Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), not 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(0.0288455i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.251 |
Dual form | 625.2.d.p.376.1 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62909 | + | 1.18361i | −1.15194 | + | 0.836936i | −0.988738 | − | 0.149657i | \(-0.952183\pi\) |
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(3\) | −0.934982 | + | 2.87758i | −0.539812 | + | 1.66137i | 0.193204 | + | 0.981159i | \(0.438112\pi\) |
−0.733016 | + | 0.680212i | \(0.761888\pi\) | |||||||
\(4\) | 0.634989 | − | 1.95429i | 0.317494 | − | 0.977147i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.88274 | − | 5.79449i | −0.768627 | − | 2.36559i | ||||
\(7\) | −0.369971 | −0.139836 | −0.0699180 | − | 0.997553i | \(-0.522274\pi\) | ||||
−0.0699180 | + | 0.997553i | \(0.522274\pi\) | |||||||
\(8\) | 0.0341417 | + | 0.105077i | 0.0120709 | + | 0.0371504i | ||||
\(9\) | −4.97921 | − | 3.61761i | −1.65974 | − | 1.20587i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41281 | − | 1.02647i | 0.425978 | − | 0.309491i | −0.354061 | − | 0.935222i | \(-0.615199\pi\) |
0.780039 | + | 0.625731i | \(0.215199\pi\) | |||||||
\(12\) | 5.02993 | + | 3.65446i | 1.45202 | + | 1.05495i | ||||
\(13\) | 0.903043 | + | 0.656099i | 0.250459 | + | 0.181969i | 0.705930 | − | 0.708281i | \(-0.250529\pi\) |
−0.455471 | + | 0.890251i | \(0.650529\pi\) | |||||||
\(14\) | 0.602718 | − | 0.437900i | 0.161083 | − | 0.117034i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.14486 | + | 2.28487i | 0.786214 | + | 0.571218i | ||||
\(17\) | −1.69588 | − | 5.21940i | −0.411312 | − | 1.26589i | −0.915508 | − | 0.402300i | \(-0.868211\pi\) |
0.504196 | − | 0.863590i | \(-0.331789\pi\) | |||||||
\(18\) | 12.3934 | 2.92116 | ||||||||
\(19\) | −1.15949 | − | 3.56855i | −0.266005 | − | 0.818681i | −0.991460 | − | 0.130411i | \(-0.958370\pi\) |
0.725455 | − | 0.688270i | \(-0.241630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.345917 | − | 1.06462i | 0.0754852 | − | 0.232319i | ||||
\(22\) | −1.08667 | + | 3.34442i | −0.231678 | + | 0.713032i | ||||
\(23\) | 5.86229 | − | 4.25920i | 1.22237 | − | 0.888106i | 0.226078 | − | 0.974109i | \(-0.427410\pi\) |
0.996295 | + | 0.0860037i | \(0.0274097\pi\) | |||||||
\(24\) | −0.334290 | −0.0682366 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.24770 | −0.440811 | ||||||||
\(27\) | 7.72199 | − | 5.61035i | 1.48610 | − | 1.07971i | ||||
\(28\) | −0.234928 | + | 0.723033i | −0.0443972 | + | 0.136640i | ||||
\(29\) | 1.29566 | − | 3.98762i | 0.240598 | − | 0.740483i | −0.755732 | − | 0.654881i | \(-0.772719\pi\) |
0.996329 | − | 0.0856020i | \(-0.0272814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0944614 | + | 0.290722i | 0.0169658 | + | 0.0522153i | 0.959181 | − | 0.282793i | \(-0.0912609\pi\) |
−0.942215 | + | 0.335008i | \(0.891261\pi\) | |||||||
\(32\) | −8.04862 | −1.42281 | ||||||||
\(33\) | 1.63279 | + | 5.02520i | 0.284231 | + | 0.874774i | ||||
\(34\) | 8.94046 | + | 6.49562i | 1.53328 | + | 1.11399i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.2316 | + | 7.43371i | −1.70527 | + | 1.23895i | ||||
\(37\) | −7.45878 | − | 5.41912i | −1.22622 | − | 0.890898i | −0.229616 | − | 0.973281i | \(-0.573747\pi\) |
−0.996601 | + | 0.0823830i | \(0.973747\pi\) | |||||||
\(38\) | 6.11267 | + | 4.44111i | 0.991606 | + | 0.720444i | ||||
\(39\) | −2.73230 | + | 1.98514i | −0.437519 | + | 0.317876i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.38688 | + | 2.46071i | 0.528941 | + | 0.384298i | 0.819962 | − | 0.572419i | \(-0.193995\pi\) |
−0.291020 | + | 0.956717i | \(0.593995\pi\) | |||||||
\(42\) | 0.696562 | + | 2.14380i | 0.107482 | + | 0.330795i | ||||
\(43\) | −7.17118 | −1.09359 | −0.546797 | − | 0.837265i | \(-0.684153\pi\) | ||||
−0.546797 | + | 0.837265i | \(0.684153\pi\) | |||||||
\(44\) | −1.10890 | − | 3.41284i | −0.167173 | − | 0.514505i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50900 | + | 13.8773i | −0.664816 | + | 2.04609i | ||||
\(47\) | −0.250388 | + | 0.770615i | −0.0365229 | + | 0.112406i | −0.967656 | − | 0.252274i | \(-0.918822\pi\) |
0.931133 | + | 0.364680i | \(0.118822\pi\) | |||||||
\(48\) | −9.51528 | + | 6.91325i | −1.37341 | + | 0.997842i | ||||
\(49\) | −6.86312 | −0.980446 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.6048 | 2.32514 | ||||||||
\(52\) | 1.85563 | − | 1.34820i | 0.257330 | − | 0.186961i | ||||
\(53\) | 1.20983 | − | 3.72347i | 0.166183 | − | 0.511457i | −0.832939 | − | 0.553365i | \(-0.813343\pi\) |
0.999121 | + | 0.0419076i | \(0.0133435\pi\) | |||||||
\(54\) | −5.93940 | + | 18.2796i | −0.808249 | + | 2.48754i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0126314 | − | 0.0388756i | −0.00168795 | − | 0.00519497i | ||||
\(57\) | 11.3529 | 1.50372 | ||||||||
\(58\) | 2.60903 | + | 8.02976i | 0.342582 | + | 1.05436i | ||||
\(59\) | 1.50265 | + | 1.09174i | 0.195629 | + | 0.142132i | 0.681288 | − | 0.732016i | \(-0.261420\pi\) |
−0.485659 | + | 0.874148i | \(0.661420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.83835 | + | 5.69490i | −1.00360 | + | 0.729157i | −0.962857 | − | 0.270013i | \(-0.912972\pi\) |
−0.0407418 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(62\) | −0.497987 | − | 0.361809i | −0.0632444 | − | 0.0459498i | ||||
\(63\) | 1.84217 | + | 1.33841i | 0.232091 | + | 0.168624i | ||||
\(64\) | 6.82224 | − | 4.95665i | 0.852780 | − | 0.619581i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.60781 | − | 6.25394i | −1.05955 | − | 0.769807i | ||||
\(67\) | 3.85346 | + | 11.8597i | 0.470775 | + | 1.44890i | 0.851572 | + | 0.524238i | \(0.175650\pi\) |
−0.380796 | + | 0.924659i | \(0.624350\pi\) | |||||||
\(68\) | −11.2771 | −1.36755 | ||||||||
\(69\) | 6.77506 | + | 20.8515i | 0.815621 | + | 2.51022i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.60830 | − | 11.1052i | 0.428227 | − | 1.31795i | −0.471644 | − | 0.881789i | \(-0.656339\pi\) |
0.899871 | − | 0.436157i | \(-0.143661\pi\) | |||||||
\(72\) | 0.210130 | − | 0.646713i | 0.0247641 | − | 0.0762159i | ||||
\(73\) | 2.77604 | − | 2.01691i | 0.324910 | − | 0.236061i | −0.413358 | − | 0.910569i | \(-0.635644\pi\) |
0.738268 | + | 0.674508i | \(0.235644\pi\) | |||||||
\(74\) | 18.5652 | 2.15816 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.71026 | −0.884427 | ||||||||
\(77\) | −0.522699 | + | 0.379763i | −0.0595671 | + | 0.0432780i | ||||
\(78\) | 2.10156 | − | 6.46794i | 0.237955 | − | 0.732350i | ||||
\(79\) | 1.75937 | − | 5.41480i | 0.197945 | − | 0.609212i | −0.801984 | − | 0.597345i | \(-0.796222\pi\) |
0.999930 | − | 0.0118675i | \(-0.00377764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.21864 | + | 9.90596i | 0.357627 | + | 1.10066i | ||||
\(82\) | −8.43005 | −0.930943 | ||||||||
\(83\) | −2.20444 | − | 6.78456i | −0.241969 | − | 0.744703i | −0.996120 | − | 0.0880023i | \(-0.971952\pi\) |
0.754152 | − | 0.656700i | \(-0.228048\pi\) | |||||||
\(84\) | −1.86093 | − | 1.35205i | −0.203044 | − | 0.147520i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.6825 | − | 8.48784i | 1.25976 | − | 0.915268i | ||||
\(87\) | 10.2633 | + | 7.45671i | 1.10034 | + | 0.799443i | ||||
\(88\) | 0.156094 | + | 0.113409i | 0.0166397 | + | 0.0120894i | ||||
\(89\) | −1.23779 | + | 0.899307i | −0.131205 | + | 0.0953263i | −0.651452 | − | 0.758690i | \(-0.725840\pi\) |
0.520247 | + | 0.854016i | \(0.325840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.334100 | − | 0.242738i | −0.0350232 | − | 0.0254458i | ||||
\(92\) | −4.60125 | − | 14.1612i | −0.479714 | − | 1.47641i | ||||
\(93\) | −0.924896 | −0.0959072 | ||||||||
\(94\) | −0.504199 | − | 1.55176i | −0.0520042 | − | 0.160052i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.52531 | − | 23.1605i | 0.768049 | − | 2.36381i | ||||
\(97\) | −1.97691 | + | 6.08430i | −0.200725 | + | 0.617767i | 0.799137 | + | 0.601149i | \(0.205290\pi\) |
−0.999862 | + | 0.0166186i | \(0.994710\pi\) | |||||||
\(98\) | 11.1807 | − | 8.12323i | 1.12942 | − | 0.820570i | ||||
\(99\) | −10.7480 | −1.08022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2487 | −1.21879 | −0.609396 | − | 0.792866i | \(-0.708588\pi\) | ||||
−0.609396 | + | 0.792866i | \(0.708588\pi\) | |||||||
\(102\) | −27.0508 | + | 19.6536i | −2.67843 | + | 1.94599i | ||||
\(103\) | 2.36933 | − | 7.29204i | 0.233457 | − | 0.718506i | −0.763866 | − | 0.645375i | \(-0.776701\pi\) |
0.997322 | − | 0.0731305i | \(-0.0232990\pi\) | |||||||
\(104\) | −0.0381097 | + | 0.117290i | −0.00373696 | + | 0.0115012i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.43619 | + | 7.49783i | 0.236624 | + | 0.728254i | ||||
\(107\) | 0.758003 | 0.0732789 | 0.0366394 | − | 0.999329i | \(-0.488335\pi\) | ||||
0.0366394 | + | 0.999329i | \(0.488335\pi\) | |||||||
\(108\) | −6.06091 | − | 18.6536i | −0.583211 | − | 1.79494i | ||||
\(109\) | 2.64419 | + | 1.92111i | 0.253267 | + | 0.184009i | 0.707174 | − | 0.707040i | \(-0.249970\pi\) |
−0.453906 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.5678 | − | 16.3965i | 2.14204 | − | 1.55628i | ||||
\(112\) | −1.16351 | − | 0.845337i | −0.109941 | − | 0.0798768i | ||||
\(113\) | 0.686012 | + | 0.498417i | 0.0645346 | + | 0.0468871i | 0.619585 | − | 0.784930i | \(-0.287301\pi\) |
−0.555050 | + | 0.831817i | \(0.687301\pi\) | |||||||
