Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.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: | \(32.1078466528\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38084 | −1.68350 | −0.841752 | − | 0.539864i | \(-0.818476\pi\) | ||||
−0.841752 | + | 0.539864i | \(0.818476\pi\) | |||||||
\(3\) | 2.66837 | 1.54058 | 0.770291 | − | 0.637692i | \(-0.220111\pi\) | ||||
0.770291 | + | 0.637692i | \(0.220111\pi\) | |||||||
\(4\) | 3.66838 | 1.83419 | ||||||||
\(5\) | −4.16670 | −1.86341 | −0.931703 | − | 0.363221i | \(-0.881677\pi\) | ||||
−0.931703 | + | 0.363221i | \(0.881677\pi\) | |||||||
\(6\) | −6.35294 | −2.59358 | ||||||||
\(7\) | 0.560262 | 0.211759 | 0.105879 | − | 0.994379i | \(-0.466234\pi\) | ||||
0.105879 | + | 0.994379i | \(0.466234\pi\) | |||||||
\(8\) | −3.97213 | −1.40436 | ||||||||
\(9\) | 4.12018 | 1.37339 | ||||||||
\(10\) | 9.92023 | 3.13705 | ||||||||
\(11\) | −1.82936 | −0.551574 | −0.275787 | − | 0.961219i | \(-0.588938\pi\) | ||||
−0.275787 | + | 0.961219i | \(0.588938\pi\) | |||||||
\(12\) | 9.78858 | 2.82572 | ||||||||
\(13\) | 1.30969 | 0.363243 | 0.181622 | − | 0.983369i | \(-0.441865\pi\) | ||||
0.181622 | + | 0.983369i | \(0.441865\pi\) | |||||||
\(14\) | −1.33389 | −0.356497 | ||||||||
\(15\) | −11.1183 | −2.87073 | ||||||||
\(16\) | 2.12024 | 0.530059 | ||||||||
\(17\) | −4.02107 | −0.975254 | −0.487627 | − | 0.873052i | \(-0.662137\pi\) | ||||
−0.487627 | + | 0.873052i | \(0.662137\pi\) | |||||||
\(18\) | −9.80948 | −2.31212 | ||||||||
\(19\) | 5.81746 | 1.33462 | 0.667308 | − | 0.744781i | \(-0.267446\pi\) | ||||
0.667308 | + | 0.744781i | \(0.267446\pi\) | |||||||
\(20\) | −15.2850 | −3.41784 | ||||||||
\(21\) | 1.49498 | 0.326232 | ||||||||
\(22\) | 4.35541 | 0.928577 | ||||||||
\(23\) | −5.24785 | −1.09425 | −0.547126 | − | 0.837050i | \(-0.684278\pi\) | ||||
−0.547126 | + | 0.837050i | \(0.684278\pi\) | |||||||
\(24\) | −10.5991 | −2.16353 | ||||||||
\(25\) | 12.3614 | 2.47228 | ||||||||
\(26\) | −3.11816 | −0.611521 | ||||||||
\(27\) | 2.98906 | 0.575246 | ||||||||
\(28\) | 2.05525 | 0.388406 | ||||||||
\(29\) | 3.27096 | 0.607402 | 0.303701 | − | 0.952767i | \(-0.401778\pi\) | ||||
0.303701 | + | 0.952767i | \(0.401778\pi\) | |||||||
\(30\) | 26.4708 | 4.83289 | ||||||||
\(31\) | 2.14223 | 0.384756 | 0.192378 | − | 0.981321i | \(-0.438380\pi\) | ||||
0.192378 | + | 0.981321i | \(0.438380\pi\) | |||||||
\(32\) | 2.89633 | 0.512003 | ||||||||
\(33\) | −4.88141 | −0.849745 | ||||||||
\(34\) | 9.57351 | 1.64184 | ||||||||
\(35\) | −2.33444 | −0.394593 | ||||||||
\(36\) | 15.1144 | 2.51907 | ||||||||
\(37\) | 2.43535 | 0.400369 | 0.200184 | − | 0.979758i | \(-0.435846\pi\) | ||||
0.200184 | + | 0.979758i | \(0.435846\pi\) | |||||||
\(38\) | −13.8504 | −2.24683 | ||||||||
\(39\) | 3.49474 | 0.559606 | ||||||||
\(40\) | 16.5507 | 2.61689 | ||||||||
\(41\) | −4.46905 | −0.697948 | −0.348974 | − | 0.937132i | \(-0.613470\pi\) | ||||
−0.348974 | + | 0.937132i | \(0.613470\pi\) | |||||||
\(42\) | −3.55931 | −0.549213 | ||||||||
\(43\) | 1.06332 | 0.162154 | 0.0810772 | − | 0.996708i | \(-0.474164\pi\) | ||||
0.0810772 | + | 0.996708i | \(0.474164\pi\) | |||||||
\(44\) | −6.71079 | −1.01169 | ||||||||
\(45\) | −17.1676 | −2.55919 | ||||||||
\(46\) | 12.4943 | 1.84218 | ||||||||
\(47\) | 8.35299 | 1.21841 | 0.609205 | − | 0.793013i | \(-0.291489\pi\) | ||||
0.609205 | + | 0.793013i | \(0.291489\pi\) | |||||||
\(48\) | 5.65757 | 0.816600 | ||||||||
\(49\) | −6.68611 | −0.955158 | ||||||||
\(50\) | −29.4305 | −4.16210 | ||||||||
\(51\) | −10.7297 | −1.50246 | ||||||||
\(52\) | 4.80444 | 0.666256 | ||||||||
\(53\) | −0.265567 | −0.0364784 | −0.0182392 | − | 0.999834i | \(-0.505806\pi\) | ||||
−0.0182392 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(54\) | −7.11647 | −0.968429 | ||||||||
\(55\) | 7.62241 | 1.02781 | ||||||||
\(56\) | −2.22543 | −0.297386 | ||||||||
\(57\) | 15.5231 | 2.05609 | ||||||||
\(58\) | −7.78761 | −1.02256 | ||||||||
\(59\) | −10.8592 | −1.41375 | −0.706875 | − | 0.707338i | \(-0.749896\pi\) | ||||
−0.706875 | + | 0.707338i | \(0.749896\pi\) | |||||||
\(60\) | −40.7861 | −5.26546 | ||||||||
\(61\) | −0.768975 | −0.0984571 | −0.0492286 | − | 0.998788i | \(-0.515676\pi\) | ||||
−0.0492286 | + | 0.998788i | \(0.515676\pi\) | |||||||
\(62\) | −5.10030 | −0.647739 | ||||||||
\(63\) | 2.30838 | 0.290829 | ||||||||
\(64\) | −11.1362 | −1.39202 | ||||||||
\(65\) | −5.45709 | −0.676869 | ||||||||
\(66\) | 11.6218 | 1.43055 | ||||||||
\(67\) | −3.01625 | −0.368493 | −0.184247 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184247 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(68\) | −14.7508 | −1.78880 | ||||||||
\(69\) | −14.0032 | −1.68579 | ||||||||
\(70\) | 5.55792 | 0.664299 | ||||||||
\(71\) | 9.16272 | 1.08741 | 0.543707 | − | 0.839275i | \(-0.317020\pi\) | ||||
0.543707 | + | 0.839275i | \(0.317020\pi\) | |||||||
\(72\) | −16.3659 | −1.92874 | ||||||||
\(73\) | −6.34436 | −0.742551 | −0.371275 | − | 0.928523i | \(-0.621079\pi\) | ||||
−0.371275 | + | 0.928523i | \(0.621079\pi\) | |||||||
\(74\) | −5.79817 | −0.674023 | ||||||||
\(75\) | 32.9848 | 3.80875 | ||||||||
\(76\) | 21.3406 | 2.44794 | ||||||||
\(77\) | −1.02492 | −0.116801 | ||||||||
\(78\) | −8.32039 | −0.942099 | ||||||||
\(79\) | −10.4576 | −1.17657 | −0.588284 | − | 0.808654i | \(-0.700196\pi\) | ||||
−0.588284 | + | 0.808654i | \(0.700196\pi\) | |||||||
\(80\) | −8.83440 | −0.987715 | ||||||||
\(81\) | −4.38463 | −0.487182 | ||||||||
\(82\) | 10.6401 | 1.17500 | ||||||||
\(83\) | 3.79116 | 0.416134 | 0.208067 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208067 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(84\) | 5.48416 | 0.598371 | ||||||||
\(85\) | 16.7546 | 1.81729 | ||||||||
\(86\) | −2.53158 | −0.272988 | ||||||||
\(87\) | 8.72812 | 0.935752 | ||||||||
\(88\) | 7.26647 | 0.774608 | ||||||||
\(89\) | 9.92127 | 1.05165 | 0.525826 | − | 0.850592i | \(-0.323756\pi\) | ||||
0.525826 | + | 0.850592i | \(0.323756\pi\) | |||||||
\(90\) | 40.8732 | 4.30841 | ||||||||
\(91\) | 0.733770 | 0.0769200 | ||||||||
\(92\) | −19.2511 | −2.00706 | ||||||||
\(93\) | 5.71626 | 0.592749 | ||||||||
\(94\) | −19.8871 | −2.05120 | ||||||||
\(95\) | −24.2396 | −2.48693 | ||||||||
\(96\) | 7.72847 | 0.788783 | ||||||||
\(97\) | 0.579578 | 0.0588472 | 0.0294236 | − | 0.999567i | \(-0.490633\pi\) | ||||
0.0294236 | + | 0.999567i | \(0.490633\pi\) | |||||||
\(98\) | 15.9185 | 1.60801 | ||||||||
\(99\) | −7.53731 | −0.757528 | ||||||||
\(100\) | 45.3463 | 4.53463 | ||||||||
\(101\) | 6.41810 | 0.638625 | 0.319312 | − | 0.947650i | \(-0.396548\pi\) | ||||
0.319312 | + | 0.947650i | \(0.396548\pi\) | |||||||
\(102\) | 25.5457 | 2.52940 | ||||||||
\(103\) | −0.374609 | −0.0369114 | −0.0184557 | − | 0.999830i | \(-0.505875\pi\) | ||||
−0.0184557 | + | 0.999830i | \(0.505875\pi\) | |||||||
\(104\) | −5.20227 | −0.510124 | ||||||||
\(105\) | −6.22915 | −0.607903 | ||||||||
\(106\) | 0.632271 | 0.0614115 | ||||||||
\(107\) | −6.37575 | −0.616367 | −0.308184 | − | 0.951327i | \(-0.599721\pi\) | ||||
−0.308184 | + | 0.951327i | \(0.599721\pi\) | |||||||
\(108\) | 10.9650 | 1.05511 | ||||||||
