Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
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: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(95\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.80236 | −1.61794 | −0.808972 | − | 0.587847i | \(-0.799976\pi\) | ||||
−0.808972 | + | 0.587847i | \(0.799976\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73987 | 0.778095 | 0.389047 | − | 0.921218i | \(-0.372804\pi\) | ||||
0.389047 | + | 0.921218i | \(0.372804\pi\) | |||||||
\(6\) | −2.80236 | −1.14406 | ||||||||
\(7\) | −0.386891 | −0.146231 | −0.0731155 | − | 0.997323i | \(-0.523294\pi\) | ||||
−0.0731155 | + | 0.997323i | \(0.523294\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.85324 | 1.61775 | ||||||||
\(10\) | 1.73987 | 0.550196 | ||||||||
\(11\) | −4.11288 | −1.24008 | −0.620040 | − | 0.784570i | \(-0.712884\pi\) | ||||
−0.620040 | + | 0.784570i | \(0.712884\pi\) | |||||||
\(12\) | −2.80236 | −0.808972 | ||||||||
\(13\) | 1.80933 | 0.501817 | 0.250909 | − | 0.968011i | \(-0.419271\pi\) | ||||
0.250909 | + | 0.968011i | \(0.419271\pi\) | |||||||
\(14\) | −0.386891 | −0.103401 | ||||||||
\(15\) | −4.87575 | −1.25891 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.50517 | 0.850129 | 0.425064 | − | 0.905163i | \(-0.360251\pi\) | ||||
0.425064 | + | 0.905163i | \(0.360251\pi\) | |||||||
\(18\) | 4.85324 | 1.14392 | ||||||||
\(19\) | −5.80916 | −1.33271 | −0.666357 | − | 0.745633i | \(-0.732147\pi\) | ||||
−0.666357 | + | 0.745633i | \(0.732147\pi\) | |||||||
\(20\) | 1.73987 | 0.389047 | ||||||||
\(21\) | 1.08421 | 0.236594 | ||||||||
\(22\) | −4.11288 | −0.876870 | ||||||||
\(23\) | −1.15032 | −0.239859 | −0.119929 | − | 0.992782i | \(-0.538267\pi\) | ||||
−0.119929 | + | 0.992782i | \(0.538267\pi\) | |||||||
\(24\) | −2.80236 | −0.572030 | ||||||||
\(25\) | −1.97284 | −0.394569 | ||||||||
\(26\) | 1.80933 | 0.354838 | ||||||||
\(27\) | −5.19344 | −0.999479 | ||||||||
\(28\) | −0.386891 | −0.0731155 | ||||||||
\(29\) | −1.45658 | −0.270481 | −0.135240 | − | 0.990813i | \(-0.543181\pi\) | ||||
−0.135240 | + | 0.990813i | \(0.543181\pi\) | |||||||
\(30\) | −4.87575 | −0.890187 | ||||||||
\(31\) | −3.46348 | −0.622059 | −0.311030 | − | 0.950400i | \(-0.600674\pi\) | ||||
−0.311030 | + | 0.950400i | \(0.600674\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.5258 | 2.00638 | ||||||||
\(34\) | 3.50517 | 0.601132 | ||||||||
\(35\) | −0.673141 | −0.113782 | ||||||||
\(36\) | 4.85324 | 0.808873 | ||||||||
\(37\) | 3.24261 | 0.533082 | 0.266541 | − | 0.963824i | \(-0.414119\pi\) | ||||
0.266541 | + | 0.963824i | \(0.414119\pi\) | |||||||
\(38\) | −5.80916 | −0.942371 | ||||||||
\(39\) | −5.07039 | −0.811912 | ||||||||
\(40\) | 1.73987 | 0.275098 | ||||||||
\(41\) | 9.43456 | 1.47343 | 0.736715 | − | 0.676203i | \(-0.236376\pi\) | ||||
0.736715 | + | 0.676203i | \(0.236376\pi\) | |||||||
\(42\) | 1.08421 | 0.167297 | ||||||||
\(43\) | 7.39336 | 1.12748 | 0.563739 | − | 0.825953i | \(-0.309363\pi\) | ||||
0.563739 | + | 0.825953i | \(0.309363\pi\) | |||||||
\(44\) | −4.11288 | −0.620040 | ||||||||
\(45\) | 8.44402 | 1.25876 | ||||||||
\(46\) | −1.15032 | −0.169606 | ||||||||
\(47\) | −7.80327 | −1.13822 | −0.569112 | − | 0.822260i | \(-0.692713\pi\) | ||||
−0.569112 | + | 0.822260i | \(0.692713\pi\) | |||||||
\(48\) | −2.80236 | −0.404486 | ||||||||
\(49\) | −6.85032 | −0.978616 | ||||||||
\(50\) | −1.97284 | −0.279002 | ||||||||
\(51\) | −9.82276 | −1.37546 | ||||||||
\(52\) | 1.80933 | 0.250909 | ||||||||
\(53\) | −0.0764819 | −0.0105056 | −0.00525280 | − | 0.999986i | \(-0.501672\pi\) | ||||
−0.00525280 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(54\) | −5.19344 | −0.706738 | ||||||||
\(55\) | −7.15589 | −0.964900 | ||||||||
\(56\) | −0.386891 | −0.0517005 | ||||||||
\(57\) | 16.2794 | 2.15626 | ||||||||
\(58\) | −1.45658 | −0.191259 | ||||||||
\(59\) | 14.6403 | 1.90601 | 0.953004 | − | 0.302956i | \(-0.0979737\pi\) | ||||
0.953004 | + | 0.302956i | \(0.0979737\pi\) | |||||||
\(60\) | −4.87575 | −0.629457 | ||||||||
\(61\) | 2.69798 | 0.345441 | 0.172720 | − | 0.984971i | \(-0.444744\pi\) | ||||
0.172720 | + | 0.984971i | \(0.444744\pi\) | |||||||
\(62\) | −3.46348 | −0.439862 | ||||||||
\(63\) | −1.87767 | −0.236565 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.14800 | 0.390461 | ||||||||
\(66\) | 11.5258 | 1.41873 | ||||||||
\(67\) | 2.31609 | 0.282955 | 0.141477 | − | 0.989941i | \(-0.454815\pi\) | ||||
0.141477 | + | 0.989941i | \(0.454815\pi\) | |||||||
\(68\) | 3.50517 | 0.425064 | ||||||||
\(69\) | 3.22362 | 0.388078 | ||||||||
\(70\) | −0.673141 | −0.0804557 | ||||||||
\(71\) | 9.43413 | 1.11963 | 0.559813 | − | 0.828619i | \(-0.310873\pi\) | ||||
0.559813 | + | 0.828619i | \(0.310873\pi\) | |||||||
\(72\) | 4.85324 | 0.571960 | ||||||||
\(73\) | 2.25900 | 0.264396 | 0.132198 | − | 0.991223i | \(-0.457797\pi\) | ||||
0.132198 | + | 0.991223i | \(0.457797\pi\) | |||||||
\(74\) | 3.24261 | 0.376946 | ||||||||
\(75\) | 5.52862 | 0.638390 | ||||||||
\(76\) | −5.80916 | −0.666357 | ||||||||
\(77\) | 1.59124 | 0.181338 | ||||||||
\(78\) | −5.07039 | −0.574109 | ||||||||
\(79\) | 4.01325 | 0.451526 | 0.225763 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225763 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(80\) | 1.73987 | 0.194524 | ||||||||
\(81\) | −0.00579824 | −0.000644249 0 | ||||||||
\(82\) | 9.43456 | 1.04187 | ||||||||
\(83\) | −14.2396 | −1.56299 | −0.781497 | − | 0.623909i | \(-0.785544\pi\) | ||||
−0.781497 | + | 0.623909i | \(0.785544\pi\) | |||||||
\(84\) | 1.08421 | 0.118297 | ||||||||
\(85\) | 6.09855 | 0.661481 | ||||||||
\(86\) | 7.39336 | 0.797247 | ||||||||
\(87\) | 4.08187 | 0.437623 | ||||||||
\(88\) | −4.11288 | −0.438435 | ||||||||
\(89\) | 2.19901 | 0.233095 | 0.116547 | − | 0.993185i | \(-0.462817\pi\) | ||||
0.116547 | + | 0.993185i | \(0.462817\pi\) | |||||||
\(90\) | 8.44402 | 0.890077 | ||||||||
\(91\) | −0.700012 | −0.0733812 | ||||||||
\(92\) | −1.15032 | −0.119929 | ||||||||
\(93\) | 9.70593 | 1.00646 | ||||||||
\(94\) | −7.80327 | −0.804846 | ||||||||
\(95\) | −10.1072 | −1.03698 | ||||||||
\(96\) | −2.80236 | −0.286015 | ||||||||
\(97\) | −9.19795 | −0.933911 | −0.466955 | − | 0.884281i | \(-0.654649\pi\) | ||||
−0.466955 | + | 0.884281i | \(0.654649\pi\) | |||||||
\(98\) | −6.85032 | −0.691986 | ||||||||
\(99\) | −19.9608 | −2.00614 | ||||||||
\(100\) | −1.97284 | −0.197284 | ||||||||
\(101\) | 13.2816 | 1.32157 | 0.660784 | − | 0.750576i | \(-0.270224\pi\) | ||||
0.660784 | + | 0.750576i | \(0.270224\pi\) | |||||||
\(102\) | −9.82276 | −0.972598 | ||||||||
\(103\) | 3.02225 | 0.297791 | 0.148896 | − | 0.988853i | \(-0.452428\pi\) | ||||
0.148896 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(104\) | 1.80933 | 0.177419 | ||||||||
\(105\) | 1.88639 | 0.184092 | ||||||||
\(106\) | −0.0764819 | −0.00742858 | ||||||||
\(107\) | −10.5944 | −1.02420 | −0.512102 | − | 0.858925i | \(-0.671133\pi\) | ||||
−0.512102 | + | 0.858925i | \(0.671133\pi\) | |||||||
\(108\) | −5.19344 | −0.499739 | ||||||||
\(109\) | 11.8288 | 1.13299 | 0.566497 | − | 0.824064i | \(-0.308298\pi\) | ||||
0.566497 | + | 0.824064i | \(0.308298\pi\) | |||||||
