Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(4.65113077458\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3257317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 34x^{2} - 27x + 10 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.17343\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.863638 | −0.152671 | −0.0763356 | − | 0.997082i | \(-0.524322\pi\) | ||||
−0.0763356 | + | 0.997082i | \(0.524322\pi\) | |||||||
\(3\) | 7.07413 | 0.453806 | 0.226903 | − | 0.973917i | \(-0.427140\pi\) | ||||
0.226903 | + | 0.973917i | \(0.427140\pi\) | |||||||
\(4\) | −31.2541 | −0.976692 | ||||||||
\(5\) | −44.4758 | −0.795607 | −0.397803 | − | 0.917471i | \(-0.630227\pi\) | ||||
−0.397803 | + | 0.917471i | \(0.630227\pi\) | |||||||
\(6\) | −6.10949 | −0.0692830 | ||||||||
\(7\) | −36.7447 | −0.283433 | −0.141716 | − | 0.989907i | \(-0.545262\pi\) | ||||
−0.141716 | + | 0.989907i | \(0.545262\pi\) | |||||||
\(8\) | 54.6287 | 0.301784 | ||||||||
\(9\) | −192.957 | −0.794060 | ||||||||
\(10\) | 38.4110 | 0.121466 | ||||||||
\(11\) | −302.283 | −0.753237 | −0.376619 | − | 0.926368i | \(-0.622913\pi\) | ||||
−0.376619 | + | 0.926368i | \(0.622913\pi\) | |||||||
\(12\) | −221.096 | −0.443228 | ||||||||
\(13\) | −373.472 | −0.612915 | −0.306457 | − | 0.951884i | \(-0.599144\pi\) | ||||
−0.306457 | + | 0.951884i | \(0.599144\pi\) | |||||||
\(14\) | 31.7341 | 0.0432720 | ||||||||
\(15\) | −314.627 | −0.361051 | ||||||||
\(16\) | 952.953 | 0.930618 | ||||||||
\(17\) | 280.365 | 0.235289 | 0.117645 | − | 0.993056i | \(-0.462466\pi\) | ||||
0.117645 | + | 0.993056i | \(0.462466\pi\) | |||||||
\(18\) | 166.645 | 0.121230 | ||||||||
\(19\) | 1371.41 | 0.871532 | 0.435766 | − | 0.900060i | \(-0.356478\pi\) | ||||
0.435766 | + | 0.900060i | \(0.356478\pi\) | |||||||
\(20\) | 1390.05 | 0.777062 | ||||||||
\(21\) | −259.937 | −0.128623 | ||||||||
\(22\) | 261.063 | 0.114998 | ||||||||
\(23\) | 1861.10 | 0.733586 | 0.366793 | − | 0.930303i | \(-0.380456\pi\) | ||||
0.366793 | + | 0.930303i | \(0.380456\pi\) | |||||||
\(24\) | 386.450 | 0.136951 | ||||||||
\(25\) | −1146.91 | −0.367010 | ||||||||
\(26\) | 322.545 | 0.0935744 | ||||||||
\(27\) | −3084.01 | −0.814155 | ||||||||
\(28\) | 1148.42 | 0.276826 | ||||||||
\(29\) | −841.000 | −0.185695 | ||||||||
\(30\) | 271.724 | 0.0551220 | ||||||||
\(31\) | 1472.03 | 0.275114 | 0.137557 | − | 0.990494i | \(-0.456075\pi\) | ||||
0.137557 | + | 0.990494i | \(0.456075\pi\) | |||||||
\(32\) | −2571.12 | −0.443862 | ||||||||
\(33\) | −2138.39 | −0.341823 | ||||||||
\(34\) | −242.134 | −0.0359219 | ||||||||
\(35\) | 1634.25 | 0.225501 | ||||||||
\(36\) | 6030.69 | 0.775552 | ||||||||
\(37\) | −11730.4 | −1.40867 | −0.704335 | − | 0.709868i | \(-0.748755\pi\) | ||||
−0.704335 | + | 0.709868i | \(0.748755\pi\) | |||||||
\(38\) | −1184.40 | −0.133058 | ||||||||
\(39\) | −2641.99 | −0.278144 | ||||||||
\(40\) | −2429.65 | −0.240101 | ||||||||
\(41\) | −2177.39 | −0.202291 | −0.101145 | − | 0.994872i | \(-0.532251\pi\) | ||||
−0.101145 | + | 0.994872i | \(0.532251\pi\) | |||||||
\(42\) | 224.491 | 0.0196371 | ||||||||
\(43\) | −9679.03 | −0.798290 | −0.399145 | − | 0.916888i | \(-0.630693\pi\) | ||||
−0.399145 | + | 0.916888i | \(0.630693\pi\) | |||||||
\(44\) | 9447.58 | 0.735680 | ||||||||
\(45\) | 8581.90 | 0.631760 | ||||||||
\(46\) | −1607.32 | −0.111997 | ||||||||
\(47\) | −15909.1 | −1.05051 | −0.525255 | − | 0.850945i | \(-0.676030\pi\) | ||||
−0.525255 | + | 0.850945i | \(0.676030\pi\) | |||||||
\(48\) | 6741.31 | 0.422320 | ||||||||
\(49\) | −15456.8 | −0.919666 | ||||||||
\(50\) | 990.512 | 0.0560318 | ||||||||
\(51\) | 1983.34 | 0.106776 | ||||||||
\(52\) | 11672.6 | 0.598629 | ||||||||
\(53\) | 24359.3 | 1.19117 | 0.595586 | − | 0.803291i | \(-0.296920\pi\) | ||||
0.595586 | + | 0.803291i | \(0.296920\pi\) | |||||||
\(54\) | 2663.47 | 0.124298 | ||||||||
\(55\) | 13444.3 | 0.599280 | ||||||||
\(56\) | −2007.32 | −0.0855353 | ||||||||
\(57\) | 9701.53 | 0.395506 | ||||||||
\(58\) | 726.320 | 0.0283503 | ||||||||
\(59\) | 36304.7 | 1.35779 | 0.678894 | − | 0.734236i | \(-0.262459\pi\) | ||||
0.678894 | + | 0.734236i | \(0.262459\pi\) | |||||||
\(60\) | 9833.40 | 0.352635 | ||||||||
\(61\) | −22316.1 | −0.767880 | −0.383940 | − | 0.923358i | \(-0.625433\pi\) | ||||
−0.383940 | + | 0.923358i | \(0.625433\pi\) | |||||||
\(62\) | −1271.30 | −0.0420019 | ||||||||
\(63\) | 7090.14 | 0.225063 | ||||||||
\(64\) | −28274.0 | −0.862853 | ||||||||
\(65\) | 16610.5 | 0.487639 | ||||||||
\(66\) | 1846.79 | 0.0521865 | ||||||||
\(67\) | −54808.6 | −1.49163 | −0.745817 | − | 0.666151i | \(-0.767940\pi\) | ||||
−0.745817 | + | 0.666151i | \(0.767940\pi\) | |||||||
\(68\) | −8762.58 | −0.229805 | ||||||||
\(69\) | 13165.7 | 0.332905 | ||||||||
\(70\) | −1411.40 | −0.0344275 | ||||||||
\(71\) | 27790.4 | 0.654258 | 0.327129 | − | 0.944980i | \(-0.393919\pi\) | ||||
0.327129 | + | 0.944980i | \(0.393919\pi\) | |||||||
\(72\) | −10541.0 | −0.239635 | ||||||||
\(73\) | 31685.5 | 0.695910 | 0.347955 | − | 0.937511i | \(-0.386876\pi\) | ||||
0.347955 | + | 0.937511i | \(0.386876\pi\) | |||||||
\(74\) | 10130.8 | 0.215063 | ||||||||
\(75\) | −8113.36 | −0.166551 | ||||||||
\(76\) | −42862.2 | −0.851218 | ||||||||
\(77\) | 11107.3 | 0.213492 | ||||||||
\(78\) | 2281.73 | 0.0424646 | ||||||||
\(79\) | −55328.4 | −0.997426 | −0.498713 | − | 0.866767i | \(-0.666194\pi\) | ||||
−0.498713 | + | 0.866767i | \(0.666194\pi\) | |||||||
\(80\) | −42383.3 | −0.740406 | ||||||||
\(81\) | 25071.8 | 0.424592 | ||||||||
\(82\) | 1880.47 | 0.0308839 | ||||||||
\(83\) | −46888.8 | −0.747092 | −0.373546 | − | 0.927612i | \(-0.621858\pi\) | ||||
−0.373546 | + | 0.927612i | \(0.621858\pi\) | |||||||
\(84\) | 8124.10 | 0.125625 | ||||||||
\(85\) | −12469.5 | −0.187198 | ||||||||
\(86\) | 8359.18 | 0.121876 | ||||||||
\(87\) | −5949.34 | −0.0842696 | ||||||||
\(88\) | −16513.3 | −0.227315 | ||||||||
\(89\) | 2564.30 | 0.0343157 | 0.0171579 | − | 0.999853i | \(-0.494538\pi\) | ||||
0.0171579 | + | 0.999853i | \(0.494538\pi\) | |||||||
\(90\) | −7411.65 | −0.0964515 | ||||||||
\(91\) | 13723.1 | 0.173720 | ||||||||
\(92\) | −58167.2 | −0.716487 | ||||||||
\(93\) | 10413.3 | 0.124848 | ||||||||
\(94\) | 13739.7 | 0.160382 | ||||||||
\(95\) | −60994.5 | −0.693396 | ||||||||
\(96\) | −18188.5 | −0.201427 | ||||||||
\(97\) | 34940.3 | 0.377048 | 0.188524 | − | 0.982069i | \(-0.439630\pi\) | ||||
0.188524 | + | 0.982069i | \(0.439630\pi\) | |||||||
\(98\) | 13349.1 | 0.140406 | ||||||||
\(99\) | 58327.5 | 0.598116 | ||||||||
\(100\) | 35845.6 | 0.358456 | ||||||||
\(101\) | 170224. | 1.66042 | 0.830210 | − | 0.557451i | \(-0.188221\pi\) | ||||
0.830210 | + | 0.557451i | \(0.188221\pi\) | |||||||
\(102\) | −1712.89 | −0.0163015 | ||||||||
\(103\) | 83962.9 | 0.779820 | 0.389910 | − | 0.920853i | \(-0.372506\pi\) | ||||
0.389910 | + | 0.920853i | \(0.372506\pi\) | |||||||
\(104\) | −20402.3 | −0.184968 | ||||||||
\(105\) | 11560.9 | 0.102334 | ||||||||
\(106\) | −21037.6 | −0.181858 | ||||||||
\(107\) | 16842.4 | 0.142215 | 0.0711074 | − | 0.997469i | \(-0.477347\pi\) | ||||
0.0711074 | + | 0.997469i | \(0.477347\pi\) | |||||||
\(108\) | 96388.2 | 0.795178 | ||||||||
\(109\) | −3855.63 | −0.0310834 | −0.0155417 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155417 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(110\) | −11611.0 | −0.0914928 | ||||||||
