Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
Defining polynomial: | \(x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-8.14464\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.14464 | −0.719892 | −0.359946 | − | 0.932973i | \(-0.617205\pi\) | ||||
−0.359946 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −61.6648 | −0.481756 | ||||||||
\(5\) | −54.3103 | −0.194307 | −0.0971533 | − | 0.995269i | \(-0.530974\pi\) | ||||
−0.0971533 | + | 0.995269i | \(0.530974\pi\) | |||||||
\(6\) | 219.905 | 0.415630 | ||||||||
\(7\) | −413.400 | −0.455541 | −0.227770 | − | 0.973715i | \(-0.573144\pi\) | ||||
−0.227770 | + | 0.973715i | \(0.573144\pi\) | |||||||
\(8\) | 1544.75 | 1.06670 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 442.338 | 0.139880 | ||||||||
\(11\) | 5302.90 | 1.20126 | 0.600632 | − | 0.799525i | \(-0.294916\pi\) | ||||
0.600632 | + | 0.799525i | \(0.294916\pi\) | |||||||
\(12\) | 1664.95 | 0.278142 | ||||||||
\(13\) | −13494.1 | −1.70349 | −0.851747 | − | 0.523953i | \(-0.824457\pi\) | ||||
−0.851747 | + | 0.523953i | \(0.824457\pi\) | |||||||
\(14\) | 3367.00 | 0.327940 | ||||||||
\(15\) | 1466.38 | 0.112183 | ||||||||
\(16\) | −4688.37 | −0.286155 | ||||||||
\(17\) | 13725.3 | 0.677566 | 0.338783 | − | 0.940865i | \(-0.389985\pi\) | ||||
0.338783 | + | 0.940865i | \(0.389985\pi\) | |||||||
\(18\) | −5937.45 | −0.239964 | ||||||||
\(19\) | −57847.2 | −1.93484 | −0.967420 | − | 0.253177i | \(-0.918525\pi\) | ||||
−0.967420 | + | 0.253177i | \(0.918525\pi\) | |||||||
\(20\) | 3349.03 | 0.0936083 | ||||||||
\(21\) | 11161.8 | 0.263007 | ||||||||
\(22\) | −43190.2 | −0.864780 | ||||||||
\(23\) | −11834.5 | −0.202815 | −0.101408 | − | 0.994845i | \(-0.532335\pi\) | ||||
−0.101408 | + | 0.994845i | \(0.532335\pi\) | |||||||
\(24\) | −41708.3 | −0.615862 | ||||||||
\(25\) | −75175.4 | −0.962245 | ||||||||
\(26\) | 109904. | 1.22633 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 25492.2 | 0.219460 | ||||||||
\(29\) | −137312. | −1.04548 | −0.522739 | − | 0.852493i | \(-0.675090\pi\) | ||||
−0.522739 | + | 0.852493i | \(0.675090\pi\) | |||||||
\(30\) | −11943.1 | −0.0807596 | ||||||||
\(31\) | 110476. | 0.666044 | 0.333022 | − | 0.942919i | \(-0.391932\pi\) | ||||
0.333022 | + | 0.942919i | \(0.391932\pi\) | |||||||
\(32\) | −159543. | −0.860703 | ||||||||
\(33\) | −143178. | −0.693550 | ||||||||
\(34\) | −111788. | −0.487774 | ||||||||
\(35\) | 22451.9 | 0.0885146 | ||||||||
\(36\) | −44953.6 | −0.160585 | ||||||||
\(37\) | 154147. | 0.500297 | 0.250149 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250149 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(38\) | 471145. | 1.39288 | ||||||||
\(39\) | 364339. | 0.983513 | ||||||||
\(40\) | −83896.0 | −0.207268 | ||||||||
\(41\) | 58042.4 | 0.131523 | 0.0657615 | − | 0.997835i | \(-0.479052\pi\) | ||||
0.0657615 | + | 0.997835i | \(0.479052\pi\) | |||||||
\(42\) | −90908.9 | −0.189336 | ||||||||
\(43\) | −607469. | −1.16516 | −0.582578 | − | 0.812775i | \(-0.697956\pi\) | ||||
−0.582578 | + | 0.812775i | \(0.697956\pi\) | |||||||
\(44\) | −327002. | −0.578716 | ||||||||
\(45\) | −39592.2 | −0.0647689 | ||||||||
\(46\) | 96387.4 | 0.146005 | ||||||||
\(47\) | −765556. | −1.07556 | −0.537780 | − | 0.843085i | \(-0.680737\pi\) | ||||
−0.537780 | + | 0.843085i | \(0.680737\pi\) | |||||||
\(48\) | 126586. | 0.165212 | ||||||||
\(49\) | −652643. | −0.792483 | ||||||||
\(50\) | 612277. | 0.692712 | ||||||||
\(51\) | −370584. | −0.391193 | ||||||||
\(52\) | 832107. | 0.820668 | ||||||||
\(53\) | 779953. | 0.719619 | 0.359810 | − | 0.933026i | \(-0.382842\pi\) | ||||
0.359810 | + | 0.933026i | \(0.382842\pi\) | |||||||
\(54\) | 160311. | 0.138543 | ||||||||
\(55\) | −288002. | −0.233414 | ||||||||
\(56\) | −638601. | −0.485927 | ||||||||
\(57\) | 1.56188e6 | 1.11708 | ||||||||
\(58\) | 1.11836e6 | 0.752630 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −90423.9 | −0.0540448 | ||||||||
\(61\) | 745383. | 0.420460 | 0.210230 | − | 0.977652i | \(-0.432579\pi\) | ||||
0.210230 | + | 0.977652i | \(0.432579\pi\) | |||||||
\(62\) | −899790. | −0.479480 | ||||||||
\(63\) | −301369. | −0.151847 | ||||||||
\(64\) | 1.89953e6 | 0.905768 | ||||||||
\(65\) | 732866. | 0.331000 | ||||||||
\(66\) | 1.16614e6 | 0.499281 | ||||||||
\(67\) | −343978. | −0.139723 | −0.0698616 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698616 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(68\) | −846369. | −0.326421 | ||||||||
\(69\) | 319530. | 0.117095 | ||||||||
\(70\) | −182863. | −0.0637209 | ||||||||
\(71\) | 4.41562e6 | 1.46416 | 0.732078 | − | 0.681221i | \(-0.238551\pi\) | ||||
0.732078 | + | 0.681221i | \(0.238551\pi\) | |||||||
\(72\) | 1.12612e6 | 0.355568 | ||||||||
\(73\) | 1.38449e6 | 0.416544 | 0.208272 | − | 0.978071i | \(-0.433216\pi\) | ||||
0.208272 | + | 0.978071i | \(0.433216\pi\) | |||||||
\(74\) | −1.25547e6 | −0.360160 | ||||||||
\(75\) | 2.02974e6 | 0.555552 | ||||||||
\(76\) | 3.56714e6 | 0.932121 | ||||||||
\(77\) | −2.19222e6 | −0.547225 | ||||||||
\(78\) | −2.96742e6 | −0.708023 | ||||||||
\(79\) | −6.92496e6 | −1.58024 | −0.790119 | − | 0.612953i | \(-0.789981\pi\) | ||||
−0.790119 | + | 0.612953i | \(0.789981\pi\) | |||||||
\(80\) | 254627. | 0.0556019 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −472735. | −0.0946824 | ||||||||
\(83\) | 4.41025e6 | 0.846623 | 0.423312 | − | 0.905984i | \(-0.360868\pi\) | ||||
0.423312 | + | 0.905984i | \(0.360868\pi\) | |||||||
\(84\) | −688290. | −0.126705 | ||||||||
\(85\) | −745427. | −0.131655 | ||||||||
\(86\) | 4.94762e6 | 0.838787 | ||||||||
\(87\) | 3.70742e6 | 0.603607 | ||||||||
\(88\) | 8.19166e6 | 1.28139 | ||||||||
\(89\) | −2.65103e6 | −0.398612 | −0.199306 | − | 0.979937i | \(-0.563869\pi\) | ||||
−0.199306 | + | 0.979937i | \(0.563869\pi\) | |||||||
\(90\) | 322465. | 0.0466266 | ||||||||
\(91\) | 5.57844e6 | 0.776011 | ||||||||
\(92\) | 729769. | 0.0977075 | ||||||||
\(93\) | −2.98286e6 | −0.384541 | ||||||||
\(94\) | 6.23518e6 | 0.774287 | ||||||||
\(95\) | 3.14170e6 | 0.375952 | ||||||||
\(96\) | 4.30767e6 | 0.496927 | ||||||||
\(97\) | 531245. | 0.0591009 | 0.0295504 | − | 0.999563i | \(-0.490592\pi\) | ||||
0.0295504 | + | 0.999563i | \(0.490592\pi\) | |||||||
\(98\) | 5.31555e6 | 0.570502 | ||||||||
\(99\) | 3.86581e6 | 0.400422 | ||||||||
\(100\) | 4.63567e6 | 0.463567 | ||||||||
\(101\) | 2.90692e6 | 0.280742 | 0.140371 | − | 0.990099i | \(-0.455170\pi\) | ||||
0.140371 | + | 0.990099i | \(0.455170\pi\) | |||||||
\(102\) | 3.01827e6 | 0.281616 | ||||||||
\(103\) | 1.71445e7 | 1.54595 | 0.772974 | − | 0.634438i | \(-0.218768\pi\) | ||||
0.772974 | + | 0.634438i | \(0.218768\pi\) | |||||||
\(104\) | −2.08450e7 | −1.81712 | ||||||||
\(105\) | −606201. | −0.0511039 | ||||||||
\(106\) | −6.35244e6 | −0.518048 | ||||||||
\(107\) | −7.73354e6 | −0.610289 | −0.305144 | − | 0.952306i | \(-0.598705\pi\) | ||||
−0.305144 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(108\) | 1.21375e6 | 0.0927140 | ||||||||
\(109\) | 5.26465e6 | 0.389383 | 0.194691 | − | 0.980865i | \(-0.437629\pi\) | ||||
0.194691 | + | 0.980865i | \(0.437629\pi\) | |||||||
\(110\) | 2.34567e6 | 0.168033 | ||||||||
\(111\) | −4.16196e6 | −0.288847 | ||||||||
\(112\) | 1.93817e6 | 0.130355 | ||||||||
\(113\) | 2.92949e7 | 1.90993 | 0.954966 | − | 0.296716i | \(-0.0958915\pi\) | ||||
0.954966 | + | 0.296716i | \(0.0958915\pi\) | |||||||
