Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.4 | ||
Root | \(-1.11000 + 1.92258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.i.165.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22001 | 1.56978 | 0.784891 | − | 0.619633i | \(-0.212719\pi\) | ||||
0.784891 | + | 0.619633i | \(0.212719\pi\) | |||||||
\(3\) | 0.274776 | − | 0.475925i | 0.158642 | − | 0.274776i | −0.775737 | − | 0.631056i | \(-0.782622\pi\) |
0.934379 | + | 0.356280i | \(0.115955\pi\) | |||||||
\(4\) | 2.92843 | 1.46422 | ||||||||
\(5\) | −2.11000 | + | 3.65463i | −0.943622 | + | 1.63440i | −0.185136 | + | 0.982713i | \(0.559273\pi\) |
−0.758486 | + | 0.651689i | \(0.774061\pi\) | |||||||
\(6\) | 0.610004 | − | 1.05656i | 0.249033 | − | 0.431338i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.06113 | 0.728720 | ||||||||
\(9\) | 1.34900 | + | 2.33653i | 0.449666 | + | 0.778844i | ||||
\(10\) | −4.68423 | + | 8.11332i | −1.48128 | + | 2.56566i | ||||
\(11\) | 0.274776 | − | 0.475925i | 0.0828480 | − | 0.143497i | −0.821624 | − | 0.570030i | \(-0.806932\pi\) |
0.904472 | + | 0.426533i | \(0.140265\pi\) | |||||||
\(12\) | 0.804662 | − | 1.39372i | 0.232286 | − | 0.402331i | ||||
\(13\) | 2.95900 | + | 2.06017i | 0.820679 | + | 0.571389i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.15956 | + | 2.00841i | 0.299396 | + | 0.518569i | ||||
\(16\) | −1.28114 | −0.320285 | ||||||||
\(17\) | 2.37888 | 0.576964 | 0.288482 | − | 0.957485i | \(-0.406849\pi\) | ||||
0.288482 | + | 0.957485i | \(0.406849\pi\) | |||||||
\(18\) | 2.99478 | + | 5.18712i | 0.705877 | + | 1.22262i | ||||
\(19\) | −1.80534 | − | 3.12694i | −0.414174 | − | 0.717370i | 0.581168 | − | 0.813784i | \(-0.302596\pi\) |
−0.995341 | + | 0.0964139i | \(0.969263\pi\) | |||||||
\(20\) | −6.17901 | + | 10.7024i | −1.38167 | + | 2.39312i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.610004 | − | 1.05656i | 0.130053 | − | 0.225259i | ||||
\(23\) | 5.81890 | 1.21332 | 0.606662 | − | 0.794960i | \(-0.292508\pi\) | ||||
0.606662 | + | 0.794960i | \(0.292508\pi\) | |||||||
\(24\) | 0.566349 | − | 0.980945i | 0.115605 | − | 0.200235i | ||||
\(25\) | −6.40423 | − | 11.0925i | −1.28085 | − | 2.21849i | ||||
\(26\) | 6.56900 | + | 4.57360i | 1.28829 | + | 0.896957i | ||||
\(27\) | 3.13134 | 0.602626 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.79945 | + | 3.11673i | 0.334149 | + | 0.578762i | 0.983321 | − | 0.181879i | \(-0.0582179\pi\) |
−0.649172 | + | 0.760641i | \(0.724885\pi\) | |||||||
\(30\) | 2.57422 | + | 4.45868i | 0.469986 | + | 0.814040i | ||||
\(31\) | −2.57422 | − | 4.45868i | −0.462344 | − | 0.800803i | 0.536733 | − | 0.843752i | \(-0.319658\pi\) |
−0.999077 | + | 0.0429489i | \(0.986325\pi\) | |||||||
\(32\) | −6.96640 | −1.23150 | ||||||||
\(33\) | −0.151003 | − | 0.261545i | −0.0262863 | − | 0.0455292i | ||||
\(34\) | 5.28114 | 0.905708 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.95045 | + | 6.84238i | 0.658408 | + | 1.14040i | ||||
\(37\) | −0.329543 | −0.0541766 | −0.0270883 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270883 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(38\) | −4.00787 | − | 6.94184i | −0.650163 | − | 1.12611i | ||||
\(39\) | 1.79355 | − | 0.842178i | 0.287198 | − | 0.134856i | ||||
\(40\) | −4.34900 | + | 7.53268i | −0.687637 | + | 1.19102i | ||||
\(41\) | −3.14579 | − | 5.44866i | −0.491289 | − | 0.850938i | 0.508660 | − | 0.860967i | \(-0.330141\pi\) |
−0.999950 | + | 0.0100292i | \(0.996808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61000 | + | 2.78861i | −0.245523 | + | 0.425259i | −0.962279 | − | 0.272066i | \(-0.912293\pi\) |
0.716755 | + | 0.697325i | \(0.245626\pi\) | |||||||
\(44\) | 0.804662 | − | 1.39372i | 0.121307 | − | 0.210111i | ||||
\(45\) | −11.3856 | −1.69726 | ||||||||
\(46\) | 12.9180 | 1.90466 | ||||||||
\(47\) | 4.10479 | − | 7.10970i | 0.598745 | − | 1.03706i | −0.394262 | − | 0.918998i | \(-0.629000\pi\) |
0.993007 | − | 0.118058i | \(-0.0376669\pi\) | |||||||
\(48\) | −0.352026 | + | 0.609727i | −0.0508106 | + | 0.0880065i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.2174 | − | 24.6253i | −2.01065 | − | 3.48255i | ||||
\(51\) | 0.653659 | − | 1.13217i | 0.0915306 | − | 0.158536i | ||||
\(52\) | 8.66524 | + | 6.03308i | 1.20165 | + | 0.836638i | ||||
\(53\) | −1.32933 | − | 2.30247i | −0.182598 | − | 0.316269i | 0.760167 | − | 0.649728i | \(-0.225117\pi\) |
−0.942764 | + | 0.333459i | \(0.891784\pi\) | |||||||
\(54\) | 6.95160 | 0.945992 | ||||||||
\(55\) | 1.15956 | + | 2.00841i | 0.156354 | + | 0.270814i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.98426 | −0.262821 | ||||||||
\(58\) | 3.99478 | + | 6.91917i | 0.524541 | + | 0.908531i | ||||
\(59\) | 1.80753 | 0.235320 | 0.117660 | − | 0.993054i | \(-0.462461\pi\) | ||||
0.117660 | + | 0.993054i | \(0.462461\pi\) | |||||||
\(60\) | 3.39568 | + | 5.88149i | 0.438381 | + | 0.759297i | ||||
\(61\) | 0.304662 | + | 0.527691i | 0.0390080 | + | 0.0675639i | 0.884870 | − | 0.465838i | \(-0.154247\pi\) |
−0.845862 | + | 0.533401i | \(0.820914\pi\) | |||||||
\(62\) | −5.71479 | − | 9.89831i | −0.725779 | − | 1.25709i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9032 | −1.61290 | ||||||||
\(65\) | −13.7727 | + | 6.46709i | −1.70829 | + | 0.802144i | ||||
\(66\) | −0.335228 | − | 0.580633i | −0.0412638 | − | 0.0714709i | ||||
\(67\) | −5.18490 | + | 8.98052i | −0.633437 | + | 1.09714i | 0.353407 | + | 0.935470i | \(0.385023\pi\) |
−0.986844 | + | 0.161675i | \(0.948310\pi\) | |||||||
\(68\) | 6.96640 | 0.844801 | ||||||||
\(69\) | 1.59889 | − | 2.76936i | 0.192484 | − | 0.333392i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.59889 | − | 9.69756i | 0.664466 | − | 1.15089i | −0.314964 | − | 0.949104i | \(-0.601992\pi\) |
0.979430 | − | 0.201785i | \(-0.0646743\pi\) | |||||||
\(72\) | 2.78046 | + | 4.81590i | 0.327680 | + | 0.567559i | ||||
\(73\) | 2.45310 | + | 4.24890i | 0.287114 | + | 0.497296i | 0.973120 | − | 0.230300i | \(-0.0739707\pi\) |
−0.686005 | + | 0.727596i | \(0.740637\pi\) | |||||||
\(74\) | −0.731589 | −0.0850455 | ||||||||
\(75\) | −7.03891 | −0.812783 | ||||||||
\(76\) | −5.28682 | − | 9.15705i | −0.606440 | − | 1.05039i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.98169 | − | 1.86964i | 0.450838 | − | 0.211695i | ||||
\(79\) | 7.00855 | − | 12.1392i | 0.788524 | − | 1.36576i | −0.138348 | − | 0.990384i | \(-0.544179\pi\) |
0.926871 | − | 0.375379i | \(-0.122488\pi\) | |||||||
\(80\) | 2.70321 | − | 4.68210i | 0.302228 | − | 0.523474i | ||||
\(81\) | −3.18657 | + | 5.51931i | −0.354064 | + | 0.613257i | ||||
\(82\) | −6.98367 | − | 12.0961i | −0.771217 | − | 1.33579i | ||||
\(83\) | 5.73159 | 0.629124 | 0.314562 | − | 0.949237i | \(-0.398142\pi\) | ||||
0.314562 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.01945 | + | 8.69395i | −0.544436 | + | 0.942991i | ||||
\(86\) | −3.57422 | + | 6.19073i | −0.385418 | + | 0.667564i | ||||
\(87\) | 1.97777 | 0.212040 | ||||||||
\(88\) | 0.566349 | − | 0.980945i | 0.0603730 | − | 0.104569i | ||||
\(89\) | 7.46755 | 0.791559 | 0.395779 | − | 0.918346i | \(-0.370474\pi\) | ||||
0.395779 | + | 0.918346i | \(0.370474\pi\) | |||||||
\(90\) | −25.2760 | −2.66433 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 17.0403 | 1.77657 | ||||||||
\(93\) | −2.82933 | −0.293388 | ||||||||
\(94\) | 9.11266 | − | 15.7836i | 0.939899 | − | 1.62795i | ||||
\(95\) | 15.2371 | 1.56329 | ||||||||
\(96\) | −1.91420 | + | 3.31549i | −0.195367 | + | 0.338386i | ||||
\(97\) | −3.42035 | + | 5.92422i | −0.347284 | + | 0.601514i | −0.985766 | − | 0.168123i | \(-0.946229\pi\) |
0.638482 | + | 0.769637i | \(0.279563\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.48269 | 0.149015 | ||||||||
\(100\) | −18.7544 | − | 32.4835i | −1.87544 | − | 3.24835i | ||||
\(101\) | 2.87956 | − | 4.98755i | 0.286527 | − | 0.496280i | −0.686451 | − | 0.727176i | \(-0.740832\pi\) |
0.972978 | + | 0.230896i | \(0.0741658\pi\) | |||||||
\(102\) | 1.45113 | − | 2.51343i | 0.143683 | − | 0.248866i | ||||
\(103\) | 0.285888 | − | 0.495173i | 0.0281694 | − | 0.0487908i | −0.851597 | − | 0.524197i | \(-0.824366\pi\) |
0.879766 | + | 0.475406i | \(0.157699\pi\) | |||||||
\(104\) | 6.09889 | + | 4.24629i | 0.598045 | + | 0.416383i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.95113 | − | 5.11150i | −0.286639 | − | 0.496473i | ||||
\(107\) | 4.07157 | 0.393613 | 0.196807 | − | 0.980442i | \(-0.436943\pi\) | ||||
0.196807 | + | 0.980442i | \(0.436943\pi\) | |||||||
\(108\) | 9.16992 | 0.882376 | ||||||||
\(109\) | −7.65434 | − | 13.2577i | −0.733153 | − | 1.26986i | −0.955529 | − | 0.294897i | \(-0.904715\pi\) |
0.222376 | − | 0.974961i | \(-0.428619\pi\) | |||||||
\(110\) | 2.57422 | + | 4.45868i | 0.245442 | + | 0.425119i | ||||
\(111\) | −0.0905505 | + | 0.156838i | −0.00859467 | + | 0.0148864i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.08846 | + | 10.5455i | −0.572754 | + | 0.992039i | 0.423528 | + | 0.905883i | \(0.360792\pi\) |
−0.996282 | + | 0.0861558i | \(0.972542\pi\) | |||||||
\(114\) | −4.40506 | −0.412572 | ||||||||
\(115\) | −12.2779 | + | 21.2659i | −1.14492 | + | 1.98306i | ||||
\(116\) | 5.26956 | + | 9.12714i | 0.489266 | + | 0.847434i | ||||