\(114\) | −18.4949 | + | 13.4373i | −1.73221 | + | 1.25852i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.97027 | − | 5.06419i | −0.647173 | − | 0.470199i | ||||
\(117\) | −2.12293 | − | 6.53372i | −0.196265 | − | 0.604042i | ||||
\(118\) | −3.74015 | −0.344309 | ||||||||
\(119\) | 0.627429 | + | 1.93103i | 0.0575163 | + | 0.177017i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.45679 | + | 7.56122i | −0.223344 | + | 0.687384i | ||||
\(122\) | 6.02890 | − | 18.5550i | 0.545831 | − | 1.67989i | ||||
\(123\) | −10.2476 | + | 7.44528i | −0.923990 | + | 0.671318i | ||||
\(124\) | 0.628139 | 0.0564086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.58521 | −0.408483 | ||||||||
\(127\) | 11.5872 | − | 8.41857i | 1.02819 | − | 0.747027i | 0.0602479 | − | 0.998183i | \(-0.480811\pi\) |
0.967947 | + | 0.251156i | \(0.0808109\pi\) | |||||||
\(128\) | −0.273031 | + | 0.840302i | −0.0241327 | + | 0.0742729i | ||||
\(129\) | 6.70492 | − | 20.6356i | 0.590335 | − | 1.81686i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.13789 | − | 15.8128i | −0.448899 | − | 1.38157i | −0.878150 | − | 0.478385i | \(-0.841222\pi\) |
0.429251 | − | 0.903185i | \(-0.358778\pi\) | |||||||
\(132\) | 10.8575 | 0.945025 | ||||||||
\(133\) | 0.428978 | + | 1.32026i | 0.0371972 | + | 0.114481i | ||||
\(134\) | −20.3149 | − | 14.7596i | −1.75494 | − | 1.27504i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.490539 | − | 0.356398i | 0.0420634 | − | 0.0305609i | ||||
\(137\) | −2.48521 | − | 1.80561i | −0.212326 | − | 0.154264i | 0.476540 | − | 0.879153i | \(-0.341891\pi\) |
−0.688865 | + | 0.724889i | \(0.741891\pi\) | |||||||
\(138\) | −35.7171 | − | 25.9500i | −3.04044 | − | 2.20901i | ||||
\(139\) | 12.7178 | − | 9.23999i | 1.07871 | − | 0.783726i | 0.101249 | − | 0.994861i | \(-0.467716\pi\) |
0.977457 | + | 0.211135i | \(0.0677161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.98340 | − | 1.44102i | −0.167032 | − | 0.121356i | ||||
\(142\) | 7.26593 | + | 22.3622i | 0.609743 | + | 1.87660i | ||||
\(143\) | 1.94929 | 0.163008 | ||||||||
\(144\) | −7.39313 | − | 22.7537i | −0.616094 | − | 1.89614i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.13520 | + | 6.57146i | −0.176710 | + | 0.543858i | ||||
\(147\) | 6.41689 | − | 19.7492i | 0.529256 | − | 1.62888i | ||||
\(148\) | −15.3268 | + | 11.1356i | −1.25986 | + | 0.915339i | ||||
\(149\) | 14.8504 | 1.21660 | 0.608298 | − | 0.793709i | \(-0.291853\pi\) | ||||
0.608298 | + | 0.793709i | \(0.291853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.712013 | −0.0579428 | −0.0289714 | − | 0.999580i | \(-0.509223\pi\) | ||||
−0.0289714 | + | 0.999580i | \(0.509223\pi\) | |||||||
\(152\) | 0.335386 | − | 0.243672i | 0.0272034 | − | 0.0197644i | ||||
\(153\) | −10.4376 | + | 32.1235i | −0.843828 | + | 2.59703i | ||||
\(154\) | 0.402036 | − | 1.23734i | 0.0323970 | − | 0.0997076i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.14456 | + | 6.60027i | 0.171702 | + | 0.528444i | ||||
\(157\) | 22.0704 | 1.76141 | 0.880704 | − | 0.473667i | \(-0.157070\pi\) | ||||
0.880704 | + | 0.473667i | \(0.157070\pi\) | |||||||
\(158\) | 3.54280 | + | 10.9036i | 0.281850 | + | 0.867445i | ||||
\(159\) | 9.58340 | + | 6.96275i | 0.760013 | + | 0.552182i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.16888 | + | 1.57578i | −0.170932 | + | 0.124189i | ||||
\(162\) | −16.9682 | − | 12.3281i | −1.33315 | − | 0.968589i | ||||
\(163\) | −10.6482 | − | 7.73637i | −0.834031 | − | 0.605959i | 0.0866658 | − | 0.996237i | \(-0.472379\pi\) |
−0.920697 | + | 0.390278i | \(0.872379\pi\) | |||||||
\(164\) | 6.95958 | − | 5.05643i | 0.543452 | − | 0.394841i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.6215 | + | 8.44350i | 0.902002 | + | 0.655343i | ||||
\(167\) | −3.21628 | − | 9.89870i | −0.248883 | − | 0.765984i | −0.994973 | − | 0.100139i | \(-0.968071\pi\) |
0.746090 | − | 0.665845i | \(-0.231929\pi\) | |||||||
\(168\) | 0.123678 | 0.00954194 | ||||||||
\(169\) | −3.63220 | − | 11.1788i | −0.279400 | − | 0.859905i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.13626 | + | 21.9631i | −0.545723 | + | 1.67956i | ||||
\(172\) | −4.55362 | + | 14.0146i | −0.347210 | + | 1.06860i | ||||
\(173\) | −7.43686 | + | 5.40320i | −0.565414 | + | 0.410797i | −0.833436 | − | 0.552615i | \(-0.813630\pi\) |
0.268022 | + | 0.963413i | \(0.413630\pi\) | |||||||
\(174\) | −25.5457 | −1.93661 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.78842 | 0.511697 | ||||||||
\(177\) | −4.54652 | + | 3.30324i | −0.341737 | + | 0.248287i | ||||
\(178\) | 0.952050 | − | 2.93011i | 0.0713592 | − | 0.219621i | ||||
\(179\) | −6.70175 | + | 20.6259i | −0.500913 | + | 1.54165i | 0.306623 | + | 0.951831i | \(0.400801\pi\) |
−0.807535 | + | 0.589819i | \(0.799199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.32749 | + | 10.2410i | 0.247331 | + | 0.761205i | 0.995244 | + | 0.0974094i | \(0.0310556\pi\) |
−0.747914 | + | 0.663796i | \(0.768944\pi\) | |||||||
\(182\) | 0.831586 | 0.0616413 | ||||||||
\(183\) | −9.05880 | − | 27.8801i | −0.669645 | − | 2.06096i | ||||
\(184\) | 0.647694 | + | 0.470577i | 0.0477486 | + | 0.0346914i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50674 | − | 1.09471i | 0.110480 | − | 0.0802682i | ||||
\(187\) | −7.75349 | − | 5.63324i | −0.566992 | − | 0.411944i | ||||
\(188\) | 1.34702 | + | 0.978664i | 0.0982412 | + | 0.0713764i | ||||
\(189\) | −2.85692 | + | 2.07567i | −0.207810 | + | 0.150983i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.10615 | + | 2.25675i | 0.224753 | + | 0.163293i | 0.694464 | − | 0.719528i | \(-0.255642\pi\) |
−0.469711 | + | 0.882820i | \(0.655642\pi\) | |||||||
\(192\) | 7.88447 | + | 24.2659i | 0.569013 | + | 1.75124i | ||||
\(193\) | 10.5334 | 0.758208 | 0.379104 | − | 0.925354i | \(-0.376232\pi\) | ||||
0.379104 | + | 0.925354i | \(0.376232\pi\) | |||||||
\(194\) | −3.98084 | − | 12.2518i | −0.285808 | − | 0.879627i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.35801 | + | 13.4126i | −0.311286 | + | 0.958040i | ||||
\(197\) | 2.98295 | − | 9.18057i | 0.212526 | − | 0.654088i | −0.786794 | − | 0.617216i | \(-0.788260\pi\) |
0.999320 | − | 0.0368724i | \(-0.0117395\pi\) | |||||||
\(198\) | 17.5096 | − | 12.7214i | 1.24435 | − | 0.904073i | ||||
\(199\) | −15.8462 | −1.12331 | −0.561654 | − | 0.827372i | \(-0.689835\pi\) | ||||
−0.561654 | + | 0.827372i | \(0.689835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.7302 | −2.66129 | ||||||||
\(202\) | 19.9543 | − | 14.4976i | 1.40398 | − | 1.02005i | ||||
\(203\) | −0.479356 | + | 1.47531i | −0.0336442 | + | 0.103546i | ||||
\(204\) | 10.5439 | − | 32.4508i | 0.738220 | − | 2.27201i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.77104 | + | 14.6838i | 0.332414 | + | 1.02307i | ||||
\(207\) | −44.5978 | −3.09976 | ||||||||
\(208\) | 1.34084 | + | 4.12667i | 0.0929703 | + | 0.286133i | ||||
\(209\) | −5.30113 | − | 3.85150i | −0.366687 | − | 0.266414i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.86623 | + | 4.26207i | −0.403848 | + | 0.293413i | −0.771107 | − | 0.636706i | \(-0.780296\pi\) |
0.367258 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(212\) | −6.50852 | − | 4.72872i | −0.447007 | − | 0.324770i | ||||
\(213\) | 28.5824 | + | 20.7663i | 1.95843 | + | 1.42289i | ||||
\(214\) | −1.23486 | + | 0.897176i | −0.0844131 | + | 0.0613297i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.853162 | + | 0.619859i | 0.0580503 | + | 0.0421760i | ||||
\(217\) | −0.0349480 | − | 0.107559i | −0.00237243 | − | 0.00730158i | ||||
\(218\) | −6.58147 | −0.445753 | ||||||||
\(219\) | 3.20827 | + | 9.87403i | 0.216795 | + | 0.667225i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.89298 | − | 5.82601i | 0.127336 | − | 0.391900i | ||||
\(222\) | −17.3581 | + | 53.4227i | −1.16500 | + | 3.58550i | ||||
\(223\) | 18.4984 | − | 13.4399i | 1.23875 | − | 0.900003i | 0.241233 | − | 0.970467i | \(-0.422448\pi\) |
0.997514 | + | 0.0704644i | \(0.0224481\pi\) | |||||||
\(224\) | 2.97776 | 0.198960 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.70751 | −0.113582 | ||||||||
\(227\) | −0.538335 | + | 0.391123i | −0.0357305 | + | 0.0259597i | −0.605507 | − | 0.795840i | \(-0.707030\pi\) |
0.569777 | + | 0.821800i | \(0.307030\pi\) | |||||||
\(228\) | 7.20895 | − | 22.1869i | 0.477424 | − | 1.46936i | ||||
\(229\) | −7.25362 | + | 22.3243i | −0.479332 | + | 1.47523i | 0.360692 | + | 0.932685i | \(0.382541\pi\) |
−0.840025 | + | 0.542548i | \(0.817459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.604084 | − | 1.85918i | −0.0397458 | − | 0.122325i | ||||
\(232\) | 0.463245 | 0.0304135 | ||||||||
\(233\) | −5.50954 | − | 16.9566i | −0.360942 | − | 1.11087i | −0.952483 | − | 0.304591i | \(-0.901480\pi\) |
0.591541 | − | 0.806275i | \(-0.298520\pi\) | |||||||
\(234\) | 11.1918 | + | 8.13132i | 0.731631 | + | 0.531561i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.08775 | − | 2.24338i | 0.200995 | − | 0.146032i | ||||
\(237\) | 13.9365 | + | 10.1255i | 0.905274 | + | 0.657720i | ||||
\(238\) | −3.30771 | − | 2.40320i | −0.214407 | − | 0.155776i | ||||
\(239\) | 19.3117 | − | 14.0308i | 1.24917 | − | 0.907575i | 0.250997 | − | 0.967988i | \(-0.419242\pi\) |
0.998173 | + | 0.0604129i | \(0.0192417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.40859 | + | 2.47649i | 0.219567 | + | 0.159524i | 0.692132 | − | 0.721771i | \(-0.256672\pi\) |
−0.472565 | + | 0.881296i | \(0.656672\pi\) | |||||||
