Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.20 | ||
Character | \(\chi\) | \(=\) | 1110.1009 |
Dual form | 1110.2.bb.e.1099.20 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.961633 | + | 2.01873i | −0.430055 | + | 0.902803i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.02191 | − | 1.74470i | 1.14217 | − | 0.659434i | 0.195205 | − | 0.980762i | \(-0.437463\pi\) |
0.946968 | + | 0.321329i | \(0.104129\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.84216 | + | 1.26745i | −0.582543 | + | 0.400804i | ||||
\(11\) | 5.35806 | 1.61552 | 0.807758 | − | 0.589515i | \(-0.200681\pi\) | ||||
0.807758 | + | 0.589515i | \(0.200681\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 2.41469 | − | 1.39412i | 0.669715 | − | 0.386660i | −0.126254 | − | 0.991998i | \(-0.540295\pi\) |
0.795969 | + | 0.605338i | \(0.206962\pi\) | |||||||
\(14\) | 3.48940 | 0.932580 | ||||||||
\(15\) | −0.176566 | − | 2.22909i | −0.0455890 | − | 0.575548i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.818404 | − | 0.472506i | −0.198492 | − | 0.114599i | 0.397460 | − | 0.917620i | \(-0.369892\pi\) |
−0.595952 | + | 0.803020i | \(0.703225\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −0.113008 | − | 0.195735i | −0.0259258 | − | 0.0449047i | 0.852771 | − | 0.522284i | \(-0.174920\pi\) |
−0.878697 | + | 0.477380i | \(0.841587\pi\) | |||||||
\(20\) | −2.22909 | + | 0.176566i | −0.498439 | + | 0.0394812i | ||||
\(21\) | −1.74470 | + | 3.02191i | −0.380724 | + | 0.659434i | ||||
\(22\) | 4.64021 | + | 2.67903i | 0.989297 | + | 0.571171i | ||||
\(23\) | − | 0.422746i | − | 0.0881487i | −0.999028 | − | 0.0440743i | \(-0.985966\pi\) | ||
0.999028 | − | 0.0440743i | \(-0.0140338\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −3.15052 | − | 3.88255i | −0.630105 | − | 0.776510i | ||||
\(26\) | 2.78824 | 0.546820 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 3.02191 | + | 1.74470i | 0.571086 | + | 0.329717i | ||||
\(29\) | −2.54265 | −0.472157 | −0.236079 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236079 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(30\) | 0.961633 | − | 2.01873i | 0.175569 | − | 0.368568i | ||||
\(31\) | 9.36492 | 1.68199 | 0.840995 | − | 0.541043i | \(-0.181970\pi\) | ||||
0.840995 | + | 0.541043i | \(0.181970\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −4.64021 | + | 2.67903i | −0.807758 | + | 0.466359i | ||||
\(34\) | −0.472506 | − | 0.818404i | −0.0810341 | − | 0.140355i | ||||
\(35\) | 0.616107 | + | 7.77816i | 0.104141 | + | 1.31475i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.05542 | − | 0.576064i | −0.995505 | − | 0.0947044i | ||||
\(38\) | − | 0.226016i | − | 0.0366646i | ||||||
\(39\) | −1.39412 | + | 2.41469i | −0.223238 | + | 0.386660i | ||||
\(40\) | −2.01873 | − | 0.961633i | −0.319189 | − | 0.152047i | ||||
\(41\) | 4.96770 | + | 8.60431i | 0.775825 | + | 1.34377i | 0.934330 | + | 0.356410i | \(0.115999\pi\) |
−0.158505 | + | 0.987358i | \(0.550667\pi\) | |||||||
\(42\) | −3.02191 | + | 1.74470i | −0.466290 | + | 0.269213i | ||||
\(43\) | 0.646192i | 0.0985434i | 0.998785 | + | 0.0492717i | \(0.0156900\pi\) | ||||
−0.998785 | + | 0.0492717i | \(0.984310\pi\) | |||||||
\(44\) | 2.67903 | + | 4.64021i | 0.403879 | + | 0.699539i | ||||
\(45\) | 1.26745 | + | 1.84216i | 0.188941 | + | 0.274613i | ||||
\(46\) | 0.211373 | − | 0.366109i | 0.0311653 | − | 0.0539798i | ||||
\(47\) | 2.57116i | 0.375043i | 0.982261 | + | 0.187521i | \(0.0600454\pi\) | ||||
−0.982261 | + | 0.187521i | \(0.939955\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 2.58794 | − | 4.48245i | 0.369706 | − | 0.640349i | ||||
\(50\) | −0.787159 | − | 4.93765i | −0.111321 | − | 0.698289i | ||||
\(51\) | 0.945012 | 0.132328 | ||||||||
\(52\) | 2.41469 | + | 1.39412i | 0.334857 | + | 0.193330i | ||||
\(53\) | 1.84610 | + | 1.06585i | 0.253582 | + | 0.146405i | 0.621403 | − | 0.783491i | \(-0.286563\pi\) |
−0.367821 | + | 0.929896i | \(0.619896\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −5.15248 | + | 10.8165i | −0.694761 | + | 1.45849i | ||||
\(56\) | 1.74470 | + | 3.02191i | 0.233145 | + | 0.403819i | ||||
\(57\) | 0.195735 | + | 0.113008i | 0.0259258 | + | 0.0149682i | ||||
\(58\) | −2.20200 | − | 1.27132i | −0.289136 | − | 0.166933i | ||||
\(59\) | −7.21013 | + | 12.4883i | −0.938679 | + | 1.62584i | −0.170740 | + | 0.985316i | \(0.554616\pi\) |
−0.767939 | + | 0.640523i | \(0.778718\pi\) | |||||||
\(60\) | 1.84216 | − | 1.26745i | 0.237822 | − | 0.163628i | ||||
\(61\) | 1.10285 | + | 1.91019i | 0.141205 | + | 0.244574i | 0.927951 | − | 0.372703i | \(-0.121569\pi\) |
−0.786746 | + | 0.617277i | \(0.788236\pi\) | |||||||
\(62\) | 8.11026 | + | 4.68246i | 1.03000 | + | 0.594673i | ||||
\(63\) | − | 3.48940i | − | 0.439623i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.492308 | + | 6.21524i | 0.0610633 | + | 0.770905i | ||||
\(66\) | −5.35806 | −0.659531 | ||||||||
\(67\) | −6.10664 | + | 3.52567i | −0.746045 | + | 0.430729i | −0.824263 | − | 0.566207i | \(-0.808410\pi\) |
0.0782179 | + | 0.996936i | \(0.475077\pi\) | |||||||
\(68\) | − | 0.945012i | − | 0.114599i | ||||||
\(69\) | 0.211373 | + | 0.366109i | 0.0254463 | + | 0.0440743i | ||||
\(70\) | −3.35552 | + | 7.04414i | −0.401061 | + | 0.841936i | ||||
\(71\) | −0.0551786 | − | 0.0955722i | −0.00654850 | − | 0.0113423i | 0.862733 | − | 0.505660i | \(-0.168751\pi\) |
−0.869281 | + | 0.494318i | \(0.835418\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 3.85069i | − | 0.450689i | −0.974279 | − | 0.225345i | \(-0.927649\pi\) | ||
0.974279 | − | 0.225345i | \(-0.0723508\pi\) | |||||||
\(74\) | −4.95612 | − | 3.52660i | −0.576137 | − | 0.409959i | ||||
\(75\) | 4.66971 | + | 1.78712i | 0.539212 | + | 0.206359i | ||||
\(76\) | 0.113008 | − | 0.195735i | 0.0129629 | − | 0.0224524i | ||||
\(77\) | 16.1915 | − | 9.34819i | 1.84520 | − | 1.06533i | ||||
\(78\) | −2.41469 | + | 1.39412i | −0.273410 | + | 0.157853i | ||||
\(79\) | −8.57940 | − | 14.8599i | −0.965257 | − | 1.67187i | −0.708922 | − | 0.705287i | \(-0.750818\pi\) |
−0.256335 | − | 0.966588i | \(-0.582515\pi\) | |||||||
\(80\) | −1.26745 | − | 1.84216i | −0.141706 | − | 0.205960i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 9.93540i | 1.09718i | ||||||||
\(83\) | −0.732895 | − | 0.423137i | −0.0804456 | − | 0.0464453i | 0.459238 | − | 0.888313i | \(-0.348123\pi\) |
−0.539683 | + | 0.841868i | \(0.681456\pi\) | |||||||
\(84\) | −3.48940 | −0.380724 | ||||||||
\(85\) | 1.74086 | − | 1.19776i | 0.188823 | − | 0.129915i | ||||
\(86\) | −0.323096 | + | 0.559619i | −0.0348404 | + | 0.0603453i | ||||
\(87\) | 2.20200 | − | 1.27132i | 0.236079 | − | 0.136300i | ||||
\(88\) | 5.35806i | 0.571171i | ||||||||
\(89\) | 5.12898 | − | 8.88366i | 0.543671 | − | 0.941666i | −0.455018 | − | 0.890482i | \(-0.650367\pi\) |
0.998689 | − | 0.0511836i | \(-0.0162994\pi\) | |||||||
\(90\) | 0.176566 | + | 2.22909i | 0.0186116 | + | 0.234966i | ||||
\(91\) | 4.86464 | − | 8.42581i | 0.509953 | − | 0.883265i | ||||
\(92\) | 0.366109 | − | 0.211373i | 0.0381695 | − | 0.0220372i | ||||
\(93\) | −8.11026 | + | 4.68246i | −0.840995 | + | 0.485549i | ||||
\(94\) | −1.28558 | + | 2.22669i | −0.132598 | + | 0.229666i | ||||
\(95\) | 0.503808 | − | 0.0399066i | 0.0516896 | − | 0.00409433i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 7.24454i | − | 0.735571i | −0.929911 | − | 0.367786i | \(-0.880116\pi\) | ||
0.929911 | − | 0.367786i | \(-0.119884\pi\) | |||||||
\(98\) | 4.48245 | − | 2.58794i | 0.452795 | − | 0.261422i | ||||
\(99\) | 2.67903 | − | 4.64021i | 0.269253 | − | 0.466359i | ||||
\(100\) | 1.78712 | − | 4.66971i | 0.178712 | − | 0.466971i | ||||
\(101\) | −0.455491 | −0.0453230 | −0.0226615 | − | 0.999743i | \(-0.507214\pi\) | ||||
−0.0226615 | + | 0.999743i | \(0.507214\pi\) | |||||||
\(102\) | 0.818404 | + | 0.472506i | 0.0810341 | + | 0.0467850i | ||||
\(103\) | 3.64174i | 0.358832i | 0.983773 | + | 0.179416i | \(0.0574207\pi\) | ||||
−0.983773 | + | 0.179416i | \(0.942579\pi\) | |||||||
\(104\) | 1.39412 | + | 2.41469i | 0.136705 | + | 0.236780i | ||||
\(105\) | −4.42265 | − | 6.42803i | −0.431606 | − | 0.627312i | ||||
\(106\) | 1.06585 | + | 1.84610i | 0.103524 | + | 0.179309i | ||||
\(107\) | −12.9077 | + | 7.45225i | −1.24783 | + | 0.720436i | −0.970677 | − | 0.240389i | \(-0.922725\pi\) |
−0.277155 | + | 0.960825i | \(0.589392\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −5.64828 | + | 9.78311i | −0.541007 | + | 0.937052i | 0.457839 | + | 0.889035i | \(0.348624\pi\) |
−0.998847 | + | 0.0480172i | \(0.984710\pi\) | |||||||
\(110\) | −9.87041 | + | 6.79109i | −0.941107 | + | 0.647505i | ||||
\(111\) | 5.53218 | − | 2.52883i | 0.525092 | − | 0.240025i | ||||
\(112\) | 3.48940i | 0.329717i | ||||||||
\(113\) | −5.26885 | − | 3.04197i | −0.495652 | − | 0.286165i | 0.231264 | − | 0.972891i | \(-0.425714\pi\) |
−0.726916 | + | 0.686726i | \(0.759047\pi\) | |||||||
\(114\) | 0.113008 | + | 0.195735i | 0.0105842 | + | 0.0183323i | ||||
\(115\) | 0.853410 | + | 0.406527i | 0.0795809 | + | 0.0379088i | ||||
\(116\) | −1.27132 | − | 2.20200i | −0.118039 | − | 0.204450i | ||||
\(117\) | − | 2.78824i | − | 0.257773i | ||||||
\(118\) | −12.4883 | + | 7.21013i | −1.14964 | + | 0.663746i | ||||
\(119\) | −3.29752 | −0.302283 | ||||||||
\(120\) | 2.22909 | − | 0.176566i | 0.203487 | − | 0.0161182i | ||||
\(121\) | 17.7088 | 1.60989 | ||||||||
\(122\) | 2.20569i | 0.199694i | ||||||||
\(123\) | −8.60431 | − | 4.96770i | −0.775825 | − | 0.447923i | ||||
\(124\) | 4.68246 | + | 8.11026i | 0.420497 | + | 0.728323i | ||||
\(125\) | 10.8675 | − | 2.62646i | 0.972015 | − | 0.234918i | ||||
