Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.a (trivial) |
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: | yes |
Analytic conductor: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.552409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.55241 | 1.09772 | 0.548860 | − | 0.835915i | \(-0.315062\pi\) | ||||
0.548860 | + | 0.835915i | \(0.315062\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.409975 | 0.204988 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.55241 | 0.633769 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.46837 | −0.872700 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.43075 | 1.33592 | 0.667961 | − | 0.744196i | \(-0.267167\pi\) | ||||
0.667961 | + | 0.744196i | \(0.267167\pi\) | |||||||
\(12\) | 0.409975 | 0.118350 | ||||||||
\(13\) | 1.73246 | 0.480498 | 0.240249 | − | 0.970711i | \(-0.422771\pi\) | ||||
0.240249 | + | 0.970711i | \(0.422771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.65187 | −1.16297 | ||||||||
\(17\) | −2.73246 | −0.662719 | −0.331359 | − | 0.943505i | \(-0.607507\pi\) | ||||
−0.331359 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(18\) | 1.55241 | 0.365906 | ||||||||
\(19\) | 0.305156 | 0.0700076 | 0.0350038 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350038 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.87834 | 1.46647 | ||||||||
\(23\) | 7.02423 | 1.46465 | 0.732327 | − | 0.680954i | \(-0.238434\pi\) | ||||
0.732327 | + | 0.680954i | \(0.238434\pi\) | |||||||
\(24\) | −2.46837 | −0.503854 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.68949 | 0.527452 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.79430 | −1.44737 | −0.723683 | − | 0.690132i | \(-0.757552\pi\) | ||||
−0.723683 | + | 0.690132i | \(0.757552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.28487 | 0.949190 | 0.474595 | − | 0.880204i | \(-0.342594\pi\) | ||||
0.474595 | + | 0.880204i | \(0.342594\pi\) | |||||||
\(32\) | −2.28487 | −0.403912 | ||||||||
\(33\) | 4.43075 | 0.771295 | ||||||||
\(34\) | −4.24190 | −0.727479 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.409975 | 0.0683292 | ||||||||
\(37\) | 3.67406 | 0.604013 | 0.302006 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302006 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(38\) | 0.473727 | 0.0768487 | ||||||||
\(39\) | 1.73246 | 0.277415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.71562 | 1.04880 | 0.524402 | − | 0.851471i | \(-0.324289\pi\) | ||||
0.524402 | + | 0.851471i | \(0.324289\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.71562 | 1.48162 | 0.740809 | − | 0.671715i | \(-0.234442\pi\) | ||||
0.740809 | + | 0.671715i | \(0.234442\pi\) | |||||||
\(44\) | 1.81650 | 0.273848 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.9045 | 1.60778 | ||||||||
\(47\) | 1.81650 | 0.264964 | 0.132482 | − | 0.991185i | \(-0.457705\pi\) | ||||
0.132482 | + | 0.991185i | \(0.457705\pi\) | |||||||
\(48\) | −4.65187 | −0.671440 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.73246 | −0.382621 | ||||||||
\(52\) | 0.710265 | 0.0984961 | ||||||||
\(53\) | 1.71513 | 0.235591 | 0.117796 | − | 0.993038i | \(-0.462417\pi\) | ||||
0.117796 | + | 0.993038i | \(0.462417\pi\) | |||||||
\(54\) | 1.55241 | 0.211256 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.305156 | 0.0404189 | ||||||||
\(58\) | −12.1000 | −1.58880 | ||||||||
\(59\) | 1.14243 | 0.148732 | 0.0743661 | − | 0.997231i | \(-0.476307\pi\) | ||||
0.0743661 | + | 0.997231i | \(0.476307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.55635 | −1.22357 | −0.611783 | − | 0.791026i | \(-0.709547\pi\) | ||||
−0.611783 | + | 0.791026i | \(0.709547\pi\) | |||||||
\(62\) | 8.20428 | 1.04194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.75669 | 0.719586 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.87834 | 0.846666 | ||||||||
\(67\) | 8.38433 | 1.02431 | 0.512154 | − | 0.858893i | \(-0.328848\pi\) | ||||
0.512154 | + | 0.858893i | \(0.328848\pi\) | |||||||
\(68\) | −1.12024 | −0.135849 | ||||||||
\(69\) | 7.02423 | 0.845618 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2888 | 1.22106 | 0.610529 | − | 0.791994i | \(-0.290957\pi\) | ||||
0.610529 | + | 0.791994i | \(0.290957\pi\) | |||||||
\(72\) | −2.46837 | −0.290900 | ||||||||
\(73\) | −12.8204 | −1.50052 | −0.750260 | − | 0.661143i | \(-0.770072\pi\) | ||||
−0.750260 | + | 0.661143i | \(0.770072\pi\) | |||||||
\(74\) | 5.70365 | 0.663036 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.125106 | 0.0143507 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.68949 | 0.304524 | ||||||||
\(79\) | 6.71372 | 0.755352 | 0.377676 | − | 0.925938i | \(-0.376723\pi\) | ||||
0.377676 | + | 0.925938i | \(0.376723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.4254 | 1.15129 | ||||||||
\(83\) | 5.09946 | 0.559739 | 0.279869 | − | 0.960038i | \(-0.409709\pi\) | ||||
0.279869 | + | 0.960038i | \(0.409709\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 15.0826 | 1.62640 | ||||||||
\(87\) | −7.79430 | −0.835637 | ||||||||
\(88\) | −10.9367 | −1.16586 | ||||||||
\(89\) | −4.07065 | −0.431489 | −0.215744 | − | 0.976450i | \(-0.569218\pi\) | ||||
−0.215744 | + | 0.976450i | \(0.569218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.87976 | 0.300236 | ||||||||
\(93\) | 5.28487 | 0.548015 | ||||||||
\(94\) | 2.81995 | 0.290856 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.28487 | −0.233198 | ||||||||
\(97\) | −2.87834 | −0.292252 | −0.146126 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146126 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.43075 | 0.445308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.21767 | −0.718185 | −0.359092 | − | 0.933302i | \(-0.616914\pi\) | ||||
−0.359092 | + | 0.933302i | \(0.616914\pi\) | |||||||
\(102\) | −4.24190 | −0.420010 | ||||||||
\(103\) | −11.2734 | −1.11080 | −0.555400 | − | 0.831583i | \(-0.687435\pi\) | ||||
−0.555400 | + | 0.831583i | \(0.687435\pi\) | |||||||
\(104\) | −4.27635 | −0.419331 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.66259 | 0.258613 | ||||||||
\(107\) | 6.91596 | 0.668591 | 0.334296 | − | 0.942468i | \(-0.391502\pi\) | ||||
0.334296 | + | 0.942468i | \(0.391502\pi\) | |||||||
\(108\) | 0.409975 | 0.0394499 | ||||||||
\(109\) | 4.42195 | 0.423546 | 0.211773 | − | 0.977319i | \(-0.432076\pi\) | ||||
