Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
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([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(9.89232559565\) |
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: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + 80362197690736 x^{8} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.17 | ||
Root | \(11.9161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.4 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.9161i | 1.48951i | 0.667339 | + | 0.744754i | \(0.267433\pi\) | ||||
−0.667339 | + | 0.744754i | \(0.732567\pi\) | |||||||
\(3\) | − | 41.5647i | − | 1.53943i | −0.638386 | − | 0.769717i | \(-0.720397\pi\) | ||
0.638386 | − | 0.769717i | \(-0.279603\pi\) | |||||||
\(4\) | −77.9927 | −1.21864 | ||||||||
\(5\) | 111.502i | 0.892019i | 0.895028 | + | 0.446010i | \(0.147155\pi\) | ||||
−0.895028 | + | 0.446010i | \(0.852845\pi\) | |||||||
\(6\) | 495.288 | 2.29300 | ||||||||
\(7\) | 49.3353i | 0.143835i | 0.997411 | + | 0.0719173i | \(0.0229118\pi\) | ||||
−0.997411 | + | 0.0719173i | \(0.977088\pi\) | |||||||
\(8\) | − | 166.738i | − | 0.325659i | ||||||
\(9\) | −998.624 | −1.36985 | ||||||||
\(10\) | −1328.67 | −1.32867 | ||||||||
\(11\) | −2545.27 | −1.91230 | −0.956149 | − | 0.292881i | \(-0.905386\pi\) | ||||
−0.956149 | + | 0.292881i | \(0.905386\pi\) | |||||||
\(12\) | 3241.74i | 1.87601i | ||||||||
\(13\) | −277.606 | −0.126357 | −0.0631783 | − | 0.998002i | \(-0.520124\pi\) | ||||
−0.0631783 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(14\) | −587.882 | −0.214243 | ||||||||
\(15\) | 4634.57 | 1.37320 | ||||||||
\(16\) | −3004.67 | −0.733563 | ||||||||
\(17\) | −532.079 | −0.108300 | −0.0541501 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541501 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(18\) | − | 11899.7i | − | 2.04041i | ||||||
\(19\) | 6002.14i | 0.875075i | 0.899200 | + | 0.437537i | \(0.144149\pi\) | ||||
−0.899200 | + | 0.437537i | \(0.855851\pi\) | |||||||
\(20\) | − | 8696.37i | − | 1.08705i | ||||||
\(21\) | 2050.61 | 0.221424 | ||||||||
\(22\) | − | 30329.6i | − | 2.84838i | ||||||
\(23\) | −18510.7 | −1.52139 | −0.760694 | − | 0.649110i | \(-0.775141\pi\) | ||||
−0.760694 | + | 0.649110i | \(0.775141\pi\) | |||||||
\(24\) | −6930.40 | −0.501331 | ||||||||
\(25\) | 3192.21 | 0.204301 | ||||||||
\(26\) | − | 3307.97i | − | 0.188209i | ||||||
\(27\) | 11206.8i | 0.569367i | ||||||||
\(28\) | − | 3847.79i | − | 0.175282i | ||||||
\(29\) | 27049.2i | 1.10907i | 0.832159 | + | 0.554537i | \(0.187105\pi\) | ||||
−0.832159 | + | 0.554537i | \(0.812895\pi\) | |||||||
\(30\) | 55225.8i | 2.04540i | ||||||||
\(31\) | 26111.0 | 0.876474 | 0.438237 | − | 0.898860i | \(-0.355603\pi\) | ||||
0.438237 | + | 0.898860i | \(0.355603\pi\) | |||||||
\(32\) | − | 46475.1i | − | 1.41831i | ||||||
\(33\) | 105793.i | 2.94386i | ||||||||
\(34\) | − | 6340.29i | − | 0.161314i | ||||||
\(35\) | −5501.00 | −0.128303 | ||||||||
\(36\) | 77885.4 | 1.66935 | ||||||||
\(37\) | − | 2171.52i | − | 0.0428705i | −0.999770 | − | 0.0214352i | \(-0.993176\pi\) | ||
0.999770 | − | 0.0214352i | \(-0.00682357\pi\) | |||||||
\(38\) | −71521.9 | −1.30343 | ||||||||
\(39\) | 11538.6i | 0.194518i | ||||||||
\(40\) | 18591.6 | 0.290494 | ||||||||
\(41\) | −82696.8 | −1.19988 | −0.599939 | − | 0.800046i | \(-0.704809\pi\) | ||||
−0.599939 | + | 0.800046i | \(0.704809\pi\) | |||||||
\(42\) | 24435.2i | 0.329813i | ||||||||
\(43\) | 74033.4 | − | 28990.0i | 0.931156 | − | 0.364622i | ||||
\(44\) | 198512. | 2.33039 | ||||||||
\(45\) | − | 111349.i | − | 1.22194i | ||||||
\(46\) | − | 220575.i | − | 2.26612i | ||||||
\(47\) | −16828.5 | −0.162088 | −0.0810442 | − | 0.996711i | \(-0.525826\pi\) | ||||
−0.0810442 | + | 0.996711i | \(0.525826\pi\) | |||||||
\(48\) | 124888.i | 1.12927i | ||||||||
\(49\) | 115215. | 0.979312 | ||||||||
\(50\) | 38038.6i | 0.304308i | ||||||||
\(51\) | 22115.7i | 0.166721i | ||||||||
\(52\) | 21651.2 | 0.153983 | ||||||||
\(53\) | −80461.4 | −0.540456 | −0.270228 | − | 0.962796i | \(-0.587099\pi\) | ||||
−0.270228 | + | 0.962796i | \(0.587099\pi\) | |||||||
\(54\) | −133542. | −0.848077 | ||||||||
\(55\) | − | 283804.i | − | 1.70581i | ||||||
\(56\) | 8226.04 | 0.0468411 | ||||||||
\(57\) | 249477. | 1.34712 | ||||||||
\(58\) | −322320. | −1.65197 | ||||||||
\(59\) | 151135. | 0.735881 | 0.367941 | − | 0.929849i | \(-0.380063\pi\) | ||||
0.367941 | + | 0.929849i | \(0.380063\pi\) | |||||||
\(60\) | −361462. | −1.67344 | ||||||||
\(61\) | 348035.i | 1.53332i | 0.642053 | + | 0.766660i | \(0.278083\pi\) | ||||
−0.642053 | + | 0.766660i | \(0.721917\pi\) | |||||||
\(62\) | 311141.i | 1.30551i | ||||||||
\(63\) | − | 49267.4i | − | 0.197033i | ||||||
\(64\) | 361501. | 1.37902 | ||||||||
\(65\) | − | 30953.7i | − | 0.112713i | ||||||
\(66\) | −1.26064e6 | −4.38490 | ||||||||
\(67\) | 261022. | 0.867867 | 0.433934 | − | 0.900945i | \(-0.357125\pi\) | ||||
0.433934 | + | 0.900945i | \(0.357125\pi\) | |||||||
\(68\) | 41498.3 | 0.131979 | ||||||||
\(69\) | 769393.i | 2.34208i | ||||||||
\(70\) | − | 65550.3i | − | 0.191109i | ||||||
\(71\) | − | 495540.i | − | 1.38453i | −0.721642 | − | 0.692267i | \(-0.756612\pi\) | ||
0.721642 | − | 0.692267i | \(-0.243388\pi\) | |||||||
\(72\) | 166508.i | 0.446106i | ||||||||
\(73\) | − | 304044.i | − | 0.781570i | −0.920482 | − | 0.390785i | \(-0.872204\pi\) | ||
0.920482 | − | 0.390785i | \(-0.127796\pi\) | |||||||
\(74\) | 25876.0 | 0.0638559 | ||||||||
\(75\) | − | 132683.i | − | 0.314508i | ||||||
\(76\) | − | 468123.i | − | 1.06640i | ||||||
\(77\) | − | 125572.i | − | 0.275055i | ||||||
\(78\) | −137495. | −0.289736 | ||||||||
\(79\) | −289935. | −0.588056 | −0.294028 | − | 0.955797i | \(-0.594996\pi\) | ||||
−0.294028 | + | 0.955797i | \(0.594996\pi\) | |||||||
\(80\) | − | 335029.i | − | 0.654353i | ||||||
\(81\) | −262188. | −0.493352 | ||||||||
\(82\) | − | 985421.i | − | 1.78723i | ||||||
\(83\) | 435765. | 0.762110 | 0.381055 | − | 0.924552i | \(-0.375561\pi\) | ||||
0.381055 | + | 0.924552i | \(0.375561\pi\) | |||||||
\(84\) | −159932. | −0.269835 | ||||||||
\(85\) | − | 59328.1i | − | 0.0966059i | ||||||
\(86\) | 345446. | + | 882187.i | 0.543107 | + | 1.38696i | ||||
\(87\) | 1.12429e6 | 1.70734 | ||||||||
\(88\) | 424392.i | 0.622758i | ||||||||
\(89\) | 1.28127e6i | 1.81748i | 0.417365 | + | 0.908739i | \(0.362954\pi\) | ||||
−0.417365 | + | 0.908739i | \(0.637046\pi\) | |||||||
\(90\) | 1.32684e6 | 1.82009 | ||||||||
\(91\) | − | 13695.7i | − | 0.0181745i | ||||||
\(92\) | 1.44370e6 | 1.85402 | ||||||||
\(93\) | − | 1.08530e6i | − | 1.34927i | ||||||
\(94\) | − | 200530.i | − | 0.241432i | ||||||
\(95\) | −669253. | −0.780584 | ||||||||
\(96\) | −1.93172e6 | −2.18339 | ||||||||
\(97\) | −291513. | −0.319406 | −0.159703 | − | 0.987165i | \(-0.551054\pi\) | ||||
−0.159703 | + | 0.987165i | \(0.551054\pi\) | |||||||
\(98\) | 1.37291e6i | 1.45869i | ||||||||
\(99\) | 2.54177e6 | 2.61957 | ||||||||
\(100\) | −248969. | −0.248969 | ||||||||
\(101\) | −1.83351e6 | −1.77959 | −0.889793 | − | 0.456365i | \(-0.849151\pi\) | ||||
−0.889793 | + | 0.456365i | \(0.849151\pi\) | |||||||
\(102\) | −263532. | −0.248332 | ||||||||
\(103\) | −1.58097e6 | −1.44682 | −0.723408 | − | 0.690421i | \(-0.757425\pi\) | ||||
−0.723408 | + | 0.690421i | \(0.757425\pi\) | |||||||
\(104\) | 46287.3i | 0.0411492i | ||||||||
\(105\) | 228648.i | 0.197514i | ||||||||
\(106\) | − | 958784.i | − | 0.805014i | ||||||
\(107\) | 1.41201e6 | 1.15262 | 0.576312 | − | 0.817230i | \(-0.304491\pi\) | ||||
0.576312 | + | 0.817230i | \(0.304491\pi\) | |||||||
\(108\) | − | 874052.i | − | 0.693851i | ||||||
\(109\) | −738817. | −0.570502 | −0.285251 | − | 0.958453i | \(-0.592077\pi\) | ||||
