Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(146,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.e (of order \(3\), degree \(2\), 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.146 |
Dual form | 845.2.e.c.191.1 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20711 | − | 2.09077i | −0.853553 | − | 1.47840i | −0.877981 | − | 0.478696i | \(-0.841110\pi\) |
0.0244272 | − | 0.999702i | \(-0.492224\pi\) | |||||||
\(3\) | 0.707107 | + | 1.22474i | 0.408248 | + | 0.707107i | 0.994694 | − | 0.102882i | \(-0.0328064\pi\) |
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(4\) | −1.91421 | + | 3.31552i | −0.957107 | + | 1.65776i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.70711 | − | 2.95680i | 0.696923 | − | 1.20711i | ||||
\(7\) | 2.41421 | − | 4.18154i | 0.912487 | − | 1.58047i | 0.101947 | − | 0.994790i | \(-0.467493\pi\) |
0.810539 | − | 0.585684i | \(-0.199174\pi\) | |||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.20711 | + | 2.09077i | 0.381721 | + | 0.661160i | ||||
\(11\) | 1.70711 | + | 2.95680i | 0.514712 | + | 0.891507i | 0.999854 | + | 0.0170722i | \(0.00543450\pi\) |
−0.485142 | + | 0.874435i | \(0.661232\pi\) | |||||||
\(12\) | −5.41421 | −1.56295 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −11.6569 | −3.11543 | ||||||||
\(15\) | −0.707107 | − | 1.22474i | −0.182574 | − | 0.316228i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −0.414214 | + | 0.717439i | −0.100462 | + | 0.174005i | −0.911875 | − | 0.410468i | \(-0.865365\pi\) |
0.811413 | + | 0.584473i | \(0.198699\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | 0.292893 | − | 0.507306i | 0.0671943 | − | 0.116384i | −0.830471 | − | 0.557062i | \(-0.811929\pi\) |
0.897665 | + | 0.440678i | \(0.145262\pi\) | |||||||
\(20\) | 1.91421 | − | 3.31552i | 0.428031 | − | 0.741372i | ||||
\(21\) | 6.82843 | 1.49008 | ||||||||
\(22\) | 4.12132 | − | 7.13834i | 0.878668 | − | 1.52190i | ||||
\(23\) | −0.707107 | − | 1.22474i | −0.147442 | − | 0.255377i | 0.782839 | − | 0.622224i | \(-0.213771\pi\) |
−0.930281 | + | 0.366847i | \(0.880437\pi\) | |||||||
\(24\) | 3.12132 | + | 5.40629i | 0.637137 | + | 1.10355i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 9.24264 | + | 16.0087i | 1.74669 | + | 3.02536i | ||||
\(29\) | 2.82843 | + | 4.89898i | 0.525226 | + | 0.909718i | 0.999568 | + | 0.0293774i | \(0.00935245\pi\) |
−0.474343 | + | 0.880340i | \(0.657314\pi\) | |||||||
\(30\) | −1.70711 | + | 2.95680i | −0.311674 | + | 0.539835i | ||||
\(31\) | −1.75736 | −0.315631 | −0.157816 | − | 0.987469i | \(-0.550445\pi\) | ||||
−0.157816 | + | 0.987469i | \(0.550445\pi\) | |||||||
\(32\) | 0.792893 | − | 1.37333i | 0.140165 | − | 0.242773i | ||||
\(33\) | −2.41421 | + | 4.18154i | −0.420261 | + | 0.727913i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −2.41421 | + | 4.18154i | −0.408077 | + | 0.706809i | ||||
\(36\) | 1.91421 | + | 3.31552i | 0.319036 | + | 0.552586i | ||||
\(37\) | −4.24264 | − | 7.34847i | −0.697486 | − | 1.20808i | −0.969335 | − | 0.245741i | \(-0.920969\pi\) |
0.271850 | − | 0.962340i | \(-0.412365\pi\) | |||||||
\(38\) | −1.41421 | −0.229416 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | −1.58579 | − | 2.74666i | −0.247658 | − | 0.428957i | 0.715217 | − | 0.698902i | \(-0.246328\pi\) |
−0.962876 | + | 0.269945i | \(0.912994\pi\) | |||||||
\(42\) | −8.24264 | − | 14.2767i | −1.27187 | − | 2.20294i | ||||
\(43\) | 5.53553 | − | 9.58783i | 0.844161 | − | 1.46213i | −0.0421868 | − | 0.999110i | \(-0.513432\pi\) |
0.886348 | − | 0.463020i | \(-0.153234\pi\) | |||||||
\(44\) | −13.0711 | −1.97054 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −1.70711 | + | 2.95680i | −0.251699 | + | 0.435956i | ||||
\(47\) | 4.82843 | 0.704298 | 0.352149 | − | 0.935944i | \(-0.385451\pi\) | ||||
0.352149 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(48\) | 2.12132 | − | 3.67423i | 0.306186 | − | 0.530330i | ||||
\(49\) | −8.15685 | − | 14.1281i | −1.16526 | − | 2.01830i | ||||
\(50\) | −1.20711 | − | 2.09077i | −0.170711 | − | 0.295680i | ||||
\(51\) | −1.17157 | −0.164053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.48528 | 0.341380 | 0.170690 | − | 0.985325i | \(-0.445400\pi\) | ||||
0.170690 | + | 0.985325i | \(0.445400\pi\) | |||||||
\(54\) | −6.82843 | − | 11.8272i | −0.929231 | − | 1.60948i | ||||
\(55\) | −1.70711 | − | 2.95680i | −0.230186 | − | 0.398694i | ||||
\(56\) | 10.6569 | − | 18.4582i | 1.42408 | − | 2.46658i | ||||
\(57\) | 0.828427 | 0.109728 | ||||||||
\(58\) | 6.82843 | − | 11.8272i | 0.896616 | − | 1.55299i | ||||
\(59\) | 0.878680 | − | 1.52192i | 0.114394 | − | 0.198137i | −0.803143 | − | 0.595786i | \(-0.796841\pi\) |
0.917537 | + | 0.397649i | \(0.130174\pi\) | |||||||
\(60\) | 5.41421 | 0.698972 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 2.12132 | + | 3.67423i | 0.269408 | + | 0.466628i | ||||
\(63\) | −2.41421 | − | 4.18154i | −0.304162 | − | 0.526825i | ||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.6569 | 1.43486 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | −1.58579 | − | 2.74666i | −0.192305 | − | 0.333082i | ||||
\(69\) | 1.00000 | − | 1.73205i | 0.120386 | − | 0.208514i | ||||
\(70\) | 11.6569 | 1.39326 | ||||||||
\(71\) | 5.94975 | − | 10.3053i | 0.706105 | − | 1.22301i | −0.260186 | − | 0.965558i | \(-0.583784\pi\) |
0.966291 | − | 0.257451i | \(-0.0828827\pi\) | |||||||
\(72\) | 2.20711 | − | 3.82282i | 0.260110 | − | 0.450524i | ||||
\(73\) | −8.48528 | −0.993127 | −0.496564 | − | 0.868000i | \(-0.665405\pi\) | ||||
−0.496564 | + | 0.868000i | \(0.665405\pi\) | |||||||
\(74\) | −10.2426 | + | 17.7408i | −1.19068 | + | 2.06232i | ||||
\(75\) | 0.707107 | + | 1.22474i | 0.0816497 | + | 0.141421i | ||||
\(76\) | 1.12132 | + | 1.94218i | 0.128624 | + | 0.222784i | ||||
\(77\) | 16.4853 | 1.87867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 1.50000 | + | 2.59808i | 0.167705 | + | 0.290474i | ||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | −3.82843 | + | 6.63103i | −0.422779 | + | 0.732275i | ||||
\(83\) | 3.17157 | 0.348125 | 0.174063 | − | 0.984735i | \(-0.444310\pi\) | ||||
0.174063 | + | 0.984735i | \(0.444310\pi\) | |||||||
\(84\) | −13.0711 | + | 22.6398i | −1.42617 | + | 2.47020i | ||||
\(85\) | 0.414214 | − | 0.717439i | 0.0449278 | − | 0.0778172i | ||||
\(86\) | −26.7279 | −2.88215 | ||||||||
\(87\) | −4.00000 | + | 6.92820i | −0.428845 | + | 0.742781i | ||||
\(88\) | 7.53553 | + | 13.0519i | 0.803291 | + | 1.39134i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 2.41421 | 0.254480 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.41421 | 0.564471 | ||||||||
\(93\) | −1.24264 | − | 2.15232i | −0.128856 | − | 0.223185i | ||||
\(94\) | −5.82843 | − | 10.0951i | −0.601156 | − | 1.04123i | ||||
\(95\) | −0.292893 | + | 0.507306i | −0.0300502 | + | 0.0520485i | ||||
\(96\) | 2.24264 | 0.228889 | ||||||||
\(97\) | −3.82843 | + | 6.63103i | −0.388718 | + | 0.673279i | −0.992277 | − | 0.124039i | \(-0.960415\pi\) |
0.603559 | + | 0.797318i | \(0.293749\pi\) | |||||||
\(98\) | −19.6924 | + | 34.1082i | −1.98923 | + | 3.44545i | ||||
\(99\) | 3.41421 | 0.343141 | ||||||||
\(100\) | −1.91421 | + | 3.31552i | −0.191421 | + | 0.331552i | ||||
\(101\) | 1.82843 | + | 3.16693i | 0.181935 | + | 0.315121i | 0.942540 | − | 0.334095i | \(-0.108431\pi\) |
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(102\) | 1.41421 | + | 2.44949i | 0.140028 | + | 0.242536i | ||||
\(103\) | 14.5858 | 1.43718 | 0.718590 | − | 0.695434i | \(-0.244788\pi\) | ||||
0.718590 | + | 0.695434i | \(0.244788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.82843 | −0.666386 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 4.70711 | + | 8.15295i | 0.455053 | + | 0.788175i | 0.998691 | − | 0.0511445i | \(-0.0162869\pi\) |
−0.543638 | + | 0.839320i | \(0.682954\pi\) | |||||||
\(108\) | −10.8284 | + | 18.7554i | −1.04197 | + | 1.80474i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −4.12132 | + | 7.13834i | −0.392952 | + | 0.680614i | ||||
\(111\) | 6.00000 | − | 10.3923i | 0.569495 | − | 0.986394i | ||||
\(112\) | −14.4853 | −1.36873 | ||||||||
\(113\) | 4.41421 | − | 7.64564i | 0.415254 | − | 0.719242i | −0.580201 | − | 0.814473i | \(-0.697026\pi\) |
0.995455 | + | 0.0952319i | \(0.0303593\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0.707107 | + | 1.22474i | 0.0659380 | + | 0.114208i | ||||
\(116\) | −21.6569 | −2.01079 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.24264 | −0.390567 | ||||||||
\(119\) | 2.00000 | + | 3.46410i | 0.183340 | + | 0.317554i | ||||
\(120\) | −3.12132 | − | 5.40629i | −0.284936 | − | 0.493524i | ||||
\(121\) | −0.328427 | + | 0.568852i | −0.0298570 | + | 0.0517139i | ||||
\(122\) | −19.3137 | −1.74858 | ||||||||
\(123\) | 2.24264 | − | 3.88437i | 0.202212 | − | 0.350242i | ||||
\(124\) | 3.36396 | − | 5.82655i | 0.302093 | − | 0.523240i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.82843 | + | 10.0951i | −0.519238 | + | 0.899346i | ||||
\(127\) | 3.29289 | + | 5.70346i | 0.292197 | + | 0.506100i | 0.974329 | − | 0.225129i | \(-0.0722804\pi\) |
