Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.991381711347.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(-0.335166 + 0.580525i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.i.961.4 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.377302 | + | 1.69046i | 0.217836 | + | 0.975985i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.42494 | 0.637251 | 0.318626 | − | 0.947881i | \(-0.396779\pi\) | ||||
0.318626 | + | 0.947881i | \(0.396779\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21529 | + | 1.44655i | −0.837299 | + | 0.546745i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71529 | + | 1.27563i | −0.905095 | + | 0.425209i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.93077 | 1.48668 | 0.743342 | − | 0.668911i | \(-0.233239\pi\) | ||||
0.743342 | + | 0.668911i | \(0.233239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37730 | + | 2.38556i | −0.381995 | + | 0.661635i | −0.991347 | − | 0.131265i | \(-0.958096\pi\) |
0.609352 | + | 0.792900i | \(0.291429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.537632 | + | 2.40879i | 0.138816 | + | 0.621948i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.559839 | − | 0.969670i | 0.135781 | − | 0.235180i | −0.790115 | − | 0.612959i | \(-0.789979\pi\) |
0.925896 | + | 0.377780i | \(0.123312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00752 | + | 3.47713i | 0.460557 | + | 0.797709i | 0.998989 | − | 0.0449606i | \(-0.0143162\pi\) |
−0.538431 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.28116 | − | 3.19906i | −0.716009 | − | 0.698092i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.43661 | −1.13361 | −0.566806 | − | 0.823851i | \(-0.691821\pi\) | ||||
−0.566806 | + | 0.823851i | \(0.691821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96955 | −0.593911 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.18087 | − | 4.10878i | −0.612160 | − | 0.790734i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.40555 | + | 5.89858i | 0.632394 | + | 1.09534i | 0.987061 | + | 0.160346i | \(0.0512611\pi\) |
−0.354667 | + | 0.934993i | \(0.615406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25292 | + | 2.17012i | 0.225031 | + | 0.389765i | 0.956329 | − | 0.292294i | \(-0.0944184\pi\) |
−0.731298 | + | 0.682058i | \(0.761085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.86039 | + | 8.33526i | 0.323853 | + | 1.45098i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.15664 | + | 2.06124i | −0.533570 | + | 0.348414i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.709787 | + | 1.22939i | 0.116688 | + | 0.202110i | 0.918453 | − | 0.395529i | \(-0.129439\pi\) |
−0.801765 | + | 0.597639i | \(0.796106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.55234 | − | 1.42819i | −0.728958 | − | 0.228694i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.124384 | − | 0.215440i | 0.0194256 | − | 0.0336460i | −0.856149 | − | 0.516729i | \(-0.827150\pi\) |
0.875575 | + | 0.483083i | \(0.160483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.498313 | + | 0.863104i | 0.0759921 | + | 0.131622i | 0.901517 | − | 0.432743i | \(-0.142454\pi\) |
−0.825525 | + | 0.564365i | \(0.809121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.86911 | + | 1.81769i | −0.576773 | + | 0.270965i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.73790 | + | 8.20628i | −0.691093 | + | 1.19701i | 0.280387 | + | 0.959887i | \(0.409537\pi\) |
−0.971480 | + | 0.237122i | \(0.923796\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.81498 | − | 6.40905i | 0.402140 | − | 0.915578i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85041 | + | 0.580525i | 0.259110 | + | 0.0812898i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.410229 | + | 0.710537i | −0.0563493 | + | 0.0975998i | −0.892824 | − | 0.450406i | \(-0.851279\pi\) |
0.836475 | + | 0.548005i | \(0.184613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.02604 | 0.947392 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.12050 | + | 4.70556i | −0.678226 | + | 0.623267i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.29204 | − | 5.70197i | −0.428586 | − | 0.742334i | 0.568161 | − | 0.822917i | \(-0.307655\pi\) |
−0.996748 | + | 0.0805836i | \(0.974322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0376322 | + | 0.0651809i | −0.00481831 | + | 0.00834556i | −0.868425 | − | 0.495821i | \(-0.834867\pi\) |
0.863606 | + | 0.504167i | \(0.168200\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.16988 | − | 6.75368i | 0.525355 | − | 0.850883i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.96257 | + | 3.39927i | −0.243427 | + | 0.421628i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.29385 | − | 10.9013i | −0.768916 | − | 1.33180i | −0.938151 | − | 0.346226i | \(-0.887463\pi\) |
0.169235 | − | 0.985576i | \(-0.445870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.05125 | − | 9.19035i | −0.246941 | − | 1.10639i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0804951 | −0.00955301 | −0.00477651 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477651 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.34551 | − | 9.25869i | 0.625644 | − | 1.08365i | −0.362772 | − | 0.931878i | \(-0.618170\pi\) |
0.988416 | − | 0.151769i | \(-0.0484971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.12042 | − | 5.01990i | −0.129375 | − | 0.579648i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.9231 | + | 7.13261i | −1.24480 | + | 0.812837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.922457 | + | 1.59774i | −0.103785 | + | 0.179760i | −0.913241 | − | 0.407420i | \(-0.866429\pi\) |
0.809456 | + | 0.587180i | \(0.199762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.74555 | − | 6.92738i | 0.638395 | − | 0.769709i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.23583 | + | 12.5328i | 0.794236 | + | 1.37566i | 0.923323 | + | 0.384023i | \(0.125462\pi\) |
−0.129088 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.797736 | − | 1.38172i | 0.0865266 | − | 0.149868i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.68637 | + | 7.98248i | −0.931277 | + | 0.855811i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.76292 | + | 11.7137i | 0.716868 | + | 1.24165i | 0.962235 | + | 0.272222i | \(0.0877584\pi\) |
−0.245366 | + | 0.969430i | \(0.578908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.399711 | − | 7.27703i | −0.0419011 | − | 0.762840i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.19576 | + | 2.93679i | −0.331385 | + | 0.304531i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.86059 | + | 4.95469i | 0.293491 | + | 0.508341i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.70160 | + | 4.67930i | 0.274306 | + | 0.475111i | 0.969960 | − | 0.243266i | \(-0.0782187\pi\) |
−0.695654 | + | 0.718377i | \(0.744885\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.3885 | + | 6.28982i | −1.34559 | + | 0.632151i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.13540 | −0.510991 | −0.255496 | − | 0.966810i | \(-0.582239\pi\) | ||||
−0.255496 | + | 0.966810i | \(0.582239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2112 | 1.40027 | 0.700137 | − | 0.714009i | \(-0.253122\pi\) | ||||
0.700137 | + | 0.714009i | \(0.253122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.67545 | − | 4.55846i | −0.456277 | − | 0.444860i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.83015 | − | 6.63401i | −0.370274 | − | 0.641334i | 0.619333 | − | 0.785128i | \(-0.287403\pi\) |
−0.989608 | + | 0.143794i | \(0.954070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.849394 | + | 1.47119i | −0.0813572 | + | 0.140915i | −0.903833 | − | 0.427885i | \(-0.859259\pi\) |
0.822476 | + | 0.568800i | \(0.192592\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.81042 | + | 1.66371i | −0.171838 | + | 0.157913i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.300351 | + | 0.520224i | −0.0282547 | + | 0.0489385i | −0.879807 | − | 0.475331i | \(-0.842328\pi\) |
