Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,2,Mod(349,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.b (of order \(2\), degree \(1\), 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: | \(5.78915414654\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 29) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.349 |
Dual form | 725.2.b.b.349.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/725\mathbb{Z}\right)^\times\).
\(n\) | \(176\) | \(552\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.41421i | − 1.70711i | −0.521005 | − | 0.853553i | \(-0.674443\pi\) | ||||
0.521005 | − | 0.853553i | \(-0.325557\pi\) | |||||||
\(3\) | − 2.41421i | − 1.39385i | −0.717146 | − | 0.696923i | \(-0.754552\pi\) | ||||
0.717146 | − | 0.696923i | \(-0.245448\pi\) | |||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.82843 | −2.37945 | ||||||||
\(7\) | − 2.82843i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 4.41421i | 1.56066i | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.414214 | −0.124890 | −0.0624450 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | 9.24264i | 2.66812i | ||||||||
\(13\) | 3.82843i | 1.06181i | 0.847430 | + | 0.530907i | \(0.178149\pi\) | ||||
−0.847430 | + | 0.530907i | \(0.821851\pi\) | |||||||
\(14\) | −6.82843 | −1.82497 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0.828427i | 0.200923i | 0.994941 | + | 0.100462i | \(0.0320319\pi\) | ||||
−0.994941 | + | 0.100462i | \(0.967968\pi\) | |||||||
\(18\) | 6.82843i | 1.60948i | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.82843 | −1.49008 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | − 3.65685i | − 0.762507i | −0.924471 | − | 0.381253i | \(-0.875493\pi\) | ||||
0.924471 | − | 0.381253i | \(-0.124507\pi\) | |||||||
\(24\) | 10.6569 | 2.17532 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.24264 | 1.81263 | ||||||||
\(27\) | − 0.414214i | − 0.0797154i | ||||||||
\(28\) | 10.8284i | 2.04638i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0711 | 1.80882 | 0.904409 | − | 0.426667i | \(-0.140313\pi\) | ||||
0.904409 | + | 0.426667i | \(0.140313\pi\) | |||||||
\(32\) | 1.58579i | 0.280330i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.8284 | 1.80474 | ||||||||
\(37\) | − 4.00000i | − 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 14.4853i | 2.34982i | ||||||||
\(39\) | 9.24264 | 1.48001 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.48528 | −0.700483 | −0.350242 | − | 0.936659i | \(-0.613901\pi\) | ||||
−0.350242 | + | 0.936659i | \(0.613901\pi\) | |||||||
\(42\) | 16.4853i | 2.54373i | ||||||||
\(43\) | − 3.58579i | − 0.546827i | −0.961897 | − | 0.273414i | \(-0.911847\pi\) | ||||
0.961897 | − | 0.273414i | \(-0.0881528\pi\) | |||||||
\(44\) | 1.58579 | 0.239066 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.82843 | −1.30168 | ||||||||
\(47\) | − 3.24264i | − 0.472988i | −0.971633 | − | 0.236494i | \(-0.924002\pi\) | ||||
0.971633 | − | 0.236494i | \(-0.0759983\pi\) | |||||||
\(48\) | − 7.24264i | − 1.04539i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | − 14.6569i | − 2.03254i | ||||||||
\(53\) | − 9.48528i | − 1.30290i | −0.758690 | − | 0.651452i | \(-0.774160\pi\) | ||||
0.758690 | − | 0.651452i | \(-0.225840\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.4853 | 1.66842 | ||||||||
\(57\) | 14.4853i | 1.91862i | ||||||||
\(58\) | 2.41421i | 0.317002i | ||||||||
\(59\) | 3.65685 | 0.476082 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.82843 | −0.618217 | −0.309108 | − | 0.951027i | \(-0.600031\pi\) | ||||
−0.309108 | + | 0.951027i | \(0.600031\pi\) | |||||||
\(62\) | − 24.3137i | − 3.08784i | ||||||||
\(63\) | 8.00000i | 1.00791i | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.41421 | 0.297169 | ||||||||
\(67\) | 5.65685i | 0.691095i | 0.938401 | + | 0.345547i | \(0.112307\pi\) | ||||
−0.938401 | + | 0.345547i | \(0.887693\pi\) | |||||||
\(68\) | − 3.17157i | − 0.384610i | ||||||||
\(69\) | −8.82843 | −1.06282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.82843 | −1.04774 | −0.523871 | − | 0.851798i | \(-0.675513\pi\) | ||||
−0.523871 | + | 0.851798i | \(0.675513\pi\) | |||||||
\(72\) | − 12.4853i | − 1.47140i | ||||||||
\(73\) | − 4.00000i | − 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | −9.65685 | −1.12259 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.9706 | 2.63490 | ||||||||
\(77\) | 1.17157i | 0.133513i | ||||||||
\(78\) | − 22.3137i | − 2.52653i | ||||||||
\(79\) | 2.41421 | 0.271620 | 0.135810 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135810 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 10.8284i | 1.19580i | ||||||||
\(83\) | − 7.65685i | − 0.840449i | −0.907420 | − | 0.420224i | \(-0.861951\pi\) | ||||
0.907420 | − | 0.420224i | \(-0.138049\pi\) | |||||||
\(84\) | 26.1421 | 2.85234 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.65685 | −0.933493 | ||||||||
\(87\) | 2.41421i | 0.258831i | ||||||||
\(88\) | − 1.82843i | − 0.194911i | ||||||||
\(89\) | 12.4853 | 1.32344 | 0.661719 | − | 0.749752i | \(-0.269827\pi\) | ||||
0.661719 | + | 0.749752i | \(0.269827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8284 | 1.13513 | ||||||||
\(92\) | 14.0000i | 1.45960i | ||||||||
\(93\) | − 24.3137i | − 2.52121i | ||||||||
\(94\) | −7.82843 | −0.807441 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.82843 | 0.390737 | ||||||||
\(97\) | 4.48528i | 0.455411i | 0.973730 | + | 0.227706i | \(0.0731224\pi\) | ||||
−0.973730 | + | 0.227706i | \(0.926878\pi\) | |||||||
\(98\) | 2.41421i | 0.243872i | ||||||||
\(99\) | 1.17157 | 0.117748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.34315 | −0.233152 | −0.116576 | − | 0.993182i | \(-0.537192\pi\) | ||||
−0.116576 | + | 0.993182i | \(0.537192\pi\) | |||||||
\(102\) | − 4.82843i | − 0.478086i | ||||||||
\(103\) | 4.82843i | 0.475759i | 0.971295 | + | 0.237880i | \(0.0764523\pi\) | ||||
−0.971295 | + | 0.237880i | \(0.923548\pi\) | |||||||
\(104\) | −16.8995 | −1.65713 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.8995 | −2.22420 | ||||||||
\(107\) | − 14.8284i | − 1.43352i | −0.697321 | − | 0.716759i | \(-0.745625\pi\) | ||||
0.697321 | − | 0.716759i | \(-0.254375\pi\) | |||||||
\(108\) | 1.58579i | 0.152592i | ||||||||
\(109\) | −12.6569 | −1.21231 | −0.606153 | − | 0.795348i | \(-0.707288\pi\) | ||||
−0.606153 | + | 0.795348i | \(0.707288\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.65685 | −0.916588 | ||||||||
\(112\) | − 8.48528i | − 0.801784i | ||||||||
\(113\) | 13.3137i | 1.25245i | 0.779643 | + | 0.626224i | \(0.215401\pi\) | ||||
−0.779643 | + | 0.626224i | \(0.784599\pi\) | |||||||
