Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-9.16809\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.1681 | −1.97426 | −0.987129 | − | 0.159926i | \(-0.948874\pi\) | ||||
−0.987129 | + | 0.159926i | \(0.948874\pi\) | |||||||
\(3\) | −28.1764 | −1.80752 | −0.903760 | − | 0.428040i | \(-0.859204\pi\) | ||||
−0.903760 | + | 0.428040i | \(0.859204\pi\) | |||||||
\(4\) | 92.7262 | 2.89769 | ||||||||
\(5\) | −10.1483 | −0.181538 | −0.0907688 | − | 0.995872i | \(-0.528932\pi\) | ||||
−0.0907688 | + | 0.995872i | \(0.528932\pi\) | |||||||
\(6\) | 314.677 | 3.56851 | ||||||||
\(7\) | 135.849 | 1.04788 | 0.523939 | − | 0.851756i | \(-0.324462\pi\) | ||||
0.523939 | + | 0.851756i | \(0.324462\pi\) | |||||||
\(8\) | −678.196 | −3.74654 | ||||||||
\(9\) | 550.912 | 2.26713 | ||||||||
\(10\) | 113.337 | 0.358402 | ||||||||
\(11\) | −74.1258 | −0.184709 | −0.0923544 | − | 0.995726i | \(-0.529439\pi\) | ||||
−0.0923544 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(12\) | −2612.70 | −5.23764 | ||||||||
\(13\) | −252.408 | −0.414233 | −0.207117 | − | 0.978316i | \(-0.566408\pi\) | ||||
−0.207117 | + | 0.978316i | \(0.566408\pi\) | |||||||
\(14\) | −1517.17 | −2.06878 | ||||||||
\(15\) | 285.942 | 0.328133 | ||||||||
\(16\) | 4606.91 | 4.49894 | ||||||||
\(17\) | 233.541 | 0.195993 | 0.0979967 | − | 0.995187i | \(-0.468757\pi\) | ||||
0.0979967 | + | 0.995187i | \(0.468757\pi\) | |||||||
\(18\) | −6152.64 | −4.47590 | ||||||||
\(19\) | 550.209 | 0.349658 | 0.174829 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174829 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(20\) | −941.010 | −0.526040 | ||||||||
\(21\) | −3827.74 | −1.89406 | ||||||||
\(22\) | 827.844 | 0.364663 | ||||||||
\(23\) | 1951.63 | 0.769269 | 0.384634 | − | 0.923069i | \(-0.374328\pi\) | ||||
0.384634 | + | 0.923069i | \(0.374328\pi\) | |||||||
\(24\) | 19109.1 | 6.77194 | ||||||||
\(25\) | −3022.01 | −0.967044 | ||||||||
\(26\) | 2818.92 | 0.817803 | ||||||||
\(27\) | −8675.87 | −2.29036 | ||||||||
\(28\) | 12596.8 | 3.03643 | ||||||||
\(29\) | −4679.01 | −1.03314 | −0.516570 | − | 0.856245i | \(-0.672791\pi\) | ||||
−0.516570 | + | 0.856245i | \(0.672791\pi\) | |||||||
\(30\) | −3193.42 | −0.647819 | ||||||||
\(31\) | 3331.10 | 0.622563 | 0.311281 | − | 0.950318i | \(-0.399242\pi\) | ||||
0.311281 | + | 0.950318i | \(0.399242\pi\) | |||||||
\(32\) | −29748.1 | −5.13553 | ||||||||
\(33\) | 2088.60 | 0.333865 | ||||||||
\(34\) | −2608.21 | −0.386942 | ||||||||
\(35\) | −1378.63 | −0.190229 | ||||||||
\(36\) | 51084.0 | 6.56944 | ||||||||
\(37\) | −13497.0 | −1.62081 | −0.810407 | − | 0.585867i | \(-0.800754\pi\) | ||||
−0.810407 | + | 0.585867i | \(0.800754\pi\) | |||||||
\(38\) | −6144.79 | −0.690316 | ||||||||
\(39\) | 7111.96 | 0.748735 | ||||||||
\(40\) | 6882.51 | 0.680137 | ||||||||
\(41\) | 8205.81 | 0.762363 | 0.381181 | − | 0.924500i | \(-0.375517\pi\) | ||||
0.381181 | + | 0.924500i | \(0.375517\pi\) | |||||||
\(42\) | 42748.5 | 3.73937 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | −6873.41 | −0.535230 | ||||||||
\(45\) | −5590.80 | −0.411569 | ||||||||
\(46\) | −21796.0 | −1.51873 | ||||||||
\(47\) | −22043.6 | −1.45559 | −0.727793 | − | 0.685797i | \(-0.759454\pi\) | ||||
−0.727793 | + | 0.685797i | \(0.759454\pi\) | |||||||
\(48\) | −129806. | −8.13192 | ||||||||
\(49\) | 1647.91 | 0.0980493 | ||||||||
\(50\) | 33750.1 | 1.90919 | ||||||||
\(51\) | −6580.36 | −0.354262 | ||||||||
\(52\) | −23404.8 | −1.20032 | ||||||||
\(53\) | 6348.62 | 0.310449 | 0.155224 | − | 0.987879i | \(-0.450390\pi\) | ||||
0.155224 | + | 0.987879i | \(0.450390\pi\) | |||||||
\(54\) | 96892.9 | 4.52176 | ||||||||
\(55\) | 752.248 | 0.0335316 | ||||||||
\(56\) | −92132.1 | −3.92592 | ||||||||
\(57\) | −15502.9 | −0.632015 | ||||||||
\(58\) | 52255.6 | 2.03968 | ||||||||
\(59\) | −14937.7 | −0.558669 | −0.279334 | − | 0.960194i | \(-0.590114\pi\) | ||||
−0.279334 | + | 0.960194i | \(0.590114\pi\) | |||||||
\(60\) | 26514.3 | 0.950829 | ||||||||
\(61\) | −23854.4 | −0.820812 | −0.410406 | − | 0.911903i | \(-0.634613\pi\) | ||||
−0.410406 | + | 0.911903i | \(0.634613\pi\) | |||||||
\(62\) | −37202.0 | −1.22910 | ||||||||
\(63\) | 74840.8 | 2.37567 | ||||||||
\(64\) | 184809. | 5.63992 | ||||||||
\(65\) | 2561.50 | 0.0751989 | ||||||||
\(66\) | −23325.7 | −0.659136 | ||||||||
\(67\) | 38603.2 | 1.05060 | 0.525299 | − | 0.850918i | \(-0.323953\pi\) | ||||
0.525299 | + | 0.850918i | \(0.323953\pi\) | |||||||
\(68\) | 21655.4 | 0.567929 | ||||||||
\(69\) | −54990.0 | −1.39047 | ||||||||
\(70\) | 15396.7 | 0.375562 | ||||||||
\(71\) | 4917.85 | 0.115779 | 0.0578894 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578894 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(72\) | −373626. | −8.49388 | ||||||||
\(73\) | 5260.97 | 0.115547 | 0.0577735 | − | 0.998330i | \(-0.481600\pi\) | ||||
0.0577735 | + | 0.998330i | \(0.481600\pi\) | |||||||
\(74\) | 150736. | 3.19991 | ||||||||
\(75\) | 85149.6 | 1.74795 | ||||||||
\(76\) | 51018.8 | 1.01320 | ||||||||
\(77\) | −10069.9 | −0.193552 | ||||||||
\(78\) | −79427.0 | −1.47820 | ||||||||
\(79\) | −26865.7 | −0.484318 | −0.242159 | − | 0.970237i | \(-0.577856\pi\) | ||||
−0.242159 | + | 0.970237i | \(0.577856\pi\) | |||||||
\(80\) | −46752.1 | −0.816726 | ||||||||
\(81\) | 110584. | 1.87274 | ||||||||
\(82\) | −91643.2 | −1.50510 | ||||||||
\(83\) | 48430.7 | 0.771659 | 0.385830 | − | 0.922570i | \(-0.373915\pi\) | ||||
0.385830 | + | 0.922570i | \(0.373915\pi\) | |||||||
\(84\) | −354932. | −5.48841 | ||||||||
\(85\) | −2370.04 | −0.0355802 | ||||||||
\(86\) | 20649.8 | 0.301072 | ||||||||
\(87\) | 131838. | 1.86742 | ||||||||
\(88\) | 50271.8 | 0.692019 | ||||||||
\(89\) | −117672. | −1.57470 | −0.787352 | − | 0.616504i | \(-0.788549\pi\) | ||||
−0.787352 | + | 0.616504i | \(0.788549\pi\) | |||||||
\(90\) | 62438.5 | 0.812543 | ||||||||
\(91\) | −34289.3 | −0.434066 | ||||||||
\(92\) | 180967. | 2.22911 | ||||||||
\(93\) | −93858.5 | −1.12529 | ||||||||
\(94\) | 246185. | 2.87370 | ||||||||
\(95\) | −5583.67 | −0.0634762 | ||||||||
\(96\) | 838197. | 9.28257 | ||||||||
\(97\) | −62399.7 | −0.673369 | −0.336684 | − | 0.941618i | \(-0.609306\pi\) | ||||
−0.336684 | + | 0.941618i | \(0.609306\pi\) | |||||||
\(98\) | −18404.1 | −0.193575 | ||||||||
\(99\) | −40836.8 | −0.418759 | ||||||||
\(100\) | −280220. | −2.80220 | ||||||||
\(101\) | −184829. | −1.80288 | −0.901441 | − | 0.432902i | \(-0.857490\pi\) | ||||
−0.901441 | + | 0.432902i | \(0.857490\pi\) | |||||||
\(102\) | 73490.1 | 0.699405 | ||||||||
\(103\) | −131556. | −1.22185 | −0.610924 | − | 0.791689i | \(-0.709202\pi\) | ||||
−0.610924 | + | 0.791689i | \(0.709202\pi\) | |||||||
\(104\) | 171182. | 1.55194 | ||||||||
\(105\) | 38844.9 | 0.343843 | ||||||||
\(106\) | −70902.0 | −0.612906 | ||||||||
\(107\) | −26372.2 | −0.222683 | −0.111341 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111341 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(108\) | −804481. | −6.63676 | ||||||||
\(109\) | −171471. | −1.38237 | −0.691183 | − | 0.722680i | \(-0.742910\pi\) | ||||
−0.691183 | + | 0.722680i | \(0.742910\pi\) | |||||||
\(110\) | −8401.17 | −0.0662000 | ||||||||
\(111\) | 380298. | 2.92965 | ||||||||
\(112\) | 625844. | 4.71434 | ||||||||
\(113\) | 108442. | 0.798917 | 0.399459 | − | 0.916751i | \(-0.369198\pi\) | ||||
