Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1133,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.d (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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.3 | ||
Root | \(1.69547 - 0.354107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1133 |
Dual form | 1134.2.d.a.1133.11 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.79035 | −0.800669 | −0.400334 | − | 0.916369i | \(-0.631106\pi\) | ||||
−0.400334 | + | 0.916369i | \(0.631106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.28052 | − | 1.34136i | 0.861954 | − | 0.506987i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.79035i | 0.566158i | ||||||||
\(11\) | 2.40150i | 0.724081i | 0.932162 | + | 0.362040i | \(0.117920\pi\) | ||||
−0.932162 | + | 0.362040i | \(0.882080\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89133i | 1.35661i | 0.734781 | + | 0.678305i | \(0.237285\pi\) | ||||
−0.734781 | + | 0.678305i | \(0.762715\pi\) | |||||||
\(14\) | −1.34136 | − | 2.28052i | −0.358494 | − | 0.609493i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.66466 | −0.888812 | −0.444406 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444406 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.01701i | − | 0.692150i | −0.938207 | − | 0.346075i | \(-0.887514\pi\) | ||
0.938207 | − | 0.346075i | \(-0.112486\pi\) | |||||||
\(20\) | 1.79035 | 0.400334 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.40150 | 0.512002 | ||||||||
\(23\) | 3.76638i | 0.785345i | 0.919678 | + | 0.392673i | \(0.128449\pi\) | ||||
−0.919678 | + | 0.392673i | \(0.871551\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79465 | −0.358930 | ||||||||
\(26\) | 4.89133 | 0.959268 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.28052 | + | 1.34136i | −0.430977 | + | 0.253493i | ||||
\(29\) | 6.56103i | 1.21835i | 0.793035 | + | 0.609176i | \(0.208500\pi\) | ||||
−0.793035 | + | 0.609176i | \(0.791500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.64661i | 0.834556i | 0.908779 | + | 0.417278i | \(0.137016\pi\) | ||||
−0.908779 | + | 0.417278i | \(0.862984\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.66466i | 0.628485i | ||||||||
\(35\) | −4.08292 | + | 2.40150i | −0.690140 | + | 0.405928i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.36404 | 1.53944 | 0.769719 | − | 0.638382i | \(-0.220396\pi\) | ||||
0.769719 | + | 0.638382i | \(0.220396\pi\) | |||||||
\(38\) | −3.01701 | −0.489424 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.79035i | − | 0.283079i | ||||||
\(41\) | −8.08188 | −1.26218 | −0.631088 | − | 0.775711i | \(-0.717392\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.96254 | 1.06178 | 0.530888 | − | 0.847442i | \(-0.321858\pi\) | ||||
0.530888 | + | 0.847442i | \(0.321858\pi\) | |||||||
\(44\) | − | 2.40150i | − | 0.362040i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.76638 | 0.555323 | ||||||||
\(47\) | 5.13604 | 0.749169 | 0.374584 | − | 0.927193i | \(-0.377785\pi\) | ||||
0.374584 | + | 0.927193i | \(0.377785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.40150 | − | 6.11799i | 0.485929 | − | 0.873998i | ||||
\(50\) | 1.79465i | 0.253802i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.89133i | − | 0.678305i | ||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.29953i | − | 0.579749i | ||||||
\(56\) | 1.34136 | + | 2.28052i | 0.179247 | + | 0.304747i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.56103 | 0.861506 | ||||||||
\(59\) | 14.5900 | 1.89946 | 0.949729 | − | 0.313073i | \(-0.101359\pi\) | ||||
0.949729 | + | 0.313073i | \(0.101359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3283i | 1.45044i | 0.688518 | + | 0.725219i | \(0.258262\pi\) | ||||
−0.688518 | + | 0.725219i | \(0.741738\pi\) | |||||||
\(62\) | 4.64661 | 0.590120 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 8.75718i | − | 1.08619i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.570231 | 0.0696648 | 0.0348324 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348324 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(68\) | 3.66466 | 0.444406 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.40150 | + | 4.08292i | 0.287035 | + | 0.488002i | ||||
\(71\) | 5.96254i | 0.707623i | 0.935317 | + | 0.353811i | \(0.115115\pi\) | ||||
−0.935317 | + | 0.353811i | \(0.884885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3814i | 1.44913i | 0.689204 | + | 0.724567i | \(0.257960\pi\) | ||||
−0.689204 | + | 0.724567i | \(0.742040\pi\) | |||||||
\(74\) | − | 9.36404i | − | 1.08855i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.01701i | 0.346075i | ||||||||
\(77\) | 3.22128 | + | 5.47667i | 0.367099 | + | 0.624124i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.03663 | 0.341647 | 0.170824 | − | 0.985302i | \(-0.445357\pi\) | ||||
0.170824 | + | 0.985302i | \(0.445357\pi\) | |||||||
\(80\) | −1.79035 | −0.200167 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.08188i | 0.892494i | ||||||||
\(83\) | −14.0054 | −1.53729 | −0.768646 | − | 0.639674i | \(-0.779069\pi\) | ||||
−0.768646 | + | 0.639674i | \(0.779069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.56103 | 0.711644 | ||||||||
\(86\) | − | 6.96254i | − | 0.750790i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.40150 | −0.256001 | ||||||||
\(89\) | 3.74863 | 0.397354 | 0.198677 | − | 0.980065i | \(-0.436336\pi\) | ||||
0.198677 | + | 0.980065i | \(0.436336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.56103 | + | 11.1547i | 0.687783 | + | 1.16934i | ||||
\(92\) | − | 3.76638i | − | 0.392673i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 5.13604i | − | 0.529742i | ||||||
\(95\) | 5.40150i | 0.554183i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.51087i | 0.559545i | 0.960066 | + | 0.279772i | \(0.0902590\pi\) | ||||
−0.960066 | + | 0.279772i | \(0.909741\pi\) | |||||||
\(98\) | −6.11799 | − | 3.40150i | −0.618010 | − | 0.343604i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.79465 | 0.179465 | ||||||||
\(101\) | −0.250324 | −0.0249082 | −0.0124541 | − | 0.999922i | \(-0.503964\pi\) | ||||
−0.0124541 | + | 0.999922i | \(0.503964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.167931i | − | 0.0165468i | −0.999966 | − | 0.00827339i | \(-0.997366\pi\) | ||
0.999966 | − | 0.00827339i | \(-0.00263353\pi\) | |||||||
\(104\) | −4.89133 | −0.479634 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.99080i | − | 0.772500i | −0.922394 | − | 0.386250i | \(-0.873770\pi\) | ||
0.922394 | − | 0.386250i | \(-0.126230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9533 | −1.81540 | −0.907700 | − | 0.419619i | \(-0.862164\pi\) | ||||
−0.907700 | + | 0.419619i | \(0.862164\pi\) | |||||||
\(110\) | −4.29953 | −0.409944 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.28052 | − | 1.34136i | 0.215488 | − | 0.126747i | ||||
\(113\) | − | 1.15953i | − | 0.109079i | −0.998512 | − | 0.0545396i | \(-0.982631\pi\) | ||
