Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(844,845)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.844");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.d (of order \(2\), degree \(1\), 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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 22x^{10} + 147x^{8} + 390x^{6} + 413x^{4} + 128x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 844.9 | ||
Root | \(0.187333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.844 |
Dual form | 845.2.d.d.844.10 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18733 | 0.839571 | 0.419786 | − | 0.907623i | \(-0.362105\pi\) | ||||
0.419786 | + | 0.907623i | \(0.362105\pi\) | |||||||
\(3\) | − | 0.345110i | − | 0.199249i | −0.995025 | − | 0.0996247i | \(-0.968236\pi\) | ||
0.995025 | − | 0.0996247i | \(-0.0317642\pi\) | |||||||
\(4\) | −0.590239 | −0.295120 | ||||||||
\(5\) | −1.71029 | − | 1.44045i | −0.764867 | − | 0.644189i | ||||
\(6\) | − | 0.409761i | − | 0.167284i | ||||||
\(7\) | −2.02956 | −0.767100 | −0.383550 | − | 0.923520i | \(-0.625299\pi\) | ||||
−0.383550 | + | 0.923520i | \(0.625299\pi\) | |||||||
\(8\) | −3.07548 | −1.08735 | ||||||||
\(9\) | 2.88090 | 0.960300 | ||||||||
\(10\) | −2.03069 | − | 1.71029i | −0.642160 | − | 0.540842i | ||||
\(11\) | 3.88090i | 1.17014i | 0.810985 | + | 0.585068i | \(0.198932\pi\) | ||||
−0.810985 | + | 0.585068i | \(0.801068\pi\) | |||||||
\(12\) | 0.203698i | 0.0588024i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.40976 | −0.644036 | ||||||||
\(15\) | −0.497113 | + | 0.590239i | −0.128354 | + | 0.152399i | ||||
\(16\) | −2.47114 | −0.617785 | ||||||||
\(17\) | 5.45014i | 1.32185i | 0.750450 | + | 0.660927i | \(0.229837\pi\) | ||||
−0.750450 | + | 0.660927i | \(0.770163\pi\) | |||||||
\(18\) | 3.42059 | 0.806240 | ||||||||
\(19\) | 5.88090i | 1.34917i | 0.738197 | + | 0.674585i | \(0.235678\pi\) | ||||
−0.738197 | + | 0.674585i | \(0.764322\pi\) | |||||||
\(20\) | 1.00948 | + | 0.850210i | 0.225727 | + | 0.190113i | ||||
\(21\) | 0.700420i | 0.152844i | ||||||||
\(22\) | 4.60792i | 0.982412i | ||||||||
\(23\) | − | 0.345110i | − | 0.0719604i | −0.999353 | − | 0.0359802i | \(-0.988545\pi\) | ||
0.999353 | − | 0.0359802i | \(-0.0114553\pi\) | |||||||
\(24\) | 1.06138i | 0.216653i | ||||||||
\(25\) | 0.850210 | + | 4.92718i | 0.170042 | + | 0.985437i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.02956i | − | 0.390588i | ||||||
\(28\) | 1.19792 | 0.226386 | ||||||||
\(29\) | −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 | ||||
\(31\) | − | 1.18048i | − | 0.212020i | −0.994365 | − | 0.106010i | \(-0.966192\pi\) | ||
0.994365 | − | 0.106010i | \(-0.0338076\pi\) | |||||||
\(32\) | 3.21689 | 0.568671 | ||||||||
\(33\) | 1.33934 | 0.233149 | ||||||||
\(34\) | 6.47114i | 1.10979i | ||||||||
\(35\) | 3.47114 | + | 2.92347i | 0.586730 | + | 0.494157i | ||||
\(36\) | −1.70042 | −0.283403 | ||||||||
\(37\) | −5.45014 | −0.895998 | −0.447999 | − | 0.894034i | \(-0.647863\pi\) | ||||
−0.447999 | + | 0.894034i | \(0.647863\pi\) | |||||||
\(38\) | 6.98259i | 1.13273i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.25997 | + | 4.43007i | 0.831674 | + | 0.700456i | ||||
\(41\) | − | 0.180479i | − | 0.0281861i | −0.999901 | − | 0.0140930i | \(-0.995514\pi\) | ||
0.999901 | − | 0.0140930i | \(-0.00448610\pi\) | |||||||
\(42\) | 0.831632i | 0.128324i | ||||||||
\(43\) | − | 1.33934i | − | 0.204247i | −0.994772 | − | 0.102123i | \(-0.967436\pi\) | ||
0.994772 | − | 0.102123i | \(-0.0325637\pi\) | |||||||
\(44\) | − | 2.29066i | − | 0.345330i | ||||||
\(45\) | −4.92718 | − | 4.14979i | −0.734501 | − | 0.618614i | ||||
\(46\) | − | 0.409761i | − | 0.0604159i | ||||||
\(47\) | −12.2807 | −1.79133 | −0.895664 | − | 0.444731i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444731i | \(0.853299\pi\) | |||||||
\(48\) | 0.852815i | 0.123093i | ||||||||
\(49\) | −2.88090 | −0.411557 | ||||||||
\(50\) | 1.00948 | + | 5.85021i | 0.142762 | + | 0.827345i | ||||
\(51\) | 1.88090 | 0.263379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.42636i | − | 0.333286i | −0.986017 | − | 0.166643i | \(-0.946707\pi\) | ||
0.986017 | − | 0.166643i | \(-0.0532928\pi\) | |||||||
\(54\) | − | 2.40976i | − | 0.327927i | ||||||
\(55\) | 5.59024 | − | 6.63748i | 0.753788 | − | 0.894997i | ||||
\(56\) | 6.24186 | 0.834103 | ||||||||
\(57\) | 2.02956 | 0.268821 | ||||||||
\(58\) | −3.56200 | −0.467714 | ||||||||
\(59\) | 7.06138i | 0.919313i | 0.888097 | + | 0.459657i | \(0.152027\pi\) | ||||
−0.888097 | + | 0.459657i | \(0.847973\pi\) | |||||||
\(60\) | 0.293416 | − | 0.348383i | 0.0378798 | − | 0.0449760i | ||||
\(61\) | 6.76180 | 0.865760 | 0.432880 | − | 0.901452i | \(-0.357497\pi\) | ||||
0.432880 | + | 0.901452i | \(0.357497\pi\) | |||||||
\(62\) | − | 1.40162i | − | 0.178006i | ||||||
\(63\) | −5.84695 | −0.736646 | ||||||||
\(64\) | 8.76180 | 1.09522 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.59024 | 0.195745 | ||||||||
\(67\) | −4.40422 | −0.538062 | −0.269031 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269031 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(68\) | − | 3.21689i | − | 0.390105i | ||||||
\(69\) | −0.119101 | −0.0143381 | ||||||||
\(70\) | 4.12140 | + | 3.47114i | 0.492601 | + | 0.414880i | ||||
\(71\) | 1.88090i | 0.223222i | 0.993752 | + | 0.111611i | \(0.0356010\pi\) | ||||
−0.993752 | + | 0.111611i | \(0.964399\pi\) | |||||||
\(72\) | −8.86014 | −1.04418 | ||||||||
\(73\) | 8.86014 | 1.03700 | 0.518501 | − | 0.855077i | \(-0.326490\pi\) | ||||
0.518501 | + | 0.855077i | \(0.326490\pi\) | |||||||
\(74\) | −6.47114 | −0.752255 | ||||||||
\(75\) | 1.70042 | − | 0.293416i | 0.196348 | − | 0.0338808i | ||||
\(76\) | − | 3.47114i | − | 0.398167i | ||||||
\(77\) | − | 7.87651i | − | 0.897611i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1805 | −1.25790 | −0.628951 | − | 0.777445i | \(-0.716515\pi\) | ||||
−0.628951 | + | 0.777445i | \(0.716515\pi\) | |||||||
\(80\) | 4.22637 | + | 3.55955i | 0.472523 | + | 0.397970i | ||||
\(81\) | 7.94228 | 0.882475 | ||||||||
\(82\) | − | 0.214289i | − | 0.0236642i | ||||||
\(83\) | −7.83540 | −0.860047 | −0.430024 | − | 0.902818i | \(-0.641495\pi\) | ||||
−0.430024 | + | 0.902818i | \(0.641495\pi\) | |||||||
\(84\) | − | 0.413416i | − | 0.0451073i | ||||||
\(85\) | 7.85066 | − | 9.32135i | 0.851523 | − | 1.01104i | ||||
\(86\) | − | 1.59024i | − | 0.171480i | ||||||
\(87\) | 1.03533i | 0.110999i | ||||||||
\(88\) | − | 11.9356i | − | 1.27234i | ||||||
\(89\) | − | 12.2419i | − | 1.29763i | −0.760944 | − | 0.648817i | \(-0.775264\pi\) | ||
0.760944 | − | 0.648817i | \(-0.224736\pi\) | |||||||
\(90\) | −5.85021 | − | 4.92718i | −0.616666 | − | 0.519371i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.203698i | 0.0212369i | ||||||||
\(93\) | −0.407395 | −0.0422449 | ||||||||
\(94\) | −14.5813 | −1.50395 | ||||||||
\(95\) | 8.47114 | − | 10.0581i | 0.869120 | − | 1.03194i | ||||
\(96\) | − | 1.11018i | − | 0.113307i | ||||||
\(97\) | −5.80585 | −0.589494 | −0.294747 | − | 0.955575i | \(-0.595235\pi\) | ||||
−0.294747 | + | 0.955575i | \(0.595235\pi\) | |||||||
\(98\) | −3.42059 | −0.345532 | ||||||||
\(99\) | 11.1805i | 1.12368i | ||||||||
\(100\) | −0.501828 | − | 2.90822i | −0.0501828 | − | 0.290822i | ||||
\(101\) | 5.94228 | 0.591279 | 0.295639 | − | 0.955300i | \(-0.404467\pi\) | ||||
0.295639 | + | 0.955300i | \(0.404467\pi\) | |||||||
\(102\) | 2.23325 | 0.221125 | ||||||||
\(103\) | − | 6.43378i | − | 0.633939i | −0.948436 | − | 0.316970i | \(-0.897335\pi\) | ||
0.948436 | − | 0.316970i | \(-0.102665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00892 | − | 1.19792i | 0.0984605 | − | 0.116905i | ||||
\(106\) | − | 2.88090i | − | 0.279818i | ||||||
\(107\) | 17.6792i | 1.70911i | 0.519360 | + | 0.854555i | \(0.326170\pi\) | ||||
−0.519360 | + | 0.854555i | \(0.673830\pi\) | |||||||
\(108\) | 1.19792i | 0.115270i | ||||||||
\(109\) | 5.76180i | 0.551880i | 0.961175 | + | 0.275940i | \(0.0889891\pi\) | ||||
−0.961175 | + | 0.275940i | \(0.911011\pi\) | |||||||
\(110\) | 6.63748 | − | 7.88090i | 0.632859 | − | 0.751414i | ||||
\(111\) | 1.88090i | 0.178527i | ||||||||
\(112\) | 5.01532 | 0.473903 | ||||||||
\(113\) | 4.75992i | 0.447776i | 0.974615 | + | 0.223888i | \(0.0718750\pi\) | ||||
−0.974615 | + | 0.223888i | \(0.928125\pi\) | |||||||
\(114\) | 2.40976 | 0.225695 | ||||||||
\(115\) | −0.497113 | + | 0.590239i | −0.0463561 | + | 0.0550401i | ||||
\(116\) | 1.77072 | 0.164407 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.38421i | 0.771829i | ||||||||
\(119\) | − | 11.0614i | − | 1.01399i | ||||||
\(120\) | 1.52886 | − | 1.81527i | 0.139565 | − | 0.165711i | ||||
\(121\) | −4.06138 | −0.369216 | ||||||||
\(122\) | 8.02851 | 0.726867 | ||||||||
\(123\) | −0.0622851 | −0.00561605 | ||||||||
\(124\) | 0.696765i | 0.0625714i | ||||||||
\(125\) | 5.64325 | − | 9.65162i | 0.504748 | − | 0.863267i | ||||
\(126\) | −6.94228 | −0.618467 | ||||||||
\(127\) | 16.7061i | 1.48243i | 0.671268 | + | 0.741215i | \(0.265750\pi\) | ||||
−0.671268 | + | 0.741215i | \(0.734250\pi\) | |||||||
\(128\) | 3.96940 | 0.350848 | ||||||||
\(129\) | −0.462218 | −0.0406961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | −0.790529 | −0.0688068 | ||||||||
\(133\) | − | 11.9356i | − | 1.03495i | ||||||
\(134\) | −5.22928 | −0.451741 | ||||||||
\(135\) | −2.92347 | + | 3.47114i | −0.251613 | + | 0.298748i | ||||
\(136\) | − | 16.7618i | − | 1.43731i | ||||||
\(137\) | −1.97786 | −0.168980 | −0.0844901 | − | 0.996424i | \(-0.526926\pi\) | ||||
−0.0844901 | + | 0.996424i | \(0.526926\pi\) | |||||||
\(138\) | −0.141412 | −0.0120378 | ||||||||
\(139\) | −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 | ||||
\(141\) | 4.23820i | 0.356921i | ||||||||
\(142\) | 2.23325i | 0.187411i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.11910 | −0.593258 | ||||||||
\(145\) | 5.13088 | + | 4.32135i | 0.426097 | + | 0.358868i | ||||
\(146\) | 10.5199 | 0.870637 | ||||||||
\(147\) | 0.994227i | 0.0820025i | ||||||||
\(148\) | 3.21689 | 0.264427 | ||||||||
\(149\) | 22.3032i | 1.82715i | 0.406668 | + | 0.913576i | \(0.366691\pi\) | ||||
−0.406668 | + | 0.913576i | \(0.633309\pi\) | |||||||
\(150\) | 2.01897 | − | 0.348383i | 0.164848 | − | 0.0284453i | ||||
\(151\) | − | 19.1626i | − | 1.55943i | −0.626132 | − | 0.779717i | \(-0.715363\pi\) | ||
0.626132 | − | 0.779717i | \(-0.284637\pi\) | |||||||
\(152\) | − | 18.0866i | − | 1.46701i | ||||||
\(153\) | 15.7013i | 1.26938i | ||||||||
\(154\) | − | 9.35204i | − | 0.753609i | ||||||
\(155\) | −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 | \(-0.0796132\pi\) | |||||||
\(158\) | −13.2750 | −1.05610 | ||||||||
\(159\) | −0.837361 | −0.0664071 | ||||||||
\(160\) | −5.50183 | − | 4.63377i | −0.434958 | − | 0.366332i | ||||
\(161\) | 0.700420i | 0.0552008i | ||||||||
\(162\) | 9.43013 | 0.740901 | ||||||||
\(163\) | 11.9356 | 0.934870 | 0.467435 | − | 0.884027i | \(-0.345178\pi\) | ||||
0.467435 | + | 0.884027i | \(0.345178\pi\) | |||||||
\(164\) | 0.106526i | 0.00831826i | ||||||||
\(165\) | −2.29066 | − | 1.92925i | −0.178328 | − | 0.150192i | ||||
\(166\) | −9.30323 | −0.722071 | ||||||||
\(167\) | 2.02956 | 0.157052 | 0.0785259 | − | 0.996912i | \(-0.474979\pi\) | ||||
0.0785259 | + | 0.996912i | \(0.474979\pi\) | |||||||
\(168\) | − | 2.15413i | − | 0.166195i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.32135 | − | 11.0675i | 0.714915 | − | 0.848842i | ||||
\(171\) | 16.9423i | 1.29561i | ||||||||
\(172\) | 0.790529i | 0.0602773i | ||||||||
\(173\) | 1.33934i | 0.101828i | 0.998703 | + | 0.0509139i | \(0.0162134\pi\) | ||||
−0.998703 | + | 0.0509139i | \(0.983787\pi\) | |||||||
\(174\) | 1.22928i | 0.0931916i | ||||||||
\(175\) | −1.72555 | − | 10.0000i | −0.130439 | − | 0.755929i | ||||
\(176\) | − | 9.59024i | − | 0.722891i | ||||||
\(177\) | 2.43695 | 0.183173 | ||||||||
\(178\) | − | 14.5352i | − | 1.08946i | ||||||
\(179\) | 20.2240 | 1.51161 | 0.755807 | − | 0.654794i | \(-0.227245\pi\) | ||||
0.755807 | + | 0.654794i | \(0.227245\pi\) | |||||||
\(180\) | 2.90822 | + | 2.44937i | 0.216766 | + | 0.182565i | ||||
\(181\) | −19.8232 | −1.47345 | −0.736723 | − | 0.676195i | \(-0.763628\pi\) | ||||
−0.736723 | + | 0.676195i | \(0.763628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.33356i | − | 0.172502i | ||||||
\(184\) | 1.06138i | 0.0782458i | ||||||||
\(185\) | 9.32135 | + | 7.85066i | 0.685319 | + | 0.577192i | ||||
\(186\) | −0.483714 | −0.0354676 | ||||||||
\(187\) | −21.1515 | −1.54675 | ||||||||
\(188\) | 7.24857 | 0.528656 | ||||||||
\(189\) | 4.11910i | 0.299621i | ||||||||
\(190\) | 10.0581 | − | 11.9423i | 0.729689 | − | 0.866384i | ||||
\(191\) | 1.53778 | 0.111270 | 0.0556350 | − | 0.998451i | \(-0.482282\pi\) | ||||
0.0556350 | + | 0.998451i | \(0.482282\pi\) | |||||||
\(192\) | − | 3.02378i | − | 0.218223i | ||||||
\(193\) | 21.2032 | 1.52624 | 0.763118 | − | 0.646259i | \(-0.223667\pi\) | ||||
0.763118 | + | 0.646259i | \(0.223667\pi\) | |||||||
\(194\) | −6.89347 | −0.494923 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70042 | 0.121459 | ||||||||
\(197\) | −9.25695 | −0.659530 | −0.329765 | − | 0.944063i | \(-0.606970\pi\) | ||||
−0.329765 | + | 0.944063i | \(0.606970\pi\) | |||||||
\(198\) | 13.2750i | 0.943410i | ||||||||
\(199\) | −17.4045 | −1.23377 | −0.616886 | − | 0.787053i | \(-0.711606\pi\) | ||||
−0.616886 | + | 0.787053i | \(0.711606\pi\) | |||||||
\(200\) | −2.61480 | − | 15.1534i | −0.184894 | − | 1.07151i | ||||
\(201\) | 1.51994i | 0.107208i | ||||||||
\(202\) | 7.05546 | 0.496421 | ||||||||
\(203\) | 6.08867 | 0.427341 | ||||||||
\(204\) | −1.11018 | −0.0777282 | ||||||||
\(205\) | −0.259971 | + | 0.308672i | −0.0181571 | + | 0.0215586i | ||||
\(206\) | − | 7.63904i | − | 0.532237i | ||||||
\(207\) | − | 0.994227i | − | 0.0691036i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.8232 | −1.57871 | ||||||||
\(210\) | 1.19792 | − | 1.42234i | 0.0826646 | − | 0.0981505i | ||||
\(211\) | −7.28174 | −0.501296 | −0.250648 | − | 0.968078i | \(-0.580644\pi\) | ||||
−0.250648 | + | 0.968078i | \(0.580644\pi\) | |||||||
\(212\) | 1.43213i | 0.0983594i | ||||||||
\(213\) | 0.649117 | 0.0444768 | ||||||||
\(214\) | 20.9911i | 1.43492i | ||||||||
\(215\) | −1.92925 | + | 2.29066i | −0.131574 | + | 0.156222i | ||||
\(216\) | 6.24186i | 0.424705i | ||||||||
\(217\) | 2.39585i | 0.162641i | ||||||||
\(218\) | 6.84118i | 0.463343i | ||||||||
\(219\) | − | 3.05772i | − | 0.206622i | ||||||
\(220\) | −3.29958 | + | 3.91770i | −0.222458 | + | 0.264131i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.23325i | 0.149886i | ||||||||
\(223\) | 19.4670 | 1.30361 | 0.651804 | − | 0.758388i | \(-0.274013\pi\) | ||||
0.651804 | + | 0.758388i | \(0.274013\pi\) | |||||||
\(224\) | −6.52886 | −0.436228 | ||||||||
\(225\) | 2.44937 | + | 14.1947i | 0.163291 | + | 0.946315i | ||||
\(226\) | 5.65162i | 0.375940i | ||||||||
\(227\) | 4.81162 | 0.319358 | 0.159679 | − | 0.987169i | \(-0.448954\pi\) | ||||
0.159679 | + | 0.987169i | \(0.448954\pi\) | |||||||
\(228\) | −1.19792 | −0.0793345 | ||||||||
\(229\) | − | 1.52360i | − | 0.100682i | −0.998732 | − | 0.0503410i | \(-0.983969\pi\) | ||
0.998732 | − | 0.0503410i | \(-0.0160308\pi\) | |||||||
\(230\) | −0.590239 | + | 0.700811i | −0.0389192 | + | 0.0462101i | ||||
\(231\) | −2.71826 | −0.178848 | ||||||||
\(232\) | 9.22643 | 0.605745 | ||||||||
\(233\) | − | 13.9652i | − | 0.914889i | −0.889238 | − | 0.457445i | \(-0.848765\pi\) | ||
0.889238 | − | 0.457445i | \(-0.151235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.0037 | + | 17.6898i | 1.37013 | + | 1.15395i | ||||
\(236\) | − | 4.16790i | − | 0.271307i | ||||||
\(237\) | 3.85849i | 0.250636i | ||||||||
\(238\) | − | 13.1335i | − | 0.851321i | ||||||
\(239\) | 4.00000i | 0.258738i | 0.991596 | + | 0.129369i | \(0.0412952\pi\) | ||||
−0.991596 | + | 0.129369i | \(0.958705\pi\) | |||||||
\(240\) | 1.22844 | − | 1.45856i | 0.0792952 | − | 0.0941499i | ||||
\(241\) | − | 17.4659i | − | 1.12508i | −0.826771 | − | 0.562538i | \(-0.809825\pi\) | ||
0.826771 | − | 0.562538i | \(-0.190175\pi\) | |||||||
\(242\) | −4.82221 | −0.309983 | ||||||||
\(243\) | − | 8.82963i | − | 0.566421i | ||||||
\(244\) | −3.99108 | −0.255503 | ||||||||
\(245\) | 4.92718 | + | 4.14979i | 0.314786 | + | 0.265120i | ||||
\(246\) | −0.0739531 | −0.00471508 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.63054i | 0.230539i | ||||||||
\(249\) | 2.70408i | 0.171364i | ||||||||
\(250\) | 6.70042 | − | 11.4597i | 0.423772 | − | 0.724774i | ||||
\(251\) | −9.29958 | −0.586984 | −0.293492 | − | 0.955961i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955961i | \(0.594817\pi\) | |||||||
\(252\) | 3.45110 | 0.217399 | ||||||||
\(253\) | 1.33934 | 0.0842034 | ||||||||
\(254\) | 19.8358i | 1.24461i | ||||||||
\(255\) | −3.21689 | − | 2.70934i | −0.201449 | − | 0.169665i | ||||
\(256\) | −12.8106 | −0.800663 | ||||||||
\(257\) | − | 10.8897i | − | 0.679281i | −0.940555 | − | 0.339640i | \(-0.889695\pi\) | ||
0.940555 | − | 0.339640i | \(-0.110305\pi\) | |||||||
\(258\) | −0.548807 | −0.0341673 | ||||||||
\(259\) | 11.0614 | 0.687321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.64270 | −0.534970 | ||||||||
\(262\) | 11.8733 | 0.733537 | ||||||||
\(263\) | 13.4406i | 0.828785i | 0.910098 | + | 0.414392i | \(0.136006\pi\) | ||||
−0.910098 | + | 0.414392i | \(0.863994\pi\) | |||||||
\(264\) | −4.11910 | −0.253513 | ||||||||
\(265\) | −3.49505 | + | 4.14979i | −0.214699 | + | 0.254920i | ||||
\(266\) | − | 14.1716i | − | 0.868914i | ||||||
\(267\) | −4.22479 | −0.258553 | ||||||||
\(268\) | 2.59955 | 0.158793 | ||||||||
\(269\) | −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 | ||||
\(271\) | 22.0037i | 1.33663i | 0.743880 | + | 0.668313i | \(0.232983\pi\) | ||||
−0.743880 | + | 0.668313i | \(0.767017\pi\) | |||||||
\(272\) | − | 13.4681i | − | 0.816621i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.34838 | −0.141871 | ||||||||
\(275\) | −19.1219 | + | 3.29958i | −1.15309 | + | 0.198972i | ||||
\(276\) | 0.0702980 | 0.00423144 | ||||||||
\(277\) | − | 9.89547i | − | 0.594561i | −0.954790 | − | 0.297281i | \(-0.903920\pi\) | ||
0.954790 | − | 0.297281i | \(-0.0960797\pi\) | |||||||
\(278\) | −10.3303 | −0.619570 | ||||||||
\(279\) | − | 3.40084i | − | 0.203603i | ||||||
\(280\) | −10.6754 | − | 8.99108i | −0.637978 | − | 0.537320i | ||||
\(281\) | 4.06138i | 0.242281i | 0.992635 | + | 0.121141i | \(0.0386552\pi\) | ||||
−0.992635 | + | 0.121141i | \(0.961345\pi\) | |||||||
\(282\) | 5.03216i | 0.299661i | ||||||||
\(283\) | − | 6.08867i | − | 0.361934i | −0.983489 | − | 0.180967i | \(-0.942077\pi\) | ||
0.983489 | − | 0.180967i | \(-0.0579227\pi\) | |||||||
\(284\) | − | 1.11018i | − | 0.0658771i | ||||||
\(285\) | −3.47114 | − | 2.92347i | −0.205613 | − | 0.173172i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.366292i | 0.0216215i | ||||||||
\(288\) | 9.26754 | 0.546095 | ||||||||
\(289\) | −12.7041 | −0.747299 | ||||||||
\(290\) | 6.09207 | + | 5.13088i | 0.357738 | + | 0.301296i | ||||
\(291\) | 2.00366i | 0.117456i | ||||||||
\(292\) | −5.22960 | −0.306039 | ||||||||
\(293\) | −9.79208 | −0.572060 | −0.286030 | − | 0.958221i | \(-0.592336\pi\) | ||||
−0.286030 | + | 0.958221i | \(0.592336\pi\) | |||||||
\(294\) | 1.18048i | 0.0688469i | ||||||||
\(295\) | 10.1716 | − | 12.0770i | 0.592211 | − | 0.703152i | ||||
\(296\) | 16.7618 | 0.974260 | ||||||||
\(297\) | 7.87651 | 0.457041 | ||||||||
\(298\) | 26.4814i | 1.53402i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00366 | + | 0.173186i | −0.0579461 | + | 0.00999888i | ||||
\(301\) | 2.71826i | 0.156678i | ||||||||
\(302\) | − | 22.7524i | − | 1.30926i | ||||||
\(303\) | − | 2.05074i | − | 0.117812i | ||||||
\(304\) | − | 14.5325i | − | 0.833497i | ||||||
\(305\) | −11.5647 | − | 9.74003i | −0.662191 | − | 0.557712i | ||||
\(306\) | 18.6427i | 1.06573i | ||||||||
\(307\) | 22.1046 | 1.26158 | 0.630788 | − | 0.775955i | \(-0.282732\pi\) | ||||
0.630788 | + | 0.775955i | \(0.282732\pi\) | |||||||
\(308\) | 4.64902i | 0.264903i | ||||||||
\(309\) | −2.22036 | −0.126312 | ||||||||
\(310\) | −2.01897 | + | 2.39719i | −0.114670 | + | 0.136151i | ||||
\(311\) | −7.63904 | −0.433170 | −0.216585 | − | 0.976264i | \(-0.569492\pi\) | ||||
−0.216585 | + | 0.976264i | \(0.569492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.1425i | − | 1.47766i | −0.673891 | − | 0.738831i | \(-0.735378\pi\) | ||
0.673891 | − | 0.738831i | \(-0.264622\pi\) | |||||||
\(314\) | − | 7.36461i | − | 0.415609i | ||||||
\(315\) | 10.0000 | + | 8.42223i | 0.563436 | + | 0.474539i | ||||
\(316\) | 6.59916 | 0.371232 | ||||||||
\(317\) | 11.8428 | 0.665159 | 0.332580 | − | 0.943075i | \(-0.392081\pi\) | ||||
0.332580 | + | 0.943075i | \(0.392081\pi\) | |||||||
\(318\) | −0.994227 | −0.0557535 | ||||||||
\(319\) | − | 11.6427i | − | 0.651866i | ||||||
\(320\) | −14.9852 | − | 12.6209i | −0.837701 | − | 0.705531i | ||||
\(321\) | 6.10126 | 0.340539 | ||||||||
\(322\) | 0.831632i | 0.0463451i | ||||||||
\(323\) | −32.0518 | −1.78341 | ||||||||
\(324\) | −4.68785 | −0.260436 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.1716 | 0.784890 | ||||||||
\(327\) | 1.98845 | 0.109962 | ||||||||
\(328\) | 0.555059i | 0.0306480i | ||||||||
\(329\) | 24.9244 | 1.37413 | ||||||||
\(330\) | −2.71978 | − | 2.29066i | −0.149719 | − | 0.126097i | ||||
\(331\) | 12.7004i | 0.698078i | 0.937108 | + | 0.349039i | \(0.113492\pi\) | ||||
−0.937108 | + | 0.349039i | \(0.886508\pi\) | |||||||
\(332\) | 4.62476 | 0.253817 | ||||||||
\(333\) | −15.7013 | −0.860427 | ||||||||
\(334\) | 2.40976 | 0.131856 | ||||||||
\(335\) | 7.53252 | + | 6.34406i | 0.411545 | + | 0.346613i | ||||
\(336\) | − | 1.73084i | − | 0.0944248i | ||||||
\(337\) | 15.2939i | 0.833113i | 0.909110 | + | 0.416556i | \(0.136763\pi\) | ||||
−0.909110 | + | 0.416556i | \(0.863237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.64270 | 0.0892191 | ||||||||
\(340\) | −4.63377 | + | 5.50183i | −0.251301 | + | 0.298378i | ||||
\(341\) | 4.58132 | 0.248092 | ||||||||
\(342\) | 20.1161i | 1.08776i | ||||||||
\(343\) | 20.0538 | 1.08281 | ||||||||
\(344\) | 4.11910i | 0.222087i | ||||||||
\(345\) | 0.203698 | + | 0.171559i | 0.0109667 | + | 0.00923642i | ||||
\(346\) | 1.59024i | 0.0854918i | ||||||||
\(347\) | 12.2396i | 0.657058i | 0.944494 | + | 0.328529i | \(0.106553\pi\) | ||||
−0.944494 | + | 0.328529i | \(0.893447\pi\) | |||||||
\(348\) | − | 0.611093i | − | 0.0327580i | ||||||
\(349\) | − | 18.7004i | − | 1.00101i | −0.865733 | − | 0.500505i | \(-0.833148\pi\) | ||
0.865733 | − | 0.500505i | \(-0.166852\pi\) | |||||||
\(350\) | −2.04880 | − | 11.8733i | −0.109513 | − | 0.634656i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4844i | 0.665422i | ||||||||
\(353\) | −1.30883 | −0.0696617 | −0.0348309 | − | 0.999393i | \(-0.511089\pi\) | ||||
−0.0348309 | + | 0.999393i | \(0.511089\pi\) | |||||||
\(354\) | 2.89347 | 0.153786 | ||||||||
\(355\) | 2.70934 | − | 3.21689i | 0.143797 | − | 0.170735i | ||||
\(356\) | 7.22563i | 0.382957i | ||||||||
\(357\) | −3.81739 | −0.202038 | ||||||||
