Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.91293 | −1.68178 | −0.840890 | − | 0.541206i | \(-0.817968\pi\) | ||||
−0.840890 | + | 0.541206i | \(0.817968\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.71400 | 1.21374 | 0.606869 | − | 0.794802i | \(-0.292425\pi\) | ||||
0.606869 | + | 0.794802i | \(0.292425\pi\) | |||||||
\(6\) | 2.91293 | 1.18920 | ||||||||
\(7\) | 1.04550 | 0.395163 | 0.197582 | − | 0.980286i | \(-0.436691\pi\) | ||||
0.197582 | + | 0.980286i | \(0.436691\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.48515 | 1.82838 | ||||||||
\(10\) | −2.71400 | −0.858242 | ||||||||
\(11\) | 1.91532 | 0.577492 | 0.288746 | − | 0.957406i | \(-0.406762\pi\) | ||||
0.288746 | + | 0.957406i | \(0.406762\pi\) | |||||||
\(12\) | −2.91293 | −0.840890 | ||||||||
\(13\) | −0.807158 | −0.223865 | −0.111933 | − | 0.993716i | \(-0.535704\pi\) | ||||
−0.111933 | + | 0.993716i | \(0.535704\pi\) | |||||||
\(14\) | −1.04550 | −0.279423 | ||||||||
\(15\) | −7.90569 | −2.04124 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.06854 | 0.744231 | 0.372115 | − | 0.928186i | \(-0.378633\pi\) | ||||
0.372115 | + | 0.928186i | \(0.378633\pi\) | |||||||
\(18\) | −5.48515 | −1.29286 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.71400 | 0.606869 | ||||||||
\(21\) | −3.04548 | −0.664577 | ||||||||
\(22\) | −1.91532 | −0.408348 | ||||||||
\(23\) | 8.03994 | 1.67644 | 0.838222 | − | 0.545329i | \(-0.183595\pi\) | ||||
0.838222 | + | 0.545329i | \(0.183595\pi\) | |||||||
\(24\) | 2.91293 | 0.594599 | ||||||||
\(25\) | 2.36580 | 0.473159 | ||||||||
\(26\) | 0.807158 | 0.158297 | ||||||||
\(27\) | −7.23905 | −1.39316 | ||||||||
\(28\) | 1.04550 | 0.197582 | ||||||||
\(29\) | 3.67644 | 0.682698 | 0.341349 | − | 0.939937i | \(-0.389116\pi\) | ||||
0.341349 | + | 0.939937i | \(0.389116\pi\) | |||||||
\(30\) | 7.90569 | 1.44337 | ||||||||
\(31\) | −5.42951 | −0.975168 | −0.487584 | − | 0.873076i | \(-0.662122\pi\) | ||||
−0.487584 | + | 0.873076i | \(0.662122\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.57920 | −0.971214 | ||||||||
\(34\) | −3.06854 | −0.526251 | ||||||||
\(35\) | 2.83750 | 0.479624 | ||||||||
\(36\) | 5.48515 | 0.914191 | ||||||||
\(37\) | −11.8395 | −1.94640 | −0.973198 | − | 0.229969i | \(-0.926138\pi\) | ||||
−0.973198 | + | 0.229969i | \(0.926138\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.35119 | 0.376492 | ||||||||
\(40\) | −2.71400 | −0.429121 | ||||||||
\(41\) | 3.89041 | 0.607580 | 0.303790 | − | 0.952739i | \(-0.401748\pi\) | ||||
0.303790 | + | 0.952739i | \(0.401748\pi\) | |||||||
\(42\) | 3.04548 | 0.469927 | ||||||||
\(43\) | 5.87343 | 0.895690 | 0.447845 | − | 0.894111i | \(-0.352192\pi\) | ||||
0.447845 | + | 0.894111i | \(0.352192\pi\) | |||||||
\(44\) | 1.91532 | 0.288746 | ||||||||
\(45\) | 14.8867 | 2.21918 | ||||||||
\(46\) | −8.03994 | −1.18542 | ||||||||
\(47\) | 9.31636 | 1.35893 | 0.679466 | − | 0.733707i | \(-0.262212\pi\) | ||||
0.679466 | + | 0.733707i | \(0.262212\pi\) | |||||||
\(48\) | −2.91293 | −0.420445 | ||||||||
\(49\) | −5.90692 | −0.843846 | ||||||||
\(50\) | −2.36580 | −0.334574 | ||||||||
\(51\) | −8.93844 | −1.25163 | ||||||||
\(52\) | −0.807158 | −0.111933 | ||||||||
\(53\) | 10.1275 | 1.39112 | 0.695561 | − | 0.718468i | \(-0.255156\pi\) | ||||
0.695561 | + | 0.718468i | \(0.255156\pi\) | |||||||
\(54\) | 7.23905 | 0.985110 | ||||||||
\(55\) | 5.19819 | 0.700924 | ||||||||
\(56\) | −1.04550 | −0.139711 | ||||||||
\(57\) | −2.91293 | −0.385827 | ||||||||
\(58\) | −3.67644 | −0.482740 | ||||||||
\(59\) | 13.2760 | 1.72838 | 0.864192 | − | 0.503162i | \(-0.167830\pi\) | ||||
0.864192 | + | 0.503162i | \(0.167830\pi\) | |||||||
\(60\) | −7.90569 | −1.02062 | ||||||||
\(61\) | −3.81249 | −0.488139 | −0.244070 | − | 0.969758i | \(-0.578483\pi\) | ||||
−0.244070 | + | 0.969758i | \(0.578483\pi\) | |||||||
\(62\) | 5.42951 | 0.689548 | ||||||||
\(63\) | 5.73474 | 0.722509 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.19063 | −0.271714 | ||||||||
\(66\) | 5.57920 | 0.686752 | ||||||||
\(67\) | −14.6917 | −1.79488 | −0.897441 | − | 0.441135i | \(-0.854576\pi\) | ||||
−0.897441 | + | 0.441135i | \(0.854576\pi\) | |||||||
\(68\) | 3.06854 | 0.372115 | ||||||||
\(69\) | −23.4198 | −2.81941 | ||||||||
\(70\) | −2.83750 | −0.339146 | ||||||||
\(71\) | −2.83404 | −0.336339 | −0.168169 | − | 0.985758i | \(-0.553786\pi\) | ||||
−0.168169 | + | 0.985758i | \(0.553786\pi\) | |||||||
\(72\) | −5.48515 | −0.646431 | ||||||||
\(73\) | −1.08964 | −0.127533 | −0.0637665 | − | 0.997965i | \(-0.520311\pi\) | ||||
−0.0637665 | + | 0.997965i | \(0.520311\pi\) | |||||||
\(74\) | 11.8395 | 1.37631 | ||||||||
\(75\) | −6.89139 | −0.795750 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 2.00248 | 0.228204 | ||||||||
\(78\) | −2.35119 | −0.266220 | ||||||||
\(79\) | 12.7905 | 1.43904 | 0.719522 | − | 0.694470i | \(-0.244361\pi\) | ||||
0.719522 | + | 0.694470i | \(0.244361\pi\) | |||||||
\(80\) | 2.71400 | 0.303434 | ||||||||
\(81\) | 4.63139 | 0.514599 | ||||||||
\(82\) | −3.89041 | −0.429624 | ||||||||
\(83\) | 6.89354 | 0.756665 | 0.378332 | − | 0.925670i | \(-0.376498\pi\) | ||||
0.378332 | + | 0.925670i | \(0.376498\pi\) | |||||||
\(84\) | −3.04548 | −0.332289 | ||||||||
\(85\) | 8.32803 | 0.903301 | ||||||||
\(86\) | −5.87343 | −0.633349 | ||||||||
\(87\) | −10.7092 | −1.14815 | ||||||||
\(88\) | −1.91532 | −0.204174 | ||||||||
\(89\) | 1.63592 | 0.173407 | 0.0867036 | − | 0.996234i | \(-0.472367\pi\) | ||||
0.0867036 | + | 0.996234i | \(0.472367\pi\) | |||||||
\(90\) | −14.8867 | −1.56919 | ||||||||
\(91\) | −0.843886 | −0.0884633 | ||||||||
\(92\) | 8.03994 | 0.838222 | ||||||||
\(93\) | 15.8158 | 1.64002 | ||||||||
\(94\) | −9.31636 | −0.960909 | ||||||||
\(95\) | 2.71400 | 0.278451 | ||||||||
\(96\) | 2.91293 | 0.297299 | ||||||||
\(97\) | 9.41240 | 0.955685 | 0.477842 | − | 0.878446i | \(-0.341419\pi\) | ||||
0.477842 | + | 0.878446i | \(0.341419\pi\) | |||||||
\(98\) | 5.90692 | 0.596689 | ||||||||
\(99\) | 10.5058 | 1.05588 | ||||||||
\(100\) | 2.36580 | 0.236580 | ||||||||
\(101\) | 10.8568 | 1.08030 | 0.540148 | − | 0.841570i | \(-0.318368\pi\) | ||||
0.540148 | + | 0.841570i | \(0.318368\pi\) | |||||||
\(102\) | 8.93844 | 0.885038 | ||||||||
\(103\) | 7.73903 | 0.762550 | 0.381275 | − | 0.924462i | \(-0.375485\pi\) | ||||
0.381275 | + | 0.924462i | \(0.375485\pi\) | |||||||
\(104\) | 0.807158 | 0.0791483 | ||||||||
\(105\) | −8.26542 | −0.806623 | ||||||||
\(106\) | −10.1275 | −0.983671 | ||||||||
\(107\) | 13.6331 | 1.31796 | 0.658981 | − | 0.752159i | \(-0.270988\pi\) | ||||
0.658981 | + | 0.752159i | \(0.270988\pi\) | |||||||
\(108\) | −7.23905 | −0.696578 | ||||||||
\(109\) | −10.6938 | −1.02428 | −0.512139 | − | 0.858902i | \(-0.671147\pi\) | ||||
−0.512139 | + | 0.858902i | \(0.671147\pi\) | |||||||
\(110\) | −5.19819 | −0.495628 | ||||||||
\(111\) | 34.4875 | 3.27341 | ||||||||
\(112\) | 1.04550 | 0.0987908 | ||||||||
\(113\) | 4.89338 | 0.460331 | 0.230165 | − | 0.973152i | \(-0.426073\pi\) | ||||
0.230165 | + | 0.973152i | \(0.426073\pi\) | |||||||
\(114\) | 2.91293 | 0.272821 | ||||||||
