Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.230234 | 0.102964 | 0.0514819 | − | 0.998674i | \(-0.483606\pi\) | ||||
0.0514819 | + | 0.998674i | \(0.483606\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.59819 | 1.73795 | 0.868977 | − | 0.494853i | \(-0.164778\pi\) | ||||
0.868977 | + | 0.494853i | \(0.164778\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.230234 | −0.0728065 | ||||||||
\(11\) | −4.50283 | −1.35765 | −0.678827 | − | 0.734299i | \(-0.737511\pi\) | ||||
−0.678827 | + | 0.734299i | \(0.737511\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.15403 | 0.320070 | 0.160035 | − | 0.987111i | \(-0.448839\pi\) | ||||
0.160035 | + | 0.987111i | \(0.448839\pi\) | |||||||
\(14\) | −4.59819 | −1.22892 | ||||||||
\(15\) | −0.230234 | −0.0594462 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.42662 | −1.80122 | −0.900610 | − | 0.434628i | \(-0.856880\pi\) | ||||
−0.900610 | + | 0.434628i | \(0.856880\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −5.94699 | −1.36433 | −0.682167 | − | 0.731197i | \(-0.738962\pi\) | ||||
−0.682167 | + | 0.731197i | \(0.738962\pi\) | |||||||
\(20\) | 0.230234 | 0.0514819 | ||||||||
\(21\) | −4.59819 | −1.00341 | ||||||||
\(22\) | 4.50283 | 0.960006 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.94699 | −0.989398 | ||||||||
\(26\) | −1.15403 | −0.226323 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.59819 | 0.868977 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0.230234 | 0.0420348 | ||||||||
\(31\) | 6.50283 | 1.16794 | 0.583971 | − | 0.811774i | \(-0.301498\pi\) | ||||
0.583971 | + | 0.811774i | \(0.301498\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.50283 | 0.783842 | ||||||||
\(34\) | 7.42662 | 1.27365 | ||||||||
\(35\) | 1.05866 | 0.178946 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.29175 | 1.19876 | 0.599378 | − | 0.800466i | \(-0.295415\pi\) | ||||
0.599378 | + | 0.800466i | \(0.295415\pi\) | |||||||
\(38\) | 5.94699 | 0.964730 | ||||||||
\(39\) | −1.15403 | −0.184792 | ||||||||
\(40\) | −0.230234 | −0.0364032 | ||||||||
\(41\) | 0.0953661 | 0.0148937 | 0.00744684 | − | 0.999972i | \(-0.497630\pi\) | ||||
0.00744684 | + | 0.999972i | \(0.497630\pi\) | |||||||
\(42\) | 4.59819 | 0.709517 | ||||||||
\(43\) | 0.941339 | 0.143553 | 0.0717764 | − | 0.997421i | \(-0.477133\pi\) | ||||
0.0717764 | + | 0.997421i | \(0.477133\pi\) | |||||||
\(44\) | −4.50283 | −0.678827 | ||||||||
\(45\) | 0.230234 | 0.0343213 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −0.598193 | −0.0872554 | −0.0436277 | − | 0.999048i | \(-0.513892\pi\) | ||||
−0.0436277 | + | 0.999048i | \(0.513892\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 14.1434 | 2.02048 | ||||||||
\(50\) | 4.94699 | 0.699610 | ||||||||
\(51\) | 7.42662 | 1.03993 | ||||||||
\(52\) | 1.15403 | 0.160035 | ||||||||
\(53\) | 13.3736 | 1.83701 | 0.918503 | − | 0.395413i | \(-0.129399\pi\) | ||||
0.918503 | + | 0.395413i | \(0.129399\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.03670 | −0.139789 | ||||||||
\(56\) | −4.59819 | −0.614459 | ||||||||
\(57\) | 5.94699 | 0.787698 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −2.94134 | −0.382930 | −0.191465 | − | 0.981499i | \(-0.561324\pi\) | ||||
−0.191465 | + | 0.981499i | \(0.561324\pi\) | |||||||
\(60\) | −0.230234 | −0.0297231 | ||||||||
\(61\) | 10.8883 | 1.39411 | 0.697054 | − | 0.717019i | \(-0.254494\pi\) | ||||
0.697054 | + | 0.717019i | \(0.254494\pi\) | |||||||
\(62\) | −6.50283 | −0.825860 | ||||||||
\(63\) | 4.59819 | 0.579318 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.265697 | 0.0329556 | ||||||||
\(66\) | −4.50283 | −0.554260 | ||||||||
\(67\) | 2.09251 | 0.255641 | 0.127820 | − | 0.991797i | \(-0.459202\pi\) | ||||
0.127820 | + | 0.991797i | \(0.459202\pi\) | |||||||
\(68\) | −7.42662 | −0.900610 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.05866 | −0.126534 | ||||||||
\(71\) | 10.9633 | 1.30110 | 0.650552 | − | 0.759462i | \(-0.274538\pi\) | ||||
0.650552 | + | 0.759462i | \(0.274538\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.3928 | −1.45046 | −0.725232 | − | 0.688504i | \(-0.758268\pi\) | ||||
−0.725232 | + | 0.688504i | \(0.758268\pi\) | |||||||
\(74\) | −7.29175 | −0.847649 | ||||||||
\(75\) | 4.94699 | 0.571229 | ||||||||
\(76\) | −5.94699 | −0.682167 | ||||||||
\(77\) | −20.7049 | −2.35954 | ||||||||
\(78\) | 1.15403 | 0.130668 | ||||||||
\(79\) | 16.5276 | 1.85950 | 0.929752 | − | 0.368185i | \(-0.120021\pi\) | ||||
0.929752 | + | 0.368185i | \(0.120021\pi\) | |||||||
\(80\) | 0.230234 | 0.0257410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.0953661 | −0.0105314 | ||||||||
\(83\) | −1.71676 | −0.188439 | −0.0942193 | − | 0.995551i | \(-0.530035\pi\) | ||||
−0.0942193 | + | 0.995551i | \(0.530035\pi\) | |||||||
\(84\) | −4.59819 | −0.501704 | ||||||||
\(85\) | −1.70986 | −0.185461 | ||||||||
\(86\) | −0.941339 | −0.101507 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 4.50283 | 0.480003 | ||||||||
\(89\) | 12.5700 | 1.33242 | 0.666209 | − | 0.745765i | \(-0.267916\pi\) | ||||
0.666209 | + | 0.745765i | \(0.267916\pi\) | |||||||
\(90\) | −0.230234 | −0.0242688 | ||||||||
\(91\) | 5.30644 | 0.556266 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.50283 | −0.674312 | ||||||||
\(94\) | 0.598193 | 0.0616989 | ||||||||
\(95\) | −1.36920 | −0.140477 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.82277 | −0.185075 | −0.0925373 | − | 0.995709i | \(-0.529498\pi\) | ||||
−0.0925373 | + | 0.995709i | \(0.529498\pi\) | |||||||
\(98\) | −14.1434 | −1.42870 | ||||||||
\(99\) | −4.50283 | −0.452551 | ||||||||
\(100\) | −4.94699 | −0.494699 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | −7.42662 | −0.735345 | ||||||||
\(103\) | −11.9119 | −1.17371 | −0.586857 | − | 0.809690i | \(-0.699635\pi\) | ||||
−0.586857 | + | 0.809690i | \(0.699635\pi\) | |||||||
\(104\) | −1.15403 | −0.113162 | ||||||||
\(105\) | −1.05866 | −0.103315 | ||||||||
\(106\) | −13.3736 | −1.29896 | ||||||||
\(107\) | 12.0819 | 1.16800 | 0.583999 | − | 0.811755i | \(-0.301487\pi\) | ||||
0.583999 | + | 0.811755i | \(0.301487\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.71676 | 0.739131 | 0.369566 | − | 0.929205i | \(-0.379506\pi\) | ||||
0.369566 | + | 0.929205i | \(0.379506\pi\) | |||||||
\(110\) | 1.03670 | 0.0988459 | ||||||||
\(111\) | −7.29175 | −0.692102 | ||||||||
\(112\) | 4.59819 | 0.434488 | ||||||||
\(113\) | 8.65810 | 0.814485 | 0.407243 | − | 0.913320i | \(-0.366490\pi\) | ||||
0.407243 | + | 0.913320i | \(0.366490\pi\) | |||||||
\(114\) | −5.94699 | −0.556987 | ||||||||
\(115\) | 0.230234 | 0.0214695 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 1.15403 | 0.106690 | ||||||||
\(118\) | 2.94134 | 0.270772 | ||||||||
\(119\) | −34.1490 | −3.13044 | ||||||||
\(120\) | 0.230234 | 0.0210174 | ||||||||
\(121\) | 9.27545 | 0.843223 | ||||||||
\(122\) | −10.8883 | −0.985783 | ||||||||
\(123\) | −0.0953661 | −0.00859887 | ||||||||
\(124\) | 6.50283 | 0.583971 | ||||||||
\(125\) | −2.29014 | −0.204836 | ||||||||