\(126\) | 1.74470 | − | 3.02191i | 0.155430 | − | 0.269213i | ||||
\(127\) | 10.0513 | + | 5.80313i | 0.891910 | + | 0.514945i | 0.874567 | − | 0.484905i | \(-0.161146\pi\) |
0.0173433 | + | 0.999850i | \(0.494479\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −0.323096 | − | 0.559619i | −0.0284470 | − | 0.0492717i | ||||
\(130\) | −2.68127 | + | 5.62871i | −0.235163 | + | 0.493670i | ||||
\(131\) | 8.75527 | − | 15.1646i | 0.764951 | − | 1.32493i | −0.175321 | − | 0.984511i | \(-0.556096\pi\) |
0.940272 | − | 0.340423i | \(-0.110570\pi\) | |||||||
\(132\) | −4.64021 | − | 2.67903i | −0.403879 | − | 0.233180i | ||||
\(133\) | −0.682998 | − | 0.394329i | −0.0592234 | − | 0.0341927i | ||||
\(134\) | −7.05134 | −0.609143 | ||||||||
\(135\) | −2.01873 | − | 0.961633i | −0.173744 | − | 0.0827642i | ||||
\(136\) | 0.472506 | − | 0.818404i | 0.0405170 | − | 0.0701776i | ||||
\(137\) | − | 12.0138i | − | 1.02641i | −0.858267 | − | 0.513203i | \(-0.828459\pi\) | ||
0.858267 | − | 0.513203i | \(-0.171541\pi\) | |||||||
\(138\) | 0.422746i | 0.0359865i | ||||||||
\(139\) | 8.73029 | − | 15.1213i | 0.740494 | − | 1.28257i | −0.211777 | − | 0.977318i | \(-0.567925\pi\) |
0.952271 | − | 0.305255i | \(-0.0987416\pi\) | |||||||
\(140\) | −6.42803 | + | 4.42265i | −0.543268 | + | 0.373782i | ||||
\(141\) | −1.28558 | − | 2.22669i | −0.108265 | − | 0.187521i | ||||
\(142\) | − | 0.110357i | − | 0.00926098i | ||||||
\(143\) | 12.9381 | − | 7.46979i | 1.08193 | − | 0.624655i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 2.44509 | − | 5.13291i | 0.203054 | − | 0.426265i | ||||
\(146\) | 1.92535 | − | 3.33480i | 0.159343 | − | 0.275990i | ||||
\(147\) | 5.17588i | 0.426900i | ||||||||
\(148\) | −2.52883 | − | 5.53218i | −0.207868 | − | 0.454743i | ||||
\(149\) | −4.22964 | −0.346506 | −0.173253 | − | 0.984877i | \(-0.555428\pi\) | ||||
−0.173253 | + | 0.984877i | \(0.555428\pi\) | |||||||
\(150\) | 3.15052 | + | 3.88255i | 0.257239 | + | 0.317009i | ||||
\(151\) | −7.00031 | − | 12.1249i | −0.569677 | − | 0.986710i | −0.996598 | − | 0.0824210i | \(-0.973735\pi\) |
0.426920 | − | 0.904289i | \(-0.359599\pi\) | |||||||
\(152\) | 0.195735 | − | 0.113008i | 0.0158762 | − | 0.00916614i | ||||
\(153\) | −0.818404 | + | 0.472506i | −0.0661640 | + | 0.0381998i | ||||
\(154\) | 18.6964 | 1.50660 | ||||||||
\(155\) | −9.00562 | + | 18.9052i | −0.723349 | + | 1.51850i | ||||
\(156\) | −2.78824 | −0.223238 | ||||||||
\(157\) | −7.19316 | − | 4.15298i | −0.574077 | − | 0.331444i | 0.184699 | − | 0.982795i | \(-0.440869\pi\) |
−0.758776 | + | 0.651352i | \(0.774202\pi\) | |||||||
\(158\) | − | 17.1588i | − | 1.36508i | ||||||
\(159\) | −2.13170 | −0.169055 | ||||||||
\(160\) | −0.176566 | − | 2.22909i | −0.0139587 | − | 0.176225i | ||||
\(161\) | −0.737564 | − | 1.27750i | −0.0581282 | − | 0.100681i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 4.36864 | + | 2.52224i | 0.342178 | + | 0.197557i | 0.661235 | − | 0.750179i | \(-0.270033\pi\) |
−0.319057 | + | 0.947736i | \(0.603366\pi\) | |||||||
\(164\) | −4.96770 | + | 8.60431i | −0.387912 | + | 0.671884i | ||||
\(165\) | −0.946048 | − | 11.9436i | −0.0736498 | − | 0.929806i | ||||
\(166\) | −0.423137 | − | 0.732895i | −0.0328418 | − | 0.0568836i | ||||
\(167\) | 8.33958 | − | 4.81486i | 0.645336 | − | 0.372585i | −0.141331 | − | 0.989962i | \(-0.545138\pi\) |
0.786667 | + | 0.617378i | \(0.211805\pi\) | |||||||
\(168\) | −3.02191 | − | 1.74470i | −0.233145 | − | 0.134606i | ||||
\(169\) | −2.61285 | + | 4.52558i | −0.200988 | + | 0.348122i | ||||
\(170\) | 2.10651 | − | 0.166856i | 0.161562 | − | 0.0127973i | ||||
\(171\) | −0.226016 | −0.0172838 | ||||||||
\(172\) | −0.559619 | + | 0.323096i | −0.0426705 | + | 0.0246359i | ||||
\(173\) | 8.68811 | + | 5.01608i | 0.660545 | + | 0.381366i | 0.792484 | − | 0.609892i | \(-0.208787\pi\) |
−0.131940 | + | 0.991258i | \(0.542121\pi\) | |||||||
\(174\) | 2.54265 | 0.192757 | ||||||||
\(175\) | −16.2945 | − | 6.23598i | −1.23175 | − | 0.471396i | ||||
\(176\) | −2.67903 | + | 4.64021i | −0.201939 | + | 0.349769i | ||||
\(177\) | − | 14.4203i | − | 1.08389i | ||||||
\(178\) | 8.88366 | − | 5.12898i | 0.665858 | − | 0.384433i | ||||
\(179\) | 2.92328 | 0.218496 | 0.109248 | − | 0.994015i | \(-0.465156\pi\) | ||||
0.109248 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(180\) | −0.961633 | + | 2.01873i | −0.0716759 | + | 0.150467i | ||||
\(181\) | −2.30385 | − | 3.99038i | −0.171244 | − | 0.296603i | 0.767611 | − | 0.640916i | \(-0.221445\pi\) |
−0.938855 | + | 0.344313i | \(0.888112\pi\) | |||||||
\(182\) | 8.42581 | − | 4.86464i | 0.624563 | − | 0.360591i | ||||
\(183\) | −1.91019 | − | 1.10285i | −0.141205 | − | 0.0815248i | ||||
\(184\) | 0.422746 | 0.0311653 | ||||||||
\(185\) | 6.98601 | − | 11.6703i | 0.513622 | − | 0.858017i | ||||
\(186\) | −9.36492 | −0.686669 | ||||||||
\(187\) | −4.38506 | − | 2.53171i | −0.320667 | − | 0.185137i | ||||
\(188\) | −2.22669 | + | 1.28558i | −0.162398 | + | 0.0937607i | ||||
\(189\) | 1.74470 | + | 3.02191i | 0.126908 | + | 0.219811i | ||||
\(190\) | 0.456264 | + | 0.217344i | 0.0331009 | + | 0.0157678i | ||||
\(191\) | −19.5218 | −1.41255 | −0.706273 | − | 0.707940i | \(-0.749625\pi\) | ||||
−0.706273 | + | 0.707940i | \(0.749625\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 18.3198i | 1.31869i | 0.751843 | + | 0.659343i | \(0.229165\pi\) | ||||
−0.751843 | + | 0.659343i | \(0.770835\pi\) | |||||||
\(194\) | 3.62227 | − | 6.27395i | 0.260064 | − | 0.450443i | ||||
\(195\) | −3.53397 | − | 5.13640i | −0.253073 | − | 0.367825i | ||||
\(196\) | 5.17588 | 0.369706 | ||||||||
\(197\) | 19.6610 | + | 11.3513i | 1.40079 | + | 0.808747i | 0.994474 | − | 0.104986i | \(-0.0334797\pi\) |
0.406316 | + | 0.913732i | \(0.366813\pi\) | |||||||
\(198\) | 4.64021 | − | 2.67903i | 0.329766 | − | 0.190390i | ||||
\(199\) | −9.35537 | −0.663185 | −0.331592 | − | 0.943423i | \(-0.607586\pi\) | ||||
−0.331592 | + | 0.943423i | \(0.607586\pi\) | |||||||
\(200\) | 3.88255 | − | 3.15052i | 0.274538 | − | 0.222776i | ||||
\(201\) | 3.52567 | − | 6.10664i | 0.248682 | − | 0.430729i | ||||
\(202\) | −0.394467 | − | 0.227745i | −0.0277546 | − | 0.0160241i | ||||
\(203\) | −7.68363 | + | 4.43615i | −0.539285 | + | 0.311357i | ||||
\(204\) | 0.472506 | + | 0.818404i | 0.0330820 | + | 0.0572997i | ||||
\(205\) | −22.1469 | + | 1.75425i | −1.54680 | + | 0.122522i | ||||
\(206\) | −1.82087 | + | 3.15384i | −0.126866 | + | 0.219739i | ||||
\(207\) | −0.366109 | − | 0.211373i | −0.0254463 | − | 0.0146914i | ||||
\(208\) | 2.78824i | 0.193330i | ||||||||
\(209\) | −0.605502 | − | 1.04876i | −0.0418835 | − | 0.0725443i | ||||
\(210\) | −0.616107 | − | 7.77816i | −0.0425154 | − | 0.536744i | ||||
\(211\) | −11.9052 | −0.819585 | −0.409793 | − | 0.912179i | \(-0.634399\pi\) | ||||
−0.409793 | + | 0.912179i | \(0.634399\pi\) | |||||||
\(212\) | 2.13170i | 0.146405i | ||||||||
\(213\) | 0.0955722 | + | 0.0551786i | 0.00654850 | + | 0.00378078i | ||||
\(214\) | −14.9045 | −1.01885 | ||||||||
\(215\) | −1.30449 | − | 0.621400i | −0.0889652 | − | 0.0423791i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 28.2999 | − | 16.3390i | 1.92112 | − | 1.10916i | ||||
\(218\) | −9.78311 | + | 5.64828i | −0.662596 | + | 0.382550i | ||||
\(219\) | 1.92535 | + | 3.33480i | 0.130103 | + | 0.225345i | ||||
\(220\) | −11.9436 | + | 0.946048i | −0.805235 | + | 0.0637826i | ||||
\(221\) | −2.63492 | −0.177244 | ||||||||
\(222\) | 6.05542 | + | 0.576064i | 0.406413 | + | 0.0386629i | ||||
\(223\) | − | 7.77470i | − | 0.520633i | −0.965523 | − | 0.260316i | \(-0.916173\pi\) | ||
0.965523 | − | 0.260316i | \(-0.0838269\pi\) | |||||||
\(224\) | −1.74470 | + | 3.02191i | −0.116573 | + | 0.201910i | ||||
\(225\) | −4.93765 | + | 0.787159i | −0.329177 | + | 0.0524773i | ||||
\(226\) | −3.04197 | − | 5.26885i | −0.202349 | − | 0.350479i | ||||
\(227\) | 2.15099 | − | 1.24188i | 0.142766 | − | 0.0824262i | −0.426915 | − | 0.904292i | \(-0.640400\pi\) |
0.569682 | + | 0.821865i | \(0.307066\pi\) | |||||||
\(228\) | 0.226016i | 0.0149682i | ||||||||
\(229\) | −6.90615 | − | 11.9618i | −0.456371 | − | 0.790458i | 0.542395 | − | 0.840124i | \(-0.317518\pi\) |
−0.998766 | + | 0.0496659i | \(0.984184\pi\) | |||||||
\(230\) | 0.535811 | + | 0.778767i | 0.0353303 | + | 0.0513504i | ||||
\(231\) | −9.34819 | + | 16.1915i | −0.615066 | + | 1.06533i | ||||
\(232\) | − | 2.54265i | − | 0.166933i | ||||||
\(233\) | − | 19.4701i | − | 1.27553i | −0.770232 | − | 0.637764i | \(-0.779859\pi\) | ||
0.770232 | − | 0.637764i | \(-0.220141\pi\) | |||||||
\(234\) | 1.39412 | − | 2.41469i | 0.0911366 | − | 0.157853i | ||||
\(235\) | −5.19048 | − | 2.47251i | −0.338589 | − | 0.161289i | ||||
\(236\) | −14.4203 | −0.938679 | ||||||||
\(237\) | 14.8599 | + | 8.57940i | 0.965257 | + | 0.557292i | ||||
\(238\) | −2.85574 | − | 1.64876i | −0.185110 | − | 0.106873i | ||||
\(239\) | −9.41518 | + | 16.3076i | −0.609017 | + | 1.05485i | 0.382386 | + | 0.924003i | \(0.375103\pi\) |
−0.991403 | + | 0.130846i | \(0.958231\pi\) | |||||||
\(240\) | 2.01873 | + | 0.961633i | 0.130308 | + | 0.0620731i | ||||
\(241\) | 2.85209 | + | 4.93996i | 0.183719 | + | 0.318211i | 0.943144 | − | 0.332384i | \(-0.107853\pi\) |
−0.759425 | + | 0.650595i | \(0.774520\pi\) | |||||||
\(242\) | 15.3363 | + | 8.85439i | 0.985852 | + | 0.569182i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −1.10285 | + | 1.91019i | −0.0706026 | + | 0.122287i | ||||
\(245\) | 6.56019 | + | 9.53482i | 0.419115 | + | 0.609157i | ||||
\(246\) | −4.96770 | − | 8.60431i | −0.316729 | − | 0.548591i | ||||
\(247\) | −0.545758 | − | 0.315093i | −0.0347257 | − | 0.0200489i | ||||
\(248\) | 9.36492i | 0.594673i | ||||||||
