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: | \(1\) |
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 | 1.2 | ||
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 | \(-0.684938\pi\) | ||||
−0.548860 | + | 0.835915i | \(0.684938\pi\) | |||||||
\(3\) | 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 | \(-0.511144\pi\) | ||||
−0.0350038 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.87834 | −1.46647 | ||||||||
\(23\) | −7.02423 | −1.46465 | −0.732327 | − | 0.680954i | \(-0.761566\pi\) | ||||
−0.732327 | + | 0.680954i | \(0.761566\pi\) | |||||||
\(24\) | 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 | \(-0.657406\pi\) | ||||
−0.474595 | + | 0.880204i | \(0.657406\pi\) | |||||||
\(32\) | 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 | \(-0.597656\pi\) | ||||
−0.302006 | + | 0.953306i | \(0.597656\pi\) | |||||||
\(38\) | 0.473727 | 0.0768487 | ||||||||
\(39\) | 1.73246 | 0.277415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.71562 | −1.04880 | −0.524402 | − | 0.851471i | \(-0.675711\pi\) | ||||
−0.524402 | + | 0.851471i | \(0.675711\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.71562 | −1.48162 | −0.740809 | − | 0.671715i | \(-0.765558\pi\) | ||||
−0.740809 | + | 0.671715i | \(0.765558\pi\) | |||||||
\(44\) | 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 | \(-0.537583\pi\) | ||||
−0.117796 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(54\) | −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 | \(-0.523693\pi\) | ||||
−0.0743661 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.55635 | 1.22357 | 0.611783 | − | 0.791026i | \(-0.290453\pi\) | ||||
0.611783 | + | 0.791026i | \(0.290453\pi\) | |||||||
\(62\) | 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 | \(-0.671152\pi\) | ||||
−0.512154 | + | 0.858893i | \(0.671152\pi\) | |||||||
\(68\) | −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 | \(-0.430782\pi\) | ||||
0.215744 | + | 0.976450i | \(0.430782\pi\) | |||||||
\(90\) | 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 | \(-0.383086\pi\) | ||||
0.359092 | + | 0.933302i | \(0.383086\pi\) | |||||||
\(102\) | 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 | \(-0.608498\pi\) | ||||
−0.334296 | + | 0.942468i | \(0.608498\pi\) | |||||||
\(108\) | 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 | \(-0.457027\pi\) | ||||
0.134594 | + | 0.990901i | \(0.457027\pi\) | |||||||
\(114\) | 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 | \(-0.708541\pi\) | ||||
−0.609279 | + | 0.792956i | \(0.708541\pi\) | |||||||
\(128\) | −13.5065 | −1.19382 | ||||||||
\(129\) | −9.71562 | −0.855413 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.9817 | 1.92055 | 0.960277 | − | 0.279048i | \(-0.0900189\pi\) | ||||
0.960277 | + | 0.279048i | \(0.0900189\pi\) | |||||||
\(132\) | 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 | \(-0.540931\pi\) | ||||
−0.128235 | + | 0.991744i | \(0.540931\pi\) | |||||||
\(138\) | 10.9045 | 0.928251 | ||||||||
\(139\) | −21.7364 | −1.84366 | −0.921829 | − | 0.387597i | \(-0.873305\pi\) | ||||
−0.921829 | + | 0.387597i | \(0.873305\pi\) | |||||||
\(140\) | 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 | \(-0.432215\pi\) | ||||
0.211347 | + | 0.977411i | \(0.432215\pi\) | |||||||
\(164\) | −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 | \(-0.716516\pi\) | ||||
−0.628952 | + | 0.777445i | \(0.716516\pi\) | |||||||
\(182\) | 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 | \(-0.475995\pi\) | ||||
0.0753410 | + | 0.997158i | \(0.475995\pi\) | |||||||
\(194\) | 4.46837 | 0.320810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.5798 | −1.60874 | −0.804372 | − | 0.594126i | \(-0.797498\pi\) | ||||
−0.804372 | + | 0.594126i | \(0.797498\pi\) | |||||||
\(198\) | −6.87834 | −0.488823 | ||||||||
\(199\) | −7.50408 | −0.531950 | −0.265975 | − | 0.963980i | \(-0.585694\pi\) | ||||
−0.265975 | + | 0.963980i | \(0.585694\pi\) | |||||||
\(200\) | 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 | \(-0.428334\pi\) | ||||
0.223247 | + | 0.974762i | \(0.428334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.2392 | −1.26312 | ||||||||
\(233\) | 7.41201 | 0.485577 | 0.242789 | − | 0.970079i | \(-0.421938\pi\) | ||||
0.242789 | + | 0.970079i | \(0.421938\pi\) | |||||||
\(234\) | −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 | \(-0.354764\pi\) | ||||
0.440605 | + | 0.897701i | \(0.354764\pi\) | |||||||
