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 | 943.3 | ||
Root | \(-2.35727 - 1.36097i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.943 |
Dual form | 1050.2.bc.f.157.3 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.46313 | − | 0.965926i | −0.930974 | − | 0.365086i | ||||
\(8\) | −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 | \(0.636261\pi\) | |||||||
\(12\) | 0.965926 | − | 0.258819i | 0.278839 | − | 0.0747146i | ||||
\(13\) | 4.42535 | − | 4.42535i | 1.22737 | − | 1.22737i | 0.262417 | − | 0.964954i | \(-0.415480\pi\) |
0.964954 | − | 0.262417i | \(-0.0845197\pi\) | |||||||
\(14\) | 0.295509 | − | 2.62920i | 0.0789781 | − | 0.702682i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −0.364671 | + | 1.36097i | −0.0884458 | + | 0.330084i | −0.995944 | − | 0.0899709i | \(-0.971323\pi\) |
0.907499 | + | 0.420055i | \(0.137989\pi\) | |||||||
\(18\) | −0.258819 | + | 0.965926i | −0.0610042 | + | 0.227671i | ||||
\(19\) | −1.76317 | + | 3.05390i | −0.404499 | + | 0.700613i | −0.994263 | − | 0.106963i | \(-0.965887\pi\) |
0.589764 | + | 0.807576i | \(0.299221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.12920 | + | 1.57052i | 0.464629 | + | 0.342715i | ||||
\(22\) | −2.72194 | + | 2.72194i | −0.580321 | + | 0.580321i | ||||
\(23\) | 1.36097 | − | 0.364671i | 0.283782 | − | 0.0760392i | −0.114120 | − | 0.993467i | \(-0.536405\pi\) |
0.397903 | + | 0.917428i | \(0.369738\pi\) | |||||||
\(24\) | 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 | ||||
\(28\) | 2.61609 | − | 0.395046i | 0.494395 | − | 0.0746568i | ||||
\(29\) | 6.66738i | 1.23810i | 0.785351 | + | 0.619050i | \(0.212482\pi\) | ||||
−0.785351 | + | 0.619050i | \(0.787518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.55390 | + | 2.62920i | −0.817905 | + | 0.472218i | −0.849693 | − | 0.527277i | \(-0.823213\pi\) |
0.0317885 | + | 0.999495i | \(0.489880\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −0.996301 | − | 3.71825i | −0.173434 | − | 0.647263i | ||||
\(34\) | −1.40898 | −0.241638 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.63283 | + | 9.82586i | 0.432835 | + | 1.61536i | 0.746195 | + | 0.665727i | \(0.231879\pi\) |
−0.313360 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(38\) | −3.40619 | − | 0.912685i | −0.552556 | − | 0.148057i | ||||
\(39\) | −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 | \(-0.0184436\pi\) | |||||||
\(42\) | −0.965926 | + | 2.46313i | −0.149046 | + | 0.380069i | ||||
\(43\) | −1.52070 | − | 1.52070i | −0.231904 | − | 0.231904i | 0.581583 | − | 0.813487i | \(-0.302434\pi\) |
−0.813487 | + | 0.581583i | \(0.802434\pi\) | |||||||
\(44\) | −3.33369 | − | 1.92471i | −0.502572 | − | 0.290160i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.704491 | + | 1.22021i | 0.103872 | + | 0.179911i | ||||
\(47\) | −5.07922 | + | 1.36097i | −0.740880 | + | 0.198518i | −0.609469 | − | 0.792810i | \(-0.708617\pi\) |
−0.131411 | + | 0.991328i | \(0.541951\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | −1.61979 | + | 6.04514i | −0.224625 | + | 0.838311i | ||||
\(53\) | −2.54922 | + | 9.51380i | −0.350162 | + | 1.30682i | 0.536303 | + | 0.844025i | \(0.319820\pi\) |
−0.886465 | + | 0.462796i | \(0.846846\pi\) | |||||||
\(54\) | 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 | ||||
\(58\) | −6.44019 | + | 1.72564i | −0.845638 | + | 0.226588i | ||||
\(59\) | 6.84941 | + | 11.8635i | 0.891717 | + | 1.54450i | 0.837815 | + | 0.545954i | \(0.183832\pi\) |
0.0539019 | + | 0.998546i | \(0.482834\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | −1.65017 | − | 2.06808i | −0.207901 | − | 0.260553i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.33369 | − | 1.92471i | 0.410349 | − | 0.236915i | ||||
\(67\) | −7.39689 | − | 1.98199i | −0.903673 | − | 0.242139i | −0.223080 | − | 0.974800i | \(-0.571611\pi\) |
−0.680593 | + | 0.732662i | \(0.738278\pi\) | |||||||
\(68\) | −0.364671 | − | 1.36097i | −0.0442229 | − | 0.165042i | ||||
\(69\) | −1.40898 | −0.169622 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2584 | 1.33613 | 0.668063 | − | 0.744105i | \(-0.267124\pi\) | ||||
0.668063 | + | 0.744105i | \(0.267124\pi\) | |||||||
\(72\) | −0.258819 | − | 0.965926i | −0.0305021 | − | 0.113835i | ||||
\(73\) | 10.2878 | + | 2.75660i | 1.20409 | + | 0.322636i | 0.804442 | − | 0.594031i | \(-0.202464\pi\) |
0.399652 | + | 0.916667i | \(0.369131\pi\) | |||||||
\(74\) | −8.80963 | + | 5.08624i | −1.02410 | + | 0.591263i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.52634i | − | 0.404499i | ||||||
\(77\) | −1.52070 | − | 10.0704i | −0.173299 | − | 1.14763i | ||||
\(78\) | −4.42535 | − | 4.42535i | −0.501072 | − | 0.501072i | ||||
\(79\) | 2.72849 | + | 1.57529i | 0.306979 | + | 0.177234i | 0.645574 | − | 0.763698i | \(-0.276618\pi\) |
−0.338595 | + | 0.940932i | \(0.609952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.716337 | − | 0.191942i | 0.0791062 | − | 0.0211964i | ||||
\(83\) | −0.471906 | + | 0.471906i | −0.0517984 | + | 0.0517984i | −0.732532 | − | 0.680733i | \(-0.761661\pi\) |
0.680733 | + | 0.732532i | \(0.261661\pi\) | |||||||
\(84\) | −2.62920 | − | 0.295509i | −0.286869 | − | 0.0322427i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.07529 | − | 1.86246i | 0.115952 | − | 0.200835i | ||||
\(87\) | 1.72564 | − | 6.44019i | 0.185008 | − | 0.690461i | ||||
\(88\) | 0.996301 | − | 3.71825i | 0.106206 | − | 0.396366i | ||||
\(89\) | 6.97594 | − | 12.0827i | 0.739448 | − | 1.28076i | −0.213296 | − | 0.976988i | \(-0.568420\pi\) |
0.952744 | − | 0.303774i | \(-0.0982467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.1748 | + | 6.62564i | −1.59075 | + | 0.694555i | ||||
\(92\) | −0.996301 | + | 0.996301i | −0.103872 | + | 0.103872i | ||||
\(93\) | 5.07922 | − | 1.36097i | 0.526690 | − | 0.141126i | ||||
\(94\) | −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 | \(-0.417264\pi\) |
−0.966410 | + | 0.257006i | \(0.917264\pi\) | |||||||
\(98\) | −3.26748 | + | 6.19060i | −0.330066 | + | 0.625345i | ||||
\(99\) | 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 | \(0.0798761\pi\) | |||||||
\(102\) | 1.36097 | + | 0.364671i | 0.134756 | + | 0.0361079i | ||||
\(103\) | 3.97706 | + | 14.8426i | 0.391872 | + | 1.46249i | 0.827043 | + | 0.562138i | \(0.190021\pi\) |
−0.435172 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(104\) | −6.25839 | −0.613686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.84941 | −0.956659 | ||||||||
\(107\) | 0.697125 | + | 2.60170i | 0.0673936 | + | 0.251516i | 0.991401 | − | 0.130858i | \(-0.0417732\pi\) |
−0.924008 | + | 0.382374i | \(0.875107\pi\) | |||||||
\(108\) | 0.965926 | + | 0.258819i | 0.0929463 | + | 0.0249049i | ||||
\(109\) | −14.5503 | + | 8.40064i | −1.39367 | + | 0.804636i | −0.993719 | − | 0.111901i | \(-0.964306\pi\) |
−0.399951 | + | 0.916537i | \(0.630973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 10.1725i | − | 0.965529i | ||||||
\(112\) | −2.06808 | + | 1.65017i | −0.195415 | + | 0.155926i | ||||
\(113\) | −10.2109 | − | 10.2109i | −0.960563 | − | 0.960563i | 0.0386883 | − | 0.999251i | \(-0.487682\pi\) |
−0.999251 | + | 0.0386883i | \(0.987682\pi\) | |||||||