\(110\) | −7.15589 | −0.682288 | ||||||||
\(111\) | −9.08697 | −0.862497 | ||||||||
\(112\) | −0.386891 | −0.0365578 | ||||||||
\(113\) | 5.18957 | 0.488194 | 0.244097 | − | 0.969751i | \(-0.421509\pi\) | ||||
0.244097 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(114\) | 16.2794 | 1.52470 | ||||||||
\(115\) | −2.00141 | −0.186633 | ||||||||
\(116\) | −1.45658 | −0.135240 | ||||||||
\(117\) | 8.78109 | 0.811812 | ||||||||
\(118\) | 14.6403 | 1.34775 | ||||||||
\(119\) | −1.35612 | −0.124315 | ||||||||
\(120\) | −4.87575 | −0.445093 | ||||||||
\(121\) | 5.91581 | 0.537801 | ||||||||
\(122\) | 2.69798 | 0.244264 | ||||||||
\(123\) | −26.4391 | −2.38393 | ||||||||
\(124\) | −3.46348 | −0.311030 | ||||||||
\(125\) | −12.1319 | −1.08511 | ||||||||
\(126\) | −1.87767 | −0.167276 | ||||||||
\(127\) | 13.1074 | 1.16310 | 0.581548 | − | 0.813512i | \(-0.302447\pi\) | ||||
0.581548 | + | 0.813512i | \(0.302447\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −20.7189 | −1.82420 | ||||||||
\(130\) | 3.14800 | 0.276098 | ||||||||
\(131\) | −11.0039 | −0.961413 | −0.480707 | − | 0.876881i | \(-0.659620\pi\) | ||||
−0.480707 | + | 0.876881i | \(0.659620\pi\) | |||||||
\(132\) | 11.5258 | 1.00319 | ||||||||
\(133\) | 2.24751 | 0.194884 | ||||||||
\(134\) | 2.31609 | 0.200079 | ||||||||
\(135\) | −9.03593 | −0.777689 | ||||||||
\(136\) | 3.50517 | 0.300566 | ||||||||
\(137\) | −10.9371 | −0.934417 | −0.467208 | − | 0.884147i | \(-0.654740\pi\) | ||||
−0.467208 | + | 0.884147i | \(0.654740\pi\) | |||||||
\(138\) | 3.22362 | 0.274413 | ||||||||
\(139\) | 1.06382 | 0.0902317 | 0.0451158 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451158 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(140\) | −0.673141 | −0.0568908 | ||||||||
\(141\) | 21.8676 | 1.84158 | ||||||||
\(142\) | 9.43413 | 0.791695 | ||||||||
\(143\) | −7.44155 | −0.622294 | ||||||||
\(144\) | 4.85324 | 0.404436 | ||||||||
\(145\) | −2.53427 | −0.210460 | ||||||||
\(146\) | 2.25900 | 0.186956 | ||||||||
\(147\) | 19.1971 | 1.58335 | ||||||||
\(148\) | 3.24261 | 0.266541 | ||||||||
\(149\) | −9.80560 | −0.803306 | −0.401653 | − | 0.915792i | \(-0.631564\pi\) | ||||
−0.401653 | + | 0.915792i | \(0.631564\pi\) | |||||||
\(150\) | 5.52862 | 0.451410 | ||||||||
\(151\) | 21.5320 | 1.75225 | 0.876126 | − | 0.482081i | \(-0.160119\pi\) | ||||
0.876126 | + | 0.482081i | \(0.160119\pi\) | |||||||
\(152\) | −5.80916 | −0.471185 | ||||||||
\(153\) | 17.0114 | 1.37529 | ||||||||
\(154\) | 1.59124 | 0.128226 | ||||||||
\(155\) | −6.02601 | −0.484021 | ||||||||
\(156\) | −5.07039 | −0.405956 | ||||||||
\(157\) | 13.2820 | 1.06002 | 0.530009 | − | 0.847992i | \(-0.322189\pi\) | ||||
0.530009 | + | 0.847992i | \(0.322189\pi\) | |||||||
\(158\) | 4.01325 | 0.319277 | ||||||||
\(159\) | 0.214330 | 0.0169975 | ||||||||
\(160\) | 1.73987 | 0.137549 | ||||||||
\(161\) | 0.445049 | 0.0350748 | ||||||||
\(162\) | −0.00579824 | −0.000455553 0 | ||||||||
\(163\) | 9.48035 | 0.742558 | 0.371279 | − | 0.928521i | \(-0.378919\pi\) | ||||
0.371279 | + | 0.928521i | \(0.378919\pi\) | |||||||
\(164\) | 9.43456 | 0.736715 | ||||||||
\(165\) | 20.0534 | 1.56116 | ||||||||
\(166\) | −14.2396 | −1.10520 | ||||||||
\(167\) | −21.4336 | −1.65858 | −0.829289 | − | 0.558820i | \(-0.811254\pi\) | ||||
−0.829289 | + | 0.558820i | \(0.811254\pi\) | |||||||
\(168\) | 1.08421 | 0.0836485 | ||||||||
\(169\) | −9.72634 | −0.748180 | ||||||||
\(170\) | 6.09855 | 0.467737 | ||||||||
\(171\) | −28.1933 | −2.15599 | ||||||||
\(172\) | 7.39336 | 0.563739 | ||||||||
\(173\) | 20.9886 | 1.59573 | 0.797867 | − | 0.602833i | \(-0.205962\pi\) | ||||
0.797867 | + | 0.602833i | \(0.205962\pi\) | |||||||
\(174\) | 4.08187 | 0.309446 | ||||||||
\(175\) | 0.763275 | 0.0576982 | ||||||||
\(176\) | −4.11288 | −0.310020 | ||||||||
\(177\) | −41.0275 | −3.08382 | ||||||||
\(178\) | 2.19901 | 0.164823 | ||||||||
\(179\) | 24.4083 | 1.82436 | 0.912182 | − | 0.409784i | \(-0.134396\pi\) | ||||
0.912182 | + | 0.409784i | \(0.134396\pi\) | |||||||
\(180\) | 8.44402 | 0.629380 | ||||||||
\(181\) | 22.5381 | 1.67525 | 0.837624 | − | 0.546248i | \(-0.183944\pi\) | ||||
0.837624 | + | 0.546248i | \(0.183944\pi\) | |||||||
\(182\) | −0.700012 | −0.0518884 | ||||||||
\(183\) | −7.56072 | −0.558904 | ||||||||
\(184\) | −1.15032 | −0.0848028 | ||||||||
\(185\) | 5.64173 | 0.414788 | ||||||||
\(186\) | 9.70593 | 0.711673 | ||||||||
\(187\) | −14.4164 | −1.05423 | ||||||||
\(188\) | −7.80327 | −0.569112 | ||||||||
\(189\) | 2.00930 | 0.146155 | ||||||||
\(190\) | −10.1072 | −0.733254 | ||||||||
\(191\) | 9.01860 | 0.652563 | 0.326282 | − | 0.945273i | \(-0.394204\pi\) | ||||
0.326282 | + | 0.945273i | \(0.394204\pi\) | |||||||
\(192\) | −2.80236 | −0.202243 | ||||||||
\(193\) | 19.5799 | 1.40939 | 0.704697 | − | 0.709509i | \(-0.251083\pi\) | ||||
0.704697 | + | 0.709509i | \(0.251083\pi\) | |||||||
\(194\) | −9.19795 | −0.660375 | ||||||||
\(195\) | −8.82183 | −0.631745 | ||||||||
\(196\) | −6.85032 | −0.489308 | ||||||||
\(197\) | −23.0988 | −1.64572 | −0.822861 | − | 0.568243i | \(-0.807623\pi\) | ||||
−0.822861 | + | 0.568243i | \(0.807623\pi\) | |||||||
\(198\) | −19.9608 | −1.41855 | ||||||||
\(199\) | −6.50597 | −0.461196 | −0.230598 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230598 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(200\) | −1.97284 | −0.139501 | ||||||||
\(201\) | −6.49051 | −0.457806 | ||||||||
\(202\) | 13.2816 | 0.934489 | ||||||||
\(203\) | 0.563539 | 0.0395527 | ||||||||
\(204\) | −9.82276 | −0.687731 | ||||||||
\(205\) | 16.4149 | 1.14647 | ||||||||
\(206\) | 3.02225 | 0.210570 | ||||||||
\(207\) | −5.58278 | −0.388030 | ||||||||
\(208\) | 1.80933 | 0.125454 | ||||||||
\(209\) | 23.8924 | 1.65267 | ||||||||
\(210\) | 1.88639 | 0.130173 | ||||||||
\(211\) | −16.5607 | −1.14009 | −0.570043 | − | 0.821615i | \(-0.693074\pi\) | ||||
−0.570043 | + | 0.821615i | \(0.693074\pi\) | |||||||
\(212\) | −0.0764819 | −0.00525280 | ||||||||
\(213\) | −26.4379 | −1.81149 | ||||||||
\(214\) | −10.5944 | −0.724221 | ||||||||
\(215\) | 12.8635 | 0.877284 | ||||||||
\(216\) | −5.19344 | −0.353369 | ||||||||
\(217\) | 1.33999 | 0.0909644 | ||||||||
\(218\) | 11.8288 | 0.801148 | ||||||||
\(219\) | −6.33054 | −0.427778 | ||||||||
\(220\) | −7.15589 | −0.482450 | ||||||||
\(221\) | 6.34200 | 0.426609 | ||||||||
\(222\) | −9.08697 | −0.609878 | ||||||||
\(223\) | −4.46460 | −0.298971 | −0.149486 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149486 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(224\) | −0.386891 | −0.0258502 | ||||||||
\(225\) | −9.57467 | −0.638312 | ||||||||
\(226\) | 5.18957 | 0.345205 | ||||||||
\(227\) | 6.05656 | 0.401988 | 0.200994 | − | 0.979592i | \(-0.435583\pi\) | ||||
0.200994 | + | 0.979592i | \(0.435583\pi\) | |||||||
\(228\) | 16.2794 | 1.07813 | ||||||||
\(229\) | −26.5917 | −1.75723 | −0.878616 | − | 0.477529i | \(-0.841533\pi\) | ||||
−0.878616 | + | 0.477529i | \(0.841533\pi\) | |||||||
\(230\) | −2.00141 | −0.131969 | ||||||||
\(231\) | −4.45922 | −0.293395 | ||||||||
\(232\) | −1.45658 | −0.0956293 | ||||||||
\(233\) | −0.193795 | −0.0126959 | −0.00634796 | − | 0.999980i | \(-0.502021\pi\) | ||||