0.211773 | + | 0.977319i | \(0.432076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.67406 | 0.348727 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.86151 | −0.269188 | −0.134594 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134594 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(114\) | 0.473727 | 0.0443686 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.19547 | −0.296692 | ||||||||
\(117\) | 1.73246 | 0.160166 | ||||||||
\(118\) | 1.77353 | 0.163266 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.63158 | 0.784689 | ||||||||
\(122\) | −14.8354 | −1.34313 | ||||||||
\(123\) | 6.71562 | 0.605527 | ||||||||
\(124\) | 2.16666 | 0.194572 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7325 | 1.21856 | 0.609279 | − | 0.792956i | \(-0.291459\pi\) | ||||
0.609279 | + | 0.792956i | \(0.291459\pi\) | |||||||
\(128\) | 13.5065 | 1.19382 | ||||||||
\(129\) | 9.71562 | 0.855413 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.9817 | −1.92055 | −0.960277 | − | 0.279048i | \(-0.909981\pi\) | ||||
−0.960277 | + | 0.279048i | \(0.909981\pi\) | |||||||
\(132\) | 1.81650 | 0.158106 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.0159 | 1.12440 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.74472 | 0.578355 | ||||||||
\(137\) | 3.00191 | 0.256470 | 0.128235 | − | 0.991744i | \(-0.459069\pi\) | ||||
0.128235 | + | 0.991744i | \(0.459069\pi\) | |||||||
\(138\) | 10.9045 | 0.928251 | ||||||||
\(139\) | 21.7364 | 1.84366 | 0.921829 | − | 0.387597i | \(-0.126695\pi\) | ||||
0.921829 | + | 0.387597i | \(0.126695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.81650 | 0.152977 | ||||||||
\(142\) | 15.9724 | 1.34038 | ||||||||
\(143\) | 7.67610 | 0.641908 | ||||||||
\(144\) | −4.65187 | −0.387656 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.9026 | −1.64715 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.50628 | 0.123815 | ||||||||
\(149\) | −5.21309 | −0.427073 | −0.213536 | − | 0.976935i | \(-0.568498\pi\) | ||||
−0.213536 | + | 0.976935i | \(0.568498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.71372 | −0.790491 | −0.395246 | − | 0.918576i | \(-0.629340\pi\) | ||||
−0.395246 | + | 0.918576i | \(0.629340\pi\) | |||||||
\(152\) | −0.753238 | −0.0610957 | ||||||||
\(153\) | −2.73246 | −0.220906 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.710265 | 0.0568667 | ||||||||
\(157\) | −9.47182 | −0.755934 | −0.377967 | − | 0.925819i | \(-0.623377\pi\) | ||||
−0.377967 | + | 0.925819i | \(0.623377\pi\) | |||||||
\(158\) | 10.4224 | 0.829165 | ||||||||
\(159\) | 1.71513 | 0.136019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.55241 | 0.121969 | ||||||||
\(163\) | −5.39659 | −0.422694 | −0.211347 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(164\) | 2.75324 | 0.214992 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.91645 | 0.614436 | ||||||||
\(167\) | −0.312550 | −0.0241859 | −0.0120929 | − | 0.999927i | \(-0.503849\pi\) | ||||
−0.0120929 | + | 0.999927i | \(0.503849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.99859 | −0.769122 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.305156 | 0.0233359 | ||||||||
\(172\) | 3.98316 | 0.303713 | ||||||||
\(173\) | 9.61475 | 0.730996 | 0.365498 | − | 0.930812i | \(-0.380899\pi\) | ||||
0.365498 | + | 0.930812i | \(0.380899\pi\) | |||||||
\(174\) | −12.1000 | −0.917295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.6113 | −1.55363 | ||||||||
\(177\) | 1.14243 | 0.0858706 | ||||||||
\(178\) | −6.31932 | −0.473653 | ||||||||
\(179\) | −8.85461 | −0.661824 | −0.330912 | − | 0.943662i | \(-0.607356\pi\) | ||||
−0.330912 | + | 0.943662i | \(0.607356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9234 | 1.25790 | 0.628952 | − | 0.777445i | \(-0.283484\pi\) | ||||
0.628952 | + | 0.777445i | \(0.283484\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.55635 | −0.706426 | ||||||||
\(184\) | −17.3384 | −1.27820 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.20428 | 0.601567 | ||||||||
\(187\) | −12.1069 | −0.885341 | ||||||||
\(188\) | 0.744719 | 0.0543142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.318541 | 0.0230488 | 0.0115244 | − | 0.999934i | \(-0.496332\pi\) | ||||
0.0115244 | + | 0.999934i | \(0.496332\pi\) | |||||||
\(192\) | 5.75669 | 0.415453 | ||||||||
\(193\) | −2.09334 | −0.150682 | −0.0753410 | − | 0.997158i | \(-0.524005\pi\) | ||||
−0.0753410 | + | 0.997158i | \(0.524005\pi\) | |||||||
\(194\) | −4.46837 | −0.320810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.5798 | 1.60874 | 0.804372 | − | 0.594126i | \(-0.202502\pi\) | ||||
0.804372 | + | 0.594126i | \(0.202502\pi\) | |||||||
\(198\) | 6.87834 | 0.488823 | ||||||||
\(199\) | 7.50408 | 0.531950 | 0.265975 | − | 0.963980i | \(-0.414306\pi\) | ||||
0.265975 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.38433 | 0.591385 | ||||||||
\(202\) | −11.2048 | −0.788365 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.12024 | −0.0784325 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.5009 | −1.21935 | ||||||||
\(207\) | 7.02423 | 0.488218 | ||||||||
\(208\) | −8.05918 | −0.558803 | ||||||||
\(209\) | 1.35207 | 0.0935248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.67216 | 0.528173 | 0.264087 | − | 0.964499i | \(-0.414930\pi\) | ||||
0.264087 | + | 0.964499i | \(0.414930\pi\) | |||||||
\(212\) | 0.703161 | 0.0482933 | ||||||||
\(213\) | 10.2888 | 0.704978 | ||||||||
\(214\) | 10.7364 | 0.733925 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.46837 | −0.167951 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.86467 | 0.464934 | ||||||||
\(219\) | −12.8204 | −0.866325 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.73387 | −0.318435 | ||||||||
\(222\) | 5.70365 | 0.382804 | ||||||||
\(223\) | 6.90208 | 0.462198 | 0.231099 | − | 0.972930i | \(-0.425768\pi\) | ||||
0.231099 | + | 0.972930i | \(0.425768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.44223 | −0.295493 | ||||||||
\(227\) | 6.34721 | 0.421279 | 0.210639 | − | 0.977564i | \(-0.432445\pi\) | ||||
0.210639 | + | 0.977564i | \(0.432445\pi\) | |||||||
\(228\) | 0.125106 | 0.00828538 | ||||||||
\(229\) | −6.75669 | −0.446495 | −0.223247 | − | 0.974762i | \(-0.571666\pi\) | ||||
−0.223247 | + | 0.974762i | \(0.571666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.2392 | 1.26312 | ||||||||
\(233\) | −7.41201 | −0.485577 | −0.242789 | − | 0.970079i | \(-0.578062\pi\) | ||||
