Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\), degree \(1\), 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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.8 | ||
Root | \(1.23291 + 0.692769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.q.901.7 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40101 | + | 0.192769i | 0.990667 | + | 0.136308i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.92568 | + | 0.540143i | 0.962840 | + | 0.270072i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0802864 | 0.0303454 | 0.0151727 | − | 0.999885i | \(-0.495170\pi\) | ||||
0.0151727 | + | 0.999885i | \(0.495170\pi\) | |||||||
\(8\) | 2.59378 | + | 1.12796i | 0.917041 | + | 0.398794i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.41649i | − | 0.728599i | −0.931282 | − | 0.364300i | \(-0.881308\pi\) | ||
0.931282 | − | 0.364300i | \(-0.118692\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.26785i | − | 1.46104i | −0.682892 | − | 0.730520i | \(-0.739278\pi\) | ||
0.682892 | − | 0.730520i | \(-0.260722\pi\) | |||||||
\(14\) | 0.112482 | + | 0.0154767i | 0.0300622 | + | 0.00413632i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.41649 | + | 2.08029i | 0.854123 | + | 0.520072i | ||||
\(17\) | 0.255918 | 0.0620692 | 0.0310346 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310346 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.95864i | − | 1.59642i | −0.602378 | − | 0.798211i | \(-0.705780\pi\) | ||
0.602378 | − | 0.798211i | \(-0.294220\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.465824 | − | 3.38554i | 0.0993139 | − | 0.721799i | ||||
\(23\) | 1.64542 | 0.343093 | 0.171546 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171546 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.01548 | − | 7.38033i | 0.199151 | − | 1.44740i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.154606 | + | 0.0433661i | 0.0292178 | + | 0.00819543i | ||||
\(29\) | 4.51516i | 0.838444i | 0.907884 | + | 0.419222i | \(0.137697\pi\) | ||||
−0.907884 | + | 0.419222i | \(0.862303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.29484 | 1.48980 | 0.744899 | − | 0.667177i | \(-0.232498\pi\) | ||||
0.744899 | + | 0.667177i | \(0.232498\pi\) | |||||||
\(32\) | 4.38554 | + | 3.57310i | 0.775261 | + | 0.631641i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.358545 | + | 0.0493330i | 0.0614899 | + | 0.00846053i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.67241i | − | 0.439341i | −0.975574 | − | 0.219671i | \(-0.929502\pi\) | ||
0.975574 | − | 0.219671i | \(-0.0704983\pi\) | |||||||
\(38\) | 1.34141 | − | 9.74915i | 0.217605 | − | 1.58152i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.11921 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.08890i | 0.623551i | 0.950156 | + | 0.311776i | \(0.100924\pi\) | ||||
−0.950156 | + | 0.311776i | \(0.899076\pi\) | |||||||
\(44\) | 1.30525 | − | 4.65339i | 0.196774 | − | 0.701525i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.30525 | + | 0.317185i | 0.339891 | + | 0.0467663i | ||||
\(47\) | −5.70272 | −0.831827 | −0.415914 | − | 0.909404i | \(-0.636538\pi\) | ||||
−0.415914 | + | 0.909404i | \(0.636538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99355 | −0.999079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.84539 | − | 10.1442i | 0.394585 | − | 1.40675i | ||||
\(53\) | 11.5627i | 1.58826i | 0.607749 | + | 0.794129i | \(0.292073\pi\) | ||||
−0.607749 | + | 0.794129i | \(0.707927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.208245 | + | 0.0905597i | 0.0278280 | + | 0.0121016i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.870381 | + | 6.32580i | −0.114287 | + | 0.830618i | ||||
\(59\) | 12.6963i | 1.65291i | 0.563000 | + | 0.826457i | \(0.309647\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.9403i | − | 1.52879i | −0.644746 | − | 0.764397i | \(-0.723037\pi\) | ||
0.644746 | − | 0.764397i | \(-0.276963\pi\) | |||||||
\(62\) | 11.6212 | + | 1.59899i | 1.47589 | + | 0.203071i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.45542 | + | 5.85136i | 0.681927 | + | 0.731420i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.27979i | 0.889367i | 0.895688 | + | 0.444684i | \(0.146684\pi\) | ||||
−0.895688 | + | 0.444684i | \(0.853316\pi\) | |||||||
\(68\) | 0.492816 | + | 0.138232i | 0.0597628 | + | 0.0167631i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3481 | 1.34678 | 0.673388 | − | 0.739289i | \(-0.264838\pi\) | ||||
0.673388 | + | 0.739289i | \(0.264838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0779 | −1.41361 | −0.706803 | − | 0.707411i | \(-0.749863\pi\) | ||||
−0.706803 | + | 0.707411i | \(0.749863\pi\) | |||||||
\(74\) | 0.515157 | − | 3.74408i | 0.0598857 | − | 0.435241i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.75866 | − | 13.4001i | 0.431148 | − | 1.53710i | ||||
\(77\) | − | 0.194011i | − | 0.0221096i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50539 | 0.619405 | 0.309702 | − | 0.950834i | \(-0.399771\pi\) | ||||
0.309702 | + | 0.950834i | \(0.399771\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.3751 | + | 1.56513i | 1.25617 | + | 0.172840i | ||||
\(83\) | − | 9.20811i | − | 1.01072i | −0.862908 | − | 0.505361i | \(-0.831359\pi\) | ||
0.862908 | − | 0.505361i | \(-0.168641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.788212 | + | 5.72861i | −0.0849950 | + | 0.617731i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.72570 | − | 6.26785i | 0.290561 | − | 0.668155i | ||||
\(89\) | −11.9173 | −1.26323 | −0.631615 | − | 0.775283i | \(-0.717607\pi\) | ||||
−0.631615 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.422937i | − | 0.0443358i | ||||||
\(92\) | 3.16855 | + | 0.888760i | 0.330344 | + | 0.0926597i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.98959 | − | 1.09931i | −0.824064 | − | 0.113385i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50539 | 0.863592 | 0.431796 | − | 0.901971i | \(-0.357880\pi\) | ||||
0.431796 | + | 0.901971i | \(0.357880\pi\) | |||||||
\(98\) | −9.79807 | − | 1.34814i | −0.989754 | − | 0.136183i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.56270i | 0.752516i | 0.926515 | + | 0.376258i | \(0.122789\pi\) | ||||
−0.926515 | + | 0.376258i | \(0.877211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.78544 | −0.175925 | −0.0879624 | − | 0.996124i | \(-0.528036\pi\) | ||||
−0.0879624 | + | 0.996124i | \(0.528036\pi\) | |||||||
\(104\) | 5.94192 | − | 13.6637i | 0.582653 | − | 1.33983i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.22893 | + | 16.1995i | −0.216492 | + | 1.57343i | ||||
\(107\) | − | 10.4705i | − | 1.01222i | −0.862469 | − | 0.506110i | \(-0.831083\pi\) | ||
0.862469 | − | 0.506110i | \(-0.168917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.64298i | 0.348934i | 0.984663 | + | 0.174467i | \(0.0558203\pi\) | ||||
−0.984663 | + | 0.174467i | \(0.944180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.274298 | + | 0.167019i | 0.0259187 | + | 0.0157818i | ||||
\(113\) | −8.83298 | −0.830937 | −0.415468 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415468 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.43883 | + | 8.69475i | −0.226440 | + | 0.807287i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.44744 | + | 17.7877i | −0.225305 | + | 1.63749i | ||||
\(119\) | 0.0205467 | 0.00188351 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.16057 | 0.469143 | ||||||||
\(122\) | 2.30171 | − | 16.7285i | 0.208387 | − | 1.51452i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.9732 | + | 4.48040i | 1.43444 | + | 0.402352i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.69628 | −0.771670 | −0.385835 | − | 0.922568i | \(-0.626087\pi\) | ||||
−0.385835 | + | 0.922568i | \(0.626087\pi\) | |||||||
\(128\) | 6.51516 | + | 9.24947i | 0.575864 | + | 0.817546i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.7916i | − | 0.942868i | −0.881901 | − | 0.471434i | \(-0.843736\pi\) | ||
0.881901 | − | 0.471434i | \(-0.156264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.558684i | − | 0.0484440i | ||||||
\(134\) | −1.40331 | + | 10.1991i | −0.121228 | + | 0.881066i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.663796 | + | 0.288665i | 0.0569200 | + | 0.0247528i | ||||
\(137\) | −11.5421 | −0.986112 | −0.493056 | − | 0.869997i | \(-0.664120\pi\) | ||||
−0.493056 | + | 0.869997i | \(0.664120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.214558i | − | 0.0181986i | −0.999959 | − | 0.00909928i | \(-0.997104\pi\) | ||
0.999959 | − | 0.00909928i | \(-0.00289643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.8989 | + | 2.18757i | 1.33421 | + | 0.183576i | ||||
\(143\) | −12.7297 | −1.06451 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.9212 | − | 2.32823i | −1.40041 | − | 0.192686i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.44348 | − | 5.14621i | 0.118654 | − | 0.423015i | ||||
\(149\) | − | 23.0475i | − | 1.88813i | −0.329762 | − | 0.944064i | \(-0.606969\pi\) | ||
0.329762 | − | 0.944064i | \(-0.393031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.48573 | 0.771938 | 0.385969 | − | 0.922512i | \(-0.373867\pi\) | ||||
0.385969 | + | 0.922512i | \(0.373867\pi\) | |||||||
\(152\) | 7.84906 | − | 18.0492i | 0.636643 | − | 1.46398i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0373993 | − | 0.271812i | 0.00301372 | − | 0.0219033i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.34413i | 0.506316i | 0.967425 | + | 0.253158i | \(0.0814693\pi\) | ||||
−0.967425 | + | 0.253158i | \(0.918531\pi\) | |||||||
\(158\) | 7.71313 | + | 1.06127i | 0.613624 | + | 0.0844298i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.132104 | 0.0104113 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4100i | 0.972030i | 0.873951 | + | 0.486015i | \(0.161550\pi\) | ||||
−0.873951 | + | 0.486015i | \(0.838450\pi\) | |||||||
\(164\) | 15.6350 | + | 4.38554i | 1.22089 | + | 0.342453i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.77504 | − | 12.9007i | 0.137769 | − | 1.00129i | ||||
\(167\) | −23.2654 | −1.80033 | −0.900166 | − | 0.435547i | \(-0.856555\pi\) | ||||
−0.900166 | + | 0.435547i | \(0.856555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.7503 | −1.13464 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.20859 | + | 7.87391i | −0.168403 | + | 0.600380i | ||||
\(173\) | 8.63897i | 0.656809i | 0.944537 | + | 0.328404i | \(0.106511\pi\) | ||||
−0.944537 | + | 0.328404i | \(0.893489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.02699 | − | 8.25592i | 0.378924 | − | 0.622313i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.6963 | − | 2.29728i | −1.25144 | − | 0.172188i | ||||
\(179\) | − | 9.40544i | − | 0.702996i | −0.936189 | − | 0.351498i | \(-0.885672\pi\) | ||
0.936189 | − | 0.351498i | \(-0.114328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.43487i | 0.478300i | 0.970983 | + | 0.239150i | \(0.0768688\pi\) | ||||
−0.970983 | + | 0.239150i | \(0.923131\pi\) | |||||||
\(182\) | 0.0815289 | − | 0.592540i | 0.00604333 | − | 0.0439220i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.26785 | + | 1.85596i | 0.314630 | + | 0.136823i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.618423i | − | 0.0452236i | ||||||
\(188\) | −10.9816 | − | 3.08029i | −0.800917 | − | 0.224653i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.56270 | 0.402503 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4227 | −1.32609 | −0.663046 | − | 0.748578i | \(-0.730737\pi\) | ||||
−0.663046 | + | 0.748578i | \(0.730737\pi\) | |||||||
\(194\) | 11.9162 | + | 1.63957i | 0.855531 | + | 0.117714i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.4674 | − | 3.77752i | −0.961954 | − | 0.269823i | ||||
\(197\) | 18.0239i | 1.28415i | 0.766643 | + | 0.642074i | \(0.221926\pi\) | ||||
−0.766643 | + | 0.642074i | \(0.778074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1214 | 1.42637 | 0.713183 | − | 0.700977i | \(-0.247253\pi\) | ||||
0.713183 | + | 0.700977i | \(0.247253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.45785 | + | 10.5954i | −0.102574 | + | 0.745493i | ||||
\(203\) | 0.362505i | 0.0254429i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.50143 | − | 0.344177i | −0.174283 | − | 0.0239800i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.9586 | − | 17.9976i | 0.759845 | − | 1.24791i | ||||
\(209\) | −16.8155 | −1.16315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.25592i | 0.224147i | 0.993700 | + | 0.112073i | \(0.0357492\pi\) | ||||
−0.993700 | + | 0.112073i | \(0.964251\pi\) | |||||||
\(212\) | −6.24551 | + | 22.2661i | −0.428943 | + | 1.52924i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.01838 | − | 14.6693i | 0.137974 | − | 1.00277i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.665963 | 0.0452085 | ||||||||
\(218\) | −0.702253 | + | 5.10387i | −0.0475626 | + | 0.345678i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.34814i | − | 0.0906856i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9911 | 1.80746 | 0.903730 | − | 0.428104i | \(-0.140818\pi\) | ||||
0.903730 | + | 0.428104i | \(0.140818\pi\) | |||||||
\(224\) | 0.352099 | + | 0.286871i | 0.0235256 | + | 0.0191674i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.3751 | − | 1.70272i | −0.823181 | − | 0.113263i | ||||
\(227\) | 19.8219i | 1.31563i | 0.753180 | + | 0.657814i | \(0.228519\pi\) | ||||
−0.753180 | + | 0.657814i | \(0.771481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6797i | 1.43264i | 0.697773 | + | 0.716319i | \(0.254174\pi\) | ||||
−0.697773 | + | 0.716319i | \(0.745826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.09291 | + | 11.7113i | −0.334366 | + | 0.768887i | ||||
\(233\) | −17.2733 | −1.13161 | −0.565807 | − | 0.824538i | \(-0.691435\pi\) | ||||
−0.565807 | + | 0.824538i | \(0.691435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.85781 | + | 24.4490i | −0.446405 | + | 1.59149i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0287862 | + | 0.00396076i | 0.00186594 | + | 0.000256738i | ||||
\(239\) | 16.3718 | 1.05900 | 0.529502 | − | 0.848309i | \(-0.322379\pi\) | ||||
0.529502 | + | 0.848309i | \(0.322379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.82654 | −0.439736 | −0.219868 | − | 0.975530i | \(-0.570563\pi\) | ||||
−0.219868 | + | 0.975530i | \(0.570563\pi\) | |||||||
\(242\) | 7.23003 | + | 0.994797i | 0.464764 | + | 0.0639480i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.44945 | − | 22.9931i | 0.412884 | − | 1.47198i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.6571 | −2.33243 | ||||||||
\(248\) | 21.5150 | + | 9.35624i | 1.36621 | + | 0.594122i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.96969i | 0.187445i | 0.995598 | + | 0.0937225i | \(0.0298766\pi\) | ||||
−0.995598 | + | 0.0937225i | \(0.970123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.97613i | − | 0.249977i | ||||||
\(254\) | −12.1836 | − | 1.67637i | −0.764467 | − | 0.105185i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.34482 | + | 14.2146i | 0.459051 | + | 0.888410i | ||||
\(257\) | −5.03031 | −0.313782 | −0.156891 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156891 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.214558i | − | 0.0133320i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.08029 | − | 15.1192i | 0.128521 | − | 0.934068i | ||||
\(263\) | 2.70585 | 0.166850 | 0.0834248 | − | 0.996514i | \(-0.473414\pi\) | ||||
0.0834248 | + | 0.996514i | \(0.473414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.107697 | − | 0.782724i | 0.00660331 | − | 0.0479919i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.93213 | + | 14.0185i | −0.240193 | + | 0.856319i | ||||
\(269\) | 22.3718i | 1.36403i | 0.731337 | + | 0.682017i | \(0.238897\pi\) | ||||
−0.731337 | + | 0.682017i | \(0.761103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.869741 | −0.0528330 | −0.0264165 | − | 0.999651i | \(-0.508410\pi\) | ||||
−0.0264165 | + | 0.999651i | \(0.508410\pi\) | |||||||
\(272\) | 0.874341 | + | 0.532383i | 0.0530147 | + | 0.0322804i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.1707 | − | 2.22496i | −0.976908 | − | 0.134415i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.6733i | − | 1.72281i | −0.507918 | − | 0.861406i | \(-0.669585\pi\) | ||
0.507918 | − | 0.861406i | \(-0.330415\pi\) | |||||||
\(278\) | 0.0413600 | − | 0.300599i | 0.00248061 | − | 0.0180287i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1429 | −0.903349 | −0.451674 | − | 0.892183i | \(-0.649173\pi\) | ||||
−0.451674 | + | 0.892183i | \(0.649173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.23225i | 0.370469i | 0.982694 | + | 0.185234i | \(0.0593044\pi\) | ||||
−0.982694 | + | 0.185234i | \(0.940696\pi\) | |||||||
\(284\) | 21.8529 | + | 6.12962i | 1.29673 | + | 0.363726i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.8345 | − | 2.45389i | −1.05458 | − | 0.145102i | ||||
\(287\) | 0.651862 | 0.0384782 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9345 | −0.996147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23.2581 | − | 6.52377i | −1.36108 | − | 0.381775i | ||||
\(293\) | − | 21.5054i | − | 1.25636i | −0.778069 | − | 0.628179i | \(-0.783800\pi\) | ||
0.778069 | − | 0.628179i | \(-0.216200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.01437 | − | 6.93165i | 0.175207 | − | 0.402894i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.44284 | − | 32.2899i | 0.257367 | − | 1.87051i | ||||
\(299\) | − | 8.66781i | − | 0.501272i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.328283i | 0.0189219i | ||||||||
\(302\) | 13.2896 | + | 1.82855i | 0.764733 | + | 0.105221i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.4760 | − | 23.7741i | 0.830253 | − | 1.36354i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.57706i | − | 0.204154i | −0.994777 | − | 0.102077i | \(-0.967451\pi\) | ||
0.994777 | − | 0.102077i | \(-0.0325488\pi\) | |||||||
\(308\) | 0.104794 | − | 0.373604i | 0.00597118 | − | 0.0212880i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.49461 | 0.141456 | 0.0707282 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707282 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.57246 | 0.541068 | 0.270534 | − | 0.962710i | \(-0.412800\pi\) | ||||
0.270534 | + | 0.962710i | \(0.412800\pi\) | |||||||
\(314\) | −1.22295 | + | 8.88821i | −0.0690150 | + | 0.501591i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6016 | + | 2.97370i | 0.596388 | + | 0.167284i | ||||
\(317\) | − | 3.16702i | − | 0.177877i | −0.996037 | − | 0.0889387i | \(-0.971652\pi\) | ||
0.996037 | − | 0.0889387i | \(-0.0283475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9108 | 0.610889 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.185080 | + | 0.0254656i | 0.0103141 | + | 0.00141914i | ||||
\(323\) | − | 1.78084i | − | 0.0990887i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.39227 | + | 17.3866i | −0.132495 | + | 0.962957i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.0595 | + | 9.15814i | 1.16281 | + | 0.505674i | ||||
\(329\) | −0.457851 | −0.0252421 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5118i | 0.907573i | 0.891111 | + | 0.453786i | \(0.149927\pi\) | ||||
−0.891111 | + | 0.453786i | \(0.850073\pi\) | |||||||
\(332\) | 4.97370 | − | 17.7319i | 0.272967 | − | 0.973163i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −32.5952 | − | 4.48484i | −1.78353 | − | 0.245400i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8330 | −0.644584 | −0.322292 | − | 0.946640i | \(-0.604453\pi\) | ||||
−0.322292 | + | 0.946640i | \(0.604453\pi\) | |||||||
\(338\) | −20.6653 | − | 2.84339i | −1.12405 | − | 0.154660i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.0444i | − | 1.08547i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.12349 | −0.0606628 | ||||||||
\(344\) | −4.61211 | + | 10.6057i | −0.248668 | + | 0.571822i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.66532 | + | 12.1033i | −0.0895283 | + | 0.650678i | ||||
\(347\) | 23.9713i | 1.28684i | 0.765511 | + | 0.643422i | \(0.222486\pi\) | ||||
−0.765511 | + | 0.643422i | \(0.777514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.91570i | − | 0.477247i | −0.971112 | − | 0.238623i | \(-0.923304\pi\) | ||
0.971112 | − | 0.238623i | \(-0.0766961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.63437 | − | 10.5976i | 0.460213 | − | 0.564855i | ||||
\(353\) | 7.35606 | 0.391524 | 0.195762 | − | 0.980651i | \(-0.437282\pi\) | ||||
0.195762 | + | 0.980651i | \(0.437282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −22.9489 | − | 6.43704i | −1.21629 | − | 0.341162i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.81307 | − | 13.1772i | 0.0958240 | − | 0.696434i | ||||
\(359\) | −25.2114 | −1.33061 | −0.665304 | − | 0.746572i | \(-0.731698\pi\) | ||||
−0.665304 | + | 0.746572i | \(0.731698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.4227 | −1.54856 | ||||||||
\(362\) | −1.24044 | + | 9.01534i | −0.0651961 | + | 0.473836i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.228446 | − | 0.814441i | 0.0119738 | − | 0.0426883i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.86573 | 0.306189 | 0.153094 | − | 0.988212i | \(-0.451076\pi\) | ||||
0.153094 | + | 0.988212i | \(0.451076\pi\) | |||||||
\(368\) | 5.62155 | + | 3.42294i | 0.293043 | + | 0.178433i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.928327i | 0.0481963i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5063i | 1.42422i | 0.702067 | + | 0.712111i | \(0.252261\pi\) | ||||
−0.702067 | + | 0.712111i | \(0.747739\pi\) | |||||||
\(374\) | 0.119213 | − | 0.866420i | 0.00616434 | − | 0.0448015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.7916 | − | 6.43244i | −0.762820 | − | 0.331728i | ||||
\(377\) | 23.7852 | 1.22500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7549i | 0.603807i | 0.953339 | + | 0.301903i | \(0.0976220\pi\) | ||||
−0.953339 | + | 0.301903i | \(0.902378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.79341 | + | 1.07231i | 0.398746 | + | 0.0548643i | ||||
\(383\) | 34.3335 | 1.75436 | 0.877180 | − | 0.480162i | \(-0.159422\pi\) | ||||
0.877180 | + | 0.480162i | \(0.159422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.8104 | − | 3.55131i | −1.31372 | − | 0.180757i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.3787 | + | 4.59413i | 0.831501 | + | 0.233232i | ||||
\(389\) | − | 2.89515i | − | 0.146790i | −0.997303 | − | 0.0733951i | \(-0.976617\pi\) | ||
0.997303 | − | 0.0733951i | \(-0.0233834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.421092 | 0.0212955 | ||||||||
\(392\) | −18.1398 | − | 7.88844i | −0.916196 | − | 0.398427i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.47444 | + | 25.2517i | −0.175040 | + | 1.27216i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.9099i | 1.14982i | 0.818218 | + | 0.574909i | \(0.194962\pi\) | ||||
−0.818218 | + | 0.574909i | \(0.805038\pi\) | |||||||
\(398\) | 28.1903 | + | 3.87877i | 1.41305 | + | 0.194425i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4337 | 0.620910 | 0.310455 | − | 0.950588i | \(-0.399519\pi\) | ||||
0.310455 | + | 0.950588i | \(0.399519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 43.6960i | − | 2.17665i | ||||||
\(404\) | −4.08494 | + | 14.5633i | −0.203233 | + | 0.724553i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0698797 | + | 0.507875i | −0.00346807 | + | 0.0252054i | ||||
\(407\) | −6.45785 | −0.320104 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.0886 | −1.58668 | −0.793340 | − | 0.608778i | \(-0.791660\pi\) | ||||
−0.793340 | + | 0.608778i | \(0.791660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.43819 | − | 0.964394i | −0.169388 | − | 0.0475123i | ||||
\(413\) | 1.01934i | 0.0501583i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.8226 | − | 23.1024i | 0.922853 | − | 1.13269i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.5587 | − | 3.24150i | −1.15230 | − | 0.158547i | ||||
\(419\) | − | 16.1364i | − | 0.788317i | −0.919043 | − | 0.394158i | \(-0.871036\pi\) | ||
0.919043 | − | 0.394158i | \(-0.128964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.7675i | 1.40204i | 0.713141 | + | 0.701021i | \(0.247272\pi\) | ||||
−0.713141 | + | 0.701021i | \(0.752728\pi\) | |||||||
\(422\) | −0.627639 | + | 4.56159i | −0.0305530 | + | 0.222055i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.0422 | + | 29.9911i | −0.633388 | + | 1.45650i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.958640i | − | 0.0463918i | ||||||
\(428\) | 5.65556 | − | 20.1628i | 0.273372 | − | 0.974605i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7297 | −1.19119 | −0.595594 | − | 0.803285i | \(-0.703083\pi\) | ||||
−0.595594 | + | 0.803285i | \(0.703083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.48816 | −0.215687 | −0.107844 | − | 0.994168i | \(-0.534395\pi\) | ||||
−0.107844 | + | 0.994168i | \(0.534395\pi\) | |||||||
\(434\) | 0.933023 | + | 0.128377i | 0.0447865 | + | 0.00616228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.96773 | + | 7.01522i | −0.0942373 | + | 0.335968i | ||||
\(437\) | − | 11.4499i | − | 0.547721i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.96081 | 0.284494 | 0.142247 | − | 0.989831i | \(-0.454567\pi\) | ||||
0.142247 | + | 0.989831i | \(0.454567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.259879 | − | 1.88876i | 0.0123612 | − | 0.0898392i | ||||
\(443\) | 14.2924i | 0.679053i | 0.940597 | + | 0.339526i | \(0.110267\pi\) | ||||
−0.940597 | + | 0.339526i | \(0.889733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 37.8149 | + | 5.20304i | 1.79059 | + | 0.246371i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.437996 | + | 0.469784i | 0.0206933 | + | 0.0221952i | ||||
\(449\) | −24.5529 | −1.15872 | −0.579362 | − | 0.815070i | \(-0.696698\pi\) | ||||
−0.579362 | + | 0.815070i | \(0.696698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19.6200i | − | 0.923870i | ||||||
\(452\) | −17.0095 | − | 4.77107i | −0.800060 | − | 0.224412i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.82105 | + | 27.7708i | −0.179331 | + | 1.30335i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.9108 | 1.35239 | 0.676196 | − | 0.736722i | \(-0.263627\pi\) | ||||
0.676196 | + | 0.736722i | \(0.263627\pi\) | |||||||
\(458\) | −4.17917 | + | 30.3736i | −0.195280 | + | 1.41927i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.35458i | 0.202813i | 0.994845 | + | 0.101407i | \(0.0323343\pi\) | ||||
−0.994845 | + | 0.101407i | \(0.967666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1303 | 0.517267 | 0.258634 | − | 0.965976i | \(-0.416728\pi\) | ||||
0.258634 | + | 0.965976i | \(0.416728\pi\) | |||||||
\(464\) | −9.39282 | + | 15.4260i | −0.436051 | + | 0.716134i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2002 | − | 3.32976i | −1.12105 | − | 0.154248i | ||||
\(467\) | − | 19.1257i | − | 0.885030i | −0.896761 | − | 0.442515i | \(-0.854086\pi\) | ||
0.896761 | − | 0.442515i | \(-0.145914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.584467i | 0.0269882i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.3209 | + | 32.9314i | −0.659172 | + | 1.51579i | ||||
\(473\) | 9.88079 | 0.454319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0395664 | + | 0.0110982i | 0.00181352 | + | 0.000508684i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.9371 | + | 3.15597i | 1.04912 | + | 0.144351i | ||||
\(479\) | 25.6358 | 1.17133 | 0.585666 | − | 0.810553i | \(-0.300833\pi\) | ||||
0.585666 | + | 0.810553i | \(0.300833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0779 | −0.641895 | ||||||||
\(482\) | −9.56407 | − | 1.31594i | −0.435632 | − | 0.0599395i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.93761 | + | 2.78745i | 0.451710 | + | 0.126702i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8434 | −0.581992 | −0.290996 | − | 0.956724i | \(-0.593987\pi\) | ||||
−0.290996 | + | 0.956724i | \(0.593987\pi\) | |||||||
\(488\) | 13.4681 | − | 30.9704i | 0.609673 | − | 1.40197i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9887i | 0.766689i | 0.923605 | + | 0.383344i | \(0.125228\pi\) | ||||
−0.923605 | + | 0.383344i | \(0.874772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15551i | 0.0520415i | ||||||||
\(494\) | −51.3571 | − | 7.06634i | −2.31066 | − | 0.317930i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.3393 | + | 17.2557i | 1.27247 | + | 0.774802i | ||||
\(497\) | 0.911101 | 0.0408684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0521i | 0.629060i | 0.949248 | + | 0.314530i | \(0.101847\pi\) | ||||
−0.949248 | + | 0.314530i | \(0.898153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.572463 | + | 4.16057i | −0.0255503 | + | 0.185695i | ||||
\(503\) | 9.53258 | 0.425037 | 0.212518 | − | 0.977157i | \(-0.431833\pi\) | ||||
0.212518 | + | 0.977157i | \(0.431833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.766474 | − | 5.57062i | 0.0340739 | − | 0.247644i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.7462 | − | 4.69723i | −0.742995 | − | 0.208406i | ||||
\(509\) | 30.3450i | 1.34502i | 0.740088 | + | 0.672510i | \(0.234784\pi\) | ||||
−0.740088 | + | 0.672510i | \(0.765216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.969687 | −0.0428964 | ||||||||
\(512\) | 7.55007 | + | 21.3306i | 0.333669 | + | 0.942690i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.04754 | − | 0.969687i | −0.310854 | − | 0.0427710i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.7806i | 0.606069i | ||||||||
\(518\) | 0.0413600 | − | 0.300599i | 0.00181726 | − | 0.0132075i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4245 | −0.631949 | −0.315975 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315975 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.2207i | − | 1.23401i | −0.786961 | − | 0.617003i | \(-0.788346\pi\) | ||
0.786961 | − | 0.617003i | \(-0.211654\pi\) | |||||||
\(524\) | 5.82902 | − | 20.7812i | 0.254642 | − | 0.907832i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.79093 | + | 0.521603i | 0.165292 | + | 0.0227430i | ||||
\(527\) | 2.12280 | 0.0924706 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2926 | −0.882287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.301769 | − | 1.07585i | 0.0130834 | − | 0.0466439i | ||||
\(533\) | − | 42.7708i | − | 1.85261i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.21130 | + | 18.8822i | −0.354674 | + | 0.815586i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.31258 | + | 31.3432i | −0.185929 | + | 1.35130i | ||||
\(539\) | 16.8999i | 0.727928i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.4695i | 0.579100i | 0.957163 | + | 0.289550i | \(0.0935056\pi\) | ||||
−0.957163 | + | 0.289550i | \(0.906494\pi\) | |||||||
\(542\) | −1.21852 | − | 0.167659i | −0.0523399 | − | 0.00720156i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.12234 | + | 0.914421i | 0.0481198 | + | 0.0392055i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.42773i | − | 0.189316i | −0.995510 | − | 0.0946581i | \(-0.969824\pi\) | ||
0.995510 | − | 0.0946581i | \(-0.0301758\pi\) | |||||||
\(548\) | −22.2265 | − | 6.23441i | −0.949469 | − | 0.266321i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.4193 | 1.33851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.442008 | 0.0187961 | ||||||||
\(554\) | 5.52731 | − | 40.1717i | 0.234833 | − | 1.70673i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.115892 | − | 0.413170i | 0.00491492 | − | 0.0175223i | ||||
\(557\) | − | 40.2017i | − | 1.70340i | −0.524030 | − | 0.851700i | \(-0.675572\pi\) | ||
0.524030 | − | 0.851700i | \(-0.324428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.5397 | 0.911033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.2154 | − | 2.91907i | −0.894917 | − | 0.123134i | ||||
\(563\) | 13.1128i | 0.552637i | 0.961066 | + | 0.276319i | \(0.0891145\pi\) | ||||
−0.961066 | + | 0.276319i | \(0.910885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.20138 | + | 8.73146i | −0.0504978 | + | 0.367011i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.4346 | + | 12.8002i | 1.23505 | + | 0.537086i | ||||
\(569\) | 11.0257 | 0.462222 | 0.231111 | − | 0.972927i | \(-0.425764\pi\) | ||||
0.231111 | + | 0.972927i | \(0.425764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 45.6960i | − | 1.91232i | −0.292847 | − | 0.956159i | \(-0.594603\pi\) | ||
0.292847 | − | 0.956159i | \(-0.405397\pi\) | |||||||
\(572\) | −24.5134 | − | 6.87587i | −1.02496 | − | 0.287495i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.913268 | + | 0.125659i | 0.0381191 | + | 0.00524489i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2685 | 0.718899 | 0.359449 | − | 0.933165i | \(-0.382965\pi\) | ||||
0.359449 | + | 0.933165i | \(0.382965\pi\) | |||||||
\(578\) | −23.7255 | − | 3.26444i | −0.986850 | − | 0.135783i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.739286i | − | 0.0306707i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.9411 | 1.15720 | ||||||||
\(584\) | −31.3273 | − | 13.6233i | −1.29633 | − | 0.563737i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.14557 | − | 30.1294i | 0.171252 | − | 1.24463i | ||||
\(587\) | − | 34.7155i | − | 1.43286i | −0.697657 | − | 0.716432i | \(-0.745774\pi\) | ||
0.697657 | − | 0.716432i | \(-0.254226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 57.7208i | − | 2.37835i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.55938 | − | 9.13026i | 0.228489 | − | 0.375251i | ||||
\(593\) | −9.34022 | −0.383557 | −0.191778 | − | 0.981438i | \(-0.561425\pi\) | ||||
−0.191778 | + | 0.981438i | \(0.561425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.4490 | − | 44.3822i | 0.509930 | − | 1.81797i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.67088 | − | 12.1437i | 0.0683274 | − | 0.496594i | ||||
\(599\) | 13.9110 | 0.568389 | 0.284195 | − | 0.958767i | \(-0.408274\pi\) | ||||
0.284195 | + | 0.958767i | \(0.408274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7330 | 0.478600 | 0.239300 | − | 0.970946i | \(-0.423082\pi\) | ||||
0.239300 | + | 0.970946i | \(0.423082\pi\) | |||||||
\(602\) | −0.0632826 | + | 0.459929i | −0.00257921 | + | 0.0187453i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.2665 | + | 5.12365i | 0.743253 | + | 0.208478i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8158 | 0.438998 | 0.219499 | − | 0.975613i | \(-0.429558\pi\) | ||||
0.219499 | + | 0.975613i | \(0.429558\pi\) | |||||||
\(608\) | 24.8639 | − | 30.5174i | 1.00837 | − | 1.23764i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.0411i | 1.21533i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.9632i | 0.725528i | 0.931881 | + | 0.362764i | \(0.118167\pi\) | ||||
−0.931881 | + | 0.362764i | \(0.881833\pi\) | |||||||
\(614\) | 0.689546 | − | 5.01152i | 0.0278278 | − | 0.202248i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.218837 | − | 0.503223i | 0.00881718 | − | 0.0202754i | ||||
\(617\) | 12.3576 | 0.497500 | 0.248750 | − | 0.968568i | \(-0.419980\pi\) | ||||
0.248750 | + | 0.968568i | \(0.419980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.99540i | − | 0.200782i | −0.994948 | − | 0.100391i | \(-0.967991\pi\) | ||
0.994948 | − | 0.100391i | \(-0.0320094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.49498 | + | 0.480883i | 0.140136 | + | 0.0192816i | ||||
\(623\) | −0.956795 | −0.0383332 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.4112 | + | 1.84527i | 0.536018 | + | 0.0737519i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.42674 | + | 12.2168i | −0.136742 | + | 0.487502i | ||||
\(629\) | − | 0.683917i | − | 0.0272696i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9674 | −0.715273 | −0.357636 | − | 0.933861i | \(-0.616417\pi\) | ||||
−0.357636 | + | 0.933861i | \(0.616417\pi\) | |||||||
\(632\) | 14.2798 | + | 6.20985i | 0.568019 | + | 0.247015i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.610502 | − | 4.43704i | 0.0242461 | − | 0.176217i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.8410i | 1.45969i | ||||||||
\(638\) | 15.2862 | + | 2.10327i | 0.605188 | + | 0.0832691i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.3638 | −1.08081 | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||||
−0.540403 | + | 0.841406i | \(0.681728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.27518i | − | 0.0897245i | −0.998993 | − | 0.0448623i | \(-0.985715\pi\) | ||
0.998993 | − | 0.0448623i | \(-0.0142849\pi\) | |||||||
\(644\) | 0.254391 | + | 0.0713553i | 0.0100244 | + | 0.00281179i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.343290 | − | 2.49498i | 0.0135066 | − | 0.0981638i | ||||
\(647\) | 12.4769 | 0.490516 | 0.245258 | − | 0.969458i | \(-0.421127\pi\) | ||||
0.245258 | + | 0.969458i | \(0.421127\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.6804 | 1.20431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.70320 | + | 23.8978i | −0.262518 | + | 0.935909i | ||||
\(653\) | 29.3055i | 1.14681i | 0.819271 | + | 0.573406i | \(0.194378\pi\) | ||||
−0.819271 | + | 0.573406i | \(0.805622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.7392 | + | 16.8903i | 1.08303 | + | 0.659455i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.641455 | − | 0.0882593i | −0.0250065 | − | 0.00344070i | ||||
\(659\) | 18.6009i | 0.724589i | 0.932064 | + | 0.362295i | \(0.118007\pi\) | ||||
−0.932064 | + | 0.362295i | \(0.881993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16.1318i | − | 0.627456i | −0.949513 | − | 0.313728i | \(-0.898422\pi\) | ||
0.949513 | − | 0.313728i | \(-0.101578\pi\) | |||||||
\(662\) | −3.18296 | + | 23.1333i | −0.123709 | + | 0.899102i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3864 | − | 23.8838i | 0.403069 | − | 0.926873i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.42931i | 0.287664i | ||||||||
\(668\) | −44.8018 | − | 12.5667i | −1.73343 | − | 0.486219i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8535 | −1.11388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1385 | 1.31594 | 0.657971 | − | 0.753043i | \(-0.271415\pi\) | ||||
0.657971 | + | 0.753043i | \(0.271415\pi\) | |||||||
\(674\) | −16.5782 | − | 2.28103i | −0.638567 | − | 0.0878619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.4043 | − | 7.96725i | −1.09247 | − | 0.306433i | ||||
\(677\) | 12.1940i | 0.468654i | 0.972158 | + | 0.234327i | \(0.0752886\pi\) | ||||
−0.972158 | + | 0.234327i | \(0.924711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.682867 | 0.0262060 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.86393 | − | 28.0825i | 0.147958 | − | 1.07533i | ||||
\(683\) | 21.8567i | 0.836322i | 0.908373 | + | 0.418161i | \(0.137325\pi\) | ||||
−0.908373 | + | 0.418161i | \(0.862675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.57403 | − | 0.216574i | −0.0600966 | − | 0.00826883i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.50608 | + | 13.9697i | −0.324291 | + | 0.532589i | ||||
\(689\) | 60.9106 | 2.32051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.17780i | − | 0.235015i | −0.993072 | − | 0.117507i | \(-0.962510\pi\) | ||
0.993072 | − | 0.117507i | \(-0.0374903\pi\) | |||||||
\(692\) | −4.66628 | + | 16.6359i | −0.177385 | + | 0.632402i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.62091 | + | 33.5841i | −0.175407 | + | 1.27483i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07785 | 0.0787043 | ||||||||
\(698\) | 1.71867 | − | 12.4910i | 0.0650525 | − | 0.472792i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9746i | 1.28320i | 0.767038 | + | 0.641601i | \(0.221730\pi\) | ||||
−0.767038 | + | 0.641601i | \(0.778270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.5963 | −0.701374 | ||||||||
\(704\) | 14.1398 | − | 13.1830i | 0.532912 | − | 0.496852i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3059 | + | 1.41802i | 0.387869 | + | 0.0533678i | ||||
\(707\) | 0.607181i | 0.0228354i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3441i | 0.839151i | 0.907720 | + | 0.419576i | \(0.137821\pi\) | ||||
−0.907720 | + | 0.419576i | \(0.862179\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30.9108 | − | 13.4422i | −1.15843 | − | 0.503768i | ||||
\(713\) | 13.6485 | 0.511139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.08029 | − | 18.1119i | 0.189859 | − | 0.676873i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.3216 | − | 4.85997i | −1.31819 | − | 0.181373i | ||||
\(719\) | 17.8427 | 0.665422 | 0.332711 | − | 0.943029i | \(-0.392037\pi\) | ||||
0.332711 | + | 0.943029i | \(0.392037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.143347 | −0.00533851 | ||||||||
\(722\) | −41.2216 | − | 5.67177i | −1.53411 | − | 0.211081i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.47575 | + | 12.3915i | −0.129175 | + | 0.460527i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9148 | 0.886953 | 0.443476 | − | 0.896286i | \(-0.353745\pi\) | ||||
0.443476 | + | 0.896286i | \(0.353745\pi\) | |||||||
\(728\) | 0.477055 | − | 1.09701i | 0.0176808 | − | 0.0406577i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.04642i | 0.0387034i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.6789i | − | 0.579112i | −0.957161 | − | 0.289556i | \(-0.906492\pi\) | ||
0.957161 | − | 0.289556i | \(-0.0935076\pi\) | |||||||
\(734\) | 8.21797 | + | 1.13073i | 0.303331 | + | 0.0417360i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.21603 | + | 5.87924i | 0.265987 | + | 0.216712i | ||||
\(737\) | 17.5915 | 0.647992 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 22.3083i | − | 0.820622i | −0.911946 | − | 0.410311i | \(-0.865420\pi\) | ||
0.911946 | − | 0.410311i | \(-0.134580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.178952 | + | 1.30060i | −0.00656955 | + | 0.0477465i | ||||
\(743\) | 9.78057 | 0.358814 | 0.179407 | − | 0.983775i | \(-0.442582\pi\) | ||||
0.179407 | + | 0.983775i | \(0.442582\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.30235 | + | 38.5367i | −0.194133 | + | 1.41093i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.334037 | − | 1.19089i | 0.0122136 | − | 0.0435431i | ||||
\(749\) | − | 0.840636i | − | 0.0307162i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.05399 | −0.293894 | −0.146947 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(752\) | −19.4833 | − | 11.8633i | −0.710483 | − | 0.432610i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33.3234 | + | 4.58504i | 1.21357 | + | 0.166977i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28.4889i | − | 1.03545i | −0.855549 | − | 0.517723i | \(-0.826780\pi\) | ||
0.855549 | − | 0.517723i | \(-0.173220\pi\) | |||||||
\(758\) | −2.26597 | + | 16.4687i | −0.0823037 | + | 0.598171i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.5005 | 0.779393 | 0.389697 | − | 0.920943i | \(-0.372580\pi\) | ||||
0.389697 | + | 0.920943i | \(0.372580\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.292482i | 0.0105886i | ||||||||
\(764\) | 10.7120 | + | 3.00465i | 0.387546 | + | 0.108705i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.1017 | + | 6.61842i | 1.73799 | + | 0.239133i | ||||
\(767\) | 66.8821 | 2.41497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5596 | 0.849580 | 0.424790 | − | 0.905292i | \(-0.360348\pi\) | ||||
0.424790 | + | 0.905292i | \(0.360348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −35.4762 | − | 9.95088i | −1.27682 | − | 0.358140i | ||||
\(773\) | − | 31.1655i | − | 1.12094i | −0.828173 | − | 0.560472i | \(-0.810620\pi\) | ||
0.828173 | − | 0.560472i | \(-0.189380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 22.0611 | + | 9.59373i | 0.791949 | + | 0.344395i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.558095 | − | 4.05615i | 0.0200087 | − | 0.145420i | ||||
\(779\) | − | 56.4987i | − | 2.02428i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27.4227i | − | 0.981260i | ||||||
\(782\) | 0.589955 | + | 0.0811733i | 0.0210968 | + | 0.00290275i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.8934 | − | 14.5486i | −0.853336 | − | 0.519593i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.07812i | 0.181015i | 0.995896 | + | 0.0905077i | \(0.0288490\pi\) | ||||
−0.995896 | + | 0.0905077i | \(0.971151\pi\) | |||||||
\(788\) | −9.73547 | + | 34.7082i | −0.346812 | + | 1.23643i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.709168 | −0.0252151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.8995 | −2.23363 | ||||||||
\(794\) | −4.41632 | + | 32.0972i | −0.156729 | + | 1.13909i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.7473 | + | 10.8684i | 1.37336 | + | 0.385221i | ||||
\(797\) | − | 1.43418i | − | 0.0508012i | −0.999677 | − | 0.0254006i | \(-0.991914\pi\) | ||
0.999677 | − | 0.0254006i | \(-0.00808613\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45943 | −0.0516309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.4198 | + | 2.39683i | 0.615115 | + | 0.0846350i | ||||
\(803\) | 29.1860i | 1.02995i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.42322 | − | 61.2187i | 0.296695 | − | 2.15634i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.53041 | + | 19.6160i | −0.300099 | + | 0.690088i | ||||
\(809\) | −23.7153 | −0.833787 | −0.416894 | − | 0.908955i | \(-0.636881\pi\) | ||||
−0.416894 | + | 0.908955i | \(0.636881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.8394i | 1.67987i | 0.542689 | + | 0.839933i | \(0.317406\pi\) | ||||
−0.542689 | + | 0.839933i | \(0.682594\pi\) | |||||||
\(812\) | −0.195805 | + | 0.698070i | −0.00687140 | + | 0.0244974i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.04754 | − | 1.24487i | −0.317116 | − | 0.0436327i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.4532 | 0.995451 | ||||||||
\(818\) | −44.9566 | − | 6.18568i | −1.57187 | − | 0.216277i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 51.9216i | − | 1.81208i | −0.423195 | − | 0.906038i | \(-0.639092\pi\) | ||
0.423195 | − | 0.906038i | \(-0.360908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.8542 | −0.970937 | −0.485469 | − | 0.874254i | \(-0.661351\pi\) | ||||
−0.485469 | + | 0.874254i | \(0.661351\pi\) | |||||||
\(824\) | −4.63105 | − | 2.01391i | −0.161330 | − | 0.0701577i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.196496 | + | 1.42811i | −0.00683698 | + | 0.0496902i | ||||
\(827\) | 43.9365i | 1.52782i | 0.645321 | + | 0.763912i | \(0.276724\pi\) | ||||
−0.645321 | + | 0.763912i | \(0.723276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.6898i | − | 1.44795i | −0.689827 | − | 0.723974i | \(-0.742314\pi\) | ||
0.689827 | − | 0.723974i | \(-0.257686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30.8241 | − | 28.7383i | 1.06863 | − | 0.996322i | ||||
\(833\) | −1.78978 | −0.0620121 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −32.3813 | − | 9.08277i | −1.11993 | − | 0.314134i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.11060 | − | 22.6074i | 0.107454 | − | 0.780959i | ||||
\(839\) | 25.4733 | 0.879437 | 0.439719 | − | 0.898136i | \(-0.355078\pi\) | ||||
0.439719 | + | 0.898136i | \(0.355078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61336 | 0.297012 | ||||||||
\(842\) | −5.54547 | + | 40.3037i | −0.191110 | + | 1.38896i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.75866 | + | 6.26986i | −0.0605356 | + | 0.215817i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.414324 | 0.0142363 | ||||||||
\(848\) | −24.0537 | + | 39.5038i | −0.826008 | + | 1.35657i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.39722i | − | 0.150735i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.5366i | − | 0.429245i | −0.976697 | − | 0.214622i | \(-0.931148\pi\) | ||
0.976697 | − | 0.214622i | \(-0.0688521\pi\) | |||||||
\(854\) | 0.184796 | − | 1.34307i | 0.00632358 | − | 0.0459588i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.8103 | − | 27.1581i | 0.403667 | − | 0.928246i | ||||
\(857\) | 2.61409 | 0.0892956 | 0.0446478 | − | 0.999003i | \(-0.485783\pi\) | ||||
0.0446478 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.8438i | − | 1.08650i | −0.839573 | − | 0.543248i | \(-0.817195\pi\) | ||
0.839573 | − | 0.543248i | \(-0.182805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.6467 | − | 4.76711i | −1.18007 | − | 0.162369i | ||||
\(863\) | −22.3335 | −0.760241 | −0.380121 | − | 0.924937i | \(-0.624118\pi\) | ||||
−0.380121 | + | 0.924937i | \(0.624118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.28798 | − | 0.865177i | −0.213674 | − | 0.0293999i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.28243 | + | 0.359715i | 0.0435286 | + | 0.0122095i | ||||
\(869\) | − | 13.3037i | − | 0.451298i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.3488 | 1.29940 | ||||||||
\(872\) | −4.10913 | + | 9.44910i | −0.139153 | + | 0.319987i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.20717 | − | 16.0414i | 0.0746588 | − | 0.542609i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 37.4408i | − | 1.26429i | −0.774852 | − | 0.632143i | \(-0.782176\pi\) | ||
0.774852 | − | 0.632143i | \(-0.217824\pi\) | |||||||
\(878\) | 8.35117 | + | 1.14906i | 0.281838 | + | 0.0387788i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.1952 | −1.79219 | −0.896096 | − | 0.443860i | \(-0.853609\pi\) | ||||
−0.896096 | + | 0.443860i | \(0.853609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0907i | 1.21455i | 0.794493 | + | 0.607274i | \(0.207737\pi\) | ||||
−0.794493 | + | 0.607274i | \(0.792263\pi\) | |||||||
\(884\) | 0.728188 | − | 2.59608i | 0.0244916 | − | 0.0873157i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.75513 | + | 20.0239i | −0.0925604 | + | 0.672715i | ||||
\(887\) | −43.3018 | −1.45393 | −0.726966 | − | 0.686673i | \(-0.759070\pi\) | ||||
−0.726966 | + | 0.686673i | \(0.759070\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.698192 | −0.0234166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 51.9763 | + | 14.5791i | 1.74029 | + | 0.488143i | ||||
\(893\) | 39.6832i | 1.32795i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.523078 | + | 0.742606i | 0.0174748 | + | 0.0248087i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.3990 | − | 4.73304i | −1.14791 | − | 0.157943i | ||||
\(899\) | 37.4525i | 1.24911i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.95910i | 0.0985820i | ||||||||
\(902\) | 3.78212 | − | 27.4879i | 0.125931 | − | 0.915247i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.9108 | − | 9.96324i | −0.762003 | − | 0.331372i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 8.75026i | − | 0.290548i | −0.989391 | − | 0.145274i | \(-0.953594\pi\) | ||
0.989391 | − | 0.145274i | \(-0.0464063\pi\) | |||||||
\(908\) | −10.7067 | + | 38.1707i | −0.355314 | + | 1.26674i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7438 | 0.455353 | 0.227676 | − | 0.973737i | \(-0.426887\pi\) | ||||
0.227676 | + | 0.973737i | \(0.426887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.2513 | −0.736411 | ||||||||
\(914\) | 40.5045 | + | 5.57310i | 1.33977 | + | 0.184342i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.7102 | + | 41.7483i | −0.386915 | + | 1.37940i | ||||
\(917\) | − | 0.866420i | − | 0.0286117i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.989347 | −0.0326355 | −0.0163178 | − | 0.999867i | \(-0.505194\pi\) | ||||
−0.0163178 | + | 0.999867i | \(0.505194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.839427 | + | 6.10083i | −0.0276451 | + | 0.200920i | ||||
\(923\) | − | 59.7803i | − | 1.96769i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5936 | + | 2.14557i | 0.512439 | + | 0.0705076i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.1331 | + | 19.8014i | −0.529596 | + | 0.650012i | ||||
\(929\) | 8.49434 | 0.278690 | 0.139345 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139345 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6656i | 1.59495i | ||||||||
\(932\) | −33.2629 | − | 9.33008i | −1.08956 | − | 0.305617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.68683 | − | 26.7953i | 0.120637 | − | 0.876770i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.6912 | −0.610615 | −0.305308 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305308 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(938\) | −0.112667 | + | 0.818847i | −0.00367871 | + | 0.0267363i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.03170i | − | 0.0988305i | −0.998778 | − | 0.0494152i | \(-0.984264\pi\) | ||
0.998778 | − | 0.0494152i | \(-0.0157358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3595 | 0.435045 | ||||||||
\(944\) | −26.4119 | + | 43.3767i | −0.859634 | + | 1.41179i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.8431 | + | 1.90471i | 0.450079 | + | 0.0619273i | ||||
\(947\) | − | 16.8327i | − | 0.546990i | −0.961873 | − | 0.273495i | \(-0.911820\pi\) | ||
0.961873 | − | 0.273495i | \(-0.0881797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.6243i | 2.06533i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0532937 | + | 0.0231759i | 0.00172726 | + | 0.000751134i | ||||
\(953\) | 1.73948 | 0.0563473 | 0.0281737 | − | 0.999603i | \(-0.491031\pi\) | ||||
0.0281737 | + | 0.999603i | \(0.491031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31.5269 | + | 8.84312i | 1.01965 | + | 0.286007i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.9162 | + | 4.94179i | 1.16040 | + | 0.159662i | ||||
\(959\) | −0.926677 | −0.0299240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8044 | 1.21950 | ||||||||
\(962\) | −19.7233 | − | 2.71377i | −0.635904 | − | 0.0874954i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.1457 | − | 3.68731i | −0.423395 | − | 0.118760i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3399 | 0.557615 | 0.278808 | − | 0.960347i | \(-0.410061\pi\) | ||||
0.278808 | + | 0.960347i | \(0.410061\pi\) | |||||||
\(968\) | 13.3854 | + | 5.82091i | 0.430223 | + | 0.187091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 45.4054i | − | 1.45713i | −0.684977 | − | 0.728565i | \(-0.740188\pi\) | ||
0.684977 | − | 0.728565i | \(-0.259812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.0172261i | − | 0.000552243i | ||||||
\(974\) | −17.9938 | − | 2.47581i | −0.576560 | − | 0.0793302i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.8392 | − | 40.7938i | 0.795082 | − | 1.30578i | ||||
\(977\) | 43.4336 | 1.38957 | 0.694783 | − | 0.719220i | \(-0.255501\pi\) | ||||
0.694783 | + | 0.719220i | \(0.255501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.7980i | 0.920388i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.27489 | + | 23.8014i | −0.104506 | + | 0.759533i | ||||
\(983\) | −47.4465 | −1.51331 | −0.756655 | − | 0.653815i | \(-0.773168\pi\) | ||||
−0.756655 | + | 0.653815i | \(0.773168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.222746 | + | 1.61889i | −0.00709368 | + | 0.0515558i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −70.5898 | − | 19.8001i | −2.24576 | − | 0.629924i | ||||
\(989\) | 6.72794i | 0.213936i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8434 | −0.916242 | −0.458121 | − | 0.888890i | \(-0.651477\pi\) | ||||
−0.458121 | + | 0.888890i | \(0.651477\pi\) | |||||||
\(992\) | 36.3773 | + | 29.6383i | 1.15498 | + | 0.941018i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.27646 | + | 0.175632i | 0.0404870 | + | 0.00557070i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 33.1449i | − | 1.04971i | −0.851192 | − | 0.524855i | \(-0.824119\pi\) | ||
0.851192 | − | 0.524855i | \(-0.175881\pi\) | |||||||
\(998\) | −2.70881 | + | 19.6872i | −0.0857460 | + | 0.623189i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))