\(126\) | −4.59819 | −0.409640 | ||||||||
\(127\) | 5.11167 | 0.453587 | 0.226794 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226794 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.941339 | −0.0828802 | ||||||||
\(130\) | −0.265697 | −0.0233031 | ||||||||
\(131\) | 10.3968 | 0.908374 | 0.454187 | − | 0.890906i | \(-0.349930\pi\) | ||||
0.454187 | + | 0.890906i | \(0.349930\pi\) | |||||||
\(132\) | 4.50283 | 0.391921 | ||||||||
\(133\) | −27.3454 | −2.37115 | ||||||||
\(134\) | −2.09251 | −0.180765 | ||||||||
\(135\) | −0.230234 | −0.0198154 | ||||||||
\(136\) | 7.42662 | 0.636827 | ||||||||
\(137\) | 12.7958 | 1.09322 | 0.546610 | − | 0.837387i | \(-0.315918\pi\) | ||||
0.546610 | + | 0.837387i | \(0.315918\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −2.80361 | −0.237799 | −0.118900 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118900 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(140\) | 1.05866 | 0.0894732 | ||||||||
\(141\) | 0.598193 | 0.0503769 | ||||||||
\(142\) | −10.9633 | −0.920019 | ||||||||
\(143\) | −5.19639 | −0.434544 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.230234 | −0.0191199 | ||||||||
\(146\) | 12.3928 | 1.02563 | ||||||||
\(147\) | −14.1434 | −1.16653 | ||||||||
\(148\) | 7.29175 | 0.599378 | ||||||||
\(149\) | −6.92783 | −0.567550 | −0.283775 | − | 0.958891i | \(-0.591587\pi\) | ||||
−0.283775 | + | 0.958891i | \(0.591587\pi\) | |||||||
\(150\) | −4.94699 | −0.403920 | ||||||||
\(151\) | 17.5289 | 1.42648 | 0.713240 | − | 0.700920i | \(-0.247227\pi\) | ||||
0.713240 | + | 0.700920i | \(0.247227\pi\) | |||||||
\(152\) | 5.94699 | 0.482365 | ||||||||
\(153\) | −7.42662 | −0.600407 | ||||||||
\(154\) | 20.7049 | 1.66845 | ||||||||
\(155\) | 1.49717 | 0.120256 | ||||||||
\(156\) | −1.15403 | −0.0923961 | ||||||||
\(157\) | 6.09537 | 0.486463 | 0.243232 | − | 0.969968i | \(-0.421792\pi\) | ||||
0.243232 | + | 0.969968i | \(0.421792\pi\) | |||||||
\(158\) | −16.5276 | −1.31487 | ||||||||
\(159\) | −13.3736 | −1.06060 | ||||||||
\(160\) | −0.230234 | −0.0182016 | ||||||||
\(161\) | 4.59819 | 0.362388 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.25343 | −0.0981765 | −0.0490882 | − | 0.998794i | \(-0.515632\pi\) | ||||
−0.0490882 | + | 0.998794i | \(0.515632\pi\) | |||||||
\(164\) | 0.0953661 | 0.00744684 | ||||||||
\(165\) | 1.03670 | 0.0807074 | ||||||||
\(166\) | 1.71676 | 0.133246 | ||||||||
\(167\) | −2.49879 | −0.193362 | −0.0966810 | − | 0.995315i | \(-0.530823\pi\) | ||||
−0.0966810 | + | 0.995315i | \(0.530823\pi\) | |||||||
\(168\) | 4.59819 | 0.354758 | ||||||||
\(169\) | −11.6682 | −0.897555 | ||||||||
\(170\) | 1.70986 | 0.131140 | ||||||||
\(171\) | −5.94699 | −0.454778 | ||||||||
\(172\) | 0.941339 | 0.0717764 | ||||||||
\(173\) | 6.21269 | 0.472342 | 0.236171 | − | 0.971712i | \(-0.424107\pi\) | ||||
0.236171 | + | 0.971712i | \(0.424107\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | −22.7472 | −1.71953 | ||||||||
\(176\) | −4.50283 | −0.339413 | ||||||||
\(177\) | 2.94134 | 0.221085 | ||||||||
\(178\) | −12.5700 | −0.942161 | ||||||||
\(179\) | 9.55084 | 0.713863 | 0.356932 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356932 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(180\) | 0.230234 | 0.0171606 | ||||||||
\(181\) | −14.2196 | −1.05693 | −0.528467 | − | 0.848954i | \(-0.677233\pi\) | ||||
−0.528467 | + | 0.848954i | \(0.677233\pi\) | |||||||
\(182\) | −5.30644 | −0.393340 | ||||||||
\(183\) | −10.8883 | −0.804889 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 1.67881 | 0.123429 | ||||||||
\(186\) | 6.50283 | 0.476810 | ||||||||
\(187\) | 33.4408 | 2.44543 | ||||||||
\(188\) | −0.598193 | −0.0436277 | ||||||||
\(189\) | −4.59819 | −0.334469 | ||||||||
\(190\) | 1.36920 | 0.0993323 | ||||||||
\(191\) | 2.00286 | 0.144922 | 0.0724608 | − | 0.997371i | \(-0.476915\pi\) | ||||
0.0724608 | + | 0.997371i | \(0.476915\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 21.6242 | 1.55655 | 0.778274 | − | 0.627925i | \(-0.216096\pi\) | ||||
0.778274 | + | 0.627925i | \(0.216096\pi\) | |||||||
\(194\) | 1.82277 | 0.130868 | ||||||||
\(195\) | −0.265697 | −0.0190269 | ||||||||
\(196\) | 14.1434 | 1.01024 | ||||||||
\(197\) | 2.89898 | 0.206544 | 0.103272 | − | 0.994653i | \(-0.467069\pi\) | ||||
0.103272 | + | 0.994653i | \(0.467069\pi\) | |||||||
\(198\) | 4.50283 | 0.320002 | ||||||||
\(199\) | 12.2754 | 0.870184 | 0.435092 | − | 0.900386i | \(-0.356716\pi\) | ||||
0.435092 | + | 0.900386i | \(0.356716\pi\) | |||||||
\(200\) | 4.94699 | 0.349805 | ||||||||
\(201\) | −2.09251 | −0.147594 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −4.59819 | −0.322730 | ||||||||
\(204\) | 7.42662 | 0.519967 | ||||||||
\(205\) | 0.0219565 | 0.00153351 | ||||||||
\(206\) | 11.9119 | 0.829941 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 1.15403 | 0.0800174 | ||||||||
\(209\) | 26.7783 | 1.85229 | ||||||||
\(210\) | 1.05866 | 0.0730546 | ||||||||
\(211\) | −15.8369 | −1.09026 | −0.545130 | − | 0.838352i | \(-0.683520\pi\) | ||||
−0.545130 | + | 0.838352i | \(0.683520\pi\) | |||||||
\(212\) | 13.3736 | 0.918503 | ||||||||
\(213\) | −10.9633 | −0.751193 | ||||||||
\(214\) | −12.0819 | −0.825899 | ||||||||
\(215\) | 0.216728 | 0.0147808 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 29.9013 | 2.02983 | ||||||||
\(218\) | −7.71676 | −0.522645 | ||||||||
\(219\) | 12.3928 | 0.837426 | ||||||||
\(220\) | −1.03670 | −0.0698946 | ||||||||
\(221\) | −8.57052 | −0.576516 | ||||||||
\(222\) | 7.29175 | 0.489390 | ||||||||
\(223\) | −13.6569 | −0.914531 | −0.457265 | − | 0.889330i | \(-0.651171\pi\) | ||||
−0.457265 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(224\) | −4.59819 | −0.307230 | ||||||||
\(225\) | −4.94699 | −0.329799 | ||||||||
\(226\) | −8.65810 | −0.575928 | ||||||||
\(227\) | 12.2726 | 0.814561 | 0.407280 | − | 0.913303i | \(-0.366477\pi\) | ||||
0.407280 | + | 0.913303i | \(0.366477\pi\) | |||||||
\(228\) | 5.94699 | 0.393849 | ||||||||
\(229\) | −7.37647 | −0.487451 | −0.243725 | − | 0.969844i | \(-0.578370\pi\) | ||||
−0.243725 | + | 0.969844i | \(0.578370\pi\) | |||||||
\(230\) | −0.230234 | −0.0151812 | ||||||||
\(231\) | 20.7049 | 1.36228 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 28.2020 | 1.84758 | 0.923789 | − | 0.382903i | \(-0.125076\pi\) | ||||
0.923789 | + | 0.382903i | \(0.125076\pi\) | |||||||
\(234\) | −1.15403 | −0.0754411 | ||||||||
\(235\) | −0.137724 | −0.00898415 | ||||||||
\(236\) | −2.94134 | −0.191465 | ||||||||
\(237\) | −16.5276 | −1.07359 | ||||||||
\(238\) | 34.1490 | 2.21355 | ||||||||
\(239\) | 1.14676 | 0.0741777 | 0.0370889 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370889 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(240\) | −0.230234 | −0.0148616 | ||||||||
\(241\) | 12.6406 | 0.814249 | 0.407125 | − | 0.913373i | \(-0.366531\pi\) | ||||
0.407125 | + | 0.913373i | \(0.366531\pi\) | |||||||
\(242\) | −9.27545 | −0.596248 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.8883 | 0.697054 | ||||||||