0.399459 | + | 0.916751i | \(0.369198\pi\) | |||||||
\(114\) | 173138. | 1.24776 | ||||||||
\(115\) | −19805.7 | −0.139651 | ||||||||
\(116\) | −433867. | −2.99372 | ||||||||
\(117\) | −139055. | −0.939120 | ||||||||
\(118\) | 166826. | 1.10296 | ||||||||
\(119\) | 31726.3 | 0.205377 | ||||||||
\(120\) | −193925. | −1.22936 | ||||||||
\(121\) | −155556. | −0.965883 | ||||||||
\(122\) | 266408. | 1.62049 | ||||||||
\(123\) | −231211. | −1.37799 | ||||||||
\(124\) | 308880. | 1.80400 | ||||||||
\(125\) | 62381.5 | 0.357092 | ||||||||
\(126\) | −835829. | −4.69019 | ||||||||
\(127\) | 162713. | 0.895186 | 0.447593 | − | 0.894237i | \(-0.352281\pi\) | ||||
0.447593 | + | 0.894237i | \(0.352281\pi\) | |||||||
\(128\) | −1.11202e6 | −5.99912 | ||||||||
\(129\) | 52098.3 | 0.275644 | ||||||||
\(130\) | −28607.1 | −0.148462 | ||||||||
\(131\) | −128326. | −0.653335 | −0.326667 | − | 0.945139i | \(-0.605926\pi\) | ||||
−0.326667 | + | 0.945139i | \(0.605926\pi\) | |||||||
\(132\) | 193668. | 0.967439 | ||||||||
\(133\) | 74745.3 | 0.366400 | ||||||||
\(134\) | −431125. | −2.07415 | ||||||||
\(135\) | 88045.0 | 0.415786 | ||||||||
\(136\) | −158387. | −0.734297 | ||||||||
\(137\) | 192870. | 0.877937 | 0.438968 | − | 0.898503i | \(-0.355344\pi\) | ||||
0.438968 | + | 0.898503i | \(0.355344\pi\) | |||||||
\(138\) | 614133. | 2.74514 | ||||||||
\(139\) | −276084. | −1.21200 | −0.606002 | − | 0.795463i | \(-0.707228\pi\) | ||||
−0.606002 | + | 0.795463i | \(0.707228\pi\) | |||||||
\(140\) | −127835. | −0.551226 | ||||||||
\(141\) | 621110. | 2.63100 | ||||||||
\(142\) | −54923.0 | −0.228577 | ||||||||
\(143\) | 18709.9 | 0.0765125 | ||||||||
\(144\) | 2.53800e6 | 10.1997 | ||||||||
\(145\) | 47483.8 | 0.187554 | ||||||||
\(146\) | −58755.0 | −0.228120 | ||||||||
\(147\) | −46432.4 | −0.177226 | ||||||||
\(148\) | −1.25153e6 | −4.69662 | ||||||||
\(149\) | 217182. | 0.801414 | 0.400707 | − | 0.916206i | \(-0.368764\pi\) | ||||
0.400707 | + | 0.916206i | \(0.368764\pi\) | |||||||
\(150\) | −950958. | −3.45091 | ||||||||
\(151\) | 404181. | 1.44256 | 0.721279 | − | 0.692644i | \(-0.243554\pi\) | ||||
0.721279 | + | 0.692644i | \(0.243554\pi\) | |||||||
\(152\) | −373150. | −1.31001 | ||||||||
\(153\) | 128661. | 0.444342 | ||||||||
\(154\) | 112462. | 0.382122 | ||||||||
\(155\) | −33804.8 | −0.113019 | ||||||||
\(156\) | 659465. | 2.16960 | ||||||||
\(157\) | 44527.8 | 0.144173 | 0.0720863 | − | 0.997398i | \(-0.477034\pi\) | ||||
0.0720863 | + | 0.997398i | \(0.477034\pi\) | |||||||
\(158\) | 300038. | 0.956168 | ||||||||
\(159\) | −178882. | −0.561142 | ||||||||
\(160\) | 301892. | 0.932291 | ||||||||
\(161\) | 265127. | 0.806100 | ||||||||
\(162\) | −1.23501e6 | −3.69728 | ||||||||
\(163\) | −214840. | −0.633354 | −0.316677 | − | 0.948533i | \(-0.602567\pi\) | ||||
−0.316677 | + | 0.948533i | \(0.602567\pi\) | |||||||
\(164\) | 760894. | 2.20909 | ||||||||
\(165\) | −21195.7 | −0.0606090 | ||||||||
\(166\) | −540879. | −1.52345 | ||||||||
\(167\) | −249849. | −0.693245 | −0.346623 | − | 0.938005i | \(-0.612672\pi\) | ||||
−0.346623 | + | 0.938005i | \(0.612672\pi\) | |||||||
\(168\) | 2.59596e6 | 7.09617 | ||||||||
\(169\) | −307583. | −0.828411 | ||||||||
\(170\) | 26468.8 | 0.0702444 | ||||||||
\(171\) | 303117. | 0.792721 | ||||||||
\(172\) | −171451. | −0.441894 | ||||||||
\(173\) | 148039. | 0.376064 | 0.188032 | − | 0.982163i | \(-0.439789\pi\) | ||||
0.188032 | + | 0.982163i | \(0.439789\pi\) | |||||||
\(174\) | −1.47238e6 | −3.68677 | ||||||||
\(175\) | −410537. | −1.01334 | ||||||||
\(176\) | −341491. | −0.830994 | ||||||||
\(177\) | 420892. | 1.00980 | ||||||||
\(178\) | 1.31417e6 | 3.10887 | ||||||||
\(179\) | 492820. | 1.14962 | 0.574812 | − | 0.818286i | \(-0.305075\pi\) | ||||
0.574812 | + | 0.818286i | \(0.305075\pi\) | |||||||
\(180\) | −518414. | −1.19260 | ||||||||
\(181\) | −379943. | −0.862030 | −0.431015 | − | 0.902345i | \(-0.641844\pi\) | ||||
−0.431015 | + | 0.902345i | \(0.641844\pi\) | |||||||
\(182\) | 382946. | 0.856958 | ||||||||
\(183\) | 672132. | 1.48363 | ||||||||
\(184\) | −1.32359e6 | −2.88209 | ||||||||
\(185\) | 136971. | 0.294239 | ||||||||
\(186\) | 1.04822e6 | 2.22162 | ||||||||
\(187\) | −17311.4 | −0.0362017 | ||||||||
\(188\) | −2.04402e6 | −4.21784 | ||||||||
\(189\) | −1.17861e6 | −2.40002 | ||||||||
\(190\) | 62358.9 | 0.125318 | ||||||||
\(191\) | 844630. | 1.67526 | 0.837631 | − | 0.546236i | \(-0.183940\pi\) | ||||
0.837631 | + | 0.546236i | \(0.183940\pi\) | |||||||
\(192\) | −5.20725e6 | −10.1943 | ||||||||
\(193\) | −228384. | −0.441339 | −0.220669 | − | 0.975349i | \(-0.570824\pi\) | ||||
−0.220669 | + | 0.975349i | \(0.570824\pi\) | |||||||
\(194\) | 696885. | 1.32940 | ||||||||
\(195\) | −72174.0 | −0.135923 | ||||||||
\(196\) | 152805. | 0.284117 | ||||||||
\(197\) | 405691. | 0.744783 | 0.372391 | − | 0.928076i | \(-0.378538\pi\) | ||||
0.372391 | + | 0.928076i | \(0.378538\pi\) | |||||||
\(198\) | 456069. | 0.826738 | ||||||||
\(199\) | −720104. | −1.28903 | −0.644514 | − | 0.764593i | \(-0.722940\pi\) | ||||
−0.644514 | + | 0.764593i | \(0.722940\pi\) | |||||||
\(200\) | 2.04952e6 | 3.62307 | ||||||||
\(201\) | −1.08770e6 | −1.89898 | ||||||||
\(202\) | 2.06419e6 | 3.55935 | ||||||||
\(203\) | −635638. | −1.08260 | ||||||||
\(204\) | −610172. | −1.02654 | ||||||||
\(205\) | −83274.7 | −0.138398 | ||||||||
\(206\) | 1.46923e6 | 2.41224 | ||||||||
\(207\) | 1.07518e6 | 1.74403 | ||||||||
\(208\) | −1.16282e6 | −1.86361 | ||||||||
\(209\) | −40784.7 | −0.0645850 | ||||||||
\(210\) | −433823. | −0.678835 | ||||||||
\(211\) | 626107. | 0.968149 | 0.484074 | − | 0.875027i | \(-0.339156\pi\) | ||||
0.484074 | + | 0.875027i | \(0.339156\pi\) | |||||||
\(212\) | 588684. | 0.899585 | ||||||||
\(213\) | −138567. | −0.209273 | ||||||||
\(214\) | 294527. | 0.439633 | ||||||||
\(215\) | 18764.1 | 0.0276842 | ||||||||
\(216\) | 5.88394e6 | 8.58092 | ||||||||
\(217\) | 452526. | 0.652370 | ||||||||
\(218\) | 1.91500e6 | 2.72915 | ||||||||
\(219\) | −148236. | −0.208854 | ||||||||
\(220\) | 69753.1 | 0.0971643 | ||||||||
\(221\) | −58947.7 | −0.0811870 | ||||||||
\(222\) | −4.24720e6 | −5.78389 | ||||||||
\(223\) | 513365. | 0.691296 | 0.345648 | − | 0.938364i | \(-0.387659\pi\) | ||||
0.345648 | + | 0.938364i | \(0.387659\pi\) | |||||||
\(224\) | −4.04125e6 | −5.38141 | ||||||||
\(225\) | −1.66486e6 | −2.19241 | ||||||||
\(226\) | −1.21109e6 | −1.57727 | ||||||||
\(227\) | −1.20833e6 | −1.55640 | −0.778200 | − | 0.628017i | \(-0.783867\pi\) | ||||
−0.778200 | + | 0.628017i | \(0.783867\pi\) | |||||||
\(228\) | −1.43753e6 | −1.83139 | ||||||||
\(229\) | −313322. | −0.394822 | −0.197411 | − | 0.980321i | \(-0.563253\pi\) | ||||
−0.197411 | + | 0.980321i | \(0.563253\pi\) | |||||||
\(230\) | 221191. | 0.275707 | ||||||||
\(231\) | 283734. | 0.349850 | ||||||||
\(232\) | 3.17328e6 | 3.87070 | ||||||||
\(233\) | −194052. | −0.234168 | −0.117084 | − | 0.993122i | \(-0.537355\pi\) | ||||
−0.117084 | + | 0.993122i | \(0.537355\pi\) | |||||||
\(234\) | 1.55297e6 | 1.85406 | ||||||||
\(235\) | 223704. | 0.264243 | ||||||||
\(236\) | −1.38512e6 | −1.61885 | ||||||||
\(237\) | 756980. | 0.875414 | ||||||||
\(238\) | −354322. | −0.405468 | ||||||||
\(239\) | −349700. | −0.396005 | −0.198002 | − | 0.980202i | \(-0.563445\pi\) | ||||
