Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −0.830898 | −0.479719 | −0.239859 | − | 0.970808i | \(-0.577101\pi\) | ||||
−0.239859 | + | 0.970808i | \(0.577101\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.41489 | −0.632756 | −0.316378 | − | 0.948633i | \(-0.602467\pi\) | ||||
−0.316378 | + | 0.948633i | \(0.602467\pi\) | |||||||
\(6\) | −0.830898 | −0.339213 | ||||||||
\(7\) | −0.234026 | −0.0884536 | −0.0442268 | − | 0.999022i | \(-0.514082\pi\) | ||||
−0.0442268 | + | 0.999022i | \(0.514082\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.30961 | −0.769870 | ||||||||
\(10\) | −1.41489 | −0.447426 | ||||||||
\(11\) | 3.75602 | 1.13248 | 0.566241 | − | 0.824240i | \(-0.308397\pi\) | ||||
0.566241 | + | 0.824240i | \(0.308397\pi\) | |||||||
\(12\) | −0.830898 | −0.239859 | ||||||||
\(13\) | 4.10056 | 1.13729 | 0.568646 | − | 0.822583i | \(-0.307468\pi\) | ||||
0.568646 | + | 0.822583i | \(0.307468\pi\) | |||||||
\(14\) | −0.234026 | −0.0625461 | ||||||||
\(15\) | 1.17563 | 0.303545 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.34390 | 1.78116 | 0.890579 | − | 0.454828i | \(-0.150299\pi\) | ||||
0.890579 | + | 0.454828i | \(0.150299\pi\) | |||||||
\(18\) | −2.30961 | −0.544380 | ||||||||
\(19\) | −2.51438 | −0.576838 | −0.288419 | − | 0.957504i | \(-0.593130\pi\) | ||||
−0.288419 | + | 0.957504i | \(0.593130\pi\) | |||||||
\(20\) | −1.41489 | −0.316378 | ||||||||
\(21\) | 0.194452 | 0.0424328 | ||||||||
\(22\) | 3.75602 | 0.800786 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −0.830898 | −0.169606 | ||||||||
\(25\) | −2.99810 | −0.599619 | ||||||||
\(26\) | 4.10056 | 0.804186 | ||||||||
\(27\) | 4.41174 | 0.849040 | ||||||||
\(28\) | −0.234026 | −0.0442268 | ||||||||
\(29\) | 5.16848 | 0.959762 | 0.479881 | − | 0.877334i | \(-0.340680\pi\) | ||||
0.479881 | + | 0.877334i | \(0.340680\pi\) | |||||||
\(30\) | 1.17563 | 0.214639 | ||||||||
\(31\) | −8.55210 | −1.53600 | −0.768002 | − | 0.640448i | \(-0.778749\pi\) | ||||
−0.768002 | + | 0.640448i | \(0.778749\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.12087 | −0.543273 | ||||||||
\(34\) | 7.34390 | 1.25947 | ||||||||
\(35\) | 0.331120 | 0.0559695 | ||||||||
\(36\) | −2.30961 | −0.384935 | ||||||||
\(37\) | 4.10484 | 0.674831 | 0.337415 | − | 0.941356i | \(-0.390447\pi\) | ||||
0.337415 | + | 0.941356i | \(0.390447\pi\) | |||||||
\(38\) | −2.51438 | −0.407886 | ||||||||
\(39\) | −3.40715 | −0.545580 | ||||||||
\(40\) | −1.41489 | −0.223713 | ||||||||
\(41\) | 0.450472 | 0.0703519 | 0.0351760 | − | 0.999381i | \(-0.488801\pi\) | ||||
0.0351760 | + | 0.999381i | \(0.488801\pi\) | |||||||
\(42\) | 0.194452 | 0.0300046 | ||||||||
\(43\) | −12.1209 | −1.84842 | −0.924212 | − | 0.381879i | \(-0.875277\pi\) | ||||
−0.924212 | + | 0.381879i | \(0.875277\pi\) | |||||||
\(44\) | 3.75602 | 0.566241 | ||||||||
\(45\) | 3.26783 | 0.487140 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 5.41357 | 0.789651 | 0.394825 | − | 0.918756i | \(-0.370805\pi\) | ||||
0.394825 | + | 0.918756i | \(0.370805\pi\) | |||||||
\(48\) | −0.830898 | −0.119930 | ||||||||
\(49\) | −6.94523 | −0.992176 | ||||||||
\(50\) | −2.99810 | −0.423995 | ||||||||
\(51\) | −6.10203 | −0.854455 | ||||||||
\(52\) | 4.10056 | 0.568646 | ||||||||
\(53\) | −2.60482 | −0.357800 | −0.178900 | − | 0.983867i | \(-0.557254\pi\) | ||||
−0.178900 | + | 0.983867i | \(0.557254\pi\) | |||||||
\(54\) | 4.41174 | 0.600362 | ||||||||
\(55\) | −5.31434 | −0.716585 | ||||||||
\(56\) | −0.234026 | −0.0312731 | ||||||||
\(57\) | 2.08919 | 0.276720 | ||||||||
\(58\) | 5.16848 | 0.678654 | ||||||||
\(59\) | −9.00816 | −1.17276 | −0.586381 | − | 0.810035i | \(-0.699448\pi\) | ||||
−0.586381 | + | 0.810035i | \(0.699448\pi\) | |||||||
\(60\) | 1.17563 | 0.151773 | ||||||||
\(61\) | 6.21086 | 0.795220 | 0.397610 | − | 0.917555i | \(-0.369840\pi\) | ||||
0.397610 | + | 0.917555i | \(0.369840\pi\) | |||||||
\(62\) | −8.55210 | −1.08612 | ||||||||
\(63\) | 0.540509 | 0.0680977 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.80183 | −0.719628 | ||||||||
\(66\) | −3.12087 | −0.384152 | ||||||||
\(67\) | 9.56096 | 1.16806 | 0.584029 | − | 0.811733i | \(-0.301476\pi\) | ||||
0.584029 | + | 0.811733i | \(0.301476\pi\) | |||||||
\(68\) | 7.34390 | 0.890579 | ||||||||
\(69\) | −0.830898 | −0.100028 | ||||||||
\(70\) | 0.331120 | 0.0395764 | ||||||||
\(71\) | −4.65500 | −0.552447 | −0.276223 | − | 0.961093i | \(-0.589083\pi\) | ||||
−0.276223 | + | 0.961093i | \(0.589083\pi\) | |||||||
\(72\) | −2.30961 | −0.272190 | ||||||||
\(73\) | 11.6142 | 1.35933 | 0.679667 | − | 0.733521i | \(-0.262124\pi\) | ||||
0.679667 | + | 0.733521i | \(0.262124\pi\) | |||||||
\(74\) | 4.10484 | 0.477177 | ||||||||
\(75\) | 2.49111 | 0.287649 | ||||||||
\(76\) | −2.51438 | −0.288419 | ||||||||
\(77\) | −0.879006 | −0.100172 | ||||||||
\(78\) | −3.40715 | −0.385783 | ||||||||
\(79\) | −0.169905 | −0.0191158 | −0.00955788 | − | 0.999954i | \(-0.503042\pi\) | ||||
−0.00955788 | + | 0.999954i | \(0.503042\pi\) | |||||||
\(80\) | −1.41489 | −0.158189 | ||||||||
\(81\) | 3.26312 | 0.362569 | ||||||||
\(82\) | 0.450472 | 0.0497463 | ||||||||
\(83\) | −0.454412 | −0.0498782 | −0.0249391 | − | 0.999689i | \(-0.507939\pi\) | ||||
−0.0249391 | + | 0.999689i | \(0.507939\pi\) | |||||||
\(84\) | 0.194452 | 0.0212164 | ||||||||
\(85\) | −10.3908 | −1.12704 | ||||||||
\(86\) | −12.1209 | −1.30703 | ||||||||
\(87\) | −4.29448 | −0.460416 | ||||||||
\(88\) | 3.75602 | 0.400393 | ||||||||
\(89\) | −5.74379 | −0.608841 | −0.304420 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304420 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(90\) | 3.26783 | 0.344460 | ||||||||
\(91\) | −0.959639 | −0.100597 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 7.10592 | 0.736850 | ||||||||
\(94\) | 5.41357 | 0.558367 | ||||||||
\(95\) | 3.55756 | 0.364998 | ||||||||
\(96\) | −0.830898 | −0.0848031 | ||||||||
\(97\) | 4.99562 | 0.507228 | 0.253614 | − | 0.967306i | \(-0.418381\pi\) | ||||
0.253614 | + | 0.967306i | \(0.418381\pi\) | |||||||
\(98\) | −6.94523 | −0.701574 | ||||||||
\(99\) | −8.67493 | −0.871864 | ||||||||
\(100\) | −2.99810 | −0.299810 | ||||||||
\(101\) | −0.804159 | −0.0800168 | −0.0400084 | − | 0.999199i | \(-0.512738\pi\) | ||||
−0.0400084 | + | 0.999199i | \(0.512738\pi\) | |||||||
\(102\) | −6.10203 | −0.604191 | ||||||||
\(103\) | 8.10317 | 0.798429 | 0.399215 | − | 0.916858i | \(-0.369283\pi\) | ||||
0.399215 | + | 0.916858i | \(0.369283\pi\) | |||||||
\(104\) | 4.10056 | 0.402093 | ||||||||
\(105\) | −0.275127 | −0.0268497 | ||||||||
\(106\) | −2.60482 | −0.253003 | ||||||||
\(107\) | 18.3164 | 1.77071 | 0.885355 | − | 0.464916i | \(-0.153915\pi\) | ||||
0.885355 | + | 0.464916i | \(0.153915\pi\) | |||||||
\(108\) | 4.41174 | 0.424520 | ||||||||
\(109\) | 7.66562 | 0.734233 | 0.367117 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367117 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(110\) | −5.31434 | −0.506702 | ||||||||
\(111\) | −3.41070 | −0.323729 | ||||||||
\(112\) | −0.234026 | −0.0221134 | ||||||||
\(113\) | 15.9127 | 1.49694 | 0.748469 | − | 0.663170i | \(-0.230789\pi\) | ||||