\(114\) | −1.27209e7 | −0.804177 | ||||||||
\(115\) | 642733. | 0.0394083 | ||||||||
\(116\) | 8.46729e6 | 0.503665 | ||||||||
\(117\) | −9.83716e6 | −0.567831 | ||||||||
\(118\) | 1.67274e6 | 0.0937219 | ||||||||
\(119\) | −5.67405e6 | −0.308659 | ||||||||
\(120\) | 2.26519e6 | 0.119666 | ||||||||
\(121\) | 8.63353e6 | 0.443037 | ||||||||
\(122\) | −6.07088e6 | −0.302686 | ||||||||
\(123\) | −1.56715e6 | −0.0759349 | ||||||||
\(124\) | −6.81249e6 | −0.320871 | ||||||||
\(125\) | 8.32580e6 | 0.381277 | ||||||||
\(126\) | 2.45454e6 | 0.109313 | ||||||||
\(127\) | 1.91366e7 | 0.828995 | 0.414497 | − | 0.910051i | \(-0.363957\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363957\pi\) | |||||||
\(128\) | 4.95050e6 | 0.208648 | ||||||||
\(129\) | 1.64017e7 | 0.672703 | ||||||||
\(130\) | −5.96894e6 | −0.238284 | ||||||||
\(131\) | 2.05015e6 | 0.0796775 | 0.0398387 | − | 0.999206i | \(-0.487316\pi\) | ||||
0.0398387 | + | 0.999206i | \(0.487316\pi\) | |||||||
\(132\) | 8.82905e6 | 0.334122 | ||||||||
\(133\) | 2.39141e7 | 0.881399 | ||||||||
\(134\) | 2.80157e6 | 0.100586 | ||||||||
\(135\) | 1.06899e6 | 0.0373943 | ||||||||
\(136\) | 2.12022e7 | 0.722762 | ||||||||
\(137\) | −1.22263e7 | −0.406232 | −0.203116 | − | 0.979155i | \(-0.565107\pi\) | ||||
−0.203116 | + | 0.979155i | \(0.565107\pi\) | |||||||
\(138\) | −2.60246e6 | −0.0842961 | ||||||||
\(139\) | 2.28834e7 | 0.722719 | 0.361359 | − | 0.932427i | \(-0.382313\pi\) | ||||
0.361359 | + | 0.932427i | \(0.382313\pi\) | |||||||
\(140\) | −1.38449e6 | −0.0426424 | ||||||||
\(141\) | 2.06700e7 | 0.620975 | ||||||||
\(142\) | −3.59636e7 | −1.05403 | ||||||||
\(143\) | −7.15575e7 | −2.04635 | ||||||||
\(144\) | −3.41782e6 | −0.0953851 | ||||||||
\(145\) | 7.45744e6 | 0.203143 | ||||||||
\(146\) | −1.12762e7 | −0.299866 | ||||||||
\(147\) | 1.76214e7 | 0.457540 | ||||||||
\(148\) | −9.50542e6 | −0.241021 | ||||||||
\(149\) | −1.01691e7 | −0.251843 | −0.125921 | − | 0.992040i | \(-0.540189\pi\) | ||||
−0.125921 | + | 0.992040i | \(0.540189\pi\) | |||||||
\(150\) | −1.65315e7 | −0.399938 | ||||||||
\(151\) | −5.75910e7 | −1.36124 | −0.680620 | − | 0.732636i | \(-0.738290\pi\) | ||||
−0.680620 | + | 0.732636i | \(0.738290\pi\) | |||||||
\(152\) | −8.93597e7 | −2.06390 | ||||||||
\(153\) | 1.00058e7 | 0.225855 | ||||||||
\(154\) | 1.78548e7 | 0.393943 | ||||||||
\(155\) | −6.00000e6 | −0.129417 | ||||||||
\(156\) | −2.24669e7 | −0.473813 | ||||||||
\(157\) | −1.36932e7 | −0.282395 | −0.141197 | − | 0.989981i | \(-0.545095\pi\) | ||||
−0.141197 | + | 0.989981i | \(0.545095\pi\) | |||||||
\(158\) | 5.64014e7 | 1.13760 | ||||||||
\(159\) | −2.10587e7 | −0.415472 | ||||||||
\(160\) | 8.66484e6 | 0.167240 | ||||||||
\(161\) | 4.89236e6 | 0.0923907 | ||||||||
\(162\) | −4.32840e6 | −0.0799880 | ||||||||
\(163\) | −5.01230e7 | −0.906527 | −0.453263 | − | 0.891377i | \(-0.649740\pi\) | ||||
−0.453263 | + | 0.891377i | \(0.649740\pi\) | |||||||
\(164\) | −3.57917e6 | −0.0633620 | ||||||||
\(165\) | 7.77606e6 | 0.134761 | ||||||||
\(166\) | −3.59199e7 | −0.609477 | ||||||||
\(167\) | 3.87403e6 | 0.0643659 | 0.0321829 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321829 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(168\) | 1.72422e7 | 0.280550 | ||||||||
\(169\) | 1.19341e8 | 1.90189 | ||||||||
\(170\) | 6.07124e6 | 0.0947777 | ||||||||
\(171\) | −4.21706e7 | −0.644947 | ||||||||
\(172\) | 3.74594e7 | 0.561321 | ||||||||
\(173\) | −5.96811e7 | −0.876346 | −0.438173 | − | 0.898891i | \(-0.644374\pi\) | ||||
−0.438173 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(174\) | −3.01956e7 | −0.434531 | ||||||||
\(175\) | 3.10775e7 | 0.438342 | ||||||||
\(176\) | −2.48619e7 | −0.343748 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | 2.15917e7 | 0.286957 | ||||||||
\(179\) | −1.10240e8 | −1.43666 | −0.718330 | − | 0.695703i | \(-0.755093\pi\) | ||||
−0.718330 | + | 0.695703i | \(0.755093\pi\) | |||||||
\(180\) | 2.44145e6 | 0.0312028 | ||||||||
\(181\) | −5.56564e7 | −0.697654 | −0.348827 | − | 0.937187i | \(-0.613420\pi\) | ||||
−0.348827 | + | 0.937187i | \(0.613420\pi\) | |||||||
\(182\) | −4.54344e7 | −0.558644 | ||||||||
\(183\) | −2.01253e7 | −0.242753 | ||||||||
\(184\) | −1.82813e7 | −0.216344 | ||||||||
\(185\) | −8.37176e6 | −0.0972111 | ||||||||
\(186\) | 2.42943e7 | 0.276828 | ||||||||
\(187\) | 7.27840e7 | 0.813936 | ||||||||
\(188\) | 4.72079e7 | 0.518157 | ||||||||
\(189\) | 8.13695e6 | 0.0876689 | ||||||||
\(190\) | −2.55881e7 | −0.270645 | ||||||||
\(191\) | 1.30425e7 | 0.135439 | 0.0677194 | − | 0.997704i | \(-0.478428\pi\) | ||||
0.0677194 | + | 0.997704i | \(0.478428\pi\) | |||||||
\(192\) | −5.12874e7 | −0.522946 | ||||||||
\(193\) | 1.67962e8 | 1.68175 | 0.840873 | − | 0.541232i | \(-0.182042\pi\) | ||||
0.840873 | + | 0.541232i | \(0.182042\pi\) | |||||||
\(194\) | −4.32680e6 | −0.0425462 | ||||||||
\(195\) | −1.97874e7 | −0.191103 | ||||||||
\(196\) | 4.02451e7 | 0.381783 | ||||||||
\(197\) | −3.14534e7 | −0.293114 | −0.146557 | − | 0.989202i | \(-0.546819\pi\) | ||||
−0.146557 | + | 0.989202i | \(0.546819\pi\) | |||||||
\(198\) | −3.14857e7 | −0.288260 | ||||||||
\(199\) | −5.07710e6 | −0.0456699 | −0.0228350 | − | 0.999739i | \(-0.507269\pi\) | ||||
−0.0228350 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(200\) | −1.16127e8 | −1.02643 | ||||||||
\(201\) | 9.28739e6 | 0.0806692 | ||||||||
\(202\) | −2.36758e7 | −0.202104 | ||||||||
\(203\) | 5.67647e7 | 0.476258 | ||||||||
\(204\) | 2.28520e7 | 0.188459 | ||||||||
\(205\) | −3.15230e6 | −0.0255558 | ||||||||
\(206\) | −1.39636e8 | −1.11291 | ||||||||
\(207\) | −8.62732e6 | −0.0676051 | ||||||||
\(208\) | 6.32651e7 | 0.487464 | ||||||||
\(209\) | −3.06758e8 | −2.32426 | ||||||||
\(210\) | 4.93729e6 | 0.0367893 | ||||||||
\(211\) | 2.48172e7 | 0.181871 | 0.0909357 | − | 0.995857i | \(-0.471014\pi\) | ||||
0.0909357 | + | 0.995857i | \(0.471014\pi\) | |||||||
\(212\) | −4.80956e7 | −0.346681 | ||||||||
\(213\) | −1.19222e8 | −0.845330 | ||||||||
\(214\) | 6.29870e7 | 0.439342 | ||||||||
\(215\) | 3.29918e7 | 0.226398 | ||||||||
\(216\) | −3.04054e7 | −0.205287 | ||||||||
\(217\) | −4.56709e7 | −0.303410 | ||||||||
\(218\) | −4.28787e7 | −0.280313 | ||||||||
\(219\) | −3.73813e7 | −0.240492 | ||||||||
\(220\) | 1.77596e7 | 0.112448 | ||||||||
\(221\) | −1.85210e8 | −1.15423 | ||||||||
\(222\) | 3.38977e7 | 0.207938 | ||||||||
\(223\) | −1.11098e8 | −0.670868 | −0.335434 | − | 0.942064i | \(-0.608883\pi\) | ||||
−0.335434 | + | 0.942064i | \(0.608883\pi\) | |||||||
\(224\) | 6.59552e7 | 0.392085 | ||||||||
\(225\) | −5.48029e7 | −0.320748 | ||||||||
\(226\) | −2.38597e8 | −1.37494 | ||||||||
\(227\) | 1.42670e8 | 0.809549 | 0.404774 | − | 0.914417i | \(-0.367350\pi\) | ||||
0.404774 | + | 0.914417i | \(0.367350\pi\) | |||||||
\(228\) | −9.63127e7 | −0.538160 | ||||||||
\(229\) | −8.79526e7 | −0.483977 | −0.241989 | − | 0.970279i | \(-0.577800\pi\) | ||||
−0.241989 | + | 0.970279i | \(0.577800\pi\) | |||||||
\(230\) | −5.23483e6 | −0.0283697 | ||||||||
\(231\) | 5.91899e7 | 0.315941 | ||||||||
\(232\) | −2.12113e8 | −1.11521 | ||||||||
\(233\) | 2.33751e8 | 1.21062 | 0.605311 | − | 0.795989i | \(-0.293049\pi\) | ||||
0.605311 | + | 0.795989i | \(0.293049\pi\) | |||||||
\(234\) | 8.01202e7 | 0.408777 | ||||||||
\(235\) | 4.15776e7 | 0.208988 | ||||||||
\(236\) | 1.26646e7 | 0.0627193 | ||||||||
\(237\) | 1.86974e8 | 0.912351 | ||||||||