−0.198002 | + | 0.980202i | \(0.563445\pi\) | |||||||
\(240\) | 1.31731e6 | 1.47625 | ||||||||
\(241\) | −21340.0 | −0.0236675 | −0.0118338 | − | 0.999930i | \(-0.503767\pi\) | ||||
−0.0118338 | + | 0.999930i | \(0.503767\pi\) | |||||||
\(242\) | 1.73727e6 | 1.90690 | ||||||||
\(243\) | −1.00761e6 | −1.09466 | ||||||||
\(244\) | −2.21193e6 | −2.37846 | ||||||||
\(245\) | −16723.5 | −0.0177996 | ||||||||
\(246\) | 2.58218e6 | 2.72050 | ||||||||
\(247\) | −138877. | −0.144840 | ||||||||
\(248\) | −2.25914e6 | −2.33245 | ||||||||
\(249\) | −1.36461e6 | −1.39479 | ||||||||
\(250\) | −696682. | −0.704993 | ||||||||
\(251\) | −881880. | −0.883538 | −0.441769 | − | 0.897129i | \(-0.645649\pi\) | ||||
−0.441769 | + | 0.897129i | \(0.645649\pi\) | |||||||
\(252\) | 6.93970e6 | 6.88398 | ||||||||
\(253\) | −144666. | −0.142091 | ||||||||
\(254\) | −1.81719e6 | −1.76733 | ||||||||
\(255\) | 66779.2 | 0.0643119 | ||||||||
\(256\) | 6.50526e6 | 6.20390 | ||||||||
\(257\) | −1.90048e6 | −1.79486 | −0.897428 | − | 0.441160i | \(-0.854567\pi\) | ||||
−0.897428 | + | 0.441160i | \(0.854567\pi\) | |||||||
\(258\) | −581838. | −0.544193 | ||||||||
\(259\) | −1.83355e6 | −1.69842 | ||||||||
\(260\) | 237518. | 0.217903 | ||||||||
\(261\) | −2.57772e6 | −2.34226 | ||||||||
\(262\) | 1.43315e6 | 1.28985 | ||||||||
\(263\) | −598922. | −0.533925 | −0.266963 | − | 0.963707i | \(-0.586020\pi\) | ||||
−0.266963 | + | 0.963707i | \(0.586020\pi\) | |||||||
\(264\) | −1.41648e6 | −1.25084 | ||||||||
\(265\) | −64427.5 | −0.0563581 | ||||||||
\(266\) | −834763. | −0.723367 | ||||||||
\(267\) | 3.31559e6 | 2.84631 | ||||||||
\(268\) | 3.57953e6 | 3.04431 | ||||||||
\(269\) | 1.21294e6 | 1.02202 | 0.511010 | − | 0.859575i | \(-0.329271\pi\) | ||||
0.511010 | + | 0.859575i | \(0.329271\pi\) | |||||||
\(270\) | −983294. | −0.820869 | ||||||||
\(271\) | 215767. | 0.178469 | 0.0892344 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892344 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(272\) | 1.07590e6 | 0.881762 | ||||||||
\(273\) | 966152. | 0.784583 | ||||||||
\(274\) | −2.15399e6 | −1.73327 | ||||||||
\(275\) | 224009. | 0.178622 | ||||||||
\(276\) | −5.09902e6 | −4.02915 | ||||||||
\(277\) | 235442. | 0.184368 | 0.0921838 | − | 0.995742i | \(-0.470615\pi\) | ||||
0.0921838 | + | 0.995742i | \(0.470615\pi\) | |||||||
\(278\) | 3.08333e6 | 2.39281 | ||||||||
\(279\) | 1.83514e6 | 1.41143 | ||||||||
\(280\) | 934981. | 0.712701 | ||||||||
\(281\) | 1.25852e6 | 0.950813 | 0.475407 | − | 0.879766i | \(-0.342301\pi\) | ||||
0.475407 | + | 0.879766i | \(0.342301\pi\) | |||||||
\(282\) | −6.93661e6 | −5.19427 | ||||||||
\(283\) | 1.12093e6 | 0.831982 | 0.415991 | − | 0.909369i | \(-0.363435\pi\) | ||||
0.415991 | + | 0.909369i | \(0.363435\pi\) | |||||||
\(284\) | 456013. | 0.335492 | ||||||||
\(285\) | 157328. | 0.114734 | ||||||||
\(286\) | −208954. | −0.151055 | ||||||||
\(287\) | 1.11475e6 | 0.798864 | ||||||||
\(288\) | −1.63886e7 | −11.6429 | ||||||||
\(289\) | −1.36532e6 | −0.961587 | ||||||||
\(290\) | −530303. | −0.370279 | ||||||||
\(291\) | 1.75820e6 | 1.21713 | ||||||||
\(292\) | 487830. | 0.334820 | ||||||||
\(293\) | 2.44369e6 | 1.66294 | 0.831469 | − | 0.555570i | \(-0.187500\pi\) | ||||
0.831469 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(294\) | 518561. | 0.349890 | ||||||||
\(295\) | 151592. | 0.101419 | ||||||||
\(296\) | 9.15362e6 | 6.07244 | ||||||||
\(297\) | 643106. | 0.423050 | ||||||||
\(298\) | −2.42550e6 | −1.58220 | ||||||||
\(299\) | −492607. | −0.318657 | ||||||||
\(300\) | 7.89560e6 | 5.06503 | ||||||||
\(301\) | −251185. | −0.159800 | ||||||||
\(302\) | −4.51393e6 | −2.84798 | ||||||||
\(303\) | 5.20783e6 | 3.25875 | ||||||||
\(304\) | 2.53477e6 | 1.57309 | ||||||||
\(305\) | 242080. | 0.149008 | ||||||||
\(306\) | −1.43689e6 | −0.877246 | ||||||||
\(307\) | −3.07195e6 | −1.86024 | −0.930120 | − | 0.367257i | \(-0.880297\pi\) | ||||
−0.930120 | + | 0.367257i | \(0.880297\pi\) | |||||||
\(308\) | −933744. | −0.560856 | ||||||||
\(309\) | 3.70678e6 | 2.20852 | ||||||||
\(310\) | 377535. | 0.223128 | ||||||||
\(311\) | −1.02013e6 | −0.598076 | −0.299038 | − | 0.954241i | \(-0.596666\pi\) | ||||
−0.299038 | + | 0.954241i | \(0.596666\pi\) | |||||||
\(312\) | −4.82330e6 | −2.80516 | ||||||||
\(313\) | 1.25975e6 | 0.726814 | 0.363407 | − | 0.931630i | \(-0.381613\pi\) | ||||
0.363407 | + | 0.931630i | \(0.381613\pi\) | |||||||
\(314\) | −497291. | −0.284634 | ||||||||
\(315\) | −759504. | −0.431274 | ||||||||
\(316\) | −2.49115e6 | −1.40340 | ||||||||
\(317\) | −3.42675e6 | −1.91529 | −0.957644 | − | 0.287953i | \(-0.907025\pi\) | ||||
−0.957644 | + | 0.287953i | \(0.907025\pi\) | |||||||
\(318\) | 1.99777e6 | 1.10784 | ||||||||
\(319\) | 346835. | 0.190830 | ||||||||
\(320\) | −1.87549e6 | −1.02386 | ||||||||
\(321\) | 743074. | 0.402503 | ||||||||
\(322\) | −2.96096e6 | −1.59145 | ||||||||
\(323\) | 128497. | 0.0685308 | ||||||||
\(324\) | 1.02540e7 | 5.42663 | ||||||||
\(325\) | 762780. | 0.400582 | ||||||||
\(326\) | 2.39935e6 | 1.25040 | ||||||||
\(327\) | 4.83143e6 | 2.49866 | ||||||||
\(328\) | −5.56515e6 | −2.85622 | ||||||||
\(329\) | −2.99460e6 | −1.52528 | ||||||||
\(330\) | 236715. | 0.119658 | ||||||||
\(331\) | −958608. | −0.480918 | −0.240459 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240459 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(332\) | 4.49080e6 | 2.23603 | ||||||||
\(333\) | −7.43567e6 | −3.67459 | ||||||||
\(334\) | 2.79034e6 | 1.36865 | ||||||||
\(335\) | −391756. | −0.190723 | ||||||||
\(336\) | −1.76341e7 | −8.52126 | ||||||||
\(337\) | 2.25932e6 | 1.08369 | 0.541843 | − | 0.840479i | \(-0.317727\pi\) | ||||
0.541843 | + | 0.840479i | \(0.317727\pi\) | |||||||
\(338\) | 3.43512e6 | 1.63550 | ||||||||
\(339\) | −3.05551e6 | −1.44406 | ||||||||
\(340\) | −219765. | −0.103100 | ||||||||
\(341\) | −246920. | −0.114993 | ||||||||
\(342\) | −3.38524e6 | −1.56503 | ||||||||
\(343\) | −2.05934e6 | −0.945135 | ||||||||
\(344\) | 1.25398e6 | 0.571342 | ||||||||
\(345\) | 558053. | 0.252422 | ||||||||
\(346\) | −1.65332e6 | −0.742448 | ||||||||
\(347\) | 2.66606e6 | 1.18863 | 0.594315 | − | 0.804233i | \(-0.297423\pi\) | ||||
0.594315 | + | 0.804233i | \(0.297423\pi\) | |||||||
\(348\) | 1.22248e7 | 5.41121 | ||||||||
\(349\) | −394009. | −0.173158 | −0.0865791 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865791 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(350\) | 4.58491e6 | 2.00060 | ||||||||
\(351\) | 2.18986e6 | 0.948743 | ||||||||
\(352\) | 2.20511e6 | 0.948577 | ||||||||
\(353\) | −781472. | −0.333793 | −0.166896 | − | 0.985974i | \(-0.553375\pi\) | ||||
−0.166896 | + | 0.985974i | \(0.553375\pi\) | |||||||
\(354\) | −4.70056e6 | −1.99362 | ||||||||
\(355\) | −49907.6 | −0.0210182 | ||||||||
\(356\) | −1.09113e7 | −4.56301 | ||||||||
\(357\) | −893935. | −0.371223 | ||||||||
\(358\) | −5.50385e6 | −2.26965 | ||||||||
\(359\) | −2.39149e6 | −0.979338 | −0.489669 | − | 0.871909i | \(-0.662882\pi\) | ||||
−0.489669 | + | 0.871909i | \(0.662882\pi\) | |||||||
\(360\) | 3.79166e6 | 1.54196 | ||||||||
\(361\) | −2.17337e6 | −0.877739 | ||||||||
\(362\) | 4.24324e6 | 1.70187 | ||||||||
\(363\) | 4.38303e6 | 1.74585 | ||||||||
\(364\) | −3.17952e6 | −1.25779 | ||||||||
\(365\) | −53389.7 | −0.0209761 | ||||||||
\(366\) | −7.50643e6 | −2.92908 | ||||||||