\(242\) | −4.94716 | − | 15.2258i | −0.318016 | − | 0.978752i | ||||
\(243\) | −2.87982 | −0.184741 | ||||||||
\(244\) | 6.15224 | + | 18.9347i | 0.393857 | + | 1.21217i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.88194 | − | 24.2581i | 0.502534 | − | 1.54664i | ||||
\(247\) | 1.29425 | − | 3.98329i | 0.0823511 | − | 0.253451i | ||||
\(248\) | −0.0273232 | + | 0.0198515i | −0.00173503 | + | 0.00126057i | ||||
\(249\) | 21.5842 | 1.36784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5741 | 1.23551 | 0.617755 | − | 0.786371i | \(-0.288042\pi\) | ||||
0.617755 | + | 0.786371i | \(0.288042\pi\) | |||||||
\(252\) | 3.78541 | − | 2.75026i | 0.238458 | − | 0.173250i | ||||
\(253\) | 3.91037 | − | 12.0349i | 0.245843 | − | 0.756627i | ||||
\(254\) | −8.91231 | + | 27.4293i | −0.559208 | + | 1.72106i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.66193 | + | 14.3480i | 0.291371 | + | 0.896747i | ||||
\(257\) | 18.4169 | 1.14881 | 0.574407 | − | 0.818570i | \(-0.305233\pi\) | ||||
0.574407 | + | 0.818570i | \(0.305233\pi\) | |||||||
\(258\) | 13.5015 | + | 41.5533i | 0.840566 | + | 2.58700i | ||||
\(259\) | 2.75954 | + | 2.00492i | 0.171469 | + | 0.124580i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.8770 | + | 15.1680i | −1.29226 | + | 0.938879i | ||||
\(262\) | 27.0862 | + | 19.6793i | 1.67339 | + | 1.21579i | ||||
\(263\) | −3.49860 | − | 2.54188i | −0.215733 | − | 0.156739i | 0.474671 | − | 0.880163i | \(-0.342567\pi\) |
−0.690404 | + | 0.723424i | \(0.742567\pi\) | |||||||
\(264\) | −0.472288 | + | 0.343137i | −0.0290673 | + | 0.0211186i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.26151 | − | 1.64309i | −0.138662 | − | 0.100744i | ||||
\(267\) | −1.43051 | − | 4.40267i | −0.0875461 | − | 0.269439i | ||||
\(268\) | 25.6243 | 1.56526 | ||||||||
\(269\) | 1.46442 | + | 4.50701i | 0.0892870 | + | 0.274797i | 0.985723 | − | 0.168377i | \(-0.0538525\pi\) |
−0.896436 | + | 0.443174i | \(0.853852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.07944 | − | 9.47755i | 0.187063 | − | 0.575720i | −0.812915 | − | 0.582382i | \(-0.802121\pi\) |
0.999978 | + | 0.00666226i | \(0.00212068\pi\) | |||||||
\(272\) | 6.59234 | − | 20.2891i | 0.399719 | − | 1.23021i | ||||
\(273\) | 1.01087 | − | 0.734443i | 0.0611809 | − | 0.0444505i | ||||
\(274\) | 6.18577 | 0.373696 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 45.0520 | 2.71181 | ||||||||
\(277\) | −14.2462 | + | 10.3504i | −0.855969 | + | 0.621898i | −0.926785 | − | 0.375591i | \(-0.877440\pi\) |
0.0708162 | + | 0.997489i | \(0.477440\pi\) | |||||||
\(278\) | −9.78191 | + | 30.1056i | −0.586680 | + | 1.80561i | ||||
\(279\) | 0.581377 | − | 1.78929i | 0.0348061 | − | 0.107122i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.87882 | − | 24.2485i | −0.470011 | − | 1.44655i | −0.852569 | − | 0.522614i | \(-0.824957\pi\) |
0.382558 | − | 0.923931i | \(-0.375043\pi\) | |||||||
\(282\) | 4.93674 | 0.293979 | ||||||||
\(283\) | 4.97531 | + | 15.3124i | 0.295751 | + | 0.910229i | 0.982968 | + | 0.183777i | \(0.0588324\pi\) |
−0.687217 | + | 0.726453i | \(0.741168\pi\) | |||||||
\(284\) | −19.4116 | − | 14.1034i | −1.15187 | − | 0.836881i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.17558 | + | 2.30719i | −0.187776 | + | 0.136427i | ||||
\(287\) | −1.25305 | − | 0.910392i | −0.0739650 | − | 0.0537387i | ||||
\(288\) | 40.0758 | + | 29.1168i | 2.36149 | + | 1.71572i | ||||
\(289\) | −10.6128 | + | 7.71064i | −0.624281 | + | 0.453567i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.6597 | − | 11.3774i | −0.917987 | − | 0.666957i | ||||
\(292\) | −2.17888 | − | 6.70591i | −0.127509 | − | 0.392433i | ||||
\(293\) | −24.9049 | −1.45496 | −0.727481 | − | 0.686128i | \(-0.759309\pi\) | ||||
−0.727481 | + | 0.686128i | \(0.759309\pi\) | |||||||
\(294\) | 12.9215 | + | 39.7683i | 0.753598 | + | 2.31933i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.314771 | − | 0.968766i | 0.0182957 | − | 0.0563084i | ||||
\(297\) | 5.15086 | − | 15.8527i | 0.298883 | − | 0.919868i | ||||
\(298\) | −24.1927 | + | 17.5771i | −1.40145 | + | 1.01821i | ||||
\(299\) | 8.08836 | 0.467762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65313 | 0.152924 | ||||||||
\(302\) | 1.15994 | − | 0.842742i | 0.0667468 | − | 0.0484944i | ||||
\(303\) | 11.4523 | − | 35.2466i | 0.657919 | − | 2.02487i | ||||
\(304\) | 4.50724 | − | 13.8718i | 0.258508 | − | 0.795605i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.0178 | − | 64.6862i | −1.20151 | − | 3.69786i | ||||
\(307\) | −1.74743 | −0.0997311 | −0.0498655 | − | 0.998756i | \(-0.515879\pi\) | ||||
−0.0498655 | + | 0.998756i | \(0.515879\pi\) | |||||||
\(308\) | 0.410261 | + | 1.26265i | 0.0233768 | + | 0.0719464i | ||||
\(309\) | 18.7681 | + | 13.6358i | 1.06768 | + | 0.775716i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.8262 | + | 10.7719i | −0.840718 | + | 0.610818i | −0.922571 | − | 0.385827i | \(-0.873916\pi\) |
0.0818529 | + | 0.996644i | \(0.473916\pi\) | |||||||
\(312\) | −0.301878 | − | 0.219327i | −0.0170905 | − | 0.0124170i | ||||
\(313\) | 2.67589 | + | 1.94415i | 0.151250 | + | 0.109890i | 0.660837 | − | 0.750530i | \(-0.270202\pi\) |
−0.509587 | + | 0.860419i | \(0.670202\pi\) | |||||||
\(314\) | −35.9547 | + | 26.1226i | −2.02904 | + | 1.47419i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.46493 | − | 6.87667i | −0.532444 | − | 0.386843i | ||||
\(317\) | 0.308721 | + | 0.950146i | 0.0173395 | + | 0.0533655i | 0.959352 | − | 0.282213i | \(-0.0910684\pi\) |
−0.942012 | + | 0.335578i | \(0.891068\pi\) | |||||||
\(318\) | −23.8534 | −1.33763 | ||||||||
\(319\) | −2.26264 | − | 6.96370i | −0.126684 | − | 0.389892i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.708719 | + | 2.18121i | −0.0395568 | + | 0.121743i | ||||
\(322\) | 1.66820 | − | 5.13420i | 0.0929653 | − | 0.286118i | ||||
\(323\) | −16.6593 | + | 12.1037i | −0.926948 | + | 0.673467i | ||||
\(324\) | 21.4030 | 1.18905 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 26.5037 | 1.46790 | ||||||||
\(327\) | −8.00042 | + | 5.81265i | −0.442424 | + | 0.321440i | ||||
\(328\) | −0.142931 | + | 0.439896i | −0.00789204 | + | 0.0242892i | ||||
\(329\) | 0.0926364 | − | 0.285106i | 0.00510721 | − | 0.0157184i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.38833 | − | 13.5059i | −0.241205 | − | 0.742351i | −0.996238 | − | 0.0866646i | \(-0.972379\pi\) |
0.755033 | − | 0.655687i | \(-0.227621\pi\) | |||||||
\(332\) | −14.6588 | −0.804508 | ||||||||
\(333\) | 17.5346 | + | 53.9660i | 0.960890 | + | 2.95732i | ||||
\(334\) | 16.9558 | + | 12.3191i | 0.927779 | + | 0.674071i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.52038 | − | 2.55771i | 0.192052 | − | 0.139534i | ||||
\(337\) | 10.6410 | + | 7.73114i | 0.579652 | + | 0.421142i | 0.838599 | − | 0.544750i | \(-0.183375\pi\) |
−0.258947 | + | 0.965892i | \(0.583375\pi\) | |||||||
\(338\) | 19.1484 | + | 13.9122i | 1.04154 | + | 0.756722i | ||||
\(339\) | −2.07564 | + | 1.50804i | −0.112733 | + | 0.0819056i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.431872 | + | 0.313774i | 0.0233872 | + | 0.0169918i | ||||
\(342\) | −14.3701 | − | 44.2265i | −0.777044 | − | 2.39150i | ||||
\(343\) | 5.12896 | 0.276938 | ||||||||
\(344\) | −0.244836 | − | 0.753527i | −0.0132007 | − | 0.0406275i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.72009 | − | 17.6046i | 0.307514 | − | 0.946430i | ||||
\(347\) | −4.18639 | + | 12.8844i | −0.224737 | + | 0.691670i | 0.773581 | + | 0.633698i | \(0.218464\pi\) |
−0.998318 | + | 0.0579727i | \(0.981536\pi\) | |||||||
\(348\) | 21.0897 | − | 15.3226i | 1.13053 | − | 0.821375i | ||||
\(349\) | −32.0976 | −1.71814 | −0.859072 | − | 0.511854i | \(-0.828959\pi\) | ||||
−0.859072 | + | 0.511854i | \(0.828959\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.6542 | 0.568681 | ||||||||
\(352\) | −11.3712 | + | 8.26163i | −0.606085 | + | 0.440347i | ||||
\(353\) | −5.65879 | + | 17.4160i | −0.301187 | + | 0.926958i | 0.679886 | + | 0.733318i | \(0.262029\pi\) |
−0.981073 | + | 0.193640i | \(0.937971\pi\) | |||||||
\(354\) | 3.49697 | − | 10.7626i | 0.185862 | − | 0.572024i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.971528 | + | 2.99006i | 0.0514909 | + | 0.158473i | ||||
\(357\) | −6.14332 | −0.325139 | ||||||||
\(358\) | −13.4951 | − | 41.5337i | −0.713239 | − | 2.19513i | ||||
\(359\) | 11.6793 | + | 8.48553i | 0.616412 | + | 0.447849i | 0.851666 | − | 0.524085i | \(-0.175592\pi\) |
−0.235255 | + | 0.971934i | \(0.575592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.98122 | − | 2.89253i | 0.209538 | − | 0.152238i | ||||
\(362\) | −17.5421 | − | 12.7451i | −0.921990 | − | 0.669865i | ||||
\(363\) | −19.4609 | − | 14.1392i | −1.02143 | − | 0.742116i | ||||
\(364\) | −0.686531 | + | 0.498794i | −0.0359840 | + | 0.0261439i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 47.7567 | + | 34.6973i | 2.49628 | + | 1.81365i | ||||
\(367\) | −3.21780 | − | 9.90337i | −0.167968 | − | 0.516952i | 0.831275 | − | 0.555861i | \(-0.187611\pi\) |
−0.999243 | + | 0.0389099i | \(0.987611\pi\) | |||||||
\(368\) | 28.1678 | 1.46835 | ||||||||
\(369\) | −7.96209 | − | 24.5048i | −0.414490 | − | 1.27567i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.447602 | + | 1.37758i | −0.0232383 | + | 0.0715202i | ||||
\(372\) | −0.587299 | + | 1.80752i | −0.0304500 | + | 0.0937155i | ||||
\(373\) | 8.10835 | − | 5.89106i | 0.419834 | − | 0.305028i | −0.357737 | − | 0.933822i | \(-0.616451\pi\) |
0.777571 | + | 0.628795i | \(0.216451\pi\) | |||||||
\(374\) | 19.2987 | 0.997912 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0895228 | −0.00461679 | ||||||||
\(377\) | 3.78631 | − | 2.75092i | 0.195005 | − | 0.141679i | ||||
\(378\) | 2.19741 | − | 6.76292i | 0.113022 | − | 0.347847i | ||||
\(379\) | 4.41879 | − | 13.5996i | 0.226978 | − | 0.698566i | −0.771107 | − | 0.636706i | \(-0.780297\pi\) |
0.998085 | − | 0.0618604i | \(-0.0197034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.3913 | + | 41.2142i | 0.686057 | + | 2.11147i | ||||
\(382\) | −7.73131 | −0.395568 | ||||||||
\(383\) | −1.55653 | − | 4.79051i | −0.0795351 | − | 0.244784i | 0.903381 | − | 0.428839i | \(-0.141077\pi\) |
−0.982916 | + | 0.184056i | \(0.941077\pi\) | |||||||
\(384\) | −2.16276 | − | 1.57133i | −0.110368 | − | 0.0801868i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.1598 | + | 12.4673i | −0.873412 | + | 0.634571i | ||||
\(387\) | 35.7068 | + | 25.9425i | 1.81508 | + | 1.31873i | ||||
\(388\) | 10.6352 | + | 7.72693i | 0.539921 | + | 0.392275i | ||||
\(389\) | −8.19745 | + | 5.95580i | −0.415627 | + | 0.301971i | −0.775876 | − | 0.630885i | \(-0.782692\pi\) |
0.360249 | + | 0.932856i | \(0.382692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.1722 | − | 23.3745i | −1.62702 | − | 1.18210i | ||||
\(392\) | −0.234318 | − | 0.721158i | −0.0118349 | − | 0.0364240i | ||||
\(393\) | 50.3064 | 2.53762 | ||||||||
\(394\) | 6.00667 | + | 18.4866i | 0.302612 | + | 0.931343i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.82488 | + | 21.0048i | −0.342963 | + | 1.05553i | ||||
\(397\) | −6.07772 | + | 18.7053i | −0.305032 | + | 0.938792i | 0.674633 | + | 0.738153i | \(0.264302\pi\) |
−0.979665 | + | 0.200639i | \(0.935698\pi\) | |||||||
\(398\) | 25.8150 | − | 18.7557i | 1.29399 | − | 0.940137i | ||||
\(399\) | −4.20024 | −0.210275 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0931 | −1.15321 | −0.576606 | − | 0.817022i | \(-0.695623\pi\) | ||||
−0.576606 | + | 0.817022i | \(0.695623\pi\) | |||||||
\(402\) | 61.4661 | − | 44.6577i | 3.06565 | − | 2.22732i | ||||
\(403\) | −0.105440 | + | 0.324511i | −0.00525234 | + | 0.0161650i | ||||
\(404\) | −7.77780 | + | 23.9376i | −0.386960 | + | 1.19094i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.965265 | − | 2.97078i | −0.0479053 | − | 0.147437i | ||||
\(407\) | −16.1004 | −0.798066 | ||||||||
\(408\) | 0.566917 | + | 1.74479i | 0.0280666 | + | 0.0863800i | ||||
\(409\) | −31.2554 | − | 22.7084i | −1.54548 | − | 1.12286i | −0.946779 | − | 0.321884i | \(-0.895684\pi\) |
−0.598701 | − | 0.800973i | \(-0.704316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.51941 | − | 5.46317i | 0.370905 | − | 0.269478i | ||||
\(412\) | −12.7463 | − | 9.26073i | −0.627965 | − | 0.456243i | ||||
\(413\) | −0.555938 | − | 0.403913i | −0.0273559 | − | 0.0198752i | ||||
\(414\) | 72.6539 | − | 52.7862i | 3.57074 | − | 2.59430i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.26825 | − | 5.28069i | −0.356355 | − | 0.258907i | ||||
\(417\) | 14.6979 | + | 45.2356i | 0.719760 | + | 2.21519i | ||||
\(418\) | 13.1947 | 0.645373 | ||||||||
\(419\) | −3.33402 | − | 10.2610i | −0.162877 | − | 0.501285i | 0.835996 | − | 0.548735i | \(-0.184890\pi\) |
−0.998874 | + | 0.0474503i | \(0.984890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0292 | − | 30.8666i | 0.488791 | − | 1.50434i | −0.337623 | − | 0.941281i | \(-0.609623\pi\) |
0.826414 | − | 0.563062i | \(-0.190377\pi\) | |||||||
\(422\) | 4.51203 | − | 13.8866i | 0.219642 | − | 0.675990i | ||||
\(423\) | 4.03452 | − | 2.93125i | 0.196165 | − | 0.142522i | ||||
\(424\) | 0.432557 | 0.0210068 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −71.1426 | −3.44687 | ||||||||
\(427\) | 2.89997 | − | 2.10695i | 0.140339 | − | 0.101962i | ||||
\(428\) | 0.481323 | − | 1.48136i | 0.0232656 | − | 0.0716043i | ||||
\(429\) | −1.82255 | + | 5.60924i | −0.0879936 | + | 0.270816i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.26198 | + | 13.1170i | 0.205292 | + | 0.631824i | 0.999701 | + | 0.0244412i | \(0.00778064\pi\) |
−0.794409 | + | 0.607383i | \(0.792219\pi\) | |||||||
\(432\) | 37.1035 | 1.78514 | ||||||||
\(433\) | 6.52397 | + | 20.0787i | 0.313522 | + | 0.964922i | 0.976358 | + | 0.216158i | \(0.0693525\pi\) |
−0.662836 | + | 0.748764i | \(0.730647\pi\) | |||||||
\(434\) | 0.184241 | + | 0.133859i | 0.00884385 | + | 0.00642543i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.43345 | − | 3.94763i | 0.260215 | − | 0.189057i | ||||
\(437\) | −21.9964 | − | 15.9814i | −1.05223 | − | 0.764492i | ||||
\(438\) | −16.9135 | − | 12.2884i | −0.808159 | − | 0.587162i | ||||
\(439\) | −29.4043 | + | 21.3634i | −1.40339 | + | 1.01962i | −0.409146 | + | 0.912469i | \(0.634173\pi\) |
−0.994243 | + | 0.107153i | \(0.965827\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.1730 | + | 24.8281i | 1.62728 | + | 1.18229i | ||||
\(442\) | 3.81185 | + | 11.7317i | 0.181311 | + | 0.558018i | ||||
\(443\) | −6.38810 | −0.303508 | −0.151754 | − | 0.988418i | \(-0.548492\pi\) | ||||
−0.151754 | + | 0.988418i | \(0.548492\pi\) | |||||||
\(444\) | −17.7132 | − | 54.5157i | −0.840632 | − | 2.58720i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.2281 | + | 43.7897i | −0.673722 | + | 2.07350i | ||||
\(447\) | −13.8849 | + | 42.7333i | −0.656733 | + | 2.02122i | ||||
\(448\) | −2.52403 | + | 1.83382i | −0.119249 | + | 0.0866397i | ||||
\(449\) | −35.1628 | −1.65943 | −0.829717 | − | 0.558185i | \(-0.811498\pi\) | ||||
−0.829717 | + | 0.558185i | \(0.811498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.31084 | 0.344254 | ||||||||
\(452\) | 1.40966 | − | 1.02418i | 0.0663050 | − | 0.0481734i | ||||
\(453\) | 0.665719 | − | 2.04887i | 0.0312782 | − | 0.0962644i | ||||
\(454\) | 0.414062 | − | 1.27435i | 0.0194329 | − | 0.0598083i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.387606 | + | 1.19293i | 0.0181513 | + | 0.0558640i | ||||
\(457\) | −22.2994 | −1.04312 | −0.521561 | − | 0.853214i | \(-0.674650\pi\) | ||||
−0.521561 | + | 0.853214i | \(0.674650\pi\) | |||||||
\(458\) | −14.6064 | − | 44.9538i | −0.682512 | − | 2.10056i | ||||
\(459\) | −42.3783 | − | 30.7896i | −1.97805 | − | 1.43714i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52533 | − | 1.10822i | 0.0710416 | − | 0.0516147i | −0.551698 | − | 0.834044i | \(-0.686020\pi\) |
0.622739 | + | 0.782429i | \(0.286020\pi\) | |||||||
\(462\) | 3.18464 | + | 2.31378i | 0.148163 | + | 0.107647i | ||||
\(463\) | −10.4486 | − | 7.59134i | −0.485587 | − | 0.352800i | 0.317898 | − | 0.948125i | \(-0.397023\pi\) |
−0.803485 | + | 0.595325i | \(0.797023\pi\) | |||||||
\(464\) | 13.1859 | − | 9.58009i | 0.612138 | − | 0.444745i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.0455 | + | 21.1028i | 1.34551 | + | 0.977569i | ||||
\(467\) | 0.809055 | + | 2.49002i | 0.0374386 | + | 0.115224i | 0.968029 | − | 0.250837i | \(-0.0807060\pi\) |
−0.930591 | + | 0.366062i | \(0.880706\pi\) | |||||||
\(468\) | −14.1168 | −0.652551 | ||||||||
\(469\) | −1.42567 | − | 4.38776i | −0.0658314 | − | 0.202608i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.6354 | + | 63.5093i | −0.950829 | + | 2.92635i | ||||
\(472\) | −0.0634140 | + | 0.195168i | −0.00291887 | + | 0.00898335i | ||||
\(473\) | −10.1315 | + | 7.36097i | −0.465847 | + | 0.338458i | ||||
\(474\) | −34.6885 | −1.59329 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.17221 | 0.191233 | ||||||||
\(477\) | −19.4940 | + | 14.1632i | −0.892571 | + | 0.648491i | ||||
\(478\) | −14.8537 | + | 45.7149i | −0.679391 | + | 2.09095i | ||||
\(479\) | 2.08066 | − | 6.40362i | 0.0950678 | − | 0.292589i | −0.892204 | − | 0.451634i | \(-0.850841\pi\) |
0.987271 | + | 0.159045i | \(0.0508414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.18012 | − | 9.78740i | −0.145001 | − | 0.446267i | ||||
\(482\) | −8.48409 | −0.386440 | ||||||||
\(483\) | −2.50658 | − | 7.71445i | −0.114053 | − | 0.351020i | ||||
\(484\) | 13.2168 | + | 9.60258i | 0.600765 | + | 0.436481i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.69150 | − | 3.40858i | 0.212811 | − | 0.154616i | ||||
\(487\) | −4.49648 | − | 3.26688i | −0.203755 | − | 0.148037i | 0.481229 | − | 0.876595i | \(-0.340191\pi\) |
−0.684984 | + | 0.728559i | \(0.740191\pi\) | |||||||
\(488\) | −0.866019 | − | 0.629200i | −0.0392028 | − | 0.0284825i | ||||
\(489\) | 32.2179 | − | 23.4077i | 1.45694 | − | 1.05853i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.49165 | + | 3.26338i | 0.202706 | + | 0.147274i | 0.684507 | − | 0.729006i | \(-0.260017\pi\) |
−0.481802 | + | 0.876280i | \(0.660017\pi\) | |||||||
\(492\) | 8.04319 | + | 24.7544i | 0.362615 | + | 1.11601i | ||||
\(493\) | −23.0103 | −1.03633 | ||||||||
\(494\) | 2.60619 | + | 8.02103i | 0.117258 | + | 0.360883i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.367196 | + | 1.13011i | −0.0164876 | + | 0.0507435i | ||||
\(497\) | −1.33497 | + | 4.10861i | −0.0598815 | + | 0.184296i | ||||
\(498\) | −35.1627 | + | 25.5472i | −1.57568 | + | 1.14480i | ||||
\(499\) | 19.2580 | 0.862107 | 0.431054 | − | 0.902326i | \(-0.358142\pi\) | ||||
0.431054 | + | 0.902326i | \(0.358142\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.4914 | 1.40693 | ||||||||
\(502\) | −31.8881 | + | 23.1681i | −1.42324 | + | 1.03404i | ||||