−0.242789 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(234\) | 2.68949 | 0.175817 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.468370 | 0.0304883 | ||||||||
\(237\) | 6.71372 | 0.436103 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.36355 | 0.476309 | 0.238154 | − | 0.971227i | \(-0.423458\pi\) | ||||
0.238154 | + | 0.971227i | \(0.423458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6800 | −0.881209 | −0.440605 | − | 0.897701i | \(-0.645236\pi\) | ||||
−0.440605 | + | 0.897701i | \(0.645236\pi\) | |||||||
\(242\) | 13.3998 | 0.861369 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.91787 | −0.250816 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4254 | 0.664699 | ||||||||
\(247\) | 0.528671 | 0.0336385 | ||||||||
\(248\) | −13.0450 | −0.828359 | ||||||||
\(249\) | 5.09946 | 0.323165 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4843 | −1.48231 | −0.741157 | − | 0.671331i | \(-0.765723\pi\) | ||||
−0.741157 | + | 0.671331i | \(0.765723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.1226 | 1.95666 | ||||||||
\(254\) | 21.3184 | 1.33764 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.45420 | 0.590888 | ||||||||
\(257\) | 14.5974 | 0.910562 | 0.455281 | − | 0.890348i | \(-0.349539\pi\) | ||||
0.455281 | + | 0.890348i | \(0.349539\pi\) | |||||||
\(258\) | 15.0826 | 0.939003 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.79430 | −0.482455 | ||||||||
\(262\) | −34.1247 | −2.10823 | ||||||||
\(263\) | 5.08940 | 0.313826 | 0.156913 | − | 0.987612i | \(-0.449846\pi\) | ||||
0.156913 | + | 0.987612i | \(0.449846\pi\) | |||||||
\(264\) | −10.9367 | −0.673110 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.07065 | −0.249120 | ||||||||
\(268\) | 3.43737 | 0.209971 | ||||||||
\(269\) | −30.5099 | −1.86022 | −0.930112 | − | 0.367277i | \(-0.880290\pi\) | ||||
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4880 | 1.18381 | 0.591907 | − | 0.806007i | \(-0.298375\pi\) | ||||
0.591907 | + | 0.806007i | \(0.298375\pi\) | |||||||
\(272\) | 12.7110 | 0.770720 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.66019 | 0.281532 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.87976 | 0.173341 | ||||||||
\(277\) | −25.4802 | −1.53096 | −0.765478 | − | 0.643462i | \(-0.777498\pi\) | ||||
−0.765478 | + | 0.643462i | \(0.777498\pi\) | |||||||
\(278\) | 33.7438 | 2.02382 | ||||||||
\(279\) | 5.28487 | 0.316397 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1914 | −1.32383 | −0.661914 | − | 0.749580i | \(-0.730255\pi\) | ||||
−0.661914 | + | 0.749580i | \(0.730255\pi\) | |||||||
\(282\) | 2.81995 | 0.167926 | ||||||||
\(283\) | −18.1242 | −1.07737 | −0.538685 | − | 0.842507i | \(-0.681079\pi\) | ||||
−0.538685 | + | 0.842507i | \(0.681079\pi\) | |||||||
\(284\) | 4.21816 | 0.250302 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.9165 | 0.704635 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.28487 | −0.134637 | ||||||||
\(289\) | −9.53367 | −0.560804 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.87834 | −0.168732 | ||||||||
\(292\) | −5.25606 | −0.307588 | ||||||||
\(293\) | −13.8958 | −0.811801 | −0.405901 | − | 0.913917i | \(-0.633042\pi\) | ||||
−0.405901 | + | 0.913917i | \(0.633042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.06895 | −0.527122 | ||||||||
\(297\) | 4.43075 | 0.257098 | ||||||||
\(298\) | −8.09285 | −0.468806 | ||||||||
\(299\) | 12.1692 | 0.703763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.0797 | −0.867737 | ||||||||
\(303\) | −7.21767 | −0.414644 | ||||||||
\(304\) | −1.41955 | −0.0814166 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.24190 | −0.242493 | ||||||||
\(307\) | 29.8332 | 1.70267 | 0.851335 | − | 0.524622i | \(-0.175793\pi\) | ||||
0.851335 | + | 0.524622i | \(0.175793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2734 | −0.641321 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5132 | −0.766266 | −0.383133 | − | 0.923693i | \(-0.625155\pi\) | ||||
−0.383133 | + | 0.923693i | \(0.625155\pi\) | |||||||
\(312\) | −4.27635 | −0.242101 | ||||||||
\(313\) | −28.9857 | −1.63837 | −0.819184 | − | 0.573531i | \(-0.805573\pi\) | ||||
−0.819184 | + | 0.573531i | \(0.805573\pi\) | |||||||
\(314\) | −14.7041 | −0.829803 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.75246 | 0.154838 | ||||||||
\(317\) | −1.15864 | −0.0650756 | −0.0325378 | − | 0.999471i | \(-0.510359\pi\) | ||||
−0.0325378 | + | 0.999471i | \(0.510359\pi\) | |||||||
\(318\) | 2.66259 | 0.149310 | ||||||||
\(319\) | −34.5346 | −1.93357 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.91596 | 0.386011 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.833827 | −0.0463954 | ||||||||
\(324\) | 0.409975 | 0.0227764 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.37772 | −0.463999 | ||||||||
\(327\) | 4.42195 | 0.244534 | ||||||||
\(328\) | −16.5766 | −0.915292 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.3491 | −1.55821 | −0.779104 | − | 0.626895i | \(-0.784326\pi\) | ||||
−0.779104 | + | 0.626895i | \(0.784326\pi\) | |||||||
\(332\) | 2.09065 | 0.114739 | ||||||||
\(333\) | 3.67406 | 0.201338 | ||||||||
\(334\) | −0.485206 | −0.0265493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9729 | −0.870101 | −0.435051 | − | 0.900406i | \(-0.643270\pi\) | ||||
−0.435051 | + | 0.900406i | \(0.643270\pi\) | |||||||
\(338\) | −15.5219 | −0.844280 | ||||||||
\(339\) | −2.86151 | −0.155416 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.4160 | 1.26805 | ||||||||
\(342\) | 0.473727 | 0.0256162 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −23.9817 | −1.29301 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.9260 | 0.802428 | ||||||||
\(347\) | −13.0120 | −0.698519 | −0.349260 | − | 0.937026i | \(-0.613567\pi\) | ||||
−0.349260 | + | 0.937026i | \(0.613567\pi\) | |||||||
\(348\) | −3.19547 | −0.171295 | ||||||||
\(349\) | −32.0724 | −1.71680 | −0.858398 | − | 0.512984i | \(-0.828540\pi\) | ||||
−0.858398 | + | 0.512984i | \(0.828540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.73246 | 0.0924718 | ||||||||
\(352\) | −10.1237 | −0.539595 | ||||||||
\(353\) | 13.3689 | 0.711555 | 0.355778 | − | 0.934571i | \(-0.384216\pi\) | ||||
0.355778 | + | 0.934571i | \(0.384216\pi\) | |||||||
\(354\) | 1.77353 | 0.0942618 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.66887 | −0.0884498 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.7460 | −0.726497 | ||||||||
