Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [250,2,Mod(51,250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(250, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("250.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.d (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: | \(1.99626005053\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 50) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(-0.983224 - 0.644389i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 250.101 |
Dual form | 250.2.d.d.151.2 |
$q$-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 \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).
\(n\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | 2.39991 | + | 1.74363i | 1.38559 | + | 1.00669i | 0.996333 | + | 0.0855571i | \(0.0272670\pi\) |
0.389254 | + | 0.921131i | \(0.372733\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.39991 | + | 1.74363i | −0.979758 | + | 0.711836i | ||||
\(7\) | −1.83337 | −0.692947 | −0.346474 | − | 0.938060i | \(-0.612621\pi\) | ||||
−0.346474 | + | 0.938060i | \(0.612621\pi\) | |||||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 1.79224 | + | 5.51595i | 0.597414 | + | 1.83865i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.566541 | + | 1.74363i | −0.170819 | + | 0.525726i | −0.999418 | − | 0.0341166i | \(-0.989138\pi\) |
0.828599 | + | 0.559842i | \(0.189138\pi\) | |||||||
\(12\) | −0.916683 | − | 2.82126i | −0.264624 | − | 0.814428i | ||||
\(13\) | 0.747156 | + | 2.29951i | 0.207224 | + | 0.637769i | 0.999615 | + | 0.0277557i | \(0.00883604\pi\) |
−0.792391 | + | 0.610014i | \(0.791164\pi\) | |||||||
\(14\) | 0.566541 | − | 1.74363i | 0.151414 | − | 0.466006i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 2.25284 | − | 1.63679i | 0.546395 | − | 0.396979i | −0.280060 | − | 0.959983i | \(-0.590354\pi\) |
0.826455 | + | 0.563003i | \(0.190354\pi\) | |||||||
\(18\) | −5.79981 | −1.36703 | ||||||||
\(19\) | 1.35294 | − | 0.982966i | 0.310385 | − | 0.225508i | −0.421677 | − | 0.906746i | \(-0.638558\pi\) |
0.732062 | + | 0.681238i | \(0.238558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.39991 | − | 3.19672i | −0.960138 | − | 0.697581i | ||||
\(22\) | −1.48322 | − | 1.07763i | −0.316224 | − | 0.229750i | ||||
\(23\) | 2.39991 | − | 7.38615i | 0.500415 | − | 1.54012i | −0.307929 | − | 0.951409i | \(-0.599636\pi\) |
0.808344 | − | 0.588710i | \(-0.200364\pi\) | |||||||
\(24\) | 2.96645 | 0.605524 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.41785 | −0.474179 | ||||||||
\(27\) | −2.56654 | + | 7.89900i | −0.493931 | + | 1.52016i | ||||
\(28\) | 1.48322 | + | 1.07763i | 0.280303 | + | 0.203652i | ||||
\(29\) | −6.13597 | − | 4.45805i | −1.13942 | − | 0.827838i | −0.152383 | − | 0.988321i | \(-0.548695\pi\) |
−0.987039 | + | 0.160483i | \(0.948695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.28304 | − | 3.11181i | 0.769256 | − | 0.558897i | −0.132479 | − | 0.991186i | \(-0.542294\pi\) |
0.901735 | + | 0.432288i | \(0.142294\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.39991 | + | 3.19672i | −0.765925 | + | 0.556477i | ||||
\(34\) | 0.860510 | + | 2.64838i | 0.147576 | + | 0.454193i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.79224 | − | 5.51595i | 0.298707 | − | 0.919325i | ||||
\(37\) | 0.406315 | + | 1.25051i | 0.0667977 | + | 0.205582i | 0.978884 | − | 0.204416i | \(-0.0655294\pi\) |
−0.912086 | + | 0.409998i | \(0.865529\pi\) | |||||||
\(38\) | 0.516776 | + | 1.59047i | 0.0838321 | + | 0.258009i | ||||
\(39\) | −2.21640 | + | 6.82138i | −0.354908 | + | 1.09229i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08621 | + | 3.34301i | 0.169637 | + | 0.522090i | 0.999348 | − | 0.0361034i | \(-0.0114946\pi\) |
−0.829711 | + | 0.558194i | \(0.811495\pi\) | |||||||
\(42\) | 4.39991 | − | 3.19672i | 0.678920 | − | 0.493265i | ||||
\(43\) | 4.30550 | 0.656583 | 0.328291 | − | 0.944576i | \(-0.393527\pi\) | ||||
0.328291 | + | 0.944576i | \(0.393527\pi\) | |||||||
\(44\) | 1.48322 | − | 1.07763i | 0.223604 | − | 0.162458i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.28304 | + | 4.56489i | 0.926383 | + | 0.673057i | ||||
\(47\) | 1.48322 | + | 1.07763i | 0.216350 | + | 0.157188i | 0.690682 | − | 0.723158i | \(-0.257310\pi\) |
−0.474332 | + | 0.880346i | \(0.657310\pi\) | |||||||
\(48\) | −0.916683 | + | 2.82126i | −0.132312 | + | 0.407214i | ||||
\(49\) | −3.63877 | −0.519824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.26057 | 1.15671 | ||||||||
\(52\) | 0.747156 | − | 2.29951i | 0.103612 | − | 0.318885i | ||||
\(53\) | −5.27267 | − | 3.83082i | −0.724257 | − | 0.526203i | 0.163485 | − | 0.986546i | \(-0.447727\pi\) |
−0.887741 | + | 0.460342i | \(0.847727\pi\) | |||||||
\(54\) | −6.71929 | − | 4.88185i | −0.914380 | − | 0.664336i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.48322 | + | 1.07763i | −0.198204 | + | 0.144004i | ||||
\(57\) | 4.96086 | 0.657082 | ||||||||
\(58\) | 6.13597 | − | 4.45805i | 0.805693 | − | 0.585370i | ||||
\(59\) | −2.79981 | − | 8.61694i | −0.364505 | − | 1.12183i | −0.950291 | − | 0.311364i | \(-0.899214\pi\) |
0.585786 | − | 0.810466i | \(-0.300786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.799717 | − | 2.46127i | 0.102393 | − | 0.315134i | −0.886717 | − | 0.462313i | \(-0.847019\pi\) |
0.989110 | + | 0.147180i | \(0.0470195\pi\) | |||||||
\(62\) | 1.63597 | + | 5.03501i | 0.207769 | + | 0.639447i | ||||
\(63\) | −3.28583 | − | 10.1128i | −0.413976 | − | 1.27409i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.68061 | − | 5.17240i | −0.206869 | − | 0.636679i | ||||
\(67\) | 7.68574 | − | 5.58402i | 0.938963 | − | 0.682196i | −0.00920814 | − | 0.999958i | \(-0.502931\pi\) |
0.948171 | + | 0.317761i | \(0.102931\pi\) | |||||||
\(68\) | −2.78467 | −0.337691 | ||||||||
\(69\) | 18.6383 | − | 13.5415i | 2.24379 | − | 1.63021i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.247156 | − | 0.179569i | −0.0293320 | − | 0.0213110i | 0.573023 | − | 0.819540i | \(-0.305771\pi\) |
−0.602355 | + | 0.798229i | \(0.705771\pi\) | |||||||
\(72\) | 4.69215 | + | 3.40904i | 0.552975 | + | 0.401760i | ||||
\(73\) | −4.61920 | + | 14.2164i | −0.540636 | + | 1.66391i | 0.190509 | + | 0.981685i | \(0.438986\pi\) |
−0.731145 | + | 0.682222i | \(0.761014\pi\) | |||||||
\(74\) | −1.31486 | −0.152850 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.67232 | −0.191829 | ||||||||
\(77\) | 1.03868 | − | 3.19672i | 0.118368 | − | 0.364300i | ||||
\(78\) | −5.80261 | − | 4.21584i | −0.657016 | − | 0.477350i | ||||
\(79\) | 2.79981 | + | 2.03418i | 0.315004 | + | 0.228864i | 0.734041 | − | 0.679106i | \(-0.237632\pi\) |
−0.419037 | + | 0.907969i | \(0.637632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.85599 | + | 4.25462i | −0.650665 | + | 0.472736i | ||||
\(82\) | −3.51505 | −0.388172 | ||||||||
\(83\) | −5.15555 | + | 3.74572i | −0.565895 | + | 0.411147i | −0.833612 | − | 0.552351i | \(-0.813731\pi\) |
0.267717 | + | 0.963498i | \(0.413731\pi\) | |||||||
\(84\) | 1.68061 | + | 5.17240i | 0.183370 | + | 0.564355i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.33047 | + | 4.09478i | −0.143469 | + | 0.441551i | ||||
\(87\) | −6.95256 | − | 21.3978i | −0.745393 | − | 2.29408i | ||||
\(88\) | 0.566541 | + | 1.74363i | 0.0603935 | + | 0.185872i | ||||
\(89\) | −1.02608 | + | 3.15794i | −0.108764 | + | 0.334741i | −0.990595 | − | 0.136824i | \(-0.956311\pi\) |
0.881832 | + | 0.471565i | \(0.156311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.36981 | − | 4.21584i | −0.143595 | − | 0.441940i | ||||
\(92\) | −6.28304 | + | 4.56489i | −0.655052 | + | 0.475923i | ||||
\(93\) | 15.7047 | 1.62851 | ||||||||
\(94\) | −1.48322 | + | 1.07763i | −0.152983 | + | 0.111149i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.39991 | − | 1.74363i | −0.244939 | − | 0.177959i | ||||
\(97\) | 8.97214 | + | 6.51864i | 0.910982 | + | 0.661867i | 0.941263 | − | 0.337674i | \(-0.109640\pi\) |
−0.0302807 | + | 0.999541i | \(0.509640\pi\) | |||||||
\(98\) | 1.12444 | − | 3.46068i | 0.113586 | − | 0.349581i | ||||
\(99\) | −10.6332 | −1.06867 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1807 | −1.31152 | −0.655762 | − | 0.754968i | \(-0.727653\pi\) | ||||
−0.655762 | + | 0.754968i | \(0.727653\pi\) | |||||||
\(102\) | −2.55266 | + | 7.85627i | −0.252751 | + | 0.777887i | ||||
\(103\) | −2.13029 | − | 1.54774i | −0.209903 | − | 0.152504i | 0.477867 | − | 0.878432i | \(-0.341410\pi\) |
−0.687770 | + | 0.725929i | \(0.741410\pi\) | |||||||
\(104\) | 1.95608 | + | 1.42118i | 0.191809 | + | 0.139358i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.27267 | − | 3.83082i | 0.512127 | − | 0.372082i | ||||
\(107\) | −18.8045 | −1.81790 | −0.908949 | − | 0.416908i | \(-0.863114\pi\) | ||||
−0.908949 | + | 0.416908i | \(0.863114\pi\) | |||||||
\(108\) | 6.71929 | − | 4.88185i | 0.646564 | − | 0.469756i | ||||
\(109\) | 3.18574 | + | 9.80470i | 0.305139 | + | 0.939120i | 0.979625 | + | 0.200833i | \(0.0643649\pi\) |
−0.674487 | + | 0.738287i | \(0.735635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.20531 | + | 3.70957i | −0.114403 | + | 0.352097i | ||||
\(112\) | −0.566541 | − | 1.74363i | −0.0535331 | − | 0.164758i | ||||
\(113\) | −1.87160 | − | 5.76019i | −0.176065 | − | 0.541873i | 0.823615 | − | 0.567149i | \(-0.191954\pi\) |