\(367\) | 3.30667e6 | 1.28152 | 0.640761 | − | 0.767741i | \(-0.278619\pi\) | ||||
0.640761 | + | 0.767741i | \(0.278619\pi\) | |||||||
\(368\) | 8.99099e6 | 3.46089 | ||||||||
\(369\) | 4.52068e6 | 1.72837 | ||||||||
\(370\) | −1.52971e6 | −0.580903 | ||||||||
\(371\) | 862453. | 0.325313 | ||||||||
\(372\) | −8.70314e6 | −3.26076 | ||||||||
\(373\) | −3.41830e6 | −1.27215 | −0.636075 | − | 0.771627i | \(-0.719443\pi\) | ||||
−0.636075 | + | 0.771627i | \(0.719443\pi\) | |||||||
\(374\) | 193336. | 0.0714715 | ||||||||
\(375\) | −1.75769e6 | −0.645452 | ||||||||
\(376\) | 1.49499e7 | 5.45341 | ||||||||
\(377\) | 1.18102e6 | 0.427960 | ||||||||
\(378\) | 1.31628e7 | 4.73826 | ||||||||
\(379\) | 3.68158e6 | 1.31655 | 0.658273 | − | 0.752779i | \(-0.271287\pi\) | ||||
0.658273 | + | 0.752779i | \(0.271287\pi\) | |||||||
\(380\) | −517752. | −0.183935 | ||||||||
\(381\) | −4.58468e6 | −1.61807 | ||||||||
\(382\) | −9.43290e6 | −3.30740 | ||||||||
\(383\) | −1.78008e6 | −0.620071 | −0.310036 | − | 0.950725i | \(-0.600341\pi\) | ||||
−0.310036 | + | 0.950725i | \(0.600341\pi\) | |||||||
\(384\) | 3.13328e7 | 10.8435 | ||||||||
\(385\) | 102192. | 0.0351370 | ||||||||
\(386\) | 2.55061e6 | 0.871317 | ||||||||
\(387\) | −1.01864e6 | −0.345734 | ||||||||
\(388\) | −5.78609e6 | −1.95122 | ||||||||
\(389\) | 3.35648e6 | 1.12463 | 0.562315 | − | 0.826923i | \(-0.309911\pi\) | ||||
0.562315 | + | 0.826923i | \(0.309911\pi\) | |||||||
\(390\) | 806046. | 0.268348 | ||||||||
\(391\) | 455786. | 0.150772 | ||||||||
\(392\) | −1.11761e6 | −0.367346 | ||||||||
\(393\) | 3.61577e6 | 1.18092 | ||||||||
\(394\) | −4.53079e6 | −1.47039 | ||||||||
\(395\) | 272640. | 0.0879219 | ||||||||
\(396\) | −3.78664e6 | −1.21343 | ||||||||
\(397\) | 2.81124e6 | 0.895202 | 0.447601 | − | 0.894233i | \(-0.352278\pi\) | ||||
0.447601 | + | 0.894233i | \(0.352278\pi\) | |||||||
\(398\) | 8.04218e6 | 2.54487 | ||||||||
\(399\) | −2.10606e6 | −0.662275 | ||||||||
\(400\) | −1.39222e7 | −4.35067 | ||||||||
\(401\) | −487846. | −0.151503 | −0.0757517 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757517 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(402\) | 1.21476e7 | 3.74907 | ||||||||
\(403\) | −840796. | −0.257886 | ||||||||
\(404\) | −1.71385e7 | −5.22420 | ||||||||
\(405\) | −1.12223e6 | −0.339973 | ||||||||
\(406\) | 7.09886e6 | 2.13734 | ||||||||
\(407\) | 1.00048e6 | 0.299379 | ||||||||
\(408\) | 4.46278e6 | 1.32726 | ||||||||
\(409\) | 5.28714e6 | 1.56283 | 0.781416 | − | 0.624010i | \(-0.214497\pi\) | ||||
0.781416 | + | 0.624010i | \(0.214497\pi\) | |||||||
\(410\) | 930019. | 0.273232 | ||||||||
\(411\) | −5.43439e6 | −1.58689 | ||||||||
\(412\) | −1.21987e7 | −3.54054 | ||||||||
\(413\) | −2.02927e6 | −0.585417 | ||||||||
\(414\) | −1.20077e7 | −3.44317 | ||||||||
\(415\) | −491487. | −0.140085 | ||||||||
\(416\) | 7.50867e6 | 2.12731 | ||||||||
\(417\) | 7.77906e6 | 2.19072 | ||||||||
\(418\) | 455487. | 0.127507 | ||||||||
\(419\) | −4.56344e6 | −1.26986 | −0.634932 | − | 0.772568i | \(-0.718972\pi\) | ||||
−0.634932 | + | 0.772568i | \(0.718972\pi\) | |||||||
\(420\) | 3.60194e6 | 0.996353 | ||||||||
\(421\) | 3.35431e6 | 0.922356 | 0.461178 | − | 0.887308i | \(-0.347427\pi\) | ||||
0.461178 | + | 0.887308i | \(0.347427\pi\) | |||||||
\(422\) | −6.99241e6 | −1.91138 | ||||||||
\(423\) | −1.21441e7 | −3.30000 | ||||||||
\(424\) | −4.30561e6 | −1.16311 | ||||||||
\(425\) | −705765. | −0.189534 | ||||||||
\(426\) | 1.54753e6 | 0.413158 | ||||||||
\(427\) | −3.24059e6 | −0.860111 | ||||||||
\(428\) | −2.44539e6 | −0.645266 | ||||||||
\(429\) | −527180. | −0.138298 | ||||||||
\(430\) | −209559. | −0.0546558 | ||||||||
\(431\) | 4.51725e6 | 1.17133 | 0.585667 | − | 0.810552i | \(-0.300833\pi\) | ||||
0.585667 | + | 0.810552i | \(0.300833\pi\) | |||||||
\(432\) | −3.99690e7 | −10.3042 | ||||||||
\(433\) | −7.39491e6 | −1.89545 | −0.947727 | − | 0.319084i | \(-0.896625\pi\) | ||||
−0.947727 | + | 0.319084i | \(0.896625\pi\) | |||||||
\(434\) | −5.05385e6 | −1.28795 | ||||||||
\(435\) | −1.33792e6 | −0.339007 | ||||||||
\(436\) | −1.58998e7 | −4.00568 | ||||||||
\(437\) | 1.07381e6 | 0.268981 | ||||||||
\(438\) | 1.65551e6 | 0.412331 | ||||||||
\(439\) | 4.68334e6 | 1.15983 | 0.579915 | − | 0.814677i | \(-0.303086\pi\) | ||||
0.579915 | + | 0.814677i | \(0.303086\pi\) | |||||||
\(440\) | −510171. | −0.125627 | ||||||||
\(441\) | 907856. | 0.222290 | ||||||||
\(442\) | 658333. | 0.160284 | ||||||||
\(443\) | −2.43782e6 | −0.590190 | −0.295095 | − | 0.955468i | \(-0.595351\pi\) | ||||
−0.295095 | + | 0.955468i | \(0.595351\pi\) | |||||||
\(444\) | 3.52636e7 | 8.48924 | ||||||||
\(445\) | 1.19417e6 | 0.285868 | ||||||||
\(446\) | −5.73331e6 | −1.36480 | ||||||||
\(447\) | −6.11940e6 | −1.44857 | ||||||||
\(448\) | 2.51061e7 | 5.90995 | ||||||||
\(449\) | 3.20725e6 | 0.750788 | 0.375394 | − | 0.926865i | \(-0.377507\pi\) | ||||
0.375394 | + | 0.926865i | \(0.377507\pi\) | |||||||
\(450\) | 1.85933e7 | 4.32839 | ||||||||
\(451\) | −608262. | −0.140815 | ||||||||
\(452\) | 1.00554e7 | 2.31502 | ||||||||
\(453\) | −1.13884e7 | −2.60745 | ||||||||
\(454\) | 1.34947e7 | 3.07273 | ||||||||
\(455\) | 347977. | 0.0787993 | ||||||||
\(456\) | 1.05140e7 | 2.36787 | ||||||||
\(457\) | 8.02184e6 | 1.79673 | 0.898366 | − | 0.439247i | \(-0.144755\pi\) | ||||
0.898366 | + | 0.439247i | \(0.144755\pi\) | |||||||
\(458\) | 3.49920e6 | 0.779481 | ||||||||
\(459\) | −2.02617e6 | −0.448895 | ||||||||
\(460\) | −1.83650e6 | −0.404666 | ||||||||
\(461\) | 4.78328e6 | 1.04827 | 0.524136 | − | 0.851635i | \(-0.324388\pi\) | ||||
0.524136 | + | 0.851635i | \(0.324388\pi\) | |||||||
\(462\) | −3.16877e6 | −0.690694 | ||||||||
\(463\) | 1.35182e6 | 0.293066 | 0.146533 | − | 0.989206i | \(-0.453189\pi\) | ||||
0.146533 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(464\) | −2.15558e7 | −4.64803 | ||||||||
\(465\) | 952500. | 0.204283 | ||||||||
\(466\) | 2.16719e6 | 0.462309 | ||||||||
\(467\) | −6.92509e6 | −1.46938 | −0.734688 | − | 0.678405i | \(-0.762671\pi\) | ||||
−0.734688 | + | 0.678405i | \(0.762671\pi\) | |||||||
\(468\) | −1.28940e7 | −2.72128 | ||||||||
\(469\) | 5.24421e6 | 1.10090 | ||||||||
\(470\) | −2.49835e6 | −0.521685 | ||||||||
\(471\) | −1.25464e6 | −0.260595 | ||||||||
\(472\) | 1.01307e7 | 2.09307 | ||||||||
\(473\) | 137059. | 0.0281678 | ||||||||
\(474\) | −8.45402e6 | −1.72829 | ||||||||
\(475\) | −1.66274e6 | −0.338135 | ||||||||
\(476\) | 2.94186e6 | 0.595121 | ||||||||
\(477\) | 3.49753e6 | 0.703827 | ||||||||
\(478\) | 3.90548e6 | 0.781816 | ||||||||
\(479\) | −4.12443e6 | −0.821343 | −0.410672 | − | 0.911783i | \(-0.634706\pi\) | ||||
−0.410672 | + | 0.911783i | \(0.634706\pi\) | |||||||
\(480\) | −8.50624e6 | −1.68513 | ||||||||
\(481\) | 3.40675e6 | 0.671395 | ||||||||
\(482\) | 238327. | 0.0467258 | ||||||||
\(483\) | −7.47033e6 | −1.45704 | ||||||||
\(484\) | −1.44242e7 | −2.79883 | ||||||||
\(485\) | 633248. | 0.122242 | ||||||||
\(486\) | 1.12531e7 | 2.16114 | ||||||||
\(487\) | −2.39619e6 | −0.457825 | −0.228913 | − | 0.973447i | \(-0.573517\pi\) | ||||
−0.228913 | + | 0.973447i | \(0.573517\pi\) | |||||||
\(488\) | 1.61779e7 | 3.07520 | ||||||||
\(489\) | 6.05343e6 | 1.14480 | ||||||||
\(490\) | 186769. | 0.0351411 | ||||||||
\(491\) | −1.38935e6 | −0.260081 | −0.130041 | − | 0.991509i | \(-0.541511\pi\) | ||||