\(114\) | 34.9706 | 3.27529 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.82843 | 0.355461 | ||||||||
\(117\) | − 10.8284i | − 1.00109i | ||||||||
\(118\) | − 8.82843i | − 0.812723i | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 11.6569i | 1.05536i | ||||||||
\(123\) | 10.8284i | 0.976366i | ||||||||
\(124\) | −38.5563 | −3.46246 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 19.3137 | 1.72060 | ||||||||
\(127\) | − 4.34315i | − 0.385392i | −0.981259 | − | 0.192696i | \(-0.938277\pi\) | ||||
0.981259 | − | 0.192696i | \(-0.0617231\pi\) | |||||||
\(128\) | − 20.5563i | − 1.81694i | ||||||||
\(129\) | −8.65685 | −0.762194 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.3137 | 1.86219 | 0.931094 | − | 0.364780i | \(-0.118856\pi\) | ||||
0.931094 | + | 0.364780i | \(0.118856\pi\) | |||||||
\(132\) | − 3.82843i | − 0.333222i | ||||||||
\(133\) | 16.9706i | 1.47153i | ||||||||
\(134\) | 13.6569 | 1.17977 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.65685 | −0.313573 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 21.3137i | 1.81434i | ||||||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.82843 | −0.659272 | ||||||||
\(142\) | 21.3137i | 1.78861i | ||||||||
\(143\) | − 1.58579i | − 0.132610i | ||||||||
\(144\) | −8.48528 | −0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.65685 | −0.799207 | ||||||||
\(147\) | 2.41421i | 0.199121i | ||||||||
\(148\) | 15.3137i | 1.25878i | ||||||||
\(149\) | 7.82843 | 0.641330 | 0.320665 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320665 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1421 | −1.15087 | −0.575435 | − | 0.817847i | \(-0.695167\pi\) | ||||
−0.575435 | + | 0.817847i | \(0.695167\pi\) | |||||||
\(152\) | − 26.4853i | − 2.14824i | ||||||||
\(153\) | − 2.34315i | − 0.189432i | ||||||||
\(154\) | 2.82843 | 0.227921 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −35.3848 | −2.83305 | ||||||||
\(157\) | 8.48528i | 0.677199i | 0.940931 | + | 0.338600i | \(0.109953\pi\) | ||||
−0.940931 | + | 0.338600i | \(0.890047\pi\) | |||||||
\(158\) | − 5.82843i | − 0.463685i | ||||||||
\(159\) | −22.8995 | −1.81605 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3431 | −0.815154 | ||||||||
\(162\) | 22.8995i | 1.79915i | ||||||||
\(163\) | − 3.92893i | − 0.307738i | −0.988091 | − | 0.153869i | \(-0.950827\pi\) | ||||
0.988091 | − | 0.153869i | \(-0.0491733\pi\) | |||||||
\(164\) | 17.1716 | 1.34087 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.4853 | −1.43474 | ||||||||
\(167\) | − 3.17157i | − 0.245424i | −0.992442 | − | 0.122712i | \(-0.960841\pi\) | ||||
0.992442 | − | 0.122712i | \(-0.0391591\pi\) | |||||||
\(168\) | − 30.1421i | − 2.32552i | ||||||||
\(169\) | −1.65685 | −0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | 1.29777 | ||||||||
\(172\) | 13.7279i | 1.04674i | ||||||||
\(173\) | − 12.3431i | − 0.938432i | −0.883083 | − | 0.469216i | \(-0.844537\pi\) | ||||
0.883083 | − | 0.469216i | \(-0.155463\pi\) | |||||||
\(174\) | 5.82843 | 0.441852 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.24264 | −0.0936676 | ||||||||
\(177\) | − 8.82843i | − 0.663585i | ||||||||
\(178\) | − 30.1421i | − 2.25925i | ||||||||
\(179\) | 6.48528 | 0.484733 | 0.242366 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.31371 | 0.617953 | 0.308977 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308977 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(182\) | − 26.1421i | − 1.93778i | ||||||||
\(183\) | 11.6569i | 0.861699i | ||||||||
\(184\) | 16.1421 | 1.19001 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −58.6985 | −4.30398 | ||||||||
\(187\) | − 0.343146i | − 0.0250933i | ||||||||
\(188\) | 12.4142i | 0.905400i | ||||||||
\(189\) | −1.17157 | −0.0852194 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3137 | 1.83164 | 0.915818 | − | 0.401594i | \(-0.131544\pi\) | ||||
0.915818 | + | 0.401594i | \(0.131544\pi\) | |||||||
\(192\) | − 23.7279i | − 1.71242i | ||||||||
\(193\) | 5.17157i | 0.372258i | 0.982525 | + | 0.186129i | \(0.0595942\pi\) | ||||
−0.982525 | + | 0.186129i | \(0.940406\pi\) | |||||||
\(194\) | 10.8284 | 0.777436 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | − 2.82843i | − 0.201008i | ||||||||
\(199\) | 0.485281 | 0.0344007 | 0.0172003 | − | 0.999852i | \(-0.494525\pi\) | ||||
0.0172003 | + | 0.999852i | \(0.494525\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.6569 | 0.963280 | ||||||||
\(202\) | 5.65685i | 0.398015i | ||||||||
\(203\) | 2.82843i | 0.198517i | ||||||||
\(204\) | −7.65685 | −0.536087 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.6569 | 0.812172 | ||||||||
\(207\) | 10.3431i | 0.718898i | ||||||||
\(208\) | 11.4853i | 0.796361i | ||||||||
\(209\) | 2.48528 | 0.171911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3848 | −1.33450 | −0.667252 | − | 0.744832i | \(-0.732529\pi\) | ||||
−0.667252 | + | 0.744832i | \(0.732529\pi\) | |||||||
\(212\) | 36.3137i | 2.49404i | ||||||||
\(213\) | 21.3137i | 1.46039i | ||||||||
\(214\) | −35.7990 | −2.44717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.82843 | 0.124409 | ||||||||
\(217\) | − 28.4853i | − 1.93371i | ||||||||
\(218\) | 30.5563i | 2.06954i | ||||||||
\(219\) | −9.65685 | −0.652550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.17157 | −0.213343 | ||||||||
\(222\) | 23.3137i | 1.56471i | ||||||||
\(223\) | 3.17157i | 0.212384i | 0.994346 | + | 0.106192i | \(0.0338659\pi\) | ||||
−0.994346 | + | 0.106192i | \(0.966134\pi\) | |||||||
\(224\) | 4.48528 | 0.299685 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.1421 | 2.13806 | ||||||||
\(227\) | − 8.14214i | − 0.540413i | −0.962802 | − | 0.270206i | \(-0.912908\pi\) | ||||
0.962802 | − | 0.270206i | \(-0.0870919\pi\) | |||||||
\(228\) | − 55.4558i | − 3.67265i | ||||||||
\(229\) | 3.51472 | 0.232259 | 0.116130 | − | 0.993234i | \(-0.462951\pi\) | ||||
0.116130 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | − 4.41421i | − 0.289807i | ||||||||
\(233\) | − 18.3137i | − 1.19977i | −0.800086 | − | 0.599885i | \(-0.795213\pi\) | ||||
0.800086 | − | 0.599885i | \(-0.204787\pi\) | |||||||
\(234\) | −26.1421 | −1.70896 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | − 5.82843i | − 0.378597i | ||||||||
\(238\) | − 5.65685i | − 0.366679i | ||||||||
\(239\) | 19.6569 | 1.27150 | 0.635748 | − | 0.771897i | \(-0.280692\pi\) | ||||
0.635748 | + | 0.771897i | \(0.280692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3137 | −1.17969 | −0.589845 | − | 0.807517i | \(-0.700811\pi\) | ||||
−0.589845 | + | 0.807517i | \(0.700811\pi\) | |||||||
\(242\) | 26.1421i | 1.68048i | ||||||||
\(243\) | 21.6569i | 1.38929i | ||||||||