0.998512 | − | 0.0545396i | \(-0.0173691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.74314i | − | 0.628801i | ||||||
\(116\) | − | 6.56103i | − | 0.609176i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.5900i | − | 1.34312i | ||||||
\(119\) | −8.35733 | + | 4.91564i | −0.766115 | + | 0.450616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23278 | 0.475707 | ||||||||
\(122\) | 11.3283 | 1.02561 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.64661i | − | 0.417278i | ||||||
\(125\) | 12.1648 | 1.08805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.40150 | 0.124363 | 0.0621817 | − | 0.998065i | \(-0.480194\pi\) | ||||
0.0621817 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.75718 | −0.768056 | ||||||||
\(131\) | −10.4918 | −0.916671 | −0.458335 | − | 0.888779i | \(-0.651554\pi\) | ||||
−0.458335 | + | 0.888779i | \(0.651554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.04690 | − | 6.88034i | −0.350911 | − | 0.596601i | ||||
\(134\) | − | 0.570231i | − | 0.0492604i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.66466i | − | 0.314242i | ||||||
\(137\) | 4.72056i | 0.403305i | 0.979457 | + | 0.201652i | \(0.0646311\pi\) | ||||
−0.979457 | + | 0.201652i | \(0.935369\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.36375i | 0.200491i | 0.994963 | + | 0.100245i | \(0.0319628\pi\) | ||||
−0.994963 | + | 0.100245i | \(0.968037\pi\) | |||||||
\(140\) | 4.08292 | − | 2.40150i | 0.345070 | − | 0.202964i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.96254 | 0.500365 | ||||||||
\(143\) | −11.7465 | −0.982295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.7465i | − | 0.975497i | ||||||
\(146\) | 12.3814 | 1.02469 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.36404 | −0.769719 | ||||||||
\(149\) | − | 17.3640i | − | 1.42252i | −0.702930 | − | 0.711259i | \(-0.748125\pi\) | ||
0.702930 | − | 0.711259i | \(-0.251875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2328 | −0.914110 | −0.457055 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457055 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(152\) | 3.01701 | 0.244712 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.47667 | − | 3.22128i | 0.441322 | − | 0.259578i | ||||
\(155\) | − | 8.31905i | − | 0.668203i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8431i | − | 1.10480i | −0.833580 | − | 0.552399i | \(-0.813713\pi\) | ||
0.833580 | − | 0.552399i | \(-0.186287\pi\) | |||||||
\(158\) | − | 3.03663i | − | 0.241581i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.79035i | 0.141540i | ||||||||
\(161\) | 5.05208 | + | 8.58930i | 0.398159 | + | 0.676931i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33577 | −0.339604 | −0.169802 | − | 0.985478i | \(-0.554313\pi\) | ||||
−0.169802 | + | 0.985478i | \(0.554313\pi\) | |||||||
\(164\) | 8.08188 | 0.631088 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.0054i | 1.08703i | ||||||||
\(167\) | −12.4151 | −0.960711 | −0.480355 | − | 0.877074i | \(-0.659492\pi\) | ||||
−0.480355 | + | 0.877074i | \(0.659492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9251 | −0.840390 | ||||||||
\(170\) | − | 6.56103i | − | 0.503208i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.96254 | −0.530888 | ||||||||
\(173\) | 17.4182 | 1.32428 | 0.662139 | − | 0.749381i | \(-0.269649\pi\) | ||||
0.662139 | + | 0.749381i | \(0.269649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.09272 | + | 2.40727i | −0.309381 | + | 0.181973i | ||||
\(176\) | 2.40150i | 0.181020i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 3.74863i | − | 0.280972i | ||||||
\(179\) | 13.1221i | 0.980789i | 0.871501 | + | 0.490395i | \(0.163147\pi\) | ||||
−0.871501 | + | 0.490395i | \(0.836853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.3577i | − | 0.992873i | −0.868073 | − | 0.496437i | \(-0.834641\pi\) | ||
0.868073 | − | 0.496437i | \(-0.165359\pi\) | |||||||
\(182\) | 11.1547 | − | 6.56103i | 0.826845 | − | 0.486336i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.76638 | −0.277661 | ||||||||
\(185\) | −16.7649 | −1.23258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.80071i | − | 0.643572i | ||||||
\(188\) | −5.13604 | −0.374584 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.40150 | 0.391866 | ||||||||
\(191\) | 9.25333i | 0.669547i | 0.942299 | + | 0.334774i | \(0.108660\pi\) | ||||
−0.942299 | + | 0.334774i | \(0.891340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.5602 | −1.76788 | −0.883941 | − | 0.467599i | \(-0.845119\pi\) | ||||
−0.883941 | + | 0.467599i | \(0.845119\pi\) | |||||||
\(194\) | 5.51087 | 0.395658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.40150 | + | 6.11799i | −0.242965 | + | 0.436999i | ||||
\(197\) | − | 12.4861i | − | 0.889598i | −0.895630 | − | 0.444799i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444799i | \(-0.146725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.179145i | − | 0.0126993i | −0.999980 | − | 0.00634964i | \(-0.997979\pi\) | ||
0.999980 | − | 0.00634964i | \(-0.00202117\pi\) | |||||||
\(200\) | − | 1.79465i | − | 0.126901i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.250324i | 0.0176127i | ||||||||
\(203\) | 8.80071 | + | 14.9625i | 0.617689 | + | 1.05016i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4694 | 1.01059 | ||||||||
\(206\) | −0.167931 | −0.0117003 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89133i | 0.339152i | ||||||||
\(209\) | 7.24536 | 0.501172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.1221 | −1.04105 | −0.520523 | − | 0.853848i | \(-0.674263\pi\) | ||||
−0.520523 | + | 0.853848i | \(0.674263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.99080 | −0.546240 | ||||||||
\(215\) | −12.4654 | −0.850131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.23278 | + | 10.5967i | 0.423109 | + | 0.719348i | ||||
\(218\) | 18.9533i | 1.28368i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.29953i | 0.289874i | ||||||||
\(221\) | − | 17.9251i | − | 1.20577i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.39524i | − | 0.562187i | −0.959680 | − | 0.281093i | \(-0.909303\pi\) | ||
0.959680 | − | 0.281093i | \(-0.0906971\pi\) | |||||||
\(224\) | −1.34136 | − | 2.28052i | −0.0896234 | − | 0.152373i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.15953 | −0.0771306 | ||||||||
\(227\) | 2.42522 | 0.160967 | 0.0804836 | − | 0.996756i | \(-0.474354\pi\) | ||||
0.0804836 | + | 0.996756i | \(0.474354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.01975i | − | 0.133469i | −0.997771 | − | 0.0667344i | \(-0.978742\pi\) | ||
0.997771 | − | 0.0667344i | \(-0.0212580\pi\) | |||||||
\(230\) | −6.74314 | −0.444630 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.56103 | −0.430753 | ||||||||
\(233\) | 12.7289i | 0.833899i | 0.908930 | + | 0.416950i | \(0.136901\pi\) | ||||
−0.908930 | + | 0.416950i | \(0.863099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.19531 | −0.599836 | ||||||||