−0.130041 | + | 0.991509i | \(0.541511\pi\) | |||||||
\(492\) | −2.14393e7 | −3.99298 | ||||||||
\(493\) | −1.09274e6 | −0.202488 | ||||||||
\(494\) | 1.55099e6 | 0.285952 | ||||||||
\(495\) | 414423. | 0.0760204 | ||||||||
\(496\) | 1.53461e7 | 2.80087 | ||||||||
\(497\) | 668084. | 0.121322 | ||||||||
\(498\) | 1.52400e7 | 2.75367 | ||||||||
\(499\) | −4.94748e6 | −0.889473 | −0.444736 | − | 0.895662i | \(-0.646703\pi\) | ||||
−0.444736 | + | 0.895662i | \(0.646703\pi\) | |||||||
\(500\) | 5.78440e6 | 1.03474 | ||||||||
\(501\) | 7.03987e6 | 1.25305 | ||||||||
\(502\) | 9.84891e6 | 1.74433 | ||||||||
\(503\) | −143778. | −0.0253381 | −0.0126690 | − | 0.999920i | \(-0.504033\pi\) | ||||
−0.0126690 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(504\) | −5.07567e7 | −8.90056 | ||||||||
\(505\) | 1.87570e6 | 0.327291 | ||||||||
\(506\) | 1.61564e6 | 0.280524 | ||||||||
\(507\) | 8.66660e6 | 1.49737 | ||||||||
\(508\) | 1.50878e7 | 2.59398 | ||||||||
\(509\) | −804164. | −0.137578 | −0.0687892 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687892 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(510\) | −745797. | −0.126968 | ||||||||
\(511\) | 714697. | 0.121079 | ||||||||
\(512\) | −3.70667e7 | −6.24897 | ||||||||
\(513\) | −4.77355e6 | −0.800844 | ||||||||
\(514\) | 2.12247e7 | 3.54351 | ||||||||
\(515\) | 1.33506e6 | 0.221811 | ||||||||
\(516\) | 4.83087e6 | 0.798733 | ||||||||
\(517\) | 1.63400e6 | 0.268860 | ||||||||
\(518\) | 2.04773e7 | 3.35311 | ||||||||
\(519\) | −4.17123e6 | −0.679744 | ||||||||
\(520\) | −1.73720e6 | −0.281735 | ||||||||
\(521\) | 1.33327e6 | 0.215191 | 0.107595 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107595 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(522\) | 2.87882e7 | 4.62422 | ||||||||
\(523\) | 870192. | 0.139111 | 0.0695554 | − | 0.997578i | \(-0.477842\pi\) | ||||
0.0695554 | + | 0.997578i | \(0.477842\pi\) | |||||||
\(524\) | −1.18992e7 | −1.89316 | ||||||||
\(525\) | 1.15675e7 | 1.83164 | ||||||||
\(526\) | 6.68881e6 | 1.05411 | ||||||||
\(527\) | 777949. | 0.122018 | ||||||||
\(528\) | 9.62201e6 | 1.50204 | ||||||||
\(529\) | −2.62748e6 | −0.408226 | ||||||||
\(530\) | 719532. | 0.111265 | ||||||||
\(531\) | −8.22937e6 | −1.26657 | ||||||||
\(532\) | 6.93085e6 | 1.06171 | ||||||||
\(533\) | −2.07121e6 | −0.315796 | ||||||||
\(534\) | −3.70288e7 | −5.61935 | ||||||||
\(535\) | 267632. | 0.0404253 | ||||||||
\(536\) | −2.61806e7 | −3.93611 | ||||||||
\(537\) | −1.38859e7 | −2.07797 | ||||||||
\(538\) | −1.35463e7 | −2.01773 | ||||||||
\(539\) | −122153. | −0.0181106 | ||||||||
\(540\) | 8.16408e6 | 1.20482 | ||||||||
\(541\) | 8.24525e6 | 1.21119 | 0.605593 | − | 0.795774i | \(-0.292936\pi\) | ||||
0.605593 | + | 0.795774i | \(0.292936\pi\) | |||||||
\(542\) | −2.40971e6 | −0.352344 | ||||||||
\(543\) | 1.07054e7 | 1.55814 | ||||||||
\(544\) | −6.94742e6 | −1.00653 | ||||||||
\(545\) | 1.74013e6 | 0.250951 | ||||||||
\(546\) | −1.07901e7 | −1.54897 | ||||||||
\(547\) | 9.45890e6 | 1.35168 | 0.675838 | − | 0.737050i | \(-0.263782\pi\) | ||||
0.675838 | + | 0.737050i | \(0.263782\pi\) | |||||||
\(548\) | 1.78841e7 | 2.54399 | ||||||||
\(549\) | −1.31417e7 | −1.86089 | ||||||||
\(550\) | −2.50175e6 | −0.352645 | ||||||||
\(551\) | −2.57443e6 | −0.361246 | ||||||||
\(552\) | 3.72940e7 | 5.20944 | ||||||||
\(553\) | −3.64967e6 | −0.507506 | ||||||||
\(554\) | −2.62944e6 | −0.363989 | ||||||||
\(555\) | −3.85936e6 | −0.531842 | ||||||||
\(556\) | −2.56002e7 | −3.51202 | ||||||||
\(557\) | −1.05787e7 | −1.44476 | −0.722380 | − | 0.691497i | \(-0.756952\pi\) | ||||
−0.722380 | + | 0.691497i | \(0.756952\pi\) | |||||||
\(558\) | −2.04950e7 | −2.78653 | ||||||||
\(559\) | 466702. | 0.0631700 | ||||||||
\(560\) | −6.35123e6 | −0.855830 | ||||||||
\(561\) | 487775. | 0.0654353 | ||||||||
\(562\) | −1.40553e7 | −1.87715 | ||||||||
\(563\) | 7.11281e6 | 0.945737 | 0.472869 | − | 0.881133i | \(-0.343219\pi\) | ||||
0.472869 | + | 0.881133i | \(0.343219\pi\) | |||||||
\(564\) | 5.75932e7 | 7.62383 | ||||||||
\(565\) | −1.10050e6 | −0.145033 | ||||||||
\(566\) | −1.25187e7 | −1.64255 | ||||||||
\(567\) | 1.50226e7 | 1.96241 | ||||||||
\(568\) | −3.33526e6 | −0.433770 | ||||||||
\(569\) | −431278. | −0.0558440 | −0.0279220 | − | 0.999610i | \(-0.508889\pi\) | ||||
−0.0279220 | + | 0.999610i | \(0.508889\pi\) | |||||||
\(570\) | −1.75705e6 | −0.226515 | ||||||||
\(571\) | −4.96062e6 | −0.636716 | −0.318358 | − | 0.947971i | \(-0.603131\pi\) | ||||
−0.318358 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(572\) | 1.73490e6 | 0.221710 | ||||||||
\(573\) | −2.37987e7 | −3.02807 | ||||||||
\(574\) | −1.24496e7 | −1.57716 | ||||||||
\(575\) | −5.89785e6 | −0.743917 | ||||||||
\(576\) | 1.01813e8 | 12.7864 | ||||||||
\(577\) | 1.02637e7 | 1.28341 | 0.641705 | − | 0.766952i | \(-0.278228\pi\) | ||||
0.641705 | + | 0.766952i | \(0.278228\pi\) | |||||||
\(578\) | 1.52480e7 | 1.89842 | ||||||||
\(579\) | 6.43505e6 | 0.797729 | ||||||||
\(580\) | 4.40299e6 | 0.543473 | ||||||||
\(581\) | 6.57926e6 | 0.808605 | ||||||||
\(582\) | −1.96357e7 | −2.40292 | ||||||||
\(583\) | −470597. | −0.0573426 | ||||||||
\(584\) | −3.56797e6 | −0.432901 | ||||||||
\(585\) | 1.41116e6 | 0.170485 | ||||||||
\(586\) | −2.72913e7 | −3.28307 | ||||||||
\(587\) | 6.47940e6 | 0.776140 | 0.388070 | − | 0.921630i | \(-0.373142\pi\) | ||||
0.388070 | + | 0.921630i | \(0.373142\pi\) | |||||||
\(588\) | −4.30550e6 | −0.513547 | ||||||||
\(589\) | 1.83280e6 | 0.217684 | ||||||||
\(590\) | −1.69299e6 | −0.200228 | ||||||||
\(591\) | −1.14309e7 | −1.34621 | ||||||||
\(592\) | −6.21795e7 | −7.29194 | ||||||||
\(593\) | −3.51558e6 | −0.410545 | −0.205272 | − | 0.978705i | \(-0.565808\pi\) | ||||
−0.205272 | + | 0.978705i | \(0.565808\pi\) | |||||||
\(594\) | −7.18226e6 | −0.835209 | ||||||||
\(595\) | −321967. | −0.0372837 | ||||||||
\(596\) | 2.01384e7 | 2.32225 | ||||||||
\(597\) | 2.02900e7 | 2.32994 | ||||||||
\(598\) | 5.50148e6 | 0.629110 | ||||||||
\(599\) | −993536. | −0.113140 | −0.0565701 | − | 0.998399i | \(-0.518016\pi\) | ||||
−0.0565701 | + | 0.998399i | \(0.518016\pi\) | |||||||
\(600\) | −5.77481e7 | −6.54877 | ||||||||
\(601\) | 6.25981e6 | 0.706928 | 0.353464 | − | 0.935448i | \(-0.385004\pi\) | ||||
0.353464 | + | 0.935448i | \(0.385004\pi\) | |||||||
\(602\) | 2.80525e6 | 0.315486 | ||||||||
\(603\) | 2.12670e7 | 2.38184 | ||||||||
\(604\) | 3.74782e7 | 4.18009 | ||||||||
\(605\) | 1.57863e6 | 0.175344 | ||||||||
\(606\) | −5.81615e7 | −6.43360 | ||||||||
\(607\) | −3.58799e6 | −0.395257 | −0.197628 | − | 0.980277i | \(-0.563324\pi\) | ||||
−0.197628 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(608\) | −1.63677e7 | −1.79568 | ||||||||
\(609\) | 1.79100e7 | 1.95683 | ||||||||
\(610\) | −2.70358e6 | −0.294181 | ||||||||
\(611\) | 5.56398e6 | 0.602952 | ||||||||
\(612\) | 1.19302e7 | 1.28757 | ||||||||
\(613\) | 7.67762e6 | 0.825231 | 0.412615 | − | 0.910905i | \(-0.364615\pi\) | ||||
0.412615 | + | 0.910905i | \(0.364615\pi\) | |||||||
\(614\) | 3.43079e7 | 3.67259 | ||||||||
\(615\) | 2.34638e6 | 0.250156 | ||||||||
\(616\) | 6.82937e6 | 0.725152 | ||||||||
\(617\) | −9.88787e6 | −1.04566 | −0.522829 | − | 0.852438i | \(-0.675123\pi\) | ||||
−0.522829 | + | 0.852438i | \(0.675123\pi\) | |||||||