\(109\) | 4.75260 | 0.455216 | 0.227608 | − | 0.973753i | \(-0.426910\pi\) | ||||
0.227608 | + | 0.973753i | \(0.426910\pi\) | |||||||
\(110\) | −18.1477 | −1.73032 | ||||||||
\(111\) | 6.49841 | 0.616801 | ||||||||
\(112\) | 1.18789 | 0.112245 | ||||||||
\(113\) | 9.30981 | 0.875794 | 0.437897 | − | 0.899025i | \(-0.355724\pi\) | ||||
0.437897 | + | 0.899025i | \(0.355724\pi\) | |||||||
\(114\) | −36.9580 | −3.46143 | ||||||||
\(115\) | 21.8662 | 2.03904 | ||||||||
\(116\) | 11.9991 | 1.11409 | ||||||||
\(117\) | 5.39617 | 0.498876 | ||||||||
\(118\) | 25.8540 | 2.38006 | ||||||||
\(119\) | −2.25285 | −0.206519 | ||||||||
\(120\) | 44.1633 | 4.03154 | ||||||||
\(121\) | −7.65343 | −0.695766 | ||||||||
\(122\) | 1.83080 | 0.165753 | ||||||||
\(123\) | −11.9251 | −1.07525 | ||||||||
\(124\) | 7.85852 | 0.705716 | ||||||||
\(125\) | −30.6728 | −2.74346 | ||||||||
\(126\) | −5.49587 | −0.489611 | ||||||||
\(127\) | −18.9546 | −1.68195 | −0.840973 | − | 0.541077i | \(-0.818017\pi\) | ||||
−0.840973 | + | 0.541077i | \(0.818017\pi\) | |||||||
\(128\) | 20.7207 | 1.83147 | ||||||||
\(129\) | 2.83732 | 0.249812 | ||||||||
\(130\) | 12.9924 | 1.13951 | ||||||||
\(131\) | −12.6620 | −1.10628 | −0.553141 | − | 0.833088i | \(-0.686571\pi\) | ||||
−0.553141 | + | 0.833088i | \(0.686571\pi\) | |||||||
\(132\) | −17.9069 | −1.55859 | ||||||||
\(133\) | 3.25930 | 0.282617 | ||||||||
\(134\) | 7.18118 | 0.620360 | ||||||||
\(135\) | −12.4545 | −1.07192 | ||||||||
\(136\) | 15.9722 | 1.36961 | ||||||||
\(137\) | −8.16415 | −0.697510 | −0.348755 | − | 0.937214i | \(-0.613395\pi\) | ||||
−0.348755 | + | 0.937214i | \(0.613395\pi\) | |||||||
\(138\) | 33.3393 | 2.83803 | ||||||||
\(139\) | −15.2059 | −1.28974 | −0.644872 | − | 0.764291i | \(-0.723089\pi\) | ||||
−0.644872 | + | 0.764291i | \(0.723089\pi\) | |||||||
\(140\) | −8.56362 | −0.723758 | ||||||||
\(141\) | 22.2889 | 1.87706 | ||||||||
\(142\) | −21.8149 | −1.83067 | ||||||||
\(143\) | −2.39590 | −0.200355 | ||||||||
\(144\) | 8.73577 | 0.727980 | ||||||||
\(145\) | −13.6291 | −1.13184 | ||||||||
\(146\) | 15.1049 | 1.25009 | ||||||||
\(147\) | −17.8410 | −1.47150 | ||||||||
\(148\) | 8.93378 | 0.734352 | ||||||||
\(149\) | 0.612543 | 0.0501815 | 0.0250907 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250907 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(150\) | −78.5313 | −6.41206 | ||||||||
\(151\) | −18.2245 | −1.48309 | −0.741544 | − | 0.670904i | \(-0.765906\pi\) | ||||
−0.741544 | + | 0.670904i | \(0.765906\pi\) | |||||||
\(152\) | −23.1077 | −1.87428 | ||||||||
\(153\) | −16.5676 | −1.33941 | ||||||||
\(154\) | 2.44017 | 0.196635 | ||||||||
\(155\) | −8.92605 | −0.716957 | ||||||||
\(156\) | 12.8200 | 1.02642 | ||||||||
\(157\) | −9.04275 | −0.721690 | −0.360845 | − | 0.932626i | \(-0.617512\pi\) | ||||
−0.360845 | + | 0.932626i | \(0.617512\pi\) | |||||||
\(158\) | 24.8977 | 1.98076 | ||||||||
\(159\) | −0.708629 | −0.0561980 | ||||||||
\(160\) | −12.0681 | −0.954070 | ||||||||
\(161\) | −2.94017 | −0.231718 | ||||||||
\(162\) | 10.4391 | 0.820172 | ||||||||
\(163\) | −2.49413 | −0.195356 | −0.0976779 | − | 0.995218i | \(-0.531141\pi\) | ||||
−0.0976779 | + | 0.995218i | \(0.531141\pi\) | |||||||
\(164\) | −16.3942 | −1.28017 | ||||||||
\(165\) | 20.3394 | 1.58342 | ||||||||
\(166\) | −9.02613 | −0.700564 | ||||||||
\(167\) | 11.6705 | 0.903093 | 0.451546 | − | 0.892248i | \(-0.350873\pi\) | ||||
0.451546 | + | 0.892248i | \(0.350873\pi\) | |||||||
\(168\) | −5.93827 | −0.458148 | ||||||||
\(169\) | −11.2847 | −0.868055 | ||||||||
\(170\) | −39.8900 | −3.05942 | ||||||||
\(171\) | 23.9690 | 1.83296 | ||||||||
\(172\) | 3.90065 | 0.297422 | ||||||||
\(173\) | −24.1908 | −1.83919 | −0.919596 | − | 0.392865i | \(-0.871484\pi\) | ||||
−0.919596 | + | 0.392865i | \(0.871484\pi\) | |||||||
\(174\) | −20.7802 | −1.57534 | ||||||||
\(175\) | 6.92562 | 0.523528 | ||||||||
\(176\) | −3.87868 | −0.292367 | ||||||||
\(177\) | −28.9764 | −2.17800 | ||||||||
\(178\) | −23.6209 | −1.77046 | ||||||||
\(179\) | 9.08790 | 0.679262 | 0.339631 | − | 0.940559i | \(-0.389698\pi\) | ||||
0.339631 | + | 0.940559i | \(0.389698\pi\) | |||||||
\(180\) | −62.9772 | −4.69404 | ||||||||
\(181\) | 18.4354 | 1.37029 | 0.685145 | − | 0.728407i | \(-0.259739\pi\) | ||||
0.685145 | + | 0.728407i | \(0.259739\pi\) | |||||||
\(182\) | −1.74698 | −0.129495 | ||||||||
\(183\) | −2.05191 | −0.151681 | ||||||||
\(184\) | 20.8451 | 1.53672 | ||||||||
\(185\) | −10.1474 | −0.746050 | ||||||||
\(186\) | −13.6095 | −0.997896 | ||||||||
\(187\) | 7.35600 | 0.537924 | ||||||||
\(188\) | 30.6419 | 2.23479 | ||||||||
\(189\) | 1.67466 | 0.121813 | ||||||||
\(190\) | 57.7106 | 4.18676 | ||||||||
\(191\) | 1.25751 | 0.0909900 | 0.0454950 | − | 0.998965i | \(-0.485513\pi\) | ||||
0.0454950 | + | 0.998965i | \(0.485513\pi\) | |||||||
\(192\) | −29.7154 | −2.14452 | ||||||||
\(193\) | −6.05436 | −0.435802 | −0.217901 | − | 0.975971i | \(-0.569921\pi\) | ||||
−0.217901 | + | 0.975971i | \(0.569921\pi\) | |||||||
\(194\) | −1.37988 | −0.0990695 | ||||||||
\(195\) | −14.5615 | −1.04277 | ||||||||
\(196\) | −24.5272 | −1.75194 | ||||||||
\(197\) | 20.5739 | 1.46583 | 0.732915 | − | 0.680320i | \(-0.238159\pi\) | ||||
0.732915 | + | 0.680320i | \(0.238159\pi\) | |||||||
\(198\) | 17.9451 | 1.27530 | ||||||||
\(199\) | −13.8188 | −0.979591 | −0.489795 | − | 0.871837i | \(-0.662928\pi\) | ||||
−0.489795 | + | 0.871837i | \(0.662928\pi\) | |||||||
\(200\) | −49.1011 | −3.47197 | ||||||||
\(201\) | −8.04845 | −0.567694 | ||||||||
\(202\) | −15.2804 | −1.07513 | ||||||||
\(203\) | 1.83259 | 0.128623 | ||||||||
\(204\) | −39.3606 | −2.75579 | ||||||||
\(205\) | 18.6212 | 1.30056 | ||||||||
\(206\) | 0.891883 | 0.0621404 | ||||||||
\(207\) | −21.6221 | −1.50284 | ||||||||
\(208\) | 2.77686 | 0.192540 | ||||||||
\(209\) | −10.6422 | −0.736140 | ||||||||
\(210\) | 14.8306 | 1.02341 | ||||||||
\(211\) | −12.0222 | −0.827645 | −0.413823 | − | 0.910358i | \(-0.635807\pi\) | ||||
−0.413823 | + | 0.910358i | \(0.635807\pi\) | |||||||
\(212\) | −0.974199 | −0.0669082 | ||||||||
\(213\) | 24.4495 | 1.67525 | ||||||||
\(214\) | 15.1796 | 1.03766 | ||||||||
\(215\) | −4.43053 | −0.302160 | ||||||||
\(216\) | −11.8730 | −0.807852 | ||||||||
\(217\) | 1.20021 | 0.0814756 | ||||||||
\(218\) | −11.3151 | −0.766359 | ||||||||
\(219\) | −16.9291 | −1.14396 | ||||||||
\(220\) | 27.9619 | 1.88519 | ||||||||
\(221\) | −5.26636 | −0.354254 | ||||||||
\(222\) | −15.4716 | −1.03839 | ||||||||
\(223\) | 24.7176 | 1.65521 | 0.827606 | − | 0.561309i | \(-0.189702\pi\) | ||||
0.827606 | + | 0.561309i | \(0.189702\pi\) | |||||||
\(224\) | 1.62270 | 0.108421 | ||||||||
\(225\) | 50.9313 | 3.39542 | ||||||||
\(226\) | −22.1651 | −1.47440 | ||||||||
\(227\) | −24.0240 | −1.59453 | −0.797266 | − | 0.603629i | \(-0.793721\pi\) | ||||
−0.797266 | + | 0.603629i | \(0.793721\pi\) | |||||||
\(228\) | 56.9447 | 3.77125 | ||||||||
\(229\) | −21.7159 | −1.43503 | −0.717514 | − | 0.696544i | \(-0.754720\pi\) | ||||
−0.717514 | + | 0.696544i | \(0.754720\pi\) | |||||||
\(230\) | −52.0599 | −3.43273 | ||||||||
\(231\) | −2.73487 | −0.179941 | ||||||||