\(236\) | −14.5900 | −0.949729 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.91564 | + | 8.35733i | 0.318633 | + | 0.541725i | ||||
\(239\) | 17.4495i | 1.12871i | 0.825531 | + | 0.564356i | \(0.190876\pi\) | ||||
−0.825531 | + | 0.564356i | \(0.809124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4332i | 0.736476i | 0.929732 | + | 0.368238i | \(0.120039\pi\) | ||||
−0.929732 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(242\) | − | 5.23278i | − | 0.336376i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.3283i | − | 0.725219i | ||||||
\(245\) | −6.08988 | + | 10.9533i | −0.389068 | + | 0.699783i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.7572 | 0.938977 | ||||||||
\(248\) | −4.64661 | −0.295060 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 12.1648i | − | 0.769369i | ||||||
\(251\) | 27.3560 | 1.72669 | 0.863347 | − | 0.504611i | \(-0.168364\pi\) | ||||
0.863347 | + | 0.504611i | \(0.168364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.04499 | −0.568653 | ||||||||
\(254\) | − | 1.40150i | − | 0.0879382i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.49673 | 0.218120 | 0.109060 | − | 0.994035i | \(-0.465216\pi\) | ||||
0.109060 | + | 0.994035i | \(0.465216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.3548 | − | 12.5606i | 1.32693 | − | 0.780475i | ||||
\(260\) | 8.75718i | 0.543097i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.4918i | 0.648184i | ||||||||
\(263\) | 9.64348i | 0.594643i | 0.954777 | + | 0.297321i | \(0.0960932\pi\) | ||||
−0.954777 | + | 0.297321i | \(0.903907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.88034 | + | 4.04690i | −0.421861 | + | 0.248131i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.570231 | −0.0348324 | ||||||||
\(269\) | 6.91107 | 0.421376 | 0.210688 | − | 0.977553i | \(-0.432430\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.6312i | − | 1.25326i | −0.779318 | − | 0.626629i | \(-0.784434\pi\) | ||
0.779318 | − | 0.626629i | \(-0.215566\pi\) | |||||||
\(272\) | −3.66466 | −0.222203 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.72056 | 0.285179 | ||||||||
\(275\) | − | 4.30986i | − | 0.259894i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5144 | −0.932168 | −0.466084 | − | 0.884740i | \(-0.654336\pi\) | ||||
−0.466084 | + | 0.884740i | \(0.654336\pi\) | |||||||
\(278\) | 2.36375 | 0.141768 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.40150 | − | 4.08292i | −0.143517 | − | 0.244001i | ||||
\(281\) | − | 13.5977i | − | 0.811168i | −0.914058 | − | 0.405584i | \(-0.867068\pi\) | ||
0.914058 | − | 0.405584i | \(-0.132932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.44783i | 0.323840i | 0.986804 | + | 0.161920i | \(0.0517687\pi\) | ||||
−0.986804 | + | 0.161920i | \(0.948231\pi\) | |||||||
\(284\) | − | 5.96254i | − | 0.353811i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7465i | 0.694587i | ||||||||
\(287\) | −18.4308 | + | 10.8407i | −1.08794 | + | 0.639907i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.57023 | −0.210014 | ||||||||
\(290\) | −11.7465 | −0.689781 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 12.3814i | − | 0.724567i | ||||||
\(293\) | 24.4622 | 1.42910 | 0.714550 | − | 0.699585i | \(-0.246632\pi\) | ||||
0.714550 | + | 0.699585i | \(0.246632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.1212 | −1.52084 | ||||||||
\(296\) | 9.36404i | 0.544274i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.3640 | −1.00587 | ||||||||
\(299\) | −18.4226 | −1.06541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.8782 | − | 9.33927i | 0.915203 | − | 0.538307i | ||||
\(302\) | 11.2328i | 0.646374i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 3.01701i | − | 0.173037i | ||||||
\(305\) | − | 20.2816i | − | 1.16132i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.2223i | 1.78195i | 0.454053 | + | 0.890975i | \(0.349978\pi\) | ||||
−0.454053 | + | 0.890975i | \(0.650022\pi\) | |||||||
\(308\) | −3.22128 | − | 5.47667i | −0.183550 | − | 0.312062i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.31905 | −0.472491 | ||||||||
\(311\) | −10.9100 | −0.618651 | −0.309325 | − | 0.950956i | \(-0.600103\pi\) | ||||
−0.309325 | + | 0.950956i | \(0.600103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.42405i | 0.193539i | 0.995307 | + | 0.0967694i | \(0.0308509\pi\) | ||||
−0.995307 | + | 0.0967694i | \(0.969149\pi\) | |||||||
\(314\) | −13.8431 | −0.781210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.03663 | −0.170824 | ||||||||
\(317\) | − | 19.0471i | − | 1.06979i | −0.844917 | − | 0.534897i | \(-0.820350\pi\) | ||
0.844917 | − | 0.534897i | \(-0.179650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.7563 | −0.882186 | ||||||||
\(320\) | 1.79035 | 0.100084 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.58930 | − | 5.05208i | 0.478663 | − | 0.281541i | ||||
\(323\) | 11.0563i | 0.615191i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 8.77821i | − | 0.486927i | ||||||
\(326\) | 4.33577i | 0.240136i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.08188i | − | 0.446247i | ||||||
\(329\) | 11.7128 | − | 6.88929i | 0.645749 | − | 0.379819i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0732502 | 0.00402620 | 0.00201310 | − | 0.999998i | \(-0.499359\pi\) | ||||
0.00201310 | + | 0.999998i | \(0.499359\pi\) | |||||||
\(332\) | 14.0054 | 0.768646 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4151i | 0.679325i | ||||||||
\(335\) | −1.02091 | −0.0557784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.23278 | −0.121627 | −0.0608136 | − | 0.998149i | \(-0.519370\pi\) | ||||
−0.0608136 | + | 0.998149i | \(0.519370\pi\) | |||||||
\(338\) | 10.9251i | 0.594246i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.56103 | −0.355822 | ||||||||
\(341\) | −11.1589 | −0.604286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.449242 | − | 18.5148i | −0.0242568 | − | 0.999706i | ||||
\(344\) | 6.96254i | 0.375395i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 17.4182i | − | 0.936406i | ||||||
\(347\) | 31.8409i | 1.70931i | 0.519195 | + | 0.854656i | \(0.326232\pi\) | ||||
−0.519195 | + | 0.854656i | \(0.673768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.7354i | − | 0.788770i | −0.918945 | − | 0.394385i | \(-0.870958\pi\) | ||
0.918945 | − | 0.394385i | \(-0.129042\pi\) | |||||||
\(350\) | 2.40727 | + | 4.09272i | 0.128674 | + | 0.218765i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.40150 | 0.128001 | ||||||||
\(353\) | −2.15957 | −0.114943 | −0.0574713 | − | 0.998347i | \(-0.518304\pi\) | ||||
−0.0574713 | + | 0.998347i | \(0.518304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.6750i | − | 0.566571i | ||||||
\(356\) | −3.74863 | −0.198677 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1221 | 0.693523 | ||||||||
\(359\) | − | 32.6448i | − | 1.72293i | −0.507820 | − | 0.861463i | \(-0.669549\pi\) | ||
