Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
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, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
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.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.22986704741655040229376.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.25838 + 0.337183i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.b.649.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −6.98615 | + | 0.440173i | −0.998021 | + | 0.0628819i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −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 | \(0.0856800\pi\) | |||||||
\(12\) | 1.73205 | + | 3.00000i | 0.144338 | + | 0.250000i | ||||
\(13\) | 3.50434 | 0.269564 | 0.134782 | − | 0.990875i | \(-0.456967\pi\) | ||||
0.134782 | + | 0.990875i | \(0.456967\pi\) | |||||||
\(14\) | 8.24500 | − | 5.47905i | 0.588928 | − | 0.391361i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.06994 | + | 7.04933i | −0.239408 | + | 0.414667i | −0.960545 | − | 0.278126i | \(-0.910287\pi\) |
0.721137 | + | 0.692793i | \(0.243620\pi\) | |||||||
\(18\) | 3.67423 | + | 2.12132i | 0.204124 | + | 0.117851i | ||||
\(19\) | 15.3628 | − | 8.86974i | 0.808571 | − | 0.466828i | −0.0378887 | − | 0.999282i | \(-0.512063\pi\) |
0.846459 | + | 0.532454i | \(0.178730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.38992 | − | 10.8604i | 0.256663 | − | 0.517163i | ||||
\(22\) | 7.83078i | 0.355945i | ||||||||
\(23\) | 10.3316 | − | 5.96495i | 0.449200 | − | 0.259346i | −0.258292 | − | 0.966067i | \(-0.583160\pi\) |
0.707492 | + | 0.706721i | \(0.249826\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.29192 | + | 2.47794i | −0.165074 | + | 0.0953054i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −6.22374 | + | 12.5405i | −0.222277 | + | 0.447876i | ||||
\(29\) | 8.52374 | 0.293922 | 0.146961 | − | 0.989142i | \(-0.453051\pi\) | ||||
0.146961 | + | 0.989142i | \(0.453051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.68072 | − | 3.85711i | −0.215507 | − | 0.124423i | 0.388361 | − | 0.921507i | \(-0.373041\pi\) |
−0.603868 | + | 0.797084i | \(0.706375\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.79536 | + | 8.30580i | 0.145314 | + | 0.251691i | ||||
\(34\) | − | 11.5115i | − | 0.338574i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −24.2950 | + | 14.0267i | −0.656621 | + | 0.379100i | −0.790988 | − | 0.611831i | \(-0.790433\pi\) |
0.134367 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(38\) | −12.5437 | + | 21.7263i | −0.330098 | + | 0.571746i | ||||
\(39\) | −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 | \(-0.0121999\pi\) | |||||||
\(42\) | 1.07820 | + | 17.1125i | 0.0256714 | + | 0.407440i | ||||
\(43\) | 43.1943i | 1.00452i | 0.864717 | + | 0.502260i | \(0.167498\pi\) | ||||
−0.864717 | + | 0.502260i | \(0.832502\pi\) | |||||||
\(44\) | −5.53720 | − | 9.59071i | −0.125845 | − | 0.217971i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.43572 | + | 14.6111i | −0.183385 | + | 0.317632i | ||||
\(47\) | 9.35524 | + | 16.2037i | 0.199048 | + | 0.344761i | 0.948220 | − | 0.317615i | \(-0.102882\pi\) |
−0.749172 | + | 0.662375i | \(0.769548\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 48.6125 | − | 6.15023i | 0.992092 | − | 0.125515i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.04933 | − | 12.2098i | −0.138222 | − | 0.239408i | ||||
\(52\) | 3.50434 | − | 6.06969i | 0.0673911 | − | 0.116725i | ||||
\(53\) | 2.44037 | + | 1.40895i | 0.0460448 | + | 0.0265840i | 0.522846 | − | 0.852427i | \(-0.324870\pi\) |
−0.476801 | + | 0.879011i | \(0.658204\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.24500 | − | 19.7598i | −0.0222321 | − | 0.352854i | ||||
\(57\) | 30.7257i | 0.539047i | ||||||||
\(58\) | −10.4394 | + | 6.02720i | −0.179990 | + | 0.103917i | ||||
\(59\) | 26.1612 | + | 15.1042i | 0.443411 | + | 0.256003i | 0.705043 | − | 0.709164i | \(-0.250928\pi\) |
−0.261633 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.0095 | + | 23.6769i | −0.672288 | + | 0.388145i | −0.796943 | − | 0.604055i | \(-0.793551\pi\) |
0.124655 | + | 0.992200i | \(0.460218\pi\) | |||||||
\(62\) | 10.9096 | 0.175961 | ||||||||
\(63\) | 11.6228 | + | 17.4903i | 0.184489 | + | 0.277624i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.7462 | − | 6.78166i | −0.177972 | − | 0.102752i | ||||
\(67\) | −5.70032 | − | 3.29108i | −0.0850794 | − | 0.0491206i | 0.456857 | − | 0.889540i | \(-0.348975\pi\) |
−0.541936 | + | 0.840420i | \(0.682309\pi\) | |||||||
\(68\) | 8.13987 | + | 14.0987i | 0.119704 | + | 0.207333i | ||||
\(69\) | 20.6632i | 0.299467i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −97.7751 | −1.37711 | −0.688557 | − | 0.725182i | \(-0.741755\pi\) | ||||
−0.688557 | + | 0.725182i | \(0.741755\pi\) | |||||||
\(72\) | 7.34847 | − | 4.24264i | 0.102062 | − | 0.0589256i | ||||
\(73\) | −30.5806 | + | 52.9672i | −0.418913 | + | 0.725578i | −0.995830 | − | 0.0912244i | \(-0.970922\pi\) |
0.576918 | + | 0.816802i | \(0.304255\pi\) | |||||||
\(74\) | 19.8368 | − | 34.3583i | 0.268064 | − | 0.464301i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 35.4790i | − | 0.466828i | ||||||
\(77\) | −17.2311 | + | 34.7197i | −0.223780 | + | 0.450906i | ||||
\(78\) | − | 8.58383i | − | 0.110049i | ||||||
\(79\) | 61.5670 | + | 106.637i | 0.779329 | + | 1.34984i | 0.932329 | + | 0.361612i | \(0.117773\pi\) |
−0.152999 | + | 0.988226i | \(0.548893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.22178 | + | 3.84823i | 0.0270948 | + | 0.0469296i | ||||
\(83\) | 89.5815 | 1.07930 | 0.539648 | − | 0.841891i | \(-0.318557\pi\) | ||||
0.539648 | + | 0.841891i | \(0.318557\pi\) | |||||||
\(84\) | −13.4209 | − | 20.1960i | −0.159772 | − | 0.240429i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −30.5430 | − | 52.9020i | −0.355151 | − | 0.615140i | ||||
\(87\) | −7.38178 | + | 12.7856i | −0.0848480 | + | 0.146961i | ||||
\(88\) | 13.5633 | + | 7.83078i | 0.154129 | + | 0.0889862i | ||||
\(89\) | 102.290 | − | 59.0573i | 1.14933 | − | 0.663566i | 0.200606 | − | 0.979672i | \(-0.435709\pi\) |
0.948724 | + | 0.316107i | \(0.102376\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.4818 | + | 1.54251i | −0.269031 | + | 0.0169507i | ||||
\(92\) | − | 23.8598i | − | 0.259346i | ||||||
\(93\) | 11.5713 | − | 6.68072i | 0.124423 | − | 0.0718357i | ||||
\(94\) | −22.9156 | − | 13.2303i | −0.243783 | − | 0.140748i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | −65.1965 | −0.672128 | −0.336064 | − | 0.941839i | \(-0.609096\pi\) | ||||
−0.336064 | + | 0.941839i | \(0.609096\pi\) | |||||||
\(98\) | −55.1890 | + | 41.9067i | −0.563153 | + | 0.427619i | ||||
\(99\) | −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 | \(0.909530\pi\) | |||||||
\(102\) | 17.2673 | + | 9.96926i | 0.169287 | + | 0.0977379i | ||||
\(103\) | 87.2421 | + | 151.108i | 0.847011 | + | 1.46707i | 0.883863 | + | 0.467746i | \(0.154934\pi\) |
−0.0368520 | + | 0.999321i | \(0.511733\pi\) | |||||||
\(104\) | 9.91176i | 0.0953054i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.98511 | −0.0375954 | ||||||||
\(107\) | −52.3741 | + | 30.2382i | −0.489477 | + | 0.282600i | −0.724358 | − | 0.689424i | \(-0.757864\pi\) |
0.234880 | + | 0.972024i | \(0.424530\pi\) | |||||||
\(108\) | 5.19615 | − | 9.00000i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −50.4057 | + | 87.3052i | −0.462437 | + | 0.800965i | −0.999082 | − | 0.0428435i | \(-0.986358\pi\) |
0.536644 | + | 0.843808i | \(0.319692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 48.5899i | − | 0.437747i | ||||||
\(112\) | 15.4971 | + | 23.3204i | 0.138367 | + | 0.208218i | ||||
\(113\) | − | 74.1876i | − | 0.656527i | −0.944586 | − | 0.328264i | \(-0.893537\pi\) | ||
0.944586 | − | 0.328264i | \(-0.106463\pi\) | |||||||
\(114\) | −21.7263 | − | 37.6311i | −0.190582 | − | 0.330098i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.52374 | − | 14.7636i | 0.0734805 | − | 0.127272i | ||||
\(117\) | −5.25650 | − | 9.10453i | −0.0449274 | − | 0.0778165i | ||||
\(118\) | −42.7211 | −0.362043 | ||||||||
\(119\) | 25.3302 | − | 51.0392i | 0.212859 | − | 0.428901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.1697 | + | 78.2362i | 0.373303 | + | 0.646580i | ||||
\(122\) | 33.4842 | − | 57.9963i | 0.274460 | − | 0.475379i | ||||
\(123\) | 4.71310 | + | 2.72111i | 0.0383179 | + | 0.0221228i | ||||
