Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(21,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} - 109104 x^{12} - 96128 x^{11} + 3580672 x^{10} - 1538048 x^{9} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.20 | ||
Root | \(2.93366 - 2.71913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 40.21 |
Dual form | 40.6.d.a.21.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65278 | + | 0.214529i | 0.999281 | + | 0.0379236i | ||||
\(3\) | 18.7876i | 1.20523i | 0.798033 | + | 0.602614i | \(0.205874\pi\) | ||||
−0.798033 | + | 0.602614i | \(0.794126\pi\) | |||||||
\(4\) | 31.9080 | + | 2.42537i | 0.997124 | + | 0.0757927i | ||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | −4.03048 | + | 106.202i | −0.0457066 | + | 1.20436i | ||||
\(7\) | −107.536 | −0.829487 | −0.414743 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414743 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(8\) | 179.848 | + | 20.5552i | 0.993532 | + | 0.113553i | ||||
\(9\) | −109.975 | −0.452573 | ||||||||
\(10\) | −5.36321 | + | 141.320i | −0.0169600 | + | 0.446892i | ||||
\(11\) | 272.206i | 0.678290i | 0.940734 | + | 0.339145i | \(0.110138\pi\) | ||||
−0.940734 | + | 0.339145i | \(0.889862\pi\) | |||||||
\(12\) | −45.5669 | + | 599.475i | −0.0913475 | + | 1.20176i | ||||
\(13\) | − | 198.402i | − | 0.325602i | −0.986659 | − | 0.162801i | \(-0.947947\pi\) | ||
0.986659 | − | 0.162801i | \(-0.0520529\pi\) | |||||||
\(14\) | −607.879 | − | 23.0696i | −0.828890 | − | 0.0314572i | ||||
\(15\) | −469.691 | −0.538994 | ||||||||
\(16\) | 1012.24 | + | 154.777i | 0.988511 | + | 0.151149i | ||||
\(17\) | 2065.79 | 1.73366 | 0.866829 | − | 0.498606i | \(-0.166154\pi\) | ||||
0.866829 | + | 0.498606i | \(0.166154\pi\) | |||||||
\(18\) | −621.667 | − | 23.5928i | −0.452248 | − | 0.0171632i | ||||
\(19\) | − | 1891.04i | − | 1.20176i | −0.799341 | − | 0.600878i | \(-0.794818\pi\) | ||
0.799341 | − | 0.600878i | \(-0.205182\pi\) | |||||||
\(20\) | −60.6342 | + | 797.699i | −0.0338955 | + | 0.445927i | ||||
\(21\) | − | 2020.35i | − | 0.999720i | ||||||
\(22\) | −58.3959 | + | 1538.72i | −0.0257232 | + | 0.677802i | ||||
\(23\) | −987.677 | −0.389310 | −0.194655 | − | 0.980872i | \(-0.562359\pi\) | ||||
−0.194655 | + | 0.980872i | \(0.562359\pi\) | |||||||
\(24\) | −386.184 | + | 3378.93i | −0.136857 | + | 1.19743i | ||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 42.5629 | − | 1121.52i | 0.0123480 | − | 0.325368i | ||||
\(27\) | 2499.22i | 0.659774i | ||||||||
\(28\) | −3431.26 | − | 260.815i | −0.827101 | − | 0.0628690i | ||||
\(29\) | − | 8015.26i | − | 1.76979i | −0.465788 | − | 0.884896i | \(-0.654229\pi\) | ||
0.465788 | − | 0.884896i | \(-0.345771\pi\) | |||||||
\(30\) | −2655.06 | − | 100.762i | −0.538606 | − | 0.0204406i | ||||
\(31\) | 827.342 | 0.154625 | 0.0773127 | − | 0.997007i | \(-0.475366\pi\) | ||||
0.0773127 | + | 0.997007i | \(0.475366\pi\) | |||||||
\(32\) | 5688.74 | + | 1092.07i | 0.982068 | + | 0.188529i | ||||
\(33\) | −5114.10 | −0.817494 | ||||||||
\(34\) | 11677.5 | + | 443.170i | 1.73241 | + | 0.0657466i | ||||
\(35\) | − | 2688.40i | − | 0.370958i | ||||||
\(36\) | −3509.09 | − | 266.730i | −0.451271 | − | 0.0343018i | ||||
\(37\) | − | 9426.30i | − | 1.13198i | −0.824414 | − | 0.565988i | \(-0.808495\pi\) | ||
0.824414 | − | 0.565988i | \(-0.191505\pi\) | |||||||
\(38\) | 405.681 | − | 10689.6i | 0.0455749 | − | 1.20089i | ||||
\(39\) | 3727.50 | 0.392425 | ||||||||
\(40\) | −513.881 | + | 4496.21i | −0.0507823 | + | 0.444321i | ||||
\(41\) | −8221.07 | −0.763780 | −0.381890 | − | 0.924208i | \(-0.624727\pi\) | ||||
−0.381890 | + | 0.924208i | \(0.624727\pi\) | |||||||
\(42\) | 433.423 | − | 11420.6i | 0.0379130 | − | 0.999001i | ||||
\(43\) | 9301.63i | 0.767164i | 0.923507 | + | 0.383582i | \(0.125310\pi\) | ||||
−0.923507 | + | 0.383582i | \(0.874690\pi\) | |||||||
\(44\) | −660.198 | + | 8685.52i | −0.0514094 | + | 0.676339i | ||||
\(45\) | − | 2749.38i | − | 0.202397i | ||||||
\(46\) | −5583.12 | − | 211.885i | −0.389030 | − | 0.0147640i | ||||
\(47\) | 13837.9 | 0.913745 | 0.456873 | − | 0.889532i | \(-0.348969\pi\) | ||||
0.456873 | + | 0.889532i | \(0.348969\pi\) | |||||||
\(48\) | −2907.89 | + | 19017.5i | −0.182169 | + | 1.19138i | ||||
\(49\) | −5242.97 | −0.311952 | ||||||||
\(50\) | −3532.99 | − | 134.080i | −0.199856 | − | 0.00758473i | ||||
\(51\) | 38811.3i | 2.08945i | ||||||||
\(52\) | 481.198 | − | 6330.60i | 0.0246783 | − | 0.324666i | ||||
\(53\) | 27751.2i | 1.35704i | 0.734582 | + | 0.678520i | \(0.237378\pi\) | ||||
−0.734582 | + | 0.678520i | \(0.762622\pi\) | |||||||
\(54\) | −536.154 | + | 14127.6i | −0.0250210 | + | 0.659299i | ||||
\(55\) | −6805.14 | −0.303340 | ||||||||
\(56\) | −19340.2 | − | 2210.43i | −0.824122 | − | 0.0941905i | ||||
\(57\) | 35528.1 | 1.44839 | ||||||||
\(58\) | 1719.50 | − | 45308.5i | 0.0671170 | − | 1.76852i | ||||
\(59\) | 25106.1i | 0.938965i | 0.882942 | + | 0.469482i | \(0.155559\pi\) | ||||
−0.882942 | + | 0.469482i | \(0.844441\pi\) | |||||||
\(60\) | −14986.9 | − | 1139.17i | −0.537444 | − | 0.0408518i | ||||
\(61\) | − | 26404.6i | − | 0.908563i | −0.890858 | − | 0.454282i | \(-0.849896\pi\) | ||
0.890858 | − | 0.454282i | \(-0.150104\pi\) | |||||||
\(62\) | 4676.79 | + | 177.488i | 0.154514 | + | 0.00586396i | ||||
\(63\) | 11826.3 | 0.375404 | ||||||||
\(64\) | 31923.0 | + | 7393.66i | 0.974212 | + | 0.225637i | ||||
\(65\) | 4960.05 | 0.145614 | ||||||||
\(66\) | −28908.9 | − | 1097.12i | −0.816905 | − | 0.0310023i | ||||
\(67\) | 38563.9i | 1.04953i | 0.851248 | + | 0.524764i | \(0.175846\pi\) | ||||
−0.851248 | + | 0.524764i | \(0.824154\pi\) | |||||||
\(68\) | 65915.1 | + | 5010.29i | 1.72867 | + | 0.131399i | ||||
\(69\) | − | 18556.1i | − | 0.469207i | ||||||
\(70\) | 576.739 | − | 15197.0i | 0.0140681 | − | 0.370691i | ||||
\(71\) | −71073.0 | −1.67324 | −0.836621 | − | 0.547782i | \(-0.815472\pi\) | ||||
−0.836621 | + | 0.547782i | \(0.815472\pi\) | |||||||
\(72\) | −19778.9 | − | 2260.57i | −0.449646 | − | 0.0513909i | ||||
\(73\) | 18622.0 | 0.408996 | 0.204498 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204498 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(74\) | 2022.21 | − | 53284.8i | 0.0429286 | − | 1.13116i | ||||
\(75\) | − | 11742.3i | − | 0.241045i | ||||||
\(76\) | 4586.46 | − | 60339.1i | 0.0910843 | − | 1.19830i | ||||
\(77\) | − | 29271.9i | − | 0.562632i | ||||||
\(78\) | 21070.8 | + | 799.656i | 0.392143 | + | 0.0148822i | ||||
\(79\) | −75599.4 | −1.36286 | −0.681429 | − | 0.731884i | \(-0.738641\pi\) | ||||
−0.681429 | + | 0.731884i | \(0.738641\pi\) | |||||||
\(80\) | −3869.43 | + | 25305.9i | −0.0675961 | + | 0.442076i | ||||
\(81\) | −73678.4 | −1.24775 | ||||||||
\(82\) | −46471.9 | − | 1763.65i | −0.763231 | − | 0.0289653i | ||||
\(83\) | − | 125298.i | − | 1.99641i | −0.0599304 | − | 0.998203i | \(-0.519088\pi\) | ||
0.0599304 | − | 0.998203i | \(-0.480912\pi\) | |||||||
\(84\) | 4900.09 | − | 64465.2i | 0.0757715 | − | 0.996845i | ||||
\(85\) | 51644.7i | 0.775315i | ||||||||
\(86\) | −1995.47 | + | 52580.1i | −0.0290936 | + | 0.766612i | ||||
\(87\) | 150588. | 2.13300 | ||||||||
\(88\) | −5595.25 | + | 48955.8i | −0.0770217 | + | 0.673903i | ||||
\(89\) | 30341.5 | 0.406034 | 0.203017 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203017 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(90\) | 589.821 | − | 15541.7i | 0.00767563 | − | 0.202251i | ||||
\(91\) | 21335.4i | 0.270083i | ||||||||
\(92\) | −31514.7 | − | 2395.48i | −0.388190 | − | 0.0295068i | ||||
\(93\) | 15543.8i | 0.186359i | ||||||||
\(94\) | 78222.6 | + | 2968.62i | 0.913088 | + | 0.0346526i | ||||
\(95\) | 47275.9 | 0.537441 | ||||||||
\(96\) | −20517.5 | + | 106878.i | −0.227220 | + | 1.18361i | ||||
\(97\) | 15635.2 | 0.168723 | 0.0843617 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843617 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(98\) | −29637.4 | − | 1124.77i | −0.311727 | − | 0.0118303i | ||||
\(99\) | − | 29935.9i | − | 0.306976i | ||||||
\(100\) | −19942.5 | − | 1515.85i | −0.199425 | − | 0.0151585i | ||||
\(101\) | − | 102692.i | − | 1.00169i | −0.865538 | − | 0.500843i | \(-0.833024\pi\) | ||
0.865538 | − | 0.500843i | \(-0.166976\pi\) | |||||||
\(102\) | −8326.12 | + | 219392.i | −0.0792396 | + | 2.08795i | ||||
\(103\) | −35981.8 | −0.334187 | −0.167093 | − | 0.985941i | \(-0.553438\pi\) | ||||
−0.167093 | + | 0.985941i | \(0.553438\pi\) | |||||||
\(104\) | 4078.20 | − | 35682.3i | 0.0369730 | − | 0.323496i | ||||
\(105\) | 50508.8 | 0.447088 | ||||||||
\(106\) | −5953.43 | + | 156872.i | −0.0514639 | + | 1.35606i | ||||
\(107\) | − | 94984.6i | − | 0.802035i | −0.916070 | − | 0.401018i | \(-0.868657\pi\) | ||
0.916070 | − | 0.401018i | \(-0.131343\pi\) | |||||||
\(108\) | −6061.52 | + | 79745.0i | −0.0500060 | + | 0.657876i | ||||
\(109\) | 173158.i | 1.39597i | 0.716113 | + | 0.697984i | \(0.245919\pi\) | ||||
−0.716113 | + | 0.697984i | \(0.754081\pi\) | |||||||
\(110\) | −38468.0 | − | 1459.90i | −0.303122 | − | 0.0115038i | ||||
\(111\) | 177098. | 1.36429 | ||||||||
\(112\) | −108852. | − | 16644.1i | −0.819957 | − | 0.125376i | ||||
\(113\) | −237780. | −1.75178 | −0.875891 | − | 0.482510i | \(-0.839725\pi\) | ||||
−0.875891 | + | 0.482510i | \(0.839725\pi\) | |||||||
\(114\) | 200833. | + | 7621.80i | 1.44735 | + | 0.0549282i | ||||
\(115\) | − | 24691.9i | − | 0.174105i | ||||||