0.507820 | − | 0.861463i | \(-0.330451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.89765 | 0.520929 | ||||||||
\(362\) | −13.3577 | −0.702067 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.56103 | − | 11.1547i | −0.343891 | − | 0.584668i | ||||
\(365\) | − | 22.1670i | − | 1.16028i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7003i | 1.55034i | 0.631751 | + | 0.775171i | \(0.282336\pi\) | ||||
−0.631751 | + | 0.775171i | \(0.717664\pi\) | |||||||
\(368\) | 3.76638i | 0.196336i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.7649i | 0.871566i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.01672 | −0.104422 | −0.0522109 | − | 0.998636i | \(-0.516627\pi\) | ||||
−0.0522109 | + | 0.998636i | \(0.516627\pi\) | |||||||
\(374\) | −8.80071 | −0.455074 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.13604i | 0.264871i | ||||||||
\(377\) | −32.0921 | −1.65283 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8709 | −0.969332 | −0.484666 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484666 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(380\) | − | 5.40150i | − | 0.277091i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.25333 | 0.473441 | ||||||||
\(383\) | −0.836511 | −0.0427437 | −0.0213719 | − | 0.999772i | \(-0.506803\pi\) | ||||
−0.0213719 | + | 0.999772i | \(0.506803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.76722 | − | 9.80515i | −0.293925 | − | 0.499717i | ||||
\(386\) | 24.5602i | 1.25008i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 5.51087i | − | 0.279772i | ||||||
\(389\) | − | 24.8219i | − | 1.25852i | −0.777195 | − | 0.629260i | \(-0.783358\pi\) | ||
0.777195 | − | 0.629260i | \(-0.216642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.8025i | − | 0.698024i | ||||||
\(392\) | 6.11799 | + | 3.40150i | 0.309005 | + | 0.171802i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.4861 | −0.629041 | ||||||||
\(395\) | −5.43662 | −0.273546 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.03390i | 0.152267i | 0.997098 | + | 0.0761336i | \(0.0242575\pi\) | ||||
−0.997098 | + | 0.0761336i | \(0.975742\pi\) | |||||||
\(398\) | −0.179145 | −0.00897975 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.79465 | −0.0897324 | ||||||||
\(401\) | 13.0771i | 0.653038i | 0.945191 | + | 0.326519i | \(0.105876\pi\) | ||||
−0.945191 | + | 0.326519i | \(0.894124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.7281 | −1.13217 | ||||||||
\(404\) | 0.250324 | 0.0124541 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.9625 | − | 8.80071i | 0.742578 | − | 0.436772i | ||||
\(407\) | 22.4878i | 1.11468i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.56709i | − | 0.275275i | −0.990483 | − | 0.137637i | \(-0.956049\pi\) | ||
0.990483 | − | 0.137637i | \(-0.0439508\pi\) | |||||||
\(410\) | − | 14.4694i | − | 0.714592i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.167931i | 0.00827339i | ||||||||
\(413\) | 33.2728 | − | 19.5705i | 1.63725 | − | 0.963000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.0746 | 1.23086 | ||||||||
\(416\) | 4.89133 | 0.239817 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7.24536i | − | 0.354382i | ||||||
\(419\) | 16.3988 | 0.801132 | 0.400566 | − | 0.916268i | \(-0.368814\pi\) | ||||
0.400566 | + | 0.916268i | \(0.368814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4578 | 0.753369 | 0.376684 | − | 0.926342i | \(-0.377064\pi\) | ||||
0.376684 | + | 0.926342i | \(0.377064\pi\) | |||||||
\(422\) | 15.1221i | 0.736131i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.57678 | 0.319021 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.1953 | + | 25.8343i | 0.735353 | + | 1.25021i | ||||
\(428\) | 7.99080i | 0.386250i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.4654i | 0.601134i | ||||||||
\(431\) | 25.0266i | 1.20549i | 0.797935 | + | 0.602744i | \(0.205926\pi\) | ||||
−0.797935 | + | 0.602744i | \(0.794074\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.25168i | 0.108209i | 0.998535 | + | 0.0541044i | \(0.0172304\pi\) | ||||
−0.998535 | + | 0.0541044i | \(0.982770\pi\) | |||||||
\(434\) | 10.5967 | − | 6.23278i | 0.508656 | − | 0.299183i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9533 | 0.907700 | ||||||||
\(437\) | 11.3632 | 0.543576 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7400i | 0.894412i | 0.894431 | + | 0.447206i | \(0.147581\pi\) | ||||
−0.894431 | + | 0.447206i | \(0.852419\pi\) | |||||||
\(440\) | 4.29953 | 0.204972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.9251 | −0.852609 | ||||||||
\(443\) | 1.20451i | 0.0572281i | 0.999591 | + | 0.0286141i | \(0.00910938\pi\) | ||||
−0.999591 | + | 0.0286141i | \(0.990891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.71136 | −0.318149 | ||||||||
\(446\) | −8.39524 | −0.397526 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.28052 | + | 1.34136i | −0.107744 | + | 0.0633733i | ||||
\(449\) | − | 26.8022i | − | 1.26487i | −0.774612 | − | 0.632436i | \(-0.782055\pi\) | ||
0.774612 | − | 0.632436i | \(-0.217945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19.4087i | − | 0.913918i | ||||||
\(452\) | 1.15953i | 0.0545396i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.42522i | − | 0.113821i | ||||||
\(455\) | −11.7465 | − | 19.9709i | −0.550686 | − | 0.936250i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8488 | 0.647821 | 0.323911 | − | 0.946088i | \(-0.395002\pi\) | ||||
0.323911 | + | 0.946088i | \(0.395002\pi\) | |||||||
\(458\) | −2.01975 | −0.0943766 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.74314i | 0.314401i | ||||||||
\(461\) | 4.80483 | 0.223783 | 0.111892 | − | 0.993720i | \(-0.464309\pi\) | ||||
0.111892 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0388 | −0.977755 | −0.488877 | − | 0.872353i | \(-0.662593\pi\) | ||||
−0.488877 | + | 0.872353i | \(0.662593\pi\) | |||||||
\(464\) | 6.56103i | 0.304588i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7289 | 0.589656 | ||||||||
\(467\) | −5.82302 | −0.269457 | −0.134729 | − | 0.990883i | \(-0.543016\pi\) | ||||
−0.134729 | + | 0.990883i | \(0.543016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30042 | − | 0.764885i | 0.0600478 | − | 0.0353191i | ||||
\(470\) | 9.19531i | 0.424148i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.5900i | 0.671560i | ||||||||
\(473\) | 16.7206i | 0.768812i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.41447i | 0.248433i | ||||||||
\(476\) | 8.35733 | − | 4.91564i | 0.383057 | − | 0.225308i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.4495 | 0.798121 | ||||||||
\(479\) | 26.9561 | 1.23166 | 0.615828 | − | 0.787881i | \(-0.288822\pi\) | ||||
0.615828 | + | 0.787881i | \(0.288822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.8026i | 2.08842i | ||||||||
\(482\) | 11.4332 | 0.520767 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.23278 | −0.237854 | ||||||||
\(485\) | − | 9.86639i | − | 0.448010i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6268 | −0.617487 | −0.308744 | − | 0.951145i | \(-0.599909\pi\) | ||||