0.851552 | + | 0.524270i | \(0.175662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.74683 | −0.722395 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.696689 | − | 8.23439i | 0.0644090 | − | 0.761270i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.162473 | + | 2.95793i | 0.0148939 | + | 0.271153i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.3125 | 1.21023 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.411122 | + | 0.128980i | 0.0370696 | + | 0.0116298i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3561 | −1.01572 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.25977 | −0.644200 | −0.322100 | − | 0.946706i | \(-0.604389\pi\) | ||||
−0.322100 | + | 0.946706i | \(0.604389\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.27103 | + | 1.16803i | −0.111908 | + | 0.102839i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4530 | 1.78698 | 0.893492 | − | 0.449079i | \(-0.148248\pi\) | ||||
0.893492 | + | 0.449079i | \(0.148248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.47708 | − | 4.79886i | −0.821767 | − | 0.416114i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.53255 | − | 5.85475i | −0.390100 | − | 0.503896i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.2116 | 1.04331 | 0.521655 | − | 0.853157i | \(-0.325315\pi\) | ||||
0.521655 | + | 0.853157i | \(0.325315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.24092 | − | 2.14933i | 0.105253 | − | 0.182304i | −0.808588 | − | 0.588375i | \(-0.799768\pi\) |
0.913842 | + | 0.406071i | \(0.133101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.6600 | − | 4.91296i | −1.31881 | − | 0.413746i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.79117 | + | 11.7626i | −0.567906 | + | 0.983642i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.85269 | + | 8.40511i | 0.402994 | + | 0.698006i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8963 | + | 2.34046i | 0.981191 | + | 0.193038i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.55593 | −0.700929 | −0.350465 | − | 0.936576i | \(-0.613976\pi\) | ||||
−0.350465 | + | 0.936576i | \(0.613976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6592 | 1.43709 | 0.718544 | − | 0.695482i | \(-0.244809\pi\) | ||||
0.718544 | + | 0.695482i | \(0.244809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.283187 | + | 3.34708i | −0.0228943 | + | 0.270595i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.78533 | + | 3.09228i | 0.143401 | + | 0.248378i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.16074 | − | 5.47457i | −0.252255 | − | 0.436918i | 0.711891 | − | 0.702289i | \(-0.247839\pi\) |
−0.964146 | + | 0.265371i | \(0.914505\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.35591 | − | 0.425387i | −0.107531 | − | 0.0337354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0436 | − | 7.86433i | 0.949172 | − | 0.619796i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.01134 | + | 6.94784i | 0.314192 | + | 0.544197i | 0.979265 | − | 0.202581i | \(-0.0649331\pi\) |
−0.665073 | + | 0.746778i | \(0.731600\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.65094 | + | 11.8772i | 0.206376 | + | 0.924640i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.06038 | + | 1.83663i | −0.0820545 | + | 0.142123i | −0.904132 | − | 0.427253i | \(-0.859482\pi\) |
0.822078 | + | 0.569375i | \(0.192815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.70608 | + | 4.68706i | 0.208160 | + | 0.360543i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.88652 | − | 6.88056i | −0.756041 | − | 0.526169i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.14404 | − | 15.8379i | 0.695208 | − | 1.20414i | −0.274902 | − | 0.961472i | \(-0.588646\pi\) |
0.970110 | − | 0.242664i | \(-0.0780212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.57841 | − | 4.29561i | 0.497281 | − | 0.324718i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.39684 | − | 7.71641i | 0.631145 | − | 0.580001i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.81276 | + | 6.60389i | −0.284979 | + | 0.493598i | −0.972604 | − | 0.232468i | \(-0.925320\pi\) |
0.687625 | + | 0.726066i | \(0.258653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5305 | 1.15438 | 0.577188 | − | 0.816611i | \(-0.304150\pi\) | ||||
0.577188 | + | 0.816611i | \(0.304150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.124384 | − | 0.0390227i | −0.00919475 | − | 0.00288464i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.01140 | + | 1.75180i | 0.0743597 | + | 0.128795i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.76044 | − | 4.78122i | 0.201863 | − | 0.349638i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9901 | + | 4.50082i | 0.944891 | + | 0.327386i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.41624 | − | 12.8453i | 0.536620 | − | 0.929454i | −0.462463 | − | 0.886639i | \(-0.653034\pi\) |
0.999083 | − | 0.0428150i | \(-0.0136326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.28387 | − | 14.3481i | −0.596286 | − | 1.03280i | −0.993364 | − | 0.115013i | \(-0.963309\pi\) |
0.397078 | − | 0.917785i | \(-0.370024\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.48680 | − | 2.03509i | −0.464529 | − | 0.145736i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.03740 | −0.287653 | −0.143826 | − | 0.989603i | \(-0.545941\pi\) | ||||
−0.143826 | + | 0.989603i | \(0.545941\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6407 | − | 21.8943i | 0.896076 | − | 1.55205i | 0.0636081 | − | 0.997975i | \(-0.479739\pi\) |
0.832468 | − | 0.554074i | \(-0.186927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0534 | − | 14.7525i | 1.13232 | − | 1.04056i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0769 | − | 8.14075i | −1.12837 | − | 0.571368i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.177240 | − | 0.306988i | 0.0123790 | − | 0.0214410i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.7619 | − | 6.93508i | 1.02603 | − | 0.482022i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.89864 | + | 17.1449i | 0.684703 | + | 1.18594i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.76246 | − | 6.51678i | 0.259019 | − | 0.448634i | −0.706961 | − | 0.707253i | \(-0.749934\pi\) |
0.965979 | + | 0.258619i | \(0.0832675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0303710 | − | 0.136073i | −0.00208099 | − | 0.00932360i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.710065 | + | 1.22987i | 0.0484261 | + | 0.0838764i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.91476 | − | 2.99502i | −0.401520 | − | 0.203315i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.6683 | + | 5.54302i | 1.19391 | + | 0.374563i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.54214 | + | 2.67106i | 0.103735 | + | 0.179675i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.49230 | − | 11.2450i | −0.434757 | − | 0.753020i | 0.562519 | − | 0.826784i | \(-0.309832\pi\) |
−0.997276 | + | 0.0737638i | \(0.976499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.06319 | − | 3.78804i | 0.537546 | − | 0.252536i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.9665 | 1.92257 | 0.961286 | − | 0.275551i | \(-0.0888603\pi\) | ||||
0.961286 | + | 0.275551i | \(0.0888603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4358 | 1.02003 | 0.510013 | − | 0.860167i | \(-0.329640\pi\) | ||||
0.510013 | + | 0.860167i | \(0.329640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.1787 | − | 15.7738i | −1.06448 | − | 1.03784i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.47324 | − | 4.28378i | −0.162027 | − | 0.280640i | 0.773568 | − | 0.633713i | \(-0.218470\pi\) |