\(124\) | −13.3614 | + | 7.71423i | −0.107754 | + | 0.0622115i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −26.6025 | − | 13.2026i | −0.211131 | − | 0.104782i | ||||
\(127\) | 151.093i | 1.18971i | 0.803833 | + | 0.594855i | \(0.202791\pi\) | ||||
−0.803833 | + | 0.594855i | \(0.797209\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −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 | \(0.641238\pi\) | |||||||
\(132\) | 19.1814 | 0.145314 | ||||||||
\(133\) | −103.423 | + | 68.7276i | −0.777615 | + | 0.516749i | ||||
\(134\) | 9.30859 | 0.0694671 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.9385 | − | 11.5115i | −0.146607 | − | 0.0846435i | ||||
\(137\) | −115.736 | − | 66.8203i | −0.844789 | − | 0.487739i | 0.0141000 | − | 0.999901i | \(-0.495512\pi\) |
−0.858889 | + | 0.512161i | \(0.828845\pi\) | |||||||
\(138\) | −14.6111 | − | 25.3072i | −0.105877 | − | 0.183385i | ||||
\(139\) | 193.762i | 1.39397i | 0.717085 | + | 0.696986i | \(0.245476\pi\) | ||||
−0.717085 | + | 0.696986i | \(0.754524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.4075 | −0.229840 | ||||||||
\(142\) | 119.750 | − | 69.1374i | 0.843306 | − | 0.486883i | ||||
\(143\) | 9.70210 | − | 16.8045i | 0.0678469 | − | 0.117514i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 86.4950i | − | 0.592432i | ||||||
\(147\) | −32.8743 | + | 78.2450i | −0.223635 | + | 0.532279i | ||||
\(148\) | 56.1068i | 0.379100i | ||||||||
\(149\) | 33.0032 | + | 57.1632i | 0.221498 | + | 0.383646i | 0.955263 | − | 0.295758i | \(-0.0955721\pi\) |
−0.733765 | + | 0.679403i | \(0.762239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4410 | + | 30.2087i | −0.115503 | + | 0.200057i | −0.917981 | − | 0.396625i | \(-0.870181\pi\) |
0.802478 | + | 0.596682i | \(0.203515\pi\) | |||||||
\(152\) | 25.0874 | + | 43.4527i | 0.165049 | + | 0.285873i | ||||
\(153\) | 24.4196 | 0.159605 | ||||||||
\(154\) | −3.44690 | − | 54.7070i | −0.0223825 | − | 0.355240i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.06969 | + | 10.5130i | 0.0389082 | + | 0.0673911i | ||||
\(157\) | 26.7503 | − | 46.3329i | 0.170384 | − | 0.295114i | −0.768170 | − | 0.640246i | \(-0.778832\pi\) |
0.938554 | + | 0.345132i | \(0.112166\pi\) | |||||||
\(158\) | −150.808 | − | 87.0689i | −0.954480 | − | 0.551069i | ||||
\(159\) | −4.22685 | + | 2.44037i | −0.0265840 | + | 0.0153483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −69.5525 | + | 46.2197i | −0.432003 | + | 0.287079i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | −178.387 | + | 102.992i | −1.09440 | + | 0.631852i | −0.934744 | − | 0.355321i | \(-0.884372\pi\) |
−0.159655 | + | 0.987173i | \(0.551038\pi\) | |||||||
\(164\) | −5.44222 | − | 3.14207i | −0.0331843 | − | 0.0191589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −109.714 | + | 63.3437i | −0.660931 | + | 0.381589i | ||||
\(167\) | −137.945 | −0.826020 | −0.413010 | − | 0.910727i | \(-0.635523\pi\) | ||||
−0.413010 | + | 0.910727i | \(0.635523\pi\) | |||||||
\(168\) | 30.7179 | + | 15.2450i | 0.182845 | + | 0.0907440i | ||||
\(169\) | −156.720 | −0.927335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46.0885 | − | 26.6092i | −0.269524 | − | 0.155609i | ||||
\(172\) | 74.8148 | + | 43.1943i | 0.434970 | + | 0.251130i | ||||
\(173\) | −110.283 | − | 191.016i | −0.637475 | − | 1.10414i | −0.985985 | − | 0.166834i | \(-0.946646\pi\) |
0.348510 | − | 0.937305i | \(-0.386688\pi\) | |||||||
\(174\) | − | 20.8788i | − | 0.119993i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.1488 | −0.125845 | ||||||||
\(177\) | −45.3126 | + | 26.1612i | −0.256003 | + | 0.147804i | ||||
\(178\) | −83.5197 | + | 144.660i | −0.469212 | + | 0.812699i | ||||
\(179\) | −36.6501 | + | 63.4798i | −0.204749 | + | 0.354636i | −0.950053 | − | 0.312089i | \(-0.898971\pi\) |
0.745304 | + | 0.666725i | \(0.232305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 61.4619i | 0.339568i | 0.985481 | + | 0.169784i | \(0.0543071\pi\) | ||||
−0.985481 | + | 0.169784i | \(0.945693\pi\) | |||||||
\(182\) | 28.8932 | − | 19.2004i | 0.158754 | − | 0.105497i | ||||
\(183\) | − | 82.0191i | − | 0.448192i | ||||||
\(184\) | 16.8714 | + | 29.2222i | 0.0916926 | + | 0.158816i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.44796 | + | 16.3643i | −0.0507955 | + | 0.0879804i | ||||
\(187\) | 22.5360 | + | 39.0336i | 0.120514 | + | 0.208736i | ||||
\(188\) | 37.4210 | 0.199048 | ||||||||
\(189\) | −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 | \(0.442231\pi\) | |||||||
\(192\) | 6.92820 | − | 12.0000i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −121.023 | − | 69.8724i | −0.627060 | − | 0.362033i | 0.152552 | − | 0.988295i | \(-0.451251\pi\) |
−0.779613 | + | 0.626262i | \(0.784584\pi\) | |||||||
\(194\) | 79.8490 | − | 46.1009i | 0.411593 | − | 0.237633i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 37.9600 | − | 90.3495i | 0.193673 | − | 0.460967i | ||||
\(197\) | 248.343i | 1.26062i | 0.776342 | + | 0.630311i | \(0.217073\pi\) | ||||
−0.776342 | + | 0.630311i | \(0.782927\pi\) | |||||||
\(198\) | 20.3450 | − | 11.7462i | 0.102752 | − | 0.0593241i | ||||
\(199\) | 106.170 | + | 61.2973i | 0.533518 | + | 0.308026i | 0.742448 | − | 0.669904i | \(-0.233665\pi\) |
−0.208930 | + | 0.977931i | \(0.566998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.87325 | − | 5.70032i | 0.0491206 | − | 0.0283598i | ||||
\(202\) | 197.421 | 0.977329 | ||||||||
\(203\) | −59.5481 | + | 3.75192i | −0.293341 | + | 0.0184824i | ||||
\(204\) | −28.1973 | −0.138222 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −213.699 | − | 123.379i | −1.03737 | − | 0.598927i | ||||
\(207\) | −30.9948 | − | 17.8949i | −0.149733 | − | 0.0864486i | ||||
\(208\) | −7.00867 | − | 12.1394i | −0.0336955 | − | 0.0583624i | ||||
\(209\) | − | 98.2271i | − | 0.469986i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 352.829 | 1.67218 | 0.836088 | − | 0.548596i | \(-0.184837\pi\) | ||||
0.836088 | + | 0.548596i | \(0.184837\pi\) | |||||||
\(212\) | 4.88074 | − | 2.81790i | 0.0230224 | − | 0.0132920i | ||||
\(213\) | 84.6757 | − | 146.663i | 0.397538 | − | 0.688557i | ||||
\(214\) | 42.7632 | − | 74.0681i | 0.199828 | − | 0.346113i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 48.3703 | + | 24.0057i | 0.222904 | + | 0.110625i | ||||
\(218\) | − | 142.569i | − | 0.653985i | ||||||
\(219\) | −52.9672 | − | 91.7418i | −0.241859 | − | 0.418913i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2624 | + | 24.7032i | −0.0645358 | + | 0.111779i | ||||
\(222\) | 34.3583 | + | 59.5103i | 0.154767 | + | 0.268064i | ||||
\(223\) | −61.7420 | −0.276870 | −0.138435 | − | 0.990372i | \(-0.544207\pi\) | ||||
−0.138435 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(224\) | −35.4700 | − | 17.6034i | −0.158348 | − | 0.0785866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 52.4586 | + | 90.8609i | 0.232118 | + | 0.402039i | ||||
\(227\) | 104.762 | − | 181.452i | 0.461505 | − | 0.799350i | −0.537531 | − | 0.843244i | \(-0.680643\pi\) |
0.999036 | + | 0.0438940i | \(0.0139764\pi\) | |||||||
\(228\) | 53.2184 | + | 30.7257i | 0.233414 | + | 0.134762i | ||||
\(229\) | 93.3568 | − | 53.8996i | 0.407671 | − | 0.235369i | −0.282117 | − | 0.959380i | \(-0.591037\pi\) |
0.689789 | + | 0.724011i | \(0.257703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37.1571 | − | 55.9148i | −0.160853 | − | 0.242055i | ||||
\(232\) | 24.1088i | 0.103917i | ||||||||
\(233\) | 283.057 | − | 163.423i | 1.21484 | − | 0.701387i | 0.251029 | − | 0.967980i | \(-0.419231\pi\) |
0.963809 | + | 0.266592i | \(0.0858978\pi\) | |||||||
\(234\) | 12.8758 | + | 7.43382i | 0.0550246 | + | 0.0317685i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 52.3224 | − | 30.2084i | 0.221705 | − | 0.128002i | ||||
\(237\) | −213.274 | −0.899892 | ||||||||
\(238\) | 5.06706 | + | 80.4211i | 0.0212902 | + | 0.337904i | ||||
\(239\) | 9.20117 | 0.0384986 | 0.0192493 | − | 0.999815i | \(-0.493872\pi\) | ||||
0.0192493 | + | 0.999815i | \(0.493872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 278.156 | + | 160.593i | 1.15417 | + | 0.666362i | 0.949900 | − | 0.312553i | \(-0.101184\pi\) |
0.204272 | + | 0.978914i | \(0.434517\pi\) | |||||||
\(242\) | −110.643 | − | 63.8796i | −0.457201 | − | 0.263965i | ||||
\(243\) | −7.79423 | − | 13.5000i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 94.7075i | 0.388145i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.69646 | −0.0312864 | ||||||||
\(247\) | 53.8365 | − | 31.0825i | 0.217962 | − | 0.125840i | ||||
\(248\) | 10.9096 | − | 18.8959i | 0.0439902 | − | 0.0761932i | ||||
\(249\) | −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 | \(-0.0122024\pi\) | |||||||
\(252\) | 41.9169 | − | 2.64104i | 0.166337 | − | 0.0104803i | ||||
\(253\) | − | 66.0583i | − | 0.261100i | ||||||
\(254\) | −106.839 | − | 185.051i | −0.420626 | − | 0.728546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 64.7109 | + | 112.083i | 0.251793 | + | 0.436119i | 0.964020 | − | 0.265831i | \(-0.0856464\pi\) |
−0.712226 | + | 0.701950i | \(0.752313\pi\) | |||||||
\(258\) | 105.804 | 0.410093 | ||||||||
\(259\) | 163.554 | − | 108.687i | 0.631483 | − | 0.419640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.7856 | − | 22.1453i | −0.0489870 | − | 0.0848480i | ||||
\(262\) | 152.538 | − | 264.203i | 0.582206 | − | 1.00841i | ||||
\(263\) | 144.561 | + | 83.4625i | 0.549663 | + | 0.317348i | 0.748986 | − | 0.662586i | \(-0.230541\pi\) |
−0.199323 | + | 0.979934i | \(0.563874\pi\) | |||||||
\(264\) | −23.4924 | + | 13.5633i | −0.0889862 | + | 0.0513762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 78.0688 | − | 157.305i | 0.293492 | − | 0.591371i | ||||
\(267\) | 204.581i | 0.766220i | ||||||||
\(268\) | −11.4006 | + | 6.58217i | −0.0425397 | + | 0.0245603i | ||||
\(269\) | −181.081 | − | 104.547i | −0.673162 | − | 0.388650i | 0.124112 | − | 0.992268i | \(-0.460392\pi\) |
−0.797274 | + | 0.603618i | \(0.793725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 123.029 | − | 71.0308i | 0.453981 | − | 0.262106i | −0.255529 | − | 0.966801i | \(-0.582250\pi\) |
0.709510 | + | 0.704695i | \(0.248916\pi\) | |||||||
\(272\) | 32.5595 | 0.119704 | ||||||||
\(273\) | 18.8881 | − | 38.0586i | 0.0691871 | − | 0.139409i | ||||
\(274\) | 188.996 | 0.689768 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35.7897 | + | 20.6632i | 0.129673 | + | 0.0748667i | ||||
\(277\) | −386.179 | − | 222.961i | −1.39415 | − | 0.804912i | −0.400377 | − | 0.916350i | \(-0.631121\pi\) |
−0.993771 | + | 0.111438i | \(0.964454\pi\) | |||||||
\(278\) | −137.010 | − | 237.309i | −0.492843 | − | 0.853630i | ||||
\(279\) | 23.1427i | 0.0829487i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 482.012 | 1.71534 | 0.857672 | − | 0.514196i | \(-0.171910\pi\) | ||||
0.857672 | + | 0.514196i | \(0.171910\pi\) | |||||||
\(282\) | 39.6909 | − | 22.9156i | 0.140748 | − | 0.0812609i | ||||
\(283\) | −108.257 | + | 187.506i | −0.382533 | + | 0.662566i | −0.991424 | − | 0.130688i | \(-0.958281\pi\) |
0.608891 | + | 0.793254i | \(0.291615\pi\) | |||||||
\(284\) | −97.7751 | + | 169.351i | −0.344278 | + | 0.596308i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.4417i | 0.0959500i | ||||||||
\(287\) | 1.38305 | + | 21.9509i | 0.00481900 | + | 0.0764841i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 111.371 | + | 192.901i | 0.385368 | + | 0.667476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 56.4618 | − | 97.7947i | 0.194027 | − | 0.336064i | ||||
\(292\) | 61.1612 | + | 105.934i | 0.209456 | + | 0.362789i | ||||
\(293\) | 383.704 | 1.30957 | 0.654786 | − | 0.755815i | \(-0.272759\pi\) | ||||
0.654786 | + | 0.755815i | \(0.272759\pi\) | |||||||
\(294\) | −15.0649 | − | 119.076i | −0.0512412 | − | 0.405020i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.6735 | − | 68.7166i | −0.134032 | − | 0.232151i | ||||
\(297\) | 14.3861 | − | 24.9174i | 0.0484379 | − | 0.0838970i | ||||
\(298\) | −80.8410 | − | 46.6736i | −0.271278 | − | 0.156623i | ||||
\(299\) | 36.2054 | − | 20.9032i | 0.121088 | − | 0.0699104i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.0130 | − | 301.762i | −0.0631661 | − | 1.00253i | ||||
\(302\) | − | 49.3305i | − | 0.163346i | ||||||
\(303\) | 209.396 | − | 120.895i | 0.691076 | − | 0.398993i | ||||
\(304\) | −61.4514 | − | 35.4790i | −0.202143 | − | 0.116707i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.9078 | + | 17.2673i | −0.0977379 | + | 0.0564290i | ||||
\(307\) | −21.1264 | −0.0688155 | −0.0344078 | − | 0.999408i | \(-0.510954\pi\) | ||||
−0.0344078 | + | 0.999408i | \(0.510954\pi\) | |||||||
\(308\) | 42.9053 | + | 64.5648i | 0.139303 | + | 0.209626i | ||||
\(309\) | −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 | \(0.622186\pi\) | |||||||
\(312\) | −14.8676 | − | 8.58383i | −0.0476527 | − | 0.0275123i | ||||
\(313\) | 1.41903 | + | 2.45782i | 0.00453363 | + | 0.00785247i | 0.868283 | − | 0.496069i | \(-0.165224\pi\) |
−0.863750 | + | 0.503921i | \(0.831890\pi\) | |||||||
\(314\) | 75.6613i | 0.240960i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 246.268 | 0.779329 | ||||||||
\(317\) | 268.338 | − | 154.925i | 0.846493 | − | 0.488723i | −0.0129730 | − | 0.999916i | \(-0.504130\pi\) |
0.859466 | + | 0.511193i | \(0.170796\pi\) | |||||||
\(318\) | 3.45121 | − | 5.97767i | 0.0108529 | − | 0.0187977i | ||||
\(319\) | 23.5988 | − | 40.8744i | 0.0739776 | − | 0.128133i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 104.748i | − | 0.326318i | ||||||
\(322\) | 52.5018 | − | 105.788i | 0.163049 | − | 0.328535i | ||||
\(323\) | 144.397i | 0.447050i | ||||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 145.652 | − | 252.278i | 0.446787 | − | 0.773857i | ||||
\(327\) | −87.3052 | − | 151.217i | −0.266988 | − | 0.462437i | ||||
\(328\) | 8.88711 | 0.0270948 | ||||||||
\(329\) | −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 | \(0.616680\pi\) | |||||||
\(332\) | 89.5815 | − | 155.160i | 0.269824 | − | 0.467349i | ||||
\(333\) | 72.8849 | + | 42.0801i | 0.218874 | + | 0.126367i | ||||
\(334\) | 168.948 | − | 97.5421i | 0.505832 | − | 0.292042i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −48.4014 | + | 3.04961i | −0.144052 | + | 0.00907622i | ||||
\(337\) | − | 155.491i | − | 0.461399i | −0.973025 | − | 0.230699i | \(-0.925899\pi\) | ||
0.973025 | − | 0.230699i | \(-0.0741014\pi\) | |||||||
\(338\) | 191.942 | − | 110.818i | 0.567874 | − | 0.327862i | ||||
\(339\) | 111.281 | + | 64.2483i | 0.328264 | + | 0.189523i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.9925 | + | 21.3576i | −0.108482 | + | 0.0626323i | ||||
\(342\) | 75.2622 | 0.220065 | ||||||||
\(343\) | −336.907 | + | 64.3643i | −0.982236 | + | 0.187651i | ||||
\(344\) | −122.172 | −0.355151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 270.138 | + | 155.964i | 0.780744 | + | 0.450763i | ||||
\(347\) | −443.844 | − | 256.253i | −1.27909 | − | 0.738482i | −0.302408 | − | 0.953179i | \(-0.597790\pi\) |
−0.976681 | + | 0.214697i | \(0.931124\pi\) | |||||||
\(348\) | 14.7636 | + | 25.5712i | 0.0424240 | + | 0.0734805i | ||||
\(349\) | 269.185i | 0.771305i | 0.922644 | + | 0.385652i | \(0.126024\pi\) | ||||
−0.922644 | + | 0.385652i | \(0.873976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.2091 | 0.0518777 | ||||||||
\(352\) | 27.1266 | − | 15.6616i | 0.0770643 | − | 0.0444931i | ||||
\(353\) | 293.231 | − | 507.890i | 0.830682 | − | 1.43878i | −0.0668166 | − | 0.997765i | \(-0.521284\pi\) |
0.897498 | − | 0.441018i | \(-0.145382\pi\) | |||||||
\(354\) | 36.9976 | − | 64.0816i | 0.104513 | − | 0.181022i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 236.229i | − | 0.663566i | ||||||
\(357\) | 54.6221 | + | 82.1966i | 0.153003 | + | 0.230242i | ||||
\(358\) | − | 103.662i | − | 0.289559i | ||||||
\(359\) | 44.4221 | + | 76.9413i | 0.123738 | + | 0.214321i | 0.921239 | − | 0.388997i | \(-0.127178\pi\) |
−0.797501 | + | 0.603318i | \(0.793845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.1554 | + | 40.1064i | −0.0641424 | + | 0.111098i | ||||
\(362\) | −43.4601 | − | 75.2751i | −0.120056 | − | 0.207942i | ||||
\(363\) | −156.472 | −0.431054 | ||||||||
\(364\) | −21.8101 | + | 43.9462i | −0.0599178 | + | 0.120731i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 57.9963 | + | 100.452i | 0.158460 | + | 0.274460i | ||||
\(367\) | 353.019 | − | 611.446i | 0.961904 | − | 1.66607i | 0.244191 | − | 0.969727i | \(-0.421478\pi\) |
0.717713 | − | 0.696339i | \(-0.245189\pi\) | |||||||
\(368\) | −41.3264 | − | 23.8598i | −0.112300 | − | 0.0648365i | ||||
\(369\) | −8.16333 | + | 4.71310i | −0.0221228 | + | 0.0127726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6690 | − | 8.76894i | −0.0476253 | − | 0.0236360i | ||||
\(372\) | − | 26.7229i | − | 0.0718357i | ||||||
