Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(109,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, 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("315.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bf (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 26x^{12} - 96x^{10} - 781x^{8} - 2400x^{6} + 16250x^{4} + 125000x^{2} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(0.717291 - 2.11790i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.109 |
Dual form | 315.2.bf.c.289.3 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.515448 | + | 0.297594i | −0.364477 | + | 0.210431i | −0.671043 | − | 0.741419i | \(-0.734153\pi\) |
0.306566 | + | 0.951849i | \(0.400820\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.822876 | + | 1.42526i | −0.411438 | + | 0.712631i | ||||
\(5\) | −2.19280 | − | 0.437757i | −0.980650 | − | 0.195771i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.68480 | + | 2.03996i | −0.636796 | + | 0.771033i | ||||
\(8\) | − | 2.16991i | − | 0.767178i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.26055 | − | 0.426923i | 0.398620 | − | 0.135005i | ||||
\(11\) | 2.68967 | − | 4.65864i | 0.810965 | − | 1.40463i | −0.101224 | − | 0.994864i | \(-0.532276\pi\) |
0.912189 | − | 0.409770i | \(-0.134391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.07992i | − | 1.13157i | −0.824554 | − | 0.565783i | \(-0.808574\pi\) | ||
0.824554 | − | 0.565783i | \(-0.191426\pi\) | |||||||
\(14\) | 0.261348 | − | 1.55288i | 0.0698483 | − | 0.415025i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(17\) | −4.27384 | − | 2.46750i | −1.03656 | − | 0.598457i | −0.117701 | − | 0.993049i | \(-0.537553\pi\) |
−0.918856 | + | 0.394592i | \(0.870886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.322876 | − | 0.559237i | −0.0740728 | − | 0.128298i | 0.826610 | − | 0.562775i | \(-0.190266\pi\) |
−0.900683 | + | 0.434478i | \(0.856933\pi\) | |||||||
\(20\) | 2.42832 | − | 2.76510i | 0.542989 | − | 0.618294i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.20172i | 0.682608i | ||||||||
\(23\) | −5.30473 | + | 3.06269i | −1.10611 | + | 0.638615i | −0.937820 | − | 0.347122i | \(-0.887159\pi\) |
−0.168293 | + | 0.985737i | \(0.553826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.61674 | + | 1.91983i | 0.923348 | + | 0.383965i | ||||
\(26\) | 1.21416 | + | 2.10299i | 0.238116 | + | 0.412430i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.52110 | − | 4.07992i | −0.287460 | − | 0.771033i | ||||
\(29\) | −2.42832 | −0.450928 | −0.225464 | − | 0.974252i | \(-0.572390\pi\) | ||||
−0.225464 | + | 0.974252i | \(0.572390\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 4.78929 | + | 2.76510i | 0.846634 | + | 0.488804i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.93725 | 0.503735 | ||||||||
\(35\) | 4.58744 | − | 3.73569i | 0.775419 | − | 0.631447i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.760548 | + | 0.439102i | −0.125033 | + | 0.0721880i | −0.561212 | − | 0.827672i | \(-0.689665\pi\) |
0.436179 | + | 0.899860i | \(0.356331\pi\) | |||||||
\(38\) | 0.332851 | + | 0.192172i | 0.0539956 | + | 0.0311744i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.949892 | + | 4.75817i | −0.150191 | + | 0.752333i | ||||
\(41\) | −11.2814 | −1.76185 | −0.880927 | − | 0.473252i | \(-0.843080\pi\) | ||||
−0.880927 | + | 0.473252i | \(0.843080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.7945i | − | 1.64614i | −0.567941 | − | 0.823069i | \(-0.692260\pi\) | ||
0.567941 | − | 0.823069i | \(-0.307740\pi\) | |||||||
\(44\) | 4.42652 | + | 7.66697i | 0.667324 | + | 1.15584i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.82288 | − | 3.15731i | 0.268768 | − | 0.465520i | ||||
\(47\) | 1.87919 | − | 1.08495i | 0.274109 | − | 0.158257i | −0.356645 | − | 0.934240i | \(-0.616079\pi\) |
0.630753 | + | 0.775983i | \(0.282746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.32288 | − | 6.87386i | −0.188982 | − | 0.981981i | ||||
\(50\) | −2.95102 | + | 0.384343i | −0.417337 | + | 0.0543544i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.81496 | + | 3.35727i | 0.806390 | + | 0.465569i | ||||
\(53\) | 6.85108 | + | 3.95547i | 0.941068 | + | 0.543326i | 0.890295 | − | 0.455384i | \(-0.150498\pi\) |
0.0507729 | + | 0.998710i | \(0.483832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.93725 | + | 9.03805i | −1.07026 | + | 1.21869i | ||||
\(56\) | 4.42652 | + | 3.65587i | 0.591519 | + | 0.488536i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.25167 | − | 0.722653i | 0.164353 | − | 0.0948890i | ||||
\(59\) | −4.16518 | + | 7.21430i | −0.542260 | + | 0.939221i | 0.456514 | + | 0.889716i | \(0.349098\pi\) |
−0.998774 | + | 0.0495053i | \(0.984236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.177124 | − | 0.306788i | −0.0226784 | − | 0.0392802i | 0.854463 | − | 0.519512i | \(-0.173886\pi\) |
−0.877142 | + | 0.480231i | \(0.840553\pi\) | |||||||
\(62\) | − | 2.97594i | − | 0.377945i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.708497 | 0.0885622 | ||||||||
\(65\) | −1.78601 | + | 8.94645i | −0.221528 | + | 1.10967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.01222 | − | 1.16176i | −0.245832 | − | 0.141931i | 0.372022 | − | 0.928224i | \(-0.378664\pi\) |
−0.617854 | + | 0.786293i | \(0.711998\pi\) | |||||||
\(68\) | 7.03367 | − | 4.06089i | 0.852958 | − | 0.492456i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.25287 | + | 3.29075i | −0.149746 | + | 0.393320i | ||||
\(71\) | 2.42832 | 0.288189 | 0.144094 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144094 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.82718 | − | 4.51902i | −0.916102 | − | 0.528912i | −0.0337124 | − | 0.999432i | \(-0.510733\pi\) |
−0.882389 | + | 0.470520i | \(0.844066\pi\) | |||||||
\(74\) | 0.261348 | − | 0.452669i | 0.0303811 | − | 0.0526217i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.06275 | 0.121905 | ||||||||
\(77\) | 4.97188 | + | 13.3357i | 0.566599 | + | 1.51975i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.96863 | + | 5.14181i | 0.333997 | + | 0.578499i | 0.983292 | − | 0.182038i | \(-0.0582693\pi\) |
−0.649295 | + | 0.760537i | \(0.724936\pi\) | |||||||
\(80\) | 1.43458 | + | 4.23580i | 0.160391 | + | 0.473576i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.81496 | − | 3.35727i | 0.642155 | − | 0.370748i | ||||
\(83\) | − | 11.6556i | − | 1.27936i | −0.768639 | − | 0.639682i | \(-0.779066\pi\) | ||
0.768639 | − | 0.639682i | \(-0.220934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.29150 | + | 7.28164i | 0.899340 | + | 0.789804i | ||||
\(86\) | 3.21236 | + | 5.56398i | 0.346398 | + | 0.599979i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.1088 | − | 5.83633i | −1.07760 | − | 0.622155i | ||||
\(89\) | −2.68967 | − | 4.65864i | −0.285104 | − | 0.493815i | 0.687530 | − | 0.726156i | \(-0.258695\pi\) |
−0.972634 | + | 0.232341i | \(0.925362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.32288 | + | 6.87386i | 0.872474 | + | 0.720577i | ||||
\(92\) | − | 10.0808i | − | 1.05100i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.645751 | + | 1.11847i | −0.0666042 | + | 0.115362i | ||||
\(95\) | 0.463192 | + | 1.36764i | 0.0475225 | + | 0.140316i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.71453i | 0.681758i | 0.940107 | + | 0.340879i | \(0.110725\pi\) | ||||
−0.940107 | + | 0.340879i | \(0.889275\pi\) | |||||||
\(98\) | 2.72749 | + | 3.14944i | 0.275518 | + | 0.318141i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.53526 | + | 5.00029i | −0.653526 | + | 0.500029i | ||||
\(101\) | −1.73686 | + | 3.00832i | −0.172824 | + | 0.299339i | −0.939406 | − | 0.342807i | \(-0.888622\pi\) |
0.766582 | + | 0.642146i | \(0.221956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.30608 | − | 3.64082i | 0.621357 | − | 0.358740i | −0.156040 | − | 0.987751i | \(-0.549873\pi\) |
0.777397 | + | 0.629010i | \(0.216540\pi\) | |||||||
\(104\) | −8.85305 | −0.868113 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.70850 | −0.457330 | ||||||||
\(107\) | −4.45643 | + | 2.57292i | −0.430820 | + | 0.248734i | −0.699696 | − | 0.714441i | \(-0.746681\pi\) |
0.268876 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.61438 | + | 11.4564i | −0.633543 | + | 1.09733i | 0.353279 | + | 0.935518i | \(0.385067\pi\) |
−0.986822 | + | 0.161810i | \(0.948267\pi\) | |||||||
\(110\) | 1.40157 | − | 7.02072i | 0.133635 | − | 0.669399i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.21812 | + | 0.878205i | 0.493066 | + | 0.0829825i | ||||
\(113\) | 15.8219i | 1.48840i | 0.667958 | + | 0.744199i | \(0.267169\pi\) | ||||
−0.667958 | + | 0.744199i | \(0.732831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9729 | − | 4.39368i | 1.20973 | − | 0.409713i | ||||
\(116\) | 1.99820 | − | 3.46099i | 0.185529 | − | 0.321345i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.95813i | − | 0.456432i | ||||||
\(119\) | 12.2342 | − | 4.56120i | 1.12151 | − | 0.418125i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.96863 | − | 15.5341i | −0.815330 | − | 1.41219i | ||||
\(122\) | 0.182597 | + | 0.105422i | 0.0165315 | + | 0.00954448i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.11438 | − | 7.12631i | −0.369482 | − | 0.639962i | ||||
\(125\) | −9.28316 | − | 6.23080i | −0.830311 | − | 0.557300i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.07992i | − | 0.362034i | −0.983480 | − | 0.181017i | \(-0.942061\pi\) | ||
0.983480 | − | 0.181017i | \(-0.0579390\pi\) | |||||||
\(128\) | −9.94376 | + | 5.74103i | −0.878913 | + | 0.507441i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.74181 | − | 5.14293i | −0.152767 | − | 0.451065i | ||||
\(131\) | −3.90383 | − | 6.76163i | −0.341079 | − | 0.590766i | 0.643554 | − | 0.765400i | \(-0.277459\pi\) |
−0.984633 | + | 0.174634i | \(0.944126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.68480 | + | 0.283551i | 0.146091 | + | 0.0245870i | ||||
\(134\) | 1.38293 | 0.119467 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.35425 | + | 9.27383i | −0.459123 | + | 0.795224i | ||||
\(137\) | −3.42554 | − | 1.97774i | −0.292663 | − | 0.168969i | 0.346479 | − | 0.938058i | \(-0.387377\pi\) |
−0.639142 | + | 0.769088i | \(0.720711\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.22876 | 0.613135 | 0.306568 | − | 0.951849i | \(-0.400819\pi\) | ||||
0.306568 | + | 0.951849i | \(0.400819\pi\) | |||||||
\(140\) | 1.54944 | + | 9.61232i | 0.130952 | + | 0.812389i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.25167 | + | 0.722653i | −0.105038 | + | 0.0606437i | ||||
\(143\) | −19.0069 | − | 10.9736i | −1.58944 | − | 0.917661i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.32482 | + | 1.06301i | 0.442202 | + | 0.0882785i | ||||
\(146\) | 5.37934 | 0.445197 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.44531i | − | 0.118803i | ||||||
\(149\) | −1.47551 | − | 2.55566i | −0.120878 | − | 0.209367i | 0.799236 | − | 0.601017i | \(-0.205238\pi\) |
−0.920114 | + | 0.391650i | \(0.871904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.46863 | − | 7.73989i | 0.363652 | − | 0.629863i | −0.624907 | − | 0.780699i | \(-0.714863\pi\) |
0.988559 | + | 0.150836i | \(0.0481965\pi\) | |||||||
\(152\) | −1.21349 | + | 0.700610i | −0.0984272 | + | 0.0568270i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.53137 | − | 5.39426i | −0.526313 | − | 0.434682i | ||||
\(155\) | 7.37754 | − | 8.40071i | 0.592578 | − | 0.674761i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1088 | − | 5.83633i | −0.806772 | − | 0.465790i | 0.0390619 | − | 0.999237i | \(-0.487563\pi\) |
−0.845834 | + | 0.533447i | \(0.820896\pi\) | |||||||
\(158\) | −3.06034 | − | 1.76689i | −0.243468 | − | 0.140566i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.29150 | − | 8.15984i | −0.734558 | − | 0.645092i | ||||
\(161\) | 2.68967 | − | 15.9815i | 0.211976 | − | 1.25952i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52110 | − | 0.878205i | 0.119141 | − | 0.0687863i | −0.439245 | − | 0.898367i | \(-0.644754\pi\) |
0.558386 | + | 0.829581i | \(0.311421\pi\) | |||||||
\(164\) | 9.28316 | − | 16.0789i | 0.724893 | − | 1.25555i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.46863 | + | 6.00784i | 0.269218 | + | 0.466299i | ||||
\(167\) | − | 12.6351i | − | 0.977733i | −0.872359 | − | 0.488867i | \(-0.837410\pi\) | ||
0.872359 | − | 0.488867i | \(-0.162590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.64575 | −0.280442 | ||||||||
\(170\) | −6.44081 | − | 1.28580i | −0.493987 | − | 0.0986166i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.3849 | + | 8.88249i | 1.17309 | + | 0.677284i | ||||
\(173\) | 8.06457 | − | 4.65608i | 0.613138 | − | 0.353995i | −0.161055 | − | 0.986945i | \(-0.551490\pi\) |
0.774193 | + | 0.632950i | \(0.218156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.6947 | + | 6.18343i | −0.884033 | + | 0.467424i | ||||
\(176\) | −10.7587 | −0.810965 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.77277 | + | 1.60086i | 0.207828 | + | 0.119989i | ||||
\(179\) | 8.33035 | − | 14.4286i | 0.622640 | − | 1.07844i | −0.366352 | − | 0.930476i | \(-0.619394\pi\) |
0.988992 | − | 0.147968i | \(-0.0472731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6458 | 0.939951 | 0.469976 | − | 0.882679i | \(-0.344263\pi\) | ||||
0.469976 | + | 0.882679i | \(0.344263\pi\) | |||||||
\(182\) | −6.33563 | − | 1.06628i | −0.469628 | − | 0.0790380i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.64575 | + | 11.5108i | 0.489931 | + | 0.848586i | ||||
\(185\) | 1.85995 | − | 0.629928i | 0.136746 | − | 0.0463133i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.9904 | + | 13.2735i | −1.68123 | + | 0.970656i | ||||
\(188\) | 3.57113i | 0.260451i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.645751 | − | 0.567102i | −0.0468477 | − | 0.0411419i | ||||
\(191\) | 5.37934 | + | 9.31728i | 0.389235 | + | 0.674175i | 0.992347 | − | 0.123482i | \(-0.0394060\pi\) |
−0.603112 | + | 0.797657i | \(0.706073\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8694 | + | 6.27543i | 0.782394 | + | 0.451715i | 0.837278 | − | 0.546777i | \(-0.184146\pi\) |
−0.0548839 | + | 0.998493i | \(0.517479\pi\) | |||||||
\(194\) | −1.99820 | − | 3.46099i | −0.143463 | − | 0.248485i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.8856 | + | 3.77089i | 0.777544 | + | 0.269349i | ||||
\(197\) | 5.91453i | 0.421393i | 0.977552 | + | 0.210697i | \(0.0675732\pi\) | ||||
−0.977552 | + | 0.210697i | \(0.932427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.82288 | − | 15.2817i | 0.625437 | − | 1.08329i | −0.363019 | − | 0.931782i | \(-0.618254\pi\) |
0.988456 | − | 0.151507i | \(-0.0484126\pi\) | |||||||
\(200\) | 4.16584 | − | 10.0179i | 0.294570 | − | 0.708372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2.06751i | − | 0.145470i | ||||||
\(203\) | 4.09124 | − | 4.95368i | 0.287149 | − | 0.347680i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.7378 | + | 4.93850i | 1.72776 | + | 0.344919i | ||||
\(206\) | −2.16697 | + | 3.75330i | −0.150980 | + | 0.261505i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.06663 | + | 4.07992i | −0.489983 | + | 0.282892i | ||||
\(209\) | −3.47371 | −0.240282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9373 | −1.02832 | −0.514161 | − | 0.857693i | \(-0.671897\pi\) | ||||
−0.514161 | + | 0.857693i | \(0.671897\pi\) | |||||||
\(212\) | −11.2752 | + | 6.50972i | −0.774382 | + | 0.447090i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.53137 | − | 2.65242i | 0.104683 | − | 0.181315i | ||||
\(215\) | −4.72535 | + | 23.6701i | −0.322266 | + | 1.61429i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.62128 | − | 12.3953i | −0.313713 | − | 0.841449i | ||||
\(218\) | − | 7.87360i | − | 0.533267i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.35021 | − | 18.7499i | −0.428131 | − | 1.26412i | ||||
\(221\) | −10.0672 | + | 17.4369i | −0.677194 | + | 1.17293i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | −13.7097 | + | 5.11131i | −0.916017 | + | 0.341514i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.70850 | − | 8.15536i | −0.313205 | − | 0.542486i | ||||
\(227\) | 3.06034 | + | 1.76689i | 0.203122 | + | 0.117273i | 0.598111 | − | 0.801413i | \(-0.295918\pi\) |
−0.394989 | + | 0.918686i | \(0.629252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.14575 | − | 1.98450i | −0.0757134 | − | 0.131139i | 0.825683 | − | 0.564135i | \(-0.190790\pi\) |
−0.901396 | + | 0.432995i | \(0.857457\pi\) | |||||||
\(230\) | −5.37934 | + | 6.12538i | −0.354703 | + | 0.403895i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.26923i | 0.345942i | ||||||||
\(233\) | 6.66848 | − | 3.85005i | 0.436867 | − | 0.252225i | −0.265401 | − | 0.964138i | \(-0.585504\pi\) |
0.702268 | + | 0.711913i | \(0.252171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.59564 | + | 1.55646i | −0.299787 | + | 0.101532i | ||||
\(236\) | −6.85484 | − | 11.8729i | −0.446212 | − | 0.772862i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.94870 | + | 5.99188i | −0.320776 | + | 0.388396i | ||||
\(239\) | 8.85305 | 0.572656 | 0.286328 | − | 0.958132i | \(-0.407565\pi\) | ||||
0.286328 | + | 0.958132i | \(0.407565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1144 | + | 24.4468i | −0.909187 | + | 1.57476i | −0.0939910 | + | 0.995573i | \(0.529962\pi\) |
−0.815196 | + | 0.579185i | \(0.803371\pi\) | |||||||
\(242\) | 9.24572 | + | 5.33802i | 0.594337 | + | 0.343141i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.583005 | 0.0373231 | ||||||||
\(245\) | −0.108279 | + | 15.6521i | −0.00691772 | + | 0.999976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.28164 | + | 1.31731i | −0.145177 | + | 0.0838182i | ||||
\(248\) | 9.39597 | + | 5.42477i | 0.596645 | + | 0.344473i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.63924 | + | 0.449039i | 0.419902 | + | 0.0283997i | ||||
\(251\) | 16.1380 | 1.01862 | 0.509311 | − | 0.860583i | \(-0.329900\pi\) | ||||
0.509311 | + | 0.860583i | \(0.329900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.9505i | 2.07158i | ||||||||
\(254\) | 1.21416 | + | 2.10299i | 0.0761832 | + | 0.131953i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.70850 | − | 4.69126i | 0.169281 | − | 0.293203i | ||||
\(257\) | −1.36375 | + | 0.787360i | −0.0850682 | + | 0.0491141i | −0.541931 | − | 0.840423i | \(-0.682306\pi\) |
0.456862 | + | 0.889537i | \(0.348973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.385622 | − | 2.29129i | 0.0239614 | − | 0.142374i | ||||
\(260\) | −11.2814 | − | 9.90735i | −0.699641 | − | 0.614428i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.02444 | + | 2.32351i | 0.248631 | + | 0.143547i | ||||
\(263\) | 12.4887 | + | 7.21033i | 0.770084 | + | 0.444608i | 0.832905 | − | 0.553417i | \(-0.186676\pi\) |
−0.0628207 | + | 0.998025i | \(0.520010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2915 | − | 11.6727i | −0.816491 | − | 0.717046i | ||||
\(266\) | −0.952811 | + | 0.355232i | −0.0584206 | + | 0.0217806i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.31161 | − | 1.91196i | 0.202289 | − | 0.116792i | ||||
\(269\) | −12.2342 | + | 21.1902i | −0.745931 | + | 1.29199i | 0.203827 | + | 0.979007i | \(0.434662\pi\) |
−0.949758 | + | 0.312984i | \(0.898671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1144 | − | 19.2507i | −0.675150 | − | 1.16939i | −0.976425 | − | 0.215857i | \(-0.930745\pi\) |
0.301275 | − | 0.953537i | \(-0.402588\pi\) | |||||||
\(272\) | 9.87000i | 0.598457i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.35425 | 0.142225 | ||||||||
\(275\) | 21.3613 | − | 16.3440i | 1.28813 | − | 0.985582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8938 | − | 8.59894i | −0.894882 | − | 0.516660i | −0.0193459 | − | 0.999813i | \(-0.506158\pi\) |
−0.875536 | + | 0.483152i | \(0.839492\pi\) | |||||||
\(278\) | −3.72605 | + | 2.15123i | −0.223473 | + | 0.129022i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.10610 | − | 9.95432i | −0.484432 | − | 0.594885i | ||||
\(281\) | 3.99641 | 0.238406 | 0.119203 | − | 0.992870i | \(-0.461966\pi\) | ||||
0.119203 | + | 0.992870i | \(0.461966\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4393 | + | 11.8007i | 1.21499 | + | 0.701476i | 0.963843 | − | 0.266472i | \(-0.0858579\pi\) |
0.251150 | + | 0.967948i | \(0.419191\pi\) | |||||||
\(284\) | −1.99820 | + | 3.46099i | −0.118572 | + | 0.205372i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.0627 | 0.772416 | ||||||||
\(287\) | 19.0069 | − | 23.0135i | 1.12194 | − | 1.35845i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.67712 | + | 6.36897i | 0.216301 | + | 0.374645i | ||||
\(290\) | −3.06101 | + | 1.03671i | −0.179749 | + | 0.0608774i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.8816 | − | 7.43719i | 0.753838 | − | 0.435228i | ||||
\(293\) | 15.1894i | 0.887371i | 0.896182 | + | 0.443686i | \(0.146329\pi\) | ||||
−0.896182 | + | 0.443686i | \(0.853671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2915 | − | 13.9962i | 0.715639 | − | 0.814889i | ||||
\(296\) | 0.952811 | + | 1.65032i | 0.0553810 | + | 0.0959228i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.52110 | + | 0.878205i | 0.0881147 | + | 0.0508730i | ||||
\(299\) | 12.4955 | + | 21.6429i | 0.722635 | + | 1.25164i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0203 | + | 18.1865i | 1.26923 | + | 1.04825i | ||||
\(302\) | 5.31935i | 0.306094i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.645751 | + | 1.11847i | −0.0370364 | + | 0.0641489i | ||||
\(305\) | 0.254099 | + | 0.750263i | 0.0145497 | + | 0.0429599i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.3996i | − | 1.16427i | −0.813093 | − | 0.582133i | \(-0.802218\pi\) | ||
0.813093 | − | 0.582133i | \(-0.197782\pi\) | |||||||
\(308\) | −23.0981 | − | 3.88739i | −1.31614 | − | 0.221505i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.30274 | + | 6.52564i | −0.0739905 | + | 0.370631i | ||||
\(311\) | −1.73686 | + | 3.00832i | −0.0984881 | + | 0.170586i | −0.911059 | − | 0.412276i | \(-0.864734\pi\) |
0.812571 | + | 0.582862i | \(0.198067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.82718 | + | 4.51902i | −0.442418 | + | 0.255430i | −0.704623 | − | 0.709582i | \(-0.748884\pi\) |
0.262205 | + | 0.965012i | \(0.415550\pi\) | |||||||
\(314\) | 6.94743 | 0.392066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.77124 | −0.549675 | ||||||||
\(317\) | 15.2485 | − | 8.80372i | 0.856441 | − | 0.494466i | −0.00637790 | − | 0.999980i | \(-0.502030\pi\) |
0.862819 | + | 0.505513i | \(0.168697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.53137 | + | 11.3127i | −0.365687 | + | 0.633388i | ||||
\(320\) | −1.55359 | − | 0.310150i | −0.0868485 | − | 0.0173379i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.36961 | + | 9.03805i | 0.187781 | + | 0.503671i | ||||
\(323\) | 3.18678i | 0.177317i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.83274 | − | 18.8359i | 0.434482 | − | 1.04483i | ||||
\(326\) | −0.522697 | + | 0.905337i | −0.0289495 | + | 0.0501420i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.4795i | 1.35166i | ||||||||
\(329\) | −0.952811 | + | 5.66142i | −0.0525302 | + | 0.312124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.79150 | − | 15.2273i | −0.483225 | − | 0.836970i | 0.516590 | − | 0.856233i | \(-0.327201\pi\) |
−0.999814 | + | 0.0192633i | \(0.993868\pi\) | |||||||
\(332\) | 16.6122 | + | 9.59108i | 0.911715 | + | 0.526379i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.76013 | + | 6.51274i | 0.205745 | + | 0.356361i | ||||
\(335\) | 3.90383 | + | 3.42836i | 0.213289 | + | 0.187311i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.2398i | − | 0.666742i | −0.942796 | − | 0.333371i | \(-0.891814\pi\) | ||
0.942796 | − | 0.333371i | \(-0.108186\pi\) | |||||||
\(338\) | 1.87919 | − | 1.08495i | 0.102215 | − | 0.0590137i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.2011 | + | 5.82569i | −0.932862 | + | 0.315942i | ||||
\(341\) | 13.4483 | + | 23.2932i | 0.728268 | + | 1.26140i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.2512 | + | 8.88249i | 0.877482 | + | 0.479610i | ||||
\(344\) | −23.4230 | −1.26288 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.77124 | + | 4.79993i | −0.148983 | + | 0.258046i | ||||
\(347\) | −16.7948 | − | 9.69651i | −0.901594 | − | 0.520536i | −0.0238772 | − | 0.999715i | \(-0.507601\pi\) |
−0.877717 | + | 0.479179i | \(0.840934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.8745 | −1.38503 | −0.692515 | − | 0.721403i | \(-0.743498\pi\) | ||||
−0.692515 | + | 0.721403i | \(0.743498\pi\) | |||||||
\(350\) | 4.18784 | − | 6.66750i | 0.223849 | − | 0.356393i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.7632 | − | 14.8744i | 1.37318 | − | 0.792807i | ||||
\(353\) | 1.36375 | + | 0.787360i | 0.0725849 | + | 0.0419069i | 0.535853 | − | 0.844311i | \(-0.319990\pi\) |
−0.463268 | + | 0.886218i | \(0.653323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.32482 | − | 1.06301i | −0.282612 | − | 0.0564189i | ||||
\(356\) | 8.85305 | 0.469211 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.91625i | 0.524090i | ||||||||
\(359\) | −9.54451 | − | 16.5316i | −0.503740 | − | 0.872503i | −0.999991 | − | 0.00432406i | \(-0.998624\pi\) |
0.496251 | − | 0.868179i | \(-0.334710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.29150 | − | 16.0934i | 0.489026 | − | 0.847019i | ||||
\(362\) | −6.51823 | + | 3.76330i | −0.342590 | + | 0.197795i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.6458 | + | 6.20595i | −0.872474 | + | 0.325280i | ||||
\(365\) | 15.1852 | + | 13.3357i | 0.794829 | + | 0.698023i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.1455 | − | 9.32160i | −0.842787 | − | 0.486583i | 0.0154235 | − | 0.999881i | \(-0.495090\pi\) |
−0.858211 | + | 0.513298i | \(0.828424\pi\) | |||||||
\(368\) | 10.6095 | + | 6.12538i | 0.553057 | + | 0.319307i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.771243 | + | 0.878205i | −0.0400950 | + | 0.0456557i | ||||