\(249\) | 0.846274 | 0.0536304 | ||||||||
\(250\) | 10.7247 | + | 3.15914i | 0.678291 | + | 0.199802i | ||||
\(251\) | −25.0920 | −1.58379 | −0.791896 | − | 0.610656i | \(-0.790906\pi\) | ||||
−0.791896 | + | 0.610656i | \(0.790906\pi\) | |||||||
\(252\) | 3.02191 | − | 1.74470i | 0.190362 | − | 0.109906i | ||||
\(253\) | − | 2.26510i | − | 0.142406i | ||||||
\(254\) | 5.80313 | + | 10.0513i | 0.364121 | + | 0.630676i | ||||
\(255\) | −0.908754 | + | 1.90772i | −0.0569084 | + | 0.119466i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 18.7134 | + | 10.8042i | 1.16731 | + | 0.673948i | 0.953046 | − | 0.302827i | \(-0.0979304\pi\) |
0.214267 | + | 0.976775i | \(0.431264\pi\) | |||||||
\(258\) | − | 0.646192i | − | 0.0402302i | ||||||
\(259\) | −19.3040 | + | 8.82407i | −1.19949 | + | 0.548301i | ||||
\(260\) | −5.13640 | + | 3.53397i | −0.318546 | + | 0.219168i | ||||
\(261\) | −1.27132 | + | 2.20200i | −0.0786929 | + | 0.136300i | ||||
\(262\) | 15.1646 | − | 8.75527i | 0.936870 | − | 0.540902i | ||||
\(263\) | −1.03776 | + | 0.599150i | −0.0639909 | + | 0.0369452i | −0.531654 | − | 0.846962i | \(-0.678429\pi\) |
0.467663 | + | 0.883907i | \(0.345096\pi\) | |||||||
\(264\) | −2.67903 | − | 4.64021i | −0.164883 | − | 0.285585i | ||||
\(265\) | −3.92693 | + | 2.70183i | −0.241229 | + | 0.165972i | ||||
\(266\) | −0.394329 | − | 0.682998i | −0.0241779 | − | 0.0418773i | ||||
\(267\) | 10.2580i | 0.627777i | ||||||||
\(268\) | −6.10664 | − | 3.52567i | −0.373023 | − | 0.215365i | ||||
\(269\) | 29.7341 | 1.81292 | 0.906461 | − | 0.422289i | \(-0.138773\pi\) | ||||
0.906461 | + | 0.422289i | \(0.138773\pi\) | |||||||
\(270\) | −1.26745 | − | 1.84216i | −0.0771347 | − | 0.112110i | ||||
\(271\) | 10.1338 | − | 17.5523i | 0.615584 | − | 1.06622i | −0.374697 | − | 0.927147i | \(-0.622253\pi\) |
0.990282 | − | 0.139076i | \(-0.0444133\pi\) | |||||||
\(272\) | 0.818404 | − | 0.472506i | 0.0496230 | − | 0.0286499i | ||||
\(273\) | 9.72929i | 0.588843i | ||||||||
\(274\) | 6.00689 | − | 10.4042i | 0.362889 | − | 0.628543i | ||||
\(275\) | −16.8807 | − | 20.8029i | −1.01794 | − | 1.25446i | ||||
\(276\) | −0.211373 | + | 0.366109i | −0.0127232 | + | 0.0220372i | ||||
\(277\) | 8.84708 | − | 5.10786i | 0.531569 | − | 0.306902i | −0.210086 | − | 0.977683i | \(-0.567374\pi\) |
0.741655 | + | 0.670781i | \(0.234041\pi\) | |||||||
\(278\) | 15.1213 | − | 8.73029i | 0.906916 | − | 0.523608i | ||||
\(279\) | 4.68246 | − | 8.11026i | 0.280332 | − | 0.485549i | ||||
\(280\) | −7.77816 | + | 0.616107i | −0.464834 | + | 0.0368194i | ||||
\(281\) | −6.76134 | + | 11.7110i | −0.403348 | + | 0.698619i | −0.994128 | − | 0.108214i | \(-0.965487\pi\) |
0.590780 | + | 0.806833i | \(0.298820\pi\) | |||||||
\(282\) | − | 2.57116i | − | 0.153111i | ||||||
\(283\) | −15.0280 | + | 8.67644i | −0.893324 | + | 0.515761i | −0.875028 | − | 0.484072i | \(-0.839157\pi\) |
−0.0182959 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(284\) | 0.0551786 | − | 0.0955722i | 0.00327425 | − | 0.00567117i | ||||
\(285\) | −0.416357 | + | 0.286464i | −0.0246629 | + | 0.0169687i | ||||
\(286\) | 14.9396 | 0.883396 | ||||||||
\(287\) | 30.0239 | + | 17.3343i | 1.77225 | + | 1.02321i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −8.05348 | − | 13.9490i | −0.473734 | − | 0.820531i | ||||
\(290\) | 4.68397 | − | 3.22268i | 0.275052 | − | 0.189243i | ||||
\(291\) | 3.62227 | + | 6.27395i | 0.212341 | + | 0.367786i | ||||
\(292\) | 3.33480 | − | 1.92535i | 0.195154 | − | 0.112672i | ||||
\(293\) | 4.57893 | − | 2.64365i | 0.267504 | − | 0.154443i | −0.360249 | − | 0.932856i | \(-0.617308\pi\) |
0.627753 | + | 0.778413i | \(0.283975\pi\) | |||||||
\(294\) | −2.58794 | + | 4.48245i | −0.150932 | + | 0.261422i | ||||
\(295\) | −18.2770 | − | 26.5645i | −1.06413 | − | 1.54664i | ||||
\(296\) | 0.576064 | − | 6.05542i | 0.0334830 | − | 0.351964i | ||||
\(297\) | 5.35806i | 0.310906i | ||||||||
\(298\) | −3.66298 | − | 2.11482i | −0.212191 | − | 0.122508i | ||||
\(299\) | −0.589360 | − | 1.02080i | −0.0340836 | − | 0.0590345i | ||||
\(300\) | 0.787159 | + | 4.93765i | 0.0454467 | + | 0.285075i | ||||
\(301\) | 1.12741 | + | 1.95273i | 0.0649829 | + | 0.112554i | ||||
\(302\) | − | 14.0006i | − | 0.805646i | ||||||
\(303\) | 0.394467 | − | 0.227745i | 0.0226615 | − | 0.0130836i | ||||
\(304\) | 0.226016 | 0.0129629 | ||||||||
\(305\) | −4.91668 | + | 0.389450i | −0.281528 | + | 0.0222998i | ||||
\(306\) | −0.945012 | −0.0540227 | ||||||||
\(307\) | 7.21345i | 0.411693i | 0.978584 | + | 0.205847i | \(0.0659948\pi\) | ||||
−0.978584 | + | 0.205847i | \(0.934005\pi\) | |||||||
\(308\) | 16.1915 | + | 9.34819i | 0.922599 | + | 0.532663i | ||||
\(309\) | −1.82087 | − | 3.15384i | −0.103586 | − | 0.179416i | ||||
\(310\) | −17.2517 | + | 11.8696i | −0.979831 | + | 0.674148i | ||||
\(311\) | −13.7569 | + | 23.8276i | −0.780082 | + | 1.35114i | 0.151812 | + | 0.988409i | \(0.451489\pi\) |
−0.931894 | + | 0.362731i | \(0.881844\pi\) | |||||||
\(312\) | −2.41469 | − | 1.39412i | −0.136705 | − | 0.0789266i | ||||
\(313\) | −30.0867 | − | 17.3706i | −1.70060 | − | 0.981843i | −0.945149 | − | 0.326638i | \(-0.894084\pi\) |
−0.755452 | − | 0.655204i | \(-0.772582\pi\) | |||||||
\(314\) | −4.15298 | − | 7.19316i | −0.234366 | − | 0.405934i | ||||
\(315\) | 7.04414 | + | 3.35552i | 0.396892 | + | 0.189062i | ||||
\(316\) | 8.57940 | − | 14.8599i | 0.482629 | − | 0.835937i | ||||
\(317\) | −6.51018 | − | 3.75866i | −0.365648 | − | 0.211107i | 0.305907 | − | 0.952061i | \(-0.401040\pi\) |
−0.671556 | + | 0.740954i | \(0.734374\pi\) | |||||||
\(318\) | −1.84610 | − | 1.06585i | −0.103524 | − | 0.0597698i | ||||
\(319\) | −13.6236 | −0.762778 | ||||||||
\(320\) | 0.961633 | − | 2.01873i | 0.0537569 | − | 0.112850i | ||||
\(321\) | 7.45225 | − | 12.9077i | 0.415944 | − | 0.720436i | ||||
\(322\) | − | 1.47513i | − | 0.0822057i | ||||||
\(323\) | 0.213587i | 0.0118843i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −13.0203 | − | 4.98294i | −0.722236 | − | 0.276404i | ||||
\(326\) | 2.52224 | + | 4.36864i | 0.139694 | + | 0.241957i | ||||
\(327\) | − | 11.2966i | − | 0.624701i | ||||||
\(328\) | −8.60431 | + | 4.96770i | −0.475094 | + | 0.274295i | ||||
\(329\) | 4.48590 | + | 7.76981i | 0.247316 | + | 0.428363i | ||||
\(330\) | 5.15248 | − | 10.8165i | 0.283635 | − | 0.595427i | ||||
\(331\) | −4.54546 | + | 7.87296i | −0.249841 | + | 0.432737i | −0.963482 | − | 0.267775i | \(-0.913712\pi\) |
0.713641 | + | 0.700512i | \(0.247045\pi\) | |||||||
\(332\) | − | 0.846274i | − | 0.0464453i | ||||||
\(333\) | −3.52660 | + | 4.95612i | −0.193256 | + | 0.271594i | ||||
\(334\) | 9.62971 | 0.526914 | ||||||||
\(335\) | −1.24502 | − | 15.7181i | −0.0680229 | − | 0.858769i | ||||
\(336\) | −1.74470 | − | 3.02191i | −0.0951811 | − | 0.164858i | ||||
\(337\) | 30.8212 | − | 17.7946i | 1.67894 | − | 0.969334i | 0.716594 | − | 0.697490i | \(-0.245700\pi\) |
0.962341 | − | 0.271843i | \(-0.0876333\pi\) | |||||||
\(338\) | −4.52558 | + | 2.61285i | −0.246159 | + | 0.142120i | ||||
\(339\) | 6.08395 | 0.330435 | ||||||||
\(340\) | 1.90772 | + | 0.908754i | 0.103461 | + | 0.0492841i | ||||
\(341\) | 50.1778 | 2.71728 | ||||||||
\(342\) | −0.195735 | − | 0.113008i | −0.0105842 | − | 0.00611076i | ||||
\(343\) | 6.36507i | 0.343681i | ||||||||
\(344\) | −0.646192 | −0.0348404 | ||||||||
\(345\) | −0.942338 | + | 0.0746424i | −0.0507338 | + | 0.00401861i | ||||
\(346\) | 5.01608 | + | 8.68811i | 0.269666 | + | 0.467076i | ||||
\(347\) | 0.659463i | 0.0354018i | 0.999843 | + | 0.0177009i | \(0.00563467\pi\) | ||||
−0.999843 | + | 0.0177009i | \(0.994365\pi\) | |||||||
\(348\) | 2.20200 | + | 1.27132i | 0.118039 | + | 0.0681501i | ||||
\(349\) | −1.60641 | + | 2.78238i | −0.0859892 | + | 0.148938i | −0.905812 | − | 0.423679i | \(-0.860738\pi\) |
0.819823 | + | 0.572617i | \(0.194072\pi\) | |||||||
\(350\) | −10.9934 | − | 13.5478i | −0.587623 | − | 0.724158i | ||||
\(351\) | 1.39412 | + | 2.41469i | 0.0744127 | + | 0.128887i | ||||
\(352\) | −4.64021 | + | 2.67903i | −0.247324 | + | 0.142793i | ||||
\(353\) | −4.06092 | − | 2.34457i | −0.216141 | − | 0.124789i | 0.388021 | − | 0.921650i | \(-0.373159\pi\) |
−0.604162 | + | 0.796861i | \(0.706492\pi\) | |||||||
\(354\) | 7.21013 | − | 12.4883i | 0.383214 | − | 0.663746i | ||||
\(355\) | 0.245996 | − | 0.0194853i | 0.0130561 | − | 0.00103417i | ||||
\(356\) | 10.2580 | 0.543671 | ||||||||
\(357\) | 2.85574 | − | 1.64876i | 0.151142 | − | 0.0872616i | ||||
\(358\) | 2.53164 | + | 1.46164i | 0.133801 | + | 0.0772502i | ||||
\(359\) | −11.1684 | −0.589444 | −0.294722 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294722 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(360\) | −1.84216 | + | 1.26745i | −0.0970905 | + | 0.0668007i | ||||
\(361\) | 9.47446 | − | 16.4102i | 0.498656 | − | 0.863697i | ||||
\(362\) | − | 4.60770i | − | 0.242175i | ||||||
\(363\) | −15.3363 | + | 8.85439i | −0.804945 | + | 0.464735i | ||||
\(364\) | 9.72929 | 0.509953 | ||||||||
\(365\) | 7.77350 | + | 3.70295i | 0.406884 | + | 0.193821i | ||||
\(366\) | −1.10285 | − | 1.91019i | −0.0576467 | − | 0.0998471i | ||||
\(367\) | 0.0843912 | − | 0.0487233i | 0.00440518 | − | 0.00254333i | −0.497796 | − | 0.867294i | \(-0.665857\pi\) |
0.502201 | + | 0.864751i | \(0.332524\pi\) | |||||||
\(368\) | 0.366109 | + | 0.211373i | 0.0190847 | + | 0.0110186i | ||||
\(369\) | 9.93540 | 0.517217 | ||||||||
\(370\) | 11.8852 | − | 6.61376i | 0.617883 | − | 0.343833i | ||||
\(371\) | 7.43833 | 0.386179 | ||||||||
\(372\) | −8.11026 | − | 4.68246i | −0.420497 | − | 0.242774i | ||||
\(373\) | 15.3660 | − | 8.87158i | 0.795623 | − | 0.459353i | −0.0463156 | − | 0.998927i | \(-0.514748\pi\) |