\(116\) | 19439.9 | − | 255750.i | 0.134137 | − | 1.76470i | ||||
\(117\) | 21819.3i | 0.147359i | ||||||||
\(118\) | −5385.97 | + | 141919.i | −0.0356090 | + | 0.938289i | ||||
\(119\) | −222147. | −1.43805 | ||||||||
\(120\) | −84473.2 | − | 9654.61i | −0.535508 | − | 0.0612043i | ||||
\(121\) | 86955.1 | 0.539923 | ||||||||
\(122\) | 5664.54 | − | 149260.i | 0.0344560 | − | 0.907910i | ||||
\(123\) | − | 154454.i | − | 0.920529i | ||||||
\(124\) | 26398.8 | + | 2006.61i | 0.154181 | + | 0.0117195i | ||||
\(125\) | − | 15625.0i | − | 0.0894427i | ||||||
\(126\) | 66851.7 | + | 2537.08i | 0.375133 | + | 0.0142367i | ||||
\(127\) | −63282.9 | −0.348158 | −0.174079 | − | 0.984732i | \(-0.555695\pi\) | ||||
−0.174079 | + | 0.984732i | \(0.555695\pi\) | |||||||
\(128\) | 178867. | + | 48643.2i | 0.964954 | + | 0.262420i | ||||
\(129\) | −174756. | −0.924607 | ||||||||
\(130\) | 28038.1 | + | 1064.07i | 0.145509 | + | 0.00552221i | ||||
\(131\) | − | 180082.i | − | 0.916835i | −0.888737 | − | 0.458417i | \(-0.848416\pi\) | ||
0.888737 | − | 0.458417i | \(-0.151584\pi\) | |||||||
\(132\) | −163180. | − | 12403.6i | −0.815142 | − | 0.0619601i | ||||
\(133\) | 203355.i | 0.996840i | ||||||||
\(134\) | −8273.05 | + | 217993.i | −0.0398019 | + | 1.04877i | ||||
\(135\) | −62480.5 | −0.295060 | ||||||||
\(136\) | 371529. | + | 42462.8i | 1.72244 | + | 0.196862i | ||||
\(137\) | 365739. | 1.66483 | 0.832414 | − | 0.554155i | \(-0.186958\pi\) | ||||
0.832414 | + | 0.554155i | \(0.186958\pi\) | |||||||
\(138\) | 3980.81 | − | 104894.i | 0.0177940 | − | 0.468869i | ||||
\(139\) | 111886.i | 0.491180i | 0.969374 | + | 0.245590i | \(0.0789817\pi\) | ||||
−0.969374 | + | 0.245590i | \(0.921018\pi\) | |||||||
\(140\) | 6520.37 | − | 85781.5i | 0.0281159 | − | 0.369891i | ||||
\(141\) | 259981.i | 1.10127i | ||||||||
\(142\) | −401760. | − | 15247.2i | −1.67204 | − | 0.0634554i | ||||
\(143\) | 54006.1 | 0.220853 | ||||||||
\(144\) | −111321. | − | 17021.6i | −0.447374 | − | 0.0684062i | ||||
\(145\) | 200381. | 0.791475 | ||||||||
\(146\) | 105266. | + | 3994.95i | 0.408702 | + | 0.0155106i | ||||
\(147\) | − | 98503.1i | − | 0.375973i | ||||||
\(148\) | 22862.2 | − | 300774.i | 0.0857955 | − | 1.12872i | ||||
\(149\) | − | 136480.i | − | 0.503621i | −0.967777 | − | 0.251811i | \(-0.918974\pi\) | ||
0.967777 | − | 0.251811i | \(-0.0810260\pi\) | |||||||
\(150\) | 2519.05 | − | 66376.5i | 0.00914132 | − | 0.240872i | ||||
\(151\) | 186354. | 0.665115 | 0.332557 | − | 0.943083i | \(-0.392088\pi\) | ||||
0.332557 | + | 0.943083i | \(0.392088\pi\) | |||||||
\(152\) | 38870.7 | − | 340100.i | 0.136463 | − | 1.19398i | ||||
\(153\) | −227186. | −0.784607 | ||||||||
\(154\) | 6279.67 | − | 165468.i | 0.0213371 | − | 0.562228i | ||||
\(155\) | 20683.6i | 0.0691506i | ||||||||
\(156\) | 118937. | + | 9040.56i | 0.391296 | + | 0.0297430i | ||||
\(157\) | 74689.6i | 0.241830i | 0.992663 | + | 0.120915i | \(0.0385829\pi\) | ||||
−0.992663 | + | 0.120915i | \(0.961417\pi\) | |||||||
\(158\) | −427347. | − | 16218.2i | −1.36188 | − | 0.0516845i | ||||
\(159\) | −521380. | −1.63554 | ||||||||
\(160\) | −27301.9 | + | 142219.i | −0.0843126 | + | 0.439194i | ||||
\(161\) | 106211. | 0.322927 | ||||||||
\(162\) | −416488. | − | 15806.1i | −1.24685 | − | 0.0473192i | ||||
\(163\) | 548779.i | 1.61781i | 0.587937 | + | 0.808907i | \(0.299940\pi\) | ||||
−0.587937 | + | 0.808907i | \(0.700060\pi\) | |||||||
\(164\) | −262317. | − | 19939.1i | −0.761583 | − | 0.0578890i | ||||
\(165\) | − | 127852.i | − | 0.365594i | ||||||
\(166\) | 26880.0 | − | 708282.i | 0.0757109 | − | 1.99497i | ||||
\(167\) | 224312. | 0.622387 | 0.311194 | − | 0.950347i | \(-0.399271\pi\) | ||||
0.311194 | + | 0.950347i | \(0.399271\pi\) | |||||||
\(168\) | 41528.8 | − | 363357.i | 0.113521 | − | 0.993254i | ||||
\(169\) | 331930. | 0.893983 | ||||||||
\(170\) | −11079.3 | + | 291936.i | −0.0294028 | + | 0.774758i | ||||
\(171\) | 207967.i | 0.543882i | ||||||||
\(172\) | −22559.9 | + | 296796.i | −0.0581454 | + | 0.764957i | ||||
\(173\) | − | 165260.i | − | 0.419809i | −0.977722 | − | 0.209905i | \(-0.932685\pi\) | ||
0.977722 | − | 0.209905i | \(-0.0673154\pi\) | |||||||
\(174\) | 851240. | + | 32305.4i | 2.13147 | + | 0.0808912i | ||||
\(175\) | 67210.1 | 0.165897 | ||||||||
\(176\) | −42131.2 | + | 275536.i | −0.102523 | + | 0.670497i | ||||
\(177\) | −471684. | −1.13167 | ||||||||
\(178\) | 171514. | + | 6509.12i | 0.405742 | + | 0.0153983i | ||||
\(179\) | − | 431975.i | − | 1.00769i | −0.863795 | − | 0.503844i | \(-0.831919\pi\) | ||
0.863795 | − | 0.503844i | \(-0.168081\pi\) | |||||||
\(180\) | 6668.26 | − | 87727.2i | 0.0153402 | − | 0.201815i | ||||
\(181\) | 216944.i | 0.492210i | 0.969243 | + | 0.246105i | \(0.0791508\pi\) | ||||
−0.969243 | + | 0.246105i | \(0.920849\pi\) | |||||||
\(182\) | −4577.05 | + | 120604.i | −0.0102425 | + | 0.269889i | ||||
\(183\) | 496080. | 1.09503 | ||||||||
\(184\) | −177632. | − | 20301.9i | −0.386792 | − | 0.0442072i | ||||
\(185\) | 235658. | 0.506235 | ||||||||
\(186\) | −3334.59 | + | 87865.8i | −0.00706741 | + | 0.186225i | ||||
\(187\) | 562319.i | 1.17592i | ||||||||
\(188\) | 441539. | + | 33562.0i | 0.911117 | + | 0.0692552i | ||||
\(189\) | − | 268756.i | − | 0.547274i | ||||||
\(190\) | 267241. | + | 10142.0i | 0.537055 | + | 0.0203817i | ||||
\(191\) | −34566.0 | −0.0685592 | −0.0342796 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342796 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(192\) | −138909. | + | 599757.i | −0.271943 | + | 1.17415i | ||||
\(193\) | −473601. | −0.915208 | −0.457604 | − | 0.889156i | \(-0.651292\pi\) | ||||
−0.457604 | + | 0.889156i | \(0.651292\pi\) | |||||||
\(194\) | 88382.7 | + | 3354.21i | 0.168602 | + | 0.00639861i | ||||
\(195\) | 93187.6i | 0.175498i | ||||||||
\(196\) | −167293. | − | 12716.1i | −0.311055 | − | 0.0236437i | ||||
\(197\) | 394784.i | 0.724760i | 0.932030 | + | 0.362380i | \(0.118036\pi\) | ||||
−0.932030 | + | 0.362380i | \(0.881964\pi\) | |||||||
\(198\) | 6422.10 | − | 169221.i | 0.0116416 | − | 0.306755i | ||||
\(199\) | −477089. | −0.854017 | −0.427009 | − | 0.904248i | \(-0.640433\pi\) | ||||
−0.427009 | + | 0.904248i | \(0.640433\pi\) | |||||||
\(200\) | −112405. | − | 12847.0i | −0.198706 | − | 0.0227106i | ||||
\(201\) | −724524. | −1.26492 | ||||||||
\(202\) | 22030.3 | − | 580493.i | 0.0379875 | − | 1.00096i | ||||
\(203\) | 861930.i | 1.46802i | ||||||||
\(204\) | −94131.6 | + | 1.23839e6i | −0.158365 | + | 2.08344i | ||||
\(205\) | − | 205527.i | − | 0.341573i | ||||||
\(206\) | −203397. | − | 7719.11i | −0.333946 | − | 0.0126736i | ||||
\(207\) | 108620. | 0.176191 | ||||||||
\(208\) | 30708.1 | − | 200829.i | 0.0492146 | − | 0.321862i | ||||
\(209\) | 514751. | 0.815139 | ||||||||
\(210\) | 285515. | + | 10835.6i | 0.446767 | + | 0.0169552i | ||||
\(211\) | − | 435894.i | − | 0.674023i | −0.941500 | − | 0.337012i | \(-0.890584\pi\) | ||
0.941500 | − | 0.337012i | \(-0.109416\pi\) | |||||||
\(212\) | −67306.9 | + | 885485.i | −0.102854 | + | 1.35314i | ||||
\(213\) | − | 1.33529e6i | − | 2.01664i | ||||||
\(214\) | 20376.9 | − | 536927.i | 0.0304161 | − | 0.801458i | ||||
\(215\) | −232541. | −0.343086 | ||||||||
\(216\) | −51372.1 | + | 449481.i | −0.0749191 | + | 0.655506i | ||||
\(217\) | −88969.2 | −0.128260 | ||||||||
\(218\) | −37147.3 | + | 978823.i | −0.0529402 | + | 1.39496i | ||||
\(219\) | 349863.i | 0.492933i | ||||||||
\(220\) | −217138. | − | 16505.0i | −0.302468 | − | 0.0229910i | ||||
\(221\) | − | 409856.i | − | 0.564483i | ||||||
\(222\) | 1.00110e6 | + | 37992.5i | 1.36331 | + | 0.0517388i | ||||
\(223\) | 1.14075e6 | 1.53613 | 0.768067 | − | 0.640369i | \(-0.221219\pi\) | ||||
0.768067 | + | 0.640369i | \(0.221219\pi\) | |||||||
\(224\) | −611746. | − | 117437.i | −0.814612 | − | 0.156382i | ||||
\(225\) | 68734.6 | 0.0905147 | ||||||||
\(226\) | −1.34412e6 | − | 51010.7i | −1.75052 | − | 0.0664339i | ||||
\(227\) | − | 1.08895e6i | − | 1.40262i | −0.712854 | − | 0.701312i | \(-0.752598\pi\) | ||
0.712854 | − | 0.701312i | \(-0.247402\pi\) | |||||||
\(228\) | 1.13363e6 | + | 86168.7i | 1.44422 | + | 0.109777i | ||||
\(229\) | − | 474386.i | − | 0.597783i | −0.954287 | − | 0.298891i | \(-0.903383\pi\) | ||
0.954287 | − | 0.298891i | \(-0.0966168\pi\) | |||||||
\(230\) | 5297.12 | − | 139578.i | 0.00660268 | − | 0.173979i | ||||
\(231\) | 549951. | 0.678100 | ||||||||
\(232\) | 164756. | − | 1.44153e6i | 0.200965 | − | 1.75835i | ||||
\(233\) | −271057. | −0.327093 | −0.163547 | − | 0.986536i | \(-0.552293\pi\) | ||||
−0.163547 | + | 0.986536i | \(0.552293\pi\) | |||||||
\(234\) | −4680.87 | + | 123340.i | −0.00558839 | + | 0.147253i | ||||
\(235\) | 345947.i | 0.408639i | ||||||||
\(236\) | −60891.5 | + | 801084.i | −0.0711667 | + | 0.936264i | ||||
\(237\) | − | 1.42033e6i | − | 1.64255i | ||||||
\(238\) | −1.25575e6 | − | 47656.8i | −1.43701 | − | 0.0545359i | ||||
\(239\) | −824404. | −0.933567 | −0.466784 | − | 0.884372i | \(-0.654587\pi\) | ||||
−0.466784 | + | 0.884372i | \(0.654587\pi\) | |||||||
\(240\) | −475438. | − | 72697.4i | −0.532802 | − | 0.0814686i | ||||
\(241\) | −86717.2 | −0.0961750 | −0.0480875 | − | 0.998843i | \(-0.515313\pi\) | ||||
−0.0480875 | + | 0.998843i | \(0.515313\pi\) | |||||||
\(242\) | 491539. | + | 18654.4i | 0.539535 | + | 0.0204758i | ||||
\(243\) | − | 776933.i | − | 0.844050i | ||||||
