Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Root | \(-2.53767i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.301 |
Dual form | 375.2.g.d.76.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05302 | + | 1.49161i | −1.45171 | + | 1.05473i | −0.466276 | + | 0.884639i | \(0.654405\pi\) |
−0.985429 | + | 0.170086i | \(0.945595\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 1.37197 | − | 4.22249i | 0.685985 | − | 2.11124i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.784184 | − | 2.41347i | −0.320142 | − | 0.985295i | ||||
\(7\) | 1.04054 | 0.393285 | 0.196643 | − | 0.980475i | \(-0.436996\pi\) | ||||
0.196643 | + | 0.980475i | \(0.436996\pi\) | |||||||
\(8\) | 1.91324 | + | 5.88835i | 0.676433 | + | 2.08185i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.40360 | + | 1.74631i | −0.724711 | + | 0.526533i | −0.887886 | − | 0.460064i | \(-0.847827\pi\) |
0.163175 | + | 0.986597i | \(0.447827\pi\) | |||||||
\(12\) | 3.59186 | + | 2.60964i | 1.03688 | + | 0.753338i | ||||
\(13\) | −4.58650 | − | 3.33228i | −1.27207 | − | 0.924209i | −0.272782 | − | 0.962076i | \(-0.587944\pi\) |
−0.999283 | + | 0.0378663i | \(0.987944\pi\) | |||||||
\(14\) | −2.13624 | + | 1.55207i | −0.570934 | + | 0.414808i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.52731 | − | 4.01583i | −1.38183 | − | 1.00396i | ||||
\(17\) | −1.57092 | − | 4.83480i | −0.381005 | − | 1.17261i | −0.939337 | − | 0.342995i | \(-0.888559\pi\) |
0.558333 | − | 0.829617i | \(-0.311441\pi\) | |||||||
\(18\) | 2.53767 | 0.598135 | ||||||||
\(19\) | −1.65990 | − | 5.10866i | −0.380808 | − | 1.17201i | −0.939476 | − | 0.342615i | \(-0.888687\pi\) |
0.558668 | − | 0.829391i | \(-0.311313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.321543 | + | 0.989608i | −0.0701665 | + | 0.215950i | ||||
\(22\) | 2.32982 | − | 7.17044i | 0.496719 | − | 1.52874i | ||||
\(23\) | −3.12312 | + | 2.26908i | −0.651215 | + | 0.473135i | −0.863685 | − | 0.504032i | \(-0.831849\pi\) |
0.212470 | + | 0.977168i | \(0.431849\pi\) | |||||||
\(24\) | −6.19138 | −1.26381 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.3866 | 2.82145 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 1.42758 | − | 4.39365i | 0.269788 | − | 0.830322i | ||||
\(29\) | 0.210038 | − | 0.646430i | 0.0390030 | − | 0.120039i | −0.929659 | − | 0.368421i | \(-0.879899\pi\) |
0.968662 | + | 0.248382i | \(0.0798987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.262699 | + | 0.808503i | 0.0471821 | + | 0.145212i | 0.971872 | − | 0.235509i | \(-0.0756759\pi\) |
−0.924690 | + | 0.380721i | \(0.875676\pi\) | |||||||
\(32\) | 4.95495 | 0.875921 | ||||||||
\(33\) | −0.918092 | − | 2.82560i | −0.159819 | − | 0.491873i | ||||
\(34\) | 10.4368 | + | 7.58275i | 1.78989 | + | 1.30043i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.59186 | + | 2.60964i | −0.598644 | + | 0.434940i | ||||
\(37\) | 1.30869 | + | 0.950818i | 0.215147 | + | 0.156313i | 0.690139 | − | 0.723676i | \(-0.257549\pi\) |
−0.474992 | + | 0.879990i | \(0.657549\pi\) | |||||||
\(38\) | 11.0279 | + | 8.01226i | 1.78897 | + | 1.29976i | ||||
\(39\) | 4.58650 | − | 3.33228i | 0.734427 | − | 0.533593i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.942740 | − | 0.684941i | −0.147231 | − | 0.106970i | 0.511731 | − | 0.859146i | \(-0.329004\pi\) |
−0.658962 | + | 0.752176i | \(0.729004\pi\) | |||||||
\(42\) | −0.815972 | − | 2.51130i | −0.125907 | − | 0.387502i | ||||
\(43\) | 5.68601 | 0.867109 | 0.433554 | − | 0.901127i | \(-0.357259\pi\) | ||||
0.433554 | + | 0.901127i | \(0.357259\pi\) | |||||||
\(44\) | 4.07613 | + | 12.5450i | 0.614500 | + | 1.89124i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.02725 | − | 9.31693i | 0.446344 | − | 1.37371i | ||||
\(47\) | 1.01555 | − | 3.12556i | 0.148134 | − | 0.455909i | −0.849267 | − | 0.527964i | \(-0.822956\pi\) |
0.997401 | + | 0.0720547i | \(0.0229556\pi\) | |||||||
\(48\) | 5.52731 | − | 4.01583i | 0.797798 | − | 0.579635i | ||||
\(49\) | −5.91729 | −0.845327 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.08361 | 0.711848 | ||||||||
\(52\) | −20.3631 | + | 14.7946i | −2.82385 | + | 2.05165i | ||||
\(53\) | 3.92023 | − | 12.0652i | 0.538485 | − | 1.65729i | −0.197511 | − | 0.980301i | \(-0.563286\pi\) |
0.735996 | − | 0.676986i | \(-0.236714\pi\) | |||||||
\(54\) | −0.784184 | + | 2.41347i | −0.106714 | + | 0.328432i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.99080 | + | 6.12704i | 0.266031 | + | 0.818760i | ||||
\(57\) | 5.37156 | 0.711481 | ||||||||
\(58\) | 0.533007 | + | 1.64043i | 0.0699873 | + | 0.215399i | ||||
\(59\) | −2.59846 | − | 1.88789i | −0.338290 | − | 0.245782i | 0.405650 | − | 0.914029i | \(-0.367045\pi\) |
−0.743940 | + | 0.668246i | \(0.767045\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.38562 | − | 3.18634i | 0.561521 | − | 0.407969i | −0.270494 | − | 0.962722i | \(-0.587187\pi\) |
0.832015 | + | 0.554753i | \(0.187187\pi\) | |||||||
\(62\) | −1.74530 | − | 1.26803i | −0.221653 | − | 0.161040i | ||||
\(63\) | −0.841811 | − | 0.611611i | −0.106058 | − | 0.0770558i | ||||
\(64\) | 0.881995 | − | 0.640807i | 0.110249 | − | 0.0801008i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.09954 | + | 4.43157i | 0.750801 | + | 0.545489i | ||||
\(67\) | −0.287120 | − | 0.883665i | −0.0350773 | − | 0.107957i | 0.931985 | − | 0.362497i | \(-0.118076\pi\) |
−0.967062 | + | 0.254540i | \(0.918076\pi\) | |||||||
\(68\) | −22.5702 | −2.73703 | ||||||||
\(69\) | −1.19292 | − | 3.67145i | −0.143611 | − | 0.441990i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.436821 | + | 1.34440i | −0.0518412 | + | 0.159551i | −0.973625 | − | 0.228153i | \(-0.926731\pi\) |
0.921784 | + | 0.387703i | \(0.126731\pi\) | |||||||
\(72\) | 1.91324 | − | 5.88835i | 0.225478 | − | 0.693949i | ||||
\(73\) | −9.16080 | + | 6.65571i | −1.07219 | + | 0.778992i | −0.976305 | − | 0.216400i | \(-0.930568\pi\) |
−0.0958862 | + | 0.995392i | \(0.530568\pi\) | |||||||
\(74\) | −4.10501 | −0.477198 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.8486 | −2.73562 | ||||||||
\(77\) | −2.50103 | + | 1.81710i | −0.285018 | + | 0.207078i | ||||
\(78\) | −4.44571 | + | 13.6825i | −0.503378 | + | 1.54924i | ||||
\(79\) | −0.447171 | + | 1.37625i | −0.0503106 | + | 0.154840i | −0.973055 | − | 0.230571i | \(-0.925941\pi\) |
0.922745 | + | 0.385412i | \(0.125941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 2.95713 | 0.326560 | ||||||||
\(83\) | −3.54616 | − | 10.9140i | −0.389242 | − | 1.19796i | −0.933356 | − | 0.358952i | \(-0.883134\pi\) |
0.544114 | − | 0.839011i | \(-0.316866\pi\) | |||||||
\(84\) | 3.73746 | + | 2.71542i | 0.407790 | + | 0.296277i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.6735 | + | 8.48129i | −1.25879 | + | 0.914561i | ||||
\(87\) | 0.549886 | + | 0.399516i | 0.0589540 | + | 0.0428326i | ||||
\(88\) | −14.8816 | − | 10.8121i | −1.58638 | − | 1.15257i | ||||
\(89\) | −7.33961 | + | 5.33254i | −0.777997 | + | 0.565248i | −0.904377 | − | 0.426734i | \(-0.859664\pi\) |
0.126380 | + | 0.991982i | \(0.459664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.77241 | − | 3.46736i | −0.500285 | − | 0.363478i | ||||
\(92\) | 5.29633 | + | 16.3004i | 0.552181 | + | 1.69944i | ||||
\(93\) | −0.850111 | −0.0881524 | ||||||||
\(94\) | 2.57715 | + | 7.93164i | 0.265812 | + | 0.818086i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.53117 | + | 4.71244i | −0.156274 | + | 0.480962i | ||||
\(97\) | −1.86315 | + | 5.73419i | −0.189174 | + | 0.582219i | −0.999995 | − | 0.00307549i | \(-0.999021\pi\) |
0.810821 | + | 0.585294i | \(0.199021\pi\) | |||||||
\(98\) | 12.1483 | − | 8.82627i | 1.22716 | − | 0.891587i | ||||
\(99\) | 2.97101 | 0.298597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.3408 | −1.52647 | −0.763236 | − | 0.646120i | \(-0.776390\pi\) | ||||
−0.763236 | + | 0.646120i | \(0.776390\pi\) | |||||||
\(102\) | −10.4368 | + | 7.58275i | −1.03339 | + | 0.750804i | ||||
\(103\) | −3.72642 | + | 11.4688i | −0.367175 | + | 1.13005i | 0.581432 | + | 0.813595i | \(0.302493\pi\) |
−0.948608 | + | 0.316455i | \(0.897507\pi\) | |||||||
\(104\) | 10.8466 | − | 33.3824i | 1.06360 | − | 3.27341i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.94827 | + | 30.6176i | 0.966261 | + | 2.97385i | ||||
\(107\) | 6.49787 | 0.628173 | 0.314086 | − | 0.949394i | \(-0.398302\pi\) | ||||
0.314086 | + | 0.949394i | \(0.398302\pi\) | |||||||
\(108\) | −1.37197 | − | 4.22249i | −0.132018 | − | 0.406309i | ||||
\(109\) | 1.86929 | + | 1.35812i | 0.179046 | + | 0.130084i | 0.673698 | − | 0.739006i | \(-0.264705\pi\) |
−0.494653 | + | 0.869091i | \(0.664705\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30869 | + | 0.950818i | −0.124215 | + | 0.0902476i | ||||
\(112\) | −5.75136 | − | 4.17861i | −0.543453 | − | 0.394841i | ||||
\(113\) | 3.13317 | + | 2.27638i | 0.294744 | + | 0.214144i | 0.725323 | − | 0.688409i | \(-0.241691\pi\) |
−0.430579 | + | 0.902553i | \(0.641691\pi\) | |||||||
\(114\) | −11.0279 | + | 8.01226i | −1.03286 | + | 0.750417i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.44138 | − | 1.77376i | −0.226676 | − | 0.164690i | ||||
\(117\) | 1.75189 | + | 5.39175i | 0.161962 | + | 0.498467i | ||||