−0.935596 | + | 0.353073i | \(0.885137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.75121 | + | 11.6934i | −0.440400 | + | 0.762795i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.04896 | − | 0.956542i | −0.198051 | − | 0.0621341i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.51732 | + | 11.2883i | −0.421571 | + | 0.730182i | −0.996093 | − | 0.0883069i | \(-0.971854\pi\) |
0.574523 | + | 0.818489i | \(0.305188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5825 | 0.939339 | 0.469670 | − | 0.882842i | \(-0.344373\pi\) | ||||
0.469670 | + | 0.882842i | \(0.344373\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8782 | + | 7.09889i | 0.890290 | + | 0.455394i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.01117 | − | 9.13249i | 0.256265 | − | 0.583453i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0599 | −0.703722 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.4561 | + | 16.9605i | −1.16961 | + | 1.07483i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0715 | 0.888187 | 0.444094 | − | 0.895980i | \(-0.353526\pi\) | ||||
0.444094 | + | 0.895980i | \(0.353526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.8067 | −1.68532 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.63672 | + | 0.827212i | 0.165118 | + | 0.0518020i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.36215 | −0.521617 | −0.260808 | − | 0.965391i | \(-0.583989\pi\) | ||||
−0.260808 | + | 0.965391i | \(0.583989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.35075 | − | 1.69670i | −0.208206 | − | 0.105428i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.7714 | − | 11.6721i | −1.03812 | − | 0.722487i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.27066 | −0.201678 | −0.100839 | − | 0.994903i | \(-0.532153\pi\) | ||||
−0.100839 | + | 0.994903i | \(0.532153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.584551 | + | 1.01247i | −0.0359087 | + | 0.0621956i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.2499 | + | 15.8520i | −1.05568 | + | 0.970129i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.69349 | + | 13.3255i | −0.469081 | + | 0.812471i | −0.999375 | − | 0.0353420i | \(-0.988748\pi\) |
0.530295 | + | 0.847813i | \(0.322081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.06308 | − | 7.03747i | −0.246815 | − | 0.427496i | 0.715825 | − | 0.698279i | \(-0.246051\pi\) |
−0.962640 | + | 0.270783i | \(0.912717\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.1507 | − | 3.42133i | 0.735393 | − | 0.207069i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.6422 | −0.882958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.8457 | 0.771826 | 0.385913 | − | 0.922535i | \(-0.373887\pi\) | ||||
0.385913 | + | 0.922535i | \(0.373887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.17029 | − | 4.29423i | −0.369406 | − | 0.257089i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.724081 | − | 1.25415i | −0.0431951 | − | 0.0748161i | 0.843620 | − | 0.536941i | \(-0.180420\pi\) |
−0.886815 | + | 0.462125i | \(0.847087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.71926 | − | 15.1022i | −0.518306 | − | 0.897732i | −0.999774 | − | 0.0212686i | \(-0.993229\pi\) |
0.481468 | − | 0.876464i | \(-0.340104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.29639 | + | 6.70513i | −0.432201 | + | 0.397178i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0360979 | + | 0.657189i | 0.00213079 | + | 0.0387926i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.87316 | + | 13.6367i | 0.463127 | + | 0.802160i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.89084 | + | 6.33244i | −0.403948 | + | 0.371214i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.900048 | + | 1.55893i | −0.0525814 | + | 0.0910736i | −0.891118 | − | 0.453772i | \(-0.850078\pi\) |
0.838537 | + | 0.544845i | \(0.183412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.69094 | − | 8.12495i | −0.273117 | − | 0.473053i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.6842 | − | 20.2594i | −0.910088 | − | 1.17557i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.48786 | − | 12.9693i | 0.433034 | − | 0.750037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.35243 | − | 1.19119i | −0.135592 | − | 0.0686589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.93760 | − | 8.68117i | −0.111312 | − | 0.498720i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0536236 | + | 0.0928787i | −0.00307048 | + | 0.00531822i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.06478 | −0.0607699 | −0.0303850 | − | 0.999538i | \(-0.509673\pi\) | ||||
−0.0303850 | + | 0.999538i | \(0.509673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.36193 | + | 24.0234i | 0.305029 | + | 1.36665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.46463 | − | 14.6612i | −0.479985 | − | 0.831359i | 0.519751 | − | 0.854318i | \(-0.326025\pi\) |
−0.999736 | + | 0.0229591i | \(0.992691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.13928 | − | 7.16944i | 0.233966 | − | 0.405241i | −0.725006 | − | 0.688743i | \(-0.758163\pi\) |
0.958972 | + | 0.283502i | \(0.0914963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.94181 | − | 9.62356i | 0.334783 | − | 0.542226i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.27371 | + | 5.67023i | −0.183870 | + | 0.318472i | −0.943195 | − | 0.332239i | \(-0.892196\pi\) |
0.759325 | + | 0.650711i | \(0.225529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.7920 | + | 29.0846i | 0.940171 | + | 1.62842i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.76938 | − | 8.97773i | 0.545274 | − | 0.501088i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.49556 | 0.250140 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.08997 | − | 7.08404i | 0.226871 | − | 0.392952i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.80747 | − | 0.880779i | −0.155253 | − | 0.0487072i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.37500 | − | 25.0329i | −0.0758062 | − | 1.38011i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3629 | + | 23.1453i | −0.734493 | + | 1.27218i | 0.220453 | + | 0.975398i | \(0.429246\pi\) |
−0.954946 | + | 0.296781i | \(0.904087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.49551 | − | 2.43271i | −0.191553 | − | 0.133312i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.96834 | − | 15.5336i | −0.489993 | − | 0.848692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.76164 | + | 8.24740i | −0.259383 | + | 0.449264i | −0.966077 | − | 0.258255i | \(-0.916853\pi\) |
0.706694 | + | 0.707520i | \(0.250186\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.992739 | − | 0.311449i | −0.0539182 | − | 0.0169156i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.17786 | + | 10.7004i | 0.334550 | + | 0.579457i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.03502 | + | 18.2699i | 0.163876 | + | 0.986481i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.92290 | − | 13.0957i | −0.157363 | − | 0.705048i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.35156 | − | 16.1974i | −0.502018 | − | 0.869521i | −0.999997 | − | 0.00233189i | \(-0.999258\pi\) |
0.497979 | − | 0.867189i | \(-0.334076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0542 | − | 26.0747i | −0.805834 | − | 1.39574i | −0.915727 | − | 0.401801i | \(-0.868384\pi\) |
0.109893 | − | 0.993943i | \(-0.464949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.1827 | − | 1.92913i | 0.757019 | − | 0.102970i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.25933 | 0.333150 | 0.166575 | − | 0.986029i | \(-0.446729\pi\) | ||||
0.166575 | + | 0.986029i | \(0.446729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.114700 | −0.00608767 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.93895 | + | 1.39069i | −0.261397 | + | 0.0736030i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.09755 | + | 8.82921i | 0.269038 | + | 0.465988i | 0.968614 | − | 0.248571i | \(-0.0799608\pi\) |
