Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(81,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.951588245534976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 81.3 | ||
Root | \(-0.390636 - 1.35919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.81 |
Dual form | 224.2.t.a.177.3 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −0.591141 | − | 0.341295i | −0.341295 | − | 0.197047i | 0.319549 | − | 0.947570i | \(-0.396468\pi\) |
−0.660845 | + | 0.750523i | \(0.729802\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.80486 | + | 1.61939i | −1.25437 | + | 0.724212i | −0.971975 | − | 0.235086i | \(-0.924463\pi\) |
−0.282397 | + | 0.959298i | \(0.591130\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.47779 | − | 2.19457i | −0.558552 | − | 0.829469i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.26704 | − | 2.19457i | −0.422345 | − | 0.731523i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.08913 | − | 1.20616i | −0.629897 | − | 0.363671i | 0.150815 | − | 0.988562i | \(-0.451810\pi\) |
−0.780712 | + | 0.624891i | \(0.785144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.09491i | − | 0.858375i | −0.903216 | − | 0.429187i | \(-0.858800\pi\) | ||
0.903216 | − | 0.429187i | \(-0.141200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21076 | 0.570815 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.97779 | + | 3.42563i | −0.479685 | + | 0.830838i | −0.999728 | − | 0.0233012i | \(-0.992582\pi\) |
0.520044 | + | 0.854140i | \(0.325916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.33831 | + | 1.35002i | −0.536444 | + | 0.309716i | −0.743637 | − | 0.668584i | \(-0.766901\pi\) |
0.207192 | + | 0.978300i | \(0.433567\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.124586 | + | 1.80166i | 0.0271870 | + | 0.393155i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.37241 | + | 2.37709i | 0.286168 | + | 0.495657i | 0.972892 | − | 0.231261i | \(-0.0742852\pi\) |
−0.686724 | + | 0.726918i | \(0.740952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.74483 | − | 4.75418i | 0.548965 | − | 0.950836i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.77750i | 0.726981i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.01745i | − | 0.374631i | −0.982300 | − | 0.187316i | \(-0.940021\pi\) | ||
0.982300 | − | 0.187316i | \(-0.0599787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.10538 | + | 1.91457i | −0.198532 | + | 0.343867i | −0.948053 | − | 0.318114i | \(-0.896951\pi\) |
0.749521 | + | 0.661981i | \(0.230284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.823314 | + | 1.42602i | 0.143321 | + | 0.248239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.69885 | + | 3.76234i | 1.30134 | + | 0.635952i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.30285 | − | 2.48425i | 0.707385 | − | 0.408409i | −0.102707 | − | 0.994712i | \(-0.532751\pi\) |
0.810092 | + | 0.586303i | \(0.199417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.05628 | + | 1.82953i | −0.169140 | + | 0.292959i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.11256 | −0.329926 | −0.164963 | − | 0.986300i | \(-0.552751\pi\) | ||||
−0.164963 | + | 0.986300i | \(0.552751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.5899i | − | 1.76745i | −0.468011 | − | 0.883723i | \(-0.655029\pi\) | ||
0.468011 | − | 0.883723i | \(-0.344971\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.10771 | + | 4.10364i | 1.05956 | + | 0.611734i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.31613 | − | 5.74371i | −0.483708 | − | 0.837807i | 0.516117 | − | 0.856518i | \(-0.327377\pi\) |
−0.999825 | + | 0.0187115i | \(0.994044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.63227 | + | 6.48623i | −0.376038 | + | 0.926604i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.33831 | − | 1.35002i | 0.327428 | − | 0.189041i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.23998 | + | 1.29325i | 0.307684 | + | 0.177642i | 0.645890 | − | 0.763431i | \(-0.276487\pi\) |
−0.338205 | + | 0.941072i | \(0.609820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.81297 | 1.05350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.84302 | 0.244114 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6283 | + | 6.13625i | 1.38369 | + | 0.798872i | 0.992594 | − | 0.121479i | \(-0.0387638\pi\) |
0.391093 | + | 0.920351i | \(0.372097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.54801 | + | 4.35784i | −0.966424 | + | 0.557965i | −0.898144 | − | 0.439701i | \(-0.855084\pi\) |
−0.0682795 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.94372 | + | 6.02371i | −0.370874 | + | 0.758916i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.01186 | + | 8.68080i | 0.621645 | + | 1.07672i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.01858 | − | 2.89748i | −0.613117 | − | 0.353983i | 0.161067 | − | 0.986943i | \(-0.448506\pi\) |
−0.774184 | + | 0.632960i | \(0.781840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.87359i | − | 0.225554i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.64663 | −0.788810 | −0.394405 | − | 0.918937i | \(-0.629049\pi\) | ||||
−0.394405 | + | 0.918937i | \(0.629049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.77890 | − | 8.27729i | 0.559328 | − | 0.968784i | −0.438225 | − | 0.898865i | \(-0.644393\pi\) |
0.997553 | − | 0.0699184i | \(-0.0222739\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.24516 | + | 1.87359i | −0.374718 | + | 0.216344i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.440297 | + | 6.36720i | 0.0501765 | + | 0.725610i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.838343 | + | 1.45205i | 0.0943209 | + | 0.163369i | 0.909325 | − | 0.416087i | \(-0.136599\pi\) |
−0.815004 | + | 0.579455i | \(0.803265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.51186 | + | 4.35067i | −0.279096 | + | 0.483408i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.47755i | − | 0.711003i | −0.934676 | − | 0.355502i | \(-0.884310\pi\) | ||
0.934676 | − | 0.355502i | \(-0.115690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 12.8112i | − | 1.38957i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.688547 | + | 1.19260i | −0.0738200 | + | 0.127860i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.98965 | − | 12.1064i | −0.740902 | − | 1.28328i | −0.952085 | − | 0.305833i | \(-0.901065\pi\) |
0.211184 | − | 0.977446i | \(-0.432268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.79200 | + | 4.57363i | −0.711995 | + | 0.479447i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.30687 | − | 0.754520i | 0.135516 | − | 0.0782401i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.37241 | − | 7.57324i | 0.448600 | − | 0.776998i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.37709 | −0.139823 | −0.0699113 | − | 0.997553i | \(-0.522272\pi\) | ||||
−0.0699113 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.11300i | 0.614379i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.689470 | + | 0.398066i | 0.0686048 | + | 0.0396090i | 0.533910 | − | 0.845541i | \(-0.320722\pi\) |
−0.465305 | + | 0.885150i | \(0.654055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.32799 | − | 2.30015i | −0.130851 | − | 0.226641i | 0.793154 | − | 0.609022i | \(-0.208438\pi\) |
−0.924005 | + | 0.382381i | \(0.875104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.26704 | − | 4.85166i | −0.318830 | − | 0.473473i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.70287 | + | 2.71520i | −0.454643 | + | 0.262489i | −0.709789 | − | 0.704414i | \(-0.751210\pi\) |
0.255146 | + | 0.966903i | \(0.417877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9614 | − | 6.90593i | −1.14570 | − | 0.661468i | −0.197862 | − | 0.980230i | \(-0.563400\pi\) |
−0.947835 | + | 0.318762i | \(0.896733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.39145 | −0.321903 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.53407 | 0.426529 | 0.213265 | − | 0.976994i | \(-0.431590\pi\) | ||||
0.213265 | + | 0.976994i | \(0.431590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.69885 | − | 4.44493i | −0.717922 | − | 0.414492i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.79200 | + | 3.92136i | −0.627921 | + | 0.362530i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.4406 | − | 0.721973i | 0.957084 | − | 0.0661831i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.59035 | − | 4.48662i | −0.235486 | − | 0.407874i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.24882 | + | 0.721006i | 0.112602 | + | 0.0650109i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.58587i | 0.141845i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4897 | 1.37448 | 0.687242 | − | 0.726428i | \(-0.258821\pi\) | ||||
0.687242 | + | 0.726428i | \(0.258821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.95558 | + | 6.85127i | −0.348270 | + | 0.603221i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5574 | + | 8.40471i | −1.27189 | + | 0.734323i | −0.975343 | − | 0.220696i | \(-0.929167\pi\) |
−0.296543 | + | 0.955020i | \(0.595834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.41824 | + | 3.13652i | 0.556532 | + | 0.271971i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.11724 | − | 10.5954i | −0.526488 | − | 0.911904i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.443721 | − | 0.768547i | 0.0379096 | − | 0.0656614i | −0.846448 | − | 0.532471i | \(-0.821263\pi\) |
0.884358 | + | 0.466810i | \(0.154597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.44264i | − | 0.207182i | −0.994620 | − | 0.103591i | \(-0.966967\pi\) | ||
0.994620 | − | 0.103591i | \(-0.0330333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.52712i | 0.381253i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.73296 | + | 6.46568i | −0.312166 | + | 0.540688i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.26704 | + | 5.65867i | 0.271312 | + | 0.469927i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.76976 | − | 2.93589i | 0.310925 | − | 0.242148i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.16541 | + | 4.71430i | −0.668936 | + | 0.386210i | −0.795673 | − | 0.605726i | \(-0.792883\pi\) |
0.126737 | + | 0.991936i | \(0.459549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.52689 | + | 6.10875i | −0.287014 | + | 0.497123i | −0.973096 | − | 0.230402i | \(-0.925996\pi\) |
0.686081 | + | 0.727525i | \(0.259329\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.0237 | 0.810370 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.16014i | − | 0.575116i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.54801 | − | 4.35784i | −0.602397 | − | 0.347794i | 0.167587 | − | 0.985857i | \(-0.446402\pi\) |
−0.769984 | + | 0.638063i | \(0.779736\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.882761 | − | 1.52899i | −0.0700075 | − | 0.121257i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.18855 | − | 6.52470i | 0.251293 | − | 0.514218i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1711 | − | 9.91376i | 1.34495 | − | 0.776505i | 0.357418 | − | 0.933945i | \(-0.383657\pi\) |
0.987529 | + | 0.157439i | \(0.0503239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.61856 | − | 2.66653i | −0.359555 | − | 0.207589i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.1600 | −1.71479 | −0.857396 | − | 0.514657i | \(-0.827919\pi\) | ||||
−0.857396 | + | 0.514657i | \(0.827919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.42151 | 0.263193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.92543 | + | 3.42105i | 0.453129 | + | 0.261614i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.8200 | − | 10.8657i | 1.43086 | − | 0.826105i | 0.433669 | − | 0.901072i | \(-0.357219\pi\) |
0.997186 | + | 0.0749674i | \(0.0238853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.4897 | + | 1.00197i | −1.09531 | + | 0.0757419i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.18855 | − | 7.25478i | −0.314830 | − | 0.545302i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.27141 | + | 1.88875i | 0.244517 | + | 0.141172i | 0.617251 | − | 0.786766i | \(-0.288246\pi\) |
−0.372734 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0326i | 1.04303i | 0.853242 | + | 0.521516i | \(0.174633\pi\) | ||||
−0.853242 | + | 0.521516i | \(0.825367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.94925 | 0.439781 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.04593 | + | 13.9360i | −0.591549 | + | 1.02459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.26374 | − | 4.77107i | 0.604304 | − | 0.348895i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.28999 | − | 5.58236i | 0.603008 | − | 0.406057i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.63945 | + | 6.30371i | 0.263341 | + | 0.456120i | 0.967128 | − | 0.254291i | \(-0.0818422\pi\) |
−0.703786 | + | 0.710412i | \(0.748509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.76704 | + | 8.25675i | −0.343139 | + | 0.594334i | −0.985014 | − | 0.172476i | \(-0.944823\pi\) |
0.641875 | + | 0.766809i | \(0.278157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.84210i | − | 0.489973i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6667i | 0.831221i | 0.909543 | + | 0.415611i | \(0.136432\pi\) | ||||
−0.909543 | + | 0.415611i | \(0.863568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.48247 | − | 16.4241i | 0.672195 | − | 1.16428i | −0.305086 | − | 0.952325i | \(-0.598685\pi\) |
0.977280 | − | 0.211950i | \(-0.0679815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.97779 | + | 3.42563i | 0.139503 | + | 0.241626i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.42744 | + | 2.98137i | −0.310745 | + | 0.209251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.92543 | − | 3.42105i | 0.413850 | − | 0.238936i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.47779 | − | 6.02371i | 0.241723 | − | 0.418677i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.51337 | 0.450540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1268i | 1.11022i | 0.831778 | + | 0.555109i | \(0.187323\pi\) | ||||
−0.831778 | + | 0.555109i | \(0.812677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.92909 | + | 2.26846i | 0.269217 | + | 0.155433i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.7685 | + | 32.5081i | 1.28000 | + | 2.21703i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.83518 | − | 0.403507i | 0.396118 | − | 0.0273918i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.65000 | + | 3.26203i | −0.381792 | + | 0.220428i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6020 | + | 6.12109i | 0.713170 | + | 0.411749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.71477 | 0.516619 | 0.258310 | − | 0.966062i | \(-0.416835\pi\) | ||||
0.258310 | + | 0.966062i | \(0.416835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.9112 | −0.927411 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.83996 | + | 1.06230i | 0.122122 | + | 0.0705074i | 0.559817 | − | 0.828616i | \(-0.310871\pi\) |
−0.437694 | + | 0.899124i | \(0.644205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.11289 | − | 4.68398i | 0.536115 | − | 0.309526i | −0.207388 | − | 0.978259i | \(-0.566496\pi\) |
0.743503 | + | 0.668733i | \(0.233163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.91282 | − | 3.91418i | 0.125854 | − | 0.257534i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.41366 | + | 7.64469i | 0.289149 | + | 0.500820i | 0.973607 | − | 0.228232i | \(-0.0732945\pi\) |
−0.684458 | + | 0.729052i | \(0.739961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.6026 | + | 10.7402i | 1.21350 | + | 0.700614i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.14449i | − | 0.0743426i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.93489 | −0.383896 | −0.191948 | − | 0.981405i | \(-0.561480\pi\) | ||||
−0.191948 | + | 0.981405i | \(0.561480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.34302 | − | 9.25439i | 0.344174 | − | 0.596128i | −0.641029 | − | 0.767517i | \(-0.721492\pi\) |
0.985203 | + | 0.171389i | \(0.0548255\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7840 | − | 7.38083i | 0.820092 | − | 0.473480i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.12057 | − | 22.4556i | −0.199366 | − | 1.43464i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.17820 | + | 7.23685i | 0.265852 | + | 0.460470i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.21076 | + | 3.82914i | −0.140101 | + | 0.242662i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.82402i | − | 0.241370i | −0.992691 | − | 0.120685i | \(-0.961491\pi\) | ||
0.992691 | − | 0.120685i | \(-0.0385091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.62141i | − | 0.416284i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.37241 | + | 7.57324i | −0.273811 | + | 0.474255i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.20291 | − | 10.7438i | −0.386927 | − | 0.670177i | 0.605108 | − | 0.796144i | \(-0.293130\pi\) |
−0.992034 | + | 0.125967i | \(0.959797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.8106 | − | 5.77170i | −0.733874 | − | 0.358636i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.42744 | + | 2.55618i | −0.274052 | + | 0.158224i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.672005 | + | 1.16395i | −0.0414376 | + | 0.0717720i | −0.886000 | − | 0.463685i | \(-0.846527\pi\) |
0.844563 | + | 0.535457i | \(0.179860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.37709 | −0.514601 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.54214i | 0.583970i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.68912 | − | 0.975212i | −0.102987 | − | 0.0594597i | 0.447622 | − | 0.894223i | \(-0.352271\pi\) |
−0.550609 | + | 0.834763i | \(0.685604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0190 | − | 22.5496i | −0.790850 | − | 1.36979i | −0.925441 | − | 0.378892i | \(-0.876305\pi\) |
0.134590 | − | 0.990901i | \(-0.457028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.57599 | − | 0.385584i | 0.337474 | − | 0.0233366i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.4686 | + | 6.62141i | −0.691583 | + | 0.399286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9578 | + | 8.05852i | 0.838641 | + | 0.484189i | 0.856802 | − | 0.515646i | \(-0.172448\pi\) |
−0.0181613 | + | 0.999835i | \(0.505781\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.60221 | 0.335396 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1313 | −0.962312 | −0.481156 | − | 0.876635i | \(-0.659783\pi\) | ||||
−0.481156 | + | 0.876635i | \(0.659783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.7949 | − | 13.1606i | −1.35501 | − | 0.782318i | −0.366068 | − | 0.930588i | \(-0.619296\pi\) |
−0.988947 | + | 0.148270i | \(0.952629\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.16942 | + | 2.98457i | −0.306210 | + | 0.176791i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.12192 | + | 4.63616i | 0.184281 | + | 0.273664i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.676686 | + | 1.17205i | 0.0398050 | + | 0.0689444i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.814056 | + | 0.469996i | 0.0477208 | + | 0.0275516i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.64929i | − | 0.563718i | −0.959456 | − | 0.281859i | \(-0.909049\pi\) | ||
0.959456 | − | 0.281859i | \(-0.0909510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.7479 | −2.31421 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.55628 | − | 7.89171i | 0.264382 | − | 0.457923i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.35688 | − | 4.24750i | 0.425460 | − | 0.245639i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.4349 | + | 17.1275i | −1.46604 | + | 0.987211i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.271716 | − | 0.470626i | −0.0156097 | − | 0.0270367i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.1141 | − | 24.4463i | 0.808169 | − | 1.39979i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2741i | 1.44247i | 0.692691 | + | 0.721235i | \(0.256425\pi\) | ||||
−0.692691 | + | 0.721235i | \(0.743575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.81295i | 0.103135i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2742 | − | 19.5275i | 0.639302 | − | 1.10730i | −0.346284 | − | 0.938130i | \(-0.612557\pi\) |
0.985586 | − | 0.169174i | \(-0.0541100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6901 | + | 21.9798i | 0.717285 | + | 1.24237i | 0.962072 | + | 0.272797i | \(0.0879486\pi\) |
−0.244787 | + | 0.969577i | \(0.578718\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.49799 | − | 21.6627i | −0.0844023 | − | 1.22055i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.8384 | + | 8.56693i | −0.833405 | + | 0.481167i | −0.855017 | − | 0.518600i | \(-0.826453\pi\) |
0.0216120 | + | 0.999766i | \(0.493120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43337 | + | 4.21473i | −0.136243 | + | 0.235979i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.70674 | 0.206890 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.6802i | − | 0.594264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7138 | − | 8.49500i | −0.816173 | − | 0.471218i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.71392 | + | 8.16475i | 0.260681 | + | 0.451512i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.70442 | + | 15.7655i | −0.424758 | + | 0.869180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.43566 | + | 4.29298i | −0.408701 | + | 0.235963i | −0.690231 | − | 0.723589i | \(-0.742491\pi\) |
0.281531 | + | 0.959552i | \(0.409158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.9037 | − | 6.29527i | −0.597521 | − | 0.344979i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.7685 | 1.02544 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.18070 | −0.173264 | −0.0866319 | − | 0.996240i | \(-0.527610\pi\) | ||||
−0.0866319 | + | 0.996240i | \(0.527610\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.68027 | − | 1.54746i | −0.145572 | − | 0.0840463i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.61856 | − | 2.66653i | 0.250109 | − | 0.144401i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1244 | − | 3.80860i | 0.978627 | − | 0.205645i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.03407 | + | 5.25516i | 0.163349 | + | 0.282929i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.0373 | − | 10.9912i | −1.02198 | − | 0.590039i | −0.107302 | − | 0.994226i | \(-0.534221\pi\) |
−0.914676 | + | 0.404187i | \(0.867554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5480i | 0.832265i | 0.909304 | + | 0.416132i | \(0.136615\pi\) | ||||
−0.909304 | + | 0.416132i | \(0.863385\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.6910 | 0.624022 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2804 | − | 23.0023i | 0.706845 | − | 1.22429i | −0.259177 | − | 0.965830i | \(-0.583451\pi\) |
0.966022 | − | 0.258461i | \(-0.0832155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.6429 | − | 10.7635i | 0.989460 | − | 0.571265i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.41824 | − | 3.13652i | −0.339689 | − | 0.166002i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5062 | − | 26.8575i | −0.818386 | − | 1.41749i | −0.906871 | − | 0.421408i | \(-0.861536\pi\) |
0.0884855 | − | 0.996077i | \(-0.471797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.85488 | + | 10.1410i | −0.308152 | + | 0.533735i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.53630i | 0.185607i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9555i | 1.62029i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.38677 | + | 11.0622i | −0.333387 | + | 0.577443i | −0.983174 | − | 0.182674i | \(-0.941525\pi\) |
0.649787 | + | 0.760117i | \(0.274858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.67669 | + | 4.63616i | 0.139343 | + | 0.241349i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.472088 | − | 6.82694i | −0.0245096 | − | 0.354437i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.73431 | − | 3.31070i | 0.296911 | − | 0.171422i | −0.344143 | − | 0.938917i | \(-0.611831\pi\) |
0.641054 | + | 0.767495i | \(0.278497\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.541251 | − | 0.937474i | 0.0279501 | − | 0.0484109i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.24384 | −0.321574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7804i | 0.964683i | 0.875983 | + | 0.482341i | \(0.160214\pi\) | ||||
−0.875983 | + | 0.482341i | \(0.839786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.15656 | − | 5.28654i | −0.469105 | − | 0.270838i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.2179 | − | 17.6980i | −0.522112 | − | 0.904325i | −0.999669 | − | 0.0257240i | \(-0.991811\pi\) |
0.477557 | − | 0.878601i | \(-0.341522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5459 | − | 17.1461i | −0.588435 | − | 0.873846i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.4349 | + | 14.6848i | −1.29293 | + | 0.746472i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.05734 | + | 1.18781i | 0.104311 | + | 0.0602242i | 0.551248 | − | 0.834341i | \(-0.314152\pi\) |
−0.446937 | + | 0.894566i | \(0.647485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8574 | −0.549082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.4740 | 0.578785 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.70287 | − | 2.71520i | −0.236627 | − | 0.136617i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1993 | − | 11.0847i | 0.963583 | − | 0.556325i | 0.0663091 | − | 0.997799i | \(-0.478878\pi\) |
0.897274 | + | 0.441474i | \(0.145544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.72360 | − | 4.04464i | −0.136351 | − | 0.202485i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1585 | − | 22.7912i | −0.657104 | − | 1.13814i | −0.981362 | − | 0.192168i | \(-0.938448\pi\) |
0.324258 | − | 0.945969i | \(-0.394885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.92543 | + | 3.42105i | 0.295167 | + | 0.170415i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 16.2707i | − | 0.808497i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.9856 | −0.594106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.331162 | − | 0.573590i | 0.0163749 | − | 0.0283622i | −0.857722 | − | 0.514114i | \(-0.828121\pi\) |
0.874097 | + | 0.485752i | \(0.161454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.524603 | + | 0.302880i | −0.0258768 | + | 0.0149399i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23998 | − | 32.3926i | −0.110222 | − | 1.59394i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4897 | + | 18.1686i | 0.514917 | + | 0.891862i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.833662 | + | 1.44395i | −0.0408246 | + | 0.0707103i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.55501i | 0.369086i | 0.982824 | + | 0.184543i | \(0.0590805\pi\) | ||||
−0.982824 | + | 0.184543i | \(0.940919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5905i | 0.613625i | 0.951770 | + | 0.306813i | \(0.0992625\pi\) | ||||
−0.951770 | + | 0.306813i | \(0.900737\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.40332 | + | 14.5550i | −0.408583 | + | 0.707687i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.8574 | + | 18.8055i | 0.526661 | + | 0.912203i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.7180 | + | 10.1246i | 1.00261 | + | 0.489966i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.41342 | − | 2.54809i | 0.213082 | − | 0.123023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.45241 | + | 11.1759i | −0.310802 | + | 0.538325i | −0.978536 | − | 0.206075i | \(-0.933931\pi\) |
0.667734 | + | 0.744400i | \(0.267264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.5815 | −1.95022 | −0.975112 | − | 0.221715i | \(-0.928835\pi\) | ||||
−0.975112 | + | 0.221715i | \(0.928835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4.46009i | − | 0.213845i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.41824 | − | 3.70557i | −0.307026 | − | 0.177262i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2273 | + | 31.5706i | 0.869941 | + | 1.50678i | 0.862055 | + | 0.506814i | \(0.169177\pi\) |
0.00788596 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.5697 | − | 2.44159i | 0.836650 | − | 0.116266i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.1274 | − | 16.2393i | 1.33637 | − | 0.771555i | 0.350104 | − | 0.936711i | \(-0.386146\pi\) |
0.986267 | + | 0.165156i | \(0.0528128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.2100 | + | 22.6379i | 1.85873 | + | 1.07314i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.43587 | 0.304406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9823 | 1.22618 | 0.613091 | − | 0.790012i | \(-0.289926\pi\) | ||||
0.613091 | + | 0.790012i | \(0.289926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.41342 | + | 2.54809i | 0.207820 | + | 0.119985i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.16978 | − | 2.40742i | 0.195913 | − | 0.113111i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.6441 | − | 23.8273i | 0.545885 | − | 1.11704i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.73448 | + | 9.93241i | 0.268248 | + | 0.464618i | 0.968409 | − | 0.249366i | \(-0.0802221\pi\) |
−0.700162 | + | 0.713984i | \(0.746889\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9403 | − | 7.47111i | −0.604004 | − | 0.348722i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 25.1973i | − | 1.17355i | −0.809749 | − | 0.586777i | \(-0.800396\pi\) | ||
0.809749 | − | 0.586777i | \(-0.199604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8223 | 1.47891 | 0.739454 | − | 0.673207i | \(-0.235084\pi\) | ||||
0.739454 | + | 0.673207i | \(0.235084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.44372 | + | 4.23265i | −0.113325 | + | 0.196284i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.3089 | − | 7.10656i | 0.569589 | − | 0.328852i | −0.187396 | − | 0.982284i | \(-0.560005\pi\) |
0.756985 | + | 0.653432i | \(0.226671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.05770 | + | 15.2955i | 0.0488398 | + | 0.706280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.97462 | + | 5.15220i | 0.137063 | + | 0.237401i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.9793 | + | 24.2129i | −0.642769 | + | 1.11331i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8223i | 0.680094i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.55438i | − | 0.300104i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.77020 | + | 9.99428i | −0.263647 | + | 0.456650i | −0.967208 | − | 0.253984i | \(-0.918259\pi\) |
0.703561 | + | 0.710635i | \(0.251592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.68855 | − | 13.3170i | −0.350568 | − | 0.607201i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.11173 | + | 2.76878i | −0.187090 | + | 0.125984i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.86255 | − | 2.23005i | 0.175390 | − | 0.101261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.80829 | + | 15.2564i | −0.399142 | + | 0.691333i | −0.993620 | − | 0.112778i | \(-0.964025\pi\) |
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.5341 | −0.612032 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8502i | 1.21173i | 0.795567 | + | 0.605866i | \(0.207173\pi\) | ||||
−0.795567 | + | 0.605866i | \(0.792827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.91105 | + | 3.99010i | 0.311258 | + | 0.179705i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.89930 | − | 17.1461i | −0.444941 | − | 0.770660i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.82233 | + | 14.5865i | 0.440592 | + | 0.654293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.21925 | − | 1.28129i | 0.0993474 | − | 0.0573583i | −0.449503 | − | 0.893279i | \(-0.648399\pi\) |
0.548851 | + | 0.835921i | \(0.315066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.0997 | + | 7.56310i | 0.585251 | + | 0.337895i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6941 | 0.655176 | 0.327588 | − | 0.944821i | \(-0.393764\pi\) | ||||
0.327588 | + | 0.944821i | \(0.393764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.57849 | −0.114741 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.02259 | − | 1.16775i | −0.0898266 | − | 0.0518614i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0283 | + | 6.36720i | −0.488821 | + | 0.282221i | −0.724085 | − | 0.689710i | \(-0.757738\pi\) |
0.235264 | + | 0.971932i | \(0.424405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.2273 | + | 1.74449i | −1.11599 | + | 0.0771716i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.09971 | − | 8.83296i | −0.225158 | − | 0.389985i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.44968 | + | 4.30107i | 0.328272 | + | 0.189528i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9992i | 0.703643i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8337 | −0.651126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0134 | + | 29.4680i | −0.745369 | + | 1.29102i | 0.204652 | + | 0.978835i | \(0.434394\pi\) |
−0.950022 | + | 0.312183i | \(0.898940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.88515 | − | 3.39779i | 0.257340 | − | 0.148575i | −0.365781 | − | 0.930701i | \(-0.619198\pi\) |
0.623120 | + | 0.782126i | \(0.285865\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.90739 | + | 4.35294i | 0.388750 | + | 0.189978i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.37241 | − | 7.57324i | −0.190465 | − | 0.329896i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.73296 | − | 13.3939i | 0.336216 | − | 0.582343i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.0994i | − | 1.34960i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.53819i | 0.283200i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.79392 | − | 15.2315i | 0.380195 | − | 0.658516i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.28924 | − | 2.23304i | −0.0556350 | − | 0.0963626i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.3226 | − | 10.3757i | 0.573845 | − | 0.446911i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3952 | − | 12.3525i | 0.919852 | − | 0.531077i | 0.0362640 | − | 0.999342i | \(-0.488454\pi\) |
0.883588 | + | 0.468266i | \(0.155121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.78924 | − | 8.29521i | 0.205526 | − | 0.355982i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.7335 | 1.91617 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.5793i | − | 1.17920i | −0.807694 | − | 0.589602i | \(-0.799284\pi\) | ||
0.807694 | − | 0.589602i | \(-0.200716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.1272 | + | 11.0431i | 0.816328 | + | 0.471307i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.72360 | + | 4.71742i | 0.116029 | + | 0.200969i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.94773 | − | 3.98563i | 0.0828261 | − | 0.169486i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.51256 | − | 5.49208i | 0.403785 | − | 0.233126i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.1575 | − | 22.6076i | −1.65916 | − | 0.957914i | −0.973106 | − | 0.230359i | \(-0.926010\pi\) |
−0.686050 | − | 0.727555i | \(-0.740657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.8698 | −1.51713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.51337 | −0.274995 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.1895 | + | 7.61497i | 0.555872 | + | 0.320933i | 0.751487 | − | 0.659748i | \(-0.229337\pi\) |
−0.195615 | + | 0.980681i | \(0.562670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7174 | + | 7.34241i | −0.535026 | + | 0.308898i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.2599 | − | 0.916930i | 0.556862 | − | 0.0385074i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.04343 | − | 12.1996i | −0.295276 | − | 0.511433i | 0.679773 | − | 0.733423i | \(-0.262078\pi\) |
−0.975049 | + | 0.221989i | \(0.928745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2480 | + | 11.1129i | 0.805505 | + | 0.465058i | 0.845392 | − | 0.534146i | \(-0.179367\pi\) |
−0.0398876 | + | 0.999204i | \(0.512700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4.96851i | − | 0.207562i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.0681 | 0.628385 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.68070 | + | 8.10721i | −0.194860 | + | 0.337507i | −0.946855 | − | 0.321662i | \(-0.895759\pi\) |
0.751995 | + | 0.659169i | \(0.229092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.63598 | − | 3.25393i | 0.234223 | − | 0.135229i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2154 | + | 9.57246i | −0.589755 | + | 0.397133i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.11974 | − | 5.40355i | −0.129206 | − | 0.223792i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.7004 | − | 21.9978i | 0.525097 | − | 0.909495i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13.0157i | − | 0.537217i | −0.963249 | − | 0.268608i | \(-0.913436\pi\) | ||
0.963249 | − | 0.268608i | \(-0.0865637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.96914i | − | 0.245954i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.98180 | − | 6.89669i | 0.163790 | − | 0.283692i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.698895 | + | 1.21052i | 0.0287002 | + | 0.0497101i | 0.880019 | − | 0.474939i | \(-0.157530\pi\) |
−0.851319 | + | 0.524649i | \(0.824197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.1151 | + | 18.9323i | −1.15261 | + | 0.776150i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2110 | + | 6.47265i | −0.458834 | + | 0.264908i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.9302 | + | 27.5919i | −0.650891 | + | 1.12738i | 0.332017 | + | 0.943274i | \(0.392271\pi\) |
−0.982907 | + | 0.184102i | \(0.941062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4927 | 1.40699 | 0.703493 | − | 0.710702i | \(-0.251623\pi\) | ||||
0.703493 | + | 0.710702i | \(0.251623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.6848i | 0.598012i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.5311 | + | 8.38955i | 0.590775 | + | 0.341084i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.61573 | − | 7.99467i | −0.187347 | − | 0.324494i | 0.757018 | − | 0.653394i | \(-0.226655\pi\) |
−0.944365 | + | 0.328900i | \(0.893322\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.63477 | − | 0.251347i | 0.147288 | − | 0.0101851i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.7763 | + | 10.2631i | −0.719152 | + | 0.415202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0431 | − | 16.1907i | −1.13265 | − | 0.653935i | −0.188049 | − | 0.982160i | \(-0.560216\pi\) |
−0.944600 | + | 0.328225i | \(0.893550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.67035 | −0.188327 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1600 | −0.409026 | −0.204513 | − | 0.978864i | \(-0.565561\pi\) | ||||
−0.204513 | + | 0.978864i | \(0.565561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.1866 | − | 18.5829i | −1.29369 | − | 0.746911i | −0.314382 | − | 0.949297i | \(-0.601797\pi\) |
−0.979306 | + | 0.202385i | \(0.935131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.97946 | + | 5.18430i | −0.360333 | + | 0.208039i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.2392 | + | 33.2301i | −0.650608 | + | 1.33133i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1560 | + | 19.3227i | 0.446240 | + | 0.772910i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.85032 | − | 2.22298i | −0.153767 | − | 0.0887774i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.6533i | 0.783630i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.31198 | 0.291085 | 0.145543 | − | 0.989352i | \(-0.453507\pi\) | ||||
0.145543 | + | 0.989352i | \(0.453507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.50401 | − | 9.53323i | 0.218765 | − | 0.378912i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −43.4463 | + | 25.0837i | −1.72411 | + | 0.995418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.0743 | + | 8.14664i | 0.795373 | + | 0.322782i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.42151 | + | 14.5865i | 0.333150 | + | 0.577032i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.85337 | + | 11.8704i | −0.270692 | + | 0.468852i | −0.969039 | − | 0.246907i | \(-0.920586\pi\) |
0.698347 | + | 0.715759i | \(0.253919\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.5812i | 1.20600i | 0.797740 | + | 0.603002i | \(0.206029\pi\) | ||||
−0.797740 | + | 0.603002i | \(0.793971\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 25.6225i | − | 1.00888i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2979 | − | 36.8891i | 0.837308 | − | 1.45026i | −0.0548287 | − | 0.998496i | \(-0.517461\pi\) |
0.892137 | − | 0.451765i | \(-0.149205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8026 | − | 25.6389i | −0.581054 | − | 1.00641i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.58712 | − | 1.75299i | −0.140591 | − | 0.0687050i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.9273 | + | 15.5465i | −1.05375 | + | 0.608381i | −0.923696 | − | 0.383126i | \(-0.874848\pi\) |
−0.130051 | + | 0.991507i | \(0.541514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.2210 | − | 47.1481i | 1.06361 | − | 1.84223i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.2201 | −0.944917 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 35.8472i | − | 1.39641i | −0.715899 | − | 0.698204i | \(-0.753983\pi\) | ||
0.715899 | − | 0.698204i | \(-0.246017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6297 | − | 13.6426i | −0.919087 | − | 0.530635i | −0.0357432 | − | 0.999361i | \(-0.511380\pi\) |
−0.883344 | + | 0.468726i | \(0.844713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.17820 | − | 7.23685i | −0.162268 | − | 0.281056i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.0815 | + | 1.59611i | −0.895063 | + | 0.0618943i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.79566 | − | 2.76878i | 0.185689 | − | 0.107208i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.56051 | − | 2.63301i | −0.176320 | − | 0.101798i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0251 | 0.811663 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.2963 | −1.24493 | −0.622465 | − | 0.782648i | \(-0.713869\pi\) | ||||
−0.622465 | + | 0.782648i | \(0.713869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.9589 | + | 10.3686i | 0.691239 | + | 0.399087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5785 | − | 7.83953i | 0.521863 | − | 0.301298i | −0.215834 | − | 0.976430i | \(-0.569247\pi\) |
0.737697 | + | 0.675132i | \(0.235914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.03506 | + | 3.02213i | 0.0780983 | + | 0.115979i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.725117 | − | 1.25594i | −0.0277865 | − | 0.0481277i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.5012 | − | 9.52698i | −0.631401 | − | 0.364540i | 0.149893 | − | 0.988702i | \(-0.452107\pi\) |
−0.781295 | + | 0.624162i | \(0.785440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.87422i | 0.109818i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.39448 | −0.243965 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00250 | − | 6.93253i | 0.152483 | − | 0.264108i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9066 | + | 15.5345i | −1.02358 | + | 0.590961i | −0.915138 | − | 0.403142i | \(-0.867918\pi\) |
−0.108438 | + | 0.994103i | \(0.534585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.4154 | − | 9.03373i | 0.509609 | − | 0.343163i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.95558 | + | 6.85127i | 0.150044 | + | 0.259883i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.17820 | − | 7.23685i | 0.158261 | − | 0.274115i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 6.02545i | − | 0.227903i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33.5258i | − | 1.26625i | −0.774048 | − | 0.633127i | \(-0.781771\pi\) | ||
0.774048 | − | 0.633127i | \(-0.218229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.70759 | + | 11.6179i | −0.252981 | + | 0.438177i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.33116 | − | 12.6979i | −0.276108 | − | 0.478232i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.145310 | − | 2.10135i | −0.00546494 | − | 0.0790293i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.16576 | − | 4.13715i | 0.269116 | − | 0.155374i | −0.359370 | − | 0.933195i | \(-0.617008\pi\) |
0.628486 | + | 0.777821i | \(0.283675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.12442 | − | 3.67960i | 0.0796720 | − | 0.137996i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.06814 | −0.227254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.1805i | − | 0.904298i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.50835 | + | 2.02555i | 0.131022 | + | 0.0756455i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.81462 | − | 3.14301i | −0.0676739 | − | 0.117215i | 0.830203 | − | 0.557461i | \(-0.188224\pi\) |
−0.897877 | + | 0.440246i | \(0.854891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.08535 | + | 6.31352i | −0.114904 | + | 0.235128i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.31696 | + | 3.64710i | −0.234930 | + | 0.135637i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.59133 | − | 5.53756i | −0.356213 | − | 0.205660i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.1550 | −1.04421 | −0.522106 | − | 0.852881i | \(-0.674853\pi\) | ||||
−0.522106 | + | 0.852881i | \(0.674853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.99500 | 0.185000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.7028 | + | 22.9224i | 1.46846 | + | 0.847816i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4264 | + | 14.6799i | −0.939145 | + | 0.542215i | −0.889692 | − | 0.456561i | \(-0.849081\pi\) |
−0.0494525 | + | 0.998776i | \(0.515748\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.81930 | + | 14.3395i | −0.214648 | + | 0.528919i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.98965 | + | 12.1064i | 0.257467 | + | 0.445946i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2457 | − | 6.49271i | −0.413680 | − | 0.238838i | 0.278690 | − | 0.960381i | \(-0.410100\pi\) |
−0.692370 | + | 0.721543i | \(0.743433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 5.70400i | − | 0.209542i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8510 | −0.801637 | −0.400819 | − | 0.916157i | \(-0.631274\pi\) | ||||
−0.400819 | + | 0.916157i | \(0.631274\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.2685 | − | 26.4459i | 0.559396 | − | 0.968903i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.2154 | + | 8.20728i | −0.520115 | + | 0.300289i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9086 | + | 6.30827i | 0.471668 | + | 0.230499i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.03724 | + | 10.4568i | 0.220302 | + | 0.381574i | 0.954900 | − | 0.296929i | \(-0.0959624\pi\) |
−0.734598 | + | 0.678503i | \(0.762629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.30512 | + | 2.26053i | −0.0475612 | + | 0.0823783i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 22.8456i | − | 0.831436i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 27.2309i | − | 0.989725i | −0.868971 | − | 0.494862i | \(-0.835218\pi\) | ||
0.868971 | − | 0.494862i | \(-0.164782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.25985 | + | 3.91418i | −0.0820275 | + | 0.142076i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2423 | − | 26.4005i | −0.552534 | − | 0.957017i | −0.998091 | − | 0.0617632i | \(-0.980328\pi\) |
0.445557 | − | 0.895254i | \(-0.353006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.52094 | + | 36.4557i | 0.0912642 | + | 1.31978i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.1151 | + | 16.2323i | −1.01650 | + | 0.586879i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.9912 | − | 32.8937i | 0.685731 | − | 1.18772i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.6991 | 1.32340 | 0.661701 | − | 0.749768i | \(-0.269835\pi\) | ||||
0.661701 | + | 0.749768i | \(0.269835\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.46809i | 0.304971i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6220 | + | 16.5249i | 1.02946 | + | 0.594359i | 0.916830 | − | 0.399277i | \(-0.130739\pi\) |
0.112631 | + | 0.993637i | \(0.464072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.06814 | + | 10.5103i | 0.217974 | + | 0.377542i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.01186 | + | 7.44278i | 0.179800 | + | 0.267008i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.93981 | − | 2.85200i | 0.176987 | − | 0.102183i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8857 | + | 8.01691i | 0.496869 | + | 0.286867i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.62093 | 0.272350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.2281 | 1.00751 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9922 | + | 8.65572i | 0.534413 | + | 0.308543i | 0.742811 | − | 0.669501i | \(-0.233492\pi\) |
−0.208399 | + | 0.978044i | \(0.566825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.794499 | − | 0.458704i | 0.0282849 | − | 0.0163303i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.70041 | − | 9.95033i | −0.238239 | − | 0.353793i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.4872 | + | 23.3604i | 0.478943 | + | 0.829553i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.95204 | + | 2.85906i | 0.175631 | + | 0.101400i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.7331i | 1.47826i | 0.673561 | + | 0.739131i | \(0.264764\pi\) | ||||
−0.673561 | + | 0.739131i | \(0.735236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.2345 | 0.928109 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7123 | + | 30.6786i | −0.625832 | + | 1.08397i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.9675 | + | 11.5282i | −0.704638 | + | 0.406823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.62258 | + | 23.4643i | 0.0571884 | + | 0.827010i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.665670 | + | 1.15297i | 0.0234327 | + | 0.0405866i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.86273 | − | 8.42250i | 0.170965 | − | 0.296119i | −0.767793 | − | 0.640698i | \(-0.778645\pi\) |
0.938757 | + | 0.344579i | \(0.111978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 55.3405i | − | 1.94327i | −0.236492 | − | 0.971633i | \(-0.575998\pi\) | ||
0.236492 | − | 0.971633i | \(-0.424002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7733i | 0.623339i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.1084 | + | 55.6134i | −1.12471 | + | 1.94805i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.6466 | + | 27.1008i | 0.547406 | + | 0.948135i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.6429 | + | 9.11056i | 0.651434 | + | 0.318349i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.5157 | − | 21.0823i | 1.27441 | − | 0.735779i | 0.298592 | − | 0.954381i | \(-0.403483\pi\) |
0.975814 | + | 0.218602i | \(0.0701496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.60689 | − | 13.1755i | 0.265160 | − | 0.459270i | −0.702446 | − | 0.711737i | \(-0.747909\pi\) |
0.967605 | + | 0.252467i | \(0.0812420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.03942 | 0.314712 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.24390i | − | 0.0432548i | −0.999766 | − | 0.0216274i | \(-0.993115\pi\) | ||
0.999766 | − | 0.0216274i | \(-0.00688475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4517 | − | 10.6531i | −0.640855 | − | 0.369998i | 0.144089 | − | 0.989565i | \(-0.453975\pi\) |
−0.784944 | + | 0.619567i | \(0.787308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.50067 | − | 9.52744i | −0.190816 | − | 0.330503i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.0134 | − | 21.8456i | −0.589478 | − | 0.756905i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 62.1557 | − | 35.8856i | 2.15099 | − | 1.24187i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.23230 | − | 4.17557i | −0.249985 | − | 0.144329i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9379 | 0.722857 | 0.361429 | − | 0.932400i | \(-0.382289\pi\) | ||||
0.361429 | + | 0.932400i | \(0.382289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9299 | 0.859651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.53586 | + | 5.50553i | 0.328432 | + | 0.189621i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.59686 | + | 5.54075i | −0.330142 | + | 0.190608i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.01820 | + | 12.3150i | −0.206788 | + | 0.423148i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.98332 | + | 15.5596i | 0.308307 | + | 0.534003i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8106 | + | 6.81884i | 0.404861 | + | 0.233747i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.4758i | − | 0.598361i | −0.954197 | − | 0.299180i | \(-0.903287\pi\) | ||
0.954197 | − | 0.299180i | \(-0.0967133\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.1600 | −0.757856 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.75517 | + | 3.04005i | −0.0599556 | + | 0.103846i | −0.894445 | − | 0.447177i | \(-0.852429\pi\) |
0.834490 | + | 0.551024i | \(0.185763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.45370 | − | 2.57134i | 0.151958 | − | 0.0877331i | −0.422093 | − | 0.906553i | \(-0.638704\pi\) |
0.574051 | + | 0.818819i | \(0.305371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.263196 | − | 3.80612i | −0.00896970 | − | 0.129712i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.1410 | − | 34.8852i | −0.685606 | − | 1.18750i | −0.973246 | − | 0.229766i | \(-0.926204\pi\) |
0.287640 | − | 0.957739i | \(-0.407129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.1916 | + | 60.9536i | −1.19655 | + | 2.07248i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.923798i | − | 0.0313738i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.04471i | − | 0.137207i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.96744 | + | 15.5321i | −0.303850 | + | 0.526284i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.74483 | + | 3.02213i | 0.0590534 | + | 0.102284i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.48031 | − | 2.34359i | 0.117656 | − | 0.0792277i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.3471 | − | 20.9850i | 1.22735 | − | 0.708613i | 0.260878 | − | 0.965372i | \(-0.415988\pi\) |
0.966476 | + | 0.256759i | \(0.0826546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.29326 | + | 5.70409i | −0.111079 | + | 0.192394i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5992 | −0.559241 | −0.279620 | − | 0.960111i | \(-0.590209\pi\) | ||||
−0.279620 | + | 0.960111i | \(0.590209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.8210i | − | 0.431462i | −0.976453 | − | 0.215731i | \(-0.930787\pi\) | ||
0.976453 | − | 0.215731i | \(-0.0692135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.4966 | + | 13.5658i | 0.789829 | + | 0.456008i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.14980 | + | 7.18766i | 0.139337 | + | 0.241338i | 0.927246 | − | 0.374454i | \(-0.122170\pi\) |
−0.787909 | + | 0.615792i | \(0.788836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.8905 | − | 33.9931i | −0.767722 | − | 1.14009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.4952 | − | 6.05942i | 0.351603 | − | 0.202998i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.5083 | + | 8.95370i | 0.518964 | + | 0.299624i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.2345 | −0.408954 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.79861 | −0.193610 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.86255 | + | 2.23005i | 0.128823 | + | 0.0743762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.86041 | + | 5.11556i | −0.295183 | + | 0.170424i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.8811 | − | 1.44395i | 0.694880 | − | 0.0480515i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.7241 | − | 39.3593i | −0.755376 | − | 1.30835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2277 | + | 8.21434i | 0.472422 | + | 0.272753i | 0.717253 | − | 0.696813i | \(-0.245399\pi\) |
−0.244831 | + | 0.969566i | \(0.578733\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.01745i | − | 0.0669147i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1630 | 1.23127 | 0.615633 | − | 0.788033i | \(-0.288900\pi\) | ||||
0.615633 | + | 0.788033i | \(0.288900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.81297 | + | 13.5325i | −0.258571 | + | 0.447859i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.6868 | + | 9.63413i | −0.551649 | + | 0.318495i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.9575 | + | 19.5268i | 1.31951 | + | 0.644831i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1528 | − | 31.4416i | −0.598806 | − | 1.03716i | −0.992998 | − | 0.118135i | \(-0.962309\pi\) |
0.394191 | − | 0.919028i | \(-0.371025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.62593 | − | 14.9406i | 0.284234 | − | 0.492308i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.5707i | 0.677094i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 27.2754i | − | 0.896809i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.36523 | + | 5.82875i | −0.110529 | + | 0.191441i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8263 | + | 18.7518i | 0.355201 | + | 0.615226i | 0.987152 | − | 0.159782i | \(-0.0510792\pi\) |
−0.631952 | + | 0.775008i | \(0.717746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.60150 | − | 18.7204i | −0.0852608 | − | 0.613536i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.3293 | + | 7.69567i | −0.436382 | + | 0.251945i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.4524 | + | 26.7644i | −0.505348 | + | 0.875288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8637 | −0.518245 | −0.259123 | − | 0.965844i | \(-0.583433\pi\) | ||||
−0.259123 | + | 0.965844i | \(0.583433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 17.3242i | − | 0.565355i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7230 | + | 7.34561i | 0.414757 | + | 0.239460i | 0.692832 | − | 0.721099i | \(-0.256363\pi\) |
−0.278075 | + | 0.960559i | \(0.589696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.89930 | − | 5.02174i | −0.0944143 | − | 0.163530i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.2123 | + | 29.0824i | −0.462325 | + | 0.946052i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0598 | + | 6.96270i | −0.391889 | + | 0.226257i | −0.682978 | − | 0.730439i | \(-0.739316\pi\) |
0.291089 | + | 0.956696i | \(0.405982\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.6175 | − | 14.7903i | −0.831579 | − | 0.480112i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6954 | 0.379250 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2883 | 0.365663 | 0.182831 | − | 0.983144i | \(-0.441474\pi\) | ||||
0.182831 | + | 0.983144i | \(0.441474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.4163 | − | 11.7873i | −0.660655 | − | 0.381430i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.87693 | − | 1.66100i | 0.0929980 | − | 0.0536924i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.34236 | + | 0.161976i | −0.0756386 | + | 0.00523047i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0563 | + | 22.6141i | 0.421170 | + | 0.729488i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.9174 | + | 6.88051i | 0.384033 | + | 0.221721i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 30.8787i | − | 0.994020i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4276 | 1.17143 | 0.585716 | − | 0.810517i | \(-0.300813\pi\) | ||||
0.585716 | + | 0.810517i | \(0.300813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.64512 | + | 6.31352i | −0.117098 | + | 0.202820i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.75503 | − | 3.32267i | 0.184688 | − | 0.106629i | −0.404806 | − | 0.914403i | \(-0.632661\pi\) |
0.589493 | + | 0.807773i | \(0.299327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.36055 | + | 3.60971i | −0.171851 | + | 0.115722i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.79861 | + | 10.0435i | 0.185704 | + | 0.321649i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.7226 | − | 39.3567i | 0.726961 | − | 1.25913i | −0.231201 | − | 0.972906i | \(-0.574265\pi\) |
0.958162 | − | 0.286227i | \(-0.0924012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.7226i | 1.07778i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.0002i | 1.11747i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.26538 | + | 16.0481i | −0.295520 | + | 0.511855i | −0.975106 | − | 0.221741i | \(-0.928826\pi\) |
0.679586 | + | 0.733596i | \(0.262159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.8930 | − | 32.7236i | −0.601980 | − | 1.04266i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.93508 | − | 6.69014i | 0.316237 | − | 0.212950i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.5503 | − | 15.9061i | 0.876047 | − | 0.505786i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.2392 | + | 31.5911i | −0.579386 | + | 1.00353i | 0.416164 | + | 0.909290i | \(0.363374\pi\) |
−0.995550 | + | 0.0942363i | \(0.969959\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.86069 | 0.185983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61.4232i | 1.94724i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.2738 | − | 7.66365i | −0.420386 | − | 0.242710i | 0.274856 | − | 0.961485i | \(-0.411370\pi\) |
−0.695243 | + | 0.718775i | \(0.744703\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.38427 | + | 16.2540i | 0.296905 | + | 0.514255i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))