Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(-2.35727 + 1.36097i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.e.493.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0.965926 | − | 2.46313i | 0.365086 | − | 0.930974i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.92471 | + | 3.33369i | 0.580321 | + | 1.00514i | 0.995441 | + | 0.0953782i | \(0.0304061\pi\) |
−0.415121 | + | 0.909766i | \(0.636261\pi\) | |||||||
\(12\) | 0.258819 | + | 0.965926i | 0.0747146 | + | 0.278839i | ||||
\(13\) | −4.42535 | − | 4.42535i | −1.22737 | − | 1.22737i | −0.964954 | − | 0.262417i | \(-0.915480\pi\) |
−0.262417 | − | 0.964954i | \(-0.584520\pi\) | |||||||
\(14\) | −0.295509 | + | 2.62920i | −0.0789781 | + | 0.702682i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −1.36097 | − | 0.364671i | −0.330084 | − | 0.0884458i | 0.0899709 | − | 0.995944i | \(-0.471323\pi\) |
−0.420055 | + | 0.907499i | \(0.637989\pi\) | |||||||
\(18\) | 0.965926 | + | 0.258819i | 0.227671 | + | 0.0610042i | ||||
\(19\) | 1.76317 | − | 3.05390i | 0.404499 | − | 0.700613i | −0.589764 | − | 0.807576i | \(-0.700779\pi\) |
0.994263 | + | 0.106963i | \(0.0341125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.12920 | + | 1.57052i | 0.464629 | + | 0.342715i | ||||
\(22\) | −2.72194 | − | 2.72194i | −0.580321 | − | 0.580321i | ||||
\(23\) | −0.364671 | − | 1.36097i | −0.0760392 | − | 0.283782i | 0.917428 | − | 0.397903i | \(-0.130262\pi\) |
−0.993467 | + | 0.114120i | \(0.963595\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.41993 | + | 3.12920i | 1.06294 | + | 0.613686i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −0.395046 | − | 2.61609i | −0.0746568 | − | 0.494395i | ||||
\(29\) | − | 6.66738i | − | 1.23810i | −0.785351 | − | 0.619050i | \(-0.787518\pi\) | ||
0.785351 | − | 0.619050i | \(-0.212482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.55390 | + | 2.62920i | −0.817905 | + | 0.472218i | −0.849693 | − | 0.527277i | \(-0.823213\pi\) |
0.0317885 | + | 0.999495i | \(0.489880\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −3.71825 | + | 0.996301i | −0.647263 | + | 0.173434i | ||||
\(34\) | 1.40898 | 0.241638 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −9.82586 | + | 2.63283i | −1.61536 | + | 0.432835i | −0.949634 | − | 0.313360i | \(-0.898545\pi\) |
−0.665727 | + | 0.746195i | \(0.731879\pi\) | |||||||
\(38\) | −0.912685 | + | 3.40619i | −0.148057 | + | 0.552556i | ||||
\(39\) | 5.41993 | − | 3.12920i | 0.867883 | − | 0.501072i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.741607i | − | 0.115820i | −0.998322 | − | 0.0579098i | \(-0.981556\pi\) | ||
0.998322 | − | 0.0579098i | \(-0.0184436\pi\) | |||||||
\(42\) | −2.46313 | − | 0.965926i | −0.380069 | − | 0.149046i | ||||
\(43\) | −1.52070 | + | 1.52070i | −0.231904 | + | 0.231904i | −0.813487 | − | 0.581583i | \(-0.802434\pi\) |
0.581583 | + | 0.813487i | \(0.302434\pi\) | |||||||
\(44\) | 3.33369 | + | 1.92471i | 0.502572 | + | 0.290160i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.704491 | + | 1.22021i | 0.103872 | + | 0.179911i | ||||
\(47\) | −1.36097 | − | 5.07922i | −0.198518 | − | 0.740880i | −0.991328 | − | 0.131411i | \(-0.958049\pi\) |
0.792810 | − | 0.609469i | \(-0.208617\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | −5.13397 | − | 4.75839i | −0.733425 | − | 0.679770i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.704491 | − | 1.22021i | 0.0986485 | − | 0.170864i | ||||
\(52\) | −6.04514 | − | 1.61979i | −0.838311 | − | 0.224625i | ||||
\(53\) | 9.51380 | + | 2.54922i | 1.30682 | + | 0.350162i | 0.844025 | − | 0.536303i | \(-0.180180\pi\) |
0.462796 | + | 0.886465i | \(0.346846\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.05868 | + | 2.42471i | 0.141472 | + | 0.324015i | ||||
\(57\) | 2.49350 | + | 2.49350i | 0.330272 | + | 0.330272i | ||||
\(58\) | 1.72564 | + | 6.44019i | 0.226588 | + | 0.845638i | ||||
\(59\) | −6.84941 | − | 11.8635i | −0.891717 | − | 1.54450i | −0.837815 | − | 0.545954i | \(-0.816168\pi\) |
−0.0539019 | − | 0.998546i | \(-0.517166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.857750 | − | 0.495222i | −0.109824 | − | 0.0634067i | 0.444082 | − | 0.895986i | \(-0.353530\pi\) |
−0.553906 | + | 0.832579i | \(0.686863\pi\) | |||||||
\(62\) | 3.71825 | − | 3.71825i | 0.472218 | − | 0.472218i | ||||
\(63\) | −2.06808 | + | 1.65017i | −0.260553 | + | 0.207901i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.33369 | − | 1.92471i | 0.410349 | − | 0.236915i | ||||
\(67\) | 1.98199 | − | 7.39689i | 0.242139 | − | 0.903673i | −0.732662 | − | 0.680593i | \(-0.761722\pi\) |
0.974800 | − | 0.223080i | \(-0.0716112\pi\) | |||||||
\(68\) | −1.36097 | + | 0.364671i | −0.165042 | + | 0.0442229i | ||||
\(69\) | 1.40898 | 0.169622 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2584 | 1.33613 | 0.668063 | − | 0.744105i | \(-0.267124\pi\) | ||||
0.668063 | + | 0.744105i | \(0.267124\pi\) | |||||||
\(72\) | 0.965926 | − | 0.258819i | 0.113835 | − | 0.0305021i | ||||
\(73\) | 2.75660 | − | 10.2878i | 0.322636 | − | 1.20409i | −0.594031 | − | 0.804442i | \(-0.702464\pi\) |
0.916667 | − | 0.399652i | \(-0.130869\pi\) | |||||||
\(74\) | 8.80963 | − | 5.08624i | 1.02410 | − | 0.591263i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.52634i | − | 0.404499i | ||||||
\(77\) | 10.0704 | − | 1.52070i | 1.14763 | − | 0.173299i | ||||
\(78\) | −4.42535 | + | 4.42535i | −0.501072 | + | 0.501072i | ||||
\(79\) | −2.72849 | − | 1.57529i | −0.306979 | − | 0.177234i | 0.338595 | − | 0.940932i | \(-0.390048\pi\) |
−0.645574 | + | 0.763698i | \(0.723382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.191942 | + | 0.716337i | 0.0211964 | + | 0.0791062i | ||||
\(83\) | 0.471906 | + | 0.471906i | 0.0517984 | + | 0.0517984i | 0.732532 | − | 0.680733i | \(-0.238339\pi\) |
−0.680733 | + | 0.732532i | \(0.738339\pi\) | |||||||
\(84\) | 2.62920 | + | 0.295509i | 0.286869 | + | 0.0322427i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.07529 | − | 1.86246i | 0.115952 | − | 0.200835i | ||||
\(87\) | 6.44019 | + | 1.72564i | 0.690461 | + | 0.185008i | ||||
\(88\) | −3.71825 | − | 0.996301i | −0.396366 | − | 0.106206i | ||||
\(89\) | −6.97594 | + | 12.0827i | −0.739448 | + | 1.28076i | 0.213296 | + | 0.976988i | \(0.431580\pi\) |
−0.952744 | + | 0.303774i | \(0.901753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.1748 | + | 6.62564i | −1.59075 | + | 0.694555i | ||||
\(92\) | −0.996301 | − | 0.996301i | −0.103872 | − | 0.103872i | ||||
\(93\) | −1.36097 | − | 5.07922i | −0.141126 | − | 0.526690i | ||||
\(94\) | 2.62920 | + | 4.55390i | 0.271181 | + | 0.469699i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 6.98682 | − | 6.98682i | 0.709404 | − | 0.709404i | −0.257006 | − | 0.966410i | \(-0.582736\pi\) |
0.966410 | + | 0.257006i | \(0.0827359\pi\) | |||||||
\(98\) | 6.19060 | + | 3.26748i | 0.625345 | + | 0.330066i | ||||
\(99\) | − | 3.84941i | − | 0.386880i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4415 | − | 7.18310i | 1.23797 | − | 0.714745i | 0.269295 | − | 0.963058i | \(-0.413209\pi\) |
0.968680 | + | 0.248313i | \(0.0798761\pi\) | |||||||
\(102\) | −0.364671 | + | 1.36097i | −0.0361079 | + | 0.134756i | ||||
\(103\) | 14.8426 | − | 3.97706i | 1.46249 | − | 0.391872i | 0.562138 | − | 0.827043i | \(-0.309979\pi\) |
0.900348 | + | 0.435172i | \(0.143312\pi\) | |||||||
\(104\) | 6.25839 | 0.613686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.84941 | −0.956659 | ||||||||
\(107\) | −2.60170 | + | 0.697125i | −0.251516 | + | 0.0673936i | −0.382374 | − | 0.924008i | \(-0.624893\pi\) |
0.130858 | + | 0.991401i | \(0.458227\pi\) | |||||||
\(108\) | 0.258819 | − | 0.965926i | 0.0249049 | − | 0.0929463i | ||||
\(109\) | 14.5503 | − | 8.40064i | 1.39367 | − | 0.804636i | 0.399951 | − | 0.916537i | \(-0.369027\pi\) |
0.993719 | + | 0.111901i | \(0.0356939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 10.1725i | − | 0.965529i | ||||||
\(112\) | −1.65017 | − | 2.06808i | −0.155926 | − | 0.195415i | ||||
\(113\) | −10.2109 | + | 10.2109i | −0.960563 | + | 0.960563i | −0.999251 | − | 0.0386883i | \(-0.987682\pi\) |
0.0386883 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(114\) | −3.05390 | − | 1.76317i | −0.286024 | − | 0.165136i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.33369 | − | 5.77412i | −0.309525 | − | 0.536113i | ||||
\(117\) | 1.61979 | + | 6.04514i | 0.149750 | + | 0.558874i | ||||
\(118\) | 9.68653 | + | 9.68653i | 0.891717 | + | 0.891717i | ||||
\(119\) | −2.21283 | + | 3.00000i | −0.202850 | + | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.90898 | + | 3.30645i | −0.173544 | + | 0.300587i | ||||
\(122\) | 0.956695 | + | 0.256346i | 0.0866151 | + | 0.0232085i | ||||
\(123\) | 0.716337 | + | 0.191942i | 0.0645900 | + | 0.0173068i | ||||
\(124\) | −2.62920 | + | 4.55390i | −0.236109 | + | 0.408952i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.57052 | − | 2.12920i | 0.139913 | − | 0.189684i | ||||
\(127\) | −14.5565 | − | 14.5565i | −1.29168 | − | 1.29168i | −0.933746 | − | 0.357936i | \(-0.883481\pi\) |