−0.00634796 | + | 0.999980i | \(0.502021\pi\) | |||||||
\(234\) | 8.78109 | 0.574038 | ||||||||
\(235\) | −13.5767 | −0.885646 | ||||||||
\(236\) | 14.6403 | 0.953004 | ||||||||
\(237\) | −11.2466 | −0.730545 | ||||||||
\(238\) | −1.35612 | −0.0879041 | ||||||||
\(239\) | 13.5686 | 0.877678 | 0.438839 | − | 0.898566i | \(-0.355390\pi\) | ||||
0.438839 | + | 0.898566i | \(0.355390\pi\) | |||||||
\(240\) | −4.87575 | −0.314729 | ||||||||
\(241\) | 15.6446 | 1.00776 | 0.503879 | − | 0.863774i | \(-0.331906\pi\) | ||||
0.503879 | + | 0.863774i | \(0.331906\pi\) | |||||||
\(242\) | 5.91581 | 0.380283 | ||||||||
\(243\) | 15.5966 | 1.00052 | ||||||||
\(244\) | 2.69798 | 0.172720 | ||||||||
\(245\) | −11.9187 | −0.761456 | ||||||||
\(246\) | −26.4391 | −1.68569 | ||||||||
\(247\) | −10.5107 | −0.668778 | ||||||||
\(248\) | −3.46348 | −0.219931 | ||||||||
\(249\) | 39.9044 | 2.52884 | ||||||||
\(250\) | −12.1319 | −0.767286 | ||||||||
\(251\) | 7.81171 | 0.493071 | 0.246535 | − | 0.969134i | \(-0.420708\pi\) | ||||
0.246535 | + | 0.969134i | \(0.420708\pi\) | |||||||
\(252\) | −1.87767 | −0.118282 | ||||||||
\(253\) | 4.73114 | 0.297444 | ||||||||
\(254\) | 13.1074 | 0.822434 | ||||||||
\(255\) | −17.0904 | −1.07024 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.3655 | 1.76939 | 0.884696 | − | 0.466168i | \(-0.154366\pi\) | ||||
0.884696 | + | 0.466168i | \(0.154366\pi\) | |||||||
\(258\) | −20.7189 | −1.28990 | ||||||||
\(259\) | −1.25454 | −0.0779531 | ||||||||
\(260\) | 3.14800 | 0.195231 | ||||||||
\(261\) | −7.06914 | −0.437569 | ||||||||
\(262\) | −11.0039 | −0.679822 | ||||||||
\(263\) | −2.05824 | −0.126916 | −0.0634582 | − | 0.997984i | \(-0.520213\pi\) | ||||
−0.0634582 | + | 0.997984i | \(0.520213\pi\) | |||||||
\(264\) | 11.5258 | 0.709363 | ||||||||
\(265\) | −0.133069 | −0.00817435 | ||||||||
\(266\) | 2.24751 | 0.137804 | ||||||||
\(267\) | −6.16243 | −0.377135 | ||||||||
\(268\) | 2.31609 | 0.141477 | ||||||||
\(269\) | 8.07102 | 0.492099 | 0.246049 | − | 0.969257i | \(-0.420867\pi\) | ||||
0.246049 | + | 0.969257i | \(0.420867\pi\) | |||||||
\(270\) | −9.03593 | −0.549909 | ||||||||
\(271\) | 6.74968 | 0.410014 | 0.205007 | − | 0.978761i | \(-0.434278\pi\) | ||||
0.205007 | + | 0.978761i | \(0.434278\pi\) | |||||||
\(272\) | 3.50517 | 0.212532 | ||||||||
\(273\) | 1.96169 | 0.118727 | ||||||||
\(274\) | −10.9371 | −0.660732 | ||||||||
\(275\) | 8.11407 | 0.489297 | ||||||||
\(276\) | 3.22362 | 0.194039 | ||||||||
\(277\) | −17.0790 | −1.02618 | −0.513089 | − | 0.858335i | \(-0.671499\pi\) | ||||
−0.513089 | + | 0.858335i | \(0.671499\pi\) | |||||||
\(278\) | 1.06382 | 0.0638034 | ||||||||
\(279\) | −16.8091 | −1.00633 | ||||||||
\(280\) | −0.673141 | −0.0402279 | ||||||||
\(281\) | −8.58496 | −0.512136 | −0.256068 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256068 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(282\) | 21.8676 | 1.30220 | ||||||||
\(283\) | −11.2073 | −0.666205 | −0.333103 | − | 0.942891i | \(-0.608096\pi\) | ||||
−0.333103 | + | 0.942891i | \(0.608096\pi\) | |||||||
\(284\) | 9.43413 | 0.559813 | ||||||||
\(285\) | 28.3241 | 1.67777 | ||||||||
\(286\) | −7.44155 | −0.440028 | ||||||||
\(287\) | −3.65015 | −0.215461 | ||||||||
\(288\) | 4.85324 | 0.285980 | ||||||||
\(289\) | −4.71378 | −0.277281 | ||||||||
\(290\) | −2.53427 | −0.148817 | ||||||||
\(291\) | 25.7760 | 1.51102 | ||||||||
\(292\) | 2.25900 | 0.132198 | ||||||||
\(293\) | 22.5845 | 1.31940 | 0.659699 | − | 0.751530i | \(-0.270684\pi\) | ||||
0.659699 | + | 0.751530i | \(0.270684\pi\) | |||||||
\(294\) | 19.1971 | 1.11960 | ||||||||
\(295\) | 25.4723 | 1.48306 | ||||||||
\(296\) | 3.24261 | 0.188473 | ||||||||
\(297\) | 21.3600 | 1.23943 | ||||||||
\(298\) | −9.80560 | −0.568023 | ||||||||
\(299\) | −2.08131 | −0.120365 | ||||||||
\(300\) | 5.52862 | 0.319195 | ||||||||
\(301\) | −2.86042 | −0.164872 | ||||||||
\(302\) | 21.5320 | 1.23903 | ||||||||
\(303\) | −37.2198 | −2.13822 | ||||||||
\(304\) | −5.80916 | −0.333178 | ||||||||
\(305\) | 4.69414 | 0.268786 | ||||||||
\(306\) | 17.0114 | 0.972478 | ||||||||
\(307\) | 12.6918 | 0.724362 | 0.362181 | − | 0.932108i | \(-0.382032\pi\) | ||||
0.362181 | + | 0.932108i | \(0.382032\pi\) | |||||||
\(308\) | 1.59124 | 0.0906692 | ||||||||
\(309\) | −8.46944 | −0.481810 | ||||||||
\(310\) | −6.02601 | −0.342255 | ||||||||
\(311\) | −19.0415 | −1.07974 | −0.539872 | − | 0.841747i | \(-0.681527\pi\) | ||||
−0.539872 | + | 0.841747i | \(0.681527\pi\) | |||||||
\(312\) | −5.07039 | −0.287054 | ||||||||
\(313\) | 15.9175 | 0.899713 | 0.449856 | − | 0.893101i | \(-0.351475\pi\) | ||||
0.449856 | + | 0.893101i | \(0.351475\pi\) | |||||||
\(314\) | 13.2820 | 0.749546 | ||||||||
\(315\) | −3.26691 | −0.184070 | ||||||||
\(316\) | 4.01325 | 0.225763 | ||||||||
\(317\) | 5.17283 | 0.290535 | 0.145267 | − | 0.989392i | \(-0.453596\pi\) | ||||
0.145267 | + | 0.989392i | \(0.453596\pi\) | |||||||
\(318\) | 0.214330 | 0.0120190 | ||||||||
\(319\) | 5.99075 | 0.335418 | ||||||||
\(320\) | 1.73987 | 0.0972618 | ||||||||
\(321\) | 29.6895 | 1.65711 | ||||||||
\(322\) | 0.445049 | 0.0248016 | ||||||||
\(323\) | −20.3621 | −1.13298 | ||||||||
\(324\) | −0.00579824 | −0.000322125 0 | ||||||||
\(325\) | −3.56952 | −0.198001 | ||||||||
\(326\) | 9.48035 | 0.525068 | ||||||||
\(327\) | −33.1486 | −1.83312 | ||||||||
\(328\) | 9.43456 | 0.520936 | ||||||||
\(329\) | 3.01902 | 0.166444 | ||||||||
\(330\) | 20.0534 | 1.10390 | ||||||||
\(331\) | 12.9156 | 0.709908 | 0.354954 | − | 0.934884i | \(-0.384497\pi\) | ||||
0.354954 | + | 0.934884i | \(0.384497\pi\) | |||||||
\(332\) | −14.2396 | −0.781497 | ||||||||
\(333\) | 15.7372 | 0.862391 | ||||||||
\(334\) | −21.4336 | −1.17279 | ||||||||
\(335\) | 4.02969 | 0.220166 | ||||||||
\(336\) | 1.08421 | 0.0591484 | ||||||||
\(337\) | 13.9400 | 0.759362 | 0.379681 | − | 0.925117i | \(-0.376034\pi\) | ||||
0.379681 | + | 0.925117i | \(0.376034\pi\) | |||||||
\(338\) | −9.72634 | −0.529043 | ||||||||
\(339\) | −14.5431 | −0.789871 | ||||||||
\(340\) | 6.09855 | 0.330740 | ||||||||
\(341\) | 14.2449 | 0.771404 | ||||||||
\(342\) | −28.1933 | −1.52452 | ||||||||
\(343\) | 5.35856 | 0.289335 | ||||||||
\(344\) | 7.39336 | 0.398623 | ||||||||
\(345\) | 5.60868 | 0.301961 | ||||||||
\(346\) | 20.9886 | 1.12835 | ||||||||
\(347\) | 32.9076 | 1.76657 | 0.883287 | − | 0.468833i | \(-0.155326\pi\) | ||||
0.883287 | + | 0.468833i | \(0.155326\pi\) | |||||||
\(348\) | 4.08187 | 0.218811 | ||||||||
\(349\) | 22.6923 | 1.21469 | 0.607344 | − | 0.794439i | \(-0.292235\pi\) | ||||
0.607344 | + | 0.794439i | \(0.292235\pi\) | |||||||
\(350\) | 0.763275 | 0.0407988 | ||||||||
\(351\) | −9.39664 | −0.501555 | ||||||||
\(352\) | −4.11288 | −0.219217 | ||||||||
\(353\) | 18.4688 | 0.982996 | 0.491498 | − | 0.870879i | \(-0.336450\pi\) | ||||
0.491498 | + | 0.870879i | \(0.336450\pi\) | |||||||
\(354\) | −41.0275 | −2.18059 | ||||||||
\(355\) | 16.4142 | 0.871175 | ||||||||
\(356\) | 2.19901 | 0.116547 | ||||||||
\(357\) | 3.80034 | 0.201135 | ||||||||
\(358\) | 24.4083 | 1.29002 | ||||||||
\(359\) | −28.4244 | −1.50018 | −0.750092 | − | 0.661334i | \(-0.769991\pi\) | ||||