\(238\) | 4.62131e7 | 0.222201 | ||||||||
\(239\) | 2.35581e8 | 1.11621 | 0.558107 | − | 0.829769i | \(-0.311528\pi\) | ||||
0.558107 | + | 0.829769i | \(0.311528\pi\) | |||||||
\(240\) | −6.87493e6 | −0.0321017 | ||||||||
\(241\) | 1.34696e8 | 0.619862 | 0.309931 | − | 0.950759i | \(-0.399694\pi\) | ||||
0.309931 | + | 0.950759i | \(0.399694\pi\) | |||||||
\(242\) | −7.03171e7 | −0.318938 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −4.59639e7 | −0.202559 | ||||||||
\(245\) | 3.54453e7 | 0.153985 | ||||||||
\(246\) | 1.27638e7 | 0.0546649 | ||||||||
\(247\) | 7.80594e8 | 3.29599 | ||||||||
\(248\) | 1.70658e8 | 0.710472 | ||||||||
\(249\) | −1.19077e8 | −0.488798 | ||||||||
\(250\) | −6.78106e7 | −0.274478 | ||||||||
\(251\) | 4.35229e8 | 1.73724 | 0.868621 | − | 0.495478i | \(-0.165007\pi\) | ||||
0.868621 | + | 0.495478i | \(0.165007\pi\) | |||||||
\(252\) | 1.85838e7 | 0.0731532 | ||||||||
\(253\) | −6.27569e7 | −0.243635 | ||||||||
\(254\) | −1.55861e8 | −0.596786 | ||||||||
\(255\) | 2.01265e7 | 0.0760113 | ||||||||
\(256\) | −2.83460e8 | −1.05597 | ||||||||
\(257\) | 2.77869e8 | 1.02112 | 0.510558 | − | 0.859844i | \(-0.329439\pi\) | ||||
0.510558 | + | 0.859844i | \(0.329439\pi\) | |||||||
\(258\) | −1.33586e8 | −0.484274 | ||||||||
\(259\) | −6.37243e7 | −0.227906 | ||||||||
\(260\) | −4.51920e7 | −0.159461 | ||||||||
\(261\) | −1.00100e8 | −0.348492 | ||||||||
\(262\) | −1.66977e7 | −0.0573592 | ||||||||
\(263\) | 1.34074e8 | 0.454463 | 0.227231 | − | 0.973841i | \(-0.427033\pi\) | ||||
0.227231 | + | 0.973841i | \(0.427033\pi\) | |||||||
\(264\) | −2.21175e8 | −0.739813 | ||||||||
\(265\) | −4.23595e7 | −0.139827 | ||||||||
\(266\) | −1.94771e8 | −0.634512 | ||||||||
\(267\) | 7.15779e7 | 0.230139 | ||||||||
\(268\) | 2.12113e7 | 0.0673124 | ||||||||
\(269\) | 4.06253e8 | 1.27252 | 0.636258 | − | 0.771476i | \(-0.280481\pi\) | ||||
0.636258 | + | 0.771476i | \(0.280481\pi\) | |||||||
\(270\) | −8.70655e6 | −0.0269199 | ||||||||
\(271\) | 4.61228e8 | 1.40774 | 0.703871 | − | 0.710328i | \(-0.251453\pi\) | ||||
0.703871 | + | 0.710328i | \(0.251453\pi\) | |||||||
\(272\) | −6.43494e7 | −0.193889 | ||||||||
\(273\) | −1.50618e8 | −0.448030 | ||||||||
\(274\) | 9.95791e7 | 0.292443 | ||||||||
\(275\) | −3.98647e8 | −1.15591 | ||||||||
\(276\) | −1.97038e7 | −0.0564114 | ||||||||
\(277\) | −2.60294e8 | −0.735843 | −0.367922 | − | 0.929857i | \(-0.619931\pi\) | ||||
−0.367922 | + | 0.929857i | \(0.619931\pi\) | |||||||
\(278\) | −1.86377e8 | −0.520279 | ||||||||
\(279\) | 8.05372e7 | 0.222015 | ||||||||
\(280\) | 3.46826e7 | 0.0944188 | ||||||||
\(281\) | −3.88226e8 | −1.04379 | −0.521894 | − | 0.853010i | \(-0.674774\pi\) | ||||
−0.521894 | + | 0.853010i | \(0.674774\pi\) | |||||||
\(282\) | −1.68350e8 | −0.447035 | ||||||||
\(283\) | 6.85015e8 | 1.79658 | 0.898292 | − | 0.439398i | \(-0.144808\pi\) | ||||
0.898292 | + | 0.439398i | \(0.144808\pi\) | |||||||
\(284\) | −2.72288e8 | −0.705365 | ||||||||
\(285\) | −8.48260e7 | −0.217056 | ||||||||
\(286\) | 5.82811e8 | 1.47315 | ||||||||
\(287\) | −2.39947e7 | −0.0599141 | ||||||||
\(288\) | −1.16307e8 | −0.286901 | ||||||||
\(289\) | −2.21954e8 | −0.540905 | ||||||||
\(290\) | −6.07382e7 | −0.146241 | ||||||||
\(291\) | −1.43436e7 | −0.0341219 | ||||||||
\(292\) | −8.53744e7 | −0.200672 | ||||||||
\(293\) | −7.03513e7 | −0.163394 | −0.0816969 | − | 0.996657i | \(-0.526034\pi\) | ||||
−0.0816969 | + | 0.996657i | \(0.526034\pi\) | |||||||
\(294\) | −1.43520e8 | −0.329379 | ||||||||
\(295\) | 1.11542e7 | 0.0252966 | ||||||||
\(296\) | 2.38118e8 | 0.533669 | ||||||||
\(297\) | −1.04377e8 | −0.231183 | ||||||||
\(298\) | 8.28235e7 | 0.181299 | ||||||||
\(299\) | 1.59695e8 | 0.345495 | ||||||||
\(300\) | −1.25163e8 | −0.267641 | ||||||||
\(301\) | 2.51128e8 | 0.530776 | ||||||||
\(302\) | 4.69058e8 | 0.979946 | ||||||||
\(303\) | −7.84868e7 | −0.162087 | ||||||||
\(304\) | 2.71209e8 | 0.553665 | ||||||||
\(305\) | −4.04820e7 | −0.0816982 | ||||||||
\(306\) | −8.14934e7 | −0.162591 | ||||||||
\(307\) | 6.19217e8 | 1.22140 | 0.610701 | − | 0.791861i | \(-0.290888\pi\) | ||||
0.610701 | + | 0.791861i | \(0.290888\pi\) | |||||||
\(308\) | 1.35183e8 | 0.263629 | ||||||||
\(309\) | −4.62902e8 | −0.892553 | ||||||||
\(310\) | 4.88679e7 | 0.0931661 | ||||||||
\(311\) | 6.09567e8 | 1.14911 | 0.574553 | − | 0.818468i | \(-0.305176\pi\) | ||||
0.574553 | + | 0.818468i | \(0.305176\pi\) | |||||||
\(312\) | 5.62814e8 | 1.04912 | ||||||||
\(313\) | −5.97609e8 | −1.10157 | −0.550785 | − | 0.834647i | \(-0.685672\pi\) | ||||
−0.550785 | + | 0.834647i | \(0.685672\pi\) | |||||||
\(314\) | 1.11526e8 | 0.203294 | ||||||||
\(315\) | 1.63674e7 | 0.0295049 | ||||||||
\(316\) | 4.27026e8 | 0.761289 | ||||||||
\(317\) | −2.89237e8 | −0.509972 | −0.254986 | − | 0.966945i | \(-0.582071\pi\) | ||||
−0.254986 | + | 0.966945i | \(0.582071\pi\) | |||||||
\(318\) | 1.71516e8 | 0.299095 | ||||||||
\(319\) | −7.28150e8 | −1.25589 | ||||||||
\(320\) | −1.03164e8 | −0.175997 | ||||||||
\(321\) | 2.08806e8 | 0.352350 | ||||||||
\(322\) | −3.98466e7 | −0.0665113 | ||||||||
\(323\) | −7.93972e8 | −1.31098 | ||||||||
\(324\) | −3.27712e7 | −0.0535284 | ||||||||
\(325\) | 1.01442e9 | 1.63918 | ||||||||
\(326\) | 4.08234e8 | 0.652601 | ||||||||
\(327\) | −1.42146e8 | −0.224810 | ||||||||
\(328\) | 8.96611e7 | 0.140296 | ||||||||
\(329\) | 3.16481e8 | 0.489962 | ||||||||
\(330\) | −6.33332e7 | −0.0970136 | ||||||||
\(331\) | −6.01918e8 | −0.912304 | −0.456152 | − | 0.889902i | \(-0.650773\pi\) | ||||
−0.456152 | + | 0.889902i | \(0.650773\pi\) | |||||||
\(332\) | −2.71957e8 | −0.407866 | ||||||||
\(333\) | 1.12373e8 | 0.166766 | ||||||||
\(334\) | −3.15526e7 | −0.0463365 | ||||||||
\(335\) | 1.86815e7 | 0.0271491 | ||||||||
\(336\) | −5.23306e7 | −0.0752607 | ||||||||
\(337\) | 4.06076e8 | 0.577966 | 0.288983 | − | 0.957334i | \(-0.406683\pi\) | ||||
0.288983 | + | 0.957334i | \(0.406683\pi\) | |||||||
\(338\) | −9.71989e8 | −1.36916 | ||||||||
\(339\) | −7.90963e8 | −1.10270 | ||||||||
\(340\) | 4.59666e7 | 0.0634258 | ||||||||
\(341\) | 5.85844e8 | 0.800095 | ||||||||
\(342\) | 3.43465e8 | 0.464292 | ||||||||
\(343\) | 6.10255e8 | 0.816549 | ||||||||
\(344\) | −9.38388e8 | −1.24288 | ||||||||
\(345\) | −1.73538e7 | −0.0227524 | ||||||||
\(346\) | 4.86082e8 | 0.630874 | ||||||||
\(347\) | 1.23529e8 | 0.158714 | 0.0793568 | − | 0.996846i | \(-0.474713\pi\) | ||||
0.0793568 | + | 0.996846i | \(0.474713\pi\) | |||||||
\(348\) | −2.28617e8 | −0.290791 | ||||||||
\(349\) | −3.88573e8 | −0.489309 | −0.244655 | − | 0.969610i | \(-0.578675\pi\) | ||||
−0.244655 | + | 0.969610i | \(0.578675\pi\) | |||||||
\(350\) | −2.53115e8 | −0.315559 | ||||||||
\(351\) | 2.65603e8 | 0.327838 | ||||||||
\(352\) | −8.46041e8 | −1.03393 | ||||||||
\(353\) | 1.30943e8 | 0.158443 | 0.0792213 | − | 0.996857i | \(-0.474757\pi\) | ||||
0.0792213 | + | 0.996857i | \(0.474757\pi\) | |||||||
\(354\) | −4.51640e7 | −0.0541104 | ||||||||
\(355\) | −2.39814e8 | −0.284495 | ||||||||
\(356\) | 1.63475e8 | 0.192034 | ||||||||
\(357\) | 1.53199e8 | 0.178204 | ||||||||
\(358\) | 8.97866e8 | 1.03424 | ||||||||
\(359\) | 1.28579e9 | 1.46669 | 0.733346 | − | 0.679856i | \(-0.237958\pi\) | ||||
0.733346 | + | 0.679856i | \(0.237958\pi\) | |||||||
\(360\) | −6.11602e7 | −0.0690892 | ||||||||
\(361\) | 2.45243e9 | 2.74361 | ||||||||
\(362\) | 4.53301e8 | 0.502235 | ||||||||
\(363\) | −2.33105e8 | −0.255787 | ||||||||
\(364\) | −3.43993e8 | −0.373848 | ||||||||
\(365\) | −7.51922e7 | −0.0809372 | ||||||||
\(366\) | 1.63914e8 | 0.174756 | ||||||||
\(367\) | 1.23889e9 | 1.30828 | 0.654139 | − | 0.756374i | \(-0.273031\pi\) | ||||
0.654139 | + | 0.756374i | \(0.273031\pi\) | |||||||
\(368\) | 5.54843e7 | 0.0580367 | ||||||||
\(369\) | 4.23129e7 | 0.0438410 | ||||||||
\(370\) | 6.81850e7 | 0.0699814 | ||||||||
\(371\) | −3.22433e8 | −0.327816 | ||||||||
\(372\) | 1.83937e8 | 0.185255 | ||||||||
\(373\) | −1.91108e8 | −0.190676 | −0.0953382 | − | 0.995445i | \(-0.530393\pi\) | ||||
−0.0953382 | + | 0.995445i | \(0.530393\pi\) | |||||||
\(374\) | −5.92800e8 | −0.585946 | ||||||||
\(375\) | −2.24796e8 | −0.220130 | ||||||||
\(376\) | −1.18259e9 | −1.14730 | ||||||||
\(377\) | 1.85289e9 | 1.78096 | ||||||||
\(378\) | −6.62726e7 | −0.0631121 | ||||||||
\(379\) | −4.82547e8 | −0.455305 | −0.227653 | − | 0.973742i | \(-0.573105\pi\) | ||||
−0.227653 | + | 0.973742i | \(0.573105\pi\) | |||||||
\(380\) | −1.93732e8 | −0.181117 | ||||||||
\(381\) | −5.16688e8 | −0.478620 | ||||||||
\(382\) | −1.06226e8 | −0.0975012 | ||||||||
\(383\) | −4.67810e8 | −0.425475 | −0.212738 | − | 0.977109i | \(-0.568238\pi\) | ||||
−0.212738 | + | 0.977109i | \(0.568238\pi\) | |||||||
\(384\) | −1.33663e8 | −0.120463 | ||||||||
\(385\) | 1.19060e8 | 0.106329 | ||||||||
\(386\) | −1.36799e9 | −1.21068 | ||||||||
\(387\) | −4.42845e8 | −0.388386 | ||||||||
\(388\) | −3.27591e7 | −0.0284722 | ||||||||
\(389\) | 2.37119e8 | 0.204241 | 0.102120 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102120 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(390\) | 1.61161e8 | 0.137573 | ||||||||
\(391\) | −1.62432e8 | −0.137421 | ||||||||
\(392\) | −1.00817e9 | −0.845344 | ||||||||
\(393\) | −5.53540e7 | −0.0460018 | ||||||||
\(394\) | 2.56177e8 | 0.211010 | ||||||||
\(395\) | 3.76097e8 | 0.307051 | ||||||||
\(396\) | −2.38384e8 | −0.192905 | ||||||||
\(397\) | −3.19338e8 | −0.256144 | −0.128072 | − | 0.991765i | \(-0.540879\pi\) | ||||
−0.128072 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(398\) | 4.13512e7 | 0.0328774 | ||||||||
\(399\) | −6.45679e8 | −0.508876 | ||||||||
\(400\) | 3.52450e8 | 0.275351 | ||||||||
\(401\) | −1.08909e9 | −0.843451 | −0.421725 | − | 0.906724i | \(-0.638575\pi\) | ||||
−0.421725 | + | 0.906724i | \(0.638575\pi\) | |||||||
\(402\) | −7.56425e7 | −0.0580731 | ||||||||
\(403\) | −1.49077e9 | −1.13460 | ||||||||
\(404\) | −1.79254e8 | −0.135249 | ||||||||
\(405\) | −2.88627e7 | −0.0215896 | ||||||||
\(406\) | −4.62328e8 | −0.342854 | ||||||||
\(407\) | 8.17424e8 | 0.600990 | ||||||||
\(408\) | −5.72460e8 | −0.417287 | ||||||||
\(409\) | 1.68562e9 | 1.21822 | 0.609112 | − | 0.793084i | \(-0.291526\pi\) | ||||
0.609112 | + | 0.793084i | \(0.291526\pi\) | |||||||
\(410\) | 2.56744e7 | 0.0183974 | ||||||||
\(411\) | 3.30111e8 | 0.234538 | ||||||||
\(412\) | −1.05721e9 | −0.744769 | ||||||||
\(413\) | 8.49037e7 | 0.0593064 | ||||||||
\(414\) | 7.02664e7 | 0.0486684 | ||||||||
\(415\) | −2.39522e8 | −0.164504 | ||||||||
\(416\) | 2.15288e9 | 1.46620 | ||||||||
\(417\) | −6.17853e8 | −0.417262 | ||||||||
\(418\) | 2.49843e9 | 1.67321 | ||||||||
\(419\) | 1.13922e9 | 0.756588 | 0.378294 | − | 0.925686i | \(-0.376511\pi\) | ||||
0.378294 | + | 0.925686i | \(0.376511\pi\) | |||||||
\(420\) | 3.73812e7 | 0.0246196 | ||||||||
\(421\) | 9.61423e8 | 0.627953 | 0.313977 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313977 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(422\) | −2.02127e8 | −0.130928 | ||||||||
\(423\) | −5.58091e8 | −0.358520 | ||||||||
\(424\) | 1.20483e9 | 0.767621 | ||||||||
\(425\) | −1.03181e9 | −0.651984 | ||||||||
\(426\) | 9.71018e8 | 0.608546 | ||||||||
\(427\) | −3.08141e8 | −0.191537 | ||||||||
\(428\) | 4.76887e8 | 0.294010 | ||||||||
\(429\) | 1.93205e9 | 1.18146 | ||||||||
\(430\) | −2.68707e8 | −0.162982 | ||||||||
\(431\) | 2.62811e8 | 0.158115 | 0.0790575 | − | 0.996870i | \(-0.474809\pi\) | ||||
0.0790575 | + | 0.996870i | \(0.474809\pi\) | |||||||
\(432\) | 9.22812e7 | 0.0550706 | ||||||||
\(433\) | −2.86742e9 | −1.69740 | −0.848698 | − | 0.528877i | \(-0.822613\pi\) | ||||
−0.848698 | + | 0.528877i | \(0.822613\pi\) | |||||||
\(434\) | 3.71973e8 | 0.218423 | ||||||||
\(435\) | −2.01351e8 | −0.117285 | ||||||||
\(436\) | −3.24643e8 | −0.187587 | ||||||||
\(437\) | 6.84590e8 | 0.392415 | ||||||||
\(438\) | 3.04457e8 | 0.173128 | ||||||||
\(439\) | −2.91897e8 | −0.164666 | −0.0823330 | − | 0.996605i | \(-0.526237\pi\) | ||||
−0.0823330 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(440\) | −4.44892e8 | −0.248983 | ||||||||
\(441\) | −4.75777e8 | −0.264161 | ||||||||
\(442\) | 1.50847e9 | 0.830920 | ||||||||
\(443\) | −2.33184e9 | −1.27434 | −0.637169 | − | 0.770724i | \(-0.719895\pi\) | ||||
−0.637169 | + | 0.770724i | \(0.719895\pi\) | |||||||
\(444\) | 2.56646e8 | 0.139154 | ||||||||
\(445\) | 1.43979e8 | 0.0774529 | ||||||||
\(446\) | 9.04850e8 | 0.482953 | ||||||||
\(447\) | 2.74565e8 | 0.145401 | ||||||||
\(448\) | −7.85267e8 | −0.412614 | ||||||||
\(449\) | −2.29986e9 | −1.19905 | −0.599527 | − | 0.800355i | \(-0.704645\pi\) | ||||
−0.599527 | + | 0.800355i | \(0.704645\pi\) | |||||||
\(450\) | 4.46350e8 | 0.230904 | ||||||||
\(451\) | 3.07793e8 | 0.157994 | ||||||||
\(452\) | −1.80646e9 | −0.920121 | ||||||||
\(453\) | 1.55496e9 | 0.785913 | ||||||||
\(454\) | −1.16200e9 | −0.582788 | ||||||||
\(455\) | −3.02967e8 | −0.150784 | ||||||||
\(456\) | 2.41271e9 | 1.19159 | ||||||||
\(457\) | 1.34778e9 | 0.660560 | 0.330280 | − | 0.943883i | \(-0.392857\pi\) | ||||
0.330280 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(458\) | 7.16343e8 | 0.348411 | ||||||||
\(459\) | −2.70156e8 | −0.130398 | ||||||||
\(460\) | −3.96340e7 | −0.0189852 | ||||||||
\(461\) | 1.79615e9 | 0.853865 | 0.426932 | − | 0.904284i | \(-0.359594\pi\) | ||||
0.426932 | + | 0.904284i | \(0.359594\pi\) | |||||||
\(462\) | −4.82080e8 | −0.227443 | ||||||||
\(463\) | −3.73066e9 | −1.74684 | −0.873418 | − | 0.486971i | \(-0.838102\pi\) | ||||
−0.873418 | + | 0.486971i | \(0.838102\pi\) | |||||||
\(464\) | 6.43768e8 | 0.299169 | ||||||||
\(465\) | 1.62000e8 | 0.0747188 | ||||||||
\(466\) | −1.90382e9 | −0.871517 | ||||||||
\(467\) | −4.18677e9 | −1.90226 | −0.951129 | − | 0.308793i | \(-0.900075\pi\) | ||||
−0.951129 | + | 0.308793i | \(0.900075\pi\) | |||||||
\(468\) | 6.06606e8 | 0.273556 | ||||||||
\(469\) | 1.42200e8 | 0.0636496 | ||||||||
\(470\) | −3.38635e8 | −0.150449 | ||||||||
\(471\) | 3.69717e8 | 0.163041 | ||||||||
\(472\) | −3.17260e8 | −0.138873 | ||||||||
\(473\) | −3.22134e9 | −1.39966 | ||||||||
\(474\) | −1.52284e9 | −0.656794 | ||||||||
\(475\) | 4.34869e9 | 1.86179 | ||||||||
\(476\) | 3.49889e8 | 0.148698 | ||||||||
\(477\) | 5.68586e8 | 0.239873 | ||||||||
\(478\) | −1.91872e9 | −0.803553 | ||||||||
\(479\) | 4.05633e9 | 1.68639 | 0.843197 | − | 0.537605i | \(-0.180671\pi\) | ||||
0.843197 | + | 0.537605i | \(0.180671\pi\) | |||||||
\(480\) | −2.33951e8 | −0.0965562 | ||||||||
\(481\) | −2.08006e9 | −0.852254 | ||||||||
\(482\) | −1.09705e9 | −0.446233 | ||||||||
\(483\) | −1.32094e8 | −0.0533418 | ||||||||
\(484\) | −5.32385e8 | −0.213436 | ||||||||
\(485\) | −2.88521e7 | −0.0114837 | ||||||||
\(486\) | 1.16867e8 | 0.0461811 | ||||||||
\(487\) | −3.44990e9 | −1.35349 | −0.676745 | − | 0.736218i | \(-0.736610\pi\) | ||||
−0.676745 | + | 0.736218i | \(0.736610\pi\) | |||||||
\(488\) | 1.15143e9 | 0.448507 | ||||||||
\(489\) | 1.35332e9 | 0.523383 | ||||||||
\(490\) | −2.88689e8 | −0.110852 | ||||||||
\(491\) | −3.70056e9 | −1.41086 | −0.705428 | − | 0.708782i | \(-0.749245\pi\) | ||||
−0.705428 | + | 0.708782i | \(0.749245\pi\) | |||||||
\(492\) | 9.66376e7 | 0.0365821 | ||||||||
\(493\) | −1.88465e9 | −0.708380 | ||||||||
\(494\) | −6.35766e9 | −2.37276 | ||||||||
\(495\) | −2.09953e8 | −0.0778045 | ||||||||
\(496\) | −5.17953e8 | −0.190592 | ||||||||
\(497\) | −1.82542e9 | −0.666982 | ||||||||
\(498\) | 9.69838e8 | 0.351882 | ||||||||
\(499\) | 3.49353e9 | 1.25867 | 0.629336 | − | 0.777133i | \(-0.283327\pi\) | ||||
0.629336 | + | 0.777133i | \(0.283327\pi\) | |||||||
\(500\) | −5.13408e8 | −0.183682 | ||||||||
\(501\) | −1.04599e8 | −0.0371616 | ||||||||
\(502\) | −3.54479e9 | −1.25063 | ||||||||
\(503\) | 3.77577e9 | 1.32287 | 0.661436 | − | 0.750002i | \(-0.269947\pi\) | ||||
0.661436 | + | 0.750002i | \(0.269947\pi\) | |||||||
\(504\) | −4.65540e8 | −0.161976 | ||||||||
\(505\) | −1.57876e8 | −0.0545501 | ||||||||
\(506\) | 5.11132e8 | 0.175391 | ||||||||
\(507\) | −3.22220e9 | −1.09806 | ||||||||
\(508\) | −1.18005e9 | −0.399373 | ||||||||
\(509\) | −2.35210e9 | −0.790575 | −0.395288 | − | 0.918557i | \(-0.629355\pi\) | ||||
−0.395288 | + | 0.918557i | \(0.629355\pi\) | |||||||
\(510\) | −1.63923e8 | −0.0547199 | ||||||||
\(511\) | −5.72349e8 | −0.189753 | ||||||||
\(512\) | 1.67502e9 | 0.551538 | ||||||||
\(513\) | 1.13861e9 | 0.372360 | ||||||||
\(514\) | −2.26315e9 | −0.735092 | ||||||||
\(515\) | −9.31124e8 | −0.300388 | ||||||||
\(516\) | −1.01140e9 | −0.324079 | ||||||||
\(517\) | −4.05967e9 | −1.29203 | ||||||||
\(518\) | 5.19011e8 | 0.164068 | ||||||||
\(519\) | 1.61139e9 | 0.505959 | ||||||||
\(520\) | 1.13210e9 | 0.353079 | ||||||||
\(521\) | −1.51952e9 | −0.470734 | −0.235367 | − | 0.971907i | \(-0.575629\pi\) | ||||
−0.235367 | + | 0.971907i | \(0.575629\pi\) | |||||||
\(522\) | 8.15281e8 | 0.250877 | ||||||||
\(523\) | 5.57185e9 | 1.70311 | 0.851556 | − | 0.524264i | \(-0.175659\pi\) | ||||
0.851556 | + | 0.524264i | \(0.175659\pi\) | |||||||
\(524\) | −1.26422e8 | −0.0383851 | ||||||||
\(525\) | −8.39093e8 | −0.253077 | ||||||||
\(526\) | −1.09198e9 | −0.327164 | ||||||||
\(527\) | 1.51632e9 | 0.451289 | ||||||||
\(528\) | 6.71272e8 | 0.198463 | ||||||||
\(529\) | −3.26477e9 | −0.958866 | ||||||||
\(530\) | 3.45003e8 | 0.100660 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −1.47465e9 | −0.424619 | ||||||||
\(533\) | −7.83227e8 | −0.224049 | ||||||||
\(534\) | −5.82977e8 | −0.165675 | ||||||||
\(535\) | 4.20011e8 | 0.118583 | ||||||||
\(536\) | −5.31360e8 | −0.149043 | ||||||||
\(537\) | 2.97648e9 | 0.829456 | ||||||||
\(538\) | −3.30878e9 | −0.916074 | ||||||||
\(539\) | −3.46090e9 | −0.951981 | ||||||||
\(540\) | −6.59190e7 | −0.0180149 | ||||||||
\(541\) | −1.01713e9 | −0.276177 | −0.138088 | − | 0.990420i | \(-0.544096\pi\) | ||||
−0.138088 | + | 0.990420i | \(0.544096\pi\) | |||||||
\(542\) | −3.75654e9 | −1.01342 | ||||||||
\(543\) | 1.50272e9 | 0.402791 | ||||||||
\(544\) | −2.18978e9 | −0.583183 | ||||||||
\(545\) | −2.85925e8 | −0.0756596 | ||||||||
\(546\) | 1.22673e9 | 0.322533 | ||||||||
\(547\) | −3.76396e8 | −0.0983308 | −0.0491654 | − | 0.998791i | \(-0.515656\pi\) | ||||
−0.0491654 | + | 0.998791i | \(0.515656\pi\) | |||||||
\(548\) | 7.53934e8 | 0.195705 | ||||||||
\(549\) | 5.43384e8 | 0.140153 | ||||||||
\(550\) | 3.24684e9 | 0.832131 | ||||||||
\(551\) | 7.94310e9 | 2.02283 | ||||||||
\(552\) | 4.93595e8 | 0.124906 | ||||||||
\(553\) | 2.86278e9 | 0.719863 | ||||||||
\(554\) | 2.12000e9 | 0.529727 | ||||||||
\(555\) | 2.26038e8 | 0.0561248 | ||||||||
\(556\) | −1.41110e9 | −0.348174 | ||||||||
\(557\) | 7.16500e9 | 1.75680 | 0.878401 | − | 0.477924i | \(-0.158611\pi\) | ||||
0.878401 | + | 0.477924i | \(0.158611\pi\) | |||||||
\(558\) | −6.55947e8 | −0.159827 | ||||||||
\(559\) | 8.19721e9 | 1.98484 | ||||||||
\(560\) | −1.05263e8 | −0.0253289 | ||||||||
\(561\) | −1.96517e9 | −0.469926 | ||||||||
\(562\) | 3.16196e9 | 0.751414 | ||||||||
\(563\) | 4.65876e9 | 1.10025 | 0.550125 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550125 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(564\) | −1.27461e9 | −0.299158 | ||||||||
\(565\) | −1.59102e9 | −0.371112 | ||||||||
\(566\) | −5.57921e9 | −1.29335 | ||||||||
\(567\) | −2.19698e8 | −0.0506157 | ||||||||
\(568\) | 6.82103e9 | 1.56182 | ||||||||
\(569\) | −4.71634e9 | −1.07328 | −0.536639 | − | 0.843812i | \(-0.680306\pi\) | ||||
−0.536639 | + | 0.843812i | \(0.680306\pi\) | |||||||
\(570\) | 6.90878e8 | 0.156257 | ||||||||
\(571\) | −8.11800e9 | −1.82483 | −0.912416 | − | 0.409265i | \(-0.865785\pi\) | ||||
−0.912416 | + | 0.409265i | \(0.865785\pi\) | |||||||
\(572\) | 4.41258e9 | 0.985840 | ||||||||
\(573\) | −3.52147e8 | −0.0781956 | ||||||||
\(574\) | 1.95429e8 | 0.0431317 | ||||||||
\(575\) | 8.89660e8 | 0.195158 | ||||||||
\(576\) | 1.38476e9 | 0.301923 | ||||||||
\(577\) | −2.96457e9 | −0.642460 | −0.321230 | − | 0.947001i | \(-0.604096\pi\) | ||||
−0.321230 | + | 0.947001i | \(0.604096\pi\) | |||||||
\(578\) | 1.80774e9 | 0.389393 | ||||||||
\(579\) | −4.53497e9 | −0.970957 | ||||||||
\(580\) | −4.59862e8 | −0.0978654 | ||||||||
\(581\) | −1.82320e9 | −0.385671 | ||||||||
\(582\) | 1.16824e8 | 0.0245641 | ||||||||
\(583\) | 4.13601e9 | 0.864453 | ||||||||
\(584\) | 2.13870e9 | 0.444329 | ||||||||
\(585\) | 5.34260e8 | 0.110333 | ||||||||
\(586\) | 5.72986e8 | 0.117626 | ||||||||
\(587\) | 4.79349e9 | 0.978180 | 0.489090 | − | 0.872233i | \(-0.337329\pi\) | ||||
0.489090 | + | 0.872233i | \(0.337329\pi\) | |||||||
\(588\) | −1.08662e9 | −0.220423 | ||||||||
\(589\) | −6.39075e9 | −1.28869 | ||||||||
\(590\) | −9.08470e7 | −0.0182108 | ||||||||
\(591\) | 8.49242e8 | 0.169229 | ||||||||
\(592\) | −7.22697e8 | −0.143163 | ||||||||
\(593\) | 6.55987e9 | 1.29183 | 0.645913 | − | 0.763411i | \(-0.276477\pi\) | ||||
0.645913 | + | 0.763411i | \(0.276477\pi\) | |||||||
\(594\) | 8.50113e8 | 0.166427 | ||||||||
\(595\) | 3.08160e8 | 0.0599745 | ||||||||
\(596\) | 6.27073e8 | 0.121327 | ||||||||
\(597\) | 1.37082e8 | 0.0263675 | ||||||||
\(598\) | −1.30066e9 | −0.248719 | ||||||||
\(599\) | 8.15165e9 | 1.54971 | 0.774857 | − | 0.632137i | \(-0.217822\pi\) | ||||
0.774857 | + | 0.632137i | \(0.217822\pi\) | |||||||
\(600\) | 3.13544e9 | 0.592610 | ||||||||
\(601\) | −3.63784e9 | −0.683570 | −0.341785 | − | 0.939778i | \(-0.611031\pi\) | ||||
−0.341785 | + | 0.939778i | \(0.611031\pi\) | |||||||
\(602\) | −2.04534e9 | −0.382102 | ||||||||
\(603\) | −2.50760e8 | −0.0465744 | ||||||||
\(604\) | 3.55133e9 | 0.655786 | ||||||||
\(605\) | −4.68890e8 | −0.0860849 | ||||||||
\(606\) | 6.39247e8 | 0.116685 | ||||||||
\(607\) | 4.53989e9 | 0.823920 | 0.411960 | − | 0.911202i | \(-0.364844\pi\) | ||||
0.411960 | + | 0.911202i | \(0.364844\pi\) | |||||||
\(608\) | 9.22913e9 | 1.66532 | ||||||||
\(609\) | −1.53265e9 | −0.274967 | ||||||||
\(610\) | 3.29712e8 | 0.0588139 | ||||||||
\(611\) | 1.03305e10 | 1.83221 | ||||||||
\(612\) | −6.17003e8 | −0.108807 | ||||||||
\(613\) | 5.71720e9 | 1.00247 | 0.501235 | − | 0.865311i | \(-0.332879\pi\) | ||||
0.501235 | + | 0.865311i | \(0.332879\pi\) | |||||||
\(614\) | −5.04330e9 | −0.879277 | ||||||||
\(615\) | 8.51122e7 | 0.0147546 | ||||||||
\(616\) | −3.38643e9 | −0.583727 | ||||||||
\(617\) | −2.37562e9 | −0.407172 | −0.203586 | − | 0.979057i | \(-0.565260\pi\) | ||||
−0.203586 | + | 0.979057i | \(0.565260\pi\) | |||||||
\(618\) | 3.77017e9 | 0.642542 | ||||||||
\(619\) | 5.60279e9 | 0.949483 | 0.474742 | − | 0.880125i | \(-0.342542\pi\) | ||||
0.474742 | + | 0.880125i | \(0.342542\pi\) | |||||||
\(620\) | 3.69989e8 | 0.0623473 | ||||||||
\(621\) | 2.32938e8 | 0.0390318 | ||||||||
\(622\) | −4.96470e9 | −0.827231 | ||||||||
\(623\) | 1.09594e9 | 0.181584 | ||||||||
\(624\) | −1.70816e9 | −0.281437 | ||||||||
\(625\) | 5.42090e9 | 0.888160 | ||||||||
\(626\) | 4.86732e9 | 0.793011 | ||||||||
\(627\) | 8.28246e9 | 1.34191 | ||||||||
\(628\) | 8.44389e8 | 0.136045 | ||||||||
\(629\) | 2.11571e9 | 0.338984 | ||||||||
\(630\) | −1.33307e8 | −0.0212403 | ||||||||
\(631\) | −1.14283e10 | −1.81083 | −0.905415 | − | 0.424527i | \(-0.860440\pi\) | ||||
−0.905415 | + | 0.424527i | \(0.860440\pi\) | |||||||
\(632\) | −1.06974e10 | −1.68565 | ||||||||
\(633\) | −6.70065e8 | −0.105003 | ||||||||
\(634\) | 2.35573e9 | 0.367124 | ||||||||
\(635\) | −1.03932e9 | −0.161079 | ||||||||
\(636\) | 1.29858e9 | 0.200156 | ||||||||
\(637\) | 8.80680e9 | 1.34999 | ||||||||
\(638\) | 5.93052e9 | 0.904108 | ||||||||
\(639\) | 3.21898e9 | 0.488052 | ||||||||
\(640\) | −2.68863e8 | −0.0405417 | ||||||||
\(641\) | −8.14000e8 | −0.122073 | −0.0610367 | − | 0.998136i | \(-0.519441\pi\) | ||||
−0.0610367 | + | 0.998136i | \(0.519441\pi\) | |||||||
\(642\) | −1.70065e9 | −0.253654 | ||||||||
\(643\) | −1.34257e10 | −1.99158 | −0.995792 | − | 0.0916394i | \(-0.970789\pi\) | ||||
−0.995792 | + | 0.0916394i | \(0.970789\pi\) | |||||||
\(644\) | −3.01686e8 | −0.0445098 | ||||||||
\(645\) | −8.90779e8 | −0.130711 | ||||||||
\(646\) | 6.46662e9 | 0.943765 | ||||||||
\(647\) | −2.58413e9 | −0.375102 | −0.187551 | − | 0.982255i | \(-0.560055\pi\) | ||||
−0.187551 | + | 0.982255i | \(0.560055\pi\) | |||||||
\(648\) | 8.20945e8 | 0.118523 | ||||||||
\(649\) | −1.08910e9 | −0.156391 | ||||||||
\(650\) | −8.26210e9 | −1.18003 | ||||||||
\(651\) | 1.23311e9 | 0.175174 | ||||||||
\(652\) | 3.09082e9 | 0.436725 | ||||||||
\(653\) | 9.14859e9 | 1.28575 | 0.642877 | − | 0.765969i | \(-0.277741\pi\) | ||||
0.642877 | + | 0.765969i | \(0.277741\pi\) | |||||||
\(654\) | 1.15773e9 | 0.161839 | ||||||||
\(655\) | −1.11344e8 | −0.0154819 | ||||||||
\(656\) | −2.72124e8 | −0.0376360 | ||||||||
\(657\) | 1.00929e9 | 0.138848 | ||||||||
\(658\) | −2.57763e9 | −0.352719 | ||||||||
\(659\) | −3.05757e9 | −0.416176 | −0.208088 | − | 0.978110i | \(-0.566724\pi\) | ||||
−0.208088 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(660\) | −4.79509e8 | −0.0649221 | ||||||||
\(661\) | −5.81198e9 | −0.782743 | −0.391371 | − | 0.920233i | \(-0.627999\pi\) | ||||
−0.391371 | + | 0.920233i | \(0.627999\pi\) | |||||||
\(662\) | 4.90241e9 | 0.656760 | ||||||||
\(663\) | 5.00068e9 | 0.666395 | ||||||||
\(664\) | 6.81275e9 | 0.903096 | ||||||||
\(665\) | −1.29878e9 | −0.171262 | ||||||||
\(666\) | −9.15238e8 | −0.120053 | ||||||||
\(667\) | 1.62501e9 | 0.212039 | ||||||||
\(668\) | −2.38891e8 | −0.0310086 | ||||||||
\(669\) | 2.99963e9 | 0.387326 | ||||||||
\(670\) | −1.52154e8 | −0.0195444 | ||||||||
\(671\) | 3.95269e9 | 0.505084 | ||||||||
\(672\) | −1.78079e9 | −0.226371 | ||||||||
\(673\) | −7.68542e9 | −0.971885 | −0.485943 | − | 0.873991i | \(-0.661524\pi\) | ||||
−0.485943 | + | 0.873991i | \(0.661524\pi\) | |||||||
\(674\) | −3.30734e9 | −0.416073 | ||||||||
\(675\) | 1.47968e9 | 0.185184 | ||||||||
\(676\) | −7.35913e9 | −0.916248 | ||||||||
\(677\) | 5.12888e9 | 0.635276 | 0.317638 | − | 0.948212i | \(-0.397110\pi\) | ||||
0.317638 | + | 0.948212i | \(0.397110\pi\) | |||||||
\(678\) | 6.44211e9 | 0.793824 | ||||||||
\(679\) | −2.19617e8 | −0.0269229 | ||||||||
\(680\) | −1.15150e9 | −0.140437 | ||||||||
\(681\) | −3.85210e9 | −0.467393 | ||||||||
\(682\) | −4.77149e9 | −0.575982 | ||||||||
\(683\) | 9.14761e9 | 1.09859 | 0.549294 | − | 0.835629i | \(-0.314897\pi\) | ||||
0.549294 | + | 0.835629i | \(0.314897\pi\) | |||||||
\(684\) | 2.60044e9 | 0.310707 | ||||||||
\(685\) | 6.64016e8 | 0.0789335 | ||||||||
\(686\) | −4.97031e9 | −0.587827 | ||||||||
\(687\) | 2.37472e9 | 0.279424 | ||||||||
\(688\) | 2.84804e9 | 0.333416 | ||||||||
\(689\) | −1.05247e10 | −1.22587 | ||||||||
\(690\) | 1.41340e8 | 0.0163793 | ||||||||
\(691\) | 1.46307e10 | 1.68691 | 0.843455 | − | 0.537200i | \(-0.180518\pi\) | ||||
0.843455 | + | 0.537200i | \(0.180518\pi\) | |||||||
\(692\) | 3.68022e9 | 0.422185 | ||||||||
\(693\) | −1.59813e9 | −0.182408 | ||||||||
\(694\) | −1.00610e9 | −0.114257 | ||||||||
\(695\) | −1.24281e9 | −0.140429 | ||||||||
\(696\) | 5.72704e9 | 0.643869 | ||||||||
\(697\) | 7.96651e8 | 0.0891155 | ||||||||
\(698\) | 3.16479e9 | 0.352250 | ||||||||
\(699\) | −6.31129e9 | −0.698953 | ||||||||
\(700\) | −1.91639e9 | −0.211174 | ||||||||
\(701\) | −5.51419e9 | −0.604601 | −0.302300 | − | 0.953213i | \(-0.597755\pi\) | ||||
−0.302300 | + | 0.953213i | \(0.597755\pi\) | |||||||
\(702\) | −2.16325e9 | −0.236008 | ||||||||
\(703\) | −8.91696e9 | −0.967996 | ||||||||
\(704\) | 1.00730e10 | 1.08807 | ||||||||
\(705\) | −1.12260e9 | −0.120660 | ||||||||
\(706\) | −1.06649e9 | −0.114061 | ||||||||
\(707\) | −1.20172e9 | −0.127890 | ||||||||
\(708\) | −3.41945e8 | −0.0362110 | ||||||||
\(709\) | 4.43575e9 | 0.467417 | 0.233709 | − | 0.972307i | \(-0.424914\pi\) | ||||
0.233709 | + | 0.972307i | \(0.424914\pi\) | |||||||
\(710\) | 1.95320e9 | 0.204806 | ||||||||
\(711\) | −5.04830e9 | −0.526746 | ||||||||
\(712\) | −4.09519e9 | −0.425201 | ||||||||
\(713\) | −1.30743e9 | −0.135084 | ||||||||
\(714\) | −1.24775e9 | −0.128288 | ||||||||
\(715\) | 3.88631e9 | 0.397619 | ||||||||
\(716\) | 6.79793e9 | 0.692119 | ||||||||
\(717\) | −6.36069e9 | −0.644447 | ||||||||
\(718\) | −1.04723e10 | −1.05586 | ||||||||
\(719\) | −5.67887e9 | −0.569785 | −0.284893 | − | 0.958559i | \(-0.591958\pi\) | ||||
−0.284893 | + | 0.958559i | \(0.591958\pi\) | |||||||
\(720\) | 1.85623e8 | 0.0185340 | ||||||||
\(721\) | −7.08754e9 | −0.704242 | ||||||||
\(722\) | −1.99742e10 | −1.97510 | ||||||||
\(723\) | −3.63679e9 | −0.357877 | ||||||||
\(724\) | 3.43204e9 | 0.336099 | ||||||||
\(725\) | 1.03225e10 | 1.00601 | ||||||||
\(726\) | 1.89856e9 | 0.184139 | ||||||||
\(727\) | −1.26294e10 | −1.21903 | −0.609514 | − | 0.792775i | \(-0.708636\pi\) | ||||
−0.609514 | + | 0.792775i | \(0.708636\pi\) | |||||||
\(728\) | 8.61731e9 | 0.827774 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 6.12414e8 | 0.0582660 | ||||||||
\(731\) | −8.33771e9 | −0.789470 | ||||||||
\(732\) | 1.24102e9 | 0.116948 | ||||||||
\(733\) | 8.87757e9 | 0.832588 | 0.416294 | − | 0.909230i | \(-0.363329\pi\) | ||||
0.416294 | + | 0.909230i | \(0.363329\pi\) | |||||||
\(734\) | −1.00903e10 | −0.941819 | ||||||||
\(735\) | −9.57023e8 | −0.0889030 | ||||||||
\(736\) | 1.88811e9 | 0.174564 | ||||||||
\(737\) | −1.82408e9 | −0.167844 | ||||||||
\(738\) | −3.44624e8 | −0.0315608 | ||||||||
\(739\) | −1.67534e10 | −1.52703 | −0.763515 | − | 0.645791i | \(-0.776528\pi\) | ||||
−0.763515 | + | 0.645791i | \(0.776528\pi\) | |||||||
\(740\) | 5.16243e8 | 0.0468320 | ||||||||
\(741\) | −2.10760e10 | −1.90294 | ||||||||
\(742\) | 2.62610e9 | 0.235992 | ||||||||
\(743\) | 1.87784e10 | 1.67957 | 0.839784 | − | 0.542921i | \(-0.182682\pi\) | ||||
0.839784 | + | 0.542921i | \(0.182682\pi\) | |||||||
\(744\) | −4.60778e9 | −0.410191 | ||||||||
\(745\) | 5.52286e8 | 0.0489347 | ||||||||
\(746\) | 1.55650e9 | 0.137266 | ||||||||
\(747\) | 3.21507e9 | 0.282208 | ||||||||
\(748\) | −4.48821e9 | −0.392118 | ||||||||
\(749\) | 3.19705e9 | 0.278011 | ||||||||
\(750\) | 1.83089e9 | 0.158470 | ||||||||
\(751\) | 2.58308e9 | 0.222535 | 0.111268 | − | 0.993790i | \(-0.464509\pi\) | ||||
0.111268 | + | 0.993790i | \(0.464509\pi\) | |||||||
\(752\) | 3.58921e9 | 0.307777 | ||||||||
\(753\) | −1.17512e10 | −1.00300 | ||||||||
\(754\) | −1.50911e10 | −1.28210 | ||||||||
\(755\) | 3.12778e9 | 0.264498 | ||||||||
\(756\) | −5.01763e8 | −0.0422350 | ||||||||
\(757\) | 5.60643e9 | 0.469733 | 0.234867 | − | 0.972028i | \(-0.424535\pi\) | ||||
0.234867 | + | 0.972028i | \(0.424535\pi\) | |||||||
\(758\) | 3.93018e9 | 0.327770 | ||||||||
\(759\) | 1.69444e9 | 0.140663 | ||||||||
\(760\) | 4.85315e9 | 0.401030 | ||||||||
\(761\) | 1.71960e8 | 0.0141443 | 0.00707216 | − | 0.999975i | \(-0.497749\pi\) | ||||
0.00707216 | + | 0.999975i | \(0.497749\pi\) | |||||||
\(762\) | 4.20824e9 | 0.344555 | ||||||||
\(763\) | −2.17641e9 | −0.177380 | ||||||||
\(764\) | −8.04260e8 | −0.0652484 | ||||||||
\(765\) | −5.43416e8 | −0.0438852 | ||||||||
\(766\) | 3.81015e9 | 0.306296 | ||||||||
\(767\) | 2.77139e9 | 0.221776 | ||||||||
\(768\) | 7.65343e9 | 0.609666 | ||||||||
\(769\) | −1.69708e10 | −1.34574 | −0.672869 | − | 0.739762i | \(-0.734938\pi\) | ||||
−0.672869 | + | 0.739762i | \(0.734938\pi\) | |||||||
\(770\) | −9.69702e8 | −0.0765457 | ||||||||
\(771\) | −7.50247e9 | −0.589541 | ||||||||
\(772\) | −1.03573e10 | −0.810191 | ||||||||
\(773\) | −5.87486e9 | −0.457477 | −0.228739 | − | 0.973488i | \(-0.573460\pi\) | ||||
−0.228739 | + | 0.973488i | \(0.573460\pi\) | |||||||
\(774\) | 3.60681e9 | 0.279596 | ||||||||
\(775\) | −8.30510e9 | −0.640898 | ||||||||
\(776\) | 8.20642e8 | 0.0630431 | ||||||||
\(777\) | 1.72056e9 | 0.131582 | ||||||||
\(778\) | −1.93125e9 | −0.147031 | ||||||||
\(779\) | −3.35759e9 | −0.254476 | ||||||||
\(780\) | 1.22018e9 | 0.0920650 | ||||||||
\(781\) | 2.34156e10 | 1.75884 | ||||||||
\(782\) | 1.32295e9 | 0.0989280 | ||||||||
\(783\) | 2.70271e9 | 0.201202 | ||||||||
\(784\) | 3.05983e9 | 0.226773 | ||||||||
\(785\) | 7.43684e8 | 0.0548712 | ||||||||
\(786\) | 4.50839e8 | 0.0331163 | ||||||||
\(787\) | 1.81450e9 | 0.132692 | 0.0663461 | − | 0.997797i | \(-0.478866\pi\) | ||||
0.0663461 | + | 0.997797i | \(0.478866\pi\) | |||||||
\(788\) | 1.93957e9 | 0.141209 | ||||||||
\(789\) | −3.61999e9 | −0.262384 | ||||||||
\(790\) | −3.06318e9 | −0.221043 | ||||||||
\(791\) | −1.21105e10 | −0.870052 | ||||||||
\(792\) | 5.97172e9 | 0.427131 | ||||||||
\(793\) | −1.00582e10 | −0.716252 | ||||||||
\(794\) | 2.60089e9 | 0.184396 | ||||||||
\(795\) | 1.14371e9 | 0.0807290 | ||||||||
\(796\) | 3.13078e8 | 0.0220017 | ||||||||
\(797\) | 7.68250e9 | 0.537525 | 0.268762 | − | 0.963207i | \(-0.413385\pi\) | ||||
0.268762 | + | 0.963207i | \(0.413385\pi\) | |||||||
\(798\) | 5.25883e9 | 0.366335 | ||||||||
\(799\) | −1.05075e10 | −0.728763 | ||||||||
\(800\) | 1.19937e10 | 0.828207 | ||||||||
\(801\) | −1.93260e9 | −0.132871 | ||||||||
\(802\) | 8.87028e9 | 0.607193 | ||||||||
\(803\) | 7.34182e9 | 0.500379 | ||||||||
\(804\) | −5.72705e8 | −0.0388629 | ||||||||
\(805\) | −2.65706e8 | −0.0179521 | ||||||||
\(806\) | 1.21418e10 | 0.816791 | ||||||||
\(807\) | −1.09688e10 | −0.734688 | ||||||||
\(808\) | 4.49047e9 | 0.299469 | ||||||||
\(809\) | −2.53283e10 | −1.68185 | −0.840924 | − | 0.541154i | \(-0.817988\pi\) | ||||
−0.840924 | + | 0.541154i | \(0.817988\pi\) | |||||||
\(810\) | 2.35077e8 | 0.0155422 | ||||||||
\(811\) | −1.04893e9 | −0.0690513 | −0.0345256 | − | 0.999404i | \(-0.510992\pi\) | ||||
−0.0345256 | + | 0.999404i | \(0.510992\pi\) | |||||||
\(812\) | −3.50038e9 | −0.229440 | ||||||||
\(813\) | −1.24531e10 | −0.812760 | ||||||||
\(814\) | −6.65763e9 | −0.432647 | ||||||||
\(815\) | 2.72220e9 | 0.176144 | ||||||||
\(816\) | 1.73743e9 | 0.111942 | ||||||||
\(817\) | 3.51404e10 | 2.25439 | ||||||||
\(818\) | −1.37287e10 | −0.876989 | ||||||||
\(819\) | 4.06668e9 | 0.258670 | ||||||||
\(820\) | 1.94386e8 | 0.0123117 | ||||||||
\(821\) | −1.22269e10 | −0.771110 | −0.385555 | − | 0.922685i | \(-0.625990\pi\) | ||||
−0.385555 | + | 0.922685i | \(0.625990\pi\) | |||||||
\(822\) | −2.68864e9 | −0.168842 | ||||||||
\(823\) | 6.96726e8 | 0.0435675 | 0.0217837 | − | 0.999763i | \(-0.493065\pi\) | ||||
0.0217837 | + | 0.999763i | \(0.493065\pi\) | |||||||
\(824\) | 2.64840e10 | 1.64907 | ||||||||
\(825\) | 1.07635e10 | 0.667365 | ||||||||
\(826\) | −6.91510e8 | −0.0426942 | ||||||||
\(827\) | −2.23328e10 | −1.37301 | −0.686505 | − | 0.727125i | \(-0.740856\pi\) | ||||
−0.686505 | + | 0.727125i | \(0.740856\pi\) | |||||||
\(828\) | 5.32001e8 | 0.0325692 | ||||||||
\(829\) | 1.33734e10 | 0.815267 | 0.407633 | − | 0.913146i | \(-0.366354\pi\) | ||||
0.407633 | + | 0.913146i | \(0.366354\pi\) | |||||||
\(830\) | 1.95082e9 | 0.118425 | ||||||||
\(831\) | 7.02794e9 | 0.424839 | ||||||||
\(832\) | −2.56324e10 | −1.54297 | ||||||||
\(833\) | −8.95774e9 | −0.536959 | ||||||||
\(834\) | 5.03219e9 | 0.300383 | ||||||||
\(835\) | −2.10400e8 | −0.0125067 | ||||||||
\(836\) | 1.89162e10 | 1.11972 | ||||||||
\(837\) | −2.17450e9 | −0.128180 | ||||||||
\(838\) | −9.27856e9 | −0.544661 | ||||||||
\(839\) | −1.68025e10 | −0.982217 | −0.491108 | − | 0.871098i | \(-0.663408\pi\) | ||||
−0.491108 | + | 0.871098i | \(0.663408\pi\) | |||||||
\(840\) | −9.36430e8 | −0.0545127 | ||||||||
\(841\) | 1.60463e9 | 0.0930226 | ||||||||
\(842\) | −7.83045e9 | −0.452058 | ||||||||
\(843\) | 1.04821e10 | 0.602631 | ||||||||
\(844\) | −1.53035e9 | −0.0876176 | ||||||||
\(845\) | −6.48145e9 | −0.369550 | ||||||||
\(846\) | 4.54545e9 | 0.258096 | ||||||||
\(847\) | −3.56910e9 | −0.201821 | ||||||||
\(848\) | −3.65671e9 | −0.205923 | ||||||||
\(849\) | −1.84954e10 | −1.03726 | ||||||||
\(850\) | 8.40370e9 | 0.469358 | ||||||||
\(851\) | −1.82424e9 | −0.101468 | ||||||||
\(852\) | 7.35177e9 | 0.407243 | ||||||||
\(853\) | −6.95279e9 | −0.383563 | −0.191782 | − | 0.981438i | \(-0.561427\pi\) | ||||
−0.191782 | + | 0.981438i | \(0.561427\pi\) | |||||||
\(854\) | 2.50970e9 | 0.137886 | ||||||||
\(855\) | 2.29030e9 | 0.125317 | ||||||||
\(856\) | −1.19464e10 | −0.650997 | ||||||||
\(857\) | −3.47269e10 | −1.88466 | −0.942330 | − | 0.334687i | \(-0.891370\pi\) | ||||
−0.942330 | + | 0.334687i | \(0.891370\pi\) | |||||||
\(858\) | −1.57359e10 | −0.850523 | ||||||||
\(859\) | −1.72796e10 | −0.930161 | −0.465081 | − | 0.885268i | \(-0.653975\pi\) | ||||
−0.465081 | + | 0.885268i | \(0.653975\pi\) | |||||||
\(860\) | −2.03443e9 | −0.109068 | ||||||||
\(861\) | 6.47858e8 | 0.0345914 | ||||||||
\(862\) | −2.14050e9 | −0.113826 | ||||||||
\(863\) | −3.64236e10 | −1.92906 | −0.964529 | − | 0.263977i | \(-0.914966\pi\) | ||||
−0.964529 | + | 0.263977i | \(0.914966\pi\) | |||||||
\(864\) | 3.14029e9 | 0.165642 | ||||||||
\(865\) | 3.24130e9 | 0.170280 | ||||||||
\(866\) | 2.33541e10 | 1.22194 | ||||||||
\(867\) | 5.99276e9 | 0.312291 | ||||||||
\(868\) | 2.81628e9 | 0.146170 | ||||||||
\(869\) | −3.67224e10 | −1.89828 | ||||||||
\(870\) | 1.63993e9 | 0.0844323 | ||||||||
\(871\) | 4.64165e9 | 0.238018 | ||||||||
\(872\) | 8.13258e9 | 0.415356 | ||||||||
\(873\) | 3.87278e8 | 0.0197003 | ||||||||
\(874\) | −5.57575e9 | −0.282496 | ||||||||
\(875\) | −3.44188e9 | −0.173687 | ||||||||
\(876\) | 2.30511e9 | 0.115858 | ||||||||
\(877\) | −2.21634e9 | −0.110953 | −0.0554763 | − | 0.998460i | \(-0.517668\pi\) | ||||
−0.0554763 | + | 0.998460i | \(0.517668\pi\) | |||||||
\(878\) | 2.37740e9 | 0.118542 | ||||||||
\(879\) | 1.89949e9 | 0.0943354 | ||||||||
\(880\) | 1.35026e9 | 0.0667925 | ||||||||
\(881\) | −2.32029e10 | −1.14321 | −0.571607 | − | 0.820528i | \(-0.693680\pi\) | ||||
−0.571607 | + | 0.820528i | \(0.693680\pi\) | |||||||
\(882\) | 3.87504e9 | 0.190167 | ||||||||
\(883\) | 1.94888e10 | 0.952624 | 0.476312 | − | 0.879276i | \(-0.341973\pi\) | ||||
0.476312 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(884\) | 1.14209e10 | 0.556057 | ||||||||
\(885\) | −3.01163e8 | −0.0146050 | ||||||||
\(886\) | 1.89920e10 | 0.917386 | ||||||||
\(887\) | 9.83405e9 | 0.473151 | 0.236575 | − | 0.971613i | \(-0.423975\pi\) | ||||
0.236575 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(888\) | −6.42920e9 | −0.308114 | ||||||||
\(889\) | −7.91107e9 | −0.377641 | ||||||||
\(890\) | −1.17265e9 | −0.0557577 | ||||||||
\(891\) | 2.81818e9 | 0.133474 | ||||||||
\(892\) | 6.85080e9 | 0.323195 | ||||||||
\(893\) | 4.42853e10 | 2.08104 | ||||||||
\(894\) | −2.23623e9 | −0.104673 | ||||||||
\(895\) | 5.98717e9 | 0.279152 | ||||||||
\(896\) | −2.04654e9 | −0.0950477 | ||||||||
\(897\) | −4.31176e9 | −0.199471 | ||||||||
\(898\) | 1.87315e10 | 0.863189 | ||||||||
\(899\) | −1.51697e10 | −0.696334 | ||||||||
\(900\) | 3.37941e9 | 0.154522 | ||||||||
\(901\) | 1.07051e10 | 0.487590 | ||||||||
\(902\) | −2.50686e9 | −0.113739 | ||||||||
\(903\) | −6.78044e9 | −0.306444 | ||||||||
\(904\) | 4.52534e10 | 2.03733 | ||||||||
\(905\) | 3.02272e9 | 0.135559 | ||||||||
\(906\) | −1.26646e10 | −0.565772 | ||||||||
\(907\) | 2.35757e10 | 1.04915 | 0.524577 | − | 0.851363i | \(-0.324224\pi\) | ||||
0.524577 | + | 0.851363i | \(0.324224\pi\) | |||||||
\(908\) | −8.79773e9 | −0.390005 | ||||||||
\(909\) | 2.11914e9 | 0.0935808 | ||||||||
\(910\) | 2.46756e9 | 0.108548 | ||||||||
\(911\) | −2.65692e10 | −1.16430 | −0.582149 | − | 0.813082i | \(-0.697788\pi\) | ||||
−0.582149 | + | 0.813082i | \(0.697788\pi\) | |||||||
\(912\) | −7.32265e9 | −0.319658 | ||||||||
\(913\) | 2.33871e10 | 1.01702 | ||||||||
\(914\) | −1.09772e10 | −0.475532 | ||||||||
\(915\) | 1.09301e9 | 0.0471685 | ||||||||
\(916\) | 5.42358e9 | 0.233159 | ||||||||
\(917\) | −8.47531e8 | −0.0362964 | ||||||||
\(918\) | 2.20032e9 | 0.0938722 | ||||||||
\(919\) | 2.32295e10 | 0.987271 | 0.493636 | − | 0.869669i | \(-0.335668\pi\) | ||||
0.493636 | + | 0.869669i | \(0.335668\pi\) | |||||||
\(920\) | 9.92863e8 | 0.0420370 | ||||||||
\(921\) | −1.67189e10 | −0.705177 | ||||||||
\(922\) | −1.46290e10 | −0.614690 | ||||||||
\(923\) | −5.95846e10 | −2.49418 | ||||||||
\(924\) | −3.64993e9 | −0.152206 | ||||||||
\(925\) | −1.15880e10 | −0.481409 | ||||||||
\(926\) | 3.03849e10 | 1.25753 | ||||||||
\(927\) | 1.24983e10 | 0.515316 | ||||||||
\(928\) | 2.19071e10 | 0.899845 | ||||||||
\(929\) | 8.90068e9 | 0.364224 | 0.182112 | − | 0.983278i | \(-0.441707\pi\) | ||||
0.182112 | + | 0.983278i | \(0.441707\pi\) | |||||||
\(930\) | −1.31943e9 | −0.0537894 | ||||||||
\(931\) | 3.77536e10 | 1.53333 | ||||||||
\(932\) | −1.44142e10 | −0.583224 | ||||||||
\(933\) | −1.64583e10 | −0.663436 | ||||||||
\(934\) | 3.40997e10 | 1.36942 | ||||||||
\(935\) | −3.95292e9 | −0.158153 | ||||||||
\(936\) | −1.51960e10 | −0.605708 | ||||||||
\(937\) | 2.70936e10 | 1.07592 | 0.537959 | − | 0.842971i | \(-0.319196\pi\) | ||||
0.537959 | + | 0.842971i | \(0.319196\pi\) | |||||||
\(938\) | −1.15817e9 | −0.0458208 | ||||||||
\(939\) | 1.61355e10 | 0.635992 | ||||||||
\(940\) | −2.56387e9 | −0.100681 | ||||||||
\(941\) | −4.63143e10 | −1.81197 | −0.905987 | − | 0.423306i | \(-0.860869\pi\) | ||||
−0.905987 | + | 0.423306i | \(0.860869\pi\) | |||||||
\(942\) | −3.01121e9 | −0.117372 | ||||||||
\(943\) | −6.86900e8 | −0.0266749 | ||||||||
\(944\) | 9.62892e8 | 0.0372542 | ||||||||
\(945\) | −4.41921e8 | −0.0170346 | ||||||||
\(946\) | 2.62367e10 | 1.00760 | ||||||||
\(947\) | 4.89914e10 | 1.87454 | 0.937271 | − | 0.348601i | \(-0.113343\pi\) | ||||
0.937271 | + | 0.348601i | \(0.113343\pi\) | |||||||
\(948\) | −1.15297e10 | −0.439531 | ||||||||
\(949\) | −1.86824e10 | −0.709580 | ||||||||
\(950\) | −3.54185e10 | −1.34029 | ||||||||
\(951\) | 7.80939e9 | 0.294432 | ||||||||
\(952\) | −8.76500e9 | −0.329248 | ||||||||
\(953\) | 3.63170e10 | 1.35921 | 0.679603 | − | 0.733580i | \(-0.262152\pi\) | ||||
0.679603 | + | 0.733580i | \(0.262152\pi\) | |||||||
\(954\) | −4.63093e9 | −0.172683 | ||||||||
\(955\) | −7.08341e8 | −0.0263166 | ||||||||
\(956\) | −1.45270e10 | −0.537743 | ||||||||
\(957\) | 1.96600e10 | 0.725091 | ||||||||
\(958\) | −3.30374e10 | −1.21402 | ||||||||
\(959\) | 5.05436e9 | 0.185055 | ||||||||
\(960\) | 2.78544e9 | 0.101612 | ||||||||
\(961\) | −1.53076e10 | −0.556385 | ||||||||
\(962\) | 1.69414e10 | 0.613530 | ||||||||
\(963\) | −5.63775e9 | −0.203430 | ||||||||
\(964\) | −8.30599e9 | −0.298622 | ||||||||
\(965\) | −9.12207e9 | −0.326774 | ||||||||
\(966\) | 1.07586e9 | 0.0384003 | ||||||||
\(967\) | −3.38245e10 | −1.20293 | −0.601463 | − | 0.798901i | \(-0.705415\pi\) | ||||
−0.601463 | + | 0.798901i | \(0.705415\pi\) | |||||||
\(968\) | 1.33367e10 | 0.472589 | ||||||||
\(969\) | 2.14373e10 | 0.756896 | ||||||||
\(970\) | 2.34990e8 | 0.00826701 | ||||||||
\(971\) | 4.01598e10 | 1.40775 | 0.703873 | − | 0.710326i | \(-0.251452\pi\) | ||||
0.703873 | + | 0.710326i | \(0.251452\pi\) | |||||||
\(972\) | 8.84822e8 | 0.0309047 | ||||||||
\(973\) | −9.46001e9 | −0.329228 | ||||||||
\(974\) | 2.80982e10 | 0.974366 | ||||||||
\(975\) | −2.73894e10 | −0.946380 | ||||||||
\(976\) | −3.49463e9 | −0.120317 | ||||||||
\(977\) | 1.49500e10 | 0.512872 | 0.256436 | − | 0.966561i | \(-0.417452\pi\) | ||||
0.256436 | + | 0.966561i | \(0.417452\pi\) | |||||||
\(978\) | −1.10223e10 | −0.376779 | ||||||||
\(979\) | −1.40582e10 | −0.478838 | ||||||||
\(980\) | −2.18572e9 | −0.0741830 | ||||||||
\(981\) | 3.83793e9 | 0.129794 | ||||||||
\(982\) | 3.01398e10 | 1.01566 | ||||||||
\(983\) | 2.98689e10 | 1.00295 | 0.501477 | − | 0.865171i | \(-0.332790\pi\) | ||||
0.501477 | + | 0.865171i | \(0.332790\pi\) | |||||||
\(984\) | −2.42085e9 | −0.0810000 | ||||||||
\(985\) | 1.70825e9 | 0.0569539 | ||||||||
\(986\) | 1.53498e10 | 0.509957 | ||||||||
\(987\) | −8.54499e9 | −0.282879 | ||||||||
\(988\) | −4.81351e10 | −1.58786 | ||||||||
\(989\) | 7.18906e9 | 0.236312 | ||||||||
\(990\) | 1.71000e9 | 0.0560108 | ||||||||
\(991\) | 1.42111e10 | 0.463842 | 0.231921 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231921 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(992\) | −1.76257e10 | −0.573266 | ||||||||
\(993\) | 1.62518e10 | 0.526719 | ||||||||
\(994\) | 1.48674e10 | 0.480155 | ||||||||
\(995\) | 2.75739e8 | 0.00887396 | ||||||||
\(996\) | 7.34284e9 | 0.235481 | ||||||||
\(997\) | 2.29718e10 | 0.734112 | 0.367056 | − | 0.930199i | \(-0.380366\pi\) | ||||
0.367056 | + | 0.930199i | \(0.380366\pi\) | |||||||
\(998\) | −2.84536e10 | −0.906108 | ||||||||
\(999\) | −3.03407e9 | −0.0962823 |
(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 | 177.8.a.c.1.6 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.c.1.12 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.6 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.c.1.12 | 17 | 3.2 | odd | 2 |