\(115\) | 21.8204 | 2.03476 | ||||||||
\(116\) | 3.67644 | 0.341349 | ||||||||
\(117\) | −4.42738 | −0.409311 | ||||||||
\(118\) | −13.2760 | −1.22215 | ||||||||
\(119\) | 3.20817 | 0.294093 | ||||||||
\(120\) | 7.90569 | 0.721687 | ||||||||
\(121\) | −7.33153 | −0.666503 | ||||||||
\(122\) | 3.81249 | 0.345167 | ||||||||
\(123\) | −11.3325 | −1.02182 | ||||||||
\(124\) | −5.42951 | −0.487584 | ||||||||
\(125\) | −7.14923 | −0.639446 | ||||||||
\(126\) | −5.73474 | −0.510891 | ||||||||
\(127\) | 4.85521 | 0.430830 | 0.215415 | − | 0.976523i | \(-0.430890\pi\) | ||||
0.215415 | + | 0.976523i | \(0.430890\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −17.1089 | −1.50635 | ||||||||
\(130\) | 2.19063 | 0.192131 | ||||||||
\(131\) | −5.42755 | −0.474207 | −0.237103 | − | 0.971484i | \(-0.576198\pi\) | ||||
−0.237103 | + | 0.971484i | \(0.576198\pi\) | |||||||
\(132\) | −5.57920 | −0.485607 | ||||||||
\(133\) | 1.04550 | 0.0906566 | ||||||||
\(134\) | 14.6917 | 1.26917 | ||||||||
\(135\) | −19.6468 | −1.69093 | ||||||||
\(136\) | −3.06854 | −0.263125 | ||||||||
\(137\) | −0.349324 | −0.0298448 | −0.0149224 | − | 0.999889i | \(-0.504750\pi\) | ||||
−0.0149224 | + | 0.999889i | \(0.504750\pi\) | |||||||
\(138\) | 23.4198 | 1.99362 | ||||||||
\(139\) | −3.98902 | −0.338344 | −0.169172 | − | 0.985587i | \(-0.554109\pi\) | ||||
−0.169172 | + | 0.985587i | \(0.554109\pi\) | |||||||
\(140\) | 2.83750 | 0.239812 | ||||||||
\(141\) | −27.1379 | −2.28542 | ||||||||
\(142\) | 2.83404 | 0.237827 | ||||||||
\(143\) | −1.54597 | −0.129280 | ||||||||
\(144\) | 5.48515 | 0.457096 | ||||||||
\(145\) | 9.97786 | 0.828616 | ||||||||
\(146\) | 1.08964 | 0.0901794 | ||||||||
\(147\) | 17.2064 | 1.41916 | ||||||||
\(148\) | −11.8395 | −0.973198 | ||||||||
\(149\) | −7.93543 | −0.650096 | −0.325048 | − | 0.945698i | \(-0.605380\pi\) | ||||
−0.325048 | + | 0.945698i | \(0.605380\pi\) | |||||||
\(150\) | 6.89139 | 0.562680 | ||||||||
\(151\) | 7.49138 | 0.609640 | 0.304820 | − | 0.952410i | \(-0.401404\pi\) | ||||
0.304820 | + | 0.952410i | \(0.401404\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 16.8314 | 1.36074 | ||||||||
\(154\) | −2.00248 | −0.161364 | ||||||||
\(155\) | −14.7357 | −1.18360 | ||||||||
\(156\) | 2.35119 | 0.188246 | ||||||||
\(157\) | 12.3973 | 0.989410 | 0.494705 | − | 0.869061i | \(-0.335276\pi\) | ||||
0.494705 | + | 0.869061i | \(0.335276\pi\) | |||||||
\(158\) | −12.7905 | −1.01756 | ||||||||
\(159\) | −29.5007 | −2.33956 | ||||||||
\(160\) | −2.71400 | −0.214561 | ||||||||
\(161\) | 8.40579 | 0.662469 | ||||||||
\(162\) | −4.63139 | −0.363877 | ||||||||
\(163\) | 20.1155 | 1.57557 | 0.787784 | − | 0.615952i | \(-0.211228\pi\) | ||||
0.787784 | + | 0.615952i | \(0.211228\pi\) | |||||||
\(164\) | 3.89041 | 0.303790 | ||||||||
\(165\) | −15.1420 | −1.17880 | ||||||||
\(166\) | −6.89354 | −0.535043 | ||||||||
\(167\) | 3.75981 | 0.290942 | 0.145471 | − | 0.989362i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989362i | \(0.453530\pi\) | |||||||
\(168\) | 3.04548 | 0.234964 | ||||||||
\(169\) | −12.3485 | −0.949884 | ||||||||
\(170\) | −8.32803 | −0.638730 | ||||||||
\(171\) | 5.48515 | 0.419460 | ||||||||
\(172\) | 5.87343 | 0.447845 | ||||||||
\(173\) | −21.6307 | −1.64456 | −0.822278 | − | 0.569086i | \(-0.807297\pi\) | ||||
−0.822278 | + | 0.569086i | \(0.807297\pi\) | |||||||
\(174\) | 10.7092 | 0.811862 | ||||||||
\(175\) | 2.47345 | 0.186975 | ||||||||
\(176\) | 1.91532 | 0.144373 | ||||||||
\(177\) | −38.6719 | −2.90676 | ||||||||
\(178\) | −1.63592 | −0.122617 | ||||||||
\(179\) | −2.94563 | −0.220167 | −0.110084 | − | 0.993922i | \(-0.535112\pi\) | ||||
−0.110084 | + | 0.993922i | \(0.535112\pi\) | |||||||
\(180\) | 14.8867 | 1.10959 | ||||||||
\(181\) | 1.09237 | 0.0811953 | 0.0405976 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405976 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(182\) | 0.843886 | 0.0625530 | ||||||||
\(183\) | 11.1055 | 0.820943 | ||||||||
\(184\) | −8.03994 | −0.592712 | ||||||||
\(185\) | −32.1323 | −2.36241 | ||||||||
\(186\) | −15.8158 | −1.15967 | ||||||||
\(187\) | 5.87725 | 0.429787 | ||||||||
\(188\) | 9.31636 | 0.679466 | ||||||||
\(189\) | −7.56845 | −0.550524 | ||||||||
\(190\) | −2.71400 | −0.196894 | ||||||||
\(191\) | −16.2655 | −1.17693 | −0.588465 | − | 0.808523i | \(-0.700267\pi\) | ||||
−0.588465 | + | 0.808523i | \(0.700267\pi\) | |||||||
\(192\) | −2.91293 | −0.210222 | ||||||||
\(193\) | 12.7920 | 0.920790 | 0.460395 | − | 0.887714i | \(-0.347708\pi\) | ||||
0.460395 | + | 0.887714i | \(0.347708\pi\) | |||||||
\(194\) | −9.41240 | −0.675771 | ||||||||
\(195\) | 6.38114 | 0.456963 | ||||||||
\(196\) | −5.90692 | −0.421923 | ||||||||
\(197\) | −9.98707 | −0.711549 | −0.355775 | − | 0.934572i | \(-0.615783\pi\) | ||||
−0.355775 | + | 0.934572i | \(0.615783\pi\) | |||||||
\(198\) | −10.5058 | −0.746617 | ||||||||
\(199\) | −9.66190 | −0.684914 | −0.342457 | − | 0.939534i | \(-0.611259\pi\) | ||||
−0.342457 | + | 0.939534i | \(0.611259\pi\) | |||||||
\(200\) | −2.36580 | −0.167287 | ||||||||
\(201\) | 42.7960 | 3.01860 | ||||||||
\(202\) | −10.8568 | −0.763884 | ||||||||
\(203\) | 3.84373 | 0.269777 | ||||||||
\(204\) | −8.93844 | −0.625816 | ||||||||
\(205\) | 10.5586 | 0.737443 | ||||||||
\(206\) | −7.73903 | −0.539204 | ||||||||
\(207\) | 44.1003 | 3.06518 | ||||||||
\(208\) | −0.807158 | −0.0559663 | ||||||||
\(209\) | 1.91532 | 0.132486 | ||||||||
\(210\) | 8.26542 | 0.570368 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 10.1275 | 0.695561 | ||||||||
\(213\) | 8.25535 | 0.565647 | ||||||||
\(214\) | −13.6331 | −0.931940 | ||||||||
\(215\) | 15.9405 | 1.08713 | ||||||||
\(216\) | 7.23905 | 0.492555 | ||||||||
\(217\) | −5.67657 | −0.385350 | ||||||||
\(218\) | 10.6938 | 0.724274 | ||||||||
\(219\) | 3.17405 | 0.214482 | ||||||||
\(220\) | 5.19819 | 0.350462 | ||||||||
\(221\) | −2.47680 | −0.166607 | ||||||||
\(222\) | −34.4875 | −2.31465 | ||||||||
\(223\) | −8.77064 | −0.587326 | −0.293663 | − | 0.955909i | \(-0.594874\pi\) | ||||
−0.293663 | + | 0.955909i | \(0.594874\pi\) | |||||||
\(224\) | −1.04550 | −0.0698556 | ||||||||
\(225\) | 12.9767 | 0.865116 | ||||||||
\(226\) | −4.89338 | −0.325503 | ||||||||
\(227\) | −6.98855 | −0.463846 | −0.231923 | − | 0.972734i | \(-0.574502\pi\) | ||||
−0.231923 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(228\) | −2.91293 | −0.192913 | ||||||||
\(229\) | 4.73353 | 0.312800 | 0.156400 | − | 0.987694i | \(-0.450011\pi\) | ||||
0.156400 | + | 0.987694i | \(0.450011\pi\) | |||||||
\(230\) | −21.8204 | −1.43879 | ||||||||
\(231\) | −5.83307 | −0.383788 | ||||||||
\(232\) | −3.67644 | −0.241370 | ||||||||
\(233\) | 13.4203 | 0.879196 | 0.439598 | − | 0.898195i | \(-0.355121\pi\) | ||||
0.439598 | + | 0.898195i | \(0.355121\pi\) | |||||||
\(234\) | 4.42738 | 0.289427 | ||||||||
\(235\) | 25.2846 | 1.64939 | ||||||||
\(236\) | 13.2760 | 0.864192 | ||||||||
\(237\) | −37.2578 | −2.42015 | ||||||||
\(238\) | −3.20817 | −0.207955 | ||||||||
\(239\) | −9.27553 | −0.599984 | −0.299992 | − | 0.953942i | \(-0.596984\pi\) | ||||