−0.285251 | + | 0.958453i | \(0.592077\pi\) | |||||||
\(110\) | 3.38182e6 | 2.54081 | ||||||||
\(111\) | −90258.5 | −0.0659962 | ||||||||
\(112\) | − | 148236.i | − | 0.105512i | ||||||
\(113\) | 1.67172e6i | 1.15859i | 0.815119 | + | 0.579293i | \(0.196671\pi\) | ||||
−0.815119 | + | 0.579293i | \(0.803329\pi\) | |||||||
\(114\) | 2.97279e6i | 2.00655i | ||||||||
\(115\) | − | 2.06399e6i | − | 1.35711i | ||||||
\(116\) | − | 2.10964e6i | − | 1.35156i | ||||||
\(117\) | 277224. | 0.173090 | ||||||||
\(118\) | 1.80093e6i | 1.09610i | ||||||||
\(119\) | − | 26250.3i | − | 0.0155773i | ||||||
\(120\) | − | 772756.i | − | 0.447197i | ||||||
\(121\) | 4.70683e6 | 2.65688 | ||||||||
\(122\) | −4.14720e6 | −2.28389 | ||||||||
\(123\) | 3.43727e6i | 1.84713i | ||||||||
\(124\) | −2.03647e6 | −1.06810 | ||||||||
\(125\) | 2.09816e6i | 1.07426i | ||||||||
\(126\) | 587074. | 0.293482 | ||||||||
\(127\) | −2.87492e6 | −1.40351 | −0.701753 | − | 0.712420i | \(-0.747599\pi\) | ||||
−0.701753 | + | 0.712420i | \(0.747599\pi\) | |||||||
\(128\) | 1.33327e6i | 0.635752i | ||||||||
\(129\) | −1.20496e6 | − | 3.07718e6i | −0.561311 | − | 1.43345i | ||||
\(130\) | 368846. | 0.167886 | ||||||||
\(131\) | − | 1.71744e6i | − | 0.763956i | −0.924171 | − | 0.381978i | \(-0.875243\pi\) | ||
0.924171 | − | 0.381978i | \(-0.124757\pi\) | |||||||
\(132\) | − | 8.25110e6i | − | 3.58749i | ||||||
\(133\) | −296117. | −0.125866 | ||||||||
\(134\) | 3.11036e6i | 1.29270i | ||||||||
\(135\) | −1.24959e6 | −0.507886 | ||||||||
\(136\) | 88717.6i | 0.0352690i | ||||||||
\(137\) | 120280.i | 0.0467771i | 0.999726 | + | 0.0233886i | \(0.00744549\pi\) | ||||
−0.999726 | + | 0.0233886i | \(0.992555\pi\) | |||||||
\(138\) | −9.16814e6 | −3.48854 | ||||||||
\(139\) | −2.80418e6 | −1.04415 | −0.522073 | − | 0.852901i | \(-0.674841\pi\) | ||||
−0.522073 | + | 0.852901i | \(0.674841\pi\) | |||||||
\(140\) | 429038. | 0.156355 | ||||||||
\(141\) | 699472.i | 0.249524i | ||||||||
\(142\) | 5.90489e6 | 2.06227 | ||||||||
\(143\) | 706581. | 0.241632 | ||||||||
\(144\) | 3.00054e6 | 1.00488 | ||||||||
\(145\) | −3.01605e6 | −0.989315 | ||||||||
\(146\) | 3.62301e6 | 1.16415 | ||||||||
\(147\) | − | 4.78888e6i | − | 1.50758i | ||||||
\(148\) | 169362.i | 0.0522435i | ||||||||
\(149\) | − | 5.36200e6i | − | 1.62094i | −0.585778 | − | 0.810471i | \(-0.699211\pi\) | ||
0.585778 | − | 0.810471i | \(-0.300789\pi\) | |||||||
\(150\) | 1.58106e6 | 0.468463 | ||||||||
\(151\) | 382921.i | 0.111219i | 0.998453 | + | 0.0556095i | \(0.0177102\pi\) | ||||
−0.998453 | + | 0.0556095i | \(0.982290\pi\) | |||||||
\(152\) | 1.00078e6 | 0.284976 | ||||||||
\(153\) | 531347. | 0.148356 | ||||||||
\(154\) | 1.49632e6 | 0.409696 | ||||||||
\(155\) | 2.91144e6i | 0.781831i | ||||||||
\(156\) | − | 899926.i | − | 0.237046i | ||||||
\(157\) | 4.70730e6i | 1.21639i | 0.793787 | + | 0.608195i | \(0.208106\pi\) | ||||
−0.793787 | + | 0.608195i | \(0.791894\pi\) | |||||||
\(158\) | − | 3.45488e6i | − | 0.875915i | ||||||
\(159\) | 3.34436e6i | 0.831996i | ||||||||
\(160\) | 5.18209e6 | 1.26516 | ||||||||
\(161\) | − | 913232.i | − | 0.218828i | ||||||
\(162\) | − | 3.12425e6i | − | 0.734853i | ||||||
\(163\) | 6.94062e6i | 1.60264i | 0.598237 | + | 0.801319i | \(0.295868\pi\) | ||||
−0.598237 | + | 0.801319i | \(0.704132\pi\) | |||||||
\(164\) | 6.44974e6 | 1.46221 | ||||||||
\(165\) | −1.17962e7 | −2.62598 | ||||||||
\(166\) | 5.19260e6i | 1.13517i | ||||||||
\(167\) | 544241. | 0.116854 | 0.0584268 | − | 0.998292i | \(-0.481392\pi\) | ||||
0.0584268 | + | 0.998292i | \(0.481392\pi\) | |||||||
\(168\) | − | 341913.i | − | 0.0721087i | ||||||
\(169\) | −4.74974e6 | −0.984034 | ||||||||
\(170\) | 706958. | 0.143895 | ||||||||
\(171\) | − | 5.99388e6i | − | 1.19873i | ||||||
\(172\) | −5.77406e6 | + | 2.26100e6i | −1.13474 | + | 0.444341i | ||||
\(173\) | 3.91149e6 | 0.755447 | 0.377724 | − | 0.925918i | \(-0.376707\pi\) | ||||
0.377724 | + | 0.925918i | \(0.376707\pi\) | |||||||
\(174\) | 1.33971e7i | 2.54310i | ||||||||
\(175\) | 157488.i | 0.0293856i | ||||||||
\(176\) | 7.64770e6 | 1.40279 | ||||||||
\(177\) | − | 6.28186e6i | − | 1.13284i | ||||||
\(178\) | −1.52676e7 | −2.70715 | ||||||||
\(179\) | − | 574368.i | − | 0.100145i | −0.998746 | − | 0.0500727i | \(-0.984055\pi\) | ||
0.998746 | − | 0.0500727i | \(-0.0159453\pi\) | |||||||
\(180\) | 8.68441e6i | 1.48910i | ||||||||
\(181\) | 2.94218e6 | 0.496173 | 0.248086 | − | 0.968738i | \(-0.420198\pi\) | ||||
0.248086 | + | 0.968738i | \(0.420198\pi\) | |||||||
\(182\) | 163199. | 0.0270710 | ||||||||
\(183\) | 1.44660e7 | 2.36044 | ||||||||
\(184\) | 3.08644e6i | 0.495454i | ||||||||
\(185\) | 242130. | 0.0382413 | ||||||||
\(186\) | 1.29325e7 | 2.00975 | ||||||||
\(187\) | 1.35428e6 | 0.207102 | ||||||||
\(188\) | 1.31250e6 | 0.197527 | ||||||||
\(189\) | −552893. | −0.0818947 | ||||||||
\(190\) | − | 7.97486e6i | − | 1.16269i | ||||||
\(191\) | 1.07146e7i | 1.53772i | 0.639418 | + | 0.768859i | \(0.279175\pi\) | ||||
−0.639418 | + | 0.768859i | \(0.720825\pi\) | |||||||
\(192\) | − | 1.50257e7i | − | 2.12291i | ||||||
\(193\) | 4.03291e6 | 0.560978 | 0.280489 | − | 0.959857i | \(-0.409503\pi\) | ||||
0.280489 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(194\) | − | 3.47369e6i | − | 0.475757i | ||||||
\(195\) | −1.28658e6 | −0.173514 | ||||||||
\(196\) | −8.98593e6 | −1.19342 | ||||||||
\(197\) | −5.70839e6 | −0.746646 | −0.373323 | − | 0.927701i | \(-0.621782\pi\) | ||||
−0.373323 | + | 0.927701i | \(0.621782\pi\) | |||||||
\(198\) | 3.02879e7i | 3.90187i | ||||||||
\(199\) | 8.41961e6i | 1.06840i | 0.845359 | + | 0.534198i | \(0.179386\pi\) | ||||
−0.845359 | + | 0.534198i | \(0.820614\pi\) | |||||||
\(200\) | − | 532261.i | − | 0.0665326i | ||||||
\(201\) | − | 1.08493e7i | − | 1.33602i | ||||||
\(202\) | − | 2.18482e7i | − | 2.65071i | ||||||
\(203\) | −1.33448e6 | −0.159523 | ||||||||
\(204\) | − | 1.72486e6i | − | 0.203172i | ||||||
\(205\) | − | 9.22089e6i | − | 1.07031i | ||||||
\(206\) | − | 1.88390e7i | − | 2.15504i | ||||||
\(207\) | 1.84853e7 | 2.08408 | ||||||||
\(208\) | 834114. | 0.0926906 | ||||||||
\(209\) | − | 1.52771e7i | − | 1.67340i | ||||||
\(210\) | −2.72458e6 | −0.294199 | ||||||||
\(211\) | − | 1.18232e7i | − | 1.25860i | −0.777164 | − | 0.629298i | \(-0.783342\pi\) | ||
0.777164 | − | 0.629298i | \(-0.216658\pi\) | |||||||
\(212\) | 6.27540e6 | 0.658619 | ||||||||
\(213\) | −2.05970e7 | −2.13140 | ||||||||
\(214\) | 1.68256e7i | 1.71684i | ||||||||
\(215\) | 3.23245e6 | + | 8.25490e6i | 0.325250 | + | 0.830609i | ||||
\(216\) | 1.86860e6 | 0.185420 | ||||||||
\(217\) | 1.28819e6i | 0.126067i | ||||||||
\(218\) | − | 8.80379e6i | − | 0.849767i | ||||||
\(219\) | −1.26375e7 | −1.20317 | ||||||||
\(220\) | 2.21346e7i | 2.07876i | ||||||||
\(221\) | 147708. | 0.0136845 | ||||||||
\(222\) | − | 1.07553e6i | − | 0.0983019i | ||||||
\(223\) | − | 1.59450e6i | − | 0.143784i | −0.997412 | − | 0.0718918i | \(-0.977096\pi\) | ||
0.997412 | − | 0.0718918i | \(-0.0229036\pi\) | |||||||
\(224\) | 2.29286e6 | 0.204002 | ||||||||
\(225\) | −3.18782e6 | −0.279863 | ||||||||
\(226\) | −1.99203e7 | −1.72572 | ||||||||
\(227\) | − | 1.36878e7i | − | 1.17019i | −0.810966 | − | 0.585093i | \(-0.801058\pi\) | ||
0.810966 | − | 0.585093i | \(-0.198942\pi\) | |||||||
\(228\) | −1.94574e7 | −1.64165 | ||||||||
\(229\) | 3.27069e6 | 0.272354 | 0.136177 | − | 0.990685i | \(-0.456518\pi\) | ||||
0.136177 | + | 0.990685i | \(0.456518\pi\) | |||||||
\(230\) | 2.45947e7 | 2.02142 | ||||||||
\(231\) | −5.21934e6 | −0.423428 | ||||||||
\(232\) | 4.51012e6 | 0.361180 | ||||||||
\(233\) | 1.71626e7i | 1.35680i | 0.734695 | + | 0.678398i | \(0.237325\pi\) | ||||
