Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.8 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.j.508.8 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.249993 | − | 0.433001i | 0.176772 | − | 0.306178i | −0.764001 | − | 0.645215i | \(-0.776768\pi\) |
0.940773 | + | 0.339037i | \(0.110101\pi\) | |||||||
\(3\) | −0.424801 | − | 0.735776i | −0.245259 | − | 0.424801i | 0.716946 | − | 0.697129i | \(-0.245540\pi\) |
−0.962204 | + | 0.272328i | \(0.912206\pi\) | |||||||
\(4\) | 0.875007 | + | 1.51556i | 0.437503 | + | 0.757778i | ||||
\(5\) | −0.521238 | + | 0.902810i | −0.233105 | + | 0.403749i | −0.958720 | − | 0.284351i | \(-0.908222\pi\) |
0.725616 | + | 0.688100i | \(0.241555\pi\) | |||||||
\(6\) | −0.424789 | −0.173420 | ||||||||
\(7\) | 2.40155 | − | 1.11021i | 0.907699 | − | 0.419621i | ||||
\(8\) | 1.87496 | 0.662897 | ||||||||
\(9\) | 1.13909 | − | 1.97296i | 0.379696 | − | 0.657653i | ||||
\(10\) | 0.260612 | + | 0.451393i | 0.0824127 | + | 0.142743i | ||||
\(11\) | 1.98365 | + | 3.43579i | 0.598094 | + | 1.03593i | 0.993102 | + | 0.117251i | \(0.0374083\pi\) |
−0.395009 | + | 0.918677i | \(0.629258\pi\) | |||||||
\(12\) | 0.743407 | − | 1.28762i | 0.214603 | − | 0.371703i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.119647 | − | 1.31742i | 0.0319770 | − | 0.352095i | ||||
\(15\) | 0.885688 | 0.228684 | ||||||||
\(16\) | −1.28129 | + | 2.21925i | −0.320322 | + | 0.554813i | ||||
\(17\) | 0.0710177 | + | 0.123006i | 0.0172243 | + | 0.0298334i | 0.874509 | − | 0.485009i | \(-0.161184\pi\) |
−0.857285 | + | 0.514843i | \(0.827850\pi\) | |||||||
\(18\) | −0.569529 | − | 0.986453i | −0.134239 | − | 0.232509i | ||||
\(19\) | 2.75488 | − | 4.77160i | 0.632014 | − | 1.09468i | −0.355126 | − | 0.934818i | \(-0.615562\pi\) |
0.987140 | − | 0.159861i | \(-0.0511046\pi\) | |||||||
\(20\) | −1.82435 | −0.407936 | ||||||||
\(21\) | −1.83705 | − | 1.29538i | −0.400877 | − | 0.282676i | ||||
\(22\) | 1.98360 | 0.422905 | ||||||||
\(23\) | −2.19549 | + | 3.80270i | −0.457791 | + | 0.792917i | −0.998844 | − | 0.0480711i | \(-0.984693\pi\) |
0.541053 | + | 0.840989i | \(0.318026\pi\) | |||||||
\(24\) | −0.796483 | − | 1.37955i | −0.162581 | − | 0.281599i | ||||
\(25\) | 1.95662 | + | 3.38897i | 0.391325 | + | 0.677794i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.48435 | −0.863013 | ||||||||
\(28\) | 3.78396 | + | 2.66823i | 0.715101 | + | 0.504249i | ||||
\(29\) | −8.39759 | −1.55939 | −0.779697 | − | 0.626157i | \(-0.784627\pi\) | ||||
−0.779697 | + | 0.626157i | \(0.784627\pi\) | |||||||
\(30\) | 0.221416 | − | 0.383504i | 0.0404249 | − | 0.0700179i | ||||
\(31\) | −1.42326 | − | 2.46516i | −0.255625 | − | 0.442756i | 0.709440 | − | 0.704766i | \(-0.248948\pi\) |
−0.965065 | + | 0.262010i | \(0.915615\pi\) | |||||||
\(32\) | 2.51558 | + | 4.35712i | 0.444696 | + | 0.770237i | ||||
\(33\) | 1.68531 | − | 2.91905i | 0.293376 | − | 0.508141i | ||||
\(34\) | 0.0710158 | 0.0121791 | ||||||||
\(35\) | −0.249465 | + | 2.74683i | −0.0421672 | + | 0.464298i | ||||
\(36\) | 3.98684 | 0.664473 | ||||||||
\(37\) | 0.421593 | − | 0.730221i | 0.0693095 | − | 0.120048i | −0.829288 | − | 0.558821i | \(-0.811254\pi\) |
0.898598 | + | 0.438774i | \(0.144587\pi\) | |||||||
\(38\) | −1.37740 | − | 2.38574i | −0.223445 | − | 0.387017i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.977298 | + | 1.69273i | −0.154524 | + | 0.267644i | ||||
\(41\) | 12.0974 | 1.88929 | 0.944647 | − | 0.328089i | \(-0.106405\pi\) | ||||
0.944647 | + | 0.328089i | \(0.106405\pi\) | |||||||
\(42\) | −1.02015 | + | 0.471607i | −0.157413 | + | 0.0727705i | ||||
\(43\) | 4.82323 | 0.735536 | 0.367768 | − | 0.929918i | \(-0.380122\pi\) | ||||
0.367768 | + | 0.929918i | \(0.380122\pi\) | |||||||
\(44\) | −3.47142 | + | 6.01267i | −0.523336 | + | 0.906444i | ||||
\(45\) | 1.18747 | + | 2.05676i | 0.177018 | + | 0.306604i | ||||
\(46\) | 1.09772 | + | 1.90130i | 0.161849 | + | 0.280331i | ||||
\(47\) | 2.27824 | − | 3.94602i | 0.332315 | − | 0.575587i | −0.650650 | − | 0.759378i | \(-0.725504\pi\) |
0.982965 | + | 0.183791i | \(0.0588369\pi\) | |||||||
\(48\) | 2.17717 | 0.314247 | ||||||||
\(49\) | 4.53485 | − | 5.33246i | 0.647836 | − | 0.761780i | ||||
\(50\) | 1.95657 | 0.276701 | ||||||||
\(51\) | 0.0603367 | − | 0.104506i | 0.00844883 | − | 0.0146338i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.139800 | + | 0.242141i | 0.0192030 | + | 0.0332606i | 0.875467 | − | 0.483278i | \(-0.160554\pi\) |
−0.856264 | + | 0.516538i | \(0.827220\pi\) | |||||||
\(54\) | −1.12106 | + | 1.94173i | −0.152557 | + | 0.264236i | ||||
\(55\) | −4.13582 | −0.557673 | ||||||||
\(56\) | 4.50280 | − | 2.08160i | 0.601711 | − | 0.278166i | ||||
\(57\) | −4.68111 | −0.620028 | ||||||||
\(58\) | −2.09934 | + | 3.63617i | −0.275657 | + | 0.477452i | ||||
\(59\) | 5.39075 | + | 9.33705i | 0.701815 | + | 1.21558i | 0.967829 | + | 0.251611i | \(0.0809602\pi\) |
−0.266013 | + | 0.963969i | \(0.585706\pi\) | |||||||
\(60\) | 0.774983 | + | 1.34231i | 0.100050 | + | 0.173292i | ||||
\(61\) | 2.93177 | − | 5.07797i | 0.375374 | − | 0.650168i | −0.615009 | − | 0.788520i | \(-0.710847\pi\) |
0.990383 | + | 0.138353i | \(0.0441808\pi\) | |||||||
\(62\) | −1.42322 | −0.180750 | ||||||||
\(63\) | 0.545169 | − | 6.00279i | 0.0686848 | − | 0.756280i | ||||
\(64\) | −2.60963 | −0.326204 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.842634 | − | 1.45949i | −0.103721 | − | 0.179650i | ||||
\(67\) | −2.57223 | − | 4.45524i | −0.314248 | − | 0.544294i | 0.665029 | − | 0.746818i | \(-0.268419\pi\) |
−0.979277 | + | 0.202523i | \(0.935086\pi\) | |||||||
\(68\) | −0.124282 | + | 0.215263i | −0.0150714 | + | 0.0261044i | ||||
\(69\) | 3.73058 | 0.449109 | ||||||||
\(70\) | 1.12701 | + | 0.794706i | 0.134704 | + | 0.0949856i | ||||
\(71\) | 3.69880 | 0.438967 | 0.219484 | − | 0.975616i | \(-0.429563\pi\) | ||||
0.219484 | + | 0.975616i | \(0.429563\pi\) | |||||||
\(72\) | 2.13574 | − | 3.69921i | 0.251700 | − | 0.435956i | ||||
\(73\) | 3.30640 | + | 5.72686i | 0.386985 | + | 0.670278i | 0.992042 | − | 0.125904i | \(-0.0401831\pi\) |
−0.605057 | + | 0.796182i | \(0.706850\pi\) | |||||||
\(74\) | −0.210791 | − | 0.365101i | −0.0245040 | − | 0.0424421i | ||||
\(75\) | 1.66235 | − | 2.87927i | 0.191952 | − | 0.332470i | ||||
\(76\) | 9.64216 | 1.10603 | ||||||||
\(77\) | 8.57829 | + | 6.04892i | 0.977587 | + | 0.689339i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.96135 | + | 10.3254i | −0.670705 | + | 1.16169i | 0.307000 | + | 0.951710i | \(0.400675\pi\) |
−0.977705 | + | 0.209985i | \(0.932658\pi\) | |||||||
\(80\) | −1.33571 | − | 2.31352i | −0.149337 | − | 0.258659i | ||||
\(81\) | −1.51231 | − | 2.61940i | −0.168035 | − | 0.291045i | ||||
\(82\) | 3.02426 | − | 5.23818i | 0.333974 | − | 0.578460i | ||||
\(83\) | 2.87321 | 0.315376 | 0.157688 | − | 0.987489i | \(-0.449596\pi\) | ||||
0.157688 | + | 0.987489i | \(0.449596\pi\) | |||||||
\(84\) | 0.355795 | − | 3.91762i | 0.0388204 | − | 0.427447i | ||||
\(85\) | −0.148068 | −0.0160603 | ||||||||
\(86\) | 1.20578 | − | 2.08846i | 0.130022 | − | 0.225205i | ||||
\(87\) | 3.56730 | + | 6.17875i | 0.382455 | + | 0.662432i | ||||
\(88\) | 3.71926 | + | 6.44195i | 0.396475 | + | 0.686714i | ||||
\(89\) | −0.873824 | + | 1.51351i | −0.0926252 | + | 0.160432i | −0.908615 | − | 0.417635i | \(-0.862859\pi\) |
0.815990 | + | 0.578066i | \(0.196193\pi\) | |||||||
\(90\) | 1.18744 | 0.125167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.68427 | −0.801141 | ||||||||
\(93\) | −1.20921 | + | 2.09440i | −0.125389 | + | 0.217180i | ||||
\(94\) | −1.13909 | − | 1.97296i | −0.117488 | − | 0.203495i | ||||
\(95\) | 2.87190 | + | 4.97427i | 0.294650 | + | 0.510350i | ||||
\(96\) | 2.13724 | − | 3.70181i | 0.218131 | − | 0.377815i | ||||
\(97\) | −2.70291 | −0.274438 | −0.137219 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137219 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(98\) | −1.17528 | − | 3.29668i | −0.118721 | − | 0.333014i | ||||
\(99\) | 9.03822 | 0.908376 | ||||||||
\(100\) | −3.42412 | + | 5.93074i | −0.342412 | + | 0.593074i | ||||
\(101\) | −5.73612 | − | 9.93524i | −0.570765 | − | 0.988594i | −0.996488 | − | 0.0837401i | \(-0.973313\pi\) |
0.425723 | − | 0.904854i | \(-0.360020\pi\) | |||||||
\(102\) | −0.0301676 | − | 0.0522517i | −0.00298703 | − | 0.00517369i | ||||
\(103\) | −2.08475 | + | 3.61090i | −0.205417 | + | 0.355792i | −0.950265 | − | 0.311441i | \(-0.899188\pi\) |
0.744849 | + | 0.667233i | \(0.232522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.12702 | − | 0.983303i | 0.207576 | − | 0.0959606i | ||||
\(106\) | 0.139796 | 0.0135782 | ||||||||
\(107\) | −4.24371 | + | 7.35032i | −0.410255 | + | 0.710583i | −0.994917 | − | 0.100694i | \(-0.967894\pi\) |
0.584662 | + | 0.811277i | \(0.301227\pi\) | |||||||
\(108\) | −3.92383 | − | 6.79628i | −0.377571 | − | 0.653972i | ||||
\(109\) | −3.21518 | − | 5.56886i | −0.307958 | − | 0.533400i | 0.669957 | − | 0.742400i | \(-0.266312\pi\) |
−0.977916 | + | 0.209000i | \(0.932979\pi\) | |||||||
\(110\) | −1.03393 | + | 1.79081i | −0.0985810 | + | 0.170747i | ||||
\(111\) | −0.716373 | −0.0679951 | ||||||||
\(112\) | −0.613225 | + | 6.75214i | −0.0579443 | + | 0.638018i | ||||
\(113\) | 10.9633 | 1.03134 | 0.515670 | − | 0.856788i | \(-0.327543\pi\) | ||||
0.515670 | + | 0.856788i | \(0.327543\pi\) | |||||||
\(114\) | −1.17025 | + | 2.02692i | −0.109603 | + | 0.189839i | ||||
\(115\) | −2.28874 | − | 3.96422i | −0.213426 | − | 0.369665i | ||||
\(116\) | −7.34795 | − | 12.7270i | −0.682240 | − | 1.18167i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.39060 | 0.496245 | ||||||||