\(114\) | 3.05390 | + | 1.76317i | 0.286024 | + | 0.165136i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.33369 | − | 5.77412i | −0.309525 | − | 0.536113i | ||||
\(117\) | 6.04514 | − | 1.61979i | 0.558874 | − | 0.149750i | ||||
\(118\) | −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 | ||||
\(122\) | 0.256346 | − | 0.956695i | 0.0232085 | − | 0.0866151i | ||||
\(123\) | −0.191942 | + | 0.716337i | −0.0173068 | + | 0.0645900i | ||||
\(124\) | 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 | −0.357936 | + | 0.933746i | \(0.616519\pi\) |
−0.933746 | + | 0.357936i | \(0.883481\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | 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 | ||||
\(133\) | 7.29275 | − | 5.81905i | 0.632362 | − | 0.504576i | ||||
\(134\) | − | 7.65782i | − | 0.661535i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.22021 | − | 0.704491i | 0.104633 | − | 0.0604096i | ||||
\(137\) | 10.9950 | + | 2.94610i | 0.939367 | + | 0.251703i | 0.695845 | − | 0.718192i | \(-0.255030\pi\) |
0.243523 | + | 0.969895i | \(0.421697\pi\) | |||||||
\(138\) | −0.364671 | − | 1.36097i | −0.0310429 | − | 0.115854i | ||||
\(139\) | −3.50510 | −0.297299 | −0.148650 | − | 0.988890i | \(-0.547493\pi\) | ||||
−0.148650 | + | 0.988890i | \(0.547493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.25839 | 0.442837 | ||||||||
\(142\) | 2.91389 | + | 10.8748i | 0.244528 | + | 0.912591i | ||||
\(143\) | 23.2702 | + | 6.23524i | 1.94596 | + | 0.521417i | ||||
\(144\) | 0.866025 | − | 0.500000i | 0.0721688 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.6507i | 0.881458i | ||||||||
\(147\) | −3.72748 | − | 5.92503i | −0.307437 | − | 0.488688i | ||||
\(148\) | −7.19303 | − | 7.19303i | −0.591263 | − | 0.591263i | ||||
\(149\) | 11.9713 | + | 6.91165i | 0.980730 | + | 0.566225i | 0.902490 | − | 0.430710i | \(-0.141737\pi\) |
0.0782393 | + | 0.996935i | \(0.475070\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.97861 | − | 5.15910i | −0.242396 | − | 0.419842i | 0.719001 | − | 0.695010i | \(-0.244600\pi\) |
−0.961396 | + | 0.275168i | \(0.911267\pi\) | |||||||
\(152\) | 3.40619 | − | 0.912685i | 0.276278 | − | 0.0740285i | ||||
\(153\) | −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 | ||||
\(157\) | 2.58387 | − | 9.64315i | 0.206216 | − | 0.769607i | −0.782860 | − | 0.622198i | \(-0.786240\pi\) |
0.989076 | − | 0.147409i | \(-0.0470934\pi\) | |||||||
\(158\) | −0.815432 | + | 3.04324i | −0.0648723 | + | 0.242107i | ||||
\(159\) | 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 | ||||
\(163\) | 1.32888 | − | 0.356071i | 0.104086 | − | 0.0278896i | −0.206400 | − | 0.978468i | \(-0.566175\pi\) |
0.310486 | + | 0.950578i | \(0.399508\pi\) | |||||||
\(164\) | 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 | \(-0.111682\pi\) |
−0.343704 | + | 0.939078i | \(0.611682\pi\) | |||||||
\(168\) | −0.395046 | − | 2.61609i | −0.0304785 | − | 0.201836i | ||||
\(169\) | − | 26.1675i | − | 2.01288i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.05390 | + | 1.76317i | −0.233538 | + | 0.134833i | ||||
\(172\) | 2.07731 | + | 0.556613i | 0.158393 | + | 0.0424414i | ||||
\(173\) | −0.439687 | − | 1.64094i | −0.0334288 | − | 0.124758i | 0.947195 | − | 0.320658i | \(-0.103904\pi\) |
−0.980624 | + | 0.195900i | \(0.937237\pi\) | |||||||
\(174\) | 6.66738 | 0.505452 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.84941 | 0.290160 | ||||||||
\(177\) | −3.54552 | − | 13.2320i | −0.266497 | − | 0.994581i | ||||
\(178\) | 13.4765 | + | 3.61101i | 1.01010 | + | 0.270657i | ||||
\(179\) | 11.9713 | − | 6.91165i | 0.894779 | − | 0.516601i | 0.0192766 | − | 0.999814i | \(-0.493864\pi\) |
0.875503 | + | 0.483213i | \(0.160530\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.36086i | − | 0.249811i | −0.992169 | − | 0.124905i | \(-0.960137\pi\) | ||
0.992169 | − | 0.124905i | \(-0.0398627\pi\) | |||||||
\(182\) | −10.3274 | − | 12.9429i | −0.765517 | − | 0.959388i | ||||
\(183\) | 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 | ||||
\(187\) | −5.23894 | + | 1.40377i | −0.383109 | + | 0.102654i | ||||
\(188\) | 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 | \(0.175208\pi\) | |||||||
\(192\) | 0.258819 | − | 0.965926i | 0.0186787 | − | 0.0697097i | ||||
\(193\) | −1.91759 | + | 7.15653i | −0.138031 | + | 0.515138i | 0.861936 | + | 0.507017i | \(0.169252\pi\) |
−0.999967 | + | 0.00812132i | \(0.997415\pi\) | |||||||
\(194\) | 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 | −0.101735 | − | 0.994811i | \(-0.532439\pi\) |
0.994811 | + | 0.101735i | \(0.0324395\pi\) | |||||||
\(198\) | −3.71825 | + | 0.996301i | −0.264244 | + | 0.0708040i | ||||
\(199\) | 0.350302 | + | 0.606741i | 0.0248323 | + | 0.0430107i | 0.878174 | − | 0.478340i | \(-0.158762\pi\) |
−0.853342 | + | 0.521351i | \(0.825428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.63187 | + | 3.82891i | 0.467776 | + | 0.270070i | ||||
\(202\) | 10.1584 | + | 10.1584i | 0.714745 | + | 0.714745i | ||||
\(203\) | 6.44019 | − | 16.4226i | 0.452013 | − | 1.15264i | ||||
\(204\) | 1.40898i | 0.0986485i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.3075 | + | 7.68310i | −0.927179 | + | 0.535307i | ||||
\(207\) | 1.36097 | + | 0.364671i | 0.0945941 | + | 0.0253464i | ||||
\(208\) | −1.61979 | − | 6.04514i | −0.112312 | − | 0.419155i | ||||
\(209\) | −13.5743 | −0.938957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4426 | −1.06311 | −0.531555 | − | 0.847024i | \(-0.678392\pi\) | ||||
−0.531555 | + | 0.847024i | \(0.678392\pi\) | |||||||
\(212\) | −2.54922 | − | 9.51380i | −0.175081 | − | 0.653410i | ||||
\(213\) | −10.8748 | − | 2.91389i | −0.745127 | − | 0.199656i | ||||
\(214\) | −2.33262 | + | 1.34674i | −0.159455 | + | 0.0920614i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 13.7564 | − | 2.07731i | 0.933848 | − | 0.141017i | ||||
\(218\) | −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 | ||||
\(222\) | 9.82586 | − | 2.63283i | 0.659469 | − | 0.176704i | ||||
\(223\) | −1.17901 | + | 1.17901i | −0.0789525 | + | 0.0789525i | −0.745480 | − | 0.666528i | \(-0.767780\pi\) |
0.666528 | + | 0.745480i | \(0.267780\pi\) | |||||||
\(224\) | −2.12920 | − | 1.57052i | −0.142263 | − | 0.104935i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.22021 | − | 12.5058i | 0.480282 | − | 0.831872i | ||||
\(227\) | 2.97938 | − | 11.1192i | 0.197749 | − | 0.738008i | −0.793790 | − | 0.608192i | \(-0.791895\pi\) |
0.991538 | − | 0.129815i | \(-0.0414384\pi\) | |||||||
\(228\) | −0.912685 | + | 3.40619i | −0.0604440 | + | 0.225580i | ||||
\(229\) | 7.80873 | − | 13.5251i | 0.516016 | − | 0.893765i | −0.483811 | − | 0.875172i | \(-0.660748\pi\) |
0.999827 | − | 0.0185931i | \(-0.00591872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.13754 | + | 10.1209i | −0.0748443 | + | 0.665904i | ||||
\(232\) | 4.71455 | − | 4.71455i | 0.309525 | − | 0.309525i | ||||
\(233\) | −28.7141 | + | 7.69393i | −1.88113 | + | 0.504046i | −0.881641 | + | 0.471920i | \(0.843561\pi\) |
−0.999484 | + | 0.0321261i | \(0.989772\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | 3.47050 | + | 1.36097i | 0.224959 | + | 0.0882187i | ||||
\(239\) | − | 7.95188i | − | 0.514364i | −0.966363 | − | 0.257182i | \(-0.917206\pi\) | ||