\(118\) | 8.15067 | 0.750330 | ||||||||
\(119\) | −1.63460 | − | 5.03078i | −0.149844 | − | 0.461171i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.671530 | + | 2.06676i | −0.0610482 | + | 0.187887i | ||||
\(122\) | −4.25101 | + | 13.0832i | −0.384868 | + | 1.18450i | ||||
\(123\) | 0.942740 | − | 0.684941i | 0.0850040 | − | 0.0617590i | ||||
\(124\) | 3.77431 | 0.338943 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.64054 | 0.235238 | ||||||||
\(127\) | 9.46046 | − | 6.87342i | 0.839480 | − | 0.609918i | −0.0827456 | − | 0.996571i | \(-0.526369\pi\) |
0.922225 | + | 0.386653i | \(0.126369\pi\) | |||||||
\(128\) | −3.91725 | + | 12.0561i | −0.346239 | + | 1.06562i | ||||
\(129\) | −1.75707 | + | 5.40772i | −0.154702 | + | 0.476123i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.46042 | − | 7.57241i | −0.214968 | − | 0.661604i | −0.999156 | − | 0.0410805i | \(-0.986920\pi\) |
0.784188 | − | 0.620524i | \(-0.213080\pi\) | |||||||
\(132\) | −13.1906 | −1.14810 | ||||||||
\(133\) | −1.72719 | − | 5.31574i | −0.149766 | − | 0.460933i | ||||
\(134\) | 1.90754 | + | 1.38591i | 0.164787 | + | 0.119725i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.4635 | − | 18.5003i | 2.18348 | − | 1.58639i | ||||
\(137\) | −8.94069 | − | 6.49579i | −0.763854 | − | 0.554973i | 0.136236 | − | 0.990676i | \(-0.456500\pi\) |
−0.900090 | + | 0.435704i | \(0.856500\pi\) | |||||||
\(138\) | 7.92545 | + | 5.75818i | 0.674659 | + | 0.490169i | ||||
\(139\) | 9.92651 | − | 7.21204i | 0.841956 | − | 0.611717i | −0.0809604 | − | 0.996717i | \(-0.525799\pi\) |
0.922916 | + | 0.385000i | \(0.125799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.65876 | + | 1.93170i | 0.223908 | + | 0.162678i | ||||
\(142\) | −1.10851 | − | 3.41164i | −0.0930241 | − | 0.286299i | ||||
\(143\) | 16.8433 | 1.40851 | ||||||||
\(144\) | 2.11124 | + | 6.49774i | 0.175937 | + | 0.541479i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.87961 | − | 27.3286i | 0.734882 | − | 2.26173i | ||||
\(147\) | 1.82854 | − | 5.62767i | 0.150816 | − | 0.464163i | ||||
\(148\) | 5.81030 | − | 4.22143i | 0.477604 | − | 0.346999i | ||||
\(149\) | −4.62832 | −0.379167 | −0.189584 | − | 0.981865i | \(-0.560714\pi\) | ||||
−0.189584 | + | 0.981865i | \(0.560714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.67249 | −0.380242 | −0.190121 | − | 0.981761i | \(-0.560888\pi\) | ||||
−0.190121 | + | 0.981761i | \(0.560888\pi\) | |||||||
\(152\) | 26.9058 | − | 19.5482i | 2.18235 | − | 1.58557i | ||||
\(153\) | −1.57092 | + | 4.83480i | −0.127002 | + | 0.390871i | ||||
\(154\) | 2.42426 | − | 7.46110i | 0.195352 | − | 0.601232i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.77800 | − | 23.9382i | −0.622738 | − | 1.91659i | ||||
\(157\) | −14.9726 | −1.19494 | −0.597472 | − | 0.801890i | \(-0.703828\pi\) | ||||
−0.597472 | + | 0.801890i | \(0.703828\pi\) | |||||||
\(158\) | −1.13477 | − | 3.49247i | −0.0902777 | − | 0.277846i | ||||
\(159\) | 10.2633 | + | 7.45672i | 0.813932 | + | 0.591357i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.24972 | + | 2.36106i | −0.256113 | + | 0.186077i | ||||
\(162\) | −2.05302 | − | 1.49161i | −0.161301 | − | 0.117192i | ||||
\(163\) | 9.63637 | + | 7.00123i | 0.754779 | + | 0.548379i | 0.897304 | − | 0.441412i | \(-0.145522\pi\) |
−0.142526 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(164\) | −4.18557 | + | 3.04099i | −0.326838 | + | 0.237462i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.5597 | + | 17.1171i | 1.82859 | + | 1.32855i | ||||
\(167\) | 3.27809 | + | 10.0889i | 0.253666 | + | 0.780704i | 0.994090 | + | 0.108563i | \(0.0346250\pi\) |
−0.740424 | + | 0.672141i | \(0.765375\pi\) | |||||||
\(168\) | −6.44235 | −0.497038 | ||||||||
\(169\) | 5.91461 | + | 18.2033i | 0.454970 | + | 1.40025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.65990 | + | 5.10866i | −0.126936 | + | 0.390669i | ||||
\(172\) | 7.80103 | − | 24.0091i | 0.594823 | − | 1.83068i | ||||
\(173\) | −1.01401 | + | 0.736719i | −0.0770935 | + | 0.0560117i | −0.625664 | − | 0.780092i | \(-0.715172\pi\) |
0.548571 | + | 0.836104i | \(0.315172\pi\) | |||||||
\(174\) | −1.72485 | −0.130760 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.2983 | 1.53004 | ||||||||
\(177\) | 2.59846 | − | 1.88789i | 0.195312 | − | 0.141902i | ||||
\(178\) | 7.11432 | − | 21.8956i | 0.533241 | − | 1.64115i | ||||
\(179\) | −6.43105 | + | 19.7927i | −0.480679 | + | 1.47938i | 0.357464 | + | 0.933927i | \(0.383642\pi\) |
−0.838143 | + | 0.545451i | \(0.816358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.14058 | − | 6.58803i | −0.159108 | − | 0.489684i | 0.839446 | − | 0.543443i | \(-0.182880\pi\) |
−0.998554 | + | 0.0537591i | \(0.982880\pi\) | |||||||
\(182\) | 14.9698 | 1.10964 | ||||||||
\(183\) | 1.67516 | + | 5.15561i | 0.123831 | + | 0.381113i | ||||
\(184\) | −19.3364 | − | 14.0487i | −1.42550 | − | 1.03569i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.74530 | − | 1.26803i | 0.127971 | − | 0.0929766i | ||||
\(187\) | 12.2189 | + | 8.87759i | 0.893538 | + | 0.649193i | ||||
\(188\) | −11.8043 | − | 8.57633i | −0.860918 | − | 0.625494i | ||||
\(189\) | 0.841811 | − | 0.611611i | 0.0612327 | − | 0.0444882i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.60494 | − | 4.79877i | −0.477916 | − | 0.347227i | 0.322602 | − | 0.946535i | \(-0.395442\pi\) |
−0.800518 | + | 0.599308i | \(0.795442\pi\) | |||||||
\(192\) | 0.336892 | + | 1.03685i | 0.0243131 | + | 0.0748280i | ||||
\(193\) | 13.9629 | 1.00507 | 0.502537 | − | 0.864556i | \(-0.332400\pi\) | ||||
0.502537 | + | 0.864556i | \(0.332400\pi\) | |||||||
\(194\) | −4.72807 | − | 14.5515i | −0.339456 | − | 1.04474i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.11834 | + | 24.9857i | −0.579881 | + | 1.78469i | ||||
\(197\) | −1.78071 | + | 5.48046i | −0.126870 | + | 0.390467i | −0.994237 | − | 0.107203i | \(-0.965811\pi\) |
0.867367 | + | 0.497669i | \(0.165811\pi\) | |||||||
\(198\) | −6.09954 | + | 4.43157i | −0.433475 | + | 0.314938i | ||||
\(199\) | −26.5748 | −1.88384 | −0.941919 | − | 0.335841i | \(-0.890980\pi\) | ||||
−0.941919 | + | 0.335841i | \(0.890980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.929140 | 0.0655365 | ||||||||
\(202\) | 31.4951 | − | 22.8825i | 2.21599 | − | 1.61001i | ||||
\(203\) | 0.218552 | − | 0.672633i | 0.0153393 | − | 0.0472096i | ||||
\(204\) | 6.97456 | − | 21.4655i | 0.488317 | − | 1.50289i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.45644 | − | 29.1039i | −0.658862 | − | 2.02777i | ||||
\(207\) | 3.86039 | 0.268315 | ||||||||
\(208\) | 11.9691 | + | 36.8371i | 0.829909 | + | 2.55420i | ||||
\(209\) | 12.9111 | + | 9.38043i | 0.893076 | + | 0.648858i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4061 | − | 15.5525i | 1.47366 | − | 1.07068i | 0.494125 | − | 0.869391i | \(-0.335488\pi\) |
0.979533 | − | 0.201285i | \(-0.0645116\pi\) | |||||||
\(212\) | −45.5669 | − | 33.1063i | −3.12954 | − | 2.27375i | ||||
\(213\) | −1.14361 | − | 0.830884i | −0.0783591 | − | 0.0569312i | ||||
\(214\) | −13.3403 | + | 9.69227i | −0.911922 | + | 0.662550i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00893 | + | 3.63920i | 0.340815 | + | 0.247616i | ||||
\(217\) | 0.273347 | + | 0.841277i | 0.0185560 | + | 0.0571096i | ||||
\(218\) | −5.86348 | −0.397125 | ||||||||
\(219\) | −3.49912 | − | 10.7692i | −0.236448 | − | 0.727713i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.90591 | + | 27.4096i | −0.599076 | + | 1.84377i | ||||
\(222\) | 1.26852 | − | 3.90410i | 0.0851374 | − | 0.262026i | ||||
\(223\) | −22.2039 | + | 16.1321i | −1.48689 | + | 1.08029i | −0.511631 | + | 0.859205i | \(0.670958\pi\) |
−0.975255 | + | 0.221081i | \(0.929042\pi\) | |||||||
\(224\) | 5.15581 | 0.344487 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.82792 | −0.653744 | ||||||||
\(227\) | 0.105302 | − | 0.0765066i | 0.00698916 | − | 0.00507792i | −0.584285 | − | 0.811548i | \(-0.698625\pi\) |
0.591274 | + | 0.806470i | \(0.298625\pi\) | |||||||
\(228\) | 7.36962 | − | 22.6813i | 0.488065 | − | 1.50211i | ||||
\(229\) | 0.873064 | − | 2.68702i | 0.0576937 | − | 0.177563i | −0.918057 | − | 0.396449i | \(-0.870242\pi\) |
0.975750 | + | 0.218886i | \(0.0702423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.955307 | − | 2.94013i | −0.0628546 | − | 0.193447i | ||||
\(232\) | 4.20826 | 0.276286 | ||||||||
\(233\) | −2.46815 | − | 7.59617i | −0.161694 | − | 0.497642i | 0.837084 | − | 0.547075i | \(-0.184259\pi\) |
−0.998777 | + | 0.0494328i | \(0.984259\pi\) | |||||||
\(234\) | −11.6390 | − | 8.45625i | −0.760867 | − | 0.552802i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.5366 | + | 8.38182i | −0.750968 | + | 0.545610i | ||||
\(237\) | −1.17071 | − | 0.850569i | −0.0760457 | − | 0.0552504i | ||||
\(238\) | 10.8598 | + | 7.89012i | 0.703938 | + | 0.511441i | ||||
\(239\) | 15.4214 | − | 11.2043i | 0.997528 | − | 0.724747i | 0.0359713 | − | 0.999353i | \(-0.488548\pi\) |
0.961557 | + | 0.274606i | \(0.0885475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0864 | − | 12.4140i | −1.10063 | − | 0.799654i | −0.119467 | − | 0.992838i | \(-0.538118\pi\) |
−0.981162 | + | 0.193184i | \(0.938118\pi\) | |||||||