−0.299992 | + | 0.953942i | \(0.596984\pi\) | |||||||
\(240\) | −7.90569 | −0.510310 | ||||||||
\(241\) | −7.87195 | −0.507077 | −0.253538 | − | 0.967325i | \(-0.581594\pi\) | ||||
−0.253538 | + | 0.967325i | \(0.581594\pi\) | |||||||
\(242\) | 7.33153 | 0.471289 | ||||||||
\(243\) | 8.22624 | 0.527714 | ||||||||
\(244\) | −3.81249 | −0.244070 | ||||||||
\(245\) | −16.0314 | −1.02421 | ||||||||
\(246\) | 11.3325 | 0.722533 | ||||||||
\(247\) | −0.807158 | −0.0513582 | ||||||||
\(248\) | 5.42951 | 0.344774 | ||||||||
\(249\) | −20.0804 | −1.27254 | ||||||||
\(250\) | 7.14923 | 0.452157 | ||||||||
\(251\) | −21.6775 | −1.36827 | −0.684135 | − | 0.729355i | \(-0.739820\pi\) | ||||
−0.684135 | + | 0.729355i | \(0.739820\pi\) | |||||||
\(252\) | 5.73474 | 0.361255 | ||||||||
\(253\) | 15.3991 | 0.968133 | ||||||||
\(254\) | −4.85521 | −0.304643 | ||||||||
\(255\) | −24.2589 | −1.51915 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.64026 | 0.164695 | 0.0823474 | − | 0.996604i | \(-0.473758\pi\) | ||||
0.0823474 | + | 0.996604i | \(0.473758\pi\) | |||||||
\(258\) | 17.1089 | 1.06515 | ||||||||
\(259\) | −12.3782 | −0.769144 | ||||||||
\(260\) | −2.19063 | −0.135857 | ||||||||
\(261\) | 20.1658 | 1.24823 | ||||||||
\(262\) | 5.42755 | 0.335315 | ||||||||
\(263\) | 8.46435 | 0.521934 | 0.260967 | − | 0.965348i | \(-0.415959\pi\) | ||||
0.260967 | + | 0.965348i | \(0.415959\pi\) | |||||||
\(264\) | 5.57920 | 0.343376 | ||||||||
\(265\) | 27.4861 | 1.68846 | ||||||||
\(266\) | −1.04550 | −0.0641039 | ||||||||
\(267\) | −4.76532 | −0.291633 | ||||||||
\(268\) | −14.6917 | −0.897441 | ||||||||
\(269\) | −18.7958 | −1.14600 | −0.573001 | − | 0.819555i | \(-0.694221\pi\) | ||||
−0.573001 | + | 0.819555i | \(0.694221\pi\) | |||||||
\(270\) | 19.6468 | 1.19567 | ||||||||
\(271\) | 12.8272 | 0.779195 | 0.389598 | − | 0.920985i | \(-0.372614\pi\) | ||||
0.389598 | + | 0.920985i | \(0.372614\pi\) | |||||||
\(272\) | 3.06854 | 0.186058 | ||||||||
\(273\) | 2.45818 | 0.148776 | ||||||||
\(274\) | 0.349324 | 0.0211034 | ||||||||
\(275\) | 4.53127 | 0.273246 | ||||||||
\(276\) | −23.4198 | −1.40970 | ||||||||
\(277\) | −14.2561 | −0.856564 | −0.428282 | − | 0.903645i | \(-0.640881\pi\) | ||||
−0.428282 | + | 0.903645i | \(0.640881\pi\) | |||||||
\(278\) | 3.98902 | 0.239245 | ||||||||
\(279\) | −29.7816 | −1.78298 | ||||||||
\(280\) | −2.83750 | −0.169573 | ||||||||
\(281\) | 0.855700 | 0.0510468 | 0.0255234 | − | 0.999674i | \(-0.491875\pi\) | ||||
0.0255234 | + | 0.999674i | \(0.491875\pi\) | |||||||
\(282\) | 27.1379 | 1.61604 | ||||||||
\(283\) | −11.0969 | −0.659642 | −0.329821 | − | 0.944044i | \(-0.606988\pi\) | ||||
−0.329821 | + | 0.944044i | \(0.606988\pi\) | |||||||
\(284\) | −2.83404 | −0.168169 | ||||||||
\(285\) | −7.90569 | −0.468292 | ||||||||
\(286\) | 1.54597 | 0.0914151 | ||||||||
\(287\) | 4.06744 | 0.240093 | ||||||||
\(288\) | −5.48515 | −0.323215 | ||||||||
\(289\) | −7.58405 | −0.446120 | ||||||||
\(290\) | −9.97786 | −0.585920 | ||||||||
\(291\) | −27.4176 | −1.60725 | ||||||||
\(292\) | −1.08964 | −0.0637665 | ||||||||
\(293\) | 24.2495 | 1.41667 | 0.708336 | − | 0.705875i | \(-0.249446\pi\) | ||||
0.708336 | + | 0.705875i | \(0.249446\pi\) | |||||||
\(294\) | −17.2064 | −1.00350 | ||||||||
\(295\) | 36.0310 | 2.09780 | ||||||||
\(296\) | 11.8395 | 0.688155 | ||||||||
\(297\) | −13.8651 | −0.804537 | ||||||||
\(298\) | 7.93543 | 0.459687 | ||||||||
\(299\) | −6.48950 | −0.375298 | ||||||||
\(300\) | −6.89139 | −0.397875 | ||||||||
\(301\) | 6.14069 | 0.353944 | ||||||||
\(302\) | −7.49138 | −0.431080 | ||||||||
\(303\) | −31.6252 | −1.81682 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −10.3471 | −0.592473 | ||||||||
\(306\) | −16.8314 | −0.962187 | ||||||||
\(307\) | −8.66246 | −0.494393 | −0.247196 | − | 0.968965i | \(-0.579509\pi\) | ||||
−0.247196 | + | 0.968965i | \(0.579509\pi\) | |||||||
\(308\) | 2.00248 | 0.114102 | ||||||||
\(309\) | −22.5432 | −1.28244 | ||||||||
\(310\) | 14.7357 | 0.836930 | ||||||||
\(311\) | −10.5945 | −0.600759 | −0.300380 | − | 0.953820i | \(-0.597113\pi\) | ||||
−0.300380 | + | 0.953820i | \(0.597113\pi\) | |||||||
\(312\) | −2.35119 | −0.133110 | ||||||||
\(313\) | −7.50496 | −0.424205 | −0.212103 | − | 0.977247i | \(-0.568031\pi\) | ||||
−0.212103 | + | 0.977247i | \(0.568031\pi\) | |||||||
\(314\) | −12.3973 | −0.699618 | ||||||||
\(315\) | 15.5641 | 0.876937 | ||||||||
\(316\) | 12.7905 | 0.719522 | ||||||||
\(317\) | −10.4072 | −0.584525 | −0.292263 | − | 0.956338i | \(-0.594408\pi\) | ||||
−0.292263 | + | 0.956338i | \(0.594408\pi\) | |||||||
\(318\) | 29.5007 | 1.65432 | ||||||||
\(319\) | 7.04157 | 0.394252 | ||||||||
\(320\) | 2.71400 | 0.151717 | ||||||||
\(321\) | −39.7123 | −2.21652 | ||||||||
\(322\) | −8.40579 | −0.468436 | ||||||||
\(323\) | 3.06854 | 0.170738 | ||||||||
\(324\) | 4.63139 | 0.257300 | ||||||||
\(325\) | −1.90957 | −0.105924 | ||||||||
\(326\) | −20.1155 | −1.11409 | ||||||||
\(327\) | 31.1502 | 1.72261 | ||||||||
\(328\) | −3.89041 | −0.214812 | ||||||||
\(329\) | 9.74029 | 0.537000 | ||||||||
\(330\) | 15.1420 | 0.833537 | ||||||||
\(331\) | −4.44099 | −0.244099 | −0.122049 | − | 0.992524i | \(-0.538947\pi\) | ||||
−0.122049 | + | 0.992524i | \(0.538947\pi\) | |||||||
\(332\) | 6.89354 | 0.378332 | ||||||||
\(333\) | −64.9412 | −3.55876 | ||||||||
\(334\) | −3.75981 | −0.205727 | ||||||||
\(335\) | −39.8734 | −2.17852 | ||||||||
\(336\) | −3.04548 | −0.166144 | ||||||||
\(337\) | −25.0304 | −1.36349 | −0.681746 | − | 0.731589i | \(-0.738779\pi\) | ||||
−0.681746 | + | 0.731589i | \(0.738779\pi\) | |||||||
\(338\) | 12.3485 | 0.671670 | ||||||||
\(339\) | −14.2541 | −0.774174 | ||||||||
\(340\) | 8.32803 | 0.451651 | ||||||||
\(341\) | −10.3993 | −0.563152 | ||||||||
\(342\) | −5.48515 | −0.296603 | ||||||||
\(343\) | −13.4942 | −0.728620 | ||||||||
\(344\) | −5.87343 | −0.316674 | ||||||||
\(345\) | −63.5613 | −3.42202 | ||||||||
\(346\) | 21.6307 | 1.16288 | ||||||||
\(347\) | 7.41359 | 0.397983 | 0.198991 | − | 0.980001i | \(-0.436233\pi\) | ||||
0.198991 | + | 0.980001i | \(0.436233\pi\) | |||||||
\(348\) | −10.7092 | −0.574073 | ||||||||
\(349\) | 4.20232 | 0.224945 | 0.112473 | − | 0.993655i | \(-0.464123\pi\) | ||||
0.112473 | + | 0.993655i | \(0.464123\pi\) | |||||||
\(350\) | −2.47345 | −0.132211 | ||||||||
\(351\) | 5.84306 | 0.311879 | ||||||||
\(352\) | −1.91532 | −0.102087 | ||||||||
\(353\) | −9.33220 | −0.496703 | −0.248351 | − | 0.968670i | \(-0.579889\pi\) | ||||
−0.248351 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(354\) | 38.6719 | 2.05539 | ||||||||
\(355\) | −7.69158 | −0.408227 | ||||||||
\(356\) | 1.63592 | 0.0867036 | ||||||||
\(357\) | −9.34517 | −0.494599 | ||||||||
\(358\) | 2.94563 | 0.155682 | ||||||||
\(359\) | 3.20438 | 0.169120 | 0.0845602 | − | 0.996418i | \(-0.473051\pi\) | ||||
0.0845602 | + | 0.996418i | \(0.473051\pi\) | |||||||
\(360\) | −14.8867 | −0.784597 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.09237 | −0.0574137 | ||||||||
\(363\) | 21.3562 | 1.12091 | ||||||||
\(364\) | −0.843886 | −0.0442317 | ||||||||