\(373\) | −44.3770 | + | 25.6211i | −0.118973 | + | 0.0686892i | −0.558306 | − | 0.829635i | \(-0.688548\pi\) |
0.439332 | + | 0.898325i | \(0.355215\pi\) | |||||||
\(374\) | −55.2018 | − | 31.8708i | −0.147598 | − | 0.0852160i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −45.8311 | + | 26.4606i | −0.121891 | + | 0.0703740i | ||||
\(377\) | 29.8701 | 0.0792309 | ||||||||
\(378\) | 42.8423 | − | 28.4700i | 0.113339 | − | 0.0753174i | ||||
\(379\) | 194.724 | 0.513784 | 0.256892 | − | 0.966440i | \(-0.417302\pi\) | ||||
0.256892 | + | 0.966440i | \(0.417302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −226.640 | − | 130.851i | −0.594855 | − | 0.343440i | ||||
\(382\) | −440.740 | − | 254.461i | −1.15377 | − | 0.666129i | ||||
\(383\) | 262.540 | + | 454.732i | 0.685482 | + | 1.18729i | 0.973285 | + | 0.229600i | \(0.0737418\pi\) |
−0.287803 | + | 0.957690i | \(0.592925\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 197.629 | 0.511993 | ||||||||
\(387\) | 112.222 | − | 64.7915i | 0.289980 | − | 0.167420i | ||||
\(388\) | −65.1965 | + | 112.924i | −0.168032 | + | 0.291040i | ||||
\(389\) | −201.765 | + | 349.467i | −0.518675 | + | 0.898372i | 0.481089 | + | 0.876672i | \(0.340241\pi\) |
−0.999765 | + | 0.0217005i | \(0.993092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 97.1079i | 0.248358i | ||||||||
\(392\) | 17.3955 | + | 137.497i | 0.0443762 | + | 0.350757i | ||||
\(393\) | − | 373.640i | − | 0.950738i | ||||||
\(394\) | −175.605 | − | 304.156i | −0.445697 | − | 0.771971i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.6116 | + | 28.7721i | −0.0419485 | + | 0.0726569i | ||||
\(397\) | 80.5960 | + | 139.596i | 0.203013 | + | 0.351628i | 0.949498 | − | 0.313774i | \(-0.101593\pi\) |
−0.746485 | + | 0.665402i | \(0.768260\pi\) | |||||||
\(398\) | −173.375 | −0.435615 | ||||||||
\(399\) | −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 | \(0.655548\pi\) | |||||||
\(402\) | −8.06147 | + | 13.9629i | −0.0200534 | + | 0.0347335i | ||||
\(403\) | −23.4115 | − | 13.5166i | −0.0580930 | − | 0.0335400i | ||||
\(404\) | −241.790 | + | 139.597i | −0.598490 | + | 0.345538i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 70.2782 | − | 46.7020i | 0.173099 | − | 0.115030i | ||||
\(407\) | 155.337i | 0.381664i | ||||||||
\(408\) | 34.5345 | − | 19.9385i | 0.0846435 | − | 0.0488689i | ||||
\(409\) | −373.605 | − | 215.701i | −0.913460 | − | 0.527386i | −0.0319171 | − | 0.999491i | \(-0.510161\pi\) |
−0.881543 | + | 0.472104i | \(0.843495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 200.461 | − | 115.736i | 0.487739 | − | 0.281596i | ||||
\(412\) | 348.969 | 0.847011 | ||||||||
\(413\) | −189.415 | − | 94.0046i | −0.458631 | − | 0.227614i | ||||
\(414\) | 50.6143 | 0.122257 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.1677 | + | 9.91176i | 0.0412684 | + | 0.0238263i | ||||
\(417\) | −290.643 | − | 167.803i | −0.696986 | − | 0.402405i | ||||
\(418\) | 69.4570 | + | 120.303i | 0.166165 | + | 0.287806i | ||||
\(419\) | − | 585.412i | − | 1.39716i | −0.715530 | − | 0.698582i | \(-0.753815\pi\) | ||
0.715530 | − | 0.698582i | \(-0.246185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 400.267 | 0.950754 | 0.475377 | − | 0.879782i | \(-0.342312\pi\) | ||||
0.475377 | + | 0.879782i | \(0.342312\pi\) | |||||||
\(422\) | −432.126 | + | 249.488i | −1.02399 | + | 0.591203i | ||||
\(423\) | 28.0657 | − | 48.6112i | 0.0663492 | − | 0.114920i | ||||
\(424\) | −3.98511 | + | 6.90241i | −0.00939885 | + | 0.0162793i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 239.499i | 0.562204i | ||||||||
\(427\) | 276.077 | − | 183.461i | 0.646550 | − | 0.429652i | ||||
\(428\) | 120.953i | 0.282600i | ||||||||
\(429\) | 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 | \(0.318294\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 2.39222 | 0.00552477 | 0.00276238 | − | 0.999996i | \(-0.499121\pi\) | ||||
0.00276238 | + | 0.999996i | \(0.499121\pi\) | |||||||
\(434\) | −76.2158 | + | 4.80210i | −0.175613 | + | 0.0110647i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 100.811 | + | 174.610i | 0.231219 | + | 0.400482i | ||||
\(437\) | 105.815 | − | 183.277i | 0.242140 | − | 0.419399i | ||||
\(438\) | 129.743 | + | 74.9069i | 0.296216 | + | 0.171020i | ||||
\(439\) | 350.264 | − | 202.225i | 0.797867 | − | 0.460649i | −0.0448578 | − | 0.998993i | \(-0.514283\pi\) |
0.842725 | + | 0.538345i | \(0.180950\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −88.8975 | − | 117.074i | −0.201582 | − | 0.265473i | ||||
\(442\) | − | 40.3402i | − | 0.0912674i | ||||||
\(443\) | 252.889 | − | 146.005i | 0.570855 | − | 0.329583i | −0.186636 | − | 0.982429i | \(-0.559758\pi\) |
0.757491 | + | 0.652846i | \(0.226425\pi\) | |||||||
\(444\) | −84.1603 | − | 48.5899i | −0.189550 | − | 0.109437i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 75.6182 | − | 43.6582i | 0.169547 | − | 0.0978883i | ||||
\(447\) | −114.326 | −0.255764 | ||||||||
\(448\) | 55.8892 | − | 3.52139i | 0.124753 | − | 0.00786024i | ||||
\(449\) | −125.680 | −0.279911 | −0.139956 | − | 0.990158i | \(-0.544696\pi\) | ||||
−0.139956 | + | 0.990158i | \(0.544696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0673 | − | 8.69913i | −0.0334087 | − | 0.0192885i | ||||
\(452\) | −128.497 | − | 74.1876i | −0.284285 | − | 0.164132i | ||||
\(453\) | −30.2087 | − | 52.3229i | −0.0666858 | − | 0.115503i | ||||
\(454\) | 296.310i | 0.652666i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −86.9054 | −0.190582 | ||||||||
\(457\) | −74.4808 | + | 43.0015i | −0.162978 | + | 0.0940952i | −0.579270 | − | 0.815135i | \(-0.696662\pi\) |
0.416293 | + | 0.909231i | \(0.363329\pi\) | |||||||
\(458\) | −76.2255 | + | 132.026i | −0.166431 | + | 0.288267i | ||||
\(459\) | −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 | \(-0.0455362\pi\) | |||||||
\(462\) | 85.0456 | + | 42.2073i | 0.184081 | + | 0.0913578i | ||||
\(463\) | 73.9873i | 0.159800i | 0.996803 | + | 0.0798999i | \(0.0254601\pi\) | ||||
−0.996803 | + | 0.0798999i | \(0.974540\pi\) | |||||||
\(464\) | −17.0475 | − | 29.5271i | −0.0367403 | − | 0.0636360i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −231.115 | + | 400.303i | −0.495956 | + | 0.859020i | ||||
\(467\) | 223.453 | + | 387.032i | 0.478486 | + | 0.828762i | 0.999696 | − | 0.0246667i | \(-0.00785244\pi\) |
−0.521210 | + | 0.853429i | \(0.674519\pi\) | |||||||
\(468\) | −21.0260 | −0.0449274 | ||||||||
\(469\) | 41.2719 | + | 20.4829i | 0.0879999 | + | 0.0436735i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.3329 | + | 80.2509i | 0.0983713 | + | 0.170384i | ||||
\(472\) | −42.7211 | + | 73.9951i | −0.0905108 | + | 0.156769i | ||||
\(473\) | 207.132 | + | 119.588i | 0.437912 | + | 0.252828i | ||||
\(474\) | 261.207 | − | 150.808i | 0.551069 | − | 0.318160i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −63.0722 | − | 94.9124i | −0.132505 | − | 0.199396i | ||||
\(477\) | − | 8.45370i | − | 0.0177226i | ||||||
\(478\) | −11.2691 | + | 6.50621i | −0.0235755 | + | 0.0136113i | ||||
\(479\) | −513.818 | − | 296.653i | −1.07269 | − | 0.619318i | −0.143775 | − | 0.989610i | \(-0.545924\pi\) |
−0.928915 | + | 0.370293i | \(0.879257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −85.1377 | + | 49.1543i | −0.177002 | + | 0.102192i | ||||
\(482\) | −454.226 | −0.942378 | ||||||||
\(483\) | −9.09539 | − | 144.356i | −0.0188310 | − | 0.298874i | ||||
\(484\) | 180.679 | 0.373303 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −709.744 | − | 409.771i | −1.45738 | − | 0.841418i | −0.458498 | − | 0.888696i | \(-0.651612\pi\) |
−0.998882 | + | 0.0472773i | \(0.984946\pi\) | |||||||
\(488\) | −66.9683 | − | 115.993i | −0.137230 | − | 0.237690i | ||||
\(489\) | − | 356.774i | − | 0.729600i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 554.724 | 1.12978 | 0.564892 | − | 0.825165i | \(-0.308918\pi\) | ||||
0.564892 | + | 0.825165i | \(0.308918\pi\) | |||||||
\(492\) | 9.42620 | − | 5.44222i | 0.0191589 | − | 0.0110614i | ||||
\(493\) | −34.6911 | + | 60.0867i | −0.0703673 | + | 0.121880i | ||||
\(494\) | −43.9574 | + | 76.1364i | −0.0889825 | + | 0.154122i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.8569i | 0.0622115i | ||||||||
\(497\) | 683.071 | − | 43.0380i | 1.37439 | − | 0.0865955i | ||||
\(498\) | − | 219.429i | − | 0.440620i | ||||||
\(499\) | 317.394 | + | 549.742i | 0.636060 | + | 1.10169i | 0.986290 | + | 0.165024i | \(0.0527701\pi\) |
