Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 214.4 | ||
Root | \(1.29589 - 0.748185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.214 |
Dual form | 441.2.h.g.373.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.239123 | 0.169086 | 0.0845428 | − | 0.996420i | \(-0.473057\pi\) | ||||
0.0845428 | + | 0.996420i | \(0.473057\pi\) | |||||||
\(3\) | 1.70316 | − | 0.315036i | 0.983320 | − | 0.181886i | ||||
\(4\) | −1.94282 | −0.971410 | ||||||||
\(5\) | 1.29589 | − | 2.24456i | 0.579542 | − | 1.00380i | −0.415990 | − | 0.909369i | \(-0.636565\pi\) |
0.995532 | − | 0.0944264i | \(-0.0301017\pi\) | |||||||
\(6\) | 0.407265 | − | 0.0753324i | 0.166265 | − | 0.0307543i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.942820 | −0.333337 | ||||||||
\(9\) | 2.80150 | − | 1.07311i | 0.933835 | − | 0.357704i | ||||
\(10\) | 0.309879 | − | 0.536725i | 0.0979922 | − | 0.169727i | ||||
\(11\) | −2.09097 | − | 3.62167i | −0.630452 | − | 1.09197i | −0.987459 | − | 0.157873i | \(-0.949536\pi\) |
0.357008 | − | 0.934101i | \(-0.383797\pi\) | |||||||
\(12\) | −3.30893 | + | 0.612058i | −0.955207 | + | 0.176686i | ||||
\(13\) | −1.84155 | − | 3.18966i | −0.510755 | − | 0.884653i | −0.999922 | − | 0.0124633i | \(-0.996033\pi\) |
0.489168 | − | 0.872190i | \(-0.337301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 4.23109i | 0.387298 | − | 1.09246i | ||||
\(16\) | 3.66019 | 0.915047 | ||||||||
\(17\) | −0.855536 | + | 1.48183i | −0.207498 | + | 0.359397i | −0.950926 | − | 0.309419i | \(-0.899865\pi\) |
0.743428 | + | 0.668816i | \(0.233199\pi\) | |||||||
\(18\) | 0.669905 | − | 0.256606i | 0.157898 | − | 0.0604826i | ||||
\(19\) | 3.57780 | + | 6.19694i | 0.820805 | + | 1.42168i | 0.905084 | + | 0.425233i | \(0.139808\pi\) |
−0.0842790 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(20\) | −2.51769 | + | 4.36077i | −0.562973 | + | 0.975097i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 2.56238 | − | 4.43818i | 0.534294 | − | 0.925424i | −0.464904 | − | 0.885361i | \(-0.653911\pi\) |
0.999197 | − | 0.0400622i | \(-0.0127556\pi\) | |||||||
\(24\) | −1.60577 | + | 0.297022i | −0.327777 | + | 0.0606294i | ||||
\(25\) | −0.858685 | − | 1.48729i | −0.171737 | − | 0.297457i | ||||
\(26\) | −0.440358 | − | 0.762722i | −0.0863613 | − | 0.149582i | ||||
\(27\) | 4.43334 | − | 2.71026i | 0.853197 | − | 0.521589i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.06238 | − | 1.84010i | 0.197279 | − | 0.341698i | −0.750366 | − | 0.661023i | \(-0.770123\pi\) |
0.947645 | + | 0.319325i | \(0.103456\pi\) | |||||||
\(30\) | 0.358685 | − | 1.01175i | 0.0654866 | − | 0.184720i | ||||
\(31\) | −6.53585 | −1.17387 | −0.586937 | − | 0.809633i | \(-0.699666\pi\) | ||||
−0.586937 | + | 0.809633i | \(0.699666\pi\) | |||||||
\(32\) | 2.76088 | 0.488059 | ||||||||
\(33\) | −4.70221 | − | 5.50955i | −0.818550 | − | 0.959089i | ||||
\(34\) | −0.204579 | + | 0.354341i | −0.0350850 | + | 0.0607689i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.44282 | + | 2.08486i | −0.907137 | + | 0.347477i | ||||
\(37\) | −0.830095 | − | 1.43777i | −0.136467 | − | 0.236367i | 0.789690 | − | 0.613506i | \(-0.210241\pi\) |
−0.926157 | + | 0.377139i | \(0.876908\pi\) | |||||||
\(38\) | 0.855536 | + | 1.48183i | 0.138786 | + | 0.240385i | ||||
\(39\) | −4.14132 | − | 4.85235i | −0.663141 | − | 0.776998i | ||||
\(40\) | −1.22180 | + | 2.11621i | −0.193183 | + | 0.334602i | ||||
\(41\) | 5.10948 | + | 8.84988i | 0.797967 | + | 1.38212i | 0.920938 | + | 0.389708i | \(0.127424\pi\) |
−0.122972 | + | 0.992410i | \(0.539242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.830095 | − | 1.43777i | 0.126588 | − | 0.219257i | −0.795764 | − | 0.605606i | \(-0.792931\pi\) |
0.922353 | + | 0.386349i | \(0.126264\pi\) | |||||||
\(44\) | 4.06238 | + | 7.03625i | 0.612427 | + | 1.06075i | ||||
\(45\) | 1.22180 | − | 7.67877i | 0.182134 | − | 1.14468i | ||||
\(46\) | 0.612725 | − | 1.06127i | 0.0903414 | − | 0.156476i | ||||
\(47\) | 9.33824 | 1.36212 | 0.681061 | − | 0.732226i | \(-0.261519\pi\) | ||||
0.681061 | + | 0.732226i | \(0.261519\pi\) | |||||||
\(48\) | 6.23389 | − | 1.15309i | 0.899784 | − | 0.166434i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.205332 | − | 0.355645i | −0.0290383 | − | 0.0502958i | ||||
\(51\) | −0.990285 | + | 2.79332i | −0.138668 | + | 0.391143i | ||||
\(52\) | 3.57780 | + | 6.19694i | 0.496152 | + | 0.859361i | ||||
\(53\) | −5.32326 | + | 9.22015i | −0.731206 | + | 1.26649i | 0.225162 | + | 0.974321i | \(0.427709\pi\) |
−0.956368 | + | 0.292164i | \(0.905625\pi\) | |||||||
\(54\) | 1.06012 | − | 0.648085i | 0.144263 | − | 0.0881932i | ||||
\(55\) | −10.8387 | −1.46149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.04583 | + | 9.42724i | 1.06570 | + | 1.24867i | ||||
\(58\) | 0.254040 | − | 0.440011i | 0.0333571 | − | 0.0577762i | ||||
\(59\) | 6.06429 | 0.789504 | 0.394752 | − | 0.918788i | \(-0.370831\pi\) | ||||
0.394752 | + | 0.918788i | \(0.370831\pi\) | |||||||
\(60\) | −2.91423 | + | 8.22024i | −0.376225 | + | 1.06123i | ||||
\(61\) | −7.98597 | −1.02250 | −0.511249 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511249 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(62\) | −1.56287 | −0.198485 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.66019 | −0.832524 | ||||||||
\(65\) | −9.54583 | −1.18401 | ||||||||
\(66\) | −1.12441 | − | 1.31746i | −0.138405 | − | 0.162168i | ||||
\(67\) | 8.26320 | 1.00951 | 0.504755 | − | 0.863262i | \(-0.331583\pi\) | ||||
0.504755 | + | 0.863262i | \(0.331583\pi\) | |||||||
\(68\) | 1.66215 | − | 2.87893i | 0.201566 | − | 0.349122i | ||||
\(69\) | 2.96596 | − | 8.36616i | 0.357060 | − | 1.00717i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.23912 | 0.740448 | 0.370224 | − | 0.928943i | \(-0.379281\pi\) | ||||
0.370224 | + | 0.928943i | \(0.379281\pi\) | |||||||
\(72\) | −2.64132 | + | 1.01175i | −0.311282 | + | 0.119236i | ||||
\(73\) | −3.57780 | + | 6.19694i | −0.418750 | + | 0.725297i | −0.995814 | − | 0.0914022i | \(-0.970865\pi\) |
0.577064 | + | 0.816699i | \(0.304198\pi\) | |||||||
\(74\) | −0.198495 | − | 0.343803i | −0.0230746 | − | 0.0399663i | ||||
\(75\) | −1.93103 | − | 2.26257i | −0.222976 | − | 0.261259i | ||||
\(76\) | −6.95103 | − | 12.0395i | −0.797338 | − | 1.38103i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.990285 | − | 1.16031i | −0.112128 | − | 0.131379i | ||||
\(79\) | −9.82846 | −1.10579 | −0.552894 | − | 0.833252i | \(-0.686477\pi\) | ||||
−0.552894 | + | 0.833252i | \(0.686477\pi\) | |||||||
\(80\) | 4.74322 | − | 8.21550i | 0.530308 | − | 0.918521i | ||||
\(81\) | 6.69686 | − | 6.01266i | 0.744096 | − | 0.668073i | ||||
\(82\) | 1.22180 | + | 2.11621i | 0.134925 | + | 0.233696i | ||||
\(83\) | −3.44733 | + | 5.97094i | −0.378393 | + | 0.655396i | −0.990829 | − | 0.135124i | \(-0.956857\pi\) |
0.612436 | + | 0.790521i | \(0.290190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.21737 | + | 3.84060i | 0.240508 | + | 0.416571i | ||||
\(86\) | 0.198495 | − | 0.343803i | 0.0214043 | − | 0.0370733i | ||||
\(87\) | 1.22971 | − | 3.46867i | 0.131839 | − | 0.371881i | ||||
\(88\) | 1.97141 | + | 3.41458i | 0.210153 | + | 0.363996i | ||||
\(89\) | 2.51769 | + | 4.36077i | 0.266875 | + | 0.462240i | 0.968053 | − | 0.250745i | \(-0.0806757\pi\) |
−0.701178 | + | 0.712986i | \(0.747342\pi\) | |||||||
\(90\) | 0.292160 | − | 1.83617i | 0.0307963 | − | 0.193550i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.97825 | + | 8.62258i | −0.519018 | + | 0.898966i | ||||
\(93\) | −11.1316 | + | 2.05903i | −1.15429 | + | 0.213511i | ||||
\(94\) | 2.23299 | 0.230315 | ||||||||
\(95\) | 18.5458 | 1.90276 | ||||||||
\(96\) | 4.70221 | − | 0.869775i | 0.479918 | − | 0.0887710i | ||||
\(97\) | −1.53167 | + | 2.65294i | −0.155518 | + | 0.269365i | −0.933247 | − | 0.359234i | \(-0.883038\pi\) |
0.777730 | + | 0.628599i | \(0.216371\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.74433 | − | 7.90228i | −0.979342 | − | 0.794209i | ||||
\(100\) | 1.66827 | + | 2.88953i | 0.166827 | + | 0.288953i | ||||
\(101\) | 5.54984 | + | 9.61260i | 0.552229 | + | 0.956489i | 0.998113 | + | 0.0613986i | \(0.0195561\pi\) |
−0.445884 | + | 0.895091i | \(0.647111\pi\) | |||||||
\(102\) | −0.236800 | + | 0.667948i | −0.0234467 | + | 0.0661367i | ||||
\(103\) | −3.99298 | + | 6.91605i | −0.393440 | + | 0.681459i | −0.992901 | − | 0.118946i | \(-0.962049\pi\) |
0.599460 | + | 0.800404i | \(0.295382\pi\) | |||||||
\(104\) | 1.73625 | + | 3.00728i | 0.170254 | + | 0.294888i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.27292 | + | 2.20475i | −0.123636 | + | 0.214145i | ||||
\(107\) | −1.97825 | − | 3.42642i | −0.191244 | − | 0.331245i | 0.754419 | − | 0.656394i | \(-0.227919\pi\) |
−0.945663 | + | 0.325149i | \(0.894586\pi\) | |||||||
\(108\) | −8.61318 | + | 5.26554i | −0.828804 | + | 0.506677i | ||||
\(109\) | −3.63160 | + | 6.29012i | −0.347844 | + | 0.602484i | −0.985866 | − | 0.167534i | \(-0.946420\pi\) |
0.638022 | + | 0.770018i | \(0.279753\pi\) | |||||||
\(110\) | −2.59179 | −0.247117 | ||||||||
\(111\) | −1.86673 | − | 2.18724i | −0.177182 | − | 0.207603i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.46457 | − | 6.00082i | −0.325920 | − | 0.564509i | 0.655778 | − | 0.754953i | \(-0.272341\pi\) |
−0.981698 | + | 0.190444i | \(0.939007\pi\) | |||||||
\(114\) | 1.92395 | + | 2.25427i | 0.180194 | + | 0.211132i | ||||
\(115\) | −6.64115 | − | 11.5028i | −0.619291 | − | 1.07264i | ||||
\(116\) | −2.06402 | + | 3.57498i | −0.191639 | + | 0.331929i | ||||
\(117\) | −8.58198 | − | 6.95966i | −0.793405 | − | 0.643421i | ||||
