Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.02529\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.02529 | −1.77671 | −0.888354 | − | 0.459159i | \(-0.848151\pi\) | ||||
−0.888354 | + | 0.459159i | \(0.848151\pi\) | |||||||
\(3\) | 8.34382 | 1.60577 | 0.802884 | − | 0.596135i | \(-0.203298\pi\) | ||||
0.802884 | + | 0.596135i | \(0.203298\pi\) | |||||||
\(4\) | 17.2535 | 2.15669 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −41.9301 | −2.85298 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −46.5017 | −2.05511 | ||||||||
\(9\) | 42.6193 | 1.57849 | ||||||||
\(10\) | −25.1265 | −0.794568 | ||||||||
\(11\) | −0.888695 | −0.0243592 | −0.0121796 | − | 0.999926i | \(-0.503877\pi\) | ||||
−0.0121796 | + | 0.999926i | \(0.503877\pi\) | |||||||
\(12\) | 143.960 | 3.46315 | ||||||||
\(13\) | 25.9574 | 0.553791 | 0.276895 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276895 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.7191 | 0.718122 | ||||||||
\(16\) | 95.6563 | 1.49463 | ||||||||
\(17\) | 96.3100 | 1.37404 | 0.687018 | − | 0.726640i | \(-0.258919\pi\) | ||||
0.687018 | + | 0.726640i | \(0.258919\pi\) | |||||||
\(18\) | −214.174 | −2.80452 | ||||||||
\(19\) | 89.0785 | 1.07558 | 0.537789 | − | 0.843079i | \(-0.319260\pi\) | ||||
0.537789 | + | 0.843079i | \(0.319260\pi\) | |||||||
\(20\) | 86.2677 | 0.964502 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.46595 | 0.0432793 | ||||||||
\(23\) | −116.532 | −1.05646 | −0.528230 | − | 0.849102i | \(-0.677144\pi\) | ||||
−0.528230 | + | 0.849102i | \(0.677144\pi\) | |||||||
\(24\) | −388.002 | −3.30002 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −130.443 | −0.983924 | ||||||||
\(27\) | 130.325 | 0.928926 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −222.663 | −1.42578 | −0.712888 | − | 0.701277i | \(-0.752613\pi\) | ||||
−0.712888 | + | 0.701277i | \(0.752613\pi\) | |||||||
\(30\) | −209.651 | −1.27589 | ||||||||
\(31\) | 12.9193 | 0.0748508 | 0.0374254 | − | 0.999299i | \(-0.488084\pi\) | ||||
0.0374254 | + | 0.999299i | \(0.488084\pi\) | |||||||
\(32\) | −108.687 | −0.600417 | ||||||||
\(33\) | −7.41511 | −0.0391153 | ||||||||
\(34\) | −483.986 | −2.44126 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 735.334 | 3.40432 | ||||||||
\(37\) | 91.2579 | 0.405478 | 0.202739 | − | 0.979233i | \(-0.435016\pi\) | ||||
0.202739 | + | 0.979233i | \(0.435016\pi\) | |||||||
\(38\) | −447.645 | −1.91099 | ||||||||
\(39\) | 216.584 | 0.889259 | ||||||||
\(40\) | −232.509 | −0.919071 | ||||||||
\(41\) | 98.4403 | 0.374971 | 0.187485 | − | 0.982267i | \(-0.439966\pi\) | ||||
0.187485 | + | 0.982267i | \(0.439966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 392.032 | 1.39033 | 0.695166 | − | 0.718850i | \(-0.255331\pi\) | ||||
0.695166 | + | 0.718850i | \(0.255331\pi\) | |||||||
\(44\) | −15.3331 | −0.0525354 | ||||||||
\(45\) | 213.097 | 0.705924 | ||||||||
\(46\) | 585.606 | 1.87702 | ||||||||
\(47\) | 220.282 | 0.683647 | 0.341823 | − | 0.939764i | \(-0.388956\pi\) | ||||
0.341823 | + | 0.939764i | \(0.388956\pi\) | |||||||
\(48\) | 798.139 | 2.40003 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −125.632 | −0.355342 | ||||||||
\(51\) | 803.594 | 2.20638 | ||||||||
\(52\) | 447.856 | 1.19436 | ||||||||
\(53\) | −228.703 | −0.592732 | −0.296366 | − | 0.955074i | \(-0.595775\pi\) | ||||
−0.296366 | + | 0.955074i | \(0.595775\pi\) | |||||||
\(54\) | −654.919 | −1.65043 | ||||||||
\(55\) | −4.44347 | −0.0108938 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 743.254 | 1.72713 | ||||||||
\(58\) | 1118.95 | 2.53319 | ||||||||
\(59\) | −13.5393 | −0.0298756 | −0.0149378 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149378 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(60\) | 719.802 | 1.54877 | ||||||||
\(61\) | −205.946 | −0.432273 | −0.216136 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216136 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(62\) | −64.9233 | −0.132988 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −219.067 | −0.427865 | ||||||||
\(65\) | 129.787 | 0.247663 | ||||||||
\(66\) | 37.2631 | 0.0694965 | ||||||||
\(67\) | 325.684 | 0.593861 | 0.296930 | − | 0.954899i | \(-0.404037\pi\) | ||||
0.296930 | + | 0.954899i | \(0.404037\pi\) | |||||||
\(68\) | 1661.69 | 2.96337 | ||||||||
\(69\) | −972.320 | −1.69643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −583.883 | −0.975975 | −0.487987 | − | 0.872851i | \(-0.662269\pi\) | ||||
−0.487987 | + | 0.872851i | \(0.662269\pi\) | |||||||
\(72\) | −1981.87 | −3.24397 | ||||||||
\(73\) | 950.353 | 1.52370 | 0.761852 | − | 0.647751i | \(-0.224290\pi\) | ||||
0.761852 | + | 0.647751i | \(0.224290\pi\) | |||||||
\(74\) | −458.597 | −0.720417 | ||||||||
\(75\) | 208.595 | 0.321154 | ||||||||
\(76\) | 1536.92 | 2.31969 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1088.40 | −1.57995 | ||||||||
\(79\) | 451.485 | 0.642988 | 0.321494 | − | 0.946912i | \(-0.395815\pi\) | ||||
0.321494 | + | 0.946912i | \(0.395815\pi\) | |||||||
\(80\) | 478.282 | 0.668419 | ||||||||
\(81\) | −63.3158 | −0.0868529 | ||||||||
\(82\) | −494.691 | −0.666213 | ||||||||
\(83\) | −164.928 | −0.218111 | −0.109056 | − | 0.994036i | \(-0.534783\pi\) | ||||
−0.109056 | + | 0.994036i | \(0.534783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 481.550 | 0.614488 | ||||||||
\(86\) | −1970.07 | −2.47021 | ||||||||
\(87\) | −1857.86 | −2.28947 | ||||||||
\(88\) | 41.3258 | 0.0500608 | ||||||||
\(89\) | −884.901 | −1.05392 | −0.526962 | − | 0.849889i | \(-0.676669\pi\) | ||||
−0.526962 | + | 0.849889i | \(0.676669\pi\) | |||||||
\(90\) | −1070.87 | −1.25422 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2010.59 | −2.27846 | ||||||||
\(93\) | 107.796 | 0.120193 | ||||||||
\(94\) | −1106.98 | −1.21464 | ||||||||
\(95\) | 445.392 | 0.481014 | ||||||||
\(96\) | −906.865 | −0.964130 | ||||||||
\(97\) | −62.1494 | −0.0650548 | −0.0325274 | − | 0.999471i | \(-0.510356\pi\) | ||||
−0.0325274 | + | 0.999471i | \(0.510356\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −37.8756 | −0.0384509 | ||||||||
\(100\) | 431.339 | 0.431339 | ||||||||
\(101\) | 562.733 | 0.554396 | 0.277198 | − | 0.960813i | \(-0.410594\pi\) | ||||
0.277198 | + | 0.960813i | \(0.410594\pi\) | |||||||
\(102\) | −4038.29 | −3.92010 | ||||||||
\(103\) | 417.039 | 0.398952 | 0.199476 | − | 0.979903i | \(-0.436076\pi\) | ||||
0.199476 | + | 0.979903i | \(0.436076\pi\) | |||||||
\(104\) | −1207.06 | −1.13810 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1149.30 | 1.05311 | ||||||||
\(107\) | 1979.39 | 1.78837 | 0.894183 | − | 0.447701i | \(-0.147757\pi\) | ||||
0.894183 | + | 0.447701i | \(0.147757\pi\) | |||||||
\(108\) | 2248.56 | 2.00341 | ||||||||
\(109\) | 1408.40 | 1.23762 | 0.618808 | − | 0.785542i | \(-0.287616\pi\) | ||||
0.618808 | + | 0.785542i | \(0.287616\pi\) | |||||||
\(110\) | 22.3297 | 0.0193551 | ||||||||
\(111\) | 761.439 | 0.651104 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −850.468 | −0.708011 | −0.354006 | − | 0.935243i | \(-0.615181\pi\) | ||||
−0.354006 | + | 0.935243i | \(0.615181\pi\) | |||||||
\(114\) | −3735.07 | −3.06861 | ||||||||
