Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(339,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.339");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.b (of order \(2\), degree \(1\), 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: | \(6\) |
Coefficient field: | 6.0.49843600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 339.2 | ||
Root | \(-1.18733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.339 |
Dual form | 845.2.b.e.339.5 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.18733i | − | 0.839571i | −0.907623 | − | 0.419786i | \(-0.862105\pi\) | ||
0.907623 | − | 0.419786i | \(-0.137895\pi\) | |||||||
\(3\) | − | 0.345110i | − | 0.199249i | −0.995025 | − | 0.0996247i | \(-0.968236\pi\) | ||
0.995025 | − | 0.0996247i | \(-0.0317642\pi\) | |||||||
\(4\) | 0.590239 | 0.295120 | ||||||||
\(5\) | −1.44045 | + | 1.71029i | −0.644189 | + | 0.764867i | ||||
\(6\) | −0.409761 | −0.167284 | ||||||||
\(7\) | − | 2.02956i | − | 0.767100i | −0.923520 | − | 0.383550i | \(-0.874701\pi\) | ||
0.923520 | − | 0.383550i | \(-0.125299\pi\) | |||||||
\(8\) | − | 3.07548i | − | 1.08735i | ||||||
\(9\) | 2.88090 | 0.960300 | ||||||||
\(10\) | 2.03069 | + | 1.71029i | 0.642160 | + | 0.540842i | ||||
\(11\) | −3.88090 | −1.17014 | −0.585068 | − | 0.810985i | \(-0.698932\pi\) | ||||
−0.585068 | + | 0.810985i | \(0.698932\pi\) | |||||||
\(12\) | − | 0.203698i | − | 0.0588024i | ||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.40976 | −0.644036 | ||||||||
\(15\) | 0.590239 | + | 0.497113i | 0.152399 | + | 0.128354i | ||||
\(16\) | −2.47114 | −0.617785 | ||||||||
\(17\) | − | 5.45014i | − | 1.32185i | −0.750450 | − | 0.660927i | \(-0.770163\pi\) | ||
0.750450 | − | 0.660927i | \(-0.229837\pi\) | |||||||
\(18\) | − | 3.42059i | − | 0.806240i | ||||||
\(19\) | 5.88090 | 1.34917 | 0.674585 | − | 0.738197i | \(-0.264322\pi\) | ||||
0.674585 | + | 0.738197i | \(0.264322\pi\) | |||||||
\(20\) | −0.850210 | + | 1.00948i | −0.190113 | + | 0.225727i | ||||
\(21\) | −0.700420 | −0.152844 | ||||||||
\(22\) | 4.60792i | 0.982412i | ||||||||
\(23\) | 0.345110i | 0.0719604i | 0.999353 | + | 0.0359802i | \(0.0114553\pi\) | ||||
−0.999353 | + | 0.0359802i | \(0.988545\pi\) | |||||||
\(24\) | −1.06138 | −0.216653 | ||||||||
\(25\) | −0.850210 | − | 4.92718i | −0.170042 | − | 0.985437i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.02956i | − | 0.390588i | ||||||
\(28\) | − | 1.19792i | − | 0.226386i | ||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0.590239 | − | 0.700811i | 0.107762 | − | 0.127950i | ||||
\(31\) | −1.18048 | −0.212020 | −0.106010 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106010 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(32\) | − | 3.21689i | − | 0.568671i | ||||||
\(33\) | 1.33934i | 0.233149i | ||||||||
\(34\) | −6.47114 | −1.10979 | ||||||||
\(35\) | 3.47114 | + | 2.92347i | 0.586730 | + | 0.494157i | ||||
\(36\) | 1.70042 | 0.283403 | ||||||||
\(37\) | − | 5.45014i | − | 0.895998i | −0.894034 | − | 0.447999i | \(-0.852137\pi\) | ||
0.894034 | − | 0.447999i | \(-0.147863\pi\) | |||||||
\(38\) | − | 6.98259i | − | 1.13273i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.25997 | + | 4.43007i | 0.831674 | + | 0.700456i | ||||
\(41\) | −0.180479 | −0.0281861 | −0.0140930 | − | 0.999901i | \(-0.504486\pi\) | ||||
−0.0140930 | + | 0.999901i | \(0.504486\pi\) | |||||||
\(42\) | 0.831632i | 0.128324i | ||||||||
\(43\) | 1.33934i | 0.204247i | 0.994772 | + | 0.102123i | \(0.0325637\pi\) | ||||
−0.994772 | + | 0.102123i | \(0.967436\pi\) | |||||||
\(44\) | −2.29066 | −0.345330 | ||||||||
\(45\) | −4.14979 | + | 4.92718i | −0.618614 | + | 0.734501i | ||||
\(46\) | 0.409761 | 0.0604159 | ||||||||
\(47\) | − | 12.2807i | − | 1.79133i | −0.444731 | − | 0.895664i | \(-0.646701\pi\) | ||
0.444731 | − | 0.895664i | \(-0.353299\pi\) | |||||||
\(48\) | 0.852815i | 0.123093i | ||||||||
\(49\) | 2.88090 | 0.411557 | ||||||||
\(50\) | −5.85021 | + | 1.00948i | −0.827345 | + | 0.142762i | ||||
\(51\) | −1.88090 | −0.263379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.42636i | − | 0.333286i | −0.986017 | − | 0.166643i | \(-0.946707\pi\) | ||
0.986017 | − | 0.166643i | \(-0.0532928\pi\) | |||||||
\(54\) | −2.40976 | −0.327927 | ||||||||
\(55\) | 5.59024 | − | 6.63748i | 0.753788 | − | 0.894997i | ||||
\(56\) | −6.24186 | −0.834103 | ||||||||
\(57\) | − | 2.02956i | − | 0.268821i | ||||||
\(58\) | 3.56200i | 0.467714i | ||||||||
\(59\) | −7.06138 | −0.919313 | −0.459657 | − | 0.888097i | \(-0.652027\pi\) | ||||
−0.459657 | + | 0.888097i | \(0.652027\pi\) | |||||||
\(60\) | 0.348383 | + | 0.293416i | 0.0449760 | + | 0.0378798i | ||||
\(61\) | 6.76180 | 0.865760 | 0.432880 | − | 0.901452i | \(-0.357497\pi\) | ||||
0.432880 | + | 0.901452i | \(0.357497\pi\) | |||||||
\(62\) | 1.40162i | 0.178006i | ||||||||
\(63\) | − | 5.84695i | − | 0.736646i | ||||||
\(64\) | −8.76180 | −1.09522 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.59024 | 0.195745 | ||||||||
\(67\) | 4.40422i | 0.538062i | 0.963132 | + | 0.269031i | \(0.0867033\pi\) | ||||
−0.963132 | + | 0.269031i | \(0.913297\pi\) | |||||||
\(68\) | − | 3.21689i | − | 0.390105i | ||||||
\(69\) | 0.119101 | 0.0143381 | ||||||||
\(70\) | 3.47114 | − | 4.12140i | 0.414880 | − | 0.492601i | ||||
\(71\) | 1.88090 | 0.223222 | 0.111611 | − | 0.993752i | \(-0.464399\pi\) | ||||
0.111611 | + | 0.993752i | \(0.464399\pi\) | |||||||
\(72\) | − | 8.86014i | − | 1.04418i | ||||||
\(73\) | 8.86014i | 1.03700i | 0.855077 | + | 0.518501i | \(0.173510\pi\) | ||||
−0.855077 | + | 0.518501i | \(0.826490\pi\) | |||||||
\(74\) | −6.47114 | −0.752255 | ||||||||
\(75\) | −1.70042 | + | 0.293416i | −0.196348 | + | 0.0338808i | ||||
\(76\) | 3.47114 | 0.398167 | ||||||||
\(77\) | 7.87651i | 0.897611i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1805 | −1.25790 | −0.628951 | − | 0.777445i | \(-0.716515\pi\) | ||||
−0.628951 | + | 0.777445i | \(0.716515\pi\) | |||||||
\(80\) | 3.55955 | − | 4.22637i | 0.397970 | − | 0.472523i | ||||
\(81\) | 7.94228 | 0.882475 | ||||||||
\(82\) | 0.214289i | 0.0236642i | ||||||||
\(83\) | 7.83540i | 0.860047i | 0.902818 | + | 0.430024i | \(0.141495\pi\) | ||||
−0.902818 | + | 0.430024i | \(0.858505\pi\) | |||||||
\(84\) | −0.413416 | −0.0451073 | ||||||||
\(85\) | 9.32135 | + | 7.85066i | 1.01104 | + | 0.851523i | ||||
\(86\) | 1.59024 | 0.171480 | ||||||||
\(87\) | 1.03533i | 0.110999i | ||||||||
\(88\) | 11.9356i | 1.27234i | ||||||||
\(89\) | 12.2419 | 1.29763 | 0.648817 | − | 0.760944i | \(-0.275264\pi\) | ||||
0.648817 | + | 0.760944i | \(0.275264\pi\) | |||||||
\(90\) | 5.85021 | + | 4.92718i | 0.616666 | + | 0.519371i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.203698i | 0.0212369i | ||||||||
\(93\) | 0.407395i | 0.0422449i | ||||||||
\(94\) | −14.5813 | −1.50395 | ||||||||
\(95\) | −8.47114 | + | 10.0581i | −0.869120 | + | 1.03194i | ||||
\(96\) | −1.11018 | −0.113307 | ||||||||
\(97\) | 5.80585i | 0.589494i | 0.955575 | + | 0.294747i | \(0.0952354\pi\) | ||||
−0.955575 | + | 0.294747i | \(0.904765\pi\) | |||||||
\(98\) | − | 3.42059i | − | 0.345532i | ||||||
\(99\) | −11.1805 | −1.12368 | ||||||||
\(100\) | −0.501828 | − | 2.90822i | −0.0501828 | − | 0.290822i | ||||
\(101\) | −5.94228 | −0.591279 | −0.295639 | − | 0.955300i | \(-0.595533\pi\) | ||||
−0.295639 | + | 0.955300i | \(0.595533\pi\) | |||||||
\(102\) | 2.23325i | 0.221125i | ||||||||
\(103\) | 6.43378i | 0.633939i | 0.948436 | + | 0.316970i | \(0.102665\pi\) | ||||
−0.948436 | + | 0.316970i | \(0.897335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00892 | − | 1.19792i | 0.0984605 | − | 0.116905i | ||||
\(106\) | −2.88090 | −0.279818 | ||||||||
\(107\) | 17.6792i | 1.70911i | 0.519360 | + | 0.854555i | \(0.326170\pi\) | ||||
−0.519360 | + | 0.854555i | \(0.673830\pi\) | |||||||