\(117\) | −0.821977 | + | 9.69296i | −0.0759918 | + | 0.896115i | ||||
\(118\) | 4.01273 | 0.369402 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.39000 | + | 4.13959i | 0.218176 | + | 0.377892i | ||||
\(121\) | 5.34900 | + | 9.26473i | 0.486272 | + | 0.842249i | ||||
\(122\) | 0.676353 | + | 1.17148i | 0.0612341 | + | 0.106061i | ||||
\(123\) | −3.45754 | −0.311756 | ||||||||
\(124\) | −7.53844 | − | 13.0570i | −0.676972 | − | 1.17255i | ||||
\(125\) | 32.9518 | 2.94730 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.980336 | − | 1.69799i | −0.0869907 | − | 0.150672i | 0.819247 | − | 0.573441i | \(-0.194392\pi\) |
−0.906238 | + | 0.422768i | \(0.861058\pi\) | |||||||
\(128\) | −14.7124 | −1.30040 | ||||||||
\(129\) | 0.884779 | + | 1.53248i | 0.0779005 | + | 0.134928i | ||||
\(130\) | −30.5755 | + | 14.3570i | −2.68165 | + | 1.25919i | ||||
\(131\) | −3.25011 | + | 5.62935i | −0.283963 | + | 0.491838i | −0.972357 | − | 0.233498i | \(-0.924983\pi\) |
0.688394 | + | 0.725337i | \(0.258316\pi\) | |||||||
\(132\) | −0.442203 | − | 0.765918i | −0.0384888 | − | 0.0666646i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.5105 | + | 19.9368i | −0.994358 | + | 1.72228i | ||||
\(135\) | −6.60714 | + | 11.4439i | −0.568652 | + | 0.984934i | ||||
\(136\) | 4.90319 | 0.420445 | ||||||||
\(137\) | −15.2576 | −1.30354 | −0.651770 | − | 0.758416i | \(-0.725973\pi\) | ||||
−0.651770 | + | 0.758416i | \(0.725973\pi\) | |||||||
\(138\) | 3.54955 | − | 6.14800i | 0.302158 | − | 0.523353i | ||||
\(139\) | −8.74801 | + | 15.1520i | −0.741997 | + | 1.28518i | 0.209588 | + | 0.977790i | \(0.432788\pi\) |
−0.951585 | + | 0.307386i | \(0.900546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.25579 | − | 3.90714i | −0.189972 | − | 0.329041i | ||||
\(142\) | 12.4296 | − | 21.5287i | 1.04307 | − | 1.80665i | ||||
\(143\) | 1.79355 | − | 0.842178i | 0.149984 | − | 0.0704264i | ||||
\(144\) | −1.72825 | − | 2.99342i | −0.144021 | − | 0.249452i | ||||
\(145\) | −15.1873 | −1.26124 | ||||||||
\(146\) | 5.44591 | + | 9.43260i | 0.450707 | + | 0.780647i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.965046 | −0.0793263 | ||||||||
\(149\) | −2.27743 | − | 3.94463i | −0.186574 | − | 0.323156i | 0.757531 | − | 0.652799i | \(-0.226405\pi\) |
−0.944106 | + | 0.329642i | \(0.893072\pi\) | |||||||
\(150\) | −15.6264 | −1.27589 | ||||||||
\(151\) | 3.16456 | + | 5.48118i | 0.257528 | + | 0.446052i | 0.965579 | − | 0.260109i | \(-0.0837586\pi\) |
−0.708051 | + | 0.706161i | \(0.750425\pi\) | |||||||
\(152\) | −3.72105 | − | 6.44504i | −0.301817 | − | 0.522762i | ||||
\(153\) | 3.20911 | + | 5.55833i | 0.259441 | + | 0.449365i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.7265 | 1.74511 | ||||||||
\(156\) | 5.25229 | − | 2.46626i | 0.420520 | − | 0.197459i | ||||
\(157\) | 8.15502 | + | 14.1249i | 0.650841 | + | 1.12729i | 0.982919 | + | 0.184038i | \(0.0589170\pi\) |
−0.332078 | + | 0.943252i | \(0.607750\pi\) | |||||||
\(158\) | 15.5590 | − | 26.9490i | 1.23781 | − | 2.14395i | ||||
\(159\) | −1.46107 | −0.115871 | ||||||||
\(160\) | 14.6991 | − | 25.4597i | 1.16207 | − | 2.01276i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.07422 | + | 12.2529i | −0.555803 | + | 0.962680i | ||||
\(163\) | −11.7999 | − | 20.4381i | −0.924241 | − | 1.60083i | −0.792778 | − | 0.609511i | \(-0.791366\pi\) |
−0.131463 | − | 0.991321i | \(-0.541967\pi\) | |||||||
\(164\) | −9.21223 | − | 15.9561i | −0.719354 | − | 1.24596i | ||||
\(165\) | 1.27447 | 0.0992173 | ||||||||
\(166\) | 12.7242 | 0.987587 | ||||||||
\(167\) | −8.91513 | − | 15.4415i | −0.689874 | − | 1.19490i | −0.971878 | − | 0.235483i | \(-0.924333\pi\) |
0.282005 | − | 0.959413i | \(-0.409001\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.51137 | + | 12.1921i | 0.347028 | + | 0.937855i | ||||
\(170\) | −11.1432 | + | 19.3006i | −0.854646 | + | 1.48029i | ||||
\(171\) | 4.87080 | − | 8.43647i | 0.372479 | − | 0.645153i | ||||
\(172\) | −4.71479 | + | 8.16626i | −0.359499 | + | 0.622671i | ||||
\(173\) | −3.78568 | − | 6.55699i | −0.287820 | − | 0.498518i | 0.685469 | − | 0.728101i | \(-0.259597\pi\) |
−0.973289 | + | 0.229583i | \(0.926264\pi\) | |||||||
\(174\) | 4.39068 | 0.332856 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.352026 | + | 0.609727i | −0.0265350 | + | 0.0459599i | ||||
\(177\) | 0.496665 | − | 0.860249i | 0.0373316 | − | 0.0646603i | ||||
\(178\) | 16.5780 | 1.24258 | ||||||||
\(179\) | 11.4017 | − | 19.7483i | 0.852201 | − | 1.47606i | −0.0270166 | − | 0.999635i | \(-0.508601\pi\) |
0.879218 | − | 0.476420i | \(-0.158066\pi\) | |||||||
\(180\) | −33.3419 | −2.48515 | ||||||||
\(181\) | −13.9294 | −1.03536 | −0.517681 | − | 0.855574i | \(-0.673205\pi\) | ||||
−0.517681 | + | 0.855574i | \(0.673205\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.334855 | 0.0247532 | ||||||||
\(184\) | 11.9935 | 0.884174 | ||||||||
\(185\) | 0.695338 | − | 1.20436i | 0.0511222 | − | 0.0885463i | ||||
\(186\) | −6.28114 | −0.460556 | ||||||||
\(187\) | 0.653659 | − | 1.13217i | 0.0478003 | − | 0.0827925i | ||||
\(188\) | 12.0206 | − | 20.8203i | 0.876692 | − | 1.51848i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33.8265 | 2.45403 | ||||||||
\(191\) | 6.33591 | + | 10.9741i | 0.458450 | + | 0.794059i | 0.998879 | − | 0.0473305i | \(-0.0150714\pi\) |
−0.540429 | + | 0.841390i | \(0.681738\pi\) | |||||||
\(192\) | −3.54548 | + | 6.14096i | −0.255873 | + | 0.443185i | ||||
\(193\) | 2.07746 | − | 3.59827i | 0.149539 | − | 0.259009i | −0.781518 | − | 0.623882i | \(-0.785554\pi\) |
0.931057 | + | 0.364873i | \(0.118888\pi\) | |||||||
\(194\) | −7.59321 | + | 13.1518i | −0.545160 | + | 0.944246i | ||||
\(195\) | −0.706545 | + | 8.33177i | −0.0505968 | + | 0.596650i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.42510 | + | 5.93245i | 0.244028 | + | 0.422669i | 0.961858 | − | 0.273549i | \(-0.0881977\pi\) |
−0.717830 | + | 0.696219i | \(0.754864\pi\) | |||||||
\(198\) | 3.29157 | 0.233922 | ||||||||
\(199\) | 0.813587 | 0.0576737 | 0.0288368 | − | 0.999584i | \(-0.490820\pi\) | ||||
0.0288368 | + | 0.999584i | \(0.490820\pi\) | |||||||
\(200\) | −13.2000 | − | 22.8630i | −0.933379 | − | 1.61666i | ||||
\(201\) | 2.84937 | + | 4.93525i | 0.200979 | + | 0.348106i | ||||
\(202\) | 6.39265 | − | 11.0724i | 0.449785 | − | 0.779051i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.91420 | − | 3.31549i | 0.134021 | − | 0.232131i | ||||
\(205\) | 26.5505 | 1.85437 | ||||||||
\(206\) | 0.634674 | − | 1.09929i | 0.0442198 | − | 0.0765910i | ||||
\(207\) | 7.84968 | + | 13.5960i | 0.545590 | + | 0.944990i | ||||
\(208\) | −3.79089 | − | 2.63937i | −0.262851 | − | 0.183007i | ||||
\(209\) | −1.98426 | −0.137254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98670 | + | 12.1013i | 0.480984 | + | 0.833089i | 0.999762 | − | 0.0218200i | \(-0.00694608\pi\) |
−0.518778 | + | 0.854909i | \(0.673613\pi\) | |||||||
\(212\) | −3.89286 | − | 6.74264i | −0.267363 | − | 0.463086i | ||||
\(213\) | −3.07688 | − | 5.32931i | −0.210824 | − | 0.365158i | ||||
\(214\) | 9.03891 | 0.617887 | ||||||||
\(215\) | −6.79423 | − | 11.7679i | −0.463363 | − | 0.802568i | ||||
\(216\) | 6.45410 | 0.439146 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.9927 | − | 29.4322i | −1.15089 | − | 1.99340i | ||||
\(219\) | 2.69621 | 0.182193 | ||||||||
\(220\) | 3.39568 | + | 5.88149i | 0.228937 | + | 0.396530i | ||||
\(221\) | 7.03912 | + | 4.90091i | 0.473502 | + | 0.329671i | ||||
\(222\) | −0.201023 | + | 0.348182i | −0.0134918 | + | 0.0233684i | ||||
\(223\) | −6.76700 | − | 11.7208i | −0.453152 | − | 0.784882i | 0.545428 | − | 0.838158i | \(-0.316367\pi\) |
−0.998580 | + | 0.0532758i | \(0.983034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.2786 | − | 29.9274i | 1.15191 | − | 1.99516i | ||||
\(226\) | −13.5164 | + | 23.4111i | −0.899099 | + | 1.55729i | ||||
\(227\) | 5.36751 | 0.356254 | 0.178127 | − | 0.984007i | \(-0.442996\pi\) | ||||
0.178127 | + | 0.984007i | \(0.442996\pi\) | |||||||
\(228\) | −5.81076 | −0.384827 | ||||||||
\(229\) | 1.54955 | − | 2.68390i | 0.102397 | − | 0.177357i | −0.810275 | − | 0.586050i | \(-0.800682\pi\) |
0.912672 | + | 0.408693i | \(0.134015\pi\) | |||||||
\(230\) | −27.2570 | + | 47.2106i | −1.79728 | + | 3.11297i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.70890 | + | 6.42399i | 0.243501 | + | 0.421756i | ||||
\(233\) | 10.1856 | − | 17.6419i | 0.667280 | − | 1.15576i | −0.311382 | − | 0.950285i | \(-0.600792\pi\) |
0.978662 | − | 0.205478i | \(-0.0658748\pi\) | |||||||
\(234\) | −1.82480 | + | 21.5185i | −0.119291 | + | 1.40671i | ||||
\(235\) | 17.3222 | + | 30.0030i | 1.12998 | + | 1.95718i | ||||
\(236\) | 5.29323 | 0.344560 | ||||||||
\(237\) | −3.85156 | − | 6.67109i | −0.250186 | − | 0.433334i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.29157 | −0.0835449 | −0.0417725 | − | 0.999127i | \(-0.513300\pi\) | ||||
−0.0417725 | + | 0.999127i | \(0.513300\pi\) | |||||||
\(240\) | −1.48555 | − | 2.57305i | −0.0958920 | − | 0.166090i | ||||
\(241\) | −2.13270 | −0.137379 | −0.0686896 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686896 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(242\) | 11.8748 | + | 20.5678i | 0.763342 | + | 1.32215i | ||||