\(242\) | −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 | \(-0.234277\pi\) | ||||
0.741157 | + | 0.671331i | \(0.234277\pi\) | |||||||
\(252\) | 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 | \(-0.550154\pi\) | ||||
−0.156913 | + | 0.987612i | \(0.550154\pi\) | |||||||
\(264\) | 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 | \(-0.119710\pi\) | ||||
0.930112 | + | 0.367277i | \(0.119710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4880 | −1.18381 | −0.591907 | − | 0.806007i | \(-0.701625\pi\) | ||||
−0.591907 | + | 0.806007i | \(0.701625\pi\) | |||||||
\(272\) | 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 | \(-0.222502\pi\) | ||||
0.765478 | + | 0.643462i | \(0.222502\pi\) | |||||||
\(278\) | 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 | \(-0.374845\pi\) | ||||
0.383133 | + | 0.923693i | \(0.374845\pi\) | |||||||
\(312\) | 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 | \(-0.489641\pi\) | ||||
0.0325378 | + | 0.999471i | \(0.489641\pi\) | |||||||
\(318\) | 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 | \(-0.356730\pi\) | ||||
0.435051 | + | 0.900406i | \(0.356730\pi\) | |||||||
\(338\) | 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 | \(-0.386433\pi\) | ||||
0.349260 | + | 0.937026i | \(0.386433\pi\) | |||||||
\(348\) | −3.19547 | −0.171295 | ||||||||
\(349\) | 32.0724 | 1.71680 | 0.858398 | − | 0.512984i | \(-0.171460\pi\) | ||||
0.858398 | + | 0.512984i | \(0.171460\pi\) | |||||||
\(350\) | 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 | \(-0.778165\pi\) | ||||
−0.766826 | + | 0.641855i | \(0.778165\pi\) | |||||||
\(374\) | 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 | \(-0.329466\pi\) | ||||
0.510484 | + | 0.859887i | \(0.329466\pi\) | |||||||
\(410\) | 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 | \(-0.542756\pi\) | ||||
−0.133920 | + | 0.990992i | \(0.542756\pi\) | |||||||
\(420\) | 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 | \(-0.581502\pi\) | ||||
−0.253259 | + | 0.967399i | \(0.581502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.34891 | 0.349552 | ||||||||
\(443\) | 19.9856 | 0.949543 | 0.474771 | − | 0.880109i | \(-0.342531\pi\) | ||||
0.474771 | + | 0.880109i | \(0.342531\pi\) | |||||||
\(444\) | −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 | \(-0.516993\pi\) | ||||
−0.0533584 | + | 0.998575i | \(0.516993\pi\) | |||||||
\(458\) | −10.4891 | −0.490126 | ||||||||
\(459\) | −2.73246 | −0.127540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0678 | −1.12095 | −0.560475 | − | 0.828171i | \(-0.689381\pi\) | ||||
−0.560475 | + | 0.828171i | \(0.689381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1290 | −0.517211 | −0.258605 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258605 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(464\) | 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 | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(480\) | 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 | \(-0.560562\pi\) | ||||
−0.189116 | + | 0.981955i | \(0.560562\pi\) | |||||||
\(488\) | 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 | \(-0.330653\pi\) | ||||
0.507274 | + | 0.861785i | \(0.330653\pi\) | |||||||
\(510\) | 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 | \(-0.305431\pi\) | ||||
0.573898 | + | 0.818927i | \(0.305431\pi\) | |||||||
\(522\) | 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 | \(-0.407428\pi\) | ||||
0.286742 | + | 0.958008i | \(0.407428\pi\) | |||||||
\(548\) | −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 | \(-0.824207\pi\) | ||||
−0.851336 | + | 0.524621i | \(0.824207\pi\) | |||||||
\(558\) | 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 | \(-0.582317\pi\) | ||||
−0.255733 | + | 0.966747i | \(0.582317\pi\) | |||||||
\(602\) | 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 | \(-0.688693\pi\) | ||||
−0.558682 | + | 0.829382i | \(0.688693\pi\) | |||||||
\(614\) | −46.3133 | −1.86905 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.4155 | 0.821896 | 0.410948 | − | 0.911659i | \(-0.365198\pi\) | ||||
0.410948 | + | 0.911659i | \(0.365198\pi\) | |||||||
\(618\) | 17.5009 | 0.703990 | ||||||||
\(619\) | −15.4422 | −0.620676 | −0.310338 | − | 0.950626i | \(-0.600442\pi\) | ||||
−0.310338 | + | 0.950626i | \(0.600442\pi\) | |||||||
\(620\) | 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 | \(-0.564487\pi\) | ||||