\(242\) | −1.70413 | − | 5.24476i | −0.109545 | − | 0.337146i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.43735 | − | 22.8898i | −0.476127 | − | 1.46537i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.913803 | + | 2.81240i | −0.0582619 | + | 0.179312i | ||||
\(247\) | −9.41036 | + | 28.9621i | −0.598767 | + | 1.84281i | ||||
\(248\) | −4.25815 | + | 3.09373i | −0.270393 | + | 0.196452i | ||||
\(249\) | 11.4756 | 0.727238 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.2224 | 1.90762 | 0.953811 | − | 0.300408i | \(-0.0971228\pi\) | ||||
0.953811 | + | 0.300408i | \(0.0971228\pi\) | |||||||
\(252\) | −3.73746 | + | 2.71542i | −0.235438 | + | 0.171056i | ||||
\(253\) | 3.54419 | − | 10.9079i | 0.222821 | − | 0.685773i | ||||
\(254\) | −9.17007 | + | 28.2226i | −0.575381 | + | 1.77084i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.26692 | − | 28.5207i | −0.579183 | − | 1.78254i | ||||
\(257\) | −5.10215 | −0.318263 | −0.159132 | − | 0.987257i | \(-0.550869\pi\) | ||||
−0.159132 | + | 0.987257i | \(0.550869\pi\) | |||||||
\(258\) | −4.45888 | − | 13.7230i | −0.277598 | − | 0.854358i | ||||
\(259\) | 1.36174 | + | 0.989360i | 0.0846142 | + | 0.0614758i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.549886 | + | 0.399516i | −0.0340371 | + | 0.0247294i | ||||
\(262\) | 16.3464 | + | 11.8763i | 1.00988 | + | 0.733722i | ||||
\(263\) | 5.19017 | + | 3.77088i | 0.320040 | + | 0.232522i | 0.736192 | − | 0.676772i | \(-0.236622\pi\) |
−0.416153 | + | 0.909295i | \(0.636622\pi\) | |||||||
\(264\) | 14.8816 | − | 10.8121i | 0.915898 | − | 0.665439i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.4749 | + | 8.33704i | 0.703574 | + | 0.511177i | ||||
\(267\) | −2.80348 | − | 8.62823i | −0.171570 | − | 0.528039i | ||||
\(268\) | −4.12518 | −0.251986 | ||||||||
\(269\) | −5.39518 | − | 16.6047i | −0.328950 | − | 1.01240i | −0.969626 | − | 0.244592i | \(-0.921346\pi\) |
0.640676 | − | 0.767811i | \(-0.278654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0294140 | + | 0.0905270i | −0.00178677 | + | 0.00549912i | −0.951946 | − | 0.306266i | \(-0.900920\pi\) |
0.950159 | + | 0.311765i | \(0.100920\pi\) | |||||||
\(272\) | −10.7328 | + | 33.0320i | −0.650769 | + | 2.00286i | ||||
\(273\) | 4.77241 | − | 3.46736i | 0.288840 | − | 0.209854i | ||||
\(274\) | 28.0446 | 1.69424 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.1393 | −1.03166 | ||||||||
\(277\) | −14.8865 | + | 10.8157i | −0.894443 | + | 0.649851i | −0.937033 | − | 0.349242i | \(-0.886439\pi\) |
0.0425895 | + | 0.999093i | \(0.486439\pi\) | |||||||
\(278\) | −9.62182 | + | 29.6129i | −0.577078 | + | 1.77606i | ||||
\(279\) | 0.262699 | − | 0.808503i | 0.0157274 | − | 0.0484038i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.54254 | + | 17.0582i | 0.330640 | + | 1.01761i | 0.968830 | + | 0.247727i | \(0.0796837\pi\) |
−0.638189 | + | 0.769879i | \(0.720316\pi\) | |||||||
\(282\) | −8.33982 | −0.496629 | ||||||||
\(283\) | 6.87252 | + | 21.1514i | 0.408529 | + | 1.25732i | 0.917912 | + | 0.396783i | \(0.129874\pi\) |
−0.509383 | + | 0.860540i | \(0.670126\pi\) | |||||||
\(284\) | 5.07740 | + | 3.68895i | 0.301288 | + | 0.218899i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −34.5796 | + | 25.1236i | −2.04474 | + | 1.48559i | ||||
\(287\) | −0.980955 | − | 0.712705i | −0.0579039 | − | 0.0420697i | ||||
\(288\) | −4.00864 | − | 2.91245i | −0.236212 | − | 0.171618i | ||||
\(289\) | −7.15424 | + | 5.19786i | −0.420837 | + | 0.305756i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.87779 | − | 3.54392i | −0.285941 | − | 0.207749i | ||||
\(292\) | 15.5353 | + | 47.8128i | 0.909136 | + | 2.79803i | ||||
\(293\) | 18.7316 | 1.09431 | 0.547155 | − | 0.837031i | \(-0.315711\pi\) | ||||
0.547155 | + | 0.837031i | \(0.315711\pi\) | |||||||
\(294\) | 4.64024 | + | 14.2812i | 0.270624 | + | 0.832896i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.09491 | + | 9.52517i | −0.179888 | + | 0.553639i | ||||
\(297\) | −0.918092 | + | 2.82560i | −0.0532731 | + | 0.163958i | ||||
\(298\) | 9.50204 | − | 6.90364i | 0.550439 | − | 0.399917i | ||||
\(299\) | 21.8854 | 1.26566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.91650 | 0.341021 | ||||||||
\(302\) | 9.59272 | − | 6.96952i | 0.551999 | − | 0.401051i | ||||
\(303\) | 4.74058 | − | 14.5900i | 0.272339 | − | 0.838174i | ||||
\(304\) | −11.3407 | + | 34.9030i | −0.650433 | + | 2.00183i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.98649 | − | 12.2692i | −0.227892 | − | 0.701381i | ||||
\(307\) | 7.03850 | 0.401708 | 0.200854 | − | 0.979621i | \(-0.435628\pi\) | ||||
0.200854 | + | 0.979621i | \(0.435628\pi\) | |||||||
\(308\) | 4.24136 | + | 13.0536i | 0.241674 | + | 0.743796i | ||||
\(309\) | −9.75590 | − | 7.08808i | −0.554994 | − | 0.403227i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6872 | − | 17.2098i | 1.34318 | − | 0.975876i | 0.343858 | − | 0.939022i | \(-0.388266\pi\) |
0.999321 | − | 0.0368546i | \(-0.0117338\pi\) | |||||||
\(312\) | 28.3967 | + | 20.6314i | 1.60765 | + | 1.16803i | ||||
\(313\) | −12.6493 | − | 9.19024i | −0.714980 | − | 0.519463i | 0.169796 | − | 0.985479i | \(-0.445689\pi\) |
−0.884776 | + | 0.466016i | \(0.845689\pi\) | |||||||
\(314\) | 30.7391 | − | 22.3333i | 1.73471 | − | 1.26034i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.19769 | + | 3.77635i | 0.292393 | + | 0.212436i | ||||
\(317\) | 1.92871 | + | 5.93596i | 0.108327 | + | 0.333397i | 0.990497 | − | 0.137535i | \(-0.0439179\pi\) |
−0.882170 | + | 0.470932i | \(0.843918\pi\) | |||||||
\(318\) | −32.1933 | −1.80531 | ||||||||
\(319\) | 0.624024 | + | 1.92055i | 0.0349386 | + | 0.107530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00795 | + | 6.17984i | −0.112073 | + | 0.344925i | ||||
\(322\) | 3.14997 | − | 9.69460i | 0.175541 | − | 0.540259i | ||||
\(323\) | −22.0918 | + | 16.0506i | −1.22922 | + | 0.893080i | ||||
\(324\) | 4.43979 | 0.246655 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.2268 | −1.67411 | ||||||||
\(327\) | −1.86929 | + | 1.35812i | −0.103372 | + | 0.0751042i | ||||
\(328\) | 2.22948 | − | 6.86164i | 0.123103 | − | 0.378871i | ||||
\(329\) | 1.05672 | − | 3.25225i | 0.0582589 | − | 0.179302i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.63073 | + | 20.4073i | 0.364458 | + | 1.12169i | 0.950320 | + | 0.311275i | \(0.100756\pi\) |
−0.585862 | + | 0.810411i | \(0.699244\pi\) | |||||||
\(332\) | −50.9493 | −2.79621 | ||||||||
\(333\) | −0.499875 | − | 1.53846i | −0.0273930 | − | 0.0843068i | ||||
\(334\) | −21.7787 | − | 15.8231i | −1.19168 | − | 0.865804i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.75136 | − | 4.17861i | 0.313763 | − | 0.227962i | ||||
\(337\) | −28.1142 | − | 20.4262i | −1.53148 | − | 1.11269i | −0.955409 | − | 0.295287i | \(-0.904585\pi\) |
−0.576072 | − | 0.817399i | \(-0.695415\pi\) | |||||||
\(338\) | −39.2950 | − | 28.5495i | −2.13736 | − | 1.55289i | ||||
\(339\) | −3.13317 | + | 2.27638i | −0.170170 | + | 0.123636i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.04332 | − | 1.48456i | −0.110652 | − | 0.0803935i | ||||
\(342\) | −4.21229 | − | 12.9641i | −0.227775 | − | 0.701019i | ||||
\(343\) | −13.4409 | −0.725740 | ||||||||
\(344\) | 10.8787 | + | 33.4812i | 0.586541 | + | 1.80519i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.982882 | − | 3.02500i | 0.0528401 | − | 0.162625i | ||||
\(347\) | 8.87623 | − | 27.3182i | 0.476501 | − | 1.46652i | −0.367421 | − | 0.930055i | \(-0.619759\pi\) |
0.843922 | − | 0.536465i | \(-0.180241\pi\) | |||||||
\(348\) | 2.44138 | − | 1.77376i | 0.130871 | − | 0.0950837i | ||||
\(349\) | −12.2834 | −0.657515 | −0.328758 | − | 0.944414i | \(-0.606630\pi\) | ||||
−0.328758 | + | 0.944414i | \(0.606630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.66922 | −0.302601 | ||||||||
\(352\) | −11.9097 | + | 8.65291i | −0.634789 | + | 0.461201i | ||||
\(353\) | −8.33663 | + | 25.6575i | −0.443714 | + | 1.36561i | 0.440174 | + | 0.897913i | \(0.354917\pi\) |
−0.883888 | + | 0.467699i | \(0.845083\pi\) | |||||||
\(354\) | −2.51870 | + | 7.75175i | −0.133867 | + | 0.412001i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.4469 | + | 38.3075i | 0.659682 | + | 2.03029i | ||||
\(357\) | 5.28968 | 0.279960 | ||||||||
\(358\) | −16.3199 | − | 50.2275i | −0.862533 | − | 2.65461i | ||||
\(359\) | −13.2875 | − | 9.65393i | −0.701287 | − | 0.509515i | 0.179064 | − | 0.983837i | \(-0.442693\pi\) |
−0.880351 | + | 0.474322i | \(0.842693\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.97178 | + | 5.79184i | −0.419567 | + | 0.304834i | ||||
\(362\) | 14.2214 | + | 10.3325i | 0.747460 | + | 0.543062i | ||||
\(363\) | −1.75809 | − | 1.27733i | −0.0922758 | − | 0.0670423i | ||||
\(364\) | −21.1885 | + | 15.3943i | −1.11058 | + | 0.806883i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.1293 | − | 8.08589i | −0.581737 | − | 0.422656i | ||||
\(367\) | −9.23816 | − | 28.4321i | −0.482228 | − | 1.48415i | −0.835956 | − | 0.548797i | \(-0.815086\pi\) |
0.353727 | − | 0.935349i | \(-0.384914\pi\) | |||||||
\(368\) | 26.3747 | 1.37487 | ||||||||
\(369\) | 0.360095 | + | 1.10826i | 0.0187458 | + | 0.0576936i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.07914 | − | 12.5543i | 0.211778 | − | 0.651787i | ||||