0.748469 | + | 0.663170i | \(0.230789\pi\) | |||||||
\(114\) | 2.08919 | 0.195671 | ||||||||
\(115\) | −1.41489 | −0.131939 | ||||||||
\(116\) | 5.16848 | 0.479881 | ||||||||
\(117\) | −9.47070 | −0.875566 | ||||||||
\(118\) | −9.00816 | −0.829268 | ||||||||
\(119\) | −1.71867 | −0.157550 | ||||||||
\(120\) | 1.17563 | 0.107319 | ||||||||
\(121\) | 3.10767 | 0.282516 | ||||||||
\(122\) | 6.21086 | 0.562305 | ||||||||
\(123\) | −0.374296 | −0.0337492 | ||||||||
\(124\) | −8.55210 | −0.768002 | ||||||||
\(125\) | 11.3164 | 1.01217 | ||||||||
\(126\) | 0.540509 | 0.0481524 | ||||||||
\(127\) | 0.658707 | 0.0584508 | 0.0292254 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292254 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.0713 | 0.886724 | ||||||||
\(130\) | −5.80183 | −0.508854 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −3.12087 | −0.271637 | ||||||||
\(133\) | 0.588430 | 0.0510234 | ||||||||
\(134\) | 9.56096 | 0.825941 | ||||||||
\(135\) | −6.24211 | −0.537235 | ||||||||
\(136\) | 7.34390 | 0.629735 | ||||||||
\(137\) | 12.3465 | 1.05483 | 0.527417 | − | 0.849606i | \(-0.323161\pi\) | ||||
0.527417 | + | 0.849606i | \(0.323161\pi\) | |||||||
\(138\) | −0.830898 | −0.0707307 | ||||||||
\(139\) | 13.3114 | 1.12906 | 0.564530 | − | 0.825412i | \(-0.309057\pi\) | ||||
0.564530 | + | 0.825412i | \(0.309057\pi\) | |||||||
\(140\) | 0.331120 | 0.0279848 | ||||||||
\(141\) | −4.49812 | −0.378810 | ||||||||
\(142\) | −4.65500 | −0.390639 | ||||||||
\(143\) | 15.4018 | 1.28796 | ||||||||
\(144\) | −2.30961 | −0.192467 | ||||||||
\(145\) | −7.31281 | −0.607296 | ||||||||
\(146\) | 11.6142 | 0.961194 | ||||||||
\(147\) | 5.77078 | 0.475966 | ||||||||
\(148\) | 4.10484 | 0.337415 | ||||||||
\(149\) | 20.3092 | 1.66380 | 0.831898 | − | 0.554928i | \(-0.187254\pi\) | ||||
0.831898 | + | 0.554928i | \(0.187254\pi\) | |||||||
\(150\) | 2.49111 | 0.203398 | ||||||||
\(151\) | 0.496065 | 0.0403692 | 0.0201846 | − | 0.999796i | \(-0.493575\pi\) | ||||
0.0201846 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(152\) | −2.51438 | −0.203943 | ||||||||
\(153\) | −16.9615 | −1.37126 | ||||||||
\(154\) | −0.879006 | −0.0708324 | ||||||||
\(155\) | 12.1003 | 0.971916 | ||||||||
\(156\) | −3.40715 | −0.272790 | ||||||||
\(157\) | −19.2148 | −1.53351 | −0.766753 | − | 0.641943i | \(-0.778129\pi\) | ||||
−0.766753 | + | 0.641943i | \(0.778129\pi\) | |||||||
\(158\) | −0.169905 | −0.0135169 | ||||||||
\(159\) | 2.16434 | 0.171643 | ||||||||
\(160\) | −1.41489 | −0.111857 | ||||||||
\(161\) | −0.234026 | −0.0184438 | ||||||||
\(162\) | 3.26312 | 0.256375 | ||||||||
\(163\) | 5.38179 | 0.421534 | 0.210767 | − | 0.977536i | \(-0.432404\pi\) | ||||
0.210767 | + | 0.977536i | \(0.432404\pi\) | |||||||
\(164\) | 0.450472 | 0.0351760 | ||||||||
\(165\) | 4.41567 | 0.343760 | ||||||||
\(166\) | −0.454412 | −0.0352692 | ||||||||
\(167\) | 18.2465 | 1.41196 | 0.705978 | − | 0.708234i | \(-0.250508\pi\) | ||||
0.705978 | + | 0.708234i | \(0.250508\pi\) | |||||||
\(168\) | 0.194452 | 0.0150023 | ||||||||
\(169\) | 3.81461 | 0.293431 | ||||||||
\(170\) | −10.3908 | −0.796937 | ||||||||
\(171\) | 5.80723 | 0.444090 | ||||||||
\(172\) | −12.1209 | −0.924212 | ||||||||
\(173\) | 17.5575 | 1.33487 | 0.667435 | − | 0.744668i | \(-0.267392\pi\) | ||||
0.667435 | + | 0.744668i | \(0.267392\pi\) | |||||||
\(174\) | −4.29448 | −0.325563 | ||||||||
\(175\) | 0.701633 | 0.0530385 | ||||||||
\(176\) | 3.75602 | 0.283121 | ||||||||
\(177\) | 7.48486 | 0.562596 | ||||||||
\(178\) | −5.74379 | −0.430515 | ||||||||
\(179\) | 3.41719 | 0.255413 | 0.127706 | − | 0.991812i | \(-0.459238\pi\) | ||||
0.127706 | + | 0.991812i | \(0.459238\pi\) | |||||||
\(180\) | 3.26783 | 0.243570 | ||||||||
\(181\) | −20.4216 | −1.51793 | −0.758964 | − | 0.651132i | \(-0.774294\pi\) | ||||
−0.758964 | + | 0.651132i | \(0.774294\pi\) | |||||||
\(182\) | −0.959639 | −0.0711331 | ||||||||
\(183\) | −5.16059 | −0.381482 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −5.80787 | −0.427003 | ||||||||
\(186\) | 7.10592 | 0.521032 | ||||||||
\(187\) | 27.5838 | 2.01713 | ||||||||
\(188\) | 5.41357 | 0.394825 | ||||||||
\(189\) | −1.03246 | −0.0751006 | ||||||||
\(190\) | 3.55756 | 0.258093 | ||||||||
\(191\) | −18.1162 | −1.31084 | −0.655420 | − | 0.755264i | \(-0.727508\pi\) | ||||
−0.655420 | + | 0.755264i | \(0.727508\pi\) | |||||||
\(192\) | −0.830898 | −0.0599649 | ||||||||
\(193\) | 1.03366 | 0.0744045 | 0.0372022 | − | 0.999308i | \(-0.488155\pi\) | ||||
0.0372022 | + | 0.999308i | \(0.488155\pi\) | |||||||
\(194\) | 4.99562 | 0.358664 | ||||||||
\(195\) | 4.82073 | 0.345219 | ||||||||
\(196\) | −6.94523 | −0.496088 | ||||||||
\(197\) | 3.09375 | 0.220421 | 0.110210 | − | 0.993908i | \(-0.464848\pi\) | ||||
0.110210 | + | 0.993908i | \(0.464848\pi\) | |||||||
\(198\) | −8.67493 | −0.616501 | ||||||||
\(199\) | 5.97114 | 0.423283 | 0.211641 | − | 0.977347i | \(-0.432119\pi\) | ||||
0.211641 | + | 0.977347i | \(0.432119\pi\) | |||||||
\(200\) | −2.99810 | −0.211997 | ||||||||
\(201\) | −7.94418 | −0.560339 | ||||||||
\(202\) | −0.804159 | −0.0565804 | ||||||||
\(203\) | −1.20956 | −0.0848944 | ||||||||
\(204\) | −6.10203 | −0.427228 | ||||||||
\(205\) | −0.637367 | −0.0445156 | ||||||||
\(206\) | 8.10317 | 0.564575 | ||||||||
\(207\) | −2.30961 | −0.160529 | ||||||||
\(208\) | 4.10056 | 0.284323 | ||||||||
\(209\) | −9.44405 | −0.653259 | ||||||||
\(210\) | −0.275127 | −0.0189856 | ||||||||
\(211\) | 4.47685 | 0.308199 | 0.154099 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154099 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(212\) | −2.60482 | −0.178900 | ||||||||
\(213\) | 3.86783 | 0.265019 | ||||||||
\(214\) | 18.3164 | 1.25208 | ||||||||
\(215\) | 17.1497 | 1.16960 | ||||||||
\(216\) | 4.41174 | 0.300181 | ||||||||
\(217\) | 2.00142 | 0.135865 | ||||||||
\(218\) | 7.66562 | 0.519181 | ||||||||
\(219\) | −9.65017 | −0.652098 | ||||||||
\(220\) | −5.31434 | −0.358293 | ||||||||
\(221\) | 30.1141 | 2.02570 | ||||||||
\(222\) | −3.41070 | −0.228911 | ||||||||
\(223\) | −10.2941 | −0.689342 | −0.344671 | − | 0.938723i | \(-0.612010\pi\) | ||||
−0.344671 | + | 0.938723i | \(0.612010\pi\) | |||||||
\(224\) | −0.234026 | −0.0156365 | ||||||||
\(225\) | 6.92443 | 0.461629 | ||||||||
\(226\) | 15.9127 | 1.05850 | ||||||||
\(227\) | 26.6259 | 1.76722 | 0.883612 | − | 0.468220i | \(-0.155104\pi\) | ||||
0.883612 | + | 0.468220i | \(0.155104\pi\) | |||||||
\(228\) | 2.08919 | 0.138360 | ||||||||
\(229\) | 18.4674 | 1.22036 | 0.610182 | − | 0.792262i | \(-0.291096\pi\) | ||||
0.610182 | + | 0.792262i | \(0.291096\pi\) | |||||||
\(230\) | −1.41489 | −0.0932948 | ||||||||
\(231\) | 0.730364 | 0.0480544 | ||||||||
\(232\) | 5.16848 | 0.339327 | ||||||||
\(233\) | −1.95218 | −0.127892 | −0.0639459 | − | 0.997953i | \(-0.520369\pi\) | ||||
−0.0639459 | + | 0.997953i | \(0.520369\pi\) | |||||||
\(234\) | −9.47070 | −0.619119 | ||||||||
\(235\) | −7.65959 | −0.499656 | ||||||||
\(236\) | −9.00816 | −0.586381 | ||||||||
\(237\) | 0.141173 | 0.00917019 | ||||||||
\(238\) | −1.71867 | −0.111405 | ||||||||