−0.308744 | + | 0.951145i | \(0.599909\pi\) | |||||||
\(488\) | −11.3283 | −0.512807 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.9533 | + | 6.08988i | 0.494821 | + | 0.275113i | ||||
\(491\) | − | 38.9630i | − | 1.75838i | −0.476475 | − | 0.879188i | \(-0.658086\pi\) | ||
0.476475 | − | 0.879188i | \(-0.341914\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 24.0440i | − | 1.08289i | ||||||
\(494\) | − | 14.7572i | − | 0.663957i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.64661i | 0.208639i | ||||||||
\(497\) | 7.99791 | + | 13.5977i | 0.358755 | + | 0.609938i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0097 | 1.16435 | 0.582176 | − | 0.813063i | \(-0.302201\pi\) | ||||
0.582176 | + | 0.813063i | \(0.302201\pi\) | |||||||
\(500\) | −12.1648 | −0.544026 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 27.3560i | − | 1.22096i | ||||||
\(503\) | −10.5271 | −0.469378 | −0.234689 | − | 0.972070i | \(-0.575407\pi\) | ||||
−0.234689 | + | 0.972070i | \(0.575407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.448168 | 0.0199432 | ||||||||
\(506\) | 9.04499i | 0.402099i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.40150 | −0.0621817 | ||||||||
\(509\) | 0.938871 | 0.0416147 | 0.0208074 | − | 0.999784i | \(-0.493376\pi\) | ||||
0.0208074 | + | 0.999784i | \(0.493376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6079 | + | 28.2360i | 0.734692 | + | 1.24909i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.49673i | − | 0.154234i | ||||||
\(515\) | 0.300656i | 0.0132485i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.3342i | 0.542459i | ||||||||
\(518\) | −12.5606 | − | 21.3548i | −0.551879 | − | 0.938278i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.75718 | 0.384028 | ||||||||
\(521\) | 39.5054 | 1.73076 | 0.865382 | − | 0.501112i | \(-0.167076\pi\) | ||||
0.865382 | + | 0.501112i | \(0.167076\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3292i | 1.06384i | 0.846794 | + | 0.531922i | \(0.178530\pi\) | ||||
−0.846794 | + | 0.531922i | \(0.821470\pi\) | |||||||
\(524\) | 10.4918 | 0.458335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.64348 | 0.420476 | ||||||||
\(527\) | − | 17.0283i | − | 0.741763i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.81436 | 0.383233 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.04690 | + | 6.88034i | 0.175455 | + | 0.298301i | ||||
\(533\) | − | 39.5311i | − | 1.71228i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3063i | 0.618516i | ||||||||
\(536\) | 0.570231i | 0.0246302i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 6.91107i | − | 0.297958i | ||||||
\(539\) | 14.6924 | + | 8.16873i | 0.632845 | + | 0.351852i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.7281 | 1.83702 | 0.918512 | − | 0.395394i | \(-0.129392\pi\) | ||||
0.918512 | + | 0.395394i | \(0.129392\pi\) | |||||||
\(542\) | −20.6312 | −0.886187 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.66466i | 0.157121i | ||||||||
\(545\) | 33.9331 | 1.45353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4953 | 1.04734 | 0.523672 | − | 0.851920i | \(-0.324562\pi\) | ||||
0.523672 | + | 0.851920i | \(0.324562\pi\) | |||||||
\(548\) | − | 4.72056i | − | 0.201652i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.30986 | −0.183773 | ||||||||
\(551\) | 19.7947 | 0.843283 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92507 | − | 4.07321i | 0.294484 | − | 0.173210i | ||||
\(554\) | 15.5144i | 0.659142i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 2.36375i | − | 0.100245i | ||||||
\(557\) | 2.54431i | 0.107806i | 0.998546 | + | 0.0539030i | \(0.0171662\pi\) | ||||
−0.998546 | + | 0.0539030i | \(0.982834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.0560i | 1.44042i | ||||||||
\(560\) | −4.08292 | + | 2.40150i | −0.172535 | + | 0.101482i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5977 | −0.573583 | ||||||||
\(563\) | −15.8141 | −0.666487 | −0.333243 | − | 0.942841i | \(-0.608143\pi\) | ||||
−0.333243 | + | 0.942841i | \(0.608143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.07596i | 0.0873363i | ||||||||
\(566\) | 5.44783 | 0.228990 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.96254 | −0.250182 | ||||||||
\(569\) | 6.38311i | 0.267594i | 0.991009 | + | 0.133797i | \(0.0427170\pi\) | ||||
−0.991009 | + | 0.133797i | \(0.957283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.82375 | −0.327414 | −0.163707 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163707 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(572\) | 11.7465 | 0.491148 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.8407 | + | 18.4308i | 0.452482 | + | 0.769289i | ||||
\(575\) | − | 6.75933i | − | 0.281884i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.3197i | − | 0.596138i | −0.954544 | − | 0.298069i | \(-0.903657\pi\) | ||
0.954544 | − | 0.298069i | \(-0.0963425\pi\) | |||||||
\(578\) | 3.57023i | 0.148502i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.7465i | 0.487749i | ||||||||
\(581\) | −31.9395 | + | 18.7863i | −1.32508 | + | 0.779387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.3814 | −0.512346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 24.4622i | − | 1.01053i | ||||||
\(587\) | −4.75150 | −0.196115 | −0.0980577 | − | 0.995181i | \(-0.531263\pi\) | ||||
−0.0980577 | + | 0.995181i | \(0.531263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0189 | 0.577637 | ||||||||
\(590\) | 26.1212i | 1.07539i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.36404 | 0.384860 | ||||||||
\(593\) | −3.58070 | −0.147042 | −0.0735208 | − | 0.997294i | \(-0.523424\pi\) | ||||
−0.0735208 | + | 0.997294i | \(0.523424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9625 | − | 8.80071i | 0.613404 | − | 0.360794i | ||||
\(596\) | 17.3640i | 0.711259i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.4226i | 0.753357i | ||||||||
\(599\) | − | 15.0655i | − | 0.615561i | −0.951457 | − | 0.307780i | \(-0.900414\pi\) | ||
0.951457 | − | 0.307780i | \(-0.0995862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.9444i | − | 0.935920i | −0.883750 | − | 0.467960i | \(-0.844989\pi\) | ||
0.883750 | − | 0.467960i | \(-0.155011\pi\) | |||||||
\(602\) | −9.33927 | − | 15.8782i | −0.380640 | − | 0.647146i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.2328 | 0.457055 | ||||||||
\(605\) | −9.36850 | −0.380884 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.4832i | − | 0.993741i | −0.867825 | − | 0.496870i | \(-0.834482\pi\) | ||
0.867825 | − | 0.496870i | \(-0.165518\pi\) | |||||||
\(608\) | −3.01701 | −0.122356 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.2816 | −0.821178 | ||||||||
\(611\) | 25.1221i | 1.01633i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.880086 | −0.0355463 | −0.0177732 | − | 0.999842i | \(-0.505658\pi\) | ||||
−0.0177732 | + | 0.999842i | \(0.505658\pi\) | |||||||
\(614\) | 31.2223 | 1.26003 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.47667 | + | 3.22128i | −0.220661 | + | 0.129789i | ||||
\(617\) | − | 13.5801i | − | 0.546714i | −0.961913 | − | 0.273357i | \(-0.911866\pi\) | ||
0.961913 | − | 0.273357i | \(-0.0881341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.4869i | − | 1.42634i | −0.700992 | − | 0.713169i | \(-0.747259\pi\) | ||
0.700992 | − | 0.713169i | \(-0.252741\pi\) | |||||||
\(620\) | 8.31905i | 0.334101i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.9100i | 0.437452i | ||||||||
\(623\) | 8.54881 | − | 5.02826i | 0.342501 | − | 0.201453i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8060 | −0.512240 | ||||||||
\(626\) | 3.42405 | 0.136853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8431i | 0.552399i | ||||||||
\(629\) | −34.3161 | −1.36827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9822 | 1.07415 | 0.537073 | − | 0.843536i | \(-0.319530\pi\) | ||||
0.537073 | + | 0.843536i | \(0.319530\pi\) | |||||||
\(632\) | 3.03663i | 0.120790i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.0471 | −0.756458 | ||||||||
\(635\) | −2.50918 | −0.0995739 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.9251 | + | 16.6379i | 1.18567 | + | 0.659216i | ||||
\(638\) | 15.7563i | 0.623800i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.79035i | − | 0.0707698i | ||||||
\(641\) | − | 1.07708i | − | 0.0425420i | −0.999774 | − | 0.0212710i | \(-0.993229\pi\) | ||
0.999774 | − | 0.0212710i | \(-0.00677128\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 38.4661i | − | 1.51695i | −0.651700 | − | 0.758477i | \(-0.725944\pi\) | ||
0.651700 | − | 0.758477i | \(-0.274056\pi\) | |||||||
\(644\) | −5.05208 | − | 8.58930i | −0.199080 | − | 0.338466i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.0563 | 0.435006 | ||||||||
\(647\) | 8.95210 | 0.351943 | 0.175972 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175972 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0380i | 1.37536i | ||||||||
\(650\) | −8.77821 | −0.344310 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.33577 | 0.169802 | ||||||||
\(653\) | − | 11.3846i | − | 0.445513i | −0.974874 | − | 0.222757i | \(-0.928494\pi\) | ||
0.974874 | − | 0.222757i | \(-0.0715055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7839 | 0.733949 | ||||||||
\(656\) | −8.08188 | −0.315544 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.88929 | − | 11.7128i | −0.268572 | − | 0.456614i | ||||
\(659\) | − | 36.3007i | − | 1.41407i | −0.707177 | − | 0.707036i | \(-0.750032\pi\) | ||
0.707177 | − | 0.707036i | \(-0.249968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.0758i | 1.40319i | 0.712578 | + | 0.701593i | \(0.247527\pi\) | ||||
−0.712578 | + | 0.701593i | \(0.752473\pi\) | |||||||
\(662\) | − | 0.0732502i | − | 0.00284695i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.0054i | − | 0.543515i | ||||||
\(665\) | 7.24536 | + | 12.3182i | 0.280963 | + | 0.477680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.7114 | −0.956828 | ||||||||
\(668\) | 12.4151 | 0.480355 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.02091i | 0.0394413i | ||||||||
\(671\) | −27.2049 | −1.05023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.57023 | −0.368905 | −0.184453 | − | 0.982841i | \(-0.559051\pi\) | ||||
−0.184453 | + | 0.982841i | \(0.559051\pi\) | |||||||
\(674\) | 2.23278i | 0.0860034i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.9251 | 0.420195 | ||||||||
\(677\) | 15.6282 | 0.600639 | 0.300320 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300320 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.39207 | + | 12.5676i | 0.283682 | + | 0.482302i | ||||
\(680\) | 6.56103i | 0.251604i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.1589i | 0.427294i | ||||||||
\(683\) | − | 11.1313i | − | 0.425926i | −0.977060 | − | 0.212963i | \(-0.931689\pi\) | ||
0.977060 | − | 0.212963i | \(-0.0683114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.45145i | − | 0.322913i | ||||||
\(686\) | −18.5148 | + | 0.449242i | −0.706899 | + | 0.0171522i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.96254 | 0.265444 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.02419i | 0.115046i | 0.998344 | + | 0.0575228i | \(0.0183202\pi\) | ||||
−0.998344 | + | 0.0575228i | \(0.981680\pi\) | |||||||
\(692\) | −17.4182 | −0.662139 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.8409 | 1.20867 | ||||||||
\(695\) | − | 4.23194i | − | 0.160527i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.6174 | 1.12184 | ||||||||
\(698\) | −14.7354 | −0.557745 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.09272 | − | 2.40727i | 0.154690 | − | 0.0909863i | ||||
\(701\) | − | 50.1486i | − | 1.89409i | −0.321103 | − | 0.947044i | \(-0.604054\pi\) | ||
0.321103 | − | 0.947044i | \(-0.395946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28.2514i | − | 1.06552i | ||||||
\(704\) | − | 2.40150i | − | 0.0905101i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.15957i | 0.0812766i | ||||||||
\(707\) | −0.570868 | + | 0.335775i | −0.0214697 | + | 0.0126281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.60770 | −0.135490 | −0.0677449 | − | 0.997703i | \(-0.521580\pi\) | ||||
−0.0677449 | + | 0.997703i | \(0.521580\pi\) | |||||||
\(710\) | −10.6750 | −0.400626 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.74863i | 0.140486i | ||||||||
\(713\) | −17.5009 | −0.655414 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0304 | 0.786493 | ||||||||
\(716\) | − | 13.1221i | − | 0.490395i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.6448 | −1.21829 | ||||||||
\(719\) | 34.3161 | 1.27977 | 0.639887 | − | 0.768469i | \(-0.278981\pi\) | ||||
0.639887 | + | 0.768469i | \(0.278981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.225257 | − | 0.382970i | −0.00838899 | − | 0.0142626i | ||||
\(722\) | − | 9.89765i | − | 0.368352i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.3577i | 0.496437i | ||||||||
\(725\) | − | 11.7747i | − | 0.437303i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4886i | 0.834057i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(728\) | −11.1547 | + | 6.56103i | −0.413422 | + | 0.243168i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.1670 | −0.820439 | ||||||||
\(731\) | −25.5154 | −0.943720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.1845i | − | 1.15182i | −0.817512 | − | 0.575912i | \(-0.804647\pi\) | ||
0.817512 | − | 0.575912i | \(-0.195353\pi\) | |||||||
\(734\) | 29.7003 | 1.09626 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.76638 | 0.138831 | ||||||||
\(737\) | 1.36941i | 0.0504429i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.08628 | 0.150316 | 0.0751581 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751581 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(740\) | 16.7649 | 0.616290 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.05821i | − | 0.0755083i | −0.999287 | − | 0.0377542i | \(-0.987980\pi\) | ||