\(244\) | 64040.9 | − | 842517.i | 0.0688625 | − | 0.905950i | ||||
\(245\) | − | 131074.i | − | 0.139509i | ||||||
\(246\) | 33134.9 | − | 873097.i | 0.0349098 | − | 0.919867i | ||||
\(247\) | −375186. | −0.391294 | ||||||||
\(248\) | 148796. | + | 17006.2i | 0.153625 | + | 0.0175581i | ||||
\(249\) | 2.35405e6 | 2.40612 | ||||||||
\(250\) | 3352.01 | − | 88324.8i | 0.00339199 | − | 0.0893784i | ||||
\(251\) | − | 411977.i | − | 0.412751i | −0.978473 | − | 0.206376i | \(-0.933833\pi\) | ||
0.978473 | − | 0.206376i | \(-0.0661669\pi\) | |||||||
\(252\) | 377354. | + | 28683.2i | 0.374324 | + | 0.0284529i | ||||
\(253\) | − | 268851.i | − | 0.264065i | ||||||
\(254\) | −357725. | − | 13576.0i | −0.347908 | − | 0.0132034i | ||||
\(255\) | −970282. | −0.934431 | ||||||||
\(256\) | 1.00066e6 | + | 313341.i | 0.954308 | + | 0.298826i | ||||
\(257\) | −88057.5 | −0.0831637 | −0.0415818 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415818 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(258\) | −987857. | − | 37490.1i | −0.923942 | − | 0.0350645i | ||||
\(259\) | 1.01367e6i | 0.938958i | ||||||||
\(260\) | 158265. | + | 12029.9i | 0.145195 | + | 0.0110365i | ||||
\(261\) | 881480.i | 0.800961i | ||||||||
\(262\) | 38632.6 | − | 1.01796e6i | 0.0347697 | − | 0.916175i | ||||
\(263\) | −126284. | −0.112579 | −0.0562896 | − | 0.998414i | \(-0.517927\pi\) | ||||
−0.0562896 | + | 0.998414i | \(0.517927\pi\) | |||||||
\(264\) | −919763. | − | 105122.i | −0.812206 | − | 0.0928286i | ||||
\(265\) | −693781. | −0.606886 | ||||||||
\(266\) | −43625.4 | + | 1.14952e6i | −0.0378038 | + | 0.996123i | ||||
\(267\) | 570045.i | 0.489363i | ||||||||
\(268\) | −93531.6 | + | 1.23049e6i | −0.0795465 | + | 1.04651i | ||||
\(269\) | 1.88178e6i | 1.58558i | 0.609495 | + | 0.792790i | \(0.291372\pi\) | ||||
−0.609495 | + | 0.792790i | \(0.708628\pi\) | |||||||
\(270\) | −353189. | − | 13403.8i | −0.294848 | − | 0.0111897i | ||||
\(271\) | −1.17095e6 | −0.968532 | −0.484266 | − | 0.874921i | \(-0.660913\pi\) | ||||
−0.484266 | + | 0.874921i | \(0.660913\pi\) | |||||||
\(272\) | 2.09106e6 | + | 319736.i | 1.71374 | + | 0.262041i | ||||
\(273\) | −400841. | −0.325511 | ||||||||
\(274\) | 2.06744e6 | + | 78461.3i | 1.66363 | + | 0.0631363i | ||||
\(275\) | − | 170128.i | − | 0.135658i | ||||||
\(276\) | 45005.4 | − | 592088.i | 0.0355625 | − | 0.467857i | ||||
\(277\) | 1.11420e6i | 0.872496i | 0.899827 | + | 0.436248i | \(0.143693\pi\) | ||||
−0.899827 | + | 0.436248i | \(0.856307\pi\) | |||||||
\(278\) | −24002.8 | + | 632470.i | −0.0186273 | + | 0.490826i | ||||
\(279\) | −90987.2 | −0.0699793 | ||||||||
\(280\) | 55260.8 | − | 483505.i | 0.0421233 | − | 0.368558i | ||||
\(281\) | −1.87861e6 | −1.41929 | −0.709646 | − | 0.704558i | \(-0.751145\pi\) | ||||
−0.709646 | + | 0.704558i | \(0.751145\pi\) | |||||||
\(282\) | −55773.4 | + | 1.46962e6i | −0.0417642 | + | 1.10048i | ||||
\(283\) | 3072.89i | 0.00228077i | 0.999999 | + | 0.00114038i | \(0.000362996\pi\) | ||||
−0.999999 | + | 0.00114038i | \(0.999637\pi\) | |||||||
\(284\) | −2.26779e6 | − | 172378.i | −1.66843 | − | 0.126820i | ||||
\(285\) | 888203.i | 0.647739i | ||||||||
\(286\) | 305285. | + | 11585.9i | 0.220694 | + | 0.00837554i | ||||
\(287\) | 884062. | 0.633546 | ||||||||
\(288\) | −625621. | − | 120101.i | −0.444458 | − | 0.0853230i | ||||
\(289\) | 2.84762e6 | 2.00557 | ||||||||
\(290\) | 1.13271e6 | + | 42987.5i | 0.790906 | + | 0.0300156i | ||||
\(291\) | 293749.i | 0.203350i | ||||||||
\(292\) | 594190. | + | 45165.2i | 0.407820 | + | 0.0309989i | ||||
\(293\) | 2.45968e6i | 1.67382i | 0.547339 | + | 0.836911i | \(0.315641\pi\) | ||||
−0.547339 | + | 0.836911i | \(0.684359\pi\) | |||||||
\(294\) | 21131.7 | − | 556817.i | 0.0142583 | − | 0.375702i | ||||
\(295\) | −627653. | −0.419918 | ||||||||
\(296\) | 193760. | − | 1.69531e6i | 0.128539 | − | 1.12465i | ||||
\(297\) | −680301. | −0.447518 | ||||||||
\(298\) | 29278.9 | − | 771493.i | 0.0190992 | − | 0.503259i | ||||
\(299\) | 195957.i | 0.126760i | ||||||||
\(300\) | 28479.3 | − | 374672.i | 0.0182695 | − | 0.240352i | ||||
\(301\) | − | 1.00026e6i | − | 0.636352i | ||||||
\(302\) | 1.05342e6 | + | 39978.3i | 0.664636 | + | 0.0252236i | ||||
\(303\) | 1.92933e6 | 1.20726 | ||||||||
\(304\) | 292689. | − | 1.91417e6i | 0.181645 | − | 1.18795i | ||||
\(305\) | 660115. | 0.406322 | ||||||||
\(306\) | −1.28423e6 | − | 48737.8i | −0.784043 | − | 0.0297552i | ||||
\(307\) | 257478.i | 0.155917i | 0.996957 | + | 0.0779585i | \(0.0248402\pi\) | ||||
−0.996957 | + | 0.0779585i | \(0.975160\pi\) | |||||||
\(308\) | 70995.2 | − | 934008.i | 0.0426434 | − | 0.561014i | ||||
\(309\) | − | 676012.i | − | 0.402771i | ||||||
\(310\) | −4437.21 | + | 116920.i | −0.00262244 | + | 0.0691009i | ||||
\(311\) | 2.43192e6 | 1.42576 | 0.712882 | − | 0.701284i | \(-0.247390\pi\) | ||||
0.712882 | + | 0.701284i | \(0.247390\pi\) | |||||||
\(312\) | 670386. | + | 76619.7i | 0.389887 | + | 0.0445609i | ||||
\(313\) | −2.62542e6 | −1.51474 | −0.757369 | − | 0.652987i | \(-0.773515\pi\) | ||||
−0.757369 | + | 0.652987i | \(0.773515\pi\) | |||||||
\(314\) | −16023.0 | + | 422204.i | −0.00917109 | + | 0.241656i | ||||
\(315\) | 295658.i | 0.167886i | ||||||||
\(316\) | −2.41222e6 | − | 183356.i | −1.35894 | − | 0.103295i | ||||
\(317\) | 2.54754e6i | 1.42388i | 0.702240 | + | 0.711940i | \(0.252183\pi\) | ||||
−0.702240 | + | 0.711940i | \(0.747817\pi\) | |||||||
\(318\) | −2.94725e6 | − | 111851.i | −1.63436 | − | 0.0620257i | ||||
\(319\) | 2.18180e6 | 1.20043 | ||||||||
\(320\) | −184841. | + | 798074.i | −0.100908 | + | 0.435681i | ||||
\(321\) | 1.78454e6 | 0.966635 | ||||||||
\(322\) | 600388. | + | 22785.3i | 0.322695 | + | 0.0122466i | ||||
\(323\) | − | 3.90648e6i | − | 2.08343i | ||||||
\(324\) | −2.35093e6 | − | 178697.i | −1.24416 | − | 0.0945704i | ||||
\(325\) | 124001.i | 0.0651205i | ||||||||
\(326\) | −117729. | + | 3.10213e6i | −0.0613534 | + | 1.61665i | ||||
\(327\) | −3.25322e6 | −1.68246 | ||||||||
\(328\) | −1.47855e6 | − | 168986.i | −0.758840 | − | 0.0867294i | ||||
\(329\) | −1.48807e6 | −0.757940 | ||||||||
\(330\) | 27428.0 | − | 722723.i | 0.0138647 | − | 0.365331i | ||||
\(331\) | 2.11710e6i | 1.06211i | 0.847336 | + | 0.531057i | \(0.178205\pi\) | ||||
−0.847336 | + | 0.531057i | \(0.821795\pi\) | |||||||
\(332\) | 303893. | − | 3.99800e6i | 0.151313 | − | 1.99066i | ||||
\(333\) | 1.03666e6i | 0.512302i | ||||||||
\(334\) | 1.26799e6 | + | 48121.2i | 0.621940 | + | 0.0236032i | ||||
\(335\) | −964097. | −0.469363 | ||||||||
\(336\) | 312704. | − | 2.04507e6i | 0.151107 | − | 0.988234i | ||||
\(337\) | −1.56954e6 | −0.752832 | −0.376416 | − | 0.926451i | \(-0.622844\pi\) | ||||
−0.376416 | + | 0.926451i | \(0.622844\pi\) | |||||||
\(338\) | 1.87633e6 | + | 71208.4i | 0.893340 | + | 0.0339031i | ||||
\(339\) | − | 4.46733e6i | − | 2.11129i | ||||||
\(340\) | −125257. | + | 1.64788e6i | −0.0587633 | + | 0.773085i | ||||
\(341\) | 225207.i | 0.104881i | ||||||||
\(342\) | −44614.9 | + | 1.17560e6i | −0.0206260 | + | 0.543491i | ||||
\(343\) | 2.37117e6 | 1.08825 | ||||||||
\(344\) | −191197. | + | 1.67288e6i | −0.0871136 | + | 0.762202i | ||||
\(345\) | 463903. | 0.209836 | ||||||||
\(346\) | 35452.9 | − | 934178.i | 0.0159207 | − | 0.419507i | ||||
\(347\) | 428538.i | 0.191058i | 0.995427 | + | 0.0955292i | \(0.0304543\pi\) | ||||
−0.995427 | + | 0.0955292i | \(0.969546\pi\) | |||||||
\(348\) | 4.80495e6 | + | 365230.i | 2.12687 | + | 0.161666i | ||||
\(349\) | − | 522898.i | − | 0.229802i | −0.993377 | − | 0.114901i | \(-0.963345\pi\) | ||
0.993377 | − | 0.114901i | \(-0.0366551\pi\) | |||||||
\(350\) | 379924. | + | 14418.5i | 0.165778 | + | 0.00629143i | ||||
\(351\) | 495850. | 0.214824 | ||||||||
\(352\) | −297269. | + | 1.54851e6i | −0.127877 | + | 0.666126i | ||||
\(353\) | 1.89389e6 | 0.808943 | 0.404472 | − | 0.914550i | \(-0.367455\pi\) | ||||
0.404472 | + | 0.914550i | \(0.367455\pi\) | |||||||
\(354\) | −2.66633e6 | − | 101190.i | −1.13085 | − | 0.0429169i | ||||
\(355\) | − | 1.77682e6i | − | 0.748297i | ||||||
\(356\) | 968136. | + | 73589.3i | 0.404866 | + | 0.0307744i | ||||
\(357\) | − | 4.17361e6i | − | 1.73317i | ||||||
\(358\) | 92671.0 | − | 2.44186e6i | 0.0382152 | − | 1.00696i | ||||
\(359\) | −2.57094e6 | −1.05282 | −0.526412 | − | 0.850229i | \(-0.676463\pi\) | ||||
−0.526412 | + | 0.850229i | \(0.676463\pi\) | |||||||
\(360\) | 56514.2 | − | 494472.i | 0.0229827 | − | 0.201088i | ||||
\(361\) | −1.09992e6 | −0.444216 | ||||||||
\(362\) | −46540.6 | + | 1.22634e6i | −0.0186664 | + | 0.491856i | ||||
\(363\) | 1.63368e6i | 0.650730i | ||||||||
\(364\) | −51746.1 | + | 680768.i | −0.0204703 | + | 0.269306i | ||||
\(365\) | 465550.i | 0.182909i | ||||||||
\(366\) | 2.80424e6 | + | 106423.i | 1.09424 | + | 0.0415274i | ||||
\(367\) | −2.47263e6 | −0.958282 | −0.479141 | − | 0.877738i | \(-0.659052\pi\) | ||||
−0.479141 | + | 0.877738i | \(0.659052\pi\) | |||||||
\(368\) | −999761. | − | 152870.i | −0.384837 | − | 0.0588439i | ||||
\(369\) | 904114. | 0.345667 | ||||||||
\(370\) | 1.33212e6 | + | 50555.3i | 0.505871 | + | 0.0191983i | ||||
\(371\) | − | 2.98426e6i | − | 1.12565i | ||||||
\(372\) | −37699.4 | + | 495971.i | −0.0141246 | + | 0.185823i | ||||
\(373\) | 2.62533e6i | 0.977038i | 0.872553 | + | 0.488519i | \(0.162463\pi\) | ||||
−0.872553 | + | 0.488519i | \(0.837537\pi\) | |||||||
