Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 44x^{2} + 19x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.122980\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −14.5171 | −1.29845 | −0.649226 | − | 0.760596i | \(-0.724907\pi\) | ||||
−0.649226 | + | 0.760596i | \(0.724907\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −18.9849 | −1.02509 | −0.512543 | − | 0.858661i | \(-0.671297\pi\) | ||||
−0.512543 | + | 0.858661i | \(0.671297\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −29.0343 | −0.918144 | ||||||||
\(11\) | 23.7792 | 0.651792 | 0.325896 | − | 0.945406i | \(-0.394334\pi\) | ||||
0.325896 | + | 0.945406i | \(0.394334\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −9.08972 | −0.193926 | −0.0969628 | − | 0.995288i | \(-0.530913\pi\) | ||||
−0.0969628 | + | 0.995288i | \(0.530913\pi\) | |||||||
\(14\) | −37.9698 | −0.724846 | ||||||||
\(15\) | 43.5514 | 0.749661 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 30.1895 | 0.430707 | 0.215354 | − | 0.976536i | \(-0.430910\pi\) | ||||
0.215354 | + | 0.976536i | \(0.430910\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 152.389 | 1.84002 | 0.920012 | − | 0.391891i | \(-0.128179\pi\) | ||||
0.920012 | + | 0.391891i | \(0.128179\pi\) | |||||||
\(20\) | −58.0685 | −0.649226 | ||||||||
\(21\) | 56.9546 | 0.591834 | ||||||||
\(22\) | 47.5585 | 0.460887 | ||||||||
\(23\) | 7.74590 | 0.0702231 | 0.0351116 | − | 0.999383i | \(-0.488821\pi\) | ||||
0.0351116 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 85.7471 | 0.685976 | ||||||||
\(26\) | −18.1794 | −0.137126 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −75.9395 | −0.512543 | ||||||||
\(29\) | 86.3277 | 0.552781 | 0.276390 | − | 0.961045i | \(-0.410862\pi\) | ||||
0.276390 | + | 0.961045i | \(0.410862\pi\) | |||||||
\(30\) | 87.1028 | 0.530091 | ||||||||
\(31\) | 143.628 | 0.832141 | 0.416071 | − | 0.909332i | \(-0.363407\pi\) | ||||
0.416071 | + | 0.909332i | \(0.363407\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −71.3377 | −0.376312 | ||||||||
\(34\) | 60.3789 | 0.304556 | ||||||||
\(35\) | 275.606 | 1.33103 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −15.9457 | −0.0708501 | −0.0354250 | − | 0.999372i | \(-0.511278\pi\) | ||||
−0.0354250 | + | 0.999372i | \(0.511278\pi\) | |||||||
\(38\) | 304.778 | 1.30109 | ||||||||
\(39\) | 27.2691 | 0.111963 | ||||||||
\(40\) | −116.137 | −0.459072 | ||||||||
\(41\) | 326.380 | 1.24322 | 0.621610 | − | 0.783327i | \(-0.286479\pi\) | ||||
0.621610 | + | 0.783327i | \(0.286479\pi\) | |||||||
\(42\) | 113.909 | 0.418490 | ||||||||
\(43\) | −216.856 | −0.769075 | −0.384537 | − | 0.923109i | \(-0.625639\pi\) | ||||
−0.384537 | + | 0.923109i | \(0.625639\pi\) | |||||||
\(44\) | 95.1170 | 0.325896 | ||||||||
\(45\) | −130.654 | −0.432817 | ||||||||
\(46\) | 15.4918 | 0.0496552 | ||||||||
\(47\) | 87.4463 | 0.271391 | 0.135695 | − | 0.990751i | \(-0.456673\pi\) | ||||
0.135695 | + | 0.990751i | \(0.456673\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 17.4255 | 0.0508032 | ||||||||
\(50\) | 171.494 | 0.485059 | ||||||||
\(51\) | −90.5684 | −0.248669 | ||||||||
\(52\) | −36.3589 | −0.0969628 | ||||||||
\(53\) | 20.1580 | 0.0522437 | 0.0261219 | − | 0.999659i | \(-0.491684\pi\) | ||||
0.0261219 | + | 0.999659i | \(0.491684\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −345.206 | −0.846320 | ||||||||
\(56\) | −151.879 | −0.362423 | ||||||||
\(57\) | −457.167 | −1.06234 | ||||||||
\(58\) | 172.655 | 0.390875 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 174.206 | 0.374831 | ||||||||
\(61\) | 298.414 | 0.626361 | 0.313181 | − | 0.949694i | \(-0.398605\pi\) | ||||
0.313181 | + | 0.949694i | \(0.398605\pi\) | |||||||
\(62\) | 287.256 | 0.588413 | ||||||||
\(63\) | −170.864 | −0.341696 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 131.957 | 0.251803 | ||||||||
\(66\) | −142.675 | −0.266093 | ||||||||
\(67\) | −297.759 | −0.542941 | −0.271470 | − | 0.962447i | \(-0.587510\pi\) | ||||
−0.271470 | + | 0.962447i | \(0.587510\pi\) | |||||||
\(68\) | 120.758 | 0.215354 | ||||||||
\(69\) | −23.2377 | −0.0405433 | ||||||||
\(70\) | 551.212 | 0.941177 | ||||||||
\(71\) | 313.600 | 0.524190 | 0.262095 | − | 0.965042i | \(-0.415587\pi\) | ||||
0.262095 | + | 0.965042i | \(0.415587\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 6.83173 | 0.0109533 | 0.00547667 | − | 0.999985i | \(-0.498257\pi\) | ||||
0.00547667 | + | 0.999985i | \(0.498257\pi\) | |||||||
\(74\) | −31.8913 | −0.0500986 | ||||||||
\(75\) | −257.241 | −0.396049 | ||||||||
\(76\) | 609.556 | 0.920012 | ||||||||
\(77\) | −451.446 | −0.668144 | ||||||||
\(78\) | 54.5383 | 0.0791698 | ||||||||
\(79\) | 75.3435 | 0.107301 | 0.0536507 | − | 0.998560i | \(-0.482914\pi\) | ||||
0.0536507 | + | 0.998560i | \(0.482914\pi\) | |||||||
\(80\) | −232.274 | −0.324613 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 652.760 | 0.879089 | ||||||||
\(83\) | 448.906 | 0.593661 | 0.296830 | − | 0.954930i | \(-0.404070\pi\) | ||||
0.296830 | + | 0.954930i | \(0.404070\pi\) | |||||||
\(84\) | 227.819 | 0.295917 | ||||||||
\(85\) | −438.264 | −0.559252 | ||||||||
\(86\) | −433.712 | −0.543818 | ||||||||
\(87\) | −258.983 | −0.319148 | ||||||||
\(88\) | 190.234 | 0.230443 | ||||||||
\(89\) | 1419.69 | 1.69087 | 0.845434 | − | 0.534079i | \(-0.179342\pi\) | ||||
0.845434 | + | 0.534079i | \(0.179342\pi\) | |||||||
\(90\) | −261.308 | −0.306048 | ||||||||
\(91\) | 172.567 | 0.198791 | ||||||||
\(92\) | 30.9836 | 0.0351116 | ||||||||
\(93\) | −430.884 | −0.480437 | ||||||||
\(94\) | 174.893 | 0.191902 | ||||||||
\(95\) | −2212.25 | −2.38918 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 622.392 | 0.651488 | 0.325744 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325744 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(98\) | 34.8510 | 0.0359233 | ||||||||
\(99\) | 214.013 | 0.217264 | ||||||||
\(100\) | 342.988 | 0.342988 | ||||||||
\(101\) | −416.885 | −0.410709 | −0.205354 | − | 0.978688i | \(-0.565835\pi\) | ||||
−0.205354 | + | 0.978688i | \(0.565835\pi\) | |||||||
\(102\) | −181.137 | −0.175835 | ||||||||
\(103\) | 86.0527 | 0.0823206 | 0.0411603 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411603 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(104\) | −72.7177 | −0.0685631 | ||||||||
\(105\) | −826.818 | −0.768468 | ||||||||
\(106\) | 40.3160 | 0.0369419 | ||||||||
\(107\) | 348.798 | 0.315136 | 0.157568 | − | 0.987508i | \(-0.449635\pi\) | ||||
0.157568 | + | 0.987508i | \(0.449635\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | 132.115 | 0.116095 | 0.0580474 | − | 0.998314i | \(-0.481513\pi\) | ||||
0.0580474 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(110\) | −690.413 | −0.598439 | ||||||||
\(111\) | 47.8370 | 0.0409053 | ||||||||
\(112\) | −303.758 | −0.256272 | ||||||||
\(113\) | 353.219 | 0.294054 | 0.147027 | − | 0.989132i | \(-0.453030\pi\) | ||||
0.147027 | + | 0.989132i | \(0.453030\pi\) | |||||||
\(114\) | −914.334 | −0.751187 | ||||||||
\(115\) | −112.448 | −0.0911813 | ||||||||
\(116\) | 345.311 | 0.276390 | ||||||||
