Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
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, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), 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 \(\Q(\zeta_{10})\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-2.53767i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.199 |
Dual form | 375.2.i.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.49161 | − | 2.05302i | −1.05473 | − | 1.45171i | −0.884639 | − | 0.466276i | \(-0.845595\pi\) |
−0.170086 | − | 0.985429i | \(-0.554405\pi\) | |||||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | −1.37197 | + | 4.22249i | −0.685985 | + | 2.11124i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.784184 | − | 2.41347i | −0.320142 | − | 0.985295i | ||||
\(7\) | 1.04054i | 0.393285i | 0.980475 | + | 0.196643i | \(0.0630039\pi\) | ||||
−0.980475 | + | 0.196643i | \(0.936996\pi\) | |||||||
\(8\) | 5.88835 | − | 1.91324i | 2.08185 | − | 0.676433i | ||||
\(9\) | 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 | \(0.447827\pi\) | |||||||
\(12\) | −2.60964 | + | 3.59186i | −0.753338 | + | 1.03688i | ||||
\(13\) | −3.33228 | + | 4.58650i | −0.924209 | + | 1.27207i | 0.0378663 | + | 0.999283i | \(0.487944\pi\) |
−0.962076 | + | 0.272782i | \(0.912056\pi\) | |||||||
\(14\) | 2.13624 | − | 1.55207i | 0.570934 | − | 0.414808i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.52731 | − | 4.01583i | −1.38183 | − | 1.00396i | ||||
\(17\) | 4.83480 | − | 1.57092i | 1.17261 | − | 0.381005i | 0.342995 | − | 0.939337i | \(-0.388559\pi\) |
0.829617 | + | 0.558333i | \(0.188559\pi\) | |||||||
\(18\) | − | 2.53767i | − | 0.598135i | ||||||
\(19\) | 1.65990 | + | 5.10866i | 0.380808 | + | 1.17201i | 0.939476 | + | 0.342615i | \(0.111313\pi\) |
−0.558668 | + | 0.829391i | \(0.688687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.321543 | + | 0.989608i | −0.0701665 | + | 0.215950i | ||||
\(22\) | 7.17044 | + | 2.32982i | 1.52874 | + | 0.496719i | ||||
\(23\) | 2.26908 | + | 3.12312i | 0.473135 | + | 0.651215i | 0.977168 | − | 0.212470i | \(-0.0681507\pi\) |
−0.504032 | + | 0.863685i | \(0.668151\pi\) | |||||||
\(24\) | 6.19138 | 1.26381 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.3866 | 2.82145 | ||||||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | −4.39365 | − | 1.42758i | −0.830322 | − | 0.269788i | ||||
\(29\) | −0.210038 | + | 0.646430i | −0.0390030 | + | 0.120039i | −0.968662 | − | 0.248382i | \(-0.920101\pi\) |
0.929659 | + | 0.368421i | \(0.120101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.262699 | + | 0.808503i | 0.0471821 | + | 0.145212i | 0.971872 | − | 0.235509i | \(-0.0756759\pi\) |
−0.924690 | + | 0.380721i | \(0.875676\pi\) | |||||||
\(32\) | 4.95495i | 0.875921i | ||||||||
\(33\) | −2.82560 | + | 0.918092i | −0.491873 | + | 0.159819i | ||||
\(34\) | −10.4368 | − | 7.58275i | −1.78989 | − | 1.30043i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.59186 | + | 2.60964i | −0.598644 | + | 0.434940i | ||||
\(37\) | −0.950818 | + | 1.30869i | −0.156313 | + | 0.215147i | −0.879990 | − | 0.474992i | \(-0.842451\pi\) |
0.723676 | + | 0.690139i | \(0.242451\pi\) | |||||||
\(38\) | 8.01226 | − | 11.0279i | 1.29976 | − | 1.78897i | ||||
\(39\) | −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 | \(0.729004\pi\) | |||||||
\(42\) | 2.51130 | − | 0.815972i | 0.387502 | − | 0.125907i | ||||
\(43\) | − | 5.68601i | − | 0.867109i | −0.901127 | − | 0.433554i | \(-0.857259\pi\) | ||
0.901127 | − | 0.433554i | \(-0.142741\pi\) | |||||||
\(44\) | −4.07613 | − | 12.5450i | −0.614500 | − | 1.89124i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.02725 | − | 9.31693i | 0.446344 | − | 1.37371i | ||||
\(47\) | 3.12556 | + | 1.01555i | 0.455909 | + | 0.148134i | 0.527964 | − | 0.849267i | \(-0.322956\pi\) |
−0.0720547 | + | 0.997401i | \(0.522956\pi\) | |||||||
\(48\) | −4.01583 | − | 5.52731i | −0.579635 | − | 0.797798i | ||||
\(49\) | 5.91729 | 0.845327 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.08361 | 0.711848 | ||||||||
\(52\) | −14.7946 | − | 20.3631i | −2.05165 | − | 2.82385i | ||||
\(53\) | −12.0652 | − | 3.92023i | −1.65729 | − | 0.538485i | −0.676986 | − | 0.735996i | \(-0.736714\pi\) |
−0.980301 | + | 0.197511i | \(0.936714\pi\) | |||||||
\(54\) | 0.784184 | − | 2.41347i | 0.106714 | − | 0.328432i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.99080 | + | 6.12704i | 0.266031 | + | 0.818760i | ||||
\(57\) | 5.37156i | 0.711481i | ||||||||
\(58\) | 1.64043 | − | 0.533007i | 0.215399 | − | 0.0699873i | ||||
\(59\) | 2.59846 | + | 1.88789i | 0.338290 | + | 0.245782i | 0.743940 | − | 0.668246i | \(-0.232955\pi\) |
−0.405650 | + | 0.914029i | \(0.632955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.38562 | − | 3.18634i | 0.561521 | − | 0.407969i | −0.270494 | − | 0.962722i | \(-0.587187\pi\) |
0.832015 | + | 0.554753i | \(0.187187\pi\) | |||||||
\(62\) | 1.26803 | − | 1.74530i | 0.161040 | − | 0.221653i | ||||
\(63\) | −0.611611 | + | 0.841811i | −0.0770558 | + | 0.106058i | ||||
\(64\) | −0.881995 | + | 0.640807i | −0.110249 | + | 0.0801008i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.09954 | + | 4.43157i | 0.750801 | + | 0.545489i | ||||
\(67\) | 0.883665 | − | 0.287120i | 0.107957 | − | 0.0350773i | −0.254540 | − | 0.967062i | \(-0.581924\pi\) |
0.362497 | + | 0.931985i | \(0.381924\pi\) | |||||||
\(68\) | 22.5702i | 2.73703i | ||||||||
\(69\) | 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 | \(0.126731\pi\) | |||||||
\(72\) | 5.88835 | + | 1.91324i | 0.693949 | + | 0.225478i | ||||
\(73\) | 6.65571 | + | 9.16080i | 0.778992 | + | 1.07219i | 0.995392 | + | 0.0958862i | \(0.0305685\pi\) |
−0.216400 | + | 0.976305i | \(0.569432\pi\) | |||||||
\(74\) | 4.10501 | 0.477198 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.8486 | −2.73562 | ||||||||
\(77\) | −1.81710 | − | 2.50103i | −0.207078 | − | 0.285018i | ||||
\(78\) | 13.6825 | + | 4.44571i | 1.54924 | + | 0.503378i | ||||
\(79\) | 0.447171 | − | 1.37625i | 0.0503106 | − | 0.154840i | −0.922745 | − | 0.385412i | \(-0.874059\pi\) |
0.973055 | + | 0.230571i | \(0.0740595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 2.95713i | 0.326560i | ||||||||
\(83\) | −10.9140 | + | 3.54616i | −1.19796 | + | 0.389242i | −0.839011 | − | 0.544114i | \(-0.816866\pi\) |
−0.358952 | + | 0.933356i | \(0.616866\pi\) | |||||||
\(84\) | −3.73746 | − | 2.71542i | −0.407790 | − | 0.296277i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.6735 | + | 8.48129i | −1.25879 | + | 0.914561i | ||||
\(87\) | −0.399516 | + | 0.549886i | −0.0428326 | + | 0.0589540i | ||||
\(88\) | −10.8121 | + | 14.8816i | −1.15257 | + | 1.58638i | ||||
\(89\) | 7.33961 | − | 5.33254i | 0.777997 | − | 0.565248i | −0.126380 | − | 0.991982i | \(-0.540336\pi\) |
0.904377 | + | 0.426734i | \(0.140336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.77241 | − | 3.46736i | −0.500285 | − | 0.363478i | ||||
\(92\) | −16.3004 | + | 5.29633i | −1.69944 | + | 0.552181i | ||||
\(93\) | 0.850111i | 0.0881524i | ||||||||
\(94\) | −2.57715 | − | 7.93164i | −0.265812 | − | 0.818086i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.53117 | + | 4.71244i | −0.156274 | + | 0.480962i | ||||
\(97\) | −5.73419 | − | 1.86315i | −0.582219 | − | 0.189174i | 0.00307549 | − | 0.999995i | \(-0.499021\pi\) |
−0.585294 | + | 0.810821i | \(0.699021\pi\) | |||||||
\(98\) | −8.82627 | − | 12.1483i | −0.891587 | − | 1.22716i | ||||
\(99\) | −2.97101 | −0.298597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.3408 | −1.52647 | −0.763236 | − | 0.646120i | \(-0.776390\pi\) | ||||
−0.763236 | + | 0.646120i | \(0.776390\pi\) | |||||||
\(102\) | −7.58275 | − | 10.4368i | −0.750804 | − | 1.03339i | ||||
\(103\) | 11.4688 | + | 3.72642i | 1.13005 | + | 0.367175i | 0.813595 | − | 0.581432i | \(-0.197507\pi\) |
0.316455 | + | 0.948608i | \(0.397507\pi\) | |||||||
\(104\) | −10.8466 | + | 33.3824i | −1.06360 | + | 3.27341i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.94827 | + | 30.6176i | 0.966261 | + | 2.97385i | ||||
\(107\) | 6.49787i | 0.628173i | 0.949394 | + | 0.314086i | \(0.101698\pi\) | ||||
−0.949394 | + | 0.314086i | \(0.898302\pi\) | |||||||
\(108\) | −4.22249 | + | 1.37197i | −0.406309 | + | 0.132018i | ||||
\(109\) | −1.86929 | − | 1.35812i | −0.179046 | − | 0.130084i | 0.494653 | − | 0.869091i | \(-0.335295\pi\) |
−0.673698 | + | 0.739006i | \(0.735295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30869 | + | 0.950818i | −0.124215 | + | 0.0902476i | ||||
\(112\) | 4.17861 | − | 5.75136i | 0.394841 | − | 0.543453i | ||||
\(113\) | 2.27638 | − | 3.13317i | 0.214144 | − | 0.294744i | −0.688409 | − | 0.725323i | \(-0.741691\pi\) |
0.902553 | + | 0.430579i | \(0.141691\pi\) | |||||||
\(114\) | 11.0279 | − | 8.01226i | 1.03286 | − | 0.750417i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.44138 | − | 1.77376i | −0.226676 | − | 0.164690i | ||||
\(117\) | −5.39175 | + | 1.75189i | −0.498467 | + | 0.161962i | ||||
\(118\) | − | 8.15067i | − | 0.750330i | ||||||
\(119\) | 1.63460 | + | 5.03078i | 0.149844 | + | 0.461171i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.671530 | + | 2.06676i | −0.0610482 | + | 0.187887i | ||||
\(122\) | −13.0832 | − | 4.25101i | −1.18450 | − | 0.384868i | ||||
\(123\) | −0.684941 | − | 0.942740i | −0.0617590 | − | 0.0850040i | ||||
\(124\) | −3.77431 | −0.338943 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.64054 | 0.235238 | ||||||||
\(127\) | 6.87342 | + | 9.46046i | 0.609918 | + | 0.839480i | 0.996571 | − | 0.0827456i | \(-0.0263689\pi\) |
−0.386653 | + | 0.922225i | \(0.626369\pi\) | |||||||
\(128\) | 12.0561 | + | 3.91725i | 1.06562 | + | 0.346239i | ||||
\(129\) | 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 | \(-0.213080\pi\) | |||||||
\(132\) | − | 13.1906i | − | 1.14810i | ||||||
\(133\) | −5.31574 | + | 1.72719i | −0.460933 | + | 0.149766i | ||||
\(134\) | −1.90754 | − | 1.38591i | −0.164787 | − | 0.119725i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.4635 | − | 18.5003i | 2.18348 | − | 1.58639i | ||||
\(137\) | 6.49579 | − | 8.94069i | 0.554973 | − | 0.763854i | −0.435704 | − | 0.900090i | \(-0.643500\pi\) |
0.990676 | + | 0.136236i | \(0.0435004\pi\) | |||||||
\(138\) | 5.75818 | − | 7.92545i | 0.490169 | − | 0.674659i | ||||
\(139\) | −9.92651 | + | 7.21204i | −0.841956 | + | 0.611717i | −0.922916 | − | 0.385000i | \(-0.874201\pi\) |
0.0809604 | + | 0.996717i | \(0.474201\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.65876 | + | 1.93170i | 0.223908 | + | 0.162678i | ||||
\(142\) | 3.41164 | − | 1.10851i | 0.286299 | − | 0.0930241i | ||||
\(143\) | − | 16.8433i | − | 1.40851i | ||||||
\(144\) | −2.11124 | − | 6.49774i | −0.175937 | − | 0.541479i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.87961 | − | 27.3286i | 0.734882 | − | 2.26173i | ||||
\(147\) | 5.62767 | + | 1.82854i | 0.464163 | + | 0.150816i | ||||
\(148\) | −4.22143 | − | 5.81030i | −0.346999 | − | 0.477604i | ||||
\(149\) | 4.62832 | 0.379167 | 0.189584 | − | 0.981865i | \(-0.439286\pi\) | ||||
0.189584 | + | 0.981865i | \(0.439286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.67249 | −0.380242 | −0.190121 | − | 0.981761i | \(-0.560888\pi\) | ||||
−0.190121 | + | 0.981761i | \(0.560888\pi\) | |||||||
\(152\) | 19.5482 | + | 26.9058i | 1.58557 | + | 2.18235i | ||||
\(153\) | 4.83480 | + | 1.57092i | 0.390871 | + | 0.127002i | ||||
\(154\) | −2.42426 | + | 7.46110i | −0.195352 | + | 0.601232i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.77800 | − | 23.9382i | −0.622738 | − | 1.91659i | ||||
\(157\) | − | 14.9726i | − | 1.19494i | −0.801890 | − | 0.597472i | \(-0.796172\pi\) | ||
0.801890 | − | 0.597472i | \(-0.203828\pi\) | |||||||
\(158\) | −3.49247 | + | 1.13477i | −0.277846 | + | 0.0902777i | ||||
\(159\) | −10.2633 | − | 7.45672i | −0.813932 | − | 0.591357i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.24972 | + | 2.36106i | −0.256113 | + | 0.186077i | ||||
\(162\) | 1.49161 | − | 2.05302i | 0.117192 | − | 0.161301i | ||||
\(163\) | 7.00123 | − | 9.63637i | 0.548379 | − | 0.754779i | −0.441412 | − | 0.897304i | \(-0.645522\pi\) |
0.989791 | + | 0.142526i | \(0.0455223\pi\) | |||||||
\(164\) | 4.18557 | − | 3.04099i | 0.326838 | − | 0.237462i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.5597 | + | 17.1171i | 1.82859 | + | 1.32855i | ||||
\(167\) | −10.0889 | + | 3.27809i | −0.780704 | + | 0.253666i | −0.672141 | − | 0.740424i | \(-0.734625\pi\) |
−0.108563 | + | 0.994090i | \(0.534625\pi\) | |||||||
\(168\) | 6.44235i | 0.497038i | ||||||||
\(169\) | −5.91461 | − | 18.2033i | −0.454970 | − | 1.40025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.65990 | + | 5.10866i | −0.126936 | + | 0.390669i | ||||
\(172\) | 24.0091 | + | 7.80103i | 1.83068 | + | 0.594823i | ||||
\(173\) | 0.736719 | + | 1.01401i | 0.0560117 | + | 0.0770935i | 0.836104 | − | 0.548571i | \(-0.184828\pi\) |
−0.780092 | + | 0.625664i | \(0.784828\pi\) | |||||||
\(174\) | 1.72485 | 0.130760 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.2983 | 1.53004 | ||||||||
\(177\) | 1.88789 | + | 2.59846i | 0.141902 | + | 0.195312i | ||||
\(178\) | −21.8956 | − | 7.11432i | −1.64115 | − | 0.533241i | ||||
\(179\) | 6.43105 | − | 19.7927i | 0.480679 | − | 1.47938i | −0.357464 | − | 0.933927i | \(-0.616358\pi\) |
0.838143 | − | 0.545451i | \(-0.183642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.14058 | − | 6.58803i | −0.159108 | − | 0.489684i | 0.839446 | − | 0.543443i | \(-0.182880\pi\) |
−0.998554 | + | 0.0537591i | \(0.982880\pi\) | |||||||
\(182\) | 14.9698i | 1.10964i | ||||||||
\(183\) | 5.15561 | − | 1.67516i | 0.381113 | − | 0.123831i | ||||
\(184\) | 19.3364 | + | 14.0487i | 1.42550 | + | 1.03569i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.74530 | − | 1.26803i | 0.127971 | − | 0.0929766i | ||||
\(187\) | −8.87759 | + | 12.2189i | −0.649193 | + | 0.893538i | ||||
\(188\) | −8.57633 | + | 11.8043i | −0.625494 | + | 0.860918i | ||||
\(189\) | −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 | \(0.795442\pi\) | |||||||
\(192\) | −1.03685 | + | 0.336892i | −0.0748280 | + | 0.0243131i | ||||
\(193\) | − | 13.9629i | − | 1.00507i | −0.864556 | − | 0.502537i | \(-0.832400\pi\) | ||
0.864556 | − | 0.502537i | \(-0.167600\pi\) | |||||||
\(194\) | 4.72807 | + | 14.5515i | 0.339456 | + | 1.04474i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.11834 | + | 24.9857i | −0.579881 | + | 1.78469i | ||||
\(197\) | −5.48046 | − | 1.78071i | −0.390467 | − | 0.126870i | 0.107203 | − | 0.994237i | \(-0.465811\pi\) |
−0.497669 | + | 0.867367i | \(0.665811\pi\) | |||||||
\(198\) | 4.43157 | + | 6.09954i | 0.314938 | + | 0.433475i | ||||
\(199\) | 26.5748 | 1.88384 | 0.941919 | − | 0.335841i | \(-0.109020\pi\) | ||||
0.941919 | + | 0.335841i | \(0.109020\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.929140 | 0.0655365 | ||||||||
\(202\) | 22.8825 | + | 31.4951i | 1.61001 | + | 2.21599i | ||||
\(203\) | −0.672633 | − | 0.218552i | −0.0472096 | − | 0.0153393i | ||||
\(204\) | −6.97456 | + | 21.4655i | −0.488317 | + | 1.50289i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.45644 | − | 29.1039i | −0.658862 | − | 2.02777i | ||||
\(207\) | 3.86039i | 0.268315i | ||||||||
\(208\) | 36.8371 | − | 11.9691i | 2.55420 | − | 0.829909i | ||||
\(209\) | −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 | \(-0.0645116\pi\) | |||||||
\(212\) | 33.1063 | − | 45.5669i | 2.27375 | − | 3.12954i | ||||
\(213\) | −0.830884 | + | 1.14361i | −0.0569312 | + | 0.0783591i | ||||
\(214\) | 13.3403 | − | 9.69227i | 0.911922 | − | 0.662550i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00893 | + | 3.63920i | 0.340815 | + | 0.247616i | ||||
\(217\) | −0.841277 | + | 0.273347i | −0.0571096 | + | 0.0185560i | ||||
\(218\) | 5.86348i | 0.397125i | ||||||||
\(219\) | 3.49912 | + | 10.7692i | 0.236448 | + | 0.727713i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.90591 | + | 27.4096i | −0.599076 | + | 1.84377i | ||||
\(222\) | 3.90410 | + | 1.26852i | 0.262026 | + | 0.0851374i | ||||
\(223\) | 16.1321 | + | 22.2039i | 1.08029 | + | 1.48689i | 0.859205 | + | 0.511631i | \(0.170958\pi\) |
0.221081 | + | 0.975255i | \(0.429042\pi\) | |||||||
\(224\) | −5.15581 | −0.344487 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.82792 | −0.653744 | ||||||||
\(227\) | 0.0765066 | + | 0.105302i | 0.00507792 | + | 0.00698916i | 0.811548 | − | 0.584285i | \(-0.198625\pi\) |
−0.806470 | + | 0.591274i | \(0.798625\pi\) | |||||||
\(228\) | −22.6813 | − | 7.36962i | −1.50211 | − | 0.488065i | ||||
\(229\) | −0.873064 | + | 2.68702i | −0.0576937 | + | 0.177563i | −0.975750 | − | 0.218886i | \(-0.929758\pi\) |
0.918057 | + | 0.396449i | \(0.129758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.955307 | − | 2.94013i | −0.0628546 | − | 0.193447i | ||||
\(232\) | 4.20826i | 0.276286i | ||||||||
\(233\) | −7.59617 | + | 2.46815i | −0.497642 | + | 0.161694i | −0.547075 | − | 0.837084i | \(-0.684259\pi\) |
0.0494328 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(234\) | 11.6390 | + | 8.45625i | 0.760867 | + | 0.552802i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.5366 | + | 8.38182i | −0.750968 | + | 0.545610i | ||||
\(237\) | 0.850569 | − | 1.17071i | 0.0552504 | − | 0.0760457i | ||||
\(238\) | 7.89012 | − | 10.8598i | 0.511441 | − | 0.703938i | ||||
\(239\) | −15.4214 | + | 11.2043i | −0.997528 | + | 0.724747i | −0.961557 | − | 0.274606i | \(-0.911452\pi\) |
−0.0359713 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0864 | − | 12.4140i | −1.10063 | − | 0.799654i | −0.119467 | − | 0.992838i | \(-0.538118\pi\) |
−0.981162 | + | 0.193184i | \(0.938118\pi\) | |||||||
\(242\) | 5.24476 | − | 1.70413i | 0.337146 | − | 0.109545i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 7.43735 | + | 22.8898i | 0.476127 | + | 1.46537i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.913803 | + | 2.81240i | −0.0582619 | + | 0.179312i | ||||
\(247\) | −28.9621 | − | 9.41036i | −1.84281 | − | 0.598767i | ||||
\(248\) | 3.09373 | + | 4.25815i | 0.196452 | + | 0.270393i | ||||
\(249\) | −11.4756 | −0.727238 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.2224 | 1.90762 | 0.953811 | − | 0.300408i | \(-0.0971228\pi\) | ||||
0.953811 | + | 0.300408i | \(0.0971228\pi\) | |||||||
\(252\) | −2.71542 | − | 3.73746i | −0.171056 | − | 0.235438i | ||||
\(253\) | −10.9079 | − | 3.54419i | −0.685773 | − | 0.222821i | ||||
\(254\) | 9.17007 | − | 28.2226i | 0.575381 | − | 1.77084i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.26692 | − | 28.5207i | −0.579183 | − | 1.78254i | ||||
\(257\) | − | 5.10215i | − | 0.318263i | −0.987257 | − | 0.159132i | \(-0.949131\pi\) | ||
0.987257 | − | 0.159132i | \(-0.0508695\pi\) | |||||||
\(258\) | −13.7230 | + | 4.45888i | −0.854358 | + | 0.277598i | ||||
\(259\) | −1.36174 | − | 0.989360i | −0.0846142 | − | 0.0614758i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.549886 | + | 0.399516i | −0.0340371 | + | 0.0247294i | ||||
\(262\) | −11.8763 | + | 16.3464i | −0.733722 | + | 1.00988i | ||||
\(263\) | 3.77088 | − | 5.19017i | 0.232522 | − | 0.320040i | −0.676772 | − | 0.736192i | \(-0.736622\pi\) |
0.909295 | + | 0.416153i | \(0.136622\pi\) | |||||||
\(264\) | −14.8816 | + | 10.8121i | −0.915898 | + | 0.665439i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.4749 | + | 8.33704i | 0.703574 | + | 0.511177i | ||||
\(267\) | 8.62823 | − | 2.80348i | 0.528039 | − | 0.171570i | ||||
\(268\) | 4.12518i | 0.251986i | ||||||||
\(269\) | 5.39518 | + | 16.6047i | 0.328950 | + | 1.01240i | 0.969626 | + | 0.244592i | \(0.0786542\pi\) |
−0.640676 | + | 0.767811i | \(0.721346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0294140 | + | 0.0905270i | −0.00178677 | + | 0.00549912i | −0.951946 | − | 0.306266i | \(-0.900920\pi\) |
0.950159 | + | 0.311765i | \(0.100920\pi\) | |||||||
\(272\) | −33.0320 | − | 10.7328i | −2.00286 | − | 0.650769i | ||||
\(273\) | −3.46736 | − | 4.77241i | −0.209854 | − | 0.288840i | ||||
\(274\) | −28.0446 | −1.69424 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.1393 | −1.03166 | ||||||||
\(277\) | −10.8157 | − | 14.8865i | −0.649851 | − | 0.894443i | 0.349242 | − | 0.937033i | \(-0.386439\pi\) |
−0.999093 | + | 0.0425895i | \(0.986439\pi\) | |||||||
\(278\) | 29.6129 | + | 9.62182i | 1.77606 | + | 0.577078i | ||||
\(279\) | −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 | \(0.720316\pi\) | |||||||
\(282\) | − | 8.33982i | − | 0.496629i | ||||||
\(283\) | 21.1514 | − | 6.87252i | 1.25732 | − | 0.408529i | 0.396783 | − | 0.917912i | \(-0.370126\pi\) |
0.860540 | + | 0.509383i | \(0.170126\pi\) | |||||||
\(284\) | −5.07740 | − | 3.68895i | −0.301288 | − | 0.218899i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −34.5796 | + | 25.1236i | −2.04474 | + | 1.48559i | ||||
\(287\) | 0.712705 | − | 0.980955i | 0.0420697 | − | 0.0579039i | ||||
\(288\) | −2.91245 | + | 4.00864i | −0.171618 | + | 0.236212i | ||||
\(289\) | 7.15424 | − | 5.19786i | 0.420837 | − | 0.305756i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.87779 | − | 3.54392i | −0.285941 | − | 0.207749i | ||||
\(292\) | −47.8128 | + | 15.5353i | −2.79803 | + | 0.909136i | ||||
\(293\) | − | 18.7316i | − | 1.09431i | −0.837031 | − | 0.547155i | \(-0.815711\pi\) | ||
0.837031 | − | 0.547155i | \(-0.184289\pi\) | |||||||
\(294\) | −4.64024 | − | 14.2812i | −0.270624 | − | 0.832896i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.09491 | + | 9.52517i | −0.179888 | + | 0.553639i | ||||
\(297\) | −2.82560 | − | 0.918092i | −0.163958 | − | 0.0532731i | ||||
\(298\) | −6.90364 | − | 9.50204i | −0.399917 | − | 0.550439i | ||||
\(299\) | −21.8854 | −1.26566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.91650 | 0.341021 | ||||||||
\(302\) | 6.96952 | + | 9.59272i | 0.401051 | + | 0.551999i | ||||
\(303\) | −14.5900 | − | 4.74058i | −0.838174 | − | 0.272339i | ||||
\(304\) | 11.3407 | − | 34.9030i | 0.650433 | − | 2.00183i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.98649 | − | 12.2692i | −0.227892 | − | 0.701381i | ||||
\(307\) | 7.03850i | 0.401708i | 0.979621 | + | 0.200854i | \(0.0643717\pi\) | ||||
−0.979621 | + | 0.200854i | \(0.935628\pi\) | |||||||
\(308\) | 13.0536 | − | 4.24136i | 0.743796 | − | 0.241674i | ||||
\(309\) | 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 | \(-0.0117338\pi\) | |||||||
\(312\) | −20.6314 | + | 28.3967i | −1.16803 | + | 1.60765i | ||||
\(313\) | −9.19024 | + | 12.6493i | −0.519463 | + | 0.714980i | −0.985479 | − | 0.169796i | \(-0.945689\pi\) |
0.466016 | + | 0.884776i | \(0.345689\pi\) | |||||||
\(314\) | −30.7391 | + | 22.3333i | −1.73471 | + | 1.26034i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.19769 | + | 3.77635i | 0.292393 | + | 0.212436i | ||||
\(317\) | −5.93596 | + | 1.92871i | −0.333397 | + | 0.108327i | −0.470932 | − | 0.882170i | \(-0.656082\pi\) |
0.137535 | + | 0.990497i | \(0.456082\pi\) | |||||||
\(318\) | 32.1933i | 1.80531i | ||||||||
\(319\) | −0.624024 | − | 1.92055i | −0.0349386 | − | 0.107530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00795 | + | 6.17984i | −0.112073 | + | 0.344925i | ||||
\(322\) | 9.69460 | + | 3.14997i | 0.540259 | + | 0.175541i | ||||
\(323\) | 16.0506 | + | 22.0918i | 0.893080 | + | 1.22922i | ||||
\(324\) | −4.43979 | −0.246655 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.2268 | −1.67411 | ||||||||
\(327\) | −1.35812 | − | 1.86929i | −0.0751042 | − | 0.103372i | ||||
\(328\) | −6.86164 | − | 2.22948i | −0.378871 | − | 0.123103i | ||||
\(329\) | −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 | \(0.699244\pi\) | |||||||
\(332\) | − | 50.9493i | − | 2.79621i | ||||||
\(333\) | −1.53846 | + | 0.499875i | −0.0843068 | + | 0.0273930i | ||||
\(334\) | 21.7787 | + | 15.8231i | 1.19168 | + | 0.865804i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.75136 | − | 4.17861i | 0.313763 | − | 0.227962i | ||||
\(337\) | 20.4262 | − | 28.1142i | 1.11269 | − | 1.53148i | 0.295287 | − | 0.955409i | \(-0.404585\pi\) |
0.817399 | − | 0.576072i | \(-0.195415\pi\) | |||||||
\(338\) | −28.5495 | + | 39.2950i | −1.55289 | + | 2.13736i | ||||
\(339\) | 3.13317 | − | 2.27638i | 0.170170 | − | 0.123636i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.04332 | − | 1.48456i | −0.110652 | − | 0.0803935i | ||||
\(342\) | 12.9641 | − | 4.21229i | 0.701019 | − | 0.227775i | ||||
\(343\) | 13.4409i | 0.725740i | ||||||||
\(344\) | −10.8787 | − | 33.4812i | −0.586541 | − | 1.80519i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.982882 | − | 3.02500i | 0.0528401 | − | 0.162625i | ||||
\(347\) | 27.3182 | + | 8.87623i | 1.46652 | + | 0.476501i | 0.930055 | − | 0.367421i | \(-0.119759\pi\) |
0.536465 | + | 0.843922i | \(0.319759\pi\) | |||||||
\(348\) | −1.77376 | − | 2.44138i | −0.0950837 | − | 0.130871i | ||||
\(349\) | 12.2834 | 0.657515 | 0.328758 | − | 0.944414i | \(-0.393370\pi\) | ||||
0.328758 | + | 0.944414i | \(0.393370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.66922 | −0.302601 | ||||||||
\(352\) | −8.65291 | − | 11.9097i | −0.461201 | − | 0.634789i | ||||
\(353\) | 25.6575 | + | 8.33663i | 1.36561 | + | 0.443714i | 0.897913 | − | 0.440174i | \(-0.145083\pi\) |
0.467699 | + | 0.883888i | \(0.345083\pi\) | |||||||
\(354\) | 2.51870 | − | 7.75175i | 0.133867 | − | 0.412001i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.4469 | + | 38.3075i | 0.659682 | + | 2.03029i | ||||
\(357\) | 5.28968i | 0.279960i | ||||||||
\(358\) | −50.2275 | + | 16.3199i | −2.65461 | + | 0.862533i | ||||
\(359\) | 13.2875 | + | 9.65393i | 0.701287 | + | 0.509515i | 0.880351 | − | 0.474322i | \(-0.157307\pi\) |
−0.179064 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.97178 | + | 5.79184i | −0.419567 | + | 0.304834i | ||||
\(362\) | −10.3325 | + | 14.2214i | −0.543062 | + | 0.747460i | ||||
\(363\) | −1.27733 | + | 1.75809i | −0.0670423 | + | 0.0922758i | ||||
\(364\) | 21.1885 | − | 15.3943i | 1.11058 | − | 0.806883i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.1293 | − | 8.08589i | −0.581737 | − | 0.422656i | ||||
\(367\) | 28.4321 | − | 9.23816i | 1.48415 | − | 0.482228i | 0.548797 | − | 0.835956i | \(-0.315086\pi\) |
0.935349 | + | 0.353727i | \(0.115086\pi\) | |||||||
\(368\) | − | 26.3747i | − | 1.37487i | ||||||
\(369\) | −0.360095 | − | 1.10826i | −0.0187458 | − | 0.0576936i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.07914 | − | 12.5543i | 0.211778 | − | 0.651787i | ||||
\(372\) | −3.58958 | − | 1.16633i | −0.186111 | − | 0.0604712i | ||||
\(373\) | −14.5951 | − | 20.0885i | −0.755706 | − | 1.04014i | −0.997559 | − | 0.0698276i | \(-0.977755\pi\) |
0.241853 | − | 0.970313i | \(-0.422245\pi\) | |||||||
\(374\) | 38.3276 | 1.98187 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.3474 | 1.04934 | ||||||||
\(377\) | −2.26494 | − | 3.11742i | −0.116650 | − | 0.160556i | ||||
\(378\) | 2.51130 | + | 0.815972i | 0.129167 | + | 0.0419690i | ||||
\(379\) | −5.99389 | + | 18.4473i | −0.307885 | + | 0.947574i | 0.670699 | + | 0.741729i | \(0.265994\pi\) |
−0.978585 | + | 0.205845i | \(0.934006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.61357 | + | 11.1214i | 0.185129 | + | 0.569768i | ||||
\(382\) | 20.7179i | 1.06002i | ||||||||
\(383\) | −10.7002 | + | 3.47670i | −0.546754 | + | 0.177651i | −0.569353 | − | 0.822094i | \(-0.692806\pi\) |
0.0225986 | + | 0.999745i | \(0.492806\pi\) | |||||||
\(384\) | 10.2555 | + | 7.45106i | 0.523349 | + | 0.380235i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.6662 | + | 20.8272i | −1.45907 | + | 1.06008i | ||||
\(387\) | 3.34215 | − | 4.60008i | 0.169891 | − | 0.233835i | ||||
\(388\) | 15.7343 | − | 21.6564i | 0.798786 | − | 1.09944i | ||||
\(389\) | 12.0558 | − | 8.75903i | 0.611252 | − | 0.444100i | −0.238603 | − | 0.971117i | \(-0.576690\pi\) |
0.849855 | + | 0.527017i | \(0.176690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8767 | + | 11.5351i | 0.802920 | + | 0.583356i | ||||
\(392\) | 34.8431 | − | 11.3212i | 1.75984 | − | 0.571807i | ||||
\(393\) | − | 7.96210i | − | 0.401635i | ||||||
\(394\) | 4.51886 | + | 13.9076i | 0.227657 | + | 0.700656i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.07613 | − | 12.5450i | 0.204833 | − | 0.630412i | ||||
\(397\) | 22.9172 | + | 7.44626i | 1.15018 | + | 0.373717i | 0.821212 | − | 0.570623i | \(-0.193298\pi\) |
0.328971 | + | 0.944340i | \(0.393298\pi\) | |||||||
\(398\) | −39.6392 | − | 54.5586i | −1.98693 | − | 2.73478i | ||||
\(399\) | −5.58930 | −0.279815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.4580 | 0.672059 | 0.336030 | − | 0.941851i | \(-0.390916\pi\) | ||||
0.336030 | + | 0.941851i | \(0.390916\pi\) | |||||||
\(402\) | −1.38591 | − | 1.90754i | −0.0691230 | − | 0.0951397i | ||||
\(403\) | −4.58358 | − | 1.48930i | −0.228325 | − | 0.0741872i | ||||
\(404\) | 21.0472 | − | 64.7765i | 1.04714 | − | 3.22275i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.554613 | + | 1.70692i | 0.0275250 | + | 0.0847132i | ||||
\(407\) | − | 4.80598i | − | 0.238224i | ||||||
\(408\) | 29.9341 | − | 9.72618i | 1.48196 | − | 0.481518i | ||||
\(409\) | −28.6988 | − | 20.8509i | −1.41906 | − | 1.03101i | −0.991925 | − | 0.126825i | \(-0.959521\pi\) |
−0.427140 | − | 0.904186i | \(-0.640479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.94069 | − | 6.49579i | 0.441012 | − | 0.320414i | ||||
\(412\) | −31.4696 | + | 43.3141i | −1.55039 | + | 2.13393i | ||||
\(413\) | −1.96441 | + | 2.70379i | −0.0966625 | + | 0.133045i | ||||
\(414\) | 7.92545 | − | 5.75818i | 0.389515 | − | 0.282999i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.7259 | − | 16.5113i | −1.11423 | − | 0.809534i | ||||
\(417\) | −11.6693 | + | 3.79159i | −0.571449 | + | 0.185675i | ||||
\(418\) | 40.4986i | 1.98085i | ||||||||
\(419\) | −4.88617 | − | 15.0381i | −0.238705 | − | 0.734659i | −0.996608 | − | 0.0822916i | \(-0.973776\pi\) |
0.757903 | − | 0.652367i | \(-0.226224\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.70244 | − | 11.3949i | 0.180446 | − | 0.555355i | −0.819394 | − | 0.573230i | \(-0.805690\pi\) |
0.999840 | + | 0.0178752i | \(0.00569015\pi\) | |||||||
\(422\) | −63.8590 | − | 20.7491i | −3.10861 | − | 1.01005i | ||||
\(423\) | 1.93170 | + | 2.65876i | 0.0939225 | + | 0.129273i | ||||
\(424\) | −78.5447 | −3.81447 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.58721 | 0.173801 | ||||||||
\(427\) | 3.31550 | + | 4.56340i | 0.160448 | + | 0.220838i | ||||
\(428\) | −27.4372 | − | 8.91488i | −1.32623 | − | 0.430917i | ||||
\(429\) | 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 | \(0.785278\pi\) | |||||||
\(432\) | − | 6.83213i | − | 0.328711i | ||||||
\(433\) | −4.06380 | + | 1.32041i | −0.195294 | + | 0.0634547i | −0.405031 | − | 0.914303i | \(-0.632739\pi\) |
0.209737 | + | 0.977758i | \(0.432739\pi\) | |||||||
\(434\) | 1.81604 | + | 1.31943i | 0.0871728 | + | 0.0633347i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.29926 | − | 6.02976i | 0.397462 | − | 0.288773i | ||||
\(437\) | −12.1885 | + | 16.7760i | −0.583055 | + | 0.802506i | ||||
\(438\) | 16.8900 | − | 23.2471i | 0.807037 | − | 1.11079i | ||||
\(439\) | −16.4289 | + | 11.9363i | −0.784111 | + | 0.569690i | −0.906210 | − | 0.422828i | \(-0.861037\pi\) |
0.122099 | + | 0.992518i | \(0.461037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.78718 | + | 3.47809i | 0.227961 | + | 0.165623i | ||||
\(442\) | 69.5565 | − | 22.6003i | 3.30847 | − | 1.07499i | ||||
\(443\) | 19.0543i | 0.905299i | 0.891689 | + | 0.452649i | \(0.149521\pi\) | ||||
−0.891689 | + | 0.452649i | \(0.850479\pi\) | |||||||
\(444\) | −2.21934 | − | 6.83041i | −0.105325 | − | 0.324157i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.5224 | − | 66.2391i | 1.01912 | − | 3.13651i | ||||
\(447\) | 4.40180 | + | 1.43023i | 0.208198 | + | 0.0676476i | ||||
\(448\) | −0.666782 | − | 0.917747i | −0.0315025 | − | 0.0433595i | ||||
\(449\) | −29.4793 | −1.39122 | −0.695608 | − | 0.718421i | \(-0.744865\pi\) | ||||
−0.695608 | + | 0.718421i | \(0.744865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.46209 | 0.163023 | ||||||||
\(452\) | 10.1066 | + | 13.9106i | 0.475376 | + | 0.654299i | ||||
\(453\) | −4.44380 | − | 1.44388i | −0.208788 | − | 0.0678394i | ||||
\(454\) | 0.102070 | − | 0.314139i | 0.00479038 | − | 0.0147433i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.2771 | + | 31.6296i | 0.481269 | + | 1.48119i | ||||
\(457\) | − | 28.3015i | − | 1.32389i | −0.749553 | − | 0.661945i | \(-0.769731\pi\) | ||
0.749553 | − | 0.661945i | \(-0.230269\pi\) | |||||||
\(458\) | 6.81877 | − | 2.21555i | 0.318620 | − | 0.103526i | ||||
\(459\) | 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 | \(0.174002\pi\) | |||||||
\(462\) | −4.61121 | + | 6.34679i | −0.214533 | + | 0.295279i | ||||
\(463\) | 5.41311 | − | 7.45051i | 0.251569 | − | 0.346254i | −0.664491 | − | 0.747296i | \(-0.731352\pi\) |
0.916060 | + | 0.401042i | \(0.131352\pi\) | |||||||
\(464\) | 3.75689 | − | 2.72954i | 0.174409 | − | 0.126716i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.3977 | + | 11.9136i | 0.759607 | + | 0.551887i | ||||
\(467\) | 10.0929 | − | 3.27938i | 0.467043 | − | 0.151752i | −0.0660353 | − | 0.997817i | \(-0.521035\pi\) |
0.533079 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(468\) | − | 25.1701i | − | 1.16349i | ||||||
\(469\) | 0.298759 | + | 0.919485i | 0.0137954 | + | 0.0424579i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.62679 | − | 14.2398i | 0.213191 | − | 0.656135i | ||||
\(472\) | 18.9126 | + | 6.14508i | 0.870524 | + | 0.282850i | ||||
\(473\) | 9.92956 | + | 13.6669i | 0.456562 | + | 0.628403i | ||||
\(474\) | −3.67220 | −0.168670 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −23.4850 | −1.07644 | ||||||||
\(477\) | −7.45672 | − | 10.2633i | −0.341420 | − | 0.469924i | ||||
\(478\) | 46.0054 | + | 14.9480i | 2.10424 | + | 0.683708i | ||||
\(479\) | −10.3849 | + | 31.9613i | −0.474496 | + | 1.46035i | 0.372140 | + | 0.928177i | \(0.378624\pi\) |
−0.846636 | + | 0.532172i | \(0.821376\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.83390 | − | 8.72184i | −0.129215 | − | 0.397682i | ||||
\(482\) | 53.5954i | 2.44120i | ||||||||
\(483\) | −3.82027 | + | 1.24128i | −0.173828 | + | 0.0564802i | ||||
\(484\) | −7.80554 | − | 5.67106i | −0.354797 | − | 0.257775i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.05302 | − | 1.49161i | 0.0931269 | − | 0.0676607i | ||||
\(487\) | −17.1919 | + | 23.6626i | −0.779039 | + | 1.07226i | 0.216348 | + | 0.976316i | \(0.430585\pi\) |
−0.995387 | + | 0.0959389i | \(0.969415\pi\) | |||||||
\(488\) | 19.7279 | − | 27.1531i | 0.893038 | − | 1.22916i | ||||
\(489\) | 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 | \(0.801967\pi\) | |||||||
\(492\) | 4.92043 | − | 1.59874i | 0.221830 | − | 0.0720769i | ||||
\(493\) | 3.45531i | 0.155619i | ||||||||
\(494\) | 23.8804 | + | 73.4964i | 1.07443 | + | 3.30676i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.79479 | − | 5.52380i | 0.0805885 | − | 0.248026i | ||||
\(497\) | −1.39889 | − | 0.454528i | −0.0627490 | − | 0.0203884i | ||||
\(498\) | 17.1171 | + | 23.5597i | 0.767036 | + | 1.05573i | ||||
\(499\) | 35.7533 | 1.60054 | 0.800268 | − | 0.599642i | \(-0.204690\pi\) | ||||
0.800268 | + | 0.599642i | \(0.204690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6081 | −0.473936 | ||||||||
\(502\) | −45.0800 | − | 62.0472i | −2.01202 | − | 2.76930i | ||||
\(503\) | −11.0744 | − | 3.59828i | −0.493782 | − | 0.160439i | 0.0515323 | − | 0.998671i | \(-0.483590\pi\) |
−0.545314 | + | 0.838232i | \(0.683590\pi\) | |||||||
\(504\) | −1.99080 | + | 6.12704i | −0.0886771 | + | 0.272920i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.99399 | + | 27.6807i | 0.399832 | + | 1.23056i | ||||
\(507\) | − | 19.1401i | − | 0.850040i | ||||||
\(508\) | −49.3768 | + | 16.0435i | −2.19074 | + | 0.711815i | ||||
\(509\) | −6.90384 | − | 5.01594i | −0.306007 | − | 0.222327i | 0.424174 | − | 0.905581i | \(-0.360564\pi\) |
−0.730181 | + | 0.683253i | \(0.760564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.53214 | + | 6.92551i | −0.421677 | + | 0.306366i | ||||
\(512\) | −29.8288 | + | 41.0558i | −1.31826 | + | 1.81443i | ||||
\(513\) | −3.15732 | + | 4.34568i | −0.139399 | + | 0.191867i | ||||
\(514\) | −10.4748 | + | 7.61040i | −0.462025 | + | 0.335681i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 20.4234 | + | 14.8384i | 0.899089 | + | 0.653226i | ||||
\(517\) | −9.28605 | + | 3.01722i | −0.408400 | + | 0.132697i | ||||
\(518\) | 4.27141i | 0.187675i | ||||||||
\(519\) | 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 | \(0.0911763\pi\) | |||||||
\(522\) | 1.64043 | + | 0.533007i | 0.0717996 | + | 0.0233291i | ||||
\(523\) | −15.9998 | − | 22.0218i | −0.699621 | − | 0.962946i | −0.999958 | − | 0.00911285i | \(-0.997099\pi\) |
0.300337 | − | 0.953833i | \(-0.402901\pi\) | |||||||
\(524\) | 35.3500 | 1.54427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.2802 | −0.709850 | ||||||||
\(527\) | 2.54019 | + | 3.49628i | 0.110653 | + | 0.152300i | ||||
\(528\) | 19.3048 | + | 6.27252i | 0.840135 | + | 0.272976i | ||||
\(529\) | 2.50224 | − | 7.70110i | 0.108793 | − | 0.334831i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.992522 | + | 3.05467i | 0.0430718 | + | 0.132561i | ||||
\(532\) | − | 24.8153i | − | 1.07588i | ||||||
\(533\) | 6.28296 | − | 2.04146i | 0.272145 | − | 0.0884253i | ||||
\(534\) | −18.6255 | − | 13.5322i | −0.806005 | − | 0.585597i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.65400 | − | 3.38133i | 0.201022 | − | 0.146051i | ||||
\(537\) | 12.2326 | − | 16.8367i | 0.527875 | − | 0.726557i | ||||
\(538\) | 26.0422 | − | 35.8440i | 1.12276 | − | 1.54535i | ||||
\(539\) | −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 | \(0.926546\pi\) | |||||||
\(542\) | 0.229728 | − | 0.0746431i | 0.00986766 | − | 0.00320620i | ||||
\(543\) | − | 6.92706i | − | 0.297269i | ||||||
\(544\) | 7.78385 | + | 23.9562i | 0.333730 | + | 1.02711i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.62592 | + | 14.2371i | −0.197971 | + | 0.609293i | ||||
\(547\) | −10.8200 | − | 3.51564i | −0.462631 | − | 0.150318i | 0.0684223 | − | 0.997656i | \(-0.478203\pi\) |
−0.531053 | + | 0.847339i | \(0.678203\pi\) | |||||||
\(548\) | 28.8399 | + | 39.6947i | 1.23198 | + | 1.69568i | ||||
\(549\) | 5.42093 | 0.231360 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.65103 | −0.155539 | ||||||||
\(552\) | 14.0487 | + | 19.3364i | 0.597954 | + | 0.823012i | ||||
\(553\) | 1.43204 | + | 0.465297i | 0.0608964 | + | 0.0197864i | ||||
\(554\) | −14.4296 | + | 44.4096i | −0.613053 | + | 1.88678i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8339 | − | 51.8093i | −0.713914 | − | 2.19720i | ||||
\(557\) | 45.7532i | 1.93862i | 0.245833 | + | 0.969312i | \(0.420938\pi\) | ||||
−0.245833 | + | 0.969312i | \(0.579062\pi\) | |||||||
\(558\) | 2.05172 | − | 0.666643i | 0.0868561 | − | 0.0282213i | ||||
\(559\) | 26.0789 | + | 18.9474i | 1.10302 | + | 0.801390i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2189 | + | 8.87759i | −0.515884 | + | 0.374812i | ||||
\(562\) | 26.7535 | − | 36.8231i | 1.12853 | − | 1.55329i | ||||
\(563\) | 5.25650 | − | 7.23495i | 0.221535 | − | 0.304917i | −0.683754 | − | 0.729712i | \(-0.739654\pi\) |
0.905289 | + | 0.424796i | \(0.139654\pi\) | |||||||
\(564\) | −11.8043 | + | 8.57633i | −0.497051 | + | 0.361129i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −45.6591 | − | 33.1733i | −1.91919 | − | 1.39438i | ||||
\(567\) | −0.989608 | + | 0.321543i | −0.0415596 | + | 0.0135035i | ||||
\(568\) | 8.75203i | 0.367227i | ||||||||
\(569\) | 0.707365 | + | 2.17704i | 0.0296543 | + | 0.0912665i | 0.964788 | − | 0.263028i | \(-0.0847211\pi\) |
−0.935134 | + | 0.354294i | \(0.884721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.50522 | + | 29.2541i | −0.397781 | + | 1.22424i | 0.528993 | + | 0.848626i | \(0.322570\pi\) |
−0.926774 | + | 0.375618i | \(0.877430\pi\) | |||||||
\(572\) | 71.1206 | + | 23.1085i | 2.97370 | + | 0.966214i | ||||
\(573\) | −4.79877 | − | 6.60494i | −0.200471 | − | 0.275925i | ||||
\(574\) | −3.07700 | −0.128431 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.09021 | −0.0454252 | ||||||||
\(577\) | 3.87484 | + | 5.33326i | 0.161312 | + | 0.222027i | 0.882020 | − | 0.471212i | \(-0.156183\pi\) |
−0.720708 | + | 0.693238i | \(0.756183\pi\) | |||||||
\(578\) | −21.3426 | − | 6.93464i | −0.887736 | − | 0.288443i | ||||
\(579\) | 4.31479 | − | 13.2795i | 0.179316 | − | 0.551879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.68991 | − | 11.3564i | −0.153083 | − | 0.471141i | ||||
\(582\) | 15.3004i | 0.634220i | ||||||||
\(583\) | 35.8459 | − | 11.6470i | 1.48458 | − | 0.482371i | ||||
\(584\) | 56.7180 | + | 41.2081i | 2.34701 | + | 1.70520i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.4563 | + | 27.9401i | −1.58861 | + | 1.15420i | ||||
\(587\) | −3.25499 | + | 4.48010i | −0.134348 | + | 0.184914i | −0.870890 | − | 0.491477i | \(-0.836457\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(588\) | −15.4420 | + | 21.2541i | −0.636817 | + | 0.876503i | ||||
\(589\) | −3.69431 | + | 2.68408i | −0.152222 | + | 0.110595i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.66196 | − | 3.38711i | −0.191767 | − | 0.139327i | ||||
\(592\) | 10.5109 | − | 3.41521i | 0.431997 | − | 0.140364i | ||||
\(593\) | 1.88122i | 0.0772524i | 0.999254 | + | 0.0386262i | \(0.0122982\pi\) | ||||
−0.999254 | + | 0.0386262i | \(0.987702\pi\) | |||||||
\(594\) | 2.32982 | + | 7.17044i | 0.0955935 | + | 0.294207i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.34992 | + | 19.5430i | −0.260103 | + | 0.800514i | ||||
\(597\) | 25.2741 | + | 8.21206i | 1.03440 | + | 0.336097i | ||||
\(598\) | 32.6444 | + | 44.9311i | 1.33493 | + | 1.83737i | ||||
\(599\) | −17.8272 | −0.728400 | −0.364200 | − | 0.931321i | \(-0.618658\pi\) | ||||
−0.364200 | + | 0.931321i | \(0.618658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.0994 | 1.35015 | 0.675077 | − | 0.737747i | \(-0.264110\pi\) | ||||
0.675077 | + | 0.737747i | \(0.264110\pi\) | |||||||
\(602\) | −8.82509 | − | 12.1467i | −0.359684 | − | 0.495062i | ||||
\(603\) | 0.883665 | + | 0.287120i | 0.0359856 | + | 0.0116924i | ||||
\(604\) | 6.41052 | − | 19.7295i | 0.260840 | − | 0.802784i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0300 | + | 37.0247i | 0.488687 | + | 1.50402i | ||||
\(607\) | − | 23.4603i | − | 0.952226i | −0.879384 | − | 0.476113i | \(-0.842045\pi\) | ||
0.879384 | − | 0.476113i | \(-0.157955\pi\) | |||||||
\(608\) | −25.3132 | + | 8.22475i | −1.02658 | + | 0.333558i | ||||
\(609\) | −0.572176 | − | 0.415710i | −0.0231857 | − | 0.0168454i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0731 | + | 10.9512i | −0.609792 | + | 0.443039i | ||||
\(612\) | −13.2664 | + | 18.2596i | −0.536263 | + | 0.738102i | ||||
\(613\) | −27.7600 | + | 38.2083i | −1.12121 | + | 1.54322i | −0.317445 | + | 0.948277i | \(0.602825\pi\) |
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(614\) | 14.4502 | − | 10.4987i | 0.583162 | − | 0.423692i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.4848 | − | 11.2504i | −0.623901 | − | 0.453290i | ||||
\(617\) | −15.4735 | + | 5.02765i | −0.622941 | + | 0.202406i | −0.603446 | − | 0.797404i | \(-0.706206\pi\) |
−0.0194952 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(618\) | − | 30.6017i | − | 1.23098i | ||||||
\(619\) | −10.9577 | − | 33.7244i | −0.440428 | − | 1.35550i | −0.887421 | − | 0.460960i | \(-0.847505\pi\) |
0.446993 | − | 0.894537i | \(-0.352495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.19292 | + | 3.67145i | −0.0478704 | + | 0.147330i | ||||
\(622\) | −70.6640 | − | 22.9601i | −2.83337 | − | 0.920617i | ||||
\(623\) | 5.54869 | + | 7.63712i | 0.222304 | + | 0.305975i | ||||
\(624\) | 38.7329 | 1.55056 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.6775 | 1.58583 | ||||||||
\(627\) | −9.38043 | − | 12.9111i | −0.374618 | − | 0.515618i | ||||
\(628\) | 63.2217 | + | 20.5420i | 2.52282 | + | 0.819714i | ||||
\(629\) | −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 | \(-0.297706\pi\) | |||||||
\(632\) | − | 8.95939i | − | 0.356385i | ||||||
\(633\) | 25.1644 | − | 8.17641i | 1.00020 | − | 0.324983i | ||||
\(634\) | 12.8138 | + | 9.30978i | 0.508901 | + | 0.369738i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 45.5669 | − | 33.1063i | 1.80684 | − | 1.31275i | ||||
\(637\) | −19.7181 | + | 27.1396i | −0.781259 | + | 1.07531i | ||||
\(638\) | −3.01213 | + | 4.14583i | −0.119251 | + | 0.164135i | ||||
\(639\) | −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 | \(0.599546\pi\) | |||||||
\(642\) | 15.6824 | − | 5.09553i | 0.618936 | − | 0.201104i | ||||
\(643\) | − | 8.08055i | − | 0.318666i | −0.987225 | − | 0.159333i | \(-0.949066\pi\) | ||
0.987225 | − | 0.159333i | \(-0.0509343\pi\) | |||||||
\(644\) | −5.51102 | − | 16.9612i | −0.217165 | − | 0.668364i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.4137 | − | 65.9045i | 0.842510 | − | 2.59298i | ||||
\(647\) | −10.4800 | − | 3.40516i | −0.412011 | − | 0.133870i | 0.0956751 | − | 0.995413i | \(-0.469499\pi\) |
−0.507686 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(648\) | 3.63920 | + | 5.00893i | 0.142961 | + | 0.196769i | ||||
\(649\) | −9.54248 | −0.374575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.884570 | −0.0346691 | ||||||||
\(652\) | 31.0840 | + | 42.7834i | 1.21734 | + | 1.67553i | ||||
\(653\) | −29.5646 | − | 9.60613i | −1.15695 | − | 0.375917i | −0.333195 | − | 0.942858i | \(-0.608127\pi\) |
−0.823758 | + | 0.566941i | \(0.808127\pi\) | |||||||
\(654\) | −1.81191 | + | 5.57650i | −0.0708515 | + | 0.218058i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.46021 | + | 7.57176i | 0.0960552 | + | 0.295628i | ||||
\(657\) | 11.3234i | 0.441767i | ||||||||
\(658\) | 8.25315 | − | 2.68161i | 0.321741 | − | 0.104540i | ||||
\(659\) | 26.2325 | + | 19.0590i | 1.02187 | + | 0.742435i | 0.966666 | − | 0.256040i | \(-0.0824178\pi\) |
0.0552080 | + | 0.998475i | \(0.482418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6268 | + | 9.17394i | −0.491128 | + | 0.356825i | −0.805618 | − | 0.592436i | \(-0.798166\pi\) |
0.314490 | + | 0.949261i | \(0.398166\pi\) | |||||||
\(662\) | 32.0061 | − | 44.0527i | 1.24395 | − | 1.71216i | ||||
\(663\) | −16.9400 | + | 23.3160i | −0.657897 | + | 0.905517i | ||||
\(664\) | −57.4806 | + | 41.7621i | −2.23068 | + | 1.62068i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.32102 | + | 2.41287i | 0.128687 | + | 0.0934966i | ||||
\(667\) | −2.49547 | + | 0.810827i | −0.0966249 | + | 0.0313953i | ||||
\(668\) | − | 47.0978i | − | 1.82227i | ||||||
\(669\) | 8.48115 | + | 26.1023i | 0.327900 | + | 1.00917i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97691 | + | 15.3173i | −0.192131 | + | 0.591320i | ||||
\(672\) | −4.90346 | − | 1.59323i | −0.189155 | − | 0.0614602i | ||||
\(673\) | −18.2373 | − | 25.1014i | −0.702995 | − | 0.967589i | −0.999919 | − | 0.0126883i | \(-0.995961\pi\) |
0.296925 | − | 0.954901i | \(-0.404039\pi\) | |||||||
\(674\) | −88.1870 | −3.39684 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 84.9778 | 3.26838 | ||||||||
\(677\) | −13.5716 | − | 18.6796i | −0.521597 | − | 0.717917i | 0.464224 | − | 0.885718i | \(-0.346333\pi\) |
−0.985821 | + | 0.167801i | \(0.946333\pi\) | |||||||
\(678\) | −9.34691 | − | 3.03700i | −0.358966 | − | 0.116635i | ||||
\(679\) | 1.93868 | − | 5.96663i | 0.0743995 | − | 0.228978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0402219 | + | 0.123790i | 0.00154131 | + | 0.00474365i | ||||
\(682\) | 6.40936i | 0.245427i | ||||||||
\(683\) | 39.3301 | − | 12.7791i | 1.50492 | − | 0.488979i | 0.563474 | − | 0.826134i | \(-0.309464\pi\) |
0.941449 | + | 0.337154i | \(0.109464\pi\) | |||||||
\(684\) | −19.2939 | − | 14.0178i | −0.737721 | − | 0.535986i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.5944 | − | 20.0485i | 1.05356 | − | 0.765457i | ||||
\(687\) | −1.66067 | + | 2.28571i | −0.0633584 | + | 0.0872053i | ||||
\(688\) | −22.8340 | + | 31.4283i | −0.870539 | + | 1.19819i | ||||
\(689\) | 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 | \(0.727091\pi\) | |||||||
\(692\) | −5.29239 | + | 1.71960i | −0.201186 | + | 0.0653694i | ||||
\(693\) | − | 3.09144i | − | 0.117434i | ||||||
\(694\) | −22.5250 | − | 69.3248i | −0.855037 | − | 2.63153i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.30042 | + | 4.00229i | −0.0492924 | + | 0.151707i | ||||
\(697\) | −5.63395 | − | 1.83058i | −0.213401 | − | 0.0693382i | ||||
\(698\) | −18.3220 | − | 25.2181i | −0.693498 | − | 0.954518i | ||||
\(699\) | −7.98709 | −0.302099 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2265 | −0.952791 | −0.476396 | − | 0.879231i | \(-0.658057\pi\) | ||||
−0.476396 | + | 0.879231i | \(0.658057\pi\) | |||||||
\(702\) | 8.45625 | + | 11.6390i | 0.319161 | + | 0.439287i | ||||
\(703\) | −8.26391 | − | 2.68511i | −0.311679 | − | 0.101271i | ||||
\(704\) | 1.00091 | − | 3.08048i | 0.0377231 | − | 0.116100i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.1556 | − | 65.1104i | −0.796203 | − | 2.45046i | ||||
\(707\) | − | 15.9627i | − | 0.600339i | ||||||
\(708\) | −13.5621 | + | 4.40658i | −0.509694 | + | 0.165610i | ||||
\(709\) | 1.26199 | + | 0.916889i | 0.0473950 | + | 0.0344345i | 0.611231 | − | 0.791453i | \(-0.290675\pi\) |
−0.563836 | + | 0.825887i | \(0.690675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17071 | − | 0.850569i | 0.0439050 | − | 0.0318988i | ||||
\(712\) | 33.0158 | − | 45.4423i | 1.23732 | − | 1.70302i | ||||
\(713\) | −1.92897 | + | 2.65500i | −0.0722404 | + | 0.0994304i | ||||
\(714\) | 10.8598 | − | 7.89012i | 0.406419 | − | 0.295280i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 74.7514 | + | 54.3100i | 2.79359 | + | 2.02966i | ||||
\(717\) | −18.1290 | + | 5.89045i | −0.677038 | + | 0.219983i | ||||
\(718\) | − | 41.6794i | − | 1.55546i | ||||||
\(719\) | −8.94304 | − | 27.5238i | −0.333519 | − | 1.02647i | −0.967447 | − | 0.253074i | \(-0.918558\pi\) |
0.633928 | − | 0.773392i | \(-0.281442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.87748 | + | 11.9336i | −0.144405 | + | 0.444432i | ||||
\(722\) | 23.7815 | + | 7.72709i | 0.885057 | + | 0.287572i | ||||
\(723\) | −12.4140 | − | 17.0864i | −0.461680 | − | 0.635448i | ||||
\(724\) | 30.7547 | 1.14299 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.51466 | 0.204668 | ||||||||
\(727\) | 21.7242 | + | 29.9008i | 0.805707 | + | 1.10896i | 0.991972 | + | 0.126461i | \(0.0403618\pi\) |
−0.186265 | + | 0.982500i | \(0.559638\pi\) | |||||||
\(728\) | −34.7355 | − | 11.2863i | −1.28739 | − | 0.418297i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.93229 | − | 27.4907i | −0.330372 | − | 1.01678i | ||||
\(732\) | 24.0678i | 0.889570i | ||||||||
\(733\) | −3.95793 | + | 1.28601i | −0.146189 | + | 0.0474998i | −0.381198 | − | 0.924494i | \(-0.624488\pi\) |
0.235008 | + | 0.971993i | \(0.424488\pi\) | |||||||
\(734\) | −61.3757 | − | 44.5921i | −2.26542 | − | 1.64592i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.4749 | + | 11.2432i | −0.570413 | + | 0.414429i | ||||
\(737\) | −1.62257 | + | 2.23328i | −0.0597682 | + | 0.0822638i | ||||
\(738\) | −1.73816 | + | 2.39237i | −0.0639824 | + | 0.0880642i | ||||
\(739\) | 15.3371 | − | 11.1431i | 0.564184 | − | 0.409904i | −0.268804 | − | 0.963195i | \(-0.586628\pi\) |
0.832988 | + | 0.553291i | \(0.186628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6366 | − | 17.8996i | −0.905050 | − | 0.657557i | ||||
\(742\) | −31.8587 | + | 10.3515i | −1.16957 | + | 0.380016i | ||||
\(743\) | 11.7060i | 0.429452i | 0.976674 | + | 0.214726i | \(0.0688859\pi\) | ||||
−0.976674 | + | 0.214726i | \(0.931114\pi\) | |||||||
\(744\) | 1.62647 | + | 5.00575i | 0.0596292 | + | 0.183520i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19.4718 | + | 59.9281i | −0.712915 | + | 2.19413i | ||||
\(747\) | −10.9140 | − | 3.54616i | −0.399321 | − | 0.129747i | ||||
\(748\) | −39.4146 | − | 54.2495i | −1.44114 | − | 1.98356i | ||||
\(749\) | −6.76126 | −0.247051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.95672 | −0.180873 | −0.0904367 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904367 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(752\) | −13.1976 | − | 18.1650i | −0.481268 | − | 0.662408i | ||||
\(753\) | 28.7432 | + | 9.33924i | 1.04746 | + | 0.340341i | ||||
\(754\) | −3.02174 | + | 9.29995i | −0.110045 | + | 0.338684i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.42758 | − | 4.39365i | −0.0519207 | − | 0.159795i | ||||
\(757\) | 18.6020i | 0.676101i | 0.941128 | + | 0.338051i | \(0.109768\pi\) | ||||
−0.941128 | + | 0.338051i | \(0.890232\pi\) | |||||||
\(758\) | 46.8132 | − | 15.2105i | 1.70033 | − | 0.552472i | ||||
\(759\) | −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 | \(0.233997\pi\) | |||||||
\(762\) | 17.4425 | − | 24.0075i | 0.631875 | − | 0.869702i | ||||
\(763\) | 1.41317 | − | 1.94507i | 0.0511603 | − | 0.0704161i | ||||
\(764\) | 29.3245 | − | 21.3055i | 1.06092 | − | 0.770806i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.0982 | + | 16.7818i | 0.834572 | + | 0.606352i | ||||
\(767\) | −17.3176 | + | 5.62682i | −0.625302 | + | 0.203173i | ||||
\(768\) | − | 29.9884i | − | 1.08211i | ||||||
\(769\) | −2.24803 | − | 6.91872i | −0.0810660 | − | 0.249495i | 0.902307 | − | 0.431095i | \(-0.141873\pi\) |
−0.983373 | + | 0.181599i | \(0.941873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.57665 | − | 4.85243i | 0.0567817 | − | 0.174756i | ||||
\(772\) | 58.9584 | + | 19.1567i | 2.12196 | + | 0.689466i | ||||
\(773\) | 5.47985 | + | 7.54237i | 0.197097 | + | 0.271280i | 0.896114 | − | 0.443825i | \(-0.146379\pi\) |
−0.699017 | + | 0.715105i | \(0.746379\pi\) | |||||||
\(774\) | −14.4292 | −0.518648 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.3296 | −1.34005 | ||||||||
\(777\) | −0.989360 | − | 1.36174i | −0.0354931 | − | 0.0488520i | ||||
\(778\) | −35.9649 | − | 11.6857i | −1.28941 | − | 0.418953i | ||||
\(779\) | 1.93427 | − | 5.95307i | 0.0693024 | − | 0.213291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29780 | − | 3.99421i | −0.0464389 | − | 0.142924i | ||||
\(782\) | − | 49.8011i | − | 1.78088i | ||||||
\(783\) | −0.646430 | + | 0.210038i | −0.0231015 | + | 0.00750614i | ||||
\(784\) | −32.7067 | − | 23.7628i | −1.16810 | − | 0.848671i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.3464 | + | 11.8763i | −0.583055 | + | 0.423615i | ||||
\(787\) | −8.73787 | + | 12.0266i | −0.311471 | + | 0.428704i | −0.935839 | − | 0.352427i | \(-0.885357\pi\) |
0.624368 | + | 0.781130i | \(0.285357\pi\) | |||||||
\(788\) | 15.0381 | − | 20.6981i | 0.535708 | − | 0.737339i | ||||
\(789\) | 5.19017 | − | 3.77088i | 0.184775 | − | 0.134247i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.26017 | + | 2.36865i | 0.115918 | + | 0.0842196i | ||||
\(792\) | −17.4943 | + | 5.68426i | −0.621634 | + | 0.201981i | ||||
\(793\) | 30.7324i | 1.09134i | ||||||||
\(794\) | −18.8962 | − | 58.1565i | −0.670600 | − | 2.06390i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.4598 | + | 112.212i | −1.29228 | + | 3.97724i | ||||
\(797\) | 9.10680 | + | 2.95898i | 0.322580 | + | 0.104812i | 0.465831 | − | 0.884874i | \(-0.345756\pi\) |
−0.143251 | + | 0.989686i | \(0.545756\pi\) | |||||||
\(798\) | 8.33704 | + | 11.4749i | 0.295128 | + | 0.406209i | ||||
\(799\) | 16.7068 | 0.591044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.07225 | 0.320552 | ||||||||
\(802\) | −20.0740 | − | 27.6295i | −0.708838 | − | 0.975632i | ||||
\(803\) | −31.9953 | − | 10.3959i | −1.12909 | − | 0.366863i | ||||
\(804\) | −1.27475 | + | 3.92328i | −0.0449570 | + | 0.138364i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.77935 | + | 11.6316i | 0.133122 | + | 0.409707i | ||||
\(807\) | 17.4592i | 0.614592i | ||||||||
\(808\) | −90.3323 | + | 29.3508i | −3.17788 | + | 1.03256i | ||||
\(809\) | 33.2859 | + | 24.1836i | 1.17027 | + | 0.850250i | 0.991041 | − | 0.133557i | \(-0.0426400\pi\) |
0.179228 | + | 0.983808i | \(0.442640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1435 | + | 25.5333i | −1.23406 | + | 0.896594i | −0.997187 | − | 0.0749479i | \(-0.976121\pi\) |
−0.236868 | + | 0.971542i | \(0.576121\pi\) | |||||||
\(812\) | 1.84566 | − | 2.54034i | 0.0647701 | − | 0.0891484i | ||||
\(813\) | −0.0559488 | + | 0.0770069i | −0.00196221 | + | 0.00270075i | ||||
\(814\) | −9.86679 | + | 7.16864i | −0.345831 | + | 0.251261i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −28.0987 | − | 20.4149i | −0.983651 | − | 0.714665i | ||||
\(817\) | 29.0479 | − | 9.43823i | 1.01626 | − | 0.330202i | ||||
\(818\) | 90.0206i | 3.14750i | ||||||||
\(819\) | −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 | \(0.00144114\pi\) | |||||||
\(822\) | −26.6720 | − | 8.66625i | −0.930292 | − | 0.302270i | ||||
\(823\) | 1.30756 | + | 1.79970i | 0.0455787 | + | 0.0627337i | 0.831198 | − | 0.555976i | \(-0.187656\pi\) |
−0.785619 | + | 0.618710i | \(0.787656\pi\) | |||||||
\(824\) | 74.6616 | 2.60096 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.48106 | 0.295094 | ||||||||
\(827\) | 18.4888 | + | 25.4476i | 0.642918 | + | 0.884900i | 0.998767 | − | 0.0496432i | \(-0.0158084\pi\) |
−0.355849 | + | 0.934543i | \(0.615808\pi\) | |||||||
\(828\) | −16.3004 | − | 5.29633i | −0.566479 | − | 0.184060i | ||||
\(829\) | −16.4690 | + | 50.6862i | −0.571990 | + | 1.76041i | 0.0742155 | + | 0.997242i | \(0.476355\pi\) |
−0.646206 | + | 0.763163i | \(0.723645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.68614 | − | 17.5001i | −0.197250 | − | 0.607073i | ||||
\(832\) | − | 6.18061i | − | 0.214274i | ||||||
\(833\) | 28.6089 | − | 9.29560i | 0.991240 | − | 0.322073i | ||||
\(834\) | 25.1903 | + | 18.3018i | 0.872267 | + | 0.633739i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 57.3223 | − | 41.6471i | 1.98253 | − | 1.44040i | ||||
\(837\) | −0.499683 | + | 0.687754i | −0.0172716 | + | 0.0237723i | ||||
\(838\) | −23.5853 | + | 32.4623i | −0.814739 | + | 1.12139i | ||||
\(839\) | −6.77415 | + | 4.92171i | −0.233870 | + | 0.169916i | −0.698548 | − | 0.715563i | \(-0.746170\pi\) |
0.464678 | + | 0.885480i | \(0.346170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0877 | + | 16.7742i | 0.796129 | + | 0.578421i | ||||
\(842\) | −28.9166 | + | 9.39558i | −0.996532 | + | 0.323793i | ||||
\(843\) | 17.9361i | 0.617750i | ||||||||
\(844\) | 36.3015 | + | 111.725i | 1.24955 | + | 3.84572i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.57715 | − | 7.93164i | 0.0886041 | − | 0.272695i | ||||
\(847\) | −2.15054 | − | 0.698751i | −0.0738933 | − | 0.0240094i | ||||
\(848\) | 50.9453 | + | 70.1202i | 1.74947 | + | 2.40794i | ||||
\(849\) | 22.2399 | 0.763273 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.24467 | −0.214064 | ||||||||
\(852\) | −3.68895 | − | 5.07740i | −0.126381 | − | 0.173949i | ||||
\(853\) | −1.16381 | − | 0.378146i | −0.0398482 | − | 0.0129475i | 0.289025 | − | 0.957322i | \(-0.406669\pi\) |
−0.328873 | + | 0.944374i | \(0.606669\pi\) | |||||||
\(854\) | 4.42332 | − | 13.6136i | 0.151363 | − | 0.465847i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4320 | + | 38.2618i | 0.424917 | + | 1.30776i | ||||
\(857\) | 14.3684i | 0.490816i | 0.969420 | + | 0.245408i | \(0.0789219\pi\) | ||||
−0.969420 | + | 0.245408i | \(0.921078\pi\) | |||||||
\(858\) | −40.6508 | + | 13.2082i | −1.38780 | + | 0.450922i | ||||
\(859\) | −8.34015 | − | 6.05947i | −0.284562 | − | 0.206747i | 0.436343 | − | 0.899781i | \(-0.356274\pi\) |
−0.720905 | + | 0.693034i | \(0.756274\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.980955 | − | 0.712705i | 0.0334308 | − | 0.0242889i | ||||
\(862\) | 21.8413 | − | 30.0619i | 0.743916 | − | 1.02391i | ||||
\(863\) | 17.7937 | − | 24.4909i | 0.605703 | − | 0.833679i | −0.390512 | − | 0.920598i | \(-0.627702\pi\) |
0.996215 | + | 0.0869190i | \(0.0277021\pi\) | |||||||
\(864\) | −4.00864 | + | 2.91245i | −0.136377 | + | 0.0990835i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.77241 | + | 6.37353i | 0.298099 | + | 0.216581i | ||||
\(867\) | 8.41031 | − | 2.73268i | 0.285629 | − | 0.0928065i | ||||
\(868\) | − | 3.92730i | − | 0.133301i | ||||||
\(869\) | 1.32855 | + | 4.08885i | 0.0450679 | + | 0.138705i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.62775 | + | 5.00969i | −0.0551541 | + | 0.169747i | ||||
\(872\) | −13.6055 | − | 4.42068i | −0.460739 | − | 0.149703i | ||||
\(873\) | −3.54392 | − | 4.87779i | −0.119944 | − | 0.165088i | ||||
\(874\) | 52.6220 | 1.77996 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.2734 | −1.69858 | ||||||||
\(877\) | 18.0065 | + | 24.7839i | 0.608037 | + | 0.836892i | 0.996414 | − | 0.0846091i | \(-0.0269641\pi\) |
−0.388377 | + | 0.921501i | \(0.626964\pi\) | |||||||
\(878\) | 49.0111 | + | 15.9247i | 1.65404 | + | 0.537431i | ||||
\(879\) | 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 | \(0.817461\pi\) | |||||||
\(882\) | − | 15.0161i | − | 0.505620i | ||||||
\(883\) | −38.2310 | + | 12.4220i | −1.28658 | + | 0.418034i | −0.870892 | − | 0.491475i | \(-0.836458\pi\) |
−0.415684 | + | 0.909509i | \(0.636458\pi\) | |||||||
\(884\) | −103.518 | − | 75.2102i | −3.48169 | − | 2.52959i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1189 | − | 28.4216i | 1.31423 | − | 0.954842i | ||||
\(887\) | 18.7169 | − | 25.7617i | 0.628453 | − | 0.864992i | −0.369481 | − | 0.929238i | \(-0.620464\pi\) |
0.997934 | + | 0.0642465i | \(0.0204644\pi\) | |||||||
\(888\) | −5.88688 | + | 8.10259i | −0.197551 | + | 0.271905i | ||||
\(889\) | −9.84394 | + | 7.15204i | −0.330155 | + | 0.239872i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.40360 | − | 1.74631i | −0.0805235 | − | 0.0585037i | ||||
\(892\) | −115.889 | + | 37.6545i | −3.88024 | + | 1.26077i | ||||
\(893\) | 17.6531i | 0.590739i | ||||||||
\(894\) | −3.62946 | − | 11.1703i | −0.121387 | − | 0.373591i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.07604 | + | 12.5448i | −0.136171 | + | 0.419091i | ||||
\(897\) | −20.8142 | − | 6.76296i | −0.694967 | − | 0.225809i | ||||
\(898\) | 43.9716 | + | 60.5217i | 1.46735 | + | 2.01964i | ||||
\(899\) | −0.577817 | −0.0192713 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.4914 | −2.14852 | ||||||||
\(902\) | −5.16407 | − | 7.10774i | −0.171945 | − | 0.236662i | ||||
\(903\) | 5.62692 | + | 1.82830i | 0.187252 | + | 0.0608419i | ||||
\(904\) | 7.40962 | − | 22.8045i | 0.246440 | − | 0.758465i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.66409 | + | 11.2769i | 0.121731 | + | 0.374651i | ||||
\(907\) | 28.8507i | 0.957970i | 0.877823 | + | 0.478985i | \(0.158995\pi\) | ||||
−0.877823 | + | 0.478985i | \(0.841005\pi\) | |||||||
\(908\) | −0.549602 | + | 0.178577i | −0.0182392 | + | 0.00592627i | ||||
\(909\) | −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 | \(0.595903\pi\) | |||||||
\(912\) | 21.5713 | − | 29.6903i | 0.714296 | − | 0.983143i | ||||
\(913\) | 20.0400 | − | 27.5827i | 0.663228 | − | 0.912855i | ||||
\(914\) | −58.1036 | + | 42.2148i | −1.92190 | + | 1.39634i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.1481 | − | 7.37301i | −0.335302 | − | 0.243611i | ||||
\(917\) | 7.87936 | − | 2.56016i | 0.260199 | − | 0.0845439i | ||||
\(918\) | − | 12.9006i | − | 0.425782i | ||||||
\(919\) | 2.58963 | + | 7.97006i | 0.0854240 | + | 0.262908i | 0.984640 | − | 0.174597i | \(-0.0558622\pi\) |
−0.899216 | + | 0.437505i | \(0.855862\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.17501 | + | 6.69401i | −0.0716692 | + | 0.220575i | ||||
\(922\) | −39.9609 | − | 12.9841i | −1.31604 | − | 0.427608i | ||||
\(923\) | −4.71046 | − | 6.48340i | −0.155047 | − | 0.213404i | ||||
\(924\) | 13.7253 | 0.451530 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.3703 | −0.767995 | ||||||||
\(927\) | 7.08808 | + | 9.75590i | 0.232803 | + | 0.320426i | ||||
\(928\) | −3.20303 | − | 1.04073i | −0.105145 | − | 0.0341636i | ||||
\(929\) | −4.42283 | + | 13.6121i | −0.145108 | + | 0.446597i | −0.997025 | − | 0.0770801i | \(-0.975440\pi\) |
0.851917 | + | 0.523677i | \(0.175440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.82212 | + | 30.2294i | 0.321907 | + | 0.990728i | ||||
\(932\) | − | 35.4610i | − | 1.16156i | ||||||
\(933\) | 27.8460 | − | 9.04771i | 0.911637 | − | 0.296209i | ||||
\(934\) | −21.7873 | − | 15.8294i | −0.712901 | − | 0.517953i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28.3967 | + | 20.6314i | −0.928177 | + | 0.674360i | ||||
\(937\) | 12.8869 | − | 17.7372i | 0.420996 | − | 0.579451i | −0.544862 | − | 0.838526i | \(-0.683418\pi\) |
0.965857 | + | 0.259075i | \(0.0834178\pi\) | |||||||
\(938\) | 1.44209 | − | 1.98487i | 0.0470859 | − | 0.0648082i | ||||
\(939\) | −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 | \(0.818932\pi\) | |||||||
\(942\) | −36.1360 | + | 11.7413i | −1.17737 | + | 0.382552i | ||||
\(943\) | − | 4.49847i | − | 0.146490i | ||||||
\(944\) | −6.78104 | − | 20.8699i | −0.220704 | − | 0.679257i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.2474 | − | 40.7712i | 0.430709 | − | 1.32559i | ||||
\(947\) | −41.4316 | − | 13.4619i | −1.34635 | − | 0.437454i | −0.454884 | − | 0.890550i | \(-0.650319\pi\) |
−0.891462 | + | 0.453096i | \(0.850319\pi\) | |||||||
\(948\) | 3.77635 | + | 5.19769i | 0.122650 | + | 0.168813i | ||||
\(949\) | −64.1947 | −2.08385 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.24144 | −0.202393 | ||||||||
\(952\) | 19.2502 | + | 26.4957i | 0.623903 | + | 0.858729i | ||||
\(953\) | 2.25561 | + | 0.732893i | 0.0730664 | + | 0.0237407i | 0.345322 | − | 0.938484i | \(-0.387770\pi\) |
−0.272256 | + | 0.962225i | \(0.587770\pi\) | |||||||
\(954\) | −9.94827 | + | 30.6176i | −0.322087 | + | 0.991282i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.1524 | − | 80.4887i | −0.845828 | − | 2.60319i | ||||
\(957\) | − | 2.01938i | − | 0.0652774i | ||||||
\(958\) | 81.1073 | − | 26.3534i | 2.62046 | − | 0.851439i | ||||
\(959\) | 9.30310 | + | 6.75910i | 0.300413 | + | 0.218263i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4949 | − | 17.7966i | 0.790157 | − | 0.574082i | ||||
\(962\) | −13.6791 | + | 18.8276i | −0.441031 | + | 0.607027i | ||||
\(963\) | −3.81935 | + | 5.25689i | −0.123077 | + | 0.169401i | ||||
\(964\) | 75.8598 | − | 55.1154i | 2.44328 | − | 1.77515i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.24672 | + | 5.99159i | 0.265334 | + | 0.192776i | ||||
\(967\) | −18.8174 | + | 6.11413i | −0.605125 | + | 0.196617i | −0.595525 | − | 0.803337i | \(-0.703056\pi\) |
−0.00960036 | + | 0.999954i | \(0.503056\pi\) | |||||||
\(968\) | 13.4546i | 0.432447i | ||||||||
\(969\) | 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 | \(-0.191169\pi\) | |||||||
\(972\) | −4.22249 | − | 1.37197i | −0.135436 | − | 0.0440059i | ||||
\(973\) | −7.50438 | − | 10.3289i | −0.240579 | − | 0.331129i | ||||
\(974\) | 74.2234 | 2.37827 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.0365 | −1.18551 | ||||||||
\(977\) | −28.0757 | − | 38.6429i | −0.898221 | − | 1.23630i | −0.971032 | − | 0.238949i | \(-0.923197\pi\) |
0.0728110 | − | 0.997346i | \(-0.476803\pi\) | |||||||
\(978\) | −28.7474 | − | 9.34058i | −0.919239 | − | 0.298679i | ||||
\(979\) | −8.32916 | + | 25.6345i | −0.266201 | + | 0.819283i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.714006 | − | 2.19749i | −0.0227965 | − | 0.0701603i | ||||
\(982\) | 35.4131i | 1.13008i | ||||||||
\(983\) | −49.3867 | + | 16.0467i | −1.57519 | + | 0.511810i | −0.960812 | − | 0.277201i | \(-0.910593\pi\) |
−0.614379 | + | 0.789011i | \(0.710593\pi\) | |||||||
\(984\) | −5.83686 | − | 4.24073i | −0.186072 | − | 0.135190i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.09383 | − | 5.15397i | 0.225914 | − | 0.164136i | ||||
\(987\) | −2.01000 | + | 2.76653i | −0.0639791 | + | 0.0880596i | ||||
\(988\) | 79.4703 | − | 109.381i | 2.52829 | − | 3.47989i | ||||
\(989\) | 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 | \(0.616229\pi\) | |||||||
\(992\) | −4.00610 | + | 1.30166i | −0.127194 | + | 0.0413277i | ||||
\(993\) | 21.4575i | 0.680933i | ||||||||
\(994\) | 1.15344 | + | 3.54994i | 0.0365850 | + | 0.112597i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.7442 | − | 48.4557i | 0.498874 | − | 1.53538i | ||||
\(997\) | 21.1625 | + | 6.87610i | 0.670222 | + | 0.217768i | 0.624309 | − | 0.781177i | \(-0.285380\pi\) |
0.0459126 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(998\) | −53.3299 | − | 73.4022i | −1.68813 | − | 2.32351i | ||||
\(999\) | −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.i.c.199.1 | 16 | ||
5.2 | odd | 4 | 375.2.g.e.301.4 | 16 | |||
5.3 | odd | 4 | 375.2.g.d.301.1 | 16 | |||
5.4 | even | 2 | 75.2.i.a.64.4 | yes | 16 | ||
15.14 | odd | 2 | 225.2.m.b.64.1 | 16 | |||
25.3 | odd | 20 | 1875.2.a.p.1.8 | 8 | |||
25.4 | even | 10 | 1875.2.b.h.1249.1 | 16 | |||
25.9 | even | 10 | inner | 375.2.i.c.49.1 | 16 | ||
25.12 | odd | 20 | 375.2.g.e.76.4 | 16 | |||
25.13 | odd | 20 | 375.2.g.d.76.1 | 16 | |||
25.16 | even | 5 | 75.2.i.a.34.4 | ✓ | 16 | ||
25.21 | even | 5 | 1875.2.b.h.1249.16 | 16 | |||
25.22 | odd | 20 | 1875.2.a.m.1.1 | 8 | |||
75.41 | odd | 10 | 225.2.m.b.109.1 | 16 | |||
75.47 | even | 20 | 5625.2.a.bd.1.8 | 8 | |||
75.53 | even | 20 | 5625.2.a.t.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.34.4 | ✓ | 16 | 25.16 | even | 5 | ||
75.2.i.a.64.4 | yes | 16 | 5.4 | even | 2 | ||
225.2.m.b.64.1 | 16 | 15.14 | odd | 2 | |||
225.2.m.b.109.1 | 16 | 75.41 | odd | 10 | |||
375.2.g.d.76.1 | 16 | 25.13 | odd | 20 | |||
375.2.g.d.301.1 | 16 | 5.3 | odd | 4 | |||
375.2.g.e.76.4 | 16 | 25.12 | odd | 20 | |||
375.2.g.e.301.4 | 16 | 5.2 | odd | 4 | |||
375.2.i.c.49.1 | 16 | 25.9 | even | 10 | inner | ||
375.2.i.c.199.1 | 16 | 1.1 | even | 1 | trivial | ||
1875.2.a.m.1.1 | 8 | 25.22 | odd | 20 | |||
1875.2.a.p.1.8 | 8 | 25.3 | odd | 20 | |||
1875.2.b.h.1249.1 | 16 | 25.4 | even | 10 | |||
1875.2.b.h.1249.16 | 16 | 25.21 | even | 5 | |||
5625.2.a.t.1.1 | 8 | 75.53 | even | 20 | |||
5625.2.a.bd.1.8 | 8 | 75.47 | even | 20 |