−0.734695 | + | 0.678398i | \(0.762675\pi\) | |||||||
\(234\) | 3.30342e6i | 0.257819i | ||||||||
\(235\) | − | 1.87642e6i | − | 0.144586i | ||||||
\(236\) | −1.17874e7 | −0.896771 | ||||||||
\(237\) | 1.20511e7i | 0.905274i | ||||||||
\(238\) | 312800. | 0.0232026 | ||||||||
\(239\) | −1.03077e7 | −0.755040 | −0.377520 | − | 0.926001i | \(-0.623223\pi\) | ||||
−0.377520 | + | 0.926001i | \(0.623223\pi\) | |||||||
\(240\) | −1.39254e7 | −1.00733 | ||||||||
\(241\) | − | 1.27257e6i | − | 0.0909143i | −0.998966 | − | 0.0454571i | \(-0.985526\pi\) | ||
0.998966 | − | 0.0454571i | \(-0.0144744\pi\) | |||||||
\(242\) | 5.60869e7i | 3.95745i | ||||||||
\(243\) | 1.90675e7i | 1.32885i | ||||||||
\(244\) | − | 2.71441e7i | − | 1.86856i | ||||||
\(245\) | 1.28468e7i | 0.873565i | ||||||||
\(246\) | −4.09587e7 | −2.75132 | ||||||||
\(247\) | − | 1.66623e6i | − | 0.110572i | ||||||
\(248\) | − | 4.35369e6i | − | 0.285432i | ||||||
\(249\) | − | 1.81124e7i | − | 1.17322i | ||||||
\(250\) | −2.50019e7 | −1.60012 | ||||||||
\(251\) | 1.41003e7 | 0.891677 | 0.445839 | − | 0.895113i | \(-0.352906\pi\) | ||||
0.445839 | + | 0.895113i | \(0.352906\pi\) | |||||||
\(252\) | 3.84250e6i | 0.240111i | ||||||||
\(253\) | 4.71148e7 | 2.90935 | ||||||||
\(254\) | − | 3.42577e7i | − | 2.09053i | ||||||
\(255\) | −2.46595e6 | −0.148718 | ||||||||
\(256\) | 7.24878e6 | 0.432061 | ||||||||
\(257\) | 1.82508e7i | 1.07518i | 0.843206 | + | 0.537591i | \(0.180666\pi\) | ||||
−0.843206 | + | 0.537591i | \(0.819334\pi\) | |||||||
\(258\) | 3.66678e7 | − | 1.43584e7i | 2.13514 | − | 0.836077i | ||||
\(259\) | 107132. | 0.00616626 | ||||||||
\(260\) | 2.41416e6i | 0.137356i | ||||||||
\(261\) | − | 2.70120e7i | − | 1.51927i | ||||||
\(262\) | 2.04652e7 | 1.13792 | ||||||||
\(263\) | 2.34584e7i | 1.28953i | 0.764381 | + | 0.644765i | \(0.223045\pi\) | ||||
−0.764381 | + | 0.644765i | \(0.776955\pi\) | |||||||
\(264\) | 1.76397e7 | 0.958694 | ||||||||
\(265\) | − | 8.97165e6i | − | 0.482097i | ||||||
\(266\) | − | 3.52855e6i | − | 0.187479i | ||||||
\(267\) | 5.32554e7 | 2.79789 | ||||||||
\(268\) | −2.03578e7 | −1.05761 | ||||||||
\(269\) | 8.18861e6 | 0.420682 | 0.210341 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210341 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(270\) | − | 1.48902e7i | − | 0.756501i | ||||||
\(271\) | 7.82358e6 | 0.393095 | 0.196548 | − | 0.980494i | \(-0.437027\pi\) | ||||
0.196548 | + | 0.980494i | \(0.437027\pi\) | |||||||
\(272\) | 1.59872e6 | 0.0794451 | ||||||||
\(273\) | −569260. | −0.0279784 | ||||||||
\(274\) | −1.43327e6 | −0.0696749 | ||||||||
\(275\) | −8.12503e6 | −0.390685 | ||||||||
\(276\) | − | 6.00070e7i | − | 2.85414i | ||||||
\(277\) | − | 1.33278e7i | − | 0.627074i | −0.949576 | − | 0.313537i | \(-0.898486\pi\) | ||
0.949576 | − | 0.313537i | \(-0.101514\pi\) | |||||||
\(278\) | − | 3.34147e7i | − | 1.55526i | ||||||
\(279\) | −2.60751e7 | −1.20064 | ||||||||
\(280\) | 917224.i | 0.0417832i | ||||||||
\(281\) | −1.46200e7 | −0.658914 | −0.329457 | − | 0.944170i | \(-0.606866\pi\) | ||||
−0.329457 | + | 0.944170i | \(0.606866\pi\) | |||||||
\(282\) | −8.33496e6 | −0.371669 | ||||||||
\(283\) | −2.77184e6 | −0.122295 | −0.0611475 | − | 0.998129i | \(-0.519476\pi\) | ||||
−0.0611475 | + | 0.998129i | \(0.519476\pi\) | |||||||
\(284\) | 3.86485e7i | 1.68724i | ||||||||
\(285\) | 2.78173e7i | 1.20166i | ||||||||
\(286\) | 8.41966e6i | 0.359912i | ||||||||
\(287\) | − | 4.07987e6i | − | 0.172584i | ||||||
\(288\) | 4.64112e7i | 1.94288i | ||||||||
\(289\) | −2.38545e7 | −0.988271 | ||||||||
\(290\) | − | 3.59395e7i | − | 1.47359i | ||||||
\(291\) | 1.21166e7i | 0.491704i | ||||||||
\(292\) | 2.37132e7i | 0.952449i | ||||||||
\(293\) | −2.86988e7 | −1.14093 | −0.570467 | − | 0.821320i | \(-0.693238\pi\) | ||||
−0.570467 | + | 0.821320i | \(0.693238\pi\) | |||||||
\(294\) | 5.70646e7 | 2.24556 | ||||||||
\(295\) | 1.68519e7i | 0.656420i | ||||||||
\(296\) | −362074. | −0.0139612 | ||||||||
\(297\) | − | 2.85244e7i | − | 1.08880i | ||||||
\(298\) | 6.38939e7 | 2.41441 | ||||||||
\(299\) | 5.13868e6 | 0.192238 | ||||||||
\(300\) | 1.03483e7i | 0.383271i | ||||||||
\(301\) | 1.43023e6 | + | 3.65246e6i | 0.0524452 | + | 0.133932i | ||||
\(302\) | −4.56292e6 | −0.165662 | ||||||||
\(303\) | 7.62092e7i | 2.73955i | ||||||||
\(304\) | − | 1.80345e7i | − | 0.641923i | ||||||
\(305\) | −3.88067e7 | −1.36775 | ||||||||
\(306\) | 6.33157e6i | 0.220977i | ||||||||
\(307\) | 3.96953e7 | 1.37190 | 0.685952 | − | 0.727646i | \(-0.259386\pi\) | ||||
0.685952 | + | 0.727646i | \(0.259386\pi\) | |||||||
\(308\) | 9.79366e6i | 0.335191i | ||||||||
\(309\) | 6.57127e7i | 2.22728i | ||||||||
\(310\) | −3.46929e7 | −1.16454 | ||||||||
\(311\) | 4.44492e7 | 1.47769 | 0.738845 | − | 0.673876i | \(-0.235372\pi\) | ||||
0.738845 | + | 0.673876i | \(0.235372\pi\) | |||||||
\(312\) | 1.92392e6 | 0.0633465 | ||||||||
\(313\) | 1.99405e7i | 0.650284i | 0.945665 | + | 0.325142i | \(0.105412\pi\) | ||||
−0.945665 | + | 0.325142i | \(0.894588\pi\) | |||||||
\(314\) | −5.60925e7 | −1.81182 | ||||||||
\(315\) | 5.49343e6 | 0.175757 | ||||||||
\(316\) | 2.26128e7 | 0.716626 | ||||||||
\(317\) | −2.35773e7 | −0.740145 | −0.370073 | − | 0.929003i | \(-0.620667\pi\) | ||||
−0.370073 | + | 0.929003i | \(0.620667\pi\) | |||||||
\(318\) | −3.98516e7 | −1.23926 | ||||||||
\(319\) | − | 6.88475e7i | − | 2.12088i | ||||||
\(320\) | 4.03083e7i | 1.23011i | ||||||||
\(321\) | − | 5.86899e7i | − | 1.77439i | ||||||
\(322\) | 1.08821e7 | 0.325947 | ||||||||
\(323\) | − | 3.19361e6i | − | 0.0947708i | ||||||
\(324\) | 2.04487e7 | 0.601217 | ||||||||
\(325\) | −886175. | −0.0258148 | ||||||||
\(326\) | −8.27049e7 | −2.38714 | ||||||||
\(327\) | 3.07087e7i | 0.878250i | ||||||||
\(328\) | 1.37887e7i | 0.390752i | ||||||||
\(329\) | − | 830239.i | − | 0.0233139i | ||||||
\(330\) | − | 1.40564e8i | − | 3.91141i | ||||||
\(331\) | − | 4.55500e7i | − | 1.25604i | −0.778196 | − | 0.628021i | \(-0.783865\pi\) | ||
0.778196 | − | 0.628021i | \(-0.216135\pi\) | |||||||
\(332\) | −3.39865e7 | −0.928735 | ||||||||
\(333\) | 2.16853e6i | 0.0587263i | ||||||||
\(334\) | 6.48522e6i | 0.174054i | ||||||||
\(335\) | 2.91046e7i | 0.774155i | ||||||||
\(336\) | −6.16140e6 | −0.162428 | ||||||||
\(337\) | −2.55279e7 | −0.666998 | −0.333499 | − | 0.942750i | \(-0.608229\pi\) | ||||
−0.333499 | + | 0.942750i | \(0.608229\pi\) | |||||||
\(338\) | − | 5.65983e7i | − | 1.46573i | ||||||
\(339\) | 6.94846e7 | 1.78357 | ||||||||
\(340\) | 4.62716e6i | 0.117727i | ||||||||
\(341\) | −6.64596e7 | −1.67608 | ||||||||
\(342\) | 7.14235e7 | 1.78551 | ||||||||
\(343\) | 1.14884e7i | 0.284693i | ||||||||
\(344\) | −4.83372e6 | − | 1.23442e7i | −0.118742 | − | 0.303240i | ||||
\(345\) | −8.57892e7 | −2.08918 | ||||||||
\(346\) | 4.66096e7i | 1.12524i | ||||||||
\(347\) | 5.97749e6i | 0.143064i | 0.997438 | + | 0.0715320i | \(0.0227888\pi\) | ||||
−0.997438 | + | 0.0715320i | \(0.977211\pi\) | |||||||
\(348\) | −8.76865e7 | −2.08063 | ||||||||
\(349\) | − | 8.42603e7i | − | 1.98220i | −0.133134 | − | 0.991098i | \(-0.542504\pi\) | ||
0.133134 | − | 0.991098i | \(-0.457496\pi\) | |||||||
\(350\) | −1.87664e6 | −0.0437701 | ||||||||
\(351\) | − | 3.11108e6i | − | 0.0719433i | ||||||
\(352\) | 1.18292e8i | 2.71223i | ||||||||
\(353\) | 4.96924e7 | 1.12971 | 0.564854 | − | 0.825191i | \(-0.308933\pi\) | ||||
0.564854 | + | 0.825191i | \(0.308933\pi\) | |||||||
\(354\) | 7.48551e7 | 1.68737 | ||||||||
\(355\) | 5.52539e7 | 1.23503 | ||||||||
\(356\) | − | 9.99293e7i | − | 2.21484i | ||||||
\(357\) | −1.09108e6 | −0.0239802 | ||||||||
\(358\) | 6.84420e6 | 0.149167 | ||||||||
\(359\) | −4.90249e7 | −1.05958 | −0.529789 | − | 0.848129i | \(-0.677729\pi\) | ||||