\(503\) | −9.62789 | + | 29.6316i | −0.429286 | + | 1.32121i | 0.469543 | + | 0.882909i | \(0.344419\pi\) |
−0.898830 | + | 0.438298i | \(0.855581\pi\) | |||||||
\(504\) | −0.0777421 | + | 0.239265i | −0.00346291 | + | 0.0106577i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.87420 | + | 24.2343i | 0.350051 | + | 1.07735i | ||||
\(507\) | 35.5638 | 1.57944 | ||||||||
\(508\) | −9.09464 | − | 27.9904i | −0.403510 | − | 1.24187i | ||||
\(509\) | 17.1714 | + | 12.4758i | 0.761109 | + | 0.552978i | 0.899250 | − | 0.437434i | \(-0.144113\pi\) |
−0.138141 | + | 0.990413i | \(0.544113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.02705 | + | 0.746198i | −0.0454342 | + | 0.0330099i | ||||
\(512\) | −26.0067 | − | 18.8949i | −1.14934 | − | 0.835046i | ||||
\(513\) | −28.9744 | − | 21.0511i | −1.27925 | − | 0.929430i | ||||
\(514\) | −30.0028 | + | 21.7983i | −1.32337 | + | 0.961483i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −36.0705 | − | 26.2068i | −1.58792 | − | 1.15369i | ||||
\(517\) | 0.437260 | + | 1.34575i | 0.0192307 | + | 0.0591859i | ||||
\(518\) | −6.86858 | −0.301788 | ||||||||
\(519\) | −8.59479 | − | 26.4520i | −0.377269 | − | 1.16112i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.41935 | − | 22.8344i | 0.325048 | − | 1.00039i | −0.646372 | − | 0.763023i | \(-0.723714\pi\) |
0.971419 | − | 0.237371i | \(-0.0762856\pi\) | |||||||
\(522\) | 16.0576 | − | 49.4203i | 0.702824 | − | 2.16307i | ||||
\(523\) | 18.4609 | − | 13.4127i | 0.807240 | − | 0.586494i | −0.105789 | − | 0.994389i | \(-0.533737\pi\) |
0.913029 | + | 0.407894i | \(0.133737\pi\) | |||||||
\(524\) | −34.1654 | −1.49252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.70813 | 0.379692 | ||||||||
\(527\) | 1.35720 | − | 0.986063i | 0.0591205 | − | 0.0429536i | ||||
\(528\) | −6.34705 | + | 19.5342i | −0.276220 | + | 0.850118i | ||||
\(529\) | 9.11826 | − | 28.0631i | 0.396446 | − | 1.22014i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.53253 | − | 10.8720i | −0.153299 | − | 0.471805i | ||||
\(532\) | 2.85257 | 0.123675 | ||||||||
\(533\) | 1.44402 | + | 4.44425i | 0.0625477 | + | 0.192502i | ||||
\(534\) | 7.54147 | + | 5.47920i | 0.326351 | + | 0.237108i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.11462 | + | 0.809822i | −0.0481445 | + | 0.0349790i | ||||
\(537\) | −53.0866 | − | 38.5696i | −2.29085 | − | 1.66440i | ||||
\(538\) | −7.72019 | − | 5.60904i | −0.332841 | − | 0.241823i | ||||
\(539\) | −9.69628 | + | 7.04476i | −0.417648 | + | 0.303439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.2538 | − | 16.1683i | −0.956766 | − | 0.695131i | −0.00436851 | − | 0.999990i | \(-0.501391\pi\) |
−0.952397 | + | 0.304859i | \(0.901391\pi\) | |||||||
\(542\) | 6.20098 | + | 19.0847i | 0.266355 | + | 0.819756i | ||||
\(543\) | −32.5803 | −1.39816 | ||||||||
\(544\) | 13.6495 | + | 42.0089i | 0.585219 | + | 1.80112i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.777518 | + | 2.39295i | −0.0332747 | + | 0.102409i | ||||
\(547\) | −0.0751603 | + | 0.231320i | −0.00321362 | + | 0.00989052i | −0.952650 | − | 0.304068i | \(-0.901655\pi\) |
0.949437 | + | 0.313958i | \(0.101655\pi\) | |||||||
\(548\) | −5.10677 | + | 3.71029i | −0.218151 | + | 0.158496i | ||||
\(549\) | 59.6308 | 2.54498 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.7323 | −0.670220 | ||||||||
\(552\) | −1.95970 | + | 1.42381i | −0.0834106 | + | 0.0606013i | ||||
\(553\) | −0.650918 | + | 2.00332i | −0.0276799 | + | 0.0851898i | ||||
\(554\) | 10.9575 | − | 33.7237i | 0.465539 | − | 1.43278i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.98203 | − | 30.7215i | −0.423333 | − | 1.30288i | ||||
\(557\) | −27.7280 | −1.17487 | −0.587436 | − | 0.809271i | \(-0.699862\pi\) | ||||
−0.587436 | + | 0.809271i | \(0.699862\pi\) | |||||||
\(558\) | 1.17070 | + | 3.60305i | 0.0495597 | + | 0.152529i | ||||
\(559\) | −6.47588 | − | 4.70500i | −0.273900 | − | 0.199000i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.4595 | − | 17.0443i | 0.990460 | − | 0.719611i | ||||
\(562\) | 41.5360 | + | 30.1777i | 1.75209 | + | 1.27297i | ||||
\(563\) | −10.0358 | − | 7.29143i | −0.422958 | − | 0.307297i | 0.355869 | − | 0.934536i | \(-0.384185\pi\) |
−0.778827 | + | 0.627239i | \(0.784185\pi\) | |||||||
\(564\) | −4.07562 | + | 2.96111i | −0.171614 | + | 0.124685i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.2291 | − | 19.0566i | −1.10249 | − | 0.801007i | ||||
\(567\) | −1.19080 | − | 3.66492i | −0.0500091 | − | 0.153912i | ||||
\(568\) | 1.29010 | 0.0541313 | ||||||||
\(569\) | −8.22214 | − | 25.3052i | −0.344690 | − | 1.06085i | −0.961749 | − | 0.273931i | \(-0.911676\pi\) |
0.617059 | − | 0.786917i | \(-0.288324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.99309 | − | 12.2895i | 0.167106 | − | 0.514298i | −0.832080 | − | 0.554656i | \(-0.812850\pi\) |
0.999185 | + | 0.0403581i | \(0.0128499\pi\) | |||||||
\(572\) | 1.23778 | − | 3.80949i | 0.0517541 | − | 0.159283i | ||||
\(573\) | −9.39817 | + | 6.82817i | −0.392614 | + | 0.285251i | ||||
\(574\) | 3.11888 | 0.130179 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −51.9006 | −2.16253 | ||||||||
\(577\) | −22.9301 | + | 16.6597i | −0.954593 | + | 0.693552i | −0.951889 | − | 0.306444i | \(-0.900861\pi\) |
−0.00270417 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(578\) | 8.16286 | − | 25.1227i | 0.339530 | − | 1.04497i | ||||
\(579\) | −9.84850 | + | 30.3106i | −0.409290 | + | 1.25966i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.815579 | + | 2.51009i | 0.0338359 | + | 0.104136i | ||||
\(582\) | 38.9775 | 1.61567 | ||||||||
\(583\) | −2.11276 | − | 6.50239i | −0.0875014 | − | 0.269302i | ||||
\(584\) | 0.306710 | + | 0.222838i | 0.0126917 | + | 0.00922108i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.5725 | − | 29.4776i | 1.67603 | − | 1.21771i | ||||
\(587\) | 6.78673 | + | 4.93085i | 0.280118 | + | 0.203518i | 0.718969 | − | 0.695042i | \(-0.244614\pi\) |
−0.438851 | + | 0.898560i | \(0.644614\pi\) | |||||||
\(588\) | −34.5210 | − | 25.0810i | −1.42362 | − | 1.03432i | ||||
\(589\) | 0.927929 | − | 0.674180i | 0.0382346 | − | 0.0277791i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6288 | + | 17.1673i | 0.971959 | + | 0.706170i | ||||
\(592\) | −11.0748 | − | 34.0847i | −0.455171 | − | 1.40087i | ||||
\(593\) | 30.9031 | 1.26904 | 0.634518 | − | 0.772908i | \(-0.281199\pi\) | ||||
0.634518 | + | 0.772908i | \(0.281199\pi\) | |||||||
\(594\) | 10.3721 | + | 31.9221i | 0.425574 | + | 1.30978i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.42986 | − | 29.0221i | 0.386262 | − | 1.18879i | ||||
\(597\) | 14.8159 | − | 45.5987i | 0.606376 | − | 1.86623i | ||||
\(598\) | −13.1767 | + | 9.57343i | −0.538835 | + | 0.391487i | ||||
\(599\) | 32.6384 | 1.33357 | 0.666784 | − | 0.745251i | \(-0.267671\pi\) | ||||
0.666784 | + | 0.745251i | \(0.267671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.9351 | 0.690796 | 0.345398 | − | 0.938456i | \(-0.387744\pi\) | ||||
0.345398 | + | 0.938456i | \(0.387744\pi\) | |||||||
\(602\) | −4.32220 | + | 3.14026i | −0.176160 | + | 0.127987i | ||||
\(603\) | 23.7167 | − | 72.9925i | 0.965819 | − | 2.97248i | ||||
\(604\) | −0.452120 | + | 1.39148i | −0.0183965 | + | 0.0566186i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23.0612 | + | 70.9751i | 0.936797 | + | 2.88317i | ||||
\(607\) | 36.3044 | 1.47355 | 0.736775 | − | 0.676138i | \(-0.236348\pi\) | ||||
0.736775 | + | 0.676138i | \(0.236348\pi\) | |||||||
\(608\) | 9.33230 | + | 28.7219i | 0.378475 | + | 1.16483i | ||||
\(609\) | −3.79712 | − | 2.75877i | −0.153867 | − | 0.111791i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.731711 | + | 0.531619i | −0.0296019 | + | 0.0215070i | ||||
\(612\) | 56.1511 | + | 40.7962i | 2.26977 | + | 1.64909i | ||||
\(613\) | 24.9129 | + | 18.1003i | 1.00622 | + | 0.731064i | 0.963414 | − | 0.268019i | \(-0.0863689\pi\) |
0.0428102 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(614\) | 2.84673 | − | 2.06827i | 0.114884 | − | 0.0834685i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0577503 | − | 0.0419580i | −0.00232682 | − | 0.00169054i | ||||
\(617\) | −10.9157 | − | 33.5949i | −0.439448 | − | 1.35248i | −0.888459 | − | 0.458955i | \(-0.848224\pi\) |
0.449011 | − | 0.893526i | \(-0.351776\pi\) | |||||||
\(618\) | −46.7145 | −1.87913 | ||||||||
\(619\) | 1.22092 | + | 3.75761i | 0.0490729 | + | 0.151031i | 0.972590 | − | 0.232526i | \(-0.0746990\pi\) |
−0.923517 | + | 0.383557i | \(0.874699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.3729 | − | 65.7791i | 0.857666 | − | 2.63962i | ||||
\(622\) | 11.4036 | − | 35.0968i | 0.457245 | − | 1.40725i | ||||
\(623\) | 0.457947 | − | 0.332718i | 0.0183472 | − | 0.0133301i | ||||
\(624\) | −13.1285 | −0.525560 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.66037 | −0.266202 | ||||||||
\(627\) | 16.0394 | − | 11.6533i | 0.640554 | − | 0.465390i | ||||
\(628\) | 14.0144 | − | 43.1320i | 0.559237 | − | 1.72116i | ||||
\(629\) | −15.6353 | + | 48.1206i | −0.623421 | + | 1.91869i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.18001 | + | 12.8648i | 0.166404 | + | 0.512138i | 0.999137 | − | 0.0415364i | \(-0.0132252\pi\) |
−0.832733 | + | 0.553674i | \(0.813225\pi\) | |||||||
\(632\) | 0.629040 | 0.0250219 | ||||||||
\(633\) | −6.77961 | − | 20.8655i | −0.269465 | − | 0.829329i | ||||
