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: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
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 | ||||||||
\(3\) | −0.936776 | −0.540848 | −0.270424 | − | 0.962741i | \(-0.587164\pi\) | ||||
−0.270424 | + | 0.962741i | \(0.587164\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.38125 | 0.617715 | 0.308857 | − | 0.951108i | \(-0.400053\pi\) | ||||
0.308857 | + | 0.951108i | \(0.400053\pi\) | |||||||
\(6\) | 0.936776 | 0.382437 | ||||||||
\(7\) | 2.49293 | 0.942237 | 0.471119 | − | 0.882070i | \(-0.343850\pi\) | ||||
0.471119 | + | 0.882070i | \(0.343850\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.12245 | −0.707483 | ||||||||
\(10\) | −1.38125 | −0.436790 | ||||||||
\(11\) | −1.29654 | −0.390922 | −0.195461 | − | 0.980712i | \(-0.562620\pi\) | ||||
−0.195461 | + | 0.980712i | \(0.562620\pi\) | |||||||
\(12\) | −0.936776 | −0.270424 | ||||||||
\(13\) | −0.532498 | −0.147688 | −0.0738441 | − | 0.997270i | \(-0.523527\pi\) | ||||
−0.0738441 | + | 0.997270i | \(0.523527\pi\) | |||||||
\(14\) | −2.49293 | −0.666262 | ||||||||
\(15\) | −1.29392 | −0.334090 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.49376 | −1.08990 | −0.544948 | − | 0.838470i | \(-0.683451\pi\) | ||||
−0.544948 | + | 0.838470i | \(0.683451\pi\) | |||||||
\(18\) | 2.12245 | 0.500266 | ||||||||
\(19\) | −6.56345 | −1.50576 | −0.752880 | − | 0.658158i | \(-0.771336\pi\) | ||||
−0.752880 | + | 0.658158i | \(0.771336\pi\) | |||||||
\(20\) | 1.38125 | 0.308857 | ||||||||
\(21\) | −2.33531 | −0.509607 | ||||||||
\(22\) | 1.29654 | 0.276423 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.936776 | 0.191219 | ||||||||
\(25\) | −3.09214 | −0.618428 | ||||||||
\(26\) | 0.532498 | 0.104431 | ||||||||
\(27\) | 4.79859 | 0.923489 | ||||||||
\(28\) | 2.49293 | 0.471119 | ||||||||
\(29\) | 9.38832 | 1.74337 | 0.871684 | − | 0.490069i | \(-0.163028\pi\) | ||||
0.871684 | + | 0.490069i | \(0.163028\pi\) | |||||||
\(30\) | 1.29392 | 0.236237 | ||||||||
\(31\) | 8.74238 | 1.57018 | 0.785089 | − | 0.619383i | \(-0.212617\pi\) | ||||
0.785089 | + | 0.619383i | \(0.212617\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.21457 | 0.211429 | ||||||||
\(34\) | 4.49376 | 0.770673 | ||||||||
\(35\) | 3.44336 | 0.582034 | ||||||||
\(36\) | −2.12245 | −0.353742 | ||||||||
\(37\) | 5.61854 | 0.923683 | 0.461841 | − | 0.886963i | \(-0.347189\pi\) | ||||
0.461841 | + | 0.886963i | \(0.347189\pi\) | |||||||
\(38\) | 6.56345 | 1.06473 | ||||||||
\(39\) | 0.498831 | 0.0798769 | ||||||||
\(40\) | −1.38125 | −0.218395 | ||||||||
\(41\) | −6.09722 | −0.952226 | −0.476113 | − | 0.879384i | \(-0.657955\pi\) | ||||
−0.476113 | + | 0.879384i | \(0.657955\pi\) | |||||||
\(42\) | 2.33531 | 0.360347 | ||||||||
\(43\) | 7.17129 | 1.09361 | 0.546806 | − | 0.837260i | \(-0.315844\pi\) | ||||
0.546806 | + | 0.837260i | \(0.315844\pi\) | |||||||
\(44\) | −1.29654 | −0.195461 | ||||||||
\(45\) | −2.93164 | −0.437023 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 6.97895 | 1.01798 | 0.508992 | − | 0.860771i | \(-0.330018\pi\) | ||||
0.508992 | + | 0.860771i | \(0.330018\pi\) | |||||||
\(48\) | −0.936776 | −0.135212 | ||||||||
\(49\) | −0.785322 | −0.112189 | ||||||||
\(50\) | 3.09214 | 0.437295 | ||||||||
\(51\) | 4.20964 | 0.589468 | ||||||||
\(52\) | −0.532498 | −0.0738441 | ||||||||
\(53\) | 0.607361 | 0.0834274 | 0.0417137 | − | 0.999130i | \(-0.486718\pi\) | ||||
0.0417137 | + | 0.999130i | \(0.486718\pi\) | |||||||
\(54\) | −4.79859 | −0.653005 | ||||||||
\(55\) | −1.79085 | −0.241478 | ||||||||
\(56\) | −2.49293 | −0.333131 | ||||||||
\(57\) | 6.14849 | 0.814387 | ||||||||
\(58\) | −9.38832 | −1.23275 | ||||||||
\(59\) | −0.436665 | −0.0568490 | −0.0284245 | − | 0.999596i | \(-0.509049\pi\) | ||||
−0.0284245 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(60\) | −1.29392 | −0.167045 | ||||||||
\(61\) | −2.24866 | −0.287911 | −0.143955 | − | 0.989584i | \(-0.545982\pi\) | ||||
−0.143955 | + | 0.989584i | \(0.545982\pi\) | |||||||
\(62\) | −8.74238 | −1.11028 | ||||||||
\(63\) | −5.29111 | −0.666617 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.735514 | −0.0912293 | ||||||||
\(66\) | −1.21457 | −0.149503 | ||||||||
\(67\) | −8.74609 | −1.06851 | −0.534253 | − | 0.845325i | \(-0.679407\pi\) | ||||
−0.534253 | + | 0.845325i | \(0.679407\pi\) | |||||||
\(68\) | −4.49376 | −0.544948 | ||||||||
\(69\) | −0.936776 | −0.112775 | ||||||||
\(70\) | −3.44336 | −0.411560 | ||||||||
\(71\) | 3.67124 | 0.435696 | 0.217848 | − | 0.975983i | \(-0.430096\pi\) | ||||
0.217848 | + | 0.975983i | \(0.430096\pi\) | |||||||
\(72\) | 2.12245 | 0.250133 | ||||||||
\(73\) | −13.3102 | −1.55784 | −0.778918 | − | 0.627125i | \(-0.784231\pi\) | ||||
−0.778918 | + | 0.627125i | \(0.784231\pi\) | |||||||
\(74\) | −5.61854 | −0.653142 | ||||||||
\(75\) | 2.89664 | 0.334476 | ||||||||
\(76\) | −6.56345 | −0.752880 | ||||||||
\(77\) | −3.23218 | −0.368341 | ||||||||
\(78\) | −0.498831 | −0.0564815 | ||||||||
\(79\) | −9.05511 | −1.01878 | −0.509390 | − | 0.860536i | \(-0.670129\pi\) | ||||
−0.509390 | + | 0.860536i | \(0.670129\pi\) | |||||||
\(80\) | 1.38125 | 0.154429 | ||||||||
\(81\) | 1.87215 | 0.208016 | ||||||||
\(82\) | 6.09722 | 0.673325 | ||||||||
\(83\) | −7.36070 | −0.807942 | −0.403971 | − | 0.914772i | \(-0.632370\pi\) | ||||
−0.403971 | + | 0.914772i | \(0.632370\pi\) | |||||||
\(84\) | −2.33531 | −0.254804 | ||||||||
\(85\) | −6.20701 | −0.673245 | ||||||||
\(86\) | −7.17129 | −0.773300 | ||||||||
\(87\) | −8.79476 | −0.942897 | ||||||||
\(88\) | 1.29654 | 0.138212 | ||||||||
\(89\) | −7.67148 | −0.813175 | −0.406588 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406588 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(90\) | 2.93164 | 0.309022 | ||||||||
\(91\) | −1.32748 | −0.139157 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −8.18965 | −0.849228 | ||||||||
\(94\) | −6.97895 | −0.719823 | ||||||||
\(95\) | −9.06579 | −0.930130 | ||||||||
\(96\) | 0.936776 | 0.0956093 | ||||||||
\(97\) | −5.31188 | −0.539340 | −0.269670 | − | 0.962953i | \(-0.586915\pi\) | ||||
−0.269670 | + | 0.962953i | \(0.586915\pi\) | |||||||
\(98\) | 0.785322 | 0.0793295 | ||||||||
\(99\) | 2.75184 | 0.276571 | ||||||||
\(100\) | −3.09214 | −0.309214 | ||||||||
\(101\) | 17.5882 | 1.75009 | 0.875046 | − | 0.484040i | \(-0.160831\pi\) | ||||
0.875046 | + | 0.484040i | \(0.160831\pi\) | |||||||
\(102\) | −4.20964 | −0.416817 | ||||||||
\(103\) | −5.88185 | −0.579556 | −0.289778 | − | 0.957094i | \(-0.593581\pi\) | ||||
−0.289778 | + | 0.957094i | \(0.593581\pi\) | |||||||
\(104\) | 0.532498 | 0.0522157 | ||||||||
\(105\) | −3.22566 | −0.314792 | ||||||||
\(106\) | −0.607361 | −0.0589921 | ||||||||
\(107\) | −2.12314 | −0.205252 | −0.102626 | − | 0.994720i | \(-0.532724\pi\) | ||||
−0.102626 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(108\) | 4.79859 | 0.461745 | ||||||||
\(109\) | 9.69916 | 0.929011 | 0.464506 | − | 0.885570i | \(-0.346232\pi\) | ||||
0.464506 | + | 0.885570i | \(0.346232\pi\) | |||||||
\(110\) | 1.79085 | 0.170751 | ||||||||
\(111\) | −5.26332 | −0.499572 | ||||||||