\(245\) | 3.25629 | 0.208037 | ||||||||
\(246\) | 0.0953661 | 0.00608032 | ||||||||
\(247\) | −6.86299 | −0.436682 | ||||||||
\(248\) | −6.50283 | −0.412930 | ||||||||
\(249\) | 1.71676 | 0.108795 | ||||||||
\(250\) | 2.29014 | 0.144841 | ||||||||
\(251\) | −5.62425 | −0.354999 | −0.177500 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177500 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(252\) | 4.59819 | 0.289659 | ||||||||
\(253\) | −4.50283 | −0.283090 | ||||||||
\(254\) | −5.11167 | −0.320735 | ||||||||
\(255\) | 1.70986 | 0.107076 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.3177 | −1.32976 | −0.664882 | − | 0.746948i | \(-0.731518\pi\) | ||||
−0.664882 | + | 0.746948i | \(0.731518\pi\) | |||||||
\(258\) | 0.941339 | 0.0586052 | ||||||||
\(259\) | 33.5289 | 2.08338 | ||||||||
\(260\) | 0.265697 | 0.0164778 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −10.3968 | −0.642317 | ||||||||
\(263\) | −1.96205 | −0.120985 | −0.0604927 | − | 0.998169i | \(-0.519267\pi\) | ||||
−0.0604927 | + | 0.998169i | \(0.519267\pi\) | |||||||
\(264\) | −4.50283 | −0.277130 | ||||||||
\(265\) | 3.07906 | 0.189145 | ||||||||
\(266\) | 27.3454 | 1.67666 | ||||||||
\(267\) | −12.5700 | −0.769271 | ||||||||
\(268\) | 2.09251 | 0.127820 | ||||||||
\(269\) | −3.85163 | −0.234838 | −0.117419 | − | 0.993082i | \(-0.537462\pi\) | ||||
−0.117419 | + | 0.993082i | \(0.537462\pi\) | |||||||
\(270\) | 0.230234 | 0.0140116 | ||||||||
\(271\) | −1.47183 | −0.0894076 | −0.0447038 | − | 0.999000i | \(-0.514234\pi\) | ||||
−0.0447038 | + | 0.999000i | \(0.514234\pi\) | |||||||
\(272\) | −7.42662 | −0.450305 | ||||||||
\(273\) | −5.30644 | −0.321160 | ||||||||
\(274\) | −12.7958 | −0.773024 | ||||||||
\(275\) | 22.2754 | 1.34326 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −24.6665 | −1.48207 | −0.741035 | − | 0.671467i | \(-0.765665\pi\) | ||||
−0.741035 | + | 0.671467i | \(0.765665\pi\) | |||||||
\(278\) | 2.80361 | 0.168150 | ||||||||
\(279\) | 6.50283 | 0.389314 | ||||||||
\(280\) | −1.05866 | −0.0632671 | ||||||||
\(281\) | −12.3081 | −0.734237 | −0.367119 | − | 0.930174i | \(-0.619656\pi\) | ||||
−0.367119 | + | 0.930174i | \(0.619656\pi\) | |||||||
\(282\) | −0.598193 | −0.0356219 | ||||||||
\(283\) | −23.8087 | −1.41528 | −0.707641 | − | 0.706572i | \(-0.750241\pi\) | ||||
−0.707641 | + | 0.706572i | \(0.750241\pi\) | |||||||
\(284\) | 10.9633 | 0.650552 | ||||||||
\(285\) | 1.36920 | 0.0811045 | ||||||||
\(286\) | 5.19639 | 0.307269 | ||||||||
\(287\) | 0.438512 | 0.0258845 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 38.1547 | 2.24439 | ||||||||
\(290\) | 0.230234 | 0.0135198 | ||||||||
\(291\) | 1.82277 | 0.106853 | ||||||||
\(292\) | −12.3928 | −0.725232 | ||||||||
\(293\) | 17.3162 | 1.01162 | 0.505811 | − | 0.862644i | \(-0.331193\pi\) | ||||
0.505811 | + | 0.862644i | \(0.331193\pi\) | |||||||
\(294\) | 14.1434 | 0.824859 | ||||||||
\(295\) | −0.677197 | −0.0394279 | ||||||||
\(296\) | −7.29175 | −0.423824 | ||||||||
\(297\) | 4.50283 | 0.261281 | ||||||||
\(298\) | 6.92783 | 0.401319 | ||||||||
\(299\) | 1.15403 | 0.0667391 | ||||||||
\(300\) | 4.94699 | 0.285615 | ||||||||
\(301\) | 4.32846 | 0.249488 | ||||||||
\(302\) | −17.5289 | −1.00867 | ||||||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | −5.94699 | −0.341083 | ||||||||
\(305\) | 2.50687 | 0.143543 | ||||||||
\(306\) | 7.42662 | 0.424552 | ||||||||
\(307\) | 0.920937 | 0.0525606 | 0.0262803 | − | 0.999655i | \(-0.491634\pi\) | ||||
0.0262803 | + | 0.999655i | \(0.491634\pi\) | |||||||
\(308\) | −20.7049 | −1.17977 | ||||||||
\(309\) | 11.9119 | 0.677644 | ||||||||
\(310\) | −1.49717 | −0.0850337 | ||||||||
\(311\) | 28.6829 | 1.62646 | 0.813229 | − | 0.581943i | \(-0.197707\pi\) | ||||
0.813229 | + | 0.581943i | \(0.197707\pi\) | |||||||
\(312\) | 1.15403 | 0.0653339 | ||||||||
\(313\) | −21.1506 | −1.19551 | −0.597753 | − | 0.801681i | \(-0.703939\pi\) | ||||
−0.597753 | + | 0.801681i | \(0.703939\pi\) | |||||||
\(314\) | −6.09537 | −0.343981 | ||||||||
\(315\) | 1.05866 | 0.0596488 | ||||||||
\(316\) | 16.5276 | 0.929752 | ||||||||
\(317\) | −27.2061 | −1.52805 | −0.764024 | − | 0.645187i | \(-0.776779\pi\) | ||||
−0.764024 | + | 0.645187i | \(0.776779\pi\) | |||||||
\(318\) | 13.3736 | 0.749955 | ||||||||
\(319\) | 4.50283 | 0.252110 | ||||||||
\(320\) | 0.230234 | 0.0128705 | ||||||||
\(321\) | −12.0819 | −0.674344 | ||||||||
\(322\) | −4.59819 | −0.256247 | ||||||||
\(323\) | 44.1661 | 2.45746 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.70896 | −0.316676 | ||||||||
\(326\) | 1.25343 | 0.0694212 | ||||||||
\(327\) | −7.71676 | −0.426738 | ||||||||
\(328\) | −0.0953661 | −0.00526571 | ||||||||
\(329\) | −2.75061 | −0.151646 | ||||||||
\(330\) | −1.03670 | −0.0570687 | ||||||||
\(331\) | 21.1833 | 1.16434 | 0.582168 | − | 0.813068i | \(-0.302204\pi\) | ||||
0.582168 | + | 0.813068i | \(0.302204\pi\) | |||||||
\(332\) | −1.71676 | −0.0942193 | ||||||||
\(333\) | 7.29175 | 0.399586 | ||||||||
\(334\) | 2.49879 | 0.136728 | ||||||||
\(335\) | 0.481767 | 0.0263218 | ||||||||
\(336\) | −4.59819 | −0.250852 | ||||||||
\(337\) | −21.5317 | −1.17291 | −0.586454 | − | 0.809982i | \(-0.699477\pi\) | ||||
−0.586454 | + | 0.809982i | \(0.699477\pi\) | |||||||
\(338\) | 11.6682 | 0.634668 | ||||||||
\(339\) | −8.65810 | −0.470243 | ||||||||
\(340\) | −1.70986 | −0.0927303 | ||||||||
\(341\) | −29.2811 | −1.58566 | ||||||||
\(342\) | 5.94699 | 0.321577 | ||||||||
\(343\) | 32.8466 | 1.77355 | ||||||||
\(344\) | −0.941339 | −0.0507536 | ||||||||
\(345\) | −0.230234 | −0.0123954 | ||||||||
\(346\) | −6.21269 | −0.333996 | ||||||||
\(347\) | −13.2845 | −0.713148 | −0.356574 | − | 0.934267i | \(-0.616055\pi\) | ||||
−0.356574 | + | 0.934267i | \(0.616055\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | 30.4392 | 1.62937 | 0.814686 | − | 0.579903i | \(-0.196909\pi\) | ||||
0.814686 | + | 0.579903i | \(0.196909\pi\) | |||||||
\(350\) | 22.7472 | 1.21589 | ||||||||
\(351\) | −1.15403 | −0.0615974 | ||||||||
\(352\) | 4.50283 | 0.240001 | ||||||||
\(353\) | 26.0847 | 1.38835 | 0.694175 | − | 0.719807i | \(-0.255770\pi\) | ||||
0.694175 | + | 0.719807i | \(0.255770\pi\) | |||||||
\(354\) | −2.94134 | −0.156330 | ||||||||
\(355\) | 2.52413 | 0.133967 | ||||||||
\(356\) | 12.5700 | 0.666209 | ||||||||
\(357\) | 34.1490 | 1.80736 | ||||||||
\(358\) | −9.55084 | −0.504778 | ||||||||
\(359\) | 29.2456 | 1.54353 | 0.771763 | − | 0.635910i | \(-0.219375\pi\) | ||||
0.771763 | + | 0.635910i | \(0.219375\pi\) | |||||||
\(360\) | −0.230234 | −0.0121344 | ||||||||
\(361\) | 16.3667 | 0.861406 | ||||||||
\(362\) | 14.2196 | 0.747365 | ||||||||
\(363\) | −9.27545 | −0.486835 | ||||||||
\(364\) | 5.30644 | 0.278133 | ||||||||
\(365\) | −2.85324 | −0.149345 | ||||||||
\(366\) | 10.8883 | 0.569142 | ||||||||
\(367\) | 25.0785 | 1.30909 | 0.654545 | − | 0.756023i | \(-0.272860\pi\) | ||||
0.654545 | + | 0.756023i | \(0.272860\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0.0953661 | 0.00496456 | ||||||||