0.966363 | − | 0.257182i | \(-0.0827940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.81069 | + | 5.66420i | −0.631962 | + | 0.364863i | −0.781512 | − | 0.623891i | \(-0.785551\pi\) |
0.149550 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(242\) | −3.68787 | − | 0.988162i | −0.237065 | − | 0.0635215i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 0.990444 | 0.0634067 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.741607 | −0.0472831 | ||||||||
\(247\) | 5.71194 | + | 21.3172i | 0.363442 | + | 1.35638i | ||||
\(248\) | 5.07922 | + | 1.36097i | 0.322531 | + | 0.0864218i | ||||
\(249\) | 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 | \(-0.231063\pi\) | |||||||
\(252\) | 2.46313 | + | 0.965926i | 0.155162 | + | 0.0608476i | ||||
\(253\) | 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 | ||||
\(257\) | 25.0314 | − | 6.70715i | 1.56142 | − | 0.418380i | 0.628305 | − | 0.777967i | \(-0.283749\pi\) |
0.933112 | + | 0.359587i | \(0.117082\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | 1.69343 | − | 6.31995i | 0.104620 | − | 0.390448i | ||||
\(263\) | −4.29407 | + | 16.0257i | −0.264784 | + | 0.988187i | 0.697599 | + | 0.716489i | \(0.254252\pi\) |
−0.962383 | + | 0.271698i | \(0.912415\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | 7.39689 | − | 1.98199i | 0.451837 | − | 0.121069i | ||||
\(269\) | 13.6804 | + | 23.6952i | 0.834110 | + | 1.44472i | 0.894753 | + | 0.446562i | \(0.147352\pi\) |
−0.0606421 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 16.3725 | − | 2.47236i | 0.990911 | − | 0.149634i | ||||
\(274\) | 11.3829i | 0.687665i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.22021 | − | 0.704491i | 0.0734483 | − | 0.0424054i | ||||
\(277\) | 20.1045 | + | 5.38699i | 1.20796 | + | 0.323673i | 0.805963 | − | 0.591966i | \(-0.201648\pi\) |
0.402001 | + | 0.915639i | \(0.368315\pi\) | |||||||
\(278\) | −0.907188 | − | 3.38567i | −0.0544095 | − | 0.203059i | ||||
\(279\) | −5.25839 | −0.314812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.89220 | 0.172534 | 0.0862670 | − | 0.996272i | \(-0.472506\pi\) | ||||
0.0862670 | + | 0.996272i | \(0.472506\pi\) | |||||||
\(282\) | 1.36097 | + | 5.07922i | 0.0810447 | + | 0.302463i | ||||
\(283\) | 20.4714 | + | 5.48531i | 1.21690 | + | 0.326068i | 0.809466 | − | 0.587167i | \(-0.199757\pi\) |
0.407435 | + | 0.913234i | \(0.366423\pi\) | |||||||
\(284\) | −9.75005 | + | 5.62920i | −0.578559 | + | 0.334031i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0911i | 1.42454i | ||||||||
\(287\) | −0.716337 | + | 1.82667i | −0.0422841 | + | 0.107825i | ||||
\(288\) | 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 | ||||
\(292\) | −10.2878 | + | 2.75660i | −0.602047 | + | 0.161318i | ||||
\(293\) | 14.1436 | − | 14.1436i | 0.826280 | − | 0.826280i | −0.160720 | − | 0.987000i | \(-0.551382\pi\) |
0.987000 | + | 0.160720i | \(0.0513816\pi\) | |||||||
\(294\) | 4.75839 | − | 5.13397i | 0.277515 | − | 0.299419i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.08624 | − | 8.80963i | 0.295632 | − | 0.512049i | ||||
\(297\) | 0.996301 | − | 3.71825i | 0.0578112 | − | 0.215754i | ||||
\(298\) | −3.57773 | + | 13.3523i | −0.207253 | + | 0.773477i | ||||
\(299\) | 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 | ||||
\(303\) | −13.8767 | + | 3.71825i | −0.797194 | + | 0.213608i | ||||
\(304\) | 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 | \(-0.338670\pi\) |
−0.874286 | + | 0.485411i | \(0.838670\pi\) | |||||||
\(308\) | 6.35217 | + | 7.96089i | 0.361948 | + | 0.453614i | ||||
\(309\) | − | 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 | \(0.532084\pi\) | |||||||
\(312\) | 6.04514 | + | 1.61979i | 0.342239 | + | 0.0917026i | ||||
\(313\) | −4.26240 | − | 15.9075i | −0.240925 | − | 0.899145i | −0.975388 | − | 0.220496i | \(-0.929232\pi\) |
0.734463 | − | 0.678649i | \(-0.237434\pi\) | |||||||
\(314\) | 9.98332 | 0.563391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.15059 | −0.177234 | ||||||||
\(317\) | 6.87988 | + | 25.6761i | 0.386412 | + | 1.44211i | 0.835928 | + | 0.548838i | \(0.184930\pi\) |
−0.449516 | + | 0.893272i | \(0.648404\pi\) | |||||||
\(318\) | 9.51380 | + | 2.54922i | 0.533507 | + | 0.142953i | ||||
\(319\) | −22.2269 | + | 12.8327i | −1.24447 | + | 0.718495i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.69348i | − | 0.150336i | ||||||
\(322\) | −0.556613 | − | 3.68603i | −0.0310189 | − | 0.205414i | ||||
\(323\) | −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 | ||||
\(327\) | 16.2288 | − | 4.34849i | 0.897455 | − | 0.240472i | ||||
\(328\) | −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 | \(0.226032\pi\) | |||||||
\(332\) | 0.172729 | − | 0.644635i | 0.00947976 | − | 0.0353789i | ||||
\(333\) | −2.63283 | + | 9.82586i | −0.144278 | + | 0.538454i | ||||
\(334\) | −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 | −0.644715 | − | 0.764423i | \(-0.723024\pi\) |
0.764423 | + | 0.644715i | \(0.223024\pi\) | |||||||
\(338\) | 25.2758 | − | 6.77264i | 1.37482 | − | 0.368383i | ||||
\(339\) | 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 | ||||
\(343\) | −8.04937 | − | 16.6796i | −0.434625 | − | 0.900611i | ||||
\(344\) | 2.15059i | 0.115952i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47122 | − | 0.849411i | 0.0790934 | − | 0.0456646i | ||||
\(347\) | −12.7957 | − | 3.42859i | −0.686908 | − | 0.184056i | −0.101549 | − | 0.994831i | \(-0.532380\pi\) |
−0.585359 | + | 0.810774i | \(0.699046\pi\) | |||||||
\(348\) | 1.72564 | + | 6.44019i | 0.0925042 | + | 0.345230i | ||||
\(349\) | −18.1788 | −0.973090 | −0.486545 | − | 0.873655i | \(-0.661743\pi\) | ||||
−0.486545 | + | 0.873655i | \(0.661743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.25839 | −0.334048 | ||||||||
\(352\) | 0.996301 | + | 3.71825i | 0.0531030 | + | 0.198183i | ||||
\(353\) | −21.0687 | − | 5.64535i | −1.12138 | − | 0.300472i | −0.349936 | − | 0.936774i | \(-0.613797\pi\) |
−0.771440 | + | 0.636302i | \(0.780463\pi\) | |||||||
\(354\) | 11.8635 | − | 6.84941i | 0.630539 | − | 0.364042i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.9519i | 0.739448i | ||||||||
\(357\) | −2.91389 | + | 2.32505i | −0.154219 | + | 0.123055i | ||||
\(358\) | 9.77455 | + | 9.77455i | 0.516601 | + | 0.516601i | ||||
\(359\) | −24.7752 | − | 14.3040i | −1.30758 | − | 0.754934i | −0.325892 | − | 0.945407i | \(-0.605664\pi\) |
−0.981692 | + | 0.190473i | \(0.938998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.28246 | + | 5.68538i | 0.172761 | + | 0.299230i | ||||
\(362\) | 3.24634 | − | 0.869854i | 0.170624 | − | 0.0457185i | ||||
\(363\) | 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 | ||||
\(367\) | 8.40733 | − | 31.3766i | 0.438859 | − | 1.63784i | −0.292800 | − | 0.956174i | \(-0.594587\pi\) |
0.731659 | − | 0.681671i | \(-0.238746\pi\) | |||||||
\(368\) | 0.364671 | − | 1.36097i | 0.0190098 | − | 0.0709456i | ||||
\(369\) | 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 | ||||
\(373\) | −21.3172 | + | 5.71194i | −1.10377 | + | 0.295753i | −0.764297 | − | 0.644865i | \(-0.776914\pi\) |
−0.339468 | + | 0.940618i | \(0.610247\pi\) | |||||||
\(374\) | −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 | ||||