−0.357936 | − | 0.933746i | \(-0.616519\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −1.07529 | − | 1.86246i | −0.0946744 | − | 0.163981i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.66631 | − | 3.27145i | −0.495068 | − | 0.285828i | 0.231607 | − | 0.972810i | \(-0.425602\pi\) |
−0.726675 | + | 0.686982i | \(0.758935\pi\) | |||||||
\(132\) | −2.72194 | + | 2.72194i | −0.236915 | + | 0.236915i | ||||
\(133\) | −5.81905 | − | 7.29275i | −0.504576 | − | 0.632362i | ||||
\(134\) | 7.65782i | 0.661535i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.22021 | − | 0.704491i | 0.104633 | − | 0.0604096i | ||||
\(137\) | −2.94610 | + | 10.9950i | −0.251703 | + | 0.939367i | 0.718192 | + | 0.695845i | \(0.244970\pi\) |
−0.969895 | + | 0.243523i | \(0.921697\pi\) | |||||||
\(138\) | −1.36097 | + | 0.364671i | −0.115854 | + | 0.0310429i | ||||
\(139\) | 3.50510 | 0.297299 | 0.148650 | − | 0.988890i | \(-0.452507\pi\) | ||||
0.148650 | + | 0.988890i | \(0.452507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.25839 | 0.442837 | ||||||||
\(142\) | −10.8748 | + | 2.91389i | −0.912591 | + | 0.244528i | ||||
\(143\) | 6.23524 | − | 23.2702i | 0.521417 | − | 1.94596i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.6507i | 0.881458i | ||||||||
\(147\) | 5.92503 | − | 3.72748i | 0.488688 | − | 0.307437i | ||||
\(148\) | −7.19303 | + | 7.19303i | −0.591263 | + | 0.591263i | ||||
\(149\) | −11.9713 | − | 6.91165i | −0.980730 | − | 0.566225i | −0.0782393 | − | 0.996935i | \(-0.524930\pi\) |
−0.902490 | + | 0.430710i | \(0.858263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.97861 | − | 5.15910i | −0.242396 | − | 0.419842i | 0.719001 | − | 0.695010i | \(-0.244600\pi\) |
−0.961396 | + | 0.275168i | \(0.911267\pi\) | |||||||
\(152\) | 0.912685 | + | 3.40619i | 0.0740285 | + | 0.276278i | ||||
\(153\) | 0.996301 | + | 0.996301i | 0.0805462 | + | 0.0805462i | ||||
\(154\) | −9.33369 | + | 4.07529i | −0.752130 | + | 0.328397i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.12920 | − | 5.41993i | 0.250536 | − | 0.433941i | ||||
\(157\) | 9.64315 | + | 2.58387i | 0.769607 | + | 0.206216i | 0.622198 | − | 0.782860i | \(-0.286240\pi\) |
0.147409 | + | 0.989076i | \(0.452907\pi\) | |||||||
\(158\) | 3.04324 | + | 0.815432i | 0.242107 | + | 0.0648723i | ||||
\(159\) | −4.92471 | + | 8.52984i | −0.390555 | + | 0.676460i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.70449 | − | 0.416367i | −0.291955 | − | 0.0328143i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −0.356071 | − | 1.32888i | −0.0278896 | − | 0.104086i | 0.950578 | − | 0.310486i | \(-0.100492\pi\) |
−0.978468 | + | 0.206400i | \(0.933825\pi\) | |||||||
\(164\) | −0.370803 | − | 0.642250i | −0.0289549 | − | 0.0501513i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.577964 | − | 0.333688i | −0.0448587 | − | 0.0258992i | ||||
\(167\) | −7.69393 | + | 7.69393i | −0.595374 | + | 0.595374i | −0.939078 | − | 0.343704i | \(-0.888318\pi\) |
0.343704 | + | 0.939078i | \(0.388318\pi\) | |||||||
\(168\) | −2.61609 | + | 0.395046i | −0.201836 | + | 0.0304785i | ||||
\(169\) | 26.1675i | 2.01288i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.05390 | + | 1.76317i | −0.233538 | + | 0.134833i | ||||
\(172\) | −0.556613 | + | 2.07731i | −0.0424414 | + | 0.158393i | ||||
\(173\) | −1.64094 | + | 0.439687i | −0.124758 | + | 0.0334288i | −0.320658 | − | 0.947195i | \(-0.603904\pi\) |
0.195900 | + | 0.980624i | \(0.437237\pi\) | |||||||
\(174\) | −6.66738 | −0.505452 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.84941 | 0.290160 | ||||||||
\(177\) | 13.2320 | − | 3.54552i | 0.994581 | − | 0.266497i | ||||
\(178\) | 3.61101 | − | 13.4765i | 0.270657 | − | 1.01010i | ||||
\(179\) | −11.9713 | + | 6.91165i | −0.894779 | + | 0.516601i | −0.875503 | − | 0.483213i | \(-0.839470\pi\) |
−0.0192766 | + | 0.999814i | \(0.506136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.36086i | − | 0.249811i | −0.992169 | − | 0.124905i | \(-0.960137\pi\) | ||
0.992169 | − | 0.124905i | \(-0.0398627\pi\) | |||||||
\(182\) | 12.9429 | − | 10.3274i | 0.959388 | − | 0.765517i | ||||
\(183\) | 0.700350 | − | 0.700350i | 0.0517713 | − | 0.0517713i | ||||
\(184\) | 1.22021 | + | 0.704491i | 0.0899554 | + | 0.0519358i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.62920 | + | 4.55390i | 0.192782 | + | 0.333908i | ||||
\(187\) | −1.40377 | − | 5.23894i | −0.102654 | − | 0.383109i | ||||
\(188\) | −3.71825 | − | 3.71825i | −0.271181 | − | 0.271181i | ||||
\(189\) | −1.05868 | − | 2.42471i | −0.0770076 | − | 0.176371i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.370803 | + | 0.642250i | −0.0268304 | + | 0.0464716i | −0.879129 | − | 0.476584i | \(-0.841875\pi\) |
0.852298 | + | 0.523056i | \(0.175208\pi\) | |||||||
\(192\) | 0.965926 | + | 0.258819i | 0.0697097 | + | 0.0186787i | ||||
\(193\) | 7.15653 | + | 1.91759i | 0.515138 | + | 0.138031i | 0.507017 | − | 0.861936i | \(-0.330748\pi\) |
0.00812132 | + | 0.999967i | \(0.497415\pi\) | |||||||
\(194\) | −4.94043 | + | 8.55707i | −0.354702 | + | 0.614362i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.82535 | − | 1.55390i | −0.487525 | − | 0.110993i | ||||
\(197\) | 12.5349 | + | 12.5349i | 0.893076 | + | 0.893076i | 0.994811 | − | 0.101735i | \(-0.0324395\pi\) |
−0.101735 | + | 0.994811i | \(0.532439\pi\) | |||||||
\(198\) | 0.996301 | + | 3.71825i | 0.0708040 | + | 0.264244i | ||||
\(199\) | −0.350302 | − | 0.606741i | −0.0248323 | − | 0.0430107i | 0.853342 | − | 0.521351i | \(-0.174572\pi\) |
−0.878174 | + | 0.478340i | \(0.841238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.63187 | + | 3.82891i | 0.467776 | + | 0.270070i | ||||
\(202\) | −10.1584 | + | 10.1584i | −0.714745 | + | 0.714745i | ||||
\(203\) | −16.4226 | − | 6.44019i | −1.15264 | − | 0.452013i | ||||
\(204\) | − | 1.40898i | − | 0.0986485i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.3075 | + | 7.68310i | −0.927179 | + | 0.535307i | ||||
\(207\) | −0.364671 | + | 1.36097i | −0.0253464 | + | 0.0945941i | ||||
\(208\) | −6.04514 | + | 1.61979i | −0.419155 | + | 0.112312i | ||||
\(209\) | 13.5743 | 0.938957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4426 | −1.06311 | −0.531555 | − | 0.847024i | \(-0.678392\pi\) | ||||
−0.531555 | + | 0.847024i | \(0.678392\pi\) | |||||||
\(212\) | 9.51380 | − | 2.54922i | 0.653410 | − | 0.175081i | ||||
\(213\) | −2.91389 | + | 10.8748i | −0.199656 | + | 0.745127i | ||||
\(214\) | 2.33262 | − | 1.34674i | 0.159455 | − | 0.0920614i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 2.07731 | + | 13.7564i | 0.141017 | + | 0.933848i | ||||
\(218\) | −11.8803 | + | 11.8803i | −0.804636 | + | 0.804636i | ||||
\(219\) | 9.22377 | + | 5.32535i | 0.623285 | + | 0.359854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.40898 | + | 7.63658i | 0.296580 | + | 0.513692i | ||||
\(222\) | 2.63283 | + | 9.82586i | 0.176704 | + | 0.659469i | ||||
\(223\) | 1.17901 | + | 1.17901i | 0.0789525 | + | 0.0789525i | 0.745480 | − | 0.666528i | \(-0.232220\pi\) |
−0.666528 | + | 0.745480i | \(0.732220\pi\) | |||||||
\(224\) | 2.12920 | + | 1.57052i | 0.142263 | + | 0.104935i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.22021 | − | 12.5058i | 0.480282 | − | 0.831872i | ||||
\(227\) | 11.1192 | + | 2.97938i | 0.738008 | + | 0.197749i | 0.608192 | − | 0.793790i | \(-0.291895\pi\) |
0.129815 | + | 0.991538i | \(0.458562\pi\) | |||||||
\(228\) | 3.40619 | + | 0.912685i | 0.225580 | + | 0.0604440i | ||||
\(229\) | −7.80873 | + | 13.5251i | −0.516016 | + | 0.893765i | 0.483811 | + | 0.875172i | \(0.339252\pi\) |
−0.999827 | + | 0.0185931i | \(0.994081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.13754 | + | 10.1209i | −0.0748443 | + | 0.665904i | ||||
\(232\) | 4.71455 | + | 4.71455i | 0.309525 | + | 0.309525i | ||||
\(233\) | 7.69393 | + | 28.7141i | 0.504046 | + | 1.88113i | 0.471920 | + | 0.881641i | \(0.343561\pi\) |
0.0321261 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(234\) | −3.12920 | − | 5.41993i | −0.204562 | − | 0.354312i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.8635 | − | 6.84941i | −0.772250 | − | 0.445859i | ||||
\(237\) | 2.22780 | − | 2.22780i | 0.144711 | − | 0.144711i | ||||
\(238\) | 1.36097 | − | 3.47050i | 0.0882187 | − | 0.224959i | ||||
\(239\) | 7.95188i | 0.514364i | 0.966363 | + | 0.257182i | \(0.0827940\pi\) | ||||
−0.966363 | + | 0.257182i | \(0.917206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.81069 | + | 5.66420i | −0.631962 | + | 0.364863i | −0.781512 | − | 0.623891i | \(-0.785551\pi\) |
0.149550 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(242\) | 0.988162 | − | 3.68787i | 0.0635215 | − | 0.237065i | ||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | −0.990444 | −0.0634067 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.741607 | −0.0472831 | ||||||||
\(247\) | −21.3172 | + | 5.71194i | −1.35638 | + | 0.363442i | ||||
\(248\) | 1.36097 | − | 5.07922i | 0.0864218 | − | 0.322531i | ||||
\(249\) | −0.577964 | + | 0.333688i | −0.0366270 | + | 0.0211466i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.0336i | − | 1.32763i | −0.747898 | − | 0.663814i | \(-0.768937\pi\) | ||
0.747898 | − | 0.663814i | \(-0.231063\pi\) | |||||||