\(374\) | −120633. | + | 3.17867e6i | −0.0445953 | + | 1.17508i | ||||
\(375\) | 293557. | 0.107799 | ||||||||
\(376\) | 2.48872e6 | + | 284441.i | 0.907835 | + | 0.103758i | ||||
\(377\) | −1.59024e6 | −0.576249 | ||||||||
\(378\) | 57655.9 | − | 1.51922e6i | 0.0207546 | − | 0.546880i | ||||
\(379\) | 2.14283e6i | 0.766284i | 0.923689 | + | 0.383142i | \(0.125158\pi\) | ||||
−0.923689 | + | 0.383142i | \(0.874842\pi\) | |||||||
\(380\) | 1.50848e6 | + | 114661.i | 0.535896 | + | 0.0407341i | ||||
\(381\) | − | 1.18894e6i | − | 0.419610i | ||||||
\(382\) | −195394. | − | 7415.39i | −0.0685098 | − | 0.00260001i | ||||
\(383\) | −641783. | −0.223559 | −0.111779 | − | 0.993733i | \(-0.535655\pi\) | ||||
−0.111779 | + | 0.993733i | \(0.535655\pi\) | |||||||
\(384\) | −913890. | + | 3.36050e6i | −0.316276 | + | 1.16299i | ||||
\(385\) | 731799. | 0.251617 | ||||||||
\(386\) | −2.67717e6 | − | 101601.i | −0.914549 | − | 0.0347080i | ||||
\(387\) | − | 1.02295e6i | − | 0.347198i | ||||||
\(388\) | 498889. | + | 37921.2i | 0.168238 | + | 0.0127880i | ||||
\(389\) | − | 2.36321e6i | − | 0.791823i | −0.918289 | − | 0.395911i | \(-0.870429\pi\) | ||
0.918289 | − | 0.395911i | \(-0.129571\pi\) | |||||||
\(390\) | −19991.4 | + | 526769.i | −0.00665551 | + | 0.175372i | ||||
\(391\) | −2.04033e6 | −0.674930 | ||||||||
\(392\) | −942941. | − | 107771.i | −0.309934 | − | 0.0354230i | ||||
\(393\) | 3.38331e6 | 1.10499 | ||||||||
\(394\) | −84692.5 | + | 2.23163e6i | −0.0274855 | + | 0.724239i | ||||
\(395\) | − | 1.88998e6i | − | 0.609489i | ||||||
\(396\) | 72605.5 | − | 955193.i | 0.0232665 | − | 0.306093i | ||||
\(397\) | − | 403888.i | − | 0.128613i | −0.997930 | − | 0.0643065i | \(-0.979516\pi\) | ||
0.997930 | − | 0.0643065i | \(-0.0204835\pi\) | |||||||
\(398\) | −2.69688e6 | − | 102349.i | −0.853403 | − | 0.0323874i | ||||
\(399\) | −3.82056e6 | −1.20142 | ||||||||
\(400\) | −632647. | − | 96735.6i | −0.197702 | − | 0.0302299i | ||||
\(401\) | 2.28335e6 | 0.709108 | 0.354554 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354554 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(402\) | −4.09558e6 | − | 155431.i | −1.26401 | − | 0.0479703i | ||||
\(403\) | − | 164146.i | − | 0.0503464i | ||||||
\(404\) | 249065. | − | 3.27668e6i | 0.0759204 | − | 0.998804i | ||||
\(405\) | − | 1.84196e6i | − | 0.558011i | ||||||
\(406\) | −184909. | + | 4.87230e6i | −0.0556726 | + | 1.46696i | ||||
\(407\) | 2.56589e6 | 0.767807 | ||||||||
\(408\) | −797775. | + | 6.98015e6i | −0.237263 | + | 2.07594i | ||||
\(409\) | 3.27964e6 | 0.969435 | 0.484717 | − | 0.874671i | \(-0.338922\pi\) | ||||
0.484717 | + | 0.874671i | \(0.338922\pi\) | |||||||
\(410\) | 44091.3 | − | 1.16180e6i | 0.0129537 | − | 0.341327i | ||||
\(411\) | 6.87136e6i | 2.00650i | ||||||||
\(412\) | −1.14810e6 | − | 87269.0i | −0.333226 | − | 0.0253289i | ||||
\(413\) | − | 2.69981e6i | − | 0.778859i | ||||||
\(414\) | 614006. | + | 23302.1i | 0.176064 | + | 0.00668181i | ||||
\(415\) | 3.13245e6 | 0.892820 | ||||||||
\(416\) | 216670. | − | 1.12866e6i | 0.0613854 | − | 0.319764i | ||||
\(417\) | −2.10208e6 | −0.591983 | ||||||||
\(418\) | 2.90978e6 | + | 110429.i | 0.814552 | + | 0.0309130i | ||||
\(419\) | 604670.i | 0.168261i | 0.996455 | + | 0.0841305i | \(0.0268113\pi\) | ||||
−0.996455 | + | 0.0841305i | \(0.973189\pi\) | |||||||
\(420\) | 1.61163e6 | + | 122502.i | 0.445802 | + | 0.0338860i | ||||
\(421\) | − | 3.46346e6i | − | 0.952367i | −0.879346 | − | 0.476184i | \(-0.842020\pi\) | ||
0.879346 | − | 0.476184i | \(-0.157980\pi\) | |||||||
\(422\) | 93511.7 | − | 2.46402e6i | 0.0255614 | − | 0.673538i | ||||
\(423\) | −1.52183e6 | −0.413537 | ||||||||
\(424\) | −570433. | + | 4.99102e6i | −0.154096 | + | 1.34826i | ||||
\(425\) | −1.29112e6 | −0.346732 | ||||||||
\(426\) | 286459. | − | 7.54813e6i | 0.0764782 | − | 2.01519i | ||||
\(427\) | 2.83945e6i | 0.753641i | ||||||||
\(428\) | 230372. | − | 3.03076e6i | 0.0607884 | − | 0.799728i | ||||
\(429\) | 1.01465e6i | 0.266178i | ||||||||
\(430\) | −1.31450e6 | − | 49886.6i | −0.342839 | − | 0.0130111i | ||||
\(431\) | 5.00345e6 | 1.29741 | 0.648704 | − | 0.761041i | \(-0.275311\pi\) | ||||
0.648704 | + | 0.761041i | \(0.275311\pi\) | |||||||
\(432\) | −386822. | + | 2.52980e6i | −0.0997244 | + | 0.652194i | ||||
\(433\) | −4.11259e6 | −1.05413 | −0.527067 | − | 0.849824i | \(-0.676708\pi\) | ||||
−0.527067 | + | 0.849824i | \(0.676708\pi\) | |||||||
\(434\) | −502924. | − | 19086.4i | −0.128167 | − | 0.00486408i | ||||
\(435\) | 3.76469e6i | 0.953908i | ||||||||
\(436\) | −419971. | + | 5.52511e6i | −0.105804 | + | 1.39195i | ||||
\(437\) | 1.86773e6i | 0.467855i | ||||||||
\(438\) | −75055.7 | + | 1.97770e6i | −0.0186938 | + | 0.492579i | ||||
\(439\) | 4.20313e6 | 1.04091 | 0.520454 | − | 0.853890i | \(-0.325763\pi\) | ||||
0.520454 | + | 0.853890i | \(0.325763\pi\) | |||||||
\(440\) | −1.22389e6 | − | 139881.i | −0.301378 | − | 0.0344451i | ||||
\(441\) | 576598. | 0.141181 | ||||||||
\(442\) | 87925.9 | − | 2.31683e6i | 0.0214073 | − | 0.564077i | ||||
\(443\) | 1.32165e6i | 0.319969i | 0.987120 | + | 0.159984i | \(0.0511443\pi\) | ||||
−0.987120 | + | 0.159984i | \(0.948856\pi\) | |||||||
\(444\) | 5.65083e6 | + | 429527.i | 1.36036 | + | 0.103403i | ||||
\(445\) | 758538.i | 0.181584i | ||||||||
\(446\) | 6.44843e6 | + | 244724.i | 1.53503 | + | 0.0582558i | ||||
\(447\) | 2.56414e6 | 0.606978 | ||||||||
\(448\) | −3.43287e6 | − | 795086.i | −0.808095 | − | 0.187163i | ||||
\(449\) | −5.52202e6 | −1.29265 | −0.646327 | − | 0.763061i | \(-0.723696\pi\) | ||||
−0.646327 | + | 0.763061i | \(0.723696\pi\) | |||||||
\(450\) | 388542. | + | 14745.5i | 0.0904495 | + | 0.00343265i | ||||
\(451\) | − | 2.23782e6i | − | 0.518064i | ||||||
\(452\) | −7.58709e6 | − | 576705.i | −1.74674 | − | 0.132772i | ||||
\(453\) | 3.50115e6i | 0.801615i | ||||||||
\(454\) | 233610. | − | 6.15557e6i | 0.0531926 | − | 1.40162i | ||||
\(455\) | −533385. | −0.120785 | ||||||||
\(456\) | 6.38968e6 | + | 730289.i | 1.43902 | + | 0.164469i | ||||
\(457\) | 3.46838e6 | 0.776849 | 0.388424 | − | 0.921481i | \(-0.373019\pi\) | ||||
0.388424 | + | 0.921481i | \(0.373019\pi\) | |||||||
\(458\) | 101769. | − | 2.68160e6i | 0.0226701 | − | 0.597352i | ||||
\(459\) | 5.16286e6i | 1.14382i | ||||||||
\(460\) | 59887.0 | − | 787869.i | 0.0131959 | − | 0.173604i | ||||
\(461\) | 2.42345e6i | 0.531107i | 0.964096 | + | 0.265554i | \(0.0855547\pi\) | ||||
−0.964096 | + | 0.265554i | \(0.914445\pi\) | |||||||
\(462\) | 3.10875e6 | + | 117980.i | 0.677612 | + | 0.0257160i | ||||
\(463\) | −6.58501e6 | −1.42759 | −0.713796 | − | 0.700354i | \(-0.753026\pi\) | ||||
−0.713796 | + | 0.700354i | \(0.753026\pi\) | |||||||
\(464\) | 1.24058e6 | − | 8.11332e6i | 0.267503 | − | 1.74946i | ||||
\(465\) | −388595. | −0.0833422 | ||||||||
\(466\) | −1.53223e6 | − | 58149.5i | −0.326858 | − | 0.0124046i | ||||
\(467\) | − | 1.15697e6i | − | 0.245488i | −0.992438 | − | 0.122744i | \(-0.960831\pi\) | ||
0.992438 | − | 0.122744i | \(-0.0391694\pi\) | |||||||
\(468\) | −52919.8 | + | 696210.i | −0.0111687 | + | 0.146935i | ||||
\(469\) | − | 4.14701e6i | − | 0.870569i | ||||||
\(470\) | −74215.5 | + | 1.95557e6i | −0.0154971 | + | 0.408345i | ||||
\(471\) | −1.40324e6 | −0.291461 | ||||||||
\(472\) | −516062. | + | 4.51529e6i | −0.106622 | + | 0.932891i | ||||
\(473\) | −2.53196e6 | −0.520359 | ||||||||
\(474\) | 304702. | − | 8.02884e6i | 0.0622916 | − | 1.64137i | ||||
\(475\) | 1.18190e6i | 0.240351i | ||||||||
\(476\) | −7.08825e6 | − | 538788.i | −1.43391 | − | 0.108993i | ||||
\(477\) | − | 3.05195e6i | − | 0.614160i | ||||||
\(478\) | −4.66018e6 | − | 176858.i | −0.932896 | − | 0.0354043i | ||||
\(479\) | −380517. | −0.0757767 | −0.0378883 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378883 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(480\) | −2.67195e6 | − | 512937.i | −0.529329 | − | 0.101616i | ||||
\(481\) | −1.87020e6 | −0.368574 | ||||||||
\(482\) | −490193. | − | 18603.3i | −0.0961059 | − | 0.00364731i | ||||
\(483\) | 1.99545e6i | 0.389201i | ||||||||
\(484\) | 2.77456e6 | + | 210898.i | 0.538370 | + | 0.0409222i | ||||
\(485\) | 390881.i | 0.0754554i | ||||||||
\(486\) | 166674. | − | 4.39184e6i | 0.0320094 | − | 0.843443i | ||||
\(487\) | 2.67715e6 | 0.511505 | 0.255753 | − | 0.966742i | \(-0.417677\pi\) | ||||
0.255753 | + | 0.966742i | \(0.417677\pi\) | |||||||
\(488\) | 542753. | − | 4.74883e6i | 0.103170 | − | 0.902687i | ||||
\(489\) | −1.03103e7 | −1.94983 | ||||||||
\(490\) | 28119.2 | − | 740935.i | 0.00529069 | − | 0.139409i | ||||
\(491\) | − | 5.10695e6i | − | 0.956000i | −0.878360 | − | 0.478000i | \(-0.841362\pi\) | ||
0.878360 | − | 0.478000i | \(-0.158638\pi\) | |||||||
\(492\) | 374609. | − | 4.92832e6i | 0.0697694 | − | 0.917881i | ||||
\(493\) | − | 1.65578e7i | − | 3.06822i | ||||||
\(494\) | −2.12084e6 | − | 80488.0i | −0.391013 | − | 0.0148393i | ||||
\(495\) | 748397. | 0.137284 | ||||||||
\(496\) | 837465. | + | 128054.i | 0.152849 | + | 0.0233715i | ||||
\(497\) | 7.64292e6 | 1.38793 | ||||||||
\(498\) | 1.33070e7 | + | 505011.i | 2.40439 | + | 0.0912489i | ||||
\(499\) | 259376.i | 0.0466313i | 0.999728 | + | 0.0233157i | \(0.00742228\pi\) | ||||
−0.999728 | + | 0.0233157i | \(0.992578\pi\) | |||||||
\(500\) | 37896.4 | − | 498562.i | 0.00677911 | − | 0.0891854i | ||||
\(501\) | 4.21429e6i | 0.750118i | ||||||||
\(502\) | 88380.7 | − | 2.32882e6i | 0.0156530 | − | 0.412454i | ||||
\(503\) | −324388. | −0.0571669 | −0.0285835 | − | 0.999591i | \(-0.509100\pi\) | ||||
−0.0285835 | + | 0.999591i | \(0.509100\pi\) | |||||||
\(504\) | 2.12695e6 | + | 243093.i | 0.372975 | + | 0.0426281i | ||||
\(505\) | 2.56729e6 | 0.447967 | ||||||||
\(506\) | 57676.2 | − | 1.51976e6i | 0.0100143 | − | 0.263875i | ||||
\(507\) | 6.23617e6i | 1.07745i | ||||||||
\(508\) | −2.01923e6 | − | 153484.i | −0.347157 | − | 0.0263879i | ||||
\(509\) | 1.13575e7i | 1.94307i | 0.236890 | + | 0.971537i | \(0.423872\pi\) | ||||
−0.236890 | + | 0.971537i | \(0.576128\pi\) | |||||||
\(510\) | −5.48479e6 | − | 208153.i | −0.933759 | − | 0.0354370i | ||||
\(511\) | −2.00254e6 | −0.339257 | ||||||||
\(512\) | 5.58932e6 | + | 1.98592e6i | 0.942289 | + | 0.334802i | ||||
\(513\) | 4.72612e6 | 0.792887 | ||||||||
\(514\) | −497770. | − | 18890.8i | −0.0831038 | − | 0.00315387i | ||||
\(515\) | − | 899544.i | − | 0.149453i | ||||||
\(516\) | −5.57610e6 | − | 423847.i | −0.921947 | − | 0.0700785i | ||||
\(517\) | 3.76675e6i | 0.619784i | ||||||||
\(518\) | −217461. | + | 5.73005e6i | −0.0356087 | + | 0.938283i | ||||
\(519\) | 3.10484e6 | 0.505966 | ||||||||
\(520\) | 892057. | + | 101955.i | 0.144672 | + | 0.0165348i | ||||
\(521\) | 9.15918e6 | 1.47830 | 0.739149 | − | 0.673541i | \(-0.235228\pi\) | ||||
0.739149 | + | 0.673541i | \(0.235228\pi\) | |||||||
\(522\) | −189103. | + | 4.98282e6i | −0.0303754 | + | 0.800385i | ||||
\(523\) | 7.08351e6i | 1.13238i | 0.824273 | + | 0.566192i | \(0.191584\pi\) | ||||
−0.824273 | + | 0.566192i | \(0.808416\pi\) | |||||||
\(524\) | 436764. | − | 5.74604e6i | 0.0694894 | − | 0.914198i | ||||
\(525\) | 1.26272e6i | 0.199944i | ||||||||
\(526\) | −713855. | − | 27091.5i | −0.112498 | − | 0.00426942i | ||||
\(527\) | 1.70911e6 | 0.268068 | ||||||||
\(528\) | −5.17667e6 | − | 791545.i | −0.808101 | − | 0.123564i | ||||
\(529\) | −5.46084e6 | −0.848438 | ||||||||
\(530\) | −3.92179e6 | − | 148836.i | −0.606450 | − | 0.0230153i | ||||
\(531\) | − | 2.76105e6i | − | 0.424950i | ||||||
\(532\) | −493210. | + | 6.48864e6i | −0.0755532 | + | 0.993973i | ||||
\(533\) | 1.63108e6i | 0.248689i | ||||||||
\(534\) | −122291. | + | 3.22234e6i | −0.0185584 | + | 0.489011i | ||||
\(535\) | 2.37461e6 | 0.358681 | ||||||||
\(536\) | −792690. | + | 6.93566e6i | −0.119177 | + | 1.04274i | ||||
\(537\) | 8.11579e6 | 1.21449 | ||||||||
\(538\) | −403696. | + | 1.06373e7i | −0.0601310 | + | 1.58444i | ||||
\(539\) | − | 1.42717e6i | − | 0.211594i | ||||||
\(540\) | −1.99362e6 | − | 151538.i | −0.294211 | − | 0.0223634i | ||||
\(541\) | − | 2.53136e6i | − | 0.371843i | −0.982565 | − | 0.185922i | \(-0.940473\pi\) | ||
0.982565 | − | 0.185922i | \(-0.0595271\pi\) | |||||||
\(542\) | −6.61911e6 | − | 251201.i | −0.967835 | − | 0.0367303i | ||||
\(543\) | −4.07586e6 | −0.593225 | ||||||||
\(544\) | 1.17517e7 | + | 2.25599e6i | 1.70257 | + | 0.326844i | ||||
\(545\) | −4.32894e6 | −0.624296 | ||||||||
\(546\) | −2.26587e6 | − | 85991.9i | −0.325277 | − | 0.0123446i | ||||
\(547\) | − | 1.30020e7i | − | 1.85798i | −0.370108 | − | 0.928989i | \(-0.620679\pi\) | ||
0.370108 | − | 0.928989i | \(-0.379321\pi\) | |||||||
\(548\) | 1.16700e7 | + | 887050.i | 1.66004 | + | 0.126182i | ||||
\(549\) | 2.90386e6i | 0.411192i | ||||||||
\(550\) | 36497.4 | − | 961700.i | 0.00514464 | − | 0.135560i | ||||
\(551\) | −1.51571e7 | −2.12686 | ||||||||
\(552\) | 381425. | − | 3.33729e6i | 0.0532797 | − | 0.466172i | ||||
\(553\) | 8.12967e6 | 1.13047 | ||||||||
\(554\) | −239027. | + | 6.29833e6i | −0.0330882 | + | 0.871868i | ||||
\(555\) | 4.42745e6i | 0.610128i | ||||||||
\(556\) | −271366. | + | 3.57007e6i | −0.0372279 | + | 0.489767i | ||||
\(557\) | 5.70438e6i | 0.779059i | 0.921014 | + | 0.389530i | \(0.127362\pi\) | ||||
−0.921014 | + | 0.389530i | \(0.872638\pi\) | |||||||
\(558\) | −514331. | − | 19519.4i | −0.0699290 | − | 0.00265387i | ||||
\(559\) | 1.84546e6 | 0.249790 | ||||||||
\(560\) | 416103. | − | 2.72130e6i | 0.0560700 | − | 0.366696i | ||||
\(561\) | −1.05646e7 | −1.41725 | ||||||||
\(562\) | −1.06194e7 | − | 403016.i | −1.41827 | − | 0.0538247i | ||||
\(563\) | − | 1.98939e6i | − | 0.264514i | −0.991215 | − | 0.132257i | \(-0.957778\pi\) | ||
0.991215 | − | 0.132257i | \(-0.0422224\pi\) | |||||||
\(564\) | −630550. | + | 8.29547e6i | −0.0834683 | + | 1.09810i | ||||
\(565\) | − | 5.94451e6i | − | 0.783420i | ||||||
\(566\) | −659.223 | + | 17370.4i | −8.64951e−5 | + | 0.00227913i | ||||
\(567\) | 7.92310e6 | 1.03499 | ||||||||
\(568\) | −1.27824e7 | − | 1.46092e6i | −1.66242 | − | 0.190001i | ||||
\(569\) | 1.30277e6 | 0.168689 | 0.0843447 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843447 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(570\) | −190545. | + | 5.02082e6i | −0.0245646 | + | 0.647273i | ||||
\(571\) | − | 2.90628e6i | − | 0.373033i | −0.982452 | − | 0.186517i | \(-0.940280\pi\) | ||
0.982452 | − | 0.186517i | \(-0.0597199\pi\) | |||||||
\(572\) | 1.72322e6 | + | 130985.i | 0.220218 | + | 0.0167390i | ||||
\(573\) | − | 649413.i | − | 0.0826294i | ||||||
\(574\) | 4.99741e6 | + | 189656.i | 0.633090 | + | 0.0240264i | ||||
\(575\) | 617298. | 0.0778619 | ||||||||
\(576\) | −3.51074e6 | − | 813120.i | −0.440902 | − | 0.102117i | ||||
\(577\) | 4.01853e6 | 0.502490 | 0.251245 | − | 0.967923i | \(-0.419160\pi\) | ||||
0.251245 | + | 0.967923i | \(0.419160\pi\) | |||||||
\(578\) | 1.60970e7 | + | 610896.i | 2.00413 | + | 0.0760585i | ||||
\(579\) | − | 8.89785e6i | − | 1.10303i | ||||||
\(580\) | 6.39376e6 | + | 485998.i | 0.789199 | + | 0.0599881i | ||||
\(581\) | 1.34741e7i | 1.65599i | ||||||||
\(582\) | −63017.6 | + | 1.66050e6i | −0.00771178 | + | 0.203204i | ||||
\(583\) | −7.55404e6 | −0.920466 | ||||||||
\(584\) | 3.34914e6 | + | 382780.i | 0.406351 | + | 0.0464426i | ||||
\(585\) | −545483. | −0.0659009 | ||||||||
\(586\) | −527671. | + | 1.39040e7i | −0.0634774 | + | 1.67262i | ||||
\(587\) | − | 1.29654e7i | − | 1.55307i | −0.630074 | − | 0.776535i | \(-0.716975\pi\) | ||
0.630074 | − | 0.776535i | \(-0.283025\pi\) | |||||||
\(588\) | 238906. | − | 3.14303e6i | 0.0284960 | − | 0.374891i | ||||
\(589\) | − | 1.56454e6i | − | 0.185822i | ||||||
\(590\) | −3.54798e6 | − | 134649.i | −0.419616 | − | 0.0159248i | ||||
\(591\) | −7.41706e6 | −0.873501 | ||||||||
\(592\) | 1.45897e6 | − | 9.54163e6i | 0.171097 | − | 1.11897i | ||||
\(593\) | −107000. | −0.0124953 | −0.00624767 | − | 0.999980i | \(-0.501989\pi\) | ||||
−0.00624767 | + | 0.999980i | \(0.501989\pi\) | |||||||
\(594\) | −3.84560e6 | − | 145944.i | −0.447196 | − | 0.0169715i | ||||
\(595\) | − | 5.55367e6i | − | 0.643114i | ||||||
\(596\) | 331015. | − | 4.35480e6i | 0.0381708 | − | 0.502173i | ||||
\(597\) | − | 8.96337e6i | − | 1.02928i | ||||||
\(598\) | −42038.4 | + | 1.10770e6i | −0.00480721 | + | 0.126669i | ||||
\(599\) | 1.06394e7 | 1.21157 | 0.605785 | − | 0.795629i | \(-0.292859\pi\) | ||||
0.605785 | + | 0.795629i | \(0.292859\pi\) | |||||||
\(600\) | 241365. | − | 2.11183e6i | 0.0273714 | − | 0.239486i | ||||
\(601\) | −6.42705e6 | −0.725814 | −0.362907 | − | 0.931825i | \(-0.618216\pi\) | ||||
−0.362907 | + | 0.931825i | \(0.618216\pi\) | |||||||
\(602\) | 214585. | − | 5.65427e6i | 0.0241328 | − | 0.635894i | ||||
\(603\) | − | 4.24108e6i | − | 0.474988i | ||||||
\(604\) | 5.94618e6 | + | 451977.i | 0.663202 | + | 0.0504109i | ||||
\(605\) | 2.17388e6i | 0.241461i | ||||||||
\(606\) | 1.09061e7 | + | 413897.i | 1.20639 | + | 0.0457836i | ||||
\(607\) | 1.96807e6 | 0.216805 | 0.108403 | − | 0.994107i | \(-0.465426\pi\) | ||||
0.108403 | + | 0.994107i | \(0.465426\pi\) | |||||||
\(608\) | 2.06515e6 | − | 1.07576e7i | 0.226565 | − | 1.18021i | ||||
\(609\) | −1.61936e7 | −1.76930 | ||||||||
\(610\) | 3.73149e6 | + | 141614.i | 0.406030 | + | 0.0154092i | ||||
\(611\) | − | 2.74546e6i | − | 0.297518i | ||||||
\(612\) | −7.24903e6 | − | 551009.i | −0.782350 | − | 0.0594675i | ||||
\(613\) | 8.12485e6i | 0.873301i | 0.899631 | + | 0.436651i | \(0.143835\pi\) | ||||
−0.899631 | + | 0.436651i | \(0.856165\pi\) | |||||||
\(614\) | −55236.3 | + | 1.45547e6i | −0.00591294 | + | 0.155805i | ||||
\(615\) | 3.86136e6 | 0.411673 | ||||||||
\(616\) | 601692. | − | 5.26451e6i | 0.0638885 | − | 0.558993i | ||||
\(617\) | 1.40750e6 | 0.148846 | 0.0744229 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744229 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(618\) | 145024. | − | 3.82135e6i | 0.0152745 | − | 0.402481i | ||||
\(619\) | − | 5.01827e6i | − | 0.526414i | −0.964739 | − | 0.263207i | \(-0.915220\pi\) | ||
0.964739 | − | 0.263207i | \(-0.0847802\pi\) | |||||||
\(620\) | −50165.2 | + | 659970.i | −0.00524111 | + | 0.0689517i | ||||
\(621\) | − | 2.46842e6i | − | 0.256856i | ||||||
\(622\) | 1.37471e7 | + | 521715.i | 1.42474 | + | 0.0540702i | ||||
\(623\) | −3.26281e6 | −0.336800 | ||||||||
\(624\) | 3.77311e6 | + | 576932.i | 0.387916 | + | 0.0593148i | ||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.48409e7 | − | 563227.i | −1.51365 | − | 0.0574444i | ||||
\(627\) | 9.67095e6i | 0.982427i | ||||||||
\(628\) | −181150. | + | 2.38319e6i | −0.0183290 | + | 0.241135i | ||||
\(629\) | − | 1.94727e7i | − | 1.96246i | ||||||
\(630\) | −63427.1 | + | 1.67129e6i | −0.00636683 | + | 0.167765i | ||||
\(631\) | 5.59458e6 | 0.559363 | 0.279682 | − | 0.960093i | \(-0.409771\pi\) | ||||
0.279682 | + | 0.960093i | \(0.409771\pi\) | |||||||
\(632\) | −1.35964e7 | − | 1.55396e6i | −1.35404 | − | 0.154756i | ||||
\(633\) | 8.18942e6 | 0.812351 | ||||||||
\(634\) | −546521. | + | 1.44007e7i | −0.0539987 | + | 1.42286i | ||||
\(635\) | − | 1.58207e6i | − | 0.155701i | ||||||
\(636\) | −1.66362e7 | − | 1.26454e6i | −1.63084 | − | 0.123962i | ||||
\(637\) | 1.04022e6i | 0.101572i | ||||||||
\(638\) | 1.23332e7 | + | 468058.i | 1.19957 | + | 0.0455248i | ||||
\(639\) | 7.81627e6 | 0.757265 | ||||||||
\(640\) | −1.21608e6 | + | 4.47169e6i | −0.117358 | + | 0.431540i | ||||
\(641\) | 3.70806e6 | 0.356453 | 0.178226 | − | 0.983990i | \(-0.442964\pi\) | ||||
0.178226 | + | 0.983990i | \(0.442964\pi\) | |||||||
\(642\) | 1.00876e7 | + | 382834.i | 0.965940 | + | 0.0366583i | ||||
\(643\) | − | 1.36989e6i | − | 0.130665i | −0.997864 | − | 0.0653325i | \(-0.979189\pi\) | ||
0.997864 | − | 0.0653325i | \(-0.0208108\pi\) | |||||||
\(644\) | 3.38897e6 | + | 257601.i | 0.321998 | + | 0.0244755i | ||||
\(645\) | − | 4.36889e6i | − | 0.413497i | ||||||
\(646\) | 838052. | − | 2.20825e7i | 0.0790114 | − | 2.08193i | ||||
\(647\) | −1.38641e7 | −1.30206 | −0.651028 | − | 0.759053i | \(-0.725662\pi\) | ||||
−0.651028 | + | 0.759053i | \(0.725662\pi\) | |||||||
\(648\) | −1.32510e7 | − | 1.51448e6i | −1.23968 | − | 0.141686i | ||||
\(649\) | −6.83402e6 | −0.636890 | ||||||||
\(650\) | −26601.8 | + | 700952.i | −0.00246961 | + | 0.0650736i | ||||
\(651\) | − | 1.67152e6i | − | 0.154582i | ||||||
\(652\) | −1.33099e6 | + | 1.75104e7i | −0.122618 | + | 1.61316i | ||||
\(653\) | 1.00652e7i | 0.923714i | 0.886954 | + | 0.461857i | \(0.152817\pi\) | ||||
−0.886954 | + | 0.461857i | \(0.847183\pi\) | |||||||
\(654\) | −1.83898e7 | − | 697909.i | −1.68125 | − | 0.0638050i | ||||
\(655\) | 4.50204e6 | 0.410021 | ||||||||
\(656\) | −8.32165e6 | − | 1.27243e6i | −0.755005 | − | 0.115445i | ||||
\(657\) | −2.04796e6 | −0.185101 | ||||||||
\(658\) | −8.41176e6 | − | 319234.i | −0.757394 | − | 0.0287438i | ||||
\(659\) | 2.94962e6i | 0.264578i | 0.991211 | + | 0.132289i | \(0.0422326\pi\) | ||||
−0.991211 | + | 0.132289i | \(0.957767\pi\) | |||||||
\(660\) | 310089. | − | 4.07951e6i | 0.0277094 | − | 0.364543i | ||||
\(661\) | 2.46213e6i | 0.219184i | 0.993977 | + | 0.109592i | \(0.0349544\pi\) | ||||
−0.993977 | + | 0.109592i | \(0.965046\pi\) | |||||||
\(662\) | −454178. | + | 1.19675e7i | −0.0402793 | + | 1.06135i | ||||
\(663\) | 7.70023e6 | 0.680331 | ||||||||
\(664\) | 2.57553e6 | − | 2.25346e7i | 0.226697 | − | 1.98349i | ||||
\(665\) | −5.08387e6 | −0.445801 | ||||||||
\(666\) | −222393. | + | 5.86002e6i | −0.0194283 | + | 0.511933i | ||||
\(667\) | 7.91648e6i | 0.688997i | ||||||||
\(668\) | 7.15733e6 | + | 544038.i | 0.620597 | + | 0.0471724i | ||||
\(669\) | 2.14320e7i | 1.85139i | ||||||||
\(670\) | −5.44983e6 | − | 206826.i | −0.469025 | − | 0.0178000i | ||||
\(671\) | 7.18748e6 | 0.616269 | ||||||||
\(672\) | 2.20637e6 | − | 1.14933e7i | 0.188476 | − | 0.981793i | ||||
\(673\) | 8.46100e6 | 0.720085 | 0.360043 | − | 0.932936i | \(-0.382762\pi\) | ||||
0.360043 | + | 0.932936i | \(0.382762\pi\) | |||||||
\(674\) | −8.87229e6 | − | 336712.i | −0.752291 | − | 0.0285501i | ||||
\(675\) | − | 1.56201e6i | − | 0.131955i | ||||||
\(676\) | 1.05912e7 | + | 805051.i | 0.891412 | + | 0.0677574i | ||||
\(677\) | 2.01968e7i | 1.69360i | 0.531913 | + | 0.846799i | \(0.321473\pi\) | ||||
−0.531913 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(678\) | 958370. | − | 2.52529e7i | 0.0800680 | − | 2.10978i | ||||
\(679\) | −1.68135e6 | −0.139954 | ||||||||
\(680\) | −1.06157e6 | + | 9.28822e6i | −0.0880392 | + | 0.770301i | ||||
\(681\) | 2.04587e7 | 1.69048 | ||||||||
\(682\) | −48313.4 | + | 1.27305e6i | −0.00397746 | + | 0.104805i | ||||
\(683\) | 5.52541e6i | 0.453224i | 0.973985 | + | 0.226612i | \(0.0727649\pi\) | ||||
−0.973985 | + | 0.226612i | \(0.927235\pi\) | |||||||
\(684\) | −504397. | + | 6.63582e6i | −0.0412223 | + | 0.542318i | ||||
\(685\) | 9.14346e6i | 0.744534i | ||||||||
\(686\) | 1.34037e7 | + | 508683.i | 1.08746 | + | 0.0412703i | ||||
\(687\) | 8.91259e6 | 0.720464 | ||||||||
\(688\) | −1.43968e6 | + | 9.41544e6i | −0.115956 | + | 0.758350i | ||||
\(689\) | 5.50590e6 | 0.441855 | ||||||||
\(690\) | 2.62234e6 | + | 99520.4i | 0.209685 | + | 0.00795773i | ||||
\(691\) | 1.66737e7i | 1.32843i | 0.747543 | + | 0.664214i | \(0.231234\pi\) | ||||
−0.747543 | + | 0.664214i | \(0.768766\pi\) | |||||||
\(692\) | 400816. | − | 5.27310e6i | 0.0318185 | − | 0.418602i | ||||
\(693\) | 3.21919e6i | 0.254632i | ||||||||
\(694\) | −91933.7 | + | 2.42244e6i | −0.00724563 | + | 0.190921i | ||||
\(695\) | −2.79716e6 | −0.219662 | ||||||||
\(696\) | 2.70830e7 | + | 3.09537e6i | 2.11921 | + | 0.242208i | ||||
\(697\) | −1.69830e7 | −1.32413 | ||||||||
\(698\) | 112177. | − | 2.95583e6i | 0.00871493 | − | 0.229637i | ||||
\(699\) | − | 5.09253e6i | − | 0.394222i | ||||||
\(700\) | 2.14454e6 | + | 163009.i | 0.165420 | + | 0.0125738i | ||||
\(701\) | − | 1.49989e7i | − | 1.15283i | −0.817157 | − | 0.576415i | \(-0.804451\pi\) | ||
0.817157 | − | 0.576415i | \(-0.195549\pi\) | |||||||
\(702\) | 2.80293e6 | + | 106374.i | 0.214669 | + | 0.00814690i | ||||
\(703\) | −1.78255e7 | −1.36036 | ||||||||
\(704\) | −2.01260e6 | + | 8.68961e6i | −0.153047 | + | 0.660798i | ||||
\(705\) | −6.49953e6 | −0.492503 | ||||||||
\(706\) | 1.07058e7 | + | 406294.i | 0.808362 | + | 0.0306781i | ||||
\(707\) | 1.10431e7i | 0.830884i | ||||||||
\(708\) | −1.50505e7 | − | 1.14401e6i | −1.12841 | − | 0.0857720i | ||||
\(709\) | − | 1.84405e7i | − | 1.37771i | −0.724900 | − | 0.688854i | \(-0.758114\pi\) | ||
0.724900 | − | 0.688854i | \(-0.241886\pi\) | |||||||
\(710\) | 381180. | − | 1.00440e7i | 0.0283781 | − | 0.747758i | ||||
\(711\) | 8.31407e6 | 0.616793 | ||||||||
\(712\) | 5.45688e6 | + | 623677.i | 0.403408 | + | 0.0461063i | ||||
\(713\) | −817147. | −0.0601972 | ||||||||
\(714\) | 895359. | − | 2.35925e7i | 0.0657282 | − | 1.73193i | ||||
\(715\) | 1.35015e6i | 0.0987684i | ||||||||
\(716\) | 1.04770e6 | − | 1.37834e7i | 0.0763754 | − | 1.00479i | ||||
\(717\) | − | 1.54886e7i | − | 1.12516i | ||||||
\(718\) | −1.45330e7 | − | 551540.i | −1.05207 | − | 0.0399269i | ||||
\(719\) | −334083. | −0.0241009 | −0.0120504 | − | 0.999927i | \(-0.503836\pi\) | ||||
−0.0120504 | + | 0.999927i | \(0.503836\pi\) | |||||||
\(720\) | 425541. | − | 2.78302e6i | 0.0305922 | − | 0.200072i | ||||
\(721\) | 3.86934e6 | 0.277204 | ||||||||
\(722\) | −6.21763e6 | − | 235965.i | −0.443897 | − | 0.0168463i | ||||
\(723\) | − | 1.62921e6i | − | 0.115913i | ||||||
\(724\) | −526168. | + | 6.92223e6i | −0.0373059 | + | 0.490794i | ||||
\(725\) | 5.00953e6i | 0.353959i | ||||||||
\(726\) | −350471. | + | 9.23485e6i | −0.0246780 | + | 0.650262i | ||||
\(727\) | −2.11438e7 | −1.48370 | −0.741851 | − | 0.670564i | \(-0.766052\pi\) | ||||
−0.741851 | + | 0.670564i | \(0.766052\pi\) | |||||||
\(728\) | −438554. | + | 3.83714e6i | −0.0306686 | + | 0.268336i | ||||
\(729\) | −3.30712e6 | −0.230479 | ||||||||
\(730\) | −99873.7 | + | 2.63165e6i | −0.00693656 | + | 0.182777i | ||||
\(731\) | 1.92152e7i | 1.33000i | ||||||||
\(732\) | 1.58289e7 | + | 1.20318e6i | 1.09188 | + | 0.0829950i | ||||
\(733\) | − | 1.48236e6i | − | 0.101904i | −0.998701 | − | 0.0509521i | \(-0.983774\pi\) | ||
0.998701 | − | 0.0509521i | \(-0.0162256\pi\) | |||||||
\(734\) | −1.39772e7 | − | 530449.i | −0.957593 | − | 0.0363415i | ||||
\(735\) | 2.46258e6 | 0.168140 | ||||||||
\(736\) | −5.61864e6 | − | 1.07862e6i | −0.382328 | − | 0.0733960i | ||||
\(737\) | −1.04973e7 | −0.711884 | ||||||||
\(738\) | 5.11076e6 | + | 193958.i | 0.345418 | + | 0.0131089i | ||||
\(739\) | 1.69772e7i | 1.14355i | 0.820411 | + | 0.571775i | \(0.193745\pi\) | ||||
−0.820411 | + | 0.571775i | \(0.806255\pi\) | |||||||
\(740\) | 7.51935e6 | + | 571556.i | 0.504779 | + | 0.0383689i | ||||
\(741\) | − | 7.04885e6i | − | 0.471599i | ||||||
\(742\) | 640209. | − | 1.68694e7i | 0.0426886 | − | 1.12484i | ||||
\(743\) | −2.01294e7 | −1.33770 | −0.668849 | − | 0.743399i | \(-0.733213\pi\) | ||||
−0.668849 | + | 0.743399i | \(0.733213\pi\) | |||||||
\(744\) | −319507. | + | 2.79553e6i | −0.0211616 | + | 0.185153i | ||||
\(745\) | 3.41201e6 | 0.225226 | ||||||||
\(746\) | −563208. | + | 1.48404e7i | −0.0370529 | + | 0.976336i | ||||
\(747\) | 1.37797e7i | 0.903520i | ||||||||
\(748\) | −1.36383e6 | + | 1.79424e7i | −0.0891264 | + | 1.17254i | ||||
\(749\) | 1.02143e7i | 0.665278i | ||||||||
\(750\) | 1.65941e6 | + | 62976.3i | 0.107721 | + | 0.00408812i | ||||
\(751\) | −1.16155e7 | −0.751514 | −0.375757 | − | 0.926718i | \(-0.622617\pi\) | ||||
−0.375757 | + | 0.926718i | \(0.622617\pi\) | |||||||
\(752\) | 1.40072e7 | + | 2.14179e6i | 0.903247 | + | 0.138112i | ||||
\(753\) | 7.74007e6 | 0.497459 | ||||||||
\(754\) | −8.98930e6 | − | 341152.i | −0.575834 | − | 0.0218534i | ||||
\(755\) | 4.65885e6i | 0.297448i | ||||||||
\(756\) | 651833. | − | 8.57547e6i | 0.0414793 | − | 0.545699i | ||||
\(757\) | − | 9.97313e6i | − | 0.632545i | −0.948668 | − | 0.316273i | \(-0.897569\pi\) | ||
0.948668 | − | 0.316273i | \(-0.102431\pi\) | |||||||
\(758\) | −459698. | + | 1.21130e7i | −0.0290603 | + | 0.765733i | ||||
\(759\) | 5.05108e6 | 0.318258 | ||||||||
\(760\) | 8.50251e6 | + | 971768.i | 0.533965 | + | 0.0610280i | ||||
\(761\) | 2.00566e7 | 1.25544 | 0.627719 | − | 0.778440i | \(-0.283989\pi\) | ||||
0.627719 | + | 0.778440i | \(0.283989\pi\) | |||||||
\(762\) | 255061. | − | 6.72080e6i | 0.0159131 | − | 0.419308i | ||||
\(763\) | − | 1.86207e7i | − | 1.15794i | ||||||
\(764\) | −1.10293e6 | − | 83835.2i | −0.0683620 | − | 0.00519628i | ||||
\(765\) | − | 5.67964e6i | − | 0.350887i | ||||||
\(766\) | −3.62786e6 | − | 137681.i | −0.223398 | − | 0.00847816i | ||||
\(767\) | 4.98110e6 | 0.305729 | ||||||||
\(768\) | −5.88695e6 | + | 1.88001e7i | −0.360153 | + | 1.15016i | ||||
\(769\) | 2.63971e7 | 1.60968 | 0.804842 | − | 0.593489i | \(-0.202250\pi\) | ||||
0.804842 | + | 0.593489i | \(0.202250\pi\) | |||||||
\(770\) | 4.13670e6 | + | 156992.i | 0.251436 | + | 0.00954223i | ||||
\(771\) | − | 1.65439e6i | − | 0.100231i | ||||||
\(772\) | −1.51117e7 | − | 1.14866e6i | −0.912575 | − | 0.0693661i | ||||
\(773\) | − | 902367.i | − | 0.0543169i | −0.999631 | − | 0.0271584i | \(-0.991354\pi\) | ||
0.999631 | − | 0.0271584i | \(-0.00864586\pi\) | |||||||
\(774\) | 219452. | − | 5.78252e6i | 0.0131670 | − | 0.346948i | ||||
\(775\) | −517089. | −0.0309251 | ||||||||
\(776\) | 2.81198e6 | + | 321386.i | 0.167632 | + | 0.0191590i | ||||
\(777\) | −1.90444e7 | −1.13166 | ||||||||
\(778\) | 506976. | − | 1.33587e7i | 0.0300288 | − | 0.791253i | ||||
\(779\) | 1.55463e7i | 0.917877i | ||||||||
\(780\) | −226014. | + | 2.97343e6i | −0.0133015 | + | 0.174993i | ||||
\(781\) | − | 1.93465e7i | − | 1.13494i | ||||||
\(782\) | −1.15335e7 | − | 437709.i | −0.674444 | − | 0.0255958i | ||||
\(783\) | 2.00319e7 | 1.16766 | ||||||||
\(784\) | −5.30712e6 | − | 811492.i | −0.308368 | − | 0.0471513i | ||||
\(785\) | −1.86724e6 | −0.108150 | ||||||||
\(786\) | 1.91251e7 | + | 725816.i | 1.10420 | + | 0.0419054i | ||||
\(787\) | − | 1.59032e7i | − | 0.915269i | −0.889140 | − | 0.457635i | \(-0.848697\pi\) | ||
0.889140 | − | 0.457635i | \(-0.151303\pi\) | |||||||
\(788\) | −957497. | + | 1.25968e7i | −0.0549315 | + | 0.722675i | ||||
\(789\) | − | 2.37258e6i | − | 0.135684i | ||||||
\(790\) | 405456. | − | 1.06837e7i | 0.0231140 | − | 0.609050i | ||||
\(791\) | 2.55700e7 | 1.45308 | ||||||||
\(792\) | 615340. | − | 5.38392e6i | 0.0348580 | − | 0.304990i | ||||
\(793\) | −5.23873e6 | −0.295830 | ||||||||
\(794\) | 86645.5 | − | 2.28309e6i | 0.00487747 | − | 0.128520i | ||||
\(795\) | − | 1.30345e7i | − | 0.731436i | ||||||
\(796\) | −1.52229e7 | − | 1.15712e6i | −0.851561 | − | 0.0647283i | ||||
\(797\) | − | 2.52099e7i | − | 1.40580i | −0.711287 | − | 0.702902i | \(-0.751887\pi\) | ||
0.711287 | − | 0.702902i | \(-0.248113\pi\) | |||||||
\(798\) | −2.15968e7 | − | 819619.i | −1.20055 | − | 0.0455622i | ||||
\(799\) | 2.85861e7 | 1.58412 | ||||||||
\(800\) | −3.55546e6 | − | 682546.i | −0.196414 | − | 0.0377057i | ||||
\(801\) | −3.33682e6 | −0.183760 | ||||||||
\(802\) | 1.29073e7 | + | 489845.i | 0.708598 | + | 0.0268920i | ||||
\(803\) | 5.06901e6i | 0.277418i | ||||||||
\(804\) | −2.31181e7 | − | 1.75724e6i | −1.26128 | − | 0.0958717i | ||||
\(805\) | 2.65527e6i | 0.144417i | ||||||||
\(806\) | 35214.1 | − | 927884.i | 0.00190932 | − | 0.0503102i | ||||
\(807\) | −3.53542e7 | −1.91099 | ||||||||
\(808\) | 2.11085e6 | − | 1.84689e7i | 0.113744 | − | 0.995206i | ||||
\(809\) | −1.43630e7 | −0.771570 | −0.385785 | − | 0.922589i | \(-0.626069\pi\) | ||||
−0.385785 | + | 0.922589i | \(0.626069\pi\) | |||||||
\(810\) | 395153. | − | 1.04122e7i | 0.0211618 | − | 0.557610i | ||||
\(811\) | − | 1.49512e7i | − | 0.798222i | −0.916903 | − | 0.399111i | \(-0.869319\pi\) | ||
0.916903 | − | 0.399111i | \(-0.130681\pi\) | |||||||
\(812\) | −2.09050e6 | + | 2.75024e7i | −0.111265 | + | 1.46380i | ||||
\(813\) | − | 2.19993e7i | − | 1.16730i | ||||||
\(814\) | 1.45044e7 | + | 550457.i | 0.767255 | + | 0.0291180i | ||||
\(815\) | −1.37195e7 | −0.723508 | ||||||||
\(816\) | −6.00709e6 | + | 3.92861e7i | −0.315819 | + | 2.06545i | ||||
\(817\) | 1.75897e7 | 0.921943 | ||||||||
\(818\) | 1.85391e7 | + | 703577.i | 0.968737 | + | 0.0367645i | ||||
\(819\) | − | 2.34637e6i | − | 0.122232i | ||||||
\(820\) | 498477. | − | 6.55793e6i | 0.0258887 | − | 0.340590i | ||||
\(821\) | − | 2.49701e7i | − | 1.29289i | −0.762960 | − | 0.646446i | \(-0.776254\pi\) | ||
0.762960 | − | 0.646446i | \(-0.223746\pi\) | |||||||
\(822\) | −1.47410e6 | + | 3.88423e7i | −0.0760936 | + | 2.00505i | ||||
\(823\) | 2.50946e7 | 1.29146 | 0.645729 | − | 0.763567i | \(-0.276554\pi\) | ||||
0.645729 | + | 0.763567i | \(0.276554\pi\) | |||||||
\(824\) | −6.47126e6 | − | 739614.i | −0.332025 | − | 0.0379478i | ||||
\(825\) | 3.19631e6 | 0.163499 | ||||||||
\(826\) | 579187. | − | 1.52615e7i | 0.0295372 | − | 0.778298i | ||||
\(827\) | − | 2.47367e7i | − | 1.25770i | −0.777526 | − | 0.628850i | \(-0.783526\pi\) | ||
0.777526 | − | 0.628850i | \(-0.216474\pi\) | |||||||
\(828\) | 3.46584e6 | + | 263443.i | 0.175684 | + | 0.0133540i | ||||
\(829\) | 1.02078e7i | 0.515878i | 0.966161 | + | 0.257939i | \(0.0830434\pi\) | ||||
−0.966161 | + | 0.257939i | \(0.916957\pi\) | |||||||
\(830\) | 1.77071e7 | + | 671999.i | 0.892177 | + | 0.0338590i | ||||
\(831\) | −2.09332e7 | −1.05156 | ||||||||
\(832\) | 1.46692e6 | − | 6.33358e6i | 0.0734678 | − | 0.317206i | ||||
\(833\) | −1.08309e7 | −0.540818 | ||||||||
\(834\) | −1.18826e7 | − | 450957.i | −0.591558 | − | 0.0224502i | ||||
\(835\) | 5.60779e6i | 0.278340i | ||||||||
\(836\) | 1.64246e7 | + | 1.24846e6i | 0.812794 | + | 0.0617816i | ||||
\(837\) | 2.06771e6i | 0.102018i | ||||||||
\(838\) | −129719. | + | 3.41807e6i | −0.00638107 | + | 0.168140i | ||||
\(839\) | 2.64451e7 | 1.29700 | 0.648501 | − | 0.761214i | \(-0.275396\pi\) | ||||
0.648501 | + | 0.761214i | \(0.275396\pi\) | |||||||
\(840\) | 9.08392e6 | + | 1.03822e6i | 0.444197 | + | 0.0507681i | ||||
\(841\) | −4.37332e7 | −2.13217 | ||||||||
\(842\) | 743010. | − | 1.95782e7i | 0.0361172 | − | 0.951682i | ||||
\(843\) | − | 3.52947e7i | − | 1.71057i | ||||||
\(844\) | 1.05720e6 | − | 1.39085e7i | 0.0510860 | − | 0.672084i | ||||
\(845\) | 8.29824e6i | 0.399801i | ||||||||
\(846\) | −8.60256e6 | − | 326475.i | −0.413239 | − | 0.0156828i | ||||
\(847\) | −9.35082e6 | −0.447859 | ||||||||
\(848\) | −4.29525e6 | + | 2.80908e7i | −0.205116 | + | 1.34145i | ||||
\(849\) | −57732.4 | −0.00274885 | ||||||||
\(850\) | −7.29841e6 | − | 276981.i | −0.346482 | − | 0.0131493i | ||||
\(851\) | 9.31014e6i | 0.440689i | ||||||||
\(852\) | 3.23858e6 | − | 4.26065e7i | 0.152846 | − | 2.01084i | ||||
\(853\) | 2.30070e7i | 1.08265i | 0.840814 | + | 0.541324i | \(0.182077\pi\) | ||||
−0.840814 | + | 0.541324i | \(0.817923\pi\) | |||||||
\(854\) | −609143. | + | 1.60508e7i | −0.0285808 | + | 0.753099i | ||||
\(855\) | −5.19919e6 | −0.243232 | ||||||||
\(856\) | 1.95243e6 | − | 1.70828e7i | 0.0910733 | − | 0.796848i | ||||
\(857\) | −1.81332e7 | −0.843379 | −0.421689 | − | 0.906740i | \(-0.638563\pi\) | ||||
−0.421689 | + | 0.906740i | \(0.638563\pi\) | |||||||
\(858\) | −217671. | + | 5.73558e6i | −0.0100944 | + | 0.265986i | ||||
\(859\) | 1.83891e6i | 0.0850310i | 0.999096 | + | 0.0425155i | \(0.0135372\pi\) | ||||
−0.999096 | + | 0.0425155i | \(0.986463\pi\) | |||||||
\(860\) | −7.41990e6 | − | 563997.i | −0.342099 | − | 0.0260034i | ||||
\(861\) | 1.66094e7i | 0.763567i | ||||||||
\(862\) | 2.82834e7 | + | 1.07338e6i | 1.29647 | + | 0.0492024i | ||||
\(863\) | 1.14230e7 | 0.522097 | 0.261049 | − | 0.965326i | \(-0.415932\pi\) | ||||
0.261049 | + | 0.965326i | \(0.415932\pi\) | |||||||
\(864\) | −2.72933e6 | + | 1.42174e7i | −0.124386 | + | 0.647942i | ||||
\(865\) | 4.13150e6 | 0.187744 | ||||||||
\(866\) | −2.32476e7 | − | 882268.i | −1.05338 | − | 0.0399766i | ||||
\(867\) | 5.35001e7i | 2.41717i | ||||||||
\(868\) | −2.83883e6 | − | 215783.i | −0.127891 | − | 0.00972116i | ||||
\(869\) | − | 2.05786e7i | − | 0.924413i | ||||||
\(870\) | −807634. | + | 2.12810e7i | −0.0361757 | + | 0.953222i | ||||
\(871\) | 7.65115e6 | 0.341729 | ||||||||
\(872\) | −3.55930e6 | + | 3.11421e7i | −0.158516 | + | 1.38694i | ||||
\(873\) | −1.71949e6 | −0.0763597 | ||||||||
\(874\) | −400682. | + | 1.05579e7i | −0.0177428 | + | 0.467519i | ||||
\(875\) | 1.68025e6i | 0.0741915i | ||||||||
\(876\) | −848547. | + | 1.11634e7i | −0.0373608 | + | 0.491515i | ||||
\(877\) | 2.12365e7i | 0.932362i | 0.884689 | + | 0.466181i | \(0.154370\pi\) | ||||
−0.884689 | + | 0.466181i | \(0.845630\pi\) | |||||||
\(878\) | 2.37594e7 | + | 901692.i | 1.04016 | + | 0.0394750i | ||||
\(879\) | −4.62116e7 | −2.01734 | ||||||||
\(880\) | −6.88840e6 | − | 1.05328e6i | −0.299855 | − | 0.0458497i | ||||
\(881\) | 1.35067e7 | 0.586287 | 0.293143 | − | 0.956069i | \(-0.405299\pi\) | ||||
0.293143 | + | 0.956069i | \(0.405299\pi\) | |||||||
\(882\) | 3.25938e6 | + | 123697.i | 0.141080 | + | 0.00535410i | ||||
\(883\) | 2.44466e7i | 1.05515i | 0.849507 | + | 0.527577i | \(0.176900\pi\) | ||||
−0.849507 | + | 0.527577i | \(0.823100\pi\) | |||||||
\(884\) | 994052. | − | 1.30777e7i | 0.0427837 | − | 0.562859i | ||||
\(885\) | − | 1.17921e7i | − | 0.506096i | ||||||
\(886\) | −283532. | + | 7.47100e6i | −0.0121344 | + | 0.319738i | ||||
\(887\) | 8.02242e6 | 0.342371 | 0.171185 | − | 0.985239i | \(-0.445240\pi\) | ||||
0.171185 | + | 0.985239i | \(0.445240\pi\) | |||||||
\(888\) | 3.18508e7 | + | 3.64029e6i | 1.35546 | + | 0.154919i | ||||
\(889\) | 6.80520e6 | 0.288793 | ||||||||
\(890\) | −162728. | + | 4.28785e6i | −0.00688632 | + | 0.181453i | ||||
\(891\) | − | 2.00557e7i | − | 0.846337i | ||||||
\(892\) | 3.63991e7 | + | 2.76674e6i | 1.53172 | + | 0.116428i | ||||
\(893\) | − | 2.61680e7i | − | 1.09810i | ||||||
\(894\) | 1.44945e7 | + | 550081.i | 0.606542 | + | 0.0230188i | ||||
\(895\) | 1.07994e7 | 0.450652 | ||||||||
\(896\) | −1.92347e7 | − | 5.23090e6i | −0.800416 | − | 0.217674i | ||||
\(897\) | −3.68157e6 | −0.152775 | ||||||||
\(898\) | −3.12148e7 | − | 1.18463e6i | −1.29172 | − | 0.0490221i | ||||
\(899\) | − | 6.63136e6i | − | 0.273655i | ||||||
\(900\) | 2.19318e6 | + | 166707.i | 0.0902543 | + | 0.00686035i | ||||
\(901\) | 5.73281e7i | 2.35264i | ||||||||
\(902\) | 480076. | − | 1.26499e7i | 0.0196469 | − | 0.517692i | ||||
\(903\) | 1.87926e7 | 0.766949 | ||||||||
\(904\) | −4.27644e7 | − | 4.88763e6i | −1.74045 | − | 0.198920i | ||||
\(905\) | −5.42359e6 | −0.220123 | ||||||||
\(906\) | −751097. | + | 1.97913e7i | −0.0304001 | + | 0.801038i | ||||
\(907\) | − | 2.02868e7i | − | 0.818831i | −0.912348 | − | 0.409416i | \(-0.865733\pi\) | ||
0.912348 | − | 0.409416i | \(-0.134267\pi\) | |||||||
\(908\) | 2.64109e6 | − | 3.47460e7i | 0.106309 | − | 1.39859i | ||||
\(909\) | 1.12935e7i | 0.453336i | ||||||||
\(910\) | −3.01511e6 | − | 114426.i | −0.120698 | − | 0.00458060i | ||||
\(911\) | 1.72893e7 | 0.690209 | 0.345104 | − | 0.938564i | \(-0.387844\pi\) | ||||
0.345104 | + | 0.938564i | \(0.387844\pi\) | |||||||
\(912\) | 3.59628e7 | + | 5.49894e6i | 1.43175 | + | 0.218923i | ||||
\(913\) | 3.41068e7 | 1.35414 | ||||||||
\(914\) | 1.96060e7 | + | 744067.i | 0.776290 | + | 0.0294609i | ||||
\(915\) | 1.24020e7i | 0.489710i | ||||||||
\(916\) | 1.15056e6 | − | 1.51367e7i | 0.0453076 | − | 0.596063i | ||||
\(917\) | 1.93653e7i | 0.760502i | ||||||||
\(918\) | −1.10758e6 | + | 2.91845e7i | −0.0433779 | + | 1.14300i | ||||
\(919\) | −2.14060e7 | −0.836079 | −0.418039 | − | 0.908429i | \(-0.637283\pi\) | ||||
−0.418039 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(920\) | 507548. | − | 4.44080e6i | 0.0197701 | − | 0.172978i | ||||
\(921\) | −4.83740e6 | −0.187916 | ||||||||
\(922\) | −519900. | + | 1.36993e7i | −0.0201415 | + | 0.530725i | ||||
\(923\) | 1.41010e7i | 0.544812i | ||||||||
\(924\) | 1.75478e7 | + | 1.33383e6i | 0.676149 | + | 0.0513950i | ||||
\(925\) | 5.89144e6i | 0.226395i | ||||||||
\(926\) | −3.72237e7 | − | 1.41267e6i | −1.42656 | − | 0.0541395i | ||||
\(927\) | 3.95710e6 | 0.151244 | ||||||||
\(928\) | 8.75326e6 | − | 4.55967e7i | 0.333657 | − | 1.73806i | ||||
\(929\) | 4.14158e7 | 1.57444 | 0.787221 | − | 0.616670i | \(-0.211519\pi\) | ||||
0.787221 | + | 0.616670i | \(0.211519\pi\) | |||||||
\(930\) | −2.19664e6 | − | 83364.7i | −0.0832823 | − | 0.00316064i | ||||
\(931\) | 9.91466e6i | 0.374890i | ||||||||
\(932\) | −8.64889e6 | − | 657414.i | −0.326152 | − | 0.0247913i | ||||
\(933\) | 4.56900e7i | 1.71837i | ||||||||
\(934\) | 248203. | − | 6.54010e6i | 0.00930979 | − | 0.245311i | ||||
\(935\) | −1.40580e7 | −0.525889 | ||||||||
\(936\) | −448501. | + | 3.92417e6i | −0.0167330 | + | 0.146406i | ||||
\(937\) | 1.39335e7 | 0.518455 | 0.259228 | − | 0.965816i | \(-0.416532\pi\) | ||||
0.259228 | + | 0.965816i | \(0.416532\pi\) | |||||||
\(938\) | 889652. | − | 2.34422e7i | 0.0330151 | − | 0.869943i | ||||
\(939\) | − | 4.93254e7i | − | 1.82560i | ||||||
\(940\) | −839049. | + | 1.10385e7i | −0.0309719 | + | 0.407464i | ||||
\(941\) | 1.51311e7i | 0.557051i | 0.960429 | + | 0.278526i | \(0.0898457\pi\) | ||||
−0.960429 | + | 0.278526i | \(0.910154\pi\) | |||||||
\(942\) | −7.93222e6 | − | 301035.i | −0.291251 | − | 0.0110532i | ||||
\(943\) | 8.11975e6 | 0.297347 | ||||||||
\(944\) | −3.88585e6 | + | 2.54133e7i | −0.141924 | + | 0.928177i | ||||
\(945\) | 6.71891e6 | 0.244748 | ||||||||
\(946\) | −1.43126e7 | − | 543177.i | −0.519985 | − | 0.0197339i | ||||
\(947\) | − | 2.72196e7i | − | 0.986296i | −0.869945 | − | 0.493148i | \(-0.835846\pi\) | ||
0.869945 | − | 0.493148i | \(-0.164154\pi\) | |||||||
\(948\) | 3.44483e6 | − | 4.53200e7i | 0.124494 | − | 1.63783i | ||||
\(949\) | − | 3.69464e6i | − | 0.133170i | ||||||
\(950\) | −253551. | + | 6.68102e6i | −0.00911499 | + | 0.240178i | ||||
\(951\) | −4.78623e7 | −1.71610 | ||||||||
\(952\) | −3.99528e7 | − | 4.56628e6i | −1.42874 | − | 0.163294i | ||||
\(953\) | −2.79494e7 | −0.996873 | −0.498437 | − | 0.866926i | \(-0.666092\pi\) | ||||
−0.498437 | + | 0.866926i | \(0.666092\pi\) | |||||||
\(954\) | 654730. | − | 1.72520e7i | 0.0232912 | − | 0.613718i | ||||
\(955\) | − | 864150.i | − | 0.0306606i | ||||||
\(956\) | −2.63051e7 | − | 1.99948e6i | −0.930882 | − | 0.0707576i | ||||
\(957\) | 4.09908e7i | 1.44679i | ||||||||
\(958\) | −2.15098e6 | − | 81631.8i | −0.0757221 | − | 0.00287373i | ||||
\(959\) | −3.93301e7 | −1.38095 | ||||||||
\(960\) | −1.49939e7 | − | 3.47273e6i | −0.525094 | − | 0.121617i | ||||
\(961\) | −2.79447e7 | −0.976091 | ||||||||
\(962\) | −1.05718e7 | − | 401210.i | −0.368309 | − | 0.0139777i | ||||
\(963\) | 1.04460e7i | 0.362980i | ||||||||
\(964\) | −2.76697e6 | − | 210321.i | −0.0958984 | − | 0.00728937i | ||||
\(965\) | − | 1.18400e7i | − | 0.409293i | ||||||
\(966\) | −428081. | + | 1.12799e7i | −0.0147599 | + | 0.388921i | ||||
\(967\) | 3.73167e7 | 1.28333 | 0.641663 | − | 0.766987i | \(-0.278245\pi\) | ||||
0.641663 | + | 0.766987i | \(0.278245\pi\) | |||||||
\(968\) | 1.56387e7 | + | 1.78738e6i | 0.536431 | + | 0.0613097i | ||||
\(969\) | 7.33936e7 | 2.51101 | ||||||||
\(970\) | −83855.2 | + | 2.20957e6i | −0.00286154 | + | 0.0754011i | ||||
\(971\) | − | 1.77774e7i | − | 0.605091i | −0.953135 | − | 0.302545i | \(-0.902164\pi\) | ||
0.953135 | − | 0.302545i | \(-0.0978364\pi\) | |||||||
\(972\) | 1.88435e6 | − | 2.47904e7i | 0.0639728 | − | 0.841622i | ||||
\(973\) | − | 1.20318e7i | − | 0.407427i | ||||||
\(974\) | 1.51333e7 | + | 574325.i | 0.511137 | + | 0.0193981i | ||||
\(975\) | −2.32969e6 | −0.0784850 | ||||||||
\(976\) | 4.08683e6 | − | 2.67277e7i | 0.137329 | − | 0.898125i | ||||
\(977\) | 1.67378e7 | 0.561000 | 0.280500 | − | 0.959854i | \(-0.409500\pi\) | ||||
0.280500 | + | 0.959854i | \(0.409500\pi\) | |||||||
\(978\) | −5.82817e7 | − | 2.21184e6i | −1.94843 | − | 0.0739448i | ||||
\(979\) | 8.25913e6i | 0.275409i | ||||||||
\(980\) | 317903. | − | 4.18232e6i | 0.0105738 | − | 0.139108i | ||||
\(981\) | − | 1.90431e7i | − | 0.631778i | ||||||
\(982\) | 1.09559e6 | − | 2.88685e7i | 0.0362550 | − | 0.955312i | ||||
\(983\) | −2.99351e7 | −0.988091 | −0.494045 | − | 0.869436i | \(-0.664482\pi\) | ||||
−0.494045 | + | 0.869436i | \(0.664482\pi\) | |||||||
\(984\) | 3.17485e6 | − | 2.77784e7i | 0.104529 | − | 0.914575i | ||||
\(985\) | −9.86961e6 | −0.324123 | ||||||||
\(986\) | 3.55212e6 | − | 9.35978e7i | 0.116358 | − | 3.06601i | ||||
\(987\) | − | 2.79574e7i | − | 0.913490i | ||||||
\(988\) | −1.19714e7 | − | 909963.i | −0.390169 | − | 0.0296573i | ||||
\(989\) | − | 9.18701e6i | − | 0.298664i | ||||||
\(990\) | 4.23053e6 | + | 160553.i | 0.137185 | + | 0.00520630i | ||||
\(991\) | 1.30589e7 | 0.422398 | 0.211199 | − | 0.977443i | \(-0.432263\pi\) | ||||
0.211199 | + | 0.977443i | \(0.432263\pi\) | |||||||
\(992\) | 4.70654e6 | + | 903519.i | 0.151853 | + | 0.0291513i | ||||
\(993\) | −3.97753e7 | −1.28009 | ||||||||
\(994\) | 4.32038e7 | + | 1.63962e6i | 1.38693 | + | 0.0526354i | ||||
\(995\) | − | 1.19272e7i | − | 0.381928i | ||||||
\(996\) | 7.51130e7 | + | 5.70944e6i | 2.39920 | + | 0.182367i | ||||
\(997\) | 7.99417e6i | 0.254704i | 0.991858 | + | 0.127352i | \(0.0406477\pi\) | ||||
−0.991858 | + | 0.127352i | \(0.959352\pi\) | |||||||
\(998\) | −55643.4 | + | 1.46619e6i | −0.00176843 | + | 0.0465978i | ||||
\(999\) | 2.35584e7 | 0.746848 |
(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 | 40.6.d.a.21.20 | yes | 20 | |
3.2 | odd | 2 | 360.6.k.b.181.1 | 20 | |||
4.3 | odd | 2 | 160.6.d.a.81.4 | 20 | |||
5.2 | odd | 4 | 200.6.f.b.149.12 | 20 | |||
5.3 | odd | 4 | 200.6.f.c.149.9 | 20 | |||
5.4 | even | 2 | 200.6.d.b.101.1 | 20 | |||
8.3 | odd | 2 | 160.6.d.a.81.17 | 20 | |||
8.5 | even | 2 | inner | 40.6.d.a.21.19 | ✓ | 20 | |
20.3 | even | 4 | 800.6.f.b.49.17 | 20 | |||
20.7 | even | 4 | 800.6.f.c.49.4 | 20 | |||
20.19 | odd | 2 | 800.6.d.c.401.17 | 20 | |||
24.5 | odd | 2 | 360.6.k.b.181.2 | 20 | |||
40.3 | even | 4 | 800.6.f.c.49.3 | 20 | |||
40.13 | odd | 4 | 200.6.f.b.149.11 | 20 | |||
40.19 | odd | 2 | 800.6.d.c.401.4 | 20 | |||
40.27 | even | 4 | 800.6.f.b.49.18 | 20 | |||
40.29 | even | 2 | 200.6.d.b.101.2 | 20 | |||
40.37 | odd | 4 | 200.6.f.c.149.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.19 | ✓ | 20 | 8.5 | even | 2 | inner | |
40.6.d.a.21.20 | yes | 20 | 1.1 | even | 1 | trivial | |
160.6.d.a.81.4 | 20 | 4.3 | odd | 2 | |||
160.6.d.a.81.17 | 20 | 8.3 | odd | 2 | |||
200.6.d.b.101.1 | 20 | 5.4 | even | 2 | |||
200.6.d.b.101.2 | 20 | 40.29 | even | 2 | |||
200.6.f.b.149.11 | 20 | 40.13 | odd | 4 | |||
200.6.f.b.149.12 | 20 | 5.2 | odd | 4 | |||
200.6.f.c.149.9 | 20 | 5.3 | odd | 4 | |||
200.6.f.c.149.10 | 20 | 40.37 | odd | 4 | |||
360.6.k.b.181.1 | 20 | 3.2 | odd | 2 | |||
360.6.k.b.181.2 | 20 | 24.5 | odd | 2 | |||
800.6.d.c.401.4 | 20 | 40.19 | odd | 2 | |||
800.6.d.c.401.17 | 20 | 20.19 | odd | 2 | |||
800.6.f.b.49.17 | 20 | 20.3 | even | 4 | |||
800.6.f.b.49.18 | 20 | 40.27 | even | 4 | |||
800.6.f.c.49.3 | 20 | 40.3 | even | 4 | |||
800.6.f.c.49.4 | 20 | 20.7 | even | 4 |