\(108\) | − | 1.19792i | − | 0.115270i | ||||||
\(109\) | 5.76180 | 0.551880 | 0.275940 | − | 0.961175i | \(-0.411011\pi\) | ||||
0.275940 | + | 0.961175i | \(0.411011\pi\) | |||||||
\(110\) | −7.88090 | − | 6.63748i | −0.751414 | − | 0.632859i | ||||
\(111\) | −1.88090 | −0.178527 | ||||||||
\(112\) | 5.01532i | 0.473903i | ||||||||
\(113\) | 4.75992i | 0.447776i | 0.974615 | + | 0.223888i | \(0.0718750\pi\) | ||||
−0.974615 | + | 0.223888i | \(0.928125\pi\) | |||||||
\(114\) | −2.40976 | −0.225695 | ||||||||
\(115\) | −0.590239 | − | 0.497113i | −0.0550401 | − | 0.0463561i | ||||
\(116\) | −1.77072 | −0.164407 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.38421i | 0.771829i | ||||||||
\(119\) | −11.0614 | −1.01399 | ||||||||
\(120\) | 1.52886 | − | 1.81527i | 0.139565 | − | 0.165711i | ||||
\(121\) | 4.06138 | 0.369216 | ||||||||
\(122\) | − | 8.02851i | − | 0.726867i | ||||||
\(123\) | 0.0622851i | 0.00561605i | ||||||||
\(124\) | −0.696765 | −0.0625714 | ||||||||
\(125\) | 9.65162 | + | 5.64325i | 0.863267 | + | 0.504748i | ||||
\(126\) | −6.94228 | −0.618467 | ||||||||
\(127\) | − | 16.7061i | − | 1.48243i | −0.671268 | − | 0.741215i | \(-0.734250\pi\) | ||
0.671268 | − | 0.741215i | \(-0.265750\pi\) | |||||||
\(128\) | 3.96940i | 0.350848i | ||||||||
\(129\) | 0.462218 | 0.0406961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 0.790529i | 0.0688068i | ||||||||
\(133\) | − | 11.9356i | − | 1.03495i | ||||||
\(134\) | 5.22928 | 0.451741 | ||||||||
\(135\) | 3.47114 | + | 2.92347i | 0.298748 | + | 0.251613i | ||||
\(136\) | −16.7618 | −1.43731 | ||||||||
\(137\) | − | 1.97786i | − | 0.168980i | −0.996424 | − | 0.0844901i | \(-0.973074\pi\) | ||
0.996424 | − | 0.0844901i | \(-0.0269261\pi\) | |||||||
\(138\) | − | 0.141412i | − | 0.0120378i | ||||||
\(139\) | −8.70042 | −0.737960 | −0.368980 | − | 0.929437i | \(-0.620293\pi\) | ||||
−0.368980 | + | 0.929437i | \(0.620293\pi\) | |||||||
\(140\) | 2.04880 | + | 1.72555i | 0.173155 | + | 0.145836i | ||||
\(141\) | −4.23820 | −0.356921 | ||||||||
\(142\) | − | 2.23325i | − | 0.187411i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.11910 | −0.593258 | ||||||||
\(145\) | 4.32135 | − | 5.13088i | 0.358868 | − | 0.426097i | ||||
\(146\) | 10.5199 | 0.870637 | ||||||||
\(147\) | − | 0.994227i | − | 0.0820025i | ||||||
\(148\) | − | 3.21689i | − | 0.264427i | ||||||
\(149\) | 22.3032 | 1.82715 | 0.913576 | − | 0.406668i | \(-0.133309\pi\) | ||||
0.913576 | + | 0.406668i | \(0.133309\pi\) | |||||||
\(150\) | 0.348383 | + | 2.01897i | 0.0284453 | + | 0.164848i | ||||
\(151\) | 19.1626 | 1.55943 | 0.779717 | − | 0.626132i | \(-0.215363\pi\) | ||||
0.779717 | + | 0.626132i | \(0.215363\pi\) | |||||||
\(152\) | − | 18.0866i | − | 1.46701i | ||||||
\(153\) | − | 15.7013i | − | 1.26938i | ||||||
\(154\) | 9.35204 | 0.753609 | ||||||||
\(155\) | 1.70042 | − | 2.01897i | 0.136581 | − | 0.162167i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.20265i | − | 0.495025i | −0.968885 | − | 0.247513i | \(-0.920387\pi\) | ||
0.968885 | − | 0.247513i | \(-0.0796132\pi\) | |||||||
\(158\) | 13.2750i | 1.05610i | ||||||||
\(159\) | −0.837361 | −0.0664071 | ||||||||
\(160\) | 5.50183 | + | 4.63377i | 0.434958 | + | 0.366332i | ||||
\(161\) | 0.700420 | 0.0552008 | ||||||||
\(162\) | − | 9.43013i | − | 0.740901i | ||||||
\(163\) | 11.9356i | 0.934870i | 0.884027 | + | 0.467435i | \(0.154822\pi\) | ||||
−0.884027 | + | 0.467435i | \(0.845178\pi\) | |||||||
\(164\) | −0.106526 | −0.00831826 | ||||||||
\(165\) | −2.29066 | − | 1.92925i | −0.178328 | − | 0.150192i | ||||
\(166\) | 9.30323 | 0.722071 | ||||||||
\(167\) | 2.02956i | 0.157052i | 0.996912 | + | 0.0785259i | \(0.0250213\pi\) | ||||
−0.996912 | + | 0.0785259i | \(0.974979\pi\) | |||||||
\(168\) | 2.15413i | 0.166195i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.32135 | − | 11.0675i | 0.714915 | − | 0.848842i | ||||
\(171\) | 16.9423 | 1.29561 | ||||||||
\(172\) | 0.790529i | 0.0602773i | ||||||||
\(173\) | − | 1.33934i | − | 0.101828i | −0.998703 | − | 0.0509139i | \(-0.983787\pi\) | ||
0.998703 | − | 0.0509139i | \(-0.0162134\pi\) | |||||||
\(174\) | 1.22928 | 0.0931916 | ||||||||
\(175\) | −10.0000 | + | 1.72555i | −0.755929 | + | 0.130439i | ||||
\(176\) | 9.59024 | 0.722891 | ||||||||
\(177\) | 2.43695i | 0.183173i | ||||||||
\(178\) | − | 14.5352i | − | 1.08946i | ||||||
\(179\) | −20.2240 | −1.51161 | −0.755807 | − | 0.654794i | \(-0.772755\pi\) | ||||
−0.755807 | + | 0.654794i | \(0.772755\pi\) | |||||||
\(180\) | −2.44937 | + | 2.90822i | −0.182565 | + | 0.216766i | ||||
\(181\) | 19.8232 | 1.47345 | 0.736723 | − | 0.676195i | \(-0.236372\pi\) | ||||
0.736723 | + | 0.676195i | \(0.236372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.33356i | − | 0.172502i | ||||||
\(184\) | 1.06138 | 0.0782458 | ||||||||
\(185\) | 9.32135 | + | 7.85066i | 0.685319 | + | 0.577192i | ||||
\(186\) | 0.483714 | 0.0354676 | ||||||||
\(187\) | 21.1515i | 1.54675i | ||||||||
\(188\) | − | 7.24857i | − | 0.528656i | ||||||
\(189\) | −4.11910 | −0.299621 | ||||||||
\(190\) | 11.9423 | + | 10.0581i | 0.866384 | + | 0.729689i | ||||
\(191\) | 1.53778 | 0.111270 | 0.0556350 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556350 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(192\) | 3.02378i | 0.218223i | ||||||||
\(193\) | 21.2032i | 1.52624i | 0.646259 | + | 0.763118i | \(0.276333\pi\) | ||||
−0.646259 | + | 0.763118i | \(0.723667\pi\) | |||||||
\(194\) | 6.89347 | 0.494923 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70042 | 0.121459 | ||||||||
\(197\) | 9.25695i | 0.659530i | 0.944063 | + | 0.329765i | \(0.106970\pi\) | ||||
−0.944063 | + | 0.329765i | \(0.893030\pi\) | |||||||
\(198\) | 13.2750i | 0.943410i | ||||||||
\(199\) | 17.4045 | 1.23377 | 0.616886 | − | 0.787053i | \(-0.288394\pi\) | ||||
0.616886 | + | 0.787053i | \(0.288394\pi\) | |||||||
\(200\) | −15.1534 | + | 2.61480i | −1.07151 | + | 0.184894i | ||||
\(201\) | 1.51994 | 0.107208 | ||||||||
\(202\) | 7.05546i | 0.496421i | ||||||||
\(203\) | 6.08867i | 0.427341i | ||||||||
\(204\) | −1.11018 | −0.0777282 | ||||||||
\(205\) | 0.259971 | − | 0.308672i | 0.0181571 | − | 0.0215586i | ||||
\(206\) | 7.63904 | 0.532237 | ||||||||
\(207\) | 0.994227i | 0.0691036i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.8232 | −1.57871 | ||||||||
\(210\) | −1.42234 | − | 1.19792i | −0.0981505 | − | 0.0826646i | ||||
\(211\) | −7.28174 | −0.501296 | −0.250648 | − | 0.968078i | \(-0.580644\pi\) | ||||
−0.250648 | + | 0.968078i | \(0.580644\pi\) | |||||||
\(212\) | − | 1.43213i | − | 0.0983594i | ||||||
\(213\) | − | 0.649117i | − | 0.0444768i | ||||||
\(214\) | 20.9911 | 1.43492 | ||||||||
\(215\) | −2.29066 | − | 1.92925i | −0.156222 | − | 0.131574i | ||||
\(216\) | −6.24186 | −0.424705 | ||||||||
\(217\) | 2.39585i | 0.162641i | ||||||||
\(218\) | − | 6.84118i | − | 0.463343i | ||||||
\(219\) | 3.05772 | 0.206622 | ||||||||
\(220\) | 3.29958 | − | 3.91770i | 0.222458 | − | 0.264131i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.23325i | 0.149886i | ||||||||
\(223\) | − | 19.4670i | − | 1.30361i | −0.758388 | − | 0.651804i | \(-0.774013\pi\) | ||
0.758388 | − | 0.651804i | \(-0.225987\pi\) | |||||||
\(224\) | −6.52886 | −0.436228 | ||||||||
\(225\) | −2.44937 | − | 14.1947i | −0.163291 | − | 0.946315i | ||||
\(226\) | 5.65162 | 0.375940 | ||||||||
\(227\) | − | 4.81162i | − | 0.319358i | −0.987169 | − | 0.159679i | \(-0.948954\pi\) | ||
0.987169 | − | 0.159679i | \(-0.0510460\pi\) | |||||||
\(228\) | − | 1.19792i | − | 0.0793345i | ||||||
\(229\) | 1.52360 | 0.100682 | 0.0503410 | − | 0.998732i | \(-0.483969\pi\) | ||||
0.0503410 | + | 0.998732i | \(0.483969\pi\) | |||||||
\(230\) | −0.590239 | + | 0.700811i | −0.0389192 | + | 0.0462101i | ||||
\(231\) | 2.71826 | 0.178848 | ||||||||
\(232\) | 9.22643i | 0.605745i | ||||||||
\(233\) | 13.9652i | 0.914889i | 0.889238 | + | 0.457445i | \(0.151235\pi\) | ||||
−0.889238 | + | 0.457445i | \(0.848765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.0037 | + | 17.6898i | 1.37013 | + | 1.15395i | ||||
\(236\) | −4.16790 | −0.271307 | ||||||||
\(237\) | 3.85849i | 0.250636i | ||||||||
\(238\) | 13.1335i | 0.851321i | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | −1.45856 | − | 1.22844i | −0.0941499 | − | 0.0792952i | ||||
\(241\) | 17.4659 | 1.12508 | 0.562538 | − | 0.826771i | \(-0.309825\pi\) | ||||
0.562538 | + | 0.826771i | \(0.309825\pi\) | |||||||
\(242\) | − | 4.82221i | − | 0.309983i | ||||||
\(243\) | − | 8.82963i | − | 0.566421i | ||||||
\(244\) | 3.99108 | 0.255503 | ||||||||
\(245\) | −4.14979 | + | 4.92718i | −0.265120 | + | 0.314786i | ||||
\(246\) | 0.0739531 | 0.00471508 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.63054i | 0.230539i | ||||||||
\(249\) | 2.70408 | 0.171364 | ||||||||
\(250\) | 6.70042 | − | 11.4597i | 0.423772 | − | 0.724774i | ||||
\(251\) | 9.29958 | 0.586984 | 0.293492 | − | 0.955961i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955961i | \(0.405183\pi\) | |||||||
\(252\) | − | 3.45110i | − | 0.217399i | ||||||
\(253\) | − | 1.33934i | − | 0.0842034i | ||||||
\(254\) | −19.8358 | −1.24461 | ||||||||
\(255\) | 2.70934 | − | 3.21689i | 0.169665 | − | 0.201449i | ||||
\(256\) | −12.8106 | −0.800663 | ||||||||
\(257\) | 10.8897i | 0.679281i | 0.940555 | + | 0.339640i | \(0.110305\pi\) | ||||
−0.940555 | + | 0.339640i | \(0.889695\pi\) | |||||||
\(258\) | − | 0.548807i | − | 0.0341673i | ||||||
\(259\) | −11.0614 | −0.687321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.64270 | −0.534970 | ||||||||
\(262\) | − | 11.8733i | − | 0.733537i | ||||||
\(263\) | 13.4406i | 0.828785i | 0.910098 | + | 0.414392i | \(0.136006\pi\) | ||||
−0.910098 | + | 0.414392i | \(0.863994\pi\) | |||||||
\(264\) | 4.11910 | 0.253513 | ||||||||
\(265\) | 4.14979 | + | 3.49505i | 0.254920 | + | 0.214699i | ||||
\(266\) | −14.1716 | −0.868914 | ||||||||
\(267\) | − | 4.22479i | − | 0.258553i | ||||||
\(268\) | 2.59955i | 0.158793i | ||||||||
\(269\) | −3.66054 | −0.223187 | −0.111593 | − | 0.993754i | \(-0.535595\pi\) | ||||
−0.111593 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(270\) | 3.47114 | − | 4.12140i | 0.211247 | − | 0.250820i | ||||
\(271\) | −22.0037 | −1.33663 | −0.668313 | − | 0.743880i | \(-0.732983\pi\) | ||||
−0.668313 | + | 0.743880i | \(0.732983\pi\) | |||||||
\(272\) | 13.4681i | 0.816621i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.34838 | −0.141871 | ||||||||
\(275\) | 3.29958 | + | 19.1219i | 0.198972 | + | 1.15309i | ||||
\(276\) | 0.0702980 | 0.00423144 | ||||||||
\(277\) | 9.89547i | 0.594561i | 0.954790 | + | 0.297281i | \(0.0960797\pi\) | ||||
−0.954790 | + | 0.297281i | \(0.903920\pi\) | |||||||
\(278\) | 10.3303i | 0.619570i | ||||||||
\(279\) | −3.40084 | −0.203603 | ||||||||
\(280\) | 8.99108 | − | 10.6754i | 0.537320 | − | 0.637978i | ||||
\(281\) | −4.06138 | −0.242281 | −0.121141 | − | 0.992635i | \(-0.538655\pi\) | ||||
−0.121141 | + | 0.992635i | \(0.538655\pi\) | |||||||
\(282\) | 5.03216i | 0.299661i | ||||||||
\(283\) | 6.08867i | 0.361934i | 0.983489 | + | 0.180967i | \(0.0579227\pi\) | ||||
−0.983489 | + | 0.180967i | \(0.942077\pi\) | |||||||
\(284\) | 1.11018 | 0.0658771 | ||||||||
\(285\) | 3.47114 | + | 2.92347i | 0.205613 | + | 0.173172i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.366292i | 0.0216215i | ||||||||
\(288\) | − | 9.26754i | − | 0.546095i | ||||||
\(289\) | −12.7041 | −0.747299 | ||||||||
\(290\) | −6.09207 | − | 5.13088i | −0.357738 | − | 0.301296i | ||||
\(291\) | 2.00366 | 0.117456 | ||||||||
\(292\) | 5.22960i | 0.306039i | ||||||||
\(293\) | − | 9.79208i | − | 0.572060i | −0.958221 | − | 0.286030i | \(-0.907664\pi\) | ||
0.958221 | − | 0.286030i | \(-0.0923356\pi\) | |||||||
\(294\) | −1.18048 | −0.0688469 | ||||||||
\(295\) | 10.1716 | − | 12.0770i | 0.592211 | − | 0.703152i | ||||
\(296\) | −16.7618 | −0.974260 | ||||||||
\(297\) | 7.87651i | 0.457041i | ||||||||
\(298\) | − | 26.4814i | − | 1.53402i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00366 | + | 0.173186i | −0.0579461 | + | 0.00999888i | ||||
\(301\) | 2.71826 | 0.156678 | ||||||||
\(302\) | − | 22.7524i | − | 1.30926i | ||||||
\(303\) | 2.05074i | 0.117812i | ||||||||
\(304\) | −14.5325 | −0.833497 | ||||||||
\(305\) | −9.74003 | + | 11.5647i | −0.557712 | + | 0.662191i | ||||
\(306\) | −18.6427 | −1.06573 | ||||||||
\(307\) | 22.1046i | 1.26158i | 0.775955 | + | 0.630788i | \(0.217268\pi\) | ||||
−0.775955 | + | 0.630788i | \(0.782732\pi\) | |||||||
\(308\) | 4.64902i | 0.264903i | ||||||||
\(309\) | 2.22036 | 0.126312 | ||||||||
\(310\) | −2.39719 | − | 2.01897i | −0.136151 | − | 0.114670i | ||||
\(311\) | 7.63904 | 0.433170 | 0.216585 | − | 0.976264i | \(-0.430508\pi\) | ||||
0.216585 | + | 0.976264i | \(0.430508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.1425i | − | 1.47766i | −0.673891 | − | 0.738831i | \(-0.735378\pi\) | ||
0.673891 | − | 0.738831i | \(-0.264622\pi\) | |||||||
\(314\) | −7.36461 | −0.415609 | ||||||||
\(315\) | 10.0000 | + | 8.42223i | 0.563436 | + | 0.474539i | ||||
\(316\) | −6.59916 | −0.371232 | ||||||||
\(317\) | − | 11.8428i | − | 0.665159i | −0.943075 | − | 0.332580i | \(-0.892081\pi\) | ||
0.943075 | − | 0.332580i | \(-0.107919\pi\) | |||||||
\(318\) | 0.994227i | 0.0557535i | ||||||||
\(319\) | 11.6427 | 0.651866 | ||||||||
\(320\) | 12.6209 | − | 14.9852i | 0.705531 | − | 0.837701i | ||||
\(321\) | 6.10126 | 0.340539 | ||||||||
\(322\) | − | 0.831632i | − | 0.0463451i | ||||||
\(323\) | − | 32.0518i | − | 1.78341i | ||||||
\(324\) | 4.68785 | 0.260436 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.1716 | 0.784890 | ||||||||
\(327\) | − | 1.98845i | − | 0.109962i | ||||||
\(328\) | 0.555059i | 0.0306480i | ||||||||
\(329\) | −24.9244 | −1.37413 | ||||||||
\(330\) | −2.29066 | + | 2.71978i | −0.126097 | + | 0.149719i | ||||
\(331\) | 12.7004 | 0.698078 | 0.349039 | − | 0.937108i | \(-0.386508\pi\) | ||||
0.349039 | + | 0.937108i | \(0.386508\pi\) | |||||||
\(332\) | 4.62476i | 0.253817i | ||||||||
\(333\) | − | 15.7013i | − | 0.860427i | ||||||
\(334\) | 2.40976 | 0.131856 | ||||||||
\(335\) | −7.53252 | − | 6.34406i | −0.411545 | − | 0.346613i | ||||
\(336\) | 1.73084 | 0.0944248 | ||||||||
\(337\) | − | 15.2939i | − | 0.833113i | −0.909110 | − | 0.416556i | \(-0.863237\pi\) | ||
0.909110 | − | 0.416556i | \(-0.136763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.64270 | 0.0892191 | ||||||||
\(340\) | 5.50183 | + | 4.63377i | 0.298378 | + | 0.251301i | ||||
\(341\) | 4.58132 | 0.248092 | ||||||||
\(342\) | − | 20.1161i | − | 1.08776i | ||||||
\(343\) | − | 20.0538i | − | 1.08281i | ||||||
\(344\) | 4.11910 | 0.222087 | ||||||||
\(345\) | −0.171559 | + | 0.203698i | −0.00923642 | + | 0.0109667i | ||||
\(346\) | −1.59024 | −0.0854918 | ||||||||
\(347\) | 12.2396i | 0.657058i | 0.944494 | + | 0.328529i | \(0.106553\pi\) | ||||
−0.944494 | + | 0.328529i | \(0.893447\pi\) | |||||||
\(348\) | 0.611093i | 0.0327580i | ||||||||
\(349\) | 18.7004 | 1.00101 | 0.500505 | − | 0.865733i | \(-0.333148\pi\) | ||||
0.500505 | + | 0.865733i | \(0.333148\pi\) | |||||||
\(350\) | 2.04880 | + | 11.8733i | 0.109513 | + | 0.634656i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4844i | 0.665422i | ||||||||
\(353\) | 1.30883i | 0.0696617i | 0.999393 | + | 0.0348309i | \(0.0110893\pi\) | ||||
−0.999393 | + | 0.0348309i | \(0.988911\pi\) | |||||||
\(354\) | 2.89347 | 0.153786 | ||||||||
\(355\) | −2.70934 | + | 3.21689i | −0.143797 | + | 0.170735i | ||||
\(356\) | 7.22563 | 0.382957 | ||||||||
\(357\) | 3.81739i | 0.202038i | ||||||||
\(358\) | 24.0127i | 1.26911i | ||||||||
\(359\) | −29.4082 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(360\) | 15.1534 | + | 12.7626i | 0.798657 | + | 0.672647i | ||||
\(361\) | 15.5850 | 0.820262 | ||||||||
\(362\) | − | 23.5367i | − | 1.23706i | ||||||
\(363\) | − | 1.40162i | − | 0.0735661i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1534 | − | 12.7626i | −0.793168 | − | 0.668024i | ||||
\(366\) | −2.77072 | −0.144828 | ||||||||
\(367\) | − | 33.4322i | − | 1.74515i | −0.488484 | − | 0.872573i | \(-0.662450\pi\) | ||
0.488484 | − | 0.872573i | \(-0.337550\pi\) | |||||||
\(368\) | − | 0.852815i | − | 0.0444560i | ||||||
\(369\) | −0.519941 | −0.0270671 | ||||||||
\(370\) | 9.32135 | − | 11.0675i | 0.484594 | − | 0.575374i | ||||
\(371\) | −4.92444 | −0.255664 | ||||||||
\(372\) | 0.240461i | 0.0124673i | ||||||||
\(373\) | 34.4781i | 1.78521i | 0.450841 | + | 0.892604i | \(0.351124\pi\) | ||||
−0.450841 | + | 0.892604i | \(0.648876\pi\) | |||||||
\(374\) | 25.1138 | 1.29861 | ||||||||
\(375\) | 1.94754 | − | 3.33087i | 0.100571 | − | 0.172005i | ||||
\(376\) | −37.7691 | −1.94779 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.89075i | 0.251553i | ||||||||
\(379\) | −17.4045 | −0.894009 | −0.447004 | − | 0.894532i | \(-0.647509\pi\) | ||||
−0.447004 | + | 0.894532i | \(0.647509\pi\) | |||||||
\(380\) | −5.00000 | + | 5.93667i | −0.256495 | + | 0.304545i | ||||
\(381\) | −5.76545 | −0.295373 | ||||||||
\(382\) | − | 1.82586i | − | 0.0934191i | ||||||
\(383\) | 1.74673i | 0.0892538i | 0.999004 | + | 0.0446269i | \(0.0142099\pi\) | ||||
−0.999004 | + | 0.0446269i | \(0.985790\pi\) | |||||||
\(384\) | 1.36988 | 0.0699063 | ||||||||
\(385\) | −13.4711 | − | 11.3457i | −0.686553 | − | 0.578231i | ||||
\(386\) | 25.1752 | 1.28138 | ||||||||
\(387\) | 3.85849i | 0.196138i | ||||||||
\(388\) | 3.42684i | 0.173971i | ||||||||
\(389\) | −22.0435 | −1.11765 | −0.558826 | − | 0.829285i | \(-0.688748\pi\) | ||||
−0.558826 | + | 0.829285i | \(0.688748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.88090 | 0.0951212 | ||||||||
\(392\) | − | 8.86014i | − | 0.447505i | ||||||
\(393\) | − | 3.45110i | − | 0.174085i | ||||||
\(394\) | 10.9911 | 0.553723 | ||||||||
\(395\) | 16.1049 | − | 19.1219i | 0.810326 | − | 0.962127i | ||||
\(396\) | −6.59916 | −0.331620 | ||||||||
\(397\) | 22.5319i | 1.13084i | 0.824802 | + | 0.565422i | \(0.191287\pi\) | ||||
−0.824802 | + | 0.565422i | \(0.808713\pi\) | |||||||
\(398\) | − | 20.6649i | − | 1.03584i | ||||||
\(399\) | −4.11910 | −0.206213 | ||||||||
\(400\) | 2.10099 | + | 12.1758i | 0.105049 | + | 0.608788i | ||||
\(401\) | 3.70408 | 0.184973 | 0.0924863 | − | 0.995714i | \(-0.470519\pi\) | ||||
0.0924863 | + | 0.995714i | \(0.470519\pi\) | |||||||
\(402\) | − | 1.80468i | − | 0.0900091i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.50737 | −0.174498 | ||||||||
\(405\) | −11.4404 | + | 13.5836i | −0.568481 | + | 0.674976i | ||||
\(406\) | 7.22928 | 0.358783 | ||||||||
\(407\) | 21.1515i | 1.04844i | ||||||||
\(408\) | 5.78466i | 0.286384i | ||||||||
\(409\) | −13.4837 | −0.666727 | −0.333363 | − | 0.942798i | \(-0.608184\pi\) | ||||
−0.333363 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(410\) | −0.366496 | − | 0.308672i | −0.0181000 | − | 0.0152442i | ||||
\(411\) | −0.682580 | −0.0336692 | ||||||||
\(412\) | 3.79747i | 0.187088i | ||||||||
\(413\) | 14.3315i | 0.705205i | ||||||||
\(414\) | 1.18048 | 0.0580174 | ||||||||
\(415\) | −13.4008 | − | 11.2865i | −0.657821 | − | 0.554033i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.00260i | 0.147038i | ||||||||
\(418\) | 27.0987i | 1.32544i | ||||||||
\(419\) | −16.8232 | −0.821866 | −0.410933 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410933 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(420\) | 0.595504 | − | 0.707062i | 0.0290576 | − | 0.0345011i | ||||
\(421\) | −17.1013 | −0.833464 | −0.416732 | − | 0.909029i | \(-0.636825\pi\) | ||||
−0.416732 | + | 0.909029i | \(0.636825\pi\) | |||||||
\(422\) | 8.64585i | 0.420874i | ||||||||
\(423\) | − | 35.3795i | − | 1.72021i | ||||||
\(424\) | −7.46222 | −0.362397 | ||||||||
\(425\) | −26.8539 | + | 4.63377i | −1.30260 | + | 0.224771i | ||||
\(426\) | −0.770718 | −0.0373414 | ||||||||
\(427\) | − | 13.7235i | − | 0.664124i | ||||||
\(428\) | 10.4349i | 0.504392i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.29066 | + | 2.71978i | −0.110465 | + | 0.131159i | ||||
\(431\) | −9.66054 | −0.465332 | −0.232666 | − | 0.972557i | \(-0.574745\pi\) | ||||
−0.232666 | + | 0.972557i | \(0.574745\pi\) | |||||||
\(432\) | 5.01532i | 0.241300i | ||||||||
\(433\) | − | 24.7727i | − | 1.19050i | −0.803541 | − | 0.595249i | \(-0.797053\pi\) | ||
0.803541 | − | 0.595249i | \(-0.202947\pi\) | |||||||
\(434\) | 2.84467 | 0.136549 | ||||||||
\(435\) | −1.77072 | − | 1.49134i | −0.0848994 | − | 0.0715043i | ||||
\(436\) | 3.40084 | 0.162871 | ||||||||
\(437\) | 2.02956i | 0.0970869i | ||||||||
\(438\) | − | 3.63054i | − | 0.173474i | ||||||
\(439\) | −7.06138 | −0.337021 | −0.168511 | − | 0.985700i | \(-0.553896\pi\) | ||||
−0.168511 | + | 0.985700i | \(0.553896\pi\) | |||||||
\(440\) | −20.4134 | − | 17.1927i | −0.973171 | − | 0.819628i | ||||
\(441\) | 8.29958 | 0.395218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.2438i | 1.81702i | 0.417865 | + | 0.908509i | \(0.362778\pi\) | ||||
−0.417865 | + | 0.908509i | \(0.637222\pi\) | |||||||
\(444\) | −1.11018 | −0.0526869 | ||||||||
\(445\) | −17.6338 | + | 20.9372i | −0.835921 | + | 0.992517i | ||||
\(446\) | −23.1138 | −1.09447 | ||||||||
\(447\) | − | 7.69707i | − | 0.364059i | ||||||
\(448\) | 17.7826i | 0.840147i | ||||||||
\(449\) | −12.4801 | −0.588970 | −0.294485 | − | 0.955656i | \(-0.595148\pi\) | ||||
−0.294485 | + | 0.955656i | \(0.595148\pi\) | |||||||
\(450\) | −16.8539 | + | 2.90822i | −0.794499 | + | 0.137095i | ||||
\(451\) | 0.700420 | 0.0329815 | ||||||||
\(452\) | 2.80950i | 0.132148i | ||||||||
\(453\) | − | 6.61322i | − | 0.310716i | ||||||
\(454\) | −5.71300 | −0.268124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24186 | −0.292302 | ||||||||
\(457\) | − | 8.23221i | − | 0.385086i | −0.981289 | − | 0.192543i | \(-0.938326\pi\) | ||
0.981289 | − | 0.192543i | \(-0.0616735\pi\) | |||||||
\(458\) | − | 1.80902i | − | 0.0845298i | ||||||
\(459\) | −11.0614 | −0.516301 | ||||||||
\(460\) | −0.348383 | − | 0.293416i | −0.0162434 | − | 0.0136806i | ||||
\(461\) | 4.54144 | 0.211516 | 0.105758 | − | 0.994392i | \(-0.466273\pi\) | ||||
0.105758 | + | 0.994392i | \(0.466273\pi\) | |||||||
\(462\) | − | 3.22748i | − | 0.150156i | ||||||
\(463\) | − | 1.98845i | − | 0.0924113i | −0.998932 | − | 0.0462056i | \(-0.985287\pi\) | ||
0.998932 | − | 0.0462056i | \(-0.0147130\pi\) | |||||||
\(464\) | 7.41342 | 0.344159 | ||||||||
\(465\) | −0.696765 | − | 0.586832i | −0.0323117 | − | 0.0272137i | ||||
\(466\) | 16.5813 | 0.768115 | ||||||||
\(467\) | − | 32.8043i | − | 1.51800i | −0.651091 | − | 0.759000i | \(-0.725688\pi\) | ||
0.651091 | − | 0.759000i | \(-0.274312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.93862 | 0.412747 | ||||||||
\(470\) | 21.0037 | − | 24.9383i | 0.968826 | − | 1.15032i | ||||
\(471\) | −2.14060 | −0.0986335 | ||||||||
\(472\) | 21.7171i | 0.999611i | ||||||||
\(473\) | − | 5.19783i | − | 0.238997i | ||||||
\(474\) | 4.58132 | 0.210427 | ||||||||
\(475\) | −5.00000 | − | 28.9763i | −0.229416 | − | 1.32952i | ||||
\(476\) | −6.52886 | −0.299250 | ||||||||
\(477\) | − | 6.99010i | − | 0.320055i | ||||||
\(478\) | − | 4.74933i | − | 0.217229i | ||||||
\(479\) | −30.8053 | −1.40753 | −0.703766 | − | 0.710432i | \(-0.748500\pi\) | ||||
−0.703766 | + | 0.710432i | \(0.748500\pi\) | |||||||
\(480\) | 1.59916 | − | 1.89874i | 0.0729913 | − | 0.0866650i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 20.7378i | − | 0.944582i | ||||||
\(483\) | − | 0.241722i | − | 0.0109987i | ||||||
\(484\) | 2.39719 | 0.108963 | ||||||||
\(485\) | −9.92970 | − | 8.36303i | −0.450885 | − | 0.379746i | ||||
\(486\) | −10.4837 | −0.475551 | ||||||||
\(487\) | 22.3251i | 1.01165i | 0.862637 | + | 0.505824i | \(0.168811\pi\) | ||||
−0.862637 | + | 0.505824i | \(0.831189\pi\) | |||||||
\(488\) | − | 20.7958i | − | 0.941380i | ||||||
\(489\) | 4.11910 | 0.186272 | ||||||||
\(490\) | 5.85021 | + | 4.92718i | 0.264286 | + | 0.222587i | ||||
\(491\) | 10.6826 | 0.482098 | 0.241049 | − | 0.970513i | \(-0.422509\pi\) | ||||
0.241049 | + | 0.970513i | \(0.422509\pi\) | |||||||
\(492\) | 0.0367631i | 0.00165741i | ||||||||
\(493\) | 16.3504i | 0.736386i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.1049 | − | 19.1219i | 0.723862 | − | 0.859466i | ||||
\(496\) | 2.91713 | 0.130983 | ||||||||
\(497\) | − | 3.81739i | − | 0.171233i | ||||||
\(498\) | − | 3.21064i | − | 0.143872i | ||||||
\(499\) | 18.8195 | 0.842477 | 0.421239 | − | 0.906950i | \(-0.361595\pi\) | ||||
0.421239 | + | 0.906950i | \(0.361595\pi\) | |||||||
\(500\) | 5.69677 | + | 3.33087i | 0.254767 | + | 0.148961i | ||||
\(501\) | 0.700420 | 0.0312925 | ||||||||
\(502\) | − | 11.0417i | − | 0.492815i | ||||||
\(503\) | 5.68128i | 0.253316i | 0.991946 | + | 0.126658i | \(0.0404250\pi\) | ||||
−0.991946 | + | 0.126658i | \(0.959575\pi\) | |||||||
\(504\) | −17.9822 | −0.800989 | ||||||||
\(505\) | 8.55955 | − | 10.1630i | 0.380895 | − | 0.452249i | ||||
\(506\) | −1.59024 | −0.0706948 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 9.86062i | − | 0.437494i | ||||||
\(509\) | 27.9244 | 1.23773 | 0.618864 | − | 0.785498i | \(-0.287593\pi\) | ||||
0.618864 | + | 0.785498i | \(0.287593\pi\) | |||||||
\(510\) | −3.81952 | − | 3.21689i | −0.169131 | − | 0.142446i | ||||
\(511\) | 17.9822 | 0.795484 | ||||||||
\(512\) | 23.1492i | 1.02306i | ||||||||
\(513\) | − | 11.9356i | − | 0.526970i | ||||||
\(514\) | 12.9297 | 0.570305 | ||||||||
\(515\) | −11.0037 | − | 9.26754i | −0.484879 | − | 0.408376i | ||||
\(516\) | 0.272820 | 0.0120102 | ||||||||
\(517\) | 47.6603i | 2.09610i | ||||||||
\(518\) | 13.1335i | 0.577055i | ||||||||
\(519\) | −0.462218 | −0.0202891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.29958 | 0.275990 | 0.137995 | − | 0.990433i | \(-0.455934\pi\) | ||||
0.137995 | + | 0.990433i | \(0.455934\pi\) | |||||||
\(522\) | 10.2618i | 0.449145i | ||||||||
\(523\) | − | 22.8571i | − | 0.999471i | −0.866178 | − | 0.499735i | \(-0.833431\pi\) | ||
0.866178 | − | 0.499735i | \(-0.166569\pi\) | |||||||
\(524\) | 5.90239 | 0.257847 | ||||||||
\(525\) | 0.595504 | + | 3.45110i | 0.0259899 | + | 0.150618i | ||||
\(526\) | 15.9585 | 0.695824 | ||||||||
\(527\) | 6.43378i | 0.280260i | ||||||||
\(528\) | − | 3.30969i | − | 0.144036i | ||||||
\(529\) | 22.8809 | 0.994822 | ||||||||
\(530\) | 4.14979 | − | 4.92718i | 0.180255 | − | 0.214023i | ||||
\(531\) | −20.3431 | −0.882816 | ||||||||
\(532\) | − | 7.04487i | − | 0.305434i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.01623 | −0.217074 | ||||||||
\(535\) | −30.2366 | − | 25.4660i | −1.30724 | − | 1.10099i | ||||
\(536\) | 13.5451 | 0.585059 | ||||||||
\(537\) | 6.97951i | 0.301188i | ||||||||
\(538\) | 4.34628i | 0.187381i | ||||||||
\(539\) | −11.1805 | −0.481577 | ||||||||
\(540\) | 2.04880 | + | 1.72555i | 0.0881664 | + | 0.0742558i | ||||
\(541\) | 9.48006 | 0.407580 | 0.203790 | − | 0.979015i | \(-0.434674\pi\) | ||||
0.203790 | + | 0.979015i | \(0.434674\pi\) | |||||||
\(542\) | 26.1257i | 1.12219i | ||||||||
\(543\) | − | 6.84118i | − | 0.293583i | ||||||
\(544\) | −17.5325 | −0.751700 | ||||||||
\(545\) | −8.29958 | + | 9.85437i | −0.355515 | + | 0.422115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3911i | 1.42770i | 0.700299 | + | 0.713850i | \(0.253050\pi\) | ||||
−0.700299 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(548\) | − | 1.16741i | − | 0.0498694i | ||||||
\(549\) | 19.4801 | 0.831389 | ||||||||
\(550\) | 22.7041 | − | 3.91770i | 0.968105 | − | 0.167051i | ||||
\(551\) | −17.6427 | −0.751604 | ||||||||
\(552\) | − | 0.366292i | − | 0.0155904i | ||||||
\(553\) | 22.6914i | 0.964937i | ||||||||
\(554\) | 11.7492 | 0.499177 | ||||||||
\(555\) | 2.70934 | − | 3.21689i | 0.115005 | − | 0.136549i | ||||
\(556\) | −5.13533 | −0.217787 | ||||||||
\(557\) | 37.7648i | 1.60015i | 0.599903 | + | 0.800073i | \(0.295206\pi\) | ||||
−0.599903 | + | 0.800073i | \(0.704794\pi\) | |||||||
\(558\) | 4.03793i | 0.170939i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.57766 | − | 7.22431i | −0.362472 | − | 0.305283i | ||||
\(561\) | 7.29958 | 0.308188 | ||||||||
\(562\) | 4.82221i | 0.203413i | ||||||||
\(563\) | − | 25.9008i | − | 1.09159i | −0.837919 | − | 0.545794i | \(-0.816228\pi\) | ||
0.837919 | − | 0.545794i | \(-0.183772\pi\) | |||||||
\(564\) | −2.50155 | −0.105334 | ||||||||
\(565\) | −8.14087 | − | 6.85643i | −0.342489 | − | 0.288452i | ||||
\(566\) | 7.22928 | 0.303869 | ||||||||
\(567\) | − | 16.1193i | − | 0.676947i | ||||||
\(568\) | − | 5.78466i | − | 0.242719i | ||||||
\(569\) | 21.5451 | 0.903217 | 0.451609 | − | 0.892216i | \(-0.350850\pi\) | ||||
0.451609 | + | 0.892216i | \(0.350850\pi\) | |||||||
\(570\) | 3.47114 | − | 4.12140i | 0.145390 | − | 0.172626i | ||||
\(571\) | −2.22036 | −0.0929192 | −0.0464596 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464596 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.530704i | − | 0.0221705i | ||||||
\(574\) | 0.434911 | 0.0181528 | ||||||||
\(575\) | 1.70042 | − | 0.293416i | 0.0709124 | − | 0.0122363i | ||||
\(576\) | −25.2419 | −1.05174 | ||||||||
\(577\) | − | 6.20265i | − | 0.258220i | −0.991630 | − | 0.129110i | \(-0.958788\pi\) | ||
0.991630 | − | 0.129110i | \(-0.0412120\pi\) | |||||||
\(578\) | 15.0840i | 0.627411i | ||||||||
\(579\) | 7.31742 | 0.304102 | ||||||||
\(580\) | 2.55063 | − | 3.02845i | 0.105909 | − | 0.125749i | ||||
\(581\) | 15.9024 | 0.659742 | ||||||||
\(582\) | − | 2.37901i | − | 0.0986130i | ||||||
\(583\) | 9.41646i | 0.389990i | ||||||||
\(584\) | 27.2492 | 1.12758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6265 | −0.480285 | ||||||||
\(587\) | − | 1.82894i | − | 0.0754883i | −0.999287 | − | 0.0377442i | \(-0.987983\pi\) | ||
0.999287 | − | 0.0377442i | \(-0.0120172\pi\) | |||||||
\(588\) | − | 0.586832i | − | 0.0242005i | ||||||
\(589\) | −6.94228 | −0.286052 | ||||||||
\(590\) | −14.3395 | − | 12.0770i | −0.590346 | − | 0.497204i | ||||
\(591\) | 3.19466 | 0.131411 | ||||||||
\(592\) | 13.4681i | 0.553534i | ||||||||
\(593\) | 0.0728761i | 0.00299266i | 0.999999 | + | 0.00149633i | \(0.000476297\pi\) | ||||
−0.999999 | + | 0.00149633i | \(0.999524\pi\) | |||||||
\(594\) | 9.35204 | 0.383719 | ||||||||
\(595\) | 15.9334 | − | 18.9182i | 0.653204 | − | 0.775571i | ||||
\(596\) | 13.1642 | 0.539229 | ||||||||
\(597\) | − | 6.00646i | − | 0.245828i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.5813 | 0.595777 | 0.297888 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297888 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(600\) | 0.902394 | + | 5.22960i | 0.0368401 | + | 0.213498i | ||||
\(601\) | −44.4082 | −1.81145 | −0.905723 | − | 0.423870i | \(-0.860671\pi\) | ||||
−0.905723 | + | 0.423870i | \(0.860671\pi\) | |||||||
\(602\) | − | 3.22748i | − | 0.131542i | ||||||
\(603\) | 12.6881i | 0.516700i | ||||||||
\(604\) | 11.3105 | 0.460220 | ||||||||
\(605\) | −5.85021 | + | 6.94615i | −0.237845 | + | 0.282401i | ||||
\(606\) | 2.43491 | 0.0989115 | ||||||||
\(607\) | − | 36.2354i | − | 1.47075i | −0.677660 | − | 0.735375i | \(-0.737006\pi\) | ||
0.677660 | − | 0.735375i | \(-0.262994\pi\) | |||||||
\(608\) | − | 18.9182i | − | 0.767235i | ||||||
\(609\) | 2.10126 | 0.0851474 | ||||||||
\(610\) | 13.7311 | + | 11.5647i | 0.555956 | + | 0.468239i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 9.26754i | − | 0.374618i | ||||||
\(613\) | − | 3.35830i | − | 0.135641i | −0.997698 | − | 0.0678203i | \(-0.978396\pi\) | ||
0.997698 | − | 0.0678203i | \(-0.0216045\pi\) | |||||||
\(614\) | 26.2455 | 1.05918 | ||||||||
\(615\) | −0.106526 | − | 0.0897185i | −0.00429553 | − | 0.00361780i | ||||
\(616\) | 24.2240 | 0.976013 | ||||||||
\(617\) | − | 21.1820i | − | 0.852754i | −0.904546 | − | 0.426377i | \(-0.859790\pi\) | ||
0.904546 | − | 0.426377i | \(-0.140210\pi\) | |||||||
\(618\) | − | 2.63631i | − | 0.106048i | ||||||
\(619\) | 25.4082 | 1.02124 | 0.510620 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510620 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(620\) | 1.00366 | − | 1.19167i | 0.0403078 | − | 0.0478587i | ||||
\(621\) | 0.700420 | 0.0281069 | ||||||||
\(622\) | − | 9.07009i | − | 0.363677i | ||||||
\(623\) | − | 24.8455i | − | 0.995416i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5543 | + | 8.37828i | −0.942171 | + | 0.335131i | ||||
\(626\) | −31.0399 | −1.24060 | ||||||||
\(627\) | 7.87651i | 0.314557i | ||||||||
\(628\) | − | 3.66105i | − | 0.146092i | ||||||
\(629\) | −29.7041 | −1.18438 | ||||||||
\(630\) | 10.0000 | − | 11.8733i | 0.398410 | − | 0.473045i | ||||
\(631\) | −43.5451 | −1.73350 | −0.866751 | − | 0.498740i | \(-0.833796\pi\) | ||||
−0.866751 | + | 0.498740i | \(0.833796\pi\) | |||||||
\(632\) | 34.3853i | 1.36777i | ||||||||
\(633\) | 2.51300i | 0.0998828i | ||||||||
\(634\) | −14.0614 | −0.558449 | ||||||||
\(635\) | 28.5724 | + | 24.0643i | 1.13386 | + | 0.954964i | ||||
\(636\) | −0.494244 | −0.0195980 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 13.8238i | − | 0.547288i | ||||||
\(639\) | 5.41868 | 0.214360 | ||||||||
\(640\) | −6.78883 | − | 5.71771i | −0.268352 | − | 0.226012i | ||||
\(641\) | 48.2854 | 1.90716 | 0.953579 | − | 0.301142i | \(-0.0973679\pi\) | ||||
0.953579 | + | 0.301142i | \(0.0973679\pi\) | |||||||
\(642\) | − | 7.24423i | − | 0.285907i | ||||||
\(643\) | − | 42.3440i | − | 1.66989i | −0.550337 | − | 0.834943i | \(-0.685501\pi\) | ||
0.550337 | − | 0.834943i | \(-0.314499\pi\) | |||||||
\(644\) | 0.413416 | 0.0162909 | ||||||||
\(645\) | −0.665802 | + | 0.790529i | −0.0262159 | + | 0.0311271i | ||||
\(646\) | −38.0561 | −1.49730 | ||||||||
\(647\) | − | 34.4052i | − | 1.35261i | −0.736622 | − | 0.676305i | \(-0.763580\pi\) | ||
0.736622 | − | 0.676305i | \(-0.236420\pi\) | |||||||
\(648\) | − | 24.4263i | − | 0.959556i | ||||||
\(649\) | 27.4045 | 1.07572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.826831 | 0.0324061 | ||||||||
\(652\) | 7.04487i | 0.275899i | ||||||||
\(653\) | 14.3315i | 0.560834i | 0.959878 | + | 0.280417i | \(0.0904727\pi\) | ||||
−0.959878 | + | 0.280417i | \(0.909527\pi\) | |||||||
\(654\) | −2.36096 | −0.0923208 | ||||||||
\(655\) | −14.4045 | + | 17.1029i | −0.562830 | + | 0.668267i | ||||
\(656\) | 0.445988 | 0.0174129 | ||||||||
\(657\) | 25.5252i | 0.995832i | ||||||||
\(658\) | 29.5936i | 1.15368i | ||||||||
\(659\) | −22.8232 | −0.889065 | −0.444532 | − | 0.895763i | \(-0.646630\pi\) | ||||
−0.444532 | + | 0.895763i | \(0.646630\pi\) | |||||||
\(660\) | −1.35204 | − | 1.13872i | −0.0526280 | − | 0.0443245i | ||||
\(661\) | −14.4187 | −0.560822 | −0.280411 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280411 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(662\) | − | 15.0796i | − | 0.586087i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.0976 | 0.935168 | ||||||||
\(665\) | 20.4134 | + | 17.1927i | 0.791598 | + | 0.666703i | ||||
\(666\) | −18.6427 | −0.722390 | ||||||||
\(667\) | − | 1.03533i | − | 0.0400881i | ||||||
\(668\) | 1.19792i | 0.0463491i | ||||||||
\(669\) | −6.71826 | −0.259743 | ||||||||
\(670\) | −7.53252 | + | 8.94361i | −0.291007 | + | 0.345522i | ||||
\(671\) | −26.2419 | −1.01306 | ||||||||
\(672\) | 2.25318i | 0.0869181i | ||||||||
\(673\) | 34.1741i | 1.31731i | 0.752443 | + | 0.658657i | \(0.228875\pi\) | ||||
−0.752443 | + | 0.658657i | \(0.771125\pi\) | |||||||
\(674\) | −18.1590 | −0.699458 | ||||||||
\(675\) | −10.0000 | + | 1.72555i | −0.384900 | + | 0.0664164i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.84695i | 0.224716i | 0.993668 | + | 0.112358i | \(0.0358404\pi\) | ||||
−0.993668 | + | 0.112358i | \(0.964160\pi\) | |||||||
\(678\) | − | 1.95043i | − | 0.0749058i | ||||||
\(679\) | 11.7833 | 0.452201 | ||||||||
\(680\) | 24.1445 | − | 28.6676i | 0.925900 | − | 1.09935i | ||||
\(681\) | −1.66054 | −0.0636319 | ||||||||
\(682\) | − | 5.43955i | − | 0.208291i | ||||||
\(683\) | − | 11.3488i | − | 0.434249i | −0.976144 | − | 0.217125i | \(-0.930332\pi\) | ||
0.976144 | − | 0.217125i | \(-0.0696678\pi\) | |||||||
\(684\) | 10.0000 | 0.382360 | ||||||||
\(685\) | 3.38273 | + | 2.84901i | 0.129247 | + | 0.108855i | ||||
\(686\) | −23.8106 | −0.909093 | ||||||||
\(687\) | − | 0.525808i | − | 0.0200608i | ||||||
\(688\) | − | 3.30969i | − | 0.126181i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.241857 | + | 0.203698i | 0.00920733 | + | 0.00775463i | ||||
\(691\) | 18.8232 | 0.716067 | 0.358034 | − | 0.933709i | \(-0.383447\pi\) | ||||
0.358034 | + | 0.933709i | \(0.383447\pi\) | |||||||
\(692\) | − | 0.790529i | − | 0.0300514i | ||||||
\(693\) | 22.6914i | 0.861976i | ||||||||
\(694\) | 14.5325 | 0.551647 | ||||||||
\(695\) | 12.5325 | − | 14.8803i | 0.475385 | − | 0.564441i | ||||
\(696\) | 3.18413 | 0.120694 | ||||||||
\(697\) | 0.983636i | 0.0372579i | ||||||||
\(698\) | − | 22.2036i | − | 0.840420i | ||||||
\(699\) | 4.81952 | 0.182291 | ||||||||
\(700\) | −5.90239 | + | 1.01849i | −0.223090 | + | 0.0384952i | ||||
\(701\) | 19.1626 | 0.723763 | 0.361881 | − | 0.932224i | \(-0.382135\pi\) | ||||
0.361881 | + | 0.932224i | \(0.382135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.0518i | − | 1.20885i | ||||||
\(704\) | 34.0037 | 1.28156 | ||||||||
\(705\) | 6.10492 | − | 7.24857i | 0.229924 | − | 0.272997i | ||||
\(706\) | 1.55401 | 0.0584860 | ||||||||
\(707\) | 12.0602i | 0.453570i | ||||||||
\(708\) | 1.43839i | 0.0540578i | ||||||||
\(709\) | 23.4837 | 0.881949 | 0.440975 | − | 0.897520i | \(-0.354633\pi\) | ||||
0.440975 | + | 0.897520i | \(0.354633\pi\) | |||||||
\(710\) | 3.81952 | + | 3.21689i | 0.143344 | + | 0.120728i | ||||
\(711\) | −32.2098 | −1.20796 | ||||||||
\(712\) | − | 37.6496i | − | 1.41098i | ||||||
\(713\) | − | 0.407395i | − | 0.0152571i | ||||||
\(714\) | 4.53252 | 0.169625 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9370 | −0.446107 | ||||||||
\(717\) | − | 1.38044i | − | 0.0515535i | ||||||
\(718\) | 34.9173i | 1.30310i | ||||||||
\(719\) | 14.1086 | 0.526161 | 0.263080 | − | 0.964774i | \(-0.415262\pi\) | ||||
0.263080 | + | 0.964774i | \(0.415262\pi\) | |||||||
\(720\) | 10.2547 | − | 12.1758i | 0.382170 | − | 0.453764i | ||||
\(721\) | 13.0577 | 0.486295 | ||||||||
\(722\) | − | 18.5046i | − | 0.688668i | ||||||
\(723\) | − | 6.02765i | − | 0.224171i | ||||||
\(724\) | 11.7004 | 0.434843 | ||||||||
\(725\) | 2.55063 | + | 14.7816i | 0.0947280 | + | 0.548973i | ||||
\(726\) | −1.66419 | −0.0617640 | ||||||||
\(727\) | 25.3762i | 0.941153i | 0.882359 | + | 0.470576i | \(0.155954\pi\) | ||||
−0.882359 | + | 0.470576i | \(0.844046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7796 | 0.769616 | ||||||||
\(730\) | −15.1534 | + | 17.9922i | −0.560854 | + | 0.665921i | ||||
\(731\) | 7.29958 | 0.269985 | ||||||||
\(732\) | − | 1.37736i | − | 0.0509087i | ||||||
\(733\) | − | 10.6692i | − | 0.394074i | −0.980396 | − | 0.197037i | \(-0.936868\pi\) | ||
0.980396 | − | 0.197037i | \(-0.0631320\pi\) | |||||||
\(734\) | −39.6952 | −1.46517 | ||||||||
\(735\) | 1.70042 | + | 1.43213i | 0.0627209 | + | 0.0528251i | ||||
\(736\) | 1.11018 | 0.0409218 | ||||||||
\(737\) | − | 17.0923i | − | 0.629605i | ||||||
\(738\) | 0.617344i | 0.0227247i | ||||||||
\(739\) | −1.41503 | −0.0520526 | −0.0260263 | − | 0.999661i | \(-0.508285\pi\) | ||||
−0.0260263 | + | 0.999661i | \(0.508285\pi\) | |||||||
