Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.6 | ||
Root | \(-0.627868 + 2.34324i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.c.49.6 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.09991 | − | 0.768349i | −0.939110 | − | 0.343616i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 2.51805i | 0.951732i | 0.879518 | + | 0.475866i | \(0.157865\pi\) | ||||
−0.879518 | + | 0.475866i | \(0.842135\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.20275 | + | 0.384547i | −0.696572 | + | 0.121604i | ||||
\(11\) | 2.88497 | 0.869851 | 0.434925 | − | 0.900467i | \(-0.356775\pi\) | ||||
0.434925 | + | 0.900467i | \(0.356775\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 4.03244 | + | 2.32813i | 1.11840 | + | 0.645707i | 0.940991 | − | 0.338431i | \(-0.109896\pi\) |
0.177406 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(14\) | 1.25902 | + | 2.18069i | 0.336488 | + | 0.582814i | ||||
\(15\) | 2.20275 | − | 0.384547i | 0.568749 | − | 0.0992896i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.31158 | − | 3.64399i | 1.53078 | − | 0.883798i | 0.531457 | − | 0.847085i | \(-0.321645\pi\) |
0.999326 | − | 0.0367122i | \(-0.0116885\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 4.11420 | − | 1.43993i | 0.943861 | − | 0.330342i | ||||
\(20\) | −1.71537 | + | 1.43440i | −0.383568 | + | 0.320743i | ||||
\(21\) | −1.25902 | − | 2.18069i | −0.274741 | − | 0.475866i | ||||
\(22\) | 2.49846 | − | 1.44248i | 0.532673 | − | 0.307539i | ||||
\(23\) | −1.48237 | − | 0.855848i | −0.309096 | − | 0.178457i | 0.337426 | − | 0.941352i | \(-0.390444\pi\) |
−0.646522 | + | 0.762895i | \(0.723777\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 3.81928 | + | 3.22694i | 0.763856 | + | 0.645387i | ||||
\(26\) | 4.65626 | 0.913167 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.18069 | + | 1.25902i | 0.412112 | + | 0.237933i | ||||
\(29\) | 2.20959 | − | 3.82712i | 0.410310 | − | 0.710678i | −0.584613 | − | 0.811312i | \(-0.698754\pi\) |
0.994923 | + | 0.100634i | \(0.0320872\pi\) | |||||||
\(30\) | 1.71537 | − | 1.43440i | 0.313182 | − | 0.261885i | ||||
\(31\) | −9.22060 | −1.65607 | −0.828035 | − | 0.560677i | \(-0.810541\pi\) | ||||
−0.828035 | + | 0.560677i | \(0.810541\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −2.49846 | + | 1.44248i | −0.434925 | + | 0.251104i | ||||
\(34\) | 3.64399 | − | 6.31158i | 0.624939 | − | 1.08243i | ||||
\(35\) | 1.93474 | − | 5.28768i | 0.327031 | − | 0.893781i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 3.26480i | 0.536730i | 0.963317 | + | 0.268365i | \(0.0864834\pi\) | ||||
−0.963317 | + | 0.268365i | \(0.913517\pi\) | |||||||
\(38\) | 2.84303 | − | 3.30411i | 0.461201 | − | 0.535998i | ||||
\(39\) | −4.65626 | −0.745598 | ||||||||
\(40\) | −0.768349 | + | 2.09991i | −0.121487 | + | 0.332026i | ||||
\(41\) | 4.48368 | + | 7.76596i | 0.700233 | + | 1.21284i | 0.968384 | + | 0.249463i | \(0.0802540\pi\) |
−0.268151 | + | 0.963377i | \(0.586413\pi\) | |||||||
\(42\) | −2.18069 | − | 1.25902i | −0.336488 | − | 0.194271i | ||||
\(43\) | −5.84894 | + | 3.37689i | −0.891955 | + | 0.514971i | −0.874582 | − | 0.484878i | \(-0.838864\pi\) |
−0.0173738 | + | 0.999849i | \(0.505531\pi\) | |||||||
\(44\) | 1.44248 | − | 2.49846i | 0.217463 | − | 0.376656i | ||||
\(45\) | −1.71537 | + | 1.43440i | −0.255712 | + | 0.213828i | ||||
\(46\) | −1.71170 | −0.252376 | ||||||||
\(47\) | 3.98083 | + | 2.29833i | 0.580664 | + | 0.335246i | 0.761397 | − | 0.648286i | \(-0.224514\pi\) |
−0.180733 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | 0.659446 | 0.0942065 | ||||||||
\(50\) | 4.92106 | + | 0.884968i | 0.695943 | + | 0.125153i | ||||
\(51\) | −3.64399 | + | 6.31158i | −0.510261 | + | 0.883798i | ||||
\(52\) | 4.03244 | − | 2.32813i | 0.559198 | − | 0.322853i | ||||
\(53\) | −9.38113 | − | 5.41620i | −1.28860 | − | 0.743972i | −0.310193 | − | 0.950673i | \(-0.600394\pi\) |
−0.978404 | + | 0.206701i | \(0.933727\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −6.05819 | − | 2.21666i | −0.816886 | − | 0.298895i | ||||
\(56\) | 2.51805 | 0.336488 | ||||||||
\(57\) | −2.84303 | + | 3.30411i | −0.376569 | + | 0.437640i | ||||
\(58\) | − | 4.41917i | − | 0.580266i | ||||||
\(59\) | 4.73274 | + | 8.19734i | 0.616150 | + | 1.06720i | 0.990182 | + | 0.139787i | \(0.0446418\pi\) |
−0.374032 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(60\) | 0.768349 | − | 2.09991i | 0.0991935 | − | 0.271098i | ||||
\(61\) | 7.50173 | − | 12.9934i | 0.960498 | − | 1.66363i | 0.239244 | − | 0.970959i | \(-0.423100\pi\) |
0.721254 | − | 0.692671i | \(-0.243566\pi\) | |||||||
\(62\) | −7.98528 | + | 4.61030i | −1.01413 | + | 0.585509i | ||||
\(63\) | 2.18069 | + | 1.25902i | 0.274741 | + | 0.158622i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.67896 | − | 7.98719i | −0.828422 | − | 0.990689i | ||||
\(66\) | −1.44248 | + | 2.49846i | −0.177558 | + | 0.307539i | ||||
\(67\) | 9.23107 | + | 5.32956i | 1.12776 | + | 0.651110i | 0.943369 | − | 0.331744i | \(-0.107637\pi\) |
0.184386 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(68\) | − | 7.28798i | − | 0.883798i | ||||||
\(69\) | 1.71170 | 0.206064 | ||||||||
\(70\) | −0.968307 | − | 5.54663i | −0.115735 | − | 0.662950i | ||||
\(71\) | −5.38040 | − | 9.31912i | −0.638536 | − | 1.10598i | −0.985754 | − | 0.168192i | \(-0.946207\pi\) |
0.347218 | − | 0.937784i | \(-0.387126\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −12.2689 | + | 7.08348i | −1.43597 | + | 0.829059i | −0.997567 | − | 0.0697187i | \(-0.977790\pi\) |
−0.438405 | + | 0.898777i | \(0.644457\pi\) | |||||||
\(74\) | 1.63240 | + | 2.82740i | 0.189763 | + | 0.328679i | ||||
\(75\) | −4.92106 | − | 0.884968i | −0.568235 | − | 0.102187i | ||||
\(76\) | 0.810083 | − | 4.28296i | 0.0929229 | − | 0.491289i | ||||
\(77\) | 7.26448i | 0.827865i | ||||||||
\(78\) | −4.03244 | + | 2.32813i | −0.456584 | + | 0.263609i | ||||
\(79\) | 4.11998 | + | 7.13601i | 0.463533 | + | 0.802864i | 0.999134 | − | 0.0416079i | \(-0.0132480\pi\) |
−0.535601 | + | 0.844471i | \(0.679915\pi\) | |||||||
\(80\) | 0.384547 | + | 2.20275i | 0.0429937 | + | 0.246275i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.76596 | + | 4.48368i | 0.857607 | + | 0.495140i | ||||
\(83\) | 7.14523i | 0.784291i | 0.919903 | + | 0.392146i | \(0.128267\pi\) | ||||
−0.919903 | + | 0.392146i | \(0.871733\pi\) | |||||||
\(84\) | −2.51805 | −0.274741 | ||||||||
\(85\) | −16.0536 | + | 2.80257i | −1.74126 | + | 0.303982i | ||||
\(86\) | −3.37689 | + | 5.84894i | −0.364139 | + | 0.630708i | ||||
\(87\) | 4.41917i | 0.473785i | ||||||||
\(88\) | − | 2.88497i | − | 0.307539i | ||||||
\(89\) | 2.37111 | − | 4.10688i | 0.251337 | − | 0.435328i | −0.712557 | − | 0.701614i | \(-0.752463\pi\) |
0.963894 | + | 0.266286i | \(0.0857964\pi\) | |||||||
\(90\) | −0.768349 | + | 2.09991i | −0.0809911 | + | 0.221350i | ||||
\(91\) | −5.86233 | + | 10.1539i | −0.614540 | + | 1.06441i | ||||
\(92\) | −1.48237 | + | 0.855848i | −0.154548 | + | 0.0892284i | ||||
\(93\) | 7.98528 | − | 4.61030i | 0.828035 | − | 0.478066i | ||||
\(94\) | 4.59667 | 0.474110 | ||||||||
\(95\) | −9.74583 | − | 0.137412i | −0.999901 | − | 0.0140982i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.98898 | + | 1.14834i | −0.201950 | + | 0.116596i | −0.597565 | − | 0.801821i | \(-0.703865\pi\) |
0.395615 | + | 0.918417i | \(0.370532\pi\) | |||||||
\(98\) | 0.571097 | − | 0.329723i | 0.0576895 | − | 0.0333070i | ||||
\(99\) | 1.44248 | − | 2.49846i | 0.144975 | − | 0.251104i | ||||
\(100\) | 4.70425 | − | 1.69412i | 0.470425 | − | 0.169412i | ||||
\(101\) | 1.68398 | − | 2.91673i | 0.167562 | − | 0.290226i | −0.770000 | − | 0.638044i | \(-0.779744\pi\) |
0.937562 | + | 0.347818i | \(0.113077\pi\) | |||||||
\(102\) | 7.28798i | 0.721618i | ||||||||
\(103\) | − | 10.9873i | − | 1.08261i | −0.840826 | − | 0.541305i | \(-0.817930\pi\) | ||
0.840826 | − | 0.541305i | \(-0.182070\pi\) | |||||||
\(104\) | 2.32813 | − | 4.03244i | 0.228292 | − | 0.395413i | ||||
\(105\) | 0.968307 | + | 5.54663i | 0.0944971 | + | 0.541296i | ||||
\(106\) | −10.8324 | −1.05214 | ||||||||
\(107\) | − | 3.35775i | − | 0.324605i | −0.986741 | − | 0.162303i | \(-0.948108\pi\) | ||
0.986741 | − | 0.162303i | \(-0.0518921\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 2.11647 | + | 3.66583i | 0.202721 | + | 0.351122i | 0.949404 | − | 0.314057i | \(-0.101688\pi\) |
−0.746683 | + | 0.665180i | \(0.768355\pi\) | |||||||
\(110\) | −6.35487 | + | 1.10941i | −0.605914 | + | 0.105778i | ||||
\(111\) | −1.63240 | − | 2.82740i | −0.154941 | − | 0.268365i | ||||
\(112\) | 2.18069 | − | 1.25902i | 0.206056 | − | 0.118966i | ||||
\(113\) | − | 18.7982i | − | 1.76839i | −0.467118 | − | 0.884195i | \(-0.654708\pi\) | ||
0.467118 | − | 0.884195i | \(-0.345292\pi\) | |||||||
\(114\) | −0.810083 | + | 4.28296i | −0.0758712 | + | 0.401136i | ||||
\(115\) | 2.45527 | + | 2.93619i | 0.228955 | + | 0.273801i | ||||
\(116\) | −2.20959 | − | 3.82712i | −0.205155 | − | 0.355339i | ||||
\(117\) | 4.03244 | − | 2.32813i | 0.372799 | − | 0.215236i | ||||
\(118\) | 8.19734 | + | 4.73274i | 0.754626 | + | 0.435684i | ||||
\(119\) | 9.17574 | + | 15.8928i | 0.841138 | + | 1.45689i | ||||
\(120\) | −0.384547 | − | 2.20275i | −0.0351042 | − | 0.201083i | ||||
\(121\) | −2.67696 | −0.243360 | ||||||||
\(122\) | − | 15.0035i | − | 1.35835i | ||||||
\(123\) | −7.76596 | − | 4.48368i | −0.700233 | − | 0.404280i | ||||
\(124\) | −4.61030 | + | 7.98528i | −0.414017 | + | 0.717099i | ||||
\(125\) | −5.54074 | − | 9.71083i | −0.495579 | − | 0.868563i | ||||
\(126\) | 2.51805 | 0.224325 | ||||||||