−0.201209 | + | 0.979548i | \(0.564487\pi\) | |||||||
\(654\) | −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 | \(-0.484850\pi\) | ||||
0.0475782 | + | 0.998868i | \(0.484850\pi\) | |||||||
\(662\) | 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 | \(-0.607945\pi\) | ||||
−0.332655 | + | 0.943049i | \(0.607945\pi\) | |||||||
\(674\) | −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 | \(-0.297181\pi\) | ||||
0.594928 | + | 0.803779i | \(0.297181\pi\) | |||||||
\(684\) | −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 | \(-0.610806\pi\) | ||||
−0.341119 | + | 0.940020i | \(0.610806\pi\) | |||||||
\(692\) | 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 | \(-0.301731\pi\) | ||||
0.583376 | + | 0.812202i | \(0.301731\pi\) | |||||||
\(720\) | 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 | \(-0.539809\pi\) | ||||
−0.124737 | + | 0.992190i | \(0.539809\pi\) | |||||||
\(744\) | −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 | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(758\) | −11.6072 | −0.421592 | ||||||||
\(759\) | −31.1226 | −1.12968 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.55508 | −0.0926215 | −0.0463108 | − | 0.998927i | \(-0.514746\pi\) | ||||
−0.0463108 | + | 0.998927i | \(0.514746\pi\) | |||||||
\(762\) | 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 | \(-0.805765\pi\) | ||||
−0.819530 | + | 0.573037i | \(0.805765\pi\) | |||||||
\(770\) | 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 | \(-0.662951\pi\) | ||||
−0.489858 | + | 0.871802i | \(0.662951\pi\) | |||||||
\(812\) | 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 | \(-0.444855\pi\) | ||||
0.172377 | + | 0.985031i | \(0.444855\pi\) | |||||||
\(824\) | −27.8269 | −0.969396 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3201 | 1.22820 | 0.614101 | − | 0.789228i | \(-0.289519\pi\) | ||||
0.614101 | + | 0.789228i | \(0.289519\pi\) | |||||||
\(828\) | −2.87976 | −0.100079 | ||||||||
\(829\) | 9.29951 | 0.322985 | 0.161493 | − | 0.986874i | \(-0.448369\pi\) | ||||
0.161493 | + | 0.986874i | \(0.448369\pi\) | |||||||
\(830\) | 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 | \(-0.543732\pi\) | ||||
−0.136957 | + | 0.990577i | \(0.543732\pi\) | |||||||
\(840\) | 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 | \(-0.687961\pi\) | ||||
−0.556774 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.7110 | 1.45474 | ||||||||
\(863\) | −37.4102 | −1.27346 | −0.636728 | − | 0.771088i | \(-0.719713\pi\) | ||||
−0.636728 | + | 0.771088i | \(0.719713\pi\) | |||||||
\(864\) | 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 | \(-0.691786\pi\) | ||||
−0.566716 | + | 0.823913i | \(0.691786\pi\) | |||||||
\(878\) | 16.4753 | 0.556014 | ||||||||
\(879\) | −13.8958 | −0.468694 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1952 | −0.410867 | −0.205433 | − | 0.978671i | \(-0.565860\pi\) | ||||
−0.205433 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.0408 | 0.371552 | 0.185776 | − | 0.982592i | \(-0.440520\pi\) | ||||
0.185776 | + | 0.982592i | \(0.440520\pi\) | |||||||
\(884\) | −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 | \(-0.406675\pi\) | ||||
0.289008 | + | 0.957327i | \(0.406675\pi\) | |||||||
\(908\) | 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 | \(-0.281255\pi\) | ||||
0.634381 | + | 0.773021i | \(0.281255\pi\) | |||||||
\(930\) | 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 | \(-0.739248\pi\) | ||||
−0.682824 | + | 0.730583i | \(0.739248\pi\) | |||||||
\(942\) | 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 | \(-0.134739\pi\) | ||||
0.911740 | + | 0.410768i | \(0.134739\pi\) | |||||||
\(948\) | 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 | \(-0.407069\pi\) | ||||
0.287821 | + | 0.957684i | \(0.407069\pi\) | |||||||
\(954\) | 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 | \(-0.618346\pi\) | ||||
−0.363290 | + | 0.931676i | \(0.618346\pi\) | |||||||
\(968\) | 21.3059 | 0.684799 | ||||||||
\(969\) | 0.833827 | 0.0267864 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.0488 | 1.31732 | 0.658660 | − | 0.752441i | \(-0.271124\pi\) | ||||
0.658660 | + | 0.752441i | \(0.271124\pi\) | |||||||
\(972\) | 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 | \(-0.600833\pi\) | ||||
−0.311504 | + | 0.950245i | \(0.600833\pi\) | |||||||
\(978\) | −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 \(a_p\))