\(378\) | −2.06808 | + | 1.65017i | −0.106371 | + | 0.0848754i | ||||
\(379\) | − | 15.8588i | − | 0.814614i | −0.913291 | − | 0.407307i | \(-0.866468\pi\) | ||
0.913291 | − | 0.407307i | \(-0.133532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.8280 | − | 10.2930i | 0.913357 | − | 0.527327i | ||||
\(382\) | −0.716337 | − | 0.191942i | −0.0366510 | − | 0.00982061i | ||||
\(383\) | 4.59325 | + | 17.1422i | 0.234704 | + | 0.875927i | 0.978282 | + | 0.207278i | \(0.0664605\pi\) |
−0.743578 | + | 0.668649i | \(0.766873\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.40898 | −0.377107 | ||||||||
\(387\) | −0.556613 | − | 2.07731i | −0.0282942 | − | 0.105596i | ||||
\(388\) | 9.54418 | + | 2.55735i | 0.484532 | + | 0.129830i | ||||
\(389\) | −30.2340 | + | 17.4556i | −1.53292 | + | 0.885034i | −0.533700 | + | 0.845674i | \(0.679199\pi\) |
−0.999225 | + | 0.0393604i | \(0.987468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.98523i | 0.100397i | ||||||||
\(392\) | −0.265576 | − | 6.99496i | −0.0134136 | − | 0.353299i | ||||
\(393\) | 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 | ||||
\(397\) | −34.8886 | + | 9.34838i | −1.75101 | + | 0.469182i | −0.984841 | − | 0.173458i | \(-0.944506\pi\) |
−0.766169 | + | 0.642640i | \(0.777839\pi\) | |||||||
\(398\) | −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 | \(0.178458\pi\) | |||||||
\(402\) | −1.98199 | + | 7.39689i | −0.0988526 | + | 0.368923i | ||||
\(403\) | −8.51750 | + | 31.7877i | −0.424287 | + | 1.58346i | ||||
\(404\) | −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 | ||||
\(408\) | −1.36097 | + | 0.364671i | −0.0673782 | + | 0.0180539i | ||||
\(409\) | 1.51216 | + | 2.61914i | 0.0747716 | + | 0.129508i | 0.900987 | − | 0.433846i | \(-0.142844\pi\) |
−0.826215 | + | 0.563354i | \(0.809511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.85786 | − | 5.69144i | −0.486252 | − | 0.280738i | ||||
\(412\) | −10.8655 | − | 10.8655i | −0.535307 | − | 0.535307i | ||||
\(413\) | −5.41167 | − | 35.8374i | −0.266291 | − | 1.76344i | ||||
\(414\) | 1.40898i | 0.0692477i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.41993 | − | 3.12920i | 0.265734 | − | 0.153421i | ||||
\(417\) | 3.38567 | + | 0.907188i | 0.165797 | + | 0.0444252i | ||||
\(418\) | −3.51330 | − | 13.1118i | −0.171841 | − | 0.641319i | ||||
\(419\) | 14.8547 | 0.725702 | 0.362851 | − | 0.931847i | \(-0.381803\pi\) | ||||
0.362851 | + | 0.931847i | \(0.381803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2920 | 1.33013 | 0.665065 | − | 0.746786i | \(-0.268404\pi\) | ||||
0.665065 | + | 0.746786i | \(0.268404\pi\) | |||||||
\(422\) | −3.99683 | − | 14.9164i | −0.194563 | − | 0.726117i | ||||
\(423\) | −5.07922 | − | 1.36097i | −0.246960 | − | 0.0661727i | ||||
\(424\) | 8.52984 | − | 4.92471i | 0.414246 | − | 0.239165i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 11.2584i | − | 0.545471i | ||||||
\(427\) | 1.63440 | + | 2.04832i | 0.0790940 | + | 0.0991250i | ||||
\(428\) | −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 | \(-0.517561\pi\) | |||||||
\(432\) | −0.965926 | + | 0.258819i | −0.0464731 | + | 0.0124524i | ||||
\(433\) | −7.65990 | + | 7.65990i | −0.368111 | + | 0.368111i | −0.866788 | − | 0.498677i | \(-0.833819\pi\) |
0.498677 | + | 0.866788i | \(0.333819\pi\) | |||||||
\(434\) | 5.56696 | + | 12.7501i | 0.267222 | + | 0.612022i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.40064 | − | 14.5503i | 0.402318 | − | 0.696835i | ||||
\(437\) | −1.28596 | + | 4.79925i | −0.0615156 | + | 0.229579i | ||||
\(438\) | 2.75660 | − | 10.2878i | 0.131716 | − | 0.491569i | ||||
\(439\) | −10.1375 | + | 17.5586i | −0.483835 | + | 0.838027i | −0.999828 | − | 0.0185660i | \(-0.994090\pi\) |
0.515992 | + | 0.856593i | \(0.327423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.06696 | + | 6.68788i | 0.0984265 | + | 0.318470i | ||||
\(442\) | −6.23524 | + | 6.23524i | −0.296580 | + | 0.296580i | ||||
\(443\) | −6.79186 | + | 1.81987i | −0.322691 | + | 0.0864647i | −0.416528 | − | 0.909123i | \(-0.636753\pi\) |
0.0938374 | + | 0.995588i | \(0.470087\pi\) | |||||||
\(444\) | 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 | ||||
\(448\) | 0.965926 | − | 2.46313i | 0.0456357 | − | 0.116372i | ||||
\(449\) | − | 4.46654i | − | 0.210789i | −0.994430 | − | 0.105394i | \(-0.966389\pi\) | ||
0.994430 | − | 0.105394i | \(-0.0336105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47229 | − | 1.42737i | 0.116415 | − | 0.0672125i | ||||
\(452\) | 13.9484 | + | 3.73746i | 0.656077 | + | 0.175795i | ||||
\(453\) | 1.54184 | + | 5.75423i | 0.0724420 | + | 0.270357i | ||||
\(454\) | 11.5114 | 0.540259 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.52634 | −0.165136 | ||||||||
\(457\) | −6.28043 | − | 23.4389i | −0.293786 | − | 1.09643i | −0.942176 | − | 0.335117i | \(-0.891224\pi\) |
0.648390 | − | 0.761308i | \(-0.275443\pi\) | |||||||
\(458\) | 15.0853 | + | 4.04210i | 0.704891 | + | 0.188875i | ||||
\(459\) | 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 | \(0.934168\pi\) | |||||||
\(462\) | −10.0704 | + | 1.52070i | −0.468518 | + | 0.0707492i | ||||
\(463\) | −1.05131 | − | 1.05131i | −0.0488583 | − | 0.0488583i | 0.682256 | − | 0.731114i | \(-0.260999\pi\) |
−0.731114 | + | 0.682256i | \(0.760999\pi\) | |||||||
\(464\) | 5.77412 | + | 3.33369i | 0.268057 | + | 0.154763i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8635 | − | 25.7444i | −0.688540 | − | 1.19259i | ||||
\(467\) | −35.7465 | + | 9.57824i | −1.65415 | + | 0.443228i | −0.960770 | − | 0.277345i | \(-0.910545\pi\) |
−0.693379 | + | 0.720573i | \(0.743879\pi\) | |||||||
\(468\) | −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 | ||||
\(472\) | 3.54552 | − | 13.2320i | 0.163196 | − | 0.609054i | ||||
\(473\) | 2.14263 | − | 7.99642i | 0.0985184 | − | 0.367676i | ||||
\(474\) | 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 | ||||
\(478\) | 7.68092 | − | 2.05810i | 0.351317 | − | 0.0941352i | ||||
\(479\) | 0.778723 | + | 1.34879i | 0.0355807 | + | 0.0616277i | 0.883267 | − | 0.468870i | \(-0.155339\pi\) |
−0.847687 | + | 0.530497i | \(0.822005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.1341 | + | 31.8317i | 2.51390 | + | 1.45140i | ||||
\(482\) | −8.01039 | − | 8.01039i | −0.364863 | − | 0.364863i | ||||
\(483\) | 3.47050 | + | 1.36097i | 0.157913 | + | 0.0619264i | ||||
\(484\) | − | 3.81796i | − | 0.173544i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 7.56068 | + | 2.02588i | 0.342607 | + | 0.0918013i | 0.426020 | − | 0.904714i | \(-0.359915\pi\) |
−0.0834127 | + | 0.996515i | \(0.526582\pi\) | |||||||
\(488\) | 0.256346 | + | 0.956695i | 0.0116042 | + | 0.0433076i | ||||
\(489\) | −1.37575 | −0.0622137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.8776 | 1.98017 | 0.990085 | − | 0.140468i | \(-0.0448608\pi\) | ||||
0.990085 | + | 0.140468i | \(0.0448608\pi\) | |||||||
\(492\) | −0.191942 | − | 0.716337i | −0.00865341 | − | 0.0322950i | ||||
\(493\) | −9.07411 | − | 2.43140i | −0.408677 | − | 0.109505i | ||||
\(494\) | −19.1125 | + | 11.0346i | −0.859913 | + | 0.496471i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.25839i | 0.236109i | ||||||||
\(497\) | −27.7308 | − | 10.8748i | −1.24390 | − | 0.487800i | ||||