−0.529789 | + | 0.848129i | \(0.677729\pi\) | |||||||
\(360\) | −1.85661e7 | −0.397935 | ||||||||
\(361\) | 1.10202e7 | 0.234244 | ||||||||
\(362\) | 3.50592e7i | 0.739053i | ||||||||
\(363\) | − | 1.95638e8i | − | 4.09009i | ||||||
\(364\) | 1.06817e6i | 0.0221480i | ||||||||
\(365\) | 3.39016e7 | 0.697175 | ||||||||
\(366\) | 1.72377e8i | 3.51590i | ||||||||
\(367\) | −5.67938e7 | −1.14895 | −0.574477 | − | 0.818520i | \(-0.694795\pi\) | ||||
−0.574477 | + | 0.818520i | \(0.694795\pi\) | |||||||
\(368\) | 5.56187e7 | 1.11603 | ||||||||
\(369\) | 8.25830e7 | 1.64366 | ||||||||
\(370\) | 2.88523e6i | 0.0569607i | ||||||||
\(371\) | − | 3.96959e6i | − | 0.0777363i | ||||||
\(372\) | 8.46452e7i | 1.64427i | ||||||||
\(373\) | − | 5.89791e7i | − | 1.13651i | −0.822854 | − | 0.568253i | \(-0.807619\pi\) | ||
0.822854 | − | 0.568253i | \(-0.192381\pi\) | |||||||
\(374\) | 1.61377e7i | 0.308481i | ||||||||
\(375\) | 8.72096e7 | 1.65375 | ||||||||
\(376\) | 2.80595e6i | 0.0527856i | ||||||||
\(377\) | − | 7.50901e6i | − | 0.140139i | ||||||
\(378\) | − | 6.58831e6i | − | 0.121983i | ||||||
\(379\) | −3.87859e7 | −0.712453 | −0.356227 | − | 0.934400i | \(-0.615937\pi\) | ||||
−0.356227 | + | 0.934400i | \(0.615937\pi\) | |||||||
\(380\) | 5.21968e7 | 0.951247 | ||||||||
\(381\) | 1.19495e8i | 2.16060i | ||||||||
\(382\) | −1.27676e8 | −2.29044 | ||||||||
\(383\) | − | 5.47849e7i | − | 0.975135i | −0.873085 | − | 0.487568i | \(-0.837884\pi\) | ||
0.873085 | − | 0.487568i | \(-0.162116\pi\) | |||||||
\(384\) | 5.54169e7 | 0.978697 | ||||||||
\(385\) | 1.40015e7 | 0.245354 | ||||||||
\(386\) | 4.80564e7i | 0.835582i | ||||||||
\(387\) | −7.39315e7 | + | 2.89501e7i | −1.27555 | + | 0.499479i | ||||
\(388\) | 2.27359e7 | 0.389239 | ||||||||
\(389\) | 5.34997e7i | 0.908872i | 0.890779 | + | 0.454436i | \(0.150159\pi\) | ||||
−0.890779 | + | 0.454436i | \(0.849841\pi\) | |||||||
\(390\) | − | 1.53310e7i | − | 0.258450i | ||||||
\(391\) | 9.84918e6 | 0.164767 | ||||||||
\(392\) | − | 1.92107e7i | − | 0.318922i | ||||||
\(393\) | −7.13850e7 | −1.17606 | ||||||||
\(394\) | − | 6.80216e7i | − | 1.11214i | ||||||
\(395\) | − | 3.23284e7i | − | 0.524558i | ||||||
\(396\) | −1.98239e8 | −3.19230 | ||||||||
\(397\) | 5.42699e7 | 0.867337 | 0.433668 | − | 0.901073i | \(-0.357219\pi\) | ||||
0.433668 | + | 0.901073i | \(0.357219\pi\) | |||||||
\(398\) | −1.00329e8 | −1.59139 | ||||||||
\(399\) | 1.23080e7i | 0.193762i | ||||||||
\(400\) | −9.59154e6 | −0.149868 | ||||||||
\(401\) | −4.38375e7 | −0.679849 | −0.339925 | − | 0.940453i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940453i | \(0.610402\pi\) | |||||||
\(402\) | 1.29281e8 | 1.99002 | ||||||||
\(403\) | −7.24857e6 | −0.110748 | ||||||||
\(404\) | 1.43000e8 | 2.16867 | ||||||||
\(405\) | − | 2.92346e7i | − | 0.440080i | ||||||
\(406\) | − | 1.59017e7i | − | 0.237611i | ||||||
\(407\) | 5.52710e6i | 0.0819811i | ||||||||
\(408\) | 3.68752e6 | 0.0542942 | ||||||||
\(409\) | 2.63760e7i | 0.385513i | 0.981247 | + | 0.192756i | \(0.0617427\pi\) | ||||
−0.981247 | + | 0.192756i | \(0.938257\pi\) | |||||||
\(410\) | 1.09877e8 | 1.59424 | ||||||||
\(411\) | 4.99942e6 | 0.0720103 | ||||||||
\(412\) | 1.23304e8 | 1.76314 | ||||||||
\(413\) | 7.45626e6i | 0.105845i | ||||||||
\(414\) | 2.20272e8i | 3.10426i | ||||||||
\(415\) | 4.85888e7i | 0.679817i | ||||||||
\(416\) | 1.29018e7i | 0.179213i | ||||||||
\(417\) | 1.16555e8i | 1.60739i | ||||||||
\(418\) | 1.82042e8 | 2.49255 | ||||||||
\(419\) | − | 7.54058e7i | − | 1.02509i | −0.858660 | − | 0.512546i | \(-0.828703\pi\) | ||
0.858660 | − | 0.512546i | \(-0.171297\pi\) | |||||||
\(420\) | − | 1.78328e7i | − | 0.240698i | ||||||
\(421\) | − | 8.94310e6i | − | 0.119851i | −0.998203 | − | 0.0599255i | \(-0.980914\pi\) | ||
0.998203 | − | 0.0599255i | \(-0.0190863\pi\) | |||||||
\(422\) | 1.40886e8 | 1.87469 | ||||||||
\(423\) | 1.68054e7 | 0.222038 | ||||||||
\(424\) | 1.34159e7i | 0.176005i | ||||||||
\(425\) | −1.69851e6 | −0.0221259 | ||||||||
\(426\) | − | 2.45435e8i | − | 3.17473i | ||||||
\(427\) | −1.71704e7 | −0.220545 | ||||||||
\(428\) | −1.10127e8 | −1.40463 | ||||||||
\(429\) | − | 2.93688e7i | − | 0.371976i | ||||||
\(430\) | −9.83660e7 | + | 3.85181e7i | −1.23720 | + | 0.484462i | ||||
\(431\) | −8.33129e7 | −1.04059 | −0.520296 | − | 0.853986i | \(-0.674178\pi\) | ||||
−0.520296 | + | 0.853986i | \(0.674178\pi\) | |||||||
\(432\) | − | 3.36729e7i | − | 0.417667i | ||||||
\(433\) | 2.94658e7i | 0.362956i | 0.983395 | + | 0.181478i | \(0.0580881\pi\) | ||||
−0.983395 | + | 0.181478i | \(0.941912\pi\) | |||||||
\(434\) | −1.53502e7 | −0.187778 | ||||||||
\(435\) | 1.25361e8i | 1.52298i | ||||||||
\(436\) | 5.76223e7 | 0.695234 | ||||||||
\(437\) | − | 1.11104e8i | − | 1.33133i | ||||||
\(438\) | − | 1.50589e8i | − | 1.79214i | ||||||
\(439\) | −4.77584e7 | −0.564490 | −0.282245 | − | 0.959342i | \(-0.591079\pi\) | ||||
−0.282245 | + | 0.959342i | \(0.591079\pi\) | |||||||
\(440\) | −4.73207e7 | −0.555512 | ||||||||
\(441\) | −1.15057e8 | −1.34151 | ||||||||
\(442\) | 1.76010e6i | 0.0203831i | ||||||||
\(443\) | 1.09518e7 | 0.125972 | 0.0629861 | − | 0.998014i | \(-0.479938\pi\) | ||||
0.0629861 | + | 0.998014i | \(0.479938\pi\) | |||||||
\(444\) | 7.03950e6 | 0.0804253 | ||||||||
\(445\) | −1.42864e8 | −1.62123 | ||||||||
\(446\) | 1.90001e7 | 0.214167 | ||||||||
\(447\) | −2.22870e8 | −2.49533 | ||||||||
\(448\) | 1.78348e7i | 0.198351i | ||||||||
\(449\) | 7.02943e7i | 0.776571i | 0.921539 | + | 0.388286i | \(0.126933\pi\) | ||||
−0.921539 | + | 0.388286i | \(0.873067\pi\) | |||||||
\(450\) | − | 3.79862e7i | − | 0.416858i | ||||||
\(451\) | 2.10486e8 | 2.29452 | ||||||||
\(452\) | − | 1.30382e8i | − | 1.41189i | ||||||
\(453\) | 1.59160e7 | 0.171214 | ||||||||
\(454\) | 1.63104e8 | 1.74300 | ||||||||
\(455\) | 1.52711e6 | 0.0162120 | ||||||||
\(456\) | − | 4.15972e7i | − | 0.438702i | ||||||
\(457\) | 7.12167e7i | 0.746162i | 0.927799 | + | 0.373081i | \(0.121699\pi\) | ||||
−0.927799 | + | 0.373081i | \(0.878301\pi\) | |||||||
\(458\) | 3.89738e7i | 0.405673i | ||||||||
\(459\) | − | 5.96293e6i | − | 0.0616626i | ||||||
\(460\) | 1.60976e8i | 1.65382i | ||||||||
\(461\) | −2.56236e7 | −0.261540 | −0.130770 | − | 0.991413i | \(-0.541745\pi\) | ||||
−0.130770 | + | 0.991413i | \(0.541745\pi\) | |||||||
\(462\) | − | 6.21940e7i | − | 0.630700i | ||||||
\(463\) | 1.17056e8i | 1.17937i | 0.807632 | + | 0.589687i | \(0.200749\pi\) | ||||
−0.807632 | + | 0.589687i | \(0.799251\pi\) | |||||||
\(464\) | − | 8.12740e7i | − | 0.813575i | ||||||
\(465\) | 1.21013e8 | 1.20358 | ||||||||
\(466\) | −2.04510e8 | −2.02096 | ||||||||
\(467\) | − | 1.05647e8i | − | 1.03730i | −0.854987 | − | 0.518650i | \(-0.826435\pi\) | ||
0.854987 | − | 0.518650i | \(-0.173565\pi\) | |||||||
\(468\) | −2.16214e7 | −0.210934 | ||||||||
\(469\) | 1.28776e7i | 0.124829i | ||||||||
\(470\) | 2.23595e7 | 0.215362 | ||||||||
\(471\) | 1.95658e8 | 1.87255 | ||||||||
\(472\) | − | 2.51998e7i | − | 0.239647i | ||||||
\(473\) | −1.88435e8 | + | 7.37873e7i | −1.78065 | + | 0.697265i | ||||
\(474\) | −1.43601e8 | −1.34841 | ||||||||
\(475\) | 1.91601e7i | 0.178779i | ||||||||
\(476\) | 2.04733e6i | 0.0189831i | ||||||||
\(477\) | 8.03508e7 | 0.740346 | ||||||||
\(478\) | − | 1.22828e8i | − | 1.12464i | ||||||
\(479\) | 2.53782e7 | 0.230916 | 0.115458 | − | 0.993312i | \(-0.463166\pi\) | ||||
0.115458 | + | 0.993312i | \(0.463166\pi\) | |||||||
\(480\) | − | 2.15392e8i | − | 1.94763i | ||||||
\(481\) | 602826.i | 0.00541697i | ||||||||
\(482\) | 1.51641e7 | 0.135418 | ||||||||
\(483\) | −3.79582e7 | −0.336872 | ||||||||
\(484\) | −3.67098e8 | −3.23777 | ||||||||
\(485\) | − | 3.25044e7i | − | 0.284916i | ||||||
\(486\) | −2.27210e8 | −1.97933 | ||||||||