\(111\) | −82982.5 | −0.639262 | ||||||||
\(112\) | −35016.0 | −0.263767 | ||||||||
\(113\) | 107319. | 0.790644 | 0.395322 | − | 0.918543i | \(-0.370633\pi\) | ||||
0.395322 | + | 0.918543i | \(0.370633\pi\) | |||||||
\(114\) | −8378.61 | −0.0603823 | ||||||||
\(115\) | −82774.0 | −0.583646 | ||||||||
\(116\) | 26284.7 | 0.181367 | ||||||||
\(117\) | 72064.0 | 0.486691 | ||||||||
\(118\) | −31354.1 | −0.207295 | ||||||||
\(119\) | −10301.9 | −0.0666886 | ||||||||
\(120\) | −17187.7 | −0.108959 | ||||||||
\(121\) | −69676.1 | −0.432634 | ||||||||
\(122\) | 19273.0 | 0.117233 | ||||||||
\(123\) | −15403.1 | −0.0918006 | ||||||||
\(124\) | −46007.0 | −0.268701 | ||||||||
\(125\) | 189996. | 1.08760 | ||||||||
\(126\) | −6123.31 | −0.0343606 | ||||||||
\(127\) | −14823.9 | −0.0815554 | −0.0407777 | − | 0.999168i | \(-0.512984\pi\) | ||||
−0.0407777 | + | 0.999168i | \(0.512984\pi\) | |||||||
\(128\) | 106694. | 0.575595 | ||||||||
\(129\) | −68470.7 | −0.362269 | ||||||||
\(130\) | −14345.4 | −0.0744484 | ||||||||
\(131\) | −313171. | −1.59442 | −0.797211 | − | 0.603701i | \(-0.793692\pi\) | ||||
−0.797211 | + | 0.603701i | \(0.793692\pi\) | |||||||
\(132\) | 66833.4 | 0.333856 | ||||||||
\(133\) | −50392.1 | −0.247020 | ||||||||
\(134\) | 47334.8 | 0.227729 | ||||||||
\(135\) | 137164. | 0.647747 | ||||||||
\(136\) | 15316.0 | 0.0710065 | ||||||||
\(137\) | −254312. | −1.15762 | −0.578810 | − | 0.815463i | \(-0.696483\pi\) | ||||
−0.578810 | + | 0.815463i | \(0.696483\pi\) | |||||||
\(138\) | −11370.4 | −0.0508250 | ||||||||
\(139\) | −390931. | −1.71618 | −0.858091 | − | 0.513498i | \(-0.828349\pi\) | ||||
−0.858091 | + | 0.513498i | \(0.828349\pi\) | |||||||
\(140\) | −51077.0 | −0.220245 | ||||||||
\(141\) | −112543. | −0.476727 | ||||||||
\(142\) | −24000.9 | −0.0998863 | ||||||||
\(143\) | 112894. | 0.461670 | ||||||||
\(144\) | −183879. | −0.738967 | ||||||||
\(145\) | 37404.1 | 0.147740 | ||||||||
\(146\) | −27364.8 | −0.106245 | ||||||||
\(147\) | −109344. | −0.417350 | ||||||||
\(148\) | 366624. | 1.37584 | ||||||||
\(149\) | 72345.7 | 0.266961 | 0.133480 | − | 0.991051i | \(-0.457385\pi\) | ||||
0.133480 | + | 0.991051i | \(0.457385\pi\) | |||||||
\(150\) | 7007.01 | 0.0254276 | ||||||||
\(151\) | −227419. | −0.811679 | −0.405840 | − | 0.913944i | \(-0.633021\pi\) | ||||
−0.405840 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(152\) | 74918.3 | 0.263014 | ||||||||
\(153\) | −54098.4 | −0.186834 | ||||||||
\(154\) | −9592.68 | −0.0325940 | ||||||||
\(155\) | −65469.6 | −0.218882 | ||||||||
\(156\) | 82573.2 | 0.271661 | ||||||||
\(157\) | 539281. | 1.74609 | 0.873044 | − | 0.487641i | \(-0.162143\pi\) | ||||
0.873044 | + | 0.487641i | \(0.162143\pi\) | |||||||
\(158\) | 47783.7 | 0.152278 | ||||||||
\(159\) | 172321. | 0.540561 | ||||||||
\(160\) | 114353. | 0.353140 | ||||||||
\(161\) | −68385.7 | −0.207922 | ||||||||
\(162\) | −21652.9 | −0.0648230 | ||||||||
\(163\) | 87996.5 | 0.259416 | 0.129708 | − | 0.991552i | \(-0.458596\pi\) | ||||
0.129708 | + | 0.991552i | \(0.458596\pi\) | |||||||
\(164\) | 68052.3 | 0.197576 | ||||||||
\(165\) | 95106.4 | 0.271957 | ||||||||
\(166\) | 40495.0 | 0.114059 | ||||||||
\(167\) | 199897. | 0.554644 | 0.277322 | − | 0.960777i | \(-0.410553\pi\) | ||||
0.277322 | + | 0.960777i | \(0.410553\pi\) | |||||||
\(168\) | −14200.0 | −0.0388164 | ||||||||
\(169\) | −231811. | −0.624335 | ||||||||
\(170\) | 10769.1 | 0.0285797 | ||||||||
\(171\) | −264623. | −0.692049 | ||||||||
\(172\) | 302510. | 0.779683 | ||||||||
\(173\) | −313797. | −0.797139 | −0.398569 | − | 0.917138i | \(-0.630493\pi\) | ||||
−0.398569 | + | 0.917138i | \(0.630493\pi\) | |||||||
\(174\) | 5138.08 | 0.0128655 | ||||||||
\(175\) | 42142.7 | 0.104023 | ||||||||
\(176\) | −288061. | −0.700976 | ||||||||
\(177\) | 256824. | 0.616172 | ||||||||
\(178\) | −2214.63 | −0.00523902 | ||||||||
\(179\) | −59814.7 | −0.139533 | −0.0697663 | − | 0.997563i | \(-0.522225\pi\) | ||||
−0.0697663 | + | 0.997563i | \(0.522225\pi\) | |||||||
\(180\) | −268220. | −0.617034 | ||||||||
\(181\) | 402231. | 0.912597 | 0.456298 | − | 0.889827i | \(-0.349175\pi\) | ||||
0.456298 | + | 0.889827i | \(0.349175\pi\) | |||||||
\(182\) | −11851.8 | −0.0265220 | ||||||||
\(183\) | −157867. | −0.348468 | ||||||||
\(184\) | 101670. | 0.221384 | ||||||||
\(185\) | 521719. | 1.12075 | ||||||||
\(186\) | −8993.35 | −0.0190607 | ||||||||
\(187\) | −84749.6 | −0.177229 | ||||||||
\(188\) | 497224. | 1.02602 | ||||||||
\(189\) | 113321. | 0.230758 | ||||||||
\(190\) | 52677.2 | 0.105862 | ||||||||
\(191\) | −903529. | −1.79209 | −0.896043 | − | 0.443967i | \(-0.853571\pi\) | ||||
−0.896043 | + | 0.443967i | \(0.853571\pi\) | |||||||
\(192\) | −200014. | −0.391568 | ||||||||
\(193\) | 1.02870e6 | 1.98791 | 0.993956 | − | 0.109780i | \(-0.0350148\pi\) | ||||
0.993956 | + | 0.109780i | \(0.0350148\pi\) | |||||||
\(194\) | −30175.7 | −0.0575644 | ||||||||
\(195\) | 117505. | 0.221293 | ||||||||
\(196\) | 483090. | 0.898230 | ||||||||
\(197\) | −866099. | −1.59002 | −0.795009 | − | 0.606598i | \(-0.792534\pi\) | ||||
−0.795009 | + | 0.606598i | \(0.792534\pi\) | |||||||
\(198\) | −50373.8 | −0.0913150 | ||||||||
\(199\) | 285836. | 0.511663 | 0.255832 | − | 0.966721i | \(-0.417651\pi\) | ||||
0.255832 | + | 0.966721i | \(0.417651\pi\) | |||||||
\(200\) | −62654.0 | −0.110758 | ||||||||
\(201\) | −387723. | −0.676911 | ||||||||
\(202\) | −147012. | −0.253498 | ||||||||
\(203\) | 30902.3 | 0.0526321 | ||||||||
\(204\) | −61987.6 | −0.104287 | ||||||||
\(205\) | 96840.9 | 0.160944 | ||||||||
\(206\) | −72513.6 | −0.119056 | ||||||||
\(207\) | −359112. | −0.582512 | ||||||||
\(208\) | −355901. | −0.570389 | ||||||||
\(209\) | −414554. | −0.656470 | ||||||||
\(210\) | −9984.43 | −0.0156234 | ||||||||
\(211\) | −918930. | −1.42094 | −0.710471 | − | 0.703727i | \(-0.751518\pi\) | ||||
−0.710471 | + | 0.703727i | \(0.751518\pi\) | |||||||
\(212\) | −761328. | −1.16341 | ||||||||
\(213\) | 196593. | 0.296906 | ||||||||
\(214\) | −14545.8 | −0.0217121 | ||||||||
\(215\) | 430482. | 0.635125 | ||||||||
\(216\) | −168476. | −0.245699 | ||||||||
\(217\) | −54089.3 | −0.0779762 | ||||||||
\(218\) | 3329.87 | 0.00474554 | ||||||||
\(219\) | 224147. | 0.315808 | ||||||||
\(220\) | −420189. | −0.585312 | ||||||||
\(221\) | −104709. | −0.144212 | ||||||||
\(222\) | 71666.8 | 0.0975969 | ||||||||
\(223\) | 486134. | 0.654626 | 0.327313 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327313 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(224\) | 94475.2 | 0.125805 | ||||||||
\(225\) | 221303. | 0.291428 | ||||||||
\(226\) | −92684.9 | −0.120708 | ||||||||
\(227\) | −557639. | −0.718271 | −0.359136 | − | 0.933285i | \(-0.616928\pi\) | ||||
−0.359136 | + | 0.933285i | \(0.616928\pi\) | |||||||
\(228\) | −303213. | −0.386287 | ||||||||
\(229\) | 440289. | 0.554816 | 0.277408 | − | 0.960752i | \(-0.410525\pi\) | ||||
0.277408 | + | 0.960752i | \(0.410525\pi\) | |||||||
\(230\) | 71486.8 | 0.0891059 | ||||||||
\(231\) | 78574.4 | 0.0968838 | ||||||||
\(232\) | −45942.7 | −0.0560398 | ||||||||
\(233\) | 1.46183e6 | 1.76403 | 0.882015 | − | 0.471221i | \(-0.156187\pi\) | ||||
0.882015 | + | 0.471221i | \(0.156187\pi\) | |||||||
\(234\) | −62237.2 | −0.0743037 | ||||||||
\(235\) | 707568. | 0.835792 | ||||||||
\(236\) | −1.13467e6 | −1.32614 | ||||||||
\(237\) | −391400. | −0.452637 | ||||||||
\(238\) | 8897.16 | 0.0101814 | ||||||||
\(239\) | 1.51292e6 | 1.71325 | 0.856627 | − | 0.515936i | \(-0.172556\pi\) | ||||
0.856627 | + | 0.515936i | \(0.172556\pi\) | |||||||
\(240\) | −299825. | −0.336000 | ||||||||
\(241\) | −800679. | −0.888006 | −0.444003 | − | 0.896025i | \(-0.646442\pi\) | ||||
−0.444003 | + | 0.896025i | \(0.646442\pi\) | |||||||
\(242\) | 60175.0 | 0.0660507 | ||||||||
\(243\) | 926776. | 1.00684 | ||||||||
\(244\) | 697470. | 0.749982 | ||||||||
\(245\) | 687454. | 0.731692 | ||||||||
\(246\) | 13302.7 | 0.0140153 | ||||||||
\(247\) | −512184. | −0.534175 | ||||||||
\(248\) | 80415.0 | 0.0830249 | ||||||||
\(249\) | −331698. | −0.339035 | ||||||||
\(250\) | −164088. | −0.166045 | ||||||||
\(251\) | 1.66023e6 | 1.66335 | 0.831676 | − | 0.555261i | \(-0.187382\pi\) | ||||
0.831676 | + | 0.555261i | \(0.187382\pi\) | |||||||
\(252\) | −221596. | −0.219817 | ||||||||
\(253\) | −562580. | −0.552564 | ||||||||
\(254\) | 12802.5 | 0.0124512 | ||||||||
\(255\) | −88210.6 | −0.0849514 | ||||||||
\(256\) | 812621. | 0.774976 | ||||||||
\(257\) | −1.00723e6 | −0.951250 | −0.475625 | − | 0.879648i | \(-0.657778\pi\) | ||||
−0.475625 | + | 0.879648i | \(0.657778\pi\) | |||||||
\(258\) | 59133.9 | 0.0553079 | ||||||||
\(259\) | 431031. | 0.399263 | ||||||||
\(260\) | −519146. | −0.476273 | ||||||||
\(261\) | 162277. | 0.147453 | ||||||||
\(262\) | 270466. | 0.243422 | ||||||||
\(263\) | 1.01326e6 | 0.903298 | 0.451649 | − | 0.892196i | \(-0.350836\pi\) | ||||
0.451649 | + | 0.892196i | \(0.350836\pi\) | |||||||
\(264\) | −116817. | −0.103157 | ||||||||
\(265\) | −1.08340e6 | −0.947705 | ||||||||
\(266\) | 43520.5 | 0.0377129 | ||||||||
\(267\) | 18140.2 | 0.0155727 | ||||||||
\(268\) | 1.71300e6 | 1.45687 | ||||||||
\(269\) | −1.45518e6 | −1.22613 | −0.613064 | − | 0.790034i | \(-0.710063\pi\) | ||||
−0.613064 | + | 0.790034i | \(0.710063\pi\) | |||||||
\(270\) | −118460. | −0.0988922 | ||||||||
\(271\) | −1.61146e6 | −1.33290 | −0.666450 | − | 0.745550i | \(-0.732187\pi\) | ||||
−0.666450 | + | 0.745550i | \(0.732187\pi\) | |||||||
\(272\) | 267175. | 0.218964 | ||||||||
\(273\) | 97079.2 | 0.0788351 | ||||||||
\(274\) | 219634. | 0.176735 | ||||||||
\(275\) | 346690. | 0.276446 | ||||||||
\(276\) | −411482. | −0.325146 | ||||||||
\(277\) | 2.06358e6 | 1.61593 | 0.807966 | − | 0.589230i | \(-0.200569\pi\) | ||||
0.807966 | + | 0.589230i | \(0.200569\pi\) | |||||||
\(278\) | 337623. | 0.262011 | ||||||||
\(279\) | −284038. | −0.218457 | ||||||||
\(280\) | 89276.9 | 0.0680525 | ||||||||
\(281\) | 21664.7 | 0.0163676 | 0.00818382 | − | 0.999967i | \(-0.497395\pi\) | ||||
0.00818382 | + | 0.999967i | \(0.497395\pi\) | |||||||
\(282\) | 97196.2 | 0.0727824 | ||||||||
\(283\) | −552726. | −0.410245 | −0.205123 | − | 0.978736i | \(-0.565759\pi\) | ||||
−0.205123 | + | 0.978736i | \(0.565759\pi\) | |||||||
\(284\) | −868565. | −0.639008 | ||||||||
\(285\) | −431483. | −0.314667 | ||||||||
\(286\) | −97499.8 | −0.0704837 | ||||||||
\(287\) | 80007.4 | 0.0573358 | ||||||||
\(288\) | 496116. | 0.352453 | ||||||||
\(289\) | −1.34125e6 | −0.944639 | ||||||||
\(290\) | −32303.6 | −0.0225557 | ||||||||
\(291\) | 247172. | 0.171107 | ||||||||
\(292\) | −990301. | −0.679689 | ||||||||
\(293\) | −1.53503e6 | −1.04459 | −0.522297 | − | 0.852764i | \(-0.674925\pi\) | ||||
−0.522297 | + | 0.852764i | \(0.674925\pi\) | |||||||
\(294\) | 94433.3 | 0.0637172 | ||||||||
\(295\) | −1.61468e6 | −1.08027 | ||||||||
\(296\) | −640817. | −0.425114 | ||||||||
\(297\) | 932244. | 0.613251 | ||||||||
\(298\) | −62480.5 | −0.0407572 | ||||||||
\(299\) | −695071. | −0.449626 | ||||||||
\(300\) | 253576. | 0.162669 | ||||||||
\(301\) | 355653. | 0.226261 | ||||||||
\(302\) | 196408. | 0.123920 | ||||||||
\(303\) | 1.20419e6 | 0.753508 | ||||||||
\(304\) | 1.30689e6 | 0.811063 | ||||||||
\(305\) | 992525. | 0.610930 | ||||||||
\(306\) | 46721.4 | 0.0285241 | ||||||||
\(307\) | −2.69140e6 | −1.62979 | −0.814895 | − | 0.579609i | \(-0.803205\pi\) | ||||
−0.814895 | + | 0.579609i | \(0.803205\pi\) | |||||||
\(308\) | −347149. | −0.208516 | ||||||||
\(309\) | 593964. | 0.353887 | ||||||||
\(310\) | 56542.1 | 0.0334170 | ||||||||
\(311\) | −1.88553e6 | −1.10543 | −0.552717 | − | 0.833369i | \(-0.686409\pi\) | ||||
−0.552717 | + | 0.833369i | \(0.686409\pi\) | |||||||
\(312\) | −144329. | −0.0839394 | ||||||||
\(313\) | −2.48142e6 | −1.43166 | −0.715828 | − | 0.698276i | \(-0.753951\pi\) | ||||
−0.715828 | + | 0.698276i | \(0.753951\pi\) | |||||||
\(314\) | −465744. | −0.266577 | ||||||||
\(315\) | −315339. | −0.179061 | ||||||||
\(316\) | 1.72924e6 | 0.974177 | ||||||||
\(317\) | 204476. | 0.114286 | 0.0571432 | − | 0.998366i | \(-0.481801\pi\) | ||||
0.0571432 | + | 0.998366i | \(0.481801\pi\) | |||||||
\(318\) | −148823. | −0.0825280 | ||||||||
\(319\) | 254220. | 0.139873 | ||||||||
\(320\) | 1.25751e6 | 0.686492 | ||||||||
\(321\) | 119145. | 0.0645379 | ||||||||
\(322\) | 59060.5 | 0.0317437 | ||||||||
\(323\) | 384496. | 0.205062 | ||||||||
\(324\) | −783596. | −0.414696 | ||||||||
\(325\) | 428338. | 0.224946 | ||||||||
\(326\) | −75997.1 | −0.0396053 | ||||||||
\(327\) | −27275.2 | −0.0141058 | ||||||||
\(328\) | −118948. | −0.0610480 | ||||||||
\(329\) | 584574. | 0.297749 | ||||||||
\(330\) | −82137.5 | −0.0415199 | ||||||||
\(331\) | 1.58800e6 | 0.796672 | 0.398336 | − | 0.917240i | \(-0.369588\pi\) | ||||
0.398336 | + | 0.917240i | \(0.369588\pi\) | |||||||
\(332\) | 1.46547e6 | 0.729678 | ||||||||
\(333\) | 2.26346e6 | 1.11857 | ||||||||
\(334\) | −172638. | −0.0846782 | ||||||||
\(335\) | 2.43766e6 | 1.18675 | ||||||||
\(336\) | −247708. | −0.119699 | ||||||||
\(337\) | −813616. | −0.390252 | −0.195126 | − | 0.980778i | \(-0.562512\pi\) | ||||
−0.195126 | + | 0.980778i | \(0.562512\pi\) | |||||||
\(338\) | 200201. | 0.0953180 | ||||||||
\(339\) | 759189. | 0.358799 | ||||||||
\(340\) | 389722. | 0.182834 | ||||||||
\(341\) | −444969. | −0.207226 | ||||||||
\(342\) | 228538. | 0.105656 | ||||||||
\(343\) | 1.18553e6 | 0.544096 | ||||||||
\(344\) | −528753. | −0.240911 | ||||||||
\(345\) | −585554. | −0.264862 | ||||||||
\(346\) | 271007. | 0.121700 | ||||||||
\(347\) | 516038. | 0.230069 | 0.115034 | − | 0.993362i | \(-0.463302\pi\) | ||||
0.115034 | + | 0.993362i | \(0.463302\pi\) | |||||||
\(348\) | 185942. | 0.0823054 | ||||||||
\(349\) | −2.65164e6 | −1.16533 | −0.582667 | − | 0.812711i | \(-0.697991\pi\) | ||||
−0.582667 | + | 0.812711i | \(0.697991\pi\) | |||||||
\(350\) | −36396.1 | −0.0158812 | ||||||||
\(351\) | 1.15179e6 | 0.499007 | ||||||||
\(352\) | 777207. | 0.334333 | ||||||||
\(353\) | 391323. | 0.167147 | 0.0835734 | − | 0.996502i | \(-0.473367\pi\) | ||||
0.0835734 | + | 0.996502i | \(0.473367\pi\) | |||||||
\(354\) | −221803. | −0.0940717 | ||||||||
\(355\) | −1.23600e6 | −0.520532 | ||||||||
\(356\) | −80144.9 | −0.0335159 | ||||||||
\(357\) | −72877.3 | −0.0302637 | ||||||||
\(358\) | 51658.3 | 0.0213026 | ||||||||
\(359\) | 3.03988e6 | 1.24486 | 0.622430 | − | 0.782675i | \(-0.286146\pi\) | ||||
0.622430 | + | 0.782675i | \(0.286146\pi\) | |||||||
\(360\) | 468818. | 0.190655 | ||||||||
\(361\) | −595334. | −0.240432 | ||||||||
\(362\) | −347382. | −0.139327 | ||||||||
\(363\) | −492898. | −0.196332 | ||||||||
\(364\) | −428905. | −0.169671 | ||||||||
\(365\) | −1.40924e6 | −0.553670 | ||||||||