\(119\) | 0.307115 | + | 0.216560i | 0.0281532 | + | 0.0198521i | ||||
\(120\) | 1.66063 | 0.151594 | ||||||||
\(121\) | −2.36975 | + | 4.10453i | −0.215432 | + | 0.373139i | ||||
\(122\) | −1.46584 | − | 2.53892i | −0.132711 | − | 0.229863i | ||||
\(123\) | −5.13898 | − | 8.90097i | −0.463366 | − | 0.802573i | ||||
\(124\) | 2.49073 | − | 4.31406i | 0.223674 | − | 0.387414i | ||||
\(125\) | −9.29184 | −0.831087 | ||||||||
\(126\) | −2.46292 | − | 1.73671i | −0.219415 | − | 0.154719i | ||||
\(127\) | −2.00787 | −0.178170 | −0.0890849 | − | 0.996024i | \(-0.528394\pi\) | ||||
−0.0890849 | + | 0.996024i | \(0.528394\pi\) | |||||||
\(128\) | −5.68356 | + | 9.84421i | −0.502360 | + | 0.870113i | ||||
\(129\) | −2.04891 | − | 3.54882i | −0.180397 | − | 0.312456i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.22511 | − | 10.7822i | 0.543890 | − | 0.942046i | −0.454785 | − | 0.890601i | \(-0.650284\pi\) |
0.998676 | − | 0.0514449i | \(-0.0163826\pi\) | |||||||
\(132\) | 5.89864 | 0.513411 | ||||||||
\(133\) | 1.31849 | − | 14.5177i | 0.114328 | − | 1.25885i | ||||
\(134\) | −2.57217 | −0.222201 | ||||||||
\(135\) | 2.33741 | − | 4.04851i | 0.201172 | − | 0.348441i | ||||
\(136\) | 0.133155 | + | 0.230631i | 0.0114180 | + | 0.0197765i | ||||
\(137\) | 2.62259 | + | 4.54246i | 0.224063 | + | 0.388088i | 0.956038 | − | 0.293243i | \(-0.0947346\pi\) |
−0.731975 | + | 0.681332i | \(0.761401\pi\) | |||||||
\(138\) | 0.932620 | − | 1.61535i | 0.0793899 | − | 0.137507i | ||||
\(139\) | −20.7385 | −1.75902 | −0.879510 | − | 0.475881i | \(-0.842129\pi\) | ||||
−0.879510 | + | 0.475881i | \(0.842129\pi\) | |||||||
\(140\) | −4.38125 | + | 2.02541i | −0.370283 | + | 0.171179i | ||||
\(141\) | −3.87119 | −0.326013 | ||||||||
\(142\) | 0.924676 | − | 1.60159i | 0.0775971 | − | 0.134402i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.91900 | + | 5.05585i | 0.243250 | + | 0.421321i | ||||
\(145\) | 4.37714 | − | 7.58143i | 0.363502 | − | 0.629604i | ||||
\(146\) | 3.30631 | 0.273633 | ||||||||
\(147\) | −5.84991 | − | 1.07141i | −0.482492 | − | 0.0883681i | ||||
\(148\) | 1.47559 | 0.121293 | ||||||||
\(149\) | −0.00568799 | + | 0.00985188i | −0.000465978 | + | 0.000807098i | −0.866258 | − | 0.499596i | \(-0.833482\pi\) |
0.865792 | + | 0.500403i | \(0.166815\pi\) | |||||||
\(150\) | −0.831153 | − | 1.43960i | −0.0678633 | − | 0.117543i | ||||
\(151\) | −9.45271 | − | 16.3726i | −0.769251 | − | 1.33238i | −0.937970 | − | 0.346717i | \(-0.887296\pi\) |
0.168719 | − | 0.985664i | \(-0.446037\pi\) | |||||||
\(152\) | 5.16529 | − | 8.94654i | 0.418960 | − | 0.725660i | ||||
\(153\) | 0.323582 | 0.0261600 | ||||||||
\(154\) | 4.76371 | − | 2.20222i | 0.383870 | − | 0.177460i | ||||
\(155\) | 2.96743 | 0.238350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.89687 | − | 17.1419i | −0.789856 | − | 1.36807i | −0.926054 | − | 0.377390i | \(-0.876822\pi\) |
0.136198 | − | 0.990682i | \(-0.456512\pi\) | |||||||
\(158\) | 2.98060 | + | 5.16255i | 0.237124 | + | 0.410710i | ||||
\(159\) | 0.118774 | − | 0.205723i | 0.00941942 | − | 0.0163149i | ||||
\(160\) | −5.24486 | −0.414643 | ||||||||
\(161\) | −1.05076 | + | 11.5698i | −0.0828117 | + | 0.911830i | ||||
\(162\) | −1.51227 | −0.118815 | ||||||||
\(163\) | 4.46627 | − | 7.73581i | 0.349825 | − | 0.605915i | −0.636393 | − | 0.771365i | \(-0.719574\pi\) |
0.986218 | + | 0.165450i | \(0.0529076\pi\) | |||||||
\(164\) | 10.5853 | + | 18.3343i | 0.826572 | + | 1.43167i | ||||
\(165\) | 1.75690 | + | 3.04304i | 0.136774 | + | 0.236900i | ||||
\(166\) | 0.718284 | − | 1.24410i | 0.0557496 | − | 0.0965612i | ||||
\(167\) | −6.13469 | −0.474716 | −0.237358 | − | 0.971422i | \(-0.576281\pi\) | ||||
−0.237358 | + | 0.971422i | \(0.576281\pi\) | |||||||
\(168\) | −3.44438 | − | 2.42879i | −0.265740 | − | 0.187385i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.0370161 | + | 0.0641138i | −0.00283900 | + | 0.00491730i | ||||
\(171\) | −6.27611 | − | 10.8705i | −0.479946 | − | 0.831291i | ||||
\(172\) | 4.22036 | + | 7.30987i | 0.321799 | + | 0.557373i | ||||
\(173\) | −12.1314 | + | 21.0122i | −0.922332 | + | 1.59753i | −0.126535 | + | 0.991962i | \(0.540386\pi\) |
−0.795797 | + | 0.605563i | \(0.792948\pi\) | |||||||
\(174\) | 3.56721 | 0.270429 | ||||||||
\(175\) | 8.46140 | + | 5.96650i | 0.639622 | + | 0.451025i | ||||
\(176\) | −10.1665 | −0.766330 | ||||||||
\(177\) | 4.57999 | − | 7.93277i | 0.344253 | − | 0.596263i | ||||
\(178\) | 0.436901 | + | 0.756734i | 0.0327471 | + | 0.0567196i | ||||
\(179\) | 2.06838 | + | 3.58253i | 0.154598 | + | 0.267771i | 0.932912 | − | 0.360103i | \(-0.117259\pi\) |
−0.778315 | + | 0.627874i | \(0.783925\pi\) | |||||||
\(180\) | −2.07809 | + | 3.59936i | −0.154892 | + | 0.268280i | ||||
\(181\) | 7.86568 | 0.584651 | 0.292326 | − | 0.956319i | \(-0.405571\pi\) | ||||
0.292326 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98167 | −0.368256 | ||||||||
\(184\) | −4.11645 | + | 7.12989i | −0.303468 | + | 0.525623i | ||||
\(185\) | 0.439501 | + | 0.761237i | 0.0323127 | + | 0.0559673i | ||||
\(186\) | 0.604586 | + | 1.04717i | 0.0443304 | + | 0.0767825i | ||||
\(187\) | −0.281749 | + | 0.488003i | −0.0206035 | + | 0.0356863i | ||||
\(188\) | 7.97389 | 0.581556 | ||||||||
\(189\) | −10.7694 | + | 4.97858i | −0.783356 | + | 0.362139i | ||||
\(190\) | 2.87182 | 0.208344 | ||||||||
\(191\) | 3.23933 | − | 5.61069i | 0.234390 | − | 0.405975i | −0.724705 | − | 0.689059i | \(-0.758024\pi\) |
0.959095 | + | 0.283084i | \(0.0913574\pi\) | |||||||
\(192\) | 1.10857 | + | 1.92011i | 0.0800044 | + | 0.138572i | ||||
\(193\) | −2.41464 | − | 4.18228i | −0.173810 | − | 0.301047i | 0.765939 | − | 0.642913i | \(-0.222274\pi\) |
−0.939749 | + | 0.341866i | \(0.888941\pi\) | |||||||
\(194\) | −0.675708 | + | 1.17036i | −0.0485130 | + | 0.0840270i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0497 | + | 2.20689i | 0.860690 | + | 0.157635i | ||||
\(197\) | −25.8362 | −1.84075 | −0.920377 | − | 0.391032i | \(-0.872118\pi\) | ||||
−0.920377 | + | 0.391032i | \(0.872118\pi\) | |||||||
\(198\) | 2.25950 | − | 3.91356i | 0.160575 | − | 0.278125i | ||||
\(199\) | −8.55731 | − | 14.8217i | −0.606612 | − | 1.05068i | −0.991795 | − | 0.127842i | \(-0.959195\pi\) |
0.385183 | − | 0.922840i | \(-0.374138\pi\) | |||||||
\(200\) | 3.66858 | + | 6.35417i | 0.259408 | + | 0.449308i | ||||
\(201\) | −2.18537 | + | 3.78518i | −0.154144 | + | 0.266986i | ||||
\(202\) | −5.73596 | −0.403581 | ||||||||
\(203\) | −20.1672 | + | 9.32312i | −1.41546 | + | 0.654355i | ||||
\(204\) | 0.211180 | 0.0147856 | ||||||||
\(205\) | −6.30561 | + | 10.9216i | −0.440403 | + | 0.762800i | ||||
\(206\) | 1.04235 | + | 1.80540i | 0.0726238 | + | 0.125788i | ||||
\(207\) | 5.00171 | + | 8.66322i | 0.347643 | + | 0.602136i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8589 | 1.51201 | ||||||||
\(210\) | 0.105970 | − | 1.16682i | 0.00731262 | − | 0.0805184i | ||||
\(211\) | 18.2911 | 1.25921 | 0.629607 | − | 0.776914i | \(-0.283216\pi\) | ||||
0.629607 | + | 0.776914i | \(0.283216\pi\) | |||||||
\(212\) | −0.244652 | + | 0.423750i | −0.0168028 | + | 0.0291032i | ||||
\(213\) | −1.57125 | − | 2.72149i | −0.107661 | − | 0.186474i | ||||
\(214\) | 2.12180 | + | 3.67506i | 0.145043 | + | 0.251222i | ||||
\(215\) | −2.51405 | + | 4.35446i | −0.171457 | + | 0.296972i | ||||
\(216\) | −8.40796 | −0.572089 | ||||||||
\(217\) | −6.15488 | − | 4.34008i | −0.417821 | − | 0.294624i | ||||
\(218\) | −3.21509 | −0.217754 | ||||||||
\(219\) | 2.80912 | − | 4.86555i | 0.189823 | − | 0.328783i | ||||
\(220\) | −3.61887 | − | 6.26806i | −0.243984 | − | 0.422593i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.179088 | + | 0.310190i | −0.0120196 | + | 0.0208186i | ||||
\(223\) | −11.5087 | −0.770679 | −0.385340 | − | 0.922775i | \(-0.625916\pi\) | ||||
−0.385340 | + | 0.922775i | \(0.625916\pi\) | |||||||
\(224\) | 10.8786 | + | 7.67099i | 0.726858 | + | 0.512539i | ||||
\(225\) | 8.91507 | 0.594338 | ||||||||
\(226\) | 2.74075 | − | 4.74711i | 0.182312 | − | 0.315773i | ||||
\(227\) | −8.95223 | − | 15.5057i | −0.594181 | − | 1.02915i | −0.993662 | − | 0.112410i | \(-0.964143\pi\) |
0.399481 | − | 0.916741i | \(-0.369190\pi\) | |||||||
\(228\) | −4.09600 | − | 7.09448i | −0.271264 | − | 0.469843i | ||||
\(229\) | 1.93175 | − | 3.34589i | 0.127654 | − | 0.221103i | −0.795113 | − | 0.606461i | \(-0.792589\pi\) |
0.922767 | + | 0.385358i | \(0.125922\pi\) | |||||||
\(230\) | −2.28868 | −0.150911 | ||||||||
\(231\) | 0.806593 | − | 8.88129i | 0.0530699 | − | 0.584346i | ||||
\(232\) | −15.7451 | −1.03372 | ||||||||
\(233\) | −12.5321 | + | 21.7062i | −0.821004 | + | 1.42202i | 0.0839312 | + | 0.996472i | \(0.473252\pi\) |
−0.904935 | + | 0.425549i | \(0.860081\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.37501 | + | 4.11363i | 0.154928 | + | 0.268344i | ||||
\(236\) | −9.43388 | + | 16.3400i | −0.614093 | + | 1.06364i | ||||
\(237\) | 10.1295 | 0.657985 | ||||||||
\(238\) | 0.170548 | − | 0.0788427i | 0.0110550 | − | 0.00511061i | ||||
\(239\) | 7.80462 | 0.504839 | 0.252419 | − | 0.967618i | \(-0.418774\pi\) | ||||
0.252419 | + | 0.967618i | \(0.418774\pi\) | |||||||
\(240\) | −1.13482 | + | 1.96557i | −0.0732524 | + | 0.126877i | ||||
\(241\) | 10.8826 | + | 18.8493i | 0.701012 | + | 1.21419i | 0.968112 | + | 0.250519i | \(0.0806012\pi\) |
−0.267100 | + | 0.963669i | \(0.586065\pi\) | |||||||
\(242\) | 1.18484 | + | 2.05221i | 0.0761647 | + | 0.131921i | ||||
\(243\) | −8.01138 | + | 13.8761i | −0.513930 | + | 0.890154i | ||||
\(244\) | 10.2613 | 0.656910 | ||||||||
\(245\) | 2.45046 | + | 6.87359i | 0.156554 | + | 0.439137i | ||||
\(246\) | −5.13884 | −0.327640 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.66855 | − | 4.62207i | −0.169453 | − | 0.293502i | ||||
\(249\) | −1.22054 | − | 2.11404i | −0.0773488 | − | 0.133972i | ||||
\(250\) | −2.32290 | + | 4.02338i | −0.146913 | + | 0.254461i | ||||
\(251\) | 7.67980 | 0.484745 | 0.242372 | − | 0.970183i | \(-0.422074\pi\) | ||||
0.242372 | + | 0.970183i | \(0.422074\pi\) | |||||||
\(252\) | 9.57458 | − | 4.42624i | 0.603142 | − | 0.278827i | ||||
\(253\) | −17.4203 | −1.09521 | ||||||||
\(254\) | −0.501955 | + | 0.869411i | −0.0314954 | + | 0.0545517i | ||||
\(255\) | 0.0628995 | + | 0.108945i | 0.00393892 | + | 0.00682241i | ||||
\(256\) | 0.232070 | + | 0.401958i | 0.0145044 | + | 0.0251224i | ||||
\(257\) | −6.81187 | + | 11.7985i | −0.424913 | + | 0.735971i | −0.996412 | − | 0.0846316i | \(-0.973029\pi\) |
0.571499 | + | 0.820603i | \(0.306362\pi\) | |||||||
\(258\) | −2.04886 | −0.127556 | ||||||||
\(259\) | 0.201775 | − | 2.22172i | 0.0125377 | − | 0.138051i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.56560 | + | 16.5681i | −0.592096 | + | 1.02554i | ||||
\(262\) | −3.11247 | − | 5.39096i | −0.192289 | − | 0.333055i | ||||
\(263\) | 5.86158 | + | 10.1525i | 0.361440 | + | 0.626033i | 0.988198 | − | 0.153181i | \(-0.0489518\pi\) |
−0.626758 | + | 0.779214i | \(0.715618\pi\) | |||||||
\(264\) | 3.15989 | − | 5.47309i | 0.194478 | − | 0.336845i | ||||
\(265\) | −0.291476 | −0.0179052 | ||||||||
\(266\) | −5.95658 | − | 4.20024i | −0.365221 | − | 0.257533i | ||||
\(267\) | 1.48481 | 0.0908686 | ||||||||
\(268\) | 4.50144 | − | 7.79673i | 0.274970 | − | 0.476261i | ||||
\(269\) | −4.59938 | − | 7.96636i | −0.280429 | − | 0.485717i | 0.691061 | − | 0.722796i | \(-0.257143\pi\) |
−0.971490 | + | 0.237079i | \(0.923810\pi\) | |||||||
\(270\) | −1.16867 | − | 2.02420i | −0.0711232 | − | 0.123189i | ||||
\(271\) | −1.28184 | + | 2.22022i | −0.0778665 | + | 0.134869i | −0.902329 | − | 0.431048i | \(-0.858144\pi\) |
0.824463 | + | 0.565916i | \(0.191477\pi\) | |||||||
\(272\) | −0.363976 | −0.0220693 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.62252 | 0.158432 | ||||||||
\(275\) | −7.76252 | + | 13.4451i | −0.468097 | + | 0.810769i | ||||
\(276\) | 3.26428 | + | 5.65391i | 0.196487 | + | 0.340325i | ||||
\(277\) | 0.466941 | + | 0.808765i | 0.0280558 | + | 0.0485940i | 0.879712 | − | 0.475506i | \(-0.157735\pi\) |
−0.851657 | + | 0.524100i | \(0.824402\pi\) | |||||||
\(278\) | −5.18450 | + | 8.97981i | −0.310945 | + | 0.538573i | ||||
\(279\) | −6.48488 | −0.388240 | ||||||||
\(280\) | −0.467736 | + | 5.15018i | −0.0279525 | + | 0.307782i | ||||
\(281\) | −6.45288 | −0.384947 | −0.192473 | − | 0.981302i | \(-0.561651\pi\) | ||||
−0.192473 | + | 0.981302i | \(0.561651\pi\) | |||||||
\(282\) | −0.967771 | + | 1.67623i | −0.0576299 | + | 0.0998180i | ||||
\(283\) | −11.0873 | − | 19.2037i | −0.659071 | − | 1.14154i | −0.980857 | − | 0.194731i | \(-0.937616\pi\) |
0.321786 | − | 0.946812i | \(-0.395717\pi\) | |||||||
\(284\) | 3.23648 | + | 5.60575i | 0.192050 | + | 0.332640i | ||||
\(285\) | 2.43997 | − | 4.22615i | 0.144531 | − | 0.250335i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0524 | − | 13.4307i | 1.71491 | − | 0.792788i | ||||
\(288\) | 11.4619 | 0.675398 | ||||||||
\(289\) | 8.48991 | − | 14.7050i | 0.499407 | − | 0.864998i | ||||
\(290\) | −2.18851 | − | 3.79061i | −0.128514 | − | 0.222593i | ||||
\(291\) | 1.14820 | + | 1.98873i | 0.0673085 | + | 0.116582i | ||||
\(292\) | −5.78625 | + | 10.0221i | −0.338615 | + | 0.586498i | ||||
\(293\) | −24.2026 | −1.41393 | −0.706964 | − | 0.707249i | \(-0.749936\pi\) | ||||
−0.706964 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(294\) | −1.92636 | + | 2.26517i | −0.112347 | + | 0.132107i | ||||
\(295\) | −11.2394 | −0.654385 | ||||||||
\(296\) | 0.790469 | − | 1.36913i | 0.0459451 | − | 0.0795792i | ||||
\(297\) | −8.89539 | − | 15.4073i | −0.516163 | − | 0.894020i | ||||
\(298\) | 0.00284392 | + | 0.00492581i | 0.000164744 | + | 0.000285345i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.81827 | 0.335918 | ||||||||
\(301\) | 11.5832 | − | 5.35481i | 0.667645 | − | 0.308646i | ||||
\(302\) | −9.45246 | −0.543928 | ||||||||
\(303\) | −4.87341 | + | 8.44100i | −0.279970 | + | 0.484923i | ||||
\(304\) | 7.05959 | + | 12.2276i | 0.404895 | + | 0.701299i | ||||
\(305\) | 3.05630 | + | 5.29366i | 0.175003 | + | 0.303114i | ||||
\(306\) | 0.0808933 | − | 0.140111i | 0.00462436 | − | 0.00800963i | ||||
\(307\) | −24.2924 | −1.38644 | −0.693220 | − | 0.720726i | \(-0.743809\pi\) | ||||
−0.693220 | + | 0.720726i | \(0.743809\pi\) | |||||||
\(308\) | −1.66142 | + | 18.2937i | −0.0946684 | + | 1.04238i | ||||
\(309\) | 3.54242 | 0.201521 | ||||||||
\(310\) | 0.741837 | − | 1.28490i | 0.0421335 | − | 0.0729774i | ||||
\(311\) | −1.99355 | − | 3.45294i | −0.113044 | − | 0.195798i | 0.803952 | − | 0.594694i | \(-0.202727\pi\) |
−0.916996 | + | 0.398896i | \(0.869393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2377 | + | 24.6604i | −0.804763 | + | 1.39389i | 0.111688 | + | 0.993743i | \(0.464374\pi\) |
−0.916451 | + | 0.400147i | \(0.868959\pi\) | |||||||
\(314\) | −9.89661 | −0.558498 | ||||||||
\(315\) | 5.13521 | + | 3.62106i | 0.289336 | + | 0.204024i | ||||
\(316\) | −20.8649 | −1.17374 | ||||||||
\(317\) | −8.40806 | + | 14.5632i | −0.472244 | + | 0.817950i | −0.999496 | − | 0.0317591i | \(-0.989889\pi\) |
0.527252 | + | 0.849709i | \(0.323222\pi\) | |||||||
\(318\) | −0.0593856 | − | 0.102859i | −0.00333018 | − | 0.00576804i | ||||
\(319\) | −16.6579 | − | 28.8523i | −0.932664 | − | 1.61542i | ||||
\(320\) | 1.36024 | − | 2.35600i | 0.0760396 | − | 0.131704i | ||||
\(321\) | 7.21093 | 0.402475 | ||||||||
\(322\) | 4.74706 | + | 3.34736i | 0.264543 | + | 0.186541i | ||||
\(323\) | 0.782582 | 0.0435440 | ||||||||
\(324\) | 2.64657 | − | 4.58399i | 0.147031 | − | 0.254666i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.23308 | − | 3.86780i | −0.123679 | − | 0.214218i | ||||
\(327\) | −2.73162 | + | 4.73131i | −0.151059 | + | 0.261642i | ||||
\(328\) | 22.6821 | 1.25241 | ||||||||
\(329\) | 1.09037 | − | 12.0059i | 0.0601139 | − | 0.661906i | ||||
\(330\) | 1.75685 | 0.0967115 | ||||||||
\(331\) | −3.10459 | + | 5.37730i | −0.170644 | + | 0.295563i | −0.938645 | − | 0.344885i | \(-0.887918\pi\) |
0.768002 | + | 0.640448i | \(0.221251\pi\) | |||||||
\(332\) | 2.51408 | + | 4.35451i | 0.137978 | + | 0.238985i | ||||
\(333\) | −0.960464 | − | 1.66357i | −0.0526331 | − | 0.0911632i | ||||
\(334\) | −1.53363 | + | 2.65633i | −0.0839165 | + | 0.145348i | ||||
\(335\) | 5.36298 | 0.293011 | ||||||||
\(336\) | 5.22857 | − | 2.41712i | 0.285242 | − | 0.131865i | ||||
\(337\) | −7.69650 | −0.419255 | −0.209628 | − | 0.977781i | \(-0.567225\pi\) | ||||
−0.209628 | + | 0.977781i | \(0.567225\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.65721 | − | 8.06653i | −0.252945 | − | 0.438114i | ||||
\(340\) | −0.129561 | − | 0.224406i | −0.00702642 | − | 0.0121701i | ||||
\(341\) | 5.64651 | − | 9.78005i | 0.305776 | − | 0.529619i | ||||
\(342\) | −6.27594 | −0.339364 | ||||||||
\(343\) | 4.97049 | − | 17.8408i | 0.268381 | − | 0.963313i | ||||
\(344\) | 9.04335 | 0.487585 | ||||||||
\(345\) | −1.94452 | + | 3.36801i | −0.104689 | + | 0.181327i | ||||
\(346\) | 6.06553 | + | 10.5058i | 0.326085 | + | 0.564795i | ||||
\(347\) | −15.2047 | − | 26.3353i | −0.816231 | − | 1.41375i | −0.908440 | − | 0.418015i | \(-0.862726\pi\) |
0.0922088 | − | 0.995740i | \(-0.470607\pi\) | |||||||
\(348\) | −6.24283 | + | 10.8129i | −0.334651 | + | 0.579632i | ||||
\(349\) | 16.1581 | 0.864924 | 0.432462 | − | 0.901652i | \(-0.357645\pi\) | ||||
0.432462 | + | 0.901652i | \(0.357645\pi\) | |||||||
\(350\) | 4.69880 | − | 2.17221i | 0.251161 | − | 0.116110i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.98008 | + | 17.2860i | −0.531940 | + | 0.921347i | ||||
\(353\) | −5.92119 | − | 10.2558i | −0.315153 | − | 0.545861i | 0.664317 | − | 0.747451i | \(-0.268723\pi\) |
−0.979470 | + | 0.201590i | \(0.935389\pi\) | |||||||
\(354\) | −2.28993 | − | 3.96628i | −0.121709 | − | 0.210805i | ||||
\(355\) | −1.92796 | + | 3.33932i | −0.102325 | + | 0.177233i | ||||
\(356\) | −3.05841 | −0.162095 | ||||||||
\(357\) | 0.0288772 | − | 0.317963i | 0.00152834 | − | 0.0168284i | ||||
\(358\) | 2.06832 | 0.109314 | ||||||||
\(359\) | 15.6826 | − | 27.1631i | 0.827698 | − | 1.43362i | −0.0721417 | − | 0.997394i | \(-0.522983\pi\) |
0.899840 | − | 0.436221i | \(-0.143683\pi\) | |||||||
\(360\) | 2.22646 | + | 3.85634i | 0.117345 | + | 0.203247i | ||||
\(361\) | −5.67876 | − | 9.83591i | −0.298882 | − | 0.517679i | ||||
\(362\) | 1.96637 | − | 3.40585i | 0.103350 | − | 0.179007i | ||||
\(363\) | 4.02669 | 0.211346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.89369 | −0.360832 | ||||||||
\(366\) | −1.24538 | + | 2.15707i | −0.0650973 | + | 0.112752i | ||||
\(367\) | −12.0387 | − | 20.8517i | −0.628415 | − | 1.08845i | −0.987870 | − | 0.155285i | \(-0.950370\pi\) |
0.359454 | − | 0.933163i | \(-0.382963\pi\) | |||||||
\(368\) | −5.62610 | − | 9.74470i | −0.293281 | − | 0.507977i | ||||
\(369\) | 13.7800 | − | 23.8676i | 0.717358 | − | 1.24250i | ||||
\(370\) | 0.439489 | 0.0228479 | ||||||||
\(371\) | 0.604564 | + | 0.426305i | 0.0313874 | + | 0.0221326i | ||||
\(372\) | −4.23225 | −0.219432 | ||||||||
\(373\) | 9.19612 | − | 15.9281i | 0.476157 | − | 0.824728i | −0.523470 | − | 0.852044i | \(-0.675363\pi\) |
0.999627 | + | 0.0273160i | \(0.00869604\pi\) | |||||||
\(374\) | 0.140871 | + | 0.243995i | 0.00728425 | + | 0.0126167i | ||||
\(375\) | 3.94718 | + | 6.83672i | 0.203831 | + | 0.353046i | ||||
\(376\) | 4.27160 | − | 7.39862i | 0.220291 | − | 0.381555i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.536539 | + | 5.90776i | −0.0275966 | + | 0.303862i | ||||
\(379\) | −8.13740 | −0.417990 | −0.208995 | − | 0.977917i | \(-0.567019\pi\) | ||||
−0.208995 | + | 0.977917i | \(0.567019\pi\) | |||||||
\(380\) | −5.02586 | + | 8.70504i | −0.257821 | + | 0.446559i | ||||
\(381\) | 0.852946 | + | 1.47735i | 0.0436977 | + | 0.0756867i | ||||
\(382\) | −1.61962 | − | 2.80527i | −0.0828671 | − | 0.143530i | ||||
\(383\) | 11.1856 | − | 19.3739i | 0.571555 | − | 0.989962i | −0.424852 | − | 0.905263i | \(-0.639674\pi\) |
0.996407 | − | 0.0846992i | \(-0.0269929\pi\) | |||||||
\(384\) | 9.65752 | 0.492833 | ||||||||
\(385\) | −9.93236 | + | 4.59164i | −0.506200 | + | 0.234012i | ||||
\(386\) | −2.41458 | −0.122899 | ||||||||
\(387\) | 5.49409 | − | 9.51604i | 0.279280 | − | 0.483727i | ||||
\(388\) | −2.36506 | − | 4.09641i | −0.120068 | − | 0.207963i | ||||
\(389\) | 10.6973 | + | 18.5283i | 0.542374 | + | 0.939420i | 0.998767 | + | 0.0496415i | \(0.0158079\pi\) |
−0.456393 | + | 0.889778i | \(0.650859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.623674 | −0.0315406 | ||||||||
\(392\) | 8.50265 | − | 9.99813i | 0.429449 | − | 0.504982i | ||||
\(393\) | −10.5777 | −0.533576 | ||||||||
\(394\) | −6.45888 | + | 11.1871i | −0.325394 | + | 0.563599i | ||||
\(395\) | −6.21456 | − | 10.7639i | −0.312689 | − | 0.541592i | ||||
\(396\) | 7.90851 | + | 13.6979i | 0.397417 | + | 0.688347i | ||||
\(397\) | 0.598365 | − | 1.03640i | 0.0300311 | − | 0.0520154i | −0.850619 | − | 0.525782i | \(-0.823773\pi\) |
0.880650 | + | 0.473767i | \(0.157106\pi\) | |||||||
\(398\) | −8.55708 | −0.428928 | ||||||||
\(399\) | −11.2419 | + | 5.19703i | −0.562799 | + | 0.260177i | ||||
\(400\) | −10.0280 | −0.501399 | ||||||||
\(401\) | −18.1375 | + | 31.4150i | −0.905741 | + | 1.56879i | −0.0858220 | + | 0.996310i | \(0.527352\pi\) |
−0.819919 | + | 0.572479i | \(0.805982\pi\) | |||||||
\(402\) | 1.09266 | + | 1.89254i | 0.0544968 | + | 0.0943913i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.0383 | − | 17.3868i | 0.499423 | − | 0.865026i | ||||
\(405\) | 3.15309 | 0.156679 | ||||||||
\(406\) | −1.00475 | + | 11.0631i | −0.0498647 | + | 0.549055i | ||||
\(407\) | 3.34518 | 0.165814 | ||||||||
\(408\) | 0.113129 | − | 0.195945i | 0.00560071 | − | 0.00970071i | ||||
\(409\) | 7.33616 | + | 12.7066i | 0.362750 | + | 0.628301i | 0.988412 | − | 0.151793i | \(-0.0485046\pi\) |
−0.625662 | + | 0.780094i | \(0.715171\pi\) | |||||||
\(410\) | 3.15272 | + | 5.46067i | 0.155702 | + | 0.269683i | ||||
\(411\) | 2.22816 | − | 3.85928i | 0.109907 | − | 0.190364i | ||||
\(412\) | −7.29669 | −0.359482 | ||||||||
\(413\) | 23.3122 | + | 16.4385i | 1.14712 | + | 0.808884i | ||||
\(414\) | 5.00158 | 0.245814 | ||||||||
\(415\) | −1.49763 | + | 2.59397i | −0.0735156 | + | 0.127333i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.80975 | + | 15.2589i | 0.431415 | + | 0.747233i | ||||
\(418\) | 5.46458 | − | 9.46494i | 0.267282 | − | 0.462945i | ||||
\(419\) | −5.93348 | −0.289870 | −0.144935 | − | 0.989441i | \(-0.546297\pi\) | ||||
−0.144935 | + | 0.989441i | \(0.546297\pi\) | |||||||
\(420\) | 3.35141 | + | 2.36322i | 0.163532 | + | 0.115314i | ||||
\(421\) | −2.63174 | −0.128263 | −0.0641317 | − | 0.997941i | \(-0.520428\pi\) | ||||
−0.0641317 | + | 0.997941i | \(0.520428\pi\) | |||||||
\(422\) | 4.57266 | − | 7.92008i | 0.222594 | − | 0.385544i | ||||
\(423\) | −5.19023 | − | 8.98974i | −0.252358 | − | 0.437096i | ||||
\(424\) | 0.262119 | + | 0.454004i | 0.0127296 | + | 0.0220484i | ||||
\(425\) | −0.277910 | + | 0.481354i | −0.0134806 | + | 0.0233491i | ||||
\(426\) | −1.57121 | −0.0761255 | ||||||||
\(427\) | 1.40315 | − | 15.4499i | 0.0679030 | − | 0.747672i | ||||
\(428\) | −14.8531 | −0.717952 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.25699 | + | 2.17717i | 0.0606175 | + | 0.104993i | ||||
\(431\) | 9.41883 | + | 16.3139i | 0.453689 | + | 0.785812i | 0.998612 | − | 0.0526738i | \(-0.0167744\pi\) |
−0.544923 | + | 0.838486i | \(0.683441\pi\) | |||||||
\(432\) | 5.74573 | − | 9.95190i | 0.276442 | − | 0.478811i | ||||
\(433\) | 19.1355 | 0.919591 | 0.459796 | − | 0.888025i | \(-0.347923\pi\) | ||||
0.459796 | + | 0.888025i | \(0.347923\pi\) | |||||||
\(434\) | −3.41794 | + | 1.58008i | −0.164066 | + | 0.0758463i | ||||
\(435\) | −7.43765 | −0.356608 | ||||||||
\(436\) | 5.62661 | − | 9.74557i | 0.269466 | − | 0.466728i | ||||
\(437\) | 12.0966 | + | 20.9520i | 0.578660 | + | 1.00227i | ||||
\(438\) | −1.40452 | − | 2.43271i | −0.0671108 | − | 0.116239i | ||||
\(439\) | 0.632554 | − | 1.09561i | 0.0301901 | − | 0.0522908i | −0.850536 | − | 0.525918i | \(-0.823722\pi\) |
0.880726 | + | 0.473627i | \(0.157055\pi\) | |||||||
\(440\) | −7.75448 | −0.369680 | ||||||||
\(441\) | −5.35512 | − | 15.0212i | −0.255006 | − | 0.715296i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.4696 | − | 18.1339i | 0.497426 | − | 0.861568i | −0.502569 | − | 0.864537i | \(-0.667612\pi\) |
0.999996 | + | 0.00296930i | \(0.000945159\pi\) | |||||||
\(444\) | −0.626831 | − | 1.08570i | −0.0297481 | − | 0.0515252i | ||||
\(445\) | −0.910940 | − | 1.57779i | −0.0431827 | − | 0.0747946i | ||||
\(446\) | −2.87710 | + | 4.98328i | −0.136234 | + | 0.235965i | ||||
\(447\) | 0.00966505 | 0.000457141 | ||||||||
\(448\) | −6.26715 | + | 2.89725i | −0.296095 | + | 0.136882i | ||||
\(449\) | 17.8632 | 0.843018 | 0.421509 | − | 0.906824i | \(-0.361501\pi\) | ||||
0.421509 | + | 0.906824i | \(0.361501\pi\) | |||||||
\(450\) | 2.22871 | − | 3.86023i | 0.105062 | − | 0.181973i | ||||
\(451\) | 23.9970 | + | 41.5640i | 1.12997 | + | 1.95717i | ||||
\(452\) | 9.59295 | + | 16.6155i | 0.451214 | + | 0.781526i | ||||
\(453\) | −8.03104 | + | 13.9102i | −0.377331 | + | 0.653557i | ||||
\(454\) | −8.95199 | −0.420138 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.77687 | −0.411015 | ||||||||
\(457\) | −3.28298 | + | 5.68629i | −0.153571 | + | 0.265994i | −0.932538 | − | 0.361072i | \(-0.882411\pi\) |
0.778966 | + | 0.627066i | \(0.215744\pi\) | |||||||
\(458\) | −0.965850 | − | 1.67290i | −0.0451312 | − | 0.0781695i | ||||
\(459\) | −0.318468 | − | 0.551603i | −0.0148648 | − | 0.0257466i | ||||
\(460\) | 4.00533 | − | 6.93744i | 0.186749 | − | 0.323460i | ||||
\(461\) | 5.11364 | 0.238166 | 0.119083 | − | 0.992884i | \(-0.462005\pi\) | ||||
0.119083 | + | 0.992884i | \(0.462005\pi\) | |||||||
\(462\) | −3.64397 | − | 2.56952i | −0.169533 | − | 0.119545i | ||||
\(463\) | 33.3239 | 1.54869 | 0.774347 | − | 0.632761i | \(-0.218079\pi\) | ||||
0.774347 | + | 0.632761i | \(0.218079\pi\) | |||||||
\(464\) | 10.7597 | − | 18.6364i | 0.499508 | − | 0.865173i | ||||
\(465\) | −1.26057 | − | 2.18336i | −0.0584574 | − | 0.101251i | ||||
\(466\) | 6.26587 | + | 10.8528i | 0.290261 | + | 0.502747i | ||||
\(467\) | 6.47472 | − | 11.2145i | 0.299614 | − | 0.518947i | −0.676433 | − | 0.736504i | \(-0.736475\pi\) |
0.976048 | + | 0.217557i | \(0.0698087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1236 | − | 7.84374i | −0.513641 | − | 0.362190i | ||||
\(470\) | 2.37494 | 0.109548 | ||||||||
\(471\) | −8.40840 | + | 14.5638i | −0.387439 | + | 0.671063i | ||||
\(472\) | 10.1074 | + | 17.5066i | 0.465231 | + | 0.805805i | ||||
\(473\) | 9.56761 | + | 16.5716i | 0.439919 | + | 0.761962i | ||||
\(474\) | 2.53232 | − | 4.38611i | 0.116313 | − | 0.201461i | ||||
\(475\) | 21.5611 | 0.989290 | ||||||||
\(476\) | −0.0594814 | + | 0.654942i | −0.00272633 | + | 0.0300192i | ||||
\(477\) | 0.636979 | 0.0291652 | ||||||||
\(478\) | 1.95110 | − | 3.37941i | 0.0892414 | − | 0.154571i | ||||
\(479\) | −13.5060 | − | 23.3930i | −0.617104 | − | 1.06885i | −0.990012 | − | 0.140987i | \(-0.954973\pi\) |
0.372908 | − | 0.927868i | \(-0.378361\pi\) | |||||||
\(480\) | 2.22802 | + | 3.85905i | 0.101695 | + | 0.176141i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.8823 | 0.495677 | ||||||||
\(483\) | 8.95917 | − | 4.14174i | 0.407656 | − | 0.188456i | ||||
\(484\) | −8.29420 | −0.377009 | ||||||||
\(485\) | 1.40886 | − | 2.44021i | 0.0639729 | − | 0.110804i | ||||
\(486\) | 4.00558 | + | 6.93788i | 0.181697 | + | 0.314708i | ||||
\(487\) | −16.0419 | − | 27.7854i | −0.726928 | − | 1.25908i | −0.958175 | − | 0.286182i | \(-0.907614\pi\) |
0.231247 | − | 0.972895i | \(-0.425720\pi\) | |||||||
\(488\) | 5.49694 | − | 9.52097i | 0.248835 | − | 0.430994i | ||||
\(489\) | −7.58910 | −0.343191 | ||||||||
\(490\) | 3.58887 | + | 0.657299i | 0.162129 | + | 0.0296937i | ||||
\(491\) | −28.6040 | −1.29088 | −0.645440 | − | 0.763811i | \(-0.723326\pi\) | ||||
−0.645440 | + | 0.763811i | \(0.723326\pi\) | |||||||
\(492\) | 8.99328 | − | 15.5768i | 0.405448 | − | 0.702257i | ||||
\(493\) | −0.596378 | − | 1.03296i | −0.0268595 | − | 0.0465220i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.71106 | + | 8.15980i | −0.211746 | + | 0.366756i | ||||
\(496\) | 7.29442 | 0.327529 | ||||||||
\(497\) | 8.88285 | − | 4.10646i | 0.398450 | − | 0.184200i | ||||
\(498\) | −1.22051 | −0.0546924 | ||||||||
\(499\) | 0.899082 | − | 1.55726i | 0.0402484 | − | 0.0697123i | −0.845199 | − | 0.534451i | \(-0.820518\pi\) |
0.885448 | + | 0.464739i | \(0.153852\pi\) | |||||||
\(500\) | −8.13042 | − | 14.0823i | −0.363603 | − | 0.629780i | ||||
\(501\) | 2.60602 | + | 4.51376i | 0.116428 | + | 0.201660i | ||||
\(502\) | 1.91990 | − | 3.32536i | 0.0856893 | − | 0.148418i | ||||
\(503\) | 29.0772 | 1.29649 | 0.648245 | − | 0.761432i | \(-0.275503\pi\) | ||||
0.648245 | + | 0.761432i | \(0.275503\pi\) | |||||||
\(504\) | 1.02217 | − | 11.2550i | 0.0455310 | − | 0.501336i | ||||
\(505\) | 11.9595 | 0.532191 | ||||||||
\(506\) | −4.35497 | + | 7.54303i | −0.193602 | + | 0.335329i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.75690 | − | 3.04304i | −0.0779499 | − | 0.135013i | ||||
\(509\) | 11.5957 | − | 20.0843i | 0.513969 | − | 0.890220i | −0.485900 | − | 0.874014i | \(-0.661508\pi\) |
0.999869 | − | 0.0162054i | \(-0.00515855\pi\) | |||||||
\(510\) | 0.0628979 | 0.00278516 | ||||||||
\(511\) | 14.2985 | + | 10.0825i | 0.632529 | + | 0.446024i | ||||
\(512\) | −22.5022 | −0.994464 | ||||||||
\(513\) | −12.3539 | + | 21.3975i | −0.545436 | + | 0.944723i | ||||
\(514\) | 3.40585 | + | 5.89910i | 0.150225 | + | 0.260198i | ||||
\(515\) | −2.17330 | − | 3.76427i | −0.0957671 | − | 0.165874i | ||||
\(516\) | 3.58562 | − | 6.21048i | 0.157848 | − | 0.273401i | ||||
\(517\) | 18.0769 | 0.795022 | ||||||||
\(518\) | −0.911564 | − | 0.642783i | −0.0400518 | − | 0.0282423i | ||||
\(519\) | 20.6137 | 0.904840 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.6255 | − | 28.7962i | −0.728376 | − | 1.26158i | −0.957569 | − | 0.288203i | \(-0.906942\pi\) |
0.229193 | − | 0.973381i | \(-0.426391\pi\) | |||||||
\(522\) | 4.78267 | + | 8.28383i | 0.209332 | + | 0.362574i | ||||
\(523\) | −19.3560 | + | 33.5256i | −0.846380 | + | 1.46597i | 0.0380367 | + | 0.999276i | \(0.487890\pi\) |
−0.884417 | + | 0.466697i | \(0.845444\pi\) | |||||||
\(524\) | 21.7881 | 0.951816 | ||||||||
\(525\) | 0.795602 | − | 8.76027i | 0.0347229 | − | 0.382330i | ||||
\(526\) | 5.86142 | 0.255570 | ||||||||
\(527\) | 0.202153 | − | 0.350140i | 0.00880594 | − | 0.0152523i | ||||
\(528\) | 4.31874 | + | 7.48028i | 0.187949 | + | 0.325537i | ||||
\(529\) | 1.85966 | + | 3.22102i | 0.0808546 | + | 0.140044i | ||||
\(530\) | −0.0728671 | + | 0.126210i | −0.00316514 | + | 0.00548219i | ||||
\(531\) | 24.5622 | 1.06591 | ||||||||
\(532\) | 23.1561 | − | 10.7049i | 1.00394 | − | 0.464115i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.371191 | − | 0.642922i | 0.0160630 | − | 0.0278220i | ||||
\(535\) | −4.42396 | − | 7.66253i | −0.191265 | − | 0.331280i | ||||
\(536\) | −4.82283 | − | 8.35338i | −0.208314 | − | 0.360811i | ||||
\(537\) | 1.75730 | − | 3.04372i | 0.0758329 | − | 0.131346i | ||||
\(538\) | −4.59926 | −0.198288 | ||||||||
\(539\) | 27.3168 | + | 5.00304i | 1.17662 | + | 0.215496i | ||||
\(540\) | 8.18100 | 0.352054 | ||||||||
\(541\) | 11.3337 | − | 19.6306i | 0.487275 | − | 0.843986i | −0.512618 | − | 0.858617i | \(-0.671324\pi\) |
0.999893 | + | 0.0146313i | \(0.00465746\pi\) | |||||||
\(542\) | 0.640905 | + | 1.11008i | 0.0275292 | + | 0.0476820i | ||||
\(543\) | −3.34135 | − | 5.78738i | −0.143391 | − | 0.248360i | ||||
\(544\) | −0.357302 | + | 0.618865i | −0.0153192 | + | 0.0265336i | ||||
\(545\) | 6.70349 | 0.287146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.21134 | −0.393848 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(548\) | −4.58957 | + | 7.94936i | −0.196057 | + | 0.339580i | ||||
\(549\) | −6.67909 | − | 11.5685i | −0.285056 | − | 0.493732i | ||||
\(550\) | 3.88116 | + | 6.72236i | 0.165493 | + | 0.286642i | ||||
\(551\) | −23.1344 | + | 40.0699i | −0.985558 | + | 1.70704i | ||||
\(552\) | 6.99468 | 0.297713 | ||||||||
\(553\) | −2.85311 | + | 31.4152i | −0.121327 | + | 1.33591i | ||||
\(554\) | 0.466928 | 0.0198379 | ||||||||
\(555\) | 0.373400 | − | 0.646748i | 0.0158500 | − | 0.0274529i | ||||
\(556\) | −18.1464 | − | 31.4304i | −0.769577 | − | 1.33295i | ||||
\(557\) | −5.66403 | − | 9.81039i | −0.239993 | − | 0.415680i | 0.720719 | − | 0.693227i | \(-0.243812\pi\) |
−0.960712 | + | 0.277547i | \(0.910478\pi\) | |||||||
\(558\) | −1.62118 | + | 2.80796i | −0.0686299 | + | 0.118871i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.77627 | − | 4.07310i | −0.244092 | − | 0.172120i | ||||
\(561\) | 0.478748 | 0.0202128 | ||||||||
\(562\) | −1.61318 | + | 2.79411i | −0.0680478 | + | 0.117862i | ||||
\(563\) | −16.3193 | − | 28.2659i | −0.687777 | − | 1.19127i | −0.972555 | − | 0.232672i | \(-0.925253\pi\) |
0.284778 | − | 0.958594i | \(-0.408080\pi\) | |||||||
\(564\) | −3.38732 | − | 5.86700i | −0.142632 | − | 0.247045i | ||||
\(565\) | −5.71448 | + | 9.89776i | −0.240410 | + | 0.416402i | ||||
\(566\) | −11.0870 | −0.466021 | ||||||||
\(567\) | −6.53998 | − | 4.61162i | −0.274653 | − | 0.193670i | ||||
\(568\) | 6.93510 | 0.290990 | ||||||||
\(569\) | −17.5045 | + | 30.3188i | −0.733829 | + | 1.27103i | 0.221407 | + | 0.975182i | \(0.428935\pi\) |
−0.955235 | + | 0.295847i | \(0.904398\pi\) | |||||||
\(570\) | −1.21995 | − | 2.11302i | −0.0510981 | − | 0.0885046i | ||||
\(571\) | −13.1273 | − | 22.7371i | −0.549360 | − | 0.951519i | −0.998319 | − | 0.0579663i | \(-0.981538\pi\) |
0.448959 | − | 0.893552i | \(-0.351795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.50428 | −0.229945 | ||||||||
\(574\) | 1.44742 | − | 15.9373i | 0.0604140 | − | 0.665211i | ||||
\(575\) | −17.1830 | −0.716580 | ||||||||
\(576\) | −2.97260 | + | 5.14870i | −0.123858 | + | 0.214529i | ||||
\(577\) | −12.2863 | − | 21.2806i | −0.511487 | − | 0.885922i | −0.999911 | − | 0.0133154i | \(-0.995761\pi\) |
0.488424 | − | 0.872606i | \(-0.337572\pi\) | |||||||
\(578\) | −4.24484 | − | 7.35228i | −0.176562 | − | 0.305815i | ||||
\(579\) | −2.05148 | + | 3.55327i | −0.0852567 | + | 0.147669i | ||||
\(580\) | 15.3201 | 0.636133 | ||||||||
\(581\) | 6.90015 | − | 3.18988i | 0.286267 | − | 0.132338i | ||||
\(582\) | 1.14817 | 0.0475930 | ||||||||
\(583\) | −0.554629 | + | 0.960646i | −0.0229704 | + | 0.0397859i | ||||
\(584\) | 6.19936 | + | 10.7376i | 0.256531 | + | 0.444325i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.05048 | + | 10.4797i | −0.249943 | + | 0.432914i | ||||
\(587\) | 20.5279 | 0.847279 | 0.423639 | − | 0.905831i | \(-0.360752\pi\) | ||||
0.423639 | + | 0.905831i | \(0.360752\pi\) | |||||||
\(588\) | −3.49493 | − | 9.80335i | −0.144129 | − | 0.404283i | ||||
\(589\) | −15.6837 | −0.646235 | ||||||||
\(590\) | −2.80978 | + | 4.86669i | −0.115677 | + | 0.200358i | ||||
\(591\) | 10.9752 | + | 19.0097i | 0.451461 | + | 0.781954i | ||||
\(592\) | 1.08036 | + | 1.87124i | 0.0444027 | + | 0.0769077i | ||||
\(593\) | −19.1417 | + | 33.1545i | −0.786057 | + | 1.36149i | 0.142308 | + | 0.989822i | \(0.454548\pi\) |
−0.928365 | + | 0.371669i | \(0.878786\pi\) | |||||||
\(594\) | −8.89515 | −0.364972 | ||||||||
\(595\) | −0.355593 | + | 0.164387i | −0.0145779 | + | 0.00673923i | ||||
\(596\) | −0.0199081 | −0.000815468 | ||||||||
\(597\) | −7.27030 | + | 12.5925i | −0.297554 | + | 0.515378i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.03567 | − | 12.1861i | −0.287470 | − | 0.497912i | 0.685735 | − | 0.727851i | \(-0.259481\pi\) |
−0.973205 | + | 0.229939i | \(0.926147\pi\) | |||||||
\(600\) | 3.11683 | − | 5.39851i | 0.127244 | − | 0.220393i | ||||
\(601\) | −20.2342 | −0.825369 | −0.412685 | − | 0.910874i | \(-0.635409\pi\) | ||||
−0.412685 | + | 0.910874i | \(0.635409\pi\) | |||||||
\(602\) | 0.577085 | − | 6.35421i | 0.0235202 | − | 0.258978i | ||||
\(603\) | −11.7200 | −0.477276 | ||||||||
\(604\) | 16.5424 | − | 28.6522i | 0.673099 | − | 1.16584i | ||||
\(605\) | −2.47041 | − | 4.27887i | −0.100436 | − | 0.173961i | ||||
\(606\) | 2.43664 | + | 4.22039i | 0.0989818 | + | 0.171441i | ||||
\(607\) | −3.27563 | + | 5.67356i | −0.132954 | + | 0.230283i | −0.924814 | − | 0.380420i | \(-0.875780\pi\) |
0.791860 | + | 0.610703i | \(0.209113\pi\) | |||||||
\(608\) | 27.7205 | 1.12422 | ||||||||
\(609\) | 15.4268 | + | 10.8781i | 0.625125 | + | 0.440803i | ||||
\(610\) | 3.05621 | 0.123742 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.283136 | + | 0.490406i | 0.0114451 | + | 0.0198235i | ||||
\(613\) | 16.6622 | + | 28.8598i | 0.672980 | + | 1.16564i | 0.977055 | + | 0.212988i | \(0.0683195\pi\) |
−0.304075 | + | 0.952648i | \(0.598347\pi\) | |||||||
\(614\) | −6.07294 | + | 10.5186i | −0.245084 | + | 0.424498i | ||||
\(615\) | 10.7145 | 0.432051 | ||||||||
\(616\) | 16.0839 | + | 11.3415i | 0.648040 | + | 0.456961i | ||||
\(617\) | −6.76038 | −0.272162 | −0.136081 | − | 0.990698i | \(-0.543451\pi\) | ||||
−0.136081 | + | 0.990698i | \(0.543451\pi\) | |||||||
\(618\) | 0.885581 | − | 1.53387i | 0.0356233 | − | 0.0617013i | ||||
\(619\) | 8.80931 | + | 15.2582i | 0.354076 | + | 0.613278i | 0.986959 | − | 0.160970i | \(-0.0514621\pi\) |
−0.632883 | + | 0.774247i | \(0.718129\pi\) | |||||||
\(620\) | 2.59652 | + | 4.49731i | 0.104279 | + | 0.180616i | ||||
\(621\) | 9.84534 | − | 17.0526i | 0.395080 | − | 0.684298i | ||||
\(622\) | −1.99350 | −0.0799321 | ||||||||
\(623\) | −0.418213 | + | 4.60489i | −0.0167554 | + | 0.184491i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.93986 | + | 8.55609i | −0.197594 | + | 0.342244i | ||||
\(626\) | 7.11866 | + | 12.3299i | 0.284519 | + | 0.492801i | ||||
\(627\) | −9.28569 | − | 16.0833i | −0.370835 | − | 0.642304i | ||||
\(628\) | 17.3197 | − | 29.9985i | 0.691130 | − | 1.19707i | ||||
\(629\) | 0.119762 | 0.00477524 | ||||||||
\(630\) | 2.85169 | − | 1.31831i | 0.113614 | − | 0.0525228i | ||||
\(631\) | 15.7519 | 0.627074 | 0.313537 | − | 0.949576i | \(-0.398486\pi\) | ||||
0.313537 | + | 0.949576i | \(0.398486\pi\) | |||||||
\(632\) | −11.1773 | + | 19.3596i | −0.444608 | + | 0.770084i | ||||
\(633\) | −7.77009 | − | 13.4582i | −0.308833 | − | 0.534915i | ||||
\(634\) | 4.20392 | + | 7.28140i | 0.166959 | + | 0.289181i | ||||
\(635\) | 1.04658 | − | 1.81273i | 0.0415322 | − | 0.0719359i | ||||
\(636\) | 0.415713 | 0.0164841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6575 | −0.659475 | ||||||||
\(639\) | 4.21327 | − | 7.29759i | 0.166674 | − | 0.288688i | ||||
\(640\) | −5.92497 | − | 10.2623i | −0.234205 | − | 0.405655i | ||||
\(641\) | 10.4702 | + | 18.1350i | 0.413550 | + | 0.716289i | 0.995275 | − | 0.0970962i | \(-0.0309554\pi\) |
−0.581725 | + | 0.813385i | \(0.697622\pi\) | |||||||
\(642\) | 1.80268 | − | 3.12234i | 0.0711463 | − | 0.123229i | ||||
\(643\) | 18.9315 | 0.746586 | 0.373293 | − | 0.927713i | \(-0.378229\pi\) | ||||
0.373293 | + | 0.927713i | \(0.378229\pi\) | |||||||
\(644\) | −18.4541 | + | 8.53118i | −0.727195 | + | 0.336176i | ||||
\(645\) | 4.27188 | 0.168205 | ||||||||
\(646\) | 0.195640 | − | 0.338859i | 0.00769736 | − | 0.0133322i | ||||
\(647\) | 18.8384 | + | 32.6291i | 0.740614 | + | 1.28278i | 0.952216 | + | 0.305426i | \(0.0987988\pi\) |
−0.211601 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(648\) | −2.83552 | − | 4.91126i | −0.111390 | − | 0.192933i | ||||
\(649\) | −21.3867 | + | 37.0429i | −0.839503 | + | 1.45406i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.578727 | + | 6.37229i | −0.0226821 | + | 0.249750i | ||||
\(652\) | 15.6321 | 0.612199 | ||||||||
\(653\) | −14.5163 | + | 25.1430i | −0.568066 | + | 0.983920i | 0.428691 | + | 0.903451i | \(0.358975\pi\) |
−0.996757 | + | 0.0804686i | \(0.974358\pi\) | |||||||
\(654\) | 1.36577 | + | 2.36559i | 0.0534060 | + | 0.0925019i | ||||
\(655\) | 6.48952 | + | 11.2402i | 0.253567 | + | 0.439190i | ||||
\(656\) | −15.5002 | + | 26.8472i | −0.605182 | + | 1.04821i | ||||
\(657\) | 15.0651 | 0.587747 | ||||||||
\(658\) | −4.92598 | − | 3.47352i | −0.192035 | − | 0.135412i | ||||
\(659\) | −1.41830 | −0.0552493 | −0.0276247 | − | 0.999618i | \(-0.508794\pi\) | ||||
−0.0276247 | + | 0.999618i | \(0.508794\pi\) | |||||||
\(660\) | −3.07459 | + | 5.32535i | −0.119678 | + | 0.207289i | ||||
\(661\) | 2.29649 | + | 3.97764i | 0.0893231 | + | 0.154712i | 0.907225 | − | 0.420645i | \(-0.138196\pi\) |
−0.817902 | + | 0.575357i | \(0.804863\pi\) | |||||||
\(662\) | 1.55225 | + | 2.68858i | 0.0603300 | + | 0.104495i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.38715 | 0.209062 | ||||||||
\(665\) | 12.4195 | + | 8.75753i | 0.481607 | + | 0.339602i | ||||
\(666\) | −0.960439 | −0.0372162 | ||||||||
\(667\) | 18.4368 | − | 31.9335i | 0.713877 | − | 1.23647i | ||||
\(668\) | −5.36789 | − | 9.29746i | −0.207690 | − | 0.359730i | ||||
\(669\) | 4.88890 | + | 8.46782i | 0.189016 | + | 0.327385i | ||||
\(670\) | 1.34071 | − | 2.32218i | 0.0517961 | − | 0.0897135i | ||||
\(671\) | 23.2624 | 0.898036 | ||||||||
\(672\) | 1.02289 | − | 11.2629i | 0.0394587 | − | 0.434475i | ||||
\(673\) | −4.20223 | −0.161984 | −0.0809920 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809920 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(674\) | −1.92407 | + | 3.33259i | −0.0741126 | + | 0.128367i | ||||
\(675\) | −8.77418 | − | 15.1973i | −0.337718 | − | 0.584945i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.04354 | + | 7.00361i | −0.155406 | + | 0.269171i | −0.933207 | − | 0.359340i | \(-0.883002\pi\) |
0.777801 | + | 0.628511i | \(0.216335\pi\) | |||||||
\(678\) | −4.65709 | −0.178854 | ||||||||
\(679\) | −6.49115 | + | 3.00080i | −0.249108 | + | 0.115160i | ||||
\(680\) | −0.277622 | −0.0106463 | ||||||||
\(681\) | −7.60583 | + | 13.1737i | −0.291456 | + | 0.504817i | ||||
\(682\) | −2.82318 | − | 4.88989i | −0.108105 | − | 0.187244i | ||||
\(683\) | 12.3433 | + | 21.3792i | 0.472302 | + | 0.818051i | 0.999498 | − | 0.0316929i | \(-0.0100898\pi\) |
−0.527196 | + | 0.849744i | \(0.676757\pi\) | |||||||
\(684\) | 10.9833 | − | 19.0236i | 0.419956 | − | 0.727386i | ||||
\(685\) | −5.46797 | −0.208920 | ||||||||
\(686\) | −6.48250 | − | 6.61231i | −0.247503 | − | 0.252459i | ||||
\(687\) | −3.28244 | −0.125233 | ||||||||
\(688\) | −6.17994 | + | 10.7040i | −0.235608 | + | 0.408085i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.972234 | + | 1.68396i | 0.0370123 | + | 0.0641072i | ||||
\(691\) | −5.62835 | + | 9.74859i | −0.214113 | + | 0.370854i | −0.952998 | − | 0.302978i | \(-0.902019\pi\) |
0.738885 | + | 0.673831i | \(0.235353\pi\) | |||||||
\(692\) | −42.4602 | −1.61409 | ||||||||
\(693\) | 21.7057 | − | 10.0344i | 0.824532 | − | 0.381174i | ||||
\(694\) | −15.2043 | −0.577147 | ||||||||
\(695\) | 10.8097 | − | 18.7230i | 0.410035 | − | 0.710202i | ||||
\(696\) | 6.68854 | + | 11.5849i | 0.253528 | + | 0.439124i | ||||
\(697\) | 0.859128 | + | 1.48805i | 0.0325418 | + | 0.0563640i | ||||
\(698\) | 4.03942 | − | 6.99648i | 0.152894 | − | 0.264821i | ||||
\(699\) | 21.2946 | 0.805434 | ||||||||
\(700\) | −1.63878 | + | 18.0445i | −0.0619402 | + | 0.682016i | ||||
\(701\) | −22.2305 | −0.839635 | −0.419818 | − | 0.907608i | \(-0.637906\pi\) | ||||
−0.419818 | + | 0.907608i | \(0.637906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.32288 | − | 4.02335i | −0.0876091 | − | 0.151743i | ||||
\(704\) | −5.17660 | − | 8.96614i | −0.195101 | − | 0.337924i | ||||
\(705\) | 2.01781 | − | 3.49495i | 0.0759951 | − | 0.131627i | ||||
\(706\) | −5.92103 | −0.222841 | ||||||||
\(707\) | −24.8058 | − | 17.4916i | −0.932918 | − | 0.657841i | ||||
\(708\) | 16.0301 | 0.602447 | ||||||||
\(709\) | 11.8870 | − | 20.5889i | 0.446427 | − | 0.773234i | −0.551723 | − | 0.834027i | \(-0.686030\pi\) |
0.998150 | + | 0.0607929i | \(0.0193629\pi\) | |||||||
\(710\) | 0.963952 | + | 1.66961i | 0.0361765 | + | 0.0626595i | ||||
\(711\) | 13.5810 | + | 23.5230i | 0.509328 | + | 0.882182i | ||||
\(712\) | −1.63838 | + | 2.83776i | −0.0614010 | + | 0.106350i | ||||
\(713\) | 12.4990 | 0.468092 | ||||||||
\(714\) | −0.130459 | − | 0.0919926i | −0.00488232 | − | 0.00344274i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.61969 | + | 6.26948i | −0.135274 | + | 0.234301i | ||||
\(717\) | −3.31541 | − | 5.74246i | −0.123816 | − | 0.214456i | ||||
\(718\) | −7.84111 | − | 13.5812i | −0.292628 | − | 0.506846i | ||||
\(719\) | −10.3904 | + | 17.9967i | −0.387496 | + | 0.671163i | −0.992112 | − | 0.125354i | \(-0.959993\pi\) |
0.604616 | + | 0.796517i | \(0.293327\pi\) | |||||||
\(720\) | −6.08597 | −0.226811 | ||||||||
\(721\) | −0.997764 | + | 10.9863i | −0.0371587 | + | 0.409150i | ||||
\(722\) | −5.67861 | −0.211336 | ||||||||
\(723\) | 9.24589 | − | 16.0144i | 0.343859 | − | 0.595580i | ||||
\(724\) | 6.88252 | + | 11.9209i | 0.255787 | + | 0.443036i | ||||
\(725\) | −16.4309 | − | 28.4592i | −0.610229 | − | 1.05695i | ||||
\(726\) | 1.00665 | − | 1.74356i | 0.0373601 | − | 0.0647097i | ||||
\(727\) | 26.7719 | 0.992915 | 0.496457 | − | 0.868061i | \(-0.334634\pi\) | ||||
0.496457 | + | 0.868061i | \(0.334634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.53910 | 0.168115 | ||||||||
\(730\) | −1.72338 | + | 2.98497i | −0.0637850 | + | 0.110479i | ||||
\(731\) | 0.342535 | + | 0.593287i | 0.0126691 | + | 0.0219435i | ||||
\(732\) | −4.35899 | − | 7.55000i | −0.161113 | − | 0.279056i | ||||
\(733\) | 2.62824 | − | 4.55224i | 0.0970761 | − | 0.168141i | −0.813397 | − | 0.581709i | \(-0.802384\pi\) |
0.910473 | + | 0.413568i | \(0.135718\pi\) | |||||||
\(734\) | −12.0384 | −0.444345 | ||||||||
\(735\) | 4.01647 | − | 4.72290i | 0.148150 | − | 0.174207i | ||||
\(736\) | −22.0917 | −0.814312 | ||||||||
\(737\) | 10.2048 | − | 17.6753i | 0.375900 | − | 0.651078i | ||||
\(738\) | −6.88981 | − | 11.9335i | −0.253617 | − | 0.439278i | ||||
\(739\) | −3.57501 | − | 6.19209i | −0.131509 | − | 0.227780i | 0.792750 | − | 0.609547i | \(-0.208649\pi\) |
−0.924258 | + | 0.381768i | \(0.875315\pi\) | |||||||
\(740\) | −0.769132 | + | 1.33218i | −0.0282738 | + | 0.0489717i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.335727 | − | 0.155204i | 0.0123249 | − | 0.00569771i | ||||
\(743\) | −0.713641 | −0.0261810 | −0.0130905 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130905 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(744\) | −2.26721 | + | 3.92692i | −0.0831198 | + | 0.143968i | ||||
\(745\) | −0.00592959 | − | 0.0102703i | −0.000217243 | − | 0.000376276i | ||||
\(746\) | −4.59794 | − | 7.96386i | −0.168342 | − | 0.291578i | ||||
\(747\) | 3.27284 | − | 5.66873i | 0.119747 | − | 0.207408i | ||||
\(748\) | −0.986128 | −0.0360564 | ||||||||
\(749\) | −2.03104 | + | 22.3636i | −0.0742127 | + | 0.817147i | ||||
\(750\) | 3.94707 | 0.144127 | ||||||||
\(751\) | 12.8507 | − | 22.2580i | 0.468927 | − | 0.812205i | −0.530442 | − | 0.847721i | \(-0.677974\pi\) |
0.999369 | + | 0.0355158i | \(0.0113074\pi\) | |||||||
\(752\) | 5.83815 | + | 10.1120i | 0.212896 | + | 0.368746i | ||||
\(753\) | −3.26238 | − | 5.65062i | −0.118888 | − | 0.205920i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.7084 | 0.717263 | ||||||||
\(756\) | −16.9686 | − | 11.9653i | −0.617142 | − | 0.435173i | ||||
\(757\) | 16.3885 | 0.595650 | 0.297825 | − | 0.954621i | \(-0.403739\pi\) | ||||
0.297825 | + | 0.954621i | \(0.403739\pi\) | |||||||
\(758\) | −2.03430 | + | 3.52350i | −0.0738889 | + | 0.127979i | ||||
\(759\) | 7.40018 | + | 12.8175i | 0.268609 | + | 0.465245i | ||||
\(760\) | 5.38468 | + | 9.32654i | 0.195323 | + | 0.338309i | ||||
\(761\) | 4.15999 | − | 7.20531i | 0.150800 | − | 0.261192i | −0.780722 | − | 0.624878i | \(-0.785149\pi\) |
0.931522 | + | 0.363686i | \(0.118482\pi\) | |||||||
\(762\) | 0.852923 | 0.0308981 | ||||||||
\(763\) | −13.9040 | − | 9.80433i | −0.503359 | − | 0.354941i | ||||
\(764\) | 11.3378 | 0.410185 | ||||||||
\(765\) | −0.168663 | + | 0.292133i | −0.00609802 | + | 0.0105621i | ||||
\(766\) | −5.59263 | − | 9.68671i | −0.202070 | − | 0.349995i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.197167 | − | 0.341504i | 0.00711466 | − | 0.0123230i | ||||
\(769\) | 25.5588 | 0.921675 | 0.460838 | − | 0.887485i | \(-0.347549\pi\) | ||||
0.460838 | + | 0.887485i | \(0.347549\pi\) | |||||||
\(770\) | −0.494838 | + | 5.44860i | −0.0178327 | + | 0.196354i | ||||
\(771\) | 11.5748 | 0.416855 | ||||||||
\(772\) | 4.22565 | − | 7.31905i | 0.152085 | − | 0.263418i | ||||
\(773\) | −4.20038 | − | 7.27528i | −0.151077 | − | 0.261674i | 0.780546 | − | 0.625098i | \(-0.214941\pi\) |
−0.931624 | + | 0.363424i | \(0.881608\pi\) | |||||||
\(774\) | −2.74697 | − | 4.75789i | −0.0987378 | − | 0.171019i | ||||
\(775\) | 5.56957 | − | 9.64678i | 0.200065 | − | 0.346523i | ||||
\(776\) | −5.06783 | −0.181925 | ||||||||
\(777\) | −1.72040 | + | 0.795326i | −0.0617191 | + | 0.0285322i | ||||
\(778\) | 10.6970 | 0.383506 | ||||||||
\(779\) | 33.3269 | − | 57.7238i | 1.19406 | − | 2.06817i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.33714 | + | 12.7083i | 0.262544 | + | 0.454739i | ||||
\(782\) | −0.155914 | + | 0.270052i | −0.00557549 | + | 0.00965703i | ||||
\(783\) | 37.6577 | 1.34578 | ||||||||
\(784\) | 6.02363 | + | 16.8964i | 0.215130 | + | 0.603443i | ||||
\(785\) | 20.6345 | 0.736476 | ||||||||
\(786\) | −2.64436 | + | 4.58017i | −0.0943212 | + | 0.163369i | ||||
\(787\) | −17.5322 | − | 30.3667i | −0.624956 | − | 1.08246i | −0.988549 | − | 0.150898i | \(-0.951784\pi\) |
0.363593 | − | 0.931558i | \(-0.381550\pi\) | |||||||
\(788\) | −22.6069 | − | 39.1562i | −0.805336 | − | 1.39488i | ||||
\(789\) | 4.98000 | − | 8.62562i | 0.177293 | − | 0.307080i | ||||
\(790\) | −6.21440 | −0.221098 | ||||||||
\(791\) | 26.3288 | − | 12.1716i | 0.936146 | − | 0.432772i | ||||
\(792\) | 16.9463 | 0.602160 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.299175 | − | 0.518186i | −0.0106173 | − | 0.0183897i | ||||
\(795\) | 0.123819 | + | 0.214461i | 0.00439142 | + | 0.00760616i | ||||
\(796\) | 14.9754 | − | 25.9382i | 0.530789 | − | 0.919354i | ||||
\(797\) | −24.5752 | −0.870500 | −0.435250 | − | 0.900310i | \(-0.643340\pi\) | ||||
−0.435250 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(798\) | −0.560080 | + | 6.16697i | −0.0198266 | + | 0.218309i | ||||
\(799\) | 0.647181 | 0.0228956 | ||||||||
\(800\) | −9.84409 | + | 17.0505i | −0.348041 | + | 0.602825i | ||||
\(801\) | 1.99073 | + | 3.44804i | 0.0703389 | + | 0.121831i | ||||
\(802\) | 9.06848 | + | 15.7071i | 0.320219 | + | 0.554636i | ||||
\(803\) | −13.1175 | + | 22.7202i | −0.462907 | + | 0.801778i | ||||
\(804\) | −7.64887 | −0.269755 | ||||||||
\(805\) | −9.89765 | − | 6.97926i | −0.348846 | − | 0.245987i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.90764 | + | 6.76823i | −0.137555 | + | 0.238253i | ||||
\(808\) | −10.7550 | − | 18.6282i | −0.378358 | − | 0.655336i | ||||
\(809\) | 15.9006 | + | 27.5406i | 0.559035 | + | 0.968277i | 0.997577 | + | 0.0695667i | \(0.0221617\pi\) |
−0.438542 | + | 0.898711i | \(0.644505\pi\) | |||||||
\(810\) | 0.788253 | − | 1.36529i | 0.0276964 | − | 0.0479715i | ||||
\(811\) | 10.3633 | 0.363905 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(812\) | −31.7762 | − | 22.4067i | −1.11512 | − | 0.786323i | ||||
\(813\) | 2.17811 | 0.0763898 | ||||||||
\(814\) | 0.836272 | − | 1.44847i | 0.0293113 | − | 0.0507687i | ||||
\(815\) | 4.65598 | + | 8.06439i | 0.163092 | + | 0.282483i | ||||
\(816\) | 0.154617 | + | 0.267805i | 0.00541269 | + | 0.00937505i | ||||
\(817\) | 13.2874 | − | 23.0145i | 0.464868 | − | 0.805176i | ||||
\(818\) | 7.33597 | 0.256496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0698 | −0.770711 | ||||||||
\(821\) | 2.02796 | − | 3.51253i | 0.0707762 | − | 0.122588i | −0.828465 | − | 0.560040i | \(-0.810786\pi\) |
0.899242 | + | 0.437452i | \(0.144119\pi\) | |||||||
\(822\) | −1.11405 | − | 1.92959i | −0.0388569 | − | 0.0673021i | ||||
\(823\) | −4.35848 | − | 7.54912i | −0.151927 | − | 0.263146i | 0.780009 | − | 0.625769i | \(-0.215215\pi\) |
−0.931936 | + | 0.362623i | \(0.881881\pi\) | |||||||
\(824\) | −3.90882 | + | 6.77027i | −0.136170 | + | 0.235854i | ||||
\(825\) | 13.1901 | 0.459220 | ||||||||
\(826\) | 12.9458 | − | 5.98472i | 0.450441 | − | 0.208235i | ||||
\(827\) | 23.5788 | 0.819915 | 0.409957 | − | 0.912105i | \(-0.365544\pi\) | ||||
0.409957 | + | 0.912105i | \(0.365544\pi\) | |||||||
\(828\) | −8.75307 | + | 15.1608i | −0.304190 | + | 0.526873i | ||||
\(829\) | 14.5203 | + | 25.1499i | 0.504311 | + | 0.873492i | 0.999988 | + | 0.00498467i | \(0.00158668\pi\) |
−0.495677 | + | 0.868507i | \(0.665080\pi\) | |||||||
\(830\) | 0.748793 | + | 1.29695i | 0.0259910 | + | 0.0450177i | ||||
\(831\) | 0.396714 | − | 0.687128i | 0.0137618 | − | 0.0238362i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.977980 | + | 0.179116i | 0.0338850 | + | 0.00620601i | ||||
\(834\) | 8.80951 | 0.305048 | ||||||||
\(835\) | 3.19763 | − | 5.53846i | 0.110659 | − | 0.191666i | ||||
\(836\) | 19.1267 | + | 33.1284i | 0.661511 | + | 1.14577i | ||||
\(837\) | 6.38240 | + | 11.0546i | 0.220608 | + | 0.382104i | ||||
\(838\) | −1.48333 | + | 2.56921i | −0.0512408 | + | 0.0887517i | ||||
\(839\) | −11.5574 | −0.399007 | −0.199503 | − | 0.979897i | \(-0.563933\pi\) | ||||
−0.199503 | + | 0.979897i | \(0.563933\pi\) | |||||||
\(840\) | 3.98807 | − | 1.84365i | 0.137602 | − | 0.0636120i | ||||
\(841\) | 41.5196 | 1.43171 | ||||||||
\(842\) | −0.657918 | + | 1.13955i | −0.0226734 | + | 0.0392714i | ||||
\(843\) | 2.74119 | + | 4.74788i | 0.0944116 | + | 0.163526i | ||||
\(844\) | 16.0049 | + | 27.7212i | 0.550910 | + | 0.954205i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.19009 | −0.178439 | ||||||||
\(847\) | −1.13417 | + | 12.4882i | −0.0389704 | + | 0.429098i | ||||
\(848\) | −0.716496 | −0.0246046 | ||||||||
\(849\) | −9.41977 | + | 16.3155i | −0.323286 | + | 0.559947i | ||||
\(850\) | 0.138951 | + | 0.240670i | 0.00476598 | + | 0.00825493i | ||||
\(851\) | 1.85121 | + | 3.20638i | 0.0634586 | + | 0.109913i | ||||
\(852\) | 2.74972 | − | 4.76265i | 0.0942038 | − | 0.163166i | ||||
\(853\) | 1.51845 | 0.0519906 | 0.0259953 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259953 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(854\) | −6.33903 | − | 4.46993i | −0.216917 | − | 0.152958i | ||||
\(855\) | 13.0854 | 0.447511 | ||||||||
\(856\) | −7.95678 | + | 13.7815i | −0.271957 | + | 0.471043i | ||||
\(857\) | 3.00060 | + | 5.19718i | 0.102498 | + | 0.177532i | 0.912713 | − | 0.408600i | \(-0.133983\pi\) |
−0.810215 | + | 0.586133i | \(0.800650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.838021 | + | 1.45150i | −0.0285929 | + | 0.0495244i | −0.879968 | − | 0.475033i | \(-0.842436\pi\) |
0.851375 | + | 0.524558i | \(0.175769\pi\) | |||||||
\(860\) | −8.79924 | −0.300051 | ||||||||
\(861\) | −22.2235 | − | 15.6707i | −0.757374 | − | 0.534057i | ||||
\(862\) | 9.41858 | 0.320798 | ||||||||
\(863\) | 21.0252 | − | 36.4167i | 0.715706 | − | 1.23964i | −0.246980 | − | 0.969021i | \(-0.579438\pi\) |
0.962687 | − | 0.270619i | \(-0.0872284\pi\) | |||||||
\(864\) | −11.2807 | − | 19.5388i | −0.383779 | − | 0.664724i | ||||
\(865\) | −12.6467 | − | 21.9047i | −0.429999 | − | 0.744781i | ||||
\(866\) | 4.78374 | − | 8.28567i | 0.162558 | − | 0.281559i | ||||
\(867\) | −14.4261 | −0.489936 | ||||||||
\(868\) | 1.19206 | − | 13.1257i | 0.0404613 | − | 0.445514i | ||||
\(869\) | −47.3010 | −1.60458 | ||||||||
\(870\) | −1.85936 | + | 3.22051i | −0.0630383 | + | 0.109186i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.02832 | − | 10.4414i | −0.204145 | − | 0.353589i | ||||
\(873\) | −3.07885 | + | 5.33272i | −0.104203 | + | 0.180485i | ||||
\(874\) | 12.0963 | 0.409164 | ||||||||
\(875\) | −22.3148 | + | 10.3159i | −0.754377 | + | 0.348742i | ||||
\(876\) | 9.83201 | 0.332193 | ||||||||
\(877\) | −15.4315 | + | 26.7281i | −0.521084 | + | 0.902545i | 0.478615 | + | 0.878025i | \(0.341139\pi\) |
−0.999699 | + | 0.0245198i | \(0.992194\pi\) | |||||||
\(878\) | −0.316268 | − | 0.547793i | −0.0106735 | − | 0.0184871i | ||||
\(879\) | 10.2813 | + | 17.8077i | 0.346778 | + | 0.600638i | ||||
\(880\) | 5.29917 | − | 9.17843i | 0.178635 | − | 0.309405i | ||||
\(881\) | −55.7338 | −1.87772 | −0.938860 | − | 0.344298i | \(-0.888117\pi\) | ||||
−0.938860 | + | 0.344298i | \(0.888117\pi\) | |||||||
\(882\) | −7.84295 | − | 1.43643i | −0.264086 | − | 0.0483671i | ||||
\(883\) | 2.92007 | 0.0982681 | 0.0491341 | − | 0.998792i | \(-0.484354\pi\) | ||||
0.0491341 | + | 0.998792i | \(0.484354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.77452 | + | 8.26971i | 0.160494 | + | 0.277983i | ||||
\(886\) | −5.23467 | − | 9.06671i | −0.175862 | − | 0.304602i | ||||
\(887\) | −0.939545 | + | 1.62734i | −0.0315468 | + | 0.0546407i | −0.881368 | − | 0.472431i | \(-0.843377\pi\) |
0.849821 | + | 0.527071i | \(0.176710\pi\) | |||||||
\(888\) | −1.34317 | −0.0450737 | ||||||||
\(889\) | −4.82200 | + | 2.22917i | −0.161725 | + | 0.0747639i | ||||
\(890\) | −0.910916 | −0.0305340 | ||||||||
\(891\) | 5.99980 | − | 10.3920i | 0.201001 | − | 0.348144i | ||||
\(892\) | −10.0702 | − | 17.4421i | −0.337175 | − | 0.584004i | ||||
\(893\) | −12.5526 | − | 21.7417i | −0.420055 | − | 0.727557i | ||||
\(894\) | 0.00241620 | − | 0.00418498i | 8.08097e−5 | − | 0.000139967i | ||||
\(895\) | −4.31246 | −0.144150 | ||||||||
\(896\) | −2.72015 | + | 29.9513i | −0.0908740 | + | 1.00060i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.46569 | − | 7.73480i | 0.149022 | − | 0.258114i | ||||
\(899\) | 11.9520 | + | 20.7014i | 0.398621 | + | 0.690431i | ||||
\(900\) | 7.80074 | + | 13.5113i | 0.260025 | + | 0.450376i | ||||
\(901\) | −0.0198566 | + | 0.0343926i | −0.000661518 | + | 0.00114578i | ||||
\(902\) | 23.9964 | 0.798991 | ||||||||
\(903\) | −8.86050 | − | 6.24793i | −0.294859 | − | 0.207918i | ||||
\(904\) | 20.5557 | 0.683672 | ||||||||
\(905\) | −4.09989 | + | 7.10121i | −0.136285 | + | 0.236052i | ||||
\(906\) | 4.01541 | + | 6.95490i | 0.133403 | + | 0.231061i | ||||
\(907\) | 17.8082 | + | 30.8447i | 0.591311 | + | 1.02418i | 0.994056 | + | 0.108868i | \(0.0347227\pi\) |
−0.402745 | + | 0.915312i | \(0.631944\pi\) | |||||||
\(908\) | 15.6665 | − | 27.1352i | 0.519912 | − | 0.900514i | ||||
\(909\) | −26.1358 | −0.866869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2844 | 1.46721 | 0.733604 | − | 0.679577i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679577i | \(0.237837\pi\) | |||||||
\(912\) | 5.99784 | − | 10.3886i | 0.198608 | − | 0.344000i | ||||
\(913\) | 5.69946 | + | 9.87175i | 0.188624 | + | 0.326707i | ||||
\(914\) | 1.64145 | + | 2.84307i | 0.0542943 | + | 0.0940404i | ||||
\(915\) | 2.59663 | − | 4.49750i | 0.0858420 | − | 0.148683i | ||||
\(916\) | 6.76118 | 0.223396 | ||||||||
\(917\) | 2.97934 | − | 32.8052i | 0.0983866 | − | 1.08332i | ||||
\(918\) | −0.318459 | −0.0105107 | ||||||||
\(919\) | −13.0564 | + | 22.6144i | −0.430691 | + | 0.745979i | −0.996933 | − | 0.0782603i | \(-0.975063\pi\) |
0.566242 | + | 0.824239i | \(0.308397\pi\) | |||||||
\(920\) | −4.29129 | − | 7.43274i | −0.141480 | − | 0.245050i | ||||
\(921\) | 10.3194 | + | 17.8738i | 0.340037 | + | 0.588961i | ||||
\(922\) | 1.27838 | − | 2.21421i | 0.0421010 | − | 0.0729211i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 14.1659 | − | 6.54875i | 0.466023 | − | 0.215438i | ||||
\(925\) | 3.29960 | 0.108490 | ||||||||
\(926\) | 8.33076 | − | 14.4293i | 0.273766 | − | 0.474176i | ||||
\(927\) | 4.74944 | + | 8.22626i | 0.155992 | + | 0.270186i | ||||
\(928\) | −21.1248 | − | 36.5893i | −0.693457 | − | 1.20110i | ||||
\(929\) | 5.01157 | − | 8.68030i | 0.164424 | − | 0.284791i | −0.772026 | − | 0.635591i | \(-0.780757\pi\) |
0.936451 | + | 0.350799i | \(0.114090\pi\) | |||||||
\(930\) | −1.26053 | −0.0413345 | ||||||||
\(931\) | −12.9514 | − | 36.3288i | −0.424464 | − | 1.19063i | ||||
\(932\) | −43.8626 | −1.43677 | ||||||||
\(933\) | −1.69373 | + | 2.93362i | −0.0554501 | + | 0.0960425i | ||||
\(934\) | −3.23727 | − | 5.60712i | −0.105927 | − | 0.183471i | ||||
\(935\) | −0.293716 | − | 0.508731i | −0.00960554 | − | 0.0166373i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.916838 | −0.0299518 | −0.0149759 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149759 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(938\) | −6.17718 | + | 2.85565i | −0.201692 | + | 0.0932404i | ||||
\(939\) | 24.1928 | 0.789501 | ||||||||
\(940\) | −4.15629 | + | 7.19891i | −0.135563 | + | 0.234803i | ||||
\(941\) | 8.54482 | + | 14.8001i | 0.278553 | + | 0.482468i | 0.971025 | − | 0.238976i | \(-0.0768118\pi\) |
−0.692472 | + | 0.721445i | \(0.743478\pi\) | |||||||
\(942\) | 4.20409 | + | 7.28169i | 0.136977 | + | 0.237250i | ||||
\(943\) | −26.5597 | + | 46.0027i | −0.864902 | + | 1.49805i | ||||
\(944\) | −27.6284 | −0.899227 | ||||||||
\(945\) | 1.11869 | − | 12.3177i | 0.0363909 | − | 0.400695i | ||||
\(946\) | 9.56735 | 0.311062 | ||||||||
\(947\) | −10.8777 | + | 18.8408i | −0.353479 | + | 0.612243i | −0.986856 | − | 0.161600i | \(-0.948335\pi\) |
0.633378 | + | 0.773843i | \(0.281668\pi\) | |||||||
\(948\) | 8.86342 | + | 15.3519i | 0.287871 | + | 0.498607i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.39012 | − | 9.33597i | 0.174879 | − | 0.302899i | ||||
\(951\) | 14.2870 | 0.463288 | ||||||||
\(952\) | 0.575828 | + | 0.406041i | 0.0186627 | + | 0.0131599i | ||||
\(953\) | −17.8081 | −0.576862 | −0.288431 | − | 0.957501i | \(-0.593134\pi\) | ||||
−0.288431 | + | 0.957501i | \(0.593134\pi\) | |||||||
\(954\) | 0.159240 | − | 0.275812i | 0.00515560 | − | 0.00892976i | ||||
\(955\) | 3.37692 | + | 5.84900i | 0.109275 | + | 0.189269i | ||||
\(956\) | 6.82909 | + | 11.8283i | 0.220869 | + | 0.382556i | ||||
\(957\) | −14.1526 | + | 24.5130i | −0.457488 | + | 0.792392i | ||||
\(958\) | −13.5056 | −0.436347 | ||||||||
\(959\) | 11.3414 | + | 7.99729i | 0.366232 | + | 0.258246i | ||||
\(960\) | −2.31132 | −0.0745975 | ||||||||
\(961\) | 11.4487 | − | 19.8297i | 0.369311 | − | 0.639666i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.66793 | + | 16.7453i | 0.311545 | + | 0.539611i | ||||
\(964\) | −19.0447 | + | 32.9865i | −0.613390 | + | 1.06242i | ||||
\(965\) | 5.03441 | 0.162063 | ||||||||
\(966\) | 0.446353 | − | 4.91474i | 0.0143612 | − | 0.158129i | ||||
\(967\) | 35.3813 | 1.13779 | 0.568893 | − | 0.822412i | \(-0.307372\pi\) | ||||
0.568893 | + | 0.822412i | \(0.307372\pi\) | |||||||
\(968\) | −4.44318 | + | 7.69582i | −0.142809 | + | 0.247353i | ||||
\(969\) | −0.332441 | − | 0.575805i | −0.0106796 | − | 0.0184975i | ||||
\(970\) | −0.704409 | − | 1.22007i | −0.0226172 | − | 0.0391742i | ||||
\(971\) | −24.8533 | + | 43.0472i | −0.797582 | + | 1.38145i | 0.123605 | + | 0.992331i | \(0.460554\pi\) |
−0.921187 | + | 0.389120i | \(0.872779\pi\) | |||||||
\(972\) | −28.0401 | −0.899385 | ||||||||
\(973\) | −49.8046 | + | 23.0242i | −1.59666 | + | 0.738122i | ||||
\(974\) | −16.0415 | −0.514002 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.51287 | + | 13.0127i | 0.240481 | + | 0.416526i | ||||
\(977\) | −30.6401 | − | 53.0701i | −0.980262 | − | 1.69786i | −0.661346 | − | 0.750081i | \(-0.730014\pi\) |
−0.318917 | − | 0.947783i | \(-0.603319\pi\) | |||||||
\(978\) | −1.89723 | + | 3.28609i | −0.0606666 | + | 0.105078i | ||||
\(979\) | −6.93346 | −0.221594 | ||||||||
\(980\) | −8.27314 | + | 9.72825i | −0.264276 | + | 0.310757i | ||||
\(981\) | −14.6495 | −0.467723 | ||||||||
\(982\) | −7.15080 | + | 12.3856i | −0.228191 | + | 0.395239i | ||||
\(983\) | −3.49481 | − | 6.05318i | −0.111467 | − | 0.193067i | 0.804895 | − | 0.593417i | \(-0.202222\pi\) |
−0.916362 | + | 0.400351i | \(0.868888\pi\) | |||||||
\(984\) | −9.63536 | − | 16.6889i | −0.307164 | − | 0.532024i | ||||
\(985\) | 13.4668 | − | 23.3252i | 0.429088 | − | 0.743203i | ||||
\(986\) | −0.596362 | −0.0189920 | ||||||||
\(987\) | −9.29684 | + | 4.29785i | −0.295922 | + | 0.136802i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.5893 | + | 18.3413i | −0.336722 | + | 0.583219i | ||||
\(990\) | 2.35547 | + | 4.07979i | 0.0748617 | + | 0.129664i | ||||
\(991\) | 16.3671 | + | 28.3486i | 0.519917 | + | 0.900522i | 0.999732 | + | 0.0231525i | \(0.00737033\pi\) |
−0.479815 | + | 0.877370i | \(0.659296\pi\) | |||||||
\(992\) | 7.16066 | − | 12.4026i | 0.227351 | − | 0.393784i | ||||
\(993\) | 5.27532 | 0.167407 | ||||||||
\(994\) | 0.442551 | − | 4.87287i | 0.0140369 | − | 0.154558i | ||||
\(995\) | 17.8416 | 0.565616 | ||||||||
\(996\) | 2.13597 | − | 3.69960i | 0.0676807 | − | 0.117226i | ||||
\(997\) | −28.8948 | − | 50.0473i | −0.915109 | − | 1.58502i | −0.806742 | − | 0.590904i | \(-0.798771\pi\) |
−0.108367 | − | 0.994111i | \(-0.534562\pi\) | |||||||
\(998\) | −0.449529 | − | 0.778607i | −0.0142296 | − | 0.0246464i | ||||
\(999\) | −1.89057 | + | 3.27456i | −0.0598150 | + | 0.103603i |
(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 | 1183.2.e.j.170.8 | 24 | ||
7.2 | even | 3 | 8281.2.a.cp.1.5 | 12 | |||
7.4 | even | 3 | inner | 1183.2.e.j.508.8 | 24 | ||
7.5 | odd | 6 | 8281.2.a.co.1.5 | 12 | |||
13.2 | odd | 12 | 91.2.u.b.30.4 | yes | 12 | ||
13.7 | odd | 12 | 91.2.k.b.23.3 | yes | 12 | ||
13.12 | even | 2 | inner | 1183.2.e.j.170.5 | 24 | ||
39.2 | even | 12 | 819.2.do.e.667.3 | 12 | |||
39.20 | even | 12 | 819.2.bm.f.478.4 | 12 | |||
91.2 | odd | 12 | 637.2.q.g.589.3 | 12 | |||
91.12 | odd | 6 | 8281.2.a.co.1.8 | 12 | |||
91.20 | even | 12 | 637.2.k.i.569.3 | 12 | |||
91.25 | even | 6 | inner | 1183.2.e.j.508.5 | 24 | ||
91.33 | even | 12 | 637.2.q.i.491.3 | 12 | |||
91.41 | even | 12 | 637.2.u.g.30.4 | 12 | |||
91.46 | odd | 12 | 91.2.u.b.88.4 | yes | 12 | ||
91.51 | even | 6 | 8281.2.a.cp.1.8 | 12 | |||
91.54 | even | 12 | 637.2.q.i.589.3 | 12 | |||
91.59 | even | 12 | 637.2.u.g.361.4 | 12 | |||
91.67 | odd | 12 | 91.2.k.b.4.4 | ✓ | 12 | ||
91.72 | odd | 12 | 637.2.q.g.491.3 | 12 | |||
91.80 | even | 12 | 637.2.k.i.459.4 | 12 | |||
273.137 | even | 12 | 819.2.do.e.361.3 | 12 | |||
273.158 | even | 12 | 819.2.bm.f.550.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.4 | ✓ | 12 | 91.67 | odd | 12 | ||
91.2.k.b.23.3 | yes | 12 | 13.7 | odd | 12 | ||
91.2.u.b.30.4 | yes | 12 | 13.2 | odd | 12 | ||
91.2.u.b.88.4 | yes | 12 | 91.46 | odd | 12 | ||
637.2.k.i.459.4 | 12 | 91.80 | even | 12 | |||
637.2.k.i.569.3 | 12 | 91.20 | even | 12 | |||
637.2.q.g.491.3 | 12 | 91.72 | odd | 12 | |||
637.2.q.g.589.3 | 12 | 91.2 | odd | 12 | |||
637.2.q.i.491.3 | 12 | 91.33 | even | 12 | |||
637.2.q.i.589.3 | 12 | 91.54 | even | 12 | |||
637.2.u.g.30.4 | 12 | 91.41 | even | 12 | |||
637.2.u.g.361.4 | 12 | 91.59 | even | 12 | |||
819.2.bm.f.478.4 | 12 | 39.20 | even | 12 | |||
819.2.bm.f.550.3 | 12 | 273.158 | even | 12 | |||
819.2.do.e.361.3 | 12 | 273.137 | even | 12 | |||
819.2.do.e.667.3 | 12 | 39.2 | even | 12 | |||
1183.2.e.j.170.5 | 24 | 13.12 | even | 2 | inner | ||
1183.2.e.j.170.8 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.e.j.508.5 | 24 | 91.25 | even | 6 | inner | ||
1183.2.e.j.508.8 | 24 | 7.4 | even | 3 | inner | ||
8281.2.a.co.1.5 | 12 | 7.5 | odd | 6 | |||
8281.2.a.co.1.8 | 12 | 91.12 | odd | 6 | |||
8281.2.a.cp.1.5 | 12 | 7.2 | even | 3 | |||
8281.2.a.cp.1.8 | 12 | 91.51 | even | 6 |