\(365\) | −2.95729 | −0.154792 | ||||||||
\(366\) | −11.1055 | −0.580494 | ||||||||
\(367\) | −10.9140 | −0.569708 | −0.284854 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284854 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(368\) | 8.03994 | 0.419111 | ||||||||
\(369\) | 21.3395 | 1.11089 | ||||||||
\(370\) | 32.1323 | 1.67048 | ||||||||
\(371\) | 10.5884 | 0.549720 | ||||||||
\(372\) | 15.8158 | 0.820009 | ||||||||
\(373\) | −17.0225 | −0.881392 | −0.440696 | − | 0.897656i | \(-0.645268\pi\) | ||||
−0.440696 | + | 0.897656i | \(0.645268\pi\) | |||||||
\(374\) | −5.87725 | −0.303906 | ||||||||
\(375\) | 20.8252 | 1.07541 | ||||||||
\(376\) | −9.31636 | −0.480455 | ||||||||
\(377\) | −2.96747 | −0.152832 | ||||||||
\(378\) | 7.56845 | 0.389279 | ||||||||
\(379\) | 24.6026 | 1.26375 | 0.631874 | − | 0.775071i | \(-0.282286\pi\) | ||||
0.631874 | + | 0.775071i | \(0.282286\pi\) | |||||||
\(380\) | 2.71400 | 0.139225 | ||||||||
\(381\) | −14.1429 | −0.724562 | ||||||||
\(382\) | 16.2655 | 0.832215 | ||||||||
\(383\) | 12.2802 | 0.627489 | 0.313744 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313744 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(384\) | 2.91293 | 0.148650 | ||||||||
\(385\) | 5.43473 | 0.276979 | ||||||||
\(386\) | −12.7920 | −0.651097 | ||||||||
\(387\) | 32.2166 | 1.63766 | ||||||||
\(388\) | 9.41240 | 0.477842 | ||||||||
\(389\) | −27.5770 | −1.39821 | −0.699104 | − | 0.715020i | \(-0.746417\pi\) | ||||
−0.699104 | + | 0.715020i | \(0.746417\pi\) | |||||||
\(390\) | −6.38114 | −0.323121 | ||||||||
\(391\) | 24.6709 | 1.24766 | ||||||||
\(392\) | 5.90692 | 0.298345 | ||||||||
\(393\) | 15.8100 | 0.797511 | ||||||||
\(394\) | 9.98707 | 0.503141 | ||||||||
\(395\) | 34.7134 | 1.74662 | ||||||||
\(396\) | 10.5058 | 0.527938 | ||||||||
\(397\) | 27.8213 | 1.39631 | 0.698155 | − | 0.715947i | \(-0.254005\pi\) | ||||
0.698155 | + | 0.715947i | \(0.254005\pi\) | |||||||
\(398\) | 9.66190 | 0.484307 | ||||||||
\(399\) | −3.04548 | −0.152464 | ||||||||
\(400\) | 2.36580 | 0.118290 | ||||||||
\(401\) | 18.2204 | 0.909882 | 0.454941 | − | 0.890522i | \(-0.349660\pi\) | ||||
0.454941 | + | 0.890522i | \(0.349660\pi\) | |||||||
\(402\) | −42.7960 | −2.13447 | ||||||||
\(403\) | 4.38247 | 0.218306 | ||||||||
\(404\) | 10.8568 | 0.540148 | ||||||||
\(405\) | 12.5696 | 0.624589 | ||||||||
\(406\) | −3.84373 | −0.190761 | ||||||||
\(407\) | −22.6764 | −1.12403 | ||||||||
\(408\) | 8.93844 | 0.442519 | ||||||||
\(409\) | −22.2303 | −1.09922 | −0.549609 | − | 0.835422i | \(-0.685223\pi\) | ||||
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(410\) | −10.5586 | −0.521451 | ||||||||
\(411\) | 1.01756 | 0.0501923 | ||||||||
\(412\) | 7.73903 | 0.381275 | ||||||||
\(413\) | 13.8801 | 0.682994 | ||||||||
\(414\) | −44.1003 | −2.16741 | ||||||||
\(415\) | 18.7091 | 0.918393 | ||||||||
\(416\) | 0.807158 | 0.0395742 | ||||||||
\(417\) | 11.6197 | 0.569020 | ||||||||
\(418\) | −1.91532 | −0.0936816 | ||||||||
\(419\) | 15.2647 | 0.745727 | 0.372864 | − | 0.927886i | \(-0.378376\pi\) | ||||
0.372864 | + | 0.927886i | \(0.378376\pi\) | |||||||
\(420\) | −8.26542 | −0.403311 | ||||||||
\(421\) | −25.8064 | −1.25773 | −0.628864 | − | 0.777515i | \(-0.716480\pi\) | ||||
−0.628864 | + | 0.777515i | \(0.716480\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 51.1016 | 2.48465 | ||||||||
\(424\) | −10.1275 | −0.491836 | ||||||||
\(425\) | 7.25955 | 0.352140 | ||||||||
\(426\) | −8.25535 | −0.399973 | ||||||||
\(427\) | −3.98597 | −0.192895 | ||||||||
\(428\) | 13.6331 | 0.658981 | ||||||||
\(429\) | 4.50330 | 0.217421 | ||||||||
\(430\) | −15.9405 | −0.768719 | ||||||||
\(431\) | 36.2604 | 1.74660 | 0.873301 | − | 0.487182i | \(-0.161975\pi\) | ||||
0.873301 | + | 0.487182i | \(0.161975\pi\) | |||||||
\(432\) | −7.23905 | −0.348289 | ||||||||
\(433\) | 18.0964 | 0.869656 | 0.434828 | − | 0.900513i | \(-0.356809\pi\) | ||||
0.434828 | + | 0.900513i | \(0.356809\pi\) | |||||||
\(434\) | 5.67657 | 0.272484 | ||||||||
\(435\) | −29.0648 | −1.39355 | ||||||||
\(436\) | −10.6938 | −0.512139 | ||||||||
\(437\) | 8.03994 | 0.384603 | ||||||||
\(438\) | −3.17405 | −0.151662 | ||||||||
\(439\) | 3.80676 | 0.181687 | 0.0908433 | − | 0.995865i | \(-0.471044\pi\) | ||||
0.0908433 | + | 0.995865i | \(0.471044\pi\) | |||||||
\(440\) | −5.19819 | −0.247814 | ||||||||
\(441\) | −32.4003 | −1.54287 | ||||||||
\(442\) | 2.47680 | 0.117809 | ||||||||
\(443\) | −18.8706 | −0.896570 | −0.448285 | − | 0.893891i | \(-0.647965\pi\) | ||||
−0.448285 | + | 0.893891i | \(0.647965\pi\) | |||||||
\(444\) | 34.4875 | 1.63670 | ||||||||
\(445\) | 4.43989 | 0.210471 | ||||||||
\(446\) | 8.77064 | 0.415302 | ||||||||
\(447\) | 23.1153 | 1.09332 | ||||||||
\(448\) | 1.04550 | 0.0493954 | ||||||||
\(449\) | 14.4551 | 0.682176 | 0.341088 | − | 0.940031i | \(-0.389205\pi\) | ||||
0.341088 | + | 0.940031i | \(0.389205\pi\) | |||||||
\(450\) | −12.9767 | −0.611729 | ||||||||
\(451\) | 7.45140 | 0.350873 | ||||||||
\(452\) | 4.89338 | 0.230165 | ||||||||
\(453\) | −21.8218 | −1.02528 | ||||||||
\(454\) | 6.98855 | 0.327989 | ||||||||
\(455\) | −2.29031 | −0.107371 | ||||||||
\(456\) | 2.91293 | 0.136410 | ||||||||
\(457\) | 15.1590 | 0.709108 | 0.354554 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354554 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(458\) | −4.73353 | −0.221183 | ||||||||
\(459\) | −22.2133 | −1.03683 | ||||||||
\(460\) | 21.8204 | 1.01738 | ||||||||
\(461\) | −14.1974 | −0.661239 | −0.330620 | − | 0.943764i | \(-0.607258\pi\) | ||||
−0.330620 | + | 0.943764i | \(0.607258\pi\) | |||||||
\(462\) | 5.83307 | 0.271379 | ||||||||
\(463\) | 28.5735 | 1.32792 | 0.663961 | − | 0.747767i | \(-0.268874\pi\) | ||||
0.663961 | + | 0.747767i | \(0.268874\pi\) | |||||||
\(464\) | 3.67644 | 0.170674 | ||||||||
\(465\) | 42.9240 | 1.99055 | ||||||||
\(466\) | −13.4203 | −0.621685 | ||||||||
\(467\) | 34.8486 | 1.61260 | 0.806300 | − | 0.591507i | \(-0.201467\pi\) | ||||
0.806300 | + | 0.591507i | \(0.201467\pi\) | |||||||
\(468\) | −4.42738 | −0.204656 | ||||||||
\(469\) | −15.3603 | −0.709271 | ||||||||
\(470\) | −25.2846 | −1.16629 | ||||||||
\(471\) | −36.1123 | −1.66397 | ||||||||
\(472\) | −13.2760 | −0.611076 | ||||||||
\(473\) | 11.2495 | 0.517254 | ||||||||
\(474\) | 37.2578 | 1.71131 | ||||||||
\(475\) | 2.36580 | 0.108550 | ||||||||
\(476\) | 3.20817 | 0.147046 | ||||||||
\(477\) | 55.5509 | 2.54350 | ||||||||
\(478\) | 9.27553 | 0.424253 | ||||||||
\(479\) | 29.9247 | 1.36730 | 0.683648 | − | 0.729812i | \(-0.260392\pi\) | ||||
0.683648 | + | 0.729812i | \(0.260392\pi\) | |||||||
\(480\) | 7.90569 | 0.360844 | ||||||||
\(481\) | 9.55632 | 0.435731 | ||||||||
\(482\) | 7.87195 | 0.358557 | ||||||||
\(483\) | −24.4854 | −1.11413 | ||||||||
\(484\) | −7.33153 | −0.333252 | ||||||||
\(485\) | 25.5453 | 1.15995 | ||||||||
\(486\) | −8.22624 | −0.373150 | ||||||||
\(487\) | −15.1429 | −0.686192 | −0.343096 | − | 0.939300i | \(-0.611476\pi\) | ||||
−0.343096 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(488\) | 3.81249 | 0.172583 | ||||||||
