Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(-0.974642 + 1.34148i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.323 |
Dual form | 363.3.h.j.245.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.974642 | + | 1.34148i | −0.487321 | + | 0.670740i | −0.979891 | − | 0.199533i | \(-0.936057\pi\) |
0.492570 | + | 0.870273i | \(0.336057\pi\) | |||||||
\(3\) | −1.09751 | − | 2.79204i | −0.365836 | − | 0.930679i | ||||
\(4\) | 0.386428 | + | 1.18930i | 0.0966070 | + | 0.297326i | ||||
\(5\) | −0.410570 | − | 0.565101i | −0.0821140 | − | 0.113020i | 0.765984 | − | 0.642860i | \(-0.222252\pi\) |
−0.848098 | + | 0.529839i | \(0.822252\pi\) | |||||||
\(6\) | 4.81514 | + | 1.24895i | 0.802523 | + | 0.208158i | ||||
\(7\) | −0.806259 | − | 2.48141i | −0.115180 | − | 0.354487i | 0.876805 | − | 0.480847i | \(-0.159671\pi\) |
−0.991985 | + | 0.126360i | \(0.959671\pi\) | |||||||
\(8\) | −8.28007 | − | 2.69036i | −1.03501 | − | 0.336295i | ||||
\(9\) | −6.59095 | + | 6.12857i | −0.732327 | + | 0.680953i | ||||
\(10\) | 1.15823 | 0.115823 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.89647 | − | 2.38419i | 0.241372 | − | 0.198683i | ||||
\(13\) | 13.8479 | + | 10.0611i | 1.06522 | + | 0.773930i | 0.975048 | − | 0.221996i | \(-0.0712573\pi\) |
0.0901753 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(14\) | 4.11458 | + | 1.33691i | 0.293898 | + | 0.0954933i | ||||
\(15\) | −1.12718 | + | 1.76653i | −0.0751453 | + | 0.117769i | ||||
\(16\) | 7.63243 | − | 5.54529i | 0.477027 | − | 0.346580i | ||||
\(17\) | 9.47072 | + | 13.0353i | 0.557101 | + | 0.766784i | 0.990954 | − | 0.134200i | \(-0.0428464\pi\) |
−0.433853 | + | 0.900984i | \(0.642846\pi\) | |||||||
\(18\) | −1.79754 | − | 14.8148i | −0.0998636 | − | 0.823043i | ||||
\(19\) | 4.92151 | − | 15.1469i | 0.259027 | − | 0.797203i | −0.733983 | − | 0.679168i | \(-0.762341\pi\) |
0.993009 | − | 0.118035i | \(-0.0376594\pi\) | |||||||
\(20\) | 0.513421 | − | 0.706663i | 0.0256710 | − | 0.0353331i | ||||
\(21\) | −6.04332 | + | 4.97448i | −0.287777 | + | 0.236880i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 23.1295i | − | 1.00563i | −0.864395 | − | 0.502814i | \(-0.832298\pi\) | ||
0.864395 | − | 0.502814i | \(-0.167702\pi\) | |||||||
\(24\) | 1.57587 | + | 26.0710i | 0.0656614 | + | 1.08629i | ||||
\(25\) | 7.57465 | − | 23.3124i | 0.302986 | − | 0.932495i | ||||
\(26\) | −26.9935 | + | 8.77071i | −1.03821 | + | 0.337335i | ||||
\(27\) | 24.3448 | + | 11.6760i | 0.901661 | + | 0.432444i | ||||
\(28\) | 2.63959 | − | 1.91777i | 0.0942710 | − | 0.0684919i | ||||
\(29\) | 5.10329 | − | 1.65816i | 0.175976 | − | 0.0571779i | −0.219704 | − | 0.975567i | \(-0.570509\pi\) |
0.395679 | + | 0.918389i | \(0.370509\pi\) | |||||||
\(30\) | −1.27117 | − | 3.23382i | −0.0423723 | − | 0.107794i | ||||
\(31\) | 3.28671 | + | 2.38793i | 0.106023 | + | 0.0770301i | 0.639533 | − | 0.768763i | \(-0.279128\pi\) |
−0.533511 | + | 0.845793i | \(0.679128\pi\) | |||||||
\(32\) | − | 19.1813i | − | 0.599415i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −26.7172 | −0.785799 | ||||||||
\(35\) | −1.07122 | + | 1.47441i | −0.0306064 | + | 0.0421260i | ||||
\(36\) | −9.83565 | − | 5.47038i | −0.273213 | − | 0.151955i | ||||
\(37\) | 19.6322 | + | 60.4217i | 0.530600 | + | 1.63302i | 0.752968 | + | 0.658057i | \(0.228621\pi\) |
−0.222368 | + | 0.974963i | \(0.571379\pi\) | |||||||
\(38\) | 15.5225 | + | 21.3649i | 0.408486 | + | 0.562233i | ||||
\(39\) | 12.8927 | − | 49.7060i | 0.330583 | − | 1.27451i | ||||
\(40\) | 1.87922 | + | 5.78366i | 0.0469806 | + | 0.144591i | ||||
\(41\) | 64.1371 | + | 20.8394i | 1.56432 | + | 0.508278i | 0.957958 | − | 0.286910i | \(-0.0926281\pi\) |
0.606362 | + | 0.795188i | \(0.292628\pi\) | |||||||
\(42\) | −0.783092 | − | 12.9553i | −0.0186450 | − | 0.308460i | ||||
\(43\) | 22.6622 | 0.527028 | 0.263514 | − | 0.964656i | \(-0.415118\pi\) | ||||
0.263514 | + | 0.964656i | \(0.415118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.16931 | + | 1.20834i | 0.137096 | + | 0.0268521i | ||||
\(46\) | 31.0277 | + | 22.5429i | 0.674515 | + | 0.490064i | ||||
\(47\) | 70.2078 | + | 22.8119i | 1.49378 | + | 0.485360i | 0.938198 | − | 0.346100i | \(-0.112494\pi\) |
0.555585 | + | 0.831460i | \(0.312494\pi\) | |||||||
\(48\) | −23.8593 | − | 15.2240i | −0.497069 | − | 0.317167i | ||||
\(49\) | 34.1345 | − | 24.8002i | 0.696622 | − | 0.506126i | ||||
\(50\) | 23.8905 | + | 32.8825i | 0.477810 | + | 0.657649i | ||||
\(51\) | 26.0009 | − | 40.7490i | 0.509822 | − | 0.799000i | ||||
\(52\) | −6.61446 | + | 20.3572i | −0.127201 | + | 0.391485i | ||||
\(53\) | 25.1873 | − | 34.6673i | 0.475232 | − | 0.654100i | −0.502348 | − | 0.864666i | \(-0.667530\pi\) |
0.977580 | + | 0.210565i | \(0.0675304\pi\) | |||||||
\(54\) | −39.3906 | + | 21.2782i | −0.729456 | + | 0.394040i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22.7154i | 0.405632i | ||||||||
\(57\) | −47.6920 | + | 2.88277i | −0.836702 | + | 0.0505749i | ||||
\(58\) | −2.74949 | + | 8.46207i | −0.0474051 | + | 0.145898i | ||||
\(59\) | 27.3316 | − | 8.88056i | 0.463247 | − | 0.150518i | −0.0680891 | − | 0.997679i | \(-0.521690\pi\) |
0.531336 | + | 0.847161i | \(0.321690\pi\) | |||||||
\(60\) | −2.53651 | − | 0.657920i | −0.0422752 | − | 0.0109653i | ||||
\(61\) | −37.4585 | + | 27.2152i | −0.614074 | + | 0.446151i | −0.850847 | − | 0.525414i | \(-0.823910\pi\) |
0.236772 | + | 0.971565i | \(0.423910\pi\) | |||||||
\(62\) | −6.40673 | + | 2.08167i | −0.103334 | + | 0.0335753i | ||||
\(63\) | 20.5215 | + | 11.4136i | 0.325739 | + | 0.181169i | ||||
\(64\) | 56.2610 | + | 40.8760i | 0.879079 | + | 0.638688i | ||||
\(65\) | − | 11.9562i | − | 0.183942i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −77.2821 | −1.15346 | −0.576732 | − | 0.816933i | \(-0.695672\pi\) | ||||
−0.576732 | + | 0.816933i | \(0.695672\pi\) | |||||||
\(68\) | −11.8432 | + | 16.3008i | −0.174165 | + | 0.239717i | ||||
\(69\) | −64.5783 | + | 25.3848i | −0.935917 | + | 0.367896i | ||||
\(70\) | −0.933834 | − | 2.87405i | −0.0133405 | − | 0.0410578i | ||||
\(71\) | −24.2537 | − | 33.3824i | −0.341601 | − | 0.470174i | 0.603307 | − | 0.797509i | \(-0.293849\pi\) |
−0.944908 | + | 0.327335i | \(0.893849\pi\) | |||||||
\(72\) | 71.0615 | − | 33.0130i | 0.986966 | − | 0.458514i | ||||
\(73\) | 17.5438 | + | 53.9942i | 0.240326 | + | 0.739647i | 0.996370 | + | 0.0851266i | \(0.0271295\pi\) |
−0.756044 | + | 0.654521i | \(0.772871\pi\) | |||||||
\(74\) | −100.189 | − | 32.5533i | −1.35390 | − | 0.439910i | ||||
\(75\) | −73.4023 | + | 4.43685i | −0.978697 | + | 0.0591579i | ||||
\(76\) | 19.9160 | 0.262053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 54.1137 | + | 65.7409i | 0.693766 | + | 0.842831i | ||||
\(79\) | −41.1994 | − | 29.9331i | −0.521512 | − | 0.378901i | 0.295661 | − | 0.955293i | \(-0.404460\pi\) |
−0.817173 | + | 0.576392i | \(0.804460\pi\) | |||||||
\(80\) | −6.26730 | − | 2.03637i | −0.0783412 | − | 0.0254546i | ||||
\(81\) | 5.88115 | − | 80.7862i | 0.0726068 | − | 0.997361i | ||||
\(82\) | −90.4664 | + | 65.7277i | −1.10325 | + | 0.801557i | ||||
\(83\) | −34.8026 | − | 47.9017i | −0.419309 | − | 0.577129i | 0.546149 | − | 0.837688i | \(-0.316093\pi\) |
−0.965458 | + | 0.260559i | \(0.916093\pi\) | |||||||
\(84\) | −8.25147 | − | 5.26505i | −0.0982317 | − | 0.0626792i | ||||
\(85\) | 3.47788 | − | 10.7038i | 0.0409163 | − | 0.125927i | ||||
\(86\) | −22.0875 | + | 30.4009i | −0.256832 | + | 0.353499i | ||||
\(87\) | −10.2306 | − | 12.4287i | −0.117593 | − | 0.142859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 38.1909i | 0.429112i | 0.976712 | + | 0.214556i | \(0.0688304\pi\) | ||||
−0.976712 | + | 0.214556i | \(0.931170\pi\) | |||||||
\(90\) | −7.63383 | + | 7.09830i | −0.0848204 | + | 0.0788700i | ||||
\(91\) | 13.8007 | − | 42.4742i | 0.151656 | − | 0.466749i | ||||
\(92\) | 27.5079 | − | 8.93786i | 0.298999 | − | 0.0971507i | ||||
\(93\) | 3.06001 | − | 11.7974i | 0.0329033 | − | 0.126854i | ||||
\(94\) | −99.0291 | + | 71.9489i | −1.05350 | + | 0.765414i | ||||
\(95\) | −10.5801 | + | 3.43769i | −0.111370 | + | 0.0361862i | ||||
\(96\) | −53.5549 | + | 21.0516i | −0.557863 | + | 0.219288i | ||||
\(97\) | −13.1808 | − | 9.57644i | −0.135885 | − | 0.0987262i | 0.517766 | − | 0.855522i | \(-0.326764\pi\) |
−0.653651 | + | 0.756796i | \(0.726764\pi\) | |||||||
\(98\) | 69.9620i | 0.713898i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 30.6525 | 0.306525 | ||||||||
\(101\) | 61.2440 | − | 84.2951i | 0.606376 | − | 0.834605i | −0.389897 | − | 0.920858i | \(-0.627490\pi\) |
0.996273 | + | 0.0862537i | \(0.0274895\pi\) | |||||||
\(102\) | 29.3224 | + | 74.5954i | 0.287474 | + | 0.731327i | ||||
\(103\) | 16.8125 | + | 51.7437i | 0.163229 | + | 0.502366i | 0.998901 | − | 0.0468618i | \(-0.0149220\pi\) |
−0.835673 | + | 0.549227i | \(0.814922\pi\) | |||||||
\(104\) | −87.5936 | − | 120.562i | −0.842246 | − | 1.15925i | ||||
\(105\) | 5.29229 | + | 1.37271i | 0.0504027 | + | 0.0130735i | ||||
\(106\) | 21.9569 | + | 67.5764i | 0.207141 | + | 0.637514i | ||||
\(107\) | 27.0164 | + | 8.77818i | 0.252490 | + | 0.0820390i | 0.432527 | − | 0.901621i | \(-0.357622\pi\) |
−0.180037 | + | 0.983660i | \(0.557622\pi\) | |||||||
\(108\) | −4.47878 | + | 33.4653i | −0.0414702 | + | 0.309864i | ||||
\(109\) | 41.2540 | 0.378477 | 0.189238 | − | 0.981931i | \(-0.439398\pi\) | ||||
0.189238 | + | 0.981931i | \(0.439398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 147.153 | − | 121.127i | 1.32570 | − | 1.09124i | ||||
\(112\) | −19.9139 | − | 14.4683i | −0.177802 | − | 0.129181i | ||||
\(113\) | −138.072 | − | 44.8625i | −1.22188 | − | 0.397013i | −0.374114 | − | 0.927383i | \(-0.622053\pi\) |
−0.847766 | + | 0.530370i | \(0.822053\pi\) | |||||||
\(114\) | 42.6154 | − | 66.7875i | 0.373820 | − | 0.585855i | ||||
\(115\) | −13.0705 | + | 9.49626i | −0.113656 | + | 0.0825762i | ||||
\(116\) | 3.94411 | + | 5.42860i | 0.0340009 | + | 0.0467983i | ||||
\(117\) | −152.931 | + | 18.5558i | −1.30710 | + | 0.158596i | ||||
\(118\) | −14.7254 | + | 45.3201i | −0.124791 | + | 0.384069i | ||||
\(119\) | 24.7101 | − | 34.0106i | 0.207648 | − | 0.285803i | ||||
\(120\) | 14.0857 | − | 11.5945i | 0.117381 | − | 0.0966207i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 76.7749i | − | 0.629303i | ||||||
\(123\) | −12.2067 | − | 201.945i | −0.0992412 | − | 1.64183i | ||||
\(124\) | −1.56990 | + | 4.83165i | −0.0126605 | + | 0.0389650i | ||||
\(125\) | −32.8917 | + | 10.6872i | −0.263134 | + | 0.0854973i | ||||
\(126\) | −35.3123 | + | 16.4050i | −0.280256 | + | 0.130198i | ||||
\(127\) | −147.873 | + | 107.436i | −1.16436 | + | 0.845955i | −0.990323 | − | 0.138785i | \(-0.955680\pi\) |
−0.174034 | + | 0.984740i | \(0.555680\pi\) | |||||||
\(128\) | −36.6987 | + | 11.9241i | −0.286709 | + | 0.0931574i | ||||
\(129\) | −24.8720 | − | 63.2737i | −0.192806 | − | 0.490494i | ||||
\(130\) | 16.0391 | + | 11.6531i | 0.123377 | + | 0.0896389i | ||||
\(131\) | − | 84.5109i | − | 0.645121i | −0.946549 | − | 0.322561i | \(-0.895456\pi\) | ||
0.946549 | − | 0.322561i | \(-0.104544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −41.5536 | −0.312433 | ||||||||
\(134\) | 75.3223 | − | 103.672i | 0.562107 | − | 0.773674i | ||||
\(135\) | −3.39714 | − | 18.5511i | −0.0251640 | − | 0.137416i | ||||
\(136\) | −43.3485 | − | 133.413i | −0.318739 | − | 0.980978i | ||||
\(137\) | 120.127 | + | 165.341i | 0.876841 | + | 1.20687i | 0.977286 | + | 0.211925i | \(0.0679733\pi\) |
−0.100445 | + | 0.994943i | \(0.532027\pi\) | |||||||
\(138\) | 28.8875 | − | 111.372i | 0.209330 | − | 0.807040i | ||||
\(139\) | 15.5254 | + | 47.7824i | 0.111694 | + | 0.343758i | 0.991243 | − | 0.132050i | \(-0.0421558\pi\) |
−0.879549 | + | 0.475808i | \(0.842156\pi\) | |||||||
\(140\) | −2.16747 | − | 0.704254i | −0.0154819 | − | 0.00503039i | ||||
\(141\) | −13.3620 | − | 221.059i | −0.0947663 | − | 1.56779i | ||||
\(142\) | 68.4204 | 0.481834 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −16.3203 | + | 83.3246i | −0.113335 | + | 0.578643i | ||||
\(145\) | −3.03229 | − | 2.20308i | −0.0209123 | − | 0.0151937i | ||||
\(146\) | −89.5311 | − | 29.0904i | −0.613227 | − | 0.199249i | ||||
\(147\) | −106.706 | − | 68.0864i | −0.725890 | − | 0.463172i | ||||
\(148\) | −64.2733 | + | 46.6973i | −0.434279 | + | 0.315522i | ||||
\(149\) | −92.5187 | − | 127.341i | −0.620931 | − | 0.854638i | 0.376490 | − | 0.926421i | \(-0.377131\pi\) |
−0.997420 | + | 0.0717830i | \(0.977131\pi\) | |||||||
\(150\) | 65.5890 | − | 102.792i | 0.437260 | − | 0.685280i | ||||
\(151\) | 52.9598 | − | 162.993i | 0.350727 | − | 1.07943i | −0.607719 | − | 0.794152i | \(-0.707915\pi\) |
0.958446 | − | 0.285274i | \(-0.0920847\pi\) | |||||||
\(152\) | −81.5009 | + | 112.176i | −0.536190 | + | 0.738002i | ||||
\(153\) | −142.309 | − | 27.8731i | −0.930124 | − | 0.182177i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.83774i | − | 0.0183080i | ||||||
\(156\) | 64.0976 | − | 3.87442i | 0.410882 | − | 0.0248360i | ||||
\(157\) | −20.1905 | + | 62.1401i | −0.128602 | + | 0.395797i | −0.994540 | − | 0.104355i | \(-0.966722\pi\) |
0.865938 | + | 0.500151i | \(0.166722\pi\) | |||||||
\(158\) | 80.3094 | − | 26.0941i | 0.508287 | − | 0.165153i | ||||
\(159\) | −124.436 | − | 32.2761i | −0.782615 | − | 0.202995i | ||||
\(160\) | −10.8394 | + | 7.87526i | −0.0677461 | + | 0.0492204i | ||||
\(161\) | −57.3937 | + | 18.6483i | −0.356483 | + | 0.115828i | ||||
\(162\) | 102.641 | + | 86.6271i | 0.633587 | + | 0.534735i | ||||
\(163\) | 12.4900 | + | 9.07449i | 0.0766256 | + | 0.0556717i | 0.625439 | − | 0.780273i | \(-0.284920\pi\) |
−0.548813 | + | 0.835945i | \(0.684920\pi\) | |||||||
\(164\) | 84.3314i | 0.514216i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 98.1792 | 0.591441 | ||||||||
\(167\) | −90.5798 | + | 124.672i | −0.542394 | + | 0.746542i | −0.988956 | − | 0.148211i | \(-0.952648\pi\) |
0.446561 | + | 0.894753i | \(0.352648\pi\) | |||||||
\(168\) | 63.4222 | − | 24.9303i | 0.377513 | − | 0.148395i | ||||
\(169\) | 38.3149 | + | 117.921i | 0.226715 | + | 0.697758i | ||||
\(170\) | 10.9693 | + | 15.0979i | 0.0645251 | + | 0.0888112i | ||||
\(171\) | 60.3912 | + | 129.994i | 0.353165 | + | 0.760199i | ||||
\(172\) | 8.75731 | + | 26.9522i | 0.0509146 | + | 0.156699i | ||||
\(173\) | 23.8744 | + | 7.75725i | 0.138002 | + | 0.0448396i | 0.377204 | − | 0.926130i | \(-0.376886\pi\) |
−0.239202 | + | 0.970970i | \(0.576886\pi\) | |||||||
\(174\) | 26.6440 | − | 1.61051i | 0.153127 | − | 0.00925582i | ||||
\(175\) | −63.9548 | −0.365456 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −54.7915 | − | 66.5642i | −0.309556 | − | 0.376069i | ||||
\(178\) | −51.2323 | − | 37.2225i | −0.287822 | − | 0.209115i | ||||
\(179\) | 58.7800 | + | 19.0988i | 0.328380 | + | 0.106697i | 0.468567 | − | 0.883428i | \(-0.344770\pi\) |
−0.140187 | + | 0.990125i | \(0.544770\pi\) | |||||||
\(180\) | 0.946908 | + | 7.80411i | 0.00526060 | + | 0.0433562i | ||||
\(181\) | 120.062 | − | 87.2301i | 0.663325 | − | 0.481934i | −0.204459 | − | 0.978875i | \(-0.565544\pi\) |
0.867784 | + | 0.496941i | \(0.165544\pi\) | |||||||
\(182\) | 43.5275 | + | 59.9104i | 0.239162 | + | 0.329178i | ||||
\(183\) | 117.097 | + | 74.7167i | 0.639874 | + | 0.408288i | ||||
\(184\) | −62.2265 | + | 191.513i | −0.338187 | + | 1.04083i | ||||
\(185\) | 26.0840 | − | 35.9015i | 0.140995 | − | 0.194062i | ||||
\(186\) | 12.8435 | + | 15.6032i | 0.0690513 | + | 0.0838880i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 92.3135i | 0.491029i | ||||||||
\(189\) | 9.34471 | − | 69.8234i | 0.0494429 | − | 0.369436i | ||||
\(190\) | 5.70024 | − | 17.5435i | 0.0300013 | − | 0.0923344i | ||||
\(191\) | 53.4521 | − | 17.3676i | 0.279854 | − | 0.0909301i | −0.165727 | − | 0.986172i | \(-0.552997\pi\) |
0.445581 | + | 0.895242i | \(0.352997\pi\) | |||||||
\(192\) | 52.3804 | − | 201.945i | 0.272815 | − | 1.05180i | ||||
\(193\) | 122.139 | − | 88.7392i | 0.632844 | − | 0.459788i | −0.224540 | − | 0.974465i | \(-0.572088\pi\) |
0.857384 | + | 0.514676i | \(0.172088\pi\) | |||||||
\(194\) | 25.6932 | − | 8.34822i | 0.132439 | − | 0.0430321i | ||||
\(195\) | −33.3823 | + | 13.1221i | −0.171191 | + | 0.0672928i | ||||
\(196\) | 42.6854 | + | 31.0128i | 0.217783 | + | 0.158228i | ||||
\(197\) | 22.3374i | 0.113388i | 0.998392 | + | 0.0566938i | \(0.0180559\pi\) | ||||
−0.998392 | + | 0.0566938i | \(0.981944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −150.930 | −0.758444 | −0.379222 | − | 0.925306i | \(-0.623808\pi\) | ||||
−0.379222 | + | 0.925306i | \(0.623808\pi\) | |||||||
\(200\) | −125.437 | + | 172.650i | −0.627186 | + | 0.863248i | ||||
\(201\) | 84.8178 | + | 215.774i | 0.421979 | + | 1.07350i | ||||
\(202\) | 53.3892 | + | 164.315i | 0.264303 | + | 0.813441i | ||||
\(203\) | −8.22915 | − | 11.3265i | −0.0405377 | − | 0.0557954i | ||||
\(204\) | 58.5104 | + | 15.1764i | 0.286815 | + | 0.0743942i | ||||
\(205\) | −14.5564 | − | 44.8000i | −0.0710068 | − | 0.218537i | ||||
\(206\) | −85.7993 | − | 27.8779i | −0.416501 | − | 0.135329i | ||||
\(207\) | 141.751 | + | 152.445i | 0.684785 | + | 0.736449i | ||||
\(208\) | 161.485 | 0.776369 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.99955 | + | 5.76159i | −0.0333312 | + | 0.0274362i | ||||
\(211\) | 146.900 | + | 106.729i | 0.696207 | + | 0.505824i | 0.878695 | − | 0.477384i | \(-0.158415\pi\) |
−0.182488 | + | 0.983208i | \(0.558415\pi\) | |||||||
\(212\) | 50.9630 | + | 16.5589i | 0.240392 | + | 0.0781079i | ||||
\(213\) | −66.5861 | + | 104.355i | −0.312611 | + | 0.489928i | ||||
\(214\) | −38.1071 | + | 27.6864i | −0.178071 | + | 0.129376i | ||||
\(215\) | −9.30442 | − | 12.8064i | −0.0432764 | − | 0.0595648i | ||||
\(216\) | −170.164 | − | 162.174i | −0.787798 | − | 0.750807i | ||||
\(217\) | 3.27551 | − | 10.0810i | 0.0150945 | − | 0.0464561i | ||||
\(218\) | −40.2078 | + | 55.3414i | −0.184440 | + | 0.253859i | ||||
\(219\) | 131.499 | − | 108.242i | 0.600454 | − | 0.494256i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 275.798i | 1.24795i | ||||||||
\(222\) | 19.0681 | + | 315.459i | 0.0858923 | + | 1.42098i | ||||
\(223\) | 58.1059 | − | 178.831i | 0.260564 | − | 0.801935i | −0.732118 | − | 0.681178i | \(-0.761468\pi\) |
0.992682 | − | 0.120757i | \(-0.0385321\pi\) | |||||||
\(224\) | −47.5967 | + | 15.4651i | −0.212485 | + | 0.0690406i | ||||
\(225\) | 92.9476 | + | 200.073i | 0.413100 | + | 0.889211i | ||||
\(226\) | 194.753 | − | 141.497i | 0.861740 | − | 0.626091i | ||||
\(227\) | 408.219 | − | 132.638i | 1.79832 | − | 0.584310i | 0.798478 | − | 0.602024i | \(-0.205639\pi\) |
0.999843 | + | 0.0177135i | \(0.00563869\pi\) | |||||||
\(228\) | −21.8580 | − | 55.6062i | −0.0958684 | − | 0.243887i | ||||
\(229\) | −109.845 | − | 79.8068i | −0.479671 | − | 0.348501i | 0.321527 | − | 0.946900i | \(-0.395804\pi\) |
−0.801198 | + | 0.598399i | \(0.795804\pi\) | |||||||
\(230\) | − | 26.7892i | − | 0.116475i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −46.7166 | −0.201365 | ||||||||
\(233\) | −192.141 | + | 264.459i | −0.824638 | + | 1.13502i | 0.164259 | + | 0.986417i | \(0.447477\pi\) |
−0.988897 | + | 0.148600i | \(0.952523\pi\) | |||||||
\(234\) | 124.161 | − | 223.239i | 0.530601 | − | 0.954012i | ||||
\(235\) | −15.9342 | − | 49.0404i | −0.0678051 | − | 0.208683i | ||||
\(236\) | 21.1233 | + | 29.0738i | 0.0895057 | + | 0.123194i | ||||
\(237\) | −38.3577 | + | 147.882i | −0.161847 | + | 0.623976i | ||||
\(238\) | 21.5410 | + | 66.2963i | 0.0905083 | + | 0.278556i | ||||
\(239\) | 88.8791 | + | 28.8786i | 0.371879 | + | 0.120831i | 0.488993 | − | 0.872288i | \(-0.337364\pi\) |
−0.117114 | + | 0.993118i | \(0.537364\pi\) | |||||||
\(240\) | 1.19280 | + | 19.7335i | 0.00497000 | + | 0.0822227i | ||||
\(241\) | −206.766 | −0.857952 | −0.428976 | − | 0.903316i | \(-0.641125\pi\) | ||||
−0.428976 | + | 0.903316i | \(0.641125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −232.013 | + | 72.2432i | −0.954785 | + | 0.297297i | ||||
\(244\) | −46.8421 | − | 34.0328i | −0.191976 | − | 0.139479i | ||||
\(245\) | −28.0292 | − | 9.10724i | −0.114405 | − | 0.0371724i | ||||
\(246\) | 282.802 | + | 180.449i | 1.14960 | + | 0.733531i | ||||
\(247\) | 220.546 | − | 160.236i | 0.892900 | − | 0.648730i | ||||
\(248\) | −20.7898 | − | 28.6147i | −0.0838297 | − | 0.115382i | ||||
\(249\) | −95.5472 | + | 149.743i | −0.383724 | + | 0.601377i | ||||
\(250\) | 17.7210 | − | 54.5397i | 0.0708841 | − | 0.218159i | ||||
\(251\) | 1.64009 | − | 2.25739i | 0.00653422 | − | 0.00899358i | −0.805737 | − | 0.592273i | \(-0.798231\pi\) |
0.812272 | + | 0.583279i | \(0.198231\pi\) | |||||||
\(252\) | −5.64417 | + | 28.8168i | −0.0223975 | + | 0.114353i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 303.081i | − | 1.19323i | ||||||
\(255\) | −33.7025 | + | 2.03717i | −0.132167 | + | 0.00798889i | ||||
\(256\) | −66.1871 | + | 203.703i | −0.258543 | + | 0.795714i | ||||
\(257\) | −380.619 | + | 123.671i | −1.48101 | + | 0.481208i | −0.934414 | − | 0.356190i | \(-0.884076\pi\) |
−0.546593 | + | 0.837398i | \(0.684076\pi\) | |||||||
\(258\) | 109.122 | + | 28.3040i | 0.422952 | + | 0.109705i | ||||
\(259\) | 134.103 | − | 97.4312i | 0.517770 | − | 0.376182i | ||||
\(260\) | 14.2196 | − | 4.62022i | 0.0546907 | − | 0.0177701i | ||||
\(261\) | −23.4734 | + | 42.2047i | −0.0899362 | + | 0.161704i | ||||
\(262\) | 113.370 | + | 82.3678i | 0.432708 | + | 0.314381i | ||||
\(263\) | 379.212i | 1.44187i | 0.693003 | + | 0.720935i | \(0.256287\pi\) | ||||
−0.693003 | + | 0.720935i | \(0.743713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.9317 | −0.112950 | ||||||||
\(266\) | 40.4999 | − | 55.7433i | 0.152255 | − | 0.209561i | ||||
\(267\) | 106.631 | − | 41.9149i | 0.399365 | − | 0.156985i | ||||
\(268\) | −29.8639 | − | 91.9118i | −0.111433 | − | 0.342954i | ||||
\(269\) | −18.3393 | − | 25.2419i | −0.0681760 | − | 0.0938362i | 0.773567 | − | 0.633714i | \(-0.218470\pi\) |
−0.841743 | + | 0.539878i | \(0.818470\pi\) | |||||||
\(270\) | 28.1969 | + | 13.5235i | 0.104433 | + | 0.0500870i | ||||
\(271\) | −160.104 | − | 492.748i | −0.590788 | − | 1.81826i | −0.574664 | − | 0.818390i | \(-0.694867\pi\) |
−0.0161246 | − | 0.999870i | \(-0.505133\pi\) | |||||||
\(272\) | 144.569 | + | 46.9734i | 0.531505 | + | 0.172696i | ||||
\(273\) | −133.736 | + | 8.08374i | −0.489875 | + | 0.0296108i | ||||
\(274\) | −338.882 | −1.23680 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −55.1450 | − | 66.9937i | −0.199801 | − | 0.242731i | ||||
\(277\) | 297.684 | + | 216.280i | 1.07467 | + | 0.780795i | 0.976746 | − | 0.214399i | \(-0.0687793\pi\) |
0.0979254 | + | 0.995194i | \(0.468779\pi\) | |||||||
\(278\) | −79.2308 | − | 25.7436i | −0.285003 | − | 0.0926031i | ||||
\(279\) | −36.2971 | + | 4.40410i | −0.130097 | + | 0.0157853i | ||||
\(280\) | 12.8365 | − | 9.32625i | 0.0458446 | − | 0.0333081i | ||||
\(281\) | 188.322 | + | 259.203i | 0.670184 | + | 0.922429i | 0.999765 | − | 0.0216982i | \(-0.00690730\pi\) |
−0.329580 | + | 0.944127i | \(0.606907\pi\) | |||||||
\(282\) | 309.569 | + | 197.528i | 1.09776 | + | 0.700456i | ||||
\(283\) | 49.6883 | − | 152.925i | 0.175577 | − | 0.540371i | −0.824082 | − | 0.566470i | \(-0.808309\pi\) |
0.999659 | + | 0.0260993i | \(0.00830861\pi\) | |||||||
\(284\) | 30.3294 | − | 41.7449i | 0.106794 | − | 0.146989i | ||||
\(285\) | 21.2100 | + | 25.7672i | 0.0744209 | + | 0.0904113i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 175.953i | − | 0.613075i | ||||||
\(288\) | 117.554 | + | 126.423i | 0.408174 | + | 0.438968i | ||||
\(289\) | 9.08071 | − | 27.9475i | 0.0314211 | − | 0.0967043i | ||||
\(290\) | 5.91079 | − | 1.92053i | 0.0203820 | − | 0.00662252i | ||||
\(291\) | −12.2717 | + | 47.3116i | −0.0421707 | + | 0.162583i | ||||
\(292\) | −57.4361 | + | 41.7298i | −0.196699 | + | 0.142910i | ||||
\(293\) | −276.702 | + | 89.9060i | −0.944377 | + | 0.306847i | −0.740429 | − | 0.672135i | \(-0.765377\pi\) |
−0.203948 | + | 0.978982i | \(0.565377\pi\) | |||||||
\(294\) | 195.336 | − | 76.7839i | 0.664410 | − | 0.261170i | ||||
\(295\) | −16.2399 | − | 11.7990i | −0.0550506 | − | 0.0399966i | ||||
\(296\) | − | 553.114i | − | 1.86863i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 260.998 | 0.875832 | ||||||||
\(299\) | 232.707 | − | 320.294i | 0.778286 | − | 1.07122i | ||||
\(300\) | −33.6414 | − | 85.5830i | −0.112138 | − | 0.285277i | ||||
\(301\) | −18.2716 | − | 56.2343i | −0.0607030 | − | 0.186825i | ||||
\(302\) | 167.035 | + | 229.905i | 0.553097 | + | 0.761273i | ||||
\(303\) | −302.571 | − | 78.4808i | −0.998583 | − | 0.259012i | ||||
\(304\) | −46.4306 | − | 142.899i | −0.152732 | − | 0.470061i | ||||
\(305\) | 30.7587 | + | 9.99411i | 0.100848 | + | 0.0327676i | ||||
\(306\) | 176.091 | − | 163.738i | 0.575462 | − | 0.535092i | ||||
\(307\) | 281.800 | 0.917915 | 0.458957 | − | 0.888458i | \(-0.348223\pi\) | ||||
0.458957 | + | 0.888458i | \(0.348223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 126.018 | − | 103.730i | 0.407826 | − | 0.335697i | ||||
\(310\) | 3.80676 | + | 2.76578i | 0.0122799 | + | 0.00892186i | ||||
\(311\) | 450.565 | + | 146.398i | 1.44876 | + | 0.470732i | 0.924618 | − | 0.380897i | \(-0.124385\pi\) |
0.524146 | + | 0.851628i | \(0.324385\pi\) | |||||||
\(312\) | −240.480 | + | 376.883i | −0.770768 | + | 1.20796i | ||||
\(313\) | 24.2496 | − | 17.6184i | 0.0774748 | − | 0.0562887i | −0.548374 | − | 0.836233i | \(-0.684753\pi\) |
0.625848 | + | 0.779945i | \(0.284753\pi\) | |||||||
\(314\) | −63.6811 | − | 87.6495i | −0.202806 | − | 0.279139i | ||||
\(315\) | −1.97567 | − | 16.2828i | −0.00627197 | − | 0.0516915i | ||||
\(316\) | 19.6790 | − | 60.5656i | 0.0622752 | − | 0.191663i | ||||
\(317\) | 93.6204 | − | 128.857i | 0.295333 | − | 0.406490i | −0.635405 | − | 0.772179i | \(-0.719167\pi\) |
0.930737 | + | 0.365689i | \(0.119167\pi\) | |||||||
\(318\) | 164.578 | − | 135.470i | 0.517541 | − | 0.426007i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 48.5757i | − | 0.151799i | ||||||
\(321\) | −5.14181 | − | 85.0651i | −0.0160181 | − | 0.265000i | ||||
\(322\) | 30.9219 | − | 95.1679i | 0.0960308 | − | 0.295552i | ||||
\(323\) | 244.054 | − | 79.2981i | 0.755586 | − | 0.245505i | ||||
\(324\) | 98.3519 | − | 24.2236i | 0.303555 | − | 0.0747641i | ||||
\(325\) | 339.441 | − | 246.618i | 1.04443 | − | 0.758825i | ||||
\(326\) | −24.3465 | + | 7.91065i | −0.0746825 | + | 0.0242658i | ||||
\(327\) | −45.2766 | − | 115.183i | −0.138461 | − | 0.352241i | ||||
\(328\) | −474.994 | − | 345.103i | −1.44815 | − | 1.05214i | ||||
\(329\) | − | 192.607i | − | 0.585431i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 332.709 | 1.00516 | 0.502582 | − | 0.864530i | \(-0.332384\pi\) | ||||
0.502582 | + | 0.864530i | \(0.332384\pi\) | |||||||
\(332\) | 43.5209 | − | 59.9014i | 0.131087 | − | 0.180426i | ||||
\(333\) | −499.694 | − | 277.919i | −1.50058 | − | 0.834591i | ||||
\(334\) | −78.9626 | − | 243.022i | −0.236415 | − | 0.727611i | ||||
\(335\) | 31.7297 | + | 43.6722i | 0.0947155 | + | 0.130365i | ||||
\(336\) | −18.5403 | + | 71.4793i | −0.0551794 | + | 0.212736i | ||||
\(337\) | −17.1212 | − | 52.6936i | −0.0508047 | − | 0.156361i | 0.922435 | − | 0.386152i | \(-0.126196\pi\) |
−0.973240 | + | 0.229791i | \(0.926196\pi\) | |||||||
\(338\) | −195.532 | − | 63.5322i | −0.578497 | − | 0.187965i | ||||
\(339\) | 26.2782 | + | 434.741i | 0.0775167 | + | 1.28242i | ||||
\(340\) | 14.0740 | 0.0413942 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −233.244 | − | 45.6840i | −0.682000 | − | 0.133579i | ||||
\(343\) | −192.491 | − | 139.853i | −0.561197 | − | 0.407733i | ||||
\(344\) | −187.645 | − | 60.9694i | −0.545478 | − | 0.177237i | ||||
\(345\) | 40.8589 | + | 26.0710i | 0.118432 | + | 0.0755682i | ||||
\(346\) | −33.6751 | + | 24.4664i | −0.0973270 | + | 0.0707122i | ||||
\(347\) | 81.4326 | + | 112.082i | 0.234676 | + | 0.323004i | 0.910071 | − | 0.414452i | \(-0.136027\pi\) |
−0.675395 | + | 0.737456i | \(0.736027\pi\) | |||||||
\(348\) | 10.8282 | − | 16.9700i | 0.0311154 | − | 0.0487645i | ||||
\(349\) | −69.9974 | + | 215.430i | −0.200566 | + | 0.617277i | 0.799301 | + | 0.600931i | \(0.205203\pi\) |
−0.999866 | + | 0.0163462i | \(0.994797\pi\) | |||||||
\(350\) | 62.3330 | − | 85.7940i | 0.178094 | − | 0.245126i | ||||
\(351\) | 219.652 | + | 406.624i | 0.625788 | + | 1.15847i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 258.939i | − | 0.733538i | −0.930312 | − | 0.366769i | \(-0.880464\pi\) | ||
0.930312 | − | 0.366769i | \(-0.119536\pi\) | |||||||
\(354\) | 142.697 | − | 8.62538i | 0.403098 | − | 0.0243655i | ||||
\(355\) | −8.90657 | + | 27.4116i | −0.0250889 | + | 0.0772157i | ||||
\(356\) | −45.4206 | + | 14.7580i | −0.127586 | + | 0.0414552i | ||||
\(357\) | −122.078 | − | 31.6647i | −0.341957 | − | 0.0886967i | ||||
\(358\) | −82.9101 | + | 60.2377i | −0.231592 | + | 0.168262i | ||||
\(359\) | −246.358 | + | 80.0466i | −0.686234 | + | 0.222971i | −0.631323 | − | 0.775520i | \(-0.717488\pi\) |
−0.0549113 | + | 0.998491i | \(0.517488\pi\) | |||||||
\(360\) | −47.8314 | − | 26.6028i | −0.132865 | − | 0.0738967i | ||||
\(361\) | 86.8492 | + | 63.0996i | 0.240580 | + | 0.174791i | ||||
\(362\) | 246.079i | 0.679775i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 55.8476 | 0.153428 | ||||||||
\(365\) | 23.3093 | − | 32.0824i | 0.0638610 | − | 0.0878971i | ||||
\(366\) | −214.358 | + | 84.2612i | −0.585679 | + | 0.230222i | ||||
\(367\) | −61.4255 | − | 189.048i | −0.167372 | − | 0.515118i | 0.831831 | − | 0.555029i | \(-0.187293\pi\) |
−0.999203 | + | 0.0399105i | \(0.987293\pi\) | |||||||
\(368\) | −128.259 | − | 176.534i | −0.348531 | − | 0.479712i | ||||
\(369\) | −550.440 | + | 255.718i | −1.49171 | + | 0.693002i | ||||
\(370\) | 22.7386 | + | 69.9823i | 0.0614557 | + | 0.189141i | ||||
\(371\) | −106.331 | − | 34.5492i | −0.286607 | − | 0.0931244i | ||||
\(372\) | 15.2131 | − | 0.919567i | 0.0408955 | − | 0.00247195i | ||||
\(373\) | −670.467 | −1.79750 | −0.898750 | − | 0.438462i | \(-0.855523\pi\) | ||||
−0.898750 | + | 0.438462i | \(0.855523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 65.9379 | + | 80.1056i | 0.175834 | + | 0.213615i | ||||
\(376\) | −519.953 | − | 377.768i | −1.38285 | − | 1.00470i | ||||
\(377\) | 87.3527 | + | 28.3826i | 0.231705 | + | 0.0752855i | ||||
\(378\) | 84.5590 | + | 80.5886i | 0.223701 | + | 0.213197i | ||||
\(379\) | −317.451 | + | 230.642i | −0.837601 | + | 0.608553i | −0.921700 | − | 0.387905i | \(-0.873199\pi\) |
0.0840983 | + | 0.996457i | \(0.473199\pi\) | |||||||
\(380\) | −8.17691 | − | 11.2546i | −0.0215182 | − | 0.0296173i | ||||
\(381\) | 462.258 | + | 294.956i | 1.21328 | + | 0.774161i | ||||
\(382\) | −28.7983 | + | 88.6321i | −0.0753883 | + | 0.232021i | ||||
\(383\) | −292.542 | + | 402.649i | −0.763817 | + | 1.05130i | 0.233070 | + | 0.972460i | \(0.425123\pi\) |
−0.996887 | + | 0.0788436i | \(0.974877\pi\) | |||||||
\(384\) | 73.5699 | + | 89.3774i | 0.191588 | + | 0.232754i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 250.336i | 0.648538i | ||||||||
\(387\) | −149.365 | + | 138.887i | −0.385957 | + | 0.358881i | ||||
\(388\) | 6.29584 | − | 19.3766i | 0.0162264 | − | 0.0499397i | ||||
\(389\) | 392.101 | − | 127.401i | 1.00797 | − | 0.327510i | 0.241926 | − | 0.970295i | \(-0.422221\pi\) |
0.766047 | + | 0.642785i | \(0.222221\pi\) | |||||||
\(390\) | 14.9328 | − | 57.5710i | 0.0382891 | − | 0.147618i | ||||
\(391\) | 301.500 | − | 219.053i | 0.771100 | − | 0.560237i | ||||
\(392\) | −349.357 | + | 113.513i | −0.891217 | + | 0.289574i | ||||
\(393\) | −235.958 | + | 92.7515i | −0.600401 | + | 0.236009i | ||||
\(394\) | −29.9651 | − | 21.7709i | −0.0760535 | − | 0.0552561i | ||||
\(395\) | 35.5715i | 0.0900544i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 171.230 | 0.431310 | 0.215655 | − | 0.976470i | \(-0.430811\pi\) | ||||
0.215655 | + | 0.976470i | \(0.430811\pi\) | |||||||
\(398\) | 147.103 | − | 202.470i | 0.369605 | − | 0.508718i | ||||
\(399\) | 45.6055 | + | 116.019i | 0.114299 | + | 0.290775i | ||||
\(400\) | −71.4608 | − | 219.934i | −0.178652 | − | 0.549835i | ||||
\(401\) | −426.743 | − | 587.361i | −1.06420 | − | 1.46474i | −0.875816 | − | 0.482646i | \(-0.839676\pi\) |
−0.188382 | − | 0.982096i | \(-0.560324\pi\) | |||||||
\(402\) | −372.124 | − | 96.5215i | −0.925681 | − | 0.240103i | ||||
\(403\) | 21.4888 | + | 66.1357i | 0.0533221 | + | 0.164108i | ||||
\(404\) | 123.919 | + | 40.2636i | 0.306729 | + | 0.0996624i | ||||
\(405\) | −48.0670 | + | 29.8450i | −0.118684 | + | 0.0736912i | ||||
\(406\) | 23.2147 | 0.0571790 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −324.919 | + | 267.453i | −0.796369 | + | 0.655521i | ||||
\(409\) | 243.830 | + | 177.153i | 0.596161 | + | 0.433137i | 0.844514 | − | 0.535533i | \(-0.179889\pi\) |
−0.248353 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(410\) | 74.2855 | + | 24.1368i | 0.181184 | + | 0.0588703i | ||||
\(411\) | 329.797 | − | 516.863i | 0.802426 | − | 1.25757i | ||||
\(412\) | −55.0420 | + | 39.9904i | −0.133597 | + | 0.0970640i | ||||
\(413\) | −44.0727 | − | 60.6608i | −0.106713 | − | 0.146878i | ||||
\(414\) | −342.658 | + | 41.5762i | −0.827676 | + | 0.100426i | ||||
\(415\) | −12.7804 | + | 39.3340i | −0.0307961 | + | 0.0947808i | ||||
\(416\) | 192.985 | − | 265.621i | 0.463905 | − | 0.638511i | ||||
\(417\) | 116.371 | − | 95.7892i | 0.279067 | − | 0.229710i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 573.195i | 1.36801i | 0.729478 | + | 0.684004i | \(0.239763\pi\) | ||||
−0.729478 | + | 0.684004i | \(0.760237\pi\) | |||||||
\(420\) | 0.412516 | + | 6.82459i | 0.000982181 | + | 0.0162490i | ||||
\(421\) | −172.827 | + | 531.908i | −0.410516 | + | 1.26344i | 0.505684 | + | 0.862719i | \(0.331240\pi\) |
−0.916200 | + | 0.400721i | \(0.868760\pi\) | |||||||
\(422\) | −286.349 | + | 93.0404i | −0.678552 | + | 0.220475i | ||||
\(423\) | −602.540 | + | 279.922i | −1.42445 | + | 0.661754i | ||||
\(424\) | −301.820 | + | 219.285i | −0.711839 | + | 0.517182i | ||||
\(425\) | 375.622 | − | 122.047i | 0.883816 | − | 0.287169i | ||||
\(426\) | −75.0920 | − | 191.032i | −0.176272 | − | 0.448433i | ||||
\(427\) | 97.7334 | + | 71.0075i | 0.228884 | + | 0.166294i | ||||
\(428\) | 35.5229i | 0.0829973i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.2480 | 0.0610420 | ||||||||
\(431\) | 117.467 | − | 161.680i | 0.272546 | − | 0.375127i | −0.650701 | − | 0.759334i | \(-0.725525\pi\) |
0.923247 | + | 0.384207i | \(0.125525\pi\) | |||||||
\(432\) | 250.557 | − | 45.8828i | 0.579993 | − | 0.106210i | ||||
\(433\) | −31.9791 | − | 98.4214i | −0.0738547 | − | 0.227301i | 0.907314 | − | 0.420453i | \(-0.138129\pi\) |
−0.981169 | + | 0.193152i | \(0.938129\pi\) | |||||||
\(434\) | 10.3310 | + | 14.2194i | 0.0238041 | + | 0.0327635i | ||||
\(435\) | −2.82313 | + | 10.8842i | −0.00648996 | + | 0.0250211i | ||||
\(436\) | 15.9417 | + | 49.0635i | 0.0365635 | + | 0.112531i | ||||
\(437\) | −350.338 | − | 113.832i | −0.801690 | − | 0.260485i | ||||
\(438\) | 17.0397 | + | 281.901i | 0.0389034 | + | 0.643610i | ||||
\(439\) | 662.550 | 1.50923 | 0.754613 | − | 0.656171i | \(-0.227825\pi\) | ||||
0.754613 | + | 0.656171i | \(0.227825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −72.9890 | + | 372.652i | −0.165508 | + | 0.845016i | ||||
\(442\) | −369.977 | − | 268.804i | −0.837051 | − | 0.608153i | ||||
\(443\) | −200.511 | − | 65.1499i | −0.452620 | − | 0.147065i | 0.0738308 | − | 0.997271i | \(-0.476478\pi\) |
−0.526451 | + | 0.850206i | \(0.676478\pi\) | |||||||
\(444\) | 200.921 | + | 128.203i | 0.452525 | + | 0.288745i | ||||
\(445\) | 21.5817 | − | 15.6801i | 0.0484983 | − | 0.0352361i | ||||
\(446\) | 183.266 | + | 252.244i | 0.410911 | + | 0.565570i | ||||
\(447\) | −254.001 | + | 398.074i | −0.568235 | + | 0.890545i | ||||
\(448\) | 56.0693 | − | 172.563i | 0.125155 | − | 0.385186i | ||||
\(449\) | 140.640 | − | 193.574i | 0.313229 | − | 0.431123i | −0.623156 | − | 0.782098i | \(-0.714150\pi\) |
0.936385 | + | 0.350975i | \(0.114150\pi\) | |||||||
\(450\) | −358.984 | − | 70.3118i | −0.797742 | − | 0.156248i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 181.546i | − | 0.401651i | ||||||
\(453\) | −513.207 | + | 31.0211i | −1.13291 | + | 0.0684793i | ||||
\(454\) | −219.936 | + | 676.892i | −0.484440 | + | 1.49095i | ||||
\(455\) | −29.6684 | + | 9.63983i | −0.0652052 | + | 0.0211864i | ||||
\(456\) | 402.649 | + | 104.439i | 0.883001 | + | 0.229033i | ||||
\(457\) | 21.5908 | − | 15.6866i | 0.0472446 | − | 0.0343252i | −0.563912 | − | 0.825835i | \(-0.690704\pi\) |
0.611157 | + | 0.791509i | \(0.290704\pi\) | |||||||
\(458\) | 214.118 | − | 69.5713i | 0.467507 | − | 0.151902i | ||||
\(459\) | 78.3626 | + | 427.923i | 0.170725 | + | 0.932294i | ||||
\(460\) | −16.3447 | − | 11.8751i | −0.0355320 | − | 0.0258155i | ||||
\(461\) | − | 393.125i | − | 0.852766i | −0.904543 | − | 0.426383i | \(-0.859788\pi\) | ||
0.904543 | − | 0.426383i | \(-0.140212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 106.954 | 0.231002 | 0.115501 | − | 0.993307i | \(-0.463153\pi\) | ||||
0.115501 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(464\) | 29.7556 | − | 40.9550i | 0.0641283 | − | 0.0882651i | ||||
\(465\) | −7.92307 | + | 3.11444i | −0.0170389 | + | 0.00669772i | ||||
\(466\) | −167.498 | − | 515.506i | −0.359438 | − | 1.10624i | ||||
\(467\) | −248.580 | − | 342.141i | −0.532291 | − | 0.732636i | 0.455186 | − | 0.890396i | \(-0.349573\pi\) |
−0.987477 | + | 0.157760i | \(0.949573\pi\) | |||||||
\(468\) | −81.1652 | − | 174.711i | −0.173430 | − | 0.373313i | ||||
\(469\) | 62.3094 | + | 191.769i | 0.132856 | + | 0.408888i | ||||
\(470\) | 81.3168 | + | 26.4214i | 0.173014 | + | 0.0562158i | ||||
\(471\) | 195.657 | − | 11.8266i | 0.415407 | − | 0.0251095i | ||||
\(472\) | −250.199 | −0.530083 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −160.996 | − | 195.588i | −0.339654 | − | 0.412634i | ||||
\(475\) | −315.831 | − | 229.464i | −0.664906 | − | 0.483083i | ||||
\(476\) | 49.9976 | + | 16.2452i | 0.105037 | + | 0.0341286i | ||||
\(477\) | 46.4532 | + | 382.853i | 0.0973862 | + | 0.802626i | ||||
\(478\) | −125.365 | + | 91.0832i | −0.262270 | + | 0.190551i | ||||
\(479\) | −317.236 | − | 436.638i | −0.662289 | − | 0.911562i | 0.337266 | − | 0.941409i | \(-0.390498\pi\) |
−0.999554 | + | 0.0298475i | \(0.990498\pi\) | |||||||
\(480\) | 33.8843 | + | 21.6208i | 0.0705924 | + | 0.0450432i | ||||
\(481\) | −336.043 | + | 1034.24i | −0.698635 | + | 2.15018i | ||||
\(482\) | 201.523 | − | 277.373i | 0.418098 | − | 0.575462i | ||||
\(483\) | 115.057 | + | 139.779i | 0.238213 | + | 0.289397i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3803i | 0.0234645i | ||||||||
\(486\) | 129.217 | − | 381.652i | 0.265878 | − | 0.785291i | ||||
\(487\) | 188.700 | − | 580.759i | 0.387474 | − | 1.19252i | −0.547195 | − | 0.837005i | \(-0.684304\pi\) |
0.934669 | − | 0.355518i | \(-0.115696\pi\) | |||||||
\(488\) | 383.378 | − | 124.567i | 0.785610 | − | 0.255260i | ||||
\(489\) | 11.6285 | − | 44.8318i | 0.0237801 | − | 0.0916805i | ||||
\(490\) | 39.5356 | − | 28.7243i | 0.0806849 | − | 0.0586210i | ||||
\(491\) | −54.0905 | + | 17.5751i | −0.110164 | + | 0.0357944i | −0.363580 | − | 0.931563i | \(-0.618446\pi\) |
0.253416 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(492\) | 235.456 | − | 92.5545i | 0.478570 | − | 0.188119i | ||||
\(493\) | 69.9465 | + | 50.8191i | 0.141879 | + | 0.103081i | ||||
\(494\) | 452.031i | 0.915043i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.3274 | 0.0772729 | ||||||||
\(497\) | −63.2806 | + | 87.0983i | −0.127325 | + | 0.175248i | ||||
\(498\) | −107.753 | − | 274.120i | −0.216371 | − | 0.550442i | ||||
\(499\) | 144.891 | + | 445.930i | 0.290363 | + | 0.893646i | 0.984740 | + | 0.174034i | \(0.0556804\pi\) |
−0.694376 | + | 0.719612i | \(0.744320\pi\) | |||||||
\(500\) | −25.4205 | − | 34.9884i | −0.0508411 | − | 0.0699767i | ||||
\(501\) | 447.502 | + | 116.073i | 0.893218 | + | 0.231683i | ||||
\(502\) | 1.42974 | + | 4.40029i | 0.00284809 | + | 0.00876552i | ||||
\(503\) | 435.748 | + | 141.583i | 0.866297 | + | 0.281477i | 0.708256 | − | 0.705955i | \(-0.249482\pi\) |
0.158041 | + | 0.987433i | \(0.449482\pi\) | |||||||
\(504\) | −139.213 | − | 149.716i | −0.276216 | − | 0.297055i | ||||
\(505\) | −72.7802 | −0.144119 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 287.189 | − | 236.396i | 0.566448 | − | 0.466265i | ||||
\(508\) | −184.917 | − | 134.350i | −0.364009 | − | 0.264468i | ||||
\(509\) | −261.397 | − | 84.9330i | −0.513550 | − | 0.166862i | 0.0407663 | − | 0.999169i | \(-0.487020\pi\) |
−0.554316 | + | 0.832306i | \(0.687020\pi\) | |||||||
\(510\) | 30.1150 | − | 47.1967i | 0.0590491 | − | 0.0925426i | ||||
\(511\) | 119.837 | − | 87.0667i | 0.234515 | − | 0.170385i | ||||
\(512\) | −299.479 | − | 412.197i | −0.584920 | − | 0.805073i | ||||
\(513\) | 296.668 | − | 311.284i | 0.578300 | − | 0.606792i | ||||
\(514\) | 205.065 | − | 631.127i | 0.398960 | − | 1.22787i | ||||
\(515\) | 22.3377 | − | 30.7452i | 0.0433741 | − | 0.0596994i | ||||
\(516\) | 65.6404 | − | 54.0310i | 0.127210 | − | 0.104711i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 274.856i | 0.530610i | ||||||||
\(519\) | −4.54380 | − | 75.1717i | −0.00875491 | − | 0.144840i | ||||
\(520\) | −32.1666 | + | 98.9985i | −0.0618588 | + | 0.190382i | ||||
\(521\) | 236.239 | − | 76.7587i | 0.453434 | − | 0.147330i | −0.0733915 | − | 0.997303i | \(-0.523382\pi\) |
0.526825 | + | 0.849974i | \(0.323382\pi\) | |||||||
\(522\) | −33.7387 | − | 72.6235i | −0.0646335 | − | 0.139126i | ||||
\(523\) | 113.737 | − | 82.6347i | 0.217470 | − | 0.158001i | −0.473717 | − | 0.880677i | \(-0.657088\pi\) |
0.691187 | + | 0.722676i | \(0.257088\pi\) | |||||||
\(524\) | 100.509 | − | 32.6574i | 0.191811 | − | 0.0623232i | ||||
\(525\) | 70.1909 | + | 178.564i | 0.133697 | + | 0.340122i | ||||
\(526\) | −508.705 | − | 369.596i | −0.967119 | − | 0.702653i | ||||
\(527\) | 65.4587i | 0.124210i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.97152 | −0.0112883 | ||||||||
\(530\) | 29.1727 | − | 40.1527i | 0.0550428 | − | 0.0757599i | ||||
\(531\) | −125.716 | + | 226.035i | −0.236753 | + | 0.425678i | ||||
\(532\) | −16.0575 | − | 49.4198i | −0.0301832 | − | 0.0928943i | ||||
\(533\) | 678.497 | + | 933.871i | 1.27298 | + | 1.75210i | ||||
\(534\) | −47.6986 | + | 183.895i | −0.0893232 | + | 0.344372i | ||||
\(535\) | −6.13159 | − | 18.8711i | −0.0114609 | − | 0.0352731i | ||||
\(536\) | 639.901 | + | 207.916i | 1.19384 | + | 0.387904i | ||||
\(537\) | −11.1871 | − | 185.077i | −0.0208326 | − | 0.344650i | ||||
\(538\) | 51.7358 | 0.0961633 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 20.7501 | − | 11.2089i | 0.0384262 | − | 0.0207572i | ||||
\(541\) | 486.149 | + | 353.208i | 0.898612 | + | 0.652880i | 0.938109 | − | 0.346340i | \(-0.112576\pi\) |
−0.0394969 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(542\) | 817.055 | + | 265.477i | 1.50748 | + | 0.489811i | ||||
\(543\) | −375.319 | − | 239.481i | −0.691195 | − | 0.441034i | ||||
\(544\) | 250.034 | − | 181.661i | 0.459622 | − | 0.333935i | ||||
\(545\) | −16.9376 | − | 23.3127i | −0.0310782 | − | 0.0427755i | ||||
\(546\) | 119.500 | − | 187.283i | 0.218865 | − | 0.343009i | ||||
\(547\) | 191.860 | − | 590.485i | 0.350750 | − | 1.07950i | −0.607683 | − | 0.794180i | \(-0.707901\pi\) |
0.958433 | − | 0.285318i | \(-0.0920992\pi\) | |||||||
\(548\) | −150.220 | + | 206.760i | −0.274124 | + | 0.377299i | ||||
\(549\) | 80.0967 | − | 408.941i | 0.145896 | − | 0.744884i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 85.4594i | − | 0.155099i | ||||||
\(552\) | 603.007 | − | 36.4491i | 1.09240 | − | 0.0660310i | ||||
\(553\) | −41.0590 | + | 126.367i | −0.0742478 | + | 0.228511i | ||||
\(554\) | −580.271 | + | 188.541i | −1.04742 | + | 0.340327i | ||||
\(555\) | −128.866 | − | 33.4252i | −0.232191 | − | 0.0602256i | ||||
\(556\) | −50.8282 | + | 36.9289i | −0.0914177 | + | 0.0664188i | ||||
\(557\) | −513.595 | + | 166.877i | −0.922074 | + | 0.299600i | −0.731317 | − | 0.682037i | \(-0.761094\pi\) |
−0.190757 | + | 0.981637i | \(0.561094\pi\) | |||||||
\(558\) | 29.4687 | − | 52.9843i | 0.0528113 | − | 0.0949539i | ||||
\(559\) | 313.824 | + | 228.006i | 0.561402 | + | 0.407883i | ||||
\(560\) | 17.1936i | 0.0307028i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −531.261 | −0.945305 | ||||||||
\(563\) | −163.796 | + | 225.446i | −0.290934 | + | 0.400437i | −0.929317 | − | 0.369282i | \(-0.879604\pi\) |
0.638383 | + | 0.769719i | \(0.279604\pi\) | |||||||
\(564\) | 257.743 | − | 101.315i | 0.456991 | − | 0.179636i | ||||
\(565\) | 31.3366 | + | 96.4441i | 0.0554630 | + | 0.170698i | ||||
\(566\) | 156.717 | + | 215.703i | 0.276886 | + | 0.381101i | ||||
\(567\) | −205.206 | + | 50.5411i | −0.361915 | + | 0.0891377i | ||||
\(568\) | 111.012 | + | 341.659i | 0.195443 | + | 0.601513i | ||||
\(569\) | −1017.22 | − | 330.514i | −1.78773 | − | 0.580869i | −0.788321 | − | 0.615264i | \(-0.789050\pi\) |
−0.999408 | + | 0.0343952i | \(0.989050\pi\) | |||||||
\(570\) | −55.2383 | + | 3.33891i | −0.0969093 | + | 0.00585774i | ||||
\(571\) | −470.660 | −0.824274 | −0.412137 | − | 0.911122i | \(-0.635217\pi\) | ||||
−0.412137 | + | 0.911122i | \(0.635217\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −107.155 | − | 130.179i | −0.187007 | − | 0.227189i | ||||
\(574\) | 236.037 | + | 171.491i | 0.411214 | + | 0.298764i | ||||
\(575\) | −539.203 | − | 175.198i | −0.937744 | − | 0.304691i | ||||
\(576\) | −621.325 | + | 75.3882i | −1.07869 | + | 0.130882i | ||||
\(577\) | −185.383 | + | 134.689i | −0.321288 | + | 0.233429i | −0.736725 | − | 0.676193i | \(-0.763629\pi\) |
0.415437 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(578\) | 28.6406 | + | 39.4204i | 0.0495512 | + | 0.0682014i | ||||
\(579\) | −381.812 | − | 243.625i | −0.659433 | − | 0.420768i | ||||
\(580\) | 1.44837 | − | 4.45764i | 0.00249720 | − | 0.00768558i | ||||
\(581\) | −90.8039 | + | 124.981i | −0.156289 | + | 0.215113i | ||||
\(582\) | −51.5071 | − | 62.5741i | −0.0885001 | − | 0.107516i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 494.275i | − | 0.846361i | ||||||
\(585\) | 73.2747 | + | 78.8030i | 0.125256 | + | 0.134706i | ||||
\(586\) | 149.079 | − | 458.817i | 0.254400 | − | 0.782964i | ||||
\(587\) | 0.704580 | − | 0.228932i | 0.00120031 | − | 0.000390003i | −0.308417 | − | 0.951251i | \(-0.599799\pi\) |
0.309617 | + | 0.950861i | \(0.399799\pi\) | |||||||
\(588\) | 39.7412 | − | 153.216i | 0.0675870 | − | 0.260571i | ||||
\(589\) | 52.3452 | − | 38.0310i | 0.0888714 | − | 0.0645688i | ||||
\(590\) | 31.6562 | − | 10.2857i | 0.0536546 | − | 0.0174334i | ||||
\(591\) | 62.3667 | − | 24.5155i | 0.105527 | − | 0.0414813i | ||||
\(592\) | 484.897 | + | 352.299i | 0.819083 | + | 0.595099i | ||||
\(593\) | − | 498.413i | − | 0.840494i | −0.907410 | − | 0.420247i | \(-0.861943\pi\) | ||
0.907410 | − | 0.420247i | \(-0.138057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.3647 | −0.0493524 | ||||||||
\(596\) | 115.695 | − | 159.241i | 0.194120 | − | 0.267183i | ||||
\(597\) | 165.647 | + | 421.403i | 0.277466 | + | 0.705868i | ||||
\(598\) | 202.862 | + | 624.344i | 0.339234 | + | 1.04405i | ||||
\(599\) | −112.504 | − | 154.848i | −0.187819 | − | 0.258511i | 0.704715 | − | 0.709490i | \(-0.251075\pi\) |
−0.892534 | + | 0.450979i | \(0.851075\pi\) | |||||||
\(600\) | 619.713 | + | 160.741i | 1.03285 | + | 0.267902i | ||||
\(601\) | −256.922 | − | 790.726i | −0.427491 | − | 1.31568i | −0.900588 | − | 0.434673i | \(-0.856864\pi\) |
0.473097 | − | 0.881010i | \(-0.343136\pi\) | |||||||
\(602\) | 93.2454 | + | 30.2973i | 0.154893 | + | 0.0503277i | ||||
\(603\) | 509.362 | − | 473.629i | 0.844713 | − | 0.785454i | ||||
\(604\) | 214.314 | 0.354824 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 400.178 | − | 329.402i | 0.660361 | − | 0.543567i | ||||
\(607\) | 638.876 | + | 464.171i | 1.05251 | + | 0.764697i | 0.972689 | − | 0.232112i | \(-0.0745636\pi\) |
0.0798256 | + | 0.996809i | \(0.474564\pi\) | |||||||
\(608\) | −290.536 | − | 94.4010i | −0.477856 | − | 0.155265i | ||||
\(609\) | −22.5923 | + | 35.4070i | −0.0370974 | + | 0.0581396i | ||||
\(610\) | −43.3856 | + | 31.5215i | −0.0711239 | + | 0.0516746i | ||||
\(611\) | 742.718 | + | 1022.26i | 1.21558 | + | 1.67310i | ||||
\(612\) | −21.8426 | − | 180.019i | −0.0356905 | − | 0.294149i | ||||
\(613\) | 85.6583 | − | 263.629i | 0.139736 | − | 0.430064i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
0.996297 | + | 0.0859829i | \(0.0274030\pi\) | |||||||
\(614\) | −274.654 | + | 378.029i | −0.447319 | + | 0.615682i | ||||
\(615\) | −109.107 | + | 89.8104i | −0.177411 | + | 0.146033i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 928.547i | − | 1.50494i | −0.658628 | − | 0.752469i | \(-0.728863\pi\) | ||
0.658628 | − | 0.752469i | \(-0.271137\pi\) | |||||||
\(618\) | 16.3294 | + | 270.151i | 0.0264230 | + | 0.437137i | ||||
\(619\) | 295.319 | − | 908.900i | 0.477091 | − | 1.46834i | −0.366025 | − | 0.930605i | \(-0.619282\pi\) |
0.843117 | − | 0.537731i | \(-0.180718\pi\) | |||||||
\(620\) | 3.37493 | − | 1.09658i | 0.00544343 | − | 0.00176868i | ||||
\(621\) | 270.060 | − | 563.083i | 0.434878 | − | 0.906735i | ||||
\(622\) | −635.529 | + | 461.739i | −1.02175 | + | 0.742346i | ||||
\(623\) | 94.7674 | − | 30.7918i | 0.152115 | − | 0.0494250i | ||||
\(624\) | −177.231 | − | 450.871i | −0.284024 | − | 0.722550i | ||||
\(625\) | −476.224 | − | 345.997i | −0.761958 | − | 0.553595i | ||||
\(626\) | 49.7019i | 0.0793961i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −81.7055 | −0.130104 | ||||||||
\(629\) | −601.686 | + | 828.149i | −0.956575 | + | 1.31661i | ||||
\(630\) | 23.7687 | + | 13.2196i | 0.0377280 | + | 0.0209835i | ||||
\(631\) | −1.62527 | − | 5.00208i | −0.00257571 | − | 0.00792722i | 0.949760 | − | 0.312978i | \(-0.101327\pi\) |