\(118\) | 1.45011 | 0.133494 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.41423 | + | 3.98916i | −0.129101 | + | 0.364158i | ||||
\(121\) | −3.24433 | + | 5.61934i | −0.294939 | + | 0.510849i | ||||
\(122\) | −1.90963 | −0.172890 | ||||||||
\(123\) | 11.4903 | + | 13.4631i | 1.03604 | + | 1.21393i | ||||
\(124\) | 12.6980 | 1.14031 | ||||||||
\(125\) | 8.50788 | 0.760968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.11109 | 0.808479 | 0.404239 | − | 0.914653i | \(-0.367536\pi\) | ||||
0.404239 | + | 0.914653i | \(0.367536\pi\) | |||||||
\(128\) | −7.11436 | −0.628827 | ||||||||
\(129\) | 0.960836 | − | 2.71026i | 0.0845969 | − | 0.238625i | ||||
\(130\) | −2.28263 | −0.200200 | ||||||||
\(131\) | 2.15143 | − | 3.72639i | 0.187971 | − | 0.325576i | −0.756602 | − | 0.653875i | \(-0.773142\pi\) |
0.944574 | + | 0.328299i | \(0.106475\pi\) | |||||||
\(132\) | 9.13555 | + | 10.7041i | 0.795148 | + | 0.931669i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.97592 | 0.170694 | ||||||||
\(135\) | −0.338175 | − | 13.4631i | −0.0291055 | − | 1.15872i | ||||
\(136\) | 0.806617 | − | 1.39710i | 0.0691668 | − | 0.119800i | ||||
\(137\) | −10.2947 | − | 17.8309i | −0.879533 | − | 1.52340i | −0.851854 | − | 0.523779i | \(-0.824522\pi\) |
−0.0276785 | − | 0.999617i | \(-0.508811\pi\) | |||||||
\(138\) | 0.709230 | − | 2.00054i | 0.0603737 | − | 0.170298i | ||||
\(139\) | 7.88067 | + | 13.6497i | 0.668429 | + | 1.15775i | 0.978343 | + | 0.206989i | \(0.0663665\pi\) |
−0.309914 | + | 0.950765i | \(0.600300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.9045 | − | 2.94188i | 1.33940 | − | 0.247751i | ||||
\(142\) | 1.49192 | 0.125199 | ||||||||
\(143\) | −7.70127 | + | 13.3390i | −0.644012 | + | 1.11546i | ||||
\(144\) | 10.2540 | − | 3.92779i | 0.854503 | − | 0.327316i | ||||
\(145\) | −2.75347 | − | 4.76915i | −0.228663 | − | 0.396056i | ||||
\(146\) | −0.855536 | + | 1.48183i | −0.0708047 | + | 0.122637i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.61273 | + | 2.79332i | 0.132565 | + | 0.229610i | ||||
\(149\) | −3.03379 | + | 5.25468i | −0.248538 | + | 0.430480i | −0.963120 | − | 0.269071i | \(-0.913283\pi\) |
0.714582 | + | 0.699551i | \(0.246617\pi\) | |||||||
\(150\) | −0.461753 | − | 0.541033i | −0.0377020 | − | 0.0441751i | ||||
\(151\) | −2.24433 | − | 3.88728i | −0.182641 | − | 0.316343i | 0.760138 | − | 0.649761i | \(-0.225131\pi\) |
−0.942779 | + | 0.333418i | \(0.891798\pi\) | |||||||
\(152\) | −3.37323 | − | 5.84260i | −0.273605 | − | 0.473897i | ||||
\(153\) | −0.806617 | + | 5.06945i | −0.0652111 | + | 0.409841i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.46978 | + | 14.6701i | −0.680309 | + | 1.17833i | ||||
\(156\) | 8.04583 | + | 9.42724i | 0.644182 | + | 0.754783i | ||||
\(157\) | 1.02891 | 0.0821163 | 0.0410582 | − | 0.999157i | \(-0.486927\pi\) | ||||
0.0410582 | + | 0.999157i | \(0.486927\pi\) | |||||||
\(158\) | −2.35021 | −0.186973 | ||||||||
\(159\) | −6.16168 | + | 17.3804i | −0.488653 | + | 1.37836i | ||||
\(160\) | 3.57780 | − | 6.19694i | 0.282850 | − | 0.489911i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.60138 | − | 1.43777i | 0.125816 | − | 0.112962i | ||||
\(163\) | −3.41423 | − | 5.91362i | −0.267423 | − | 0.463190i | 0.700772 | − | 0.713385i | \(-0.252839\pi\) |
−0.968196 | + | 0.250194i | \(0.919505\pi\) | |||||||
\(164\) | −9.92680 | − | 17.1937i | −0.775153 | − | 1.34260i | ||||
\(165\) | −18.4601 | + | 3.41458i | −1.43711 | + | 0.265825i | ||||
\(166\) | −0.824336 | + | 1.42779i | −0.0639809 | + | 0.110818i | ||||
\(167\) | −8.99716 | − | 15.5835i | −0.696221 | − | 1.20589i | −0.969767 | − | 0.244032i | \(-0.921530\pi\) |
0.273546 | − | 0.961859i | \(-0.411803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.282630 | + | 0.489530i | −0.0217408 | + | 0.0376561i | ||||
\(170\) | 0.530225 | + | 0.918376i | 0.0406664 | + | 0.0704362i | ||||
\(171\) | 16.6733 | + | 13.5214i | 1.27504 | + | 1.03401i | ||||
\(172\) | −1.61273 | + | 2.79332i | −0.122969 | + | 0.212989i | ||||
\(173\) | −0.830357 | −0.0631309 | −0.0315654 | − | 0.999502i | \(-0.510049\pi\) | ||||
−0.0315654 | + | 0.999502i | \(0.510049\pi\) | |||||||
\(174\) | 0.294052 | − | 0.829440i | 0.0222920 | − | 0.0628797i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.65335 | − | 13.2560i | −0.576893 | − | 0.999208i | ||||
\(177\) | 10.3285 | − | 1.91047i | 0.776335 | − | 0.143600i | ||||
\(178\) | 0.602038 | + | 1.04276i | 0.0451247 | + | 0.0781582i | ||||
\(179\) | −3.78947 | + | 6.56355i | −0.283238 | + | 0.490583i | −0.972180 | − | 0.234233i | \(-0.924742\pi\) |
0.688942 | + | 0.724816i | \(0.258075\pi\) | |||||||
\(180\) | −2.37373 | + | 14.9185i | −0.176927 | + | 1.11196i | ||||
\(181\) | 0.409157 | 0.0304124 | 0.0152062 | − | 0.999884i | \(-0.495160\pi\) | ||||
0.0152062 | + | 0.999884i | \(0.495160\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6014 | + | 2.51586i | −1.00544 | + | 0.185978i | ||||
\(184\) | −2.41586 | + | 4.18440i | −0.178100 | + | 0.308478i | ||||
\(185\) | −4.30286 | −0.316353 | ||||||||
\(186\) | −2.66182 | + | 0.492361i | −0.195174 | + | 0.0361017i | ||||
\(187\) | 7.15561 | 0.523270 | ||||||||
\(188\) | −18.1425 | −1.32318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.43474 | 0.321730 | ||||||||
\(191\) | 16.0241 | 1.15946 | 0.579731 | − | 0.814808i | \(-0.303158\pi\) | ||||
0.579731 | + | 0.814808i | \(0.303158\pi\) | |||||||
\(192\) | −11.3434 | + | 2.09820i | −0.818637 | + | 0.151424i | ||||
\(193\) | −12.3743 | −0.890721 | −0.445360 | − | 0.895351i | \(-0.646924\pi\) | ||||
−0.445360 | + | 0.895351i | \(0.646924\pi\) | |||||||
\(194\) | −0.366259 | + | 0.634379i | −0.0262959 | + | 0.0455458i | ||||
\(195\) | −16.2581 | + | 3.00728i | −1.16426 | + | 0.215356i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1021 | 1.64595 | 0.822977 | − | 0.568075i | \(-0.192312\pi\) | ||||
0.822977 | + | 0.568075i | \(0.192312\pi\) | |||||||
\(198\) | −2.33009 | − | 1.88962i | −0.165593 | − | 0.134289i | ||||
\(199\) | 3.37323 | − | 5.84260i | 0.239122 | − | 0.414171i | −0.721341 | − | 0.692580i | \(-0.756474\pi\) |
0.960463 | + | 0.278409i | \(0.0898072\pi\) | |||||||
\(200\) | 0.809585 | + | 1.40224i | 0.0572463 | + | 0.0991536i | ||||
\(201\) | 14.0735 | − | 2.60320i | 0.992672 | − | 0.183616i | ||||
\(202\) | 1.32710 | + | 2.29860i | 0.0933741 | + | 0.161729i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.92395 | − | 5.42692i | 0.134703 | − | 0.379961i | ||||
\(205\) | 26.4854 | 1.84982 | ||||||||
\(206\) | −0.954815 | + | 1.65379i | −0.0665251 | + | 0.115225i | ||||
\(207\) | 2.41586 | − | 15.1833i | 0.167914 | − | 1.05531i | ||||
\(208\) | −6.74043 | − | 11.6748i | −0.467365 | − | 0.809500i | ||||
\(209\) | 14.9622 | − | 25.9153i | 1.03496 | − | 1.79260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.44282 | − | 14.6234i | −0.581228 | − | 1.00672i | −0.995334 | − | 0.0964875i | \(-0.969239\pi\) |
0.414106 | − | 0.910228i | \(-0.364094\pi\) | |||||||
\(212\) | 10.3421 | − | 17.9131i | 0.710301 | − | 1.23028i | ||||
\(213\) | 10.6262 | − | 1.96555i | 0.728097 | − | 0.134677i | ||||
\(214\) | −0.473045 | − | 0.819338i | −0.0323367 | − | 0.0560088i | ||||
\(215\) | −2.15143 | − | 3.72639i | −0.146726 | − | 0.254138i | ||||
\(216\) | −4.17984 | + | 2.55528i | −0.284402 | + | 0.173865i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.868400 | + | 1.50411i | −0.0588155 | + | 0.101871i | ||||
\(219\) | −4.14132 | + | 11.6815i | −0.279844 | + | 0.789364i | ||||
\(220\) | 21.0577 | 1.41971 | ||||||||
\(221\) | 6.30206 | 0.423922 | ||||||||
\(222\) | −0.446379 | − | 0.523019i | −0.0299590 | − | 0.0351027i | ||||
\(223\) | 2.25071 | − | 3.89834i | 0.150719 | − | 0.261052i | −0.780773 | − | 0.624815i | \(-0.785175\pi\) |
0.931492 | + | 0.363762i | \(0.118508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00163 | − | 3.24517i | −0.266776 | − | 0.216345i | ||||
\(226\) | −0.828460 | − | 1.43494i | −0.0551084 | − | 0.0954505i | ||||
\(227\) | 3.03215 | + | 5.25183i | 0.201251 | + | 0.348576i | 0.948932 | − | 0.315482i | \(-0.102166\pi\) |
−0.747681 | + | 0.664058i | \(0.768833\pi\) | |||||||
\(228\) | −15.6316 | − | 18.3154i | −1.03523 | − | 1.21297i | ||||
\(229\) | 5.52466 | − | 9.56899i | 0.365080 | − | 0.632336i | −0.623709 | − | 0.781656i | \(-0.714375\pi\) |
0.988789 | + | 0.149320i | \(0.0477084\pi\) | |||||||
\(230\) | −1.58805 | − | 2.75059i | −0.104713 | − | 0.181369i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00163 | + | 1.73488i | −0.0657605 | + | 0.113901i | ||||
\(233\) | 4.06922 | + | 7.04809i | 0.266583 | + | 0.461736i | 0.967977 | − | 0.251038i | \(-0.0807719\pi\) |
−0.701394 | + | 0.712774i | \(0.747439\pi\) | |||||||
\(234\) | −2.05215 | − | 1.66422i | −0.134153 | − | 0.108793i | ||||
\(235\) | 12.1014 | − | 20.9602i | 0.789407 | − | 1.36729i | ||||
\(236\) | −11.7818 | −0.766932 | ||||||||
\(237\) | −16.7394 | + | 3.09632i | −1.08734 | + | 0.201127i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5813 | − | 18.3273i | −0.684445 | − | 1.18549i | −0.973611 | − | 0.228214i | \(-0.926711\pi\) |
0.289166 | − | 0.957279i | \(-0.406622\pi\) | |||||||
\(240\) | 5.49028 | − | 15.4866i | 0.354396 | − | 0.999655i | ||||
\(241\) | −6.84573 | − | 11.8572i | −0.440972 | − | 0.763786i | 0.556790 | − | 0.830654i | \(-0.312033\pi\) |
−0.997762 | + | 0.0668671i | \(0.978700\pi\) | |||||||
\(242\) | −0.775794 | + | 1.34371i | −0.0498699 | + | 0.0863772i | ||||
\(243\) | 9.51162 | − | 12.3503i | 0.610171 | − | 0.792270i | ||||
