Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(123,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.123");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 123.2 | ||
Character | \(\chi\) | \(=\) | 349.123 |
Dual form | 349.2.e.a.227.2 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28298 | + | 1.31808i | −1.61431 | + | 0.932024i | −0.625958 | + | 0.779857i | \(0.715292\pi\) |
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(3\) | −1.40419 | + | 2.43213i | −0.810710 | + | 1.40419i | 0.101657 | + | 0.994819i | \(0.467585\pi\) |
−0.912368 | + | 0.409372i | \(0.865748\pi\) | |||||||
\(4\) | 2.47467 | − | 4.28626i | 1.23734 | − | 2.14313i | ||||
\(5\) | 0.108819 | − | 0.188480i | 0.0486652 | − | 0.0842906i | −0.840667 | − | 0.541553i | \(-0.817837\pi\) |
0.889332 | + | 0.457262i | \(0.151170\pi\) | |||||||
\(6\) | − | 7.40335i | − | 3.02240i | ||||||
\(7\) | 3.00446 | − | 1.73462i | 1.13558 | − | 0.655627i | 0.190247 | − | 0.981736i | \(-0.439071\pi\) |
0.945332 | + | 0.326110i | \(0.105738\pi\) | |||||||
\(8\) | 7.77496i | 2.74886i | ||||||||
\(9\) | −2.44351 | − | 4.23228i | −0.814502 | − | 1.41076i | ||||
\(10\) | 0.573727i | 0.181429i | ||||||||
\(11\) | 6.40695i | 1.93177i | 0.258975 | + | 0.965884i | \(0.416615\pi\) | ||||
−0.258975 | + | 0.965884i | \(0.583385\pi\) | |||||||
\(12\) | 6.94983 | + | 12.0375i | 2.00624 | + | 3.47492i | ||||
\(13\) | 3.09197 | − | 1.78515i | 0.857558 | − | 0.495111i | −0.00563602 | − | 0.999984i | \(-0.501794\pi\) |
0.863194 | + | 0.504873i | \(0.168461\pi\) | |||||||
\(14\) | −4.57275 | + | 7.92024i | −1.22212 | + | 2.11677i | ||||
\(15\) | 0.305605 | + | 0.529323i | 0.0789068 | + | 0.136671i | ||||
\(16\) | −5.29867 | − | 9.17757i | −1.32467 | − | 2.29439i | ||||
\(17\) | 6.82681 | 1.65574 | 0.827872 | − | 0.560916i | \(-0.189551\pi\) | ||||
0.827872 | + | 0.560916i | \(0.189551\pi\) | |||||||
\(18\) | 11.1570 | + | 6.44148i | 2.62972 | + | 1.51827i | ||||
\(19\) | −2.30633 | + | 3.99469i | −0.529109 | + | 0.916444i | 0.470314 | + | 0.882499i | \(0.344141\pi\) |
−0.999424 | + | 0.0339454i | \(0.989193\pi\) | |||||||
\(20\) | −0.538582 | − | 0.932851i | −0.120431 | − | 0.208592i | ||||
\(21\) | 9.74298i | 2.12609i | ||||||||
\(22\) | −8.44488 | − | 14.6270i | −1.80045 | − | 3.11848i | ||||
\(23\) | −1.65886 | − | 2.87323i | −0.345897 | − | 0.599111i | 0.639620 | − | 0.768692i | \(-0.279092\pi\) |
−0.985516 | + | 0.169581i | \(0.945759\pi\) | |||||||
\(24\) | −18.9097 | − | 10.9175i | −3.85993 | − | 2.22853i | ||||
\(25\) | 2.47632 | + | 4.28911i | 0.495263 | + | 0.857821i | ||||
\(26\) | −4.70594 | + | 8.15093i | −0.922911 | + | 1.59853i | ||||
\(27\) | 5.29945 | 1.01988 | ||||||||
\(28\) | − | 17.1705i | − | 3.24492i | ||||||
\(29\) | 3.25863 | − | 5.64412i | 0.605113 | − | 1.04809i | −0.386920 | − | 0.922113i | \(-0.626461\pi\) |
0.992034 | − | 0.125974i | \(-0.0402055\pi\) | |||||||
\(30\) | −1.39538 | − | 0.805623i | −0.254760 | − | 0.147086i | ||||
\(31\) | −2.85706 | −0.513143 | −0.256571 | − | 0.966525i | \(-0.582593\pi\) | ||||
−0.256571 | + | 0.966525i | \(0.582593\pi\) | |||||||
\(32\) | 10.7269 | + | 6.19321i | 1.89627 | + | 1.09481i | ||||
\(33\) | −15.5825 | − | 8.99658i | −2.71257 | − | 1.56610i | ||||
\(34\) | −15.5855 | + | 8.99829i | −2.67289 | + | 1.54319i | ||||
\(35\) | − | 0.755039i | − | 0.127625i | ||||||
\(36\) | −24.1875 | −4.03125 | ||||||||
\(37\) | 0.771177 | 0.126781 | 0.0633904 | − | 0.997989i | \(-0.479809\pi\) | ||||
0.0633904 | + | 0.997989i | \(0.479809\pi\) | |||||||
\(38\) | − | 12.1597i | − | 1.97257i | ||||||
\(39\) | 10.0268i | 1.60557i | ||||||||
\(40\) | 1.46542 | + | 0.846061i | 0.231703 | + | 0.133774i | ||||
\(41\) | −4.60340 | −0.718931 | −0.359465 | − | 0.933158i | \(-0.617041\pi\) | ||||
−0.359465 | + | 0.933158i | \(0.617041\pi\) | |||||||
\(42\) | −12.8420 | − | 22.2431i | −1.98157 | − | 3.43218i | ||||
\(43\) | 5.76174 | + | 3.32654i | 0.878657 | + | 0.507293i | 0.870215 | − | 0.492671i | \(-0.163980\pi\) |
0.00844180 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(44\) | 27.4619 | + | 15.8551i | 4.14003 | + | 2.39025i | ||||
\(45\) | −1.06360 | −0.158552 | ||||||||
\(46\) | 7.57431 | + | 4.37303i | 1.11677 | + | 0.644768i | ||||
\(47\) | 2.55802i | 0.373125i | 0.982443 | + | 0.186563i | \(0.0597347\pi\) | ||||
−0.982443 | + | 0.186563i | \(0.940265\pi\) | |||||||
\(48\) | 29.7614 | 4.29569 | ||||||||
\(49\) | 2.51785 | − | 4.36104i | 0.359693 | − | 0.623006i | ||||
\(50\) | −11.3068 | − | 6.52797i | −1.59902 | − | 0.923195i | ||||
\(51\) | −9.58615 | + | 16.6037i | −1.34233 | + | 2.32498i | ||||
\(52\) | − | 17.6706i | − | 2.45048i | ||||||
\(53\) | 3.79762i | 0.521643i | 0.965387 | + | 0.260822i | \(0.0839934\pi\) | ||||
−0.965387 | + | 0.260822i | \(0.916007\pi\) | |||||||
\(54\) | −12.0986 | + | 6.98510i | −1.64640 | + | 0.950552i | ||||
\(55\) | 1.20758 | + | 0.697196i | 0.162830 | + | 0.0940099i | ||||
\(56\) | 13.4866 | + | 23.3595i | 1.80223 | + | 3.12155i | ||||
\(57\) | −6.47707 | − | 11.2186i | −0.857909 | − | 1.48594i | ||||
\(58\) | 17.1806i | 2.25592i | ||||||||
\(59\) | −7.78985 | − | 4.49747i | −1.01415 | − | 0.585521i | −0.101747 | − | 0.994810i | \(-0.532443\pi\) |
−0.912405 | + | 0.409289i | \(0.865777\pi\) | |||||||
\(60\) | 3.02509 | 0.390537 | ||||||||
\(61\) | 7.60401i | 0.973594i | 0.873515 | + | 0.486797i | \(0.161835\pi\) | ||||
−0.873515 | + | 0.486797i | \(0.838165\pi\) | |||||||
\(62\) | 6.52261 | − | 3.76583i | 0.828373 | − | 0.478261i | ||||
\(63\) | −14.6828 | − | 8.47713i | −1.84986 | − | 1.06802i | ||||
\(64\) | −11.4579 | −1.43224 | ||||||||
\(65\) | − | 0.777030i | − | 0.0963787i | ||||||
\(66\) | 47.4329 | 5.83859 | ||||||||
\(67\) | −2.56887 | −0.313837 | −0.156919 | − | 0.987612i | \(-0.550156\pi\) | ||||
−0.156919 | + | 0.987612i | \(0.550156\pi\) | |||||||
\(68\) | 16.8941 | − | 29.2615i | 2.04871 | − | 3.54848i | ||||
\(69\) | 9.31744 | 1.12169 | ||||||||
\(70\) | 0.995202 | + | 1.72374i | 0.118949 | + | 0.206026i | ||||
\(71\) | −6.09051 | + | 3.51636i | −0.722810 | + | 0.417315i | −0.815786 | − | 0.578354i | \(-0.803695\pi\) |
0.0929760 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(72\) | 32.9058 | − | 18.9982i | 3.87798 | − | 2.23895i | ||||
\(73\) | −0.243212 | + | 0.421256i | −0.0284659 | + | 0.0493043i | −0.879907 | − | 0.475145i | \(-0.842396\pi\) |
0.851442 | + | 0.524450i | \(0.175729\pi\) | |||||||
\(74\) | −1.76058 | + | 1.01647i | −0.204664 | + | 0.118163i | ||||
\(75\) | −13.9089 | −1.60606 | ||||||||
\(76\) | 11.4149 | + | 19.7711i | 1.30937 | + | 2.26790i | ||||
\(77\) | 11.1137 | + | 19.2494i | 1.26652 | + | 2.19367i | ||||
\(78\) | −13.2161 | − | 22.8909i | −1.49643 | − | 2.59189i | ||||
\(79\) | − | 3.36812i | − | 0.378944i | −0.981886 | − | 0.189472i | \(-0.939322\pi\) | ||
0.981886 | − | 0.189472i | \(-0.0606776\pi\) | |||||||
\(80\) | −2.30638 | −0.257861 | ||||||||
\(81\) | −0.110925 | + | 0.192127i | −0.0123250 | + | 0.0213475i | ||||
\(82\) | 10.5095 | − | 6.06766i | 1.16058 | − | 0.670061i | ||||
\(83\) | 6.90550 | + | 11.9607i | 0.757977 | + | 1.31286i | 0.943881 | + | 0.330287i | \(0.107146\pi\) |
−0.185903 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(84\) | 41.7610 | + | 24.1107i | 4.55649 | + | 2.63069i | ||||
\(85\) | 0.742885 | − | 1.28671i | 0.0805772 | − | 0.139564i | ||||
\(86\) | −17.5386 | −1.89124 | ||||||||
\(87\) | 9.15149 | + | 15.8508i | 0.981143 | + | 1.69939i | ||||
\(88\) | −49.8138 | −5.31017 | ||||||||
\(89\) | −2.16506 | − | 1.25000i | −0.229496 | − | 0.132500i | 0.380844 | − | 0.924639i | \(-0.375634\pi\) |
−0.610339 | + | 0.792140i | \(0.708967\pi\) | |||||||
\(90\) | 2.42817 | − | 1.40191i | 0.255952 | − | 0.147774i | ||||
\(91\) | 6.19313 | − | 10.7268i | 0.649216 | − | 1.12448i | ||||
\(92\) | −16.4206 | −1.71196 | ||||||||
\(93\) | 4.01185 | − | 6.94874i | 0.416010 | − | 0.720550i | ||||
\(94\) | −3.37167 | − | 5.83991i | −0.347762 | − | 0.602341i | ||||
\(95\) | 0.501945 | + | 0.869394i | 0.0514984 | + | 0.0891979i | ||||
\(96\) | −30.1254 | + | 17.3929i | −3.07466 | + | 1.77515i | ||||
\(97\) | −0.717554 | + | 0.414280i | −0.0728566 | + | 0.0420638i | −0.535986 | − | 0.844227i | \(-0.680060\pi\) |
0.463129 | + | 0.886291i | \(0.346727\pi\) | |||||||
\(98\) | 13.2749i | 1.34097i | ||||||||
\(99\) | 27.1160 | − | 15.6554i | 2.72526 | − | 1.57343i | ||||
\(100\) | 24.5123 | 2.45123 | ||||||||
\(101\) | − | 5.46694i | − | 0.543981i | −0.962300 | − | 0.271990i | \(-0.912318\pi\) | ||
0.962300 | − | 0.271990i | \(-0.0876819\pi\) | |||||||
\(102\) | − | 50.5413i | − | 5.00433i | ||||||
\(103\) | 3.23464i | 0.318719i | 0.987221 | + | 0.159359i | \(0.0509428\pi\) | ||||
−0.987221 | + | 0.159359i | \(0.949057\pi\) | |||||||
\(104\) | 13.8795 | + | 24.0399i | 1.36099 | + | 2.35731i | ||||
\(105\) | 1.83635 | + | 1.06022i | 0.179210 | + | 0.103467i | ||||
\(106\) | −5.00557 | − | 8.66990i | −0.486184 | − | 0.842095i | ||||
\(107\) | 3.58817 | − | 2.07163i | 0.346881 | − | 0.200272i | −0.316430 | − | 0.948616i | \(-0.602484\pi\) |
0.663311 | + | 0.748344i | \(0.269151\pi\) | |||||||
\(108\) | 13.1144 | − | 22.7148i | 1.26194 | − | 2.18574i | ||||
\(109\) | 0.302219 | − | 0.523458i | 0.0289473 | − | 0.0501382i | −0.851189 | − | 0.524860i | \(-0.824118\pi\) |
0.880136 | + | 0.474721i | \(0.157451\pi\) | |||||||
\(110\) | −3.67584 | −0.350478 | ||||||||
\(111\) | −1.08288 | + | 1.87560i | −0.102782 | + | 0.178024i | ||||
\(112\) | −31.8393 | − | 18.3824i | −3.00853 | − | 1.73698i | ||||
\(113\) | −4.74156 | + | 2.73754i | −0.446049 | + | 0.257526i | −0.706160 | − | 0.708052i | \(-0.749574\pi\) |
0.260111 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(114\) | 29.5741 | + | 17.0746i | 2.76987 | + | 1.59918i | ||||
\(115\) | −0.722061 | −0.0673325 | ||||||||
\(116\) | −16.1281 | − | 27.9347i | −1.49746 | − | 2.59367i | ||||
\(117\) | −15.1105 | − | 8.72404i | −1.39696 | − | 0.806538i | ||||
\(118\) | 23.7121 | 2.18288 | ||||||||
\(119\) | 20.5109 | − | 11.8420i | 1.88023 | − | 1.08555i | ||||
\(120\) | −4.11546 | + | 2.37606i | −0.375688 | + | 0.216904i | ||||
\(121\) | −30.0490 | −2.73173 | ||||||||
\(122\) | −10.0227 | − | 17.3598i | −0.907413 | − | 1.57169i | ||||
\(123\) | 6.46406 | − | 11.1961i | 0.582845 | − | 1.00952i | ||||
\(124\) | −7.07028 | + | 12.2461i | −0.634930 | + | 1.09973i | ||||
\(125\) | 2.16607 | 0.193739 | ||||||||
\(126\) | 44.6942 | 3.98167 | ||||||||
\(127\) | 7.90370i | 0.701340i | 0.936499 | + | 0.350670i | \(0.114046\pi\) | ||||
−0.936499 | + | 0.350670i | \(0.885954\pi\) | |||||||
\(128\) | 4.70425 | − | 2.71600i | 0.415801 | − | 0.240063i | ||||
\(129\) | −16.1812 | + | 9.34220i | −1.42467 | + | 0.822535i | ||||
\(130\) | 1.02419 | + | 1.77395i | 0.0898273 | + | 0.155585i | ||||
\(131\) | 9.21456i | 0.805080i | 0.915402 | + | 0.402540i | \(0.131873\pi\) | ||||
−0.915402 | + | 0.402540i | \(0.868127\pi\) | |||||||
\(132\) | −77.1234 | + | 44.5272i | −6.71273 | + | 3.87560i | ||||
\(133\) | 16.0025i | 1.38759i | ||||||||
\(134\) | 5.86469 | − | 3.38598i | 0.506632 | − | 0.292504i | ||||
\(135\) | 0.576679 | − | 0.998838i | 0.0496327 | − | 0.0859663i | ||||
\(136\) | 53.0782i | 4.55142i | ||||||||
\(137\) | 0.392816 | + | 0.226792i | 0.0335605 | + | 0.0193762i | 0.516686 | − | 0.856175i | \(-0.327165\pi\) |
−0.483126 | + | 0.875551i | \(0.660499\pi\) | |||||||
\(138\) | −21.2716 | + | 12.2811i | −1.81076 | + | 1.04544i | ||||
\(139\) | 8.74910 | 0.742089 | 0.371044 | − | 0.928615i | \(-0.379000\pi\) | ||||
0.371044 | + | 0.928615i | \(0.379000\pi\) | |||||||
\(140\) | −3.23629 | − | 1.86847i | −0.273517 | − | 0.157915i | ||||
\(141\) | −6.22143 | − | 3.59195i | −0.523939 | − | 0.302496i | ||||
\(142\) | 9.26968 | − | 16.0556i | 0.777894 | − | 1.34735i | ||||
\(143\) | 11.4374 | + | 19.8101i | 0.956440 | + | 1.65660i | ||||
\(144\) | −25.8947 | + | 44.8509i | −2.15789 | + | 3.73758i | ||||
\(145\) | −0.709201 | − | 1.22837i | −0.0588959 | − | 0.102011i | ||||
\(146\) | − | 1.28229i | − | 0.106123i | ||||||
\(147\) | 7.07108 | + | 12.2475i | 0.583213 | + | 1.01015i | ||||
\(148\) | 1.90841 | − | 3.30547i | 0.156871 | − | 0.271708i | ||||
\(149\) | −11.5649 | + | 6.67701i | −0.947435 | + | 0.547002i | −0.892283 | − | 0.451476i | \(-0.850898\pi\) |
−0.0551516 | + | 0.998478i | \(0.517564\pi\) | |||||||
\(150\) | 31.7538 | − | 18.3330i | 2.59268 | − | 1.49689i | ||||
\(151\) | 7.74324 | − | 13.4117i | 0.630136 | − | 1.09143i | −0.357387 | − | 0.933956i | \(-0.616332\pi\) |
0.987523 | − | 0.157472i | \(-0.0503343\pi\) | |||||||
\(152\) | −31.0585 | − | 17.9317i | −2.51918 | − | 1.45445i | ||||
\(153\) | −16.6814 | − | 28.8930i | −1.34861 | − | 2.33586i | ||||
\(154\) | −50.7446 | − | 29.2974i | −4.08911 | − | 2.36085i | ||||
\(155\) | −0.310901 | + | 0.538497i | −0.0249722 | + | 0.0432531i | ||||
\(156\) | 42.9773 | + | 24.8130i | 3.44094 | + | 1.98663i | ||||
\(157\) | 6.28571 | − | 10.8872i | 0.501654 | − | 0.868890i | −0.498344 | − | 0.866979i | \(-0.666058\pi\) |
0.999998 | − | 0.00191105i | \(-0.000608306\pi\) | |||||||
\(158\) | 4.43946 | + | 7.68937i | 0.353185 | + | 0.611734i | ||||
\(159\) | −9.23631 | − | 5.33258i | −0.732487 | − | 0.422901i | ||||
\(160\) | 2.33459 | − | 1.34787i | 0.184565 | − | 0.106559i | ||||
\(161\) | −9.96797 | − | 5.75501i | −0.785586 | − | 0.453558i | ||||
\(162\) | − | 0.584831i | − | 0.0459487i | ||||||
\(163\) | − | 7.85479i | − | 0.615234i | −0.951510 | − | 0.307617i | \(-0.900468\pi\) | ||
0.951510 | − | 0.307617i | \(-0.0995316\pi\) | |||||||
\(164\) | −11.3919 | + | 19.7314i | −0.889560 | + | 1.54076i | ||||
\(165\) | −3.39134 | + | 1.95799i | −0.264016 | + | 0.152430i | ||||
\(166\) | −31.5303 | − | 18.2040i | −2.44722 | − | 1.41291i | ||||
\(167\) | − | 14.9620i | − | 1.15780i | −0.815399 | − | 0.578899i | \(-0.803483\pi\) | ||
0.815399 | − | 0.578899i | \(-0.196517\pi\) | |||||||
\(168\) | −75.7513 | −5.84434 | ||||||||
\(169\) | −0.126489 | + | 0.219086i | −0.00972995 | + | 0.0168528i | ||||
\(170\) | 3.91673i | 0.300399i | ||||||||
\(171\) | 22.5422 | 1.72384 | ||||||||
\(172\) | 28.5169 | − | 16.4642i | 2.17439 | − | 1.25538i | ||||
\(173\) | 13.9566 | − | 8.05787i | 1.06110 | − | 0.612628i | 0.135366 | − | 0.990796i | \(-0.456779\pi\) |
0.925737 | + | 0.378167i | \(0.123446\pi\) | |||||||
\(174\) | −41.7854 | − | 24.1248i | −3.16774 | − | 1.82890i | ||||
\(175\) | 14.8800 | + | 8.59096i | 1.12482 | + | 0.649416i | ||||
\(176\) | 58.8003 | − | 33.9483i | 4.43224 | − | 2.55895i | ||||
\(177\) | 21.8769 | − | 12.6306i | 1.64437 | − | 0.949376i | ||||
\(178\) | 6.59039 | 0.493971 | ||||||||
\(179\) | 19.9344i | 1.48996i | 0.667084 | + | 0.744982i | \(0.267542\pi\) | ||||
−0.667084 | + | 0.744982i | \(0.732458\pi\) | |||||||
\(180\) | −2.63206 | + | 4.55885i | −0.196182 | + | 0.339797i | ||||
\(181\) | 13.8630 | 1.03043 | 0.515215 | − | 0.857061i | \(-0.327712\pi\) | ||||
0.515215 | + | 0.857061i | \(0.327712\pi\) | |||||||
\(182\) | 32.6522i | 2.42034i | ||||||||
\(183\) | −18.4940 | − | 10.6775i | −1.36711 | − | 0.789303i | ||||
\(184\) | 22.3393 | − | 12.8976i | 1.64687 | − | 0.950823i | ||||
\(185\) | 0.0839185 | − | 0.145351i | 0.00616981 | − | 0.0106864i | ||||
\(186\) | 21.1518i | 1.55092i | ||||||||
\(187\) | 43.7390i | 3.19852i | ||||||||
\(188\) | 10.9643 | + | 6.33026i | 0.799656 | + | 0.461682i | ||||
\(189\) | 15.9220 | − | 9.19256i | 1.15815 | − | 0.668660i | ||||
\(190\) | −2.29186 | − | 1.32321i | −0.166269 | − | 0.0959955i | ||||
\(191\) | −1.36496 | − | 2.36418i | −0.0987649 | − | 0.171066i | 0.812409 | − | 0.583088i | \(-0.198156\pi\) |
−0.911174 | + | 0.412022i | \(0.864823\pi\) | |||||||
\(192\) | 16.0891 | − | 27.8671i | 1.16113 | − | 2.01113i | ||||
\(193\) | −20.7639 | − | 11.9880i | −1.49462 | − | 0.862918i | −0.494636 | − | 0.869100i | \(-0.664699\pi\) |
−0.999981 | + | 0.00618253i | \(0.998032\pi\) | |||||||
\(194\) | 1.09211 | − | 1.89159i | 0.0784089 | − | 0.135808i | ||||
\(195\) | 1.88984 | + | 1.09110i | 0.135334 | + | 0.0781352i | ||||
\(196\) | −12.4617 | − | 21.5843i | −0.890122 | − | 1.54174i | ||||
\(197\) | 18.6911 | + | 10.7913i | 1.33168 | + | 0.768849i | 0.985558 | − | 0.169339i | \(-0.0541633\pi\) |
0.346127 | + | 0.938188i | \(0.387497\pi\) | |||||||
\(198\) | −41.2702 | + | 71.4821i | −2.93295 | + | 5.08001i | ||||
\(199\) | 18.2458 | − | 10.5342i | 1.29341 | − | 0.746751i | 0.314154 | − | 0.949372i | \(-0.398279\pi\) |
0.979257 | + | 0.202621i | \(0.0649460\pi\) | |||||||
\(200\) | −33.3476 | + | 19.2533i | −2.35803 | + | 1.36141i | ||||
\(201\) | 3.60718 | − | 6.24783i | 0.254431 | − | 0.440688i | ||||
\(202\) | 7.20587 | + | 12.4809i | 0.507003 | + | 0.878155i | ||||
\(203\) | − | 22.6100i | − | 1.58691i | ||||||
\(204\) | 47.4452 | + | 82.1775i | 3.32183 | + | 5.75357i | ||||
\(205\) | −0.500937 | + | 0.867648i | −0.0349869 | + | 0.0605991i | ||||
\(206\) | −4.26352 | − | 7.38463i | −0.297053 | − | 0.514512i | ||||
\(207\) | −8.10688 | + | 14.0415i | −0.563467 | + | 0.975954i | ||||
\(208\) | −32.7667 | − | 18.9178i | −2.27196 | − | 1.31172i | ||||
\(209\) | −25.5938 | − | 14.7766i | −1.77036 | − | 1.02212i | ||||
\(210\) | −5.58982 | −0.385734 | ||||||||
\(211\) | 4.43388 | − | 2.55990i | 0.305241 | − | 0.176231i | −0.339554 | − | 0.940587i | \(-0.610276\pi\) |
0.644795 | + | 0.764356i | \(0.276943\pi\) | |||||||
\(212\) | 16.2776 | + | 9.39787i | 1.11795 | + | 0.645448i | ||||
\(213\) | − | 19.7505i | − | 1.35328i | ||||||
\(214\) | −5.46115 | + | 9.45899i | −0.373316 | + | 0.646603i | ||||
\(215\) | 1.25397 | − | 0.723980i | 0.0855201 | − | 0.0493750i | ||||
\(216\) | 41.2030i | 2.80351i | ||||||||
\(217\) | −8.58391 | + | 4.95592i | −0.582714 | + | 0.336430i | ||||
\(218\) | 1.59339i | 0.107918i | ||||||||
\(219\) | −0.683034 | − | 1.18305i | −0.0461551 | − | 0.0799430i | ||||
\(220\) | 5.97673 | − | 3.45067i | 0.402951 | − | 0.232644i | ||||
\(221\) | 21.1083 | − | 12.1869i | 1.41990 | − | 0.819778i | ||||
\(222\) | − | 5.70930i | − | 0.383183i | ||||||
\(223\) | 25.5494 | 1.71092 | 0.855459 | − | 0.517871i | \(-0.173275\pi\) | ||||
0.855459 | + | 0.517871i | \(0.173275\pi\) | |||||||
\(224\) | 42.9716 | 2.87116 | ||||||||
\(225\) | 12.1018 | − | 20.9609i | 0.806786 | − | 1.39739i | ||||
\(226\) | 7.21661 | − | 12.4995i | 0.480042 | − | 0.831456i | ||||
\(227\) | −12.5063 | − | 21.6615i | −0.830070 | − | 1.43772i | −0.897982 | − | 0.440032i | \(-0.854967\pi\) |
0.0679123 | − | 0.997691i | \(-0.478366\pi\) | |||||||
\(228\) | −64.1145 | −4.24609 | ||||||||
\(229\) | −8.26244 | + | 4.77032i | −0.545997 | + | 0.315232i | −0.747506 | − | 0.664255i | \(-0.768749\pi\) |
0.201509 | + | 0.979487i | \(0.435416\pi\) | |||||||
\(230\) | 1.64845 | − | 0.951735i | 0.108696 | − | 0.0627555i | ||||
\(231\) | −62.4228 | −4.10712 | ||||||||
\(232\) | 43.8828 | + | 25.3357i | 2.88105 | + | 1.66337i | ||||
\(233\) | −8.17762 | − | 14.1641i | −0.535734 | − | 0.927918i | −0.999127 | − | 0.0417656i | \(-0.986702\pi\) |
0.463394 | − | 0.886153i | \(-0.346632\pi\) | |||||||
\(234\) | 45.9960 | 3.00685 | ||||||||
\(235\) | 0.482134 | + | 0.278360i | 0.0314510 | + | 0.0181582i | ||||
\(236\) | −38.5547 | + | 22.2596i | −2.50970 | + | 1.44897i | ||||
\(237\) | 8.19172 | + | 4.72949i | 0.532109 | + | 0.307213i | ||||
\(238\) | −31.2173 | + | 54.0700i | −2.02352 | + | 3.50484i | ||||
\(239\) | 23.7000 | 1.53303 | 0.766513 | − | 0.642229i | \(-0.221990\pi\) | ||||
0.766513 | + | 0.642229i | \(0.221990\pi\) | |||||||
\(240\) | 3.23860 | − | 5.60942i | 0.209051 | − | 0.362086i | ||||
\(241\) | −2.32644 | + | 4.02950i | −0.149859 | + | 0.259563i | −0.931175 | − | 0.364572i | \(-0.881215\pi\) |
0.781316 | + | 0.624135i | \(0.214549\pi\) | |||||||
\(242\) | 68.6014 | − | 39.6070i | 4.40986 | − | 2.54604i | ||||
\(243\) | 7.63766 | + | 13.2288i | 0.489956 | + | 0.848629i | ||||
\(244\) | 32.5928 | + | 18.8175i | 2.08654 | + | 1.20466i | ||||
\(245\) | −0.547978 | − | 0.949126i | −0.0350090 | − | 0.0606374i | ||||
\(246\) | 34.0806i | 2.17290i | ||||||||
\(247\) | 16.4686i | 1.04787i | ||||||||
\(248\) | − | 22.2135i | − | 1.41056i | ||||||
\(249\) | −38.7866 | −2.45800 | ||||||||
\(250\) | −4.94509 | + | 2.85505i | −0.312755 | + | 0.180569i | ||||
\(251\) | − | 15.5235i | − | 0.979834i | −0.871769 | − | 0.489917i | \(-0.837027\pi\) | ||
0.871769 | − | 0.489917i | \(-0.162973\pi\) | |||||||
\(252\) | −72.6704 | + | 41.9563i | −4.57781 | + | 2.64300i | ||||
\(253\) | 18.4087 | − | 10.6282i | 1.15734 | − | 0.668192i | ||||
\(254\) | −10.4177 | − | 18.0440i | −0.653665 | − | 1.13218i | ||||
\(255\) | 2.08630 | + | 3.61359i | 0.130649 | + | 0.226291i | ||||
\(256\) | 4.29806 | − | 7.44446i | 0.268629 | − | 0.465279i | ||||
\(257\) | 21.9740 | 1.37070 | 0.685350 | − | 0.728214i | \(-0.259649\pi\) | ||||
0.685350 | + | 0.728214i | \(0.259649\pi\) | |||||||
\(258\) | 24.6276 | − | 42.6562i | 1.53324 | − | 2.65566i | ||||
\(259\) | 2.31697 | − | 1.33770i | 0.143970 | − | 0.0831208i | ||||
\(260\) | −3.33055 | − | 1.92290i | −0.206552 | − | 0.119253i | ||||
\(261\) | −31.8500 | −1.97146 | ||||||||
\(262\) | −12.1455 | − | 21.0367i | −0.750353 | − | 1.29965i | ||||
\(263\) | −18.6259 | −1.14852 | −0.574262 | − | 0.818671i | \(-0.694711\pi\) | ||||
−0.574262 | + | 0.818671i | \(0.694711\pi\) | |||||||
\(264\) | 69.9481 | − | 121.154i | 4.30501 | − | 7.45649i | ||||
\(265\) | 0.715774 | + | 0.413252i | 0.0439696 | + | 0.0253859i | ||||
\(266\) | −21.0926 | − | 36.5334i | −1.29327 | − | 2.24001i | ||||
\(267\) | 6.08032 | − | 3.51047i | 0.372109 | − | 0.214837i | ||||
\(268\) | −6.35712 | + | 11.0108i | −0.388323 | + | 0.672595i | ||||
\(269\) | −12.0465 | −0.734488 | −0.367244 | − | 0.930125i | \(-0.619699\pi\) | ||||
−0.367244 | + | 0.930125i | \(0.619699\pi\) | |||||||
\(270\) | 3.04044i | 0.185035i | ||||||||
\(271\) | −6.94290 | − | 12.0255i | −0.421751 | − | 0.730494i | 0.574360 | − | 0.818603i | \(-0.305251\pi\) |
−0.996111 | + | 0.0881086i | \(0.971918\pi\) | |||||||
\(272\) | −36.1731 | − | 62.6536i | −2.19331 | − | 3.79893i | ||||
\(273\) | 17.3927 | + | 30.1250i | 1.05265 | + | 1.82325i | ||||
\(274\) | −1.19572 | −0.0722363 | ||||||||
\(275\) | −27.4801 | + | 15.8656i | −1.65711 | + | 0.956734i | ||||
\(276\) | 23.0576 | − | 39.9370i | 1.38791 | − | 2.40392i | ||||
\(277\) | −1.64914 | + | 0.952131i | −0.0990871 | + | 0.0572080i | −0.548725 | − | 0.836003i | \(-0.684886\pi\) |
0.449638 | + | 0.893211i | \(0.351553\pi\) | |||||||
\(278\) | −19.9740 | + | 11.5320i | −1.19796 | + | 0.691645i | ||||
\(279\) | 6.98124 | + | 12.0919i | 0.417956 | + | 0.723920i | ||||
\(280\) | 5.87039 | 0.350823 | ||||||||
\(281\) | 4.68083 | − | 8.10743i | 0.279235 | − | 0.483649i | −0.691960 | − | 0.721936i | \(-0.743253\pi\) |
0.971195 | + | 0.238287i | \(0.0765859\pi\) | |||||||
\(282\) | 18.9379 | 1.12774 | ||||||||
\(283\) | −9.32281 | −0.554184 | −0.277092 | − | 0.960843i | \(-0.589371\pi\) | ||||
−0.277092 | + | 0.960843i | \(0.589371\pi\) | |||||||
\(284\) | 34.8073i | 2.06544i | ||||||||
\(285\) | −2.81931 | −0.167001 | ||||||||
\(286\) | −52.2226 | − | 30.1507i | −3.08799 | − | 1.78285i | ||||
\(287\) | −13.8307 | + | 7.98518i | −0.816403 | + | 0.471350i | ||||
\(288\) | − | 60.5325i | − | 3.56691i | ||||||
\(289\) | 29.6053 | 1.74149 | ||||||||
\(290\) | 3.23819 | + | 1.86957i | 0.190153 | + | 0.109785i | ||||
\(291\) | − | 2.32691i | − | 0.136406i | ||||||
\(292\) | 1.20374 | + | 2.08494i | 0.0704437 | + | 0.122012i | ||||
\(293\) | −8.47896 | − | 14.6860i | −0.495346 | − | 0.857965i | 0.504639 | − | 0.863330i | \(-0.331626\pi\) |
−0.999986 | + | 0.00536528i | \(0.998292\pi\) | |||||||
\(294\) | −32.2863 | − | 18.6405i | −1.88298 | − | 1.08714i | ||||
\(295\) | −1.69536 | + | 0.978818i | −0.0987078 | + | 0.0569890i | ||||
\(296\) | 5.99587i | 0.348503i | ||||||||
\(297\) | 33.9533i | 1.97017i | ||||||||
\(298\) | 17.6017 | − | 30.4870i | 1.01964 | − | 1.76606i | ||||
\(299\) | −10.2583 | − | 5.92263i | −0.593253 | − | 0.342515i | ||||
\(300\) | −34.4200 | + | 59.6171i | −1.98724 | + | 3.44200i | ||||
\(301\) | 23.0812 | 1.33038 | ||||||||
\(302\) | 40.8249i | 2.34921i | ||||||||
\(303\) | 13.2963 | + | 7.67663i | 0.763853 | + | 0.441011i | ||||
\(304\) | 48.8821 | 2.80358 | ||||||||
\(305\) | 1.43320 | + | 0.827459i | 0.0820648 | + | 0.0473802i | ||||
\(306\) | 76.1665 | + | 43.9747i | 4.35415 | + | 2.51387i | ||||
\(307\) | 0.210027 | + | 0.363777i | 0.0119868 | + | 0.0207618i | 0.871957 | − | 0.489583i | \(-0.162851\pi\) |
−0.859970 | + | 0.510345i | \(0.829518\pi\) | |||||||
\(308\) | 110.011 | 6.26844 | ||||||||
\(309\) | −7.86707 | − | 4.54205i | −0.447542 | − | 0.258388i | ||||
\(310\) | − | 1.63917i | − | 0.0930987i | ||||||
\(311\) | − | 32.5607i | − | 1.84635i | −0.384381 | − | 0.923175i | \(-0.625585\pi\) | ||
0.384381 | − | 0.923175i | \(-0.374415\pi\) | |||||||
\(312\) | −77.9576 | −4.41348 | ||||||||
\(313\) | −0.957373 | −0.0541139 | −0.0270569 | − | 0.999634i | \(-0.508614\pi\) | ||||
−0.0270569 | + | 0.999634i | \(0.508614\pi\) | |||||||
\(314\) | 33.1403i | 1.87021i | ||||||||
\(315\) | −3.19553 | + | 1.84494i | −0.180048 | + | 0.103951i | ||||
\(316\) | −14.4367 | − | 8.33501i | −0.812126 | − | 0.468881i | ||||
\(317\) | −3.35534 | − | 1.93721i | −0.188455 | − | 0.108804i | 0.402804 | − | 0.915286i | \(-0.368036\pi\) |
−0.591259 | + | 0.806482i | \(0.701369\pi\) | |||||||
\(318\) | 28.1151 | 1.57662 | ||||||||
\(319\) | 36.1616 | + | 20.8779i | 2.02466 | + | 1.16894i | ||||
\(320\) | −1.24683 | + | 2.15958i | −0.0697000 | + | 0.120724i | ||||
\(321\) | 11.6359i | 0.649450i | ||||||||
\(322\) | 30.3423 | 1.69091 | ||||||||
\(323\) | −15.7449 | + | 27.2710i | −0.876070 | + | 1.51740i | ||||
\(324\) | 0.549006 | + | 0.950905i | 0.0305003 | + | 0.0528281i | ||||
\(325\) | 15.3134 | + | 8.84119i | 0.849434 | + | 0.490421i | ||||
\(326\) | 10.3532 | + | 17.9323i | 0.573413 | + | 0.993181i | ||||
\(327\) | 0.848745 | + | 1.47007i | 0.0469357 | + | 0.0812951i | ||||
\(328\) | − | 35.7913i | − | 1.97624i | ||||||
\(329\) | 4.43720 | + | 7.68546i | 0.244631 | + | 0.423713i | ||||
\(330\) | 5.16159 | − | 8.94013i | 0.284136 | − | 0.492138i | ||||
\(331\) | −17.1985 | − | 9.92953i | −0.945312 | − | 0.545776i | −0.0536908 | − | 0.998558i | \(-0.517099\pi\) |
−0.891622 | + | 0.452781i | \(0.850432\pi\) | |||||||
\(332\) | 68.3555 | 3.75149 | ||||||||
\(333\) | −1.88438 | − | 3.26384i | −0.103263 | − | 0.178857i | ||||
\(334\) | 19.7212 | + | 34.1581i | 1.07910 | + | 1.86905i | ||||
\(335\) | −0.279541 | + | 0.484179i | −0.0152730 | + | 0.0264536i | ||||
\(336\) | 89.4169 | − | 51.6249i | 4.87809 | − | 2.81637i | ||||
\(337\) | 7.61047 | + | 13.1817i | 0.414569 | + | 0.718054i | 0.995383 | − | 0.0959817i | \(-0.0305990\pi\) |
−0.580814 | + | 0.814036i | \(0.697266\pi\) | |||||||
\(338\) | − | 0.666892i | − | 0.0362742i | ||||||
\(339\) | − | 15.3761i | − | 0.835117i | ||||||
\(340\) | −3.67680 | − | 6.36840i | −0.199402 | − | 0.345375i | ||||
\(341\) | − | 18.3050i | − | 0.991272i | ||||||
\(342\) | −51.4634 | + | 29.7124i | −2.78282 | + | 1.60666i | ||||
\(343\) | 6.81466i | 0.367957i | ||||||||
\(344\) | −25.8637 | + | 44.7973i | −1.39448 | + | 2.41531i | ||||
\(345\) | 1.01391 | − | 1.75615i | 0.0545872 | − | 0.0945478i | ||||
\(346\) | −21.2418 | + | 36.7919i | −1.14197 | + | 1.97795i | ||||
\(347\) | 11.3854 | − | 6.57337i | 0.611201 | − | 0.352877i | −0.162235 | − | 0.986752i | \(-0.551870\pi\) |
0.773435 | + | 0.633875i | \(0.218537\pi\) | |||||||
\(348\) | 90.5878 | 4.85602 | ||||||||
\(349\) | −14.6970 | + | 11.5325i | −0.786713 | + | 0.617319i | ||||
\(350\) | −45.2943 | −2.42108 | ||||||||
\(351\) | 16.3857 | − | 9.46031i | 0.874606 | − | 0.504954i | ||||
\(352\) | −39.6796 | + | 68.7270i | −2.11493 | + | 3.66316i | ||||
\(353\) | 0.128539 | − | 0.222636i | 0.00684143 | − | 0.0118497i | −0.862584 | − | 0.505913i | \(-0.831156\pi\) |
0.869426 | + | 0.494063i | \(0.164489\pi\) | |||||||
\(354\) | −33.2964 | + | 57.6710i | −1.76968 | + | 3.06518i | ||||
\(355\) | 1.53058i | 0.0812348i | ||||||||
\(356\) | −10.7156 | + | 6.18667i | −0.567927 | + | 0.327893i | ||||
\(357\) | 66.5135i | 3.52027i | ||||||||
\(358\) | −26.2751 | − | 45.5098i | −1.38868 | − | 2.40527i | ||||
\(359\) | 28.5865i | 1.50874i | 0.656451 | + | 0.754369i | \(0.272057\pi\) | ||||
−0.656451 | + | 0.754369i | \(0.727943\pi\) | |||||||
\(360\) | − | 8.26942i | − | 0.435837i | ||||||
\(361\) | −1.13836 | − | 1.97169i | −0.0599135 | − | 0.103773i | ||||
\(362\) | −31.6491 | + | 18.2726i | −1.66344 | + | 0.960386i | ||||
\(363\) | 42.1946 | − | 73.0831i | 2.21464 | − | 3.83587i | ||||
\(364\) | −30.6519 | − | 53.0907i | −1.60660 | − | 2.78271i | ||||
\(365\) | 0.0529321 | + | 0.0916811i | 0.00277059 | + | 0.00479881i | ||||
\(366\) | 56.2952 | 2.94260 | ||||||||
\(367\) | 4.55133 | + | 2.62771i | 0.237578 | + | 0.137166i | 0.614063 | − | 0.789257i | \(-0.289534\pi\) |
−0.376485 | + | 0.926423i | \(0.622867\pi\) | |||||||
\(368\) | −17.5795 | + | 30.4487i | −0.916397 | + | 1.58725i | ||||
\(369\) | 11.2484 | + | 19.4829i | 0.585571 | + | 1.01424i | ||||
\(370\) | 0.442446i | 0.0230016i | ||||||||
\(371\) | 6.58745 | + | 11.4098i | 0.342003 | + | 0.592367i | ||||
\(372\) | −19.8561 | − | 34.3917i | −1.02949 | − | 1.78313i | ||||
\(373\) | 16.5196 | + | 9.53760i | 0.855353 | + | 0.493838i | 0.862453 | − | 0.506137i | \(-0.168927\pi\) |
−0.00710042 | + | 0.999975i | \(0.502260\pi\) | |||||||
\(374\) | −57.6516 | − | 99.8555i | −2.98109 | − | 5.16340i | ||||
\(375\) | −3.04157 | + | 5.26815i | −0.157066 | + | 0.272046i | ||||
\(376\) | −19.8885 | −1.02567 | ||||||||
\(377\) | − | 23.2686i | − | 1.19839i | ||||||
\(378\) | −24.2331 | + | 41.9729i | −1.24641 | + | 2.15885i | ||||
\(379\) | 6.45186 | + | 3.72498i | 0.331410 | + | 0.191339i | 0.656467 | − | 0.754355i | \(-0.272050\pi\) |
−0.325057 | + | 0.945694i | \(0.605384\pi\) | |||||||
\(380\) | 4.96860 | 0.254884 | ||||||||
\(381\) | −19.2228 | − | 11.0983i | −0.984815 | − | 0.568583i | ||||
\(382\) | 6.23235 | + | 3.59825i | 0.318875 | + | 0.184103i | ||||
\(383\) | 10.3513 | − | 5.97634i | 0.528928 | − | 0.305377i | −0.211652 | − | 0.977345i | \(-0.567884\pi\) |
0.740580 | + | 0.671969i | \(0.234551\pi\) | |||||||
\(384\) | 15.2551i | 0.778486i | ||||||||
\(385\) | 4.83750 | 0.246542 | ||||||||
\(386\) | 63.2048 | 3.21704 | ||||||||
\(387\) | − | 32.5137i | − | 1.65276i | ||||||
\(388\) | 4.10083i | 0.208188i | ||||||||
\(389\) | 2.30430 | + | 1.33039i | 0.116833 | + | 0.0674534i | 0.557278 | − | 0.830326i | \(-0.311846\pi\) |
−0.440445 | + | 0.897780i | \(0.645179\pi\) | |||||||
\(390\) | −5.75263 | −0.291296 | ||||||||
\(391\) | −11.3247 | − | 19.6150i | −0.572717 | − | 0.991974i | ||||
\(392\) | 33.9069 | + | 19.5762i | 1.71256 | + | 0.988745i | ||||
\(393\) | −22.4110 | − | 12.9390i | −1.13049 | − | 0.652686i | ||||
\(394\) | −56.8952 | −2.86634 | ||||||||
\(395\) | −0.634823 | − | 0.366515i | −0.0319414 | − | 0.0184414i | ||||
\(396\) | − | 154.968i | − | 7.78745i | ||||||
\(397\) | −3.42443 | −0.171867 | −0.0859335 | − | 0.996301i | \(-0.527387\pi\) | ||||
−0.0859335 | + | 0.996301i | \(0.527387\pi\) | |||||||
\(398\) | −27.7699 | + | 48.0989i | −1.39198 | + | 2.41098i | ||||
\(399\) | −38.9202 | − | 22.4706i | −1.94845 | − | 1.12494i | ||||
\(400\) | 26.2424 | − | 45.4532i | 1.31212 | − | 2.27266i | ||||
\(401\) | 7.51071i | 0.375067i | 0.982258 | + | 0.187533i | \(0.0600493\pi\) | ||||
−0.982258 | + | 0.187533i | \(0.939951\pi\) | |||||||
\(402\) | 19.0182i | 0.948544i | ||||||||
\(403\) | −8.83393 | + | 5.10027i | −0.440049 | + | 0.254063i | ||||
\(404\) | −23.4327 | − | 13.5289i | −1.16582 | − | 0.673088i | ||||
\(405\) | 0.0241414 | + | 0.0418141i | 0.00119960 | + | 0.00207776i | ||||
\(406\) | 29.8018 | + | 51.6183i | 1.47904 | + | 2.56177i | ||||
\(407\) | 4.94089i | 0.244911i | ||||||||
\(408\) | −129.093 | − | 74.5319i | −6.39106 | − | 3.68988i | ||||
\(409\) | −13.8572 | −0.685194 | −0.342597 | − | 0.939482i | \(-0.611307\pi\) | ||||
−0.342597 | + | 0.939482i | \(0.611307\pi\) | |||||||
\(410\) | − | 2.64110i | − | 0.130435i | ||||||
\(411\) | −1.10318 | + | 0.636920i | −0.0544157 | + | 0.0314169i | ||||
\(412\) | 13.8645 | + | 8.00468i | 0.683056 | + | 0.394362i | ||||
\(413\) | −31.2057 | −1.53553 | ||||||||
\(414\) | − | 42.7421i | − | 2.10066i | ||||||
\(415\) | 3.00579 | 0.147548 | ||||||||
\(416\) | 44.2232 | 2.16822 | ||||||||
\(417\) | −12.2854 | + | 21.2790i | −0.601619 | + | 1.04203i | ||||
\(418\) | 77.9069 | 3.81055 | ||||||||
\(419\) | −10.6844 | − | 18.5059i | −0.521966 | − | 0.904071i | −0.999673 | − | 0.0255526i | \(-0.991865\pi\) |
0.477708 | − | 0.878519i | \(-0.341468\pi\) | |||||||
\(420\) | 9.08875 | − | 5.24739i | 0.443485 | − | 0.256046i | ||||
\(421\) | −23.4754 | + | 13.5535i | −1.14412 | + | 0.660558i | −0.947448 | − | 0.319911i | \(-0.896347\pi\) |
−0.196673 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(422\) | −6.74831 | + | 11.6884i | −0.328503 | + | 0.568983i | ||||
\(423\) | 10.8262 | − | 6.25053i | 0.526390 | − | 0.303911i | ||||
\(424\) | −29.5263 | −1.43393 | ||||||||
\(425\) | 16.9053 | + | 29.2809i | 0.820030 | + | 1.42033i | ||||
\(426\) | 26.0328 | + | 45.0901i | 1.26129 | + | 2.18462i | ||||
\(427\) | 13.1901 | + | 22.8459i | 0.638314 | + | 1.10559i | ||||
\(428\) | − | 20.5064i | − | 0.991216i | ||||||
\(429\) | −64.2410 | −3.10158 | ||||||||
\(430\) | −1.90853 | + | 3.30567i | −0.0920374 | + | 0.159414i | ||||
\(431\) | −3.71289 | + | 2.14364i | −0.178843 | + | 0.103255i | −0.586749 | − | 0.809769i | \(-0.699593\pi\) |
0.407906 | + | 0.913024i | \(0.366259\pi\) | |||||||
\(432\) | −28.0801 | − | 48.6361i | −1.35100 | − | 2.34001i | ||||
\(433\) | −11.4270 | − | 6.59737i | −0.549146 | − | 0.317050i | 0.199632 | − | 0.979871i | \(-0.436025\pi\) |
−0.748777 | + | 0.662822i | \(0.769359\pi\) | |||||||
\(434\) | 13.0646 | − | 22.6286i | 0.627121 | − | 1.08621i | ||||
\(435\) | 3.98341 | 0.190990 | ||||||||
\(436\) | −1.49579 | − | 2.59078i | −0.0716351 | − | 0.124076i | ||||
\(437\) | 15.3036 | 0.732069 | ||||||||
\(438\) | 3.11871 | + | 1.80059i | 0.149018 | + | 0.0860354i | ||||
\(439\) | −31.5839 | + | 18.2350i | −1.50742 | + | 0.870309i | −0.507457 | + | 0.861677i | \(0.669414\pi\) |
−0.999963 | + | 0.00863178i | \(0.997252\pi\) | |||||||
\(440\) | −5.42067 | + | 9.38888i | −0.258420 | + | 0.447597i | ||||
\(441\) | −24.6095 | −1.17188 | ||||||||
\(442\) | −32.1266 | + | 55.6448i | −1.52810 | + | 2.64676i | ||||
\(443\) | 6.25521 | + | 10.8343i | 0.297194 | + | 0.514755i | 0.975493 | − | 0.220031i | \(-0.0706159\pi\) |
−0.678299 | + | 0.734786i | \(0.737283\pi\) | |||||||
\(444\) | 5.35955 | + | 9.28302i | 0.254353 | + | 0.440552i | ||||
\(445\) | −0.471198 | + | 0.272046i | −0.0223369 | + | 0.0128962i | ||||
\(446\) | −58.3289 | + | 33.6762i | −2.76196 | + | 1.59462i | ||||
\(447\) | − | 37.5032i | − | 1.77384i | ||||||
\(448\) | −34.4247 | + | 19.8751i | −1.62642 | + | 0.939011i | ||||
\(449\) | 19.4656 | 0.918640 | 0.459320 | − | 0.888271i | \(-0.348093\pi\) | ||||
0.459320 | + | 0.888271i | \(0.348093\pi\) | |||||||
\(450\) | 63.8046i | 3.00778i | ||||||||
\(451\) | − | 29.4938i | − | 1.38881i | ||||||
\(452\) | 27.0981i | 1.27459i | ||||||||
\(453\) | 21.7460 | + | 37.6652i | 1.02172 | + | 1.76966i | ||||
\(454\) | 57.1032 | + | 32.9685i | 2.67998 | + | 1.54729i | ||||
\(455\) | −1.34786 | − | 2.33456i | −0.0631885 | − | 0.109446i | ||||
\(456\) | 87.2242 | − | 50.3589i | 4.08465 | − | 2.35827i | ||||
\(457\) | 15.1313 | − | 26.2082i | 0.707812 | − | 1.22597i | −0.257855 | − | 0.966184i | \(-0.583016\pi\) |
0.965667 | − | 0.259783i | \(-0.0836511\pi\) | |||||||
\(458\) | 12.5753 | − | 21.7811i | 0.587607 | − | 1.01776i | ||||
\(459\) | 36.1783 | 1.68866 | ||||||||
\(460\) | −1.78687 | + | 3.09494i | −0.0833130 | + | 0.144302i | ||||
\(461\) | 0.828955 | + | 0.478597i | 0.0386083 | + | 0.0222905i | 0.519180 | − | 0.854665i | \(-0.326237\pi\) |
−0.480572 | + | 0.876955i | \(0.659571\pi\) | |||||||
\(462\) | 142.510 | − | 82.2783i | 6.63017 | − | 3.82793i | ||||
\(463\) | −30.5678 | − | 17.6483i | −1.42061 | − | 0.820187i | −0.424255 | − | 0.905543i | \(-0.639464\pi\) |
−0.996351 | + | 0.0853553i | \(0.972797\pi\) | |||||||
\(464\) | −69.0658 | −3.20630 | ||||||||
\(465\) | −0.873130 | − | 1.51230i | −0.0404904 | − | 0.0701315i | ||||
\(466\) | 37.3387 | + | 21.5575i | 1.72968 | + | 0.998633i | ||||
\(467\) | −28.8206 | −1.33366 | −0.666830 | − | 0.745210i | \(-0.732349\pi\) | ||||
−0.666830 | + | 0.745210i | \(0.732349\pi\) | |||||||
\(468\) | −74.7870 | + | 43.1783i | −3.45703 | + | 1.99592i | ||||
\(469\) | −7.71806 | + | 4.45603i | −0.356387 | + | 0.205760i | ||||
\(470\) | −1.46760 | −0.0676956 | ||||||||
\(471\) | 17.6527 | + | 30.5753i | 0.813392 | + | 1.40884i | ||||
\(472\) | 34.9677 | − | 60.5658i | 1.60952 | − | 2.78777i | ||||
\(473\) | −21.3130 | + | 36.9152i | −0.979972 | + | 1.69736i | ||||
\(474\) | −24.9354 | −1.14532 | ||||||||
\(475\) | −22.8449 | −1.04819 | ||||||||
\(476\) | − | 117.220i | − | 5.37277i | ||||||
\(477\) | 16.0726 | − | 9.27951i | 0.735913 | − | 0.424879i | ||||
\(478\) | −54.1067 | + | 31.2385i | −2.47478 | + | 1.42882i | ||||
\(479\) | −6.73995 | − | 11.6739i | −0.307956 | − | 0.533396i | 0.669959 | − | 0.742398i | \(-0.266312\pi\) |
−0.977915 | + | 0.209002i | \(0.932978\pi\) | |||||||
\(480\) | 7.57069i | 0.345553i | ||||||||
\(481\) | 2.38446 | − | 1.37667i | 0.108722 | − | 0.0627706i | ||||
\(482\) | − | 12.2657i | − | 0.558688i | ||||||
\(483\) | 27.9939 | − | 16.1623i | 1.27376 | − | 0.735408i | ||||
\(484\) | −74.3615 | + | 128.798i | −3.38007 | + | 5.85445i | ||||
\(485\) | 0.180326i | 0.00818817i | ||||||||
\(486\) | −34.8733 | − | 20.1341i | −1.58188 | − | 0.913301i | ||||
\(487\) | 16.4234 | − | 9.48207i | 0.744217 | − | 0.429674i | −0.0793837 | − | 0.996844i | \(-0.525295\pi\) |
0.823600 | + | 0.567170i | \(0.191962\pi\) | |||||||
\(488\) | −59.1209 | −2.67628 | ||||||||
\(489\) | 19.1039 | + | 11.0296i | 0.863907 | + | 0.498777i | ||||
\(490\) | 2.50205 | + | 1.44456i | 0.113031 | + | 0.0652585i | ||||
\(491\) | −13.5615 | + | 23.4891i | −0.612020 | + | 1.06005i | 0.378879 | + | 0.925446i | \(0.376310\pi\) |
−0.990899 | + | 0.134604i | \(0.957024\pi\) | |||||||
\(492\) | −31.9929 | − | 55.4133i | −1.44235 | − | 2.49822i | ||||
\(493\) | 22.2461 | − | 38.5313i | 1.00191 | − | 1.73536i | ||||
\(494\) | −21.7069 | − | 37.5975i | −0.976642 | − | 1.69159i | ||||
\(495\) | − | 6.81441i | − | 0.306285i | ||||||
\(496\) | 15.1386 | + | 26.2209i | 0.679744 | + | 1.17735i | ||||
\(497\) | −12.1991 | + | 21.1295i | −0.547205 | + | 0.947787i | ||||
\(498\) | 88.5491 | − | 51.1238i | 3.96798 | − | 2.29091i | ||||
\(499\) | 28.2846 | − | 16.3301i | 1.26619 | − | 0.731038i | 0.291929 | − | 0.956440i | \(-0.405703\pi\) |
0.974266 | + | 0.225402i | \(0.0723696\pi\) | |||||||
\(500\) | 5.36031 | − | 9.28432i | 0.239720 | − | 0.415208i | ||||
\(501\) | 36.3897 | + | 21.0096i | 1.62577 | + | 0.938639i | ||||
\(502\) | 20.4612 | + | 35.4399i | 0.913229 | + | 1.58176i | ||||
\(503\) | −32.1480 | − | 18.5607i | −1.43341 | − | 0.827579i | −0.436029 | − | 0.899933i | \(-0.643616\pi\) |
−0.997379 | + | 0.0723539i | \(0.976949\pi\) | |||||||
\(504\) | 65.9094 | − | 114.158i | 2.93584 | − | 5.08502i | ||||
\(505\) | −1.03041 | − | 0.594905i | −0.0458525 | − | 0.0264729i | ||||
\(506\) | −28.0178 | + | 48.5282i | −1.24554 | + | 2.15734i | ||||
\(507\) | −0.355230 | − | 0.615277i | −0.0157763 | − | 0.0273254i | ||||
\(508\) | 33.8773 | + | 19.5591i | 1.50306 | + | 0.867793i | ||||
\(509\) | 15.7310 | − | 9.08231i | 0.697265 | − | 0.402566i | −0.109063 | − | 0.994035i | \(-0.534785\pi\) |
0.806328 | + | 0.591469i | \(0.201452\pi\) | |||||||
\(510\) | −9.52599 | − | 5.49984i | −0.421818 | − | 0.243537i | ||||
\(511\) | 1.68753i | 0.0746519i | ||||||||
\(512\) | 33.5248i | 1.48160i | ||||||||
\(513\) | −12.2223 | + | 21.1697i | −0.539628 | + | 0.934663i | ||||
\(514\) | −50.1663 | + | 28.9635i | −2.21274 | + | 1.27753i | ||||
\(515\) | 0.609664 | + | 0.351989i | 0.0268650 | + | 0.0155105i | ||||
\(516\) | 92.4756i | 4.07101i | ||||||||
\(517\) | −16.3891 | −0.720791 | ||||||||
\(518\) | −3.52640 | + | 6.10791i | −0.154941 | + | 0.268366i | ||||
\(519\) | 45.2591i | 1.98666i | ||||||||
\(520\) | 6.04138 | 0.264932 | ||||||||
\(521\) | 21.5970 | − | 12.4690i | 0.946180 | − | 0.546277i | 0.0542879 | − | 0.998525i | \(-0.482711\pi\) |
0.891892 | + | 0.452248i | \(0.149378\pi\) | |||||||
\(522\) | 72.7129 | − | 41.9808i | 3.18256 | − | 1.83745i | ||||
\(523\) | −22.1910 | − | 12.8120i | −0.970344 | − | 0.560229i | −0.0710032 | − | 0.997476i | \(-0.522620\pi\) |
−0.899341 | + | 0.437247i | \(0.855953\pi\) | |||||||
\(524\) | 39.4960 | + | 22.8030i | 1.72539 | + | 0.996155i | ||||
\(525\) | −41.7887 | + | 24.1267i | −1.82381 | + | 1.05298i | ||||
\(526\) | 42.5227 | − | 24.5505i | 1.85408 | − | 1.07045i | ||||
\(527\) | −19.5046 | −0.849633 | ||||||||
\(528\) | 190.680i | 8.29828i | ||||||||
\(529\) | 5.99635 | − | 10.3860i | 0.260711 | − | 0.451565i | ||||
\(530\) | −2.17880 | −0.0946410 | ||||||||
\(531\) | 43.9584i | 1.90763i | ||||||||
\(532\) | 68.5909 | + | 39.6010i | 2.97379 | + | 1.71692i | ||||
\(533\) | −14.2336 | + | 8.21776i | −0.616525 | + | 0.355951i | ||||
\(534\) | −9.25417 | + | 16.0287i | −0.400467 | + | 0.693629i | ||||
\(535\) | − | 0.901728i | − | 0.0389851i | ||||||
\(536\) | − | 19.9729i | − | 0.862696i | ||||||
\(537\) | −48.4830 | − | 27.9917i | −2.09219 | − | 1.20793i | ||||
\(538\) | 27.5020 | − | 15.8783i | 1.18569 | − | 0.684560i | ||||
\(539\) | 27.9410 | + | 16.1317i | 1.20350 | + | 0.694843i | ||||
\(540\) | −2.85419 | − | 4.94360i | −0.122825 | − | 0.212739i | ||||
\(541\) | 2.57521 | − | 4.46040i | 0.110717 | − | 0.191767i | −0.805343 | − | 0.592810i | \(-0.798019\pi\) |
0.916060 | + | 0.401042i | \(0.131352\pi\) | |||||||
\(542\) | 31.7010 | + | 18.3026i | 1.36168 | + | 0.786164i | ||||
\(543\) | −19.4663 | + | 33.7167i | −0.835381 | + | 1.44692i | ||||
\(544\) | 73.2308 | + | 42.2798i | 3.13975 | + | 1.81273i | ||||
\(545\) | −0.0657741 | − | 0.113924i | −0.00281745 | − | 0.00487997i | ||||
\(546\) | −79.4143 | − | 45.8499i | −3.39862 | − | 1.96219i | ||||
\(547\) | −13.6498 | + | 23.6422i | −0.583625 | + | 1.01087i | 0.411421 | + | 0.911446i | \(0.365033\pi\) |
−0.995045 | + | 0.0994220i | \(0.968301\pi\) | |||||||
\(548\) | 1.94418 | − | 1.12247i | 0.0830514 | − | 0.0479497i | ||||
\(549\) | 32.1823 | − | 18.5805i | 1.37351 | − | 0.792994i | ||||
\(550\) | 41.8244 | − | 72.4420i | 1.78340 | − | 3.08894i | ||||
\(551\) | 15.0310 | + | 26.0345i | 0.640342 | + | 1.10910i | ||||
\(552\) | 72.4427i | 3.08337i | ||||||||
\(553\) | −5.84243 | − | 10.1194i | −0.248446 | − | 0.430320i | ||||
\(554\) | 2.50997 | − | 4.34740i | 0.106638 | − | 0.184703i | ||||
\(555\) | 0.235675 | + | 0.408202i | 0.0100039 | + | 0.0173272i | ||||
\(556\) | 21.6512 | − | 37.5009i | 0.918214 | − | 1.59039i | ||||
\(557\) | −32.6393 | − | 18.8443i | −1.38297 | − | 0.798458i | −0.390460 | − | 0.920620i | \(-0.627684\pi\) |
−0.992510 | + | 0.122162i | \(0.961017\pi\) | |||||||
\(558\) | −31.8761 | − | 18.4037i | −1.34942 | − | 0.779089i | ||||
\(559\) | 23.7535 | 1.00467 | ||||||||
\(560\) | −6.92942 | + | 4.00070i | −0.292822 | + | 0.169061i | ||||
\(561\) | −106.379 | − | 61.4180i | −4.49133 | − | 2.59307i | ||||
\(562\) | 24.6788i | 1.04101i | ||||||||
\(563\) | 12.5400 | − | 21.7199i | 0.528497 | − | 0.915383i | −0.470951 | − | 0.882159i | \(-0.656089\pi\) |
0.999448 | − | 0.0332240i | \(-0.0105775\pi\) | |||||||
\(564\) | −30.7920 | + | 17.7778i | −1.29658 | + | 0.748580i | ||||
\(565\) | 1.19158i | 0.0501303i | ||||||||
\(566\) | 21.2838 | − | 12.2882i | 0.894626 | − | 0.516513i | ||||
\(567\) | 0.769652i | 0.0323223i | ||||||||
\(568\) | −27.3395 | − | 47.3534i | −1.14714 | − | 1.98691i | ||||
\(569\) | 25.3438 | − | 14.6322i | 1.06247 | − | 0.613415i | 0.136353 | − | 0.990660i | \(-0.456462\pi\) |
0.926113 | + | 0.377245i | \(0.123129\pi\) | |||||||
\(570\) | 6.43643 | − | 3.71607i | 0.269592 | − | 0.155649i | ||||
\(571\) | − | 39.5659i | − | 1.65578i | −0.560889 | − | 0.827891i | \(-0.689541\pi\) | ||
0.560889 | − | 0.827891i | \(-0.310459\pi\) | |||||||
\(572\) | 113.215 | 4.73375 | ||||||||
\(573\) | 7.66665 | 0.320279 | ||||||||
\(574\) | 21.0502 | − | 36.4601i | 0.878619 | − | 1.52181i | ||||
\(575\) | 8.21574 | − | 14.2301i | 0.342620 | − | 0.593435i | ||||
\(576\) | 27.9974 | + | 48.4929i | 1.16656 | + | 2.02054i | ||||
\(577\) | −0.701671 | −0.0292109 | −0.0146055 | − | 0.999893i | \(-0.504649\pi\) | ||||
−0.0146055 | + | 0.999893i | \(0.504649\pi\) | |||||||
\(578\) | −67.5885 | + | 39.0222i | −2.81131 | + | 1.62311i | ||||
\(579\) | 58.3129 | − | 33.6670i | 2.42340 | − | 1.39915i | ||||
\(580\) | −7.02016 | −0.291496 | ||||||||
\(581\) | 41.4946 | + | 23.9569i | 1.72149 | + | 0.993900i | ||||
\(582\) | 3.06706 | + | 5.31230i | 0.127134 | + | 0.220202i | ||||
\(583\) | −24.3312 | −1.00769 | ||||||||
\(584\) | −3.27525 | − | 1.89097i | −0.135531 | − | 0.0782488i | ||||
\(585\) | −3.28861 | + | 1.89868i | −0.135967 | + | 0.0785007i | ||||
\(586\) | 38.7147 | + | 22.3519i | 1.59929 | + | 0.923349i | ||||
\(587\) | 19.1966 | − | 33.2495i | 0.792329 | − | 1.37235i | −0.132192 | − | 0.991224i | \(-0.542202\pi\) |
0.924521 | − | 0.381130i | \(-0.124465\pi\) | |||||||
\(588\) | 69.9945 | 2.88652 | ||||||||
\(589\) | 6.58933 | − | 11.4131i | 0.271509 | − | 0.470267i | ||||
\(590\) | 2.58032 | − | 4.46925i | 0.106230 | − | 0.183996i | ||||
\(591\) | −52.4917 | + | 30.3061i | −2.15922 | + | 1.24663i | ||||
\(592\) | −4.08622 | − | 7.07754i | −0.167943 | − | 0.290885i | ||||
\(593\) | 19.7042 | + | 11.3762i | 0.809156 | + | 0.467166i | 0.846663 | − | 0.532130i | \(-0.178608\pi\) |
−0.0375068 | + | 0.999296i | \(0.511942\pi\) | |||||||
\(594\) | −44.7532 | − | 77.5149i | −1.83625 | − | 3.18047i | ||||
\(595\) | − | 5.15451i | − | 0.211314i | ||||||
\(596\) | 66.0937i | 2.70730i | ||||||||
\(597\) | 59.1682i | 2.42159i | ||||||||
\(598\) | 31.2260 | 1.27693 | ||||||||
\(599\) | 32.6915 | − | 18.8745i | 1.33574 | − | 0.771190i | 0.349567 | − | 0.936911i | \(-0.386329\pi\) |
0.986173 | + | 0.165722i | \(0.0529954\pi\) | |||||||
\(600\) | − | 108.141i | − | 4.41484i | ||||||
\(601\) | 7.49723 | − | 4.32853i | 0.305818 | − | 0.176564i | −0.339235 | − | 0.940702i | \(-0.610168\pi\) |
0.645054 | + | 0.764137i | \(0.276835\pi\) | |||||||
\(602\) | −52.6940 | + | 30.4229i | −2.14765 | + | 1.23995i | ||||
\(603\) | 6.27705 | + | 10.8722i | 0.255621 | + | 0.442749i | ||||
\(604\) | −38.3240 | − | 66.3791i | −1.55938 | − | 2.70093i | ||||
\(605\) | −3.26989 | + | 5.66362i | −0.132940 | + | 0.230259i | ||||
\(606\) | −40.4737 | −1.64413 | ||||||||
\(607\) | −3.80682 | + | 6.59361i | −0.154514 | + | 0.267627i | −0.932882 | − | 0.360182i | \(-0.882715\pi\) |
0.778368 | + | 0.627809i | \(0.216048\pi\) | |||||||
\(608\) | −49.4798 | + | 28.5672i | −2.00667 | + | 1.15855i | ||||
\(609\) | 54.9905 | + | 31.7488i | 2.22833 | + | 1.28653i | ||||
\(610\) | −4.36263 | −0.176638 | ||||||||
\(611\) | 4.56644 | + | 7.90931i | 0.184738 | + | 0.319976i | ||||
\(612\) | −165.124 | −6.67473 | ||||||||
\(613\) | 3.60506 | − | 6.24414i | 0.145607 | − | 0.252198i | −0.783992 | − | 0.620770i | \(-0.786820\pi\) |
0.929599 | + | 0.368572i | \(0.120153\pi\) | |||||||
\(614\) | −0.958974 | − | 0.553664i | −0.0387010 | − | 0.0223441i | ||||
\(615\) | −1.40682 | − | 2.43669i | −0.0567285 | − | 0.0982567i | ||||
\(616\) | −149.663 | + | 86.4082i | −6.03011 | + | 3.48149i | ||||
\(617\) | 18.3661 | − | 31.8111i | 0.739392 | − | 1.28067i | −0.213377 | − | 0.976970i | \(-0.568446\pi\) |
0.952769 | − | 0.303695i | \(-0.0982204\pi\) | |||||||
\(618\) | 23.9472 | 0.963297 | ||||||||
\(619\) | 6.17107i | 0.248036i | 0.992280 | + | 0.124018i | \(0.0395781\pi\) | ||||
−0.992280 | + | 0.124018i | \(0.960422\pi\) | |||||||
\(620\) | 1.53876 | + | 2.66521i | 0.0617980 | + | 0.107037i | ||||
\(621\) | −8.79106 | − | 15.2266i | −0.352773 | − | 0.611021i | ||||
\(622\) | 42.9177 | + | 74.3356i | 1.72084 | + | 2.98058i | ||||
\(623\) | −8.67311 | −0.347481 | ||||||||
\(624\) | 92.0213 | − | 53.1285i | 3.68380 | − | 2.12684i | ||||
\(625\) | −12.1459 | + | 21.0373i | −0.485835 | + | 0.841491i | ||||
\(626\) | 2.18567 | − | 1.26189i | 0.0873567 | − | 0.0504354i | ||||
\(627\) | 71.8771 | − | 41.4983i | 2.87049 | − | 1.65728i | ||||
\(628\) | −31.1102 | − | 53.8844i | −1.24143 | − | 2.15022i | ||||
\(629\) | 5.26468 | 0.209917 | ||||||||
\(630\) | 4.86356 | − | 8.42394i | 0.193769 | − | 0.335618i | ||||
\(631\) | −25.2080 | −1.00351 | −0.501757 | − | 0.865009i | \(-0.667313\pi\) | ||||
−0.501757 | + | 0.865009i | \(0.667313\pi\) | |||||||
\(632\) | 26.1870 | 1.04166 | ||||||||
\(633\) | 14.3784i | 0.571488i | ||||||||
\(634\) | 10.2136 | 0.405633 | ||||||||
\(635\) | 1.48968 | + | 0.860070i | 0.0591163 | + | 0.0341308i | ||||
\(636\) | −45.7137 | + | 26.3928i | −1.81267 | + | 1.04654i | ||||
\(637\) | − | 17.9789i | − | 0.712351i | ||||||
\(638\) | −110.075 | −4.35791 | ||||||||
\(639\) | 29.7644 | + | 17.1845i | 1.17746 | + | 0.679807i | ||||
\(640\) | − | 1.18221i | − | 0.0467309i | ||||||
\(641\) | 1.05027 | + | 1.81913i | 0.0414834 | + | 0.0718513i | 0.886022 | − | 0.463644i | \(-0.153458\pi\) |
−0.844538 | + | 0.535495i | \(0.820125\pi\) | |||||||
\(642\) | −15.3370 | − | 26.5645i | −0.605303 | − | 1.04842i | ||||
\(643\) | 39.5176 | + | 22.8155i | 1.55842 | + | 0.899756i | 0.997408 | + | 0.0719497i | \(0.0229221\pi\) |
0.561014 | + | 0.827806i | \(0.310411\pi\) | |||||||
\(644\) | −49.3349 | + | 28.4835i | −1.94407 | + | 1.12241i | ||||
\(645\) | 4.06643i | 0.160115i | ||||||||
\(646\) | − | 83.0122i | − | 3.26607i | ||||||
\(647\) | 4.70442 | − | 8.14830i | 0.184950 | − | 0.320343i | −0.758610 | − | 0.651545i | \(-0.774121\pi\) |
0.943560 | + | 0.331203i | \(0.107454\pi\) | |||||||
\(648\) | −1.49378 | − | 0.862436i | −0.0586813 | − | 0.0338797i | ||||
\(649\) | 28.8151 | − | 49.9092i | 1.13109 | − | 1.95911i | ||||
\(650\) | −46.6136 | −1.82834 | ||||||||
\(651\) | − | 27.8362i | − | 1.09099i | ||||||
\(652\) | −33.6677 | − | 19.4380i | −1.31853 | − | 0.761252i | ||||
\(653\) | 3.54253 | 0.138630 | 0.0693150 | − | 0.997595i | \(-0.477919\pi\) | ||||
0.0693150 | + | 0.997595i | \(0.477919\pi\) | |||||||
\(654\) | −3.87534 | − | 2.23743i | −0.151538 | − | 0.0874904i | ||||
\(655\) | 1.73676 | + | 1.00272i | 0.0678607 | + | 0.0391794i | ||||
\(656\) | 24.3919 | + | 42.2481i | 0.952345 | + | 1.64951i | ||||
\(657\) | 2.37716 | 0.0927420 | ||||||||
\(658\) | −20.2601 | − | 11.6972i | −0.789821 | − | 0.456004i | ||||
\(659\) | − | 28.6458i | − | 1.11588i | −0.829881 | − | 0.557941i | \(-0.811592\pi\) | ||
0.829881 | − | 0.557941i | \(-0.188408\pi\) | |||||||
\(660\) | 19.3816i | 0.754427i | ||||||||
\(661\) | 8.95093 | 0.348151 | 0.174075 | − | 0.984732i | \(-0.444306\pi\) | ||||
0.174075 | + | 0.984732i | \(0.444306\pi\) | |||||||
\(662\) | 52.3517 | 2.03471 | ||||||||
\(663\) | 68.4508i | 2.65841i | ||||||||
\(664\) | −92.9938 | + | 53.6900i | −3.60886 | + | 2.08358i | ||||
\(665\) | 3.01614 | + | 1.74137i | 0.116961 | + | 0.0675275i | ||||
\(666\) | 8.60400 | + | 4.96752i | 0.333398 | + | 0.192488i | ||||
\(667\) | −21.6225 | −0.837227 | ||||||||
\(668\) | −64.1312 | − | 37.0262i | −2.48131 | − | 1.43259i | ||||
\(669\) | −35.8763 | + | 62.1396i | −1.38706 | + | 2.40246i | ||||
\(670\) | − | 1.47383i | − | 0.0569391i | ||||||
\(671\) | −48.7185 | −1.88076 | ||||||||
\(672\) | −60.3403 | + | 104.512i | −2.32768 | + | 4.03165i | ||||
\(673\) | 2.26628 | + | 3.92531i | 0.0873585 | + | 0.151309i | 0.906394 | − | 0.422434i | \(-0.138824\pi\) |
−0.819035 | + | 0.573743i | \(0.805491\pi\) | |||||||
\(674\) | −34.7492 | − | 20.0624i | −1.33849 | − | 0.772776i | ||||
\(675\) | 13.1231 | + | 22.7299i | 0.505109 | + | 0.874875i | ||||
\(676\) | 0.626040 | + | 1.08433i | 0.0240784 | + | 0.0417051i | ||||
\(677\) | − | 8.35832i | − | 0.321236i | −0.987017 | − | 0.160618i | \(-0.948651\pi\) | ||
0.987017 | − | 0.160618i | \(-0.0513488\pi\) | |||||||
\(678\) | 20.2670 | + | 35.1035i | 0.778349 | + | 1.34814i | ||||
\(679\) | −1.43724 | + | 2.48937i | −0.0551563 | + | 0.0955334i | ||||
\(680\) | 10.0041 | + | 5.77590i | 0.383642 | + | 0.221496i | ||||
\(681\) | 70.2447 | 2.69178 | ||||||||
\(682\) | 24.1275 | + | 41.7901i | 0.923890 | + | 1.60022i | ||||
\(683\) | 19.3498 | + | 33.5149i | 0.740400 | + | 1.28241i | 0.952313 | + | 0.305122i | \(0.0986973\pi\) |
−0.211913 | + | 0.977289i | \(0.567969\pi\) | |||||||
\(684\) | 55.7845 | − | 96.6216i | 2.13297 | − | 3.69442i | ||||
\(685\) | 0.0854915 | − | 0.0493585i | 0.00326646 | − | 0.00188589i | ||||
\(686\) | −8.98228 | − | 15.5578i | −0.342945 | − | 0.593998i | ||||
\(687\) | − | 26.7938i | − | 1.02225i | ||||||
\(688\) | − | 70.5051i | − | 2.68798i | ||||||
\(689\) | 6.77932 | + | 11.7421i | 0.258271 | + | 0.447339i | ||||
\(690\) | 5.34567i | 0.203506i | ||||||||
\(691\) | −7.88117 | + | 4.55020i | −0.299814 | + | 0.173098i | −0.642359 | − | 0.766404i | \(-0.722044\pi\) |
0.342545 | + | 0.939501i | \(0.388711\pi\) | |||||||
\(692\) | − | 79.7624i | − | 3.03211i | ||||||
\(693\) | 54.3126 | − | 94.0721i | 2.06316 | − | 3.57350i | ||||
\(694\) | −17.3285 | + | 30.0138i | −0.657779 | + | 1.13931i | ||||
\(695\) | 0.952066 | − | 1.64903i | 0.0361139 | − | 0.0625511i | ||||
\(696\) | −123.240 | + | 71.1525i | −4.67139 | + | 2.69703i | ||||
\(697\) | −31.4266 | −1.19037 | ||||||||
\(698\) | 18.3523 | − | 45.7003i | 0.694644 | − | 1.72978i | ||||
\(699\) | 45.9318 | 1.73730 | ||||||||
\(700\) | 73.6462 | − | 42.5197i | 2.78357 | − | 1.60709i | ||||
\(701\) | 11.2972 | − | 19.5673i | 0.426690 | − | 0.739049i | −0.569887 | − | 0.821723i | \(-0.693013\pi\) |
0.996577 | + | 0.0826747i | \(0.0263462\pi\) | |||||||
\(702\) | −24.9389 | + | 43.1954i | −0.941258 | + | 1.63031i | ||||
\(703\) | −1.77859 | + | 3.08061i | −0.0670809 | + | 0.116188i | ||||
\(704\) | − | 73.4101i | − | 2.76675i | ||||||
\(705\) | −1.35402 | + | 0.781742i | −0.0509952 | + | 0.0294421i | ||||
\(706\) | 0.677698i | 0.0255055i | ||||||||
\(707\) | −9.48309 | − | 16.4252i | −0.356648 | − | 0.617733i | ||||
\(708\) | − | 125.027i | − | 4.69879i | ||||||
\(709\) | 5.29684i | 0.198927i | 0.995041 | + | 0.0994634i | \(0.0317126\pi\) | ||||
−0.995041 | + | 0.0994634i | \(0.968287\pi\) | |||||||
\(710\) | −2.01743 | − | 3.49429i | −0.0757128 | − | 0.131138i | ||||
\(711\) | −14.2548 | + | 8.23003i | −0.534598 | + | 0.308650i | ||||
\(712\) | 9.71868 | − | 16.8332i | 0.364223 | − | 0.630853i | ||||
\(713\) | 4.73946 | + | 8.20899i | 0.177494 | + | 0.307429i | ||||
\(714\) | −87.6701 | − | 151.849i | −3.28097 | − | 5.68281i | ||||
\(715\) | 4.97839 | 0.186181 | ||||||||
\(716\) | 85.4439 | + | 49.3311i | 3.19319 | + | 1.84359i | ||||
\(717\) | −33.2793 | + | 57.6415i | −1.24284 | + | 2.15266i | ||||
\(718\) | −37.6793 | − | 65.2625i | −1.40618 | − | 2.43557i | ||||
\(719\) | − | 15.8281i | − | 0.590288i | −0.955453 | − | 0.295144i | \(-0.904632\pi\) | ||
0.955453 | − | 0.295144i | \(-0.0953677\pi\) | |||||||
\(720\) | 5.63565 | + | 9.76124i | 0.210028 | + | 0.363780i | ||||
\(721\) | 5.61089 | + | 9.71834i | 0.208960 | + | 0.361930i | ||||
\(722\) | 5.19769 | + | 3.00089i | 0.193438 | + | 0.111682i | ||||
\(723\) | −6.53352 | − | 11.3164i | −0.242984 | − | 0.420861i | ||||
\(724\) | 34.3065 | − | 59.4206i | 1.27499 | − | 2.20835i | ||||
\(725\) | 32.2776 | 1.19876 | ||||||||
\(726\) | 222.463i | 8.25639i | ||||||||
\(727\) | 18.1106 | − | 31.3684i | 0.671683 | − | 1.16339i | −0.305743 | − | 0.952114i | \(-0.598905\pi\) |
0.977426 | − | 0.211276i | \(-0.0677618\pi\) | |||||||
\(728\) | 83.4005 | + | 48.1513i | 3.09103 | + | 1.78461i | ||||
\(729\) | −43.5645 | −1.61350 | ||||||||
\(730\) | −0.241686 | − | 0.139538i | −0.00894521 | − | 0.00516452i | ||||
\(731\) | 39.3343 | + | 22.7097i | 1.45483 | + | 0.839948i | ||||
\(732\) | −91.5330 | + | 52.8466i | −3.38316 | + | 1.95327i | ||||
\(733\) | − | 8.81140i | − | 0.325457i | −0.986671 | − | 0.162728i | \(-0.947971\pi\) | ||
0.986671 | − | 0.162728i | \(-0.0520294\pi\) | |||||||
\(734\) | −13.8542 | −0.511366 | ||||||||
\(735\) | 3.07786 | 0.113529 | ||||||||
\(736\) | − | 41.0947i | − | 1.51477i | ||||||
\(737\) | − | 16.4586i | − | 0.606261i | ||||||
\(738\) | −51.3600 | − | 29.6527i | −1.89059 | − | 1.09153i | ||||
\(739\) | −35.3073 | −1.29880 | −0.649399 | − | 0.760447i | \(-0.724980\pi\) | ||||
−0.649399 | + | 0.760447i | \(0.724980\pi\) | |||||||
\(740\) | −0.415342 | − | 0.719393i | −0.0152683 | − | 0.0264454i | ||||
\(741\) | −40.0538 | − | 23.1251i | −1.47141 | − | 0.849520i | ||||
\(742\) | −30.0781 | − | 17.3656i | −1.10420 | − | 0.637510i | ||||
\(743\) | −25.5098 | −0.935864 | −0.467932 | − | 0.883764i | \(-0.655001\pi\) | ||||
−0.467932 | + | 0.883764i | \(0.655001\pi\) | |||||||
\(744\) | 54.0261 | + | 31.1920i | 1.98069 | + | 1.14355i | ||||
\(745\) | 2.90633i | 0.106480i | ||||||||
\(746\) | −50.2853 | −1.84108 | ||||||||
\(747\) | 33.7473 | − | 58.4520i | 1.23475 | − | 2.13865i | ||||
\(748\) | 187.477 | + | 108.240i | 6.85484 | + | 3.95764i | ||||
\(749\) | 7.18700 | − | 12.4482i | 0.262607 | − | 0.454849i | ||||
\(750\) | − | 16.0361i | − | 0.585557i | ||||||
\(751\) | 46.2312i | 1.68700i | 0.537129 | + | 0.843500i | \(0.319509\pi\) | ||||
−0.537129 | + | 0.843500i | \(0.680491\pi\) | |||||||
\(752\) | 23.4764 | − | 13.5541i | 0.856096 | − | 0.494267i | ||||
\(753\) | 37.7551 | + | 21.7979i | 1.37587 | + | 0.794361i | ||||
\(754\) | 30.6699 | + | 53.1218i | 1.11693 | + | 1.93458i | ||||
\(755\) | −1.68522 | − | 2.91889i | −0.0613314 | − | 0.106229i | ||||
\(756\) | − | 90.9944i | − | 3.30943i | ||||||
\(757\) | 41.1906 | + | 23.7814i | 1.49710 | + | 0.864350i | 0.999994 | − | 0.00334193i | \(-0.00106377\pi\) |
0.497103 | + | 0.867692i | \(0.334397\pi\) | |||||||
\(758\) | −19.6393 | −0.713332 | ||||||||
\(759\) | 59.6964i | 2.16684i | ||||||||
\(760\) | −6.75950 | + | 3.90260i | −0.245193 | + | 0.141562i | ||||
\(761\) | −34.2252 | − | 19.7599i | −1.24066 | − | 0.716296i | −0.271432 | − | 0.962458i | \(-0.587497\pi\) |
−0.969229 | + | 0.246161i | \(0.920831\pi\) | |||||||
\(762\) | 58.5138 | 2.11973 | ||||||||
\(763\) | − | 2.09694i | − | 0.0759145i | ||||||
\(764\) | −13.5113 | −0.488822 | ||||||||
\(765\) | −7.26097 | −0.262521 | ||||||||
\(766\) | −15.7546 | + | 27.2877i | −0.569236 | + | 0.985946i | ||||
\(767\) | −32.1146 | −1.15959 | ||||||||
\(768\) | 12.0706 | + | 20.9069i | 0.435560 | + | 0.754412i | ||||
\(769\) | −5.69581 | + | 3.28848i | −0.205396 | + | 0.118586i | −0.599170 | − | 0.800622i | \(-0.704503\pi\) |
0.393774 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(770\) | −11.0439 | + | 6.37621i | −0.397995 | + | 0.229783i | ||||
\(771\) | −30.8557 | + | 53.4436i | −1.11124 | + | 1.92473i | ||||
\(772\) | −102.768 | + | 59.3330i | −3.69869 | + | 2.13544i | ||||
\(773\) | −48.4808 | −1.74373 | −0.871866 | − | 0.489744i | \(-0.837090\pi\) | ||||
−0.871866 | + | 0.489744i | \(0.837090\pi\) | |||||||
\(774\) | 42.8557 | + | 74.2282i | 1.54042 | + | 2.66808i | ||||
\(775\) | −7.07498 | − | 12.2542i | −0.254141 | − | 0.440185i | ||||
\(776\) | −3.22101 | − | 5.57895i | −0.115628 | − | 0.200273i | ||||
\(777\) | 7.51357i | 0.269548i | ||||||||
\(778\) | −7.01424 | −0.251473 | ||||||||
\(779\) | 10.6170 | − | 18.3892i | 0.380393 | − | 0.658860i | ||||
\(780\) | 9.35347 | − | 5.40023i | 0.334908 | − | 0.193359i | ||||
\(781\) | −22.5291 | − | 39.0216i | −0.806155 | − | 1.39630i | ||||
\(782\) | 51.7084 | + | 29.8538i | 1.84909 | + | 1.06757i | ||||
\(783\) | 17.2690 | − | 29.9107i | 0.617143 | − | 1.06892i | ||||
\(784\) | −53.3650 | −1.90589 | ||||||||
\(785\) | −1.36801 | − | 2.36945i | −0.0488262 | − | 0.0845695i | ||||
\(786\) | 68.2186 | 2.43328 | ||||||||
\(787\) | −0.203032 | − | 0.117221i | −0.00723732 | − | 0.00417847i | 0.496377 | − | 0.868107i | \(-0.334663\pi\) |
−0.503614 | + | 0.863929i | \(0.667997\pi\) | |||||||
\(788\) | 92.5087 | − | 53.4099i | 3.29549 | − | 1.90265i | ||||
\(789\) | 26.1544 | − | 45.3007i | 0.931121 | − | 1.61275i | ||||
\(790\) | 1.93239 | 0.0687512 | ||||||||
\(791\) | −9.49722 | + | 16.4497i | −0.337682 | + | 0.584883i | ||||
\(792\) | 121.720 | + | 210.826i | 4.32514 | + | 7.49136i | ||||
\(793\) | 13.5743 | + | 23.5114i | 0.482037 | + | 0.834913i | ||||
\(794\) | 7.81790 | − | 4.51367i | 0.277447 | − | 0.160184i | ||||
\(795\) | −2.01017 | + | 1.16057i | −0.0712932 | + | 0.0411612i | ||||
\(796\) | − | 104.275i | − | 3.69593i | ||||||
\(797\) | 11.8344 | − | 6.83262i | 0.419198 | − | 0.242024i | −0.275536 | − | 0.961291i | \(-0.588855\pi\) |
0.694734 | + | 0.719267i | \(0.255522\pi\) | |||||||
\(798\) | 118.472 | 4.19387 | ||||||||
\(799\) | 17.4631i | 0.617800i | ||||||||
\(800\) | 61.3454i | 2.16889i | ||||||||
\(801\) | 12.2175i | 0.431684i | ||||||||
\(802\) | −9.89972 | − | 17.1468i | −0.349571 | − | 0.605475i | ||||
\(803\) | −2.69897 | − | 1.55825i | −0.0952445 | − | 0.0549894i | ||||
\(804\) | −17.8532 | − | 30.9227i | −0.629634 | − | 1.09056i | ||||
\(805\) | −2.16940 | + | 1.25251i | −0.0764614 | + | 0.0441450i | ||||
\(806\) | 13.4451 | − | 23.2877i | 0.473585 | − | 0.820273i | ||||
\(807\) | 16.9156 | − | 29.2987i | 0.595457 | − | 1.03136i | ||||
\(808\) | 42.5052 | 1.49533 | ||||||||
\(809\) | −4.87234 | + | 8.43915i | −0.171302 | + | 0.296705i | −0.938875 | − | 0.344257i | \(-0.888131\pi\) |
0.767573 | + | 0.640962i | \(0.221464\pi\) | |||||||
\(810\) | −0.110229 | − | 0.0636406i | −0.00387304 | − | 0.00223610i | ||||
\(811\) | −24.6705 | + | 14.2435i | −0.866299 | + | 0.500158i | −0.866117 | − | 0.499842i | \(-0.833391\pi\) |
−0.000182448 | 1.00000i | \(0.500058\pi\) | ||||||||
\(812\) | −96.9125 | − | 55.9525i | −3.40096 | − | 1.96355i | ||||
\(813\) | 38.9966 | 1.36767 | ||||||||
\(814\) | −6.51250 | − | 11.2800i | −0.228263 | − | 0.395363i | ||||
\(815\) | −1.48047 | − | 0.854748i | −0.0518585 | − | 0.0299405i | ||||
\(816\) | 203.176 | 7.11257 | ||||||||
\(817\) | −26.5770 | + | 15.3442i | −0.929812 | + | 0.536827i | ||||
\(818\) | 31.6358 | − | 18.2649i | 1.10612 | − | 0.638618i | ||||
\(819\) | −60.5318 | −2.11515 | ||||||||
\(820\) | 2.47931 | + | 4.29429i | 0.0865812 | + | 0.149963i | ||||
\(821\) | −18.4983 | + | 32.0399i | −0.645594 | + | 1.11820i | 0.338570 | + | 0.940941i | \(0.390057\pi\) |
−0.984164 | + | 0.177260i | \(0.943277\pi\) | |||||||
\(822\) | 1.67902 | − | 2.90815i | 0.0585627 | − | 0.101434i | ||||
\(823\) | −1.61445 | −0.0562762 | −0.0281381 | − | 0.999604i | \(-0.508958\pi\) | ||||
−0.0281381 | + | 0.999604i | \(0.508958\pi\) | |||||||
\(824\) | −25.1492 | −0.876114 | ||||||||
\(825\) | − | 89.1136i | − | 3.10254i | ||||||
\(826\) | 71.2421 | − | 41.1316i | 2.47883 | − | 1.43115i | ||||
\(827\) | 26.7130 | − | 15.4227i | 0.928900 | − | 0.536301i | 0.0424368 | − | 0.999099i | \(-0.486488\pi\) |
0.886464 | + | 0.462798i | \(0.153155\pi\) | |||||||
\(828\) | 40.1238 | + | 69.4964i | 1.39440 | + | 2.41517i | ||||
\(829\) | − | 18.9155i | − | 0.656963i | −0.944510 | − | 0.328482i | \(-0.893463\pi\) | ||
0.944510 | − | 0.328482i | \(-0.106537\pi\) | |||||||
\(830\) | −6.86217 | + | 3.96188i | −0.238189 | + | 0.137519i | ||||
\(831\) | − | 5.34789i | − | 0.185516i | ||||||
\(832\) | −35.4274 | + | 20.4540i | −1.22822 | + | 0.709116i | ||||
\(833\) | 17.1889 | − | 29.7720i | 0.595559 | − | 1.03154i | ||||
\(834\) | − | 64.7726i | − | 2.24289i | ||||||
\(835\) | −2.82004 | − | 1.62815i | −0.0975915 | − | 0.0563445i | ||||
\(836\) | −126.672 | + | 73.1344i | −4.38106 | + | 2.52941i | ||||
\(837\) | −15.1408 | −0.523344 | ||||||||
\(838\) | 48.7845 | + | 28.1657i | 1.68523 | + | 0.972969i | ||||
\(839\) | 7.79025 | + | 4.49770i | 0.268949 | + | 0.155278i | 0.628410 | − | 0.777882i | \(-0.283706\pi\) |
−0.359461 | + | 0.933160i | \(0.617039\pi\) | |||||||
\(840\) | −8.24316 | + | 14.2776i | −0.284416 | + | 0.492623i | ||||
\(841\) | −6.73739 | − | 11.6695i | −0.232324 | − | 0.402397i | ||||
\(842\) | 35.7293 | − | 61.8849i | 1.23131 | − | 2.13270i | ||||
\(843\) | 13.1456 | + | 22.7688i | 0.452757 | + | 0.784198i | ||||
\(844\) | − | 25.3397i | − | 0.872228i | ||||||
\(845\) | 0.0275288 | + | 0.0476813i | 0.000947020 | + | 0.00164029i | ||||
\(846\) | −16.4774 | + | 28.5397i | −0.566505 | + | 0.981216i | ||||
\(847\) | −90.2810 | + | 52.1238i | −3.10209 | + | 1.79099i | ||||
\(848\) | 34.8529 | − | 20.1224i | 1.19685 | − | 0.691004i | ||||
\(849\) | 13.0910 | − | 22.6743i | 0.449282 | − | 0.778180i | ||||
\(850\) | −77.1892 | − | 44.5652i | −2.64757 | − | 1.52857i | ||||
\(851\) | −1.27928 | − | 2.21577i | −0.0438530 | − | 0.0759557i | ||||
\(852\) | −84.6560 | − | 48.8762i | −2.90027 | − | 1.67447i | ||||
\(853\) | 11.9832 | − | 20.7556i | 0.410298 | − | 0.710657i | −0.584624 | − | 0.811304i | \(-0.698758\pi\) |
0.994922 | + | 0.100647i | \(0.0320914\pi\) | |||||||
\(854\) | −60.2256 | − | 34.7713i | −2.06088 | − | 1.18985i | ||||
\(855\) | 2.45301 | − | 4.24874i | 0.0838912 | − | 0.145304i | ||||
\(856\) | 16.1068 | + | 27.8978i | 0.550520 | + | 0.953529i | ||||
\(857\) | 48.6824 | + | 28.1068i | 1.66296 | + | 0.960110i | 0.971291 | + | 0.237894i | \(0.0764570\pi\) |
0.691668 | + | 0.722216i | \(0.256876\pi\) | |||||||
\(858\) | 146.661 | − | 84.6748i | 5.00692 | − | 2.89075i | ||||
\(859\) | −40.3154 | − | 23.2761i | −1.37554 | − | 0.794170i | −0.383923 | − | 0.923365i | \(-0.625427\pi\) |
−0.991619 | + | 0.129195i | \(0.958761\pi\) | |||||||
\(860\) | − | 7.16646i | − | 0.244374i | ||||||
\(861\) | − | 44.8509i | − | 1.52851i | ||||||
\(862\) | 5.65097 | − | 9.78777i | 0.192473 | − | 0.333373i | ||||
\(863\) | −18.6797 | + | 10.7847i | −0.635865 | + | 0.367117i | −0.783020 | − | 0.621997i | \(-0.786322\pi\) |
0.147155 | + | 0.989113i | \(0.452988\pi\) | |||||||
\(864\) | 56.8469 | + | 32.8206i | 1.93397 | + | 1.11658i | ||||
\(865\) | − | 3.50739i | − | 0.119255i | ||||||
\(866\) | 34.7835 | 1.18199 | ||||||||
\(867\) | −41.5716 | + | 72.0041i | −1.41184 | + | 2.44539i | ||||
\(868\) | 49.0572i | 1.66511i | ||||||||
\(869\) | 21.5794 | 0.732031 | ||||||||
\(870\) | −9.09406 | + | 5.25046i | −0.308318 | + | 0.178007i | ||||
\(871\) | −7.94286 | + | 4.58581i | −0.269134 | + | 0.155384i | ||||
\(872\) | 4.06986 | + | 2.34974i | 0.137823 | + | 0.0795721i | ||||
\(873\) | 3.50670 | + | 2.02459i | 0.118684 | + | 0.0685221i | ||||
\(874\) | −34.9378 | + | 20.1713i | −1.18179 | + | 0.682306i | ||||
\(875\) | 6.50785 | − | 3.75731i | 0.220006 | − | 0.127020i | ||||
\(876\) | −6.76114 | −0.228438 | ||||||||
\(877\) | − | 7.18743i | − | 0.242702i | −0.992610 | − | 0.121351i | \(-0.961277\pi\) | ||
0.992610 | − | 0.121351i | \(-0.0387227\pi\) | |||||||
\(878\) | 48.0704 | − | 83.2604i | 1.62230 | − | 2.80990i | ||||
\(879\) | 47.6243 | 1.60633 | ||||||||
\(880\) | − | 14.7769i | − | 0.498128i | ||||||
\(881\) | 34.3744 | + | 19.8461i | 1.15810 | + | 0.668630i | 0.950848 | − | 0.309657i | \(-0.100214\pi\) |
0.207253 | + | 0.978287i | \(0.433548\pi\) | |||||||
\(882\) | 56.1831 | − | 32.4373i | 1.89178 | − | 1.09222i | ||||
\(883\) | −28.3360 | + | 49.0795i | −0.953584 | + | 1.65166i | −0.216008 | + | 0.976392i | \(0.569304\pi\) |
−0.737576 | + | 0.675264i | \(0.764030\pi\) | |||||||
\(884\) | − | 120.634i | − | 4.05736i | ||||||
\(885\) | − | 5.49779i | − | 0.184806i | ||||||
\(886\) | −28.5611 | − | 16.4897i | −0.959528 | − | 0.553984i | ||||
\(887\) | 42.1909 | − | 24.3589i | 1.41663 | − | 0.817893i | 0.420631 | − | 0.907232i | \(-0.361809\pi\) |
0.996001 | + | 0.0893393i | \(0.0284755\pi\) | |||||||
\(888\) | −14.5827 | − | 8.41935i | −0.489365 | − | 0.282535i | ||||
\(889\) | 13.7099 | + | 23.7463i | 0.459817 | + | 0.796426i | ||||
\(890\) | 0.717158 | − | 1.24215i | 0.0240392 | − | 0.0416371i | ||||
\(891\) | −1.23095 | − | 0.710690i | −0.0412384 | − | 0.0238090i | ||||
\(892\) | 63.2265 | − | 109.512i | 2.11698 | − | 3.66672i | ||||
\(893\) | −10.2185 | − | 5.89964i | −0.341949 | − | 0.197424i | ||||
\(894\) | 49.4322 | + | 85.6191i | 1.65326 | + | 2.86353i | ||||
\(895\) | 3.75722 | + | 2.16923i | 0.125590 | + | 0.0725094i | ||||
\(896\) | 9.42249 | − | 16.3202i | 0.314783 | − | 0.545221i | ||||
\(897\) | 28.8092 | − | 16.6330i | 0.961912 | − | 0.555360i | ||||
\(898\) | −44.4397 | + | 25.6573i | −1.48297 | + | 0.856194i | ||||
\(899\) | −9.31010 | + | 16.1256i | −0.310509 | + | 0.537818i | ||||
\(900\) | −59.8960 | − | 103.743i | −1.99653 | − | 3.45810i | ||||
\(901\) | 25.9256i | 0.863708i | ||||||||
\(902\) | 38.8752 | + | 67.3338i | 1.29440 | + | 2.24197i | ||||
\(903\) | −32.4104 | + | 56.1365i | −1.07855 | + | 1.86811i | ||||
\(904\) | −21.2843 | − | 36.8655i | −0.707905 | − | 1.22613i | ||||
\(905\) | 1.50856 | − | 2.61290i | 0.0501461 | − | 0.0868556i | ||||
\(906\) | −99.2914 | − | 57.3259i | −3.29874 | − | 1.90453i | ||||
\(907\) | 16.4803 | + | 9.51492i | 0.547220 | + | 0.315938i | 0.748000 | − | 0.663699i | \(-0.231014\pi\) |
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(908\) | −123.796 | −4.10830 | ||||||||
\(909\) | −23.1376 | + | 13.3585i | −0.767426 | + | 0.443073i | ||||
\(910\) | 6.15426 | + | 3.55317i | 0.204012 | + | 0.117786i | ||||
\(911\) | − | 32.6074i | − | 1.08033i | −0.841558 | − | 0.540166i | \(-0.818361\pi\) | ||
0.841558 | − | 0.540166i | \(-0.181639\pi\) | |||||||
\(912\) | −68.6398 | + | 118.888i | −2.27289 | + | 3.93676i | ||||
\(913\) | −76.6315 | + | 44.2432i | −2.53613 | + | 1.46424i | ||||
\(914\) | 79.7771i | 2.63879i | ||||||||
\(915\) | −4.02498 | + | 2.32382i | −0.133062 | + | 0.0768231i | ||||
\(916\) | 47.2200i | 1.56019i | ||||||||
\(917\) | 15.9838 | + | 27.6848i | 0.527832 | + | 0.914231i | ||||
\(918\) | −82.5946 | + | 47.6860i | −2.72603 | + | 1.57387i | ||||
\(919\) | −11.1771 | + | 6.45309i | −0.368698 | + | 0.212868i | −0.672889 | − | 0.739743i | \(-0.734947\pi\) |
0.304191 | + | 0.952611i | \(0.401614\pi\) | |||||||
\(920\) | − | 5.61399i | − | 0.185088i | ||||||
\(921\) | −1.17967 | −0.0388714 | ||||||||
\(922\) | −2.52332 | −0.0831011 | ||||||||
\(923\) | −12.5544 | + | 21.7449i | −0.413234 | + | 0.715743i | ||||
\(924\) | −154.476 | + | 267.560i | −5.08189 | + | 8.80209i | ||||
\(925\) | 1.90968 | + | 3.30766i | 0.0627899 | + | 0.108755i | ||||
\(926\) | 93.0477 | 3.05774 | ||||||||
\(927\) | 13.6899 | − | 7.90386i | 0.449635 | − | 0.259597i | ||||
\(928\) | 69.9104 | − | 40.3628i | 2.29492 | − | 1.32497i | ||||
\(929\) | 3.19382 | 0.104786 | 0.0523929 | − | 0.998627i | \(-0.483315\pi\) | ||||
0.0523929 | + | 0.998627i | \(0.483315\pi\) | |||||||
\(930\) | 3.98668 | + | 2.30171i | 0.130728 | + | 0.0754761i | ||||
\(931\) | 11.6140 | + | 20.1160i | 0.380633 | + | 0.659276i | ||||
\(932\) | −80.9478 | −2.65153 | ||||||||
\(933\) | 79.1919 | + | 45.7215i | 2.59263 | + | 1.49685i | ||||
\(934\) | 65.7970 | − | 37.9879i | 2.15294 | − | 1.24300i | ||||
\(935\) | 8.24391 | + | 4.75963i | 0.269605 | + | 0.155656i | ||||
\(936\) | 67.8291 | − | 117.483i | 2.21706 | − | 3.84006i | ||||
\(937\) | 3.15113 | 0.102943 | 0.0514715 | − | 0.998674i | \(-0.483609\pi\) | ||||
0.0514715 | + | 0.998674i | \(0.483609\pi\) | |||||||
\(938\) | 11.7468 | − | 20.3461i | 0.383547 | − | 0.664323i | ||||
\(939\) | 1.34433 | − | 2.32845i | 0.0438707 | − | 0.0759863i | ||||
\(940\) | 2.38625 | − | 1.37770i | 0.0778309 | − | 0.0449357i | ||||
\(941\) | −9.20714 | − | 15.9472i | −0.300144 | − | 0.519865i | 0.676024 | − | 0.736879i | \(-0.263701\pi\) |
−0.976168 | + | 0.217014i | \(0.930368\pi\) | |||||||
\(942\) | −80.6015 | − | 46.5353i | −2.62614 | − | 1.51620i | ||||
\(943\) | 7.63641 | + | 13.2267i | 0.248676 | + | 0.430719i | ||||
\(944\) | 95.3226i | 3.10249i | ||||||||
\(945\) | − | 4.00129i | − | 0.130162i | ||||||
\(946\) | − | 112.369i | − | 3.65343i | ||||||
\(947\) | −3.98310 | −0.129433 | −0.0647166 | − | 0.997904i | \(-0.520614\pi\) | ||||
−0.0647166 | + | 0.997904i | \(0.520614\pi\) | |||||||
\(948\) | 40.5437 | − | 23.4079i | 1.31680 | − | 0.760253i | ||||
\(949\) | 1.73668i | 0.0563751i | ||||||||
\(950\) | 52.1544 | − | 30.1114i | 1.69211 | − | 0.976942i | ||||
\(951\) | 9.42307 | − | 5.44041i | 0.305564 | − | 0.176417i | ||||
\(952\) | 92.0707 | + | 159.471i | 2.98403 | + | 5.16849i | ||||
\(953\) | −5.76690 | − | 9.98856i | −0.186808 | − | 0.323561i | 0.757376 | − | 0.652979i | \(-0.226481\pi\) |
−0.944184 | + | 0.329418i | \(0.893148\pi\) | |||||||
\(954\) | −24.4623 | + | 42.3699i | −0.791996 | + | 1.37178i | ||||
\(955\) | −0.594132 | −0.0192257 | ||||||||
\(956\) | 58.6498 | − | 101.584i | 1.89687 | − | 3.28547i | ||||
\(957\) | −101.556 | + | 58.6331i | −3.28283 | + | 1.89534i | ||||
\(958\) | 30.7744 | + | 17.7676i | 0.994276 | + | 0.574045i | ||||
\(959\) | 1.57360 | 0.0508142 | ||||||||
\(960\) | −3.50158 | − | 6.06492i | −0.113013 | − | 0.195744i | ||||
\(961\) | −22.8372 | −0.736685 | ||||||||
\(962\) | −3.62911 | + | 6.28581i | −0.117007 | + | 0.202663i | ||||
\(963\) | −17.5354 | − | 10.1241i | −0.565071 | − | 0.326244i | ||||
\(964\) | 11.5143 | + | 19.9434i | 0.370852 | + | 0.642334i | ||||
\(965\) | −4.51900 | + | 2.60904i | −0.145472 | + | 0.0839881i | ||||
\(966\) | −42.6063 | + | 73.7963i | −1.37084 | + | 2.37436i | ||||
\(967\) | 36.0912 | 1.16061 | 0.580307 | − | 0.814398i | \(-0.302933\pi\) | ||||
0.580307 | + | 0.814398i | \(0.302933\pi\) | |||||||
\(968\) | − | 233.630i | − | 7.50915i | ||||||
\(969\) | −44.2177 | − | 76.5873i | −1.42048 | − | 2.46034i | ||||
\(970\) | −0.237684 | − | 0.411681i | −0.00763157 | − | 0.0132183i | ||||
\(971\) | −15.6128 | − | 27.0421i | −0.501038 | − | 0.867824i | −0.999999 | − | 0.00119933i | \(-0.999618\pi\) |
0.498961 | − | 0.866624i | \(-0.333715\pi\) | |||||||
\(972\) | 75.6028 | 2.42496 | ||||||||
\(973\) | 26.2863 | − | 15.1764i | 0.842700 | − | 0.486533i | ||||
\(974\) | −24.9963 | + | 43.2948i | −0.800932 | + | 1.38726i | ||||
\(975\) | −43.0058 | + | 24.8294i | −1.37729 | + | 0.795178i | ||||
\(976\) | 69.7864 | − | 40.2912i | 2.23381 | − | 1.28969i | ||||
\(977\) | 8.79013 | + | 15.2249i | 0.281221 | + | 0.487089i | 0.971686 | − | 0.236277i | \(-0.0759272\pi\) |
−0.690465 | + | 0.723366i | \(0.742594\pi\) | |||||||
\(978\) | −58.1517 | −1.85949 | ||||||||
\(979\) | 8.00867 | − | 13.8714i | 0.255958 | − | 0.443333i | ||||
\(980\) | −5.42427 | −0.173272 | ||||||||
\(981\) | −2.95389 | −0.0943105 | ||||||||
\(982\) | − | 71.5004i | − | 2.28167i | ||||||
\(983\) | −22.6095 | −0.721131 | −0.360565 | − | 0.932734i | \(-0.617416\pi\) | ||||
−0.360565 | + | 0.932734i | \(0.617416\pi\) | |||||||
\(984\) | 87.0491 | + | 50.2578i | 2.77502 | + | 1.60216i | ||||
\(985\) | 4.06788 | − | 2.34859i | 0.129613 | − | 0.0748324i | ||||
\(986\) | 117.289i | 3.73523i | ||||||||
\(987\) | −24.9227 | −0.793299 | ||||||||
\(988\) | 70.5887 | + | 40.7544i | 2.24573 | + | 1.29657i | ||||
\(989\) | − | 22.0731i | − | 0.701884i | ||||||
\(990\) | 8.98194 | + | 15.5572i | 0.285465 | + | 0.494440i | ||||
\(991\) | 27.4050 | + | 47.4668i | 0.870548 | + | 1.50783i | 0.861431 | + | 0.507875i | \(0.169569\pi\) |
0.00911717 | + | 0.999958i | \(0.497098\pi\) | |||||||
\(992\) | −30.6475 | − | 17.6943i | −0.973059 | − | 0.561796i | ||||
\(993\) | 48.2998 | − | 27.8859i | 1.53275 | − | 0.884933i | ||||
\(994\) | − | 64.3177i | − | 2.04003i | ||||||
\(995\) | − | 4.58528i | − | 0.145363i | ||||||
\(996\) | −95.9841 | + | 166.249i | −3.04137 | + | 5.26781i | ||||
\(997\) | −23.9347 | − | 13.8187i | −0.758018 | − | 0.437642i | 0.0705657 | − | 0.997507i | \(-0.477520\pi\) |
−0.828584 | + | 0.559865i | \(0.810853\pi\) | |||||||
\(998\) | −43.0489 | + | 74.5629i | −1.36269 | + | 2.36025i | ||||
\(999\) | 4.08682 | 0.129301 |
(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 | 349.2.e.a.123.2 | ✓ | 58 | |
349.227 | even | 6 | inner | 349.2.e.a.227.2 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.e.a.123.2 | ✓ | 58 | 1.1 | even | 1 | trivial | |
349.2.e.a.227.2 | yes | 58 | 349.227 | even | 6 | inner |