\(370\) | −1.67881 | −0.0872772 | ||||||||
\(371\) | 61.4944 | 3.19263 | ||||||||
\(372\) | −6.50283 | −0.337156 | ||||||||
\(373\) | 36.4257 | 1.88605 | 0.943025 | − | 0.332723i | \(-0.107967\pi\) | ||||
0.943025 | + | 0.332723i | \(0.107967\pi\) | |||||||
\(374\) | −33.4408 | −1.72918 | ||||||||
\(375\) | 2.29014 | 0.118262 | ||||||||
\(376\) | 0.598193 | 0.0308494 | ||||||||
\(377\) | −1.15403 | −0.0594354 | ||||||||
\(378\) | 4.59819 | 0.236506 | ||||||||
\(379\) | −22.0847 | −1.13442 | −0.567208 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567208 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(380\) | −1.36920 | −0.0702385 | ||||||||
\(381\) | −5.11167 | −0.261879 | ||||||||
\(382\) | −2.00286 | −0.102475 | ||||||||
\(383\) | 30.2118 | 1.54375 | 0.771875 | − | 0.635774i | \(-0.219319\pi\) | ||||
0.771875 | + | 0.635774i | \(0.219319\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −4.76697 | −0.242947 | ||||||||
\(386\) | −21.6242 | −1.10065 | ||||||||
\(387\) | 0.941339 | 0.0478509 | ||||||||
\(388\) | −1.82277 | −0.0925373 | ||||||||
\(389\) | −34.5622 | −1.75237 | −0.876187 | − | 0.481972i | \(-0.839921\pi\) | ||||
−0.876187 | + | 0.481972i | \(0.839921\pi\) | |||||||
\(390\) | 0.265697 | 0.0134541 | ||||||||
\(391\) | −7.42662 | −0.375580 | ||||||||
\(392\) | −14.1434 | −0.714348 | ||||||||
\(393\) | −10.3968 | −0.524450 | ||||||||
\(394\) | −2.89898 | −0.146049 | ||||||||
\(395\) | 3.80523 | 0.191462 | ||||||||
\(396\) | −4.50283 | −0.226276 | ||||||||
\(397\) | −20.8981 | −1.04884 | −0.524422 | − | 0.851458i | \(-0.675719\pi\) | ||||
−0.524422 | + | 0.851458i | \(0.675719\pi\) | |||||||
\(398\) | −12.2754 | −0.615313 | ||||||||
\(399\) | 27.3454 | 1.36898 | ||||||||
\(400\) | −4.94699 | −0.247350 | ||||||||
\(401\) | −6.97056 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(402\) | 2.09251 | 0.104365 | ||||||||
\(403\) | 7.50444 | 0.373823 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0.230234 | 0.0114404 | ||||||||
\(406\) | 4.59819 | 0.228204 | ||||||||
\(407\) | −32.8335 | −1.62750 | ||||||||
\(408\) | −7.42662 | −0.367672 | ||||||||
\(409\) | 0.857280 | 0.0423897 | 0.0211949 | − | 0.999775i | \(-0.493253\pi\) | ||||
0.0211949 | + | 0.999775i | \(0.493253\pi\) | |||||||
\(410\) | −0.0219565 | −0.00108436 | ||||||||
\(411\) | −12.7958 | −0.631171 | ||||||||
\(412\) | −11.9119 | −0.586857 | ||||||||
\(413\) | −13.5248 | −0.665514 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −0.395256 | −0.0194024 | ||||||||
\(416\) | −1.15403 | −0.0565809 | ||||||||
\(417\) | 2.80361 | 0.137294 | ||||||||
\(418\) | −26.7783 | −1.30977 | ||||||||
\(419\) | −3.35166 | −0.163739 | −0.0818695 | − | 0.996643i | \(-0.526089\pi\) | ||||
−0.0818695 | + | 0.996643i | \(0.526089\pi\) | |||||||
\(420\) | −1.05866 | −0.0516574 | ||||||||
\(421\) | −28.7798 | −1.40264 | −0.701322 | − | 0.712845i | \(-0.747406\pi\) | ||||
−0.701322 | + | 0.712845i | \(0.747406\pi\) | |||||||
\(422\) | 15.8369 | 0.770930 | ||||||||
\(423\) | −0.598193 | −0.0290851 | ||||||||
\(424\) | −13.3736 | −0.649480 | ||||||||
\(425\) | 36.7394 | 1.78212 | ||||||||
\(426\) | 10.9633 | 0.531173 | ||||||||
\(427\) | 50.0666 | 2.42289 | ||||||||
\(428\) | 12.0819 | 0.583999 | ||||||||
\(429\) | 5.19639 | 0.250884 | ||||||||
\(430\) | −0.216728 | −0.0104516 | ||||||||
\(431\) | 8.84597 | 0.426096 | 0.213048 | − | 0.977042i | \(-0.431661\pi\) | ||||
0.213048 | + | 0.977042i | \(0.431661\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 2.74775 | 0.132048 | 0.0660242 | − | 0.997818i | \(-0.478969\pi\) | ||||
0.0660242 | + | 0.997818i | \(0.478969\pi\) | |||||||
\(434\) | −29.9013 | −1.43531 | ||||||||
\(435\) | 0.230234 | 0.0110389 | ||||||||
\(436\) | 7.71676 | 0.369566 | ||||||||
\(437\) | −5.94699 | −0.284483 | ||||||||
\(438\) | −12.3928 | −0.592150 | ||||||||
\(439\) | 16.4385 | 0.784567 | 0.392284 | − | 0.919844i | \(-0.371685\pi\) | ||||
0.392284 | + | 0.919844i | \(0.371685\pi\) | |||||||
\(440\) | 1.03670 | 0.0494230 | ||||||||
\(441\) | 14.1434 | 0.673494 | ||||||||
\(442\) | 8.57052 | 0.407658 | ||||||||
\(443\) | −29.1751 | −1.38615 | −0.693075 | − | 0.720865i | \(-0.743745\pi\) | ||||
−0.693075 | + | 0.720865i | \(0.743745\pi\) | |||||||
\(444\) | −7.29175 | −0.346051 | ||||||||
\(445\) | 2.89404 | 0.137191 | ||||||||
\(446\) | 13.6569 | 0.646671 | ||||||||
\(447\) | 6.92783 | 0.327675 | ||||||||
\(448\) | 4.59819 | 0.217244 | ||||||||
\(449\) | −30.8777 | −1.45721 | −0.728604 | − | 0.684935i | \(-0.759830\pi\) | ||||
−0.728604 | + | 0.684935i | \(0.759830\pi\) | |||||||
\(450\) | 4.94699 | 0.233203 | ||||||||
\(451\) | −0.429417 | −0.0202205 | ||||||||
\(452\) | 8.65810 | 0.407243 | ||||||||
\(453\) | −17.5289 | −0.823579 | ||||||||
\(454\) | −12.2726 | −0.575981 | ||||||||
\(455\) | 1.22172 | 0.0572753 | ||||||||
\(456\) | −5.94699 | −0.278493 | ||||||||
\(457\) | −21.0797 | −0.986068 | −0.493034 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493034 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(458\) | 7.37647 | 0.344680 | ||||||||
\(459\) | 7.42662 | 0.346645 | ||||||||
\(460\) | 0.230234 | 0.0107347 | ||||||||
\(461\) | −14.3504 | −0.668365 | −0.334183 | − | 0.942508i | \(-0.608460\pi\) | ||||
−0.334183 | + | 0.942508i | \(0.608460\pi\) | |||||||
\(462\) | −20.7049 | −0.963278 | ||||||||
\(463\) | 31.9436 | 1.48455 | 0.742273 | − | 0.670098i | \(-0.233748\pi\) | ||||
0.742273 | + | 0.670098i | \(0.233748\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −1.49717 | −0.0694297 | ||||||||
\(466\) | −28.2020 | −1.30643 | ||||||||
\(467\) | −3.07180 | −0.142146 | −0.0710729 | − | 0.997471i | \(-0.522642\pi\) | ||||
−0.0710729 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(468\) | 1.15403 | 0.0533449 | ||||||||
\(469\) | 9.62176 | 0.444292 | ||||||||
\(470\) | 0.137724 | 0.00635276 | ||||||||
\(471\) | −6.09537 | −0.280860 | ||||||||
\(472\) | 2.94134 | 0.135386 | ||||||||
\(473\) | −4.23868 | −0.194895 | ||||||||
\(474\) | 16.5276 | 0.759140 | ||||||||
\(475\) | 29.4197 | 1.34987 | ||||||||
\(476\) | −34.1490 | −1.56522 | ||||||||
\(477\) | 13.3736 | 0.612336 | ||||||||
\(478\) | −1.14676 | −0.0524516 | ||||||||
\(479\) | −0.637695 | −0.0291370 | −0.0145685 | − | 0.999894i | \(-0.504637\pi\) | ||||
−0.0145685 | + | 0.999894i | \(0.504637\pi\) | |||||||
\(480\) | 0.230234 | 0.0105087 | ||||||||
\(481\) | 8.41488 | 0.383686 | ||||||||
\(482\) | −12.6406 | −0.575761 | ||||||||
\(483\) | −4.59819 | −0.209225 | ||||||||
\(484\) | 9.27545 | 0.421611 | ||||||||
\(485\) | −0.419665 | −0.0190560 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.6430 | 0.935425 | 0.467713 | − | 0.883881i | \(-0.345078\pi\) | ||||
0.467713 | + | 0.883881i | \(0.345078\pi\) | |||||||
\(488\) | −10.8883 | −0.492892 | ||||||||
\(489\) | 1.25343 | 0.0566822 | ||||||||
\(490\) | −3.25629 | −0.147104 | ||||||||
\(491\) | 17.5819 | 0.793460 | 0.396730 | − | 0.917935i | \(-0.370145\pi\) | ||||
0.396730 | + | 0.917935i | \(0.370145\pi\) | |||||||
\(492\) | −0.0953661 | −0.00429944 | ||||||||
\(493\) | 7.42662 | 0.334478 | ||||||||
\(494\) | 6.86299 | 0.308781 | ||||||||
\(495\) | −1.03670 | −0.0465964 | ||||||||
\(496\) | 6.50283 | 0.291986 | ||||||||
\(497\) | 50.4113 | 2.26126 | ||||||||
\(498\) | −1.71676 | −0.0769298 | ||||||||
\(499\) | −9.35607 | −0.418835 | −0.209418 | − | 0.977826i | \(-0.567157\pi\) | ||||
−0.209418 | + | 0.977826i | \(0.567157\pi\) | |||||||
\(500\) | −2.29014 | −0.102418 | ||||||||
\(501\) | 2.49879 | 0.111638 | ||||||||
\(502\) | 5.62425 | 0.251022 | ||||||||
\(503\) | −43.1722 | −1.92495 | −0.962477 | − | 0.271362i | \(-0.912526\pi\) | ||||
−0.962477 | + | 0.271362i | \(0.912526\pi\) | |||||||
\(504\) | −4.59819 | −0.204820 | ||||||||
\(505\) | −2.30234 | −0.102453 | ||||||||
\(506\) | 4.50283 | 0.200175 | ||||||||
\(507\) | 11.6682 | 0.518204 | ||||||||
\(508\) | 5.11167 | 0.226794 | ||||||||
\(509\) | −31.7692 | −1.40815 | −0.704073 | − | 0.710127i | \(-0.748637\pi\) | ||||
−0.704073 | + | 0.710127i | \(0.748637\pi\) | |||||||
\(510\) | −1.70986 | −0.0757140 | ||||||||
\(511\) | −56.9844 | −2.52084 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.94699 | 0.262566 | ||||||||
\(514\) | 21.3177 | 0.940286 | ||||||||
\(515\) | −2.74253 | −0.120850 | ||||||||
\(516\) | −0.941339 | −0.0414401 | ||||||||
\(517\) | 2.69356 | 0.118463 | ||||||||
\(518\) | −33.5289 | −1.47317 | ||||||||
\(519\) | −6.21269 | −0.272707 | ||||||||
\(520\) | −0.265697 | −0.0116516 | ||||||||
\(521\) | −35.1440 | −1.53969 | −0.769844 | − | 0.638232i | \(-0.779666\pi\) | ||||
−0.769844 | + | 0.638232i | \(0.779666\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 30.6026 | 1.33816 | 0.669079 | − | 0.743191i | \(-0.266689\pi\) | ||||
0.669079 | + | 0.743191i | \(0.266689\pi\) | |||||||
\(524\) | 10.3968 | 0.454187 | ||||||||
\(525\) | 22.7472 | 0.992770 | ||||||||
\(526\) | 1.96205 | 0.0855496 | ||||||||
\(527\) | −48.2940 | −2.10372 | ||||||||
\(528\) | 4.50283 | 0.195960 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.07906 | −0.133746 | ||||||||
\(531\) | −2.94134 | −0.127643 | ||||||||
\(532\) | −27.3454 | −1.18557 | ||||||||
\(533\) | 0.110055 | 0.00476702 | ||||||||
\(534\) | 12.5700 | 0.543957 | ||||||||
\(535\) | 2.78166 | 0.120262 | ||||||||
\(536\) | −2.09251 | −0.0903827 | ||||||||
\(537\) | −9.55084 | −0.412149 | ||||||||
\(538\) | 3.85163 | 0.166055 | ||||||||
\(539\) | −63.6852 | −2.74311 | ||||||||
\(540\) | −0.230234 | −0.00990770 | ||||||||
\(541\) | −5.76197 | −0.247727 | −0.123863 | − | 0.992299i | \(-0.539528\pi\) | ||||
−0.123863 | + | 0.992299i | \(0.539528\pi\) | |||||||
\(542\) | 1.47183 | 0.0632207 | ||||||||
\(543\) | 14.2196 | 0.610221 | ||||||||
\(544\) | 7.42662 | 0.318414 | ||||||||
\(545\) | 1.77666 | 0.0761038 | ||||||||
\(546\) | 5.30644 | 0.227095 | ||||||||
\(547\) | −19.5044 | −0.833950 | −0.416975 | − | 0.908918i | \(-0.636910\pi\) | ||||
−0.416975 | + | 0.908918i | \(0.636910\pi\) | |||||||
\(548\) | 12.7958 | 0.546610 | ||||||||
\(549\) | 10.8883 | 0.464703 | ||||||||
\(550\) | −22.2754 | −0.949828 | ||||||||
\(551\) | 5.94699 | 0.253350 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 75.9973 | 3.23173 | ||||||||
\(554\) | 24.6665 | 1.04798 | ||||||||
\(555\) | −1.67881 | −0.0712615 | ||||||||
\(556\) | −2.80361 | −0.118900 | ||||||||
\(557\) | 32.8193 | 1.39060 | 0.695300 | − | 0.718720i | \(-0.255272\pi\) | ||||
0.695300 | + | 0.718720i | \(0.255272\pi\) | |||||||
\(558\) | −6.50283 | −0.275287 | ||||||||
\(559\) | 1.08633 | 0.0459469 | ||||||||
\(560\) | 1.05866 | 0.0447366 | ||||||||
\(561\) | −33.4408 | −1.41187 | ||||||||
\(562\) | 12.3081 | 0.519184 | ||||||||
\(563\) | 25.0440 | 1.05548 | 0.527739 | − | 0.849407i | \(-0.323040\pi\) | ||||
0.527739 | + | 0.849407i | \(0.323040\pi\) | |||||||
\(564\) | 0.598193 | 0.0251885 | ||||||||
\(565\) | 1.99339 | 0.0838626 | ||||||||
\(566\) | 23.8087 | 1.00076 | ||||||||
\(567\) | 4.59819 | 0.193106 | ||||||||
\(568\) | −10.9633 | −0.460010 | ||||||||
\(569\) | 3.80808 | 0.159643 | 0.0798216 | − | 0.996809i | \(-0.474565\pi\) | ||||
0.0798216 | + | 0.996809i | \(0.474565\pi\) | |||||||
\(570\) | −1.36920 | −0.0573495 | ||||||||
\(571\) | −2.36392 | −0.0989269 | −0.0494635 | − | 0.998776i | \(-0.515751\pi\) | ||||
−0.0494635 | + | 0.998776i | \(0.515751\pi\) | |||||||
\(572\) | −5.19639 | −0.217272 | ||||||||
\(573\) | −2.00286 | −0.0836705 | ||||||||
\(574\) | −0.438512 | −0.0183031 | ||||||||
\(575\) | −4.94699 | −0.206304 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.8956 | 0.953156 | 0.476578 | − | 0.879132i | \(-0.341877\pi\) | ||||
0.476578 | + | 0.879132i | \(0.341877\pi\) | |||||||
\(578\) | −38.1547 | −1.58703 | ||||||||
\(579\) | −21.6242 | −0.898673 | ||||||||
\(580\) | −0.230234 | −0.00955996 | ||||||||
\(581\) | −7.89398 | −0.327498 | ||||||||
\(582\) | −1.82277 | −0.0755564 | ||||||||
\(583\) | −60.2191 | −2.49402 | ||||||||
\(584\) | 12.3928 | 0.512817 | ||||||||
\(585\) | 0.265697 | 0.0109852 | ||||||||
\(586\) | −17.3162 | −0.715325 | ||||||||
\(587\) | 14.2550 | 0.588369 | 0.294184 | − | 0.955749i | \(-0.404952\pi\) | ||||
0.294184 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(588\) | −14.1434 | −0.583263 | ||||||||
\(589\) | −38.6723 | −1.59346 | ||||||||
\(590\) | 0.677197 | 0.0278798 | ||||||||
\(591\) | −2.89898 | −0.119248 | ||||||||
\(592\) | 7.29175 | 0.299689 | ||||||||
\(593\) | 13.5044 | 0.554561 | 0.277280 | − | 0.960789i | \(-0.410567\pi\) | ||||
0.277280 | + | 0.960789i | \(0.410567\pi\) | |||||||
\(594\) | −4.50283 | −0.184753 | ||||||||
\(595\) | −7.86228 | −0.322322 | ||||||||
\(596\) | −6.92783 | −0.283775 | ||||||||
\(597\) | −12.2754 | −0.502401 | ||||||||
\(598\) | −1.15403 | −0.0471917 | ||||||||
\(599\) | −29.7855 | −1.21700 | −0.608501 | − | 0.793553i | \(-0.708229\pi\) | ||||
−0.608501 | + | 0.793553i | \(0.708229\pi\) | |||||||
\(600\) | −4.94699 | −0.201960 | ||||||||
\(601\) | 35.9819 | 1.46773 | 0.733867 | − | 0.679293i | \(-0.237714\pi\) | ||||
0.733867 | + | 0.679293i | \(0.237714\pi\) | |||||||
\(602\) | −4.32846 | −0.176415 | ||||||||
\(603\) | 2.09251 | 0.0852136 | ||||||||
\(604\) | 17.5289 | 0.713240 | ||||||||
\(605\) | 2.13553 | 0.0868215 | ||||||||
\(606\) | −10.0000 | −0.406222 | ||||||||
\(607\) | 30.7871 | 1.24961 | 0.624805 | − | 0.780781i | \(-0.285179\pi\) | ||||
0.624805 | + | 0.780781i | \(0.285179\pi\) | |||||||
\(608\) | 5.94699 | 0.241182 | ||||||||
\(609\) | 4.59819 | 0.186328 | ||||||||
\(610\) | −2.50687 | −0.101500 | ||||||||
\(611\) | −0.690331 | −0.0279278 | ||||||||
\(612\) | −7.42662 | −0.300203 | ||||||||
\(613\) | 18.2155 | 0.735719 | 0.367859 | − | 0.929881i | \(-0.380091\pi\) | ||||
0.367859 | + | 0.929881i | \(0.380091\pi\) | |||||||
\(614\) | −0.920937 | −0.0371660 | ||||||||
\(615\) | −0.0219565 | −0.000885373 0 | ||||||||
\(616\) | 20.7049 | 0.834223 | ||||||||
\(617\) | −17.4592 | −0.702882 | −0.351441 | − | 0.936210i | \(-0.614308\pi\) | ||||
−0.351441 | + | 0.936210i | \(0.614308\pi\) | |||||||
\(618\) | −11.9119 | −0.479167 | ||||||||
\(619\) | −14.3781 | −0.577904 | −0.288952 | − | 0.957344i | \(-0.593307\pi\) | ||||
−0.288952 | + | 0.957344i | \(0.593307\pi\) | |||||||
\(620\) | 1.49717 | 0.0601279 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −28.6829 | −1.15008 | ||||||||
\(623\) | 57.7993 | 2.31568 | ||||||||
\(624\) | −1.15403 | −0.0461981 | ||||||||
\(625\) | 24.2077 | 0.968308 | ||||||||
\(626\) | 21.1506 | 0.845350 | ||||||||
\(627\) | −26.7783 | −1.06942 | ||||||||
\(628\) | 6.09537 | 0.243232 | ||||||||
\(629\) | −54.1531 | −2.15922 | ||||||||
\(630\) | −1.05866 | −0.0421781 | ||||||||
\(631\) | −9.02357 | −0.359223 | −0.179611 | − | 0.983738i | \(-0.557484\pi\) | ||||
−0.179611 | + | 0.983738i | \(0.557484\pi\) | |||||||
\(632\) | −16.5276 | −0.657434 | ||||||||
\(633\) | 15.8369 | 0.629462 | ||||||||
\(634\) | 27.2061 | 1.08049 | ||||||||
\(635\) | 1.17688 | 0.0467031 | ||||||||
\(636\) | −13.3736 | −0.530298 | ||||||||
\(637\) | 16.3218 | 0.646695 | ||||||||
\(638\) | −4.50283 | −0.178269 | ||||||||
\(639\) | 10.9633 | 0.433701 | ||||||||
\(640\) | −0.230234 | −0.00910081 | ||||||||
\(641\) | −16.3826 | −0.647076 | −0.323538 | − | 0.946215i | \(-0.604872\pi\) | ||||
−0.323538 | + | 0.946215i | \(0.604872\pi\) | |||||||
\(642\) | 12.0819 | 0.476833 | ||||||||
\(643\) | −36.6733 | −1.44625 | −0.723127 | − | 0.690715i | \(-0.757296\pi\) | ||||
−0.723127 | + | 0.690715i | \(0.757296\pi\) | |||||||
\(644\) | 4.59819 | 0.181194 | ||||||||
\(645\) | −0.216728 | −0.00853367 | ||||||||
\(646\) | −44.1661 | −1.73769 | ||||||||
\(647\) | 30.5028 | 1.19919 | 0.599595 | − | 0.800304i | \(-0.295328\pi\) | ||||
0.599595 | + | 0.800304i | \(0.295328\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 13.2443 | 0.519886 | ||||||||
\(650\) | 5.70896 | 0.223924 | ||||||||
\(651\) | −29.9013 | −1.17192 | ||||||||
\(652\) | −1.25343 | −0.0490882 | ||||||||
\(653\) | −17.6601 | −0.691092 | −0.345546 | − | 0.938402i | \(-0.612306\pi\) | ||||
−0.345546 | + | 0.938402i | \(0.612306\pi\) | |||||||
\(654\) | 7.71676 | 0.301749 | ||||||||
\(655\) | 2.39370 | 0.0935297 | ||||||||
\(656\) | 0.0953661 | 0.00372342 | ||||||||
\(657\) | −12.3928 | −0.483488 | ||||||||
\(658\) | 2.75061 | 0.107230 | ||||||||
\(659\) | 15.7473 | 0.613427 | 0.306714 | − | 0.951802i | \(-0.400771\pi\) | ||||
0.306714 | + | 0.951802i | \(0.400771\pi\) | |||||||
\(660\) | 1.03670 | 0.0403537 | ||||||||
\(661\) | −34.4640 | −1.34049 | −0.670247 | − | 0.742138i | \(-0.733812\pi\) | ||||
−0.670247 | + | 0.742138i | \(0.733812\pi\) | |||||||
\(662\) | −21.1833 | −0.823310 | ||||||||
\(663\) | 8.57052 | 0.332852 | ||||||||
\(664\) | 1.71676 | 0.0666231 | ||||||||
\(665\) | −6.29585 | −0.244143 | ||||||||
\(666\) | −7.29175 | −0.282550 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −2.49879 | −0.0966810 | ||||||||
\(669\) | 13.6569 | 0.528004 | ||||||||
\(670\) | −0.481767 | −0.0186123 | ||||||||
\(671\) | −49.0283 | −1.89272 | ||||||||
\(672\) | 4.59819 | 0.177379 | ||||||||
\(673\) | 47.2426 | 1.82107 | 0.910535 | − | 0.413432i | \(-0.135670\pi\) | ||||
0.910535 | + | 0.413432i | \(0.135670\pi\) | |||||||
\(674\) | 21.5317 | 0.829372 | ||||||||
\(675\) | 4.94699 | 0.190410 | ||||||||
\(676\) | −11.6682 | −0.448778 | ||||||||
\(677\) | −5.38141 | −0.206824 | −0.103412 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103412 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(678\) | 8.65810 | 0.332512 | ||||||||
\(679\) | −8.38146 | −0.321651 | ||||||||
\(680\) | 1.70986 | 0.0655702 | ||||||||
\(681\) | −12.2726 | −0.470287 | ||||||||
\(682\) | 29.2811 | 1.12123 | ||||||||
\(683\) | −14.7945 | −0.566097 | −0.283048 | − | 0.959106i | \(-0.591346\pi\) | ||||
−0.283048 | + | 0.959106i | \(0.591346\pi\) | |||||||
\(684\) | −5.94699 | −0.227389 | ||||||||
\(685\) | 2.94604 | 0.112562 | ||||||||
\(686\) | −32.8466 | −1.25409 | ||||||||
\(687\) | 7.37647 | 0.281430 | ||||||||
\(688\) | 0.941339 | 0.0358882 | ||||||||
\(689\) | 15.4335 | 0.587970 | ||||||||
\(690\) | 0.230234 | 0.00876487 | ||||||||
\(691\) | −17.0310 | −0.647889 | −0.323945 | − | 0.946076i | \(-0.605009\pi\) | ||||
−0.323945 | + | 0.946076i | \(0.605009\pi\) | |||||||
\(692\) | 6.21269 | 0.236171 | ||||||||
\(693\) | −20.7049 | −0.786513 | ||||||||
\(694\) | 13.2845 | 0.504272 | ||||||||
\(695\) | −0.645488 | −0.0244848 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −0.708248 | −0.0268268 | ||||||||
\(698\) | −30.4392 | −1.15214 | ||||||||
\(699\) | −28.2020 | −1.06670 | ||||||||
\(700\) | −22.7472 | −0.859764 | ||||||||
\(701\) | 38.9065 | 1.46948 | 0.734740 | − | 0.678349i | \(-0.237304\pi\) | ||||
0.734740 | + | 0.678349i | \(0.237304\pi\) | |||||||
\(702\) | 1.15403 | 0.0435560 | ||||||||
\(703\) | −43.3640 | −1.63550 | ||||||||
\(704\) | −4.50283 | −0.169707 | ||||||||
\(705\) | 0.137724 | 0.00518700 | ||||||||
\(706\) | −26.0847 | −0.981711 | ||||||||
\(707\) | −45.9819 | −1.72933 | ||||||||
\(708\) | 2.94134 | 0.110542 | ||||||||
\(709\) | −13.2849 | −0.498923 | −0.249462 | − | 0.968385i | \(-0.580254\pi\) | ||||
−0.249462 | + | 0.968385i | \(0.580254\pi\) | |||||||
\(710\) | −2.52413 | −0.0947287 | ||||||||
\(711\) | 16.5276 | 0.619835 | ||||||||
\(712\) | −12.5700 | −0.471081 | ||||||||
\(713\) | 6.50283 | 0.243533 | ||||||||
\(714\) | −34.1490 | −1.27800 | ||||||||
\(715\) | −1.19639 | −0.0447423 | ||||||||
\(716\) | 9.55084 | 0.356932 | ||||||||
\(717\) | −1.14676 | −0.0428265 | ||||||||
\(718\) | −29.2456 | −1.09144 | ||||||||
\(719\) | −3.73430 | −0.139266 | −0.0696330 | − | 0.997573i | \(-0.522183\pi\) | ||||
−0.0696330 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(720\) | 0.230234 | 0.00858032 | ||||||||
\(721\) | −54.7732 | −2.03986 | ||||||||
\(722\) | −16.3667 | −0.609106 | ||||||||
\(723\) | −12.6406 | −0.470107 | ||||||||
\(724\) | −14.2196 | −0.528467 | ||||||||
\(725\) | 4.94699 | 0.183727 | ||||||||
\(726\) | 9.27545 | 0.344244 | ||||||||
\(727\) | 26.6547 | 0.988569 | 0.494284 | − | 0.869300i | \(-0.335430\pi\) | ||||
0.494284 | + | 0.869300i | \(0.335430\pi\) | |||||||
\(728\) | −5.30644 | −0.196670 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.85324 | 0.105603 | ||||||||
\(731\) | −6.99096 | −0.258570 | ||||||||
\(732\) | −10.8883 | −0.402444 | ||||||||
\(733\) | 37.7912 | 1.39585 | 0.697925 | − | 0.716171i | \(-0.254107\pi\) | ||||
0.697925 | + | 0.716171i | \(0.254107\pi\) | |||||||
\(734\) | −25.0785 | −0.925666 | ||||||||
\(735\) | −3.25629 | −0.120110 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −9.42221 | −0.347072 | ||||||||
\(738\) | −0.0953661 | −0.00351048 | ||||||||
\(739\) | 14.5477 | 0.535145 | 0.267572 | − | 0.963538i | \(-0.413779\pi\) | ||||
0.267572 | + | 0.963538i | \(0.413779\pi\) | |||||||
\(740\) | 1.67881 | 0.0617143 | ||||||||
\(741\) | 6.86299 | 0.252118 | ||||||||
\(742\) | −61.4944 | −2.25753 | ||||||||
\(743\) | −27.2725 | −1.00053 | −0.500266 | − | 0.865872i | \(-0.666764\pi\) | ||||
−0.500266 | + | 0.865872i | \(0.666764\pi\) | |||||||
\(744\) | 6.50283 | 0.238405 | ||||||||
\(745\) | −1.59502 | −0.0584372 | ||||||||
\(746\) | −36.4257 | −1.33364 | ||||||||