0.841938 | + | 0.539574i | \(0.181415\pi\) | |||||||
\(374\) | −2.53171 | − | 4.38506i | −0.130912 | − | 0.226746i | ||||
\(375\) | −8.09826 | + | 7.70831i | −0.418193 | + | 0.398056i | ||||
\(376\) | −2.57116 | −0.132598 | ||||||||
\(377\) | −6.13970 | + | 3.54476i | −0.316211 | + | 0.182564i | ||||
\(378\) | 3.48940i | 0.179475i | ||||||||
\(379\) | −9.09367 | + | 15.7507i | −0.467111 | + | 0.809059i | −0.999294 | − | 0.0375697i | \(-0.988038\pi\) |
0.532183 | + | 0.846629i | \(0.321372\pi\) | |||||||
\(380\) | 0.286464 | + | 0.416357i | 0.0146953 | + | 0.0213587i | ||||
\(381\) | −11.6063 | −0.594607 | ||||||||
\(382\) | −16.9063 | − | 9.76088i | −0.865004 | − | 0.499410i | ||||
\(383\) | 11.9039 | − | 6.87272i | 0.608261 | − | 0.351180i | −0.164023 | − | 0.986456i | \(-0.552447\pi\) |
0.772285 | + | 0.635277i | \(0.219114\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 3.30114 | + | 41.6758i | 0.168241 | + | 2.12400i | ||||
\(386\) | −9.15988 | + | 15.8654i | −0.466226 | + | 0.807527i | ||||
\(387\) | 0.559619 | + | 0.323096i | 0.0284470 | + | 0.0164239i | ||||
\(388\) | 6.27395 | − | 3.62227i | 0.318512 | − | 0.183893i | ||||
\(389\) | −1.90141 | − | 3.29334i | −0.0964053 | − | 0.166979i | 0.813789 | − | 0.581161i | \(-0.197401\pi\) |
−0.910194 | + | 0.414182i | \(0.864068\pi\) | |||||||
\(390\) | −0.492308 | − | 6.21524i | −0.0249290 | − | 0.314721i | ||||
\(391\) | −0.199750 | + | 0.345977i | −0.0101018 | + | 0.0174968i | ||||
\(392\) | 4.48245 | + | 2.58794i | 0.226398 | + | 0.130711i | ||||
\(393\) | 17.5105i | 0.883290i | ||||||||
\(394\) | 11.3513 | + | 19.6610i | 0.571870 | + | 0.990508i | ||||
\(395\) | 38.2484 | − | 3.02965i | 1.92449 | − | 0.152438i | ||||
\(396\) | 5.35806 | 0.269253 | ||||||||
\(397\) | 10.6416i | 0.534087i | 0.963684 | + | 0.267043i | \(0.0860467\pi\) | ||||
−0.963684 | + | 0.267043i | \(0.913953\pi\) | |||||||
\(398\) | −8.10199 | − | 4.67769i | −0.406116 | − | 0.234471i | ||||
\(399\) | 0.788658 | 0.0394823 | ||||||||
\(400\) | 4.93765 | − | 0.787159i | 0.246882 | − | 0.0393580i | ||||
\(401\) | −37.4003 | −1.86768 | −0.933841 | − | 0.357688i | \(-0.883565\pi\) | ||||
−0.933841 | + | 0.357688i | \(0.883565\pi\) | |||||||
\(402\) | 6.10664 | − | 3.52567i | 0.304572 | − | 0.175845i | ||||
\(403\) | 22.6134 | − | 13.0558i | 1.12645 | − | 0.650358i | ||||
\(404\) | −0.227745 | − | 0.394467i | −0.0113308 | − | 0.0196255i | ||||
\(405\) | 2.22909 | − | 0.176566i | 0.110764 | − | 0.00877361i | ||||
\(406\) | −8.87230 | −0.440325 | ||||||||
\(407\) | −32.4453 | − | 3.08659i | −1.60825 | − | 0.152996i | ||||
\(408\) | 0.945012i | 0.0467850i | ||||||||
\(409\) | −4.23490 | + | 7.33506i | −0.209402 | + | 0.362695i | −0.951526 | − | 0.307567i | \(-0.900485\pi\) |
0.742124 | + | 0.670262i | \(0.233818\pi\) | |||||||
\(410\) | −20.0569 | − | 9.55421i | −0.990539 | − | 0.471849i | ||||
\(411\) | 6.00689 | + | 10.4042i | 0.296298 | + | 0.513203i | ||||
\(412\) | −3.15384 | + | 1.82087i | −0.155379 | + | 0.0897079i | ||||
\(413\) | 50.3180i | 2.47599i | ||||||||
\(414\) | −0.211373 | − | 0.366109i | −0.0103884 | − | 0.0179933i | ||||
\(415\) | 1.55897 | − | 1.07261i | 0.0765270 | − | 0.0526525i | ||||
\(416\) | −1.39412 | + | 2.41469i | −0.0683525 | + | 0.118390i | ||||
\(417\) | 17.4606i | 0.855048i | ||||||||
\(418\) | − | 1.21100i | − | 0.0592322i | ||||||
\(419\) | 7.22921 | − | 12.5214i | 0.353170 | − | 0.611709i | −0.633633 | − | 0.773634i | \(-0.718437\pi\) |
0.986803 | + | 0.161925i | \(0.0517704\pi\) | |||||||
\(420\) | 3.35552 | − | 7.04414i | 0.163732 | − | 0.343719i | ||||
\(421\) | 29.1100 | 1.41873 | 0.709366 | − | 0.704840i | \(-0.248981\pi\) | ||||
0.709366 | + | 0.704840i | \(0.248981\pi\) | |||||||
\(422\) | −10.3102 | − | 5.95258i | −0.501891 | − | 0.289767i | ||||
\(423\) | 2.22669 | + | 1.28558i | 0.108265 | + | 0.0625071i | ||||
\(424\) | −1.06585 | + | 1.84610i | −0.0517622 | + | 0.0896547i | ||||
\(425\) | 0.743875 | + | 4.66614i | 0.0360832 | + | 0.226341i | ||||
\(426\) | 0.0551786 | + | 0.0955722i | 0.00267341 | + | 0.00463049i | ||||
\(427\) | 6.66540 | + | 3.84827i | 0.322561 | + | 0.186231i | ||||
\(428\) | −12.9077 | − | 7.45225i | −0.623916 | − | 0.360218i | ||||
\(429\) | −7.46979 | + | 12.9381i | −0.360645 | + | 0.624655i | ||||
\(430\) | −0.819019 | − | 1.19039i | −0.0394966 | − | 0.0574058i | ||||
\(431\) | −6.48910 | − | 11.2395i | −0.312569 | − | 0.541386i | 0.666349 | − | 0.745640i | \(-0.267856\pi\) |
−0.978918 | + | 0.204255i | \(0.934523\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 11.1872i | 0.537624i | 0.963193 | + | 0.268812i | \(0.0866310\pi\) | ||||
−0.963193 | + | 0.268812i | \(0.913369\pi\) | |||||||
\(434\) | 32.6779 | 1.56859 | ||||||||
\(435\) | 0.448943 | + | 5.66778i | 0.0215252 | + | 0.271749i | ||||
\(436\) | −11.2966 | −0.541007 | ||||||||
\(437\) | −0.0827463 | + | 0.0477736i | −0.00395829 | + | 0.00228532i | ||||
\(438\) | 3.85069i | 0.183993i | ||||||||
\(439\) | −12.9368 | − | 22.4072i | −0.617441 | − | 1.06944i | −0.989951 | − | 0.141411i | \(-0.954836\pi\) |
0.372510 | − | 0.928028i | \(-0.378497\pi\) | |||||||
\(440\) | −10.8165 | − | 5.15248i | −0.515655 | − | 0.245635i | ||||
\(441\) | −2.58794 | − | 4.48245i | −0.123235 | − | 0.213450i | ||||
\(442\) | −2.28191 | − | 1.31746i | −0.108539 | − | 0.0626653i | ||||
\(443\) | − | 39.0089i | − | 1.85337i | −0.375843 | − | 0.926683i | \(-0.622647\pi\) | ||
0.375843 | − | 0.926683i | \(-0.377353\pi\) | |||||||
\(444\) | 4.95612 | + | 3.52660i | 0.235207 | + | 0.167365i | ||||
\(445\) | 13.0015 | + | 18.8968i | 0.616330 | + | 0.895796i | ||||
\(446\) | 3.88735 | − | 6.73309i | 0.184071 | − | 0.318821i | ||||
\(447\) | 3.66298 | − | 2.11482i | 0.173253 | − | 0.100028i | ||||
\(448\) | −3.02191 | + | 1.74470i | −0.142772 | + | 0.0824292i | ||||
\(449\) | −20.3811 | − | 35.3011i | −0.961842 | − | 1.66596i | −0.717869 | − | 0.696178i | \(-0.754882\pi\) |
−0.243973 | − | 0.969782i | \(-0.578451\pi\) | |||||||
\(450\) | −4.66971 | − | 1.78712i | −0.220132 | − | 0.0842459i | ||||
\(451\) | 26.6172 | + | 46.1024i | 1.25336 | + | 2.17088i | ||||
\(452\) | − | 6.08395i | − | 0.286165i | ||||||
\(453\) | 12.1249 | + | 7.00031i | 0.569677 | + | 0.328903i | ||||
\(454\) | 2.48375 | 0.116568 | ||||||||
\(455\) | 12.3314 | + | 17.9229i | 0.578106 | + | 0.840240i | ||||
\(456\) | −0.113008 | + | 0.195735i | −0.00529208 | + | 0.00916614i | ||||
\(457\) | 1.09441 | − | 0.631857i | 0.0511943 | − | 0.0295570i | −0.474184 | − | 0.880426i | \(-0.657257\pi\) |
0.525379 | + | 0.850869i | \(0.323924\pi\) | |||||||
\(458\) | − | 13.8123i | − | 0.645406i | ||||||
\(459\) | 0.472506 | − | 0.818404i | 0.0220547 | − | 0.0381998i | ||||
\(460\) | 0.0746424 | + | 0.942338i | 0.00348022 | + | 0.0439367i | ||||
\(461\) | −12.2631 | + | 21.2402i | −0.571148 | + | 0.989257i | 0.425301 | + | 0.905052i | \(0.360168\pi\) |
−0.996448 | + | 0.0842048i | \(0.973165\pi\) | |||||||
\(462\) | −16.1915 | + | 9.34819i | −0.753299 | + | 0.434917i | ||||
\(463\) | −23.6943 | + | 13.6799i | −1.10117 | + | 0.635760i | −0.936528 | − | 0.350593i | \(-0.885980\pi\) |
−0.164641 | + | 0.986353i | \(0.552647\pi\) | |||||||
\(464\) | 1.27132 | − | 2.20200i | 0.0590197 | − | 0.102225i | ||||
\(465\) | −1.65352 | − | 20.8752i | −0.0766803 | − | 0.968065i | ||||
\(466\) | 9.73505 | − | 16.8616i | 0.450967 | − | 0.781098i | ||||
\(467\) | 34.6935i | 1.60543i | 0.596366 | + | 0.802713i | \(0.296611\pi\) | ||||
−0.596366 | + | 0.802713i | \(0.703389\pi\) | |||||||
\(468\) | 2.41469 | − | 1.39412i | 0.111619 | − | 0.0644433i | ||||
\(469\) | −12.3025 | + | 21.3085i | −0.568075 | + | 0.983935i | ||||
\(470\) | −3.25883 | − | 4.73650i | −0.150319 | − | 0.218478i | ||||
\(471\) | 8.30595 | 0.382718 | ||||||||
\(472\) | −12.4883 | − | 7.21013i | −0.574821 | − | 0.331873i | ||||
\(473\) | 3.46234i | 0.159198i | ||||||||
\(474\) | 8.57940 | + | 14.8599i | 0.394065 | + | 0.682540i | ||||
\(475\) | −0.403918 | + | 1.05543i | −0.0185330 | + | 0.0484263i | ||||
\(476\) | −1.64876 | − | 2.85574i | −0.0755708 | − | 0.130892i | ||||
\(477\) | 1.84610 | − | 1.06585i | 0.0845273 | − | 0.0488018i | ||||
\(478\) | −16.3076 | + | 9.41518i | −0.745891 | + | 0.430640i | ||||
\(479\) | −4.76098 | + | 8.24626i | −0.217535 | + | 0.376781i | −0.954054 | − | 0.299636i | \(-0.903135\pi\) |
0.736519 | + | 0.676417i | \(0.236468\pi\) | |||||||
\(480\) | 1.26745 | + | 1.84216i | 0.0578511 | + | 0.0840828i | ||||
\(481\) | −15.4251 | + | 7.05098i | −0.703323 | + | 0.321497i | ||||
\(482\) | 5.70418i | 0.259818i | ||||||||
\(483\) | 1.27750 | + | 0.737564i | 0.0581282 | + | 0.0335603i | ||||
\(484\) | 8.85439 | + | 15.3363i | 0.402472 | + | 0.697103i | ||||
\(485\) | 14.6247 | + | 6.96658i | 0.664075 | + | 0.316336i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 37.4997i | 1.69928i | 0.527367 | + | 0.849638i | \(0.323179\pi\) | ||||
−0.527367 | + | 0.849638i | \(0.676821\pi\) | |||||||
\(488\) | −1.91019 | + | 1.10285i | −0.0864701 | + | 0.0499235i | ||||
\(489\) | −5.04447 | −0.228119 | ||||||||
\(490\) | 0.913882 | + | 11.5375i | 0.0412850 | + | 0.521211i | ||||
\(491\) | 12.0268 | 0.542760 | 0.271380 | − | 0.962472i | \(-0.412520\pi\) | ||||
0.271380 | + | 0.962472i | \(0.412520\pi\) | |||||||
\(492\) | − | 9.93540i | − | 0.447923i | ||||||
\(493\) | 2.08091 | + | 1.20141i | 0.0937195 | + | 0.0541090i | ||||
\(494\) | −0.315093 | − | 0.545758i | −0.0141767 | − | 0.0245548i | ||||
\(495\) | 6.79109 | + | 9.87041i | 0.305237 | + | 0.443642i | ||||
\(496\) | −4.68246 | + | 8.11026i | −0.210249 | + | 0.364161i | ||||
\(497\) | −0.333489 | − | 0.192540i | −0.0149590 | − | 0.00863661i | ||||