\(489\) | −58.5950 | −2.64976 | ||||||||
\(490\) | 16.0314 | 0.724224 | ||||||||
\(491\) | −22.6136 | −1.02054 | −0.510268 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510268 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(492\) | −11.3325 | −0.510908 | ||||||||
\(493\) | 11.2813 | 0.508085 | ||||||||
\(494\) | 0.807158 | 0.0363157 | ||||||||
\(495\) | 28.5128 | 1.28156 | ||||||||
\(496\) | −5.42951 | −0.243792 | ||||||||
\(497\) | −2.96300 | −0.132909 | ||||||||
\(498\) | 20.0804 | 0.899824 | ||||||||
\(499\) | −15.5567 | −0.696412 | −0.348206 | − | 0.937418i | \(-0.613209\pi\) | ||||
−0.348206 | + | 0.937418i | \(0.613209\pi\) | |||||||
\(500\) | −7.14923 | −0.319723 | ||||||||
\(501\) | −10.9520 | −0.489301 | ||||||||
\(502\) | 21.6775 | 0.967513 | ||||||||
\(503\) | −25.4643 | −1.13540 | −0.567699 | − | 0.823236i | \(-0.692166\pi\) | ||||
−0.567699 | + | 0.823236i | \(0.692166\pi\) | |||||||
\(504\) | −5.73474 | −0.255446 | ||||||||
\(505\) | 29.4655 | 1.31120 | ||||||||
\(506\) | −15.3991 | −0.684573 | ||||||||
\(507\) | 35.9703 | 1.59750 | ||||||||
\(508\) | 4.85521 | 0.215415 | ||||||||
\(509\) | 36.0825 | 1.59933 | 0.799665 | − | 0.600446i | \(-0.205010\pi\) | ||||
0.799665 | + | 0.600446i | \(0.205010\pi\) | |||||||
\(510\) | 24.2589 | 1.07420 | ||||||||
\(511\) | −1.13922 | −0.0503963 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.23905 | −0.319612 | ||||||||
\(514\) | −2.64026 | −0.116457 | ||||||||
\(515\) | 21.0037 | 0.925535 | ||||||||
\(516\) | −17.1089 | −0.753177 | ||||||||
\(517\) | 17.8439 | 0.784772 | ||||||||
\(518\) | 12.3782 | 0.543867 | ||||||||
\(519\) | 63.0088 | 2.76578 | ||||||||
\(520\) | 2.19063 | 0.0960653 | ||||||||
\(521\) | 34.7028 | 1.52036 | 0.760178 | − | 0.649715i | \(-0.225112\pi\) | ||||
0.760178 | + | 0.649715i | \(0.225112\pi\) | |||||||
\(522\) | −20.1658 | −0.882633 | ||||||||
\(523\) | −18.2068 | −0.796126 | −0.398063 | − | 0.917358i | \(-0.630317\pi\) | ||||
−0.398063 | + | 0.917358i | \(0.630317\pi\) | |||||||
\(524\) | −5.42755 | −0.237103 | ||||||||
\(525\) | −7.20498 | −0.314451 | ||||||||
\(526\) | −8.46435 | −0.369063 | ||||||||
\(527\) | −16.6607 | −0.725750 | ||||||||
\(528\) | −5.57920 | −0.242804 | ||||||||
\(529\) | 41.6407 | 1.81046 | ||||||||
\(530\) | −27.4861 | −1.19392 | ||||||||
\(531\) | 72.8206 | 3.16015 | ||||||||
\(532\) | 1.04550 | 0.0453283 | ||||||||
\(533\) | −3.14018 | −0.136016 | ||||||||
\(534\) | 4.76532 | 0.206215 | ||||||||
\(535\) | 37.0003 | 1.59966 | ||||||||
\(536\) | 14.6917 | 0.634586 | ||||||||
\(537\) | 8.58042 | 0.370272 | ||||||||
\(538\) | 18.7958 | 0.810345 | ||||||||
\(539\) | −11.3137 | −0.487314 | ||||||||
\(540\) | −19.6468 | −0.845463 | ||||||||
\(541\) | 20.1527 | 0.866434 | 0.433217 | − | 0.901290i | \(-0.357378\pi\) | ||||
0.433217 | + | 0.901290i | \(0.357378\pi\) | |||||||
\(542\) | −12.8272 | −0.550974 | ||||||||
\(543\) | −3.18200 | −0.136553 | ||||||||
\(544\) | −3.06854 | −0.131563 | ||||||||
\(545\) | −29.0229 | −1.24321 | ||||||||
\(546\) | −2.45818 | −0.105200 | ||||||||
\(547\) | 32.4207 | 1.38621 | 0.693105 | − | 0.720837i | \(-0.256242\pi\) | ||||
0.693105 | + | 0.720837i | \(0.256242\pi\) | |||||||
\(548\) | −0.349324 | −0.0149224 | ||||||||
\(549\) | −20.9121 | −0.892505 | ||||||||
\(550\) | −4.53127 | −0.193214 | ||||||||
\(551\) | 3.67644 | 0.156622 | ||||||||
\(552\) | 23.4198 | 0.996812 | ||||||||
\(553\) | 13.3725 | 0.568657 | ||||||||
\(554\) | 14.2561 | 0.605683 | ||||||||
\(555\) | 93.5991 | 3.97306 | ||||||||
\(556\) | −3.98902 | −0.169172 | ||||||||
\(557\) | 36.4455 | 1.54425 | 0.772124 | − | 0.635472i | \(-0.219195\pi\) | ||||
0.772124 | + | 0.635472i | \(0.219195\pi\) | |||||||
\(558\) | 29.7816 | 1.26076 | ||||||||
\(559\) | −4.74079 | −0.200514 | ||||||||
\(560\) | 2.83750 | 0.119906 | ||||||||
\(561\) | −17.1200 | −0.722808 | ||||||||
\(562\) | −0.855700 | −0.0360955 | ||||||||
\(563\) | −15.9781 | −0.673398 | −0.336699 | − | 0.941612i | \(-0.609310\pi\) | ||||
−0.336699 | + | 0.941612i | \(0.609310\pi\) | |||||||
\(564\) | −27.1379 | −1.14271 | ||||||||
\(565\) | 13.2806 | 0.558721 | ||||||||
\(566\) | 11.0969 | 0.466437 | ||||||||
\(567\) | 4.84214 | 0.203351 | ||||||||
\(568\) | 2.83404 | 0.118914 | ||||||||
\(569\) | 36.9401 | 1.54861 | 0.774306 | − | 0.632812i | \(-0.218099\pi\) | ||||
0.774306 | + | 0.632812i | \(0.218099\pi\) | |||||||
\(570\) | 7.90569 | 0.331133 | ||||||||
\(571\) | 8.56438 | 0.358408 | 0.179204 | − | 0.983812i | \(-0.442648\pi\) | ||||
0.179204 | + | 0.983812i | \(0.442648\pi\) | |||||||
\(572\) | −1.54597 | −0.0646402 | ||||||||
\(573\) | 47.3802 | 1.97934 | ||||||||
\(574\) | −4.06744 | −0.169772 | ||||||||
\(575\) | 19.0209 | 0.793225 | ||||||||
\(576\) | 5.48515 | 0.228548 | ||||||||
\(577\) | −39.5768 | −1.64761 | −0.823803 | − | 0.566876i | \(-0.808152\pi\) | ||||
−0.823803 | + | 0.566876i | \(0.808152\pi\) | |||||||
\(578\) | 7.58405 | 0.315455 | ||||||||
\(579\) | −37.2622 | −1.54857 | ||||||||
\(580\) | 9.97786 | 0.414308 | ||||||||
\(581\) | 7.20722 | 0.299006 | ||||||||
\(582\) | 27.4176 | 1.13650 | ||||||||
\(583\) | 19.3975 | 0.803361 | ||||||||
\(584\) | 1.08964 | 0.0450897 | ||||||||
\(585\) | −12.0159 | −0.496797 | ||||||||
\(586\) | −24.2495 | −1.00174 | ||||||||
\(587\) | −15.0877 | −0.622736 | −0.311368 | − | 0.950289i | \(-0.600787\pi\) | ||||
−0.311368 | + | 0.950289i | \(0.600787\pi\) | |||||||
\(588\) | 17.2064 | 0.709582 | ||||||||
\(589\) | −5.42951 | −0.223719 | ||||||||
\(590\) | −36.0310 | −1.48337 | ||||||||
\(591\) | 29.0916 | 1.19667 | ||||||||
\(592\) | −11.8395 | −0.486599 | ||||||||
\(593\) | 14.8139 | 0.608334 | 0.304167 | − | 0.952619i | \(-0.401622\pi\) | ||||
0.304167 | + | 0.952619i | \(0.401622\pi\) | |||||||
\(594\) | 13.8651 | 0.568893 | ||||||||
\(595\) | 8.70698 | 0.356951 | ||||||||
\(596\) | −7.93543 | −0.325048 | ||||||||
\(597\) | 28.1444 | 1.15187 | ||||||||
\(598\) | 6.48950 | 0.265375 | ||||||||
\(599\) | 18.8276 | 0.769276 | 0.384638 | − | 0.923068i | \(-0.374326\pi\) | ||||
0.384638 | + | 0.923068i | \(0.374326\pi\) | |||||||
\(600\) | 6.89139 | 0.281340 | ||||||||
\(601\) | −26.6665 | −1.08775 | −0.543874 | − | 0.839167i | \(-0.683043\pi\) | ||||
−0.543874 | + | 0.839167i | \(0.683043\pi\) | |||||||
\(602\) | −6.14069 | −0.250276 | ||||||||
\(603\) | −80.5863 | −3.28173 | ||||||||
\(604\) | 7.49138 | 0.304820 | ||||||||
\(605\) | −19.8978 | −0.808960 | ||||||||
\(606\) | 31.6252 | 1.28469 | ||||||||
\(607\) | −2.06850 | −0.0839579 | −0.0419790 | − | 0.999118i | \(-0.513366\pi\) | ||||
−0.0419790 | + | 0.999118i | \(0.513366\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −11.1965 | −0.453705 | ||||||||
\(610\) | 10.3471 | 0.418942 | ||||||||
\(611\) | −7.51978 | −0.304218 | ||||||||
\(612\) | 16.8314 | 0.680369 | ||||||||
\(613\) | 23.4376 | 0.946634 | 0.473317 | − | 0.880892i | \(-0.343056\pi\) | ||||
0.473317 | + | 0.880892i | \(0.343056\pi\) | |||||||
\(614\) | 8.66246 | 0.349588 | ||||||||
\(615\) | −30.7564 | −1.24022 | ||||||||
\(616\) | −2.00248 | −0.0806821 | ||||||||