\(115\) | −582.659 | −0.472463 | ||||||||
\(116\) | −3841.73 | −3.07496 | ||||||||
\(117\) | 1106.28 | 0.874154 | ||||||||
\(118\) | 68.0387 | 0.0530803 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1940.01 | −1.47582 | ||||||||
\(121\) | −1330.21 | −0.999407 | ||||||||
\(122\) | 1034.94 | 0.768023 | ||||||||
\(123\) | 821.368 | 0.602116 | ||||||||
\(124\) | 222.904 | 0.161430 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 885.282 | 0.618552 | 0.309276 | − | 0.950972i | \(-0.399913\pi\) | ||||
0.309276 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(128\) | 1970.37 | 1.36061 | ||||||||
\(129\) | 3271.04 | 2.23255 | ||||||||
\(130\) | −652.216 | −0.440024 | ||||||||
\(131\) | −1807.09 | −1.20524 | −0.602620 | − | 0.798028i | \(-0.705877\pi\) | ||||
−0.602620 | + | 0.798028i | \(0.705877\pi\) | |||||||
\(132\) | −127.937 | −0.0843597 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1636.66 | −1.05512 | ||||||||
\(135\) | 651.623 | 0.415428 | ||||||||
\(136\) | −4478.58 | −2.82379 | ||||||||
\(137\) | 1931.87 | 1.20475 | 0.602374 | − | 0.798214i | \(-0.294222\pi\) | ||||
0.602374 | + | 0.798214i | \(0.294222\pi\) | |||||||
\(138\) | 4886.19 | 3.01406 | ||||||||
\(139\) | −2597.93 | −1.58528 | −0.792640 | − | 0.609690i | \(-0.791294\pi\) | ||||
−0.792640 | + | 0.609690i | \(0.791294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1837.99 | 1.09778 | ||||||||
\(142\) | 2934.18 | 1.73402 | ||||||||
\(143\) | −23.0682 | −0.0134899 | ||||||||
\(144\) | 4076.81 | 2.35926 | ||||||||
\(145\) | −1113.32 | −0.637627 | ||||||||
\(146\) | −4775.80 | −2.70718 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1574.52 | 0.874492 | ||||||||
\(149\) | −2923.55 | −1.60743 | −0.803713 | − | 0.595017i | \(-0.797145\pi\) | ||||
−0.803713 | + | 0.595017i | \(0.797145\pi\) | |||||||
\(150\) | −1048.25 | −0.570597 | ||||||||
\(151\) | 265.714 | 0.143202 | 0.0716009 | − | 0.997433i | \(-0.477189\pi\) | ||||
0.0716009 | + | 0.997433i | \(0.477189\pi\) | |||||||
\(152\) | −4142.30 | −2.21043 | ||||||||
\(153\) | 4104.67 | 2.16891 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 64.5965 | 0.0334743 | ||||||||
\(156\) | 3736.83 | 1.91786 | ||||||||
\(157\) | −1748.45 | −0.888798 | −0.444399 | − | 0.895829i | \(-0.646583\pi\) | ||||
−0.444399 | + | 0.895829i | \(0.646583\pi\) | |||||||
\(158\) | −2268.84 | −1.14240 | ||||||||
\(159\) | −1908.26 | −0.951791 | ||||||||
\(160\) | −543.435 | −0.268515 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 318.180 | 0.154312 | ||||||||
\(163\) | −3261.20 | −1.56710 | −0.783548 | − | 0.621331i | \(-0.786592\pi\) | ||||
−0.783548 | + | 0.621331i | \(0.786592\pi\) | |||||||
\(164\) | 1698.44 | 0.808696 | ||||||||
\(165\) | −37.0755 | −0.0174929 | ||||||||
\(166\) | 828.812 | 0.387520 | ||||||||
\(167\) | −1244.32 | −0.576579 | −0.288289 | − | 0.957543i | \(-0.593086\pi\) | ||||
−0.288289 | + | 0.957543i | \(0.593086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1523.22 | −0.693316 | ||||||||
\(170\) | −2419.93 | −1.09177 | ||||||||
\(171\) | 3796.46 | 1.69779 | ||||||||
\(172\) | 6763.93 | 2.99852 | ||||||||
\(173\) | −3800.34 | −1.67014 | −0.835071 | − | 0.550142i | \(-0.814574\pi\) | ||||
−0.835071 | + | 0.550142i | \(0.814574\pi\) | |||||||
\(174\) | 9336.30 | 4.06772 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −85.0093 | −0.0364080 | ||||||||
\(177\) | −112.969 | −0.0479733 | ||||||||
\(178\) | 4446.88 | 1.87252 | ||||||||
\(179\) | 1701.63 | 0.710534 | 0.355267 | − | 0.934765i | \(-0.384390\pi\) | ||||
0.355267 | + | 0.934765i | \(0.384390\pi\) | |||||||
\(180\) | 3676.67 | 1.52246 | ||||||||
\(181\) | 2366.84 | 0.971966 | 0.485983 | − | 0.873968i | \(-0.338462\pi\) | ||||
0.485983 | + | 0.873968i | \(0.338462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1718.37 | −0.694130 | ||||||||
\(184\) | 5418.93 | 2.17114 | ||||||||
\(185\) | 456.289 | 0.181335 | ||||||||
\(186\) | −541.708 | −0.213548 | ||||||||
\(187\) | −85.5902 | −0.0334705 | ||||||||
\(188\) | 3800.64 | 1.47442 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2238.23 | −0.854621 | ||||||||
\(191\) | −2230.48 | −0.844982 | −0.422491 | − | 0.906367i | \(-0.638844\pi\) | ||||
−0.422491 | + | 0.906367i | \(0.638844\pi\) | |||||||
\(192\) | −1827.85 | −0.687052 | ||||||||
\(193\) | −235.689 | −0.0879028 | −0.0439514 | − | 0.999034i | \(-0.513995\pi\) | ||||
−0.0439514 | + | 0.999034i | \(0.513995\pi\) | |||||||
\(194\) | 312.319 | 0.115583 | ||||||||
\(195\) | 1082.92 | 0.397689 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3232.17 | 1.16895 | 0.584473 | − | 0.811413i | \(-0.301301\pi\) | ||||
0.584473 | + | 0.811413i | \(0.301301\pi\) | |||||||
\(198\) | 190.336 | 0.0683160 | ||||||||
\(199\) | −3792.29 | −1.35090 | −0.675448 | − | 0.737408i | \(-0.736050\pi\) | ||||
−0.675448 | + | 0.737408i | \(0.736050\pi\) | |||||||
\(200\) | −1162.54 | −0.411021 | ||||||||
\(201\) | 2717.45 | 0.953603 | ||||||||
\(202\) | −2827.90 | −0.985000 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 13864.8 | 4.75849 | ||||||||
\(205\) | 492.201 | 0.167692 | ||||||||
\(206\) | −2095.74 | −0.708821 | ||||||||
\(207\) | −4966.51 | −1.66761 | ||||||||
\(208\) | 2482.99 | 0.827712 | ||||||||
\(209\) | −79.1636 | −0.0262003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 728.206 | 0.237591 | 0.118796 | − | 0.992919i | \(-0.462097\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462097\pi\) | |||||||
\(212\) | −3945.94 | −1.27834 | ||||||||
\(213\) | −4871.82 | −1.56719 | ||||||||
\(214\) | −9947.03 | −3.17741 | ||||||||
\(215\) | 1960.16 | 0.621775 | ||||||||
\(216\) | −6060.32 | −1.90904 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7077.61 | −2.19888 | ||||||||
\(219\) | 7929.57 | 2.44672 | ||||||||
\(220\) | −76.6657 | −0.0234945 | ||||||||
\(221\) | 2499.95 | 0.760928 | ||||||||
\(222\) | −3826.45 | −1.15682 | ||||||||
\(223\) | −3994.75 | −1.19959 | −0.599795 | − | 0.800154i | \(-0.704751\pi\) | ||||
−0.599795 | + | 0.800154i | \(0.704751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1065.48 | 0.315699 | ||||||||
\(226\) | 4273.85 | 1.25793 | ||||||||
\(227\) | −465.315 | −0.136053 | −0.0680265 | − | 0.997684i | \(-0.521670\pi\) | ||||
−0.0680265 | + | 0.997684i | \(0.521670\pi\) | |||||||
\(228\) | 12823.8 | 3.72489 | ||||||||
\(229\) | 5090.75 | 1.46902 | 0.734512 | − | 0.678596i | \(-0.237411\pi\) | ||||
0.734512 | + | 0.678596i | \(0.237411\pi\) | |||||||
\(230\) | 2928.03 | 0.839429 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10354.2 | 2.93012 | ||||||||
\(233\) | −1659.26 | −0.466530 | −0.233265 | − | 0.972413i | \(-0.574941\pi\) | ||||
−0.233265 | + | 0.972413i | \(0.574941\pi\) | |||||||
\(234\) | −5559.40 | −1.55312 | ||||||||
\(235\) | 1101.41 | 0.305736 | ||||||||
\(236\) | −233.600 | −0.0644325 | ||||||||
\(237\) | 3767.11 | 1.03249 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1300.53 | −0.351983 | −0.175992 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175992 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(240\) | 3990.70 | 1.07333 | ||||||||
\(241\) | −896.001 | −0.239488 | −0.119744 | − | 0.992805i | \(-0.538207\pi\) | ||||