\(243\) | 6.44819 | + | 11.1686i | 0.413652 | + | 0.716466i | ||||
\(244\) | 0.892184 | + | 1.54531i | 0.0571162 | + | 0.0989282i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.67577 | −0.489389 | ||||||||
\(247\) | 1.10004 | − | 12.9719i | 0.0699938 | − | 0.825385i | ||||
\(248\) | −5.30581 | − | 9.18993i | −0.336919 | − | 0.583561i | ||||
\(249\) | 1.57490 | − | 2.72781i | 0.0998053 | − | 0.172868i | ||||
\(250\) | 73.1532 | 4.62662 | ||||||||
\(251\) | −15.3856 | + | 26.6486i | −0.971128 | + | 1.68204i | −0.278964 | + | 0.960302i | \(0.589991\pi\) |
−0.692164 | + | 0.721741i | \(0.743342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.59889 | − | 2.76936i | 0.100521 | − | 0.174108i | ||||
\(254\) | −2.17635 | − | 3.76955i | −0.136557 | − | 0.236523i | ||||
\(255\) | 2.75845 | + | 4.77777i | 0.172741 | + | 0.299196i | ||||
\(256\) | −6.85521 | −0.428451 | ||||||||
\(257\) | 1.47361 | 0.0919213 | 0.0459607 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459607 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(258\) | 1.96422 | + | 3.40212i | 0.122287 | + | 0.211807i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −40.3324 | + | 18.9385i | −2.50131 | + | 1.17451i | ||||
\(261\) | −4.85489 | + | 8.40892i | −0.300510 | + | 0.520499i | ||||
\(262\) | −7.21526 | + | 12.4972i | −0.445760 | + | 0.772079i | ||||
\(263\) | −3.33847 | + | 5.78240i | −0.205859 | + | 0.356558i | −0.950406 | − | 0.311012i | \(-0.899332\pi\) |
0.744547 | + | 0.667570i | \(0.232665\pi\) | |||||||
\(264\) | −0.311238 | − | 0.539079i | −0.0191553 | − | 0.0331780i | ||||
\(265\) | 11.2196 | 0.689214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.05190 | − | 3.55400i | 0.125574 | − | 0.217501i | ||||
\(268\) | −15.1837 | + | 26.2989i | −0.927489 | + | 1.60646i | ||||
\(269\) | −7.57573 | −0.461900 | −0.230950 | − | 0.972966i | \(-0.574183\pi\) | ||||
−0.230950 | + | 0.972966i | \(0.574183\pi\) | |||||||
\(270\) | −14.6679 | + | 25.4055i | −0.892660 | + | 1.54613i | ||||
\(271\) | −20.5680 | −1.24942 | −0.624709 | − | 0.780858i | \(-0.714782\pi\) | ||||
−0.624709 | + | 0.780858i | \(0.714782\pi\) | |||||||
\(272\) | −3.04768 | −0.184793 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.8719 | −2.04628 | ||||||||
\(275\) | −7.03891 | −0.424462 | ||||||||
\(276\) | 4.68225 | − | 8.10989i | 0.281838 | − | 0.488158i | ||||
\(277\) | 5.70541 | 0.342805 | 0.171402 | − | 0.985201i | \(-0.445170\pi\) | ||||
0.171402 | + | 0.985201i | \(0.445170\pi\) | |||||||
\(278\) | −19.4207 | + | 33.6376i | −1.16477 | + | 2.01745i | ||||
\(279\) | 6.94523 | − | 12.0295i | 0.415800 | − | 0.720187i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.37315 | −0.380190 | −0.190095 | − | 0.981766i | \(-0.560880\pi\) | ||||
−0.190095 | + | 0.981766i | \(0.560880\pi\) | |||||||
\(282\) | −5.00787 | − | 8.67389i | −0.298214 | − | 0.516523i | ||||
\(283\) | 13.5097 | − | 23.3995i | 0.803068 | − | 1.39096i | −0.114519 | − | 0.993421i | \(-0.536533\pi\) |
0.917587 | − | 0.397534i | \(-0.130134\pi\) | |||||||
\(284\) | 16.3960 | − | 28.3987i | 0.972923 | − | 1.68515i | ||||
\(285\) | 4.18679 | − | 7.25173i | 0.248004 | − | 0.429555i | ||||
\(286\) | 3.98169 | − | 1.86964i | 0.235443 | − | 0.110554i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.39766 | − | 16.2772i | −0.553762 | − | 0.959144i | ||||
\(289\) | −11.3409 | −0.667113 | ||||||||
\(290\) | −33.7160 | −1.97987 | ||||||||
\(291\) | 1.87966 | + | 3.25566i | 0.110187 | + | 0.190850i | ||||
\(292\) | 7.18376 | + | 12.4426i | 0.420398 | + | 0.728150i | ||||
\(293\) | −2.43736 | + | 4.22163i | −0.142392 | + | 0.246630i | −0.928397 | − | 0.371590i | \(-0.878813\pi\) |
0.786005 | + | 0.618220i | \(0.212146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.81389 | + | 6.60586i | −0.222053 | + | 0.384608i | ||||
\(296\) | −0.679232 | −0.0394796 | ||||||||
\(297\) | 0.860415 | − | 1.49028i | 0.0499264 | − | 0.0864750i | ||||
\(298\) | −5.05592 | − | 8.75710i | −0.292881 | − | 0.507285i | ||||
\(299\) | 17.2181 | + | 11.9879i | 0.995750 | + | 0.693281i | ||||
\(300\) | −20.6130 | −1.19009 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.02535 | + | 12.1683i | 0.404263 | + | 0.700205i | ||||
\(303\) | −1.58247 | − | 2.74091i | −0.0909104 | − | 0.157461i | ||||
\(304\) | 2.31290 | + | 4.00605i | 0.132654 | + | 0.229763i | ||||
\(305\) | −2.57135 | −0.147235 | ||||||||
\(306\) | 7.12424 | + | 12.3395i | 0.407266 | + | 0.705405i | ||||
\(307\) | −16.1760 | −0.923212 | −0.461606 | − | 0.887085i | \(-0.652727\pi\) | ||||
−0.461606 | + | 0.887085i | \(0.652727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.157110 | − | 0.272123i | −0.00893769 | − | 0.0154805i | ||||
\(310\) | 48.2329 | 2.73945 | ||||||||
\(311\) | −0.654032 | − | 1.13282i | −0.0370868 | − | 0.0642362i | 0.846886 | − | 0.531774i | \(-0.178474\pi\) |
−0.883973 | + | 0.467538i | \(0.845141\pi\) | |||||||
\(312\) | 3.69674 | − | 1.73584i | 0.209287 | − | 0.0982726i | ||||
\(313\) | 6.59889 | − | 11.4296i | 0.372991 | − | 0.646040i | −0.617033 | − | 0.786937i | \(-0.711665\pi\) |
0.990024 | + | 0.140897i | \(0.0449988\pi\) | |||||||
\(314\) | 18.1042 | + | 31.3574i | 1.02168 | + | 1.76960i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.5241 | − | 35.5488i | 1.15457 | − | 1.99977i | ||||
\(317\) | 4.03776 | − | 6.99360i | 0.226783 | − | 0.392800i | −0.730070 | − | 0.683373i | \(-0.760512\pi\) |
0.956853 | + | 0.290573i | \(0.0938458\pi\) | |||||||
\(318\) | −3.24359 | −0.181892 | ||||||||
\(319\) | 1.97777 | 0.110734 | ||||||||
\(320\) | 27.2258 | − | 47.1564i | 1.52197 | − | 2.63613i | ||||
\(321\) | 1.11877 | − | 1.93776i | 0.0624435 | − | 0.108155i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.29470 | − | 7.43863i | −0.238963 | − | 0.413897i | ||||
\(324\) | −9.33168 | + | 16.1629i | −0.518426 | + | 0.897941i | ||||
\(325\) | 3.90226 | − | 46.0164i | 0.216458 | − | 2.55253i | ||||
\(326\) | −26.1959 | − | 45.3726i | −1.45086 | − | 2.51296i | ||||
\(327\) | −8.41290 | −0.465234 | ||||||||
\(328\) | −6.48388 | − | 11.2304i | −0.358012 | − | 0.620096i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.82933 | 0.155750 | ||||||||
\(331\) | 7.47256 | + | 12.9429i | 0.410729 | + | 0.711403i | 0.994970 | − | 0.100177i | \(-0.0319409\pi\) |
−0.584241 | + | 0.811580i | \(0.698608\pi\) | |||||||
\(332\) | 16.7846 | 0.921174 | ||||||||
\(333\) | −0.444553 | − | 0.769988i | −0.0243613 | − | 0.0421951i | ||||
\(334\) | −19.7917 | − | 34.2802i | −1.08295 | − | 1.87573i | ||||
\(335\) | −21.8803 | − | 37.8979i | −1.19545 | − | 2.07058i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1695 | −0.935282 | −0.467641 | − | 0.883918i | \(-0.654896\pi\) | ||||
−0.467641 | + | 0.883918i | \(0.654896\pi\) | |||||||
\(338\) | 10.0153 | + | 27.0666i | 0.544759 | + | 1.47223i | ||||
\(339\) | 3.34592 | + | 5.79530i | 0.181725 | + | 0.314758i | ||||
\(340\) | −14.6991 | + | 25.4597i | −0.797173 | + | 1.38074i | ||||
\(341\) | −2.82933 | −0.153217 | ||||||||
\(342\) | 10.8132 | − | 18.7290i | 0.584712 | − | 1.01275i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.31843 | + | 5.74769i | −0.178918 | + | 0.309895i | ||||
\(345\) | 6.74733 | + | 11.6867i | 0.363264 | + | 0.629192i | ||||
\(346\) | −8.40423 | − | 14.5566i | −0.451814 | − | 0.782565i | ||||
\(347\) | −3.93845 | −0.211427 | −0.105713 | − | 0.994397i | \(-0.533713\pi\) | ||||
−0.105713 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(348\) | 5.79178 | 0.310472 | ||||||||
\(349\) | 8.58883 | + | 14.8763i | 0.459750 | + | 0.796310i | 0.998947 | − | 0.0458695i | \(-0.0146058\pi\) |
−0.539198 | + | 0.842179i | \(0.681272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.26563 | + | 6.45110i | 0.494563 | + | 0.344334i | ||||
\(352\) | −1.91420 | + | 3.31549i | −0.102027 | + | 0.176716i | ||||
\(353\) | −9.09821 | + | 15.7586i | −0.484249 | + | 0.838744i | −0.999836 | − | 0.0180932i | \(-0.994240\pi\) |
0.515587 | + | 0.856837i | \(0.327574\pi\) | |||||||
\(354\) | 1.10260 | − | 1.90976i | 0.0586025 | − | 0.101503i | ||||
\(355\) | 23.6274 | + | 40.9238i | 1.25401 | + | 2.17201i | ||||
\(356\) | 21.8682 | 1.15901 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.3118 | − | 43.8413i | 1.33777 | − | 2.31709i | ||||
\(359\) | −8.15631 | + | 14.1272i | −0.430474 | + | 0.745603i | −0.996914 | − | 0.0785003i | \(-0.974987\pi\) |
0.566440 | + | 0.824103i | \(0.308320\pi\) | |||||||
\(360\) | −23.4671 | −1.23683 | ||||||||
\(361\) | 2.98148 | − | 5.16408i | 0.156920 | − | 0.271794i | ||||
\(362\) | −30.9233 | −1.62529 | ||||||||
\(363\) | 5.87909 | 0.308572 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.7042 | −1.08371 | ||||||||
\(366\) | 0.743381 | 0.0388571 | ||||||||
\(367\) | −18.0982 | + | 31.3469i | −0.944716 | + | 1.63630i | −0.188398 | + | 0.982093i | \(0.560329\pi\) |
−0.756319 | + | 0.654203i | \(0.773004\pi\) | |||||||
\(368\) | −7.45482 | −0.388610 | ||||||||
\(369\) | 8.48731 | − | 14.7005i | 0.441832 | − | 0.765275i | ||||
\(370\) | 1.54366 | − | 2.67369i | 0.0802508 | − | 0.138998i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.28551 | −0.429584 | ||||||||
\(373\) | −4.89892 | − | 8.48518i | −0.253657 | − | 0.439346i | 0.710873 | − | 0.703320i | \(-0.248300\pi\) |