\(487\) | 2.41863e7 | 0.209403 | 0.104701 | − | 0.994504i | \(-0.466611\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466611\pi\) | |||||||
\(488\) | 5.80304e7 | 0.499340 | ||||||||
\(489\) | 2.88485e8 | 2.46715 | ||||||||
\(490\) | −1.53083e8 | −1.30118 | ||||||||
\(491\) | − | 4.10861e7i | − | 0.347097i | −0.984825 | − | 0.173548i | \(-0.944477\pi\) | ||
0.984825 | − | 0.173548i | \(-0.0555233\pi\) | |||||||
\(492\) | − | 2.68082e8i | − | 2.25098i | ||||||
\(493\) | − | 1.43923e7i | − | 0.120113i | ||||||
\(494\) | 1.98549e7 | 0.164697 | ||||||||
\(495\) | 2.83413e8i | 2.33671i | ||||||||
\(496\) | −7.84551e7 | −0.642949 | ||||||||
\(497\) | 2.44476e7 | 0.199144 | ||||||||
\(498\) | 2.15829e8 | 1.74752 | ||||||||
\(499\) | 6.96419e7i | 0.560491i | 0.959928 | + | 0.280246i | \(0.0904159\pi\) | ||||
−0.959928 | + | 0.280246i | \(0.909584\pi\) | |||||||
\(500\) | − | 1.63641e8i | − | 1.30913i | ||||||
\(501\) | − | 2.26212e7i | − | 0.179888i | ||||||
\(502\) | 1.68020e8i | 1.32816i | ||||||||
\(503\) | 3.35079e7i | 0.263296i | 0.991297 | + | 0.131648i | \(0.0420268\pi\) | ||||
−0.991297 | + | 0.131648i | \(0.957973\pi\) | |||||||
\(504\) | −8.21473e6 | −0.0641655 | ||||||||
\(505\) | − | 2.04441e8i | − | 1.58742i | ||||||
\(506\) | 5.61423e8i | 4.33350i | ||||||||
\(507\) | 1.97422e8i | 1.51485i | ||||||||
\(508\) | 2.24223e8 | 1.71036 | ||||||||
\(509\) | −3.31260e7 | −0.251198 | −0.125599 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125599 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(510\) | − | 2.93845e7i | − | 0.221517i | ||||||
\(511\) | 1.50001e7 | 0.112417 | ||||||||
\(512\) | 1.71706e8i | 1.27931i | ||||||||
\(513\) | −6.72651e7 | −0.498239 | ||||||||
\(514\) | −2.17478e8 | −1.60149 | ||||||||
\(515\) | − | 1.76283e8i | − | 1.29059i | ||||||
\(516\) | 9.39780e7 | + | 2.39997e8i | 0.684033 | + | 1.74686i | ||||
\(517\) | 4.28331e7 | 0.309961 | ||||||||
\(518\) | 1.27660e6i | 0.00918469i | ||||||||
\(519\) | − | 1.62580e8i | − | 1.16296i | ||||||
\(520\) | −5.16114e6 | −0.0367059 | ||||||||
\(521\) | − | 2.11591e8i | − | 1.49618i | −0.663598 | − | 0.748090i | \(-0.730971\pi\) | ||
0.663598 | − | 0.748090i | \(-0.269029\pi\) | |||||||
\(522\) | 3.21877e8 | 2.26297 | ||||||||
\(523\) | − | 1.63093e7i | − | 0.114007i | −0.998374 | − | 0.0570034i | \(-0.981845\pi\) | ||
0.998374 | − | 0.0570034i | \(-0.0181546\pi\) | |||||||
\(524\) | 1.33948e8i | 0.930984i | ||||||||
\(525\) | 6.54596e6 | 0.0452372 | ||||||||
\(526\) | −2.79532e8 | −1.92077 | ||||||||
\(527\) | −1.38931e7 | −0.0949223 | ||||||||
\(528\) | − | 3.17874e8i | − | 2.15950i | ||||||
\(529\) | 1.94612e8 | 1.31462 | ||||||||
\(530\) | 1.06907e8 | 0.718088 | ||||||||
\(531\) | −1.50927e8 | −1.00805 | ||||||||
\(532\) | 2.30950e7 | 0.153385 | ||||||||
\(533\) | 2.29571e7 | 0.151613 | ||||||||
\(534\) | 6.34595e8i | 4.16747i | ||||||||
\(535\) | 1.57443e8i | 1.02816i | ||||||||
\(536\) | − | 4.35222e7i | − | 0.282629i | ||||||
\(537\) | −2.38734e7 | −0.154167 | ||||||||
\(538\) | 9.75760e7i | 0.626609i | ||||||||
\(539\) | −2.93253e8 | −1.87274 | ||||||||
\(540\) | 9.74589e7 | 0.618928 | ||||||||
\(541\) | 5.73217e7 | 0.362016 | 0.181008 | − | 0.983482i | \(-0.442064\pi\) | ||||
0.181008 | + | 0.983482i | \(0.442064\pi\) | |||||||
\(542\) | 9.32264e7i | 0.585519i | ||||||||
\(543\) | − | 1.22291e8i | − | 0.763825i | ||||||
\(544\) | 2.47284e7i | 0.153603i | ||||||||
\(545\) | − | 8.23798e7i | − | 0.508899i | ||||||
\(546\) | − | 6.78334e6i | − | 0.0416740i | ||||||
\(547\) | 1.30026e8 | 0.794455 | 0.397228 | − | 0.917720i | \(-0.369972\pi\) | ||||
0.397228 | + | 0.917720i | \(0.369972\pi\) | |||||||
\(548\) | − | 9.38100e6i | − | 0.0570043i | ||||||
\(549\) | − | 3.47556e8i | − | 2.10043i | ||||||
\(550\) | − | 9.68184e7i | − | 0.581929i | ||||||
\(551\) | −1.62353e8 | −0.970522 | ||||||||
\(552\) | 1.28287e8 | 0.762719 | ||||||||
\(553\) | − | 1.43040e7i | − | 0.0845829i | ||||||
\(554\) | 1.58815e8 | 0.934031 | ||||||||
\(555\) | − | 1.00640e7i | − | 0.0588699i | ||||||
\(556\) | 2.18705e8 | 1.27243 | ||||||||
\(557\) | 2.40668e8 | 1.39268 | 0.696341 | − | 0.717711i | \(-0.254810\pi\) | ||||
0.696341 | + | 0.717711i | \(0.254810\pi\) | |||||||
\(558\) | − | 3.10713e8i | − | 1.78837i | ||||||
\(559\) | −2.05521e7 | + | 8.04778e6i | −0.117658 | + | 0.0460724i | ||||
\(560\) | 1.65287e7 | 0.0941185 | ||||||||
\(561\) | − | 5.62904e7i | − | 0.318820i | ||||||
\(562\) | − | 1.74213e8i | − | 0.981459i | ||||||
\(563\) | 2.85376e8 | 1.59916 | 0.799580 | − | 0.600559i | \(-0.205055\pi\) | ||||
0.799580 | + | 0.600559i | \(0.205055\pi\) | |||||||
\(564\) | − | 5.45537e7i | − | 0.304079i | ||||||
\(565\) | −1.86401e8 | −1.03348 | ||||||||
\(566\) | − | 3.30294e7i | − | 0.182159i | ||||||
\(567\) | − | 1.29351e7i | − | 0.0709611i | ||||||
\(568\) | −8.26251e7 | −0.450886 | ||||||||
\(569\) | 1.77690e8 | 0.964552 | 0.482276 | − | 0.876019i | \(-0.339810\pi\) | ||||
0.482276 | + | 0.876019i | \(0.339810\pi\) | |||||||
\(570\) | −3.31473e8 | −1.78988 | ||||||||
\(571\) | − | 5.26888e6i | − | 0.0283015i | −0.999900 | − | 0.0141508i | \(-0.995496\pi\) | ||
0.999900 | − | 0.0141508i | \(-0.00450448\pi\) | |||||||
\(572\) | −5.51081e7 | −0.294461 | ||||||||
\(573\) | 4.45350e8 | 2.36722 | ||||||||
\(574\) | 4.86160e7 | 0.257065 | ||||||||
\(575\) | −5.90901e7 | −0.310822 | ||||||||
\(576\) | −3.61004e8 | −1.88906 | ||||||||
\(577\) | − | 5.49076e7i | − | 0.285828i | −0.989735 | − | 0.142914i | \(-0.954353\pi\) | ||
0.989735 | − | 0.142914i | \(-0.0456472\pi\) | |||||||
\(578\) | − | 2.84251e8i | − | 1.47204i | ||||||
\(579\) | − | 1.67627e8i | − | 0.863589i | ||||||
\(580\) | 2.35230e8 | 1.20561 | ||||||||
\(581\) | 2.14986e7i | 0.109618i | ||||||||
\(582\) | −1.44383e8 | −0.732397 | ||||||||
\(583\) | 2.04796e8 | 1.03351 | ||||||||
\(584\) | −5.06955e7 | −0.254525 | ||||||||
\(585\) | 3.09111e7i | 0.154400i | ||||||||
\(586\) | − | 3.41977e8i | − | 1.69943i | ||||||
\(587\) | 1.92743e8i | 0.952936i | 0.879192 | + | 0.476468i | \(0.158083\pi\) | ||||
−0.879192 | + | 0.476468i | \(0.841917\pi\) | |||||||
\(588\) | 3.73497e8i | 1.83720i | ||||||||
\(589\) | 1.56722e8i | 0.766980i | ||||||||
\(590\) | −2.00808e8 | −0.977743 | ||||||||
\(591\) | 2.37267e8i | 1.14941i | ||||||||
\(592\) | 6.52470e6i | 0.0314482i | ||||||||
\(593\) | 3.30813e8i | 1.58642i | 0.608948 | + | 0.793210i | \(0.291592\pi\) | ||||
−0.608948 | + | 0.793210i | \(0.708408\pi\) | |||||||
\(594\) | 3.39899e8 | 1.62178 | ||||||||
\(595\) | 2.92697e6 | 0.0138953 | ||||||||
\(596\) | 4.18196e8i | 1.97534i | ||||||||
\(597\) | 3.49958e8 | 1.64473 | ||||||||
\(598\) | 6.12329e7i | 0.286340i | ||||||||
\(599\) | 3.28927e7 | 0.153045 | 0.0765226 | − | 0.997068i | \(-0.475618\pi\) | ||||
0.0765226 | + | 0.997068i | \(0.475618\pi\) | |||||||
\(600\) | −2.21233e7 | −0.102423 | ||||||||
\(601\) | − | 7.51027e7i | − | 0.345965i | −0.984925 | − | 0.172983i | \(-0.944660\pi\) | ||
0.984925 | − | 0.172983i | \(-0.0553404\pi\) | |||||||
\(602\) | −4.35229e7 | + | 1.70427e7i | −0.199493 | + | 0.0781176i | ||||
\(603\) | −2.60663e8 | −1.18885 | ||||||||
\(604\) | − | 2.98651e7i | − | 0.135535i | ||||||
\(605\) | 5.24823e8i | 2.36999i | ||||||||
\(606\) | −9.08114e8 | −4.08059 | ||||||||
\(607\) | − | 3.49954e8i | − | 1.56475i | −0.622809 | − | 0.782374i | \(-0.714009\pi\) | ||
0.622809 | − | 0.782374i | \(-0.285991\pi\) | |||||||
\(608\) | 2.78950e8 | 1.24113 | ||||||||
\(609\) | 5.54672e7i | 0.245575i | ||||||||
\(610\) | − | 4.62423e8i | − | 2.03728i | ||||||
\(611\) | 4.67169e6 | 0.0204810 | ||||||||
\(612\) | −4.14412e7 | −0.180791 | ||||||||
\(613\) | 1.29934e8 | 0.564081 | 0.282041 | − | 0.959402i | \(-0.408989\pi\) | ||||