\(359\) | −13.1195 | −0.692420 | −0.346210 | − | 0.938157i | \(-0.612531\pi\) | ||||
−0.346210 | + | 0.938157i | \(0.612531\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9069 | −0.995099 | ||||||||
\(362\) | 26.2720 | 1.38082 | ||||||||
\(363\) | 8.63158 | 0.453041 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −14.8354 | −0.775457 | ||||||||
\(367\) | 13.1360 | 0.685691 | 0.342846 | − | 0.939392i | \(-0.388609\pi\) | ||||
0.342846 | + | 0.939392i | \(0.388609\pi\) | |||||||
\(368\) | −32.6758 | −1.70334 | ||||||||
\(369\) | 6.71562 | 0.349601 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.16666 | 0.112336 | ||||||||
\(373\) | 29.6197 | 1.53365 | 0.766826 | − | 0.641855i | \(-0.221835\pi\) | ||||
0.766826 | + | 0.641855i | \(0.221835\pi\) | |||||||
\(374\) | −18.7948 | −0.971856 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.48379 | −0.231234 | ||||||||
\(377\) | −13.5033 | −0.695456 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.47689 | 0.384062 | 0.192031 | − | 0.981389i | \(-0.438493\pi\) | ||||
0.192031 | + | 0.981389i | \(0.438493\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7325 | 0.703535 | ||||||||
\(382\) | 0.494506 | 0.0253012 | ||||||||
\(383\) | −23.7391 | −1.21301 | −0.606505 | − | 0.795080i | \(-0.707429\pi\) | ||||
−0.606505 | + | 0.795080i | \(0.707429\pi\) | |||||||
\(384\) | 13.5065 | 0.689250 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.24972 | −0.165406 | ||||||||
\(387\) | 9.71562 | 0.493873 | ||||||||
\(388\) | −1.18005 | −0.0599079 | ||||||||
\(389\) | −14.1305 | −0.716443 | −0.358221 | − | 0.933637i | \(-0.616617\pi\) | ||||
−0.358221 | + | 0.933637i | \(0.616617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.1934 | −0.970653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.9817 | −1.10883 | ||||||||
\(394\) | 35.0531 | 1.76595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.81650 | 0.0912825 | ||||||||
\(397\) | 11.2696 | 0.565604 | 0.282802 | − | 0.959178i | \(-0.408736\pi\) | ||||
0.282802 | + | 0.959178i | \(0.408736\pi\) | |||||||
\(398\) | 11.6494 | 0.583932 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2968 | 1.16339 | 0.581694 | − | 0.813407i | \(-0.302390\pi\) | ||||
0.581694 | + | 0.813407i | \(0.302390\pi\) | |||||||
\(402\) | 13.0159 | 0.649175 | ||||||||
\(403\) | 9.15582 | 0.456084 | ||||||||
\(404\) | −2.95906 | −0.147219 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.2789 | 0.806914 | ||||||||
\(408\) | 6.74472 | 0.333913 | ||||||||
\(409\) | −20.6478 | −1.02097 | −0.510484 | − | 0.859887i | \(-0.670534\pi\) | ||||
−0.510484 | + | 0.859887i | \(0.670534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00191 | 0.148073 | ||||||||
\(412\) | −4.62181 | −0.227700 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.9045 | 0.535926 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.95844 | −0.194079 | ||||||||
\(417\) | 21.7364 | 1.06444 | ||||||||
\(418\) | 2.09897 | 0.102664 | ||||||||
\(419\) | 5.48254 | 0.267839 | 0.133920 | − | 0.990992i | \(-0.457244\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.78079 | −0.184264 | −0.0921322 | − | 0.995747i | \(-0.529368\pi\) | ||||
−0.0921322 | + | 0.995747i | \(0.529368\pi\) | |||||||
\(422\) | 11.9103 | 0.579786 | ||||||||
\(423\) | 1.81650 | 0.0883212 | ||||||||
\(424\) | −4.23358 | −0.205601 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.9724 | 0.773868 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.83537 | 0.137053 | ||||||||
\(429\) | 7.67610 | 0.370606 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.5127 | −1.32524 | −0.662621 | − | 0.748955i | \(-0.730556\pi\) | ||||
−0.662621 | + | 0.748955i | \(0.730556\pi\) | |||||||
\(432\) | −4.65187 | −0.223813 | ||||||||
\(433\) | 8.75514 | 0.420745 | 0.210373 | − | 0.977621i | \(-0.432532\pi\) | ||||
0.210373 | + | 0.977621i | \(0.432532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.81289 | 0.0868216 | ||||||||
\(437\) | 2.14349 | 0.102537 | ||||||||
\(438\) | −19.9026 | −0.950982 | ||||||||
\(439\) | 10.6127 | 0.506517 | 0.253259 | − | 0.967399i | \(-0.418498\pi\) | ||||
0.253259 | + | 0.967399i | \(0.418498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.34891 | −0.349552 | ||||||||
\(443\) | −19.9856 | −0.949543 | −0.474771 | − | 0.880109i | \(-0.657469\pi\) | ||||
−0.474771 | + | 0.880109i | \(0.657469\pi\) | |||||||
\(444\) | 1.50628 | 0.0714847 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7149 | 0.507363 | ||||||||
\(447\) | −5.21309 | −0.246571 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.02578 | 0.142795 | 0.0713976 | − | 0.997448i | \(-0.477254\pi\) | ||||
0.0713976 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7553 | 1.40112 | ||||||||
\(452\) | −1.17315 | −0.0551802 | ||||||||
\(453\) | −9.71372 | −0.456390 | ||||||||
\(454\) | 9.85346 | 0.462446 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.753238 | −0.0352736 | ||||||||
\(457\) | 2.28135 | 0.106717 | 0.0533584 | − | 0.998575i | \(-0.483007\pi\) | ||||
0.0533584 | + | 0.998575i | \(0.483007\pi\) | |||||||
\(458\) | −10.4891 | −0.490126 | ||||||||
\(459\) | −2.73246 | −0.127540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0678 | 1.12095 | 0.560475 | − | 0.828171i | \(-0.310619\pi\) | ||||
0.560475 | + | 0.828171i | \(0.310619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1290 | 0.517211 | 0.258605 | − | 0.965983i | \(-0.416737\pi\) | ||||
0.258605 | + | 0.965983i | \(0.416737\pi\) | |||||||
\(464\) | 36.2581 | 1.68324 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5065 | −0.533027 | ||||||||
\(467\) | −28.5766 | −1.32237 | −0.661185 | − | 0.750223i | \(-0.729946\pi\) | ||||
−0.661185 | + | 0.750223i | \(0.729946\pi\) | |||||||
\(468\) | 0.710265 | 0.0328320 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.47182 | −0.436438 | ||||||||
\(472\) | −2.81995 | −0.129799 | ||||||||
\(473\) | 43.0475 | 1.97933 | ||||||||
\(474\) | 10.4224 | 0.478718 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.71513 | 0.0785305 | ||||||||
\(478\) | 11.4312 | 0.522853 | ||||||||
\(479\) | 5.58009 | 0.254961 | 0.127480 | − | 0.991841i | \(-0.459311\pi\) | ||||
0.127480 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.36517 | 0.290227 | ||||||||