\(112\) | 2.49293 | 0.235559 | ||||||||
\(113\) | 0.192906 | 0.0181470 | 0.00907352 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907352 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(114\) | −6.14849 | −0.575858 | ||||||||
\(115\) | 1.38125 | 0.128802 | ||||||||
\(116\) | 9.38832 | 0.871684 | ||||||||
\(117\) | 1.13020 | 0.104487 | ||||||||
\(118\) | 0.436665 | 0.0401983 | ||||||||
\(119\) | −11.2026 | −1.02694 | ||||||||
\(120\) | 1.29392 | 0.118119 | ||||||||
\(121\) | −9.31898 | −0.847180 | ||||||||
\(122\) | 2.24866 | 0.203584 | ||||||||
\(123\) | 5.71173 | 0.515009 | ||||||||
\(124\) | 8.74238 | 0.785089 | ||||||||
\(125\) | −11.1773 | −0.999727 | ||||||||
\(126\) | 5.29111 | 0.471370 | ||||||||
\(127\) | −11.7953 | −1.04666 | −0.523330 | − | 0.852130i | \(-0.675310\pi\) | ||||
−0.523330 | + | 0.852130i | \(0.675310\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.71789 | −0.591477 | ||||||||
\(130\) | 0.735514 | 0.0645088 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 1.21457 | 0.105715 | ||||||||
\(133\) | −16.3622 | −1.41878 | ||||||||
\(134\) | 8.74609 | 0.755547 | ||||||||
\(135\) | 6.62806 | 0.570453 | ||||||||
\(136\) | 4.49376 | 0.385336 | ||||||||
\(137\) | 3.16549 | 0.270446 | 0.135223 | − | 0.990815i | \(-0.456825\pi\) | ||||
0.135223 | + | 0.990815i | \(0.456825\pi\) | |||||||
\(138\) | 0.936776 | 0.0797437 | ||||||||
\(139\) | 20.6429 | 1.75090 | 0.875452 | − | 0.483305i | \(-0.160564\pi\) | ||||
0.875452 | + | 0.483305i | \(0.160564\pi\) | |||||||
\(140\) | 3.44336 | 0.291017 | ||||||||
\(141\) | −6.53771 | −0.550575 | ||||||||
\(142\) | −3.67124 | −0.308084 | ||||||||
\(143\) | 0.690405 | 0.0577345 | ||||||||
\(144\) | −2.12245 | −0.176871 | ||||||||
\(145\) | 12.9676 | 1.07690 | ||||||||
\(146\) | 13.3102 | 1.10156 | ||||||||
\(147\) | 0.735671 | 0.0606771 | ||||||||
\(148\) | 5.61854 | 0.461841 | ||||||||
\(149\) | −11.5985 | −0.950184 | −0.475092 | − | 0.879936i | \(-0.657585\pi\) | ||||
−0.475092 | + | 0.879936i | \(0.657585\pi\) | |||||||
\(150\) | −2.89664 | −0.236510 | ||||||||
\(151\) | −3.10142 | −0.252390 | −0.126195 | − | 0.992005i | \(-0.540277\pi\) | ||||
−0.126195 | + | 0.992005i | \(0.540277\pi\) | |||||||
\(152\) | 6.56345 | 0.532366 | ||||||||
\(153\) | 9.53778 | 0.771083 | ||||||||
\(154\) | 3.23218 | 0.260456 | ||||||||
\(155\) | 12.0754 | 0.969922 | ||||||||
\(156\) | 0.498831 | 0.0399385 | ||||||||
\(157\) | 3.16050 | 0.252235 | 0.126118 | − | 0.992015i | \(-0.459748\pi\) | ||||
0.126118 | + | 0.992015i | \(0.459748\pi\) | |||||||
\(158\) | 9.05511 | 0.720386 | ||||||||
\(159\) | −0.568961 | −0.0451216 | ||||||||
\(160\) | −1.38125 | −0.109198 | ||||||||
\(161\) | 2.49293 | 0.196470 | ||||||||
\(162\) | −1.87215 | −0.147090 | ||||||||
\(163\) | −11.5854 | −0.907441 | −0.453721 | − | 0.891144i | \(-0.649904\pi\) | ||||
−0.453721 | + | 0.891144i | \(0.649904\pi\) | |||||||
\(164\) | −6.09722 | −0.476113 | ||||||||
\(165\) | 1.67763 | 0.130603 | ||||||||
\(166\) | 7.36070 | 0.571301 | ||||||||
\(167\) | −9.73825 | −0.753569 | −0.376784 | − | 0.926301i | \(-0.622970\pi\) | ||||
−0.376784 | + | 0.926301i | \(0.622970\pi\) | |||||||
\(168\) | 2.33531 | 0.180173 | ||||||||
\(169\) | −12.7164 | −0.978188 | ||||||||
\(170\) | 6.20701 | 0.476056 | ||||||||
\(171\) | 13.9306 | 1.06530 | ||||||||
\(172\) | 7.17129 | 0.546806 | ||||||||
\(173\) | −9.97288 | −0.758224 | −0.379112 | − | 0.925351i | \(-0.623770\pi\) | ||||
−0.379112 | + | 0.925351i | \(0.623770\pi\) | |||||||
\(174\) | 8.79476 | 0.666729 | ||||||||
\(175\) | −7.70848 | −0.582706 | ||||||||
\(176\) | −1.29654 | −0.0977304 | ||||||||
\(177\) | 0.409058 | 0.0307467 | ||||||||
\(178\) | 7.67148 | 0.575002 | ||||||||
\(179\) | −11.7814 | −0.880584 | −0.440292 | − | 0.897855i | \(-0.645125\pi\) | ||||
−0.440292 | + | 0.897855i | \(0.645125\pi\) | |||||||
\(180\) | −2.93164 | −0.218512 | ||||||||
\(181\) | 1.37301 | 0.102055 | 0.0510274 | − | 0.998697i | \(-0.483750\pi\) | ||||
0.0510274 | + | 0.998697i | \(0.483750\pi\) | |||||||
\(182\) | 1.32748 | 0.0983992 | ||||||||
\(183\) | 2.10649 | 0.155716 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 7.76062 | 0.570572 | ||||||||
\(186\) | 8.18965 | 0.600495 | ||||||||
\(187\) | 5.82634 | 0.426064 | ||||||||
\(188\) | 6.97895 | 0.508992 | ||||||||
\(189\) | 11.9625 | 0.870146 | ||||||||
\(190\) | 9.06579 | 0.657701 | ||||||||
\(191\) | 0.683085 | 0.0494263 | 0.0247131 | − | 0.999695i | \(-0.492133\pi\) | ||||
0.0247131 | + | 0.999695i | \(0.492133\pi\) | |||||||
\(192\) | −0.936776 | −0.0676060 | ||||||||
\(193\) | −0.407793 | −0.0293536 | −0.0146768 | − | 0.999892i | \(-0.504672\pi\) | ||||
−0.0146768 | + | 0.999892i | \(0.504672\pi\) | |||||||
\(194\) | 5.31188 | 0.381371 | ||||||||
\(195\) | 0.689012 | 0.0493412 | ||||||||
\(196\) | −0.785322 | −0.0560944 | ||||||||
\(197\) | −7.19013 | −0.512275 | −0.256138 | − | 0.966640i | \(-0.582450\pi\) | ||||
−0.256138 | + | 0.966640i | \(0.582450\pi\) | |||||||
\(198\) | −2.75184 | −0.195565 | ||||||||
\(199\) | 3.59473 | 0.254824 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(200\) | 3.09214 | 0.218647 | ||||||||
\(201\) | 8.19313 | 0.577899 | ||||||||
\(202\) | −17.5882 | −1.23750 | ||||||||
\(203\) | 23.4044 | 1.64267 | ||||||||
\(204\) | 4.20964 | 0.294734 | ||||||||
\(205\) | −8.42180 | −0.588204 | ||||||||
\(206\) | 5.88185 | 0.409808 | ||||||||
\(207\) | −2.12245 | −0.147520 | ||||||||
\(208\) | −0.532498 | −0.0369221 | ||||||||
\(209\) | 8.50978 | 0.588634 | ||||||||
\(210\) | 3.22566 | 0.222592 | ||||||||
\(211\) | −25.4830 | −1.75432 | −0.877160 | − | 0.480198i | \(-0.840565\pi\) | ||||
−0.877160 | + | 0.480198i | \(0.840565\pi\) | |||||||
\(212\) | 0.607361 | 0.0417137 | ||||||||
\(213\) | −3.43913 | −0.235645 | ||||||||
\(214\) | 2.12314 | 0.145135 | ||||||||
\(215\) | 9.90536 | 0.675540 | ||||||||
\(216\) | −4.79859 | −0.326503 | ||||||||
\(217\) | 21.7941 | 1.47948 | ||||||||
\(218\) | −9.69916 | −0.656910 | ||||||||
\(219\) | 12.4686 | 0.842553 | ||||||||
\(220\) | −1.79085 | −0.120739 | ||||||||
\(221\) | 2.39292 | 0.160965 | ||||||||
\(222\) | 5.26332 | 0.353251 | ||||||||
\(223\) | −25.4651 | −1.70527 | −0.852635 | − | 0.522507i | \(-0.824997\pi\) | ||||
−0.852635 | + | 0.522507i | \(0.824997\pi\) | |||||||
\(224\) | −2.49293 | −0.166566 | ||||||||
\(225\) | 6.56292 | 0.437528 | ||||||||
\(226\) | −0.192906 | −0.0128319 | ||||||||
\(227\) | 11.8102 | 0.783871 | 0.391936 | − | 0.919993i | \(-0.371806\pi\) | ||||
0.391936 | + | 0.919993i | \(0.371806\pi\) | |||||||
\(228\) | 6.14849 | 0.407193 | ||||||||
\(229\) | −20.8857 | −1.38017 | −0.690083 | − | 0.723731i | \(-0.742426\pi\) | ||||
−0.690083 | + | 0.723731i | \(0.742426\pi\) | |||||||
\(230\) | −1.38125 | −0.0910771 | ||||||||
\(231\) | 3.02783 | 0.199216 | ||||||||
\(232\) | −9.38832 | −0.616374 | ||||||||
\(233\) | 14.9353 | 0.978442 | 0.489221 | − | 0.872160i | \(-0.337281\pi\) | ||||
0.489221 | + | 0.872160i | \(0.337281\pi\) | |||||||
\(234\) | −1.13020 | −0.0738835 | ||||||||
\(235\) | 9.63969 | 0.628824 | ||||||||
\(236\) | −0.436665 | −0.0284245 | ||||||||
\(237\) | 8.48262 | 0.551005 | ||||||||
