Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,4,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("570.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(33.6310887033\) |
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: | \( x^{4} - x^{3} - 410x^{2} + 4362x - 12540 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(12.2089\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 17.1829 | 0.927789 | 0.463894 | − | 0.885891i | \(-0.346452\pi\) | ||||
0.463894 | + | 0.885891i | \(0.346452\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 29.2349 | 0.801333 | 0.400666 | − | 0.916224i | \(-0.368779\pi\) | ||||
0.400666 | + | 0.916224i | \(0.368779\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −69.9219 | −1.49176 | −0.745879 | − | 0.666082i | \(-0.767970\pi\) | ||||
−0.745879 | + | 0.666082i | \(0.767970\pi\) | |||||||
\(14\) | 34.3658 | 0.656046 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 94.5904 | 1.34950 | 0.674751 | − | 0.738045i | \(-0.264251\pi\) | ||||
0.674751 | + | 0.738045i | \(0.264251\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 51.5487 | 0.535659 | ||||||||
\(22\) | 58.4699 | 0.566628 | ||||||||
\(23\) | −8.21713 | −0.0744952 | −0.0372476 | − | 0.999306i | \(-0.511859\pi\) | ||||
−0.0372476 | + | 0.999306i | \(0.511859\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −139.844 | −1.05483 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 68.7316 | 0.463894 | ||||||||
\(29\) | 216.520 | 1.38644 | 0.693219 | − | 0.720727i | \(-0.256192\pi\) | ||||
0.693219 | + | 0.720727i | \(0.256192\pi\) | |||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | −227.097 | −1.31574 | −0.657869 | − | 0.753132i | \(-0.728542\pi\) | ||||
−0.657869 | + | 0.753132i | \(0.728542\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 87.7048 | 0.462650 | ||||||||
\(34\) | 189.181 | 0.954242 | ||||||||
\(35\) | 85.9144 | 0.414920 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −5.48766 | −0.0243828 | −0.0121914 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121914 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | −209.766 | −0.861267 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −423.214 | −1.61207 | −0.806035 | − | 0.591867i | \(-0.798391\pi\) | ||||
−0.806035 | + | 0.591867i | \(0.798391\pi\) | |||||||
\(42\) | 103.097 | 0.378768 | ||||||||
\(43\) | 267.242 | 0.947769 | 0.473885 | − | 0.880587i | \(-0.342851\pi\) | ||||
0.473885 | + | 0.880587i | \(0.342851\pi\) | |||||||
\(44\) | 116.940 | 0.400666 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −16.4343 | −0.0526761 | ||||||||
\(47\) | −6.59371 | −0.0204636 | −0.0102318 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102318 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −47.7483 | −0.139208 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 283.771 | 0.779136 | ||||||||
\(52\) | −279.688 | −0.745879 | ||||||||
\(53\) | −206.172 | −0.534338 | −0.267169 | − | 0.963650i | \(-0.586088\pi\) | ||||
−0.267169 | + | 0.963650i | \(0.586088\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 146.175 | 0.358367 | ||||||||
\(56\) | 137.463 | 0.328023 | ||||||||
\(57\) | 57.0000 | 0.132453 | ||||||||
\(58\) | 433.040 | 0.980360 | ||||||||
\(59\) | 208.532 | 0.460146 | 0.230073 | − | 0.973173i | \(-0.426104\pi\) | ||||
0.230073 | + | 0.973173i | \(0.426104\pi\) | |||||||
\(60\) | 60.0000 | 0.129099 | ||||||||
\(61\) | 510.064 | 1.07061 | 0.535303 | − | 0.844660i | \(-0.320197\pi\) | ||||
0.535303 | + | 0.844660i | \(0.320197\pi\) | |||||||
\(62\) | −454.195 | −0.930367 | ||||||||
\(63\) | 154.646 | 0.309263 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −349.610 | −0.667134 | ||||||||
\(66\) | 175.410 | 0.327143 | ||||||||
\(67\) | 1010.47 | 1.84251 | 0.921257 | − | 0.388956i | \(-0.127164\pi\) | ||||
0.921257 | + | 0.388956i | \(0.127164\pi\) | |||||||
\(68\) | 378.362 | 0.674751 | ||||||||
\(69\) | −24.6514 | −0.0430098 | ||||||||
\(70\) | 171.829 | 0.293393 | ||||||||
\(71\) | 334.247 | 0.558701 | 0.279351 | − | 0.960189i | \(-0.409881\pi\) | ||||
0.279351 | + | 0.960189i | \(0.409881\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −866.693 | −1.38957 | −0.694786 | − | 0.719217i | \(-0.744501\pi\) | ||||
−0.694786 | + | 0.719217i | \(0.744501\pi\) | |||||||
\(74\) | −10.9753 | −0.0172413 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 76.0000 | 0.114708 | ||||||||
\(77\) | 502.341 | 0.743468 | ||||||||
\(78\) | −419.532 | −0.609008 | ||||||||
\(79\) | 502.538 | 0.715695 | 0.357848 | − | 0.933780i | \(-0.383511\pi\) | ||||
0.357848 | + | 0.933780i | \(0.383511\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −846.428 | −1.13991 | ||||||||
\(83\) | −478.314 | −0.632551 | −0.316276 | − | 0.948667i | \(-0.602432\pi\) | ||||
−0.316276 | + | 0.948667i | \(0.602432\pi\) | |||||||
\(84\) | 206.195 | 0.267830 | ||||||||
\(85\) | 472.952 | 0.603516 | ||||||||
\(86\) | 534.485 | 0.670174 | ||||||||
\(87\) | 649.559 | 0.800461 | ||||||||
\(88\) | 233.879 | 0.283314 | ||||||||
\(89\) | −1150.25 | −1.36996 | −0.684978 | − | 0.728563i | \(-0.740188\pi\) | ||||
−0.684978 | + | 0.728563i | \(0.740188\pi\) | |||||||
\(90\) | 90.0000 | 0.105409 | ||||||||
\(91\) | −1201.46 | −1.38404 | ||||||||
\(92\) | −32.8685 | −0.0372476 | ||||||||
\(93\) | −681.292 | −0.759642 | ||||||||
\(94\) | −13.1874 | −0.0144700 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −1394.30 | −1.45948 | −0.729742 | − | 0.683723i | \(-0.760360\pi\) | ||||
−0.729742 | + | 0.683723i | \(0.760360\pi\) | |||||||
\(98\) | −95.4967 | −0.0984349 | ||||||||
\(99\) | 263.114 | 0.267111 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 1962.77 | 1.93369 | 0.966847 | − | 0.255357i | \(-0.0821931\pi\) | ||||
0.966847 | + | 0.255357i | \(0.0821931\pi\) | |||||||
\(102\) | 567.542 | 0.550932 | ||||||||
\(103\) | 1511.69 | 1.44612 | 0.723062 | − | 0.690783i | \(-0.242734\pi\) | ||||
0.723062 | + | 0.690783i | \(0.242734\pi\) | |||||||
\(104\) | −559.375 | −0.527416 | ||||||||
\(105\) | 257.743 | 0.239554 | ||||||||
\(106\) | −412.344 | −0.377834 | ||||||||
\(107\) | −1034.13 | −0.934332 | −0.467166 | − | 0.884170i | \(-0.654725\pi\) | ||||
−0.467166 | + | 0.884170i | \(0.654725\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −489.446 | −0.430096 | −0.215048 | − | 0.976603i | \(-0.568991\pi\) | ||||
−0.215048 | + | 0.976603i | \(0.568991\pi\) | |||||||
\(110\) | 292.349 | 0.253404 | ||||||||
\(111\) | −16.4630 | −0.0140774 | ||||||||
\(112\) | 274.926 | 0.231947 | ||||||||
\(113\) | 598.992 | 0.498659 | 0.249329 | − | 0.968419i | \(-0.419790\pi\) | ||||
0.249329 | + | 0.968419i | \(0.419790\pi\) | |||||||
\(114\) | 114.000 | 0.0936586 | ||||||||
\(115\) | −41.0857 | −0.0333153 | ||||||||
\(116\) | 866.079 | 0.693219 | ||||||||
\(117\) | −629.297 | −0.497253 | ||||||||
\(118\) | 417.065 | 0.325372 | ||||||||
\(119\) | 1625.34 | 1.25205 | ||||||||
\(120\) | 120.000 | 0.0912871 | ||||||||
\(121\) | −476.319 | −0.357865 | ||||||||
\(122\) | 1020.13 | 0.757033 | ||||||||
\(123\) | −1269.64 | −0.930730 | ||||||||
\(124\) | −908.389 | −0.657869 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 309.292 | 0.218682 | ||||||||
\(127\) | −1621.31 | −1.13282 | −0.566411 | − | 0.824123i | \(-0.691668\pi\) | ||||
−0.566411 | + | 0.824123i | \(0.691668\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 801.727 | 0.547195 | ||||||||
\(130\) | −699.219 | −0.471735 | ||||||||
\(131\) | −2133.74 | −1.42309 | −0.711547 | − | 0.702639i | \(-0.752005\pi\) | ||||
−0.711547 | + | 0.702639i | \(0.752005\pi\) | |||||||
\(132\) | 350.819 | 0.231325 | ||||||||
\(133\) | 326.475 | 0.212849 | ||||||||
\(134\) | 2020.94 | 1.30285 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 756.723 | 0.477121 | ||||||||
\(137\) | 822.308 | 0.512807 | 0.256403 | − | 0.966570i | \(-0.417462\pi\) | ||||
0.256403 | + | 0.966570i | \(0.417462\pi\) | |||||||
\(138\) | −49.3028 | −0.0304126 | ||||||||
\(139\) | 423.232 | 0.258259 | 0.129130 | − | 0.991628i | \(-0.458782\pi\) | ||||
0.129130 | + | 0.991628i | \(0.458782\pi\) | |||||||
\(140\) | 343.658 | 0.207460 | ||||||||
\(141\) | −19.7811 | −0.0118147 | ||||||||
\(142\) | 668.493 | 0.395061 | ||||||||
\(143\) | −2044.16 | −1.19539 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 1082.60 | 0.620034 | ||||||||
\(146\) | −1733.39 | −0.982576 | ||||||||
\(147\) | −143.245 | −0.0803718 | ||||||||
\(148\) | −21.9506 | −0.0121914 | ||||||||
\(149\) | −1387.73 | −0.763003 | −0.381502 | − | 0.924368i | \(-0.624593\pi\) | ||||
−0.381502 | + | 0.924368i | \(0.624593\pi\) | |||||||
\(150\) | 150.000 | 0.0816497 | ||||||||
\(151\) | 1687.63 | 0.909518 | 0.454759 | − | 0.890614i | \(-0.349725\pi\) | ||||
0.454759 | + | 0.890614i | \(0.349725\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | 851.313 | 0.449834 | ||||||||
\(154\) | 1004.68 | 0.525711 | ||||||||
\(155\) | −1135.49 | −0.588416 | ||||||||
\(156\) | −839.063 | −0.430633 | ||||||||
\(157\) | −1875.67 | −0.953468 | −0.476734 | − | 0.879048i | \(-0.658179\pi\) | ||||
−0.476734 | + | 0.879048i | \(0.658179\pi\) | |||||||
\(158\) | 1005.08 | 0.506073 | ||||||||
\(159\) | −618.517 | −0.308500 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | −141.194 | −0.0691158 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 879.526 | 0.422637 | 0.211318 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211318 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(164\) | −1692.86 | −0.806035 | ||||||||
\(165\) | 438.524 | 0.206903 | ||||||||
\(166\) | −956.627 | −0.447281 | ||||||||
\(167\) | −3292.23 | −1.52551 | −0.762756 | − | 0.646686i | \(-0.776154\pi\) | ||||
−0.762756 | + | 0.646686i | \(0.776154\pi\) | |||||||
\(168\) | 412.389 | 0.189384 | ||||||||
\(169\) | 2692.07 | 1.22534 | ||||||||
\(170\) | 945.904 | 0.426750 | ||||||||
\(171\) | 171.000 | 0.0764719 | ||||||||
\(172\) | 1068.97 | 0.473885 | ||||||||
\(173\) | −1861.03 | −0.817868 | −0.408934 | − | 0.912564i | \(-0.634099\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634099\pi\) | |||||||
\(174\) | 1299.12 | 0.566011 | ||||||||
\(175\) | 429.572 | 0.185558 | ||||||||
\(176\) | 467.759 | 0.200333 | ||||||||
\(177\) | 625.597 | 0.265665 | ||||||||
\(178\) | −2300.50 | −0.968706 | ||||||||
\(179\) | −2869.30 | −1.19811 | −0.599055 | − | 0.800708i | \(-0.704457\pi\) | ||||
−0.599055 | + | 0.800708i | \(0.704457\pi\) | |||||||
\(180\) | 180.000 | 0.0745356 | ||||||||
\(181\) | −2402.69 | −0.986689 | −0.493344 | − | 0.869834i | \(-0.664226\pi\) | ||||
−0.493344 | + | 0.869834i | \(0.664226\pi\) | |||||||
\(182\) | −2402.92 | −0.978661 | ||||||||
\(183\) | 1530.19 | 0.618115 | ||||||||
\(184\) | −65.7371 | −0.0263380 | ||||||||
\(185\) | −27.4383 | −0.0109043 | ||||||||
\(186\) | −1362.58 | −0.537148 | ||||||||
\(187\) | 2765.34 | 1.08140 | ||||||||
\(188\) | −26.3748 | −0.0102318 | ||||||||
\(189\) | 463.938 | 0.178553 | ||||||||
\(190\) | 190.000 | 0.0725476 | ||||||||
\(191\) | −746.471 | −0.282789 | −0.141395 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141395 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 646.067 | 0.240958 | 0.120479 | − | 0.992716i | \(-0.461557\pi\) | ||||
0.120479 | + | 0.992716i | \(0.461557\pi\) | |||||||
\(194\) | −2788.60 | −1.03201 | ||||||||
\(195\) | −1048.83 | −0.385170 | ||||||||
\(196\) | −190.993 | −0.0696040 | ||||||||
\(197\) | 4906.46 | 1.77447 | 0.887236 | − | 0.461316i | \(-0.152623\pi\) | ||||
0.887236 | + | 0.461316i | \(0.152623\pi\) | |||||||
\(198\) | 526.229 | 0.188876 | ||||||||
\(199\) | −1166.24 | −0.415438 | −0.207719 | − | 0.978189i | \(-0.566604\pi\) | ||||
−0.207719 | + | 0.978189i | \(0.566604\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | 3031.41 | 1.06378 | ||||||||
\(202\) | 3925.54 | 1.36733 | ||||||||
\(203\) | 3720.44 | 1.28632 | ||||||||
\(204\) | 1135.08 | 0.389568 | ||||||||
\(205\) | −2116.07 | −0.720940 | ||||||||
\(206\) | 3023.37 | 1.02256 | ||||||||
\(207\) | −73.9542 | −0.0248317 | ||||||||
\(208\) | −1118.75 | −0.372939 | ||||||||
\(209\) | 555.464 | 0.183838 | ||||||||
\(210\) | 515.487 | 0.169390 | ||||||||
\(211\) | −5519.45 | −1.80083 | −0.900414 | − | 0.435035i | \(-0.856736\pi\) | ||||
−0.900414 | + | 0.435035i | \(0.856736\pi\) | |||||||
\(212\) | −824.689 | −0.267169 | ||||||||
\(213\) | 1002.74 | 0.322566 | ||||||||
\(214\) | −2068.27 | −0.660672 | ||||||||
\(215\) | 1336.21 | 0.423855 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −3902.19 | −1.22073 | ||||||||
\(218\) | −978.893 | −0.304124 | ||||||||
\(219\) | −2600.08 | −0.802270 | ||||||||
\(220\) | 584.699 | 0.179184 | ||||||||
\(221\) | −6613.94 | −2.01313 | ||||||||
\(222\) | −32.9259 | −0.00995425 | ||||||||
\(223\) | 1393.07 | 0.418326 | 0.209163 | − | 0.977881i | \(-0.432926\pi\) | ||||
0.209163 | + | 0.977881i | \(0.432926\pi\) | |||||||
\(224\) | 549.852 | 0.164011 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 1197.98 | 0.352605 | ||||||||
\(227\) | −4179.18 | −1.22195 | −0.610974 | − | 0.791651i | \(-0.709222\pi\) | ||||
−0.610974 | + | 0.791651i | \(0.709222\pi\) | |||||||
\(228\) | 228.000 | 0.0662266 | ||||||||
\(229\) | 2796.83 | 0.807074 | 0.403537 | − | 0.914963i | \(-0.367781\pi\) | ||||
0.403537 | + | 0.914963i | \(0.367781\pi\) | |||||||
\(230\) | −82.1713 | −0.0235575 | ||||||||
\(231\) | 1507.02 | 0.429241 | ||||||||
\(232\) | 1732.16 | 0.490180 | ||||||||
\(233\) | −4967.60 | −1.39673 | −0.698365 | − | 0.715742i | \(-0.746089\pi\) | ||||
−0.698365 | + | 0.715742i | \(0.746089\pi\) | |||||||
\(234\) | −1258.59 | −0.351611 | ||||||||
\(235\) | −32.9685 | −0.00915162 | ||||||||
\(236\) | 834.129 | 0.230073 | ||||||||
\(237\) | 1507.61 | 0.413207 | ||||||||
\(238\) | 3250.67 | 0.885335 | ||||||||
\(239\) | 4698.63 | 1.27167 | 0.635835 | − | 0.771825i | \(-0.280656\pi\) | ||||
0.635835 | + | 0.771825i | \(0.280656\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −67.0326 | −0.0179168 | −0.00895840 | − | 0.999960i | \(-0.502852\pi\) | ||||
−0.00895840 | + | 0.999960i | \(0.502852\pi\) | |||||||
\(242\) | −952.638 | −0.253049 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2040.26 | 0.535303 | ||||||||
\(245\) | −238.742 | −0.0622557 | ||||||||
\(246\) | −2539.28 | −0.658125 | ||||||||
\(247\) | −1328.52 | −0.342233 | ||||||||
\(248\) | −1816.78 | −0.465184 | ||||||||
\(249\) | −1434.94 | −0.365204 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −5378.10 | −1.35244 | −0.676221 | − | 0.736699i | \(-0.736384\pi\) | ||||
−0.676221 | + | 0.736699i | \(0.736384\pi\) | |||||||
\(252\) | 618.584 | 0.154631 | ||||||||
\(253\) | −240.227 | −0.0596955 | ||||||||
\(254\) | −3242.63 | −0.801026 | ||||||||
\(255\) | 1418.86 | 0.348440 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2751.52 | −0.667840 | −0.333920 | − | 0.942601i | \(-0.608372\pi\) | ||||
−0.333920 | + | 0.942601i | \(0.608372\pi\) | |||||||
\(258\) | 1603.45 | 0.386925 | ||||||||
\(259\) | −94.2938 | −0.0226221 | ||||||||
\(260\) | −1398.44 | −0.333567 | ||||||||
\(261\) | 1948.68 | 0.462146 | ||||||||
\(262\) | −4267.47 | −1.00628 | ||||||||
\(263\) | −1557.63 | −0.365201 | −0.182600 | − | 0.983187i | \(-0.558451\pi\) | ||||
−0.182600 | + | 0.983187i | \(0.558451\pi\) | |||||||
\(264\) | 701.638 | 0.163571 | ||||||||
\(265\) | −1030.86 | −0.238963 | ||||||||
\(266\) | 652.950 | 0.150507 | ||||||||
\(267\) | −3450.75 | −0.790945 | ||||||||
\(268\) | 4041.87 | 0.921257 | ||||||||
\(269\) | −1660.54 | −0.376375 | −0.188187 | − | 0.982133i | \(-0.560261\pi\) | ||||
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(270\) | 270.000 | 0.0608581 | ||||||||
\(271\) | 1880.00 | 0.421409 | 0.210704 | − | 0.977550i | \(-0.432424\pi\) | ||||
0.210704 | + | 0.977550i | \(0.432424\pi\) | |||||||
\(272\) | 1513.45 | 0.337376 | ||||||||
\(273\) | −3604.38 | −0.799074 | ||||||||
\(274\) | 1644.62 | 0.362609 | ||||||||
\(275\) | 730.873 | 0.160267 | ||||||||
\(276\) | −98.6056 | −0.0215049 | ||||||||
\(277\) | −8624.73 | −1.87079 | −0.935397 | − | 0.353599i | \(-0.884958\pi\) | ||||
−0.935397 | + | 0.353599i | \(0.884958\pi\) | |||||||
\(278\) | 846.464 | 0.182617 | ||||||||
\(279\) | −2043.88 | −0.438579 | ||||||||
\(280\) | 687.316 | 0.146696 | ||||||||
\(281\) | −928.020 | −0.197014 | −0.0985071 | − | 0.995136i | \(-0.531407\pi\) | ||||
−0.0985071 | + | 0.995136i | \(0.531407\pi\) | |||||||
\(282\) | −39.5623 | −0.00835425 | ||||||||
\(283\) | −2306.23 | −0.484420 | −0.242210 | − | 0.970224i | \(-0.577872\pi\) | ||||
−0.242210 | + | 0.970224i | \(0.577872\pi\) | |||||||
\(284\) | 1336.99 | 0.279351 | ||||||||
\(285\) | 285.000 | 0.0592349 | ||||||||
\(286\) | −4088.32 | −0.845272 | ||||||||
\(287\) | −7272.04 | −1.49566 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 4034.34 | 0.821156 | ||||||||
\(290\) | 2165.20 | 0.438430 | ||||||||
\(291\) | −4182.91 | −0.842633 | ||||||||
\(292\) | −3466.77 | −0.694786 | ||||||||
\(293\) | 2760.03 | 0.550317 | 0.275158 | − | 0.961399i | \(-0.411270\pi\) | ||||
0.275158 | + | 0.961399i | \(0.411270\pi\) | |||||||
\(294\) | −286.490 | −0.0568314 | ||||||||
\(295\) | 1042.66 | 0.205783 | ||||||||
\(296\) | −43.9012 | −0.00862064 | ||||||||
\(297\) | 789.343 | 0.154217 | ||||||||
\(298\) | −2775.46 | −0.539525 | ||||||||
\(299\) | 574.558 | 0.111129 | ||||||||
\(300\) | 300.000 | 0.0577350 | ||||||||
\(301\) | 4592.00 | 0.879330 | ||||||||
\(302\) | 3375.26 | 0.643127 | ||||||||
\(303\) | 5888.31 | 1.11642 | ||||||||
\(304\) | 304.000 | 0.0573539 | ||||||||
\(305\) | 2550.32 | 0.478790 | ||||||||
\(306\) | 1702.63 | 0.318081 | ||||||||
\(307\) | 5771.80 | 1.07301 | 0.536505 | − | 0.843897i | \(-0.319744\pi\) | ||||
0.536505 | + | 0.843897i | \(0.319744\pi\) | |||||||
\(308\) | 2009.36 | 0.371734 | ||||||||
\(309\) | 4535.06 | 0.834920 | ||||||||
\(310\) | −2270.97 | −0.416073 | ||||||||
\(311\) | −6175.04 | −1.12590 | −0.562949 | − | 0.826491i | \(-0.690333\pi\) | ||||
−0.562949 | + | 0.826491i | \(0.690333\pi\) | |||||||
\(312\) | −1678.13 | −0.304504 | ||||||||
\(313\) | 11040.3 | 1.99372 | 0.996862 | − | 0.0791558i | \(-0.0252224\pi\) | ||||
0.996862 | + | 0.0791558i | \(0.0252224\pi\) | |||||||
\(314\) | −3751.33 | −0.674203 | ||||||||
\(315\) | 773.230 | 0.138307 | ||||||||
\(316\) | 2010.15 | 0.357848 | ||||||||
\(317\) | −1426.52 | −0.252748 | −0.126374 | − | 0.991983i | \(-0.540334\pi\) | ||||
−0.126374 | + | 0.991983i | \(0.540334\pi\) | |||||||
\(318\) | −1237.03 | −0.218143 | ||||||||
\(319\) | 6329.94 | 1.11100 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | −3102.40 | −0.539437 | ||||||||
\(322\) | −282.388 | −0.0488723 | ||||||||
\(323\) | 1797.22 | 0.309597 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −1748.05 | −0.298352 | ||||||||
\(326\) | 1759.05 | 0.298849 | ||||||||
\(327\) | −1468.34 | −0.248316 | ||||||||
\(328\) | −3385.71 | −0.569953 | ||||||||
\(329\) | −113.299 | −0.0189859 | ||||||||
\(330\) | 877.048 | 0.146303 | ||||||||
\(331\) | −900.393 | −0.149517 | −0.0747584 | − | 0.997202i | \(-0.523819\pi\) | ||||
−0.0747584 | + | 0.997202i | \(0.523819\pi\) | |||||||
\(332\) | −1913.25 | −0.316276 | ||||||||
\(333\) | −49.3889 | −0.00812761 | ||||||||
\(334\) | −6584.46 | −1.07870 | ||||||||
\(335\) | 5052.34 | 0.823997 | ||||||||
\(336\) | 824.779 | 0.133915 | ||||||||
\(337\) | 7663.82 | 1.23880 | 0.619399 | − | 0.785076i | \(-0.287376\pi\) | ||||
0.619399 | + | 0.785076i | \(0.287376\pi\) | |||||||
\(338\) | 5384.15 | 0.866447 | ||||||||
\(339\) | 1796.98 | 0.287901 | ||||||||
\(340\) | 1891.81 | 0.301758 | ||||||||
\(341\) | −6639.17 | −1.05434 | ||||||||
\(342\) | 342.000 | 0.0540738 | ||||||||
\(343\) | −6714.19 | −1.05694 | ||||||||
\(344\) | 2137.94 | 0.335087 | ||||||||
\(345\) | −123.257 | −0.0192346 | ||||||||
\(346\) | −3722.05 | −0.578320 | ||||||||
\(347\) | −10905.5 | −1.68714 | −0.843569 | − | 0.537021i | \(-0.819549\pi\) | ||||
−0.843569 | + | 0.537021i | \(0.819549\pi\) | |||||||
\(348\) | 2598.24 | 0.400230 | ||||||||
\(349\) | −2473.62 | −0.379397 | −0.189699 | − | 0.981842i | \(-0.560751\pi\) | ||||
−0.189699 | + | 0.981842i | \(0.560751\pi\) | |||||||
\(350\) | 859.144 | 0.131209 | ||||||||
\(351\) | −1887.89 | −0.287089 | ||||||||
\(352\) | 935.518 | 0.141657 | ||||||||
\(353\) | −4926.69 | −0.742836 | −0.371418 | − | 0.928466i | \(-0.621128\pi\) | ||||
−0.371418 | + | 0.928466i | \(0.621128\pi\) | |||||||
\(354\) | 1251.19 | 0.187854 | ||||||||
\(355\) | 1671.23 | 0.249859 | ||||||||
\(356\) | −4601.00 | −0.684978 | ||||||||
\(357\) | 4876.01 | 0.722873 | ||||||||
\(358\) | −5738.61 | −0.847192 | ||||||||
\(359\) | 7595.97 | 1.11671 | 0.558356 | − | 0.829601i | \(-0.311432\pi\) | ||||
0.558356 | + | 0.829601i | \(0.311432\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −4805.38 | −0.697694 | ||||||||
\(363\) | −1428.96 | −0.206614 | ||||||||
\(364\) | −4805.84 | −0.692018 | ||||||||
\(365\) | −4333.47 | −0.621435 | ||||||||
\(366\) | 3060.38 | 0.437073 | ||||||||
\(367\) | 5177.70 | 0.736441 | 0.368221 | − | 0.929738i | \(-0.379967\pi\) | ||||
0.368221 | + | 0.929738i | \(0.379967\pi\) | |||||||
\(368\) | −131.474 | −0.0186238 | ||||||||
\(369\) | −3808.92 | −0.537357 | ||||||||
\(370\) | −54.8766 | −0.00771053 | ||||||||
\(371\) | −3542.63 | −0.495753 | ||||||||
\(372\) | −2725.17 | −0.379821 | ||||||||
\(373\) | 4912.63 | 0.681947 | 0.340974 | − | 0.940073i | \(-0.389243\pi\) | ||||
0.340974 | + | 0.940073i | \(0.389243\pi\) | |||||||
\(374\) | 5530.69 | 0.764666 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | −52.7497 | −0.00723499 | ||||||||
\(377\) | −15139.5 | −2.06823 | ||||||||
\(378\) | 927.876 | 0.126256 | ||||||||
\(379\) | −6166.88 | −0.835809 | −0.417904 | − | 0.908491i | \(-0.637235\pi\) | ||||
−0.417904 | + | 0.908491i | \(0.637235\pi\) | |||||||
\(380\) | 380.000 | 0.0512989 | ||||||||
\(381\) | −4863.94 | −0.654035 | ||||||||
\(382\) | −1492.94 | −0.199962 | ||||||||
\(383\) | −6827.55 | −0.910891 | −0.455446 | − | 0.890264i | \(-0.650520\pi\) | ||||
−0.455446 | + | 0.890264i | \(0.650520\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 2511.70 | 0.332489 | ||||||||
\(386\) | 1292.13 | 0.170383 | ||||||||
\(387\) | 2405.18 | 0.315923 | ||||||||
\(388\) | −5577.21 | −0.729742 | ||||||||
\(389\) | 1891.05 | 0.246479 | 0.123239 | − | 0.992377i | \(-0.460672\pi\) | ||||
0.123239 | + | 0.992377i | \(0.460672\pi\) | |||||||
\(390\) | −2097.66 | −0.272356 | ||||||||
\(391\) | −777.262 | −0.100531 | ||||||||
\(392\) | −381.987 | −0.0492175 | ||||||||
\(393\) | −6401.21 | −0.821624 | ||||||||
\(394\) | 9812.92 | 1.25474 | ||||||||
\(395\) | 2512.69 | 0.320069 | ||||||||
\(396\) | 1052.46 | 0.133555 | ||||||||
\(397\) | 9658.62 | 1.22104 | 0.610519 | − | 0.792001i | \(-0.290961\pi\) | ||||
0.610519 | + | 0.792001i | \(0.290961\pi\) | |||||||
\(398\) | −2332.47 | −0.293759 | ||||||||
\(399\) | 979.425 | 0.122889 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 2062.75 | 0.256880 | 0.128440 | − | 0.991717i | \(-0.459003\pi\) | ||||
0.128440 | + | 0.991717i | \(0.459003\pi\) | |||||||
\(402\) | 6062.81 | 0.752203 | ||||||||
\(403\) | 15879.1 | 1.96276 | ||||||||
\(404\) | 7851.08 | 0.966847 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 7440.87 | 0.909567 | ||||||||
\(407\) | −160.431 | −0.0195388 | ||||||||
\(408\) | 2270.17 | 0.275466 | ||||||||
\(409\) | −6421.95 | −0.776394 | −0.388197 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388197 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(410\) | −4232.14 | −0.509782 | ||||||||
\(411\) | 2466.92 | 0.296069 | ||||||||
\(412\) | 6046.74 | 0.723062 | ||||||||
\(413\) | 3583.19 | 0.426918 | ||||||||
\(414\) | −147.908 | −0.0175587 | ||||||||
\(415\) | −2391.57 | −0.282885 | ||||||||
\(416\) | −2237.50 | −0.263708 | ||||||||
\(417\) | 1269.70 | 0.149106 | ||||||||
\(418\) | 1110.93 | 0.129993 | ||||||||
\(419\) | 3671.43 | 0.428070 | 0.214035 | − | 0.976826i | \(-0.431339\pi\) | ||||
0.214035 | + | 0.976826i | \(0.431339\pi\) | |||||||
\(420\) | 1030.97 | 0.119777 | ||||||||
\(421\) | −5940.10 | −0.687655 | −0.343827 | − | 0.939033i | \(-0.611723\pi\) | ||||
−0.343827 | + | 0.939033i | \(0.611723\pi\) | |||||||
\(422\) | −11038.9 | −1.27338 | ||||||||
\(423\) | −59.3434 | −0.00682122 | ||||||||
\(424\) | −1649.38 | −0.188917 | ||||||||
\(425\) | 2364.76 | 0.269900 | ||||||||
\(426\) | 2005.48 | 0.228089 | ||||||||
\(427\) | 8764.37 | 0.993297 | ||||||||
\(428\) | −4136.53 | −0.467166 | ||||||||
\(429\) | −6132.49 | −0.690161 | ||||||||
\(430\) | 2672.42 | 0.299711 | ||||||||
\(431\) | −17677.0 | −1.97557 | −0.987785 | − | 0.155825i | \(-0.950196\pi\) | ||||
−0.987785 | + | 0.155825i | \(0.950196\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 13703.0 | 1.52084 | 0.760421 | − | 0.649430i | \(-0.224993\pi\) | ||||
0.760421 | + | 0.649430i | \(0.224993\pi\) | |||||||
\(434\) | −7804.38 | −0.863184 | ||||||||
\(435\) | 3247.80 | 0.357977 | ||||||||
\(436\) | −1957.79 | −0.215048 | ||||||||
\(437\) | −156.126 | −0.0170904 | ||||||||
\(438\) | −5200.16 | −0.567290 | ||||||||
\(439\) | −2745.97 | −0.298538 | −0.149269 | − | 0.988797i | \(-0.547692\pi\) | ||||
−0.149269 | + | 0.988797i | \(0.547692\pi\) | |||||||
\(440\) | 1169.40 | 0.126702 | ||||||||
\(441\) | −429.735 | −0.0464027 | ||||||||
\(442\) | −13227.9 | −1.42350 | ||||||||
\(443\) | 8941.76 | 0.958997 | 0.479499 | − | 0.877543i | \(-0.340819\pi\) | ||||
0.479499 | + | 0.877543i | \(0.340819\pi\) | |||||||
\(444\) | −65.8519 | −0.00703872 | ||||||||
\(445\) | −5751.24 | −0.612663 | ||||||||
\(446\) | 2786.14 | 0.295801 | ||||||||
\(447\) | −4163.20 | −0.440520 | ||||||||
\(448\) | 1099.70 | 0.115974 | ||||||||
\(449\) | 8770.30 | 0.921818 | 0.460909 | − | 0.887448i | \(-0.347524\pi\) | ||||
0.460909 | + | 0.887448i | \(0.347524\pi\) | |||||||
\(450\) | 450.000 | 0.0471405 | ||||||||
\(451\) | −12372.6 | −1.29181 | ||||||||
\(452\) | 2395.97 | 0.249329 | ||||||||
\(453\) | 5062.89 | 0.525111 | ||||||||
\(454\) | −8358.36 | −0.864047 | ||||||||
\(455\) | −6007.30 | −0.618960 | ||||||||
\(456\) | 456.000 | 0.0468293 | ||||||||
\(457\) | 14319.3 | 1.46571 | 0.732856 | − | 0.680384i | \(-0.238187\pi\) | ||||
0.732856 | + | 0.680384i | \(0.238187\pi\) | |||||||
\(458\) | 5593.67 | 0.570688 | ||||||||
\(459\) | 2553.94 | 0.259712 | ||||||||
\(460\) | −164.343 | −0.0166576 | ||||||||
\(461\) | 2579.44 | 0.260599 | 0.130300 | − | 0.991475i | \(-0.458406\pi\) | ||||
0.130300 | + | 0.991475i | \(0.458406\pi\) | |||||||
\(462\) | 3014.04 | 0.303519 | ||||||||
\(463\) | 19134.6 | 1.92065 | 0.960324 | − | 0.278888i | \(-0.0899657\pi\) | ||||
0.960324 | + | 0.278888i | \(0.0899657\pi\) | |||||||
\(464\) | 3464.32 | 0.346610 | ||||||||
\(465\) | −3406.46 | −0.339722 | ||||||||
\(466\) | −9935.20 | −0.987637 | ||||||||
\(467\) | 12280.1 | 1.21682 | 0.608409 | − | 0.793624i | \(-0.291808\pi\) | ||||
0.608409 | + | 0.793624i | \(0.291808\pi\) | |||||||
\(468\) | −2517.19 | −0.248626 | ||||||||
\(469\) | 17362.8 | 1.70946 | ||||||||
\(470\) | −65.9371 | −0.00647117 | ||||||||
\(471\) | −5627.00 | −0.550485 | ||||||||
\(472\) | 1668.26 | 0.162686 | ||||||||
\(473\) | 7812.81 | 0.759479 | ||||||||
\(474\) | 3015.23 | 0.292181 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 6501.34 | 0.626027 | ||||||||
\(477\) | −1855.55 | −0.178113 | ||||||||
\(478\) | 9397.26 | 0.899206 | ||||||||
\(479\) | 1427.43 | 0.136160 | 0.0680802 | − | 0.997680i | \(-0.478313\pi\) | ||||
0.0680802 | + | 0.997680i | \(0.478313\pi\) | |||||||
\(480\) | 480.000 | 0.0456435 | ||||||||
\(481\) | 383.707 | 0.0363733 | ||||||||
\(482\) | −134.065 | −0.0126691 | ||||||||
\(483\) | −423.582 | −0.0399041 | ||||||||
\(484\) | −1905.28 | −0.178933 | ||||||||
\(485\) | −6971.51 | −0.652701 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 14257.2 | 1.32660 | 0.663301 | − | 0.748353i | \(-0.269155\pi\) | ||||
0.663301 | + | 0.748353i | \(0.269155\pi\) | |||||||
\(488\) | 4080.51 | 0.378517 | ||||||||
\(489\) | 2638.58 | 0.244010 | ||||||||
\(490\) | −477.483 | −0.0440214 | ||||||||
\(491\) | −17429.3 | −1.60198 | −0.800990 | − | 0.598678i | \(-0.795693\pi\) | ||||
−0.800990 | + | 0.598678i | \(0.795693\pi\) | |||||||
\(492\) | −5078.57 | −0.465365 | ||||||||
\(493\) | 20480.7 | 1.87100 | ||||||||
\(494\) | −2657.03 | −0.241995 | ||||||||
\(495\) | 1315.57 | 0.119456 | ||||||||
\(496\) | −3633.56 | −0.328935 | ||||||||
\(497\) | 5743.32 | 0.518357 | ||||||||
\(498\) | −2869.88 | −0.258238 | ||||||||
\(499\) | −6280.73 | −0.563455 | −0.281728 | − | 0.959494i | \(-0.590907\pi\) | ||||
−0.281728 | + | 0.959494i | \(0.590907\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | −9876.69 | −0.880755 | ||||||||
\(502\) | −10756.2 | −0.956321 | ||||||||
\(503\) | 6433.48 | 0.570288 | 0.285144 | − | 0.958485i | \(-0.407959\pi\) | ||||
0.285144 | + | 0.958485i | \(0.407959\pi\) | |||||||
\(504\) | 1237.17 | 0.109341 | ||||||||
\(505\) | 9813.86 | 0.864774 | ||||||||
\(506\) | −480.455 | −0.0422111 | ||||||||
\(507\) | 8076.22 | 0.707451 | ||||||||
\(508\) | −6485.26 | −0.566411 | ||||||||
\(509\) | 18989.4 | 1.65362 | 0.826808 | − | 0.562485i | \(-0.190155\pi\) | ||||
0.826808 | + | 0.562485i | \(0.190155\pi\) | |||||||
\(510\) | 2837.71 | 0.246384 | ||||||||
\(511\) | −14892.3 | −1.28923 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 513.000 | 0.0441511 | ||||||||
\(514\) | −5503.03 | −0.472234 | ||||||||
\(515\) | 7558.43 | 0.646726 | ||||||||
\(516\) | 3206.91 | 0.273597 | ||||||||
\(517\) | −192.767 | −0.0163982 | ||||||||
\(518\) | −188.588 | −0.0159963 | ||||||||
\(519\) | −5583.08 | −0.472197 | ||||||||
\(520\) | −2796.88 | −0.235868 | ||||||||
\(521\) | 7232.61 | 0.608189 | 0.304094 | − | 0.952642i | \(-0.401646\pi\) | ||||
0.304094 | + | 0.952642i | \(0.401646\pi\) | |||||||
\(522\) | 3897.36 | 0.326787 | ||||||||
\(523\) | 7864.04 | 0.657496 | 0.328748 | − | 0.944418i | \(-0.393373\pi\) | ||||
0.328748 | + | 0.944418i | \(0.393373\pi\) | |||||||
\(524\) | −8534.94 | −0.711547 | ||||||||
\(525\) | 1288.72 | 0.107132 | ||||||||
\(526\) | −3115.27 | −0.258236 | ||||||||
\(527\) | −21481.2 | −1.77559 | ||||||||
\(528\) | 1403.28 | 0.115662 | ||||||||
\(529\) | −12099.5 | −0.994450 | ||||||||
\(530\) | −2061.72 | −0.168973 | ||||||||
\(531\) | 1876.79 | 0.153382 | ||||||||
\(532\) | 1305.90 | 0.106425 | ||||||||
\(533\) | 29591.9 | 2.40482 | ||||||||
\(534\) | −6901.49 | −0.559282 | ||||||||
\(535\) | −5170.67 | −0.417846 | ||||||||
\(536\) | 8083.75 | 0.651427 | ||||||||
\(537\) | −8607.91 | −0.691729 | ||||||||
\(538\) | −3321.08 | −0.266137 | ||||||||
\(539\) | −1395.92 | −0.111552 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | 19267.3 | 1.53117 | 0.765587 | − | 0.643332i | \(-0.222449\pi\) | ||||
0.765587 | + | 0.643332i | \(0.222449\pi\) | |||||||
\(542\) | 3760.00 | 0.297981 | ||||||||
\(543\) | −7208.08 | −0.569665 | ||||||||
\(544\) | 3026.89 | 0.238561 | ||||||||
\(545\) | −2447.23 | −0.192345 | ||||||||
\(546\) | −7208.76 | −0.565030 | ||||||||
\(547\) | 7054.21 | 0.551401 | 0.275700 | − | 0.961244i | \(-0.411090\pi\) | ||||
0.275700 | + | 0.961244i | \(0.411090\pi\) | |||||||
\(548\) | 3289.23 | 0.256403 | ||||||||
\(549\) | 4590.57 | 0.356869 | ||||||||
\(550\) | 1461.75 | 0.113326 | ||||||||
\(551\) | 4113.88 | 0.318071 | ||||||||
\(552\) | −197.211 | −0.0152063 | ||||||||
\(553\) | 8635.05 | 0.664014 | ||||||||
\(554\) | −17249.5 | −1.32285 | ||||||||
\(555\) | −82.3148 | −0.00629562 | ||||||||
\(556\) | 1692.93 | 0.129130 | ||||||||
\(557\) | 7105.83 | 0.540546 | 0.270273 | − | 0.962784i | \(-0.412886\pi\) | ||||
0.270273 | + | 0.962784i | \(0.412886\pi\) | |||||||
\(558\) | −4087.75 | −0.310122 | ||||||||
\(559\) | −18686.1 | −1.41384 | ||||||||
\(560\) | 1374.63 | 0.103730 | ||||||||
\(561\) | 8296.03 | 0.624347 | ||||||||
\(562\) | −1856.04 | −0.139310 | ||||||||
\(563\) | 1180.00 | 0.0883323 | 0.0441661 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441661 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(564\) | −79.1245 | −0.00590735 | ||||||||
\(565\) | 2994.96 | 0.223007 | ||||||||
\(566\) | −4612.45 | −0.342537 | ||||||||
\(567\) | 1391.81 | 0.103088 | ||||||||
\(568\) | 2673.97 | 0.197531 | ||||||||
\(569\) | 2692.66 | 0.198387 | 0.0991936 | − | 0.995068i | \(-0.468374\pi\) | ||||
0.0991936 | + | 0.995068i | \(0.468374\pi\) | |||||||
\(570\) | 570.000 | 0.0418854 | ||||||||
\(571\) | −10754.0 | −0.788160 | −0.394080 | − | 0.919076i | \(-0.628937\pi\) | ||||
−0.394080 | + | 0.919076i | \(0.628937\pi\) | |||||||
\(572\) | −8176.65 | −0.597697 | ||||||||
\(573\) | −2239.41 | −0.163268 | ||||||||
\(574\) | −14544.1 | −1.05759 | ||||||||
\(575\) | −205.428 | −0.0148990 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 16146.3 | 1.16495 | 0.582476 | − | 0.812848i | \(-0.302084\pi\) | ||||
0.582476 | + | 0.812848i | \(0.302084\pi\) | |||||||
\(578\) | 8068.68 | 0.580645 | ||||||||
\(579\) | 1938.20 | 0.139117 | ||||||||
\(580\) | 4330.40 | 0.310017 | ||||||||
\(581\) | −8218.81 | −0.586874 | ||||||||
\(582\) | −8365.81 | −0.595832 | ||||||||
\(583\) | −6027.43 | −0.428183 | ||||||||
\(584\) | −6933.54 | −0.491288 | ||||||||
\(585\) | −3146.49 | −0.222378 | ||||||||
\(586\) | 5520.06 | 0.389133 | ||||||||
\(587\) | 19339.4 | 1.35984 | 0.679918 | − | 0.733288i | \(-0.262015\pi\) | ||||
0.679918 | + | 0.733288i | \(0.262015\pi\) | |||||||
\(588\) | −572.980 | −0.0401859 | ||||||||
\(589\) | −4314.85 | −0.301851 | ||||||||
\(590\) | 2085.32 | 0.145511 | ||||||||
\(591\) | 14719.4 | 1.02449 | ||||||||
\(592\) | −87.8025 | −0.00609571 | ||||||||
\(593\) | 15453.7 | 1.07016 | 0.535082 | − | 0.844800i | \(-0.320281\pi\) | ||||
0.535082 | + | 0.844800i | \(0.320281\pi\) | |||||||
\(594\) | 1578.69 | 0.109048 | ||||||||
\(595\) | 8126.68 | 0.559935 | ||||||||
\(596\) | −5550.93 | −0.381502 | ||||||||
\(597\) | −3498.71 | −0.239853 | ||||||||
\(598\) | 1149.12 | 0.0785800 | ||||||||
\(599\) | 15789.0 | 1.07700 | 0.538500 | − | 0.842626i | \(-0.318991\pi\) | ||||
0.538500 | + | 0.842626i | \(0.318991\pi\) | |||||||
\(600\) | 600.000 | 0.0408248 | ||||||||
\(601\) | −4673.39 | −0.317191 | −0.158595 | − | 0.987344i | \(-0.550697\pi\) | ||||
−0.158595 | + | 0.987344i | \(0.550697\pi\) | |||||||
\(602\) | 9183.99 | 0.621780 | ||||||||
\(603\) | 9094.22 | 0.614171 | ||||||||
\(604\) | 6750.51 | 0.454759 | ||||||||
\(605\) | −2381.59 | −0.160042 | ||||||||
\(606\) | 11776.6 | 0.789427 | ||||||||
\(607\) | 10101.9 | 0.675488 | 0.337744 | − | 0.941238i | \(-0.390336\pi\) | ||||
0.337744 | + | 0.941238i | \(0.390336\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | 11161.3 | 0.742658 | ||||||||
\(610\) | 5100.64 | 0.338555 | ||||||||
\(611\) | 461.045 | 0.0305268 | ||||||||
\(612\) | 3405.25 | 0.224917 | ||||||||
\(613\) | −8592.15 | −0.566123 | −0.283062 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283062 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(614\) | 11543.6 | 0.758732 | ||||||||
\(615\) | −6348.21 | −0.416235 | ||||||||
\(616\) | 4018.72 | 0.262856 | ||||||||
\(617\) | −14952.7 | −0.975646 | −0.487823 | − | 0.872943i | \(-0.662209\pi\) | ||||
−0.487823 | + | 0.872943i | \(0.662209\pi\) | |||||||
\(618\) | 9070.11 | 0.590378 | ||||||||
\(619\) | −25121.9 | −1.63124 | −0.815618 | − | 0.578591i | \(-0.803603\pi\) | ||||
−0.815618 | + | 0.578591i | \(0.803603\pi\) | |||||||
\(620\) | −4541.95 | −0.294208 | ||||||||
\(621\) | −221.863 | −0.0143366 | ||||||||
\(622\) | −12350.1 | −0.796131 | ||||||||
\(623\) | −19764.6 | −1.27103 | ||||||||
\(624\) | −3356.25 | −0.215317 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 22080.6 | 1.40978 | ||||||||
\(627\) | 1666.39 | 0.106139 | ||||||||
\(628\) | −7502.66 | −0.476734 | ||||||||
\(629\) | −519.080 | −0.0329047 | ||||||||
\(630\) | 1546.46 | 0.0977975 | ||||||||
\(631\) | 18777.7 | 1.18468 | 0.592338 | − | 0.805690i | \(-0.298205\pi\) | ||||
0.592338 | + | 0.805690i | \(0.298205\pi\) | |||||||
\(632\) | 4020.30 | 0.253037 | ||||||||
\(633\) | −16558.3 | −1.03971 | ||||||||
\(634\) | −2853.03 | −0.178720 | ||||||||
\(635\) | −8106.57 | −0.506613 | ||||||||
\(636\) | −2474.07 | −0.154250 | ||||||||
\(637\) | 3338.66 | 0.207665 | ||||||||
\(638\) | 12659.9 | 0.785595 | ||||||||
\(639\) | 3008.22 | 0.186234 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | 25392.7 | 1.56466 | 0.782332 | − | 0.622862i | \(-0.214030\pi\) | ||||
0.782332 | + | 0.622862i | \(0.214030\pi\) | |||||||
\(642\) | −6204.80 | −0.381439 | ||||||||
\(643\) | 215.451 | 0.0132139 | 0.00660696 | − | 0.999978i | \(-0.497897\pi\) | ||||
0.00660696 | + | 0.999978i | \(0.497897\pi\) | |||||||
\(644\) | −564.776 | −0.0345579 | ||||||||
\(645\) | 4008.64 | 0.244713 | ||||||||
\(646\) | 3594.43 | 0.218918 | ||||||||
\(647\) | −19929.7 | −1.21100 | −0.605501 | − | 0.795844i | \(-0.707027\pi\) | ||||
−0.605501 | + | 0.795844i | \(0.707027\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 6096.43 | 0.368730 | ||||||||
\(650\) | −3496.10 | −0.210966 | ||||||||
\(651\) | −11706.6 | −0.704787 | ||||||||
\(652\) | 3518.11 | 0.211318 | ||||||||
\(653\) | 18648.1 | 1.11754 | 0.558771 | − | 0.829322i | \(-0.311273\pi\) | ||||
0.558771 | + | 0.829322i | \(0.311273\pi\) | |||||||
\(654\) | −2936.68 | −0.175586 | ||||||||
\(655\) | −10668.7 | −0.636427 | ||||||||
\(656\) | −6771.42 | −0.403018 | ||||||||
\(657\) | −7800.24 | −0.463191 | ||||||||
\(658\) | −226.598 | −0.0134251 | ||||||||
\(659\) | −8105.95 | −0.479155 | −0.239577 | − | 0.970877i | \(-0.577009\pi\) | ||||
−0.239577 | + | 0.970877i | \(0.577009\pi\) | |||||||
\(660\) | 1754.10 | 0.103452 | ||||||||
\(661\) | −4872.33 | −0.286704 | −0.143352 | − | 0.989672i | \(-0.545788\pi\) | ||||
−0.143352 | + | 0.989672i | \(0.545788\pi\) | |||||||
\(662\) | −1800.79 | −0.105724 | ||||||||
\(663\) | −19841.8 | −1.16228 | ||||||||
\(664\) | −3826.51 | −0.223641 | ||||||||
\(665\) | 1632.37 | 0.0951891 | ||||||||
\(666\) | −98.7778 | −0.00574709 | ||||||||
\(667\) | −1779.17 | −0.103283 | ||||||||
\(668\) | −13168.9 | −0.762756 | ||||||||
\(669\) | 4179.20 | 0.241521 | ||||||||
\(670\) | 10104.7 | 0.582654 | ||||||||
\(671\) | 14911.7 | 0.857912 | ||||||||
\(672\) | 1649.56 | 0.0946920 | ||||||||
\(673\) | 12953.6 | 0.741937 | 0.370969 | − | 0.928645i | \(-0.379026\pi\) | ||||
0.370969 | + | 0.928645i | \(0.379026\pi\) | |||||||
\(674\) | 15327.6 | 0.875962 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 10768.3 | 0.612671 | ||||||||
\(677\) | 6098.11 | 0.346188 | 0.173094 | − | 0.984905i | \(-0.444624\pi\) | ||||
0.173094 | + | 0.984905i | \(0.444624\pi\) | |||||||
\(678\) | 3593.95 | 0.203577 | ||||||||
\(679\) | −23958.1 | −1.35409 | ||||||||
\(680\) | 3783.62 | 0.213375 | ||||||||
\(681\) | −12537.5 | −0.705491 | ||||||||
\(682\) | −13278.3 | −0.745534 | ||||||||
\(683\) | 27530.4 | 1.54234 | 0.771171 | − | 0.636628i | \(-0.219671\pi\) | ||||
0.771171 | + | 0.636628i | \(0.219671\pi\) | |||||||
\(684\) | 684.000 | 0.0382360 | ||||||||
\(685\) | 4111.54 | 0.229334 | ||||||||
\(686\) | −13428.4 | −0.747373 | ||||||||
\(687\) | 8390.50 | 0.465965 | ||||||||
\(688\) | 4275.88 | 0.236942 | ||||||||
\(689\) | 14416.0 | 0.797103 | ||||||||
\(690\) | −246.514 | −0.0136009 | ||||||||
\(691\) | −26669.7 | −1.46825 | −0.734127 | − | 0.679012i | \(-0.762408\pi\) | ||||
−0.734127 | + | 0.679012i | \(0.762408\pi\) | |||||||
\(692\) | −7444.11 | −0.408934 | ||||||||
\(693\) | 4521.06 | 0.247823 | ||||||||
\(694\) | −21811.0 | −1.19299 | ||||||||
\(695\) | 2116.16 | 0.115497 | ||||||||
\(696\) | 5196.47 | 0.283006 | ||||||||
\(697\) | −40032.0 | −2.17549 | ||||||||
\(698\) | −4947.23 | −0.268274 | ||||||||
\(699\) | −14902.8 | −0.806403 | ||||||||
\(700\) | 1718.29 | 0.0927789 | ||||||||
\(701\) | −5377.33 | −0.289727 | −0.144864 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144864 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(702\) | −3775.78 | −0.203003 | ||||||||
\(703\) | −104.265 | −0.00559381 | ||||||||
\(704\) | 1871.04 | 0.100167 | ||||||||
\(705\) | −98.9056 | −0.00528369 | ||||||||
\(706\) | −9853.38 | −0.525265 | ||||||||
\(707\) | 33726.1 | 1.79406 | ||||||||
\(708\) | 2502.39 | 0.132833 | ||||||||
\(709\) | −14906.2 | −0.789580 | −0.394790 | − | 0.918771i | \(-0.629183\pi\) | ||||
−0.394790 | + | 0.918771i | \(0.629183\pi\) | |||||||
\(710\) | 3342.47 | 0.176677 | ||||||||
\(711\) | 4522.84 | 0.238565 | ||||||||
\(712\) | −9201.99 | −0.484353 | ||||||||
\(713\) | 1866.09 | 0.0980162 | ||||||||
\(714\) | 9752.02 | 0.511149 | ||||||||
\(715\) | −10220.8 | −0.534597 | ||||||||
\(716\) | −11477.2 | −0.599055 | ||||||||
\(717\) | 14095.9 | 0.734199 | ||||||||
\(718\) | 15191.9 | 0.789635 | ||||||||
\(719\) | −17007.1 | −0.882140 | −0.441070 | − | 0.897473i | \(-0.645401\pi\) | ||||
−0.441070 | + | 0.897473i | \(0.645401\pi\) | |||||||
\(720\) | 720.000 | 0.0372678 | ||||||||
\(721\) | 25975.1 | 1.34170 | ||||||||
\(722\) | 722.000 | 0.0372161 | ||||||||
\(723\) | −201.098 | −0.0103443 | ||||||||
\(724\) | −9610.77 | −0.493344 | ||||||||
\(725\) | 5412.99 | 0.277288 | ||||||||
\(726\) | −2857.91 | −0.146098 | ||||||||
\(727\) | 25491.3 | 1.30044 | 0.650221 | − | 0.759745i | \(-0.274676\pi\) | ||||
0.650221 | + | 0.759745i | \(0.274676\pi\) | |||||||
\(728\) | −9611.68 | −0.489331 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −8666.93 | −0.439421 | ||||||||
\(731\) | 25278.6 | 1.27902 | ||||||||
\(732\) | 6120.77 | 0.309057 | ||||||||
\(733\) | −18043.7 | −0.909223 | −0.454611 | − | 0.890690i | \(-0.650222\pi\) | ||||
−0.454611 | + | 0.890690i | \(0.650222\pi\) | |||||||
\(734\) | 10355.4 | 0.520743 | ||||||||
\(735\) | −716.225 | −0.0359433 | ||||||||
\(736\) | −262.948 | −0.0131690 | ||||||||
\(737\) | 29541.0 | 1.47647 | ||||||||
\(738\) | −7617.85 | −0.379969 | ||||||||
\(739\) | −4482.52 | −0.223129 | −0.111564 | − | 0.993757i | \(-0.535586\pi\) | ||||
−0.111564 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(740\) | −109.753 | −0.00545217 | ||||||||
\(741\) | −3985.55 | −0.197588 | ||||||||
\(742\) | −7085.27 | −0.350550 | ||||||||
\(743\) | −1934.60 | −0.0955230 | −0.0477615 | − | 0.998859i | \(-0.515209\pi\) | ||||
−0.0477615 | + | 0.998859i | \(0.515209\pi\) | |||||||
\(744\) | −5450.34 | −0.268574 | ||||||||
\(745\) | −6938.66 | −0.341225 | ||||||||
\(746\) | 9825.26 | 0.482210 | ||||||||
\(747\) | −4304.82 | −0.210850 | ||||||||
\(748\) | 11061.4 | 0.540700 | ||||||||
\(749\) | −17769.4 | −0.866862 | ||||||||
\(750\) | 750.000 | 0.0365148 | ||||||||
\(751\) | 6102.74 | 0.296528 | 0.148264 | − | 0.988948i | \(-0.452632\pi\) | ||||
0.148264 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(752\) | −105.499 | −0.00511591 | ||||||||
\(753\) | −16134.3 | −0.780833 | ||||||||
\(754\) | −30279.0 | −1.46246 | ||||||||
\(755\) | 8438.14 | 0.406749 | ||||||||
\(756\) | 1855.75 | 0.0892765 | ||||||||
\(757\) | −40052.0 | −1.92301 | −0.961503 | − | 0.274796i | \(-0.911390\pi\) | ||||
−0.961503 | + | 0.274796i | \(0.911390\pi\) | |||||||
\(758\) | −12333.8 | −0.591006 | ||||||||
\(759\) | −720.682 | −0.0344652 | ||||||||
\(760\) | 760.000 | 0.0362738 | ||||||||
\(761\) | −10449.7 | −0.497770 | −0.248885 | − | 0.968533i | \(-0.580064\pi\) | ||||
−0.248885 | + | 0.968533i | \(0.580064\pi\) | |||||||
\(762\) | −9727.88 | −0.462472 | ||||||||
\(763\) | −8410.10 | −0.399038 | ||||||||
\(764\) | −2985.88 | −0.141395 | ||||||||
\(765\) | 4256.57 | 0.201172 | ||||||||
\(766\) | −13655.1 | −0.644097 | ||||||||
\(767\) | −14581.0 | −0.686426 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 6903.59 | 0.323732 | 0.161866 | − | 0.986813i | \(-0.448249\pi\) | ||||
0.161866 | + | 0.986813i | \(0.448249\pi\) | |||||||
\(770\) | 5023.41 | 0.235105 | ||||||||
\(771\) | −8254.55 | −0.385578 | ||||||||
\(772\) | 2584.27 | 0.120479 | ||||||||
\(773\) | −26849.0 | −1.24928 | −0.624639 | − | 0.780914i | \(-0.714754\pi\) | ||||
−0.624639 | + | 0.780914i | \(0.714754\pi\) | |||||||
\(774\) | 4810.36 | 0.223391 | ||||||||
\(775\) | −5677.43 | −0.263148 | ||||||||
\(776\) | −11154.4 | −0.516005 | ||||||||
\(777\) | −282.881 | −0.0130609 | ||||||||
\(778\) | 3782.11 | 0.174287 | ||||||||
\(779\) | −8041.06 | −0.369834 | ||||||||
\(780\) | −4195.32 | −0.192585 | ||||||||
\(781\) | 9771.68 | 0.447706 | ||||||||
\(782\) | −1554.52 | −0.0710865 | ||||||||
\(783\) | 5846.03 | 0.266820 | ||||||||
\(784\) | −763.973 | −0.0348020 | ||||||||
\(785\) | −9378.33 | −0.426404 | ||||||||
\(786\) | −12802.4 | −0.580976 | ||||||||
\(787\) | 13804.1 | 0.625239 | 0.312620 | − | 0.949878i | \(-0.398793\pi\) | ||||
0.312620 | + | 0.949878i | \(0.398793\pi\) | |||||||
\(788\) | 19625.8 | 0.887236 | ||||||||
\(789\) | −4672.90 | −0.210849 | ||||||||
\(790\) | 5025.38 | 0.226323 | ||||||||
\(791\) | 10292.4 | 0.462650 | ||||||||
\(792\) | 2104.91 | 0.0944380 | ||||||||
\(793\) | −35664.6 | −1.59709 | ||||||||
\(794\) | 19317.2 | 0.863405 | ||||||||
\(795\) | −3092.58 | −0.137966 | ||||||||
\(796\) | −4664.94 | −0.207719 | ||||||||
\(797\) | 14190.6 | 0.630684 | 0.315342 | − | 0.948978i | \(-0.397881\pi\) | ||||
0.315342 | + | 0.948978i | \(0.397881\pi\) | |||||||
\(798\) | 1958.85 | 0.0868954 | ||||||||
\(799\) | −623.702 | −0.0276157 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | −10352.2 | −0.456652 | ||||||||
\(802\) | 4125.50 | 0.181642 | ||||||||
\(803\) | −25337.7 | −1.11351 | ||||||||
\(804\) | 12125.6 | 0.531888 | ||||||||
\(805\) | −705.970 | −0.0309095 | ||||||||
\(806\) | 31758.2 | 1.38788 | ||||||||
\(807\) | −4981.62 | −0.217300 | ||||||||
\(808\) | 15702.2 | 0.683664 | ||||||||
\(809\) | 23720.0 | 1.03084 | 0.515422 | − | 0.856937i | \(-0.327635\pi\) | ||||
0.515422 | + | 0.856937i | \(0.327635\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | 23359.2 | 1.01141 | 0.505704 | − | 0.862707i | \(-0.331233\pi\) | ||||
0.505704 | + | 0.862707i | \(0.331233\pi\) | |||||||
\(812\) | 14881.7 | 0.643161 | ||||||||
\(813\) | 5639.99 | 0.243300 | ||||||||
\(814\) | −320.862 | −0.0138160 | ||||||||
\(815\) | 4397.63 | 0.189009 | ||||||||
\(816\) | 4540.34 | 0.194784 | ||||||||
\(817\) | 5077.61 | 0.217433 | ||||||||
\(818\) | −12843.9 | −0.548994 | ||||||||
\(819\) | −10813.1 | −0.461345 | ||||||||
\(820\) | −8464.28 | −0.360470 | ||||||||
\(821\) | −13199.5 | −0.561103 | −0.280551 | − | 0.959839i | \(-0.590517\pi\) | ||||
−0.280551 | + | 0.959839i | \(0.590517\pi\) | |||||||
\(822\) | 4933.85 | 0.209352 | ||||||||
\(823\) | −11817.2 | −0.500513 | −0.250256 | − | 0.968180i | \(-0.580515\pi\) | ||||
−0.250256 | + | 0.968180i | \(0.580515\pi\) | |||||||
\(824\) | 12093.5 | 0.511282 | ||||||||
\(825\) | 2192.62 | 0.0925300 | ||||||||
\(826\) | 7166.38 | 0.301877 | ||||||||
\(827\) | −33124.4 | −1.39280 | −0.696402 | − | 0.717652i | \(-0.745217\pi\) | ||||
−0.696402 | + | 0.717652i | \(0.745217\pi\) | |||||||
\(828\) | −295.817 | −0.0124159 | ||||||||
\(829\) | 21452.5 | 0.898764 | 0.449382 | − | 0.893340i | \(-0.351644\pi\) | ||||
0.449382 | + | 0.893340i | \(0.351644\pi\) | |||||||
\(830\) | −4783.14 | −0.200030 | ||||||||
\(831\) | −25874.2 | −1.08010 | ||||||||
\(832\) | −4475.00 | −0.186470 | ||||||||
\(833\) | −4516.53 | −0.187862 | ||||||||
\(834\) | 2539.39 | 0.105434 | ||||||||
\(835\) | −16461.2 | −0.682230 | ||||||||
\(836\) | 2221.85 | 0.0919192 | ||||||||
\(837\) | −6131.63 | −0.253214 | ||||||||
\(838\) | 7342.86 | 0.302691 | ||||||||
\(839\) | −4748.27 | −0.195386 | −0.0976928 | − | 0.995217i | \(-0.531146\pi\) | ||||
−0.0976928 | + | 0.995217i | \(0.531146\pi\) | |||||||
\(840\) | 2061.95 | 0.0846951 | ||||||||
\(841\) | 22491.8 | 0.922212 | ||||||||
\(842\) | −11880.2 | −0.486245 | ||||||||
\(843\) | −2784.06 | −0.113746 | ||||||||
\(844\) | −22077.8 | −0.900414 | ||||||||
\(845\) | 13460.4 | 0.547989 | ||||||||
\(846\) | −118.687 | −0.00482333 | ||||||||
\(847\) | −8184.53 | −0.332024 | ||||||||
\(848\) | −3298.76 | −0.133585 | ||||||||
\(849\) | −6918.68 | −0.279680 | ||||||||
\(850\) | 4729.52 | 0.190848 | ||||||||
\(851\) | 45.0928 | 0.00181641 | ||||||||
\(852\) | 4010.96 | 0.161283 | ||||||||
\(853\) | 16832.9 | 0.675672 | 0.337836 | − | 0.941205i | \(-0.390305\pi\) | ||||
0.337836 | + | 0.941205i | \(0.390305\pi\) | |||||||
\(854\) | 17528.7 | 0.702367 | ||||||||
\(855\) | 855.000 | 0.0341993 | ||||||||
\(856\) | −8273.07 | −0.330336 | ||||||||
\(857\) | 22016.2 | 0.877548 | 0.438774 | − | 0.898597i | \(-0.355413\pi\) | ||||
0.438774 | + | 0.898597i | \(0.355413\pi\) | |||||||
\(858\) | −12265.0 | −0.488018 | ||||||||
\(859\) | −44154.2 | −1.75381 | −0.876904 | − | 0.480666i | \(-0.840395\pi\) | ||||
−0.876904 | + | 0.480666i | \(0.840395\pi\) | |||||||
\(860\) | 5344.85 | 0.211928 | ||||||||
\(861\) | −21816.1 | −0.863520 | ||||||||
\(862\) | −35354.0 | −1.39694 | ||||||||
\(863\) | 18091.3 | 0.713598 | 0.356799 | − | 0.934181i | \(-0.383868\pi\) | ||||
0.356799 | + | 0.934181i | \(0.383868\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −9305.13 | −0.365762 | ||||||||
\(866\) | 27406.0 | 1.07540 | ||||||||
\(867\) | 12103.0 | 0.474095 | ||||||||
\(868\) | −15608.8 | −0.610363 | ||||||||
\(869\) | 14691.7 | 0.573510 | ||||||||
\(870\) | 6495.59 | 0.253128 | ||||||||
\(871\) | −70653.9 | −2.74858 | ||||||||
\(872\) | −3915.57 | −0.152062 | ||||||||
\(873\) | −12548.7 | −0.486495 | ||||||||
\(874\) | −312.251 | −0.0120847 | ||||||||
\(875\) | 2147.86 | 0.0829840 | ||||||||
\(876\) | −10400.3 | −0.401135 | ||||||||