\(371\) | −19.6117 | + | 7.31173i | −1.01819 | + | 0.379606i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7088 | + | 11.9562i | −1.07226 | + | 0.619069i | −0.928798 | − | 0.370587i | \(-0.879157\pi\) |
−0.143461 | + | 0.989656i | \(0.545823\pi\) | |||||||
\(374\) | 7.90024 | − | 13.6836i | 0.408512 | − | 0.707563i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.35425 | − | 4.07768i | −0.121411 | − | 0.210290i | ||||
\(377\) | 9.90735i | 0.510255i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.29150 | 0.117707 | 0.0588533 | − | 0.998267i | \(-0.481256\pi\) | ||||
0.0588533 | + | 0.998267i | \(0.481256\pi\) | |||||||
\(380\) | −2.33039 | − | 0.465224i | −0.119546 | − | 0.0238655i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.54553 | − | 3.20172i | −0.283734 | − | 0.163814i | ||||
\(383\) | 12.3061 | − | 7.10491i | 0.628811 | − | 0.363044i | −0.151481 | − | 0.988460i | \(-0.548404\pi\) |
0.780291 | + | 0.625416i | \(0.215071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.06454 | − | 31.4190i | −0.258113 | − | 1.60126i | ||||
\(386\) | −7.47012 | −0.380219 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.56997 | − | 5.52523i | −0.485842 | − | 0.280501i | ||||
\(389\) | −15.4465 | + | 26.7542i | −0.783171 | + | 1.35649i | 0.146915 | + | 0.989149i | \(0.453066\pi\) |
−0.930086 | + | 0.367343i | \(0.880268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.2288 | 1.52873 | ||||||||
\(392\) | −14.9156 | + | 2.87052i | −0.753354 | + | 0.144983i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.76013 | − | 3.04863i | −0.0886740 | − | 0.153588i | ||||
\(395\) | −4.25874 | − | 12.5745i | −0.214280 | − | 0.632692i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.5060 | − | 15.8806i | 1.38049 | − | 0.797023i | 0.388268 | − | 0.921546i | \(-0.373073\pi\) |
0.992217 | + | 0.124523i | \(0.0397400\pi\) | |||||||
\(398\) | 10.5025i | 0.526445i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.29150 | − | 9.91625i | −0.0645751 | − | 0.495813i | ||||
\(401\) | −19.6117 | − | 33.9685i | −0.979363 | − | 1.69631i | −0.664715 | − | 0.747097i | \(-0.731447\pi\) |
−0.314648 | − | 0.949208i | \(-0.601886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6666 | + | 10.1998i | 0.880035 | + | 0.508088i | ||||
\(404\) | −2.85843 | − | 4.95095i | −0.142212 | − | 0.246319i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.634637 | + | 3.77089i | −0.0314965 | + | 0.187146i | ||||
\(407\) | 4.72416i | 0.234168i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7915 | − | 22.1555i | 0.632499 | − | 1.09552i | −0.354540 | − | 0.935041i | \(-0.615363\pi\) |
0.987039 | − | 0.160480i | \(-0.0513041\pi\) | |||||||
\(410\) | −14.2207 | + | 4.81628i | −0.702310 | + | 0.237859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.9838i | 0.590398i | ||||||||
\(413\) | −7.69938 | − | 20.6515i | −0.378862 | − | 1.01619i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.10230 | + | 25.5583i | −0.250462 | + | 1.25461i | ||||
\(416\) | 11.2814 | − | 19.5399i | 0.553115 | − | 0.958023i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.79052 | − | 1.03376i | 0.0875771 | − | 0.0505627i | ||||
\(419\) | 17.7061 | 0.864999 | 0.432500 | − | 0.901634i | \(-0.357632\pi\) | ||||
0.432500 | + | 0.901634i | \(0.357632\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.22876 | −0.449782 | −0.224891 | − | 0.974384i | \(-0.572203\pi\) | ||||
−0.224891 | + | 0.974384i | \(0.572203\pi\) | |||||||
\(422\) | 7.69938 | − | 4.44524i | 0.374800 | − | 0.216391i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.58301 | − | 14.8662i | 0.416828 | − | 0.721967i | ||||
\(425\) | −14.9940 | − | 19.5968i | −0.727317 | − | 0.950586i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.924256 | + | 0.155551i | 0.0447279 | + | 0.00752766i | ||||
\(428\) | − | 8.46878i | − | 0.409354i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.60840 | − | 13.6069i | −0.222237 | − | 0.656184i | ||||
\(431\) | 10.3286 | − | 17.8896i | 0.497509 | − | 0.861711i | −0.502487 | − | 0.864585i | \(-0.667581\pi\) |
0.999996 | + | 0.00287387i | \(0.000914782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.8287i | 1.62570i | 0.582472 | + | 0.812851i | \(0.302086\pi\) | ||||
−0.582472 | + | 0.812851i | \(0.697914\pi\) | |||||||
\(434\) | 6.07080 | + | 5.01387i | 0.291408 | + | 0.240674i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.8856 | − | 18.8544i | −0.521327 | − | 0.902964i | ||||
\(437\) | 3.42554 | + | 1.97774i | 0.163866 | + | 0.0946079i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.1144 | + | 26.1789i | 0.721370 | + | 1.24945i | 0.960451 | + | 0.278450i | \(0.0898206\pi\) |
−0.239081 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(440\) | 19.6117 | + | 17.2231i | 0.934952 | + | 0.821079i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.9838i | − | 0.570009i | ||||||
\(443\) | 14.5505 | − | 8.40071i | 0.691313 | − | 0.399130i | −0.112791 | − | 0.993619i | \(-0.535979\pi\) |
0.804104 | + | 0.594489i | \(0.202646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.85855 | + | 11.3929i | 0.182913 | + | 0.540075i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.19368 | + | 1.44531i | −0.0563960 | + | 0.0682843i | ||||
\(449\) | 22.5627 | 1.06480 | 0.532401 | − | 0.846492i | \(-0.321290\pi\) | ||||
0.532401 | + | 0.846492i | \(0.321290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.3431 | + | 52.5559i | −1.42880 | + | 2.47476i | ||||
\(452\) | −22.5503 | − | 13.0194i | −1.06068 | − | 0.612383i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.10326 | −0.0987111 | ||||||||
\(455\) | −15.2413 | − | 18.7164i | −0.714524 | − | 0.877438i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7754 | + | 16.0361i | −1.29928 | + | 0.750139i | −0.980279 | − | 0.197617i | \(-0.936680\pi\) |
−0.318999 | + | 0.947755i | \(0.603347\pi\) | |||||||
\(458\) | 1.18115 | + | 0.681937i | 0.0551915 | + | 0.0318648i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.41296 | + | 22.1053i | −0.205755 | + | 1.03066i | ||||
\(461\) | −16.1380 | −0.751622 | −0.375811 | − | 0.926696i | \(-0.622636\pi\) | ||||
−0.375811 | + | 0.926696i | \(0.622636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.5090i | − | 0.813712i | −0.913492 | − | 0.406856i | \(-0.866625\pi\) | ||
0.913492 | − | 0.406856i | \(-0.133375\pi\) | |||||||
\(464\) | 2.42832 | + | 4.20597i | 0.112732 | + | 0.195257i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.29150 | + | 3.96900i | −0.106152 | + | 0.183860i | ||||
\(467\) | −35.5868 | + | 20.5460i | −1.64676 | + | 0.950757i | −0.668412 | + | 0.743791i | \(0.733026\pi\) |
−0.978348 | + | 0.206966i | \(0.933641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.76013 | − | 2.14752i | 0.265978 | − | 0.0991632i | ||||
\(470\) | 1.90562 | − | 2.16991i | 0.0878998 | − | 0.100090i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.6544 | + | 9.03805i | 0.720550 | + | 0.416010i | ||||
\(473\) | −50.2875 | − | 29.0335i | −2.31222 | − | 1.33496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.416995 | − | 3.20172i | −0.0191330 | − | 0.146905i | ||||
\(476\) | −3.56630 | + | 21.1902i | −0.163461 | + | 0.971252i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.56329 | + | 2.63461i | −0.208720 | + | 0.120504i | ||||
\(479\) | 6.33215 | − | 10.9676i | 0.289323 | − | 0.501122i | −0.684325 | − | 0.729177i | \(-0.739903\pi\) |
0.973648 | + | 0.228055i | \(0.0732364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.79150 | + | 3.10297i | 0.0816855 | + | 0.141483i | ||||
\(482\) | − | 16.8014i | − | 0.765284i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29.5203 | 1.34183 | ||||||||
\(485\) | 2.93933 | − | 14.7236i | 0.133468 | − | 0.668565i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7088 | − | 11.9562i | −0.938404 | − | 0.541788i | −0.0489441 | − | 0.998802i | \(-0.515586\pi\) |
−0.889460 | + | 0.457014i | \(0.848919\pi\) | |||||||
\(488\) | −0.665702 | + | 0.384343i | −0.0301349 | + | 0.0173984i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.60216 | − | 8.10007i | −0.207904 | − | 0.365924i | ||||
\(491\) | 36.2724 | 1.63695 | 0.818476 | − | 0.574541i | \(-0.194819\pi\) | ||||
0.818476 | + | 0.574541i | \(0.194819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3782 | + | 5.99188i | 0.467413 | + | 0.269861i | ||||
\(494\) | 0.784045 | − | 1.35801i | 0.0352759 | − | 0.0610996i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | −4.09124 | + | 4.95368i | −0.183517 | + | 0.222203i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | − | 4.33013i | −0.111915 | − | 0.193843i | 0.804627 | − | 0.593780i | \(-0.202365\pi\) |
