Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 126.1 | ||
Root | \(-2.04679i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.126 |
Dual form | 625.2.d.q.501.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.823534 | − | 2.53458i | −0.582327 | − | 1.79222i | −0.609751 | − | 0.792593i | \(-0.708731\pi\) |
0.0274246 | − | 0.999624i | \(-0.491269\pi\) | |||||||
\(3\) | 0.614111 | − | 0.446178i | 0.354557 | − | 0.257601i | −0.396221 | − | 0.918155i | \(-0.629679\pi\) |
0.750778 | + | 0.660554i | \(0.229679\pi\) | |||||||
\(4\) | −4.12784 | + | 2.99905i | −2.06392 | + | 1.49953i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.63661 | − | 1.18907i | −0.668144 | − | 0.485435i | ||||
\(7\) | 2.04213 | 0.771852 | 0.385926 | − | 0.922530i | \(-0.373882\pi\) | ||||
0.385926 | + | 0.922530i | \(0.373882\pi\) | |||||||
\(8\) | 6.68866 | + | 4.85960i | 2.36480 | + | 1.71813i | ||||
\(9\) | −0.748993 | + | 2.30516i | −0.249664 | + | 0.768388i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.416762 | + | 1.28266i | 0.125659 | + | 0.386737i | 0.994020 | − | 0.109194i | \(-0.0348269\pi\) |
−0.868362 | + | 0.495931i | \(0.834827\pi\) | |||||||
\(12\) | −1.19684 | + | 3.68350i | −0.345498 | + | 1.06333i | ||||
\(13\) | −0.407790 | + | 1.25505i | −0.113101 | + | 0.348088i | −0.991546 | − | 0.129754i | \(-0.958581\pi\) |
0.878445 | + | 0.477843i | \(0.158581\pi\) | |||||||
\(14\) | −1.68176 | − | 5.17593i | −0.449470 | − | 1.38333i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.65530 | − | 11.2498i | 0.913824 | − | 2.81246i | ||||
\(17\) | 3.30659 | + | 2.40238i | 0.801966 | + | 0.582663i | 0.911490 | − | 0.411321i | \(-0.134933\pi\) |
−0.109524 | + | 0.993984i | \(0.534933\pi\) | |||||||
\(18\) | 6.45944 | 1.52250 | ||||||||
\(19\) | 3.95350 | + | 2.87239i | 0.906996 | + | 0.658971i | 0.940253 | − | 0.340476i | \(-0.110588\pi\) |
−0.0332573 | + | 0.999447i | \(0.510588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.25409 | − | 0.911152i | 0.273666 | − | 0.198830i | ||||
\(22\) | 2.90779 | − | 2.11263i | 0.619943 | − | 0.450415i | ||||
\(23\) | 0.845525 | + | 2.60226i | 0.176304 | + | 0.542608i | 0.999691 | − | 0.0248727i | \(-0.00791806\pi\) |
−0.823387 | + | 0.567481i | \(0.807918\pi\) | |||||||
\(24\) | 6.27582 | 1.28105 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.51685 | 0.689711 | ||||||||
\(27\) | 1.27226 | + | 3.91560i | 0.244846 | + | 0.753558i | ||||
\(28\) | −8.42958 | + | 6.12445i | −1.59304 | + | 1.15741i | ||||
\(29\) | 3.73696 | − | 2.71506i | 0.693937 | − | 0.504175i | −0.184015 | − | 0.982923i | \(-0.558910\pi\) |
0.877952 | + | 0.478749i | \(0.158910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.79035 | − | 4.20694i | −1.03998 | − | 0.755588i | −0.0696967 | − | 0.997568i | \(-0.522203\pi\) |
−0.970281 | + | 0.241980i | \(0.922203\pi\) | |||||||
\(32\) | −14.9886 | −2.64963 | ||||||||
\(33\) | 0.828234 | + | 0.601747i | 0.144177 | + | 0.104751i | ||||
\(34\) | 3.36593 | − | 10.3593i | 0.577252 | − | 1.77660i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.82158 | − | 11.7616i | −0.636930 | − | 1.96027i | ||||
\(37\) | 2.67188 | − | 8.22321i | 0.439255 | − | 1.35189i | −0.449408 | − | 0.893327i | \(-0.648365\pi\) |
0.888663 | − | 0.458561i | \(-0.151635\pi\) | |||||||
\(38\) | 4.02445 | − | 12.3860i | 0.652851 | − | 2.00927i | ||||
\(39\) | 0.309547 | + | 0.952686i | 0.0495671 | + | 0.152552i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12094 | + | 9.60527i | −0.487409 | + | 1.50009i | 0.341051 | + | 0.940045i | \(0.389217\pi\) |
−0.828461 | + | 0.560047i | \(0.810783\pi\) | |||||||
\(42\) | −3.34217 | − | 2.42823i | −0.515709 | − | 0.374684i | ||||
\(43\) | −2.43460 | −0.371272 | −0.185636 | − | 0.982619i | \(-0.559435\pi\) | ||||
−0.185636 | + | 0.982619i | \(0.559435\pi\) | |||||||
\(44\) | −5.56710 | − | 4.04474i | −0.839272 | − | 0.609767i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.89930 | − | 4.28610i | 0.869805 | − | 0.631950i | ||||
\(47\) | 6.12581 | − | 4.45066i | 0.893542 | − | 0.649196i | −0.0432572 | − | 0.999064i | \(-0.513774\pi\) |
0.936799 | + | 0.349868i | \(0.113774\pi\) | |||||||
\(48\) | −2.77467 | − | 8.53956i | −0.400489 | − | 1.23258i | ||||
\(49\) | −2.82971 | −0.404244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.10250 | 0.434437 | ||||||||
\(52\) | −2.08067 | − | 6.40363i | −0.288536 | − | 0.888024i | ||||
\(53\) | −0.502597 | + | 0.365158i | −0.0690371 | + | 0.0501584i | −0.621769 | − | 0.783201i | \(-0.713586\pi\) |
0.552731 | + | 0.833359i | \(0.313586\pi\) | |||||||
\(54\) | 8.87665 | − | 6.44926i | 1.20796 | − | 0.877634i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.6591 | + | 9.92393i | 1.82528 | + | 1.32614i | ||||
\(57\) | 3.70948 | 0.491333 | ||||||||
\(58\) | −9.95905 | − | 7.23568i | −1.30769 | − | 0.950091i | ||||
\(59\) | −3.50462 | + | 10.7861i | −0.456262 | + | 1.40423i | 0.413385 | + | 0.910557i | \(0.364347\pi\) |
−0.869647 | + | 0.493674i | \(0.835653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.200093 | + | 0.615822i | 0.0256192 | + | 0.0788479i | 0.963049 | − | 0.269327i | \(-0.0868014\pi\) |
−0.937429 | + | 0.348175i | \(0.886801\pi\) | |||||||
\(62\) | −5.89425 | + | 18.1407i | −0.748571 | + | 2.30387i | ||||
\(63\) | −1.52954 | + | 4.70744i | −0.192704 | + | 0.593082i | ||||
\(64\) | 5.03301 | + | 15.4900i | 0.629127 | + | 1.93625i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.843096 | − | 2.59478i | 0.103778 | − | 0.319396i | ||||
\(67\) | 8.84972 | + | 6.42970i | 1.08117 | + | 0.785513i | 0.977886 | − | 0.209139i | \(-0.0670662\pi\) |
0.103280 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(68\) | −20.8539 | −2.52891 | ||||||||
\(69\) | 1.68031 | + | 1.22082i | 0.202286 | + | 0.146969i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.38846 | − | 1.73532i | 0.283458 | − | 0.205945i | −0.436966 | − | 0.899478i | \(-0.643947\pi\) |
0.720424 | + | 0.693533i | \(0.243947\pi\) | |||||||
\(72\) | −16.2119 | + | 11.7787i | −1.91060 | + | 1.38813i | ||||
\(73\) | −4.18378 | − | 12.8763i | −0.489674 | − | 1.50706i | −0.825095 | − | 0.564993i | \(-0.808879\pi\) |
0.335421 | − | 0.942068i | \(-0.391121\pi\) | |||||||
\(74\) | −23.0428 | −2.67867 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.9339 | −2.86011 | ||||||||
\(77\) | 0.851083 | + | 2.61936i | 0.0969899 | + | 0.298504i | ||||
\(78\) | 2.15974 | − | 1.56914i | 0.244542 | − | 0.177670i | ||||
\(79\) | −1.52847 | + | 1.11050i | −0.171966 | + | 0.124941i | −0.670439 | − | 0.741964i | \(-0.733894\pi\) |
0.498473 | + | 0.866905i | \(0.333894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.35431 | − | 2.43705i | −0.372701 | − | 0.270783i | ||||
\(82\) | 26.9155 | 2.97232 | ||||||||
\(83\) | 1.92126 | + | 1.39588i | 0.210886 | + | 0.153218i | 0.688214 | − | 0.725507i | \(-0.258395\pi\) |
−0.477328 | + | 0.878725i | \(0.658395\pi\) | |||||||
\(84\) | −2.44410 | + | 7.52218i | −0.266674 | + | 0.820737i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00497 | + | 6.17067i | 0.216202 | + | 0.665401i | ||||
\(87\) | 1.08351 | − | 3.33470i | 0.116164 | − | 0.357517i | ||||
\(88\) | −3.44564 | + | 10.6046i | −0.367307 | + | 1.13045i | ||||
\(89\) | 2.26782 | + | 6.97963i | 0.240388 | + | 0.739840i | 0.996361 | + | 0.0852361i | \(0.0271644\pi\) |
−0.755972 | + | 0.654604i | \(0.772836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.832761 | + | 2.56297i | −0.0872970 | + | 0.268673i | ||||
\(92\) | −11.2945 | − | 8.20593i | −1.17753 | − | 0.855527i | ||||
\(93\) | −5.43296 | −0.563371 | ||||||||
\(94\) | −16.3254 | − | 11.8611i | −1.68383 | − | 1.22338i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.20465 | + | 6.68757i | −0.939445 | + | 0.682547i | ||||
\(97\) | 4.69161 | − | 3.40865i | 0.476361 | − | 0.346096i | −0.323554 | − | 0.946210i | \(-0.604878\pi\) |
0.799915 | + | 0.600113i | \(0.204878\pi\) | |||||||
\(98\) | 2.33036 | + | 7.17212i | 0.235402 | + | 0.724493i | ||||
\(99\) | −3.26890 | −0.328537 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5536 | 1.14962 | 0.574812 | − | 0.818285i | \(-0.305075\pi\) | ||||
0.574812 | + | 0.818285i | \(0.305075\pi\) | |||||||
\(102\) | −2.55502 | − | 7.86353i | −0.252984 | − | 0.778606i | ||||
\(103\) | 9.39037 | − | 6.82250i | 0.925260 | − | 0.672241i | −0.0195675 | − | 0.999809i | \(-0.506229\pi\) |
0.944828 | + | 0.327568i | \(0.106229\pi\) | |||||||
\(104\) | −8.82661 | + | 6.41291i | −0.865520 | + | 0.628837i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.33943 | + | 0.973152i | 0.130097 | + | 0.0945208i | ||||
\(107\) | −10.1703 | −0.983204 | −0.491602 | − | 0.870820i | \(-0.663588\pi\) | ||||
−0.491602 | + | 0.870820i | \(0.663588\pi\) | |||||||
\(108\) | −16.9948 | − | 12.3474i | −1.63532 | − | 1.18813i | ||||
\(109\) | 0.369198 | − | 1.13628i | 0.0353628 | − | 0.108835i | −0.931817 | − | 0.362928i | \(-0.881777\pi\) |
0.967180 | + | 0.254093i | \(0.0817769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.02818 | − | 6.24210i | −0.192506 | − | 0.592474i | ||||
\(112\) | 7.46459 | − | 22.9736i | 0.705337 | − | 2.17080i | ||||
\(113\) | −1.38519 | + | 4.26318i | −0.130308 | + | 0.401046i | −0.994831 | − | 0.101547i | \(-0.967621\pi\) |
0.864523 | + | 0.502593i | \(0.167621\pi\) | |||||||