\(618\) | −4.13976e7 | −4.36018 | ||||||||
\(619\) | 759066. | 0.0796256 | 0.0398128 | − | 0.999207i | \(-0.487324\pi\) | ||||
0.0398128 | + | 0.999207i | \(0.487324\pi\) | |||||||
\(620\) | −3.13459e6 | −0.327493 | ||||||||
\(621\) | −1.69321e7 | −1.76190 | ||||||||
\(622\) | 1.13930e7 | 1.18076 | ||||||||
\(623\) | −1.59856e7 | −1.65010 | ||||||||
\(624\) | 3.27642e7 | 3.36851 | ||||||||
\(625\) | 8.81073e6 | 0.902218 | ||||||||
\(626\) | −1.40690e7 | −1.43492 | ||||||||
\(627\) | 1.14917e6 | 0.116739 | ||||||||
\(628\) | 4.12890e6 | 0.417768 | ||||||||
\(629\) | −3.15211e6 | −0.317669 | ||||||||
\(630\) | 8.48221e6 | 0.851447 | ||||||||
\(631\) | −8.94214e6 | −0.894063 | −0.447031 | − | 0.894518i | \(-0.647519\pi\) | ||||
−0.447031 | + | 0.894518i | \(0.647519\pi\) | |||||||
\(632\) | 1.82202e7 | 1.81451 | ||||||||
\(633\) | −1.76415e7 | −1.74995 | ||||||||
\(634\) | 3.82703e7 | 3.78127 | ||||||||
\(635\) | −1.65126e6 | −0.162510 | ||||||||
\(636\) | −1.65870e7 | −1.62602 | ||||||||
\(637\) | −415947. | −0.0406153 | ||||||||
\(638\) | −3.87349e6 | −0.376748 | ||||||||
\(639\) | 2.70930e6 | 0.262485 | ||||||||
\(640\) | 1.12851e7 | 1.08907 | ||||||||
\(641\) | −1.38335e6 | −0.132981 | −0.0664903 | − | 0.997787i | \(-0.521180\pi\) | ||||
−0.0664903 | + | 0.997787i | \(0.521180\pi\) | |||||||
\(642\) | −8.29872e6 | −0.794646 | ||||||||
\(643\) | 1.42540e7 | 1.35959 | 0.679797 | − | 0.733400i | \(-0.262068\pi\) | ||||
0.679797 | + | 0.733400i | \(0.262068\pi\) | |||||||
\(644\) | 2.45842e7 | 2.33583 | ||||||||
\(645\) | −528707. | −0.0500398 | ||||||||
\(646\) | −1.43506e6 | −0.135297 | ||||||||
\(647\) | −9.93069e6 | −0.932650 | −0.466325 | − | 0.884613i | \(-0.654422\pi\) | ||||
−0.466325 | + | 0.884613i | \(0.654422\pi\) | |||||||
\(648\) | −7.49973e7 | −7.01630 | ||||||||
\(649\) | 1.10727e6 | 0.103191 | ||||||||
\(650\) | −8.51880e6 | −0.790852 | ||||||||
\(651\) | −1.27506e7 | −1.17917 | ||||||||
\(652\) | −1.99213e7 | −1.83527 | ||||||||
\(653\) | −1.48917e7 | −1.36666 | −0.683330 | − | 0.730110i | \(-0.739469\pi\) | ||||
−0.683330 | + | 0.730110i | \(0.739469\pi\) | |||||||
\(654\) | −5.39578e7 | −4.93299 | ||||||||
\(655\) | 1.30228e6 | 0.118605 | ||||||||
\(656\) | 3.78035e7 | 3.42982 | ||||||||
\(657\) | 2.89833e6 | 0.261960 | ||||||||
\(658\) | 3.34439e7 | 3.01129 | ||||||||
\(659\) | −834285. | −0.0748343 | −0.0374172 | − | 0.999300i | \(-0.511913\pi\) | ||||
−0.0374172 | + | 0.999300i | \(0.511913\pi\) | |||||||
\(660\) | −1.96539e6 | −0.175626 | ||||||||
\(661\) | 9.69443e6 | 0.863016 | 0.431508 | − | 0.902109i | \(-0.357982\pi\) | ||||
0.431508 | + | 0.902109i | \(0.357982\pi\) | |||||||
\(662\) | 1.07058e7 | 0.949456 | ||||||||
\(663\) | 1.66094e6 | 0.146747 | ||||||||
\(664\) | −3.28455e7 | −2.89105 | ||||||||
\(665\) | −758535. | −0.0665153 | ||||||||
\(666\) | 8.30422e7 | 7.25460 | ||||||||
\(667\) | −9.13170e6 | −0.794762 | ||||||||
\(668\) | −2.31676e7 | −2.00881 | ||||||||
\(669\) | −1.44648e7 | −1.24953 | ||||||||
\(670\) | 4.37516e6 | 0.376537 | ||||||||
\(671\) | 1.76823e6 | 0.151611 | ||||||||
\(672\) | 1.13868e8 | 9.72700 | ||||||||
\(673\) | −5.45965e6 | −0.464651 | −0.232326 | − | 0.972638i | \(-0.574634\pi\) | ||||
−0.232326 | + | 0.972638i | \(0.574634\pi\) | |||||||
\(674\) | −2.52323e7 | −2.13948 | ||||||||
\(675\) | 2.62186e7 | 2.21488 | ||||||||
\(676\) | −2.85210e7 | −2.40048 | ||||||||
\(677\) | 503614. | 0.0422305 | 0.0211152 | − | 0.999777i | \(-0.493278\pi\) | ||||
0.0211152 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(678\) | 3.41242e7 | 2.85094 | ||||||||
\(679\) | −8.47692e6 | −0.705609 | ||||||||
\(680\) | 1.60735e6 | 0.133302 | ||||||||
\(681\) | 3.40465e7 | 2.81322 | ||||||||
\(682\) | 2.75763e6 | 0.227026 | ||||||||
\(683\) | −9.08309e6 | −0.745044 | −0.372522 | − | 0.928023i | \(-0.621507\pi\) | ||||
−0.372522 | + | 0.928023i | \(0.621507\pi\) | |||||||
\(684\) | 2.81069e7 | 2.29706 | ||||||||
\(685\) | −1.95729e6 | −0.159378 | ||||||||
\(686\) | 2.29989e7 | 1.86594 | ||||||||
\(687\) | 8.82829e6 | 0.713649 | ||||||||
\(688\) | −8.51818e6 | −0.686082 | ||||||||
\(689\) | −1.60244e6 | −0.128598 | ||||||||
\(690\) | −6.23238e6 | −0.498347 | ||||||||
\(691\) | 2.14373e7 | 1.70795 | 0.853976 | − | 0.520313i | \(-0.174185\pi\) | ||||
0.853976 | + | 0.520313i | \(0.174185\pi\) | |||||||
\(692\) | 1.37271e7 | 1.08972 | ||||||||
\(693\) | −5.54763e6 | −0.438808 | ||||||||
\(694\) | −2.97748e7 | −2.34666 | ||||||||
\(695\) | 2.80177e6 | 0.220024 | ||||||||
\(696\) | −8.94119e7 | −6.99636 | ||||||||
\(697\) | 1.91640e6 | 0.149418 | ||||||||
\(698\) | 4.40033e6 | 0.341859 | ||||||||
\(699\) | 5.46770e6 | 0.423264 | ||||||||
\(700\) | −3.80675e7 | −2.93636 | ||||||||
\(701\) | −2.39509e7 | −1.84088 | −0.920442 | − | 0.390878i | \(-0.872171\pi\) | ||||
−0.920442 | + | 0.390878i | \(0.872171\pi\) | |||||||
\(702\) | −2.44565e7 | −1.87306 | ||||||||
\(703\) | −7.42618e6 | −0.566731 | ||||||||
\(704\) | −1.36991e7 | −1.04174 | ||||||||
\(705\) | −6.30319e6 | −0.477625 | ||||||||
\(706\) | 8.72755e6 | 0.658993 | ||||||||
\(707\) | −2.51088e7 | −1.88920 | ||||||||
\(708\) | 3.90277e7 | 2.92611 | ||||||||
\(709\) | 1.01183e7 | 0.755949 | 0.377975 | − | 0.925816i | \(-0.376621\pi\) | ||||
0.377975 | + | 0.925816i | \(0.376621\pi\) | |||||||
\(710\) | 557372. | 0.0414954 | ||||||||
\(711\) | −1.48006e7 | −1.09801 | ||||||||
\(712\) | 7.98048e7 | 5.89969 | ||||||||
\(713\) | 6.50107e6 | 0.478918 | ||||||||
\(714\) | 9.98355e6 | 0.732891 | ||||||||
\(715\) | −189873. | −0.0138899 | ||||||||
\(716\) | 4.56973e7 | 3.33126 | ||||||||
\(717\) | 9.85329e6 | 0.715787 | ||||||||
\(718\) | 2.67084e7 | 1.93347 | ||||||||
\(719\) | −1.59945e6 | −0.115384 | −0.0576922 | − | 0.998334i | \(-0.518374\pi\) | ||||
−0.0576922 | + | 0.998334i | \(0.518374\pi\) | |||||||
\(720\) | −2.57563e7 | −1.85162 | ||||||||
\(721\) | −1.78717e7 | −1.28035 | ||||||||
\(722\) | 2.42724e7 | 1.73288 | ||||||||
\(723\) | 601287. | 0.0427795 | ||||||||
\(724\) | −3.52307e7 | −2.49790 | ||||||||
\(725\) | 1.41400e7 | 0.999091 | ||||||||
\(726\) | −4.89500e7 | −3.44676 | ||||||||
\(727\) | −2.36374e7 | −1.65868 | −0.829340 | − | 0.558744i | \(-0.811284\pi\) | ||||
−0.829340 | + | 0.558744i | \(0.811284\pi\) | |||||||
\(728\) | 2.32549e7 | 1.62624 | ||||||||
\(729\) | 1.51921e6 | 0.105876 | ||||||||
\(730\) | 596261. | 0.0414123 | ||||||||
\(731\) | −431818. | −0.0298887 | ||||||||
\(732\) | 6.23242e7 | 4.29912 | ||||||||
\(733\) | −8.73268e6 | −0.600327 | −0.300163 | − | 0.953888i | \(-0.597041\pi\) | ||||
−0.300163 | + | 0.953888i | \(0.597041\pi\) | |||||||
\(734\) | −3.69292e7 | −2.53005 | ||||||||
\(735\) | 471208. | 0.0321732 | ||||||||
\(736\) | −5.80574e7 | −3.95060 | ||||||||
\(737\) | −2.86150e6 | −0.194055 | ||||||||
\(738\) | −5.04874e7 | −3.41226 | ||||||||
\(739\) | 1.45547e7 | 0.980378 | 0.490189 | − | 0.871616i | \(-0.336928\pi\) | ||||
0.490189 | + | 0.871616i | \(0.336928\pi\) | |||||||
\(740\) | 1.27008e7 | 0.852614 | ||||||||
\(741\) | 3.91307e6 | 0.261801 | ||||||||
\(742\) | −9.63195e6 | −0.642251 | ||||||||
\(743\) | 1.04520e7 | 0.694591 | 0.347296 | − | 0.937756i | \(-0.387100\pi\) | ||||
0.347296 | + | 0.937756i | \(0.387100\pi\) | |||||||
\(744\) | 6.36544e7 | 4.21596 | ||||||||
\(745\) | −2.20401e6 | −0.145487 | ||||||||
\(746\) | 3.81759e7 | 2.51155 | ||||||||