\(252\) | −0.965926 | + | 2.46313i | −0.0608476 | + | 0.155162i | ||||
\(253\) | 3.83517 | − | 3.83517i | 0.241115 | − | 0.241115i | ||||
\(254\) | 17.8280 | + | 10.2930i | 1.11863 | + | 0.645841i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.70715 | + | 25.0314i | 0.418380 | + | 1.56142i | 0.777967 | + | 0.628305i | \(0.216251\pi\) |
−0.359587 | + | 0.933112i | \(0.617082\pi\) | |||||||
\(258\) | 1.52070 | + | 1.52070i | 0.0946744 | + | 0.0946744i | ||||
\(259\) | −3.00606 | + | 26.7454i | −0.186787 | + | 1.66188i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.33369 | + | 5.77412i | −0.206350 | + | 0.357409i | ||||
\(262\) | 6.31995 | + | 1.69343i | 0.390448 | + | 0.104620i | ||||
\(263\) | 16.0257 | + | 4.29407i | 0.988187 | + | 0.264784i | 0.716489 | − | 0.697599i | \(-0.245748\pi\) |
0.271698 | + | 0.962383i | \(0.412415\pi\) | |||||||
\(264\) | 1.92471 | − | 3.33369i | 0.118457 | − | 0.205174i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.50828 | + | 5.53818i | 0.460362 | + | 0.339568i | ||||
\(267\) | −9.86547 | − | 9.86547i | −0.603757 | − | 0.603757i | ||||
\(268\) | −1.98199 | − | 7.39689i | −0.121069 | − | 0.451837i | ||||
\(269\) | −13.6804 | − | 23.6952i | −0.834110 | − | 1.44472i | −0.894753 | − | 0.446562i | \(-0.852648\pi\) |
0.0606421 | − | 0.998160i | \(-0.480685\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.828972 | − | 0.478607i | −0.0503565 | − | 0.0290733i | 0.474610 | − | 0.880196i | \(-0.342589\pi\) |
−0.524967 | + | 0.851123i | \(0.675922\pi\) | |||||||
\(272\) | −0.996301 | + | 0.996301i | −0.0604096 | + | 0.0604096i | ||||
\(273\) | −2.47236 | − | 16.3725i | −0.149634 | − | 0.990911i | ||||
\(274\) | − | 11.3829i | − | 0.687665i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.22021 | − | 0.704491i | 0.0734483 | − | 0.0424054i | ||||
\(277\) | −5.38699 | + | 20.1045i | −0.323673 | + | 1.20796i | 0.591966 | + | 0.805963i | \(0.298352\pi\) |
−0.915639 | + | 0.402001i | \(0.868315\pi\) | |||||||
\(278\) | −3.38567 | + | 0.907188i | −0.203059 | + | 0.0544095i | ||||
\(279\) | 5.25839 | 0.314812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.89220 | 0.172534 | 0.0862670 | − | 0.996272i | \(-0.472506\pi\) | ||||
0.0862670 | + | 0.996272i | \(0.472506\pi\) | |||||||
\(282\) | −5.07922 | + | 1.36097i | −0.302463 | + | 0.0810447i | ||||
\(283\) | 5.48531 | − | 20.4714i | 0.326068 | − | 1.21690i | −0.587167 | − | 0.809466i | \(-0.699757\pi\) |
0.913234 | − | 0.407435i | \(-0.133577\pi\) | |||||||
\(284\) | 9.75005 | − | 5.62920i | 0.578559 | − | 0.334031i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0911i | 1.42454i | ||||||||
\(287\) | −1.82667 | − | 0.716337i | −0.107825 | − | 0.0422841i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | −13.0032 | − | 7.50738i | −0.764892 | − | 0.441611i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.94043 | + | 8.55707i | 0.289613 | + | 0.501625i | ||||
\(292\) | −2.75660 | − | 10.2878i | −0.161318 | − | 0.602047i | ||||
\(293\) | −14.1436 | − | 14.1436i | −0.826280 | − | 0.826280i | 0.160720 | − | 0.987000i | \(-0.448618\pi\) |
−0.987000 | + | 0.160720i | \(0.948618\pi\) | |||||||
\(294\) | −4.75839 | + | 5.13397i | −0.277515 | + | 0.299419i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.08624 | − | 8.80963i | 0.295632 | − | 0.512049i | ||||
\(297\) | 3.71825 | + | 0.996301i | 0.215754 | + | 0.0578112i | ||||
\(298\) | 13.3523 | + | 3.57773i | 0.773477 | + | 0.207253i | ||||
\(299\) | −4.40898 | + | 7.63658i | −0.254978 | + | 0.441635i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.27679 | + | 5.21455i | 0.131232 | + | 0.300561i | ||||
\(302\) | 4.21239 | + | 4.21239i | 0.242396 | + | 0.242396i | ||||
\(303\) | 3.71825 | + | 13.8767i | 0.213608 | + | 0.797194i | ||||
\(304\) | −1.76317 | − | 3.05390i | −0.101125 | − | 0.175153i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.22021 | − | 0.704491i | −0.0697550 | − | 0.0402731i | ||||
\(307\) | 6.81363 | − | 6.81363i | 0.388874 | − | 0.388874i | −0.485411 | − | 0.874286i | \(-0.661330\pi\) |
0.874286 | + | 0.485411i | \(0.161330\pi\) | |||||||
\(308\) | 7.96089 | − | 6.35217i | 0.453614 | − | 0.361948i | ||||
\(309\) | 15.3662i | 0.874152i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8568 | + | 10.3096i | −1.01257 | + | 0.584605i | −0.911942 | − | 0.410319i | \(-0.865417\pi\) |
−0.100624 | + | 0.994925i | \(0.532084\pi\) | |||||||
\(312\) | −1.61979 | + | 6.04514i | −0.0917026 | + | 0.342239i | ||||
\(313\) | −15.9075 | + | 4.26240i | −0.899145 | + | 0.240925i | −0.678649 | − | 0.734463i | \(-0.737434\pi\) |
−0.220496 | + | 0.975388i | \(0.570768\pi\) | |||||||
\(314\) | −9.98332 | −0.563391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.15059 | −0.177234 | ||||||||
\(317\) | −25.6761 | + | 6.87988i | −1.44211 | + | 0.386412i | −0.893272 | − | 0.449516i | \(-0.851596\pi\) |
−0.548838 | + | 0.835928i | \(0.684930\pi\) | |||||||
\(318\) | 2.54922 | − | 9.51380i | 0.142953 | − | 0.533507i | ||||
\(319\) | 22.2269 | − | 12.8327i | 1.24447 | − | 0.718495i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.69348i | − | 0.150336i | ||||||
\(322\) | 3.68603 | − | 0.556613i | 0.205414 | − | 0.0310189i | ||||
\(323\) | −3.51330 | + | 3.51330i | −0.195485 | + | 0.195485i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.687877 | + | 1.19144i | 0.0380980 | + | 0.0659876i | ||||
\(327\) | 4.34849 | + | 16.2288i | 0.240472 | + | 0.897455i | ||||
\(328\) | 0.524395 | + | 0.524395i | 0.0289549 | + | 0.0289549i | ||||
\(329\) | −13.8253 | − | 1.55390i | −0.762216 | − | 0.0856694i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.37347 | + | 5.84303i | −0.185423 | + | 0.321162i | −0.943719 | − | 0.330749i | \(-0.892699\pi\) |
0.758296 | + | 0.651910i | \(0.226032\pi\) | |||||||
\(332\) | 0.644635 | + | 0.172729i | 0.0353789 | + | 0.00947976i | ||||
\(333\) | 9.82586 | + | 2.63283i | 0.538454 | + | 0.144278i | ||||
\(334\) | 5.44043 | − | 9.42310i | 0.297687 | − | 0.515609i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.42471 | − | 1.05868i | 0.132279 | − | 0.0577557i | ||||
\(337\) | 2.19755 | + | 2.19755i | 0.119708 | + | 0.119708i | 0.764423 | − | 0.644715i | \(-0.223024\pi\) |
−0.644715 | + | 0.764423i | \(0.723024\pi\) | |||||||
\(338\) | −6.77264 | − | 25.2758i | −0.368383 | − | 1.37482i | ||||
\(339\) | −7.22021 | − | 12.5058i | −0.392148 | − | 0.679221i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5298 | − | 10.1209i | −0.949294 | − | 0.548075i | ||||
\(342\) | 2.49350 | − | 2.49350i | 0.134833 | − | 0.134833i | ||||
\(343\) | −16.6796 | + | 8.04937i | −0.900611 | + | 0.434625i | ||||
\(344\) | − | 2.15059i | − | 0.115952i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47122 | − | 0.849411i | 0.0790934 | − | 0.0456646i | ||||
\(347\) | 3.42859 | − | 12.7957i | 0.184056 | − | 0.686908i | −0.810774 | − | 0.585359i | \(-0.800954\pi\) |
0.994831 | − | 0.101549i | \(-0.0323798\pi\) | |||||||
\(348\) | 6.44019 | − | 1.72564i | 0.345230 | − | 0.0925042i | ||||
\(349\) | 18.1788 | 0.973090 | 0.486545 | − | 0.873655i | \(-0.338257\pi\) | ||||
0.486545 | + | 0.873655i | \(0.338257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.25839 | −0.334048 | ||||||||
\(352\) | −3.71825 | + | 0.996301i | −0.198183 | + | 0.0531030i | ||||
\(353\) | −5.64535 | + | 21.0687i | −0.300472 | + | 1.12138i | 0.636302 | + | 0.771440i | \(0.280463\pi\) |
−0.936774 | + | 0.349936i | \(0.886203\pi\) | |||||||
\(354\) | −11.8635 | + | 6.84941i | −0.630539 | + | 0.364042i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.9519i | 0.739448i | ||||||||
\(357\) | −2.32505 | − | 2.91389i | −0.123055 | − | 0.154219i | ||||
\(358\) | 9.77455 | − | 9.77455i | 0.516601 | − | 0.516601i | ||||
\(359\) | 24.7752 | + | 14.3040i | 1.30758 | + | 0.754934i | 0.981692 | − | 0.190473i | \(-0.0610022\pi\) |
0.325892 | + | 0.945407i | \(0.394336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.28246 | + | 5.68538i | 0.172761 | + | 0.299230i | ||||
\(362\) | 0.869854 | + | 3.24634i | 0.0457185 | + | 0.170624i | ||||
\(363\) | −2.69971 | − | 2.69971i | −0.141698 | − | 0.141698i | ||||
\(364\) | −9.82891 | + | 13.3253i | −0.515175 | + | 0.698438i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.495222 | + | 0.857750i | −0.0258857 | + | 0.0448353i | ||||
\(367\) | 31.3766 | + | 8.40733i | 1.63784 | + | 0.438859i | 0.956174 | − | 0.292800i | \(-0.0945870\pi\) |
0.681671 | + | 0.731659i | \(0.261254\pi\) | |||||||
\(368\) | −1.36097 | − | 0.364671i | −0.0709456 | − | 0.0190098i | ||||
\(369\) | −0.370803 | + | 0.642250i | −0.0193033 | + | 0.0334342i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4687 | − | 20.9713i | 0.803093 | − | 1.08878i | ||||
\(372\) | −3.71825 | − | 3.71825i | −0.192782 | − | 0.192782i | ||||
\(373\) | 5.71194 | + | 21.3172i | 0.295753 | + | 1.10377i | 0.940618 | + | 0.339468i | \(0.110247\pi\) |
−0.644865 | + | 0.764297i | \(0.723086\pi\) | |||||||
\(374\) | 2.71188 | + | 4.69711i | 0.140228 | + | 0.242882i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.55390 | + | 2.62920i | 0.234850 | + | 0.135590i | ||||
\(377\) | −29.5055 | + | 29.5055i | −1.51961 | + | 1.51961i | ||||