−0.699575 | + | 0.714559i | \(0.746628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.43970 | − | 2.49364i | 0.0757739 | − | 0.131244i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.02285 | + | 22.5042i | 0.263631 | + | 1.18117i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.61701 | − | 13.1931i | 0.398693 | − | 0.690556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6557 | 1.49581 | 0.747906 | − | 0.663804i | \(-0.231059\pi\) | ||||
0.747906 | + | 0.663804i | \(0.231059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0629181 | + | 0.743649i | −0.00327538 | + | 0.0387128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.119054 | − | 2.16746i | −0.00618097 | − | 0.112529i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0734 | −0.832249 | −0.416124 | − | 0.909308i | \(-0.636612\pi\) | ||||
−0.416124 | + | 0.909308i | \(0.636612\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.28469 | − | 19.1970i | −0.221260 | − | 0.991330i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.7619 | −0.966286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.01893 | 0.0523388 | 0.0261694 | − | 0.999658i | \(-0.491669\pi\) | ||||
0.0261694 | + | 0.999658i | \(0.491669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.73913 | − | 12.2723i | −0.140330 | − | 0.628730i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.5865 | 0.592044 | 0.296022 | − | 0.955181i | \(-0.404340\pi\) | ||||
0.296022 | + | 0.955181i | \(0.404340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.5647 | + | 10.1635i | −0.793250 | + | 0.517981i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.45406 | − | 1.70791i | −0.124747 | − | 0.0868181i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8135 | 0.903181 | 0.451590 | − | 0.892225i | \(-0.350857\pi\) | ||||
0.451590 | + | 0.892225i | \(0.350857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.04363 | + | 5.27172i | −0.153923 | + | 0.266602i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.71695 | + | 34.5749i | 0.389269 | + | 1.74407i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.31444 | + | 2.27668i | −0.0661369 | + | 0.114552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.54229 | − | 11.3316i | −0.328348 | − | 0.568715i | 0.653836 | − | 0.756636i | \(-0.273159\pi\) |
−0.982184 | + | 0.187921i | \(0.939825\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.53653 | − | 17.8312i | 0.227111 | − | 0.892677i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1033 | 0.704285 | 0.352143 | − | 0.935946i | \(-0.385453\pi\) | ||||
0.352143 | + | 0.935946i | \(0.385453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.90259 | −0.343842 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.18706 | − | 9.87108i | 0.406818 | − | 0.490498i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.49980 | + | 6.06183i | 0.173479 | + | 0.300474i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.32300 | + | 2.29150i | 0.0654179 | + | 0.113307i | 0.896879 | − | 0.442275i | \(-0.145829\pi\) |
−0.831461 | + | 0.555583i | \(0.812495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.60747 | + | 20.6432i | 0.227270 | + | 1.01825i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5410 | + | 7.86940i | 0.764722 | + | 0.387228i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3106 | + | 17.8585i | 0.506128 | + | 0.876639i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.10155 | + | 1.28677i | 0.200854 | + | 0.0630133i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.7567 | + | 29.0235i | −0.818619 | + | 1.41789i | 0.0880816 | + | 0.996113i | \(0.471926\pi\) |
−0.906700 | + | 0.421776i | \(0.861407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.41950 | − | 4.19071i | −0.117919 | − | 0.204242i | 0.801024 | − | 0.598633i | \(-0.204289\pi\) |
−0.918943 | + | 0.394390i | \(0.870956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.39660 | − | 28.3262i | 0.116527 | − | 1.37727i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.66247 | + | 2.87949i | −0.0806418 | + | 0.139676i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0109214 | − | 0.198831i | −0.000528522 | − | 0.00962212i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.4466 | − | 7.04210i | −1.08373 | − | 0.339996i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6643 | + | 30.5954i | −0.850858 | + | 1.47373i | 0.0295774 | + | 0.999562i | \(0.490584\pi\) |
−0.880435 | + | 0.474166i | \(0.842749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.47404 | 0.263066 | 0.131533 | − | 0.991312i | \(-0.458010\pi\) | ||||
0.131533 | + | 0.991312i | \(0.458010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.3775 | + | 11.3745i | −0.593458 | + | 0.545367i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.9141 | − | 18.9038i | −0.522093 | − | 0.904292i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.19906 | − | 5.54093i | 0.152683 | − | 0.264454i | −0.779530 | − | 0.626365i | \(-0.784542\pi\) |
0.932213 | + | 0.361911i | \(0.117875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.532064 | + | 20.9933i | 0.0253364 | + | 0.999679i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.19341 | + | 5.53115i | −0.151723 | + | 0.262793i | −0.931861 | − | 0.362815i | \(-0.881816\pi\) |
0.780138 | + | 0.625608i | \(0.215149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.63674 | + | 16.6913i | 0.456825 | + | 0.791245i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.22817 | − | 14.4634i | −0.152687 | − | 0.684097i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.7460 | −0.554327 | −0.277163 | − | 0.960823i | \(-0.589394\pi\) | ||||
−0.277163 | + | 0.960823i | \(0.589394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.613311 | − | 1.06229i | 0.0288797 | − | 0.0500210i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.66287 | + | 29.8522i | 0.313049 | + | 1.40258i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.569564 | − | 10.3693i | −0.0267016 | − | 0.486121i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.26120 | + | 9.11266i | −0.246108 | + | 0.426272i | −0.962443 | − | 0.271485i | \(-0.912485\pi\) |
0.716334 | + | 0.697757i | \(0.245819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.76494 | + | 0.784145i | −0.269084 | + | 0.0366007i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.54278 | − | 6.13627i | −0.165004 | − | 0.285794i | 0.771653 | − | 0.636044i | \(-0.219430\pi\) |
−0.936657 | + | 0.350249i | \(0.886097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3760 | + | 28.3641i | −0.761059 | + | 1.31819i | 0.181246 | + | 0.983438i | \(0.441987\pi\) |
−0.942305 | + | 0.334755i | \(0.891346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.55376 | + | 4.18475i | −0.211176 | + | 0.194063i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.96216 | − | 3.39856i | −0.0907978 | − | 0.157266i | 0.817049 | − | 0.576568i | \(-0.195608\pi\) |
−0.907847 | + | 0.419301i | \(0.862275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.7119 | + | 15.0450i | 1.37197 | + | 0.694716i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.06196 | − | 7.40867i | 0.371476 | − | 0.341373i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.45707 | + | 4.25577i | 0.112976 | + | 0.195681i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.96145 | − | 10.3255i | −0.273530 | − | 0.473768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.207509 | − | 2.45261i | 0.00950117 | − | 0.112297i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0865 | −0.735010 | −0.367505 | − | 0.930022i | \(-0.619788\pi\) | ||||
−0.367505 | + | 0.930022i | \(0.619788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.91036 | −0.178297 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.8384 | + | 17.3920i | 0.811675 | + | 0.791365i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.84961 | + | 6.66771i | 0.174802 | + | 0.302765i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.75172 | − | 3.03407i | 0.0793781 | − | 0.137487i | −0.823604 | − | 0.567166i | \(-0.808040\pi\) |