−0.916542 | + | 0.399937i | \(0.869032\pi\) | |||||||
\(500\) | 16.5194 | − | 8.10377i | 0.738771 | − | 0.362412i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.31830 | + | 4.80257i | −0.371264 | + | 0.214349i | ||||
\(503\) | 15.8219i | 0.705463i | 0.935725 | + | 0.352731i | \(0.114747\pi\) | ||||
−0.935725 | + | 0.352731i | \(0.885253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.12549 | − | 5.83633i | 0.228081 | − | 0.259713i | ||||
\(506\) | −9.80586 | − | 16.9842i | −0.435924 | − | 0.755042i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.81496 | + | 3.35727i | 0.257997 | + | 0.148955i | ||||
\(509\) | −10.7587 | − | 18.6346i | −0.476870 | − | 0.825963i | 0.522779 | − | 0.852468i | \(-0.324895\pi\) |
−0.999649 | + | 0.0265057i | \(0.991562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4059 | − | 8.35347i | 0.991178 | − | 0.369536i | ||||
\(512\) | − | 19.7400i | − | 0.872393i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.468627 | − | 0.811686i | 0.0206702 | − | 0.0358019i | ||||
\(515\) | −15.4218 | + | 5.22305i | −0.679564 | + | 0.230155i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.6727i | − | 0.513363i | ||||||
\(518\) | 0.483106 | + | 1.29580i | 0.0212264 | + | 0.0569341i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.4130 | + | 3.87548i | 0.851315 | + | 0.169951i | ||||
\(521\) | 8.33035 | − | 14.4286i | 0.364959 | − | 0.632128i | −0.623810 | − | 0.781576i | \(-0.714416\pi\) |
0.988770 | + | 0.149448i | \(0.0477495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.01222 | + | 1.16176i | −0.0879882 | + | 0.0508000i | −0.543349 | − | 0.839507i | \(-0.682844\pi\) |
0.455360 | + | 0.890307i | \(0.349510\pi\) | |||||||
\(524\) | 12.8495 | 0.561331 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.58301 | −0.374237 | ||||||||
\(527\) | 21.3692 | − | 12.3375i | 0.930856 | − | 0.537430i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.26013 | − | 12.5749i | 0.315658 | − | 0.546735i | ||||
\(530\) | 10.3248 | + | 2.06118i | 0.448480 | + | 0.0895318i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.79052 | + | 2.16796i | −0.0776288 | + | 0.0939930i | ||||
\(533\) | 46.0271i | 1.99365i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8984 | − | 3.69107i | 0.471178 | − | 0.159579i | ||||
\(536\) | −2.52090 | + | 4.36633i | −0.108886 | + | 0.188597i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.5633i | − | 0.627867i | ||||||
\(539\) | −35.5810 | − | 12.3256i | −1.53258 | − | 0.530901i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.7915 | − | 25.6196i | −0.635936 | − | 1.10147i | −0.986316 | − | 0.164866i | \(-0.947281\pi\) |
0.350380 | − | 0.936608i | \(-0.386053\pi\) | |||||||
\(542\) | 11.4578 | + | 6.61514i | 0.492153 | + | 0.284145i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.6458 | − | 23.6351i | −0.585057 | − | 1.01335i | ||||
\(545\) | 19.5191 | − | 22.2262i | 0.836108 | − | 0.952065i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.6394i | 1.39556i | 0.716313 | + | 0.697779i | \(0.245828\pi\) | ||||
−0.716313 | + | 0.697779i | \(0.754172\pi\) | |||||||
\(548\) | 5.63758 | − | 3.25486i | 0.240826 | − | 0.139041i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.14674 | + | 14.7815i | −0.262098 | + | 0.630285i | ||||
\(551\) | 0.784045 | + | 1.35801i | 0.0334015 | + | 0.0578530i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.4906 | − | 2.60706i | −0.658729 | − | 0.110864i | ||||
\(554\) | 10.2360 | 0.434885 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.94837 | + | 10.3029i | −0.252267 | + | 0.436939i | ||||
\(557\) | −1.57869 | − | 0.911455i | −0.0668911 | − | 0.0386196i | 0.466181 | − | 0.884689i | \(-0.345629\pi\) |
−0.533073 | + | 0.846070i | \(0.678963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.0405 | −1.86272 | ||||||||
\(560\) | −11.0578 | − | 4.20999i | −0.467279 | − | 0.177905i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.05994 | + | 1.18931i | −0.0868934 | + | 0.0501679i | ||||
\(563\) | −7.51678 | − | 4.33981i | −0.316794 | − | 0.182901i | 0.333168 | − | 0.942867i | \(-0.391882\pi\) |
−0.649963 | + | 0.759966i | \(0.725216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.92614 | − | 34.6942i | 0.291385 | − | 1.45960i | ||||
\(566\) | −14.0472 | −0.590449 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 5.26923i | − | 0.221092i | ||||||
\(569\) | −11.5427 | − | 19.9926i | −0.483896 | − | 0.838132i | 0.515933 | − | 0.856629i | \(-0.327445\pi\) |
−0.999829 | + | 0.0184967i | \(0.994112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.26013 | + | 3.91466i | −0.0945835 | + | 0.163823i | −0.909435 | − | 0.415847i | \(-0.863485\pi\) |
0.814851 | + | 0.579670i | \(0.196819\pi\) | |||||||
\(572\) | 31.2806 | − | 18.0599i | 1.30791 | − | 0.755121i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.94837 | + | 17.5186i | −0.123062 | + | 0.731213i | ||||
\(575\) | −30.3704 | + | 3.95547i | −1.26653 | + | 0.164955i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.1877 | + | 11.0780i | 0.798793 | + | 0.461183i | 0.843049 | − | 0.537837i | \(-0.180758\pi\) |
−0.0442559 | + | 0.999020i | \(0.514092\pi\) | |||||||
\(578\) | −3.79073 | − | 2.18858i | −0.157674 | − | 0.0910329i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.89674 | + | 6.71453i | −0.244849 | + | 0.278806i | ||||
\(581\) | 23.7769 | + | 19.6373i | 0.986432 | + | 0.814694i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.8542 | − | 21.2778i | 1.52635 | − | 0.881237i | ||||
\(584\) | −9.80586 | + | 16.9842i | −0.405769 | + | 0.702813i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.52026 | − | 7.82932i | −0.186730 | − | 0.323426i | ||||
\(587\) | 44.2789i | 1.82758i | 0.406182 | + | 0.913792i | \(0.366860\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22876 | 0.133039 | ||||||||
\(590\) | −2.17045 | + | 10.8722i | −0.0893561 | + | 0.447600i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.52110 | + | 0.878205i | 0.0625166 | + | 0.0360940i | ||||
\(593\) | −21.9170 | + | 12.6538i | −0.900022 | + | 0.519628i | −0.877207 | − | 0.480112i | \(-0.840596\pi\) |
−0.0228149 | + | 0.999740i | \(0.507263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.8238 | + | 4.64621i | −1.18166 | + | 0.190476i | ||||
\(596\) | 4.85664 | 0.198936 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.8816 | − | 7.43719i | −0.526767 | − | 0.304129i | ||||
\(599\) | −12.2342 | + | 21.1902i | −0.499875 | + | 0.865809i | −1.00000 | 0.000144290i | \(-0.999954\pi\) | |
0.500125 | + | 0.865953i | \(0.333287\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1033 | 0.942402 | 0.471201 | − | 0.882026i | \(-0.343821\pi\) | ||||
0.471201 | + | 0.882026i | \(0.343821\pi\) | |||||||
\(602\) | −16.7625 | − | 2.82111i | −0.683188 | − | 0.114980i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.35425 | + | 12.7379i | 0.299240 | + | 0.518299i | ||||
\(605\) | 12.8662 | + | 37.9893i | 0.523087 | + | 1.54448i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1455 | + | 9.32160i | −0.655325 | + | 0.378352i | −0.790493 | − | 0.612471i | \(-0.790176\pi\) |
0.135169 | + | 0.990823i | \(0.456842\pi\) | |||||||
\(608\) | − | 3.57113i | − | 0.144828i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.354249 | − | 0.311103i | −0.0143431 | − | 0.0125962i | ||||
\(611\) | −4.42652 | − | 7.66697i | −0.179078 | − | 0.310172i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4938 | − | 14.7188i | −1.02968 | − | 0.594488i | −0.112789 | − | 0.993619i | \(-0.535978\pi\) |
−0.916894 | + | 0.399131i | \(0.869312\pi\) | |||||||
\(614\) | 6.07080 | + | 10.5149i | 0.244997 | + | 0.424348i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.9373 | − | 10.7885i | 1.16592 | − | 0.434682i | ||||
\(617\) | 13.8628i | 0.558096i | 0.960277 | + | 0.279048i | \(0.0900189\pi\) | ||||
−0.960277 | + | 0.279048i | \(0.909981\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.50000 | − | 11.2583i | 0.261257 | − | 0.452510i | −0.705319 | − | 0.708890i | \(-0.749196\pi\) |
0.966576 | + | 0.256379i | \(0.0825296\pi\) | |||||||
\(620\) | 5.90241 | + | 17.4277i | 0.237047 | + | 0.699912i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 2.06751i | − | 0.0828997i | ||||||
\(623\) | 14.0350 | + | 2.36208i | 0.562301 | + | 0.0946347i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6285 | + | 17.7267i | 0.705142 | + | 0.709067i | ||||
\(626\) | 2.68967 | − | 4.65864i | 0.107501 | − | 0.186197i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.6366 | − | 9.60515i | 0.663873 | − | 0.383287i | ||||