\(634\) | −1.62753 | − | 1.18247i | −0.0646376 | − | 0.0469620i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.6926 | − | 14.3075i | 0.780863 | − | 0.567330i | ||||
\(637\) | −6.19769 | − | 4.50289i | −0.245562 | − | 0.178411i | ||||
\(638\) | 11.9283 | + | 8.66644i | 0.472247 | + | 0.343108i | ||||
\(639\) | −58.1408 | + | 42.2418i | −2.30002 | + | 1.67106i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2273 | + | 21.2349i | 1.15441 | + | 0.838727i | 0.989061 | − | 0.147508i | \(-0.0471253\pi\) |
0.165348 | + | 0.986235i | \(0.447125\pi\) | |||||||
\(642\) | −1.42713 | − | 4.39224i | −0.0563242 | − | 0.173348i | ||||
\(643\) | 7.35135 | 0.289909 | 0.144954 | − | 0.989438i | \(-0.453696\pi\) | ||||
0.144954 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(644\) | 1.70233 | + | 5.23924i | 0.0670813 | + | 0.206455i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.8136 | − | 39.4361i | 0.504143 | − | 1.55159i | ||||
\(647\) | −13.5042 | + | 41.5615i | −0.530903 | + | 1.63395i | 0.221435 | + | 0.975175i | \(0.428926\pi\) |
−0.752338 | + | 0.658777i | \(0.771074\pi\) | |||||||
\(648\) | −0.931001 | + | 0.676412i | −0.0365732 | + | 0.0265720i | ||||
\(649\) | 3.24359 | 0.127322 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.342185 | 0.0134113 | ||||||||
\(652\) | −21.8806 | + | 15.8972i | −0.856912 | + | 0.622583i | ||||
\(653\) | 11.0766 | − | 34.0902i | 0.433459 | − | 1.33405i | −0.461198 | − | 0.887297i | \(-0.652580\pi\) |
0.894657 | − | 0.446754i | \(-0.147420\pi\) | |||||||
\(654\) | 6.15355 | − | 18.9387i | 0.240623 | − | 0.740561i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.02883 | + | 15.4771i | 0.196343 | + | 0.604281i | ||||
\(657\) | −21.1189 | −0.823925 | ||||||||
\(658\) | 0.186539 | + | 0.574109i | 0.00727205 | + | 0.0223811i | ||||
\(659\) | −0.0552680 | − | 0.0401545i | −0.00215294 | − | 0.00156420i | 0.586708 | − | 0.809798i | \(-0.300424\pi\) |
−0.588861 | + | 0.808234i | \(0.700424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3235 | − | 15.4924i | 0.829388 | − | 0.602585i | −0.0899985 | − | 0.995942i | \(-0.528686\pi\) |
0.919386 | + | 0.393357i | \(0.128686\pi\) | |||||||
\(662\) | 23.1347 | + | 16.8083i | 0.899154 | + | 0.653274i | ||||
\(663\) | 14.9949 | + | 10.8944i | 0.582353 | + | 0.423104i | ||||
\(664\) | 0.637640 | − | 0.463273i | 0.0247452 | − | 0.0179785i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −92.4399 | − | 67.1615i | −3.58197 | − | 2.60246i | ||||
\(667\) | −9.38858 | − | 28.8951i | −0.363527 | − | 1.11882i | ||||
\(668\) | −21.3873 | −0.827498 | ||||||||
\(669\) | 21.3787 | + | 65.7968i | 0.826547 | + | 2.54385i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.22848 | + | 16.0916i | −0.201843 | + | 0.621210i | ||||
\(672\) | −2.78415 | + | 8.56873i | −0.107401 | + | 0.330546i | ||||
\(673\) | −4.10740 | + | 2.98420i | −0.158329 | + | 0.115032i | −0.664129 | − | 0.747618i | \(-0.731197\pi\) |
0.505800 | + | 0.862651i | \(0.331197\pi\) | |||||||
\(674\) | −26.4858 | −1.02019 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.1530 | −0.928962 | ||||||||
\(677\) | 31.1883 | − | 22.6596i | 1.19866 | − | 0.870879i | 0.204510 | − | 0.978865i | \(-0.434440\pi\) |
0.994152 | + | 0.107985i | \(0.0344399\pi\) | |||||||
\(678\) | 1.59649 | − | 4.91348i | 0.0613127 | − | 0.188701i | ||||
\(679\) | 0.731400 | − | 2.25102i | 0.0280686 | − | 0.0863861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.622154 | − | 1.91479i | −0.0238410 | − | 0.0733750i | ||||
\(682\) | −1.07494 | −0.0411618 | ||||||||
\(683\) | −11.3141 | − | 34.8213i | −0.432923 | − | 1.33240i | −0.895200 | − | 0.445664i | \(-0.852968\pi\) |
0.462277 | − | 0.886735i | \(-0.347032\pi\) | |||||||
\(684\) | 38.3910 | + | 27.8927i | 1.46792 | + | 1.06650i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.35555 | + | 6.07066i | −0.319016 | + | 0.231779i | ||||
\(687\) | −57.4580 | − | 41.7457i | −2.19216 | − | 1.59270i | ||||
\(688\) | −22.5523 | − | 16.3852i | −0.859799 | − | 0.624680i | ||||
\(689\) | 3.53549 | − | 2.56868i | 0.134691 | − | 0.0978590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.7664 | − | 17.2673i | −0.904115 | − | 0.656878i | 0.0354046 | − | 0.999373i | \(-0.488728\pi\) |
−0.939520 | + | 0.342495i | \(0.888728\pi\) | |||||||
\(692\) | 5.83711 | + | 17.9648i | 0.221894 | + | 0.682919i | ||||
\(693\) | 3.97647 | 0.151053 | ||||||||
\(694\) | −8.43001 | − | 25.9449i | −0.319999 | − | 0.984855i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.433125 | + | 1.33302i | −0.0164176 | + | 0.0505281i | ||||
\(697\) | 7.09967 | − | 21.8505i | 0.268919 | − | 0.827648i | ||||
\(698\) | 52.2900 | − | 37.9909i | 1.97920 | − | 1.43798i | ||||
\(699\) | 53.9454 | 2.04040 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.566147 | −0.0213831 | −0.0106915 | − | 0.999943i | \(-0.503403\pi\) | ||||
−0.0106915 | + | 0.999943i | \(0.503403\pi\) | |||||||
\(702\) | −17.3567 | + | 12.6104i | −0.655088 | + | 0.475949i | ||||
\(703\) | −10.6900 | + | 32.9004i | −0.403181 | + | 1.24086i | ||||
\(704\) | 4.55069 | − | 14.0056i | 0.171511 | − | 0.527856i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.3949 | − | 35.0700i | −0.428854 | − | 1.31988i | ||||
\(707\) | 4.53167 | 0.170431 | ||||||||
\(708\) | 3.56852 | + | 10.9828i | 0.134113 | + | 0.412758i | ||||
\(709\) | −0.531732 | − | 0.386326i | −0.0199696 | − | 0.0145088i | 0.577756 | − | 0.816210i | \(-0.303929\pi\) |
−0.597725 | + | 0.801701i | \(0.703929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.3489 | + | 20.5967i | −1.06317 | + | 0.772437i | ||||
\(712\) | −0.136757 | − | 0.0993597i | −0.00512518 | − | 0.00372366i | ||||
\(713\) | 1.79201 | + | 1.30197i | 0.0671112 | + | 0.0487591i | ||||
\(714\) | 10.0080 | − | 7.27126i | 0.374541 | − | 0.272120i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36.0535 | + | 26.1944i | 1.34738 | + | 0.978931i | ||||
\(717\) | 22.3186 | + | 68.6894i | 0.833502 | + | 2.56525i | ||||
\(718\) | −29.0702 | −1.08489 | ||||||||
\(719\) | 10.8481 | + | 33.3870i | 0.404566 | + | 1.24513i | 0.921257 | + | 0.388954i | \(0.127163\pi\) |
−0.516692 | + | 0.856172i | \(0.672837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.876583 | + | 2.69785i | −0.0326457 | + | 0.100473i | ||||
\(722\) | −3.06217 | + | 9.42439i | −0.113962 | + | 0.350739i | ||||
\(723\) | −10.3133 | + | 7.49301i | −0.383554 | + | 0.278668i | ||||
\(724\) | 22.1268 | 0.822336 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 48.4389 | 1.79774 | ||||||||
\(727\) | −33.3461 | + | 24.2273i | −1.23674 | + | 0.898542i | −0.997377 | − | 0.0723882i | \(-0.976938\pi\) |
−0.239361 | + | 0.970931i | \(0.576938\pi\) | |||||||
\(728\) | 0.0140995 | − | 0.0433938i | 0.000522562 | − | 0.00160828i | ||||
\(729\) | −6.96334 | + | 21.4310i | −0.257901 | + | 0.793739i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1615 | + | 37.4292i | 0.449809 | + | 1.38437i | ||||
\(732\) | −60.2382 | −2.22647 | ||||||||
\(733\) | 12.3941 | + | 38.1452i | 0.457787 | + | 1.40892i | 0.867832 | + | 0.496858i | \(0.165513\pi\) |
−0.410045 | + | 0.912065i | \(0.634487\pi\) | |||||||
\(734\) | 16.9638 | + | 12.3249i | 0.626144 | + | 0.454920i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.1834 | + | 34.2807i | −1.73920 | + | 1.26360i | ||||
\(737\) | 17.6178 | + | 12.8001i | 0.648961 | + | 0.471498i | ||||
\(738\) | 41.9750 | + | 30.4966i | 1.54512 | + | 1.12260i | ||||
\(739\) | 23.0921 | − | 16.7774i | 0.849457 | − | 0.617167i | −0.0755391 | − | 0.997143i | \(-0.524068\pi\) |
0.924996 | + | 0.379976i | \(0.124068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2521 | + | 7.44861i | 0.376621 | + | 0.273632i | ||||
\(742\) | −0.901322 | − | 2.77398i | −0.0330886 | − | 0.101836i | ||||
\(743\) | −29.6851 | −1.08904 | −0.544520 | − | 0.838748i | \(-0.683288\pi\) | ||||
−0.544520 | + | 0.838748i | \(0.683288\pi\) | |||||||
\(744\) | −0.0315775 | − | 0.0971855i | −0.00115769 | − | 0.00356299i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.23657 | + | 19.1942i | −0.228337 | + | 0.702749i | ||||
\(747\) | −13.5675 | + | 41.7566i | −0.496410 | + | 1.52779i | ||||
\(748\) | −15.9324 | + | 11.5756i | −0.582546 | + | 0.423245i | ||||
\(749\) | −0.280439 | −0.0102470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.2113 | 1.64978 | 0.824892 | − | 0.565290i | \(-0.191236\pi\) | ||||
0.824892 | + | 0.565290i | \(0.191236\pi\) | |||||||
\(752\) | −2.54819 | + | 1.85137i | −0.0929230 | + | 0.0675125i | ||||
\(753\) | −18.3015 | + | 56.3261i | −0.666943 | + | 2.05264i | ||||
\(754\) | −2.91225 | + | 8.96300i | −0.106058 | + | 0.326413i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.24236 | + | 6.90128i | 0.0815539 | + | 0.250997i | ||||
\(757\) | −5.69813 | −0.207102 | −0.103551 | − | 0.994624i | \(-0.533020\pi\) | ||||
−0.103551 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(758\) | 8.89798 | + | 27.3852i | 0.323189 | + | 0.994674i | ||||
\(759\) | 30.9752 | + | 22.5048i | 1.12433 | + | 0.816873i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.6796 | − | 24.4697i | 1.22088 | − | 0.887025i | 0.224711 | − | 0.974425i | \(-0.427856\pi\) |
0.996173 | + | 0.0874009i | \(0.0278561\pi\) | |||||||
\(762\) | −70.5970 | − | 51.2917i | −2.55746 | − | 1.85810i | ||||
\(763\) | −0.978273 | − | 0.710757i | −0.0354159 | − | 0.0257311i | ||||
\(764\) | 6.38272 | − | 4.63732i | 0.230919 | − | 0.167772i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.20582 | + | 5.96188i | 0.296488 | + | 0.215411i | ||||