0.902982 | + | 0.429679i | \(0.141373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2315 | + | 9.40242i | −0.462686 | + | 0.425192i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5546 | − | 35.6017i | 0.927618 | − | 1.60668i | 0.140321 | − | 0.990106i | \(-0.455186\pi\) |
0.787296 | − | 0.616575i | \(-0.211480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.62624 | 0.343468 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.0777 | + | 8.96261i | −0.857480 | + | 0.402839i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.178320 | − | 0.116440i | 0.00799873 | − | 0.00522306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.8297 | −0.529571 | −0.264785 | − | 0.964307i | \(-0.585301\pi\) | ||||
−0.264785 | + | 0.964307i | \(0.585301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.50482 | − | 1.09956i | −0.156584 | − | 0.0491247i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.8595 | −0.974665 | −0.487332 | − | 0.873217i | \(-0.662030\pi\) | ||||
−0.487332 | + | 0.873217i | \(0.662030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.31762 | −0.325630 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.90226 | + | 6.34294i | −0.306540 | + | 0.281700i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8966 | 0.748930 | 0.374465 | − | 0.927241i | \(-0.377826\pi\) | ||||
0.374465 | + | 0.927241i | \(0.377826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55134 | + | 28.2432i | 0.0686271 | + | 1.24941i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.90108 | − | 19.3088i | 0.348841 | − | 0.852503i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.2501 | 0.892326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.3615 | + | 40.4633i | −1.02744 | + | 1.77957i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.2234 | + | 9.48190i | 1.32666 | + | 0.416209i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2466 | + | 29.8720i | −0.755587 | + | 1.30872i | 0.189495 | + | 0.981882i | \(0.439315\pi\) |
−0.945082 | + | 0.326834i | \(0.894018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.995615 | − | 1.72445i | −0.0435352 | − | 0.0754051i | 0.843437 | − | 0.537229i | \(-0.180529\pi\) |
−0.886972 | + | 0.461823i | \(0.847195\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.74359 | + | 9.49977i | 0.425245 | + | 0.414604i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.80573 | 0.122220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.55673 | 0.285075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.2124 | + | 11.2831i | 0.703558 | + | 0.489644i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.342629 | + | 0.593452i | 0.0148409 | + | 0.0257052i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.45772 | − | 9.45305i | −0.235958 | − | 0.408691i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.6021 | − | 3.95364i | −0.543823 | − | 0.170612i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.8800 | − | 31.6016i | 0.597856 | − | 1.36118i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0681 | − | 26.0988i | −0.647830 | − | 1.12207i | −0.983640 | − | 0.180145i | \(-0.942343\pi\) |
0.335810 | − | 0.941930i | \(-0.390990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.85971 | + | 26.2537i | 0.251464 | + | 1.12665i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.21033 | + | 2.09636i | −0.0518450 | + | 0.0897982i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.68070 | − | 13.3034i | −0.328403 | − | 0.568810i | 0.653792 | − | 0.756674i | \(-0.273177\pi\) |
−0.982195 | + | 0.187864i | \(0.939844\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0190357 | − | 0.224990i | 0.000812426 | − | 0.00960232i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6734 | + | 23.6831i | −0.582508 | + | 1.00893i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.267709 | − | 4.87384i | −0.0113842 | − | 0.207257i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.57974 | + | 2.37069i | −0.109504 | + | 0.100630i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.6412 | + | 20.1631i | −0.493252 | + | 0.854338i | −0.999970 | − | 0.00777438i | \(-0.997525\pi\) |
0.506718 | + | 0.862112i | \(0.330859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.74531 | −0.116114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.12397 | + | 2.86244i | 0.385214 | + | 0.120852i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.27942 | + | 3.94808i | 0.0960663 | + | 0.166392i | 0.910053 | − | 0.414492i | \(-0.136041\pi\) |
−0.813987 | + | 0.580883i | \(0.802707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.427982 | + | 0.741286i | −0.0180053 | + | 0.0311861i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.70724 | + | 23.6574i | −0.113693 | + | 0.993516i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.09976 | + | 15.7612i | −0.381482 | + | 0.660746i | −0.991274 | − | 0.131815i | \(-0.957919\pi\) |
0.609793 | + | 0.792561i | \(0.291253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.52275 | − | 14.7618i | −0.356666 | − | 0.617763i | 0.630736 | − | 0.775998i | \(-0.282753\pi\) |
−0.987402 | + | 0.158234i | \(0.949420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.5126 | + | 7.69027i | 1.02403 | + | 0.321266i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.1443 | 0.673264 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.70473 | + | 9.88088i | −0.237491 | + | 0.411346i | −0.959994 | − | 0.280022i | \(-0.909658\pi\) |
0.722503 | + | 0.691368i | \(0.242992\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.1293 | − | 19.4171i | 0.878103 | − | 0.806947i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.1588 | − | 17.2968i | −1.41715 | − | 0.717592i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.02275 | + | 3.50350i | −0.0837736 | + | 0.145100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.992739 | − | 11.7335i | 0.0410447 | − | 0.485120i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.52544 | − | 4.37420i | −0.104236 | − | 0.180543i | 0.809190 | − | 0.587548i | \(-0.199906\pi\) |
−0.913426 | + | 0.407005i | \(0.866573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.03052 | + | 8.71312i | −0.207279 | + | 0.359018i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.52332 | − | 6.82504i | −0.0626610 | − | 0.280745i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.98892 | − | 17.3013i | −0.410196 | − | 0.710480i | 0.584715 | − | 0.811239i | \(-0.301206\pi\) |
−0.994911 | + | 0.100759i | \(0.967873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.231513 | + | 4.21487i | 0.00949113 | + | 0.172793i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.7808 | + | 13.1078i | 1.70997 | + | 0.536465i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.19660 | + | 3.80463i | 0.0897508 | + | 0.155453i | 0.907406 | − | 0.420256i | \(-0.138060\pi\) |
−0.817655 | + | 0.575709i | \(0.804726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1778 | + | 21.0926i | 0.496743 | + | 0.860385i | 0.999993 | − | 0.00375637i | \(-0.00119569\pi\) |
−0.503250 | + | 0.864141i | \(0.667862\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.9955 | + | 21.5715i | 1.26224 | + | 0.878457i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.9695 | 0.771221 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.1256 | −0.532752 | −0.266376 | − | 0.963869i | \(-0.585826\pi\) | ||||
−0.266376 | + | 0.963869i | \(0.585826\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.69574 | − | 30.2487i | 0.311847 | − | 1.22574i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0510 | − | 22.6051i | −0.527988 | − | 0.914502i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2403 | + | 40.2534i | −0.938667 | + | 1.62582i | −0.170707 | + | 0.985322i | \(0.554605\pi\) |