\(740\) | 5.50183 | + | 4.63377i | 0.202251 | + | 0.170341i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.84695i | 0.214648i | ||||||||
\(743\) | − | 29.8777i | − | 1.09611i | −0.836443 | − | 0.548053i | \(-0.815369\pi\) | ||
0.836443 | − | 0.548053i | \(-0.184631\pi\) | |||||||
\(744\) | 1.25293 | 0.0459348 | ||||||||
\(745\) | −32.1267 | + | 38.1451i | −1.17703 | + | 1.39753i | ||||
\(746\) | 40.9370 | 1.49881 | ||||||||
\(747\) | 22.5730i | 0.825903i | ||||||||
\(748\) | 12.4844i | 0.456476i | ||||||||
\(749\) | 35.8809 | 1.31106 | ||||||||
\(750\) | −3.95485 | − | 2.31238i | −0.144411 | − | 0.0844362i | ||||
\(751\) | −19.9858 | −0.729293 | −0.364646 | − | 0.931146i | \(-0.618810\pi\) | ||||
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(752\) | 30.3474i | 1.10666i | ||||||||
\(753\) | − | 3.20938i | − | 0.116956i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.6028 | + | 32.7737i | −1.00457 | + | 1.19276i | ||||
\(756\) | −2.43126 | −0.0884239 | ||||||||
\(757\) | − | 17.0923i | − | 0.621232i | −0.950535 | − | 0.310616i | \(-0.899465\pi\) | ||
0.950535 | − | 0.310616i | \(-0.100535\pi\) | |||||||
\(758\) | 20.6649i | 0.750584i | ||||||||
\(759\) | −0.462218 | −0.0167775 | ||||||||
\(760\) | 30.9334 | + | 26.0528i | 1.12207 | + | 0.945034i | ||||
\(761\) | 42.2240 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(762\) | 6.84552i | 0.247987i | ||||||||
\(763\) | − | 11.6939i | − | 0.423347i | ||||||
\(764\) | 0.907659 | 0.0328380 | ||||||||
\(765\) | 26.8539 | + | 22.6170i | 0.970904 | + | 0.817718i | ||||
\(766\) | 2.07395 | 0.0749350 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.42107i | 0.159531i | ||||||||
\(769\) | −23.7655 | −0.857004 | −0.428502 | − | 0.903541i | \(-0.640959\pi\) | ||||
−0.428502 | + | 0.903541i | \(0.640959\pi\) | |||||||
\(770\) | −13.4711 | + | 15.9947i | −0.485466 | + | 0.576410i | ||||
\(771\) | 3.75814 | 0.135346 | ||||||||
\(772\) | 12.5149i | 0.450422i | ||||||||
\(773\) | − | 0.284086i | − | 0.0102179i | −0.999987 | − | 0.00510894i | \(-0.998374\pi\) | ||
0.999987 | − | 0.00510894i | \(-0.00162623\pi\) | |||||||
\(774\) | 4.58132 | 0.164672 | ||||||||
\(775\) | 1.00366 | + | 5.81644i | 0.0360524 | + | 0.208933i | ||||
\(776\) | 17.8557 | 0.640984 | ||||||||
\(777\) | 3.81739i | 0.136948i | ||||||||
\(778\) | 26.1730i | 0.938349i | ||||||||
\(779\) | −1.06138 | −0.0380278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29958 | −0.261199 | ||||||||
\(782\) | − | 2.23325i | − | 0.0798610i | ||||||
\(783\) | 6.08867i | 0.217591i | ||||||||
\(784\) | −7.11910 | −0.254254 | ||||||||
\(785\) | 10.6084 | + | 8.93460i | 0.378628 | + | 0.318890i | ||||
\(786\) | −4.09761 | −0.146157 | ||||||||
\(787\) | − | 24.1341i | − | 0.860289i | −0.902760 | − | 0.430145i | \(-0.858463\pi\) | ||
0.902760 | − | 0.430145i | \(-0.141537\pi\) | |||||||
\(788\) | 5.46381i | 0.194640i | ||||||||
\(789\) | 4.63849 | 0.165135 | ||||||||
\(790\) | −22.7041 | − | 19.1219i | −0.807775 | − | 0.680327i | ||||
\(791\) | 9.66054 | 0.343489 | ||||||||
\(792\) | 34.3853i | 1.22183i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 26.7529 | 0.949424 | ||||||||
\(795\) | 1.20618 | − | 1.43213i | 0.0427787 | − | 0.0507926i | ||||
\(796\) | 10.2728 | 0.364110 | ||||||||
\(797\) | − | 34.3442i | − | 1.21653i | −0.793732 | − | 0.608267i | \(-0.791865\pi\) | ||
0.793732 | − | 0.608267i | \(-0.208135\pi\) | |||||||
\(798\) | 4.89075i | 0.173131i | ||||||||
\(799\) | −66.9317 | −2.36787 | ||||||||
\(800\) | −15.8502 | + | 2.73503i | −0.560390 | + | 0.0966980i | ||||
\(801\) | 35.2676 | 1.24612 | ||||||||
\(802\) | − | 4.39797i | − | 0.155298i | ||||||
\(803\) | − | 34.3853i | − | 1.21343i | ||||||
\(804\) | 0.897129 | 0.0316393 | ||||||||
\(805\) | −1.00892 | + | 1.19792i | −0.0355598 | + | 0.0422213i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26329i | 0.0444698i | ||||||||
\(808\) | 18.2753i | 0.642924i | ||||||||
\(809\) | 47.6862 | 1.67656 | 0.838279 | − | 0.545241i | \(-0.183562\pi\) | ||||
0.838279 | + | 0.545241i | \(0.183562\pi\) | |||||||
\(810\) | 16.1283 | + | 13.5836i | 0.566691 | + | 0.477280i | ||||
\(811\) | −24.5992 | −0.863793 | −0.431897 | − | 0.901923i | \(-0.642155\pi\) | ||||
−0.431897 | + | 0.901923i | \(0.642155\pi\) | |||||||
\(812\) | 3.59377i | 0.126117i | ||||||||
\(813\) | 7.59368i | 0.266322i | ||||||||
\(814\) | 25.1138 | 0.880239 | ||||||||
\(815\) | −20.4134 | − | 17.1927i | −0.715051 | − | 0.602233i | ||||
\(816\) | 4.64796 | 0.162711 | ||||||||
\(817\) | 7.87651i | 0.275564i | ||||||||
\(818\) | 16.0097i | 0.559765i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.153445 | − | 0.182190i | 0.00535853 | − | 0.00636236i | ||||
\(821\) | −17.2996 | −0.603759 | −0.301880 | − | 0.953346i | \(-0.597614\pi\) | ||||
−0.301880 | + | 0.953346i | \(0.597614\pi\) | |||||||
\(822\) | 0.810450i | 0.0282677i | ||||||||
\(823\) | 32.5625i | 1.13506i | 0.823353 | + | 0.567529i | \(0.192101\pi\) | ||||
−0.823353 | + | 0.567529i | \(0.807899\pi\) | |||||||
\(824\) | 19.7869 | 0.689311 | ||||||||
\(825\) | 6.59916 | − | 1.13872i | 0.229753 | − | 0.0396451i | ||||
\(826\) | 17.0162 | 0.592070 | ||||||||
\(827\) | 15.4702i | 0.537951i | 0.963147 | + | 0.268976i | \(0.0866851\pi\) | ||||
−0.963147 | + | 0.268976i | \(0.913315\pi\) | |||||||
\(828\) | 0.586832i | 0.0203938i | ||||||||
\(829\) | 14.5236 | 0.504425 | 0.252213 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252213 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(830\) | −13.4008 | + | 15.9113i | −0.465150 | + | 0.552288i | ||||
\(831\) | 3.41503 | 0.118466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 15.7013i | − | 0.544018i | ||||||
\(834\) | 3.56509 | 0.123449 | ||||||||
\(835\) | −3.47114 | − | 2.92347i | −0.120124 | − | 0.101171i | ||||
\(836\) | −13.4711 | −0.465909 | ||||||||
\(837\) | 2.39585i | 0.0828127i | ||||||||
\(838\) | 19.9747i | 0.690015i | ||||||||
\(839\) | 0.815866 | 0.0281668 | 0.0140834 | − | 0.999901i | \(-0.495517\pi\) | ||||
0.0140834 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(840\) | −3.68419 | − | 3.10291i | −0.127117 | − | 0.107061i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 20.3049i | 0.699753i | ||||||||
\(843\) | 1.40162i | 0.0482744i | ||||||||
\(844\) | −4.29797 | −0.147942 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −42.0073 | −1.44424 | ||||||||
\(847\) | − | 8.24280i | − | 0.283226i | ||||||
\(848\) | 5.99587i | 0.205899i | ||||||||
\(849\) | 2.10126 | 0.0721151 | ||||||||
\(850\) | 5.50183 | + | 31.8845i | 0.188711 | + | 1.09363i | ||||
\(851\) | 1.88090 | 0.0644764 | ||||||||
\(852\) | − | 0.383134i | − | 0.0131260i | ||||||
\(853\) | 20.0856i | 0.687719i | 0.939021 | + | 0.343859i | \(0.111734\pi\) | ||||
−0.939021 | + | 0.343859i | \(0.888266\pi\) | |||||||
\(854\) | −16.2943 | −0.557580 | ||||||||
\(855\) | −24.4045 | + | 28.9763i | −0.834616 | + | 0.990968i | ||||
\(856\) | 54.3719 | 1.85839 | ||||||||
\(857\) | 40.7886i | 1.39331i | 0.717406 | + | 0.696656i | \(0.245329\pi\) | ||||
−0.717406 | + | 0.696656i | \(0.754671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1301 | 1.36922 | 0.684610 | − | 0.728909i | \(-0.259972\pi\) | ||||
0.684610 | + | 0.728909i | \(0.259972\pi\) | |||||||
\(860\) | −1.35204 | − | 1.13872i | −0.0461041 | − | 0.0388300i | ||||
\(861\) | 0.126411 | 0.00430808 | ||||||||
\(862\) | 11.4703i | 0.390679i | ||||||||
\(863\) | − | 20.8275i | − | 0.708977i | −0.935060 | − | 0.354489i | \(-0.884655\pi\) | ||
0.935060 | − | 0.354489i | \(-0.115345\pi\) | |||||||
\(864\) | −6.52886 | −0.222116 | ||||||||
\(865\) | 2.29066 | + | 1.92925i | 0.0778848 | + | 0.0655964i | ||||
\(866\) | −29.4134 | −0.999509 | ||||||||
\(867\) | 4.38430i | 0.148899i | ||||||||
\(868\) | 1.41412i | 0.0479985i | ||||||||
\(869\) | 43.3903 | 1.47192 | ||||||||