\(238\) | 11.2026 | 0.726157 | ||||||||
\(239\) | −11.7803 | −0.762006 | −0.381003 | − | 0.924574i | \(-0.624421\pi\) | ||||
−0.381003 | + | 0.924574i | \(0.624421\pi\) | |||||||
\(240\) | −1.29392 | −0.0835225 | ||||||||
\(241\) | 0.115681 | 0.00745169 | 0.00372585 | − | 0.999993i | \(-0.498814\pi\) | ||||
0.00372585 | + | 0.999993i | \(0.498814\pi\) | |||||||
\(242\) | 9.31898 | 0.599047 | ||||||||
\(243\) | −16.1496 | −1.03599 | ||||||||
\(244\) | −2.24866 | −0.143955 | ||||||||
\(245\) | −1.08473 | −0.0693007 | ||||||||
\(246\) | −5.71173 | −0.364167 | ||||||||
\(247\) | 3.49502 | 0.222383 | ||||||||
\(248\) | −8.74238 | −0.555142 | ||||||||
\(249\) | 6.89533 | 0.436974 | ||||||||
\(250\) | 11.1773 | 0.706914 | ||||||||
\(251\) | −30.5995 | −1.93143 | −0.965713 | − | 0.259613i | \(-0.916405\pi\) | ||||
−0.965713 | + | 0.259613i | \(0.916405\pi\) | |||||||
\(252\) | −5.29111 | −0.333309 | ||||||||
\(253\) | −1.29654 | −0.0815128 | ||||||||
\(254\) | 11.7953 | 0.740100 | ||||||||
\(255\) | 5.81458 | 0.364123 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.16866 | 0.384790 | 0.192395 | − | 0.981318i | \(-0.438374\pi\) | ||||
0.192395 | + | 0.981318i | \(0.438374\pi\) | |||||||
\(258\) | 6.71789 | 0.418238 | ||||||||
\(259\) | 14.0066 | 0.870328 | ||||||||
\(260\) | −0.735514 | −0.0456146 | ||||||||
\(261\) | −19.9262 | −1.23340 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 5.69520 | 0.351181 | 0.175591 | − | 0.984463i | \(-0.443817\pi\) | ||||
0.175591 | + | 0.984463i | \(0.443817\pi\) | |||||||
\(264\) | −1.21457 | −0.0747515 | ||||||||
\(265\) | 0.838919 | 0.0515344 | ||||||||
\(266\) | 16.3622 | 1.00323 | ||||||||
\(267\) | 7.18646 | 0.439804 | ||||||||
\(268\) | −8.74609 | −0.534253 | ||||||||
\(269\) | 27.1772 | 1.65702 | 0.828510 | − | 0.559974i | \(-0.189189\pi\) | ||||
0.828510 | + | 0.559974i | \(0.189189\pi\) | |||||||
\(270\) | −6.62806 | −0.403371 | ||||||||
\(271\) | −19.6099 | −1.19122 | −0.595609 | − | 0.803275i | \(-0.703089\pi\) | ||||
−0.595609 | + | 0.803275i | \(0.703089\pi\) | |||||||
\(272\) | −4.49376 | −0.272474 | ||||||||
\(273\) | 1.24355 | 0.0752630 | ||||||||
\(274\) | −3.16549 | −0.191234 | ||||||||
\(275\) | 4.00909 | 0.241757 | ||||||||
\(276\) | −0.936776 | −0.0563873 | ||||||||
\(277\) | 11.5177 | 0.692032 | 0.346016 | − | 0.938229i | \(-0.387534\pi\) | ||||
0.346016 | + | 0.938229i | \(0.387534\pi\) | |||||||
\(278\) | −20.6429 | −1.23808 | ||||||||
\(279\) | −18.5553 | −1.11087 | ||||||||
\(280\) | −3.44336 | −0.205780 | ||||||||
\(281\) | 3.50568 | 0.209131 | 0.104566 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104566 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(282\) | 6.53771 | 0.389315 | ||||||||
\(283\) | −16.2648 | −0.966844 | −0.483422 | − | 0.875388i | \(-0.660606\pi\) | ||||
−0.483422 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(284\) | 3.67124 | 0.217848 | ||||||||
\(285\) | 8.49261 | 0.503059 | ||||||||
\(286\) | −0.690405 | −0.0408245 | ||||||||
\(287\) | −15.1999 | −0.897223 | ||||||||
\(288\) | 2.12245 | 0.125067 | ||||||||
\(289\) | 3.19385 | 0.187873 | ||||||||
\(290\) | −12.9676 | −0.761486 | ||||||||
\(291\) | 4.97605 | 0.291701 | ||||||||
\(292\) | −13.3102 | −0.778918 | ||||||||
\(293\) | −2.83217 | −0.165457 | −0.0827286 | − | 0.996572i | \(-0.526363\pi\) | ||||
−0.0827286 | + | 0.996572i | \(0.526363\pi\) | |||||||
\(294\) | −0.735671 | −0.0429052 | ||||||||
\(295\) | −0.603145 | −0.0351165 | ||||||||
\(296\) | −5.61854 | −0.326571 | ||||||||
\(297\) | −6.22156 | −0.361012 | ||||||||
\(298\) | 11.5985 | 0.671882 | ||||||||
\(299\) | −0.532498 | −0.0307951 | ||||||||
\(300\) | 2.89664 | 0.167238 | ||||||||
\(301\) | 17.8775 | 1.03044 | ||||||||
\(302\) | 3.10142 | 0.178467 | ||||||||
\(303\) | −16.4762 | −0.946533 | ||||||||
\(304\) | −6.56345 | −0.376440 | ||||||||
\(305\) | −3.10596 | −0.177847 | ||||||||
\(306\) | −9.53778 | −0.545238 | ||||||||
\(307\) | −23.5112 | −1.34185 | −0.670927 | − | 0.741523i | \(-0.734104\pi\) | ||||
−0.670927 | + | 0.741523i | \(0.734104\pi\) | |||||||
\(308\) | −3.23218 | −0.184170 | ||||||||
\(309\) | 5.50998 | 0.313452 | ||||||||
\(310\) | −12.0754 | −0.685839 | ||||||||
\(311\) | 10.8460 | 0.615022 | 0.307511 | − | 0.951545i | \(-0.400504\pi\) | ||||
0.307511 | + | 0.951545i | \(0.400504\pi\) | |||||||
\(312\) | −0.498831 | −0.0282408 | ||||||||
\(313\) | 19.7921 | 1.11872 | 0.559359 | − | 0.828926i | \(-0.311047\pi\) | ||||
0.559359 | + | 0.828926i | \(0.311047\pi\) | |||||||
\(314\) | −3.16050 | −0.178357 | ||||||||
\(315\) | −7.30836 | −0.411779 | ||||||||
\(316\) | −9.05511 | −0.509390 | ||||||||
\(317\) | −31.5696 | −1.77313 | −0.886564 | − | 0.462607i | \(-0.846914\pi\) | ||||
−0.886564 | + | 0.462607i | \(0.846914\pi\) | |||||||
\(318\) | 0.568961 | 0.0319058 | ||||||||
\(319\) | −12.1723 | −0.681520 | ||||||||
\(320\) | 1.38125 | 0.0772144 | ||||||||
\(321\) | 1.98891 | 0.111010 | ||||||||
\(322\) | −2.49293 | −0.138925 | ||||||||
\(323\) | 29.4946 | 1.64112 | ||||||||
\(324\) | 1.87215 | 0.104008 | ||||||||
\(325\) | 1.64656 | 0.0913346 | ||||||||
\(326\) | 11.5854 | 0.641658 | ||||||||
\(327\) | −9.08595 | −0.502454 | ||||||||
\(328\) | 6.09722 | 0.336663 | ||||||||
\(329\) | 17.3980 | 0.959183 | ||||||||
\(330\) | −1.67763 | −0.0923502 | ||||||||
\(331\) | 15.7971 | 0.868289 | 0.434144 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434144 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(332\) | −7.36070 | −0.403971 | ||||||||
\(333\) | −11.9251 | −0.653490 | ||||||||
\(334\) | 9.73825 | 0.532854 | ||||||||
\(335\) | −12.0806 | −0.660032 | ||||||||
\(336\) | −2.33531 | −0.127402 | ||||||||
\(337\) | −14.6876 | −0.800087 | −0.400043 | − | 0.916496i | \(-0.631005\pi\) | ||||
−0.400043 | + | 0.916496i | \(0.631005\pi\) | |||||||
\(338\) | 12.7164 | 0.691683 | ||||||||
\(339\) | −0.180709 | −0.00981479 | ||||||||
\(340\) | −6.20701 | −0.336623 | ||||||||
\(341\) | −11.3348 | −0.613816 | ||||||||
\(342\) | −13.9306 | −0.753281 | ||||||||
\(343\) | −19.4082 | −1.04795 | ||||||||
\(344\) | −7.17129 | −0.386650 | ||||||||
\(345\) | −1.29392 | −0.0696626 | ||||||||
\(346\) | 9.97288 | 0.536145 | ||||||||
\(347\) | −7.46473 | −0.400728 | −0.200364 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200364 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(348\) | −8.79476 | −0.471448 | ||||||||
\(349\) | −11.9085 | −0.637450 | −0.318725 | − | 0.947847i | \(-0.603255\pi\) | ||||
−0.318725 | + | 0.947847i | \(0.603255\pi\) | |||||||
\(350\) | 7.70848 | 0.412036 | ||||||||
\(351\) | −2.55524 | −0.136389 | ||||||||
\(352\) | 1.29654 | 0.0691058 | ||||||||
\(353\) | −0.279427 | −0.0148724 | −0.00743621 | − | 0.999972i | \(-0.502367\pi\) | ||||
−0.00743621 | + | 0.999972i | \(0.502367\pi\) | |||||||
\(354\) | −0.409058 | −0.0217412 | ||||||||
\(355\) | 5.07091 | 0.269136 | ||||||||
\(356\) | −7.67148 | −0.406588 | ||||||||
\(357\) | 10.4943 | 0.555419 | ||||||||
\(358\) | 11.7814 | 0.622667 | ||||||||
\(359\) | 9.12238 | 0.481461 | 0.240730 | − | 0.970592i | \(-0.422613\pi\) | ||||
0.240730 | + | 0.970592i | \(0.422613\pi\) | |||||||
\(360\) | 2.93164 | 0.154511 | ||||||||
\(361\) | 24.0789 | 1.26731 | ||||||||
\(362\) | −1.37301 | −0.0721636 | ||||||||
\(363\) | 8.72980 | 0.458196 | ||||||||
\(364\) | −1.32748 | −0.0695787 | ||||||||
\(365\) | −18.3847 | −0.962299 | ||||||||
\(366\) | −2.10649 | −0.110108 | ||||||||
\(367\) | 22.4485 | 1.17180 | 0.585900 | − | 0.810383i | \(-0.300741\pi\) | ||||
0.585900 | + | 0.810383i | \(0.300741\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 12.9410 | 0.673684 | ||||||||
\(370\) | −7.76062 | −0.403456 | ||||||||
\(371\) | 1.51411 | 0.0786084 | ||||||||
\(372\) | −8.18965 | −0.424614 | ||||||||
\(373\) | −3.66142 | −0.189581 | −0.0947905 | − | 0.995497i | \(-0.530218\pi\) | ||||
−0.0947905 | + | 0.995497i | \(0.530218\pi\) | |||||||
\(374\) | −5.82634 | −0.301273 | ||||||||
\(375\) | 10.4706 | 0.540701 | ||||||||
\(376\) | −6.97895 | −0.359912 | ||||||||
\(377\) | −4.99926 | −0.257475 | ||||||||
\(378\) | −11.9625 | −0.615286 | ||||||||
\(379\) | 18.5474 | 0.952714 | 0.476357 | − | 0.879252i | \(-0.341957\pi\) | ||||
0.476357 | + | 0.879252i | \(0.341957\pi\) | |||||||
\(380\) | −9.06579 | −0.465065 | ||||||||
\(381\) | 11.0495 | 0.566084 | ||||||||
\(382\) | −0.683085 | −0.0349496 | ||||||||
\(383\) | −3.65393 | −0.186707 | −0.0933536 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933536 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(384\) | 0.936776 | 0.0478047 | ||||||||
\(385\) | −4.46445 | −0.227530 | ||||||||
\(386\) | 0.407793 | 0.0207561 | ||||||||
\(387\) | −15.2207 | −0.773712 | ||||||||
\(388\) | −5.31188 | −0.269670 | ||||||||
\(389\) | −2.41585 | −0.122489 | −0.0612443 | − | 0.998123i | \(-0.519507\pi\) | ||||
−0.0612443 | + | 0.998123i | \(0.519507\pi\) | |||||||
\(390\) | −0.689012 | −0.0348895 | ||||||||
\(391\) | −4.49376 | −0.227259 | ||||||||
\(392\) | 0.785322 | 0.0396647 | ||||||||
\(393\) | −0.936776 | −0.0472541 | ||||||||
\(394\) | 7.19013 | 0.362233 | ||||||||
\(395\) | −12.5074 | −0.629316 | ||||||||
\(396\) | 2.75184 | 0.138285 | ||||||||
\(397\) | 15.8509 | 0.795536 | 0.397768 | − | 0.917486i | \(-0.369785\pi\) | ||||
0.397768 | + | 0.917486i | \(0.369785\pi\) | |||||||
\(398\) | −3.59473 | −0.180187 | ||||||||
\(399\) | 15.3277 | 0.767346 | ||||||||
\(400\) | −3.09214 | −0.154607 | ||||||||
\(401\) | −4.53493 | −0.226464 | −0.113232 | − | 0.993569i | \(-0.536120\pi\) | ||||
−0.113232 | + | 0.993569i | \(0.536120\pi\) | |||||||
\(402\) | −8.19313 | −0.408636 | ||||||||
\(403\) | −4.65530 | −0.231897 | ||||||||
\(404\) | 17.5882 | 0.875046 | ||||||||
\(405\) | 2.58591 | 0.128495 | ||||||||
\(406\) | −23.4044 | −1.16154 | ||||||||
\(407\) | −7.28466 | −0.361087 | ||||||||
\(408\) | −4.20964 | −0.208408 | ||||||||
\(409\) | −17.2859 | −0.854733 | −0.427366 | − | 0.904078i | \(-0.640559\pi\) | ||||
−0.427366 | + | 0.904078i | \(0.640559\pi\) | |||||||
\(410\) | 8.42180 | 0.415923 | ||||||||
\(411\) | −2.96536 | −0.146270 | ||||||||
\(412\) | −5.88185 | −0.289778 | ||||||||
\(413\) | −1.08857 | −0.0535652 | ||||||||
\(414\) | 2.12245 | 0.104313 | ||||||||
\(415\) | −10.1670 | −0.499078 | ||||||||
\(416\) | 0.532498 | 0.0261078 | ||||||||
\(417\) | −19.3377 | −0.946973 | ||||||||
\(418\) | −8.50978 | −0.416227 | ||||||||
\(419\) | 1.27685 | 0.0623781 | 0.0311890 | − | 0.999514i | \(-0.490071\pi\) | ||||
0.0311890 | + | 0.999514i | \(0.490071\pi\) | |||||||
\(420\) | −3.22566 | −0.157396 | ||||||||
\(421\) | −28.2406 | −1.37636 | −0.688181 | − | 0.725539i | \(-0.741591\pi\) | ||||
−0.688181 | + | 0.725539i | \(0.741591\pi\) | |||||||
\(422\) | 25.4830 | 1.24049 | ||||||||
\(423\) | −14.8125 | −0.720207 | ||||||||
\(424\) | −0.607361 | −0.0294961 | ||||||||
\(425\) | 13.8953 | 0.674023 | ||||||||
\(426\) | 3.43913 | 0.166626 | ||||||||
\(427\) | −5.60573 | −0.271280 | ||||||||
\(428\) | −2.12314 | −0.102626 | ||||||||
\(429\) | −0.646755 | −0.0312256 | ||||||||
\(430\) | −9.90536 | −0.477679 | ||||||||
\(431\) | 4.07729 | 0.196396 | 0.0981982 | − | 0.995167i | \(-0.468692\pi\) | ||||
0.0981982 | + | 0.995167i | \(0.468692\pi\) | |||||||
\(432\) | 4.79859 | 0.230872 | ||||||||
\(433\) | 40.1696 | 1.93043 | 0.965214 | − | 0.261460i | \(-0.0842039\pi\) | ||||
0.965214 | + | 0.261460i | \(0.0842039\pi\) | |||||||
\(434\) | −21.7941 | −1.04615 | ||||||||
\(435\) | −12.1478 | −0.582441 | ||||||||
\(436\) | 9.69916 | 0.464506 | ||||||||
\(437\) | −6.56345 | −0.313973 | ||||||||
\(438\) | −12.4686 | −0.595775 | ||||||||
\(439\) | 0.902219 | 0.0430606 | 0.0215303 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215303 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(440\) | 1.79085 | 0.0853754 | ||||||||
\(441\) | 1.66681 | 0.0793717 | ||||||||
\(442\) | −2.39292 | −0.113819 | ||||||||
\(443\) | −18.8332 | −0.894791 | −0.447395 | − | 0.894336i | \(-0.647648\pi\) | ||||
−0.447395 | + | 0.894336i | \(0.647648\pi\) | |||||||
\(444\) | −5.26332 | −0.249786 | ||||||||
\(445\) | −10.5963 | −0.502310 | ||||||||
\(446\) | 25.4651 | 1.20581 | ||||||||
\(447\) | 10.8652 | 0.513905 | ||||||||
\(448\) | 2.49293 | 0.117780 | ||||||||
\(449\) | −28.7296 | −1.35583 | −0.677917 | − | 0.735139i | \(-0.737117\pi\) | ||||
−0.677917 | + | 0.735139i | \(0.737117\pi\) | |||||||
\(450\) | −6.56292 | −0.309379 | ||||||||
\(451\) | 7.90529 | 0.372246 | ||||||||
\(452\) | 0.192906 | 0.00907352 | ||||||||
\(453\) | 2.90534 | 0.136505 | ||||||||
\(454\) | −11.8102 | −0.554281 | ||||||||
\(455\) | −1.83358 | −0.0859596 | ||||||||
\(456\) | −6.14849 | −0.287929 | ||||||||
\(457\) | 18.8061 | 0.879712 | 0.439856 | − | 0.898068i | \(-0.355029\pi\) | ||||
0.439856 | + | 0.898068i | \(0.355029\pi\) | |||||||
\(458\) | 20.8857 | 0.975924 | ||||||||
\(459\) | −21.5637 | −1.00651 | ||||||||
\(460\) | 1.38125 | 0.0644012 | ||||||||
\(461\) | 36.4941 | 1.69970 | 0.849850 | − | 0.527025i | \(-0.176693\pi\) | ||||
0.849850 | + | 0.527025i | \(0.176693\pi\) | |||||||
\(462\) | −3.02783 | −0.140867 | ||||||||
\(463\) | −22.2870 | −1.03577 | −0.517883 | − | 0.855452i | \(-0.673280\pi\) | ||||
−0.517883 | + | 0.855452i | \(0.673280\pi\) | |||||||
\(464\) | 9.38832 | 0.435842 | ||||||||
\(465\) | −11.3120 | −0.524581 | ||||||||
\(466\) | −14.9353 | −0.691863 | ||||||||
\(467\) | 36.9088 | 1.70794 | 0.853969 | − | 0.520324i | \(-0.174189\pi\) | ||||
0.853969 | + | 0.520324i | \(0.174189\pi\) | |||||||
\(468\) | 1.13020 | 0.0522435 | ||||||||
\(469\) | −21.8034 | −1.00679 | ||||||||
\(470\) | −9.63969 | −0.444646 | ||||||||
\(471\) | −2.96068 | −0.136421 | ||||||||
\(472\) | 0.436665 | 0.0200992 | ||||||||
\(473\) | −9.29786 | −0.427516 | ||||||||
\(474\) | −8.48262 | −0.389619 | ||||||||
\(475\) | 20.2951 | 0.931204 | ||||||||
\(476\) | −11.2026 | −0.513470 | ||||||||
\(477\) | −1.28909 | −0.0590235 | ||||||||
\(478\) | 11.7803 | 0.538819 | ||||||||
\(479\) | 37.6259 | 1.71917 | 0.859587 | − | 0.510990i | \(-0.170721\pi\) | ||||
0.859587 | + | 0.510990i | \(0.170721\pi\) | |||||||
\(480\) | 1.29392 | 0.0590593 | ||||||||
\(481\) | −2.99186 | −0.136417 | ||||||||
\(482\) | −0.115681 | −0.00526914 | ||||||||
\(483\) | −2.33531 | −0.106260 | ||||||||
\(484\) | −9.31898 | −0.423590 | ||||||||
\(485\) | −7.33705 | −0.333158 | ||||||||