−0.682132 | + | 0.731229i | \(0.738947\pi\) | |||||||
\(128\) | 10.2782 | + | 17.8023i | 0.908471 | + | 1.57352i | ||||
\(129\) | 15.6569 | 1.37851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | −9.24264 | − | 16.0087i | −0.804469 | − | 1.39338i | ||||
\(133\) | −1.41421 | − | 2.44949i | −0.122628 | − | 0.212398i | ||||
\(134\) | −2.41421 | + | 4.18154i | −0.208556 | + | 0.361230i | ||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | −1.82843 | + | 3.16693i | −0.156786 | + | 0.271562i | ||||
\(137\) | −8.65685 | + | 14.9941i | −0.739605 | + | 1.28103i | 0.213068 | + | 0.977037i | \(0.431654\pi\) |
−0.952673 | + | 0.303996i | \(0.901679\pi\) | |||||||
\(138\) | −4.82843 | −0.411023 | ||||||||
\(139\) | −2.24264 | + | 3.88437i | −0.190218 | + | 0.329468i | −0.945323 | − | 0.326137i | \(-0.894253\pi\) |
0.755104 | + | 0.655605i | \(0.227586\pi\) | |||||||
\(140\) | −9.24264 | − | 16.0087i | −0.781146 | − | 1.35298i | ||||
\(141\) | 3.41421 | + | 5.91359i | 0.287529 | + | 0.498014i | ||||
\(142\) | −28.7279 | −2.41079 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −2.82843 | − | 4.89898i | −0.234888 | − | 0.406838i | ||||
\(146\) | 10.2426 | + | 17.7408i | 0.847687 | + | 1.46824i | ||||
\(147\) | 11.5355 | − | 19.9801i | 0.951435 | − | 1.64793i | ||||
\(148\) | 32.4853 | 2.67027 | ||||||||
\(149\) | −5.82843 | + | 10.0951i | −0.477483 | + | 0.827025i | −0.999667 | − | 0.0258077i | \(-0.991784\pi\) |
0.522184 | + | 0.852833i | \(0.325118\pi\) | |||||||
\(150\) | 1.70711 | − | 2.95680i | 0.139385 | − | 0.241421i | ||||
\(151\) | −9.75736 | −0.794043 | −0.397021 | − | 0.917809i | \(-0.629956\pi\) | ||||
−0.397021 | + | 0.917809i | \(0.629956\pi\) | |||||||
\(152\) | 1.29289 | − | 2.23936i | 0.104867 | − | 0.181636i | ||||
\(153\) | 0.414214 | + | 0.717439i | 0.0334872 | + | 0.0580015i | ||||
\(154\) | −19.8995 | − | 34.4669i | −1.60355 | − | 2.77742i | ||||
\(155\) | 1.75736 | 0.141154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | 10.2426 | + | 17.7408i | 0.814861 | + | 1.41138i | ||||
\(159\) | 1.75736 | + | 3.04384i | 0.139368 | + | 0.241392i | ||||
\(160\) | −0.792893 | + | 1.37333i | −0.0626837 | + | 0.108571i | ||||
\(161\) | −6.82843 | −0.538155 | ||||||||
\(162\) | 6.03553 | − | 10.4539i | 0.474196 | − | 0.821332i | ||||
\(163\) | 9.48528 | − | 16.4290i | 0.742945 | − | 1.28682i | −0.208204 | − | 0.978085i | \(-0.566762\pi\) |
0.951149 | − | 0.308732i | \(-0.0999048\pi\) | |||||||
\(164\) | 12.1421 | 0.948141 | ||||||||
\(165\) | 2.41421 | − | 4.18154i | 0.187946 | − | 0.325532i | ||||
\(166\) | −3.82843 | − | 6.63103i | −0.297144 | − | 0.514668i | ||||
\(167\) | −1.58579 | − | 2.74666i | −0.122712 | − | 0.212543i | 0.798124 | − | 0.602493i | \(-0.205826\pi\) |
−0.920836 | + | 0.389950i | \(0.872492\pi\) | |||||||
\(168\) | 30.1421 | 2.32552 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −0.292893 | − | 0.507306i | −0.0223981 | − | 0.0387947i | ||||
\(172\) | 21.1924 | + | 36.7063i | 1.61590 | + | 2.79883i | ||||
\(173\) | −8.41421 | + | 14.5738i | −0.639721 | + | 1.10803i | 0.345773 | + | 0.938318i | \(0.387617\pi\) |
−0.985494 | + | 0.169711i | \(0.945717\pi\) | |||||||
\(174\) | 19.3137 | 1.46417 | ||||||||
\(175\) | 2.41421 | − | 4.18154i | 0.182497 | − | 0.316095i | ||||
\(176\) | 5.12132 | − | 8.87039i | 0.386034 | − | 0.668631i | ||||
\(177\) | 2.48528 | 0.186805 | ||||||||
\(178\) | 7.24264 | − | 12.5446i | 0.542859 | − | 0.940259i | ||||
\(179\) | −2.82843 | − | 4.89898i | −0.211407 | − | 0.366167i | 0.740748 | − | 0.671783i | \(-0.234471\pi\) |
−0.952155 | + | 0.305616i | \(0.901138\pi\) | |||||||
\(180\) | −1.91421 | − | 3.31552i | −0.142677 | − | 0.247124i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3137 | 0.836333 | ||||||||
\(184\) | −3.12132 | − | 5.40629i | −0.230107 | − | 0.398557i | ||||
\(185\) | 4.24264 | + | 7.34847i | 0.311925 | + | 0.540270i | ||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | −2.82843 | −0.206835 | ||||||||
\(188\) | −9.24264 | + | 16.0087i | −0.674089 | + | 1.16756i | ||||
\(189\) | 13.6569 | − | 23.6544i | 0.993390 | − | 1.72060i | ||||
\(190\) | 1.41421 | 0.102598 | ||||||||
\(191\) | −1.17157 | + | 2.02922i | −0.0847720 | + | 0.146829i | −0.905294 | − | 0.424785i | \(-0.860350\pi\) |
0.820522 | + | 0.571615i | \(0.193683\pi\) | |||||||
\(192\) | −6.94975 | − | 12.0373i | −0.501555 | − | 0.868718i | ||||
\(193\) | 2.17157 | + | 3.76127i | 0.156313 | + | 0.270742i | 0.933536 | − | 0.358483i | \(-0.116706\pi\) |
−0.777223 | + | 0.629225i | \(0.783372\pi\) | |||||||
\(194\) | 18.4853 | 1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 62.4558 | 4.46113 | ||||||||
\(197\) | 5.48528 | + | 9.50079i | 0.390810 | + | 0.676903i | 0.992557 | − | 0.121784i | \(-0.0388616\pi\) |
−0.601746 | + | 0.798687i | \(0.705528\pi\) | |||||||
\(198\) | −4.12132 | − | 7.13834i | −0.292889 | − | 0.507299i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 1.41421 | − | 2.44949i | 0.0997509 | − | 0.172774i | ||||
\(202\) | 4.41421 | − | 7.64564i | 0.310583 | − | 0.537946i | ||||
\(203\) | 27.3137 | 1.91705 | ||||||||
\(204\) | 2.24264 | − | 3.88437i | 0.157016 | − | 0.271960i | ||||
\(205\) | 1.58579 | + | 2.74666i | 0.110756 | + | 0.191835i | ||||
\(206\) | −17.6066 | − | 30.4955i | −1.22671 | − | 2.12472i | ||||
\(207\) | −1.41421 | −0.0982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 8.24264 | + | 14.2767i | 0.568796 | + | 0.985184i | ||||
\(211\) | −1.65685 | − | 2.86976i | −0.114063 | − | 0.197562i | 0.803342 | − | 0.595518i | \(-0.203053\pi\) |
−0.917405 | + | 0.397956i | \(0.869720\pi\) | |||||||
\(212\) | −4.75736 | + | 8.23999i | −0.326737 | + | 0.565925i | ||||
\(213\) | 16.8284 | 1.15306 | ||||||||
\(214\) | 11.3640 | − | 19.6830i | 0.776824 | − | 1.34550i | ||||
\(215\) | −5.53553 | + | 9.58783i | −0.377520 | + | 0.653884i | ||||
\(216\) | 24.9706 | 1.69903 | ||||||||
\(217\) | −4.24264 | + | 7.34847i | −0.288009 | + | 0.498847i | ||||
\(218\) | −2.41421 | − | 4.18154i | −0.163511 | − | 0.283210i | ||||
\(219\) | −6.00000 | − | 10.3923i | −0.405442 | − | 0.702247i | ||||
\(220\) | 13.0711 | 0.881251 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −28.9706 | −1.94438 | ||||||||
\(223\) | 4.75736 | + | 8.23999i | 0.318576 | + | 0.551790i | 0.980191 | − | 0.198053i | \(-0.0634619\pi\) |
−0.661615 | + | 0.749844i | \(0.730129\pi\) | |||||||
\(224\) | −3.82843 | − | 6.63103i | −0.255798 | − | 0.443054i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | −21.3137 | −1.41777 | ||||||||
\(227\) | −8.17157 | + | 14.1536i | −0.542366 | + | 0.939406i | 0.456401 | + | 0.889774i | \(0.349138\pi\) |
−0.998768 | + | 0.0496320i | \(0.984195\pi\) | |||||||
\(228\) | −1.58579 | + | 2.74666i | −0.105021 | + | 0.181902i | ||||
\(229\) | 4.82843 | 0.319071 | 0.159536 | − | 0.987192i | \(-0.449000\pi\) | ||||
0.159536 | + | 0.987192i | \(0.449000\pi\) | |||||||
\(230\) | 1.70711 | − | 2.95680i | 0.112563 | − | 0.194965i | ||||
\(231\) | 11.6569 | + | 20.1903i | 0.766965 | + | 1.32842i | ||||
\(232\) | 12.4853 | + | 21.6251i | 0.819699 | + | 1.41976i | ||||
\(233\) | −20.6274 | −1.35135 | −0.675674 | − | 0.737201i | \(-0.736147\pi\) | ||||
−0.675674 | + | 0.737201i | \(0.736147\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82843 | −0.314972 | ||||||||
\(236\) | 3.36396 | + | 5.82655i | 0.218975 | + | 0.379276i | ||||
\(237\) | −6.00000 | − | 10.3923i | −0.389742 | − | 0.675053i | ||||
\(238\) | 4.82843 | − | 8.36308i | 0.312980 | − | 0.542098i | ||||
\(239\) | 3.41421 | 0.220847 | 0.110424 | − | 0.993885i | \(-0.464779\pi\) | ||||
0.110424 | + | 0.993885i | \(0.464779\pi\) | |||||||
\(240\) | −2.12132 | + | 3.67423i | −0.136931 | + | 0.237171i | ||||
\(241\) | −7.24264 | + | 12.5446i | −0.466539 | + | 0.808070i | −0.999270 | − | 0.0382151i | \(-0.987833\pi\) |
0.532730 | + | 0.846285i | \(0.321166\pi\) | |||||||
\(242\) | 1.58579 | 0.101938 | ||||||||
\(243\) | 4.94975 | − | 8.57321i | 0.317526 | − | 0.549972i | ||||
\(244\) | 15.3137 | + | 26.5241i | 0.980360 | + | 1.69803i | ||||
\(245\) | 8.15685 | + | 14.1281i | 0.521122 | + | 0.902610i | ||||
\(246\) | −10.8284 | −0.690395 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.75736 | −0.492593 | ||||||||
\(249\) | 2.24264 | + | 3.88437i | 0.142122 | + | 0.246162i | ||||
\(250\) | 1.20711 | + | 2.09077i | 0.0763441 | + | 0.132232i | ||||
\(251\) | −9.89949 | + | 17.1464i | −0.624851 | + | 1.08227i | 0.363719 | + | 0.931509i | \(0.381507\pi\) |
−0.988570 | + | 0.150764i | \(0.951827\pi\) | |||||||
\(252\) | 18.4853 | 1.16446 | ||||||||
\(253\) | 2.41421 | − | 4.18154i | 0.151780 | − | 0.262891i | ||||
\(254\) | 7.94975 | − | 13.7694i | 0.498812 | − | 0.863967i | ||||
\(255\) | 1.17157 | 0.0733667 | ||||||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | −13.8284 | − | 23.9515i | −0.862594 | − | 1.49406i | −0.869417 | − | 0.494079i | \(-0.835505\pi\) |
0.00682332 | − | 0.999977i | \(-0.497828\pi\) | |||||||
\(258\) | −18.8995 | − | 32.7349i | −1.17663 | − | 2.03798i | ||||