\(358\) | 24.0127 | 1.26911 | ||||||||
\(359\) | 29.4082i | 1.55210i | 0.630670 | + | 0.776051i | \(0.282780\pi\) | ||||
−0.630670 | + | 0.776051i | \(0.717220\pi\) | |||||||
\(360\) | 15.1534 | + | 12.7626i | 0.798657 | + | 0.672647i | ||||
\(361\) | −15.5850 | −0.820262 | ||||||||
\(362\) | −23.5367 | −1.23706 | ||||||||
\(363\) | 1.40162i | 0.0735661i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1534 | − | 12.7626i | −0.793168 | − | 0.668024i | ||||
\(366\) | − | 2.77072i | − | 0.144828i | ||||||
\(367\) | − | 33.4322i | − | 1.74515i | −0.488484 | − | 0.872573i | \(-0.662450\pi\) | ||
0.488484 | − | 0.872573i | \(-0.337550\pi\) | |||||||
\(368\) | 0.852815i | 0.0444560i | ||||||||
\(369\) | − | 0.519941i | − | 0.0270671i | ||||||
\(370\) | 11.0675 | + | 9.32135i | 0.575374 | + | 0.484594i | ||||
\(371\) | 4.92444i | 0.255664i | ||||||||
\(372\) | 0.240461 | 0.0124673 | ||||||||
\(373\) | 34.4781i | 1.78521i | 0.450841 | + | 0.892604i | \(0.351124\pi\) | ||||
−0.450841 | + | 0.892604i | \(0.648876\pi\) | |||||||
\(374\) | −25.1138 | −1.29861 | ||||||||
\(375\) | −3.33087 | − | 1.94754i | −0.172005 | − | 0.100571i | ||||
\(376\) | 37.7691 | 1.94779 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.89075i | 0.251553i | ||||||||
\(379\) | − | 17.4045i | − | 0.894009i | −0.894532 | − | 0.447004i | \(-0.852491\pi\) | ||
0.894532 | − | 0.447004i | \(-0.147509\pi\) | |||||||
\(380\) | −5.00000 | + | 5.93667i | −0.256495 | + | 0.304545i | ||||
\(381\) | 5.76545 | 0.295373 | ||||||||
\(382\) | 1.82586 | 0.0934191 | ||||||||
\(383\) | −1.74673 | −0.0892538 | −0.0446269 | − | 0.999004i | \(-0.514210\pi\) | ||||
−0.0446269 | + | 0.999004i | \(0.514210\pi\) | |||||||
\(384\) | − | 1.36988i | − | 0.0699063i | ||||||
\(385\) | −11.3457 | + | 13.4711i | −0.578231 | + | 0.686553i | ||||
\(386\) | 25.1752 | 1.28138 | ||||||||
\(387\) | − | 3.85849i | − | 0.196138i | ||||||
\(388\) | 3.42684 | 0.173971 | ||||||||
\(389\) | 22.0435 | 1.11765 | 0.558826 | − | 0.829285i | \(-0.311252\pi\) | ||||
0.558826 | + | 0.829285i | \(0.311252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.88090 | 0.0951212 | ||||||||
\(392\) | 8.86014 | 0.447505 | ||||||||
\(393\) | − | 3.45110i | − | 0.174085i | ||||||
\(394\) | −10.9911 | −0.553723 | ||||||||
\(395\) | 19.1219 | + | 16.1049i | 0.962127 | + | 0.810326i | ||||
\(396\) | − | 6.59916i | − | 0.331620i | ||||||
\(397\) | 22.5319 | 1.13084 | 0.565422 | − | 0.824802i | \(-0.308713\pi\) | ||||
0.565422 | + | 0.824802i | \(0.308713\pi\) | |||||||
\(398\) | −20.6649 | −1.03584 | ||||||||
\(399\) | −4.11910 | −0.206213 | ||||||||
\(400\) | −2.10099 | − | 12.1758i | −0.105049 | − | 0.608788i | ||||
\(401\) | − | 3.70408i | − | 0.184973i | −0.995714 | − | 0.0924863i | \(-0.970519\pi\) | ||
0.995714 | − | 0.0924863i | \(-0.0294815\pi\) | |||||||
\(402\) | 1.80468i | 0.0900091i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.50737 | −0.174498 | ||||||||
\(405\) | −13.5836 | − | 11.4404i | −0.674976 | − | 0.568481i | ||||
\(406\) | 7.22928 | 0.358783 | ||||||||
\(407\) | − | 21.1515i | − | 1.04844i | ||||||
\(408\) | −5.78466 | −0.286384 | ||||||||
\(409\) | − | 13.4837i | − | 0.666727i | −0.942798 | − | 0.333363i | \(-0.891816\pi\) | ||
0.942798 | − | 0.333363i | \(-0.108184\pi\) | |||||||
\(410\) | −0.308672 | + | 0.366496i | −0.0152442 | + | 0.0181000i | ||||
\(411\) | 0.682580i | 0.0336692i | ||||||||
\(412\) | 3.79747i | 0.187088i | ||||||||
\(413\) | − | 14.3315i | − | 0.705205i | ||||||
\(414\) | − | 1.18048i | − | 0.0580174i | ||||||
\(415\) | 13.4008 | + | 11.2865i | 0.657821 | + | 0.554033i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.00260i | 0.147038i | ||||||||
\(418\) | −27.0987 | −1.32544 | ||||||||
\(419\) | −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 | ||||
\(421\) | − | 17.1013i | − | 0.833464i | −0.909029 | − | 0.416732i | \(-0.863175\pi\) | ||
0.909029 | − | 0.416732i | \(-0.136825\pi\) | |||||||
\(422\) | −8.64585 | −0.420874 | ||||||||
\(423\) | −35.3795 | −1.72021 | ||||||||
\(424\) | 7.46222i | 0.362397i | ||||||||
\(425\) | −26.8539 | + | 4.63377i | −1.30260 | + | 0.224771i | ||||
\(426\) | 0.770718 | 0.0373414 | ||||||||
\(427\) | −13.7235 | −0.664124 | ||||||||
\(428\) | − | 10.4349i | − | 0.504392i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.29066 | + | 2.71978i | −0.110465 | + | 0.131159i | ||||
\(431\) | − | 9.66054i | − | 0.465332i | −0.972557 | − | 0.232666i | \(-0.925255\pi\) | ||
0.972557 | − | 0.232666i | \(-0.0747448\pi\) | |||||||
\(432\) | 5.01532i | 0.241300i | ||||||||
\(433\) | 24.7727i | 1.19050i | 0.803541 | + | 0.595249i | \(0.202947\pi\) | ||||
−0.803541 | + | 0.595249i | \(0.797053\pi\) | |||||||
\(434\) | 2.84467i | 0.136549i | ||||||||
\(435\) | 1.49134 | − | 1.77072i | 0.0715043 | − | 0.0848994i | ||||
\(436\) | − | 3.40084i | − | 0.162871i | ||||||
\(437\) | 2.02956 | 0.0970869 | ||||||||
\(438\) | − | 3.63054i | − | 0.173474i | ||||||
\(439\) | 7.06138 | 0.337021 | 0.168511 | − | 0.985700i | \(-0.446104\pi\) | ||||
0.168511 | + | 0.985700i | \(0.446104\pi\) | |||||||
\(440\) | −17.1927 | + | 20.4134i | −0.819628 | + | 0.973171i | ||||
\(441\) | −8.29958 | −0.395218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.2438i | 1.81702i | 0.417865 | + | 0.908509i | \(0.362778\pi\) | ||||
−0.417865 | + | 0.908509i | \(0.637222\pi\) | |||||||
\(444\) | − | 1.11018i | − | 0.0526869i | ||||||
\(445\) | −17.6338 | + | 20.9372i | −0.835921 | + | 0.992517i | ||||
\(446\) | 23.1138 | 1.09447 | ||||||||
\(447\) | 7.69707 | 0.364059 | ||||||||
\(448\) | −17.7826 | −0.840147 | ||||||||
\(449\) | 12.4801i | 0.588970i | 0.955656 | + | 0.294485i | \(0.0951482\pi\) | ||||
−0.955656 | + | 0.294485i | \(0.904852\pi\) | |||||||
\(450\) | 2.90822 | + | 16.8539i | 0.137095 | + | 0.794499i | ||||
\(451\) | 0.700420 | 0.0329815 | ||||||||
\(452\) | − | 2.80950i | − | 0.132148i | ||||||
\(453\) | −6.61322 | −0.310716 | ||||||||
\(454\) | 5.71300 | 0.268124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24186 | −0.292302 | ||||||||
\(457\) | 8.23221 | 0.385086 | 0.192543 | − | 0.981289i | \(-0.438326\pi\) | ||||
0.192543 | + | 0.981289i | \(0.438326\pi\) | |||||||
\(458\) | − | 1.80902i | − | 0.0845298i | ||||||
\(459\) | 11.0614 | 0.516301 | ||||||||
\(460\) | 0.293416 | − | 0.348383i | 0.0136806 | − | 0.0162434i | ||||
\(461\) | 4.54144i | 0.211516i | 0.994392 | + | 0.105758i | \(0.0337269\pi\) | ||||
−0.994392 | + | 0.105758i | \(0.966273\pi\) | |||||||
\(462\) | −3.22748 | −0.150156 | ||||||||
\(463\) | −1.98845 | −0.0924113 | −0.0462056 | − | 0.998932i | \(-0.514713\pi\) | ||||
−0.0462056 | + | 0.998932i | \(0.514713\pi\) | |||||||
\(464\) | 7.41342 | 0.344159 | ||||||||
\(465\) | 0.696765 | + | 0.586832i | 0.0323117 | + | 0.0272137i | ||||
\(466\) | − | 16.5813i | − | 0.768115i | ||||||
\(467\) | 32.8043i | 1.51800i | 0.651091 | + | 0.759000i | \(0.274312\pi\) | ||||
−0.651091 | + | 0.759000i | \(0.725688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.93862 | 0.412747 | ||||||||
\(470\) | 24.9383 | + | 21.0037i | 1.15032 | + | 0.968826i | ||||
\(471\) | −2.14060 | −0.0986335 | ||||||||
\(472\) | − | 21.7171i | − | 0.999611i | ||||||
\(473\) | 5.19783 | 0.238997 | ||||||||
\(474\) | 4.58132i | 0.210427i | ||||||||
\(475\) | −28.9763 | + | 5.00000i | −1.32952 | + | 0.229416i | ||||
\(476\) | 6.52886i | 0.299250i | ||||||||
\(477\) | − | 6.99010i | − | 0.320055i | ||||||
\(478\) | 4.74933i | 0.217229i | ||||||||
\(479\) | 30.8053i | 1.40753i | 0.710432 | + | 0.703766i | \(0.248500\pi\) | ||||
−0.710432 | + | 0.703766i | \(0.751500\pi\) | |||||||
\(480\) | −1.59916 | + | 1.89874i | −0.0729913 | + | 0.0866650i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 20.7378i | − | 0.944582i | ||||||
\(483\) | 0.241722 | 0.0109987 | ||||||||
\(484\) | 2.39719 | 0.108963 | ||||||||
\(485\) | 9.92970 | + | 8.36303i | 0.450885 | + | 0.379746i | ||||
\(486\) | − | 10.4837i | − | 0.475551i | ||||||
\(487\) | −22.3251 | −1.01165 | −0.505824 | − | 0.862637i | \(-0.668811\pi\) | ||||
−0.505824 | + | 0.862637i | \(0.668811\pi\) | |||||||
\(488\) | −20.7958 | −0.941380 | ||||||||
\(489\) | − | 4.11910i | − | 0.186272i | ||||||
\(490\) | 5.85021 | + | 4.92718i | 0.264286 | + | 0.222587i | ||||
\(491\) | −10.6826 | −0.482098 | −0.241049 | − | 0.970513i | \(-0.577491\pi\) | ||||
−0.241049 | + | 0.970513i | \(0.577491\pi\) | |||||||
\(492\) | 0.0367631 | 0.00165741 | ||||||||
\(493\) | − | 16.3504i | − | 0.736386i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.1049 | − | 19.1219i | 0.723862 | − | 0.859466i | ||||
\(496\) | 2.91713i | 0.130983i | ||||||||
\(497\) | − | 3.81739i | − | 0.171233i | ||||||
\(498\) | 3.21064i | 0.143872i | ||||||||
\(499\) | 18.8195i | 0.842477i | 0.906950 | + | 0.421239i | \(0.138405\pi\) | ||||
−0.906950 | + | 0.421239i | \(0.861595\pi\) | |||||||
\(500\) | −3.33087 | + | 5.69677i | −0.148961 | + | 0.254767i | ||||
\(501\) | − | 0.700420i | − | 0.0312925i | ||||||
\(502\) | −11.0417 | −0.492815 | ||||||||
\(503\) | 5.68128i | 0.253316i | 0.991946 | + | 0.126658i | \(0.0404250\pi\) | ||||
−0.991946 | + | 0.126658i | \(0.959575\pi\) | |||||||
\(504\) | 17.9822 | 0.800989 | ||||||||
\(505\) | −10.1630 | − | 8.55955i | −0.452249 | − | 0.380895i | ||||
\(506\) | 1.59024 | 0.0706948 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 9.86062i | − | 0.437494i | ||||||
\(509\) | 27.9244i | 1.23773i | 0.785498 | + | 0.618864i | \(0.212407\pi\) | ||||
−0.785498 | + | 0.618864i | \(0.787593\pi\) | |||||||
\(510\) | −3.81952 | − | 3.21689i | −0.169131 | − | 0.142446i | ||||
\(511\) | −17.9822 | −0.795484 | ||||||||
\(512\) | −23.1492 | −1.02306 | ||||||||
\(513\) | 11.9356 | 0.526970 | ||||||||
\(514\) | − | 12.9297i | − | 0.570305i | ||||||
\(515\) | −9.26754 | + | 11.0037i | −0.408376 | + | 0.484879i | ||||
\(516\) | 0.272820 | 0.0120102 | ||||||||
\(517\) | − | 47.6603i | − | 2.09610i | ||||||
\(518\) | 13.1335 | 0.577055 | ||||||||
\(519\) | 0.462218 | 0.0202891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.29958 | 0.275990 | 0.137995 | − | 0.990433i | \(-0.455934\pi\) | ||||
0.137995 | + | 0.990433i | \(0.455934\pi\) | |||||||
\(522\) | −10.2618 | −0.449145 | ||||||||
\(523\) | − | 22.8571i | − | 0.999471i | −0.866178 | − | 0.499735i | \(-0.833431\pi\) | ||
0.866178 | − | 0.499735i | \(-0.166569\pi\) | |||||||
\(524\) | −5.90239 | −0.257847 | ||||||||
\(525\) | −3.45110 | + | 0.595504i | −0.150618 | + | 0.0259899i | ||||
\(526\) | 15.9585i | 0.695824i | ||||||||
\(527\) | 6.43378 | 0.280260 | ||||||||
\(528\) | −3.30969 | −0.144036 | ||||||||
\(529\) | 22.8809 | 0.994822 | ||||||||
\(530\) | −4.14979 | + | 4.92718i | −0.180255 | + | 0.214023i | ||||
\(531\) | 20.3431i | 0.882816i | ||||||||
\(532\) | 7.04487i | 0.305434i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.01623 | −0.217074 | ||||||||
\(535\) | 25.4660 | − | 30.2366i | 1.10099 | − | 1.30724i | ||||
\(536\) | 13.5451 | 0.585059 | ||||||||
\(537\) | − | 6.97951i | − | 0.301188i | ||||||
\(538\) | −4.34628 | −0.187381 | ||||||||
\(539\) | − | 11.1805i | − | 0.481577i | ||||||
\(540\) | 1.72555 | − | 2.04880i | 0.0742558 | − | 0.0881664i | ||||
\(541\) | − | 9.48006i | − | 0.407580i | −0.979015 | − | 0.203790i | \(-0.934674\pi\) | ||
0.979015 | − | 0.203790i | \(-0.0653259\pi\) | |||||||
\(542\) | 26.1257i | 1.12219i | ||||||||
\(543\) | 6.84118i | 0.293583i | ||||||||
\(544\) | 17.5325i | 0.751700i | ||||||||
\(545\) | 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 | \(0.746950\pi\) | |||||||
\(548\) | 1.16741 | 0.0498694 | ||||||||
\(549\) | 19.4801 | 0.831389 | ||||||||
\(550\) | −22.7041 | + | 3.91770i | −0.968105 | + | 0.167051i | ||||
\(551\) | − | 17.6427i | − | 0.751604i | ||||||
\(552\) | 0.366292 | 0.0155904 | ||||||||
\(553\) | 22.6914 | 0.964937 | ||||||||
\(554\) | − | 11.7492i | − | 0.499177i | ||||||
\(555\) | 2.70934 | − | 3.21689i | 0.115005 | − | 0.136549i | ||||
\(556\) | 5.13533 | 0.217787 | ||||||||
\(557\) | 37.7648 | 1.60015 | 0.800073 | − | 0.599903i | \(-0.204794\pi\) | ||||
0.800073 | + | 0.599903i | \(0.204794\pi\) | |||||||
\(558\) | − | 4.03793i | − | 0.170939i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.57766 | − | 7.22431i | −0.362472 | − | 0.305283i | ||||
\(561\) | 7.29958i | 0.308188i | ||||||||
\(562\) | 4.82221i | 0.203413i | ||||||||
\(563\) | 25.9008i | 1.09159i | 0.837919 | + | 0.545794i | \(0.183772\pi\) | ||||
−0.837919 | + | 0.545794i | \(0.816228\pi\) | |||||||
\(564\) | − | 2.50155i | − | 0.105334i | ||||||
\(565\) | 6.85643 | − | 8.14087i | 0.288452 | − | 0.342489i | ||||
\(566\) | − | 7.22928i | − | 0.303869i | ||||||
\(567\) | −16.1193 | −0.676947 | ||||||||
\(568\) | − | 5.78466i | − | 0.242719i | ||||||
\(569\) | −21.5451 | −0.903217 | −0.451609 | − | 0.892216i | \(-0.649150\pi\) | ||||
−0.451609 | + | 0.892216i | \(0.649150\pi\) | |||||||
\(570\) | −4.12140 | − | 3.47114i | −0.172626 | − | 0.145390i | ||||
\(571\) | 2.22036 | 0.0929192 | 0.0464596 | − | 0.998920i | \(-0.485206\pi\) | ||||
0.0464596 | + | 0.998920i | \(0.485206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.530704i | − | 0.0221705i | ||||||
\(574\) | 0.434911i | 0.0181528i | ||||||||
\(575\) | 1.70042 | − | 0.293416i | 0.0709124 | − | 0.0122363i | ||||
\(576\) | 25.2419 | 1.05174 | ||||||||
\(577\) | 6.20265 | 0.258220 | 0.129110 | − | 0.991630i | \(-0.458788\pi\) | ||||
0.129110 | + | 0.991630i | \(0.458788\pi\) | |||||||
\(578\) | −15.0840 | −0.627411 | ||||||||
\(579\) | − | 7.31742i | − | 0.304102i | ||||||
\(580\) | −3.02845 | − | 2.55063i | −0.125749 | − | 0.105909i | ||||
\(581\) | 15.9024 | 0.659742 | ||||||||
\(582\) | 2.37901i | 0.0986130i | ||||||||
\(583\) | 9.41646 | 0.389990 | ||||||||
\(584\) | −27.2492 | −1.12758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6265 | −0.480285 | ||||||||
\(587\) | 1.82894 | 0.0754883 | 0.0377442 | − | 0.999287i | \(-0.487983\pi\) | ||||
0.0377442 | + | 0.999287i | \(0.487983\pi\) | |||||||
\(588\) | − | 0.586832i | − | 0.0242005i | ||||||
\(589\) | 6.94228 | 0.286052 | ||||||||
\(590\) | 12.0770 | − | 14.3395i | 0.497204 | − | 0.590346i | ||||
\(591\) | 3.19466i | 0.131411i | ||||||||
\(592\) | 13.4681 | 0.553534 | ||||||||
\(593\) | 0.0728761 | 0.00299266 | 0.00149633 | − | 0.999999i | \(-0.499524\pi\) | ||||
0.00149633 | + | 0.999999i | \(0.499524\pi\) | |||||||
\(594\) | 9.35204 | 0.383719 | ||||||||
\(595\) | −15.9334 | + | 18.9182i | −0.653204 | + | 0.775571i | ||||
\(596\) | − | 13.1642i | − | 0.539229i | ||||||
\(597\) | 6.00646i | 0.245828i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.5813 | 0.595777 | 0.297888 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297888 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(600\) | −5.22960 | + | 0.902394i | −0.213498 | + | 0.0368401i | ||||
\(601\) | −44.4082 | −1.81145 | −0.905723 | − | 0.423870i | \(-0.860671\pi\) | ||||
−0.905723 | + | 0.423870i | \(0.860671\pi\) | |||||||
\(602\) | 3.22748i | 0.131542i | ||||||||
\(603\) | −12.6881 | −0.516700 | ||||||||
\(604\) | 11.3105i | 0.460220i | ||||||||
\(605\) | 6.94615 | + | 5.85021i | 0.282401 | + | 0.237845i | ||||
\(606\) | − | 2.43491i | − | 0.0989115i | ||||||
\(607\) | − | 36.2354i | − | 1.47075i | −0.677660 | − | 0.735375i | \(-0.737006\pi\) | ||
0.677660 | − | 0.735375i | \(-0.262994\pi\) | |||||||
\(608\) | 18.9182i | 0.767235i | ||||||||
\(609\) | − | 2.10126i | − | 0.0851474i | ||||||
\(610\) | −13.7311 | − | 11.5647i | −0.555956 | − | 0.468239i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 9.26754i | − | 0.374618i | ||||||
\(613\) | 3.35830 | 0.135641 | 0.0678203 | − | 0.997698i | \(-0.478396\pi\) | ||||
0.0678203 | + | 0.997698i | \(0.478396\pi\) | |||||||
\(614\) | 26.2455 | 1.05918 | ||||||||
\(615\) | 0.106526 | + | 0.0897185i | 0.00429553 | + | 0.00361780i | ||||
\(616\) | 24.2240i | 0.976013i | ||||||||
\(617\) | 21.1820 | 0.852754 | 0.426377 | − | 0.904546i | \(-0.359790\pi\) | ||||
0.426377 | + | 0.904546i | \(0.359790\pi\) | |||||||
\(618\) | −2.63631 | −0.106048 | ||||||||
\(619\) | − | 25.4082i | − | 1.02124i | −0.859807 | − | 0.510620i | \(-0.829416\pi\) | ||
0.859807 | − | 0.510620i | \(-0.170584\pi\) | |||||||
\(620\) | 1.00366 | − | 1.19167i | 0.0403078 | − | 0.0478587i | ||||
\(621\) | −0.700420 | −0.0281069 | ||||||||
\(622\) | −9.07009 | −0.363677 | ||||||||
\(623\) | 24.8455i | 0.995416i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5543 | + | 8.37828i | −0.942171 | + | 0.335131i | ||||
\(626\) | − | 31.0399i | − | 1.24060i | ||||||
\(627\) | 7.87651i | 0.314557i | ||||||||
\(628\) | 3.66105i | 0.146092i | ||||||||
\(629\) | − | 29.7041i | − | 1.18438i | ||||||
\(630\) | 11.8733 | + | 10.0000i | 0.473045 | + | 0.398410i | ||||
\(631\) | 43.5451i | 1.73350i | 0.498740 | + | 0.866751i | \(0.333796\pi\) | ||||
−0.498740 | + | 0.866751i | \(0.666204\pi\) | |||||||
\(632\) | 34.3853 | 1.36777 | ||||||||
\(633\) | 2.51300i | 0.0998828i | ||||||||
\(634\) | 14.0614 | 0.558449 | ||||||||
\(635\) | 24.0643 | − | 28.5724i | 0.954964 | − | 1.13386i | ||||
\(636\) | 0.494244 | 0.0195980 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 13.8238i | − | 0.547288i | ||||||
\(639\) | 5.41868i | 0.214360i | ||||||||
\(640\) | −6.78883 | − | 5.71771i | −0.268352 | − | 0.226012i | ||||
\(641\) | −48.2854 | −1.90716 | −0.953579 | − | 0.301142i | \(-0.902632\pi\) | ||||
−0.953579 | + | 0.301142i | \(0.902632\pi\) | |||||||
\(642\) | 7.24423 | 0.285907 | ||||||||
\(643\) | 42.3440 | 1.66989 | 0.834943 | − | 0.550337i | \(-0.185501\pi\) | ||||
0.834943 | + | 0.550337i | \(0.185501\pi\) | |||||||
\(644\) | − | 0.413416i | − | 0.0162909i | ||||||
\(645\) | 0.790529 | + | 0.665802i | 0.0311271 | + | 0.0262159i | ||||
\(646\) | −38.0561 | −1.49730 | ||||||||
\(647\) | 34.4052i | 1.35261i | 0.736622 | + | 0.676305i | \(0.236420\pi\) | ||||
−0.736622 | + | 0.676305i | \(0.763580\pi\) | |||||||
\(648\) | −24.4263 | −0.959556 | ||||||||
\(649\) | −27.4045 | −1.07572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.826831 | 0.0324061 | ||||||||
\(652\) | −7.04487 | −0.275899 | ||||||||
\(653\) | 14.3315i | 0.560834i | 0.959878 | + | 0.280417i | \(0.0904727\pi\) | ||||
−0.959878 | + | 0.280417i | \(0.909527\pi\) | |||||||
\(654\) | 2.36096 | 0.0923208 | ||||||||
\(655\) | −17.1029 | − | 14.4045i | −0.668267 | − | 0.562830i | ||||
\(656\) | 0.445988i | 0.0174129i | ||||||||
\(657\) | 25.5252 | 0.995832 | ||||||||
\(658\) | 29.5936 | 1.15368 | ||||||||
\(659\) | −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 | ||||
\(661\) | 14.4187i | 0.560822i | 0.959880 | + | 0.280411i | \(0.0904707\pi\) | ||||
−0.959880 | + | 0.280411i | \(0.909529\pi\) | |||||||
\(662\) | 15.0796i | 0.586087i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.0976 | 0.935168 | ||||||||
\(665\) | −17.1927 | + | 20.4134i | −0.666703 | + | 0.791598i | ||||
\(666\) | −18.6427 | −0.722390 | ||||||||
\(667\) | 1.03533i | 0.0400881i | ||||||||
\(668\) | −1.19792 | −0.0463491 | ||||||||
\(669\) | − | 6.71826i | − | 0.259743i | ||||||
\(670\) | 8.94361 | + | 7.53252i | 0.345522 | + | 0.291007i | ||||
\(671\) | 26.2419i | 1.01306i | ||||||||
\(672\) | 2.25318i | 0.0869181i | ||||||||
\(673\) | − | 34.1741i | − | 1.31731i | −0.752443 | − | 0.658657i | \(-0.771125\pi\) | ||
0.752443 | − | 0.658657i | \(-0.228875\pi\) | |||||||
\(674\) | 18.1590i | 0.699458i | ||||||||
\(675\) | 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 | \(0.964160\pi\) | |||||||
\(678\) | 1.95043 | 0.0749058 | ||||||||
\(679\) | 11.7833 | 0.452201 | ||||||||
\(680\) | −24.1445 | + | 28.6676i | −0.925900 | + | 1.09935i | ||||
\(681\) | − | 1.66054i | − | 0.0636319i | ||||||
\(682\) | 5.43955 | 0.208291 | ||||||||
\(683\) | −11.3488 | −0.434249 | −0.217125 | − | 0.976144i | \(-0.569668\pi\) | ||||
−0.217125 | + | 0.976144i | \(0.569668\pi\) | |||||||
\(684\) | − | 10.0000i | − | 0.382360i | ||||||
\(685\) | 3.38273 | + | 2.84901i | 0.129247 | + | 0.108855i | ||||
\(686\) | 23.8106 | 0.909093 | ||||||||
\(687\) | −0.525808 | −0.0200608 | ||||||||
\(688\) | 3.30969i | 0.126181i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.241857 | + | 0.203698i | 0.00920733 | + | 0.00775463i | ||||
\(691\) | 18.8232i | 0.716067i | 0.933709 | + | 0.358034i | \(0.116553\pi\) | ||||
−0.933709 | + | 0.358034i | \(0.883447\pi\) | |||||||
\(692\) | − | 0.790529i | − | 0.0300514i | ||||||
\(693\) | − | 22.6914i | − | 0.861976i | ||||||
\(694\) | 14.5325i | 0.551647i | ||||||||
\(695\) | 14.8803 | + | 12.5325i | 0.564441 | + | 0.475385i | ||||
\(696\) | − | 3.18413i | − | 0.120694i | ||||||
\(697\) | 0.983636 | 0.0372579 | ||||||||
\(698\) | − | 22.2036i | − | 0.840420i | ||||||
\(699\) | −4.81952 | −0.182291 | ||||||||
\(700\) | 1.01849 | + | 5.90239i | 0.0384952 | + | 0.223090i | ||||
\(701\) | −19.1626 | −0.723763 | −0.361881 | − | 0.932224i | \(-0.617865\pi\) | ||||
−0.361881 | + | 0.932224i | \(0.617865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.0518i | − | 1.20885i | ||||||
\(704\) | 34.0037i | 1.28156i | ||||||||
\(705\) | 6.10492 | − | 7.24857i | 0.229924 | − | 0.272997i | ||||
\(706\) | −1.55401 | −0.0584860 | ||||||||
\(707\) | −12.0602 | −0.453570 | ||||||||
\(708\) | −1.43839 | −0.0540578 | ||||||||
\(709\) | − | 23.4837i | − | 0.881949i | −0.897520 | − | 0.440975i | \(-0.854633\pi\) | ||
0.897520 | − | 0.440975i | \(-0.145367\pi\) | |||||||
\(710\) | 3.21689 | − | 3.81952i | 0.120728 | − | 0.143344i | ||||
\(711\) | −32.2098 | −1.20796 | ||||||||
\(712\) | 37.6496i | 1.41098i | ||||||||
\(713\) | −0.407395 | −0.0152571 | ||||||||
\(714\) | −4.53252 | −0.169625 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.9370 | −0.446107 | ||||||||
\(717\) | 1.38044 | 0.0515535 | ||||||||
\(718\) | 34.9173i | 1.30310i | ||||||||
\(719\) | −14.1086 | −0.526161 | −0.263080 | − | 0.964774i | \(-0.584738\pi\) | ||||
−0.263080 | + | 0.964774i | \(0.584738\pi\) | |||||||
\(720\) | 12.1758 | + | 10.2547i | 0.453764 | + | 0.382170i | ||||
\(721\) | 13.0577i | 0.486295i | ||||||||
\(722\) | −18.5046 | −0.688668 | ||||||||
\(723\) | −6.02765 | −0.224171 | ||||||||
\(724\) | 11.7004 | 0.434843 | ||||||||
\(725\) | −2.55063 | − | 14.7816i | −0.0947280 | − | 0.548973i | ||||
\(726\) | 1.66419i | 0.0617640i | ||||||||
\(727\) | − | 25.3762i | − | 0.941153i | −0.882359 | − | 0.470576i | \(-0.844046\pi\) | ||
0.882359 | − | 0.470576i | \(-0.155954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7796 | 0.769616 | ||||||||
\(730\) | −17.9922 | − | 15.1534i | −0.665921 | − | 0.560854i | ||||
\(731\) | 7.29958 | 0.269985 | ||||||||
\(732\) | 1.37736i | 0.0509087i | ||||||||
\(733\) | 10.6692 | 0.394074 | 0.197037 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197037 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(734\) | − | 39.6952i | − | 1.46517i | ||||||
\(735\) | 1.43213 | − | 1.70042i | 0.0528251 | − | 0.0627209i | ||||
\(736\) | − | 1.11018i | − | 0.0409218i | ||||||
\(737\) | − | 17.0923i | − | 0.629605i | ||||||
\(738\) | − | 0.617344i | − | 0.0227247i | ||||||
\(739\) | 1.41503i | 0.0520526i | 0.999661 | + | 0.0260263i | \(0.00828536\pi\) | ||||
−0.999661 | + | 0.0260263i | \(0.991715\pi\) | |||||||
\(740\) | −5.50183 | − | 4.63377i | −0.202251 | − | 0.170341i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.84695i | 0.214648i | ||||||||
\(743\) | 29.8777 | 1.09611 | 0.548053 | − | 0.836443i | \(-0.315369\pi\) | ||||
0.548053 | + | 0.836443i | \(0.315369\pi\) | |||||||
\(744\) | 1.25293 | 0.0459348 | ||||||||
\(745\) | 32.1267 | − | 38.1451i | 1.17703 | − | 1.39753i | ||||
\(746\) | 40.9370i | 1.49881i | ||||||||
\(747\) | −22.5730 | −0.825903 | ||||||||
\(748\) | 12.4844 | 0.456476 | ||||||||
\(749\) | − | 35.8809i | − | 1.31106i | ||||||
\(750\) | −3.95485 | − | 2.31238i | −0.144411 | − | 0.0844362i | ||||
\(751\) | 19.9858 | 0.729293 | 0.364646 | − | 0.931146i | \(-0.381190\pi\) | ||||
0.364646 | + | 0.931146i | \(0.381190\pi\) | |||||||
\(752\) | 30.3474 | 1.10666 | ||||||||
\(753\) | 3.20938i | 0.116956i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.6028 | + | 32.7737i | −1.00457 | + | 1.19276i | ||||
\(756\) | − | 2.43126i | − | 0.0884239i | ||||||
\(757\) | − | 17.0923i | − | 0.621232i | −0.950535 | − | 0.310616i | \(-0.899465\pi\) | ||
0.950535 | − | 0.310616i | \(-0.100535\pi\) | |||||||
\(758\) | − | 20.6649i | − | 0.750584i | ||||||
\(759\) | − | 0.462218i | − | 0.0167775i | ||||||
\(760\) | −26.0528 | + | 30.9334i | −0.945034 | + | 1.12207i | ||||
\(761\) | − | 42.2240i | − | 1.53062i | −0.643662 | − | 0.765310i | \(-0.722586\pi\) | ||
0.643662 | − | 0.765310i | \(-0.277414\pi\) | |||||||
\(762\) | 6.84552 | 0.247987 | ||||||||
\(763\) | − | 11.6939i | − | 0.423347i | ||||||
\(764\) | −0.907659 | −0.0328380 | ||||||||
\(765\) | 22.6170 | − | 26.8539i | 0.817718 | − | 0.970904i | ||||
\(766\) | −2.07395 | −0.0749350 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.42107i | 0.159531i | ||||||||
\(769\) | − | 23.7655i | − | 0.857004i | −0.903541 | − | 0.428502i | \(-0.859041\pi\) | ||
0.903541 | − | 0.428502i | \(-0.140959\pi\) | |||||||
\(770\) | −13.4711 | + | 15.9947i | −0.485466 | + | 0.576410i | ||||
\(771\) | −3.75814 | −0.135346 | ||||||||
\(772\) | −12.5149 | −0.450422 | ||||||||
\(773\) | 0.284086 | 0.0102179 | 0.00510894 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510894 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(774\) | − | 4.58132i | − | 0.164672i | ||||||
\(775\) | 5.81644 | − | 1.00366i | 0.208933 | − | 0.0360524i | ||||
\(776\) | 17.8557 | 0.640984 | ||||||||
\(777\) | − | 3.81739i | − | 0.136948i | ||||||
\(778\) | 26.1730 | 0.938349 | ||||||||
\(779\) | 1.06138 | 0.0380278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29958 | −0.261199 | ||||||||
\(782\) | 2.23325 | 0.0798610 | ||||||||
\(783\) | 6.08867i | 0.217591i | ||||||||
\(784\) | 7.11910 | 0.254254 | ||||||||
\(785\) | −8.93460 | + | 10.6084i | −0.318890 | + | 0.378628i | ||||
\(786\) | − | 4.09761i | − | 0.146157i | ||||||
\(787\) | −24.1341 | −0.860289 | −0.430145 | − | 0.902760i | \(-0.641537\pi\) | ||||
−0.430145 | + | 0.902760i | \(0.641537\pi\) | |||||||
\(788\) | 5.46381 | 0.194640 | ||||||||
\(789\) | 4.63849 | 0.165135 | ||||||||
\(790\) | 22.7041 | + | 19.1219i | 0.807775 | + | 0.680327i | ||||
\(791\) | − | 9.66054i | − | 0.343489i | ||||||
\(792\) | − | 34.3853i | − | 1.22183i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 26.7529 | 0.949424 | ||||||||
\(795\) | 1.43213 | + | 1.20618i | 0.0507926 | + | 0.0427787i | ||||
\(796\) | 10.2728 | 0.364110 | ||||||||
\(797\) | 34.3442i | 1.21653i | 0.793732 | + | 0.608267i | \(0.208135\pi\) | ||||
−0.793732 | + | 0.608267i | \(0.791865\pi\) | |||||||
\(798\) | −4.89075 | −0.173131 | ||||||||
\(799\) | − | 66.9317i | − | 2.36787i | ||||||
\(800\) | 2.73503 | + | 15.8502i | 0.0966980 | + | 0.560390i | ||||
\(801\) | − | 35.2676i | − | 1.24612i | ||||||
\(802\) | − | 4.39797i | − | 0.155298i | ||||||
\(803\) | 34.3853i | 1.21343i | ||||||||
\(804\) | − | 0.897129i | − | 0.0316393i | ||||||
\(805\) | 1.00892 | − | 1.19792i | 0.0355598 | − | 0.0422213i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26329i | 0.0444698i | ||||||||
\(808\) | −18.2753 | −0.642924 | ||||||||
\(809\) | 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 | ||||
\(811\) | − | 24.5992i | − | 0.863793i | −0.901923 | − | 0.431897i | \(-0.857845\pi\) | ||
0.901923 | − | 0.431897i | \(-0.142155\pi\) | |||||||
\(812\) | −3.59377 | −0.126117 | ||||||||
\(813\) | 7.59368 | 0.266322 | ||||||||
\(814\) | − | 25.1138i | − | 0.880239i | ||||||
\(815\) | −20.4134 | − | 17.1927i | −0.715051 | − | 0.602233i | ||||
\(816\) | −4.64796 | −0.162711 | ||||||||
\(817\) | 7.87651 | 0.275564 | ||||||||
\(818\) | − | 16.0097i | − | 0.559765i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.153445 | − | 0.182190i | 0.00535853 | − | 0.00636236i | ||||
\(821\) | − | 17.2996i | − | 0.603759i | −0.953346 | − | 0.301880i | \(-0.902386\pi\) | ||
0.953346 | − | 0.301880i | \(-0.0976141\pi\) | |||||||
\(822\) | 0.810450i | 0.0282677i | ||||||||
\(823\) | − | 32.5625i | − | 1.13506i | −0.823353 | − | 0.567529i | \(-0.807899\pi\) | ||
0.823353 | − | 0.567529i | \(-0.192101\pi\) | |||||||
\(824\) | 19.7869i | 0.689311i | ||||||||
\(825\) | 1.13872 | + | 6.59916i | 0.0396451 | + | 0.229753i | ||||
\(826\) | − | 17.0162i | − | 0.592070i | ||||||
\(827\) | 15.4702 | 0.537951 | 0.268976 | − | 0.963147i | \(-0.413315\pi\) | ||||
0.268976 | + | 0.963147i | \(0.413315\pi\) | |||||||
\(828\) | 0.586832i | 0.0203938i | ||||||||
\(829\) | −14.5236 | −0.504425 | −0.252213 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252213 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(830\) | 15.9113 | + | 13.4008i | 0.552288 | + | 0.465150i | ||||
\(831\) | −3.41503 | −0.118466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 15.7013i | − | 0.544018i | ||||||
\(834\) | 3.56509i | 0.123449i | ||||||||
\(835\) | −3.47114 | − | 2.92347i | −0.120124 | − | 0.101171i | ||||
\(836\) | 13.4711 | 0.465909 | ||||||||
\(837\) | −2.39585 | −0.0828127 | ||||||||
\(838\) | −19.9747 | −0.690015 | ||||||||
\(839\) | − | 0.815866i | − | 0.0281668i | −0.999901 | − | 0.0140834i | \(-0.995517\pi\) | ||
0.999901 | − | 0.0140834i | \(-0.00448304\pi\) | |||||||
\(840\) | −3.10291 | + | 3.68419i | −0.107061 | + | 0.127117i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | − | 20.3049i | − | 0.699753i | ||||||
\(843\) | 1.40162 | 0.0482744 | ||||||||
\(844\) | 4.29797 | 0.147942 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −42.0073 | −1.44424 | ||||||||
\(847\) | 8.24280 | 0.283226 | ||||||||
\(848\) | 5.99587i | 0.205899i | ||||||||
\(849\) | −2.10126 | −0.0721151 | ||||||||
\(850\) | −31.8845 | + | 5.50183i | −1.09363 | + | 0.188711i | ||||
\(851\) | 1.88090i | 0.0644764i | ||||||||
\(852\) | −0.383134 | −0.0131260 | ||||||||
\(853\) | 20.0856 | 0.687719 | 0.343859 | − | 0.939021i | \(-0.388266\pi\) | ||||
0.343859 | + | 0.939021i | \(0.388266\pi\) | |||||||
\(854\) | −16.2943 | −0.557580 | ||||||||
\(855\) | 24.4045 | − | 28.9763i | 0.834616 | − | 0.990968i | ||||
\(856\) | − | 54.3719i | − | 1.85839i | ||||||
\(857\) | − | 40.7886i | − | 1.39331i | −0.717406 | − | 0.696656i | \(-0.754671\pi\) | ||
0.717406 | − | 0.696656i | \(-0.245329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.1301 | 1.36922 | 0.684610 | − | 0.728909i | \(-0.259972\pi\) | ||||
0.684610 | + | 0.728909i | \(0.259972\pi\) | |||||||
\(860\) | 1.13872 | − | 1.35204i | 0.0388300 | − | 0.0461041i | ||||
\(861\) | 0.126411 | 0.00430808 | ||||||||
\(862\) | − | 11.4703i | − | 0.390679i | ||||||
\(863\) | 20.8275 | 0.708977 | 0.354489 | − | 0.935060i | \(-0.384655\pi\) | ||||
0.354489 | + | 0.935060i | \(0.384655\pi\) | |||||||
\(864\) | − | 6.52886i | − | 0.222116i | ||||||
\(865\) | 1.92925 | − | 2.29066i | 0.0655964 | − | 0.0778848i | ||||
\(866\) | 29.4134i | 0.999509i | ||||||||
\(867\) | 4.38430i | 0.148899i | ||||||||