\(629\) | 4.33394 | 0.172806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.16601 | 0.126037 | 0.0630184 | − | 0.998012i | \(-0.479927\pi\) | ||||
0.0630184 | + | 0.998012i | \(0.479927\pi\) | |||||||
\(632\) | 11.1573 | − | 6.44165i | 0.443812 | − | 0.256235i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.23987 | + | 9.07572i | −0.208102 | + | 0.360443i | ||||
\(635\) | −1.78601 | + | 8.94645i | −0.0708758 | + | 0.355029i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.0448 | + | 5.39723i | −1.11118 | + | 0.213846i | ||||
\(638\) | − | 7.77479i | − | 0.307807i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.3179 | − | 8.23599i | 0.961248 | − | 0.325556i | ||||
\(641\) | −11.0200 | + | 19.0872i | −0.435265 | + | 0.753900i | −0.997317 | − | 0.0732011i | \(-0.976679\pi\) |
0.562053 | + | 0.827102i | \(0.310012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.0979i | − | 1.54187i | −0.636913 | − | 0.770935i | \(-0.719789\pi\) | ||
0.636913 | − | 0.770935i | \(-0.280211\pi\) | |||||||
\(644\) | 20.5645 | + | 16.9842i | 0.810356 | + | 0.669273i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.948368 | − | 1.64262i | −0.0373130 | − | 0.0646281i | ||||
\(647\) | −21.1866 | − | 12.2321i | −0.832931 | − | 0.480893i | 0.0219243 | − | 0.999760i | \(-0.493021\pi\) |
−0.854855 | + | 0.518867i | \(0.826354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.4059 | + | 38.8081i | 0.879508 | + | 1.52335i | ||||
\(650\) | 1.56809 | + | 12.0399i | 0.0615056 | + | 0.472244i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.89061i | 0.113205i | ||||||||
\(653\) | 24.8271 | − | 14.3339i | 0.971558 | − | 0.560929i | 0.0718473 | − | 0.997416i | \(-0.477111\pi\) |
0.899711 | + | 0.436486i | \(0.143777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.60036 | + | 16.5358i | 0.218824 | + | 0.646108i | ||||
\(656\) | 11.2814 | + | 19.5399i | 0.440463 | + | 0.762905i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.19368 | − | 3.20172i | −0.0465344 | − | 0.124816i | ||||
\(659\) | −17.7061 | −0.689732 | −0.344866 | − | 0.938652i | \(-0.612076\pi\) | ||||
−0.344866 | + | 0.938652i | \(0.612076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.32288 | + | 16.1477i | −0.362618 | + | 0.628073i | −0.988391 | − | 0.151933i | \(-0.951450\pi\) |
0.625773 | + | 0.780005i | \(0.284784\pi\) | |||||||
\(662\) | 9.06312 | + | 5.23260i | 0.352248 | + | 0.203371i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.2915 | −0.981501 | ||||||||
\(665\) | −3.57031 | − | 1.35930i | −0.138451 | − | 0.0527116i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.8816 | − | 7.43719i | 0.498777 | − | 0.287969i | ||||
\(668\) | 18.0083 | + | 10.3971i | 0.696763 | + | 0.402277i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.03248 | − | 0.605385i | −0.117155 | − | 0.0233881i | ||||
\(671\) | −1.90562 | −0.0735657 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 12.2398i | − | 0.471808i | −0.971776 | − | 0.235904i | \(-0.924195\pi\) | ||
0.971776 | − | 0.235904i | \(-0.0758051\pi\) | |||||||
\(674\) | 3.64248 | + | 6.30896i | 0.140303 | + | 0.243012i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | − | 5.19615i | 0.115385 | − | 0.199852i | ||||
\(677\) | 26.2232 | − | 15.1399i | 1.00784 | − | 0.581875i | 0.0972799 | − | 0.995257i | \(-0.468986\pi\) |
0.910558 | + | 0.413382i | \(0.135652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.6974 | − | 11.3127i | −0.525657 | − | 0.434140i | ||||
\(680\) | 15.8005 | − | 17.9918i | 0.605921 | − | 0.689954i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.8638 | − | 8.00429i | −0.530874 | − | 0.306500i | ||||
\(683\) | 29.7990 | + | 17.2044i | 1.14023 | + | 0.658309i | 0.946486 | − | 0.322744i | \(-0.104605\pi\) |
0.193739 | + | 0.981053i | \(0.437939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.64575 | + | 5.83633i | 0.253921 | + | 0.222995i | ||||
\(686\) | −11.0200 | + | 0.257794i | −0.420746 | + | 0.00984264i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.6965 | + | 10.7945i | −0.712799 | + | 0.411535i | ||||
\(689\) | 16.1380 | − | 27.9518i | 0.614809 | − | 1.06488i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.14575 | − | 12.3768i | −0.271837 | − | 0.470836i | 0.697495 | − | 0.716590i | \(-0.254298\pi\) |
−0.969332 | + | 0.245754i | \(0.920965\pi\) | |||||||
\(692\) | 15.3255i | 0.582588i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.5425 | 0.438147 | ||||||||
\(695\) | −15.8512 | − | 3.16444i | −0.601271 | − | 0.120034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.2147 | + | 27.8368i | 1.82626 | + | 1.05439i | ||||
\(698\) | 13.3370 | − | 7.70010i | 0.504811 | − | 0.291453i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.810238 | − | 21.7562i | 0.0306241 | − | 0.822306i | ||||
\(701\) | −25.8513 | −0.976390 | −0.488195 | − | 0.872735i | \(-0.662344\pi\) | ||||
−0.488195 | + | 0.872735i | \(0.662344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.491125 | + | 0.283551i | 0.0185231 | + | 0.0106943i | ||||
\(704\) | 1.90562 | − | 3.30064i | 0.0718209 | − | 0.124397i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.937254 | −0.0352740 | ||||||||
\(707\) | −3.21060 | − | 8.61155i | −0.120747 | − | 0.323871i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.17712 | − | 5.50294i | −0.119319 | − | 0.206667i | 0.800179 | − | 0.599762i | \(-0.204738\pi\) |
−0.919498 | + | 0.393094i | \(0.871405\pi\) | |||||||
\(710\) | 3.06101 | − | 1.03671i | 0.114878 | − | 0.0389069i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.1088 | + | 5.83633i | −0.378844 | + | 0.218726i | ||||
\(713\) | − | 30.6269i | − | 1.14699i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.8745 | + | 32.3834i | 1.37903 | + | 1.21107i | ||||
\(716\) | 13.7097 | + | 23.7459i | 0.512355 | + | 0.887425i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.83940 | + | 5.68078i | 0.367203 | + | 0.212005i | ||||
\(719\) | 9.80586 | + | 16.9842i | 0.365697 | + | 0.633406i | 0.988888 | − | 0.148664i | \(-0.0474974\pi\) |
−0.623191 | + | 0.782070i | \(0.714164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19738 | + | 18.9982i | −0.119077 | + | 0.707531i | ||||
\(722\) | 11.0604i | 0.411625i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.4059 | + | 18.0235i | −0.386732 | + | 0.669839i | ||||
\(725\) | −11.2109 | − | 4.66195i | −0.416363 | − | 0.173140i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.5432i | 1.50366i | 0.659355 | + | 0.751832i | \(0.270830\pi\) | ||||
−0.659355 | + | 0.751832i | \(0.729170\pi\) | |||||||
\(728\) | 14.9156 | − | 18.0599i | 0.552811 | − | 0.669343i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.7958 | − | 2.35484i | −0.436582 | − | 0.0871566i | ||||
\(731\) | −26.6353 | + | 46.1337i | −0.985143 | + | 1.70632i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.07885 | + | 5.24168i | −0.335335 | + | 0.193606i | −0.658207 | − | 0.752837i | \(-0.728685\pi\) |
0.322872 | + | 0.946443i | \(0.395352\pi\) | |||||||
\(734\) | 11.0962 | 0.409568 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.8745 | −1.24863 | ||||||||
\(737\) | −10.8244 | + | 6.24947i | −0.398722 | + | 0.230202i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.96863 | − | 10.3380i | 0.219559 | − | 0.380288i | −0.735114 | − | 0.677944i | \(-0.762871\pi\) |
0.954673 | + | 0.297655i | \(0.0962047\pi\) | |||||||
\(740\) | −0.632693 | + | 3.16927i | −0.0232582 | + | 0.116505i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.93289 | − | 9.60515i | 0.291226 | − | 0.352616i | ||||
\(743\) | − | 10.6760i | − | 0.391666i | −0.980637 | − | 0.195833i | \(-0.937259\pi\) | ||
0.980637 | − | 0.195833i | \(-0.0627410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.11674 | + | 6.24995i | 0.0775513 | + | 0.228981i | ||||
\(746\) | 7.11619 | − | 12.3256i | 0.260542 | − | 0.451273i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 43.6898i | − | 1.59746i | ||||||
\(749\) | 2.25955 | − | 13.4258i | 0.0825623 | − | 0.490569i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.7288 | − | 23.7789i | −0.500969 | − | 0.867705i | −0.999999 | − | 0.00111978i | \(-0.999644\pi\) |
0.499030 | − | 0.866585i | \(-0.333690\pi\) | |||||||
\(752\) | −3.75839 | − | 2.16991i | −0.137054 | − | 0.0791284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.94837 | − | 5.10672i | −0.107373 | − | 0.185976i | ||||
\(755\) | −13.1870 | + | 15.0159i | −0.479924 | + | 0.546483i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.7992i | − | 1.48287i | −0.671023 | − | 0.741436i | \(-0.734145\pi\) | ||
0.671023 | − | 0.741436i | \(-0.265855\pi\) | |||||||
\(758\) | −1.18115 | + | 0.681937i | −0.0429013 | + | 0.0247691i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.96764 | − | 1.00508i | 0.107648 | − | 0.0364582i | ||||