\(498\) | 0.471906 | + | 0.471906i | 0.0211466 | + | 0.0211466i | ||||
\(499\) | 29.9024 | + | 17.2642i | 1.33862 | + | 0.772850i | 0.986602 | − | 0.163144i | \(-0.0521636\pi\) |
0.352014 | + | 0.935995i | \(0.385497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.44043 | − | 9.42310i | −0.243060 | − | 0.420993i | ||||
\(502\) | 20.3169 | − | 5.44389i | 0.906786 | − | 0.242973i | ||||
\(503\) | −16.9300 | + | 16.9300i | −0.754872 | + | 0.754872i | −0.975384 | − | 0.220512i | \(-0.929227\pi\) |
0.220512 | + | 0.975384i | \(0.429227\pi\) | |||||||
\(504\) | −0.295509 | + | 2.62920i | −0.0131630 | + | 0.117114i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.71188 | + | 4.69711i | −0.120558 | + | 0.208812i | ||||
\(507\) | −6.77264 | + | 25.2758i | −0.300784 | + | 1.12254i | ||||
\(508\) | 5.32805 | − | 19.8846i | 0.236394 | − | 0.882235i | ||||
\(509\) | 5.10674 | − | 8.84514i | 0.226352 | − | 0.392054i | −0.730372 | − | 0.683050i | \(-0.760653\pi\) |
0.956724 | + | 0.290996i | \(0.0939866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.6774 | − | 16.7271i | −1.00319 | − | 0.739963i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 3.40619 | − | 0.912685i | 0.150387 | − | 0.0402960i | ||||
\(514\) | 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 | ||||
\(518\) | 26.6121 | − | 4.01860i | 1.16927 | − | 0.176567i | ||||
\(519\) | 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 | \(0.457426\pi\) | |||||||
\(522\) | −6.44019 | − | 1.72564i | −0.281879 | − | 0.0755294i | ||||
\(523\) | −10.9108 | − | 40.7197i | −0.477097 | − | 1.78055i | −0.613281 | − | 0.789865i | \(-0.710151\pi\) |
0.136184 | − | 0.990684i | \(-0.456516\pi\) | |||||||
\(524\) | 6.54289 | 0.285828 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.5910 | −0.723403 | ||||||||
\(527\) | −1.91759 | − | 7.15653i | −0.0835313 | − | 0.311743i | ||||
\(528\) | −3.71825 | − | 0.996301i | −0.161816 | − | 0.0433584i | ||||
\(529\) | −18.1993 | + | 10.5074i | −0.791275 | + | 0.456843i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.6988i | 0.594478i | ||||||||
\(532\) | −3.40619 | + | 8.68582i | −0.147677 | + | 0.376578i | ||||
\(533\) | −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 | ||||
\(537\) | −13.3523 | + | 3.57773i | −0.576194 | + | 0.154391i | ||||
\(538\) | −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 | \(0.00407455\pi\) | |||||||
\(542\) | 0.247745 | − | 0.924599i | 0.0106416 | − | 0.0397149i | ||||
\(543\) | −0.869854 | + | 3.24634i | −0.0373290 | + | 0.139314i | ||||
\(544\) | −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 | −0.918483 | − | 0.395462i | \(-0.870585\pi\) |
0.395462 | + | 0.918483i | \(0.370585\pi\) | |||||||
\(548\) | −10.9950 | + | 2.94610i | −0.469684 | + | 0.125851i | ||||
\(549\) | −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 | ||||
\(553\) | −5.19900 | − | 6.51567i | −0.221084 | − | 0.277074i | ||||
\(554\) | 20.8137i | 0.884291i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.03551 | − | 1.75255i | 0.128734 | − | 0.0743248i | ||||
\(557\) | −34.7179 | − | 9.30265i | −1.47105 | − | 0.394166i | −0.567757 | − | 0.823196i | \(-0.692189\pi\) |
−0.903290 | + | 0.429031i | \(0.858855\pi\) | |||||||
\(558\) | −1.36097 | − | 5.07922i | −0.0576146 | − | 0.215020i | ||||
\(559\) | −13.4592 | −0.569265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.42375 | 0.228991 | ||||||||
\(562\) | 0.748555 | + | 2.79365i | 0.0315759 | + | 0.117843i | ||||
\(563\) | 31.9435 | + | 8.55924i | 1.34626 | + | 0.360729i | 0.858752 | − | 0.512391i | \(-0.171240\pi\) |
0.487506 | + | 0.873120i | \(0.337907\pi\) | |||||||
\(564\) | −4.55390 | + | 2.62920i | −0.191754 | + | 0.110709i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.1936i | 0.890833i | ||||||||
\(567\) | −0.395046 | − | 2.61609i | −0.0165904 | − | 0.109866i | ||||
\(568\) | −7.96089 | − | 7.96089i | −0.334031 | − | 0.334031i | ||||
\(569\) | −14.4472 | − | 8.34107i | −0.605656 | − | 0.349676i | 0.165607 | − | 0.986192i | \(-0.447042\pi\) |
−0.771264 | + | 0.636516i | \(0.780375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21754 | − | 2.10885i | −0.0509527 | − | 0.0882526i | 0.839424 | − | 0.543477i | \(-0.182892\pi\) |
−0.890377 | + | 0.455224i | \(0.849559\pi\) | |||||||
\(572\) | −23.2702 | + | 6.23524i | −0.972978 | + | 0.260709i | ||||
\(573\) | 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 | ||||
\(577\) | −0.464598 | + | 1.73390i | −0.0193415 | + | 0.0721834i | −0.974922 | − | 0.222547i | \(-0.928563\pi\) |
0.955581 | + | 0.294730i | \(0.0952297\pi\) | |||||||
\(578\) | −3.88611 | + | 14.5032i | −0.161641 | + | 0.603252i | ||||
\(579\) | 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 | ||||
\(583\) | −36.6225 | + | 9.81298i | −1.51675 | + | 0.406412i | ||||
\(584\) | −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 | 0.982622 | + | 0.185619i | \(0.0594290\pi\) |
0.185619 | + | 0.982622i | \(0.440571\pi\) | |||||||
\(588\) | 6.19060 | + | 3.26748i | 0.255296 | + | 0.134749i | ||||
\(589\) | − | 18.5429i | − | 0.764047i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.3521 | + | 8.86353i | −0.631500 | + | 0.364597i | ||||
\(592\) | 9.82586 | + | 2.63283i | 0.403840 | + | 0.108209i | ||||
\(593\) | −0.710130 | − | 2.65024i | −0.0291616 | − | 0.108832i | 0.949811 | − | 0.312824i | \(-0.101275\pi\) |
−0.978973 | + | 0.203992i | \(0.934608\pi\) | |||||||
\(594\) | 3.84941 | 0.157943 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8233 | −0.566225 | ||||||||
\(597\) | −0.181330 | − | 0.676732i | −0.00742133 | − | 0.0276968i | ||||
\(598\) | 8.51750 | + | 2.28226i | 0.348306 | + | 0.0933284i | ||||
\(599\) | 27.3558 | − | 15.7939i | 1.11773 | − | 0.645321i | 0.176909 | − | 0.984227i | \(-0.443390\pi\) |
0.940820 | + | 0.338906i | \(0.110057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.59089i | − | 0.187266i | −0.995607 | − | 0.0936332i | \(-0.970152\pi\) | ||
0.995607 | − | 0.0936332i | \(-0.0298481\pi\) | |||||||
\(602\) | −4.44759 | + | 3.54883i | −0.181270 | + | 0.144640i | ||||
\(603\) | −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 | ||||
\(607\) | −16.4732 | + | 4.41399i | −0.668628 | + | 0.179158i | −0.577137 | − | 0.816648i | \(-0.695830\pi\) |
−0.0914911 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 0.364671 | − | 1.36097i | 0.0147410 | − | 0.0550140i | ||||
\(613\) | 2.92689 | − | 10.9233i | 0.118216 | − | 0.441188i | −0.881291 | − | 0.472573i | \(-0.843325\pi\) |
0.999507 | + | 0.0313851i | \(0.00999182\pi\) | |||||||
\(614\) | 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 | −0.637889 | − | 0.770128i | \(-0.720192\pi\) |
0.770128 | + | 0.637889i | \(0.220192\pi\) | |||||||
\(618\) | 14.8426 | − | 3.97706i | 0.597057 | − | 0.159981i | ||||
\(619\) | −12.8766 | − | 22.3029i | −0.517554 | − | 0.896429i | −0.999792 | − | 0.0203891i | \(-0.993510\pi\) |
0.482239 | − | 0.876040i | \(-0.339824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.22021 | − | 0.704491i | −0.0489655 | − | 0.0282703i | ||||
\(622\) | −14.5800 | − | 14.5800i | −0.584605 | − | 0.584605i | ||||
\(623\) | −28.8536 | + | 23.0229i | −1.15599 | + | 0.922394i | ||||