\(767\) | 0.640669 | + | 1.97178i | 0.0231332 | + | 0.0711967i | ||||
\(768\) | −45.6462 | −1.64712 | ||||||||
\(769\) | −4.92142 | − | 15.1466i | −0.177471 | − | 0.546200i | 0.822267 | − | 0.569102i | \(-0.192709\pi\) |
−0.999738 | + | 0.0229027i | \(0.992709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.2195 | + | 52.9960i | −0.620144 | + | 1.90861i | ||||
\(772\) | 6.68857 | − | 20.5853i | 0.240727 | − | 0.740881i | ||||
\(773\) | −38.6969 | + | 28.1149i | −1.39183 | + | 1.01122i | −0.396169 | + | 0.918178i | \(0.629660\pi\) |
−0.995662 | + | 0.0930462i | \(0.970340\pi\) | |||||||
\(774\) | −88.8755 | −3.19456 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.706817 | −0.0253732 | ||||||||
\(777\) | −8.34943 | + | 6.06622i | −0.299534 | + | 0.217624i | ||||
\(778\) | 6.30510 | − | 19.4051i | 0.226049 | − | 0.695706i | ||||
\(779\) | 4.85410 | − | 14.9394i | 0.173916 | − | 0.535259i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.30128 | − | 19.3933i | −0.225477 | − | 0.693948i | ||||
\(782\) | 80.0778 | 2.86358 | ||||||||
\(783\) | −12.3669 | − | 38.0615i | −0.441958 | − | 1.36021i | ||||
\(784\) | −21.5835 | − | 15.6813i | −0.770840 | − | 0.560048i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −81.9538 | + | 59.5429i | −2.92319 | + | 2.12383i | ||||
\(787\) | 32.8106 | + | 23.8383i | 1.16957 | + | 0.849743i | 0.990957 | − | 0.134177i | \(-0.0428390\pi\) |
0.178613 | + | 0.983919i | \(0.442839\pi\) | |||||||
\(788\) | −16.0474 | − | 11.6591i | −0.571665 | − | 0.415339i | ||||
\(789\) | 10.5856 | − | 7.69088i | 0.376857 | − | 0.273802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.253805 | − | 0.184400i | −0.00902426 | − | 0.00655651i | ||||
\(792\) | −0.366956 | − | 1.12937i | −0.0130392 | − | 0.0401306i | ||||
\(793\) | −10.8148 | −0.384044 | ||||||||
\(794\) | −12.2385 | − | 37.6663i | −0.434329 | − | 1.33673i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0622 | + | 30.9682i | −0.356644 | + | 1.09764i | ||||
\(797\) | −8.60045 | + | 26.4695i | −0.304644 | + | 0.937596i | 0.675166 | + | 0.737665i | \(0.264072\pi\) |
−0.979810 | + | 0.199931i | \(0.935928\pi\) | |||||||
\(798\) | 6.84258 | − | 4.97143i | 0.242225 | − | 0.175987i | ||||
\(799\) | 4.44678 | 0.157316 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.41656 | 0.332718 | ||||||||
\(802\) | 37.6207 | − | 27.3331i | 1.32843 | − | 0.965164i | ||||
\(803\) | 1.85172 | − | 5.69901i | 0.0653458 | − | 0.201114i | ||||
\(804\) | −23.9583 | + | 73.7360i | −0.844943 | + | 2.60047i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.212321 | − | 0.653458i | −0.00747870 | − | 0.0230171i | ||||
\(807\) | −14.3385 | −0.504738 | ||||||||
\(808\) | −0.418191 | − | 1.28706i | −0.0147119 | − | 0.0452786i | ||||
\(809\) | 6.67201 | + | 4.84750i | 0.234575 | + | 0.170429i | 0.698863 | − | 0.715255i | \(-0.253690\pi\) |
−0.464288 | + | 0.885684i | \(0.653690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.8503 | − | 10.7894i | 0.521465 | − | 0.378867i | −0.295690 | − | 0.955284i | \(-0.595550\pi\) |
0.817156 | + | 0.576417i | \(0.195550\pi\) | |||||||
\(812\) | 2.57880 | + | 1.87361i | 0.0904981 | + | 0.0657507i | ||||
\(813\) | 24.3932 | + | 17.7227i | 0.855506 | + | 0.621561i | ||||
\(814\) | 26.2290 | − | 19.0565i | 0.919327 | − | 0.667930i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 52.2198 | + | 37.9399i | 1.82806 | + | 1.32816i | ||||
\(817\) | 8.31491 | + | 25.5907i | 0.290902 | + | 0.895304i | ||||
\(818\) | 77.7957 | 2.72006 | ||||||||
\(819\) | 0.785424 | + | 2.41729i | 0.0274449 | + | 0.0844669i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.90209 | + | 15.0871i | −0.171084 | + | 0.526543i | −0.999433 | − | 0.0336695i | \(-0.989281\pi\) |
0.828349 | + | 0.560213i | \(0.189281\pi\) | |||||||
\(822\) | −5.78358 | + | 17.8000i | −0.201725 | + | 0.620847i | ||||
\(823\) | −26.2692 | + | 19.0857i | −0.915685 | + | 0.665284i | −0.942446 | − | 0.334358i | \(-0.891481\pi\) |
0.0267610 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(824\) | 0.847120 | 0.0295108 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.38375 | 0.0481468 | ||||||||
\(827\) | 23.2953 | − | 16.9250i | 0.810057 | − | 0.588541i | −0.103790 | − | 0.994599i | \(-0.533097\pi\) |
0.913847 | + | 0.406058i | \(0.133097\pi\) | |||||||
\(828\) | −28.3191 | + | 87.1572i | −0.984156 | + | 3.02892i | ||||
\(829\) | −2.65515 | + | 8.17171i | −0.0922172 | + | 0.283815i | −0.986518 | − | 0.163650i | \(-0.947673\pi\) |
0.894301 | + | 0.447465i | \(0.147673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.4643 | − | 50.6719i | −0.571141 | − | 1.75779i | ||||
\(832\) | 9.41283 | 0.326331 | ||||||||
\(833\) | 11.6391 | + | 35.8213i | 0.403270 | + | 1.24114i | ||||
\(834\) | −77.4854 | − | 56.2964i | −2.68310 | − | 1.94939i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.8931 | + | 7.91432i | −0.376746 | + | 0.273722i | ||||
\(837\) | 2.36049 | + | 1.71499i | 0.0815903 | + | 0.0592788i | ||||
\(838\) | 17.5765 | + | 12.7700i | 0.607168 | + | 0.441134i | ||||
\(839\) | 38.0676 | − | 27.6577i | 1.31424 | − | 0.954850i | 0.314253 | − | 0.949339i | \(-0.398246\pi\) |
0.999985 | − | 0.00551066i | \(-0.00175411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.23907 | + | 6.71258i | 0.318589 | + | 0.231468i | ||||
\(842\) | 20.1954 | + | 62.1551i | 0.695979 | + | 2.14200i | ||||
\(843\) | 77.1436 | 2.65697 | ||||||||
\(844\) | 4.60435 | + | 14.1707i | 0.158488 | + | 0.487776i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.10317 | + | 9.55056i | −0.106689 | + | 0.328355i | ||||
\(847\) | 0.908942 | − | 2.79744i | 0.0312316 | − | 0.0961210i | ||||
\(848\) | 12.3124 | − | 8.94546i | 0.422809 | − | 0.307188i | ||||
\(849\) | −48.7145 | −1.67188 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −66.8067 | −2.29011 | ||||||||
\(852\) | 58.7331 | − | 42.6721i | 2.01216 | − | 1.46192i | ||||
\(853\) | 5.77526 | − | 17.7744i | 0.197741 | − | 0.608585i | −0.802192 | − | 0.597066i | \(-0.796333\pi\) |
0.999934 | − | 0.0115193i | \(-0.00366680\pi\) | |||||||
\(854\) | −2.23052 | + | 6.86483i | −0.0763268 | + | 0.234910i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0258795 | + | 0.0796489i | 0.000884543 | + | 0.00272234i | ||||
\(857\) | −3.06228 | −0.104606 | −0.0523028 | − | 0.998631i | \(-0.516656\pi\) | ||||
−0.0523028 | + | 0.998631i | \(0.516656\pi\) | |||||||
\(858\) | −3.67002 | − | 11.2952i | −0.125292 | − | 0.385610i | ||||
\(859\) | −13.7261 | − | 9.97258i | −0.468328 | − | 0.340260i | 0.328462 | − | 0.944517i | \(-0.393470\pi\) |
−0.796789 | + | 0.604257i | \(0.793470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.79130 | − | 2.75454i | 0.129207 | − | 0.0938745i | ||||
\(862\) | −22.4685 | − | 16.3243i | −0.765281 | − | 0.556009i | ||||
\(863\) | −17.7150 | − | 12.8707i | −0.603025 | − | 0.438124i | 0.243926 | − | 0.969794i | \(-0.421565\pi\) |
−0.846951 | + | 0.531670i | \(0.821565\pi\) | |||||||
\(864\) | −62.1514 | + | 45.1556i | −2.11443 | + | 1.53622i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −34.3935 | − | 24.9883i | −1.16874 | − | 0.849137i | ||||
\(867\) | −12.2652 | − | 37.7484i | −0.416548 | − | 1.28200i | ||||
\(868\) | −0.232393 | −0.00788795 | ||||||||
\(869\) | −3.07245 | − | 9.45601i | −0.104226 | − | 0.320773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.30132 | + | 13.2381i | −0.145745 | + | 0.448556i | ||||
\(872\) | −0.111588 | + | 0.343434i | −0.00377886 | + | 0.0116301i | ||||
\(873\) | 31.8541 | − | 23.1434i | 1.07810 | − | 0.783284i | ||||
\(874\) | 54.7499 | 1.85194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.3340 | 0.720808 | ||||||||
\(877\) | 37.8879 | − | 27.5272i | 1.27938 | − | 0.929527i | 0.279850 | − | 0.960044i | \(-0.409715\pi\) |
0.999534 | + | 0.0305170i | \(0.00971537\pi\) | |||||||
\(878\) | 22.6164 | − | 69.6061i | 0.763266 | − | 2.34909i | ||||
\(879\) | 23.2857 | − | 71.6659i | 0.785406 | − | 2.41723i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.00869502 | + | 0.0267605i | 0.000292943 | + | 0.000901585i | 0.951203 | − | 0.308566i | \(-0.0998491\pi\) |
−0.950910 | + | 0.309468i | \(0.899849\pi\) | |||||||
\(882\) | −85.0576 | −2.86404 | ||||||||
\(883\) | 9.04544 | + | 27.8390i | 0.304403 | + | 0.936857i | 0.979899 | + | 0.199493i | \(0.0639297\pi\) |
−0.675496 | + | 0.737364i | \(0.736070\pi\) | |||||||
\(884\) | −10.1837 | − | 7.39890i | −0.342515 | − | 0.248852i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.4068 | − | 7.56099i | 0.349624 | − | 0.254016i | ||||
\(887\) | 16.0830 | + | 11.6850i | 0.540014 | + | 0.392343i | 0.824090 | − | 0.566458i | \(-0.191687\pi\) |
−0.284076 | + | 0.958802i | \(0.591687\pi\) | |||||||
\(888\) | 2.49340 | + | 1.81156i | 0.0836729 | + | 0.0607919i | ||||
\(889\) | −4.28692 | + | 3.11463i | −0.143779 | + | 0.104461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.7155 | + | 10.6914i | 0.492986 | + | 0.358175i | ||||
\(892\) | −14.5192 | − | 44.6856i | −0.486140 | − | 1.49618i | ||||
\(893\) | 3.04030 | 0.101740 | ||||||||
\(894\) | −27.9596 | − | 86.0508i | −0.935108 | − | 2.87797i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.101014 | − | 0.310888i | 0.00337462 | − | 0.0103860i | ||||
\(897\) | −7.56247 | + | 23.2749i | −0.252504 | + | 0.777126i | ||||
\(898\) | 57.2834 | − | 41.6188i | 1.91157 | − | 1.38884i | ||||