0.999287 | − | 0.0377542i | \(-0.0120204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.0877i | 1.13897i | ||||||||
\(746\) | 2.01672i | 0.0738374i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.80071i | 0.321786i | ||||||||
\(749\) | −10.7185 | − | 18.2231i | −0.391647 | − | 0.665859i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8105 | 0.868859 | 0.434429 | − | 0.900706i | \(-0.356950\pi\) | ||||
0.434429 | + | 0.900706i | \(0.356950\pi\) | |||||||
\(752\) | 5.13604 | 0.187292 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.0921i | 1.16873i | ||||||||
\(755\) | 20.1106 | 0.731900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0754 | 0.366197 | 0.183098 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183098 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(758\) | 18.8709i | 0.685421i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.40150 | −0.195933 | ||||||||
\(761\) | 27.8735 | 1.01041 | 0.505207 | − | 0.862998i | \(-0.331416\pi\) | ||||
0.505207 | + | 0.862998i | \(0.331416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.2234 | + | 25.4233i | −1.56479 | + | 0.920384i | ||||
\(764\) | − | 9.25333i | − | 0.334774i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.836511i | 0.0302244i | ||||||||
\(767\) | 71.3645i | 2.57682i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.17261i | 0.258651i | 0.991602 | + | 0.129326i | \(0.0412812\pi\) | ||||
−0.991602 | + | 0.129326i | \(0.958719\pi\) | |||||||
\(770\) | −9.80515 | + | 5.76722i | −0.353353 | + | 0.207836i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.5602 | 0.883941 | ||||||||
\(773\) | 2.14153 | 0.0770255 | 0.0385128 | − | 0.999258i | \(-0.487738\pi\) | ||||
0.0385128 | + | 0.999258i | \(0.487738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.33903i | − | 0.299547i | ||||||
\(776\) | −5.51087 | −0.197829 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.8219 | −0.889907 | ||||||||
\(779\) | 24.3831i | 0.873615i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3191 | −0.512376 | ||||||||
\(782\) | −13.8025 | −0.493578 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.40150 | − | 6.11799i | 0.121482 | − | 0.218500i | ||||
\(785\) | 24.7839i | 0.884577i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.3552i | − | 0.654292i | −0.944974 | − | 0.327146i | \(-0.893913\pi\) | ||
0.944974 | − | 0.327146i | \(-0.106087\pi\) | |||||||
\(788\) | 12.4861i | 0.444799i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.43662i | 0.193426i | ||||||||
\(791\) | −1.55534 | − | 2.64432i | −0.0553017 | − | 0.0940212i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.4103 | −1.96768 | ||||||||
\(794\) | 3.03390 | 0.107669 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.179145i | 0.00634964i | ||||||||
\(797\) | 24.8452 | 0.880062 | 0.440031 | − | 0.897982i | \(-0.354967\pi\) | ||||
0.440031 | + | 0.897982i | \(0.354967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8219 | −0.665870 | ||||||||
\(800\) | 1.79465i | 0.0634504i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.0771 | 0.461768 | ||||||||
\(803\) | −29.7340 | −1.04929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.04499 | − | 15.3778i | −0.318794 | − | 0.541998i | ||||
\(806\) | 22.7281i | 0.800562i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 0.250324i | − | 0.00880637i | ||||||
\(809\) | 37.7861i | 1.32849i | 0.747516 | + | 0.664244i | \(0.231246\pi\) | ||||
−0.747516 | + | 0.664244i | \(0.768754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5165i | 1.28227i | 0.767429 | + | 0.641134i | \(0.221536\pi\) | ||||
−0.767429 | + | 0.641134i | \(0.778464\pi\) | |||||||
\(812\) | −8.80071 | − | 14.9625i | −0.308844 | − | 0.525082i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.4878 | 0.788196 | ||||||||
\(815\) | 7.76255 | 0.271910 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21.0060i | − | 0.734909i | ||||||
\(818\) | −5.56709 | −0.194649 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.4694 | −0.505293 | ||||||||
\(821\) | 6.37558i | 0.222509i | 0.993792 | + | 0.111255i | \(0.0354869\pi\) | ||||
−0.993792 | + | 0.111255i | \(0.964513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0587 | 0.978064 | 0.489032 | − | 0.872266i | \(-0.337350\pi\) | ||||
0.489032 | + | 0.872266i | \(0.337350\pi\) | |||||||
\(824\) | 0.167931 | 0.00585017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.5705 | − | 33.2728i | −0.680944 | − | 1.15771i | ||||
\(827\) | 0.581579i | 0.0202235i | 0.999949 | + | 0.0101117i | \(0.00321872\pi\) | ||||
−0.999949 | + | 0.0101117i | \(0.996781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.9246i | 1.80342i | 0.432346 | + | 0.901708i | \(0.357686\pi\) | ||||
−0.432346 | + | 0.901708i | \(0.642314\pi\) | |||||||
\(830\) | − | 25.0746i | − | 0.870351i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.89133i | − | 0.169576i | ||||||
\(833\) | −12.4654 | + | 22.4204i | −0.431900 | + | 0.776820i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2274 | 0.769211 | ||||||||
\(836\) | −7.24536 | −0.250586 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 16.3988i | − | 0.566486i | ||||||
\(839\) | −6.66075 | −0.229955 | −0.114977 | − | 0.993368i | \(-0.536680\pi\) | ||||
−0.114977 | + | 0.993368i | \(0.536680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0471 | −0.484384 | ||||||||
\(842\) | − | 15.4578i | − | 0.532712i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.1221 | 0.520523 | ||||||||
\(845\) | 19.5597 | 0.672874 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.9334 | − | 7.01904i | 0.410038 | − | 0.241177i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 6.57678i | − | 0.225582i | ||||||
\(851\) | 35.2686i | 1.20899i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.2034i | − | 0.760229i | −0.924939 | − | 0.380115i | \(-0.875885\pi\) | ||
0.924939 | − | 0.380115i | \(-0.124115\pi\) | |||||||
\(854\) | 25.8343 | − | 15.1953i | 0.884033 | − | 0.519973i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.99080 | 0.273120 | ||||||||
\(857\) | −15.2966 | −0.522522 | −0.261261 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261261 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.25646i | − | 0.145229i | −0.997360 | − | 0.0726143i | \(-0.976866\pi\) | ||
0.997360 | − | 0.0726143i | \(-0.0231342\pi\) | |||||||
\(860\) | 12.4654 | 0.425066 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.0266 | 0.852409 | ||||||||
\(863\) | 23.6624i | 0.805476i | 0.915315 | + | 0.402738i | \(0.131941\pi\) | ||||
−0.915315 | + | 0.402738i | \(0.868059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.1846 | −1.06031 | ||||||||
\(866\) | 2.25168 | 0.0765151 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.23278 | − | 10.5967i | −0.211554 | − | 0.359674i | ||||
\(869\) | 7.29247i | 0.247380i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.78919i | 0.0945079i | ||||||||
\(872\) | − | 18.9533i | − | 0.641841i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.3632i | − | 0.384367i | ||||||
\(875\) | 27.7420 | − | 16.3174i | 0.937851 | − | 0.551628i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3923 | −0.688599 | −0.344300 | − | 0.938860i | \(-0.611884\pi\) | ||||
−0.344300 | + | 0.938860i | \(0.611884\pi\) | |||||||
\(878\) | 18.7400 | 0.632445 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 4.29953i | − | 0.144937i | ||||||
\(881\) | −32.4586 | −1.09356 | −0.546780 | − | 0.837276i | \(-0.684147\pi\) | ||||
−0.546780 | + | 0.837276i | \(0.684147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.8311 | −0.835632 | −0.417816 | − | 0.908532i | \(-0.637204\pi\) | ||||
−0.417816 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(884\) | 17.9251i | 0.602885i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.20451 | 0.0404664 | ||||||||
\(887\) | −9.72119 | −0.326405 | −0.163203 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163203 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.19615 | − | 1.87992i | 0.107196 | − | 0.0630506i | ||||
\(890\) | 6.71136i | 0.224965i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.39524i | 0.281093i | ||||||||
\(893\) | − | 15.4955i | − | 0.518537i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 23.4931i | − | 0.785287i | ||||||
\(896\) | 1.34136 | + | 2.28052i | 0.0448117 | + | 0.0761867i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.8022 | −0.894400 | ||||||||
\(899\) | −30.4865 | −1.01678 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −19.4087 | −0.646238 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.15953 | 0.0385653 | ||||||||
\(905\) | 23.9150i | 0.794963i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0863 | −0.534136 | −0.267068 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267068 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(908\) | −2.42522 | −0.0804836 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.9709 | + | 11.7465i | −0.662029 | + | 0.389394i | ||||
\(911\) | − | 31.1870i | − | 1.03327i | −0.856206 | − | 0.516635i | \(-0.827184\pi\) | ||
0.856206 | − | 0.516635i | \(-0.172816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 33.6340i | − | 1.11312i | ||||||
\(914\) | − | 13.8488i | − | 0.458079i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.01975i | 0.0667344i | ||||||||
\(917\) | −23.9267 | + | 14.0733i | −0.790128 | + | 0.464740i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.7664 | 0.849955 | 0.424977 | − | 0.905204i | \(-0.360282\pi\) | ||||
0.424977 | + | 0.905204i | \(0.360282\pi\) | |||||||
\(920\) | 6.74314 | 0.222315 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 4.80483i | − | 0.158239i | ||||||
\(923\) | −29.1647 | −0.959968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.8052 | −0.552550 | ||||||||
\(926\) | 21.0388i | 0.691377i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.56103 | 0.215376 | ||||||||
\(929\) | −54.7487 | −1.79625 | −0.898124 | − | 0.439743i | \(-0.855069\pi\) | ||||
−0.898124 | + | 0.439743i | \(0.855069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.4580 | − | 10.2624i | −0.604938 | − | 0.336336i | ||||
\(932\) | − | 12.7289i | − | 0.416950i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.82302i | 0.190535i | ||||||||
\(935\) | 15.7563i | 0.515288i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.2065i | − | 1.90152i | −0.309924 | − | 0.950761i | \(-0.600304\pi\) | ||
0.309924 | − | 0.950761i | \(-0.399696\pi\) | |||||||
\(938\) | −0.764885 | − | 1.30042i | −0.0249744 | − | 0.0424602i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.19531 | 0.299918 | ||||||||
\(941\) | 33.3316 | 1.08658 | 0.543289 | − | 0.839545i | \(-0.317179\pi\) | ||||
0.543289 | + | 0.839545i | \(0.317179\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30.4394i | − | 0.991245i | ||||||
\(944\) | 14.5900 | 0.474864 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.7206 | 0.543632 | ||||||||
\(947\) | 7.61522i | 0.247461i | 0.992316 | + | 0.123731i | \(0.0394859\pi\) | ||||
−0.992316 | + | 0.123731i | \(0.960514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.5615 | −1.96591 | ||||||||
\(950\) | 5.41447 | 0.175669 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.91564 | − | 8.35733i | −0.159317 | − | 0.270862i | ||||
\(953\) | 55.7861i | 1.80709i | 0.428495 | + | 0.903544i | \(0.359044\pi\) | ||||
−0.428495 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.5667i | − | 0.536085i | ||||||
\(956\) | − | 17.4495i | − | 0.564356i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 26.9561i | − | 0.870912i | ||||||
\(959\) | 6.33197 | + | 10.7653i | 0.204470 | + | 0.347630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.40903 | 0.303517 | ||||||||
\(962\) | 45.8026 | 1.47673 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 11.4332i | − | 0.368238i | ||||||
\(965\) | 43.9713 | 1.41549 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.6739 | 0.857775 | 0.428887 | − | 0.903358i | \(-0.358906\pi\) | ||||
0.428887 | + | 0.903358i | \(0.358906\pi\) | |||||||
\(968\) | 5.23278i | 0.168188i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.86639 | −0.316791 | ||||||||
\(971\) | 8.59942 | 0.275968 | 0.137984 | − | 0.990434i | \(-0.455938\pi\) | ||||
0.137984 | + | 0.990434i | \(0.455938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.17064 | + | 5.39057i | 0.101646 | + | 0.172814i | ||||
\(974\) | 13.6268i | 0.436630i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.3283i | 0.362610i | ||||||||
\(977\) | − | 14.7771i | − | 0.472761i | −0.971661 | − | 0.236380i | \(-0.924039\pi\) | ||
0.971661 | − | 0.236380i | \(-0.0759612\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00235i | 0.287716i | ||||||||
\(980\) | 6.08988 | − | 10.9533i | 0.194534 | − | 0.349891i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38.9630 | −1.24336 | ||||||||
\(983\) | 20.5135 | 0.654280 | 0.327140 | − | 0.944976i | \(-0.393915\pi\) | ||||
0.327140 | + | 0.944976i | \(0.393915\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3545i | 0.712273i | ||||||||
\(986\) | −24.0440 | −0.765716 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.7572 | −0.469489 | ||||||||
\(989\) | 26.2236i | 0.833861i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.29294 | −0.295200 | −0.147600 | − | 0.989047i | \(-0.547155\pi\) | ||||
−0.147600 | + | 0.989047i | \(0.547155\pi\) | |||||||
\(992\) | 4.64661 | 0.147530 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.5977 | − | 7.99791i | 0.431291 | − | 0.253678i | ||||
\(995\) | 0.320733i | 0.0101679i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 0.0199668i | − | 0.000632354i | −1.00000 | 0.000316177i | \(-0.999899\pi\) | |||
1.00000 | 0.000316177i | \(-0.000100642\pi\) | ||||||||
\(998\) | − | 26.0097i | − | 0.823322i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))