\(117\) | −81.8074 | −0.0646419 | ||||||||
\(118\) | 118.000 | 0.0920575 | ||||||||
\(119\) | −573.143 | −0.441512 | ||||||||
\(120\) | 348.411 | 0.265045 | ||||||||
\(121\) | −765.547 | −0.575167 | ||||||||
\(122\) | 596.829 | 0.442904 | ||||||||
\(123\) | −979.140 | −0.717773 | ||||||||
\(124\) | 574.512 | 0.416071 | ||||||||
\(125\) | 569.840 | 0.407744 | ||||||||
\(126\) | −341.728 | −0.241615 | ||||||||
\(127\) | −1970.59 | −1.37686 | −0.688430 | − | 0.725303i | \(-0.741700\pi\) | ||||
−0.688430 | + | 0.725303i | \(0.741700\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 650.568 | 0.444026 | ||||||||
\(130\) | 263.913 | 0.178052 | ||||||||
\(131\) | −1308.78 | −0.872891 | −0.436446 | − | 0.899731i | \(-0.643763\pi\) | ||||
−0.436446 | + | 0.899731i | \(0.643763\pi\) | |||||||
\(132\) | −285.351 | −0.188156 | ||||||||
\(133\) | −2893.09 | −1.88618 | ||||||||
\(134\) | −595.518 | −0.383917 | ||||||||
\(135\) | 391.963 | 0.249887 | ||||||||
\(136\) | 241.516 | 0.152278 | ||||||||
\(137\) | 770.739 | 0.480647 | 0.240324 | − | 0.970693i | \(-0.422746\pi\) | ||||
0.240324 | + | 0.970693i | \(0.422746\pi\) | |||||||
\(138\) | −46.4754 | −0.0286685 | ||||||||
\(139\) | 1567.36 | 0.956415 | 0.478207 | − | 0.878247i | \(-0.341287\pi\) | ||||
0.478207 | + | 0.878247i | \(0.341287\pi\) | |||||||
\(140\) | 1102.42 | 0.665513 | ||||||||
\(141\) | −262.339 | −0.156687 | ||||||||
\(142\) | 627.200 | 0.370658 | ||||||||
\(143\) | −216.147 | −0.126399 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1253.23 | −0.717759 | ||||||||
\(146\) | 13.6635 | 0.00774518 | ||||||||
\(147\) | −52.2765 | −0.0293313 | ||||||||
\(148\) | −63.7827 | −0.0354250 | ||||||||
\(149\) | −628.560 | −0.345595 | −0.172798 | − | 0.984957i | \(-0.555281\pi\) | ||||
−0.172798 | + | 0.984957i | \(0.555281\pi\) | |||||||
\(150\) | −514.482 | −0.280049 | ||||||||
\(151\) | 1057.42 | 0.569881 | 0.284940 | − | 0.958545i | \(-0.408026\pi\) | ||||
0.284940 | + | 0.958545i | \(0.408026\pi\) | |||||||
\(152\) | 1219.11 | 0.650547 | ||||||||
\(153\) | 271.705 | 0.143569 | ||||||||
\(154\) | −902.892 | −0.472449 | ||||||||
\(155\) | −2085.07 | −1.08049 | ||||||||
\(156\) | 109.077 | 0.0559815 | ||||||||
\(157\) | −2184.80 | −1.11061 | −0.555305 | − | 0.831647i | \(-0.687399\pi\) | ||||
−0.555305 | + | 0.831647i | \(0.687399\pi\) | |||||||
\(158\) | 150.687 | 0.0758735 | ||||||||
\(159\) | −60.4741 | −0.0301629 | ||||||||
\(160\) | −464.548 | −0.229536 | ||||||||
\(161\) | −147.055 | −0.0719848 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −847.798 | −0.407391 | −0.203695 | − | 0.979034i | \(-0.565295\pi\) | ||||
−0.203695 | + | 0.979034i | \(0.565295\pi\) | |||||||
\(164\) | 1305.52 | 0.621610 | ||||||||
\(165\) | 1035.62 | 0.488623 | ||||||||
\(166\) | 897.812 | 0.419782 | ||||||||
\(167\) | 1327.98 | 0.615343 | 0.307672 | − | 0.951493i | \(-0.400450\pi\) | ||||
0.307672 | + | 0.951493i | \(0.400450\pi\) | |||||||
\(168\) | 455.637 | 0.209245 | ||||||||
\(169\) | −2114.38 | −0.962393 | ||||||||
\(170\) | −876.529 | −0.395451 | ||||||||
\(171\) | 1371.50 | 0.613341 | ||||||||
\(172\) | −867.424 | −0.384537 | ||||||||
\(173\) | 3125.82 | 1.37371 | 0.686854 | − | 0.726796i | \(-0.258991\pi\) | ||||
0.686854 | + | 0.726796i | \(0.258991\pi\) | |||||||
\(174\) | −517.966 | −0.225672 | ||||||||
\(175\) | −1627.90 | −0.703185 | ||||||||
\(176\) | 380.468 | 0.162948 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | 2839.39 | 1.19562 | ||||||||
\(179\) | 4682.86 | 1.95538 | 0.977692 | − | 0.210044i | \(-0.0673607\pi\) | ||||
0.977692 | + | 0.210044i | \(0.0673607\pi\) | |||||||
\(180\) | −522.617 | −0.216409 | ||||||||
\(181\) | −132.858 | −0.0545593 | −0.0272796 | − | 0.999628i | \(-0.508684\pi\) | ||||
−0.0272796 | + | 0.999628i | \(0.508684\pi\) | |||||||
\(182\) | 345.134 | 0.140566 | ||||||||
\(183\) | −895.243 | −0.361630 | ||||||||
\(184\) | 61.9672 | 0.0248276 | ||||||||
\(185\) | 231.485 | 0.0919954 | ||||||||
\(186\) | −861.769 | −0.339720 | ||||||||
\(187\) | 717.883 | 0.280732 | ||||||||
\(188\) | 349.785 | 0.135695 | ||||||||
\(189\) | 512.592 | 0.197278 | ||||||||
\(190\) | −4424.50 | −1.68941 | ||||||||
\(191\) | −3273.78 | −1.24022 | −0.620111 | − | 0.784514i | \(-0.712913\pi\) | ||||
−0.620111 | + | 0.784514i | \(0.712913\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 340.402 | 0.126957 | 0.0634784 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634784 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(194\) | 1244.78 | 0.460672 | ||||||||
\(195\) | −395.870 | −0.145379 | ||||||||
\(196\) | 69.7020 | 0.0254016 | ||||||||
\(197\) | 4671.06 | 1.68934 | 0.844668 | − | 0.535291i | \(-0.179798\pi\) | ||||
0.844668 | + | 0.535291i | \(0.179798\pi\) | |||||||
\(198\) | 428.026 | 0.153629 | ||||||||
\(199\) | −1282.92 | −0.457004 | −0.228502 | − | 0.973543i | \(-0.573383\pi\) | ||||
−0.228502 | + | 0.973543i | \(0.573383\pi\) | |||||||
\(200\) | 685.976 | 0.242529 | ||||||||
\(201\) | 893.277 | 0.313467 | ||||||||
\(202\) | −833.770 | −0.290415 | ||||||||
\(203\) | −1638.92 | −0.566648 | ||||||||
\(204\) | −362.274 | −0.124334 | ||||||||
\(205\) | −4738.10 | −1.61426 | ||||||||
\(206\) | 172.105 | 0.0582095 | ||||||||
\(207\) | 69.7131 | 0.0234077 | ||||||||
\(208\) | −145.435 | −0.0484814 | ||||||||
\(209\) | 3623.70 | 1.19931 | ||||||||
\(210\) | −1653.64 | −0.543389 | ||||||||
\(211\) | 918.289 | 0.299610 | 0.149805 | − | 0.988716i | \(-0.452135\pi\) | ||||
0.149805 | + | 0.988716i | \(0.452135\pi\) | |||||||
\(212\) | 80.6321 | 0.0261219 | ||||||||
\(213\) | −940.800 | −0.302641 | ||||||||
\(214\) | 697.595 | 0.222835 | ||||||||
\(215\) | 3148.13 | 0.998606 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −2726.76 | −0.853017 | ||||||||
\(218\) | 264.230 | 0.0820914 | ||||||||
\(219\) | −20.4952 | −0.00632392 | ||||||||
\(220\) | −1380.83 | −0.423160 | ||||||||
\(221\) | −274.414 | −0.0835252 | ||||||||
\(222\) | 95.6740 | 0.0289244 | ||||||||
\(223\) | −4775.60 | −1.43407 | −0.717035 | − | 0.697037i | \(-0.754501\pi\) | ||||
−0.717035 | + | 0.697037i | \(0.754501\pi\) | |||||||
\(224\) | −607.516 | −0.181211 | ||||||||
\(225\) | 771.723 | 0.228659 | ||||||||
\(226\) | 706.438 | 0.207927 | ||||||||
\(227\) | −3348.25 | −0.978992 | −0.489496 | − | 0.872006i | \(-0.662819\pi\) | ||||
−0.489496 | + | 0.872006i | \(0.662819\pi\) | |||||||
\(228\) | −1828.67 | −0.531169 | ||||||||
\(229\) | 667.923 | 0.192741 | 0.0963703 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963703 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(230\) | −224.896 | −0.0644749 | ||||||||
\(231\) | 1354.34 | 0.385753 | ||||||||
\(232\) | 690.621 | 0.195438 | ||||||||
\(233\) | 3641.88 | 1.02398 | 0.511990 | − | 0.858991i | \(-0.328908\pi\) | ||||
0.511990 | + | 0.858991i | \(0.328908\pi\) | |||||||
\(234\) | −163.615 | −0.0457087 | ||||||||
\(235\) | −1269.47 | −0.352387 | ||||||||
\(236\) | 236.000 | 0.0650945 | ||||||||
\(237\) | −226.031 | −0.0619505 | ||||||||
\(238\) | −1146.29 | −0.312196 | ||||||||
\(239\) | −4829.87 | −1.30719 | −0.653595 | − | 0.756844i | \(-0.726740\pi\) | ||||