−0.750092 | + | 0.661334i | \(0.769991\pi\) | |||||||
\(360\) | 8.44402 | 0.445039 | ||||||||
\(361\) | 14.7464 | 0.776125 | ||||||||
\(362\) | 22.5381 | 1.18458 | ||||||||
\(363\) | −16.5782 | −0.870132 | ||||||||
\(364\) | −0.700012 | −0.0366906 | ||||||||
\(365\) | 3.93037 | 0.205725 | ||||||||
\(366\) | −7.56072 | −0.395205 | ||||||||
\(367\) | 6.84530 | 0.357322 | 0.178661 | − | 0.983911i | \(-0.442823\pi\) | ||||
0.178661 | + | 0.983911i | \(0.442823\pi\) | |||||||
\(368\) | −1.15032 | −0.0599646 | ||||||||
\(369\) | 45.7882 | 2.38364 | ||||||||
\(370\) | 5.64173 | 0.293300 | ||||||||
\(371\) | 0.0295901 | 0.00153624 | ||||||||
\(372\) | 9.70593 | 0.503229 | ||||||||
\(373\) | −13.5581 | −0.702012 | −0.351006 | − | 0.936373i | \(-0.614160\pi\) | ||||
−0.351006 | + | 0.936373i | \(0.614160\pi\) | |||||||
\(374\) | −14.4164 | −0.745452 | ||||||||
\(375\) | 33.9979 | 1.75564 | ||||||||
\(376\) | −7.80327 | −0.402423 | ||||||||
\(377\) | −2.63543 | −0.135732 | ||||||||
\(378\) | 2.00930 | 0.103347 | ||||||||
\(379\) | 33.7983 | 1.73610 | 0.868051 | − | 0.496475i | \(-0.165373\pi\) | ||||
0.868051 | + | 0.496475i | \(0.165373\pi\) | |||||||
\(380\) | −10.1072 | −0.518489 | ||||||||
\(381\) | −36.7318 | −1.88183 | ||||||||
\(382\) | 9.01860 | 0.461432 | ||||||||
\(383\) | 0.153092 | 0.00782263 | 0.00391131 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00391131 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(384\) | −2.80236 | −0.143007 | ||||||||
\(385\) | 2.76855 | 0.141098 | ||||||||
\(386\) | 19.5799 | 0.996592 | ||||||||
\(387\) | 35.8817 | 1.82397 | ||||||||
\(388\) | −9.19795 | −0.466955 | ||||||||
\(389\) | −10.8983 | −0.552564 | −0.276282 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276282 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(390\) | −8.82183 | −0.446711 | ||||||||
\(391\) | −4.03207 | −0.203911 | ||||||||
\(392\) | −6.85032 | −0.345993 | ||||||||
\(393\) | 30.8369 | 1.55551 | ||||||||
\(394\) | −23.0988 | −1.16370 | ||||||||
\(395\) | 6.98255 | 0.351330 | ||||||||
\(396\) | −19.9608 | −1.00307 | ||||||||
\(397\) | 9.43226 | 0.473391 | 0.236696 | − | 0.971584i | \(-0.423936\pi\) | ||||
0.236696 | + | 0.971584i | \(0.423936\pi\) | |||||||
\(398\) | −6.50597 | −0.326115 | ||||||||
\(399\) | −6.29835 | −0.315312 | ||||||||
\(400\) | −1.97284 | −0.0986421 | ||||||||
\(401\) | −9.90263 | −0.494514 | −0.247257 | − | 0.968950i | \(-0.579529\pi\) | ||||
−0.247257 | + | 0.968950i | \(0.579529\pi\) | |||||||
\(402\) | −6.49051 | −0.323717 | ||||||||
\(403\) | −6.26657 | −0.312160 | ||||||||
\(404\) | 13.2816 | 0.660784 | ||||||||
\(405\) | −0.0100882 | −0.000501287 0 | ||||||||
\(406\) | 0.563539 | 0.0279680 | ||||||||
\(407\) | −13.3365 | −0.661065 | ||||||||
\(408\) | −9.82276 | −0.486299 | ||||||||
\(409\) | −30.5749 | −1.51183 | −0.755917 | − | 0.654668i | \(-0.772809\pi\) | ||||
−0.755917 | + | 0.654668i | \(0.772809\pi\) | |||||||
\(410\) | 16.4149 | 0.810676 | ||||||||
\(411\) | 30.6496 | 1.51183 | ||||||||
\(412\) | 3.02225 | 0.148896 | ||||||||
\(413\) | −5.66421 | −0.278718 | ||||||||
\(414\) | −5.58278 | −0.274379 | ||||||||
\(415\) | −24.7750 | −1.21616 | ||||||||
\(416\) | 1.80933 | 0.0887096 | ||||||||
\(417\) | −2.98120 | −0.145990 | ||||||||
\(418\) | 23.8924 | 1.16862 | ||||||||
\(419\) | 19.7963 | 0.967110 | 0.483555 | − | 0.875314i | \(-0.339345\pi\) | ||||
0.483555 | + | 0.875314i | \(0.339345\pi\) | |||||||
\(420\) | 1.88639 | 0.0920462 | ||||||||
\(421\) | −14.7606 | −0.719386 | −0.359693 | − | 0.933071i | \(-0.617119\pi\) | ||||
−0.359693 | + | 0.933071i | \(0.617119\pi\) | |||||||
\(422\) | −16.5607 | −0.806163 | ||||||||
\(423\) | −37.8711 | −1.84136 | ||||||||
\(424\) | −0.0764819 | −0.00371429 | ||||||||
\(425\) | −6.91515 | −0.335434 | ||||||||
\(426\) | −26.4379 | −1.28092 | ||||||||
\(427\) | −1.04382 | −0.0505142 | ||||||||
\(428\) | −10.5944 | −0.512102 | ||||||||
\(429\) | 20.8539 | 1.00684 | ||||||||
\(430\) | 12.8635 | 0.620333 | ||||||||
\(431\) | 10.8736 | 0.523763 | 0.261882 | − | 0.965100i | \(-0.415657\pi\) | ||||
0.261882 | + | 0.965100i | \(0.415657\pi\) | |||||||
\(432\) | −5.19344 | −0.249870 | ||||||||
\(433\) | −29.3690 | −1.41138 | −0.705691 | − | 0.708520i | \(-0.749363\pi\) | ||||
−0.705691 | + | 0.708520i | \(0.749363\pi\) | |||||||
\(434\) | 1.33999 | 0.0643215 | ||||||||
\(435\) | 7.10194 | 0.340512 | ||||||||
\(436\) | 11.8288 | 0.566497 | ||||||||
\(437\) | 6.68240 | 0.319663 | ||||||||
\(438\) | −6.33054 | −0.302485 | ||||||||
\(439\) | 33.4954 | 1.59865 | 0.799324 | − | 0.600900i | \(-0.205191\pi\) | ||||
0.799324 | + | 0.600900i | \(0.205191\pi\) | |||||||
\(440\) | −7.15589 | −0.341144 | ||||||||
\(441\) | −33.2462 | −1.58315 | ||||||||
\(442\) | 6.34200 | 0.301658 | ||||||||
\(443\) | 5.91776 | 0.281161 | 0.140581 | − | 0.990069i | \(-0.455103\pi\) | ||||
0.140581 | + | 0.990069i | \(0.455103\pi\) | |||||||
\(444\) | −9.08697 | −0.431249 | ||||||||
\(445\) | 3.82600 | 0.181370 | ||||||||
\(446\) | −4.46460 | −0.211405 | ||||||||
\(447\) | 27.4789 | 1.29971 | ||||||||
\(448\) | −0.386891 | −0.0182789 | ||||||||
\(449\) | 12.2918 | 0.580085 | 0.290042 | − | 0.957014i | \(-0.406331\pi\) | ||||
0.290042 | + | 0.957014i | \(0.406331\pi\) | |||||||
\(450\) | −9.57467 | −0.451354 | ||||||||
\(451\) | −38.8032 | −1.82717 | ||||||||
\(452\) | 5.18957 | 0.244097 | ||||||||
\(453\) | −60.3406 | −2.83505 | ||||||||
\(454\) | 6.05656 | 0.284248 | ||||||||
\(455\) | −1.21793 | −0.0570975 | ||||||||
\(456\) | 16.2794 | 0.762352 | ||||||||
\(457\) | 20.5618 | 0.961841 | 0.480920 | − | 0.876764i | \(-0.340303\pi\) | ||||
0.480920 | + | 0.876764i | \(0.340303\pi\) | |||||||
\(458\) | −26.5917 | −1.24255 | ||||||||
\(459\) | −18.2039 | −0.849686 | ||||||||
\(460\) | −2.00141 | −0.0933163 | ||||||||
\(461\) | 15.8977 | 0.740428 | 0.370214 | − | 0.928947i | \(-0.379284\pi\) | ||||
0.370214 | + | 0.928947i | \(0.379284\pi\) | |||||||
\(462\) | −4.45922 | −0.207462 | ||||||||
\(463\) | −12.0243 | −0.558817 | −0.279409 | − | 0.960172i | \(-0.590138\pi\) | ||||
−0.279409 | + | 0.960172i | \(0.590138\pi\) | |||||||
\(464\) | −1.45658 | −0.0676201 | ||||||||
\(465\) | 16.8871 | 0.783119 | ||||||||
\(466\) | −0.193795 | −0.00897737 | ||||||||
\(467\) | 26.3272 | 1.21828 | 0.609139 | − | 0.793064i | \(-0.291515\pi\) | ||||
0.609139 | + | 0.793064i | \(0.291515\pi\) | |||||||
\(468\) | 8.78109 | 0.405906 | ||||||||
\(469\) | −0.896073 | −0.0413768 | ||||||||
\(470\) | −13.5767 | −0.626247 | ||||||||
\(471\) | −37.2210 | −1.71505 | ||||||||
\(472\) | 14.6403 | 0.673876 | ||||||||
\(473\) | −30.4080 | −1.39816 | ||||||||
\(474\) | −11.2466 | −0.516573 | ||||||||
\(475\) | 11.4606 | 0.525847 | ||||||||
\(476\) | −1.35612 | −0.0621576 | ||||||||
\(477\) | −0.371185 | −0.0169954 | ||||||||
\(478\) | 13.5686 | 0.620612 | ||||||||
\(479\) | 12.8252 | 0.585996 | 0.292998 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292998 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(480\) | −4.87575 | −0.222547 | ||||||||
\(481\) | 5.86694 | 0.267510 | ||||||||
\(482\) | 15.6446 | 0.712592 | ||||||||
\(483\) | −1.24719 | −0.0567490 | ||||||||
\(484\) | 5.91581 | 0.268900 | ||||||||