\(114\) | −3.05489 | − | 9.40198i | −0.286116 | − | 0.880576i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.28297 | + | 22.4147i | −0.676207 | + | 2.08115i | ||||
\(117\) | −2.58766 | − | 1.88005i | −0.239230 | − | 0.173811i | ||||
\(118\) | 30.2244 | 2.78238 | ||||||||
\(119\) | 6.75249 | + | 4.90597i | 0.619000 | + | 0.449729i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.42765 | − | 5.39651i | 0.675241 | − | 0.490591i | ||||
\(122\) | 1.39606 | − | 1.01430i | 0.126394 | − | 0.0918304i | ||||
\(123\) | 2.36905 | + | 7.29120i | 0.213610 | + | 0.657425i | ||||
\(124\) | 36.5185 | 3.27946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.1910 | 1.17515 | ||||||||
\(127\) | 1.29072 | + | 3.97242i | 0.114533 | + | 0.352495i | 0.991849 | − | 0.127417i | \(-0.0406686\pi\) |
−0.877317 | + | 0.479912i | \(0.840669\pi\) | |||||||
\(128\) | 10.8638 | − | 7.89300i | 0.960231 | − | 0.697649i | ||||
\(129\) | −1.49511 | + | 1.08626i | −0.131637 | + | 0.0956400i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.74187 | − | 1.99209i | −0.239559 | − | 0.174049i | 0.461528 | − | 0.887126i | \(-0.347301\pi\) |
−0.701087 | + | 0.713076i | \(0.747301\pi\) | |||||||
\(132\) | −5.22349 | −0.454646 | ||||||||
\(133\) | 8.07356 | + | 5.86579i | 0.700067 | + | 0.508628i | ||||
\(134\) | 9.00853 | − | 27.7254i | 0.778218 | − | 2.39511i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.4421 | + | 32.1374i | 0.895401 | + | 2.75576i | ||||
\(137\) | 2.57596 | − | 7.92798i | 0.220079 | − | 0.677333i | −0.778675 | − | 0.627427i | \(-0.784108\pi\) |
0.998754 | − | 0.0499056i | \(-0.0158920\pi\) | |||||||
\(138\) | 1.71047 | − | 5.26427i | 0.145605 | − | 0.448125i | ||||
\(139\) | −1.06102 | − | 3.26550i | −0.0899949 | − | 0.276976i | 0.895922 | − | 0.444211i | \(-0.146516\pi\) |
−0.985917 | + | 0.167235i | \(0.946516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77614 | − | 5.46640i | 0.149578 | − | 0.460354i | ||||
\(142\) | −6.36528 | − | 4.62465i | −0.534163 | − | 0.388092i | ||||
\(143\) | −1.77976 | −0.148831 | ||||||||
\(144\) | 23.1950 | + | 16.8521i | 1.93291 | + | 1.40434i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −29.1906 | + | 21.2082i | −2.41583 | + | 1.75520i | ||||
\(147\) | −1.73775 | + | 1.26255i | −0.143328 | + | 0.104134i | ||||
\(148\) | 13.6327 | + | 41.9572i | 1.12060 | + | 3.44886i | ||||
\(149\) | 9.96023 | 0.815974 | 0.407987 | − | 0.912988i | \(-0.366231\pi\) | ||||
0.407987 | + | 0.912988i | \(0.366231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0404 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827134\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827134\pi\) | |||||||
\(152\) | 12.4850 | + | 38.4249i | 1.01267 | + | 3.11667i | ||||
\(153\) | −8.01450 | + | 5.82287i | −0.647934 | + | 0.470751i | ||||
\(154\) | 5.93808 | − | 4.31427i | 0.478504 | − | 0.347654i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.13491 | − | 3.00419i | −0.331058 | − | 0.240528i | ||||
\(157\) | −7.80843 | −0.623181 | −0.311590 | − | 0.950217i | \(-0.600862\pi\) | ||||
−0.311590 | + | 0.950217i | \(0.600862\pi\) | |||||||
\(158\) | 4.07339 | + | 2.95949i | 0.324062 | + | 0.235445i | ||||
\(159\) | −0.145725 | + | 0.448495i | −0.0115567 | + | 0.0355680i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.72667 | + | 5.31415i | 0.136081 | + | 0.418813i | ||||
\(162\) | −3.41450 | + | 10.5088i | −0.268269 | + | 0.825646i | ||||
\(163\) | 3.60887 | − | 11.1070i | 0.282668 | − | 0.869963i | −0.704420 | − | 0.709784i | \(-0.748793\pi\) |
0.987088 | − | 0.160180i | \(-0.0512074\pi\) | |||||||
\(164\) | −15.9240 | − | 49.0089i | −1.24345 | − | 3.82695i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.95574 | − | 6.01914i | 0.151795 | − | 0.467176i | ||||
\(167\) | 6.07732 | + | 4.41543i | 0.470277 | + | 0.341676i | 0.797549 | − | 0.603254i | \(-0.206129\pi\) |
−0.327272 | + | 0.944930i | \(0.606129\pi\) | |||||||
\(168\) | 12.8160 | 0.988779 | ||||||||
\(169\) | 9.10836 | + | 6.61761i | 0.700643 | + | 0.509047i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.58248 | + | 6.96208i | −0.732790 | + | 0.532403i | ||||
\(172\) | 10.0496 | − | 7.30148i | 0.766276 | − | 0.556732i | ||||
\(173\) | −1.64206 | − | 5.05374i | −0.124843 | − | 0.384229i | 0.869029 | − | 0.494761i | \(-0.164744\pi\) |
−0.993873 | + | 0.110532i | \(0.964744\pi\) | |||||||
\(174\) | −9.34436 | −0.708394 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.9532 | 1.20251 | ||||||||
\(177\) | 2.66029 | + | 8.18754i | 0.199960 | + | 0.615413i | ||||
\(178\) | 15.8228 | − | 11.4959i | 1.18597 | − | 0.861657i | ||||
\(179\) | −1.05718 | + | 0.768083i | −0.0790171 | + | 0.0574093i | −0.626592 | − | 0.779347i | \(-0.715551\pi\) |
0.547575 | + | 0.836756i | \(0.315551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3120 | + | 11.8513i | 1.21246 | + | 0.880904i | 0.995452 | − | 0.0952662i | \(-0.0303702\pi\) |
0.217008 | + | 0.976170i | \(0.430370\pi\) | |||||||
\(182\) | 7.18186 | 0.532355 | ||||||||
\(183\) | 0.397645 | + | 0.288906i | 0.0293947 | + | 0.0213565i | ||||
\(184\) | −6.99050 | + | 21.5145i | −0.515346 | + | 1.58607i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.47423 | + | 13.7703i | 0.328066 | + | 1.00968i | ||||
\(187\) | −1.70338 | + | 5.24247i | −0.124563 | + | 0.383367i | ||||
\(188\) | −11.9386 | + | 36.7433i | −0.870713 | + | 2.67978i | ||||
\(189\) | 2.59811 | + | 7.99616i | 0.188985 | + | 0.581635i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.58074 | − | 20.2534i | 0.476166 | − | 1.46549i | −0.368213 | − | 0.929741i | \(-0.620030\pi\) |
0.844379 | − | 0.535746i | \(-0.179970\pi\) | |||||||
\(192\) | 10.0021 | + | 7.26697i | 0.721842 | + | 0.524449i | ||||
\(193\) | 7.99352 | 0.575386 | 0.287693 | − | 0.957723i | \(-0.407112\pi\) | ||||
0.287693 | + | 0.957723i | \(0.407112\pi\) | |||||||
\(194\) | −12.5032 | − | 9.08411i | −0.897677 | − | 0.652201i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.6806 | − | 8.48644i | 0.834328 | − | 0.606175i | ||||
\(197\) | −17.5568 | + | 12.7558i | −1.25087 | + | 0.908811i | −0.998272 | − | 0.0587600i | \(-0.981285\pi\) |
−0.252599 | + | 0.967571i | \(0.581285\pi\) | |||||||
\(198\) | 2.69205 | + | 8.28528i | 0.191316 | + | 0.588810i | ||||
\(199\) | 9.34240 | 0.662265 | 0.331133 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331133 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.30350 | 0.585684 | ||||||||
\(202\) | −9.51477 | − | 29.2834i | −0.669457 | − | 2.06038i | ||||
\(203\) | 7.63136 | − | 5.54451i | 0.535617 | − | 0.389148i | ||||
\(204\) | −12.8066 | + | 9.30456i | −0.896643 | + | 0.651450i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −25.0254 | − | 18.1820i | −1.74361 | − | 1.26680i | ||||
\(207\) | −6.63192 | −0.460951 | ||||||||
\(208\) | 12.6285 | + | 9.17516i | 0.875631 | + | 0.636183i | ||||
\(209\) | −2.03663 | + | 6.26812i | −0.140877 | + | 0.433575i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.12649 | − | 6.54467i | −0.146394 | − | 0.450554i | 0.850794 | − | 0.525500i | \(-0.176122\pi\) |
−0.997188 | + | 0.0749460i | \(0.976122\pi\) | |||||||
\(212\) | 0.979513 | − | 3.01463i | 0.0672732 | − | 0.207046i | ||||
\(213\) | 0.692520 | − | 2.13136i | 0.0474507 | − | 0.146038i | ||||
\(214\) | 8.37562 | + | 25.7775i | 0.572546 | + | 1.76211i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.5186 | + | 32.3728i | −0.715697 | + | 2.20269i | ||||
\(217\) | −11.8246 | − | 8.59111i | −0.802709 | − | 0.583202i | ||||
\(218\) | −3.18402 | −0.215649 | ||||||||
\(219\) | −8.31444 | − | 6.04079i | −0.561838 | − | 0.408199i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.36350 | + | 3.17027i | −0.293521 | + | 0.213255i | ||||
\(222\) | −14.1508 | + | 10.2812i | −0.949740 | + | 0.690026i | ||||
\(223\) | −2.63127 | − | 8.09821i | −0.176203 | − | 0.542296i | 0.823484 | − | 0.567340i | \(-0.192028\pi\) |
−0.999686 | + | 0.0250437i | \(0.992028\pi\) | |||||||
\(224\) | −30.6086 | −2.04512 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.9461 | 0.794643 | ||||||||
\(227\) | −6.48428 | − | 19.9566i | −0.430377 | − | 1.32456i | −0.897751 | − | 0.440504i | \(-0.854800\pi\) |
0.467374 | − | 0.884060i | \(-0.345200\pi\) | |||||||
\(228\) | −15.3122 | + | 11.1249i | −1.01407 | + | 0.736767i | ||||
\(229\) | −24.0787 | + | 17.4942i | −1.59116 | + | 1.15605i | −0.688908 | + | 0.724849i | \(0.741910\pi\) |
−0.902256 | + | 0.431200i | \(0.858090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.69136 | + | 1.22884i | 0.111283 | + | 0.0808521i | ||||
\(232\) | 38.1894 | 2.50726 | ||||||||
\(233\) | −1.83771 | − | 1.33518i | −0.120392 | − | 0.0874703i | 0.525960 | − | 0.850510i | \(-0.323706\pi\) |
−0.646352 | + | 0.763039i | \(0.723706\pi\) | |||||||
\(234\) | −2.63410 | + | 8.10692i | −0.172196 | + | 0.529966i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.8816 | − | 55.0338i | −1.16399 | − | 3.58240i | ||||
\(237\) | −0.443171 | + | 1.36394i | −0.0287870 | + | 0.0885973i | ||||
\(238\) | 6.87366 | − | 21.1549i | 0.445553 | − | 1.37127i | ||||
\(239\) | 4.76838 | + | 14.6756i | 0.308441 | + | 0.949283i | 0.978371 | + | 0.206859i | \(0.0663240\pi\) |
−0.669930 | + | 0.742424i | \(0.733676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.49621 | + | 4.60486i | −0.0963793 | + | 0.296625i | −0.987611 | − | 0.156924i | \(-0.949842\pi\) |
0.891231 | + | 0.453549i | \(0.149842\pi\) | |||||||
\(242\) | −19.7948 | − | 14.3818i | −1.27246 | − | 0.924494i | ||||
\(243\) | −15.4986 | −0.994235 | ||||||||
\(244\) | −2.67283 | − | 1.94192i | −0.171110 | − | 0.124319i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16.5291 | − | 12.0091i | 1.05386 | − | 0.765672i | ||||
\(247\) | −5.21719 | + | 3.79051i | −0.331962 | + | 0.241184i | ||||
\(248\) | −18.2857 | − | 56.2776i | −1.16114 | − | 3.57363i | ||||
\(249\) | 1.80268 | 0.114240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.8293 | −1.12537 | −0.562687 | − | 0.826670i | \(-0.690232\pi\) | ||||
−0.562687 | + | 0.826670i | \(0.690232\pi\) | |||||||
\(252\) | −7.80416 | − | 24.0187i | −0.491616 | − | 1.51304i | ||||
\(253\) | −2.98544 | + | 2.16905i | −0.187693 | + | 0.136367i | ||||
\(254\) | 9.00545 | − | 6.54284i | 0.565052 | − | 0.410534i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.59889 | − | 1.88820i | −0.162431 | − | 0.118013i | ||||
\(257\) | −5.88929 | −0.367364 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(258\) | 3.98449 | + | 2.89490i | 0.248064 | + | 0.180229i | ||||
\(259\) | 5.45633 | − | 16.7929i | 0.339040 | − | 1.04346i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.45971 | + | 10.6479i | 0.214150 | + | 0.659087i | ||||
\(262\) | −2.79107 | + | 8.59004i | −0.172433 | + | 0.530695i | ||||
\(263\) | −7.31668 | + | 22.5184i | −0.451166 | + | 1.38855i | 0.424412 | + | 0.905469i | \(0.360481\pi\) |
−0.875578 | + | 0.483077i | \(0.839519\pi\) | |||||||
\(264\) | 2.61553 | + | 8.04977i | 0.160975 | + | 0.495429i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.21844 | − | 25.2938i | 0.503905 | − | 1.55086i | ||||
\(267\) | 4.50685 | + | 3.27442i | 0.275815 | + | 0.200391i | ||||
\(268\) | −55.8132 | −3.40934 | ||||||||
\(269\) | −11.1208 | − | 8.07972i | −0.678046 | − | 0.492629i | 0.194663 | − | 0.980870i | \(-0.437639\pi\) |
−0.872709 | + | 0.488241i | \(0.837639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.06667 | + | 4.40769i | −0.368524 | + | 0.267748i | −0.756599 | − | 0.653880i | \(-0.773140\pi\) |
0.388075 | + | 0.921628i | \(0.373140\pi\) | |||||||
\(272\) | 39.1130 | − | 28.4172i | 2.37157 | − | 1.72305i | ||||
\(273\) | 0.632134 | + | 1.94551i | 0.0382585 | + | 0.117748i | ||||
\(274\) | −22.2155 | −1.34209 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.5974 | −0.637887 | ||||||||
\(277\) | −0.876983 | − | 2.69908i | −0.0526928 | − | 0.162172i | 0.921247 | − | 0.388978i | \(-0.127172\pi\) |
−0.973940 | + | 0.226806i | \(0.927172\pi\) | |||||||
\(278\) | −7.40287 | + | 5.37850i | −0.443994 | + | 0.322581i | ||||
\(279\) | 14.0346 | − | 10.1967i | 0.840231 | − | 0.610463i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5758 | + | 13.4961i | 1.10814 | + | 0.805110i | 0.982370 | − | 0.186949i | \(-0.0598600\pi\) |
0.125770 | + | 0.992059i | \(0.459860\pi\) | |||||||
\(282\) | −15.3177 | −0.912158 | ||||||||
\(283\) | −20.3263 | − | 14.7679i | −1.20827 | − | 0.877861i | −0.213200 | − | 0.977009i | \(-0.568388\pi\) |
−0.995073 | + | 0.0991475i | \(0.968388\pi\) | |||||||
\(284\) | −4.65488 | + | 14.3262i | −0.276216 | + | 0.850106i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.46569 | + | 4.51093i | 0.0866681 | + | 0.266737i | ||||
\(287\) | −6.37337 | + | 19.6152i | −0.376208 | + | 1.15785i | ||||
\(288\) | 11.2263 | − | 34.5511i | 0.661519 | − | 2.03595i | ||||
\(289\) | −0.0911657 | − | 0.280579i | −0.00536269 | − | 0.0165047i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.36030 | − | 4.18658i | 0.0797424 | − | 0.245422i | ||||
\(292\) | 55.8868 | + | 40.6041i | 3.27053 | + | 2.37618i | ||||
\(293\) | 28.8755 | 1.68692 | 0.843461 | − | 0.537190i | \(-0.180514\pi\) | ||||
0.843461 | + | 0.537190i | \(0.180514\pi\) | |||||||
\(294\) | 4.63114 | + | 3.36472i | 0.270093 | + | 0.196234i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 57.8329 | − | 42.0180i | 3.36147 | − | 2.44225i | ||||
\(297\) | −4.49217 | + | 3.26375i | −0.260662 | + | 0.189382i | ||||
\(298\) | −8.20259 | − | 25.2450i | −0.475163 | − | 1.46240i | ||||
\(299\) | −3.61076 | −0.208816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.97176 | −0.286567 | ||||||||
\(302\) | 17.3275 | + | 53.3286i | 0.997087 | + | 3.06872i | ||||
\(303\) | 7.09518 | − | 5.15495i | 0.407607 | − | 0.296144i | ||||
\(304\) | 46.7652 | − | 33.9769i | 2.68217 | − | 1.94871i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 21.3587 | + | 15.5180i | 1.22100 | + | 0.887107i | ||||
\(307\) | −23.9526 | −1.36704 | −0.683522 | − | 0.729930i | \(-0.739553\pi\) | ||||
−0.683522 | + | 0.729930i | \(0.739553\pi\) | |||||||
\(308\) | −11.3687 | − | 8.25987i | −0.647794 | − | 0.470650i | ||||
\(309\) | 2.72268 | − | 8.37954i | 0.154888 | − | 0.476695i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.05567 | − | 9.40438i | −0.173271 | − | 0.533273i | 0.826279 | − | 0.563261i | \(-0.190453\pi\) |
−0.999550 | + | 0.0299874i | \(0.990453\pi\) | |||||||
\(312\) | −2.55922 | + | 7.87647i | −0.144887 | + | 0.445917i | ||||
\(313\) | 5.80289 | − | 17.8595i | 0.327999 | − | 1.00948i | −0.642070 | − | 0.766646i | \(-0.721924\pi\) |
0.970069 | − | 0.242831i | \(-0.0780759\pi\) | |||||||
\(314\) | 6.43051 | + | 19.7911i | 0.362895 | + | 1.11687i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.97884 | − | 9.16792i | 0.167573 | − | 0.515736i | ||||
\(317\) | −20.9388 | − | 15.2130i | −1.17604 | − | 0.854445i | −0.184323 | − | 0.982866i | \(-0.559009\pi\) |
−0.991720 | + | 0.128421i | \(0.959009\pi\) | |||||||
\(318\) | 1.25676 | 0.0704754 | ||||||||
\(319\) | 5.03994 | + | 3.66173i | 0.282182 | + | 0.205017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.24571 | + | 4.53778i | −0.348602 | + | 0.253274i | ||||
\(322\) | 12.0471 | − | 8.75276i | 0.671361 | − | 0.487772i | ||||
\(323\) | 6.17206 | + | 18.9956i | 0.343422 | + | 1.05695i | ||||
\(324\) | 21.1549 | 1.17527 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.1234 | −1.72377 | ||||||||
\(327\) | −0.280252 | − | 0.862527i | −0.0154980 | − | 0.0476978i | ||||
\(328\) | −67.5527 | + | 49.0799i | −3.72997 | + | 2.70998i | ||||
\(329\) | 12.5097 | − | 9.08883i | 0.689682 | − | 0.501083i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.04965 | − | 0.762612i | −0.0576938 | − | 0.0419170i | 0.558565 | − | 0.829461i | \(-0.311352\pi\) |
−0.616258 | + | 0.787544i | \(0.711352\pi\) | |||||||
\(332\) | −12.1170 | −0.665006 | ||||||||
\(333\) | 16.9546 | + | 12.3183i | 0.929109 | + | 0.675037i | ||||
\(334\) | 6.18637 | − | 19.0397i | 0.338503 | − | 1.04181i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.66624 | − | 17.4389i | −0.309119 | − | 0.951369i | ||||
\(337\) | 3.48476 | − | 10.7250i | 0.189827 | − | 0.584228i | −0.810171 | − | 0.586194i | \(-0.800626\pi\) |
0.999998 | + | 0.00196599i | \(0.000625795\pi\) | |||||||
\(338\) | 9.27181 | − | 28.5357i | 0.504320 | − | 1.55214i | ||||
\(339\) | 1.05147 | + | 3.23610i | 0.0571082 | + | 0.175761i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.98288 | − | 9.18036i | 0.161532 | − | 0.497145i | ||||
\(342\) | 25.5374 | + | 18.5540i | 1.38091 | + | 1.00329i | ||||
\(343\) | −20.0735 | −1.08387 | ||||||||
\(344\) | −16.2842 | − | 11.8312i | −0.877985 | − | 0.637893i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.4568 | + | 8.32385i | −0.615921 | + | 0.447493i | ||||
\(347\) | 1.74344 | − | 1.26668i | 0.0935926 | − | 0.0679990i | −0.540005 | − | 0.841662i | \(-0.681578\pi\) |
0.633597 | + | 0.773663i | \(0.281578\pi\) | |||||||
\(348\) | 5.52838 | + | 17.0146i | 0.296352 | + | 0.912078i | ||||
\(349\) | 5.60904 | 0.300245 | 0.150122 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150122 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.43309 | −0.289997 | ||||||||
\(352\) | −6.24668 | − | 19.2253i | −0.332949 | − | 1.02471i | ||||
\(353\) | −14.9643 | + | 10.8722i | −0.796471 | + | 0.578670i | −0.909877 | − | 0.414879i | \(-0.863824\pi\) |
0.113406 | + | 0.993549i | \(0.463824\pi\) | |||||||
\(354\) | 18.5611 | − | 13.4854i | 0.986512 | − | 0.716743i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −30.2935 | − | 22.0095i | −1.60555 | − | 1.16650i | ||||
\(357\) | 6.33571 | 0.335321 | ||||||||
\(358\) | 2.81739 | + | 2.04695i | 0.148904 | + | 0.108185i | ||||
\(359\) | 3.47489 | − | 10.6946i | 0.183398 | − | 0.564440i | −0.816520 | − | 0.577318i | \(-0.804099\pi\) |
0.999917 | + | 0.0128782i | \(0.00409938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50825 | + | 4.64193i | 0.0793818 | + | 0.244312i | ||||
\(362\) | 16.6047 | − | 51.1040i | 0.872723 | − | 2.68596i | ||||
\(363\) | 2.15360 | − | 6.62810i | 0.113035 | − | 0.347885i | ||||
\(364\) | −4.24899 | − | 13.0770i | −0.222707 | − | 0.685423i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.404780 | − | 1.24578i | 0.0211582 | − | 0.0651182i | ||||
\(367\) | −23.1117 | − | 16.7916i | −1.20642 | − | 0.876517i | −0.211521 | − | 0.977374i | \(-0.567842\pi\) |
−0.994901 | + | 0.100857i | \(0.967842\pi\) | |||||||
\(368\) | 32.3656 | 1.68718 | ||||||||
\(369\) | −19.8042 | − | 14.3886i | −1.03096 | − | 0.749039i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.02637 | + | 0.745700i | −0.0532864 | + | 0.0387148i | ||||
\(372\) | 22.4264 | − | 16.2937i | 1.16275 | − | 0.844790i | ||||
\(373\) | −4.35244 | − | 13.3954i | −0.225361 | − | 0.693590i | −0.998255 | − | 0.0590544i | \(-0.981191\pi\) |
0.772894 | − | 0.634535i | \(-0.218809\pi\) | |||||||
\(374\) | 14.6902 | 0.759613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 62.6020 | 3.22845 | ||||||||
\(377\) | 1.88364 | + | 5.79725i | 0.0970125 | + | 0.298574i | ||||
\(378\) | 18.1273 | − | 13.1702i | 0.932366 | − | 0.677403i | ||||
\(379\) | −17.7905 | + | 12.9256i | −0.913839 | + | 0.663943i | −0.941983 | − | 0.335661i | \(-0.891040\pi\) |
0.0281442 | + | 0.999604i | \(0.491040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.56505 | + | 1.86361i | 0.131411 | + | 0.0954759i | ||||
\(382\) | −56.7534 | −2.90376 | ||||||||
\(383\) | −11.9278 | − | 8.66607i | −0.609484 | − | 0.442816i | 0.239749 | − | 0.970835i | \(-0.422935\pi\) |
−0.849232 | + | 0.528019i | \(0.822935\pi\) | |||||||
\(384\) | 3.14988 | − | 9.69435i | 0.160742 | − | 0.494712i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.58294 | − | 20.2602i | −0.335063 | − | 1.03122i | ||||
\(387\) | 1.82350 | − | 5.61214i | 0.0926935 | − | 0.285281i | ||||
\(388\) | −9.14349 | + | 28.1408i | −0.464190 | + | 1.42863i | ||||
\(389\) | −4.40558 | − | 13.5590i | −0.223372 | − | 0.687468i | −0.998453 | − | 0.0556059i | \(-0.982291\pi\) |
0.775081 | − | 0.631862i | \(-0.217709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.45581 | + | 10.6359i | −0.174768 | + | 0.537879i | ||||
\(392\) | −18.9270 | − | 13.7513i | −0.955957 | − | 0.694543i | ||||
\(393\) | −2.57264 | −0.129772 | ||||||||
\(394\) | 46.7891 | + | 33.9943i | 2.35720 | + | 1.71261i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 13.4935 | − | 9.80360i | 0.678074 | − | 0.492650i | ||||
\(397\) | −4.44203 | + | 3.22732i | −0.222939 | + | 0.161975i | −0.693649 | − | 0.720314i | \(-0.743998\pi\) |
0.470710 | + | 0.882288i | \(0.343998\pi\) | |||||||
\(398\) | −7.69378 | − | 23.6790i | −0.385655 | − | 1.18692i | ||||
\(399\) | 7.57525 | 0.379237 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.7528 | 1.33597 | 0.667985 | − | 0.744175i | \(-0.267157\pi\) | ||||
0.667985 | + | 0.744175i | \(0.267157\pi\) | |||||||
\(402\) | −6.83821 | − | 21.0459i | −0.341059 | − | 1.04967i | ||||
\(403\) | 7.64117 | − | 5.55163i | 0.380634 | − | 0.276546i | ||||
\(404\) | −47.6913 | + | 34.6498i | −2.37273 | + | 1.72389i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.3377 | − | 14.7762i | −1.00934 | − | 0.733330i | ||||
\(407\) | 11.6612 | 0.578022 | ||||||||
\(408\) | 20.7516 | + | 15.0769i | 1.02736 | + | 0.746418i | ||||
\(409\) | 1.58646 | − | 4.88262i | 0.0784453 | − | 0.241430i | −0.904142 | − | 0.427233i | \(-0.859489\pi\) |
0.982587 | + | 0.185803i | \(0.0594886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.95536 | − | 6.01799i | −0.0964510 | − | 0.296846i | ||||
\(412\) | −18.3009 | + | 56.3244i | −0.901621 | + | 2.77490i | ||||
\(413\) | −7.15688 | + | 22.0266i | −0.352167 | + | 1.08386i | ||||
\(414\) | 5.46162 | + | 16.8091i | 0.268424 | + | 0.826123i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.11220 | − | 18.8114i | 0.299675 | − | 0.922306i | ||||
\(417\) | −2.10858 | − | 1.53197i | −0.103258 | − | 0.0750210i | ||||
\(418\) | 17.5643 | 0.859096 | ||||||||
\(419\) | −25.7685 | − | 18.7219i | −1.25887 | − | 0.914625i | −0.260171 | − | 0.965562i | \(-0.583779\pi\) |
−0.998702 | + | 0.0509374i | \(0.983779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.49213 | + | 1.81064i | −0.121459 | + | 0.0882451i | −0.646856 | − | 0.762612i | \(-0.723917\pi\) |
0.525397 | + | 0.850857i | \(0.323917\pi\) | |||||||
\(422\) | −14.8367 | + | 10.7795i | −0.722241 | + | 0.524739i | ||||
\(423\) | 5.67132 | + | 17.4545i | 0.275749 | + | 0.848668i | ||||
\(424\) | −5.13623 | −0.249437 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.97240 | −0.289364 | ||||||||
\(427\) | 0.408615 | + | 1.25759i | 0.0197743 | + | 0.0608589i | ||||
\(428\) | 41.9815 | − | 30.5014i | 2.02925 | − | 1.47434i | ||||
\(429\) | −1.09297 | + | 0.794088i | −0.0527690 | + | 0.0383389i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.8882 | − | 13.7231i | −0.909813 | − | 0.661018i | 0.0311549 | − | 0.999515i | \(-0.490081\pi\) |
−0.940967 | + | 0.338497i | \(0.890081\pi\) | |||||||
\(432\) | 48.7004 | 2.34310 | ||||||||
\(433\) | 6.64539 | + | 4.82816i | 0.319357 | + | 0.232026i | 0.735901 | − | 0.677089i | \(-0.236759\pi\) |
−0.416544 | + | 0.909116i | \(0.636759\pi\) | |||||||
\(434\) | −12.0368 | + | 37.0455i | −0.577786 | + | 1.77824i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.88376 | + | 5.79761i | 0.0902156 | + | 0.277655i | ||||
\(437\) | −4.13191 | + | 12.7167i | −0.197656 | + | 0.608323i | ||||
\(438\) | −8.46363 | + | 26.0484i | −0.404408 | + | 1.24464i | ||||
\(439\) | −7.51274 | − | 23.1218i | −0.358564 | − | 1.10355i | −0.953914 | − | 0.300079i | \(-0.902987\pi\) |
0.595351 | − | 0.803466i | \(-0.297013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.11943 | − | 6.52295i | 0.100925 | − | 0.310617i | ||||
\(442\) | 11.6288 | + | 8.44881i | 0.553125 | + | 0.401869i | ||||
\(443\) | −0.0631363 | −0.00299970 | −0.00149985 | − | 0.999999i | \(-0.500477\pi\) | ||||
−0.00149985 | + | 0.999999i | \(0.500477\pi\) | |||||||
\(444\) | 27.0924 | + | 19.6838i | 1.28575 | + | 0.934150i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.3586 | + | 13.3383i | −0.869305 | + | 0.631587i | ||||
\(447\) | 6.11668 | − | 4.44403i | 0.289309 | − | 0.210195i | ||||
\(448\) | 10.2781 | + | 31.6326i | 0.485593 | + | 1.49450i | ||||
\(449\) | −11.5711 | −0.546074 | −0.273037 | − | 0.962004i | \(-0.588028\pi\) | ||||
−0.273037 | + | 0.962004i | \(0.588028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6210 | −0.641389 | ||||||||
\(452\) | −7.06764 | − | 21.7520i | −0.332434 | − | 1.02313i | ||||
\(453\) | −12.9212 | + | 9.38777i | −0.607089 | + | 0.441076i | ||||
\(454\) | −45.2414 | + | 32.8698i | −2.12328 | + | 1.54266i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.8115 | + | 18.0266i | 1.16190 | + | 0.844173i | ||||
\(457\) | 41.3967 | 1.93646 | 0.968228 | − | 0.250071i | \(-0.0804539\pi\) | ||||
0.968228 | + | 0.250071i | \(0.0804539\pi\) | |||||||
\(458\) | 64.1700 | + | 46.6222i | 2.99847 | + | 2.17851i | ||||
\(459\) | −5.19993 | + | 16.0037i | −0.242712 | + | 0.746991i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.07604 | + | 27.9332i | 0.422713 | + | 1.30098i | 0.905167 | + | 0.425056i | \(0.139746\pi\) |
−0.482453 | + | 0.875922i | \(0.660254\pi\) | |||||||
\(462\) | 1.72171 | − | 5.29888i | 0.0801012 | − | 0.246526i | ||||
\(463\) | 9.44049 | − | 29.0548i | 0.438737 | − | 1.35029i | −0.450472 | − | 0.892791i | \(-0.648744\pi\) |
0.889208 | − | 0.457502i | \(-0.151256\pi\) | |||||||
\(464\) | −16.8843 | − | 51.9646i | −0.783835 | − | 2.41240i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.87069 | + | 5.75738i | −0.0866579 | + | 0.266706i | ||||
\(467\) | 26.4669 | + | 19.2293i | 1.22474 | + | 0.889827i | 0.996485 | − | 0.0837742i | \(-0.0266974\pi\) |
0.228257 | + | 0.973601i | \(0.426697\pi\) | |||||||
\(468\) | 16.3198 | 0.754384 | ||||||||
\(469\) | 18.0723 | + | 13.1303i | 0.834500 | + | 0.606300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.79524 | + | 3.48395i | −0.220953 | + | 0.160532i | ||||
\(472\) | −75.8573 | + | 55.1136i | −3.49162 | + | 2.53681i | ||||
\(473\) | −1.01465 | − | 3.12277i | −0.0466536 | − | 0.143585i | ||||
\(474\) | 3.82197 | 0.175549 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −42.5864 | −1.95195 | ||||||||
\(477\) | −0.465308 | − | 1.43207i | −0.0213050 | − | 0.0655700i | ||||
\(478\) | 33.2694 | − | 24.1716i | 1.52171 | − | 1.10559i | ||||
\(479\) | 9.97945 | − | 7.25050i | 0.455973 | − | 0.331284i | −0.335977 | − | 0.941870i | \(-0.609066\pi\) |
0.791949 | + | 0.610587i | \(0.209066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.23098 | + | 6.70670i | 0.420896 | + | 0.305799i | ||||
\(482\) | 12.9036 | 0.587741 | ||||||||
\(483\) | 3.43142 | + | 2.49307i | 0.156135 | + | 0.113439i | ||||
\(484\) | −14.4758 | + | 44.5518i | −0.657989 | + | 2.02508i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.7636 | + | 39.2824i | 0.578970 | + | 1.78189i | ||||
\(487\) | −10.9071 | + | 33.5687i | −0.494249 | + | 1.52114i | 0.323875 | + | 0.946100i | \(0.395014\pi\) |
−0.818124 | + | 0.575042i | \(0.804986\pi\) | |||||||
\(488\) | −1.65429 | + | 5.09139i | −0.0748864 | + | 0.230476i | ||||
\(489\) | −2.73943 | − | 8.43109i | −0.123881 | − | 0.381267i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.73278 | − | 14.5660i | 0.213587 | − | 0.657354i | −0.785664 | − | 0.618654i | \(-0.787678\pi\) |
0.999251 | − | 0.0386999i | \(-0.0123216\pi\) | |||||||
\(492\) | −31.6457 | − | 22.9920i | −1.42670 | − | 1.03656i | ||||
\(493\) | 18.8792 | 0.850278 | ||||||||
\(494\) | 13.9039 | + | 10.1018i | 0.625565 | + | 0.454500i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.4929 | + | 49.7630i | −3.07542 | + | 2.23442i | ||||
\(497\) | 4.87755 | − | 3.54375i | 0.218788 | − | 0.158959i | ||||
\(498\) | −1.48457 | − | 4.56903i | −0.0665250 | − | 0.204743i | ||||
\(499\) | −35.1777 | −1.57477 | −0.787386 | − | 0.616461i | \(-0.788566\pi\) | ||||
−0.787386 | + | 0.616461i | \(0.788566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.70221 | 0.254756 | ||||||||
\(502\) | 14.6830 | + | 45.1897i | 0.655335 | + | 2.01691i | ||||
\(503\) | 5.93409 | − | 4.31137i | 0.264588 | − | 0.192235i | −0.447579 | − | 0.894244i | \(-0.647714\pi\) |
0.712167 | + | 0.702010i | \(0.247714\pi\) | |||||||
\(504\) | −33.1069 | + | 24.0535i | −1.47470 | + | 1.07143i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.95622 | + | 5.78054i | 0.353697 | + | 0.256976i | ||||
\(507\) | 8.54617 | 0.379549 | ||||||||
\(508\) | −17.2413 | − | 12.5266i | −0.764961 | − | 0.555777i | ||||
\(509\) | 1.76355 | − | 5.42765i | 0.0781681 | − | 0.240577i | −0.904335 | − | 0.426824i | \(-0.859633\pi\) |
0.982503 | + | 0.186247i | \(0.0596325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.54381 | − | 26.2951i | −0.377956 | − | 1.16323i | ||||
\(512\) | 5.65366 | − | 17.4002i | 0.249859 | − | 0.768987i | ||||
\(513\) | −6.21726 | + | 19.1348i | −0.274499 | + | 0.844820i | ||||
\(514\) | 4.85003 | + | 14.9269i | 0.213926 | + | 0.658395i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.91382 | − | 8.96783i | 0.128274 | − | 0.394787i | ||||
\(517\) | 8.26171 | + | 6.00249i | 0.363350 | + | 0.263989i | ||||
\(518\) | −47.0563 | −2.06753 | ||||||||
\(519\) | −3.26327 | − | 2.37090i | −0.143242 | − | 0.104071i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7705 | − | 19.4499i | 1.17283 | − | 0.852114i | 0.181489 | − | 0.983393i | \(-0.441908\pi\) |
0.991346 | + | 0.131279i | \(0.0419082\pi\) | |||||||
\(522\) | 24.1387 | − | 17.5378i | 1.05652 | − | 0.767608i | ||||
\(523\) | 9.72536 | + | 29.9316i | 0.425260 | + | 1.30882i | 0.902745 | + | 0.430177i | \(0.141549\pi\) |
−0.477484 | + | 0.878640i | \(0.658451\pi\) | |||||||
\(524\) | 17.2924 | 0.755421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 63.1002 | 2.75130 | ||||||||
\(527\) | −9.03967 | − | 27.8213i | −0.393774 | − | 1.21191i | ||||
\(528\) | 9.79700 | − | 7.11794i | 0.426360 | − | 0.309768i | ||||
\(529\) | 12.5506 | − | 9.11851i | 0.545676 | − | 0.396457i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.2388 | − | 16.1574i | −0.965082 | − | 0.701173i | ||||
\(532\) | −50.9182 | −2.20758 | ||||||||
\(533\) | −10.7824 | − | 7.83388i | −0.467038 | − | 0.339323i | ||||
\(534\) | 4.58772 | − | 14.1196i | 0.198530 | − | 0.611013i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27.9471 | + | 86.0122i | 1.20713 | + | 3.71516i | ||||
\(537\) | −0.306522 | + | 0.943377i | −0.0132274 | + | 0.0407097i | ||||
\(538\) | −11.3203 | + | 34.8404i | −0.488054 | + | 1.50208i | ||||
\(539\) | −1.17932 | − | 3.62956i | −0.0507968 | − | 0.156336i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.06905 | + | 21.7563i | −0.303922 | + | 0.935376i | 0.676155 | + | 0.736759i | \(0.263645\pi\) |
−0.980077 | + | 0.198617i | \(0.936355\pi\) | |||||||
\(542\) | 16.1678 | + | 11.7466i | 0.694464 | + | 0.504558i | ||||
\(543\) | 15.3052 | 0.656808 | ||||||||
\(544\) | −49.5611 | − | 36.0083i | −2.12492 | − | 1.54384i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.41046 | − | 3.20439i | 0.188750 | − | 0.137135i | ||||
\(547\) | 14.3639 | − | 10.4360i | 0.614157 | − | 0.446211i | −0.236719 | − | 0.971578i | \(-0.576072\pi\) |
0.850876 | + | 0.525367i | \(0.176072\pi\) | |||||||
\(548\) | 13.1433 | + | 40.4508i | 0.561453 | + | 1.72797i | ||||
\(549\) | −1.56944 | −0.0669820 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.5728 | 0.961634 | ||||||||
\(552\) | 5.30636 | + | 16.3313i | 0.225854 | + | 0.695107i | ||||
\(553\) | −3.12133 | + | 2.26778i | −0.132733 | + | 0.0964359i | ||||
\(554\) | −6.11879 | + | 4.44556i | −0.259962 | + | 0.188874i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.1731 | + | 10.2974i | 0.601075 | + | 0.436706i | ||||
\(557\) | 2.27448 | 0.0963727 | 0.0481864 | − | 0.998838i | \(-0.484656\pi\) | ||||
0.0481864 | + | 0.998838i | \(0.484656\pi\) | |||||||
\(558\) | −37.4024 | − | 27.1745i | −1.58337 | − | 1.15039i | ||||
\(559\) | 0.992805 | − | 3.05554i | 0.0419912 | − | 0.129236i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29301 | + | 3.97946i | 0.0545908 | + | 0.168013i | ||||
\(562\) | 18.9091 | − | 58.1963i | 0.797633 | − | 2.45486i | ||||
\(563\) | 0.122896 | − | 0.378234i | 0.00517943 | − | 0.0159407i | −0.948433 | − | 0.316976i | \(-0.897332\pi\) |
0.953613 | + | 0.301036i | \(0.0973324\pi\) | |||||||
\(564\) | 9.06239 | + | 27.8912i | 0.381595 | + | 1.17443i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.6910 | + | 63.6804i | −0.869709 | + | 2.67669i | ||||
\(567\) | −6.84994 | − | 4.97677i | −0.287670 | − | 0.209005i | ||||
\(568\) | 24.4086 | 1.02416 | ||||||||
\(569\) | 9.05098 | + | 6.57592i | 0.379437 | + | 0.275677i | 0.761113 | − | 0.648619i | \(-0.224653\pi\) |
−0.381676 | + | 0.924296i | \(0.624653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3004 | − | 11.1164i | 0.640303 | − | 0.465207i | −0.219651 | − | 0.975578i | \(-0.570492\pi\) |
0.859954 | + | 0.510371i | \(0.170492\pi\) | |||||||
\(572\) | 7.34655 | − | 5.33758i | 0.307175 | − | 0.223176i | ||||
\(573\) | −4.99533 | − | 15.3740i | −0.208683 | − | 0.642259i | ||||
\(574\) | 54.9649 | 2.29419 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −39.4768 | −1.64486 | ||||||||
\(577\) | 1.85969 | + | 5.72355i | 0.0774201 | + | 0.238274i | 0.982275 | − | 0.187446i | \(-0.0600208\pi\) |
−0.904855 | + | 0.425720i | \(0.860021\pi\) | |||||||
\(578\) | −0.636071 | + | 0.462133i | −0.0264571 | + | 0.0192222i | ||||
\(579\) | 4.90891 | − | 3.56653i | 0.204007 | − | 0.148220i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.92347 | + | 2.85057i | 0.162773 | + | 0.118261i | ||||
\(582\) | −11.7315 | −0.486285 | ||||||||
\(583\) | −0.677839 | − | 0.492479i | −0.0280732 | − | 0.0203964i | ||||
\(584\) | 34.5900 | − | 106.457i | 1.43134 | − | 4.40522i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.7799 | − | 73.1871i | −0.982340 | − | 3.02333i | ||||
\(587\) | 5.04705 | − | 15.5332i | 0.208314 | − | 0.641125i | −0.791247 | − | 0.611497i | \(-0.790568\pi\) |
0.999561 | − | 0.0296279i | \(-0.00943225\pi\) | |||||||
\(588\) | 3.38671 | − | 10.4232i | 0.139666 | − | 0.429847i | ||||
\(589\) | −10.8082 | − | 33.2643i | −0.445345 | − | 1.37063i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.09049 | + | 15.6669i | −0.209395 | + | 0.644451i | ||||
\(592\) | −82.7434 | − | 60.1166i | −3.40073 | − | 2.47078i | ||||
\(593\) | −8.40604 | −0.345195 | −0.172597 | − | 0.984992i | \(-0.555216\pi\) | ||||
−0.172597 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(594\) | 11.9717 | + | 8.69794i | 0.491204 | + | 0.356881i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −41.1142 | + | 29.8712i | −1.68410 | + | 1.22357i | ||||
\(597\) | 5.73727 | − | 4.16837i | 0.234811 | − | 0.170600i | ||||
\(598\) | 2.97358 | + | 9.15175i | 0.121599 | + | 0.374243i | ||||
\(599\) | 13.1918 | 0.539001 | 0.269501 | − | 0.963000i | \(-0.413141\pi\) | ||||
0.269501 | + | 0.963000i | \(0.413141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.06690 | −0.247474 | −0.123737 | − | 0.992315i | \(-0.539488\pi\) | ||||
−0.123737 | + | 0.992315i | \(0.539488\pi\) | |||||||
\(602\) | 4.09441 | + | 12.6013i | 0.166876 | + | 0.513591i | ||||
\(603\) | −21.4499 | + | 15.5843i | −0.873508 | + | 0.634641i | ||||
\(604\) | 86.8516 | − | 63.1014i | 3.53394 | − | 2.56756i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.9087 | − | 13.7380i | −0.768115 | − | 0.558068i | ||||
\(607\) | 14.9141 | 0.605345 | 0.302672 | − | 0.953095i | \(-0.402121\pi\) | ||||
0.302672 | + | 0.953095i | \(0.402121\pi\) | |||||||
\(608\) | −59.2574 | − | 43.0530i | −2.40321 | − | 1.74603i | ||||
\(609\) | 2.21267 | − | 6.80988i | 0.0896617 | − | 0.275950i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.08776 | + | 9.50314i | 0.124917 | + | 0.384456i | ||||
\(612\) | 15.6195 | − | 48.0718i | 0.631380 | − | 1.94319i | ||||
\(613\) | 11.2721 | − | 34.6919i | 0.455275 | − | 1.40119i | −0.415536 | − | 0.909577i | \(-0.636406\pi\) |
0.870812 | − | 0.491617i | \(-0.163594\pi\) | |||||||
\(614\) | 19.7257 | + | 60.7096i | 0.796066 | + | 2.45004i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.03645 | + | 21.6560i | −0.283507 | + | 0.872543i | ||||
\(617\) | 13.1336 | + | 9.54215i | 0.528741 | + | 0.384153i | 0.819886 | − | 0.572526i | \(-0.194036\pi\) |
−0.291146 | + | 0.956679i | \(0.594036\pi\) | |||||||
\(618\) | −23.4808 | −0.944537 | ||||||||
\(619\) | 8.11932 | + | 5.89903i | 0.326343 | + | 0.237102i | 0.738877 | − | 0.673840i | \(-0.235356\pi\) |
−0.412534 | + | 0.910942i | \(0.635356\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.11368 | + | 6.62148i | −0.365719 | + | 0.265711i | ||||
\(622\) | −21.3197 | + | 15.4896i | −0.854841 | + | 0.621078i | ||||
\(623\) | 4.63118 | + | 14.2533i | 0.185544 | + | 0.571047i | ||||
\(624\) | 11.8491 | 0.474342 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.0451 | −2.00020 | ||||||||
\(627\) | 1.54597 | + | 4.75802i | 0.0617403 | + | 0.190017i | ||||
\(628\) | 32.2320 | − | 23.4179i | 1.28619 | − | 0.934475i | ||||
\(629\) | 28.5901 | − | 20.7719i | 1.13996 | − | 0.828231i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2657 | − | 16.9035i | −0.926194 | − | 0.672920i | 0.0188637 | − | 0.999822i | \(-0.493995\pi\) |
−0.945058 | + | 0.326902i | \(0.893995\pi\) | |||||||
\(632\) | −15.6200 | −0.621330 | ||||||||
\(633\) | −4.22599 | − | 3.07036i | −0.167968 | − | 0.122036i | ||||
\(634\) | −21.3146 | + | 65.5995i | −0.846510 | + | 2.60529i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.743531 | − | 2.28835i | −0.0294829 | − | 0.0907391i | ||||
\(637\) | 1.15393 | − | 3.55143i | 0.0457203 | − | 0.140713i | ||||
\(638\) | 5.13037 | − | 15.7897i | 0.203113 | − | 0.625119i | ||||
\(639\) | 2.21125 | + | 6.80554i | 0.0874759 | + | 0.269223i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.63761 | + | 17.3508i | −0.222672 | + | 0.685315i | 0.775847 | + | 0.630921i | \(0.217323\pi\) |
−0.998520 | + | 0.0543939i | \(0.982677\pi\) | |||||||
\(642\) | 16.6449 | + | 12.0932i | 0.656922 | + | 0.477282i | ||||
\(643\) | 33.9734 | 1.33978 | 0.669890 | − | 0.742461i | \(-0.266341\pi\) | ||||
0.669890 | + | 0.742461i | \(0.266341\pi\) | |||||||
\(644\) | −23.0648 | − | 16.7576i | −0.908881 | − | 0.660341i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 43.0630 | − | 31.2871i | 1.69429 | − | 1.23097i | ||||
\(647\) | 38.3254 | − | 27.8450i | 1.50673 | − | 1.09470i | 0.539123 | − | 0.842227i | \(-0.318756\pi\) |
0.967604 | − | 0.252473i | \(-0.0812440\pi\) | |||||||
\(648\) | −10.5928 | − | 32.6012i | −0.416124 | − | 1.28070i | ||||
\(649\) | −15.2955 | −0.600402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.0948 | −0.434840 | ||||||||
\(652\) | 18.4135 | + | 56.6709i | 0.721128 | + | 2.21940i | ||||
\(653\) | −30.2540 | + | 21.9808i | −1.18393 | + | 0.860175i | −0.992609 | − | 0.121353i | \(-0.961277\pi\) |
−0.191319 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(654\) | −1.95534 | + | 1.42064i | −0.0764600 | + | 0.0555514i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 96.6499 | + | 70.2202i | 3.77354 | + | 2.74164i | ||||
\(657\) | 32.8157 | 1.28026 | ||||||||
\(658\) | −33.3385 | − | 24.2218i | −1.29967 | − | 0.944266i | ||||
\(659\) | −2.92996 | + | 9.01748i | −0.114135 | + | 0.351271i | −0.991766 | − | 0.128066i | \(-0.959123\pi\) |
0.877631 | + | 0.479337i | \(0.159123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.71344 | − | 8.35112i | −0.105541 | − | 0.324821i | 0.884316 | − | 0.466888i | \(-0.154625\pi\) |
−0.989857 | + | 0.142067i | \(0.954625\pi\) | |||||||
\(662\) | −1.06848 | + | 3.28845i | −0.0415277 | + | 0.127809i | ||||
\(663\) | −1.26517 | + | 3.89379i | −0.0491351 | + | 0.151222i | ||||
\(664\) | 6.06727 | + | 18.6731i | 0.235456 | + | 0.724658i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.2589 | − | 53.1174i | 0.668768 | − | 2.05826i | ||||
\(667\) | 10.2250 | + | 7.42889i | 0.395913 | + | 0.287648i | ||||
\(668\) | −38.3283 | −1.48297 | ||||||||
\(669\) | −5.22913 | − | 3.79919i | −0.202170 | − | 0.146885i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.706500 | + | 0.513303i | −0.0272741 | + | 0.0198158i | ||||
\(672\) | −18.7971 | + | 13.6569i | −0.725113 | + | 0.526825i | ||||
\(673\) | −14.8408 | − | 45.6753i | −0.572072 | − | 1.76066i | −0.645941 | − | 0.763387i | \(-0.723535\pi\) |
0.0738696 | − | 0.997268i | \(-0.476465\pi\) | |||||||
\(674\) | −30.0531 | −1.15760 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.4444 | −2.20940 | ||||||||
\(677\) | 4.76354 | + | 14.6607i | 0.183078 | + | 0.563455i | 0.999910 | − | 0.0134203i | \(-0.00427195\pi\) |
−0.816832 | + | 0.576875i | \(0.804272\pi\) | |||||||
\(678\) | 7.33623 | − | 5.33008i | 0.281746 | − | 0.204701i | ||||
\(679\) | 9.58087 | − | 6.96091i | 0.367680 | − | 0.267135i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.8862 | − | 9.36240i | −0.493802 | − | 0.358768i | ||||
\(682\) | −25.7248 | −0.985055 | ||||||||
\(683\) | −22.5086 | − | 16.3534i | −0.861267 | − | 0.625747i | 0.0669626 | − | 0.997755i | \(-0.478669\pi\) |
−0.928229 | + | 0.372009i | \(0.878669\pi\) | |||||||
\(684\) | 18.6753 | − | 57.4767i | 0.714068 | − | 2.19768i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.5312 | + | 50.8779i | 0.631166 | + | 1.94253i | ||||
\(687\) | −6.98146 | + | 21.4867i | −0.266359 | + | 0.819770i | ||||
\(688\) | −8.89917 | + | 27.3888i | −0.339278 | + | 1.04419i | ||||
\(689\) | −0.253338 | − | 0.779693i | −0.00965139 | − | 0.0297039i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.21931 | + | 19.1411i | −0.236594 | + | 0.728161i | 0.760312 | + | 0.649558i | \(0.225046\pi\) |
−0.996906 | + | 0.0786030i | \(0.974954\pi\) | |||||||
\(692\) | 21.9346 | + | 15.9364i | 0.833827 | + | 0.605811i | ||||
\(693\) | −6.67552 | −0.253582 | ||||||||
\(694\) | −4.64628 | − | 3.37572i | −0.176370 | − | 0.128141i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 23.4525 | − | 17.0393i | 0.888966 | − | 0.645871i | ||||
\(697\) | −33.3952 | + | 24.2630i | −1.26493 | + | 0.919028i | ||||
\(698\) | −4.61923 | − | 14.2165i | −0.174841 | − | 0.538104i | ||||
\(699\) | −1.72428 | −0.0652184 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.6216 | 1.19433 | 0.597166 | − | 0.802118i | \(-0.296293\pi\) | ||||
0.597166 | + | 0.802118i | \(0.296293\pi\) | |||||||
\(702\) | 4.47433 | + | 13.7706i | 0.168873 | + | 0.519737i | ||||
\(703\) | 34.1836 | − | 24.8358i | 1.28926 | − | 0.936701i | ||||
\(704\) | −17.7709 | + | 12.9113i | −0.669766 | + | 0.486614i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 39.8801 | + | 28.9746i | 1.50091 | + | 1.09047i | ||||
\(707\) | 23.5939 | 0.887340 | ||||||||
\(708\) | −35.5361 | − | 25.8185i | −1.33553 | − | 0.970319i | ||||
\(709\) | −1.47094 | + | 4.52710i | −0.0552425 | + | 0.170019i | −0.974871 | − | 0.222771i | \(-0.928490\pi\) |
0.919628 | + | 0.392790i | \(0.128490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41507 | − | 4.35513i | −0.0530692 | − | 0.163330i | ||||
\(712\) | −18.7495 | + | 57.7051i | −0.702668 | + | 2.16259i | ||||
\(713\) | 6.05165 | − | 18.6251i | 0.226636 | − | 0.697514i | ||||
\(714\) | −5.21767 | − | 16.0583i | −0.195266 | − | 0.600968i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.06033 | − | 6.34105i | 0.0769982 | − | 0.236976i | ||||
\(717\) | 9.47621 | + | 6.88487i | 0.353896 | + | 0.257120i | ||||
\(718\) | −29.9680 | −1.11840 | ||||||||
\(719\) | 18.6662 | + | 13.5618i | 0.696133 | + | 0.505770i | 0.878670 | − | 0.477429i | \(-0.158431\pi\) |
−0.182538 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.1763 | − | 13.9324i | 0.714164 | − | 0.518871i | ||||
\(722\) | 10.5232 | − | 7.64557i | 0.391634 | − | 0.284539i | ||||
\(723\) | 1.13575 | + | 3.49547i | 0.0422389 | + | 0.129998i | ||||
\(724\) | −102.876 | −3.82336 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.5730 | −0.689309 | ||||||||
\(727\) | −4.81470 | − | 14.8181i | −0.178567 | − | 0.549574i | 0.821211 | − | 0.570624i | \(-0.193299\pi\) |
−0.999778 | + | 0.0210509i | \(0.993299\pi\) | |||||||
\(728\) | −18.0251 | + | 13.0960i | −0.668054 | + | 0.485369i | ||||
\(729\) | 0.545079 | − | 0.396023i | 0.0201881 | − | 0.0146675i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.05022 | − | 5.84882i | −0.297748 | − | 0.216327i | ||||
\(732\) | −2.50786 | −0.0926931 | ||||||||
\(733\) | 13.9325 | + | 10.1226i | 0.514609 | + | 0.373886i | 0.814569 | − | 0.580066i | \(-0.196973\pi\) |
−0.299960 | + | 0.953952i | \(0.596973\pi\) | |||||||
\(734\) | −23.5264 | + | 72.4069i | −0.868377 | + | 2.67259i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.6732 | − | 39.0041i | −0.467141 | − | 1.43771i | ||||
\(737\) | −4.55891 | + | 14.0309i | −0.167929 | + | 0.516834i | ||||
\(738\) | −20.1595 | + | 62.0447i | −0.742083 | + | 2.28390i | ||||
\(739\) | −8.49421 | − | 26.1425i | −0.312464 | − | 0.961667i | −0.976786 | − | 0.214219i | \(-0.931279\pi\) |
0.664321 | − | 0.747447i | \(-0.268721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.51269 | + | 4.65559i | −0.0555701 | + | 0.171027i | ||||
\(742\) | 2.73529 | + | 1.98730i | 0.100415 | + | 0.0729561i | ||||
\(743\) | −48.4801 | −1.77856 | −0.889280 | − | 0.457362i | \(-0.848794\pi\) | ||||
−0.889280 | + | 0.457362i | \(0.848794\pi\) | |||||||
\(744\) | −36.3392 | − | 26.4020i | −1.33226 | − | 0.967944i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.3674 | + | 22.0632i | −1.11183 | + | 0.807792i | ||||
\(747\) | −4.65675 | + | 3.38332i | −0.170381 | + | 0.123789i | ||||
\(748\) | −8.69114 | − | 26.7486i | −0.317780 | − | 0.978025i | ||||
\(749\) | −20.7691 | −0.758888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.29720 | 0.120316 | 0.0601582 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601582 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(752\) | −27.6776 | − | 85.1830i | −1.00930 | − | 3.10630i | ||||
\(753\) | −10.9491 | + | 7.95502i | −0.399009 | + | 0.289897i | ||||
\(754\) | 13.1423 | − | 9.54847i | 0.478616 | − | 0.347735i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −34.7055 | − | 25.2150i | −1.26223 | − | 0.917061i | ||||
\(757\) | 35.7934 | 1.30093 | 0.650466 | − | 0.759535i | \(-0.274574\pi\) | ||||
0.650466 | + | 0.759535i | \(0.274574\pi\) | |||||||
\(758\) | 47.4120 | + | 34.4468i | 1.72208 | + | 1.25117i | ||||
\(759\) | −0.865609 | + | 2.66407i | −0.0314196 | + | 0.0966996i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.205221 | − | 0.631606i | −0.00743927 | − | 0.0228957i | 0.947268 | − | 0.320442i | \(-0.103832\pi\) |
−0.954707 | + | 0.297547i | \(0.903832\pi\) | |||||||
\(762\) | 2.61107 | − | 8.03606i | 0.0945892 | − | 0.291116i | ||||
\(763\) | 0.753950 | − | 2.32042i | 0.0272948 | − | 0.0840049i | ||||
\(764\) | 33.5769 | + | 103.339i | 1.21477 | + | 3.73867i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.1419 | + | 37.3688i | −0.438703 | + | 1.35019i | ||||
\(767\) | −12.1079 | − | 8.79694i | −0.437193 | − | 0.317639i | ||||
\(768\) | −2.43848 | −0.0879911 | ||||||||
\(769\) | −20.7990 | − | 15.1114i | −0.750032 | − | 0.544930i | 0.145805 | − | 0.989313i | \(-0.453423\pi\) |
−0.895837 | + | 0.444383i | \(0.853423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.61667 | + | 2.62767i | −0.130251 | + | 0.0946331i | ||||
\(772\) | −32.9960 | + | 23.9730i | −1.18755 | + | 0.862806i | ||||
\(773\) | 11.9113 | + | 36.6593i | 0.428420 | + | 1.31854i | 0.899681 | + | 0.436548i | \(0.143799\pi\) |
−0.471260 | + | 0.881994i | \(0.656201\pi\) | |||||||
\(774\) | −15.7261 | −0.565264 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 47.9453 | 1.72114 | ||||||||
\(777\) | −4.14181 | − | 12.7472i | −0.148586 | − | 0.457302i | ||||
\(778\) | −30.7382 | + | 22.3326i | −1.10202 | + | 0.800662i | ||||
\(779\) | −39.9287 | + | 29.0099i | −1.43060 | + | 1.03939i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.22125 | + | 2.34038i | 0.115265 | + | 0.0837452i | ||||
\(782\) | 29.8034 | 1.06577 | ||||||||
\(783\) | 15.3855 | + | 11.1782i | 0.549832 | + | 0.399476i | ||||
\(784\) | −10.3434 | + | 31.8338i | −0.369408 | + | 1.13692i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.11866 | + | 6.52055i | 0.0755699 | + | 0.232580i | ||||
\(787\) | 11.1961 | − | 34.4579i | 0.399096 | − | 1.22829i | −0.526629 | − | 0.850095i | \(-0.676544\pi\) |
0.925725 | − | 0.378197i | \(-0.123456\pi\) | |||||||
\(788\) | 34.2165 | − | 105.308i | 1.21891 | − | 3.75143i | ||||
\(789\) | 5.55396 | + | 17.0933i | 0.197726 | + | 0.608539i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.82874 | + | 8.70596i | −0.100578 | + | 0.309548i | ||||
\(792\) | −21.8646 | − | 15.8856i | −0.776924 | − | 0.564468i | ||||
\(793\) | −0.854482 | −0.0303436 | ||||||||
\(794\) | 11.8381 | + | 8.60085i | 0.420117 | + | 0.305233i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −38.5639 | + | 28.0183i | −1.36686 | + | 0.993084i | ||||
\(797\) | 27.3671 | − | 19.8833i | 0.969392 | − | 0.704304i | 0.0140788 | − | 0.999901i | \(-0.495518\pi\) |
0.955313 | + | 0.295597i | \(0.0955184\pi\) | |||||||
\(798\) | −6.23847 | − | 19.2000i | −0.220840 | − | 0.679674i | ||||
\(799\) | 30.9478 | 1.09485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7878 | −0.628501 | ||||||||
\(802\) | −22.0318 | − | 67.8070i | −0.777971 | − | 2.39435i | ||||
\(803\) | 14.7724 | − | 10.7328i | 0.521305 | − | 0.378751i | ||||
\(804\) | −34.2755 | + | 24.9026i | −1.20880 | + | 0.878248i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.3638 | − | 14.7952i | −0.717284 | − | 0.521138i | ||||
\(807\) | −10.4344 | −0.367308 | ||||||||
\(808\) | 77.2780 | + | 56.1458i | 2.71863 | + | 1.97520i | ||||
\(809\) | −0.452429 | + | 1.39243i | −0.0159066 | + | 0.0489554i | −0.958695 | − | 0.284437i | \(-0.908193\pi\) |
0.942788 | + | 0.333392i | \(0.108193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5734 | − | 38.6971i | −0.441513 | − | 1.35884i | −0.886263 | − | 0.463182i | \(-0.846707\pi\) |
0.444750 | − | 0.895655i | \(-0.353293\pi\) | |||||||
\(812\) | −14.8728 | + | 45.7737i | −0.521932 | + | 1.60634i | ||||
\(813\) | −1.75899 | + | 5.41362i | −0.0616906 | + | 0.189864i | ||||
\(814\) | −9.60336 | − | 29.5561i | −0.336598 | − | 1.03594i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.3406 | − | 34.9027i | 0.396999 | − | 1.22184i | ||||
\(817\) | −9.62518 | − | 6.99311i | −0.336743 | − | 0.244658i | ||||
\(818\) | −13.6819 | −0.478375 | ||||||||
\(819\) | −5.28434 | − | 3.83930i | −0.184650 | − | 0.134156i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.2327 | − | 17.6061i | 0.845729 | − | 0.614458i | −0.0782364 | − | 0.996935i | \(-0.524929\pi\) |
0.923965 | + | 0.382477i | \(0.124929\pi\) | |||||||
\(822\) | −13.6428 | + | 9.91204i | −0.475846 | + | 0.345722i | ||||
\(823\) | −5.85182 | − | 18.0100i | −0.203981 | − | 0.627790i | −0.999754 | − | 0.0221943i | \(-0.992935\pi\) |
0.795772 | − | 0.605596i | \(-0.207065\pi\) | |||||||
\(824\) | 95.9636 | 3.34305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 61.7221 | 2.14759 | ||||||||
\(827\) | −6.26188 | − | 19.2721i | −0.217747 | − | 0.670156i | −0.998947 | − | 0.0458757i | \(-0.985392\pi\) |
0.781200 | − | 0.624281i | \(-0.214608\pi\) | |||||||
\(828\) | 27.3755 | − | 19.8895i | 0.951365 | − | 0.691207i | ||||
\(829\) | −13.4621 | + | 9.78077i | −0.467557 | + | 0.339700i | −0.796488 | − | 0.604654i | \(-0.793311\pi\) |
0.328931 | + | 0.944354i | \(0.393311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.74283 | − | 1.26624i | −0.0604582 | − | 0.0439254i | ||||
\(832\) | −21.4932 | −0.745142 | ||||||||
\(833\) | −9.35670 | − | 6.79804i | −0.324190 | − | 0.235538i | ||||
\(834\) | −2.14641 | + | 6.60599i | −0.0743243 | + | 0.228747i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.3915 | − | 31.9818i | −0.359398 | − | 1.10611i | ||||
\(837\) | 9.10588 | − | 28.0250i | 0.314745 | − | 0.968686i | ||||
\(838\) | −26.2309 | + | 80.7304i | −0.906131 | + | 2.78878i | ||||
\(839\) | −2.20535 | − | 6.78737i | −0.0761371 | − | 0.234326i | 0.905744 | − | 0.423826i | \(-0.139313\pi\) |
−0.981881 | + | 0.189500i | \(0.939313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.36816 | + | 7.28846i | −0.0816608 | + | 0.251326i | ||||
\(842\) | 6.64156 | + | 4.82537i | 0.228883 | + | 0.166293i | ||||
\(843\) | 17.4293 | 0.600295 | ||||||||
\(844\) | 28.4056 | + | 20.6379i | 0.977762 | + | 0.710385i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 39.5693 | − | 28.7488i | 1.36042 | − | 0.988404i | ||||
\(847\) | 15.1682 | − | 11.0204i | 0.521186 | − | 0.378664i | ||||
\(848\) | 2.27083 | + | 6.98891i | 0.0779807 | + | 0.240000i | ||||
\(849\) | −19.0717 | −0.654539 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.6581 | 0.810988 | ||||||||
\(852\) | 3.53344 | + | 10.8748i | 0.121054 | + | 0.372565i | ||||
\(853\) | 25.7472 | − | 18.7064i | 0.881566 | − | 0.640495i | −0.0520993 | − | 0.998642i | \(-0.516591\pi\) |
0.933665 | + | 0.358147i | \(0.116591\pi\) | |||||||
\(854\) | 2.85094 | − | 2.07133i | 0.0975573 | − | 0.0708795i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −68.0260 | − | 49.4238i | −2.32508 | − | 1.68927i | ||||
\(857\) | −43.1535 | −1.47409 | −0.737047 | − | 0.675842i | \(-0.763780\pi\) | ||||
−0.737047 | + | 0.675842i | \(0.763780\pi\) | |||||||
\(858\) | 2.91277 | + | 2.11625i | 0.0994405 | + | 0.0722477i | ||||
\(859\) | 9.54599 | − | 29.3795i | 0.325705 | − | 1.00242i | −0.645416 | − | 0.763831i | \(-0.723316\pi\) |
0.971121 | − | 0.238586i | \(-0.0766839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.83791 | + | 14.8896i | 0.164876 | + | 0.507435i | ||||
\(862\) | −19.2271 | + | 59.1750i | −0.654879 | + | 2.01551i | ||||
\(863\) | −11.8017 | + | 36.3218i | −0.401734 | + | 1.23641i | 0.521858 | + | 0.853032i | \(0.325239\pi\) |
−0.923592 | + | 0.383377i | \(0.874761\pi\) | |||||||
\(864\) | −19.0693 | − | 58.6893i | −0.648751 | − | 1.99665i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.76464 | − | 20.8194i | 0.229872 | − | 0.707472i | ||||
\(867\) | −0.181174 | − | 0.131631i | −0.00615299 | − | 0.00447041i | ||||
\(868\) | 74.5754 | 2.53125 | ||||||||
\(869\) | −2.06141 | − | 1.49770i | −0.0699284 | − | 0.0508059i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6784 | + | 8.48487i | −0.395708 | + | 0.287499i | ||||
\(872\) | 7.99128 | − | 5.80601i | 0.270619 | − | 0.196616i | ||||
\(873\) | 4.34352 | + | 13.3680i | 0.147006 | + | 0.452438i | ||||
\(874\) | 35.6343 | 1.20535 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 52.4373 | 1.77169 | ||||||||
\(877\) | 9.80348 | + | 30.1720i | 0.331040 | + | 1.01884i | 0.968640 | + | 0.248469i | \(0.0799273\pi\) |
−0.637600 | + | 0.770368i | \(0.720073\pi\) | |||||||
\(878\) | −52.4171 | + | 38.0832i | −1.76899 | + | 1.28525i | ||||
\(879\) | 17.7327 | − | 12.8836i | 0.598110 | − | 0.434553i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0994 | + | 22.5950i | 1.04776 | + | 0.761245i | 0.971786 | − | 0.235864i | \(-0.0757921\pi\) |
0.0759780 | + | 0.997109i | \(0.475792\pi\) | |||||||
\(882\) | −18.2783 | −0.615464 | ||||||||
\(883\) | −9.82933 | − | 7.14142i | −0.330783 | − | 0.240328i | 0.409980 | − | 0.912095i | \(-0.365536\pi\) |
−0.740763 | + | 0.671767i | \(0.765536\pi\) | |||||||
\(884\) | 8.50404 | − | 26.1727i | 0.286022 | − | 0.880284i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0519949 | + | 0.160024i | 0.00174680 | + | 0.00537611i | ||||
\(887\) | −7.49154 | + | 23.0566i | −0.251541 | + | 0.774165i | 0.742950 | + | 0.669347i | \(0.233426\pi\) |
−0.994491 | + | 0.104818i | \(0.966574\pi\) | |||||||
\(888\) | 16.7683 | − | 51.6074i | 0.562706 | − | 1.73183i | ||||
\(889\) | 2.63581 | + | 8.11219i | 0.0884022 | + | 0.272074i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.72796 | − | 5.31812i | 0.0578889 | − | 0.178164i | ||||
\(892\) | 35.1484 | + | 25.5368i | 1.17686 | + | 0.855036i | ||||
\(893\) | 37.0025 | 1.23824 | ||||||||
\(894\) | −16.3010 | − | 11.8434i | −0.545188 | − | 0.396102i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.1852 | − | 16.1185i | 0.741157 | − | 0.538482i | ||||
\(897\) | −2.21741 | + | 1.61104i | −0.0740370 | + | 0.0537911i | ||||
\(898\) | 9.52919 | + | 29.3278i | 0.317993 | + | 0.978683i | ||||
\(899\) | −33.0604 | −1.10263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.53913 | −0.0845908 | ||||||||
\(902\) | 11.2174 | + | 34.5235i | 0.373498 | + | 1.14951i | ||||
\(903\) | −3.05321 | + | 2.21829i | −0.101604 | + | 0.0738200i | ||||
\(904\) | −29.9824 | + | 21.7835i | −0.997200 | + | 0.724508i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.4350 | + | 25.0185i | 1.14403 | + | 0.831185i | ||||
\(907\) | −32.5046 | −1.07930 | −0.539649 | − | 0.841890i | \(-0.681443\pi\) | ||||
−0.539649 | + | 0.841890i | \(0.681443\pi\) | |||||||
\(908\) | 86.6168 | + | 62.9308i | 2.87448 | + | 2.08843i | ||||
\(909\) | −8.65356 | + | 26.6329i | −0.287020 | + | 0.883358i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6665 | + | 42.0612i | 0.452792 | + | 1.39355i | 0.873708 | + | 0.486451i | \(0.161709\pi\) |
−0.420916 | + | 0.907100i | \(0.638291\pi\) | |||||||
\(912\) | 13.5593 | − | 41.7311i | 0.448992 | − | 1.38186i | ||||
\(913\) | −0.989732 | + | 3.04608i | −0.0327554 | + | 0.100811i | ||||
\(914\) | −34.0916 | − | 104.923i | −1.12765 | − | 3.47055i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.9270 | − | 144.426i | 1.55051 | − | 4.77198i | ||||
\(917\) | −5.59926 | − | 4.06810i | −0.184904 | − | 0.134340i | ||||
\(918\) | 44.8450 | 1.48011 | ||||||||
\(919\) | 32.1937 | + | 23.3901i | 1.06197 | + | 0.771568i | 0.974452 | − | 0.224594i | \(-0.0721057\pi\) |
0.0875203 | + | 0.996163i | \(0.472106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.7095 | + | 10.6871i | −0.484695 | + | 0.352152i | ||||
\(922\) | 63.3244 | − | 46.0079i | 2.08548 | − | 1.51519i | ||||
\(923\) | 1.20392 | + | 3.70529i | 0.0396275 | + | 0.121961i | ||||
\(924\) | −10.6670 | −0.350920 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −81.4163 | −2.67551 | ||||||||
\(927\) | 8.69366 | + | 26.7563i | 0.285537 | + | 0.878794i | ||||
\(928\) | −56.0118 | + | 40.6949i | −1.83868 | + | 1.33588i | ||||
\(929\) | 5.37690 | − | 3.90655i | 0.176410 | − | 0.128170i | −0.496076 | − | 0.868279i | \(-0.665226\pi\) |
0.672487 | + | 0.740109i | \(0.265226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1873 | − | 8.12803i | −0.366648 | − | 0.266385i | ||||
\(932\) | 11.5900 | 0.379644 | ||||||||
\(933\) | −6.07254 | − | 4.41196i | −0.198806 | − | 0.144441i | ||||
\(934\) | 26.9418 | − | 82.9184i | 0.881563 | − | 2.71317i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.17174 | − | 25.1500i | −0.267102 | − | 0.822054i | ||||
\(937\) | 0.0709458 | − | 0.218349i | 0.00231770 | − | 0.00713314i | −0.949891 | − | 0.312581i | \(-0.898806\pi\) |
0.952209 | + | 0.305448i | \(0.0988063\pi\) | |||||||
\(938\) | 18.3966 | − | 56.6188i | 0.600669 | − | 1.84867i | ||||
\(939\) | −4.40487 | − | 13.5568i | −0.143748 | − | 0.442410i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.75990 | − | 26.9602i | 0.285565 | − | 0.878877i | −0.700664 | − | 0.713491i | \(-0.747113\pi\) |
0.986229 | − | 0.165386i | \(-0.0528871\pi\) | |||||||
\(942\) | 12.7794 | + | 9.28476i | 0.416375 | + | 0.302514i | ||||
\(943\) | −27.6342 | −0.899894 | ||||||||
\(944\) | 108.532 | + | 78.8528i | 3.53240 | + | 2.56644i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.07929 | + | 5.14341i | −0.230168 | + | 0.167227i | ||||
\(947\) | −38.8357 | + | 28.2158i | −1.26199 | + | 0.916891i | −0.998854 | − | 0.0478673i | \(-0.984758\pi\) |
−0.263138 | + | 0.964758i | \(0.584758\pi\) | |||||||
\(948\) | −2.26118 | − | 6.95921i | −0.0734399 | − | 0.226025i | ||||
\(949\) | 17.8666 | 0.579973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6464 | −0.637080 | ||||||||
\(952\) | 21.3241 | + | 65.6288i | 0.691117 | + | 2.12704i | ||||
\(953\) | 21.7533 | − | 15.8047i | 0.704657 | − | 0.511963i | −0.176789 | − | 0.984249i | \(-0.556571\pi\) |
0.881446 | + | 0.472286i | \(0.156571\pi\) | |||||||
\(954\) | −3.24650 | + | 2.35872i | −0.105109 | + | 0.0763663i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −63.6958 | − | 46.2777i | −2.06007 | − | 1.49673i | ||||
\(957\) | 4.72886 | 0.152862 | ||||||||
\(958\) | −26.5954 | − | 19.3227i | −0.859257 | − | 0.624287i | ||||
\(959\) | 5.26043 | − | 16.1900i | 0.169868 | − | 0.522801i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.25033 | + | 19.2365i | 0.201624 | + | 0.620534i | ||||
\(962\) | 9.39662 | − | 28.9198i | 0.302959 | − | 0.932412i | ||||
\(963\) | 7.61752 | − | 23.4443i | 0.245471 | − | 0.755482i | ||||
\(964\) | −7.63410 | − | 23.4953i | −0.245878 | − | 0.756734i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.49299 | − | 10.7503i | 0.112385 | − | 0.345886i | ||||
\(967\) | 3.05821 | + | 2.22192i | 0.0983456 | + | 0.0714522i | 0.635871 | − | 0.771795i | \(-0.280641\pi\) |
−0.537526 | + | 0.843247i | \(0.680641\pi\) | |||||||
\(968\) | 75.9059 | 2.43971 | ||||||||
\(969\) | 12.2658 | + | 8.91159i | 0.394033 | + | 0.286282i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.13176 | + | 6.63461i | −0.293052 | + | 0.212915i | −0.724590 | − | 0.689180i | \(-0.757971\pi\) |
0.431538 | + | 0.902095i | \(0.357971\pi\) | |||||||
\(972\) | 63.9757 | − | 46.4811i | 2.05202 | − | 1.49088i | ||||
\(973\) | −2.16675 | − | 6.66857i | −0.0694628 | − | 0.213784i | ||||
\(974\) | 94.0648 | 3.01403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.65930 | 0.245168 | ||||||||
\(977\) | 6.26679 | + | 19.2872i | 0.200492 | + | 0.617052i | 0.999868 | + | 0.0162210i | \(0.00516354\pi\) |
−0.799376 | + | 0.600831i | \(0.794836\pi\) | |||||||
\(978\) | −19.1132 | + | 13.8866i | −0.611174 | + | 0.444044i | ||||
\(979\) | −8.00738 | + | 5.81770i | −0.255917 | + | 0.185934i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.34277 | + | 1.70213i | 0.0747990 | + | 0.0543447i | ||||
\(982\) | −40.8162 | −1.30250 | ||||||||
\(983\) | 22.9055 | + | 16.6418i | 0.730570 | + | 0.530790i | 0.889744 | − | 0.456460i | \(-0.150883\pi\) |
−0.159173 | + | 0.987251i | \(0.550883\pi\) | |||||||
\(984\) | −19.5865 | + | 60.2810i | −0.624394 | + | 1.92169i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.5477 | − | 47.8509i | −0.495139 | − | 1.52388i | ||||
\(987\) | 3.62711 | − | 11.1631i | 0.115452 | − | 0.355325i | ||||
\(988\) | 10.1678 | − | 31.2933i | 0.323481 | − | 0.995571i | ||||
\(989\) | −2.05851 | − | 6.33544i | −0.0654568 | − | 0.201455i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.37346 | − | 22.6932i | 0.234226 | − | 0.720873i | −0.762997 | − | 0.646402i | \(-0.776273\pi\) |
0.997223 | − | 0.0744712i | \(-0.0237269\pi\) | |||||||
\(992\) | 86.7892 | + | 63.0560i | 2.75556 | + | 2.00203i | ||||
\(993\) | −0.984859 | −0.0312536 | ||||||||
\(994\) | −12.9987 | − | 9.44413i | −0.412295 | − | 0.299550i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.44117 | + | 5.40632i | −0.235782 | + | 0.171306i | ||||
\(997\) | −11.0609 | + | 8.03620i | −0.350301 | + | 0.254509i | −0.748996 | − | 0.662575i | \(-0.769464\pi\) |
0.398694 | + | 0.917084i | \(0.369464\pi\) | |||||||
\(998\) | 28.9701 | + | 89.1607i | 0.917031 | + | 2.82233i | ||||
\(999\) | 35.5982 | 1.12628 |
(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 | 625.2.d.q.126.1 | 16 | ||
5.2 | odd | 4 | 625.2.e.j.499.8 | 32 | |||
5.3 | odd | 4 | 625.2.e.j.499.1 | 32 | |||
5.4 | even | 2 | 625.2.d.m.126.4 | 16 | |||
25.2 | odd | 20 | 625.2.b.d.624.1 | 16 | |||
25.3 | odd | 20 | 625.2.e.j.124.8 | 32 | |||
25.4 | even | 10 | 625.2.d.m.501.4 | 16 | |||
25.6 | even | 5 | 625.2.d.p.376.4 | 16 | |||
25.8 | odd | 20 | 625.2.e.k.249.8 | 32 | |||
25.9 | even | 10 | 625.2.d.n.251.1 | 16 | |||
25.11 | even | 5 | 625.2.a.e.1.1 | ✓ | 8 | ||
25.12 | odd | 20 | 625.2.e.k.374.8 | 32 | |||
25.13 | odd | 20 | 625.2.e.k.374.1 | 32 | |||
25.14 | even | 10 | 625.2.a.g.1.8 | yes | 8 | ||
25.16 | even | 5 | 625.2.d.p.251.4 | 16 | |||
25.17 | odd | 20 | 625.2.e.k.249.1 | 32 | |||
25.19 | even | 10 | 625.2.d.n.376.1 | 16 | |||
25.21 | even | 5 | inner | 625.2.d.q.501.1 | 16 | ||
25.22 | odd | 20 | 625.2.e.j.124.1 | 32 | |||
25.23 | odd | 20 | 625.2.b.d.624.16 | 16 | |||
75.11 | odd | 10 | 5625.2.a.be.1.8 | 8 | |||
75.14 | odd | 10 | 5625.2.a.s.1.1 | 8 | |||
100.11 | odd | 10 | 10000.2.a.bn.1.5 | 8 | |||
100.39 | odd | 10 | 10000.2.a.be.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.1 | ✓ | 8 | 25.11 | even | 5 | ||
625.2.a.g.1.8 | yes | 8 | 25.14 | even | 10 | ||
625.2.b.d.624.1 | 16 | 25.2 | odd | 20 | |||
625.2.b.d.624.16 | 16 | 25.23 | odd | 20 | |||
625.2.d.m.126.4 | 16 | 5.4 | even | 2 | |||
625.2.d.m.501.4 | 16 | 25.4 | even | 10 | |||
625.2.d.n.251.1 | 16 | 25.9 | even | 10 | |||
625.2.d.n.376.1 | 16 | 25.19 | even | 10 | |||
625.2.d.p.251.4 | 16 | 25.16 | even | 5 | |||
625.2.d.p.376.4 | 16 | 25.6 | even | 5 | |||
625.2.d.q.126.1 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.q.501.1 | 16 | 25.21 | even | 5 | inner | ||
625.2.e.j.124.1 | 32 | 25.22 | odd | 20 | |||
625.2.e.j.124.8 | 32 | 25.3 | odd | 20 | |||
625.2.e.j.499.1 | 32 | 5.3 | odd | 4 | |||
625.2.e.j.499.8 | 32 | 5.2 | odd | 4 | |||
625.2.e.k.249.1 | 32 | 25.17 | odd | 20 | |||
625.2.e.k.249.8 | 32 | 25.8 | odd | 20 | |||
625.2.e.k.374.1 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.374.8 | 32 | 25.12 | odd | 20 | |||
5625.2.a.s.1.1 | 8 | 75.14 | odd | 10 | |||
5625.2.a.be.1.8 | 8 | 75.11 | odd | 10 | |||
10000.2.a.be.1.4 | 8 | 100.39 | odd | 10 | |||
10000.2.a.bn.1.5 | 8 | 100.11 | odd | 10 |