\(366\) | 136340. | 0.0532010 | ||||||||
\(367\) | 1.02897e6 | 0.398785 | 0.199392 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199392 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(368\) | 1.77354e6 | 0.682688 | ||||||||
\(369\) | 420141. | 0.160631 | ||||||||
\(370\) | −450577. | −0.171106 | ||||||||
\(371\) | −895074. | −0.337617 | ||||||||
\(372\) | −325460. | −0.121938 | ||||||||
\(373\) | −4.42358e6 | −1.64627 | −0.823136 | − | 0.567844i | \(-0.807778\pi\) | ||||
−0.823136 | + | 0.567844i | \(0.807778\pi\) | |||||||
\(374\) | 73193.0 | 0.0270577 | ||||||||
\(375\) | 1.34406e6 | 0.493560 | ||||||||
\(376\) | −869091. | −0.317027 | ||||||||
\(377\) | 314090. | 0.113815 | ||||||||
\(378\) | −97868.5 | −0.0352301 | ||||||||
\(379\) | −4.23499e6 | −1.51445 | −0.757223 | − | 0.653156i | \(-0.773445\pi\) | ||||
−0.757223 | + | 0.653156i | \(0.773445\pi\) | |||||||
\(380\) | 1.90633e6 | 0.677234 | ||||||||
\(381\) | −104866. | −0.0370103 | ||||||||
\(382\) | 780323. | 0.273600 | ||||||||
\(383\) | −894484. | −0.311584 | −0.155792 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155792 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(384\) | 754770. | 0.261208 | ||||||||
\(385\) | −494005. | −0.169856 | ||||||||
\(386\) | −888428. | −0.303497 | ||||||||
\(387\) | 1.86763e6 | 0.633891 | ||||||||
\(388\) | −1.09203e6 | −0.368260 | ||||||||
\(389\) | 3.60641e6 | 1.20837 | 0.604186 | − | 0.796843i | \(-0.293498\pi\) | ||||
0.604186 | + | 0.796843i | \(0.293498\pi\) | |||||||
\(390\) | −101481. | −0.0337851 | ||||||||
\(391\) | 521789. | 0.172605 | ||||||||
\(392\) | −844386. | −0.277540 | ||||||||
\(393\) | −2.21541e6 | −0.723557 | ||||||||
\(394\) | 747996. | 0.242750 | ||||||||
\(395\) | 2.46077e6 | 0.793559 | ||||||||
\(396\) | −1.82297e6 | −0.584175 | ||||||||
\(397\) | −1.96195e6 | −0.624757 | −0.312379 | − | 0.949958i | \(-0.601126\pi\) | ||||
−0.312379 | + | 0.949958i | \(0.601126\pi\) | |||||||
\(398\) | −246859. | −0.0781162 | ||||||||
\(399\) | −356480. | −0.112099 | ||||||||
\(400\) | −1.09295e6 | −0.341546 | ||||||||
\(401\) | −721116. | −0.223947 | −0.111973 | − | 0.993711i | \(-0.535717\pi\) | ||||
−0.111973 | + | 0.993711i | \(0.535717\pi\) | |||||||
\(402\) | 334853. | 0.103345 | ||||||||
\(403\) | −549762. | −0.168621 | ||||||||
\(404\) | −5.32021e6 | −1.62172 | ||||||||
\(405\) | −1.11509e6 | −0.337809 | ||||||||
\(406\) | −26688.4 | −0.00803540 | ||||||||
\(407\) | 3.54590e6 | 1.06106 | ||||||||
\(408\) | 108347. | 0.0322231 | ||||||||
\(409\) | 1.33383e6 | 0.394269 | 0.197135 | − | 0.980376i | \(-0.436836\pi\) | ||||
0.197135 | + | 0.980376i | \(0.436836\pi\) | |||||||
\(410\) | −83635.5 | −0.0245715 | ||||||||
\(411\) | −1.79904e6 | −0.525334 | ||||||||
\(412\) | −2.62419e6 | −0.761644 | ||||||||
\(413\) | −1.33400e6 | −0.384842 | ||||||||
\(414\) | 310143. | 0.0889327 | ||||||||
\(415\) | 2.08542e6 | 0.594391 | ||||||||
\(416\) | 960244. | 0.272050 | ||||||||
\(417\) | −2.76550e6 | −0.778813 | ||||||||
\(418\) | 358024. | 0.100224 | ||||||||
\(419\) | −4.51294e6 | −1.25581 | −0.627905 | − | 0.778290i | \(-0.716087\pi\) | ||||
−0.627905 | + | 0.778290i | \(0.716087\pi\) | |||||||
\(420\) | −361326. | −0.0999483 | ||||||||
\(421\) | 982181. | 0.270076 | 0.135038 | − | 0.990840i | \(-0.456884\pi\) | ||||
0.135038 | + | 0.990840i | \(0.456884\pi\) | |||||||
\(422\) | 793623. | 0.216937 | ||||||||
\(423\) | 3.06976e6 | 0.834168 | ||||||||
\(424\) | 1.33071e6 | 0.359476 | ||||||||
\(425\) | −321553. | −0.0863535 | ||||||||
\(426\) | −169785. | −0.0453290 | ||||||||
\(427\) | 819998. | 0.217642 | ||||||||
\(428\) | −526395. | −0.138900 | ||||||||
\(429\) | 798629. | 0.209508 | ||||||||
\(430\) | −371781. | −0.0969652 | ||||||||
\(431\) | 5.31784e6 | 1.37893 | 0.689465 | − | 0.724319i | \(-0.257846\pi\) | ||||
0.689465 | + | 0.724319i | \(0.257846\pi\) | |||||||
\(432\) | −2.93892e6 | −0.757667 | ||||||||
\(433\) | 679278. | 0.174112 | 0.0870558 | − | 0.996203i | \(-0.472254\pi\) | ||||
0.0870558 | + | 0.996203i | \(0.472254\pi\) | |||||||
\(434\) | 46713.6 | 0.0119047 | ||||||||
\(435\) | 264602. | 0.0670454 | ||||||||
\(436\) | 120504. | 0.0303589 | ||||||||
\(437\) | 2.55234e6 | 0.639344 | ||||||||
\(438\) | −193582. | −0.0482147 | ||||||||
\(439\) | 3.53619e6 | 0.875739 | 0.437870 | − | 0.899039i | \(-0.355733\pi\) | ||||
0.437870 | + | 0.899039i | \(0.355733\pi\) | |||||||
\(440\) | 734442. | 0.180853 | ||||||||
\(441\) | 2.98250e6 | 0.730270 | ||||||||
\(442\) | 90430.5 | 0.0220170 | ||||||||
\(443\) | −1.35298e6 | −0.327553 | −0.163776 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163776 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(444\) | 2.59355e6 | 0.624362 | ||||||||
\(445\) | −114049. | −0.0273018 | ||||||||
\(446\) | −419844. | −0.0999425 | ||||||||
\(447\) | 511783. | 0.121148 | ||||||||
\(448\) | 1.03892e6 | 0.244561 | ||||||||
\(449\) | −2.04554e6 | −0.478843 | −0.239421 | − | 0.970916i | \(-0.576958\pi\) | ||||
−0.239421 | + | 0.970916i | \(0.576958\pi\) | |||||||
\(450\) | −191126. | −0.0444927 | ||||||||
\(451\) | 658186. | 0.152373 | ||||||||
\(452\) | −3.35416e6 | −0.772215 | ||||||||
\(453\) | −1.60879e6 | −0.368345 | ||||||||
\(454\) | 481598. | 0.109659 | ||||||||
\(455\) | −610347. | −0.138213 | ||||||||
\(456\) | 529982. | 0.119357 | ||||||||
\(457\) | 8.48379e6 | 1.90020 | 0.950100 | − | 0.311944i | \(-0.100980\pi\) | ||||
0.950100 | + | 0.311944i | \(0.100980\pi\) | |||||||
\(458\) | −380250. | −0.0847044 | ||||||||
\(459\) | −864651. | −0.191562 | ||||||||
\(460\) | 2.58703e6 | 0.570042 | ||||||||
\(461\) | −2.06795e6 | −0.453198 | −0.226599 | − | 0.973988i | \(-0.572761\pi\) | ||||
−0.226599 | + | 0.973988i | \(0.572761\pi\) | |||||||
\(462\) | −67859.9 | −0.0147914 | ||||||||
\(463\) | −368290. | −0.0798430 | −0.0399215 | − | 0.999203i | \(-0.512711\pi\) | ||||
−0.0399215 | + | 0.999203i | \(0.512711\pi\) | |||||||
\(464\) | −801433. | −0.172811 | ||||||||
\(465\) | −463141. | −0.0993300 | ||||||||
\(466\) | −1.26249e6 | −0.269317 | ||||||||
\(467\) | −2.78365e6 | −0.590640 | −0.295320 | − | 0.955398i | \(-0.595426\pi\) | ||||
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(468\) | −2.25230e6 | −0.475347 | ||||||||
\(469\) | 2.01393e6 | 0.422777 | ||||||||
\(470\) | −611082. | −0.127601 | ||||||||
\(471\) | 3.81494e6 | 0.792385 | ||||||||
\(472\) | 1.98328e6 | 0.409759 | ||||||||
\(473\) | 2.92580e6 | 0.601302 | ||||||||
\(474\) | 338028. | 0.0691047 | ||||||||
\(475\) | −1.57288e6 | −0.319861 | ||||||||
\(476\) | 321978. | 0.0651342 | ||||||||
\(477\) | −4.70028e6 | −0.945863 | ||||||||
\(478\) | −1.30662e6 | −0.261564 | ||||||||
\(479\) | 1.49820e6 | 0.298352 | 0.149176 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149176 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(480\) | 808946. | 0.160257 | ||||||||
\(481\) | 4.38099e6 | 0.863394 | ||||||||
\(482\) | 691497. | 0.135573 | ||||||||
\(483\) | −483770. | −0.0943563 | ||||||||
\(484\) | 2.17767e6 | 0.422550 | ||||||||
\(485\) | −1.55399e6 | −0.299982 | ||||||||
\(486\) | −800399. | −0.153715 | ||||||||
\(487\) | 7.95675e6 | 1.52024 | 0.760122 | − | 0.649781i | \(-0.225139\pi\) | ||||
0.760122 | + | 0.649781i | \(0.225139\pi\) | |||||||
\(488\) | −1.21910e6 | −0.231734 | ||||||||
\(489\) | 622498. | 0.117724 | ||||||||
\(490\) | −593712. | −0.111708 | ||||||||