\(747\) | 2.66811e7 | 1.74945 | ||||||||
\(748\) | −1.60522e6 | −0.104902 | ||||||||
\(749\) | −3.58263e6 | −0.233344 | ||||||||
\(750\) | 1.96300e7 | 1.27429 | ||||||||
\(751\) | −2.90334e6 | −0.187844 | −0.0939221 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939221 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(752\) | −1.01553e8 | −6.54859 | ||||||||
\(753\) | 2.48482e7 | 1.59701 | ||||||||
\(754\) | −1.31897e7 | −0.844904 | ||||||||
\(755\) | −4.10173e6 | −0.261879 | ||||||||
\(756\) | −1.09288e8 | −6.95452 | ||||||||
\(757\) | −8.00481e6 | −0.507705 | −0.253852 | − | 0.967243i | \(-0.581698\pi\) | ||||
−0.253852 | + | 0.967243i | \(0.581698\pi\) | |||||||
\(758\) | −4.11162e7 | −2.59920 | ||||||||
\(759\) | 4.07618e6 | 0.256832 | ||||||||
\(760\) | 3.78682e6 | 0.237816 | ||||||||
\(761\) | 1.58931e7 | 0.994826 | 0.497413 | − | 0.867514i | \(-0.334283\pi\) | ||||
0.497413 | + | 0.867514i | \(0.334283\pi\) | |||||||
\(762\) | 5.12021e7 | 3.19448 | ||||||||
\(763\) | −2.32941e7 | −1.44855 | ||||||||
\(764\) | 7.83193e7 | 4.85440 | ||||||||
\(765\) | −1.30568e6 | −0.0806648 | ||||||||
\(766\) | 1.98801e7 | 1.22418 | ||||||||
\(767\) | 3.77040e6 | 0.231419 | ||||||||
\(768\) | −1.83295e8 | −11.2137 | ||||||||
\(769\) | 1.55997e7 | 0.951264 | 0.475632 | − | 0.879644i | \(-0.342219\pi\) | ||||
0.475632 | + | 0.879644i | \(0.342219\pi\) | |||||||
\(770\) | −1.14129e6 | −0.0693696 | ||||||||
\(771\) | 5.35487e7 | 3.24424 | ||||||||
\(772\) | −2.11772e7 | −1.27887 | ||||||||
\(773\) | −2.37032e7 | −1.42678 | −0.713392 | − | 0.700765i | \(-0.752842\pi\) | ||||
−0.713392 | + | 0.700765i | \(0.752842\pi\) | |||||||
\(774\) | 1.13762e7 | 0.682568 | ||||||||
\(775\) | −1.00666e7 | −0.602046 | ||||||||
\(776\) | 4.23192e7 | 2.52280 | ||||||||
\(777\) | 5.16630e7 | 3.06992 | ||||||||
\(778\) | −3.74855e7 | −2.22031 | ||||||||
\(779\) | 4.51491e6 | 0.266567 | ||||||||
\(780\) | −6.69243e6 | −0.393865 | ||||||||
\(781\) | −364539. | −0.0213854 | ||||||||
\(782\) | −5.09026e6 | −0.297662 | ||||||||
\(783\) | 4.05945e7 | 2.36626 | ||||||||
\(784\) | 7.59180e6 | 0.441118 | ||||||||
\(785\) | −451880. | −0.0261727 | ||||||||
\(786\) | −4.03812e7 | −2.33143 | ||||||||
\(787\) | 2.03168e7 | 1.16928 | 0.584639 | − | 0.811294i | \(-0.301236\pi\) | ||||
0.584639 | + | 0.811294i | \(0.301236\pi\) | |||||||
\(788\) | 3.76182e7 | 2.15815 | ||||||||
\(789\) | 1.68755e7 | 0.965081 | ||||||||
\(790\) | −3.04487e6 | −0.173580 | ||||||||
\(791\) | 1.47317e7 | 0.837168 | ||||||||
\(792\) | 2.76954e7 | 1.56890 | ||||||||
\(793\) | 6.02104e6 | 0.340007 | ||||||||
\(794\) | −3.13961e7 | −1.76736 | ||||||||
\(795\) | 1.81534e6 | 0.101868 | ||||||||
\(796\) | −6.67725e7 | −3.73521 | ||||||||
\(797\) | −9.05526e6 | −0.504958 | −0.252479 | − | 0.967602i | \(-0.581246\pi\) | ||||
−0.252479 | + | 0.967602i | \(0.581246\pi\) | |||||||
\(798\) | 2.35206e7 | 1.30750 | ||||||||
\(799\) | −5.14809e6 | −0.285285 | ||||||||
\(800\) | 8.98993e7 | 4.96628 | ||||||||
\(801\) | −6.48271e7 | −3.57006 | ||||||||
\(802\) | 5.44831e6 | 0.299107 | ||||||||
\(803\) | −389974. | −0.0213426 | ||||||||
\(804\) | −1.00859e8 | −5.50266 | ||||||||
\(805\) | −2.69058e6 | −0.146337 | ||||||||
\(806\) | 9.39008e6 | 0.509134 | ||||||||
\(807\) | −3.41764e7 | −1.84732 | ||||||||
\(808\) | 1.25350e8 | 6.75457 | ||||||||
\(809\) | −6.37396e6 | −0.342403 | −0.171202 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171202 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(810\) | 1.25332e7 | 0.671195 | ||||||||
\(811\) | 8.10409e6 | 0.432665 | 0.216333 | − | 0.976320i | \(-0.430590\pi\) | ||||
0.216333 | + | 0.976320i | \(0.430590\pi\) | |||||||
\(812\) | −5.89403e7 | −3.13706 | ||||||||
\(813\) | −6.07956e6 | −0.322586 | ||||||||
\(814\) | −1.11734e7 | −0.591051 | ||||||||
\(815\) | 2.18025e6 | 0.114977 | ||||||||
\(816\) | −3.03152e7 | −1.59380 | ||||||||
\(817\) | −1.01734e6 | −0.0533224 | ||||||||
\(818\) | −5.90473e7 | −3.08544 | ||||||||
\(819\) | −1.88904e7 | −0.984083 | ||||||||
\(820\) | −7.72175e6 | −0.401034 | ||||||||
\(821\) | −1.15491e6 | −0.0597983 | −0.0298992 | − | 0.999553i | \(-0.509519\pi\) | ||||
−0.0298992 | + | 0.999553i | \(0.509519\pi\) | |||||||
\(822\) | 6.06917e7 | 3.13293 | ||||||||
\(823\) | −5.41617e6 | −0.278736 | −0.139368 | − | 0.990241i | \(-0.544507\pi\) | ||||
−0.139368 | + | 0.990241i | \(0.544507\pi\) | |||||||
\(824\) | 8.92207e7 | 4.57770 | ||||||||
\(825\) | −6.31178e6 | −0.322862 | ||||||||
\(826\) | 2.26631e7 | 1.15576 | ||||||||
\(827\) | 2.73522e7 | 1.39068 | 0.695342 | − | 0.718679i | \(-0.255253\pi\) | ||||
0.695342 | + | 0.718679i | \(0.255253\pi\) | |||||||
\(828\) | 9.96971e7 | 5.05367 | ||||||||
\(829\) | −2.13862e7 | −1.08081 | −0.540403 | − | 0.841407i | \(-0.681728\pi\) | ||||
−0.540403 | + | 0.841407i | \(0.681728\pi\) | |||||||
\(830\) | 5.48898e6 | 0.276564 | ||||||||
\(831\) | −6.63392e6 | −0.333248 | ||||||||
\(832\) | −4.66472e7 | −2.33624 | ||||||||
\(833\) | 384856. | 0.0192170 | ||||||||
\(834\) | −8.68772e7 | −4.32505 | ||||||||
\(835\) | 2.53554e6 | 0.125850 | ||||||||
\(836\) | −3.78181e6 | −0.187148 | ||||||||
\(837\) | −2.89002e7 | −1.42589 | ||||||||
\(838\) | 5.09649e7 | 2.50704 | ||||||||
\(839\) | −1.45057e7 | −0.711432 | −0.355716 | − | 0.934594i | \(-0.615763\pi\) | ||||
−0.355716 | + | 0.934594i | \(0.615763\pi\) | |||||||
\(840\) | −2.63444e7 | −1.28822 | ||||||||
\(841\) | 1.38197e6 | 0.0673766 | ||||||||
\(842\) | −3.74613e7 | −1.82097 | ||||||||
\(843\) | −3.54607e7 | −1.71861 | ||||||||
\(844\) | 5.80565e7 | 2.80540 | ||||||||
\(845\) | 3.12143e6 | 0.150388 | ||||||||
\(846\) | 1.35626e8 | 6.51505 | ||||||||
\(847\) | −2.11322e7 | −1.01213 | ||||||||
\(848\) | 2.92476e7 | 1.39669 | ||||||||
\(849\) | −3.15839e7 | −1.50382 | ||||||||
\(850\) | 7.88205e6 | 0.374190 | ||||||||
\(851\) | −2.63412e7 | −1.24684 | ||||||||
\(852\) | −1.28488e7 | −0.606408 | ||||||||
\(853\) | −1.15298e7 | −0.542563 | −0.271282 | − | 0.962500i | \(-0.587447\pi\) | ||||
−0.271282 | + | 0.962500i | \(0.587447\pi\) | |||||||
\(854\) | 3.61912e7 | 1.69808 | ||||||||
\(855\) | −3.07611e6 | −0.143909 | ||||||||
\(856\) | 1.78855e7 | 0.834289 | ||||||||
\(857\) | 2.85360e7 | 1.32722 | 0.663608 | − | 0.748080i | \(-0.269024\pi\) | ||||
0.663608 | + | 0.748080i | \(0.269024\pi\) | |||||||
\(858\) | 5.88759e6 | 0.273036 | ||||||||
\(859\) | −2.75999e7 | −1.27622 | −0.638109 | − | 0.769946i | \(-0.720283\pi\) | ||||
−0.638109 | + | 0.769946i | \(0.720283\pi\) | |||||||
\(860\) | 1.73993e6 | 0.0802204 | ||||||||
\(861\) | −3.14097e7 | −1.44396 | ||||||||
\(862\) | −5.04490e7 | −2.31251 | ||||||||
\(863\) | 6.90832e6 | 0.315752 | 0.157876 | − | 0.987459i | \(-0.449535\pi\) | ||||
0.157876 | + | 0.987459i | \(0.449535\pi\) | |||||||
\(864\) | 2.58091e8 | 11.7622 | ||||||||
\(865\) | −1.50234e6 | −0.0682698 | ||||||||
\(866\) | 8.25870e7 | 3.74211 | ||||||||
\(867\) | 3.84697e7 | 1.73809 | ||||||||
\(868\) | 4.19610e7 | 1.89037 | ||||||||
\(869\) | 1.99144e6 | 0.0894578 | ||||||||
\(870\) | 1.49421e7 | 0.669287 | ||||||||
\(871\) | −9.74377e6 | −0.435193 | ||||||||
\(872\) | 1.16291e8 | 5.17909 | ||||||||
\(873\) | −3.43767e7 | −1.52661 | ||||||||
\(874\) | −1.19924e7 | −0.531038 | ||||||||
\(875\) | 8.47445e6 | 0.374189 | ||||||||
\(876\) | −1.37453e7 | −0.605194 | ||||||||