\(259\) | −40.9706 | −2.54579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65685 | 0.350150 | ||||||||
\(262\) | 20.4853 | + | 35.4815i | 1.26558 | + | 2.19206i | ||||
\(263\) | 5.29289 | + | 9.16756i | 0.326374 | + | 0.565296i | 0.981789 | − | 0.189972i | \(-0.0608399\pi\) |
−0.655416 | + | 0.755268i | \(0.727507\pi\) | |||||||
\(264\) | −10.6569 | + | 18.4582i | −0.655884 | + | 1.13602i | ||||
\(265\) | −2.48528 | −0.152670 | ||||||||
\(266\) | −3.41421 | + | 5.91359i | −0.209339 | + | 0.362586i | ||||
\(267\) | −4.24264 | + | 7.34847i | −0.259645 | + | 0.449719i | ||||
\(268\) | 7.65685 | 0.467717 | ||||||||
\(269\) | 12.6569 | − | 21.9223i | 0.771702 | − | 1.33663i | −0.164928 | − | 0.986306i | \(-0.552739\pi\) |
0.936630 | − | 0.350321i | \(-0.113928\pi\) | |||||||
\(270\) | 6.82843 | + | 11.8272i | 0.415565 | + | 0.719779i | ||||
\(271\) | 13.3640 | + | 23.1471i | 0.811803 | + | 1.40608i | 0.911601 | + | 0.411076i | \(0.134847\pi\) |
−0.0997982 | + | 0.995008i | \(0.531820\pi\) | |||||||
\(272\) | 2.48528 | 0.150692 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 41.7990 | 2.52517 | ||||||||
\(275\) | 1.70711 | + | 2.95680i | 0.102942 | + | 0.178301i | ||||
\(276\) | 3.82843 | + | 6.63103i | 0.230444 | + | 0.399141i | ||||
\(277\) | 6.41421 | − | 11.1097i | 0.385393 | − | 0.667520i | −0.606431 | − | 0.795136i | \(-0.707399\pi\) |
0.991824 | + | 0.127616i | \(0.0407326\pi\) | |||||||
\(278\) | 10.8284 | 0.649446 | ||||||||
\(279\) | −0.878680 | + | 1.52192i | −0.0526052 | + | 0.0911148i | ||||
\(280\) | −10.6569 | + | 18.4582i | −0.636869 | + | 1.10309i | ||||
\(281\) | −21.7990 | −1.30042 | −0.650209 | − | 0.759755i | \(-0.725319\pi\) | ||||
−0.650209 | + | 0.759755i | \(0.725319\pi\) | |||||||
\(282\) | 8.24264 | − | 14.2767i | 0.490842 | − | 0.850163i | ||||
\(283\) | 8.36396 | + | 14.4868i | 0.497186 | + | 0.861151i | 0.999995 | − | 0.00324643i | \(-0.00103337\pi\) |
−0.502809 | + | 0.864398i | \(0.667700\pi\) | |||||||
\(284\) | 22.7782 | + | 39.4530i | 1.35164 | + | 2.34110i | ||||
\(285\) | −0.828427 | −0.0490718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.3137 | −0.903940 | ||||||||
\(288\) | −0.792893 | − | 1.37333i | −0.0467217 | − | 0.0809243i | ||||
\(289\) | 8.15685 | + | 14.1281i | 0.479815 | + | 0.831064i | ||||
\(290\) | −6.82843 | + | 11.8272i | −0.400979 | + | 0.694516i | ||||
\(291\) | −10.8284 | −0.634774 | ||||||||
\(292\) | 16.2426 | − | 28.1331i | 0.950529 | − | 1.64636i | ||||
\(293\) | 13.0711 | − | 22.6398i | 0.763620 | − | 1.32263i | −0.177353 | − | 0.984147i | \(-0.556753\pi\) |
0.940973 | − | 0.338481i | \(-0.109913\pi\) | |||||||
\(294\) | −55.6985 | −3.24840 | ||||||||
\(295\) | −0.878680 | + | 1.52192i | −0.0511587 | + | 0.0886095i | ||||
\(296\) | −18.7279 | − | 32.4377i | −1.08854 | − | 1.88540i | ||||
\(297\) | 9.65685 | + | 16.7262i | 0.560348 | + | 0.970550i | ||||
\(298\) | 28.1421 | 1.63023 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.41421 | −0.312590 | ||||||||
\(301\) | −26.7279 | − | 46.2941i | −1.54057 | − | 2.66835i | ||||
\(302\) | 11.7782 | + | 20.4004i | 0.677758 | + | 1.17391i | ||||
\(303\) | −2.58579 | + | 4.47871i | −0.148550 | + | 0.257295i | ||||
\(304\) | −1.75736 | −0.100791 | ||||||||
\(305\) | −4.00000 | + | 6.92820i | −0.229039 | + | 0.396708i | ||||
\(306\) | 1.00000 | − | 1.73205i | 0.0571662 | − | 0.0990148i | ||||
\(307\) | −24.8284 | −1.41703 | −0.708517 | − | 0.705694i | \(-0.750635\pi\) | ||||
−0.708517 | + | 0.705694i | \(0.750635\pi\) | |||||||
\(308\) | −31.5563 | + | 54.6572i | −1.79809 | + | 3.11438i | ||||
\(309\) | 10.3137 | + | 17.8639i | 0.586726 | + | 1.01624i | ||||
\(310\) | −2.12132 | − | 3.67423i | −0.120483 | − | 0.208683i | ||||
\(311\) | 8.48528 | 0.481156 | 0.240578 | − | 0.970630i | \(-0.422663\pi\) | ||||
0.240578 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.82843 | −0.272919 | −0.136459 | − | 0.990646i | \(-0.543572\pi\) | ||||
−0.136459 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(314\) | −21.7279 | − | 37.6339i | −1.22618 | − | 2.12380i | ||||
\(315\) | 2.41421 | + | 4.18154i | 0.136026 | + | 0.235603i | ||||
\(316\) | 16.2426 | − | 28.1331i | 0.913720 | − | 1.58261i | ||||
\(317\) | 2.14214 | 0.120314 | 0.0601572 | − | 0.998189i | \(-0.480840\pi\) | ||||
0.0601572 | + | 0.998189i | \(0.480840\pi\) | |||||||
\(318\) | 4.24264 | − | 7.34847i | 0.237915 | − | 0.412082i | ||||
\(319\) | −9.65685 | + | 16.7262i | −0.540680 | + | 0.936485i | ||||
\(320\) | 9.82843 | 0.549426 | ||||||||
\(321\) | −6.65685 | + | 11.5300i | −0.371549 | + | 0.643542i | ||||
\(322\) | 8.24264 | + | 14.2767i | 0.459344 | + | 0.795608i | ||||
\(323\) | 0.242641 | + | 0.420266i | 0.0135009 | + | 0.0233842i | ||||
\(324\) | −19.1421 | −1.06345 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −45.7990 | −2.53657 | ||||||||
\(327\) | 1.41421 | + | 2.44949i | 0.0782062 | + | 0.135457i | ||||
\(328\) | −7.00000 | − | 12.1244i | −0.386510 | − | 0.669456i | ||||
\(329\) | 11.6569 | − | 20.1903i | 0.642663 | − | 1.11313i | ||||
\(330\) | −11.6569 | −0.641689 | ||||||||
\(331\) | −13.0208 | + | 22.5527i | −0.715689 | + | 1.23961i | 0.247005 | + | 0.969014i | \(0.420554\pi\) |
−0.962693 | + | 0.270595i | \(0.912780\pi\) | |||||||
\(332\) | −6.07107 | + | 10.5154i | −0.333193 | + | 0.577107i | ||||
\(333\) | −8.48528 | −0.464991 | ||||||||
\(334\) | −3.82843 | + | 6.63103i | −0.209482 | + | 0.362834i | ||||
\(335\) | 1.00000 | + | 1.73205i | 0.0546358 | + | 0.0946320i | ||||
\(336\) | −10.2426 | − | 17.7408i | −0.558782 | − | 0.967839i | ||||
\(337\) | 12.8284 | 0.698809 | 0.349404 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349404 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.4853 | 0.678107 | ||||||||
\(340\) | 1.58579 | + | 2.74666i | 0.0860013 | + | 0.148959i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | −0.707107 | + | 1.22474i | −0.0382360 | + | 0.0662266i | ||||
\(343\) | −44.9706 | −2.42818 | ||||||||
\(344\) | 24.4350 | − | 42.3227i | 1.31745 | − | 2.28189i | ||||
\(345\) | −1.00000 | + | 1.73205i | −0.0538382 | + | 0.0932505i | ||||
\(346\) | 40.6274 | 2.18414 | ||||||||
\(347\) | 2.12132 | − | 3.67423i | 0.113878 | − | 0.197243i | −0.803452 | − | 0.595369i | \(-0.797006\pi\) |
0.917331 | + | 0.398126i | \(0.130339\pi\) | |||||||
\(348\) | −15.3137 | − | 26.5241i | −0.820901 | − | 1.42184i | ||||
\(349\) | 9.24264 | + | 16.0087i | 0.494747 | + | 0.856927i | 0.999982 | − | 0.00605481i | \(-0.00192732\pi\) |
−0.505234 | + | 0.862982i | \(0.668594\pi\) | |||||||
\(350\) | −11.6569 | −0.623085 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.41421 | 0.288579 | ||||||||
\(353\) | 7.41421 | + | 12.8418i | 0.394619 | + | 0.683500i | 0.993052 | − | 0.117673i | \(-0.0375433\pi\) |
−0.598434 | + | 0.801172i | \(0.704210\pi\) | |||||||
\(354\) | −3.00000 | − | 5.19615i | −0.159448 | − | 0.276172i | ||||
\(355\) | −5.94975 | + | 10.3053i | −0.315780 | + | 0.546947i | ||||
\(356\) | −22.9706 | −1.21744 | ||||||||
\(357\) | −2.82843 | + | 4.89898i | −0.149696 | + | 0.259281i | ||||
\(358\) | −6.82843 | + | 11.8272i | −0.360894 | + | 0.625086i | ||||
\(359\) | 8.10051 | 0.427528 | 0.213764 | − | 0.976885i | \(-0.431428\pi\) | ||||
0.213764 | + | 0.976885i | \(0.431428\pi\) | |||||||
\(360\) | −2.20711 | + | 3.82282i | −0.116325 | + | 0.201480i | ||||
\(361\) | 9.32843 | + | 16.1573i | 0.490970 | + | 0.850385i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.928932 | −0.0487563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.48528 | 0.444140 | ||||||||
\(366\) | −13.6569 | − | 23.6544i | −0.713855 | − | 1.23643i | ||||
\(367\) | −17.7782 | − | 30.7927i | −0.928013 | − | 1.60737i | −0.786642 | − | 0.617409i | \(-0.788182\pi\) |
−0.141371 | − | 0.989957i | \(-0.545151\pi\) | |||||||
\(368\) | −2.12132 | + | 3.67423i | −0.110581 | + | 0.191533i | ||||
\(369\) | −3.17157 | −0.165105 | ||||||||
\(370\) | 10.2426 | − | 17.7408i | 0.532490 | − | 0.922299i | ||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | 9.51472 | 0.493315 | ||||||||
\(373\) | 1.34315 | − | 2.32640i | 0.0695455 | − | 0.120456i | −0.829156 | − | 0.559018i | \(-0.811178\pi\) |
0.898701 | + | 0.438561i | \(0.144512\pi\) | |||||||
\(374\) | 3.41421 | + | 5.91359i | 0.176545 | + | 0.305785i | ||||
\(375\) | −0.707107 | − | 1.22474i | −0.0365148 | − | 0.0632456i | ||||
\(376\) | 21.3137 | 1.09917 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −65.9411 | −3.39165 | ||||||||
\(379\) | 14.5355 | + | 25.1763i | 0.746640 | + | 1.29322i | 0.949425 | + | 0.313995i | \(0.101668\pi\) |
−0.202784 | + | 0.979223i | \(0.564999\pi\) | |||||||
\(380\) | −1.12132 | − | 1.94218i | −0.0575225 | − | 0.0996319i | ||||
\(381\) | −4.65685 | + | 8.06591i | −0.238578 | + | 0.413229i | ||||
\(382\) | 5.65685 | 0.289430 | ||||||||
\(383\) | −14.5563 | + | 25.2123i | −0.743795 | + | 1.28829i | 0.206961 | + | 0.978349i | \(0.433643\pi\) |
−0.950756 | + | 0.309941i | \(0.899691\pi\) | |||||||
\(384\) | −14.5355 | + | 25.1763i | −0.741763 | + | 1.28477i | ||||
\(385\) | −16.4853 | −0.840168 | ||||||||
\(386\) | 5.24264 | − | 9.08052i | 0.266843 | − | 0.462186i | ||||
\(387\) | −5.53553 | − | 9.58783i | −0.281387 | − | 0.487377i | ||||
\(388\) | −14.6569 | − | 25.3864i | −0.744089 | − | 1.28880i | ||||
\(389\) | 28.6274 | 1.45147 | 0.725734 | − | 0.687976i | \(-0.241500\pi\) | ||||
0.725734 | + | 0.687976i | \(0.241500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.17157 | 0.0592490 | ||||||||
\(392\) | −36.0061 | − | 62.3644i | −1.81858 | − | 3.14988i | ||||
\(393\) | −12.0000 | − | 20.7846i | −0.605320 | − | 1.04844i | ||||
\(394\) | 13.2426 | − | 22.9369i | 0.667155 | − | 1.15555i | ||||
\(395\) | 8.48528 | 0.426941 | ||||||||
\(396\) | −6.53553 | + | 11.3199i | −0.328423 | + | 0.568845i | ||||
\(397\) | 5.89949 | − | 10.2182i | 0.296087 | − | 0.512838i | −0.679150 | − | 0.733999i | \(-0.737651\pi\) |
0.975237 | + | 0.221161i | \(0.0709848\pi\) | |||||||
\(398\) | 9.65685 | 0.484054 | ||||||||
\(399\) | 2.00000 | − | 3.46410i | 0.100125 | − | 0.173422i | ||||
\(400\) | −1.50000 | − | 2.59808i | −0.0750000 | − | 0.129904i | ||||
\(401\) | −2.65685 | − | 4.60181i | −0.132677 | − | 0.229803i | 0.792031 | − | 0.610481i | \(-0.209024\pi\) |
−0.924708 | + | 0.380678i | \(0.875691\pi\) | |||||||
\(402\) | −6.82843 | −0.340571 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −2.50000 | − | 4.33013i | −0.124226 | − | 0.215166i | ||||
\(406\) | −32.9706 | − | 57.1067i | −1.63630 | − | 2.83416i | ||||
\(407\) | 14.4853 | − | 25.0892i | 0.718009 | − | 1.24363i | ||||
\(408\) | −5.17157 | −0.256031 | ||||||||
\(409\) | 3.58579 | − | 6.21076i | 0.177306 | − | 0.307103i | −0.763651 | − | 0.645629i | \(-0.776595\pi\) |
0.940957 | + | 0.338527i | \(0.109929\pi\) | |||||||
\(410\) | 3.82843 | − | 6.63103i | 0.189073 | − | 0.327483i | ||||
\(411\) | −24.4853 | −1.20777 | ||||||||
\(412\) | −27.9203 | + | 48.3594i | −1.37553 | + | 2.38250i | ||||
\(413\) | −4.24264 | − | 7.34847i | −0.208767 | − | 0.361595i | ||||
\(414\) | 1.70711 | + | 2.95680i | 0.0838997 | + | 0.145319i | ||||
\(415\) | −3.17157 | −0.155686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.34315 | −0.310625 | ||||||||
\(418\) | −2.41421 | − | 4.18154i | −0.118083 | − | 0.204526i | ||||
\(419\) | −5.41421 | − | 9.37769i | −0.264502 | − | 0.458130i | 0.702931 | − | 0.711258i | \(-0.251874\pi\) |
−0.967433 | + | 0.253127i | \(0.918541\pi\) | |||||||
\(420\) | 13.0711 | − | 22.6398i | 0.637803 | − | 1.10471i | ||||
\(421\) | 34.9706 | 1.70436 | 0.852180 | − | 0.523248i | \(-0.175280\pi\) | ||||
0.852180 | + | 0.523248i | \(0.175280\pi\) | |||||||
\(422\) | −4.00000 | + | 6.92820i | −0.194717 | + | 0.337260i | ||||
\(423\) | 2.41421 | − | 4.18154i | 0.117383 | − | 0.203313i | ||||
\(424\) | 10.9706 | 0.532778 | ||||||||
\(425\) | −0.414214 | + | 0.717439i | −0.0200923 | + | 0.0348009i | ||||
\(426\) | −20.3137 | − | 35.1844i | −0.984202 | − | 1.70469i | ||||
\(427\) | −19.3137 | − | 33.4523i | −0.934656 | − | 1.61887i | ||||
\(428\) | −36.0416 | −1.74214 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.7279 | 1.28893 | ||||||||
\(431\) | 20.1924 | + | 34.9742i | 0.972633 | + | 1.68465i | 0.687534 | + | 0.726152i | \(0.258693\pi\) |
0.285099 | + | 0.958498i | \(0.407974\pi\) | |||||||
\(432\) | −8.48528 | − | 14.6969i | −0.408248 | − | 0.707107i | ||||
\(433\) | −3.82843 | + | 6.63103i | −0.183982 | + | 0.318667i | −0.943233 | − | 0.332131i | \(-0.892232\pi\) |
0.759251 | + | 0.650798i | \(0.225566\pi\) | |||||||
\(434\) | 20.4853 | 0.983325 | ||||||||
\(435\) | 4.00000 | − | 6.92820i | 0.191785 | − | 0.332182i | ||||
\(436\) | −3.82843 | + | 6.63103i | −0.183348 | + | 0.317569i | ||||
\(437\) | −0.828427 | −0.0396290 | ||||||||
\(438\) | −14.4853 | + | 25.0892i | −0.692134 | + | 1.19881i | ||||
\(439\) | −0.485281 | − | 0.840532i | −0.0231612 | − | 0.0401164i | 0.854212 | − | 0.519924i | \(-0.174040\pi\) |
−0.877374 | + | 0.479808i | \(0.840706\pi\) | |||||||
\(440\) | −7.53553 | − | 13.0519i | −0.359242 | − | 0.622226i | ||||
\(441\) | −16.3137 | −0.776843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.41421 | −0.447283 | −0.223641 | − | 0.974671i | \(-0.571794\pi\) | ||||
−0.223641 | + | 0.974671i | \(0.571794\pi\) | |||||||
\(444\) | 22.9706 | + | 39.7862i | 1.09013 | + | 1.88817i | ||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | 11.4853 | − | 19.8931i | 0.543844 | − | 0.941965i | ||||
\(447\) | −16.4853 | −0.779727 | ||||||||
\(448\) | −23.7279 | + | 41.0980i | −1.12104 | + | 1.94170i | ||||
\(449\) | −16.5563 | + | 28.6764i | −0.781342 | + | 1.35332i | 0.149817 | + | 0.988714i | \(0.452131\pi\) |
−0.931160 | + | 0.364611i | \(0.881202\pi\) | |||||||
\(450\) | −2.41421 | −0.113807 | ||||||||
\(451\) | 5.41421 | − | 9.37769i | 0.254945 | − | 0.441578i | ||||
\(452\) | 16.8995 | + | 29.2708i | 0.794885 | + | 1.37678i | ||||
\(453\) | −6.89949 | − | 11.9503i | −0.324167 | − | 0.561473i | ||||
\(454\) | 39.4558 | 1.85175 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.65685 | 0.171248 | ||||||||
\(457\) | −9.00000 | − | 15.5885i | −0.421002 | − | 0.729197i | 0.575036 | − | 0.818128i | \(-0.304988\pi\) |
−0.996038 | + | 0.0889312i | \(0.971655\pi\) | |||||||
\(458\) | −5.82843 | − | 10.0951i | −0.272345 | − | 0.471715i | ||||
\(459\) | −2.34315 | + | 4.05845i | −0.109369 | + | 0.189432i | ||||
\(460\) | −5.41421 | −0.252439 | ||||||||
\(461\) | 4.75736 | − | 8.23999i | 0.221572 | − | 0.383775i | −0.733713 | − | 0.679459i | \(-0.762214\pi\) |
0.955286 | + | 0.295685i | \(0.0955478\pi\) | |||||||
\(462\) | 28.1421 | − | 48.7436i | 1.30929 | − | 2.26776i | ||||
\(463\) | 4.34315 | 0.201843 | 0.100922 | − | 0.994894i | \(-0.467821\pi\) | ||||
0.100922 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(464\) | 8.48528 | − | 14.6969i | 0.393919 | − | 0.682288i | ||||
\(465\) | 1.24264 | + | 2.15232i | 0.0576261 | + | 0.0998113i | ||||
\(466\) | 24.8995 | + | 43.1272i | 1.15345 | + | 1.99783i | ||||
\(467\) | −13.4142 | −0.620736 | −0.310368 | − | 0.950617i | \(-0.600452\pi\) | ||||
−0.310368 | + | 0.950617i | \(0.600452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.65685 | −0.445912 | ||||||||
\(470\) | 5.82843 | + | 10.0951i | 0.268845 | + | 0.465654i | ||||
\(471\) | 12.7279 | + | 22.0454i | 0.586472 | + | 1.01580i | ||||
\(472\) | 3.87868 | − | 6.71807i | 0.178531 | − | 0.309224i | ||||
\(473\) | 37.7990 | 1.73800 | ||||||||
\(474\) | −14.4853 | + | 25.0892i | −0.665331 | + | 1.15239i | ||||
\(475\) | 0.292893 | − | 0.507306i | 0.0134389 | − | 0.0232768i | ||||
\(476\) | −15.3137 | −0.701903 | ||||||||
\(477\) | 1.24264 | − | 2.15232i | 0.0568966 | − | 0.0985478i | ||||
\(478\) | −4.12132 | − | 7.13834i | −0.188505 | − | 0.326500i | ||||
\(479\) | −15.3640 | − | 26.6112i | −0.701997 | − | 1.21589i | −0.967764 | − | 0.251858i | \(-0.918959\pi\) |
0.265767 | − | 0.964037i | \(-0.414375\pi\) | |||||||
\(480\) | −2.24264 | −0.102362 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.9706 | 1.59287 | ||||||||
\(483\) | −4.82843 | − | 8.36308i | −0.219701 | − | 0.380533i | ||||
\(484\) | −1.25736 | − | 2.17781i | −0.0571527 | − | 0.0989914i | ||||
\(485\) | 3.82843 | − | 6.63103i | 0.173840 | − | 0.301100i | ||||
\(486\) | −23.8995 | −1.08410 | ||||||||
\(487\) | −5.48528 | + | 9.50079i | −0.248562 | + | 0.430522i | −0.963127 | − | 0.269047i | \(-0.913291\pi\) |
0.714565 | + | 0.699569i | \(0.246625\pi\) | |||||||
\(488\) | 17.6569 | − | 30.5826i | 0.799288 | − | 1.38441i | ||||
\(489\) | 26.8284 | 1.21322 | ||||||||
\(490\) | 19.6924 | − | 34.1082i | 0.889611 | − | 1.54085i | ||||
\(491\) | −2.58579 | − | 4.47871i | −0.116695 | − | 0.202122i | 0.801761 | − | 0.597645i | \(-0.203897\pi\) |
−0.918456 | + | 0.395523i | \(0.870563\pi\) | |||||||
\(492\) | 8.58579 | + | 14.8710i | 0.387077 | + | 0.670437i | ||||
\(493\) | −4.68629 | −0.211060 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.41421 | −0.153457 | ||||||||
\(496\) | 2.63604 | + | 4.56575i | 0.118362 | + | 0.205008i | ||||
\(497\) | −28.7279 | − | 49.7582i | −1.28862 | − | 2.23196i | ||||
\(498\) | 5.41421 | − | 9.37769i | 0.242617 | − | 0.420224i | ||||
\(499\) | −41.5563 | −1.86032 | −0.930159 | − | 0.367157i | \(-0.880331\pi\) | ||||
−0.930159 | + | 0.367157i | \(0.880331\pi\) | |||||||
\(500\) | 1.91421 | − | 3.31552i | 0.0856062 | − | 0.148274i | ||||
\(501\) | 2.24264 | − | 3.88437i | 0.100194 | − | 0.173541i | ||||
\(502\) | 47.7990 | 2.13337 | ||||||||
\(503\) | −18.9497 | + | 32.8219i | −0.844927 | + | 1.46346i | 0.0407567 | + | 0.999169i | \(0.487023\pi\) |
−0.885684 | + | 0.464288i | \(0.846310\pi\) | |||||||
\(504\) | −10.6569 | − | 18.4582i | −0.474694 | − | 0.822194i | ||||
\(505\) | −1.82843 | − | 3.16693i | −0.0813639 | − | 0.140926i | ||||
\(506\) | −11.6569 | −0.518210 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.2132 | −1.11866 | ||||||||
\(509\) | 20.5563 | + | 35.6046i | 0.911144 | + | 1.57815i | 0.812451 | + | 0.583030i | \(0.198133\pi\) |
0.0986936 | + | 0.995118i | \(0.468534\pi\) | |||||||
\(510\) | −1.41421 | − | 2.44949i | −0.0626224 | − | 0.108465i | ||||
\(511\) | −20.4853 | + | 35.4815i | −0.906215 | + | 1.56961i | ||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | 1.65685 | − | 2.86976i | 0.0731519 | − | 0.126703i | ||||
\(514\) | −33.3848 | + | 57.8241i | −1.47254 | + | 2.55051i | ||||
\(515\) | −14.5858 | −0.642727 | ||||||||
\(516\) | −29.9706 | + | 51.9105i | −1.31938 | + | 2.28523i | ||||
\(517\) | 8.24264 | + | 14.2767i | 0.362511 | + | 0.627887i | ||||
\(518\) | 49.4558 | + | 85.6600i | 2.17297 | + | 3.76369i | ||||
\(519\) | −23.7990 | −1.04466 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.6569 | −0.773561 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(522\) | −6.82843 | − | 11.8272i | −0.298872 | − | 0.517662i | ||||
\(523\) | 9.87868 | + | 17.1104i | 0.431965 | + | 0.748184i | 0.997042 | − | 0.0768531i | \(-0.0244872\pi\) |
−0.565078 | + | 0.825038i | \(0.691154\pi\) | |||||||
\(524\) | 32.4853 | − | 56.2662i | 1.41913 | − | 2.45800i | ||||
\(525\) | 6.82843 | 0.298017 | ||||||||
\(526\) | 12.7782 | − | 22.1324i | 0.557155 | − | 0.965021i | ||||
\(527\) | 0.727922 | − | 1.26080i | 0.0317088 | − | 0.0549212i | ||||
\(528\) | 14.4853 | 0.630391 | ||||||||
\(529\) | 10.5000 | − | 18.1865i | 0.456522 | − | 0.790719i | ||||
\(530\) | 3.00000 | + | 5.19615i | 0.130312 | + | 0.225706i | ||||
\(531\) | −0.878680 | − | 1.52192i | −0.0381314 | − | 0.0660456i | ||||
\(532\) | 10.8284 | 0.469472 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.4853 | 0.886485 | ||||||||
\(535\) | −4.70711 | − | 8.15295i | −0.203506 | − | 0.352483i | ||||
\(536\) | −4.41421 | − | 7.64564i | −0.190665 | − | 0.330241i | ||||
\(537\) | 4.00000 | − | 6.92820i | 0.172613 | − | 0.298974i | ||||
\(538\) | −61.1127 | −2.63476 | ||||||||
\(539\) | 27.8492 | − | 48.2363i | 1.19955 | − | 2.07768i | ||||
\(540\) | 10.8284 | − | 18.7554i | 0.465981 | − | 0.807103i | ||||
\(541\) | 7.17157 | 0.308330 | 0.154165 | − | 0.988045i | \(-0.450731\pi\) | ||||
0.154165 | + | 0.988045i | \(0.450731\pi\) | |||||||
\(542\) | 32.2635 | − | 55.8819i | 1.38583 | − | 2.40034i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.656854 | + | 1.13770i | 0.0281624 | + | 0.0487787i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2132 | 0.564956 | 0.282478 | − | 0.959274i | \(-0.408844\pi\) | ||||
0.282478 | + | 0.959274i | \(0.408844\pi\) | |||||||
\(548\) | −33.1421 | − | 57.4039i | −1.41576 | − | 2.45217i | ||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | 4.12132 | − | 7.13834i | 0.175734 | − | 0.304380i | ||||
\(551\) | 3.31371 | 0.141169 | ||||||||
\(552\) | 4.41421 | − | 7.64564i | 0.187881 | − | 0.325420i | ||||
\(553\) | −20.4853 | + | 35.4815i | −0.871123 | + | 1.50883i | ||||
\(554\) | −30.9706 | −1.31581 | ||||||||
\(555\) | −6.00000 | + | 10.3923i | −0.254686 | + | 0.441129i | ||||
\(556\) | −8.58579 | − | 14.8710i | −0.364118 | − | 0.630672i | ||||
\(557\) | −17.8995 | − | 31.0028i | −0.758426 | − | 1.31363i | −0.943653 | − | 0.330937i | \(-0.892635\pi\) |
0.185227 | − | 0.982696i | \(-0.440698\pi\) | |||||||
\(558\) | 4.24264 | 0.179605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.4853 | 0.612115 | ||||||||
\(561\) | −2.00000 | − | 3.46410i | −0.0844401 | − | 0.146254i | ||||
\(562\) | 26.3137 | + | 45.5767i | 1.10998 | + | 1.92254i | ||||
\(563\) | 3.87868 | − | 6.71807i | 0.163467 | − | 0.283133i | −0.772643 | − | 0.634841i | \(-0.781066\pi\) |
0.936110 | + | 0.351708i | \(0.114399\pi\) | |||||||
\(564\) | −26.1421 | −1.10078 | ||||||||
\(565\) | −4.41421 | + | 7.64564i | −0.185707 | + | 0.321655i | ||||
\(566\) | 20.1924 | − | 34.9742i | 0.848749 | − | 1.47008i | ||||
\(567\) | 24.1421 | 1.01387 | ||||||||
\(568\) | 26.2635 | − | 45.4896i | 1.10199 | − | 1.90870i | ||||
\(569\) | 5.17157 | + | 8.95743i | 0.216804 | + | 0.375515i | 0.953829 | − | 0.300350i | \(-0.0971035\pi\) |
−0.737025 | + | 0.675865i | \(0.763770\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | −11.5147 | −0.481876 | −0.240938 | − | 0.970541i | \(-0.577455\pi\) | ||||
−0.240938 | + | 0.970541i | \(0.577455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.31371 | −0.138432 | ||||||||
\(574\) | 18.4853 | + | 32.0174i | 0.771561 | + | 1.33638i | ||||
\(575\) | −0.707107 | − | 1.22474i | −0.0294884 | − | 0.0510754i | ||||
\(576\) | −4.91421 | + | 8.51167i | −0.204759 | + | 0.354653i | ||||
\(577\) | 34.8284 | 1.44993 | 0.724963 | − | 0.688788i | \(-0.241857\pi\) | ||||
0.724963 | + | 0.688788i | \(0.241857\pi\) | |||||||
\(578\) | 19.6924 | − | 34.1082i | 0.819095 | − | 1.41871i | ||||
\(579\) | −3.07107 | + | 5.31925i | −0.127629 | + | 0.221060i | ||||
\(580\) | 21.6569 | 0.899252 | ||||||||
\(581\) | 7.65685 | − | 13.2621i | 0.317660 | − | 0.550203i | ||||
\(582\) | 13.0711 | + | 22.6398i | 0.541813 | + | 0.938448i | ||||
\(583\) | 4.24264 | + | 7.34847i | 0.175712 | + | 0.304342i | ||||
\(584\) | −37.4558 | −1.54993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −63.1127 | −2.60716 | ||||||||
\(587\) | 10.1716 | + | 17.6177i | 0.419826 | + | 0.727160i | 0.995922 | − | 0.0902226i | \(-0.0287579\pi\) |
−0.576096 | + | 0.817382i | \(0.695425\pi\) | |||||||
\(588\) | 44.1630 | + | 76.4925i | 1.82125 | + | 3.15450i | ||||
\(589\) | −0.514719 | + | 0.891519i | −0.0212086 | + | 0.0367344i | ||||
\(590\) | 4.24264 | 0.174667 | ||||||||
\(591\) | −7.75736 | + | 13.4361i | −0.319095 | + | 0.552689i | ||||
\(592\) | −12.7279 | + | 22.0454i | −0.523114 | + | 0.906061i | ||||
\(593\) | 24.6274 | 1.01133 | 0.505663 | − | 0.862731i | \(-0.331248\pi\) | ||||
0.505663 | + | 0.862731i | \(0.331248\pi\) | |||||||
\(594\) | 23.3137 | − | 40.3805i | 0.956573 | − | 1.65683i | ||||
\(595\) | −2.00000 | − | 3.46410i | −0.0819920 | − | 0.142014i | ||||
\(596\) | −22.3137 | − | 38.6485i | −0.914005 | − | 1.58310i | ||||
\(597\) | −5.65685 | −0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4558 | 1.04010 | 0.520049 | − | 0.854137i | \(-0.325914\pi\) | ||||
0.520049 | + | 0.854137i | \(0.325914\pi\) | |||||||
\(600\) | 3.12132 | + | 5.40629i | 0.127427 | + | 0.220711i | ||||
\(601\) | 22.3137 | + | 38.6485i | 0.910195 | + | 1.57650i | 0.813788 | + | 0.581162i | \(0.197402\pi\) |
0.0964075 | + | 0.995342i | \(0.469265\pi\) | |||||||
\(602\) | −64.5269 | + | 111.764i | −2.62992 | + | 4.55516i | ||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 18.6777 | − | 32.3507i | 0.759984 | − | 1.31633i | ||||
\(605\) | 0.328427 | − | 0.568852i | 0.0133525 | − | 0.0231271i | ||||
\(606\) | 12.4853 | 0.507180 | ||||||||
\(607\) | −15.8787 | + | 27.5027i | −0.644496 | + | 1.11630i | 0.339922 | + | 0.940454i | \(0.389599\pi\) |
−0.984418 | + | 0.175846i | \(0.943734\pi\) | |||||||
\(608\) | −0.464466 | − | 0.804479i | −0.0188366 | − | 0.0326259i | ||||
\(609\) | 19.3137 | + | 33.4523i | 0.782631 | + | 1.35556i | ||||
\(610\) | 19.3137 | 0.781989 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.17157 | −0.128203 | ||||||||
\(613\) | −7.34315 | − | 12.7187i | −0.296587 | − | 0.513704i | 0.678766 | − | 0.734355i | \(-0.262515\pi\) |
−0.975353 | + | 0.220651i | \(0.929182\pi\) | |||||||
\(614\) | 29.9706 | + | 51.9105i | 1.20951 | + | 2.09494i | ||||
\(615\) | −2.24264 | + | 3.88437i | −0.0904320 | + | 0.156633i | ||||
\(616\) | 72.7696 | 2.93197 | ||||||||
\(617\) | 5.48528 | − | 9.50079i | 0.220829 | − | 0.382487i | −0.734231 | − | 0.678900i | \(-0.762457\pi\) |
0.955060 | + | 0.296413i | \(0.0957904\pi\) | |||||||
\(618\) | 24.8995 | − | 43.1272i | 1.00160 | − | 1.73483i | ||||
\(619\) | −1.75736 | −0.0706342 | −0.0353171 | − | 0.999376i | \(-0.511244\pi\) | ||||
−0.0353171 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(620\) | −3.36396 | + | 5.82655i | −0.135100 | + | 0.234000i | ||||
\(621\) | −4.00000 | − | 6.92820i | −0.160514 | − | 0.278019i | ||||
\(622\) | −10.2426 | − | 17.7408i | −0.410692 | − | 0.711340i | ||||
\(623\) | 28.9706 | 1.16068 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.82843 | + | 10.0951i | 0.232951 | + | 0.403483i | ||||
\(627\) | 1.41421 | + | 2.44949i | 0.0564782 | + | 0.0978232i | ||||
\(628\) | −34.4558 | + | 59.6793i | −1.37494 | + | 2.38146i | ||||
\(629\) | 7.02944 | 0.280282 | ||||||||
\(630\) | 5.82843 | − | 10.0951i | 0.232210 | − | 0.402200i | ||||
\(631\) | −4.87868 | + | 8.45012i | −0.194217 | + | 0.336394i | −0.946644 | − | 0.322282i | \(-0.895550\pi\) |
0.752426 | + | 0.658676i | \(0.228883\pi\) | |||||||
\(632\) | −37.4558 | −1.48991 | ||||||||
\(633\) | 2.34315 | − | 4.05845i | 0.0931317 | − | 0.161309i | ||||
\(634\) | −2.58579 | − | 4.47871i | −0.102695 | − | 0.177872i | ||||
\(635\) | −3.29289 | − | 5.70346i | −0.130674 | − | 0.226335i | ||||
\(636\) | −13.4558 | −0.533559 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 46.6274 | 1.84600 | ||||||||
\(639\) | −5.94975 | − | 10.3053i | −0.235368 | − | 0.407670i | ||||
\(640\) | −10.2782 | − | 17.8023i | −0.406281 | − | 0.703699i | ||||
\(641\) | −23.8284 | + | 41.2720i | −0.941166 | + | 1.63015i | −0.177915 | + | 0.984046i | \(0.556935\pi\) |
−0.763251 | + | 0.646102i | \(0.776398\pi\) | |||||||
\(642\) | 32.1421 | 1.26855 | ||||||||
\(643\) | 4.75736 | − | 8.23999i | 0.187612 | − | 0.324953i | −0.756842 | − | 0.653598i | \(-0.773259\pi\) |
0.944454 | + | 0.328645i | \(0.106592\pi\) | |||||||
\(644\) | 13.0711 | − | 22.6398i | 0.515072 | − | 0.892131i | ||||
\(645\) | −15.6569 | −0.616488 | ||||||||
\(646\) | 0.585786 | − | 1.01461i | 0.0230475 | − | 0.0399194i | ||||
\(647\) | −4.70711 | − | 8.15295i | −0.185055 | − | 0.320525i | 0.758540 | − | 0.651627i | \(-0.225913\pi\) |
−0.943595 | + | 0.331101i | \(0.892580\pi\) | |||||||
\(648\) | 11.0355 | + | 19.1141i | 0.433517 | + | 0.750873i | ||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 36.3137 | + | 62.8972i | 1.42215 | + | 2.46324i | ||||
\(653\) | −23.4853 | − | 40.6777i | −0.919050 | − | 1.59184i | −0.800861 | − | 0.598850i | \(-0.795624\pi\) |
−0.118189 | − | 0.992991i | \(-0.537709\pi\) | |||||||
\(654\) | 3.41421 | − | 5.91359i | 0.133506 | − | 0.231240i | ||||
\(655\) | 16.9706 | 0.663095 | ||||||||
\(656\) | −4.75736 | + | 8.23999i | −0.185744 | + | 0.321717i | ||||
\(657\) | −4.24264 | + | 7.34847i | −0.165521 | + | 0.286691i | ||||
\(658\) | −56.2843 | −2.19419 | ||||||||
\(659\) | −8.92893 | + | 15.4654i | −0.347822 | + | 0.602445i | −0.985862 | − | 0.167558i | \(-0.946412\pi\) |
0.638040 | + | 0.770003i | \(0.279745\pi\) | |||||||
\(660\) | 9.24264 | + | 16.0087i | 0.359769 | + | 0.623139i | ||||
\(661\) | 14.7990 | + | 25.6326i | 0.575614 | + | 0.996993i | 0.995975 | + | 0.0896356i | \(0.0285702\pi\) |
−0.420361 | + | 0.907357i | \(0.638096\pi\) | |||||||
\(662\) | 62.8701 | 2.44351 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.0000 | 0.543305 | ||||||||
\(665\) | 1.41421 | + | 2.44949i | 0.0548408 | + | 0.0949871i | ||||
\(666\) | 10.2426 | + | 17.7408i | 0.396894 | + | 0.687441i | ||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 12.1421 | 0.469793 | ||||||||
\(669\) | −6.72792 | + | 11.6531i | −0.260116 | + | 0.450535i | ||||
\(670\) | 2.41421 | − | 4.18154i | 0.0932692 | − | 0.161547i | ||||
\(671\) | 27.3137 | 1.05443 | ||||||||
\(672\) | 5.41421 | − | 9.37769i | 0.208858 | − | 0.361752i | ||||
\(673\) | −3.24264 | − | 5.61642i | −0.124995 | − | 0.216497i | 0.796736 | − | 0.604327i | \(-0.206558\pi\) |
−0.921731 | + | 0.387830i | \(0.873225\pi\) | |||||||
\(674\) | −15.4853 | − | 26.8213i | −0.596471 | − | 1.03312i | ||||
\(675\) | 5.65685 | 0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.1421 | −0.774125 | −0.387063 | − | 0.922053i | \(-0.626510\pi\) | ||||
−0.387063 | + | 0.922053i | \(0.626510\pi\) | |||||||
\(678\) | −15.0711 | − | 26.1039i | −0.578801 | − | 1.00251i | ||||
\(679\) | 18.4853 | + | 32.0174i | 0.709400 | + | 1.22872i | ||||
\(680\) | 1.82843 | − | 3.16693i | 0.0701170 | − | 0.121446i | ||||
\(681\) | −23.1127 | −0.885681 | ||||||||
\(682\) | −7.24264 | + | 12.5446i | −0.277335 | + | 0.480358i | ||||
\(683\) | 5.34315 | − | 9.25460i | 0.204450 | − | 0.354117i | −0.745507 | − | 0.666497i | \(-0.767793\pi\) |
0.949957 | + | 0.312380i | \(0.101126\pi\) | |||||||
\(684\) | 2.24264 | 0.0857495 | ||||||||
\(685\) | 8.65685 | − | 14.9941i | 0.330761 | − | 0.572896i | ||||
\(686\) | 54.2843 | + | 94.0231i | 2.07258 | + | 3.58982i | ||||
\(687\) | 3.41421 | + | 5.91359i | 0.130260 | + | 0.225618i | ||||
\(688\) | −33.2132 | −1.26624 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.82843 | 0.183815 | ||||||||
\(691\) | 3.46447 | + | 6.00063i | 0.131795 | + | 0.228275i | 0.924368 | − | 0.381501i | \(-0.124593\pi\) |
−0.792574 | + | 0.609776i | \(0.791259\pi\) | |||||||
\(692\) | −32.2132 | − | 55.7949i | −1.22456 | − | 2.12100i | ||||
\(693\) | 8.24264 | − | 14.2767i | 0.313112 | − | 0.542326i | ||||
\(694\) | −10.2426 | −0.388805 | ||||||||
\(695\) | 2.24264 | − | 3.88437i | 0.0850682 | − | 0.147342i | ||||
\(696\) | −17.6569 | + | 30.5826i | −0.669281 | + | 1.15923i | ||||
\(697\) | 2.62742 | 0.0995205 | ||||||||
\(698\) | 22.3137 | − | 38.6485i | 0.844586 | − | 1.46287i | ||||
\(699\) | −14.5858 | − | 25.2633i | −0.551685 | − | 0.955547i | ||||
\(700\) | 9.24264 | + | 16.0087i | 0.349339 | + | 0.605073i | ||||
\(701\) | 14.6863 | 0.554694 | 0.277347 | − | 0.960770i | \(-0.410545\pi\) | ||||
0.277347 | + | 0.960770i | \(0.410545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.97056 | −0.187468 | ||||||||
\(704\) | −16.7782 | − | 29.0607i | −0.632351 | − | 1.09526i | ||||
\(705\) | −3.41421 | − | 5.91359i | −0.128587 | − | 0.222719i | ||||
\(706\) | 17.8995 | − | 31.0028i | 0.673656 | − | 1.16681i | ||||
\(707\) | 17.6569 | 0.664054 | ||||||||
\(708\) | −4.75736 | + | 8.23999i | −0.178793 | + | 0.309678i | ||||
\(709\) | 22.5563 | − | 39.0687i | 0.847121 | − | 1.46726i | −0.0366445 | − | 0.999328i | \(-0.511667\pi\) |
0.883766 | − | 0.467929i | \(-0.155000\pi\) | |||||||
\(710\) | 28.7279 | 1.07814 | ||||||||
\(711\) | −4.24264 | + | 7.34847i | −0.159111 | + | 0.275589i | ||||
\(712\) | 13.2426 | + | 22.9369i | 0.496289 | + | 0.859598i | ||||
\(713\) | 1.24264 | + | 2.15232i | 0.0465373 | + | 0.0806049i | ||||
\(714\) | 13.6569 | 0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.6569 | 0.809355 | ||||||||
\(717\) | 2.41421 | + | 4.18154i | 0.0901605 | + | 0.156162i | ||||
\(718\) | −9.77817 | − | 16.9363i | −0.364918 | − | 0.632057i | ||||
\(719\) | −14.4853 | + | 25.0892i | −0.540210 | + | 0.935671i | 0.458682 | + | 0.888601i | \(0.348322\pi\) |
−0.998892 | + | 0.0470703i | \(0.985012\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 35.2132 | − | 60.9911i | 1.31141 | − | 2.27143i | ||||
\(722\) | 22.5208 | − | 39.0072i | 0.838138 | − | 1.45170i | ||||
\(723\) | −20.4853 | −0.761856 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.82843 | + | 4.89898i | 0.105045 | + | 0.181944i | ||||
\(726\) | 1.12132 | + | 1.94218i | 0.0416161 | + | 0.0720812i | ||||
\(727\) | −51.3553 | −1.90466 | −0.952332 | − | 0.305063i | \(-0.901322\pi\) | ||||
−0.952332 | + | 0.305063i | \(0.901322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −10.2426 | − | 17.7408i | −0.379097 | − | 0.656616i | ||||
\(731\) | 4.58579 | + | 7.94282i | 0.169611 | + | 0.293776i | ||||
\(732\) | −21.6569 | + | 37.5108i | −0.800460 | + | 1.38644i | ||||
\(733\) | −21.3137 | −0.787240 | −0.393620 | − | 0.919273i | \(-0.628777\pi\) | ||||
−0.393620 | + | 0.919273i | \(0.628777\pi\) | |||||||
\(734\) | −42.9203 | + | 74.3402i | −1.58422 | + | 2.74395i | ||||
\(735\) | −11.5355 | + | 19.9801i | −0.425495 | + | 0.736978i | ||||
\(736\) | −2.24264 | −0.0826648 | ||||||||
\(737\) | 3.41421 | − | 5.91359i | 0.125764 | − | 0.217830i | ||||
\(738\) | 3.82843 | + | 6.63103i | 0.140926 | + | 0.244092i | ||||
\(739\) | 2.63604 | + | 4.56575i | 0.0969683 | + | 0.167954i | 0.910428 | − | 0.413667i | \(-0.135752\pi\) |
−0.813460 | + | 0.581621i | \(0.802419\pi\) | |||||||
\(740\) | −32.4853 | −1.19418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.9706 | −1.06354 | ||||||||
\(743\) | −10.7574 | − | 18.6323i | −0.394649 | − | 0.683553i | 0.598407 | − | 0.801192i | \(-0.295801\pi\) |
−0.993056 | + | 0.117640i | \(0.962467\pi\) | |||||||
\(744\) | −5.48528 | − | 9.50079i | −0.201100 | − | 0.348316i | ||||
\(745\) | 5.82843 | − | 10.0951i | 0.213537 | − | 0.369857i | ||||
\(746\) | −6.48528 | −0.237443 | ||||||||
\(747\) | 1.58579 | − | 2.74666i | 0.0580209 | − | 0.100495i | ||||
\(748\) | 5.41421 | − | 9.37769i | 0.197963 | − | 0.342882i | ||||
\(749\) | 45.4558 | 1.66092 | ||||||||
\(750\) | −1.70711 | + | 2.95680i | −0.0623347 | + | 0.107967i | ||||
\(751\) | 13.7574 | + | 23.8284i | 0.502013 | + | 0.869512i | 0.999997 | + | 0.00232617i | \(0.000740444\pi\) |
−0.497984 | + | 0.867186i | \(0.665926\pi\) | |||||||
\(752\) | −7.24264 | − | 12.5446i | −0.264112 | − | 0.457455i | ||||
\(753\) | −28.0000 | −1.02038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.75736 | 0.355107 | ||||||||
\(756\) | 52.2843 | + | 90.5590i | 1.90156 | + | 3.29360i | ||||
\(757\) | 12.0711 | + | 20.9077i | 0.438730 | + | 0.759903i | 0.997592 | − | 0.0693577i | \(-0.0220950\pi\) |
−0.558861 | + | 0.829261i | \(0.688762\pi\) | |||||||
\(758\) | 35.0919 | − | 60.7809i | 1.27459 | − | 2.20766i | ||||
\(759\) | 6.82843 | 0.247856 | ||||||||
\(760\) | −1.29289 | + | 2.23936i | −0.0468982 | + | 0.0812300i | ||||
\(761\) | 4.31371 | − | 7.47156i | 0.156372 | − | 0.270844i | −0.777186 | − | 0.629271i | \(-0.783354\pi\) |
0.933558 | + | 0.358427i | \(0.116687\pi\) | |||||||
\(762\) | 22.4853 | 0.814556 | ||||||||
\(763\) | 4.82843 | − | 8.36308i | 0.174801 | − | 0.302764i | ||||
\(764\) | −4.48528 | − | 7.76874i | −0.162272 | − | 0.281063i | ||||
\(765\) | −0.414214 | − | 0.717439i | −0.0149759 | − | 0.0259391i | ||||
\(766\) | 70.2843 | 2.53947 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 42.3848 | 1.52943 | ||||||||
\(769\) | −11.4853 | − | 19.8931i | −0.414170 | − | 0.717363i | 0.581171 | − | 0.813781i | \(-0.302595\pi\) |
−0.995341 | + | 0.0964182i | \(0.969261\pi\) | |||||||
\(770\) | 19.8995 | + | 34.4669i | 0.717128 | + | 1.24210i | ||||
\(771\) | 19.5563 | − | 33.8726i | 0.704305 | − | 1.21989i | ||||
\(772\) | −16.6274 | −0.598434 | ||||||||
\(773\) | −11.0711 | + | 19.1757i | −0.398199 | + | 0.689700i | −0.993504 | − | 0.113799i | \(-0.963698\pi\) |