−0.767960 | + | 0.640497i | \(0.778728\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.585823 | + | 0.183789i | 0.0236227 | + | 0.00741108i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1948 | − | 24.5862i | 0.571463 | − | 0.989803i | −0.424953 | − | 0.905215i | \(-0.639709\pi\) |
0.996416 | − | 0.0845873i | \(-0.0269572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.9212 | −1.28302 | −0.641511 | − | 0.767114i | \(-0.721692\pi\) | ||||
−0.641511 | + | 0.767114i | \(0.721692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.2932 | + | 22.3378i | 0.693951 | + | 0.896385i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.9263 | − | 16.1663i | −1.27910 | − | 0.647691i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.33399 | −0.0533594 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.2480 | + | 23.2020i | −1.00831 | + | 0.926601i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.58947 | 0.0633762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.7184 | −1.54135 | −0.770677 | − | 0.637226i | \(-0.780082\pi\) | ||||
−0.770677 | + | 0.637226i | \(0.780082\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.4359 | + | 3.90149i | 0.494283 | + | 0.155070i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3447 | −0.410517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.4121 | + | 15.5425i | 0.452163 | + | 0.615816i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.218567 | − | 0.102682i | 0.00864639 | − | 0.00406202i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4001 | −1.59571 | −0.797854 | − | 0.602851i | \(-0.794032\pi\) | ||||
−0.797854 | + | 0.602851i | \(0.794032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.27355 | + | 10.8661i | −0.247405 | + | 0.428517i | −0.962805 | − | 0.270198i | \(-0.912911\pi\) |
0.715400 | + | 0.698715i | \(0.246244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.81113 | + | 1.66437i | −0.0713132 | + | 0.0655344i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2774 | + | 29.9253i | −0.679245 | + | 1.17649i | 0.295964 | + | 0.955199i | \(0.404359\pi\) |
−0.975209 | + | 0.221287i | \(0.928974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2323 | − | 28.1151i | −0.637173 | − | 1.10362i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.83130 | − | 11.1287i | 0.110967 | − | 0.436167i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2944 | −0.872446 | −0.436223 | − | 0.899839i | \(-0.643684\pi\) | ||||
−0.436223 | + | 0.899839i | \(0.643684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.1442 | 1.13876 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.70395 | + | 31.9589i | −0.105491 | + | 1.24683i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.57493 | − | 6.19196i | −0.139259 | − | 0.241204i | 0.787957 | − | 0.615730i | \(-0.211139\pi\) |
−0.927217 | + | 0.374526i | \(0.877806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.4530 | − | 37.1577i | −0.834425 | − | 1.44527i | −0.894498 | − | 0.447072i | \(-0.852467\pi\) |
0.0600736 | − | 0.998194i | \(-0.480866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.93346 | + | 3.61471i | −0.152763 | + | 0.140384i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.5043 | − | 6.83807i | −0.523672 | − | 0.265169i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5146 | − | 32.0683i | −0.716889 | − | 1.24169i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.5596 | − | 15.2177i | 0.640232 | − | 0.588351i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.185556 | + | 0.321392i | −0.00716331 | + | 0.0124072i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8270 | − | 32.6094i | −0.725729 | − | 1.25700i | −0.958673 | − | 0.284510i | \(-0.908169\pi\) |
0.232944 | − | 0.972490i | \(-0.425164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.44578 | + | 12.2012i | 0.363568 | + | 0.469626i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.1808 | − | 22.8298i | 0.506580 | − | 0.877422i | −0.493391 | − | 0.869808i | \(-0.664243\pi\) |
0.999971 | − | 0.00761453i | \(-0.00242380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.7537 | − | 6.45800i | −0.489440 | − | 0.247835i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9291 | + | 48.9666i | 0.418805 | + | 1.87640i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.96588 | + | 3.40500i | −0.0752222 | + | 0.130289i | −0.901183 | − | 0.433439i | \(-0.857300\pi\) |
0.825961 | + | 0.563728i | \(0.190633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.4008 | 0.664850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.82396 | + | 26.0936i | 0.222198 | + | 0.995531i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.13002 | − | 1.95725i | −0.0430503 | − | 0.0745653i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.95052 | − | 17.2348i | 0.378536 | − | 0.655643i | −0.612314 | − | 0.790615i | \(-0.709761\pi\) |
0.990849 | + | 0.134972i | \(0.0430944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20.5607 | − | 33.3008i | 0.781037 | − | 1.26499i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.76823 | − | 3.06266i | 0.0670727 | − | 0.116173i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.139270 | − | 0.241223i | −0.00527524 | − | 0.00913699i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.30838 | − | 5.79718i | 0.238605 | − | 0.219270i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.7908 | 1.65396 | 0.826979 | − | 0.562234i | \(-0.190058\pi\) | ||||
0.826979 | + | 0.562234i | \(0.190058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.84983 | + | 4.93604i | −0.107483 | + | 0.186166i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.3145 | − | 7.00066i | −0.840412 | − | 0.263660i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3764 | − | 7.42861i | 0.427853 | − | 0.279382i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.3172 | + | 38.6545i | −0.838139 | + | 1.45170i | 0.0533097 | + | 0.998578i | \(0.483023\pi\) |
−0.891449 | + | 0.453121i | \(0.850310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.466612 | − | 5.51504i | 0.0174993 | − | 0.206830i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.81163 | − | 11.7981i | −0.255097 | − | 0.441842i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.67699 | + | 16.7610i | −0.361899 | + | 0.626827i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.5414 | − | 6.75814i | −0.804480 | − | 0.252387i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.5096 | + | 33.7917i | 0.727586 | + | 1.26022i | 0.957901 | + | 0.287100i | \(0.0926912\pi\) |
−0.230315 | + | 0.973116i | \(0.573976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.4819 | + | 20.5572i | −1.17245 | + | 0.765592i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.50200 | + | 24.6510i | 0.204622 | + | 0.916781i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.1130 | − | 17.5162i | −0.375586 | − | 0.650534i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2554 | + | 19.4949i | 0.417439 | + | 0.723025i | 0.995681 | − | 0.0928402i | \(-0.0295946\pi\) |
−0.578242 | + | 0.815865i | \(0.696261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.76407 | + | 26.1390i | −0.250521 | + | 0.968111i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11590 | 0.0412731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.897039 | −0.0331329 | −0.0165664 | − | 0.999863i | \(-0.505274\pi\) | ||||
−0.0165664 | + | 0.999863i | \(0.505274\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.9515 | + | 3.33501i | 0.625266 | + | 0.123014i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.0335 | − | 53.7517i | −1.14314 | − | 1.97997i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.79032 | + | 3.10092i | −0.0658578 | + | 0.114069i | −0.897074 | − | 0.441880i | \(-0.854312\pi\) |
0.831216 | + | 0.555949i | \(0.187645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.17291 | − | 18.6962i | −0.153296 | − | 0.686823i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.7964 | − | 42.9486i | 0.909691 | − | 1.57563i | 0.0951977 | − | 0.995458i | \(-0.469652\pi\) |
0.814493 | − | 0.580173i | \(-0.197015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1917 | −0.446668 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.6346 | − | 24.8000i | −1.30380 | − | 0.907384i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0813 | + | 9.15573i | 0.660676 | + | 0.334543i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9030 | 1.56555 | 0.782776 | − | 0.622304i | \(-0.213803\pi\) | ||||
0.782776 | + | 0.622304i | \(0.213803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.30922 | + | 23.7873i | 0.193479 | + | 0.866858i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.1633 | 0.915786 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8029 | 0.501677 | 0.250838 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250838 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.1142 | − | 45.3155i | −0.367123 | − | 1.64485i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7197 | 1.47609 | 0.738044 | − | 0.674752i | \(-0.235749\pi\) | ||||
0.738044 | + | 0.674752i | \(0.235749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.246505 | − | 4.48781i | −0.00892410 | − | 0.162470i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.403524 | + | 4.76938i | −0.0145894 | + | 0.172437i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.1365 | 0.654871 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.57381 | − | 9.65413i | 0.200997 | − | 0.348137i | −0.747853 | − | 0.663864i | \(-0.768915\pi\) |
0.948850 | + | 0.315728i | \(0.102249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.15506 | − | 14.1359i | −0.113627 | − | 0.509090i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.462831 | + | 0.801647i | −0.0166469 | + | 0.0288332i | −0.874229 | − | 0.485514i | \(-0.838632\pi\) |
0.857582 | + | 0.514347i | \(0.171966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.72061 | − | 6.44428i | −0.133648 | − | 0.231485i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.60395 | − | 6.30447i | 0.0575415 | − | 0.226172i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.998817 | 0.0357863 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.396903 | −0.0142023 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.4033 | − | 32.7553i | 0.478996 | − | 1.17058i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.50386 | − | 7.80092i | −0.160750 | − | 0.278427i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.5120 | + | 19.9393i | 0.410358 | + | 0.710761i | 0.994929 | − | 0.100582i | \(-0.0320704\pi\) |
−0.584571 | + | 0.811343i | \(0.698737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.23403 | − | 5.52891i | −0.0439325 | − | 0.196834i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0871659 | − | 1.58692i | −0.00309926 | − | 0.0564243i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.103662 | − | 0.179548i | −0.00368114 | − | 0.00637593i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.93209 | − | 0.606149i | −0.0685242 | − | 0.0214979i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.3925 | − | 19.7325i | 0.403544 | − | 0.698960i | −0.590606 | − | 0.806960i | \(-0.701111\pi\) |
0.994151 | + | 0.108000i | \(0.0344447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.30492 | + | 9.18839i | 0.187675 | + | 0.325062i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.3056 | − | 23.1791i | −1.17680 | − | 0.818995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.3575 | − | 45.6525i | 0.930135 | − | 1.61104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.1614 | − | 11.2062i | 0.604861 | − | 0.394966i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.4290 | − | 7.97776i | −0.895143 | − | 0.280831i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.73753 | − | 11.6697i | 0.236879 | − | 0.410286i | −0.722938 | − | 0.690913i | \(-0.757209\pi\) |
0.959817 | + | 0.280627i | \(0.0905422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7348 | 1.07924 | 0.539622 | − | 0.841907i | \(-0.318567\pi\) | ||||
0.539622 | + | 0.841907i | \(0.318567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.3635 | − | 9.52372i | 0.363465 | − | 0.334011i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.71590 | + | 9.90023i | 0.200219 | + | 0.346790i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00075 | + | 3.46540i | −0.0699974 | + | 0.121239i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3681 | + | 19.2493i | 0.362291 | + | 0.672626i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.49319 | − | 14.7106i | 0.296414 | − | 0.513405i | −0.678899 | − | 0.734232i | \(-0.737542\pi\) |
0.975313 | + | 0.220827i | \(0.0708757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.29157 | − | 16.0935i | −0.323884 | − | 0.560983i | 0.657402 | − | 0.753540i | \(-0.271655\pi\) |
−0.981286 | + | 0.192557i | \(0.938322\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.52453 | − | 24.7520i | −0.192340 | − | 0.861754i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5419 | −0.505670 | −0.252835 | − | 0.967509i | \(-0.581363\pi\) | ||||
−0.252835 | + | 0.967509i | \(0.581363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.78717 | − | 8.29161i | 0.166265 | − | 0.287980i | −0.770839 | − | 0.637030i | \(-0.780163\pi\) |
0.937104 | + | 0.349051i | \(0.113496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.84673 | + | 21.7152i | 0.168131 | + | 0.753291i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.63872 | − | 6.31764i | −0.160722 | − | 0.218893i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.51097 | + | 2.61708i | −0.0522894 | + | 0.0905678i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.93115 | − | 12.0508i | 0.170446 | − | 0.416538i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2303 | − | 36.7720i | −0.732952 | − | 1.26951i | −0.955616 | − | 0.294615i | \(-0.904809\pi\) |
0.222664 | − | 0.974895i | \(-0.428525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.69551 | + | 15.0611i | −0.299845 | + | 0.519347i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.84688 | − | 1.69722i | 0.0636100 | − | 0.0584554i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.85599 | + | 6.67877i | 0.132650 | + | 0.229757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4911 | + | 19.2572i | −1.01332 | + | 0.661687i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.2398 | − | 20.4376i | 0.763268 | − | 0.701417i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.85883 | − | 6.68370i | −0.132279 | − | 0.229114i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.14039 | + | 12.3675i | 0.244482 | + | 0.423456i | 0.961986 | − | 0.273099i | \(-0.0880486\pi\) |
−0.717504 | + | 0.696555i | \(0.754715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.0877 | − | 9.80436i | −0.481788 | − | 0.335302i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.7790 | 1.18803 | 0.594013 | − | 0.804455i | \(-0.297543\pi\) | ||||
0.594013 | + | 0.804455i | \(0.297543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6486 | 0.431564 | 0.215782 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215782 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.09733 | + | 0.308981i | −0.0373969 | + | 0.0105300i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.2398 | − | 22.9321i | −0.450690 | − | 0.780617i | 0.547739 | − | 0.836649i | \(-0.315489\pi\) |