\(491\) | −1.87342e6 | −0.350697 | −0.175348 | − | 0.984506i | \(-0.556105\pi\) | ||||
−0.175348 | + | 0.984506i | \(0.556105\pi\) | |||||||
\(492\) | 481411. | 0.0896609 | ||||||||
\(493\) | −235787. | −0.0436921 | ||||||||
\(494\) | 442341. | 0.0815530 | ||||||||
\(495\) | −2.59416e6 | −0.475865 | ||||||||
\(496\) | 1.40277e6 | 0.256026 | ||||||||
\(497\) | −1.02115e6 | −0.185438 | ||||||||
\(498\) | 286467. | 0.0517608 | ||||||||
\(499\) | −352286. | −0.0633350 | −0.0316675 | − | 0.999498i | \(-0.510082\pi\) | ||||
−0.0316675 | + | 0.999498i | \(0.510082\pi\) | |||||||
\(500\) | −5.93817e6 | −1.06225 | ||||||||
\(501\) | 1.41410e6 | 0.251701 | ||||||||
\(502\) | −1.43384e6 | −0.253946 | ||||||||
\(503\) | −3.57266e6 | −0.629611 | −0.314805 | − | 0.949156i | \(-0.601939\pi\) | ||||
−0.314805 | + | 0.949156i | \(0.601939\pi\) | |||||||
\(504\) | 387325. | 0.0679202 | ||||||||
\(505\) | −7.57085e6 | −1.32104 | ||||||||
\(506\) | 485865. | 0.0843606 | ||||||||
\(507\) | −1.63986e6 | −0.283327 | ||||||||
\(508\) | 463308. | 0.0796545 | ||||||||
\(509\) | −1.05719e7 | −1.80867 | −0.904337 | − | 0.426819i | \(-0.859634\pi\) | ||||
−0.904337 | + | 0.426819i | \(0.859634\pi\) | |||||||
\(510\) | 76182.1 | 0.0129696 | ||||||||
\(511\) | −1.16427e6 | −0.197243 | ||||||||
\(512\) | −4.11603e6 | −0.693911 | ||||||||
\(513\) | −4.22945e6 | −0.709562 | ||||||||
\(514\) | 869880. | 0.145228 | ||||||||
\(515\) | −3.73431e6 | −0.620430 | ||||||||
\(516\) | 2.13999e6 | 0.353825 | ||||||||
\(517\) | 4.80903e6 | 0.791282 | ||||||||
\(518\) | −372255. | −0.0609559 | ||||||||
\(519\) | −2.21984e6 | −0.361746 | ||||||||
\(520\) | 907408. | 0.147162 | ||||||||
\(521\) | 7.42701e6 | 1.19872 | 0.599362 | − | 0.800478i | \(-0.295421\pi\) | ||||
0.599362 | + | 0.800478i | \(0.295421\pi\) | |||||||
\(522\) | −140148. | −0.0225119 | ||||||||
\(523\) | −1.03292e7 | −1.65125 | −0.825623 | − | 0.564222i | \(-0.809176\pi\) | ||||
−0.825623 | + | 0.564222i | \(0.809176\pi\) | |||||||
\(524\) | 9.78788e6 | 1.55726 | ||||||||
\(525\) | 298123. | 0.0472060 | ||||||||
\(526\) | −875089. | −0.137908 | ||||||||
\(527\) | 412706. | 0.0647313 | ||||||||
\(528\) | −2.03778e6 | −0.318107 | ||||||||
\(529\) | −2.97263e6 | −0.461851 | ||||||||
\(530\) | 935663. | 0.144687 | ||||||||
\(531\) | −7.00523e6 | −1.07817 | ||||||||
\(532\) | 1.57496e6 | 0.241263 | ||||||||
\(533\) | 813193. | 0.123987 | ||||||||
\(534\) | −15666.5 | −0.00237750 | ||||||||
\(535\) | −749079. | −0.113147 | ||||||||
\(536\) | −2.99412e6 | −0.450151 | ||||||||
\(537\) | −423137. | −0.0633207 | ||||||||
\(538\) | 1.25675e6 | 0.187194 | ||||||||
\(539\) | 4.67233e6 | 0.692726 | ||||||||
\(540\) | −4.28694e6 | −0.632649 | ||||||||
\(541\) | 4.60833e6 | 0.676941 | 0.338470 | − | 0.940977i | \(-0.390091\pi\) | ||||
0.338470 | + | 0.940977i | \(0.390091\pi\) | |||||||
\(542\) | 1.39172e6 | 0.203495 | ||||||||
\(543\) | 2.84543e6 | 0.414142 | ||||||||
\(544\) | −720854. | −0.104436 | ||||||||
\(545\) | 171482. | 0.0247302 | ||||||||
\(546\) | −83841.3 | −0.0120358 | ||||||||
\(547\) | −1.79146e6 | −0.255999 | −0.127999 | − | 0.991774i | \(-0.540856\pi\) | ||||
−0.127999 | + | 0.991774i | \(0.540856\pi\) | |||||||
\(548\) | 7.94831e6 | 1.13064 | ||||||||
\(549\) | 4.30604e6 | 0.609743 | ||||||||
\(550\) | −299415. | −0.0422052 | ||||||||
\(551\) | −1.15336e6 | −0.161839 | ||||||||
\(552\) | 719224. | 0.100465 | ||||||||
\(553\) | 2.03303e6 | 0.282703 | ||||||||
\(554\) | −1.78219e6 | −0.246706 | ||||||||
\(555\) | 3.69071e6 | 0.508601 | ||||||||
\(556\) | 1.22182e7 | 1.67618 | ||||||||
\(557\) | 1.07840e7 | 1.47280 | 0.736399 | − | 0.676548i | \(-0.236525\pi\) | ||||
0.736399 | + | 0.676548i | \(0.236525\pi\) | |||||||
\(558\) | 245306. | 0.0333521 | ||||||||
\(559\) | 3.61485e6 | 0.489284 | ||||||||
\(560\) | 1.55736e6 | 0.209855 | ||||||||
\(561\) | −599530. | −0.0804273 | ||||||||
\(562\) | −18710.4 | −0.00249887 | ||||||||
\(563\) | −1.40598e7 | −1.86942 | −0.934710 | − | 0.355411i | \(-0.884341\pi\) | ||||
−0.934710 | + | 0.355411i | \(0.884341\pi\) | |||||||
\(564\) | 3.51743e6 | 0.465615 | ||||||||
\(565\) | −4.77310e6 | −0.629041 | ||||||||
\(566\) | 477355. | 0.0626326 | ||||||||
\(567\) | −921255. | −0.120343 | ||||||||
\(568\) | 1.51815e6 | 0.197444 | ||||||||
\(569\) | 4.09890e6 | 0.530746 | 0.265373 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265373 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(570\) | 372645. | 0.0480406 | ||||||||
\(571\) | −2.46148e6 | −0.315941 | −0.157971 | − | 0.987444i | \(-0.550495\pi\) | ||||
−0.157971 | + | 0.987444i | \(0.550495\pi\) | |||||||
\(572\) | −3.52841e6 | −0.450909 | ||||||||
\(573\) | −6.39168e6 | −0.813259 | ||||||||
\(574\) | −69097.5 | −0.00875351 | ||||||||
\(575\) | −2.13451e6 | −0.269233 | ||||||||
\(576\) | 5.45565e6 | 0.685157 | ||||||||
\(577\) | 7.09785e6 | 0.887539 | 0.443770 | − | 0.896141i | \(-0.353641\pi\) | ||||
0.443770 | + | 0.896141i | \(0.353641\pi\) | |||||||
\(578\) | 1.15836e6 | 0.144219 | ||||||||
\(579\) | 7.27718e6 | 0.902125 | ||||||||
\(580\) | −1.16903e6 | −0.144297 | ||||||||
\(581\) | 1.72292e6 | 0.211750 | ||||||||
\(582\) | −213467. | −0.0261230 | ||||||||
\(583\) | −7.36339e6 | −0.897235 | ||||||||
\(584\) | 1.73094e6 | 0.210014 | ||||||||
\(585\) | −3.20510e6 | −0.387215 | ||||||||
\(586\) | 1.32571e6 | 0.159479 | ||||||||
\(587\) | −1.43549e7 | −1.71951 | −0.859753 | − | 0.510710i | \(-0.829383\pi\) | ||||
−0.859753 | + | 0.510710i | \(0.829383\pi\) | |||||||
\(588\) | 3.41744e6 | 0.407622 | ||||||||
\(589\) | 2.01876e6 | 0.239770 | ||||||||
\(590\) | 1.39450e6 | 0.164925 | ||||||||
\(591\) | −6.12690e6 | −0.721559 | ||||||||
\(592\) | −1.11785e7 | −1.31093 | ||||||||
\(593\) | 1.01492e7 | 1.18521 | 0.592606 | − | 0.805493i | \(-0.298099\pi\) | ||||
0.592606 | + | 0.805493i | \(0.298099\pi\) | |||||||
\(594\) | −805122. | −0.0936258 | ||||||||
\(595\) | 458187. | 0.0530579 | ||||||||
\(596\) | −2.26110e6 | −0.260738 | ||||||||
\(597\) | 2.02204e6 | 0.232196 | ||||||||
\(598\) | 600290. | 0.0686449 | ||||||||
\(599\) | −8.76777e6 | −0.998440 | −0.499220 | − | 0.866475i | \(-0.666380\pi\) | ||||
−0.499220 | + | 0.866475i | \(0.666380\pi\) | |||||||
\(600\) | −443222. | −0.0502624 | ||||||||
\(601\) | 1.49619e7 | 1.68966 | 0.844831 | − | 0.535034i | \(-0.179701\pi\) | ||||
0.844831 | + | 0.535034i | \(0.179701\pi\) | |||||||
\(602\) | −307156. | −0.0345436 | ||||||||
\(603\) | 1.05757e7 | 1.18445 | ||||||||
\(604\) | 7.10779e6 | 0.792760 | ||||||||
\(605\) | 3.09890e6 | 0.344206 | ||||||||
\(606\) | −1.03998e6 | −0.115039 | ||||||||
\(607\) | 7.03290e6 | 0.774752 | 0.387376 | − | 0.921922i | \(-0.373382\pi\) | ||||
0.387376 | + | 0.921922i | \(0.373382\pi\) | |||||||
\(608\) | −3.52606e6 | −0.386840 | ||||||||
\(609\) | 218607. | 0.0238847 | ||||||||
\(610\) | −857182. | −0.0932714 | ||||||||
\(611\) | 5.94159e6 | 0.643873 | ||||||||
\(612\) | 1.69080e6 | 0.182479 | ||||||||
\(613\) | −806845. | −0.0867239 | −0.0433620 | − | 0.999059i | \(-0.513807\pi\) | ||||
−0.0433620 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(614\) | 2.32439e6 | 0.248822 | ||||||||
\(615\) | 685065. | 0.0730372 | ||||||||
\(616\) | 606777. | 0.0644284 | ||||||||
\(617\) | 7.36483e6 | 0.778843 | 0.389421 | − | 0.921060i | \(-0.372675\pi\) | ||||
0.389421 | + | 0.921060i | \(0.372675\pi\) | |||||||
\(618\) | −512970. | −0.0540283 | ||||||||
\(619\) | −1.30528e7 | −1.36923 | −0.684617 | − | 0.728903i | \(-0.740031\pi\) | ||||
−0.684617 | + | 0.728903i | \(0.740031\pi\) | |||||||
\(620\) | 2.04620e6 | 0.213781 | ||||||||
\(621\) | −5.73967e6 | −0.597253 | ||||||||
\(622\) | 1.62842e6 | 0.168768 | ||||||||
\(623\) | −94224.4 | −0.00972620 | ||||||||
\(624\) | −2.51769e6 | −0.258846 | ||||||||
\(625\) | −4.86615e6 | −0.498294 | ||||||||
\(626\) | 2.14305e6 | 0.218573 | ||||||||
\(627\) | −2.93261e6 | −0.297910 | ||||||||
\(628\) | −1.68548e7 | −1.70539 | ||||||||
\(629\) | −3.28880e6 | −0.331445 | ||||||||
\(630\) | 272339. | 0.0273375 | ||||||||
\(631\) | 2.89105e6 | 0.289056 | 0.144528 | − | 0.989501i | \(-0.453834\pi\) | ||||
0.144528 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(632\) | −3.02252e6 | −0.301007 | ||||||||
\(633\) | −6.50063e6 | −0.644831 | ||||||||
\(634\) | −176594. | −0.0174482 | ||||||||
\(635\) | 659304. | 0.0648860 | ||||||||
\(636\) | −5.38573e6 | −0.527961 | ||||||||
\(637\) | 5.77270e6 | 0.563677 | ||||||||
\(638\) | −219554. | −0.0213545 | ||||||||
\(639\) | −5.36234e6 | −0.519520 | ||||||||
\(640\) | −4.74532e6 | −0.457947 | ||||||||
\(641\) | −1.31397e7 | −1.26311 | −0.631555 | − | 0.775331i | \(-0.717583\pi\) | ||||
−0.631555 | + | 0.775331i | \(0.717583\pi\) | |||||||
\(642\) | −102899. | −0.00985307 | ||||||||
\(643\) | −1.17266e7 | −1.11852 | −0.559259 | − | 0.828993i | \(-0.688914\pi\) | ||||
−0.559259 | + | 0.828993i | \(0.688914\pi\) | |||||||
\(644\) | 2.13734e6 | 0.203076 | ||||||||
\(645\) | 3.04529e6 | 0.288223 | ||||||||
\(646\) | −332065. | −0.0313071 | ||||||||
\(647\) | 1.10662e7 | 1.03929 | 0.519646 | − | 0.854382i | \(-0.326064\pi\) | ||||
0.519646 | + | 0.854382i | \(0.326064\pi\) | |||||||
\(648\) | 1.36964e6 | 0.128135 | ||||||||
\(649\) | −1.09743e7 | −1.02274 | ||||||||
\(650\) | −369929. | −0.0343427 | ||||||||
\(651\) | −382635. | −0.0353860 | ||||||||
\(652\) | −2.75025e6 | −0.253369 | ||||||||
\(653\) | −3.44597e6 | −0.316249 | −0.158124 | − | 0.987419i | \(-0.550545\pi\) | ||||
−0.158124 | + | 0.987419i | \(0.550545\pi\) | |||||||
\(654\) | 23555.9 | 0.00215355 | ||||||||
\(655\) | 1.39285e7 | 1.26853 | ||||||||
\(656\) | −2.07495e6 | −0.188255 | ||||||||
\(657\) | −6.11392e6 | −0.552594 | ||||||||
\(658\) | −504860. | −0.0454576 | ||||||||
\(659\) | −9.12181e6 | −0.818215 | −0.409108 | − | 0.912486i | \(-0.634160\pi\) | ||||
−0.409108 | + | 0.912486i | \(0.634160\pi\) | |||||||
\(660\) | −2.97247e6 | −0.265618 | ||||||||
\(661\) | 1.68113e7 | 1.49657 | 0.748287 | − | 0.663375i | \(-0.230877\pi\) | ||||
0.748287 | + | 0.663375i | \(0.230877\pi\) | |||||||
\(662\) | −1.37145e6 | −0.121629 | ||||||||
\(663\) | −740723. | −0.0654443 | ||||||||
\(664\) | −2.56147e6 | −0.225460 | ||||||||
\(665\) | 2.24123e6 | 0.196531 | ||||||||
\(666\) | −1.95481e6 | −0.170773 | ||||||||
\(667\) | −1.56519e6 | −0.136224 | ||||||||
\(668\) | −6.24760e6 | −0.541716 | ||||||||
\(669\) | 3.43897e6 | 0.297073 | ||||||||
\(670\) | −2.10525e6 | −0.181183 | ||||||||
\(671\) | 6.74577e6 | 0.578396 | ||||||||
\(672\) | 668330. | 0.0570910 | ||||||||
\(673\) | 8.53511e6 | 0.726393 | 0.363196 | − | 0.931713i | \(-0.381685\pi\) | ||||
0.363196 | + | 0.931713i | \(0.381685\pi\) | |||||||
\(674\) | 702670. | 0.0595802 | ||||||||
\(675\) | 3.53708e6 | 0.298803 | ||||||||
\(676\) | 7.24506e6 | 0.609783 | ||||||||
\(677\) | −912690. | −0.0765335 | −0.0382667 | − | 0.999268i | \(-0.512184\pi\) | ||||
−0.0382667 | + | 0.999268i | \(0.512184\pi\) | |||||||
\(678\) | −655665. | −0.0547782 | ||||||||
\(679\) | −1.28387e6 | −0.106868 | ||||||||
\(680\) | −681191. | −0.0564932 | ||||||||
\(681\) | −3.94481e6 | −0.325955 | ||||||||
\(682\) | 384292. | 0.0316374 | ||||||||
\(683\) | −4.20567e6 | −0.344972 | −0.172486 | − | 0.985012i | \(-0.555180\pi\) | ||||
−0.172486 | + | 0.985012i | \(0.555180\pi\) | |||||||
\(684\) | 8.27055e6 | 0.675918 | ||||||||
\(685\) | 1.13107e7 | 0.921010 | ||||||||
\(686\) | −1.02386e6 | −0.0830677 | ||||||||
\(687\) | 3.11466e6 | 0.251779 | ||||||||
\(688\) | −9.22366e6 | −0.742903 | ||||||||
\(689\) | −9.09751e6 | −0.730087 | ||||||||
\(690\) | 505707. | 0.0404367 | ||||||||
\(691\) | 6.23030e6 | 0.496379 | 0.248190 | − | 0.968711i | \(-0.420164\pi\) | ||||
0.248190 | + | 0.968711i | \(0.420164\pi\) | |||||||
\(692\) | 9.80746e6 | 0.778559 | ||||||||
\(693\) | −2.14323e6 | −0.169525 | ||||||||
\(694\) | −445670. | −0.0351249 | ||||||||
\(695\) | 1.73870e7 | 1.36541 | ||||||||
\(696\) | −325005. | −0.0254312 | ||||||||
\(697\) | −610464. | −0.0475968 | ||||||||
\(698\) | 2.29005e6 | 0.177913 | ||||||||
\(699\) | 1.03412e7 | 0.800527 | ||||||||
\(700\) | −1.31713e6 | −0.101598 | ||||||||
\(701\) | 1.69453e7 | 1.30243 | 0.651215 | − | 0.758893i | \(-0.274259\pi\) | ||||
0.651215 | + | 0.758893i | \(0.274259\pi\) | |||||||
\(702\) | −994733. | −0.0761840 | ||||||||
\(703\) | −1.60872e7 | −1.22770 | ||||||||
\(704\) | 8.54673e6 | 0.649933 | ||||||||
\(705\) | 5.00542e6 | 0.379287 | ||||||||
\(706\) | −337961. | −0.0255185 | ||||||||
\(707\) | −6.25484e6 | −0.470617 | ||||||||
\(708\) | −8.02680e6 | −0.601810 | ||||||||
\(709\) | −1.87326e7 | −1.39953 | −0.699766 | − | 0.714372i | \(-0.746712\pi\) | ||||
−0.699766 | + | 0.714372i | \(0.746712\pi\) | |||||||
\(710\) | 1.06746e6 | 0.0794702 | ||||||||
\(711\) | 1.06760e7 | 0.792016 | ||||||||
\(712\) | 140084. | 0.0103559 | ||||||||
\(713\) | 2.73960e6 | 0.201820 | ||||||||
\(714\) | 62939.6 | 0.00462039 | ||||||||
\(715\) | −5.02106e6 | −0.367308 | ||||||||
\(716\) | 1.86946e6 | 0.136280 | ||||||||
\(717\) | 1.07026e7 | 0.777485 | ||||||||
\(718\) | −2.62536e6 | −0.190054 | ||||||||
\(719\) | 2.15611e6 | 0.155542 | 0.0777711 | − | 0.996971i | \(-0.475220\pi\) | ||||
0.0777711 | + | 0.996971i | \(0.475220\pi\) | |||||||
\(720\) | 8.17814e6 | 0.587927 | ||||||||
\(721\) | −3.08519e6 | −0.221026 | ||||||||
\(722\) | 514154. | 0.0367071 | ||||||||
\(723\) | −5.66410e6 | −0.402982 | ||||||||
\(724\) | −1.25714e7 | −0.891326 | ||||||||
\(725\) | 964548. | 0.0681520 | ||||||||
\(726\) | 425686. | 0.0299742 | ||||||||
\(727\) | 4.87466e6 | 0.342065 | 0.171032 | − | 0.985265i | \(-0.445290\pi\) | ||||
0.171032 | + | 0.985265i | \(0.445290\pi\) | |||||||
\(728\) | 749677. | 0.0524259 | ||||||||
\(729\) | 463697. | 0.0323159 | ||||||||
\(730\) | 1.21707e6 | 0.0845295 | ||||||||
\(731\) | −2.71367e6 | −0.187829 | ||||||||
\(732\) | 4.93399e6 | 0.340346 | ||||||||
\(733\) | 5.15920e6 | 0.354669 | 0.177334 | − | 0.984151i | \(-0.443253\pi\) | ||||
0.177334 | + | 0.984151i | \(0.443253\pi\) | |||||||
\(734\) | −888660. | −0.0608829 | ||||||||
\(735\) | 4.86314e6 | 0.332046 | ||||||||
\(736\) | −4.78513e6 | −0.325611 | ||||||||
\(737\) | 1.65677e7 | 1.12355 | ||||||||
\(738\) | −362850. | −0.0245237 | ||||||||
\(739\) | −4.60821e6 | −0.310400 | −0.155200 | − | 0.987883i | \(-0.549602\pi\) | ||||
−0.155200 | + | 0.987883i | \(0.549602\pi\) | |||||||
\(740\) | −1.63059e7 | −1.09462 | ||||||||
\(741\) | −3.62325e6 | −0.242411 | ||||||||
\(742\) | 773020. | 0.0515444 | ||||||||
\(743\) | 2.50473e7 | 1.66452 | 0.832261 | − | 0.554384i | \(-0.187046\pi\) | ||||
0.832261 | + | 0.554384i | \(0.187046\pi\) | |||||||
\(744\) | 568866. | 0.0376771 | ||||||||
\(745\) | −3.21763e6 | −0.212396 | ||||||||
\(746\) | 3.82037e6 | 0.251338 | ||||||||
\(747\) | 9.04751e6 | 0.593236 | ||||||||
\(748\) | 2.64878e6 | 0.173098 | ||||||||
\(749\) | −618870. | −0.0403083 | ||||||||
\(750\) | −1.16078e6 | −0.0753524 | ||||||||
\(751\) | −1.87279e7 | −1.21168 | −0.605841 | − | 0.795586i | \(-0.707163\pi\) | ||||
−0.605841 | + | 0.795586i | \(0.707163\pi\) | |||||||
\(752\) | −1.51606e7 | −0.977623 | ||||||||
\(753\) | 1.17447e7 | 0.754839 | ||||||||
\(754\) | −271260. | −0.0173763 | ||||||||
\(755\) | 1.01146e7 | 0.645778 | ||||||||
\(756\) | −3.54176e6 | −0.225379 | ||||||||
\(757\) | −5.50814e6 | −0.349354 | −0.174677 | − | 0.984626i | \(-0.555888\pi\) | ||||
−0.174677 | + | 0.984626i | \(0.555888\pi\) | |||||||
\(758\) | 3.65750e6 | 0.231212 | ||||||||
\(759\) | −3.97976e6 | −0.250757 | ||||||||
\(760\) | −3.33205e6 | −0.209256 | ||||||||
\(761\) | −2.67826e7 | −1.67645 | −0.838226 | − | 0.545323i | \(-0.816407\pi\) | ||||
−0.838226 | + | 0.545323i | \(0.816407\pi\) | |||||||
\(762\) | 90566.4 | 0.00565040 | ||||||||
\(763\) | 141674. | 0.00881005 | ||||||||
\(764\) | 2.82390e7 | 1.75032 | ||||||||
\(765\) | 2.40607e6 | 0.148646 | ||||||||
\(766\) | 772511. | 0.0475699 | ||||||||
\(767\) | −1.35588e7 | −0.832209 | ||||||||
\(768\) | 5.74859e6 | 0.351689 | ||||||||
\(769\) | 1.76374e7 | 1.07552 | 0.537761 | − | 0.843097i | \(-0.319270\pi\) | ||||
0.537761 | + | 0.843097i | \(0.319270\pi\) | |||||||
\(770\) | 426642. | 0.0259320 | ||||||||
\(771\) | −7.12526e6 | −0.431683 | ||||||||
\(772\) | −3.21512e7 | −1.94158 | ||||||||
\(773\) | −6.59079e6 | −0.396724 | −0.198362 | − | 0.980129i | \(-0.563562\pi\) | ||||
−0.198362 | + | 0.980129i | \(0.563562\pi\) | |||||||
\(774\) | −1.61296e6 | −0.0967768 | ||||||||
\(775\) | −1.68828e6 | −0.100970 | ||||||||
\(776\) | 1.90874e6 | 0.113787 | ||||||||
\(777\) | 3.04917e6 | 0.181188 | ||||||||
\(778\) | −3.11463e6 | −0.184484 | ||||||||
\(779\) | −2.98609e6 | −0.176303 | ||||||||
\(780\) | −3.67250e6 | −0.216135 | ||||||||
\(781\) | −8.40056e6 | −0.492811 | ||||||||
\(782\) | −450637. | −0.0263518 | ||||||||
\(783\) | 2.59366e6 | 0.151185 | ||||||||
\(784\) | −1.47296e7 | −0.855858 | ||||||||
\(785\) | −2.39849e7 | −1.38920 | ||||||||
\(786\) | 1.91331e6 | 0.110466 | ||||||||
\(787\) | 1.83730e7 | 1.05741 | 0.528704 | − | 0.848806i | \(-0.322678\pi\) | ||||
0.528704 | + | 0.848806i | \(0.322678\pi\) | |||||||
\(788\) | 2.70692e7 | 1.55296 | ||||||||
\(789\) | 7.16792e6 | 0.409922 | ||||||||
\(790\) | −2.12522e6 | −0.121153 | ||||||||
\(791\) | −3.94341e6 | −0.224094 | ||||||||
\(792\) | 3.18635e6 | 0.180502 | ||||||||
\(793\) | 8.33444e6 | 0.470645 | ||||||||
\(794\) | 1.69441e6 | 0.0953824 | ||||||||
\(795\) | −7.66409e6 | −0.430074 | ||||||||
\(796\) | −8.93356e6 | −0.499737 | ||||||||
\(797\) | −3.06769e7 | −1.71067 | −0.855334 | − | 0.518078i | \(-0.826648\pi\) | ||||
−0.855334 | + | 0.518078i | \(0.826648\pi\) | |||||||
\(798\) | 307870. | 0.0171143 | ||||||||
\(799\) | −4.46035e6 | −0.247174 | ||||||||
\(800\) | 2.94884e6 | 0.162902 | ||||||||
\(801\) | −494798. | −0.0272488 | ||||||||
\(802\) | 622784. | 0.0341902 | ||||||||
\(803\) | −9.57797e6 | −0.524185 | ||||||||
\(804\) | 1.21180e7 | 0.661134 | ||||||||
\(805\) | 3.04151e6 | 0.165424 | ||||||||
\(806\) | 474796. | 0.0257436 | ||||||||
\(807\) | −1.02941e7 | −0.556423 | ||||||||
\(808\) | 9.29912e6 | 0.501088 | ||||||||
\(809\) | −2.81720e6 | −0.151338 | −0.0756688 | − | 0.997133i | \(-0.524109\pi\) | ||||
−0.0756688 | + | 0.997133i | \(0.524109\pi\) | |||||||
\(810\) | 963031. | 0.0515736 | ||||||||
\(811\) | −1.57819e7 | −0.842574 | −0.421287 | − | 0.906927i | \(-0.638421\pi\) | ||||
−0.421287 | + | 0.906927i | \(0.638421\pi\) | |||||||
\(812\) | −965825. | −0.0514053 | ||||||||
\(813\) | −1.13997e7 | −0.604877 | ||||||||
\(814\) | −3.06238e6 | −0.161994 | ||||||||
\(815\) | −3.91371e6 | −0.206393 | ||||||||
\(816\) | 1.89003e6 | 0.0993673 | ||||||||
\(817\) | −1.32739e7 | −0.695735 | ||||||||
\(818\) | −1.15195e6 | −0.0601935 | ||||||||
\(819\) | −2.64797e6 | −0.137944 | ||||||||
\(820\) | −3.02668e6 | −0.157192 | ||||||||
\(821\) | −2.40563e6 | −0.124558 | −0.0622789 | − | 0.998059i | \(-0.519837\pi\) | ||||
−0.0622789 | + | 0.998059i | \(0.519837\pi\) | |||||||
\(822\) | 1.55372e6 | 0.0802034 | ||||||||
\(823\) | 4.47397e6 | 0.230247 | 0.115123 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115123 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(824\) | 4.58678e6 | 0.235337 | ||||||||
\(825\) | 2.45253e6 | 0.125453 | ||||||||
\(826\) | 1.15210e6 | 0.0587542 | ||||||||
\(827\) | 2.36054e7 | 1.20018 | 0.600091 | − | 0.799932i | \(-0.295131\pi\) | ||||
0.600091 | + | 0.799932i | \(0.295131\pi\) | |||||||
\(828\) | 1.12237e7 | 0.568934 | ||||||||
\(829\) | −7.52668e6 | −0.380380 | −0.190190 | − | 0.981747i | \(-0.560910\pi\) | ||||
−0.190190 | + | 0.981747i | \(0.560910\pi\) | |||||||
\(830\) | −1.80105e6 | −0.0907464 | ||||||||
\(831\) | 1.45981e7 | 0.733319 | ||||||||
\(832\) | 1.05595e7 | 0.528855 | ||||||||
\(833\) | −4.33356e6 | −0.216388 | ||||||||
\(834\) | 2.38839e6 | 0.118902 | ||||||||
\(835\) | −8.89056e6 | −0.441279 | ||||||||
\(836\) | 1.29565e7 | 0.641169 | ||||||||
\(837\) | −4.53976e6 | −0.223985 | ||||||||
\(838\) | 3.89754e6 | 0.191726 | ||||||||
\(839\) | −7.28878e6 | −0.357478 | −0.178739 | − | 0.983896i | \(-0.557202\pi\) | ||||
−0.178739 | + | 0.983896i | \(0.557202\pi\) | |||||||
\(840\) | 631556. | 0.0308826 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | −848249. | −0.0412328 | ||||||||
\(843\) | 153259. | 0.00742773 | ||||||||
\(844\) | 2.87204e7 | 1.38782 | ||||||||
\(845\) | 1.03100e7 | 0.496725 | ||||||||
\(846\) | −2.65116e6 | −0.127353 | ||||||||
\(847\) | 2.56023e6 | 0.122623 | ||||||||
\(848\) | 2.32132e7 | 1.10853 | ||||||||
\(849\) | −3.91005e6 | −0.186172 | ||||||||
\(850\) | 277705. | 0.0131837 | ||||||||
\(851\) | −2.18315e7 | −1.03338 | ||||||||
\(852\) | −6.14434e6 | −0.289985 | ||||||||
\(853\) | 2.18767e7 | 1.02946 | 0.514729 | − | 0.857353i | \(-0.327893\pi\) | ||||
0.514729 | + | 0.857353i | \(0.327893\pi\) | |||||||
\(854\) | −708182. | −0.0332277 | ||||||||
\(855\) | 1.17693e7 | 0.550599 | ||||||||
\(856\) | 920079. | 0.0429181 | ||||||||
\(857\) | −1.62738e7 | −0.756897 | −0.378448 | − | 0.925622i | \(-0.623542\pi\) | ||||
−0.378448 | + | 0.925622i | \(0.623542\pi\) | |||||||
\(858\) | −689726. | −0.0319859 | ||||||||
\(859\) | 1.50220e7 | 0.694615 | 0.347308 | − | 0.937751i | \(-0.387096\pi\) | ||||
0.347308 | + | 0.937751i | \(0.387096\pi\) | |||||||
\(860\) | −1.34544e7 | −0.620321 | ||||||||
\(861\) | 565983. | 0.0260193 | ||||||||
\(862\) | −4.59269e6 | −0.210523 | ||||||||
\(863\) | 2.24278e7 | 1.02508 | 0.512542 | − | 0.858662i | \(-0.328704\pi\) | ||||
0.512542 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(864\) | 7.92938e6 | 0.361372 | ||||||||
\(865\) | 1.39564e7 | 0.634209 | ||||||||
\(866\) | −586650. | −0.0265818 | ||||||||
\(867\) | −9.48819e6 | −0.428682 | ||||||||
\(868\) | 1.69051e6 | 0.0761587 | ||||||||
\(869\) | 1.67248e7 | 0.751298 | ||||||||
\(870\) | −228520. | −0.0102359 | ||||||||
\(871\) | 2.04695e7 | 0.914244 | ||||||||
\(872\) | −210628. | −0.00938047 | ||||||||
\(873\) | −6.74196e6 | −0.299399 | ||||||||
\(874\) | −2.20430e6 | −0.0976093 | ||||||||
\(875\) | −6.98136e6 | −0.308262 | ||||||||
\(876\) | −7.00552e6 | −0.308447 | ||||||||
\(877\) | 1.25450e7 | 0.550771 | 0.275385 | − | 0.961334i | \(-0.411195\pi\) | ||||
0.275385 | + | 0.961334i | \(0.411195\pi\) | |||||||
\(878\) | −3.05399e6 | −0.133700 | ||||||||
\(879\) | −1.08590e7 | −0.474043 | ||||||||
\(880\) | 1.28117e7 | 0.557701 | ||||||||
\(881\) | 7.60341e6 | 0.330042 | 0.165021 | − | 0.986290i | \(-0.447231\pi\) | ||||
0.165021 | + | 0.986290i | \(0.447231\pi\) | |||||||
\(882\) | −2.57580e6 | −0.111491 | ||||||||
\(883\) | 2.15220e7 | 0.928923 | 0.464462 | − | 0.885593i | \(-0.346248\pi\) | ||||
0.464462 | + | 0.885593i | \(0.346248\pi\) | |||||||
\(884\) | 3.27258e6 | 0.140851 | ||||||||
\(885\) | −1.14224e7 | −0.490231 | ||||||||
\(886\) | 1.16848e6 | 0.0500079 | ||||||||
\(887\) | −333279. | −0.0142232 | −0.00711162 | − | 0.999975i | \(-0.502264\pi\) | ||||
−0.00711162 | + | 0.999975i | \(0.502264\pi\) | |||||||
\(888\) | −4.53322e6 | −0.192919 | ||||||||
\(889\) | 544700. | 0.0231155 | ||||||||
\(890\) | 98497.2 | 0.00416820 | ||||||||
\(891\) | −7.57876e6 | −0.319819 | ||||||||
\(892\) | −1.51937e7 | −0.639368 | ||||||||
\(893\) | −2.18178e7 | −0.915552 | ||||||||
\(894\) | −441995. | −0.0184958 | ||||||||
\(895\) | 2.66031e6 | 0.111013 | ||||||||
\(896\) | −3.92046e6 | −0.163142 | ||||||||
\(897\) | −4.91702e6 | −0.204043 | ||||||||
\(898\) | 1.76661e6 | 0.0731055 | ||||||||
\(899\) | −1.23798e6 | −0.0510873 | ||||||||
\(900\) | −6.91664e6 | −0.284635 | ||||||||
\(901\) | 6.82950e6 | 0.280270 | ||||||||
\(902\) | −568435. | −0.0232629 | ||||||||
\(903\) | 2.51594e6 | 0.102679 | ||||||||
\(904\) | 5.86270e6 | 0.238603 | ||||||||
\(905\) | −1.78895e7 | −0.726068 | ||||||||
\(906\) | 1.38941e6 | 0.0562356 | ||||||||
\(907\) | 1.65687e7 | 0.668759 | 0.334380 | − | 0.942439i | \(-0.391473\pi\) | ||||
0.334380 | + | 0.942439i | \(0.391473\pi\) | |||||||
\(908\) | 1.74285e7 | 0.701529 | ||||||||
\(909\) | −3.28459e7 | −1.31847 | ||||||||
\(910\) | 527119. | 0.0211011 | ||||||||
\(911\) | 1.30648e7 | 0.521561 | 0.260781 | − | 0.965398i | \(-0.416020\pi\) | ||||
0.260781 | + | 0.965398i | \(0.416020\pi\) | |||||||
\(912\) | 9.24510e6 | 0.368065 | ||||||||
\(913\) | 1.41737e7 | 0.562737 | ||||||||
\(914\) | −7.32693e6 | −0.290106 | ||||||||
\(915\) | 7.02125e6 | 0.277244 | ||||||||
\(916\) | −1.37608e7 | −0.541884 | ||||||||
\(917\) | 1.15074e7 | 0.451911 | ||||||||
\(918\) | 746746. | 0.0292460 | ||||||||
\(919\) | −7.30805e6 | −0.285439 | −0.142719 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142719 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(920\) | −4.52184e6 | −0.176135 | ||||||||
\(921\) | −1.90393e7 | −0.739608 | ||||||||
\(922\) | 1.78596e6 | 0.0691902 | ||||||||
\(923\) | −1.03789e7 | −0.401004 | ||||||||
\(924\) | −2.45578e6 | −0.0946256 | ||||||||
\(925\) | 1.34537e7 | 0.516996 | ||||||||
\(926\) | 318069. | 0.0121897 | ||||||||
\(927\) | −1.62012e7 | −0.619224 | ||||||||
\(928\) | 2.16232e6 | 0.0824231 | ||||||||
\(929\) | 2.69866e7 | 1.02591 | 0.512955 | − | 0.858416i | \(-0.328551\pi\) | ||||
0.512955 | + | 0.858416i | \(0.328551\pi\) | |||||||
\(930\) | 399986. | 0.0151648 | ||||||||
\(931\) | −2.11976e7 | −0.801518 | ||||||||
\(932\) | −4.56881e7 | −1.72291 | ||||||||
\(933\) | −1.33385e7 | −0.501652 | ||||||||
\(934\) | 2.40407e6 | 0.0901737 | ||||||||
\(935\) | 3.76930e6 | 0.141004 | ||||||||
\(936\) | 3.93676e6 | 0.146876 | ||||||||
\(937\) | −2.15536e7 | −0.801993 | −0.400997 | − | 0.916080i | \(-0.631336\pi\) | ||||
−0.400997 | + | 0.916080i | \(0.631336\pi\) | |||||||
\(938\) | −1.73930e6 | −0.0645459 | ||||||||
\(939\) | −1.75539e7 | −0.649694 | ||||||||
\(940\) | −2.21144e7 | −0.816311 | ||||||||
\(941\) | −1.22668e7 | −0.451602 | −0.225801 | − | 0.974173i | \(-0.572500\pi\) | ||||
−0.225801 | + | 0.974173i | \(0.572500\pi\) | |||||||
\(942\) | −3.29473e6 | −0.120974 | ||||||||
\(943\) | −4.05234e6 | −0.148398 | ||||||||
\(944\) | 3.45966e7 | 1.26358 | ||||||||
\(945\) | −5.04005e6 | −0.183593 | ||||||||
\(946\) | −2.52684e6 | −0.0918014 | ||||||||
\(947\) | 5.13280e7 | 1.85986 | 0.929928 | − | 0.367741i | \(-0.119869\pi\) | ||||
0.929928 | + | 0.367741i | \(0.119869\pi\) | |||||||
\(948\) | 1.22329e7 | 0.442087 | ||||||||
\(949\) | −1.18336e7 | −0.426533 | ||||||||
\(950\) | 1.35840e6 | 0.0488335 | ||||||||
\(951\) | 1.44649e6 | 0.0518638 | ||||||||
\(952\) | −562782. | −0.0201255 | ||||||||
\(953\) | −3.30301e7 | −1.17809 | −0.589044 | − | 0.808101i | \(-0.700496\pi\) | ||||
−0.589044 | + | 0.808101i | \(0.700496\pi\) | |||||||
\(954\) | 4.05934e6 | 0.144406 | ||||||||
\(955\) | 4.01852e7 | 1.42580 | ||||||||
\(956\) | −4.72851e7 | −1.67332 | ||||||||
\(957\) | 1.79838e6 | 0.0634750 | ||||||||
\(958\) | −1.29390e6 | −0.0455498 | ||||||||
\(959\) | 9.34463e6 | 0.328107 | ||||||||
\(960\) | 8.89576e6 | 0.311534 | ||||||||
\(961\) | −2.64623e7 | −0.924312 | ||||||||
\(962\) | −3.78359e6 | −0.131815 | ||||||||
\(963\) | −3.24986e6 | −0.112927 | ||||||||
\(964\) | 2.50245e7 | 0.867307 | ||||||||
\(965\) | −4.57524e7 | −1.58160 | ||||||||
\(966\) | 417802. | 0.0144055 | ||||||||
\(967\) | −7.77281e6 | −0.267308 | −0.133654 | − | 0.991028i | \(-0.542671\pi\) | ||||
−0.133654 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(968\) | −3.80632e6 | −0.130562 | ||||||||
\(969\) | 2.71997e6 | 0.0930583 | ||||||||
\(970\) | 1.34209e6 | 0.0457986 | ||||||||
\(971\) | 2.31111e7 | 0.786635 | 0.393317 | − | 0.919403i | \(-0.371327\pi\) | ||||
0.393317 | + | 0.919403i | \(0.371327\pi\) | |||||||
\(972\) | −2.89656e7 | −0.983369 | ||||||||
\(973\) | 1.43647e7 | 0.486422 | ||||||||
\(974\) | −6.87175e6 | −0.232097 | ||||||||
\(975\) | 3.03012e6 | 0.102082 | ||||||||
\(976\) | −2.12662e7 | −0.714603 | ||||||||
\(977\) | 1.04792e7 | 0.351231 | 0.175616 | − | 0.984459i | \(-0.443808\pi\) | ||||
0.175616 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(978\) | −537613. | −0.0179731 | ||||||||
\(979\) | −775143. | −0.0258479 | ||||||||
\(980\) | −2.14858e7 | −0.714638 | ||||||||
\(981\) | 743969. | 0.0246821 | ||||||||
\(982\) | 1.61796e6 | 0.0535413 | ||||||||
\(983\) | 3.94189e7 | 1.30113 | 0.650565 | − | 0.759450i | \(-0.274532\pi\) | ||||
0.650565 | + | 0.759450i | \(0.274532\pi\) | |||||||
\(984\) | −841452. | −0.0277039 | ||||||||
\(985\) | 3.85204e7 | 1.26503 | ||||||||
\(986\) | 203635. | 0.00667052 | ||||||||
\(987\) | 4.13535e6 | 0.135120 | ||||||||
\(988\) | 1.60079e7 | 0.521724 | ||||||||
\(989\) | −1.80137e7 | −0.585615 | ||||||||
\(990\) | 2.24042e6 | 0.0726508 | ||||||||
\(991\) | −4.53294e7 | −1.46621 | −0.733104 | − | 0.680117i | \(-0.761929\pi\) | ||||
−0.733104 | + | 0.680117i | \(0.761929\pi\) | |||||||
\(992\) | −3.78477e6 | −0.122113 | ||||||||
\(993\) | 1.12337e7 | 0.361534 | ||||||||
\(994\) | 881905. | 0.0283110 | ||||||||
\(995\) | −1.27128e7 | −0.407083 | ||||||||
\(996\) | 1.03669e7 | 0.331132 | ||||||||
\(997\) | 4.74723e7 | 1.51253 | 0.756263 | − | 0.654268i | \(-0.227023\pi\) | ||||
0.756263 | + | 0.654268i | \(0.227023\pi\) | |||||||
\(998\) | 304247. | 0.00966942 | ||||||||
\(999\) | 3.61768e7 | 1.14687 |
(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 | 29.6.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 261.6.a.a.1.3 | 4 | |||
4.3 | odd | 2 | 464.6.a.i.1.1 | 4 | |||
5.4 | even | 2 | 725.6.a.a.1.3 | 4 | |||
29.28 | even | 2 | 841.6.a.a.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
261.6.a.a.1.3 | 4 | 3.2 | odd | 2 | |||
464.6.a.i.1.1 | 4 | 4.3 | odd | 2 | |||
725.6.a.a.1.3 | 4 | 5.4 | even | 2 | |||
841.6.a.a.1.3 | 4 | 29.28 | even | 2 |