\(761\) | −2.25955 | − | 3.91366i | −0.0819087 | − | 0.141870i | 0.822161 | − | 0.569255i | \(-0.192768\pi\) |
−0.904070 | + | 0.427385i | \(0.859435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.2268 | − | 32.7949i | −0.442638 | − | 1.18726i | ||||
\(764\) | −17.7061 | −0.640584 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.22876 | + | 7.32442i | −0.152791 | + | 0.264642i | ||||
\(767\) | 29.4338 | + | 16.9936i | 1.06279 | + | 0.613603i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6458 | 0.888749 | 0.444374 | − | 0.895841i | \(-0.353426\pi\) | ||||
0.444374 | + | 0.895841i | \(0.353426\pi\) | |||||||
\(770\) | 11.9606 | + | 14.6877i | 0.431031 | + | 0.529307i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8883 | + | 10.3278i | −0.643813 | + | 0.371706i | ||||
\(773\) | 16.5799 | + | 9.57241i | 0.596338 | + | 0.344296i | 0.767599 | − | 0.640930i | \(-0.221451\pi\) |
−0.171262 | + | 0.985226i | \(0.554784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.8549 | + | 15.1915i | −0.713210 | + | 0.545695i | ||||
\(776\) | 14.5699 | 0.523030 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 18.3872i | − | 0.659213i | ||||||
\(779\) | 3.64248 | + | 6.30896i | 0.130505 | + | 0.226042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.53137 | − | 11.3127i | 0.233711 | − | 0.404799i | ||||
\(782\) | −15.5813 | + | 8.99590i | −0.557188 | + | 0.321693i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.5830 | + | 9.16515i | −0.377964 | + | 0.327327i | ||||
\(785\) | 19.6117 | + | 17.2231i | 0.699972 | + | 0.614719i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6122 | − | 7.28164i | −0.449575 | − | 0.259562i | 0.258076 | − | 0.966125i | \(-0.416912\pi\) |
−0.707651 | + | 0.706562i | \(0.750245\pi\) | |||||||
\(788\) | −8.42976 | − | 4.86693i | −0.300298 | − | 0.173377i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.93725 | + | 5.21412i | 0.211238 | + | 0.185510i | ||||
\(791\) | −32.2760 | − | 26.6568i | −1.14760 | − | 0.947805i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.25167 | + | 0.722653i | −0.0444482 | + | 0.0256622i | ||||
\(794\) | −9.45193 | + | 16.3712i | −0.335436 | + | 0.580993i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.5203 | + | 25.1498i | 0.514657 | + | 0.891412i | ||||
\(797\) | − | 3.53378i | − | 0.125173i | −0.998040 | − | 0.0625865i | \(-0.980065\pi\) | ||
0.998040 | − | 0.0625865i | \(-0.0199349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7085 | −0.378839 | ||||||||
\(800\) | 16.8024 | + | 21.9603i | 0.594054 | + | 0.776414i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.2176 | + | 11.6727i | 0.713910 | + | 0.412176i | ||||
\(803\) | −42.1050 | + | 24.3093i | −1.48585 | + | 0.857858i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.8939 | + | 33.8667i | −0.454450 | + | 1.19365i | ||||
\(806\) | −12.1416 | −0.427670 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.52778 | + | 3.76882i | 0.229647 | + | 0.132587i | ||||
\(809\) | 22.4702 | − | 38.9194i | 0.790009 | − | 1.36833i | −0.135952 | − | 0.990715i | \(-0.543409\pi\) |
0.925961 | − | 0.377620i | \(-0.123257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.2288 | 1.41262 | 0.706311 | − | 0.707901i | \(-0.250358\pi\) | ||||
0.706311 | + | 0.707901i | \(0.250358\pi\) | |||||||
\(812\) | 3.69370 | + | 9.90735i | 0.129624 | + | 0.347680i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.40588 | − | 2.43506i | −0.0492761 | − | 0.0853487i | ||||
\(815\) | −3.71990 | + | 1.25986i | −0.130302 | + | 0.0441309i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.03666 | + | 3.48527i | −0.211196 | + | 0.121934i | ||||
\(818\) | 15.2267i | 0.532389i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.3948 | + | 31.1941i | −0.956667 | + | 1.08934i | ||||
\(821\) | 8.59170 | + | 14.8813i | 0.299852 | + | 0.519360i | 0.976102 | − | 0.217313i | \(-0.0697292\pi\) |
−0.676250 | + | 0.736673i | \(0.736396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.6870 | − | 24.0680i | −1.45312 | − | 0.838957i | −0.454459 | − | 0.890768i | \(-0.650167\pi\) |
−0.998657 | + | 0.0518109i | \(0.983501\pi\) | |||||||
\(824\) | −7.90024 | − | 13.6836i | −0.275218 | − | 0.476691i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.1144 | + | 8.35347i | 0.351924 | + | 0.290654i | ||||
\(827\) | − | 31.0112i | − | 1.07837i | −0.842189 | − | 0.539183i | \(-0.818733\pi\) | ||
0.842189 | − | 0.539183i | \(-0.181267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.5516 | − | 26.9362i | 0.540131 | − | 0.935533i | −0.458766 | − | 0.888557i | \(-0.651708\pi\) |
0.998896 | − | 0.0469761i | \(-0.0149585\pi\) | |||||||
\(830\) | −4.97603 | − | 14.6924i | −0.172721 | − | 0.509981i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.89061i | − | 0.100214i | ||||||
\(833\) | −11.3075 | + | 32.6420i | −0.391782 | + | 1.13098i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.53110 | + | 27.7062i | −0.191412 | + | 0.958814i | ||||
\(836\) | 2.85843 | − | 4.95095i | 0.0988610 | − | 0.171232i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.12657 | + | 5.26923i | −0.315272 | + | 0.182022i | ||||
\(839\) | −42.6972 | −1.47407 | −0.737035 | − | 0.675855i | \(-0.763775\pi\) | ||||
−0.737035 | + | 0.675855i | \(0.763775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1033 | −0.796664 | ||||||||
\(842\) | 4.75694 | − | 2.74642i | 0.163935 | − | 0.0946480i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.2915 | − | 21.2895i | 0.423091 | − | 0.732815i | ||||
\(845\) | 7.99440 | + | 1.59595i | 0.275016 | + | 0.0549024i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.7994 | + | 7.87629i | 1.60804 | + | 0.270633i | ||||
\(848\) | − | 15.8219i | − | 0.543326i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.5605 | + | 5.63902i | 0.465122 | + | 0.193417i | ||||
\(851\) | 2.68967 | − | 4.65864i | 0.0922006 | − | 0.159696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.63461i | 0.0902075i | 0.998982 | + | 0.0451037i | \(0.0143618\pi\) | ||||
−0.998982 | + | 0.0451037i | \(0.985638\pi\) | |||||||
\(854\) | −0.522697 | + | 0.194874i | −0.0178863 | + | 0.00666846i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.58301 | + | 9.67005i | 0.190823 | + | 0.330515i | ||||
\(857\) | −41.4393 | − | 23.9250i | −1.41554 | − | 0.817262i | −0.419637 | − | 0.907692i | \(-0.637843\pi\) |
−0.995903 | + | 0.0904296i | \(0.971176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.53137 | + | 14.7768i | 0.291087 | + | 0.504177i | 0.974067 | − | 0.226260i | \(-0.0726499\pi\) |
−0.682980 | + | 0.730437i | \(0.739317\pi\) | |||||||
\(860\) | −29.8477 | − | 26.2124i | −1.01780 | − | 0.893835i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.2949i | 0.418765i | ||||||||
\(863\) | −38.1317 | + | 22.0153i | −1.29802 | + | 0.749411i | −0.980061 | − | 0.198695i | \(-0.936330\pi\) |
−0.317956 | + | 0.948105i | \(0.602997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7222 | + | 6.67953i | −0.670575 | + | 0.227111i | ||||
\(866\) | −10.0672 | − | 17.4369i | −0.342098 | − | 0.592531i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.4693 | + | 3.61327i | 0.728716 | + | 0.122642i | ||||
\(869\) | 31.9385 | 1.08344 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.73987 | + | 8.20970i | −0.160604 | + | 0.278175i | ||||
\(872\) | 24.8594 | + | 14.3526i | 0.841846 | + | 0.486040i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.35425 | −0.0796336 | ||||||||
\(875\) | 28.3509 | − | 8.43961i | 0.958435 | − | 0.285311i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.2843 | − | 15.7526i | 0.921324 | − | 0.531927i | 0.0372670 | − | 0.999305i | \(-0.488135\pi\) |
0.884057 | + | 0.467379i | \(0.154801\pi\) | |||||||
\(878\) | −15.5813 | − | 8.99590i | −0.525845 | − | 0.303597i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.5916 | + | 4.70968i | 0.795273 | + | 0.158763i | ||||
\(881\) | 45.9857 | 1.54930 | 0.774649 | − | 0.632392i | \(-0.217927\pi\) | ||||
0.774649 | + | 0.632392i | \(0.217927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.8449i | − | 0.735140i | −0.929996 | − | 0.367570i | \(-0.880190\pi\) | ||
0.929996 | − | 0.367570i | \(-0.119810\pi\) | |||||||
\(884\) | −16.5681 | − | 28.6968i | −0.557246 | − | 0.965179i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.00000 | + | 8.66025i | −0.167978 | + | 0.290947i | ||||
\(887\) | 0.0323423 | − | 0.0186729i | 0.00108595 | − | 0.000626973i | −0.499457 | − | 0.866339i | \(-0.666467\pi\) |
0.500543 | + | 0.865712i | \(0.333134\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.32288 | + | 6.87386i | 0.279140 | + | 0.230542i | ||||