−0.999681 | + | 0.0252760i | \(0.991954\pi\) | |||||||
\(114\) | −1.53299 | + | 4.71806i | −0.143578 | + | 0.441886i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.34373 | + | 7.21327i | 0.217610 | + | 0.669735i | ||||
\(117\) | −11.3449 | + | 8.24255i | −1.04884 | + | 0.762024i | ||||
\(118\) | 9.06039 | 0.834076 | ||||||||
\(119\) | −4.13029 | + | 3.00083i | −0.378623 | + | 0.275086i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.17989 | + | 4.48996i | 0.561809 | + | 0.408178i | ||||
\(122\) | 2.09369 | + | 1.52115i | 0.189553 | + | 0.137719i | ||||
\(123\) | −3.22218 | + | 9.91686i | −0.290535 | + | 0.894174i | ||||
\(124\) | −5.29413 | −0.475427 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.6332 | 0.947279 | ||||||||
\(127\) | −0.102986 | + | 0.316957i | −0.00913850 | + | 0.0281254i | −0.955522 | − | 0.294921i | \(-0.904707\pi\) |
0.946383 | + | 0.323046i | \(0.104707\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 10.3328 | + | 7.50722i | 0.909753 | + | 0.660974i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.18910 | − | 3.04356i | 0.366003 | − | 0.265917i | −0.389548 | − | 0.921006i | \(-0.627369\pi\) |
0.755552 | + | 0.655089i | \(0.227369\pi\) | |||||||
\(132\) | 5.43858 | 0.473368 | ||||||||
\(133\) | −2.48043 | + | 1.80214i | −0.215080 | + | 0.156265i | ||||
\(134\) | 2.93569 | + | 9.03513i | 0.253605 | + | 0.780516i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.860510 | − | 2.64838i | 0.0737881 | − | 0.227096i | ||||
\(137\) | 6.03299 | + | 18.5676i | 0.515433 | + | 1.58634i | 0.782493 | + | 0.622660i | \(0.213948\pi\) |
−0.267060 | + | 0.963680i | \(0.586052\pi\) | |||||||
\(138\) | 7.11920 | + | 21.9106i | 0.606026 | + | 1.86516i | ||||
\(139\) | −2.45825 | + | 7.56572i | −0.208506 | + | 0.641716i | 0.791045 | + | 0.611758i | \(0.209537\pi\) |
−0.999551 | + | 0.0299582i | \(0.990463\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.68061 | + | 5.17240i | 0.141533 | + | 0.435595i | ||||
\(142\) | 0.247156 | − | 0.179569i | 0.0207409 | − | 0.0150691i | ||||
\(143\) | −4.43280 | −0.370689 | ||||||||
\(144\) | −4.69215 | + | 3.40904i | −0.391012 | + | 0.284087i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0932 | − | 8.78624i | −1.00084 | − | 0.727154i | ||||
\(147\) | −8.73271 | − | 6.34468i | −0.720262 | − | 0.523301i | ||||
\(148\) | 0.406315 | − | 1.25051i | 0.0333989 | − | 0.102791i | ||||
\(149\) | −1.67955 | −0.137594 | −0.0687969 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687969 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2664 | −1.73063 | −0.865316 | − | 0.501227i | \(-0.832882\pi\) | ||||
−0.865316 | + | 0.501227i | \(0.832882\pi\) | |||||||
\(152\) | 0.516776 | − | 1.59047i | 0.0419161 | − | 0.129004i | ||||
\(153\) | 13.0661 | + | 9.49306i | 1.05633 | + | 0.767468i | ||||
\(154\) | 2.71929 | + | 1.97568i | 0.219127 | + | 0.159205i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.80261 | − | 4.21584i | 0.464581 | − | 0.337538i | ||||
\(157\) | −10.4514 | −0.834113 | −0.417056 | − | 0.908881i | \(-0.636938\pi\) | ||||
−0.417056 | + | 0.908881i | \(0.636938\pi\) | |||||||
\(158\) | −2.79981 | + | 2.03418i | −0.222741 | + | 0.161831i | ||||
\(159\) | −5.97437 | − | 18.3872i | −0.473798 | − | 1.45820i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.39991 | + | 13.5415i | −0.346761 | + | 1.06722i | ||||
\(162\) | −2.23679 | − | 6.88413i | −0.175739 | − | 0.540868i | ||||
\(163\) | −3.21706 | − | 9.90109i | −0.251980 | − | 0.775513i | −0.994410 | − | 0.105590i | \(-0.966327\pi\) |
0.742430 | − | 0.669923i | \(-0.233673\pi\) | |||||||
\(164\) | 1.08621 | − | 3.34301i | 0.0848187 | − | 0.261045i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.96924 | − | 6.06071i | −0.152843 | − | 0.470402i | ||||
\(167\) | 1.71650 | − | 1.24711i | 0.132826 | − | 0.0965041i | −0.519388 | − | 0.854538i | \(-0.673840\pi\) |
0.652215 | + | 0.758034i | \(0.273840\pi\) | |||||||
\(168\) | −5.43858 | −0.419596 | ||||||||
\(169\) | 5.78772 | − | 4.20502i | 0.445209 | − | 0.323463i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.84678 | + | 5.70102i | 0.600059 | + | 0.435968i | ||||
\(172\) | −3.48322 | − | 2.53071i | −0.265593 | − | 0.192965i | ||||
\(173\) | 5.59774 | − | 17.2281i | 0.425588 | − | 1.30983i | −0.476841 | − | 0.878989i | \(-0.658218\pi\) |
0.902430 | − | 0.430837i | \(-0.141782\pi\) | |||||||
\(174\) | 22.4990 | 1.70564 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.83337 | −0.138195 | ||||||||
\(177\) | 8.30550 | − | 25.5617i | 0.624280 | − | 1.92134i | ||||
\(178\) | −2.68630 | − | 1.95171i | −0.201347 | − | 0.146287i | ||||
\(179\) | −8.54361 | − | 6.20730i | −0.638579 | − | 0.463955i | 0.220782 | − | 0.975323i | \(-0.429139\pi\) |
−0.859362 | + | 0.511368i | \(0.829139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6886 | + | 10.6719i | −1.09180 | + | 0.793237i | −0.979702 | − | 0.200460i | \(-0.935756\pi\) |
−0.112096 | + | 0.993697i | \(0.535756\pi\) | |||||||
\(182\) | 4.43280 | 0.328581 | ||||||||
\(183\) | 6.21081 | − | 4.51242i | 0.459116 | − | 0.333567i | ||||
\(184\) | −2.39991 | − | 7.38615i | −0.176923 | − | 0.544514i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.85303 | + | 14.9361i | −0.355842 | + | 1.09517i | ||||
\(187\) | 1.57763 | + | 4.85544i | 0.115368 | + | 0.355065i | ||||
\(188\) | −0.566541 | − | 1.74363i | −0.0413193 | − | 0.127168i | ||||
\(189\) | 4.70541 | − | 14.4818i | 0.342268 | − | 1.05339i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76906 | − | 20.8330i | −0.489792 | − | 1.50742i | −0.824919 | − | 0.565251i | \(-0.808779\pi\) |
0.335127 | − | 0.942173i | \(-0.391221\pi\) | |||||||
\(192\) | 2.39991 | − | 1.74363i | 0.173198 | − | 0.125836i | ||||
\(193\) | −27.4248 | −1.97408 | −0.987041 | − | 0.160465i | \(-0.948700\pi\) | ||||
−0.987041 | + | 0.160465i | \(0.948700\pi\) | |||||||
\(194\) | −8.97214 | + | 6.51864i | −0.644162 | + | 0.468011i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.94383 | + | 2.13882i | 0.210273 | + | 0.152773i | ||||
\(197\) | −0.909110 | − | 0.660507i | −0.0647714 | − | 0.0470592i | 0.554928 | − | 0.831898i | \(-0.312746\pi\) |
−0.619700 | + | 0.784839i | \(0.712746\pi\) | |||||||
\(198\) | 3.28583 | − | 10.1128i | 0.233514 | − | 0.718682i | ||||
\(199\) | 25.4992 | 1.80759 | 0.903794 | − | 0.427968i | \(-0.140770\pi\) | ||||
0.903794 | + | 0.427968i | \(0.140770\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.1815 | 1.98777 | ||||||||
\(202\) | 4.07305 | − | 12.5355i | 0.286579 | − | 0.881998i | ||||
\(203\) | 11.2495 | + | 8.17323i | 0.789559 | + | 0.573648i | ||||
\(204\) | −6.68294 | − | 4.85544i | −0.467900 | − | 0.339949i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.13029 | − | 1.54774i | 0.148424 | − | 0.107836i | ||||
\(207\) | 45.0429 | 3.13070 | ||||||||
\(208\) | −1.95608 | + | 1.42118i | −0.135630 | + | 0.0985408i | ||||
\(209\) | 0.947439 | + | 2.91592i | 0.0655358 | + | 0.201698i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58341 | − | 20.2617i | 0.453221 | − | 1.39487i | −0.419990 | − | 0.907529i | \(-0.637967\pi\) |
0.873211 | − | 0.487342i | \(-0.162033\pi\) | |||||||
\(212\) | 2.01398 | + | 6.19839i | 0.138321 | + | 0.425708i | ||||
\(213\) | −0.280048 | − | 0.861899i | −0.0191886 | − | 0.0590564i | ||||
\(214\) | 5.81090 | − | 17.8841i | 0.397225 | − | 1.22253i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.56654 | + | 7.89900i | 0.174631 | + | 0.537459i | ||||
\(217\) | −7.85237 | + | 5.70508i | −0.533054 | + | 0.387286i | ||||
\(218\) | −10.3093 | −0.698232 | ||||||||
\(219\) | −35.8739 | + | 26.0639i | −2.42413 | + | 1.76124i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.44703 | + | 3.95750i | 0.366407 | + | 0.266210i | ||||
\(222\) | −3.15555 | − | 2.29264i | −0.211786 | − | 0.153872i | ||||
\(223\) | −1.00280 | + | 3.08629i | −0.0671522 | + | 0.206673i | −0.979002 | − | 0.203851i | \(-0.934654\pi\) |
0.911850 | + | 0.410524i | \(0.134654\pi\) | |||||||
\(224\) | 1.83337 | 0.122497 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.05662 | 0.402880 | ||||||||
\(227\) | −5.06085 | + | 15.5757i | −0.335901 | + | 1.03380i | 0.630376 | + | 0.776290i | \(0.282901\pi\) |
−0.966277 | + | 0.257506i | \(0.917099\pi\) | |||||||
\(228\) | −4.01342 | − | 2.91592i | −0.265795 | − | 0.193111i | ||||
\(229\) | 4.11788 | + | 2.99181i | 0.272117 | + | 0.197705i | 0.715472 | − | 0.698642i | \(-0.246212\pi\) |
−0.443355 | + | 0.896346i | \(0.646212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.06664 | − | 5.86076i | 0.530746 | − | 0.385609i | ||||
\(232\) | −7.58448 | −0.497946 | ||||||||
\(233\) | −1.34536 | + | 0.977464i | −0.0881378 | + | 0.0640358i | −0.630981 | − | 0.775798i | \(-0.717348\pi\) |
0.542844 | + | 0.839834i | \(0.317348\pi\) | |||||||
\(234\) | −4.33337 | − | 13.3367i | −0.283281 | − | 0.871849i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.79981 | + | 8.61694i | −0.182252 | + | 0.560915i | ||||
\(237\) | 3.17242 | + | 9.76370i | 0.206071 | + | 0.634221i | ||||
\(238\) | −1.57763 | − | 4.85544i | −0.102263 | − | 0.314732i | ||||
\(239\) | 3.95536 | − | 12.1733i | 0.255851 | − | 0.787428i | −0.737810 | − | 0.675009i | \(-0.764140\pi\) |
0.993661 | − | 0.112420i | \(-0.0358601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.122209 | + | 0.376121i | 0.00787219 | + | 0.0242281i | 0.954915 | − | 0.296878i | \(-0.0959454\pi\) |
−0.947043 | + | 0.321106i | \(0.895945\pi\) | |||||||
\(242\) | −6.17989 | + | 4.48996i | −0.397259 | + | 0.288625i | ||||
\(243\) | 3.44417 | 0.220944 | ||||||||
\(244\) | −2.09369 | + | 1.52115i | −0.134034 | + | 0.0973817i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.43579 | − | 6.12896i | −0.537846 | − | 0.390768i | ||||
\(247\) | 3.27120 | + | 2.37666i | 0.208141 | + | 0.151223i | ||||
\(248\) | 1.63597 | − | 5.03501i | 0.103885 | − | 0.319724i | ||||
\(249\) | −18.9040 | −1.19799 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.36589 | 0.591170 | 0.295585 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295585 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(252\) | −3.28583 | + | 10.1128i | −0.206988 | + | 0.637044i | ||||
\(253\) | 11.5191 | + | 8.36912i | 0.724200 | + | 0.526162i | ||||
\(254\) | −0.269620 | − | 0.195890i | −0.0169175 | − | 0.0122913i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 4.97926 | 0.310598 | 0.155299 | − | 0.987868i | \(-0.450366\pi\) | ||||
0.155299 | + | 0.987868i | \(0.450366\pi\) | |||||||
\(258\) | −10.3328 | + | 7.50722i | −0.643292 | + | 0.467379i | ||||
\(259\) | −0.744923 | − | 2.29264i | −0.0462873 | − | 0.142458i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.5932 | − | 41.8356i | 0.841399 | − | 2.58956i | ||||
\(262\) | 1.60009 | + | 4.92458i | 0.0988541 | + | 0.304242i | ||||
\(263\) | 6.12199 | + | 18.8416i | 0.377498 | + | 1.16182i | 0.941778 | + | 0.336236i | \(0.109154\pi\) |
−0.564279 | + | 0.825584i | \(0.690846\pi\) | |||||||
\(264\) | −1.68061 | + | 5.17240i | −0.103435 | + | 0.318339i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.947439 | − | 2.91592i | −0.0580912 | − | 0.178786i | ||||
\(267\) | −7.96878 | + | 5.78966i | −0.487681 | + | 0.354321i | ||||
\(268\) | −9.50010 | −0.580311 | ||||||||
\(269\) | −11.9685 | + | 8.69564i | −0.729734 | + | 0.530183i | −0.889479 | − | 0.456976i | \(-0.848933\pi\) |
0.159745 | + | 0.987158i | \(0.448933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1583 | + | 7.38047i | 0.617075 | + | 0.448331i | 0.851899 | − | 0.523707i | \(-0.175451\pi\) |
−0.234823 | + | 0.972038i | \(0.575451\pi\) | |||||||
\(272\) | 2.25284 | + | 1.63679i | 0.136599 | + | 0.0992448i | ||||
\(273\) | 4.06347 | − | 12.5061i | 0.245932 | − | 0.756902i | ||||
\(274\) | −19.5232 | −1.17944 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −23.0382 | −1.38674 | ||||||||
\(277\) | 1.95664 | − | 6.02193i | 0.117563 | − | 0.361823i | −0.874910 | − | 0.484286i | \(-0.839079\pi\) |
0.992473 | + | 0.122463i | \(0.0390794\pi\) | |||||||
\(278\) | −6.43579 | − | 4.67587i | −0.385993 | − | 0.280440i | ||||
\(279\) | 24.8408 | + | 18.0479i | 1.48718 | + | 1.08050i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2525 | − | 11.8082i | 0.969545 | − | 0.704416i | 0.0141971 | − | 0.999899i | \(-0.495481\pi\) |
0.955348 | + | 0.295484i | \(0.0954808\pi\) | |||||||
\(282\) | −5.43858 | −0.323863 | ||||||||
\(283\) | 1.46981 | − | 1.06788i | 0.0873709 | − | 0.0634787i | −0.543242 | − | 0.839576i | \(-0.682803\pi\) |
0.630613 | + | 0.776097i | \(0.282803\pi\) | |||||||
\(284\) | 0.0944052 | + | 0.290549i | 0.00560192 | + | 0.0172409i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.36981 | − | 4.21584i | 0.0809986 | − | 0.249288i | ||||
\(287\) | −1.99142 | − | 6.12896i | −0.117550 | − | 0.361781i | ||||
\(288\) | −1.79224 | − | 5.51595i | −0.105609 | − | 0.325031i | ||||
\(289\) | −2.85705 | + | 8.79311i | −0.168062 | + | 0.517242i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.1662 | + | 31.2882i | 0.595951 | + | 1.83415i | ||||
\(292\) | 12.0932 | − | 8.78624i | 0.707702 | − | 0.514176i | ||||
\(293\) | 6.85931 | 0.400725 | 0.200363 | − | 0.979722i | \(-0.435788\pi\) | ||||
0.200363 | + | 0.979722i | \(0.435788\pi\) | |||||||
\(294\) | 8.73271 | − | 6.34468i | 0.509302 | − | 0.370030i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.06375 | + | 0.772856i | 0.0618290 | + | 0.0449214i | ||||
\(297\) | −12.3189 | − | 8.95022i | −0.714816 | − | 0.519344i | ||||
\(298\) | 0.519009 | − | 1.59734i | 0.0300654 | − | 0.0925317i | ||||
\(299\) | 18.7776 | 1.08594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.89356 | −0.454977 | ||||||||
\(302\) | 6.57167 | − | 20.2255i | 0.378157 | − | 1.16385i | ||||
\(303\) | −31.6323 | − | 22.9822i | −1.81723 | − | 1.32030i | ||||
\(304\) | 1.35294 | + | 0.982966i | 0.0775963 | + | 0.0563770i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.0661 | + | 9.49306i | −0.746938 | + | 0.542682i | ||||
\(307\) | 2.89526 | 0.165241 | 0.0826206 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826206 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(308\) | −2.71929 | + | 1.97568i | −0.154946 | + | 0.112575i | ||||
\(309\) | −2.41379 | − | 7.42888i | −0.137316 | − | 0.422614i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.38090 | + | 19.6384i | −0.361828 | + | 1.11359i | 0.590116 | + | 0.807318i | \(0.299082\pi\) |
−0.951944 | + | 0.306272i | \(0.900918\pi\) | |||||||
\(312\) | 2.21640 | + | 6.82138i | 0.125479 | + | 0.386184i | ||||
\(313\) | −5.07629 | − | 15.6232i | −0.286929 | − | 0.883076i | −0.985814 | − | 0.167842i | \(-0.946320\pi\) |
0.698885 | − | 0.715234i | \(-0.253680\pi\) | |||||||
\(314\) | 3.22966 | − | 9.93987i | 0.182260 | − | 0.560939i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.06943 | − | 3.29138i | −0.0601603 | − | 0.185154i | ||||
\(317\) | 13.3535 | − | 9.70191i | 0.750009 | − | 0.544914i | −0.145820 | − | 0.989311i | \(-0.546582\pi\) |
0.895830 | + | 0.444397i | \(0.146582\pi\) | |||||||
\(318\) | 19.3335 | 1.08417 | ||||||||
\(319\) | 11.2495 | − | 8.17323i | 0.629850 | − | 0.457613i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −45.1290 | − | 32.7881i | −2.51885 | − | 1.83005i | ||||
\(322\) | −11.5191 | − | 8.36912i | −0.641935 | − | 0.466393i | ||||
\(323\) | 1.43905 | − | 4.42894i | 0.0800709 | − | 0.246433i | ||||
\(324\) | 7.23840 | 0.402133 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.4106 | 0.576591 | ||||||||
\(327\) | −9.45033 | + | 29.0851i | −0.522605 | + | 1.60841i | ||||
\(328\) | 2.84373 | + | 2.06609i | 0.157019 | + | 0.114081i | ||||
\(329\) | −2.71929 | − | 1.97568i | −0.149919 | − | 0.108923i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2245 | + | 16.1471i | −1.22157 | + | 0.887522i | −0.996229 | − | 0.0867577i | \(-0.972349\pi\) |
−0.225340 | + | 0.974280i | \(0.572349\pi\) | |||||||
\(332\) | 6.37261 | 0.349742 | ||||||||
\(333\) | −6.16953 | + | 4.48242i | −0.338088 | + | 0.245635i | ||||
\(334\) | 0.655643 | + | 2.01786i | 0.0358752 | + | 0.110413i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.68061 | − | 5.17240i | 0.0916851 | − | 0.282178i | ||||
\(337\) | 0.848317 | + | 2.61085i | 0.0462108 | + | 0.142222i | 0.971500 | − | 0.237041i | \(-0.0761775\pi\) |
−0.925289 | + | 0.379263i | \(0.876178\pi\) | |||||||
\(338\) | 2.21071 | + | 6.80387i | 0.120247 | + | 0.370082i | ||||
\(339\) | 5.55200 | − | 17.0873i | 0.301543 | − | 0.928054i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.99934 | + | 9.23102i | 0.162423 | + | 0.499888i | ||||
\(342\) | −7.84678 | + | 5.70102i | −0.424305 | + | 0.308276i | ||||
\(343\) | 19.5048 | 1.05316 | ||||||||
\(344\) | 3.48322 | − | 2.53071i | 0.187803 | − | 0.136447i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.6551 | + | 10.6475i | 0.787862 | + | 0.572415i | ||||
\(347\) | −17.2637 | − | 12.5428i | −0.926762 | − | 0.673332i | 0.0184361 | − | 0.999830i | \(-0.494131\pi\) |
−0.945198 | + | 0.326498i | \(0.894131\pi\) | |||||||
\(348\) | −6.95256 | + | 21.3978i | −0.372697 | + | 1.14704i | ||||
\(349\) | −16.7650 | −0.897411 | −0.448705 | − | 0.893680i | \(-0.648115\pi\) | ||||
−0.448705 | + | 0.893680i | \(0.648115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0814 | −1.07187 | ||||||||
\(352\) | 0.566541 | − | 1.74363i | 0.0301967 | − | 0.0929360i | ||||
\(353\) | 2.41785 | + | 1.75667i | 0.128689 | + | 0.0934981i | 0.650268 | − | 0.759705i | \(-0.274657\pi\) |
−0.521579 | + | 0.853203i | \(0.674657\pi\) | |||||||
\(354\) | 21.7441 | + | 15.7980i | 1.15569 | + | 0.839654i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.68630 | − | 1.95171i | 0.142374 | − | 0.103441i | ||||
\(357\) | −15.1447 | −0.801540 | ||||||||
\(358\) | 8.54361 | − | 6.20730i | 0.451544 | − | 0.328066i | ||||
\(359\) | 2.07194 | + | 6.37678i | 0.109353 | + | 0.336554i | 0.990727 | − | 0.135865i | \(-0.0433812\pi\) |
−0.881375 | + | 0.472418i | \(0.843381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00711 | + | 15.4103i | −0.263532 | + | 0.811068i | ||||
\(362\) | −5.61056 | − | 17.2675i | −0.294884 | − | 0.907561i | ||||
\(363\) | 7.00233 | + | 21.5510i | 0.367527 | + | 1.13113i | ||||
\(364\) | −1.36981 | + | 4.21584i | −0.0717976 | + | 0.220970i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.37232 | + | 7.30124i | 0.124003 | + | 0.381642i | ||||
\(367\) | 3.24949 | − | 2.36089i | 0.169622 | − | 0.123237i | −0.499736 | − | 0.866178i | \(-0.666570\pi\) |
0.669357 | + | 0.742941i | \(0.266570\pi\) | |||||||
\(368\) | 7.76626 | 0.404844 | ||||||||
\(369\) | −16.4931 | + | 11.9830i | −0.858598 | + | 0.623808i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.66673 | + | 7.02329i | 0.501872 | + | 0.364631i | ||||
\(372\) | −12.7054 | − | 9.23102i | −0.658745 | − | 0.478606i | ||||
\(373\) | −8.21467 | + | 25.2822i | −0.425340 | + | 1.30906i | 0.477329 | + | 0.878725i | \(0.341605\pi\) |
−0.902669 | + | 0.430336i | \(0.858395\pi\) | |||||||
\(374\) | −5.10532 | −0.263990 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.83337 | 0.0945486 | ||||||||
\(377\) | 5.66679 | − | 17.4406i | 0.291855 | − | 0.898236i | ||||
\(378\) | 12.3189 | + | 8.95022i | 0.633617 | + | 0.460350i | ||||
\(379\) | 12.6431 | + | 9.18578i | 0.649435 | + | 0.471842i | 0.863079 | − | 0.505070i | \(-0.168533\pi\) |
−0.213644 | + | 0.976912i | \(0.568533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.799814 | + | 0.581099i | −0.0409757 | + | 0.0297706i | ||||
\(382\) | 21.9051 | 1.12076 | ||||||||
\(383\) | 10.8776 | − | 7.90306i | 0.555821 | − | 0.403828i | −0.274106 | − | 0.961699i | \(-0.588382\pi\) |
0.829927 | + | 0.557872i | \(0.188382\pi\) | |||||||
\(384\) | 0.916683 | + | 2.82126i | 0.0467793 | + | 0.143972i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.47474 | − | 26.0826i | 0.431353 | − | 1.32757i | ||||
\(387\) | 7.71650 | + | 23.7489i | 0.392252 | + | 1.20723i | ||||
\(388\) | −3.42705 | − | 10.5474i | −0.173982 | − | 0.535462i | ||||
\(389\) | −7.75991 | + | 23.8826i | −0.393443 | + | 1.21089i | 0.536724 | + | 0.843758i | \(0.319662\pi\) |
−0.930167 | + | 0.367136i | \(0.880338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.68294 | − | 20.5680i | −0.337971 | − | 1.04017i | ||||
\(392\) | −2.94383 | + | 2.13882i | −0.148686 | + | 0.108026i | ||||
\(393\) | 15.3603 | 0.774825 | ||||||||
\(394\) | 0.909110 | − | 0.660507i | 0.0458003 | − | 0.0332759i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.60242 | + | 6.25003i | 0.432288 | + | 0.314076i | ||||
\(397\) | 2.84628 | + | 2.06794i | 0.142850 | + | 0.103787i | 0.656915 | − | 0.753964i | \(-0.271861\pi\) |
−0.514065 | + | 0.857751i | \(0.671861\pi\) | |||||||
\(398\) | −7.87968 | + | 24.2511i | −0.394972 | + | 1.21560i | ||||
\(399\) | −9.09507 | −0.455323 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8696 | 1.49161 | 0.745807 | − | 0.666162i | \(-0.232064\pi\) | ||||
0.745807 | + | 0.666162i | \(0.232064\pi\) | |||||||
\(402\) | −8.70858 | + | 26.8022i | −0.434344 | + | 1.33677i | ||||
\(403\) | 10.3557 | + | 7.52388i | 0.515856 | + | 0.374791i | ||||
\(404\) | 10.6634 | + | 7.74739i | 0.530523 | + | 0.385447i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2495 | + | 8.17323i | −0.558303 | + | 0.405631i | ||||
\(407\) | −2.41062 | −0.119490 | ||||||||
\(408\) | 6.68294 | − | 4.85544i | 0.330855 | − | 0.240380i | ||||
\(409\) | −11.9784 | − | 36.8656i | −0.592291 | − | 1.82289i | −0.567771 | − | 0.823186i | \(-0.692194\pi\) |
−0.0245200 | − | 0.999699i | \(-0.507806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.8965 | + | 55.0799i | −0.882772 | + | 2.71689i | ||||
\(412\) | 0.813697 | + | 2.50430i | 0.0400880 | + | 0.123378i | ||||
\(413\) | 5.13308 | + | 15.7980i | 0.252582 | + | 0.777369i | ||||
\(414\) | −13.9190 | + | 42.8383i | −0.684082 | + | 2.10539i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.747156 | − | 2.29951i | −0.0366323 | − | 0.112743i | ||||
\(417\) | −19.0914 | + | 13.8707i | −0.934911 | + | 0.679253i | ||||
\(418\) | −3.06598 | −0.149962 | ||||||||
\(419\) | 15.2988 | − | 11.1152i | 0.747395 | − | 0.543014i | −0.147624 | − | 0.989044i | \(-0.547162\pi\) |
0.895018 | + | 0.446030i | \(0.147162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8414 | + | 12.9625i | 0.869536 | + | 0.631755i | 0.930462 | − | 0.366388i | \(-0.119406\pi\) |
−0.0609265 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(422\) | 17.2356 | + | 12.5224i | 0.839016 | + | 0.609581i | ||||
\(423\) | −3.28583 | + | 10.1128i | −0.159763 | + | 0.491699i | ||||
\(424\) | −6.51738 | −0.316512 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.906255 | 0.0439082 | ||||||||
\(427\) | −1.46617 | + | 4.51242i | −0.0709531 | + | 0.218371i | ||||
\(428\) | 15.2131 | + | 11.0530i | 0.735355 | + | 0.534267i | ||||
\(429\) | −10.6383 | − | 7.72918i | −0.513622 | − | 0.373168i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.44763 | − | 5.41102i | 0.358740 | − | 0.260640i | −0.393787 | − | 0.919202i | \(-0.628835\pi\) |
0.752526 | + | 0.658562i | \(0.228835\pi\) | |||||||
\(432\) | −8.30550 | −0.399599 | ||||||||
\(433\) | 28.1516 | − | 20.4533i | 1.35288 | − | 0.982923i | 0.354015 | − | 0.935240i | \(-0.384816\pi\) |
0.998862 | − | 0.0476837i | \(-0.0151840\pi\) | |||||||
\(434\) | −2.99934 | − | 9.23102i | −0.143973 | − | 0.443103i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.18574 | − | 9.80470i | 0.152569 | − | 0.469560i | ||||
\(437\) | −4.01342 | − | 12.3520i | −0.191988 | − | 0.590878i | ||||
\(438\) | −13.7026 | − | 42.1723i | −0.654736 | − | 2.01507i | ||||
\(439\) | −2.58025 | + | 7.94118i | −0.123148 | + | 0.379012i | −0.993559 | − | 0.113314i | \(-0.963853\pi\) |
0.870411 | + | 0.492326i | \(0.163853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.52155 | − | 20.0713i | −0.310550 | − | 0.955775i | ||||
\(442\) | −5.44703 | + | 3.95750i | −0.259089 | + | 0.188239i | ||||
\(443\) | 1.19887 | 0.0569599 | 0.0284799 | − | 0.999594i | \(-0.490933\pi\) | ||||
0.0284799 | + | 0.999594i | \(0.490933\pi\) | |||||||
\(444\) | 3.15555 | − | 2.29264i | 0.149756 | − | 0.108804i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.62535 | − | 1.90743i | −0.124314 | − | 0.0903194i | ||||
\(447\) | −4.03076 | − | 2.92852i | −0.190648 | − | 0.138514i | ||||
\(448\) | −0.566541 | + | 1.74363i | −0.0267666 | + | 0.0823790i | ||||
\(449\) | 32.7953 | 1.54771 | 0.773853 | − | 0.633365i | \(-0.218327\pi\) | ||||
0.773853 | + | 0.633365i | \(0.218327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.44437 | −0.303453 | ||||||||
\(452\) | −1.87160 | + | 5.76019i | −0.0880326 | + | 0.270936i | ||||
\(453\) | −51.0373 | − | 37.0808i | −2.39794 | − | 1.74221i | ||||
\(454\) | −13.2495 | − | 9.62631i | −0.621829 | − | 0.451785i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.01342 | − | 2.91592i | 0.187946 | − | 0.136550i | ||||
\(457\) | −19.7884 | −0.925664 | −0.462832 | − | 0.886446i | \(-0.653167\pi\) | ||||
−0.462832 | + | 0.886446i | \(0.653167\pi\) | |||||||
\(458\) | −4.11788 | + | 2.99181i | −0.192416 | + | 0.139798i | ||||
\(459\) | 7.14697 | + | 21.9961i | 0.333592 | + | 1.02669i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.90468 | − | 8.93970i | 0.135285 | − | 0.416363i | −0.860350 | − | 0.509704i | \(-0.829755\pi\) |
0.995634 | + | 0.0933412i | \(0.0297547\pi\) | |||||||
\(462\) | 3.08118 | + | 9.48290i | 0.143350 | + | 0.441185i | ||||
\(463\) | −5.47977 | − | 16.8650i | −0.254666 | − | 0.783783i | −0.993895 | − | 0.110328i | \(-0.964810\pi\) |
0.739229 | − | 0.673454i | \(-0.235190\pi\) | |||||||
\(464\) | 2.34373 | − | 7.21327i | 0.108805 | − | 0.334868i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.513883 | − | 1.58157i | −0.0238052 | − | 0.0732649i | ||||
\(467\) | 17.6857 | − | 12.8494i | 0.818398 | − | 0.594601i | −0.0978549 | − | 0.995201i | \(-0.531198\pi\) |
0.916253 | + | 0.400599i | \(0.131198\pi\) | |||||||
\(468\) | 14.0231 | 0.648216 | ||||||||
\(469\) | −14.0908 | + | 10.2375i | −0.650651 | + | 0.472726i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.0824 | − | 18.2234i | −1.15574 | − | 0.839691i | ||||
\(472\) | −7.33001 | − | 5.32556i | −0.337391 | − | 0.245129i | ||||
\(473\) | −2.43924 | + | 7.50722i | −0.112157 | + | 0.345182i | ||||
\(474\) | −10.2662 | −0.471541 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.10532 | 0.234002 | ||||||||
\(477\) | 11.6807 | − | 35.9495i | 0.534823 | − | 1.64602i | ||||
\(478\) | 10.3553 | + | 7.52354i | 0.473639 | + | 0.344119i | ||||
\(479\) | 4.94352 | + | 3.59168i | 0.225875 | + | 0.164108i | 0.694967 | − | 0.719041i | \(-0.255419\pi\) |
−0.469092 | + | 0.883149i | \(0.655419\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.57198 | + | 1.86865i | −0.117272 | + | 0.0852031i | ||||
\(482\) | −0.395477 | −0.0180135 | ||||||||
\(483\) | −34.1708 | + | 24.8266i | −1.55483 | + | 1.12965i | ||||
\(484\) | −2.36051 | − | 7.26490i | −0.107296 | − | 0.330223i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.06431 | + | 3.27560i | −0.0482780 | + | 0.148584i | ||||
\(487\) | −1.56421 | − | 4.81415i | −0.0708812 | − | 0.218150i | 0.909340 | − | 0.416053i | \(-0.136587\pi\) |
−0.980222 | + | 0.197903i | \(0.936587\pi\) | |||||||
\(488\) | −0.799717 | − | 2.46127i | −0.0362015 | − | 0.111417i | ||||
\(489\) | 9.54324 | − | 29.3711i | 0.431560 | − | 1.32821i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.736165 | + | 2.26568i | 0.0332227 | + | 0.102249i | 0.966293 | − | 0.257446i | \(-0.0828809\pi\) |
−0.933070 | + | 0.359695i | \(0.882881\pi\) | |||||||
\(492\) | 8.43579 | − | 6.12896i | 0.380315 | − | 0.276315i | ||||
\(493\) | −21.1203 | −0.951209 | ||||||||
\(494\) | −3.27120 | + | 2.37666i | −0.147178 | + | 0.106931i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.28304 | + | 3.11181i | 0.192314 | + | 0.139724i | ||||
\(497\) | 0.453127 | + | 0.329216i | 0.0203255 | + | 0.0147674i | ||||
\(498\) | 5.84166 | − | 17.9788i | 0.261771 | − | 0.805648i | ||||
\(499\) | −0.0503313 | −0.00225314 | −0.00112657 | − | 0.999999i | \(-0.500359\pi\) | ||||
−0.00112657 | + | 0.999999i | \(0.500359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.29393 | 0.281192 | ||||||||
\(502\) | −2.89422 | + | 8.90749i | −0.129175 | + | 0.397561i | ||||
\(503\) | −4.37744 | − | 3.18040i | −0.195181 | − | 0.141807i | 0.485903 | − | 0.874013i | \(-0.338491\pi\) |
−0.681083 | + | 0.732206i | \(0.738491\pi\) | |||||||
\(504\) | −8.60242 | − | 6.25003i | −0.383182 | − | 0.278398i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.5191 | + | 8.36912i | −0.512087 | + | 0.372053i | ||||
\(507\) | 21.2220 | 0.942502 | ||||||||
\(508\) | 0.269620 | − | 0.195890i | 0.0119625 | − | 0.00869123i | ||||
\(509\) | 5.85472 | + | 18.0190i | 0.259506 | + | 0.798678i | 0.992908 | + | 0.118883i | \(0.0379312\pi\) |
−0.733402 | + | 0.679795i | \(0.762069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.46868 | − | 26.0639i | 0.374632 | − | 1.15300i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | 4.29208 | + | 13.2097i | 0.189500 | + | 0.583221i | ||||
\(514\) | −1.53868 | + | 4.73556i | −0.0678681 | + | 0.208877i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.94678 | − | 12.1469i | −0.173747 | − | 0.534739i | ||||
\(517\) | −2.71929 | + | 1.97568i | −0.119594 | + | 0.0868904i | ||||
\(518\) | 2.41062 | 0.105917 | ||||||||
\(519\) | 43.4735 | − | 31.5854i | 1.90828 | − | 1.38644i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.0817 | − | 22.5822i | −1.36171 | − | 0.989342i | −0.998334 | − | 0.0577005i | \(-0.981623\pi\) |
−0.363379 | − | 0.931642i | \(-0.618377\pi\) | |||||||
\(522\) | 35.5875 | + | 25.8558i | 1.55762 | + | 1.13168i | ||||
\(523\) | 3.79057 | − | 11.6662i | 0.165750 | − | 0.510127i | −0.833341 | − | 0.552760i | \(-0.813575\pi\) |
0.999091 | + | 0.0426332i | \(0.0135747\pi\) | |||||||
\(524\) | −5.17801 | −0.226202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.8112 | −0.863809 | ||||||||
\(527\) | 4.55565 | − | 14.0208i | 0.198447 | − | 0.610757i | ||||
\(528\) | −4.39991 | − | 3.19672i | −0.191481 | − | 0.139119i | ||||
\(529\) | −30.1883 | − | 21.9331i | −1.31254 | − | 0.953613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.5127 | − | 30.8873i | 1.84489 | − | 1.34039i | ||||
\(532\) | 3.06598 | 0.132927 | ||||||||
\(533\) | −6.87572 | + | 4.99550i | −0.297820 | + | 0.216379i | ||||
\(534\) | −3.04380 | − | 9.36786i | −0.131718 | − | 0.405387i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.93569 | − | 9.03513i | 0.126803 | − | 0.390258i | ||||
\(537\) | −9.68061 | − | 29.7939i | −0.417749 | − | 1.28570i | ||||
\(538\) | −4.57157 | − | 14.0698i | −0.197094 | − | 0.606594i | ||||
\(539\) | 2.06151 | − | 6.34468i | 0.0887957 | − | 0.273285i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9872 | + | 39.9704i | 0.558362 | + | 1.71846i | 0.686896 | + | 0.726756i | \(0.258973\pi\) |
−0.128534 | + | 0.991705i | \(0.541027\pi\) | |||||||
\(542\) | −10.1583 | + | 7.38047i | −0.436338 | + | 0.317018i | ||||
\(543\) | −53.8593 | −2.31132 | ||||||||
\(544\) | −2.25284 | + | 1.63679i | −0.0965899 | + | 0.0701767i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.6383 | + | 7.72918i | 0.455277 | + | 0.330778i | ||||
\(547\) | 15.6719 | + | 11.3863i | 0.670080 | + | 0.486842i | 0.870052 | − | 0.492960i | \(-0.164085\pi\) |
−0.199972 | + | 0.979802i | \(0.564085\pi\) | |||||||
\(548\) | 6.03299 | − | 18.5676i | 0.257717 | − | 0.793170i | ||||
\(549\) | 15.0096 | 0.640592 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6837 | −0.540344 | ||||||||
\(552\) | 7.11920 | − | 21.9106i | 0.303013 | − | 0.932579i | ||||
\(553\) | −5.13308 | − | 3.72940i | −0.218281 | − | 0.158590i | ||||
\(554\) | 5.12256 | + | 3.72176i | 0.217637 | + | 0.158122i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.43579 | − | 4.67587i | 0.272938 | − | 0.198301i | ||||
\(557\) | −8.54685 | −0.362142 | −0.181071 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181071 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(558\) | −24.8408 | + | 18.0479i | −1.05160 | + | 0.764029i | ||||
\(559\) | 3.21688 | + | 9.90054i | 0.136060 | + | 0.418748i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.67995 | + | 14.4034i | −0.197588 | + | 0.608113i | ||||
\(562\) | 6.20792 | + | 19.1060i | 0.261865 | + | 0.805938i | ||||
\(563\) | 7.24949 | + | 22.3116i | 0.305529 | + | 0.940323i | 0.979479 | + | 0.201546i | \(0.0645964\pi\) |
−0.673950 | + | 0.738777i | \(0.735404\pi\) | |||||||
\(564\) | 1.68061 | − | 5.17240i | 0.0707667 | − | 0.217797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.561416 | + | 1.72786i | 0.0235981 | + | 0.0726274i | ||||
\(567\) | 10.7362 | − | 7.80028i | 0.450877 | − | 0.327581i | ||||
\(568\) | −0.305502 | −0.0128186 | ||||||||
\(569\) | 5.74445 | − | 4.17359i | 0.240820 | − | 0.174966i | −0.460829 | − | 0.887489i | \(-0.652448\pi\) |
0.701649 | + | 0.712523i | \(0.252448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.67745 | + | 7.03108i | 0.404989 | + | 0.294241i | 0.771570 | − | 0.636145i | \(-0.219472\pi\) |
−0.366581 | + | 0.930386i | \(0.619472\pi\) | |||||||
\(572\) | 3.58621 | + | 2.60553i | 0.149947 | + | 0.108943i | ||||
\(573\) | 20.0801 | − | 61.8001i | 0.838856 | − | 2.58173i | ||||
\(574\) | 6.44437 | 0.268983 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.79981 | 0.241659 | ||||||||
\(577\) | −12.8457 | + | 39.5350i | −0.534774 | + | 1.64587i | 0.209362 | + | 0.977838i | \(0.432861\pi\) |
−0.744137 | + | 0.668027i | \(0.767139\pi\) | |||||||
\(578\) | −7.47987 | − | 5.43444i | −0.311121 | − | 0.226043i | ||||
\(579\) | −65.8171 | − | 47.8189i | −2.73526 | − | 1.98729i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.45200 | − | 6.86728i | 0.392135 | − | 0.284903i | ||||
\(582\) | −32.8984 | −1.36368 | ||||||||
\(583\) | 9.66673 | − | 7.02329i | 0.400355 | − | 0.290875i | ||||
\(584\) | 4.61920 | + | 14.2164i | 0.191144 | + | 0.588280i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.11964 | + | 6.52359i | −0.0875617 | + | 0.269487i | ||||
\(587\) | −5.91072 | − | 18.1913i | −0.243962 | − | 0.750836i | −0.995806 | − | 0.0914953i | \(-0.970835\pi\) |
0.751844 | − | 0.659341i | \(-0.229165\pi\) | |||||||
\(588\) | 3.33560 | + | 10.2659i | 0.137558 | + | 0.423359i | ||||
\(589\) | 2.73588 | − | 8.42016i | 0.112730 | − | 0.346947i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.03010 | − | 3.17031i | −0.0423725 | − | 0.130409i | ||||
\(592\) | −1.06375 | + | 0.772856i | −0.0437197 | + | 0.0317642i | ||||
\(593\) | −0.538428 | −0.0221106 | −0.0110553 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110553 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(594\) | 12.3189 | − | 8.95022i | 0.505451 | − | 0.367232i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.35878 | + | 0.987213i | 0.0556579 | + | 0.0404378i | ||||
\(597\) | 61.1956 | + | 44.4612i | 2.50457 | + | 1.81968i | ||||
\(598\) | −5.80261 | + | 17.8586i | −0.237286 | + | 0.730292i | ||||
\(599\) | −38.4209 | −1.56983 | −0.784917 | − | 0.619601i | \(-0.787295\pi\) | ||||
−0.784917 | + | 0.619601i | \(0.787295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6034 | 0.799639 | 0.399820 | − | 0.916594i | \(-0.369073\pi\) | ||||
0.399820 | + | 0.916594i | \(0.369073\pi\) | |||||||
\(602\) | 2.43924 | − | 7.50722i | 0.0994162 | − | 0.305971i | ||||
\(603\) | 44.5759 | + | 32.3863i | 1.81527 | + | 1.31887i | ||||
\(604\) | 17.2048 | + | 12.5001i | 0.700055 | + | 0.508620i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 31.6323 | − | 22.9822i | 1.28498 | − | 0.933590i | ||||
\(607\) | 32.4415 | 1.31676 | 0.658381 | − | 0.752685i | \(-0.271242\pi\) | ||||
0.658381 | + | 0.752685i | \(0.271242\pi\) | |||||||
\(608\) | −1.35294 | + | 0.982966i | −0.0548688 | + | 0.0398646i | ||||
\(609\) | 12.7466 | + | 39.2300i | 0.516518 | + | 1.58968i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.36981 | + | 4.21584i | −0.0554166 | + | 0.170555i | ||||
\(612\) | −4.99080 | − | 15.3601i | −0.201741 | − | 0.620895i | ||||
\(613\) | 7.25273 | + | 22.3216i | 0.292935 | + | 0.901561i | 0.983907 | + | 0.178680i | \(0.0571826\pi\) |
−0.690972 | + | 0.722881i | \(0.742817\pi\) | |||||||
\(614\) | −0.894685 | + | 2.75356i | −0.0361065 | + | 0.111124i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.03868 | − | 3.19672i | −0.0418495 | − | 0.128799i | ||||
\(617\) | 14.0876 | − | 10.2353i | 0.567147 | − | 0.412056i | −0.266921 | − | 0.963718i | \(-0.586006\pi\) |
0.834068 | + | 0.551662i | \(0.186006\pi\) | |||||||
\(618\) | 7.81119 | 0.314212 | ||||||||
\(619\) | −10.1801 | + | 7.39624i | −0.409171 | + | 0.297280i | −0.773266 | − | 0.634082i | \(-0.781378\pi\) |
0.364095 | + | 0.931362i | \(0.381378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 52.1838 | + | 37.9137i | 2.09406 | + | 1.52143i | ||||
\(622\) | −16.7054 | − | 12.1372i | −0.669826 | − | 0.486657i | ||||
\(623\) | 1.88117 | − | 5.78966i | 0.0753676 | − | 0.231958i | ||||
\(624\) | −7.17242 | −0.287127 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.4272 | 0.656563 | ||||||||
\(627\) | −2.81053 | + | 8.64992i | −0.112242 | + | 0.345445i | ||||
\(628\) | 8.45536 | + | 6.14318i | 0.337406 | + | 0.245140i | ||||
\(629\) | 2.96218 | + | 2.15215i | 0.118110 | + | 0.0858118i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.7653 | + | 24.5319i | −1.34418 | + | 0.976601i | −0.344897 | + | 0.938640i | \(0.612086\pi\) |
−0.999279 | + | 0.0379610i | \(0.987914\pi\) | |||||||
\(632\) | 3.46076 | 0.137662 | ||||||||
\(633\) | 51.1285 | − | 37.1470i | 2.03218 | − | 1.47646i | ||||
\(634\) | 5.10060 | + | 15.6980i | 0.202571 | + | 0.623448i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.97437 | + | 18.3872i | −0.236899 | + | 0.729101i | ||||
\(637\) | −2.71873 | − | 8.36739i | −0.107720 | − | 0.331528i | ||||
\(638\) | 4.29692 | + | 13.2246i | 0.170117 | + | 0.523565i | ||||
\(639\) | 0.547533 | − | 1.68513i | 0.0216601 | − | 0.0666628i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.44926 | − | 13.6934i | −0.175735 | − | 0.540858i | 0.823931 | − | 0.566690i | \(-0.191776\pi\) |
−0.999666 | + | 0.0258324i | \(0.991776\pi\) | |||||||
\(642\) | 45.1290 | − | 32.7881i | 1.78110 | − | 1.29404i | ||||
\(643\) | −30.1666 | −1.18966 | −0.594828 | − | 0.803853i | \(-0.702780\pi\) | ||||
−0.594828 | + | 0.803853i | \(0.702780\pi\) | |||||||
\(644\) | 11.5191 | − | 8.36912i | 0.453916 | − | 0.329790i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.76748 | + | 2.73724i | 0.148230 | + | 0.107695i | ||||
\(647\) | −8.64660 | − | 6.28212i | −0.339933 | − | 0.246976i | 0.404701 | − | 0.914449i | \(-0.367376\pi\) |
−0.744633 | + | 0.667474i | \(0.767376\pi\) | |||||||
\(648\) | −2.23679 | + | 6.88413i | −0.0878693 | + | 0.270434i | ||||
\(649\) | 16.6110 | 0.652039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.7925 | −1.12847 | ||||||||
\(652\) | −3.21706 | + | 9.90109i | −0.125990 | + | 0.387757i | ||||
\(653\) | 8.22432 | + | 5.97532i | 0.321843 | + | 0.233832i | 0.736961 | − | 0.675935i | \(-0.236260\pi\) |
−0.415119 | + | 0.909767i | \(0.636260\pi\) | |||||||
\(654\) | −24.7413 | − | 17.9756i | −0.967461 | − | 0.702902i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.84373 | + | 2.06609i | −0.111029 | + | 0.0806674i | ||||
\(657\) | −86.6959 | −3.38233 | ||||||||
\(658\) | 2.71929 | − | 1.97568i | 0.106009 | − | 0.0770201i | ||||
\(659\) | 9.61668 | + | 29.5971i | 0.374613 | + | 1.15294i | 0.943740 | + | 0.330689i | \(0.107281\pi\) |
−0.569127 | + | 0.822250i | \(0.692719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8131 | − | 39.4347i | 0.498372 | − | 1.53383i | −0.313262 | − | 0.949667i | \(-0.601422\pi\) |
0.811635 | − | 0.584165i | \(-0.198578\pi\) | |||||||
\(662\) | −8.48901 | − | 26.1265i | −0.329935 | − | 1.01543i | ||||
\(663\) | 6.17194 | + | 18.9953i | 0.239698 | + | 0.737715i | ||||
\(664\) | −1.96924 | + | 6.06071i | −0.0764215 | + | 0.235201i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.35655 | − | 7.25271i | −0.0913144 | − | 0.281037i | ||||
\(667\) | −47.6536 | + | 34.6224i | −1.84515 | + | 1.34058i | ||||
\(668\) | −2.12171 | −0.0820913 | ||||||||
\(669\) | −7.78797 | + | 5.65829i | −0.301100 | + | 0.218762i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.83849 | + | 2.78883i | 0.148183 | + | 0.107661i | ||||
\(672\) | 4.39991 | + | 3.19672i | 0.169730 | + | 0.123316i | ||||
\(673\) | −0.662831 | + | 2.03998i | −0.0255503 | + | 0.0786356i | −0.963019 | − | 0.269435i | \(-0.913163\pi\) |
0.937468 | + | 0.348071i | \(0.113163\pi\) | |||||||
\(674\) | −2.74521 | −0.105742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.15401 | −0.275154 | ||||||||
\(677\) | −12.8391 | + | 39.5147i | −0.493446 | + | 1.51867i | 0.325918 | + | 0.945398i | \(0.394327\pi\) |
−0.819364 | + | 0.573274i | \(0.805673\pi\) | |||||||
\(678\) | 14.5353 | + | 10.5605i | 0.558226 | + | 0.405575i | ||||
\(679\) | −16.4492 | − | 11.9510i | −0.631263 | − | 0.458639i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.3039 | + | 28.5560i | −1.50613 | + | 1.09427i | ||||
\(682\) | −9.70607 | −0.371665 | ||||||||
\(683\) | −23.3247 | + | 16.9464i | −0.892495 | + | 0.648436i | −0.936527 | − | 0.350595i | \(-0.885980\pi\) |
0.0440323 | + | 0.999030i | \(0.485980\pi\) | |||||||
\(684\) | −2.99720 | − | 9.22445i | −0.114601 | − | 0.352706i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.02730 | + | 18.5501i | −0.230123 | + | 0.708247i | ||||
\(687\) | 4.66589 | + | 14.3601i | 0.178015 | + | 0.547874i | ||||
\(688\) | 1.33047 | + | 4.09478i | 0.0507238 | + | 0.156112i | ||||
\(689\) | 4.86950 | − | 14.9868i | 0.185513 | − | 0.570951i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2050 | − | 46.7963i | −0.578426 | − | 1.78021i | −0.624204 | − | 0.781262i | \(-0.714576\pi\) |
0.0457774 | − | 0.998952i | \(-0.485424\pi\) | |||||||
\(692\) | −14.6551 | + | 10.6475i | −0.557103 | + | 0.404759i | ||||
\(693\) | 19.4945 | 0.740535 | ||||||||
\(694\) | 17.2637 | − | 12.5428i | 0.655319 | − | 0.476117i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.2021 | − | 13.2246i | −0.689947 | − | 0.501276i | ||||
\(697\) | 7.91886 | + | 5.75339i | 0.299948 | + | 0.217925i | ||||
\(698\) | 5.18067 | − | 15.9445i | 0.196091 | − | 0.603507i | ||||
\(699\) | −4.93309 | −0.186587 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9783 | −0.943419 | −0.471709 | − | 0.881754i | \(-0.656363\pi\) | ||||
−0.471709 | + | 0.881754i | \(0.656363\pi\) | |||||||
\(702\) | 6.20551 | − | 19.0986i | 0.234212 | − | 0.720830i | ||||
\(703\) | 1.77893 | + | 1.29247i | 0.0670935 | + | 0.0487462i | ||||
\(704\) | 1.48322 | + | 1.07763i | 0.0559011 | + | 0.0406145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.41785 | + | 1.75667i | −0.0909969 | + | 0.0661131i | ||||
\(707\) | 24.1650 | 0.908817 | ||||||||
\(708\) | −21.7441 | + | 15.7980i | −0.817193 | + | 0.593725i | ||||
\(709\) | 3.02602 | + | 9.31312i | 0.113644 | + | 0.349762i | 0.991662 | − | 0.128867i | \(-0.0411340\pi\) |
−0.878017 | + | 0.478629i | \(0.841134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.20252 | + | 19.0894i | −0.232613 | + | 0.715908i | ||||
\(712\) | 1.02608 | + | 3.15794i | 0.0384538 | + | 0.118349i | ||||
\(713\) | −12.7054 | − | 39.1032i | −0.475821 | − | 1.46443i | ||||
\(714\) | 4.67995 | − | 14.4034i | 0.175143 | − | 0.539034i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.26337 | + | 10.0436i | 0.121958 | + | 0.375348i | ||||
\(717\) | 30.7184 | − | 22.3182i | 1.14720 | − | 0.833488i | ||||
\(718\) | −6.70494 | −0.250226 | ||||||||
\(719\) | 6.94474 | − | 5.04565i | 0.258995 | − | 0.188171i | −0.450709 | − | 0.892671i | \(-0.648829\pi\) |
0.709704 | + | 0.704500i | \(0.248829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.90559 | + | 2.83758i | 0.145452 | + | 0.105677i | ||||
\(722\) | −13.1088 | − | 9.52408i | −0.487858 | − | 0.354450i | ||||
\(723\) | −0.362527 | + | 1.11574i | −0.0134825 | + | 0.0414950i | ||||
\(724\) | 18.1561 | 0.674768 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.6600 | −0.840992 | ||||||||
\(727\) | 7.42142 | − | 22.8408i | 0.275245 | − | 0.847118i | −0.713909 | − | 0.700238i | \(-0.753077\pi\) |
0.989154 | − | 0.146880i | \(-0.0469230\pi\) | |||||||
\(728\) | −3.58621 | − | 2.60553i | −0.132914 | − | 0.0965675i | ||||
\(729\) | 25.8337 | + | 18.7693i | 0.956802 | + | 0.695157i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.69962 | − | 7.04719i | 0.358754 | − | 0.260650i | ||||
\(732\) | −7.67698 | −0.283749 | ||||||||
\(733\) | −15.3787 | + | 11.1733i | −0.568025 | + | 0.412695i | −0.834387 | − | 0.551178i | \(-0.814178\pi\) |
0.266362 | + | 0.963873i | \(0.414178\pi\) | |||||||
\(734\) | 1.24119 | + | 3.82000i | 0.0458133 | + | 0.140999i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39991 | + | 7.38615i | −0.0884617 | + | 0.272257i | ||||
\(737\) | 5.38220 | + | 16.5647i | 0.198256 | + | 0.610168i | ||||
\(738\) | −6.29981 | − | 19.3888i | −0.231899 | − | 0.713713i | ||||
\(739\) | −6.42507 | + | 19.7743i | −0.236350 | + | 0.727411i | 0.760589 | + | 0.649233i | \(0.224910\pi\) |
−0.996939 | + | 0.0781776i | \(0.975090\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.70653 | + | 11.4075i | 0.136163 | + | 0.419066i | ||||
\(742\) | −9.66673 | + | 7.02329i | −0.354877 | + | 0.257833i | ||||
\(743\) | −6.53365 | −0.239696 | −0.119848 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119848 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(744\) | 12.7054 | − | 9.23102i | 0.465803 | − | 0.338426i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21.5063 | − | 15.6252i | −0.787401 | − | 0.572080i | ||||
\(747\) | −29.9012 | − | 21.7245i | −1.09403 | − | 0.794858i | ||||
\(748\) | 1.57763 | − | 4.85544i | 0.0576838 | − | 0.177533i | ||||
\(749\) | 34.4755 | 1.25971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9879 | 1.02129 | 0.510646 | − | 0.859791i | \(-0.329406\pi\) | ||||
0.510646 | + | 0.859791i | \(0.329406\pi\) | |||||||
\(752\) | −0.566541 | + | 1.74363i | −0.0206596 | + | 0.0635838i | ||||
\(753\) | 22.4773 | + | 16.3307i | 0.819117 | + | 0.595123i | ||||
\(754\) | 14.8359 | + | 10.7789i | 0.540290 | + | 0.392544i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.3189 | + | 8.95022i | −0.448035 | + | 0.325516i | ||||
\(757\) | −4.48558 | −0.163031 | −0.0815156 | − | 0.996672i | \(-0.525976\pi\) | ||||
−0.0815156 | + | 0.996672i | \(0.525976\pi\) | |||||||
\(758\) | −12.6431 | + | 9.18578i | −0.459220 | + | 0.333643i | ||||
\(759\) | 13.0521 | + | 40.1702i | 0.473761 | + | 1.45809i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.138770 | − | 0.427091i | 0.00503042 | − | 0.0154820i | −0.948510 | − | 0.316748i | \(-0.897409\pi\) |
0.953540 | + | 0.301266i | \(0.0974091\pi\) | |||||||
\(762\) | −0.305502 | − | 0.940237i | −0.0110672 | − | 0.0340612i | ||||
\(763\) | −5.84063 | − | 17.9756i | −0.211445 | − | 0.650760i | ||||
\(764\) | −6.76906 | + | 20.8330i | −0.244896 | + | 0.753712i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.15489 | + | 12.7874i | 0.150122 | + | 0.462028i | ||||
\(767\) | 17.7228 | − | 12.8764i | 0.639935 | − | 0.464940i | ||||
\(768\) | −2.96645 | −0.107042 | ||||||||
\(769\) | −16.9783 | + | 12.3355i | −0.612254 | + | 0.444829i | −0.850207 | − | 0.526448i | \(-0.823524\pi\) |
0.237953 | + | 0.971277i | \(0.423524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9498 | + | 8.68202i | 0.430360 | + | 0.312675i | ||||
\(772\) | 22.1872 | + | 16.1199i | 0.798533 | + | 0.580168i | ||||
\(773\) | −10.8283 | + | 33.3262i | −0.389468 | + | 1.19866i | 0.543718 | + | 0.839268i | \(0.317016\pi\) |
−0.933187 | + | 0.359392i | \(0.882984\pi\) | |||||||
\(774\) | −24.9711 | −0.897568 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.0902 | 0.398114 | ||||||||
\(777\) | 2.20978 | − | 6.80099i | 0.0792753 | − | 0.243984i | ||||
\(778\) | −20.3157 | − | 14.7602i | −0.728354 | − | 0.529180i | ||||
\(779\) | 4.75564 | + | 3.45517i | 0.170388 | + | 0.123794i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.453127 | − | 0.329216i | 0.0162142 | − | 0.0117803i | ||||
\(782\) | 21.6265 | 0.773361 | ||||||||
\(783\) | 50.9623 | − | 37.0263i | 1.82125 | − | 1.32321i | ||||
\(784\) | −1.12444 | − | 3.46068i | −0.0401586 | − | 0.123596i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.74659 | + | 14.6085i | −0.169305 | + | 0.521068i | ||||
\(787\) | −12.1132 | − | 37.2807i | −0.431790 | − | 1.32891i | −0.896340 | − | 0.443367i | \(-0.853784\pi\) |
0.464550 | − | 0.885547i | \(-0.346216\pi\) | |||||||
\(788\) | 0.347249 | + | 1.06872i | 0.0123702 | + | 0.0380717i | ||||
\(789\) | −18.1606 | + | 55.8925i | −0.646534 | + | 1.98983i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.43132 | + | 10.5605i | 0.122004 | + | 0.375489i | ||||
\(792\) | −8.60242 | + | 6.25003i | −0.305674 | + | 0.222085i | ||||
\(793\) | 6.25724 | 0.222201 | ||||||||
\(794\) | −2.84628 | + | 2.06794i | −0.101011 | + | 0.0733884i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.6293 | − | 14.9880i | −0.731185 | − | 0.531237i | ||||
\(797\) | −6.98479 | − | 5.07475i | −0.247414 | − | 0.179757i | 0.457166 | − | 0.889381i | \(-0.348865\pi\) |
−0.704580 | + | 0.709625i | \(0.748865\pi\) | |||||||
\(798\) | 2.81053 | − | 8.64992i | 0.0994917 | − | 0.306204i | ||||
\(799\) | 5.10532 | 0.180613 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.2580 | −0.680448 | ||||||||
\(802\) | −9.23020 | + | 28.4076i | −0.325930 | + | 1.00311i | ||||
\(803\) | −22.1713 | − | 16.1084i | −0.782408 | − | 0.568453i | ||||
\(804\) | −22.7993 | − | 16.5647i | −0.804071 | − | 0.584192i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.3557 | + | 7.52388i | −0.364765 | + | 0.265017i | ||||
\(807\) | −43.8854 | −1.54484 | ||||||||
\(808\) | −10.6634 | + | 7.74739i | −0.375136 | + | 0.272552i | ||||
\(809\) | −14.1830 | − | 43.6508i | −0.498648 | − | 1.53468i | −0.811194 | − | 0.584778i | \(-0.801182\pi\) |
0.312546 | − | 0.949903i | \(-0.398818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1734 | − | 37.4660i | 0.427467 | − | 1.31561i | −0.473145 | − | 0.880984i | \(-0.656881\pi\) |
0.900612 | − | 0.434623i | \(-0.143119\pi\) | |||||||
\(812\) | −4.29692 | − | 13.2246i | −0.150792 | − | 0.464091i | ||||
\(813\) | 11.5102 | + | 35.4249i | 0.403682 | + | 1.24240i | ||||
\(814\) | 0.744923 | − | 2.29264i | 0.0261096 | − | 0.0803569i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.55266 | + | 7.85627i | 0.0893609 | + | 0.275025i | ||||
\(817\) | 5.82507 | − | 4.23216i | 0.203794 | − | 0.148065i | ||||
\(818\) | 38.7628 | 1.35531 | ||||||||
\(819\) | 20.7993 | − | 15.1116i | 0.726788 | − | 0.528042i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.0672 | − | 16.0328i | −0.770152 | − | 0.559548i | 0.131855 | − | 0.991269i | \(-0.457907\pi\) |
−0.902007 | + | 0.431721i | \(0.857907\pi\) | |||||||
\(822\) | −46.8538 | − | 34.0413i | −1.63421 | − | 1.18733i | ||||
\(823\) | −1.89701 | + | 5.83841i | −0.0661258 | + | 0.203514i | −0.978660 | − | 0.205486i | \(-0.934122\pi\) |
0.912534 | + | 0.409000i | \(0.134122\pi\) | |||||||
\(824\) | −2.63318 | −0.0917311 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.6110 | −0.577971 | ||||||||
\(827\) | −13.6170 | + | 41.9087i | −0.473508 | + | 1.45731i | 0.374451 | + | 0.927247i | \(0.377831\pi\) |
−0.847959 | + | 0.530062i | \(0.822169\pi\) | |||||||
\(828\) | −36.4404 | − | 26.4755i | −1.26639 | − | 0.920088i | ||||
\(829\) | −3.80236 | − | 2.76257i | −0.132061 | − | 0.0959481i | 0.519794 | − | 0.854292i | \(-0.326009\pi\) |
−0.651855 | + | 0.758344i | \(0.726009\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.1958 | − | 11.0404i | 0.527136 | − | 0.382987i | ||||
\(832\) | 2.41785 | 0.0838238 | ||||||||
\(833\) | −8.19758 | + | 5.95589i | −0.284029 | + | 0.206359i | ||||
\(834\) | −7.29228 | − | 22.4433i | −0.252511 | − | 0.777149i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.947439 | − | 2.91592i | 0.0327679 | − | 0.100849i | ||||
\(837\) | 13.5876 | + | 41.8183i | 0.469656 | + | 1.44545i | ||||
\(838\) | 5.84362 | + | 17.9848i | 0.201864 | + | 0.621275i | ||||
\(839\) | −14.2747 | + | 43.9331i | −0.492819 | + | 1.51674i | 0.327509 | + | 0.944848i | \(0.393791\pi\) |
−0.820328 | + | 0.571893i | \(0.806209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.81451 | + | 27.1283i | 0.303949 | + | 0.935458i | ||||
\(842\) | −17.8414 | + | 12.9625i | −0.614855 | + | 0.446718i | ||||
\(843\) | 59.5937 | 2.05252 | ||||||||
\(844\) | −17.2356 | + | 12.5224i | −0.593274 | + | 0.431039i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.60242 | − | 6.25003i | −0.295757 | − | 0.214880i | ||||
\(847\) | −11.3300 | − | 8.23173i | −0.389304 | − | 0.282846i | ||||
\(848\) | 2.01398 | − | 6.19839i | 0.0691604 | − | 0.212854i | ||||
\(849\) | 5.38938 | 0.184963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2116 | 0.350048 | ||||||||
\(852\) | −0.280048 | + | 0.861899i | −0.00959429 | + | 0.0295282i | ||||
\(853\) | 10.2282 | + | 7.43121i | 0.350206 | + | 0.254440i | 0.748956 | − | 0.662620i | \(-0.230556\pi\) |
−0.398749 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(854\) | −3.83849 | − | 2.78883i | −0.131350 | − | 0.0954317i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.2131 | + | 11.0530i | −0.519974 | + | 0.377783i | ||||
\(857\) | 19.4162 | 0.663245 | 0.331623 | − | 0.943412i | \(-0.392404\pi\) | ||||
0.331623 | + | 0.943412i | \(0.392404\pi\) | |||||||
\(858\) | 10.6383 | − | 7.72918i | 0.363186 | − | 0.263870i | ||||
\(859\) | 2.88593 | + | 8.88197i | 0.0984665 | + | 0.303049i | 0.988142 | − | 0.153545i | \(-0.0490691\pi\) |
−0.889675 | + | 0.456594i | \(0.849069\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.90744 | − | 18.1812i | 0.201325 | − | 0.619615i | ||||
\(862\) | 2.84474 | + | 8.75521i | 0.0968923 | + | 0.298204i | ||||
\(863\) | 5.05071 | + | 15.5445i | 0.171928 | + | 0.529141i | 0.999480 | − | 0.0322489i | \(-0.0102669\pi\) |
−0.827552 | + | 0.561390i | \(0.810267\pi\) | |||||||
\(864\) | 2.56654 | − | 7.89900i | 0.0873155 | − | 0.268729i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.7529 | + | 33.0941i | 0.365400 | + | 1.12458i | ||||
\(867\) | −22.1886 | + | 16.1210i | −0.753565 | + | 0.547497i | ||||
\(868\) | 9.70607 | 0.329445 | ||||||||
\(869\) | −5.13308 | + | 3.72940i | −0.174128 | + | 0.126511i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5829 | + | 13.5013i | 0.629659 | + | 0.457474i | ||||
\(872\) | 8.34038 | + | 6.05964i | 0.282441 | + | 0.205205i | ||||
\(873\) | −19.8763 | + | 61.1728i | −0.672709 | + | 2.07039i | ||||
\(874\) | 12.9877 | 0.439315 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.3426 | 1.49820 | ||||||||
\(877\) | 10.9717 | − | 33.7673i | 0.370487 | − | 1.14024i | −0.575986 | − | 0.817459i | \(-0.695382\pi\) |
0.946473 | − | 0.322782i | \(-0.104618\pi\) | |||||||
\(878\) | −6.75517 | − | 4.90792i | −0.227976 | − | 0.165634i | ||||
\(879\) | 16.4617 | + | 11.9601i | 0.555240 | + | 0.403405i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5378 | − | 18.5543i | 0.860390 | − | 0.625110i | −0.0676008 | − | 0.997712i | \(-0.521534\pi\) |
0.927991 | + | 0.372602i | \(0.121534\pi\) | |||||||
\(882\) | 21.1042 | 0.710615 | ||||||||
\(883\) | 28.2592 | − | 20.5315i | 0.950997 | − | 0.690940i | −4.54670e−5 | − | 1.00000i | \(-0.500014\pi\) |
0.951042 | + | 0.309060i | \(0.100014\pi\) | |||||||
\(884\) | −2.08058 | − | 6.40337i | −0.0699775 | − | 0.215369i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.370470 | + | 1.14019i | −0.0124462 | + | 0.0383054i | ||||
\(887\) | 13.2668 | + | 40.8311i | 0.445456 | + | 1.37097i | 0.881982 | + | 0.471282i | \(0.156209\pi\) |
−0.436526 | + | 0.899692i | \(0.643791\pi\) | |||||||
\(888\) | 1.20531 | + | 3.70957i | 0.0404476 | + | 0.124485i | ||||
\(889\) | 0.188810 | − | 0.581099i | 0.00633250 | − | 0.0194894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.10085 | − | 12.6211i | −0.137384 | − | 0.422823i | ||||
\(892\) | 2.62535 | − | 1.90743i | 0.0879033 | − | 0.0638655i | ||||
\(893\) | 3.06598 | 0.102599 | ||||||||
\(894\) | 4.03076 | − | 2.92852i | 0.134809 | − | 0.0979442i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.48322 | − | 1.07763i | −0.0495510 | − | 0.0360009i | ||||
\(897\) | 45.0646 | + | 32.7413i | 1.50466 | + | 1.09320i | ||||
\(898\) | −10.1343 | + | 31.1902i | −0.338186 | + | 1.04083i | ||||
\(899\) | −40.1532 | −1.33918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1487 | −0.604622 | ||||||||
\(902\) | 1.99142 | − | 6.12896i | 0.0663070 | − | 0.204072i | ||||
\(903\) | −18.9438 | − | 13.7635i | −0.630410 | − | 0.458020i | ||||
\(904\) | −4.89991 | − | 3.55999i | −0.162968 | − | 0.118404i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 51.0373 | − | 37.0808i | 1.69560 | − | 1.23193i | ||||
\(907\) | 39.8259 | 1.32240 | 0.661199 | − | 0.750211i | \(-0.270048\pi\) | ||||
0.661199 | + | 0.750211i | \(0.270048\pi\) | |||||||
\(908\) | 13.2495 | − | 9.62631i | 0.439700 | − | 0.319460i | ||||
\(909\) | −23.6229 | − | 72.7038i | −0.783522 | − | 2.41143i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.522189 | + | 1.60713i | −0.0173009 | + | 0.0532467i | −0.959334 | − | 0.282273i | \(-0.908912\pi\) |
0.942033 | + | 0.335519i | \(0.108912\pi\) | |||||||
\(912\) | 1.53299 | + | 4.71806i | 0.0507623 | + | 0.156230i | ||||
\(913\) | −3.61034 | − | 11.1115i | −0.119485 | − | 0.367737i | ||||
\(914\) | 6.11496 | − | 18.8199i | 0.202265 | − | 0.622508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.57289 | − | 4.84085i | −0.0519697 | − | 0.159946i | ||||
\(917\) | −7.68015 | + | 5.57995i | −0.253621 | + | 0.184266i | ||||
\(918\) | −23.1281 | −0.763340 | ||||||||
\(919\) | 24.2013 | − | 17.5833i | 0.798327 | − | 0.580019i | −0.112096 | − | 0.993697i | \(-0.535756\pi\) |
0.910423 | + | 0.413679i | \(0.135756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.94836 | + | 5.04828i | 0.228956 | + | 0.166346i | ||||
\(922\) | 7.60456 | + | 5.52504i | 0.250443 | + | 0.181957i | ||||
\(923\) | 0.228257 | − | 0.702504i | 0.00751318 | − | 0.0231232i | ||||
\(924\) | −9.97091 | −0.328019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.7329 | 0.582739 | ||||||||
\(927\) | 4.71929 | − | 14.5245i | 0.155002 | − | 0.477047i | ||||
\(928\) | 6.13597 | + | 4.45805i | 0.201423 | + | 0.146343i | ||||
\(929\) | 12.8664 | + | 9.34795i | 0.422131 | + | 0.306696i | 0.778495 | − | 0.627651i | \(-0.215983\pi\) |
−0.356363 | + | 0.934347i | \(0.615983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.92303 | + | 3.57679i | −0.161346 | + | 0.117225i | ||||
\(932\) | 1.66296 | 0.0544721 | ||||||||
\(933\) | −49.5557 | + | 36.0043i | −1.62238 | + | 1.17873i | ||||
\(934\) | 6.75535 | + | 20.7908i | 0.221042 | + | 0.680297i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.33337 | + | 13.3367i | −0.141640 | + | 0.435925i | ||||
\(937\) | −14.2973 | − | 44.0026i | −0.467073 | − | 1.43750i | −0.856357 | − | 0.516384i | \(-0.827278\pi\) |
0.389284 | − | 0.921118i | \(-0.372722\pi\) | |||||||
\(938\) | −5.38220 | − | 16.5647i | −0.175735 | − | 0.540856i | ||||
\(939\) | 15.0585 | − | 46.3454i | 0.491417 | − | 1.51243i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.60650 | − | 11.0997i | −0.117569 | − | 0.361839i | 0.874906 | − | 0.484294i | \(-0.160923\pi\) |
−0.992474 | + | 0.122455i | \(0.960923\pi\) | |||||||
\(942\) | 25.0824 | − | 18.2234i | 0.817228 | − | 0.593751i | ||||
\(943\) | 27.2988 | 0.888971 | ||||||||
\(944\) | 7.33001 | − | 5.32556i | 0.238571 | − | 0.173332i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.38602 | − | 4.63972i | −0.207628 | − | 0.150850i | ||||
\(947\) | −2.37336 | − | 1.72435i | −0.0771238 | − | 0.0560337i | 0.548555 | − | 0.836114i | \(-0.315178\pi\) |
−0.625679 | + | 0.780081i | \(0.715178\pi\) | |||||||
\(948\) | 3.17242 | − | 9.76370i | 0.103035 | − | 0.317110i | ||||
\(949\) | −36.1421 | −1.17322 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.9638 | 1.58776 | ||||||||
\(952\) | −1.57763 | + | 4.85544i | −0.0511313 | + | 0.157366i | ||||
\(953\) | −8.03924 | − | 5.84085i | −0.260417 | − | 0.189204i | 0.449914 | − | 0.893072i | \(-0.351455\pi\) |
−0.710331 | + | 0.703868i | \(0.751455\pi\) | |||||||
\(954\) | 30.5805 | + | 22.2180i | 0.990080 | + | 0.719335i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.3553 | + | 7.52354i | −0.334913 | + | 0.243329i | ||||
\(957\) | 41.2488 | 1.33339 | ||||||||
\(958\) | −4.94352 | + | 3.59168i | −0.159718 | + | 0.116042i | ||||
\(959\) | −11.0607 | − | 34.0413i | −0.357168 | − | 1.09925i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.918471 | + | 2.82676i | −0.0296281 | + | 0.0911859i | ||||
\(962\) | −0.982407 | − | 3.02354i | −0.0316741 | − | 0.0974828i | ||||
\(963\) | −33.7021 | − | 103.725i | −1.08604 | − | 3.34248i | ||||
\(964\) | 0.122209 | − | 0.376121i | 0.00393610 | − | 0.0121141i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.0521 | − | 40.1702i | −0.419944 | − | 1.29246i | ||||
\(967\) | 36.7193 | − | 26.6781i | 1.18081 | − | 0.857910i | 0.188549 | − | 0.982064i | \(-0.439621\pi\) |
0.992263 | + | 0.124153i | \(0.0396215\pi\) | |||||||
\(968\) | 7.63877 | 0.245519 | ||||||||
\(969\) | 11.1760 | − | 8.11987i | 0.359026 | − | 0.260848i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.78844 | + | 2.75246i | 0.121577 | + | 0.0883307i | 0.646912 | − | 0.762565i | \(-0.276060\pi\) |
−0.525335 | + | 0.850895i | \(0.676060\pi\) | |||||||
\(972\) | −2.78640 | − | 2.02444i | −0.0893737 | − | 0.0649338i | ||||
\(973\) | 4.50688 | − | 13.8707i | 0.144484 | − | 0.444675i | ||||
\(974\) | 5.06189 | 0.162194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.58794 | 0.0828379 | ||||||||
\(977\) | −0.991339 | + | 3.05103i | −0.0317157 | + | 0.0976110i | −0.965661 | − | 0.259804i | \(-0.916342\pi\) |
0.933946 | + | 0.357415i | \(0.116342\pi\) | |||||||
\(978\) | 24.9845 | + | 18.1523i | 0.798917 | + | 0.580447i | ||||
\(979\) | −4.92498 | − | 3.57820i | −0.157403 | − | 0.114360i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.3726 | + | 35.1448i | −1.54442 | + | 1.12209i | ||||
\(982\) | −2.38228 | −0.0760216 | ||||||||
\(983\) | 15.8337 | − | 11.5038i | 0.505015 | − | 0.366915i | −0.305914 | − | 0.952059i | \(-0.598962\pi\) |
0.810929 | + | 0.585144i | \(0.198962\pi\) | |||||||
\(984\) | 3.22218 | + | 9.91686i | 0.102719 | + | 0.316138i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.52652 | − | 20.0866i | 0.207847 | − | 0.639687i | ||||
\(987\) | −3.08118 | − | 9.48290i | −0.0980751 | − | 0.301844i | ||||
\(988\) | −1.24949 | − | 3.84552i | −0.0397514 | − | 0.122342i | ||||
\(989\) | 10.3328 | − | 31.8011i | 0.328564 | − | 1.01122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9762 | + | 43.0144i | 0.443969 | + | 1.36640i | 0.883610 | + | 0.468223i | \(0.155106\pi\) |
−0.439641 | + | 0.898173i | \(0.644894\pi\) | |||||||
\(992\) | −4.28304 | + | 3.11181i | −0.135987 | + | 0.0988000i | ||||
\(993\) | −81.4913 | −2.58605 | ||||||||
\(994\) | −0.453127 | + | 0.329216i | −0.0143723 | + | 0.0104421i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.2937 | + | 11.1115i | 0.484598 | + | 0.352081i | ||||
\(997\) | −46.9808 | − | 34.1335i | −1.48790 | − | 1.08102i | −0.974904 | − | 0.222626i | \(-0.928537\pi\) |
−0.512991 | − | 0.858394i | \(-0.671463\pi\) | |||||||
\(998\) | 0.0155532 | − | 0.0478679i | 0.000492329 | − | 0.00151523i | ||||
\(999\) | −10.9206 | −0.345512 |
(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 | 250.2.d.d.101.2 | 8 | ||
5.2 | odd | 4 | 250.2.e.c.149.2 | 16 | |||
5.3 | odd | 4 | 250.2.e.c.149.3 | 16 | |||
5.4 | even | 2 | 50.2.d.b.21.1 | ✓ | 8 | ||
15.14 | odd | 2 | 450.2.h.e.271.1 | 8 | |||
20.19 | odd | 2 | 400.2.u.d.321.2 | 8 | |||
25.6 | even | 5 | inner | 250.2.d.d.151.2 | 8 | ||
25.8 | odd | 20 | 250.2.e.c.99.2 | 16 | |||
25.9 | even | 10 | 1250.2.a.l.1.4 | 4 | |||
25.12 | odd | 20 | 1250.2.b.e.1249.4 | 8 | |||
25.13 | odd | 20 | 1250.2.b.e.1249.5 | 8 | |||
25.16 | even | 5 | 1250.2.a.f.1.1 | 4 | |||
25.17 | odd | 20 | 250.2.e.c.99.3 | 16 | |||
25.19 | even | 10 | 50.2.d.b.31.1 | yes | 8 | ||
75.44 | odd | 10 | 450.2.h.e.181.1 | 8 | |||
100.19 | odd | 10 | 400.2.u.d.81.2 | 8 | |||
100.59 | odd | 10 | 10000.2.a.t.1.1 | 4 | |||
100.91 | odd | 10 | 10000.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.21.1 | ✓ | 8 | 5.4 | even | 2 | ||
50.2.d.b.31.1 | yes | 8 | 25.19 | even | 10 | ||
250.2.d.d.101.2 | 8 | 1.1 | even | 1 | trivial | ||
250.2.d.d.151.2 | 8 | 25.6 | even | 5 | inner | ||
250.2.e.c.99.2 | 16 | 25.8 | odd | 20 | |||
250.2.e.c.99.3 | 16 | 25.17 | odd | 20 | |||
250.2.e.c.149.2 | 16 | 5.2 | odd | 4 | |||
250.2.e.c.149.3 | 16 | 5.3 | odd | 4 | |||
400.2.u.d.81.2 | 8 | 100.19 | odd | 10 | |||
400.2.u.d.321.2 | 8 | 20.19 | odd | 2 | |||
450.2.h.e.181.1 | 8 | 75.44 | odd | 10 | |||
450.2.h.e.271.1 | 8 | 15.14 | odd | 2 | |||
1250.2.a.f.1.1 | 4 | 25.16 | even | 5 | |||
1250.2.a.l.1.4 | 4 | 25.9 | even | 10 | |||
1250.2.b.e.1249.4 | 8 | 25.12 | odd | 20 | |||
1250.2.b.e.1249.5 | 8 | 25.13 | odd | 20 | |||
10000.2.a.t.1.1 | 4 | 100.59 | odd | 10 | |||
10000.2.a.x.1.4 | 4 | 100.91 | odd | 10 |