−0.119744 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(242\) | 6684.69 | 1.77565 | ||||||||
\(243\) | −4047.06 | −1.06839 | ||||||||
\(244\) | −3553.29 | −0.932280 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4127.61 | −1.06978 | ||||||||
\(247\) | 2312.24 | 0.595645 | ||||||||
\(248\) | −600.770 | −0.153826 | ||||||||
\(249\) | −1376.13 | −0.350236 | ||||||||
\(250\) | −628.161 | −0.158914 | ||||||||
\(251\) | −383.031 | −0.0963216 | −0.0481608 | − | 0.998840i | \(-0.515336\pi\) | ||||
−0.0481608 | + | 0.998840i | \(0.515336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 103.561 | 0.0257345 | ||||||||
\(254\) | −4448.80 | −1.09899 | ||||||||
\(255\) | 4017.97 | 0.986725 | ||||||||
\(256\) | −8149.15 | −1.98954 | ||||||||
\(257\) | −7323.87 | −1.77763 | −0.888815 | − | 0.458267i | \(-0.848470\pi\) | ||||
−0.888815 | + | 0.458267i | \(0.848470\pi\) | |||||||
\(258\) | −16437.9 | −3.96659 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2239.28 | 0.534132 | ||||||||
\(261\) | −9489.75 | −2.25058 | ||||||||
\(262\) | 9081.17 | 2.14136 | ||||||||
\(263\) | −6762.89 | −1.58562 | −0.792810 | − | 0.609469i | \(-0.791383\pi\) | ||||
−0.792810 | + | 0.609469i | \(0.791383\pi\) | |||||||
\(264\) | 344.815 | 0.0803860 | ||||||||
\(265\) | −1143.52 | −0.265078 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7383.45 | −1.69236 | ||||||||
\(268\) | 5619.21 | 1.28077 | ||||||||
\(269\) | 1918.70 | 0.434888 | 0.217444 | − | 0.976073i | \(-0.430228\pi\) | ||||
0.217444 | + | 0.976073i | \(0.430228\pi\) | |||||||
\(270\) | −3274.60 | −0.738095 | ||||||||
\(271\) | −1428.96 | −0.320308 | −0.160154 | − | 0.987092i | \(-0.551199\pi\) | ||||
−0.160154 | + | 0.987092i | \(0.551199\pi\) | |||||||
\(272\) | 9212.67 | 2.05368 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9708.19 | −2.14049 | ||||||||
\(275\) | −22.2174 | −0.00487185 | ||||||||
\(276\) | −16776.0 | −3.65868 | ||||||||
\(277\) | −6269.22 | −1.35986 | −0.679930 | − | 0.733277i | \(-0.737990\pi\) | ||||
−0.679930 | + | 0.733277i | \(0.737990\pi\) | |||||||
\(278\) | 13055.4 | 2.81658 | ||||||||
\(279\) | 550.612 | 0.118152 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 486.921 | 0.103371 | 0.0516856 | − | 0.998663i | \(-0.483541\pi\) | ||||
0.0516856 | + | 0.998663i | \(0.483541\pi\) | |||||||
\(282\) | −9236.44 | −1.95043 | ||||||||
\(283\) | −6054.15 | −1.27167 | −0.635834 | − | 0.771826i | \(-0.719344\pi\) | ||||
−0.635834 | + | 0.771826i | \(0.719344\pi\) | |||||||
\(284\) | −10074.1 | −2.10488 | ||||||||
\(285\) | 3716.27 | 0.772396 | ||||||||
\(286\) | 115.924 | 0.0239676 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4632.17 | −0.947753 | ||||||||
\(289\) | 4362.62 | 0.887976 | ||||||||
\(290\) | 5594.74 | 1.13288 | ||||||||
\(291\) | −518.563 | −0.104463 | ||||||||
\(292\) | 16397.0 | 3.28616 | ||||||||
\(293\) | 2506.54 | 0.499773 | 0.249887 | − | 0.968275i | \(-0.419607\pi\) | ||||
0.249887 | + | 0.968275i | \(0.419607\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −67.6963 | −0.0133608 | ||||||||
\(296\) | −4243.65 | −0.833301 | ||||||||
\(297\) | −115.819 | −0.0226279 | ||||||||
\(298\) | 14691.7 | 2.85593 | ||||||||
\(299\) | −3024.86 | −0.585057 | ||||||||
\(300\) | 3599.01 | 0.692630 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1335.29 | −0.254428 | ||||||||
\(303\) | 4695.34 | 0.890232 | ||||||||
\(304\) | 8520.92 | 1.60759 | ||||||||
\(305\) | −1029.73 | −0.193318 | ||||||||
\(306\) | −20627.1 | −3.85351 | ||||||||
\(307\) | 5201.02 | 0.966898 | 0.483449 | − | 0.875372i | \(-0.339384\pi\) | ||||
0.483449 | + | 0.875372i | \(0.339384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3479.70 | 0.640625 | ||||||||
\(310\) | −324.616 | −0.0594741 | ||||||||
\(311\) | 3263.68 | 0.595069 | 0.297534 | − | 0.954711i | \(-0.403836\pi\) | ||||
0.297534 | + | 0.954711i | \(0.403836\pi\) | |||||||
\(312\) | −10071.5 | −1.82752 | ||||||||
\(313\) | 3986.24 | 0.719857 | 0.359929 | − | 0.932980i | \(-0.382801\pi\) | ||||
0.359929 | + | 0.932980i | \(0.382801\pi\) | |||||||
\(314\) | 8786.46 | 1.57914 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7789.72 | 1.38673 | ||||||||
\(317\) | −6429.56 | −1.13918 | −0.569590 | − | 0.821929i | \(-0.692898\pi\) | ||||
−0.569590 | + | 0.821929i | \(0.692898\pi\) | |||||||
\(318\) | 9589.55 | 1.69105 | ||||||||
\(319\) | 197.880 | 0.0347308 | ||||||||
\(320\) | −1095.33 | −0.191347 | ||||||||
\(321\) | 16515.7 | 2.87170 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8579.15 | 1.47788 | ||||||||
\(324\) | −1092.42 | −0.187315 | ||||||||
\(325\) | 648.934 | 0.110758 | ||||||||
\(326\) | 16388.5 | 2.78427 | ||||||||
\(327\) | 11751.4 | 1.98733 | ||||||||
\(328\) | −4577.64 | −0.770604 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 186.315 | 0.0310798 | ||||||||
\(331\) | −5773.29 | −0.958696 | −0.479348 | − | 0.877625i | \(-0.659127\pi\) | ||||
−0.479348 | + | 0.877625i | \(0.659127\pi\) | |||||||
\(332\) | −2845.59 | −0.470398 | ||||||||
\(333\) | 3889.35 | 0.640045 | ||||||||
\(334\) | 6253.09 | 1.02441 | ||||||||
\(335\) | 1628.42 | 0.265582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10674.0 | −1.72536 | −0.862681 | − | 0.505748i | \(-0.831217\pi\) | ||||
−0.862681 | + | 0.505748i | \(0.831217\pi\) | |||||||
\(338\) | 7654.60 | 1.23182 | ||||||||
\(339\) | −7096.15 | −1.13690 | ||||||||
\(340\) | 8308.45 | 1.32526 | ||||||||
\(341\) | −11.4813 | −0.00182331 | ||||||||
\(342\) | −19078.3 | −3.01648 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18230.1 | −2.85728 | ||||||||
\(345\) | −4861.60 | −0.758666 | ||||||||
\(346\) | 19097.8 | 2.96736 | ||||||||
\(347\) | 8501.97 | 1.31530 | 0.657651 | − | 0.753323i | \(-0.271550\pi\) | ||||
0.657651 | + | 0.753323i | \(0.271550\pi\) | |||||||
\(348\) | −32054.7 | −4.93768 | ||||||||
\(349\) | −4158.79 | −0.637865 | −0.318933 | − | 0.947777i | \(-0.603324\pi\) | ||||
−0.318933 | + | 0.947777i | \(0.603324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3382.89 | 0.514430 | ||||||||
\(352\) | 96.5896 | 0.0146257 | ||||||||
\(353\) | 5043.63 | 0.760469 | 0.380234 | − | 0.924890i | \(-0.375843\pi\) | ||||
0.380234 | + | 0.924890i | \(0.375843\pi\) | |||||||
\(354\) | 567.703 | 0.0852346 | ||||||||
\(355\) | −2919.42 | −0.436469 | ||||||||
\(356\) | −15267.7 | −2.27299 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8551.17 | −1.26241 | ||||||||
\(359\) | 9501.30 | 1.39682 | 0.698412 | − | 0.715696i | \(-0.253890\pi\) | ||||
0.698412 | + | 0.715696i | \(0.253890\pi\) | |||||||
\(360\) | −9909.36 | −1.45075 | ||||||||
\(361\) | 1075.97 | 0.156870 | ||||||||
\(362\) | −11894.1 | −1.72690 | ||||||||
\(363\) | −11099.0 | −1.60482 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4751.77 | 0.681421 | ||||||||
\(366\) | 8635.33 | 1.23327 | ||||||||
\(367\) | 6606.52 | 0.939666 | 0.469833 | − | 0.882755i | \(-0.344314\pi\) | ||||
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(368\) | −11147.0 | −1.57902 | ||||||||
\(369\) | 4195.46 | 0.591888 | ||||||||
\(370\) | −2292.99 | −0.322180 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1859.87 | 0.259220 | ||||||||
\(373\) | −8719.88 | −1.21045 | −0.605226 | − | 0.796054i | \(-0.706917\pi\) | ||||
−0.605226 | + | 0.796054i | \(0.706917\pi\) | |||||||
\(374\) | 430.116 | 0.0594673 | ||||||||
\(375\) | 1042.98 | 0.143624 | ||||||||
\(376\) | −10243.5 | −1.40497 | ||||||||
\(377\) | −5779.75 | −0.789582 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11457.2 | 1.55281 | 0.776405 | − | 0.630235i | \(-0.217041\pi\) | ||||
0.776405 | + | 0.630235i | \(0.217041\pi\) | |||||||
\(380\) | 7684.59 | 1.03740 | ||||||||
\(381\) | 7386.63 | 0.993251 | ||||||||
\(382\) | 11208.8 | 1.50129 | ||||||||
\(383\) | 4797.61 | 0.640069 | 0.320034 | − | 0.947406i | \(-0.396306\pi\) | ||||
0.320034 | + | 0.947406i | \(0.396306\pi\) | |||||||
\(384\) | 16440.4 | 2.18482 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1184.40 | 0.156178 | ||||||||
\(387\) | 16708.1 | 2.19463 | ||||||||
\(388\) | −1072.30 | −0.140303 | ||||||||
\(389\) | 390.521 | 0.0509003 | 0.0254501 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254501 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(390\) | −5441.98 | −0.706577 | ||||||||
\(391\) | −11223.2 | −1.45161 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15078.1 | −1.93534 | ||||||||
\(394\) | −16242.6 | −2.07688 | ||||||||
\(395\) | 2257.43 | 0.287553 | ||||||||
\(396\) | −653.487 | −0.0829267 | ||||||||
\(397\) | −15361.7 | −1.94202 | −0.971009 | − | 0.239041i | \(-0.923167\pi\) | ||||
−0.971009 | + | 0.239041i | \(0.923167\pi\) | |||||||
\(398\) | 19057.3 | 2.40015 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2391.41 | 0.298926 | ||||||||
\(401\) | 7181.72 | 0.894359 | 0.447180 | − | 0.894444i | \(-0.352428\pi\) | ||||
0.447180 | + | 0.894444i | \(0.352428\pi\) | |||||||
\(402\) | −13656.0 | −1.69427 | ||||||||
\(403\) | 335.351 | 0.0414517 | ||||||||
\(404\) | 9709.14 | 1.19566 | ||||||||
\(405\) | −316.579 | −0.0388418 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −81.1004 | −0.00987714 | ||||||||
\(408\) | −37368.5 | −4.53435 | ||||||||
\(409\) | −2177.35 | −0.263235 | −0.131617 | − | 0.991301i | \(-0.542017\pi\) | ||||
−0.131617 | + | 0.991301i | \(0.542017\pi\) | |||||||
\(410\) | −2473.46 | −0.297940 | ||||||||
\(411\) | 16119.1 | 1.93455 | ||||||||
\(412\) | 7195.40 | 0.860417 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 24958.1 | 2.96286 | ||||||||
\(415\) | −824.641 | −0.0975422 | ||||||||
\(416\) | −2821.23 | −0.332505 | ||||||||
\(417\) | −21676.7 | −2.54559 | ||||||||
\(418\) | 397.820 | 0.0465503 | ||||||||
\(419\) | −6832.55 | −0.796639 | −0.398320 | − | 0.917247i | \(-0.630407\pi\) | ||||
−0.398320 | + | 0.917247i | \(0.630407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2198.26 | 0.254482 | 0.127241 | − | 0.991872i | \(-0.459388\pi\) | ||||
0.127241 | + | 0.991872i | \(0.459388\pi\) | |||||||
\(422\) | −3659.44 | −0.422130 | ||||||||
\(423\) | 9388.25 | 1.07913 | ||||||||
\(424\) | 10635.1 | 1.21813 | ||||||||
\(425\) | 2407.75 | 0.274807 | ||||||||
\(426\) | 24482.3 | 2.78444 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 34151.5 | 3.85696 | ||||||||
\(429\) | −192.477 | −0.0216617 | ||||||||
\(430\) | −9850.36 | −1.10471 | ||||||||
\(431\) | 12854.6 | 1.43663 | 0.718313 | − | 0.695720i | \(-0.244915\pi\) | ||||
0.718313 | + | 0.695720i | \(0.244915\pi\) | |||||||
\(432\) | 12466.4 | 1.38840 | ||||||||
\(433\) | 4590.69 | 0.509502 | 0.254751 | − | 0.967007i | \(-0.418007\pi\) | ||||
0.254751 | + | 0.967007i | \(0.418007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9289.31 | −1.02388 | ||||||||
\(436\) | 24299.9 | 2.66916 | ||||||||
\(437\) | −10380.5 | −1.13631 | ||||||||
\(438\) | −39848.4 | −4.34710 | ||||||||
\(439\) | −2598.82 | −0.282540 | −0.141270 | − | 0.989971i | \(-0.545119\pi\) | ||||
−0.141270 | + | 0.989971i | \(0.545119\pi\) | |||||||
\(440\) | 206.629 | 0.0223879 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12563.0 | −1.35195 | ||||||||
\(443\) | 1708.96 | 0.183285 | 0.0916426 | − | 0.995792i | \(-0.470788\pi\) | ||||
0.0916426 | + | 0.995792i | \(0.470788\pi\) | |||||||
\(444\) | 13137.5 | 1.40423 | ||||||||
\(445\) | −4424.50 | −0.471329 | ||||||||
\(446\) | 20074.8 | 2.13132 | ||||||||
\(447\) | −24393.6 | −2.58115 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1428.21 | −0.150115 | −0.0750573 | − | 0.997179i | \(-0.523914\pi\) | ||||
−0.0750573 | + | 0.997179i | \(0.523914\pi\) | |||||||
\(450\) | −5354.36 | −0.560904 | ||||||||
\(451\) | −87.4834 | −0.00913399 | ||||||||
\(452\) | −14673.6 | −1.52696 | ||||||||
\(453\) | 2217.07 | 0.229949 | ||||||||
\(454\) | 2338.34 | 0.241727 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −34562.6 | −3.54944 | ||||||||
\(457\) | 13802.7 | 1.41283 | 0.706417 | − | 0.707796i | \(-0.250310\pi\) | ||||
0.706417 | + | 0.707796i | \(0.250310\pi\) | |||||||
\(458\) | −25582.5 | −2.61003 | ||||||||
\(459\) | 12551.6 | 1.27638 | ||||||||
\(460\) | −10052.9 | −1.01896 | ||||||||
\(461\) | −9698.29 | −0.979815 | −0.489907 | − | 0.871775i | \(-0.662969\pi\) | ||||
−0.489907 | + | 0.871775i | \(0.662969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2757.52 | 0.276788 | 0.138394 | − | 0.990377i | \(-0.455806\pi\) | ||||
0.138394 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(464\) | −21299.2 | −2.13101 | ||||||||
\(465\) | 538.982 | 0.0537520 | ||||||||
\(466\) | 8338.24 | 0.828887 | ||||||||
\(467\) | 5292.92 | 0.524469 | 0.262235 | − | 0.965004i | \(-0.415541\pi\) | ||||
0.262235 | + | 0.965004i | \(0.415541\pi\) | |||||||
\(468\) | 19087.3 | 1.88528 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5534.90 | −0.543204 | ||||||||
\(471\) | −14588.7 | −1.42720 | ||||||||
\(472\) | 629.599 | 0.0613975 | ||||||||
\(473\) | −348.396 | −0.0338674 | ||||||||
\(474\) | −18930.8 | −1.83443 | ||||||||
\(475\) | 2226.96 | 0.215116 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9747.18 | −0.935624 | ||||||||
\(478\) | 6535.52 | 0.625371 | ||||||||
\(479\) | −9319.53 | −0.888977 | −0.444489 | − | 0.895784i | \(-0.646615\pi\) | ||||
−0.444489 | + | 0.895784i | \(0.646615\pi\) | |||||||
\(480\) | −4534.32 | −0.431172 | ||||||||
\(481\) | 2368.81 | 0.224550 | ||||||||
\(482\) | 4502.67 | 0.425500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22950.8 | −2.15541 | ||||||||
\(485\) | −310.747 | −0.0290934 | ||||||||
\(486\) | 20337.7 | 1.89822 | ||||||||
\(487\) | −3499.65 | −0.325635 | −0.162818 | − | 0.986656i | \(-0.552058\pi\) | ||||
−0.162818 | + | 0.986656i | \(0.552058\pi\) | |||||||
\(488\) | 9576.83 | 0.888367 | ||||||||
\(489\) | −27210.8 | −2.51639 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −54.5901 | −0.00501755 | −0.00250877 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250877 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(492\) | 14171.5 | 1.29858 | ||||||||
\(493\) | −21444.7 | −1.95907 | ||||||||
\(494\) | −11619.7 | −1.05829 | ||||||||
\(495\) | −189.378 | −0.0171958 | ||||||||
\(496\) | 1235.81 | 0.111874 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6915.45 | 0.622267 | ||||||||
\(499\) | −7930.98 | −0.711502 | −0.355751 | − | 0.934581i | \(-0.615775\pi\) | ||||
−0.355751 | + | 0.934581i | \(0.615775\pi\) | |||||||
\(500\) | 2156.69 | 0.192900 | ||||||||
\(501\) | −10382.4 | −0.925852 | ||||||||
\(502\) | 1924.84 | 0.171135 | ||||||||
\(503\) | 21662.2 | 1.92022 | 0.960109 | − | 0.279625i | \(-0.0902103\pi\) | ||||
0.960109 | + | 0.279625i | \(0.0902103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2813.66 | 0.247934 | ||||||||
\(506\) | −520.425 | −0.0457228 | ||||||||
\(507\) | −12709.4 | −1.11331 | ||||||||
\(508\) | 15274.2 | 1.33403 | ||||||||
\(509\) | −6913.22 | −0.602010 | −0.301005 | − | 0.953623i | \(-0.597322\pi\) | ||||
−0.301005 | + | 0.953623i | \(0.597322\pi\) | |||||||
\(510\) | −20191.5 | −1.75312 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25188.9 | 2.17422 | ||||||||
\(513\) | 11609.1 | 0.999133 | ||||||||
\(514\) | 36804.6 | 3.15833 | ||||||||
\(515\) | 2085.19 | 0.178417 | ||||||||
\(516\) | 56437.0 | 4.81493 | ||||||||
\(517\) | −195.763 | −0.0166531 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31709.4 | −2.68186 | ||||||||
\(520\) | −6035.31 | −0.508973 | ||||||||
\(521\) | −2680.16 | −0.225374 | −0.112687 | − | 0.993631i | \(-0.535946\pi\) | ||||
−0.112687 | + | 0.993631i | \(0.535946\pi\) | |||||||
\(522\) | 47688.8 | 3.99862 | ||||||||
\(523\) | −835.518 | −0.0698559 | −0.0349280 | − | 0.999390i | \(-0.511120\pi\) | ||||
−0.0349280 | + | 0.999390i | \(0.511120\pi\) | |||||||
\(524\) | −31178.8 | −2.59933 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33985.5 | 2.81718 | ||||||||
\(527\) | 1244.26 | 0.102848 | ||||||||
\(528\) | −709.302 | −0.0584629 | ||||||||
\(529\) | 1412.67 | 0.116106 | ||||||||
\(530\) | 5746.50 | 0.470966 | ||||||||
\(531\) | −577.034 | −0.0471585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2555.25 | 0.207655 | ||||||||
\(534\) | 37104.0 | 3.00683 | ||||||||
\(535\) | 9896.97 | 0.799782 | ||||||||
\(536\) | −15144.9 | −1.22045 | ||||||||
\(537\) | 14198.1 | 1.14095 | ||||||||
\(538\) | −9642.00 | −0.772669 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11242.8 | 0.895951 | ||||||||
\(541\) | 10319.5 | 0.820090 | 0.410045 | − | 0.912065i | \(-0.365513\pi\) | ||||
0.410045 | + | 0.912065i | \(0.365513\pi\) | |||||||
\(542\) | 7180.96 | 0.569093 | ||||||||
\(543\) | 19748.5 | 1.56075 | ||||||||
\(544\) | −10467.7 | −0.824994 | ||||||||
\(545\) | 7042.00 | 0.553479 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12465.4 | 0.974373 | 0.487186 | − | 0.873298i | \(-0.338023\pi\) | ||||
0.487186 | + | 0.873298i | \(0.338023\pi\) | |||||||
\(548\) | 33331.5 | 2.59827 | ||||||||
\(549\) | −8777.27 | −0.682340 | ||||||||
\(550\) | 111.649 | 0.00865585 | ||||||||
\(551\) | −19834.5 | −1.53354 | ||||||||
\(552\) | 45214.6 | 3.48634 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 31504.7 | 2.41607 | ||||||||
\(555\) | 3807.19 | 0.291183 | ||||||||
\(556\) | −44823.6 | −3.41896 | ||||||||
\(557\) | −8750.27 | −0.665639 | −0.332819 | − | 0.942991i | \(-0.608000\pi\) | ||||
−0.332819 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(558\) | −2766.98 | −0.209921 | ||||||||
\(559\) | 10176.1 | 0.769952 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −714.149 | −0.0537458 | ||||||||
\(562\) | −2446.92 | −0.183660 | ||||||||
\(563\) | 12033.1 | 0.900774 | 0.450387 | − | 0.892833i | \(-0.351286\pi\) | ||||
0.450387 | + | 0.892833i | \(0.351286\pi\) | |||||||
\(564\) | 31711.8 | 2.36757 | ||||||||
\(565\) | −4252.34 | −0.316632 | ||||||||
\(566\) | 30423.9 | 2.25938 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27151.6 | 2.00573 | ||||||||
\(569\) | −12824.3 | −0.944856 | −0.472428 | − | 0.881369i | \(-0.656622\pi\) | ||||
−0.472428 | + | 0.881369i | \(0.656622\pi\) | |||||||
\(570\) | −18675.3 | −1.37232 | ||||||||
\(571\) | −21514.0 | −1.57676 | −0.788382 | − | 0.615186i | \(-0.789081\pi\) | ||||
−0.788382 | + | 0.615186i | \(0.789081\pi\) | |||||||
\(572\) | −398.008 | −0.0290936 | ||||||||
\(573\) | −18610.7 | −1.35685 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2913.30 | −0.211292 | ||||||||
\(576\) | −9336.48 | −0.675382 | ||||||||
\(577\) | 9538.51 | 0.688203 | 0.344102 | − | 0.938932i | \(-0.388184\pi\) | ||||
0.344102 | + | 0.938932i | \(0.388184\pi\) | |||||||
\(578\) | −21923.5 | −1.57767 | ||||||||
\(579\) | −1966.54 | −0.141152 | ||||||||
\(580\) | −19208.6 | −1.37517 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2605.93 | 0.185600 | ||||||||
\(583\) | 203.247 | 0.0144385 | ||||||||
\(584\) | −44193.1 | −3.13137 | ||||||||
\(585\) | 5531.42 | 0.390934 | ||||||||
\(586\) | −12596.1 | −0.887952 | ||||||||
\(587\) | 25729.6 | 1.80916 | 0.904579 | − | 0.426306i | \(-0.140185\pi\) | ||||
0.904579 | + | 0.426306i | \(0.140185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1150.83 | 0.0805080 | ||||||||
\(590\) | 340.194 | 0.0237382 | ||||||||
\(591\) | 26968.6 | 1.87706 | ||||||||
\(592\) | 8729.39 | 0.606040 | ||||||||
\(593\) | −15379.9 | −1.06505 | −0.532526 | − | 0.846414i | \(-0.678757\pi\) | ||||
−0.532526 | + | 0.846414i | \(0.678757\pi\) | |||||||
\(594\) | 582.023 | 0.0402032 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −50441.6 | −3.46672 | ||||||||
\(597\) | −31642.2 | −2.16923 | ||||||||
\(598\) | 15200.8 | 1.03948 | ||||||||
\(599\) | 12267.5 | 0.836791 | 0.418395 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418395 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(600\) | −9700.05 | −0.660005 | ||||||||
\(601\) | 17025.4 | 1.15554 | 0.577770 | − | 0.816200i | \(-0.303923\pi\) | ||||
0.577770 | + | 0.816200i | \(0.303923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13880.4 | 0.937405 | ||||||||
\(604\) | 4584.50 | 0.308842 | ||||||||
\(605\) | −6651.05 | −0.446948 | ||||||||
\(606\) | −23595.5 | −1.58168 | ||||||||
\(607\) | 25674.7 | 1.71681 | 0.858407 | − | 0.512970i | \(-0.171455\pi\) | ||||
0.858407 | + | 0.512970i | \(0.171455\pi\) | |||||||
\(608\) | −9681.67 | −0.645796 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5174.69 | 0.343470 | ||||||||
\(611\) | 5717.93 | 0.378597 | ||||||||
\(612\) | 70820.0 | 4.67766 | ||||||||
\(613\) | −12436.0 | −0.819389 | −0.409695 | − | 0.912223i | \(-0.634365\pi\) | ||||
−0.409695 | + | 0.912223i | \(0.634365\pi\) | |||||||
\(614\) | −26136.6 | −1.71790 | ||||||||
\(615\) | 4106.84 | 0.269274 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9794.06 | 0.639050 | 0.319525 | − | 0.947578i | \(-0.396477\pi\) | ||||
0.319525 | + | 0.947578i | \(0.396477\pi\) | |||||||
\(618\) | −17486.5 | −1.13820 | ||||||||
\(619\) | 18198.0 | 1.18164 | 0.590822 | − | 0.806802i | \(-0.298803\pi\) | ||||
0.590822 | + | 0.806802i | \(0.298803\pi\) | |||||||
\(620\) | 1114.52 | 0.0721938 | ||||||||
\(621\) | −15187.0 | −0.981372 | ||||||||
\(622\) | −16401.0 | −1.05726 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 20717.6 | 1.32911 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −20032.0 | −1.27898 | ||||||||
\(627\) | −660.526 | −0.0420716 | ||||||||
\(628\) | −30166.9 | −1.91686 | ||||||||
\(629\) | 8789.05 | 0.557142 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 92.7119 | 0.00584914 | 0.00292457 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292457 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(632\) | −20994.8 | −1.32141 | ||||||||