\(485\) | −16.0033 | −0.726671 | ||||||||
\(486\) | 15.5966 | 0.707475 | ||||||||
\(487\) | 32.0639 | 1.45295 | 0.726476 | − | 0.687191i | \(-0.241157\pi\) | ||||
0.726476 | + | 0.687191i | \(0.241157\pi\) | |||||||
\(488\) | 2.69798 | 0.122132 | ||||||||
\(489\) | −26.5674 | −1.20142 | ||||||||
\(490\) | −11.9187 | −0.538431 | ||||||||
\(491\) | −30.6227 | −1.38198 | −0.690991 | − | 0.722863i | \(-0.742826\pi\) | ||||
−0.690991 | + | 0.722863i | \(0.742826\pi\) | |||||||
\(492\) | −26.4391 | −1.19197 | ||||||||
\(493\) | −5.10557 | −0.229943 | ||||||||
\(494\) | −10.5107 | −0.472898 | ||||||||
\(495\) | −34.7292 | −1.56096 | ||||||||
\(496\) | −3.46348 | −0.155515 | ||||||||
\(497\) | −3.64998 | −0.163724 | ||||||||
\(498\) | 39.9044 | 1.78816 | ||||||||
\(499\) | 17.3833 | 0.778184 | 0.389092 | − | 0.921199i | \(-0.372789\pi\) | ||||
0.389092 | + | 0.921199i | \(0.372789\pi\) | |||||||
\(500\) | −12.1319 | −0.542553 | ||||||||
\(501\) | 60.0646 | 2.68349 | ||||||||
\(502\) | 7.81171 | 0.348654 | ||||||||
\(503\) | −28.4946 | −1.27051 | −0.635255 | − | 0.772303i | \(-0.719105\pi\) | ||||
−0.635255 | + | 0.772303i | \(0.719105\pi\) | |||||||
\(504\) | −1.87767 | −0.0836382 | ||||||||
\(505\) | 23.1083 | 1.02830 | ||||||||
\(506\) | 4.73114 | 0.210325 | ||||||||
\(507\) | 27.2567 | 1.21051 | ||||||||
\(508\) | 13.1074 | 0.581548 | ||||||||
\(509\) | 28.4529 | 1.26115 | 0.630576 | − | 0.776128i | \(-0.282819\pi\) | ||||
0.630576 | + | 0.776128i | \(0.282819\pi\) | |||||||
\(510\) | −17.0904 | −0.756773 | ||||||||
\(511\) | −0.873987 | −0.0386629 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 30.1696 | 1.33202 | ||||||||
\(514\) | 28.3655 | 1.25115 | ||||||||
\(515\) | 5.25833 | 0.231710 | ||||||||
\(516\) | −20.7189 | −0.912098 | ||||||||
\(517\) | 32.0940 | 1.41149 | ||||||||
\(518\) | −1.25454 | −0.0551212 | ||||||||
\(519\) | −58.8177 | −2.58181 | ||||||||
\(520\) | 3.14800 | 0.138049 | ||||||||
\(521\) | −16.1382 | −0.707026 | −0.353513 | − | 0.935430i | \(-0.615013\pi\) | ||||
−0.353513 | + | 0.935430i | \(0.615013\pi\) | |||||||
\(522\) | −7.06914 | −0.309408 | ||||||||
\(523\) | 44.4285 | 1.94272 | 0.971362 | − | 0.237605i | \(-0.0763624\pi\) | ||||
0.971362 | + | 0.237605i | \(0.0763624\pi\) | |||||||
\(524\) | −11.0039 | −0.480707 | ||||||||
\(525\) | −2.13897 | −0.0933525 | ||||||||
\(526\) | −2.05824 | −0.0897434 | ||||||||
\(527\) | −12.1401 | −0.528830 | ||||||||
\(528\) | 11.5258 | 0.501596 | ||||||||
\(529\) | −21.6768 | −0.942468 | ||||||||
\(530\) | −0.133069 | −0.00578014 | ||||||||
\(531\) | 71.0530 | 3.08344 | ||||||||
\(532\) | 2.24751 | 0.0974420 | ||||||||
\(533\) | 17.0702 | 0.739393 | ||||||||
\(534\) | −6.16243 | −0.266675 | ||||||||
\(535\) | −18.4330 | −0.796927 | ||||||||
\(536\) | 2.31609 | 0.100040 | ||||||||
\(537\) | −68.4010 | −2.95172 | ||||||||
\(538\) | 8.07102 | 0.347966 | ||||||||
\(539\) | 28.1745 | 1.21356 | ||||||||
\(540\) | −9.03593 | −0.388845 | ||||||||
\(541\) | 16.8128 | 0.722840 | 0.361420 | − | 0.932403i | \(-0.382292\pi\) | ||||
0.361420 | + | 0.932403i | \(0.382292\pi\) | |||||||
\(542\) | 6.74968 | 0.289923 | ||||||||
\(543\) | −63.1601 | −2.71046 | ||||||||
\(544\) | 3.50517 | 0.150283 | ||||||||
\(545\) | 20.5806 | 0.881577 | ||||||||
\(546\) | 1.96169 | 0.0839525 | ||||||||
\(547\) | 36.3759 | 1.55532 | 0.777660 | − | 0.628685i | \(-0.216407\pi\) | ||||
0.777660 | + | 0.628685i | \(0.216407\pi\) | |||||||
\(548\) | −10.9371 | −0.467208 | ||||||||
\(549\) | 13.0939 | 0.558836 | ||||||||
\(550\) | 8.11407 | 0.345985 | ||||||||
\(551\) | 8.46153 | 0.360473 | ||||||||
\(552\) | 3.22362 | 0.137206 | ||||||||
\(553\) | −1.55269 | −0.0660272 | ||||||||
\(554\) | −17.0790 | −0.725617 | ||||||||
\(555\) | −15.8102 | −0.671104 | ||||||||
\(556\) | 1.06382 | 0.0451158 | ||||||||
\(557\) | −9.03837 | −0.382968 | −0.191484 | − | 0.981496i | \(-0.561330\pi\) | ||||
−0.191484 | + | 0.981496i | \(0.561330\pi\) | |||||||
\(558\) | −16.8091 | −0.711585 | ||||||||
\(559\) | 13.3770 | 0.565787 | ||||||||
\(560\) | −0.673141 | −0.0284454 | ||||||||
\(561\) | 40.3999 | 1.70568 | ||||||||
\(562\) | −8.58496 | −0.362135 | ||||||||
\(563\) | 10.2278 | 0.431049 | 0.215525 | − | 0.976498i | \(-0.430854\pi\) | ||||
0.215525 | + | 0.976498i | \(0.430854\pi\) | |||||||
\(564\) | 21.8676 | 0.920792 | ||||||||
\(565\) | 9.02919 | 0.379861 | ||||||||
\(566\) | −11.2073 | −0.471078 | ||||||||
\(567\) | 0.00224329 | 9.42092e−5 0 | ||||||||
\(568\) | 9.43413 | 0.395847 | ||||||||
\(569\) | 27.3976 | 1.14857 | 0.574283 | − | 0.818657i | \(-0.305281\pi\) | ||||
0.574283 | + | 0.818657i | \(0.305281\pi\) | |||||||
\(570\) | 28.3241 | 1.18636 | ||||||||
\(571\) | −21.5018 | −0.899823 | −0.449912 | − | 0.893073i | \(-0.648545\pi\) | ||||
−0.449912 | + | 0.893073i | \(0.648545\pi\) | |||||||
\(572\) | −7.44155 | −0.311147 | ||||||||
\(573\) | −25.2734 | −1.05581 | ||||||||
\(574\) | −3.65015 | −0.152354 | ||||||||
\(575\) | 2.26940 | 0.0946406 | ||||||||
\(576\) | 4.85324 | 0.202218 | ||||||||
\(577\) | −11.8311 | −0.492533 | −0.246267 | − | 0.969202i | \(-0.579204\pi\) | ||||
−0.246267 | + | 0.969202i | \(0.579204\pi\) | |||||||
\(578\) | −4.71378 | −0.196067 | ||||||||
\(579\) | −54.8700 | −2.28032 | ||||||||
\(580\) | −2.53427 | −0.105230 | ||||||||
\(581\) | 5.50915 | 0.228558 | ||||||||
\(582\) | 25.7760 | 1.06845 | ||||||||
\(583\) | 0.314561 | 0.0130278 | ||||||||
\(584\) | 2.25900 | 0.0934781 | ||||||||
\(585\) | 15.2780 | 0.631667 | ||||||||
\(586\) | 22.5845 | 0.932955 | ||||||||
\(587\) | 34.7490 | 1.43425 | 0.717123 | − | 0.696946i | \(-0.245458\pi\) | ||||
0.717123 | + | 0.696946i | \(0.245458\pi\) | |||||||
\(588\) | 19.1971 | 0.791674 | ||||||||
\(589\) | 20.1199 | 0.829027 | ||||||||
\(590\) | 25.4723 | 1.04868 | ||||||||
\(591\) | 64.7312 | 2.66269 | ||||||||
\(592\) | 3.24261 | 0.133270 | ||||||||
\(593\) | 0.158235 | 0.00649795 | 0.00324897 | − | 0.999995i | \(-0.498966\pi\) | ||||
0.00324897 | + | 0.999995i | \(0.498966\pi\) | |||||||
\(594\) | 21.3600 | 0.876413 | ||||||||
\(595\) | −2.35947 | −0.0967290 | ||||||||
\(596\) | −9.80560 | −0.401653 | ||||||||
\(597\) | 18.2321 | 0.746189 | ||||||||
\(598\) | −2.08131 | −0.0851110 | ||||||||
\(599\) | 25.6606 | 1.04846 | 0.524232 | − | 0.851576i | \(-0.324353\pi\) | ||||
0.524232 | + | 0.851576i | \(0.324353\pi\) | |||||||
\(600\) | 5.52862 | 0.225705 | ||||||||
\(601\) | −29.1463 | −1.18890 | −0.594450 | − | 0.804132i | \(-0.702630\pi\) | ||||
−0.594450 | + | 0.804132i | \(0.702630\pi\) | |||||||
\(602\) | −2.86042 | −0.116582 | ||||||||
\(603\) | 11.2405 | 0.457749 | ||||||||
\(604\) | 21.5320 | 0.876126 | ||||||||
\(605\) | 10.2928 | 0.418460 | ||||||||
\(606\) | −37.2198 | −1.51195 | ||||||||
\(607\) | −9.56400 | −0.388191 | −0.194095 | − | 0.980983i | \(-0.562177\pi\) | ||||
−0.194095 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(608\) | −5.80916 | −0.235593 | ||||||||
\(609\) | −1.57924 | −0.0639940 | ||||||||
\(610\) | 4.69414 | 0.190060 | ||||||||
\(611\) | −14.1187 | −0.571180 | ||||||||
\(612\) | 17.0114 | 0.687646 | ||||||||
\(613\) | 17.3910 | 0.702417 | 0.351209 | − | 0.936297i | \(-0.385771\pi\) | ||||
0.351209 | + | 0.936297i | \(0.385771\pi\) | |||||||
\(614\) | 12.6918 | 0.512201 | ||||||||
\(615\) | −46.0006 | −1.85492 | ||||||||
\(616\) | 1.59124 | 0.0641128 | ||||||||
\(617\) | 43.3429 | 1.74492 | 0.872461 | − | 0.488684i | \(-0.162523\pi\) | ||||
0.872461 | + | 0.488684i | \(0.162523\pi\) | |||||||
\(618\) | −8.46944 | −0.340691 | ||||||||
\(619\) | 37.2868 | 1.49868 | 0.749341 | − | 0.662184i | \(-0.230370\pi\) | ||||
0.749341 | + | 0.662184i | \(0.230370\pi\) | |||||||
\(620\) | −6.02601 | −0.242011 | ||||||||
\(621\) | 5.97413 | 0.239734 | ||||||||
\(622\) | −19.0415 | −0.763494 | ||||||||
\(623\) | −0.850778 | −0.0340857 | ||||||||
\(624\) | −5.07039 | −0.202978 | ||||||||
\(625\) | −11.2437 | −0.449747 | ||||||||
\(626\) | 15.9175 | 0.636193 | ||||||||
\(627\) | −66.9552 | −2.67393 | ||||||||
\(628\) | 13.2820 | 0.530009 | ||||||||
\(629\) | 11.3659 | 0.453188 | ||||||||
\(630\) | −3.26691 | −0.130157 | ||||||||
\(631\) | −3.99272 | −0.158948 | −0.0794739 | − | 0.996837i | \(-0.525324\pi\) | ||||
−0.0794739 | + | 0.996837i | \(0.525324\pi\) | |||||||
\(632\) | 4.01325 | 0.159639 | ||||||||
\(633\) | 46.4091 | 1.84460 | ||||||||
\(634\) | 5.17283 | 0.205439 | ||||||||
\(635\) | 22.8053 | 0.905000 | ||||||||
\(636\) | 0.214330 | 0.00849874 | ||||||||
\(637\) | −12.3945 | −0.491086 | ||||||||
\(638\) | 5.99075 | 0.237176 | ||||||||
\(639\) | 45.7861 | 1.81127 | ||||||||
\(640\) | 1.73987 | 0.0687745 | ||||||||
\(641\) | 26.2367 | 1.03629 | 0.518143 | − | 0.855294i | \(-0.326623\pi\) | ||||
0.518143 | + | 0.855294i | \(0.326623\pi\) | |||||||
\(642\) | 29.6895 | 1.17175 | ||||||||
\(643\) | −29.1591 | −1.14992 | −0.574962 | − | 0.818180i | \(-0.694983\pi\) | ||||
−0.574962 | + | 0.818180i | \(0.694983\pi\) | |||||||
\(644\) | 0.445049 | 0.0175374 | ||||||||
\(645\) | −36.0482 | −1.41940 | ||||||||
\(646\) | −20.3621 | −0.801136 | ||||||||
\(647\) | −31.9971 | −1.25793 | −0.628967 | − | 0.777432i | \(-0.716522\pi\) | ||||
−0.628967 | + | 0.777432i | \(0.716522\pi\) | |||||||
\(648\) | −0.00579824 | −0.000227777 0 | ||||||||
\(649\) | −60.2140 | −2.36361 | ||||||||
\(650\) | −3.56952 | −0.140008 | ||||||||
\(651\) | −3.75513 | −0.147175 | ||||||||
\(652\) | 9.48035 | 0.371279 | ||||||||
\(653\) | 7.21785 | 0.282456 | 0.141228 | − | 0.989977i | \(-0.454895\pi\) | ||||
0.141228 | + | 0.989977i | \(0.454895\pi\) | |||||||
\(654\) | −33.1486 | −1.29621 | ||||||||
\(655\) | −19.1454 | −0.748071 | ||||||||
\(656\) | 9.43456 | 0.368358 | ||||||||
\(657\) | 10.9635 | 0.427726 | ||||||||
\(658\) | 3.01902 | 0.117693 | ||||||||
\(659\) | 18.7844 | 0.731736 | 0.365868 | − | 0.930667i | \(-0.380772\pi\) | ||||
0.365868 | + | 0.930667i | \(0.380772\pi\) | |||||||
\(660\) | 20.0534 | 0.780578 | ||||||||
\(661\) | −12.5128 | −0.486693 | −0.243346 | − | 0.969939i | \(-0.578245\pi\) | ||||
−0.243346 | + | 0.969939i | \(0.578245\pi\) | |||||||
\(662\) | 12.9156 | 0.501980 | ||||||||
\(663\) | −17.7726 | −0.690230 | ||||||||
\(664\) | −14.2396 | −0.552602 | ||||||||
\(665\) | 3.91039 | 0.151638 | ||||||||
\(666\) | 15.7372 | 0.609802 | ||||||||
\(667\) | 1.67554 | 0.0648771 | ||||||||
\(668\) | −21.4336 | −0.829289 | ||||||||
\(669\) | 12.5114 | 0.483719 | ||||||||
\(670\) | 4.02969 | 0.155681 | ||||||||
\(671\) | −11.0965 | −0.428375 | ||||||||
\(672\) | 1.08421 | 0.0418243 | ||||||||
\(673\) | −21.3003 | −0.821065 | −0.410533 | − | 0.911846i | \(-0.634657\pi\) | ||||
−0.410533 | + | 0.911846i | \(0.634657\pi\) | |||||||
\(674\) | 13.9400 | 0.536950 | ||||||||
\(675\) | 10.2458 | 0.394363 | ||||||||
\(676\) | −9.72634 | −0.374090 | ||||||||
\(677\) | 37.3958 | 1.43724 | 0.718618 | − | 0.695405i | \(-0.244775\pi\) | ||||
0.718618 | + | 0.695405i | \(0.244775\pi\) | |||||||
\(678\) | −14.5431 | −0.558523 | ||||||||
\(679\) | 3.55860 | 0.136567 | ||||||||
\(680\) | 6.09855 | 0.233869 | ||||||||
\(681\) | −16.9727 | −0.650395 | ||||||||
\(682\) | 14.2449 | 0.545465 | ||||||||
\(683\) | −1.67716 | −0.0641747 | −0.0320874 | − | 0.999485i | \(-0.510215\pi\) | ||||
−0.0320874 | + | 0.999485i | \(0.510215\pi\) | |||||||
\(684\) | −28.1933 | −1.07800 | ||||||||
\(685\) | −19.0291 | −0.727065 | ||||||||
\(686\) | 5.35856 | 0.204591 | ||||||||
\(687\) | 74.5197 | 2.84310 | ||||||||
\(688\) | 7.39336 | 0.281869 | ||||||||
\(689\) | −0.138381 | −0.00527189 | ||||||||
\(690\) | 5.60868 | 0.213519 | ||||||||
\(691\) | −48.6176 | −1.84950 | −0.924750 | − | 0.380574i | \(-0.875726\pi\) | ||||
−0.924750 | + | 0.380574i | \(0.875726\pi\) | |||||||
\(692\) | 20.9886 | 0.797867 | ||||||||
\(693\) | 7.72265 | 0.293359 | ||||||||
\(694\) | 32.9076 | 1.24916 | ||||||||
\(695\) | 1.85090 | 0.0702088 | ||||||||
\(696\) | 4.08187 | 0.154723 | ||||||||
\(697\) | 33.0697 | 1.25261 | ||||||||
\(698\) | 22.6923 | 0.858915 | ||||||||
\(699\) | 0.543084 | 0.0205413 | ||||||||
\(700\) | 0.763275 | 0.0288491 | ||||||||
\(701\) | −14.5282 | −0.548723 | −0.274362 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274362 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(702\) | −9.39664 | −0.354653 | ||||||||
\(703\) | −18.8369 | −0.710445 | ||||||||
\(704\) | −4.11288 | −0.155010 | ||||||||
\(705\) | 38.0468 | 1.43293 | ||||||||
\(706\) | 18.4688 | 0.695083 | ||||||||
\(707\) | −5.13853 | −0.193254 | ||||||||
\(708\) | −41.0275 | −1.54191 | ||||||||
\(709\) | −2.07261 | −0.0778385 | −0.0389193 | − | 0.999242i | \(-0.512392\pi\) | ||||
−0.0389193 | + | 0.999242i | \(0.512392\pi\) | |||||||
\(710\) | 16.4142 | 0.616014 | ||||||||
\(711\) | 19.4773 | 0.730455 | ||||||||
\(712\) | 2.19901 | 0.0824115 | ||||||||
\(713\) | 3.98411 | 0.149206 | ||||||||
\(714\) | 3.80034 | 0.142224 | ||||||||
\(715\) | −12.9474 | −0.484203 | ||||||||
\(716\) | 24.4083 | 0.912182 | ||||||||
\(717\) | −38.0241 | −1.42004 | ||||||||
\(718\) | −28.4244 | −1.06079 | ||||||||
\(719\) | 18.9765 | 0.707703 | 0.353851 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353851 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(720\) | 8.44402 | 0.314690 | ||||||||
\(721\) | −1.16928 | −0.0435463 | ||||||||
\(722\) | 14.7464 | 0.548804 | ||||||||
\(723\) | −43.8418 | −1.63050 | ||||||||
\(724\) | 22.5381 | 0.837624 | ||||||||
\(725\) | 2.87361 | 0.106723 | ||||||||
\(726\) | −16.5782 | −0.615276 | ||||||||
\(727\) | 14.1840 | 0.526057 | 0.263029 | − | 0.964788i | \(-0.415279\pi\) | ||||
0.263029 | + | 0.964788i | \(0.415279\pi\) | |||||||
\(728\) | −0.700012 | −0.0259442 | ||||||||
\(729\) | −43.6899 | −1.61814 | ||||||||
\(730\) | 3.93037 | 0.145470 | ||||||||
\(731\) | 25.9150 | 0.958501 | ||||||||
\(732\) | −7.56072 | −0.279452 | ||||||||
\(733\) | 28.5554 | 1.05472 | 0.527358 | − | 0.849643i | \(-0.323183\pi\) | ||||
0.527358 | + | 0.849643i | \(0.323183\pi\) | |||||||
\(734\) | 6.84530 | 0.252665 | ||||||||
\(735\) | 33.4005 | 1.23199 | ||||||||
\(736\) | −1.15032 | −0.0424014 | ||||||||
\(737\) | −9.52579 | −0.350887 | ||||||||
\(738\) | 45.7882 | 1.68549 | ||||||||
\(739\) | 49.9825 | 1.83864 | 0.919319 | − | 0.393514i | \(-0.128741\pi\) | ||||
0.919319 | + | 0.393514i | \(0.128741\pi\) | |||||||
\(740\) | 5.64173 | 0.207394 | ||||||||
\(741\) | 29.4547 | 1.08205 | ||||||||
\(742\) | 0.0295901 | 0.00108629 | ||||||||
\(743\) | −10.3475 | −0.379611 | −0.189806 | − | 0.981822i | \(-0.560786\pi\) | ||||
−0.189806 | + | 0.981822i | \(0.560786\pi\) | |||||||
\(744\) | 9.70593 | 0.355837 | ||||||||
\(745\) | −17.0605 | −0.625048 | ||||||||
\(746\) | −13.5581 | −0.496398 | ||||||||
\(747\) | −69.1079 | −2.52853 | ||||||||
\(748\) | −14.4164 | −0.527114 | ||||||||
\(749\) | 4.09889 | 0.149770 | ||||||||
\(750\) | 33.9979 | 1.24143 | ||||||||
\(751\) | −12.1440 | −0.443142 | −0.221571 | − | 0.975144i | \(-0.571118\pi\) | ||||
−0.221571 | + | 0.975144i | \(0.571118\pi\) | |||||||
\(752\) | −7.80327 | −0.284556 | ||||||||
\(753\) | −21.8912 | −0.797761 | ||||||||
\(754\) | −2.63543 | −0.0959769 | ||||||||
\(755\) | 37.4630 | 1.36342 | ||||||||
\(756\) | 2.00930 | 0.0730774 | ||||||||
\(757\) | 6.34007 | 0.230434 | 0.115217 | − | 0.993340i | \(-0.463244\pi\) | ||||
0.115217 | + | 0.993340i | \(0.463244\pi\) | |||||||
\(758\) | 33.7983 | 1.22761 | ||||||||
\(759\) | −13.2584 | −0.481248 | ||||||||
\(760\) | −10.1072 | −0.366627 | ||||||||
\(761\) | −29.0587 | −1.05338 | −0.526689 | − | 0.850058i | \(-0.676567\pi\) | ||||
−0.526689 | + | 0.850058i | \(0.676567\pi\) | |||||||
\(762\) | −36.7318 | −1.33065 | ||||||||
\(763\) | −4.57646 | −0.165679 | ||||||||
\(764\) | 9.01860 | 0.326282 | ||||||||
\(765\) | 29.5977 | 1.07011 | ||||||||
\(766\) | 0.153092 | 0.00553143 | ||||||||
\(767\) | 26.4891 | 0.956468 | ||||||||
\(768\) | −2.80236 | −0.101122 | ||||||||
\(769\) | −8.60300 | −0.310232 | −0.155116 | − | 0.987896i | \(-0.549575\pi\) | ||||
−0.155116 | + | 0.987896i | \(0.549575\pi\) | |||||||
\(770\) | 2.76855 | 0.0997716 | ||||||||
\(771\) | −79.4905 | −2.86278 | ||||||||
\(772\) | 19.5799 | 0.704697 | ||||||||
\(773\) | −39.4896 | −1.42034 | −0.710171 | − | 0.704030i | \(-0.751382\pi\) | ||||
−0.710171 | + | 0.704030i | \(0.751382\pi\) | |||||||
\(774\) | 35.8817 | 1.28974 | ||||||||
\(775\) | 6.83290 | 0.245445 | ||||||||
\(776\) | −9.19795 | −0.330187 | ||||||||
\(777\) | 3.51567 | 0.126124 | ||||||||
\(778\) | −10.8983 | −0.390721 | ||||||||
\(779\) | −54.8069 | −1.96366 | ||||||||
\(780\) | −8.82183 | −0.315872 | ||||||||
\(781\) | −38.8015 | −1.38843 | ||||||||
\(782\) | −4.03207 | −0.144187 | ||||||||
\(783\) | 7.56468 | 0.270340 | ||||||||
\(784\) | −6.85032 | −0.244654 | ||||||||
\(785\) | 23.1090 | 0.824795 | ||||||||
\(786\) | 30.8369 | 1.09991 | ||||||||
\(787\) | −43.8216 | −1.56207 | −0.781036 | − | 0.624486i | \(-0.785308\pi\) | ||||
−0.781036 | + | 0.624486i | \(0.785308\pi\) | |||||||
\(788\) | −23.0988 | −0.822861 | ||||||||
\(789\) | 5.76793 | 0.205344 | ||||||||
\(790\) | 6.98255 | 0.248428 | ||||||||
\(791\) | −2.00780 | −0.0713891 | ||||||||
\(792\) | −19.9608 | −0.709276 | ||||||||
\(793\) | 4.88153 | 0.173348 | ||||||||
\(794\) | 9.43226 | 0.334738 | ||||||||
\(795\) | 0.372907 | 0.0132256 | ||||||||
\(796\) | −6.50597 | −0.230598 | ||||||||
\(797\) | −19.5989 | −0.694229 | −0.347115 | − | 0.937823i | \(-0.612839\pi\) | ||||
−0.347115 | + | 0.937823i | \(0.612839\pi\) | |||||||
\(798\) | −6.29835 | −0.222959 | ||||||||
\(799\) | −27.3518 | −0.967637 | ||||||||
\(800\) | −1.97284 | −0.0697505 | ||||||||
\(801\) | 10.6723 | 0.377088 | ||||||||
\(802\) | −9.90263 | −0.349674 | ||||||||
\(803\) | −9.29101 | −0.327872 | ||||||||
\(804\) | −6.49051 | −0.228903 | ||||||||
\(805\) | 0.774328 | 0.0272915 | ||||||||
\(806\) | −6.26657 | −0.220730 | ||||||||
\(807\) | −22.6179 | −0.796189 | ||||||||
\(808\) | 13.2816 | 0.467245 | ||||||||
\(809\) | 8.58664 | 0.301890 | 0.150945 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150945 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(810\) | −0.0100882 | −0.000354463 0 | ||||||||
\(811\) | 29.3272 | 1.02982 | 0.514909 | − | 0.857245i | \(-0.327826\pi\) | ||||
0.514909 | + | 0.857245i | \(0.327826\pi\) | |||||||
\(812\) | 0.563539 | 0.0197763 | ||||||||
\(813\) | −18.9150 | −0.663380 | ||||||||
\(814\) | −13.3365 | −0.467443 | ||||||||
\(815\) | 16.4946 | 0.577781 | ||||||||
\(816\) | −9.82276 | −0.343865 | ||||||||
\(817\) | −42.9492 | −1.50260 | ||||||||
\(818\) | −30.5749 | −1.06903 | ||||||||
\(819\) | −3.39733 | −0.118712 | ||||||||
\(820\) | 16.4149 | 0.573234 | ||||||||
\(821\) | −6.41377 | −0.223842 | −0.111921 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111921 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(822\) | 30.6496 | 1.06903 | ||||||||
\(823\) | 35.2079 | 1.22727 | 0.613635 | − | 0.789590i | \(-0.289707\pi\) | ||||
0.613635 | + | 0.789590i | \(0.289707\pi\) | |||||||
\(824\) | 3.02225 | 0.105285 | ||||||||
\(825\) | −22.7386 | −0.791656 | ||||||||
\(826\) | −5.66421 | −0.197083 | ||||||||
\(827\) | −50.6697 | −1.76196 | −0.880978 | − | 0.473157i | \(-0.843114\pi\) | ||||
−0.880978 | + | 0.473157i | \(0.843114\pi\) | |||||||
\(828\) | −5.58278 | −0.194015 | ||||||||
\(829\) | −19.0272 | −0.660841 | −0.330420 | − | 0.943834i | \(-0.607191\pi\) | ||||
−0.330420 | + | 0.943834i | \(0.607191\pi\) | |||||||
\(830\) | −24.7750 | −0.859953 | ||||||||
\(831\) | 47.8616 | 1.66030 | ||||||||
\(832\) | 1.80933 | 0.0627271 | ||||||||
\(833\) | −24.0115 | −0.831950 | ||||||||
\(834\) | −2.98120 | −0.103230 | ||||||||
\(835\) | −37.2917 | −1.29053 | ||||||||
\(836\) | 23.8924 | 0.826336 | ||||||||
\(837\) | 17.9874 | 0.621735 | ||||||||
\(838\) | 19.7963 | 0.683850 | ||||||||
\(839\) | −31.5069 | −1.08774 | −0.543869 | − | 0.839170i | \(-0.683041\pi\) | ||||
−0.543869 | + | 0.839170i | \(0.683041\pi\) | |||||||
\(840\) | 1.88639 | 0.0650865 | ||||||||
\(841\) | −26.8784 | −0.926840 | ||||||||
\(842\) | −14.7606 | −0.508683 | ||||||||
\(843\) | 24.0582 | 0.828607 | ||||||||
\(844\) | −16.5607 | −0.570043 | ||||||||
\(845\) | −16.9226 | −0.582155 | ||||||||
\(846\) | −37.8711 | −1.30204 | ||||||||
\(847\) | −2.28877 | −0.0786432 | ||||||||
\(848\) | −0.0764819 | −0.00262640 | ||||||||
\(849\) | 31.4069 | 1.07788 | ||||||||
\(850\) | −6.91515 | −0.237188 | ||||||||
\(851\) | −3.73004 | −0.127864 | ||||||||
\(852\) | −26.4379 | −0.905746 | ||||||||
\(853\) | 6.43711 | 0.220402 | 0.110201 | − | 0.993909i | \(-0.464850\pi\) | ||||
0.110201 | + | 0.993909i | \(0.464850\pi\) | |||||||
\(854\) | −1.04382 | −0.0357189 | ||||||||
\(855\) | −49.0527 | −1.67757 | ||||||||
\(856\) | −10.5944 | −0.362111 | ||||||||
\(857\) | −20.9885 | −0.716952 | −0.358476 | − | 0.933539i | \(-0.616704\pi\) | ||||
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(858\) | 20.8539 | 0.711941 | ||||||||
\(859\) | −33.2709 | −1.13519 | −0.567595 | − | 0.823308i | \(-0.692126\pi\) | ||||
−0.567595 | + | 0.823308i | \(0.692126\pi\) | |||||||
\(860\) | 12.8635 | 0.438642 | ||||||||
\(861\) | 10.2290 | 0.348605 | ||||||||
\(862\) | 10.8736 | 0.370357 | ||||||||
\(863\) | −38.9050 | −1.32434 | −0.662171 | − | 0.749353i | \(-0.730365\pi\) | ||||
−0.662171 | + | 0.749353i | \(0.730365\pi\) | |||||||
\(864\) | −5.19344 | −0.176685 | ||||||||
\(865\) | 36.5175 | 1.24163 | ||||||||
\(866\) | −29.3690 | −0.997998 | ||||||||
\(867\) | 13.2097 | 0.448626 | ||||||||
\(868\) | 1.33999 | 0.0454822 | ||||||||
\(869\) | −16.5060 | −0.559929 | ||||||||
\(870\) | 7.10194 | 0.240778 | ||||||||
\(871\) | 4.19056 | 0.141992 | ||||||||
\(872\) | 11.8288 | 0.400574 | ||||||||
\(873\) | −44.6399 | −1.51083 | ||||||||
\(874\) | 6.68240 | 0.226036 | ||||||||
\(875\) | 4.69371 | 0.158676 | ||||||||
\(876\) | −6.33054 | −0.213889 | ||||||||
\(877\) | 26.1977 | 0.884632 | 0.442316 | − | 0.896859i | \(-0.354157\pi\) | ||||
0.442316 | + | 0.896859i | \(0.354157\pi\) | |||||||
\(878\) | 33.4954 | 1.13042 | ||||||||
\(879\) | −63.2898 | −2.13471 | ||||||||
\(880\) | −7.15589 | −0.241225 | ||||||||
\(881\) | −24.2765 | −0.817895 | −0.408948 | − | 0.912558i | \(-0.634104\pi\) | ||||
−0.408948 | + | 0.912558i | \(0.634104\pi\) | |||||||
\(882\) | −33.2462 | −1.11946 | ||||||||
\(883\) | −13.9387 | −0.469076 | −0.234538 | − | 0.972107i | \(-0.575358\pi\) | ||||
−0.234538 | + | 0.972107i | \(0.575358\pi\) | |||||||
\(884\) | 6.34200 | 0.213305 | ||||||||
\(885\) | −71.3827 | −2.39950 | ||||||||
\(886\) | 5.91776 | 0.198811 | ||||||||
\(887\) | 16.7014 | 0.560778 | 0.280389 | − | 0.959886i | \(-0.409537\pi\) | ||||
0.280389 | + | 0.959886i | \(0.409537\pi\) | |||||||
\(888\) | −9.08697 | −0.304939 | ||||||||
\(889\) | −5.07115 | −0.170081 | ||||||||
\(890\) | 3.82600 | 0.128248 | ||||||||
\(891\) | 0.0238475 | 0.000798921 0 | ||||||||
\(892\) | −4.46460 | −0.149486 | ||||||||
\(893\) | 45.3305 | 1.51693 | ||||||||
\(894\) | 27.4789 | 0.919030 | ||||||||
\(895\) | 42.4674 | 1.41953 | ||||||||
\(896\) | −0.386891 | −0.0129251 | ||||||||
\(897\) | 5.83258 | 0.194744 | ||||||||
\(898\) | 12.2918 | 0.410182 | ||||||||
\(899\) | 5.04484 | 0.168255 | ||||||||
\(900\) | −9.57467 | −0.319156 | ||||||||
\(901\) | −0.268082 | −0.00893111 | ||||||||
\(902\) | −38.8032 | −1.29201 | ||||||||
\(903\) | 8.01595 | 0.266754 | ||||||||
\(904\) | 5.18957 | 0.172603 | ||||||||
\(905\) | 39.2135 | 1.30350 | ||||||||
\(906\) | −60.3406 | −2.00468 | ||||||||
\(907\) | −34.8498 | −1.15717 | −0.578584 | − | 0.815623i | \(-0.696395\pi\) | ||||
−0.578584 | + | 0.815623i | \(0.696395\pi\) | |||||||
\(908\) | 6.05656 | 0.200994 | ||||||||
\(909\) | 64.4587 | 2.13796 | ||||||||
\(910\) | −1.21793 | −0.0403741 | ||||||||
\(911\) | −18.4574 | −0.611520 | −0.305760 | − | 0.952109i | \(-0.598910\pi\) | ||||
−0.305760 | + | 0.952109i | \(0.598910\pi\) | |||||||
\(912\) | 16.2794 | 0.539064 | ||||||||
\(913\) | 58.5656 | 1.93824 | ||||||||
\(914\) | 20.5618 | 0.680124 | ||||||||
\(915\) | −13.1547 | −0.434881 | ||||||||
\(916\) | −26.5917 | −0.878616 | ||||||||
\(917\) | 4.25730 | 0.140588 | ||||||||
\(918\) | −18.2039 | −0.600818 | ||||||||
\(919\) | −48.9446 | −1.61453 | −0.807266 | − | 0.590188i | \(-0.799054\pi\) | ||||
−0.807266 | + | 0.590188i | \(0.799054\pi\) | |||||||
\(920\) | −2.00141 | −0.0659846 | ||||||||
\(921\) | −35.5672 | −1.17198 | ||||||||
\(922\) | 15.8977 | 0.523562 | ||||||||
\(923\) | 17.0694 | 0.561847 | ||||||||
\(924\) | −4.45922 | −0.146698 | ||||||||
\(925\) | −6.39716 | −0.210337 | ||||||||
\(926\) | −12.0243 | −0.395143 | ||||||||
\(927\) | 14.6677 | 0.481750 | ||||||||
\(928\) | −1.45658 | −0.0478147 | ||||||||
\(929\) | 58.1360 | 1.90738 | 0.953690 | − | 0.300791i | \(-0.0972505\pi\) | ||||
0.953690 | + | 0.300791i | \(0.0972505\pi\) | |||||||
\(930\) | 16.8871 | 0.553749 | ||||||||
\(931\) | 39.7946 | 1.30422 | ||||||||
\(932\) | −0.193795 | −0.00634796 | ||||||||
\(933\) | 53.3611 | 1.74697 | ||||||||
\(934\) | 26.3272 | 0.861452 | ||||||||
\(935\) | −25.0826 | −0.820290 | ||||||||
\(936\) | 8.78109 | 0.287019 | ||||||||
\(937\) | −24.6344 | −0.804771 | −0.402386 | − | 0.915470i | \(-0.631819\pi\) | ||||
−0.402386 | + | 0.915470i | \(0.631819\pi\) | |||||||
\(938\) | −0.896073 | −0.0292578 | ||||||||
\(939\) | −44.6067 | −1.45569 | ||||||||
\(940\) | −13.5767 | −0.442823 | ||||||||
\(941\) | 41.0314 | 1.33758 | 0.668792 | − | 0.743449i | \(-0.266811\pi\) | ||||
0.668792 | + | 0.743449i | \(0.266811\pi\) | |||||||
\(942\) | −37.2210 | −1.21272 | ||||||||
\(943\) | −10.8528 | −0.353415 | ||||||||
\(944\) | 14.6403 | 0.476502 | ||||||||
\(945\) | 3.49592 | 0.113722 | ||||||||
\(946\) | −30.4080 | −0.988650 | ||||||||
\(947\) | 17.7566 | 0.577012 | 0.288506 | − | 0.957478i | \(-0.406842\pi\) | ||||
0.288506 | + | 0.957478i | \(0.406842\pi\) | |||||||
\(948\) | −11.2466 | −0.365272 | ||||||||
\(949\) | 4.08727 | 0.132678 | ||||||||
\(950\) | 11.4606 | 0.371830 | ||||||||
\(951\) | −14.4961 | −0.470069 | ||||||||
\(952\) | −1.35612 | −0.0439521 | ||||||||
\(953\) | 7.20625 | 0.233433 | 0.116717 | − | 0.993165i | \(-0.462763\pi\) | ||||
0.116717 | + | 0.993165i | \(0.462763\pi\) | |||||||
\(954\) | −0.371185 | −0.0120175 | ||||||||
\(955\) | 15.6912 | 0.507756 | ||||||||
\(956\) | 13.5686 | 0.438839 | ||||||||
\(957\) | −16.7883 | −0.542688 | ||||||||
\(958\) | 12.8252 | 0.414362 | ||||||||
\(959\) | 4.23145 | 0.136641 | ||||||||
\(960\) | −4.87575 | −0.157364 | ||||||||
\(961\) | −19.0043 | −0.613042 | ||||||||
\(962\) | 5.86694 | 0.189158 | ||||||||
\(963\) | −51.4174 | −1.65690 | ||||||||
\(964\) | 15.6446 | 0.503879 | ||||||||
\(965\) | 34.0666 | 1.09664 | ||||||||
\(966\) | −1.24719 | −0.0401276 | ||||||||
\(967\) | −6.79547 | −0.218528 | −0.109264 | − | 0.994013i | \(-0.534849\pi\) | ||||
−0.109264 | + | 0.994013i | \(0.534849\pi\) | |||||||
\(968\) | 5.91581 | 0.190141 | ||||||||
\(969\) | 57.0620 | 1.83310 | ||||||||
\(970\) | −16.0033 | −0.513834 | ||||||||
\(971\) | −11.0555 | −0.354787 | −0.177394 | − | 0.984140i | \(-0.556767\pi\) | ||||
−0.177394 | + | 0.984140i | \(0.556767\pi\) | |||||||
\(972\) | 15.5966 | 0.500261 | ||||||||
\(973\) | −0.411581 | −0.0131947 | ||||||||
\(974\) | 32.0639 | 1.02739 | ||||||||
\(975\) | 10.0031 | 0.320355 | ||||||||
\(976\) | 2.69798 | 0.0863602 | ||||||||
\(977\) | −53.8767 | −1.72367 | −0.861834 | − | 0.507191i | \(-0.830684\pi\) | ||||
−0.861834 | + | 0.507191i | \(0.830684\pi\) | |||||||
\(978\) | −26.5674 | −0.849531 | ||||||||
\(979\) | −9.04428 | −0.289057 | ||||||||
\(980\) | −11.9187 | −0.380728 | ||||||||
\(981\) | 57.4080 | 1.83290 | ||||||||
\(982\) | −30.6227 | −0.977209 | ||||||||
\(983\) | 22.6631 | 0.722842 | 0.361421 | − | 0.932403i | \(-0.382292\pi\) | ||||
0.361421 | + | 0.932403i | \(0.382292\pi\) | |||||||
\(984\) | −26.4391 | −0.842847 | ||||||||
\(985\) | −40.1890 | −1.28053 | ||||||||
\(986\) | −5.10557 | −0.162594 | ||||||||
\(987\) | −8.46038 | −0.269297 | ||||||||
\(988\) | −10.5107 | −0.334389 | ||||||||
\(989\) | −8.50474 | −0.270435 | ||||||||
\(990\) | −34.7292 | −1.10377 | ||||||||
\(991\) | 22.9896 | 0.730290 | 0.365145 | − | 0.930951i | \(-0.381019\pi\) | ||||
0.365145 | + | 0.930951i | \(0.381019\pi\) | |||||||
\(992\) | −3.46348 | −0.109966 | ||||||||
\(993\) | −36.1943 | −1.14859 | ||||||||
\(994\) | −3.64998 | −0.115770 | ||||||||
\(995\) | −11.3196 | −0.358854 | ||||||||
\(996\) | 39.9044 | 1.26442 | ||||||||
\(997\) | 32.0237 | 1.01420 | 0.507101 | − | 0.861887i | \(-0.330717\pi\) | ||||
0.507101 | + | 0.861887i | \(0.330717\pi\) | |||||||
\(998\) | 17.3833 | 0.550259 | ||||||||
\(999\) | −16.8403 | −0.532804 |
(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 | 8002.2.a.g.1.6 | ✓ | 95 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.g.1.6 | ✓ | 95 | 1.1 | even | 1 | trivial |