0.595305 | + | 0.803500i | \(0.297031\pi\) | |||||||
\(774\) | −13.3640 | + | 23.1471i | −0.480358 | + | 0.832004i | ||||
\(775\) | −1.75736 | −0.0631262 | ||||||||
\(776\) | −16.8995 | + | 29.2708i | −0.606657 | + | 1.05076i | ||||
\(777\) | −28.9706 | − | 50.1785i | −1.03931 | − | 1.80014i | ||||
\(778\) | −34.5563 | − | 59.8534i | −1.23891 | − | 2.14585i | ||||
\(779\) | −1.85786 | −0.0665649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.6274 | 1.45376 | ||||||||
\(782\) | −1.41421 | − | 2.44949i | −0.0505722 | − | 0.0875936i | ||||
\(783\) | 16.0000 | + | 27.7128i | 0.571793 | + | 0.990375i | ||||
\(784\) | −24.4706 | + | 42.3843i | −0.873949 | + | 1.51372i | ||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −28.9706 | + | 50.1785i | −1.03335 | + | 1.78981i | ||||
\(787\) | 11.2426 | − | 19.4728i | 0.400757 | − | 0.694131i | −0.593061 | − | 0.805158i | \(-0.702081\pi\) |
0.993817 | + | 0.111027i | \(0.0354139\pi\) | |||||||
\(788\) | −42.0000 | −1.49619 | ||||||||
\(789\) | −7.48528 | + | 12.9649i | −0.266483 | + | 0.461562i | ||||
\(790\) | −10.2426 | − | 17.7408i | −0.364417 | − | 0.631188i | ||||
\(791\) | −21.3137 | − | 36.9164i | −0.757828 | − | 1.31260i | ||||
\(792\) | 15.0711 | 0.535527 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −28.4853 | −1.01090 | ||||||||
\(795\) | −1.75736 | − | 3.04384i | −0.0623271 | − | 0.107954i | ||||
\(796\) | −7.65685 | − | 13.2621i | −0.271390 | − | 0.470061i | ||||
\(797\) | 11.4853 | − | 19.8931i | 0.406830 | − | 0.704649i | −0.587703 | − | 0.809077i | \(-0.699968\pi\) |
0.994533 | + | 0.104427i | \(0.0333010\pi\) | |||||||
\(798\) | −9.65685 | −0.341849 | ||||||||
\(799\) | −2.00000 | + | 3.46410i | −0.0707549 | + | 0.122551i | ||||
\(800\) | 0.792893 | − | 1.37333i | 0.0280330 | − | 0.0485546i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | −6.41421 | + | 11.1097i | −0.226494 | + | 0.392299i | ||||
\(803\) | −14.4853 | − | 25.0892i | −0.511174 | − | 0.885380i | ||||
\(804\) | 5.41421 | + | 9.37769i | 0.190945 | + | 0.330726i | ||||
\(805\) | 6.82843 | 0.240670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.7990 | 1.26018 | ||||||||
\(808\) | 8.07107 | + | 13.9795i | 0.283939 | + | 0.491797i | ||||
\(809\) | −22.6274 | − | 39.1918i | −0.795538 | − | 1.37791i | −0.922497 | − | 0.386004i | \(-0.873855\pi\) |
0.126960 | − | 0.991908i | \(-0.459478\pi\) | |||||||
\(810\) | −6.03553 | + | 10.4539i | −0.212067 | + | 0.367311i | ||||
\(811\) | 28.3848 | 0.996724 | 0.498362 | − | 0.866969i | \(-0.333935\pi\) | ||||
0.498362 | + | 0.866969i | \(0.333935\pi\) | |||||||
\(812\) | −52.2843 | + | 90.5590i | −1.83482 | + | 3.17800i | ||||
\(813\) | −18.8995 | + | 32.7349i | −0.662834 | + | 1.14806i | ||||
\(814\) | −69.9411 | −2.45144 | ||||||||
\(815\) | −9.48528 | + | 16.4290i | −0.332255 | + | 0.575482i | ||||
\(816\) | 1.75736 | + | 3.04384i | 0.0615199 | + | 0.106556i | ||||
\(817\) | −3.24264 | − | 5.61642i | −0.113446 | − | 0.196494i | ||||
\(818\) | −17.3137 | −0.605360 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.1421 | −0.424022 | ||||||||
\(821\) | −25.6274 | − | 44.3880i | −0.894403 | − | 1.54915i | −0.834542 | − | 0.550945i | \(-0.814267\pi\) |
−0.0598613 | − | 0.998207i | \(-0.519066\pi\) | |||||||
\(822\) | 29.5563 | + | 51.1931i | 1.03090 | + | 1.78556i | ||||
\(823\) | 1.19239 | − | 2.06528i | 0.0415640 | − | 0.0719910i | −0.844495 | − | 0.535563i | \(-0.820099\pi\) |
0.886059 | + | 0.463572i | \(0.153433\pi\) | |||||||
\(824\) | 64.3848 | 2.24295 | ||||||||
\(825\) | −2.41421 | + | 4.18154i | −0.0840521 | + | 0.145583i | ||||
\(826\) | −10.2426 | + | 17.7408i | −0.356387 | + | 0.617280i | ||||
\(827\) | −56.1421 | −1.95225 | −0.976127 | − | 0.217202i | \(-0.930307\pi\) | ||||
−0.976127 | + | 0.217202i | \(0.930307\pi\) | |||||||
\(828\) | 2.70711 | − | 4.68885i | 0.0940785 | − | 0.162949i | ||||
\(829\) | −20.4853 | − | 35.4815i | −0.711483 | − | 1.23233i | −0.964300 | − | 0.264811i | \(-0.914690\pi\) |
0.252817 | − | 0.967514i | \(-0.418643\pi\) | |||||||
\(830\) | 3.82843 | + | 6.63103i | 0.132887 | + | 0.230166i | ||||
\(831\) | 18.1421 | 0.629344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.5147 | 0.468257 | ||||||||
\(834\) | 7.65685 | + | 13.2621i | 0.265135 | + | 0.459228i | ||||
\(835\) | 1.58579 | + | 2.74666i | 0.0548784 | + | 0.0950522i | ||||
\(836\) | −3.82843 | + | 6.63103i | −0.132409 | + | 0.229339i | ||||
\(837\) | −9.94113 | −0.343616 | ||||||||
\(838\) | −13.0711 | + | 22.6398i | −0.451533 | + | 0.782077i | ||||
\(839\) | 3.36396 | − | 5.82655i | 0.116137 | − | 0.201155i | −0.802097 | − | 0.597194i | \(-0.796282\pi\) |
0.918234 | + | 0.396039i | \(0.129616\pi\) | |||||||
\(840\) | −30.1421 | −1.04000 | ||||||||
\(841\) | −1.50000 | + | 2.59808i | −0.0517241 | + | 0.0895888i | ||||
\(842\) | −42.2132 | − | 73.1154i | −1.45476 | − | 2.51972i | ||||
\(843\) | −15.4142 | − | 26.6982i | −0.530894 | − | 0.919535i | ||||
\(844\) | 12.6863 | 0.436680 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.6569 | −0.400771 | ||||||||
\(847\) | 1.58579 | + | 2.74666i | 0.0544883 | + | 0.0943764i | ||||
\(848\) | −3.72792 | − | 6.45695i | −0.128017 | − | 0.221733i | ||||
\(849\) | −11.8284 | + | 20.4874i | −0.405951 | + | 0.703127i | ||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | −32.2132 | + | 55.7949i | −1.10361 | + | 1.91150i | ||||
\(853\) | 13.4558 | 0.460719 | 0.230360 | − | 0.973106i | \(-0.426010\pi\) | ||||
0.230360 | + | 0.973106i | \(0.426010\pi\) | |||||||
\(854\) | −46.6274 | + | 80.7611i | −1.59556 | + | 2.76359i | ||||
\(855\) | 0.292893 | + | 0.507306i | 0.0100167 | + | 0.0173495i | ||||
\(856\) | 20.7782 | + | 35.9889i | 0.710183 | + | 1.23007i | ||||
\(857\) | 11.6569 | 0.398191 | 0.199095 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199095 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7990 | −0.948489 | −0.474245 | − | 0.880393i | \(-0.657279\pi\) | ||||
−0.474245 | + | 0.880393i | \(0.657279\pi\) | |||||||
\(860\) | −21.1924 | − | 36.7063i | −0.722654 | − | 1.25167i | ||||
\(861\) | −10.8284 | − | 18.7554i | −0.369032 | − | 0.639182i | ||||
\(862\) | 48.7487 | − | 84.4353i | 1.66039 | − | 2.87588i | ||||
\(863\) | 31.4558 | 1.07077 | 0.535385 | − | 0.844608i | \(-0.320167\pi\) | ||||
0.535385 | + | 0.844608i | \(0.320167\pi\) | |||||||
\(864\) | 4.48528 | − | 7.76874i | 0.152592 | − | 0.264298i | ||||
\(865\) | 8.41421 | − | 14.5738i | 0.286092 | − | 0.495526i | ||||
\(866\) | 18.4853 | 0.628155 | ||||||||
\(867\) | −11.5355 | + | 19.9801i | −0.391767 | + | 0.678561i | ||||
\(868\) | −16.2426 | − | 28.1331i | −0.551311 | − | 0.954899i | ||||
\(869\) | −14.4853 | − | 25.0892i | −0.491380 | − | 0.851094i | ||||
\(870\) | −19.3137 | −0.654796 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | 3.82843 | + | 6.63103i | 0.129573 | + | 0.224426i | ||||
\(874\) | 1.00000 | + | 1.73205i | 0.0338255 | + | 0.0585875i | ||||
\(875\) | −2.41421 | + | 4.18154i | −0.0816153 | + | 0.141362i | ||||
\(876\) | 45.9411 | 1.55221 | ||||||||
\(877\) | 12.6569 | − | 21.9223i | 0.427392 | − | 0.740264i | −0.569249 | − | 0.822165i | \(-0.692766\pi\) |
0.996640 | + | 0.0819013i | \(0.0260992\pi\) | |||||||
\(878\) | −1.17157 | + | 2.02922i | −0.0395387 | + | 0.0684830i | ||||
\(879\) | 36.9706 | 1.24699 | ||||||||
\(880\) | −5.12132 | + | 8.87039i | −0.172640 | + | 0.299021i | ||||
\(881\) | −9.51472 | − | 16.4800i | −0.320559 | − | 0.555225i | 0.660044 | − | 0.751227i | \(-0.270537\pi\) |
−0.980603 | + | 0.196002i | \(0.937204\pi\) | |||||||
\(882\) | 19.6924 | + | 34.1082i | 0.663077 | + | 1.14848i | ||||
\(883\) | −23.7574 | −0.799499 | −0.399749 | − | 0.916624i | \(-0.630903\pi\) | ||||
−0.399749 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.48528 | −0.0835418 | ||||||||
\(886\) | 11.3640 | + | 19.6830i | 0.381780 | + | 0.661262i | ||||
\(887\) | 11.1924 | + | 19.3858i | 0.375804 | + | 0.650911i | 0.990447 | − | 0.137894i | \(-0.0440334\pi\) |
−0.614643 | + | 0.788805i | \(0.710700\pi\) | |||||||
\(888\) | 26.4853 | − | 45.8739i | 0.888788 | − | 1.53943i | ||||
\(889\) | 31.7990 | 1.06650 | ||||||||
\(890\) | −7.24264 | + | 12.5446i | −0.242774 | + | 0.420497i | ||||
\(891\) | −8.53553 | + | 14.7840i | −0.285951 | + | 0.495282i | ||||
\(892\) | −36.4264 | −1.21965 | ||||||||
\(893\) | 1.41421 | − | 2.44949i | 0.0473249 | − | 0.0819690i | ||||
\(894\) | 19.8995 | + | 34.4669i | 0.665539 | + | 1.15275i | ||||
\(895\) | 2.82843 | + | 4.89898i | 0.0945439 | + | 0.163755i | ||||
\(896\) | 99.2548 | 3.31587 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 79.9411 | 2.66767 | ||||||||
\(899\) | −4.97056 | − | 8.60927i | −0.165778 | − | 0.287135i | ||||
\(900\) | 1.91421 | + | 3.31552i | 0.0638071 | + | 0.110517i | ||||
\(901\) | −1.02944 | + | 1.78304i | −0.0342955 | + | 0.0594016i | ||||
\(902\) | −26.1421 | −0.870438 | ||||||||
\(903\) | 37.7990 | − | 65.4698i | 1.25787 | − | 2.17870i | ||||
\(904\) | 19.4853 | − | 33.7495i | 0.648071 | − | 1.12249i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.6569 | + | 28.8505i | −0.553387 | + | 0.958494i | ||||