−0.350230 | + | 0.936664i | \(0.613897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 119.464 | − | 206.918i | 0.238451 | − | 0.413010i | ||||
\(502\) | 13.6043 | + | 23.5634i | 0.0271003 | + | 0.0469390i | ||||
\(503\) | −120.116 | −0.238800 | −0.119400 | − | 0.992846i | \(-0.538097\pi\) | ||||
−0.119400 | + | 0.992846i | \(0.538097\pi\) | |||||||
\(504\) | −49.4700 | + | 32.8743i | −0.0981547 | + | 0.0652268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.7103 | + | 80.9046i | 0.0923128 | + | 0.159890i | ||||
\(507\) | 135.723 | − | 235.079i | 0.267699 | − | 0.463668i | ||||
\(508\) | 261.701 | + | 151.093i | 0.515160 | + | 0.297428i | ||||
\(509\) | −51.1082 | + | 29.5073i | −0.100409 | + | 0.0579712i | −0.549364 | − | 0.835583i | \(-0.685130\pi\) |
0.448955 | + | 0.893555i | \(0.351796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 190.326 | − | 383.497i | 0.372458 | − | 0.750484i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 79.8277 | − | 46.0885i | 0.155609 | − | 0.0898412i | ||||
\(514\) | −158.509 | − | 91.5150i | −0.308383 | − | 0.178045i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −129.583 | + | 74.8148i | −0.251130 | + | 0.144990i | ||||
\(517\) | 103.604 | 0.200394 | ||||||||
\(518\) | −123.459 | + | 248.764i | −0.238338 | + | 0.480239i | ||||
\(519\) | 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 | \(-0.715471\pi\) | |||||||
\(522\) | 31.3182 | + | 18.0816i | 0.0599966 | + | 0.0346391i | ||||
\(523\) | 345.682 | + | 598.739i | 0.660960 | + | 1.14482i | 0.980364 | + | 0.197197i | \(0.0631840\pi\) |
−0.319404 | + | 0.947619i | \(0.603483\pi\) | |||||||
\(524\) | 431.442i | 0.823363i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −236.068 | −0.448798 | ||||||||
\(527\) | 54.3802 | − | 31.3964i | 0.103188 | − | 0.0595757i | ||||
\(528\) | 19.1814 | − | 33.2232i | 0.0363285 | − | 0.0629227i | ||||
\(529\) | −193.339 | + | 334.872i | −0.365479 | + | 0.633029i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 90.6251i | − | 0.170669i | ||||||
\(532\) | 15.6169 | + | 247.861i | 0.0293551 | + | 0.465905i | ||||
\(533\) | − | 11.0109i | − | 0.0206583i | ||||||
\(534\) | −144.660 | − | 250.559i | −0.270900 | − | 0.469212i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.30859 | − | 16.1229i | 0.0173668 | − | 0.0300801i | ||||
\(537\) | −63.4798 | − | 109.950i | −0.118212 | − | 0.204749i | ||||
\(538\) | 295.703 | 0.549635 | ||||||||
\(539\) | 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 | \(-0.333597\pi\) | |||||||
\(542\) | −100.453 | + | 173.989i | −0.185337 | + | 0.321013i | ||||
\(543\) | −92.1928 | − | 53.2275i | −0.169784 | − | 0.0980249i | ||||
\(544\) | −39.8771 | + | 23.0230i | −0.0733034 | + | 0.0423217i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.77837 | + | 59.9679i | 0.00692010 | + | 0.109831i | ||||
\(547\) | 318.491i | 0.582251i | 0.956685 | + | 0.291126i | \(0.0940297\pi\) | ||||
−0.956685 | + | 0.291126i | \(0.905970\pi\) | |||||||
\(548\) | −231.472 | + | 133.641i | −0.422395 | + | 0.243870i | ||||
\(549\) | 123.029 | + | 71.0306i | 0.224096 | + | 0.129382i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130.949 | − | 75.6034i | 0.237657 | − | 0.137211i | ||||
\(552\) | −58.4444 | −0.105877 | ||||||||
\(553\) | −477.055 | − | 717.883i | −0.862667 | − | 1.29816i | ||||
\(554\) | 630.628 | 1.13832 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 335.606 | + | 193.762i | 0.603607 | + | 0.348493i | ||||
\(557\) | 499.660 | + | 288.479i | 0.897055 | + | 0.517915i | 0.876244 | − | 0.481869i | \(-0.160042\pi\) |
0.0208114 | + | 0.999783i | \(0.493375\pi\) | |||||||
\(558\) | −16.3643 | − | 28.3439i | −0.0293268 | − | 0.0507955i | ||||
\(559\) | 151.367i | 0.270783i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −78.0672 | −0.139157 | ||||||||
\(562\) | −590.342 | + | 340.834i | −1.05043 | + | 0.606466i | ||||
\(563\) | −177.985 | + | 308.279i | −0.316137 | + | 0.547565i | −0.979678 | − | 0.200574i | \(-0.935719\pi\) |
0.663542 | + | 0.748139i | \(0.269053\pi\) | |||||||
\(564\) | −32.4075 | + | 56.1314i | −0.0574601 | + | 0.0995238i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 306.196i | − | 0.540983i | ||||||
\(567\) | 28.0068 | − | 56.4324i | 0.0493948 | − | 0.0995281i | ||||
\(568\) | − | 276.550i | − | 0.486883i | ||||||
\(569\) | −186.085 | − | 322.308i | −0.327038 | − | 0.566447i | 0.654885 | − | 0.755729i | \(-0.272717\pi\) |
−0.981923 | + | 0.189282i | \(0.939384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 82.9355 | − | 143.649i | 0.145246 | − | 0.251574i | −0.784219 | − | 0.620485i | \(-0.786936\pi\) |
0.929465 | + | 0.368911i | \(0.120269\pi\) | |||||||
\(572\) | −19.4042 | − | 33.6091i | −0.0339234 | − | 0.0587571i | ||||
\(573\) | −623.300 | −1.08778 | ||||||||
\(574\) | −17.2155 | − | 25.9063i | −0.0299922 | − | 0.0451330i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 8.06639 | − | 13.9714i | 0.0139799 | − | 0.0242139i | −0.858951 | − | 0.512058i | \(-0.828883\pi\) |
0.872931 | + | 0.487844i | \(0.162217\pi\) | |||||||
\(578\) | −272.803 | − | 157.503i | −0.471977 | − | 0.272496i | ||||
\(579\) | 209.617 | − | 121.023i | 0.362033 | − | 0.209020i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −625.830 | + | 39.4314i | −1.07716 | + | 0.0678681i | ||||
\(582\) | 159.698i | 0.274395i | ||||||||
\(583\) | 13.5128 | − | 7.80164i | 0.0231781 | − | 0.0133819i | ||||
\(584\) | −149.814 | − | 86.4950i | −0.256530 | − | 0.148108i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −469.940 | + | 271.320i | −0.801945 | + | 0.463003i | ||||
\(587\) | 204.516 | 0.348409 | 0.174205 | − | 0.984709i | \(-0.444265\pi\) | ||||
0.174205 | + | 0.984709i | \(0.444265\pi\) | |||||||
\(588\) | 102.650 | + | 135.185i | 0.174575 | + | 0.229906i | ||||
\(589\) | −136.846 | −0.232337 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −372.514 | − | 215.071i | −0.630311 | − | 0.363910i | ||||
\(592\) | 97.1799 | + | 56.1068i | 0.164155 | + | 0.0947751i | ||||
\(593\) | −345.011 | − | 597.577i | −0.581806 | − | 1.00772i | −0.995265 | − | 0.0971952i | \(-0.969013\pi\) |
0.413459 | − | 0.910523i | \(-0.364320\pi\) | |||||||
\(594\) | 40.6899i | 0.0685016i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 132.013 | 0.221498 | ||||||||
\(597\) | −183.892 | + | 106.170i | −0.308026 | + | 0.177839i | ||||
\(598\) | −29.5616 | + | 51.2022i | −0.0494341 | + | 0.0856224i | ||||
\(599\) | −477.775 | + | 827.531i | −0.797622 | + | 1.38152i | 0.123539 | + | 0.992340i | \(0.460575\pi\) |
−0.921161 | + | 0.389182i | \(0.872758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 587.954i | 0.978293i | 0.872202 | + | 0.489146i | \(0.162692\pi\) | ||||
−0.872202 | + | 0.489146i | \(0.837308\pi\) | |||||||
\(602\) | 236.664 | + | 356.137i | 0.393130 | + | 0.591590i | ||||
\(603\) | 19.7465i | 0.0327471i | ||||||||
\(604\) | 34.8820 | + | 60.4173i | 0.0577516 | + | 0.100029i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −170.971 | + | 296.131i | −0.282131 | + | 0.488665i | ||||
\(607\) | 259.483 | + | 449.438i | 0.427485 | + | 0.740425i | 0.996649 | − | 0.0817986i | \(-0.0260664\pi\) |
−0.569164 | + | 0.822224i | \(0.692733\pi\) | |||||||
\(608\) | 100.350 | 0.165049 | ||||||||
\(609\) | 45.9423 | − | 92.5714i | 0.0754389 | − | 0.152006i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.7839 | + | 56.7834i | 0.0536561 | + | 0.0929351i | ||||
\(612\) | 24.4196 | − | 42.2960i | 0.0399013 | − | 0.0691111i | ||||
\(613\) | 110.465 | + | 63.7771i | 0.180204 | + | 0.104041i | 0.587389 | − | 0.809305i | \(-0.300156\pi\) |
−0.407184 | + | 0.913346i | \(0.633489\pi\) | |||||||
\(614\) | 25.8744 | − | 14.9386i | 0.0421407 | − | 0.0243300i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −98.2022 | − | 48.7368i | −0.159419 | − | 0.0791182i | ||||
\(617\) | 486.581i | 0.788624i | 0.918977 | + | 0.394312i | \(0.129017\pi\) | ||||
−0.918977 | + | 0.394312i | \(0.870983\pi\) | |||||||
\(618\) | 370.137 | − | 213.699i | 0.598927 | − | 0.345791i | ||||
\(619\) | −370.662 | − | 214.002i | −0.598808 | − | 0.345722i | 0.169765 | − | 0.985485i | \(-0.445699\pi\) |
−0.768572 | + | 0.639763i | \(0.779033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 53.6846 | − | 30.9948i | 0.0864486 | − | 0.0499111i | ||||
\(622\) | −122.522 | −0.196980 | ||||||||
\(623\) | −688.620 | + | 457.609i | −1.10533 | + | 0.734524i | ||||