\(232\) | −12.9927 | −0.853011 | ||||||||
\(233\) | 9.74286 | 0.638276 | 0.319138 | − | 0.947708i | \(-0.396607\pi\) | ||||
0.319138 | + | 0.947708i | \(0.396607\pi\) | |||||||
\(234\) | −12.8474 | −0.839860 | ||||||||
\(235\) | −34.8044 | −2.27039 | ||||||||
\(236\) | −39.8357 | −2.59308 | ||||||||
\(237\) | −27.9046 | −1.81260 | ||||||||
\(238\) | 5.36367 | 0.347675 | ||||||||
\(239\) | −12.8171 | −0.829068 | −0.414534 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414534 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(240\) | −23.5734 | −1.52166 | ||||||||
\(241\) | −12.3571 | −0.795988 | −0.397994 | − | 0.917388i | \(-0.630293\pi\) | ||||
−0.397994 | + | 0.917388i | \(0.630293\pi\) | |||||||
\(242\) | 18.2216 | 1.17133 | ||||||||
\(243\) | −20.6670 | −1.32579 | ||||||||
\(244\) | −2.82089 | −0.180589 | ||||||||
\(245\) | 27.8590 | 1.77985 | ||||||||
\(246\) | 28.3916 | 1.81018 | ||||||||
\(247\) | 7.61908 | 0.484790 | ||||||||
\(248\) | −8.50923 | −0.540337 | ||||||||
\(249\) | 10.1162 | 0.641089 | ||||||||
\(250\) | 73.0269 | 4.61863 | ||||||||
\(251\) | 16.8649 | 1.06450 | 0.532252 | − | 0.846586i | \(-0.321346\pi\) | ||||
0.532252 | + | 0.846586i | \(0.321346\pi\) | |||||||
\(252\) | 8.46801 | 0.533435 | ||||||||
\(253\) | 9.60022 | 0.603561 | ||||||||
\(254\) | 45.1277 | 2.83156 | ||||||||
\(255\) | 44.7075 | 2.79969 | ||||||||
\(256\) | −27.0603 | −1.69127 | ||||||||
\(257\) | −3.47728 | −0.216907 | −0.108453 | − | 0.994102i | \(-0.534590\pi\) | ||||
−0.108453 | + | 0.994102i | \(0.534590\pi\) | |||||||
\(258\) | −6.75520 | −0.420560 | ||||||||
\(259\) | 1.36443 | 0.0847817 | ||||||||
\(260\) | −20.0187 | −1.24151 | ||||||||
\(261\) | 13.4769 | 0.834202 | ||||||||
\(262\) | 30.1461 | 1.86243 | ||||||||
\(263\) | −23.8585 | −1.47118 | −0.735590 | − | 0.677427i | \(-0.763095\pi\) | ||||
−0.735590 | + | 0.677427i | \(0.763095\pi\) | |||||||
\(264\) | 19.3896 | 1.19335 | ||||||||
\(265\) | 1.10654 | 0.0679740 | ||||||||
\(266\) | −7.75986 | −0.475787 | ||||||||
\(267\) | 26.4736 | 1.62016 | ||||||||
\(268\) | −11.0647 | −0.675886 | ||||||||
\(269\) | −29.1615 | −1.77801 | −0.889005 | − | 0.457898i | \(-0.848603\pi\) | ||||
−0.889005 | + | 0.457898i | \(0.848603\pi\) | |||||||
\(270\) | 29.6522 | 1.80458 | ||||||||
\(271\) | 6.14253 | 0.373132 | 0.186566 | − | 0.982442i | \(-0.440264\pi\) | ||||
0.186566 | + | 0.982442i | \(0.440264\pi\) | |||||||
\(272\) | −8.52563 | −0.516942 | ||||||||
\(273\) | 1.95797 | 0.118502 | ||||||||
\(274\) | 19.4375 | 1.17426 | ||||||||
\(275\) | −22.6135 | −1.36365 | ||||||||
\(276\) | −51.3690 | −3.09205 | ||||||||
\(277\) | 24.7645 | 1.48796 | 0.743979 | − | 0.668204i | \(-0.232936\pi\) | ||||
0.743979 | + | 0.668204i | \(0.232936\pi\) | |||||||
\(278\) | 36.2026 | 2.17129 | ||||||||
\(279\) | 8.82640 | 0.528422 | ||||||||
\(280\) | 9.27272 | 0.554151 | ||||||||
\(281\) | 30.0022 | 1.78978 | 0.894890 | − | 0.446286i | \(-0.147254\pi\) | ||||
0.894890 | + | 0.446286i | \(0.147254\pi\) | |||||||
\(282\) | −53.0661 | −3.16004 | ||||||||
\(283\) | −7.65221 | −0.454877 | −0.227438 | − | 0.973792i | \(-0.573035\pi\) | ||||
−0.227438 | + | 0.973792i | \(0.573035\pi\) | |||||||
\(284\) | 33.6123 | 1.99452 | ||||||||
\(285\) | −64.6802 | −3.83133 | ||||||||
\(286\) | 5.70425 | 0.337299 | ||||||||
\(287\) | −2.50384 | −0.147797 | ||||||||
\(288\) | 11.9334 | 0.703183 | ||||||||
\(289\) | −0.830968 | −0.0488804 | ||||||||
\(290\) | 32.4487 | 1.90545 | ||||||||
\(291\) | 1.54653 | 0.0906590 | ||||||||
\(292\) | −23.2735 | −1.36198 | ||||||||
\(293\) | 20.0380 | 1.17063 | 0.585315 | − | 0.810806i | \(-0.300971\pi\) | ||||
0.585315 | + | 0.810806i | \(0.300971\pi\) | |||||||
\(294\) | 42.4765 | 2.47728 | ||||||||
\(295\) | 45.2471 | 2.63439 | ||||||||
\(296\) | −9.67353 | −0.562262 | ||||||||
\(297\) | −5.46808 | −0.317290 | ||||||||
\(298\) | −1.45836 | −0.0844808 | ||||||||
\(299\) | −6.87306 | −0.397479 | ||||||||
\(300\) | 121.001 | 6.98597 | ||||||||
\(301\) | 0.595736 | 0.0343377 | ||||||||
\(302\) | 43.3895 | 2.49679 | ||||||||
\(303\) | 17.1258 | 0.983854 | ||||||||
\(304\) | 12.3344 | 0.707426 | ||||||||
\(305\) | 3.20409 | 0.183466 | ||||||||
\(306\) | 39.4446 | 2.25490 | ||||||||
\(307\) | 3.32726 | 0.189897 | 0.0949485 | − | 0.995482i | \(-0.469731\pi\) | ||||
0.0949485 | + | 0.995482i | \(0.469731\pi\) | |||||||
\(308\) | −3.75980 | −0.214234 | ||||||||
\(309\) | −0.999595 | −0.0568650 | ||||||||
\(310\) | 21.2514 | 1.20700 | ||||||||
\(311\) | −5.46479 | −0.309880 | −0.154940 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154940 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(312\) | −13.8816 | −0.785888 | ||||||||
\(313\) | 2.18662 | 0.123595 | 0.0617976 | − | 0.998089i | \(-0.480317\pi\) | ||||
0.0617976 | + | 0.998089i | \(0.480317\pi\) | |||||||
\(314\) | 21.5293 | 1.21497 | ||||||||
\(315\) | −9.61834 | −0.541932 | ||||||||
\(316\) | −38.3623 | −2.15805 | ||||||||
\(317\) | −6.15646 | −0.345781 | −0.172891 | − | 0.984941i | \(-0.555311\pi\) | ||||
−0.172891 | + | 0.984941i | \(0.555311\pi\) | |||||||
\(318\) | 1.68713 | 0.0946096 | ||||||||
\(319\) | −5.98377 | −0.335027 | ||||||||
\(320\) | 46.4010 | 2.59390 | ||||||||
\(321\) | −17.0129 | −0.949565 | ||||||||
\(322\) | 7.00006 | 0.390098 | ||||||||
\(323\) | −23.3924 | −1.30159 | ||||||||
\(324\) | −16.0845 | −0.893583 | ||||||||
\(325\) | 16.1896 | 0.898039 | ||||||||
\(326\) | 5.93812 | 0.328882 | ||||||||
\(327\) | 12.6817 | 0.701298 | ||||||||
\(328\) | 17.7517 | 0.980171 | ||||||||
\(329\) | 4.67986 | 0.258009 | ||||||||
\(330\) | −48.4247 | −2.66569 | ||||||||
\(331\) | −20.5437 | −1.12919 | −0.564593 | − | 0.825370i | \(-0.690967\pi\) | ||||
−0.564593 | + | 0.825370i | \(0.690967\pi\) | |||||||
\(332\) | 13.9074 | 0.763268 | ||||||||
\(333\) | 10.0341 | 0.549865 | ||||||||
\(334\) | −27.7856 | −1.52036 | ||||||||
\(335\) | 12.5678 | 0.686652 | ||||||||
\(336\) | 3.16972 | 0.172922 | ||||||||
\(337\) | −15.1554 | −0.825566 | −0.412783 | − | 0.910829i | \(-0.635443\pi\) | ||||
−0.412783 | + | 0.910829i | \(0.635443\pi\) | |||||||
\(338\) | 26.8670 | 1.46137 | ||||||||
\(339\) | 24.8420 | 1.34923 | ||||||||
\(340\) | 61.4623 | 3.33326 | ||||||||
\(341\) | −3.91892 | −0.212222 | ||||||||
\(342\) | −57.0663 | −3.08579 | ||||||||
\(343\) | −7.66780 | −0.414022 | ||||||||
\(344\) | −4.22364 | −0.227723 | ||||||||
\(345\) | 58.3471 | 3.14130 | ||||||||
\(346\) | 57.5943 | 3.09629 | ||||||||
\(347\) | −2.73738 | −0.146950 | −0.0734751 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734751 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(348\) | 32.0180 | 1.71635 | ||||||||
\(349\) | −28.3742 | −1.51884 | −0.759418 | − | 0.650603i | \(-0.774516\pi\) | ||||
−0.759418 | + | 0.650603i | \(0.774516\pi\) | |||||||
\(350\) | −16.4888 | −0.881362 | ||||||||
\(351\) | 3.91475 | 0.208954 | ||||||||
\(352\) | −5.29844 | −0.282408 | ||||||||
\(353\) | −12.8986 | −0.686524 | −0.343262 | − | 0.939240i | \(-0.611532\pi\) | ||||
−0.343262 | + | 0.939240i | \(0.611532\pi\) | |||||||
\(354\) | 68.9880 | 3.66667 | ||||||||
\(355\) | −38.1783 | −2.02630 | ||||||||
\(356\) | 36.3950 | 1.92893 | ||||||||