\(244\) | 18.4853 | 1.18340 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.1421 | 1.66676 | ||||||||
\(247\) | − 22.9706i | − 1.46158i | ||||||||
\(248\) | 44.4558i | 2.82295i | ||||||||
\(249\) | −18.4853 | −1.17146 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0711 | 1.26687 | 0.633437 | − | 0.773794i | \(-0.281643\pi\) | ||||
0.633437 | + | 0.773794i | \(0.281643\pi\) | |||||||
\(252\) | − 30.6274i | − 1.92935i | ||||||||
\(253\) | 1.51472i | 0.0952295i | ||||||||
\(254\) | −10.4853 | −0.657905 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | − 18.1716i | − 1.13351i | −0.823886 | − | 0.566756i | \(-0.808198\pi\) | ||||
0.823886 | − | 0.566756i | \(-0.191802\pi\) | |||||||
\(258\) | 20.8995i | 1.30115i | ||||||||
\(259\) | −11.3137 | −0.703000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | − 51.4558i | − 3.17895i | ||||||||
\(263\) | − 2.75736i | − 0.170026i | −0.996380 | − | 0.0850130i | \(-0.972907\pi\) | ||||
0.996380 | − | 0.0850130i | \(-0.0270932\pi\) | |||||||
\(264\) | −4.41421 | −0.271676 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 40.9706 | 2.51207 | ||||||||
\(267\) | − 30.1421i | − 1.84467i | ||||||||
\(268\) | − 21.6569i | − 1.32290i | ||||||||
\(269\) | −31.4558 | −1.91790 | −0.958948 | − | 0.283581i | \(-0.908478\pi\) | ||||
−0.958948 | + | 0.283581i | \(0.908478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5563 | 1.00573 | 0.502863 | − | 0.864366i | \(-0.332280\pi\) | ||||
0.502863 | + | 0.864366i | \(0.332280\pi\) | |||||||
\(272\) | 2.48528i | 0.150692i | ||||||||
\(273\) | − 26.1421i | − 1.58219i | ||||||||
\(274\) | 28.9706 | 1.75018 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 33.7990 | 2.03446 | ||||||||
\(277\) | − 17.3137i | − 1.04028i | −0.854081 | − | 0.520140i | \(-0.825880\pi\) | ||||
0.854081 | − | 0.520140i | \(-0.174120\pi\) | |||||||
\(278\) | 33.7990i | 2.02713i | ||||||||
\(279\) | −28.4853 | −1.70537 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.9706 | 1.90720 | 0.953602 | − | 0.301070i | \(-0.0973439\pi\) | ||||
0.953602 | + | 0.301070i | \(0.0973439\pi\) | |||||||
\(282\) | 18.8995i | 1.12545i | ||||||||
\(283\) | − 11.6569i | − 0.692928i | −0.938063 | − | 0.346464i | \(-0.887382\pi\) | ||||
0.938063 | − | 0.346464i | \(-0.112618\pi\) | |||||||
\(284\) | 33.7990 | 2.00560 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.82843 | −0.226380 | ||||||||
\(287\) | 12.6863i | 0.748848i | ||||||||
\(288\) | − 4.48528i | − 0.264298i | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8284 | 0.634774 | ||||||||
\(292\) | 15.3137i | 0.896167i | ||||||||
\(293\) | − 7.65685i | − 0.447318i | −0.974667 | − | 0.223659i | \(-0.928200\pi\) | ||||
0.974667 | − | 0.223659i | \(-0.0718002\pi\) | |||||||
\(294\) | 5.82843 | 0.339921 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.6569 | 1.02628 | ||||||||
\(297\) | 0.171573i | 0.00995567i | ||||||||
\(298\) | − 18.8995i | − 1.09482i | ||||||||
\(299\) | 14.0000 | 0.809641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1421 | −0.584583 | ||||||||
\(302\) | 34.1421i | 1.96466i | ||||||||
\(303\) | 5.65685i | 0.324978i | ||||||||
\(304\) | −18.0000 | −1.03237 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.65685 | −0.323381 | ||||||||
\(307\) | 2.89949i | 0.165483i | 0.996571 | + | 0.0827415i | \(0.0263676\pi\) | ||||
−0.996571 | + | 0.0827415i | \(0.973632\pi\) | |||||||
\(308\) | − 4.48528i | − 0.255573i | ||||||||
\(309\) | 11.6569 | 0.663135 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.68629 | 0.152326 | 0.0761628 | − | 0.997095i | \(-0.475733\pi\) | ||||
0.0761628 | + | 0.997095i | \(0.475733\pi\) | |||||||
\(312\) | 40.7990i | 2.30979i | ||||||||
\(313\) | − 9.82843i | − 0.555536i | −0.960648 | − | 0.277768i | \(-0.910405\pi\) | ||||
0.960648 | − | 0.277768i | \(-0.0895946\pi\) | |||||||
\(314\) | 20.4853 | 1.15605 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.24264 | −0.519939 | ||||||||
\(317\) | − 31.4558i | − 1.76674i | −0.468680 | − | 0.883368i | \(-0.655270\pi\) | ||||
0.468680 | − | 0.883368i | \(-0.344730\pi\) | |||||||
\(318\) | 55.2843i | 3.10019i | ||||||||
\(319\) | 0.414214 | 0.0231915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.7990 | −1.99810 | ||||||||
\(322\) | 24.9706i | 1.39156i | ||||||||
\(323\) | − 4.97056i | − 0.276570i | ||||||||
\(324\) | 36.3137 | 2.01743 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.48528 | −0.525341 | ||||||||
\(327\) | 30.5563i | 1.68977i | ||||||||
\(328\) | − 19.7990i | − 1.09322i | ||||||||
\(329\) | −9.17157 | −0.505645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41421 | −0.132697 | −0.0663486 | − | 0.997797i | \(-0.521135\pi\) | ||||
−0.0663486 | + | 0.997797i | \(0.521135\pi\) | |||||||
\(332\) | 29.3137i | 1.60880i | ||||||||
\(333\) | 11.3137i | 0.619987i | ||||||||
\(334\) | −7.65685 | −0.418964 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.4853 | −1.11756 | ||||||||
\(337\) | 21.7990i | 1.18747i | 0.804662 | + | 0.593733i | \(0.202347\pi\) | ||||
−0.804662 | + | 0.593733i | \(0.797653\pi\) | |||||||
\(338\) | 4.00000i | 0.217571i | ||||||||
\(339\) | 32.1421 | 1.74572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.17157 | −0.225903 | ||||||||
\(342\) | − 40.9706i | − 2.21543i | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | 15.8284 | 0.853412 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.7990 | −1.60200 | ||||||||
\(347\) | 2.48528i | 0.133417i | 0.997773 | + | 0.0667084i | \(0.0212497\pi\) | ||||
−0.997773 | + | 0.0667084i | \(0.978750\pi\) | |||||||
\(348\) | − 9.24264i | − 0.495458i | ||||||||
\(349\) | 5.14214 | 0.275252 | 0.137626 | − | 0.990484i | \(-0.456053\pi\) | ||||
0.137626 | + | 0.990484i | \(0.456053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.58579 | 0.0846430 | ||||||||
\(352\) | − 0.656854i | − 0.0350104i | ||||||||
\(353\) | − 26.9706i | − 1.43550i | −0.696302 | − | 0.717749i | \(-0.745172\pi\) | ||||
0.696302 | − | 0.717749i | \(-0.254828\pi\) | |||||||
\(354\) | −21.3137 | −1.13281 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −47.7990 | −2.53334 | ||||||||
\(357\) | − 5.65685i | − 0.299392i | ||||||||
\(358\) | − 15.6569i | − 0.827490i | ||||||||
\(359\) | −3.92893 | −0.207361 | −0.103681 | − | 0.994611i | \(-0.533062\pi\) | ||||
−0.103681 | + | 0.994611i | \(0.533062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | − 20.0711i | − 1.05491i | ||||||||
\(363\) | 26.1421i | 1.37211i | ||||||||
\(364\) | −41.4558 | −2.17288 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 28.1421 | 1.47101 | ||||||||
\(367\) | 18.0000i | 0.939592i | 0.882775 | + | 0.469796i | \(0.155673\pi\) | ||||
−0.882775 | + | 0.469796i | \(0.844327\pi\) | |||||||
\(368\) | − 10.9706i | − 0.571880i | ||||||||