\(624\) | 24.2787 | 0.0389082 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.47589 | − | 2.00680i | −0.00555254 | − | 0.00320576i | ||||
\(627\) | 147.341 | + | 85.0671i | 0.234993 | + | 0.135673i | ||||
\(628\) | −53.5006 | − | 92.6658i | −0.0851921 | − | 0.147557i | ||||
\(629\) | − | 228.351i | − | 0.363038i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −64.4987 | −0.102217 | −0.0511083 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511083 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(632\) | −301.616 | + | 174.138i | −0.477240 | + | 0.275535i | ||||
\(633\) | −305.559 | + | 529.244i | −0.482716 | + | 0.836088i | ||||
\(634\) | −219.097 | + | 379.488i | −0.345579 | + | 0.598561i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.76149i | 0.0153483i | ||||||||
\(637\) | 170.354 | − | 21.5525i | 0.267432 | − | 0.0338343i | ||||
\(638\) | 66.7476i | 0.104620i | ||||||||
\(639\) | 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 | \(0.981228\pi\) | |||||||
\(642\) | 74.0681 | + | 128.290i | 0.115371 | + | 0.199828i | ||||
\(643\) | −1092.83 | −1.69958 | −0.849788 | − | 0.527124i | \(-0.823270\pi\) | ||||
−0.849788 | + | 0.527124i | \(0.823270\pi\) | |||||||
\(644\) | 10.5025 | + | 166.688i | 0.0163082 | + | 0.258833i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −102.104 | − | 176.850i | −0.158056 | − | 0.273761i | ||||
\(647\) | 257.546 | − | 446.083i | 0.398062 | − | 0.689463i | −0.595425 | − | 0.803411i | \(-0.703016\pi\) |
0.993487 | + | 0.113948i | \(0.0363496\pi\) | |||||||
\(648\) | −22.0454 | − | 12.7279i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 144.860 | − | 83.6349i | 0.223205 | − | 0.128867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −77.8984 | + | 51.7659i | −0.119660 | + | 0.0795175i | ||||
\(652\) | 411.967i | 0.631852i | ||||||||
\(653\) | 681.245 | − | 393.317i | 1.04325 | − | 0.602323i | 0.122501 | − | 0.992468i | \(-0.460909\pi\) |
0.920753 | + | 0.390145i | \(0.127575\pi\) | |||||||
\(654\) | 213.853 | + | 123.468i | 0.326993 | + | 0.188789i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.8844 | + | 6.28413i | −0.0165921 | + | 0.00957947i | ||||
\(657\) | 183.484 | 0.279275 | ||||||||
\(658\) | 165.915 | + | 82.3420i | 0.252151 | + | 0.125140i | ||||
\(659\) | 819.425 | 1.24344 | 0.621719 | − | 0.783241i | \(-0.286435\pi\) | ||||
0.621719 | + | 0.783241i | \(0.286435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −889.453 | − | 513.526i | −1.34562 | − | 0.776892i | −0.357991 | − | 0.933725i | \(-0.616538\pi\) |
−0.987625 | + | 0.156833i | \(0.949872\pi\) | |||||||
\(662\) | −510.216 | − | 294.573i | −0.770718 | − | 0.444974i | ||||
\(663\) | −24.7032 | − | 42.7873i | −0.0372598 | − | 0.0645358i | ||||
\(664\) | 253.375i | 0.381589i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −119.021 | −0.178710 | ||||||||
\(667\) | 88.0639 | − | 50.8437i | 0.132030 | − | 0.0762275i | ||||
\(668\) | −137.945 | + | 238.928i | −0.206505 | + | 0.357677i | ||||
\(669\) | 53.4701 | − | 92.6130i | 0.0799254 | − | 0.138435i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 262.207i | 0.390771i | ||||||||
\(672\) | 57.1230 | − | 37.9600i | 0.0850045 | − | 0.0564881i | ||||
\(673\) | − | 669.779i | − | 0.995213i | −0.867403 | − | 0.497607i | \(-0.834212\pi\) | ||
0.867403 | − | 0.497607i | \(-0.165788\pi\) | |||||||
\(674\) | 109.949 | + | 190.437i | 0.163129 | + | 0.282548i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −156.720 | + | 271.446i | −0.231834 | + | 0.401548i | ||||
\(677\) | 454.099 | + | 786.522i | 0.670751 | + | 1.16178i | 0.977691 | + | 0.210047i | \(0.0673616\pi\) |
−0.306940 | + | 0.951729i | \(0.599305\pi\) | |||||||
\(678\) | −181.722 | −0.268026 | ||||||||
\(679\) | 455.472 | − | 28.6977i | 0.670798 | − | 0.0422647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 181.452 | + | 314.285i | 0.266450 | + | 0.461505i | ||||
\(682\) | 30.2042 | − | 52.3153i | 0.0442877 | − | 0.0767086i | ||||
\(683\) | 572.733 | + | 330.668i | 0.838555 | + | 0.484140i | 0.856773 | − | 0.515694i | \(-0.172466\pi\) |
−0.0182177 | + | 0.999834i | \(0.505799\pi\) | |||||||
\(684\) | −92.1770 | + | 53.2184i | −0.134762 | + | 0.0778047i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 367.112 | − | 317.059i | 0.535149 | − | 0.462185i | ||||
\(687\) | 186.714i | 0.271781i | ||||||||
\(688\) | 149.630 | − | 86.3887i | 0.217485 | − | 0.125565i | ||||
\(689\) | 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 | \(0.397493\pi\) | |||||||
\(692\) | −441.133 | −0.637475 | ||||||||
\(693\) | 116.051 | − | 7.31198i | 0.167462 | − | 0.0105512i | ||||
\(694\) | 724.794 | 1.04437 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −36.1632 | − | 20.8788i | −0.0519586 | − | 0.0299983i | ||||
\(697\) | 22.1495 | + | 12.7880i | 0.0317783 | + | 0.0183472i | ||||
\(698\) | −190.343 | − | 329.683i | −0.272697 | − | 0.472326i | ||||
\(699\) | 566.115i | 0.809892i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −415.967 | −0.593391 | −0.296696 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296696 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(702\) | −22.3015 | + | 12.8758i | −0.0317685 | + | 0.0183415i | ||||
\(703\) | −248.827 | + | 430.980i | −0.353950 | + | 0.613059i | ||||
\(704\) | −22.1488 | + | 38.3629i | −0.0314614 | + | 0.0544927i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 829.382i | 1.17476i | ||||||||
\(707\) | 875.313 | + | 434.409i | 1.23807 | + | 0.614440i | ||||
\(708\) | 104.645i | 0.147804i | ||||||||
\(709\) | 136.620 | + | 236.632i | 0.192693 | + | 0.333755i | 0.946142 | − | 0.323752i | \(-0.104944\pi\) |
−0.753449 | + | 0.657507i | \(0.771611\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 184.701 | − | 319.912i | 0.259776 | − | 0.449946i | ||||
\(712\) | 167.039 | + | 289.321i | 0.234606 | + | 0.406349i | ||||
\(713\) | −92.0300 | −0.129074 | ||||||||
\(714\) | −125.020 | − | 62.0462i | −0.175098 | − | 0.0868994i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 73.3002 | + | 126.960i | 0.102375 | + | 0.177318i | ||||
\(717\) | −7.96845 | + | 13.8018i | −0.0111136 | + | 0.0192493i | ||||
\(718\) | −108.811 | − | 62.8223i | −0.151548 | − | 0.0874962i | ||||
\(719\) | −361.463 | + | 208.691i | −0.502731 | + | 0.290252i | −0.729840 | − | 0.683617i | \(-0.760406\pi\) |
0.227110 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −676.000 | − | 1017.26i | −0.937587 | − | 1.41090i | ||||
\(722\) | − | 65.4934i | − | 0.0907111i | ||||||
\(723\) | −481.779 | + | 278.156i | −0.666362 | + | 0.384724i | ||||
\(724\) | 106.455 | + | 61.4619i | 0.147037 | + | 0.0848921i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 191.639 | − | 110.643i | 0.263965 | − | 0.152400i | ||||
\(727\) | −357.267 | −0.491426 | −0.245713 | − | 0.969343i | \(-0.579022\pi\) | ||||
−0.245713 | + | 0.969343i | \(0.579022\pi\) | |||||||
\(728\) | −4.36289 | − | 69.2450i | −0.00599298 | − | 0.0951167i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −304.491 | − | 175.798i | −0.416541 | − | 0.240490i | ||||
\(732\) | −142.061 | − | 82.0191i | −0.194073 | − | 0.112048i | ||||
\(733\) | 215.521 | + | 373.293i | 0.294026 | + | 0.509267i | 0.974758 | − | 0.223265i | \(-0.0716716\pi\) |
−0.680732 | + | 0.732532i | \(0.738338\pi\) | |||||||
\(734\) | 998.488i | 1.36034i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 67.4858 | 0.0916926 | ||||||||
\(737\) | −31.5638 | + | 18.2234i | −0.0428274 | + | 0.0247264i | ||||
\(738\) | 6.66533 | − | 11.5447i | 0.00903161 | − | 0.0156432i | ||||
\(739\) | 159.512 | − | 276.282i | 0.215848 | − | 0.373860i | −0.737687 | − | 0.675143i | \(-0.764082\pi\) |
0.953535 | + | 0.301284i | \(0.0974151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 107.673i | 0.145308i | ||||||||
\(742\) | 27.8406 | − | 1.75414i | 0.0375210 | − | 0.00236407i | ||||
\(743\) | 1303.33i | 1.75414i | 0.480360 | + | 0.877072i | \(0.340506\pi\) | ||||
−0.480360 | + | 0.877072i | \(0.659494\pi\) | |||||||
\(744\) | 18.8959 | + | 32.7287i | 0.0253977 | + | 0.0439902i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36.2337 | − | 62.7585i | 0.0485706 | − | 0.0841267i | ||||
\(747\) | −134.372 | − | 232.740i | −0.179883 | − | 0.311566i | ||||
\(748\) | 90.1442 | 0.120514 | ||||||||
\(749\) | 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 | \(-0.471698\pi\) | |||||||
\(752\) | 37.4210 | − | 64.8150i | 0.0497619 | − | 0.0861901i | ||||
\(753\) | 28.8591 | + | 16.6618i | 0.0383255 | + | 0.0221273i | ||||
\(754\) | −36.5832 | + | 21.1213i | −0.0485188 | + | 0.0280124i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −32.3395 | + | 65.1625i | −0.0427771 | + | 0.0861938i | ||||
\(757\) | 1206.22i | 1.59342i | 0.604359 | + | 0.796712i | \(0.293429\pi\) | ||||
−0.604359 | + | 0.796712i | \(0.706571\pi\) | |||||||
\(758\) | −238.487 | + | 137.691i | −0.314627 | + | 0.181650i | ||||
\(759\) | 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 | \(0.382908\pi\) | |||||||
\(762\) | 370.101 | 0.485697 | ||||||||
\(763\) | 313.712 | − | 632.114i | 0.411156 | − | 0.828459i | ||||
\(764\) | 719.725 | 0.942048 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −643.088 | − | 371.287i | −0.839540 | − | 0.484709i | ||||
\(767\) | 91.6777 | + | 52.9301i | 0.119528 | + | 0.0690093i | ||||
\(768\) | −13.8564 | − | 24.0000i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | − | 1341.44i | − | 1.74440i | −0.489149 | − | 0.872200i | \(-0.662693\pi\) | ||
0.489149 | − | 0.872200i | \(-0.337307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −224.165 | −0.290746 | ||||||||
\(772\) | −242.045 | + | 139.745i | −0.313530 | + | 0.181017i | ||||
\(773\) | −90.0279 | + | 155.933i | −0.116466 | + | 0.201724i | −0.918365 | − | 0.395735i | \(-0.870490\pi\) |
0.801899 | + | 0.597460i | \(0.203823\pi\) | |||||||
\(774\) | −91.6290 | + | 158.706i | −0.118384 | + | 0.205047i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 184.403i | − | 0.237633i | ||||||
\(777\) | 21.3880 | + | 339.456i | 0.0275264 | + | 0.436881i | ||||
\(778\) | − | 570.677i | − | 0.733518i | ||||||
\(779\) | −27.8693 | − | 48.2711i | −0.0357758 | − | 0.0619654i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −270.700 | + | 468.866i | −0.346607 | + | 0.600341i | ||||
\(782\) | −68.6657 | − | 118.932i | −0.0878078 | − | 0.152087i | ||||
\(783\) | 44.2907 | 0.0565654 | ||||||||
\(784\) | −118.530 | − | 156.098i | −0.151186 | − | 0.199105i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 264.203 | + | 457.614i | 0.336137 | + | 0.582206i | ||||
\(787\) | 584.386 | − | 1012.19i | 0.742549 | − | 1.28613i | −0.208783 | − | 0.977962i | \(-0.566950\pi\) |
0.951331 | − | 0.308170i | \(-0.0997166\pi\) | |||||||
\(788\) | 430.142 | + | 248.343i | 0.545866 | + | 0.315156i | ||||
\(789\) | −250.387 | + | 144.561i | −0.317348 | + | 0.183221i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.6554 | + | 518.285i | 0.0412837 | + | 0.655228i | ||||
\(792\) | − | 46.9847i | − | 0.0593241i | ||||||
\(793\) | −143.711 | + | 82.9717i | −0.181225 | + | 0.104630i | ||||
\(794\) | −197.419 | − | 113.980i | −0.248639 | − | 0.143552i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 212.340 | − | 122.595i | 0.266759 | − | 0.154013i | ||||
\(797\) | −1242.38 | −1.55883 | −0.779413 | − | 0.626510i | \(-0.784483\pi\) | ||||
−0.779413 | + | 0.626510i | \(0.784483\pi\) | |||||||
\(798\) | 168.348 | + | 253.333i | 0.210962 | + | 0.317460i | ||||
\(799\) | −152.301 | −0.190614 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −306.871 | − | 177.172i | −0.383110 | − | 0.221189i | ||||
\(802\) | −520.531 | − | 300.529i | −0.649041 | − | 0.374724i | ||||
\(803\) | 169.331 | + | 293.290i | 0.210873 | + | 0.365243i | ||||
\(804\) | − | 22.8013i | − | 0.0283598i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.2308 | 0.0474327 | ||||||||
\(807\) | 313.641 | − | 181.081i | 0.388650 | − | 0.224387i | ||||
\(808\) | 197.421 | − | 341.942i | 0.244332 | − | 0.423196i | ||||
\(809\) | −44.8275 | + | 77.6435i | −0.0554110 | + | 0.0959747i | −0.892400 | − | 0.451244i | \(-0.850980\pi\) |
0.836989 | + | 0.547219i | \(0.184314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 234.127i | − | 0.288689i | −0.989527 | − | 0.144345i | \(-0.953893\pi\) | ||
0.989527 | − | 0.144345i | \(-0.0461074\pi\) | |||||||
\(812\) | −53.0496 | + | 106.892i | −0.0653320 | + | 0.131641i | ||||
\(813\) | 246.058i | 0.302654i | ||||||||
\(814\) | −109.840 | − | 190.249i | −0.134939 | − | 0.233721i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −28.1973 | + | 48.8392i | −0.0345556 | + | 0.0598520i | ||||
\(817\) | 383.123 | + | 663.588i | 0.468938 | + | 0.812225i | ||||
\(818\) | 610.095 | 0.745837 | ||||||||
\(819\) | 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 | \(0.965794\pi\) | |||||||
\(822\) | −163.676 | + | 283.494i | −0.199119 | + | 0.344884i | ||||
\(823\) | 745.037 | + | 430.147i | 0.905269 | + | 0.522657i | 0.878906 | − | 0.476995i | \(-0.158274\pi\) |
0.0263632 | + | 0.999652i | \(0.491607\pi\) | |||||||
\(824\) | −427.398 | + | 246.758i | −0.518686 | + | 0.299464i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 298.456 | − | 18.8047i | 0.361327 | − | 0.0227660i | ||||
\(827\) | 703.661i | 0.850860i | 0.904991 | + | 0.425430i | \(0.139877\pi\) | ||||
−0.904991 | + | 0.425430i | \(0.860123\pi\) | |||||||
\(828\) | −61.9896 | + | 35.7897i | −0.0748667 | + | 0.0432243i | ||||
\(829\) | −1282.06 | − | 740.196i | −1.54651 | − | 0.892878i | −0.998404 | − | 0.0564693i | \(-0.982016\pi\) |
−0.548106 | − | 0.836409i | \(-0.684651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 668.882 | − | 386.179i | 0.804912 | − | 0.464716i | ||||
\(832\) | −28.0347 | −0.0336955 | ||||||||
\(833\) | −154.495 | + | 367.717i | −0.185468 | + | 0.441437i | ||||
\(834\) | 474.618 | 0.569086 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −170.134 | − | 98.2271i | −0.203510 | − | 0.117496i | ||||
\(837\) | −34.7140 | − | 20.0422i | −0.0414743 | − | 0.0239452i | ||||
\(838\) | 413.949 | + | 716.980i | 0.493972 | + | 0.855585i | ||||
\(839\) | − | 1377.82i | − | 1.64222i | −0.570769 | − | 0.821111i | \(-0.693355\pi\) | ||
0.570769 | − | 0.821111i | \(-0.306645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −768.346 | −0.913610 | ||||||||
\(842\) | −490.225 | + | 283.032i | −0.582215 | + | 0.336142i | ||||
\(843\) | −417.435 | + | 723.018i | −0.495177 | + | 0.857672i | ||||
\(844\) | 352.829 | − | 611.118i | 0.418044 | − | 0.724073i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 79.3818i | 0.0938319i | ||||||||
\(847\) | −350.000 | − | 526.687i | −0.413223 | − | 0.621827i | ||||
\(848\) | − | 11.2716i | − | 0.0132920i | ||||||
\(849\) | −187.506 | − | 324.770i | −0.220855 | − | 0.382533i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −167.337 | + | 289.837i | −0.196636 | + | 0.340584i | ||||
\(852\) | −169.351 | − | 293.325i | −0.198769 | − | 0.344278i | ||||
\(853\) | 383.511 | 0.449602 | 0.224801 | − | 0.974405i | \(-0.427827\pi\) | ||||
0.224801 | + | 0.974405i | \(0.427827\pi\) | |||||||
\(854\) | −208.397 | + | 419.909i | −0.244024 | + | 0.491697i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −85.5265 | − | 148.136i | −0.0999141 | − | 0.173056i | ||||
\(857\) | 164.125 | − | 284.273i | 0.191512 | − | 0.331708i | −0.754240 | − | 0.656599i | \(-0.771994\pi\) |
0.945751 | + | 0.324891i | \(0.105328\pi\) | |||||||
\(858\) | −41.1625 | − | 23.7652i | −0.0479750 | − | 0.0276984i | ||||
\(859\) | 168.842 | − | 97.4811i | 0.196557 | − | 0.113482i | −0.398492 | − | 0.917172i | \(-0.630466\pi\) |
0.595048 | + | 0.803690i | \(0.297133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.1242 | − | 16.9355i | −0.0396332 | − | 0.0196696i | ||||
\(862\) | − | 558.985i | − | 0.648474i | ||||||
\(863\) | −463.984 | + | 267.881i | −0.537641 | + | 0.310407i | −0.744122 | − | 0.668043i | \(-0.767132\pi\) |
0.206481 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.92986 | + | 1.69156i | −0.00338321 | + | 0.00195330i | ||||
\(867\) | −385.801 | −0.444984 | ||||||||
\(868\) | 89.9493 | − | 59.7741i | 0.103628 | − | 0.0688641i | ||||
\(869\) | 681.818 | 0.784601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.9758 | − | 11.5331i | −0.0229344 | − | 0.0132412i | ||||
\(872\) | −246.936 | − | 142.569i | −0.283184 | − | 0.163496i | ||||
\(873\) | 97.7947 | + | 169.385i | 0.112021 | + | 0.194027i | ||||
\(874\) | 299.291i | 0.342438i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −211.869 | −0.241859 | ||||||||
\(877\) | −1045.48 | + | 603.606i | −1.19210 | + | 0.688262i | −0.958784 | − | 0.284138i | \(-0.908293\pi\) |
−0.233321 | + | 0.972400i | \(0.574959\pi\) | |||||||
\(878\) | −285.989 | + | 495.348i | −0.325728 | + | 0.564177i | ||||
\(879\) | −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 | \(0.883711\pi\) | |||||||
\(882\) | 191.660 | + | 80.5253i | 0.217302 | + | 0.0912985i | ||||