\(482\) | −21.2370 | −0.967320 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.53873 | 0.160852 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.55241 | 0.0704187 | ||||||||
\(487\) | 8.34684 | 0.378232 | 0.189116 | − | 0.981955i | \(-0.439438\pi\) | ||||
0.189116 | + | 0.981955i | \(0.439438\pi\) | |||||||
\(488\) | 23.5886 | 1.06781 | ||||||||
\(489\) | −5.39659 | −0.244042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.557405 | 0.0251554 | 0.0125777 | − | 0.999921i | \(-0.495996\pi\) | ||||
0.0125777 | + | 0.999921i | \(0.495996\pi\) | |||||||
\(492\) | 2.75324 | 0.124126 | ||||||||
\(493\) | 21.2976 | 0.959197 | ||||||||
\(494\) | 0.820713 | 0.0369256 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.5845 | −1.10388 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.91645 | 0.354745 | ||||||||
\(499\) | −26.0337 | −1.16543 | −0.582713 | − | 0.812678i | \(-0.698009\pi\) | ||||
−0.582713 | + | 0.812678i | \(0.698009\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.312550 | −0.0139637 | ||||||||
\(502\) | −36.4572 | −1.62717 | ||||||||
\(503\) | −5.52409 | −0.246307 | −0.123154 | − | 0.992388i | \(-0.539301\pi\) | ||||
−0.123154 | + | 0.992388i | \(0.539301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 48.3151 | 2.14787 | ||||||||
\(507\) | −9.99859 | −0.444053 | ||||||||
\(508\) | 5.62997 | 0.249789 | ||||||||
\(509\) | −22.8893 | −1.01455 | −0.507274 | − | 0.861785i | \(-0.669347\pi\) | ||||
−0.507274 | + | 0.861785i | \(0.669347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12.3362 | −0.545186 | ||||||||
\(513\) | 0.305156 | 0.0134730 | ||||||||
\(514\) | 22.6612 | 0.999541 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.98316 | 0.175349 | ||||||||
\(517\) | 8.04846 | 0.353971 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.61475 | 0.422041 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.1989 | −1.14780 | −0.573898 | − | 0.818927i | \(-0.694569\pi\) | ||||
−0.573898 | + | 0.818927i | \(0.694569\pi\) | |||||||
\(522\) | −12.1000 | −0.529601 | ||||||||
\(523\) | 26.8760 | 1.17521 | 0.587603 | − | 0.809149i | \(-0.300072\pi\) | ||||
0.587603 | + | 0.809149i | \(0.300072\pi\) | |||||||
\(524\) | −9.01197 | −0.393690 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.90083 | 0.344493 | ||||||||
\(527\) | −14.4407 | −0.629046 | ||||||||
\(528\) | −20.6113 | −0.896992 | ||||||||
\(529\) | 26.3398 | 1.14521 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.14243 | 0.0495774 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.6345 | 0.503948 | ||||||||
\(534\) | −6.31932 | −0.273464 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.6956 | −0.893915 | ||||||||
\(537\) | −8.85461 | −0.382104 | ||||||||
\(538\) | −47.3639 | −2.04200 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7844 | −0.807606 | −0.403803 | − | 0.914846i | \(-0.632312\pi\) | ||||
−0.403803 | + | 0.914846i | \(0.632312\pi\) | |||||||
\(542\) | 30.2534 | 1.29949 | ||||||||
\(543\) | 16.9234 | 0.726251 | ||||||||
\(544\) | 6.24331 | 0.267680 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4126 | −0.573483 | −0.286742 | − | 0.958008i | \(-0.592572\pi\) | ||||
−0.286742 | + | 0.958008i | \(0.592572\pi\) | |||||||
\(548\) | 1.23071 | 0.0525732 | ||||||||
\(549\) | −9.55635 | −0.407855 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.37848 | −0.101327 | ||||||||
\(552\) | −17.3384 | −0.737971 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −39.5557 | −1.68056 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.91138 | 0.377927 | ||||||||
\(557\) | 40.1845 | 1.70267 | 0.851336 | − | 0.524621i | \(-0.175793\pi\) | ||||
0.851336 | + | 0.524621i | \(0.175793\pi\) | |||||||
\(558\) | 8.20428 | 0.347315 | ||||||||
\(559\) | 16.8319 | 0.711914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.1069 | −0.511152 | ||||||||
\(562\) | −34.4501 | −1.45319 | ||||||||
\(563\) | 25.1879 | 1.06154 | 0.530772 | − | 0.847514i | \(-0.321902\pi\) | ||||
0.530772 | + | 0.847514i | \(0.321902\pi\) | |||||||
\(564\) | 0.744719 | 0.0313583 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.1362 | −1.18265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.3966 | −1.06562 | ||||||||
\(569\) | −11.0351 | −0.462617 | −0.231309 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231309 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.7147 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294834\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(572\) | 3.14701 | 0.131583 | ||||||||
\(573\) | 0.318541 | 0.0133073 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.75669 | 0.239862 | ||||||||
\(577\) | 6.86405 | 0.285754 | 0.142877 | − | 0.989740i | \(-0.454365\pi\) | ||||
0.142877 | + | 0.989740i | \(0.454365\pi\) | |||||||
\(578\) | −14.8002 | −0.615605 | ||||||||
\(579\) | −2.09334 | −0.0869963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.46837 | −0.185220 | ||||||||
\(583\) | 7.59933 | 0.314732 | ||||||||
\(584\) | 31.6456 | 1.30950 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.5720 | −0.891130 | ||||||||
\(587\) | −9.03965 | −0.373106 | −0.186553 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186553 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61271 | 0.0664506 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.5798 | 0.928809 | ||||||||
\(592\) | −17.0913 | −0.702447 | ||||||||
\(593\) | 5.10798 | 0.209760 | 0.104880 | − | 0.994485i | \(-0.466554\pi\) | ||||
0.104880 | + | 0.994485i | \(0.466554\pi\) | |||||||
\(594\) | 6.87834 | 0.282222 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.13724 | −0.0875446 | ||||||||
\(597\) | 7.50408 | 0.307121 | ||||||||
\(598\) | 18.8916 | 0.772534 | ||||||||
\(599\) | −29.9443 | −1.22349 | −0.611745 | − | 0.791055i | \(-0.709532\pi\) | ||||
−0.611745 | + | 0.791055i | \(0.709532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5387 | 0.511466 | 0.255733 | − | 0.966747i | \(-0.417683\pi\) | ||||
0.255733 | + | 0.966747i | \(0.417683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.38433 | 0.341436 | ||||||||
\(604\) | −3.98238 | −0.162041 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.2048 | −0.455163 | ||||||||
\(607\) | −9.59805 | −0.389573 | −0.194786 | − | 0.980846i | \(-0.562401\pi\) | ||||
−0.194786 | + | 0.980846i | \(0.562401\pi\) | |||||||
\(608\) | −0.697242 | −0.0282769 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.14701 | 0.127314 | ||||||||
\(612\) | −1.12024 | −0.0452830 | ||||||||