\(617\) | −0.367420 | −0.0147918 | −0.00739589 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739589 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(618\) | 22.5432 | 0.906822 | ||||||||
\(619\) | 31.6786 | 1.27327 | 0.636636 | − | 0.771165i | \(-0.280326\pi\) | ||||
0.636636 | + | 0.771165i | \(0.280326\pi\) | |||||||
\(620\) | −14.7357 | −0.591799 | ||||||||
\(621\) | −58.2016 | −2.33555 | ||||||||
\(622\) | 10.5945 | 0.424801 | ||||||||
\(623\) | 1.71036 | 0.0685241 | ||||||||
\(624\) | 2.35119 | 0.0941230 | ||||||||
\(625\) | −31.2320 | −1.24928 | ||||||||
\(626\) | 7.50496 | 0.299958 | ||||||||
\(627\) | −5.57920 | −0.222812 | ||||||||
\(628\) | 12.3973 | 0.494705 | ||||||||
\(629\) | −36.3299 | −1.44857 | ||||||||
\(630\) | −15.5641 | −0.620088 | ||||||||
\(631\) | 4.56729 | 0.181821 | 0.0909104 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909104 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(632\) | −12.7905 | −0.508779 | ||||||||
\(633\) | 2.91293 | 0.115778 | ||||||||
\(634\) | 10.4072 | 0.413322 | ||||||||
\(635\) | 13.1770 | 0.522915 | ||||||||
\(636\) | −29.5007 | −1.16978 | ||||||||
\(637\) | 4.76782 | 0.188908 | ||||||||
\(638\) | −7.04157 | −0.278779 | ||||||||
\(639\) | −15.5451 | −0.614955 | ||||||||
\(640\) | −2.71400 | −0.107280 | ||||||||
\(641\) | 15.0650 | 0.595030 | 0.297515 | − | 0.954717i | \(-0.403842\pi\) | ||||
0.297515 | + | 0.954717i | \(0.403842\pi\) | |||||||
\(642\) | 39.7123 | 1.56732 | ||||||||
\(643\) | −38.5647 | −1.52084 | −0.760422 | − | 0.649429i | \(-0.775008\pi\) | ||||
−0.760422 | + | 0.649429i | \(0.775008\pi\) | |||||||
\(644\) | 8.40579 | 0.331234 | ||||||||
\(645\) | −46.4335 | −1.82832 | ||||||||
\(646\) | −3.06854 | −0.120730 | ||||||||
\(647\) | 6.94107 | 0.272882 | 0.136441 | − | 0.990648i | \(-0.456434\pi\) | ||||
0.136441 | + | 0.990648i | \(0.456434\pi\) | |||||||
\(648\) | −4.63139 | −0.181938 | ||||||||
\(649\) | 25.4278 | 0.998128 | ||||||||
\(650\) | 1.90957 | 0.0748996 | ||||||||
\(651\) | 16.5354 | 0.648075 | ||||||||
\(652\) | 20.1155 | 0.787784 | ||||||||
\(653\) | −10.4388 | −0.408501 | −0.204250 | − | 0.978919i | \(-0.565476\pi\) | ||||
−0.204250 | + | 0.978919i | \(0.565476\pi\) | |||||||
\(654\) | −31.1502 | −1.21807 | ||||||||
\(655\) | −14.7304 | −0.575563 | ||||||||
\(656\) | 3.89041 | 0.151895 | ||||||||
\(657\) | −5.97684 | −0.233179 | ||||||||
\(658\) | −9.74029 | −0.379716 | ||||||||
\(659\) | −32.5868 | −1.26940 | −0.634701 | − | 0.772758i | \(-0.718877\pi\) | ||||
−0.634701 | + | 0.772758i | \(0.718877\pi\) | |||||||
\(660\) | −15.1420 | −0.589400 | ||||||||
\(661\) | 3.64918 | 0.141937 | 0.0709684 | − | 0.997479i | \(-0.477391\pi\) | ||||
0.0709684 | + | 0.997479i | \(0.477391\pi\) | |||||||
\(662\) | 4.44099 | 0.172604 | ||||||||
\(663\) | 7.21473 | 0.280197 | ||||||||
\(664\) | −6.89354 | −0.267521 | ||||||||
\(665\) | 2.83750 | 0.110033 | ||||||||
\(666\) | 64.9412 | 2.51642 | ||||||||
\(667\) | 29.5584 | 1.14450 | ||||||||
\(668\) | 3.75981 | 0.145471 | ||||||||
\(669\) | 25.5482 | 0.987752 | ||||||||
\(670\) | 39.8734 | 1.54044 | ||||||||
\(671\) | −7.30215 | −0.281897 | ||||||||
\(672\) | 3.04548 | 0.117482 | ||||||||
\(673\) | 42.3897 | 1.63400 | 0.817002 | − | 0.576635i | \(-0.195634\pi\) | ||||
0.817002 | + | 0.576635i | \(0.195634\pi\) | |||||||
\(674\) | 25.0304 | 0.964135 | ||||||||
\(675\) | −17.1261 | −0.659185 | ||||||||
\(676\) | −12.3485 | −0.474942 | ||||||||
\(677\) | −23.5502 | −0.905106 | −0.452553 | − | 0.891738i | \(-0.649487\pi\) | ||||
−0.452553 | + | 0.891738i | \(0.649487\pi\) | |||||||
\(678\) | 14.2541 | 0.547424 | ||||||||
\(679\) | 9.84070 | 0.377651 | ||||||||
\(680\) | −8.32803 | −0.319365 | ||||||||
\(681\) | 20.3571 | 0.780087 | ||||||||
\(682\) | 10.3993 | 0.398208 | ||||||||
\(683\) | 23.5248 | 0.900152 | 0.450076 | − | 0.892990i | \(-0.351397\pi\) | ||||
0.450076 | + | 0.892990i | \(0.351397\pi\) | |||||||
\(684\) | 5.48515 | 0.209730 | ||||||||
\(685\) | −0.948065 | −0.0362237 | ||||||||
\(686\) | 13.4942 | 0.515212 | ||||||||
\(687\) | −13.7884 | −0.526061 | ||||||||
\(688\) | 5.87343 | 0.223923 | ||||||||
\(689\) | −8.17450 | −0.311424 | ||||||||
\(690\) | 63.5613 | 2.41974 | ||||||||
\(691\) | 9.29670 | 0.353663 | 0.176831 | − | 0.984241i | \(-0.443415\pi\) | ||||
0.176831 | + | 0.984241i | \(0.443415\pi\) | |||||||
\(692\) | −21.6307 | −0.822278 | ||||||||
\(693\) | 10.9839 | 0.417243 | ||||||||
\(694\) | −7.41359 | −0.281416 | ||||||||
\(695\) | −10.8262 | −0.410661 | ||||||||
\(696\) | 10.7092 | 0.405931 | ||||||||
\(697\) | 11.9379 | 0.452180 | ||||||||
\(698\) | −4.20232 | −0.159060 | ||||||||
\(699\) | −39.0925 | −1.47861 | ||||||||
\(700\) | 2.47345 | 0.0934876 | ||||||||
\(701\) | 16.3585 | 0.617853 | 0.308927 | − | 0.951086i | \(-0.400030\pi\) | ||||
0.308927 | + | 0.951086i | \(0.400030\pi\) | |||||||
\(702\) | −5.84306 | −0.220532 | ||||||||
\(703\) | −11.8395 | −0.446534 | ||||||||
\(704\) | 1.91532 | 0.0721865 | ||||||||
\(705\) | −73.6522 | −2.77390 | ||||||||
\(706\) | 9.33220 | 0.351222 | ||||||||
\(707\) | 11.3509 | 0.426893 | ||||||||
\(708\) | −38.6719 | −1.45338 | ||||||||
\(709\) | −23.7095 | −0.890430 | −0.445215 | − | 0.895424i | \(-0.646873\pi\) | ||||
−0.445215 | + | 0.895424i | \(0.646873\pi\) | |||||||
\(710\) | 7.69158 | 0.288660 | ||||||||
\(711\) | 70.1578 | 2.63112 | ||||||||
\(712\) | −1.63592 | −0.0613087 | ||||||||
\(713\) | −43.6529 | −1.63481 | ||||||||
\(714\) | 9.34517 | 0.349734 | ||||||||
\(715\) | −4.19576 | −0.156913 | ||||||||
\(716\) | −2.94563 | −0.110084 | ||||||||
\(717\) | 27.0189 | 1.00904 | ||||||||
\(718\) | −3.20438 | −0.119586 | ||||||||
\(719\) | 41.1896 | 1.53611 | 0.768056 | − | 0.640383i | \(-0.221224\pi\) | ||||
0.768056 | + | 0.640383i | \(0.221224\pi\) | |||||||
\(720\) | 14.8867 | 0.554794 | ||||||||
\(721\) | 8.09118 | 0.301331 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 22.9304 | 0.852791 | ||||||||
\(724\) | 1.09237 | 0.0405976 | ||||||||
\(725\) | 8.69771 | 0.323025 | ||||||||
\(726\) | −21.3562 | −0.792604 | ||||||||
\(727\) | 17.9195 | 0.664598 | 0.332299 | − | 0.943174i | \(-0.392176\pi\) | ||||
0.332299 | + | 0.943174i | \(0.392176\pi\) | |||||||
\(728\) | 0.843886 | 0.0312765 | ||||||||
\(729\) | −37.8566 | −1.40210 | ||||||||
\(730\) | 2.95729 | 0.109454 | ||||||||
\(731\) | 18.0229 | 0.666600 | ||||||||
\(732\) | 11.1055 | 0.410471 | ||||||||
\(733\) | −17.0730 | −0.630606 | −0.315303 | − | 0.948991i | \(-0.602106\pi\) | ||||
−0.315303 | + | 0.948991i | \(0.602106\pi\) | |||||||
\(734\) | 10.9140 | 0.402845 | ||||||||
\(735\) | 46.6983 | 1.72249 | ||||||||
\(736\) | −8.03994 | −0.296356 | ||||||||
\(737\) | −28.1394 | −1.03653 | ||||||||
\(738\) | −21.3395 | −0.785517 | ||||||||
\(739\) | 14.6540 | 0.539055 | 0.269528 | − | 0.962993i | \(-0.413132\pi\) | ||||
0.269528 | + | 0.962993i | \(0.413132\pi\) | |||||||
\(740\) | −32.1323 | −1.18121 | ||||||||
\(741\) | 2.35119 | 0.0863732 | ||||||||
\(742\) | −10.5884 | −0.388711 | ||||||||
\(743\) | −16.5949 | −0.608809 | −0.304405 | − | 0.952543i | \(-0.598458\pi\) | ||||
−0.304405 | + | 0.952543i | \(0.598458\pi\) | |||||||
\(744\) | −15.8158 | −0.579834 | ||||||||
\(745\) | −21.5368 | −0.789046 | ||||||||
\(746\) | 17.0225 | 0.623238 | ||||||||
\(747\) | 37.8121 | 1.38347 | ||||||||
\(748\) | 5.87725 | 0.214894 | ||||||||
\(749\) | 14.2535 | 0.520810 | ||||||||
\(750\) | −20.8252 | −0.760428 | ||||||||
\(751\) | 53.5990 | 1.95586 | 0.977928 | − | 0.208940i | \(-0.0670015\pi\) | ||||
0.977928 | + | 0.208940i | \(0.0670015\pi\) | |||||||
\(752\) | 9.31636 | 0.339733 | ||||||||
\(753\) | 63.1449 | 2.30113 | ||||||||
\(754\) | 2.96747 | 0.108069 | ||||||||
\(755\) | 20.3316 | 0.739943 | ||||||||
\(756\) | −7.56845 | −0.275262 | ||||||||
\(757\) | −10.2731 | −0.373383 | −0.186692 | − | 0.982419i | \(-0.559777\pi\) | ||||
−0.186692 | + | 0.982419i | \(0.559777\pi\) | |||||||
\(758\) | −24.6026 | −0.893605 | ||||||||
\(759\) | −44.8564 | −1.62819 | ||||||||
\(760\) | −2.71400 | −0.0984471 | ||||||||
\(761\) | −43.8690 | −1.59025 | −0.795125 | − | 0.606445i | \(-0.792595\pi\) | ||||
−0.795125 | + | 0.606445i | \(0.792595\pi\) | |||||||
\(762\) | 14.1429 | 0.512342 | ||||||||
\(763\) | −11.1804 | −0.404757 | ||||||||
\(764\) | −16.2655 | −0.588465 | ||||||||
\(765\) | 45.6804 | 1.65158 | ||||||||
\(766\) | −12.2802 | −0.443702 | ||||||||
\(767\) | −10.7158 | −0.386925 | ||||||||
\(768\) | −2.91293 | −0.105111 | ||||||||
\(769\) | −44.9736 | −1.62179 | −0.810895 | − | 0.585192i | \(-0.801019\pi\) | ||||
−0.810895 | + | 0.585192i | \(0.801019\pi\) | |||||||
\(770\) | −5.43473 | −0.195854 | ||||||||
\(771\) | −7.69088 | −0.276980 | ||||||||
\(772\) | 12.7920 | 0.460395 | ||||||||
\(773\) | −4.49899 | −0.161817 | −0.0809087 | − | 0.996722i | \(-0.525782\pi\) | ||||
−0.0809087 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(774\) | −32.2166 | −1.15800 | ||||||||
\(775\) | −12.8451 | −0.461410 | ||||||||
\(776\) | −9.41240 | −0.337886 | ||||||||
\(777\) | 36.0568 | 1.29353 | ||||||||
\(778\) | 27.5770 | 0.988682 | ||||||||
\(779\) | 3.89041 | 0.139388 | ||||||||
\(780\) | 6.38114 | 0.228481 | ||||||||
\(781\) | −5.42810 | −0.194233 | ||||||||
\(782\) | −24.6709 | −0.882230 | ||||||||
\(783\) | −26.6139 | −0.951104 | ||||||||
\(784\) | −5.90692 | −0.210962 | ||||||||
\(785\) | 33.6462 | 1.20088 | ||||||||
\(786\) | −15.8100 | −0.563926 | ||||||||
\(787\) | 44.2455 | 1.57718 | 0.788591 | − | 0.614919i | \(-0.210811\pi\) | ||||
0.788591 | + | 0.614919i | \(0.210811\pi\) | |||||||
\(788\) | −9.98707 | −0.355775 | ||||||||
\(789\) | −24.6560 | −0.877778 | ||||||||
\(790\) | −34.7134 | −1.23505 | ||||||||
\(791\) | 5.11605 | 0.181906 | ||||||||
\(792\) | −10.5058 | −0.373309 | ||||||||
\(793\) | 3.07728 | 0.109277 | ||||||||
\(794\) | −27.8213 | −0.987340 | ||||||||
\(795\) | −80.0649 | −2.83961 | ||||||||
\(796\) | −9.66190 | −0.342457 | ||||||||
\(797\) | 32.1688 | 1.13948 | 0.569738 | − | 0.821826i | \(-0.307045\pi\) | ||||
0.569738 | + | 0.821826i | \(0.307045\pi\) | |||||||
\(798\) | 3.04548 | 0.107809 | ||||||||
\(799\) | 28.5877 | 1.01136 | ||||||||
\(800\) | −2.36580 | −0.0836435 | ||||||||
\(801\) | 8.97326 | 0.317055 | ||||||||
\(802\) | −18.2204 | −0.643383 | ||||||||
\(803\) | −2.08702 | −0.0736492 | ||||||||
\(804\) | 42.7960 | 1.50930 | ||||||||
\(805\) | 22.8133 | 0.804063 | ||||||||
\(806\) | −4.38247 | −0.154366 | ||||||||
\(807\) | 54.7509 | 1.92732 | ||||||||
\(808\) | −10.8568 | −0.381942 | ||||||||
\(809\) | 51.7237 | 1.81851 | 0.909254 | − | 0.416242i | \(-0.136653\pi\) | ||||
0.909254 | + | 0.416242i | \(0.136653\pi\) | |||||||
\(810\) | −12.5696 | −0.441651 | ||||||||
\(811\) | −34.6043 | −1.21512 | −0.607560 | − | 0.794274i | \(-0.707852\pi\) | ||||
−0.607560 | + | 0.794274i | \(0.707852\pi\) | |||||||
\(812\) | 3.84373 | 0.134888 | ||||||||
\(813\) | −37.3646 | −1.31043 | ||||||||
\(814\) | 22.6764 | 0.794808 | ||||||||
\(815\) | 54.5935 | 1.91233 | ||||||||
\(816\) | −8.93844 | −0.312908 | ||||||||
\(817\) | 5.87343 | 0.205485 | ||||||||
\(818\) | 22.2303 | 0.777264 | ||||||||
\(819\) | −4.62884 | −0.161745 | ||||||||
\(820\) | 10.5586 | 0.368721 | ||||||||
\(821\) | 54.1266 | 1.88903 | 0.944516 | − | 0.328466i | \(-0.106531\pi\) | ||||
0.944516 | + | 0.328466i | \(0.106531\pi\) | |||||||
\(822\) | −1.01756 | −0.0354913 | ||||||||
\(823\) | −10.9317 | −0.381057 | −0.190528 | − | 0.981682i | \(-0.561020\pi\) | ||||
−0.190528 | + | 0.981682i | \(0.561020\pi\) | |||||||
\(824\) | −7.73903 | −0.269602 | ||||||||
\(825\) | −13.1993 | −0.459539 | ||||||||
\(826\) | −13.8801 | −0.482949 | ||||||||
\(827\) | 44.7518 | 1.55617 | 0.778087 | − | 0.628156i | \(-0.216190\pi\) | ||||
0.778087 | + | 0.628156i | \(0.216190\pi\) | |||||||
\(828\) | 44.1003 | 1.53259 | ||||||||
\(829\) | 35.6891 | 1.23954 | 0.619768 | − | 0.784785i | \(-0.287227\pi\) | ||||
0.619768 | + | 0.784785i | \(0.287227\pi\) | |||||||
\(830\) | −18.7091 | −0.649402 | ||||||||
\(831\) | 41.5269 | 1.44055 | ||||||||
\(832\) | −0.807158 | −0.0279832 | ||||||||
\(833\) | −18.1256 | −0.628016 | ||||||||
\(834\) | −11.6197 | −0.402358 | ||||||||
\(835\) | 10.2041 | 0.353128 | ||||||||
\(836\) | 1.91532 | 0.0662429 | ||||||||
\(837\) | 39.3045 | 1.35856 | ||||||||
\(838\) | −15.2647 | −0.527309 | ||||||||
\(839\) | −6.52818 | −0.225378 | −0.112689 | − | 0.993630i | \(-0.535946\pi\) | ||||
−0.112689 | + | 0.993630i | \(0.535946\pi\) | |||||||
\(840\) | 8.26542 | 0.285184 | ||||||||
\(841\) | −15.4838 | −0.533924 | ||||||||
\(842\) | 25.8064 | 0.889348 | ||||||||
\(843\) | −2.49259 | −0.0858495 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −33.5138 | −1.15291 | ||||||||
\(846\) | −51.1016 | −1.75691 | ||||||||
\(847\) | −7.66514 | −0.263377 | ||||||||
\(848\) | 10.1275 | 0.347780 | ||||||||
\(849\) | 32.3244 | 1.10937 | ||||||||
\(850\) | −7.25955 | −0.249000 | ||||||||
\(851\) | −95.1886 | −3.26302 | ||||||||
\(852\) | 8.25535 | 0.282824 | ||||||||
\(853\) | 8.43031 | 0.288648 | 0.144324 | − | 0.989530i | \(-0.453899\pi\) | ||||
0.144324 | + | 0.989530i | \(0.453899\pi\) | |||||||
\(854\) | 3.98597 | 0.136397 | ||||||||
\(855\) | 14.8867 | 0.509114 | ||||||||
\(856\) | −13.6331 | −0.465970 | ||||||||
\(857\) | −1.19404 | −0.0407875 | −0.0203937 | − | 0.999792i | \(-0.506492\pi\) | ||||
−0.0203937 | + | 0.999792i | \(0.506492\pi\) | |||||||
\(858\) | −4.50330 | −0.153740 | ||||||||
\(859\) | −3.24234 | −0.110627 | −0.0553136 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553136 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(860\) | 15.9405 | 0.543566 | ||||||||
\(861\) | −11.8482 | −0.403784 | ||||||||
\(862\) | −36.2604 | −1.23503 | ||||||||
\(863\) | −41.2472 | −1.40407 | −0.702036 | − | 0.712141i | \(-0.747725\pi\) | ||||
−0.702036 | + | 0.712141i | \(0.747725\pi\) | |||||||
\(864\) | 7.23905 | 0.246278 | ||||||||
\(865\) | −58.7059 | −1.99606 | ||||||||
\(866\) | −18.0964 | −0.614940 | ||||||||
\(867\) | 22.0918 | 0.750276 | ||||||||
\(868\) | −5.67657 | −0.192675 | ||||||||
\(869\) | 24.4980 | 0.831036 | ||||||||
\(870\) | 29.0648 | 0.985388 | ||||||||
\(871\) | 11.8586 | 0.401812 | ||||||||
\(872\) | 10.6938 | 0.362137 | ||||||||
\(873\) | 51.6284 | 1.74736 | ||||||||
\(874\) | −8.03994 | −0.271955 | ||||||||
\(875\) | −7.47454 | −0.252686 | ||||||||
\(876\) | 3.17405 | 0.107241 | ||||||||
\(877\) | 30.9878 | 1.04639 | 0.523193 | − | 0.852215i | \(-0.324741\pi\) | ||||
0.523193 | + | 0.852215i | \(0.324741\pi\) | |||||||
\(878\) | −3.80676 | −0.128472 | ||||||||
\(879\) | −70.6371 | −2.38253 | ||||||||
\(880\) | 5.19819 | 0.175231 | ||||||||
\(881\) | −6.68498 | −0.225223 | −0.112611 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112611 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(882\) | 32.4003 | 1.09098 | ||||||||
\(883\) | −26.4231 | −0.889208 | −0.444604 | − | 0.895727i | \(-0.646656\pi\) | ||||
−0.444604 | + | 0.895727i | \(0.646656\pi\) | |||||||
\(884\) | −2.47680 | −0.0833037 | ||||||||
\(885\) | −104.956 | −3.52804 | ||||||||
\(886\) | 18.8706 | 0.633971 | ||||||||
\(887\) | 50.2495 | 1.68721 | 0.843606 | − | 0.536963i | \(-0.180428\pi\) | ||||
0.843606 | + | 0.536963i | \(0.180428\pi\) | |||||||
\(888\) | −34.4875 | −1.15732 | ||||||||
\(889\) | 5.07614 | 0.170248 | ||||||||
\(890\) | −4.43989 | −0.148825 | ||||||||
\(891\) | 8.87062 | 0.297177 | ||||||||
\(892\) | −8.77064 | −0.293663 | ||||||||
\(893\) | 9.31636 | 0.311760 | ||||||||
\(894\) | −23.1153 | −0.773092 | ||||||||
\(895\) | −7.99445 | −0.267225 | ||||||||
\(896\) | −1.04550 | −0.0349278 | ||||||||
\(897\) | 18.9035 | 0.631168 | ||||||||
\(898\) | −14.4551 | −0.482372 | ||||||||
\(899\) | −19.9612 | −0.665745 | ||||||||
\(900\) | 12.9767 | 0.432558 | ||||||||
\(901\) | 31.0767 | 1.03532 | ||||||||
\(902\) | −7.45140 | −0.248104 | ||||||||
\(903\) | −17.8874 | −0.595255 | ||||||||
\(904\) | −4.89338 | −0.162751 | ||||||||
\(905\) | 2.96469 | 0.0985498 | ||||||||
\(906\) | 21.8218 | 0.724982 | ||||||||
\(907\) | −12.2095 | −0.405410 | −0.202705 | − | 0.979240i | \(-0.564973\pi\) | ||||
−0.202705 | + | 0.979240i | \(0.564973\pi\) | |||||||
\(908\) | −6.98855 | −0.231923 | ||||||||
\(909\) | 59.5513 | 1.97519 | ||||||||
\(910\) | 2.29031 | 0.0759230 | ||||||||
\(911\) | −6.16492 | −0.204253 | −0.102126 | − | 0.994771i | \(-0.532565\pi\) | ||||
−0.102126 | + | 0.994771i | \(0.532565\pi\) | |||||||
\(912\) | −2.91293 | −0.0964567 | ||||||||
\(913\) | 13.2034 | 0.436968 | ||||||||
\(914\) | −15.1590 | −0.501415 | ||||||||
\(915\) | 30.1403 | 0.996409 | ||||||||
\(916\) | 4.73353 | 0.156400 | ||||||||
\(917\) | −5.67452 | −0.187389 | ||||||||
\(918\) | 22.2133 | 0.733149 | ||||||||
\(919\) | −51.1872 | −1.68851 | −0.844255 | − | 0.535941i | \(-0.819957\pi\) | ||||
−0.844255 | + | 0.535941i | \(0.819957\pi\) | |||||||
\(920\) | −21.8204 | −0.719397 | ||||||||
\(921\) | 25.2331 | 0.831460 | ||||||||
\(922\) | 14.1974 | 0.467567 | ||||||||
\(923\) | 2.28752 | 0.0752945 | ||||||||
\(924\) | −5.83307 | −0.191894 | ||||||||
\(925\) | −28.0098 | −0.920955 | ||||||||
\(926\) | −28.5735 | −0.938983 | ||||||||
\(927\) | 42.4497 | 1.39423 | ||||||||
\(928\) | −3.67644 | −0.120685 | ||||||||
\(929\) | 0.900308 | 0.0295381 | 0.0147691 | − | 0.999891i | \(-0.495299\pi\) | ||||
0.0147691 | + | 0.999891i | \(0.495299\pi\) | |||||||
\(930\) | −42.9240 | −1.40753 | ||||||||
\(931\) | −5.90692 | −0.193592 | ||||||||
\(932\) | 13.4203 | 0.439598 | ||||||||
\(933\) | 30.8610 | 1.01034 | ||||||||
\(934\) | −34.8486 | −1.14028 | ||||||||
\(935\) | 15.9509 | 0.521649 | ||||||||
\(936\) | 4.42738 | 0.144713 | ||||||||
\(937\) | 57.8114 | 1.88861 | 0.944307 | − | 0.329065i | \(-0.106733\pi\) | ||||
0.944307 | + | 0.329065i | \(0.106733\pi\) | |||||||
\(938\) | 15.3603 | 0.501530 | ||||||||
\(939\) | 21.8614 | 0.713420 | ||||||||
\(940\) | 25.2846 | 0.824693 | ||||||||
\(941\) | −47.3129 | −1.54236 | −0.771179 | − | 0.636619i | \(-0.780333\pi\) | ||||
−0.771179 | + | 0.636619i | \(0.780333\pi\) | |||||||
\(942\) | 36.1123 | 1.17660 | ||||||||
\(943\) | 31.2787 | 1.01857 | ||||||||
\(944\) | 13.2760 | 0.432096 | ||||||||
\(945\) | −20.5408 | −0.668192 | ||||||||
\(946\) | −11.2495 | −0.365754 | ||||||||
\(947\) | −13.5857 | −0.441477 | −0.220738 | − | 0.975333i | \(-0.570847\pi\) | ||||
−0.220738 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(948\) | −37.2578 | −1.21008 | ||||||||
\(949\) | 0.879513 | 0.0285502 | ||||||||
\(950\) | −2.36580 | −0.0767566 | ||||||||
\(951\) | 30.3153 | 0.983042 | ||||||||
\(952\) | −3.20817 | −0.103977 | ||||||||
\(953\) | 18.3927 | 0.595798 | 0.297899 | − | 0.954597i | \(-0.403714\pi\) | ||||
0.297899 | + | 0.954597i | \(0.403714\pi\) | |||||||
\(954\) | −55.5509 | −1.79853 | ||||||||
\(955\) | −44.1445 | −1.42848 | ||||||||
\(956\) | −9.27553 | −0.299992 | ||||||||
\(957\) | −20.5116 | −0.663046 | ||||||||
\(958\) | −29.9247 | −0.966824 | ||||||||
\(959\) | −0.365219 | −0.0117936 | ||||||||
\(960\) | −7.90569 | −0.255155 | ||||||||
\(961\) | −1.52046 | −0.0490472 | ||||||||
\(962\) | −9.55632 | −0.308108 | ||||||||
\(963\) | 74.7796 | 2.40974 | ||||||||
\(964\) | −7.87195 | −0.253538 | ||||||||
\(965\) | 34.7176 | 1.11760 | ||||||||
\(966\) | 24.4854 | 0.787806 | ||||||||
\(967\) | −4.34796 | −0.139821 | −0.0699105 | − | 0.997553i | \(-0.522271\pi\) | ||||
−0.0699105 | + | 0.997553i | \(0.522271\pi\) | |||||||
\(968\) | 7.33153 | 0.235644 | ||||||||
\(969\) | −8.93844 | −0.287144 | ||||||||
\(970\) | −25.5453 | −0.820209 | ||||||||
\(971\) | −54.2533 | −1.74107 | −0.870535 | − | 0.492106i | \(-0.836227\pi\) | ||||
−0.870535 | + | 0.492106i | \(0.836227\pi\) | |||||||
\(972\) | 8.22624 | 0.263857 | ||||||||
\(973\) | −4.17053 | −0.133701 | ||||||||
\(974\) | 15.1429 | 0.485211 | ||||||||
\(975\) | 5.56244 | 0.178141 | ||||||||
\(976\) | −3.81249 | −0.122035 | ||||||||
\(977\) | −24.2978 | −0.777356 | −0.388678 | − | 0.921374i | \(-0.627068\pi\) | ||||
−0.388678 | + | 0.921374i | \(0.627068\pi\) | |||||||
\(978\) | 58.5950 | 1.87366 | ||||||||
\(979\) | 3.13332 | 0.100141 | ||||||||
\(980\) | −16.0314 | −0.512104 | ||||||||
\(981\) | −58.6569 | −1.87277 | ||||||||
\(982\) | 22.6136 | 0.721628 | ||||||||
\(983\) | 41.2528 | 1.31576 | 0.657880 | − | 0.753123i | \(-0.271453\pi\) | ||||
0.657880 | + | 0.753123i | \(0.271453\pi\) | |||||||
\(984\) | 11.3325 | 0.361266 | ||||||||
\(985\) | −27.1049 | −0.863634 | ||||||||
\(986\) | −11.2813 | −0.359270 | ||||||||
\(987\) | −28.3728 | −0.903115 | ||||||||
\(988\) | −0.807158 | −0.0256791 | ||||||||
\(989\) | 47.2221 | 1.50157 | ||||||||
\(990\) | −28.5128 | −0.906197 | ||||||||
\(991\) | 7.73665 | 0.245763 | 0.122881 | − | 0.992421i | \(-0.460787\pi\) | ||||
0.122881 | + | 0.992421i | \(0.460787\pi\) | |||||||
\(992\) | 5.42951 | 0.172387 | ||||||||
\(993\) | 12.9363 | 0.410520 | ||||||||
\(994\) | 2.96300 | 0.0939806 | ||||||||
\(995\) | −26.2224 | −0.831306 | ||||||||
\(996\) | −20.0804 | −0.636272 | ||||||||
\(997\) | −5.75421 | −0.182238 | −0.0911188 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911188 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(998\) | 15.5567 | 0.492438 | ||||||||
\(999\) | 85.7065 | 2.71163 |
(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 | 8018.2.a.i.1.3 | ✓ | 43 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.i.1.3 | ✓ | 43 | 1.1 | even | 1 | trivial |