\(127\) | −13.6465 | − | 7.87880i | −1.21093 | − | 0.699131i | −0.247968 | − | 0.968768i | \(-0.579763\pi\) |
−0.962962 | + | 0.269637i | \(0.913096\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 3.37689 | − | 5.84894i | 0.297318 | − | 0.514971i | ||||
\(130\) | −9.77774 | − | 3.57763i | −0.857565 | − | 0.313779i | ||||
\(131\) | 3.28357 | + | 5.68732i | 0.286887 | + | 0.496903i | 0.973065 | − | 0.230531i | \(-0.0740462\pi\) |
−0.686178 | + | 0.727434i | \(0.740713\pi\) | |||||||
\(132\) | 2.88497i | 0.251104i | ||||||||
\(133\) | 3.62581 | + | 10.3597i | 0.314397 | + | 0.898303i | ||||
\(134\) | 10.6591 | 0.920808 | ||||||||
\(135\) | 0.768349 | − | 2.09991i | 0.0661290 | − | 0.180732i | ||||
\(136\) | −3.64399 | − | 6.31158i | −0.312470 | − | 0.541213i | ||||
\(137\) | −12.5023 | − | 7.21818i | −1.06814 | − | 0.616691i | −0.140467 | − | 0.990085i | \(-0.544861\pi\) |
−0.927673 | + | 0.373394i | \(0.878194\pi\) | |||||||
\(138\) | 1.48237 | − | 0.855848i | 0.126188 | − | 0.0728547i | ||||
\(139\) | −3.09728 | + | 5.36464i | −0.262708 | + | 0.455023i | −0.966960 | − | 0.254926i | \(-0.917949\pi\) |
0.704253 | + | 0.709949i | \(0.251282\pi\) | |||||||
\(140\) | −3.61190 | − | 4.31937i | −0.305261 | − | 0.365054i | ||||
\(141\) | −4.59667 | −0.387109 | ||||||||
\(142\) | −9.31912 | − | 5.38040i | −0.782043 | − | 0.451513i | ||||
\(143\) | 11.6335 | + | 6.71658i | 0.972838 | + | 0.561668i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −7.58051 | + | 6.33888i | −0.629527 | + | 0.526416i | ||||
\(146\) | −7.08348 | + | 12.2689i | −0.586233 | + | 1.01539i | ||||
\(147\) | −0.571097 | + | 0.329723i | −0.0471033 | + | 0.0271951i | ||||
\(148\) | 2.82740 | + | 1.63240i | 0.232411 | + | 0.134183i | ||||
\(149\) | −5.99475 | − | 10.3832i | −0.491109 | − | 0.850626i | 0.508838 | − | 0.860862i | \(-0.330075\pi\) |
−0.999948 | + | 0.0102357i | \(0.996742\pi\) | |||||||
\(150\) | −4.70425 | + | 1.69412i | −0.384100 | + | 0.138325i | ||||
\(151\) | −5.51534 | −0.448832 | −0.224416 | − | 0.974493i | \(-0.572047\pi\) | ||||
−0.224416 | + | 0.974493i | \(0.572047\pi\) | |||||||
\(152\) | −1.43993 | − | 4.11420i | −0.116794 | − | 0.333705i | ||||
\(153\) | − | 7.28798i | − | 0.589198i | ||||||
\(154\) | 3.63224 | + | 6.29123i | 0.292694 | + | 0.506961i | ||||
\(155\) | 19.3625 | + | 7.08464i | 1.55523 | + | 0.569052i | ||||
\(156\) | −2.32813 | + | 4.03244i | −0.186399 | + | 0.322853i | ||||
\(157\) | 10.6341 | − | 6.13962i | 0.848696 | − | 0.489995i | −0.0115149 | − | 0.999934i | \(-0.503665\pi\) |
0.860211 | + | 0.509939i | \(0.170332\pi\) | |||||||
\(158\) | 7.13601 | + | 4.11998i | 0.567710 | + | 0.327768i | ||||
\(159\) | 10.8324 | 0.859065 | ||||||||
\(160\) | 1.43440 | + | 1.71537i | 0.113400 | + | 0.135612i | ||||
\(161\) | 2.15507 | − | 3.73268i | 0.169843 | − | 0.294177i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | − | 3.45801i | − | 0.270852i | −0.990787 | − | 0.135426i | \(-0.956760\pi\) | ||
0.990787 | − | 0.135426i | \(-0.0432403\pi\) | |||||||
\(164\) | 8.96736 | 0.700233 | ||||||||
\(165\) | 6.35487 | − | 1.10941i | 0.494726 | − | 0.0863671i | ||||
\(166\) | 3.57262 | + | 6.18795i | 0.277289 | + | 0.480278i | ||||
\(167\) | 5.37144 | + | 3.10120i | 0.415654 | + | 0.239978i | 0.693216 | − | 0.720730i | \(-0.256193\pi\) |
−0.277562 | + | 0.960708i | \(0.589526\pi\) | |||||||
\(168\) | −2.18069 | + | 1.25902i | −0.168244 | + | 0.0971357i | ||||
\(169\) | 4.34036 | + | 7.51773i | 0.333874 | + | 0.578287i | ||||
\(170\) | −12.5016 | + | 10.4539i | −0.958826 | + | 0.801779i | ||||
\(171\) | 0.810083 | − | 4.28296i | 0.0619486 | − | 0.327526i | ||||
\(172\) | 6.75378i | 0.514971i | ||||||||
\(173\) | −12.4712 | + | 7.20026i | −0.948169 | + | 0.547425i | −0.892512 | − | 0.451025i | \(-0.851059\pi\) |
−0.0556571 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(174\) | 2.20959 | + | 3.82712i | 0.167508 | + | 0.290133i | ||||
\(175\) | −8.12557 | + | 9.61712i | −0.614235 | + | 0.726986i | ||||
\(176\) | −1.44248 | − | 2.49846i | −0.108731 | − | 0.188328i | ||||
\(177\) | −8.19734 | − | 4.73274i | −0.616150 | − | 0.355734i | ||||
\(178\) | − | 4.74222i | − | 0.355444i | ||||||
\(179\) | −1.94176 | −0.145134 | −0.0725670 | − | 0.997364i | \(-0.523119\pi\) | ||||
−0.0725670 | + | 0.997364i | \(0.523119\pi\) | |||||||
\(180\) | 0.384547 | + | 2.20275i | 0.0286624 | + | 0.164184i | ||||
\(181\) | −8.81480 | + | 15.2677i | −0.655199 | + | 1.13484i | 0.326645 | + | 0.945147i | \(0.394082\pi\) |
−0.981844 | + | 0.189691i | \(0.939251\pi\) | |||||||
\(182\) | 11.7247i | 0.869090i | ||||||||
\(183\) | 15.0035i | 1.10909i | ||||||||
\(184\) | −0.855848 | + | 1.48237i | −0.0630940 | + | 0.109282i | ||||
\(185\) | 2.50851 | − | 6.85581i | 0.184429 | − | 0.504049i | ||||
\(186\) | 4.61030 | − | 7.98528i | 0.338044 | − | 0.585509i | ||||
\(187\) | 18.2087 | − | 10.5128i | 1.33155 | − | 0.768772i | ||||
\(188\) | 3.98083 | − | 2.29833i | 0.290332 | − | 0.167623i | ||||
\(189\) | −2.51805 | −0.183161 | ||||||||
\(190\) | −8.50884 | + | 4.75391i | −0.617296 | + | 0.344885i | ||||
\(191\) | −4.61377 | −0.333840 | −0.166920 | − | 0.985970i | \(-0.553382\pi\) | ||||
−0.166920 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −21.7202 | + | 12.5401i | −1.56345 | + | 0.902659i | −0.566547 | + | 0.824030i | \(0.691721\pi\) |
−0.996904 | + | 0.0786292i | \(0.974946\pi\) | |||||||
\(194\) | −1.14834 | + | 1.98898i | −0.0824458 | + | 0.142800i | ||||
\(195\) | 9.77774 | + | 3.57763i | 0.700198 | + | 0.256200i | ||||
\(196\) | 0.329723 | − | 0.571097i | 0.0235516 | − | 0.0407926i | ||||
\(197\) | − | 3.62439i | − | 0.258227i | −0.991630 | − | 0.129113i | \(-0.958787\pi\) | ||
0.991630 | − | 0.129113i | \(-0.0412131\pi\) | |||||||
\(198\) | − | 2.88497i | − | 0.205026i | ||||||
\(199\) | 0.298493 | − | 0.517005i | 0.0211596 | − | 0.0366495i | −0.855252 | − | 0.518213i | \(-0.826598\pi\) |
0.876411 | + | 0.481563i | \(0.159931\pi\) | |||||||
\(200\) | 3.22694 | − | 3.81928i | 0.228179 | − | 0.270064i | ||||
\(201\) | −10.6591 | −0.751837 | ||||||||
\(202\) | − | 3.36795i | − | 0.236968i | ||||||
\(203\) | 9.63686 | + | 5.56384i | 0.676375 | + | 0.390505i | ||||
\(204\) | 3.64399 | + | 6.31158i | 0.255130 | + | 0.441899i | ||||
\(205\) | −3.44837 | − | 19.7529i | −0.240845 | − | 1.37960i | ||||
\(206\) | −5.49365 | − | 9.51527i | −0.382760 | − | 0.662961i | ||||
\(207\) | −1.48237 | + | 0.855848i | −0.103032 | + | 0.0594856i | ||||
\(208\) | − | 4.65626i | − | 0.322853i | ||||||
\(209\) | 11.8693 | − | 4.15415i | 0.821018 | − | 0.287349i | ||||
\(210\) | 3.61190 | + | 4.31937i | 0.249244 | + | 0.298065i | ||||
\(211\) | 11.4644 | + | 19.8569i | 0.789242 | + | 1.36701i | 0.926432 | + | 0.376462i | \(0.122859\pi\) |
−0.137191 | + | 0.990545i | \(0.543807\pi\) | |||||||
\(212\) | −9.38113 | + | 5.41620i | −0.644299 | + | 0.371986i | ||||
\(213\) | 9.31912 | + | 5.38040i | 0.638536 | + | 0.368659i | ||||
\(214\) | −1.67887 | − | 2.90789i | −0.114765 | − | 0.198779i | ||||
\(215\) | 14.8769 | − | 2.59715i | 1.01460 | − | 0.177124i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − | 23.2179i | − | 1.57613i | ||||||
\(218\) | 3.66583 | + | 2.11647i | 0.248281 | + | 0.143345i | ||||
\(219\) | 7.08348 | − | 12.2689i | 0.478657 | − | 0.829059i | ||||
\(220\) | −4.94878 | + | 4.13821i | −0.333647 | + | 0.278998i | ||||
\(221\) | 33.9347 | 2.28270 | ||||||||
\(222\) | −2.82740 | − | 1.63240i | −0.189763 | − | 0.109560i | ||||
\(223\) | −9.74016 | + | 5.62349i | −0.652250 | + | 0.376576i | −0.789318 | − | 0.613985i | \(-0.789565\pi\) |
0.137068 | + | 0.990562i | \(0.456232\pi\) | |||||||
\(224\) | 1.25902 | − | 2.18069i | 0.0841220 | − | 0.145704i | ||||
\(225\) | 4.70425 | − | 1.69412i | 0.313616 | − | 0.112942i | ||||
\(226\) | −9.39912 | − | 16.2798i | −0.625220 | − | 1.08291i | ||||
\(227\) | 8.82814i | 0.585944i | 0.956121 | + | 0.292972i | \(0.0946443\pi\) | ||||
−0.956121 | + | 0.292972i | \(0.905356\pi\) | |||||||
\(228\) | 1.43993 | + | 4.11420i | 0.0953616 | + | 0.272469i | ||||
\(229\) | 22.2817 | 1.47241 | 0.736207 | − | 0.676756i | \(-0.236615\pi\) | ||||
0.736207 | + | 0.676756i | \(0.236615\pi\) | |||||||
\(230\) | 3.59442 | + | 1.31518i | 0.237009 | + | 0.0867205i | ||||
\(231\) | −3.63224 | − | 6.29123i | −0.238984 | − | 0.413932i | ||||
\(232\) | −3.82712 | − | 2.20959i | −0.251263 | − | 0.145066i | ||||
\(233\) | 5.35318 | − | 3.09066i | 0.350699 | − | 0.202476i | −0.314294 | − | 0.949326i | \(-0.601768\pi\) |
0.664993 | + | 0.746850i | \(0.268435\pi\) | |||||||
\(234\) | 2.32813 | − | 4.03244i | 0.152195 | − | 0.263609i | ||||
\(235\) | −6.59348 | − | 7.88497i | −0.430111 | − | 0.514359i | ||||
\(236\) | 9.46547 | 0.616150 | ||||||||
\(237\) | −7.13601 | − | 4.11998i | −0.463533 | − | 0.267621i | ||||
\(238\) | 15.8928 | + | 9.17574i | 1.03018 | + | 0.594775i | ||||
\(239\) | −18.1898 | −1.17660 | −0.588299 | − | 0.808644i | \(-0.700202\pi\) | ||||
−0.588299 | + | 0.808644i | \(0.700202\pi\) | |||||||
\(240\) | −1.43440 | − | 1.71537i | −0.0925904 | − | 0.110726i | ||||
\(241\) | −1.24768 | + | 2.16104i | −0.0803699 | + | 0.139205i | −0.903409 | − | 0.428780i | \(-0.858943\pi\) |
0.823039 | + | 0.567985i | \(0.192277\pi\) | |||||||
\(242\) | −2.31831 | + | 1.33848i | −0.149027 | + | 0.0860407i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −7.50173 | − | 12.9934i | −0.480249 | − | 0.831815i | ||||
\(245\) | −1.38478 | − | 0.506685i | −0.0884703 | − | 0.0323709i | ||||
\(246\) | −8.96736 | −0.571738 | ||||||||
\(247\) | 19.9426 | + | 3.77195i | 1.26892 | + | 0.240004i | ||||
\(248\) | 9.22060i | 0.585509i | ||||||||
\(249\) | −3.57262 | − | 6.18795i | −0.226405 | − | 0.392146i | ||||
\(250\) | −9.65384 | − | 5.63945i | −0.610562 | − | 0.356670i | ||||
\(251\) | 10.6317 | − | 18.4147i | 0.671069 | − | 1.16232i | −0.306533 | − | 0.951860i | \(-0.599169\pi\) |
0.977601 | − | 0.210465i | \(-0.0674977\pi\) | |||||||
\(252\) | 2.18069 | − | 1.25902i | 0.137371 | − | 0.0793110i | ||||
\(253\) | −4.27660 | − | 2.46910i | −0.268867 | − | 0.155231i | ||||
\(254\) | −15.7576 | −0.988720 | ||||||||
\(255\) | 12.5016 | − | 10.4539i | 0.782878 | − | 0.654649i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.03779 | + | 2.90857i | 0.314249 | + | 0.181432i | 0.648826 | − | 0.760937i | \(-0.275260\pi\) |
−0.334577 | + | 0.942368i | \(0.608594\pi\) | |||||||
\(258\) | − | 6.75378i | − | 0.420472i | ||||||
\(259\) | −8.22092 | −0.510823 | ||||||||
\(260\) | −10.2566 | + | 1.79055i | −0.636087 | + | 0.111045i | ||||
\(261\) | −2.20959 | − | 3.82712i | −0.136770 | − | 0.236893i | ||||
\(262\) | 5.68732 | + | 3.28357i | 0.351364 | + | 0.202860i | ||||
\(263\) | −14.9606 | + | 8.63749i | −0.922508 | + | 0.532610i | −0.884434 | − | 0.466665i | \(-0.845456\pi\) |
−0.0380737 | + | 0.999275i | \(0.512122\pi\) | |||||||
\(264\) | 1.44248 | + | 2.49846i | 0.0887788 | + | 0.153769i | ||||
\(265\) | 15.5380 | + | 18.5815i | 0.954494 | + | 1.14145i | ||||
\(266\) | 8.31991 | + | 7.15889i | 0.510126 | + | 0.438940i | ||||
\(267\) | 4.74222i | 0.290219i | ||||||||
\(268\) | 9.23107 | − | 5.32956i | 0.563878 | − | 0.325555i | ||||
\(269\) | −4.82743 | − | 8.36136i | −0.294334 | − | 0.509801i | 0.680496 | − | 0.732752i | \(-0.261764\pi\) |
−0.974830 | + | 0.222951i | \(0.928431\pi\) | |||||||
\(270\) | −0.384547 | − | 2.20275i | −0.0234028 | − | 0.134055i | ||||
\(271\) | −3.21818 | − | 5.57406i | −0.195491 | − | 0.338600i | 0.751571 | − | 0.659653i | \(-0.229297\pi\) |
−0.947061 | + | 0.321053i | \(0.895963\pi\) | |||||||
\(272\) | −6.31158 | − | 3.64399i | −0.382696 | − | 0.220949i | ||||
\(273\) | − | 11.7247i | − | 0.709609i | ||||||
\(274\) | −14.4364 | −0.872133 | ||||||||
\(275\) | 11.0185 | + | 9.30961i | 0.664440 | + | 0.561390i | ||||
\(276\) | 0.855848 | − | 1.48237i | 0.0515160 | − | 0.0892284i | ||||
\(277\) | − | 11.1309i | − | 0.668791i | −0.942433 | − | 0.334396i | \(-0.891468\pi\) | ||
0.942433 | − | 0.334396i | \(-0.108532\pi\) | |||||||
\(278\) | 6.19455i | 0.371525i | ||||||||
\(279\) | −4.61030 | + | 7.98528i | −0.276012 | + | 0.478066i | ||||
\(280\) | −5.28768 | − | 1.93474i | −0.315999 | − | 0.115623i | ||||
\(281\) | −2.84358 | + | 4.92523i | −0.169634 | + | 0.293815i | −0.938291 | − | 0.345846i | \(-0.887592\pi\) |
0.768657 | + | 0.639661i | \(0.220925\pi\) | |||||||
\(282\) | −3.98083 | + | 2.29833i | −0.237055 | + | 0.136864i | ||||
\(283\) | 6.24466 | − | 3.60536i | 0.371207 | − | 0.214316i | −0.302779 | − | 0.953061i | \(-0.597914\pi\) |
0.673985 | + | 0.738745i | \(0.264581\pi\) | |||||||
\(284\) | −10.7608 | −0.638536 | ||||||||
\(285\) | 8.50884 | − | 4.75391i | 0.504020 | − | 0.281597i | ||||
\(286\) | 13.4332 | 0.794319 | ||||||||
\(287\) | −19.5550 | + | 11.2901i | −1.15430 | + | 0.666434i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 18.0573 | − | 31.2762i | 1.06220 | − | 1.83978i | ||||
\(290\) | −3.39547 | + | 9.27989i | −0.199389 | + | 0.544934i | ||||
\(291\) | 1.14834 | − | 1.98898i | 0.0673167 | − | 0.116596i | ||||
\(292\) | 14.1670i | 0.829059i | ||||||||
\(293\) | 9.26719i | 0.541395i | 0.962664 | + | 0.270697i | \(0.0872543\pi\) | ||||
−0.962664 | + | 0.270697i | \(0.912746\pi\) | |||||||
\(294\) | −0.329723 | + | 0.571097i | −0.0192298 | + | 0.0333070i | ||||
\(295\) | −3.63992 | − | 20.8501i | −0.211924 | − | 1.21394i | ||||
\(296\) | 3.26480 | 0.189763 | ||||||||
\(297\) | 2.88497i | 0.167403i | ||||||||
\(298\) | −10.3832 | − | 5.99475i | −0.601484 | − | 0.347267i | ||||
\(299\) | −3.98505 | − | 6.90231i | −0.230461 | − | 0.399171i | ||||
\(300\) | −3.22694 | + | 3.81928i | −0.186307 | + | 0.220506i | ||||
\(301\) | −8.50316 | − | 14.7279i | −0.490114 | − | 0.848902i | ||||
\(302\) | −4.77643 | + | 2.75767i | −0.274852 | + | 0.158686i | ||||
\(303\) | 3.36795i | 0.193484i | ||||||||
\(304\) | −3.30411 | − | 2.84303i | −0.189504 | − | 0.163059i | ||||
\(305\) | −25.7364 | + | 21.5210i | −1.47366 | + | 1.23229i | ||||
\(306\) | −3.64399 | − | 6.31158i | −0.208313 | − | 0.360809i | ||||
\(307\) | 8.89602 | − | 5.13612i | 0.507722 | − | 0.293134i | −0.224175 | − | 0.974549i | \(-0.571969\pi\) |
0.731897 | + | 0.681415i | \(0.238635\pi\) | |||||||
\(308\) | 6.29123 | + | 3.63224i | 0.358476 | + | 0.206966i | ||||
\(309\) | 5.49365 | + | 9.51527i | 0.312523 | + | 0.541305i | ||||
\(310\) | 20.3107 | − | 3.54576i | 1.15357 | − | 0.201385i | ||||
\(311\) | −11.4317 | −0.648232 | −0.324116 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324116 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(312\) | 4.65626i | 0.263609i | ||||||||
\(313\) | 3.42825 | + | 1.97930i | 0.193776 | + | 0.111877i | 0.593749 | − | 0.804650i | \(-0.297647\pi\) |
−0.399973 | + | 0.916527i | \(0.630981\pi\) | |||||||
\(314\) | 6.13962 | − | 10.6341i | 0.346479 | − | 0.600118i | ||||
\(315\) | −3.61190 | − | 4.31937i | −0.203507 | − | 0.243369i | ||||
\(316\) | 8.23995 | 0.463533 | ||||||||
\(317\) | −19.0052 | − | 10.9727i | −1.06744 | − | 0.616286i | −0.139958 | − | 0.990157i | \(-0.544697\pi\) |
−0.927480 | + | 0.373872i | \(0.878030\pi\) | |||||||
\(318\) | 9.38113 | − | 5.41620i | 0.526068 | − | 0.303725i | ||||
\(319\) | 6.37459 | − | 11.0411i | 0.356908 | − | 0.618184i | ||||
\(320\) | 2.09991 | + | 0.768349i | 0.117389 | + | 0.0429520i | ||||
\(321\) | 1.67887 | + | 2.90789i | 0.0937055 | + | 0.162303i | ||||
\(322\) | − | 4.31013i | − | 0.240194i | ||||||
\(323\) | 20.7200 | − | 24.0803i | 1.15289 | − | 1.33986i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 7.88828 | + | 21.9042i | 0.437563 | + | 1.21503i | ||||
\(326\) | −1.72900 | − | 2.99472i | −0.0957606 | − | 0.165862i | ||||
\(327\) | −3.66583 | − | 2.11647i | −0.202721 | − | 0.117041i | ||||
\(328\) | 7.76596 | − | 4.48368i | 0.428803 | − | 0.247570i | ||||
\(329\) | −5.78731 | + | 10.0239i | −0.319065 | + | 0.552636i | ||||
\(330\) | 4.94878 | − | 4.13821i | 0.272421 | − | 0.227801i | ||||
\(331\) | 7.44789 | 0.409373 | 0.204687 | − | 0.978828i | \(-0.434382\pi\) | ||||
0.204687 | + | 0.978828i | \(0.434382\pi\) | |||||||
\(332\) | 6.18795 | + | 3.57262i | 0.339608 | + | 0.196073i | ||||
\(333\) | 2.82740 | + | 1.63240i | 0.154941 | + | 0.0894551i | ||||
\(334\) | 6.20240 | 0.339380 | ||||||||
\(335\) | −15.2895 | − | 18.2843i | −0.835354 | − | 0.998979i | ||||
\(336\) | −1.25902 | + | 2.18069i | −0.0686853 | + | 0.118966i | ||||
\(337\) | −4.04725 | + | 2.33668i | −0.220468 | + | 0.127287i | −0.606167 | − | 0.795338i | \(-0.707294\pi\) |
0.385699 | + | 0.922625i | \(0.373960\pi\) | |||||||
\(338\) | 7.51773 | + | 4.34036i | 0.408911 | + | 0.236085i | ||||
\(339\) | 9.39912 | + | 16.2798i | 0.510490 | + | 0.884195i | ||||
\(340\) | −5.59972 | + | 15.3041i | −0.303687 | + | 0.829983i | ||||
\(341\) | −26.6011 | −1.44053 | ||||||||
\(342\) | −1.43993 | − | 4.11420i | −0.0778624 | − | 0.222470i | ||||
\(343\) | 19.2868i | 1.04139i | ||||||||
\(344\) | 3.37689 | + | 5.84894i | 0.182070 | + | 0.315354i | ||||
\(345\) | −3.59442 | − | 1.31518i | −0.193517 | − | 0.0708070i | ||||
\(346\) | −7.20026 | + | 12.4712i | −0.387088 | + | 0.670456i | ||||
\(347\) | −11.8564 | + | 6.84531i | −0.636486 | + | 0.367475i | −0.783260 | − | 0.621695i | \(-0.786444\pi\) |
0.146774 | + | 0.989170i | \(0.453111\pi\) | |||||||
\(348\) | 3.82712 | + | 2.20959i | 0.205155 | + | 0.118446i | ||||
\(349\) | 34.7901 | 1.86227 | 0.931137 | − | 0.364671i | \(-0.118818\pi\) | ||||
0.931137 | + | 0.364671i | \(0.118818\pi\) | |||||||
\(350\) | −2.22839 | + | 12.3915i | −0.119113 | + | 0.662351i | ||||
\(351\) | −2.32813 | + | 4.03244i | −0.124266 | + | 0.215236i | ||||
\(352\) | −2.49846 | − | 1.44248i | −0.133168 | − | 0.0768847i | ||||
\(353\) | − | 3.05876i | − | 0.162802i | −0.996681 | − | 0.0814008i | \(-0.974061\pi\) | ||
0.996681 | − | 0.0814008i | \(-0.0259394\pi\) | |||||||
\(354\) | −9.46547 | −0.503084 | ||||||||
\(355\) | 4.13803 | + | 23.7034i | 0.219624 | + | 1.25805i | ||||
\(356\) | −2.37111 | − | 4.10688i | −0.125668 | − | 0.217664i | ||||
\(357\) | −15.8928 | − | 9.17574i | −0.841138 | − | 0.485631i | ||||
\(358\) | −1.68161 | + | 0.970880i | −0.0888760 | + | 0.0513126i | ||||
\(359\) | 8.49408 | + | 14.7122i | 0.448300 | + | 0.776479i | 0.998276 | − | 0.0587020i | \(-0.0186962\pi\) |
−0.549975 | + | 0.835181i | \(0.685363\pi\) | |||||||
\(360\) | 1.43440 | + | 1.71537i | 0.0755997 | + | 0.0904078i | ||||
\(361\) | 14.8532 | − | 11.8483i | 0.781748 | − | 0.623595i | ||||
\(362\) | 17.6296i | 0.926592i | ||||||||
\(363\) | 2.31831 | − | 1.33848i | 0.121680 | − | 0.0702519i | ||||
\(364\) | 5.86233 | + | 10.1539i | 0.307270 | + | 0.532207i | ||||
\(365\) | 31.2063 | − | 5.44786i | 1.63341 | − | 0.285154i | ||||
\(366\) | 7.50173 | + | 12.9934i | 0.392121 | + | 0.679174i | ||||
\(367\) | −4.66821 | − | 2.69519i | −0.243679 | − | 0.140688i | 0.373188 | − | 0.927756i | \(-0.378265\pi\) |
−0.616866 | + | 0.787068i | \(0.711598\pi\) | |||||||
\(368\) | 1.71170i | 0.0892284i | ||||||||
\(369\) | 8.96736 | 0.466822 | ||||||||
\(370\) | −1.25547 | − | 7.19156i | −0.0652688 | − | 0.373871i | ||||
\(371\) | 13.6382 | − | 23.6221i | 0.708062 | − | 1.22640i | ||||
\(372\) | − | 9.22060i | − | 0.478066i | ||||||
\(373\) | 3.85586i | 0.199649i | 0.995005 | + | 0.0998244i | \(0.0318281\pi\) | ||||
−0.995005 | + | 0.0998244i | \(0.968172\pi\) | |||||||
\(374\) | 10.5128 | − | 18.2087i | 0.543604 | − | 0.941550i | ||||
\(375\) | 9.65384 | + | 5.63945i | 0.498522 | + | 0.291220i | ||||
\(376\) | 2.29833 | − | 3.98083i | 0.118527 | − | 0.205296i | ||||
\(377\) | 17.8200 | − | 10.2884i | 0.917779 | − | 0.529880i | ||||
\(378\) | −2.18069 | + | 1.25902i | −0.112163 | + | 0.0647571i | ||||
\(379\) | −13.6566 | −0.701495 | −0.350747 | − | 0.936470i | \(-0.614072\pi\) | ||||
−0.350747 | + | 0.936470i | \(0.614072\pi\) | |||||||
\(380\) | −4.99192 | + | 8.37143i | −0.256080 | + | 0.429445i | ||||
\(381\) | 15.7576 | 0.807287 | ||||||||
\(382\) | −3.99564 | + | 2.30688i | −0.204435 | + | 0.118030i | ||||
\(383\) | 6.30771 | − | 3.64176i | 0.322309 | − | 0.186085i | −0.330112 | − | 0.943942i | \(-0.607087\pi\) |
0.652421 | + | 0.757857i | \(0.273753\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 5.58166 | − | 15.2548i | 0.284468 | − | 0.777456i | ||||
\(386\) | −12.5401 | + | 21.7202i | −0.638276 | + | 1.10553i | ||||
\(387\) | 6.75378i | 0.343314i | ||||||||
\(388\) | 2.29667i | 0.116596i | ||||||||
\(389\) | −9.81327 | + | 16.9971i | −0.497553 | + | 0.861786i | −0.999996 | − | 0.00282365i | \(-0.999101\pi\) |
0.502443 | + | 0.864610i | \(0.332435\pi\) | |||||||
\(390\) | 10.2566 | − | 1.79055i | 0.519362 | − | 0.0906680i | ||||
\(391\) | −12.4748 | −0.630879 | ||||||||
\(392\) | − | 0.659446i | − | 0.0333070i | ||||||
\(393\) | −5.68732 | − | 3.28357i | −0.286887 | − | 0.165634i | ||||
\(394\) | −1.81219 | − | 3.13881i | −0.0912969 | − | 0.158131i | ||||
\(395\) | −3.16865 | − | 18.1506i | −0.159432 | − | 0.913255i | ||||
\(396\) | −1.44248 | − | 2.49846i | −0.0724876 | − | 0.125552i | ||||
\(397\) | 10.0280 | − | 5.78964i | 0.503288 | − | 0.290574i | −0.226782 | − | 0.973946i | \(-0.572821\pi\) |
0.730071 | + | 0.683372i | \(0.239487\pi\) | |||||||
\(398\) | − | 0.596986i | − | 0.0299242i | ||||||
\(399\) | −8.31991 | − | 7.15889i | −0.416516 | − | 0.358393i | ||||
\(400\) | 0.884968 | − | 4.92106i | 0.0442484 | − | 0.246053i | ||||
\(401\) | 0.738065 | + | 1.27837i | 0.0368572 | + | 0.0638386i | 0.883866 | − | 0.467741i | \(-0.154932\pi\) |
−0.847008 | + | 0.531580i | \(0.821599\pi\) | |||||||
\(402\) | −9.23107 | + | 5.32956i | −0.460404 | + | 0.265814i | ||||
\(403\) | −37.1815 | − | 21.4667i | −1.85214 | − | 1.06933i | ||||
\(404\) | −1.68398 | − | 2.91673i | −0.0837810 | − | 0.145113i | ||||
\(405\) | 0.384547 | + | 2.20275i | 0.0191083 | + | 0.109456i | ||||
\(406\) | 11.1277 | 0.552258 | ||||||||
\(407\) | 9.41885i | 0.466875i | ||||||||
\(408\) | 6.31158 | + | 3.64399i | 0.312470 | + | 0.180404i | ||||
\(409\) | 0.325761 | − | 0.564235i | 0.0161078 | − | 0.0278996i | −0.857859 | − | 0.513885i | \(-0.828206\pi\) |
0.873967 | + | 0.485985i | \(0.161539\pi\) | |||||||
\(410\) | −12.8628 | − | 15.3823i | −0.635249 | − | 0.759678i | ||||
\(411\) | 14.4364 | 0.712093 | ||||||||
\(412\) | −9.51527 | − | 5.49365i | −0.468784 | − | 0.270653i | ||||
\(413\) | −20.6413 | + | 11.9172i | −1.01569 | + | 0.586409i | ||||
\(414\) | −0.855848 | + | 1.48237i | −0.0420627 | + | 0.0728547i | ||||
\(415\) | 5.49003 | − | 15.0044i | 0.269495 | − | 0.736536i | ||||
\(416\) | −2.32813 | − | 4.03244i | −0.114146 | − | 0.197706i | ||||
\(417\) | − | 6.19455i | − | 0.303349i | ||||||
\(418\) | 8.20206 | − | 9.53226i | 0.401176 | − | 0.466238i | ||||
\(419\) | −25.9557 | −1.26802 | −0.634010 | − | 0.773325i | \(-0.718592\pi\) | ||||
−0.634010 | + | 0.773325i | \(0.718592\pi\) | |||||||
\(420\) | 5.28768 | + | 1.93474i | 0.258012 | + | 0.0944056i | ||||
\(421\) | 14.9470 | + | 25.8890i | 0.728473 | + | 1.26175i | 0.957528 | + | 0.288339i | \(0.0931032\pi\) |
−0.229055 | + | 0.973414i | \(0.573564\pi\) | |||||||
\(422\) | 19.8569 | + | 11.4644i | 0.966620 | + | 0.558078i | ||||
\(423\) | 3.98083 | − | 2.29833i | 0.193555 | − | 0.111749i | ||||
\(424\) | −5.41620 | + | 9.38113i | −0.263034 | + | 0.455588i | ||||
\(425\) | 35.8646 | + | 6.44963i | 1.73969 | + | 0.312853i | ||||
\(426\) | 10.7608 | 0.521362 | ||||||||
\(427\) | 32.7179 | + | 18.8897i | 1.58333 | + | 0.914136i | ||||
\(428\) | −2.90789 | − | 1.67887i | −0.140558 | − | 0.0811514i | ||||
\(429\) | −13.4332 | −0.648559 | ||||||||
\(430\) | 11.5852 | − | 9.68765i | 0.558688 | − | 0.467180i | ||||
\(431\) | −13.7123 | + | 23.7503i | −0.660496 | + | 1.14401i | 0.319989 | + | 0.947421i | \(0.396321\pi\) |
−0.980485 | + | 0.196592i | \(0.937013\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 9.75555 | + | 5.63237i | 0.468822 | + | 0.270674i | 0.715746 | − | 0.698360i | \(-0.246087\pi\) |
−0.246925 | + | 0.969035i | \(0.579420\pi\) | |||||||
\(434\) | −11.6089 | − | 20.1073i | −0.557247 | − | 0.965181i | ||||
\(435\) | 3.39547 | − | 9.27989i | 0.162800 | − | 0.444936i | ||||
\(436\) | 4.23293 | 0.202721 | ||||||||
\(437\) | −7.33113 | − | 1.38662i | −0.350696 | − | 0.0663308i | ||||
\(438\) | − | 14.1670i | − | 0.676924i | ||||||
\(439\) | −7.89796 | − | 13.6797i | −0.376949 | − | 0.652895i | 0.613668 | − | 0.789564i | \(-0.289693\pi\) |
−0.990617 | + | 0.136670i | \(0.956360\pi\) | |||||||
\(440\) | −2.21666 | + | 6.05819i | −0.105675 | + | 0.288813i | ||||
\(441\) | 0.329723 | − | 0.571097i | 0.0157011 | − | 0.0271951i | ||||
\(442\) | 29.3883 | − | 16.9674i | 1.39786 | − | 0.807055i | ||||
\(443\) | 6.09413 | + | 3.51845i | 0.289541 | + | 0.167167i | 0.637735 | − | 0.770256i | \(-0.279872\pi\) |
−0.348194 | + | 0.937423i | \(0.613205\pi\) | |||||||
\(444\) | −3.26480 | −0.154941 | ||||||||
\(445\) | −8.13464 | + | 6.80226i | −0.385619 | + | 0.322458i | ||||
\(446\) | −5.62349 | + | 9.74016i | −0.266280 | + | 0.461210i | ||||
\(447\) | 10.3832 | + | 5.99475i | 0.491109 | + | 0.283542i | ||||
\(448\) | − | 2.51805i | − | 0.118966i | ||||||
\(449\) | −16.3890 | −0.773444 | −0.386722 | − | 0.922196i | \(-0.626393\pi\) | ||||
−0.386722 | + | 0.922196i | \(0.626393\pi\) | |||||||
\(450\) | 3.22694 | − | 3.81928i | 0.152119 | − | 0.180043i | ||||
\(451\) | 12.9353 | + | 22.4046i | 0.609098 | + | 1.05499i | ||||
\(452\) | −16.2798 | − | 9.39912i | −0.765735 | − | 0.442097i | ||||
\(453\) | 4.77643 | − | 2.75767i | 0.224416 | − | 0.129567i | ||||
\(454\) | 4.41407 | + | 7.64539i | 0.207163 | + | 0.358816i | ||||
\(455\) | 20.1121 | − | 16.8179i | 0.942870 | − | 0.788436i | ||||
\(456\) | 3.30411 | + | 2.84303i | 0.154729 | + | 0.133137i | ||||
\(457\) | − | 11.5975i | − | 0.542508i | −0.962508 | − | 0.271254i | \(-0.912562\pi\) | ||
0.962508 | − | 0.271254i | \(-0.0874383\pi\) | |||||||
\(458\) | 19.2965 | − | 11.1408i | 0.901666 | − | 0.520577i | ||||
\(459\) | 3.64399 | + | 6.31158i | 0.170087 | + | 0.294599i | ||||
\(460\) | 3.77045 | − | 0.658228i | 0.175798 | − | 0.0306900i | ||||
\(461\) | 2.39232 | + | 4.14363i | 0.111422 | + | 0.192988i | 0.916344 | − | 0.400393i | \(-0.131126\pi\) |
−0.804922 | + | 0.593381i | \(0.797793\pi\) | |||||||
\(462\) | −6.29123 | − | 3.63224i | −0.292694 | − | 0.168987i | ||||
\(463\) | − | 12.1559i | − | 0.564934i | −0.959277 | − | 0.282467i | \(-0.908847\pi\) | ||
0.959277 | − | 0.282467i | \(-0.0911527\pi\) | |||||||
\(464\) | −4.41917 | −0.205155 | ||||||||
\(465\) | −20.3107 | + | 3.54576i | −0.941887 | + | 0.164430i | ||||
\(466\) | 3.09066 | − | 5.35318i | 0.143172 | − | 0.247981i | ||||
\(467\) | − | 1.60463i | − | 0.0742533i | −0.999311 | − | 0.0371266i | \(-0.988180\pi\) | ||
0.999311 | − | 0.0371266i | \(-0.0118205\pi\) | |||||||
\(468\) | − | 4.65626i | − | 0.215236i | ||||||
\(469\) | −13.4201 | + | 23.2443i | −0.619682 | + | 1.07332i | ||||
\(470\) | −9.65260 | − | 3.53184i | −0.445241 | − | 0.162912i | ||||
\(471\) | −6.13962 | + | 10.6341i | −0.282899 | + | 0.489995i | ||||
\(472\) | 8.19734 | − | 4.73274i | 0.377313 | − | 0.217842i | ||||
\(473\) | −16.8740 | + | 9.74222i | −0.775868 | + | 0.447948i | ||||
\(474\) | −8.23995 | −0.378473 | ||||||||
\(475\) | 20.3598 | + | 7.77675i | 0.934172 | + | 0.356822i | ||||
\(476\) | 18.3515 | 0.841138 | ||||||||
\(477\) | −9.38113 | + | 5.41620i | −0.429532 | + | 0.247991i | ||||
\(478\) | −15.7528 | + | 9.09488i | −0.720516 | + | 0.415990i | ||||
\(479\) | −17.2940 | + | 29.9541i | −0.790184 | + | 1.36864i | 0.135669 | + | 0.990754i | \(0.456682\pi\) |
−0.925853 | + | 0.377884i | \(0.876652\pi\) | |||||||
\(480\) | −2.09991 | − | 0.768349i | −0.0958475 | − | 0.0350702i | ||||
\(481\) | −7.60088 | + | 13.1651i | −0.346570 | + | 0.600277i | ||||
\(482\) | 2.49535i | 0.113660i | ||||||||
\(483\) | 4.31013i | 0.196118i | ||||||||
\(484\) | −1.33848 | + | 2.31831i | −0.0608399 | + | 0.105378i | ||||
\(485\) | 5.05901 | − | 0.883179i | 0.229718 | − | 0.0401031i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 24.3737i | 1.10448i | 0.833687 | + | 0.552238i | \(0.186226\pi\) | ||||
−0.833687 | + | 0.552238i | \(0.813774\pi\) | |||||||
\(488\) | −12.9934 | − | 7.50173i | −0.588182 | − | 0.339587i | ||||
\(489\) | 1.72900 | + | 2.99472i | 0.0781882 | + | 0.135426i | ||||
\(490\) | −1.45260 | + | 0.253588i | −0.0656216 | + | 0.0114559i | ||||
\(491\) | 5.45453 | + | 9.44752i | 0.246159 | + | 0.426360i | 0.962457 | − | 0.271434i | \(-0.0874980\pi\) |
−0.716298 | + | 0.697795i | \(0.754165\pi\) | |||||||
\(492\) | −7.76596 | + | 4.48368i | −0.350117 | + | 0.202140i | ||||
\(493\) | − | 32.2069i | − | 1.45052i | ||||||
\(494\) | 19.1568 | − | 6.70468i | 0.861903 | − | 0.301658i | ||||
\(495\) | −4.94878 | + | 4.13821i | −0.222431 | + | 0.185999i | ||||
\(496\) | 4.61030 | + | 7.98528i | 0.207009 | + | 0.358549i | ||||
\(497\) | 23.4660 | − | 13.5481i | 1.05259 | − | 0.607715i | ||||
\(498\) | −6.18795 | − | 3.57262i | −0.277289 | − | 0.160093i | ||||
\(499\) | −5.54788 | − | 9.60920i | −0.248357 | − | 0.430167i | 0.714713 | − | 0.699418i | \(-0.246557\pi\) |
−0.963070 | + | 0.269251i | \(0.913224\pi\) | |||||||
\(500\) | −11.1802 | − | 0.0569884i | −0.499994 | − | 0.00254860i | ||||
\(501\) | −6.20240 | −0.277103 | ||||||||
\(502\) | − | 21.2635i | − | 0.949034i | ||||||
\(503\) | −17.0870 | − | 9.86519i | −0.761872 | − | 0.439867i | 0.0680955 | − | 0.997679i | \(-0.478308\pi\) |
−0.829967 | + | 0.557812i | \(0.811641\pi\) | |||||||
\(504\) | 1.25902 | − | 2.18069i | 0.0560813 | − | 0.0971357i | ||||
\(505\) | −5.77728 | + | 4.83101i | −0.257085 | + | 0.214977i | ||||
\(506\) | −4.93819 | −0.219529 | ||||||||
\(507\) | −7.51773 | − | 4.34036i | −0.333874 | − | 0.192762i | ||||
\(508\) | −13.6465 | + | 7.87880i | −0.605465 | + | 0.349565i | ||||
\(509\) | −16.6873 | + | 28.9033i | −0.739653 | + | 1.28112i | 0.212999 | + | 0.977052i | \(0.431677\pi\) |
−0.952652 | + | 0.304064i | \(0.901656\pi\) | |||||||
\(510\) | 5.59972 | − | 15.3041i | 0.247960 | − | 0.677679i | ||||
\(511\) | −17.8365 | − | 30.8938i | −0.789042 | − | 1.36666i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.43993 | + | 4.11420i | 0.0635744 | + | 0.181646i | ||||
\(514\) | 5.81714 | 0.256583 | ||||||||
\(515\) | −8.44208 | + | 23.0724i | −0.372002 | + | 1.01669i | ||||
\(516\) | −3.37689 | − | 5.84894i | −0.148659 | − | 0.257485i | ||||
\(517\) | 11.4846 | + | 6.63062i | 0.505091 | + | 0.291614i | ||||
\(518\) | −7.11953 | + | 4.11046i | −0.312814 | + | 0.180603i | ||||
\(519\) | 7.20026 | − | 12.4712i | 0.316056 | − | 0.547425i | ||||
\(520\) | −7.98719 | + | 6.67896i | −0.350261 | + | 0.292892i | ||||
\(521\) | −32.4955 | −1.42366 | −0.711828 | − | 0.702354i | \(-0.752132\pi\) | ||||
−0.711828 | + | 0.702354i | \(0.752132\pi\) | |||||||
\(522\) | −3.82712 | − | 2.20959i | −0.167508 | − | 0.0967110i | ||||
\(523\) | 8.12396 | + | 4.69037i | 0.355236 | + | 0.205096i | 0.666989 | − | 0.745068i | \(-0.267583\pi\) |
−0.311753 | + | 0.950163i | \(0.600916\pi\) | |||||||
\(524\) | 6.56715 | 0.286887 | ||||||||
\(525\) | 2.22839 | − | 12.3915i | 0.0972550 | − | 0.540807i | ||||
\(526\) | −8.63749 | + | 14.9606i | −0.376612 | + | 0.652312i | ||||
\(527\) | −58.1966 | + | 33.5998i | −2.53508 | + | 1.46363i | ||||
\(528\) | 2.49846 | + | 1.44248i | 0.108731 | + | 0.0627761i | ||||
\(529\) | −10.0350 | − | 17.3812i | −0.436306 | − | 0.755705i | ||||
\(530\) | 22.7471 | + | 8.32306i | 0.988071 | + | 0.361531i | ||||
\(531\) | 9.46547 | 0.410767 | ||||||||
\(532\) | 10.7847 | + | 2.03983i | 0.467576 | + | 0.0884376i | ||||
\(533\) | 41.7543i | 1.80858i | ||||||||
\(534\) | 2.37111 | + | 4.10688i | 0.102608 | + | 0.177722i | ||||
\(535\) | −2.57992 | + | 7.05098i | −0.111540 | + | 0.304840i | ||||
\(536\) | 5.32956 | − | 9.23107i | 0.230202 | − | 0.398722i | ||||
\(537\) | 1.68161 | − | 0.970880i | 0.0725670 | − | 0.0418966i | ||||
\(538\) | −8.36136 | − | 4.82743i | −0.360484 | − | 0.208125i | ||||
\(539\) | 1.90248 | 0.0819456 | ||||||||
\(540\) | −1.43440 | − | 1.71537i | −0.0617269 | − | 0.0738176i | ||||
\(541\) | 18.8739 | − | 32.6906i | 0.811453 | − | 1.40548i | −0.100394 | − | 0.994948i | \(-0.532010\pi\) |
0.911847 | − | 0.410530i | \(-0.134656\pi\) | |||||||
\(542\) | −5.57406 | − | 3.21818i | −0.239426 | − | 0.138233i | ||||
\(543\) | − | 17.6296i | − | 0.756559i | ||||||
\(544\) | −7.28798 | −0.312470 | ||||||||
\(545\) | −1.62776 | − | 9.32410i | −0.0697256 | − | 0.399401i | ||||
\(546\) | −5.86233 | − | 10.1539i | −0.250885 | − | 0.434545i | ||||
\(547\) | −5.07734 | − | 2.93141i | −0.217092 | − | 0.125338i | 0.387511 | − | 0.921865i | \(-0.373335\pi\) |
−0.604603 | + | 0.796527i | \(0.706668\pi\) | |||||||
\(548\) | −12.5023 | + | 7.21818i | −0.534070 | + | 0.308345i | ||||
\(549\) | −7.50173 | − | 12.9934i | −0.320166 | − | 0.554544i | ||||
\(550\) | 14.1971 | + | 2.55311i | 0.605366 | + | 0.108865i | ||||
\(551\) | 3.57990 | − | 18.9272i | 0.152509 | − | 0.806324i | ||||
\(552\) | − | 1.71170i | − | 0.0728547i | ||||||
\(553\) | −17.9688 | + | 10.3743i | −0.764111 | + | 0.441160i | ||||
\(554\) | −5.56545 | − | 9.63965i | −0.236453 | − | 0.409549i | ||||
\(555\) | 1.25547 | + | 7.19156i | 0.0532917 | + | 0.305265i | ||||
\(556\) | 3.09728 | + | 5.36464i | 0.131354 | + | 0.227511i | ||||
\(557\) | 18.3570 | + | 10.5984i | 0.777809 | + | 0.449068i | 0.835653 | − | 0.549257i | \(-0.185089\pi\) |
−0.0578442 | + | 0.998326i | \(0.518423\pi\) | |||||||
\(558\) | 9.22060i | 0.390339i | ||||||||
\(559\) | −31.4473 | −1.33008 | ||||||||
\(560\) | −5.54663 | + | 0.968307i | −0.234388 | + | 0.0409184i | ||||
\(561\) | −10.5128 | + | 18.2087i | −0.443851 | + | 0.768772i | ||||
\(562\) | 5.68717i | 0.239899i | ||||||||
\(563\) | 26.4882i | 1.11634i | 0.829725 | + | 0.558172i | \(0.188497\pi\) | ||||
−0.829725 | + | 0.558172i | \(0.811503\pi\) | |||||||
\(564\) | −2.29833 | + | 3.98083i | −0.0967773 | + | 0.167623i | ||||
\(565\) | −14.4436 | + | 39.4747i | −0.607647 | + | 1.66071i | ||||
\(566\) | 3.60536 | − | 6.24466i | 0.151544 | − | 0.262483i | ||||
\(567\) | 2.18069 | − | 1.25902i | 0.0915804 | − | 0.0528740i | ||||
\(568\) | −9.31912 | + | 5.38040i | −0.391022 | + | 0.225757i | ||||
\(569\) | −21.8861 | −0.917514 | −0.458757 | − | 0.888562i | \(-0.651705\pi\) | ||||
−0.458757 | + | 0.888562i | \(0.651705\pi\) | |||||||
\(570\) | 4.99192 | − | 8.37143i | 0.209088 | − | 0.350640i | ||||
\(571\) | −14.0325 | −0.587242 | −0.293621 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293621 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(572\) | 11.6335 | − | 6.71658i | 0.486419 | − | 0.280834i | ||||
\(573\) | 3.99564 | − | 2.30688i | 0.166920 | − | 0.0963714i | ||||
\(574\) | −11.2901 | + | 19.5550i | −0.471240 | + | 0.816212i | ||||
\(575\) | −2.89983 | − | 8.05225i | −0.120931 | − | 0.335802i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 27.9608i | − | 1.16402i | −0.813180 | − | 0.582012i | \(-0.802266\pi\) | ||
0.813180 | − | 0.582012i | \(-0.197734\pi\) | |||||||
\(578\) | − | 36.1147i | − | 1.50217i | ||||||
\(579\) | 12.5401 | − | 21.7202i | 0.521150 | − | 0.902659i | ||||
\(580\) | 1.69938 | + | 9.73435i | 0.0705629 | + | 0.404197i | ||||
\(581\) | −17.9920 | −0.746435 | ||||||||
\(582\) | − | 2.29667i | − | 0.0952002i | ||||||
\(583\) | −27.0643 | − | 15.6256i | −1.12089 | − | 0.647145i | ||||
\(584\) | 7.08348 | + | 12.2689i | 0.293117 | + | 0.507693i | ||||
\(585\) | −10.2566 | + | 1.79055i | −0.424058 | + | 0.0740301i | ||||
\(586\) | 4.63359 | + | 8.02562i | 0.191412 | + | 0.331535i | ||||
\(587\) | 9.03637 | − | 5.21715i | 0.372971 | − | 0.215335i | −0.301785 | − | 0.953376i | \(-0.597582\pi\) |
0.674756 | + | 0.738041i | \(0.264249\pi\) | |||||||
\(588\) | 0.659446i | 0.0271951i | ||||||||
\(589\) | −37.9354 | + | 13.2770i | −1.56310 | + | 0.547070i | ||||
\(590\) | −13.5773 | − | 16.2368i | −0.558969 | − | 0.668457i | ||||
\(591\) | 1.81219 | + | 3.13881i | 0.0745436 | + | 0.129113i | ||||
\(592\) | 2.82740 | − | 1.63240i | 0.116206 | − | 0.0670913i | ||||
\(593\) | 4.77660 | + | 2.75777i | 0.196152 | + | 0.113248i | 0.594859 | − | 0.803830i | \(-0.297208\pi\) |
−0.398708 | + | 0.917078i | \(0.630541\pi\) | |||||||
\(594\) | 1.44248 | + | 2.49846i | 0.0591858 | + | 0.102513i | ||||
\(595\) | −7.05700 | − | 40.4238i | −0.289309 | − | 1.65721i | ||||
\(596\) | −11.9895 | −0.491109 | ||||||||
\(597\) | 0.596986i | 0.0244330i | ||||||||
\(598\) | −6.90231 | − | 3.98505i | −0.282256 | − | 0.162961i | ||||
\(599\) | 22.5946 | − | 39.1349i | 0.923189 | − | 1.59901i | 0.128741 | − | 0.991678i | \(-0.458907\pi\) |
0.794448 | − | 0.607332i | \(-0.207760\pi\) | |||||||
\(600\) | −0.884968 | + | 4.92106i | −0.0361287 | + | 0.200901i | ||||
\(601\) | −10.2025 | −0.416167 | −0.208083 | − | 0.978111i | \(-0.566723\pi\) | ||||
−0.208083 | + | 0.978111i | \(0.566723\pi\) | |||||||
\(602\) | −14.7279 | − | 8.50316i | −0.600265 | − | 0.346563i | ||||
\(603\) | 9.23107 | − | 5.32956i | 0.375918 | − | 0.217037i | ||||
\(604\) | −2.75767 | + | 4.77643i | −0.112208 | + | 0.194350i | ||||
\(605\) | 5.62138 | + | 2.05684i | 0.228542 | + | 0.0836224i | ||||
\(606\) | 1.68398 | + | 2.91673i | 0.0684069 | + | 0.118484i | ||||
\(607\) | − | 6.78955i | − | 0.275579i | −0.990462 | − | 0.137790i | \(-0.956000\pi\) | ||
0.990462 | − | 0.137790i | \(-0.0439998\pi\) | |||||||
\(608\) | −4.28296 | − | 0.810083i | −0.173697 | − | 0.0328532i | ||||
\(609\) | −11.1277 | −0.450916 | ||||||||
\(610\) | −11.5279 | + | 31.5060i | −0.466751 | + | 1.27564i | ||||
\(611\) | 10.7016 | + | 18.5358i | 0.432942 | + | 0.749877i | ||||
\(612\) | −6.31158 | − | 3.64399i | −0.255130 | − | 0.147300i | ||||
\(613\) | −20.8847 | + | 12.0578i | −0.843524 | + | 0.487009i | −0.858460 | − | 0.512880i | \(-0.828579\pi\) |
0.0149366 | + | 0.999888i | \(0.495245\pi\) | |||||||
\(614\) | 5.13612 | − | 8.89602i | 0.207277 | − | 0.359014i | ||||
\(615\) | 12.8628 | + | 15.3823i | 0.518679 | + | 0.620275i | ||||
\(616\) | 7.26448 | 0.292694 | ||||||||
\(617\) | −33.6188 | − | 19.4098i | −1.35344 | − | 0.781410i | −0.364712 | − | 0.931121i | \(-0.618832\pi\) |
−0.988730 | + | 0.149711i | \(0.952166\pi\) | |||||||
\(618\) | 9.51527 | + | 5.49365i | 0.382760 | + | 0.220987i | ||||
\(619\) | −43.0532 | −1.73046 | −0.865228 | − | 0.501379i | \(-0.832826\pi\) | ||||
−0.865228 | + | 0.501379i | \(0.832826\pi\) | |||||||
\(620\) | 15.8167 | − | 13.2261i | 0.635215 | − | 0.531172i | ||||
\(621\) | 0.855848 | − | 1.48237i | 0.0343440 | − | 0.0594856i | ||||
\(622\) | −9.90014 | + | 5.71585i | −0.396959 | + | 0.229185i | ||||
\(623\) | 10.3413 | + | 5.97056i | 0.414316 | + | 0.239205i | ||||
\(624\) | 2.32813 | + | 4.03244i | 0.0931997 | + | 0.161427i | ||||
\(625\) | 4.17378 | + | 24.6491i | 0.166951 | + | 0.985965i | ||||
\(626\) | 3.95860 | 0.158217 | ||||||||
\(627\) | −8.20206 | + | 9.53226i | −0.327559 | + | 0.380682i | ||||
\(628\) | − | 12.2792i | − | 0.489995i | ||||||
\(629\) | 11.8969 | + | 20.6061i | 0.474361 | + | 0.821617i | ||||
\(630\) | −5.28768 | − | 1.93474i | −0.210666 | − | 0.0770818i | ||||
\(631\) | 20.9642 | − | 36.3110i | 0.834571 | − | 1.44552i | −0.0598078 | − | 0.998210i | \(-0.519049\pi\) |
0.894379 | − | 0.447310i | \(-0.147618\pi\) | |||||||
\(632\) | 7.13601 | − | 4.11998i | 0.283855 | − | 0.163884i | ||||
\(633\) | −19.8569 | − | 11.4644i | −0.789242 | − | 0.455669i | ||||
\(634\) | −21.9453 | −0.871560 | ||||||||
\(635\) | 22.6028 | + | 27.0301i | 0.896964 | + | 1.07266i | ||||
\(636\) | 5.41620 | − | 9.38113i | 0.214766 | − | 0.371986i | ||||
\(637\) | 2.65917 | + | 1.53527i | 0.105360 | + | 0.0608298i | ||||
\(638\) | − | 12.7492i | − | 0.504745i | ||||||
\(639\) | −10.7608 | −0.425691 | ||||||||
\(640\) | 2.20275 | − | 0.384547i | 0.0870715 | − | 0.0152006i | ||||
\(641\) | 0.126170 | + | 0.218532i | 0.00498340 | + | 0.00863150i | 0.868506 | − | 0.495678i | \(-0.165080\pi\) |
−0.863523 | + | 0.504310i | \(0.831747\pi\) | |||||||
\(642\) | 2.90789 | + | 1.67887i | 0.114765 | + | 0.0662598i | ||||
\(643\) | 35.9135 | − | 20.7347i | 1.41629 | − | 0.817696i | 0.420320 | − | 0.907376i | \(-0.361918\pi\) |
0.995971 | + | 0.0896801i | \(0.0285845\pi\) | |||||||
\(644\) | −2.15507 | − | 3.73268i | −0.0849215 | − | 0.147088i | ||||
\(645\) | −11.5852 | + | 9.68765i | −0.456167 | + | 0.381451i | ||||
\(646\) | 5.90387 | − | 31.2142i | 0.232285 | − | 1.22810i | ||||
\(647\) | − | 11.3601i | − | 0.446612i | −0.974748 | − | 0.223306i | \(-0.928315\pi\) | ||
0.974748 | − | 0.223306i | \(-0.0716848\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 13.6538 | + | 23.6491i | 0.535958 | + | 0.928307i | ||||
\(650\) | 17.7835 | + | 15.0254i | 0.697528 | + | 0.589346i | ||||
\(651\) | 11.6089 | + | 20.1073i | 0.454991 | + | 0.788067i | ||||
\(652\) | −2.99472 | − | 1.72900i | −0.117282 | − | 0.0677130i | ||||
\(653\) | − | 14.1285i | − | 0.552889i | −0.961030 | − | 0.276444i | \(-0.910844\pi\) | ||
0.961030 | − | 0.276444i | \(-0.0891562\pi\) | |||||||
\(654\) | −4.23293 | −0.165521 | ||||||||
\(655\) | −2.52538 | − | 14.4658i | −0.0986746 | − | 0.565226i | ||||
\(656\) | 4.48368 | − | 7.76596i | 0.175058 | − | 0.303210i | ||||
\(657\) | 14.1670i | 0.552706i | ||||||||
\(658\) | 11.5746i | 0.451225i | ||||||||
\(659\) | −14.6536 | + | 25.3808i | −0.570823 | + | 0.988695i | 0.425658 | + | 0.904884i | \(0.360043\pi\) |
−0.996482 | + | 0.0838112i | \(0.973291\pi\) | |||||||
\(660\) | 2.21666 | − | 6.05819i | 0.0862835 | − | 0.235815i | ||||
\(661\) | 0.0305882 | − | 0.0529803i | 0.00118974 | − | 0.00206070i | −0.865430 | − | 0.501030i | \(-0.832955\pi\) |
0.866620 | + | 0.498969i | \(0.166288\pi\) | |||||||
\(662\) | 6.45007 | − | 3.72395i | 0.250689 | − | 0.144735i | ||||
\(663\) | −29.3883 | + | 16.9674i | −1.14135 | + | 0.658958i | ||||
\(664\) | 7.14523 | 0.277289 | ||||||||
\(665\) | 0.346010 | − | 24.5404i | 0.0134177 | − | 0.951637i | ||||
\(666\) | 3.26480 | 0.126509 | ||||||||
\(667\) | −6.55086 | + | 3.78214i | −0.253650 | + | 0.146445i | ||||
\(668\) | 5.37144 | − | 3.10120i | 0.207827 | − | 0.119989i | ||||
\(669\) | 5.62349 | − | 9.74016i | 0.217417 | − | 0.376576i | ||||
\(670\) | −22.3832 | − | 8.18993i | −0.864740 | − | 0.316405i | ||||
\(671\) | 21.6422 | − | 37.4855i | 0.835489 | − | 1.44711i | ||||
\(672\) | 2.51805i | 0.0971357i | ||||||||
\(673\) | 29.7678i | 1.14747i | 0.819042 | + | 0.573733i | \(0.194505\pi\) | ||||
−0.819042 | + | 0.573733i | \(0.805495\pi\) | |||||||
\(674\) | −2.33668 | + | 4.04725i | −0.0900055 | + | 0.155894i | ||||
\(675\) | −3.22694 | + | 3.81928i | −0.124205 | + | 0.147004i | ||||
\(676\) | 8.68073 | 0.333874 | ||||||||
\(677\) | − | 14.3460i | − | 0.551360i | −0.961249 | − | 0.275680i | \(-0.911097\pi\) | ||
0.961249 | − | 0.275680i | \(-0.0889031\pi\) | |||||||
\(678\) | 16.2798 | + | 9.39912i | 0.625220 | + | 0.360971i | ||||
\(679\) | −2.89157 | − | 5.00834i | −0.110968 | − | 0.192202i | ||||
\(680\) | 2.80257 | + | 16.0536i | 0.107474 | + | 0.615629i | ||||
\(681\) | −4.41407 | − | 7.64539i | −0.169148 | − | 0.292972i | ||||
\(682\) | −23.0373 | + | 13.3006i | −0.882143 | + | 0.509305i | ||||
\(683\) | − | 39.5539i | − | 1.51349i | −0.653712 | − | 0.756744i | \(-0.726789\pi\) | ||
0.653712 | − | 0.756744i | \(-0.273211\pi\) | |||||||
\(684\) | −3.30411 | − | 2.84303i | −0.126336 | − | 0.108706i | ||||
\(685\) | 20.7076 | + | 24.7637i | 0.791196 | + | 0.946171i | ||||
\(686\) | 9.64342 | + | 16.7029i | 0.368187 | + | 0.637719i | ||||
\(687\) | −19.2965 | + | 11.1408i | −0.736207 | + | 0.425049i | ||||
\(688\) | 5.84894 | + | 3.37689i | 0.222989 | + | 0.128743i | ||||
\(689\) | −25.2192 | − | 43.6810i | −0.960775 | − | 1.66411i | ||||
\(690\) | −3.77045 | + | 0.658228i | −0.143538 | + | 0.0250583i | ||||
\(691\) | −32.4212 | −1.23336 | −0.616681 | − | 0.787213i | \(-0.711523\pi\) | ||||
−0.616681 | + | 0.787213i | \(0.711523\pi\) | |||||||
\(692\) | 14.4005i | 0.547425i | ||||||||
\(693\) | 6.29123 | + | 3.63224i | 0.238984 | + | 0.137977i | ||||
\(694\) | −6.84531 | + | 11.8564i | −0.259844 | + | 0.450064i | ||||
\(695\) | 10.6259 | − | 8.88550i | 0.403065 | − | 0.337046i | ||||
\(696\) | 4.41917 | 0.167508 | ||||||||
\(697\) | 56.5982 | + | 32.6770i | 2.14381 | + | 1.23773i | ||||
\(698\) | 30.1291 | − | 17.3951i | 1.14040 | − | 0.658413i | ||||
\(699\) | −3.09066 | + | 5.35318i | −0.116900 | + | 0.202476i | ||||
\(700\) | 4.26588 | + | 11.8455i | 0.161235 | + | 0.447718i | ||||
\(701\) | 10.1662 | + | 17.6084i | 0.383972 | + | 0.665059i | 0.991626 | − | 0.129143i | \(-0.0412226\pi\) |
−0.607654 | + | 0.794202i | \(0.707889\pi\) | |||||||
\(702\) | 4.65626i | 0.175739i | ||||||||
\(703\) | 4.70108 | + | 13.4320i | 0.177305 | + | 0.506599i | ||||
\(704\) | −2.88497 | −0.108731 | ||||||||
\(705\) | 9.65260 | + | 3.53184i | 0.363538 | + | 0.133017i | ||||
\(706\) | −1.52938 | − | 2.64897i | −0.0575590 | − | 0.0996952i | ||||
\(707\) | 7.34447 | + | 4.24033i | 0.276217 | + | 0.159474i | ||||
\(708\) | −8.19734 | + | 4.73274i | −0.308075 | + | 0.177867i | ||||
\(709\) | 20.1591 | − | 34.9165i | 0.757089 | − | 1.31132i | −0.187240 | − | 0.982314i | \(-0.559954\pi\) |
0.944329 | − | 0.329003i | \(-0.106712\pi\) | |||||||
\(710\) | 15.4353 | + | 18.4587i | 0.579278 | + | 0.692743i | ||||
\(711\) | 8.23995 | 0.309022 | ||||||||
\(712\) | −4.10688 | − | 2.37111i | −0.153912 | − | 0.0888610i | ||||
\(713\) | 13.6684 | + | 7.89144i | 0.511885 | + | 0.295537i | ||||
\(714\) | −18.3515 | −0.686787 | ||||||||
\(715\) | −19.2686 | − | 23.0428i | −0.720604 | − | 0.861752i | ||||
\(716\) | −0.970880 | + | 1.68161i | −0.0362835 | + | 0.0628448i | ||||
\(717\) | 15.7528 | − | 9.09488i | 0.588299 | − | 0.339655i | ||||
\(718\) | 14.7122 | + | 8.49408i | 0.549054 | + | 0.316996i | ||||
\(719\) | −14.5708 | − | 25.2374i | −0.543401 | − | 0.941198i | −0.998706 | − | 0.0508623i | \(-0.983803\pi\) |
0.455305 | − | 0.890336i | \(-0.349530\pi\) | |||||||
\(720\) | 2.09991 | + | 0.768349i | 0.0782592 | + | 0.0286347i | ||||
\(721\) | 27.6665 | 1.03035 | ||||||||
\(722\) | 6.93911 | − | 17.6875i | 0.258247 | − | 0.658262i | ||||
\(723\) | − | 2.49535i | − | 0.0928031i | ||||||
\(724\) | 8.81480 | + | 15.2677i | 0.327600 | + | 0.567419i | ||||
\(725\) | 20.7889 | − | 7.48663i | 0.772080 | − | 0.278047i | ||||
\(726\) | 1.33848 | − | 2.31831i | 0.0496756 | − | 0.0860407i | ||||
\(727\) | 15.6863 | − | 9.05647i | 0.581771 | − | 0.335886i | −0.180066 | − | 0.983655i | \(-0.557631\pi\) |
0.761837 | + | 0.647769i | \(0.224298\pi\) | |||||||
\(728\) | 10.1539 | + | 5.86233i | 0.376327 | + | 0.217273i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 24.3015 | − | 20.3212i | 0.899440 | − | 0.752120i | ||||
\(731\) | −24.6107 | + | 42.6270i | −0.910260 | + | 1.57662i | ||||
\(732\) | 12.9934 | + | 7.50173i | 0.480249 | + | 0.277272i | ||||
\(733\) | 8.31171i | 0.307000i | 0.988149 | + | 0.153500i | \(0.0490545\pi\) | ||||
−0.988149 | + | 0.153500i | \(0.950946\pi\) | |||||||
\(734\) | −5.39039 | −0.198963 | ||||||||
\(735\) | 1.45260 | − | 0.253588i | 0.0535798 | − | 0.00935373i | ||||
\(736\) | 0.855848 | + | 1.48237i | 0.0315470 | + | 0.0546410i | ||||
\(737\) | 26.6314 | + | 15.3756i | 0.980979 | + | 0.566368i | ||||
\(738\) | 7.76596 | − | 4.48368i | 0.285869 | − | 0.165047i | ||||
\(739\) | 7.63311 | + | 13.2209i | 0.280788 | + | 0.486340i | 0.971579 | − | 0.236715i | \(-0.0760708\pi\) |
−0.690791 | + | 0.723055i | \(0.742737\pi\) | |||||||
\(740\) | −4.68305 | − | 5.60034i | −0.172152 | − | 0.205872i | ||||
\(741\) | −19.1568 | + | 6.70468i | −0.703741 | + | 0.246303i | ||||
\(742\) | − | 27.2765i | − | 1.00135i | ||||||
\(743\) | 29.0049 | − | 16.7460i | 1.06409 | − | 0.614351i | 0.137528 | − | 0.990498i | \(-0.456084\pi\) |
0.926560 | + | 0.376147i | \(0.122751\pi\) | |||||||
\(744\) | −4.61030 | − | 7.98528i | −0.169022 | − | 0.292754i | ||||
\(745\) | 4.61053 | + | 26.4099i | 0.168917 | + | 0.967585i | ||||
\(746\) | 1.92793 | + | 3.33927i | 0.0705865 | + | 0.122259i | ||||
\(747\) | 6.18795 | + | 3.57262i | 0.226405 | + | 0.130715i | ||||
\(748\) | − | 21.0256i | − | 0.768772i | ||||||
\(749\) | 8.45496 | 0.308937 | ||||||||
\(750\) | 11.1802 | + | 0.0569884i | 0.408243 | + | 0.00208092i | ||||
\(751\) | −10.0737 | + | 17.4481i | −0.367594 | + | 0.636691i | −0.989189 | − | 0.146648i | \(-0.953152\pi\) |
0.621595 | + | 0.783339i | \(0.286485\pi\) | |||||||
\(752\) | − | 4.59667i | − | 0.167623i | ||||||
\(753\) | 21.2635i | 0.774883i | ||||||||
\(754\) | 10.2884 | − | 17.8200i | 0.374682 | − | 0.648968i | ||||
\(755\) | 11.5817 | + | 4.23771i | 0.421503 | + | 0.154226i | ||||
\(756\) | −1.25902 | + | 2.18069i | −0.0457902 | + | 0.0793110i | ||||
\(757\) | 26.9406 | − | 15.5542i | 0.979174 | − | 0.565327i | 0.0771537 | − | 0.997019i | \(-0.475417\pi\) |
0.902021 | + | 0.431693i | \(0.142083\pi\) | |||||||
\(758\) | −11.8270 | + | 6.82832i | −0.429576 | + | 0.248016i | ||||
\(759\) | 4.93819 | 0.179245 | ||||||||
\(760\) | −0.137412 | + | 9.74583i | −0.00498446 | + | 0.353518i | ||||
\(761\) | 2.73496 | 0.0991421 | 0.0495710 | − | 0.998771i | \(-0.484215\pi\) | ||||
0.0495710 | + | 0.998771i | \(0.484215\pi\) | |||||||
\(762\) | 13.6465 | − | 7.87880i | 0.494360 | − | 0.285419i | ||||
\(763\) | −9.23072 | + | 5.32936i | −0.334174 | + | 0.192936i | ||||
\(764\) | −2.30688 | + | 3.99564i | −0.0834601 | + | 0.144557i | ||||
\(765\) | −5.59972 | + | 15.3041i | −0.202458 | + | 0.553322i | ||||
\(766\) | 3.64176 | − | 6.30771i | 0.131582 | − | 0.227907i | ||||
\(767\) | 44.0737i | 1.59141i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 11.3522 | − | 19.6626i | 0.409371 | − | 0.709052i | −0.585448 | − | 0.810710i | \(-0.699081\pi\) |
0.994819 | + | 0.101658i | \(0.0324147\pi\) | |||||||
\(770\) | −2.79354 | − | 16.0019i | −0.100672 | − | 0.576667i | ||||
\(771\) | −5.81714 | −0.209499 | ||||||||
\(772\) | 25.0803i | 0.902659i | ||||||||
\(773\) | −11.9910 | − | 6.92302i | −0.431287 | − | 0.249004i | 0.268608 | − | 0.963250i | \(-0.413437\pi\) |
−0.699895 | + | 0.714246i | \(0.746770\pi\) | |||||||
\(774\) | 3.37689 | + | 5.84894i | 0.121380 | + | 0.210236i | ||||
\(775\) | −35.2161 | − | 29.7543i | −1.26500 | − | 1.06881i | ||||
\(776\) | 1.14834 | + | 1.98898i | 0.0412229 | + | 0.0714002i | ||||
\(777\) | 7.11953 | − | 4.11046i | 0.255412 | − | 0.147462i | ||||
\(778\) | 19.6265i | 0.703646i | ||||||||
\(779\) | 29.6292 | + | 25.4945i | 1.06158 | + | 0.913435i | ||||
\(780\) | 7.98719 | − | 6.67896i | 0.285987 | − | 0.239145i | ||||
\(781\) | −15.5223 | − | 26.8854i | −0.555431 | − | 0.962034i | ||||
\(782\) | −10.8035 | + | 6.23741i | −0.386333 | + | 0.223049i | ||||
\(783\) | 3.82712 | + | 2.20959i | 0.136770 | + | 0.0789642i | ||||
\(784\) | −0.329723 | − | 0.571097i | −0.0117758 | − | 0.0203963i | ||||
\(785\) | −27.0481 | + | 4.72194i | −0.965389 | + | 0.168533i | ||||
\(786\) | −6.56715 | −0.234242 | ||||||||
\(787\) | 0.272719i | 0.00972137i | 0.999988 | + | 0.00486069i | \(0.00154721\pi\) | ||||
−0.999988 | + | 0.00486069i | \(0.998453\pi\) | |||||||
\(788\) | −3.13881 | − | 1.81219i | −0.111815 | − | 0.0645567i | ||||
\(789\) | 8.63749 | − | 14.9606i | 0.307503 | − | 0.532610i | ||||
\(790\) | −11.8194 | − | 14.1345i | −0.420516 | − | 0.502884i | ||||
\(791\) | 47.3348 | 1.68303 | ||||||||
\(792\) | −2.49846 | − | 1.44248i | −0.0887788 | − | 0.0512564i | ||||
\(793\) | 60.5005 | − | 34.9300i | 2.14843 | − | 1.24040i | ||||
\(794\) | 5.78964 | − | 10.0280i | 0.205467 | − | 0.355879i | ||||
\(795\) | −22.7471 | − | 8.32306i | −0.806757 | − | 0.295189i | ||||
\(796\) | −0.298493 | − | 0.517005i | −0.0105798 | − | 0.0183248i | ||||
\(797\) | − | 2.18853i | − | 0.0775216i | −0.999249 | − | 0.0387608i | \(-0.987659\pi\) | ||
0.999249 | − | 0.0387608i | \(-0.0123410\pi\) | |||||||
\(798\) | −10.7847 | − | 2.03983i | −0.381774 | − | 0.0722090i | ||||
\(799\) | 33.5004 | 1.18516 | ||||||||
\(800\) | −1.69412 | − | 4.70425i | −0.0598964 | − | 0.166320i | ||||
\(801\) | −2.37111 | − | 4.10688i | −0.0837790 | − | 0.145109i | ||||
\(802\) | 1.27837 | + | 0.738065i | 0.0451407 | + | 0.0260620i | ||||
\(803\) | −35.3955 | + | 20.4356i | −1.24908 | + | 0.721157i | ||||
\(804\) | −5.32956 | + | 9.23107i | −0.187959 | + | 0.325555i | ||||
\(805\) | −7.39346 | + | 6.18247i | −0.260585 | + | 0.217903i | ||||
\(806\) | −42.9335 | −1.51227 | ||||||||
\(807\) | 8.36136 | + | 4.82743i | 0.294334 | + | 0.169934i | ||||
\(808\) | −2.91673 | − | 1.68398i | −0.102610 | − | 0.0592421i | ||||
\(809\) | 8.89531 | 0.312743 | 0.156371 | − | 0.987698i | \(-0.450020\pi\) | ||||
0.156371 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(810\) | 1.43440 | + | 1.71537i | 0.0503998 | + | 0.0602719i | ||||
\(811\) | 6.06868 | − | 10.5113i | 0.213100 | − | 0.369101i | −0.739583 | − | 0.673065i | \(-0.764977\pi\) |
0.952683 | + | 0.303965i | \(0.0983106\pi\) | |||||||
\(812\) | 9.63686 | − | 5.56384i | 0.338187 | − | 0.195253i | ||||
\(813\) | 5.57406 | + | 3.21818i | 0.195491 | + | 0.112867i | ||||
\(814\) | 4.70943 | + | 8.15697i | 0.165065 | + | 0.285902i | ||||
\(815\) | −2.65696 | + | 7.26152i | −0.0930691 | + | 0.254360i | ||||
\(816\) | 7.28798 | 0.255130 | ||||||||
\(817\) | −19.2012 | + | 22.3152i | −0.671765 | + | 0.780711i | ||||
\(818\) | − | 0.651522i | − | 0.0227799i | ||||||
\(819\) | 5.86233 | + | 10.1539i | 0.204847 | + | 0.354805i | ||||
\(820\) | −18.8307 | − | 6.89006i | −0.657596 | − | 0.240611i | ||||
\(821\) | 21.4432 | − | 37.1408i | 0.748374 | − | 1.29622i | −0.200228 | − | 0.979749i | \(-0.564168\pi\) |
0.948602 | − | 0.316472i | \(-0.102498\pi\) | |||||||
\(822\) | 12.5023 | − | 7.21818i | 0.436066 | − | 0.251763i | ||||
\(823\) | 27.1468 | + | 15.6732i | 0.946278 | + | 0.546334i | 0.891923 | − | 0.452188i | \(-0.149356\pi\) |
0.0543553 | + | 0.998522i | \(0.482690\pi\) | |||||||
\(824\) | −10.9873 | −0.382760 | ||||||||
\(825\) | −14.1971 | − | 2.55311i | −0.494280 | − | 0.0888877i | ||||
\(826\) | −11.9172 | + | 20.6413i | −0.414654 | + | 0.718202i | ||||
\(827\) | −28.4166 | − | 16.4063i | −0.988143 | − | 0.570505i | −0.0834244 | − | 0.996514i | \(-0.526586\pi\) |
−0.904719 | + | 0.426009i | \(0.859919\pi\) | |||||||
\(828\) | 1.71170i | 0.0594856i | ||||||||
\(829\) | −51.8181 | −1.79972 | −0.899858 | − | 0.436182i | \(-0.856330\pi\) | ||||
−0.899858 | + | 0.436182i | \(0.856330\pi\) | |||||||
\(830\) | −2.74768 | − | 15.7392i | −0.0953733 | − | 0.546315i | ||||
\(831\) | 5.56545 | + | 9.63965i | 0.193063 | + | 0.334396i | ||||
\(832\) | −4.03244 | − | 2.32813i | −0.139800 | − | 0.0807133i | ||||
\(833\) | 4.16214 | − | 2.40301i | 0.144210 | − | 0.0832595i | ||||
\(834\) | −3.09728 | − | 5.36464i | −0.107250 | − | 0.185762i | ||||
\(835\) | −8.89675 | − | 10.6394i | −0.307885 | − | 0.368192i | ||||
\(836\) | 2.33706 | − | 12.3562i | 0.0808290 | − | 0.427348i | ||||
\(837\) | − | 9.22060i | − | 0.318711i | ||||||
\(838\) | −22.4783 | + | 12.9779i | −0.776500 | + | 0.448313i | ||||
\(839\) | 0.433475 | + | 0.750801i | 0.0149652 | + | 0.0259205i | 0.873411 | − | 0.486984i | \(-0.161903\pi\) |
−0.858446 | + | 0.512904i | \(0.828570\pi\) | |||||||
\(840\) | 5.54663 | − | 0.968307i | 0.191377 | − | 0.0334098i | ||||
\(841\) | 4.73545 | + | 8.20204i | 0.163291 | + | 0.282829i | ||||
\(842\) | 25.8890 | + | 14.9470i | 0.892194 | + | 0.515109i | ||||
\(843\) | − | 5.68717i | − | 0.195876i | ||||||
\(844\) | 22.9288 | 0.789242 | ||||||||
\(845\) | −3.33815 | − | 19.1215i | −0.114836 | − | 0.657800i | ||||
\(846\) | 2.29833 | − | 3.98083i | 0.0790183 | − | 0.136864i | ||||
\(847\) | − | 6.74070i | − | 0.231613i | ||||||
\(848\) | 10.8324i | 0.371986i | ||||||||
\(849\) | −3.60536 | + | 6.24466i | −0.123736 | + | 0.214316i | ||||
\(850\) | 34.2845 | − | 12.3468i | 1.17595 | − | 0.423490i | ||||
\(851\) | 2.79418 | − | 4.83966i | 0.0957831 | − | 0.165901i | ||||
\(852\) | 9.31912 | − | 5.38040i | 0.319268 | − | 0.184329i | ||||
\(853\) | 1.05924 | − | 0.611551i | 0.0362676 | − | 0.0209391i | −0.481757 | − | 0.876305i | \(-0.660001\pi\) |
0.518024 | + | 0.855366i | \(0.326668\pi\) | |||||||
\(854\) | 37.7794 | 1.29278 | ||||||||
\(855\) | −4.99192 | + | 8.37143i | −0.170720 | + | 0.286297i | ||||
\(856\) | −3.35775 | −0.114765 | ||||||||
\(857\) | −14.7442 | + | 8.51258i | −0.503653 | + | 0.290784i | −0.730221 | − | 0.683211i | \(-0.760583\pi\) |
0.226568 | + | 0.973995i | \(0.427249\pi\) | |||||||
\(858\) | −11.6335 | + | 6.71658i | −0.397160 | + | 0.229300i | ||||
\(859\) | −4.21282 | + | 7.29683i | −0.143740 | + | 0.248964i | −0.928902 | − | 0.370326i | \(-0.879246\pi\) |
0.785162 | + | 0.619290i | \(0.212579\pi\) | |||||||
\(860\) | 5.18926 | − | 14.1824i | 0.176952 | − | 0.483614i | ||||
\(861\) | 11.2901 | − | 19.5550i | 0.384766 | − | 0.666434i | ||||
\(862\) | 27.4245i | 0.934083i | ||||||||
\(863\) | − | 6.06986i | − | 0.206620i | −0.994649 | − | 0.103310i | \(-0.967057\pi\) | ||
0.994649 | − | 0.103310i | \(-0.0329434\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 31.7208 | − | 5.53768i | 1.07854 | − | 0.188287i | ||||
\(866\) | 11.2647 | 0.382791 | ||||||||
\(867\) | 36.1147i | 1.22652i | ||||||||
\(868\) | −20.1073 | − | 11.6089i | −0.682486 | − | 0.394033i | ||||
\(869\) | 11.8860 | + | 20.5872i | 0.403205 | + | 0.698371i | ||||
\(870\) | −1.69938 | − | 9.73435i | −0.0576144 | − | 0.330025i | ||||
\(871\) | 24.8158 | + | 42.9822i | 0.840852 | + | 1.45640i | ||||
\(872\) | 3.66583 | − | 2.11647i | 0.124141 | − | 0.0716726i | ||||
\(873\) | 2.29667i | 0.0777307i | ||||||||
\(874\) | −7.04226 | + | 2.46472i | −0.238208 | + | 0.0833705i | ||||
\(875\) | 24.4523 | − | 13.9518i | 0.826639 | − | 0.471659i | ||||
\(876\) | −7.08348 | − | 12.2689i | −0.239329 | − | 0.414529i | ||||
\(877\) | −29.4618 | + | 17.0098i | −0.994855 | + | 0.574380i | −0.906722 | − | 0.421729i | \(-0.861423\pi\) |
−0.0881333 | + | 0.996109i | \(0.528090\pi\) | |||||||
\(878\) | −13.6797 | − | 7.89796i | −0.461666 | − | 0.266543i | ||||
\(879\) | −4.63359 | − | 8.02562i | −0.156287 | − | 0.270697i | ||||
\(880\) | 1.10941 | + | 6.35487i | 0.0373981 | + | 0.214223i | ||||
\(881\) | 37.8182 | 1.27413 | 0.637064 | − | 0.770811i | \(-0.280149\pi\) | ||||
0.637064 | + | 0.770811i | \(0.280149\pi\) | |||||||
\(882\) | − | 0.659446i | − | 0.0222047i | ||||||
\(883\) | −39.0605 | − | 22.5516i | −1.31449 | − | 0.758921i | −0.331653 | − | 0.943401i | \(-0.607606\pi\) |
−0.982836 | + | 0.184480i | \(0.940940\pi\) | |||||||
\(884\) | 16.9674 | − | 29.3883i | 0.570674 | − | 0.988436i | ||||
\(885\) | 13.5773 | + | 16.2368i | 0.456397 | + | 0.545793i | ||||
\(886\) | 7.03690 | 0.236409 | ||||||||
\(887\) | 37.0666 | + | 21.4004i | 1.24457 | + | 0.718555i | 0.970022 | − | 0.243017i | \(-0.0781372\pi\) |
0.274552 | + | 0.961572i | \(0.411471\pi\) | |||||||
\(888\) | −2.82740 | + | 1.63240i | −0.0948814 | + | 0.0547798i | ||||
\(889\) | 19.8392 | − | 34.3625i | 0.665385 | − | 1.15248i | ||||
\(890\) | −3.64368 | + | 9.95825i | −0.122136 | + | 0.333801i | ||||
\(891\) | −1.44248 | − | 2.49846i | −0.0483250 | − | 0.0837014i | ||||
\(892\) | 11.2470i | 0.376576i | ||||||||
\(893\) | 19.6873 | + | 3.72368i | 0.658812 | + | 0.124608i | ||||
\(894\) | 11.9895 | 0.400989 | ||||||||
\(895\) | 4.07753 | + | 1.49195i | 0.136297 | + | 0.0498704i | ||||
\(896\) | −1.25902 | − | 2.18069i | −0.0420610 | − | 0.0728518i | ||||
\(897\) | 6.90231 | + | 3.98505i | 0.230461 | + | 0.133057i | ||||
\(898\) | −14.1933 | + | 8.19449i | −0.473635 | + | 0.273454i | ||||
\(899\) | −20.3737 | + | 35.2883i | −0.679502 | + | 1.17693i | ||||
\(900\) | 0.884968 | − | 4.92106i | 0.0294989 | − | 0.164035i | ||||
\(901\) | −78.9463 | −2.63008 | ||||||||
\(902\) | 22.4046 | + | 12.9353i | 0.745990 | + | 0.430698i | ||||
\(903\) | 14.7279 | + | 8.50316i | 0.490114 | + | 0.282967i | ||||
\(904\) | −18.7982 | −0.625220 | ||||||||
\(905\) | 30.2412 | − | 25.2880i | 1.00525 | − | 0.840601i | ||||
\(906\) | 2.75767 | − | 4.77643i | 0.0916175 | − | 0.158686i | ||||
\(907\) | 26.2663 | − | 15.1648i | 0.872157 | − | 0.503540i | 0.00409285 | − | 0.999992i | \(-0.498697\pi\) |
0.868065 | + | 0.496451i | \(0.165364\pi\) | |||||||
\(908\) | 7.64539 | + | 4.41407i | 0.253721 | + | 0.146486i | ||||
\(909\) | −1.68398 | − | 2.91673i | −0.0558540 | − | 0.0967419i | ||||
\(910\) | 9.00864 | − | 24.6208i | 0.298634 | − | 0.816171i | ||||
\(911\) | 35.4194 | 1.17350 | 0.586748 | − | 0.809770i | \(-0.300408\pi\) | ||||
0.586748 | + | 0.809770i | \(0.300408\pi\) | |||||||
\(912\) | 4.28296 | + | 0.810083i | 0.141823 | + | 0.0268245i | ||||
\(913\) | 20.6138i | 0.682216i | ||||||||
\(914\) | −5.79875 | − | 10.0437i | −0.191805 | − | 0.332217i | ||||
\(915\) | 11.5279 | − | 31.5060i | 0.381100 | − | 1.04155i | ||||
\(916\) | 11.1408 | − | 19.2965i | 0.368104 | − | 0.637574i | ||||
\(917\) | −14.3209 | + | 8.26819i | −0.472918 | + | 0.273040i | ||||
\(918\) | 6.31158 | + | 3.64399i | 0.208313 | + | 0.120270i | ||||
\(919\) | −17.0531 | −0.562531 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(920\) | 2.93619 | − | 2.45527i | 0.0968033 | − | 0.0809477i | ||||
\(921\) | −5.13612 | + | 8.89602i | −0.169241 | + | 0.293134i | ||||
\(922\) | 4.14363 | + | 2.39232i | 0.136463 | + | 0.0787870i | ||||
\(923\) | − | 50.1050i | − | 1.64923i | ||||||
\(924\) | −7.26448 | −0.238984 | ||||||||
\(925\) | −10.5353 | + | 12.4692i | −0.346399 | + | 0.409985i | ||||
\(926\) | −6.07796 | − | 10.5273i | −0.199734 | − | 0.345950i | ||||
\(927\) | −9.51527 | − | 5.49365i | −0.312523 | − | 0.180435i | ||||
\(928\) | −3.82712 | + | 2.20959i | −0.125631 | + | 0.0725332i | ||||
\(929\) | −16.0271 | − | 27.7598i | −0.525834 | − | 0.910771i | −0.999547 | − | 0.0300916i | \(-0.990420\pi\) |
0.473714 | − | 0.880679i | \(-0.342913\pi\) | |||||||
\(930\) | −15.8167 | + | 13.2261i | −0.518651 | + | 0.433700i | ||||
\(931\) | 2.71309 | − | 0.949555i | 0.0889179 | − | 0.0311204i | ||||
\(932\) | − | 6.18132i | − | 0.202476i | ||||||
\(933\) | 9.90014 | − | 5.71585i | 0.324116 | − | 0.187128i | ||||
\(934\) | −0.802313 | − | 1.38965i | −0.0262525 | − | 0.0454706i | ||||
\(935\) | −46.3142 | + | 8.08533i | −1.51464 | + | 0.264419i | ||||
\(936\) | −2.32813 | − | 4.03244i | −0.0760973 | − | 0.131804i | ||||
\(937\) | −22.9312 | − | 13.2393i | −0.749128 | − | 0.432509i | 0.0762506 | − | 0.997089i | \(-0.475705\pi\) |
−0.825379 | + | 0.564579i | \(0.809038\pi\) | |||||||
\(938\) | 26.8402i | 0.876362i | ||||||||
\(939\) | −3.95860 | −0.129184 | ||||||||
\(940\) | −10.1253 | + | 1.76763i | −0.330252 | + | 0.0576539i | ||||
\(941\) | −7.18502 | + | 12.4448i | −0.234225 | + | 0.405689i | −0.959047 | − | 0.283247i | \(-0.908589\pi\) |
0.724822 | + | 0.688936i | \(0.241922\pi\) | |||||||
\(942\) | 12.2792i | 0.400079i | ||||||||
\(943\) | − | 15.3494i | − | 0.499845i | ||||||
\(944\) | 4.73274 | − | 8.19734i | 0.154037 | − | 0.266801i | ||||
\(945\) | 5.28768 | + | 1.93474i | 0.172008 | + | 0.0629371i | ||||
\(946\) | −9.74222 | + | 16.8740i | −0.316747 | + | 0.548622i | ||||
\(947\) | 39.4692 | − | 22.7875i | 1.28258 | − | 0.740495i | 0.305257 | − | 0.952270i | \(-0.401258\pi\) |
0.977318 | + | 0.211775i | \(0.0679243\pi\) | |||||||
\(948\) | −7.13601 | + | 4.11998i | −0.231767 | + | 0.133811i | ||||
\(949\) | −65.9650 | −2.14132 | ||||||||
\(950\) | 21.5205 | − | 3.44504i | 0.698217 | − | 0.111772i | ||||
\(951\) | 21.9453 | 0.711625 | ||||||||
\(952\) | 15.8928 | − | 9.17574i | 0.515090 | − | 0.297387i | ||||
\(953\) | 46.7123 | − | 26.9694i | 1.51316 | − | 0.873623i | 0.513278 | − | 0.858222i | \(-0.328431\pi\) |
0.999881 | − | 0.0154010i | \(-0.00490249\pi\) | |||||||
\(954\) | −5.41620 | + | 9.38113i | −0.175356 | + | 0.303725i | ||||
\(955\) | 9.68851 | + | 3.54498i | 0.313513 | + | 0.114713i | ||||
\(956\) | −9.09488 | + | 15.7528i | −0.294149 | + | 0.509482i | ||||
\(957\) | 12.7492i | 0.412122i | ||||||||
\(958\) | 34.5880i | 1.11749i | ||||||||
\(959\) | 18.1757 | − | 31.4813i | 0.586924 | − | 1.01658i | ||||
\(960\) | −2.20275 | + | 0.384547i | −0.0710936 | + | 0.0124112i | ||||
\(961\) | 54.0195 | 1.74257 | ||||||||
\(962\) | 15.2018i | 0.490124i | ||||||||
\(963\) | −2.90789 | − | 1.67887i | −0.0937055 | − | 0.0541009i | ||||
\(964\) | 1.24768 | + | 2.16104i | 0.0401849 | + | 0.0696023i | ||||
\(965\) | 55.2457 | − | 9.64454i | 1.77842 | − | 0.310469i | ||||
\(966\) | 2.15507 | + | 3.73268i | 0.0693381 | + | 0.120097i | ||||
\(967\) | −19.5534 | + | 11.2892i | −0.628795 | + | 0.363035i | −0.780285 | − | 0.625424i | \(-0.784926\pi\) |
0.151490 | + | 0.988459i | \(0.451593\pi\) | |||||||
\(968\) | 2.67696i | 0.0860407i | ||||||||
\(969\) | −5.90387 | + | 31.2142i | −0.189660 | + | 1.00274i | ||||
\(970\) | 3.93964 | − | 3.29436i | 0.126494 | − | 0.105776i | ||||
\(971\) | −29.4664 | − | 51.0372i | −0.945621 | − | 1.63786i | −0.754504 | − | 0.656296i | \(-0.772122\pi\) |
−0.191117 | − | 0.981567i | \(-0.561211\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −13.5084 | − | 7.79909i | −0.433060 | − | 0.250027i | ||||
\(974\) | 12.1868 | + | 21.1082i | 0.390491 | + | 0.676350i | ||||
\(975\) | −17.7835 | − | 15.0254i | −0.569529 | − | 0.481199i | ||||
\(976\) | −15.0035 | −0.480249 | ||||||||
\(977\) | 1.86548i | 0.0596821i | 0.999555 | + | 0.0298411i | \(0.00950012\pi\) | ||||
−0.999555 | + | 0.0298411i | \(0.990500\pi\) | |||||||
\(978\) | 2.99472 | + | 1.72900i | 0.0957606 | + | 0.0552874i | ||||
\(979\) | 6.84057 | − | 11.8482i | 0.218626 | − | 0.378671i | ||||
\(980\) | −1.13119 | + | 0.945912i | −0.0361346 | + | 0.0302160i | ||||
\(981\) | 4.23293 | 0.135147 | ||||||||
\(982\) | 9.44752 | + | 5.45453i | 0.301482 | + | 0.174061i | ||||
\(983\) | −38.1239 | + | 22.0109i | −1.21597 | + | 0.702038i | −0.964052 | − | 0.265712i | \(-0.914393\pi\) |
−0.251913 | + | 0.967750i | \(0.581060\pi\) | |||||||
\(984\) | −4.48368 | + | 7.76596i | −0.142934 | + | 0.247570i | ||||
\(985\) | −2.78479 | + | 7.61090i | −0.0887309 | + | 0.242503i | ||||
\(986\) | −16.1034 | − | 27.8920i | −0.512838 | − | 0.888261i | ||||
\(987\) | − | 11.5746i | − | 0.368424i | ||||||
\(988\) | 13.2379 | − | 15.3848i | 0.421154 | − | 0.489456i | ||||
\(989\) | 11.5604 | 0.367600 | ||||||||
\(990\) | −2.21666 | + | 6.05819i | −0.0704502 | + | 0.192542i | ||||
\(991\) | 16.2964 | + | 28.2263i | 0.517674 | + | 0.896637i | 0.999789 | + | 0.0205293i | \(0.00653513\pi\) |
−0.482116 | + | 0.876108i | \(0.660132\pi\) | |||||||
\(992\) | 7.98528 | + | 4.61030i | 0.253533 | + | 0.146377i | ||||
\(993\) | −6.45007 | + | 3.72395i | −0.204687 | + | 0.118176i | ||||
\(994\) | 13.5481 | − | 23.4660i | 0.429719 | − | 0.744296i | ||||
\(995\) | −1.02405 | + | 0.856319i | −0.0324646 | + | 0.0271471i | ||||
\(996\) | −7.14523 | −0.226405 | ||||||||
\(997\) | 16.4589 | + | 9.50256i | 0.521259 | + | 0.300949i | 0.737450 | − | 0.675402i | \(-0.236030\pi\) |
−0.216190 | + | 0.976351i | \(0.569363\pi\) | |||||||
\(998\) | −9.60920 | − | 5.54788i | −0.304174 | − | 0.175615i | ||||
\(999\) | −3.26480 | −0.103294 |
(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 | 570.2.q.c.349.6 | yes | 20 | |
3.2 | odd | 2 | 1710.2.t.c.919.5 | 20 | |||
5.4 | even | 2 | inner | 570.2.q.c.349.3 | yes | 20 | |
15.14 | odd | 2 | 1710.2.t.c.919.8 | 20 | |||
19.11 | even | 3 | inner | 570.2.q.c.49.3 | ✓ | 20 | |
57.11 | odd | 6 | 1710.2.t.c.1189.8 | 20 | |||
95.49 | even | 6 | inner | 570.2.q.c.49.6 | yes | 20 | |
285.239 | odd | 6 | 1710.2.t.c.1189.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.3 | ✓ | 20 | 19.11 | even | 3 | inner | |
570.2.q.c.49.6 | yes | 20 | 95.49 | even | 6 | inner | |
570.2.q.c.349.3 | yes | 20 | 5.4 | even | 2 | inner | |
570.2.q.c.349.6 | yes | 20 | 1.1 | even | 1 | trivial | |
1710.2.t.c.919.5 | 20 | 3.2 | odd | 2 | |||
1710.2.t.c.919.8 | 20 | 15.14 | odd | 2 | |||
1710.2.t.c.1189.5 | 20 | 285.239 | odd | 6 | |||
1710.2.t.c.1189.8 | 20 | 57.11 | odd | 6 |