−0.653595 | + | 0.756844i | \(0.726740\pi\) | |||||||
\(240\) | 696.822 | 0.187415 | ||||||||
\(241\) | 5698.29 | 1.52307 | 0.761533 | − | 0.648126i | \(-0.224447\pi\) | ||||
0.761533 | + | 0.648126i | \(0.224447\pi\) | |||||||
\(242\) | −1531.09 | −0.406705 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1193.66 | 0.313181 | ||||||||
\(245\) | −252.968 | −0.0659655 | ||||||||
\(246\) | −1958.28 | −0.507542 | ||||||||
\(247\) | −1385.17 | −0.356828 | ||||||||
\(248\) | 1149.02 | 0.294206 | ||||||||
\(249\) | −1346.72 | −0.342750 | ||||||||
\(250\) | 1139.68 | 0.288319 | ||||||||
\(251\) | 2138.32 | 0.537727 | 0.268863 | − | 0.963178i | \(-0.413352\pi\) | ||||
0.268863 | + | 0.963178i | \(0.413352\pi\) | |||||||
\(252\) | −683.456 | −0.170848 | ||||||||
\(253\) | 184.192 | 0.0457709 | ||||||||
\(254\) | −3941.17 | −0.973587 | ||||||||
\(255\) | 1314.79 | 0.322885 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4379.06 | 1.06287 | 0.531437 | − | 0.847098i | \(-0.321652\pi\) | ||||
0.531437 | + | 0.847098i | \(0.321652\pi\) | |||||||
\(258\) | 1301.14 | 0.313973 | ||||||||
\(259\) | 302.727 | 0.0726275 | ||||||||
\(260\) | 527.826 | 0.125902 | ||||||||
\(261\) | 776.949 | 0.184260 | ||||||||
\(262\) | −2617.56 | −0.617227 | ||||||||
\(263\) | −6374.29 | −1.49451 | −0.747254 | − | 0.664539i | \(-0.768628\pi\) | ||||
−0.747254 | + | 0.664539i | \(0.768628\pi\) | |||||||
\(264\) | −570.702 | −0.133047 | ||||||||
\(265\) | −292.637 | −0.0678359 | ||||||||
\(266\) | −5786.18 | −1.33373 | ||||||||
\(267\) | −4259.08 | −0.976224 | ||||||||
\(268\) | −1191.04 | −0.271470 | ||||||||
\(269\) | 8643.02 | 1.95901 | 0.979506 | − | 0.201417i | \(-0.0645546\pi\) | ||||
0.979506 | + | 0.201417i | \(0.0645546\pi\) | |||||||
\(270\) | 783.925 | 0.176697 | ||||||||
\(271\) | −7810.17 | −1.75068 | −0.875339 | − | 0.483510i | \(-0.839362\pi\) | ||||
−0.875339 | + | 0.483510i | \(0.839362\pi\) | |||||||
\(272\) | 483.032 | 0.107677 | ||||||||
\(273\) | −517.701 | −0.114772 | ||||||||
\(274\) | 1541.48 | 0.339869 | ||||||||
\(275\) | 2039.00 | 0.447114 | ||||||||
\(276\) | −92.9508 | −0.0202717 | ||||||||
\(277\) | −1071.20 | −0.232354 | −0.116177 | − | 0.993229i | \(-0.537064\pi\) | ||||
−0.116177 | + | 0.993229i | \(0.537064\pi\) | |||||||
\(278\) | 3134.72 | 0.676287 | ||||||||
\(279\) | 1292.65 | 0.277380 | ||||||||
\(280\) | 2204.85 | 0.470589 | ||||||||
\(281\) | 7587.19 | 1.61073 | 0.805363 | − | 0.592782i | \(-0.201970\pi\) | ||||
0.805363 | + | 0.592782i | \(0.201970\pi\) | |||||||
\(282\) | −524.678 | −0.110795 | ||||||||
\(283\) | 8951.10 | 1.88017 | 0.940085 | − | 0.340941i | \(-0.110746\pi\) | ||||
0.940085 | + | 0.340941i | \(0.110746\pi\) | |||||||
\(284\) | 1254.40 | 0.262095 | ||||||||
\(285\) | 6636.76 | 1.37939 | ||||||||
\(286\) | −432.293 | −0.0893777 | ||||||||
\(287\) | −6196.29 | −1.27441 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4001.60 | −0.814491 | ||||||||
\(290\) | −2506.46 | −0.507532 | ||||||||
\(291\) | −1867.18 | −0.376137 | ||||||||
\(292\) | 27.3269 | 0.00547667 | ||||||||
\(293\) | −1422.92 | −0.283713 | −0.141856 | − | 0.989887i | \(-0.545307\pi\) | ||||
−0.141856 | + | 0.989887i | \(0.545307\pi\) | |||||||
\(294\) | −104.553 | −0.0207403 | ||||||||
\(295\) | −856.511 | −0.169044 | ||||||||
\(296\) | −127.565 | −0.0250493 | ||||||||
\(297\) | −642.040 | −0.125437 | ||||||||
\(298\) | −1257.12 | −0.244373 | ||||||||
\(299\) | −70.4080 | −0.0136181 | ||||||||
\(300\) | −1028.96 | −0.198024 | ||||||||
\(301\) | 4116.98 | 0.788369 | ||||||||
\(302\) | 2114.85 | 0.402967 | ||||||||
\(303\) | 1250.65 | 0.237123 | ||||||||
\(304\) | 2438.23 | 0.460006 | ||||||||
\(305\) | −4332.12 | −0.813300 | ||||||||
\(306\) | 543.410 | 0.101519 | ||||||||
\(307\) | 7310.99 | 1.35915 | 0.679577 | − | 0.733605i | \(-0.262163\pi\) | ||||
0.679577 | + | 0.733605i | \(0.262163\pi\) | |||||||
\(308\) | −1805.78 | −0.334072 | ||||||||
\(309\) | −258.158 | −0.0475278 | ||||||||
\(310\) | −4170.14 | −0.764025 | ||||||||
\(311\) | 974.108 | 0.177610 | 0.0888048 | − | 0.996049i | \(-0.471695\pi\) | ||||
0.0888048 | + | 0.996049i | \(0.471695\pi\) | |||||||
\(312\) | 218.153 | 0.0395849 | ||||||||
\(313\) | 540.790 | 0.0976591 | 0.0488295 | − | 0.998807i | \(-0.484451\pi\) | ||||
0.0488295 | + | 0.998807i | \(0.484451\pi\) | |||||||
\(314\) | −4369.60 | −0.785320 | ||||||||
\(315\) | 2480.45 | 0.443675 | ||||||||
\(316\) | 301.374 | 0.0536507 | ||||||||
\(317\) | 2666.13 | 0.472381 | 0.236190 | − | 0.971707i | \(-0.424101\pi\) | ||||
0.236190 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(318\) | −120.948 | −0.0213284 | ||||||||
\(319\) | 2052.81 | 0.360298 | ||||||||
\(320\) | −929.096 | −0.162306 | ||||||||
\(321\) | −1046.39 | −0.181944 | ||||||||
\(322\) | −294.110 | −0.0509009 | ||||||||
\(323\) | 4600.55 | 0.792511 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −779.416 | −0.133028 | ||||||||
\(326\) | −1695.60 | −0.288069 | ||||||||
\(327\) | −396.345 | −0.0670273 | ||||||||
\(328\) | 2611.04 | 0.439544 | ||||||||
\(329\) | −1660.16 | −0.278199 | ||||||||
\(330\) | 2071.24 | 0.345509 | ||||||||
\(331\) | 1412.61 | 0.234574 | 0.117287 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117287 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(332\) | 1795.62 | 0.296830 | ||||||||
\(333\) | −143.511 | −0.0236167 | ||||||||
\(334\) | 2655.96 | 0.435114 | ||||||||
\(335\) | 4322.60 | 0.704983 | ||||||||
\(336\) | 911.274 | 0.147959 | ||||||||
\(337\) | −426.538 | −0.0689466 | −0.0344733 | − | 0.999406i | \(-0.510975\pi\) | ||||
−0.0344733 | + | 0.999406i | \(0.510975\pi\) | |||||||
\(338\) | −4228.75 | −0.680514 | ||||||||
\(339\) | −1059.66 | −0.169772 | ||||||||
\(340\) | −1753.06 | −0.279626 | ||||||||
\(341\) | 3415.37 | 0.542383 | ||||||||
\(342\) | 2743.00 | 0.433698 | ||||||||
\(343\) | 6180.99 | 0.973009 | ||||||||
\(344\) | −1734.85 | −0.271909 | ||||||||
\(345\) | 337.345 | 0.0526436 | ||||||||
\(346\) | 6251.63 | 0.971358 | ||||||||
\(347\) | 224.184 | 0.0346826 | 0.0173413 | − | 0.999850i | \(-0.494480\pi\) | ||||
0.0173413 | + | 0.999850i | \(0.494480\pi\) | |||||||
\(348\) | −1035.93 | −0.159574 | ||||||||
\(349\) | 11037.8 | 1.69296 | 0.846479 | − | 0.532422i | \(-0.178718\pi\) | ||||
0.846479 | + | 0.532422i | \(0.178718\pi\) | |||||||
\(350\) | −3255.79 | −0.497227 | ||||||||
\(351\) | 245.422 | 0.0373210 | ||||||||
\(352\) | 760.936 | 0.115222 | ||||||||
\(353\) | 9820.44 | 1.48071 | 0.740353 | − | 0.672219i | \(-0.234658\pi\) | ||||
0.740353 | + | 0.672219i | \(0.234658\pi\) | |||||||
\(354\) | −354.000 | −0.0531494 | ||||||||
\(355\) | −4552.57 | −0.680635 | ||||||||
\(356\) | 5678.78 | 0.845434 | ||||||||
\(357\) | 1719.43 | 0.254907 | ||||||||
\(358\) | 9365.73 | 1.38267 | ||||||||
\(359\) | 4391.53 | 0.645616 | 0.322808 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322808 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(360\) | −1045.23 | −0.153024 | ||||||||
\(361\) | 16363.4 | 2.38569 | ||||||||
\(362\) | −265.715 | −0.0385792 | ||||||||
\(363\) | 2296.64 | 0.332073 | ||||||||
\(364\) | 690.269 | 0.0993953 | ||||||||
\(365\) | −99.1772 | −0.0142224 | ||||||||
\(366\) | −1790.49 | −0.255711 | ||||||||
\(367\) | −2173.35 | −0.309123 | −0.154561 | − | 0.987983i | \(-0.549396\pi\) | ||||
−0.154561 | + | 0.987983i | \(0.549396\pi\) | |||||||
\(368\) | 123.934 | 0.0175558 | ||||||||
\(369\) | 2937.42 | 0.414407 | ||||||||
\(370\) | 462.971 | 0.0650505 | ||||||||
\(371\) | −382.698 | −0.0535544 | ||||||||
\(372\) | −1723.54 | −0.240218 | ||||||||
\(373\) | 9445.30 | 1.31115 | 0.655575 | − | 0.755130i | \(-0.272426\pi\) | ||||
0.655575 | + | 0.755130i | \(0.272426\pi\) | |||||||
\(374\) | 1435.77 | 0.198507 | ||||||||
\(375\) | −1709.52 | −0.235411 | ||||||||
\(376\) | 699.570 | 0.0959510 | ||||||||
\(377\) | −784.694 | −0.107198 | ||||||||
\(378\) | 1025.18 | 0.139497 | ||||||||
\(379\) | −4028.86 | −0.546039 | −0.273019 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273019 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(380\) | −8849.01 | −1.19459 | ||||||||
\(381\) | 5911.76 | 0.794930 | ||||||||
\(382\) | −6547.56 | −0.876970 | ||||||||
\(383\) | 1787.00 | 0.238411 | 0.119206 | − | 0.992870i | \(-0.461965\pi\) | ||||
0.119206 | + | 0.992870i | \(0.461965\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 6553.70 | 0.867552 | ||||||||
\(386\) | 680.804 | 0.0897720 | ||||||||
\(387\) | −1951.70 | −0.256358 | ||||||||
\(388\) | 2489.57 | 0.325744 | ||||||||
\(389\) | −5491.07 | −0.715702 | −0.357851 | − | 0.933779i | \(-0.616490\pi\) | ||||
−0.357851 | + | 0.933779i | \(0.616490\pi\) | |||||||
\(390\) | −791.740 | −0.102798 | ||||||||
\(391\) | 233.845 | 0.0302456 | ||||||||
\(392\) | 139.404 | 0.0179617 | ||||||||
\(393\) | 3926.34 | 0.503964 | ||||||||
\(394\) | 9342.12 | 1.19454 | ||||||||
\(395\) | −1093.77 | −0.139326 | ||||||||
\(396\) | 856.053 | 0.108632 | ||||||||
\(397\) | −11750.8 | −1.48554 | −0.742768 | − | 0.669549i | \(-0.766487\pi\) | ||||
−0.742768 | + | 0.669549i | \(0.766487\pi\) | |||||||
\(398\) | −2565.84 | −0.323151 | ||||||||
\(399\) | 8679.26 | 1.08899 | ||||||||
\(400\) | 1371.95 | 0.171494 | ||||||||
\(401\) | −4123.69 | −0.513535 | −0.256767 | − | 0.966473i | \(-0.582657\pi\) | ||||
−0.256767 | + | 0.966473i | \(0.582657\pi\) | |||||||
\(402\) | 1786.55 | 0.221655 | ||||||||
\(403\) | −1305.54 | −0.161374 | ||||||||
\(404\) | −1667.54 | −0.205354 | ||||||||
\(405\) | −1175.89 | −0.144272 | ||||||||
\(406\) | −3277.84 | −0.400681 | ||||||||
\(407\) | −379.176 | −0.0461795 | ||||||||
\(408\) | −724.547 | −0.0879177 | ||||||||
\(409\) | −14142.8 | −1.70982 | −0.854910 | − | 0.518776i | \(-0.826388\pi\) | ||||
−0.854910 | + | 0.518776i | \(0.826388\pi\) | |||||||
\(410\) | −9476.20 | −1.14145 | ||||||||
\(411\) | −2312.22 | −0.277502 | ||||||||
\(412\) | 344.211 | 0.0411603 | ||||||||
\(413\) | −1120.11 | −0.133455 | ||||||||
\(414\) | 139.426 | 0.0165517 | ||||||||
\(415\) | −6516.83 | −0.770840 | ||||||||
\(416\) | −290.871 | −0.0342815 | ||||||||
\(417\) | −4702.08 | −0.552186 | ||||||||
\(418\) | 7247.40 | 0.848042 | ||||||||
\(419\) | −13489.9 | −1.57285 | −0.786425 | − | 0.617686i | \(-0.788070\pi\) | ||||
−0.786425 | + | 0.617686i | \(0.788070\pi\) | |||||||
\(420\) | −3307.27 | −0.384234 | ||||||||
\(421\) | 11198.4 | 1.29638 | 0.648189 | − | 0.761479i | \(-0.275527\pi\) | ||||
0.648189 | + | 0.761479i | \(0.275527\pi\) | |||||||
\(422\) | 1836.58 | 0.211856 | ||||||||
\(423\) | 787.017 | 0.0904635 | ||||||||
\(424\) | 161.264 | 0.0184709 | ||||||||
\(425\) | 2588.66 | 0.295455 | ||||||||
\(426\) | −1881.60 | −0.214000 | ||||||||
\(427\) | −5665.36 | −0.642075 | ||||||||
\(428\) | 1395.19 | 0.157568 | ||||||||
\(429\) | 648.440 | 0.0729766 | ||||||||
\(430\) | 6296.25 | 0.706121 | ||||||||
\(431\) | −9819.96 | −1.09747 | −0.548737 | − | 0.835995i | \(-0.684891\pi\) | ||||
−0.548737 | + | 0.835995i | \(0.684891\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −6816.67 | −0.756554 | −0.378277 | − | 0.925692i | \(-0.623483\pi\) | ||||
−0.378277 | + | 0.925692i | \(0.623483\pi\) | |||||||
\(434\) | −5453.52 | −0.603174 | ||||||||
\(435\) | 3759.69 | 0.414398 | ||||||||
\(436\) | 528.460 | 0.0580474 | ||||||||
\(437\) | 1180.39 | 0.129212 | ||||||||
\(438\) | −40.9904 | −0.00447168 | ||||||||
\(439\) | −17813.6 | −1.93666 | −0.968331 | − | 0.249670i | \(-0.919678\pi\) | ||||
−0.968331 | + | 0.249670i | \(0.919678\pi\) | |||||||
\(440\) | −2761.65 | −0.299219 | ||||||||
\(441\) | 156.830 | 0.0169344 | ||||||||
\(442\) | −548.827 | −0.0590612 | ||||||||
\(443\) | −14194.9 | −1.52239 | −0.761194 | − | 0.648524i | \(-0.775386\pi\) | ||||
−0.761194 | + | 0.648524i | \(0.775386\pi\) | |||||||
\(444\) | 191.348 | 0.0204526 | ||||||||
\(445\) | −20609.9 | −2.19551 | ||||||||
\(446\) | −9551.19 | −1.01404 | ||||||||
\(447\) | 1885.68 | 0.199529 | ||||||||
\(448\) | −1215.03 | −0.128136 | ||||||||
\(449\) | −1846.28 | −0.194057 | −0.0970284 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970284 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(450\) | 1543.45 | 0.161686 | ||||||||
\(451\) | 7761.07 | 0.810321 | ||||||||
\(452\) | 1412.88 | 0.147027 | ||||||||
\(453\) | −3172.27 | −0.329021 | ||||||||
\(454\) | −6696.50 | −0.692252 | ||||||||
\(455\) | −2505.18 | −0.258120 | ||||||||
\(456\) | −3657.34 | −0.375593 | ||||||||
\(457\) | −10310.4 | −1.05536 | −0.527681 | − | 0.849443i | \(-0.676938\pi\) | ||||
−0.527681 | + | 0.849443i | \(0.676938\pi\) | |||||||
\(458\) | 1335.85 | 0.136288 | ||||||||
\(459\) | −815.116 | −0.0828896 | ||||||||
\(460\) | −449.793 | −0.0455907 | ||||||||
\(461\) | −118.971 | −0.0120196 | −0.00600982 | − | 0.999982i | \(-0.501913\pi\) | ||||
−0.00600982 | + | 0.999982i | \(0.501913\pi\) | |||||||
\(462\) | 2708.68 | 0.272768 | ||||||||
\(463\) | −16512.4 | −1.65745 | −0.828724 | − | 0.559658i | \(-0.810933\pi\) | ||||
−0.828724 | + | 0.559658i | \(0.810933\pi\) | |||||||
\(464\) | 1381.24 | 0.138195 | ||||||||
\(465\) | 6255.20 | 0.623824 | ||||||||
\(466\) | 7283.76 | 0.724064 | ||||||||
\(467\) | 9651.70 | 0.956375 | 0.478188 | − | 0.878258i | \(-0.341294\pi\) | ||||
0.478188 | + | 0.878258i | \(0.341294\pi\) | |||||||
\(468\) | −327.230 | −0.0323209 | ||||||||
\(469\) | 5652.92 | 0.556562 | ||||||||
\(470\) | −2538.94 | −0.249176 | ||||||||
\(471\) | 6554.39 | 0.641211 | ||||||||
\(472\) | 472.000 | 0.0460287 | ||||||||
\(473\) | −5156.67 | −0.501277 | ||||||||
\(474\) | −452.061 | −0.0438056 | ||||||||
\(475\) | 13066.9 | 1.26221 | ||||||||
\(476\) | −2292.57 | −0.220756 | ||||||||
\(477\) | 181.422 | 0.0174146 | ||||||||
\(478\) | −9659.75 | −0.924323 | ||||||||
\(479\) | −698.299 | −0.0666098 | −0.0333049 | − | 0.999445i | \(-0.510603\pi\) | ||||
−0.0333049 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(480\) | 1393.64 | 0.132523 | ||||||||
\(481\) | 144.942 | 0.0137396 | ||||||||
\(482\) | 11396.6 | 1.07697 | ||||||||
\(483\) | 441.165 | 0.0415604 | ||||||||
\(484\) | −3062.19 | −0.287584 | ||||||||
\(485\) | −9035.35 | −0.845926 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −495.933 | −0.0461455 | −0.0230728 | − | 0.999734i | \(-0.507345\pi\) | ||||
−0.0230728 | + | 0.999734i | \(0.507345\pi\) | |||||||
\(488\) | 2387.31 | 0.221452 | ||||||||
\(489\) | 2543.40 | 0.235207 | ||||||||
\(490\) | −505.937 | −0.0466447 | ||||||||
\(491\) | 15858.8 | 1.45763 | 0.728815 | − | 0.684711i | \(-0.240072\pi\) | ||||
0.728815 | + | 0.684711i | \(0.240072\pi\) | |||||||
\(492\) | −3916.56 | −0.358887 | ||||||||
\(493\) | 2606.19 | 0.238087 | ||||||||
\(494\) | −2770.35 | −0.252315 | ||||||||
\(495\) | −3106.86 | −0.282107 | ||||||||
\(496\) | 2298.05 | 0.208035 | ||||||||
\(497\) | −5953.66 | −0.537340 | ||||||||
\(498\) | −2693.44 | −0.242361 | ||||||||
\(499\) | −3175.90 | −0.284915 | −0.142458 | − | 0.989801i | \(-0.545500\pi\) | ||||
−0.142458 | + | 0.989801i | \(0.545500\pi\) | |||||||
\(500\) | 2279.36 | 0.203872 | ||||||||
\(501\) | −3983.95 | −0.355269 | ||||||||
\(502\) | 4276.64 | 0.380230 | ||||||||
\(503\) | −2673.46 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(504\) | −1366.91 | −0.120808 | ||||||||
\(505\) | 6051.97 | 0.533286 | ||||||||
\(506\) | 368.383 | 0.0323649 | ||||||||
\(507\) | 6343.13 | 0.555638 | ||||||||
\(508\) | −7882.34 | −0.688430 | ||||||||
\(509\) | −13398.4 | −1.16675 | −0.583374 | − | 0.812204i | \(-0.698268\pi\) | ||||
−0.583374 | + | 0.812204i | \(0.698268\pi\) | |||||||
\(510\) | 2629.59 | 0.228314 | ||||||||
\(511\) | −129.700 | −0.0112281 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −4114.50 | −0.354113 | ||||||||
\(514\) | 8758.13 | 0.751565 | ||||||||
\(515\) | −1249.24 | −0.106889 | ||||||||
\(516\) | 2602.27 | 0.222013 | ||||||||
\(517\) | 2079.41 | 0.176890 | ||||||||
\(518\) | 605.453 | 0.0513554 | ||||||||
\(519\) | −9377.45 | −0.793110 | ||||||||
\(520\) | 1055.65 | 0.0890258 | ||||||||
\(521\) | 5203.78 | 0.437585 | 0.218792 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218792 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(522\) | 1553.90 | 0.130292 | ||||||||
\(523\) | 15363.7 | 1.28453 | 0.642264 | − | 0.766483i | \(-0.277995\pi\) | ||||
0.642264 | + | 0.766483i | \(0.277995\pi\) | |||||||
\(524\) | −5235.13 | −0.436446 | ||||||||
\(525\) | 4883.69 | 0.405984 | ||||||||
\(526\) | −12748.6 | −1.05678 | ||||||||
\(527\) | 4336.06 | 0.358409 | ||||||||
\(528\) | −1141.40 | −0.0940781 | ||||||||
\(529\) | −12107.0 | −0.995069 | ||||||||
\(530\) | −585.273 | −0.0479672 | ||||||||
\(531\) | 531.000 | 0.0433963 | ||||||||
\(532\) | −11572.4 | −0.943092 | ||||||||
\(533\) | −2966.70 | −0.241092 | ||||||||
\(534\) | −8518.17 | −0.690294 | ||||||||
\(535\) | −5063.54 | −0.409189 | ||||||||
\(536\) | −2382.07 | −0.191959 | ||||||||
\(537\) | −14048.6 | −1.12894 | ||||||||
\(538\) | 17286.0 | 1.38523 | ||||||||
\(539\) | 414.366 | 0.0331131 | ||||||||
\(540\) | 1567.85 | 0.124944 | ||||||||
\(541\) | 4815.08 | 0.382655 | 0.191327 | − | 0.981526i | \(-0.438721\pi\) | ||||
0.191327 | + | 0.981526i | \(0.438721\pi\) | |||||||
\(542\) | −15620.3 | −1.23792 | ||||||||
\(543\) | 398.573 | 0.0314998 | ||||||||
\(544\) | 966.063 | 0.0761390 | ||||||||
\(545\) | −1917.93 | −0.150743 | ||||||||
\(546\) | −1035.40 | −0.0811560 | ||||||||
\(547\) | 15456.4 | 1.20816 | 0.604082 | − | 0.796922i | \(-0.293540\pi\) | ||||
0.604082 | + | 0.796922i | \(0.293540\pi\) | |||||||
\(548\) | 3082.95 | 0.240324 | ||||||||
\(549\) | 2685.73 | 0.208787 | ||||||||
\(550\) | 4078.00 | 0.316157 | ||||||||
\(551\) | 13155.4 | 1.01713 | ||||||||
\(552\) | −185.902 | −0.0143342 | ||||||||
\(553\) | −1430.39 | −0.109993 | ||||||||
\(554\) | −2142.39 | −0.164299 | ||||||||
\(555\) | −694.456 | −0.0531135 | ||||||||
\(556\) | 6269.43 | 0.478207 | ||||||||
\(557\) | −15326.4 | −1.16589 | −0.582944 | − | 0.812512i | \(-0.698099\pi\) | ||||
−0.582944 | + | 0.812512i | \(0.698099\pi\) | |||||||
\(558\) | 2585.31 | 0.196138 | ||||||||
\(559\) | 1971.16 | 0.149143 | ||||||||
\(560\) | 4409.69 | 0.332756 | ||||||||
\(561\) | −2153.65 | −0.162080 | ||||||||
\(562\) | 15174.4 | 1.13896 | ||||||||
\(563\) | −20801.2 | −1.55713 | −0.778565 | − | 0.627564i | \(-0.784052\pi\) | ||||
−0.778565 | + | 0.627564i | \(0.784052\pi\) | |||||||
\(564\) | −1049.36 | −0.0783437 | ||||||||
\(565\) | −5127.73 | −0.381815 | ||||||||
\(566\) | 17902.2 | 1.32948 | ||||||||
\(567\) | −1537.77 | −0.113899 | ||||||||
\(568\) | 2508.80 | 0.185329 | ||||||||
\(569\) | −12363.3 | −0.910889 | −0.455445 | − | 0.890264i | \(-0.650520\pi\) | ||||
−0.455445 | + | 0.890264i | \(0.650520\pi\) | |||||||
\(570\) | 13273.5 | 0.975379 | ||||||||
\(571\) | 15498.3 | 1.13587 | 0.567935 | − | 0.823073i | \(-0.307743\pi\) | ||||
0.567935 | + | 0.823073i | \(0.307743\pi\) | |||||||
\(572\) | −864.586 | −0.0631996 | ||||||||
\(573\) | 9821.34 | 0.716043 | ||||||||
\(574\) | −12392.6 | −0.901143 | ||||||||
\(575\) | 664.188 | 0.0481714 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 11548.5 | 0.833223 | 0.416612 | − | 0.909085i | \(-0.363217\pi\) | ||||
0.416612 | + | 0.909085i | \(0.363217\pi\) | |||||||
\(578\) | −8003.19 | −0.575932 | ||||||||
\(579\) | −1021.21 | −0.0732986 | ||||||||
\(580\) | −5012.92 | −0.358880 | ||||||||
\(581\) | −8522.43 | −0.608554 | ||||||||
\(582\) | −3734.35 | −0.265969 | ||||||||
\(583\) | 479.343 | 0.0340520 | ||||||||
\(584\) | 54.6539 | 0.00387259 | ||||||||
\(585\) | 1187.61 | 0.0839344 | ||||||||
\(586\) | −2845.84 | −0.200615 | ||||||||
\(587\) | −17238.5 | −1.21211 | −0.606057 | − | 0.795421i | \(-0.707250\pi\) | ||||
−0.606057 | + | 0.795421i | \(0.707250\pi\) | |||||||
\(588\) | −209.106 | −0.0146656 | ||||||||
\(589\) | 21887.4 | 1.53116 | ||||||||
\(590\) | −1713.02 | −0.119532 | ||||||||
\(591\) | −14013.2 | −0.975338 | ||||||||
\(592\) | −255.131 | −0.0177125 | ||||||||
\(593\) | −13806.2 | −0.956072 | −0.478036 | − | 0.878340i | \(-0.658651\pi\) | ||||
−0.478036 | + | 0.878340i | \(0.658651\pi\) | |||||||
\(594\) | −1284.08 | −0.0886977 | ||||||||
\(595\) | 8320.40 | 0.573282 | ||||||||
\(596\) | −2514.24 | −0.172798 | ||||||||
\(597\) | 3848.76 | 0.263851 | ||||||||
\(598\) | −140.816 | −0.00962943 | ||||||||
\(599\) | −28580.6 | −1.94953 | −0.974767 | − | 0.223223i | \(-0.928342\pi\) | ||||
−0.974767 | + | 0.223223i | \(0.928342\pi\) | |||||||
\(600\) | −2057.93 | −0.140024 | ||||||||
\(601\) | −2557.49 | −0.173581 | −0.0867905 | − | 0.996227i | \(-0.527661\pi\) | ||||
−0.0867905 | + | 0.996227i | \(0.527661\pi\) | |||||||
\(602\) | 8233.97 | 0.557461 | ||||||||
\(603\) | −2679.83 | −0.180980 | ||||||||
\(604\) | 4229.70 | 0.284940 | ||||||||
\(605\) | 11113.6 | 0.746827 | ||||||||
\(606\) | 2501.31 | 0.167671 | ||||||||
\(607\) | 5944.14 | 0.397471 | 0.198736 | − | 0.980053i | \(-0.436316\pi\) | ||||
0.198736 | + | 0.980053i | \(0.436316\pi\) | |||||||
\(608\) | 4876.45 | 0.325273 | ||||||||
\(609\) | 4916.76 | 0.327155 | ||||||||
\(610\) | −8664.24 | −0.575090 | ||||||||
\(611\) | −794.862 | −0.0526296 | ||||||||
\(612\) | 1086.82 | 0.0717845 | ||||||||
\(613\) | 9848.25 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(614\) | 14622.0 | 0.961067 | ||||||||
\(615\) | 14214.3 | 0.931994 | ||||||||
\(616\) | −3611.57 | −0.236224 | ||||||||
\(617\) | −13450.9 | −0.877656 | −0.438828 | − | 0.898571i | \(-0.644606\pi\) | ||||
−0.438828 | + | 0.898571i | \(0.644606\pi\) | |||||||
\(618\) | −516.316 | −0.0336072 | ||||||||
\(619\) | −16407.2 | −1.06537 | −0.532683 | − | 0.846315i | \(-0.678816\pi\) | ||||
−0.532683 | + | 0.846315i | \(0.678816\pi\) | |||||||
\(620\) | −8340.27 | −0.540247 | ||||||||
\(621\) | −209.139 | −0.0135144 | ||||||||
\(622\) | 1948.22 | 0.125589 | ||||||||
\(623\) | −26952.7 | −1.73329 | ||||||||
\(624\) | 436.306 | 0.0279908 | ||||||||
\(625\) | −18990.8 | −1.21541 | ||||||||
\(626\) | 1081.58 | 0.0690554 | ||||||||
\(627\) | −10871.1 | −0.692424 | ||||||||
\(628\) | −8739.19 | −0.555305 | ||||||||
\(629\) | −481.391 | −0.0305156 | ||||||||
\(630\) | 4960.91 | 0.313726 | ||||||||
\(631\) | −4817.91 | −0.303959 | −0.151979 | − | 0.988384i | \(-0.548565\pi\) | ||||
−0.151979 | + | 0.988384i | \(0.548565\pi\) | |||||||
\(632\) | 602.748 | 0.0379368 | ||||||||
\(633\) | −2754.87 | −0.172980 | ||||||||
\(634\) | 5332.26 | 0.334024 | ||||||||
\(635\) | 28607.2 | 1.78779 | ||||||||
\(636\) | −241.896 | −0.0150815 | ||||||||
\(637\) | −158.393 | −0.00985205 | ||||||||
\(638\) | 4105.61 | 0.254769 | ||||||||
\(639\) | 2822.40 | 0.174730 | ||||||||
\(640\) | −1858.19 | −0.114768 | ||||||||
\(641\) | −1980.91 | −0.122061 | −0.0610305 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610305 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(642\) | −2092.79 | −0.128654 | ||||||||
\(643\) | −14075.8 | −0.863292 | −0.431646 | − | 0.902043i | \(-0.642067\pi\) | ||||
−0.431646 | + | 0.902043i | \(0.642067\pi\) | |||||||
\(644\) | −588.220 | −0.0359924 | ||||||||
\(645\) | −9444.38 | −0.576546 | ||||||||
\(646\) | 9201.09 | 0.560390 | ||||||||
\(647\) | 13170.6 | 0.800296 | 0.400148 | − | 0.916451i | \(-0.368959\pi\) | ||||
0.400148 | + | 0.916451i | \(0.368959\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 1402.98 | 0.0848561 | ||||||||
\(650\) | −1558.83 | −0.0940653 | ||||||||
\(651\) | 8180.29 | 0.492490 | ||||||||
\(652\) | −3391.19 | −0.203695 | ||||||||
\(653\) | 17815.8 | 1.06766 | 0.533832 | − | 0.845591i | \(-0.320751\pi\) | ||||
0.533832 | + | 0.845591i | \(0.320751\pi\) | |||||||
\(654\) | −792.690 | −0.0473955 | ||||||||
\(655\) | 18999.8 | 1.13341 | ||||||||
\(656\) | 5222.08 | 0.310805 | ||||||||
\(657\) | 61.4856 | 0.00365111 | ||||||||
\(658\) | −3320.31 | −0.196716 | ||||||||
\(659\) | −29695.3 | −1.75533 | −0.877666 | − | 0.479273i | \(-0.840901\pi\) | ||||
−0.877666 | + | 0.479273i | \(0.840901\pi\) | |||||||
\(660\) | 4142.48 | 0.244312 | ||||||||
\(661\) | 30236.1 | 1.77919 | 0.889596 | − | 0.456748i | \(-0.150986\pi\) | ||||
0.889596 | + | 0.456748i | \(0.150986\pi\) | |||||||
\(662\) | 2825.22 | 0.165869 | ||||||||
\(663\) | 823.241 | 0.0482233 | ||||||||
\(664\) | 3591.25 | 0.209891 | ||||||||
\(665\) | 41999.3 | 2.44912 | ||||||||
\(666\) | −287.022 | −0.0166995 | ||||||||
\(667\) | 668.685 | 0.0388180 | ||||||||
\(668\) | 5311.93 | 0.307672 | ||||||||
\(669\) | 14326.8 | 0.827961 | ||||||||
\(670\) | 8645.21 | 0.498498 | ||||||||
\(671\) | 7096.07 | 0.408257 | ||||||||
\(672\) | 1822.55 | 0.104622 | ||||||||
\(673\) | −28150.8 | −1.61238 | −0.806191 | − | 0.591655i | \(-0.798475\pi\) | ||||
−0.806191 | + | 0.591655i | \(0.798475\pi\) | |||||||
\(674\) | −853.075 | −0.0487526 | ||||||||
\(675\) | −2315.17 | −0.132016 | ||||||||
\(676\) | −8457.51 | −0.481196 | ||||||||
\(677\) | 8280.59 | 0.470087 | 0.235043 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235043 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(678\) | −2119.32 | −0.120047 | ||||||||
\(679\) | −11816.0 | −0.667832 | ||||||||
\(680\) | −3506.12 | −0.197726 | ||||||||
\(681\) | 10044.7 | 0.565221 | ||||||||
\(682\) | 6830.74 | 0.383523 | ||||||||
\(683\) | 23754.0 | 1.33078 | 0.665390 | − | 0.746496i | \(-0.268265\pi\) | ||||
0.665390 | + | 0.746496i | \(0.268265\pi\) | |||||||
\(684\) | 5486.01 | 0.306671 | ||||||||
\(685\) | −11188.9 | −0.624097 | ||||||||
\(686\) | 12362.0 | 0.688021 | ||||||||
\(687\) | −2003.77 | −0.111279 | ||||||||
\(688\) | −3469.69 | −0.192269 | ||||||||
\(689\) | −183.231 | −0.0101314 | ||||||||
\(690\) | 674.689 | 0.0372246 | ||||||||
\(691\) | 2606.85 | 0.143516 | 0.0717578 | − | 0.997422i | \(-0.477139\pi\) | ||||
0.0717578 | + | 0.997422i | \(0.477139\pi\) | |||||||
\(692\) | 12503.3 | 0.686854 | ||||||||
\(693\) | −4063.01 | −0.222715 | ||||||||
\(694\) | 448.369 | 0.0245243 | ||||||||
\(695\) | −22753.6 | −1.24186 | ||||||||
\(696\) | −2071.86 | −0.112836 | ||||||||
\(697\) | 9853.24 | 0.535464 | ||||||||
\(698\) | 22075.7 | 1.19710 | ||||||||
\(699\) | −10925.6 | −0.591195 | ||||||||
\(700\) | −6511.59 | −0.351593 | ||||||||
\(701\) | −8619.02 | −0.464388 | −0.232194 | − | 0.972670i | \(-0.574590\pi\) | ||||
−0.232194 | + | 0.972670i | \(0.574590\pi\) | |||||||
\(702\) | 490.845 | 0.0263899 | ||||||||
\(703\) | −2429.95 | −0.130366 | ||||||||
\(704\) | 1521.87 | 0.0814740 | ||||||||
\(705\) | 3808.41 | 0.203451 | ||||||||
\(706\) | 19640.9 | 1.04702 | ||||||||
\(707\) | 7914.51 | 0.421012 | ||||||||
\(708\) | −708.000 | −0.0375823 | ||||||||
\(709\) | −22526.1 | −1.19321 | −0.596606 | − | 0.802534i | \(-0.703484\pi\) | ||||
−0.596606 | + | 0.802534i | \(0.703484\pi\) | |||||||
\(710\) | −9105.15 | −0.481282 | ||||||||
\(711\) | 678.092 | 0.0357671 | ||||||||
\(712\) | 11357.6 | 0.597812 | ||||||||
\(713\) | 1112.53 | 0.0584355 | ||||||||
\(714\) | 3438.86 | 0.180247 | ||||||||
\(715\) | 3137.83 | 0.164123 | ||||||||
\(716\) | 18731.5 | 0.977692 | ||||||||
\(717\) | 14489.6 | 0.754707 | ||||||||
\(718\) | 8783.07 | 0.456520 | ||||||||
\(719\) | −14465.6 | −0.750313 | −0.375157 | − | 0.926961i | \(-0.622411\pi\) | ||||
−0.375157 | + | 0.926961i | \(0.622411\pi\) | |||||||
\(720\) | −2090.47 | −0.108204 | ||||||||
\(721\) | −1633.70 | −0.0843858 | ||||||||
\(722\) | 32726.9 | 1.68694 | ||||||||
\(723\) | −17094.9 | −0.879343 | ||||||||
\(724\) | −531.430 | −0.0272796 | ||||||||
\(725\) | 7402.34 | 0.379195 | ||||||||
\(726\) | 4593.28 | 0.234811 | ||||||||
\(727\) | −5354.94 | −0.273183 | −0.136591 | − | 0.990627i | \(-0.543615\pi\) | ||||
−0.136591 | + | 0.990627i | \(0.543615\pi\) | |||||||
\(728\) | 1380.54 | 0.0702831 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −198.354 | −0.0100567 | ||||||||
\(731\) | −6546.77 | −0.331246 | ||||||||
\(732\) | −3580.97 | −0.180815 | ||||||||
\(733\) | −19575.6 | −0.986413 | −0.493206 | − | 0.869912i | \(-0.664175\pi\) | ||||
−0.493206 | + | 0.869912i | \(0.664175\pi\) | |||||||
\(734\) | −4346.70 | −0.218583 | ||||||||
\(735\) | 758.905 | 0.0380852 | ||||||||
\(736\) | 247.869 | 0.0124138 | ||||||||
\(737\) | −7080.48 | −0.353885 | ||||||||
\(738\) | 5874.84 | 0.293030 | ||||||||
\(739\) | −1620.91 | −0.0806850 | −0.0403425 | − | 0.999186i | \(-0.512845\pi\) | ||||
−0.0403425 | + | 0.999186i | \(0.512845\pi\) | |||||||
\(740\) | 925.941 | 0.0459977 | ||||||||
\(741\) | 4155.52 | 0.206015 | ||||||||
\(742\) | −765.395 | −0.0378686 | ||||||||
\(743\) | −1746.91 | −0.0862554 | −0.0431277 | − | 0.999070i | \(-0.513732\pi\) | ||||
−0.0431277 | + | 0.999070i | \(0.513732\pi\) | |||||||
\(744\) | −3447.07 | −0.169860 | ||||||||
\(745\) | 9124.89 | 0.448739 | ||||||||
\(746\) | 18890.6 | 0.927123 | ||||||||
\(747\) | 4040.16 | 0.197887 | ||||||||
\(748\) | 2871.53 | 0.140366 | ||||||||
\(749\) | −6621.88 | −0.323042 | ||||||||
\(750\) | −3419.04 | −0.166461 | ||||||||
\(751\) | 18511.7 | 0.899467 | 0.449734 | − | 0.893163i | \(-0.351519\pi\) | ||||
0.449734 | + | 0.893163i | \(0.351519\pi\) | |||||||
\(752\) | 1399.14 | 0.0678476 | ||||||||
\(753\) | −6414.96 | −0.310457 | ||||||||
\(754\) | −1569.39 | −0.0758007 | ||||||||
\(755\) | −15350.8 | −0.739963 | ||||||||
\(756\) | 2050.37 | 0.0986390 | ||||||||
\(757\) | 24433.2 | 1.17311 | 0.586553 | − | 0.809911i | \(-0.300485\pi\) | ||||
0.586553 | + | 0.809911i | \(0.300485\pi\) | |||||||
\(758\) | −8057.72 | −0.386108 | ||||||||
\(759\) | −552.575 | −0.0264258 | ||||||||
\(760\) | −17698.0 | −0.844703 | ||||||||
\(761\) | 22235.4 | 1.05918 | 0.529588 | − | 0.848255i | \(-0.322347\pi\) | ||||
0.529588 | + | 0.848255i | \(0.322347\pi\) | |||||||
\(762\) | 11823.5 | 0.562101 | ||||||||
\(763\) | −2508.19 | −0.119007 | ||||||||
\(764\) | −13095.1 | −0.620111 | ||||||||
\(765\) | −3944.38 | −0.186417 | ||||||||
\(766\) | 3574.00 | 0.168582 | ||||||||
\(767\) | −536.293 | −0.0252470 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 18702.6 | 0.877027 | 0.438513 | − | 0.898725i | \(-0.355505\pi\) | ||||
0.438513 | + | 0.898725i | \(0.355505\pi\) | |||||||
\(770\) | 13107.4 | 0.613452 | ||||||||
\(771\) | −13137.2 | −0.613650 | ||||||||
\(772\) | 1361.61 | 0.0634784 | ||||||||
\(773\) | −947.968 | −0.0441087 | −0.0220544 | − | 0.999757i | \(-0.507021\pi\) | ||||
−0.0220544 | + | 0.999757i | \(0.507021\pi\) | |||||||
\(774\) | −3903.41 | −0.181273 | ||||||||
\(775\) | 12315.7 | 0.570829 | ||||||||
\(776\) | 4979.14 | 0.230336 | ||||||||
\(777\) | −908.180 | −0.0419315 | ||||||||
\(778\) | −10982.1 | −0.506078 | ||||||||
\(779\) | 49736.8 | 2.28755 | ||||||||
\(780\) | −1583.48 | −0.0726893 | ||||||||
\(781\) | 7457.18 | 0.341663 | ||||||||
\(782\) | 467.689 | 0.0213869 | ||||||||
\(783\) | −2330.85 | −0.106383 | ||||||||
\(784\) | 278.808 | 0.0127008 | ||||||||
\(785\) | 31717.0 | 1.44207 | ||||||||
\(786\) | 7852.69 | 0.356356 | ||||||||
\(787\) | −27044.5 | −1.22495 | −0.612473 | − | 0.790491i | \(-0.709825\pi\) | ||||
−0.612473 | + | 0.790491i | \(0.709825\pi\) | |||||||
\(788\) | 18684.2 | 0.844668 | ||||||||
\(789\) | 19122.9 | 0.862854 | ||||||||
\(790\) | −2187.54 | −0.0985181 | ||||||||
\(791\) | −6705.82 | −0.301431 | ||||||||
\(792\) | 1712.11 | 0.0768144 | ||||||||
\(793\) | −2712.50 | −0.121468 | ||||||||
\(794\) | −23501.7 | −1.05043 | ||||||||
\(795\) | 877.910 | 0.0391651 | ||||||||
\(796\) | −5131.68 | −0.228502 | ||||||||
\(797\) | −1335.55 | −0.0593569 | −0.0296785 | − | 0.999559i | \(-0.509448\pi\) | ||||
−0.0296785 | + | 0.999559i | \(0.509448\pi\) | |||||||
\(798\) | 17358.5 | 0.770032 | ||||||||
\(799\) | 2639.96 | 0.116890 | ||||||||
\(800\) | 2743.91 | 0.121265 | ||||||||
\(801\) | 12777.3 | 0.563623 | ||||||||
\(802\) | −8247.38 | −0.363124 | ||||||||
\(803\) | 162.454 | 0.00713930 | ||||||||
\(804\) | 3573.11 | 0.156734 | ||||||||
\(805\) | 2134.82 | 0.0934688 | ||||||||
\(806\) | −2611.08 | −0.114108 | ||||||||
\(807\) | −25929.0 | −1.13104 | ||||||||
\(808\) | −3335.08 | −0.145208 | ||||||||
\(809\) | 10946.3 | 0.475714 | 0.237857 | − | 0.971300i | \(-0.423555\pi\) | ||||
0.237857 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(810\) | −2351.78 | −0.102016 | ||||||||
\(811\) | −19857.3 | −0.859781 | −0.429891 | − | 0.902881i | \(-0.641448\pi\) | ||||
−0.429891 | + | 0.902881i | \(0.641448\pi\) | |||||||
\(812\) | −6555.68 | −0.283324 | ||||||||
\(813\) | 23430.5 | 1.01075 | ||||||||
\(814\) | −758.352 | −0.0326538 | ||||||||
\(815\) | 12307.6 | 0.528977 | ||||||||
\(816\) | −1449.09 | −0.0621672 | ||||||||
\(817\) | −33046.5 | −1.41512 | ||||||||
\(818\) | −28285.6 | −1.20903 | ||||||||
\(819\) | 1553.10 | 0.0662636 | ||||||||
\(820\) | −18952.4 | −0.807130 | ||||||||
\(821\) | 16339.2 | 0.694569 | 0.347285 | − | 0.937760i | \(-0.387104\pi\) | ||||
0.347285 | + | 0.937760i | \(0.387104\pi\) | |||||||
\(822\) | −4624.43 | −0.196223 | ||||||||
\(823\) | 26132.8 | 1.10684 | 0.553421 | − | 0.832902i | \(-0.313322\pi\) | ||||
0.553421 | + | 0.832902i | \(0.313322\pi\) | |||||||
\(824\) | 688.421 | 0.0291047 | ||||||||
\(825\) | −6117.00 | −0.258141 | ||||||||
\(826\) | −2240.22 | −0.0943669 | ||||||||
\(827\) | 40384.2 | 1.69806 | 0.849030 | − | 0.528345i | \(-0.177187\pi\) | ||||
0.849030 | + | 0.528345i | \(0.177187\pi\) | |||||||
\(828\) | 278.852 | 0.0117039 | ||||||||
\(829\) | 25800.6 | 1.08093 | 0.540465 | − | 0.841367i | \(-0.318248\pi\) | ||||
0.540465 | + | 0.841367i | \(0.318248\pi\) | |||||||
\(830\) | −13033.7 | −0.545066 | ||||||||
\(831\) | 3213.59 | 0.134149 | ||||||||
\(832\) | −581.742 | −0.0242407 | ||||||||
\(833\) | 526.067 | 0.0218813 | ||||||||
\(834\) | −9404.15 | −0.390455 | ||||||||
\(835\) | −19278.5 | −0.798994 | ||||||||
\(836\) | 14494.8 | 0.599656 | ||||||||
\(837\) | −3877.96 | −0.160146 | ||||||||
\(838\) | −26979.8 | −1.11217 | ||||||||
\(839\) | −6044.78 | −0.248736 | −0.124368 | − | 0.992236i | \(-0.539690\pi\) | ||||
−0.124368 | + | 0.992236i | \(0.539690\pi\) | |||||||
\(840\) | −6614.54 | −0.271694 | ||||||||
\(841\) | −16936.5 | −0.694433 | ||||||||
\(842\) | 22396.8 | 0.916678 | ||||||||
\(843\) | −22761.6 | −0.929953 | ||||||||
\(844\) | 3673.16 | 0.149805 | ||||||||
\(845\) | 30694.7 | 1.24962 | ||||||||
\(846\) | 1574.03 | 0.0639674 | ||||||||
\(847\) | 14533.8 | 0.589596 | ||||||||
\(848\) | 322.528 | 0.0130609 | ||||||||
\(849\) | −26853.3 | −1.08552 | ||||||||
\(850\) | 5177.32 | 0.208918 | ||||||||
\(851\) | −123.514 | −0.00497531 | ||||||||
\(852\) | −3763.20 | −0.151321 | ||||||||
\(853\) | 6900.19 | 0.276973 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(854\) | −11330.7 | −0.454015 | ||||||||
\(855\) | −19910.3 | −0.796394 | ||||||||
\(856\) | 2790.38 | 0.111417 | ||||||||
\(857\) | −17424.7 | −0.694534 | −0.347267 | − | 0.937766i | \(-0.612890\pi\) | ||||
−0.347267 | + | 0.937766i | \(0.612890\pi\) | |||||||
\(858\) | 1296.88 | 0.0516023 | ||||||||
\(859\) | −41478.4 | −1.64753 | −0.823764 | − | 0.566933i | \(-0.808130\pi\) | ||||
−0.823764 | + | 0.566933i | \(0.808130\pi\) | |||||||
\(860\) | 12592.5 | 0.499303 | ||||||||
\(861\) | 18588.9 | 0.735780 | ||||||||
\(862\) | −19639.9 | −0.776031 | ||||||||
\(863\) | −14024.1 | −0.553168 | −0.276584 | − | 0.960990i | \(-0.589202\pi\) | ||||
−0.276584 | + | 0.960990i | \(0.589202\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −45377.9 | −1.78369 | ||||||||
\(866\) | −13633.3 | −0.534965 | ||||||||
\(867\) | 12004.8 | 0.470247 | ||||||||
\(868\) | −10907.0 | −0.426508 | ||||||||
\(869\) | 1791.61 | 0.0699382 | ||||||||
\(870\) | 7519.38 | 0.293024 | ||||||||
\(871\) | 2706.54 | 0.105290 | ||||||||
\(872\) | 1056.92 | 0.0410457 | ||||||||
\(873\) | 5601.53 | 0.217163 | ||||||||
\(874\) | 2360.78 | 0.0913668 | ||||||||