\(877\) | 17188.7 | 0.661825 | 0.330913 | − | 0.943661i | \(-0.392643\pi\) | ||||
0.330913 | + | 0.943661i | \(0.392643\pi\) | |||||||
\(878\) | −5491.94 | −0.211098 | ||||||||
\(879\) | 8280.09 | 0.317725 | ||||||||
\(880\) | 2338.79 | 0.0895918 | ||||||||
\(881\) | −36459.5 | −1.39427 | −0.697135 | − | 0.716940i | \(-0.745542\pi\) | ||||
−0.697135 | + | 0.716940i | \(0.745542\pi\) | |||||||
\(882\) | −859.470 | −0.0328116 | ||||||||
\(883\) | −39492.5 | −1.50513 | −0.752565 | − | 0.658518i | \(-0.771184\pi\) | ||||
−0.752565 | + | 0.658518i | \(0.771184\pi\) | |||||||
\(884\) | −26455.8 | −1.00657 | ||||||||
\(885\) | 3127.98 | 0.118809 | ||||||||
\(886\) | 17883.5 | 0.678113 | ||||||||
\(887\) | −11920.3 | −0.451232 | −0.225616 | − | 0.974216i | \(-0.572439\pi\) | ||||
−0.225616 | + | 0.974216i | \(0.572439\pi\) | |||||||
\(888\) | −131.704 | −0.00497713 | ||||||||
\(889\) | −27858.9 | −1.05102 | ||||||||
\(890\) | −11502.5 | −0.433218 | ||||||||
\(891\) | 2368.03 | 0.0890370 | ||||||||
\(892\) | 5572.27 | 0.209163 | ||||||||
\(893\) | −125.280 | −0.00469468 | ||||||||
\(894\) | −8326.39 | −0.311495 | ||||||||
\(895\) | −14346.5 | −0.535811 | ||||||||
\(896\) | 2199.41 | 0.0820057 | ||||||||
\(897\) | 1723.67 | 0.0641603 | ||||||||
\(898\) | 17540.6 | 0.651823 | ||||||||
\(899\) | −49171.1 | −1.82419 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | −19501.9 | −0.721091 | ||||||||
\(902\) | −24745.3 | −0.913444 | ||||||||
\(903\) | 13776.0 | 0.507681 | ||||||||
\(904\) | 4791.94 | 0.176303 | ||||||||
\(905\) | −12013.5 | −0.441261 | ||||||||
\(906\) | 10125.8 | 0.371309 | ||||||||
\(907\) | −45690.1 | −1.67267 | −0.836337 | − | 0.548215i | \(-0.815307\pi\) | ||||
−0.836337 | + | 0.548215i | \(0.815307\pi\) | |||||||
\(908\) | −16716.7 | −0.610974 | ||||||||
\(909\) | 17664.9 | 0.644564 | ||||||||
\(910\) | −12014.6 | −0.437671 | ||||||||
\(911\) | −32444.3 | −1.17994 | −0.589971 | − | 0.807424i | \(-0.700861\pi\) | ||||
−0.589971 | + | 0.807424i | \(0.700861\pi\) | |||||||
\(912\) | 912.000 | 0.0331133 | ||||||||
\(913\) | −13983.5 | −0.506884 | ||||||||
\(914\) | 28638.7 | 1.03641 | ||||||||
\(915\) | 7650.96 | 0.276429 | ||||||||
\(916\) | 11187.3 | 0.403537 | ||||||||
\(917\) | −36663.7 | −1.32033 | ||||||||
\(918\) | 5107.88 | 0.183644 | ||||||||
\(919\) | −30990.9 | −1.11240 | −0.556201 | − | 0.831048i | \(-0.687741\pi\) | ||||
−0.556201 | + | 0.831048i | \(0.687741\pi\) | |||||||
\(920\) | −328.685 | −0.0117787 | ||||||||
\(921\) | 17315.4 | 0.619502 | ||||||||
\(922\) | 5158.87 | 0.184272 | ||||||||
\(923\) | −23371.2 | −0.833447 | ||||||||
\(924\) | 6028.09 | 0.214621 | ||||||||
\(925\) | −137.191 | −0.00487657 | ||||||||
\(926\) | 38269.2 | 1.35810 | ||||||||
\(927\) | 13605.2 | 0.482041 | ||||||||
\(928\) | 6928.63 | 0.245090 | ||||||||
\(929\) | 18596.6 | 0.656766 | 0.328383 | − | 0.944545i | \(-0.393496\pi\) | ||||
0.328383 | + | 0.944545i | \(0.393496\pi\) | |||||||
\(930\) | −6812.92 | −0.240220 | ||||||||
\(931\) | −907.218 | −0.0319365 | ||||||||
\(932\) | −19870.4 | −0.698365 | ||||||||
\(933\) | −18525.1 | −0.650038 | ||||||||
\(934\) | 24560.1 | 0.860420 | ||||||||
\(935\) | 13826.7 | 0.483617 | ||||||||
\(936\) | −5034.38 | −0.175805 | ||||||||
\(937\) | 38908.0 | 1.35653 | 0.678266 | − | 0.734816i | \(-0.262732\pi\) | ||||
0.678266 | + | 0.734816i | \(0.262732\pi\) | |||||||
\(938\) | 34725.5 | 1.20877 | ||||||||
\(939\) | 33121.0 | 1.15108 | ||||||||
\(940\) | −131.874 | −0.00457581 | ||||||||
\(941\) | −30289.8 | −1.04933 | −0.524665 | − | 0.851309i | \(-0.675809\pi\) | ||||
−0.524665 | + | 0.851309i | \(0.675809\pi\) | |||||||
\(942\) | −11254.0 | −0.389252 | ||||||||
\(943\) | 3477.60 | 0.120092 | ||||||||
\(944\) | 3336.52 | 0.115036 | ||||||||
\(945\) | 2319.69 | 0.0798513 | ||||||||
\(946\) | 15625.6 | 0.537033 | ||||||||
\(947\) | 5350.55 | 0.183600 | 0.0918002 | − | 0.995777i | \(-0.470738\pi\) | ||||
0.0918002 | + | 0.995777i | \(0.470738\pi\) | |||||||
\(948\) | 6030.46 | 0.206603 | ||||||||
\(949\) | 60600.8 | 2.07290 | ||||||||
\(950\) | 950.000 | 0.0324443 | ||||||||
\(951\) | −4279.55 | −0.145924 | ||||||||
\(952\) | 13002.7 | 0.442668 | ||||||||
\(953\) | 18445.6 | 0.626978 | 0.313489 | − | 0.949592i | \(-0.398502\pi\) | ||||
0.313489 | + | 0.949592i | \(0.398502\pi\) | |||||||
\(954\) | −3711.10 | −0.125945 | ||||||||
\(955\) | −3732.36 | −0.126467 | ||||||||
\(956\) | 18794.5 | 0.635835 | ||||||||
\(957\) | 18989.8 | 0.641435 | ||||||||
\(958\) | 2854.85 | 0.0962799 | ||||||||
\(959\) | 14129.6 | 0.475776 | ||||||||
\(960\) | 960.000 | 0.0322749 | ||||||||
\(961\) | 21782.2 | 0.731167 | ||||||||
\(962\) | 767.415 | 0.0257198 | ||||||||
\(963\) | −9307.20 | −0.311444 | ||||||||
\(964\) | −268.130 | −0.00895840 | ||||||||
\(965\) | 3230.33 | 0.107760 | ||||||||
\(966\) | −847.164 | −0.0282164 | ||||||||
\(967\) | 2251.28 | 0.0748670 | 0.0374335 | − | 0.999299i | \(-0.488082\pi\) | ||||
0.0374335 | + | 0.999299i | \(0.488082\pi\) | |||||||
\(968\) | −3810.55 | −0.126525 | ||||||||
\(969\) | 5391.65 | 0.178746 | ||||||||
\(970\) | −13943.0 | −0.461529 | ||||||||
\(971\) | −15117.4 | −0.499630 | −0.249815 | − | 0.968294i | \(-0.580370\pi\) | ||||
−0.249815 | + | 0.968294i | \(0.580370\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 7272.35 | 0.239610 | ||||||||
\(974\) | 28514.4 | 0.938049 | ||||||||
\(975\) | −5244.14 | −0.172253 | ||||||||
\(976\) | 8161.02 | 0.267652 | ||||||||
\(977\) | −52640.2 | −1.72376 | −0.861878 | − | 0.507116i | \(-0.830712\pi\) | ||||
−0.861878 | + | 0.507116i | \(0.830712\pi\) | |||||||
\(978\) | 5277.16 | 0.172541 | ||||||||
\(979\) | −33627.4 | −1.09779 | ||||||||
\(980\) | −954.967 | −0.0311279 | ||||||||
\(981\) | −4405.02 | −0.143365 | ||||||||
\(982\) | −34858.5 | −1.13277 | ||||||||
\(983\) | −3111.24 | −0.100949 | −0.0504746 | − | 0.998725i | \(-0.516073\pi\) | ||||
−0.0504746 | + | 0.998725i | \(0.516073\pi\) | |||||||
\(984\) | −10157.1 | −0.329063 | ||||||||
\(985\) | 24532.3 | 0.793568 | ||||||||
\(986\) | 40961.4 | 1.32300 | ||||||||
\(987\) | −339.897 | −0.0109615 | ||||||||
\(988\) | −5314.07 | −0.171116 | ||||||||
\(989\) | −2195.97 | −0.0706043 | ||||||||
\(990\) | 2631.14 | 0.0844679 | ||||||||
\(991\) | 20100.4 | 0.644308 | 0.322154 | − | 0.946687i | \(-0.395593\pi\) | ||||
0.322154 | + | 0.946687i | \(0.395593\pi\) | |||||||
\(992\) | −7267.11 | −0.232592 | ||||||||
\(993\) | −2701.18 | −0.0863236 | ||||||||
\(994\) | 11486.6 | 0.366534 | ||||||||
\(995\) | −5831.18 | −0.185790 | ||||||||
\(996\) | −5739.76 | −0.182602 | ||||||||
\(997\) | 53308.1 | 1.69337 | 0.846683 | − | 0.532098i | \(-0.178596\pi\) | ||||
0.846683 | + | 0.532098i | \(0.178596\pi\) | |||||||
\(998\) | −12561.5 | −0.398423 | ||||||||
\(999\) | −148.167 | −0.00469248 |
(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 | 570.4.a.s.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 1710.4.a.bc.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.4.a.s.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1710.4.a.bc.1.3 | 4 | 3.2 | odd | 2 |