\(624\) | 6.25839i | 0.250536i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.2623 | − | 8.23433i | 0.570035 | − | 0.329110i | ||||
\(627\) | 13.1118 | + | 3.51330i | 0.523635 | + | 0.140308i | ||||
\(628\) | 2.58387 | + | 9.64315i | 0.103108 | + | 0.384804i | ||||
\(629\) | −14.3328 | −0.571488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5189 | 1.41399 | 0.706993 | − | 0.707221i | \(-0.250051\pi\) | ||||
0.706993 | + | 0.707221i | \(0.250051\pi\) | |||||||
\(632\) | −0.815432 | − | 3.04324i | −0.0324362 | − | 0.121053i | ||||
\(633\) | 14.9164 | + | 3.99683i | 0.592872 | + | 0.158860i | ||||
\(634\) | −23.0205 | + | 13.2909i | −0.914262 | + | 0.527849i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.84941i | 0.390555i | ||||||||
\(637\) | 43.7772 | − | 1.66208i | 1.73452 | − | 0.0658540i | ||||
\(638\) | −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 | \(0.755297\pi\) | |||||||
\(642\) | 2.60170 | − | 0.697125i | 0.102681 | − | 0.0275133i | ||||
\(643\) | 25.5136 | − | 25.5136i | 1.00616 | − | 1.00616i | 0.00617772 | − | 0.999981i | \(-0.498034\pi\) |
0.999981 | − | 0.00617772i | \(-0.00196644\pi\) | |||||||
\(644\) | 3.41637 | − | 1.49166i | 0.134624 | − | 0.0587797i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.48428 | − | 4.30289i | 0.0977426 | − | 0.169295i | ||||
\(647\) | −8.44686 | + | 31.5241i | −0.332080 | + | 1.23934i | 0.574920 | + | 0.818210i | \(0.305033\pi\) |
−0.907000 | + | 0.421130i | \(0.861633\pi\) | |||||||
\(648\) | 0.258819 | − | 0.965926i | 0.0101674 | − | 0.0379452i | ||||
\(649\) | −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 | ||||
\(653\) | 18.0668 | − | 4.84099i | 0.707010 | − | 0.189443i | 0.112642 | − | 0.993636i | \(-0.464069\pi\) |
0.594368 | + | 0.804193i | \(0.297402\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 2.07731 | + | 13.7564i | 0.0809820 | + | 0.536282i | ||||
\(659\) | − | 43.5871i | − | 1.69791i | −0.528462 | − | 0.848957i | \(-0.677231\pi\) | ||
0.528462 | − | 0.848957i | \(-0.322769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3300 | − | 12.3149i | 0.829642 | − | 0.478994i | −0.0240879 | − | 0.999710i | \(-0.507668\pi\) |
0.853730 | + | 0.520716i | \(0.174335\pi\) | |||||||
\(662\) | −6.51705 | − | 1.74624i | −0.253292 | − | 0.0678695i | ||||
\(663\) | −2.28226 | − | 8.51750i | −0.0886355 | − | 0.330792i | ||||
\(664\) | 0.667375 | 0.0258992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.1725 | −0.394176 | ||||||||
\(667\) | 2.43140 | + | 9.07411i | 0.0941442 | + | 0.351351i | ||||
\(668\) | −10.5101 | − | 2.81617i | −0.406648 | − | 0.108961i | ||||
\(669\) | 1.44399 | − | 0.833688i | 0.0558279 | − | 0.0322322i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.81263i | − | 0.147185i | ||||||
\(672\) | 1.65017 | + | 2.06808i | 0.0636565 | + | 0.0797779i | ||||
\(673\) | 11.4796 | + | 11.4796i | 0.442506 | + | 0.442506i | 0.892853 | − | 0.450348i | \(-0.148700\pi\) |
−0.450348 | + | 0.892853i | \(0.648700\pi\) | |||||||
\(674\) | 2.69144 | + | 1.55390i | 0.103670 | + | 0.0598541i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0837 | + | 22.6617i | 0.503221 | + | 0.871604i | ||||
\(677\) | 16.0065 | − | 4.28892i | 0.615179 | − | 0.164837i | 0.0622438 | − | 0.998061i | \(-0.480174\pi\) |
0.552935 | + | 0.833224i | \(0.313508\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | 5.23894 | − | 19.5520i | 0.200609 | − | 0.748685i | ||||
\(683\) | −3.60132 | + | 13.4403i | −0.137801 | + | 0.514279i | 0.862170 | + | 0.506619i | \(0.169105\pi\) |
−0.999971 | + | 0.00765999i | \(0.997562\pi\) | |||||||
\(684\) | 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 | ||||
\(688\) | −2.07731 | + | 0.556613i | −0.0791967 | + | 0.0212207i | ||||
\(689\) | 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 | ||||
\(693\) | 3.71825 | − | 9.48158i | 0.141244 | − | 0.360176i | ||||
\(694\) | − | 13.2471i | − | 0.502851i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.77412 | + | 3.33369i | −0.218867 | + | 0.126363i | ||||
\(697\) | 1.00931 | + | 0.270443i | 0.0382302 | + | 0.0102438i | ||||
\(698\) | −4.70503 | − | 17.5594i | −0.178088 | − | 0.664633i | ||||
\(699\) | 29.7271 | 1.12438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2732 | 1.03009 | 0.515047 | − | 0.857162i | \(-0.327775\pi\) | ||||
0.515047 | + | 0.857162i | \(0.327775\pi\) | |||||||
\(702\) | −1.61979 | − | 6.04514i | −0.0611351 | − | 0.228159i | ||||
\(703\) | −34.6493 | − | 9.28426i | −1.30682 | − | 0.350163i | ||||
\(704\) | −3.33369 | + | 1.92471i | −0.125643 | + | 0.0725401i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 21.8120i | − | 0.820904i | ||||||
\(707\) | −37.5833 | + | 5.67532i | −1.41347 | + | 0.213442i | ||||
\(708\) | 9.68653 | + | 9.68653i | 0.364042 | + | 0.364042i | ||||
\(709\) | −22.7497 | − | 13.1345i | −0.854382 | − | 0.493278i | 0.00774478 | − | 0.999970i | \(-0.497535\pi\) |
−0.862127 | + | 0.506692i | \(0.830868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.57529 | + | 2.72849i | 0.0590782 | + | 0.102326i | ||||
\(712\) | −13.4765 | + | 3.61101i | −0.505052 | + | 0.135328i | ||||
\(713\) | −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 | ||||
\(717\) | −2.05810 | + | 7.68092i | −0.0768610 | + | 0.286849i | ||||
\(718\) | 7.40427 | − | 27.6331i | 0.276325 | − | 1.03126i | ||||
\(719\) | −10.2929 | + | 17.8279i | −0.383862 | + | 0.664869i | −0.991611 | − | 0.129261i | \(-0.958740\pi\) |
0.607748 | + | 0.794130i | \(0.292073\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.54085 | − | 40.4008i | 0.169110 | − | 1.50460i | ||||
\(722\) | −4.64209 | + | 4.64209i | −0.172761 | + | 0.172761i | ||||
\(723\) | 10.9424 | − | 2.93201i | 0.406952 | − | 0.109043i | ||||
\(724\) | 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 | \(-0.185833\pi\) |
−0.551209 | + | 0.834367i | \(0.685833\pi\) | |||||||
\(728\) | 15.4152 | + | 6.04514i | 0.571326 | + | 0.224048i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.62418 | − | 1.51507i | 0.0970588 | − | 0.0560369i | ||||
\(732\) | −0.956695 | − | 0.256346i | −0.0353605 | − | 0.00947481i | ||||
\(733\) | −3.65082 | − | 13.6250i | −0.134846 | − | 0.503252i | −0.999998 | − | 0.00174331i | \(-0.999445\pi\) |
0.865152 | − | 0.501509i | \(-0.167222\pi\) | |||||||
\(734\) | 32.4834 | 1.19899 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.40898 | 0.0519358 | ||||||||
\(737\) | −7.62949 | − | 28.4737i | −0.281036 | − | 1.04884i | ||||
\(738\) | 0.716337 | + | 0.191942i | 0.0263687 | + | 0.00706548i | ||||
\(739\) | 17.0208 | − | 9.82696i | 0.626120 | − | 0.361490i | −0.153128 | − | 0.988206i | \(-0.548935\pi\) |
0.779248 | + | 0.626716i | \(0.215601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 22.0692i | − | 0.810734i | ||||||
\(742\) | 24.2603 | + | 9.51380i | 0.890625 | + | 0.349263i | ||||
\(743\) | 20.7983 | + | 20.7983i | 0.763016 | + | 0.763016i | 0.976866 | − | 0.213851i | \(-0.0686006\pi\) |
−0.213851 | + | 0.976866i | \(0.568601\pi\) | |||||||
\(744\) | −4.55390 | − | 2.62920i | −0.166954 | − | 0.0963910i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.0346 | − | 19.1125i | −0.404006 | − | 0.699759i | ||||
\(747\) | −0.644635 | + | 0.172729i | −0.0235860 | + | 0.00631984i | ||||