0.282041 | + | 0.959402i | \(0.408989\pi\) | |||||||
\(614\) | 4.73012e8i | 2.04346i | ||||||||
\(615\) | −3.83264e8 | −1.64768 | ||||||||
\(616\) | −2.09375e7 | −0.0895741 | ||||||||
\(617\) | 3.41618e8 | 1.45441 | 0.727203 | − | 0.686423i | \(-0.240820\pi\) | ||||
0.727203 | + | 0.686423i | \(0.240820\pi\) | |||||||
\(618\) | −7.83037e8 | −3.31755 | ||||||||
\(619\) | −1.53447e8 | −0.646972 | −0.323486 | − | 0.946233i | \(-0.604855\pi\) | ||||
−0.323486 | + | 0.946233i | \(0.604855\pi\) | |||||||
\(620\) | − | 2.27071e8i | − | 0.952768i | ||||||
\(621\) | − | 2.07447e8i | − | 0.866229i | ||||||
\(622\) | 5.29660e8i | 2.20103i | ||||||||
\(623\) | −6.32116e7 | −0.261416 | ||||||||
\(624\) | − | 3.46697e7i | − | 0.142691i | ||||||
\(625\) | −1.84072e8 | −0.753960 | ||||||||
\(626\) | −2.37612e8 | −0.968604 | ||||||||
\(627\) | −6.34986e8 | −2.57609 | ||||||||
\(628\) | − | 3.67135e8i | − | 1.48234i | ||||||
\(629\) | 1.15542e6i | 0.00464288i | ||||||||
\(630\) | 6.54601e7i | 0.261791i | ||||||||
\(631\) | 1.27596e8i | 0.507866i | 0.967222 | + | 0.253933i | \(0.0817243\pi\) | ||||
−0.967222 | + | 0.253933i | \(0.918276\pi\) | |||||||
\(632\) | 4.83430e7i | 0.191506i | ||||||||
\(633\) | −4.91426e8 | −1.93753 | ||||||||
\(634\) | − | 2.80949e8i | − | 1.10245i | ||||||
\(635\) | − | 3.20560e8i | − | 1.25195i | ||||||
\(636\) | − | 2.60835e8i | − | 1.01390i | ||||||
\(637\) | −3.19843e7 | −0.123743 | ||||||||
\(638\) | 8.20391e8 | 3.15907 | ||||||||
\(639\) | 4.94858e8i | 1.89661i | ||||||||
\(640\) | −1.48663e8 | −0.567103 | ||||||||
\(641\) | 8.34287e7i | 0.316768i | 0.987378 | + | 0.158384i | \(0.0506284\pi\) | ||||
−0.987378 | + | 0.158384i | \(0.949372\pi\) | |||||||
\(642\) | 6.99353e8 | 2.64296 | ||||||||
\(643\) | −3.32211e8 | −1.24963 | −0.624815 | − | 0.780773i | \(-0.714826\pi\) | ||||
−0.624815 | + | 0.780773i | \(0.714826\pi\) | |||||||
\(644\) | 7.12254e7i | 0.266672i | ||||||||
\(645\) | 3.43113e8 | − | 1.34356e8i | 1.27867 | − | 0.500700i | ||||
\(646\) | 3.80553e7 | 0.141162 | ||||||||
\(647\) | 2.30541e8i | 0.851206i | 0.904910 | + | 0.425603i | \(0.139938\pi\) | ||||
−0.904910 | + | 0.425603i | \(0.860062\pi\) | |||||||
\(648\) | 4.37165e7i | 0.160665i | ||||||||
\(649\) | −3.84678e8 | −1.40722 | ||||||||
\(650\) | − | 1.05597e7i | − | 0.0384514i | ||||||
\(651\) | 5.35434e7 | 0.194072 | ||||||||
\(652\) | − | 5.41317e8i | − | 1.95303i | ||||||
\(653\) | − | 2.83522e8i | − | 1.01823i | −0.860697 | − | 0.509117i | \(-0.829972\pi\) | ||
0.860697 | − | 0.509117i | \(-0.170028\pi\) | |||||||
\(654\) | −3.65927e8 | −1.30816 | ||||||||
\(655\) | 1.91499e8 | 0.681464 | ||||||||
\(656\) | 2.48477e8 | 0.880186 | ||||||||
\(657\) | 3.03626e8i | 1.07064i | ||||||||
\(658\) | 9.89319e6 | 0.0347263 | ||||||||
\(659\) | 3.17640e8 | 1.10989 | 0.554943 | − | 0.831888i | \(-0.312740\pi\) | ||||
0.554943 | + | 0.831888i | \(0.312740\pi\) | |||||||
\(660\) | 9.20018e8 | 3.20011 | ||||||||
\(661\) | 2.93585e8 | 1.01655 | 0.508277 | − | 0.861194i | \(-0.330283\pi\) | ||||
0.508277 | + | 0.861194i | \(0.330283\pi\) | |||||||
\(662\) | 5.42776e8 | 1.87088 | ||||||||
\(663\) | − | 6.13944e6i | − | 0.0210663i | ||||||
\(664\) | − | 7.26584e7i | − | 0.248188i | ||||||
\(665\) | − | 3.30178e7i | − | 0.112275i | ||||||
\(666\) | −2.58404e7 | −0.0874734 | ||||||||
\(667\) | − | 5.00701e8i | − | 1.68733i | ||||||
\(668\) | −4.24468e7 | −0.142402 | ||||||||
\(669\) | −6.62748e7 | −0.221345 | ||||||||
\(670\) | −3.46813e8 | −1.15311 | ||||||||
\(671\) | − | 8.85841e8i | − | 2.93217i | ||||||
\(672\) | − | 9.53021e7i | − | 0.314047i | ||||||
\(673\) | 3.04183e8i | 0.997906i | 0.866629 | + | 0.498953i | \(0.166282\pi\) | ||||
−0.866629 | + | 0.498953i | \(0.833718\pi\) | |||||||
\(674\) | − | 3.04192e8i | − | 0.993499i | ||||||
\(675\) | 3.57746e7i | 0.116322i | ||||||||
\(676\) | 3.70445e8 | 1.19918 | ||||||||
\(677\) | 4.01476e8i | 1.29388i | 0.762541 | + | 0.646940i | \(0.223952\pi\) | ||||
−0.762541 | + | 0.646940i | \(0.776048\pi\) | |||||||
\(678\) | 8.27983e8i | 2.65664i | ||||||||
\(679\) | − | 1.43819e7i | − | 0.0459416i | ||||||
\(680\) | −9.89223e6 | −0.0314606 | ||||||||
\(681\) | −5.68928e8 | −1.80142 | ||||||||
\(682\) | − | 7.91937e8i | − | 2.49653i | ||||||
\(683\) | −1.64796e8 | −0.517232 | −0.258616 | − | 0.965980i | \(-0.583266\pi\) | ||||
−0.258616 | + | 0.965980i | \(0.583266\pi\) | |||||||
\(684\) | 4.67479e8i | 1.46081i | ||||||||
\(685\) | −1.34116e7 | −0.0417261 | ||||||||
\(686\) | −1.36897e8 | −0.424053 | ||||||||
\(687\) | − | 1.35945e8i | − | 0.419270i | ||||||
\(688\) | −2.22446e8 | + | 8.71054e7i | −0.683062 | + | 0.267473i | ||||
\(689\) | 2.23365e7 | 0.0682902 | ||||||||
\(690\) | − | 1.02227e9i | − | 3.11185i | ||||||
\(691\) | 5.47737e8i | 1.66011i | 0.557679 | + | 0.830057i | \(0.311692\pi\) | ||||
−0.557679 | + | 0.830057i | \(0.688308\pi\) | |||||||
\(692\) | −3.05068e8 | −0.920615 | ||||||||
\(693\) | 1.25399e8i | 0.376785i | ||||||||
\(694\) | −7.12282e7 | −0.213095 | ||||||||
\(695\) | − | 3.12672e8i | − | 0.931398i | ||||||
\(696\) | − | 1.87462e8i | − | 0.556013i | ||||||
\(697\) | 4.40012e7 | 0.129947 | ||||||||
\(698\) | 1.00405e9 | 2.95250 | ||||||||
\(699\) | 7.13357e8 | 2.08870 | ||||||||
\(700\) | − | 1.22829e7i | − | 0.0358103i | ||||||
\(701\) | −3.75496e8 | −1.09006 | −0.545030 | − | 0.838416i | \(-0.683482\pi\) | ||||
−0.545030 | + | 0.838416i | \(0.683482\pi\) | |||||||
\(702\) | 3.70719e7 | 0.107160 | ||||||||
\(703\) | 1.30338e7 | 0.0375149 | ||||||||
\(704\) | −9.20118e8 | −2.63709 | ||||||||
\(705\) | −7.79928e7 | −0.222581 | ||||||||
\(706\) | 5.92138e8i | 1.68271i | ||||||||
\(707\) | − | 9.04566e7i | − | 0.255966i | ||||||
\(708\) | 4.89939e8i | 1.38052i | ||||||||
\(709\) | 1.86689e8 | 0.523818 | 0.261909 | − | 0.965093i | \(-0.415648\pi\) | ||||
0.261909 | + | 0.965093i | \(0.415648\pi\) | |||||||
\(710\) | 6.58409e8i | 1.83959i | ||||||||
\(711\) | 2.89536e8 | 0.805552 | ||||||||
\(712\) | 2.13635e8 | 0.591879 | ||||||||
\(713\) | −4.83334e8 | −1.33346 | ||||||||
\(714\) | − | 1.30014e7i | − | 0.0357188i | ||||||
\(715\) | 7.87855e7i | 0.215540i | ||||||||
\(716\) | 4.47965e7i | 0.122041i | ||||||||
\(717\) | 4.28438e8i | 1.16233i | ||||||||
\(718\) | − | 5.84184e8i | − | 1.57825i | ||||||
\(719\) | −6.32011e8 | −1.70035 | −0.850174 | − | 0.526501i | \(-0.823504\pi\) | ||||
−0.850174 | + | 0.526501i | \(0.823504\pi\) | |||||||
\(720\) | 3.34568e8i | 0.896368i | ||||||||
\(721\) | − | 7.79978e7i | − | 0.208102i | ||||||
\(722\) | 1.31318e8i | 0.348909i | ||||||||
\(723\) | −5.28942e7 | −0.139956 | ||||||||
\(724\) | −2.29468e8 | −0.604654 | ||||||||
\(725\) | 8.63466e7i | 0.226585i | ||||||||
\(726\) | 2.33124e9 | 6.09223 | ||||||||
\(727\) | 6.56629e7i | 0.170890i | 0.996343 | + | 0.0854451i | \(0.0272312\pi\) | ||||
−0.996343 | + | 0.0854451i | \(0.972769\pi\) | |||||||
\(728\) | −2.28360e6 | −0.00591868 | ||||||||
\(729\) | 6.01402e8 | 1.55232 | ||||||||
\(730\) | 4.03974e8i | 1.03845i | ||||||||
\(731\) | −3.93916e7 | + | 1.54250e7i | −0.100844 | + | 0.0394886i | ||||
\(732\) | −1.12824e9 | −2.87652 | ||||||||
\(733\) | 2.03328e8i | 0.516281i | 0.966107 | + | 0.258141i | \(0.0831098\pi\) | ||||
−0.966107 | + | 0.258141i | \(0.916890\pi\) | |||||||
\(734\) | − | 6.76759e8i | − | 1.71138i | ||||||
\(735\) | 5.33972e8 | 1.34480 | ||||||||
\(736\) | 8.60289e8i | 2.15780i | ||||||||
\(737\) | −6.64372e8 | −1.65962 | ||||||||
\(738\) | 9.84065e8i | 2.44824i | ||||||||
\(739\) | 6.14810e8i | 1.52338i | 0.647943 | + | 0.761688i | \(0.275629\pi\) | ||||
−0.647943 | + | 0.761688i | \(0.724371\pi\) | |||||||
\(740\) | −1.88843e7 | −0.0466022 | ||||||||
\(741\) | −6.92562e7 | −0.170217 | ||||||||
\(742\) | 4.73019e7 | 0.115789 | ||||||||