\(357\) | −6.01144 | −0.318159 | ||||||||
\(358\) | −21.6368 | −1.14354 | ||||||||
\(359\) | −6.66198 | −0.351606 | −0.175803 | − | 0.984425i | \(-0.556252\pi\) | ||||
−0.175803 | + | 0.984425i | \(0.556252\pi\) | |||||||
\(360\) | 68.1919 | 3.59403 | ||||||||
\(361\) | 14.8428 | 0.781203 | ||||||||
\(362\) | −43.8916 | −2.30689 | ||||||||
\(363\) | −20.4222 | −1.07189 | ||||||||
\(364\) | 2.69174 | 0.141086 | ||||||||
\(365\) | 26.4350 | 1.38367 | ||||||||
\(366\) | 4.88525 | 0.255356 | ||||||||
\(367\) | −4.38158 | −0.228717 | −0.114358 | − | 0.993440i | \(-0.536481\pi\) | ||||
−0.114358 | + | 0.993440i | \(0.536481\pi\) | |||||||
\(368\) | −11.1267 | −0.580018 | ||||||||
\(369\) | −18.4133 | −0.958559 | ||||||||
\(370\) | 24.1592 | 1.25598 | ||||||||
\(371\) | −0.148787 | −0.00772463 | ||||||||
\(372\) | 20.9694 | 1.08721 | ||||||||
\(373\) | 34.2259 | 1.77215 | 0.886075 | − | 0.463542i | \(-0.153422\pi\) | ||||
0.886075 | + | 0.463542i | \(0.153422\pi\) | |||||||
\(374\) | −17.5134 | −0.905598 | ||||||||
\(375\) | −81.8463 | −4.22652 | ||||||||
\(376\) | −33.1792 | −1.71109 | ||||||||
\(377\) | 4.28394 | 0.220634 | ||||||||
\(378\) | −3.98708 | −0.205073 | ||||||||
\(379\) | −20.3815 | −1.04693 | −0.523465 | − | 0.852047i | \(-0.675361\pi\) | ||||
−0.523465 | + | 0.852047i | \(0.675361\pi\) | |||||||
\(380\) | −88.9201 | −4.56150 | ||||||||
\(381\) | −50.5777 | −2.59118 | ||||||||
\(382\) | −2.99392 | −0.153182 | ||||||||
\(383\) | −5.13673 | −0.262475 | −0.131237 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131237 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(384\) | 55.2904 | 2.82153 | ||||||||
\(385\) | 4.27054 | 0.217647 | ||||||||
\(386\) | 14.4144 | 0.733675 | ||||||||
\(387\) | 4.38106 | 0.222702 | ||||||||
\(388\) | 2.12611 | 0.107937 | ||||||||
\(389\) | 6.09040 | 0.308796 | 0.154398 | − | 0.988009i | \(-0.450656\pi\) | ||||
0.154398 | + | 0.988009i | \(0.450656\pi\) | |||||||
\(390\) | 34.6686 | 1.75551 | ||||||||
\(391\) | 21.1020 | 1.06717 | ||||||||
\(392\) | 26.5581 | 1.34139 | ||||||||
\(393\) | −33.7868 | −1.70432 | ||||||||
\(394\) | −48.9831 | −2.46773 | ||||||||
\(395\) | 43.5736 | 2.19242 | ||||||||
\(396\) | −27.6497 | −1.38945 | ||||||||
\(397\) | 23.4678 | 1.17782 | 0.588908 | − | 0.808200i | \(-0.299558\pi\) | ||||
0.588908 | + | 0.808200i | \(0.299558\pi\) | |||||||
\(398\) | 32.9003 | 1.64915 | ||||||||
\(399\) | 8.69701 | 0.435395 | ||||||||
\(400\) | 26.2091 | 1.31046 | ||||||||
\(401\) | 14.1673 | 0.707481 | 0.353741 | − | 0.935344i | \(-0.384910\pi\) | ||||
0.353741 | + | 0.935344i | \(0.384910\pi\) | |||||||
\(402\) | 19.1620 | 0.955715 | ||||||||
\(403\) | 2.80566 | 0.139760 | ||||||||
\(404\) | 23.5440 | 1.17136 | ||||||||
\(405\) | 18.2695 | 0.907817 | ||||||||
\(406\) | −4.36310 | −0.216537 | ||||||||
\(407\) | −4.45514 | −0.220833 | ||||||||
\(408\) | 42.6198 | 2.10999 | ||||||||
\(409\) | −8.44876 | −0.417764 | −0.208882 | − | 0.977941i | \(-0.566982\pi\) | ||||
−0.208882 | + | 0.977941i | \(0.566982\pi\) | |||||||
\(410\) | −44.3340 | −2.18950 | ||||||||
\(411\) | −21.7849 | −1.07457 | ||||||||
\(412\) | −1.37421 | −0.0677024 | ||||||||
\(413\) | −6.08400 | −0.299374 | ||||||||
\(414\) | 51.4787 | 2.53004 | ||||||||
\(415\) | −15.7966 | −0.775427 | ||||||||
\(416\) | 3.79330 | 0.185982 | ||||||||
\(417\) | −40.5748 | −1.98696 | ||||||||
\(418\) | 25.3374 | 1.23929 | ||||||||
\(419\) | 8.55376 | 0.417879 | 0.208939 | − | 0.977929i | \(-0.432999\pi\) | ||||
0.208939 | + | 0.977929i | \(0.432999\pi\) | |||||||
\(420\) | −22.8509 | −1.11501 | ||||||||
\(421\) | −14.5625 | −0.709734 | −0.354867 | − | 0.934917i | \(-0.615474\pi\) | ||||
−0.354867 | + | 0.934917i | \(0.615474\pi\) | |||||||
\(422\) | 28.6230 | 1.39334 | ||||||||
\(423\) | 34.4159 | 1.67336 | ||||||||
\(424\) | 1.05487 | 0.0512288 | ||||||||
\(425\) | −49.7061 | −2.41110 | ||||||||
\(426\) | −58.2102 | −2.82030 | ||||||||
\(427\) | −0.430827 | −0.0208492 | ||||||||
\(428\) | −23.3887 | −1.13053 | ||||||||
\(429\) | −6.39314 | −0.308664 | ||||||||
\(430\) | 10.5484 | 0.508687 | ||||||||
\(431\) | −16.3159 | −0.785909 | −0.392955 | − | 0.919558i | \(-0.628547\pi\) | ||||
−0.392955 | + | 0.919558i | \(0.628547\pi\) | |||||||
\(432\) | 6.33752 | 0.304914 | ||||||||
\(433\) | −8.60560 | −0.413559 | −0.206779 | − | 0.978388i | \(-0.566298\pi\) | ||||
−0.206779 | + | 0.978388i | \(0.566298\pi\) | |||||||
\(434\) | −2.85750 | −0.137165 | ||||||||
\(435\) | −36.3675 | −1.74369 | ||||||||
\(436\) | 17.4343 | 0.834952 | ||||||||
\(437\) | −30.5292 | −1.46041 | ||||||||
\(438\) | 40.3053 | 1.92586 | ||||||||
\(439\) | 34.5914 | 1.65096 | 0.825480 | − | 0.564432i | \(-0.190905\pi\) | ||||
0.825480 | + | 0.564432i | \(0.190905\pi\) | |||||||
\(440\) | −30.2772 | −1.44341 | ||||||||
\(441\) | −27.5480 | −1.31181 | ||||||||
\(442\) | 12.5383 | 0.596388 | ||||||||
\(443\) | −18.8616 | −0.896140 | −0.448070 | − | 0.893998i | \(-0.647889\pi\) | ||||
−0.448070 | + | 0.893998i | \(0.647889\pi\) | |||||||
\(444\) | 23.8386 | 1.13133 | ||||||||
\(445\) | −41.3390 | −1.95966 | ||||||||
\(446\) | −58.8485 | −2.78656 | ||||||||
\(447\) | 1.63449 | 0.0773087 | ||||||||
\(448\) | −6.23916 | −0.294773 | ||||||||
\(449\) | −25.4699 | −1.20200 | −0.601000 | − | 0.799249i | \(-0.705231\pi\) | ||||
−0.601000 | + | 0.799249i | \(0.705231\pi\) | |||||||
\(450\) | −121.259 | −5.71620 | ||||||||
\(451\) | 8.17552 | 0.384970 | ||||||||
\(452\) | 34.1519 | 1.60637 | ||||||||
\(453\) | −48.6297 | −2.28482 | ||||||||
\(454\) | 57.1973 | 2.68440 | ||||||||
\(455\) | −3.05740 | −0.143333 | ||||||||
\(456\) | −61.6599 | −2.88749 | ||||||||
\(457\) | −19.4634 | −0.910461 | −0.455231 | − | 0.890374i | \(-0.650443\pi\) | ||||
−0.455231 | + | 0.890374i | \(0.650443\pi\) | |||||||
\(458\) | 51.7020 | 2.41588 | ||||||||
\(459\) | −12.0192 | −0.561010 | ||||||||
\(460\) | 80.2136 | 3.73998 | ||||||||
\(461\) | 16.2206 | 0.755471 | 0.377735 | − | 0.925914i | \(-0.376703\pi\) | ||||
0.377735 | + | 0.925914i | \(0.376703\pi\) | |||||||
\(462\) | 6.51127 | 0.302932 | ||||||||
\(463\) | 5.87666 | 0.273112 | 0.136556 | − | 0.990632i | \(-0.456397\pi\) | ||||
0.136556 | + | 0.990632i | \(0.456397\pi\) | |||||||
\(464\) | 6.93520 | 0.321959 | ||||||||
\(465\) | −23.8180 | −1.10453 | ||||||||
\(466\) | −23.1962 | −1.07454 | ||||||||
\(467\) | −37.2094 | −1.72184 | −0.860922 | − | 0.508737i | \(-0.830113\pi\) | ||||
−0.860922 | + | 0.508737i | \(0.830113\pi\) | |||||||
\(468\) | 19.7952 | 0.915033 | ||||||||
\(469\) | −1.68989 | −0.0780317 | ||||||||
\(470\) | 82.8636 | 3.82222 | ||||||||
\(471\) | −24.1294 | −1.11182 | ||||||||
\(472\) | 43.1343 | 1.98541 | ||||||||
\(473\) | −1.94519 | −0.0894401 | ||||||||
\(474\) | 66.4363 | 3.05152 | ||||||||
\(475\) | 71.9120 | 3.29955 | ||||||||
\(476\) | −8.26431 | −0.378794 | ||||||||
\(477\) | −1.09418 | −0.0500992 | ||||||||
\(478\) | 30.5153 | 1.39574 | ||||||||
\(479\) | 21.9563 | 1.00321 | 0.501605 | − | 0.865097i | \(-0.332743\pi\) | ||||
0.501605 | + | 0.865097i | \(0.332743\pi\) | |||||||
\(480\) | −32.2022 | −1.46982 | ||||||||
\(481\) | 3.18956 | 0.145431 | ||||||||
\(482\) | 29.4201 | 1.34005 | ||||||||