\(748\) | 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 | \(0.0232915\pi\) | |||||||
\(752\) | −1.36097 | + | 5.07922i | −0.0496296 | + | 0.185220i | ||||
\(753\) | −5.44389 | + | 20.3169i | −0.198386 | + | 0.740388i | ||||
\(754\) | −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 | 0.110699 | − | 0.993854i | \(-0.464691\pi\) |
0.993854 | − | 0.110699i | \(-0.0353090\pi\) | |||||||
\(758\) | 15.3185 | − | 4.10457i | 0.556392 | − | 0.149085i | ||||
\(759\) | −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 | ||||
\(763\) | 43.9537 | − | 6.63729i | 1.59123 | − | 0.240286i | ||||
\(764\) | − | 0.741607i | − | 0.0268304i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.3693 | + | 8.87347i | −0.555316 | + | 0.320612i | ||||
\(767\) | 82.8113 | + | 22.1892i | 2.99014 | + | 0.801207i | ||||
\(768\) | 0.258819 | + | 0.965926i | 0.00933933 | + | 0.0348548i | ||||
\(769\) | −27.3976 | −0.987984 | −0.493992 | − | 0.869466i | \(-0.664463\pi\) | ||||
−0.493992 | + | 0.869466i | \(0.664463\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.9144 | −0.933285 | ||||||||
\(772\) | −1.91759 | − | 7.15653i | −0.0690154 | − | 0.257569i | ||||
\(773\) | 4.67901 | + | 1.25374i | 0.168292 | + | 0.0450938i | 0.341981 | − | 0.939707i | \(-0.388902\pi\) |
−0.173689 | + | 0.984801i | \(0.555569\pi\) | |||||||
\(774\) | 1.86246 | − | 1.07529i | 0.0669449 | − | 0.0386507i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.88086i | 0.354702i | ||||||||
\(777\) | −9.82586 | + | 25.0561i | −0.352501 | + | 0.898882i | ||||
\(778\) | −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 | ||||
\(782\) | −1.91759 | + | 0.513816i | −0.0685727 | + | 0.0183740i | ||||
\(783\) | 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 | ||||
\(787\) | 13.5953 | − | 50.7385i | 0.484621 | − | 1.80863i | −0.0971384 | − | 0.995271i | \(-0.530969\pi\) |
0.581760 | − | 0.813361i | \(-0.302364\pi\) | |||||||
\(788\) | −4.58810 | + | 17.1230i | −0.163444 | + | 0.609982i | ||||
\(789\) | 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 | ||||
\(793\) | −5.98738 | + | 1.60431i | −0.212618 | + | 0.0569708i | ||||
\(794\) | −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 | \(-0.321168\pi\) |
−0.846288 | + | 0.532726i | \(0.821168\pi\) | |||||||
\(798\) | −5.81905 | − | 7.29275i | −0.205992 | − | 0.258161i | ||||
\(799\) | − | 7.40898i | − | 0.262111i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0827 | − | 6.97594i | 0.426920 | − | 0.246483i | ||||
\(802\) | −1.43267 | − | 0.383884i | −0.0505895 | − | 0.0135554i | ||||
\(803\) | 10.6113 | + | 39.6019i | 0.374465 | + | 1.39752i | ||||
\(804\) | −7.65782 | −0.270070 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.9091 | −1.15917 | ||||||||
\(807\) | −7.08151 | − | 26.4286i | −0.249281 | − | 0.930329i | ||||
\(808\) | −13.8767 | − | 3.71825i | −0.488180 | − | 0.130807i | ||||
\(809\) | 17.1675 | − | 9.91165i | 0.603577 | − | 0.348475i | −0.166871 | − | 0.985979i | \(-0.553366\pi\) |
0.770447 | + | 0.637504i | \(0.220033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.73982i | − | 0.271782i | −0.990724 | − | 0.135891i | \(-0.956610\pi\) | ||
0.990724 | − | 0.135891i | \(-0.0433897\pi\) | |||||||
\(812\) | 2.63392 | + | 17.4425i | 0.0924326 | + | 0.612111i | ||||
\(813\) | 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 | ||||
\(817\) | 7.32530 | − | 1.96281i | 0.256280 | − | 0.0686700i | ||||
\(818\) | −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 | \(0.936137\pi\) | |||||||
\(822\) | 2.94610 | − | 10.9950i | 0.102757 | − | 0.383495i | ||||
\(823\) | −9.28104 | + | 34.6373i | −0.323517 | + | 1.20738i | 0.592278 | + | 0.805734i | \(0.298229\pi\) |
−0.915795 | + | 0.401647i | \(0.868438\pi\) | |||||||
\(824\) | 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 | −0.346881 | − | 0.937909i | \(-0.612759\pi\) |
0.937909 | + | 0.346881i | \(0.112759\pi\) | |||||||
\(828\) | −1.36097 | + | 0.364671i | −0.0472971 | + | 0.0126732i | ||||
\(829\) | −12.8699 | − | 22.2913i | −0.446991 | − | 0.774210i | 0.551198 | − | 0.834374i | \(-0.314171\pi\) |
−0.998188 | + | 0.0601642i | \(0.980838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0252 | − | 10.4069i | −0.625288 | − | 0.361010i | ||||
\(832\) | 4.42535 | + | 4.42535i | 0.153421 | + | 0.153421i | ||||
\(833\) | −8.34825 | + | 5.25195i | −0.289250 | + | 0.181969i | ||||
\(834\) | 3.50510i | 0.121372i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.7557 | − | 6.78717i | 0.406580 | − | 0.234739i | ||||
\(837\) | 5.07922 | + | 1.36097i | 0.175563 | + | 0.0470421i | ||||
\(838\) | 3.84469 | + | 14.3486i | 0.132813 | + | 0.495664i | ||||
\(839\) | −39.3234 | −1.35759 | −0.678797 | − | 0.734326i | \(-0.737499\pi\) | ||||
−0.678797 | + | 0.734326i | \(0.737499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4539 | −0.532893 | ||||||||
\(842\) | 7.06368 | + | 26.3620i | 0.243431 | + | 0.908495i | ||||
\(843\) | −2.79365 | − | 0.748555i | −0.0962183 | − | 0.0257816i | ||||
\(844\) | 13.3736 | − | 7.72128i | 0.460340 | − | 0.265777i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 5.25839i | − | 0.180787i | ||||||
\(847\) | 7.89585 | − | 6.30028i | 0.271305 | − | 0.216480i | ||||
\(848\) | 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 | ||||
\(852\) | 10.8748 | − | 2.91389i | 0.372564 | − | 0.0998281i | ||||
\(853\) | −11.4032 | + | 11.4032i | −0.390439 | + | 0.390439i | −0.874844 | − | 0.484405i | \(-0.839036\pi\) |
0.484405 | + | 0.874844i | \(0.339036\pi\) | |||||||
\(854\) | −1.55551 | + | 2.10885i | −0.0532284 | + | 0.0721634i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.34674 | − | 2.33262i | 0.0460307 | − | 0.0797275i | ||||
\(857\) | −0.673539 | + | 2.51368i | −0.0230077 | + | 0.0858658i | −0.976475 | − | 0.215630i | \(-0.930819\pi\) |
0.953467 | + | 0.301496i | \(0.0974860\pi\) | |||||||
\(858\) | 6.23524 | − | 23.2702i | 0.212868 | − | 0.794433i | ||||
\(859\) | −11.6663 | + | 20.2066i | −0.398049 | + | 0.689442i | −0.993485 | − | 0.113961i | \(-0.963646\pi\) |
0.595436 | + | 0.803403i | \(0.296979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.16471 | − | 1.57903i | 0.0396931 | − | 0.0538131i | ||||
\(862\) | 26.1971 | − | 26.1971i | 0.892278 | − | 0.892278i | ||||
\(863\) | 40.2335 | − | 10.7805i | 1.36957 | − | 0.366974i | 0.502246 | − | 0.864725i | \(-0.332507\pi\) |
0.867320 | + | 0.497751i | \(0.165841\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | −10.8748 | + | 8.67722i | −0.369114 | + | 0.294524i | ||||
\(869\) | 12.1279i | 0.411411i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.5048 | + | 23.9628i | −1.40634 | + | 0.811949i | ||||
\(872\) | 16.2288 | + | 4.34849i | 0.549576 | + | 0.147259i | ||||
\(873\) | −2.55735 | − | 9.54418i | −0.0865533 | − | 0.323021i | ||||
\(874\) | −4.96855 | −0.168064 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6507 | 0.359854 | ||||||||
\(877\) | 10.1242 | + | 37.7842i | 0.341871 | + | 1.27588i | 0.896225 | + | 0.443600i | \(0.146299\pi\) |
−0.554354 | + | 0.832281i | \(0.687035\pi\) | |||||||
\(878\) | −19.5841 | − | 5.24754i | −0.660931 | − | 0.177096i | ||||
\(879\) | −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 | \(0.939264\pi\) | |||||||
\(882\) | −5.92503 | + | 3.72748i | −0.199506 | + | 0.125511i | ||||