\(613\) | 27.6646 | 1.11736 | 0.558682 | − | 0.829382i | \(-0.311307\pi\) | ||||
0.558682 | + | 0.829382i | \(0.311307\pi\) | |||||||
\(614\) | 46.3133 | 1.86905 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4155 | −0.821896 | −0.410948 | − | 0.911659i | \(-0.634802\pi\) | ||||
−0.410948 | + | 0.911659i | \(0.634802\pi\) | |||||||
\(618\) | −17.5009 | −0.703990 | ||||||||
\(619\) | 15.4422 | 0.620676 | 0.310338 | − | 0.950626i | \(-0.399558\pi\) | ||||
0.310338 | + | 0.950626i | \(0.399558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.02423 | 0.281873 | ||||||||
\(622\) | −20.9781 | −0.841145 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.05918 | −0.322625 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −44.9977 | −1.79847 | ||||||||
\(627\) | 1.35207 | 0.0539966 | ||||||||
\(628\) | −3.88321 | −0.154957 | ||||||||
\(629\) | −10.0392 | −0.400290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1722 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774705\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774705\pi\) | |||||||
\(632\) | −16.5719 | −0.659196 | ||||||||
\(633\) | 7.67216 | 0.304941 | ||||||||
\(634\) | −1.79868 | −0.0714347 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.703161 | 0.0278822 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −53.6119 | −2.12252 | ||||||||
\(639\) | 10.2888 | 0.407019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.7801 | −0.662776 | −0.331388 | − | 0.943495i | \(-0.607517\pi\) | ||||
−0.331388 | + | 0.943495i | \(0.607517\pi\) | |||||||
\(642\) | 10.7364 | 0.423732 | ||||||||
\(643\) | 14.2002 | 0.560001 | 0.280001 | − | 0.960000i | \(-0.409665\pi\) | ||||
0.280001 | + | 0.960000i | \(0.409665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.29444 | −0.0509291 | ||||||||
\(647\) | −14.4885 | −0.569602 | −0.284801 | − | 0.958587i | \(-0.591928\pi\) | ||||
−0.284801 | + | 0.958587i | \(0.591928\pi\) | |||||||
\(648\) | −2.46837 | −0.0969667 | ||||||||
\(649\) | 5.06185 | 0.198695 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.21247 | −0.0866469 | ||||||||
\(653\) | 10.2833 | 0.402418 | 0.201209 | − | 0.979548i | \(-0.435513\pi\) | ||||
0.201209 | + | 0.979548i | \(0.435513\pi\) | |||||||
\(654\) | 6.86467 | 0.268430 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −31.2402 | −1.21973 | ||||||||
\(657\) | −12.8204 | −0.500173 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.9773 | 0.583433 | 0.291717 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291717 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.44647 | −0.0951565 | −0.0475782 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475782 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(662\) | −44.0094 | −1.71048 | ||||||||
\(663\) | −4.73387 | −0.183848 | ||||||||
\(664\) | −12.5874 | −0.488484 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.70365 | 0.221012 | ||||||||
\(667\) | −54.7490 | −2.11989 | ||||||||
\(668\) | −0.128138 | −0.00495780 | ||||||||
\(669\) | 6.90208 | 0.266850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.3418 | −1.63459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.2596 | 0.665310 | 0.332655 | − | 0.943049i | \(-0.392055\pi\) | ||||
0.332655 | + | 0.943049i | \(0.392055\pi\) | |||||||
\(674\) | −24.7965 | −0.955127 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.09917 | −0.157660 | ||||||||
\(677\) | −11.6384 | −0.447298 | −0.223649 | − | 0.974670i | \(-0.571797\pi\) | ||||
−0.223649 | + | 0.974670i | \(0.571797\pi\) | |||||||
\(678\) | −4.44223 | −0.170603 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.34721 | 0.243225 | ||||||||
\(682\) | 36.3511 | 1.39196 | ||||||||
\(683\) | −31.0960 | −1.18986 | −0.594928 | − | 0.803779i | \(-0.702819\pi\) | ||||
−0.594928 | + | 0.803779i | \(0.702819\pi\) | |||||||
\(684\) | 0.125106 | 0.00478356 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.75669 | −0.257784 | ||||||||
\(688\) | −45.1958 | −1.72307 | ||||||||
\(689\) | 2.97140 | 0.113201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.9339 | 0.682238 | 0.341119 | − | 0.940020i | \(-0.389194\pi\) | ||||
0.341119 | + | 0.940020i | \(0.389194\pi\) | |||||||
\(692\) | 3.94181 | 0.149845 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.1999 | −0.766778 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 19.2392 | 0.729261 | ||||||||
\(697\) | −18.3502 | −0.695062 | ||||||||
\(698\) | −49.7895 | −1.88456 | ||||||||
\(699\) | −7.41201 | −0.280348 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.04488 | 0.266081 | 0.133041 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133041 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(702\) | 2.68949 | 0.101508 | ||||||||
\(703\) | 1.12116 | 0.0422855 | ||||||||
\(704\) | 25.5065 | 0.961312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.7540 | 0.781088 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.468370 | 0.0176024 | ||||||||
\(709\) | −25.9243 | −0.973609 | −0.486804 | − | 0.873511i | \(-0.661838\pi\) | ||||
−0.486804 | + | 0.873511i | \(0.661838\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.71372 | 0.251784 | ||||||||
\(712\) | 10.0479 | 0.376560 | ||||||||
\(713\) | 37.1221 | 1.39023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.63017 | −0.135666 | ||||||||
\(717\) | 7.36355 | 0.274997 | ||||||||
\(718\) | −20.3668 | −0.760082 | ||||||||
\(719\) | −31.2855 | −1.16675 | −0.583376 | − | 0.812202i | \(-0.698269\pi\) | ||||
−0.583376 | + | 0.812202i | \(0.698269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.3512 | −1.09234 | ||||||||
\(723\) | −13.6800 | −0.508766 | ||||||||
\(724\) | 6.93815 | 0.257854 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.3998 | 0.497311 | ||||||||
\(727\) | 22.8312 | 0.846761 | 0.423380 | − | 0.905952i | \(-0.360843\pi\) | ||||
0.423380 | + | 0.905952i | \(0.360843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.5475 | −0.981896 | ||||||||
\(732\) | −3.91787 | −0.144809 | ||||||||
\(733\) | −5.95434 | −0.219929 | −0.109964 | − | 0.993936i | \(-0.535074\pi\) | ||||
−0.109964 | + | 0.993936i | \(0.535074\pi\) | |||||||
\(734\) | 20.3924 | 0.752696 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.0494 | −0.591590 | ||||||||
\(737\) | 37.1489 | 1.36840 | ||||||||
\(738\) | 10.4254 | 0.383764 | ||||||||
\(739\) | 41.5079 | 1.52689 | 0.763446 | − | 0.645872i | \(-0.223506\pi\) | ||||