−0.964530 | + | 0.263974i | \(0.914967\pi\) | |||||||
\(374\) | 1.45113 | − | 2.51343i | 0.0750361 | − | 0.129966i | ||||
\(375\) | 9.05435 | − | 15.6826i | 0.467564 | − | 0.809845i | ||||
\(376\) | 8.46051 | − | 14.6540i | 0.436317 | − | 0.755724i | ||||
\(377\) | −1.09645 | + | 12.9296i | −0.0564699 | + | 0.665907i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.53275 | − | 11.3151i | −0.335565 | − | 0.581216i | 0.648028 | − | 0.761616i | \(-0.275594\pi\) |
−0.983593 | + | 0.180401i | \(0.942261\pi\) | |||||||
\(380\) | 44.6209 | 2.28900 | ||||||||
\(381\) | −1.07749 | −0.0552014 | ||||||||
\(382\) | 14.0658 | + | 24.3626i | 0.719667 | + | 1.24650i | ||||
\(383\) | 13.8965 | + | 24.0694i | 0.710076 | + | 1.22989i | 0.964828 | + | 0.262881i | \(0.0846726\pi\) |
−0.254753 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(384\) | −4.04260 | + | 7.00199i | −0.206298 | + | 0.357319i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.61198 | − | 7.98818i | 0.234744 | − | 0.406588i | ||||
\(387\) | −8.68756 | −0.441614 | ||||||||
\(388\) | −10.0163 | + | 17.3487i | −0.508499 | + | 0.880747i | ||||
\(389\) | −6.85233 | − | 11.8686i | −0.347427 | − | 0.601761i | 0.638365 | − | 0.769734i | \(-0.279611\pi\) |
−0.985792 | + | 0.167973i | \(0.946278\pi\) | |||||||
\(390\) | −1.56854 | + | 18.4966i | −0.0794259 | + | 0.936611i | ||||
\(391\) | 13.8425 | 0.700044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78610 | + | 3.09361i | 0.0900968 | + | 0.156052i | ||||
\(394\) | 7.60375 | + | 13.1701i | 0.383071 | + | 0.663499i | ||||
\(395\) | 29.5761 | + | 51.2274i | 1.48814 | + | 2.57753i | ||||
\(396\) | 4.34195 | 0.218191 | ||||||||
\(397\) | 3.95597 | + | 6.85194i | 0.198545 | + | 0.343889i | 0.948057 | − | 0.318101i | \(-0.103045\pi\) |
−0.749512 | + | 0.661991i | \(0.769712\pi\) | |||||||
\(398\) | 1.80617 | 0.0905351 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.20472 | + | 14.2110i | 0.410236 | + | 0.710549i | ||||
\(401\) | −16.5442 | −0.826180 | −0.413090 | − | 0.910690i | \(-0.635550\pi\) | ||||
−0.413090 | + | 0.910690i | \(0.635550\pi\) | |||||||
\(402\) | 6.32562 | + | 10.9563i | 0.315493 | + | 0.546451i | ||||
\(403\) | 1.56854 | − | 18.4966i | 0.0781344 | − | 0.921381i | ||||
\(404\) | 8.43261 | − | 14.6057i | 0.419538 | − | 0.726661i | ||||
\(405\) | −13.4474 | − | 23.2915i | −0.668205 | − | 1.15737i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0905505 | + | 0.156838i | −0.00448842 | + | 0.00777417i | ||||
\(408\) | 1.34728 | − | 2.33355i | 0.0667002 | − | 0.115528i | ||||
\(409\) | −25.7819 | −1.27483 | −0.637416 | − | 0.770520i | \(-0.719997\pi\) | ||||
−0.637416 | + | 0.770520i | \(0.719997\pi\) | |||||||
\(410\) | 58.9423 | 2.91095 | ||||||||
\(411\) | −4.19240 | + | 7.26146i | −0.206796 | + | 0.358181i | ||||
\(412\) | 0.837205 | − | 1.45008i | 0.0412461 | − | 0.0714404i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 17.4263 | + | 30.1833i | 0.856458 | + | 1.48343i | ||||
\(415\) | −12.0937 | + | 20.9469i | −0.593655 | + | 1.02824i | ||||
\(416\) | −20.6136 | − | 14.3520i | −1.01066 | − | 0.703665i | ||||
\(417\) | 4.80748 | + | 8.32680i | 0.235423 | + | 0.407765i | ||||
\(418\) | −4.40506 | −0.215459 | ||||||||
\(419\) | 11.8436 | + | 20.5137i | 0.578596 | + | 1.00216i | 0.995641 | + | 0.0932720i | \(0.0297326\pi\) |
−0.417044 | + | 0.908886i | \(0.636934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8246 | −1.01493 | −0.507465 | − | 0.861672i | \(-0.669417\pi\) | ||||
−0.507465 | + | 0.861672i | \(0.669417\pi\) | |||||||
\(422\) | 15.5105 | + | 26.8650i | 0.755041 | + | 1.30777i | ||||
\(423\) | 22.1494 | 1.07694 | ||||||||
\(424\) | −2.73993 | − | 4.74570i | −0.133063 | − | 0.230471i | ||||
\(425\) | −15.2349 | − | 26.3877i | −0.739002 | − | 1.27999i | ||||
\(426\) | −6.83069 | − | 11.8311i | −0.330948 | − | 0.573219i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.9233 | 0.576335 | ||||||||
\(429\) | 0.0920100 | − | 1.08501i | 0.00444228 | − | 0.0523846i | ||||
\(430\) | −15.0832 | − | 26.1249i | −0.727378 | − | 1.25986i | ||||
\(431\) | −9.97521 | + | 17.2776i | −0.480489 | + | 0.832232i | −0.999749 | − | 0.0223845i | \(-0.992874\pi\) |
0.519260 | + | 0.854616i | \(0.326208\pi\) | |||||||
\(432\) | −4.01168 | −0.193012 | ||||||||
\(433\) | 0.00834083 | − | 0.0144467i | 0.000400835 | − | 0.000694266i | −0.865825 | − | 0.500347i | \(-0.833206\pi\) |
0.866226 | + | 0.499653i | \(0.166539\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.17311 | + | 7.22804i | −0.200085 | + | 0.346558i | ||||
\(436\) | −22.4152 | − | 38.8243i | −1.07349 | − | 1.85935i | ||||
\(437\) | −10.5051 | − | 18.1954i | −0.502527 | − | 0.870402i | ||||
\(438\) | 5.98561 | 0.286004 | ||||||||
\(439\) | −13.4960 | −0.644130 | −0.322065 | − | 0.946718i | \(-0.604377\pi\) | ||||
−0.322065 | + | 0.946718i | \(0.604377\pi\) | |||||||
\(440\) | 2.39000 | + | 4.13959i | 0.113939 | + | 0.197347i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.6269 | + | 10.8801i | 0.743296 | + | 0.517512i | ||||
\(443\) | 7.50552 | − | 12.9999i | 0.356598 | − | 0.617646i | −0.630792 | − | 0.775952i | \(-0.717270\pi\) |
0.987390 | + | 0.158306i | \(0.0506032\pi\) | |||||||
\(444\) | −0.265171 | + | 0.459290i | −0.0125845 | + | 0.0217969i | ||||
\(445\) | −15.7566 | + | 27.2912i | −0.746933 | + | 1.29373i | ||||
\(446\) | −15.0228 | − | 26.0202i | −0.711350 | − | 1.23209i | ||||
\(447\) | −2.50313 | −0.118394 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.8918 | − | 20.5972i | 0.561210 | − | 0.972044i | −0.436181 | − | 0.899859i | \(-0.643669\pi\) |
0.997391 | − | 0.0721852i | \(-0.0229973\pi\) | |||||||
\(450\) | 38.3586 | − | 66.4390i | 1.80824 | − | 3.13196i | ||||
\(451\) | −3.45754 | −0.162809 | ||||||||
\(452\) | −17.8297 | + | 30.8819i | −0.838636 | + | 1.45256i | ||||
\(453\) | 3.47818 | 0.163419 | ||||||||
\(454\) | 11.9159 | 0.559242 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.08981 | −0.191523 | ||||||||
\(457\) | 18.1313 | 0.848148 | 0.424074 | − | 0.905627i | \(-0.360600\pi\) | ||||
0.424074 | + | 0.905627i | \(0.360600\pi\) | |||||||
\(458\) | 3.44002 | − | 5.95828i | 0.160741 | − | 0.278412i | ||||
\(459\) | 7.44909 | 0.347694 | ||||||||
\(460\) | −35.9550 | + | 62.2759i | −1.67641 | + | 2.90363i | ||||
\(461\) | −3.03980 | + | 5.26508i | −0.141577 | + | 0.245219i | −0.928091 | − | 0.372354i | \(-0.878551\pi\) |
0.786513 | + | 0.617573i | \(0.211884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.19289 | 0.241334 | 0.120667 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120667 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(464\) | −2.30534 | − | 3.99297i | −0.107023 | − | 0.185369i | ||||
\(465\) | 5.96990 | − | 10.3402i | 0.276848 | − | 0.479514i | ||||
\(466\) | 22.6121 | − | 39.1653i | 1.04748 | − | 1.81430i | ||||
\(467\) | −4.34984 | + | 7.53414i | −0.201287 | + | 0.348638i | −0.948943 | − | 0.315447i | \(-0.897846\pi\) |
0.747657 | + | 0.664085i | \(0.231179\pi\) | |||||||
\(468\) | −2.40711 | + | 28.3852i | −0.111268 | + | 1.31211i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 38.4555 | + | 66.6069i | 1.77382 | + | 3.07235i | ||||
\(471\) | 8.96320 | 0.413002 | ||||||||
\(472\) | 3.72556 | 0.171483 | ||||||||
\(473\) | 0.884779 | + | 1.53248i | 0.0406822 | + | 0.0704636i | ||||
\(474\) | −8.55049 | − | 14.8099i | −0.392737 | − | 0.680240i | ||||
\(475\) | −23.1237 | + | 40.0513i | −1.06099 | + | 1.83768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.58653 | − | 6.21205i | 0.164216 | − | 0.284430i | ||||
\(478\) | −2.86730 | −0.131147 | ||||||||
\(479\) | 12.1094 | − | 20.9741i | 0.553294 | − | 0.958332i | −0.444741 | − | 0.895659i | \(-0.646704\pi\) |
0.998034 | − | 0.0626730i | \(-0.0199625\pi\) | |||||||
\(480\) | −8.07793 | − | 13.9914i | −0.368705 | − | 0.638616i | ||||
\(481\) | −0.975119 | − | 0.678916i | −0.0444616 | − | 0.0309559i | ||||
\(482\) | −4.73461 | −0.215655 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6642 | + | 27.1312i | 0.712009 | + | 1.23323i | ||||
\(485\) | −14.4339 | − | 25.0003i | −0.655410 | − | 1.13520i | ||||
\(486\) | 14.3150 | + | 24.7944i | 0.649343 | + | 1.12470i | ||||
\(487\) | 1.77393 | 0.0803846 | 0.0401923 | − | 0.999192i | \(-0.487203\pi\) | ||||
0.0401923 | + | 0.999192i | \(0.487203\pi\) | |||||||
\(488\) | 0.627949 | + | 1.08764i | 0.0284259 | + | 0.0492351i | ||||
\(489\) | −12.9693 | −0.586493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.34483 | + | 5.79342i | 0.150950 | + | 0.261453i | 0.931577 | − | 0.363544i | \(-0.118433\pi\) |
−0.780627 | + | 0.624997i | \(0.785100\pi\) | |||||||
\(492\) | −10.1252 | −0.456479 | ||||||||
\(493\) | 4.28067 | + | 7.41434i | 0.192792 | + | 0.333925i | ||||
\(494\) | 2.44210 | − | 28.7978i | 0.109875 | − | 1.29568i | ||||
\(495\) | −3.12847 | + | 5.41867i | −0.140614 | + | 0.243551i | ||||
\(496\) | 3.29794 | + | 5.71220i | 0.148082 | + | 0.256485i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.49629 | − | 6.05575i | 0.156673 | − | 0.271365i | ||||
\(499\) | −12.3194 | + | 21.3378i | −0.551491 | + | 0.955210i | 0.446677 | + | 0.894695i | \(0.352607\pi\) |
−0.998167 | + | 0.0605143i | \(0.980726\pi\) | |||||||
\(500\) | 96.4972 | 4.31548 | ||||||||
\(501\) | −9.79864 | −0.437771 | ||||||||
\(502\) | −34.1560 | + | 59.1600i | −1.52446 | + | 2.64044i | ||||
\(503\) | 16.5726 | − | 28.7046i | 0.738936 | − | 1.27987i | −0.214039 | − | 0.976825i | \(-0.568662\pi\) |
0.952975 | − | 0.303049i | \(-0.0980046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1518 | + | 21.0475i | 0.540747 | + | 0.936601i | ||||
\(506\) | 3.54955 | − | 6.14800i | 0.157797 | − | 0.273312i | ||||
\(507\) | 7.04215 | + | 1.20302i | 0.312753 | + | 0.0534279i | ||||
\(508\) | −2.87085 | − | 4.97246i | −0.127373 | − | 0.220617i | ||||
\(509\) | 27.6580 | 1.22592 | 0.612961 | − | 0.790114i | \(-0.289978\pi\) | ||||
0.612961 | + | 0.790114i | \(0.289978\pi\) | |||||||
\(510\) | 6.12377 | + | 10.6067i | 0.271165 | + | 0.469672i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.2061 | 0.627828 | ||||||||
\(513\) | −5.65314 | − | 9.79152i | −0.249592 | − | 0.432306i | ||||
\(514\) | 3.27143 | 0.144296 | ||||||||
\(515\) | 1.20645 | + | 2.08963i | 0.0531626 | + | 0.0920802i | ||||
\(516\) | 2.59102 | + | 4.48778i | 0.114063 | + | 0.197563i | ||||
\(517\) | −2.25579 | − | 3.90714i | −0.0992096 | − | 0.171836i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.16085 | −0.182641 | ||||||||
\(520\) | −28.3873 | + | 13.3295i | −1.24487 | + | 0.584538i | ||||
\(521\) | 0.711083 | + | 1.23163i | 0.0311531 | + | 0.0539587i | 0.881182 | − | 0.472778i | \(-0.156749\pi\) |
−0.850029 | + | 0.526737i | \(0.823415\pi\) | |||||||
\(522\) | −10.7779 | + | 18.6679i | −0.471736 | + | 0.817070i | ||||
\(523\) | 3.36178 | 0.147000 | 0.0735002 | − | 0.997295i | \(-0.476583\pi\) | ||||
0.0735002 | + | 0.997295i | \(0.476583\pi\) | |||||||
\(524\) | −9.51772 | + | 16.4852i | −0.415784 | + | 0.720158i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.41143 | + | 12.8370i | −0.323154 | + | 0.559718i | ||||
\(527\) | −6.12377 | − | 10.6067i | −0.266756 | − | 0.462034i | ||||
\(528\) | 0.193456 | + | 0.335076i | 0.00841910 | + | 0.0145823i | ||||
\(529\) | 10.8596 | 0.472156 | ||||||||
\(530\) | 24.9076 | 1.08192 | ||||||||
\(531\) | 2.43835 | + | 4.22335i | 0.105815 | + | 0.183278i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.91681 | − | 22.6035i | 0.0830260 | − | 0.979065i | ||||
\(534\) | 4.55524 | − | 7.88990i | 0.197124 | − | 0.341429i | ||||
\(535\) | −8.59102 | + | 14.8801i | −0.371422 | + | 0.643322i | ||||
\(536\) | −10.6868 | + | 18.5100i | −0.461598 | + | 0.799512i | ||||
\(537\) | −6.26580 | − | 10.8527i | −0.270389 | − | 0.468328i | ||||
\(538\) | −16.8182 | −0.725083 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.3486 | + | 33.5127i | −0.832630 | + | 1.44216i | ||||
\(541\) | −3.88144 | + | 6.72286i | −0.166876 | + | 0.289038i | −0.937320 | − | 0.348470i | \(-0.886701\pi\) |
0.770444 | + | 0.637508i | \(0.220035\pi\) | |||||||
\(542\) | −45.6612 | −1.96131 | ||||||||
\(543\) | −3.82745 | + | 6.62934i | −0.164252 | + | 0.284492i | ||||
\(544\) | −16.5723 | −0.710530 | ||||||||
\(545\) | 64.6027 | 2.76728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.19247 | −0.264771 | −0.132385 | − | 0.991198i | \(-0.542264\pi\) | ||||
−0.132385 | + | 0.991198i | \(0.542264\pi\) | |||||||
\(548\) | −44.6808 | −1.90867 | ||||||||
\(549\) | −0.821977 | + | 1.42371i | −0.0350811 | + | 0.0607623i | ||||
\(550\) | −15.6264 | −0.666313 | ||||||||
\(551\) | 6.49723 | − | 11.2535i | 0.276791 | − | 0.479416i | ||||
\(552\) | 3.29553 | − | 5.70802i | 0.140267 | − | 0.242949i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.6661 | 0.538129 | ||||||||
\(555\) | −0.382124 | − | 0.661858i | −0.0162202 | − | 0.0280943i | ||||
\(556\) | −25.6180 | + | 44.3717i | −1.08644 | + | 1.88178i | ||||
\(557\) | −14.7729 | + | 25.5874i | −0.625948 | + | 1.08417i | 0.362409 | + | 0.932019i | \(0.381954\pi\) |
−0.988357 | + | 0.152154i | \(0.951379\pi\) | |||||||
\(558\) | 15.4185 | − | 26.7056i | 0.652716 | − | 1.13054i | ||||
\(559\) | −10.5090 | + | 4.93461i | −0.444484 | + | 0.208712i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.359219 | − | 0.622186i | −0.0151662 | − | 0.0262687i | ||||
\(562\) | −14.1484 | −0.596816 | ||||||||
\(563\) | −6.46736 | −0.272567 | −0.136283 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136283 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(564\) | −6.60593 | − | 11.4418i | −0.278160 | − | 0.481787i | ||||
\(565\) | −25.6933 | − | 44.5022i | −1.08093 | − | 1.87222i | ||||
\(566\) | 29.9916 | − | 51.9470i | 1.26064 | − | 2.18350i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.5401 | − | 19.9880i | 0.484210 | − | 0.838676i | ||||
\(569\) | 21.6956 | 0.909526 | 0.454763 | − | 0.890612i | \(-0.349724\pi\) | ||||
0.454763 | + | 0.890612i | \(0.349724\pi\) | |||||||
\(570\) | 9.29470 | − | 16.0989i | 0.389312 | − | 0.674308i | ||||
\(571\) | 8.32088 | + | 14.4122i | 0.348218 | + | 0.603131i | 0.985933 | − | 0.167141i | \(-0.0534536\pi\) |
−0.637715 | + | 0.770272i | \(0.720120\pi\) | |||||||
\(572\) | 5.25229 | − | 2.46626i | 0.219609 | − | 0.103120i | ||||
\(573\) | 6.96381 | 0.290917 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.2656 | − | 64.5459i | −1.55408 | − | 2.69175i | ||||
\(576\) | −17.4064 | − | 30.1487i | −0.725265 | − | 1.25620i | ||||
\(577\) | −1.32120 | − | 2.28839i | −0.0550024 | − | 0.0952669i | 0.837213 | − | 0.546877i | \(-0.184183\pi\) |
−0.892216 | + | 0.451610i | \(0.850850\pi\) | |||||||
\(578\) | −25.1769 | −1.04722 | ||||||||
\(579\) | −1.14167 | − | 1.97743i | −0.0474462 | − | 0.0821793i | ||||
\(580\) | −44.4752 | −1.84673 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.17286 | + | 7.22760i | 0.172970 | + | 0.299594i | ||||
\(583\) | −1.46107 | −0.0605114 | ||||||||
\(584\) | 5.05617 | + | 8.75755i | 0.209226 | + | 0.362390i | ||||
\(585\) | −33.6899 | − | 23.4562i | −1.39290 | − | 0.969795i | ||||
\(586\) | −5.41096 | + | 9.37205i | −0.223525 | + | 0.387156i | ||||
\(587\) | 3.69407 | + | 6.39832i | 0.152471 | + | 0.264087i | 0.932135 | − | 0.362110i | \(-0.117944\pi\) |
−0.779664 | + | 0.626198i | \(0.784610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.29470 | + | 16.0989i | −0.382981 | + | 0.663343i | ||||
\(590\) | −8.46687 | + | 14.6651i | −0.348576 | + | 0.603751i | ||||
\(591\) | 3.76453 | 0.154852 | ||||||||
\(592\) | 0.422191 | 0.0173519 | ||||||||
\(593\) | 23.4515 | − | 40.6192i | 0.963037 | − | 1.66803i | 0.248238 | − | 0.968699i | \(-0.420149\pi\) |
0.714799 | − | 0.699330i | \(-0.246518\pi\) | |||||||
\(594\) | 1.91013 | − | 3.30844i | 0.0783735 | − | 0.135747i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.66931 | − | 11.5516i | −0.273186 | − | 0.473171i | ||||
\(597\) | 0.223554 | − | 0.387207i | 0.00914945 | − | 0.0158473i | ||||
\(598\) | 38.2244 | + | 26.6133i | 1.56311 | + | 1.08830i | ||||
\(599\) | −0.811449 | − | 1.40547i | −0.0331549 | − | 0.0574260i | 0.848972 | − | 0.528438i | \(-0.177222\pi\) |
−0.882127 | + | 0.471012i | \(0.843889\pi\) | |||||||
\(600\) | −14.5081 | −0.592291 | ||||||||
\(601\) | −23.5174 | − | 40.7333i | −0.959293 | − | 1.66154i | −0.724223 | − | 0.689566i | \(-0.757801\pi\) |
−0.235070 | − | 0.971978i | \(-0.575532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.9777 | −1.13934 | ||||||||
\(604\) | 9.26721 | + | 16.0513i | 0.377077 | + | 0.653117i | ||||
\(605\) | −45.1456 | −1.83543 | ||||||||
\(606\) | −3.51309 | − | 6.08485i | −0.142709 | − | 0.247180i | ||||
\(607\) | −14.1935 | − | 24.5838i | −0.576095 | − | 0.997825i | −0.995922 | − | 0.0902211i | \(-0.971243\pi\) |
0.419827 | − | 0.907604i | \(-0.362091\pi\) | |||||||
\(608\) | 12.5767 | + | 21.7836i | 0.510054 | + | 0.883440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.70843 | −0.231127 | ||||||||
\(611\) | 26.7933 | − | 12.5810i | 1.08394 | − | 0.508974i | ||||
\(612\) | 9.39766 | + | 16.2772i | 0.379878 | + | 0.657968i | ||||
\(613\) | 23.7782 | − | 41.1851i | 0.960393 | − | 1.66345i | 0.238878 | − | 0.971050i | \(-0.423220\pi\) |
0.721514 | − | 0.692399i | \(-0.243446\pi\) | |||||||
\(614\) | −35.9108 | −1.44924 | ||||||||
\(615\) | 7.29543 | − | 12.6360i | 0.294180 | − | 0.509535i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.24338 | − | 14.2780i | 0.331866 | − | 0.574809i | −0.651012 | − | 0.759068i | \(-0.725655\pi\) |
0.982878 | + | 0.184259i | \(0.0589885\pi\) | |||||||
\(618\) | −0.348786 | − | 0.604115i | −0.0140302 | − | 0.0243011i | ||||
\(619\) | −15.9706 | − | 27.6619i | −0.641912 | − | 1.11182i | −0.985006 | − | 0.172523i | \(-0.944808\pi\) |
0.343094 | − | 0.939301i | \(-0.388525\pi\) | |||||||
\(620\) | 63.6245 | 2.55522 | ||||||||
\(621\) | 18.2209 | 0.731181 | ||||||||
\(622\) | −1.45196 | − | 2.51486i | −0.0582182 | − | 0.100837i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.29779 | + | 1.07895i | −0.0919851 | + | 0.0431925i | ||||
\(625\) | −37.5072 | + | 64.9644i | −1.50029 | + | 2.59858i | ||||
\(626\) | 14.6496 | − | 25.3738i | 0.585515 | − | 1.01414i | ||||
\(627\) | −0.545225 | + | 0.944357i | −0.0217742 | + | 0.0377140i | ||||
\(628\) | 23.8814 | + | 41.3639i | 0.952973 | + | 1.65060i | ||||
\(629\) | −0.783945 | −0.0312579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.59577 | + | 11.4242i | −0.262573 | + | 0.454790i | −0.966925 | − | 0.255061i | \(-0.917905\pi\) |