\(378\) | 1.65017 | + | 2.06808i | 0.0848754 | + | 0.106371i | ||||
\(379\) | 15.8588i | 0.814614i | 0.913291 | + | 0.407307i | \(0.133532\pi\) | ||||
−0.913291 | + | 0.407307i | \(0.866468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.8280 | − | 10.2930i | 0.913357 | − | 0.527327i | ||||
\(382\) | 0.191942 | − | 0.716337i | 0.00982061 | − | 0.0366510i | ||||
\(383\) | 17.1422 | − | 4.59325i | 0.875927 | − | 0.234704i | 0.207278 | − | 0.978282i | \(-0.433540\pi\) |
0.668649 | + | 0.743578i | \(0.266873\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.40898 | −0.377107 | ||||||||
\(387\) | 2.07731 | − | 0.556613i | 0.105596 | − | 0.0282942i | ||||
\(388\) | 2.55735 | − | 9.54418i | 0.129830 | − | 0.484532i | ||||
\(389\) | 30.2340 | − | 17.4556i | 1.53292 | − | 0.885034i | 0.533700 | − | 0.845674i | \(-0.320801\pi\) |
0.999225 | − | 0.0393604i | \(-0.0125320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.98523i | 0.100397i | ||||||||
\(392\) | 6.99496 | − | 0.265576i | 0.353299 | − | 0.0134136i | ||||
\(393\) | 4.62652 | − | 4.62652i | 0.233377 | − | 0.233377i | ||||
\(394\) | −15.3521 | − | 8.86353i | −0.773427 | − | 0.446538i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.92471 | − | 3.33369i | −0.0967201 | − | 0.167524i | ||||
\(397\) | −9.34838 | − | 34.8886i | −0.469182 | − | 1.75101i | −0.642640 | − | 0.766169i | \(-0.722161\pi\) |
0.173458 | − | 0.984841i | \(-0.444506\pi\) | |||||||
\(398\) | 0.495402 | + | 0.495402i | 0.0248323 | + | 0.0248323i | ||||
\(399\) | 8.55034 | − | 3.73327i | 0.428052 | − | 0.186897i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.741607 | + | 1.28450i | −0.0370341 | + | 0.0641449i | −0.883948 | − | 0.467585i | \(-0.845124\pi\) |
0.846914 | + | 0.531729i | \(0.178458\pi\) | |||||||
\(402\) | −7.39689 | − | 1.98199i | −0.368923 | − | 0.0988526i | ||||
\(403\) | 31.7877 | + | 8.51750i | 1.58346 | + | 0.424287i | ||||
\(404\) | 7.18310 | − | 12.4415i | 0.357373 | − | 0.618987i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.5298 | + | 1.97027i | 0.869991 | + | 0.0977828i | ||||
\(407\) | −27.6889 | − | 27.6889i | −1.37249 | − | 1.37249i | ||||
\(408\) | 0.364671 | + | 1.36097i | 0.0180539 | + | 0.0673782i | ||||
\(409\) | −1.51216 | − | 2.61914i | −0.0747716 | − | 0.129508i | 0.826215 | − | 0.563354i | \(-0.190489\pi\) |
−0.900987 | + | 0.433846i | \(0.857156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.85786 | − | 5.69144i | −0.486252 | − | 0.280738i | ||||
\(412\) | 10.8655 | − | 10.8655i | 0.535307 | − | 0.535307i | ||||
\(413\) | −35.8374 | + | 5.41167i | −1.76344 | + | 0.266291i | ||||
\(414\) | − | 1.40898i | − | 0.0692477i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.41993 | − | 3.12920i | 0.265734 | − | 0.153421i | ||||
\(417\) | −0.907188 | + | 3.38567i | −0.0444252 | + | 0.165797i | ||||
\(418\) | −13.1118 | + | 3.51330i | −0.641319 | + | 0.171841i | ||||
\(419\) | −14.8547 | −0.725702 | −0.362851 | − | 0.931847i | \(-0.618197\pi\) | ||||
−0.362851 | + | 0.931847i | \(0.618197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2920 | 1.33013 | 0.665065 | − | 0.746786i | \(-0.268404\pi\) | ||||
0.665065 | + | 0.746786i | \(0.268404\pi\) | |||||||
\(422\) | 14.9164 | − | 3.99683i | 0.726117 | − | 0.194563i | ||||
\(423\) | −1.36097 | + | 5.07922i | −0.0661727 | + | 0.246960i | ||||
\(424\) | −8.52984 | + | 4.92471i | −0.414246 | + | 0.239165i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 11.2584i | − | 0.545471i | ||||||
\(427\) | −2.04832 | + | 1.63440i | −0.0991250 | + | 0.0790940i | ||||
\(428\) | −1.90458 | + | 1.90458i | −0.0920614 | + | 0.0920614i | ||||
\(429\) | 20.8635 | + | 12.0456i | 1.00730 | + | 0.581565i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5242 | − | 32.0848i | −0.892278 | − | 1.54547i | −0.837138 | − | 0.546992i | \(-0.815773\pi\) |
−0.0551401 | − | 0.998479i | \(-0.517561\pi\) | |||||||
\(432\) | −0.258819 | − | 0.965926i | −0.0124524 | − | 0.0464731i | ||||
\(433\) | 7.65990 | + | 7.65990i | 0.368111 | + | 0.368111i | 0.866788 | − | 0.498677i | \(-0.166181\pi\) |
−0.498677 | + | 0.866788i | \(0.666181\pi\) | |||||||
\(434\) | −5.56696 | − | 12.7501i | −0.267222 | − | 0.612022i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.40064 | − | 14.5503i | 0.402318 | − | 0.696835i | ||||
\(437\) | −4.79925 | − | 1.28596i | −0.229579 | − | 0.0615156i | ||||
\(438\) | −10.2878 | − | 2.75660i | −0.491569 | − | 0.131716i | ||||
\(439\) | 10.1375 | − | 17.5586i | 0.483835 | − | 0.838027i | −0.515992 | − | 0.856593i | \(-0.672577\pi\) |
0.999828 | + | 0.0185660i | \(0.00591009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.06696 | + | 6.68788i | 0.0984265 | + | 0.318470i | ||||
\(442\) | −6.23524 | − | 6.23524i | −0.296580 | − | 0.296580i | ||||
\(443\) | 1.81987 | + | 6.79186i | 0.0864647 | + | 0.322691i | 0.995588 | − | 0.0938374i | \(-0.0299134\pi\) |
−0.909123 | + | 0.416528i | \(0.863247\pi\) | |||||||
\(444\) | −5.08624 | − | 8.80963i | −0.241382 | − | 0.418086i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.44399 | − | 0.833688i | −0.0683749 | − | 0.0394763i | ||||
\(447\) | 9.77455 | − | 9.77455i | 0.462320 | − | 0.462320i | ||||
\(448\) | −2.46313 | − | 0.965926i | −0.116372 | − | 0.0456357i | ||||
\(449\) | 4.46654i | 0.210789i | 0.994430 | + | 0.105394i | \(0.0336105\pi\) | ||||
−0.994430 | + | 0.105394i | \(0.966389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47229 | − | 1.42737i | 0.116415 | − | 0.0672125i | ||||
\(452\) | −3.73746 | + | 13.9484i | −0.175795 | + | 0.656077i | ||||
\(453\) | 5.75423 | − | 1.54184i | 0.270357 | − | 0.0724420i | ||||
\(454\) | −11.5114 | −0.540259 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.52634 | −0.165136 | ||||||||
\(457\) | 23.4389 | − | 6.28043i | 1.09643 | − | 0.293786i | 0.335117 | − | 0.942176i | \(-0.391224\pi\) |
0.761308 | + | 0.648390i | \(0.224557\pi\) | |||||||
\(458\) | 4.04210 | − | 15.0853i | 0.188875 | − | 0.704891i | ||||
\(459\) | −1.22021 | + | 0.704491i | −0.0569547 | + | 0.0328828i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.81796i | 0.410694i | 0.978689 | + | 0.205347i | \(0.0658322\pi\) | ||||
−0.978689 | + | 0.205347i | \(0.934168\pi\) | |||||||
\(462\) | −1.52070 | − | 10.0704i | −0.0707492 | − | 0.468518i | ||||
\(463\) | −1.05131 | + | 1.05131i | −0.0488583 | + | 0.0488583i | −0.731114 | − | 0.682256i | \(-0.760999\pi\) |
0.682256 | + | 0.731114i | \(0.260999\pi\) | |||||||
\(464\) | −5.77412 | − | 3.33369i | −0.268057 | − | 0.154763i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8635 | − | 25.7444i | −0.688540 | − | 1.19259i | ||||
\(467\) | −9.57824 | − | 35.7465i | −0.443228 | − | 1.65415i | −0.720573 | − | 0.693379i | \(-0.756121\pi\) |
0.277345 | − | 0.960770i | \(-0.410545\pi\) | |||||||
\(468\) | 4.42535 | + | 4.42535i | 0.204562 | + | 0.204562i | ||||
\(469\) | −16.3050 | − | 12.0267i | −0.752895 | − | 0.555343i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.99166 | + | 8.64581i | −0.230004 | + | 0.398378i | ||||
\(472\) | 13.2320 | + | 3.54552i | 0.609054 | + | 0.163196i | ||||
\(473\) | −7.99642 | − | 2.14263i | −0.367676 | − | 0.0985184i | ||||
\(474\) | −1.57529 | + | 2.72849i | −0.0723557 | + | 0.125324i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.416367 | + | 3.70449i | −0.0190841 | + | 0.169795i | ||||
\(477\) | −6.96459 | − | 6.96459i | −0.318886 | − | 0.318886i | ||||
\(478\) | −2.05810 | − | 7.68092i | −0.0941352 | − | 0.351317i | ||||
\(479\) | −0.778723 | − | 1.34879i | −0.0355807 | − | 0.0616277i | 0.847687 | − | 0.530497i | \(-0.177995\pi\) |
−0.883267 | + | 0.468870i | \(0.844661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.1341 | + | 31.8317i | 2.51390 | + | 1.45140i | ||||
\(482\) | 8.01039 | − | 8.01039i | 0.364863 | − | 0.364863i | ||||
\(483\) | 1.36097 | − | 3.47050i | 0.0619264 | − | 0.157913i | ||||
\(484\) | 3.81796i | 0.173544i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −2.02588 | + | 7.56068i | −0.0918013 | + | 0.342607i | −0.996515 | − | 0.0834127i | \(-0.973418\pi\) |
0.904714 | + | 0.426020i | \(0.140085\pi\) | |||||||
\(488\) | 0.956695 | − | 0.256346i | 0.0433076 | − | 0.0116042i | ||||
\(489\) | 1.37575 | 0.0622137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.8776 | 1.98017 | 0.990085 | − | 0.140468i | \(-0.0448608\pi\) | ||||
0.990085 | + | 0.140468i | \(0.0448608\pi\) | |||||||
\(492\) | 0.716337 | − | 0.191942i | 0.0322950 | − | 0.00865341i | ||||
\(493\) | −2.43140 | + | 9.07411i | −0.109505 | + | 0.408677i | ||||
\(494\) | 19.1125 | − | 11.0346i | 0.859913 | − | 0.496471i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.25839i | 0.236109i | ||||||||
\(497\) | 10.8748 | − | 27.7308i | 0.487800 | − | 1.24390i | ||||
\(498\) | 0.471906 | − | 0.471906i | 0.0211466 | − | 0.0211466i | ||||
\(499\) | −29.9024 | − | 17.2642i | −1.33862 | − | 0.772850i | −0.352014 | − | 0.935995i | \(-0.614503\pi\) |
−0.986602 | + | 0.163144i | \(0.947836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.44043 | − | 9.42310i | −0.243060 | − | 0.420993i | ||||
\(502\) | 5.44389 | + | 20.3169i | 0.242973 | + | 0.906786i | ||||
\(503\) | 16.9300 | + | 16.9300i | 0.754872 | + | 0.754872i | 0.975384 | − | 0.220512i | \(-0.0707728\pi\) |
−0.220512 | + | 0.975384i | \(0.570773\pi\) | |||||||
\(504\) | 0.295509 | − | 2.62920i | 0.0131630 | − | 0.117114i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.71188 | + | 4.69711i | −0.120558 | + | 0.208812i | ||||
\(507\) | −25.2758 | − | 6.77264i | −1.12254 | − | 0.300784i | ||||
\(508\) | −19.8846 | − | 5.32805i | −0.882235 | − | 0.236394i | ||||
\(509\) | −5.10674 | + | 8.84514i | −0.226352 | + | 0.392054i | −0.956724 | − | 0.290996i | \(-0.906013\pi\) |
0.730372 | + | 0.683050i | \(0.239347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.6774 | − | 16.7271i | −1.00319 | − | 0.739963i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.912685 | − | 3.40619i | −0.0402960 | − | 0.150387i | ||||
\(514\) | −12.9572 | − | 22.4426i | −0.571518 | − | 0.989899i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.86246 | − | 1.07529i | −0.0819904 | − | 0.0473372i | ||||
\(517\) | 14.3131 | − | 14.3131i | 0.629487 | − | 0.629487i | ||||
\(518\) | −4.01860 | − | 26.6121i | −0.176567 | − | 1.16927i | ||||
\(519\) | − | 1.69882i | − | 0.0745700i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0251 | + | 8.67476i | −0.658263 | + | 0.380048i | −0.791615 | − | 0.611021i | \(-0.790759\pi\) |
0.133352 | + | 0.991069i | \(0.457426\pi\) | |||||||
\(522\) | 1.72564 | − | 6.44019i | 0.0755294 | − | 0.281879i | ||||
\(523\) | −40.7197 | + | 10.9108i | −1.78055 | + | 0.477097i | −0.990684 | − | 0.136184i | \(-0.956516\pi\) |
−0.789865 | + | 0.613281i | \(0.789849\pi\) | |||||||
\(524\) | −6.54289 | −0.285828 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.5910 | −0.723403 | ||||||||
\(527\) | 7.15653 | − | 1.91759i | 0.311743 | − | 0.0835313i | ||||
\(528\) | −0.996301 | + | 3.71825i | −0.0433584 | + | 0.161816i | ||||
\(529\) | 18.1993 | − | 10.5074i | 0.791275 | − | 0.456843i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.6988i | 0.594478i | ||||||||
\(532\) | −8.68582 | − | 3.40619i | −0.376578 | − | 0.147677i | ||||
\(533\) | −3.28187 | + | 3.28187i | −0.142154 | + | 0.142154i | ||||
\(534\) | 12.0827 | + | 6.97594i | 0.522869 | + | 0.301878i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.82891 | + | 6.63187i | 0.165384 | + | 0.286453i | ||||
\(537\) | −3.57773 | − | 13.3523i | −0.154391 | − | 0.576194i | ||||
\(538\) | 19.3470 | + | 19.3470i | 0.834110 | + | 0.834110i | ||||
\(539\) | 5.98161 | − | 26.2736i | 0.257646 | − | 1.13168i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3709 | − | 19.6950i | 0.488874 | − | 0.846754i | −0.511044 | − | 0.859554i | \(-0.670741\pi\) |
0.999918 | + | 0.0128002i | \(0.00407455\pi\) | |||||||
\(542\) | 0.924599 | + | 0.247745i | 0.0397149 | + | 0.0106416i | ||||
\(543\) | 3.24634 | + | 0.869854i | 0.139314 | + | 0.0373290i | ||||
\(544\) | 0.704491 | − | 1.22021i | 0.0302048 | − | 0.0523163i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.62564 | + | 15.1748i | 0.283551 | + | 0.649420i | ||||
\(547\) | −12.2324 | − | 12.2324i | −0.523021 | − | 0.523021i | 0.395462 | − | 0.918483i | \(-0.370585\pi\) |
−0.918483 | + | 0.395462i | \(0.870585\pi\) | |||||||
\(548\) | 2.94610 | + | 10.9950i | 0.125851 | + | 0.469684i | ||||
\(549\) | 0.495222 | + | 0.857750i | 0.0211356 | + | 0.0366079i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.3615 | − | 11.7557i | −0.867430 | − | 0.500811i | ||||
\(552\) | −0.996301 | + | 0.996301i | −0.0424054 | + | 0.0424054i | ||||
\(553\) | −6.51567 | + | 5.19900i | −0.277074 | + | 0.221084i | ||||
\(554\) | − | 20.8137i | − | 0.884291i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.03551 | − | 1.75255i | 0.128734 | − | 0.0743248i | ||||
\(557\) | 9.30265 | − | 34.7179i | 0.394166 | − | 1.47105i | −0.429031 | − | 0.903290i | \(-0.641145\pi\) |
0.823196 | − | 0.567757i | \(-0.192189\pi\) | |||||||
\(558\) | −5.07922 | + | 1.36097i | −0.215020 | + | 0.0576146i | ||||
\(559\) | 13.4592 | 0.569265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.42375 | 0.228991 | ||||||||
\(562\) | −2.79365 | + | 0.748555i | −0.117843 | + | 0.0315759i | ||||
\(563\) | 8.55924 | − | 31.9435i | 0.360729 | − | 1.34626i | −0.512391 | − | 0.858752i | \(-0.671240\pi\) |
0.873120 | − | 0.487506i | \(-0.162093\pi\) | |||||||
\(564\) | 4.55390 | − | 2.62920i | 0.191754 | − | 0.110709i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.1936i | 0.890833i | ||||||||
\(567\) | 2.61609 | − | 0.395046i | 0.109866 | − | 0.0165904i | ||||
\(568\) | −7.96089 | + | 7.96089i | −0.334031 | + | 0.334031i | ||||
\(569\) | 14.4472 | + | 8.34107i | 0.605656 | + | 0.349676i | 0.771264 | − | 0.636516i | \(-0.219625\pi\) |
−0.165607 | + | 0.986192i | \(0.552958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21754 | − | 2.10885i | −0.0509527 | − | 0.0882526i | 0.839424 | − | 0.543477i | \(-0.182892\pi\) |
−0.890377 | + | 0.455224i | \(0.849559\pi\) | |||||||
\(572\) | −6.23524 | − | 23.2702i | −0.260709 | − | 0.972978i | ||||
\(573\) | −0.524395 | − | 0.524395i | −0.0219069 | − | 0.0219069i | ||||
\(574\) | 1.94983 | + | 0.219151i | 0.0813843 | + | 0.00914720i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −1.73390 | − | 0.464598i | −0.0721834 | − | 0.0193415i | 0.222547 | − | 0.974922i | \(-0.428563\pi\) |
−0.294730 | + | 0.955581i | \(0.595230\pi\) | |||||||
\(578\) | 14.5032 | + | 3.88611i | 0.603252 | + | 0.161641i | ||||
\(579\) | −3.70449 | + | 6.41637i | −0.153953 | + | 0.266655i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.61819 | − | 0.706537i | 0.0671338 | − | 0.0293121i | ||||
\(582\) | −6.98682 | − | 6.98682i | −0.289613 | − | 0.289613i | ||||
\(583\) | 9.81298 | + | 36.6225i | 0.406412 | + | 1.51675i | ||||
\(584\) | 5.32535 | + | 9.22377i | 0.220365 | + | 0.381683i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.3223 | + | 10.0011i | 0.715580 | + | 0.413140i | ||||
\(587\) | −28.3042 | + | 28.3042i | −1.16824 | + | 1.16824i | −0.185619 | + | 0.982622i | \(0.559429\pi\) |
−0.982622 | + | 0.185619i | \(0.940571\pi\) | |||||||
\(588\) | 3.26748 | − | 6.19060i | 0.134749 | − | 0.255296i | ||||
\(589\) | 18.5429i | 0.764047i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.3521 | + | 8.86353i | −0.631500 | + | 0.364597i | ||||
\(592\) | −2.63283 | + | 9.82586i | −0.108209 | + | 0.403840i | ||||
\(593\) | −2.65024 | + | 0.710130i | −0.108832 | + | 0.0291616i | −0.312824 | − | 0.949811i | \(-0.601275\pi\) |
0.203992 | + | 0.978973i | \(0.434608\pi\) | |||||||
\(594\) | −3.84941 | −0.157943 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8233 | −0.566225 | ||||||||
\(597\) | 0.676732 | − | 0.181330i | 0.0276968 | − | 0.00742133i | ||||
\(598\) | 2.28226 | − | 8.51750i | 0.0933284 | − | 0.348306i | ||||
\(599\) | −27.3558 | + | 15.7939i | −1.11773 | + | 0.645321i | −0.940820 | − | 0.338906i | \(-0.889943\pi\) |
−0.176909 | + | 0.984227i | \(0.556610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.59089i | − | 0.187266i | −0.995607 | − | 0.0936332i | \(-0.970152\pi\) | ||
0.995607 | − | 0.0936332i | \(-0.0298481\pi\) | |||||||
\(602\) | −3.54883 | − | 4.44759i | −0.144640 | − | 0.181270i | ||||
\(603\) | −5.41490 | + | 5.41490i | −0.220512 | + | 0.220512i | ||||
\(604\) | −5.15910 | − | 2.97861i | −0.209921 | − | 0.121198i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.18310 | − | 12.4415i | −0.291793 | − | 0.505401i | ||||
\(607\) | −4.41399 | − | 16.4732i | −0.179158 | − | 0.668628i | −0.995806 | − | 0.0914911i | \(-0.970837\pi\) |
0.816648 | − | 0.577137i | \(-0.195830\pi\) | |||||||
\(608\) | 2.49350 | + | 2.49350i | 0.101125 | + | 0.101125i | ||||
\(609\) | 10.4712 | − | 14.1962i | 0.424315 | − | 0.575257i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4545 | + | 28.5001i | −0.665680 | + | 1.15299i | ||||
\(612\) | 1.36097 | + | 0.364671i | 0.0550140 | + | 0.0147410i | ||||
\(613\) | −10.9233 | − | 2.92689i | −0.441188 | − | 0.118216i | 0.0313851 | − | 0.999507i | \(-0.490008\pi\) |
−0.472573 | + | 0.881291i | \(0.656675\pi\) | |||||||
\(614\) | −4.81796 | + | 8.34496i | −0.194437 | + | 0.336775i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.04556 | + | 8.19615i | −0.243583 | + | 0.330232i | ||||
\(617\) | 3.28476 | + | 3.28476i | 0.132240 | + | 0.132240i | 0.770128 | − | 0.637889i | \(-0.220192\pi\) |
−0.637889 | + | 0.770128i | \(0.720192\pi\) | |||||||
\(618\) | −3.97706 | − | 14.8426i | −0.159981 | − | 0.597057i | ||||
\(619\) | 12.8766 | + | 22.3029i | 0.517554 | + | 0.896429i | 0.999792 | + | 0.0203891i | \(0.00649049\pi\) |
−0.482239 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.22021 | − | 0.704491i | −0.0489655 | − | 0.0282703i | ||||
\(622\) | 14.5800 | − | 14.5800i | 0.584605 | − | 0.584605i | ||||
\(623\) | 23.0229 | + | 28.8536i | 0.922394 | + | 1.15599i | ||||
\(624\) | − | 6.25839i | − | 0.250536i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.2623 | − | 8.23433i | 0.570035 | − | 0.329110i | ||||
\(627\) | −3.51330 | + | 13.1118i | −0.140308 | + | 0.523635i | ||||
\(628\) | 9.64315 | − | 2.58387i | 0.384804 | − | 0.103108i | ||||
\(629\) | 14.3328 | 0.571488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5189 | 1.41399 | 0.706993 | − | 0.707221i | \(-0.250051\pi\) | ||||
0.706993 | + | 0.707221i | \(0.250051\pi\) | |||||||
\(632\) | 3.04324 | − | 0.815432i | 0.121053 | − | 0.0324362i | ||||
\(633\) | 3.99683 | − | 14.9164i | 0.158860 | − | 0.592872i | ||||
\(634\) | 23.0205 | − | 13.2909i | 0.914262 | − | 0.527849i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.84941i | 0.390555i | ||||||||
\(637\) | 1.66208 | + | 43.7772i | 0.0658540 | + | 1.73452i | ||||
\(638\) | −18.1482 | + | 18.1482i | −0.718495 | + | 0.718495i | ||||
\(639\) | −9.75005 | − | 5.62920i | −0.385706 | − | 0.222688i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.14492 | + | 10.6433i | 0.242710 | + | 0.420386i | 0.961485 | − | 0.274857i | \(-0.0886304\pi\) |
−0.718775 | + | 0.695242i | \(0.755297\pi\) | |||||||
\(642\) | 0.697125 | + | 2.60170i | 0.0275133 | + | 0.102681i | ||||
\(643\) | −25.5136 | − | 25.5136i | −1.00616 | − | 1.00616i | −0.999981 | − | 0.00617772i | \(-0.998034\pi\) |
−0.00617772 | − | 0.999981i | \(-0.501966\pi\) | |||||||
\(644\) | −3.41637 | + | 1.49166i | −0.134624 | + | 0.0587797i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.48428 | − | 4.30289i | 0.0977426 | − | 0.169295i | ||||
\(647\) | −31.5241 | − | 8.44686i | −1.23934 | − | 0.332080i | −0.421130 | − | 0.907000i | \(-0.638367\pi\) |
−0.818210 | + | 0.574920i | \(0.805033\pi\) | |||||||
\(648\) | −0.965926 | − | 0.258819i | −0.0379452 | − | 0.0101674i | ||||
\(649\) | 26.3662 | − | 45.6676i | 1.03496 | − | 1.79261i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8253 | − | 1.55390i | −0.541858 | − | 0.0609022i | ||||
\(652\) | −0.972804 | − | 0.972804i | −0.0380980 | − | 0.0380980i | ||||
\(653\) | −4.84099 | − | 18.0668i | −0.189443 | − | 0.707010i | −0.993636 | − | 0.112642i | \(-0.964069\pi\) |
0.804193 | − | 0.594368i | \(-0.202598\pi\) | |||||||
\(654\) | −8.40064 | − | 14.5503i | −0.328491 | − | 0.568963i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.642250 | − | 0.370803i | −0.0250757 | − | 0.0144774i | ||||
\(657\) | −7.53118 | + | 7.53118i | −0.293819 | + | 0.293819i | ||||
\(658\) | 13.7564 | − | 2.07731i | 0.536282 | − | 0.0809820i | ||||
\(659\) | 43.5871i | 1.69791i | 0.528462 | + | 0.848957i | \(0.322769\pi\) | ||||
−0.528462 | + | 0.848957i | \(0.677231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3300 | − | 12.3149i | 0.829642 | − | 0.478994i | −0.0240879 | − | 0.999710i | \(-0.507668\pi\) |
0.853730 | + | 0.520716i | \(0.174335\pi\) | |||||||
\(662\) | 1.74624 | − | 6.51705i | 0.0678695 | − | 0.253292i | ||||
\(663\) | −8.51750 | + | 2.28226i | −0.330792 | + | 0.0886355i | ||||
\(664\) | −0.667375 | −0.0258992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.1725 | −0.394176 | ||||||||
\(667\) | −9.07411 | + | 2.43140i | −0.351351 | + | 0.0941442i | ||||
\(668\) | −2.81617 | + | 10.5101i | −0.108961 | + | 0.406648i | ||||
\(669\) | −1.44399 | + | 0.833688i | −0.0558279 | + | 0.0322322i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.81263i | − | 0.147185i | ||||||
\(672\) | −2.06808 | + | 1.65017i | −0.0797779 | + | 0.0636565i | ||||
\(673\) | 11.4796 | − | 11.4796i | 0.442506 | − | 0.442506i | −0.450348 | − | 0.892853i | \(-0.648700\pi\) |
0.892853 | + | 0.450348i | \(0.148700\pi\) | |||||||
\(674\) | −2.69144 | − | 1.55390i | −0.103670 | − | 0.0598541i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0837 | + | 22.6617i | 0.503221 | + | 0.871604i | ||||
\(677\) | 4.28892 | + | 16.0065i | 0.164837 | + | 0.615179i | 0.998061 | + | 0.0622438i | \(0.0198256\pi\) |
−0.833224 | + | 0.552935i | \(0.813508\pi\) | |||||||
\(678\) | 10.2109 | + | 10.2109i | 0.392148 | + | 0.392148i | ||||
\(679\) | −10.4607 | − | 23.9582i | −0.401444 | − | 0.919430i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.75572 | + | 9.96921i | −0.220560 | + | 0.382021i | ||||
\(682\) | 19.5520 | + | 5.23894i | 0.748685 | + | 0.200609i | ||||
\(683\) | 13.4403 | + | 3.60132i | 0.514279 | + | 0.137801i | 0.506619 | − | 0.862170i | \(-0.330895\pi\) |
0.00765999 | + | 0.999971i | \(0.497562\pi\) | |||||||
\(684\) | −1.76317 | + | 3.05390i | −0.0674165 | + | 0.116769i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.0279 | − | 12.0921i | 0.535587 | − | 0.461678i | ||||
\(687\) | −11.0432 | − | 11.0432i | −0.421325 | − | 0.421325i | ||||
\(688\) | 0.556613 | + | 2.07731i | 0.0212207 | + | 0.0791967i | ||||
\(689\) | −30.8207 | − | 53.3831i | −1.17418 | − | 2.03373i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.05178 | + | 2.33929i | 0.154137 | + | 0.0889909i | 0.575085 | − | 0.818094i | \(-0.304969\pi\) |
−0.420948 | + | 0.907085i | \(0.638302\pi\) | |||||||
\(692\) | −1.20125 | + | 1.20125i | −0.0456646 | + | 0.0456646i | ||||
\(693\) | −9.48158 | − | 3.71825i | −0.360176 | − | 0.141244i | ||||
\(694\) | 13.2471i | 0.502851i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.77412 | + | 3.33369i | −0.218867 | + | 0.126363i | ||||
\(697\) | −0.270443 | + | 1.00931i | −0.0102438 | + | 0.0382302i | ||||
\(698\) | −17.5594 | + | 4.70503i | −0.664633 | + | 0.178088i | ||||
\(699\) | −29.7271 | −1.12438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2732 | 1.03009 | 0.515047 | − | 0.857162i | \(-0.327775\pi\) | ||||
0.515047 | + | 0.857162i | \(0.327775\pi\) | |||||||
\(702\) | 6.04514 | − | 1.61979i | 0.228159 | − | 0.0611351i | ||||
\(703\) | −9.28426 | + | 34.6493i | −0.350163 | + | 1.30682i | ||||
\(704\) | 3.33369 | − | 1.92471i | 0.125643 | − | 0.0725401i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 21.8120i | − | 0.820904i | ||||||
\(707\) | −5.67532 | − | 37.5833i | −0.213442 | − | 1.41347i | ||||
\(708\) | 9.68653 | − | 9.68653i | 0.364042 | − | 0.364042i | ||||
\(709\) | 22.7497 | + | 13.1345i | 0.854382 | + | 0.493278i | 0.862127 | − | 0.506692i | \(-0.169132\pi\) |
−0.00774478 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.57529 | + | 2.72849i | 0.0590782 | + | 0.102326i | ||||
\(712\) | −3.61101 | − | 13.4765i | −0.135328 | − | 0.505052i | ||||
\(713\) | 5.23894 | + | 5.23894i | 0.196200 | + | 0.196200i | ||||
\(714\) | 3.00000 | + | 2.21283i | 0.112272 | + | 0.0828131i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.91165 | + | 11.9713i | −0.258301 | + | 0.447390i | ||||
\(717\) | −7.68092 | − | 2.05810i | −0.286849 | − | 0.0768610i | ||||
\(718\) | −27.6331 | − | 7.40427i | −1.03126 | − | 0.276325i | ||||
\(719\) | 10.2929 | − | 17.8279i | 0.383862 | − | 0.664869i | −0.607748 | − | 0.794130i | \(-0.707927\pi\) |
0.991611 | + | 0.129261i | \(0.0412604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.54085 | − | 40.4008i | 0.169110 | − | 1.50460i | ||||
\(722\) | −4.64209 | − | 4.64209i | −0.172761 | − | 0.172761i | ||||
\(723\) | −2.93201 | − | 10.9424i | −0.109043 | − | 0.406952i | ||||
\(724\) | −1.68043 | − | 2.91059i | −0.0624527 | − | 0.108171i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.30645 | + | 1.90898i | 0.122714 | + | 0.0708490i | ||||
\(727\) | −7.63477 | + | 7.63477i | −0.283158 | + | 0.283158i | −0.834367 | − | 0.551209i | \(-0.814167\pi\) |
0.551209 | + | 0.834367i | \(0.314167\pi\) | |||||||
\(728\) | 6.04514 | − | 15.4152i | 0.224048 | − | 0.571326i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.62418 | − | 1.51507i | 0.0970588 | − | 0.0560369i | ||||
\(732\) | 0.256346 | − | 0.956695i | 0.00947481 | − | 0.0353605i | ||||
\(733\) | −13.6250 | + | 3.65082i | −0.503252 | + | 0.134846i | −0.501509 | − | 0.865152i | \(-0.667222\pi\) |
−0.00174331 | + | 0.999998i | \(0.500555\pi\) | |||||||
\(734\) | −32.4834 | −1.19899 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.40898 | 0.0519358 | ||||||||
\(737\) | 28.4737 | − | 7.62949i | 1.04884 | − | 0.281036i | ||||
\(738\) | 0.191942 | − | 0.716337i | 0.00706548 | − | 0.0263687i | ||||
\(739\) | −17.0208 | + | 9.82696i | −0.626120 | + | 0.361490i | −0.779248 | − | 0.626716i | \(-0.784399\pi\) |
0.153128 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 22.0692i | − | 0.810734i | ||||||
\(742\) | −9.51380 | + | 24.2603i | −0.349263 | + | 0.890625i | ||||
\(743\) | 20.7983 | − | 20.7983i | 0.763016 | − | 0.763016i | −0.213851 | − | 0.976866i | \(-0.568601\pi\) |
0.976866 | + | 0.213851i | \(0.0686006\pi\) | |||||||
\(744\) | 4.55390 | + | 2.62920i | 0.166954 | + | 0.0963910i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.0346 | − | 19.1125i | −0.404006 | − | 0.699759i | ||||
\(747\) | −0.172729 | − | 0.644635i | −0.00631984 | − | 0.0235860i | ||||
\(748\) | −3.83517 | − | 3.83517i | −0.140228 | − | 0.140228i | ||||
\(749\) | −0.795948 | + | 7.08170i | −0.0290833 | + | 0.258760i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9305 | − | 20.6642i | 0.435350 | − | 0.754048i | −0.561975 | − | 0.827155i | \(-0.689958\pi\) |
0.997324 | + | 0.0731070i | \(0.0232915\pi\) | |||||||
\(752\) | −5.07922 | − | 1.36097i | −0.185220 | − | 0.0496296i | ||||
\(753\) | 20.3169 | + | 5.44389i | 0.740388 | + | 0.198386i | ||||
\(754\) | 20.8635 | − | 36.1367i | 0.759805 | − | 1.31602i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.12920 | − | 1.57052i | −0.0774381 | − | 0.0571191i | ||||
\(757\) | 30.3903 | + | 30.3903i | 1.10455 | + | 1.10455i | 0.993854 | + | 0.110699i | \(0.0353090\pi\) |
0.110699 | + | 0.993854i | \(0.464691\pi\) | |||||||
\(758\) | −4.10457 | − | 15.3185i | −0.149085 | − | 0.556392i | ||||
\(759\) | 2.71188 | + | 4.69711i | 0.0984349 | + | 0.170494i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.111347 | + | 0.0642865i | 0.00403634 | + | 0.00233038i | 0.502017 | − | 0.864858i | \(-0.332592\pi\) |
−0.497980 | + | 0.867188i | \(0.665925\pi\) | |||||||
\(762\) | −14.5565 | + | 14.5565i | −0.527327 | + | 0.527327i | ||||
\(763\) | −6.63729 | − | 43.9537i | −0.240286 | − | 1.59123i | ||||
\(764\) | 0.741607i | 0.0268304i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.3693 | + | 8.87347i | −0.555316 | + | 0.320612i | ||||
\(767\) | −22.1892 | + | 82.8113i | −0.801207 | + | 2.99014i | ||||
\(768\) | 0.965926 | − | 0.258819i | 0.0348548 | − | 0.00933933i | ||||
\(769\) | 27.3976 | 0.987984 | 0.493992 | − | 0.869466i | \(-0.335537\pi\) | ||||
0.493992 | + | 0.869466i | \(0.335537\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.9144 | −0.933285 | ||||||||
\(772\) | 7.15653 | − | 1.91759i | 0.257569 | − | 0.0690154i | ||||
\(773\) | 1.25374 | − | 4.67901i | 0.0450938 | − | 0.168292i | −0.939707 | − | 0.341981i | \(-0.888902\pi\) |
0.984801 | + | 0.173689i | \(0.0555687\pi\) | |||||||
\(774\) | −1.86246 | + | 1.07529i | −0.0669449 | + | 0.0386507i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.88086i | 0.354702i | ||||||||
\(777\) | −25.0561 | − | 9.82586i | −0.898882 | − | 0.352501i | ||||
\(778\) | −24.6860 | + | 24.6860i | −0.885034 | + | 0.885034i | ||||
\(779\) | −2.26479 | − | 1.30758i | −0.0811447 | − | 0.0468489i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.6691 | + | 37.5320i | 0.775381 | + | 1.34300i | ||||
\(782\) | −0.513816 | − | 1.91759i | −0.0183740 | − | 0.0685727i | ||||
\(783\) | −4.71455 | − | 4.71455i | −0.168484 | − | 0.168484i | ||||
\(784\) | −6.68788 | + | 2.06696i | −0.238853 | + | 0.0738199i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.27145 | + | 5.66631i | −0.116689 | + | 0.202111i | ||||
\(787\) | 50.7385 | + | 13.5953i | 1.80863 | + | 0.484621i | 0.995271 | − | 0.0971384i | \(-0.0309689\pi\) |
0.813361 | + | 0.581760i | \(0.197636\pi\) | |||||||
\(788\) | 17.1230 | + | 4.58810i | 0.609982 | + | 0.163444i | ||||
\(789\) | −8.29551 | + | 14.3682i | −0.295328 | + | 0.511523i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2878 | + | 35.0138i | 0.543571 | + | 1.24495i | ||||
\(792\) | 2.72194 | + | 2.72194i | 0.0967201 | + | 0.0967201i | ||||
\(793\) | 1.60431 | + | 5.98738i | 0.0569708 | + | 0.212618i | ||||
\(794\) | 18.0597 | + | 31.2803i | 0.640914 | + | 1.11010i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.606741 | − | 0.350302i | −0.0215054 | − | 0.0124161i | ||||
\(797\) | 8.85221 | − | 8.85221i | 0.313561 | − | 0.313561i | −0.532726 | − | 0.846288i | \(-0.678832\pi\) |
0.846288 | + | 0.532726i | \(0.178832\pi\) | |||||||
\(798\) | −7.29275 | + | 5.81905i | −0.258161 | + | 0.205992i | ||||
\(799\) | 7.40898i | 0.262111i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0827 | − | 6.97594i | 0.426920 | − | 0.246483i | ||||
\(802\) | 0.383884 | − | 1.43267i | 0.0135554 | − | 0.0505895i | ||||
\(803\) | 39.6019 | − | 10.6113i | 1.39752 | − | 0.374465i | ||||
\(804\) | 7.65782 | 0.270070 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.9091 | −1.15917 | ||||||||
\(807\) | 26.4286 | − | 7.08151i | 0.930329 | − | 0.249281i | ||||
\(808\) | −3.71825 | + | 13.8767i | −0.130807 | + | 0.488180i | ||||
\(809\) | −17.1675 | + | 9.91165i | −0.603577 | + | 0.348475i | −0.770447 | − | 0.637504i | \(-0.779967\pi\) |
0.166871 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.73982i | − | 0.271782i | −0.990724 | − | 0.135891i | \(-0.956610\pi\) | ||
0.990724 | − | 0.135891i | \(-0.0433897\pi\) | |||||||
\(812\) | −17.4425 | + | 2.63392i | −0.612111 | + | 0.0924326i | ||||
\(813\) | 0.676853 | − | 0.676853i | 0.0237383 | − | 0.0237383i | ||||
\(814\) | 33.9119 | + | 19.5790i | 1.18861 | + | 0.686245i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.704491 | − | 1.22021i | −0.0246621 | − | 0.0427160i | ||||
\(817\) | 1.96281 | + | 7.32530i | 0.0686700 | + | 0.256280i | ||||
\(818\) | 2.13852 | + | 2.13852i | 0.0747716 | + | 0.0747716i | ||||
\(819\) | 16.4545 | + | 1.84941i | 0.574968 | + | 0.0646236i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9844 | + | 32.8819i | −0.662560 | + | 1.14759i | 0.317381 | + | 0.948298i | \(0.397197\pi\) |
−0.979941 | + | 0.199289i | \(0.936137\pi\) | |||||||
\(822\) | 10.9950 | + | 2.94610i | 0.383495 | + | 0.102757i | ||||
\(823\) | 34.6373 | + | 9.28104i | 1.20738 | + | 0.323517i | 0.805734 | − | 0.592278i | \(-0.201771\pi\) |
0.401647 | + | 0.915795i | \(0.368438\pi\) | |||||||
\(824\) | −7.68310 | + | 13.3075i | −0.267653 | + | 0.463589i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.2156 | − | 14.5027i | 1.15572 | − | 0.504612i | ||||
\(827\) | 16.9966 | + | 16.9966i | 0.591029 | + | 0.591029i | 0.937909 | − | 0.346881i | \(-0.112759\pi\) |
−0.346881 | + | 0.937909i | \(0.612759\pi\) | |||||||
\(828\) | 0.364671 | + | 1.36097i | 0.0126732 | + | 0.0472971i | ||||
\(829\) | 12.8699 | + | 22.2913i | 0.446991 | + | 0.774210i | 0.998188 | − | 0.0601642i | \(-0.0191624\pi\) |
−0.551198 | + | 0.834374i | \(0.685829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0252 | − | 10.4069i | −0.625288 | − | 0.361010i | ||||
\(832\) | −4.42535 | + | 4.42535i | −0.153421 | + | 0.153421i | ||||
\(833\) | 5.25195 | + | 8.34825i | 0.181969 | + | 0.289250i | ||||
\(834\) | − | 3.50510i | − | 0.121372i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.7557 | − | 6.78717i | 0.406580 | − | 0.234739i | ||||
\(837\) | −1.36097 | + | 5.07922i | −0.0470421 | + | 0.175563i | ||||
\(838\) | 14.3486 | − | 3.84469i | 0.495664 | − | 0.132813i | ||||
\(839\) | 39.3234 | 1.35759 | 0.678797 | − | 0.734326i | \(-0.262501\pi\) | ||||
0.678797 | + | 0.734326i | \(0.262501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4539 | −0.532893 | ||||||||
\(842\) | −26.3620 | + | 7.06368i | −0.908495 | + | 0.243431i | ||||
\(843\) | −0.748555 | + | 2.79365i | −0.0257816 | + | 0.0962183i | ||||
\(844\) | −13.3736 | + | 7.72128i | −0.460340 | + | 0.265777i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 5.25839i | − | 0.180787i | ||||||
\(847\) | 6.30028 | + | 7.89585i | 0.216480 | + | 0.271305i | ||||
\(848\) | 6.96459 | − | 6.96459i | 0.239165 | − | 0.239165i | ||||
\(849\) | 18.3542 | + | 10.5968i | 0.629914 | + | 0.363681i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.16642 | + | 12.4126i | 0.245662 | + | 0.425499i | ||||
\(852\) | 2.91389 | + | 10.8748i | 0.0998281 | + | 0.372564i | ||||
\(853\) | 11.4032 | + | 11.4032i | 0.390439 | + | 0.390439i | 0.874844 | − | 0.484405i | \(-0.160964\pi\) |
−0.484405 | + | 0.874844i | \(0.660964\pi\) | |||||||
\(854\) | 1.55551 | − | 2.10885i | 0.0532284 | − | 0.0721634i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.34674 | − | 2.33262i | 0.0460307 | − | 0.0797275i | ||||
\(857\) | −2.51368 | − | 0.673539i | −0.0858658 | − | 0.0230077i | 0.215630 | − | 0.976475i | \(-0.430819\pi\) |
−0.301496 | + | 0.953467i | \(0.597486\pi\) | |||||||
\(858\) | −23.2702 | − | 6.23524i | −0.794433 | − | 0.212868i | ||||
\(859\) | 11.6663 | − | 20.2066i | 0.398049 | − | 0.689442i | −0.595436 | − | 0.803403i | \(-0.703021\pi\) |
0.993485 | + | 0.113961i | \(0.0363539\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.16471 | − | 1.57903i | 0.0396931 | − | 0.0538131i | ||||
\(862\) | 26.1971 | + | 26.1971i | 0.892278 | + | 0.892278i | ||||
\(863\) | −10.7805 | − | 40.2335i | −0.366974 | − | 1.36957i | −0.864725 | − | 0.502246i | \(-0.832507\pi\) |
0.497751 | − | 0.867320i | \(-0.334159\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.38142 | − | 5.41637i | −0.318794 | − | 0.184056i | ||||
\(867\) | 10.6170 | − | 10.6170i | 0.360574 | − | 0.360574i | ||||
\(868\) | 8.67722 | + | 10.8748i | 0.294524 | + | 0.369114i | ||||
\(869\) | − | 12.1279i | − | 0.411411i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.5048 | + | 23.9628i | −1.40634 | + | 0.811949i | ||||
\(872\) | −4.34849 | + | 16.2288i | −0.147259 | + | 0.549576i | ||||
\(873\) | −9.54418 | + | 2.55735i | −0.323021 | + | 0.0865533i | ||||
\(874\) | 4.96855 | 0.168064 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6507 | 0.359854 | ||||||||
\(877\) | −37.7842 | + | 10.1242i | −1.27588 | + | 0.341871i | −0.832281 | − | 0.554354i | \(-0.812965\pi\) |
−0.443600 | + | 0.896225i | \(0.646299\pi\) | |||||||
\(878\) | −5.24754 | + | 19.5841i | −0.177096 | + | 0.660931i | ||||
\(879\) | 17.3223 | − | 10.0011i | 0.584268 | − | 0.337327i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2584i | 0.379305i | 0.981851 | + | 0.189652i | \(0.0607361\pi\) | ||||
−0.981851 | + | 0.189652i | \(0.939264\pi\) | |||||||
\(882\) | −3.72748 | − | 5.92503i | −0.125511 | − | 0.199506i | ||||
\(883\) | −16.2037 | + | 16.2037i | −0.545297 | + | 0.545297i | −0.925077 | − | 0.379780i | \(-0.876000\pi\) |
0.379780 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(884\) | 7.63658 | + | 4.40898i | 0.256846 | + | 0.148290i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.51572 | − | 6.08941i | −0.118113 | − | 0.204578i | ||||
\(887\) | −3.39548 | − | 12.6721i | −0.114009 | − | 0.425488i | 0.885202 | − | 0.465207i | \(-0.154020\pi\) |
−0.999211 | + | 0.0397194i | \(0.987354\pi\) | |||||||
\(888\) | 7.19303 | + | 7.19303i | 0.241382 | + | 0.241382i | ||||
\(889\) | −49.9150 | + | 21.7940i | −1.67410 | + | 0.730948i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.92471 | + | 3.33369i | −0.0644801 | + | 0.111683i | ||||
\(892\) | 1.61056 | + | 0.431548i | 0.0539256 | + | 0.0144493i | ||||
\(893\) | −17.9111 | − | 4.79925i | −0.599371 | − | 0.160601i | ||||
\(894\) | −6.91165 | + | 11.9713i | −0.231160 | + | 0.400381i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.62920 | + | 0.295509i | 0.0878353 | + | 0.00987226i | ||||
\(897\) | −6.23524 | − | 6.23524i | −0.208189 | − | 0.208189i | ||||
\(898\) | −1.15602 | − | 4.31434i | −0.0385770 | − | 0.143971i | ||||
\(899\) | 17.5298 | + | 30.3626i | 0.584653 | + | 1.01265i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0184 | − | 6.93882i | −0.400391 | − | 0.231166i | ||||
\(902\) | −2.01861 | + | 2.01861i | −0.0672125 | + | 0.0672125i | ||||
\(903\) | −5.62614 | + | 0.849583i | −0.187226 | + | 0.0282723i | ||||
\(904\) | − | 14.4404i | − | 0.480282i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.15910 | + | 2.97861i | −0.171400 | + | 0.0989576i | ||||
\(907\) | 2.64146 | − | 9.85808i | 0.0877084 | − | 0.327332i | −0.908105 | − | 0.418743i | \(-0.862471\pi\) |
0.995813 | + | 0.0914106i | \(0.0291376\pi\) | |||||||
\(908\) | 11.1192 | − | 2.97938i | 0.369004 | − | 0.0988743i | ||||
\(909\) | −14.3662 | −0.476497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.10568 | 0.0366328 | 0.0183164 | − | 0.999832i | \(-0.494169\pi\) | ||||
0.0183164 | + | 0.999832i | \(0.494169\pi\) | |||||||
\(912\) | 3.40619 | − | 0.912685i | 0.112790 | − | 0.0302220i | ||||
\(913\) | −0.664907 | + | 2.48147i | −0.0220052 | + | 0.0821245i | ||||
\(914\) | −21.0147 | + | 12.1329i | −0.695106 | + | 0.401320i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.6175i | 0.516016i | ||||||||
\(917\) | −13.5312 | + | 10.7969i | −0.446840 | + | 0.356544i | ||||
\(918\) | 0.996301 | − | 0.996301i | 0.0328828 | − | 0.0328828i | ||||
\(919\) | −35.1784 | − | 20.3103i | −1.16043 | − | 0.669974i | −0.209023 | − | 0.977911i | \(-0.567028\pi\) |
−0.951407 | + | 0.307937i | \(0.900362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.81796 | + | 8.34496i | 0.158757 | + | 0.274976i | ||||
\(922\) | −2.28226 | − | 8.51750i | −0.0751621 | − | 0.280509i | ||||
\(923\) | −49.8224 | − | 49.8224i | −1.63992 | − | 1.63992i | ||||
\(924\) | 4.07529 | + | 9.33369i | 0.134067 | + | 0.307056i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.743385 | − | 1.28758i | 0.0244291 | − | 0.0423125i | ||||
\(927\) | −14.8426 | − | 3.97706i | −0.487495 | − | 0.130624i | ||||
\(928\) | 6.44019 | + | 1.72564i | 0.211410 | + | 0.0566470i | ||||
\(929\) | −9.48534 | + | 16.4291i | −0.311204 | + | 0.539021i | −0.978623 | − | 0.205661i | \(-0.934066\pi\) |
0.667419 | + | 0.744682i | \(0.267399\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.5837 | + | 7.28879i | −0.772926 | + | 0.238881i | ||||
\(932\) | 21.0202 | + | 21.0202i | 0.688540 | + | 0.688540i | ||||
\(933\) | −5.33665 | − | 19.9167i | −0.174714 | − | 0.652042i | ||||
\(934\) | 18.5037 | + | 32.0494i | 0.605461 | + | 1.04869i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.41993 | − | 3.12920i | −0.177156 | − | 0.102281i | ||||
\(937\) | −1.26931 | + | 1.26931i | −0.0414664 | + | 0.0414664i | −0.727536 | − | 0.686070i | \(-0.759335\pi\) |
0.686070 | + | 0.727536i | \(0.259335\pi\) | |||||||
\(938\) | 18.8622 | + | 7.39689i | 0.615872 | + | 0.241517i | ||||
\(939\) | − | 16.4687i | − | 0.537434i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.9611 | + | 25.9583i | −1.46569 | + | 0.846216i | −0.999265 | − | 0.0383456i | \(-0.987791\pi\) |
−0.466424 | + | 0.884561i | \(0.654458\pi\) | |||||||
\(942\) | 2.58387 | − | 9.64315i | 0.0841872 | − | 0.314191i | ||||
\(943\) | −1.00931 | + | 0.270443i | −0.0328675 | + | 0.00880683i | ||||
\(944\) | −13.6988 | −0.445859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.27850 | 0.269157 | ||||||||
\(947\) | 26.5843 | − | 7.12325i | 0.863875 | − | 0.231475i | 0.200437 | − | 0.979706i | \(-0.435764\pi\) |
0.663437 | + | 0.748232i | \(0.269097\pi\) | |||||||
\(948\) | 0.815432 | − | 3.04324i | 0.0264840 | − | 0.0988397i | ||||
\(949\) | −57.7260 | + | 33.3281i | −1.87387 | + | 1.08188i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 26.5818i | − | 0.861974i | ||||||
\(952\) | −0.556613 | − | 3.68603i | −0.0180399 | − | 0.119465i | ||||
\(953\) | 24.6409 | − | 24.6409i | 0.798197 | − | 0.798197i | −0.184614 | − | 0.982811i | \(-0.559103\pi\) |
0.982811 | + | 0.184614i | \(0.0591035\pi\) | |||||||
\(954\) | 8.52984 | + | 4.92471i | 0.276164 | + | 0.159443i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.97594 | + | 6.88653i | 0.128591 | + | 0.222726i | ||||
\(957\) | 6.64271 | + | 24.7909i | 0.214728 | + | 0.801377i | ||||
\(958\) | 1.10128 | + | 1.10128i | 0.0355807 | + | 0.0355807i | ||||
\(959\) | 24.2364 | + | 17.8770i | 0.782633 | + | 0.577278i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.67465 | + | 2.90058i | −0.0540210 | + | 0.0935671i | ||||
\(962\) | −61.4941 | − | 16.4773i | −1.98265 | − | 0.531249i | ||||
\(963\) | 2.60170 | + | 0.697125i | 0.0838388 | + | 0.0224645i | ||||
\(964\) | −5.66420 | + | 9.81069i | −0.182432 | + | 0.315981i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.416367 | + | 3.70449i | −0.0133964 | + | 0.119190i | ||||
\(967\) | 36.8801 | + | 36.8801i | 1.18598 | + | 1.18598i | 0.978168 | + | 0.207814i | \(0.0666350\pi\) |
0.207814 | + | 0.978168i | \(0.433365\pi\) | |||||||
\(968\) | −0.988162 | − | 3.68787i | −0.0317607 | − | 0.118533i | ||||
\(969\) | −2.48428 | − | 4.30289i | −0.0798065 | − | 0.138229i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.6973 | + | 25.2287i | 1.40231 | + | 0.809626i | 0.994630 | − | 0.103497i | \(-0.0330031\pi\) |
0.407684 | + | 0.913123i | \(0.366336\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 3.38567 | − | 8.63351i | 0.108540 | − | 0.276778i | ||||
\(974\) | − | 7.82739i | − | 0.250806i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.857750 | + | 0.495222i | −0.0274559 | + | 0.0158517i | ||||
\(977\) | 9.28012 | − | 34.6339i | 0.296897 | − | 1.10804i | −0.642801 | − | 0.766033i | \(-0.722228\pi\) |
0.939699 | − | 0.342003i | \(-0.111105\pi\) | |||||||
\(978\) | −1.32888 | + | 0.356071i | −0.0424928 | + | 0.0113859i | ||||
\(979\) | −53.7065 | −1.71647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8013 | −0.536424 | ||||||||
\(982\) | −42.3826 | + | 11.3564i | −1.35248 | + | 0.362396i | ||||
\(983\) | −1.13061 | + | 4.21948i | −0.0360607 | + | 0.134580i | −0.981609 | − | 0.190900i | \(-0.938859\pi\) |
0.945549 | + | 0.325480i | \(0.105526\pi\) | |||||||
\(984\) | −0.642250 | + | 0.370803i | −0.0204742 | + | 0.0118208i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 9.39421i | − | 0.299173i | ||||||
\(987\) | 5.07922 | − | 12.9521i | 0.161673 | − | 0.412269i | ||||
\(988\) | −15.6053 | + | 15.6053i | −0.496471 | + | 0.496471i | ||||
\(989\) | 2.62418 | + | 1.51507i | 0.0834441 | + | 0.0481765i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3772 | − | 19.7059i | −0.361409 | − | 0.625978i | 0.626784 | − | 0.779193i | \(-0.284371\pi\) |
−0.988193 | + | 0.153214i | \(0.951037\pi\) | |||||||
\(992\) | −1.36097 | − | 5.07922i | −0.0432109 | − | 0.161265i | ||||
\(993\) | −4.77081 | − | 4.77081i | −0.151397 | − | 0.151397i | ||||
\(994\) | −3.32696 | + | 29.6005i | −0.105525 | + | 0.938872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.333688 | + | 0.577964i | −0.0105733 | + | 0.0183135i | ||||
\(997\) | 26.5703 | + | 7.11948i | 0.841489 | + | 0.225476i | 0.653720 | − | 0.756737i | \(-0.273208\pi\) |
0.187769 | + | 0.982213i | \(0.439874\pi\) | |||||||
\(998\) | 33.3518 | + | 8.93659i | 1.05573 | + | 0.282883i | ||||
\(999\) | −5.08624 | + | 8.80963i | −0.160922 | + | 0.278724i |
(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 | 1050.2.bc.e.607.1 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.f.943.2 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.f.943.3 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.e.607.4 | yes | 16 | |
7.3 | odd | 6 | 1050.2.bc.f.157.3 | yes | 16 | ||
35.3 | even | 12 | inner | 1050.2.bc.e.493.2 | ✓ | 16 | |
35.17 | even | 12 | inner | 1050.2.bc.e.493.3 | yes | 16 | |
35.24 | odd | 6 | 1050.2.bc.f.157.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.493.2 | ✓ | 16 | 35.3 | even | 12 | inner | |
1050.2.bc.e.493.3 | yes | 16 | 35.17 | even | 12 | inner | |
1050.2.bc.e.607.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.2.bc.e.607.4 | yes | 16 | 5.4 | even | 2 | inner | |
1050.2.bc.f.157.2 | yes | 16 | 35.24 | odd | 6 | ||
1050.2.bc.f.157.3 | yes | 16 | 7.3 | odd | 6 | ||
1050.2.bc.f.943.2 | yes | 16 | 5.2 | odd | 4 | ||
1050.2.bc.f.943.3 | yes | 16 | 5.3 | odd | 4 |