0.763446 | + | 0.645872i | \(0.223506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.528671 | 0.0194212 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.80015 | 0.249473 | 0.124737 | − | 0.992190i | \(-0.460191\pi\) | ||||
0.124737 | + | 0.992190i | \(0.460191\pi\) | |||||||
\(744\) | −13.0450 | −0.478253 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.9820 | 1.68352 | ||||||||
\(747\) | 5.09946 | 0.186580 | ||||||||
\(748\) | −4.96351 | −0.181484 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6113 | 0.861588 | 0.430794 | − | 0.902450i | \(-0.358233\pi\) | ||||
0.430794 | + | 0.902450i | \(0.358233\pi\) | |||||||
\(752\) | −8.45012 | −0.308144 | ||||||||
\(753\) | −23.4843 | −0.855815 | ||||||||
\(754\) | −20.9627 | −0.763416 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.2267 | −0.589769 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(758\) | 11.6072 | 0.421592 | ||||||||
\(759\) | 31.1226 | 1.12968 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.55508 | 0.0926215 | 0.0463108 | − | 0.998927i | \(-0.485254\pi\) | ||||
0.0463108 | + | 0.998927i | \(0.485254\pi\) | |||||||
\(762\) | 21.3184 | 0.772284 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.130594 | 0.00472473 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.8528 | −1.33154 | ||||||||
\(767\) | 1.97922 | 0.0714655 | ||||||||
\(768\) | 9.45420 | 0.341149 | ||||||||
\(769\) | 45.4525 | 1.63906 | 0.819530 | − | 0.573037i | \(-0.194235\pi\) | ||||
0.819530 | + | 0.573037i | \(0.194235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5974 | 0.525713 | ||||||||
\(772\) | −0.858217 | −0.0308879 | ||||||||
\(773\) | −51.4891 | −1.85194 | −0.925968 | − | 0.377603i | \(-0.876749\pi\) | ||||
−0.925968 | + | 0.377603i | \(0.876749\pi\) | |||||||
\(774\) | 15.0826 | 0.542134 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.10482 | 0.255048 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9363 | −0.786453 | ||||||||
\(779\) | 2.04931 | 0.0734243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.5872 | 1.63124 | ||||||||
\(782\) | −29.7961 | −1.06550 | ||||||||
\(783\) | −7.79430 | −0.278546 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −34.1247 | −1.21719 | ||||||||
\(787\) | 20.1514 | 0.718321 | 0.359161 | − | 0.933276i | \(-0.383063\pi\) | ||||
0.359161 | + | 0.933276i | \(0.383063\pi\) | |||||||
\(788\) | 9.25716 | 0.329773 | ||||||||
\(789\) | 5.08940 | 0.181187 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.9367 | −0.388620 | ||||||||
\(793\) | −16.5560 | −0.587920 | ||||||||
\(794\) | 17.4950 | 0.620874 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.07649 | 0.109043 | ||||||||
\(797\) | −13.0702 | −0.462971 | −0.231486 | − | 0.972838i | \(-0.574359\pi\) | ||||
−0.231486 | + | 0.972838i | \(0.574359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.96351 | −0.175596 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.07065 | −0.143830 | ||||||||
\(802\) | 36.1662 | 1.27707 | ||||||||
\(803\) | −56.8042 | −2.00458 | ||||||||
\(804\) | 3.43737 | 0.121227 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.2136 | 0.500652 | ||||||||
\(807\) | −30.5099 | −1.07400 | ||||||||
\(808\) | 17.8159 | 0.626760 | ||||||||
\(809\) | −1.73720 | −0.0610765 | −0.0305383 | − | 0.999534i | \(-0.509722\pi\) | ||||
−0.0305383 | + | 0.999534i | \(0.509722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9004 | 0.979715 | 0.489858 | − | 0.871802i | \(-0.337049\pi\) | ||||
0.489858 | + | 0.871802i | \(0.337049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4880 | 0.683475 | ||||||||
\(814\) | 25.2715 | 0.885765 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.7110 | 0.444976 | ||||||||
\(817\) | 2.96478 | 0.103725 | ||||||||
\(818\) | −32.0538 | −1.12074 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.9360 | 0.591070 | 0.295535 | − | 0.955332i | \(-0.404502\pi\) | ||||
0.295535 | + | 0.955332i | \(0.404502\pi\) | |||||||
\(822\) | 4.66019 | 0.162543 | ||||||||
\(823\) | −9.89031 | −0.344755 | −0.172377 | − | 0.985031i | \(-0.555145\pi\) | ||||
−0.172377 | + | 0.985031i | \(0.555145\pi\) | |||||||
\(824\) | 27.8269 | 0.969396 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.3201 | −1.22820 | −0.614101 | − | 0.789228i | \(-0.710481\pi\) | ||||
−0.614101 | + | 0.789228i | \(0.710481\pi\) | |||||||
\(828\) | 2.87976 | 0.100079 | ||||||||
\(829\) | −9.29951 | −0.322985 | −0.161493 | − | 0.986874i | \(-0.551631\pi\) | ||||
−0.161493 | + | 0.986874i | \(0.551631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.4802 | −0.883898 | ||||||||
\(832\) | 9.97323 | 0.345760 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 33.7438 | 1.16845 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.554316 | 0.0191714 | ||||||||
\(837\) | 5.28487 | 0.182672 | ||||||||
\(838\) | 8.51114 | 0.294012 | ||||||||
\(839\) | 7.93405 | 0.273914 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.7512 | 1.09487 | ||||||||
\(842\) | −5.86933 | −0.202271 | ||||||||
\(843\) | −22.1914 | −0.764312 | ||||||||
\(844\) | 3.14539 | 0.108269 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.81995 | 0.0969519 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.97857 | −0.273985 | ||||||||
\(849\) | −18.1242 | −0.622020 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.8075 | 0.884669 | ||||||||
\(852\) | 4.21816 | 0.144512 | ||||||||
\(853\) | 30.0757 | 1.02977 | 0.514887 | − | 0.857258i | \(-0.327834\pi\) | ||||
0.514887 | + | 0.857258i | \(0.327834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.0711 | −0.583480 | ||||||||
\(857\) | 47.1373 | 1.61018 | 0.805090 | − | 0.593153i | \(-0.202117\pi\) | ||||
0.805090 | + | 0.593153i | \(0.202117\pi\) | |||||||
\(858\) | 11.9165 | 0.406821 | ||||||||
\(859\) | 32.6367 | 1.11355 | 0.556774 | − | 0.830664i | \(-0.312039\pi\) | ||||
0.556774 | + | 0.830664i | \(0.312039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.7110 | −1.45474 | ||||||||
\(863\) | 37.4102 | 1.27346 | 0.636728 | − | 0.771088i | \(-0.280287\pi\) | ||||
0.636728 | + | 0.771088i | \(0.280287\pi\) | |||||||
\(864\) | −2.28487 | −0.0777328 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.5916 | 0.461860 | ||||||||
\(867\) | −9.53367 | −0.323780 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.7468 | 1.00909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5255 | 0.492178 | ||||||||