\(747\) | −1.71676 | −0.0628129 | ||||||||
\(748\) | 33.4408 | 1.22272 | ||||||||
\(749\) | 55.5547 | 2.02993 | ||||||||
\(750\) | −2.29014 | −0.0836240 | ||||||||
\(751\) | 46.6547 | 1.70245 | 0.851227 | − | 0.524797i | \(-0.175859\pi\) | ||||
0.851227 | + | 0.524797i | \(0.175859\pi\) | |||||||
\(752\) | −0.598193 | −0.0218139 | ||||||||
\(753\) | 5.62425 | 0.204959 | ||||||||
\(754\) | 1.15403 | 0.0420272 | ||||||||
\(755\) | 4.03575 | 0.146876 | ||||||||
\(756\) | −4.59819 | −0.167235 | ||||||||
\(757\) | −44.5955 | −1.62085 | −0.810425 | − | 0.585842i | \(-0.800764\pi\) | ||||
−0.810425 | + | 0.585842i | \(0.800764\pi\) | |||||||
\(758\) | 22.0847 | 0.802153 | ||||||||
\(759\) | 4.50283 | 0.163442 | ||||||||
\(760\) | 1.36920 | 0.0496661 | ||||||||
\(761\) | 12.0153 | 0.435556 | 0.217778 | − | 0.975998i | \(-0.430119\pi\) | ||||
0.217778 | + | 0.975998i | \(0.430119\pi\) | |||||||
\(762\) | 5.11167 | 0.185176 | ||||||||
\(763\) | 35.4831 | 1.28458 | ||||||||
\(764\) | 2.00286 | 0.0724608 | ||||||||
\(765\) | −1.70986 | −0.0618202 | ||||||||
\(766\) | −30.2118 | −1.09160 | ||||||||
\(767\) | −3.39439 | −0.122564 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −19.5603 | −0.705363 | −0.352681 | − | 0.935743i | \(-0.614730\pi\) | ||||
−0.352681 | + | 0.935743i | \(0.614730\pi\) | |||||||
\(770\) | 4.76697 | 0.171790 | ||||||||
\(771\) | 21.3177 | 0.767740 | ||||||||
\(772\) | 21.6242 | 0.778274 | ||||||||
\(773\) | −14.7871 | −0.531855 | −0.265927 | − | 0.963993i | \(-0.585678\pi\) | ||||
−0.265927 | + | 0.963993i | \(0.585678\pi\) | |||||||
\(774\) | −0.941339 | −0.0338357 | ||||||||
\(775\) | −32.1694 | −1.15556 | ||||||||
\(776\) | 1.82277 | 0.0654338 | ||||||||
\(777\) | −33.5289 | −1.20284 | ||||||||
\(778\) | 34.5622 | 1.23912 | ||||||||
\(779\) | −0.567142 | −0.0203200 | ||||||||
\(780\) | −0.265697 | −0.00951346 | ||||||||
\(781\) | −49.3658 | −1.76645 | ||||||||
\(782\) | 7.42662 | 0.265575 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 14.1434 | 0.505121 | ||||||||
\(785\) | 1.40336 | 0.0500881 | ||||||||
\(786\) | 10.3968 | 0.370842 | ||||||||
\(787\) | 4.83569 | 0.172374 | 0.0861869 | − | 0.996279i | \(-0.472532\pi\) | ||||
0.0861869 | + | 0.996279i | \(0.472532\pi\) | |||||||
\(788\) | 2.89898 | 0.103272 | ||||||||
\(789\) | 1.96205 | 0.0698509 | ||||||||
\(790\) | −3.80523 | −0.135384 | ||||||||
\(791\) | 39.8116 | 1.41554 | ||||||||
\(792\) | 4.50283 | 0.160001 | ||||||||
\(793\) | 12.5654 | 0.446212 | ||||||||
\(794\) | 20.8981 | 0.741645 | ||||||||
\(795\) | −3.07906 | −0.109203 | ||||||||
\(796\) | 12.2754 | 0.435092 | ||||||||
\(797\) | −5.42128 | −0.192032 | −0.0960158 | − | 0.995380i | \(-0.530610\pi\) | ||||
−0.0960158 | + | 0.995380i | \(0.530610\pi\) | |||||||
\(798\) | −27.3454 | −0.968017 | ||||||||
\(799\) | 4.44255 | 0.157166 | ||||||||
\(800\) | 4.94699 | 0.174903 | ||||||||
\(801\) | 12.5700 | 0.444139 | ||||||||
\(802\) | 6.97056 | 0.246139 | ||||||||
\(803\) | 55.8025 | 1.96923 | ||||||||
\(804\) | −2.09251 | −0.0737971 | ||||||||
\(805\) | 1.05866 | 0.0373129 | ||||||||
\(806\) | −7.50444 | −0.264333 | ||||||||
\(807\) | 3.85163 | 0.135584 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | 31.5215 | 1.10824 | 0.554118 | − | 0.832438i | \(-0.313056\pi\) | ||||
0.554118 | + | 0.832438i | \(0.313056\pi\) | |||||||
\(810\) | −0.230234 | −0.00808961 | ||||||||
\(811\) | 34.4856 | 1.21095 | 0.605476 | − | 0.795864i | \(-0.292983\pi\) | ||||
0.605476 | + | 0.795864i | \(0.292983\pi\) | |||||||
\(812\) | −4.59819 | −0.161365 | ||||||||
\(813\) | 1.47183 | 0.0516195 | ||||||||
\(814\) | 32.8335 | 1.15081 | ||||||||
\(815\) | −0.288583 | −0.0101086 | ||||||||
\(816\) | 7.42662 | 0.259984 | ||||||||
\(817\) | −5.59813 | −0.195854 | ||||||||
\(818\) | −0.857280 | −0.0299741 | ||||||||
\(819\) | 5.30644 | 0.185422 | ||||||||
\(820\) | 0.0219565 | 0.000766756 0 | ||||||||
\(821\) | 18.8206 | 0.656845 | 0.328422 | − | 0.944531i | \(-0.393483\pi\) | ||||
0.328422 | + | 0.944531i | \(0.393483\pi\) | |||||||
\(822\) | 12.7958 | 0.446306 | ||||||||
\(823\) | 29.0593 | 1.01294 | 0.506472 | − | 0.862256i | \(-0.330949\pi\) | ||||
0.506472 | + | 0.862256i | \(0.330949\pi\) | |||||||
\(824\) | 11.9119 | 0.414971 | ||||||||
\(825\) | −22.2754 | −0.775532 | ||||||||
\(826\) | 13.5248 | 0.470589 | ||||||||
\(827\) | 14.7447 | 0.512725 | 0.256362 | − | 0.966581i | \(-0.417476\pi\) | ||||
0.256362 | + | 0.966581i | \(0.417476\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −45.6422 | −1.58522 | −0.792609 | − | 0.609730i | \(-0.791278\pi\) | ||||
−0.792609 | + | 0.609730i | \(0.791278\pi\) | |||||||
\(830\) | 0.395256 | 0.0137196 | ||||||||
\(831\) | 24.6665 | 0.855673 | ||||||||
\(832\) | 1.15403 | 0.0400087 | ||||||||
\(833\) | −105.037 | −3.63933 | ||||||||
\(834\) | −2.80361 | −0.0970812 | ||||||||
\(835\) | −0.575306 | −0.0199093 | ||||||||
\(836\) | 26.7783 | 0.926146 | ||||||||
\(837\) | −6.50283 | −0.224771 | ||||||||
\(838\) | 3.35166 | 0.115781 | ||||||||
\(839\) | −5.37295 | −0.185495 | −0.0927475 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927475 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(840\) | 1.05866 | 0.0365273 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 28.7798 | 0.991818 | ||||||||
\(843\) | 12.3081 | 0.423912 | ||||||||
\(844\) | −15.8369 | −0.545130 | ||||||||
\(845\) | −2.68642 | −0.0924158 | ||||||||
\(846\) | 0.598193 | 0.0205663 | ||||||||
\(847\) | 42.6503 | 1.46548 | ||||||||
\(848\) | 13.3736 | 0.459252 | ||||||||
\(849\) | 23.8087 | 0.817114 | ||||||||
\(850\) | −36.7394 | −1.26015 | ||||||||
\(851\) | 7.29175 | 0.249958 | ||||||||
\(852\) | −10.9633 | −0.375596 | ||||||||
\(853\) | 42.6974 | 1.46193 | 0.730966 | − | 0.682414i | \(-0.239070\pi\) | ||||
0.730966 | + | 0.682414i | \(0.239070\pi\) | |||||||
\(854\) | −50.0666 | −1.71325 | ||||||||
\(855\) | −1.36920 | −0.0468257 | ||||||||
\(856\) | −12.0819 | −0.412949 | ||||||||
\(857\) | 48.5254 | 1.65760 | 0.828799 | − | 0.559547i | \(-0.189025\pi\) | ||||
0.828799 | + | 0.559547i | \(0.189025\pi\) | |||||||
\(858\) | −5.19639 | −0.177402 | ||||||||
\(859\) | 24.3112 | 0.829487 | 0.414744 | − | 0.909938i | \(-0.363871\pi\) | ||||
0.414744 | + | 0.909938i | \(0.363871\pi\) | |||||||
\(860\) | 0.216728 | 0.00739038 | ||||||||
\(861\) | −0.438512 | −0.0149444 | ||||||||
\(862\) | −8.84597 | −0.301295 | ||||||||
\(863\) | 41.2092 | 1.40278 | 0.701390 | − | 0.712778i | \(-0.252563\pi\) | ||||
0.701390 | + | 0.712778i | \(0.252563\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.43037 | 0.0486342 | ||||||||
\(866\) | −2.74775 | −0.0933723 | ||||||||
\(867\) | −38.1547 | −1.29580 | ||||||||
\(868\) | 29.9013 | 1.01491 | ||||||||
\(869\) | −74.4211 | −2.52456 | ||||||||
\(870\) | −0.230234 | −0.00780567 | ||||||||
\(871\) | 2.41481 | 0.0818228 | ||||||||
\(872\) | −7.71676 | −0.261322 | ||||||||
\(873\) | −1.82277 | −0.0616915 | ||||||||
\(874\) | 5.94699 | 0.201160 | ||||||||
\(875\) | −10.5305 | −0.355996 | ||||||||
\(876\) | 12.3928 | 0.418713 | ||||||||
\(877\) | −24.3674 | −0.822830 | −0.411415 | − | 0.911448i | \(-0.634965\pi\) | ||||
−0.411415 | + | 0.911448i | \(0.634965\pi\) | |||||||
\(878\) | −16.4385 | −0.554773 | ||||||||
\(879\) | −17.3162 | −0.584061 | ||||||||
\(880\) | −1.03670 | −0.0349473 | ||||||||
\(881\) | −11.9890 | −0.403919 | −0.201959 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201959 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(882\) | −14.1434 | −0.476232 | ||||||||
\(883\) | −48.3787 | −1.62807 | −0.814037 | − | 0.580813i | \(-0.802735\pi\) | ||||
−0.814037 | + | 0.580813i | \(0.802735\pi\) | |||||||
\(884\) | −8.57052 | −0.288258 | ||||||||
\(885\) | 0.677197 | 0.0227637 | ||||||||
\(886\) | 29.1751 | 0.980156 | ||||||||
\(887\) | 41.8351 | 1.40469 | 0.702343 | − | 0.711839i | \(-0.252137\pi\) | ||||
0.702343 | + | 0.711839i | \(0.252137\pi\) | |||||||
\(888\) | 7.29175 | 0.244695 | ||||||||
\(889\) | 23.5044 | 0.788314 | ||||||||
\(890\) | −2.89404 | −0.0970086 | ||||||||
\(891\) | −4.50283 | −0.150850 | ||||||||
\(892\) | −13.6569 | −0.457265 | ||||||||
\(893\) | 3.55745 | 0.119045 | ||||||||
\(894\) | −6.92783 | −0.231701 | ||||||||
\(895\) | 2.19893 | 0.0735021 | ||||||||
\(896\) | −4.59819 | −0.153615 | ||||||||
\(897\) | −1.15403 | −0.0385319 | ||||||||
\(898\) | 30.8777 | 1.03040 | ||||||||
\(899\) | −6.50283 | −0.216881 | ||||||||
\(900\) | −4.94699 | −0.164900 | ||||||||
\(901\) | −99.3207 | −3.30885 | ||||||||
\(902\) | 0.429417 | 0.0142980 | ||||||||
\(903\) | −4.32846 | −0.144042 | ||||||||
\(904\) | −8.65810 | −0.287964 | ||||||||
\(905\) | −3.27383 | −0.108826 | ||||||||
\(906\) | 17.5289 | 0.582358 | ||||||||
\(907\) | −0.443449 | −0.0147245 | −0.00736223 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736223 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(908\) | 12.2726 | 0.407280 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | −1.22172 | −0.0404998 | ||||||||
\(911\) | 44.0010 | 1.45782 | 0.728910 | − | 0.684610i | \(-0.240027\pi\) | ||||
0.728910 | + | 0.684610i | \(0.240027\pi\) | |||||||
\(912\) | 5.94699 | 0.196925 | ||||||||
\(913\) | 7.73026 | 0.255834 | ||||||||
\(914\) | 21.0797 | 0.697255 | ||||||||
\(915\) | −2.50687 | −0.0828744 | ||||||||
\(916\) | −7.37647 | −0.243725 | ||||||||
\(917\) | 47.8065 | 1.57871 | ||||||||
\(918\) | −7.42662 | −0.245115 | ||||||||
\(919\) | −52.5556 | −1.73365 | −0.866825 | − | 0.498613i | \(-0.833843\pi\) | ||||
−0.866825 | + | 0.498613i | \(0.833843\pi\) | |||||||
\(920\) | −0.230234 | −0.00759060 | ||||||||
\(921\) | −0.920937 | −0.0303459 | ||||||||
\(922\) | 14.3504 | 0.472606 | ||||||||
\(923\) | 12.6519 | 0.416444 | ||||||||
\(924\) | 20.7049 | 0.681140 | ||||||||
\(925\) | −36.0722 | −1.18605 | ||||||||
\(926\) | −31.9436 | −1.04973 | ||||||||
\(927\) | −11.9119 | −0.391238 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −51.6298 | −1.69392 | −0.846960 | − | 0.531656i | \(-0.821570\pi\) | ||||
−0.846960 | + | 0.531656i | \(0.821570\pi\) | |||||||
\(930\) | 1.49717 | 0.0490942 | ||||||||
\(931\) | −84.1106 | −2.75661 | ||||||||
\(932\) | 28.2020 | 0.923789 | ||||||||
\(933\) | −28.6829 | −0.939036 | ||||||||
\(934\) | 3.07180 | 0.100512 | ||||||||
\(935\) | 7.69921 | 0.251791 | ||||||||
\(936\) | −1.15403 | −0.0377206 | ||||||||
\(937\) | 12.2804 | 0.401183 | 0.200591 | − | 0.979675i | \(-0.435714\pi\) | ||||
0.200591 | + | 0.979675i | \(0.435714\pi\) | |||||||
\(938\) | −9.62176 | −0.314162 | ||||||||
\(939\) | 21.1506 | 0.690225 | ||||||||
\(940\) | −0.137724 | −0.00449208 | ||||||||
\(941\) | −36.4257 | −1.18744 | −0.593721 | − | 0.804671i | \(-0.702342\pi\) | ||||
−0.593721 | + | 0.804671i | \(0.702342\pi\) | |||||||
\(942\) | 6.09537 | 0.198598 | ||||||||
\(943\) | 0.0953661 | 0.00310555 | ||||||||
\(944\) | −2.94134 | −0.0957324 | ||||||||
\(945\) | −1.05866 | −0.0344383 | ||||||||
\(946\) | 4.23868 | 0.137812 | ||||||||
\(947\) | 2.22738 | 0.0723801 | 0.0361900 | − | 0.999345i | \(-0.488478\pi\) | ||||
0.0361900 | + | 0.999345i | \(0.488478\pi\) | |||||||
\(948\) | −16.5276 | −0.536793 | ||||||||
\(949\) | −14.3016 | −0.464250 | ||||||||
\(950\) | −29.4197 | −0.954502 | ||||||||
\(951\) | 27.2061 | 0.882219 | ||||||||
\(952\) | 34.1490 | 1.10678 | ||||||||
\(953\) | 16.1524 | 0.523228 | 0.261614 | − | 0.965173i | \(-0.415745\pi\) | ||||
0.261614 | + | 0.965173i | \(0.415745\pi\) | |||||||
\(954\) | −13.3736 | −0.432987 | ||||||||
\(955\) | 0.461126 | 0.0149217 | ||||||||
\(956\) | 1.14676 | 0.0370889 | ||||||||
\(957\) | −4.50283 | −0.145556 | ||||||||
\(958\) | 0.637695 | 0.0206030 | ||||||||
\(959\) | 58.8377 | 1.89997 | ||||||||
\(960\) | −0.230234 | −0.00743078 | ||||||||
\(961\) | 11.2868 | 0.364089 | ||||||||
\(962\) | −8.41488 | −0.271307 | ||||||||
\(963\) | 12.0819 | 0.389333 | ||||||||
\(964\) | 12.6406 | 0.407125 | ||||||||
\(965\) | 4.97864 | 0.160268 | ||||||||
\(966\) | 4.59819 | 0.147944 | ||||||||
\(967\) | −1.46208 | −0.0470174 | −0.0235087 | − | 0.999724i | \(-0.507484\pi\) | ||||
−0.0235087 | + | 0.999724i | \(0.507484\pi\) | |||||||
\(968\) | −9.27545 | −0.298124 | ||||||||
\(969\) | −44.1661 | −1.41882 | ||||||||
\(970\) | 0.419665 | 0.0134746 | ||||||||
\(971\) | 6.24440 | 0.200392 | 0.100196 | − | 0.994968i | \(-0.468053\pi\) | ||||
0.100196 | + | 0.994968i | \(0.468053\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −12.8916 | −0.413284 | ||||||||
\(974\) | −20.6430 | −0.661446 | ||||||||
\(975\) | 5.70896 | 0.182833 | ||||||||
\(976\) | 10.8883 | 0.348527 | ||||||||
\(977\) | −13.8899 | −0.444379 | −0.222189 | − | 0.975004i | \(-0.571320\pi\) | ||||
−0.222189 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(978\) | −1.25343 | −0.0400804 | ||||||||
\(979\) | −56.6005 | −1.80896 | ||||||||
\(980\) | 3.25629 | 0.104018 | ||||||||
\(981\) | 7.71676 | 0.246377 | ||||||||
\(982\) | −17.5819 | −0.561061 | ||||||||
\(983\) | 27.5406 | 0.878407 | 0.439204 | − | 0.898387i | \(-0.355261\pi\) | ||||
0.439204 | + | 0.898387i | \(0.355261\pi\) | |||||||
\(984\) | 0.0953661 | 0.00304016 | ||||||||
\(985\) | 0.667444 | 0.0212665 | ||||||||
\(986\) | −7.42662 | −0.236512 | ||||||||
\(987\) | 2.75061 | 0.0875528 | ||||||||
\(988\) | −6.86299 | −0.218341 | ||||||||
\(989\) | 0.941339 | 0.0299328 | ||||||||
\(990\) | 1.03670 | 0.0329486 | ||||||||
\(991\) | −4.94289 | −0.157016 | −0.0785081 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785081 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(992\) | −6.50283 | −0.206465 | ||||||||
\(993\) | −21.1833 | −0.672230 | ||||||||
\(994\) | −50.4113 | −1.59895 | ||||||||
\(995\) | 2.82623 | 0.0895975 | ||||||||
\(996\) | 1.71676 | 0.0543976 | ||||||||
\(997\) | 10.2437 | 0.324423 | 0.162211 | − | 0.986756i | \(-0.448137\pi\) | ||||
0.162211 | + | 0.986756i | \(0.448137\pi\) | |||||||
\(998\) | 9.35607 | 0.296161 | ||||||||
\(999\) | −7.29175 | −0.230701 |
(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 | 4002.2.a.ba.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.ba.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |