Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + 164 x^{7} + 2332 x^{6} - 440 x^{5} - 1344 x^{4} + 244 x^{3} + 295 x^{2} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.52769\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | 0.527686 | 0.304660 | 0.152330 | − | 0.988330i | \(-0.451322\pi\) | ||||
0.152330 | + | 0.988330i | \(0.451322\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.527686 | 0.215427 | ||||||||
\(7\) | −1.45681 | −0.550622 | −0.275311 | − | 0.961355i | \(-0.588781\pi\) | ||||
−0.275311 | + | 0.961355i | \(0.588781\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.72155 | −0.907182 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.62149 | −0.790410 | −0.395205 | − | 0.918593i | \(-0.629327\pi\) | ||||
−0.395205 | + | 0.918593i | \(0.629327\pi\) | |||||||
\(12\) | 0.527686 | 0.152330 | ||||||||
\(13\) | 1.24353 | 0.344894 | 0.172447 | − | 0.985019i | \(-0.444833\pi\) | ||||
0.172447 | + | 0.985019i | \(0.444833\pi\) | |||||||
\(14\) | −1.45681 | −0.389348 | ||||||||
\(15\) | 0.527686 | 0.136248 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.45768 | 0.596074 | 0.298037 | − | 0.954554i | \(-0.403668\pi\) | ||||
0.298037 | + | 0.954554i | \(0.403668\pi\) | |||||||
\(18\) | −2.72155 | −0.641475 | ||||||||
\(19\) | −1.20341 | −0.276081 | −0.138041 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138041 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.768738 | −0.167752 | ||||||||
\(22\) | −2.62149 | −0.558905 | ||||||||
\(23\) | −1.35625 | −0.282798 | −0.141399 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141399 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(24\) | 0.527686 | 0.107714 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.24353 | 0.243877 | ||||||||
\(27\) | −3.01918 | −0.581042 | ||||||||
\(28\) | −1.45681 | −0.275311 | ||||||||
\(29\) | 0.521590 | 0.0968568 | 0.0484284 | − | 0.998827i | \(-0.484579\pi\) | ||||
0.0484284 | + | 0.998827i | \(0.484579\pi\) | |||||||
\(30\) | 0.527686 | 0.0963419 | ||||||||
\(31\) | −2.53028 | −0.454452 | −0.227226 | − | 0.973842i | \(-0.572966\pi\) | ||||
−0.227226 | + | 0.973842i | \(0.572966\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.38333 | −0.240806 | ||||||||
\(34\) | 2.45768 | 0.421488 | ||||||||
\(35\) | −1.45681 | −0.246246 | ||||||||
\(36\) | −2.72155 | −0.453591 | ||||||||
\(37\) | −10.7002 | −1.75910 | −0.879552 | − | 0.475803i | \(-0.842158\pi\) | ||||
−0.879552 | + | 0.475803i | \(0.842158\pi\) | |||||||
\(38\) | −1.20341 | −0.195219 | ||||||||
\(39\) | 0.656195 | 0.105075 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −4.79988 | −0.749616 | −0.374808 | − | 0.927103i | \(-0.622291\pi\) | ||||
−0.374808 | + | 0.927103i | \(0.622291\pi\) | |||||||
\(42\) | −0.768738 | −0.118619 | ||||||||
\(43\) | −6.82716 | −1.04113 | −0.520566 | − | 0.853822i | \(-0.674279\pi\) | ||||
−0.520566 | + | 0.853822i | \(0.674279\pi\) | |||||||
\(44\) | −2.62149 | −0.395205 | ||||||||
\(45\) | −2.72155 | −0.405704 | ||||||||
\(46\) | −1.35625 | −0.199968 | ||||||||
\(47\) | 7.76806 | 1.13309 | 0.566544 | − | 0.824031i | \(-0.308280\pi\) | ||||
0.566544 | + | 0.824031i | \(0.308280\pi\) | |||||||
\(48\) | 0.527686 | 0.0761650 | ||||||||
\(49\) | −4.87771 | −0.696816 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.29688 | 0.181600 | ||||||||
\(52\) | 1.24353 | 0.172447 | ||||||||
\(53\) | 2.85206 | 0.391761 | 0.195880 | − | 0.980628i | \(-0.437244\pi\) | ||||
0.195880 | + | 0.980628i | \(0.437244\pi\) | |||||||
\(54\) | −3.01918 | −0.410859 | ||||||||
\(55\) | −2.62149 | −0.353482 | ||||||||
\(56\) | −1.45681 | −0.194674 | ||||||||
\(57\) | −0.635024 | −0.0841110 | ||||||||
\(58\) | 0.521590 | 0.0684881 | ||||||||
\(59\) | 4.64954 | 0.605318 | 0.302659 | − | 0.953099i | \(-0.402126\pi\) | ||||
0.302659 | + | 0.953099i | \(0.402126\pi\) | |||||||
\(60\) | 0.527686 | 0.0681240 | ||||||||
\(61\) | −5.90552 | −0.756124 | −0.378062 | − | 0.925780i | \(-0.623409\pi\) | ||||
−0.378062 | + | 0.925780i | \(0.623409\pi\) | |||||||
\(62\) | −2.53028 | −0.321346 | ||||||||
\(63\) | 3.96477 | 0.499514 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.24353 | 0.154241 | ||||||||
\(66\) | −1.38333 | −0.170276 | ||||||||
\(67\) | −2.08902 | −0.255214 | −0.127607 | − | 0.991825i | \(-0.540730\pi\) | ||||
−0.127607 | + | 0.991825i | \(0.540730\pi\) | |||||||
\(68\) | 2.45768 | 0.298037 | ||||||||
\(69\) | −0.715675 | −0.0861571 | ||||||||
\(70\) | −1.45681 | −0.174122 | ||||||||
\(71\) | 9.96266 | 1.18235 | 0.591175 | − | 0.806543i | \(-0.298664\pi\) | ||||
0.591175 | + | 0.806543i | \(0.298664\pi\) | |||||||
\(72\) | −2.72155 | −0.320737 | ||||||||
\(73\) | −5.44302 | −0.637057 | −0.318529 | − | 0.947913i | \(-0.603189\pi\) | ||||
−0.318529 | + | 0.947913i | \(0.603189\pi\) | |||||||
\(74\) | −10.7002 | −1.24387 | ||||||||
\(75\) | 0.527686 | 0.0609320 | ||||||||
\(76\) | −1.20341 | −0.138041 | ||||||||
\(77\) | 3.81902 | 0.435217 | ||||||||
\(78\) | 0.656195 | 0.0742995 | ||||||||
\(79\) | −9.71634 | −1.09317 | −0.546587 | − | 0.837402i | \(-0.684073\pi\) | ||||
−0.546587 | + | 0.837402i | \(0.684073\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 6.57146 | 0.730162 | ||||||||
\(82\) | −4.79988 | −0.530058 | ||||||||
\(83\) | −17.4608 | −1.91657 | −0.958284 | − | 0.285816i | \(-0.907735\pi\) | ||||
−0.958284 | + | 0.285816i | \(0.907735\pi\) | |||||||
\(84\) | −0.768738 | −0.0838762 | ||||||||
\(85\) | 2.45768 | 0.266572 | ||||||||
\(86\) | −6.82716 | −0.736191 | ||||||||
\(87\) | 0.275236 | 0.0295084 | ||||||||
\(88\) | −2.62149 | −0.279452 | ||||||||
\(89\) | 5.36866 | 0.569077 | 0.284538 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284538 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(90\) | −2.72155 | −0.286876 | ||||||||
\(91\) | −1.81159 | −0.189906 | ||||||||
\(92\) | −1.35625 | −0.141399 | ||||||||
\(93\) | −1.33519 | −0.138453 | ||||||||
\(94\) | 7.76806 | 0.801214 | ||||||||
\(95\) | −1.20341 | −0.123467 | ||||||||
\(96\) | 0.527686 | 0.0538568 | ||||||||
\(97\) | −13.4933 | −1.37003 | −0.685017 | − | 0.728527i | \(-0.740205\pi\) | ||||
−0.685017 | + | 0.728527i | \(0.740205\pi\) | |||||||
\(98\) | −4.87771 | −0.492723 | ||||||||
\(99\) | 7.13452 | 0.717046 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.06770 | 0.504255 | 0.252127 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252127 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(102\) | 1.29688 | 0.128410 | ||||||||
\(103\) | 9.02142 | 0.888907 | 0.444453 | − | 0.895802i | \(-0.353398\pi\) | ||||
0.444453 | + | 0.895802i | \(0.353398\pi\) | |||||||
\(104\) | 1.24353 | 0.121938 | ||||||||
\(105\) | −0.768738 | −0.0750212 | ||||||||
\(106\) | 2.85206 | 0.277017 | ||||||||
\(107\) | 6.53561 | 0.631822 | 0.315911 | − | 0.948789i | \(-0.397690\pi\) | ||||
0.315911 | + | 0.948789i | \(0.397690\pi\) | |||||||
\(108\) | −3.01918 | −0.290521 | ||||||||
\(109\) | −1.18883 | −0.113869 | −0.0569345 | − | 0.998378i | \(-0.518133\pi\) | ||||
−0.0569345 | + | 0.998378i | \(0.518133\pi\) | |||||||
\(110\) | −2.62149 | −0.249950 | ||||||||
\(111\) | −5.64636 | −0.535929 | ||||||||
\(112\) | −1.45681 | −0.137655 | ||||||||
\(113\) | −4.78861 | −0.450474 | −0.225237 | − | 0.974304i | \(-0.572316\pi\) | ||||
−0.225237 | + | 0.974304i | \(0.572316\pi\) | |||||||
\(114\) | −0.635024 | −0.0594754 | ||||||||
\(115\) | −1.35625 | −0.126471 | ||||||||
\(116\) | 0.521590 | 0.0484284 | ||||||||
\(117\) | −3.38433 | −0.312882 | ||||||||
\(118\) | 4.64954 | 0.428025 | ||||||||
\(119\) | −3.58036 | −0.328211 | ||||||||
\(120\) | 0.527686 | 0.0481710 | ||||||||
\(121\) | −4.12777 | −0.375251 | ||||||||
\(122\) | −5.90552 | −0.534661 | ||||||||
\(123\) | −2.53283 | −0.228378 | ||||||||
\(124\) | −2.53028 | −0.227226 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.96477 | 0.353210 | ||||||||
\(127\) | −3.81154 | −0.338219 | −0.169110 | − | 0.985597i | \(-0.554089\pi\) | ||||
−0.169110 | + | 0.985597i | \(0.554089\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.60260 | −0.317191 | ||||||||
\(130\) | 1.24353 | 0.109065 | ||||||||
\(131\) | 2.67702 | 0.233892 | 0.116946 | − | 0.993138i | \(-0.462690\pi\) | ||||
0.116946 | + | 0.993138i | \(0.462690\pi\) | |||||||
\(132\) | −1.38333 | −0.120403 | ||||||||
\(133\) | 1.75314 | 0.152017 | ||||||||
\(134\) | −2.08902 | −0.180464 | ||||||||
\(135\) | −3.01918 | −0.259850 | ||||||||
\(136\) | 2.45768 | 0.210744 | ||||||||
\(137\) | −13.4125 | −1.14591 | −0.572954 | − | 0.819588i | \(-0.694203\pi\) | ||||
−0.572954 | + | 0.819588i | \(0.694203\pi\) | |||||||
\(138\) | −0.715675 | −0.0609223 | ||||||||
\(139\) | −17.3453 | −1.47121 | −0.735603 | − | 0.677413i | \(-0.763101\pi\) | ||||
−0.735603 | + | 0.677413i | \(0.763101\pi\) | |||||||
\(140\) | −1.45681 | −0.123123 | ||||||||
\(141\) | 4.09910 | 0.345207 | ||||||||
\(142\) | 9.96266 | 0.836048 | ||||||||
\(143\) | −3.25991 | −0.272608 | ||||||||
\(144\) | −2.72155 | −0.226796 | ||||||||
\(145\) | 0.521590 | 0.0433157 | ||||||||
\(146\) | −5.44302 | −0.450468 | ||||||||
\(147\) | −2.57390 | −0.212292 | ||||||||
\(148\) | −10.7002 | −0.879552 | ||||||||
\(149\) | −20.3630 | −1.66820 | −0.834101 | − | 0.551612i | \(-0.814013\pi\) | ||||
−0.834101 | + | 0.551612i | \(0.814013\pi\) | |||||||
\(150\) | 0.527686 | 0.0430854 | ||||||||
\(151\) | −9.03664 | −0.735391 | −0.367696 | − | 0.929946i | \(-0.619853\pi\) | ||||
−0.367696 | + | 0.929946i | \(0.619853\pi\) | |||||||
\(152\) | −1.20341 | −0.0976095 | ||||||||
\(153\) | −6.68868 | −0.540748 | ||||||||
\(154\) | 3.81902 | 0.307745 | ||||||||
\(155\) | −2.53028 | −0.203237 | ||||||||
\(156\) | 0.656195 | 0.0525377 | ||||||||
\(157\) | 7.93990 | 0.633673 | 0.316836 | − | 0.948480i | \(-0.397379\pi\) | ||||
0.316836 | + | 0.948480i | \(0.397379\pi\) | |||||||
\(158\) | −9.71634 | −0.772991 | ||||||||
\(159\) | 1.50499 | 0.119354 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.97580 | 0.155715 | ||||||||
\(162\) | 6.57146 | 0.516303 | ||||||||
\(163\) | 17.2900 | 1.35426 | 0.677130 | − | 0.735863i | \(-0.263223\pi\) | ||||
0.677130 | + | 0.735863i | \(0.263223\pi\) | |||||||
\(164\) | −4.79988 | −0.374808 | ||||||||
\(165\) | −1.38333 | −0.107692 | ||||||||
\(166\) | −17.4608 | −1.35522 | ||||||||
\(167\) | −9.42282 | −0.729160 | −0.364580 | − | 0.931172i | \(-0.618787\pi\) | ||||
−0.364580 | + | 0.931172i | \(0.618787\pi\) | |||||||
\(168\) | −0.768738 | −0.0593094 | ||||||||
\(169\) | −11.4536 | −0.881048 | ||||||||
\(170\) | 2.45768 | 0.188495 | ||||||||
\(171\) | 3.27514 | 0.250456 | ||||||||
\(172\) | −6.82716 | −0.520566 | ||||||||
\(173\) | 1.86070 | 0.141466 | 0.0707331 | − | 0.997495i | \(-0.477466\pi\) | ||||
0.0707331 | + | 0.997495i | \(0.477466\pi\) | |||||||
\(174\) | 0.275236 | 0.0208656 | ||||||||
\(175\) | −1.45681 | −0.110124 | ||||||||
\(176\) | −2.62149 | −0.197603 | ||||||||
\(177\) | 2.45350 | 0.184416 | ||||||||
\(178\) | 5.36866 | 0.402398 | ||||||||
\(179\) | 10.0718 | 0.752805 | 0.376402 | − | 0.926456i | \(-0.377161\pi\) | ||||
0.376402 | + | 0.926456i | \(0.377161\pi\) | |||||||
\(180\) | −2.72155 | −0.202852 | ||||||||
\(181\) | −0.752269 | −0.0559157 | −0.0279579 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279579 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(182\) | −1.81159 | −0.134284 | ||||||||
\(183\) | −3.11626 | −0.230361 | ||||||||
\(184\) | −1.35625 | −0.0999841 | ||||||||
\(185\) | −10.7002 | −0.786695 | ||||||||
\(186\) | −1.33519 | −0.0979012 | ||||||||
\(187\) | −6.44278 | −0.471143 | ||||||||
\(188\) | 7.76806 | 0.566544 | ||||||||
\(189\) | 4.39837 | 0.319934 | ||||||||
\(190\) | −1.20341 | −0.0873046 | ||||||||
\(191\) | −3.15540 | −0.228317 | −0.114158 | − | 0.993463i | \(-0.536417\pi\) | ||||
−0.114158 | + | 0.993463i | \(0.536417\pi\) | |||||||
\(192\) | 0.527686 | 0.0380825 | ||||||||
\(193\) | −7.76219 | −0.558734 | −0.279367 | − | 0.960184i | \(-0.590125\pi\) | ||||
−0.279367 | + | 0.960184i | \(0.590125\pi\) | |||||||
\(194\) | −13.4933 | −0.968760 | ||||||||
\(195\) | 0.656195 | 0.0469911 | ||||||||
\(196\) | −4.87771 | −0.348408 | ||||||||
\(197\) | −14.2092 | −1.01237 | −0.506183 | − | 0.862426i | \(-0.668944\pi\) | ||||
−0.506183 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(198\) | 7.13452 | 0.507028 | ||||||||
\(199\) | 8.59075 | 0.608982 | 0.304491 | − | 0.952515i | \(-0.401514\pi\) | ||||
0.304491 | + | 0.952515i | \(0.401514\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.10235 | −0.0777535 | ||||||||
\(202\) | 5.06770 | 0.356562 | ||||||||
\(203\) | −0.759857 | −0.0533315 | ||||||||
\(204\) | 1.29688 | 0.0907999 | ||||||||
\(205\) | −4.79988 | −0.335238 | ||||||||
\(206\) | 9.02142 | 0.628552 | ||||||||
\(207\) | 3.69110 | 0.256549 | ||||||||
\(208\) | 1.24353 | 0.0862235 | ||||||||
\(209\) | 3.15474 | 0.218218 | ||||||||
\(210\) | −0.768738 | −0.0530480 | ||||||||
\(211\) | 27.1324 | 1.86787 | 0.933937 | − | 0.357438i | \(-0.116350\pi\) | ||||
0.933937 | + | 0.357438i | \(0.116350\pi\) | |||||||
\(212\) | 2.85206 | 0.195880 | ||||||||
\(213\) | 5.25716 | 0.360215 | ||||||||
\(214\) | 6.53561 | 0.446765 | ||||||||
\(215\) | −6.82716 | −0.465608 | ||||||||
\(216\) | −3.01918 | −0.205429 | ||||||||
\(217\) | 3.68613 | 0.250231 | ||||||||
\(218\) | −1.18883 | −0.0805175 | ||||||||
\(219\) | −2.87221 | −0.194086 | ||||||||
\(220\) | −2.62149 | −0.176741 | ||||||||
\(221\) | 3.05620 | 0.205582 | ||||||||
\(222\) | −5.64636 | −0.378959 | ||||||||
\(223\) | 23.7152 | 1.58809 | 0.794044 | − | 0.607860i | \(-0.207972\pi\) | ||||
0.794044 | + | 0.607860i | \(0.207972\pi\) | |||||||
\(224\) | −1.45681 | −0.0973371 | ||||||||
\(225\) | −2.72155 | −0.181436 | ||||||||
\(226\) | −4.78861 | −0.318534 | ||||||||
\(227\) | 11.4333 | 0.758857 | 0.379429 | − | 0.925221i | \(-0.376121\pi\) | ||||
0.379429 | + | 0.925221i | \(0.376121\pi\) | |||||||
\(228\) | −0.635024 | −0.0420555 | ||||||||
\(229\) | −4.78887 | −0.316457 | −0.158229 | − | 0.987402i | \(-0.550578\pi\) | ||||
−0.158229 | + | 0.987402i | \(0.550578\pi\) | |||||||
\(230\) | −1.35625 | −0.0894285 | ||||||||
\(231\) | 2.01524 | 0.132593 | ||||||||
\(232\) | 0.521590 | 0.0342441 | ||||||||
\(233\) | −28.5022 | −1.86724 | −0.933621 | − | 0.358262i | \(-0.883369\pi\) | ||||
−0.933621 | + | 0.358262i | \(0.883369\pi\) | |||||||
\(234\) | −3.38433 | −0.221241 | ||||||||
\(235\) | 7.76806 | 0.506733 | ||||||||
\(236\) | 4.64954 | 0.302659 | ||||||||
\(237\) | −5.12718 | −0.333046 | ||||||||
\(238\) | −3.58036 | −0.232080 | ||||||||
\(239\) | 17.5347 | 1.13423 | 0.567114 | − | 0.823639i | \(-0.308060\pi\) | ||||
0.567114 | + | 0.823639i | \(0.308060\pi\) | |||||||
\(240\) | 0.527686 | 0.0340620 | ||||||||
\(241\) | 17.6740 | 1.13848 | 0.569241 | − | 0.822171i | \(-0.307237\pi\) | ||||
0.569241 | + | 0.822171i | \(0.307237\pi\) | |||||||
\(242\) | −4.12777 | −0.265343 | ||||||||
\(243\) | 12.5252 | 0.803493 | ||||||||
\(244\) | −5.90552 | −0.378062 | ||||||||
\(245\) | −4.87771 | −0.311625 | ||||||||
\(246\) | −2.53283 | −0.161488 | ||||||||
\(247\) | −1.49648 | −0.0952188 | ||||||||
\(248\) | −2.53028 | −0.160673 | ||||||||
\(249\) | −9.21381 | −0.583902 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 22.0973 | 1.39477 | 0.697386 | − | 0.716696i | \(-0.254347\pi\) | ||||
0.697386 | + | 0.716696i | \(0.254347\pi\) | |||||||
\(252\) | 3.96477 | 0.249757 | ||||||||
\(253\) | 3.55540 | 0.223526 | ||||||||
\(254\) | −3.81154 | −0.239157 | ||||||||
\(255\) | 1.29688 | 0.0812139 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.0526 | −1.56274 | −0.781369 | − | 0.624069i | \(-0.785478\pi\) | ||||
−0.781369 | + | 0.624069i | \(0.785478\pi\) | |||||||
\(258\) | −3.60260 | −0.224288 | ||||||||
\(259\) | 15.5882 | 0.968601 | ||||||||
\(260\) | 1.24353 | 0.0771206 | ||||||||
\(261\) | −1.41953 | −0.0878668 | ||||||||
\(262\) | 2.67702 | 0.165387 | ||||||||
\(263\) | −26.5018 | −1.63417 | −0.817086 | − | 0.576516i | \(-0.804412\pi\) | ||||
−0.817086 | + | 0.576516i | \(0.804412\pi\) | |||||||
\(264\) | −1.38333 | −0.0851379 | ||||||||
\(265\) | 2.85206 | 0.175201 | ||||||||
\(266\) | 1.75314 | 0.107492 | ||||||||
\(267\) | 2.83297 | 0.173375 | ||||||||
\(268\) | −2.08902 | −0.127607 | ||||||||
\(269\) | 13.0978 | 0.798584 | 0.399292 | − | 0.916824i | \(-0.369256\pi\) | ||||
0.399292 | + | 0.916824i | \(0.369256\pi\) | |||||||
\(270\) | −3.01918 | −0.183742 | ||||||||
\(271\) | −10.8390 | −0.658420 | −0.329210 | − | 0.944257i | \(-0.606782\pi\) | ||||
−0.329210 | + | 0.944257i | \(0.606782\pi\) | |||||||
\(272\) | 2.45768 | 0.149018 | ||||||||
\(273\) | −0.955951 | −0.0578568 | ||||||||
\(274\) | −13.4125 | −0.810279 | ||||||||
\(275\) | −2.62149 | −0.158082 | ||||||||
\(276\) | −0.715675 | −0.0430786 | ||||||||
\(277\) | 2.62756 | 0.157875 | 0.0789374 | − | 0.996880i | \(-0.474847\pi\) | ||||
0.0789374 | + | 0.996880i | \(0.474847\pi\) | |||||||
\(278\) | −17.3453 | −1.04030 | ||||||||
\(279\) | 6.88628 | 0.412271 | ||||||||
\(280\) | −1.45681 | −0.0870610 | ||||||||
\(281\) | 14.3946 | 0.858713 | 0.429356 | − | 0.903135i | \(-0.358740\pi\) | ||||
0.429356 | + | 0.903135i | \(0.358740\pi\) | |||||||
\(282\) | 4.09910 | 0.244098 | ||||||||
\(283\) | −10.7074 | −0.636488 | −0.318244 | − | 0.948009i | \(-0.603093\pi\) | ||||
−0.318244 | + | 0.948009i | \(0.603093\pi\) | |||||||
\(284\) | 9.96266 | 0.591175 | ||||||||
\(285\) | −0.635024 | −0.0376156 | ||||||||
\(286\) | −3.25991 | −0.192763 | ||||||||
\(287\) | 6.99251 | 0.412755 | ||||||||
\(288\) | −2.72155 | −0.160369 | ||||||||
\(289\) | −10.9598 | −0.644696 | ||||||||
\(290\) | 0.521590 | 0.0306288 | ||||||||
\(291\) | −7.12021 | −0.417394 | ||||||||
\(292\) | −5.44302 | −0.318529 | ||||||||
\(293\) | 10.1084 | 0.590536 | 0.295268 | − | 0.955414i | \(-0.404591\pi\) | ||||
0.295268 | + | 0.955414i | \(0.404591\pi\) | |||||||
\(294\) | −2.57390 | −0.150113 | ||||||||
\(295\) | 4.64954 | 0.270707 | ||||||||
\(296\) | −10.7002 | −0.621937 | ||||||||
\(297\) | 7.91477 | 0.459262 | ||||||||
\(298\) | −20.3630 | −1.17960 | ||||||||
\(299\) | −1.68654 | −0.0975352 | ||||||||
\(300\) | 0.527686 | 0.0304660 | ||||||||
\(301\) | 9.94586 | 0.573270 | ||||||||
\(302\) | −9.03664 | −0.520000 | ||||||||
\(303\) | 2.67416 | 0.153626 | ||||||||
\(304\) | −1.20341 | −0.0690204 | ||||||||
\(305\) | −5.90552 | −0.338149 | ||||||||
\(306\) | −6.68868 | −0.382366 | ||||||||
\(307\) | −32.0679 | −1.83021 | −0.915105 | − | 0.403216i | \(-0.867892\pi\) | ||||
−0.915105 | + | 0.403216i | \(0.867892\pi\) | |||||||
\(308\) | 3.81902 | 0.217609 | ||||||||
\(309\) | 4.76048 | 0.270814 | ||||||||
\(310\) | −2.53028 | −0.143710 | ||||||||
\(311\) | 0.533714 | 0.0302642 | 0.0151321 | − | 0.999886i | \(-0.495183\pi\) | ||||
0.0151321 | + | 0.999886i | \(0.495183\pi\) | |||||||
\(312\) | 0.656195 | 0.0371497 | ||||||||
\(313\) | 23.4850 | 1.32745 | 0.663725 | − | 0.747977i | \(-0.268975\pi\) | ||||
0.663725 | + | 0.747977i | \(0.268975\pi\) | |||||||
\(314\) | 7.93990 | 0.448074 | ||||||||
\(315\) | 3.96477 | 0.223390 | ||||||||
\(316\) | −9.71634 | −0.546587 | ||||||||
\(317\) | 30.0676 | 1.68877 | 0.844383 | − | 0.535740i | \(-0.179967\pi\) | ||||
0.844383 | + | 0.535740i | \(0.179967\pi\) | |||||||
\(318\) | 1.50499 | 0.0843959 | ||||||||
\(319\) | −1.36735 | −0.0765566 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 3.44875 | 0.192491 | ||||||||
\(322\) | 1.97580 | 0.110107 | ||||||||
\(323\) | −2.95759 | −0.164565 | ||||||||
\(324\) | 6.57146 | 0.365081 | ||||||||
\(325\) | 1.24353 | 0.0689788 | ||||||||
\(326\) | 17.2900 | 0.957607 | ||||||||
\(327\) | −0.627328 | −0.0346913 | ||||||||
\(328\) | −4.79988 | −0.265029 | ||||||||
\(329\) | −11.3166 | −0.623903 | ||||||||
\(330\) | −1.38333 | −0.0761497 | ||||||||
\(331\) | 9.77668 | 0.537375 | 0.268687 | − | 0.963227i | \(-0.413410\pi\) | ||||
0.268687 | + | 0.963227i | \(0.413410\pi\) | |||||||
\(332\) | −17.4608 | −0.958284 | ||||||||
\(333\) | 29.1211 | 1.59583 | ||||||||
\(334\) | −9.42282 | −0.515594 | ||||||||
\(335\) | −2.08902 | −0.114135 | ||||||||
\(336\) | −0.768738 | −0.0419381 | ||||||||
\(337\) | −14.5929 | −0.794925 | −0.397463 | − | 0.917618i | \(-0.630109\pi\) | ||||
−0.397463 | + | 0.917618i | \(0.630109\pi\) | |||||||
\(338\) | −11.4536 | −0.622995 | ||||||||
\(339\) | −2.52688 | −0.137242 | ||||||||
\(340\) | 2.45768 | 0.133286 | ||||||||
\(341\) | 6.63312 | 0.359203 | ||||||||
\(342\) | 3.27514 | 0.177099 | ||||||||
\(343\) | 17.3035 | 0.934304 | ||||||||
\(344\) | −6.82716 | −0.368096 | ||||||||
\(345\) | −0.715675 | −0.0385306 | ||||||||
\(346\) | 1.86070 | 0.100032 | ||||||||
\(347\) | −19.4971 | −1.04666 | −0.523330 | − | 0.852130i | \(-0.675310\pi\) | ||||
−0.523330 | + | 0.852130i | \(0.675310\pi\) | |||||||
\(348\) | 0.275236 | 0.0147542 | ||||||||
\(349\) | −6.24943 | −0.334524 | −0.167262 | − | 0.985912i | \(-0.553493\pi\) | ||||
−0.167262 | + | 0.985912i | \(0.553493\pi\) | |||||||
\(350\) | −1.45681 | −0.0778697 | ||||||||
\(351\) | −3.75445 | −0.200398 | ||||||||
\(352\) | −2.62149 | −0.139726 | ||||||||
\(353\) | 8.57783 | 0.456552 | 0.228276 | − | 0.973596i | \(-0.426691\pi\) | ||||
0.228276 | + | 0.973596i | \(0.426691\pi\) | |||||||
\(354\) | 2.45350 | 0.130402 | ||||||||
\(355\) | 9.96266 | 0.528763 | ||||||||
\(356\) | 5.36866 | 0.284538 | ||||||||
\(357\) | −1.88931 | −0.0999928 | ||||||||
\(358\) | 10.0718 | 0.532313 | ||||||||
\(359\) | 9.90321 | 0.522671 | 0.261336 | − | 0.965248i | \(-0.415837\pi\) | ||||
0.261336 | + | 0.965248i | \(0.415837\pi\) | |||||||
\(360\) | −2.72155 | −0.143438 | ||||||||
\(361\) | −17.5518 | −0.923779 | ||||||||
\(362\) | −0.752269 | −0.0395384 | ||||||||
\(363\) | −2.17817 | −0.114324 | ||||||||
\(364\) | −1.81159 | −0.0949531 | ||||||||
\(365\) | −5.44302 | −0.284901 | ||||||||
\(366\) | −3.11626 | −0.162890 | ||||||||
\(367\) | 32.8695 | 1.71577 | 0.857886 | − | 0.513840i | \(-0.171777\pi\) | ||||
0.857886 | + | 0.513840i | \(0.171777\pi\) | |||||||
\(368\) | −1.35625 | −0.0706994 | ||||||||
\(369\) | 13.0631 | 0.680038 | ||||||||
\(370\) | −10.7002 | −0.556278 | ||||||||
\(371\) | −4.15491 | −0.215712 | ||||||||
\(372\) | −1.33519 | −0.0692266 | ||||||||
\(373\) | 6.77078 | 0.350577 | 0.175289 | − | 0.984517i | \(-0.443914\pi\) | ||||
0.175289 | + | 0.984517i | \(0.443914\pi\) | |||||||
\(374\) | −6.44278 | −0.333148 | ||||||||
\(375\) | 0.527686 | 0.0272496 | ||||||||
\(376\) | 7.76806 | 0.400607 | ||||||||
\(377\) | 0.648614 | 0.0334053 | ||||||||
\(378\) | 4.39837 | 0.226228 | ||||||||
\(379\) | 34.9977 | 1.79771 | 0.898857 | − | 0.438242i | \(-0.144399\pi\) | ||||
0.898857 | + | 0.438242i | \(0.144399\pi\) | |||||||
\(380\) | −1.20341 | −0.0617337 | ||||||||
\(381\) | −2.01130 | −0.103042 | ||||||||
\(382\) | −3.15540 | −0.161444 | ||||||||
\(383\) | −1.92123 | −0.0981701 | −0.0490851 | − | 0.998795i | \(-0.515631\pi\) | ||||
−0.0490851 | + | 0.998795i | \(0.515631\pi\) | |||||||
\(384\) | 0.527686 | 0.0269284 | ||||||||
\(385\) | 3.81902 | 0.194635 | ||||||||
\(386\) | −7.76219 | −0.395085 | ||||||||
\(387\) | 18.5804 | 0.944496 | ||||||||
\(388\) | −13.4933 | −0.685017 | ||||||||
\(389\) | −19.8128 | −1.00455 | −0.502274 | − | 0.864709i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864709i | \(0.667503\pi\) | |||||||
\(390\) | 0.656195 | 0.0332277 | ||||||||
\(391\) | −3.33322 | −0.168568 | ||||||||
\(392\) | −4.87771 | −0.246361 | ||||||||
\(393\) | 1.41263 | 0.0712575 | ||||||||
\(394\) | −14.2092 | −0.715851 | ||||||||
\(395\) | −9.71634 | −0.488882 | ||||||||
\(396\) | 7.13452 | 0.358523 | ||||||||
\(397\) | 24.4796 | 1.22860 | 0.614299 | − | 0.789073i | \(-0.289439\pi\) | ||||
0.614299 | + | 0.789073i | \(0.289439\pi\) | |||||||
\(398\) | 8.59075 | 0.430616 | ||||||||
\(399\) | 0.925108 | 0.0463133 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.26064 | −0.312641 | −0.156321 | − | 0.987706i | \(-0.549963\pi\) | ||||
−0.156321 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(402\) | −1.10235 | −0.0549800 | ||||||||
\(403\) | −3.14649 | −0.156738 | ||||||||
\(404\) | 5.06770 | 0.252127 | ||||||||
\(405\) | 6.57146 | 0.326538 | ||||||||
\(406\) | −0.759857 | −0.0377111 | ||||||||
\(407\) | 28.0506 | 1.39041 | ||||||||
\(408\) | 1.29688 | 0.0642052 | ||||||||
\(409\) | 17.3216 | 0.856499 | 0.428250 | − | 0.903661i | \(-0.359130\pi\) | ||||
0.428250 | + | 0.903661i | \(0.359130\pi\) | |||||||
\(410\) | −4.79988 | −0.237049 | ||||||||
\(411\) | −7.07760 | −0.349112 | ||||||||
\(412\) | 9.02142 | 0.444453 | ||||||||
\(413\) | −6.77349 | −0.333302 | ||||||||
\(414\) | 3.69110 | 0.181408 | ||||||||
\(415\) | −17.4608 | −0.857116 | ||||||||
\(416\) | 1.24353 | 0.0609692 | ||||||||
\(417\) | −9.15286 | −0.448218 | ||||||||
\(418\) | 3.15474 | 0.154303 | ||||||||
\(419\) | −24.5868 | −1.20114 | −0.600572 | − | 0.799571i | \(-0.705060\pi\) | ||||
−0.600572 | + | 0.799571i | \(0.705060\pi\) | |||||||
\(420\) | −0.768738 | −0.0375106 | ||||||||
\(421\) | −37.1346 | −1.80983 | −0.904916 | − | 0.425591i | \(-0.860066\pi\) | ||||
−0.904916 | + | 0.425591i | \(0.860066\pi\) | |||||||
\(422\) | 27.1324 | 1.32079 | ||||||||
\(423\) | −21.1411 | −1.02792 | ||||||||
\(424\) | 2.85206 | 0.138508 | ||||||||
\(425\) | 2.45768 | 0.119215 | ||||||||
\(426\) | 5.25716 | 0.254710 | ||||||||
\(427\) | 8.60321 | 0.416339 | ||||||||
\(428\) | 6.53561 | 0.315911 | ||||||||
\(429\) | −1.72021 | −0.0830526 | ||||||||
\(430\) | −6.82716 | −0.329235 | ||||||||
\(431\) | 15.0911 | 0.726911 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(432\) | −3.01918 | −0.145261 | ||||||||
\(433\) | 29.4439 | 1.41498 | 0.707492 | − | 0.706722i | \(-0.249827\pi\) | ||||
0.707492 | + | 0.706722i | \(0.249827\pi\) | |||||||
\(434\) | 3.68613 | 0.176940 | ||||||||
\(435\) | 0.275236 | 0.0131966 | ||||||||
\(436\) | −1.18883 | −0.0569345 | ||||||||
\(437\) | 1.63213 | 0.0780752 | ||||||||
\(438\) | −2.87221 | −0.137239 | ||||||||
\(439\) | −12.8585 | −0.613702 | −0.306851 | − | 0.951758i | \(-0.599275\pi\) | ||||
−0.306851 | + | 0.951758i | \(0.599275\pi\) | |||||||
\(440\) | −2.62149 | −0.124975 | ||||||||
\(441\) | 13.2749 | 0.632139 | ||||||||
\(442\) | 3.05620 | 0.145369 | ||||||||
\(443\) | 8.99480 | 0.427356 | 0.213678 | − | 0.976904i | \(-0.431456\pi\) | ||||
0.213678 | + | 0.976904i | \(0.431456\pi\) | |||||||
\(444\) | −5.64636 | −0.267964 | ||||||||
\(445\) | 5.36866 | 0.254499 | ||||||||
\(446\) | 23.7152 | 1.12295 | ||||||||
\(447\) | −10.7453 | −0.508234 | ||||||||
\(448\) | −1.45681 | −0.0688277 | ||||||||
\(449\) | 2.15083 | 0.101504 | 0.0507519 | − | 0.998711i | \(-0.483838\pi\) | ||||
0.0507519 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(450\) | −2.72155 | −0.128295 | ||||||||
\(451\) | 12.5829 | 0.592504 | ||||||||
\(452\) | −4.78861 | −0.225237 | ||||||||
\(453\) | −4.76851 | −0.224044 | ||||||||
\(454\) | 11.4333 | 0.536593 | ||||||||
\(455\) | −1.81159 | −0.0849286 | ||||||||
\(456\) | −0.635024 | −0.0297377 | ||||||||
\(457\) | 33.5887 | 1.57121 | 0.785606 | − | 0.618728i | \(-0.212352\pi\) | ||||
0.785606 | + | 0.618728i | \(0.212352\pi\) | |||||||
\(458\) | −4.78887 | −0.223769 | ||||||||
\(459\) | −7.42017 | −0.346344 | ||||||||
\(460\) | −1.35625 | −0.0632355 | ||||||||
\(461\) | −30.9832 | −1.44303 | −0.721515 | − | 0.692398i | \(-0.756554\pi\) | ||||
−0.721515 | + | 0.692398i | \(0.756554\pi\) | |||||||
\(462\) | 2.01524 | 0.0937576 | ||||||||
\(463\) | −17.2054 | −0.799602 | −0.399801 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399801 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(464\) | 0.521590 | 0.0242142 | ||||||||
\(465\) | −1.33519 | −0.0619182 | ||||||||
\(466\) | −28.5022 | −1.32034 | ||||||||
\(467\) | 2.17888 | 0.100826 | 0.0504132 | − | 0.998728i | \(-0.483946\pi\) | ||||
0.0504132 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(468\) | −3.38433 | −0.156441 | ||||||||
\(469\) | 3.04330 | 0.140526 | ||||||||
\(470\) | 7.76806 | 0.358314 | ||||||||
\(471\) | 4.18978 | 0.193055 | ||||||||
\(472\) | 4.64954 | 0.214012 | ||||||||
\(473\) | 17.8974 | 0.822921 | ||||||||
\(474\) | −5.12718 | −0.235499 | ||||||||
\(475\) | −1.20341 | −0.0552163 | ||||||||
\(476\) | −3.58036 | −0.164106 | ||||||||
\(477\) | −7.76202 | −0.355399 | ||||||||
\(478\) | 17.5347 | 0.802020 | ||||||||
\(479\) | 29.3115 | 1.33928 | 0.669639 | − | 0.742687i | \(-0.266449\pi\) | ||||
0.669639 | + | 0.742687i | \(0.266449\pi\) | |||||||
\(480\) | 0.527686 | 0.0240855 | ||||||||
\(481\) | −13.3061 | −0.606704 | ||||||||
\(482\) | 17.6740 | 0.805028 | ||||||||
\(483\) | 1.04260 | 0.0474400 | ||||||||
\(484\) | −4.12777 | −0.187626 | ||||||||
\(485\) | −13.4933 | −0.612697 | ||||||||
\(486\) | 12.5252 | 0.568155 | ||||||||
\(487\) | −2.85069 | −0.129177 | −0.0645884 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645884 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(488\) | −5.90552 | −0.267330 | ||||||||
\(489\) | 9.12372 | 0.412589 | ||||||||
\(490\) | −4.87771 | −0.220352 | ||||||||
\(491\) | −22.3198 | −1.00728 | −0.503638 | − | 0.863915i | \(-0.668006\pi\) | ||||
−0.503638 | + | 0.863915i | \(0.668006\pi\) | |||||||
\(492\) | −2.53283 | −0.114189 | ||||||||
\(493\) | 1.28190 | 0.0577338 | ||||||||
\(494\) | −1.49648 | −0.0673299 | ||||||||
\(495\) | 7.13452 | 0.320673 | ||||||||
\(496\) | −2.53028 | −0.113613 | ||||||||
\(497\) | −14.5137 | −0.651028 | ||||||||
\(498\) | −9.21381 | −0.412881 | ||||||||
\(499\) | −39.3315 | −1.76072 | −0.880361 | − | 0.474305i | \(-0.842699\pi\) | ||||
−0.880361 | + | 0.474305i | \(0.842699\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −4.97229 | −0.222146 | ||||||||
\(502\) | 22.0973 | 0.986252 | ||||||||
\(503\) | 22.7238 | 1.01320 | 0.506602 | − | 0.862180i | \(-0.330902\pi\) | ||||
0.506602 | + | 0.862180i | \(0.330902\pi\) | |||||||
\(504\) | 3.96477 | 0.176605 | ||||||||
\(505\) | 5.06770 | 0.225510 | ||||||||
\(506\) | 3.55540 | 0.158057 | ||||||||
\(507\) | −6.04392 | −0.268420 | ||||||||
\(508\) | −3.81154 | −0.169110 | ||||||||
\(509\) | −4.55005 | −0.201677 | −0.100839 | − | 0.994903i | \(-0.532153\pi\) | ||||
−0.100839 | + | 0.994903i | \(0.532153\pi\) | |||||||
\(510\) | 1.29688 | 0.0574269 | ||||||||
\(511\) | 7.92944 | 0.350778 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.63332 | 0.160415 | ||||||||
\(514\) | −25.0526 | −1.10502 | ||||||||
\(515\) | 9.02142 | 0.397531 | ||||||||
\(516\) | −3.60260 | −0.158596 | ||||||||
\(517\) | −20.3639 | −0.895605 | ||||||||
\(518\) | 15.5882 | 0.684905 | ||||||||
\(519\) | 0.981865 | 0.0430991 | ||||||||
\(520\) | 1.24353 | 0.0545325 | ||||||||
\(521\) | 27.4148 | 1.20106 | 0.600531 | − | 0.799601i | \(-0.294956\pi\) | ||||
0.600531 | + | 0.799601i | \(0.294956\pi\) | |||||||
\(522\) | −1.41953 | −0.0621312 | ||||||||
\(523\) | 29.8544 | 1.30544 | 0.652720 | − | 0.757599i | \(-0.273628\pi\) | ||||
0.652720 | + | 0.757599i | \(0.273628\pi\) | |||||||
\(524\) | 2.67702 | 0.116946 | ||||||||
\(525\) | −0.768738 | −0.0335505 | ||||||||
\(526\) | −26.5018 | −1.15553 | ||||||||
\(527\) | −6.21861 | −0.270887 | ||||||||
\(528\) | −1.38333 | −0.0602016 | ||||||||
\(529\) | −21.1606 | −0.920025 | ||||||||
\(530\) | 2.85206 | 0.123886 | ||||||||
\(531\) | −12.6539 | −0.549134 | ||||||||
\(532\) | 1.75314 | 0.0760083 | ||||||||
\(533\) | −5.96881 | −0.258538 | ||||||||
\(534\) | 2.83297 | 0.122595 | ||||||||
\(535\) | 6.53561 | 0.282559 | ||||||||
\(536\) | −2.08902 | −0.0902318 | ||||||||
\(537\) | 5.31478 | 0.229349 | ||||||||
\(538\) | 13.0978 | 0.564685 | ||||||||
\(539\) | 12.7869 | 0.550770 | ||||||||
\(540\) | −3.01918 | −0.129925 | ||||||||
\(541\) | −36.0471 | −1.54978 | −0.774892 | − | 0.632094i | \(-0.782196\pi\) | ||||
−0.774892 | + | 0.632094i | \(0.782196\pi\) | |||||||
\(542\) | −10.8390 | −0.465573 | ||||||||
\(543\) | −0.396962 | −0.0170353 | ||||||||
\(544\) | 2.45768 | 0.105372 | ||||||||
\(545\) | −1.18883 | −0.0509237 | ||||||||
\(546\) | −0.955951 | −0.0409109 | ||||||||
\(547\) | 5.24440 | 0.224235 | 0.112117 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112117 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(548\) | −13.4125 | −0.572954 | ||||||||
\(549\) | 16.0721 | 0.685943 | ||||||||
\(550\) | −2.62149 | −0.111781 | ||||||||
\(551\) | −0.627687 | −0.0267404 | ||||||||
\(552\) | −0.715675 | −0.0304612 | ||||||||
\(553\) | 14.1549 | 0.601925 | ||||||||
\(554\) | 2.62756 | 0.111634 | ||||||||
\(555\) | −5.64636 | −0.239675 | ||||||||
\(556\) | −17.3453 | −0.735603 | ||||||||
\(557\) | 21.1447 | 0.895930 | 0.447965 | − | 0.894051i | \(-0.352149\pi\) | ||||
0.447965 | + | 0.894051i | \(0.352149\pi\) | |||||||
\(558\) | 6.88628 | 0.291519 | ||||||||
\(559\) | −8.48979 | −0.359080 | ||||||||
\(560\) | −1.45681 | −0.0615614 | ||||||||
\(561\) | −3.39977 | −0.143538 | ||||||||
\(562\) | 14.3946 | 0.607202 | ||||||||
\(563\) | 15.0001 | 0.632177 | 0.316089 | − | 0.948730i | \(-0.397630\pi\) | ||||
0.316089 | + | 0.948730i | \(0.397630\pi\) | |||||||
\(564\) | 4.09910 | 0.172603 | ||||||||
\(565\) | −4.78861 | −0.201458 | ||||||||
\(566\) | −10.7074 | −0.450065 | ||||||||
\(567\) | −9.57336 | −0.402043 | ||||||||
\(568\) | 9.96266 | 0.418024 | ||||||||
\(569\) | 38.6940 | 1.62214 | 0.811069 | − | 0.584950i | \(-0.198886\pi\) | ||||
0.811069 | + | 0.584950i | \(0.198886\pi\) | |||||||
\(570\) | −0.635024 | −0.0265982 | ||||||||
\(571\) | 9.73147 | 0.407249 | 0.203625 | − | 0.979049i | \(-0.434728\pi\) | ||||
0.203625 | + | 0.979049i | \(0.434728\pi\) | |||||||
\(572\) | −3.25991 | −0.136304 | ||||||||
\(573\) | −1.66506 | −0.0695590 | ||||||||
\(574\) | 6.99251 | 0.291862 | ||||||||
\(575\) | −1.35625 | −0.0565596 | ||||||||
\(576\) | −2.72155 | −0.113398 | ||||||||
\(577\) | −19.5085 | −0.812148 | −0.406074 | − | 0.913840i | \(-0.633102\pi\) | ||||
−0.406074 | + | 0.913840i | \(0.633102\pi\) | |||||||
\(578\) | −10.9598 | −0.455869 | ||||||||
\(579\) | −4.09600 | −0.170224 | ||||||||
\(580\) | 0.521590 | 0.0216578 | ||||||||
\(581\) | 25.4370 | 1.05530 | ||||||||
\(582\) | −7.12021 | −0.295142 | ||||||||
\(583\) | −7.47667 | −0.309652 | ||||||||
\(584\) | −5.44302 | −0.225234 | ||||||||
\(585\) | −3.38433 | −0.139925 | ||||||||
\(586\) | 10.1084 | 0.417572 | ||||||||
\(587\) | 14.7817 | 0.610106 | 0.305053 | − | 0.952335i | \(-0.401326\pi\) | ||||
0.305053 | + | 0.952335i | \(0.401326\pi\) | |||||||
\(588\) | −2.57390 | −0.106146 | ||||||||
\(589\) | 3.04497 | 0.125466 | ||||||||
\(590\) | 4.64954 | 0.191419 | ||||||||
\(591\) | −7.49802 | −0.308427 | ||||||||
\(592\) | −10.7002 | −0.439776 | ||||||||
\(593\) | 3.20171 | 0.131478 | 0.0657392 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657392 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(594\) | 7.91477 | 0.324747 | ||||||||
\(595\) | −3.58036 | −0.146781 | ||||||||
\(596\) | −20.3630 | −0.834101 | ||||||||
\(597\) | 4.53322 | 0.185533 | ||||||||
\(598\) | −1.68654 | −0.0689678 | ||||||||
\(599\) | −41.1127 | −1.67982 | −0.839910 | − | 0.542726i | \(-0.817392\pi\) | ||||
−0.839910 | + | 0.542726i | \(0.817392\pi\) | |||||||
\(600\) | 0.527686 | 0.0215427 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 9.94586 | 0.405363 | ||||||||
\(603\) | 5.68536 | 0.231526 | ||||||||
\(604\) | −9.03664 | −0.367696 | ||||||||
\(605\) | −4.12777 | −0.167818 | ||||||||
\(606\) | 2.67416 | 0.108630 | ||||||||
\(607\) | −32.6049 | −1.32339 | −0.661696 | − | 0.749772i | \(-0.730163\pi\) | ||||
−0.661696 | + | 0.749772i | \(0.730163\pi\) | |||||||
\(608\) | −1.20341 | −0.0488048 | ||||||||
\(609\) | −0.400966 | −0.0162480 | ||||||||
\(610\) | −5.90552 | −0.239107 | ||||||||
\(611\) | 9.65984 | 0.390795 | ||||||||
\(612\) | −6.68868 | −0.270374 | ||||||||
\(613\) | 38.4767 | 1.55406 | 0.777030 | − | 0.629464i | \(-0.216725\pi\) | ||||
0.777030 | + | 0.629464i | \(0.216725\pi\) | |||||||
\(614\) | −32.0679 | −1.29415 | ||||||||
\(615\) | −2.53283 | −0.102134 | ||||||||
\(616\) | 3.81902 | 0.153873 | ||||||||
\(617\) | −44.5065 | −1.79176 | −0.895882 | − | 0.444293i | \(-0.853455\pi\) | ||||
−0.895882 | + | 0.444293i | \(0.853455\pi\) | |||||||
\(618\) | 4.76048 | 0.191495 | ||||||||
\(619\) | −47.8908 | −1.92489 | −0.962447 | − | 0.271471i | \(-0.912490\pi\) | ||||
−0.962447 | + | 0.271471i | \(0.912490\pi\) | |||||||
\(620\) | −2.53028 | −0.101619 | ||||||||
\(621\) | 4.09477 | 0.164317 | ||||||||
\(622\) | 0.533714 | 0.0214000 | ||||||||
\(623\) | −7.82111 | −0.313346 | ||||||||
\(624\) | 0.656195 | 0.0262688 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.4850 | 0.938649 | ||||||||
\(627\) | 1.66471 | 0.0664822 | ||||||||
\(628\) | 7.93990 | 0.316836 | ||||||||
\(629\) | −26.2977 | −1.04856 | ||||||||
\(630\) | 3.96477 | 0.157960 | ||||||||
\(631\) | −36.4674 | −1.45174 | −0.725872 | − | 0.687830i | \(-0.758564\pi\) | ||||
−0.725872 | + | 0.687830i | \(0.758564\pi\) | |||||||
\(632\) | −9.71634 | −0.386495 | ||||||||
\(633\) | 14.3174 | 0.569066 | ||||||||
\(634\) | 30.0676 | 1.19414 | ||||||||
\(635\) | −3.81154 | −0.151256 | ||||||||
\(636\) | 1.50499 | 0.0596769 | ||||||||
\(637\) | −6.06559 | −0.240327 | ||||||||
\(638\) | −1.36735 | −0.0541337 | ||||||||
\(639\) | −27.1139 | −1.07261 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −4.68407 | −0.185010 | −0.0925048 | − | 0.995712i | \(-0.529487\pi\) | ||||
−0.0925048 | + | 0.995712i | \(0.529487\pi\) | |||||||
\(642\) | 3.44875 | 0.136112 | ||||||||
\(643\) | −6.04543 | −0.238409 | −0.119204 | − | 0.992870i | \(-0.538034\pi\) | ||||
−0.119204 | + | 0.992870i | \(0.538034\pi\) | |||||||
\(644\) | 1.97580 | 0.0778573 | ||||||||
\(645\) | −3.60260 | −0.141852 | ||||||||
\(646\) | −2.95759 | −0.116365 | ||||||||
\(647\) | −34.4331 | −1.35370 | −0.676852 | − | 0.736120i | \(-0.736656\pi\) | ||||
−0.676852 | + | 0.736120i | \(0.736656\pi\) | |||||||
\(648\) | 6.57146 | 0.258151 | ||||||||
\(649\) | −12.1887 | −0.478450 | ||||||||
\(650\) | 1.24353 | 0.0487754 | ||||||||
\(651\) | 1.94512 | 0.0762354 | ||||||||
\(652\) | 17.2900 | 0.677130 | ||||||||
\(653\) | −2.60127 | −0.101796 | −0.0508978 | − | 0.998704i | \(-0.516208\pi\) | ||||
−0.0508978 | + | 0.998704i | \(0.516208\pi\) | |||||||
\(654\) | −0.627328 | −0.0245305 | ||||||||
\(655\) | 2.67702 | 0.104600 | ||||||||
\(656\) | −4.79988 | −0.187404 | ||||||||
\(657\) | 14.8134 | 0.577927 | ||||||||
\(658\) | −11.3166 | −0.441166 | ||||||||
\(659\) | −27.1201 | −1.05645 | −0.528225 | − | 0.849105i | \(-0.677142\pi\) | ||||
−0.528225 | + | 0.849105i | \(0.677142\pi\) | |||||||
\(660\) | −1.38333 | −0.0538459 | ||||||||
\(661\) | 36.9919 | 1.43882 | 0.719409 | − | 0.694586i | \(-0.244413\pi\) | ||||
0.719409 | + | 0.694586i | \(0.244413\pi\) | |||||||
\(662\) | 9.77668 | 0.379981 | ||||||||
\(663\) | 1.61272 | 0.0626327 | ||||||||
\(664\) | −17.4608 | −0.677609 | ||||||||
\(665\) | 1.75314 | 0.0679839 | ||||||||
\(666\) | 29.1211 | 1.12842 | ||||||||
\(667\) | −0.707407 | −0.0273909 | ||||||||
\(668\) | −9.42282 | −0.364580 | ||||||||
\(669\) | 12.5142 | 0.483827 | ||||||||
\(670\) | −2.08902 | −0.0807058 | ||||||||
\(671\) | 15.4813 | 0.597648 | ||||||||
\(672\) | −0.768738 | −0.0296547 | ||||||||
\(673\) | 8.65152 | 0.333491 | 0.166746 | − | 0.986000i | \(-0.446674\pi\) | ||||
0.166746 | + | 0.986000i | \(0.446674\pi\) | |||||||
\(674\) | −14.5929 | −0.562097 | ||||||||
\(675\) | −3.01918 | −0.116208 | ||||||||
\(676\) | −11.4536 | −0.440524 | ||||||||
\(677\) | 33.6014 | 1.29141 | 0.645703 | − | 0.763589i | \(-0.276564\pi\) | ||||
0.645703 | + | 0.763589i | \(0.276564\pi\) | |||||||
\(678\) | −2.52688 | −0.0970444 | ||||||||
\(679\) | 19.6571 | 0.754370 | ||||||||
\(680\) | 2.45768 | 0.0942476 | ||||||||
\(681\) | 6.03322 | 0.231193 | ||||||||
\(682\) | 6.63312 | 0.253995 | ||||||||
\(683\) | −6.53157 | −0.249924 | −0.124962 | − | 0.992162i | \(-0.539881\pi\) | ||||
−0.124962 | + | 0.992162i | \(0.539881\pi\) | |||||||
\(684\) | 3.27514 | 0.125228 | ||||||||
\(685\) | −13.4125 | −0.512466 | ||||||||
\(686\) | 17.3035 | 0.660653 | ||||||||
\(687\) | −2.52702 | −0.0964119 | ||||||||
\(688\) | −6.82716 | −0.260283 | ||||||||
\(689\) | 3.54663 | 0.135116 | ||||||||
\(690\) | −0.715675 | −0.0272453 | ||||||||
\(691\) | 45.6707 | 1.73740 | 0.868698 | − | 0.495342i | \(-0.164957\pi\) | ||||
0.868698 | + | 0.495342i | \(0.164957\pi\) | |||||||
\(692\) | 1.86070 | 0.0707331 | ||||||||
\(693\) | −10.3936 | −0.394821 | ||||||||
\(694\) | −19.4971 | −0.740100 | ||||||||
\(695\) | −17.3453 | −0.657944 | ||||||||
\(696\) | 0.275236 | 0.0104328 | ||||||||
\(697\) | −11.7966 | −0.446826 | ||||||||
\(698\) | −6.24943 | −0.236544 | ||||||||
\(699\) | −15.0402 | −0.568874 | ||||||||
\(700\) | −1.45681 | −0.0550622 | ||||||||
\(701\) | −34.5577 | −1.30523 | −0.652614 | − | 0.757690i | \(-0.726328\pi\) | ||||
−0.652614 | + | 0.757690i | \(0.726328\pi\) | |||||||
\(702\) | −3.75445 | −0.141703 | ||||||||
\(703\) | 12.8768 | 0.485656 | ||||||||
\(704\) | −2.62149 | −0.0988013 | ||||||||
\(705\) | 4.09910 | 0.154381 | ||||||||
\(706\) | 8.57783 | 0.322831 | ||||||||
\(707\) | −7.38267 | −0.277654 | ||||||||
\(708\) | 2.45350 | 0.0922081 | ||||||||
\(709\) | 43.1652 | 1.62110 | 0.810551 | − | 0.585668i | \(-0.199168\pi\) | ||||
0.810551 | + | 0.585668i | \(0.199168\pi\) | |||||||
\(710\) | 9.96266 | 0.373892 | ||||||||
\(711\) | 26.4435 | 0.991708 | ||||||||
\(712\) | 5.36866 | 0.201199 | ||||||||
\(713\) | 3.43169 | 0.128518 | ||||||||
\(714\) | −1.88931 | −0.0707056 | ||||||||
\(715\) | −3.25991 | −0.121914 | ||||||||
\(716\) | 10.0718 | 0.376402 | ||||||||
\(717\) | 9.25284 | 0.345554 | ||||||||
\(718\) | 9.90321 | 0.369584 | ||||||||
\(719\) | 3.40341 | 0.126926 | 0.0634628 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634628 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(720\) | −2.72155 | −0.101426 | ||||||||
\(721\) | −13.1425 | −0.489451 | ||||||||
\(722\) | −17.5518 | −0.653210 | ||||||||
\(723\) | 9.32633 | 0.346850 | ||||||||
\(724\) | −0.752269 | −0.0279579 | ||||||||
\(725\) | 0.521590 | 0.0193714 | ||||||||
\(726\) | −2.17817 | −0.0808393 | ||||||||
\(727\) | 32.4078 | 1.20194 | 0.600969 | − | 0.799272i | \(-0.294782\pi\) | ||||
0.600969 | + | 0.799272i | \(0.294782\pi\) | |||||||
\(728\) | −1.81159 | −0.0671420 | ||||||||
\(729\) | −13.1050 | −0.485370 | ||||||||
\(730\) | −5.44302 | −0.201455 | ||||||||
\(731\) | −16.7789 | −0.620591 | ||||||||
\(732\) | −3.11626 | −0.115180 | ||||||||
\(733\) | −6.04603 | −0.223315 | −0.111658 | − | 0.993747i | \(-0.535616\pi\) | ||||
−0.111658 | + | 0.993747i | \(0.535616\pi\) | |||||||
\(734\) | 32.8695 | 1.21323 | ||||||||
\(735\) | −2.57390 | −0.0949398 | ||||||||
\(736\) | −1.35625 | −0.0499921 | ||||||||
\(737\) | 5.47635 | 0.201724 | ||||||||
\(738\) | 13.0631 | 0.480859 | ||||||||
\(739\) | 25.4319 | 0.935526 | 0.467763 | − | 0.883854i | \(-0.345060\pi\) | ||||
0.467763 | + | 0.883854i | \(0.345060\pi\) | |||||||
\(740\) | −10.7002 | −0.393348 | ||||||||
\(741\) | −0.789673 | −0.0290094 | ||||||||
\(742\) | −4.15491 | −0.152532 | ||||||||
\(743\) | 30.5313 | 1.12008 | 0.560042 | − | 0.828464i | \(-0.310785\pi\) | ||||
0.560042 | + | 0.828464i | \(0.310785\pi\) | |||||||
\(744\) | −1.33519 | −0.0489506 | ||||||||
\(745\) | −20.3630 | −0.746042 | ||||||||
\(746\) | 6.77078 | 0.247896 | ||||||||
\(747\) | 47.5203 | 1.73868 | ||||||||
\(748\) | −6.44278 | −0.235571 | ||||||||
\(749\) | −9.52114 | −0.347895 | ||||||||
\(750\) | 0.527686 | 0.0192684 | ||||||||
\(751\) | 17.7883 | 0.649106 | 0.324553 | − | 0.945867i | \(-0.394786\pi\) | ||||
0.324553 | + | 0.945867i | \(0.394786\pi\) | |||||||
\(752\) | 7.76806 | 0.283272 | ||||||||
\(753\) | 11.6605 | 0.424931 | ||||||||
\(754\) | 0.648614 | 0.0236211 | ||||||||
\(755\) | −9.03664 | −0.328877 | ||||||||
\(756\) | 4.39837 | 0.159967 | ||||||||
\(757\) | −45.4058 | −1.65030 | −0.825151 | − | 0.564913i | \(-0.808910\pi\) | ||||
−0.825151 | + | 0.564913i | \(0.808910\pi\) | |||||||
\(758\) | 34.9977 | 1.27118 | ||||||||
\(759\) | 1.87614 | 0.0680995 | ||||||||
\(760\) | −1.20341 | −0.0436523 | ||||||||
\(761\) | 25.8410 | 0.936735 | 0.468367 | − | 0.883534i | \(-0.344842\pi\) | ||||
0.468367 | + | 0.883534i | \(0.344842\pi\) | |||||||
\(762\) | −2.01130 | −0.0728616 | ||||||||
\(763\) | 1.73189 | 0.0626987 | ||||||||
\(764\) | −3.15540 | −0.114158 | ||||||||
\(765\) | −6.68868 | −0.241830 | ||||||||
\(766\) | −1.92123 | −0.0694168 | ||||||||
\(767\) | 5.78185 | 0.208771 | ||||||||
\(768\) | 0.527686 | 0.0190412 | ||||||||
\(769\) | 29.3539 | 1.05853 | 0.529264 | − | 0.848457i | \(-0.322468\pi\) | ||||
0.529264 | + | 0.848457i | \(0.322468\pi\) | |||||||
\(770\) | 3.81902 | 0.137628 | ||||||||
\(771\) | −13.2199 | −0.476104 | ||||||||
\(772\) | −7.76219 | −0.279367 | ||||||||
\(773\) | 13.7170 | 0.493366 | 0.246683 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246683 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(774\) | 18.5804 | 0.667860 | ||||||||
\(775\) | −2.53028 | −0.0908904 | ||||||||
\(776\) | −13.4933 | −0.484380 | ||||||||
\(777\) | 8.22566 | 0.295094 | ||||||||
\(778\) | −19.8128 | −0.710323 | ||||||||
\(779\) | 5.77623 | 0.206955 | ||||||||
\(780\) | 0.656195 | 0.0234956 | ||||||||
\(781\) | −26.1171 | −0.934542 | ||||||||
\(782\) | −3.33322 | −0.119196 | ||||||||
\(783\) | −1.57478 | −0.0562779 | ||||||||
\(784\) | −4.87771 | −0.174204 | ||||||||
\(785\) | 7.93990 | 0.283387 | ||||||||
\(786\) | 1.41263 | 0.0503867 | ||||||||
\(787\) | −40.2677 | −1.43539 | −0.717695 | − | 0.696358i | \(-0.754803\pi\) | ||||
−0.717695 | + | 0.696358i | \(0.754803\pi\) | |||||||
\(788\) | −14.2092 | −0.506183 | ||||||||
\(789\) | −13.9846 | −0.497867 | ||||||||
\(790\) | −9.71634 | −0.345692 | ||||||||
\(791\) | 6.97609 | 0.248041 | ||||||||
\(792\) | 7.13452 | 0.253514 | ||||||||
\(793\) | −7.34371 | −0.260783 | ||||||||
\(794\) | 24.4796 | 0.868750 | ||||||||
\(795\) | 1.50499 | 0.0533767 | ||||||||
\(796\) | 8.59075 | 0.304491 | ||||||||
\(797\) | −20.0391 | −0.709821 | −0.354910 | − | 0.934900i | \(-0.615489\pi\) | ||||
−0.354910 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(798\) | 0.925108 | 0.0327485 | ||||||||
\(799\) | 19.0914 | 0.675404 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −14.6111 | −0.516257 | ||||||||
\(802\) | −6.26064 | −0.221071 | ||||||||
\(803\) | 14.2689 | 0.503537 | ||||||||
\(804\) | −1.10235 | −0.0388768 | ||||||||
\(805\) | 1.97580 | 0.0696377 | ||||||||
\(806\) | −3.14649 | −0.110830 | ||||||||
\(807\) | 6.91151 | 0.243297 | ||||||||
\(808\) | 5.06770 | 0.178281 | ||||||||
\(809\) | −48.4907 | −1.70484 | −0.852422 | − | 0.522855i | \(-0.824867\pi\) | ||||
−0.852422 | + | 0.522855i | \(0.824867\pi\) | |||||||
\(810\) | 6.57146 | 0.230898 | ||||||||
\(811\) | 38.1208 | 1.33860 | 0.669301 | − | 0.742992i | \(-0.266594\pi\) | ||||
0.669301 | + | 0.742992i | \(0.266594\pi\) | |||||||
\(812\) | −0.759857 | −0.0266657 | ||||||||
\(813\) | −5.71957 | −0.200594 | ||||||||
\(814\) | 28.0506 | 0.983171 | ||||||||
\(815\) | 17.2900 | 0.605644 | ||||||||
\(816\) | 1.29688 | 0.0454000 | ||||||||
\(817\) | 8.21588 | 0.287437 | ||||||||
\(818\) | 17.3216 | 0.605636 | ||||||||
\(819\) | 4.93032 | 0.172279 | ||||||||
\(820\) | −4.79988 | −0.167619 | ||||||||
\(821\) | −20.7438 | −0.723964 | −0.361982 | − | 0.932185i | \(-0.617900\pi\) | ||||
−0.361982 | + | 0.932185i | \(0.617900\pi\) | |||||||
\(822\) | −7.07760 | −0.246860 | ||||||||
\(823\) | 49.2294 | 1.71603 | 0.858015 | − | 0.513625i | \(-0.171698\pi\) | ||||
0.858015 | + | 0.513625i | \(0.171698\pi\) | |||||||
\(824\) | 9.02142 | 0.314276 | ||||||||
\(825\) | −1.38333 | −0.0481613 | ||||||||
\(826\) | −6.77349 | −0.235680 | ||||||||
\(827\) | 32.5946 | 1.13343 | 0.566713 | − | 0.823915i | \(-0.308215\pi\) | ||||
0.566713 | + | 0.823915i | \(0.308215\pi\) | |||||||
\(828\) | 3.69110 | 0.128275 | ||||||||
\(829\) | −0.215824 | −0.00749589 | −0.00374795 | − | 0.999993i | \(-0.501193\pi\) | ||||
−0.00374795 | + | 0.999993i | \(0.501193\pi\) | |||||||
\(830\) | −17.4608 | −0.606072 | ||||||||
\(831\) | 1.38653 | 0.0480981 | ||||||||
\(832\) | 1.24353 | 0.0431117 | ||||||||
\(833\) | −11.9878 | −0.415354 | ||||||||
\(834\) | −9.15286 | −0.316938 | ||||||||
\(835\) | −9.42282 | −0.326090 | ||||||||
\(836\) | 3.15474 | 0.109109 | ||||||||
\(837\) | 7.63938 | 0.264056 | ||||||||
\(838\) | −24.5868 | −0.849337 | ||||||||
\(839\) | 13.6258 | 0.470413 | 0.235207 | − | 0.971945i | \(-0.424423\pi\) | ||||
0.235207 | + | 0.971945i | \(0.424423\pi\) | |||||||
\(840\) | −0.768738 | −0.0265240 | ||||||||
\(841\) | −28.7279 | −0.990619 | ||||||||
\(842\) | −37.1346 | −1.27974 | ||||||||
\(843\) | 7.59586 | 0.261615 | ||||||||
\(844\) | 27.1324 | 0.933937 | ||||||||
\(845\) | −11.4536 | −0.394017 | ||||||||
\(846\) | −21.1411 | −0.726848 | ||||||||
\(847\) | 6.01336 | 0.206622 | ||||||||
\(848\) | 2.85206 | 0.0979402 | ||||||||
\(849\) | −5.65014 | −0.193912 | ||||||||
\(850\) | 2.45768 | 0.0842976 | ||||||||
\(851\) | 14.5122 | 0.497471 | ||||||||
\(852\) | 5.25716 | 0.180107 | ||||||||
\(853\) | −41.4481 | −1.41916 | −0.709578 | − | 0.704627i | \(-0.751114\pi\) | ||||
−0.709578 | + | 0.704627i | \(0.751114\pi\) | |||||||
\(854\) | 8.60321 | 0.294396 | ||||||||
\(855\) | 3.27514 | 0.112007 | ||||||||
\(856\) | 6.53561 | 0.223383 | ||||||||
\(857\) | −56.5055 | −1.93019 | −0.965095 | − | 0.261900i | \(-0.915651\pi\) | ||||
−0.965095 | + | 0.261900i | \(0.915651\pi\) | |||||||
\(858\) | −1.72021 | −0.0587271 | ||||||||
\(859\) | −25.9645 | −0.885899 | −0.442949 | − | 0.896547i | \(-0.646068\pi\) | ||||
−0.442949 | + | 0.896547i | \(0.646068\pi\) | |||||||
\(860\) | −6.82716 | −0.232804 | ||||||||
\(861\) | 3.68985 | 0.125750 | ||||||||
\(862\) | 15.0911 | 0.514004 | ||||||||
\(863\) | 1.50224 | 0.0511368 | 0.0255684 | − | 0.999673i | \(-0.491860\pi\) | ||||
0.0255684 | + | 0.999673i | \(0.491860\pi\) | |||||||
\(864\) | −3.01918 | −0.102715 | ||||||||
\(865\) | 1.86070 | 0.0632656 | ||||||||
\(866\) | 29.4439 | 1.00054 | ||||||||
\(867\) | −5.78335 | −0.196413 | ||||||||
\(868\) | 3.68613 | 0.125116 | ||||||||
\(869\) | 25.4713 | 0.864056 | ||||||||
\(870\) | 0.275236 | 0.00933137 | ||||||||
\(871\) | −2.59776 | −0.0880218 | ||||||||
\(872\) | −1.18883 | −0.0402588 | ||||||||
\(873\) | 36.7225 | 1.24287 | ||||||||
\(874\) | 1.63213 | 0.0552075 | ||||||||
\(875\) | −1.45681 | −0.0492491 | ||||||||
\(876\) | −2.87221 | −0.0970429 | ||||||||
\(877\) | 57.2813 | 1.93425 | 0.967126 | − | 0.254299i | \(-0.0818448\pi\) | ||||
0.967126 | + | 0.254299i | \(0.0818448\pi\) | |||||||
\(878\) | −12.8585 | −0.433953 | ||||||||
\(879\) | 5.33404 | 0.179913 | ||||||||
\(880\) | −2.62149 | −0.0883706 | ||||||||
\(881\) | 20.1691 | 0.679513 | 0.339757 | − | 0.940513i | \(-0.389655\pi\) | ||||
0.339757 | + | 0.940513i | \(0.389655\pi\) | |||||||
\(882\) | 13.2749 | 0.446990 | ||||||||
\(883\) | −21.0001 | −0.706710 | −0.353355 | − | 0.935489i | \(-0.614959\pi\) | ||||
−0.353355 | + | 0.935489i | \(0.614959\pi\) | |||||||
\(884\) | 3.05620 | 0.102791 | ||||||||
\(885\) | 2.45350 | 0.0824735 | ||||||||
\(886\) | 8.99480 | 0.302186 | ||||||||
\(887\) | 34.3226 | 1.15244 | 0.576220 | − | 0.817295i | \(-0.304527\pi\) | ||||
0.576220 | + | 0.817295i | \(0.304527\pi\) | |||||||
\(888\) | −5.64636 | −0.189479 | ||||||||
\(889\) | 5.55268 | 0.186231 | ||||||||
\(890\) | 5.36866 | 0.179958 | ||||||||
\(891\) | −17.2270 | −0.577128 | ||||||||
\(892\) | 23.7152 | 0.794044 | ||||||||
\(893\) | −9.34817 | −0.312825 | ||||||||
\(894\) | −10.7453 | −0.359376 | ||||||||
\(895\) | 10.0718 | 0.336665 | ||||||||
\(896\) | −1.45681 | −0.0486686 | ||||||||
\(897\) | −0.889965 | −0.0297151 | ||||||||
\(898\) | 2.15083 | 0.0717740 | ||||||||
\(899\) | −1.31977 | −0.0440168 | ||||||||
\(900\) | −2.72155 | −0.0907182 | ||||||||
\(901\) | 7.00944 | 0.233518 | ||||||||
\(902\) | 12.5829 | 0.418964 | ||||||||
\(903\) | 5.24829 | 0.174652 | ||||||||
\(904\) | −4.78861 | −0.159267 | ||||||||
\(905\) | −0.752269 | −0.0250063 | ||||||||
\(906\) | −4.76851 | −0.158423 | ||||||||
\(907\) | −23.1385 | −0.768302 | −0.384151 | − | 0.923270i | \(-0.625506\pi\) | ||||
−0.384151 | + | 0.923270i | \(0.625506\pi\) | |||||||
\(908\) | 11.4333 | 0.379429 | ||||||||
\(909\) | −13.7920 | −0.457451 | ||||||||
\(910\) | −1.81159 | −0.0600536 | ||||||||
\(911\) | 34.2913 | 1.13612 | 0.568060 | − | 0.822987i | \(-0.307694\pi\) | ||||
0.568060 | + | 0.822987i | \(0.307694\pi\) | |||||||
\(912\) | −0.635024 | −0.0210277 | ||||||||
\(913\) | 45.7733 | 1.51488 | ||||||||
\(914\) | 33.5887 | 1.11101 | ||||||||
\(915\) | −3.11626 | −0.103020 | ||||||||
\(916\) | −4.78887 | −0.158229 | ||||||||
\(917\) | −3.89990 | −0.128786 | ||||||||
\(918\) | −7.42017 | −0.244902 | ||||||||
\(919\) | −53.1213 | −1.75231 | −0.876155 | − | 0.482030i | \(-0.839900\pi\) | ||||
−0.876155 | + | 0.482030i | \(0.839900\pi\) | |||||||
\(920\) | −1.35625 | −0.0447143 | ||||||||
\(921\) | −16.9218 | −0.557591 | ||||||||
\(922\) | −30.9832 | −1.02038 | ||||||||
\(923\) | 12.3889 | 0.407785 | ||||||||
\(924\) | 2.01524 | 0.0662966 | ||||||||
\(925\) | −10.7002 | −0.351821 | ||||||||
\(926\) | −17.2054 | −0.565404 | ||||||||
\(927\) | −24.5522 | −0.806400 | ||||||||
\(928\) | 0.521590 | 0.0171220 | ||||||||
\(929\) | 25.6258 | 0.840755 | 0.420377 | − | 0.907349i | \(-0.361898\pi\) | ||||
0.420377 | + | 0.907349i | \(0.361898\pi\) | |||||||
\(930\) | −1.33519 | −0.0437828 | ||||||||
\(931\) | 5.86989 | 0.192378 | ||||||||
\(932\) | −28.5022 | −0.933621 | ||||||||
\(933\) | 0.281634 | 0.00922028 | ||||||||
\(934\) | 2.17888 | 0.0712950 | ||||||||
\(935\) | −6.44278 | −0.210702 | ||||||||
\(936\) | −3.38433 | −0.110620 | ||||||||
\(937\) | −15.3419 | −0.501199 | −0.250600 | − | 0.968091i | \(-0.580628\pi\) | ||||
−0.250600 | + | 0.968091i | \(0.580628\pi\) | |||||||
\(938\) | 3.04330 | 0.0993672 | ||||||||
\(939\) | 12.3927 | 0.404421 | ||||||||
\(940\) | 7.76806 | 0.253366 | ||||||||
\(941\) | −12.9629 | −0.422577 | −0.211289 | − | 0.977424i | \(-0.567766\pi\) | ||||
−0.211289 | + | 0.977424i | \(0.567766\pi\) | |||||||
\(942\) | 4.18978 | 0.136510 | ||||||||
\(943\) | 6.50984 | 0.211990 | ||||||||
\(944\) | 4.64954 | 0.151330 | ||||||||
\(945\) | 4.39837 | 0.143079 | ||||||||
\(946\) | 17.8974 | 0.581893 | ||||||||
\(947\) | −34.3424 | −1.11598 | −0.557988 | − | 0.829849i | \(-0.688427\pi\) | ||||
−0.557988 | + | 0.829849i | \(0.688427\pi\) | |||||||
\(948\) | −5.12718 | −0.166523 | ||||||||
\(949\) | −6.76857 | −0.219717 | ||||||||
\(950\) | −1.20341 | −0.0390438 | ||||||||
\(951\) | 15.8663 | 0.514499 | ||||||||
\(952\) | −3.58036 | −0.116040 | ||||||||
\(953\) | 56.7450 | 1.83815 | 0.919076 | − | 0.394080i | \(-0.128937\pi\) | ||||
0.919076 | + | 0.394080i | \(0.128937\pi\) | |||||||
\(954\) | −7.76202 | −0.251305 | ||||||||
\(955\) | −3.15540 | −0.102106 | ||||||||
\(956\) | 17.5347 | 0.567114 | ||||||||
\(957\) | −0.721530 | −0.0233237 | ||||||||
\(958\) | 29.3115 | 0.947012 | ||||||||
\(959\) | 19.5395 | 0.630962 | ||||||||
\(960\) | 0.527686 | 0.0170310 | ||||||||
\(961\) | −24.5977 | −0.793474 | ||||||||
\(962\) | −13.3061 | −0.429005 | ||||||||
\(963\) | −17.7870 | −0.573177 | ||||||||
\(964\) | 17.6740 | 0.569241 | ||||||||
\(965\) | −7.76219 | −0.249874 | ||||||||
\(966\) | 1.04260 | 0.0335452 | ||||||||
\(967\) | 39.3646 | 1.26588 | 0.632940 | − | 0.774200i | \(-0.281848\pi\) | ||||
0.632940 | + | 0.774200i | \(0.281848\pi\) | |||||||
\(968\) | −4.12777 | −0.132671 | ||||||||
\(969\) | −1.56068 | −0.0501363 | ||||||||
\(970\) | −13.4933 | −0.433243 | ||||||||
\(971\) | −15.2564 | −0.489601 | −0.244801 | − | 0.969573i | \(-0.578722\pi\) | ||||
−0.244801 | + | 0.969573i | \(0.578722\pi\) | |||||||
\(972\) | 12.5252 | 0.401747 | ||||||||
\(973\) | 25.2687 | 0.810079 | ||||||||
\(974\) | −2.85069 | −0.0913418 | ||||||||
\(975\) | 0.656195 | 0.0210151 | ||||||||
\(976\) | −5.90552 | −0.189031 | ||||||||
\(977\) | −14.6568 | −0.468914 | −0.234457 | − | 0.972126i | \(-0.575331\pi\) | ||||
−0.234457 | + | 0.972126i | \(0.575331\pi\) | |||||||
\(978\) | 9.12372 | 0.291744 | ||||||||
\(979\) | −14.0739 | −0.449804 | ||||||||
\(980\) | −4.87771 | −0.155813 | ||||||||
\(981\) | 3.23545 | 0.103300 | ||||||||
\(982\) | −22.3198 | −0.712252 | ||||||||
\(983\) | 36.2154 | 1.15509 | 0.577546 | − | 0.816358i | \(-0.304010\pi\) | ||||
0.577546 | + | 0.816358i | \(0.304010\pi\) | |||||||
\(984\) | −2.53283 | −0.0807438 | ||||||||
\(985\) | −14.2092 | −0.452744 | ||||||||
\(986\) | 1.28190 | 0.0408240 | ||||||||
\(987\) | −5.97161 | −0.190078 | ||||||||
\(988\) | −1.49648 | −0.0476094 | ||||||||
\(989\) | 9.25933 | 0.294430 | ||||||||
\(990\) | 7.13452 | 0.226750 | ||||||||
\(991\) | 24.9078 | 0.791223 | 0.395612 | − | 0.918418i | \(-0.370533\pi\) | ||||
0.395612 | + | 0.918418i | \(0.370533\pi\) | |||||||
\(992\) | −2.53028 | −0.0803365 | ||||||||
\(993\) | 5.15902 | 0.163717 | ||||||||
\(994\) | −14.5137 | −0.460346 | ||||||||
\(995\) | 8.59075 | 0.272345 | ||||||||
\(996\) | −9.21381 | −0.291951 | ||||||||
\(997\) | −57.8545 | −1.83227 | −0.916135 | − | 0.400870i | \(-0.868708\pi\) | ||||
−0.916135 | + | 0.400870i | \(0.868708\pi\) | |||||||
\(998\) | −39.3315 | −1.24502 | ||||||||
\(999\) | 32.3059 | 1.02211 |
(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 | 6010.2.a.c.1.11 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.11 | ✓ | 16 | 1.1 | even | 1 | trivial |