\(872\) | −10.9150 | −0.369628 | ||||||||
\(873\) | −2.87834 | −0.0974172 | ||||||||
\(874\) | 3.32757 | 0.112557 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.25606 | −0.177586 | ||||||||
\(877\) | 33.5657 | 1.13343 | 0.566716 | − | 0.823913i | \(-0.308214\pi\) | ||||
0.566716 | + | 0.823913i | \(0.308214\pi\) | |||||||
\(878\) | 16.4753 | 0.556014 | ||||||||
\(879\) | −13.8958 | −0.468694 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1952 | 0.410867 | 0.205433 | − | 0.978671i | \(-0.434140\pi\) | ||||
0.205433 | + | 0.978671i | \(0.434140\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0408 | −0.371552 | −0.185776 | − | 0.982592i | \(-0.559480\pi\) | ||||
−0.185776 | + | 0.982592i | \(0.559480\pi\) | |||||||
\(884\) | −1.94077 | −0.0652752 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.0258 | −1.04233 | ||||||||
\(887\) | −1.56093 | −0.0524108 | −0.0262054 | − | 0.999657i | \(-0.508342\pi\) | ||||
−0.0262054 | + | 0.999657i | \(0.508342\pi\) | |||||||
\(888\) | −9.06895 | −0.304334 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.43075 | 0.148436 | ||||||||
\(892\) | 2.82968 | 0.0947448 | ||||||||
\(893\) | 0.554316 | 0.0185495 | ||||||||
\(894\) | −8.09285 | −0.270665 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.1692 | 0.406318 | ||||||||
\(898\) | 4.69724 | 0.156749 | ||||||||
\(899\) | −41.1919 | −1.37383 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.68653 | −0.156131 | ||||||||
\(902\) | 46.1924 | 1.53804 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.06326 | 0.234921 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.0797 | −0.500988 | ||||||||
\(907\) | −17.4078 | −0.578016 | −0.289008 | − | 0.957327i | \(-0.593325\pi\) | ||||
−0.289008 | + | 0.957327i | \(0.593325\pi\) | |||||||
\(908\) | 2.60220 | 0.0863569 | ||||||||
\(909\) | −7.21767 | −0.239395 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3203 | −0.606978 | −0.303489 | − | 0.952835i | \(-0.598152\pi\) | ||||
−0.303489 | + | 0.952835i | \(0.598152\pi\) | |||||||
\(912\) | −1.41955 | −0.0470059 | ||||||||
\(913\) | 22.5945 | 0.747767 | ||||||||
\(914\) | 3.54158 | 0.117145 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.77007 | −0.0915258 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.24190 | −0.140003 | ||||||||
\(919\) | 22.5927 | 0.745264 | 0.372632 | − | 0.927979i | \(-0.378455\pi\) | ||||
0.372632 | + | 0.927979i | \(0.378455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.8332 | 0.983037 | ||||||||
\(922\) | 37.3631 | 1.23049 | ||||||||
\(923\) | 17.8249 | 0.586715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.2768 | 0.567752 | ||||||||
\(927\) | −11.2734 | −0.370267 | ||||||||
\(928\) | 17.8090 | 0.584608 | ||||||||
\(929\) | −38.6712 | −1.26876 | −0.634381 | − | 0.773021i | \(-0.718745\pi\) | ||||
−0.634381 | + | 0.773021i | \(0.718745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.03874 | −0.0995372 | ||||||||
\(933\) | −13.5132 | −0.442404 | ||||||||
\(934\) | −44.3626 | −1.45159 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.27635 | −0.139777 | ||||||||
\(937\) | −46.7921 | −1.52863 | −0.764316 | − | 0.644842i | \(-0.776923\pi\) | ||||
−0.764316 | + | 0.644842i | \(0.776923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.9857 | −0.945912 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.8922 | 1.36565 | 0.682824 | − | 0.730583i | \(-0.260752\pi\) | ||||
0.682824 | + | 0.730583i | \(0.260752\pi\) | |||||||
\(942\) | −14.7041 | −0.479087 | ||||||||
\(943\) | 47.1721 | 1.53613 | ||||||||
\(944\) | −5.31446 | −0.172971 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 66.8274 | 2.17275 | ||||||||
\(947\) | −56.1146 | −1.82348 | −0.911740 | − | 0.410768i | \(-0.865261\pi\) | ||||
−0.911740 | + | 0.410768i | \(0.865261\pi\) | |||||||
\(948\) | 2.75246 | 0.0893956 | ||||||||
\(949\) | −22.2109 | −0.720996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.15864 | −0.0375714 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7705 | −0.575643 | −0.287821 | − | 0.957684i | \(-0.592931\pi\) | ||||
−0.287821 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(954\) | 2.66259 | 0.0862044 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.01887 | 0.0976373 | ||||||||
\(957\) | −34.5346 | −1.11635 | ||||||||
\(958\) | 8.66259 | 0.279875 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.07016 | −0.0990375 | ||||||||
\(962\) | 9.88135 | 0.318587 | ||||||||
\(963\) | 6.91596 | 0.222864 | ||||||||
\(964\) | −5.60848 | −0.180637 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5942 | 0.726579 | 0.363290 | − | 0.931676i | \(-0.381654\pi\) | ||||
0.363290 | + | 0.931676i | \(0.381654\pi\) | |||||||
\(968\) | −21.3059 | −0.684799 | ||||||||
\(969\) | −0.833827 | −0.0267864 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.0488 | −1.31732 | −0.658660 | − | 0.752441i | \(-0.728876\pi\) | ||||
−0.658660 | + | 0.752441i | \(0.728876\pi\) | |||||||
\(972\) | 0.409975 | 0.0131500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.9577 | 0.415192 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.4549 | 1.42297 | ||||||||
\(977\) | 19.4734 | 0.623008 | 0.311504 | − | 0.950245i | \(-0.399167\pi\) | ||||
0.311504 | + | 0.950245i | \(0.399167\pi\) | |||||||
\(978\) | −8.37772 | −0.267890 | ||||||||
\(979\) | −18.0361 | −0.576435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.42195 | 0.141182 | ||||||||
\(982\) | 0.865321 | 0.0276135 | ||||||||
\(983\) | 51.7272 | 1.64984 | 0.824920 | − | 0.565249i | \(-0.191220\pi\) | ||||
0.824920 | + | 0.565249i | \(0.191220\pi\) | |||||||
\(984\) | −16.5766 | −0.528444 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 33.0626 | 1.05293 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.216742 | 0.00689548 | ||||||||
\(989\) | 68.2448 | 2.17006 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.9499 | 1.14198 | 0.570992 | − | 0.820955i | \(-0.306559\pi\) | ||||
0.570992 | + | 0.820955i | \(0.306559\pi\) | |||||||
\(992\) | −12.0752 | −0.383389 | ||||||||
\(993\) | −28.3491 | −0.899632 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.09065 | 0.0662449 | ||||||||
\(997\) | 56.0599 | 1.77544 | 0.887718 | − | 0.460388i | \(-0.152290\pi\) | ||||
0.887718 | + | 0.460388i | \(0.152290\pi\) | |||||||
\(998\) | −40.4149 | −1.27931 | ||||||||
\(999\) | 3.67406 | 0.116242 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))