\(372\) | −1.16633 | + | 3.58958i | −0.0604712 | + | 0.186111i | ||||
\(373\) | 20.0885 | − | 14.5951i | 1.04014 | − | 0.755706i | 0.0698276 | − | 0.997559i | \(-0.477755\pi\) |
0.970313 | + | 0.241853i | \(0.0777551\pi\) | |||||||
\(374\) | −38.3276 | −1.98187 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.3474 | 1.04934 | ||||||||
\(377\) | −3.11742 | + | 2.26494i | −0.160556 | + | 0.116650i | ||||
\(378\) | −0.815972 | + | 2.51130i | −0.0419690 | + | 0.129167i | ||||
\(379\) | 5.99389 | − | 18.4473i | 0.307885 | − | 0.947574i | −0.670699 | − | 0.741729i | \(-0.734006\pi\) |
0.978585 | − | 0.205845i | \(-0.0659941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.61357 | + | 11.1214i | 0.185129 | + | 0.569768i | ||||
\(382\) | 20.7179 | 1.06002 | ||||||||
\(383\) | −3.47670 | − | 10.7002i | −0.177651 | − | 0.546754i | 0.822094 | − | 0.569353i | \(-0.192806\pi\) |
−0.999745 | + | 0.0225986i | \(0.992806\pi\) | |||||||
\(384\) | −10.2555 | − | 7.45106i | −0.523349 | − | 0.380235i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.6662 | + | 20.8272i | −1.45907 | + | 1.06008i | ||||
\(387\) | −4.60008 | − | 3.34215i | −0.233835 | − | 0.169891i | ||||
\(388\) | 21.6564 | + | 15.7343i | 1.09944 | + | 0.798786i | ||||
\(389\) | −12.0558 | + | 8.75903i | −0.611252 | + | 0.444100i | −0.849855 | − | 0.527017i | \(-0.823310\pi\) |
0.238603 | + | 0.971117i | \(0.423310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8767 | + | 11.5351i | 0.802920 | + | 0.583356i | ||||
\(392\) | −11.3212 | − | 34.8431i | −0.571807 | − | 1.75984i | ||||
\(393\) | 7.96210 | 0.401635 | ||||||||
\(394\) | −4.51886 | − | 13.9076i | −0.227657 | − | 0.700656i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.07613 | − | 12.5450i | 0.204833 | − | 0.630412i | ||||
\(397\) | 7.44626 | − | 22.9172i | 0.373717 | − | 1.15018i | −0.570623 | − | 0.821212i | \(-0.693298\pi\) |
0.944340 | − | 0.328971i | \(-0.106702\pi\) | |||||||
\(398\) | 54.5586 | − | 39.6392i | 2.73478 | − | 1.98693i | ||||
\(399\) | 5.58930 | 0.279815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4580 | 0.672059 | 0.336030 | − | 0.941851i | \(-0.390916\pi\) | ||||
0.336030 | + | 0.941851i | \(0.390916\pi\) | |||||||
\(402\) | −1.90754 | + | 1.38591i | −0.0951397 | + | 0.0691230i | ||||
\(403\) | 1.48930 | − | 4.58358i | 0.0741872 | − | 0.228325i | ||||
\(404\) | −21.0472 | + | 64.7765i | −1.04714 | + | 3.22275i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.554613 | + | 1.70692i | 0.0275250 | + | 0.0847132i | ||||
\(407\) | −4.80598 | −0.238224 | ||||||||
\(408\) | 9.72618 | + | 29.9341i | 0.481518 | + | 1.48196i | ||||
\(409\) | 28.6988 | + | 20.8509i | 1.41906 | + | 1.03101i | 0.991925 | + | 0.126825i | \(0.0404788\pi\) |
0.427140 | + | 0.904186i | \(0.359521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.94069 | − | 6.49579i | 0.441012 | − | 0.320414i | ||||
\(412\) | 43.3141 | + | 31.4696i | 2.13393 | + | 1.55039i | ||||
\(413\) | −2.70379 | − | 1.96441i | −0.133045 | − | 0.0966625i | ||||
\(414\) | −7.92545 | + | 5.75818i | −0.389515 | + | 0.282999i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.7259 | − | 16.5113i | −1.11423 | − | 0.809534i | ||||
\(417\) | 3.79159 | + | 11.6693i | 0.185675 | + | 0.571449i | ||||
\(418\) | −40.4986 | −1.98085 | ||||||||
\(419\) | 4.88617 | + | 15.0381i | 0.238705 | + | 0.734659i | 0.996608 | + | 0.0822916i | \(0.0262239\pi\) |
−0.757903 | + | 0.652367i | \(0.773776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.70244 | − | 11.3949i | 0.180446 | − | 0.555355i | −0.819394 | − | 0.573230i | \(-0.805690\pi\) |
0.999840 | + | 0.0178752i | \(0.00569015\pi\) | |||||||
\(422\) | −20.7491 | + | 63.8590i | −1.01005 | + | 3.10861i | ||||
\(423\) | −2.65876 | + | 1.93170i | −0.129273 | + | 0.0939225i | ||||
\(424\) | 78.5447 | 3.81447 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.58721 | 0.173801 | ||||||||
\(427\) | 4.56340 | − | 3.31550i | 0.220838 | − | 0.160448i | ||||
\(428\) | 8.91488 | − | 27.4372i | 0.430917 | − | 1.32623i | ||||
\(429\) | −5.20486 | + | 16.0189i | −0.251293 | + | 0.773401i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.52486 | + | 13.9261i | 0.217955 | + | 0.670797i | 0.998931 | + | 0.0462350i | \(0.0147223\pi\) |
−0.780976 | + | 0.624562i | \(0.785278\pi\) | |||||||
\(432\) | −6.83213 | −0.328711 | ||||||||
\(433\) | −1.32041 | − | 4.06380i | −0.0634547 | − | 0.195294i | 0.914303 | − | 0.405031i | \(-0.132739\pi\) |
−0.977758 | + | 0.209737i | \(0.932739\pi\) | |||||||
\(434\) | −1.81604 | − | 1.31943i | −0.0871728 | − | 0.0633347i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.29926 | − | 6.02976i | 0.397462 | − | 0.288773i | ||||
\(437\) | 16.7760 | + | 12.1885i | 0.802506 | + | 0.583055i | ||||
\(438\) | 23.2471 | + | 16.8900i | 1.11079 | + | 0.807037i | ||||
\(439\) | 16.4289 | − | 11.9363i | 0.784111 | − | 0.569690i | −0.122099 | − | 0.992518i | \(-0.538963\pi\) |
0.906210 | + | 0.422828i | \(0.138963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.78718 | + | 3.47809i | 0.227961 | + | 0.165623i | ||||
\(442\) | −22.6003 | − | 69.5565i | −1.07499 | − | 3.30847i | ||||
\(443\) | −19.0543 | −0.905299 | −0.452649 | − | 0.891689i | \(-0.649521\pi\) | ||||
−0.452649 | + | 0.891689i | \(0.649521\pi\) | |||||||
\(444\) | 2.21934 | + | 6.83041i | 0.105325 | + | 0.324157i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.5224 | − | 66.2391i | 1.01912 | − | 3.13651i | ||||
\(447\) | 1.43023 | − | 4.40180i | 0.0676476 | − | 0.208198i | ||||
\(448\) | 0.917747 | − | 0.666782i | 0.0433595 | − | 0.0315025i | ||||
\(449\) | 29.4793 | 1.39122 | 0.695608 | − | 0.718421i | \(-0.255135\pi\) | ||||
0.695608 | + | 0.718421i | \(0.255135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.46209 | 0.163023 | ||||||||
\(452\) | 13.9106 | − | 10.1066i | 0.654299 | − | 0.475376i | ||||
\(453\) | 1.44388 | − | 4.44380i | 0.0678394 | − | 0.208788i | ||||
\(454\) | −0.102070 | + | 0.314139i | −0.00479038 | + | 0.0147433i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.2771 | + | 31.6296i | 0.481269 | + | 1.48119i | ||||
\(457\) | −28.3015 | −1.32389 | −0.661945 | − | 0.749553i | \(-0.730269\pi\) | ||||
−0.661945 | + | 0.749553i | \(0.730269\pi\) | |||||||
\(458\) | 2.21555 | + | 6.81877i | 0.103526 | + | 0.318620i | ||||
\(459\) | −4.11273 | − | 2.98807i | −0.191966 | − | 0.139471i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3953 | − | 9.73223i | 0.623879 | − | 0.453275i | −0.230395 | − | 0.973097i | \(-0.574002\pi\) |
0.854274 | + | 0.519822i | \(0.174002\pi\) | |||||||
\(462\) | 6.34679 | + | 4.61121i | 0.295279 | + | 0.214533i | ||||
\(463\) | 7.45051 | + | 5.41311i | 0.346254 | + | 0.251569i | 0.747296 | − | 0.664491i | \(-0.231352\pi\) |
−0.401042 | + | 0.916060i | \(0.631352\pi\) | |||||||
\(464\) | −3.75689 | + | 2.72954i | −0.174409 | + | 0.126716i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.3977 | + | 11.9136i | 0.759607 | + | 0.551887i | ||||
\(467\) | −3.27938 | − | 10.0929i | −0.151752 | − | 0.467043i | 0.846066 | − | 0.533079i | \(-0.178965\pi\) |
−0.997817 | + | 0.0660353i | \(0.978965\pi\) | |||||||
\(468\) | 25.1701 | 1.16349 | ||||||||
\(469\) | −0.298759 | − | 0.919485i | −0.0137954 | − | 0.0424579i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.62679 | − | 14.2398i | 0.213191 | − | 0.656135i | ||||
\(472\) | 6.14508 | − | 18.9126i | 0.282850 | − | 0.870524i | ||||
\(473\) | −13.6669 | + | 9.92956i | −0.628403 | + | 0.456562i | ||||
\(474\) | 3.67220 | 0.168670 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −23.4850 | −1.07644 | ||||||||
\(477\) | −10.2633 | + | 7.45672i | −0.469924 | + | 0.341420i | ||||
\(478\) | −14.9480 | + | 46.0054i | −0.683708 | + | 2.10424i | ||||
\(479\) | 10.3849 | − | 31.9613i | 0.474496 | − | 1.46035i | −0.372140 | − | 0.928177i | \(-0.621376\pi\) |
0.846636 | − | 0.532172i | \(-0.178624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.83390 | − | 8.72184i | −0.129215 | − | 0.397682i | ||||
\(482\) | 53.5954 | 2.44120 | ||||||||
\(483\) | −1.24128 | − | 3.82027i | −0.0564802 | − | 0.173828i | ||||
\(484\) | 7.80554 | + | 5.67106i | 0.354797 | + | 0.257775i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.05302 | − | 1.49161i | 0.0931269 | − | 0.0676607i | ||||
\(487\) | 23.6626 | + | 17.1919i | 1.07226 | + | 0.779039i | 0.976316 | − | 0.216348i | \(-0.0694147\pi\) |
0.0959389 | + | 0.995387i | \(0.469415\pi\) | |||||||
\(488\) | 27.1531 | + | 19.7279i | 1.22916 | + | 0.893038i | ||||
\(489\) | −9.63637 | + | 7.00123i | −0.435772 | + | 0.316607i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2898 | − | 8.20251i | −0.509501 | − | 0.370174i | 0.303133 | − | 0.952948i | \(-0.401967\pi\) |
−0.812634 | + | 0.582774i | \(0.801967\pi\) | |||||||
\(492\) | −1.59874 | − | 4.92043i | −0.0720769 | − | 0.221830i | ||||
\(493\) | −3.45531 | −0.155619 | ||||||||
\(494\) | −23.8804 | − | 73.4964i | −1.07443 | − | 3.30676i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.79479 | − | 5.52380i | 0.0805885 | − | 0.248026i | ||||
\(497\) | −0.454528 | + | 1.39889i | −0.0203884 | + | 0.0627490i | ||||
\(498\) | −23.5597 | + | 17.1171i | −1.05573 | + | 0.767036i | ||||