\(875\) | −10818.3 | −0.417973 | ||||||||
\(876\) | −81.9808 | −0.00316196 | ||||||||
\(877\) | 7506.31 | 0.289019 | 0.144510 | − | 0.989503i | \(-0.453840\pi\) | ||||
0.144510 | + | 0.989503i | \(0.453840\pi\) | |||||||
\(878\) | −35627.1 | −1.36943 | ||||||||
\(879\) | 4268.75 | 0.163802 | ||||||||
\(880\) | −5523.30 | −0.211580 | ||||||||
\(881\) | 13812.2 | 0.528201 | 0.264101 | − | 0.964495i | \(-0.414925\pi\) | ||||
0.264101 | + | 0.964495i | \(0.414925\pi\) | |||||||
\(882\) | 313.659 | 0.0119744 | ||||||||
\(883\) | 11579.6 | 0.441318 | 0.220659 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220659 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(884\) | −1097.65 | −0.0417626 | ||||||||
\(885\) | 2569.53 | 0.0975976 | ||||||||
\(886\) | −28389.7 | −1.07649 | ||||||||
\(887\) | 17903.3 | 0.677714 | 0.338857 | − | 0.940838i | \(-0.389960\pi\) | ||||
0.338857 | + | 0.940838i | \(0.389960\pi\) | |||||||
\(888\) | 382.696 | 0.0144622 | ||||||||
\(889\) | 37411.3 | 1.41140 | ||||||||
\(890\) | −41219.8 | −1.55246 | ||||||||
\(891\) | 1926.12 | 0.0724213 | ||||||||
\(892\) | −19102.4 | −0.717035 | ||||||||
\(893\) | 13325.9 | 0.499365 | ||||||||
\(894\) | 3771.36 | 0.141089 | ||||||||
\(895\) | −67981.7 | −2.53897 | ||||||||
\(896\) | −2430.06 | −0.0906057 | ||||||||
\(897\) | 211.224 | 0.00786239 | ||||||||
\(898\) | −3692.57 | −0.137219 | ||||||||
\(899\) | 12399.1 | 0.459992 | ||||||||
\(900\) | 3086.89 | 0.114329 | ||||||||
\(901\) | 608.560 | 0.0225017 | ||||||||
\(902\) | 15522.1 | 0.572983 | ||||||||
\(903\) | −12350.9 | −0.455165 | ||||||||
\(904\) | 2825.75 | 0.103964 | ||||||||
\(905\) | 1928.71 | 0.0708426 | ||||||||
\(906\) | −6344.55 | −0.232653 | ||||||||
\(907\) | 48047.8 | 1.75899 | 0.879493 | − | 0.475912i | \(-0.157882\pi\) | ||||
0.879493 | + | 0.475912i | \(0.157882\pi\) | |||||||
\(908\) | −13393.0 | −0.489496 | ||||||||
\(909\) | −3751.96 | −0.136903 | ||||||||
\(910\) | −5010.36 | −0.182518 | ||||||||
\(911\) | 32038.1 | 1.16517 | 0.582584 | − | 0.812770i | \(-0.302042\pi\) | ||||
0.582584 | + | 0.812770i | \(0.302042\pi\) | |||||||
\(912\) | −7314.68 | −0.265585 | ||||||||
\(913\) | 10674.7 | 0.386943 | ||||||||
\(914\) | −20620.8 | −0.746254 | ||||||||
\(915\) | 12996.4 | 0.469559 | ||||||||
\(916\) | 2671.69 | 0.0963703 | ||||||||
\(917\) | 24847.1 | 0.894790 | ||||||||
\(918\) | −1630.23 | −0.0586118 | ||||||||
\(919\) | 41966.1 | 1.50635 | 0.753175 | − | 0.657821i | \(-0.228522\pi\) | ||||
0.753175 | + | 0.657821i | \(0.228522\pi\) | |||||||
\(920\) | −899.586 | −0.0322375 | ||||||||
\(921\) | −21933.0 | −0.784708 | ||||||||
\(922\) | −237.943 | −0.00849916 | ||||||||
\(923\) | −2850.54 | −0.101654 | ||||||||
\(924\) | 5417.35 | 0.192876 | ||||||||
\(925\) | −1367.29 | −0.0486015 | ||||||||
\(926\) | −33024.9 | −1.17199 | ||||||||
\(927\) | 774.474 | 0.0274402 | ||||||||
\(928\) | 2762.49 | 0.0977188 | ||||||||
\(929\) | −11790.5 | −0.416399 | −0.208200 | − | 0.978086i | \(-0.566760\pi\) | ||||
−0.208200 | + | 0.978086i | \(0.566760\pi\) | |||||||
\(930\) | 12510.4 | 0.441110 | ||||||||
\(931\) | 2655.46 | 0.0934792 | ||||||||
\(932\) | 14567.5 | 0.511990 | ||||||||
\(933\) | −2922.32 | −0.102543 | ||||||||
\(934\) | 19303.4 | 0.676259 | ||||||||
\(935\) | −10421.6 | −0.364516 | ||||||||
\(936\) | −654.460 | −0.0228544 | ||||||||
\(937\) | −2254.98 | −0.0786201 | −0.0393101 | − | 0.999227i | \(-0.512516\pi\) | ||||
−0.0393101 | + | 0.999227i | \(0.512516\pi\) | |||||||
\(938\) | 11305.8 | 0.393549 | ||||||||
\(939\) | −1622.37 | −0.0563835 | ||||||||
\(940\) | −5077.88 | −0.176194 | ||||||||
\(941\) | 4345.03 | 0.150525 | 0.0752625 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752625 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(942\) | 13108.8 | 0.453405 | ||||||||
\(943\) | 2528.11 | 0.0873028 | ||||||||
\(944\) | 944.000 | 0.0325472 | ||||||||
\(945\) | −7441.36 | −0.256156 | ||||||||
\(946\) | −10313.3 | −0.354456 | ||||||||
\(947\) | −43486.4 | −1.49221 | −0.746103 | − | 0.665831i | \(-0.768077\pi\) | ||||
−0.746103 | + | 0.665831i | \(0.768077\pi\) | |||||||
\(948\) | −904.122 | −0.0309752 | ||||||||
\(949\) | −62.0985 | −0.00212413 | ||||||||
\(950\) | 26133.8 | 0.892519 | ||||||||
\(951\) | −7998.39 | −0.272729 | ||||||||
\(952\) | −4585.15 | −0.156098 | ||||||||
\(953\) | −11476.4 | −0.390091 | −0.195046 | − | 0.980794i | \(-0.562485\pi\) | ||||
−0.195046 | + | 0.980794i | \(0.562485\pi\) | |||||||
\(954\) | 362.844 | 0.0123140 | ||||||||
\(955\) | 47525.9 | 1.61037 | ||||||||
\(956\) | −19319.5 | −0.653595 | ||||||||
\(957\) | −6158.42 | −0.208018 | ||||||||
\(958\) | −1396.60 | −0.0471002 | ||||||||
\(959\) | −14632.4 | −0.492705 | ||||||||
\(960\) | 2787.29 | 0.0937077 | ||||||||
\(961\) | −9161.96 | −0.307541 | ||||||||
\(962\) | 289.883 | 0.00971540 | ||||||||
\(963\) | 3139.18 | 0.105045 | ||||||||
\(964\) | 22793.2 | 0.761533 | ||||||||
\(965\) | −4941.66 | −0.164847 | ||||||||
\(966\) | 882.330 | 0.0293877 | ||||||||
\(967\) | −30998.7 | −1.03087 | −0.515436 | − | 0.856928i | \(-0.672370\pi\) | ||||
−0.515436 | + | 0.856928i | \(0.672370\pi\) | |||||||
\(968\) | −6124.38 | −0.203352 | ||||||||
\(969\) | −13801.6 | −0.457557 | ||||||||
\(970\) | −18070.7 | −0.598160 | ||||||||
\(971\) | −27050.2 | −0.894009 | −0.447004 | − | 0.894532i | \(-0.647509\pi\) | ||||
−0.447004 | + | 0.894532i | \(0.647509\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −29756.1 | −0.980408 | ||||||||
\(974\) | −991.866 | −0.0326298 | ||||||||
\(975\) | 2338.25 | 0.0768040 | ||||||||
\(976\) | 4774.63 | 0.156590 | ||||||||
\(977\) | 7821.75 | 0.256131 | 0.128066 | − | 0.991766i | \(-0.459123\pi\) | ||||
0.128066 | + | 0.991766i | \(0.459123\pi\) | |||||||
\(978\) | 5086.79 | 0.166317 | ||||||||
\(979\) | 33759.3 | 1.10210 | ||||||||
\(980\) | −1011.87 | −0.0329828 | ||||||||
\(981\) | 1189.04 | 0.0386982 | ||||||||
\(982\) | 31717.5 | 1.03070 | ||||||||
\(983\) | 47680.9 | 1.54709 | 0.773543 | − | 0.633744i | \(-0.218483\pi\) | ||||
0.773543 | + | 0.633744i | \(0.218483\pi\) | |||||||
\(984\) | −7833.12 | −0.253771 | ||||||||
\(985\) | −67810.3 | −2.19352 | ||||||||
\(986\) | 5212.37 | 0.168353 | ||||||||
\(987\) | 4980.47 | 0.160618 | ||||||||
\(988\) | −5540.69 | −0.178414 | ||||||||
\(989\) | −1679.74 | −0.0540068 | ||||||||
\(990\) | −6213.72 | −0.199480 | ||||||||
\(991\) | 11338.7 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(992\) | 4596.10 | 0.147103 | ||||||||
\(993\) | −4237.83 | −0.135431 | ||||||||
\(994\) | −11907.3 | −0.379957 | ||||||||
\(995\) | 18624.3 | 0.593398 | ||||||||
\(996\) | −5386.87 | −0.171375 | ||||||||
\(997\) | −20391.1 | −0.647735 | −0.323868 | − | 0.946102i | \(-0.604983\pi\) | ||||
−0.323868 | + | 0.946102i | \(0.604983\pi\) | |||||||
\(998\) | −6351.80 | −0.201466 | ||||||||
\(999\) | 430.533 | 0.0136351 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 354.4.a.h.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 1062.4.a.n.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.a.h.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1062.4.a.n.1.4 | 4 | 3.2 | odd | 2 |