\(483\) | −7.84545 | −0.356980 | ||||||||
\(484\) | −28.0757 | −1.27617 | ||||||||
\(485\) | −2.41493 | −0.109656 | ||||||||
\(486\) | 49.2047 | 2.23197 | ||||||||
\(487\) | 29.3037 | 1.32788 | 0.663939 | − | 0.747787i | \(-0.268884\pi\) | ||||
0.663939 | + | 0.747787i | \(0.268884\pi\) | |||||||
\(488\) | 3.05447 | 0.138269 | ||||||||
\(489\) | −6.65527 | −0.300962 | ||||||||
\(490\) | −66.3277 | −2.99638 | ||||||||
\(491\) | 6.45589 | 0.291350 | 0.145675 | − | 0.989332i | \(-0.453465\pi\) | ||||
0.145675 | + | 0.989332i | \(0.453465\pi\) | |||||||
\(492\) | −43.7456 | −1.97221 | ||||||||
\(493\) | −13.1528 | −0.592371 | ||||||||
\(494\) | −18.1398 | −0.816147 | ||||||||
\(495\) | 31.4057 | 1.41158 | ||||||||
\(496\) | 4.54204 | 0.203944 | ||||||||
\(497\) | 5.13352 | 0.230270 | ||||||||
\(498\) | −24.0850 | −1.07928 | ||||||||
\(499\) | 0.103492 | 0.00463294 | 0.00231647 | − | 0.999997i | \(-0.499263\pi\) | ||||
0.00231647 | + | 0.999997i | \(0.499263\pi\) | |||||||
\(500\) | −112.519 | −5.03202 | ||||||||
\(501\) | 31.1413 | 1.39129 | ||||||||
\(502\) | −40.1526 | −1.79210 | ||||||||
\(503\) | −0.466966 | −0.0208210 | −0.0104105 | − | 0.999946i | \(-0.503314\pi\) | ||||
−0.0104105 | + | 0.999946i | \(0.503314\pi\) | |||||||
\(504\) | −9.16919 | −0.408428 | ||||||||
\(505\) | −26.7423 | −1.19002 | ||||||||
\(506\) | −22.8565 | −1.01610 | ||||||||
\(507\) | −30.1117 | −1.33731 | ||||||||
\(508\) | −69.5325 | −3.08501 | ||||||||
\(509\) | −4.45931 | −0.197656 | −0.0988278 | − | 0.995105i | \(-0.531509\pi\) | ||||
−0.0988278 | + | 0.995105i | \(0.531509\pi\) | |||||||
\(510\) | −106.441 | −4.71329 | ||||||||
\(511\) | −3.55450 | −0.157242 | ||||||||
\(512\) | 22.9846 | 1.01579 | ||||||||
\(513\) | 17.3888 | 0.767732 | ||||||||
\(514\) | 8.27883 | 0.365164 | ||||||||
\(515\) | 1.56089 | 0.0687808 | ||||||||
\(516\) | 10.4084 | 0.458203 | ||||||||
\(517\) | −15.2807 | −0.672043 | ||||||||
\(518\) | −3.24849 | −0.142730 | ||||||||
\(519\) | −64.5499 | −2.83343 | ||||||||
\(520\) | 21.6763 | 0.950568 | ||||||||
\(521\) | −26.6586 | −1.16793 | −0.583967 | − | 0.811777i | \(-0.698500\pi\) | ||||
−0.583967 | + | 0.811777i | \(0.698500\pi\) | |||||||
\(522\) | −32.0864 | −1.40438 | ||||||||
\(523\) | −27.7048 | −1.21145 | −0.605724 | − | 0.795675i | \(-0.707116\pi\) | ||||
−0.605724 | + | 0.795675i | \(0.707116\pi\) | |||||||
\(524\) | −46.4489 | −2.02913 | ||||||||
\(525\) | 18.4801 | 0.806538 | ||||||||
\(526\) | 56.8032 | 2.47674 | ||||||||
\(527\) | −8.61408 | −0.375235 | ||||||||
\(528\) | −10.3497 | −0.450415 | ||||||||
\(529\) | 4.53992 | 0.197388 | ||||||||
\(530\) | −2.63448 | −0.114435 | ||||||||
\(531\) | −44.7420 | −1.94164 | ||||||||
\(532\) | 11.9563 | 0.518373 | ||||||||
\(533\) | −5.85308 | −0.253525 | ||||||||
\(534\) | −63.0293 | −2.72754 | ||||||||
\(535\) | 26.5659 | 1.14854 | ||||||||
\(536\) | 11.9809 | 0.517497 | ||||||||
\(537\) | 24.2499 | 1.04646 | ||||||||
\(538\) | 69.4288 | 2.99329 | ||||||||
\(539\) | 12.2313 | 0.526840 | ||||||||
\(540\) | −45.6879 | −1.96610 | ||||||||
\(541\) | 10.1376 | 0.435849 | 0.217925 | − | 0.975966i | \(-0.430071\pi\) | ||||
0.217925 | + | 0.975966i | \(0.430071\pi\) | |||||||
\(542\) | −14.6243 | −0.628169 | ||||||||
\(543\) | 49.1923 | 2.11104 | ||||||||
\(544\) | −11.6463 | −0.499333 | ||||||||
\(545\) | −19.8027 | −0.848252 | ||||||||
\(546\) | −4.66160 | −0.199498 | ||||||||
\(547\) | 15.4358 | 0.659987 | 0.329993 | − | 0.943983i | \(-0.392953\pi\) | ||||
0.329993 | + | 0.943983i | \(0.392953\pi\) | |||||||
\(548\) | −29.9492 | −1.27937 | ||||||||
\(549\) | −3.16832 | −0.135221 | ||||||||
\(550\) | 53.8390 | 2.29570 | ||||||||
\(551\) | 19.0287 | 0.810649 | ||||||||
\(552\) | 55.6225 | 2.36745 | ||||||||
\(553\) | −5.85897 | −0.249149 | ||||||||
\(554\) | −58.9603 | −2.50498 | ||||||||
\(555\) | −27.0769 | −1.14935 | ||||||||
\(556\) | −55.7808 | −2.36563 | ||||||||
\(557\) | −27.9681 | −1.18505 | −0.592524 | − | 0.805553i | \(-0.701869\pi\) | ||||
−0.592524 | + | 0.805553i | \(0.701869\pi\) | |||||||
\(558\) | −21.0142 | −0.889602 | ||||||||
\(559\) | 1.39262 | 0.0589015 | ||||||||
\(560\) | −4.94957 | −0.209158 | ||||||||
\(561\) | 19.6285 | 0.828717 | ||||||||
\(562\) | −71.4303 | −3.01310 | ||||||||
\(563\) | 19.6267 | 0.827168 | 0.413584 | − | 0.910466i | \(-0.364277\pi\) | ||||
0.413584 | + | 0.910466i | \(0.364277\pi\) | |||||||
\(564\) | 81.7639 | 3.44288 | ||||||||
\(565\) | −38.7912 | −1.63196 | ||||||||
\(566\) | 18.2187 | 0.765787 | ||||||||
\(567\) | −2.45654 | −0.103165 | ||||||||
\(568\) | −36.3955 | −1.52712 | ||||||||
\(569\) | 22.1947 | 0.930451 | 0.465226 | − | 0.885192i | \(-0.345973\pi\) | ||||
0.465226 | + | 0.885192i | \(0.345973\pi\) | |||||||
\(570\) | 153.993 | 6.45006 | ||||||||
\(571\) | 25.8293 | 1.08092 | 0.540462 | − | 0.841368i | \(-0.318249\pi\) | ||||
0.540462 | + | 0.841368i | \(0.318249\pi\) | |||||||
\(572\) | −8.78907 | −0.367489 | ||||||||
\(573\) | 3.35549 | 0.140178 | ||||||||
\(574\) | 5.96122 | 0.248817 | ||||||||
\(575\) | −64.8708 | −2.70530 | ||||||||
\(576\) | −45.8830 | −1.91179 | ||||||||
\(577\) | −5.64704 | −0.235089 | −0.117545 | − | 0.993068i | \(-0.537502\pi\) | ||||
−0.117545 | + | 0.993068i | \(0.537502\pi\) | |||||||
\(578\) | 1.97840 | 0.0822905 | ||||||||
\(579\) | −16.1553 | −0.671389 | ||||||||
\(580\) | −49.9967 | −2.07600 | ||||||||
\(581\) | 2.12404 | 0.0881201 | ||||||||
\(582\) | −3.68202 | −0.152625 | ||||||||
\(583\) | 0.485818 | 0.0201205 | ||||||||
\(584\) | 25.2006 | 1.04281 | ||||||||
\(585\) | −22.4842 | −0.929609 | ||||||||
\(586\) | −47.7071 | −1.97076 | ||||||||
\(587\) | −19.0641 | −0.786860 | −0.393430 | − | 0.919355i | \(-0.628712\pi\) | ||||
−0.393430 | + | 0.919355i | \(0.628712\pi\) | |||||||
\(588\) | −65.4475 | −2.69901 | ||||||||
\(589\) | 12.4624 | 0.513502 | ||||||||
\(590\) | −107.726 | −4.43501 | ||||||||
\(591\) | 54.8988 | 2.25823 | ||||||||
\(592\) | 5.16352 | 0.212219 | ||||||||
\(593\) | −10.2334 | −0.420237 | −0.210119 | − | 0.977676i | \(-0.567385\pi\) | ||||
−0.210119 | + | 0.977676i | \(0.567385\pi\) | |||||||
\(594\) | 13.0186 | 0.534160 | ||||||||
\(595\) | 9.38697 | 0.384828 | ||||||||
\(596\) | 2.24704 | 0.0920423 | ||||||||
\(597\) | −36.8737 | −1.50914 | ||||||||
\(598\) | 16.3636 | 0.669159 | ||||||||
\(599\) | 23.7118 | 0.968838 | 0.484419 | − | 0.874836i | \(-0.339031\pi\) | ||||
0.484419 | + | 0.874836i | \(0.339031\pi\) | |||||||
\(600\) | −131.020 | −5.34886 | ||||||||
\(601\) | 45.2643 | 1.84637 | 0.923184 | − | 0.384359i | \(-0.125577\pi\) | ||||
0.923184 | + | 0.384359i | \(0.125577\pi\) | |||||||
\(602\) | −1.41835 | −0.0578076 | ||||||||
\(603\) | −12.4275 | −0.506086 | ||||||||
\(604\) | −66.8543 | −2.72026 | ||||||||
\(605\) | 31.8896 | 1.29650 | ||||||||
\(606\) | −40.7738 | −1.65632 | ||||||||
\(607\) | −15.0406 | −0.610479 | −0.305240 | − | 0.952276i | \(-0.598737\pi\) | ||||
−0.305240 | + | 0.952276i | \(0.598737\pi\) | |||||||
\(608\) | 16.8493 | 0.683328 | ||||||||
\(609\) | 4.89003 | 0.198154 | ||||||||
\(610\) | −7.62841 | −0.308865 | ||||||||
\(611\) | 10.9398 | 0.442579 | ||||||||
\(612\) | −60.7761 | −2.45673 | ||||||||
