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: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(-0.671462 - 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.p.901.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.671462 | + | 1.24464i | −0.474795 | + | 0.880096i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.09828 | − | 1.67146i | −0.549139 | − | 0.835731i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.68585 | −1.77108 | −0.885542 | − | 0.464560i | \(-0.846213\pi\) | ||||
−0.885542 | + | 0.464560i | \(0.846213\pi\) | |||||||
\(8\) | 2.81783 | − | 0.244644i | 0.996252 | − | 0.0864948i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.29273i | − | 0.691284i | −0.938366 | − | 0.345642i | \(-0.887661\pi\) | ||
0.938366 | − | 0.345642i | \(-0.112339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.97858i | 1.38081i | 0.723424 | + | 0.690404i | \(0.242567\pi\) | ||||
−0.723424 | + | 0.690404i | \(0.757433\pi\) | |||||||
\(14\) | 3.14637 | − | 5.83221i | 0.840902 | − | 1.55872i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58757 | + | 3.67146i | −0.396892 | + | 0.917865i | ||||
\(17\) | −2.97858 | −0.722411 | −0.361206 | − | 0.932486i | \(-0.617635\pi\) | ||||
−0.361206 | + | 0.932486i | \(0.617635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68585i | 0.616175i | 0.951358 | + | 0.308088i | \(0.0996890\pi\) | ||||
−0.951358 | + | 0.308088i | \(0.900311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.85363 | + | 1.53948i | 0.608397 | + | 0.328218i | ||||
\(23\) | 2.68585 | 0.560038 | 0.280019 | − | 0.959995i | \(-0.409659\pi\) | ||||
0.280019 | + | 0.959995i | \(0.409659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.19656 | − | 3.34292i | −1.21524 | − | 0.655601i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.14637 | + | 7.83221i | 0.972572 | + | 1.48015i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.97858 | −1.25339 | −0.626695 | − | 0.779265i | \(-0.715593\pi\) | ||||
−0.626695 | + | 0.779265i | \(0.715593\pi\) | |||||||
\(32\) | −3.50367 | − | 4.44120i | −0.619368 | − | 0.785101i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | − | 3.70727i | 0.342997 | − | 0.635791i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.39312i | − | 0.722224i | −0.932523 | − | 0.361112i | \(-0.882397\pi\) | ||
0.932523 | − | 0.361112i | \(-0.117603\pi\) | |||||||
\(38\) | −3.34292 | − | 1.80344i | −0.542294 | − | 0.292557i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3717 | 1.77596 | 0.887980 | − | 0.459882i | \(-0.152108\pi\) | ||||
0.887980 | + | 0.459882i | \(0.152108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.37169i | − | 1.42917i | −0.699549 | − | 0.714585i | \(-0.746616\pi\) | ||
0.699549 | − | 0.714585i | \(-0.253384\pi\) | |||||||
\(44\) | −3.83221 | + | 2.51806i | −0.577728 | + | 0.379611i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.80344 | + | 3.34292i | −0.265903 | + | 0.492887i | ||||
\(47\) | 7.27131 | 1.06063 | 0.530315 | − | 0.847801i | \(-0.322074\pi\) | ||||
0.530315 | + | 0.847801i | \(0.322074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.9572 | 2.13674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.32150 | − | 5.46787i | 1.15398 | − | 0.758257i | ||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.2039 | + | 1.14637i | −1.76445 | + | 0.153190i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.48929 | + | 1.34292i | 0.326860 | + | 0.176334i | ||||
\(59\) | − | 1.70727i | − | 0.222267i | −0.993805 | − | 0.111134i | \(-0.964552\pi\) | ||
0.993805 | − | 0.111134i | \(-0.0354482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.58546i | 0.587108i | 0.955942 | + | 0.293554i | \(0.0948381\pi\) | ||||
−0.955942 | + | 0.293554i | \(0.905162\pi\) | |||||||
\(62\) | 4.68585 | − | 8.68585i | 0.595103 | − | 1.10310i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.88030 | − | 1.37873i | 0.985037 | − | 0.172341i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 3.27131 | + | 4.97858i | 0.396704 | + | 0.603741i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.585462 | −0.0694816 | −0.0347408 | − | 0.999396i | \(-0.511061\pi\) | ||||
−0.0347408 | + | 0.999396i | \(0.511061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 5.46787 | + | 2.94981i | 0.635626 | + | 0.342908i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.48929 | − | 2.94981i | 0.514957 | − | 0.338366i | ||||
\(77\) | 10.7434i | 1.22432i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02142 | 0.114919 | 0.0574595 | − | 0.998348i | \(-0.481700\pi\) | ||||
0.0574595 | + | 0.998348i | \(0.481700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.63565 | + | 14.1537i | −0.843217 | + | 1.56302i | ||||
\(83\) | − | 13.3717i | − | 1.46773i | −0.679293 | − | 0.733867i | \(-0.737714\pi\) | ||
0.679293 | − | 0.733867i | \(-0.262286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.6644 | + | 6.29273i | 1.25781 | + | 0.678563i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.560904 | − | 6.46052i | −0.0597925 | − | 0.688694i | ||||
\(89\) | −3.37169 | −0.357399 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 23.3288i | − | 2.44553i | ||||||
\(92\) | −2.94981 | − | 4.48929i | −0.307539 | − | 0.468041i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.88240 | + | 9.05019i | −0.503581 | + | 0.933456i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.95715 | 0.401788 | 0.200894 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200894 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(98\) | −10.0432 | + | 18.6163i | −1.01451 | + | 1.88053i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6430 | 1.44282 | 0.721409 | − | 0.692509i | \(-0.243495\pi\) | ||||
0.721409 | + | 0.692509i | \(0.243495\pi\) | |||||||
\(104\) | 1.21798 | + | 14.0288i | 0.119433 | + | 1.37563i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.48929 | + | 1.34292i | 0.241781 | + | 0.130436i | ||||
\(107\) | − | 11.3288i | − | 1.09520i | −0.836740 | − | 0.547600i | \(-0.815541\pi\) | ||
0.836740 | − | 0.547600i | \(-0.184459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.37169i | − | 0.897645i | −0.893621 | − | 0.448823i | \(-0.851843\pi\) | ||
0.893621 | − | 0.448823i | \(-0.148157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.43910 | − | 17.2039i | 0.702929 | − | 1.62562i | ||||
\(113\) | 19.7648 | 1.85932 | 0.929658 | − | 0.368423i | \(-0.120102\pi\) | ||||
0.929658 | + | 0.368423i | \(0.120102\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.34292 | + | 2.19656i | −0.310383 | + | 0.203945i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.12494 | + | 1.14637i | 0.195617 | + | 0.105531i | ||||
\(119\) | 13.9572 | 1.27945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.74338 | 0.522126 | ||||||||
\(122\) | −5.70727 | − | 3.07896i | −0.516712 | − | 0.278756i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.66442 | + | 11.6644i | 0.688286 | + | 1.04750i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.64300 | −0.589471 | −0.294735 | − | 0.955579i | \(-0.595232\pi\) | ||||
−0.294735 | + | 0.955579i | \(0.595232\pi\) | |||||||
\(128\) | −3.57529 | + | 10.7339i | −0.316014 | + | 0.948755i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.07896i | − | 0.618492i | −0.950982 | − | 0.309246i | \(-0.899923\pi\) | ||
0.950982 | − | 0.309246i | \(-0.100077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 12.5855i | − | 1.09130i | ||||||
\(134\) | 4.97858 | + | 2.68585i | 0.430084 | + | 0.232022i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.39312 | + | 0.728692i | −0.719704 | + | 0.0624848i | ||||
\(137\) | −14.9786 | −1.27971 | −0.639853 | − | 0.768497i | \(-0.721005\pi\) | ||||
−0.639853 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.64300i | 0.393814i | 0.980422 | + | 0.196907i | \(0.0630897\pi\) | ||||
−0.980422 | + | 0.196907i | \(0.936910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.393115 | − | 0.728692i | 0.0329895 | − | 0.0611505i | ||||
\(143\) | 11.4145 | 0.954532 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.02877 | + | 7.46787i | −0.333423 | + | 0.618045i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.34292 | + | 4.82487i | −0.603585 | + | 0.396601i | ||||
\(149\) | − | 2.00000i | − | 0.163846i | −0.996639 | − | 0.0819232i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819232i | \(-0.0261062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.35027 | −0.679535 | −0.339768 | − | 0.940509i | \(-0.610348\pi\) | ||||
−0.339768 | + | 0.940509i | \(0.610348\pi\) | |||||||
\(152\) | 0.657077 | + | 7.56825i | 0.0532960 | + | 0.613866i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.3717 | − | 7.21377i | −1.07752 | − | 0.581302i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3503i | 1.78375i | 0.452286 | + | 0.891873i | \(0.350609\pi\) | ||||
−0.452286 | + | 0.891873i | \(0.649391\pi\) | |||||||
\(158\) | −0.685846 | + | 1.27131i | −0.0545630 | + | 0.101140i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5855 | −0.991873 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.37169i | 0.107439i | 0.998556 | + | 0.0537196i | \(0.0171077\pi\) | ||||
−0.998556 | + | 0.0537196i | \(0.982892\pi\) | |||||||
\(164\) | −12.4893 | − | 19.0073i | −0.975250 | − | 1.48422i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6430 | + | 8.97858i | 1.29175 | + | 0.696873i | ||||
\(167\) | 11.2713 | 0.872200 | 0.436100 | − | 0.899898i | \(-0.356359\pi\) | ||||
0.436100 | + | 0.899898i | \(0.356359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7862 | −0.906633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.6644 | + | 10.2927i | −1.19440 | + | 0.784813i | ||||
\(173\) | − | 10.7862i | − | 0.820062i | −0.912072 | − | 0.410031i | \(-0.865518\pi\) | ||
0.912072 | − | 0.410031i | \(-0.134482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.41767 | + | 3.63986i | 0.634506 | + | 0.274365i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.26396 | − | 4.19656i | 0.169691 | − | 0.314545i | ||||
\(179\) | − | 3.66442i | − | 0.273892i | −0.990579 | − | 0.136946i | \(-0.956271\pi\) | ||
0.990579 | − | 0.136946i | \(-0.0437287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.62831i | − | 0.492678i | −0.969184 | − | 0.246339i | \(-0.920772\pi\) | ||
0.969184 | − | 0.246339i | \(-0.0792277\pi\) | |||||||
\(182\) | 29.0361 | + | 15.6644i | 2.15230 | + | 1.16112i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.56825 | − | 0.657077i | 0.557939 | − | 0.0484404i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82908i | 0.499392i | ||||||||
\(188\) | −7.98592 | − | 12.1537i | −0.582433 | − | 0.886401i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.21377 | −0.0873690 | −0.0436845 | − | 0.999045i | \(-0.513910\pi\) | ||||
−0.0436845 | + | 0.999045i | \(0.513910\pi\) | |||||||
\(194\) | −2.65708 | + | 4.92525i | −0.190767 | + | 0.353612i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.4271 | − | 25.0003i | −1.17337 | − | 1.78574i | ||||
\(197\) | 23.9572i | 1.70688i | 0.521194 | + | 0.853438i | \(0.325487\pi\) | ||||
−0.521194 | + | 0.853438i | \(0.674513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.350269 | 0.0248299 | 0.0124150 | − | 0.999923i | \(-0.496048\pi\) | ||||
0.0124150 | + | 0.999923i | \(0.496048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.48929 | − | 1.34292i | −0.175146 | − | 0.0944877i | ||||
\(203\) | 9.37169i | 0.657764i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.83221 | + | 18.2253i | −0.685043 | + | 1.26982i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.2787 | − | 7.90383i | −1.26740 | − | 0.548032i | ||||
\(209\) | 6.15792 | 0.425952 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1004i | 0.970710i | 0.874317 | + | 0.485355i | \(0.161310\pi\) | ||||
−0.874317 | + | 0.485355i | \(0.838690\pi\) | |||||||
\(212\) | −3.34292 | + | 2.19656i | −0.229593 | + | 0.150860i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.1004 | + | 7.60688i | 0.963882 | + | 0.519996i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.7005 | 2.21986 | ||||||||
\(218\) | 11.6644 | + | 6.29273i | 0.790014 | + | 0.426198i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.8291i | − | 0.997512i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.72869 | 0.450587 | 0.225293 | − | 0.974291i | \(-0.427666\pi\) | ||||
0.225293 | + | 0.974291i | \(0.427666\pi\) | |||||||
\(224\) | 16.4177 | + | 20.8108i | 1.09695 | + | 1.39048i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.2713 | + | 24.6002i | −0.882794 | + | 1.63638i | ||||
\(227\) | 9.95715i | 0.660880i | 0.943827 | + | 0.330440i | \(0.107197\pi\) | ||||
−0.943827 | + | 0.330440i | \(0.892803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.3288i | − | 0.748631i | −0.927301 | − | 0.374316i | \(-0.877878\pi\) | ||
0.927301 | − | 0.374316i | \(-0.122122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.489289 | − | 5.63565i | −0.0321234 | − | 0.369999i | ||||
\(233\) | −18.9786 | −1.24333 | −0.621664 | − | 0.783284i | \(-0.713543\pi\) | ||||
−0.621664 | + | 0.783284i | \(0.713543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.85363 | + | 1.87506i | −0.185756 | + | 0.122056i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.37169 | + | 17.3717i | −0.607477 | + | 1.12604i | ||||
\(239\) | −2.62831 | −0.170011 | −0.0850055 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850055 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7862 | 0.694802 | 0.347401 | − | 0.937717i | \(-0.387064\pi\) | ||||
0.347401 | + | 0.937717i | \(0.387064\pi\) | |||||||
\(242\) | −3.85646 | + | 7.14847i | −0.247903 | + | 0.459521i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.66442 | − | 5.03612i | 0.490664 | − | 0.322404i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3717 | −0.850820 | ||||||||
\(248\) | −19.6644 | + | 1.70727i | −1.24869 | + | 0.108412i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 30.9933i | − | 1.95628i | −0.207952 | − | 0.978139i | \(-0.566680\pi\) | ||
0.207952 | − | 0.978139i | \(-0.433320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.15792i | − | 0.387145i | ||||||
\(254\) | 4.46052 | − | 8.26817i | 0.279878 | − | 0.518791i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9593 | − | 11.6574i | −0.684954 | − | 0.728587i | ||||
\(257\) | 20.9357 | 1.30594 | 0.652968 | − | 0.757386i | \(-0.273524\pi\) | ||||
0.652968 | + | 0.757386i | \(0.273524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.5855i | 1.27912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.81079 | + | 4.75325i | 0.544332 | + | 0.293657i | ||||
\(263\) | −19.2713 | −1.18832 | −0.594160 | − | 0.804347i | \(-0.702515\pi\) | ||||
−0.594160 | + | 0.804347i | \(0.702515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.6644 | + | 8.45065i | 0.960447 | + | 0.518143i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.68585 | + | 4.39312i | −0.408403 | + | 0.268352i | ||||
\(269\) | 24.7434i | 1.50863i | 0.656512 | + | 0.754315i | \(0.272031\pi\) | ||||
−0.656512 | + | 0.754315i | \(0.727969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.5640 | 1.67440 | 0.837198 | − | 0.546900i | \(-0.184192\pi\) | ||||
0.837198 | + | 0.546900i | \(0.184192\pi\) | |||||||
\(272\) | 4.72869 | − | 10.9357i | 0.286719 | − | 0.663076i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0575 | − | 18.6430i | 0.607598 | − | 1.12626i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3074i | 1.22015i | 0.792342 | + | 0.610077i | \(0.208862\pi\) | ||||
−0.792342 | + | 0.610077i | \(0.791138\pi\) | |||||||
\(278\) | −5.77888 | − | 3.11760i | −0.346594 | − | 0.186981i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7862 | 0.643453 | 0.321726 | − | 0.946833i | \(-0.395737\pi\) | ||||
0.321726 | + | 0.946833i | \(0.395737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000i | 1.18888i | 0.804141 | + | 0.594438i | \(0.202626\pi\) | ||||
−0.804141 | + | 0.594438i | \(0.797374\pi\) | |||||||
\(284\) | 0.643000 | + | 0.978577i | 0.0381551 | + | 0.0580679i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.66442 | + | 14.2070i | −0.453207 | + | 0.840080i | ||||
\(287\) | −53.2860 | −3.14537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.12808 | −0.478122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.58967 | − | 10.0288i | −0.385631 | − | 0.586889i | ||||
\(293\) | − | 21.9143i | − | 1.28025i | −0.768272 | − | 0.640124i | \(-0.778883\pi\) | ||
0.768272 | − | 0.640124i | \(-0.221117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.07475 | − | 12.3790i | −0.0624686 | − | 0.719517i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.48929 | + | 1.34292i | 0.144201 | + | 0.0777934i | ||||
\(299\) | 13.3717i | 0.773305i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.9143i | 2.53118i | ||||||||
\(302\) | 5.60688 | − | 10.3931i | 0.322640 | − | 0.598057i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.86098 | − | 4.26396i | −0.565566 | − | 0.244555i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.5426i | − | 1.51487i | −0.652912 | − | 0.757434i | \(-0.726453\pi\) | ||
0.652912 | − | 0.757434i | \(-0.273547\pi\) | |||||||
\(308\) | 17.9572 | − | 11.7992i | 1.02320 | − | 0.672324i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2008 | −0.691842 | −0.345921 | − | 0.938264i | \(-0.612434\pi\) | ||||
−0.345921 | + | 0.938264i | \(0.612434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9572 | −0.901952 | −0.450976 | − | 0.892536i | \(-0.648924\pi\) | ||||
−0.450976 | + | 0.892536i | \(0.648924\pi\) | |||||||
\(314\) | −27.8181 | − | 15.0073i | −1.56987 | − | 0.846914i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.12181 | − | 1.70727i | −0.0631066 | − | 0.0960414i | ||||
\(317\) | − | 33.5296i | − | 1.88321i | −0.336718 | − | 0.941605i | \(-0.609317\pi\) | ||
0.336718 | − | 0.941605i | \(-0.390683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.58546 | −0.256737 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.45065 | − | 15.6644i | 0.470937 | − | 0.872944i | ||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.70727 | − | 0.921039i | −0.0945569 | − | 0.0510116i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 32.0435 | − | 2.78202i | 1.76930 | − | 0.153611i | ||||
\(329\) | −34.0722 | −1.87846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.8568i | − | 1.09143i | −0.837972 | − | 0.545713i | \(-0.816259\pi\) | ||
0.837972 | − | 0.545713i | \(-0.183741\pi\) | |||||||
\(332\) | −22.3503 | + | 14.6858i | −1.22663 | + | 0.805991i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.56825 | + | 14.0288i | −0.414116 | + | 0.767620i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.17092 | −0.390625 | −0.195313 | − | 0.980741i | \(-0.562572\pi\) | ||||
−0.195313 | + | 0.980741i | \(0.562572\pi\) | |||||||
\(338\) | 7.91400 | − | 14.6697i | 0.430465 | − | 0.797925i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37.2860 | −2.01325 | ||||||||
\(344\) | −2.29273 | − | 26.4078i | −0.123616 | − | 1.42381i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4250 | + | 7.24254i | 0.721734 | + | 0.389361i | ||||
\(347\) | 0.786230i | 0.0422071i | 0.999777 | + | 0.0211035i | \(0.00671796\pi\) | ||||
−0.999777 | + | 0.0211035i | \(0.993282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.15792i | 0.329626i | 0.986325 | + | 0.164813i | \(0.0527021\pi\) | ||||
−0.986325 | + | 0.164813i | \(0.947298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.1825 | + | 8.03298i | −0.542728 | + | 0.428159i | ||||
\(353\) | 21.7220 | 1.15614 | 0.578072 | − | 0.815986i | \(-0.303805\pi\) | ||||
0.578072 | + | 0.815986i | \(0.303805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.70306 | + | 5.63565i | 0.196262 | + | 0.298689i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.56090 | + | 2.46052i | 0.241051 | + | 0.130042i | ||||
\(359\) | −0.585462 | −0.0308995 | −0.0154498 | − | 0.999881i | \(-0.504918\pi\) | ||||
−0.0154498 | + | 0.999881i | \(0.504918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7862 | 0.620328 | ||||||||
\(362\) | 8.24989 | + | 4.45065i | 0.433604 | + | 0.233921i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −38.9933 | + | 25.6216i | −2.04380 | + | 1.34294i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.485078 | 0.0253209 | 0.0126604 | − | 0.999920i | \(-0.495970\pi\) | ||||
0.0126604 | + | 0.999920i | \(0.495970\pi\) | |||||||
\(368\) | −4.26396 | + | 9.86098i | −0.222274 | + | 0.514039i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.37169i | 0.486554i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.3931i | 0.641691i | 0.947132 | + | 0.320846i | \(0.103967\pi\) | ||||
−0.947132 | + | 0.320846i | \(0.896033\pi\) | |||||||
\(374\) | −8.49977 | − | 4.58546i | −0.439513 | − | 0.237109i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.4893 | − | 1.77888i | 1.05665 | − | 0.0917389i | ||||
\(377\) | 9.95715 | 0.512820 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.0147i | − | 1.33629i | −0.744033 | − | 0.668143i | \(-0.767090\pi\) | ||
0.744033 | − | 0.668143i | \(-0.232910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.37169 | + | 9.95715i | −0.274840 | + | 0.509452i | ||||
\(383\) | 6.68585 | 0.341631 | 0.170815 | − | 0.985303i | \(-0.445360\pi\) | ||||
0.170815 | + | 0.985303i | \(0.445360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.815000 | − | 1.51071i | 0.0414824 | − | 0.0768932i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.34606 | − | 6.61423i | −0.220638 | − | 0.335787i | ||||
\(389\) | − | 29.9143i | − | 1.51672i | −0.651838 | − | 0.758358i | \(-0.726002\pi\) | ||
0.651838 | − | 0.758358i | \(-0.273998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 42.1467 | − | 3.65918i | 2.12873 | − | 0.184817i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.8181 | − | 16.0863i | −1.50222 | − | 0.810416i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.76481i | − | 0.490082i | −0.969513 | − | 0.245041i | \(-0.921199\pi\) | ||
0.969513 | − | 0.245041i | \(-0.0788014\pi\) | |||||||
\(398\) | −0.235192 | + | 0.435961i | −0.0117891 | + | 0.0218527i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.58546 | 0.328862 | 0.164431 | − | 0.986389i | \(-0.447421\pi\) | ||||
0.164431 | + | 0.986389i | \(0.447421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 34.7434i | − | 1.73069i | ||||||
\(404\) | 3.34292 | − | 2.19656i | 0.166317 | − | 0.109283i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.6644 | − | 6.29273i | −0.578896 | − | 0.312303i | ||||
\(407\) | −10.0722 | −0.499262 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.9143 | −1.28138 | −0.640690 | − | 0.767800i | \(-0.721352\pi\) | ||||
−0.640690 | + | 0.767800i | \(0.721352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.0821 | − | 24.4752i | −0.792308 | − | 1.20581i | ||||
\(413\) | 8.00000i | 0.393654i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22.1109 | − | 17.4433i | 1.08407 | − | 0.855229i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.13481 | + | 7.66442i | −0.202240 | + | 0.374879i | ||||
\(419\) | 12.2499i | 0.598446i | 0.954183 | + | 0.299223i | \(0.0967275\pi\) | ||||
−0.954183 | + | 0.299223i | \(0.903273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.67115i | − | 0.227658i | −0.993500 | − | 0.113829i | \(-0.963688\pi\) | ||
0.993500 | − | 0.113829i | \(-0.0363116\pi\) | |||||||
\(422\) | −17.5500 | − | 9.46787i | −0.854319 | − | 0.460888i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.489289 | − | 5.63565i | −0.0237620 | − | 0.273692i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 21.4868i | − | 1.03982i | ||||||
\(428\) | −18.9357 | + | 12.4422i | −0.915293 | + | 0.601418i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.585462 | −0.0282007 | −0.0141004 | − | 0.999901i | \(-0.504488\pi\) | ||||
−0.0141004 | + | 0.999901i | \(0.504488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9143 | 1.05313 | 0.526567 | − | 0.850133i | \(-0.323479\pi\) | ||||
0.526567 | + | 0.850133i | \(0.323479\pi\) | |||||||
\(434\) | −21.9572 | + | 40.7005i | −1.05398 | + | 1.95369i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.6644 | + | 10.2927i | −0.750190 | + | 0.492932i | ||||
\(437\) | 7.21377i | 0.345081i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39312 | −0.114217 | −0.0571086 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571086 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.4569 | + | 9.95715i | 0.877906 | + | 0.473614i | ||||
\(443\) | − | 20.7005i | − | 0.983512i | −0.870733 | − | 0.491756i | \(-0.836355\pi\) | ||
0.870733 | − | 0.491756i | \(-0.163645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.51806 | + | 8.37483i | −0.213936 | + | 0.396560i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −36.9259 | + | 6.46052i | −1.74458 | + | 0.305231i | ||||
\(449\) | 37.9143 | 1.78929 | 0.894643 | − | 0.446781i | \(-0.147430\pi\) | ||||
0.894643 | + | 0.446781i | \(0.147430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 26.0722i | − | 1.22769i | ||||||
\(452\) | −21.7073 | − | 33.0361i | −1.02102 | − | 1.55389i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.3931 | − | 6.68585i | −0.581638 | − | 0.313782i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.7005 | −1.81033 | −0.905167 | − | 0.425055i | \(-0.860255\pi\) | ||||
−0.905167 | + | 0.425055i | \(0.860255\pi\) | |||||||
\(458\) | 14.1004 | + | 7.60688i | 0.658868 | + | 0.355446i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.74338i | 0.220921i | 0.993880 | + | 0.110461i | \(0.0352326\pi\) | ||||
−0.993880 | + | 0.110461i | \(0.964767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.3142 | −0.711709 | −0.355855 | − | 0.934541i | \(-0.615810\pi\) | ||||
−0.355855 | + | 0.934541i | \(0.615810\pi\) | |||||||
\(464\) | 7.34292 | + | 3.17513i | 0.340887 | + | 0.147402i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7434 | − | 23.6216i | 0.590326 | − | 1.09425i | ||||
\(467\) | − | 30.5426i | − | 1.41334i | −0.707541 | − | 0.706672i | \(-0.750196\pi\) | ||
0.707541 | − | 0.706672i | \(-0.249804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7434i | 0.865489i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.417674 | − | 4.81079i | −0.0192250 | − | 0.221435i | ||||
\(473\) | −21.4868 | −0.987963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.3288 | − | 23.3288i | −0.702597 | − | 1.06928i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.76481 | − | 3.27131i | 0.0807204 | − | 0.149626i | ||||
\(479\) | −3.32885 | −0.152099 | −0.0760494 | − | 0.997104i | \(-0.524231\pi\) | ||||
−0.0760494 | + | 0.997104i | \(0.524231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.8715 | 0.997253 | ||||||||
\(482\) | −7.24254 | + | 13.4250i | −0.329889 | + | 0.611493i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.30784 | − | 9.59985i | −0.286720 | − | 0.436357i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1004 | 0.548321 | 0.274160 | − | 0.961684i | \(-0.411600\pi\) | ||||
0.274160 | + | 0.961684i | \(0.411600\pi\) | |||||||
\(488\) | 1.12181 | + | 12.9210i | 0.0507818 | + | 0.584908i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.2927i | − | 0.645022i | −0.946566 | − | 0.322511i | \(-0.895473\pi\) | ||
0.946566 | − | 0.322511i | \(-0.104527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.95715i | 0.268297i | ||||||||
\(494\) | 8.97858 | − | 16.6430i | 0.403965 | − | 0.748804i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.0790 | − | 25.6216i | 0.497460 | − | 1.15044i | ||||
\(497\) | 2.74338 | 0.123058 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.22846i | − | 0.413123i | −0.978434 | − | 0.206561i | \(-0.933773\pi\) | ||
0.978434 | − | 0.206561i | \(-0.0662273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.5756 | + | 20.8108i | 1.72171 | + | 0.928831i | ||||
\(503\) | −14.1004 | −0.628705 | −0.314353 | − | 0.949306i | \(-0.601787\pi\) | ||||
−0.314353 | + | 0.949306i | \(0.601787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.66442 | + | 4.13481i | 0.340725 | + | 0.183815i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.29587 | + | 11.1035i | 0.323702 | + | 0.492639i | ||||
\(509\) | − | 43.4011i | − | 1.92372i | −0.273544 | − | 0.961859i | \(-0.588196\pi\) | ||
0.273544 | − | 0.961859i | \(-0.411804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1151 | −1.24374 | ||||||||
\(512\) | 21.8680 | − | 5.81289i | 0.966439 | − | 0.256896i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.0575 | + | 26.0575i | −0.620051 | + | 1.14935i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.6712i | − | 0.733196i | ||||||
\(518\) | −25.6216 | − | 13.8223i | −1.12575 | − | 0.607319i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5725i | 0.593482i | 0.954958 | + | 0.296741i | \(0.0958998\pi\) | ||||
−0.954958 | + | 0.296741i | \(0.904100\pi\) | |||||||
\(524\) | −11.8322 | + | 7.77467i | −0.516893 | + | 0.339638i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9399 | − | 23.9859i | 0.564208 | − | 1.04584i | ||||
\(527\) | 20.7862 | 0.905462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7862 | −0.686358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.0361 | + | 13.8223i | −0.912031 | + | 0.599275i | ||||
\(533\) | 56.6148i | 2.45226i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.978577 | − | 11.2713i | −0.0422681 | − | 0.486846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.7967 | − | 16.6142i | −1.32774 | − | 0.716290i | ||||
\(539\) | − | 34.2927i | − | 1.47709i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.2860i | 1.60305i | 0.597961 | + | 0.801525i | \(0.295978\pi\) | ||||
−0.597961 | + | 0.801525i | \(0.704022\pi\) | |||||||
\(542\) | −18.5082 | + | 34.3074i | −0.794995 | + | 1.47363i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.4360 | + | 13.2285i | 0.447438 | + | 0.567166i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.200768i | − | 0.00858424i | −0.999991 | − | 0.00429212i | \(-0.998634\pi\) | ||
0.999991 | − | 0.00429212i | \(-0.00136623\pi\) | |||||||
\(548\) | 16.4507 | + | 25.0361i | 0.702737 | + | 1.06949i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.37169 | 0.228842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.78623 | −0.203531 | ||||||||
\(554\) | −25.2755 | − | 13.6357i | −1.07385 | − | 0.579323i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.76060 | − | 5.09931i | 0.329123 | − | 0.216259i | ||||
\(557\) | − | 9.21377i | − | 0.390400i | −0.980763 | − | 0.195200i | \(-0.937464\pi\) | ||
0.980763 | − | 0.195200i | \(-0.0625356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6577 | 1.97341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.24254 | + | 13.4250i | −0.305508 | + | 0.566300i | ||||
\(563\) | 36.7005i | 1.54674i | 0.633953 | + | 0.773372i | \(0.281431\pi\) | ||||
−0.633953 | + | 0.773372i | \(0.718569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.8929 | − | 13.4292i | −1.04633 | − | 0.564473i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.64973 | + | 0.143230i | −0.0692212 | + | 0.00600979i | ||||
\(569\) | −13.4145 | −0.562367 | −0.281183 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281183 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.6858i | − | 0.781978i | −0.920395 | − | 0.390989i | \(-0.872133\pi\) | ||
0.920395 | − | 0.390989i | \(-0.127867\pi\) | |||||||
\(572\) | −12.5363 | − | 19.0790i | −0.524171 | − | 0.797731i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 35.7795 | − | 66.3221i | 1.49341 | − | 2.76823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.78623 | 0.115992 | 0.0579961 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579961 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(578\) | 5.45769 | − | 10.1166i | 0.227010 | − | 0.420794i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.6577i | 2.59948i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.58546 | −0.189910 | ||||||||
\(584\) | 16.9070 | − | 1.46787i | 0.699615 | − | 0.0607407i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.2755 | + | 14.7146i | 1.12674 | + | 0.607855i | ||||
\(587\) | 27.3288i | 1.12798i | 0.825781 | + | 0.563991i | \(0.190735\pi\) | ||||
−0.825781 | + | 0.563991i | \(0.809265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18.7434i | − | 0.772308i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.1292 | + | 6.97437i | 0.662904 | + | 0.286645i | ||||
\(593\) | −6.97858 | −0.286576 | −0.143288 | − | 0.989681i | \(-0.545767\pi\) | ||||
−0.143288 | + | 0.989681i | \(0.545767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.34292 | + | 2.19656i | −0.136931 | + | 0.0899745i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.6430 | − | 8.97858i | −0.680583 | − | 0.367161i | ||||
\(599\) | −36.4998 | −1.49134 | −0.745670 | − | 0.666315i | \(-0.767870\pi\) | ||||
−0.745670 | + | 0.666315i | \(0.767870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5725 | −0.635214 | −0.317607 | − | 0.948222i | \(-0.602879\pi\) | ||||
−0.317607 | + | 0.948222i | \(0.602879\pi\) | |||||||
\(602\) | −54.6577 | − | 29.4868i | −2.22768 | − | 1.20179i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.17092 | + | 13.9572i | 0.373160 | + | 0.567909i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2285 | 1.26752 | 0.633762 | − | 0.773528i | \(-0.281510\pi\) | ||||
0.633762 | + | 0.773528i | \(0.281510\pi\) | |||||||
\(608\) | 11.9284 | − | 9.41033i | 0.483760 | − | 0.381639i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.2008i | 1.46453i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.978577i | − | 0.0395244i | −0.999805 | − | 0.0197622i | \(-0.993709\pi\) | ||
0.999805 | − | 0.0197622i | \(-0.00629091\pi\) | |||||||
\(614\) | 33.0361 | + | 17.8223i | 1.33323 | + | 0.719251i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.62831 | + | 30.2730i | 0.105898 | + | 1.21973i | ||||
\(617\) | 32.9357 | 1.32594 | 0.662971 | − | 0.748645i | \(-0.269295\pi\) | ||||
0.662971 | + | 0.748645i | \(0.269295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.35700i | − | 0.134929i | −0.997722 | − | 0.0674646i | \(-0.978509\pi\) | ||
0.997722 | − | 0.0674646i | \(-0.0214910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.19235 | − | 15.1856i | 0.328483 | − | 0.608888i | ||||
\(623\) | 15.7992 | 0.632983 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.7146 | − | 19.8610i | 0.428242 | − | 0.793804i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.3576 | − | 24.5468i | 1.49073 | − | 0.979525i | ||||
\(629\) | 13.0852i | 0.521742i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.7648 | −1.10530 | −0.552650 | − | 0.833414i | \(-0.686383\pi\) | ||||
−0.552650 | + | 0.833414i | \(0.686383\pi\) | |||||||
\(632\) | 2.87819 | − | 0.249885i | 0.114488 | − | 0.00993990i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41.7324 | + | 22.5138i | 1.65741 | + | 0.894139i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 74.4653i | 2.95042i | ||||||||
\(638\) | 3.07896 | − | 5.70727i | 0.121897 | − | 0.225953i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.1281 | 0.834509 | 0.417254 | − | 0.908790i | \(-0.362992\pi\) | ||||
0.417254 | + | 0.908790i | \(0.362992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.2860i | − | 1.15493i | −0.816416 | − | 0.577464i | \(-0.804043\pi\) | ||
0.816416 | − | 0.577464i | \(-0.195957\pi\) | |||||||
\(644\) | 13.8223 | + | 21.0361i | 0.544677 | + | 0.828939i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.95715 | + | 5.37169i | 0.391759 | + | 0.211346i | ||||
\(647\) | 15.6728 | 0.616163 | 0.308082 | − | 0.951360i | \(-0.400313\pi\) | ||||
0.308082 | + | 0.951360i | \(0.400313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.91431 | −0.153650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.29273 | − | 1.50650i | 0.0897903 | − | 0.0589991i | ||||
\(653\) | 17.5296i | 0.685987i | 0.939338 | + | 0.342993i | \(0.111441\pi\) | ||||
−0.939338 | + | 0.342993i | \(0.888559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.0533 | + | 41.7507i | −0.704864 | + | 1.63009i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.8782 | − | 42.4078i | 0.891885 | − | 1.65323i | ||||
\(659\) | 23.8652i | 0.929656i | 0.885401 | + | 0.464828i | \(0.153884\pi\) | ||||
−0.885401 | + | 0.464828i | \(0.846116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.1579i | − | 1.17301i | −0.809947 | − | 0.586504i | \(-0.800504\pi\) | ||
0.809947 | − | 0.586504i | \(-0.199496\pi\) | |||||||
\(662\) | 24.7146 | + | 13.3331i | 0.960561 | + | 0.518204i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.27131 | − | 37.6791i | −0.126951 | − | 1.46223i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.37169i | − | 0.207993i | ||||||
\(668\) | −12.3790 | − | 18.8396i | −0.478959 | − | 0.728924i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5132 | 0.405859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000 | 0.693849 | 0.346925 | − | 0.937893i | \(-0.387226\pi\) | ||||
0.346925 | + | 0.937893i | \(0.387226\pi\) | |||||||
\(674\) | 4.81500 | − | 8.92525i | 0.185467 | − | 0.343788i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.9446 | + | 19.7002i | 0.497868 | + | 0.757701i | ||||
\(677\) | 9.61531i | 0.369546i | 0.982781 | + | 0.184773i | \(0.0591550\pi\) | ||||
−0.982781 | + | 0.184773i | \(0.940845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5426 | −0.711600 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.9143 | − | 10.7434i | −0.762558 | − | 0.411385i | ||||
\(683\) | 18.6283i | 0.712792i | 0.934335 | + | 0.356396i | \(0.115995\pi\) | ||||
−0.934335 | + | 0.356396i | \(0.884005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.0361 | − | 46.4078i | 0.955883 | − | 1.77186i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 34.4078 | + | 14.8782i | 1.31179 | + | 0.567226i | ||||
\(689\) | 9.95715 | 0.379337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.4292i | − | 0.510872i | −0.966826 | − | 0.255436i | \(-0.917781\pi\) | ||
0.966826 | − | 0.255436i | \(-0.0822190\pi\) | |||||||
\(692\) | −18.0288 | + | 11.8463i | −0.685351 | + | 0.450328i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.978577 | − | 0.527923i | −0.0371463 | − | 0.0200397i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.8715 | −1.28297 | ||||||||
\(698\) | −7.66442 | − | 4.13481i | −0.290103 | − | 0.156505i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.1709i | − | 0.724076i | −0.932163 | − | 0.362038i | \(-0.882081\pi\) | ||
0.932163 | − | 0.362038i | \(-0.117919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7992 | 0.445016 | ||||||||
\(704\) | −3.16106 | − | 18.0674i | −0.119137 | − | 0.680941i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.5855 | + | 27.0361i | −0.548931 | + | 1.01752i | ||||
\(707\) | − | 9.37169i | − | 0.352459i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4145i | 0.578905i | 0.957192 | + | 0.289453i | \(0.0934732\pi\) | ||||
−0.957192 | + | 0.289453i | \(0.906527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.50085 | + | 0.824865i | −0.356059 | + | 0.0309131i | ||||
\(713\) | −18.7434 | −0.701945 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.12494 | + | 4.02456i | −0.228900 | + | 0.150405i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.393115 | − | 0.728692i | 0.0146709 | − | 0.0271945i | ||||
\(719\) | −20.7862 | −0.775196 | −0.387598 | − | 0.921829i | \(-0.626695\pi\) | ||||
−0.387598 | + | 0.921829i | \(0.626695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −68.6148 | −2.55535 | ||||||||
\(722\) | −7.91400 | + | 14.6697i | −0.294529 | + | 0.545948i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.0790 | + | 7.27973i | −0.411746 | + | 0.270549i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3012 | −0.456224 | −0.228112 | − | 0.973635i | \(-0.573255\pi\) | ||||
−0.228112 | + | 0.973635i | \(0.573255\pi\) | |||||||
\(728\) | −5.70727 | − | 65.7367i | −0.211525 | − | 2.43636i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.9143i | 1.03245i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9227i | 1.32684i | 0.748249 | + | 0.663418i | \(0.230895\pi\) | ||||
−0.748249 | + | 0.663418i | \(0.769105\pi\) | |||||||
\(734\) | −0.325711 | + | 0.603749i | −0.0120222 | + | 0.0222848i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.41033 | − | 11.9284i | −0.346869 | − | 0.439686i | ||||
\(737\) | −9.17092 | −0.337815 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.0277i | 1.06780i | 0.845547 | + | 0.533900i | \(0.179274\pi\) | ||||
−0.845547 | + | 0.533900i | \(0.820726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.6644 | − | 6.29273i | −0.428214 | − | 0.231013i | ||||
\(743\) | 2.60015 | 0.0953904 | 0.0476952 | − | 0.998862i | \(-0.484812\pi\) | ||||
0.0476952 | + | 0.998862i | \(0.484812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.4250 | − | 8.32150i | −0.564750 | − | 0.304672i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.4145 | − | 7.50023i | 0.417357 | − | 0.274236i | ||||
\(749\) | 53.0852i | 1.93969i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8929 | −0.397487 | −0.198744 | − | 0.980052i | \(-0.563686\pi\) | ||||
−0.198744 | + | 0.980052i | \(0.563686\pi\) | |||||||
\(752\) | −11.5437 | + | 26.6963i | −0.420955 | + | 0.973515i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.68585 | + | 12.3931i | −0.243484 | + | 0.451331i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.3503i | − | 1.24848i | −0.781232 | − | 0.624241i | \(-0.785408\pi\) | ||
0.781232 | − | 0.624241i | \(-0.214592\pi\) | |||||||
\(758\) | 32.3790 | + | 17.4679i | 1.17606 | + | 0.634461i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0852 | 0.691839 | 0.345920 | − | 0.938264i | \(-0.387567\pi\) | ||||
0.345920 | + | 0.938264i | \(0.387567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.9143i | 1.58980i | ||||||||
\(764\) | −8.78623 | − | 13.3717i | −0.317875 | − | 0.483771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.48929 | + | 8.32150i | −0.162205 | + | 0.300668i | ||||
\(767\) | 8.49977 | 0.306909 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.8715 | 1.14931 | 0.574657 | − | 0.818394i | \(-0.305135\pi\) | ||||
0.574657 | + | 0.818394i | \(0.305135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.33306 | + | 2.02877i | 0.0479778 | + | 0.0730170i | ||||
\(773\) | − | 11.9572i | − | 0.430069i | −0.976606 | − | 0.215034i | \(-0.931014\pi\) | ||
0.976606 | − | 0.215034i | \(-0.0689864\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.1506 | − | 0.968095i | 0.400282 | − | 0.0347526i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.2327 | + | 20.0863i | 1.33486 | + | 0.720129i | ||||
\(779\) | 30.5426i | 1.09430i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34231i | 0.0480315i | ||||||||
\(782\) | 5.37169 | − | 9.95715i | 0.192091 | − | 0.356067i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.7455 | + | 54.9146i | −0.848053 | + | 1.96124i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.0852i | − | 1.17936i | −0.807637 | − | 0.589681i | \(-0.799254\pi\) | ||
0.807637 | − | 0.589681i | \(-0.200746\pi\) | |||||||
\(788\) | 40.0435 | − | 26.3116i | 1.42649 | − | 0.937313i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.6148 | −3.29300 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8291 | −0.810684 | ||||||||
\(794\) | 12.1537 | + | 6.55669i | 0.431319 | + | 0.232688i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.384694 | − | 0.585462i | −0.0136351 | − | 0.0207511i | ||||
\(797\) | − | 10.0000i | − | 0.354218i | −0.984191 | − | 0.177109i | \(-0.943325\pi\) | ||
0.984191 | − | 0.177109i | \(-0.0566745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.6582 | −0.766210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.42188 | + | 8.19656i | −0.156142 | + | 0.289431i | ||||
\(803\) | − | 13.7564i | − | 0.485452i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.2432 | + | 23.3288i | 1.52318 | + | 0.821724i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.489289 | + | 5.63565i | 0.0172131 | + | 0.198262i | ||||
\(809\) | 30.6148 | 1.07636 | 0.538180 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538180 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.9290i | 1.89370i | 0.321670 | + | 0.946852i | \(0.395756\pi\) | ||||
−0.321670 | + | 0.946852i | \(0.604244\pi\) | |||||||
\(812\) | 15.6644 | − | 10.2927i | 0.549713 | − | 0.361204i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.76312 | − | 12.5363i | 0.237047 | − | 0.439399i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.1709 | 0.880619 | ||||||||
\(818\) | 17.4005 | − | 32.2541i | 0.608393 | − | 1.12774i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12.6577i | − | 0.441757i | −0.975301 | − | 0.220878i | \(-0.929108\pi\) | ||
0.975301 | − | 0.220878i | \(-0.0708924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.8139 | 0.690670 | 0.345335 | − | 0.938479i | \(-0.387765\pi\) | ||||
0.345335 | + | 0.938479i | \(0.387765\pi\) | |||||||
\(824\) | 41.2614 | − | 3.58233i | 1.43741 | − | 0.124796i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.95715 | − | 5.37169i | −0.346454 | − | 0.186905i | ||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.3717i | − | 1.43690i | −0.695580 | − | 0.718449i | \(-0.744852\pi\) | ||
0.695580 | − | 0.718449i | \(-0.255148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.86412 | + | 39.2327i | 0.237970 | + | 1.36015i | ||||
\(833\) | −44.5510 | −1.54360 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.76312 | − | 10.2927i | −0.233907 | − | 0.355982i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.2467 | − | 8.22533i | −0.526690 | − | 0.284139i | ||||
\(839\) | −20.9013 | −0.721593 | −0.360797 | − | 0.932645i | \(-0.617495\pi\) | ||||
−0.360797 | + | 0.932645i | \(0.617495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 5.81392 | + | 3.13650i | 0.200361 | + | 0.108091i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.5682 | − | 15.4862i | 0.811253 | − | 0.533055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.9126 | −0.924728 | ||||||||
\(848\) | 7.34292 | + | 3.17513i | 0.252157 | + | 0.109035i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 11.7992i | − | 0.404472i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.63673i | − | 0.227237i | −0.993524 | − | 0.113619i | \(-0.963756\pi\) | ||
0.993524 | − | 0.113619i | \(-0.0362442\pi\) | |||||||
\(854\) | 26.7434 | + | 14.4275i | 0.915140 | + | 0.493700i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.77154 | − | 31.9227i | −0.0947292 | − | 1.09110i | ||||
\(857\) | 9.80765 | 0.335023 | 0.167512 | − | 0.985870i | \(-0.446427\pi\) | ||||
0.167512 | + | 0.985870i | \(0.446427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.3864i | 1.34385i | 0.740621 | + | 0.671923i | \(0.234531\pi\) | ||||
−0.740621 | + | 0.671923i | \(0.765469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.393115 | − | 0.728692i | 0.0133896 | − | 0.0248193i | ||||
\(863\) | 7.07054 | 0.240684 | 0.120342 | − | 0.992732i | \(-0.461601\pi\) | ||||
0.120342 | + | 0.992732i | \(0.461601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.7146 | + | 27.2755i | −0.500023 | + | 0.926860i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −35.9143 | − | 54.6577i | −1.21901 | − | 1.85520i | ||||
\(869\) | − | 2.34185i | − | 0.0794417i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9143 | 0.674771 | ||||||||
\(872\) | −2.29273 | − | 26.4078i | −0.0776417 | − | 0.894281i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.97858 | − | 4.84377i | −0.303705 | − | 0.163843i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 23.1365i | − | 0.781264i | −0.920547 | − | 0.390632i | \(-0.872256\pi\) | ||
0.920547 | − | 0.390632i | \(-0.127744\pi\) | |||||||
\(878\) | 1.60688 | − | 2.97858i | 0.0542297 | − | 0.100522i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.4569 | −0.958738 | −0.479369 | − | 0.877613i | \(-0.659134\pi\) | ||||
−0.479369 | + | 0.877613i | \(0.659134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.2003i | 1.38650i | 0.720697 | + | 0.693250i | \(0.243822\pi\) | ||||
−0.720697 | + | 0.693250i | \(0.756178\pi\) | |||||||
\(884\) | −24.7862 | + | 16.2865i | −0.833651 | + | 0.547773i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.7648 | + | 13.8996i | 0.865586 | + | 0.466967i | ||||
\(887\) | −3.55777 | −0.119458 | −0.0597291 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597291 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.1281 | 1.04400 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.38998 | − | 11.2467i | −0.247435 | − | 0.376569i | ||||
\(893\) | 19.5296i | 0.653534i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.7533 | − | 50.2976i | 0.559687 | − | 1.68032i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.4580 | + | 47.1898i | −0.849544 | + | 1.57474i | ||||
\(899\) | 13.9572i | 0.465497i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.95715i | 0.198462i | ||||||||
\(902\) | 32.4507 | + | 17.5065i | 1.08049 | + | 0.582903i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 55.6938 | − | 4.83535i | 1.85235 | − | 0.160821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.6577i | 1.68206i | 0.540988 | + | 0.841031i | \(0.318051\pi\) | ||||
−0.540988 | + | 0.841031i | \(0.681949\pi\) | |||||||
\(908\) | 16.6430 | − | 10.9357i | 0.552317 | − | 0.362915i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.4569 | 0.876557 | 0.438279 | − | 0.898839i | \(-0.355588\pi\) | ||||
0.438279 | + | 0.898839i | \(0.355588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.6577 | −1.01462 | ||||||||
\(914\) | 25.9859 | − | 48.1684i | 0.859538 | − | 1.59327i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.9357 | + | 12.4422i | −0.625654 | + | 0.411103i | ||||
\(917\) | 33.1709i | 1.09540i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.8077 | 0.983264 | 0.491632 | − | 0.870803i | \(-0.336401\pi\) | ||||
0.491632 | + | 0.870803i | \(0.336401\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.90383 | − | 3.18500i | −0.194432 | − | 0.104892i | ||||
\(923\) | − | 2.91477i | − | 0.0959407i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.2829 | − | 19.0607i | 0.337916 | − | 0.626373i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.88240 | + | 7.00735i | −0.291579 | + | 0.230027i | ||||
\(929\) | 8.82908 | 0.289673 | 0.144836 | − | 0.989456i | \(-0.453734\pi\) | ||||
0.144836 | + | 0.989456i | \(0.453734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.1726i | 1.31660i | ||||||||
\(932\) | 20.8438 | + | 31.7220i | 0.682760 | + | 1.03909i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.0147 | + | 20.5082i | 1.24388 | + | 0.671049i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.2302 | 1.37960 | 0.689799 | − | 0.724000i | \(-0.257699\pi\) | ||||
0.689799 | + | 0.724000i | \(0.257699\pi\) | |||||||
\(938\) | −23.3288 | − | 12.5855i | −0.761714 | − | 0.410930i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 32.7434i | − | 1.06740i | −0.845673 | − | 0.533702i | \(-0.820800\pi\) | ||
0.845673 | − | 0.533702i | \(-0.179200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.5426 | 0.994604 | ||||||||
\(944\) | 6.26817 | + | 2.71040i | 0.204012 | + | 0.0882162i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.4275 | − | 26.7434i | 0.469080 | − | 0.869502i | ||||
\(947\) | − | 15.9143i | − | 0.517146i | −0.965992 | − | 0.258573i | \(-0.916748\pi\) | ||
0.965992 | − | 0.258573i | \(-0.0832522\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8715i | 0.969669i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39.3288 | − | 3.41454i | 1.27466 | − | 0.110666i | ||||
\(953\) | 55.6791 | 1.80362 | 0.901812 | − | 0.432129i | \(-0.142238\pi\) | ||||
0.901812 | + | 0.432129i | \(0.142238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.88661 | + | 4.39312i | 0.0933598 | + | 0.142083i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.23519 | − | 4.14323i | 0.0722158 | − | 0.133862i | ||||
\(959\) | 70.1873 | 2.26647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7005 | 0.570985 | ||||||||
\(962\) | −14.6858 | + | 27.2222i | −0.473491 | + | 0.877679i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.8463 | − | 18.0288i | −0.381543 | − | 0.580668i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7581 | 1.76090 | 0.880451 | − | 0.474138i | \(-0.157240\pi\) | ||||
0.880451 | + | 0.474138i | \(0.157240\pi\) | |||||||
\(968\) | 16.1839 | − | 1.40509i | 0.520169 | − | 0.0451612i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.3221i | 0.973083i | 0.873657 | + | 0.486542i | \(0.161742\pi\) | ||||
−0.873657 | + | 0.486542i | \(0.838258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 21.7564i | − | 0.697478i | ||||||
\(974\) | −8.12494 | + | 15.0607i | −0.260340 | + | 0.482575i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.8353 | − | 7.27973i | −0.538886 | − | 0.233018i | ||||
\(977\) | −29.7220 | −0.950890 | −0.475445 | − | 0.879746i | \(-0.657713\pi\) | ||||
−0.475445 | + | 0.879746i | \(0.657713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.73038i | 0.247064i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.7894 | + | 9.59702i | 0.567681 | + | 0.306253i | ||||
\(983\) | −49.5443 | −1.58022 | −0.790109 | − | 0.612966i | \(-0.789976\pi\) | ||||
−0.790109 | + | 0.612966i | \(0.789976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.41454 | − | 4.00000i | −0.236127 | − | 0.127386i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6858 | + | 22.3503i | 0.467219 | + | 0.711057i | ||||
\(989\) | − | 25.1709i | − | 0.800389i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0937 | 0.606530 | 0.303265 | − | 0.952906i | \(-0.401923\pi\) | ||||
0.303265 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(992\) | 24.4507 | + | 30.9933i | 0.776309 | + | 0.984037i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.84208 | + | 3.41454i | −0.0584271 | + | 0.108303i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.8500i | − | 1.23039i | −0.788374 | − | 0.615197i | \(-0.789077\pi\) | ||
0.788374 | − | 0.615197i | \(-0.210923\pi\) | |||||||
\(998\) | 11.4862 | + | 6.19656i | 0.363588 | + | 0.196149i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))