\(907\) | −4.60660 | − | 7.97887i | −0.152960 | − | 0.264934i | 0.779355 | − | 0.626583i | \(-0.215547\pi\) |
−0.932314 | + | 0.361649i | \(0.882214\pi\) | |||||||
\(908\) | −31.2843 | − | 54.1859i | −1.03821 | − | 1.79822i | ||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | −1.24264 | − | 2.15232i | −0.0411479 | − | 0.0712703i | ||||
\(913\) | 5.41421 | + | 9.37769i | 0.179184 | + | 0.310356i | ||||
\(914\) | −21.7279 | + | 37.6339i | −0.718696 | + | 1.24482i | ||||
\(915\) | −11.3137 | −0.374020 | ||||||||
\(916\) | −9.24264 | + | 16.0087i | −0.305385 | + | 0.528943i | ||||
\(917\) | −40.9706 | + | 70.9631i | −1.35297 | + | 2.34341i | ||||
\(918\) | 11.3137 | 0.373408 | ||||||||
\(919\) | −0.242641 | + | 0.420266i | −0.00800398 | + | 0.0138633i | −0.870000 | − | 0.493052i | \(-0.835881\pi\) |
0.861996 | + | 0.506916i | \(0.169214\pi\) | |||||||
\(920\) | 3.12132 | + | 5.40629i | 0.102907 | + | 0.178240i | ||||
\(921\) | −17.5563 | − | 30.4085i | −0.578501 | − | 1.00199i | ||||
\(922\) | −22.9706 | −0.756495 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −89.2548 | −2.93627 | ||||||||
\(925\) | −4.24264 | − | 7.34847i | −0.139497 | − | 0.241616i | ||||
\(926\) | −5.24264 | − | 9.08052i | −0.172284 | − | 0.298404i | ||||
\(927\) | 7.29289 | − | 12.6317i | 0.239530 | − | 0.414878i | ||||
\(928\) | 8.97056 | 0.294473 | ||||||||
\(929\) | 8.41421 | − | 14.5738i | 0.276061 | − | 0.478152i | −0.694341 | − | 0.719646i | \(-0.744304\pi\) |
0.970402 | + | 0.241494i | \(0.0776374\pi\) | |||||||
\(930\) | 3.00000 | − | 5.19615i | 0.0983739 | − | 0.170389i | ||||
\(931\) | −9.55635 | −0.313197 | ||||||||
\(932\) | 39.4853 | − | 68.3905i | 1.29338 | − | 2.24021i | ||||
\(933\) | 6.00000 | + | 10.3923i | 0.196431 | + | 0.340229i | ||||
\(934\) | 16.1924 | + | 28.0460i | 0.529831 | + | 0.917694i | ||||
\(935\) | 2.82843 | 0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9706 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(938\) | 11.6569 | + | 20.1903i | 0.380610 | + | 0.659235i | ||||
\(939\) | −3.41421 | − | 5.91359i | −0.111419 | − | 0.192983i | ||||
\(940\) | 9.24264 | − | 16.0087i | 0.301462 | − | 0.522147i | ||||
\(941\) | −18.7696 | −0.611870 | −0.305935 | − | 0.952052i | \(-0.598969\pi\) | ||||
−0.305935 | + | 0.952052i | \(0.598969\pi\) | |||||||
\(942\) | 30.7279 | − | 53.2223i | 1.00117 | − | 1.73408i | ||||
\(943\) | −2.24264 | + | 3.88437i | −0.0730304 | + | 0.126492i | ||||
\(944\) | −5.27208 | −0.171592 | ||||||||
\(945\) | −13.6569 | + | 23.6544i | −0.444258 | + | 0.769477i | ||||
\(946\) | −45.6274 | − | 79.0290i | −1.48348 | − | 2.56945i | ||||
\(947\) | 8.55635 | + | 14.8200i | 0.278044 | + | 0.481586i | 0.970899 | − | 0.239491i | \(-0.0769806\pi\) |
−0.692855 | + | 0.721077i | \(0.743647\pi\) | |||||||
\(948\) | 45.9411 | 1.49210 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.41421 | −0.0458831 | ||||||||
\(951\) | 1.51472 | + | 2.62357i | 0.0491181 | + | 0.0850751i | ||||
\(952\) | 8.82843 | + | 15.2913i | 0.286131 | + | 0.495593i | ||||
\(953\) | −17.6274 | + | 30.5316i | −0.571008 | + | 0.989015i | 0.425455 | + | 0.904980i | \(0.360114\pi\) |
−0.996463 | + | 0.0840352i | \(0.973219\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 1.17157 | − | 2.02922i | 0.0379112 | − | 0.0656641i | ||||
\(956\) | −6.53553 | + | 11.3199i | −0.211374 | + | 0.366111i | ||||
\(957\) | −27.3137 | −0.882927 | ||||||||
\(958\) | −37.0919 | + | 64.2450i | −1.19838 | + | 2.07566i | ||||
\(959\) | 41.7990 | + | 72.3980i | 1.34976 | + | 2.33785i | ||||
\(960\) | 6.94975 | + | 12.0373i | 0.224302 | + | 0.388503i | ||||
\(961\) | −27.9117 | −0.900377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.41421 | 0.303369 | ||||||||
\(964\) | −27.7279 | − | 48.0262i | −0.893056 | − | 1.54682i | ||||
\(965\) | −2.17157 | − | 3.76127i | −0.0699054 | − | 0.121080i | ||||
\(966\) | −11.6569 | + | 20.1903i | −0.375053 | + | 0.649611i | ||||
\(967\) | −47.9411 | −1.54168 | −0.770841 | − | 0.637027i | \(-0.780164\pi\) | ||||
−0.770841 | + | 0.637027i | \(0.780164\pi\) | |||||||
\(968\) | −1.44975 | + | 2.51104i | −0.0465966 | + | 0.0807078i | ||||
\(969\) | −0.343146 | + | 0.594346i | −0.0110234 | + | 0.0190931i | ||||
\(970\) | −18.4853 | −0.593527 | ||||||||
\(971\) | −22.1421 | + | 38.3513i | −0.710575 | + | 1.23075i | 0.254067 | + | 0.967187i | \(0.418232\pi\) |
−0.964642 | + | 0.263565i | \(0.915102\pi\) | |||||||
\(972\) | 18.9497 | + | 32.8219i | 0.607813 | + | 1.05276i | ||||
\(973\) | 10.8284 | + | 18.7554i | 0.347143 | + | 0.601270i | ||||
\(974\) | 26.4853 | 0.848643 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0000 | −0.768221 | ||||||||
\(977\) | −19.7574 | − | 34.2208i | −0.632094 | − | 1.09482i | −0.987123 | − | 0.159964i | \(-0.948862\pi\) |
0.355029 | − | 0.934855i | \(-0.384471\pi\) | |||||||
\(978\) | −32.3848 | − | 56.0921i | −1.03555 | − | 1.79363i | ||||
\(979\) | −10.2426 | + | 17.7408i | −0.327356 | + | 0.566998i | ||||
\(980\) | −62.4558 | −1.99508 | ||||||||
\(981\) | 1.00000 | − | 1.73205i | 0.0319275 | − | 0.0553001i | ||||
\(982\) | −6.24264 | + | 10.8126i | −0.199211 | + | 0.345043i | ||||
\(983\) | 1.02944 | 0.0328339 | 0.0164170 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164170 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(984\) | 9.89949 | − | 17.1464i | 0.315584 | − | 0.546608i | ||||
\(985\) | −5.48528 | − | 9.50079i | −0.174776 | − | 0.302720i | ||||
\(986\) | 5.65685 | + | 9.79796i | 0.180151 | + | 0.312031i | ||||
\(987\) | 32.9706 | 1.04946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.6569 | −0.497859 | ||||||||
\(990\) | 4.12132 | + | 7.13834i | 0.130984 | + | 0.226871i | ||||
\(991\) | −24.4853 | − | 42.4098i | −0.777801 | − | 1.34719i | −0.933207 | − | 0.359340i | \(-0.883002\pi\) |
0.155406 | − | 0.987851i | \(-0.450331\pi\) | |||||||
\(992\) | −1.39340 | + | 2.41344i | −0.0442404 | + | 0.0766267i | ||||
\(993\) | −36.8284 | −1.16871 | ||||||||
\(994\) | −69.3553 | + | 120.127i | −2.19982 | + | 3.81020i | ||||
\(995\) | 2.00000 | − | 3.46410i | 0.0634043 | − | 0.109819i | ||||
\(996\) | −17.1716 | −0.544102 | ||||||||
\(997\) | −14.4142 | + | 24.9662i | −0.456503 | + | 0.790686i | −0.998773 | − | 0.0495181i | \(-0.984231\pi\) |
0.542271 | + | 0.840204i | \(0.317565\pi\) | |||||||
\(998\) | 50.1630 | + | 86.8848i | 1.58788 | + | 2.75029i | ||||
\(999\) | −24.0000 | − | 41.5692i | −0.759326 | − | 1.31519i |
(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 | 845.2.e.c.146.1 | 4 | ||
13.2 | odd | 12 | 845.2.c.b.506.1 | 4 | |||
13.3 | even | 3 | 845.2.a.g.1.2 | 2 | |||
13.4 | even | 6 | 845.2.e.h.191.2 | 4 | |||
13.5 | odd | 4 | 845.2.m.f.361.1 | 8 | |||
13.6 | odd | 12 | 845.2.m.f.316.4 | 8 | |||
13.7 | odd | 12 | 845.2.m.f.316.1 | 8 | |||
13.8 | odd | 4 | 845.2.m.f.361.4 | 8 | |||
13.9 | even | 3 | inner | 845.2.e.c.191.1 | 4 | ||
13.10 | even | 6 | 65.2.a.b.1.1 | ✓ | 2 | ||
13.11 | odd | 12 | 845.2.c.b.506.4 | 4 | |||
13.12 | even | 2 | 845.2.e.h.146.2 | 4 | |||
39.23 | odd | 6 | 585.2.a.m.1.2 | 2 | |||
39.29 | odd | 6 | 7605.2.a.x.1.1 | 2 | |||
52.23 | odd | 6 | 1040.2.a.j.1.2 | 2 | |||
65.23 | odd | 12 | 325.2.b.f.274.4 | 4 | |||
65.29 | even | 6 | 4225.2.a.r.1.1 | 2 | |||
65.49 | even | 6 | 325.2.a.i.1.2 | 2 | |||
65.62 | odd | 12 | 325.2.b.f.274.1 | 4 | |||
91.62 | odd | 6 | 3185.2.a.j.1.1 | 2 | |||
104.75 | odd | 6 | 4160.2.a.z.1.1 | 2 | |||
104.101 | even | 6 | 4160.2.a.bf.1.2 | 2 | |||
143.10 | odd | 6 | 7865.2.a.j.1.2 | 2 | |||
156.23 | even | 6 | 9360.2.a.cd.1.1 | 2 | |||
195.23 | even | 12 | 2925.2.c.r.2224.1 | 4 | |||
195.62 | even | 12 | 2925.2.c.r.2224.4 | 4 | |||
195.179 | odd | 6 | 2925.2.a.u.1.1 | 2 | |||
260.179 | odd | 6 | 5200.2.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.b.1.1 | ✓ | 2 | 13.10 | even | 6 | ||
325.2.a.i.1.2 | 2 | 65.49 | even | 6 | |||
325.2.b.f.274.1 | 4 | 65.62 | odd | 12 | |||
325.2.b.f.274.4 | 4 | 65.23 | odd | 12 | |||
585.2.a.m.1.2 | 2 | 39.23 | odd | 6 | |||
845.2.a.g.1.2 | 2 | 13.3 | even | 3 | |||
845.2.c.b.506.1 | 4 | 13.2 | odd | 12 | |||
845.2.c.b.506.4 | 4 | 13.11 | odd | 12 | |||
845.2.e.c.146.1 | 4 | 1.1 | even | 1 | trivial | ||
845.2.e.c.191.1 | 4 | 13.9 | even | 3 | inner | ||
845.2.e.h.146.2 | 4 | 13.12 | even | 2 | |||
845.2.e.h.191.2 | 4 | 13.4 | even | 6 | |||
845.2.m.f.316.1 | 8 | 13.7 | odd | 12 | |||
845.2.m.f.316.4 | 8 | 13.6 | odd | 12 | |||
845.2.m.f.361.1 | 8 | 13.5 | odd | 4 | |||
845.2.m.f.361.4 | 8 | 13.8 | odd | 4 | |||
1040.2.a.j.1.2 | 2 | 52.23 | odd | 6 | |||
2925.2.a.u.1.1 | 2 | 195.179 | odd | 6 | |||
2925.2.c.r.2224.1 | 4 | 195.23 | even | 12 | |||
2925.2.c.r.2224.4 | 4 | 195.62 | even | 12 | |||
3185.2.a.j.1.1 | 2 | 91.62 | odd | 6 | |||
4160.2.a.z.1.1 | 2 | 104.75 | odd | 6 | |||
4160.2.a.bf.1.2 | 2 | 104.101 | even | 6 | |||
4225.2.a.r.1.1 | 2 | 65.29 | even | 6 | |||
5200.2.a.bu.1.1 | 2 | 260.179 | odd | 6 | |||
7605.2.a.x.1.1 | 2 | 39.29 | odd | 6 | |||
7865.2.a.j.1.2 | 2 | 143.10 | odd | 6 | |||
9360.2.a.cd.1.1 | 2 | 156.23 | even | 6 |