\(499\) | −35.7533 | −1.60054 | −0.800268 | − | 0.599642i | \(-0.795310\pi\) | ||||
−0.800268 | + | 0.599642i | \(0.795310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6081 | −0.473936 | ||||||||
\(502\) | −62.0472 | + | 45.0800i | −2.76930 | + | 2.01202i | ||||
\(503\) | 3.59828 | − | 11.0744i | 0.160439 | − | 0.493782i | −0.838232 | − | 0.545314i | \(-0.816410\pi\) |
0.998671 | + | 0.0515323i | \(0.0164105\pi\) | |||||||
\(504\) | 1.99080 | − | 6.12704i | 0.0886771 | − | 0.272920i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.99399 | + | 27.6807i | 0.399832 | + | 1.23056i | ||||
\(507\) | −19.1401 | −0.850040 | ||||||||
\(508\) | −16.0435 | − | 49.3768i | −0.711815 | − | 2.19074i | ||||
\(509\) | 6.90384 | + | 5.01594i | 0.306007 | + | 0.222327i | 0.730181 | − | 0.683253i | \(-0.239436\pi\) |
−0.424174 | + | 0.905581i | \(0.639436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.53214 | + | 6.92551i | −0.421677 | + | 0.306366i | ||||
\(512\) | 41.0558 | + | 29.8288i | 1.81443 | + | 1.31826i | ||||
\(513\) | −4.34568 | − | 3.15732i | −0.191867 | − | 0.139399i | ||||
\(514\) | 10.4748 | − | 7.61040i | 0.462025 | − | 0.335681i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 20.4234 | + | 14.8384i | 0.899089 | + | 0.653226i | ||||
\(517\) | 3.01722 | + | 9.28605i | 0.132697 | + | 0.408400i | ||||
\(518\) | −4.27141 | −0.187675 | ||||||||
\(519\) | −0.387316 | − | 1.19204i | −0.0170013 | − | 0.0523246i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.390998 | − | 1.20337i | 0.0171299 | − | 0.0527205i | −0.942126 | − | 0.335259i | \(-0.891176\pi\) |
0.959256 | + | 0.282538i | \(0.0911763\pi\) | |||||||
\(522\) | 0.533007 | − | 1.64043i | 0.0233291 | − | 0.0717996i | ||||
\(523\) | 22.0218 | − | 15.9998i | 0.962946 | − | 0.699621i | 0.00911285 | − | 0.999958i | \(-0.497099\pi\) |
0.953833 | + | 0.300337i | \(0.0970993\pi\) | |||||||
\(524\) | −35.3500 | −1.54427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.2802 | −0.709850 | ||||||||
\(527\) | 3.49628 | − | 2.54019i | 0.152300 | − | 0.110653i | ||||
\(528\) | −6.27252 | + | 19.3048i | −0.272976 | + | 0.840135i | ||||
\(529\) | −2.50224 | + | 7.70110i | −0.108793 | + | 0.334831i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.992522 | + | 3.05467i | 0.0430718 | + | 0.132561i | ||||
\(532\) | −24.8153 | −1.07588 | ||||||||
\(533\) | 2.04146 | + | 6.28296i | 0.0884253 | + | 0.272145i | ||||
\(534\) | 18.6255 | + | 13.5322i | 0.806005 | + | 0.585597i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.65400 | − | 3.38133i | 0.201022 | − | 0.146051i | ||||
\(537\) | −16.8367 | − | 12.2326i | −0.726557 | − | 0.527875i | ||||
\(538\) | 35.8440 | + | 26.0422i | 1.54535 | + | 1.12276i | ||||
\(539\) | 14.2228 | − | 10.3334i | 0.612618 | − | 0.445093i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.5804 | − | 17.8587i | −1.05679 | − | 0.767805i | −0.0833007 | − | 0.996524i | \(-0.526546\pi\) |
−0.973492 | + | 0.228719i | \(0.926546\pi\) | |||||||
\(542\) | −0.0746431 | − | 0.229728i | −0.00320620 | − | 0.00986766i | ||||
\(543\) | 6.92706 | 0.297269 | ||||||||
\(544\) | −7.78385 | − | 23.9562i | −0.333730 | − | 1.02711i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.62592 | + | 14.2371i | −0.197971 | + | 0.609293i | ||||
\(547\) | −3.51564 | + | 10.8200i | −0.150318 | + | 0.462631i | −0.997656 | − | 0.0684223i | \(-0.978203\pi\) |
0.847339 | + | 0.531053i | \(0.178203\pi\) | |||||||
\(548\) | −39.6947 | + | 28.8399i | −1.69568 | + | 1.23198i | ||||
\(549\) | −5.42093 | −0.231360 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.65103 | −0.155539 | ||||||||
\(552\) | 19.3364 | − | 14.0487i | 0.823012 | − | 0.597954i | ||||
\(553\) | −0.465297 | + | 1.43204i | −0.0197864 | + | 0.0608964i | ||||
\(554\) | 14.4296 | − | 44.4096i | 0.613053 | − | 1.88678i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8339 | − | 51.8093i | −0.713914 | − | 2.19720i | ||||
\(557\) | 45.7532 | 1.93862 | 0.969312 | − | 0.245833i | \(-0.0790616\pi\) | ||||
0.969312 | + | 0.245833i | \(0.0790616\pi\) | |||||||
\(558\) | 0.666643 | + | 2.05172i | 0.0282213 | + | 0.0868561i | ||||
\(559\) | −26.0789 | − | 18.9474i | −1.10302 | − | 0.801390i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2189 | + | 8.87759i | −0.515884 | + | 0.374812i | ||||
\(562\) | −36.8231 | − | 26.7535i | −1.55329 | − | 1.12853i | ||||
\(563\) | 7.23495 | + | 5.25650i | 0.304917 | + | 0.221535i | 0.729712 | − | 0.683754i | \(-0.239654\pi\) |
−0.424796 | + | 0.905289i | \(0.639654\pi\) | |||||||
\(564\) | 11.8043 | − | 8.57633i | 0.497051 | − | 0.361129i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −45.6591 | − | 33.1733i | −1.91919 | − | 1.39438i | ||||
\(567\) | 0.321543 | + | 0.989608i | 0.0135035 | + | 0.0415596i | ||||
\(568\) | −8.75203 | −0.367227 | ||||||||
\(569\) | −0.707365 | − | 2.17704i | −0.0296543 | − | 0.0912665i | 0.935134 | − | 0.354294i | \(-0.115279\pi\) |
−0.964788 | + | 0.263028i | \(0.915279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.50522 | + | 29.2541i | −0.397781 | + | 1.22424i | 0.528993 | + | 0.848626i | \(0.322570\pi\) |
−0.926774 | + | 0.375618i | \(0.877430\pi\) | |||||||
\(572\) | 23.1085 | − | 71.1206i | 0.966214 | − | 2.97370i | ||||
\(573\) | 6.60494 | − | 4.79877i | 0.275925 | − | 0.200471i | ||||
\(574\) | 3.07700 | 0.128431 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.09021 | −0.0454252 | ||||||||
\(577\) | 5.33326 | − | 3.87484i | 0.222027 | − | 0.161312i | −0.471212 | − | 0.882020i | \(-0.656183\pi\) |
0.693238 | + | 0.720708i | \(0.256183\pi\) | |||||||
\(578\) | 6.93464 | − | 21.3426i | 0.288443 | − | 0.887736i | ||||
\(579\) | −4.31479 | + | 13.2795i | −0.179316 | + | 0.551879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.68991 | − | 11.3564i | −0.153083 | − | 0.471141i | ||||
\(582\) | 15.3004 | 0.634220 | ||||||||
\(583\) | 11.6470 | + | 35.8459i | 0.482371 | + | 1.48458i | ||||
\(584\) | −56.7180 | − | 41.2081i | −2.34701 | − | 1.70520i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.4563 | + | 27.9401i | −1.58861 | + | 1.15420i | ||||
\(587\) | 4.48010 | + | 3.25499i | 0.184914 | + | 0.134348i | 0.676391 | − | 0.736543i | \(-0.263543\pi\) |
−0.491477 | + | 0.870890i | \(0.663543\pi\) | |||||||
\(588\) | −21.2541 | − | 15.4420i | −0.876503 | − | 0.636817i | ||||
\(589\) | 3.69431 | − | 2.68408i | 0.152222 | − | 0.110595i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.66196 | − | 3.38711i | −0.191767 | − | 0.139327i | ||||
\(592\) | −3.41521 | − | 10.5109i | −0.140364 | − | 0.431997i | ||||
\(593\) | −1.88122 | −0.0772524 | −0.0386262 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386262 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(594\) | −2.32982 | − | 7.17044i | −0.0955935 | − | 0.294207i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.34992 | + | 19.5430i | −0.260103 | + | 0.800514i | ||||
\(597\) | 8.21206 | − | 25.2741i | 0.336097 | − | 1.03440i | ||||
\(598\) | −44.9311 | + | 32.6444i | −1.83737 | + | 1.33493i | ||||
\(599\) | 17.8272 | 0.728400 | 0.364200 | − | 0.931321i | \(-0.381342\pi\) | ||||
0.364200 | + | 0.931321i | \(0.381342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.0994 | 1.35015 | 0.675077 | − | 0.737747i | \(-0.264110\pi\) | ||||
0.675077 | + | 0.737747i | \(0.264110\pi\) | |||||||
\(602\) | −12.1467 | + | 8.82509i | −0.495062 | + | 0.359684i | ||||
\(603\) | −0.287120 | + | 0.883665i | −0.0116924 | + | 0.0359856i | ||||
\(604\) | −6.41052 | + | 19.7295i | −0.260840 | + | 0.802784i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0300 | + | 37.0247i | 0.488687 | + | 1.50402i | ||||
\(607\) | −23.4603 | −0.952226 | −0.476113 | − | 0.879384i | \(-0.657955\pi\) | ||||
−0.476113 | + | 0.879384i | \(0.657955\pi\) | |||||||
\(608\) | −8.22475 | − | 25.3132i | −0.333558 | − | 1.02658i | ||||
\(609\) | 0.572176 | + | 0.415710i | 0.0231857 | + | 0.0168454i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0731 | + | 10.9512i | −0.609792 | + | 0.443039i | ||||
\(612\) | 18.2596 | + | 13.2664i | 0.738102 | + | 0.536263i | ||||
\(613\) | −38.2083 | − | 27.7600i | −1.54322 | − | 1.12121i | −0.948277 | − | 0.317445i | \(-0.897175\pi\) |
−0.594942 | − | 0.803769i | \(-0.702825\pi\) | |||||||
\(614\) | −14.4502 | + | 10.4987i | −0.583162 | + | 0.423692i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.4848 | − | 11.2504i | −0.623901 | − | 0.453290i | ||||
\(617\) | 5.02765 | + | 15.4735i | 0.202406 | + | 0.622941i | 0.999810 | + | 0.0194952i | \(0.00620592\pi\) |
−0.797404 | + | 0.603446i | \(0.793794\pi\) | |||||||
\(618\) | 30.6017 | 1.23098 | ||||||||
\(619\) | 10.9577 | + | 33.7244i | 0.440428 | + | 1.35550i | 0.887421 | + | 0.460960i | \(0.152495\pi\) |
−0.446993 | + | 0.894537i | \(0.647505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.19292 | + | 3.67145i | −0.0478704 | + | 0.147330i | ||||
\(622\) | −22.9601 | + | 70.6640i | −0.920617 | + | 2.83337i | ||||
\(623\) | −7.63712 | + | 5.54869i | −0.305975 | + | 0.222304i | ||||
\(624\) | −38.7329 | −1.55056 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.6775 | 1.58583 | ||||||||
\(627\) | −12.9111 | + | 9.38043i | −0.515618 | + | 0.374618i | ||||
\(628\) | −20.5420 | + | 63.2217i | −0.819714 | + | 2.52282i | ||||