\(890\) | −5.37934 | − | 4.72416i | −0.180316 | − | 0.158354i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.21349 | − | 0.700610i | −0.0406080 | − | 0.0234450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.5830 | + | 27.9923i | −0.821719 | + | 0.935681i | ||||
\(896\) | 5.04180 | − | 29.9574i | 0.168435 | − | 1.00081i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.6299 | + | 6.71453i | −0.388095 | + | 0.224067i | ||||
\(899\) | 6.07080 | − | 10.5149i | 0.202472 | − | 0.350693i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.5203 | − | 33.8101i | −0.650314 | − | 1.12638i | ||||
\(902\) | − | 36.1197i | − | 1.20266i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34.3320 | 1.14187 | ||||||||
\(905\) | −27.7296 | − | 5.53576i | −0.921763 | − | 0.184015i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.760548 | − | 0.439102i | −0.0252536 | − | 0.0145802i | 0.487320 | − | 0.873223i | \(-0.337975\pi\) |
−0.512574 | + | 0.858643i | \(0.671308\pi\) | |||||||
\(908\) | −5.03657 | + | 2.90786i | −0.167144 | + | 0.0965008i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.4260 | + | 5.11160i | 0.445067 | + | 0.169448i | ||||
\(911\) | −1.56809 | −0.0519532 | −0.0259766 | − | 0.999663i | \(-0.508270\pi\) | ||||
−0.0259766 | + | 0.999663i | \(0.508270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.2991 | − | 31.3496i | −1.79704 | − | 1.03752i | ||||
\(914\) | 9.54451 | − | 16.5316i | 0.315704 | − | 0.546816i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.77124 | 0.124605 | ||||||||
\(917\) | 20.3706 | + | 3.42836i | 0.672698 | + | 0.113214i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.43725 | − | 7.68555i | −0.146372 | − | 0.253523i | 0.783512 | − | 0.621376i | \(-0.213426\pi\) |
−0.929884 | + | 0.367853i | \(0.880093\pi\) | |||||||
\(920\) | −9.53388 | − | 28.1501i | −0.314323 | − | 0.928080i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.31830 | − | 4.80257i | 0.273949 | − | 0.158164i | ||||
\(923\) | − | 9.90735i | − | 0.326104i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.35425 | + | 0.567102i | −0.143167 | + | 0.0186462i | ||||
\(926\) | 5.21057 | + | 9.02497i | 0.171230 | + | 0.296579i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.6299 | − | 6.71453i | −0.381771 | − | 0.220415i | ||||
\(929\) | −6.68608 | − | 11.5806i | −0.219363 | − | 0.379948i | 0.735250 | − | 0.677796i | \(-0.237065\pi\) |
−0.954613 | + | 0.297848i | \(0.903731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.41699 | + | 2.95920i | −0.111987 | + | 0.0969840i | ||||
\(932\) | 12.6724i | 0.415100i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.2288 | − | 21.1808i | 0.400137 | − | 0.693058i | ||||
\(935\) | 56.2239 | − | 19.0420i | 1.83872 | − | 0.622739i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.255999i | 0.00836312i | 0.999991 | + | 0.00418156i | \(0.00133104\pi\) | ||||
−0.999991 | + | 0.00418156i | \(0.998669\pi\) | |||||||
\(938\) | −2.32996 | + | 2.82111i | −0.0760758 | + | 0.0921126i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.56329 | − | 7.83077i | 0.0509887 | − | 0.255411i | ||||
\(941\) | 15.9692 | − | 27.6595i | 0.520582 | − | 0.901675i | −0.479131 | − | 0.877743i | \(-0.659048\pi\) |
0.999714 | − | 0.0239319i | \(-0.00761847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.8447 | − | 34.5513i | 1.94881 | − | 1.12515i | ||||
\(944\) | 16.6607 | 0.542260 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.5608 | 1.12367 | ||||||||
\(947\) | −25.3102 | + | 14.6128i | −0.822470 | + | 0.474853i | −0.851268 | − | 0.524732i | \(-0.824166\pi\) |
0.0287974 | + | 0.999585i | \(0.490832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.4373 | + | 31.9343i | −0.598499 | + | 1.03663i | ||||
\(950\) | 1.16775 | + | 1.52622i | 0.0378868 | + | 0.0495172i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.89739 | − | 26.5470i | −0.320776 | − | 0.860394i | ||||
\(953\) | − | 57.6827i | − | 1.86852i | −0.356587 | − | 0.934262i | \(-0.616060\pi\) | ||
0.356587 | − | 0.934262i | \(-0.383940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.71710 | − | 22.7858i | −0.249720 | − | 0.737330i | ||||
\(956\) | −7.28496 | + | 12.6179i | −0.235612 | + | 0.408093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.53764i | 0.243530i | ||||||||
\(959\) | 9.80586 | − | 3.65587i | 0.316648 | − | 0.118054i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | −1.84685 | − | 1.06628i | −0.0595449 | − | 0.0343783i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.2288 | − | 40.2334i | −0.748148 | − | 1.29583i | ||||
\(965\) | −21.0872 | − | 18.5189i | −0.678822 | − | 0.596145i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2235i | 0.778976i | 0.921032 | + | 0.389488i | \(0.127348\pi\) | ||||
−0.921032 | + | 0.389488i | \(0.872652\pi\) | |||||||
\(968\) | −33.7076 | + | 19.4611i | −1.08340 | + | 0.625503i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.86659 | + | 8.46399i | 0.0920406 | + | 0.271762i | ||||
\(971\) | −11.1888 | − | 19.3795i | −0.359065 | − | 0.621919i | 0.628740 | − | 0.777616i | \(-0.283571\pi\) |
−0.987805 | + | 0.155697i | \(0.950238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.1790 | + | 14.7464i | −0.390442 | + | 0.472747i | ||||
\(974\) | 14.2324 | 0.456035 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.354249 | + | 0.613577i | −0.0113392 | + | 0.0196401i | ||||
\(977\) | −50.1696 | − | 28.9654i | −1.60507 | − | 0.926686i | −0.990452 | − | 0.137859i | \(-0.955978\pi\) |
−0.614615 | − | 0.788827i | \(-0.710689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.9373 | −0.924839 | ||||||||
\(980\) | −22.2193 | − | 13.0341i | −0.709768 | − | 0.416358i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.6965 | + | 10.7945i | −0.596631 | + | 0.344465i | ||||
\(983\) | 5.85252 | + | 3.37896i | 0.186667 | + | 0.107772i | 0.590421 | − | 0.807095i | \(-0.298962\pi\) |
−0.403755 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.58913 | − | 12.9694i | 0.0824965 | − | 0.413239i | ||||
\(986\) | −7.13259 | −0.227148 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 4.33592i | − | 0.137944i | ||||||
\(989\) | 33.0601 | + | 57.2617i | 1.05125 | + | 1.82082i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.19738 | − | 14.1983i | 0.260398 | − | 0.451023i | −0.705949 | − | 0.708262i | \(-0.749479\pi\) |
0.966348 | + | 0.257239i | \(0.0828127\pi\) | |||||||
\(992\) | −23.9464 | + | 13.8255i | −0.760300 | + | 0.438959i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.634637 | − | 3.77089i | 0.0201295 | − | 0.119605i | ||||
\(995\) | −26.0365 | + | 29.6474i | −0.825411 | + | 0.939885i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5060 | + | 15.8806i | 0.871123 | + | 0.502943i | 0.867721 | − | 0.497051i | \(-0.165584\pi\) |
0.00340163 | + | 0.999994i | \(0.498917\pi\) | |||||||
\(998\) | 2.57724 | + | 1.48797i | 0.0815811 | + | 0.0471009i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.bf.c.109.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 315.2.bf.c.109.6 | yes | 16 | |
5.4 | even | 2 | inner | 315.2.bf.c.109.5 | yes | 16 | |
7.2 | even | 3 | inner | 315.2.bf.c.289.5 | yes | 16 | |
7.3 | odd | 6 | 2205.2.d.r.1324.3 | 8 | |||
7.4 | even | 3 | 2205.2.d.p.1324.4 | 8 | |||
15.14 | odd | 2 | inner | 315.2.bf.c.109.4 | yes | 16 | |
21.2 | odd | 6 | inner | 315.2.bf.c.289.4 | yes | 16 | |
21.11 | odd | 6 | 2205.2.d.p.1324.5 | 8 | |||
21.17 | even | 6 | 2205.2.d.r.1324.6 | 8 | |||
35.4 | even | 6 | 2205.2.d.p.1324.6 | 8 | |||
35.9 | even | 6 | inner | 315.2.bf.c.289.3 | yes | 16 | |
35.24 | odd | 6 | 2205.2.d.r.1324.5 | 8 | |||
105.44 | odd | 6 | inner | 315.2.bf.c.289.6 | yes | 16 | |
105.59 | even | 6 | 2205.2.d.r.1324.4 | 8 | |||
105.74 | odd | 6 | 2205.2.d.p.1324.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bf.c.109.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
315.2.bf.c.109.4 | yes | 16 | 15.14 | odd | 2 | inner | |
315.2.bf.c.109.5 | yes | 16 | 5.4 | even | 2 | inner | |
315.2.bf.c.109.6 | yes | 16 | 3.2 | odd | 2 | inner | |
315.2.bf.c.289.3 | yes | 16 | 35.9 | even | 6 | inner | |
315.2.bf.c.289.4 | yes | 16 | 21.2 | odd | 6 | inner | |
315.2.bf.c.289.5 | yes | 16 | 7.2 | even | 3 | inner | |
315.2.bf.c.289.6 | yes | 16 | 105.44 | odd | 6 | inner | |
2205.2.d.p.1324.3 | 8 | 105.74 | odd | 6 | |||
2205.2.d.p.1324.4 | 8 | 7.4 | even | 3 | |||
2205.2.d.p.1324.5 | 8 | 21.11 | odd | 6 | |||
2205.2.d.p.1324.6 | 8 | 35.4 | even | 6 | |||
2205.2.d.r.1324.3 | 8 | 7.3 | odd | 6 | |||
2205.2.d.r.1324.4 | 8 | 105.59 | even | 6 | |||
2205.2.d.r.1324.5 | 8 | 35.24 | odd | 6 | |||
2205.2.d.r.1324.6 | 8 | 21.17 | even | 6 |