\(883\) | 177.196i | 0.200675i | 0.994953 | + | 0.100337i | \(0.0319922\pi\) | ||||
−0.994953 | + | 0.100337i | \(0.968008\pi\) | |||||||
\(884\) | 28.5248 | + | 49.4065i | 0.0322679 | + | 0.0558897i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −206.483 | + | 357.639i | −0.233051 | + | 0.403655i | ||||
\(887\) | −636.205 | − | 1101.94i | −0.717255 | − | 1.24232i | −0.962083 | − | 0.272755i | \(-0.912065\pi\) |
0.244829 | − | 0.969566i | \(-0.421268\pi\) | |||||||
\(888\) | 137.433 | 0.154767 | ||||||||
\(889\) | −66.5072 | − | 1055.56i | −0.0748112 | − | 1.18736i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9174 | + | 43.1582i | 0.0279657 | + | 0.0484379i | ||||
\(892\) | −61.7420 | + | 106.940i | −0.0692175 | + | 0.119888i | ||||
\(893\) | 287.446 | + | 165.957i | 0.321888 | + | 0.185842i | ||||
\(894\) | 140.021 | − | 80.8410i | 0.156623 | − | 0.0904261i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −65.9600 | + | 43.8324i | −0.0736161 | + | 0.0489201i | ||||
\(897\) | 72.4108i | 0.0807255i | ||||||||
\(898\) | 153.926 | − | 88.8693i | 0.171410 | − | 0.0989636i | ||||
\(899\) | −56.9447 | − | 32.8770i | −0.0633423 | − | 0.0365707i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8643 | + | 11.4687i | −0.0220470 | + | 0.0127288i | ||||
\(902\) | 24.6048 | 0.0272781 | ||||||||
\(903\) | 469.109 | + | 232.814i | 0.519500 | + | 0.257823i | ||||
\(904\) | 209.834 | 0.232118 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 73.9958 | + | 42.7215i | 0.0816731 | + | 0.0471540i | ||||
\(907\) | 155.255 | + | 89.6364i | 0.171174 | + | 0.0988273i | 0.583139 | − | 0.812372i | \(-0.301824\pi\) |
−0.411965 | + | 0.911200i | \(0.635158\pi\) | |||||||
\(908\) | −209.523 | − | 362.905i | −0.230752 | − | 0.399675i | ||||
\(909\) | 418.792i | 0.460718i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 684.893 | 0.751803 | 0.375902 | − | 0.926660i | \(-0.377333\pi\) | ||||
0.375902 | + | 0.926660i | \(0.377333\pi\) | |||||||
\(912\) | 106.437 | − | 61.4514i | 0.116707 | − | 0.0673809i | ||||
\(913\) | 248.015 | − | 429.575i | 0.271649 | − | 0.470510i | ||||
\(914\) | 60.8133 | − | 105.332i | 0.0665353 | − | 0.115243i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 215.598i | − | 0.235369i | ||||||
\(917\) | 1257.67 | − | 835.763i | 1.37151 | − | 0.911410i | ||||
\(918\) | − | 59.8156i | − | 0.0651586i | ||||||
\(919\) | 470.376 | + | 814.715i | 0.511835 | + | 0.886523i | 0.999906 | + | 0.0137197i | \(0.00436726\pi\) |
−0.488071 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2960 | − | 31.6896i | 0.0198653 | − | 0.0344078i | ||||
\(922\) | 92.9481 | + | 160.991i | 0.100811 | + | 0.174611i | ||||
\(923\) | −342.637 | −0.371221 | ||||||||
\(924\) | −134.004 | + | 8.44315i | −0.145026 | + | 0.00913761i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.3169 | − | 90.6156i | −0.0564978 | − | 0.0978570i | ||||
\(927\) | 261.726 | − | 453.324i | 0.282337 | − | 0.489022i | ||||
\(928\) | 41.7576 | + | 24.1088i | 0.0449975 | + | 0.0259793i | ||||
\(929\) | −5.55322 | + | 3.20616i | −0.00597764 | + | 0.00345119i | −0.502986 | − | 0.864295i | \(-0.667765\pi\) |
0.497008 | + | 0.867746i | \(0.334432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 692.275 | − | 525.665i | 0.743582 | − | 0.564624i | ||||
\(932\) | − | 653.693i | − | 0.701387i | ||||||
\(933\) | −129.954 | + | 75.0288i | −0.139286 | + | 0.0804167i | ||||
\(934\) | −547.346 | − | 316.010i | −0.586023 | − | 0.338341i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 25.7515 | − | 14.8676i | 0.0275123 | − | 0.0158842i | ||||
\(937\) | −867.253 | −0.925564 | −0.462782 | − | 0.886472i | \(-0.653149\pi\) | ||||
−0.462782 | + | 0.886472i | \(0.653149\pi\) | |||||||
\(938\) | −65.0312 | + | 4.09739i | −0.0693296 | + | 0.00436822i | ||||
\(939\) | −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 | \(0.766041\pi\) | |||||||
\(942\) | −113.492 | − | 65.5246i | −0.120480 | − | 0.0695590i | ||||
\(943\) | −18.7423 | − | 32.4626i | −0.0198752 | − | 0.0344248i | ||||
\(944\) | − | 120.833i | − | 0.128002i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −338.246 | −0.357553 | ||||||||
\(947\) | 648.272 | − | 374.280i | 0.684553 | − | 0.395227i | −0.117015 | − | 0.993130i | \(-0.537333\pi\) |
0.801568 | + | 0.597903i | \(0.203999\pi\) | |||||||
\(948\) | −213.274 | + | 369.402i | −0.224973 | + | 0.389665i | ||||
\(949\) | −107.165 | + | 185.615i | −0.112924 | + | 0.195590i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 536.677i | 0.564329i | ||||||||
\(952\) | 144.361 | + | 71.6447i | 0.151639 | + | 0.0752571i | ||||
\(953\) | − | 21.6304i | − | 0.0226972i | −0.999936 | − | 0.0113486i | \(-0.996388\pi\) | ||
0.999936 | − | 0.0113486i | \(-0.00361244\pi\) | |||||||
\(954\) | 5.97767 | + | 10.3536i | 0.00626590 | + | 0.0108529i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.20117 | − | 15.9369i | 0.00962466 | − | 0.0166704i | ||||
\(957\) | 40.8744 | + | 70.7965i | 0.0427110 | + | 0.0739776i | ||||
\(958\) | 839.062 | 0.875847 | ||||||||
\(959\) | 837.962 | + | 415.872i | 0.873787 | + | 0.433652i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −450.745 | − | 780.714i | −0.469038 | − | 0.812397i | ||||
\(962\) | 69.5147 | − | 120.403i | 0.0722606 | − | 0.125159i | ||||
\(963\) | 157.122 | + | 90.7146i | 0.163159 | + | 0.0941999i | ||||
\(964\) | 556.311 | − | 321.186i | 0.577086 | − | 0.333181i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 113.215 | + | 170.368i | 0.117200 | + | 0.176365i | ||||
\(967\) | 452.988i | 0.468447i | 0.972183 | + | 0.234224i | \(0.0752548\pi\) | ||||
−0.972183 | + | 0.234224i | \(0.924745\pi\) | |||||||
\(968\) | −221.285 | + | 127.759i | −0.228601 | + | 0.131983i | ||||
\(969\) | −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 | \(0.0967791\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −85.2889 | − | 1353.65i | −0.0876556 | − | 1.39121i | ||||
\(974\) | 1159.01 | 1.18995 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 164.038 | + | 94.7075i | 0.168072 | + | 0.0970364i | ||||
\(977\) | −1019.58 | − | 588.653i | −1.04358 | − | 0.602511i | −0.122734 | − | 0.992440i | \(-0.539166\pi\) |
−0.920845 | + | 0.389929i | \(0.872500\pi\) | |||||||
\(978\) | 252.278 | + | 436.957i | 0.257952 | + | 0.446787i | ||||
\(979\) | − | 654.025i | − | 0.668054i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 302.434 | 0.308292 | ||||||||
\(982\) | −679.395 | + | 392.249i | −0.691848 | + | 0.399439i | ||||
\(983\) | −401.275 | + | 695.029i | −0.408215 | + | 0.707049i | −0.994690 | − | 0.102918i | \(-0.967182\pi\) |
0.586475 | + | 0.809967i | \(0.300515\pi\) | |||||||
\(984\) | −7.69646 | + | 13.3307i | −0.00782161 | + | 0.0135474i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 98.1212i | − | 0.0995144i | ||||||
\(987\) | 226.404 | − | 14.2649i | 0.229386 | − | 0.0144528i | ||||
\(988\) | − | 124.330i | − | 0.125840i | ||||||
\(989\) | 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 | \(0.137140\pi\) | |||||||
\(992\) | −21.8191 | − | 37.7918i | −0.0219951 | − | 0.0380966i | ||||
\(993\) | −721.554 | −0.726640 | ||||||||
\(994\) | −806.155 | + | 535.715i | −0.811021 | + | 0.538948i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 155.160 | + | 268.745i | 0.155783 | + | 0.269824i | ||||
\(997\) | 466.550 | − | 808.088i | 0.467953 | − | 0.810519i | −0.531376 | − | 0.847136i | \(-0.678325\pi\) |
0.999329 | + | 0.0366170i | \(0.0116582\pi\) | |||||||
\(998\) | −777.453 | − | 448.862i | −0.779011 | − | 0.449762i | ||||
\(999\) | −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.q.b.199.1 | 16 | ||
5.2 | odd | 4 | 1050.3.p.d.451.1 | yes | 8 | ||
5.3 | odd | 4 | 1050.3.p.c.451.4 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1050.3.q.b.199.8 | 16 | ||
7.5 | odd | 6 | inner | 1050.3.q.b.649.8 | 16 | ||
35.12 | even | 12 | 1050.3.p.d.901.1 | yes | 8 | ||
35.19 | odd | 6 | inner | 1050.3.q.b.649.1 | 16 | ||
35.33 | even | 12 | 1050.3.p.c.901.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.4 | ✓ | 8 | 5.3 | odd | 4 | ||
1050.3.p.c.901.4 | yes | 8 | 35.33 | even | 12 | ||
1050.3.p.d.451.1 | yes | 8 | 5.2 | odd | 4 | ||
1050.3.p.d.901.1 | yes | 8 | 35.12 | even | 12 | ||
1050.3.q.b.199.1 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.q.b.199.8 | 16 | 5.4 | even | 2 | inner | ||
1050.3.q.b.649.1 | 16 | 35.19 | odd | 6 | inner | ||
1050.3.q.b.649.8 | 16 | 7.5 | odd | 6 | inner |