\(629\) | 2.54117 | − | 7.82091i | 0.101323 | − | 0.311840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.03453 | − | 27.8054i | −0.359659 | − | 1.10692i | −0.953258 | − | 0.302156i | \(-0.902294\pi\) |
0.593599 | − | 0.804761i | \(-0.297706\pi\) | |||||||
\(632\) | −8.95939 | −0.356385 | ||||||||
\(633\) | 8.17641 | + | 25.1644i | 0.324983 | + | 1.00020i | ||||
\(634\) | −12.8138 | − | 9.30978i | −0.508901 | − | 0.369738i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 45.5669 | − | 33.1063i | 1.80684 | − | 1.31275i | ||||
\(637\) | 27.1396 | + | 19.7181i | 1.07531 | + | 0.781259i | ||||
\(638\) | −4.14583 | − | 3.01213i | −0.164135 | − | 0.119251i | ||||
\(639\) | 1.14361 | − | 0.830884i | 0.0452406 | − | 0.0328692i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7145 | + | 9.23764i | 0.502194 | + | 0.364865i | 0.809854 | − | 0.586631i | \(-0.199546\pi\) |
−0.307661 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(642\) | −5.09553 | − | 15.6824i | −0.201104 | − | 0.618936i | ||||
\(643\) | 8.08055 | 0.318666 | 0.159333 | − | 0.987225i | \(-0.449066\pi\) | ||||
0.159333 | + | 0.987225i | \(0.449066\pi\) | |||||||
\(644\) | 5.51102 | + | 16.9612i | 0.217165 | + | 0.668364i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.4137 | − | 65.9045i | 0.842510 | − | 2.59298i | ||||
\(647\) | −3.40516 | + | 10.4800i | −0.133870 | + | 0.412011i | −0.995413 | − | 0.0956751i | \(-0.969499\pi\) |
0.861542 | + | 0.507686i | \(0.169499\pi\) | |||||||
\(648\) | −5.00893 | + | 3.63920i | −0.196769 | + | 0.142961i | ||||
\(649\) | 9.54248 | 0.374575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.884570 | −0.0346691 | ||||||||
\(652\) | 42.7834 | − | 31.0840i | 1.67553 | − | 1.21734i | ||||
\(653\) | 9.60613 | − | 29.5646i | 0.375917 | − | 1.15695i | −0.566941 | − | 0.823758i | \(-0.691873\pi\) |
0.942858 | − | 0.333195i | \(-0.108127\pi\) | |||||||
\(654\) | 1.81191 | − | 5.57650i | 0.0708515 | − | 0.218058i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.46021 | + | 7.57176i | 0.0960552 | + | 0.295628i | ||||
\(657\) | 11.3234 | 0.441767 | ||||||||
\(658\) | 2.68161 | + | 8.25315i | 0.104540 | + | 0.321741i | ||||
\(659\) | −26.2325 | − | 19.0590i | −1.02187 | − | 0.742435i | −0.0552080 | − | 0.998475i | \(-0.517582\pi\) |
−0.966666 | + | 0.256040i | \(0.917582\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6268 | + | 9.17394i | −0.491128 | + | 0.356825i | −0.805618 | − | 0.592436i | \(-0.798166\pi\) |
0.314490 | + | 0.949261i | \(0.398166\pi\) | |||||||
\(662\) | −44.0527 | − | 32.0061i | −1.71216 | − | 1.24395i | ||||
\(663\) | −23.3160 | − | 16.9400i | −0.905517 | − | 0.657897i | ||||
\(664\) | 57.4806 | − | 41.7621i | 2.23068 | − | 1.62068i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.32102 | + | 2.41287i | 0.128687 | + | 0.0934966i | ||||
\(667\) | 0.810827 | + | 2.49547i | 0.0313953 | + | 0.0966249i | ||||
\(668\) | 47.0978 | 1.82227 | ||||||||
\(669\) | −8.48115 | − | 26.1023i | −0.327900 | − | 1.00917i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97691 | + | 15.3173i | −0.192131 | + | 0.591320i | ||||
\(672\) | −1.59323 | + | 4.90346i | −0.0614602 | + | 0.189155i | ||||
\(673\) | 25.1014 | − | 18.2373i | 0.967589 | − | 0.702995i | 0.0126883 | − | 0.999919i | \(-0.495961\pi\) |
0.954901 | + | 0.296925i | \(0.0959611\pi\) | |||||||
\(674\) | 88.1870 | 3.39684 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 84.9778 | 3.26838 | ||||||||
\(677\) | −18.6796 | + | 13.5716i | −0.717917 | + | 0.521597i | −0.885718 | − | 0.464224i | \(-0.846333\pi\) |
0.167801 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(678\) | 3.03700 | − | 9.34691i | 0.116635 | − | 0.358966i | ||||
\(679\) | −1.93868 | + | 5.96663i | −0.0743995 | + | 0.228978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0402219 | + | 0.123790i | 0.00154131 | + | 0.00474365i | ||||
\(682\) | 6.40936 | 0.245427 | ||||||||
\(683\) | 12.7791 | + | 39.3301i | 0.488979 | + | 1.50492i | 0.826134 | + | 0.563474i | \(0.190536\pi\) |
−0.337154 | + | 0.941449i | \(0.609464\pi\) | |||||||
\(684\) | 19.2939 | + | 14.0178i | 0.737721 | + | 0.535986i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.5944 | − | 20.0485i | 1.05356 | − | 0.765457i | ||||
\(687\) | 2.28571 | + | 1.66067i | 0.0872053 | + | 0.0633584i | ||||
\(688\) | −31.4283 | − | 22.8340i | −1.19819 | − | 0.870539i | ||||
\(689\) | −58.1849 | + | 42.2738i | −2.21667 | + | 1.61050i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.61557 | − | 2.62686i | −0.137543 | − | 0.0999306i | 0.516886 | − | 0.856054i | \(-0.327091\pi\) |
−0.654429 | + | 0.756123i | \(0.727091\pi\) | |||||||
\(692\) | 1.71960 | + | 5.29239i | 0.0653694 | + | 0.201186i | ||||
\(693\) | 3.09144 | 0.117434 | ||||||||
\(694\) | 22.5250 | + | 69.3248i | 0.855037 | + | 2.63153i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.30042 | + | 4.00229i | −0.0492924 | + | 0.151707i | ||||
\(697\) | −1.83058 | + | 5.63395i | −0.0693382 | + | 0.213401i | ||||
\(698\) | 25.2181 | − | 18.3220i | 0.954518 | − | 0.693498i | ||||
\(699\) | 7.98709 | 0.302099 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2265 | −0.952791 | −0.476396 | − | 0.879231i | \(-0.658057\pi\) | ||||
−0.476396 | + | 0.879231i | \(0.658057\pi\) | |||||||
\(702\) | 11.6390 | − | 8.45625i | 0.439287 | − | 0.319161i | ||||
\(703\) | 2.68511 | − | 8.26391i | 0.101271 | − | 0.311679i | ||||
\(704\) | −1.00091 | + | 3.08048i | −0.0377231 | + | 0.116100i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.1556 | − | 65.1104i | −0.796203 | − | 2.45046i | ||||
\(707\) | −15.9627 | −0.600339 | ||||||||
\(708\) | −4.40658 | − | 13.5621i | −0.165610 | − | 0.509694i | ||||
\(709\) | −1.26199 | − | 0.916889i | −0.0473950 | − | 0.0344345i | 0.563836 | − | 0.825887i | \(-0.309325\pi\) |
−0.611231 | + | 0.791453i | \(0.709325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17071 | − | 0.850569i | 0.0439050 | − | 0.0318988i | ||||
\(712\) | −45.4423 | − | 33.0158i | −1.70302 | − | 1.23732i | ||||
\(713\) | −2.65500 | − | 1.92897i | −0.0994304 | − | 0.0722404i | ||||
\(714\) | −10.8598 | + | 7.89012i | −0.406419 | + | 0.295280i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 74.7514 | + | 54.3100i | 2.79359 | + | 2.02966i | ||||
\(717\) | 5.89045 | + | 18.1290i | 0.219983 | + | 0.677038i | ||||
\(718\) | 41.6794 | 1.55546 | ||||||||
\(719\) | 8.94304 | + | 27.5238i | 0.333519 | + | 1.02647i | 0.967447 | + | 0.253074i | \(0.0814416\pi\) |
−0.633928 | + | 0.773392i | \(0.718558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.87748 | + | 11.9336i | −0.144405 | + | 0.444432i | ||||
\(722\) | 7.72709 | − | 23.7815i | 0.287572 | − | 0.885057i | ||||
\(723\) | 17.0864 | − | 12.4140i | 0.635448 | − | 0.461680i | ||||
\(724\) | −30.7547 | −1.14299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.51466 | 0.204668 | ||||||||
\(727\) | 29.9008 | − | 21.7242i | 1.10896 | − | 0.805707i | 0.126461 | − | 0.991972i | \(-0.459638\pi\) |
0.982500 | + | 0.186265i | \(0.0596382\pi\) | |||||||
\(728\) | 11.2863 | − | 34.7355i | 0.418297 | − | 1.28739i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.93229 | − | 27.4907i | −0.330372 | − | 1.01678i | ||||
\(732\) | 24.0678 | 0.889570 | ||||||||
\(733\) | −1.28601 | − | 3.95793i | −0.0474998 | − | 0.146189i | 0.924494 | − | 0.381198i | \(-0.124488\pi\) |
−0.971993 | + | 0.235008i | \(0.924488\pi\) | |||||||
\(734\) | 61.3757 | + | 44.5921i | 2.26542 | + | 1.64592i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.4749 | + | 11.2432i | −0.570413 | + | 0.414429i | ||||
\(737\) | 2.23328 | + | 1.62257i | 0.0822638 | + | 0.0597682i | ||||
\(738\) | −2.39237 | − | 1.73816i | −0.0880642 | − | 0.0639824i | ||||
\(739\) | −15.3371 | + | 11.1431i | −0.564184 | + | 0.409904i | −0.832988 | − | 0.553291i | \(-0.813372\pi\) |
0.268804 | + | 0.963195i | \(0.413372\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6366 | − | 17.8996i | −0.905050 | − | 0.657557i | ||||
\(742\) | 10.3515 | + | 31.8587i | 0.380016 | + | 1.16957i | ||||
\(743\) | −11.7060 | −0.429452 | −0.214726 | − | 0.976674i | \(-0.568886\pi\) | ||||
−0.214726 | + | 0.976674i | \(0.568886\pi\) | |||||||
\(744\) | −1.62647 | − | 5.00575i | −0.0596292 | − | 0.183520i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19.4718 | + | 59.9281i | −0.712915 | + | 2.19413i | ||||
\(747\) | −3.54616 | + | 10.9140i | −0.129747 | + | 0.399321i | ||||
\(748\) | 54.2495 | − | 39.4146i | 1.98356 | − | 1.44114i | ||||
\(749\) | 6.76126 | 0.247051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.95672 | −0.180873 | −0.0904367 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904367 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(752\) | −18.1650 | + | 13.1976i | −0.662408 | + | 0.481268i | ||||
\(753\) | −9.33924 | + | 28.7432i | −0.340341 | + | 1.04746i | ||||
\(754\) | 3.02174 | − | 9.29995i | 0.110045 | − | 0.338684i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.42758 | − | 4.39365i | −0.0519207 | − | 0.159795i | ||||
\(757\) | 18.6020 | 0.676101 | 0.338051 | − | 0.941128i | \(-0.390232\pi\) | ||||
0.338051 | + | 0.941128i | \(0.390232\pi\) | |||||||
\(758\) | 15.2105 | + | 46.8132i | 0.552472 | + | 1.70033i | ||||