−0.952336 | + | 0.305051i | \(0.901327\pi\) | |||||||
\(632\) | 260.603 | + | 358.690i | 0.412347 | + | 0.567547i | ||||
\(633\) | 136.767 | − | 527.285i | 0.216062 | − | 0.832994i | ||||
\(634\) | 81.6132 | + | 251.180i | 0.128728 | + | 0.396183i | ||||
\(635\) | 121.425 | + | 39.4533i | 0.191220 | + | 0.0621311i | ||||
\(636\) | −9.69935 | − | 160.464i | −0.0152506 | − | 0.252302i | ||||
\(637\) | 722.207 | 1.13376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 364.441 | + | 71.3807i | 0.570330 | + | 0.111707i | ||||
\(640\) | 21.8058 | + | 15.8428i | 0.0340715 | + | 0.0247544i | ||||
\(641\) | −462.217 | − | 150.183i | −0.721087 | − | 0.234296i | −0.0745928 | − | 0.997214i | \(-0.523766\pi\) |
−0.646495 | + | 0.762919i | \(0.723766\pi\) | |||||||
\(642\) | 119.124 | + | 76.0103i | 0.185552 | + | 0.118396i | ||||
\(643\) | 597.765 | − | 434.302i | 0.929650 | − | 0.675430i | −0.0162570 | − | 0.999868i | \(-0.505175\pi\) |
0.945907 | + | 0.324437i | \(0.105175\pi\) | |||||||
\(644\) | −44.3570 | − | 61.0522i | −0.0688774 | − | 0.0948016i | ||||
\(645\) | −25.5444 | + | 40.0335i | −0.0396037 | + | 0.0620674i | ||||
\(646\) | −131.489 | + | 404.681i | −0.203543 | + | 0.626441i | ||||
\(647\) | −676.121 | + | 930.601i | −1.04501 | + | 1.43833i | −0.151953 | + | 0.988388i | \(0.548556\pi\) |
−0.893057 | + | 0.449945i | \(0.851444\pi\) | |||||||
\(648\) | −266.040 | + | 653.093i | −0.410556 | + | 1.00786i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 695.717i | 1.07033i | ||||||||
\(651\) | −31.7413 | + | 1.91862i | −0.0487578 | + | 0.00294720i | ||||
\(652\) | −5.96585 | + | 18.3610i | −0.00915007 | + | 0.0281610i | ||||
\(653\) | −575.439 | + | 186.971i | −0.881224 | + | 0.286327i | −0.714465 | − | 0.699671i | \(-0.753330\pi\) |
−0.166758 | + | 0.985998i | \(0.553330\pi\) | |||||||
\(654\) | 198.644 | + | 51.5242i | 0.303736 | + | 0.0787831i | ||||
\(655\) | −47.7572 | + | 34.6976i | −0.0729117 | + | 0.0529735i | ||||
\(656\) | 605.083 | − | 196.603i | 0.922382 | − | 0.299700i | ||||
\(657\) | −446.538 | − | 248.355i | −0.679662 | − | 0.378013i | ||||
\(658\) | 258.378 | + | 187.723i | 0.392672 | + | 0.285293i | ||||
\(659\) | 956.314i | 1.45116i | 0.688138 | + | 0.725580i | \(0.258428\pi\) | ||||
−0.688138 | + | 0.725580i | \(0.741572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 57.8747 | 0.0875563 | 0.0437781 | − | 0.999041i | \(-0.486061\pi\) | ||||
0.0437781 | + | 0.999041i | \(0.486061\pi\) | |||||||
\(662\) | −324.272 | + | 446.323i | −0.489837 | + | 0.674203i | ||||
\(663\) | 770.037 | − | 302.690i | 1.16144 | − | 0.456547i | ||||
\(664\) | 159.295 | + | 490.261i | 0.239903 | + | 0.738345i | ||||
\(665\) | 17.0607 | + | 23.4820i | 0.0256551 | + | 0.0353113i | ||||
\(666\) | 859.845 | − | 399.458i | 1.29106 | − | 0.599786i | ||||
\(667\) | −38.3523 | − | 118.036i | −0.0574997 | − | 0.176966i | ||||
\(668\) | −183.276 | − | 59.5499i | −0.274365 | − | 0.0891466i | ||||
\(669\) | −563.076 | + | 34.0355i | −0.841668 | + | 0.0508751i | ||||
\(670\) | −89.5104 | −0.133598 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 95.4169 | + | 115.919i | 0.141989 | + | 0.172498i | ||||
\(673\) | 688.997 | + | 500.586i | 1.02377 | + | 0.743813i | 0.967052 | − | 0.254578i | \(-0.0819365\pi\) |
0.0567178 | + | 0.998390i | \(0.481936\pi\) | |||||||
\(674\) | 87.3744 | + | 28.3897i | 0.129636 | + | 0.0421212i | ||||
\(675\) | 456.599 | − | 479.095i | 0.676443 | − | 0.709770i | ||||
\(676\) | −125.438 | + | 91.1361i | −0.185559 | + | 0.134817i | ||||
\(677\) | −158.543 | − | 218.215i | −0.234184 | − | 0.322327i | 0.675710 | − | 0.737168i | \(-0.263837\pi\) |
−0.909894 | + | 0.414841i | \(0.863837\pi\) | |||||||
\(678\) | −608.807 | − | 388.465i | −0.897946 | − | 0.572957i | ||||
\(679\) | −13.1359 | + | 40.4282i | −0.0193460 | + | 0.0595408i | ||||
\(680\) | −57.5942 | + | 79.2717i | −0.0846974 | + | 0.116576i | ||||
\(681\) | −818.355 | − | 994.191i | −1.20170 | − | 1.45990i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 254.016i | 0.371913i | 0.982558 | + | 0.185956i | \(0.0595383\pi\) | ||||
−0.982558 | + | 0.185956i | \(0.940462\pi\) | |||||||
\(684\) | −131.265 | + | 122.057i | −0.191908 | + | 0.178445i | ||||
\(685\) | 44.1137 | − | 135.768i | 0.0643996 | − | 0.198201i | ||||
\(686\) | 375.219 | − | 121.916i | 0.546966 | − | 0.177720i | ||||
\(687\) | −102.268 | + | 394.279i | −0.148862 | + | 0.573914i | ||||
\(688\) | 172.968 | − | 125.668i | 0.251407 | − | 0.182658i | ||||
\(689\) | 697.582 | − | 226.658i | 1.01246 | − | 0.328967i | ||||
\(690\) | −74.7965 | + | 29.4014i | −0.108401 | + | 0.0426108i | ||||
\(691\) | 306.290 | + | 222.532i | 0.443256 | + | 0.322044i | 0.786927 | − | 0.617046i | \(-0.211671\pi\) |
−0.343672 | + | 0.939090i | \(0.611671\pi\) | |||||||
\(692\) | 31.3914i | 0.0453634i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −229.724 | −0.331014 | ||||||||
\(695\) | 20.6276 | − | 28.3915i | 0.0296800 | − | 0.0408510i | ||||
\(696\) | 51.2719 | + | 130.435i | 0.0736666 | + | 0.187406i | ||||
\(697\) | 335.776 | + | 1033.41i | 0.481745 | + | 1.48266i | ||||
\(698\) | −220.772 | − | 303.867i | −0.316293 | − | 0.435339i | ||||
\(699\) | 949.256 | + | 246.218i | 1.35802 | + | 0.352243i | ||||
\(700\) | −24.7139 | − | 76.0616i | −0.0353056 | − | 0.108659i | ||||
\(701\) | −304.289 | − | 98.8694i | −0.434078 | − | 0.141040i | 0.0838238 | − | 0.996481i | \(-0.473287\pi\) |
−0.517902 | + | 0.855440i | \(0.673287\pi\) | |||||||
\(702\) | −759.559 | − | 101.654i | −1.08199 | − | 0.144807i | ||||
\(703\) | 1011.82 | 1.43929 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −119.435 | + | 98.3111i | −0.169411 | + | 0.139448i | ||||
\(706\) | 347.361 | + | 252.373i | 0.492013 | + | 0.357468i | ||||
\(707\) | −258.549 | − | 84.0077i | −0.365699 | − | 0.118823i | ||||
\(708\) | 57.9921 | − | 90.8859i | 0.0819097 | − | 0.128370i | ||||
\(709\) | 184.876 | − | 134.320i | 0.260755 | − | 0.189450i | −0.449725 | − | 0.893167i | \(-0.648478\pi\) |
0.710480 | + | 0.703717i | \(0.248478\pi\) | |||||||
\(710\) | −28.0914 | − | 38.6645i | −0.0395653 | − | 0.0544570i | ||||
\(711\) | 454.991 | − | 55.2061i | 0.639931 | − | 0.0776457i | ||||
\(712\) | 102.747 | − | 316.223i | 0.144308 | − | 0.444134i | ||||
\(713\) | 55.2316 | − | 76.0198i | 0.0774636 | − | 0.106620i | ||||
\(714\) | 161.460 | − | 132.904i | 0.226135 | − | 0.186140i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 77.2875i | 0.107943i | ||||||||
\(717\) | −16.9156 | − | 279.848i | −0.0235922 | − | 0.390304i | ||||
\(718\) | 132.730 | − | 408.501i | 0.184861 | − | 0.568943i | ||||
\(719\) | −765.742 | + | 248.805i | −1.06501 | + | 0.346043i | −0.788542 | − | 0.614981i | \(-0.789164\pi\) |
−0.276467 | + | 0.961023i | \(0.589164\pi\) | |||||||
\(720\) | 53.7874 | − | 24.9880i | 0.0747048 | − | 0.0347056i | ||||
\(721\) | 114.842 | − | 83.4376i | 0.159282 | − | 0.115725i | ||||
\(722\) | −169.294 | + | 55.0069i | −0.234479 | + | 0.0761868i | ||||
\(723\) | 226.928 | + | 577.300i | 0.313870 | + | 0.798478i | ||||
\(724\) | 150.138 | + | 109.082i | 0.207373 | + | 0.150665i | ||||
\(725\) | − | 131.530i | − | 0.181420i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1002.31 | −1.37869 | −0.689345 | − | 0.724434i | \(-0.742101\pi\) | ||||
−0.689345 | + | 0.724434i | \(0.742101\pi\) | |||||||
\(728\) | −228.541 | + | 314.560i | −0.313930 | + | 0.432088i | ||||
\(729\) | 456.342 | + | 568.501i | 0.625984 | + | 0.779836i | ||||
\(730\) | 20.3198 | + | 62.5378i | 0.0278353 | + | 0.0856682i | ||||
\(731\) | 214.627 | + | 295.409i | 0.293608 | + | 0.404117i | ||||
\(732\) | −43.6112 | + | 168.136i | −0.0595781 | + | 0.229694i | ||||
\(733\) | 223.915 | + | 689.141i | 0.305478 | + | 0.940165i | 0.979498 | + | 0.201452i | \(0.0645660\pi\) |
−0.674020 | + | 0.738713i | \(0.735434\pi\) | |||||||
\(734\) | 313.472 | + | 101.853i | 0.427074 | + | 0.138765i | ||||
\(735\) | 5.33456 | + | 88.2538i | 0.00725790 | + | 0.120073i | ||||
\(736\) | −443.653 | −0.602789 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 193.442 | − | 987.637i | 0.262117 | − | 1.33826i | ||||
\(739\) | −696.026 | − | 505.693i | −0.941849 | − | 0.684293i | 0.00701624 | − | 0.999975i | \(-0.497767\pi\) |
−0.948865 | + | 0.315682i | \(0.897767\pi\) | |||||||
\(740\) | 52.7774 | + | 17.1484i | 0.0713208 | + | 0.0231735i | ||||
\(741\) | −689.438 | − | 439.913i | −0.930415 | − | 0.593675i | ||||
\(742\) | 149.982 | − | 108.968i | 0.202132 | − | 0.146858i | ||||
\(743\) | −229.421 | − | 315.771i | −0.308776 | − | 0.424994i | 0.626223 | − | 0.779644i | \(-0.284600\pi\) |
−0.934999 | + | 0.354650i | \(0.884600\pi\) | |||||||
\(744\) | −57.0762 | + | 89.4507i | −0.0767154 | + | 0.120229i | ||||
\(745\) | −33.9752 | + | 104.565i | −0.0456043 | + | 0.140355i | ||||
\(746\) | 653.465 | − | 899.418i | 0.875959 | − | 1.20565i | ||||
\(747\) | 522.951 | + | 102.427i | 0.700069 | + | 0.137118i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 74.1164i | − | 0.0989538i | ||||||
\(750\) | −171.726 | + | 10.3801i | −0.228968 | + | 0.0138401i | ||||
\(751\) | −266.909 | + | 821.461i | −0.355405 | + | 1.09382i | 0.600370 | + | 0.799722i | \(0.295020\pi\) |
−0.955774 | + | 0.294101i | \(0.904980\pi\) | |||||||
\(752\) | 662.355 | − | 215.212i | 0.880791 | − | 0.286186i | ||||
\(753\) | −8.10273 | − | 2.10168i | −0.0107606 | − | 0.00279108i | ||||
\(754\) | −123.212 | + | 89.5190i | −0.163412 | + | 0.118725i | ||||
\(755\) | −113.851 | + | 36.9926i | −0.150797 | + | 0.0489968i | ||||
\(756\) | 86.6523 | − | 15.8680i | 0.114619 | − | 0.0209895i | ||||
\(757\) | 683.966 | + | 496.931i | 0.903522 | + | 0.656447i | 0.939368 | − | 0.342910i | \(-0.111413\pi\) |
−0.0358461 | + | 0.999357i | \(0.511413\pi\) | |||||||
\(758\) | − | 650.647i | − | 0.858373i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 96.8528 | 0.127438 | ||||||||
\(761\) | 103.379 | − | 142.289i | 0.135847 | − | 0.186977i | −0.735674 | − | 0.677336i | \(-0.763134\pi\) |
0.871521 | + | 0.490359i | \(0.163134\pi\) | |||||||
\(762\) | −846.213 | + | 332.634i | −1.11052 | + | 0.436528i | ||||
\(763\) | −33.2614 | − | 102.368i | −0.0435929 | − | 0.134165i | ||||
\(764\) | 41.3108 | + | 56.8594i | 0.0540717 | + | 0.0744233i | ||||
\(765\) | 42.6767 | + | 91.8628i | 0.0557865 | + | 0.120082i | ||||
\(766\) | −255.022 | − | 784.878i | −0.332927 | − | 1.02464i | ||||
\(767\) | 467.833 | + | 152.008i | 0.609951 | + | 0.198185i | ||||
\(768\) | 641.387 | − | 38.7690i | 0.835139 | − | 0.0504805i | ||||
\(769\) | −1341.04 | −1.74388 | −0.871941 | − | 0.489611i | \(-0.837139\pi\) | ||||
−0.871941 | + | 0.489611i | \(0.837139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 763.025 | + | 926.972i | 0.989657 | + | 1.20230i | ||||
\(772\) | 152.736 | + | 110.969i | 0.197844 | + | 0.143742i | ||||
\(773\) | 746.230 | + | 242.465i | 0.965368 | + | 0.313667i | 0.748945 | − | 0.662632i | \(-0.230561\pi\) |
0.216424 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(774\) | −40.7363 | − | 335.736i | −0.0526309 | − | 0.433767i | ||||
\(775\) | 80.5641 | − | 58.5332i | 0.103954 | − | 0.0755268i | ||||
\(776\) | 83.3742 | + | 114.755i | 0.107441 | + | 0.147880i | ||||
\(777\) | −419.210 | − | 267.488i | −0.539524 | − | 0.344257i | ||||
\(778\) | −211.252 | + | 650.167i | −0.271532 | + | 0.835690i | ||||
\(779\) | 631.303 | − | 868.914i | 0.810402 | − | 1.11542i | ||||
\(780\) | −28.5060 | − | 34.6309i | −0.0365461 | − | 0.0443986i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 617.954i | 0.790222i | ||||||||
\(783\) | 143.599 | + | 19.2184i | 0.183396 | + | 0.0245446i | ||||
\(784\) | 123.005 | − | 378.571i | 0.156894 | − | 0.482871i | ||||
\(785\) | 43.4051 | − | 14.1032i | 0.0552931 | − | 0.0179658i | ||||
\(786\) | 105.550 | − | 406.932i | 0.134287 | − | 0.517725i | ||||
\(787\) | −1171.82 | + | 851.375i | −1.48897 | + | 1.08180i | −0.514442 | + | 0.857525i | \(0.672001\pi\) |
−0.974526 | + | 0.224273i | \(0.927999\pi\) | |||||||
\(788\) | −26.5659 | + | 8.63178i | −0.0337130 | + | 0.0109540i | ||||
\(789\) | 1058.77 | − | 416.189i | 1.34192 | − | 0.527489i | ||||
\(790\) | −47.7184 | − | 34.6695i | −0.0604031 | − | 0.0438854i | ||||
\(791\) | 378.785i | 0.478869i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −792.536 | −0.999415 | ||||||||
\(794\) | −166.888 | + | 229.702i | −0.210186 | + | 0.289297i | ||||
\(795\) | 32.8503 | + | 83.5704i | 0.0413211 | + | 0.105120i | ||||
\(796\) | −58.3237 | − | 179.502i | −0.0732709 | − | 0.225505i | ||||
\(797\) | −203.605 | − | 280.238i | −0.255464 | − | 0.351616i | 0.661951 | − | 0.749547i | \(-0.269728\pi\) |
−0.917416 | + | 0.397931i | \(0.869728\pi\) | |||||||
\(798\) | −200.086 | − | 51.8984i | −0.250735 | − | 0.0650355i | ||||
\(799\) | 367.558 | + | 1131.23i | 0.460022 | + | 1.41580i | ||||
\(800\) | −447.162 | − | 145.292i | −0.558952 | − | 0.181615i | ||||
\(801\) | −234.056 | − | 251.714i | −0.292205 | − | 0.314250i | ||||
\(802\) | 1203.85 | 1.50107 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −223.845 | + | 184.255i | −0.278414 | + | 0.229173i | ||||
\(805\) | 34.1023 | + | 24.7768i | 0.0423631 | + | 0.0307786i | ||||
\(806\) | −109.664 | − | 35.6318i | −0.136059 | − | 0.0442082i | ||||
\(807\) | −50.3488 | + | 78.9074i | −0.0623901 | + | 0.0977787i | ||||
\(808\) | −733.888 | + | 533.201i | −0.908277 | + | 0.659902i | ||||
\(809\) | −307.526 | − | 423.274i | −0.380131 | − | 0.523206i | 0.575488 | − | 0.817810i | \(-0.304812\pi\) |
−0.955619 | + | 0.294604i | \(0.904812\pi\) | |||||||
\(810\) | 6.81172 | − | 93.5690i | 0.00840954 | − | 0.115517i | ||||
\(811\) | 319.359 | − | 982.886i | 0.393784 | − | 1.21194i | −0.536120 | − | 0.844142i | \(-0.680111\pi\) |
0.929904 | − | 0.367802i | \(-0.119889\pi\) | |||||||
\(812\) | 10.2906 | − | 14.1638i | 0.0126732 | − | 0.0174431i | ||||
\(813\) | −1200.06 | + | 987.811i | −1.47608 | + | 1.21502i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 10.7838i | − | 0.0132317i | ||||||
\(816\) | −27.5146 | − | 455.196i | −0.0337189 | − | 0.557839i | ||||
\(817\) | 111.532 | − | 343.261i | 0.136514 | − | 0.420148i | ||||
\(818\) | −475.294 | + | 154.432i | −0.581044 | + | 0.188793i | ||||
\(819\) | 169.346 | + | 364.524i | 0.206772 | + | 0.445084i | ||||
\(820\) | 47.6558 | − | 34.6239i | 0.0581168 | − | 0.0422243i | ||||
\(821\) | −92.9928 | + | 30.2152i | −0.113268 | + | 0.0368029i | −0.365102 | − | 0.930967i | \(-0.618966\pi\) |
0.251835 | + | 0.967770i | \(0.418966\pi\) | |||||||
\(822\) | 371.927 | + | 946.172i | 0.452465 | + | 1.15106i | ||||
\(823\) | −583.839 | − | 424.184i | −0.709404 | − | 0.515412i | 0.173578 | − | 0.984820i | \(-0.444467\pi\) |
−0.882981 | + | 0.469408i | \(0.844467\pi\) | |||||||
\(824\) | − | 473.673i | − | 0.574846i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 124.330 | 0.150521 | ||||||||
\(827\) | 722.545 | − | 994.498i | 0.873694 | − | 1.20254i | −0.104433 | − | 0.994532i | \(-0.533303\pi\) |
0.978128 | − | 0.208005i | \(-0.0666971\pi\) | |||||||
\(828\) | −126.527 | + | 227.493i | −0.152810 | + | 0.274750i | ||||
\(829\) | −59.7651 | − | 183.938i | −0.0720930 | − | 0.221879i | 0.908517 | − | 0.417847i | \(-0.137215\pi\) |
−0.980610 | + | 0.195968i | \(0.937215\pi\) | |||||||
\(830\) | −40.3095 | − | 55.4812i | −0.0485656 | − | 0.0668448i | ||||
\(831\) | 277.151 | − | 1068.51i | 0.333515 | − | 1.28582i | ||||
\(832\) | 367.840 | + | 1132.09i | 0.442115 | + | 1.36069i | ||||
\(833\) | 646.556 | + | 210.079i | 0.776178 | + | 0.252195i | ||||
\(834\) | 15.0793 | + | 249.469i | 0.0180807 | + | 0.299124i | ||||
\(835\) | 107.642 | 0.128912 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.1329 | + | 96.5094i | 0.0622854 | + | 0.115304i | ||||
\(838\) | −768.930 | − | 558.660i | −0.917577 | − | 0.666659i | ||||
\(839\) | 554.741 | + | 180.246i | 0.661193 | + | 0.214835i | 0.620343 | − | 0.784331i | \(-0.286993\pi\) |
0.0408501 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(840\) | −40.1274 | − | 25.6043i | −0.0477707 | − | 0.0304813i | ||||
\(841\) | −657.089 | + | 477.403i | −0.781319 | + | 0.567661i | ||||
\(842\) | −545.099 | − | 750.264i | −0.647386 | − | 0.891050i | ||||
\(843\) | 517.019 | − | 810.279i | 0.613308 | − | 0.961185i | ||||
\(844\) | −70.1668 | + | 215.951i | −0.0831360 | + | 0.255866i | ||||
\(845\) | 50.9064 | − | 70.0667i | 0.0602443 | − | 0.0829192i | ||||
\(846\) | 211.752 | − | 1081.12i | 0.250297 | − | 1.27792i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 404.267i | − | 0.476730i | ||||||
\(849\) | −481.506 | + | 29.1049i | −0.567144 | + | 0.0342814i | ||||
\(850\) | −202.373 | + | 622.841i | −0.238086 | + | 0.732754i | ||||
\(851\) | 1397.52 | − | 454.082i | 1.64221 | − | 0.533587i | ||||
\(852\) | −149.840 | − | 38.8655i | −0.175869 | − | 0.0456168i | ||||
\(853\) | −348.868 | + | 253.468i | −0.408990 | + | 0.297148i | −0.773193 | − | 0.634171i | \(-0.781341\pi\) |
0.364203 | + | 0.931320i | \(0.381341\pi\) | |||||||
\(854\) | −190.510 | + | 61.9005i | −0.223080 | + | 0.0724830i | ||||
\(855\) | 48.6649 | − | 87.4988i | 0.0569180 | − | 0.102338i | ||||
\(856\) | −200.082 | − | 145.368i | −0.233740 | − | 0.169822i | ||||
\(857\) | 580.461i | 0.677317i | 0.940909 | + | 0.338659i | \(0.109973\pi\) | ||||
−0.940909 | + | 0.338659i | \(0.890027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −812.241 | −0.945566 | −0.472783 | − | 0.881179i | \(-0.656751\pi\) | ||||
−0.472783 | + | 0.881179i | \(0.656751\pi\) | |||||||
\(860\) | 11.6352 | − | 16.0145i | 0.0135294 | − | 0.0186216i | ||||
\(861\) | −491.266 | + | 193.110i | −0.570576 | + | 0.224285i | ||||
\(862\) | 102.402 | + | 315.160i | 0.118795 | + | 0.365614i | ||||
\(863\) | 369.257 | + | 508.239i | 0.427876 | + | 0.588921i | 0.967464 | − | 0.253008i | \(-0.0814199\pi\) |
−0.539588 | + | 0.841929i | \(0.681420\pi\) | |||||||
\(864\) | 223.961 | − | 466.965i | 0.259214 | − | 0.540469i | ||||
\(865\) | −5.41846 | − | 16.6763i | −0.00626412 | − | 0.0192790i | ||||
\(866\) | 163.198 | + | 53.0264i | 0.188451 | + | 0.0612314i | ||||
\(867\) | −87.9967 | + | 5.31902i | −0.101496 | + | 0.00613497i | ||||
\(868\) | 13.2551 | 0.0152708 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −11.8493 | − | 14.3953i | −0.0136199 | − | 0.0165464i | ||||
\(871\) | −1070.19 | − | 777.542i | −1.22870 | − | 0.892700i | ||||
\(872\) | −341.586 | − | 110.988i | −0.391727 | − | 0.127280i | ||||
\(873\) | 145.564 | − | 17.6619i | 0.166740 | − | 0.0202313i | ||||
\(874\) | 494.158 | − | 359.026i | 0.565398 | − | 0.410785i | ||||
\(875\) | 53.0385 | + | 73.0012i | 0.0606154 | + | 0.0834299i | ||||
\(876\) | 179.548 | + | 114.565i | 0.204963 | + | 0.130782i | ||||
\(877\) | −371.068 | + | 1142.03i | −0.423111 | + | 1.30220i | 0.481680 | + | 0.876347i | \(0.340027\pi\) |
−0.904791 | + | 0.425855i | \(0.859973\pi\) | |||||||
\(878\) | −645.749 | + | 888.797i | −0.735477 | + | 1.01230i | ||||
\(879\) | 554.704 | + | 673.891i | 0.631063 | + | 0.766656i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 131.219i | 0.148943i | 0.997223 | + | 0.0744714i | \(0.0237269\pi\) | ||||
−0.997223 | + | 0.0744714i | \(0.976273\pi\) | |||||||
\(882\) | −428.767 | − | 461.116i | −0.486131 | − | 0.522807i | ||||
\(883\) | −39.2451 | + | 120.784i | −0.0444452 | + | 0.136788i | −0.970817 | − | 0.239823i | \(-0.922911\pi\) |
0.926371 | + | 0.376611i | \(0.122911\pi\) | |||||||
\(884\) | −328.007 | + | 106.576i | −0.371048 | + | 0.120561i | ||||
\(885\) | −15.1198 | + | 58.2920i | −0.0170845 | + | 0.0658667i | ||||
\(886\) | 282.823 | − | 205.483i | 0.319214 | − | 0.231922i | ||||
\(887\) | −1136.31 | + | 369.209i | −1.28107 | + | 0.416245i | −0.868957 | − | 0.494888i | \(-0.835209\pi\) |
−0.412113 | + | 0.911133i | \(0.635209\pi\) | |||||||
\(888\) | −1544.31 | + | 607.047i | −1.73909 | + | 0.683612i | ||||
\(889\) | 385.818 | + | 280.313i | 0.433991 | + | 0.315313i | ||||
\(890\) | 44.2339i | 0.0497010i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 235.138 | 0.263608 | ||||||||
\(893\) | 691.057 | − | 951.158i | 0.773860 | − | 1.06513i | ||||
\(894\) | −286.448 | − | 728.716i | −0.320411 | − | 0.815119i | ||||
\(895\) | −13.3406 | − | 41.0580i | −0.0149057 | − | 0.0458749i | ||||
\(896\) | 59.1774 | + | 81.4507i | 0.0660462 | + | 0.0909048i | ||||
\(897\) | −1149.67 | − | 298.202i | −1.28169 | − | 0.332443i | ||||
\(898\) | 122.602 | + | 377.331i | 0.136528 | + | 0.420190i | ||||
\(899\) | 20.7326 | + | 6.73643i | 0.0230618 | + | 0.00749325i | ||||
\(900\) | −202.029 | + | 187.856i | −0.224477 | + | 0.208729i | ||||
\(901\) | 690.442 | 0.766306 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −136.955 | + | 112.733i | −0.151667 | + | 0.124842i | ||||
\(904\) | 1022.55 | + | 742.929i | 1.13114 | + | 0.821824i | ||||
\(905\) | −98.5876 | − | 32.0331i | −0.108937 | − | 0.0353956i | ||||
\(906\) | 458.579 | − | 718.692i | 0.506158 | − | 0.793258i | ||||
\(907\) | −424.397 | + | 308.342i | −0.467913 | + | 0.339958i | −0.796627 | − | 0.604471i | \(-0.793385\pi\) |
0.328715 | + | 0.944429i | \(0.393385\pi\) | |||||||
\(908\) | 315.494 | + | 434.241i | 0.347461 | + | 0.478239i | ||||
\(909\) | 112.953 | + | 930.922i | 0.124261 | + | 1.02412i | ||||
\(910\) | 15.9844 | − | 49.1949i | 0.0175653 | − | 0.0540603i | ||||
\(911\) | 103.220 | − | 142.070i | 0.113304 | − | 0.155950i | −0.748598 | − | 0.663024i | \(-0.769273\pi\) |
0.861903 | + | 0.507074i | \(0.169273\pi\) | |||||||
\(912\) | −348.020 | + | 286.468i | −0.381601 | + | 0.314110i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 44.2524i | 0.0484162i | ||||||||
\(915\) | −5.85404 | − | 96.8481i | −0.00639786 | − | 0.105845i | ||||
\(916\) | 52.4674 | − | 161.478i | 0.0572788 | − | 0.176286i | ||||
\(917\) | −209.706 | + | 68.1377i | −0.228687 | + | 0.0743050i | ||||
\(918\) | −650.425 | − | 311.950i | −0.708524 | − | 0.339815i | ||||
\(919\) | −1055.86 | + | 767.124i | −1.14892 | + | 0.834738i | −0.988337 | − | 0.152285i | \(-0.951337\pi\) |
−0.160581 | + | 0.987023i | \(0.551337\pi\) | |||||||
\(920\) | 133.773 | − | 43.4654i | 0.145405 | − | 0.0472450i | ||||
\(921\) | −309.278 | − | 786.796i | −0.335807 | − | 0.854284i | ||||
\(922\) | 527.369 | + | 383.156i | 0.571984 | + | 0.415571i | ||||
\(923\) | − | 706.294i | − | 0.765216i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1557.28 | 1.68355 | ||||||||
\(926\) | −104.242 | + | 143.476i | −0.112572 | + | 0.154942i | ||||
\(927\) | −427.925 | − | 238.003i | −0.461624 | − | 0.256745i | ||||
\(928\) | −31.8056 | − | 97.8877i | −0.0342733 | − | 0.105482i | ||||
\(929\) | −916.652 | − | 1261.66i | −0.986708 | − | 1.35809i | −0.933136 | − | 0.359524i | \(-0.882939\pi\) |
−0.0535724 | − | 0.998564i | \(-0.517061\pi\) | |||||||
\(930\) | 3.54419 | − | 13.6641i | 0.00381096 | − | 0.0146926i | ||||
\(931\) | −207.651 | − | 639.084i | −0.223041 | − | 0.686449i | ||||
\(932\) | −388.770 | − | 126.319i | −0.417136 | − | 0.135536i | ||||
\(933\) | −85.7523 | − | 1418.67i | −0.0919102 | − | 1.52054i | ||||
\(934\) | 701.251 | 0.750804 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1316.20 | + | 257.795i | 1.40620 | + | 0.275422i | ||||
\(937\) | −581.968 | − | 422.824i | −0.621097 | − | 0.451253i | 0.232208 | − | 0.972666i | \(-0.425405\pi\) |
−0.853305 | + | 0.521413i | \(0.825405\pi\) | |||||||
\(938\) | −317.983 | − | 103.319i | −0.339001 | − | 0.110148i | ||||
\(939\) | −75.8053 | − | 48.3695i | −0.0807298 | − | 0.0515117i | ||||
\(940\) | 52.1664 | − | 37.9011i | 0.0554962 | − | 0.0403204i | ||||
\(941\) | 689.641 | + | 949.209i | 0.732881 | + | 1.00872i | 0.998997 | + | 0.0447831i | \(0.0142597\pi\) |
−0.266116 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(942\) | −174.830 | + | 273.996i | −0.185595 | + | 0.290866i | ||||
\(943\) | 482.004 | − | 1483.46i | 0.511139 | − | 1.57312i | ||||
\(944\) | 159.361 | − | 219.342i | 0.168815 | − | 0.232353i | ||||
\(945\) | −43.2940 | + | 23.3867i | −0.0458137 | + | 0.0247478i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 266.119i | − | 0.281013i | −0.990080 | − | 0.140506i | \(-0.955127\pi\) | ||
0.990080 | − | 0.140506i | \(-0.0448730\pi\) | |||||||
\(948\) | −190.699 | + | 11.5269i | −0.201160 | + | 0.0121592i | ||||
\(949\) | −300.296 | + | 924.216i | −0.316434 | + | 0.973884i | ||||
\(950\) | 615.643 | − | 200.035i | 0.648046 | − | 0.210563i | ||||
\(951\) | −462.524 | − | 119.969i | −0.486356 | − | 0.126151i | ||||
\(952\) | −296.102 | + | 215.131i | −0.311032 | + | 0.225978i | ||||
\(953\) | −121.881 | + | 39.6016i | −0.127892 | + | 0.0415547i | −0.372264 | − | 0.928127i | \(-0.621418\pi\) |
0.244372 | + | 0.969682i | \(0.421418\pi\) | |||||||
\(954\) | −558.864 | − | 310.828i | −0.585811 | − | 0.325816i | ||||
\(955\) | −31.7603 | − | 23.0752i | −0.0332569 | − | 0.0241625i | ||||
\(956\) | 116.864i | 0.122242i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 894.933 | 0.934168 | ||||||||
\(959\) | 313.425 | − | 431.393i | 0.326825 | − | 0.449836i | ||||
\(960\) | −135.625 | + | 53.3122i | −0.141276 | + | 0.0555336i | ||||
\(961\) | −291.865 | − | 898.268i | −0.303710 | − | 0.934723i | ||||
\(962\) | −1059.88 | − | 1458.80i | −1.10175 | − | 1.51643i | ||||
\(963\) | −231.862 | + | 107.716i | −0.240770 | + | 0.111854i | ||||
\(964\) | −79.9003 | − | 245.908i | −0.0828841 | − | 0.255091i | ||||
\(965\) | −100.293 | − | 32.5872i | −0.103931 | − | 0.0337692i | ||||
\(966\) | −299.649 | + | 18.1125i | −0.310196 | + | 0.0187500i | ||||
\(967\) | −1324.17 | −1.36936 | −0.684682 | − | 0.728842i | \(-0.740059\pi\) | ||||
−0.684682 | + | 0.728842i | \(0.740059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −489.255 | − | 594.379i | −0.504907 | − | 0.613394i | ||||
\(970\) | −15.2664 | − | 11.0917i | −0.0157386 | − | 0.0114348i | ||||
\(971\) | 556.252 | + | 180.737i | 0.572865 | + | 0.186135i | 0.581102 | − | 0.813831i | \(-0.302622\pi\) |
−0.00823681 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(972\) | −175.575 | − | 248.017i | −0.180633 | − | 0.255161i | ||||
\(973\) | 106.050 | − | 77.0500i | 0.108993 | − | 0.0791881i | ||||
\(974\) | 595.161 | + | 819.169i | 0.611048 | + | 0.841036i | ||||
\(975\) | −1061.11 | − | 677.066i | −1.08831 | − | 0.694427i | ||||
\(976\) | −134.984 | + | 415.437i | −0.138303 | + | 0.425652i | ||||
\(977\) | −406.363 | + | 559.311i | −0.415930 | + | 0.572478i | −0.964652 | − | 0.263526i | \(-0.915114\pi\) |
0.548722 | + | 0.836005i | \(0.315114\pi\) | |||||||
\(978\) | 48.8073 | + | 59.2943i | 0.0499052 | + | 0.0606281i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 36.8545i | − | 0.0376066i | ||||||
\(981\) | −271.903 | + | 252.828i | −0.277169 | + | 0.257725i | ||||
\(982\) | 29.1423 | − | 89.6907i | 0.0296764 | − | 0.0913347i | ||||
\(983\) | −623.407 | + | 202.557i | −0.634188 | + | 0.206060i | −0.608430 | − | 0.793608i | \(-0.708200\pi\) |
−0.0257588 | + | 0.999668i | \(0.508200\pi\) | |||||||
\(984\) | −442.231 | + | 1704.96i | −0.449422 | + | 1.73268i | ||||
\(985\) | 12.6229 | − | 9.17105i | 0.0128151 | − | 0.00931071i | ||||
\(986\) | −136.346 | + | 44.3013i | −0.138281 | + | 0.0449304i | ||||
\(987\) | −537.765 | + | 211.388i | −0.544848 | + | 0.214172i | ||||
\(988\) | 275.795 | + | 200.377i | 0.279144 | + | 0.202810i | ||||
\(989\) | − | 524.164i | − | 0.529994i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 95.0559 | 0.0959192 | 0.0479596 | − | 0.998849i | \(-0.484728\pi\) | ||||
0.0479596 | + | 0.998849i | \(0.484728\pi\) | |||||||
\(992\) | 45.8036 | − | 63.0433i | 0.0461730 | − | 0.0635517i | ||||
\(993\) | −365.151 | − | 928.937i | −0.367726 | − | 0.935485i | ||||
\(994\) | −55.1646 | − | 169.779i | −0.0554976 | − | 0.170804i | ||||
\(995\) | 61.9675 | + | 85.2909i | 0.0622789 | + | 0.0857195i | ||||
\(996\) | −215.012 | − | 55.7697i | −0.215875 | − | 0.0559937i | ||||
\(997\) | 241.467 | + | 743.158i | 0.242193 | + | 0.745394i | 0.996085 | + | 0.0883960i | \(0.0281741\pi\) |
−0.753892 | + | 0.656998i | \(0.771826\pi\) | |||||||
\(998\) | −739.422 | − | 240.253i | −0.740904 | − | 0.240734i | ||||
\(999\) | −227.541 | + | 1700.18i | −0.227769 | + | 1.70188i |
(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 | 363.3.h.j.323.2 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.j.323.3 | 16 | ||
11.2 | odd | 10 | 363.3.h.o.269.2 | 16 | |||
11.3 | even | 5 | inner | 363.3.h.j.245.3 | 16 | ||
11.4 | even | 5 | 363.3.h.n.251.2 | 16 | |||
11.5 | even | 5 | 363.3.b.l.122.4 | 8 | |||
11.6 | odd | 10 | 363.3.b.m.122.5 | 8 | |||
11.7 | odd | 10 | 363.3.h.o.251.3 | 16 | |||
11.8 | odd | 10 | 33.3.h.b.14.2 | ✓ | 16 | ||
11.9 | even | 5 | 363.3.h.n.269.3 | 16 | |||
11.10 | odd | 2 | 33.3.h.b.26.3 | yes | 16 | ||
33.2 | even | 10 | 363.3.h.o.269.3 | 16 | |||
33.5 | odd | 10 | 363.3.b.l.122.5 | 8 | |||
33.8 | even | 10 | 33.3.h.b.14.3 | yes | 16 | ||
33.14 | odd | 10 | inner | 363.3.h.j.245.2 | 16 | ||
33.17 | even | 10 | 363.3.b.m.122.4 | 8 | |||
33.20 | odd | 10 | 363.3.h.n.269.2 | 16 | |||
33.26 | odd | 10 | 363.3.h.n.251.3 | 16 | |||
33.29 | even | 10 | 363.3.h.o.251.2 | 16 | |||
33.32 | even | 2 | 33.3.h.b.26.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.h.b.14.2 | ✓ | 16 | 11.8 | odd | 10 | ||
33.3.h.b.14.3 | yes | 16 | 33.8 | even | 10 | ||
33.3.h.b.26.2 | yes | 16 | 33.32 | even | 2 | ||
33.3.h.b.26.3 | yes | 16 | 11.10 | odd | 2 | ||
363.3.b.l.122.4 | 8 | 11.5 | even | 5 | |||
363.3.b.l.122.5 | 8 | 33.5 | odd | 10 | |||
363.3.b.m.122.4 | 8 | 33.17 | even | 10 | |||
363.3.b.m.122.5 | 8 | 11.6 | odd | 10 | |||
363.3.h.j.245.2 | 16 | 33.14 | odd | 10 | inner | ||
363.3.h.j.245.3 | 16 | 11.3 | even | 5 | inner | ||
363.3.h.j.323.2 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.j.323.3 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.n.251.2 | 16 | 11.4 | even | 5 | |||
363.3.h.n.251.3 | 16 | 33.26 | odd | 10 | |||
363.3.h.n.269.2 | 16 | 33.20 | odd | 10 | |||
363.3.h.n.269.3 | 16 | 11.9 | even | 5 | |||
363.3.h.o.251.2 | 16 | 33.29 | even | 10 | |||
363.3.h.o.251.3 | 16 | 11.7 | odd | 10 | |||
363.3.h.o.269.2 | 16 | 11.2 | odd | 10 | |||
363.3.h.o.269.3 | 16 | 33.2 | even | 10 |