\(633\) | 6076.02 | 0.381516 | ||||||||
\(634\) | 32310.4 | 2.02399 | ||||||||
\(635\) | 4426.41 | 0.276625 | ||||||||
\(636\) | −32924.2 | −2.05272 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −994.403 | −0.0617066 | ||||||||
\(639\) | −24884.7 | −1.54057 | ||||||||
\(640\) | 9851.85 | 0.608482 | ||||||||
\(641\) | 12888.6 | 0.794179 | 0.397090 | − | 0.917780i | \(-0.370020\pi\) | ||||
0.397090 | + | 0.917780i | \(0.370020\pi\) | |||||||
\(642\) | −82996.2 | −5.10218 | ||||||||
\(643\) | −24478.5 | −1.50130 | −0.750651 | − | 0.660699i | \(-0.770260\pi\) | ||||
−0.750651 | + | 0.660699i | \(0.770260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16355.2 | 0.998427 | ||||||||
\(646\) | −43112.7 | −2.62577 | ||||||||
\(647\) | −6675.03 | −0.405599 | −0.202799 | − | 0.979220i | \(-0.565004\pi\) | ||||
−0.202799 | + | 0.979220i | \(0.565004\pi\) | |||||||
\(648\) | 2944.29 | 0.178492 | ||||||||
\(649\) | 12.0323 | 0.000727747 0 | ||||||||
\(650\) | −3261.08 | −0.196785 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56267.2 | −3.37974 | ||||||||
\(653\) | 2382.08 | 0.142753 | 0.0713767 | − | 0.997449i | \(-0.477261\pi\) | ||||
0.0713767 | + | 0.997449i | \(0.477261\pi\) | |||||||
\(654\) | −59054.3 | −3.53090 | ||||||||
\(655\) | −9035.47 | −0.539000 | ||||||||
\(656\) | 9416.44 | 0.560442 | ||||||||
\(657\) | 40503.4 | 2.40516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −384.150 | −0.0227077 | −0.0113538 | − | 0.999936i | \(-0.503614\pi\) | ||||
−0.0113538 | + | 0.999936i | \(0.503614\pi\) | |||||||
\(660\) | −639.684 | −0.0377268 | ||||||||
\(661\) | −29320.5 | −1.72532 | −0.862660 | − | 0.505784i | \(-0.831203\pi\) | ||||
−0.862660 | + | 0.505784i | \(0.831203\pi\) | |||||||
\(662\) | 29012.4 | 1.70332 | ||||||||
\(663\) | 20859.2 | 1.22187 | ||||||||
\(664\) | 7669.44 | 0.448241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19545.1 | −1.13717 | ||||||||
\(667\) | 25947.4 | 1.50628 | ||||||||
\(668\) | −21469.0 | −1.24350 | ||||||||
\(669\) | −33331.5 | −1.92626 | ||||||||
\(670\) | −8183.29 | −0.471863 | ||||||||
\(671\) | 183.023 | 0.0105298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24841.9 | −1.42286 | −0.711431 | − | 0.702756i | \(-0.751952\pi\) | ||||
−0.711431 | + | 0.702756i | \(0.751952\pi\) | |||||||
\(674\) | 53639.7 | 3.06547 | ||||||||
\(675\) | 3258.12 | 0.185785 | ||||||||
\(676\) | −26280.9 | −1.49527 | ||||||||
\(677\) | 483.632 | 0.0274556 | 0.0137278 | − | 0.999906i | \(-0.495630\pi\) | ||||
0.0137278 | + | 0.999906i | \(0.495630\pi\) | |||||||
\(678\) | 35660.2 | 2.01994 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22392.9 | −1.26284 | ||||||||
\(681\) | −3882.50 | −0.218470 | ||||||||
\(682\) | 57.6970 | 0.00323949 | ||||||||
\(683\) | −6436.97 | −0.360620 | −0.180310 | − | 0.983610i | \(-0.557710\pi\) | ||||
−0.180310 | + | 0.983610i | \(0.557710\pi\) | |||||||
\(684\) | 65502.4 | 3.66162 | ||||||||
\(685\) | 9659.33 | 0.538780 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42476.3 | 2.35891 | ||||||||
\(688\) | 37500.3 | 2.07803 | ||||||||
\(689\) | −5936.53 | −0.328250 | ||||||||
\(690\) | 24431.0 | 1.34793 | ||||||||
\(691\) | 17783.5 | 0.979042 | 0.489521 | − | 0.871992i | \(-0.337172\pi\) | ||||
0.489521 | + | 0.871992i | \(0.337172\pi\) | |||||||
\(692\) | −65569.4 | −3.60198 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42724.9 | −2.33691 | ||||||||
\(695\) | −12989.7 | −0.708959 | ||||||||
\(696\) | 86393.8 | 4.70510 | ||||||||
\(697\) | 9480.79 | 0.515223 | ||||||||
\(698\) | 20899.1 | 1.13330 | ||||||||
\(699\) | −13844.5 | −0.749139 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23546.2 | 1.26866 | 0.634328 | − | 0.773064i | \(-0.281277\pi\) | ||||
0.634328 | + | 0.773064i | \(0.281277\pi\) | |||||||
\(702\) | −17000.0 | −0.913993 | ||||||||
\(703\) | 8129.11 | 0.436124 | ||||||||
\(704\) | 194.684 | 0.0104225 | ||||||||
\(705\) | 9189.95 | 0.490941 | ||||||||
\(706\) | −25345.7 | −1.35113 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1949.12 | −0.103464 | ||||||||
\(709\) | −23563.8 | −1.24818 | −0.624088 | − | 0.781354i | \(-0.714529\pi\) | ||||
−0.624088 | + | 0.781354i | \(0.714529\pi\) | |||||||
\(710\) | 14670.9 | 0.775478 | ||||||||
\(711\) | 19242.0 | 1.01495 | ||||||||
\(712\) | 41149.4 | 2.16593 | ||||||||
\(713\) | −1505.51 | −0.0790769 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −115.341 | −0.00603287 | ||||||||
\(716\) | 29359.1 | 1.53240 | ||||||||
\(717\) | −10851.3 | −0.565204 | ||||||||
\(718\) | −47746.8 | −2.48175 | ||||||||
\(719\) | −25106.5 | −1.30224 | −0.651122 | − | 0.758973i | \(-0.725701\pi\) | ||||
−0.651122 | + | 0.758973i | \(0.725701\pi\) | |||||||
\(720\) | 20384.0 | 1.05509 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5407.07 | −0.278712 | ||||||||
\(723\) | −7476.07 | −0.384562 | ||||||||
\(724\) | 40836.4 | 2.09623 | ||||||||
\(725\) | −5566.58 | −0.285155 | ||||||||
\(726\) | 55775.9 | 2.85129 | ||||||||
\(727\) | 20502.4 | 1.04593 | 0.522965 | − | 0.852354i | \(-0.324826\pi\) | ||||
0.522965 | + | 0.852354i | \(0.324826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32058.4 | −1.62874 | ||||||||
\(730\) | −23879.0 | −1.21069 | ||||||||
\(731\) | 37756.6 | 1.91037 | ||||||||
\(732\) | −29648.0 | −1.49703 | ||||||||
\(733\) | −9984.38 | −0.503112 | −0.251556 | − | 0.967843i | \(-0.580942\pi\) | ||||
−0.251556 | + | 0.967843i | \(0.580942\pi\) | |||||||
\(734\) | −33199.7 | −1.66951 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12665.5 | 0.634316 | ||||||||
\(737\) | −289.434 | −0.0144660 | ||||||||
\(738\) | −21083.4 | −1.05161 | ||||||||
\(739\) | −20692.0 | −1.03000 | −0.514999 | − | 0.857191i | \(-0.672208\pi\) | ||||
−0.514999 | + | 0.857191i | \(0.672208\pi\) | |||||||
\(740\) | 7872.61 | 0.391085 | ||||||||
\(741\) | 19292.9 | 0.956469 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4015.42 | 0.198266 | 0.0991330 | − | 0.995074i | \(-0.468393\pi\) | ||||
0.0991330 | + | 0.995074i | \(0.468393\pi\) | |||||||
\(744\) | −5012.72 | −0.247010 | ||||||||
\(745\) | −14617.7 | −0.718863 | ||||||||
\(746\) | 43819.9 | 2.15062 | ||||||||
\(747\) | −7029.12 | −0.344287 | ||||||||
\(748\) | −1476.73 | −0.0721855 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5241.26 | −0.255179 | ||||||||
\(751\) | 19406.6 | 0.942950 | 0.471475 | − | 0.881879i | \(-0.343722\pi\) | ||||
0.471475 | + | 0.881879i | \(0.343722\pi\) | |||||||
\(752\) | 21071.3 | 1.02180 | ||||||||
\(753\) | −3195.94 | −0.154670 | ||||||||
\(754\) | 29044.9 | 1.40286 | ||||||||
\(755\) | 1328.57 | 0.0640418 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14626.8 | −0.702274 | −0.351137 | − | 0.936324i | \(-0.614205\pi\) | ||||
−0.351137 | + | 0.936324i | \(0.614205\pi\) | |||||||
\(758\) | −57575.6 | −2.75889 | ||||||||
\(759\) | 864.096 | 0.0413237 | ||||||||
\(760\) | −20711.5 | −0.988533 | ||||||||
\(761\) | 22296.4 | 1.06208 | 0.531040 | − | 0.847347i | \(-0.321801\pi\) | ||||
0.531040 | + | 0.847347i | \(0.321801\pi\) | |||||||
\(762\) | −37120.0 | −1.76472 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −38483.6 | −1.82237 | ||||||||
\(765\) | 20523.3 | 0.969964 | ||||||||
\(766\) | −24109.4 | −1.13722 | ||||||||
\(767\) | −351.443 | −0.0165448 | ||||||||
\(768\) | −67995.0 | −3.19474 | ||||||||
\(769\) | 8658.29 | 0.406015 | 0.203008 | − | 0.979177i | \(-0.434928\pi\) | ||||
0.203008 | + | 0.979177i | \(0.434928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −61109.1 | −2.85446 | ||||||||
\(772\) | −4066.46 | −0.189579 | ||||||||
\(773\) | −4583.16 | −0.213253 | −0.106627 | − | 0.994299i | \(-0.534005\pi\) | ||||
−0.106627 | + | 0.994299i | \(0.534005\pi\) | |||||||
\(774\) | −83963.1 | −3.89921 | ||||||||
\(775\) | 322.983 | 0.0149702 | ||||||||
\(776\) | 2890.05 | 0.133694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1962.48 | −0.0904350 | ||||||||
\(779\) | 8768.91 | 0.403310 | ||||||||
\(780\) | 18684.2 | 0.857693 | ||||||||
\(781\) | 518.894 | 0.0237740 | ||||||||
\(782\) | 56399.8 | 2.57909 | ||||||||
\(783\) | −29018.5 | −1.32444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8742.24 | −0.397483 | ||||||||
\(786\) | 75771.6 | 3.43853 | ||||||||
\(787\) | −21374.1 | −0.968111 | −0.484055 | − | 0.875037i | \(-0.660837\pi\) | ||||
−0.484055 | + | 0.875037i | \(0.660837\pi\) | |||||||
\(788\) | 55766.3 | 2.52106 | ||||||||
\(789\) | −56428.4 | −2.54614 | ||||||||
\(790\) | −11344.2 | −0.510898 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1761.28 | 0.0790206 | ||||||||
\(793\) | −5345.81 | −0.239389 | ||||||||
\(794\) | 77197.0 | 3.45040 | ||||||||
\(795\) | −9541.29 | −0.425654 | ||||||||
\(796\) | −65430.4 | −2.91347 | ||||||||
\(797\) | −13930.6 | −0.619131 | −0.309565 | − | 0.950878i | \(-0.600184\pi\) | ||||
−0.309565 | + | 0.950878i | \(0.600184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21215.3 | 0.939355 | ||||||||
\(800\) | −2717.18 | −0.120083 | ||||||||
\(801\) | −37713.9 | −1.66361 | ||||||||
\(802\) | −36090.2 | −1.58902 | ||||||||
\(803\) | −844.574 | −0.0371163 | ||||||||
\(804\) | 46885.6 | 2.05663 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1685.24 | −0.0736476 | ||||||||
\(807\) | 16009.2 | 0.698330 | ||||||||
\(808\) | −26168.1 | −1.13934 | ||||||||
\(809\) | 23831.6 | 1.03569 | 0.517845 | − | 0.855475i | \(-0.326734\pi\) | ||||
0.517845 | + | 0.855475i | \(0.326734\pi\) | |||||||
\(810\) | 1590.90 | 0.0690106 | ||||||||
\(811\) | −14512.4 | −0.628358 | −0.314179 | − | 0.949364i | \(-0.601729\pi\) | ||||
−0.314179 | + | 0.949364i | \(0.601729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11923.0 | −0.514340 | ||||||||
\(814\) | 407.553 | 0.0175488 | ||||||||
\(815\) | −16306.0 | −0.700827 | ||||||||
\(816\) | 76868.8 | 3.29773 | ||||||||
\(817\) | 34921.6 | 1.49541 | ||||||||
\(818\) | 10941.8 | 0.467692 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8492.22 | 0.361660 | ||||||||
\(821\) | −395.767 | −0.0168238 | −0.00841191 | − | 0.999965i | \(-0.502678\pi\) | ||||
−0.00841191 | + | 0.999965i | \(0.502678\pi\) | |||||||
\(822\) | −81003.4 | −3.43712 | ||||||||
\(823\) | 17250.2 | 0.730625 | 0.365312 | − | 0.930885i | \(-0.380962\pi\) | ||||
0.365312 | + | 0.930885i | \(0.380962\pi\) | |||||||
\(824\) | −19393.0 | −0.819888 | ||||||||
\(825\) | −185.378 | −0.00782306 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43760.3 | 1.84002 | 0.920009 | − | 0.391897i | \(-0.128181\pi\) | ||||
0.920009 | + | 0.391897i | \(0.128181\pi\) | |||||||
\(828\) | −85689.8 | −3.59653 | ||||||||
\(829\) | −15250.8 | −0.638939 | −0.319470 | − | 0.947597i | \(-0.603505\pi\) | ||||
−0.319470 | + | 0.947597i | \(0.603505\pi\) | |||||||
\(830\) | 4144.06 | 0.173304 | ||||||||
\(831\) | −52309.3 | −2.18362 | ||||||||
\(832\) | −5686.40 | −0.236948 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 108932. | 4.52278 | ||||||||
\(835\) | −6221.62 | −0.257854 | ||||||||
\(836\) | −1365.85 | −0.0565059 | ||||||||
\(837\) | 1683.70 | 0.0695309 | ||||||||
\(838\) | 34335.5 | 1.41540 | ||||||||
\(839\) | 15948.9 | 0.656276 | 0.328138 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328138 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25189.9 | 1.03284 | ||||||||
\(842\) | −11046.9 | −0.452140 | ||||||||
\(843\) | 4062.78 | 0.165990 | ||||||||
\(844\) | 12564.1 | 0.512411 | ||||||||
\(845\) | −7616.08 | −0.310060 | ||||||||
\(846\) | −47178.7 | −1.91730 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −21876.9 | −0.885916 | ||||||||
\(849\) | −50514.8 | −2.04200 | ||||||||
\(850\) | −12099.6 | −0.488252 | ||||||||
\(851\) | −10634.4 | −0.428371 | ||||||||
\(852\) | −84056.1 | −3.37995 | ||||||||
\(853\) | 18372.1 | 0.737456 | 0.368728 | − | 0.929537i | \(-0.379793\pi\) | ||||
0.368728 | + | 0.929537i | \(0.379793\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18982.3 | 0.759276 | ||||||||
\(856\) | −92045.2 | −3.67528 | ||||||||
\(857\) | 45484.2 | 1.81296 | 0.906482 | − | 0.422244i | \(-0.138758\pi\) | ||||
0.906482 | + | 0.422244i | \(0.138758\pi\) | |||||||
\(858\) | 967.251 | 0.0384865 | ||||||||
\(859\) | 35623.5 | 1.41497 | 0.707485 | − | 0.706728i | \(-0.249830\pi\) | ||||
0.707485 | + | 0.706728i | \(0.249830\pi\) | |||||||
\(860\) | 33819.7 | 1.34098 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −64598.3 | −2.55247 | ||||||||
\(863\) | 7274.95 | 0.286955 | 0.143478 | − | 0.989654i | \(-0.454172\pi\) | ||||
0.143478 | + | 0.989654i | \(0.454172\pi\) | |||||||
\(864\) | −14164.6 | −0.557743 | ||||||||
\(865\) | −19001.7 | −0.746911 | ||||||||
\(866\) | −23069.5 | −0.905236 | ||||||||
\(867\) | 36400.9 | 1.42588 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −401.233 | −0.0156627 | ||||||||
\(870\) | 46681.5 | 1.81914 | ||||||||
\(871\) | 8453.90 | 0.328874 | ||||||||
\(872\) | −65493.0 | −2.54343 | ||||||||
\(873\) | −2648.76 | −0.102688 | ||||||||
\(874\) | 52164.9 | 2.01888 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 136813. | 5.27682 | ||||||||
\(877\) | 20656.4 | 0.795345 | 0.397672 | − | 0.917527i | \(-0.369818\pi\) | ||||
0.397672 | + | 0.917527i | \(0.369818\pi\) | |||||||
\(878\) | 13059.8 | 0.501990 | ||||||||
\(879\) | 20914.1 | 0.802520 | ||||||||
\(880\) | −425.046 | −0.0162822 | ||||||||
\(881\) | −13163.2 | −0.503383 | −0.251691 | − | 0.967808i | \(-0.580987\pi\) | ||||
−0.251691 | + | 0.967808i | \(0.580987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1426.38 | −0.0543620 | −0.0271810 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271810 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(884\) | 43133.1 | 1.64109 | ||||||||
\(885\) | −564.846 | −0.0214543 | ||||||||
\(886\) | −8588.04 | −0.325644 | ||||||||
\(887\) | −36168.2 | −1.36912 | −0.684560 | − | 0.728957i | \(-0.740006\pi\) | ||||
−0.684560 | + | 0.728957i | \(0.740006\pi\) | |||||||
\(888\) | −35408.2 | −1.33809 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 22234.4 | 0.837415 | ||||||||
\(891\) | 56.2684 | 0.00211567 | ||||||||
\(892\) | −68923.6 | −2.58715 | ||||||||
\(893\) | 19622.4 | 0.735316 | ||||||||
\(894\) | 122585. | 4.58596 | ||||||||
\(895\) | 8508.14 | 0.317761 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25238.9 | −0.939466 | ||||||||
\(898\) | 7177.17 | 0.266710 | ||||||||
\(899\) | −2876.66 | −0.106721 | ||||||||