\(870\) | −1.77072 | + | 2.10243i | −0.0600330 | + | 0.0712792i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 17.7203i | − | 0.600084i | ||||||
\(873\) | 16.7261i | 0.566091i | ||||||||
\(874\) | 2.40976 | 0.0815114 | ||||||||
\(875\) | 11.4533 | − | 19.5885i | 0.387192 | − | 0.662212i | ||||
\(876\) | 1.80479 | 0.0609782 | ||||||||
\(877\) | − | 46.5944i | − | 1.57338i | −0.617347 | − | 0.786691i | \(-0.711793\pi\) | ||
0.617347 | − | 0.786691i | \(-0.288207\pi\) | |||||||
\(878\) | 8.38421i | 0.282953i | ||||||||
\(879\) | −3.37935 | −0.113982 | ||||||||
\(880\) | −13.8143 | + | 16.4021i | −0.465678 | + | 0.552916i | ||||
\(881\) | 23.8447 | 0.803347 | 0.401674 | − | 0.915783i | \(-0.368429\pi\) | ||||
0.401674 | + | 0.915783i | \(0.368429\pi\) | |||||||
\(882\) | − | 9.85437i | − | 0.331814i | ||||||
\(883\) | 37.2496i | 1.25355i | 0.779201 | + | 0.626774i | \(0.215625\pi\) | ||||
−0.779201 | + | 0.626774i | \(0.784375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.16790 | − | 3.51031i | −0.140103 | − | 0.117998i | ||||
\(886\) | 45.4082 | 1.52552 | ||||||||
\(887\) | 28.5795i | 0.959605i | 0.877377 | + | 0.479802i | \(0.159292\pi\) | ||||
−0.877377 | + | 0.479802i | \(0.840708\pi\) | |||||||
\(888\) | 5.78466i | 0.194121i | ||||||||
\(889\) | −33.9060 | −1.13717 | ||||||||
\(890\) | 24.8594 | + | 20.9372i | 0.833289 | + | 0.701816i | ||||
\(891\) | −30.8232 | −1.03262 | ||||||||
\(892\) | − | 11.4902i | − | 0.384720i | ||||||
\(893\) | − | 72.2217i | − | 2.41681i | ||||||
\(894\) | −9.13899 | −0.305653 | ||||||||
\(895\) | 29.1317 | − | 34.5890i | 0.973765 | − | 1.15618i | ||||
\(896\) | 8.05611 | 0.269136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.8180i | 0.494483i | ||||||||
\(899\) | 3.54144 | 0.118114 | ||||||||
\(900\) | −1.44571 | − | 8.37828i | −0.0481905 | − | 0.279276i | ||||
\(901\) | −13.2240 | −0.440556 | ||||||||
\(902\) | − | 0.831632i | − | 0.0276903i | ||||||
\(903\) | − | 0.938099i | − | 0.0312180i | ||||||
\(904\) | 14.6390 | 0.486887 | ||||||||
\(905\) | −28.5543 | + | 33.9035i | −0.949177 | + | 1.12699i | ||||
\(906\) | −7.85209 | −0.260868 | ||||||||
\(907\) | 6.41386i | 0.212969i | 0.994314 | + | 0.106484i | \(0.0339594\pi\) | ||||
−0.994314 | + | 0.106484i | \(0.966041\pi\) | |||||||
\(908\) | − | 2.84001i | − | 0.0942489i | ||||||
\(909\) | −17.1191 | −0.567805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.2204 | 0.736193 | 0.368097 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368097 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(912\) | 5.01532i | 0.166074i | ||||||||
\(913\) | − | 30.4084i | − | 1.00637i | ||||||
\(914\) | −9.77437 | −0.323308 | ||||||||
\(915\) | 3.99108 | + | 3.36138i | 0.131941 | + | 0.111124i | ||||
\(916\) | 0.899287 | 0.0297133 | ||||||||
\(917\) | − | 20.2956i | − | 0.670219i | ||||||
\(918\) | 13.1335i | 0.433472i | ||||||||
\(919\) | −26.1264 | −0.861831 | −0.430915 | − | 0.902392i | \(-0.641809\pi\) | ||||
−0.430915 | + | 0.902392i | \(0.641809\pi\) | |||||||
\(920\) | −1.52886 | + | 1.81527i | −0.0504051 | + | 0.0598476i | ||||
\(921\) | 7.62851 | 0.251368 | ||||||||
\(922\) | − | 5.39220i | − | 0.177583i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.60442 | 0.0527817 | ||||||||
\(925\) | −26.8539 | + | 4.63377i | −0.882950 | + | 0.152357i | ||||
\(926\) | −2.36096 | −0.0775859 | ||||||||
\(927\) | 18.5351i | 0.608772i | ||||||||
\(928\) | 9.65067i | 0.316799i | ||||||||
\(929\) | −23.9423 | −0.785521 | −0.392760 | − | 0.919641i | \(-0.628480\pi\) | ||||
−0.392760 | + | 0.919641i | \(0.628480\pi\) | |||||||
\(930\) | −0.696765 | + | 0.827293i | −0.0228478 | + | 0.0271280i | ||||
\(931\) | 16.9423 | 0.555261 | ||||||||
\(932\) | 8.24280i | 0.270002i | ||||||||
\(933\) | − | 2.63631i | − | 0.0863089i | ||||||
\(934\) | −38.9496 | −1.27447 | ||||||||
\(935\) | −36.1752 | − | 30.4676i | −1.18306 | − | 0.996397i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.5046i | − | 0.604518i | −0.953226 | − | 0.302259i | \(-0.902259\pi\) | ||
0.953226 | − | 0.302259i | \(-0.0977407\pi\) | |||||||
\(938\) | − | 10.6131i | − | 0.346531i | ||||||
\(939\) | −9.02204 | −0.294423 | ||||||||
\(940\) | 12.3972 | + | 10.4412i | 0.404352 | + | 0.340554i | ||||
\(941\) | 14.3788 | 0.468735 | 0.234368 | − | 0.972148i | \(-0.424698\pi\) | ||||
0.234368 | + | 0.972148i | \(0.424698\pi\) | |||||||
\(942\) | 2.54160i | 0.0828098i | ||||||||
\(943\) | − | 0.0622851i | − | 0.00202828i | ||||||
\(944\) | 17.4496 | 0.567938 | ||||||||
\(945\) | 5.93336 | − | 7.04487i | 0.193012 | − | 0.229170i | ||||
\(946\) | −6.17156 | −0.200655 | ||||||||
\(947\) | − | 58.3188i | − | 1.89511i | −0.319596 | − | 0.947554i | \(-0.603547\pi\) | ||
0.319596 | − | 0.947554i | \(-0.396453\pi\) | |||||||
\(948\) | 2.27744i | 0.0739677i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −34.4045 | + | 5.93667i | −1.11623 | + | 0.192611i | ||||
\(951\) | −4.08708 | −0.132533 | ||||||||
\(952\) | 34.0190i | 1.10256i | ||||||||
\(953\) | 13.7995i | 0.447010i | 0.974703 | + | 0.223505i | \(0.0717499\pi\) | ||||
−0.974703 | + | 0.223505i | \(0.928250\pi\) | |||||||
\(954\) | −8.29958 | −0.268709 | ||||||||
\(955\) | −2.21510 | + | 2.63006i | −0.0716788 | + | 0.0851067i | ||||
\(956\) | 2.36096 | 0.0763588 | ||||||||
\(957\) | − | 4.01801i | − | 0.129884i | ||||||
\(958\) | 36.5762i | 1.18172i | ||||||||
\(959\) | −4.01419 | −0.129625 | ||||||||
\(960\) | −5.17156 | − | 4.35561i | −0.166911 | − | 0.140577i | ||||
\(961\) | −29.6065 | −0.955047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9319i | 1.64126i | ||||||||
\(964\) | 10.3090 | 0.332032 | ||||||||
\(965\) | −36.2636 | − | 30.5421i | −1.16737 | − | 0.983184i | ||||
\(966\) | −0.287005 | −0.00923422 | ||||||||
\(967\) | − | 30.3474i | − | 0.975906i | −0.872870 | − | 0.487953i | \(-0.837744\pi\) | ||
0.872870 | − | 0.487953i | \(-0.162256\pi\) | |||||||
\(968\) | − | 12.4907i | − | 0.401466i | ||||||
\(969\) | −11.0614 | −0.355343 | ||||||||
\(970\) | −9.92970 | + | 11.7899i | −0.318824 | + | 0.378550i | ||||
\(971\) | 44.1013 | 1.41528 | 0.707638 | − | 0.706575i | \(-0.249761\pi\) | ||||
0.707638 | + | 0.706575i | \(0.249761\pi\) | |||||||
\(972\) | − | 5.21160i | − | 0.167162i | ||||||
\(973\) | 17.6580i | 0.566089i | ||||||||
\(974\) | 26.5074 | 0.849351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.7093 | −0.534853 | ||||||||
\(977\) | 22.3220i | 0.714143i | 0.934077 | + | 0.357071i | \(0.116225\pi\) | ||||
−0.934077 | + | 0.357071i | \(0.883775\pi\) | |||||||
\(978\) | − | 4.89075i | − | 0.156389i | ||||||
\(979\) | −47.5094 | −1.51841 | ||||||||
\(980\) | −2.44937 | + | 2.90822i | −0.0782422 | + | 0.0928996i | ||||
\(981\) | 16.5992 | 0.529970 | ||||||||
\(982\) | − | 12.6838i | − | 0.404756i | ||||||
\(983\) | 4.03793i | 0.128790i | 0.997924 | + | 0.0643950i | \(0.0205118\pi\) | ||||
−0.997924 | + | 0.0643950i | \(0.979488\pi\) | |||||||
\(984\) | 0.191556 | 0.00610659 | ||||||||
\(985\) | −15.8321 | − | 13.3342i | −0.504453 | − | 0.424862i | ||||
\(986\) | 19.4134 | 0.618249 | ||||||||
\(987\) | 8.60167i | 0.273794i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.462218 | −0.0146977 | ||||||||
\(990\) | −22.7041 | − | 19.1219i | −0.721583 | − | 0.607734i | ||||
\(991\) | 29.6500 | 0.941864 | 0.470932 | − | 0.882170i | \(-0.343918\pi\) | ||||
0.470932 | + | 0.882170i | \(0.343918\pi\) | |||||||
\(992\) | 3.79747i | 0.120570i | ||||||||
\(993\) | − | 4.38304i | − | 0.139092i | ||||||
\(994\) | −4.53252 | −0.143763 | ||||||||
\(995\) | −25.0703 | + | 29.7668i | −0.794782 | + | 0.943671i | ||||
\(996\) | 1.59605 | 0.0505728 | ||||||||
\(997\) | 22.1762i | 0.702327i | 0.936314 | + | 0.351164i | \(0.114214\pi\) | ||||
−0.936314 | + | 0.351164i | \(0.885786\pi\) | |||||||
\(998\) | − | 22.3450i | − | 0.707320i | ||||||
\(999\) | −11.0614 | −0.349967 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))