\(498\) | 0.732895 | + | 0.423137i | 0.0328418 | + | 0.0189612i | ||||
\(499\) | −19.6299 | − | 33.9999i | −0.878753 | − | 1.52204i | −0.852710 | − | 0.522384i | \(-0.825043\pi\) |
−0.0260427 | − | 0.999661i | \(-0.508291\pi\) | |||||||
\(500\) | 7.70831 | + | 8.09826i | 0.344726 | + | 0.362165i | ||||
\(501\) | −4.81486 | + | 8.33958i | −0.215112 | + | 0.372585i | ||||
\(502\) | −21.7303 | − | 12.5460i | −0.969871 | − | 0.559955i | ||||
\(503\) | −13.5890 | − | 7.84562i | −0.605904 | − | 0.349819i | 0.165456 | − | 0.986217i | \(-0.447090\pi\) |
−0.771361 | + | 0.636398i | \(0.780424\pi\) | |||||||
\(504\) | 3.48940 | 0.155430 | ||||||||
\(505\) | 0.438015 | − | 0.919512i | 0.0194914 | − | 0.0409178i | ||||
\(506\) | 1.13255 | − | 1.96163i | 0.0503480 | − | 0.0872052i | ||||
\(507\) | − | 5.22569i | − | 0.232081i | ||||||
\(508\) | 11.6063i | 0.514945i | ||||||||
\(509\) | −0.129495 | + | 0.224293i | −0.00573978 | + | 0.00994160i | −0.868881 | − | 0.495021i | \(-0.835160\pi\) |
0.863141 | + | 0.504963i | \(0.168494\pi\) | |||||||
\(510\) | −1.74086 | + | 1.19776i | −0.0770868 | + | 0.0530376i | ||||
\(511\) | −6.71829 | − | 11.6364i | −0.297200 | − | 0.514765i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0.195735 | − | 0.113008i | 0.00864192 | − | 0.00498942i | ||||
\(514\) | 10.8042 | + | 18.7134i | 0.476553 | + | 0.825415i | ||||
\(515\) | −7.35169 | − | 3.50202i | −0.323954 | − | 0.154317i | ||||
\(516\) | 0.323096 | − | 0.559619i | 0.0142235 | − | 0.0246359i | ||||
\(517\) | 13.7764i | 0.605887i | ||||||||
\(518\) | −21.1298 | − | 2.01012i | −0.928389 | − | 0.0883194i | ||||
\(519\) | −10.0322 | −0.440363 | ||||||||
\(520\) | −6.21524 | + | 0.492308i | −0.272556 | + | 0.0215891i | ||||
\(521\) | −3.78019 | − | 6.54748i | −0.165613 | − | 0.286850i | 0.771260 | − | 0.636521i | \(-0.219627\pi\) |
−0.936873 | + | 0.349670i | \(0.886294\pi\) | |||||||
\(522\) | −2.20200 | + | 1.27132i | −0.0963787 | + | 0.0556443i | ||||
\(523\) | 7.28454 | − | 4.20573i | 0.318531 | − | 0.183904i | −0.332207 | − | 0.943207i | \(-0.607793\pi\) |
0.650737 | + | 0.759303i | \(0.274460\pi\) | |||||||
\(524\) | 17.5105 | 0.764951 | ||||||||
\(525\) | 17.2294 | − | 2.74671i | 0.751953 | − | 0.119876i | ||||
\(526\) | −1.19830 | −0.0522483 | ||||||||
\(527\) | −7.66429 | − | 4.42498i | −0.333862 | − | 0.192755i | ||||
\(528\) | − | 5.35806i | − | 0.233180i | ||||||
\(529\) | 22.8213 | 0.992230 | ||||||||
\(530\) | −4.75173 | + | 0.376384i | −0.206402 | + | 0.0163491i | ||||
\(531\) | 7.21013 | + | 12.4883i | 0.312893 | + | 0.541946i | ||||
\(532\) | − | 0.788658i | − | 0.0341927i | ||||||
\(533\) | 23.9909 | + | 13.8512i | 1.03916 | + | 0.599961i | ||||
\(534\) | −5.12898 | + | 8.88366i | −0.221953 | + | 0.384433i | ||||
\(535\) | −2.63162 | − | 33.2234i | −0.113775 | − | 1.43637i | ||||
\(536\) | −3.52567 | − | 6.10664i | −0.152286 | − | 0.263767i | ||||
\(537\) | −2.53164 | + | 1.46164i | −0.109248 | + | 0.0630745i | ||||
\(538\) | 25.7505 | + | 14.8671i | 1.11018 | + | 0.640965i | ||||
\(539\) | 13.8663 | − | 24.0172i | 0.597265 | − | 1.03449i | ||||
\(540\) | −0.176566 | − | 2.22909i | −0.00759817 | − | 0.0959246i | ||||
\(541\) | −11.4565 | −0.492552 | −0.246276 | − | 0.969200i | \(-0.579207\pi\) | ||||
−0.246276 | + | 0.969200i | \(0.579207\pi\) | |||||||
\(542\) | 17.5523 | − | 10.1338i | 0.753934 | − | 0.435284i | ||||
\(543\) | 3.99038 | + | 2.30385i | 0.171244 | + | 0.0988677i | ||||
\(544\) | 0.945012 | 0.0405170 | ||||||||
\(545\) | −14.3179 | − | 20.8101i | −0.613310 | − | 0.891407i | ||||
\(546\) | −4.86464 | + | 8.42581i | −0.208188 | + | 0.360591i | ||||
\(547\) | − | 21.4063i | − | 0.915266i | −0.889141 | − | 0.457633i | \(-0.848697\pi\) | ||
0.889141 | − | 0.457633i | \(-0.151303\pi\) | |||||||
\(548\) | 10.4042 | − | 6.00689i | 0.444447 | − | 0.256602i | ||||
\(549\) | 2.20569 | 0.0941367 | ||||||||
\(550\) | −4.21765 | − | 26.4562i | −0.179841 | − | 1.12810i | ||||
\(551\) | 0.287339 | + | 0.497685i | 0.0122410 | + | 0.0212021i | ||||
\(552\) | −0.366109 | + | 0.211373i | −0.0155826 | + | 0.00899664i | ||||
\(553\) | −51.8522 | − | 29.9369i | −2.20498 | − | 1.27305i | ||||
\(554\) | 10.2157 | 0.434024 | ||||||||
\(555\) | −0.214918 | + | 13.5998i | −0.00912275 | + | 0.577278i | ||||
\(556\) | 17.4606 | 0.740494 | ||||||||
\(557\) | −32.3309 | − | 18.6663i | −1.36991 | − | 0.790915i | −0.378990 | − | 0.925401i | \(-0.623728\pi\) |
−0.990916 | + | 0.134486i | \(0.957062\pi\) | |||||||
\(558\) | 8.11026 | − | 4.68246i | 0.343335 | − | 0.198224i | ||||
\(559\) | 0.900871 | + | 1.56035i | 0.0381028 | + | 0.0659960i | ||||
\(560\) | −7.04414 | − | 3.35552i | −0.297669 | − | 0.141796i | ||||
\(561\) | 5.06343 | 0.213778 | ||||||||
\(562\) | −11.7110 | + | 6.76134i | −0.493998 | + | 0.285210i | ||||
\(563\) | 31.5978i | 1.33169i | 0.746090 | + | 0.665845i | \(0.231929\pi\) | ||||
−0.746090 | + | 0.665845i | \(0.768071\pi\) | |||||||
\(564\) | 1.28558 | − | 2.22669i | 0.0541327 | − | 0.0937607i | ||||
\(565\) | 11.2076 | − | 7.71112i | 0.471508 | − | 0.324409i | ||||
\(566\) | −17.3529 | −0.729396 | ||||||||
\(567\) | −3.02191 | − | 1.74470i | −0.126908 | − | 0.0732704i | ||||
\(568\) | 0.0955722 | − | 0.0551786i | 0.00401012 | − | 0.00231524i | ||||
\(569\) | 31.0452 | 1.30148 | 0.650740 | − | 0.759300i | \(-0.274459\pi\) | ||||
0.650740 | + | 0.759300i | \(0.274459\pi\) | |||||||
\(570\) | −0.503808 | + | 0.0399066i | −0.0211022 | + | 0.00167150i | ||||
\(571\) | −20.5791 | + | 35.6441i | −0.861210 | + | 1.49166i | 0.00955188 | + | 0.999954i | \(0.496959\pi\) |
−0.870762 | + | 0.491705i | \(0.836374\pi\) | |||||||
\(572\) | 12.9381 | + | 7.46979i | 0.540967 | + | 0.312328i | ||||
\(573\) | 16.9063 | − | 9.76088i | 0.706273 | − | 0.407767i | ||||
\(574\) | 17.3343 | + | 30.0239i | 0.723519 | + | 1.25317i | ||||
\(575\) | −1.64133 | + | 1.33187i | −0.0684483 | + | 0.0555429i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.4946 | + | 12.9873i | 0.936464 | + | 0.540668i | 0.888850 | − | 0.458198i | \(-0.151505\pi\) |
0.0476141 | + | 0.998866i | \(0.484838\pi\) | |||||||
\(578\) | − | 16.1070i | − | 0.669961i | ||||||
\(579\) | −9.15988 | − | 15.8654i | −0.380672 | − | 0.659343i | ||||
\(580\) | 5.66778 | − | 0.448943i | 0.235342 | − | 0.0186414i | ||||
\(581\) | −2.95298 | −0.122510 | ||||||||
\(582\) | 7.24454i | 0.300296i | ||||||||
\(583\) | 9.89153 | + | 5.71088i | 0.409665 | + | 0.236520i | ||||
\(584\) | 3.85069 | 0.159343 | ||||||||
\(585\) | 5.62871 | + | 2.68127i | 0.232718 | + | 0.110857i | ||||
\(586\) | 5.28729 | 0.218416 | ||||||||
\(587\) | −34.1658 | + | 19.7256i | −1.41017 | + | 0.814163i | −0.995404 | − | 0.0957642i | \(-0.969471\pi\) |
−0.414768 | + | 0.909927i | \(0.636137\pi\) | |||||||
\(588\) | −4.48245 | + | 2.58794i | −0.184853 | + | 0.106725i | ||||
\(589\) | −1.05831 | − | 1.83305i | −0.0436069 | − | 0.0755293i | ||||
\(590\) | −2.54612 | − | 32.1440i | −0.104822 | − | 1.32335i | ||||
\(591\) | −22.7026 | −0.933860 | ||||||||
\(592\) | 3.52660 | − | 4.95612i | 0.144942 | − | 0.203695i | ||||
\(593\) | − | 14.9931i | − | 0.615692i | −0.951436 | − | 0.307846i | \(-0.900392\pi\) | ||
0.951436 | − | 0.307846i | \(-0.0996082\pi\) | |||||||
\(594\) | −2.67903 | + | 4.64021i | −0.109922 | + | 0.190390i | ||||
\(595\) | 3.17100 | − | 6.65679i | 0.129998 | − | 0.272902i | ||||
\(596\) | −2.11482 | − | 3.66298i | −0.0866264 | − | 0.150041i | ||||
\(597\) | 8.10199 | − | 4.67769i | 0.331592 | − | 0.191445i | ||||
\(598\) | − | 1.17872i | − | 0.0482014i | ||||||
\(599\) | 1.48089 | + | 2.56497i | 0.0605074 | + | 0.104802i | 0.894692 | − | 0.446683i | \(-0.147395\pi\) |
−0.834185 | + | 0.551485i | \(0.814061\pi\) | |||||||
\(600\) | −1.78712 | + | 4.66971i | −0.0729591 | + | 0.190640i | ||||
\(601\) | 18.6906 | − | 32.3730i | 0.762404 | − | 1.32052i | −0.179205 | − | 0.983812i | \(-0.557353\pi\) |
0.941608 | − | 0.336710i | \(-0.109314\pi\) | |||||||
\(602\) | 2.25482i | 0.0918996i | ||||||||
\(603\) | 7.05134i | 0.287153i | ||||||||
\(604\) | 7.00031 | − | 12.1249i | 0.284839 | − | 0.493355i | ||||
\(605\) | −17.0293 | + | 35.7492i | −0.692341 | + | 1.45341i | ||||
\(606\) | 0.455491 | 0.0185031 | ||||||||
\(607\) | 8.14822 | + | 4.70438i | 0.330726 | + | 0.190945i | 0.656163 | − | 0.754619i | \(-0.272178\pi\) |
−0.325437 | + | 0.945564i | \(0.605512\pi\) | |||||||
\(608\) | 0.195735 | + | 0.113008i | 0.00793811 | + | 0.00458307i | ||||
\(609\) | 4.43615 | − | 7.68363i | 0.179762 | − | 0.311357i | ||||
\(610\) | −4.45270 | − | 2.12107i | −0.180284 | − | 0.0858795i | ||||
\(611\) | 3.58452 | + | 6.20856i | 0.145014 | + | 0.251172i | ||||
\(612\) | −0.818404 | − | 0.472506i | −0.0330820 | − | 0.0190999i | ||||
\(613\) | −40.6211 | − | 23.4526i | −1.64067 | − | 0.947241i | −0.980596 | − | 0.196041i | \(-0.937191\pi\) |
−0.660074 | − | 0.751200i | \(-0.729475\pi\) | |||||||
\(614\) | −3.60673 | + | 6.24703i | −0.145556 | + | 0.252110i | ||||
\(615\) | 18.3026 | − | 12.5927i | 0.738033 | − | 0.507785i | ||||
\(616\) | 9.34819 | + | 16.1915i | 0.376649 | + | 0.652376i | ||||
\(617\) | −38.2288 | − | 22.0714i | −1.53903 | − | 0.888562i | −0.998896 | − | 0.0469854i | \(-0.985039\pi\) |
−0.540138 | − | 0.841576i | \(-0.681628\pi\) | |||||||
\(618\) | − | 3.64174i | − | 0.146492i | ||||||
\(619\) | 43.6928 | 1.75616 | 0.878080 | − | 0.478513i | \(-0.158824\pi\) | ||||
0.878080 | + | 0.478513i | \(0.158824\pi\) | |||||||
\(620\) | −20.8752 | + | 1.65352i | −0.838369 | + | 0.0664071i | ||||
\(621\) | 0.422746 | 0.0169642 | ||||||||
\(622\) | −23.8276 | + | 13.7569i | −0.955401 | + | 0.551601i | ||||
\(623\) | − | 35.7941i | − | 1.43406i | ||||||
\(624\) | −1.39412 | − | 2.41469i | −0.0558096 | − | 0.0966650i | ||||
\(625\) | −5.14839 | + | 24.4641i | −0.205936 | + | 0.978566i | ||||
\(626\) | −17.3706 | − | 30.0867i | −0.694268 | − | 1.20251i | ||||
\(627\) | 1.04876 | + | 0.605502i | 0.0418835 | + | 0.0241814i | ||||
\(628\) | − | 8.30595i | − | 0.331444i | ||||||
\(629\) | 4.68359 | + | 3.33268i | 0.186747 | + | 0.132882i | ||||
\(630\) | 4.42265 | + | 6.42803i | 0.176202 | + | 0.256099i | ||||
\(631\) | 16.8066 | − | 29.1099i | 0.669061 | − | 1.15885i | −0.309107 | − | 0.951027i | \(-0.600030\pi\) |
0.978167 | − | 0.207819i | \(-0.0666367\pi\) | |||||||
\(632\) | 14.8599 | − | 8.57940i | 0.591097 | − | 0.341270i | ||||
\(633\) | 10.3102 | − | 5.95258i | 0.409793 | − | 0.236594i | ||||
\(634\) | −3.75866 | − | 6.51018i | −0.149275 | − | 0.258552i | ||||
\(635\) | −21.3806 | + | 14.7104i | −0.848464 | + | 0.583764i | ||||
\(636\) | −1.06585 | − | 1.84610i | −0.0422636 | − | 0.0732027i | ||||
\(637\) | − | 14.4316i | − | 0.571802i | ||||||
\(638\) | −11.7984 | − | 6.81182i | −0.467104 | − | 0.269683i | ||||
\(639\) | −0.110357 | −0.00436567 | ||||||||
\(640\) | 1.84216 | − | 1.26745i | 0.0728179 | − | 0.0501005i | ||||
\(641\) | 0.214823 | − | 0.372084i | 0.00848500 | − | 0.0146964i | −0.861752 | − | 0.507330i | \(-0.830632\pi\) |
0.870237 | + | 0.492634i | \(0.163966\pi\) | |||||||
\(642\) | 12.9077 | − | 7.45225i | 0.509425 | − | 0.294117i | ||||
\(643\) | 35.5391i | 1.40153i | 0.713394 | + | 0.700763i | \(0.247157\pi\) | ||||
−0.713394 | + | 0.700763i | \(0.752843\pi\) | |||||||
\(644\) | 0.737564 | − | 1.27750i | 0.0290641 | − | 0.0503405i | ||||
\(645\) | 1.44042 | − | 0.114095i | 0.0567164 | − | 0.00449250i | ||||
\(646\) | −0.106794 | + | 0.184972i | −0.00420174 | + | 0.00727763i | ||||
\(647\) | −30.9881 | + | 17.8910i | −1.21827 | + | 0.703367i | −0.964547 | − | 0.263910i | \(-0.914988\pi\) |
−0.253721 | + | 0.967278i | \(0.581654\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −38.6323 | + | 66.9131i | −1.51645 | + | 2.62657i | ||||
\(650\) | −8.78443 | − | 10.8255i | −0.344554 | − | 0.424611i | ||||
\(651\) | −16.3390 | + | 28.2999i | −0.640374 | + | 1.10916i | ||||
\(652\) | 5.04447i | 0.197557i | ||||||||
\(653\) | 24.4769 | − | 14.1318i | 0.957857 | − | 0.553019i | 0.0623441 | − | 0.998055i | \(-0.480142\pi\) |
0.895513 | + | 0.445036i | \(0.146809\pi\) | |||||||
\(654\) | 5.64828 | − | 9.78311i | 0.220865 | − | 0.382550i | ||||
\(655\) | 22.1938 | + | 32.2573i | 0.867183 | + | 1.26040i | ||||
\(656\) | −9.93540 | −0.387912 | ||||||||
\(657\) | −3.33480 | − | 1.92535i | −0.130103 | − | 0.0751149i | ||||
\(658\) | 8.97180i | 0.349757i | ||||||||
\(659\) | 6.79717 | + | 11.7730i | 0.264780 | + | 0.458612i | 0.967506 | − | 0.252848i | \(-0.0813673\pi\) |
−0.702726 | + | 0.711461i | \(0.748034\pi\) | |||||||
\(660\) | 9.87041 | − | 6.79109i | 0.384205 | − | 0.264343i | ||||
\(661\) | −10.2764 | − | 17.7992i | −0.399705 | − | 0.692310i | 0.593984 | − | 0.804477i | \(-0.297554\pi\) |
−0.993689 | + | 0.112167i | \(0.964221\pi\) | |||||||
\(662\) | −7.87296 | + | 4.54546i | −0.305991 | + | 0.176664i | ||||
\(663\) | 2.28191 | − | 1.31746i | 0.0886221 | − | 0.0511660i | ||||
\(664\) | 0.423137 | − | 0.732895i | 0.0164209 | − | 0.0284418i | ||||
\(665\) | 1.45284 | − | 0.999587i | 0.0563386 | − | 0.0387623i | ||||
\(666\) | −5.53218 | + | 2.52883i | −0.214368 | + | 0.0979900i | ||||
\(667\) | 1.07489i | 0.0416201i | ||||||||
\(668\) | 8.33958 | + | 4.81486i | 0.322668 | + | 0.186292i | ||||
\(669\) | 3.88735 | + | 6.73309i | 0.150294 | + | 0.260316i | ||||
\(670\) | 6.78080 | − | 14.2347i | 0.261965 | − | 0.549936i | ||||
\(671\) | 5.90912 | + | 10.2349i | 0.228119 | + | 0.395114i | ||||
\(672\) | − | 3.48940i | − | 0.134606i | ||||||
\(673\) | −3.30721 | + | 1.90942i | −0.127483 | + | 0.0736026i | −0.562386 | − | 0.826875i | \(-0.690116\pi\) |
0.434902 | + | 0.900478i | \(0.356783\pi\) | |||||||
\(674\) | 35.5892 | 1.37085 | ||||||||
\(675\) | 3.88255 | − | 3.15052i | 0.149439 | − | 0.121264i | ||||
\(676\) | −5.22569 | −0.200988 | ||||||||
\(677\) | − | 17.3483i | − | 0.666749i | −0.942795 | − | 0.333374i | \(-0.891813\pi\) | ||
0.942795 | − | 0.333374i | \(-0.108187\pi\) | |||||||
\(678\) | 5.26885 | + | 3.04197i | 0.202349 | + | 0.116826i | ||||
\(679\) | −12.6395 | − | 21.8923i | −0.485060 | − | 0.840149i | ||||
\(680\) | 1.19776 | + | 1.74086i | 0.0459319 | + | 0.0667591i | ||||
\(681\) | −1.24188 | + | 2.15099i | −0.0475888 | + | 0.0824262i | ||||
\(682\) | 43.4552 | + | 25.0889i | 1.66399 | + | 0.960704i | ||||
\(683\) | 10.6376 | + | 6.14161i | 0.407035 | + | 0.235002i | 0.689515 | − | 0.724271i | \(-0.257824\pi\) |
−0.282480 | + | 0.959273i | \(0.591157\pi\) | |||||||
\(684\) | −0.113008 | − | 0.195735i | −0.00432096 | − | 0.00748412i | ||||
\(685\) | 24.2525 | + | 11.5528i | 0.926642 | + | 0.441411i | ||||
\(686\) | −3.18253 | + | 5.51231i | −0.121510 | + | 0.210461i | ||||
\(687\) | 11.9618 | + | 6.90615i | 0.456371 | + | 0.263486i | ||||
\(688\) | −0.559619 | − | 0.323096i | −0.0213353 | − | 0.0123179i | ||||
\(689\) | 5.94369 | 0.226437 | ||||||||
\(690\) | −0.853410 | − | 0.406527i | −0.0324887 | − | 0.0154762i | ||||
\(691\) | 18.8467 | − | 32.6434i | 0.716961 | − | 1.24181i | −0.245238 | − | 0.969463i | \(-0.578866\pi\) |
0.962198 | − | 0.272350i | \(-0.0878007\pi\) | |||||||
\(692\) | 10.0322i | 0.381366i | ||||||||
\(693\) | − | 18.6964i | − | 0.710217i | ||||||
\(694\) | −0.329731 | + | 0.571111i | −0.0125164 | + | 0.0216791i | ||||
\(695\) | 22.1305 | + | 32.1652i | 0.839457 | + | 1.22010i | ||||
\(696\) | 1.27132 | + | 2.20200i | 0.0481894 | + | 0.0834664i | ||||
\(697\) | − | 9.38907i | − | 0.355636i | ||||||
\(698\) | −2.78238 | + | 1.60641i | −0.105315 | + | 0.0608035i | ||||
\(699\) | 9.73505 | + | 16.8616i | 0.368213 | + | 0.637764i | ||||
\(700\) | −2.74671 | − | 17.2294i | −0.103816 | − | 0.651211i | ||||
\(701\) | −5.17241 | + | 8.95888i | −0.195359 | + | 0.338372i | −0.947018 | − | 0.321180i | \(-0.895921\pi\) |
0.751659 | + | 0.659552i | \(0.229254\pi\) | |||||||
\(702\) | 2.78824i | 0.105236i | ||||||||
\(703\) | 0.571554 | + | 1.25036i | 0.0215566 | + | 0.0471582i | ||||
\(704\) | −5.35806 | −0.201939 | ||||||||
\(705\) | 5.73134 | − | 0.453979i | 0.215855 | − | 0.0170978i | ||||
\(706\) | −2.34457 | − | 4.06092i | −0.0882392 | − | 0.152835i | ||||
\(707\) | −1.37645 | + | 0.794694i | −0.0517668 | + | 0.0298875i | ||||
\(708\) | 12.4883 | − | 7.21013i | 0.469339 | − | 0.270973i | ||||
\(709\) | −2.97502 | −0.111729 | −0.0558647 | − | 0.998438i | \(-0.517792\pi\) | ||||
−0.0558647 | + | 0.998438i | \(0.517792\pi\) | |||||||
\(710\) | 0.222781 | + | 0.106123i | 0.00836084 | + | 0.00398273i | ||||
\(711\) | −17.1588 | −0.643505 | ||||||||
\(712\) | 8.88366 | + | 5.12898i | 0.332929 | + | 0.192217i | ||||
\(713\) | − | 3.95899i | − | 0.148265i | ||||||
\(714\) | 3.29752 | 0.123407 | ||||||||
\(715\) | 2.63781 | + | 33.3016i | 0.0986486 | + | 1.24541i | ||||
\(716\) | 1.46164 | + | 2.53164i | 0.0546241 | + | 0.0946117i | ||||
\(717\) | − | 18.8304i | − | 0.703232i | ||||||
\(718\) | −9.67209 | − | 5.58418i | −0.360959 | − | 0.208400i | ||||
\(719\) | 10.5764 | − | 18.3189i | 0.394434 | − | 0.683181i | −0.598594 | − | 0.801052i | \(-0.704274\pi\) |
0.993029 | + | 0.117872i | \(0.0376072\pi\) | |||||||
\(720\) | −2.22909 | + | 0.176566i | −0.0830731 | + | 0.00658021i | ||||
\(721\) | 6.35374 | + | 11.0050i | 0.236626 | + | 0.409848i | ||||
\(722\) | 16.4102 | − | 9.47446i | 0.610726 | − | 0.352603i | ||||
\(723\) | −4.93996 | − | 2.85209i | −0.183719 | − | 0.106070i | ||||
\(724\) | 2.30385 | − | 3.99038i | 0.0856219 | − | 0.148301i | ||||
\(725\) | 8.01067 | + | 9.87195i | 0.297509 | + | 0.366635i | ||||
\(726\) | −17.7088 | −0.657235 | ||||||||
\(727\) | 36.5774 | − | 21.1180i | 1.35658 | − | 0.783223i | 0.367421 | − | 0.930055i | \(-0.380241\pi\) |
0.989162 | + | 0.146832i | \(0.0469075\pi\) | |||||||
\(728\) | 8.42581 | + | 4.86464i | 0.312281 | + | 0.180296i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.88057 | + | 7.09360i | 0.180638 | + | 0.262546i | ||||
\(731\) | 0.305330 | − | 0.528846i | 0.0112930 | − | 0.0195601i | ||||
\(732\) | − | 2.20569i | − | 0.0815248i | ||||||
\(733\) | −11.8396 | + | 6.83559i | −0.437305 | + | 0.252478i | −0.702454 | − | 0.711729i | \(-0.747912\pi\) |
0.265149 | + | 0.964208i | \(0.414579\pi\) | |||||||
\(734\) | 0.0974465 | 0.00359682 | ||||||||
\(735\) | −10.4487 | − | 4.97730i | −0.385406 | − | 0.183590i | ||||
\(736\) | 0.211373 | + | 0.366109i | 0.00779132 | + | 0.0134950i | ||||
\(737\) | −32.7198 | + | 18.8908i | −1.20525 | + | 0.695850i | ||||
\(738\) | 8.60431 | + | 4.96770i | 0.316729 | + | 0.182864i | ||||
\(739\) | 39.9570 | 1.46984 | 0.734922 | − | 0.678152i | \(-0.237219\pi\) | ||||
0.734922 | + | 0.678152i | \(0.237219\pi\) | |||||||
\(740\) | 13.5998 | + | 0.214918i | 0.499938 | + | 0.00790053i | ||||
\(741\) | 0.630187 | 0.0231505 | ||||||||
\(742\) | 6.44178 | + | 3.71917i | 0.236485 | + | 0.136535i | ||||
\(743\) | −45.8728 | + | 26.4847i | −1.68291 | + | 0.971628i | −0.723197 | + | 0.690642i | \(0.757328\pi\) |
−0.959712 | + | 0.280985i | \(0.909339\pi\) | |||||||
\(744\) | −4.68246 | − | 8.11026i | −0.171667 | − | 0.297337i | ||||
\(745\) | 4.06736 | − | 8.53850i | 0.149017 | − | 0.312826i | ||||
\(746\) | 17.7432 | 0.649623 | ||||||||
\(747\) | −0.732895 | + | 0.423137i | −0.0268152 | + | 0.0154818i | ||||
\(748\) | − | 5.06343i | − | 0.185137i | ||||||
\(749\) | −26.0039 | + | 45.0400i | −0.950160 | + | 1.64573i | ||||
\(750\) | −10.8675 | + | 2.62646i | −0.396824 | + | 0.0959049i | ||||
\(751\) | 32.7746 | 1.19596 | 0.597981 | − | 0.801510i | \(-0.295970\pi\) | ||||
0.597981 | + | 0.801510i | \(0.295970\pi\) | |||||||
\(752\) | −2.22669 | − | 1.28558i | −0.0811991 | − | 0.0468803i | ||||
\(753\) | 21.7303 | − | 12.5460i | 0.791896 | − | 0.457201i | ||||
\(754\) | −7.08952 | −0.258185 | ||||||||
\(755\) | 31.2086 | − | 2.47203i | 1.13580 | − | 0.0899663i | ||||
\(756\) | −1.74470 | + | 3.02191i | −0.0634540 | + | 0.109906i | ||||
\(757\) | 12.5773 | + | 7.26150i | 0.457129 | + | 0.263924i | 0.710836 | − | 0.703357i | \(-0.248317\pi\) |
−0.253707 | + | 0.967281i | \(0.581650\pi\) | |||||||
\(758\) | −15.7507 | + | 9.09367i | −0.572091 | + | 0.330297i | ||||
\(759\) | 1.13255 | + | 1.96163i | 0.0411089 | + | 0.0712028i | ||||
\(760\) | 0.0399066 | + | 0.503808i | 0.00144756 | + | 0.0182750i | ||||
\(761\) | −5.09320 | + | 8.82168i | −0.184628 | + | 0.319786i | −0.943451 | − | 0.331511i | \(-0.892441\pi\) |
0.758823 | + | 0.651297i | \(0.225775\pi\) | |||||||
\(762\) | −10.0513 | − | 5.80313i | −0.364121 | − | 0.210225i | ||||
\(763\) | 39.4182i | 1.42703i | ||||||||
\(764\) | −9.76088 | − | 16.9063i | −0.353136 | − | 0.611650i | ||||
\(765\) | −0.166856 | − | 2.10651i | −0.00603271 | − | 0.0761611i | ||||
\(766\) | 13.7454 | 0.496643 | ||||||||
\(767\) | 40.2072i | 1.45180i | ||||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −10.9529 | −0.394973 | −0.197486 | − | 0.980306i | \(-0.563278\pi\) | ||||
−0.197486 | + | 0.980306i | \(0.563278\pi\) | |||||||
\(770\) | −17.9791 | + | 37.7429i | −0.647920 | + | 1.36016i | ||||
\(771\) | −21.6084 | −0.778208 | ||||||||
\(772\) | −15.8654 | + | 9.15988i | −0.571007 | + | 0.329671i | ||||
\(773\) | 17.6750 | − | 10.2047i | 0.635725 | − | 0.367036i | −0.147241 | − | 0.989101i | \(-0.547039\pi\) |
0.782966 | + | 0.622065i | \(0.213706\pi\) | |||||||
\(774\) | 0.323096 | + | 0.559619i | 0.0116135 | + | 0.0201151i | ||||
\(775\) | −29.5044 | − | 36.3598i | −1.05983 | − | 1.30608i | ||||
\(776\) | 7.24454 | 0.260064 | ||||||||
\(777\) | 12.3057 | − | 17.2939i | 0.441464 | − | 0.620414i | ||||
\(778\) | − | 3.80282i | − | 0.136338i | ||||||
\(779\) | 1.12278 | − | 1.94471i | 0.0402277 | − | 0.0696764i | ||||
\(780\) | 2.68127 | − | 5.62871i | 0.0960048 | − | 0.201540i | ||||
\(781\) | −0.295650 | − | 0.512081i | −0.0105792 | − | 0.0183237i | ||||
\(782\) | −0.345977 | + | 0.199750i | −0.0123721 | + | 0.00714305i | ||||
\(783\) | − | 2.54265i | − | 0.0908667i | ||||||
\(784\) | 2.58794 | + | 4.48245i | 0.0924265 | + | 0.160087i | ||||
\(785\) | 15.3009 | − | 10.5274i | 0.546113 | − | 0.375739i | ||||
\(786\) | −8.75527 | + | 15.1646i | −0.312290 | + | 0.540902i | ||||
\(787\) | 7.53315i | 0.268528i | 0.990946 | + | 0.134264i | \(0.0428670\pi\) | ||||
−0.990946 | + | 0.134264i | \(0.957133\pi\) | |||||||
\(788\) | 22.7026i | 0.808747i | ||||||||
\(789\) | 0.599150 | − | 1.03776i | 0.0213303 | − | 0.0369452i | ||||
\(790\) | 34.6389 | + | 16.5005i | 1.23240 | + | 0.587060i | ||||
\(791\) | −21.2293 | −0.754827 | ||||||||
\(792\) | 4.64021 | + | 2.67903i | 0.164883 | + | 0.0951951i | ||||
\(793\) | 5.32607 | + | 3.07501i | 0.189134 | + | 0.109197i | ||||
\(794\) | −5.32080 | + | 9.21590i | −0.188828 | + | 0.327060i | ||||
\(795\) | 2.04991 | − | 4.30331i | 0.0727028 | − | 0.152623i | ||||
\(796\) | −4.67769 | − | 8.10199i | −0.165796 | − | 0.287167i | ||||
\(797\) | 31.0699 | + | 17.9382i | 1.10055 | + | 0.635404i | 0.936366 | − | 0.351025i | \(-0.114167\pi\) |
0.164186 | + | 0.986429i | \(0.447500\pi\) | |||||||
\(798\) | 0.682998 | + | 0.394329i | 0.0241779 | + | 0.0139591i | ||||
\(799\) | 1.21489 | − | 2.10425i | 0.0429797 | − | 0.0744430i | ||||
\(800\) | 4.66971 | + | 1.78712i | 0.165099 | + | 0.0631844i | ||||
\(801\) | −5.12898 | − | 8.88366i | −0.181224 | − | 0.313889i | ||||
\(802\) | −32.3896 | − | 18.7002i | −1.14372 | − | 0.660326i | ||||
\(803\) | − | 20.6322i | − | 0.728096i | ||||||
\(804\) | 7.05134 | 0.248682 | ||||||||
\(805\) | 3.28819 | − | 0.260457i | 0.115893 | − | 0.00917990i | ||||
\(806\) | 26.1117 | 0.919745 | ||||||||
\(807\) | −25.7505 | + | 14.8671i | −0.906461 | + | 0.523346i | ||||
\(808\) | − | 0.455491i | − | 0.0160241i | ||||||
\(809\) | −8.74968 | − | 15.1549i | −0.307622 | − | 0.532818i | 0.670219 | − | 0.742163i | \(-0.266200\pi\) |
−0.977842 | + | 0.209345i | \(0.932867\pi\) | |||||||
\(810\) | 2.01873 | + | 0.961633i | 0.0709309 | + | 0.0337883i | ||||
\(811\) | 0.0371742 | + | 0.0643876i | 0.00130536 | + | 0.00226096i | 0.866677 | − | 0.498869i | \(-0.166251\pi\) |
−0.865372 | + | 0.501130i | \(0.832918\pi\) | |||||||
\(812\) | −7.68363 | − | 4.43615i | −0.269643 | − | 0.155678i | ||||
\(813\) | 20.2676i | 0.710816i | ||||||||
\(814\) | −26.5552 | − | 18.8957i | −0.930758 | − | 0.662294i | ||||
\(815\) | −9.29274 | + | 6.39363i | −0.325510 | + | 0.223959i | ||||
\(816\) | −0.472506 | + | 0.818404i | −0.0165410 | + | 0.0286499i | ||||
\(817\) | 0.126483 | − | 0.0730248i | 0.00442507 | − | 0.00255481i | ||||
\(818\) | −7.33506 | + | 4.23490i | −0.256464 | + | 0.148070i | ||||
\(819\) | −4.86464 | − | 8.42581i | −0.169984 | − | 0.294422i | ||||
\(820\) | −12.5927 | − | 18.3026i | −0.439755 | − | 0.639156i | ||||
\(821\) | 0.260419 | + | 0.451060i | 0.00908870 | + | 0.0157421i | 0.870534 | − | 0.492108i | \(-0.163774\pi\) |
−0.861445 | + | 0.507850i | \(0.830440\pi\) | |||||||
\(822\) | 12.0138i | 0.419029i | ||||||||
\(823\) | 48.1533 | + | 27.8013i | 1.67852 | + | 0.969094i | 0.962606 | + | 0.270905i | \(0.0873228\pi\) |
0.715913 | + | 0.698189i | \(0.246011\pi\) | |||||||
\(824\) | −3.64174 | −0.126866 | ||||||||
\(825\) | 25.0206 | + | 9.57552i | 0.871105 | + | 0.333377i | ||||
\(826\) | −25.1590 | + | 43.5767i | −0.875393 | + | 1.51623i | ||||
\(827\) | −14.7494 | + | 8.51556i | −0.512886 | + | 0.296115i | −0.734019 | − | 0.679129i | \(-0.762358\pi\) |
0.221133 | + | 0.975244i | \(0.429024\pi\) | |||||||
\(828\) | − | 0.422746i | − | 0.0146914i | ||||||
\(829\) | −28.5172 | + | 49.3933i | −0.990444 | + | 1.71550i | −0.375787 | + | 0.926706i | \(0.622628\pi\) |
−0.614658 | + | 0.788794i | \(0.710706\pi\) | |||||||
\(830\) | 1.88642 | − | 0.149423i | 0.0654785 | − | 0.00518654i | ||||
\(831\) | −5.10786 | + | 8.84708i | −0.177190 | + | 0.306902i | ||||
\(832\) | −2.41469 | + | 1.39412i | −0.0837143 | + | 0.0483325i | ||||
\(833\) | −4.23596 | + | 2.44563i | −0.146767 | + | 0.0847362i | ||||
\(834\) | −8.73029 | + | 15.1213i | −0.302305 | + | 0.523608i | ||||
\(835\) | 1.70027 | + | 21.4655i | 0.0588404 | + | 0.742843i | ||||
\(836\) | 0.605502 | − | 1.04876i | 0.0209417 | − | 0.0362722i | ||||
\(837\) | 9.36492i | 0.323699i | ||||||||
\(838\) | 12.5214 | − | 7.22921i | 0.432543 | − | 0.249729i | ||||
\(839\) | −12.5634 | + | 21.7605i | −0.433738 | + | 0.751256i | −0.997192 | − | 0.0748914i | \(-0.976139\pi\) |
0.563454 | + | 0.826148i | \(0.309472\pi\) | |||||||
\(840\) | 6.42803 | − | 4.42265i | 0.221788 | − | 0.152596i | ||||
\(841\) | −22.5350 | −0.777067 | ||||||||
\(842\) | 25.2100 | + | 14.5550i | 0.868793 | + | 0.501598i | ||||
\(843\) | − | 13.5227i | − | 0.465746i | ||||||
\(844\) | −5.95258 | − | 10.3102i | −0.204896 | − | 0.354891i | ||||
\(845\) | −6.62332 | − | 9.62657i | −0.227849 | − | 0.331164i | ||||
\(846\) | 1.28558 | + | 2.22669i | 0.0441992 | + | 0.0765553i | ||||
\(847\) | 53.5143 | − | 30.8965i | 1.83877 | − | 1.06162i | ||||
\(848\) | −1.84610 | + | 1.06585i | −0.0633954 | + | 0.0366014i | ||||
\(849\) | 8.67644 | − | 15.0280i | 0.297775 | − | 0.515761i | ||||
\(850\) | −1.68885 | + | 4.41293i | −0.0579272 | + | 0.151362i | ||||
\(851\) | −0.243529 | + | 2.55991i | −0.00834806 | + | 0.0877525i | ||||
\(852\) | 0.110357i | 0.00378078i | ||||||||
\(853\) | 27.0501 | + | 15.6174i | 0.926178 | + | 0.534729i | 0.885601 | − | 0.464447i | \(-0.153747\pi\) |
0.0405775 | + | 0.999176i | \(0.487080\pi\) | |||||||
\(854\) | 3.84827 | + | 6.66540i | 0.131685 | + | 0.228085i | ||||
\(855\) | 0.217344 | − | 0.456264i | 0.00743301 | − | 0.0156039i | ||||
\(856\) | −7.45225 | − | 12.9077i | −0.254713 | − | 0.441175i | ||||
\(857\) | 6.91686i | 0.236275i | 0.992997 | + | 0.118138i | \(0.0376924\pi\) | ||||
−0.992997 | + | 0.118138i | \(0.962308\pi\) | |||||||
\(858\) | −12.9381 | + | 7.46979i | −0.441698 | + | 0.255014i | ||||
\(859\) | −42.8829 | −1.46314 | −0.731572 | − | 0.681764i | \(-0.761213\pi\) | ||||
−0.731572 | + | 0.681764i | \(0.761213\pi\) | |||||||
\(860\) | −0.114095 | − | 1.44042i | −0.00389062 | − | 0.0491179i | ||||
\(861\) | −34.6686 | −1.18150 | ||||||||
\(862\) | − | 12.9782i | − | 0.442039i | ||||||
\(863\) | 12.0069 | + | 6.93219i | 0.408720 | + | 0.235974i | 0.690240 | − | 0.723581i | \(-0.257505\pi\) |
−0.281520 | + | 0.959555i | \(0.590838\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −18.4809 | + | 12.7153i | −0.628369 | + | 0.432333i | ||||
\(866\) | −5.59361 | + | 9.68842i | −0.190079 | + | 0.329226i | ||||
\(867\) | 13.9490 | + | 8.05348i | 0.473734 | + | 0.273510i | ||||
\(868\) | 28.2999 | + | 16.3390i | 0.960562 | + | 0.554580i | ||||
\(869\) | −45.9689 | − | 79.6205i | −1.55939 | − | 2.70094i | ||||
\(870\) | −2.44509 | + | 5.13291i | −0.0828964 | + | 0.174022i | ||||
\(871\) | −9.83044 | + | 17.0268i | −0.333092 | + | 0.576932i | ||||
\(872\) | −9.78311 | − | 5.64828i | −0.331298 | − | 0.191275i | ||||
\(873\) | −6.27395 | − | 3.62227i | −0.212341 | − | 0.122595i | ||||
\(874\) | −0.0955472 | −0.00323193 | ||||||||
\(875\) | 28.2580 | − | 26.8974i | 0.955296 | − | 0.909297i | ||||
\(876\) | −1.92535 | + | 3.33480i | −0.0650514 | + | 0.112672i | ||||
\(877\) | 49.0704i | 1.65699i | 0.559997 | + | 0.828495i | \(0.310802\pi\) | ||||
−0.559997 | + | 0.828495i | \(0.689198\pi\) | |||||||
\(878\) | − | 25.8737i | − | 0.873194i | ||||||
\(879\) | −2.64365 | + | 4.57893i | −0.0891680 | + | 0.154443i | ||||
\(880\) | −6.79109 | − | 9.87041i | −0.228928 | − | 0.332732i | ||||
\(881\) | −22.6821 | − | 39.2866i | −0.764180 | − | 1.32360i | −0.940679 | − | 0.339298i | \(-0.889811\pi\) |
0.176499 | − | 0.984301i | \(-0.443523\pi\) | |||||||
\(882\) | − | 5.17588i | − | 0.174281i | ||||||
\(883\) | 29.1537 | − | 16.8319i | 0.981098 | − | 0.566437i | 0.0784969 | − | 0.996914i | \(-0.474988\pi\) |
0.902602 | + | 0.430477i | \(0.141655\pi\) | |||||||
\(884\) | −1.31746 | − | 2.28191i | −0.0443110 | − | 0.0767490i | ||||
\(885\) | 29.1106 | + | 13.8670i | 0.978541 | + | 0.466134i | ||||
\(886\) | 19.5044 | − | 33.7827i | 0.655264 | − | 1.13495i | ||||
\(887\) | − | 56.7645i | − | 1.90596i | −0.303027 | − | 0.952982i | \(-0.597997\pi\) | ||
0.303027 | − | 0.952982i | \(-0.402003\pi\) | |||||||
\(888\) | 2.52883 | + | 5.53218i | 0.0848618 | + | 0.185648i | ||||
\(889\) | 40.4988 | 1.35829 | ||||||||
\(890\) | 1.81120 | + | 22.8659i | 0.0607116 | + | 0.766466i | ||||
\(891\) | −2.67903 | − | 4.64021i | −0.0897508 | − | 0.155453i | ||||
\(892\) | 6.73309 | − | 3.88735i | 0.225441 | − | 0.130158i | ||||
\(893\) | 0.503267 | − | 0.290561i | 0.0168412 | − | 0.00972327i | ||||
\(894\) | 4.22964 | 0.141460 | ||||||||
\(895\) | −2.81112 | + | 5.90131i | −0.0939655 | + | 0.197259i | ||||
\(896\) | −3.48940 | −0.116573 | ||||||||
\(897\) | 1.02080 | + | 0.589360i | 0.0340836 | + | 0.0196782i | ||||
\(898\) | − | 40.7622i | − | 1.36025i | ||||||
\(899\) | −23.8117 | −0.794164 | ||||||||
\(900\) | −3.15052 | − | 3.88255i | −0.105017 | − | 0.129418i | ||||
\(901\) | −1.00724 | − | 1.74459i | −0.0335560 | − | 0.0581207i | ||||
\(902\) | 53.2345i | 1.77251i | ||||||||
\(903\) | −1.95273 | − | 1.12741i | −0.0649829 | − | 0.0375179i | ||||
\(904\) | 3.04197 | − | 5.26885i | 0.101175 | − | 0.175239i | ||||
\(905\) | 10.2710 | − | 0.813561i | 0.341418 | − | 0.0270437i | ||||
\(906\) | 7.00031 | + | 12.1249i | 0.232570 | + | 0.402823i | ||||
\(907\) | 38.3848 | − | 22.1615i | 1.27455 | − | 0.735859i | 0.298706 | − | 0.954345i | \(-0.403445\pi\) |
0.975840 | + | 0.218486i | \(0.0701118\pi\) | |||||||
\(908\) | 2.15099 | + | 1.24188i | 0.0713831 | + | 0.0412131i | ||||
\(909\) | −0.227745 | + | 0.394467i | −0.00755384 | + | 0.0130836i | ||||
\(910\) | 1.71786 | + | 21.6874i | 0.0569464 | + | 0.718931i | ||||
\(911\) | −25.1276 | −0.832515 | −0.416258 | − | 0.909247i | \(-0.636659\pi\) | ||||
−0.416258 | + | 0.909247i | \(0.636659\pi\) | |||||||
\(912\) | −0.195735 | + | 0.113008i | −0.00648144 | + | 0.00374206i | ||||
\(913\) | −3.92689 | − | 2.26719i | −0.129961 | − | 0.0750331i | ||||
\(914\) | 1.26371 | 0.0418000 | ||||||||
\(915\) | 4.06325 | − | 2.79561i | 0.134327 | − | 0.0924202i | ||||
\(916\) | 6.90615 | − | 11.9618i | 0.228186 | − | 0.395229i | ||||
\(917\) | − | 61.1012i | − | 2.01774i | ||||||
\(918\) | 0.818404 | − | 0.472506i | 0.0270114 | − | 0.0155950i | ||||
\(919\) | 6.33494 | 0.208970 | 0.104485 | − | 0.994526i | \(-0.466681\pi\) | ||||
0.104485 | + | 0.994526i | \(0.466681\pi\) | |||||||
\(920\) | −0.406527 | + | 0.853410i | −0.0134028 | + | 0.0281361i | ||||
\(921\) | −3.60673 | − | 6.24703i | −0.118846 | − | 0.205847i | ||||
\(922\) | −21.2402 | + | 12.2631i | −0.699510 | + | 0.403862i | ||||
\(923\) | −0.266479 | − | 0.153852i | −0.00877125 | − | 0.00506409i | ||||
\(924\) | −18.6964 | −0.615066 | ||||||||
\(925\) | 16.8412 | + | 25.3254i | 0.553734 | + | 0.832694i | ||||
\(926\) | −27.3599 | −0.899101 | ||||||||
\(927\) | 3.15384 | + | 1.82087i | 0.103586 | + | 0.0598053i | ||||
\(928\) | 2.20200 | − | 1.27132i | 0.0722840 | − | 0.0417332i | ||||
\(929\) | −2.80470 | − | 4.85788i | −0.0920191 | − | 0.159382i | 0.816342 | − | 0.577569i | \(-0.195999\pi\) |
−0.908361 | + | 0.418188i | \(0.862665\pi\) | |||||||
\(930\) | 9.00562 | − | 18.9052i | 0.295306 | − | 0.619927i | ||||
\(931\) | −1.16983 | −0.0383396 | ||||||||
\(932\) | 16.8616 | − | 9.73505i | 0.552320 | − | 0.318882i | ||||
\(933\) | − | 27.5138i | − | 0.900761i | ||||||
\(934\) | −17.3468 | + | 30.0455i | −0.567604 | + | 0.983119i | ||||
\(935\) | 9.32765 | − | 6.41766i | 0.305047 | − | 0.209880i | ||||
\(936\) | 2.78824 | 0.0911366 | ||||||||
\(937\) | −17.1782 | − | 9.91785i | −0.561188 | − | 0.324002i | 0.192434 | − | 0.981310i | \(-0.438362\pi\) |
−0.753622 | + | 0.657308i | \(0.771695\pi\) | |||||||
\(938\) | −21.3085 | + | 12.3025i | −0.695747 | + | 0.401690i | ||||
\(939\) | 34.7411 | 1.13373 | ||||||||
\(940\) | −0.453979 | − | 5.73134i | −0.0148071 | − | 0.186936i | ||||
\(941\) | 13.6103 | − | 23.5738i | 0.443684 | − | 0.768484i | −0.554275 | − | 0.832334i | \(-0.687004\pi\) |
0.997960 | + | 0.0638496i | \(0.0203378\pi\) | |||||||
\(942\) | 7.19316 | + | 4.15298i | 0.234366 | + | 0.135311i | ||||
\(943\) | 3.63744 | − | 2.10008i | 0.118451 | − | 0.0683879i | ||||
\(944\) | −7.21013 | − | 12.4883i | −0.234670 | − | 0.406460i | ||||
\(945\) | −7.77816 | + | 0.616107i | −0.253024 | + | 0.0200420i | ||||
\(946\) | −1.73117 | + | 2.99847i | −0.0562851 | + | 0.0974887i | ||||
\(947\) | −28.8262 | − | 16.6428i | −0.936726 | − | 0.540819i | −0.0477935 | − | 0.998857i | \(-0.515219\pi\) |
−0.888932 | + | 0.458038i | \(0.848552\pi\) | |||||||
\(948\) | 17.1588i | 0.557292i | ||||||||
\(949\) | −5.36834 | − | 9.29823i | −0.174264 | − | 0.301833i | ||||
\(950\) | −0.877517 | + | 0.712068i | −0.0284704 | + | 0.0231025i | ||||
\(951\) | 7.51731 | 0.243766 | ||||||||
\(952\) | − | 3.29752i | − | 0.106873i | ||||||
\(953\) | −5.30657 | − | 3.06375i | −0.171897 | − | 0.0992446i | 0.411583 | − | 0.911372i | \(-0.364976\pi\) |
−0.583480 | + | 0.812128i | \(0.698309\pi\) | |||||||
\(954\) | 2.13170 | 0.0690162 | ||||||||
\(955\) | 18.7728 | − | 39.4091i | 0.607473 | − | 1.27525i | ||||
\(956\) | −18.8304 | −0.609017 | ||||||||
\(957\) | 11.7984 | − | 6.81182i | 0.381389 | − | 0.220195i | ||||
\(958\) | −8.24626 | + | 4.76098i | −0.266425 | + | 0.153820i | ||||
\(959\) | −20.9604 | − | 36.3045i | −0.676847 | − | 1.17233i | ||||
\(960\) | 0.176566 | + | 2.22909i | 0.00569863 | + | 0.0719434i | ||||
\(961\) | 56.7018 | 1.82909 | ||||||||
\(962\) | −16.8840 | − | 1.60621i | −0.544362 | − | 0.0517862i | ||||
\(963\) | 14.9045i | 0.480291i | ||||||||
\(964\) | −2.85209 | + | 4.93996i | −0.0918596 | + | 0.159105i | ||||
\(965\) | −36.9826 | − | 17.6169i | −1.19051 | − | 0.567108i | ||||
\(966\) | 0.737564 | + | 1.27750i | 0.0237307 | + | 0.0411029i | ||||
\(967\) | −35.0030 | + | 20.2090i | −1.12562 | + | 0.649877i | −0.942830 | − | 0.333275i | \(-0.891846\pi\) |
−0.182790 | + | 0.983152i | \(0.558513\pi\) | |||||||
\(968\) | 17.7088i | 0.569182i | ||||||||
\(969\) | −0.106794 | − | 0.184972i | −0.00343071 | − | 0.00594216i | ||||
\(970\) | 9.18211 | + | 13.3456i | 0.294820 | + | 0.428502i | ||||
\(971\) | −12.2091 | + | 21.1467i | −0.391808 | + | 0.678631i | −0.992688 | − | 0.120708i | \(-0.961483\pi\) |
0.600880 | + | 0.799339i | \(0.294817\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 60.9269i | − | 1.95323i | ||||||
\(974\) | −18.7499 | + | 32.4757i | −0.600785 | + | 1.04059i | ||||
\(975\) | 13.7674 | − | 2.19479i | 0.440909 | − | 0.0702896i | ||||
\(976\) | −2.20569 | −0.0706026 | ||||||||
\(977\) | −43.4550 | − | 25.0888i | −1.39025 | − | 0.802661i | −0.396907 | − | 0.917859i | \(-0.629916\pi\) |
−0.993343 | + | 0.115198i | \(0.963250\pi\) | |||||||
\(978\) | −4.36864 | − | 2.52224i | −0.139694 | − | 0.0806522i | ||||
\(979\) | 27.4814 | − | 47.5991i | 0.878309 | − | 1.52128i | ||||
\(980\) | −4.97730 | + | 10.4487i | −0.158994 | + | 0.333771i | ||||
\(981\) | 5.64828 | + | 9.78311i | 0.180336 | + | 0.312351i | ||||
\(982\) | 10.4155 | + | 6.01338i | 0.332372 | + | 0.191895i | ||||
\(983\) | −39.7753 | − | 22.9643i | −1.26863 | − | 0.732446i | −0.293904 | − | 0.955835i | \(-0.594955\pi\) |
−0.974729 | + | 0.223389i | \(0.928288\pi\) | |||||||
\(984\) | 4.96770 | − | 8.60431i | 0.158365 | − | 0.274295i | ||||
\(985\) | −41.8219 | + | 28.7745i | −1.33256 | + | 0.916831i | ||||
\(986\) | 1.20141 | + | 2.08091i | 0.0382608 | + | 0.0662697i | ||||
\(987\) | −7.76981 | − | 4.48590i | −0.247316 | − | 0.142788i | ||||
\(988\) | − | 0.630187i | − | 0.0200489i | ||||||
\(989\) | 0.273175 | 0.00868647 | ||||||||
\(990\) | 0.946048 | + | 11.9436i | 0.0300674 | + | 0.379592i | ||||
\(991\) | 44.5033 | 1.41369 | 0.706847 | − | 0.707366i | \(-0.250117\pi\) | ||||
0.706847 | + | 0.707366i | \(0.250117\pi\) | |||||||
\(992\) | −8.11026 | + | 4.68246i | −0.257501 | + | 0.148668i | ||||
\(993\) | − | 9.09091i | − | 0.288491i | ||||||
\(994\) | −0.192540 | − | 0.333489i | −0.00610700 | − | 0.0105776i | ||||
\(995\) | 8.99643 | − | 18.8859i | 0.285206 | − | 0.598725i | ||||
\(996\) | 0.423137 | + | 0.732895i | 0.0134076 | + | 0.0232227i | ||||
\(997\) | −8.02005 | − | 4.63038i | −0.253998 | − | 0.146646i | 0.367596 | − | 0.929986i | \(-0.380181\pi\) |
−0.621593 | + | 0.783340i | \(0.713514\pi\) | |||||||
\(998\) | − | 39.2597i | − | 1.24274i | ||||||
\(999\) | 0.576064 | − | 6.05542i | 0.0182259 | − | 0.191585i |
(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 | 1110.2.bb.e.1009.20 | yes | 40 | |
5.4 | even | 2 | inner | 1110.2.bb.e.1009.1 | ✓ | 40 | |
37.26 | even | 3 | inner | 1110.2.bb.e.1099.1 | yes | 40 | |
185.174 | even | 6 | inner | 1110.2.bb.e.1099.20 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.e.1009.1 | ✓ | 40 | 5.4 | even | 2 | inner | |
1110.2.bb.e.1009.20 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.bb.e.1099.1 | yes | 40 | 37.26 | even | 3 | inner | |
1110.2.bb.e.1099.20 | yes | 40 | 185.174 | even | 6 | inner |