\(759\) | 9.27881 | + | 6.74145i | 0.336799 | + | 0.244699i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.18925 | − | 6.67638i | 0.333110 | − | 0.242019i | −0.408639 | − | 0.912696i | \(-0.633997\pi\) |
0.741749 | + | 0.670677i | \(0.233997\pi\) | |||||||
\(762\) | −24.0075 | − | 17.4425i | −0.869702 | − | 0.631875i | ||||
\(763\) | 1.94507 | + | 1.41317i | 0.0704161 | + | 0.0511603i | ||||
\(764\) | −29.3245 | + | 21.3055i | −1.06092 | + | 0.770806i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.0982 | + | 16.7818i | 0.834572 | + | 0.606352i | ||||
\(767\) | 5.62682 | + | 17.3176i | 0.203173 | + | 0.625302i | ||||
\(768\) | 29.9884 | 1.08211 | ||||||||
\(769\) | 2.24803 | + | 6.91872i | 0.0810660 | + | 0.249495i | 0.983373 | − | 0.181599i | \(-0.0581274\pi\) |
−0.902307 | + | 0.431095i | \(0.858127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.57665 | − | 4.85243i | 0.0567817 | − | 0.174756i | ||||
\(772\) | 19.1567 | − | 58.9584i | 0.689466 | − | 2.12196i | ||||
\(773\) | −7.54237 | + | 5.47985i | −0.271280 | + | 0.197097i | −0.715105 | − | 0.699017i | \(-0.753621\pi\) |
0.443825 | + | 0.896114i | \(0.353621\pi\) | |||||||
\(774\) | 14.4292 | 0.518648 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.3296 | −1.34005 | ||||||||
\(777\) | −1.36174 | + | 0.989360i | −0.0488520 | + | 0.0354931i | ||||
\(778\) | 11.6857 | − | 35.9649i | 0.418953 | − | 1.28941i | ||||
\(779\) | −1.93427 | + | 5.95307i | −0.0693024 | + | 0.213291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29780 | − | 3.99421i | −0.0464389 | − | 0.142924i | ||||
\(782\) | −49.8011 | −1.78088 | ||||||||
\(783\) | −0.210038 | − | 0.646430i | −0.00750614 | − | 0.0231015i | ||||
\(784\) | 32.7067 | + | 23.7628i | 1.16810 | + | 0.848671i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.3464 | + | 11.8763i | −0.583055 | + | 0.423615i | ||||
\(787\) | 12.0266 | + | 8.73787i | 0.428704 | + | 0.311471i | 0.781130 | − | 0.624368i | \(-0.214643\pi\) |
−0.352427 | + | 0.935839i | \(0.614643\pi\) | |||||||
\(788\) | 20.6981 | + | 15.0381i | 0.737339 | + | 0.535708i | ||||
\(789\) | −5.19017 | + | 3.77088i | −0.184775 | + | 0.134247i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.26017 | + | 2.36865i | 0.115918 | + | 0.0842196i | ||||
\(792\) | 5.68426 | + | 17.4943i | 0.201981 | + | 0.621634i | ||||
\(793\) | −30.7324 | −1.09134 | ||||||||
\(794\) | 18.8962 | + | 58.1565i | 0.670600 | + | 2.06390i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.4598 | + | 112.212i | −1.29228 | + | 3.97724i | ||||
\(797\) | 2.95898 | − | 9.10680i | 0.104812 | − | 0.322580i | −0.884874 | − | 0.465831i | \(-0.845756\pi\) |
0.989686 | + | 0.143251i | \(0.0457556\pi\) | |||||||
\(798\) | −11.4749 | + | 8.33704i | −0.406209 | + | 0.295128i | ||||
\(799\) | −16.7068 | −0.591044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.07225 | 0.320552 | ||||||||
\(802\) | −27.6295 | + | 20.0740i | −0.975632 | + | 0.708838i | ||||
\(803\) | 10.3959 | − | 31.9953i | 0.366863 | − | 1.12909i | ||||
\(804\) | 1.27475 | − | 3.92328i | 0.0449570 | − | 0.138364i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.77935 | + | 11.6316i | 0.133122 | + | 0.409707i | ||||
\(807\) | 17.4592 | 0.614592 | ||||||||
\(808\) | −29.3508 | − | 90.3323i | −1.03256 | − | 3.17788i | ||||
\(809\) | −33.2859 | − | 24.1836i | −1.17027 | − | 0.850250i | −0.179228 | − | 0.983808i | \(-0.557360\pi\) |
−0.991041 | + | 0.133557i | \(0.957360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1435 | + | 25.5333i | −1.23406 | + | 0.896594i | −0.997187 | − | 0.0749479i | \(-0.976121\pi\) |
−0.236868 | + | 0.971542i | \(0.576121\pi\) | |||||||
\(812\) | −2.54034 | − | 1.84566i | −0.0891484 | − | 0.0647701i | ||||
\(813\) | −0.0770069 | − | 0.0559488i | −0.00270075 | − | 0.00196221i | ||||
\(814\) | 9.86679 | − | 7.16864i | 0.345831 | − | 0.251261i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −28.0987 | − | 20.4149i | −0.983651 | − | 0.714665i | ||||
\(817\) | −9.43823 | − | 29.0479i | −0.330202 | − | 1.01626i | ||||
\(818\) | −90.0206 | −3.14750 | ||||||||
\(819\) | 1.82290 | + | 5.61031i | 0.0636973 | + | 0.196040i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.39595 | − | 16.6070i | 0.188320 | − | 0.579589i | −0.811670 | − | 0.584116i | \(-0.801441\pi\) |
0.999990 | + | 0.00452746i | \(0.00144114\pi\) | |||||||
\(822\) | −8.66625 | + | 26.6720i | −0.302270 | + | 0.930292i | ||||
\(823\) | −1.79970 | + | 1.30756i | −0.0627337 | + | 0.0455787i | −0.618710 | − | 0.785619i | \(-0.712344\pi\) |
0.555976 | + | 0.831198i | \(0.312344\pi\) | |||||||
\(824\) | −74.6616 | −2.60096 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.48106 | 0.295094 | ||||||||
\(827\) | 25.4476 | − | 18.4888i | 0.884900 | − | 0.642918i | −0.0496432 | − | 0.998767i | \(-0.515808\pi\) |
0.934543 | + | 0.355849i | \(0.115808\pi\) | |||||||
\(828\) | 5.29633 | − | 16.3004i | 0.184060 | − | 0.566479i | ||||
\(829\) | 16.4690 | − | 50.6862i | 0.571990 | − | 1.76041i | −0.0742155 | − | 0.997242i | \(-0.523645\pi\) |
0.646206 | − | 0.763163i | \(-0.276355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.68614 | − | 17.5001i | −0.197250 | − | 0.607073i | ||||
\(832\) | −6.18061 | −0.214274 | ||||||||
\(833\) | 9.29560 | + | 28.6089i | 0.322073 | + | 0.991240i | ||||
\(834\) | −25.1903 | − | 18.3018i | −0.872267 | − | 0.633739i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 57.3223 | − | 41.6471i | 1.98253 | − | 1.44040i | ||||
\(837\) | 0.687754 | + | 0.499683i | 0.0237723 | + | 0.0172716i | ||||
\(838\) | −32.4623 | − | 23.5853i | −1.12139 | − | 0.814739i | ||||
\(839\) | 6.77415 | − | 4.92171i | 0.233870 | − | 0.169916i | −0.464678 | − | 0.885480i | \(-0.653830\pi\) |
0.698548 | + | 0.715563i | \(0.253830\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0877 | + | 16.7742i | 0.796129 | + | 0.578421i | ||||
\(842\) | 9.39558 | + | 28.9166i | 0.323793 | + | 0.996532i | ||||
\(843\) | −17.9361 | −0.617750 | ||||||||
\(844\) | −36.3015 | − | 111.725i | −1.24955 | − | 3.84572i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.57715 | − | 7.93164i | 0.0886041 | − | 0.272695i | ||||
\(847\) | −0.698751 | + | 2.15054i | −0.0240094 | + | 0.0738933i | ||||
\(848\) | −70.1202 | + | 50.9453i | −2.40794 | + | 1.74947i | ||||
\(849\) | −22.2399 | −0.763273 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.24467 | −0.214064 | ||||||||
\(852\) | −5.07740 | + | 3.68895i | −0.173949 | + | 0.126381i | ||||
\(853\) | 0.378146 | − | 1.16381i | 0.0129475 | − | 0.0398482i | −0.944374 | − | 0.328873i | \(-0.893331\pi\) |
0.957322 | + | 0.289025i | \(0.0933311\pi\) | |||||||
\(854\) | −4.42332 | + | 13.6136i | −0.151363 | + | 0.465847i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4320 | + | 38.2618i | 0.424917 | + | 1.30776i | ||||
\(857\) | 14.3684 | 0.490816 | 0.245408 | − | 0.969420i | \(-0.421078\pi\) | ||||
0.245408 | + | 0.969420i | \(0.421078\pi\) | |||||||
\(858\) | −13.2082 | − | 40.6508i | −0.450922 | − | 1.38780i | ||||
\(859\) | 8.34015 | + | 6.05947i | 0.284562 | + | 0.206747i | 0.720905 | − | 0.693034i | \(-0.243726\pi\) |
−0.436343 | + | 0.899781i | \(0.643726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.980955 | − | 0.712705i | 0.0334308 | − | 0.0242889i | ||||
\(862\) | −30.0619 | − | 21.8413i | −1.02391 | − | 0.743916i | ||||
\(863\) | 24.4909 | + | 17.7937i | 0.833679 | + | 0.605703i | 0.920598 | − | 0.390512i | \(-0.127702\pi\) |
−0.0869190 | + | 0.996215i | \(0.527702\pi\) | |||||||
\(864\) | 4.00864 | − | 2.91245i | 0.136377 | − | 0.0990835i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.77241 | + | 6.37353i | 0.298099 | + | 0.216581i | ||||
\(867\) | −2.73268 | − | 8.41031i | −0.0928065 | − | 0.285629i | ||||
\(868\) | 3.92730 | 0.133301 | ||||||||
\(869\) | −1.32855 | − | 4.08885i | −0.0450679 | − | 0.138705i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.62775 | + | 5.00969i | −0.0551541 | + | 0.169747i | ||||
\(872\) | −4.42068 | + | 13.6055i | −0.149703 | + | 0.460739i | ||||
\(873\) | 4.87779 | − | 3.54392i | 0.165088 | − | 0.119944i | ||||
\(874\) | −52.6220 | −1.77996 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.2734 | −1.69858 | ||||||||
\(877\) | 24.7839 | − | 18.0065i | 0.836892 | − | 0.608037i | −0.0846091 | − | 0.996414i | \(-0.526964\pi\) |
0.921501 | + | 0.388377i | \(0.126964\pi\) | |||||||
\(878\) | −15.9247 | + | 49.0111i | −0.537431 | + | 1.65404i | ||||
\(879\) | −5.78837 | + | 17.8148i | −0.195237 | + | 0.600877i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.70359 | + | 14.4762i | 0.158468 | + | 0.487714i | 0.998496 | − | 0.0548293i | \(-0.0174615\pi\) |
−0.840028 | + | 0.542543i | \(0.817461\pi\) | |||||||
\(882\) | −15.0161 | −0.505620 | ||||||||
\(883\) | −12.4220 | − | 38.2310i | −0.418034 | − | 1.28658i | −0.909509 | − | 0.415684i | \(-0.863542\pi\) |
0.491475 | − | 0.870892i | \(-0.336458\pi\) | |||||||
\(884\) | 103.518 | + | 75.2102i | 3.48169 | + | 2.52959i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1189 | − | 28.4216i | 1.31423 | − | 0.954842i | ||||
\(887\) | −25.7617 | − | 18.7169i | −0.864992 | − | 0.628453i | 0.0642465 | − | 0.997934i | \(-0.479536\pi\) |
−0.929238 | + | 0.369481i | \(0.879536\pi\) | |||||||