\(486\) | 16.1496 | 0.732559 | ||||||||
\(487\) | 38.7739 | 1.75701 | 0.878506 | − | 0.477731i | \(-0.158541\pi\) | ||||
0.878506 | + | 0.477731i | \(0.158541\pi\) | |||||||
\(488\) | 2.24866 | 0.101792 | ||||||||
\(489\) | 10.8530 | 0.490788 | ||||||||
\(490\) | 1.08473 | 0.0490030 | ||||||||
\(491\) | −8.16329 | −0.368404 | −0.184202 | − | 0.982888i | \(-0.558970\pi\) | ||||
−0.184202 | + | 0.982888i | \(0.558970\pi\) | |||||||
\(492\) | 5.71173 | 0.257505 | ||||||||
\(493\) | −42.1888 | −1.90009 | ||||||||
\(494\) | −3.49502 | −0.157249 | ||||||||
\(495\) | 3.80099 | 0.170842 | ||||||||
\(496\) | 8.74238 | 0.392544 | ||||||||
\(497\) | 9.15213 | 0.410529 | ||||||||
\(498\) | −6.89533 | −0.308987 | ||||||||
\(499\) | −32.2183 | −1.44229 | −0.721145 | − | 0.692784i | \(-0.756384\pi\) | ||||
−0.721145 | + | 0.692784i | \(0.756384\pi\) | |||||||
\(500\) | −11.1773 | −0.499864 | ||||||||
\(501\) | 9.12257 | 0.407566 | ||||||||
\(502\) | 30.5995 | 1.36572 | ||||||||
\(503\) | 23.9695 | 1.06875 | 0.534373 | − | 0.845249i | \(-0.320548\pi\) | ||||
0.534373 | + | 0.845249i | \(0.320548\pi\) | |||||||
\(504\) | 5.29111 | 0.235685 | ||||||||
\(505\) | 24.2937 | 1.08106 | ||||||||
\(506\) | 1.29654 | 0.0576382 | ||||||||
\(507\) | 11.9125 | 0.529051 | ||||||||
\(508\) | −11.7953 | −0.523330 | ||||||||
\(509\) | −4.33842 | −0.192297 | −0.0961485 | − | 0.995367i | \(-0.530652\pi\) | ||||
−0.0961485 | + | 0.995367i | \(0.530652\pi\) | |||||||
\(510\) | −5.81458 | −0.257474 | ||||||||
\(511\) | −33.1813 | −1.46785 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −31.4953 | −1.39055 | ||||||||
\(514\) | −6.16866 | −0.272088 | ||||||||
\(515\) | −8.12432 | −0.358000 | ||||||||
\(516\) | −6.71789 | −0.295739 | ||||||||
\(517\) | −9.04848 | −0.397952 | ||||||||
\(518\) | −14.0066 | −0.615415 | ||||||||
\(519\) | 9.34236 | 0.410084 | ||||||||
\(520\) | 0.735514 | 0.0322544 | ||||||||
\(521\) | 12.2003 | 0.534503 | 0.267252 | − | 0.963627i | \(-0.413885\pi\) | ||||
0.267252 | + | 0.963627i | \(0.413885\pi\) | |||||||
\(522\) | 19.9262 | 0.872148 | ||||||||
\(523\) | −11.3549 | −0.496517 | −0.248258 | − | 0.968694i | \(-0.579858\pi\) | ||||
−0.248258 | + | 0.968694i | \(0.579858\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 7.22112 | 0.315155 | ||||||||
\(526\) | −5.69520 | −0.248323 | ||||||||
\(527\) | −39.2861 | −1.71133 | ||||||||
\(528\) | 1.21457 | 0.0528573 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.838919 | −0.0364403 | ||||||||
\(531\) | 0.926801 | 0.0402197 | ||||||||
\(532\) | −16.3622 | −0.709391 | ||||||||
\(533\) | 3.24676 | 0.140633 | ||||||||
\(534\) | −7.18646 | −0.310989 | ||||||||
\(535\) | −2.93259 | −0.126787 | ||||||||
\(536\) | 8.74609 | 0.377774 | ||||||||
\(537\) | 11.0366 | 0.476262 | ||||||||
\(538\) | −27.1772 | −1.17169 | ||||||||
\(539\) | 1.01820 | 0.0438570 | ||||||||
\(540\) | 6.62806 | 0.285226 | ||||||||
\(541\) | −9.31967 | −0.400684 | −0.200342 | − | 0.979726i | \(-0.564205\pi\) | ||||
−0.200342 | + | 0.979726i | \(0.564205\pi\) | |||||||
\(542\) | 19.6099 | 0.842318 | ||||||||
\(543\) | −1.28620 | −0.0551961 | ||||||||
\(544\) | 4.49376 | 0.192668 | ||||||||
\(545\) | 13.3970 | 0.573864 | ||||||||
\(546\) | −1.24355 | −0.0532190 | ||||||||
\(547\) | −31.0071 | −1.32577 | −0.662883 | − | 0.748723i | \(-0.730668\pi\) | ||||
−0.662883 | + | 0.748723i | \(0.730668\pi\) | |||||||
\(548\) | 3.16549 | 0.135223 | ||||||||
\(549\) | 4.77266 | 0.203692 | ||||||||
\(550\) | −4.00909 | −0.170948 | ||||||||
\(551\) | −61.6198 | −2.62509 | ||||||||
\(552\) | 0.936776 | 0.0398718 | ||||||||
\(553\) | −22.5737 | −0.959932 | ||||||||
\(554\) | −11.5177 | −0.489340 | ||||||||
\(555\) | −7.26997 | −0.308593 | ||||||||
\(556\) | 20.6429 | 0.875452 | ||||||||
\(557\) | −32.2904 | −1.36819 | −0.684094 | − | 0.729393i | \(-0.739802\pi\) | ||||
−0.684094 | + | 0.729393i | \(0.739802\pi\) | |||||||
\(558\) | 18.5553 | 0.785507 | ||||||||
\(559\) | −3.81869 | −0.161514 | ||||||||
\(560\) | 3.44336 | 0.145509 | ||||||||
\(561\) | −5.45797 | −0.230436 | ||||||||
\(562\) | −3.50568 | −0.147878 | ||||||||
\(563\) | −21.8210 | −0.919646 | −0.459823 | − | 0.888011i | \(-0.652087\pi\) | ||||
−0.459823 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(564\) | −6.53771 | −0.275287 | ||||||||
\(565\) | 0.266451 | 0.0112097 | ||||||||
\(566\) | 16.2648 | 0.683662 | ||||||||
\(567\) | 4.66712 | 0.196001 | ||||||||
\(568\) | −3.67124 | −0.154042 | ||||||||
\(569\) | −21.6536 | −0.907767 | −0.453883 | − | 0.891061i | \(-0.649962\pi\) | ||||
−0.453883 | + | 0.891061i | \(0.649962\pi\) | |||||||
\(570\) | −8.49261 | −0.355716 | ||||||||
\(571\) | −23.4711 | −0.982237 | −0.491118 | − | 0.871093i | \(-0.663412\pi\) | ||||
−0.491118 | + | 0.871093i | \(0.663412\pi\) | |||||||
\(572\) | 0.690405 | 0.0288673 | ||||||||
\(573\) | −0.639897 | −0.0267321 | ||||||||
\(574\) | 15.1999 | 0.634432 | ||||||||
\(575\) | −3.09214 | −0.128951 | ||||||||
\(576\) | −2.12245 | −0.0884354 | ||||||||
\(577\) | −13.2931 | −0.553398 | −0.276699 | − | 0.960957i | \(-0.589240\pi\) | ||||
−0.276699 | + | 0.960957i | \(0.589240\pi\) | |||||||
\(578\) | −3.19385 | −0.132847 | ||||||||
\(579\) | 0.382011 | 0.0158758 | ||||||||
\(580\) | 12.9676 | 0.538452 | ||||||||
\(581\) | −18.3497 | −0.761273 | ||||||||
\(582\) | −4.97605 | −0.206264 | ||||||||
\(583\) | −0.787468 | −0.0326136 | ||||||||
\(584\) | 13.3102 | 0.550779 | ||||||||
\(585\) | 1.56109 | 0.0645432 | ||||||||
\(586\) | 2.83217 | 0.116996 | ||||||||
\(587\) | 4.88252 | 0.201523 | 0.100762 | − | 0.994911i | \(-0.467872\pi\) | ||||
0.100762 | + | 0.994911i | \(0.467872\pi\) | |||||||
\(588\) | 0.735671 | 0.0303386 | ||||||||
\(589\) | −57.3802 | −2.36431 | ||||||||
\(590\) | 0.603145 | 0.0248311 | ||||||||
\(591\) | 6.73554 | 0.277063 | ||||||||
\(592\) | 5.61854 | 0.230921 | ||||||||
\(593\) | −14.9675 | −0.614642 | −0.307321 | − | 0.951606i | \(-0.599432\pi\) | ||||
−0.307321 | + | 0.951606i | \(0.599432\pi\) | |||||||
\(594\) | 6.22156 | 0.255274 | ||||||||
\(595\) | −15.4736 | −0.634357 | ||||||||
\(596\) | −11.5985 | −0.475092 | ||||||||
\(597\) | −3.36746 | −0.137821 | ||||||||
\(598\) | 0.532498 | 0.0217755 | ||||||||
\(599\) | −27.8084 | −1.13622 | −0.568109 | − | 0.822953i | \(-0.692325\pi\) | ||||
−0.568109 | + | 0.822953i | \(0.692325\pi\) | |||||||
\(600\) | −2.89664 | −0.118255 | ||||||||
\(601\) | −36.3320 | −1.48201 | −0.741007 | − | 0.671498i | \(-0.765651\pi\) | ||||
−0.741007 | + | 0.671498i | \(0.765651\pi\) | |||||||
\(602\) | −17.8775 | −0.728632 | ||||||||
\(603\) | 18.5632 | 0.755950 | ||||||||
\(604\) | −3.10142 | −0.126195 | ||||||||
\(605\) | −12.8719 | −0.523316 | ||||||||
\(606\) | 16.4762 | 0.669300 | ||||||||
\(607\) | −45.0589 | −1.82889 | −0.914443 | − | 0.404716i | \(-0.867370\pi\) | ||||
−0.914443 | + | 0.404716i | \(0.867370\pi\) | |||||||
\(608\) | 6.56345 | 0.266183 | ||||||||
\(609\) | −21.9247 | −0.888433 | ||||||||
\(610\) | 3.10596 | 0.125757 | ||||||||
\(611\) | −3.71627 | −0.150344 | ||||||||
\(612\) | 9.53778 | 0.385542 | ||||||||
\(613\) | −14.2772 | −0.576650 | −0.288325 | − | 0.957533i | \(-0.593098\pi\) | ||||
−0.288325 | + | 0.957533i | \(0.593098\pi\) | |||||||
\(614\) | 23.5112 | 0.948835 | ||||||||
\(615\) | 7.88934 | 0.318129 | ||||||||
\(616\) | 3.23218 | 0.130228 | ||||||||
\(617\) | 29.5515 | 1.18970 | 0.594849 | − | 0.803837i | \(-0.297212\pi\) | ||||
0.594849 | + | 0.803837i | \(0.297212\pi\) | |||||||
\(618\) | −5.50998 | −0.221644 | ||||||||
\(619\) | 8.68462 | 0.349064 | 0.174532 | − | 0.984651i | \(-0.444159\pi\) | ||||
0.174532 | + | 0.984651i | \(0.444159\pi\) | |||||||
\(620\) | 12.0754 | 0.484961 | ||||||||
\(621\) | 4.79859 | 0.192561 | ||||||||
\(622\) | −10.8460 | −0.434886 | ||||||||
\(623\) | −19.1244 | −0.766204 | ||||||||
\(624\) | 0.498831 | 0.0199692 | ||||||||
\(625\) | 0.0220452 | 0.000881808 0 | ||||||||
\(626\) | −19.7921 | −0.791053 | ||||||||
\(627\) | −7.97176 | −0.318361 | ||||||||
\(628\) | 3.16050 | 0.126118 | ||||||||
\(629\) | −25.2484 | −1.00672 | ||||||||
\(630\) | 7.30836 | 0.291172 | ||||||||
\(631\) | 2.13449 | 0.0849726 | 0.0424863 | − | 0.999097i | \(-0.486472\pi\) | ||||
0.0424863 | + | 0.999097i | \(0.486472\pi\) | |||||||
\(632\) | 9.05511 | 0.360193 | ||||||||
\(633\) | 23.8718 | 0.948820 | ||||||||
\(634\) | 31.5696 | 1.25379 | ||||||||
\(635\) | −16.2922 | −0.646537 | ||||||||
\(636\) | −0.568961 | −0.0225608 | ||||||||
\(637\) | 0.418182 | 0.0165690 | ||||||||
\(638\) | 12.1723 | 0.481907 | ||||||||
\(639\) | −7.79202 | −0.308248 | ||||||||
\(640\) | −1.38125 | −0.0545988 | ||||||||
\(641\) | 7.84892 | 0.310014 | 0.155007 | − | 0.987913i | \(-0.450460\pi\) | ||||
0.155007 | + | 0.987913i | \(0.450460\pi\) | |||||||
\(642\) | −1.98891 | −0.0784959 | ||||||||
\(643\) | 31.3502 | 1.23633 | 0.618165 | − | 0.786049i | \(-0.287876\pi\) | ||||
0.618165 | + | 0.786049i | \(0.287876\pi\) | |||||||
\(644\) | 2.49293 | 0.0982350 | ||||||||
\(645\) | −9.27911 | −0.365364 | ||||||||
\(646\) | −29.4946 | −1.16045 | ||||||||
\(647\) | 19.8691 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(648\) | −1.87215 | −0.0735448 | ||||||||
\(649\) | 0.566154 | 0.0222235 | ||||||||
\(650\) | −1.64656 | −0.0645833 | ||||||||
\(651\) | −20.4162 | −0.800174 | ||||||||
\(652\) | −11.5854 | −0.453721 | ||||||||
\(653\) | 3.89288 | 0.152340 | 0.0761702 | − | 0.997095i | \(-0.475731\pi\) | ||||
0.0761702 | + | 0.997095i | \(0.475731\pi\) | |||||||
\(654\) | 9.08595 | 0.355289 | ||||||||
\(655\) | 1.38125 | 0.0539700 | ||||||||
\(656\) | −6.09722 | −0.238056 | ||||||||
\(657\) | 28.2502 | 1.10214 | ||||||||
\(658\) | −17.3980 | −0.678245 | ||||||||
\(659\) | −19.7748 | −0.770317 | −0.385159 | − | 0.922850i | \(-0.625853\pi\) | ||||
−0.385159 | + | 0.922850i | \(0.625853\pi\) | |||||||
\(660\) | 1.67763 | 0.0653015 | ||||||||
\(661\) | −21.7597 | −0.846354 | −0.423177 | − | 0.906047i | \(-0.639085\pi\) | ||||
−0.423177 | + | 0.906047i | \(0.639085\pi\) | |||||||
\(662\) | −15.7971 | −0.613973 | ||||||||
\(663\) | −2.24163 | −0.0870575 | ||||||||
\(664\) | 7.36070 | 0.285651 | ||||||||
\(665\) | −22.6003 | −0.876403 | ||||||||
\(666\) | 11.9251 | 0.462087 | ||||||||
\(667\) | 9.38832 | 0.363517 | ||||||||
\(668\) | −9.73825 | −0.376784 | ||||||||
\(669\) | 23.8551 | 0.922292 | ||||||||
\(670\) | 12.0806 | 0.466713 | ||||||||
\(671\) | 2.91547 | 0.112551 | ||||||||
\(672\) | 2.33531 | 0.0900867 | ||||||||
\(673\) | −6.64428 | −0.256118 | −0.128059 | − | 0.991767i | \(-0.540875\pi\) | ||||
−0.128059 | + | 0.991767i | \(0.540875\pi\) | |||||||
\(674\) | 14.6876 | 0.565747 | ||||||||
\(675\) | −14.8379 | −0.571112 | ||||||||
\(676\) | −12.7164 | −0.489094 | ||||||||
\(677\) | 29.4872 | 1.13328 | 0.566642 | − | 0.823964i | \(-0.308242\pi\) | ||||
0.566642 | + | 0.823964i | \(0.308242\pi\) | |||||||
\(678\) | 0.180709 | 0.00694010 | ||||||||
\(679\) | −13.2421 | −0.508186 | ||||||||
\(680\) | 6.20701 | 0.238028 | ||||||||
\(681\) | −11.0635 | −0.423955 | ||||||||
\(682\) | 11.3348 | 0.434034 | ||||||||
\(683\) | 24.3576 | 0.932016 | 0.466008 | − | 0.884780i | \(-0.345692\pi\) | ||||
0.466008 | + | 0.884780i | \(0.345692\pi\) | |||||||
\(684\) | 13.9306 | 0.532650 | ||||||||
\(685\) | 4.37234 | 0.167059 | ||||||||
\(686\) | 19.4082 | 0.741010 | ||||||||
\(687\) | 19.5652 | 0.746460 | ||||||||
\(688\) | 7.17129 | 0.273403 | ||||||||
\(689\) | −0.323418 | −0.0123213 | ||||||||
\(690\) | 1.29392 | 0.0492589 | ||||||||
\(691\) | −47.7353 | −1.81594 | −0.907969 | − | 0.419038i | \(-0.862367\pi\) | ||||
−0.907969 | + | 0.419038i | \(0.862367\pi\) | |||||||
\(692\) | −9.97288 | −0.379112 | ||||||||
\(693\) | 6.86014 | 0.260595 | ||||||||
\(694\) | 7.46473 | 0.283357 | ||||||||
\(695\) | 28.5130 | 1.08156 | ||||||||
\(696\) | 8.79476 | 0.333364 | ||||||||
\(697\) | 27.3994 | 1.03783 | ||||||||
\(698\) | 11.9085 | 0.450745 | ||||||||
\(699\) | −13.9910 | −0.529188 | ||||||||
\(700\) | −7.70848 | −0.291353 | ||||||||
\(701\) | 44.1090 | 1.66598 | 0.832988 | − | 0.553292i | \(-0.186629\pi\) | ||||
0.832988 | + | 0.553292i | \(0.186629\pi\) | |||||||
\(702\) | 2.55524 | 0.0964412 | ||||||||
\(703\) | −36.8770 | −1.39084 | ||||||||
\(704\) | −1.29654 | −0.0488652 | ||||||||
\(705\) | −9.03023 | −0.340098 | ||||||||
\(706\) | 0.279427 | 0.0105164 | ||||||||
\(707\) | 43.8461 | 1.64900 | ||||||||
\(708\) | 0.409058 | 0.0153733 | ||||||||
\(709\) | 2.29225 | 0.0860872 | 0.0430436 | − | 0.999073i | \(-0.486295\pi\) | ||||
0.0430436 | + | 0.999073i | \(0.486295\pi\) | |||||||
\(710\) | −5.07091 | −0.190308 | ||||||||
\(711\) | 19.2190 | 0.720770 | ||||||||
\(712\) | 7.67148 | 0.287501 | ||||||||
\(713\) | 8.74238 | 0.327405 | ||||||||
\(714\) | −10.4943 | −0.392740 | ||||||||
\(715\) | 0.953623 | 0.0356635 | ||||||||
\(716\) | −11.7814 | −0.440292 | ||||||||
\(717\) | 11.0355 | 0.412129 | ||||||||
\(718\) | −9.12238 | −0.340444 | ||||||||
\(719\) | −21.5034 | −0.801942 | −0.400971 | − | 0.916091i | \(-0.631327\pi\) | ||||
−0.400971 | + | 0.916091i | \(0.631327\pi\) | |||||||
\(720\) | −2.93164 | −0.109256 | ||||||||
\(721\) | −14.6630 | −0.546079 | ||||||||
\(722\) | −24.0789 | −0.896124 | ||||||||
\(723\) | −0.108368 | −0.00403023 | ||||||||
\(724\) | 1.37301 | 0.0510274 | ||||||||
\(725\) | −29.0300 | −1.07815 | ||||||||
\(726\) | −8.72980 | −0.323993 | ||||||||
\(727\) | 34.2339 | 1.26967 | 0.634833 | − | 0.772650i | \(-0.281069\pi\) | ||||
0.634833 | + | 0.772650i | \(0.281069\pi\) | |||||||
\(728\) | 1.32748 | 0.0491996 | ||||||||
\(729\) | 9.51208 | 0.352299 | ||||||||
\(730\) | 18.3847 | 0.680448 | ||||||||
\(731\) | −32.2260 | −1.19192 | ||||||||
\(732\) | 2.10649 | 0.0778580 | ||||||||
\(733\) | −37.9137 | −1.40037 | −0.700187 | − | 0.713960i | \(-0.746900\pi\) | ||||
−0.700187 | + | 0.713960i | \(0.746900\pi\) | |||||||
\(734\) | −22.4485 | −0.828588 | ||||||||
\(735\) | 1.01615 | 0.0374812 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 11.3397 | 0.417702 | ||||||||
\(738\) | −12.9410 | −0.476367 | ||||||||
\(739\) | −40.8369 | −1.50221 | −0.751105 | − | 0.660182i | \(-0.770479\pi\) | ||||
−0.751105 | + | 0.660182i | \(0.770479\pi\) | |||||||
\(740\) | 7.76062 | 0.285286 | ||||||||
\(741\) | −3.27405 | −0.120275 | ||||||||
\(742\) | −1.51411 | −0.0555846 | ||||||||
\(743\) | −42.0599 | −1.54303 | −0.771513 | − | 0.636213i | \(-0.780500\pi\) | ||||
−0.771513 | + | 0.636213i | \(0.780500\pi\) | |||||||
\(744\) | 8.18965 | 0.300247 | ||||||||
\(745\) | −16.0204 | −0.586943 | ||||||||
\(746\) | 3.66142 | 0.134054 | ||||||||
\(747\) | 15.6227 | 0.571605 | ||||||||
\(748\) | 5.82634 | 0.213032 | ||||||||
\(749\) | −5.29283 | −0.193396 | ||||||||
\(750\) | −10.4706 | −0.382333 | ||||||||
\(751\) | 20.4074 | 0.744678 | 0.372339 | − | 0.928097i | \(-0.378556\pi\) | ||||
0.372339 | + | 0.928097i | \(0.378556\pi\) | |||||||
\(752\) | 6.97895 | 0.254496 | ||||||||
\(753\) | 28.6649 | 1.04461 | ||||||||
\(754\) | 4.99926 | 0.182062 | ||||||||
\(755\) | −4.28385 | −0.155905 | ||||||||
\(756\) | 11.9625 | 0.435073 | ||||||||
\(757\) | 16.8969 | 0.614129 | 0.307065 | − | 0.951689i | \(-0.400653\pi\) | ||||
0.307065 | + | 0.951689i | \(0.400653\pi\) | |||||||
\(758\) | −18.5474 | −0.673671 | ||||||||
\(759\) | 1.21457 | 0.0440860 | ||||||||
\(760\) | 9.06579 | 0.328851 | ||||||||
\(761\) | 21.7485 | 0.788383 | 0.394192 | − | 0.919028i | \(-0.371025\pi\) | ||||
0.394192 | + | 0.919028i | \(0.371025\pi\) | |||||||
\(762\) | −11.0495 | −0.400282 | ||||||||
\(763\) | 24.1793 | 0.875349 | ||||||||
\(764\) | 0.683085 | 0.0247131 | ||||||||
\(765\) | 13.1741 | 0.476310 | ||||||||
\(766\) | 3.65393 | 0.132022 | ||||||||
\(767\) | 0.232523 | 0.00839593 | ||||||||
\(768\) | −0.936776 | −0.0338030 | ||||||||
\(769\) | −8.84077 | −0.318806 | −0.159403 | − | 0.987214i | \(-0.550957\pi\) | ||||
−0.159403 | + | 0.987214i | \(0.550957\pi\) | |||||||
\(770\) | 4.46445 | 0.160888 | ||||||||
\(771\) | −5.77865 | −0.208113 | ||||||||
\(772\) | −0.407793 | −0.0146768 | ||||||||
\(773\) | 38.0472 | 1.36846 | 0.684232 | − | 0.729264i | \(-0.260138\pi\) | ||||
0.684232 | + | 0.729264i | \(0.260138\pi\) | |||||||
\(774\) | 15.2207 | 0.547097 | ||||||||
\(775\) | −27.0327 | −0.971042 | ||||||||
\(776\) | 5.31188 | 0.190686 | ||||||||
\(777\) | −13.1211 | −0.470715 | ||||||||
\(778\) | 2.41585 | 0.0866125 | ||||||||
\(779\) | 40.0188 | 1.43382 | ||||||||
\(780\) | 0.689012 | 0.0246706 | ||||||||
\(781\) | −4.75991 | −0.170323 | ||||||||
\(782\) | 4.49376 | 0.160696 | ||||||||
\(783\) | 45.0507 | 1.60998 | ||||||||
\(784\) | −0.785322 | −0.0280472 | ||||||||
\(785\) | 4.36545 | 0.155810 | ||||||||
\(786\) | 0.936776 | 0.0334137 | ||||||||
\(787\) | 47.6748 | 1.69942 | 0.849711 | − | 0.527249i | \(-0.176776\pi\) | ||||
0.849711 | + | 0.527249i | \(0.176776\pi\) | |||||||
\(788\) | −7.19013 | −0.256138 | ||||||||
\(789\) | −5.33513 | −0.189936 | ||||||||
\(790\) | 12.5074 | 0.444993 | ||||||||
\(791\) | 0.480899 | 0.0170988 | ||||||||
\(792\) | −2.75184 | −0.0977824 | ||||||||
\(793\) | 1.19740 | 0.0425211 | ||||||||
\(794\) | −15.8509 | −0.562529 | ||||||||
\(795\) | −0.785879 | −0.0278723 | ||||||||
\(796\) | 3.59473 | 0.127412 | ||||||||
\(797\) | 2.00493 | 0.0710183 | 0.0355091 | − | 0.999369i | \(-0.488695\pi\) | ||||
0.0355091 | + | 0.999369i | \(0.488695\pi\) | |||||||
\(798\) | −15.3277 | −0.542595 | ||||||||
\(799\) | −31.3617 | −1.10950 | ||||||||
\(800\) | 3.09214 | 0.109324 | ||||||||
\(801\) | 16.2823 | 0.575308 | ||||||||
\(802\) | 4.53493 | 0.160134 | ||||||||
\(803\) | 17.2572 | 0.608992 | ||||||||
\(804\) | 8.19313 | 0.288950 | ||||||||
\(805\) | 3.44336 | 0.121362 | ||||||||
\(806\) | 4.65530 | 0.163976 | ||||||||
\(807\) | −25.4589 | −0.896196 | ||||||||
\(808\) | −17.5882 | −0.618751 | ||||||||
\(809\) | 4.24063 | 0.149093 | 0.0745464 | − | 0.997218i | \(-0.476249\pi\) | ||||
0.0745464 | + | 0.997218i | \(0.476249\pi\) | |||||||
\(810\) | −2.58591 | −0.0908595 | ||||||||
\(811\) | −9.37816 | −0.329312 | −0.164656 | − | 0.986351i | \(-0.552651\pi\) | ||||
−0.164656 | + | 0.986351i | \(0.552651\pi\) | |||||||
\(812\) | 23.4044 | 0.821333 | ||||||||
\(813\) | 18.3701 | 0.644268 | ||||||||
\(814\) | 7.28466 | 0.255327 | ||||||||
\(815\) | −16.0024 | −0.560540 | ||||||||
\(816\) | 4.20964 | 0.147367 | ||||||||
\(817\) | −47.0684 | −1.64672 | ||||||||
\(818\) | 17.2859 | 0.604387 | ||||||||
\(819\) | 2.81750 | 0.0984516 | ||||||||
\(820\) | −8.42180 | −0.294102 | ||||||||
\(821\) | −3.94270 | −0.137601 | −0.0688005 | − | 0.997630i | \(-0.521917\pi\) | ||||
−0.0688005 | + | 0.997630i | \(0.521917\pi\) | |||||||
\(822\) | 2.96536 | 0.103429 | ||||||||
\(823\) | 7.82578 | 0.272789 | 0.136395 | − | 0.990655i | \(-0.456448\pi\) | ||||
0.136395 | + | 0.990655i | \(0.456448\pi\) | |||||||
\(824\) | 5.88185 | 0.204904 | ||||||||
\(825\) | −3.75562 | −0.130754 | ||||||||
\(826\) | 1.08857 | 0.0378763 | ||||||||
\(827\) | −27.3167 | −0.949895 | −0.474947 | − | 0.880014i | \(-0.657533\pi\) | ||||
−0.474947 | + | 0.880014i | \(0.657533\pi\) | |||||||
\(828\) | −2.12245 | −0.0737602 | ||||||||
\(829\) | 31.7497 | 1.10271 | 0.551356 | − | 0.834270i | \(-0.314111\pi\) | ||||
0.551356 | + | 0.834270i | \(0.314111\pi\) | |||||||
\(830\) | 10.1670 | 0.352901 | ||||||||
\(831\) | −10.7895 | −0.374284 | ||||||||
\(832\) | −0.532498 | −0.0184610 | ||||||||
\(833\) | 3.52905 | 0.122274 | ||||||||
\(834\) | 19.3377 | 0.669611 | ||||||||
\(835\) | −13.4510 | −0.465491 | ||||||||
\(836\) | 8.50978 | 0.294317 | ||||||||
\(837\) | 41.9511 | 1.45004 | ||||||||
\(838\) | −1.27685 | −0.0441080 | ||||||||
\(839\) | −51.7729 | −1.78740 | −0.893699 | − | 0.448667i | \(-0.851899\pi\) | ||||
−0.893699 | + | 0.448667i | \(0.851899\pi\) | |||||||
\(840\) | 3.22566 | 0.111296 | ||||||||
\(841\) | 59.1406 | 2.03933 | ||||||||
\(842\) | 28.2406 | 0.973235 | ||||||||
\(843\) | −3.28404 | −0.113108 | ||||||||
\(844\) | −25.4830 | −0.877160 | ||||||||
\(845\) | −17.5646 | −0.604241 | ||||||||
\(846\) | 14.8125 | 0.509263 | ||||||||
\(847\) | −23.2315 | −0.798245 | ||||||||
\(848\) | 0.607361 | 0.0208569 | ||||||||
\(849\) | 15.2365 | 0.522915 | ||||||||
\(850\) | −13.8953 | −0.476606 | ||||||||
\(851\) | 5.61854 | 0.192601 | ||||||||
\(852\) | −3.43913 | −0.117823 | ||||||||
\(853\) | 14.3979 | 0.492976 | 0.246488 | − | 0.969146i | \(-0.420723\pi\) | ||||
0.246488 | + | 0.969146i | \(0.420723\pi\) | |||||||
\(854\) | 5.60573 | 0.191824 | ||||||||
\(855\) | 19.2417 | 0.658052 | ||||||||
\(856\) | 2.12314 | 0.0725674 | ||||||||
\(857\) | 11.9525 | 0.408290 | 0.204145 | − | 0.978941i | \(-0.434559\pi\) | ||||
0.204145 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(858\) | 0.646755 | 0.0220798 | ||||||||
\(859\) | −14.4561 | −0.493236 | −0.246618 | − | 0.969113i | \(-0.579319\pi\) | ||||
−0.246618 | + | 0.969113i | \(0.579319\pi\) | |||||||
\(860\) | 9.90536 | 0.337770 | ||||||||
\(861\) | 14.2389 | 0.485261 | ||||||||
\(862\) | −4.07729 | −0.138873 | ||||||||
\(863\) | 5.33211 | 0.181507 | 0.0907535 | − | 0.995873i | \(-0.471072\pi\) | ||||
0.0907535 | + | 0.995873i | \(0.471072\pi\) | |||||||
\(864\) | −4.79859 | −0.163251 | ||||||||
\(865\) | −13.7751 | −0.468366 | ||||||||
\(866\) | −40.1696 | −1.36502 | ||||||||
\(867\) | −2.99192 | −0.101611 | ||||||||
\(868\) | 21.7941 | 0.739740 | ||||||||
\(869\) | 11.7403 | 0.398263 | ||||||||
\(870\) | 12.1478 | 0.411848 | ||||||||
\(871\) | 4.65728 | 0.157806 | ||||||||
\(872\) | −9.69916 | −0.328455 | ||||||||
\(873\) | 11.2742 | 0.381574 | ||||||||
\(874\) | 6.56345 | 0.222012 | ||||||||
\(875\) | −27.8642 | −0.941980 | ||||||||
\(876\) | 12.4686 | 0.421277 | ||||||||
\(877\) | 42.8468 | 1.44683 | 0.723417 | − | 0.690411i | \(-0.242570\pi\) | ||||
0.723417 | + | 0.690411i | \(0.242570\pi\) | |||||||
\(878\) | −0.902219 | −0.0304484 | ||||||||
\(879\) | 2.65311 | 0.0894872 | ||||||||
\(880\) | −1.79085 | −0.0603695 | ||||||||
\(881\) | −13.9353 | −0.469493 | −0.234747 | − | 0.972057i | \(-0.575426\pi\) | ||||
−0.234747 | + | 0.972057i | \(0.575426\pi\) | |||||||
\(882\) | −1.66681 | −0.0561243 | ||||||||
\(883\) | 18.3696 | 0.618185 | 0.309092 | − | 0.951032i | \(-0.399975\pi\) | ||||
0.309092 | + | 0.951032i | \(0.399975\pi\) | |||||||
\(884\) | 2.39292 | 0.0804824 | ||||||||
\(885\) | 0.565012 | 0.0189927 | ||||||||
\(886\) | 18.8332 | 0.632713 | ||||||||
\(887\) | −7.62969 | −0.256180 | −0.128090 | − | 0.991763i | \(-0.540885\pi\) | ||||
−0.128090 | + | 0.991763i | \(0.540885\pi\) | |||||||
\(888\) | 5.26332 | 0.176625 | ||||||||
\(889\) | −29.4047 | −0.986202 | ||||||||
\(890\) | 10.5963 | 0.355187 | ||||||||
\(891\) | −2.42731 | −0.0813180 | ||||||||
\(892\) | −25.4651 | −0.852635 | ||||||||
\(893\) | −45.8060 | −1.53284 | ||||||||
\(894\) | −10.8652 | −0.363386 | ||||||||
\(895\) | −16.2731 | −0.543950 | ||||||||
\(896\) | −2.49293 | −0.0832828 | ||||||||
\(897\) | 0.498831 | 0.0166555 | ||||||||
\(898\) | 28.7296 | 0.958719 | ||||||||
\(899\) | 82.0763 | 2.73740 | ||||||||
\(900\) | 6.56292 | 0.218764 | ||||||||
\(901\) | −2.72933 | −0.0909272 | ||||||||
\(902\) | −7.90529 | −0.263217 | ||||||||
\(903\) | −16.7472 | −0.557312 | ||||||||
\(904\) | −0.192906 | −0.00641595 | ||||||||
\(905\) | 1.89647 | 0.0630407 | ||||||||
\(906\) | −2.90534 | −0.0965234 | ||||||||
\(907\) | −18.3669 | −0.609862 | −0.304931 | − | 0.952374i | \(-0.598633\pi\) | ||||
−0.304931 | + | 0.952374i | \(0.598633\pi\) | |||||||
\(908\) | 11.8102 | 0.391936 | ||||||||
\(909\) | −37.3301 | −1.23816 | ||||||||
\(910\) | 1.83358 | 0.0607826 | ||||||||
\(911\) | 23.7045 | 0.785366 | 0.392683 | − | 0.919674i | \(-0.371547\pi\) | ||||
0.392683 | + | 0.919674i | \(0.371547\pi\) | |||||||
\(912\) | 6.14849 | 0.203597 | ||||||||
\(913\) | 9.54344 | 0.315842 | ||||||||
\(914\) | −18.8061 | −0.622050 | ||||||||
\(915\) | 2.90959 | 0.0961881 | ||||||||
\(916\) | −20.8857 | −0.690083 | ||||||||
\(917\) | 2.49293 | 0.0823237 | ||||||||
\(918\) | 21.5637 | 0.711708 | ||||||||
\(919\) | 26.8920 | 0.887086 | 0.443543 | − | 0.896253i | \(-0.353721\pi\) | ||||
0.443543 | + | 0.896253i | \(0.353721\pi\) | |||||||
\(920\) | −1.38125 | −0.0455385 | ||||||||
\(921\) | 22.0247 | 0.725739 | ||||||||
\(922\) | −36.4941 | −1.20187 | ||||||||
\(923\) | −1.95493 | −0.0643472 | ||||||||
\(924\) | 3.02783 | 0.0996082 | ||||||||
\(925\) | −17.3733 | −0.571231 | ||||||||
\(926\) | 22.2870 | 0.732397 | ||||||||
\(927\) | 12.4839 | 0.410026 | ||||||||
\(928\) | −9.38832 | −0.308187 | ||||||||
\(929\) | 17.1007 | 0.561056 | 0.280528 | − | 0.959846i | \(-0.409490\pi\) | ||||
0.280528 | + | 0.959846i | \(0.409490\pi\) | |||||||
\(930\) | 11.3120 | 0.370934 | ||||||||
\(931\) | 5.15442 | 0.168929 | ||||||||
\(932\) | 14.9353 | 0.489221 | ||||||||
\(933\) | −10.1603 | −0.332633 | ||||||||
\(934\) | −36.9088 | −1.20769 | ||||||||
\(935\) | 8.04764 | 0.263186 | ||||||||
\(936\) | −1.13020 | −0.0369417 | ||||||||
\(937\) | 54.5264 | 1.78130 | 0.890650 | − | 0.454690i | \(-0.150250\pi\) | ||||
0.890650 | + | 0.454690i | \(0.150250\pi\) | |||||||
\(938\) | 21.8034 | 0.711905 | ||||||||
\(939\) | −18.5408 | −0.605056 | ||||||||
\(940\) | 9.63969 | 0.314412 | ||||||||
\(941\) | 21.9661 | 0.716074 | 0.358037 | − | 0.933707i | \(-0.383446\pi\) | ||||
0.358037 | + | 0.933707i | \(0.383446\pi\) | |||||||
\(942\) | 2.96068 | 0.0964642 | ||||||||
\(943\) | −6.09722 | −0.198553 | ||||||||
\(944\) | −0.436665 | −0.0142122 | ||||||||
\(945\) | 16.5233 | 0.537502 | ||||||||
\(946\) | 9.29786 | 0.302300 | ||||||||
\(947\) | 13.7835 | 0.447904 | 0.223952 | − | 0.974600i | \(-0.428104\pi\) | ||||
0.223952 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(948\) | 8.48262 | 0.275503 | ||||||||
\(949\) | 7.08763 | 0.230074 | ||||||||
\(950\) | −20.2951 | −0.658461 | ||||||||
\(951\) | 29.5737 | 0.958992 | ||||||||
\(952\) | 11.2026 | 0.363078 | ||||||||
\(953\) | 17.3360 | 0.561568 | 0.280784 | − | 0.959771i | \(-0.409406\pi\) | ||||
0.280784 | + | 0.959771i | \(0.409406\pi\) | |||||||
\(954\) | 1.28909 | 0.0417359 | ||||||||
\(955\) | 0.943512 | 0.0305313 | ||||||||
\(956\) | −11.7803 | −0.381003 | ||||||||
\(957\) | 11.4028 | 0.368599 | ||||||||
\(958\) | −37.6259 | −1.21564 | ||||||||
\(959\) | 7.89134 | 0.254825 | ||||||||
\(960\) | −1.29392 | −0.0417612 | ||||||||
\(961\) | 45.4292 | 1.46546 | ||||||||
\(962\) | 2.99186 | 0.0964615 | ||||||||
\(963\) | 4.50626 | 0.145212 | ||||||||
\(964\) | 0.115681 | 0.00372585 | ||||||||
\(965\) | −0.563265 | −0.0181322 | ||||||||
\(966\) | 2.33531 | 0.0751375 | ||||||||
\(967\) | −41.0432 | −1.31986 | −0.659930 | − | 0.751327i | \(-0.729414\pi\) | ||||
−0.659930 | + | 0.751327i | \(0.729414\pi\) | |||||||
\(968\) | 9.31898 | 0.299523 | ||||||||
\(969\) | −27.6298 | −0.887597 | ||||||||
\(970\) | 7.33705 | 0.235579 | ||||||||
\(971\) | −21.5678 | −0.692144 | −0.346072 | − | 0.938208i | \(-0.612485\pi\) | ||||
−0.346072 | + | 0.938208i | \(0.612485\pi\) | |||||||
\(972\) | −16.1496 | −0.517997 | ||||||||
\(973\) | 51.4611 | 1.64977 | ||||||||
\(974\) | −38.7739 | −1.24240 | ||||||||
\(975\) | −1.54246 | −0.0493981 | ||||||||
\(976\) | −2.24866 | −0.0719777 | ||||||||
\(977\) | 15.2171 | 0.486837 | 0.243419 | − | 0.969921i | \(-0.421731\pi\) | ||||
0.243419 | + | 0.969921i | \(0.421731\pi\) | |||||||
\(978\) | −10.8530 | −0.347039 | ||||||||
\(979\) | 9.94638 | 0.317888 | ||||||||
\(980\) | −1.08473 | −0.0346504 | ||||||||
\(981\) | −20.5860 | −0.657260 | ||||||||
\(982\) | 8.16329 | 0.260501 | ||||||||
\(983\) | 4.11398 | 0.131215 | 0.0656077 | − | 0.997845i | \(-0.479101\pi\) | ||||
0.0656077 | + | 0.997845i | \(0.479101\pi\) | |||||||
\(984\) | −5.71173 | −0.182083 | ||||||||
\(985\) | −9.93138 | −0.316440 | ||||||||
\(986\) | 42.1888 | 1.34357 | ||||||||
\(987\) | −16.2980 | −0.518772 | ||||||||
\(988\) | 3.49502 | 0.111192 | ||||||||
\(989\) | 7.17129 | 0.228034 | ||||||||
\(990\) | −3.80099 | −0.120803 | ||||||||
\(991\) | 8.21859 | 0.261072 | 0.130536 | − | 0.991444i | \(-0.458330\pi\) | ||||
0.130536 | + | 0.991444i | \(0.458330\pi\) | |||||||
\(992\) | −8.74238 | −0.277571 | ||||||||
\(993\) | −14.7984 | −0.469612 | ||||||||
\(994\) | −9.15213 | −0.290288 | ||||||||
\(995\) | 4.96523 | 0.157408 | ||||||||
\(996\) | 6.89533 | 0.218487 | ||||||||
\(997\) | −1.29169 | −0.0409083 | −0.0204541 | − | 0.999791i | \(-0.506511\pi\) | ||||
−0.0204541 | + | 0.999791i | \(0.506511\pi\) | |||||||
\(998\) | 32.2183 | 1.01985 | ||||||||
\(999\) | 26.9611 | 0.853011 |
(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.i.1.10 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.i.1.10 | ✓ | 25 | 1.1 | even | 1 | trivial |