\(868\) | − | 1.41412i | − | 0.0479985i | ||||||
\(869\) | − | 43.3903i | − | 1.47192i | ||||||
\(870\) | 1.77072 | − | 2.10243i | 0.0600330 | − | 0.0712792i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 17.7203i | − | 0.600084i | ||||||
\(873\) | −16.7261 | −0.566091 | ||||||||
\(874\) | 2.40976 | 0.0815114 | ||||||||
\(875\) | −11.4533 | + | 19.5885i | −0.387192 | + | 0.662212i | ||||
\(876\) | 1.80479i | 0.0609782i | ||||||||
\(877\) | 46.5944 | 1.57338 | 0.786691 | − | 0.617347i | \(-0.211793\pi\) | ||||
0.786691 | + | 0.617347i | \(0.211793\pi\) | |||||||
\(878\) | 8.38421 | 0.282953 | ||||||||
\(879\) | 3.37935i | 0.113982i | ||||||||
\(880\) | −13.8143 | + | 16.4021i | −0.465678 | + | 0.552916i | ||||
\(881\) | −23.8447 | −0.803347 | −0.401674 | − | 0.915783i | \(-0.631571\pi\) | ||||
−0.401674 | + | 0.915783i | \(0.631571\pi\) | |||||||
\(882\) | −9.85437 | −0.331814 | ||||||||
\(883\) | − | 37.2496i | − | 1.25355i | −0.779201 | − | 0.626774i | \(-0.784375\pi\) | ||
0.779201 | − | 0.626774i | \(-0.215625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.16790 | − | 3.51031i | −0.140103 | − | 0.117998i | ||||
\(886\) | 45.4082i | 1.52552i | ||||||||
\(887\) | 28.5795i | 0.959605i | 0.877377 | + | 0.479802i | \(0.159292\pi\) | ||||
−0.877377 | + | 0.479802i | \(0.840708\pi\) | |||||||
\(888\) | − | 5.78466i | − | 0.194121i | ||||||
\(889\) | − | 33.9060i | − | 1.13717i | ||||||
\(890\) | −20.9372 | + | 24.8594i | −0.701816 | + | 0.833289i | ||||
\(891\) | 30.8232i | 1.03262i | ||||||||
\(892\) | −11.4902 | −0.384720 | ||||||||
\(893\) | − | 72.2217i | − | 2.41681i | ||||||
\(894\) | 9.13899 | 0.305653 | ||||||||
\(895\) | −34.5890 | − | 29.1317i | −1.15618 | − | 0.973765i | ||||
\(896\) | −8.05611 | −0.269136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.8180i | 0.494483i | ||||||||
\(899\) | 3.54144i | 0.118114i | ||||||||
\(900\) | −1.44571 | − | 8.37828i | −0.0481905 | − | 0.279276i | ||||
\(901\) | 13.2240 | 0.440556 | ||||||||
\(902\) | 0.831632 | 0.0276903 | ||||||||
\(903\) | 0.938099 | 0.0312180 | ||||||||
\(904\) | − | 14.6390i | − | 0.486887i | ||||||
\(905\) | 33.9035 | + | 28.5543i | 1.12699 | + | 0.949177i | ||||
\(906\) | −7.85209 | −0.260868 | ||||||||
\(907\) | − | 6.41386i | − | 0.212969i | −0.994314 | − | 0.106484i | \(-0.966041\pi\) | ||
0.994314 | − | 0.106484i | \(-0.0339594\pi\) | |||||||
\(908\) | −2.84001 | −0.0942489 | ||||||||
\(909\) | 17.1191 | 0.567805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.2204 | 0.736193 | 0.368097 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368097 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(912\) | −5.01532 | −0.166074 | ||||||||
\(913\) | − | 30.4084i | − | 1.00637i | ||||||
\(914\) | 9.77437 | 0.323308 | ||||||||
\(915\) | −3.36138 | + | 3.99108i | −0.111124 | + | 0.131941i | ||||
\(916\) | 0.899287i | 0.0297133i | ||||||||
\(917\) | −20.2956 | −0.670219 | ||||||||
\(918\) | 13.1335 | 0.433472 | ||||||||
\(919\) | −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 | ||||
\(921\) | − | 7.62851i | − | 0.251368i | ||||||
\(922\) | 5.39220i | 0.177583i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.60442 | 0.0527817 | ||||||||
\(925\) | −4.63377 | − | 26.8539i | −0.152357 | − | 0.882950i | ||||
\(926\) | −2.36096 | −0.0775859 | ||||||||
\(927\) | − | 18.5351i | − | 0.608772i | ||||||
\(928\) | −9.65067 | −0.316799 | ||||||||
\(929\) | − | 23.9423i | − | 0.785521i | −0.919641 | − | 0.392760i | \(-0.871520\pi\) | ||
0.919641 | − | 0.392760i | \(-0.128480\pi\) | |||||||
\(930\) | 0.827293 | + | 0.696765i | 0.0271280 | + | 0.0228478i | ||||
\(931\) | − | 16.9423i | − | 0.555261i | ||||||
\(932\) | 8.24280i | 0.270002i | ||||||||
\(933\) | 2.63631i | 0.0863089i | ||||||||
\(934\) | 38.9496i | 1.27447i | ||||||||
\(935\) | 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 | \(-0.0977407\pi\) | |||||||
\(938\) | 10.6131 | 0.346531 | ||||||||
\(939\) | −9.02204 | −0.294423 | ||||||||
\(940\) | −12.3972 | − | 10.4412i | −0.404352 | − | 0.340554i | ||||
\(941\) | 14.3788i | 0.468735i | 0.972148 | + | 0.234368i | \(0.0753020\pi\) | ||||
−0.972148 | + | 0.234368i | \(0.924698\pi\) | |||||||
\(942\) | −2.54160 | −0.0828098 | ||||||||
\(943\) | −0.0622851 | −0.00202828 | ||||||||
\(944\) | − | 17.4496i | − | 0.567938i | ||||||
\(945\) | 5.93336 | − | 7.04487i | 0.193012 | − | 0.229170i | ||||
\(946\) | 6.17156 | 0.200655 | ||||||||
\(947\) | −58.3188 | −1.89511 | −0.947554 | − | 0.319596i | \(-0.896453\pi\) | ||||
−0.947554 | + | 0.319596i | \(0.896453\pi\) | |||||||
\(948\) | − | 2.27744i | − | 0.0739677i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −34.4045 | + | 5.93667i | −1.11623 | + | 0.192611i | ||||
\(951\) | − | 4.08708i | − | 0.132533i | ||||||
\(952\) | 34.0190i | 1.10256i | ||||||||
\(953\) | − | 13.7995i | − | 0.447010i | −0.974703 | − | 0.223505i | \(-0.928250\pi\) | ||
0.974703 | − | 0.223505i | \(-0.0717499\pi\) | |||||||
\(954\) | − | 8.29958i | − | 0.268709i | ||||||
\(955\) | −2.63006 | − | 2.21510i | −0.0851067 | − | 0.0716788i | ||||
\(956\) | − | 2.36096i | − | 0.0763588i | ||||||
\(957\) | −4.01801 | −0.129884 | ||||||||
\(958\) | 36.5762i | 1.18172i | ||||||||
\(959\) | 4.01419 | 0.129625 | ||||||||
\(960\) | −4.35561 | + | 5.17156i | −0.140577 | + | 0.166911i | ||||
\(961\) | 29.6065 | 0.955047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9319i | 1.64126i | ||||||||
\(964\) | 10.3090i | 0.332032i | ||||||||
\(965\) | −36.2636 | − | 30.5421i | −1.16737 | − | 0.983184i | ||||
\(966\) | 0.287005 | 0.00923422 | ||||||||
\(967\) | 30.3474 | 0.975906 | 0.487953 | − | 0.872870i | \(-0.337744\pi\) | ||||
0.487953 | + | 0.872870i | \(0.337744\pi\) | |||||||
\(968\) | 12.4907 | 0.401466 | ||||||||
\(969\) | 11.0614i | 0.355343i | ||||||||
\(970\) | 11.7899 | + | 9.92970i | 0.378550 | + | 0.318824i | ||||
\(971\) | 44.1013 | 1.41528 | 0.707638 | − | 0.706575i | \(-0.249761\pi\) | ||||
0.707638 | + | 0.706575i | \(0.249761\pi\) | |||||||
\(972\) | 5.21160i | 0.167162i | ||||||||
\(973\) | 17.6580 | 0.566089 | ||||||||
\(974\) | −26.5074 | −0.849351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.7093 | −0.534853 | ||||||||
\(977\) | −22.3220 | −0.714143 | −0.357071 | − | 0.934077i | \(-0.616225\pi\) | ||||
−0.357071 | + | 0.934077i | \(0.616225\pi\) | |||||||
\(978\) | − | 4.89075i | − | 0.156389i | ||||||
\(979\) | 47.5094 | 1.51841 | ||||||||
\(980\) | −2.90822 | − | 2.44937i | −0.0928996 | − | 0.0782422i | ||||
\(981\) | 16.5992i | 0.529970i | ||||||||
\(982\) | −12.6838 | −0.404756 | ||||||||
\(983\) | 4.03793 | 0.128790 | 0.0643950 | − | 0.997924i | \(-0.479488\pi\) | ||||
0.0643950 | + | 0.997924i | \(0.479488\pi\) | |||||||
\(984\) | 0.191556 | 0.00610659 | ||||||||
\(985\) | 15.8321 | + | 13.3342i | 0.504453 | + | 0.424862i | ||||
\(986\) | − | 19.4134i | − | 0.618249i | ||||||
\(987\) | − | 8.60167i | − | 0.273794i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.462218 | −0.0146977 | ||||||||
\(990\) | 19.1219 | − | 22.7041i | 0.607734 | − | 0.721583i | ||||
\(991\) | 29.6500 | 0.941864 | 0.470932 | − | 0.882170i | \(-0.343918\pi\) | ||||
0.470932 | + | 0.882170i | \(0.343918\pi\) | |||||||
\(992\) | − | 3.79747i | − | 0.120570i | ||||||
\(993\) | 4.38304 | 0.139092 | ||||||||
\(994\) | − | 4.53252i | − | 0.143763i | ||||||
\(995\) | 29.7668 | + | 25.0703i | 0.943671 | + | 0.794782i | ||||
\(996\) | − | 1.59605i | − | 0.0505728i | ||||||
\(997\) | 22.1762i | 0.702327i | 0.936314 | + | 0.351164i | \(0.114214\pi\) | ||||
−0.936314 | + | 0.351164i | \(0.885786\pi\) | |||||||
\(998\) | 22.3450i | 0.707320i | ||||||||
\(999\) | 11.0614i | 0.349967i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))