\(369\) | 12.6863 | 0.660422 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.8284 | −1.39286 | ||||||||
\(372\) | 93.0833i | 4.82614i | ||||||||
\(373\) | 26.3137i | 1.36247i | 0.732064 | + | 0.681236i | \(0.238557\pi\) | ||||
−0.732064 | + | 0.681236i | \(0.761443\pi\) | |||||||
\(374\) | −0.828427 | −0.0428369 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.3137 | 0.738173 | ||||||||
\(377\) | − 3.82843i | − 0.197174i | ||||||||
\(378\) | 2.82843i | 0.145479i | ||||||||
\(379\) | 6.97056 | 0.358054 | 0.179027 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179027 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4853 | −0.537177 | ||||||||
\(382\) | − 61.1127i | − 3.12680i | ||||||||
\(383\) | 3.51472i | 0.179594i | 0.995960 | + | 0.0897969i | \(0.0286218\pi\) | ||||
−0.995960 | + | 0.0897969i | \(0.971378\pi\) | |||||||
\(384\) | −49.6274 | −2.53254 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4853 | 0.635484 | ||||||||
\(387\) | 10.1421i | 0.515554i | ||||||||
\(388\) | − 17.1716i | − 0.871755i | ||||||||
\(389\) | −3.02944 | −0.153599 | −0.0767993 | − | 0.997047i | \(-0.524470\pi\) | ||||
−0.0767993 | + | 0.997047i | \(0.524470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.02944 | 0.153205 | ||||||||
\(392\) | − 4.41421i | − 0.222951i | ||||||||
\(393\) | − 51.4558i | − 2.59560i | ||||||||
\(394\) | 4.82843 | 0.243253 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.48528 | −0.225394 | ||||||||
\(397\) | 19.3431i | 0.970805i | 0.874291 | + | 0.485402i | \(0.161327\pi\) | ||||
−0.874291 | + | 0.485402i | \(0.838673\pi\) | |||||||
\(398\) | − 1.17157i | − 0.0587256i | ||||||||
\(399\) | 40.9706 | 2.05109 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6569 | −0.931679 | −0.465839 | − | 0.884869i | \(-0.654248\pi\) | ||||
−0.465839 | + | 0.884869i | \(0.654248\pi\) | |||||||
\(402\) | − 32.9706i | − 1.64442i | ||||||||
\(403\) | 38.5563i | 1.92063i | ||||||||
\(404\) | 8.97056 | 0.446302 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.82843 | 0.338889 | ||||||||
\(407\) | 1.65685i | 0.0821272i | ||||||||
\(408\) | 8.82843i | 0.437072i | ||||||||
\(409\) | 18.9706 | 0.938034 | 0.469017 | − | 0.883189i | \(-0.344608\pi\) | ||||
0.469017 | + | 0.883189i | \(0.344608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.9706 | 1.42901 | ||||||||
\(412\) | − 18.4853i | − 0.910704i | ||||||||
\(413\) | − 10.3431i | − 0.508953i | ||||||||
\(414\) | 24.9706 | 1.22724 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.07107 | −0.297659 | ||||||||
\(417\) | 33.7990i | 1.65514i | ||||||||
\(418\) | − 6.00000i | − 0.293470i | ||||||||
\(419\) | 9.51472 | 0.464824 | 0.232412 | − | 0.972617i | \(-0.425338\pi\) | ||||
0.232412 | + | 0.972617i | \(0.425338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.1127 | 1.80876 | 0.904381 | − | 0.426726i | \(-0.140333\pi\) | ||||
0.904381 | + | 0.426726i | \(0.140333\pi\) | |||||||
\(422\) | 46.7990i | 2.27814i | ||||||||
\(423\) | 9.17157i | 0.445937i | ||||||||
\(424\) | 41.8701 | 2.03339 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 51.4558 | 2.49304 | ||||||||
\(427\) | 13.6569i | 0.660901i | ||||||||
\(428\) | 56.7696i | 2.74406i | ||||||||
\(429\) | −3.82843 | −0.184838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6569 | 0.946837 | 0.473419 | − | 0.880838i | \(-0.343020\pi\) | ||||
0.473419 | + | 0.880838i | \(0.343020\pi\) | |||||||
\(432\) | − 1.24264i | − 0.0597866i | ||||||||
\(433\) | − 30.6274i | − 1.47186i | −0.677058 | − | 0.735930i | \(-0.736745\pi\) | ||||
0.677058 | − | 0.735930i | \(-0.263255\pi\) | |||||||
\(434\) | −68.7696 | −3.30104 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 48.4558 | 2.32061 | ||||||||
\(437\) | 21.9411i | 1.04959i | ||||||||
\(438\) | 23.3137i | 1.11397i | ||||||||
\(439\) | 0.343146 | 0.0163775 | 0.00818873 | − | 0.999966i | \(-0.497393\pi\) | ||||
0.00818873 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82843 | 0.134687 | ||||||||
\(442\) | 7.65685i | 0.364199i | ||||||||
\(443\) | 24.3431i | 1.15658i | 0.815832 | + | 0.578289i | \(0.196279\pi\) | ||||
−0.815832 | + | 0.578289i | \(0.803721\pi\) | |||||||
\(444\) | 36.9706 | 1.75455 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.65685 | 0.362563 | ||||||||
\(447\) | − 18.8995i | − 0.893915i | ||||||||
\(448\) | − 27.7990i | − 1.31338i | ||||||||
\(449\) | 34.9706 | 1.65036 | 0.825181 | − | 0.564868i | \(-0.191073\pi\) | ||||
0.825181 | + | 0.564868i | \(0.191073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85786 | 0.0874834 | ||||||||
\(452\) | − 50.9706i | − 2.39745i | ||||||||
\(453\) | 34.1421i | 1.60414i | ||||||||
\(454\) | −19.6569 | −0.922542 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −63.9411 | −2.99432 | ||||||||
\(457\) | 1.02944i | 0.0481550i | 0.999710 | + | 0.0240775i | \(0.00766485\pi\) | ||||
−0.999710 | + | 0.0240775i | \(0.992335\pi\) | |||||||
\(458\) | − 8.48528i | − 0.396491i | ||||||||
\(459\) | 0.343146 | 0.0160167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | − 6.82843i | − 0.317687i | ||||||||
\(463\) | 26.0000i | 1.20832i | 0.796862 | + | 0.604161i | \(0.206492\pi\) | ||||
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.2132 | −2.04814 | ||||||||
\(467\) | − 38.3553i | − 1.77487i | −0.460930 | − | 0.887437i | \(-0.652484\pi\) | ||||
0.460930 | − | 0.887437i | \(-0.347516\pi\) | |||||||
\(468\) | 41.4558i | 1.91630i | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.4853 | 0.943912 | ||||||||
\(472\) | 16.1421i | 0.743002i | ||||||||
\(473\) | 1.48528i | 0.0682933i | ||||||||
\(474\) | −14.0711 | −0.646306 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.97056 | −0.411165 | ||||||||
\(477\) | 26.8284i | 1.22839i | ||||||||
\(478\) | − 47.4558i | − 2.17058i | ||||||||
\(479\) | −6.89949 | −0.315246 | −0.157623 | − | 0.987499i | \(-0.550383\pi\) | ||||
−0.157623 | + | 0.987499i | \(0.550383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.3137 | 0.698245 | ||||||||
\(482\) | 44.2132i | 2.01386i | ||||||||
\(483\) | 24.9706i | 1.13620i | ||||||||
\(484\) | 41.4558 | 1.88436 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 52.2843 | 2.37166 | ||||||||
\(487\) | − 11.5147i | − 0.521782i | −0.965368 | − | 0.260891i | \(-0.915984\pi\) | ||||
0.965368 | − | 0.260891i | \(-0.0840163\pi\) | |||||||
\(488\) | − 21.3137i | − 0.964826i | ||||||||
\(489\) | −9.48528 | −0.428939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2426 | −0.958667 | −0.479333 | − | 0.877633i | \(-0.659122\pi\) | ||||
−0.479333 | + | 0.877633i | \(0.659122\pi\) | |||||||
\(492\) | − 41.4558i | − 1.86897i | ||||||||
\(493\) | − 0.828427i | − 0.0373105i | ||||||||