\(239\) | −1.46566 | −0.0948056 | −0.0474028 | − | 0.998876i | \(-0.515094\pi\) | ||||
−0.0474028 | + | 0.998876i | \(0.515094\pi\) | |||||||
\(240\) | 1.17563 | 0.0758863 | ||||||||
\(241\) | −29.9828 | −1.93136 | −0.965681 | − | 0.259732i | \(-0.916366\pi\) | ||||
−0.965681 | + | 0.259732i | \(0.916366\pi\) | |||||||
\(242\) | 3.10767 | 0.199769 | ||||||||
\(243\) | −15.9465 | −1.02297 | ||||||||
\(244\) | 6.21086 | 0.397610 | ||||||||
\(245\) | 9.82671 | 0.627806 | ||||||||
\(246\) | −0.374296 | −0.0238643 | ||||||||
\(247\) | −10.3104 | −0.656033 | ||||||||
\(248\) | −8.55210 | −0.543059 | ||||||||
\(249\) | 0.377570 | 0.0239275 | ||||||||
\(250\) | 11.3164 | 0.715712 | ||||||||
\(251\) | −4.98723 | −0.314791 | −0.157396 | − | 0.987536i | \(-0.550310\pi\) | ||||
−0.157396 | + | 0.987536i | \(0.550310\pi\) | |||||||
\(252\) | 0.540509 | 0.0340489 | ||||||||
\(253\) | 3.75602 | 0.236139 | ||||||||
\(254\) | 0.658707 | 0.0413309 | ||||||||
\(255\) | 8.63368 | 0.540662 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.8339 | 1.48672 | 0.743358 | − | 0.668894i | \(-0.233232\pi\) | ||||
0.743358 | + | 0.668894i | \(0.233232\pi\) | |||||||
\(258\) | 10.0713 | 0.627009 | ||||||||
\(259\) | −0.960639 | −0.0596912 | ||||||||
\(260\) | −5.80183 | −0.359814 | ||||||||
\(261\) | −11.9372 | −0.738892 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 7.87510 | 0.485600 | 0.242800 | − | 0.970076i | \(-0.421934\pi\) | ||||
0.242800 | + | 0.970076i | \(0.421934\pi\) | |||||||
\(264\) | −3.12087 | −0.192076 | ||||||||
\(265\) | 3.68553 | 0.226400 | ||||||||
\(266\) | 0.588430 | 0.0360790 | ||||||||
\(267\) | 4.77250 | 0.292072 | ||||||||
\(268\) | 9.56096 | 0.584029 | ||||||||
\(269\) | 9.11359 | 0.555665 | 0.277833 | − | 0.960630i | \(-0.410384\pi\) | ||||
0.277833 | + | 0.960630i | \(0.410384\pi\) | |||||||
\(270\) | −6.24211 | −0.379883 | ||||||||
\(271\) | −6.46382 | −0.392649 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(272\) | 7.34390 | 0.445290 | ||||||||
\(273\) | 0.797361 | 0.0482585 | ||||||||
\(274\) | 12.3465 | 0.745880 | ||||||||
\(275\) | −11.2609 | −0.679058 | ||||||||
\(276\) | −0.830898 | −0.0500142 | ||||||||
\(277\) | 2.70561 | 0.162564 | 0.0812822 | − | 0.996691i | \(-0.474099\pi\) | ||||
0.0812822 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(278\) | 13.3114 | 0.798367 | ||||||||
\(279\) | 19.7520 | 1.18252 | ||||||||
\(280\) | 0.331120 | 0.0197882 | ||||||||
\(281\) | −7.31543 | −0.436402 | −0.218201 | − | 0.975904i | \(-0.570019\pi\) | ||||
−0.218201 | + | 0.975904i | \(0.570019\pi\) | |||||||
\(282\) | −4.49812 | −0.267859 | ||||||||
\(283\) | −5.09365 | −0.302786 | −0.151393 | − | 0.988474i | \(-0.548376\pi\) | ||||
−0.151393 | + | 0.988474i | \(0.548376\pi\) | |||||||
\(284\) | −4.65500 | −0.276223 | ||||||||
\(285\) | −2.95597 | −0.175096 | ||||||||
\(286\) | 15.4018 | 0.910727 | ||||||||
\(287\) | −0.105422 | −0.00622288 | ||||||||
\(288\) | −2.30961 | −0.136095 | ||||||||
\(289\) | 36.9329 | 2.17252 | ||||||||
\(290\) | −7.31281 | −0.429423 | ||||||||
\(291\) | −4.15084 | −0.243327 | ||||||||
\(292\) | 11.6142 | 0.679667 | ||||||||
\(293\) | −15.9117 | −0.929573 | −0.464786 | − | 0.885423i | \(-0.653869\pi\) | ||||
−0.464786 | + | 0.885423i | \(0.653869\pi\) | |||||||
\(294\) | 5.77078 | 0.336559 | ||||||||
\(295\) | 12.7455 | 0.742073 | ||||||||
\(296\) | 4.10484 | 0.238589 | ||||||||
\(297\) | 16.5706 | 0.961523 | ||||||||
\(298\) | 20.3092 | 1.17648 | ||||||||
\(299\) | 4.10056 | 0.237142 | ||||||||
\(300\) | 2.49111 | 0.143824 | ||||||||
\(301\) | 2.83661 | 0.163500 | ||||||||
\(302\) | 0.496065 | 0.0285453 | ||||||||
\(303\) | 0.668173 | 0.0383856 | ||||||||
\(304\) | −2.51438 | −0.144210 | ||||||||
\(305\) | −8.78767 | −0.503180 | ||||||||
\(306\) | −16.9615 | −0.969627 | ||||||||
\(307\) | 18.8530 | 1.07600 | 0.538000 | − | 0.842945i | \(-0.319180\pi\) | ||||
0.538000 | + | 0.842945i | \(0.319180\pi\) | |||||||
\(308\) | −0.879006 | −0.0500860 | ||||||||
\(309\) | −6.73290 | −0.383022 | ||||||||
\(310\) | 12.1003 | 0.687248 | ||||||||
\(311\) | −13.4179 | −0.760862 | −0.380431 | − | 0.924809i | \(-0.624224\pi\) | ||||
−0.380431 | + | 0.924809i | \(0.624224\pi\) | |||||||
\(312\) | −3.40715 | −0.192892 | ||||||||
\(313\) | 16.6992 | 0.943893 | 0.471946 | − | 0.881627i | \(-0.343552\pi\) | ||||
0.471946 | + | 0.881627i | \(0.343552\pi\) | |||||||
\(314\) | −19.2148 | −1.08435 | ||||||||
\(315\) | −0.764758 | −0.0430893 | ||||||||
\(316\) | −0.169905 | −0.00955788 | ||||||||
\(317\) | −28.0772 | −1.57698 | −0.788488 | − | 0.615051i | \(-0.789136\pi\) | ||||
−0.788488 | + | 0.615051i | \(0.789136\pi\) | |||||||
\(318\) | 2.16434 | 0.121370 | ||||||||
\(319\) | 19.4129 | 1.08691 | ||||||||
\(320\) | −1.41489 | −0.0790945 | ||||||||
\(321\) | −15.2190 | −0.849443 | ||||||||
\(322\) | −0.234026 | −0.0130418 | ||||||||
\(323\) | −18.4654 | −1.02744 | ||||||||
\(324\) | 3.26312 | 0.181285 | ||||||||
\(325\) | −12.2939 | −0.681942 | ||||||||
\(326\) | 5.38179 | 0.298070 | ||||||||
\(327\) | −6.36935 | −0.352226 | ||||||||
\(328\) | 0.450472 | 0.0248732 | ||||||||
\(329\) | −1.26692 | −0.0698474 | ||||||||
\(330\) | 4.41567 | 0.243075 | ||||||||
\(331\) | −1.21324 | −0.0666855 | −0.0333428 | − | 0.999444i | \(-0.510615\pi\) | ||||
−0.0333428 | + | 0.999444i | \(0.510615\pi\) | |||||||
\(332\) | −0.454412 | −0.0249391 | ||||||||
\(333\) | −9.48056 | −0.519532 | ||||||||
\(334\) | 18.2465 | 0.998403 | ||||||||
\(335\) | −13.5277 | −0.739096 | ||||||||
\(336\) | 0.194452 | 0.0106082 | ||||||||
\(337\) | 0.992259 | 0.0540518 | 0.0270259 | − | 0.999635i | \(-0.491396\pi\) | ||||
0.0270259 | + | 0.999635i | \(0.491396\pi\) | |||||||
\(338\) | 3.81461 | 0.207487 | ||||||||
\(339\) | −13.2218 | −0.718110 | ||||||||
\(340\) | −10.3908 | −0.563520 | ||||||||
\(341\) | −32.1219 | −1.73950 | ||||||||
\(342\) | 5.80723 | 0.314019 | ||||||||
\(343\) | 3.26355 | 0.176215 | ||||||||
\(344\) | −12.1209 | −0.653517 | ||||||||
\(345\) | 1.17563 | 0.0632936 | ||||||||
\(346\) | 17.5575 | 0.943896 | ||||||||
\(347\) | −10.7069 | −0.574777 | −0.287388 | − | 0.957814i | \(-0.592787\pi\) | ||||
−0.287388 | + | 0.957814i | \(0.592787\pi\) | |||||||
\(348\) | −4.29448 | −0.230208 | ||||||||
\(349\) | −18.7164 | −1.00187 | −0.500934 | − | 0.865485i | \(-0.667010\pi\) | ||||
−0.500934 | + | 0.865485i | \(0.667010\pi\) | |||||||
\(350\) | 0.701633 | 0.0375039 | ||||||||
\(351\) | 18.0906 | 0.965606 | ||||||||
\(352\) | 3.75602 | 0.200196 | ||||||||
\(353\) | 37.3705 | 1.98903 | 0.994516 | − | 0.104584i | \(-0.0333512\pi\) | ||||
0.994516 | + | 0.104584i | \(0.0333512\pi\) | |||||||
\(354\) | 7.48486 | 0.397816 | ||||||||
\(355\) | 6.58629 | 0.349564 | ||||||||
\(356\) | −5.74379 | −0.304420 | ||||||||
\(357\) | 1.42803 | 0.0755796 | ||||||||
\(358\) | 3.41719 | 0.180604 | ||||||||
\(359\) | −5.79181 | −0.305680 | −0.152840 | − | 0.988251i | \(-0.548842\pi\) | ||||
−0.152840 | + | 0.988251i | \(0.548842\pi\) | |||||||
\(360\) | 3.26783 | 0.172230 | ||||||||
\(361\) | −12.6779 | −0.667258 | ||||||||
\(362\) | −20.4216 | −1.07334 | ||||||||
\(363\) | −2.58216 | −0.135528 | ||||||||
\(364\) | −0.959639 | −0.0502987 | ||||||||
\(365\) | −16.4327 | −0.860127 | ||||||||
\(366\) | −5.16059 | −0.269749 | ||||||||
\(367\) | −20.8003 | −1.08577 | −0.542884 | − | 0.839807i | \(-0.682668\pi\) | ||||
−0.542884 | + | 0.839807i | \(0.682668\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.04041 | −0.0541618 | ||||||||
\(370\) | −5.80787 | −0.301937 | ||||||||
\(371\) | 0.609597 | 0.0316487 | ||||||||
\(372\) | 7.10592 | 0.368425 | ||||||||
\(373\) | 29.8137 | 1.54369 | 0.771847 | − | 0.635809i | \(-0.219333\pi\) | ||||
0.771847 | + | 0.635809i | \(0.219333\pi\) | |||||||
\(374\) | 27.5838 | 1.42633 | ||||||||
\(375\) | −9.40277 | −0.485557 | ||||||||
\(376\) | 5.41357 | 0.279184 | ||||||||
\(377\) | 21.1937 | 1.09153 | ||||||||
\(378\) | −1.03246 | −0.0531042 | ||||||||
\(379\) | 21.9308 | 1.12651 | 0.563254 | − | 0.826284i | \(-0.309549\pi\) | ||||
0.563254 | + | 0.826284i | \(0.309549\pi\) | |||||||
\(380\) | 3.55756 | 0.182499 | ||||||||
\(381\) | −0.547318 | −0.0280399 | ||||||||
\(382\) | −18.1162 | −0.926904 | ||||||||
\(383\) | −10.3428 | −0.528494 | −0.264247 | − | 0.964455i | \(-0.585123\pi\) | ||||
−0.264247 | + | 0.964455i | \(0.585123\pi\) | |||||||
\(384\) | −0.830898 | −0.0424016 | ||||||||
\(385\) | 1.24369 | 0.0633845 | ||||||||
\(386\) | 1.03366 | 0.0526119 | ||||||||
\(387\) | 27.9946 | 1.42305 | ||||||||
\(388\) | 4.99562 | 0.253614 | ||||||||
\(389\) | 0.575240 | 0.0291658 | 0.0145829 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145829 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(390\) | 4.82073 | 0.244107 | ||||||||
\(391\) | 7.34390 | 0.371397 | ||||||||
\(392\) | −6.94523 | −0.350787 | ||||||||
\(393\) | −0.830898 | −0.0419132 | ||||||||
\(394\) | 3.09375 | 0.155861 | ||||||||
\(395\) | 0.240396 | 0.0120956 | ||||||||
\(396\) | −8.67493 | −0.435932 | ||||||||
\(397\) | −9.25444 | −0.464467 | −0.232234 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232234 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(398\) | 5.97114 | 0.299306 | ||||||||
\(399\) | −0.488925 | −0.0244769 | ||||||||
\(400\) | −2.99810 | −0.149905 | ||||||||
\(401\) | −15.9794 | −0.797971 | −0.398986 | − | 0.916957i | \(-0.630638\pi\) | ||||
−0.398986 | + | 0.916957i | \(0.630638\pi\) | |||||||
\(402\) | −7.94418 | −0.396220 | ||||||||
\(403\) | −35.0684 | −1.74688 | ||||||||
\(404\) | −0.804159 | −0.0400084 | ||||||||
\(405\) | −4.61695 | −0.229418 | ||||||||
\(406\) | −1.20956 | −0.0600294 | ||||||||
\(407\) | 15.4178 | 0.764234 | ||||||||
\(408\) | −6.10203 | −0.302096 | ||||||||
\(409\) | −23.7683 | −1.17527 | −0.587633 | − | 0.809127i | \(-0.699940\pi\) | ||||
−0.587633 | + | 0.809127i | \(0.699940\pi\) | |||||||
\(410\) | −0.637367 | −0.0314773 | ||||||||
\(411\) | −10.2587 | −0.506024 | ||||||||
\(412\) | 8.10317 | 0.399215 | ||||||||
\(413\) | 2.10814 | 0.103735 | ||||||||
\(414\) | −2.30961 | −0.113511 | ||||||||
\(415\) | 0.642941 | 0.0315608 | ||||||||
\(416\) | 4.10056 | 0.201047 | ||||||||
\(417\) | −11.0604 | −0.541632 | ||||||||
\(418\) | −9.44405 | −0.461924 | ||||||||
\(419\) | 31.5720 | 1.54240 | 0.771198 | − | 0.636596i | \(-0.219658\pi\) | ||||
0.771198 | + | 0.636596i | \(0.219658\pi\) | |||||||
\(420\) | −0.275127 | −0.0134248 | ||||||||
\(421\) | −21.3439 | −1.04024 | −0.520118 | − | 0.854094i | \(-0.674112\pi\) | ||||
−0.520118 | + | 0.854094i | \(0.674112\pi\) | |||||||
\(422\) | 4.47685 | 0.217929 | ||||||||
\(423\) | −12.5032 | −0.607928 | ||||||||
\(424\) | −2.60482 | −0.126501 | ||||||||
\(425\) | −22.0177 | −1.06802 | ||||||||
\(426\) | 3.86783 | 0.187397 | ||||||||
\(427\) | −1.45350 | −0.0703400 | ||||||||
\(428\) | 18.3164 | 0.885355 | ||||||||
\(429\) | −12.7973 | −0.617860 | ||||||||
\(430\) | 17.1497 | 0.827034 | ||||||||
\(431\) | −7.09641 | −0.341822 | −0.170911 | − | 0.985286i | \(-0.554671\pi\) | ||||
−0.170911 | + | 0.985286i | \(0.554671\pi\) | |||||||
\(432\) | 4.41174 | 0.212260 | ||||||||
\(433\) | −7.58377 | −0.364453 | −0.182226 | − | 0.983257i | \(-0.558330\pi\) | ||||
−0.182226 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(434\) | 2.00142 | 0.0960710 | ||||||||
\(435\) | 6.07620 | 0.291331 | ||||||||
\(436\) | 7.66562 | 0.367117 | ||||||||
\(437\) | −2.51438 | −0.120279 | ||||||||
\(438\) | −9.65017 | −0.461103 | ||||||||
\(439\) | 25.1129 | 1.19858 | 0.599288 | − | 0.800534i | \(-0.295451\pi\) | ||||
0.599288 | + | 0.800534i | \(0.295451\pi\) | |||||||
\(440\) | −5.31434 | −0.253351 | ||||||||
\(441\) | 16.0408 | 0.763846 | ||||||||
\(442\) | 30.1141 | 1.43238 | ||||||||
\(443\) | −29.8716 | −1.41924 | −0.709621 | − | 0.704583i | \(-0.751134\pi\) | ||||
−0.709621 | + | 0.704583i | \(0.751134\pi\) | |||||||
\(444\) | −3.41070 | −0.161865 | ||||||||
\(445\) | 8.12681 | 0.385248 | ||||||||
\(446\) | −10.2941 | −0.487439 | ||||||||
\(447\) | −16.8749 | −0.798155 | ||||||||
\(448\) | −0.234026 | −0.0110567 | ||||||||
\(449\) | −7.12677 | −0.336333 | −0.168167 | − | 0.985759i | \(-0.553785\pi\) | ||||
−0.168167 | + | 0.985759i | \(0.553785\pi\) | |||||||
\(450\) | 6.92443 | 0.326421 | ||||||||
\(451\) | 1.69198 | 0.0796723 | ||||||||
\(452\) | 15.9127 | 0.748469 | ||||||||
\(453\) | −0.412179 | −0.0193659 | ||||||||
\(454\) | 26.6259 | 1.24962 | ||||||||
\(455\) | 1.35778 | 0.0636537 | ||||||||
\(456\) | 2.08919 | 0.0978354 | ||||||||
\(457\) | −29.1112 | −1.36177 | −0.680883 | − | 0.732392i | \(-0.738404\pi\) | ||||
−0.680883 | + | 0.732392i | \(0.738404\pi\) | |||||||
\(458\) | 18.4674 | 0.862927 | ||||||||
\(459\) | 32.3994 | 1.51227 | ||||||||
\(460\) | −1.41489 | −0.0659694 | ||||||||
\(461\) | 33.8785 | 1.57788 | 0.788940 | − | 0.614471i | \(-0.210630\pi\) | ||||
0.788940 | + | 0.614471i | \(0.210630\pi\) | |||||||
\(462\) | 0.730364 | 0.0339796 | ||||||||
\(463\) | 4.68072 | 0.217532 | 0.108766 | − | 0.994067i | \(-0.465310\pi\) | ||||
0.108766 | + | 0.994067i | \(0.465310\pi\) | |||||||
\(464\) | 5.16848 | 0.239941 | ||||||||
\(465\) | −10.0541 | −0.466246 | ||||||||
\(466\) | −1.95218 | −0.0904332 | ||||||||
\(467\) | −28.6923 | −1.32772 | −0.663860 | − | 0.747857i | \(-0.731083\pi\) | ||||
−0.663860 | + | 0.747857i | \(0.731083\pi\) | |||||||
\(468\) | −9.47070 | −0.437783 | ||||||||
\(469\) | −2.23751 | −0.103319 | ||||||||
\(470\) | −7.65959 | −0.353310 | ||||||||
\(471\) | 15.9655 | 0.735652 | ||||||||
\(472\) | −9.00816 | −0.414634 | ||||||||
\(473\) | −45.5264 | −2.09331 | ||||||||
\(474\) | 0.141173 | 0.00648431 | ||||||||
\(475\) | 7.53835 | 0.345883 | ||||||||
\(476\) | −1.71867 | −0.0787749 | ||||||||
\(477\) | 6.01612 | 0.275459 | ||||||||
\(478\) | −1.46566 | −0.0670377 | ||||||||
\(479\) | −32.2915 | −1.47544 | −0.737719 | − | 0.675108i | \(-0.764097\pi\) | ||||
−0.737719 | + | 0.675108i | \(0.764097\pi\) | |||||||
\(480\) | 1.17563 | 0.0536597 | ||||||||
\(481\) | 16.8321 | 0.767479 | ||||||||
\(482\) | −29.9828 | −1.36568 | ||||||||
\(483\) | 0.194452 | 0.00884786 | ||||||||
\(484\) | 3.10767 | 0.141258 | ||||||||
\(485\) | −7.06823 | −0.320952 | ||||||||
\(486\) | −15.9465 | −0.723350 | ||||||||
\(487\) | −32.0737 | −1.45340 | −0.726698 | − | 0.686957i | \(-0.758946\pi\) | ||||
−0.726698 | + | 0.686957i | \(0.758946\pi\) | |||||||
\(488\) | 6.21086 | 0.281153 | ||||||||
\(489\) | −4.47172 | −0.202218 | ||||||||
\(490\) | 9.82671 | 0.443926 | ||||||||
\(491\) | −6.59041 | −0.297421 | −0.148711 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148711 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(492\) | −0.374296 | −0.0168746 | ||||||||
\(493\) | 37.9568 | 1.70949 | ||||||||
\(494\) | −10.3104 | −0.463885 | ||||||||
\(495\) | 12.2740 | 0.551677 | ||||||||
\(496\) | −8.55210 | −0.384001 | ||||||||
\(497\) | 1.08939 | 0.0488659 | ||||||||
\(498\) | 0.377570 | 0.0169193 | ||||||||
\(499\) | 7.32680 | 0.327993 | 0.163996 | − | 0.986461i | \(-0.447561\pi\) | ||||
0.163996 | + | 0.986461i | \(0.447561\pi\) | |||||||
\(500\) | 11.3164 | 0.506085 | ||||||||
\(501\) | −15.1610 | −0.677342 | ||||||||
\(502\) | −4.98723 | −0.222591 | ||||||||
\(503\) | −33.3411 | −1.48660 | −0.743302 | − | 0.668956i | \(-0.766741\pi\) | ||||
−0.743302 | + | 0.668956i | \(0.766741\pi\) | |||||||
\(504\) | 0.540509 | 0.0240762 | ||||||||
\(505\) | 1.13779 | 0.0506311 | ||||||||
\(506\) | 3.75602 | 0.166975 | ||||||||
\(507\) | −3.16955 | −0.140765 | ||||||||
\(508\) | 0.658707 | 0.0292254 | ||||||||
\(509\) | 26.8676 | 1.19089 | 0.595443 | − | 0.803398i | \(-0.296977\pi\) | ||||
0.595443 | + | 0.803398i | \(0.296977\pi\) | |||||||
\(510\) | 8.63368 | 0.382306 | ||||||||
\(511\) | −2.71801 | −0.120238 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.0928 | −0.489759 | ||||||||
\(514\) | 23.8339 | 1.05127 | ||||||||
\(515\) | −11.4651 | −0.505211 | ||||||||
\(516\) | 10.0713 | 0.443362 | ||||||||
\(517\) | 20.3335 | 0.894265 | ||||||||
\(518\) | −0.960639 | −0.0422080 | ||||||||
\(519\) | −14.5885 | −0.640363 | ||||||||
\(520\) | −5.80183 | −0.254427 | ||||||||
\(521\) | −24.5976 | −1.07764 | −0.538820 | − | 0.842421i | \(-0.681130\pi\) | ||||
−0.538820 | + | 0.842421i | \(0.681130\pi\) | |||||||
\(522\) | −11.9372 | −0.522475 | ||||||||
\(523\) | 21.8706 | 0.956335 | 0.478167 | − | 0.878269i | \(-0.341301\pi\) | ||||
0.478167 | + | 0.878269i | \(0.341301\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | −0.582985 | −0.0254436 | ||||||||
\(526\) | 7.87510 | 0.343371 | ||||||||
\(527\) | −62.8058 | −2.73586 | ||||||||
\(528\) | −3.12087 | −0.135818 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 3.68553 | 0.160089 | ||||||||
\(531\) | 20.8053 | 0.902874 | ||||||||
\(532\) | 0.588430 | 0.0255117 | ||||||||
\(533\) | 1.84719 | 0.0800107 | ||||||||
\(534\) | 4.77250 | 0.206526 | ||||||||
\(535\) | −25.9156 | −1.12043 | ||||||||
\(536\) | 9.56096 | 0.412971 | ||||||||
\(537\) | −2.83934 | −0.122526 | ||||||||
\(538\) | 9.11359 | 0.392915 | ||||||||
\(539\) | −26.0864 | −1.12362 | ||||||||
\(540\) | −6.24211 | −0.268618 | ||||||||
\(541\) | −24.0710 | −1.03489 | −0.517446 | − | 0.855716i | \(-0.673117\pi\) | ||||
−0.517446 | + | 0.855716i | \(0.673117\pi\) | |||||||
\(542\) | −6.46382 | −0.277645 | ||||||||
\(543\) | 16.9683 | 0.728179 | ||||||||
\(544\) | 7.34390 | 0.314867 | ||||||||
\(545\) | −10.8460 | −0.464591 | ||||||||
\(546\) | 0.797361 | 0.0341239 | ||||||||
\(547\) | 38.5541 | 1.64845 | 0.824227 | − | 0.566260i | \(-0.191610\pi\) | ||||
0.824227 | + | 0.566260i | \(0.191610\pi\) | |||||||
\(548\) | 12.3465 | 0.527417 | ||||||||
\(549\) | −14.3447 | −0.612216 | ||||||||
\(550\) | −11.2609 | −0.480167 | ||||||||
\(551\) | −12.9955 | −0.553627 | ||||||||
\(552\) | −0.830898 | −0.0353654 | ||||||||
\(553\) | 0.0397621 | 0.00169086 | ||||||||
\(554\) | 2.70561 | 0.114950 | ||||||||
\(555\) | 4.82575 | 0.204842 | ||||||||
\(556\) | 13.3114 | 0.564530 | ||||||||
\(557\) | 18.1129 | 0.767470 | 0.383735 | − | 0.923443i | \(-0.374638\pi\) | ||||
0.383735 | + | 0.923443i | \(0.374638\pi\) | |||||||
\(558\) | 19.7520 | 0.836170 | ||||||||
\(559\) | −49.7026 | −2.10220 | ||||||||
\(560\) | 0.331120 | 0.0139924 | ||||||||
\(561\) | −22.9193 | −0.967656 | ||||||||
\(562\) | −7.31543 | −0.308583 | ||||||||
\(563\) | −12.9892 | −0.547429 | −0.273715 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273715 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(564\) | −4.49812 | −0.189405 | ||||||||
\(565\) | −22.5146 | −0.947197 | ||||||||
\(566\) | −5.09365 | −0.214102 | ||||||||
\(567\) | −0.763656 | −0.0320705 | ||||||||
\(568\) | −4.65500 | −0.195319 | ||||||||
\(569\) | −5.17296 | −0.216862 | −0.108431 | − | 0.994104i | \(-0.534583\pi\) | ||||
−0.108431 | + | 0.994104i | \(0.534583\pi\) | |||||||
\(570\) | −2.95597 | −0.123812 | ||||||||
\(571\) | 16.5056 | 0.690737 | 0.345368 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345368 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(572\) | 15.4018 | 0.643981 | ||||||||
\(573\) | 15.0527 | 0.628835 | ||||||||
\(574\) | −0.105422 | −0.00440024 | ||||||||
\(575\) | −2.99810 | −0.125029 | ||||||||
\(576\) | −2.30961 | −0.0962337 | ||||||||
\(577\) | 21.7339 | 0.904793 | 0.452397 | − | 0.891817i | \(-0.350569\pi\) | ||||
0.452397 | + | 0.891817i | \(0.350569\pi\) | |||||||
\(578\) | 36.9329 | 1.53621 | ||||||||
\(579\) | −0.858866 | −0.0356932 | ||||||||
\(580\) | −7.31281 | −0.303648 | ||||||||
\(581\) | 0.106344 | 0.00441190 | ||||||||
\(582\) | −4.15084 | −0.172058 | ||||||||
\(583\) | −9.78376 | −0.405202 | ||||||||
\(584\) | 11.6142 | 0.480597 | ||||||||
\(585\) | 13.4000 | 0.554020 | ||||||||
\(586\) | −15.9117 | −0.657307 | ||||||||
\(587\) | −2.84193 | −0.117299 | −0.0586496 | − | 0.998279i | \(-0.518679\pi\) | ||||
−0.0586496 | + | 0.998279i | \(0.518679\pi\) | |||||||
\(588\) | 5.77078 | 0.237983 | ||||||||
\(589\) | 21.5032 | 0.886025 | ||||||||
\(590\) | 12.7455 | 0.524725 | ||||||||
\(591\) | −2.57059 | −0.105740 | ||||||||
\(592\) | 4.10484 | 0.168708 | ||||||||
\(593\) | −3.74209 | −0.153669 | −0.0768346 | − | 0.997044i | \(-0.524481\pi\) | ||||
−0.0768346 | + | 0.997044i | \(0.524481\pi\) | |||||||
\(594\) | 16.5706 | 0.679899 | ||||||||
\(595\) | 2.43172 | 0.0996906 | ||||||||
\(596\) | 20.3092 | 0.831898 | ||||||||
\(597\) | −4.96140 | −0.203057 | ||||||||
\(598\) | 4.10056 | 0.167684 | ||||||||
\(599\) | 17.3354 | 0.708304 | 0.354152 | − | 0.935188i | \(-0.384770\pi\) | ||||
0.354152 | + | 0.935188i | \(0.384770\pi\) | |||||||
\(600\) | 2.49111 | 0.101699 | ||||||||
\(601\) | 15.4098 | 0.628577 | 0.314289 | − | 0.949328i | \(-0.398234\pi\) | ||||
0.314289 | + | 0.949328i | \(0.398234\pi\) | |||||||
\(602\) | 2.83661 | 0.115612 | ||||||||
\(603\) | −22.0821 | −0.899252 | ||||||||
\(604\) | 0.496065 | 0.0201846 | ||||||||
\(605\) | −4.39701 | −0.178764 | ||||||||
\(606\) | 0.668173 | 0.0271427 | ||||||||
\(607\) | 17.9299 | 0.727750 | 0.363875 | − | 0.931448i | \(-0.381453\pi\) | ||||
0.363875 | + | 0.931448i | \(0.381453\pi\) | |||||||
\(608\) | −2.51438 | −0.101972 | ||||||||
\(609\) | 1.00502 | 0.0407254 | ||||||||
\(610\) | −8.78767 | −0.355802 | ||||||||
\(611\) | 22.1987 | 0.898063 | ||||||||
\(612\) | −16.9615 | −0.685630 | ||||||||
\(613\) | 23.0127 | 0.929474 | 0.464737 | − | 0.885449i | \(-0.346149\pi\) | ||||
0.464737 | + | 0.885449i | \(0.346149\pi\) | |||||||
\(614\) | 18.8530 | 0.760846 | ||||||||
\(615\) | 0.529587 | 0.0213550 | ||||||||
\(616\) | −0.879006 | −0.0354162 | ||||||||
\(617\) | 47.2047 | 1.90039 | 0.950195 | − | 0.311655i | \(-0.100883\pi\) | ||||
0.950195 | + | 0.311655i | \(0.100883\pi\) | |||||||
\(618\) | −6.73290 | −0.270837 | ||||||||
\(619\) | −16.9935 | −0.683025 | −0.341513 | − | 0.939877i | \(-0.610939\pi\) | ||||
−0.341513 | + | 0.939877i | \(0.610939\pi\) | |||||||
\(620\) | 12.1003 | 0.485958 | ||||||||
\(621\) | 4.41174 | 0.177037 | ||||||||
\(622\) | −13.4179 | −0.538011 | ||||||||
\(623\) | 1.34420 | 0.0538541 | ||||||||
\(624\) | −3.40715 | −0.136395 | ||||||||
\(625\) | −1.02093 | −0.0408371 | ||||||||
\(626\) | 16.6992 | 0.667433 | ||||||||
\(627\) | 7.84704 | 0.313381 | ||||||||
\(628\) | −19.2148 | −0.766753 | ||||||||
\(629\) | 30.1455 | 1.20198 | ||||||||
\(630\) | −0.764758 | −0.0304687 | ||||||||
\(631\) | 40.8166 | 1.62488 | 0.812442 | − | 0.583041i | \(-0.198138\pi\) | ||||
0.812442 | + | 0.583041i | \(0.198138\pi\) | |||||||
\(632\) | −0.169905 | −0.00675844 | ||||||||
\(633\) | −3.71980 | −0.147849 | ||||||||
\(634\) | −28.0772 | −1.11509 | ||||||||
\(635\) | −0.931995 | −0.0369851 | ||||||||
\(636\) | 2.16434 | 0.0858217 | ||||||||
\(637\) | −28.4794 | −1.12839 | ||||||||
\(638\) | 19.4129 | 0.768564 | ||||||||
\(639\) | 10.7512 | 0.425312 | ||||||||
\(640\) | −1.41489 | −0.0559283 | ||||||||
\(641\) | 43.0727 | 1.70127 | 0.850634 | − | 0.525758i | \(-0.176218\pi\) | ||||
0.850634 | + | 0.525758i | \(0.176218\pi\) | |||||||
\(642\) | −15.2190 | −0.600647 | ||||||||
\(643\) | 13.4348 | 0.529818 | 0.264909 | − | 0.964273i | \(-0.414658\pi\) | ||||
0.264909 | + | 0.964273i | \(0.414658\pi\) | |||||||
\(644\) | −0.234026 | −0.00922192 | ||||||||
\(645\) | −14.2497 | −0.561080 | ||||||||
\(646\) | −18.4654 | −0.726510 | ||||||||
\(647\) | 2.28741 | 0.0899275 | 0.0449638 | − | 0.998989i | \(-0.485683\pi\) | ||||
0.0449638 | + | 0.998989i | \(0.485683\pi\) | |||||||
\(648\) | 3.26312 | 0.128188 | ||||||||
\(649\) | −33.8348 | −1.32813 | ||||||||
\(650\) | −12.2939 | −0.482206 | ||||||||
\(651\) | −1.66297 | −0.0651770 | ||||||||
\(652\) | 5.38179 | 0.210767 | ||||||||
\(653\) | 32.2933 | 1.26374 | 0.631868 | − | 0.775076i | \(-0.282288\pi\) | ||||
0.631868 | + | 0.775076i | \(0.282288\pi\) | |||||||
\(654\) | −6.36935 | −0.249061 | ||||||||
\(655\) | −1.41489 | −0.0552842 | ||||||||
\(656\) | 0.450472 | 0.0175880 | ||||||||
\(657\) | −26.8241 | −1.04651 | ||||||||
\(658\) | −1.26692 | −0.0493896 | ||||||||
\(659\) | −49.3134 | −1.92098 | −0.960488 | − | 0.278322i | \(-0.910222\pi\) | ||||
−0.960488 | + | 0.278322i | \(0.910222\pi\) | |||||||
\(660\) | 4.41567 | 0.171880 | ||||||||
\(661\) | 7.79175 | 0.303064 | 0.151532 | − | 0.988452i | \(-0.451579\pi\) | ||||
0.151532 | + | 0.988452i | \(0.451579\pi\) | |||||||
\(662\) | −1.21324 | −0.0471538 | ||||||||
\(663\) | −25.0218 | −0.971765 | ||||||||
\(664\) | −0.454412 | −0.0176346 | ||||||||
\(665\) | −0.832562 | −0.0322854 | ||||||||
\(666\) | −9.48056 | −0.367364 | ||||||||
\(667\) | 5.16848 | 0.200124 | ||||||||
\(668\) | 18.2465 | 0.705978 | ||||||||
\(669\) | 8.55332 | 0.330691 | ||||||||
\(670\) | −13.5277 | −0.522619 | ||||||||
\(671\) | 23.3281 | 0.900572 | ||||||||
\(672\) | 0.194452 | 0.00750114 | ||||||||
\(673\) | 13.3627 | 0.515094 | 0.257547 | − | 0.966266i | \(-0.417086\pi\) | ||||
0.257547 | + | 0.966266i | \(0.417086\pi\) | |||||||
\(674\) | 0.992259 | 0.0382204 | ||||||||
\(675\) | −13.2268 | −0.509101 | ||||||||
\(676\) | 3.81461 | 0.146716 | ||||||||
\(677\) | 5.47408 | 0.210386 | 0.105193 | − | 0.994452i | \(-0.466454\pi\) | ||||
0.105193 | + | 0.994452i | \(0.466454\pi\) | |||||||
\(678\) | −13.2218 | −0.507780 | ||||||||
\(679\) | −1.16910 | −0.0448661 | ||||||||
\(680\) | −10.3908 | −0.398469 | ||||||||
\(681\) | −22.1234 | −0.847771 | ||||||||
\(682\) | −32.1219 | −1.23001 | ||||||||
\(683\) | 28.7084 | 1.09850 | 0.549249 | − | 0.835659i | \(-0.314914\pi\) | ||||
0.549249 | + | 0.835659i | \(0.314914\pi\) | |||||||
\(684\) | 5.80723 | 0.222045 | ||||||||
\(685\) | −17.4689 | −0.667453 | ||||||||
\(686\) | 3.26355 | 0.124603 | ||||||||
\(687\) | −15.3446 | −0.585431 | ||||||||
\(688\) | −12.1209 | −0.462106 | ||||||||
\(689\) | −10.6812 | −0.406923 | ||||||||
\(690\) | 1.17563 | 0.0447553 | ||||||||
\(691\) | −50.0073 | −1.90237 | −0.951184 | − | 0.308624i | \(-0.900132\pi\) | ||||
−0.951184 | + | 0.308624i | \(0.900132\pi\) | |||||||
\(692\) | 17.5575 | 0.667435 | ||||||||
\(693\) | 2.03016 | 0.0771194 | ||||||||
\(694\) | −10.7069 | −0.406429 | ||||||||
\(695\) | −18.8342 | −0.714420 | ||||||||
\(696\) | −4.29448 | −0.162782 | ||||||||
\(697\) | 3.30822 | 0.125308 | ||||||||
\(698\) | −18.7164 | −0.708428 | ||||||||
\(699\) | 1.62206 | 0.0613521 | ||||||||
\(700\) | 0.701633 | 0.0265192 | ||||||||
\(701\) | 46.4162 | 1.75312 | 0.876559 | − | 0.481295i | \(-0.159833\pi\) | ||||
0.876559 | + | 0.481295i | \(0.159833\pi\) | |||||||
\(702\) | 18.0906 | 0.682786 | ||||||||
\(703\) | −10.3211 | −0.389268 | ||||||||
\(704\) | 3.75602 | 0.141560 | ||||||||
\(705\) | 6.36433 | 0.239695 | ||||||||
\(706\) | 37.3705 | 1.40646 | ||||||||
\(707\) | 0.188194 | 0.00707777 | ||||||||
\(708\) | 7.48486 | 0.281298 | ||||||||
\(709\) | 30.4219 | 1.14252 | 0.571259 | − | 0.820770i | \(-0.306455\pi\) | ||||
0.571259 | + | 0.820770i | \(0.306455\pi\) | |||||||
\(710\) | 6.58629 | 0.247179 | ||||||||
\(711\) | 0.392413 | 0.0147166 | ||||||||
\(712\) | −5.74379 | −0.215258 | ||||||||
\(713\) | −8.55210 | −0.320279 | ||||||||
\(714\) | 1.42803 | 0.0534429 | ||||||||
\(715\) | −21.7918 | −0.814966 | ||||||||
\(716\) | 3.41719 | 0.127706 | ||||||||
\(717\) | 1.21781 | 0.0454801 | ||||||||
\(718\) | −5.79181 | −0.216148 | ||||||||
\(719\) | 27.2627 | 1.01673 | 0.508364 | − | 0.861142i | \(-0.330251\pi\) | ||||
0.508364 | + | 0.861142i | \(0.330251\pi\) | |||||||
\(720\) | 3.26783 | 0.121785 | ||||||||
\(721\) | −1.89635 | −0.0706239 | ||||||||
\(722\) | −12.6779 | −0.471823 | ||||||||
\(723\) | 24.9126 | 0.926511 | ||||||||
\(724\) | −20.4216 | −0.758964 | ||||||||
\(725\) | −15.4956 | −0.575492 | ||||||||
\(726\) | −2.58216 | −0.0958329 | ||||||||
\(727\) | 26.3797 | 0.978369 | 0.489185 | − | 0.872180i | \(-0.337294\pi\) | ||||
0.489185 | + | 0.872180i | \(0.337294\pi\) | |||||||
\(728\) | −0.959639 | −0.0355666 | ||||||||
\(729\) | 3.46058 | 0.128170 | ||||||||
\(730\) | −16.4327 | −0.608202 | ||||||||
\(731\) | −89.0149 | −3.29234 | ||||||||
\(732\) | −5.16059 | −0.190741 | ||||||||
\(733\) | 44.4526 | 1.64189 | 0.820946 | − | 0.571005i | \(-0.193447\pi\) | ||||
0.820946 | + | 0.571005i | \(0.193447\pi\) | |||||||
\(734\) | −20.8003 | −0.767755 | ||||||||
\(735\) | −8.16499 | −0.301170 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 35.9111 | 1.32280 | ||||||||
\(738\) | −1.04041 | −0.0382982 | ||||||||
\(739\) | −32.3513 | −1.19006 | −0.595030 | − | 0.803703i | \(-0.702860\pi\) | ||||
−0.595030 | + | 0.803703i | \(0.702860\pi\) | |||||||
\(740\) | −5.80787 | −0.213502 | ||||||||
\(741\) | 8.56686 | 0.314711 | ||||||||
\(742\) | 0.609597 | 0.0223790 | ||||||||
\(743\) | 12.1524 | 0.445827 | 0.222914 | − | 0.974838i | \(-0.428443\pi\) | ||||
0.222914 | + | 0.974838i | \(0.428443\pi\) | |||||||
\(744\) | 7.10592 | 0.260516 | ||||||||
\(745\) | −28.7352 | −1.05278 | ||||||||
\(746\) | 29.8137 | 1.09156 | ||||||||
\(747\) | 1.04951 | 0.0383997 | ||||||||
\(748\) | 27.5838 | 1.00856 | ||||||||
\(749\) | −4.28651 | −0.156626 | ||||||||
\(750\) | −9.40277 | −0.343341 | ||||||||
\(751\) | 30.9411 | 1.12906 | 0.564528 | − | 0.825414i | \(-0.309058\pi\) | ||||
0.564528 | + | 0.825414i | \(0.309058\pi\) | |||||||
\(752\) | 5.41357 | 0.197413 | ||||||||
\(753\) | 4.14388 | 0.151011 | ||||||||
\(754\) | 21.1937 | 0.771828 | ||||||||
\(755\) | −0.701875 | −0.0255438 | ||||||||
\(756\) | −1.03246 | −0.0375503 | ||||||||
\(757\) | −20.8625 | −0.758261 | −0.379131 | − | 0.925343i | \(-0.623777\pi\) | ||||
−0.379131 | + | 0.925343i | \(0.623777\pi\) | |||||||
\(758\) | 21.9308 | 0.796562 | ||||||||
\(759\) | −3.12087 | −0.113280 | ||||||||
\(760\) | 3.55756 | 0.129046 | ||||||||
\(761\) | −34.0386 | −1.23390 | −0.616949 | − | 0.787003i | \(-0.711632\pi\) | ||||
−0.616949 | + | 0.787003i | \(0.711632\pi\) | |||||||
\(762\) | −0.547318 | −0.0198272 | ||||||||
\(763\) | −1.79396 | −0.0649455 | ||||||||
\(764\) | −18.1162 | −0.655420 | ||||||||
\(765\) | 23.9987 | 0.867673 | ||||||||
\(766\) | −10.3428 | −0.373702 | ||||||||
\(767\) | −36.9385 | −1.33377 | ||||||||
\(768\) | −0.830898 | −0.0299824 | ||||||||
\(769\) | −42.9030 | −1.54712 | −0.773561 | − | 0.633722i | \(-0.781527\pi\) | ||||
−0.773561 | + | 0.633722i | \(0.781527\pi\) | |||||||
\(770\) | 1.24369 | 0.0448196 | ||||||||
\(771\) | −19.8035 | −0.713206 | ||||||||
\(772\) | 1.03366 | 0.0372022 | ||||||||
\(773\) | −45.7995 | −1.64729 | −0.823647 | − | 0.567103i | \(-0.808064\pi\) | ||||
−0.823647 | + | 0.567103i | \(0.808064\pi\) | |||||||
\(774\) | 27.9946 | 1.00625 | ||||||||
\(775\) | 25.6400 | 0.921017 | ||||||||
\(776\) | 4.99562 | 0.179332 | ||||||||
\(777\) | 0.798192 | 0.0286350 | ||||||||
\(778\) | 0.575240 | 0.0206233 | ||||||||
\(779\) | −1.13266 | −0.0405817 | ||||||||
\(780\) | 4.82073 | 0.172610 | ||||||||
\(781\) | −17.4843 | −0.625636 | ||||||||
\(782\) | 7.34390 | 0.262617 | ||||||||
\(783\) | 22.8020 | 0.814877 | ||||||||
\(784\) | −6.94523 | −0.248044 | ||||||||
\(785\) | 27.1867 | 0.970335 | ||||||||
\(786\) | −0.830898 | −0.0296371 | ||||||||
\(787\) | 29.8640 | 1.06454 | 0.532269 | − | 0.846575i | \(-0.321340\pi\) | ||||
0.532269 | + | 0.846575i | \(0.321340\pi\) | |||||||
\(788\) | 3.09375 | 0.110210 | ||||||||
\(789\) | −6.54341 | −0.232951 | ||||||||
\(790\) | 0.240396 | 0.00855289 | ||||||||
\(791\) | −3.72398 | −0.132410 | ||||||||
\(792\) | −8.67493 | −0.308250 | ||||||||
\(793\) | 25.4680 | 0.904396 | ||||||||
\(794\) | −9.25444 | −0.328428 | ||||||||
\(795\) | −3.06230 | −0.108608 | ||||||||
\(796\) | 5.97114 | 0.211641 | ||||||||
\(797\) | −42.0432 | −1.48925 | −0.744623 | − | 0.667485i | \(-0.767371\pi\) | ||||
−0.744623 | + | 0.667485i | \(0.767371\pi\) | |||||||
\(798\) | −0.488925 | −0.0173078 | ||||||||
\(799\) | 39.7568 | 1.40649 | ||||||||
\(800\) | −2.99810 | −0.105999 | ||||||||
\(801\) | 13.2659 | 0.468728 | ||||||||
\(802\) | −15.9794 | −0.564251 | ||||||||
\(803\) | 43.6230 | 1.53942 | ||||||||
\(804\) | −7.94418 | −0.280170 | ||||||||
\(805\) | 0.331120 | 0.0116705 | ||||||||
\(806\) | −35.0684 | −1.23523 | ||||||||
\(807\) | −7.57246 | −0.266563 | ||||||||
\(808\) | −0.804159 | −0.0282902 | ||||||||
\(809\) | −31.1472 | −1.09508 | −0.547538 | − | 0.836781i | \(-0.684435\pi\) | ||||
−0.547538 | + | 0.836781i | \(0.684435\pi\) | |||||||
\(810\) | −4.61695 | −0.162223 | ||||||||
\(811\) | 46.0408 | 1.61671 | 0.808356 | − | 0.588694i | \(-0.200358\pi\) | ||||
0.808356 | + | 0.588694i | \(0.200358\pi\) | |||||||
\(812\) | −1.20956 | −0.0424472 | ||||||||
\(813\) | 5.37078 | 0.188361 | ||||||||
\(814\) | 15.4178 | 0.540395 | ||||||||
\(815\) | −7.61462 | −0.266729 | ||||||||
\(816\) | −6.10203 | −0.213614 | ||||||||
\(817\) | 30.4766 | 1.06624 | ||||||||
\(818\) | −23.7683 | −0.831039 | ||||||||
\(819\) | 2.21639 | 0.0774469 | ||||||||
\(820\) | −0.637367 | −0.0222578 | ||||||||
\(821\) | −14.1999 | −0.495578 | −0.247789 | − | 0.968814i | \(-0.579704\pi\) | ||||
−0.247789 | + | 0.968814i | \(0.579704\pi\) | |||||||
\(822\) | −10.2587 | −0.357813 | ||||||||
\(823\) | −0.278519 | −0.00970855 | −0.00485427 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485427 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(824\) | 8.10317 | 0.282287 | ||||||||
\(825\) | 9.35666 | 0.325757 | ||||||||
\(826\) | 2.10814 | 0.0733517 | ||||||||
\(827\) | −33.7245 | −1.17272 | −0.586358 | − | 0.810052i | \(-0.699439\pi\) | ||||
−0.586358 | + | 0.810052i | \(0.699439\pi\) | |||||||
\(828\) | −2.30961 | −0.0802645 | ||||||||
\(829\) | −40.4962 | −1.40649 | −0.703246 | − | 0.710947i | \(-0.748267\pi\) | ||||
−0.703246 | + | 0.710947i | \(0.748267\pi\) | |||||||
\(830\) | 0.642941 | 0.0223168 | ||||||||
\(831\) | −2.24808 | −0.0779852 | ||||||||
\(832\) | 4.10056 | 0.142161 | ||||||||
\(833\) | −51.0051 | −1.76722 | ||||||||
\(834\) | −11.0604 | −0.382992 | ||||||||
\(835\) | −25.8167 | −0.893424 | ||||||||
\(836\) | −9.44405 | −0.326629 | ||||||||
\(837\) | −37.7297 | −1.30413 | ||||||||
\(838\) | 31.5720 | 1.09064 | ||||||||
\(839\) | 15.1626 | 0.523470 | 0.261735 | − | 0.965140i | \(-0.415705\pi\) | ||||
0.261735 | + | 0.965140i | \(0.415705\pi\) | |||||||
\(840\) | −0.275127 | −0.00949279 | ||||||||
\(841\) | −2.28683 | −0.0788563 | ||||||||
\(842\) | −21.3439 | −0.735558 | ||||||||
\(843\) | 6.07837 | 0.209350 | ||||||||
\(844\) | 4.47685 | 0.154099 | ||||||||
\(845\) | −5.39724 | −0.185671 | ||||||||
\(846\) | −12.5032 | −0.429870 | ||||||||
\(847\) | −0.727277 | −0.0249895 | ||||||||
\(848\) | −2.60482 | −0.0894500 | ||||||||
\(849\) | 4.23230 | 0.145252 | ||||||||
\(850\) | −22.0177 | −0.755202 | ||||||||
\(851\) | 4.10484 | 0.140712 | ||||||||
\(852\) | 3.86783 | 0.132510 | ||||||||
\(853\) | 2.84635 | 0.0974572 | 0.0487286 | − | 0.998812i | \(-0.484483\pi\) | ||||
0.0487286 | + | 0.998812i | \(0.484483\pi\) | |||||||
\(854\) | −1.45350 | −0.0497379 | ||||||||
\(855\) | −8.21657 | −0.281001 | ||||||||
\(856\) | 18.3164 | 0.626040 | ||||||||
\(857\) | 28.7344 | 0.981547 | 0.490774 | − | 0.871287i | \(-0.336714\pi\) | ||||
0.490774 | + | 0.871287i | \(0.336714\pi\) | |||||||
\(858\) | −12.7973 | −0.436893 | ||||||||
\(859\) | −53.3194 | −1.81923 | −0.909617 | − | 0.415448i | \(-0.863625\pi\) | ||||
−0.909617 | + | 0.415448i | \(0.863625\pi\) | |||||||
\(860\) | 17.1497 | 0.584801 | ||||||||
\(861\) | 0.0875951 | 0.00298523 | ||||||||
\(862\) | −7.09641 | −0.241705 | ||||||||
\(863\) | −15.8333 | −0.538972 | −0.269486 | − | 0.963004i | \(-0.586854\pi\) | ||||
−0.269486 | + | 0.963004i | \(0.586854\pi\) | |||||||
\(864\) | 4.41174 | 0.150090 | ||||||||
\(865\) | −24.8418 | −0.844648 | ||||||||
\(866\) | −7.58377 | −0.257707 | ||||||||
\(867\) | −30.6875 | −1.04220 | ||||||||
\(868\) | 2.00142 | 0.0679325 | ||||||||
\(869\) | −0.638165 | −0.0216483 | ||||||||
\(870\) | 6.07620 | 0.206002 | ||||||||
\(871\) | 39.2053 | 1.32842 | ||||||||
\(872\) | 7.66562 | 0.259591 | ||||||||
\(873\) | −11.5379 | −0.390499 | ||||||||
\(874\) | −2.51438 | −0.0850501 | ||||||||
\(875\) | −2.64833 | −0.0895300 | ||||||||
\(876\) | −9.65017 | −0.326049 | ||||||||
\(877\) | 46.9103 | 1.58405 | 0.792023 | − | 0.610491i | \(-0.209028\pi\) | ||||
0.792023 | + | 0.610491i | \(0.209028\pi\) | |||||||
\(878\) | 25.1129 | 0.847521 | ||||||||
\(879\) | 13.2210 | 0.445934 | ||||||||
\(880\) | −5.31434 | −0.179146 | ||||||||
\(881\) | 4.70541 | 0.158529 | 0.0792646 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792646 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(882\) | 16.0408 | 0.540121 | ||||||||
\(883\) | 5.74717 | 0.193408 | 0.0967039 | − | 0.995313i | \(-0.469170\pi\) | ||||
0.0967039 | + | 0.995313i | \(0.469170\pi\) | |||||||
\(884\) | 30.1141 | 1.01285 | ||||||||
\(885\) | −10.5902 | −0.355986 | ||||||||
\(886\) | −29.8716 | −1.00356 | ||||||||
\(887\) | −2.10416 | −0.0706507 | −0.0353253 | − | 0.999376i | \(-0.511247\pi\) | ||||
−0.0353253 | + | 0.999376i | \(0.511247\pi\) | |||||||
\(888\) | −3.41070 | −0.114456 | ||||||||
\(889\) | −0.154155 | −0.00517018 | ||||||||
\(890\) | 8.12681 | 0.272411 | ||||||||
\(891\) | 12.2563 | 0.410603 | ||||||||
\(892\) | −10.2941 | −0.344671 | ||||||||
\(893\) | −13.6118 | −0.455501 | ||||||||
\(894\) | −16.8749 | −0.564381 | ||||||||
\(895\) | −4.83494 | −0.161614 | ||||||||
\(896\) | −0.234026 | −0.00781826 | ||||||||
\(897\) | −3.40715 | −0.113761 | ||||||||
\(898\) | −7.12677 | −0.237823 | ||||||||
\(899\) | −44.2014 | −1.47420 | ||||||||
\(900\) | 6.92443 | 0.230814 | ||||||||
\(901\) | −19.1296 | −0.637298 | ||||||||
\(902\) | 1.69198 | 0.0563368 | ||||||||
\(903\) | −2.35694 | −0.0784339 | ||||||||
\(904\) | 15.9127 | 0.529248 | ||||||||
\(905\) | 28.8943 | 0.960479 | ||||||||
\(906\) | −0.412179 | −0.0136937 | ||||||||
\(907\) | −41.6827 | −1.38405 | −0.692025 | − | 0.721873i | \(-0.743281\pi\) | ||||
−0.692025 | + | 0.721873i | \(0.743281\pi\) | |||||||
\(908\) | 26.6259 | 0.883612 | ||||||||
\(909\) | 1.85729 | 0.0616025 | ||||||||
\(910\) | 1.35778 | 0.0450099 | ||||||||
\(911\) | 31.9920 | 1.05994 | 0.529972 | − | 0.848015i | \(-0.322202\pi\) | ||||
0.529972 | + | 0.848015i | \(0.322202\pi\) | |||||||
\(912\) | 2.08919 | 0.0691800 | ||||||||
\(913\) | −1.70678 | −0.0564862 | ||||||||
\(914\) | −29.1112 | −0.962914 | ||||||||
\(915\) | 7.30165 | 0.241385 | ||||||||
\(916\) | 18.4674 | 0.610182 | ||||||||
\(917\) | −0.234026 | −0.00772822 | ||||||||
\(918\) | 32.3994 | 1.06934 | ||||||||
\(919\) | 43.0366 | 1.41965 | 0.709824 | − | 0.704379i | \(-0.248775\pi\) | ||||
0.709824 | + | 0.704379i | \(0.248775\pi\) | |||||||
\(920\) | −1.41489 | −0.0466474 | ||||||||
\(921\) | −15.6649 | −0.516177 | ||||||||
\(922\) | 33.8785 | 1.11573 | ||||||||
\(923\) | −19.0881 | −0.628293 | ||||||||
\(924\) | 0.730364 | 0.0240272 | ||||||||
\(925\) | −12.3067 | −0.404642 | ||||||||
\(926\) | 4.68072 | 0.153818 | ||||||||
\(927\) | −18.7152 | −0.614686 | ||||||||
\(928\) | 5.16848 | 0.169664 | ||||||||
\(929\) | −17.3584 | −0.569509 | −0.284755 | − | 0.958600i | \(-0.591912\pi\) | ||||
−0.284755 | + | 0.958600i | \(0.591912\pi\) | |||||||
\(930\) | −10.0541 | −0.329686 | ||||||||
\(931\) | 17.4629 | 0.572325 | ||||||||
\(932\) | −1.95218 | −0.0639459 | ||||||||
\(933\) | 11.1489 | 0.365000 | ||||||||
\(934\) | −28.6923 | −0.938839 | ||||||||
\(935\) | −39.0280 | −1.27635 | ||||||||
\(936\) | −9.47070 | −0.309559 | ||||||||
\(937\) | 38.3766 | 1.25371 | 0.626854 | − | 0.779136i | \(-0.284342\pi\) | ||||
0.626854 | + | 0.779136i | \(0.284342\pi\) | |||||||
\(938\) | −2.23751 | −0.0730574 | ||||||||
\(939\) | −13.8753 | −0.452803 | ||||||||
\(940\) | −7.65959 | −0.249828 | ||||||||
\(941\) | −10.6999 | −0.348807 | −0.174404 | − | 0.984674i | \(-0.555800\pi\) | ||||
−0.174404 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(942\) | 15.9655 | 0.520184 | ||||||||
\(943\) | 0.450472 | 0.0146694 | ||||||||
\(944\) | −9.00816 | −0.293191 | ||||||||
\(945\) | 1.46082 | 0.0475204 | ||||||||
\(946\) | −45.5264 | −1.48019 | ||||||||
\(947\) | −41.6905 | −1.35476 | −0.677380 | − | 0.735634i | \(-0.736885\pi\) | ||||
−0.677380 | + | 0.735634i | \(0.736885\pi\) | |||||||
\(948\) | 0.141173 | 0.00458510 | ||||||||
\(949\) | 47.6245 | 1.54596 | ||||||||
\(950\) | 7.53835 | 0.244576 | ||||||||
\(951\) | 23.3293 | 0.756505 | ||||||||
\(952\) | −1.71867 | −0.0557023 | ||||||||
\(953\) | 10.5881 | 0.342982 | 0.171491 | − | 0.985186i | \(-0.445141\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445141\pi\) | |||||||
\(954\) | 6.01612 | 0.194779 | ||||||||
\(955\) | 25.6323 | 0.829443 | ||||||||
\(956\) | −1.46566 | −0.0474028 | ||||||||
\(957\) | −16.1301 | −0.521413 | ||||||||
\(958\) | −32.2915 | −1.04329 | ||||||||
\(959\) | −2.88941 | −0.0933038 | ||||||||
\(960\) | 1.17563 | 0.0379432 | ||||||||
\(961\) | 42.1385 | 1.35931 | ||||||||
\(962\) | 16.8321 | 0.542690 | ||||||||
\(963\) | −42.3036 | −1.36322 | ||||||||
\(964\) | −29.9828 | −0.965681 | ||||||||
\(965\) | −1.46251 | −0.0470799 | ||||||||
\(966\) | 0.194452 | 0.00625638 | ||||||||
\(967\) | 1.37294 | 0.0441508 | 0.0220754 | − | 0.999756i | \(-0.492973\pi\) | ||||
0.0220754 | + | 0.999756i | \(0.492973\pi\) | |||||||
\(968\) | 3.10767 | 0.0998844 | ||||||||
\(969\) | 15.3428 | 0.492882 | ||||||||
\(970\) | −7.06823 | −0.226947 | ||||||||
\(971\) | −36.7515 | −1.17941 | −0.589706 | − | 0.807618i | \(-0.700756\pi\) | ||||
−0.589706 | + | 0.807618i | \(0.700756\pi\) | |||||||
\(972\) | −15.9465 | −0.511486 | ||||||||
\(973\) | −3.11522 | −0.0998695 | ||||||||
\(974\) | −32.0737 | −1.02771 | ||||||||
\(975\) | 10.2150 | 0.327140 | ||||||||
\(976\) | 6.21086 | 0.198805 | ||||||||
\(977\) | −33.7415 | −1.07949 | −0.539743 | − | 0.841830i | \(-0.681478\pi\) | ||||
−0.539743 | + | 0.841830i | \(0.681478\pi\) | |||||||
\(978\) | −4.47172 | −0.142990 | ||||||||
\(979\) | −21.5738 | −0.689501 | ||||||||
\(980\) | 9.82671 | 0.313903 | ||||||||
\(981\) | −17.7046 | −0.565264 | ||||||||
\(982\) | −6.59041 | −0.210308 | ||||||||
\(983\) | 6.19255 | 0.197512 | 0.0987559 | − | 0.995112i | \(-0.468514\pi\) | ||||
0.0987559 | + | 0.995112i | \(0.468514\pi\) | |||||||
\(984\) | −0.374296 | −0.0119321 | ||||||||
\(985\) | −4.37731 | −0.139473 | ||||||||
\(986\) | 37.9568 | 1.20879 | ||||||||
\(987\) | 1.05268 | 0.0335071 | ||||||||
\(988\) | −10.3104 | −0.328016 | ||||||||
\(989\) | −12.1209 | −0.385423 | ||||||||
\(990\) | 12.2740 | 0.390095 | ||||||||
\(991\) | −45.1645 | −1.43470 | −0.717349 | − | 0.696714i | \(-0.754645\pi\) | ||||
−0.717349 | + | 0.696714i | \(0.754645\pi\) | |||||||
\(992\) | −8.55210 | −0.271530 | ||||||||
\(993\) | 1.00808 | 0.0319903 | ||||||||
\(994\) | 1.08939 | 0.0345534 | ||||||||
\(995\) | −8.44848 | −0.267835 | ||||||||
\(996\) | 0.377570 | 0.0119638 | ||||||||
\(997\) | −35.3467 | −1.11944 | −0.559720 | − | 0.828682i | \(-0.689091\pi\) | ||||
−0.559720 | + | 0.828682i | \(0.689091\pi\) | |||||||
\(998\) | 7.32680 | 0.231926 | ||||||||
\(999\) | 18.1095 | 0.572958 |
(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 | 6026.2.a.m.1.16 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.m.1.16 | ✓ | 41 | 1.1 | even | 1 | trivial |