0.704352 | + | 0.709851i | \(0.251238\pi\) | |||||||
\(632\) | 14.4456 | − | 25.0204i | 0.574613 | − | 0.995259i | ||||
\(633\) | 7.67910 | 0.305217 | ||||||||
\(634\) | 8.96386 | − | 15.5259i | 0.356000 | − | 0.616610i | ||||
\(635\) | 8.27405 | 0.328346 | ||||||||
\(636\) | −4.27865 | −0.169660 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.39068 | 0.173829 | ||||||||
\(639\) | 30.2115 | 1.19515 | ||||||||
\(640\) | 31.0432 | − | 53.7684i | 1.22709 | − | 2.12538i | ||||
\(641\) | −47.1627 | −1.86282 | −0.931408 | − | 0.363978i | \(-0.881418\pi\) | ||||
−0.931408 | + | 0.363978i | \(0.881418\pi\) | |||||||
\(642\) | 2.48367 | − | 4.30184i | 0.0980227 | − | 0.169780i | ||||
\(643\) | −1.40679 | + | 2.43664i | −0.0554785 | + | 0.0960916i | −0.892431 | − | 0.451184i | \(-0.851002\pi\) |
0.836952 | + | 0.547276i | \(0.184335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.46755 | −0.294035 | ||||||||
\(646\) | −9.53426 | − | 16.5138i | −0.375121 | − | 0.649728i | ||||
\(647\) | 12.9891 | − | 22.4979i | 0.510656 | − | 0.884482i | −0.489268 | − | 0.872134i | \(-0.662736\pi\) |
0.999924 | − | 0.0123485i | \(-0.00393074\pi\) | |||||||
\(648\) | −6.56795 | + | 11.3760i | −0.258014 | + | 0.446893i | ||||
\(649\) | 0.496665 | − | 0.860249i | 0.0194958 | − | 0.0337677i | ||||
\(650\) | 8.66304 | − | 102.157i | 0.339792 | − | 4.00692i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −34.5553 | − | 59.8515i | −1.35329 | − | 2.34397i | ||||
\(653\) | −26.8426 | −1.05043 | −0.525216 | − | 0.850969i | \(-0.676015\pi\) | ||||
−0.525216 | + | 0.850969i | \(0.676015\pi\) | |||||||
\(654\) | −18.6767 | −0.730317 | ||||||||
\(655\) | −13.7155 | − | 23.7559i | −0.535908 | − | 0.928219i | ||||
\(656\) | 4.03019 | + | 6.98050i | 0.157353 | + | 0.272543i | ||||
\(657\) | −6.61846 | + | 11.4635i | −0.258211 | + | 0.447234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.78666 | + | 13.4869i | −0.303325 | + | 0.525375i | −0.976887 | − | 0.213756i | \(-0.931430\pi\) |
0.673562 | + | 0.739131i | \(0.264764\pi\) | |||||||
\(660\) | 3.73220 | 0.145276 | ||||||||
\(661\) | 16.6902 | − | 28.9083i | 0.649174 | − | 1.12440i | −0.334146 | − | 0.942521i | \(-0.608448\pi\) |
0.983320 | − | 0.181881i | \(-0.0582187\pi\) | |||||||
\(662\) | 16.5891 | + | 28.7332i | 0.644755 | + | 1.11675i | ||||
\(663\) | 4.26665 | − | 2.00344i | 0.165703 | − | 0.0778073i | ||||
\(664\) | 11.8136 | 0.458455 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.986911 | − | 1.70938i | −0.0382420 | − | 0.0662371i | ||||
\(667\) | 10.4708 | + | 18.1359i | 0.405431 | + | 0.702227i | ||||
\(668\) | −26.1074 | − | 45.2193i | −1.01013 | − | 1.74959i | ||||
\(669\) | −7.43762 | −0.287555 | ||||||||
\(670\) | −48.5745 | − | 84.1335i | −1.87660 | − | 3.25036i | ||||
\(671\) | 0.334855 | 0.0129269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.427076 | − | 0.739717i | −0.0164626 | − | 0.0285140i | 0.857677 | − | 0.514189i | \(-0.171907\pi\) |
−0.874139 | + | 0.485675i | \(0.838574\pi\) | |||||||
\(674\) | −38.1164 | −1.46819 | ||||||||
\(675\) | −20.0538 | − | 34.7342i | −0.771872 | − | 1.33692i | ||||
\(676\) | 13.2113 | + | 35.7038i | 0.508125 | + | 1.37322i | ||||
\(677\) | −12.2725 | + | 21.2565i | −0.471669 | + | 0.816955i | −0.999475 | − | 0.0324100i | \(-0.989682\pi\) |
0.527805 | + | 0.849365i | \(0.323015\pi\) | |||||||
\(678\) | 7.42797 | + | 12.8656i | 0.285269 | + | 0.494101i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.3458 | + | 17.9194i | −0.396742 | + | 0.687177i | ||||
\(681\) | 1.47486 | − | 2.55454i | 0.0565168 | − | 0.0978900i | ||||
\(682\) | −6.28114 | −0.240517 | ||||||||
\(683\) | −43.0372 | −1.64677 | −0.823387 | − | 0.567480i | \(-0.807918\pi\) | ||||
−0.823387 | + | 0.567480i | \(0.807918\pi\) | |||||||
\(684\) | 14.2638 | − | 24.7057i | 0.545391 | − | 0.944645i | ||||
\(685\) | 32.1935 | − | 55.7608i | 1.23005 | − | 2.13051i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.851558 | − | 1.47494i | −0.0324889 | − | 0.0562725i | ||||
\(688\) | 2.06264 | − | 3.57260i | 0.0786374 | − | 0.136204i | ||||
\(689\) | 0.809995 | − | 9.55167i | 0.0308583 | − | 0.363890i | ||||
\(690\) | 14.9791 | + | 25.9446i | 0.570246 | + | 0.987695i | ||||
\(691\) | 25.8195 | 0.982220 | 0.491110 | − | 0.871097i | \(-0.336591\pi\) | ||||
0.491110 | + | 0.871097i | \(0.336591\pi\) | |||||||
\(692\) | −11.0861 | − | 19.2017i | −0.421431 | − | 0.729939i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.74338 | −0.331894 | ||||||||
\(695\) | −36.9167 | − | 63.9416i | −1.40033 | − | 2.42544i | ||||
\(696\) | 4.07646 | 0.154518 | ||||||||
\(697\) | −7.48346 | − | 12.9617i | −0.283456 | − | 0.490961i | ||||
\(698\) | 19.0673 | + | 33.0255i | 0.721707 | + | 1.25003i | ||||
\(699\) | −5.59750 | − | 9.69515i | −0.211717 | − | 0.366704i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.3178 | 0.616313 | 0.308156 | − | 0.951336i | \(-0.400288\pi\) | ||||
0.308156 | + | 0.951336i | \(0.400288\pi\) | |||||||
\(702\) | 20.5698 | + | 14.3215i | 0.776356 | + | 0.540530i | ||||
\(703\) | 0.594938 | + | 1.03046i | 0.0224385 | + | 0.0388647i | ||||
\(704\) | −3.54548 | + | 6.14096i | −0.133625 | + | 0.231446i | ||||
\(705\) | 19.0389 | 0.717047 | ||||||||
\(706\) | −20.1981 | + | 34.9841i | −0.760166 | + | 1.31665i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.45445 | − | 2.51918i | 0.0546616 | − | 0.0946767i | ||||
\(709\) | 11.1897 | + | 19.3811i | 0.420238 | + | 0.727874i | 0.995963 | − | 0.0897702i | \(-0.0286133\pi\) |
−0.575725 | + | 0.817644i | \(0.695280\pi\) | |||||||
\(710\) | 52.4529 | + | 90.8511i | 1.96852 | + | 3.40958i | ||||
\(711\) | 37.8181 | 1.41829 | ||||||||
\(712\) | 15.3916 | 0.576825 | ||||||||
\(713\) | −14.9791 | − | 25.9446i | −0.560973 | − | 0.971634i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.706545 | + | 8.33177i | −0.0264233 | + | 0.311590i | ||||
\(716\) | 33.3891 | − | 57.8315i | 1.24781 | − | 2.16127i | ||||
\(717\) | −0.354893 | + | 0.614692i | −0.0132537 | + | 0.0229561i | ||||
\(718\) | −18.1071 | + | 31.3624i | −0.675750 | + | 1.17043i | ||||
\(719\) | −11.3723 | − | 19.6973i | −0.424113 | − | 0.734586i | 0.572224 | − | 0.820098i | \(-0.306081\pi\) |
−0.996337 | + | 0.0855115i | \(0.972748\pi\) | |||||||
\(720\) | 14.5865 | 0.543606 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.61892 | − | 11.4643i | 0.246331 | − | 0.426657i | ||||
\(723\) | −0.586013 | + | 1.01500i | −0.0217941 | + | 0.0377484i | ||||
\(724\) | −40.7913 | −1.51599 | ||||||||
\(725\) | 23.0481 | − | 39.9205i | 0.855986 | − | 1.48261i | ||||
\(726\) | 13.0516 | 0.484392 | ||||||||
\(727\) | −18.7274 | −0.694561 | −0.347280 | − | 0.937761i | \(-0.612895\pi\) | ||||
−0.347280 | + | 0.937761i | \(0.612895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.0322 | −0.445638 | ||||||||
\(730\) | −45.9636 | −1.70119 | ||||||||
\(731\) | −3.83001 | + | 6.63377i | −0.141658 | + | 0.245359i | ||||
\(732\) | 0.980601 | 0.0362441 | ||||||||
\(733\) | −0.846341 | + | 1.46591i | −0.0312603 | + | 0.0541445i | −0.881232 | − | 0.472683i | \(-0.843285\pi\) |
0.849972 | + | 0.526828i | \(0.176619\pi\) | |||||||
\(734\) | −40.1781 | + | 69.5904i | −1.48300 | + | 2.56863i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −40.5368 | −1.49421 | ||||||||
\(737\) | 2.84937 | + | 4.93525i | 0.104958 | + | 0.181792i | ||||
\(738\) | 18.8419 | − | 32.6351i | 0.693580 | − | 1.20132i | ||||
\(739\) | −23.4581 | + | 40.6305i | −0.862919 | + | 1.49462i | 0.00618065 | + | 0.999981i | \(0.498033\pi\) |
−0.869099 | + | 0.494638i | \(0.835301\pi\) | |||||||
\(740\) | 2.03625 | − | 3.52689i | 0.0748541 | − | 0.129651i | ||||
\(741\) | −5.87141 | − | 4.08791i | −0.215692 | − | 0.150173i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.44831 | − | 11.1688i | −0.236566 | − | 0.409744i | 0.723161 | − | 0.690680i | \(-0.242688\pi\) |
−0.959727 | + | 0.280936i | \(0.909355\pi\) | |||||||
\(744\) | −5.83163 | −0.213798 | ||||||||
\(745\) | 19.2216 | 0.704223 | ||||||||
\(746\) | −10.8756 | − | 18.8372i | −0.398186 | − | 0.689678i | ||||
\(747\) | 7.73189 | + | 13.3920i | 0.282895 | + | 0.489989i | ||||
\(748\) | 1.91420 | − | 3.31549i | 0.0699900 | − | 0.121226i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 20.1007 | − | 34.8155i | 0.733974 | − | 1.27128i | ||||
\(751\) | −45.6333 | −1.66518 | −0.832591 | − | 0.553888i | \(-0.813144\pi\) | ||||
−0.832591 | + | 0.553888i | \(0.813144\pi\) | |||||||
\(752\) | −5.25881 | + | 9.10852i | −0.191769 | + | 0.332154i | ||||
\(753\) | 8.45515 | + | 14.6447i | 0.308123 | + | 0.533684i | ||||
\(754\) | −2.43412 | + | 28.7038i | −0.0886454 | + | 1.04533i | ||||
\(755\) | −26.7089 | −0.972038 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0782 | + | 33.0445i | 0.693410 | + | 1.20102i | 0.970714 | + | 0.240239i | \(0.0772260\pi\) |
−0.277303 | + | 0.960782i | \(0.589441\pi\) | |||||||
\(758\) | −14.5028 | − | 25.1195i | −0.526764 | − | 0.912382i | ||||
\(759\) | −0.878673 | − | 1.52191i | −0.0318938 | − | 0.0552417i | ||||
\(760\) | 31.4057 | 1.13920 | ||||||||
\(761\) | 21.3672 | + | 37.0092i | 0.774562 | + | 1.34158i | 0.935040 | + | 0.354542i | \(0.115363\pi\) |
−0.160478 | + | 0.987039i | \(0.551304\pi\) | |||||||