\(888\) | −8.10259 | − | 5.88688i | −0.271905 | − | 0.197551i | ||||
\(889\) | 9.84394 | − | 7.15204i | 0.330155 | − | 0.239872i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.40360 | − | 1.74631i | −0.0805235 | − | 0.0585037i | ||||
\(892\) | 37.6545 | + | 115.889i | 1.26077 | + | 3.88024i | ||||
\(893\) | −17.6531 | −0.590739 | ||||||||
\(894\) | 3.62946 | + | 11.1703i | 0.121387 | + | 0.373591i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.07604 | + | 12.5448i | −0.136171 | + | 0.419091i | ||||
\(897\) | −6.76296 | + | 20.8142i | −0.225809 | + | 0.694967i | ||||
\(898\) | −60.5217 | + | 43.9716i | −2.01964 | + | 1.46735i | ||||
\(899\) | 0.577817 | 0.0192713 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.4914 | −2.14852 | ||||||||
\(902\) | −7.10774 | + | 5.16407i | −0.236662 | + | 0.171945i | ||||
\(903\) | −1.82830 | + | 5.62692i | −0.0608419 | + | 0.187252i | ||||
\(904\) | −7.40962 | + | 22.8045i | −0.246440 | + | 0.758465i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.66409 | + | 11.2769i | 0.121731 | + | 0.374651i | ||||
\(907\) | 28.8507 | 0.957970 | 0.478985 | − | 0.877823i | \(-0.341005\pi\) | ||||
0.478985 | + | 0.877823i | \(0.341005\pi\) | |||||||
\(908\) | −0.178577 | − | 0.549602i | −0.00592627 | − | 0.0182392i | ||||
\(909\) | 12.4110 | + | 9.01712i | 0.411647 | + | 0.299079i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1370 | + | 28.4347i | −1.29667 | + | 0.942084i | −0.999917 | − | 0.0128711i | \(-0.995903\pi\) |
−0.296750 | + | 0.954955i | \(0.595903\pi\) | |||||||
\(912\) | −29.6903 | − | 21.5713i | −0.983143 | − | 0.714296i | ||||
\(913\) | 27.5827 | + | 20.0400i | 0.912855 | + | 0.663228i | ||||
\(914\) | 58.1036 | − | 42.2148i | 1.92190 | − | 1.39634i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.1481 | − | 7.37301i | −0.335302 | − | 0.243611i | ||||
\(917\) | −2.56016 | − | 7.87936i | −0.0845439 | − | 0.260199i | ||||
\(918\) | 12.9006 | 0.425782 | ||||||||
\(919\) | −2.58963 | − | 7.97006i | −0.0854240 | − | 0.262908i | 0.899216 | − | 0.437505i | \(-0.144138\pi\) |
−0.984640 | + | 0.174597i | \(0.944138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.17501 | + | 6.69401i | −0.0716692 | + | 0.220575i | ||||
\(922\) | −12.9841 | + | 39.9609i | −0.427608 | + | 1.31604i | ||||
\(923\) | 6.48340 | − | 4.71046i | 0.213404 | − | 0.155047i | ||||
\(924\) | −13.7253 | −0.451530 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.3703 | −0.767995 | ||||||||
\(927\) | 9.75590 | − | 7.08808i | 0.320426 | − | 0.232803i | ||||
\(928\) | 1.04073 | − | 3.20303i | 0.0341636 | − | 0.105145i | ||||
\(929\) | 4.42283 | − | 13.6121i | 0.145108 | − | 0.446597i | −0.851917 | − | 0.523677i | \(-0.824560\pi\) |
0.997025 | + | 0.0770801i | \(0.0245597\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.82212 | + | 30.2294i | 0.321907 | + | 0.990728i | ||||
\(932\) | −35.4610 | −1.16156 | ||||||||
\(933\) | 9.04771 | + | 27.8460i | 0.296209 | + | 0.911637i | ||||
\(934\) | 21.7873 | + | 15.8294i | 0.712901 | + | 0.517953i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28.3967 | + | 20.6314i | −0.928177 | + | 0.674360i | ||||
\(937\) | −17.7372 | − | 12.8869i | −0.579451 | − | 0.420996i | 0.259075 | − | 0.965857i | \(-0.416582\pi\) |
−0.838526 | + | 0.544862i | \(0.816582\pi\) | |||||||
\(938\) | 1.98487 | + | 1.44209i | 0.0648082 | + | 0.0470859i | ||||
\(939\) | 12.6493 | − | 9.19024i | 0.412794 | − | 0.299912i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.1167 | − | 13.1625i | −0.590586 | − | 0.429086i | 0.251939 | − | 0.967743i | \(-0.418932\pi\) |
−0.842525 | + | 0.538657i | \(0.818932\pi\) | |||||||
\(942\) | 11.7413 | + | 36.1360i | 0.382552 | + | 1.17737i | ||||
\(943\) | 4.49847 | 0.146490 | ||||||||
\(944\) | 6.78104 | + | 20.8699i | 0.220704 | + | 0.679257i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.2474 | − | 40.7712i | 0.430709 | − | 1.32559i | ||||
\(947\) | −13.4619 | + | 41.4316i | −0.437454 | + | 1.34635i | 0.453096 | + | 0.891462i | \(0.350319\pi\) |
−0.890550 | + | 0.454884i | \(0.849681\pi\) | |||||||
\(948\) | −5.19769 | + | 3.77635i | −0.168813 | + | 0.122650i | ||||
\(949\) | 64.1947 | 2.08385 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.24144 | −0.202393 | ||||||||
\(952\) | 26.4957 | − | 19.2502i | 0.858729 | − | 0.623903i | ||||
\(953\) | −0.732893 | + | 2.25561i | −0.0237407 | + | 0.0730664i | −0.962225 | − | 0.272256i | \(-0.912230\pi\) |
0.938484 | + | 0.345322i | \(0.112230\pi\) | |||||||
\(954\) | 9.94827 | − | 30.6176i | 0.322087 | − | 0.991282i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.1524 | − | 80.4887i | −0.845828 | − | 2.60319i | ||||
\(957\) | −2.01938 | −0.0652774 | ||||||||
\(958\) | 26.3534 | + | 81.1073i | 0.851439 | + | 2.62046i | ||||
\(959\) | −9.30310 | − | 6.75910i | −0.300413 | − | 0.218263i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4949 | − | 17.7966i | 0.790157 | − | 0.574082i | ||||
\(962\) | 18.8276 | + | 13.6791i | 0.607027 | + | 0.441031i | ||||
\(963\) | −5.25689 | − | 3.81935i | −0.169401 | − | 0.123077i | ||||
\(964\) | −75.8598 | + | 55.1154i | −2.44328 | + | 1.77515i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.24672 | + | 5.99159i | 0.265334 | + | 0.192776i | ||||
\(967\) | 6.11413 | + | 18.8174i | 0.196617 | + | 0.605125i | 0.999954 | + | 0.00960036i | \(0.00305594\pi\) |
−0.803337 | + | 0.595525i | \(0.796944\pi\) | |||||||
\(968\) | −13.4546 | −0.432447 | ||||||||
\(969\) | −8.43831 | − | 25.9704i | −0.271077 | − | 0.834291i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.2604 | − | 46.9668i | 0.489731 | − | 1.50724i | −0.335279 | − | 0.942119i | \(-0.608831\pi\) |
0.825010 | − | 0.565118i | \(-0.191169\pi\) | |||||||
\(972\) | −1.37197 | + | 4.22249i | −0.0440059 | + | 0.135436i | ||||
\(973\) | 10.3289 | − | 7.50438i | 0.331129 | − | 0.240579i | ||||
\(974\) | −74.2234 | −2.37827 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.0365 | −1.18551 | ||||||||
\(977\) | −38.6429 | + | 28.0757i | −1.23630 | + | 0.898221i | −0.997346 | − | 0.0728110i | \(-0.976803\pi\) |
−0.238949 | + | 0.971032i | \(0.576803\pi\) | |||||||
\(978\) | 9.34058 | − | 28.7474i | 0.298679 | − | 0.919239i | ||||
\(979\) | 8.32916 | − | 25.6345i | 0.266201 | − | 0.819283i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.714006 | − | 2.19749i | −0.0227965 | − | 0.0701603i | ||||
\(982\) | 35.4131 | 1.13008 | ||||||||
\(983\) | −16.0467 | − | 49.3867i | −0.511810 | − | 1.57519i | −0.789011 | − | 0.614379i | \(-0.789407\pi\) |
0.277201 | − | 0.960812i | \(-0.410593\pi\) | |||||||
\(984\) | 5.83686 | + | 4.24073i | 0.186072 | + | 0.135190i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.09383 | − | 5.15397i | 0.225914 | − | 0.164136i | ||||
\(987\) | 2.76653 | + | 2.01000i | 0.0880596 | + | 0.0639791i | ||||
\(988\) | 109.381 | + | 79.4703i | 3.47989 | + | 2.52829i | ||||
\(989\) | −17.7581 | + | 12.9020i | −0.564674 | + | 0.410260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.2509 | + | 9.62734i | 0.420929 | + | 0.305823i | 0.778011 | − | 0.628250i | \(-0.216229\pi\) |
−0.357083 | + | 0.934073i | \(0.616229\pi\) | |||||||
\(992\) | 1.30166 | + | 4.00610i | 0.0413277 | + | 0.127194i | ||||
\(993\) | −21.4575 | −0.680933 | ||||||||
\(994\) | −1.15344 | − | 3.54994i | −0.0365850 | − | 0.112597i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.7442 | − | 48.4557i | 0.498874 | − | 1.53538i | ||||
\(997\) | 6.87610 | − | 21.1625i | 0.217768 | − | 0.670222i | −0.781177 | − | 0.624309i | \(-0.785380\pi\) |
0.998945 | − | 0.0459126i | \(-0.0146196\pi\) | |||||||
\(998\) | 73.4022 | − | 53.3299i | 2.32351 | − | 1.68813i | ||||
\(999\) | 1.61763 | 0.0511795 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 375.2.g.d.301.1 | 16 | ||
5.2 | odd | 4 | 375.2.i.c.199.1 | 16 | |||
5.3 | odd | 4 | 75.2.i.a.64.4 | yes | 16 | ||
5.4 | even | 2 | 375.2.g.e.301.4 | 16 | |||
15.8 | even | 4 | 225.2.m.b.64.1 | 16 | |||
25.3 | odd | 20 | 1875.2.b.h.1249.1 | 16 | |||
25.4 | even | 10 | 1875.2.a.m.1.1 | 8 | |||
25.9 | even | 10 | 375.2.g.e.76.4 | 16 | |||
25.12 | odd | 20 | 75.2.i.a.34.4 | ✓ | 16 | ||
25.13 | odd | 20 | 375.2.i.c.49.1 | 16 | |||
25.16 | even | 5 | inner | 375.2.g.d.76.1 | 16 | ||
25.21 | even | 5 | 1875.2.a.p.1.8 | 8 | |||
25.22 | odd | 20 | 1875.2.b.h.1249.16 | 16 | |||
75.29 | odd | 10 | 5625.2.a.bd.1.8 | 8 | |||
75.62 | even | 20 | 225.2.m.b.109.1 | 16 | |||
75.71 | odd | 10 | 5625.2.a.t.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.4 | ✓ | 16 | 25.12 | odd | 20 | ||
75.2.i.a.64.4 | yes | 16 | 5.3 | odd | 4 | ||
225.2.m.b.64.1 | 16 | 15.8 | even | 4 | |||
225.2.m.b.109.1 | 16 | 75.62 | even | 20 | |||
375.2.g.d.76.1 | 16 | 25.16 | even | 5 | inner | ||
375.2.g.d.301.1 | 16 | 1.1 | even | 1 | trivial | ||
375.2.g.e.76.4 | 16 | 25.9 | even | 10 | |||
375.2.g.e.301.4 | 16 | 5.4 | even | 2 | |||
375.2.i.c.49.1 | 16 | 25.13 | odd | 20 | |||
375.2.i.c.199.1 | 16 | 5.2 | odd | 4 | |||
1875.2.a.m.1.1 | 8 | 25.4 | even | 10 | |||
1875.2.a.p.1.8 | 8 | 25.21 | even | 5 | |||
1875.2.b.h.1249.1 | 16 | 25.3 | odd | 20 | |||
1875.2.b.h.1249.16 | 16 | 25.22 | odd | 20 | |||
5625.2.a.t.1.1 | 8 | 75.71 | odd | 10 | |||
5625.2.a.bd.1.8 | 8 | 75.29 | odd | 10 |