−0.998429 | + | 0.0560318i | \(0.982155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0297 | − | 22.5681i | 0.443022 | − | 0.767337i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.0817 | + | 18.4544i | −0.682011 | + | 0.626744i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.54843 | + | 7.87811i | −0.154295 | + | 0.267247i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.6741 | 1.17489 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.3047 | − | 9.25942i | −0.450294 | − | 0.313384i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.1570 | − | 16.4272i | 0.850463 | − | 0.555341i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.4534 | 0.960805 | 0.480402 | − | 0.877048i | \(-0.340491\pi\) | ||||
0.480402 | + | 0.877048i | \(0.340491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.97489 | − | 0.933305i | −0.100341 | − | 0.0314796i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3637 | −0.686071 | −0.343036 | − | 0.939322i | \(-0.611455\pi\) | ||||
−0.343036 | + | 0.939322i | \(0.611455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.1950 | −1.65554 | −0.827772 | − | 0.561065i | \(-0.810392\pi\) | ||||
−0.827772 | + | 0.561065i | \(0.810392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.9650 | − | 10.9954i | 0.402198 | − | 0.369606i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.21692 | 0.141590 | 0.0707952 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707952 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0825 | − | 10.5016i | 0.539388 | − | 0.352213i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.3300 | − | 34.1573i | 0.949092 | − | 1.14431i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.0457 | −1.27315 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.43294 | + | 9.41013i | −0.181603 | + | 0.314546i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.7493 | + | 7.76453i | 0.826355 | + | 0.259250i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.53374 | + | 14.7809i | −0.284616 | + | 0.492970i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.459325 | + | 0.795574i | 0.0153023 | + | 0.0265044i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.12607 | − | 4.42612i | 0.0374733 | − | 0.147292i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.1301 | 0.735628 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.9851 | −1.59332 | −0.796659 | − | 0.604429i | \(-0.793401\pi\) | ||||
−0.796659 | + | 0.604429i | \(0.793401\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.9441 | − | 6.55085i | 0.462496 | − | 0.217278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8667 | + | 22.2858i | 0.426294 | + | 0.738362i | 0.996540 | − | 0.0831113i | \(-0.0264857\pi\) |
−0.570247 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.6782 | + | 61.7965i | 1.18078 | + | 2.04517i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.177240 | − | 0.0556049i | −0.00585937 | − | 0.00183824i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45.3092 | + | 29.5863i | −1.49624 | + | 0.977024i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.13478 | − | 1.96550i | −0.0374330 | − | 0.0648359i | 0.846702 | − | 0.532068i | \(-0.178585\pi\) |
−0.884135 | + | 0.467232i | \(0.845251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.401742 | − | 1.79996i | −0.0132379 | − | 0.0593106i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.110866 | − | 0.192026i | 0.00364920 | − | 0.00632060i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.10775 | − | 3.65073i | −0.0693024 | − | 0.120035i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.5875 | + | 18.1282i | −1.26738 | + | 0.595408i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.9248 | + | 39.7069i | −0.752138 | + | 1.30274i | 0.194647 | + | 0.980873i | \(0.437644\pi\) |
−0.946785 | + | 0.321868i | \(0.895689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9362 | − | 3.07824i | 0.915573 | − | 0.100885i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.5903 | − | 19.8408i | 0.706836 | − | 0.649558i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.93346 | − | 6.81294i | 0.128638 | − | 0.222807i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.2075 | −1.83622 | −0.918110 | − | 0.396325i | \(-0.870285\pi\) | ||||
−0.918110 | + | 0.396325i | \(0.870285\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6814 | + | 4.29222i | 0.446475 | + | 0.140071i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6402 | + | 30.5536i | 0.575053 | + | 0.996020i | 0.996036 | + | 0.0889519i | \(0.0283517\pi\) |
−0.420983 | + | 0.907068i | \(0.638315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.676229 | + | 1.17126i | −0.0220210 | + | 0.0381415i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.5101 | + | 6.41338i | 0.602133 | + | 0.208627i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.3565 | + | 43.9188i | −0.823976 | + | 1.42717i | 0.0787236 | + | 0.996896i | \(0.474916\pi\) |
−0.902699 | + | 0.430272i | \(0.858418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7248 | + | 25.5040i | 0.477986 | + | 0.827896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.8204 | − | 3.39467i | −0.350877 | − | 0.110080i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.9988 | 0.842184 | 0.421092 | − | 0.907018i | \(-0.361647\pi\) | ||||
0.421092 | + | 0.907018i | \(0.361647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.5677 | − | 18.3038i | 0.341962 | − | 0.592296i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.8305 | + | 39.3598i | −1.38451 | + | 1.27232i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.0522 | + | 17.6647i | −0.873562 | + | 0.570424i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3604 | − | 21.4088i | 0.398722 | − | 0.690607i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.8625 | + | 13.1274i | 0.607834 | + | 0.423024i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.8040 | − | 20.4451i | −0.379984 | − | 0.658152i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9810 | − | 22.4838i | 0.417442 | − | 0.723031i | −0.578239 | − | 0.815867i | \(-0.696260\pi\) |
0.995681 | + | 0.0928360i | \(0.0295932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.69619 | + | 7.59955i | 0.0544893 | + | 0.244133i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.97206 | + | 6.87981i | 0.127469 | + | 0.220783i | 0.922696 | − | 0.385530i | \(-0.125981\pi\) |
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.360130 | + | 6.55643i | 0.0115452 | + | 0.210189i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5184 | + | 4.24110i | 0.432936 | + | 0.135824i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.1274 | + | 45.2540i | 0.835889 | + | 1.44780i | 0.893304 | + | 0.449452i | \(0.148381\pi\) |
−0.0574149 | + | 0.998350i | \(0.518286\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.3464 | + | 57.7577i | 1.06576 | + | 1.84594i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.429654 | − | 5.07822i | 0.0137178 | − | 0.162135i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.8379 | 1.23874 | 0.619369 | − | 0.785100i | \(-0.287389\pi\) | ||||
0.619369 | + | 0.785100i | \(0.287389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.75304 | −0.183307 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.7982 | − | 11.7693i | 1.33045 | − | 0.374622i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.70914 | − | 4.69236i | −0.0861455 | − | 0.149208i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4689 | − | 26.7929i | 0.491385 | − | 0.851104i | −0.508565 | − | 0.861023i | \(-0.669824\pi\) |
0.999951 | + | 0.00991892i | \(0.00315734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44.1679 | − | 13.8567i | −1.40163 | − | 0.439728i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0122 | − | 31.1981i | 0.571025 | − | 0.989045i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.0670 | 1.49063 | 0.745313 | − | 0.666714i | \(-0.232300\pi\) | ||||
0.745313 | + | 0.666714i | \(0.232300\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.79353 | − | 6.82688i | 0.0883834 | − | 0.215993i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))