\(762\) | −2.39203 | −0.0866543 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.5543 | + | 32.1370i | 0.671271 | + | 1.16267i | ||||
\(765\) | −27.0849 | −0.979257 | ||||||||
\(766\) | 30.8502 | + | 53.4342i | 1.11466 | + | 1.93066i | ||||
\(767\) | 5.34848 | + | 3.72382i | 0.193122 | + | 0.134459i | ||||
\(768\) | −1.88364 | + | 3.26257i | −0.0679702 | + | 0.117728i | ||||
\(769\) | 10.8088 | + | 18.7215i | 0.389777 | + | 0.675113i | 0.992419 | − | 0.122898i | \(-0.0392189\pi\) |
−0.602643 | + | 0.798011i | \(0.705886\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.404912 | − | 0.701329i | 0.0145826 | − | 0.0252577i | ||||
\(772\) | 6.08371 | − | 10.5373i | 0.218958 | − | 0.379246i | ||||
\(773\) | −10.0011 | −0.359716 | −0.179858 | − | 0.983693i | \(-0.557564\pi\) | ||||
−0.179858 | + | 0.983693i | \(0.557564\pi\) | |||||||
\(774\) | −19.2865 | −0.693237 | ||||||||
\(775\) | −32.9718 | + | 57.1089i | −1.18438 | + | 2.05141i | ||||
\(776\) | −7.04980 | + | 12.2106i | −0.253073 | + | 0.438335i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.2122 | − | 26.3484i | −0.545385 | − | 0.944634i | ||||
\(779\) | −11.3584 | + | 19.6734i | −0.406958 | + | 0.704872i | ||||
\(780\) | −2.06907 | + | 24.3990i | −0.0740847 | + | 0.873625i | ||||
\(781\) | −3.07688 | − | 5.32931i | −0.110099 | − | 0.190698i | ||||
\(782\) | 30.7304 | 1.09892 | ||||||||
\(783\) | 5.63467 | + | 9.75954i | 0.201367 | + | 0.348778i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −68.8285 | −2.45659 | ||||||||
\(786\) | 3.96515 | + | 6.86785i | 0.141432 | + | 0.244968i | ||||
\(787\) | −41.7878 | −1.48957 | −0.744787 | − | 0.667302i | \(-0.767449\pi\) | ||||
−0.744787 | + | 0.667302i | \(0.767449\pi\) | |||||||
\(788\) | 10.0302 | + | 17.3728i | 0.357310 | + | 0.618880i | ||||
\(789\) | 1.83466 | + | 3.17772i | 0.0653156 | + | 0.113130i | ||||
\(790\) | 65.6593 | + | 113.725i | 2.33605 | + | 4.04616i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.05601 | 0.108591 | ||||||||
\(793\) | −0.185638 | + | 2.18909i | −0.00659221 | + | 0.0777370i | ||||
\(794\) | 8.78229 | + | 15.2114i | 0.311672 | + | 0.539831i | ||||
\(795\) | 3.08287 | − | 5.33968i | 0.109338 | − | 0.189379i | ||||
\(796\) | 2.38254 | 0.0844468 | ||||||||
\(797\) | −11.3856 | + | 19.7204i | −0.403297 | + | 0.698531i | −0.994122 | − | 0.108269i | \(-0.965469\pi\) |
0.590825 | + | 0.806800i | \(0.298803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.76481 | − | 16.9131i | 0.345454 | − | 0.598344i | ||||
\(800\) | 44.6145 | + | 77.2745i | 1.57736 | + | 2.73207i | ||||
\(801\) | 10.0737 | + | 17.4482i | 0.355937 | + | 0.616501i | ||||
\(802\) | −36.7283 | −1.29692 | ||||||||
\(803\) | 2.69621 | 0.0951473 | ||||||||
\(804\) | 8.34419 | + | 14.4526i | 0.294277 | + | 0.509703i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.48216 | − | 41.0626i | 0.122654 | − | 1.44637i | ||||
\(807\) | −2.08163 | + | 3.60548i | −0.0732767 | + | 0.126919i | ||||
\(808\) | 5.93516 | − | 10.2800i | 0.208798 | − | 0.361649i | ||||
\(809\) | 18.7851 | − | 32.5367i | 0.660449 | − | 1.14393i | −0.320049 | − | 0.947401i | \(-0.603699\pi\) |
0.980498 | − | 0.196530i | \(-0.0629672\pi\) | |||||||
\(810\) | −29.8533 | − | 51.7074i | −1.04894 | − | 1.81681i | ||||
\(811\) | −11.5936 | −0.407106 | −0.203553 | − | 0.979064i | \(-0.565249\pi\) | ||||
−0.203553 | + | 0.979064i | \(0.565249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.65159 | + | 9.78884i | −0.198210 | + | 0.343309i | ||||
\(814\) | −0.201023 | + | 0.348182i | −0.00704584 | + | 0.0122038i | ||||
\(815\) | 99.5915 | 3.48854 | ||||||||
\(816\) | −0.837429 | + | 1.45047i | −0.0293159 | + | 0.0507766i | ||||
\(817\) | 11.6264 | 0.406757 | ||||||||
\(818\) | −57.2359 | −2.00121 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 77.7514 | 2.71520 | ||||||||
\(821\) | 31.0243 | 1.08276 | 0.541378 | − | 0.840780i | \(-0.317903\pi\) | ||||
0.541378 | + | 0.840780i | \(0.317903\pi\) | |||||||
\(822\) | −9.30717 | + | 16.1205i | −0.324625 | + | 0.562267i | ||||
\(823\) | 29.0775 | 1.01358 | 0.506789 | − | 0.862070i | \(-0.330832\pi\) | ||||
0.506789 | + | 0.862070i | \(0.330832\pi\) | |||||||
\(824\) | 0.589253 | − | 1.02062i | 0.0205276 | − | 0.0355549i | ||||
\(825\) | −1.93412 | + | 3.34999i | −0.0673374 | + | 0.116632i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8920 | 0.517846 | 0.258923 | − | 0.965898i | \(-0.416632\pi\) | ||||
0.258923 | + | 0.965898i | \(0.416632\pi\) | |||||||
\(828\) | 22.9873 | + | 39.8151i | 0.798863 | + | 1.38367i | ||||
\(829\) | −2.18594 | + | 3.78617i | −0.0759210 | + | 0.131499i | −0.901486 | − | 0.432807i | \(-0.857523\pi\) |
0.825565 | + | 0.564306i | \(0.190856\pi\) | |||||||
\(830\) | −26.8481 | + | 46.5022i | −0.931909 | + | 1.61411i | ||||
\(831\) | 1.56771 | − | 2.71535i | 0.0543832 | − | 0.0941944i | ||||
\(832\) | −38.1806 | − | 26.5828i | −1.32367 | − | 0.921593i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.6726 | + | 18.4856i | 0.369563 | + | 0.640103i | ||||
\(835\) | 75.2439 | 2.60392 | ||||||||
\(836\) | −5.81076 | −0.200969 | ||||||||
\(837\) | −8.06076 | − | 13.9616i | −0.278621 | − | 0.482585i | ||||
\(838\) | 26.2928 | + | 45.5405i | 0.908270 | + | 1.57317i | ||||
\(839\) | 11.4109 | − | 19.7643i | 0.393948 | − | 0.682338i | −0.599018 | − | 0.800735i | \(-0.704442\pi\) |
0.992966 | + | 0.118397i | \(0.0377756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.02399 | − | 13.8980i | 0.276689 | − | 0.479240i | ||||
\(842\) | −46.2308 | −1.59322 | ||||||||
\(843\) | −1.75119 | + | 3.03314i | −0.0603140 | + | 0.104467i | ||||
\(844\) | 20.4601 | + | 35.4379i | 0.704265 | + | 1.21982i | ||||
\(845\) | −54.0767 | − | 9.23799i | −1.86030 | − | 0.317797i | ||||
\(846\) | 49.1718 | 1.69056 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.70306 | + | 2.94979i | 0.0584833 | + | 0.101296i | ||||
\(849\) | −7.42427 | − | 12.8592i | −0.254800 | − | 0.441327i | ||||
\(850\) | −33.8216 | − | 58.5808i | −1.16007 | − | 2.00931i | ||||
\(851\) | −1.91758 | −0.0657338 | ||||||||
\(852\) | −9.01043 | − | 15.6065i | −0.308692 | − | 0.534671i | ||||
\(853\) | −23.3549 | −0.799656 | −0.399828 | − | 0.916590i | \(-0.630930\pi\) | ||||
−0.399828 | + | 0.916590i | \(0.630930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.5548 | + | 35.6020i | 0.702960 | + | 1.21756i | ||||
\(856\) | 8.39203 | 0.286834 | ||||||||
\(857\) | −21.7653 | − | 37.6986i | −0.743488 | − | 1.28776i | −0.950898 | − | 0.309505i | \(-0.899837\pi\) |
0.207410 | − | 0.978254i | \(-0.433497\pi\) | |||||||
\(858\) | 0.204263 | − | 2.40872i | 0.00697342 | − | 0.0822324i | ||||
\(859\) | 10.2557 | − | 17.7633i | 0.349919 | − | 0.606078i | −0.636316 | − | 0.771429i | \(-0.719542\pi\) |
0.986235 | + | 0.165351i | \(0.0528757\pi\) | |||||||
\(860\) | −19.8965 | − | 34.4617i | −0.678464 | − | 1.17513i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.1451 | + | 38.3564i | −0.754263 | + | 1.30642i | ||||
\(863\) | 25.3339 | − | 43.8796i | 0.862376 | − | 1.49368i | −0.00725258 | − | 0.999974i | \(-0.502309\pi\) |
0.869629 | − | 0.493706i | \(-0.164358\pi\) | |||||||
\(864\) | −21.8142 | −0.742133 | ||||||||
\(865\) | 31.9512 | 1.08637 | ||||||||
\(866\) | 0.0185167 | − | 0.0320719i | 0.000629224 | − | 0.00108985i | ||||
\(867\) | −3.11621 | + | 5.39743i | −0.105832 | + | 0.183306i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.85156 | − | 6.67109i | −0.130655 | − | 0.226301i | ||||
\(870\) | −9.26434 | + | 16.0463i | −0.314091 | + | 0.544021i | ||||
\(871\) | −33.8436 | + | 15.8916i | −1.14675 | + | 0.538465i | ||||
\(872\) | −15.7766 | − | 27.3259i | −0.534263 | − | 0.925371i | ||||
\(873\) | −18.4562 | −0.624647 | ||||||||
\(874\) | −23.3214 | − | 40.3939i | −0.788858 | − | 1.36634i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.89568 | 0.266770 | ||||||||
\(877\) | 23.5180 | + | 40.7344i | 0.794148 | + | 1.37550i | 0.923379 | + | 0.383890i | \(0.125416\pi\) |
−0.129231 | + | 0.991615i | \(0.541251\pi\) | |||||||
\(878\) | −29.9613 | −1.01114 | ||||||||
\(879\) | 1.33945 | + | 2.32000i | 0.0451787 | + | 0.0782517i | ||||
\(880\) | −1.48555 | − | 2.57305i | −0.0500780 | − | 0.0867376i | ||||
\(881\) | −8.05674 | − | 13.9547i | −0.271439 | − | 0.470145i | 0.697792 | − | 0.716301i | \(-0.254166\pi\) |
−0.969230 | + | 0.246155i | \(0.920833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0733 | 1.41588 | 0.707940 | − | 0.706273i | \(-0.249625\pi\) | ||||
0.707940 | + | 0.706273i | \(0.249625\pi\) | |||||||
\(884\) | 20.6136 | + | 14.3520i | 0.693310 | + | 0.482710i | ||||
\(885\) | 2.09593 | + | 3.63026i | 0.0704539 | + | 0.122030i | ||||
\(886\) | 16.6623 | − | 28.8600i | 0.559782 | − | 0.969570i | ||||
\(887\) | 41.7628 | 1.40226 | 0.701128 | − | 0.713035i | \(-0.252680\pi\) | ||||
0.701128 | + | 0.713035i | \(0.252680\pi\) | |||||||
\(888\) | −0.186636 | + | 0.323264i | −0.00626311 | + | 0.0108480i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −34.9797 | + | 60.5866i | −1.17252 | + | 2.03087i | ||||
\(891\) | 1.75119 | + | 3.03314i | 0.0586669 | + | 0.101614i | ||||
\(892\) | −19.8167 | − | 34.3236i | −0.663513 | − | 1.14924i | ||||
\(893\) | −29.6422 | −0.991938 | ||||||||
\(894\) | −5.55697 | −0.185853 | ||||||||