\(877\) | 1.00172e7 | 0.439790 | 0.219895 | − | 0.975524i | \(-0.429429\pi\) | ||||
0.219895 | + | 0.975524i | \(0.429429\pi\) | |||||||
\(878\) | −5.23040e7 | −2.28981 | ||||||||
\(879\) | −6.88544e7 | −3.00580 | ||||||||
\(880\) | 3.46554e6 | 0.150857 | ||||||||
\(881\) | 2.80779e7 | 1.21878 | 0.609389 | − | 0.792871i | \(-0.291415\pi\) | ||||
0.609389 | + | 0.792871i | \(0.291415\pi\) | |||||||
\(882\) | −1.01390e7 | −0.438859 | ||||||||
\(883\) | 2.54617e7 | 1.09897 | 0.549485 | − | 0.835504i | \(-0.314824\pi\) | ||||
0.549485 | + | 0.835504i | \(0.314824\pi\) | |||||||
\(884\) | −5.46600e6 | −0.235255 | ||||||||
\(885\) | −4.27132e6 | −0.183318 | ||||||||
\(886\) | 2.72258e7 | 1.16519 | ||||||||
\(887\) | 1.53530e7 | 0.655216 | 0.327608 | − | 0.944814i | \(-0.393757\pi\) | ||||
0.327608 | + | 0.944814i | \(0.393757\pi\) | |||||||
\(888\) | −2.57916e8 | −10.9761 | ||||||||
\(889\) | 2.21044e7 | 0.938046 | ||||||||
\(890\) | −1.33366e7 | −0.564377 | ||||||||
\(891\) | −8.19709e6 | −0.345912 | ||||||||
\(892\) | 4.76024e7 | 2.00317 | ||||||||
\(893\) | −1.21286e7 | −0.508958 | ||||||||
\(894\) | 6.83420e7 | 2.85986 | ||||||||
\(895\) | −5.00126e6 | −0.208700 | ||||||||
\(896\) | −1.51067e8 | −6.28635 | ||||||||
\(897\) | 1.38799e7 | 0.575978 | ||||||||
\(898\) | −3.58189e7 | −1.48225 | ||||||||
\(899\) | −1.55862e7 | −0.643194 | ||||||||
\(900\) | −1.54377e8 | −6.35294 | ||||||||
\(901\) | 1.48267e6 | 0.0608459 | ||||||||
\(902\) | 6.79313e6 | 0.278006 | ||||||||
\(903\) | 7.07749e6 | 0.288842 | ||||||||
\(904\) | −7.35450e7 | −2.99317 | ||||||||
\(905\) | 3.85576e6 | 0.156491 | ||||||||
\(906\) | 1.27186e8 | 5.14778 | ||||||||
\(907\) | −2.57735e7 | −1.04029 | −0.520146 | − | 0.854077i | \(-0.674123\pi\) | ||||
−0.520146 | + | 0.854077i | \(0.674123\pi\) | |||||||
\(908\) | −1.12044e8 | −4.50997 | ||||||||
\(909\) | −1.01825e8 | −4.08737 | ||||||||
\(910\) | −3.88624e6 | −0.155570 | ||||||||
\(911\) | 1.30975e7 | 0.522869 | 0.261435 | − | 0.965221i | \(-0.415804\pi\) | ||||
0.261435 | + | 0.965221i | \(0.415804\pi\) | |||||||
\(912\) | −7.14207e7 | −2.84340 | ||||||||
\(913\) | −3.58997e6 | −0.142532 | ||||||||
\(914\) | −8.95886e7 | −3.54721 | ||||||||
\(915\) | −6.82097e6 | −0.269335 | ||||||||
\(916\) | −2.90531e7 | −1.14407 | ||||||||
\(917\) | −1.74329e7 | −0.684616 | ||||||||
\(918\) | 2.26285e7 | 0.886235 | ||||||||
\(919\) | 2.00241e7 | 0.782104 | 0.391052 | − | 0.920369i | \(-0.372111\pi\) | ||||
0.391052 | + | 0.920369i | \(0.372111\pi\) | |||||||
\(920\) | 1.34321e7 | 0.523208 | ||||||||
\(921\) | 8.65568e7 | 3.36242 | ||||||||
\(922\) | −5.34201e7 | −2.06956 | ||||||||
\(923\) | −1.24130e6 | −0.0479594 | ||||||||
\(924\) | 2.63096e7 | 1.01376 | ||||||||
\(925\) | 4.07881e7 | 1.56740 | ||||||||
\(926\) | −1.50972e7 | −0.578588 | ||||||||
\(927\) | −7.24758e7 | −2.77009 | ||||||||
\(928\) | 1.39192e8 | 5.30571 | ||||||||
\(929\) | 2.20794e7 | 0.839361 | 0.419681 | − | 0.907672i | \(-0.362142\pi\) | ||||
0.419681 | + | 0.907672i | \(0.362142\pi\) | |||||||
\(930\) | −1.06376e7 | −0.403308 | ||||||||
\(931\) | 906698. | 0.0342838 | ||||||||
\(932\) | −1.79937e7 | −0.678549 | ||||||||
\(933\) | 2.87438e7 | 1.08103 | ||||||||
\(934\) | 7.73400e7 | 2.90093 | ||||||||
\(935\) | 175681. | 0.00657197 | ||||||||
\(936\) | 9.43063e7 | 3.51845 | ||||||||
\(937\) | 3.08266e7 | 1.14704 | 0.573518 | − | 0.819193i | \(-0.305578\pi\) | ||||
0.573518 | + | 0.819193i | \(0.305578\pi\) | |||||||
\(938\) | −5.85678e7 | −2.17346 | ||||||||
\(939\) | −3.54953e7 | −1.31373 | ||||||||
\(940\) | 2.07432e7 | 0.765697 | ||||||||
\(941\) | 2.58954e7 | 0.953342 | 0.476671 | − | 0.879082i | \(-0.341843\pi\) | ||||
0.476671 | + | 0.879082i | \(0.341843\pi\) | |||||||
\(942\) | 1.40119e7 | 0.514481 | ||||||||
\(943\) | 1.60147e7 | 0.586462 | ||||||||
\(944\) | −6.88168e7 | −2.51342 | ||||||||
\(945\) | 1.19608e7 | 0.435694 | ||||||||
\(946\) | −1.53068e6 | −0.0556106 | ||||||||
\(947\) | 3.84495e7 | 1.39321 | 0.696604 | − | 0.717456i | \(-0.254693\pi\) | ||||
0.696604 | + | 0.717456i | \(0.254693\pi\) | |||||||
\(948\) | 7.01919e7 | 2.53668 | ||||||||
\(949\) | −1.32791e6 | −0.0478634 | ||||||||
\(950\) | 1.85696e7 | 0.667566 | ||||||||
\(951\) | 9.65536e7 | 3.46192 | ||||||||
\(952\) | −2.15167e7 | −0.769454 | ||||||||
\(953\) | 4.30967e7 | 1.53713 | 0.768567 | − | 0.639769i | \(-0.220970\pi\) | ||||
0.768567 | + | 0.639769i | \(0.220970\pi\) | |||||||
\(954\) | −3.90608e7 | −1.38954 | ||||||||
\(955\) | −8.57152e6 | −0.304123 | ||||||||
\(956\) | −3.24263e7 | −1.14750 | ||||||||
\(957\) | −9.77259e6 | −0.344929 | ||||||||
\(958\) | 4.60620e7 | 1.62154 | ||||||||
\(959\) | 2.62012e7 | 0.919971 | ||||||||
\(960\) | 5.28446e7 | 1.85064 | ||||||||
\(961\) | −1.75329e7 | −0.612416 | ||||||||
\(962\) | −3.80469e7 | −1.32551 | ||||||||
\(963\) | −1.45288e7 | −0.504850 | ||||||||
\(964\) | −1.97878e6 | −0.0685812 | ||||||||
\(965\) | 2.31770e6 | 0.0801196 | ||||||||
\(966\) | 8.34293e7 | 2.87658 | ||||||||
\(967\) | 1.74442e7 | 0.599910 | 0.299955 | − | 0.953953i | \(-0.403028\pi\) | ||||
0.299955 | + | 0.953953i | \(0.403028\pi\) | |||||||
\(968\) | 1.05498e8 | 3.61872 | ||||||||
\(969\) | −3.62058e6 | −0.123871 | ||||||||
\(970\) | −7.07217e6 | −0.241337 | ||||||||
\(971\) | −1.03144e7 | −0.351071 | −0.175536 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175536 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(972\) | −9.34323e7 | −3.17199 | ||||||||
\(973\) | −3.75057e7 | −1.27003 | ||||||||
\(974\) | 2.67609e7 | 0.903865 | ||||||||
\(975\) | −2.14924e7 | −0.724059 | ||||||||
\(976\) | −1.09895e8 | −3.69278 | ||||||||
\(977\) | −3.92840e7 | −1.31668 | −0.658338 | − | 0.752722i | \(-0.728740\pi\) | ||||
−0.658338 | + | 0.752722i | \(0.728740\pi\) | |||||||
\(978\) | −6.76052e7 | −2.26013 | ||||||||
\(979\) | 8.72255e6 | 0.290862 | ||||||||
\(980\) | −1.55070e6 | −0.0515779 | ||||||||
\(981\) | −9.44652e7 | −3.13400 | ||||||||
\(982\) | 1.55164e7 | 0.513467 | ||||||||
\(983\) | 2.20437e7 | 0.727613 | 0.363807 | − | 0.931474i | \(-0.381477\pi\) | ||||
0.363807 | + | 0.931474i | \(0.381477\pi\) | |||||||
\(984\) | 1.56806e8 | 5.16268 | ||||||||
\(985\) | −4.11706e6 | −0.135206 | ||||||||
\(986\) | 1.22038e7 | 0.399764 | ||||||||
\(987\) | 8.43771e7 | 2.75697 | ||||||||
\(988\) | −1.28776e7 | −0.419702 | ||||||||
\(989\) | −3.60856e6 | −0.117312 | ||||||||
\(990\) | −4.62831e6 | −0.150084 | ||||||||
\(991\) | −3.97800e7 | −1.28671 | −0.643356 | − | 0.765567i | \(-0.722458\pi\) | ||||
−0.643356 | + | 0.765567i | \(0.722458\pi\) | |||||||
\(992\) | −9.90940e7 | −3.19719 | ||||||||
\(993\) | 2.70102e7 | 0.869269 | ||||||||
\(994\) | −7.46122e6 | −0.239521 | ||||||||
\(995\) | 7.30780e6 | 0.234007 | ||||||||
\(996\) | −1.26535e8 | −4.04167 | ||||||||
\(997\) | −2.94784e7 | −0.939218 | −0.469609 | − | 0.882875i | \(-0.655605\pi\) | ||||
−0.469609 | + | 0.882875i | \(0.655605\pi\) | |||||||
\(998\) | 5.52539e7 | 1.75605 | ||||||||
\(999\) | 1.17098e8 | 3.71225 |
(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 | 43.6.a.a.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 387.6.a.c.1.8 | 8 | |||
4.3 | odd | 2 | 688.6.a.e.1.8 | 8 | |||
5.4 | even | 2 | 1075.6.a.a.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
387.6.a.c.1.8 | 8 | 3.2 | odd | 2 | |||
688.6.a.e.1.8 | 8 | 4.3 | odd | 2 | |||
1075.6.a.a.1.8 | 8 | 5.4 | even | 2 |