\(494\) | −55.4558 | −2.49508 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.2132 | 1.35661 | ||||||||
\(497\) | 24.9706i | 1.12008i | ||||||||
\(498\) | 44.6274i | 1.99980i | ||||||||
\(499\) | −18.9706 | −0.849239 | −0.424620 | − | 0.905372i | \(-0.639592\pi\) | ||||
−0.424620 | + | 0.905372i | \(0.639592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.65685 | −0.342083 | ||||||||
\(502\) | − 48.4558i | − 2.16269i | ||||||||
\(503\) | − 0.272078i | − 0.0121314i | −0.999982 | − | 0.00606568i | \(-0.998069\pi\) | ||||
0.999982 | − | 0.00606568i | \(-0.00193078\pi\) | |||||||
\(504\) | −35.3137 | −1.57300 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.65685 | 0.162567 | ||||||||
\(507\) | 4.00000i | 0.177646i | ||||||||
\(508\) | 16.6274i | 0.737722i | ||||||||
\(509\) | 10.5147 | 0.466057 | 0.233028 | − | 0.972470i | \(-0.425137\pi\) | ||||
0.233028 | + | 0.972470i | \(0.425137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3137 | −0.500489 | ||||||||
\(512\) | 31.2426i | 1.38074i | ||||||||
\(513\) | 2.48528i | 0.109728i | ||||||||
\(514\) | −43.8701 | −1.93503 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33.1421 | 1.45900 | ||||||||
\(517\) | 1.34315i | 0.0590715i | ||||||||
\(518\) | 27.3137i | 1.20010i | ||||||||
\(519\) | −29.7990 | −1.30803 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.1421 | −1.27674 | −0.638370 | − | 0.769730i | \(-0.720391\pi\) | ||||
−0.638370 | + | 0.769730i | \(0.720391\pi\) | |||||||
\(522\) | − 6.82843i | − 0.298872i | ||||||||
\(523\) | − 4.68629i | − 0.204917i | −0.994737 | − | 0.102459i | \(-0.967329\pi\) | ||||
0.994737 | − | 0.102459i | \(-0.0326709\pi\) | |||||||
\(524\) | −81.5980 | −3.56462 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.65685 | −0.290253 | ||||||||
\(527\) | 8.34315i | 0.363433i | ||||||||
\(528\) | 3.00000i | 0.130558i | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3431 | −0.448854 | ||||||||
\(532\) | − 64.9706i | − 2.81683i | ||||||||
\(533\) | − 17.1716i | − 0.743783i | ||||||||
\(534\) | −72.7696 | −3.14905 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.9706 | −1.07856 | ||||||||
\(537\) | − 15.6569i | − 0.675643i | ||||||||
\(538\) | 75.9411i | 3.27405i | ||||||||
\(539\) | 0.414214 | 0.0178414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3431 | −0.444687 | −0.222343 | − | 0.974968i | \(-0.571371\pi\) | ||||
−0.222343 | + | 0.974968i | \(0.571371\pi\) | |||||||
\(542\) | − 39.9706i | − 1.71688i | ||||||||
\(543\) | − 20.0711i | − 0.861332i | ||||||||
\(544\) | −1.31371 | −0.0563248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −63.1127 | −2.70097 | ||||||||
\(547\) | 35.7990i | 1.53065i | 0.643641 | + | 0.765327i | \(0.277423\pi\) | ||||
−0.643641 | + | 0.765327i | \(0.722577\pi\) | |||||||
\(548\) | − 45.9411i | − 1.96251i | ||||||||
\(549\) | 13.6569 | 0.582860 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | − 38.9706i | − 1.65870i | ||||||||
\(553\) | − 6.82843i | − 0.290374i | ||||||||
\(554\) | −41.7990 | −1.77587 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 53.5980 | 2.27306 | ||||||||
\(557\) | − 17.3137i | − 0.733605i | −0.930299 | − | 0.366803i | \(-0.880452\pi\) | ||||
0.930299 | − | 0.366803i | \(-0.119548\pi\) | |||||||
\(558\) | 68.7696i | 2.91125i | ||||||||
\(559\) | 13.7279 | 0.580629 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.828427 | −0.0349762 | ||||||||
\(562\) | − 77.1838i | − 3.25580i | ||||||||
\(563\) | 0.757359i | 0.0319189i | 0.999873 | + | 0.0159594i | \(0.00508026\pi\) | ||||
−0.999873 | + | 0.0159594i | \(0.994920\pi\) | |||||||
\(564\) | 29.9706 | 1.26199 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.1421 | −1.18290 | ||||||||
\(567\) | 26.8284i | 1.12669i | ||||||||
\(568\) | − 38.9706i | − 1.63517i | ||||||||
\(569\) | 39.6569 | 1.66250 | 0.831251 | − | 0.555897i | \(-0.187625\pi\) | ||||
0.831251 | + | 0.555897i | \(0.187625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6274 | 0.612138 | 0.306069 | − | 0.952009i | \(-0.400986\pi\) | ||||
0.306069 | + | 0.952009i | \(0.400986\pi\) | |||||||
\(572\) | 6.07107i | 0.253844i | ||||||||
\(573\) | − 61.1127i | − 2.55302i | ||||||||
\(574\) | 30.6274 | 1.27836 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −27.7990 | −1.15829 | ||||||||
\(577\) | − 29.7990i | − 1.24055i | −0.784385 | − | 0.620274i | \(-0.787021\pi\) | ||||
0.784385 | − | 0.620274i | \(-0.212979\pi\) | |||||||
\(578\) | − 39.3848i | − 1.63819i | ||||||||
\(579\) | 12.4853 | 0.518871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6569 | −0.898478 | ||||||||
\(582\) | − 26.1421i | − 1.08363i | ||||||||
\(583\) | 3.92893i | 0.162720i | ||||||||
\(584\) | 17.6569 | 0.730646 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.4853 | −0.763620 | ||||||||
\(587\) | 7.65685i | 0.316032i | 0.987437 | + | 0.158016i | \(0.0505098\pi\) | ||||
−0.987437 | + | 0.158016i | \(0.949490\pi\) | |||||||
\(588\) | − 9.24264i | − 0.381160i | ||||||||
\(589\) | −60.4264 | −2.48983 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.82843 | 0.198615 | ||||||||
\(592\) | − 12.0000i | − 0.493197i | ||||||||
\(593\) | 19.4853i | 0.800165i | 0.916479 | + | 0.400082i | \(0.131018\pi\) | ||||
−0.916479 | + | 0.400082i | \(0.868982\pi\) | |||||||
\(594\) | 0.414214 | 0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.9706 | −1.22764 | ||||||||
\(597\) | − 1.17157i | − 0.0479493i | ||||||||
\(598\) | − 33.7990i | − 1.38214i | ||||||||
\(599\) | −9.87006 | −0.403280 | −0.201640 | − | 0.979460i | \(-0.564627\pi\) | ||||
−0.201640 | + | 0.979460i | \(0.564627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1716 | −0.700443 | −0.350222 | − | 0.936667i | \(-0.613894\pi\) | ||||
−0.350222 | + | 0.936667i | \(0.613894\pi\) | |||||||
\(602\) | 24.4853i | 0.997946i | ||||||||
\(603\) | − 16.0000i | − 0.651570i | ||||||||
\(604\) | 54.1421 | 2.20301 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.6569 | 0.554772 | ||||||||
\(607\) | − 7.72792i | − 0.313667i | −0.987625 | − | 0.156833i | \(-0.949871\pi\) | ||||
0.987625 | − | 0.156833i | \(-0.0501286\pi\) | |||||||
\(608\) | − 9.51472i | − 0.385873i | ||||||||
\(609\) | 6.82843 | 0.276702 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4142 | 0.502225 | ||||||||
\(612\) | 8.97056i | 0.362614i | ||||||||
\(613\) | 9.00000i | 0.363507i | 0.983344 | + | 0.181753i | \(0.0581772\pi\) | ||||
−0.983344 | + | 0.181753i | \(0.941823\pi\) | |||||||
\(614\) | 7.00000 | 0.282497 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.17157 | −0.208369 | ||||||||
\(617\) | 0.686292i | 0.0276291i | 0.999905 | + | 0.0138145i | \(0.00439744\pi\) | ||||
−0.999905 | + | 0.0138145i | \(0.995603\pi\) | |||||||
\(618\) | − 28.1421i | − 1.13204i | ||||||||
\(619\) | −33.5858 | −1.34993 | −0.674963 | − | 0.737851i | \(-0.735841\pi\) | ||||
−0.674963 | + | 0.737851i | \(0.735841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51472 | −0.0607836 | ||||||||
\(622\) | − 6.48528i | − 0.260036i | ||||||||
\(623\) | − 35.3137i | − 1.41481i | ||||||||
\(624\) | 27.7279 | 1.11001 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.7279 | −0.948358 | ||||||||
\(627\) | − 6.00000i | − 0.239617i | ||||||||
\(628\) | − 32.4853i | − 1.29630i | ||||||||
\(629\) | 3.31371 | 0.132126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.8284 | −1.46612 | −0.733058 | − | 0.680166i | \(-0.761908\pi\) | ||||
−0.733058 | + | 0.680166i | \(0.761908\pi\) | |||||||
\(632\) | 10.6569i | 0.423907i | ||||||||
\(633\) | 46.7990i | 1.86009i | ||||||||
\(634\) | −75.9411 | −3.01601 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 87.6690 | 3.47630 | ||||||||
\(637\) | − 3.82843i | − 0.151688i | ||||||||
\(638\) | − 1.00000i | − 0.0395904i | ||||||||
\(639\) | 24.9706 | 0.987820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7990 | 0.703018 | 0.351509 | − | 0.936185i | \(-0.385669\pi\) | ||||
0.351509 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(642\) | 86.4264i | 3.41098i | ||||||||
\(643\) | − 32.4853i | − 1.28109i | −0.767919 | − | 0.640547i | \(-0.778708\pi\) | ||||
0.767919 | − | 0.640547i | \(-0.221292\pi\) | |||||||
\(644\) | 39.5980 | 1.56038 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 39.6569i | 1.55907i | 0.626358 | + | 0.779536i | \(0.284545\pi\) | ||||
−0.626358 | + | 0.779536i | \(0.715455\pi\) | |||||||
\(648\) | − 41.8701i | − 1.64481i | ||||||||
\(649\) | −1.51472 | −0.0594579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −68.7696 | −2.69529 | ||||||||
\(652\) | 15.0416i | 0.589076i | ||||||||
\(653\) | 30.1421i | 1.17955i | 0.807567 | + | 0.589776i | \(0.200784\pi\) | ||||
−0.807567 | + | 0.589776i | \(0.799216\pi\) | |||||||
\(654\) | 73.7696 | 2.88462 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.4558 | −0.525362 | ||||||||
\(657\) | 11.3137i | 0.441390i | ||||||||
\(658\) | 22.1421i | 0.863190i | ||||||||
\(659\) | −14.4142 | −0.561498 | −0.280749 | − | 0.959781i | \(-0.590583\pi\) | ||||
−0.280749 | + | 0.959781i | \(0.590583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.3137 | 1.29575 | 0.647877 | − | 0.761745i | \(-0.275657\pi\) | ||||
0.647877 | + | 0.761745i | \(0.275657\pi\) | |||||||
\(662\) | 5.82843i | 0.226528i | ||||||||
\(663\) | 7.65685i | 0.297368i | ||||||||
\(664\) | 33.7990 | 1.31166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.3137 | 1.05838 | ||||||||
\(667\) | 3.65685i | 0.141594i | ||||||||
\(668\) | 12.1421i | 0.469793i | ||||||||
\(669\) | 7.65685 | 0.296031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | − 10.8284i | − 0.417716i | ||||||||
\(673\) | 21.6274i | 0.833676i | 0.908981 | + | 0.416838i | \(0.136862\pi\) | ||||
−0.908981 | + | 0.416838i | \(0.863138\pi\) | |||||||
\(674\) | 52.6274 | 2.02713 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.34315 | 0.243967 | ||||||||
\(677\) | − 22.0000i | − 0.845529i | −0.906240 | − | 0.422764i | \(-0.861060\pi\) | ||||
0.906240 | − | 0.422764i | \(-0.138940\pi\) | |||||||
\(678\) | − 77.5980i | − 2.98013i | ||||||||
\(679\) | 12.6863 | 0.486855 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.6569 | −0.753252 | ||||||||
\(682\) | 10.0711i | 0.385641i | ||||||||
\(683\) | − 20.9706i | − 0.802416i | −0.915987 | − | 0.401208i | \(-0.868590\pi\) | ||||
0.915987 | − | 0.401208i | \(-0.131410\pi\) | |||||||
\(684\) | −64.9706 | −2.48421 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −40.9706 | −1.56426 | ||||||||
\(687\) | − 8.48528i | − 0.323734i | ||||||||
\(688\) | − 10.7574i | − 0.410120i | ||||||||
\(689\) | 36.3137 | 1.38344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.0000 | 1.82601 | 0.913003 | − | 0.407953i | \(-0.133757\pi\) | ||||
0.913003 | + | 0.407953i | \(0.133757\pi\) | |||||||
\(692\) | 47.2548i | 1.79636i | ||||||||
\(693\) | − 3.31371i | − 0.125877i | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.6569 | −0.403947 | ||||||||
\(697\) | − 3.71573i | − 0.140743i | ||||||||
\(698\) | − 12.4142i | − 0.469885i | ||||||||
\(699\) | −44.2132 | −1.67230 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.1127 | −1.51504 | −0.757518 | − | 0.652814i | \(-0.773588\pi\) | ||||
−0.757518 | + | 0.652814i | \(0.773588\pi\) | |||||||
\(702\) | − 3.82843i | − 0.144495i | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | −4.07107 | −0.153434 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −65.1127 | −2.45055 | ||||||||
\(707\) | 6.62742i | 0.249250i | ||||||||
\(708\) | 33.7990i | 1.27024i | ||||||||
\(709\) | −29.1421 | −1.09446 | −0.547228 | − | 0.836984i | \(-0.684317\pi\) | ||||
−0.547228 | + | 0.836984i | \(0.684317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.82843 | −0.256086 | ||||||||
\(712\) | 55.1127i | 2.06544i | ||||||||
\(713\) | − 36.8284i | − 1.37924i | ||||||||
\(714\) | −13.6569 | −0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.8284 | −0.927882 | ||||||||
\(717\) | − 47.4558i | − 1.77227i | ||||||||
\(718\) | 9.48528i | 0.353988i | ||||||||
\(719\) | 20.1421 | 0.751175 | 0.375587 | − | 0.926787i | \(-0.377441\pi\) | ||||
0.375587 | + | 0.926787i | \(0.377441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6569 | 0.508608 | ||||||||
\(722\) | − 41.0416i | − 1.52741i | ||||||||
\(723\) | 44.2132i | 1.64431i | ||||||||
\(724\) | −31.8284 | −1.18289 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 63.1127 | 2.34233 | ||||||||
\(727\) | 1.31371i | 0.0487228i | 0.999703 | + | 0.0243614i | \(0.00775523\pi\) | ||||
−0.999703 | + | 0.0243614i | \(0.992245\pi\) | |||||||
\(728\) | 47.7990i | 1.77155i | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.97056 | 0.109870 | ||||||||
\(732\) | − 44.6274i | − 1.64948i | ||||||||
\(733\) | 41.2548i | 1.52378i | 0.647705 | + | 0.761891i | \(0.275729\pi\) | ||||
−0.647705 | + | 0.761891i | \(0.724271\pi\) | |||||||
\(734\) | 43.4558 | 1.60398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.79899 | 0.213754 | ||||||||
\(737\) | − 2.34315i | − 0.0863109i | ||||||||
\(738\) | − 30.6274i | − 1.12741i | ||||||||
\(739\) | −4.07107 | −0.149757 | −0.0748783 | − | 0.997193i | \(-0.523857\pi\) | ||||
−0.0748783 | + | 0.997193i | \(0.523857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −55.4558 | −2.03722 | ||||||||
\(742\) | 64.7696i | 2.37777i | ||||||||
\(743\) | − 23.6569i | − 0.867886i | −0.900940 | − | 0.433943i | \(-0.857122\pi\) | ||||
0.900940 | − | 0.433943i | \(-0.142878\pi\) | |||||||
\(744\) | 107.326 | 3.93476 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 63.5269 | 2.32589 | ||||||||
\(747\) | 21.6569i | 0.792383i | ||||||||
\(748\) | 1.31371i | 0.0480339i | ||||||||
\(749\) | −41.9411 | −1.53250 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3137 | 0.923710 | 0.461855 | − | 0.886955i | \(-0.347184\pi\) | ||||
0.461855 | + | 0.886955i | \(0.347184\pi\) | |||||||
\(752\) | − 9.72792i | − 0.354741i | ||||||||
\(753\) | − 48.4558i | − 1.76583i | ||||||||
\(754\) | −9.24264 | −0.336597 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.48528 | 0.163128 | ||||||||
\(757\) | 25.5147i | 0.927348i | 0.886006 | + | 0.463674i | \(0.153469\pi\) | ||||
−0.886006 | + | 0.463674i | \(0.846531\pi\) | |||||||
\(758\) | − 16.8284i | − 0.611236i | ||||||||
\(759\) | 3.65685 | 0.132735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.5980 | 1.65293 | 0.826463 | − | 0.562991i | \(-0.190350\pi\) | ||||
0.826463 | + | 0.562991i | \(0.190350\pi\) | |||||||
\(762\) | 25.3137i | 0.917019i | ||||||||
\(763\) | 35.7990i | 1.29601i | ||||||||
\(764\) | −96.9117 | −3.50614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.48528 | 0.306586 | ||||||||
\(767\) | 14.0000i | 0.505511i | ||||||||
\(768\) | 72.3553i | 2.61090i | ||||||||
\(769\) | 49.1127 | 1.77105 | 0.885525 | − | 0.464592i | \(-0.153799\pi\) | ||||
0.885525 | + | 0.464592i | \(0.153799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.8701 | −1.57994 | ||||||||
\(772\) | − 19.7990i | − 0.712581i | ||||||||
\(773\) | 19.5147i | 0.701896i | 0.936395 | + | 0.350948i | \(0.114141\pi\) | ||||
−0.936395 | + | 0.350948i | \(0.885859\pi\) | |||||||
\(774\) | 24.4853 | 0.880105 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | 27.3137i | 0.979874i | ||||||||
\(778\) | 7.31371i | 0.262209i | ||||||||
\(779\) | 26.9117 | 0.964211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.65685 | 0.130853 | ||||||||
\(782\) | − 7.31371i | − 0.261538i | ||||||||
\(783\) | 0.414214i | 0.0148028i | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −124.225 | −4.43097 | ||||||||
\(787\) | − 54.0833i | − 1.92786i | −0.266156 | − | 0.963930i | \(-0.585754\pi\) | ||||
0.266156 | − | 0.963930i | \(-0.414246\pi\) | |||||||
\(788\) | − 7.65685i | − 0.272764i | ||||||||
\(789\) | −6.65685 | −0.236990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.6569 | 1.33892 | ||||||||
\(792\) | 5.17157i | 0.183764i | ||||||||
\(793\) | − 18.4853i | − 0.656432i | ||||||||
\(794\) | 46.6985 | 1.65727 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.85786 | −0.0658503 | ||||||||
\(797\) | 51.7401i | 1.83273i | 0.400345 | + | 0.916364i | \(0.368890\pi\) | ||||
−0.400345 | + | 0.916364i | \(0.631110\pi\) | |||||||
\(798\) | − 98.9117i | − 3.50144i | ||||||||
\(799\) | 2.68629 | 0.0950342 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.3137 | −1.24775 | ||||||||
\(802\) | 45.0416i | 1.59048i | ||||||||
\(803\) | 1.65685i | 0.0584691i | ||||||||
\(804\) | −52.2843 | −1.84392 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 93.0833 | 3.27872 | ||||||||
\(807\) | 75.9411i | 2.67325i | ||||||||
\(808\) | − 10.3431i | − 0.363871i | ||||||||
\(809\) | −36.2843 | −1.27569 | −0.637844 | − | 0.770166i | \(-0.720173\pi\) | ||||
−0.637844 | + | 0.770166i | \(0.720173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8284 | 0.380238 | 0.190119 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190119 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(812\) | − 10.8284i | − 0.380003i | ||||||||
\(813\) | − 39.9706i | − 1.40183i | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.00000 | 0.210042 | ||||||||
\(817\) | 21.5147i | 0.752705i | ||||||||
\(818\) | − 45.7990i | − 1.60132i | ||||||||
\(819\) | −30.6274 | −1.07021 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48528 | −0.0518367 | −0.0259183 | − | 0.999664i | \(-0.508251\pi\) | ||||
−0.0259183 | + | 0.999664i | \(0.508251\pi\) | |||||||
\(822\) | − 69.9411i | − 2.43948i | ||||||||
\(823\) | 54.2843i | 1.89223i | 0.323830 | + | 0.946115i | \(0.395029\pi\) | ||||
−0.323830 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(824\) | −21.3137 | −0.742498 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.9706 | −0.868837 | ||||||||
\(827\) | 32.8995i | 1.14403i | 0.820244 | + | 0.572014i | \(0.193838\pi\) | ||||
−0.820244 | + | 0.572014i | \(0.806162\pi\) | |||||||
\(828\) | − 39.5980i | − 1.37612i | ||||||||
\(829\) | 29.7990 | 1.03496 | 0.517481 | − | 0.855695i | \(-0.326870\pi\) | ||||
0.517481 | + | 0.855695i | \(0.326870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −41.7990 | −1.44999 | ||||||||
\(832\) | 37.6274i | 1.30450i | ||||||||
\(833\) | − 0.828427i | − 0.0287033i | ||||||||
\(834\) | 81.5980 | 2.82551 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.51472 | −0.329073 | ||||||||
\(837\) | − 4.17157i | − 0.144191i | ||||||||
\(838\) | − 22.9706i | − 0.793505i | ||||||||
\(839\) | 7.92893 | 0.273737 | 0.136869 | − | 0.990589i | \(-0.456296\pi\) | ||||
0.136869 | + | 0.990589i | \(0.456296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − 89.5980i | − 3.08775i | ||||||||
\(843\) | − 77.1838i | − 2.65835i | ||||||||
\(844\) | 74.2132 | 2.55452 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.1421 | 0.761262 | ||||||||
\(847\) | 30.6274i | 1.05237i | ||||||||
\(848\) | − 28.4558i | − 0.977178i | ||||||||
\(849\) | −28.1421 | −0.965836 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6274 | −0.501421 | ||||||||
\(852\) | − 81.5980i | − 2.79550i | ||||||||
\(853\) | 22.9706i | 0.786497i | 0.919432 | + | 0.393249i | \(0.128649\pi\) | ||||
−0.919432 | + | 0.393249i | \(0.871351\pi\) | |||||||
\(854\) | 32.9706 | 1.12823 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 65.4558 | 2.23723 | ||||||||
\(857\) | − 6.17157i | − 0.210817i | −0.994429 | − | 0.105408i | \(-0.966385\pi\) | ||||
0.994429 | − | 0.105408i | \(-0.0336150\pi\) | |||||||
\(858\) | 9.24264i | 0.315539i | ||||||||
\(859\) | −19.7279 | −0.673108 | −0.336554 | − | 0.941664i | \(-0.609261\pi\) | ||||
−0.336554 | + | 0.941664i | \(0.609261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.6274 | 1.04378 | ||||||||
\(862\) | − 47.4558i | − 1.61635i | ||||||||
\(863\) | − 17.1127i | − 0.582523i | −0.956643 | − | 0.291262i | \(-0.905925\pi\) | ||||
0.956643 | − | 0.291262i | \(-0.0940750\pi\) | |||||||
\(864\) | 0.656854 | 0.0223466 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −73.9411 | −2.51262 | ||||||||
\(867\) | − 39.3848i | − 1.33758i | ||||||||
\(868\) | 109.054i | 3.70153i | ||||||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6569 | −0.733815 | ||||||||
\(872\) | − 55.8701i | − 1.89200i | ||||||||
\(873\) | − 12.6863i | − 0.429366i | ||||||||
\(874\) | 52.9706 | 1.79176 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 36.9706 | 1.24912 | ||||||||
\(877\) | − 37.1421i | − 1.25420i | −0.778938 | − | 0.627100i | \(-0.784242\pi\) | ||||
0.778938 | − | 0.627100i | \(-0.215758\pi\) | |||||||
\(878\) | − 0.828427i | − 0.0279581i | ||||||||
\(879\) | −18.4853 | −0.623493 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0000 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(882\) | − 6.82843i | − 0.229925i | ||||||||
\(883\) | − 38.4264i | − 1.29315i | −0.762850 | − | 0.646576i | \(-0.776200\pi\) | ||||
0.762850 | − | 0.646576i | \(-0.223800\pi\) | |||||||
\(884\) | 12.1421 | 0.408384 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 58.7696 | 1.97440 | ||||||||
\(887\) | 17.1005i | 0.574179i | 0.957904 | + | 0.287089i | \(0.0926877\pi\) | ||||
−0.957904 | + | 0.287089i | \(0.907312\pi\) | |||||||
\(888\) | − 42.6274i | − 1.43048i | ||||||||
\(889\) | −12.2843 | −0.412001 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.92893 | 0.131624 | ||||||||
\(892\) | − 12.1421i | − 0.406549i | ||||||||
\(893\) | 19.4558i | 0.651065i | ||||||||
\(894\) | −45.6274 | −1.52601 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −58.1421 | −1.94239 | ||||||||
\(897\) | − 33.7990i | − 1.12852i | ||||||||
\(898\) | − 84.4264i | − 2.81735i | ||||||||
\(899\) | −10.0711 | −0.335889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.85786 | 0.261783 | ||||||||
\(902\) | − 4.48528i | − 0.149344i | ||||||||
\(903\) | 24.4853i | 0.814819i | ||||||||
\(904\) | −58.7696 | −1.95465 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 82.4264 | 2.73843 | ||||||||
\(907\) | 22.2843i | 0.739937i | 0.929044 | + | 0.369969i | \(0.120632\pi\) | ||||
−0.929044 | + | 0.369969i | \(0.879368\pi\) | |||||||
\(908\) | 31.1716i | 1.03446i | ||||||||
\(909\) | 6.62742 | 0.219818 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4437 | −0.511671 | −0.255835 | − | 0.966720i | \(-0.582351\pi\) | ||||
−0.255835 | + | 0.966720i | \(0.582351\pi\) | |||||||
\(912\) | 43.4558i | 1.43897i | ||||||||
\(913\) | 3.17157i | 0.104964i | ||||||||
\(914\) | 2.48528 | 0.0822058 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.4558 | −0.444594 | ||||||||
\(917\) | − 60.2843i | − 1.99076i | ||||||||
\(918\) | − 0.828427i | − 0.0273422i | ||||||||
\(919\) | −8.14214 | −0.268584 | −0.134292 | − | 0.990942i | \(-0.542876\pi\) | ||||
−0.134292 | + | 0.990942i | \(0.542876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.00000 | 0.230658 | ||||||||
\(922\) | − 33.7990i | − 1.11311i | ||||||||
\(923\) | − 33.7990i | − 1.11251i | ||||||||
\(924\) | −10.8284 | −0.356229 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 62.7696 | 2.06274 | ||||||||
\(927\) | − 13.6569i | − 0.448550i | ||||||||
\(928\) | − 1.58579i | − 0.0520560i | ||||||||
\(929\) | −18.6863 | −0.613077 | −0.306539 | − | 0.951858i | \(-0.599171\pi\) | ||||
−0.306539 | + | 0.951858i | \(0.599171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 70.1127i | 2.29662i | ||||||||
\(933\) | − 6.48528i | − 0.212319i | ||||||||
\(934\) | −92.5980 | −3.02990 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 47.7990 | 1.56236 | ||||||||
\(937\) | − 16.6274i | − 0.543194i | −0.962411 | − | 0.271597i | \(-0.912448\pi\) | ||||
0.962411 | − | 0.271597i | \(-0.0875518\pi\) | |||||||
\(938\) | − 38.6274i | − 1.26123i | ||||||||
\(939\) | −23.7279 | −0.774331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.5980 | −1.84504 | −0.922521 | − | 0.385948i | \(-0.873875\pi\) | ||||
−0.922521 | + | 0.385948i | \(0.873875\pi\) | |||||||
\(942\) | − 49.4558i | − 1.61136i | ||||||||
\(943\) | 16.4020i | 0.534123i | ||||||||
\(944\) | 10.9706 | 0.357061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.58579 | 0.116584 | ||||||||
\(947\) | 2.61522i | 0.0849834i | 0.999097 | + | 0.0424917i | \(0.0135296\pi\) | ||||
−0.999097 | + | 0.0424917i | \(0.986470\pi\) | |||||||
\(948\) | 22.3137i | 0.724716i | ||||||||
\(949\) | 15.3137 | 0.497104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −75.9411 | −2.46256 | ||||||||
\(952\) | 10.3431i | 0.335223i | ||||||||
\(953\) | 35.6274i | 1.15409i | 0.816714 | + | 0.577043i | \(0.195793\pi\) | ||||
−0.816714 | + | 0.577043i | \(0.804207\pi\) | |||||||
\(954\) | 64.7696 | 2.09699 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −75.2548 | −2.43392 | ||||||||
\(957\) | − 1.00000i | − 0.0323254i | ||||||||
\(958\) | 16.6569i | 0.538159i | ||||||||
\(959\) | 33.9411 | 1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.4264 | 2.27182 | ||||||||
\(962\) | − 36.9706i | − 1.19198i | ||||||||
\(963\) | 41.9411i | 1.35153i | ||||||||
\(964\) | 70.1127 | 2.25818 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 60.2843 | 1.93961 | ||||||||
\(967\) | − 35.2426i | − 1.13333i | −0.823949 | − | 0.566663i | \(-0.808234\pi\) | ||||
0.823949 | − | 0.566663i | \(-0.191766\pi\) | |||||||
\(968\) | − 47.7990i | − 1.53632i | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6569 | −0.502452 | −0.251226 | − | 0.967928i | \(-0.580834\pi\) | ||||
−0.251226 | + | 0.967928i | \(0.580834\pi\) | |||||||
\(972\) | − 82.9117i | − 2.65939i | ||||||||
\(973\) | 39.5980i | 1.26945i | ||||||||
\(974\) | −27.7990 | −0.890737 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.4853 | −0.463663 | ||||||||
\(977\) | 36.1716i | 1.15723i | 0.815600 | + | 0.578616i | \(0.196407\pi\) | ||||
−0.815600 | + | 0.578616i | \(0.803593\pi\) | |||||||
\(978\) | 22.8995i | 0.732245i | ||||||||
\(979\) | −5.17157 | −0.165284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.7990 | 1.14297 | ||||||||
\(982\) | 51.2843i | 1.63655i | ||||||||
\(983\) | 21.8701i | 0.697547i | 0.937207 | + | 0.348773i | \(0.113402\pi\) | ||||
−0.937207 | + | 0.348773i | \(0.886598\pi\) | |||||||
\(984\) | −47.7990 | −1.52378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.00000 | −0.0636930 | ||||||||
\(987\) | 22.1421i | 0.704792i | ||||||||
\(988\) | 87.9411i | 2.79778i | ||||||||
\(989\) | −13.1127 | −0.416960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.8284 | −0.407508 | −0.203754 | − | 0.979022i | \(-0.565314\pi\) | ||||
−0.203754 | + | 0.979022i | \(0.565314\pi\) | |||||||
\(992\) | 15.9706i | 0.507066i | ||||||||
\(993\) | 5.82843i | 0.184960i | ||||||||
\(994\) | 60.2843 | 1.91210 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 70.7696 | 2.24242 | ||||||||
\(997\) | 28.2843i | 0.895772i | 0.894091 | + | 0.447886i | \(0.147823\pi\) | ||||
−0.894091 | + | 0.447886i | \(0.852177\pi\) | |||||||
\(998\) | 45.7990i | 1.44974i | ||||||||
\(999\) | −1.65685 | −0.0524205 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))