\(743\) | 2.10819e8i | 0.513977i | 0.966414 | + | 0.256989i | \(0.0827303\pi\) | ||||
−0.966414 | + | 0.256989i | \(0.917270\pi\) | |||||||
\(744\) | −1.80960e8 | −0.439403 | ||||||||
\(745\) | 5.97876e8 | 1.44591 | ||||||||
\(746\) | 7.02799e8 | 1.69284 | ||||||||
\(747\) | −4.35165e8 | −1.04398 | ||||||||
\(748\) | −1.05624e8 | −0.252382 | ||||||||
\(749\) | 6.96620e7i | 0.165787i | ||||||||
\(750\) | 1.03920e9i | 2.46328i | ||||||||
\(751\) | − | 5.50957e8i | − | 1.30076i | −0.759608 | − | 0.650381i | \(-0.774609\pi\) | ||
0.759608 | − | 0.650381i | \(-0.225391\pi\) | |||||||
\(752\) | 5.05642e7 | 0.118902 | ||||||||
\(753\) | − | 5.86075e8i | − | 1.37268i | ||||||
\(754\) | 8.94778e7 | 0.208738 | ||||||||
\(755\) | −4.26967e7 | −0.0992094 | ||||||||
\(756\) | 4.31216e7 | 0.0997997 | ||||||||
\(757\) | 5.62713e8i | 1.29718i | 0.761139 | + | 0.648589i | \(0.224640\pi\) | ||||
−0.761139 | + | 0.648589i | \(0.775360\pi\) | |||||||
\(758\) | − | 4.62175e8i | − | 1.06120i | ||||||
\(759\) | − | 1.95831e9i | − | 4.47875i | ||||||
\(760\) | 1.11590e8i | 0.254204i | ||||||||
\(761\) | − | 5.58509e8i | − | 1.26729i | −0.773624 | − | 0.633645i | \(-0.781558\pi\) | ||
0.773624 | − | 0.633645i | \(-0.218442\pi\) | |||||||
\(762\) | −1.42391e9 | −3.21824 | ||||||||
\(763\) | − | 3.64497e7i | − | 0.0820579i | ||||||
\(764\) | − | 8.35662e8i | − | 1.87392i | ||||||
\(765\) | 5.92465e7i | 0.132336i | ||||||||
\(766\) | 6.52821e8 | 1.45247 | ||||||||
\(767\) | −4.19558e7 | −0.0929835 | ||||||||
\(768\) | − | 3.01293e8i | − | 0.665129i | ||||||
\(769\) | −2.08570e8 | −0.458640 | −0.229320 | − | 0.973351i | \(-0.573650\pi\) | ||||
−0.229320 | + | 0.973351i | \(0.573650\pi\) | |||||||
\(770\) | 1.66843e8i | 0.365457i | ||||||||
\(771\) | 7.58588e8 | 1.65517 | ||||||||
\(772\) | −3.14537e8 | −0.683628 | ||||||||
\(773\) | − | 1.37228e8i | − | 0.297101i | −0.988905 | − | 0.148550i | \(-0.952539\pi\) | ||
0.988905 | − | 0.148550i | \(-0.0474607\pi\) | |||||||
\(774\) | −3.44971e8 | − | 8.80973e8i | −0.743978 | − | 1.89994i | ||||
\(775\) | 8.33518e7 | 0.179065 | ||||||||
\(776\) | 4.86062e7i | 0.104017i | ||||||||
\(777\) | − | 4.45293e6i | − | 0.00949254i | ||||||
\(778\) | −6.37506e8 | −1.35377 | ||||||||
\(779\) | − | 4.96358e8i | − | 1.04998i | ||||||
\(780\) | 1.00344e8 | 0.211450 | ||||||||
\(781\) | 1.26128e9i | 2.64764i | ||||||||
\(782\) | 1.17363e8i | 0.245421i | ||||||||
\(783\) | −3.03136e8 | −0.631470 | ||||||||
\(784\) | −3.46184e8 | −0.718387 | ||||||||
\(785\) | −5.24876e8 | −1.08504 | ||||||||
\(786\) | − | 8.50628e8i | − | 1.75175i | ||||||
\(787\) | −7.68149e8 | −1.57587 | −0.787937 | − | 0.615756i | \(-0.788851\pi\) | ||||
−0.787937 | + | 0.615756i | \(0.788851\pi\) | |||||||
\(788\) | 4.45213e8 | 0.909890 | ||||||||
\(789\) | 9.75042e8 | 1.98515 | ||||||||
\(790\) | 3.85228e8 | 0.781333 | ||||||||
\(791\) | −8.24748e7 | −0.166645 | ||||||||
\(792\) | − | 4.23808e8i | − | 0.853088i | ||||||
\(793\) | − | 9.66163e7i | − | 0.193745i | ||||||
\(794\) | 6.46684e8i | 1.29191i | ||||||||
\(795\) | −3.72904e8 | −0.742156 | ||||||||
\(796\) | − | 6.56668e8i | − | 1.30199i | ||||||
\(797\) | 2.01201e8 | 0.397424 | 0.198712 | − | 0.980058i | \(-0.436324\pi\) | ||||
0.198712 | + | 0.980058i | \(0.436324\pi\) | |||||||
\(798\) | −1.46663e8 | −0.288611 | ||||||||
\(799\) | 8.95410e6 | 0.0175542 | ||||||||
\(800\) | − | 1.48358e8i | − | 0.289762i | ||||||
\(801\) | − | 1.27950e9i | − | 2.48968i | ||||||
\(802\) | − | 5.22371e8i | − | 1.01264i | ||||||
\(803\) | 7.73873e8i | 1.49459i | ||||||||
\(804\) | 8.46167e8i | 1.62813i | ||||||||
\(805\) | 1.01828e8 | 0.195199 | ||||||||
\(806\) | − | 8.63744e7i | − | 0.164960i | ||||||
\(807\) | − | 3.40357e8i | − | 0.647611i | ||||||
\(808\) | 3.05715e8i | 0.579539i | ||||||||
\(809\) | 7.12252e8 | 1.34520 | 0.672602 | − | 0.740004i | \(-0.265177\pi\) | ||||
0.672602 | + | 0.740004i | \(0.265177\pi\) | |||||||
\(810\) | 3.48361e8 | 0.655503 | ||||||||
\(811\) | − | 4.96725e8i | − | 0.931223i | −0.884989 | − | 0.465611i | \(-0.845834\pi\) | ||
0.884989 | − | 0.465611i | \(-0.154166\pi\) | |||||||
\(812\) | 1.04080e8 | 0.194401 | ||||||||
\(813\) | − | 3.25185e8i | − | 0.605144i | ||||||
\(814\) | −6.58613e7 | −0.122112 | ||||||||
\(815\) | −7.73896e8 | −1.42958 | ||||||||
\(816\) | − | 6.64505e7i | − | 0.122300i | ||||||
\(817\) | 1.74002e8 | + | 4.44359e8i | 0.319071 | + | 0.814831i | ||||
\(818\) | −3.14298e8 | −0.574225 | ||||||||
\(819\) | 1.36769e7i | 0.0248964i | ||||||||
\(820\) | 7.19162e8i | 1.30432i | ||||||||
\(821\) | −5.21938e7 | −0.0943169 | −0.0471585 | − | 0.998887i | \(-0.515017\pi\) | ||||
−0.0471585 | + | 0.998887i | \(0.515017\pi\) | |||||||
\(822\) | 5.95735e7i | 0.107260i | ||||||||
\(823\) | 3.65976e8 | 0.656527 | 0.328264 | − | 0.944586i | \(-0.393537\pi\) | ||||
0.328264 | + | 0.944586i | \(0.393537\pi\) | |||||||
\(824\) | 2.63608e8i | 0.471169i | ||||||||
\(825\) | 3.37714e8i | 0.601433i | ||||||||
\(826\) | −8.88493e7 | −0.157657 | ||||||||
\(827\) | 4.96995e8 | 0.878689 | 0.439345 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439345 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(828\) | −1.44172e9 | −2.53974 | ||||||||
\(829\) | − | 1.08959e8i | − | 0.191249i | −0.995417 | − | 0.0956247i | \(-0.969515\pi\) | ||
0.995417 | − | 0.0956247i | \(-0.0304849\pi\) | |||||||
\(830\) | −5.78988e8 | −1.01259 | ||||||||
\(831\) | −5.53965e8 | −0.965338 | ||||||||
\(832\) | −1.00355e8 | −0.174248 | ||||||||
\(833\) | −6.13035e7 | −0.106060 | ||||||||
\(834\) | −1.38887e9 | −2.39422 | ||||||||
\(835\) | 6.06842e7i | 0.104236i | ||||||||
\(836\) | 1.19150e9i | 2.03927i | ||||||||
\(837\) | 2.92622e8i | 0.499035i | ||||||||
\(838\) | 8.98540e8 | 1.52688 | ||||||||
\(839\) | − | 2.51998e8i | − | 0.426689i | −0.976977 | − | 0.213344i | \(-0.931564\pi\) | ||
0.976977 | − | 0.213344i | \(-0.0684356\pi\) | |||||||
\(840\) | 3.81241e7 | 0.0643224 | ||||||||
\(841\) | −1.36836e8 | −0.230044 | ||||||||
\(842\) | 1.06567e8 | 0.178519 | ||||||||
\(843\) | 6.07677e8i | 1.01435i | ||||||||
\(844\) | 9.22121e8i | 1.53377i | ||||||||
\(845\) | − | 5.29608e8i | − | 0.877777i | ||||||
\(846\) | 2.00254e8i | 0.330727i | ||||||||
\(847\) | 2.32213e8i | 0.382152i | ||||||||
\(848\) | 2.41760e8 | 0.396458 | ||||||||
\(849\) | 1.15211e8i | 0.188265i | ||||||||
\(850\) | − | 2.02395e7i | − | 0.0329567i | ||||||
\(851\) | 4.01964e7i | 0.0652227i | ||||||||
\(852\) | 1.60641e9 | 2.59740 | ||||||||
\(853\) | −5.32924e8 | −0.858654 | −0.429327 | − | 0.903149i | \(-0.641249\pi\) | ||||
−0.429327 | + | 0.903149i | \(0.641249\pi\) | |||||||
\(854\) | − | 2.04603e8i | − | 0.328503i | ||||||
\(855\) | 6.68332e8 | 1.06929 | ||||||||
\(856\) | − | 2.35436e8i | − | 0.375362i | ||||||
\(857\) | −8.90239e8 | −1.41437 | −0.707187 | − | 0.707027i | \(-0.750036\pi\) | ||||
−0.707187 | + | 0.707027i | \(0.750036\pi\) | |||||||
\(858\) | 3.49961e8 | 0.554061 | ||||||||
\(859\) | 2.45194e8i | 0.386839i | 0.981116 | + | 0.193419i | \(0.0619578\pi\) | ||||
−0.981116 | + | 0.193419i | \(0.938042\pi\) | |||||||
\(860\) | −2.52108e8 | − | 6.43822e8i | −0.396361 | − | 1.01221i | ||||
\(861\) | −1.69579e8 | −0.265682 | ||||||||
\(862\) | − | 9.92763e8i | − | 1.54997i | ||||||
\(863\) | 161936.i | 0.000251948i | 1.00000 | 0.000125974i | \(4.00988e-5\pi\) | |||||
−1.00000 | 0.000125974i | \(0.999960\pi\) | ||||||||
\(864\) | 5.20840e8 | 0.807538 | ||||||||
\(865\) | 4.36141e8i | 0.673874i | ||||||||
\(866\) | −3.51116e8 | −0.540626 | ||||||||
\(867\) | 9.91503e8i | 1.52138i | ||||||||
\(868\) | − | 1.00470e8i | − | 0.153630i | ||||||
\(869\) | 7.37962e8 | 1.12454 | ||||||||
\(870\) | −1.49381e9 | −2.26850 | ||||||||
\(871\) | −7.24613e7 | −0.109661 | ||||||||
\(872\) | 1.23188e8i | 0.185789i | ||||||||
\(873\) | 2.91112e8 | 0.437539 | ||||||||
\(874\) | 1.32392e9 | 1.98303 | ||||||||
\(875\) | −1.03514e8 | −0.154516 | ||||||||
\(876\) | 9.85632e8 | 1.46623 | ||||||||
\(877\) | 4.36338e8 | 0.646881 | 0.323440 | − | 0.946249i | \(-0.395161\pi\) | ||||
0.323440 | + | 0.946249i | \(0.395161\pi\) | |||||||
\(878\) | − | 5.69093e8i | − | 0.840813i | ||||||
\(879\) | 1.19286e9i | 1.75639i | ||||||||
\(880\) | 8.52738e8i | 1.25132i | ||||||||
\(881\) | 2.05667e8 | 0.300771 | 0.150386 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150386 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(882\) | − | 1.37102e9i | − | 1.99820i | ||||||
\(883\) | −5.99629e8 | −0.870965 | −0.435482 | − | 0.900197i | \(-0.643422\pi\) | ||||
−0.435482 | + | 0.900197i | \(0.643422\pi\) | |||||||
\(884\) | −1.15202e7 | −0.0166764 | ||||||||
\(885\) | 7.00443e8 | 1.01052 | ||||||||
\(886\) | 1.30502e8i | 0.187637i | ||||||||
\(887\) | − | 5.68254e7i | − | 0.0814277i | −0.999171 | − | 0.0407138i | \(-0.987037\pi\) | ||
0.999171 | − | 0.0407138i | \(-0.0129632\pi\) | |||||||
\(888\) | 1.50495e7i | 0.0214923i | ||||||||
\(889\) | − | 1.41835e8i | − | 0.201873i | ||||||
\(890\) | − | 1.70238e9i | − | 2.41483i | ||||||
\(891\) | 6.67338e8 | 0.943437 | ||||||||
\(892\) | 1.24359e8i | 0.175220i | ||||||||
\(893\) | − | 1.01007e8i | − | 0.141840i | ||||||
\(894\) | − | 2.65573e9i | − | 3.71682i | ||||||
\(895\) | 6.40434e7 | 0.0893316 | ||||||||
\(896\) | −6.57771e7 | −0.0914431 | ||||||||
\(897\) | − | 2.13588e8i | − | 0.295937i | ||||||
\(898\) | −8.37632e8 | −1.15671 | ||||||||
\(899\) | 7.06282e8i | 0.972074i | ||||||||
\(900\) | 2.48626e8 | 0.341051 | ||||||||
\(901\) | 4.28119e7 | 0.0585315 | ||||||||
\(902\) | 2.50816e9i | 3.41771i | ||||||||
\(903\) | 1.51813e8 | − | 5.94470e7i | 0.206180 | − | 0.0807359i | ||||
\(904\) | 2.78739e8 | 0.377304 | ||||||||
\(905\) | 3.28060e8i | 0.442596i | ||||||||
\(906\) | 1.89656e8i | 0.255025i | ||||||||
\(907\) | −1.66416e7 | −0.0223035 | −0.0111518 | − | 0.999938i | \(-0.503550\pi\) | ||||
−0.0111518 | + | 0.999938i | \(0.503550\pi\) | |||||||
\(908\) | 1.06755e9i | 1.42603i | ||||||||
\(909\) | 1.83099e9 | 2.43777 | ||||||||
\(910\) | 1.81971e7i | 0.0241479i | ||||||||
\(911\) | − | 8.19723e8i | − | 1.08421i | −0.840312 | − | 0.542103i | \(-0.817628\pi\) | ||
0.840312 | − | 0.542103i | \(-0.182372\pi\) | |||||||
\(912\) | −7.49597e8 | −0.988197 | ||||||||
\(913\) | −1.10914e9 | −1.45738 | ||||||||
\(914\) | −8.48623e8 | −1.11142 | ||||||||
\(915\) | 1.61299e9i | 2.10556i | ||||||||
\(916\) | −2.55090e8 | −0.331900 | ||||||||
\(917\) | 8.47305e7 | 0.109883 | ||||||||
\(918\) | 7.10547e7 | 0.0918469 | ||||||||
\(919\) | −1.31103e8 | −0.168914 | −0.0844569 | − | 0.996427i | \(-0.526916\pi\) | ||||
−0.0844569 | + | 0.996427i | \(0.526916\pi\) | |||||||
\(920\) | −3.44145e8 | −0.441955 | ||||||||
\(921\) | − | 1.64992e9i | − | 2.11196i | ||||||
\(922\) | − | 3.05333e8i | − | 0.389565i | ||||||
\(923\) | 1.37565e8i | 0.174945i | ||||||||
\(924\) | 4.07070e8 | 0.516005 | ||||||||
\(925\) | − | 6.93194e6i | − | 0.00875849i | ||||||
\(926\) | −1.39485e9 | −1.75669 | ||||||||
\(927\) | 1.57880e9 | 1.98193 | ||||||||
\(928\) | 1.25711e9 | 1.57301 | ||||||||
\(929\) | − | 1.02715e9i | − | 1.28111i | −0.767911 | − | 0.640557i | \(-0.778704\pi\) | ||
0.767911 | − | 0.640557i | \(-0.221296\pi\) | |||||||
\(930\) | 1.44200e9i | 1.79274i | ||||||||
\(931\) | 6.91536e8i | 0.856971i | ||||||||
\(932\) | − | 1.33855e9i | − | 1.65344i | ||||||
\(933\) | − | 1.84752e9i | − | 2.27480i | ||||||
\(934\) | 1.25889e9 | 1.54507 | ||||||||
\(935\) | 1.51006e8i | 0.184739i | ||||||||
\(936\) | − | 4.62236e7i | − | 0.0563685i | ||||||
\(937\) | 7.28893e8i | 0.886023i | 0.896516 | + | 0.443012i | \(0.146090\pi\) | ||||
−0.896516 | + | 0.443012i | \(0.853910\pi\) | |||||||
\(938\) | −1.53450e8 | −0.185934 | ||||||||
\(939\) | 8.28821e8 | 1.00107 | ||||||||
\(940\) | 1.46347e8i | 0.176198i | ||||||||
\(941\) | −1.27276e9 | −1.52749 | −0.763745 | − | 0.645518i | \(-0.776642\pi\) | ||||
−0.763745 | + | 0.645518i | \(0.776642\pi\) | |||||||
\(942\) | 2.33147e9i | 2.78918i | ||||||||
\(943\) | 1.53078e9 | 1.82548 | ||||||||
\(944\) | −4.54110e8 | −0.539815 | ||||||||
\(945\) | − | 6.16489e7i | − | 0.0730516i | ||||||
\(946\) | −8.79254e8 | − | 2.24540e9i | −1.03858 | − | 2.65229i | ||||
\(947\) | 1.42519e9 | 1.67812 | 0.839062 | − | 0.544037i | \(-0.183105\pi\) | ||||
0.839062 | + | 0.544037i | \(0.183105\pi\) | |||||||
\(948\) | − | 9.39894e8i | − | 1.10320i | ||||||
\(949\) | 8.44043e7i | 0.0987565i | ||||||||
\(950\) | −2.28313e8 | −0.266293 | ||||||||
\(951\) | 9.79985e8i | 1.13940i | ||||||||
\(952\) | −4.37691e6 | −0.00507290 | ||||||||
\(953\) | 8.71160e8i | 1.00651i | 0.864137 | + | 0.503257i | \(0.167865\pi\) | ||||
−0.864137 | + | 0.503257i | \(0.832135\pi\) | |||||||
\(954\) | 9.57465e8i | 1.10275i | ||||||||
\(955\) | −1.19471e9 | −1.37167 | ||||||||
\(956\) | 8.03928e8 | 0.920118 | ||||||||
\(957\) | −2.86162e9 | −3.26495 | ||||||||
\(958\) | 3.02408e8i | 0.343951i | ||||||||
\(959\) | −5.93407e6 | −0.00672817 | ||||||||
\(960\) | 1.67540e9 | 1.89367 | ||||||||
\(961\) | −2.05718e8 | −0.231794 | ||||||||
\(962\) | −7.18331e6 | −0.00806862 | ||||||||
\(963\) | −1.41007e9 | −1.57893 | ||||||||
\(964\) | 9.92515e7i | 0.110791i | ||||||||
\(965\) | 4.49679e8i | 0.500404i | ||||||||
\(966\) | − | 4.52313e8i | − | 0.501773i | ||||||
\(967\) | 7.72698e6 | 0.00854536 | 0.00427268 | − | 0.999991i | \(-0.498640\pi\) | ||||
0.00427268 | + | 0.999991i | \(0.498640\pi\) | |||||||
\(968\) | − | 7.84806e8i | − | 0.865239i | ||||||
\(969\) | −1.32742e8 | −0.145893 | ||||||||
\(970\) | 3.87325e8 | 0.424385 | ||||||||
\(971\) | 1.09201e9 | 1.19280 | 0.596399 | − | 0.802688i | \(-0.296598\pi\) | ||||
0.596399 | + | 0.802688i | \(0.296598\pi\) | |||||||
\(972\) | − | 1.48713e9i | − | 1.61938i | ||||||
\(973\) | − | 1.38345e8i | − | 0.150184i | ||||||
\(974\) | 2.88205e8i | 0.311907i | ||||||||
\(975\) | 3.68336e7i | 0.0397402i | ||||||||
\(976\) | − | 1.04573e9i | − | 1.12479i | ||||||
\(977\) | 9.17565e8 | 0.983905 | 0.491952 | − | 0.870622i | \(-0.336283\pi\) | ||||
0.491952 | + | 0.870622i | \(0.336283\pi\) | |||||||
\(978\) | 3.43760e9i | 3.67485i | ||||||||
\(979\) | − | 3.26116e9i | − | 3.47556i | ||||||
\(980\) | − | 1.00195e9i | − | 1.06456i | ||||||
\(981\) | 7.37800e8 | 0.781505 | ||||||||
\(982\) | 4.89585e8 | 0.517003 | ||||||||
\(983\) | 1.28685e8i | 0.135477i | 0.997703 | + | 0.0677387i | \(0.0215784\pi\) | ||||
−0.997703 | + | 0.0677387i | \(0.978422\pi\) | |||||||
\(984\) | 5.73122e8 | 0.601536 | ||||||||
\(985\) | − | 6.36499e8i | − | 0.666023i | ||||||
\(986\) | 1.71500e8 | 0.178909 | ||||||||
\(987\) | −3.45086e7 | −0.0358902 | ||||||||
\(988\) | 1.29953e8i | 0.134746i | ||||||||
\(989\) | −1.37041e9 | + | 5.36626e8i | −1.41665 | + | 0.554731i | ||||
\(990\) | −3.37717e9 | −3.48055 | ||||||||
\(991\) | 6.68907e8i | 0.687298i | 0.939098 | + | 0.343649i | \(0.111663\pi\) | ||||
−0.939098 | + | 0.343649i | \(0.888337\pi\) | |||||||
\(992\) | − | 1.21351e9i | − | 1.24311i | ||||||
\(993\) | −1.89327e9 | −1.93359 | ||||||||
\(994\) | 2.91319e8i | 0.296626i | ||||||||
\(995\) | −9.38807e8 | −0.953031 | ||||||||
\(996\) | 1.41264e9i | 1.42973i | ||||||||
\(997\) | − | 4.51285e8i | − | 0.455371i | −0.973735 | − | 0.227685i | \(-0.926884\pi\) | ||
0.973735 | − | 0.227685i | \(-0.0731157\pi\) | |||||||
\(998\) | −8.29857e8 | −0.834856 | ||||||||
\(999\) | 2.43359e7 | 0.0244090 |
(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 | 43.7.b.b.42.17 | yes | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.4 | ✓ | 20 | 43.42 | odd | 2 | inner | |
43.7.b.b.42.17 | yes | 20 | 1.1 | even | 1 | trivial |