\(900\) | 18383.3 | 0.680865 | ||||||||
\(901\) | −22026.4 | −0.814436 | ||||||||
\(902\) | 439.629 | 0.0162284 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39548.2 | 1.45504 | ||||||||
\(905\) | 11834.2 | 0.434676 | ||||||||
\(906\) | −11141.4 | −0.408552 | ||||||||
\(907\) | 212.271 | 0.00777105 | 0.00388552 | − | 0.999992i | \(-0.498763\pi\) | ||||
0.00388552 | + | 0.999992i | \(0.498763\pi\) | |||||||
\(908\) | −8028.33 | −0.293425 | ||||||||
\(909\) | 23983.3 | 0.875111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36810.6 | −1.33874 | −0.669369 | − | 0.742930i | \(-0.733436\pi\) | ||||
−0.669369 | + | 0.742930i | \(0.733436\pi\) | |||||||
\(912\) | 71097.0 | 2.58142 | ||||||||
\(913\) | 146.571 | 0.00531302 | ||||||||
\(914\) | −69362.8 | −2.51019 | ||||||||
\(915\) | −8591.87 | −0.310425 | ||||||||
\(916\) | 87833.5 | 3.16823 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −63075.3 | −2.26775 | ||||||||
\(919\) | 32727.7 | 1.17474 | 0.587371 | − | 0.809318i | \(-0.300163\pi\) | ||||
0.587371 | + | 0.809318i | \(0.300163\pi\) | |||||||
\(920\) | 27094.7 | 0.970961 | ||||||||
\(921\) | 43396.3 | 1.55261 | ||||||||
\(922\) | 48736.7 | 1.74084 | ||||||||
\(923\) | −15156.1 | −0.540486 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2281.45 | 0.0810957 | ||||||||
\(926\) | −13857.3 | −0.491771 | ||||||||
\(927\) | 17773.9 | 0.629743 | ||||||||
\(928\) | 24200.6 | 0.856060 | ||||||||
\(929\) | 6359.40 | 0.224591 | 0.112296 | − | 0.993675i | \(-0.464180\pi\) | ||||
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(930\) | −2708.54 | −0.0955016 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28628.0 | −1.00616 | ||||||||
\(933\) | 27231.6 | 0.955543 | ||||||||
\(934\) | −26598.5 | −0.931829 | ||||||||
\(935\) | −427.951 | −0.0149684 | ||||||||
\(936\) | −51444.2 | −1.79648 | ||||||||
\(937\) | −29540.8 | −1.02994 | −0.514971 | − | 0.857208i | \(-0.672197\pi\) | ||||
−0.514971 | + | 0.857208i | \(0.672197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33260.4 | 1.15592 | ||||||||
\(940\) | 19003.2 | 0.659379 | ||||||||
\(941\) | 19002.1 | 0.658291 | 0.329145 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329145 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(942\) | 73312.6 | 2.53573 | ||||||||
\(943\) | −11471.4 | −0.396141 | ||||||||
\(944\) | −1295.12 | −0.0446530 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1750.79 | 0.0601725 | ||||||||
\(947\) | 21320.8 | 0.731609 | 0.365804 | − | 0.930692i | \(-0.380794\pi\) | ||||
0.365804 | + | 0.930692i | \(0.380794\pi\) | |||||||
\(948\) | 64996.0 | 2.22676 | ||||||||
\(949\) | 24668.7 | 0.843813 | ||||||||
\(950\) | −11191.1 | −0.382198 | ||||||||
\(951\) | −53647.1 | −1.82926 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16523.3 | 0.561640 | 0.280820 | − | 0.959760i | \(-0.409394\pi\) | ||||
0.280820 | + | 0.959760i | \(0.409394\pi\) | |||||||
\(954\) | 48982.4 | 1.66233 | ||||||||
\(955\) | −11152.4 | −0.377888 | ||||||||
\(956\) | −22438.7 | −0.759120 | ||||||||
\(957\) | 1651.07 | 0.0557697 | ||||||||
\(958\) | 46833.3 | 1.57945 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9139.27 | −0.307259 | ||||||||
\(961\) | −29624.1 | −0.994397 | ||||||||
\(962\) | −11904.0 | −0.398960 | ||||||||
\(963\) | 84360.4 | 2.82292 | ||||||||
\(964\) | −15459.2 | −0.516501 | ||||||||
\(965\) | −1178.44 | −0.0393113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11517.9 | 0.383031 | 0.191515 | − | 0.981490i | \(-0.438660\pi\) | ||||
0.191515 | + | 0.981490i | \(0.438660\pi\) | |||||||
\(968\) | 61857.1 | 2.05389 | ||||||||
\(969\) | 71582.9 | 2.37314 | ||||||||
\(970\) | 1561.59 | 0.0516904 | ||||||||
\(971\) | 20328.0 | 0.671838 | 0.335919 | − | 0.941891i | \(-0.390953\pi\) | ||||
0.335919 | + | 0.941891i | \(0.390953\pi\) | |||||||
\(972\) | −69826.1 | −2.30419 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17586.8 | 0.578559 | ||||||||
\(975\) | 5414.59 | 0.177852 | ||||||||
\(976\) | −19700.0 | −0.646088 | ||||||||
\(977\) | −2142.66 | −0.0701635 | −0.0350817 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350817 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(978\) | 136742. | 4.47090 | ||||||||
\(979\) | 786.407 | 0.0256728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 60025.0 | 1.95357 | ||||||||
\(982\) | 274.331 | 0.00891472 | ||||||||
\(983\) | 23277.0 | 0.755260 | 0.377630 | − | 0.925957i | \(-0.376739\pi\) | ||||
0.377630 | + | 0.925957i | \(0.376739\pi\) | |||||||
\(984\) | −38195.0 | −1.23741 | ||||||||
\(985\) | 16160.8 | 0.522769 | ||||||||
\(986\) | 107766. | 3.48069 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39894.4 | 1.28462 | ||||||||
\(989\) | −45684.2 | −1.46883 | ||||||||
\(990\) | 951.678 | 0.0305518 | ||||||||
\(991\) | 7542.57 | 0.241774 | 0.120887 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120887 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(992\) | −1404.16 | −0.0449417 | ||||||||
\(993\) | −48171.2 | −1.53944 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18961.4 | −0.604139 | ||||||||
\(996\) | −23743.1 | −0.755351 | ||||||||
\(997\) | 48108.9 | 1.52821 | 0.764104 | − | 0.645093i | \(-0.223181\pi\) | ||||
0.764104 | + | 0.645093i | \(0.223181\pi\) | |||||||
\(998\) | 39855.5 | 1.26413 | ||||||||
\(999\) | 11893.2 | 0.376659 |
(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 | 245.4.a.n.1.1 | 5 | ||
3.2 | odd | 2 | 2205.4.a.bt.1.5 | 5 | |||
5.4 | even | 2 | 1225.4.a.bf.1.5 | 5 | |||
7.2 | even | 3 | 245.4.e.o.116.5 | 10 | |||
7.3 | odd | 6 | 35.4.e.c.16.5 | yes | 10 | ||
7.4 | even | 3 | 245.4.e.o.226.5 | 10 | |||
7.5 | odd | 6 | 35.4.e.c.11.5 | ✓ | 10 | ||
7.6 | odd | 2 | 245.4.a.m.1.1 | 5 | |||
21.5 | even | 6 | 315.4.j.g.46.1 | 10 | |||
21.17 | even | 6 | 315.4.j.g.226.1 | 10 | |||
21.20 | even | 2 | 2205.4.a.bu.1.5 | 5 | |||
28.3 | even | 6 | 560.4.q.n.401.2 | 10 | |||
28.19 | even | 6 | 560.4.q.n.81.2 | 10 | |||
35.3 | even | 12 | 175.4.k.d.149.2 | 20 | |||
35.12 | even | 12 | 175.4.k.d.74.2 | 20 | |||
35.17 | even | 12 | 175.4.k.d.149.9 | 20 | |||
35.19 | odd | 6 | 175.4.e.d.151.1 | 10 | |||
35.24 | odd | 6 | 175.4.e.d.51.1 | 10 | |||
35.33 | even | 12 | 175.4.k.d.74.9 | 20 | |||
35.34 | odd | 2 | 1225.4.a.bg.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.5 | ✓ | 10 | 7.5 | odd | 6 | ||
35.4.e.c.16.5 | yes | 10 | 7.3 | odd | 6 | ||
175.4.e.d.51.1 | 10 | 35.24 | odd | 6 | |||
175.4.e.d.151.1 | 10 | 35.19 | odd | 6 | |||
175.4.k.d.74.2 | 20 | 35.12 | even | 12 | |||
175.4.k.d.74.9 | 20 | 35.33 | even | 12 | |||
175.4.k.d.149.2 | 20 | 35.3 | even | 12 | |||
175.4.k.d.149.9 | 20 | 35.17 | even | 12 | |||
245.4.a.m.1.1 | 5 | 7.6 | odd | 2 | |||
245.4.a.n.1.1 | 5 | 1.1 | even | 1 | trivial | ||
245.4.e.o.116.5 | 10 | 7.2 | even | 3 | |||
245.4.e.o.226.5 | 10 | 7.4 | even | 3 | |||
315.4.j.g.46.1 | 10 | 21.5 | even | 6 | |||
315.4.j.g.226.1 | 10 | 21.17 | even | 6 | |||
560.4.q.n.81.2 | 10 | 28.19 | even | 6 | |||
560.4.q.n.401.2 | 10 | 28.3 | even | 6 | |||
1225.4.a.bf.1.5 | 5 | 5.4 | even | 2 | |||
1225.4.a.bg.1.5 | 5 | 35.34 | odd | 2 | |||
2205.4.a.bt.1.5 | 5 | 3.2 | odd | 2 | |||
2205.4.a.bu.1.5 | 5 | 21.20 | even | 2 |