\(883\) | −16.2037 | − | 16.2037i | −0.545297 | − | 0.545297i | 0.379780 | − | 0.925077i | \(-0.376000\pi\) |
−0.925077 | + | 0.379780i | \(0.876000\pi\) | |||||||
\(884\) | −7.63658 | − | 4.40898i | −0.256846 | − | 0.148290i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.51572 | − | 6.08941i | −0.118113 | − | 0.204578i | ||||
\(887\) | −12.6721 | + | 3.39548i | −0.425488 | + | 0.114009i | −0.465207 | − | 0.885202i | \(-0.654020\pi\) |
0.0397194 | + | 0.999211i | \(0.487354\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | 0.431548 | − | 1.61056i | 0.0144493 | − | 0.0539256i | ||||
\(893\) | 4.79925 | − | 17.9111i | 0.160601 | − | 0.599371i | ||||
\(894\) | 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 | ||||
\(898\) | 4.31434 | − | 1.15602i | 0.143971 | − | 0.0385770i | ||||
\(899\) | −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 | ||||
\(903\) | −0.849583 | − | 5.62614i | −0.0282723 | − | 0.187226i | ||||
\(904\) | 14.4404i | 0.480282i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.15910 | + | 2.97861i | −0.171400 | + | 0.0989576i | ||||
\(907\) | −9.85808 | − | 2.64146i | −0.327332 | − | 0.0877084i | 0.0914106 | − | 0.995813i | \(-0.470862\pi\) |
−0.418743 | + | 0.908105i | \(0.637529\pi\) | |||||||
\(908\) | 2.97938 | + | 11.1192i | 0.0988743 | + | 0.369004i | ||||
\(909\) | 14.3662 | 0.476497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.10568 | 0.0366328 | 0.0183164 | − | 0.999832i | \(-0.494169\pi\) | ||||
0.0183164 | + | 0.999832i | \(0.494169\pi\) | |||||||
\(912\) | −0.912685 | − | 3.40619i | −0.0302220 | − | 0.112790i | ||||
\(913\) | −2.48147 | − | 0.664907i | −0.0821245 | − | 0.0220052i | ||||
\(914\) | 21.0147 | − | 12.1329i | 0.695106 | − | 0.401320i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.6175i | 0.516016i | ||||||||
\(917\) | 10.7969 | + | 13.5312i | 0.356544 | + | 0.446840i | ||||
\(918\) | 0.996301 | + | 0.996301i | 0.0328828 | + | 0.0328828i | ||||
\(919\) | 35.1784 | + | 20.3103i | 1.16043 | + | 0.669974i | 0.951407 | − | 0.307937i | \(-0.0996385\pi\) |
0.209023 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.81796 | + | 8.34496i | 0.158757 | + | 0.274976i | ||||
\(922\) | −8.51750 | + | 2.28226i | −0.280509 | + | 0.0751621i | ||||
\(923\) | 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 | ||||
\(927\) | −3.97706 | + | 14.8426i | −0.130624 | + | 0.487495i | ||||
\(928\) | −1.72564 | + | 6.44019i | −0.0566470 | + | 0.211410i | ||||
\(929\) | 9.48534 | − | 16.4291i | 0.311204 | − | 0.539021i | −0.667419 | − | 0.744682i | \(-0.732601\pi\) |
0.978623 | + | 0.205661i | \(0.0659345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.5837 | + | 7.28879i | −0.772926 | + | 0.238881i | ||||
\(932\) | 21.0202 | − | 21.0202i | 0.688540 | − | 0.688540i | ||||
\(933\) | 19.9167 | − | 5.33665i | 0.652042 | − | 0.174714i | ||||
\(934\) | −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 | \(-0.240665\pi\) |
−0.686070 | + | 0.727536i | \(0.740665\pi\) | |||||||
\(938\) | −7.39689 | + | 18.8622i | −0.241517 | + | 0.615872i | ||||
\(939\) | 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 | \(0.654458\pi\) | |||||||
\(942\) | −9.64315 | − | 2.58387i | −0.314191 | − | 0.0841872i | ||||
\(943\) | −0.270443 | − | 1.00931i | −0.00880683 | − | 0.0328675i | ||||
\(944\) | 13.6988 | 0.445859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.27850 | 0.269157 | ||||||||
\(947\) | −7.12325 | − | 26.5843i | −0.231475 | − | 0.863875i | −0.979706 | − | 0.200437i | \(-0.935764\pi\) |
0.748232 | − | 0.663437i | \(-0.230903\pi\) | |||||||
\(948\) | 3.04324 | + | 0.815432i | 0.0988397 | + | 0.0264840i | ||||
\(949\) | 57.7260 | − | 33.3281i | 1.87387 | − | 1.08188i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 26.5818i | − | 0.861974i | ||||||
\(952\) | −3.68603 | + | 0.556613i | −0.119465 | + | 0.0180399i | ||||
\(953\) | 24.6409 | + | 24.6409i | 0.798197 | + | 0.798197i | 0.982811 | − | 0.184614i | \(-0.0591035\pi\) |
−0.184614 | + | 0.982811i | \(0.559103\pi\) | |||||||
\(954\) | −8.52984 | − | 4.92471i | −0.276164 | − | 0.159443i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.97594 | + | 6.88653i | 0.128591 | + | 0.222726i | ||||
\(957\) | 24.7909 | − | 6.64271i | 0.801377 | − | 0.214728i | ||||
\(958\) | −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 | ||||
\(962\) | −16.4773 | + | 61.4941i | −0.531249 | + | 1.98265i | ||||
\(963\) | −0.697125 | + | 2.60170i | −0.0224645 | + | 0.0838388i | ||||
\(964\) | 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 | 0.207814 | − | 0.978168i | \(-0.433365\pi\) |
0.978168 | − | 0.207814i | \(-0.0666350\pi\) | |||||||
\(968\) | 3.68787 | − | 0.988162i | 0.118533 | − | 0.0317607i | ||||
\(969\) | 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 | ||||
\(973\) | 8.63351 | + | 3.38567i | 0.276778 | + | 0.108540i | ||||
\(974\) | 7.82739i | 0.250806i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.857750 | + | 0.495222i | −0.0274559 | + | 0.0158517i | ||||
\(977\) | −34.6339 | − | 9.28012i | −1.10804 | − | 0.296897i | −0.342003 | − | 0.939699i | \(-0.611105\pi\) |
−0.766033 | + | 0.642801i | \(0.777772\pi\) | |||||||
\(978\) | −0.356071 | − | 1.32888i | −0.0113859 | − | 0.0424928i | ||||
\(979\) | 53.7065 | 1.71647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8013 | −0.536424 | ||||||||
\(982\) | 11.3564 | + | 42.3826i | 0.362396 | + | 1.35248i | ||||
\(983\) | −4.21948 | − | 1.13061i | −0.134580 | − | 0.0360607i | 0.190900 | − | 0.981609i | \(-0.438859\pi\) |
−0.325480 | + | 0.945549i | \(0.605526\pi\) | |||||||
\(984\) | 0.642250 | − | 0.370803i | 0.0204742 | − | 0.0118208i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 9.39421i | − | 0.299173i | ||||||
\(987\) | −12.9521 | − | 5.07922i | −0.412269 | − | 0.161673i | ||||
\(988\) | −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 | \(0.951037\pi\) | |||||||
\(992\) | −5.07922 | + | 1.36097i | −0.161265 | + | 0.0432109i | ||||
\(993\) | 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 | ||||
\(997\) | 7.11948 | − | 26.5703i | 0.225476 | − | 0.841489i | −0.756737 | − | 0.653720i | \(-0.773208\pi\) |
0.982213 | − | 0.187769i | \(-0.0601258\pi\) | |||||||
\(998\) | −8.93659 | + | 33.3518i | −0.282883 | + | 1.05573i | ||||
\(999\) | 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.f.943.3 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.e.607.1 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.e.607.4 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.f.943.2 | yes | 16 | |
7.3 | odd | 6 | 1050.2.bc.e.493.2 | ✓ | 16 | ||
35.3 | even | 12 | inner | 1050.2.bc.f.157.2 | yes | 16 | |
35.17 | even | 12 | inner | 1050.2.bc.f.157.3 | yes | 16 | |
35.24 | odd | 6 | 1050.2.bc.e.493.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.493.2 | ✓ | 16 | 7.3 | odd | 6 | ||
1050.2.bc.e.493.3 | yes | 16 | 35.24 | odd | 6 | ||
1050.2.bc.e.607.1 | yes | 16 | 5.2 | odd | 4 | ||
1050.2.bc.e.607.4 | yes | 16 | 5.3 | odd | 4 | ||
1050.2.bc.f.157.2 | yes | 16 | 35.3 | even | 12 | inner | |
1050.2.bc.f.157.3 | yes | 16 | 35.17 | even | 12 | inner | |
1050.2.bc.f.943.2 | yes | 16 | 5.4 | even | 2 | inner | |
1050.2.bc.f.943.3 | yes | 16 | 1.1 | even | 1 | trivial |