\(899\) | 1.28168 | 0.0427465 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.4860 | −0.715801 | ||||||||
\(902\) | −11.9100 | + | 8.65316i | −0.396561 | + | 0.288119i | ||||
\(903\) | −2.48063 | + | 7.63459i | −0.0825501 | + | 0.254063i | ||||
\(904\) | −0.0289507 | + | 0.0891010i | −0.000962885 | + | 0.00296346i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.34054 | + | 4.12575i | 0.0445364 | + | 0.137069i | ||||
\(907\) | 14.2958 | 0.474685 | 0.237343 | − | 0.971426i | \(-0.423724\pi\) | ||||
0.237343 | + | 0.971426i | \(0.423724\pi\) | |||||||
\(908\) | 0.422533 | + | 1.30042i | 0.0140223 | + | 0.0431561i | ||||
\(909\) | 60.9890 | + | 44.3111i | 2.02288 | + | 1.46971i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.6953 | + | 11.4033i | −0.520009 | + | 0.377808i | −0.816607 | − | 0.577194i | \(-0.804148\pi\) |
0.296599 | + | 0.955002i | \(0.404148\pi\) | |||||||
\(912\) | 35.7031 | + | 25.9399i | 1.18225 | + | 0.858954i | ||||
\(913\) | −10.0786 | − | 7.32251i | −0.333552 | − | 0.242340i | ||||
\(914\) | 36.3278 | − | 26.3937i | 1.20162 | − | 0.873025i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.0224 | + | 28.3514i | 1.28934 | + | 0.936757i | ||||
\(917\) | 1.90087 | + | 5.85028i | 0.0627723 | + | 0.193193i | ||||
\(918\) | 105.481 | 3.48139 | ||||||||
\(919\) | 1.32851 | + | 4.08873i | 0.0438234 | + | 0.134875i | 0.970574 | − | 0.240802i | \(-0.0774104\pi\) |
−0.926751 | + | 0.375676i | \(0.877410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.63381 | − | 5.02836i | 0.0538360 | − | 0.165690i | ||||
\(922\) | −1.17321 | + | 3.61077i | −0.0386376 | + | 0.118914i | ||||
\(923\) | 10.5446 | − | 7.66108i | 0.347079 | − | 0.252167i | ||||
\(924\) | −4.01697 | −0.132149 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.0069 | 0.854639 | ||||||||
\(927\) | −38.1771 | + | 27.7373i | −1.25390 | + | 0.911013i | ||||
\(928\) | −10.4283 | + | 32.0949i | −0.342324 | + | 1.05357i | ||||
\(929\) | 13.2975 | − | 40.9256i | 0.436277 | − | 1.34272i | −0.455495 | − | 0.890239i | \(-0.650538\pi\) |
0.891772 | − | 0.452485i | \(-0.149462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.95773 | + | 24.4914i | 0.260804 | + | 0.802672i | ||||
\(932\) | −36.6368 | −1.20008 | ||||||||
\(933\) | −17.1347 | − | 52.7352i | −0.560965 | − | 1.72647i | ||||
\(934\) | −4.26522 | − | 3.09887i | −0.139562 | − | 0.101398i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.614064 | − | 0.446144i | 0.0200713 | − | 0.0145827i | ||||
\(937\) | 13.7378 | + | 9.98109i | 0.448794 | + | 0.326068i | 0.789119 | − | 0.614240i | \(-0.210537\pi\) |
−0.340325 | + | 0.940308i | \(0.610537\pi\) | |||||||
\(938\) | 7.51593 | + | 5.46064i | 0.245404 | + | 0.178296i | ||||
\(939\) | −8.09634 | + | 5.88233i | −0.264214 | + | 0.191963i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.5985 | + | 10.6064i | 0.475898 | + | 0.345760i | 0.799735 | − | 0.600353i | \(-0.204973\pi\) |
−0.323837 | + | 0.946113i | \(0.604973\pi\) | |||||||
\(942\) | −41.5529 | − | 127.887i | −1.35387 | − | 4.16677i | ||||
\(943\) | 30.3355 | 0.987860 | ||||||||
\(944\) | 2.23114 | + | 6.86673i | 0.0726173 | + | 0.223493i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.79268 | − | 23.9834i | 0.253362 | − | 0.779768i | ||||
\(947\) | −2.22762 | + | 6.85590i | −0.0723879 | + | 0.222787i | −0.980704 | − | 0.195497i | \(-0.937368\pi\) |
0.908317 | + | 0.418284i | \(0.137368\pi\) | |||||||
\(948\) | 28.6377 | − | 20.8065i | 0.930109 | − | 0.675764i | ||||
\(949\) | 3.83017 | 0.124333 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.02277 | −0.0980200 | ||||||||
\(952\) | −0.181486 | + | 0.131857i | −0.00588198 | + | 0.00427351i | ||||
\(953\) | −4.26444 | + | 13.1246i | −0.138139 | + | 0.425147i | −0.996065 | − | 0.0886255i | \(-0.971753\pi\) |
0.857926 | + | 0.513773i | \(0.171753\pi\) | |||||||
\(954\) | 14.9939 | − | 46.1465i | 0.485446 | − | 1.49405i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.1575 | − | 46.6501i | −0.490230 | − | 1.50877i | ||||
\(957\) | 22.1541 | 0.716141 | ||||||||
\(958\) | 4.18977 | + | 12.8948i | 0.135365 | + | 0.416611i | ||||
\(959\) | 0.919456 | + | 0.668024i | 0.0296908 | + | 0.0215716i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0039 | − | 18.1664i | 0.806578 | − | 0.586014i | ||||
\(962\) | 16.7651 | + | 12.1806i | 0.540530 | + | 0.392718i | ||||
\(963\) | −3.77426 | − | 2.74216i | −0.121624 | − | 0.0883648i | ||||
\(964\) | 7.00420 | − | 5.08885i | 0.225590 | − | 0.163901i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.2143 | + | 9.60076i | 0.425164 | + | 0.308900i | ||||
\(967\) | −4.60299 | − | 14.1666i | −0.148022 | − | 0.455566i | 0.849365 | − | 0.527806i | \(-0.176985\pi\) |
−0.997387 | + | 0.0722402i | \(0.976985\pi\) | |||||||
\(968\) | −0.878391 | −0.0282326 | ||||||||
\(969\) | −19.2532 | − | 59.2551i | −0.618501 | − | 1.90355i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2970 | − | 37.8461i | 0.394628 | − | 1.21454i | −0.534623 | − | 0.845091i | \(-0.679546\pi\) |
0.929251 | − | 0.369449i | \(-0.120454\pi\) | |||||||
\(972\) | −1.82866 | + | 5.62803i | −0.0586542 | + | 0.180519i | ||||
\(973\) | −4.70521 | + | 3.41853i | −0.150842 | + | 0.109593i | ||||
\(974\) | 11.1919 | 0.358611 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.6626 | −1.20555 | ||||||||
\(977\) | 25.0493 | − | 18.1994i | 0.801399 | − | 0.582251i | −0.109925 | − | 0.993940i | \(-0.535061\pi\) |
0.911324 | + | 0.411689i | \(0.135061\pi\) | |||||||
\(978\) | −24.7805 | + | 76.2665i | −0.792393 | + | 2.43873i | ||||
\(979\) | −0.825653 | + | 2.54110i | −0.0263880 | + | 0.0812138i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.21613 | − | 19.1313i | −0.198466 | − | 0.610815i | ||||
\(982\) | −11.1799 | −0.356764 | ||||||||
\(983\) | 8.57673 | + | 26.3965i | 0.273555 | + | 0.841916i | 0.989598 | + | 0.143860i | \(0.0459515\pi\) |
−0.716043 | + | 0.698056i | \(0.754049\pi\) | |||||||
\(984\) | −1.13220 | − | 0.822590i | −0.0360932 | − | 0.0262232i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 37.4859 | − | 27.2351i | 1.19379 | − | 0.867342i | ||||
\(987\) | 0.733800 | + | 0.533137i | 0.0233571 | + | 0.0169699i | ||||
\(988\) | −6.96269 | − | 5.05869i | −0.221513 | − | 0.160938i | ||||
\(989\) | −42.0395 | + | 30.5435i | −1.33678 | + | 0.971227i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1498 | − | 8.82736i | −0.385952 | − | 0.280410i | 0.377843 | − | 0.925870i | \(-0.376666\pi\) |
−0.763795 | + | 0.645459i | \(0.776666\pi\) | |||||||
\(992\) | −0.760284 | − | 2.33991i | −0.0241390 | − | 0.0742923i | ||||
\(993\) | 42.9673 | 1.36353 | ||||||||
\(994\) | −2.68819 | − | 8.27339i | −0.0852641 | − | 0.262416i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.7057 | − | 42.1819i | 0.434283 | − | 1.33659i | ||||
\(997\) | 5.53566 | − | 17.0370i | 0.175316 | − | 0.539568i | −0.824332 | − | 0.566107i | \(-0.808449\pi\) |
0.999648 | + | 0.0265394i | \(0.00844875\pi\) | |||||||
\(998\) | −31.3731 | + | 22.7939i | −0.993099 | + | 0.721528i | ||||
\(999\) | −87.9999 | −2.78419 |
(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 | 625.2.d.p.251.1 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.374.2 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.374.7 | 32 | |||
5.4 | even | 2 | 625.2.d.n.251.4 | 16 | |||
25.2 | odd | 20 | 625.2.e.j.499.2 | 32 | |||
25.3 | odd | 20 | 625.2.b.d.624.4 | 16 | |||
25.4 | even | 10 | 625.2.a.g.1.1 | yes | 8 | ||
25.6 | even | 5 | 625.2.d.q.501.4 | 16 | |||
25.8 | odd | 20 | 625.2.e.j.124.2 | 32 | |||
25.9 | even | 10 | 625.2.d.n.376.4 | 16 | |||
25.11 | even | 5 | 625.2.d.q.126.4 | 16 | |||
25.12 | odd | 20 | 625.2.e.k.249.7 | 32 | |||
25.13 | odd | 20 | 625.2.e.k.249.2 | 32 | |||
25.14 | even | 10 | 625.2.d.m.126.1 | 16 | |||
25.16 | even | 5 | inner | 625.2.d.p.376.1 | 16 | ||
25.17 | odd | 20 | 625.2.e.j.124.7 | 32 | |||
25.19 | even | 10 | 625.2.d.m.501.1 | 16 | |||
25.21 | even | 5 | 625.2.a.e.1.8 | ✓ | 8 | ||
25.22 | odd | 20 | 625.2.b.d.624.13 | 16 | |||
25.23 | odd | 20 | 625.2.e.j.499.7 | 32 | |||
75.29 | odd | 10 | 5625.2.a.s.1.8 | 8 | |||
75.71 | odd | 10 | 5625.2.a.be.1.1 | 8 | |||
100.71 | odd | 10 | 10000.2.a.bn.1.7 | 8 | |||
100.79 | odd | 10 | 10000.2.a.be.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.8 | ✓ | 8 | 25.21 | even | 5 | ||
625.2.a.g.1.1 | yes | 8 | 25.4 | even | 10 | ||
625.2.b.d.624.4 | 16 | 25.3 | odd | 20 | |||
625.2.b.d.624.13 | 16 | 25.22 | odd | 20 | |||
625.2.d.m.126.1 | 16 | 25.14 | even | 10 | |||
625.2.d.m.501.1 | 16 | 25.19 | even | 10 | |||
625.2.d.n.251.4 | 16 | 5.4 | even | 2 | |||
625.2.d.n.376.4 | 16 | 25.9 | even | 10 | |||
625.2.d.p.251.1 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.p.376.1 | 16 | 25.16 | even | 5 | inner | ||
625.2.d.q.126.4 | 16 | 25.11 | even | 5 | |||
625.2.d.q.501.4 | 16 | 25.6 | even | 5 | |||
625.2.e.j.124.2 | 32 | 25.8 | odd | 20 | |||
625.2.e.j.124.7 | 32 | 25.17 | odd | 20 | |||
625.2.e.j.499.2 | 32 | 25.2 | odd | 20 | |||
625.2.e.j.499.7 | 32 | 25.23 | odd | 20 | |||
625.2.e.k.249.2 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.249.7 | 32 | 25.12 | odd | 20 | |||
625.2.e.k.374.2 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.374.7 | 32 | 5.3 | odd | 4 | |||
5625.2.a.s.1.8 | 8 | 75.29 | odd | 10 | |||
5625.2.a.be.1.1 | 8 | 75.71 | odd | 10 | |||
10000.2.a.be.1.2 | 8 | 100.79 | odd | 10 | |||
10000.2.a.bn.1.7 | 8 | 100.71 | odd | 10 |