\(613\) | −34.0823 | −1.37657 | −0.688286 | − | 0.725440i | \(-0.741636\pi\) | ||||
−0.688286 | + | 0.725440i | \(0.741636\pi\) | |||||||
\(614\) | −7.92167 | −0.319692 | ||||||||
\(615\) | 49.6882 | 2.00362 | ||||||||
\(616\) | 4.07112 | 0.164030 | ||||||||
\(617\) | −48.4114 | −1.94897 | −0.974484 | − | 0.224455i | \(-0.927940\pi\) | ||||
−0.974484 | + | 0.224455i | \(0.927940\pi\) | |||||||
\(618\) | 2.37987 | 0.0957325 | ||||||||
\(619\) | 0.00242124 | 9.73180e−5 0 | 4.86590e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.86590e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(620\) | −32.7441 | −1.31504 | ||||||||
\(621\) | −15.6862 | −0.629464 | ||||||||
\(622\) | 13.0108 | 0.521684 | ||||||||
\(623\) | 5.55851 | 0.222697 | ||||||||
\(624\) | 7.40967 | 0.296624 | ||||||||
\(625\) | 65.9974 | 2.63990 | ||||||||
\(626\) | −5.20598 | −0.208073 | ||||||||
\(627\) | −28.3974 | −1.13408 | ||||||||
\(628\) | −33.1722 | −1.32372 | ||||||||
\(629\) | −9.79272 | −0.390461 | ||||||||
\(630\) | 22.8997 | 0.912345 | ||||||||
\(631\) | 22.2712 | 0.886604 | 0.443302 | − | 0.896372i | \(-0.353807\pi\) | ||||
0.443302 | + | 0.896372i | \(0.353807\pi\) | |||||||
\(632\) | 41.5388 | 1.65233 | ||||||||
\(633\) | −32.0797 | −1.27506 | ||||||||
\(634\) | 14.6575 | 0.582125 | ||||||||
\(635\) | 78.9780 | 3.13415 | ||||||||
\(636\) | −2.59952 | −0.103078 | ||||||||
\(637\) | −8.75674 | −0.346955 | ||||||||
\(638\) | 14.2464 | 0.564019 | ||||||||
\(639\) | 37.7521 | 1.49345 | ||||||||
\(640\) | −86.3370 | −3.41277 | ||||||||
\(641\) | −13.0279 | −0.514571 | −0.257286 | − | 0.966335i | \(-0.582828\pi\) | ||||
−0.257286 | + | 0.966335i | \(0.582828\pi\) | |||||||
\(642\) | 40.5048 | 1.59860 | ||||||||
\(643\) | 32.5917 | 1.28529 | 0.642645 | − | 0.766164i | \(-0.277837\pi\) | ||||
0.642645 | + | 0.766164i | \(0.277837\pi\) | |||||||
\(644\) | −10.7856 | −0.425014 | ||||||||
\(645\) | −11.8223 | −0.465502 | ||||||||
\(646\) | 55.6935 | 2.19123 | ||||||||
\(647\) | −12.9421 | −0.508808 | −0.254404 | − | 0.967098i | \(-0.581879\pi\) | ||||
−0.254404 | + | 0.967098i | \(0.581879\pi\) | |||||||
\(648\) | 17.4163 | 0.684179 | ||||||||
\(649\) | 19.8655 | 0.779787 | ||||||||
\(650\) | −38.5448 | −1.51185 | ||||||||
\(651\) | 3.20260 | 0.125520 | ||||||||
\(652\) | −9.14943 | −0.358319 | ||||||||
\(653\) | −42.2076 | −1.65171 | −0.825856 | − | 0.563881i | \(-0.809308\pi\) | ||||
−0.825856 | + | 0.563881i | \(0.809308\pi\) | |||||||
\(654\) | −30.1930 | −1.18064 | ||||||||
\(655\) | 52.7587 | 2.06145 | ||||||||
\(656\) | −9.47544 | −0.369954 | ||||||||
\(657\) | −26.1399 | −1.01982 | ||||||||
\(658\) | −11.1420 | −0.434360 | ||||||||
\(659\) | 14.3099 | 0.557435 | 0.278718 | − | 0.960373i | \(-0.410091\pi\) | ||||
0.278718 | + | 0.960373i | \(0.410091\pi\) | |||||||
\(660\) | 74.6126 | 2.90429 | ||||||||
\(661\) | −36.1449 | −1.40587 | −0.702937 | − | 0.711253i | \(-0.748128\pi\) | ||||
−0.702937 | + | 0.711253i | \(0.748128\pi\) | |||||||
\(662\) | 48.9113 | 1.90099 | ||||||||
\(663\) | −14.0526 | −0.545758 | ||||||||
\(664\) | −15.0590 | −0.584402 | ||||||||
\(665\) | −13.5805 | −0.526630 | ||||||||
\(666\) | −23.8895 | −0.925700 | ||||||||
\(667\) | −17.1655 | −0.664651 | ||||||||
\(668\) | 42.8119 | 1.65644 | ||||||||
\(669\) | 65.9556 | 2.54999 | ||||||||
\(670\) | −29.9219 | −1.15598 | ||||||||
\(671\) | 1.40673 | 0.0543064 | ||||||||
\(672\) | 4.32996 | 0.167032 | ||||||||
\(673\) | −24.2053 | −0.933044 | −0.466522 | − | 0.884509i | \(-0.654493\pi\) | ||||
−0.466522 | + | 0.884509i | \(0.654493\pi\) | |||||||
\(674\) | 36.0825 | 1.38984 | ||||||||
\(675\) | 36.9490 | 1.42217 | ||||||||
\(676\) | −41.3966 | −1.59218 | ||||||||
\(677\) | −9.22875 | −0.354690 | −0.177345 | − | 0.984149i | \(-0.556751\pi\) | ||||
−0.177345 | + | 0.984149i | \(0.556751\pi\) | |||||||
\(678\) | −59.1447 | −2.27144 | ||||||||
\(679\) | 0.324715 | 0.0124614 | ||||||||
\(680\) | −66.5515 | −2.55214 | ||||||||
\(681\) | −64.1050 | −2.45651 | ||||||||
\(682\) | 9.33031 | 0.357276 | ||||||||
\(683\) | 18.8516 | 0.721337 | 0.360668 | − | 0.932694i | \(-0.382549\pi\) | ||||
0.360668 | + | 0.932694i | \(0.382549\pi\) | |||||||
\(684\) | 87.9274 | 3.36199 | ||||||||
\(685\) | 34.0176 | 1.29974 | ||||||||
\(686\) | 18.2558 | 0.697008 | ||||||||
\(687\) | −57.9461 | −2.21078 | ||||||||
\(688\) | 2.25448 | 0.0859514 | ||||||||
\(689\) | −0.347810 | −0.0132505 | ||||||||
\(690\) | −138.915 | −5.28840 | ||||||||
\(691\) | 7.54841 | 0.287155 | 0.143578 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143578 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(692\) | −88.7410 | −3.37343 | ||||||||
\(693\) | −4.22287 | −0.160413 | ||||||||
\(694\) | 6.51725 | 0.247391 | ||||||||
\(695\) | 63.3583 | 2.40332 | ||||||||
\(696\) | −34.6692 | −1.31413 | ||||||||
\(697\) | 17.9704 | 0.680677 | ||||||||
\(698\) | 67.5543 | 2.55697 | ||||||||
\(699\) | 25.9975 | 0.983317 | ||||||||
\(700\) | 25.4058 | 0.960249 | ||||||||
\(701\) | −6.22755 | −0.235211 | −0.117606 | − | 0.993060i | \(-0.537522\pi\) | ||||
−0.117606 | + | 0.993060i | \(0.537522\pi\) | |||||||
\(702\) | −9.32038 | −0.351775 | ||||||||
\(703\) | 14.1675 | 0.534339 | ||||||||
\(704\) | 20.3721 | 0.767801 | ||||||||
\(705\) | −92.8710 | −3.49773 | ||||||||
\(706\) | 30.7095 | 1.15577 | ||||||||
\(707\) | 3.59581 | 0.135234 | ||||||||
\(708\) | −106.296 | −3.99486 | ||||||||
\(709\) | 19.5869 | 0.735601 | 0.367801 | − | 0.929905i | \(-0.380111\pi\) | ||||
0.367801 | + | 0.929905i | \(0.380111\pi\) | |||||||
\(710\) | 90.8963 | 3.41128 | ||||||||
\(711\) | −43.0871 | −1.61589 | ||||||||
\(712\) | −39.4086 | −1.47690 | ||||||||
\(713\) | −11.2421 | −0.421021 | ||||||||
\(714\) | 14.3122 | 0.535622 | ||||||||
\(715\) | 9.98301 | 0.373343 | ||||||||
\(716\) | 33.3379 | 1.24589 | ||||||||
\(717\) | −34.2007 | −1.27725 | ||||||||
\(718\) | 15.8611 | 0.591930 | ||||||||
\(719\) | −44.1287 | −1.64572 | −0.822861 | − | 0.568242i | \(-0.807624\pi\) | ||||
−0.822861 | + | 0.568242i | \(0.807624\pi\) | |||||||
\(720\) | −36.3993 | −1.35652 | ||||||||
\(721\) | −0.209879 | −0.00781631 | ||||||||
\(722\) | −35.3384 | −1.31516 | ||||||||
\(723\) | −32.9731 | −1.22628 | ||||||||
\(724\) | 67.6279 | 2.51337 | ||||||||
\(725\) | 40.4336 | 1.50167 | ||||||||
\(726\) | 48.6218 | 1.80452 | ||||||||
\(727\) | 2.08144 | 0.0771962 | 0.0385981 | − | 0.999255i | \(-0.487711\pi\) | ||||
0.0385981 | + | 0.999255i | \(0.487711\pi\) | |||||||
\(728\) | −2.91463 | −0.108023 | ||||||||
\(729\) | −41.9933 | −1.55531 | ||||||||
\(730\) | −62.9375 | −2.32942 | ||||||||
\(731\) | −4.27568 | −0.158142 | ||||||||
\(732\) | −7.52717 | −0.278212 | ||||||||
\(733\) | 30.1434 | 1.11337 | 0.556687 | − | 0.830723i | \(-0.312072\pi\) | ||||
0.556687 | + | 0.830723i | \(0.312072\pi\) | |||||||
\(734\) | 10.4318 | 0.385046 | ||||||||
\(735\) | 74.3381 | 2.74200 | ||||||||
\(736\) | −15.1995 | −0.560261 | ||||||||
\(737\) | 5.51781 | 0.203251 | ||||||||
\(738\) | 43.8391 | 1.61374 | ||||||||
\(739\) | −30.5553 | −1.12399 | −0.561997 | − | 0.827139i | \(-0.689967\pi\) | ||||
−0.561997 | + | 0.827139i | \(0.689967\pi\) | |||||||
\(740\) | −37.2244 | −1.36840 | ||||||||
\(741\) | 20.3305 | 0.746859 | ||||||||
\(742\) | 0.354237 | 0.0130044 | ||||||||
\(743\) | 8.32637 | 0.305465 | 0.152733 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152733 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(744\) | −22.7058 | −0.832433 | ||||||||
\(745\) | −2.55228 | −0.0935085 | ||||||||
\(746\) | −81.4862 | −2.98342 | ||||||||
\(747\) | 15.6203 | 0.571516 | ||||||||
\(748\) | 26.9846 | 0.986654 | ||||||||
\(749\) | −3.57209 | −0.130521 | ||||||||
\(750\) | 194.863 | 7.11538 | ||||||||
\(751\) | 10.6928 | 0.390186 | 0.195093 | − | 0.980785i | \(-0.437499\pi\) | ||||
0.195093 | + | 0.980785i | \(0.437499\pi\) | |||||||
\(752\) | 17.7103 | 0.645829 | ||||||||
\(753\) | 45.0018 | 1.63996 | ||||||||
\(754\) | −10.1994 | −0.371439 | ||||||||
\(755\) | 75.9361 | 2.76360 | ||||||||
\(756\) | 6.14327 | 0.223429 | ||||||||
\(757\) | −6.33427 | −0.230223 | −0.115111 | − | 0.993353i | \(-0.536723\pi\) | ||||
−0.115111 | + | 0.993353i | \(0.536723\pi\) | |||||||
\(758\) | 48.5251 | 1.76251 | ||||||||
\(759\) | 25.6169 | 0.929835 | ||||||||
\(760\) | 96.2830 | 3.49255 | ||||||||
\(761\) | −52.2078 | −1.89253 | −0.946266 | − | 0.323389i | \(-0.895178\pi\) | ||||
−0.946266 | + | 0.323389i | \(0.895178\pi\) | |||||||
\(762\) | 120.417 | 4.36226 | ||||||||
\(763\) | 2.66270 | 0.0963961 | ||||||||
\(764\) | 4.61301 | 0.166893 | ||||||||
\(765\) | 69.0321 | 2.49586 | ||||||||
\(766\) | 12.2297 | 0.441877 | ||||||||
\(767\) | −14.2222 | −0.513535 | ||||||||
\(768\) | −72.2067 | −2.60553 | ||||||||
\(769\) | 28.9390 | 1.04357 | 0.521784 | − | 0.853077i | \(-0.325267\pi\) | ||||
0.521784 | + | 0.853077i | \(0.325267\pi\) | |||||||
\(770\) | −10.1675 | −0.366410 | ||||||||
\(771\) | −9.27866 | −0.334163 | ||||||||
\(772\) | −22.2097 | −0.799344 | ||||||||
\(773\) | 1.28957 | 0.0463825 | 0.0231913 | − | 0.999731i | \(-0.492617\pi\) | ||||
0.0231913 | + | 0.999731i | \(0.492617\pi\) | |||||||
\(774\) | −10.4306 | −0.374920 | ||||||||
\(775\) | 26.4810 | 0.951226 | ||||||||
\(776\) | −2.30216 | −0.0826427 | ||||||||
\(777\) | 3.64081 | 0.130613 | ||||||||
\(778\) | −14.5003 | −0.519859 | ||||||||
\(779\) | −25.9985 | −0.931494 | ||||||||
\(780\) | −53.4172 | −1.91264 | ||||||||
\(781\) | −16.7619 | −0.599789 | ||||||||
\(782\) | −50.2404 | −1.79659 | ||||||||
\(783\) | 9.77710 | 0.349405 | ||||||||
\(784\) | −14.1761 | −0.506290 | ||||||||
\(785\) | 37.6785 | 1.34480 | ||||||||
\(786\) | 80.4408 | 2.86923 | ||||||||
\(787\) | 22.6115 | 0.806014 | 0.403007 | − | 0.915197i | \(-0.367965\pi\) | ||||
0.403007 | + | 0.915197i | \(0.367965\pi\) | |||||||
\(788\) | 75.4729 | 2.68861 | ||||||||
\(789\) | −63.6633 | −2.26647 | ||||||||
\(790\) | −103.742 | −3.69096 | ||||||||
\(791\) | 5.21593 | 0.185457 | ||||||||
\(792\) | 29.9392 | 1.06384 | ||||||||
\(793\) | −1.00712 | −0.0357639 | ||||||||
\(794\) | −55.8730 | −1.98286 | ||||||||
\(795\) | 2.95265 | 0.104720 | ||||||||
\(796\) | −50.6927 | −1.79675 | ||||||||
\(797\) | 37.0376 | 1.31194 | 0.655969 | − | 0.754787i | \(-0.272260\pi\) | ||||
0.655969 | + | 0.754787i | \(0.272260\pi\) | |||||||
\(798\) | −20.7061 | −0.732990 | ||||||||
\(799\) | −33.5880 | −1.18826 | ||||||||
\(800\) | 35.8027 | 1.26582 | ||||||||
\(801\) | 40.8775 | 1.44433 | ||||||||
\(802\) | −33.7300 | −1.19105 | ||||||||
\(803\) | 11.6061 | 0.409571 | ||||||||
\(804\) | −29.5248 | −1.04126 | ||||||||
\(805\) | 12.2508 | 0.431784 | ||||||||
\(806\) | −6.67982 | −0.235287 | ||||||||
\(807\) | −77.8137 | −2.73917 | ||||||||
\(808\) | −25.4935 | −0.896859 | ||||||||
\(809\) | −2.77415 | −0.0975338 | −0.0487669 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487669 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(810\) | −43.4966 | −1.52831 | ||||||||
\(811\) | 49.0223 | 1.72141 | 0.860703 | − | 0.509108i | \(-0.170025\pi\) | ||||
0.860703 | + | 0.509108i | \(0.170025\pi\) | |||||||
\(812\) | 6.72264 | 0.235918 | ||||||||
\(813\) | 16.3905 | 0.574840 | ||||||||
\(814\) | 10.6069 | 0.371773 | ||||||||
\(815\) | 10.3923 | 0.364027 | ||||||||
\(816\) | −22.7495 | −0.796392 | ||||||||
\(817\) | 6.18581 | 0.216414 | ||||||||
\(818\) | 20.1151 | 0.703308 | ||||||||
\(819\) | 3.02327 | 0.105641 | ||||||||
\(820\) | 68.3096 | 2.38547 | ||||||||
\(821\) | 27.2442 | 0.950830 | 0.475415 | − | 0.879762i | \(-0.342298\pi\) | ||||
0.475415 | + | 0.879762i | \(0.342298\pi\) | |||||||
\(822\) | 51.8664 | 1.80905 | ||||||||
\(823\) | 18.5906 | 0.648026 | 0.324013 | − | 0.946053i | \(-0.394968\pi\) | ||||
0.324013 | + | 0.946053i | \(0.394968\pi\) | |||||||
\(824\) | 1.48800 | 0.0518368 | ||||||||
\(825\) | −60.3411 | −2.10081 | ||||||||
\(826\) | 14.4850 | 0.503998 | ||||||||
\(827\) | 53.7216 | 1.86808 | 0.934041 | − | 0.357165i | \(-0.116257\pi\) | ||||
0.934041 | + | 0.357165i | \(0.116257\pi\) | |||||||
\(828\) | −79.3180 | −2.75649 | ||||||||
\(829\) | −8.10921 | −0.281645 | −0.140822 | − | 0.990035i | \(-0.544975\pi\) | ||||
−0.140822 | + | 0.990035i | \(0.544975\pi\) | |||||||
\(830\) | 37.6092 | 1.30543 | ||||||||
\(831\) | 66.0809 | 2.29232 | ||||||||
\(832\) | −14.5849 | −0.505641 | ||||||||
\(833\) | 26.8853 | 0.931521 | ||||||||
\(834\) | 96.6019 | 3.34505 | ||||||||
\(835\) | −48.6276 | −1.68283 | ||||||||
\(836\) | −39.0398 | −1.35022 | ||||||||
\(837\) | 6.40327 | 0.221329 | ||||||||
\(838\) | −20.3651 | −0.703501 | ||||||||
\(839\) | −15.4939 | −0.534909 | −0.267455 | − | 0.963570i | \(-0.586183\pi\) | ||||
−0.267455 | + | 0.963570i | \(0.586183\pi\) | |||||||
\(840\) | 24.7430 | 0.853715 | ||||||||
\(841\) | −18.3008 | −0.631063 | ||||||||
\(842\) | 34.6710 | 1.19484 | ||||||||
\(843\) | 80.0569 | 2.75731 | ||||||||
\(844\) | −44.1021 | −1.51806 | ||||||||
\(845\) | 47.0200 | 1.61754 | ||||||||
\(846\) | −81.9385 | −2.81711 | ||||||||
\(847\) | −4.28792 | −0.147335 | ||||||||
\(848\) | −0.563064 | −0.0193357 | ||||||||
\(849\) | −20.4189 | −0.700775 | ||||||||
\(850\) | 118.342 | 4.05910 | ||||||||
\(851\) | −12.7803 | −0.438105 | ||||||||
\(852\) | 89.6900 | 3.07273 | ||||||||
\(853\) | 45.4994 | 1.55787 | 0.778935 | − | 0.627105i | \(-0.215760\pi\) | ||||
0.778935 | + | 0.627105i | \(0.215760\pi\) | |||||||
\(854\) | 1.02573 | 0.0350997 | ||||||||
\(855\) | −99.8717 | −3.41554 | ||||||||
\(856\) | 25.3253 | 0.865602 | ||||||||
\(857\) | 33.7720 | 1.15363 | 0.576814 | − | 0.816875i | \(-0.304296\pi\) | ||||
0.576814 | + | 0.816875i | \(0.304296\pi\) | |||||||
\(858\) | 15.2210 | 0.519637 | ||||||||
\(859\) | −43.6086 | −1.48791 | −0.743953 | − | 0.668232i | \(-0.767051\pi\) | ||||
−0.743953 | + | 0.668232i | \(0.767051\pi\) | |||||||
\(860\) | −16.2528 | −0.554218 | ||||||||
\(861\) | −6.68116 | −0.227693 | ||||||||
\(862\) | 38.8455 | 1.32308 | ||||||||
\(863\) | −17.7026 | −0.602603 | −0.301302 | − | 0.953529i | \(-0.597421\pi\) | ||||
−0.301302 | + | 0.953529i | \(0.597421\pi\) | |||||||
\(864\) | 8.65731 | 0.294528 | ||||||||
\(865\) | 100.796 | 3.42716 | ||||||||
\(866\) | 20.4885 | 0.696228 | ||||||||
\(867\) | −2.21733 | −0.0753044 | ||||||||
\(868\) | 4.40283 | 0.149442 | ||||||||
\(869\) | 19.1307 | 0.648964 | ||||||||
\(870\) | 86.5850 | 2.93550 | ||||||||
\(871\) | −3.95035 | −0.133853 | ||||||||
\(872\) | −18.8779 | −0.639288 | ||||||||
\(873\) | 2.38797 | 0.0808204 | ||||||||
\(874\) | 72.6849 | 2.45860 | ||||||||
\(875\) | −17.1848 | −0.580952 | ||||||||
\(876\) | −62.1022 | −2.09824 | ||||||||
\(877\) | −52.7771 | −1.78215 | −0.891077 | − | 0.453852i | \(-0.850050\pi\) | ||||
−0.891077 | + | 0.453852i | \(0.850050\pi\) | |||||||
\(878\) | −82.3565 | −2.77940 | ||||||||
\(879\) | 53.4686 | 1.80345 | ||||||||
\(880\) | 16.1613 | 0.544798 | ||||||||
\(881\) | 31.5553 | 1.06313 | 0.531563 | − | 0.847019i | \(-0.321605\pi\) | ||||
0.531563 | + | 0.847019i | \(0.321605\pi\) | |||||||
\(882\) | 65.5872 | 2.20844 | ||||||||
\(883\) | −20.2880 | −0.682747 | −0.341373 | − | 0.939928i | \(-0.610892\pi\) | ||||
−0.341373 | + | 0.939928i | \(0.610892\pi\) | |||||||
\(884\) | −19.3190 | −0.649769 | ||||||||
\(885\) | 120.736 | 4.05850 | ||||||||
\(886\) | 44.9063 | 1.50866 | ||||||||
\(887\) | −19.2722 | −0.647098 | −0.323549 | − | 0.946211i | \(-0.604876\pi\) | ||||
−0.323549 | + | 0.946211i | \(0.604876\pi\) | |||||||
\(888\) | −25.8125 | −0.866212 | ||||||||
\(889\) | −10.6195 | −0.356167 | ||||||||
\(890\) | 98.4213 | 3.29909 | ||||||||
\(891\) | 8.02109 | 0.268717 | ||||||||
\(892\) | 90.6734 | 3.03597 | ||||||||
\(893\) | 48.5932 | 1.62611 | ||||||||
\(894\) | −3.89145 | −0.130150 | ||||||||
\(895\) | −37.8666 | −1.26574 | ||||||||
\(896\) | 11.6090 | 0.387830 | ||||||||
\(897\) | −18.3399 | −0.612350 | ||||||||
\(898\) | 60.6397 | 2.02357 | ||||||||
\(899\) | 7.00715 | 0.233702 | ||||||||
\(900\) | 186.835 | 6.22784 | ||||||||
\(901\) | 1.06786 | 0.0355757 | ||||||||
\(902\) | −19.4646 | −0.648099 | ||||||||
\(903\) | 1.58964 | 0.0529000 | ||||||||
\(904\) | −36.9798 | −1.22993 | ||||||||
\(905\) | −76.8147 | −2.55341 | ||||||||
\(906\) | 115.779 | 3.84651 | ||||||||
\(907\) | 40.3930 | 1.34123 | 0.670613 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670613 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(908\) | −88.1292 | −2.92467 | ||||||||
\(909\) | 26.4437 | 0.877084 | ||||||||
\(910\) | 7.27917 | 0.241302 | ||||||||
\(911\) | −57.1724 | −1.89421 | −0.947103 | − | 0.320928i | \(-0.896005\pi\) | ||||
−0.947103 | + | 0.320928i | \(0.896005\pi\) | |||||||
\(912\) | 32.9127 | 1.08985 | ||||||||
\(913\) | −6.93541 | −0.229529 | ||||||||
\(914\) | 46.3392 | 1.53277 | ||||||||
\(915\) | 8.54969 | 0.282644 | ||||||||
\(916\) | −79.6622 | −2.63211 | ||||||||
\(917\) | −7.09402 | −0.234265 | ||||||||
\(918\) | 28.6158 | 0.944463 | ||||||||
\(919\) | 29.8217 | 0.983726 | 0.491863 | − | 0.870673i | \(-0.336316\pi\) | ||||
0.491863 | + | 0.870673i | \(0.336316\pi\) | |||||||
\(920\) | −86.8555 | −2.86354 | ||||||||
\(921\) | 8.87836 | 0.292552 | ||||||||
\(922\) | −38.6187 | −1.27184 | ||||||||
\(923\) | 12.0003 | 0.394996 | ||||||||
\(924\) | −10.0325 | −0.330046 | ||||||||
\(925\) | 30.1043 | 0.989825 | ||||||||
\(926\) | −13.9914 | −0.459785 | ||||||||
\(927\) | −1.54346 | −0.0506939 | ||||||||
\(928\) | 9.47377 | 0.310992 | ||||||||
\(929\) | 23.3100 | 0.764775 | 0.382388 | − | 0.924002i | \(-0.375102\pi\) | ||||
0.382388 | + | 0.924002i | \(0.375102\pi\) | |||||||
\(930\) | 56.7067 | 1.85949 | ||||||||
\(931\) | −38.8962 | −1.27477 | ||||||||
\(932\) | 35.7405 | 1.17072 | ||||||||
\(933\) | −14.5821 | −0.477395 | ||||||||
\(934\) | 88.5894 | 2.89873 | ||||||||
\(935\) | −30.6503 | −1.00237 | ||||||||
\(936\) | −21.4343 | −0.700602 | ||||||||
\(937\) | 26.2774 | 0.858446 | 0.429223 | − | 0.903198i | \(-0.358787\pi\) | ||||
0.429223 | + | 0.903198i | \(0.358787\pi\) | |||||||
\(938\) | 4.02334 | 0.131367 | ||||||||
\(939\) | 5.83471 | 0.190409 | ||||||||
\(940\) | −127.676 | −4.16433 | ||||||||
\(941\) | 25.9370 | 0.845523 | 0.422761 | − | 0.906241i | \(-0.361061\pi\) | ||||
0.422761 | + | 0.906241i | \(0.361061\pi\) | |||||||
\(942\) | 57.4481 | 1.87176 | ||||||||
\(943\) | 23.4529 | 0.763732 | ||||||||
\(944\) | −23.0241 | −0.749371 | ||||||||
\(945\) | −6.97780 | −0.226988 | ||||||||
\(946\) | 4.63119 | 0.150573 | ||||||||
\(947\) | 52.6402 | 1.71058 | 0.855289 | − | 0.518151i | \(-0.173380\pi\) | ||||
0.855289 | + | 0.518151i | \(0.173380\pi\) | |||||||
\(948\) | −102.365 | −3.32465 | ||||||||
\(949\) | −8.30915 | −0.269726 | ||||||||
\(950\) | −171.211 | −5.55481 | ||||||||
\(951\) | −16.4277 | −0.532705 | ||||||||
\(952\) | 8.94863 | 0.290027 | ||||||||
\(953\) | −3.42258 | −0.110868 | −0.0554341 | − | 0.998462i | \(-0.517654\pi\) | ||||
−0.0554341 | + | 0.998462i | \(0.517654\pi\) | |||||||
\(954\) | 2.60507 | 0.0843423 | ||||||||
\(955\) | −5.23966 | −0.169551 | ||||||||
\(956\) | −47.0179 | −1.52067 | ||||||||
\(957\) | −15.9669 | −0.516136 | ||||||||
\(958\) | −52.2744 | −1.68891 | ||||||||
\(959\) | −4.57406 | −0.147704 | ||||||||
\(960\) | 123.815 | 3.99611 | ||||||||
\(961\) | −26.4108 | −0.851963 | ||||||||
\(962\) | −7.59381 | −0.244834 | ||||||||
\(963\) | −26.2693 | −0.846516 | ||||||||
\(964\) | −45.3303 | −1.45999 | ||||||||
\(965\) | 25.2267 | 0.812077 | ||||||||
\(966\) | 18.6787 | 0.600978 | ||||||||
\(967\) | 38.2377 | 1.22964 | 0.614821 | − | 0.788667i | \(-0.289228\pi\) | ||||
0.614821 | + | 0.788667i | \(0.289228\pi\) | |||||||
\(968\) | 30.4004 | 0.977107 | ||||||||
\(969\) | −62.4196 | −2.00521 | ||||||||
\(970\) | 5.74955 | 0.184607 | ||||||||
\(971\) | −18.4539 | −0.592213 | −0.296106 | − | 0.955155i | \(-0.595688\pi\) | ||||
−0.296106 | + | 0.955155i | \(0.595688\pi\) | |||||||
\(972\) | −75.8144 | −2.43175 | ||||||||
\(973\) | −8.51926 | −0.273115 | ||||||||
\(974\) | −69.7673 | −2.23549 | ||||||||
\(975\) | 43.1999 | 1.38350 | ||||||||
\(976\) | −1.63041 | −0.0521881 | ||||||||
\(977\) | −45.7969 | −1.46517 | −0.732587 | − | 0.680673i | \(-0.761687\pi\) | ||||
−0.732587 | + | 0.680673i | \(0.761687\pi\) | |||||||
\(978\) | 15.8451 | 0.506670 | ||||||||
\(979\) | −18.1496 | −0.580064 | ||||||||
\(980\) | 102.197 | 3.26458 | ||||||||
\(981\) | 19.5816 | 0.625191 | ||||||||
\(982\) | −15.3704 | −0.490490 | ||||||||
\(983\) | 14.4013 | 0.459331 | 0.229665 | − | 0.973270i | \(-0.426237\pi\) | ||||
0.229665 | + | 0.973270i | \(0.426237\pi\) | |||||||
\(984\) | 47.3679 | 1.51003 | ||||||||
\(985\) | −85.7254 | −2.73144 | ||||||||
\(986\) | 31.3146 | 0.997259 | ||||||||
\(987\) | 12.4876 | 0.397484 | ||||||||
\(988\) | 27.9496 | 0.889197 | ||||||||
\(989\) | −5.58013 | −0.177438 | ||||||||
\(990\) | −74.7719 | −2.37641 | ||||||||
\(991\) | 19.6799 | 0.625152 | 0.312576 | − | 0.949893i | \(-0.398808\pi\) | ||||
0.312576 | + | 0.949893i | \(0.398808\pi\) | |||||||
\(992\) | 6.20461 | 0.196997 | ||||||||
\(993\) | −54.8182 | −1.73960 | ||||||||
\(994\) | −12.2221 | −0.387660 | ||||||||
\(995\) | 57.5789 | 1.82537 | ||||||||
\(996\) | 37.1101 | 1.17588 | ||||||||
\(997\) | −6.83553 | −0.216484 | −0.108242 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108242 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(998\) | −0.246398 | −0.00779958 | ||||||||
\(999\) | 7.27941 | 0.230310 |
(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 | 4021.2.a.b.1.15 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.b.1.15 | ✓ | 151 | 1.1 | even | 1 | trivial |