\(895\) | 48.1151 | + | 83.3379i | 1.60831 | + | 2.78568i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4365 | − | 4.90055i | 0.348464 | − | 0.163625i | ||||
\(898\) | 26.3999 | − | 45.7260i | 0.880977 | − | 1.52590i | ||||
\(899\) | 9.26434 | − | 16.0463i | 0.308983 | − | 0.535174i | ||||
\(900\) | 50.5992 | − | 87.6404i | 1.68664 | − | 2.92135i | ||||
\(901\) | −3.16233 | − | 5.47731i | −0.105352 | − | 0.182476i | ||||
\(902\) | −7.67577 | −0.255575 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5491 | + | 21.7357i | −0.417377 | + | 0.722919i | ||||
\(905\) | 29.3910 | − | 50.9068i | 0.976991 | − | 1.69220i | ||||
\(906\) | 7.72158 | 0.256532 | ||||||||
\(907\) | 7.71125 | − | 13.3563i | 0.256048 | − | 0.443488i | −0.709132 | − | 0.705076i | \(-0.750913\pi\) |
0.965180 | + | 0.261588i | \(0.0842463\pi\) | |||||||
\(908\) | 15.7184 | 0.521634 | ||||||||
\(909\) | 15.5381 | 0.515366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5462 | 1.24396 | 0.621981 | − | 0.783033i | \(-0.286328\pi\) | ||||
0.621981 | + | 0.783033i | \(0.286328\pi\) | |||||||
\(912\) | 2.54211 | 0.0841776 | ||||||||
\(913\) | 1.57490 | − | 2.72781i | 0.0521216 | − | 0.0902773i | ||||
\(914\) | 40.2517 | 1.33141 | ||||||||
\(915\) | −0.706545 | + | 1.22377i | −0.0233577 | + | 0.0404567i | ||||
\(916\) | 4.53776 | − | 7.85963i | 0.149932 | − | 0.259689i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 16.5370 | 0.545804 | ||||||||
\(919\) | 4.73732 | + | 8.20528i | 0.156270 | + | 0.270667i | 0.933521 | − | 0.358524i | \(-0.116720\pi\) |
−0.777251 | + | 0.629191i | \(0.783386\pi\) | |||||||
\(920\) | −25.3064 | + | 43.8319i | −0.834326 | + | 1.44510i | ||||
\(921\) | −4.44476 | + | 7.69856i | −0.146460 | + | 0.253676i | ||||
\(922\) | −6.74837 | + | 11.6885i | −0.222246 | + | 0.384941i | ||||
\(923\) | 36.5458 | − | 17.1604i | 1.20292 | − | 0.564842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.11047 | + | 3.65545i | 0.0693919 | + | 0.120190i | ||||
\(926\) | 11.5283 | 0.378842 | ||||||||
\(927\) | 1.54265 | 0.0506672 | ||||||||
\(928\) | −12.5357 | − | 21.7124i | −0.411503 | − | 0.712745i | ||||
\(929\) | 17.9220 | + | 31.0418i | 0.588001 | + | 1.01845i | 0.994494 | + | 0.104793i | \(0.0334181\pi\) |
−0.406493 | + | 0.913654i | \(0.633249\pi\) | |||||||
\(930\) | 13.2532 | − | 22.9553i | 0.434591 | − | 0.752733i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.8278 | − | 51.6633i | 0.977043 | − | 1.69229i | ||||
\(933\) | −0.718848 | −0.0235340 | ||||||||
\(934\) | −9.65668 | + | 16.7259i | −0.315976 | + | 0.547287i | ||||
\(935\) | 2.75845 | + | 4.77777i | 0.0902108 | + | 0.156250i | ||||
\(936\) | −1.69420 | + | 19.9785i | −0.0553768 | + | 0.653017i | ||||
\(937\) | 31.3709 | 1.02484 | 0.512422 | − | 0.858734i | \(-0.328748\pi\) | ||||
0.512422 | + | 0.858734i | \(0.328748\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.62643 | − | 6.28116i | −0.118344 | − | 0.204978i | ||||
\(940\) | 50.7270 | + | 87.8618i | 1.65453 | + | 2.86574i | ||||
\(941\) | 22.3922 | + | 38.7844i | 0.729964 | + | 1.26433i | 0.956898 | + | 0.290425i | \(0.0937966\pi\) |
−0.226934 | + | 0.973910i | \(0.572870\pi\) | |||||||
\(942\) | 19.8984 | 0.648324 | ||||||||
\(943\) | −18.3050 | − | 31.7052i | −0.596093 | − | 1.03246i | ||||
\(944\) | −2.31570 | −0.0753695 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.96422 | + | 3.40212i | 0.0638622 | + | 0.110613i | ||||
\(947\) | −35.0674 | −1.13954 | −0.569768 | − | 0.821805i | \(-0.692967\pi\) | ||||
−0.569768 | + | 0.821805i | \(0.692967\pi\) | |||||||
\(948\) | −11.2790 | − | 19.5359i | −0.366326 | − | 0.634495i | ||||
\(949\) | −1.49474 | + | 17.6263i | −0.0485212 | + | 0.572175i | ||||
\(950\) | −51.3347 | + | 88.9143i | −1.66552 | + | 2.88476i | ||||
\(951\) | −2.21896 | − | 3.84334i | −0.0719546 | − | 0.124629i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.4852 | + | 51.0699i | −0.955120 | + | 1.65432i | −0.221027 | + | 0.975268i | \(0.570941\pi\) |
−0.734093 | + | 0.679048i | \(0.762393\pi\) | |||||||
\(954\) | 7.96212 | − | 13.7908i | 0.257783 | − | 0.446494i | ||||
\(955\) | −53.4752 | −1.73042 | ||||||||
\(956\) | −3.78229 | −0.122328 | ||||||||
\(957\) | 0.543444 | − | 0.941273i | 0.0175671 | − | 0.0304270i | ||||
\(958\) | 26.8830 | − | 46.5627i | 0.868550 | − | 1.50437i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −14.9620 | − | 25.9149i | −0.482895 | − | 0.836399i | ||||
\(961\) | 2.24677 | − | 3.89152i | 0.0724765 | − | 0.125533i | ||||
\(962\) | −2.16477 | − | 1.50720i | −0.0697950 | − | 0.0485941i | ||||
\(963\) | 5.49253 | + | 9.51334i | 0.176994 | + | 0.306563i | ||||
\(964\) | −6.24547 | −0.201153 | ||||||||
\(965\) | 8.76690 | + | 15.1847i | 0.282217 | + | 0.488813i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3671 | 0.976540 | 0.488270 | − | 0.872693i | \(-0.337628\pi\) | ||||
0.488270 | + | 0.872693i | \(0.337628\pi\) | |||||||
\(968\) | 11.0250 | + | 19.0958i | 0.354357 | + | 0.613764i | ||||
\(969\) | −4.72031 | −0.151638 | ||||||||
\(970\) | −32.0434 | − | 55.5008i | −1.02885 | − | 1.78202i | ||||
\(971\) | −24.7588 | − | 42.8834i | −0.794546 | − | 1.37619i | −0.923127 | − | 0.384495i | \(-0.874375\pi\) |
0.128581 | − | 0.991699i | \(-0.458958\pi\) | |||||||
\(972\) | 18.8831 | + | 32.7065i | 0.605676 | + | 1.04906i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.93815 | 0.126186 | ||||||||
\(975\) | −20.8281 | − | 14.5014i | −0.667034 | − | 0.464416i | ||||
\(976\) | −0.390315 | − | 0.676045i | −0.0124937 | − | 0.0216397i | ||||
\(977\) | 5.43356 | − | 9.41120i | 0.173835 | − | 0.301091i | −0.765923 | − | 0.642933i | \(-0.777717\pi\) |
0.939757 | + | 0.341842i | \(0.111051\pi\) | |||||||
\(978\) | −28.7920 | −0.920666 | ||||||||
\(979\) | 2.05190 | − | 3.55400i | 0.0655790 | − | 0.113586i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6514 | − | 35.7692i | 0.659347 | − | 1.14202i | ||||
\(982\) | 7.42555 | + | 12.8614i | 0.236959 | + | 0.410425i | ||||
\(983\) | 1.17417 | + | 2.03371i | 0.0374501 | + | 0.0648654i | 0.884143 | − | 0.467217i | \(-0.154743\pi\) |
−0.846693 | + | 0.532082i | \(0.821410\pi\) | |||||||
\(984\) | −7.12645 | −0.227183 | ||||||||
\(985\) | −28.9079 | −0.921082 | ||||||||
\(986\) | 9.50312 | + | 16.4599i | 0.302641 | + | 0.524190i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.22139 | − | 37.9875i | 0.102486 | − | 1.20854i | ||||
\(989\) | −9.36845 | + | 16.2266i | −0.297899 | + | 0.515977i | ||||
\(990\) | −6.94523 | + | 12.0295i | −0.220734 | + | 0.382322i | ||||
\(991\) | −12.2408 | + | 21.2016i | −0.388841 | + | 0.673492i | −0.992294 | − | 0.123907i | \(-0.960458\pi\) |
0.603453 | + | 0.797398i | \(0.293791\pi\) | |||||||
\(992\) | 17.9331 | + | 31.0610i | 0.569375 | + | 0.986187i | ||||
\(993\) | 8.21311 | 0.260635 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.71667 | + | 2.97336i | −0.0544222 | + | 0.0942620i | ||||
\(996\) | 4.61199 | − | 7.98821i | 0.146137 | − | 0.253116i | ||||
\(997\) | 6.62341 | 0.209766 | 0.104883 | − | 0.994485i | \(-0.466553\pi\) | ||||
0.104883 | + | 0.994485i | \(0.466553\pi\) | |||||||
\(998\) | −27.3491 | + | 47.3700i | −0.865720 | + | 1.49947i | ||||
\(999\) | −1.03191 | −0.0326482 |
(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 | 637.2.h.i.471.4 | 8 | ||
7.2 | even | 3 | 637.2.f.i.393.1 | 8 | |||
7.3 | odd | 6 | 637.2.g.k.263.1 | 8 | |||
7.4 | even | 3 | 637.2.g.j.263.1 | 8 | |||
7.5 | odd | 6 | 91.2.f.c.29.1 | yes | 8 | ||
7.6 | odd | 2 | 637.2.h.h.471.4 | 8 | |||
13.9 | even | 3 | 637.2.g.j.373.1 | 8 | |||
21.5 | even | 6 | 819.2.o.h.757.4 | 8 | |||
28.19 | even | 6 | 1456.2.s.q.1121.2 | 8 | |||
91.9 | even | 3 | 637.2.f.i.295.1 | 8 | |||
91.16 | even | 3 | 8281.2.a.bp.1.4 | 4 | |||
91.23 | even | 6 | 8281.2.a.bt.1.1 | 4 | |||
91.48 | odd | 6 | 637.2.g.k.373.1 | 8 | |||
91.54 | even | 12 | 1183.2.c.g.337.2 | 8 | |||
91.61 | odd | 6 | 91.2.f.c.22.1 | ✓ | 8 | ||
91.68 | odd | 6 | 1183.2.a.k.1.4 | 4 | |||
91.74 | even | 3 | inner | 637.2.h.i.165.4 | 8 | ||
91.75 | odd | 6 | 1183.2.a.l.1.1 | 4 | |||
91.87 | odd | 6 | 637.2.h.h.165.4 | 8 | |||
91.89 | even | 12 | 1183.2.c.g.337.7 | 8 | |||
273.152 | even | 6 | 819.2.o.h.568.4 | 8 | |||
364.243 | even | 6 | 1456.2.s.q.113.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.c.22.1 | ✓ | 8 | 91.61 | odd | 6 | ||
91.2.f.c.29.1 | yes | 8 | 7.5 | odd | 6 | ||
637.2.f.i.295.1 | 8 | 91.9 | even | 3 | |||
637.2.f.i.393.1 | 8 | 7.2 | even | 3 | |||
637.2.g.j.263.1 | 8 | 7.4 | even | 3 | |||
637.2.g.j.373.1 | 8 | 13.9 | even | 3 | |||
637.2.g.k.263.1 | 8 | 7.3 | odd | 6 | |||
637.2.g.k.373.1 | 8 | 91.48 | odd | 6 | |||
637.2.h.h.165.4 | 8 | 91.87 | odd | 6 | |||
637.2.h.h.471.4 | 8 | 7.6 | odd | 2 | |||
637.2.h.i.165.4 | 8 | 91.74 | even | 3 | inner | ||
637.2.h.i.471.4 | 8 | 1.1 | even | 1 | trivial | ||
819.2.o.h.568.4 | 8 | 273.152 | even | 6 | |||
819.2.o.h.757.4 | 8 | 21.5 | even | 6 | |||
1183.2.a.k.1.4 | 4 | 91.68 | odd | 6 | |||
1183.2.a.l.1.1 | 4 | 91.75 | odd | 6 | |||
1183.2.c.g.337.2 | 8 | 91.54 | even | 12 | |||
1183.2.c.g.337.7 | 8 | 91.89 | even | 12 | |||
1456.2.s.q.113.2 | 8 | 364.243 | even | 6 | |||
1456.2.s.q.1121.2 | 8 | 28.19 | even | 6 | |||
8281.2.a.bp.1.4 | 4 | 91.16 | even | 3 | |||
8281.2.a.bt.1.1 | 4 | 91.23 | even | 6 |