\(244\) | 15.5153 | 0.993265 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.74759 | + | 3.21934i | 0.175180 | + | 0.205257i | ||||
\(247\) | 13.1774 | − | 22.8240i | 0.838460 | − | 1.45225i | ||||
\(248\) | 6.16213 | 0.391296 | ||||||||
\(249\) | −3.99028 | + | 11.2555i | −0.252874 | + | 0.713288i | ||||
\(250\) | 2.03443 | 0.128669 | ||||||||
\(251\) | 15.2040 | 0.959667 | 0.479833 | − | 0.877360i | \(-0.340697\pi\) | ||||
0.479833 | + | 0.877360i | \(0.340697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.4315 | −1.34738 | ||||||||
\(254\) | 2.17867 | 0.136702 | ||||||||
\(255\) | 4.98646 | + | 5.84260i | 0.312264 | + | 0.365878i | ||||
\(256\) | 11.6192 | 0.726198 | ||||||||
\(257\) | −12.8107 | + | 22.1889i | −0.799112 | + | 1.38410i | 0.121082 | + | 0.992642i | \(0.461363\pi\) |
−0.920195 | + | 0.391461i | \(0.871970\pi\) | |||||||
\(258\) | 0.229758 | − | 0.648085i | 0.0143041 | − | 0.0403480i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.5458 | 1.15016 | ||||||||
\(261\) | 1.00163 | − | 6.29510i | 0.0619996 | − | 0.389657i | ||||
\(262\) | 0.514457 | − | 0.891066i | 0.0317833 | − | 0.0550502i | ||||
\(263\) | −3.55034 | − | 6.14938i | −0.218924 | − | 0.379187i | 0.735556 | − | 0.677464i | \(-0.236921\pi\) |
−0.954479 | + | 0.298278i | \(0.903588\pi\) | |||||||
\(264\) | 4.43334 | + | 5.19451i | 0.272853 | + | 0.319700i | ||||
\(265\) | 13.7968 | + | 23.8967i | 0.847528 | + | 1.46796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.66182 | + | 6.63392i | 0.346498 | + | 0.405989i | ||||
\(268\) | −16.0539 | −0.980649 | ||||||||
\(269\) | 8.21572 | − | 14.2301i | 0.500922 | − | 0.867622i | −0.499078 | − | 0.866557i | \(-0.666328\pi\) |
0.999999 | − | 0.00106448i | \(-0.000338834\pi\) | |||||||
\(270\) | −0.0808656 | − | 3.21934i | −0.00492132 | − | 0.195923i | ||||
\(271\) | −6.34899 | − | 10.9968i | −0.385674 | − | 0.668007i | 0.606189 | − | 0.795321i | \(-0.292698\pi\) |
−0.991862 | + | 0.127314i | \(0.959364\pi\) | |||||||
\(272\) | −3.13143 | + | 5.42379i | −0.189871 | + | 0.328865i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.46169 | − | 4.26378i | −0.148716 | − | 0.257584i | ||||
\(275\) | −3.59097 | + | 6.21975i | −0.216544 | + | 0.375065i | ||||
\(276\) | −5.76233 | + | 16.2539i | −0.346851 | + | 0.978373i | ||||
\(277\) | 0.414230 | + | 0.717468i | 0.0248887 | + | 0.0431084i | 0.878201 | − | 0.478291i | \(-0.158744\pi\) |
−0.853313 | + | 0.521399i | \(0.825410\pi\) | |||||||
\(278\) | 1.88445 | + | 3.26396i | 0.113022 | + | 0.195760i | ||||
\(279\) | −18.3102 | + | 7.01370i | −1.09620 | + | 0.419899i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.60985 | + | 4.52039i | −0.155690 | + | 0.269664i | −0.933310 | − | 0.359071i | \(-0.883094\pi\) |
0.777620 | + | 0.628735i | \(0.216427\pi\) | |||||||
\(282\) | 3.80314 | − | 0.703472i | 0.226474 | − | 0.0418911i | ||||
\(283\) | −7.35417 | −0.437160 | −0.218580 | − | 0.975819i | \(-0.570142\pi\) | ||||
−0.218580 | + | 0.975819i | \(0.570142\pi\) | |||||||
\(284\) | −12.1215 | −0.719278 | ||||||||
\(285\) | 31.5865 | − | 5.84260i | 1.87102 | − | 0.346086i | ||||
\(286\) | −1.84155 | + | 3.18966i | −0.108893 | + | 0.188609i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.73461 | − | 2.96273i | 0.455766 | − | 0.174581i | ||||
\(289\) | 7.03611 | + | 12.1869i | 0.413889 | + | 0.716877i | ||||
\(290\) | −0.658419 | − | 1.14041i | −0.0386637 | − | 0.0669674i | ||||
\(291\) | −1.77292 | + | 5.00091i | −0.103930 | + | 0.293158i | ||||
\(292\) | 6.95103 | − | 12.0395i | 0.406778 | − | 0.704561i | ||||
\(293\) | −3.91286 | − | 6.77728i | −0.228592 | − | 0.395933i | 0.728799 | − | 0.684728i | \(-0.240079\pi\) |
−0.957391 | + | 0.288795i | \(0.906745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.85868 | − | 13.6116i | 0.457550 | − | 0.792500i | ||||
\(296\) | 0.782630 | + | 1.35556i | 0.0454895 | + | 0.0787900i | ||||
\(297\) | −19.0856 | − | 10.3890i | −1.10746 | − | 0.602833i | ||||
\(298\) | −0.725450 | + | 1.25652i | −0.0420242 | + | 0.0727881i | ||||
\(299\) | −18.8750 | −1.09157 | ||||||||
\(300\) | 3.75164 | + | 4.39576i | 0.216601 | + | 0.253790i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.536670 | − | 0.929540i | −0.0308819 | − | 0.0534890i | ||||
\(303\) | 12.4806 | + | 14.6234i | 0.716990 | + | 0.840092i | ||||
\(304\) | 13.0954 | + | 22.6820i | 0.751075 | + | 1.30090i | ||||
\(305\) | −10.3490 | + | 17.9249i | −0.592580 | + | 1.02638i | ||||
\(306\) | −0.192881 | + | 1.21222i | −0.0110263 | + | 0.0692982i | ||||
\(307\) | 22.6709 | 1.29390 | 0.646948 | − | 0.762534i | \(-0.276045\pi\) | ||||
0.646948 | + | 0.762534i | \(0.276045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.62188 | + | 13.0371i | −0.262930 | + | 0.741653i | ||||
\(310\) | −2.02532 | + | 3.50796i | −0.115030 | + | 0.199239i | ||||
\(311\) | −32.3176 | −1.83256 | −0.916281 | − | 0.400536i | \(-0.868824\pi\) | ||||
−0.916281 | + | 0.400536i | \(0.868824\pi\) | |||||||
\(312\) | 3.90451 | + | 4.57489i | 0.221050 | + | 0.259002i | ||||
\(313\) | −24.3196 | −1.37462 | −0.687312 | − | 0.726362i | \(-0.741209\pi\) | ||||
−0.687312 | + | 0.726362i | \(0.741209\pi\) | |||||||
\(314\) | 0.246037 | 0.0138847 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.0949 | 1.07417 | ||||||||
\(317\) | 5.13844 | 0.288603 | 0.144302 | − | 0.989534i | \(-0.453906\pi\) | ||||
0.144302 | + | 0.989534i | \(0.453906\pi\) | |||||||
\(318\) | −1.47340 | + | 4.15606i | −0.0826242 | + | 0.233060i | ||||
\(319\) | −8.88564 | −0.497500 | ||||||||
\(320\) | −8.63090 | + | 14.9492i | −0.482482 | + | 0.835684i | ||||
\(321\) | −4.44872 | − | 5.21253i | −0.248303 | − | 0.290935i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2438 | −0.681262 | ||||||||
\(324\) | −13.0108 | + | 11.6815i | −0.722822 | + | 0.648973i | ||||
\(325\) | −3.16263 | + | 5.47783i | −0.175431 | + | 0.303855i | ||||
\(326\) | −0.816422 | − | 1.41408i | −0.0452174 | − | 0.0783189i | ||||
\(327\) | −4.20358 | + | 11.8572i | −0.232459 | + | 0.655702i | ||||
\(328\) | −4.81732 | − | 8.34384i | −0.265992 | − | 0.460712i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.41423 | + | 0.816506i | −0.242995 | + | 0.0449472i | ||||
\(331\) | −11.6979 | −0.642977 | −0.321488 | − | 0.946913i | \(-0.604183\pi\) | ||||
−0.321488 | + | 0.946913i | \(0.604183\pi\) | |||||||
\(332\) | 6.69753 | − | 11.6005i | 0.367575 | − | 0.636658i | ||||
\(333\) | −3.86840 | − | 3.13713i | −0.211987 | − | 0.171913i | ||||
\(334\) | −2.15143 | − | 3.72639i | −0.117721 | − | 0.203899i | ||||
\(335\) | 10.7082 | − | 18.5472i | 0.585053 | − | 1.01334i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8473 | + | 29.1804i | 0.917733 | + | 1.58956i | 0.802850 | + | 0.596181i | \(0.203316\pi\) |
0.114883 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(338\) | −0.0675835 | + | 0.117058i | −0.00367606 | + | 0.00636711i | ||||
\(339\) | −7.79119 | − | 9.12888i | −0.423160 | − | 0.495813i | ||||
\(340\) | −4.30795 | − | 7.46159i | −0.233631 | − | 0.404661i | ||||
\(341\) | 13.6663 | + | 23.6707i | 0.740071 | + | 1.28184i | ||||
\(342\) | 3.98696 | + | 3.23327i | 0.215590 | + | 0.174835i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.782630 | + | 1.35556i | −0.0421966 | + | 0.0730866i | ||||
\(345\) | −14.9347 | − | 17.4989i | −0.804059 | − | 0.942111i | ||||
\(346\) | −0.198558 | −0.0106745 | ||||||||
\(347\) | 27.3114 | 1.46615 | 0.733075 | − | 0.680148i | \(-0.238084\pi\) | ||||
0.733075 | + | 0.680148i | \(0.238084\pi\) | |||||||
\(348\) | −2.38910 | + | 6.73900i | −0.128069 | + | 0.361248i | ||||
\(349\) | −11.4585 | + | 19.8467i | −0.613358 | + | 1.06237i | 0.377312 | + | 0.926086i | \(0.376848\pi\) |
−0.990670 | + | 0.136281i | \(0.956485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.8090 | − | 9.14978i | −0.897200 | − | 0.488379i | ||||
\(352\) | −5.77292 | − | 9.99898i | −0.307697 | − | 0.532948i | ||||
\(353\) | −5.13466 | − | 8.89349i | −0.273290 | − | 0.473353i | 0.696412 | − | 0.717642i | \(-0.254779\pi\) |
−0.969702 | + | 0.244289i | \(0.921445\pi\) | |||||||
\(354\) | 2.46978 | − | 0.456838i | 0.131267 | − | 0.0242806i | ||||
\(355\) | 8.08525 | − | 14.0041i | 0.429120 | − | 0.743258i | ||||
\(356\) | −4.89142 | − | 8.47218i | −0.259245 | − | 0.449025i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.906150 | + | 1.56950i | −0.0478915 | + | 0.0829505i | ||||
\(359\) | −5.05034 | − | 8.74745i | −0.266547 | − | 0.461673i | 0.701421 | − | 0.712747i | \(-0.252549\pi\) |
−0.967968 | + | 0.251075i | \(0.919216\pi\) | |||||||
\(360\) | −1.15193 | + | 7.23970i | −0.0607122 | + | 0.381566i | ||||
\(361\) | −16.1014 | + | 27.8884i | −0.847441 | + | 1.46781i | ||||
\(362\) | 0.0978390 | 0.00514231 | ||||||||
\(363\) | −3.75531 | + | 10.5927i | −0.197103 | + | 0.555973i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.27292 | + | 16.0612i | 0.485367 | + | 0.840680i | ||||
\(366\) | −3.25241 | + | 0.601602i | −0.170006 | + | 0.0314462i | ||||
\(367\) | 3.88768 | + | 6.73367i | 0.202935 | + | 0.351494i | 0.949473 | − | 0.313849i | \(-0.101619\pi\) |
−0.746538 | + | 0.665343i | \(0.768285\pi\) | |||||||
\(368\) | 9.37880 | − | 16.2446i | 0.488904 | − | 0.846806i | ||||
\(369\) | 23.8111 | + | 19.3099i | 1.23956 | + | 1.00523i | ||||
\(370\) | −1.02891 | −0.0534907 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 21.6267 | − | 4.00032i | 1.12129 | − | 0.207407i | ||||
\(373\) | −12.0555 | + | 20.8808i | −0.624212 | + | 1.08117i | 0.364480 | + | 0.931211i | \(0.381247\pi\) |
−0.988693 | + | 0.149957i | \(0.952087\pi\) | |||||||
\(374\) | 1.71107 | 0.0884775 | ||||||||
\(375\) | 14.4903 | − | 2.68029i | 0.748275 | − | 0.138409i | ||||
\(376\) | −8.80428 | −0.454046 | ||||||||
\(377\) | −7.82573 | −0.403045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3581 | −0.686161 | −0.343081 | − | 0.939306i | \(-0.611470\pi\) | ||||
−0.343081 | + | 0.939306i | \(0.611470\pi\) | |||||||
\(380\) | −36.0312 | −1.84836 | ||||||||
\(381\) | 15.5176 | − | 2.87032i | 0.794993 | − | 0.147051i | ||||
\(382\) | 3.83173 | 0.196048 | ||||||||
\(383\) | 4.62020 | − | 8.00242i | 0.236081 | − | 0.408905i | −0.723505 | − | 0.690319i | \(-0.757470\pi\) |
0.959586 | + | 0.281414i | \(0.0908035\pi\) | |||||||
\(384\) | −12.1169 | + | 2.24128i | −0.618337 | + | 0.114375i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.95898 | −0.150608 | ||||||||
\(387\) | 0.782630 | − | 4.91870i | 0.0397833 | − | 0.250031i | ||||
\(388\) | 2.97577 | − | 5.15418i | 0.151072 | − | 0.261664i | ||||
\(389\) | −5.22421 | − | 9.04859i | −0.264878 | − | 0.458782i | 0.702654 | − | 0.711532i | \(-0.251998\pi\) |
−0.967532 | + | 0.252750i | \(0.918665\pi\) | |||||||
\(390\) | −3.88768 | + | 0.719110i | −0.196861 | + | 0.0364136i | ||||
\(391\) | 4.38442 | + | 7.59404i | 0.221730 | + | 0.384047i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.49028 | − | 7.02441i | 0.125618 | − | 0.354335i | ||||
\(394\) | 5.52424 | 0.278307 | ||||||||
\(395\) | −12.7366 | + | 22.0605i | −0.640850 | + | 1.10999i | ||||
\(396\) | 18.9315 | + | 15.3527i | 0.951342 | + | 0.771502i | ||||
\(397\) | 0.204579 | + | 0.354341i | 0.0102675 | + | 0.0177838i | 0.871114 | − | 0.491082i | \(-0.163398\pi\) |
−0.860846 | + | 0.508866i | \(0.830065\pi\) | |||||||
\(398\) | 0.806617 | − | 1.39710i | 0.0404321 | − | 0.0700304i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.14295 | − | 5.44375i | −0.157147 | − | 0.272187i | ||||
\(401\) | −7.62640 | + | 13.2093i | −0.380844 | + | 0.659641i | −0.991183 | − | 0.132499i | \(-0.957700\pi\) |
0.610339 | + | 0.792140i | \(0.291033\pi\) | |||||||
\(402\) | 3.36531 | − | 0.622486i | 0.167847 | − | 0.0310468i | ||||
\(403\) | 12.0361 | + | 20.8472i | 0.599562 | + | 1.03847i | ||||
\(404\) | −10.7823 | − | 18.6756i | −0.536441 | − | 0.929143i | ||||
\(405\) | −4.81732 | − | 22.8232i | −0.239375 | − | 1.13410i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.47141 | + | 6.01266i | −0.172071 | + | 0.298036i | ||||
\(408\) | 0.933660 | − | 2.63360i | 0.0462231 | − | 0.130383i | ||||
\(409\) | −6.12670 | −0.302946 | −0.151473 | − | 0.988461i | \(-0.548402\pi\) | ||||
−0.151473 | + | 0.988461i | \(0.548402\pi\) | |||||||
\(410\) | 6.33327 | 0.312778 | ||||||||
\(411\) | −23.1508 | − | 27.1257i | −1.14195 | − | 1.33801i | ||||
\(412\) | 7.75765 | − | 13.4366i | 0.382192 | − | 0.661976i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.577690 | − | 3.63068i | 0.0283919 | − | 0.178438i | ||||
\(415\) | 8.93474 | + | 15.4754i | 0.438589 | + | 0.759659i | ||||
\(416\) | −5.08430 | − | 8.80626i | −0.249278 | − | 0.431763i | ||||
\(417\) | 17.7222 | + | 20.7650i | 0.867859 | + | 1.01686i | ||||
\(418\) | 3.57780 | − | 6.19694i | 0.174996 | − | 0.303102i | ||||
\(419\) | −0.781437 | − | 1.35349i | −0.0381757 | − | 0.0661223i | 0.846306 | − | 0.532697i | \(-0.178821\pi\) |
−0.884482 | + | 0.466574i | \(0.845488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.6316 | + | 20.1465i | −0.566889 | + | 0.981881i | 0.429982 | + | 0.902838i | \(0.358520\pi\) |
−0.996871 | + | 0.0790438i | \(0.974813\pi\) | |||||||
\(422\) | −2.01887 | − | 3.49679i | −0.0982773 | − | 0.170221i | ||||
\(423\) | 26.1611 | − | 10.0210i | 1.27200 | − | 0.487237i | ||||
\(424\) | 5.01887 | − | 8.69295i | 0.243738 | − | 0.422167i | ||||
\(425\) | 2.93854 | 0.142540 | ||||||||
\(426\) | 2.54098 | − | 0.470008i | 0.123111 | − | 0.0227720i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.84338 | + | 6.65692i | 0.185777 | + | 0.321775i | ||||
\(429\) | −8.91423 | + | 25.1446i | −0.430383 | + | 1.21399i | ||||
\(430\) | −0.514457 | − | 0.891066i | −0.0248093 | − | 0.0429710i | ||||
\(431\) | −0.502879 | + | 0.871011i | −0.0242228 | + | 0.0419551i | −0.877883 | − | 0.478876i | \(-0.841044\pi\) |
0.853660 | + | 0.520831i | \(0.174378\pi\) | |||||||
\(432\) | 16.2269 | − | 9.92005i | 0.780716 | − | 0.477279i | ||||
\(433\) | 13.1071 | 0.629889 | 0.314945 | − | 0.949110i | \(-0.398014\pi\) | ||||
0.314945 | + | 0.949110i | \(0.398014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.19205 | − | 7.25518i | −0.296886 | − | 0.347859i | ||||
\(436\) | 7.05555 | − | 12.2206i | 0.337899 | − | 0.585259i | ||||
\(437\) | 36.6708 | 1.75420 | ||||||||
\(438\) | −0.990285 | + | 2.79332i | −0.0473176 | + | 0.133470i | ||||
\(439\) | 18.6141 | 0.888402 | 0.444201 | − | 0.895927i | \(-0.353488\pi\) | ||||
0.444201 | + | 0.895927i | \(0.353488\pi\) | |||||||
\(440\) | 10.2190 | 0.487170 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.50697 | 0.0716792 | ||||||||
\(443\) | −1.11901 | −0.0531656 | −0.0265828 | − | 0.999647i | \(-0.508463\pi\) | ||||
−0.0265828 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(444\) | 3.62672 | + | 4.24941i | 0.172117 | + | 0.201668i | ||||
\(445\) | 13.0506 | 0.618660 | ||||||||
\(446\) | 0.538197 | − | 0.932185i | 0.0254844 | − | 0.0441402i | ||||
\(447\) | −3.51162 | + | 9.90531i | −0.166094 | + | 0.468505i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.4419 | −1.86138 | −0.930689 | − | 0.365813i | \(-0.880791\pi\) | ||||
−0.930689 | + | 0.365813i | \(0.880791\pi\) | |||||||
\(450\) | −0.956884 | − | 0.775997i | −0.0451079 | − | 0.0365808i | ||||
\(451\) | 21.3676 | − | 37.0097i | 1.00616 | − | 1.74272i | ||||
\(452\) | 6.73104 | + | 11.6585i | 0.316602 | + | 0.548370i | ||||
\(453\) | −5.04708 | − | 5.91362i | −0.237132 | − | 0.277846i | ||||
\(454\) | 0.725057 | + | 1.25584i | 0.0340286 | + | 0.0589393i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.58577 | − | 8.88819i | −0.355236 | − | 0.416228i | ||||
\(457\) | −34.2405 | −1.60170 | −0.800852 | − | 0.598863i | \(-0.795619\pi\) | ||||
−0.800852 | + | 0.598863i | \(0.795619\pi\) | |||||||
\(458\) | 1.32107 | − | 2.28817i | 0.0617297 | − | 0.106919i | ||||
\(459\) | 0.223260 | + | 8.88819i | 0.0104209 | + | 0.414865i | ||||
\(460\) | 12.9026 | + | 22.3479i | 0.601585 | + | 1.04198i | ||||
\(461\) | −10.1938 | + | 17.6561i | −0.474772 | + | 0.822328i | −0.999583 | − | 0.0288903i | \(-0.990803\pi\) |
0.524811 | + | 0.851219i | \(0.324136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.40451 | − | 5.89679i | −0.158221 | − | 0.274047i | 0.776006 | − | 0.630725i | \(-0.217243\pi\) |
−0.934227 | + | 0.356678i | \(0.883909\pi\) | |||||||
\(464\) | 3.88852 | − | 6.73511i | 0.180520 | − | 0.312670i | ||||
\(465\) | −9.80378 | + | 27.6538i | −0.454639 | + | 1.28241i | ||||
\(466\) | 0.973045 | + | 1.68536i | 0.0450754 | + | 0.0780729i | ||||
\(467\) | −12.3956 | − | 21.4698i | −0.573598 | − | 0.993502i | −0.996192 | − | 0.0871825i | \(-0.972214\pi\) |
0.422594 | − | 0.906319i | \(-0.361120\pi\) | |||||||
\(468\) | 16.6733 | + | 13.5214i | 0.770721 | + | 0.625026i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.89372 | − | 5.01207i | 0.133477 | − | 0.231190i | ||||
\(471\) | 1.75241 | − | 0.324145i | 0.0807466 | − | 0.0149358i | ||||
\(472\) | −5.71754 | −0.263171 | ||||||||
\(473\) | −6.94282 | −0.319231 | ||||||||
\(474\) | −4.00279 | + | 0.740401i | −0.183854 | + | 0.0340078i | ||||
\(475\) | 6.14441 | − | 10.6424i | 0.281925 | − | 0.488309i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.01887 | + | 31.5428i | −0.229798 | + | 1.44424i | ||||
\(478\) | −2.53022 | − | 4.38248i | −0.115730 | − | 0.200450i | ||||
\(479\) | 5.54984 | + | 9.61260i | 0.253579 | + | 0.439211i | 0.964508 | − | 0.264052i | \(-0.0850590\pi\) |
−0.710930 | + | 0.703263i | \(0.751726\pi\) | |||||||
\(480\) | 4.14132 | − | 11.6815i | 0.189024 | − | 0.533186i | ||||
\(481\) | −3.05733 | + | 5.29545i | −0.139402 | + | 0.241452i | ||||
\(482\) | −1.63697 | − | 2.83532i | −0.0745621 | − | 0.129145i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.30314 | − | 10.9174i | 0.286506 | − | 0.496244i | ||||
\(485\) | 3.96978 | + | 6.87585i | 0.180258 | + | 0.312216i | ||||
\(486\) | 2.27445 | − | 2.95324i | 0.103171 | − | 0.133962i | ||||
\(487\) | 5.01887 | − | 8.69295i | 0.227427 | − | 0.393915i | −0.729618 | − | 0.683855i | \(-0.760302\pi\) |
0.957045 | + | 0.289940i | \(0.0936354\pi\) | |||||||
\(488\) | 7.52933 | 0.340837 | ||||||||
\(489\) | −7.67798 | − | 8.99623i | −0.347210 | − | 0.406824i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.19398 | + | 10.7283i | 0.279530 | + | 0.484161i | 0.971268 | − | 0.237988i | \(-0.0764879\pi\) |
−0.691738 | + | 0.722149i | \(0.743155\pi\) | |||||||
\(492\) | −22.3236 | − | 26.1563i | −1.00642 | − | 1.17922i | ||||
\(493\) | 1.81781 | + | 3.14854i | 0.0818702 | + | 0.141803i | ||||
\(494\) | 3.15103 | − | 5.45774i | 0.141772 | − | 0.245556i | ||||
\(495\) | −30.3647 | + | 11.6312i | −1.36479 | + | 0.522782i | ||||
\(496\) | −23.9225 | −1.07415 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.954170 | + | 2.69145i | −0.0427574 | + | 0.120607i | ||||
\(499\) | −5.11109 | + | 8.85267i | −0.228804 | + | 0.396300i | −0.957454 | − | 0.288586i | \(-0.906815\pi\) |
0.728650 | + | 0.684886i | \(0.240148\pi\) | |||||||
\(500\) | −16.5293 | −0.739212 | ||||||||
\(501\) | −20.2330 | − | 23.7068i | −0.903943 | − | 1.05914i | ||||
\(502\) | 3.63562 | 0.162266 | ||||||||
\(503\) | −8.45753 | −0.377102 | −0.188551 | − | 0.982063i | \(-0.560379\pi\) | ||||
−0.188551 | + | 0.982063i | \(0.560379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.7680 | 1.28016 | ||||||||
\(506\) | −5.12476 | −0.227824 | ||||||||
\(507\) | −0.327145 | + | 0.922786i | −0.0145290 | + | 0.0409824i | ||||
\(508\) | −17.7012 | −0.785364 | ||||||||
\(509\) | 5.28286 | − | 9.15018i | 0.234159 | − | 0.405574i | −0.724869 | − | 0.688886i | \(-0.758100\pi\) |
0.959028 | + | 0.283312i | \(0.0914332\pi\) | |||||||
\(510\) | 1.19238 | + | 1.39710i | 0.0527994 | + | 0.0618647i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.0071 | 0.751616 | ||||||||
\(513\) | 32.6569 | + | 17.7764i | 1.44184 | + | 0.784847i | ||||
\(514\) | −3.06335 | + | 5.30587i | −0.135118 | + | 0.234032i | ||||
\(515\) | 10.3490 | + | 17.9249i | 0.456030 | + | 0.789867i | ||||
\(516\) | −1.86673 | + | 5.26554i | −0.0821783 | + | 0.231802i | ||||
\(517\) | −19.5260 | − | 33.8200i | −0.858752 | − | 1.48740i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.41423 | + | 0.261592i | −0.0620778 | + | 0.0114826i | ||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | −9.87788 | + | 17.1090i | −0.432758 | + | 0.749558i | −0.997110 | − | 0.0759760i | \(-0.975793\pi\) |
0.564352 | + | 0.825534i | \(0.309126\pi\) | |||||||
\(522\) | 0.239514 | − | 1.50531i | 0.0104833 | − | 0.0658854i | ||||
\(523\) | 16.2641 | + | 28.1702i | 0.711179 | + | 1.23180i | 0.964415 | + | 0.264394i | \(0.0851718\pi\) |
−0.253236 | + | 0.967405i | \(0.581495\pi\) | |||||||
\(524\) | −4.17984 | + | 7.23970i | −0.182597 | + | 0.316268i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.848970 | − | 1.47046i | −0.0370168 | − | 0.0641150i | ||||
\(527\) | 5.59166 | − | 9.68504i | 0.243577 | − | 0.421887i | ||||
\(528\) | −17.2110 | − | 20.1660i | −0.749012 | − | 0.877612i | ||||
\(529\) | −1.63160 | − | 2.82601i | −0.0709391 | − | 0.122870i | ||||
\(530\) | 3.29913 | + | 5.71426i | 0.143305 | + | 0.248211i | ||||
\(531\) | 16.9891 | − | 6.50767i | 0.737266 | − | 0.282409i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.8187 | − | 32.5950i | 0.815130 | − | 1.41185i | ||||
\(534\) | 1.35387 | + | 1.58632i | 0.0585879 | + | 0.0686470i | ||||
\(535\) | −10.2544 | −0.443336 | ||||||||
\(536\) | −7.79071 | −0.336507 | ||||||||
\(537\) | −4.38631 | + | 12.3726i | −0.189283 | + | 0.533917i | ||||
\(538\) | 1.96457 | − | 3.40274i | 0.0846987 | − | 0.146702i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.657014 | + | 26.1563i | 0.0282734 | + | 1.12559i | ||||
\(541\) | −7.61109 | − | 13.1828i | −0.327226 | − | 0.566773i | 0.654734 | − | 0.755859i | \(-0.272781\pi\) |
−0.981960 | + | 0.189087i | \(0.939447\pi\) | |||||||
\(542\) | −1.51819 | − | 2.62959i | −0.0652119 | − | 0.112950i | ||||
\(543\) | 0.696860 | − | 0.128899i | 0.0299051 | − | 0.00553159i | ||||
\(544\) | −2.36203 | + | 4.09116i | −0.101271 | + | 0.175407i | ||||
\(545\) | 9.41234 | + | 16.3027i | 0.403180 | + | 0.698329i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.6871 | + | 20.2427i | −0.499706 | + | 0.865517i | −1.00000 | 0.000339172i | \(-0.999892\pi\) | |
0.500294 | + | 0.865856i | \(0.333225\pi\) | |||||||
\(548\) | 20.0007 | + | 34.6422i | 0.854387 | + | 1.47984i | ||||
\(549\) | −22.3727 | + | 8.56984i | −0.954845 | + | 0.365752i | ||||
\(550\) | −0.858685 | + | 1.48729i | −0.0366144 | + | 0.0634181i | ||||
\(551\) | 15.2040 | 0.647711 | ||||||||
\(552\) | −2.79637 | + | 7.88779i | −0.119021 | + | 0.335726i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.0990521 | + | 0.171563i | 0.00420832 | + | 0.00728902i | ||||
\(555\) | −7.32846 | + | 1.35556i | −0.311076 | + | 0.0575401i | ||||
\(556\) | −15.3107 | − | 26.5189i | −0.649319 | − | 1.12465i | ||||
\(557\) | −13.8337 | + | 23.9606i | −0.586151 | + | 1.01524i | 0.408580 | + | 0.912723i | \(0.366024\pi\) |
−0.994731 | + | 0.102521i | \(0.967309\pi\) | |||||||
\(558\) | −4.37840 | + | 1.67714i | −0.185352 | + | 0.0709990i | ||||
\(559\) | −6.11465 | −0.258622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1871 | − | 2.25427i | 0.514542 | − | 0.0951755i | ||||
\(562\) | −0.624075 | + | 1.08093i | −0.0263250 | + | 0.0455963i | ||||
\(563\) | −8.55824 | −0.360687 | −0.180343 | − | 0.983604i | \(-0.557721\pi\) | ||||
−0.180343 | + | 0.983604i | \(0.557721\pi\) | |||||||
\(564\) | −30.8996 | + | 5.71554i | −1.30111 | + | 0.240668i | ||||
\(565\) | −17.9589 | −0.755536 | ||||||||
\(566\) | −1.75855 | −0.0739175 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.88237 | −0.246819 | ||||||||
\(569\) | 13.7278 | 0.575498 | 0.287749 | − | 0.957706i | \(-0.407093\pi\) | ||||
0.287749 | + | 0.957706i | \(0.407093\pi\) | |||||||
\(570\) | 7.55307 | − | 1.39710i | 0.316363 | − | 0.0585181i | ||||
\(571\) | 10.7174 | 0.448508 | 0.224254 | − | 0.974531i | \(-0.428005\pi\) | ||||
0.224254 | + | 0.974531i | \(0.428005\pi\) | |||||||
\(572\) | 14.9622 | − | 25.9153i | 0.625600 | − | 1.08357i | ||||
\(573\) | 27.2916 | − | 5.04816i | 1.14012 | − | 0.210890i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.80111 | −0.367032 | ||||||||
\(576\) | −18.6586 | + | 7.14713i | −0.777440 | + | 0.297797i | ||||
\(577\) | −22.8177 | + | 39.5214i | −0.949912 | + | 1.64530i | −0.204307 | + | 0.978907i | \(0.565494\pi\) |
−0.745605 | + | 0.666389i | \(0.767839\pi\) | |||||||
\(578\) | 1.68250 | + | 2.91417i | 0.0699827 | + | 0.121214i | ||||
\(579\) | −21.0754 | + | 3.89834i | −0.875863 | + | 0.162010i | ||||
\(580\) | 5.34950 | + | 9.26560i | 0.222126 | + | 0.384733i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.423945 | + | 1.19583i | −0.0175731 | + | 0.0495689i | ||||
\(583\) | 44.5231 | 1.84396 | ||||||||
\(584\) | 3.37323 | − | 5.84260i | 0.139585 | − | 0.241768i | ||||
\(585\) | −26.7427 | + | 10.2437i | −1.10567 | + | 0.423527i | ||||
\(586\) | −0.935657 | − | 1.62060i | −0.0386516 | − | 0.0669466i | ||||
\(587\) | −5.10948 | + | 8.84988i | −0.210891 | + | 0.365274i | −0.951994 | − | 0.306118i | \(-0.900970\pi\) |
0.741103 | + | 0.671392i | \(0.234303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.3840 | − | 40.5023i | −0.963521 | − | 1.66887i | ||||
\(590\) | 1.87919 | − | 3.25486i | 0.0773652 | − | 0.134000i | ||||
\(591\) | 39.3465 | − | 7.27798i | 1.61850 | − | 0.299376i | ||||
\(592\) | −3.03831 | − | 5.26250i | −0.124874 | − | 0.216287i | ||||
\(593\) | 5.69804 | + | 9.86929i | 0.233990 | + | 0.405283i | 0.958979 | − | 0.283478i | \(-0.0914883\pi\) |
−0.724988 | + | 0.688761i | \(0.758155\pi\) | |||||||
\(594\) | −4.56382 | − | 2.48426i | −0.187256 | − | 0.101930i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.89411 | − | 10.2089i | 0.241432 | − | 0.418173i | ||||
\(597\) | 3.90451 | − | 11.0136i | 0.159801 | − | 0.450755i | ||||
\(598\) | −4.51346 | −0.184569 | ||||||||
\(599\) | −34.5746 | −1.41268 | −0.706339 | − | 0.707874i | \(-0.749655\pi\) | ||||
−0.706339 | + | 0.707874i | \(0.749655\pi\) | |||||||
\(600\) | 1.82061 | + | 2.13320i | 0.0743261 | + | 0.0870873i | ||||
\(601\) | −19.4207 | + | 33.6376i | −0.792187 | + | 1.37211i | 0.132423 | + | 0.991193i | \(0.457724\pi\) |
−0.924610 | + | 0.380915i | \(0.875609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.1494 | − | 8.86734i | 0.942716 | − | 0.361106i | ||||
\(604\) | 4.36032 | + | 7.55230i | 0.177419 | + | 0.307299i | ||||
\(605\) | 8.40861 | + | 14.5641i | 0.341858 | + | 0.592116i | ||||
\(606\) | 2.98439 | + | 3.49679i | 0.121233 | + | 0.142048i | ||||
\(607\) | −20.6662 | + | 35.7950i | −0.838817 | + | 1.45287i | 0.0520683 | + | 0.998644i | \(0.483419\pi\) |
−0.890885 | + | 0.454229i | \(0.849915\pi\) | |||||||
\(608\) | 9.87788 | + | 17.1090i | 0.400601 | + | 0.693861i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.47468 | + | 4.28627i | −0.100197 | + | 0.173546i | ||||
\(611\) | −17.1969 | − | 29.7858i | −0.695710 | − | 1.20501i | ||||
\(612\) | 1.56711 | − | 9.84903i | 0.0633467 | − | 0.398123i | ||||
\(613\) | 14.3285 | − | 24.8176i | 0.578721 | − | 1.00237i | −0.416905 | − | 0.908950i | \(-0.636885\pi\) |
0.995626 | − | 0.0934244i | \(-0.0297813\pi\) | |||||||
\(614\) | 5.42114 | 0.218779 | ||||||||
\(615\) | 45.1088 | − | 8.34384i | 1.81896 | − | 0.336456i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8518 | + | 29.1883i | 0.678430 | + | 1.17508i | 0.975454 | + | 0.220205i | \(0.0706726\pi\) |
−0.297024 | + | 0.954870i | \(0.595994\pi\) | |||||||
\(618\) | −1.10520 | + | 3.11747i | −0.0444577 | + | 0.125403i | ||||
\(619\) | 0.719036 | + | 1.24541i | 0.0289005 | + | 0.0500571i | 0.880114 | − | 0.474763i | \(-0.157466\pi\) |
−0.851213 | + | 0.524820i | \(0.824133\pi\) | |||||||
\(620\) | 16.4552 | − | 28.5013i | 0.660859 | − | 1.14464i | ||||
\(621\) | −0.668677 | − | 26.6207i | −0.0268331 | − | 1.06825i | ||||
\(622\) | −7.72789 | −0.309860 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.1580 | − | 17.7605i | −0.606806 | − | 0.710990i | ||||
\(625\) | 15.3187 | − | 26.5328i | 0.612750 | − | 1.06131i | ||||
\(626\) | −5.81538 | −0.232429 | ||||||||
\(627\) | 17.3187 | − | 48.8514i | 0.691644 | − | 1.95094i | ||||
\(628\) | −1.99900 | −0.0797686 | ||||||||
\(629\) | 2.84071 | 0.113266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7680 | −1.22486 | −0.612428 | − | 0.790527i | \(-0.709807\pi\) | ||||
−0.612428 | + | 0.790527i | \(0.709807\pi\) | |||||||
\(632\) | 9.26647 | 0.368600 | ||||||||
\(633\) | −18.9864 | − | 22.2462i | −0.754640 | − | 0.884206i | ||||
\(634\) | 1.22872 | 0.0487987 | ||||||||
\(635\) | 11.8070 | − | 20.4503i | 0.468547 | − | 0.811547i | ||||
\(636\) | 11.9710 | − | 33.7670i | 0.474682 | − | 1.33895i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.12476 | −0.0841202 | ||||||||
\(639\) | 17.4789 | − | 6.69528i | 0.691456 | − | 0.264861i | ||||
\(640\) | −9.21946 | + | 15.9686i | −0.364431 | + | 0.631213i | ||||
\(641\) | −4.61956 | − | 8.00132i | −0.182462 | − | 0.316033i | 0.760257 | − | 0.649623i | \(-0.225073\pi\) |
−0.942718 | + | 0.333590i | \(0.891740\pi\) | |||||||
\(642\) | −1.06379 | − | 1.24644i | −0.0419845 | − | 0.0491929i | ||||
\(643\) | −12.7795 | − | 22.1348i | −0.503976 | − | 0.872912i | −0.999989 | − | 0.00459728i | \(-0.998537\pi\) |
0.496013 | − | 0.868315i | \(-0.334797\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.83818 | − | 5.66886i | −0.190503 | − | 0.223211i | ||||
\(646\) | −2.92777 | −0.115192 | ||||||||
\(647\) | 14.1556 | − | 24.5181i | 0.556512 | − | 0.963908i | −0.441272 | − | 0.897374i | \(-0.645472\pi\) |
0.997784 | − | 0.0665343i | \(-0.0211942\pi\) | |||||||
\(648\) | −6.31393 | + | 5.66886i | −0.248035 | + | 0.222694i | ||||
\(649\) | −12.6803 | − | 21.9629i | −0.497744 | − | 0.862118i | ||||
\(650\) | −0.756258 | + | 1.30988i | −0.0296629 | + | 0.0513776i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.63323 | + | 11.4891i | 0.259778 | + | 0.449948i | ||||
\(653\) | 4.17511 | − | 7.23150i | 0.163385 | − | 0.282990i | −0.772696 | − | 0.634776i | \(-0.781092\pi\) |
0.936080 | + | 0.351786i | \(0.114426\pi\) | |||||||
\(654\) | −1.00517 | + | 2.83532i | −0.0393054 | + | 0.110870i | ||||
\(655\) | −5.57605 | − | 9.65801i | −0.217874 | − | 0.377370i | ||||
\(656\) | 18.7017 | + | 32.3922i | 0.730177 | + | 1.26470i | ||||
\(657\) | −3.37323 | + | 21.2001i | −0.131602 | + | 0.827096i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7862 | − | 29.0745i | 0.653897 | − | 1.13258i | −0.328272 | − | 0.944583i | \(-0.606466\pi\) |
0.982169 | − | 0.188000i | \(-0.0602005\pi\) | |||||||
\(660\) | 35.8646 | − | 6.63392i | 1.39603 | − | 0.258225i | ||||
\(661\) | 16.9534 | 0.659410 | 0.329705 | − | 0.944084i | \(-0.393051\pi\) | ||||
0.329705 | + | 0.944084i | \(0.393051\pi\) | |||||||
\(662\) | −2.79725 | −0.108718 | ||||||||
\(663\) | 10.7334 | − | 1.98537i | 0.416851 | − | 0.0771055i | ||||
\(664\) | 3.25021 | − | 5.62952i | 0.126133 | − | 0.218468i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.925025 | − | 0.750160i | −0.0358440 | − | 0.0290681i | ||||
\(667\) | −5.44445 | − | 9.43007i | −0.210810 | − | 0.365134i | ||||
\(668\) | 17.4799 | + | 30.2760i | 0.676316 | + | 1.17141i | ||||
\(669\) | 2.60520 | − | 7.34856i | 0.100723 | − | 0.284112i | ||||
\(670\) | 2.56059 | − | 4.43507i | 0.0989242 | − | 0.171342i | ||||
\(671\) | 16.6984 | + | 28.9225i | 0.644636 | + | 1.11654i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2157 | − | 38.4788i | 0.856354 | − | 1.48325i | −0.0190299 | − | 0.999819i | \(-0.506058\pi\) |
0.875384 | − | 0.483429i | \(-0.160609\pi\) | |||||||
\(674\) | 4.02859 | + | 6.97772i | 0.155175 | + | 0.268772i | ||||
\(675\) | −7.83777 | − | 4.26639i | −0.301676 | − | 0.164213i | ||||
\(676\) | 0.549100 | − | 0.951068i | 0.0211192 | − | 0.0365796i | ||||
\(677\) | 14.3736 | 0.552423 | 0.276212 | − | 0.961097i | \(-0.410921\pi\) | ||||
0.276212 | + | 0.961097i | \(0.410921\pi\) | |||||||
\(678\) | −1.86306 | − | 2.18293i | −0.0715502 | − | 0.0838349i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.09058 | − | 3.62099i | −0.0801701 | − | 0.138859i | ||||
\(681\) | 6.81875 | + | 7.98947i | 0.261295 | + | 0.306157i | ||||
\(682\) | 3.26793 | + | 5.66021i | 0.125135 | + | 0.216741i | ||||
\(683\) | 16.1546 | − | 27.9806i | 0.618138 | − | 1.07065i | −0.371687 | − | 0.928358i | \(-0.621220\pi\) |
0.989825 | − | 0.142289i | \(-0.0454462\pi\) | |||||||
\(684\) | −32.3931 | − | 26.2696i | −1.23858 | − | 1.00444i | ||||
\(685\) | −53.3632 | −2.03890 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.39480 | − | 18.0380i | 0.243977 | − | 0.688192i | ||||
\(688\) | 3.03831 | − | 5.26250i | 0.115834 | − | 0.200631i | ||||
\(689\) | 39.2122 | 1.49387 | ||||||||
\(690\) | −3.57124 | − | 4.18440i | −0.135955 | − | 0.159297i | ||||
\(691\) | 28.9962 | 1.10307 | 0.551533 | − | 0.834153i | \(-0.314043\pi\) | ||||
0.551533 | + | 0.834153i | \(0.314043\pi\) | |||||||
\(692\) | 1.61323 | 0.0613259 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.53078 | 0.247905 | ||||||||
\(695\) | 40.8500 | 1.54953 | ||||||||
\(696\) | −1.15939 | + | 3.27033i | −0.0439467 | + | 0.123962i | ||||
\(697\) | −17.4854 | −0.662306 | ||||||||
\(698\) | −2.73999 | + | 4.74580i | −0.103710 | + | 0.179631i | ||||
\(699\) | 9.15093 | + | 10.7221i | 0.346120 | + | 0.405546i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.3912 | −0.996783 | −0.498392 | − | 0.866952i | \(-0.666076\pi\) | ||||
−0.498392 | + | 0.866952i | \(0.666076\pi\) | |||||||
\(702\) | −4.01943 | − | 2.18793i | −0.151704 | − | 0.0825780i | ||||
\(703\) | 5.93984 | − | 10.2881i | 0.224025 | − | 0.388023i | ||||
\(704\) | 13.9263 | + | 24.1210i | 0.524866 | + | 0.909095i | ||||
\(705\) | 14.0074 | − | 39.5109i | 0.527548 | − | 1.48807i | ||||
\(706\) | −1.22782 | − | 2.12664i | −0.0462095 | − | 0.0800372i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.0663 | + | 3.71170i | −0.754139 | + | 0.139494i | ||||
\(709\) | −7.88564 | −0.296151 | −0.148076 | − | 0.988976i | \(-0.547308\pi\) | ||||
−0.148076 | + | 0.988976i | \(0.547308\pi\) | |||||||
\(710\) | 1.93337 | − | 3.34870i | 0.0725581 | − | 0.125674i | ||||
\(711\) | −27.5345 | + | 10.5470i | −1.03262 | + | 0.395545i | ||||
\(712\) | −2.37373 | − | 4.11142i | −0.0889592 | − | 0.154082i | ||||
\(713\) | −16.7473 | + | 29.0073i | −0.627193 | + | 1.08633i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.9601 | + | 34.5718i | 0.746464 | + | 1.29291i | ||||
\(716\) | 7.36225 | − | 12.7518i | 0.275140 | − | 0.476557i | ||||
\(717\) | −23.7953 | − | 27.8808i | −0.888652 | − | 1.04123i | ||||
\(718\) | −1.20765 | − | 2.09172i | −0.0450693 | − | 0.0780623i | ||||
\(719\) | −16.5754 | − | 28.7095i | −0.618159 | − | 1.07068i | −0.989822 | − | 0.142314i | \(-0.954546\pi\) |
0.371663 | − | 0.928368i | \(-0.378788\pi\) | |||||||
\(720\) | 4.47200 | − | 28.1058i | 0.166662 | − | 1.04744i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.85021 | + | 6.66877i | −0.143290 | + | 0.248186i | ||||
\(723\) | −15.3948 | − | 18.0380i | −0.572539 | − | 0.670840i | ||||
\(724\) | −0.794919 | −0.0295429 | ||||||||
\(725\) | −3.64900 | −0.135521 | ||||||||
\(726\) | −0.897982 | + | 2.53296i | −0.0333273 | + | 0.0940070i | ||||
\(727\) | 16.5502 | − | 28.6658i | 0.613814 | − | 1.06316i | −0.376777 | − | 0.926304i | \(-0.622968\pi\) |
0.990591 | − | 0.136853i | \(-0.0436989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.3090 | − | 24.0310i | 0.455890 | − | 0.890036i | ||||
\(730\) | 2.21737 | + | 3.84060i | 0.0820685 | + | 0.142147i | ||||
\(731\) | 1.42035 | + | 2.46012i | 0.0525337 | + | 0.0909910i | ||||
\(732\) | 26.4250 | − | 4.88787i | 0.976697 | − | 0.180661i | ||||
\(733\) | −22.2795 | + | 38.5892i | −0.822911 | + | 1.42532i | 0.0805946 | + | 0.996747i | \(0.474318\pi\) |
−0.903505 | + | 0.428577i | \(0.859015\pi\) | |||||||
\(734\) | 0.929636 | + | 1.61018i | 0.0343135 | + | 0.0594327i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.07442 | − | 12.2533i | 0.260767 | − | 0.451661i | ||||
\(737\) | −17.2781 | − | 29.9266i | −0.636448 | − | 1.10236i | ||||
\(738\) | 5.69380 | + | 4.61745i | 0.209592 | + | 0.169971i | ||||
\(739\) | −19.9045 | + | 34.4756i | −0.732199 | + | 1.26821i | 0.223742 | + | 0.974648i | \(0.428173\pi\) |
−0.955941 | + | 0.293558i | \(0.905161\pi\) | |||||||
\(740\) | 8.35969 | 0.307308 | ||||||||
\(741\) | 15.2529 | − | 43.0242i | 0.560329 | − | 1.58053i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.37072 | − | 9.30237i | −0.197033 | − | 0.341271i | 0.750532 | − | 0.660834i | \(-0.229797\pi\) |
−0.947565 | + | 0.319563i | \(0.896464\pi\) | |||||||
\(744\) | 10.4951 | − | 1.94129i | 0.384769 | − | 0.0711712i | ||||
\(745\) | 7.86295 | + | 13.6190i | 0.288076 | + | 0.498962i | ||||
\(746\) | −2.88276 | + | 4.99309i | −0.105545 | + | 0.182810i | ||||
\(747\) | −3.25021 | + | 20.4270i | −0.118919 | + | 0.747385i | ||||
\(748\) | −13.9021 | −0.508310 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.46496 | − | 0.640919i | 0.126523 | − | 0.0234031i | ||||
\(751\) | −9.85705 | + | 17.0729i | −0.359689 | + | 0.622999i | −0.987909 | − | 0.155036i | \(-0.950450\pi\) |
0.628220 | + | 0.778036i | \(0.283784\pi\) | |||||||
\(752\) | 34.1797 | 1.24641 | ||||||||
\(753\) | 25.8948 | − | 4.78980i | 0.943659 | − | 0.174550i | ||||
\(754\) | −1.87131 | −0.0681492 | ||||||||
\(755\) | −11.6336 | −0.423391 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3549 | 1.28499 | 0.642497 | − | 0.766288i | \(-0.277898\pi\) | ||||
0.642497 | + | 0.766288i | \(0.277898\pi\) | |||||||
\(758\) | −3.19424 | −0.116020 | ||||||||
\(759\) | −36.5012 | + | 6.75168i | −1.32491 | + | 0.245070i | ||||
\(760\) | −17.4854 | −0.634261 | ||||||||
\(761\) | −19.5572 | + | 33.8741i | −0.708948 | + | 1.22793i | 0.256300 | + | 0.966597i | \(0.417497\pi\) |
−0.965248 | + | 0.261336i | \(0.915837\pi\) | |||||||
\(762\) | 3.71063 | − | 0.686360i | 0.134422 | − | 0.0248642i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −31.1319 | −1.12631 | ||||||||
\(765\) | 10.3334 | + | 8.37997i | 0.373604 | + | 0.302978i | ||||
\(766\) | 1.10480 | − | 1.91357i | 0.0399180 | − | 0.0691399i | ||||
\(767\) | −11.1677 | − | 19.3430i | −0.403243 | − | 0.698437i | ||||
\(768\) | 19.7893 | − | 3.66045i | 0.714085 | − | 0.132085i | ||||
\(769\) | −18.9240 | − | 32.7773i | −0.682415 | − | 1.18198i | −0.974242 | − | 0.225507i | \(-0.927596\pi\) |
0.291826 | − | 0.956471i | \(-0.405737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.8285 | + | 41.8270i | −0.534034 | + | 1.50636i | ||||
\(772\) | 24.0410 | 0.865255 | ||||||||
\(773\) | 14.9133 | − | 25.8305i | 0.536393 | − | 0.929059i | −0.462702 | − | 0.886514i | \(-0.653120\pi\) |
0.999095 | − | 0.0425453i | \(-0.0135467\pi\) | |||||||
\(774\) | 0.187145 | − | 1.17617i | 0.00672679 | − | 0.0422767i | ||||
\(775\) | 5.61224 | + | 9.72068i | 0.201598 | + | 0.349177i | ||||
\(776\) | 1.44409 | − | 2.50124i | 0.0518399 | − | 0.0897894i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.24923 | − | 2.16373i | −0.0447870 | − | 0.0775734i | ||||
\(779\) | −36.5614 | + | 63.3263i | −1.30995 | + | 2.26890i | ||||
\(780\) | 31.5865 | − | 5.84260i | 1.13098 | − | 0.209199i | ||||
\(781\) | −13.0458 | − | 22.5960i | −0.466817 | − | 0.808550i | ||||
\(782\) | 1.04842 | + | 1.81591i | 0.0374913 | + | 0.0649369i | ||||
\(783\) | −0.277238 | − | 11.0371i | −0.00990768 | − | 0.394434i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.33336 | − | 2.30946i | 0.0475898 | − | 0.0824280i | ||||
\(786\) | 0.595485 | − | 1.67970i | 0.0212402 | − | 0.0599129i | ||||
\(787\) | −17.6206 | −0.628107 | −0.314053 | − | 0.949405i | \(-0.601687\pi\) | ||||
−0.314053 | + | 0.949405i | \(0.601687\pi\) | |||||||
\(788\) | −44.8832 | −1.59890 | ||||||||
\(789\) | −7.98407 | − | 9.35488i | −0.284241 | − | 0.333043i | ||||
\(790\) | −3.04563 | + | 5.27518i | −0.108359 | + | 0.187683i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.18715 | + | 7.45043i | 0.326451 | + | 0.264739i | ||||
\(793\) | 14.7066 | + | 25.4725i | 0.522246 | + | 0.904556i | ||||
\(794\) | 0.0489195 | + | 0.0847311i | 0.00173609 | + | 0.00300699i | ||||
\(795\) | 31.0264 | + | 36.3534i | 1.10039 | + | 1.28932i | ||||
\(796\) | −6.55357 | + | 11.3511i | −0.232285 | + | 0.402330i | ||||
\(797\) | 5.06056 | + | 8.76515i | 0.179254 | + | 0.310477i | 0.941625 | − | 0.336663i | \(-0.109298\pi\) |
−0.762371 | + | 0.647140i | \(0.775965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.98921 | + | 13.8377i | −0.282638 | + | 0.489543i | ||||
\(800\) | −2.37072 | − | 4.10621i | −0.0838177 | − | 0.145177i | ||||
\(801\) | 11.7329 | + | 9.51495i | 0.414562 | + | 0.336194i | ||||
\(802\) | −1.82365 | + | 3.15865i | −0.0643953 | + | 0.111536i | ||||
\(803\) | 29.9244 | 1.05601 | ||||||||
\(804\) | −27.3424 | + | 5.05756i | −0.964291 | + | 0.178366i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.87812 | + | 4.98504i | 0.101377 | + | 0.175591i | ||||
\(807\) | 9.50972 | − | 26.8243i | 0.334758 | − | 0.944260i | ||||
\(808\) | −5.23250 | − | 9.06295i | −0.184079 | − | 0.318834i | ||||
\(809\) | 23.5735 | − | 40.8305i | 0.828799 | − | 1.43552i | −0.0701816 | − | 0.997534i | \(-0.522358\pi\) |
0.898981 | − | 0.437988i | \(-0.144309\pi\) | |||||||
\(810\) | −1.15193 | − | 5.45757i | −0.0404748 | − | 0.191759i | ||||
\(811\) | −21.0577 | −0.739435 | −0.369717 | − | 0.929144i | \(-0.620546\pi\) | ||||
−0.369717 | + | 0.929144i | \(0.620546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.2777 | − | 16.7291i | −0.500742 | − | 0.586715i | ||||
\(814\) | −0.830095 | + | 1.43777i | −0.0290948 | + | 0.0503937i | ||||
\(815\) | −17.6979 | −0.619931 | ||||||||
\(816\) | −3.62463 | + | 10.2241i | −0.126887 | + | 0.357915i | ||||
\(817\) | 11.8797 | 0.415617 | ||||||||
\(818\) | −1.46504 | −0.0512238 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.4563 | −1.79693 | ||||||||
\(821\) | 11.1604 | 0.389499 | 0.194750 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194750 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(822\) | −5.53590 | − | 6.48638i | −0.193087 | − | 0.226238i | ||||
\(823\) | 9.43474 | 0.328874 | 0.164437 | − | 0.986388i | \(-0.447419\pi\) | ||||
0.164437 | + | 0.986388i | \(0.447419\pi\) | |||||||
\(824\) | 3.76466 | − | 6.52059i | 0.131148 | − | 0.227156i | ||||
\(825\) | −4.15656 | + | 11.7245i | −0.144713 | + | 0.408195i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.2646 | 0.600348 | 0.300174 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300174 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(828\) | −4.69359 | + | 29.4984i | −0.163114 | + | 1.02514i | ||||
\(829\) | −24.2263 | + | 41.9612i | −0.841415 | + | 1.45737i | 0.0472838 | + | 0.998881i | \(0.484943\pi\) |
−0.888699 | + | 0.458492i | \(0.848390\pi\) | |||||||
\(830\) | 2.13650 | + | 3.70053i | 0.0741591 | + | 0.128447i | ||||
\(831\) | 0.931528 | + | 1.09146i | 0.0323143 | + | 0.0378625i | ||||
\(832\) | 12.2651 | + | 21.2438i | 0.425215 | + | 0.736495i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.23779 | + | 4.96538i | 0.146743 | + | 0.171937i | ||||
\(835\) | −46.6375 | −1.61396 | ||||||||
\(836\) | −29.0688 | + | 50.3487i | −1.00537 | + | 1.74135i | ||||
\(837\) | −28.9757 | + | 17.7138i | −1.00155 | + | 0.612280i | ||||
\(838\) | −0.186860 | − | 0.323651i | −0.00645497 | − | 0.0111803i | ||||
\(839\) | −7.43429 | + | 12.8766i | −0.256660 | + | 0.444548i | −0.965345 | − | 0.260977i | \(-0.915955\pi\) |
0.708685 | + | 0.705525i | \(0.249289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2427 | + | 21.2050i | 0.422162 | + | 0.731206i | ||||
\(842\) | −2.78139 | + | 4.81750i | −0.0958529 | + | 0.166022i | ||||
\(843\) | −3.02090 | + | 8.52113i | −0.104045 | + | 0.293483i | ||||
\(844\) | 16.4029 | + | 28.4106i | 0.564610 | + | 0.977934i | ||||
\(845\) | 0.732518 | + | 1.26876i | 0.0251994 | + | 0.0436466i | ||||
\(846\) | 6.25574 | − | 2.39625i | 0.215077 | − | 0.0823848i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.4841 | + | 33.7475i | −0.669088 | + | 1.15889i | ||||
\(849\) | −12.5253 | + | 2.31683i | −0.429868 | + | 0.0795132i | ||||
\(850\) | 0.702674 | 0.0241015 | ||||||||
\(851\) | −8.50808 | −0.291653 | ||||||||
\(852\) | −20.6448 | + | 3.81870i | −0.707281 | + | 0.130827i | ||||
\(853\) | 3.99900 | − | 6.92648i | 0.136923 | − | 0.237158i | −0.789407 | − | 0.613870i | \(-0.789612\pi\) |
0.926331 | + | 0.376712i | \(0.122945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 51.9562 | − | 19.9018i | 1.77687 | − | 0.680626i | ||||
\(856\) | 1.86513 | + | 3.23050i | 0.0637488 | + | 0.110416i | ||||
\(857\) | −21.5661 | − | 37.3536i | −0.736684 | − | 1.27597i | −0.953980 | − | 0.299869i | \(-0.903057\pi\) |
0.217296 | − | 0.976106i | \(-0.430276\pi\) | |||||||
\(858\) | −2.13160 | + | 6.01266i | −0.0727716 | + | 0.205269i | ||||
\(859\) | −1.22180 | + | 2.11621i | −0.0416871 | + | 0.0722042i | −0.886116 | − | 0.463463i | \(-0.846607\pi\) |
0.844429 | + | 0.535667i | \(0.179940\pi\) | |||||||
\(860\) | 4.17984 | + | 7.23970i | 0.142531 | + | 0.246872i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.120250 | + | 0.208279i | −0.00409573 | + | 0.00709401i | ||||
\(863\) | −12.8594 | − | 22.2731i | −0.437738 | − | 0.758185i | 0.559777 | − | 0.828644i | \(-0.310887\pi\) |
−0.997515 | + | 0.0704589i | \(0.977554\pi\) | |||||||
\(864\) | 12.2399 | − | 7.48268i | 0.416410 | − | 0.254566i | ||||
\(865\) | −1.07605 | + | 1.86378i | −0.0365870 | + | 0.0633705i | ||||
\(866\) | 3.13422 | 0.106505 | ||||||||
\(867\) | 15.8229 | + | 18.5396i | 0.537375 | + | 0.629639i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.5510 | + | 35.5954i | 0.697146 | + | 1.20749i | ||||
\(870\) | −1.48066 | − | 1.73488i | −0.0501992 | − | 0.0588180i | ||||
\(871\) | −15.2171 | − | 26.3568i | −0.515612 | − | 0.893067i | ||||
\(872\) | 3.42395 | − | 5.93045i | 0.115949 | − | 0.200830i | ||||
\(873\) | −1.44409 | + | 9.07587i | −0.0488751 | + | 0.307172i | ||||
\(874\) | 8.76884 | 0.296611 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.04583 | − | 22.6951i | 0.271843 | − | 0.766796i | ||||
\(877\) | 10.9795 | − | 19.0170i | 0.370751 | − | 0.642160i | −0.618930 | − | 0.785446i | \(-0.712434\pi\) |
0.989681 | + | 0.143286i | \(0.0457670\pi\) | |||||||
\(878\) | 4.45106 | 0.150216 | ||||||||
\(879\) | −8.79931 | − | 10.3101i | −0.296794 | − | 0.347751i | ||||
\(880\) | −39.6718 | −1.33733 | ||||||||
\(881\) | 35.0576 | 1.18112 | 0.590560 | − | 0.806994i | \(-0.298907\pi\) | ||||
0.590560 | + | 0.806994i | \(0.298907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3009 | 0.885097 | 0.442549 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442549 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(884\) | −12.2438 | −0.411803 | ||||||||
\(885\) | 9.09644 | − | 25.6586i | 0.305774 | − | 0.862503i | ||||
\(886\) | −0.267580 | −0.00898954 | ||||||||
\(887\) | 23.9090 | − | 41.4116i | 0.802785 | − | 1.39046i | −0.114991 | − | 0.993366i | \(-0.536684\pi\) |
0.917776 | − | 0.397098i | \(-0.129983\pi\) | |||||||
\(888\) | 1.75999 | + | 2.06217i | 0.0590615 | + | 0.0692019i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.12071 | 0.104607 | ||||||||
\(891\) | −35.7788 | − | 11.6815i | −1.19864 | − | 0.391345i | ||||
\(892\) | −4.37272 | + | 7.57378i | −0.146410 | + | 0.253589i | ||||
\(893\) | 33.4104 | + | 57.8685i | 1.11804 | + | 1.93650i | ||||
\(894\) | −0.839710 | + | 2.36859i | −0.0280841 | + | 0.0792175i | ||||
\(895\) | 9.82150 | + | 17.0113i | 0.328296 | + | 0.568626i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.1472 | + | 5.94631i | −1.07336 | + | 0.198542i | ||||
\(898\) | −9.43147 | −0.314732 | ||||||||
\(899\) | −6.94357 | + | 12.0266i | −0.231581 | + | 0.401110i | ||||
\(900\) | 7.77446 | + | 6.30479i | 0.259149 | + | 0.210160i | ||||
\(901\) | −9.10848 | − | 15.7764i | −0.303448 | − | 0.525587i | ||||
\(902\) | 5.10948 | − | 8.84988i | 0.170127 | − | 0.294669i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.26647 | + | 5.65769i | 0.108641 | + | 0.188172i | ||||
\(905\) | 0.530225 | − | 0.918376i | 0.0176253 | − | 0.0305279i | ||||
\(906\) | −1.20687 | − | 1.41409i | −0.0400957 | − | 0.0469798i | ||||
\(907\) | 9.55718 | + | 16.5535i | 0.317341 | + | 0.549651i | 0.979932 | − | 0.199330i | \(-0.0638767\pi\) |
−0.662591 | + | 0.748981i | \(0.730543\pi\) | |||||||
\(908\) | −5.89092 | − | 10.2034i | −0.195497 | − | 0.338611i | ||||
\(909\) | 25.8633 | + | 20.9741i | 0.857831 | + | 0.695669i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.02928 | − | 15.6392i | 0.299153 | − | 0.518149i | −0.676789 | − | 0.736177i | \(-0.736629\pi\) |
0.975942 | + | 0.218028i | \(0.0699625\pi\) | |||||||
\(912\) | 29.4493 | + | 34.5055i | 0.975163 | + | 1.14259i | ||||
\(913\) | 28.8330 | 0.954234 | ||||||||
\(914\) | −8.18770 | −0.270825 | ||||||||
\(915\) | −11.9789 | + | 33.7893i | −0.396012 | + | 1.11704i | ||||
\(916\) | −10.7334 | + | 18.5908i | −0.354642 | + | 0.614258i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0533866 | + | 2.12537i | 0.00176202 | + | 0.0701478i | ||||
\(919\) | −8.10464 | − | 14.0377i | −0.267348 | − | 0.463060i | 0.700828 | − | 0.713330i | \(-0.252814\pi\) |
−0.968176 | + | 0.250270i | \(0.919481\pi\) | |||||||
\(920\) | 6.26141 | + | 10.8451i | 0.206433 | + | 0.357552i | ||||
\(921\) | 38.6122 | − | 7.14215i | 1.27231 | − | 0.235342i | ||||
\(922\) | −2.43757 | + | 4.22199i | −0.0802771 | + | 0.139044i | ||||
\(923\) | −11.4897 | − | 19.9007i | −0.378187 | − | 0.655039i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42558 | + | 2.46918i | −0.0468728 | + | 0.0811860i | ||||
\(926\) | −0.814099 | − | 1.41006i | −0.0267529 | − | 0.0463375i | ||||
\(927\) | −3.76466 | + | 23.6603i | −0.123648 | + | 0.777105i | ||||
\(928\) | 2.93310 | − | 5.08029i | 0.0962839 | − | 0.166769i | ||||
\(929\) | −22.6829 | −0.744203 | −0.372102 | − | 0.928192i | \(-0.621363\pi\) | ||||
−0.372102 | + | 0.928192i | \(0.621363\pi\) | |||||||
\(930\) | −2.34431 | + | 6.61266i | −0.0768730 | + | 0.216838i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.90576 | − | 13.6932i | −0.258962 | − | 0.448535i | ||||
\(933\) | −55.0420 | + | 10.1812i | −1.80199 | + | 0.333317i | ||||
\(934\) | −2.96407 | − | 5.13392i | −0.0969873 | − | 0.167987i | ||||
\(935\) | 9.27292 | − | 16.0612i | 0.303257 | − | 0.525256i | ||||
\(936\) | 8.09127 | + | 6.56171i | 0.264471 | + | 0.214476i | ||||
\(937\) | 51.2933 | 1.67568 | 0.837840 | − | 0.545915i | \(-0.183818\pi\) | ||||
0.837840 | + | 0.545915i | \(0.183818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.4201 | + | 7.66154i | −1.35169 | + | 0.250025i | ||||
\(940\) | −23.5108 | + | 40.7219i | −0.766838 | + | 1.32820i | ||||
\(941\) | −31.9318 | −1.04095 | −0.520474 | − | 0.853878i | \(-0.674245\pi\) | ||||
−0.520474 | + | 0.853878i | \(0.674245\pi\) | |||||||
\(942\) | 0.419041 | − | 0.0775106i | 0.0136531 | − | 0.00252543i | ||||
\(943\) | 52.3697 | 1.70539 | ||||||||
\(944\) | 22.1965 | 0.722433 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.66019 | −0.0539774 | ||||||||
\(947\) | −4.49330 | −0.146013 | −0.0730063 | − | 0.997331i | \(-0.523259\pi\) | ||||
−0.0730063 | + | 0.997331i | \(0.523259\pi\) | |||||||
\(948\) | 32.5217 | − | 6.01559i | 1.05626 | − | 0.195377i | ||||
\(949\) | 26.3549 | 0.855515 | ||||||||
\(950\) | 1.46927 | − | 2.54485i | 0.0476695 | − | 0.0825660i | ||||
\(951\) | 8.75158 | − | 1.61879i | 0.283789 | − | 0.0524929i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.14635 | 0.0371340 | 0.0185670 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185670 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(954\) | −1.20013 | + | 7.54261i | −0.0388556 | + | 0.244201i | ||||
\(955\) | 20.7655 | − | 35.9669i | 0.671956 | − | 1.16386i | ||||
\(956\) | 20.5575 | + | 35.6066i | 0.664876 | + | 1.15160i | ||||
\(957\) | −15.1337 | + | 2.79929i | −0.489202 | + | 0.0904883i | ||||
\(958\) | 1.32710 | + | 2.29860i | 0.0428765 | + | 0.0742643i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.99028 | + | 28.1799i | −0.322435 | + | 0.909501i | ||||
\(961\) | 11.7174 | 0.377980 | ||||||||
\(962\) | −0.731078 | + | 1.26626i | −0.0235709 | + | 0.0408260i | ||||
\(963\) | −9.21900 | − | 7.47626i | −0.297078 | − | 0.240919i | ||||
\(964\) | 13.3000 | + | 23.0363i | 0.428365 | + | 0.741950i | ||||
\(965\) | −16.0358 | + | 27.7748i | −0.516210 | + | 0.894102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.8080 | − | 42.9686i | −0.797770 | − | 1.38178i | −0.921065 | − | 0.389408i | \(-0.872680\pi\) |
0.123295 | − | 0.992370i | \(-0.460654\pi\) | |||||||
\(968\) | 3.05881 | − | 5.29802i | 0.0983140 | − | 0.170285i | ||||
\(969\) | −20.8531 | + | 3.85722i | −0.669898 | + | 0.123912i | ||||
\(970\) | 0.949266 | + | 1.64418i | 0.0304791 | + | 0.0527913i | ||||
\(971\) | 2.56661 | + | 4.44550i | 0.0823664 | + | 0.142663i | 0.904266 | − | 0.426970i | \(-0.140419\pi\) |
−0.821900 | + | 0.569632i | \(0.807086\pi\) | |||||||
\(972\) | −18.4794 | + | 23.9943i | −0.592726 | + | 0.769619i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.20013 | − | 2.07869i | 0.0384546 | − | 0.0666054i | ||||
\(975\) | −3.66075 | + | 10.3260i | −0.117238 | + | 0.330695i | ||||
\(976\) | −29.2302 | −0.935634 | ||||||||
\(977\) | 31.1948 | 0.998011 | 0.499006 | − | 0.866599i | \(-0.333699\pi\) | ||||
0.499006 | + | 0.866599i | \(0.333699\pi\) | |||||||
\(978\) | −1.83598 | − | 2.15121i | −0.0587083 | − | 0.0687881i | ||||
\(979\) | 10.5288 | − | 18.2365i | 0.336503 | − | 0.582840i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.42395 | + | 21.5189i | −0.109318 | + | 0.687046i | ||||
\(982\) | 1.48113 | + | 2.56538i | 0.0472646 | + | 0.0818647i | ||||
\(983\) | −10.1700 | − | 17.6150i | −0.324374 | − | 0.561832i | 0.657012 | − | 0.753880i | \(-0.271820\pi\) |
−0.981385 | + | 0.192049i | \(0.938487\pi\) | |||||||
\(984\) | −10.8333 | − | 12.6933i | −0.345352 | − | 0.404647i | ||||
\(985\) | 29.9378 | − | 51.8539i | 0.953899 | − | 1.65220i | ||||
\(986\) | 0.434681 | + | 0.752890i | 0.0138431 | + | 0.0239769i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.6014 | + | 44.3429i | −0.814488 | + | 1.41074i | ||||
\(989\) | −4.25404 | − | 7.36821i | −0.135271 | − | 0.234296i | ||||
\(990\) | −7.26091 | + | 2.78128i | −0.230767 | + | 0.0883949i | ||||
\(991\) | 6.48276 | − | 11.2285i | 0.205932 | − | 0.356684i | −0.744498 | − | 0.667625i | \(-0.767311\pi\) |
0.950429 | + | 0.310941i | \(0.100644\pi\) | |||||||
\(992\) | −18.0447 | −0.572919 | ||||||||
\(993\) | −19.9235 | + | 3.68527i | −0.632252 | + | 0.116948i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.74269 | − | 15.1428i | −0.277162 | − | 0.480059i | ||||
\(996\) | 7.75241 | − | 21.8674i | 0.245644 | − | 0.692895i | ||||
\(997\) | 24.7408 | + | 42.8523i | 0.783548 | + | 1.35715i | 0.929863 | + | 0.367907i | \(0.119926\pi\) |
−0.146314 | + | 0.989238i | \(0.546741\pi\) | |||||||
\(998\) | −1.22218 | + | 2.11688i | −0.0386875 | + | 0.0670086i | ||||
\(999\) | −7.57681 | − | 4.12434i | −0.239720 | − | 0.130488i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.h.g.214.4 | 12 | ||
3.2 | odd | 2 | 1323.2.h.g.802.3 | 12 | |||
7.2 | even | 3 | 441.2.g.g.79.3 | 12 | |||
7.3 | odd | 6 | 441.2.f.g.295.4 | yes | 12 | ||
7.4 | even | 3 | 441.2.f.g.295.3 | yes | 12 | ||
7.5 | odd | 6 | 441.2.g.g.79.4 | 12 | |||
7.6 | odd | 2 | inner | 441.2.h.g.214.3 | 12 | ||
9.4 | even | 3 | 441.2.g.g.67.3 | 12 | |||
9.5 | odd | 6 | 1323.2.g.g.361.4 | 12 | |||
21.2 | odd | 6 | 1323.2.g.g.667.4 | 12 | |||
21.5 | even | 6 | 1323.2.g.g.667.3 | 12 | |||
21.11 | odd | 6 | 1323.2.f.g.883.3 | 12 | |||
21.17 | even | 6 | 1323.2.f.g.883.4 | 12 | |||
21.20 | even | 2 | 1323.2.h.g.802.4 | 12 | |||
63.4 | even | 3 | 441.2.f.g.148.3 | ✓ | 12 | ||
63.5 | even | 6 | 1323.2.h.g.226.4 | 12 | |||
63.11 | odd | 6 | 3969.2.a.bd.1.4 | 6 | |||
63.13 | odd | 6 | 441.2.g.g.67.4 | 12 | |||
63.23 | odd | 6 | 1323.2.h.g.226.3 | 12 | |||
63.25 | even | 3 | 3969.2.a.be.1.3 | 6 | |||
63.31 | odd | 6 | 441.2.f.g.148.4 | yes | 12 | ||
63.32 | odd | 6 | 1323.2.f.g.442.3 | 12 | |||
63.38 | even | 6 | 3969.2.a.bd.1.3 | 6 | |||
63.40 | odd | 6 | inner | 441.2.h.g.373.3 | 12 | ||
63.41 | even | 6 | 1323.2.g.g.361.3 | 12 | |||
63.52 | odd | 6 | 3969.2.a.be.1.4 | 6 | |||
63.58 | even | 3 | inner | 441.2.h.g.373.4 | 12 | ||
63.59 | even | 6 | 1323.2.f.g.442.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.3 | ✓ | 12 | 63.4 | even | 3 | ||
441.2.f.g.148.4 | yes | 12 | 63.31 | odd | 6 | ||
441.2.f.g.295.3 | yes | 12 | 7.4 | even | 3 | ||
441.2.f.g.295.4 | yes | 12 | 7.3 | odd | 6 | ||
441.2.g.g.67.3 | 12 | 9.4 | even | 3 | |||
441.2.g.g.67.4 | 12 | 63.13 | odd | 6 | |||
441.2.g.g.79.3 | 12 | 7.2 | even | 3 | |||
441.2.g.g.79.4 | 12 | 7.5 | odd | 6 | |||
441.2.h.g.214.3 | 12 | 7.6 | odd | 2 | inner | ||
441.2.h.g.214.4 | 12 | 1.1 | even | 1 | trivial | ||
441.2.h.g.373.3 | 12 | 63.40 | odd | 6 | inner | ||
441.2.h.g.373.4 | 12 | 63.58 | even | 3 | inner | ||
1323.2.f.g.442.3 | 12 | 63.32 | odd | 6 | |||
1323.2.f.g.442.4 | 12 | 63.59 | even | 6 | |||
1323.2.f.g.883.3 | 12 | 21.11 | odd | 6 | |||
1323.2.f.g.883.4 | 12 | 21.17 | even | 6 | |||
1323.2.g.g.361.3 | 12 | 63.41 | even | 6 | |||
1323.2.g.g.361.4 | 12 | 9.5 | odd | 6 | |||
1323.2.g.g.667.3 | 12 | 21.5 | even | 6 | |||
1323.2.g.g.667.4 | 12 | 21.2 | odd | 6 | |||
1323.2.h.g.226.3 | 12 | 63.23 | odd | 6 | |||
1323.2.h.g.226.4 | 12 | 63.5 | even | 6 | |||
1323.2.h.g.802.3 | 12 | 3.2 | odd | 2 | |||
1323.2.h.g.802.4 | 12 | 21.20 | even | 2 | |||
3969.2.a.bd.1.3 | 6 | 63.38 | even | 6 | |||
3969.2.a.bd.1.4 | 6 | 63.11 | odd | 6 | |||
3969.2.a.be.1.3 | 6 | 63.25 | even | 3 | |||
3969.2.a.be.1.4 | 6 | 63.52 | odd | 6 |