Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.65028\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.675556 | 0.390033 | 0.195016 | − | 0.980800i | \(-0.437524\pi\) | ||||
0.195016 | + | 0.980800i | \(0.437524\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.675556 | −0.275795 | ||||||||
\(7\) | −1.96617 | −0.743142 | −0.371571 | − | 0.928404i | \(-0.621181\pi\) | ||||
−0.371571 | + | 0.928404i | \(0.621181\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.54362 | −0.847875 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.702842 | −0.211915 | −0.105957 | − | 0.994371i | \(-0.533791\pi\) | ||||
−0.105957 | + | 0.994371i | \(0.533791\pi\) | |||||||
\(12\) | 0.675556 | 0.195016 | ||||||||
\(13\) | 3.63999 | 1.00955 | 0.504775 | − | 0.863251i | \(-0.331575\pi\) | ||||
0.504775 | + | 0.863251i | \(0.331575\pi\) | |||||||
\(14\) | 1.96617 | 0.525481 | ||||||||
\(15\) | 0.675556 | 0.174428 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.463370 | −0.112384 | −0.0561919 | − | 0.998420i | \(-0.517896\pi\) | ||||
−0.0561919 | + | 0.998420i | \(0.517896\pi\) | |||||||
\(18\) | 2.54362 | 0.599538 | ||||||||
\(19\) | 1.64115 | 0.376505 | 0.188252 | − | 0.982121i | \(-0.439718\pi\) | ||||
0.188252 | + | 0.982121i | \(0.439718\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.32826 | −0.289850 | ||||||||
\(22\) | 0.702842 | 0.149846 | ||||||||
\(23\) | −3.53333 | −0.736750 | −0.368375 | − | 0.929677i | \(-0.620086\pi\) | ||||
−0.368375 | + | 0.929677i | \(0.620086\pi\) | |||||||
\(24\) | −0.675556 | −0.137897 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.63999 | −0.713860 | ||||||||
\(27\) | −3.74503 | −0.720731 | ||||||||
\(28\) | −1.96617 | −0.371571 | ||||||||
\(29\) | 2.53753 | 0.471208 | 0.235604 | − | 0.971849i | \(-0.424293\pi\) | ||||
0.235604 | + | 0.971849i | \(0.424293\pi\) | |||||||
\(30\) | −0.675556 | −0.123339 | ||||||||
\(31\) | −6.10965 | −1.09733 | −0.548663 | − | 0.836044i | \(-0.684863\pi\) | ||||
−0.548663 | + | 0.836044i | \(0.684863\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.474809 | −0.0826537 | ||||||||
\(34\) | 0.463370 | 0.0794673 | ||||||||
\(35\) | −1.96617 | −0.332343 | ||||||||
\(36\) | −2.54362 | −0.423937 | ||||||||
\(37\) | 5.76322 | 0.947468 | 0.473734 | − | 0.880668i | \(-0.342906\pi\) | ||||
0.473734 | + | 0.880668i | \(0.342906\pi\) | |||||||
\(38\) | −1.64115 | −0.266229 | ||||||||
\(39\) | 2.45902 | 0.393758 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.14911 | 1.11650 | 0.558251 | − | 0.829672i | \(-0.311472\pi\) | ||||
0.558251 | + | 0.829672i | \(0.311472\pi\) | |||||||
\(42\) | 1.32826 | 0.204955 | ||||||||
\(43\) | −6.31705 | −0.963342 | −0.481671 | − | 0.876352i | \(-0.659970\pi\) | ||||
−0.481671 | + | 0.876352i | \(0.659970\pi\) | |||||||
\(44\) | −0.702842 | −0.105957 | ||||||||
\(45\) | −2.54362 | −0.379181 | ||||||||
\(46\) | 3.53333 | 0.520961 | ||||||||
\(47\) | 5.97612 | 0.871707 | 0.435854 | − | 0.900018i | \(-0.356447\pi\) | ||||
0.435854 | + | 0.900018i | \(0.356447\pi\) | |||||||
\(48\) | 0.675556 | 0.0975082 | ||||||||
\(49\) | −3.13418 | −0.447739 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.313032 | −0.0438333 | ||||||||
\(52\) | 3.63999 | 0.504775 | ||||||||
\(53\) | −4.57721 | −0.628729 | −0.314364 | − | 0.949302i | \(-0.601791\pi\) | ||||
−0.314364 | + | 0.949302i | \(0.601791\pi\) | |||||||
\(54\) | 3.74503 | 0.509634 | ||||||||
\(55\) | −0.702842 | −0.0947711 | ||||||||
\(56\) | 1.96617 | 0.262741 | ||||||||
\(57\) | 1.10869 | 0.146849 | ||||||||
\(58\) | −2.53753 | −0.333194 | ||||||||
\(59\) | −2.56548 | −0.333997 | −0.166998 | − | 0.985957i | \(-0.553407\pi\) | ||||
−0.166998 | + | 0.985957i | \(0.553407\pi\) | |||||||
\(60\) | 0.675556 | 0.0872139 | ||||||||
\(61\) | −9.20668 | −1.17879 | −0.589397 | − | 0.807843i | \(-0.700635\pi\) | ||||
−0.589397 | + | 0.807843i | \(0.700635\pi\) | |||||||
\(62\) | 6.10965 | 0.775926 | ||||||||
\(63\) | 5.00120 | 0.630092 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.63999 | 0.451485 | ||||||||
\(66\) | 0.474809 | 0.0584450 | ||||||||
\(67\) | 2.71402 | 0.331570 | 0.165785 | − | 0.986162i | \(-0.446984\pi\) | ||||
0.165785 | + | 0.986162i | \(0.446984\pi\) | |||||||
\(68\) | −0.463370 | −0.0561919 | ||||||||
\(69\) | −2.38696 | −0.287357 | ||||||||
\(70\) | 1.96617 | 0.235002 | ||||||||
\(71\) | −3.57818 | −0.424651 | −0.212326 | − | 0.977199i | \(-0.568104\pi\) | ||||
−0.212326 | + | 0.977199i | \(0.568104\pi\) | |||||||
\(72\) | 2.54362 | 0.299769 | ||||||||
\(73\) | −1.05604 | −0.123600 | −0.0617999 | − | 0.998089i | \(-0.519684\pi\) | ||||
−0.0617999 | + | 0.998089i | \(0.519684\pi\) | |||||||
\(74\) | −5.76322 | −0.669961 | ||||||||
\(75\) | 0.675556 | 0.0780065 | ||||||||
\(76\) | 1.64115 | 0.188252 | ||||||||
\(77\) | 1.38191 | 0.157483 | ||||||||
\(78\) | −2.45902 | −0.278429 | ||||||||
\(79\) | −7.77888 | −0.875192 | −0.437596 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437596 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 5.10089 | 0.566766 | ||||||||
\(82\) | −7.14911 | −0.789487 | ||||||||
\(83\) | −5.64286 | −0.619384 | −0.309692 | − | 0.950837i | \(-0.600226\pi\) | ||||
−0.309692 | + | 0.950837i | \(0.600226\pi\) | |||||||
\(84\) | −1.32826 | −0.144925 | ||||||||
\(85\) | −0.463370 | −0.0502595 | ||||||||
\(86\) | 6.31705 | 0.681186 | ||||||||
\(87\) | 1.71424 | 0.183786 | ||||||||
\(88\) | 0.702842 | 0.0749232 | ||||||||
\(89\) | 2.42510 | 0.257060 | 0.128530 | − | 0.991706i | \(-0.458974\pi\) | ||||
0.128530 | + | 0.991706i | \(0.458974\pi\) | |||||||
\(90\) | 2.54362 | 0.268121 | ||||||||
\(91\) | −7.15683 | −0.750240 | ||||||||
\(92\) | −3.53333 | −0.368375 | ||||||||
\(93\) | −4.12741 | −0.427993 | ||||||||
\(94\) | −5.97612 | −0.616390 | ||||||||
\(95\) | 1.64115 | 0.168378 | ||||||||
\(96\) | −0.675556 | −0.0689487 | ||||||||
\(97\) | 14.3124 | 1.45321 | 0.726604 | − | 0.687057i | \(-0.241098\pi\) | ||||
0.726604 | + | 0.687057i | \(0.241098\pi\) | |||||||
\(98\) | 3.13418 | 0.316599 | ||||||||
\(99\) | 1.78776 | 0.179677 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.1101 | 1.10549 | 0.552747 | − | 0.833349i | \(-0.313580\pi\) | ||||
0.552747 | + | 0.833349i | \(0.313580\pi\) | |||||||
\(102\) | 0.313032 | 0.0309948 | ||||||||
\(103\) | −13.5007 | −1.33026 | −0.665130 | − | 0.746727i | \(-0.731624\pi\) | ||||
−0.665130 | + | 0.746727i | \(0.731624\pi\) | |||||||
\(104\) | −3.63999 | −0.356930 | ||||||||
\(105\) | −1.32826 | −0.129625 | ||||||||
\(106\) | 4.57721 | 0.444578 | ||||||||
\(107\) | −9.98140 | −0.964939 | −0.482469 | − | 0.875913i | \(-0.660260\pi\) | ||||
−0.482469 | + | 0.875913i | \(0.660260\pi\) | |||||||
\(108\) | −3.74503 | −0.360366 | ||||||||
\(109\) | −17.3033 | −1.65736 | −0.828678 | − | 0.559725i | \(-0.810907\pi\) | ||||
−0.828678 | + | 0.559725i | \(0.810907\pi\) | |||||||
\(110\) | 0.702842 | 0.0670133 | ||||||||
\(111\) | 3.89338 | 0.369543 | ||||||||
\(112\) | −1.96617 | −0.185786 | ||||||||
\(113\) | −15.8435 | −1.49043 | −0.745215 | − | 0.666824i | \(-0.767653\pi\) | ||||
−0.745215 | + | 0.666824i | \(0.767653\pi\) | |||||||
\(114\) | −1.10869 | −0.103838 | ||||||||
\(115\) | −3.53333 | −0.329485 | ||||||||
\(116\) | 2.53753 | 0.235604 | ||||||||
\(117\) | −9.25876 | −0.855972 | ||||||||
\(118\) | 2.56548 | 0.236171 | ||||||||
\(119\) | 0.911064 | 0.0835171 | ||||||||
\(120\) | −0.675556 | −0.0616696 | ||||||||
\(121\) | −10.5060 | −0.955092 | ||||||||
\(122\) | 9.20668 | 0.833534 | ||||||||
\(123\) | 4.82962 | 0.435472 | ||||||||
\(124\) | −6.10965 | −0.548663 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.00120 | −0.445542 | ||||||||
\(127\) | −2.46196 | −0.218463 | −0.109232 | − | 0.994016i | \(-0.534839\pi\) | ||||
−0.109232 | + | 0.994016i | \(0.534839\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.26753 | −0.375735 | ||||||||
\(130\) | −3.63999 | −0.319248 | ||||||||
\(131\) | −12.1540 | −1.06190 | −0.530950 | − | 0.847403i | \(-0.678165\pi\) | ||||
−0.530950 | + | 0.847403i | \(0.678165\pi\) | |||||||
\(132\) | −0.474809 | −0.0413268 | ||||||||
\(133\) | −3.22677 | −0.279797 | ||||||||
\(134\) | −2.71402 | −0.234456 | ||||||||
\(135\) | −3.74503 | −0.322321 | ||||||||
\(136\) | 0.463370 | 0.0397336 | ||||||||
\(137\) | −14.9534 | −1.27755 | −0.638777 | − | 0.769392i | \(-0.720559\pi\) | ||||
−0.638777 | + | 0.769392i | \(0.720559\pi\) | |||||||
\(138\) | 2.38696 | 0.203192 | ||||||||
\(139\) | −21.8514 | −1.85341 | −0.926704 | − | 0.375792i | \(-0.877371\pi\) | ||||
−0.926704 | + | 0.375792i | \(0.877371\pi\) | |||||||
\(140\) | −1.96617 | −0.166172 | ||||||||
\(141\) | 4.03721 | 0.339994 | ||||||||
\(142\) | 3.57818 | 0.300274 | ||||||||
\(143\) | −2.55833 | −0.213939 | ||||||||
\(144\) | −2.54362 | −0.211969 | ||||||||
\(145\) | 2.53753 | 0.210730 | ||||||||
\(146\) | 1.05604 | 0.0873982 | ||||||||
\(147\) | −2.11731 | −0.174633 | ||||||||
\(148\) | 5.76322 | 0.473734 | ||||||||
\(149\) | 3.79711 | 0.311071 | 0.155536 | − | 0.987830i | \(-0.450290\pi\) | ||||
0.155536 | + | 0.987830i | \(0.450290\pi\) | |||||||
\(150\) | −0.675556 | −0.0551589 | ||||||||
\(151\) | −5.98467 | −0.487026 | −0.243513 | − | 0.969898i | \(-0.578300\pi\) | ||||
−0.243513 | + | 0.969898i | \(0.578300\pi\) | |||||||
\(152\) | −1.64115 | −0.133114 | ||||||||
\(153\) | 1.17864 | 0.0952873 | ||||||||
\(154\) | −1.38191 | −0.111357 | ||||||||
\(155\) | −6.10965 | −0.490739 | ||||||||
\(156\) | 2.45902 | 0.196879 | ||||||||
\(157\) | 18.7300 | 1.49482 | 0.747409 | − | 0.664364i | \(-0.231297\pi\) | ||||
0.747409 | + | 0.664364i | \(0.231297\pi\) | |||||||
\(158\) | 7.77888 | 0.618854 | ||||||||
\(159\) | −3.09217 | −0.245225 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 6.94712 | 0.547510 | ||||||||
\(162\) | −5.10089 | −0.400764 | ||||||||
\(163\) | 24.0979 | 1.88750 | 0.943748 | − | 0.330666i | \(-0.107273\pi\) | ||||
0.943748 | + | 0.330666i | \(0.107273\pi\) | |||||||
\(164\) | 7.14911 | 0.558251 | ||||||||
\(165\) | −0.474809 | −0.0369638 | ||||||||
\(166\) | 5.64286 | 0.437971 | ||||||||
\(167\) | −6.60551 | −0.511150 | −0.255575 | − | 0.966789i | \(-0.582265\pi\) | ||||
−0.255575 | + | 0.966789i | \(0.582265\pi\) | |||||||
\(168\) | 1.32826 | 0.102477 | ||||||||
\(169\) | 0.249501 | 0.0191924 | ||||||||
\(170\) | 0.463370 | 0.0355389 | ||||||||
\(171\) | −4.17446 | −0.319229 | ||||||||
\(172\) | −6.31705 | −0.481671 | ||||||||
\(173\) | −15.0557 | −1.14466 | −0.572332 | − | 0.820022i | \(-0.693961\pi\) | ||||
−0.572332 | + | 0.820022i | \(0.693961\pi\) | |||||||
\(174\) | −1.71424 | −0.129957 | ||||||||
\(175\) | −1.96617 | −0.148628 | ||||||||
\(176\) | −0.702842 | −0.0529787 | ||||||||
\(177\) | −1.73312 | −0.130270 | ||||||||
\(178\) | −2.42510 | −0.181769 | ||||||||
\(179\) | 12.5215 | 0.935904 | 0.467952 | − | 0.883754i | \(-0.344992\pi\) | ||||
0.467952 | + | 0.883754i | \(0.344992\pi\) | |||||||
\(180\) | −2.54362 | −0.189591 | ||||||||
\(181\) | −23.0329 | −1.71202 | −0.856012 | − | 0.516956i | \(-0.827065\pi\) | ||||
−0.856012 | + | 0.516956i | \(0.827065\pi\) | |||||||
\(182\) | 7.15683 | 0.530500 | ||||||||
\(183\) | −6.21963 | −0.459768 | ||||||||
\(184\) | 3.53333 | 0.260480 | ||||||||
\(185\) | 5.76322 | 0.423721 | ||||||||
\(186\) | 4.12741 | 0.302637 | ||||||||
\(187\) | 0.325676 | 0.0238158 | ||||||||
\(188\) | 5.97612 | 0.435854 | ||||||||
\(189\) | 7.36337 | 0.535606 | ||||||||
\(190\) | −1.64115 | −0.119061 | ||||||||
\(191\) | 15.0467 | 1.08874 | 0.544371 | − | 0.838844i | \(-0.316768\pi\) | ||||
0.544371 | + | 0.838844i | \(0.316768\pi\) | |||||||
\(192\) | 0.675556 | 0.0487541 | ||||||||
\(193\) | −19.7068 | −1.41852 | −0.709262 | − | 0.704945i | \(-0.750972\pi\) | ||||
−0.709262 | + | 0.704945i | \(0.750972\pi\) | |||||||
\(194\) | −14.3124 | −1.02757 | ||||||||
\(195\) | 2.45902 | 0.176094 | ||||||||
\(196\) | −3.13418 | −0.223870 | ||||||||
\(197\) | 15.6305 | 1.11363 | 0.556813 | − | 0.830638i | \(-0.312024\pi\) | ||||
0.556813 | + | 0.830638i | \(0.312024\pi\) | |||||||
\(198\) | −1.78776 | −0.127051 | ||||||||
\(199\) | −6.63045 | −0.470020 | −0.235010 | − | 0.971993i | \(-0.575512\pi\) | ||||
−0.235010 | + | 0.971993i | \(0.575512\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 1.83347 | 0.129323 | ||||||||
\(202\) | −11.1101 | −0.781703 | ||||||||
\(203\) | −4.98922 | −0.350174 | ||||||||
\(204\) | −0.313032 | −0.0219167 | ||||||||
\(205\) | 7.14911 | 0.499315 | ||||||||
\(206\) | 13.5007 | 0.940636 | ||||||||
\(207\) | 8.98746 | 0.624671 | ||||||||
\(208\) | 3.63999 | 0.252388 | ||||||||
\(209\) | −1.15347 | −0.0797869 | ||||||||
\(210\) | 1.32826 | 0.0916586 | ||||||||
\(211\) | 18.7194 | 1.28870 | 0.644350 | − | 0.764731i | \(-0.277128\pi\) | ||||
0.644350 | + | 0.764731i | \(0.277128\pi\) | |||||||
\(212\) | −4.57721 | −0.314364 | ||||||||
\(213\) | −2.41726 | −0.165628 | ||||||||
\(214\) | 9.98140 | 0.682315 | ||||||||
\(215\) | −6.31705 | −0.430820 | ||||||||
\(216\) | 3.74503 | 0.254817 | ||||||||
\(217\) | 12.0126 | 0.815469 | ||||||||
\(218\) | 17.3033 | 1.17193 | ||||||||
\(219\) | −0.713412 | −0.0482079 | ||||||||
\(220\) | −0.702842 | −0.0473856 | ||||||||
\(221\) | −1.68666 | −0.113457 | ||||||||
\(222\) | −3.89338 | −0.261307 | ||||||||
\(223\) | −7.21360 | −0.483059 | −0.241529 | − | 0.970394i | \(-0.577649\pi\) | ||||
−0.241529 | + | 0.970394i | \(0.577649\pi\) | |||||||
\(224\) | 1.96617 | 0.131370 | ||||||||
\(225\) | −2.54362 | −0.169575 | ||||||||
\(226\) | 15.8435 | 1.05389 | ||||||||
\(227\) | 19.4540 | 1.29120 | 0.645602 | − | 0.763674i | \(-0.276606\pi\) | ||||
0.645602 | + | 0.763674i | \(0.276606\pi\) | |||||||
\(228\) | 1.10869 | 0.0734245 | ||||||||
\(229\) | 11.2055 | 0.740479 | 0.370239 | − | 0.928936i | \(-0.379276\pi\) | ||||
0.370239 | + | 0.928936i | \(0.379276\pi\) | |||||||
\(230\) | 3.53333 | 0.232981 | ||||||||
\(231\) | 0.933555 | 0.0614234 | ||||||||
\(232\) | −2.53753 | −0.166597 | ||||||||
\(233\) | 17.7284 | 1.16143 | 0.580714 | − | 0.814108i | \(-0.302773\pi\) | ||||
0.580714 | + | 0.814108i | \(0.302773\pi\) | |||||||
\(234\) | 9.25876 | 0.605264 | ||||||||
\(235\) | 5.97612 | 0.389839 | ||||||||
\(236\) | −2.56548 | −0.166998 | ||||||||
\(237\) | −5.25507 | −0.341353 | ||||||||
\(238\) | −0.911064 | −0.0590555 | ||||||||
\(239\) | −13.2487 | −0.856990 | −0.428495 | − | 0.903544i | \(-0.640956\pi\) | ||||
−0.428495 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(240\) | 0.675556 | 0.0436070 | ||||||||
\(241\) | 6.61312 | 0.425989 | 0.212994 | − | 0.977053i | \(-0.431678\pi\) | ||||
0.212994 | + | 0.977053i | \(0.431678\pi\) | |||||||
\(242\) | 10.5060 | 0.675352 | ||||||||
\(243\) | 14.6810 | 0.941789 | ||||||||
\(244\) | −9.20668 | −0.589397 | ||||||||
\(245\) | −3.13418 | −0.200235 | ||||||||
\(246\) | −4.82962 | −0.307926 | ||||||||
\(247\) | 5.97375 | 0.380100 | ||||||||
\(248\) | 6.10965 | 0.387963 | ||||||||
\(249\) | −3.81207 | −0.241580 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −26.0274 | −1.64283 | −0.821417 | − | 0.570329i | \(-0.806816\pi\) | ||||
−0.821417 | + | 0.570329i | \(0.806816\pi\) | |||||||
\(252\) | 5.00120 | 0.315046 | ||||||||
\(253\) | 2.48337 | 0.156128 | ||||||||
\(254\) | 2.46196 | 0.154477 | ||||||||
\(255\) | −0.313032 | −0.0196029 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.14027 | −0.507776 | −0.253888 | − | 0.967234i | \(-0.581710\pi\) | ||||
−0.253888 | + | 0.967234i | \(0.581710\pi\) | |||||||
\(258\) | 4.26753 | 0.265685 | ||||||||
\(259\) | −11.3315 | −0.704104 | ||||||||
\(260\) | 3.63999 | 0.225742 | ||||||||
\(261\) | −6.45452 | −0.399525 | ||||||||
\(262\) | 12.1540 | 0.750877 | ||||||||
\(263\) | 2.11090 | 0.130164 | 0.0650820 | − | 0.997880i | \(-0.479269\pi\) | ||||
0.0650820 | + | 0.997880i | \(0.479269\pi\) | |||||||
\(264\) | 0.474809 | 0.0292225 | ||||||||
\(265\) | −4.57721 | −0.281176 | ||||||||
\(266\) | 3.22677 | 0.197846 | ||||||||
\(267\) | 1.63829 | 0.100262 | ||||||||
\(268\) | 2.71402 | 0.165785 | ||||||||
\(269\) | −19.0580 | −1.16199 | −0.580993 | − | 0.813909i | \(-0.697336\pi\) | ||||
−0.580993 | + | 0.813909i | \(0.697336\pi\) | |||||||
\(270\) | 3.74503 | 0.227915 | ||||||||
\(271\) | −5.04991 | −0.306760 | −0.153380 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153380 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(272\) | −0.463370 | −0.0280959 | ||||||||
\(273\) | −4.83484 | −0.292618 | ||||||||
\(274\) | 14.9534 | 0.903367 | ||||||||
\(275\) | −0.702842 | −0.0423829 | ||||||||
\(276\) | −2.38696 | −0.143678 | ||||||||
\(277\) | −9.21670 | −0.553778 | −0.276889 | − | 0.960902i | \(-0.589303\pi\) | ||||
−0.276889 | + | 0.960902i | \(0.589303\pi\) | |||||||
\(278\) | 21.8514 | 1.31056 | ||||||||
\(279\) | 15.5407 | 0.930394 | ||||||||
\(280\) | 1.96617 | 0.117501 | ||||||||
\(281\) | −6.57568 | −0.392272 | −0.196136 | − | 0.980577i | \(-0.562839\pi\) | ||||
−0.196136 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(282\) | −4.03721 | −0.240412 | ||||||||
\(283\) | 18.7413 | 1.11406 | 0.557028 | − | 0.830494i | \(-0.311942\pi\) | ||||
0.557028 | + | 0.830494i | \(0.311942\pi\) | |||||||
\(284\) | −3.57818 | −0.212326 | ||||||||
\(285\) | 1.10869 | 0.0656729 | ||||||||
\(286\) | 2.55833 | 0.151277 | ||||||||
\(287\) | −14.0564 | −0.829721 | ||||||||
\(288\) | 2.54362 | 0.149884 | ||||||||
\(289\) | −16.7853 | −0.987370 | ||||||||
\(290\) | −2.53753 | −0.149009 | ||||||||
\(291\) | 9.66886 | 0.566798 | ||||||||
\(292\) | −1.05604 | −0.0617999 | ||||||||
\(293\) | 20.3420 | 1.18839 | 0.594195 | − | 0.804321i | \(-0.297471\pi\) | ||||
0.594195 | + | 0.804321i | \(0.297471\pi\) | |||||||
\(294\) | 2.11731 | 0.123484 | ||||||||
\(295\) | −2.56548 | −0.149368 | ||||||||
\(296\) | −5.76322 | −0.334981 | ||||||||
\(297\) | 2.63216 | 0.152734 | ||||||||
\(298\) | −3.79711 | −0.219961 | ||||||||
\(299\) | −12.8613 | −0.743786 | ||||||||
\(300\) | 0.675556 | 0.0390033 | ||||||||
\(301\) | 12.4204 | 0.715900 | ||||||||
\(302\) | 5.98467 | 0.344379 | ||||||||
\(303\) | 7.50548 | 0.431179 | ||||||||
\(304\) | 1.64115 | 0.0941261 | ||||||||
\(305\) | −9.20668 | −0.527173 | ||||||||
\(306\) | −1.17864 | −0.0673783 | ||||||||
\(307\) | −9.26421 | −0.528737 | −0.264368 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264368 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(308\) | 1.38191 | 0.0787414 | ||||||||
\(309\) | −9.12046 | −0.518845 | ||||||||
\(310\) | 6.10965 | 0.347005 | ||||||||
\(311\) | −10.3280 | −0.585650 | −0.292825 | − | 0.956166i | \(-0.594595\pi\) | ||||
−0.292825 | + | 0.956166i | \(0.594595\pi\) | |||||||
\(312\) | −2.45902 | −0.139214 | ||||||||
\(313\) | −24.1184 | −1.36325 | −0.681626 | − | 0.731701i | \(-0.738727\pi\) | ||||
−0.681626 | + | 0.731701i | \(0.738727\pi\) | |||||||
\(314\) | −18.7300 | −1.05700 | ||||||||
\(315\) | 5.00120 | 0.281786 | ||||||||
\(316\) | −7.77888 | −0.437596 | ||||||||
\(317\) | 19.8911 | 1.11720 | 0.558598 | − | 0.829438i | \(-0.311339\pi\) | ||||
0.558598 | + | 0.829438i | \(0.311339\pi\) | |||||||
\(318\) | 3.09217 | 0.173400 | ||||||||
\(319\) | −1.78348 | −0.0998558 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −6.74300 | −0.376358 | ||||||||
\(322\) | −6.94712 | −0.387148 | ||||||||
\(323\) | −0.760457 | −0.0423130 | ||||||||
\(324\) | 5.10089 | 0.283383 | ||||||||
\(325\) | 3.63999 | 0.201910 | ||||||||
\(326\) | −24.0979 | −1.33466 | ||||||||
\(327\) | −11.6894 | −0.646423 | ||||||||
\(328\) | −7.14911 | −0.394743 | ||||||||
\(329\) | −11.7501 | −0.647803 | ||||||||
\(330\) | 0.474809 | 0.0261374 | ||||||||
\(331\) | −25.8891 | −1.42299 | −0.711496 | − | 0.702691i | \(-0.751982\pi\) | ||||
−0.711496 | + | 0.702691i | \(0.751982\pi\) | |||||||
\(332\) | −5.64286 | −0.309692 | ||||||||
\(333\) | −14.6595 | −0.803334 | ||||||||
\(334\) | 6.60551 | 0.361437 | ||||||||
\(335\) | 2.71402 | 0.148283 | ||||||||
\(336\) | −1.32826 | −0.0724625 | ||||||||
\(337\) | 14.9572 | 0.814770 | 0.407385 | − | 0.913257i | \(-0.366441\pi\) | ||||
0.407385 | + | 0.913257i | \(0.366441\pi\) | |||||||
\(338\) | −0.249501 | −0.0135711 | ||||||||
\(339\) | −10.7032 | −0.581317 | ||||||||
\(340\) | −0.463370 | −0.0251298 | ||||||||
\(341\) | 4.29412 | 0.232539 | ||||||||
\(342\) | 4.17446 | 0.225729 | ||||||||
\(343\) | 19.9255 | 1.07588 | ||||||||
\(344\) | 6.31705 | 0.340593 | ||||||||
\(345\) | −2.38696 | −0.128510 | ||||||||
\(346\) | 15.0557 | 0.809400 | ||||||||
\(347\) | 27.7319 | 1.48873 | 0.744363 | − | 0.667776i | \(-0.232753\pi\) | ||||
0.744363 | + | 0.667776i | \(0.232753\pi\) | |||||||
\(348\) | 1.71424 | 0.0918932 | ||||||||
\(349\) | 2.15312 | 0.115254 | 0.0576270 | − | 0.998338i | \(-0.481647\pi\) | ||||
0.0576270 | + | 0.998338i | \(0.481647\pi\) | |||||||
\(350\) | 1.96617 | 0.105096 | ||||||||
\(351\) | −13.6319 | −0.727615 | ||||||||
\(352\) | 0.702842 | 0.0374616 | ||||||||
\(353\) | 6.05838 | 0.322455 | 0.161228 | − | 0.986917i | \(-0.448455\pi\) | ||||
0.161228 | + | 0.986917i | \(0.448455\pi\) | |||||||
\(354\) | 1.73312 | 0.0921145 | ||||||||
\(355\) | −3.57818 | −0.189910 | ||||||||
\(356\) | 2.42510 | 0.128530 | ||||||||
\(357\) | 0.615475 | 0.0325744 | ||||||||
\(358\) | −12.5215 | −0.661784 | ||||||||
\(359\) | −26.0891 | −1.37693 | −0.688465 | − | 0.725270i | \(-0.741715\pi\) | ||||
−0.688465 | + | 0.725270i | \(0.741715\pi\) | |||||||
\(360\) | 2.54362 | 0.134061 | ||||||||
\(361\) | −16.3066 | −0.858244 | ||||||||
\(362\) | 23.0329 | 1.21058 | ||||||||
\(363\) | −7.09740 | −0.372517 | ||||||||
\(364\) | −7.15683 | −0.375120 | ||||||||
\(365\) | −1.05604 | −0.0552755 | ||||||||
\(366\) | 6.21963 | 0.325105 | ||||||||
\(367\) | 2.08709 | 0.108945 | 0.0544725 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544725 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(368\) | −3.53333 | −0.184187 | ||||||||
\(369\) | −18.1846 | −0.946654 | ||||||||
\(370\) | −5.76322 | −0.299616 | ||||||||
\(371\) | 8.99958 | 0.467235 | ||||||||
\(372\) | −4.12741 | −0.213996 | ||||||||
\(373\) | −28.8649 | −1.49457 | −0.747284 | − | 0.664504i | \(-0.768643\pi\) | ||||
−0.747284 | + | 0.664504i | \(0.768643\pi\) | |||||||
\(374\) | −0.325676 | −0.0168403 | ||||||||
\(375\) | 0.675556 | 0.0348856 | ||||||||
\(376\) | −5.97612 | −0.308195 | ||||||||
\(377\) | 9.23658 | 0.475708 | ||||||||
\(378\) | −7.36337 | −0.378731 | ||||||||
\(379\) | 7.44485 | 0.382416 | 0.191208 | − | 0.981550i | \(-0.438759\pi\) | ||||
0.191208 | + | 0.981550i | \(0.438759\pi\) | |||||||
\(380\) | 1.64115 | 0.0841890 | ||||||||
\(381\) | −1.66319 | −0.0852079 | ||||||||
\(382\) | −15.0467 | −0.769858 | ||||||||
\(383\) | −18.3001 | −0.935092 | −0.467546 | − | 0.883969i | \(-0.654862\pi\) | ||||
−0.467546 | + | 0.883969i | \(0.654862\pi\) | |||||||
\(384\) | −0.675556 | −0.0344743 | ||||||||
\(385\) | 1.38191 | 0.0704285 | ||||||||
\(386\) | 19.7068 | 1.00305 | ||||||||
\(387\) | 16.0682 | 0.816793 | ||||||||
\(388\) | 14.3124 | 0.726604 | ||||||||
\(389\) | 22.2317 | 1.12719 | 0.563597 | − | 0.826050i | \(-0.309417\pi\) | ||||
0.563597 | + | 0.826050i | \(0.309417\pi\) | |||||||
\(390\) | −2.45902 | −0.124517 | ||||||||
\(391\) | 1.63724 | 0.0827987 | ||||||||
\(392\) | 3.13418 | 0.158300 | ||||||||
\(393\) | −8.21071 | −0.414176 | ||||||||
\(394\) | −15.6305 | −0.787452 | ||||||||
\(395\) | −7.77888 | −0.391398 | ||||||||
\(396\) | 1.78776 | 0.0898385 | ||||||||
\(397\) | 3.83234 | 0.192340 | 0.0961699 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961699 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(398\) | 6.63045 | 0.332354 | ||||||||
\(399\) | −2.17987 | −0.109130 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | −1.83347 | −0.0914453 | ||||||||
\(403\) | −22.2390 | −1.10781 | ||||||||
\(404\) | 11.1101 | 0.552747 | ||||||||
\(405\) | 5.10089 | 0.253465 | ||||||||
\(406\) | 4.98922 | 0.247611 | ||||||||
\(407\) | −4.05063 | −0.200782 | ||||||||
\(408\) | 0.313032 | 0.0154974 | ||||||||
\(409\) | 20.3572 | 1.00660 | 0.503300 | − | 0.864112i | \(-0.332119\pi\) | ||||
0.503300 | + | 0.864112i | \(0.332119\pi\) | |||||||
\(410\) | −7.14911 | −0.353069 | ||||||||
\(411\) | −10.1019 | −0.498288 | ||||||||
\(412\) | −13.5007 | −0.665130 | ||||||||
\(413\) | 5.04416 | 0.248207 | ||||||||
\(414\) | −8.98746 | −0.441709 | ||||||||
\(415\) | −5.64286 | −0.276997 | ||||||||
\(416\) | −3.63999 | −0.178465 | ||||||||
\(417\) | −14.7618 | −0.722890 | ||||||||
\(418\) | 1.15347 | 0.0564178 | ||||||||
\(419\) | 20.8407 | 1.01814 | 0.509068 | − | 0.860726i | \(-0.329990\pi\) | ||||
0.509068 | + | 0.860726i | \(0.329990\pi\) | |||||||
\(420\) | −1.32826 | −0.0648124 | ||||||||
\(421\) | 23.1118 | 1.12640 | 0.563200 | − | 0.826321i | \(-0.309570\pi\) | ||||
0.563200 | + | 0.826321i | \(0.309570\pi\) | |||||||
\(422\) | −18.7194 | −0.911248 | ||||||||
\(423\) | −15.2010 | −0.739098 | ||||||||
\(424\) | 4.57721 | 0.222289 | ||||||||
\(425\) | −0.463370 | −0.0224767 | ||||||||
\(426\) | 2.41726 | 0.117117 | ||||||||
\(427\) | 18.1019 | 0.876012 | ||||||||
\(428\) | −9.98140 | −0.482469 | ||||||||
\(429\) | −1.72830 | −0.0834430 | ||||||||
\(430\) | 6.31705 | 0.304635 | ||||||||
\(431\) | −26.9560 | −1.29842 | −0.649212 | − | 0.760608i | \(-0.724901\pi\) | ||||
−0.649212 | + | 0.760608i | \(0.724901\pi\) | |||||||
\(432\) | −3.74503 | −0.180183 | ||||||||
\(433\) | 1.05846 | 0.0508662 | 0.0254331 | − | 0.999677i | \(-0.491904\pi\) | ||||
0.0254331 | + | 0.999677i | \(0.491904\pi\) | |||||||
\(434\) | −12.0126 | −0.576624 | ||||||||
\(435\) | 1.71424 | 0.0821917 | ||||||||
\(436\) | −17.3033 | −0.828678 | ||||||||
\(437\) | −5.79871 | −0.277390 | ||||||||
\(438\) | 0.713412 | 0.0340882 | ||||||||
\(439\) | −26.9332 | −1.28545 | −0.642725 | − | 0.766097i | \(-0.722196\pi\) | ||||
−0.642725 | + | 0.766097i | \(0.722196\pi\) | |||||||
\(440\) | 0.702842 | 0.0335067 | ||||||||
\(441\) | 7.97216 | 0.379627 | ||||||||
\(442\) | 1.68666 | 0.0802262 | ||||||||
\(443\) | 3.79606 | 0.180356 | 0.0901782 | − | 0.995926i | \(-0.471256\pi\) | ||||
0.0901782 | + | 0.995926i | \(0.471256\pi\) | |||||||
\(444\) | 3.89338 | 0.184772 | ||||||||
\(445\) | 2.42510 | 0.114961 | ||||||||
\(446\) | 7.21360 | 0.341574 | ||||||||
\(447\) | 2.56516 | 0.121328 | ||||||||
\(448\) | −1.96617 | −0.0928928 | ||||||||
\(449\) | −19.9784 | −0.942841 | −0.471420 | − | 0.881909i | \(-0.656258\pi\) | ||||
−0.471420 | + | 0.881909i | \(0.656258\pi\) | |||||||
\(450\) | 2.54362 | 0.119908 | ||||||||
\(451\) | −5.02469 | −0.236603 | ||||||||
\(452\) | −15.8435 | −0.745215 | ||||||||
\(453\) | −4.04298 | −0.189956 | ||||||||
\(454\) | −19.4540 | −0.913020 | ||||||||
\(455\) | −7.15683 | −0.335517 | ||||||||
\(456\) | −1.10869 | −0.0519190 | ||||||||
\(457\) | −12.0619 | −0.564231 | −0.282115 | − | 0.959380i | \(-0.591036\pi\) | ||||
−0.282115 | + | 0.959380i | \(0.591036\pi\) | |||||||
\(458\) | −11.2055 | −0.523598 | ||||||||
\(459\) | 1.73533 | 0.0809985 | ||||||||
\(460\) | −3.53333 | −0.164742 | ||||||||
\(461\) | −23.7685 | −1.10701 | −0.553504 | − | 0.832847i | \(-0.686710\pi\) | ||||
−0.553504 | + | 0.832847i | \(0.686710\pi\) | |||||||
\(462\) | −0.933555 | −0.0434329 | ||||||||
\(463\) | −25.5650 | −1.18810 | −0.594052 | − | 0.804426i | \(-0.702473\pi\) | ||||
−0.594052 | + | 0.804426i | \(0.702473\pi\) | |||||||
\(464\) | 2.53753 | 0.117802 | ||||||||
\(465\) | −4.12741 | −0.191404 | ||||||||
\(466\) | −17.7284 | −0.821254 | ||||||||
\(467\) | 1.38486 | 0.0640835 | 0.0320418 | − | 0.999487i | \(-0.489799\pi\) | ||||
0.0320418 | + | 0.999487i | \(0.489799\pi\) | |||||||
\(468\) | −9.25876 | −0.427986 | ||||||||
\(469\) | −5.33623 | −0.246404 | ||||||||
\(470\) | −5.97612 | −0.275658 | ||||||||
\(471\) | 12.6532 | 0.583028 | ||||||||
\(472\) | 2.56548 | 0.118086 | ||||||||
\(473\) | 4.43989 | 0.204146 | ||||||||
\(474\) | 5.25507 | 0.241373 | ||||||||
\(475\) | 1.64115 | 0.0753009 | ||||||||
\(476\) | 0.911064 | 0.0417586 | ||||||||
\(477\) | 11.6427 | 0.533083 | ||||||||
\(478\) | 13.2487 | 0.605983 | ||||||||
\(479\) | −9.15088 | −0.418114 | −0.209057 | − | 0.977903i | \(-0.567039\pi\) | ||||
−0.209057 | + | 0.977903i | \(0.567039\pi\) | |||||||
\(480\) | −0.675556 | −0.0308348 | ||||||||
\(481\) | 20.9781 | 0.956517 | ||||||||
\(482\) | −6.61312 | −0.301219 | ||||||||
\(483\) | 4.69317 | 0.213547 | ||||||||
\(484\) | −10.5060 | −0.477546 | ||||||||
\(485\) | 14.3124 | 0.649894 | ||||||||
\(486\) | −14.6810 | −0.665945 | ||||||||
\(487\) | 9.41697 | 0.426724 | 0.213362 | − | 0.976973i | \(-0.431559\pi\) | ||||
0.213362 | + | 0.976973i | \(0.431559\pi\) | |||||||
\(488\) | 9.20668 | 0.416767 | ||||||||
\(489\) | 16.2795 | 0.736185 | ||||||||
\(490\) | 3.13418 | 0.141588 | ||||||||
\(491\) | 21.6913 | 0.978917 | 0.489458 | − | 0.872027i | \(-0.337195\pi\) | ||||
0.489458 | + | 0.872027i | \(0.337195\pi\) | |||||||
\(492\) | 4.82962 | 0.217736 | ||||||||
\(493\) | −1.17582 | −0.0529561 | ||||||||
\(494\) | −5.97375 | −0.268772 | ||||||||
\(495\) | 1.78776 | 0.0803540 | ||||||||
\(496\) | −6.10965 | −0.274331 | ||||||||
\(497\) | 7.03530 | 0.315577 | ||||||||
\(498\) | 3.81207 | 0.170823 | ||||||||
\(499\) | −38.4965 | −1.72334 | −0.861670 | − | 0.507468i | \(-0.830581\pi\) | ||||
−0.861670 | + | 0.507468i | \(0.830581\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −4.46239 | −0.199365 | ||||||||
\(502\) | 26.0274 | 1.16166 | ||||||||
\(503\) | −18.5035 | −0.825029 | −0.412515 | − | 0.910951i | \(-0.635349\pi\) | ||||
−0.412515 | + | 0.910951i | \(0.635349\pi\) | |||||||
\(504\) | −5.00120 | −0.222771 | ||||||||
\(505\) | 11.1101 | 0.494392 | ||||||||
\(506\) | −2.48337 | −0.110399 | ||||||||
\(507\) | 0.168552 | 0.00748566 | ||||||||
\(508\) | −2.46196 | −0.109232 | ||||||||
\(509\) | 29.3133 | 1.29929 | 0.649644 | − | 0.760239i | \(-0.274918\pi\) | ||||
0.649644 | + | 0.760239i | \(0.274918\pi\) | |||||||
\(510\) | 0.313032 | 0.0138613 | ||||||||
\(511\) | 2.07635 | 0.0918522 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.14614 | −0.271359 | ||||||||
\(514\) | 8.14027 | 0.359052 | ||||||||
\(515\) | −13.5007 | −0.594910 | ||||||||
\(516\) | −4.26753 | −0.187867 | ||||||||
\(517\) | −4.20027 | −0.184728 | ||||||||
\(518\) | 11.3315 | 0.497877 | ||||||||
\(519\) | −10.1710 | −0.446456 | ||||||||
\(520\) | −3.63999 | −0.159624 | ||||||||
\(521\) | −28.6667 | −1.25591 | −0.627956 | − | 0.778249i | \(-0.716108\pi\) | ||||
−0.627956 | + | 0.778249i | \(0.716108\pi\) | |||||||
\(522\) | 6.45452 | 0.282507 | ||||||||
\(523\) | 35.7366 | 1.56265 | 0.781326 | − | 0.624123i | \(-0.214543\pi\) | ||||
0.781326 | + | 0.624123i | \(0.214543\pi\) | |||||||
\(524\) | −12.1540 | −0.530950 | ||||||||
\(525\) | −1.32826 | −0.0579700 | ||||||||
\(526\) | −2.11090 | −0.0920398 | ||||||||
\(527\) | 2.83103 | 0.123322 | ||||||||
\(528\) | −0.474809 | −0.0206634 | ||||||||
\(529\) | −10.5156 | −0.457200 | ||||||||
\(530\) | 4.57721 | 0.198821 | ||||||||
\(531\) | 6.52561 | 0.283187 | ||||||||
\(532\) | −3.22677 | −0.139898 | ||||||||
\(533\) | 26.0226 | 1.12717 | ||||||||
\(534\) | −1.63829 | −0.0708959 | ||||||||
\(535\) | −9.98140 | −0.431534 | ||||||||
\(536\) | −2.71402 | −0.117228 | ||||||||
\(537\) | 8.45900 | 0.365033 | ||||||||
\(538\) | 19.0580 | 0.821648 | ||||||||
\(539\) | 2.20283 | 0.0948826 | ||||||||
\(540\) | −3.74503 | −0.161160 | ||||||||
\(541\) | 34.4528 | 1.48124 | 0.740620 | − | 0.671924i | \(-0.234532\pi\) | ||||
0.740620 | + | 0.671924i | \(0.234532\pi\) | |||||||
\(542\) | 5.04991 | 0.216912 | ||||||||
\(543\) | −15.5600 | −0.667745 | ||||||||
\(544\) | 0.463370 | 0.0198668 | ||||||||
\(545\) | −17.3033 | −0.741192 | ||||||||
\(546\) | 4.83484 | 0.206912 | ||||||||
\(547\) | −23.5201 | −1.00565 | −0.502824 | − | 0.864389i | \(-0.667705\pi\) | ||||
−0.502824 | + | 0.864389i | \(0.667705\pi\) | |||||||
\(548\) | −14.9534 | −0.638777 | ||||||||
\(549\) | 23.4183 | 0.999470 | ||||||||
\(550\) | 0.702842 | 0.0299693 | ||||||||
\(551\) | 4.16446 | 0.177412 | ||||||||
\(552\) | 2.38696 | 0.101596 | ||||||||
\(553\) | 15.2946 | 0.650392 | ||||||||
\(554\) | 9.21670 | 0.391580 | ||||||||
\(555\) | 3.89338 | 0.165265 | ||||||||
\(556\) | −21.8514 | −0.926704 | ||||||||
\(557\) | 7.16891 | 0.303757 | 0.151878 | − | 0.988399i | \(-0.451468\pi\) | ||||
0.151878 | + | 0.988399i | \(0.451468\pi\) | |||||||
\(558\) | −15.5407 | −0.657888 | ||||||||
\(559\) | −22.9940 | −0.972542 | ||||||||
\(560\) | −1.96617 | −0.0830859 | ||||||||
\(561\) | 0.220012 | 0.00928893 | ||||||||
\(562\) | 6.57568 | 0.277378 | ||||||||
\(563\) | −6.13281 | −0.258467 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(564\) | 4.03721 | 0.169997 | ||||||||
\(565\) | −15.8435 | −0.666541 | ||||||||
\(566\) | −18.7413 | −0.787757 | ||||||||
\(567\) | −10.0292 | −0.421188 | ||||||||
\(568\) | 3.57818 | 0.150137 | ||||||||
\(569\) | −36.2932 | −1.52149 | −0.760745 | − | 0.649050i | \(-0.775166\pi\) | ||||
−0.760745 | + | 0.649050i | \(0.775166\pi\) | |||||||
\(570\) | −1.10869 | −0.0464378 | ||||||||
\(571\) | −4.27540 | −0.178920 | −0.0894600 | − | 0.995990i | \(-0.528514\pi\) | ||||
−0.0894600 | + | 0.995990i | \(0.528514\pi\) | |||||||
\(572\) | −2.55833 | −0.106969 | ||||||||
\(573\) | 10.1649 | 0.424645 | ||||||||
\(574\) | 14.0564 | 0.586701 | ||||||||
\(575\) | −3.53333 | −0.147350 | ||||||||
\(576\) | −2.54362 | −0.105984 | ||||||||
\(577\) | 13.9229 | 0.579616 | 0.289808 | − | 0.957085i | \(-0.406408\pi\) | ||||
0.289808 | + | 0.957085i | \(0.406408\pi\) | |||||||
\(578\) | 16.7853 | 0.698176 | ||||||||
\(579\) | −13.3130 | −0.553271 | ||||||||
\(580\) | 2.53753 | 0.105365 | ||||||||
\(581\) | 11.0948 | 0.460291 | ||||||||
\(582\) | −9.66886 | −0.400787 | ||||||||
\(583\) | 3.21706 | 0.133237 | ||||||||
\(584\) | 1.05604 | 0.0436991 | ||||||||
\(585\) | −9.25876 | −0.382802 | ||||||||
\(586\) | −20.3420 | −0.840319 | ||||||||
\(587\) | −30.9970 | −1.27938 | −0.639692 | − | 0.768631i | \(-0.720938\pi\) | ||||
−0.639692 | + | 0.768631i | \(0.720938\pi\) | |||||||
\(588\) | −2.11731 | −0.0873165 | ||||||||
\(589\) | −10.0268 | −0.413148 | ||||||||
\(590\) | 2.56548 | 0.105619 | ||||||||
\(591\) | 10.5593 | 0.434350 | ||||||||
\(592\) | 5.76322 | 0.236867 | ||||||||
\(593\) | 29.1063 | 1.19525 | 0.597625 | − | 0.801775i | \(-0.296111\pi\) | ||||
0.597625 | + | 0.801775i | \(0.296111\pi\) | |||||||
\(594\) | −2.63216 | −0.107999 | ||||||||
\(595\) | 0.911064 | 0.0373500 | ||||||||
\(596\) | 3.79711 | 0.155536 | ||||||||
\(597\) | −4.47924 | −0.183323 | ||||||||
\(598\) | 12.8613 | 0.525936 | ||||||||
\(599\) | 34.1254 | 1.39433 | 0.697163 | − | 0.716912i | \(-0.254445\pi\) | ||||
0.697163 | + | 0.716912i | \(0.254445\pi\) | |||||||
\(600\) | −0.675556 | −0.0275795 | ||||||||
\(601\) | 34.7085 | 1.41579 | 0.707895 | − | 0.706318i | \(-0.249645\pi\) | ||||
0.707895 | + | 0.706318i | \(0.249645\pi\) | |||||||
\(602\) | −12.4204 | −0.506218 | ||||||||
\(603\) | −6.90345 | −0.281130 | ||||||||
\(604\) | −5.98467 | −0.243513 | ||||||||
\(605\) | −10.5060 | −0.427130 | ||||||||
\(606\) | −7.50548 | −0.304889 | ||||||||
\(607\) | 3.38718 | 0.137481 | 0.0687407 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687407 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(608\) | −1.64115 | −0.0665572 | ||||||||
\(609\) | −3.37050 | −0.136579 | ||||||||
\(610\) | 9.20668 | 0.372768 | ||||||||
\(611\) | 21.7530 | 0.880032 | ||||||||
\(612\) | 1.17864 | 0.0476436 | ||||||||
\(613\) | −44.1473 | −1.78309 | −0.891547 | − | 0.452928i | \(-0.850379\pi\) | ||||
−0.891547 | + | 0.452928i | \(0.850379\pi\) | |||||||
\(614\) | 9.26421 | 0.373873 | ||||||||
\(615\) | 4.82962 | 0.194749 | ||||||||
\(616\) | −1.38191 | −0.0556786 | ||||||||
\(617\) | 24.2323 | 0.975555 | 0.487777 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487777 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(618\) | 9.12046 | 0.366879 | ||||||||
\(619\) | −32.1593 | −1.29259 | −0.646295 | − | 0.763088i | \(-0.723682\pi\) | ||||
−0.646295 | + | 0.763088i | \(0.723682\pi\) | |||||||
\(620\) | −6.10965 | −0.245369 | ||||||||
\(621\) | 13.2324 | 0.530999 | ||||||||
\(622\) | 10.3280 | 0.414117 | ||||||||
\(623\) | −4.76816 | −0.191032 | ||||||||
\(624\) | 2.45902 | 0.0984394 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.1184 | 0.963965 | ||||||||
\(627\) | −0.779231 | −0.0311195 | ||||||||
\(628\) | 18.7300 | 0.747409 | ||||||||
\(629\) | −2.67050 | −0.106480 | ||||||||
\(630\) | −5.00120 | −0.199252 | ||||||||
\(631\) | −39.2786 | −1.56366 | −0.781829 | − | 0.623493i | \(-0.785713\pi\) | ||||
−0.781829 | + | 0.623493i | \(0.785713\pi\) | |||||||
\(632\) | 7.77888 | 0.309427 | ||||||||
\(633\) | 12.6460 | 0.502635 | ||||||||
\(634\) | −19.8911 | −0.789977 | ||||||||
\(635\) | −2.46196 | −0.0976998 | ||||||||
\(636\) | −3.09217 | −0.122612 | ||||||||
\(637\) | −11.4084 | −0.452015 | ||||||||
\(638\) | 1.78348 | 0.0706087 | ||||||||
\(639\) | 9.10154 | 0.360051 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 31.9114 | 1.26042 | 0.630212 | − | 0.776423i | \(-0.282968\pi\) | ||||
0.630212 | + | 0.776423i | \(0.282968\pi\) | |||||||
\(642\) | 6.74300 | 0.266125 | ||||||||
\(643\) | 28.2686 | 1.11480 | 0.557402 | − | 0.830243i | \(-0.311798\pi\) | ||||
0.557402 | + | 0.830243i | \(0.311798\pi\) | |||||||
\(644\) | 6.94712 | 0.273755 | ||||||||
\(645\) | −4.26753 | −0.168034 | ||||||||
\(646\) | 0.760457 | 0.0299198 | ||||||||
\(647\) | 5.22465 | 0.205402 | 0.102701 | − | 0.994712i | \(-0.467251\pi\) | ||||
0.102701 | + | 0.994712i | \(0.467251\pi\) | |||||||
\(648\) | −5.10089 | −0.200382 | ||||||||
\(649\) | 1.80312 | 0.0707788 | ||||||||
\(650\) | −3.63999 | −0.142772 | ||||||||
\(651\) | 8.11520 | 0.318060 | ||||||||
\(652\) | 24.0979 | 0.943748 | ||||||||
\(653\) | 9.99605 | 0.391176 | 0.195588 | − | 0.980686i | \(-0.437339\pi\) | ||||
0.195588 | + | 0.980686i | \(0.437339\pi\) | |||||||
\(654\) | 11.6894 | 0.457090 | ||||||||
\(655\) | −12.1540 | −0.474896 | ||||||||
\(656\) | 7.14911 | 0.279126 | ||||||||
\(657\) | 2.68616 | 0.104797 | ||||||||
\(658\) | 11.7501 | 0.458066 | ||||||||
\(659\) | 31.5145 | 1.22763 | 0.613816 | − | 0.789449i | \(-0.289634\pi\) | ||||
0.613816 | + | 0.789449i | \(0.289634\pi\) | |||||||
\(660\) | −0.474809 | −0.0184819 | ||||||||
\(661\) | 43.0557 | 1.67467 | 0.837336 | − | 0.546688i | \(-0.184112\pi\) | ||||
0.837336 | + | 0.546688i | \(0.184112\pi\) | |||||||
\(662\) | 25.8891 | 1.00621 | ||||||||
\(663\) | −1.13943 | −0.0442520 | ||||||||
\(664\) | 5.64286 | 0.218985 | ||||||||
\(665\) | −3.22677 | −0.125129 | ||||||||
\(666\) | 14.6595 | 0.568043 | ||||||||
\(667\) | −8.96593 | −0.347162 | ||||||||
\(668\) | −6.60551 | −0.255575 | ||||||||
\(669\) | −4.87320 | −0.188409 | ||||||||
\(670\) | −2.71402 | −0.104852 | ||||||||
\(671\) | 6.47084 | 0.249804 | ||||||||
\(672\) | 1.32826 | 0.0512387 | ||||||||
\(673\) | 19.2058 | 0.740331 | 0.370165 | − | 0.928966i | \(-0.379301\pi\) | ||||
0.370165 | + | 0.928966i | \(0.379301\pi\) | |||||||
\(674\) | −14.9572 | −0.576129 | ||||||||
\(675\) | −3.74503 | −0.144146 | ||||||||
\(676\) | 0.249501 | 0.00959619 | ||||||||
\(677\) | 29.2520 | 1.12425 | 0.562123 | − | 0.827054i | \(-0.309985\pi\) | ||||
0.562123 | + | 0.827054i | \(0.309985\pi\) | |||||||
\(678\) | 10.7032 | 0.411053 | ||||||||
\(679\) | −28.1407 | −1.07994 | ||||||||
\(680\) | 0.463370 | 0.0177694 | ||||||||
\(681\) | 13.1422 | 0.503612 | ||||||||
\(682\) | −4.29412 | −0.164430 | ||||||||
\(683\) | 19.8552 | 0.759737 | 0.379869 | − | 0.925040i | \(-0.375969\pi\) | ||||
0.379869 | + | 0.925040i | \(0.375969\pi\) | |||||||
\(684\) | −4.17446 | −0.159614 | ||||||||
\(685\) | −14.9534 | −0.571339 | ||||||||
\(686\) | −19.9255 | −0.760760 | ||||||||
\(687\) | 7.56993 | 0.288811 | ||||||||
\(688\) | −6.31705 | −0.240835 | ||||||||
\(689\) | −16.6610 | −0.634733 | ||||||||
\(690\) | 2.38696 | 0.0908701 | ||||||||
\(691\) | −31.8422 | −1.21133 | −0.605667 | − | 0.795718i | \(-0.707094\pi\) | ||||
−0.605667 | + | 0.795718i | \(0.707094\pi\) | |||||||
\(692\) | −15.0557 | −0.572332 | ||||||||
\(693\) | −3.51505 | −0.133526 | ||||||||
\(694\) | −27.7319 | −1.05269 | ||||||||
\(695\) | −21.8514 | −0.828869 | ||||||||
\(696\) | −1.71424 | −0.0649783 | ||||||||
\(697\) | −3.31268 | −0.125477 | ||||||||
\(698\) | −2.15312 | −0.0814969 | ||||||||
\(699\) | 11.9766 | 0.452995 | ||||||||
\(700\) | −1.96617 | −0.0743142 | ||||||||
\(701\) | 31.8457 | 1.20280 | 0.601398 | − | 0.798950i | \(-0.294611\pi\) | ||||
0.601398 | + | 0.798950i | \(0.294611\pi\) | |||||||
\(702\) | 13.6319 | 0.514501 | ||||||||
\(703\) | 9.45829 | 0.356726 | ||||||||
\(704\) | −0.702842 | −0.0264893 | ||||||||
\(705\) | 4.03721 | 0.152050 | ||||||||
\(706\) | −6.05838 | −0.228010 | ||||||||
\(707\) | −21.8443 | −0.821540 | ||||||||
\(708\) | −1.73312 | −0.0651348 | ||||||||
\(709\) | −39.1770 | −1.47132 | −0.735661 | − | 0.677350i | \(-0.763128\pi\) | ||||
−0.735661 | + | 0.677350i | \(0.763128\pi\) | |||||||
\(710\) | 3.57818 | 0.134287 | ||||||||
\(711\) | 19.7865 | 0.742053 | ||||||||
\(712\) | −2.42510 | −0.0908845 | ||||||||
\(713\) | 21.5874 | 0.808454 | ||||||||
\(714\) | −0.615475 | −0.0230336 | ||||||||
\(715\) | −2.55833 | −0.0956763 | ||||||||
\(716\) | 12.5215 | 0.467952 | ||||||||
\(717\) | −8.95027 | −0.334254 | ||||||||
\(718\) | 26.0891 | 0.973636 | ||||||||
\(719\) | −10.4263 | −0.388836 | −0.194418 | − | 0.980919i | \(-0.562282\pi\) | ||||
−0.194418 | + | 0.980919i | \(0.562282\pi\) | |||||||
\(720\) | −2.54362 | −0.0947953 | ||||||||
\(721\) | 26.5446 | 0.988573 | ||||||||
\(722\) | 16.3066 | 0.606870 | ||||||||
\(723\) | 4.46754 | 0.166149 | ||||||||
\(724\) | −23.0329 | −0.856012 | ||||||||
\(725\) | 2.53753 | 0.0942415 | ||||||||
\(726\) | 7.09740 | 0.263409 | ||||||||
\(727\) | 18.9553 | 0.703014 | 0.351507 | − | 0.936185i | \(-0.385669\pi\) | ||||
0.351507 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(728\) | 7.15683 | 0.265250 | ||||||||
\(729\) | −5.38481 | −0.199438 | ||||||||
\(730\) | 1.05604 | 0.0390857 | ||||||||
\(731\) | 2.92713 | 0.108264 | ||||||||
\(732\) | −6.21963 | −0.229884 | ||||||||
\(733\) | −31.9555 | −1.18030 | −0.590151 | − | 0.807293i | \(-0.700932\pi\) | ||||
−0.590151 | + | 0.807293i | \(0.700932\pi\) | |||||||
\(734\) | −2.08709 | −0.0770358 | ||||||||
\(735\) | −2.11731 | −0.0780982 | ||||||||
\(736\) | 3.53333 | 0.130240 | ||||||||
\(737\) | −1.90753 | −0.0702646 | ||||||||
\(738\) | 18.1846 | 0.669386 | ||||||||
\(739\) | 52.0858 | 1.91601 | 0.958004 | − | 0.286755i | \(-0.0925766\pi\) | ||||
0.958004 | + | 0.286755i | \(0.0925766\pi\) | |||||||
\(740\) | 5.76322 | 0.211860 | ||||||||
\(741\) | 4.03560 | 0.148252 | ||||||||
\(742\) | −8.99958 | −0.330385 | ||||||||
\(743\) | 38.5288 | 1.41349 | 0.706743 | − | 0.707470i | \(-0.250164\pi\) | ||||
0.706743 | + | 0.707470i | \(0.250164\pi\) | |||||||
\(744\) | 4.12741 | 0.151318 | ||||||||
\(745\) | 3.79711 | 0.139115 | ||||||||
\(746\) | 28.8649 | 1.05682 | ||||||||
\(747\) | 14.3533 | 0.525160 | ||||||||
\(748\) | 0.325676 | 0.0119079 | ||||||||
\(749\) | 19.6251 | 0.717087 | ||||||||
\(750\) | −0.675556 | −0.0246678 | ||||||||
\(751\) | 11.6188 | 0.423977 | 0.211988 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211988 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(752\) | 5.97612 | 0.217927 | ||||||||
\(753\) | −17.5830 | −0.640759 | ||||||||
\(754\) | −9.23658 | −0.336376 | ||||||||
\(755\) | −5.98467 | −0.217805 | ||||||||
\(756\) | 7.36337 | 0.267803 | ||||||||
\(757\) | −1.94600 | −0.0707286 | −0.0353643 | − | 0.999374i | \(-0.511259\pi\) | ||||
−0.0353643 | + | 0.999374i | \(0.511259\pi\) | |||||||
\(758\) | −7.44485 | −0.270409 | ||||||||
\(759\) | 1.67766 | 0.0608951 | ||||||||
\(760\) | −1.64115 | −0.0595306 | ||||||||
\(761\) | −41.4858 | −1.50386 | −0.751930 | − | 0.659243i | \(-0.770877\pi\) | ||||
−0.751930 | + | 0.659243i | \(0.770877\pi\) | |||||||
\(762\) | 1.66319 | 0.0602511 | ||||||||
\(763\) | 34.0212 | 1.23165 | ||||||||
\(764\) | 15.0467 | 0.544371 | ||||||||
\(765\) | 1.17864 | 0.0426138 | ||||||||
\(766\) | 18.3001 | 0.661210 | ||||||||
\(767\) | −9.33830 | −0.337186 | ||||||||
\(768\) | 0.675556 | 0.0243770 | ||||||||
\(769\) | −29.7575 | −1.07308 | −0.536541 | − | 0.843874i | \(-0.680269\pi\) | ||||
−0.536541 | + | 0.843874i | \(0.680269\pi\) | |||||||
\(770\) | −1.38191 | −0.0498004 | ||||||||
\(771\) | −5.49921 | −0.198049 | ||||||||
\(772\) | −19.7068 | −0.709262 | ||||||||
\(773\) | 19.3525 | 0.696061 | 0.348030 | − | 0.937483i | \(-0.386851\pi\) | ||||
0.348030 | + | 0.937483i | \(0.386851\pi\) | |||||||
\(774\) | −16.0682 | −0.577560 | ||||||||
\(775\) | −6.10965 | −0.219465 | ||||||||
\(776\) | −14.3124 | −0.513786 | ||||||||
\(777\) | −7.65505 | −0.274623 | ||||||||
\(778\) | −22.2317 | −0.797046 | ||||||||
\(779\) | 11.7327 | 0.420368 | ||||||||
\(780\) | 2.45902 | 0.0880469 | ||||||||
\(781\) | 2.51489 | 0.0899899 | ||||||||
\(782\) | −1.63724 | −0.0585475 | ||||||||
\(783\) | −9.50313 | −0.339614 | ||||||||
\(784\) | −3.13418 | −0.111935 | ||||||||
\(785\) | 18.7300 | 0.668503 | ||||||||
\(786\) | 8.21071 | 0.292866 | ||||||||
\(787\) | 20.6864 | 0.737390 | 0.368695 | − | 0.929550i | \(-0.379805\pi\) | ||||
0.368695 | + | 0.929550i | \(0.379805\pi\) | |||||||
\(788\) | 15.6305 | 0.556813 | ||||||||
\(789\) | 1.42604 | 0.0507682 | ||||||||
\(790\) | 7.77888 | 0.276760 | ||||||||
\(791\) | 31.1510 | 1.10760 | ||||||||
\(792\) | −1.78776 | −0.0635254 | ||||||||
\(793\) | −33.5122 | −1.19005 | ||||||||
\(794\) | −3.83234 | −0.136005 | ||||||||
\(795\) | −3.09217 | −0.109668 | ||||||||
\(796\) | −6.63045 | −0.235010 | ||||||||
\(797\) | 35.4361 | 1.25521 | 0.627606 | − | 0.778531i | \(-0.284035\pi\) | ||||
0.627606 | + | 0.778531i | \(0.284035\pi\) | |||||||
\(798\) | 2.17987 | 0.0771664 | ||||||||
\(799\) | −2.76916 | −0.0979657 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −6.16855 | −0.217955 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | 0.742227 | 0.0261926 | ||||||||
\(804\) | 1.83347 | 0.0646616 | ||||||||
\(805\) | 6.94712 | 0.244854 | ||||||||
\(806\) | 22.2390 | 0.783337 | ||||||||
\(807\) | −12.8747 | −0.453213 | ||||||||
\(808\) | −11.1101 | −0.390851 | ||||||||
\(809\) | 27.9959 | 0.984283 | 0.492142 | − | 0.870515i | \(-0.336214\pi\) | ||||
0.492142 | + | 0.870515i | \(0.336214\pi\) | |||||||
\(810\) | −5.10089 | −0.179227 | ||||||||
\(811\) | 22.3971 | 0.786469 | 0.393234 | − | 0.919438i | \(-0.371356\pi\) | ||||
0.393234 | + | 0.919438i | \(0.371356\pi\) | |||||||
\(812\) | −4.98922 | −0.175087 | ||||||||
\(813\) | −3.41150 | −0.119647 | ||||||||
\(814\) | 4.05063 | 0.141975 | ||||||||
\(815\) | 24.0979 | 0.844114 | ||||||||
\(816\) | −0.313032 | −0.0109583 | ||||||||
\(817\) | −10.3672 | −0.362703 | ||||||||
\(818\) | −20.3572 | −0.711774 | ||||||||
\(819\) | 18.2043 | 0.636109 | ||||||||
\(820\) | 7.14911 | 0.249658 | ||||||||
\(821\) | 20.9374 | 0.730722 | 0.365361 | − | 0.930866i | \(-0.380946\pi\) | ||||
0.365361 | + | 0.930866i | \(0.380946\pi\) | |||||||
\(822\) | 10.1019 | 0.352343 | ||||||||
\(823\) | 47.8076 | 1.66647 | 0.833234 | − | 0.552921i | \(-0.186487\pi\) | ||||
0.833234 | + | 0.552921i | \(0.186487\pi\) | |||||||
\(824\) | 13.5007 | 0.470318 | ||||||||
\(825\) | −0.474809 | −0.0165307 | ||||||||
\(826\) | −5.04416 | −0.175509 | ||||||||
\(827\) | −14.9690 | −0.520522 | −0.260261 | − | 0.965538i | \(-0.583809\pi\) | ||||
−0.260261 | + | 0.965538i | \(0.583809\pi\) | |||||||
\(828\) | 8.98746 | 0.312336 | ||||||||
\(829\) | −21.5059 | −0.746929 | −0.373465 | − | 0.927644i | \(-0.621830\pi\) | ||||
−0.373465 | + | 0.927644i | \(0.621830\pi\) | |||||||
\(830\) | 5.64286 | 0.195866 | ||||||||
\(831\) | −6.22640 | −0.215991 | ||||||||
\(832\) | 3.63999 | 0.126194 | ||||||||
\(833\) | 1.45228 | 0.0503186 | ||||||||
\(834\) | 14.7618 | 0.511160 | ||||||||
\(835\) | −6.60551 | −0.228593 | ||||||||
\(836\) | −1.15347 | −0.0398934 | ||||||||
\(837\) | 22.8808 | 0.790877 | ||||||||
\(838\) | −20.8407 | −0.719931 | ||||||||
\(839\) | 13.8121 | 0.476846 | 0.238423 | − | 0.971161i | \(-0.423370\pi\) | ||||
0.238423 | + | 0.971161i | \(0.423370\pi\) | |||||||
\(840\) | 1.32826 | 0.0458293 | ||||||||
\(841\) | −22.5609 | −0.777963 | ||||||||
\(842\) | −23.1118 | −0.796485 | ||||||||
\(843\) | −4.44224 | −0.152999 | ||||||||
\(844\) | 18.7194 | 0.644350 | ||||||||
\(845\) | 0.249501 | 0.00858310 | ||||||||
\(846\) | 15.2010 | 0.522621 | ||||||||
\(847\) | 20.6566 | 0.709770 | ||||||||
\(848\) | −4.57721 | −0.157182 | ||||||||
\(849\) | 12.6608 | 0.434518 | ||||||||
\(850\) | 0.463370 | 0.0158935 | ||||||||
\(851\) | −20.3634 | −0.698047 | ||||||||
\(852\) | −2.41726 | −0.0828140 | ||||||||
\(853\) | −9.04546 | −0.309711 | −0.154855 | − | 0.987937i | \(-0.549491\pi\) | ||||
−0.154855 | + | 0.987937i | \(0.549491\pi\) | |||||||
\(854\) | −18.1019 | −0.619434 | ||||||||
\(855\) | −4.17446 | −0.142763 | ||||||||
\(856\) | 9.98140 | 0.341157 | ||||||||
\(857\) | −1.35948 | −0.0464389 | −0.0232194 | − | 0.999730i | \(-0.507392\pi\) | ||||
−0.0232194 | + | 0.999730i | \(0.507392\pi\) | |||||||
\(858\) | 1.72830 | 0.0590031 | ||||||||
\(859\) | −6.15779 | −0.210101 | −0.105051 | − | 0.994467i | \(-0.533500\pi\) | ||||
−0.105051 | + | 0.994467i | \(0.533500\pi\) | |||||||
\(860\) | −6.31705 | −0.215410 | ||||||||
\(861\) | −9.49586 | −0.323618 | ||||||||
\(862\) | 26.9560 | 0.918124 | ||||||||
\(863\) | 6.62312 | 0.225454 | 0.112727 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112727 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(864\) | 3.74503 | 0.127409 | ||||||||
\(865\) | −15.0557 | −0.511909 | ||||||||
\(866\) | −1.05846 | −0.0359678 | ||||||||
\(867\) | −11.3394 | −0.385106 | ||||||||
\(868\) | 12.0126 | 0.407735 | ||||||||
\(869\) | 5.46732 | 0.185466 | ||||||||
\(870\) | −1.71424 | −0.0581183 | ||||||||
\(871\) | 9.87900 | 0.334737 | ||||||||
\(872\) | 17.3033 | 0.585964 | ||||||||
\(873\) | −36.4054 | −1.23214 | ||||||||
\(874\) | 5.79871 | 0.196144 | ||||||||
\(875\) | −1.96617 | −0.0664687 | ||||||||
\(876\) | −0.713412 | −0.0241040 | ||||||||
\(877\) | −25.9471 | −0.876170 | −0.438085 | − | 0.898934i | \(-0.644343\pi\) | ||||
−0.438085 | + | 0.898934i | \(0.644343\pi\) | |||||||
\(878\) | 26.9332 | 0.908950 | ||||||||
\(879\) | 13.7421 | 0.463511 | ||||||||
\(880\) | −0.702842 | −0.0236928 | ||||||||
\(881\) | −32.5527 | −1.09673 | −0.548365 | − | 0.836239i | \(-0.684749\pi\) | ||||
−0.548365 | + | 0.836239i | \(0.684749\pi\) | |||||||
\(882\) | −7.97216 | −0.268437 | ||||||||
\(883\) | −17.9716 | −0.604793 | −0.302396 | − | 0.953182i | \(-0.597787\pi\) | ||||
−0.302396 | + | 0.953182i | \(0.597787\pi\) | |||||||
\(884\) | −1.68666 | −0.0567285 | ||||||||
\(885\) | −1.73312 | −0.0582583 | ||||||||
\(886\) | −3.79606 | −0.127531 | ||||||||
\(887\) | 22.3570 | 0.750674 | 0.375337 | − | 0.926889i | \(-0.377527\pi\) | ||||
0.375337 | + | 0.926889i | \(0.377527\pi\) | |||||||
\(888\) | −3.89338 | −0.130653 | ||||||||
\(889\) | 4.84063 | 0.162349 | ||||||||
\(890\) | −2.42510 | −0.0812896 | ||||||||
\(891\) | −3.58512 | −0.120106 | ||||||||
\(892\) | −7.21360 | −0.241529 | ||||||||
\(893\) | 9.80769 | 0.328202 | ||||||||
\(894\) | −2.56516 | −0.0857919 | ||||||||
\(895\) | 12.5215 | 0.418549 | ||||||||
\(896\) | 1.96617 | 0.0656851 | ||||||||
\(897\) | −8.68851 | −0.290101 | ||||||||
\(898\) | 19.9784 | 0.666689 | ||||||||
\(899\) | −15.5034 | −0.517068 | ||||||||
\(900\) | −2.54362 | −0.0847875 | ||||||||
\(901\) | 2.12094 | 0.0706589 | ||||||||
\(902\) | 5.02469 | 0.167304 | ||||||||
\(903\) | 8.39068 | 0.279224 | ||||||||
\(904\) | 15.8435 | 0.526947 | ||||||||
\(905\) | −23.0329 | −0.765641 | ||||||||
\(906\) | 4.04298 | 0.134319 | ||||||||
\(907\) | 1.71251 | 0.0568629 | 0.0284315 | − | 0.999596i | \(-0.490949\pi\) | ||||
0.0284315 | + | 0.999596i | \(0.490949\pi\) | |||||||
\(908\) | 19.4540 | 0.645602 | ||||||||
\(909\) | −28.2599 | −0.937320 | ||||||||
\(910\) | 7.15683 | 0.237247 | ||||||||
\(911\) | 48.8985 | 1.62008 | 0.810040 | − | 0.586374i | \(-0.199445\pi\) | ||||
0.810040 | + | 0.586374i | \(0.199445\pi\) | |||||||
\(912\) | 1.10869 | 0.0367123 | ||||||||
\(913\) | 3.96603 | 0.131257 | ||||||||
\(914\) | 12.0619 | 0.398971 | ||||||||
\(915\) | −6.21963 | −0.205615 | ||||||||
\(916\) | 11.2055 | 0.370239 | ||||||||
\(917\) | 23.8968 | 0.789143 | ||||||||
\(918\) | −1.73533 | −0.0572746 | ||||||||
\(919\) | −22.4082 | −0.739177 | −0.369589 | − | 0.929195i | \(-0.620501\pi\) | ||||
−0.369589 | + | 0.929195i | \(0.620501\pi\) | |||||||
\(920\) | 3.53333 | 0.116490 | ||||||||
\(921\) | −6.25850 | −0.206225 | ||||||||
\(922\) | 23.7685 | 0.782773 | ||||||||
\(923\) | −13.0245 | −0.428707 | ||||||||
\(924\) | 0.933555 | 0.0307117 | ||||||||
\(925\) | 5.76322 | 0.189494 | ||||||||
\(926\) | 25.5650 | 0.840117 | ||||||||
\(927\) | 34.3406 | 1.12789 | ||||||||
\(928\) | −2.53753 | −0.0832985 | ||||||||
\(929\) | −8.82972 | −0.289694 | −0.144847 | − | 0.989454i | \(-0.546269\pi\) | ||||
−0.144847 | + | 0.989454i | \(0.546269\pi\) | |||||||
\(930\) | 4.12741 | 0.135343 | ||||||||
\(931\) | −5.14364 | −0.168576 | ||||||||
\(932\) | 17.7284 | 0.580714 | ||||||||
\(933\) | −6.97718 | −0.228423 | ||||||||
\(934\) | −1.38486 | −0.0453139 | ||||||||
\(935\) | 0.325676 | 0.0106507 | ||||||||
\(936\) | 9.25876 | 0.302632 | ||||||||
\(937\) | −39.4540 | −1.28891 | −0.644453 | − | 0.764644i | \(-0.722915\pi\) | ||||
−0.644453 | + | 0.764644i | \(0.722915\pi\) | |||||||
\(938\) | 5.33623 | 0.174234 | ||||||||
\(939\) | −16.2933 | −0.531713 | ||||||||
\(940\) | 5.97612 | 0.194920 | ||||||||
\(941\) | 36.8693 | 1.20190 | 0.600952 | − | 0.799285i | \(-0.294788\pi\) | ||||
0.600952 | + | 0.799285i | \(0.294788\pi\) | |||||||
\(942\) | −12.6532 | −0.412263 | ||||||||
\(943\) | −25.2601 | −0.822583 | ||||||||
\(944\) | −2.56548 | −0.0834991 | ||||||||
\(945\) | 7.36337 | 0.239530 | ||||||||
\(946\) | −4.43989 | −0.144353 | ||||||||
\(947\) | 33.8844 | 1.10110 | 0.550548 | − | 0.834804i | \(-0.314419\pi\) | ||||
0.550548 | + | 0.834804i | \(0.314419\pi\) | |||||||
\(948\) | −5.25507 | −0.170677 | ||||||||
\(949\) | −3.84396 | −0.124780 | ||||||||
\(950\) | −1.64115 | −0.0532458 | ||||||||
\(951\) | 13.4376 | 0.435743 | ||||||||
\(952\) | −0.911064 | −0.0295278 | ||||||||
\(953\) | 12.8001 | 0.414635 | 0.207317 | − | 0.978274i | \(-0.433527\pi\) | ||||
0.207317 | + | 0.978274i | \(0.433527\pi\) | |||||||
\(954\) | −11.6427 | −0.376947 | ||||||||
\(955\) | 15.0467 | 0.486901 | ||||||||
\(956\) | −13.2487 | −0.428495 | ||||||||
\(957\) | −1.20484 | −0.0389470 | ||||||||
\(958\) | 9.15088 | 0.295651 | ||||||||
\(959\) | 29.4009 | 0.949405 | ||||||||
\(960\) | 0.675556 | 0.0218035 | ||||||||
\(961\) | 6.32782 | 0.204123 | ||||||||
\(962\) | −20.9781 | −0.676360 | ||||||||
\(963\) | 25.3889 | 0.818147 | ||||||||
\(964\) | 6.61312 | 0.212994 | ||||||||
\(965\) | −19.7068 | −0.634383 | ||||||||
\(966\) | −4.69317 | −0.151000 | ||||||||
\(967\) | −16.6147 | −0.534293 | −0.267147 | − | 0.963656i | \(-0.586081\pi\) | ||||
−0.267147 | + | 0.963656i | \(0.586081\pi\) | |||||||
\(968\) | 10.5060 | 0.337676 | ||||||||
\(969\) | −0.513732 | −0.0165034 | ||||||||
\(970\) | −14.3124 | −0.459545 | ||||||||
\(971\) | −38.9312 | −1.24936 | −0.624681 | − | 0.780880i | \(-0.714771\pi\) | ||||
−0.624681 | + | 0.780880i | \(0.714771\pi\) | |||||||
\(972\) | 14.6810 | 0.470894 | ||||||||
\(973\) | 42.9635 | 1.37735 | ||||||||
\(974\) | −9.41697 | −0.301739 | ||||||||
\(975\) | 2.45902 | 0.0787515 | ||||||||
\(976\) | −9.20668 | −0.294699 | ||||||||
\(977\) | −11.9325 | −0.381755 | −0.190878 | − | 0.981614i | \(-0.561133\pi\) | ||||
−0.190878 | + | 0.981614i | \(0.561133\pi\) | |||||||
\(978\) | −16.2795 | −0.520561 | ||||||||
\(979\) | −1.70446 | −0.0544749 | ||||||||
\(980\) | −3.13418 | −0.100118 | ||||||||
\(981\) | 44.0131 | 1.40523 | ||||||||
\(982\) | −21.6913 | −0.692199 | ||||||||
\(983\) | 13.2389 | 0.422254 | 0.211127 | − | 0.977459i | \(-0.432287\pi\) | ||||
0.211127 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(984\) | −4.82962 | −0.153963 | ||||||||
\(985\) | 15.6305 | 0.498029 | ||||||||
\(986\) | 1.17582 | 0.0374456 | ||||||||
\(987\) | −7.93784 | −0.252664 | ||||||||
\(988\) | 5.97375 | 0.190050 | ||||||||
\(989\) | 22.3202 | 0.709742 | ||||||||
\(990\) | −1.78776 | −0.0568189 | ||||||||
\(991\) | 25.3896 | 0.806526 | 0.403263 | − | 0.915084i | \(-0.367876\pi\) | ||||
0.403263 | + | 0.915084i | \(0.367876\pi\) | |||||||
\(992\) | 6.10965 | 0.193982 | ||||||||
\(993\) | −17.4895 | −0.555013 | ||||||||
\(994\) | −7.03530 | −0.223146 | ||||||||
\(995\) | −6.63045 | −0.210199 | ||||||||
\(996\) | −3.81207 | −0.120790 | ||||||||
\(997\) | −13.2384 | −0.419263 | −0.209632 | − | 0.977780i | \(-0.567226\pi\) | ||||
−0.209632 | + | 0.977780i | \(0.567226\pi\) | |||||||
\(998\) | 38.4965 | 1.21859 | ||||||||
\(999\) | −21.5834 | −0.682870 |
(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 | 4010.2.a.i.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.i.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |