Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,8,Mod(1,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(4.68577538226\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 15.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.0000 | −1.94454 | −0.972272 | − | 0.233854i | \(-0.924866\pi\) | ||||
−0.972272 | + | 0.233854i | \(0.924866\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 356.000 | 2.78125 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | −594.000 | −1.12268 | ||||||||
\(7\) | −420.000 | −0.462814 | −0.231407 | − | 0.972857i | \(-0.574333\pi\) | ||||
−0.231407 | + | 0.972857i | \(0.574333\pi\) | |||||||
\(8\) | −5016.00 | −3.46372 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2750.00 | 0.869626 | ||||||||
\(11\) | −2944.00 | −0.666904 | −0.333452 | − | 0.942767i | \(-0.608214\pi\) | ||||
−0.333452 | + | 0.942767i | \(0.608214\pi\) | |||||||
\(12\) | 9612.00 | 1.60576 | ||||||||
\(13\) | −11006.0 | −1.38940 | −0.694701 | − | 0.719299i | \(-0.744463\pi\) | ||||
−0.694701 | + | 0.719299i | \(0.744463\pi\) | |||||||
\(14\) | 9240.00 | 0.899961 | ||||||||
\(15\) | −3375.00 | −0.258199 | ||||||||
\(16\) | 64784.0 | 3.95410 | ||||||||
\(17\) | −16546.0 | −0.816811 | −0.408406 | − | 0.912801i | \(-0.633915\pi\) | ||||
−0.408406 | + | 0.912801i | \(0.633915\pi\) | |||||||
\(18\) | −16038.0 | −0.648181 | ||||||||
\(19\) | −25364.0 | −0.848360 | −0.424180 | − | 0.905578i | \(-0.639438\pi\) | ||||
−0.424180 | + | 0.905578i | \(0.639438\pi\) | |||||||
\(20\) | −44500.0 | −1.24381 | ||||||||
\(21\) | −11340.0 | −0.267206 | ||||||||
\(22\) | 64768.0 | 1.29682 | ||||||||
\(23\) | −5880.00 | −0.100770 | −0.0503848 | − | 0.998730i | \(-0.516045\pi\) | ||||
−0.0503848 | + | 0.998730i | \(0.516045\pi\) | |||||||
\(24\) | −135432. | −1.99978 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | 242132. | 2.70175 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −149520. | −1.28720 | ||||||||
\(29\) | 163042. | 1.24139 | 0.620693 | − | 0.784054i | \(-0.286852\pi\) | ||||
0.620693 | + | 0.784054i | \(0.286852\pi\) | |||||||
\(30\) | 74250.0 | 0.502079 | ||||||||
\(31\) | −201600. | −1.21542 | −0.607708 | − | 0.794161i | \(-0.707911\pi\) | ||||
−0.607708 | + | 0.794161i | \(0.707911\pi\) | |||||||
\(32\) | −783200. | −4.22520 | ||||||||
\(33\) | −79488.0 | −0.385037 | ||||||||
\(34\) | 364012. | 1.58833 | ||||||||
\(35\) | 52500.0 | 0.206977 | ||||||||
\(36\) | 259524. | 0.927083 | ||||||||
\(37\) | 120530. | 0.391191 | 0.195596 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195596 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(38\) | 558008. | 1.64967 | ||||||||
\(39\) | −297162. | −0.802171 | ||||||||
\(40\) | 627000. | 1.54902 | ||||||||
\(41\) | −115910. | −0.262650 | −0.131325 | − | 0.991339i | \(-0.541923\pi\) | ||||
−0.131325 | + | 0.991339i | \(0.541923\pi\) | |||||||
\(42\) | 249480. | 0.519593 | ||||||||
\(43\) | −19148.0 | −0.0367269 | −0.0183634 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183634 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(44\) | −1.04806e6 | −1.85483 | ||||||||
\(45\) | −91125.0 | −0.149071 | ||||||||
\(46\) | 129360. | 0.195951 | ||||||||
\(47\) | 841016. | 1.18158 | 0.590788 | − | 0.806827i | \(-0.298817\pi\) | ||||
0.590788 | + | 0.806827i | \(0.298817\pi\) | |||||||
\(48\) | 1.74917e6 | 2.28290 | ||||||||
\(49\) | −647143. | −0.785804 | ||||||||
\(50\) | −343750. | −0.388909 | ||||||||
\(51\) | −446742. | −0.471586 | ||||||||
\(52\) | −3.91814e6 | −3.86427 | ||||||||
\(53\) | 501890. | 0.463066 | 0.231533 | − | 0.972827i | \(-0.425626\pi\) | ||||
0.231533 | + | 0.972827i | \(0.425626\pi\) | |||||||
\(54\) | −433026. | −0.374228 | ||||||||
\(55\) | 368000. | 0.298249 | ||||||||
\(56\) | 2.10672e6 | 1.60306 | ||||||||
\(57\) | −684828. | −0.489801 | ||||||||
\(58\) | −3.58692e6 | −2.41393 | ||||||||
\(59\) | −1.58618e6 | −1.00547 | −0.502735 | − | 0.864440i | \(-0.667673\pi\) | ||||
−0.502735 | + | 0.864440i | \(0.667673\pi\) | |||||||
\(60\) | −1.20150e6 | −0.718116 | ||||||||
\(61\) | −372962. | −0.210383 | −0.105191 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105191 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(62\) | 4.43520e6 | 2.36343 | ||||||||
\(63\) | −306180. | −0.154271 | ||||||||
\(64\) | 8.93805e6 | 4.26199 | ||||||||
\(65\) | 1.37575e6 | 0.621359 | ||||||||
\(66\) | 1.74874e6 | 0.748722 | ||||||||
\(67\) | 4.56104e6 | 1.85269 | 0.926344 | − | 0.376678i | \(-0.122934\pi\) | ||||
0.926344 | + | 0.376678i | \(0.122934\pi\) | |||||||
\(68\) | −5.89038e6 | −2.27176 | ||||||||
\(69\) | −158760. | −0.0581794 | ||||||||
\(70\) | −1.15500e6 | −0.402475 | ||||||||
\(71\) | 1.51283e6 | 0.501633 | 0.250817 | − | 0.968035i | \(-0.419301\pi\) | ||||
0.250817 | + | 0.968035i | \(0.419301\pi\) | |||||||
\(72\) | −3.65666e6 | −1.15457 | ||||||||
\(73\) | −1.52291e6 | −0.458189 | −0.229094 | − | 0.973404i | \(-0.573576\pi\) | ||||
−0.229094 | + | 0.973404i | \(0.573576\pi\) | |||||||
\(74\) | −2.65166e6 | −0.760688 | ||||||||
\(75\) | 421875. | 0.115470 | ||||||||
\(76\) | −9.02958e6 | −2.35950 | ||||||||
\(77\) | 1.23648e6 | 0.308652 | ||||||||
\(78\) | 6.53756e6 | 1.55986 | ||||||||
\(79\) | 4.23192e6 | 0.965701 | 0.482850 | − | 0.875703i | \(-0.339601\pi\) | ||||
0.482850 | + | 0.875703i | \(0.339601\pi\) | |||||||
\(80\) | −8.09800e6 | −1.76833 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 2.55002e6 | 0.510734 | ||||||||
\(83\) | −1.85420e6 | −0.355946 | −0.177973 | − | 0.984035i | \(-0.556954\pi\) | ||||
−0.177973 | + | 0.984035i | \(0.556954\pi\) | |||||||
\(84\) | −4.03704e6 | −0.743166 | ||||||||
\(85\) | 2.06825e6 | 0.365289 | ||||||||
\(86\) | 421256. | 0.0714170 | ||||||||
\(87\) | 4.40213e6 | 0.716714 | ||||||||
\(88\) | 1.47671e7 | 2.30997 | ||||||||
\(89\) | −6.88817e6 | −1.03571 | −0.517856 | − | 0.855468i | \(-0.673270\pi\) | ||||
−0.517856 | + | 0.855468i | \(0.673270\pi\) | |||||||
\(90\) | 2.00475e6 | 0.289875 | ||||||||
\(91\) | 4.62252e6 | 0.643034 | ||||||||
\(92\) | −2.09328e6 | −0.280266 | ||||||||
\(93\) | −5.44320e6 | −0.701720 | ||||||||
\(94\) | −1.85024e7 | −2.29763 | ||||||||
\(95\) | 3.17050e6 | 0.379398 | ||||||||
\(96\) | −2.11464e7 | −2.43942 | ||||||||
\(97\) | 3.70003e6 | 0.411628 | 0.205814 | − | 0.978591i | \(-0.434016\pi\) | ||||
0.205814 | + | 0.978591i | \(0.434016\pi\) | |||||||
\(98\) | 1.42371e7 | 1.52803 | ||||||||
\(99\) | −2.14618e6 | −0.222301 | ||||||||
\(100\) | 5.56250e6 | 0.556250 | ||||||||
\(101\) | −1.80025e7 | −1.73863 | −0.869314 | − | 0.494259i | \(-0.835439\pi\) | ||||
−0.869314 | + | 0.494259i | \(0.835439\pi\) | |||||||
\(102\) | 9.82832e6 | 0.917020 | ||||||||
\(103\) | −5.37207e6 | −0.484408 | −0.242204 | − | 0.970225i | \(-0.577870\pi\) | ||||
−0.242204 | + | 0.970225i | \(0.577870\pi\) | |||||||
\(104\) | 5.52061e7 | 4.81250 | ||||||||
\(105\) | 1.41750e6 | 0.119498 | ||||||||
\(106\) | −1.10416e7 | −0.900452 | ||||||||
\(107\) | −1.15398e7 | −0.910655 | −0.455327 | − | 0.890324i | \(-0.650478\pi\) | ||||
−0.455327 | + | 0.890324i | \(0.650478\pi\) | |||||||
\(108\) | 7.00715e6 | 0.535252 | ||||||||
\(109\) | −1.57179e6 | −0.116253 | −0.0581263 | − | 0.998309i | \(-0.518513\pi\) | ||||
−0.0581263 | + | 0.998309i | \(0.518513\pi\) | |||||||
\(110\) | −8.09600e6 | −0.579957 | ||||||||
\(111\) | 3.25431e6 | 0.225854 | ||||||||
\(112\) | −2.72093e7 | −1.83001 | ||||||||
\(113\) | −2.52050e7 | −1.64328 | −0.821640 | − | 0.570007i | \(-0.806940\pi\) | ||||
−0.821640 | + | 0.570007i | \(0.806940\pi\) | |||||||
\(114\) | 1.50662e7 | 0.952439 | ||||||||
\(115\) | 735000. | 0.0450656 | ||||||||
\(116\) | 5.80430e7 | 3.45260 | ||||||||
\(117\) | −8.02337e6 | −0.463134 | ||||||||
\(118\) | 3.48959e7 | 1.95518 | ||||||||
\(119\) | 6.94932e6 | 0.378031 | ||||||||
\(120\) | 1.69290e7 | 0.894328 | ||||||||
\(121\) | −1.08200e7 | −0.555239 | ||||||||
\(122\) | 8.20516e6 | 0.409098 | ||||||||
\(123\) | −3.12957e6 | −0.151641 | ||||||||
\(124\) | −7.17696e7 | −3.38037 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | 6.73596e6 | 0.299987 | ||||||||
\(127\) | 3.94080e7 | 1.70715 | 0.853574 | − | 0.520971i | \(-0.174430\pi\) | ||||
0.853574 | + | 0.520971i | \(0.174430\pi\) | |||||||
\(128\) | −9.63875e7 | −4.06243 | ||||||||
\(129\) | −516996. | −0.0212043 | ||||||||
\(130\) | −3.02665e7 | −1.20826 | ||||||||
\(131\) | 1.41082e7 | 0.548305 | 0.274153 | − | 0.961686i | \(-0.411603\pi\) | ||||
0.274153 | + | 0.961686i | \(0.411603\pi\) | |||||||
\(132\) | −2.82977e7 | −1.07088 | ||||||||
\(133\) | 1.06529e7 | 0.392633 | ||||||||
\(134\) | −1.00343e8 | −3.60263 | ||||||||
\(135\) | −2.46038e6 | −0.0860663 | ||||||||
\(136\) | 8.29947e7 | 2.82920 | ||||||||
\(137\) | −8.00512e6 | −0.265978 | −0.132989 | − | 0.991118i | \(-0.542458\pi\) | ||||
−0.132989 | + | 0.991118i | \(0.542458\pi\) | |||||||
\(138\) | 3.49272e6 | 0.113132 | ||||||||
\(139\) | 4.60716e7 | 1.45506 | 0.727532 | − | 0.686074i | \(-0.240667\pi\) | ||||
0.727532 | + | 0.686074i | \(0.240667\pi\) | |||||||
\(140\) | 1.86900e7 | 0.575654 | ||||||||
\(141\) | 2.27074e7 | 0.682183 | ||||||||
\(142\) | −3.32823e7 | −0.975448 | ||||||||
\(143\) | 3.24017e7 | 0.926598 | ||||||||
\(144\) | 4.72275e7 | 1.31803 | ||||||||
\(145\) | −2.03802e7 | −0.555164 | ||||||||
\(146\) | 3.35040e7 | 0.890968 | ||||||||
\(147\) | −1.74729e7 | −0.453684 | ||||||||
\(148\) | 4.29087e7 | 1.08800 | ||||||||
\(149\) | 7.23525e7 | 1.79185 | 0.895925 | − | 0.444206i | \(-0.146514\pi\) | ||||
0.895925 | + | 0.444206i | \(0.146514\pi\) | |||||||
\(150\) | −9.28125e6 | −0.224537 | ||||||||
\(151\) | −3.70062e7 | −0.874692 | −0.437346 | − | 0.899293i | \(-0.644082\pi\) | ||||
−0.437346 | + | 0.899293i | \(0.644082\pi\) | |||||||
\(152\) | 1.27226e8 | 2.93848 | ||||||||
\(153\) | −1.20620e7 | −0.272270 | ||||||||
\(154\) | −2.72026e7 | −0.600188 | ||||||||
\(155\) | 2.52000e7 | 0.543550 | ||||||||
\(156\) | −1.05790e8 | −2.23104 | ||||||||
\(157\) | −7.85080e7 | −1.61907 | −0.809534 | − | 0.587073i | \(-0.800280\pi\) | ||||
−0.809534 | + | 0.587073i | \(0.800280\pi\) | |||||||
\(158\) | −9.31022e7 | −1.87785 | ||||||||
\(159\) | 1.35510e7 | 0.267351 | ||||||||
\(160\) | 9.79000e7 | 1.88957 | ||||||||
\(161\) | 2.46960e6 | 0.0466376 | ||||||||
\(162\) | −1.16917e7 | −0.216060 | ||||||||
\(163\) | −4.68184e7 | −0.846759 | −0.423380 | − | 0.905952i | \(-0.639156\pi\) | ||||
−0.423380 | + | 0.905952i | \(0.639156\pi\) | |||||||
\(164\) | −4.12640e7 | −0.730495 | ||||||||
\(165\) | 9.93600e6 | 0.172194 | ||||||||
\(166\) | 4.07925e7 | 0.692153 | ||||||||
\(167\) | −2.50043e7 | −0.415438 | −0.207719 | − | 0.978188i | \(-0.566604\pi\) | ||||
−0.207719 | + | 0.978188i | \(0.566604\pi\) | |||||||
\(168\) | 5.68814e7 | 0.925525 | ||||||||
\(169\) | 5.83835e7 | 0.930437 | ||||||||
\(170\) | −4.55015e7 | −0.710321 | ||||||||
\(171\) | −1.84904e7 | −0.282787 | ||||||||
\(172\) | −6.81669e6 | −0.102147 | ||||||||
\(173\) | 5.30671e7 | 0.779227 | 0.389613 | − | 0.920979i | \(-0.372609\pi\) | ||||
0.389613 | + | 0.920979i | \(0.372609\pi\) | |||||||
\(174\) | −9.68469e7 | −1.39368 | ||||||||
\(175\) | −6.56250e6 | −0.0925627 | ||||||||
\(176\) | −1.90724e8 | −2.63701 | ||||||||
\(177\) | −4.28268e7 | −0.580509 | ||||||||
\(178\) | 1.51540e8 | 2.01399 | ||||||||
\(179\) | 4.22054e7 | 0.550025 | 0.275012 | − | 0.961441i | \(-0.411318\pi\) | ||||
0.275012 | + | 0.961441i | \(0.411318\pi\) | |||||||
\(180\) | −3.24405e7 | −0.414604 | ||||||||
\(181\) | −1.00020e8 | −1.25376 | −0.626879 | − | 0.779116i | \(-0.715668\pi\) | ||||
−0.626879 | + | 0.779116i | \(0.715668\pi\) | |||||||
\(182\) | −1.01695e8 | −1.25041 | ||||||||
\(183\) | −1.00700e7 | −0.121465 | ||||||||
\(184\) | 2.94941e7 | 0.349038 | ||||||||
\(185\) | −1.50662e7 | −0.174946 | ||||||||
\(186\) | 1.19750e8 | 1.36453 | ||||||||
\(187\) | 4.87114e7 | 0.544735 | ||||||||
\(188\) | 2.99402e8 | 3.28626 | ||||||||
\(189\) | −8.26686e6 | −0.0890685 | ||||||||
\(190\) | −6.97510e7 | −0.737756 | ||||||||
\(191\) | 6.17610e7 | 0.641354 | 0.320677 | − | 0.947189i | \(-0.396090\pi\) | ||||
0.320677 | + | 0.947189i | \(0.396090\pi\) | |||||||
\(192\) | 2.41327e8 | 2.46066 | ||||||||
\(193\) | −7.67419e7 | −0.768390 | −0.384195 | − | 0.923252i | \(-0.625521\pi\) | ||||
−0.384195 | + | 0.923252i | \(0.625521\pi\) | |||||||
\(194\) | −8.14007e7 | −0.800428 | ||||||||
\(195\) | 3.71452e7 | 0.358742 | ||||||||
\(196\) | −2.30383e8 | −2.18552 | ||||||||
\(197\) | −1.81032e8 | −1.68703 | −0.843516 | − | 0.537105i | \(-0.819518\pi\) | ||||
−0.843516 | + | 0.537105i | \(0.819518\pi\) | |||||||
\(198\) | 4.72159e7 | 0.432275 | ||||||||
\(199\) | 6.16084e7 | 0.554185 | 0.277092 | − | 0.960843i | \(-0.410629\pi\) | ||||
0.277092 | + | 0.960843i | \(0.410629\pi\) | |||||||
\(200\) | −7.83750e7 | −0.692744 | ||||||||
\(201\) | 1.23148e8 | 1.06965 | ||||||||
\(202\) | 3.96054e8 | 3.38084 | ||||||||
\(203\) | −6.84776e7 | −0.574530 | ||||||||
\(204\) | −1.59040e8 | −1.31160 | ||||||||
\(205\) | 1.44888e7 | 0.117461 | ||||||||
\(206\) | 1.18185e8 | 0.941952 | ||||||||
\(207\) | −4.28652e6 | −0.0335899 | ||||||||
\(208\) | −7.13013e8 | −5.49383 | ||||||||
\(209\) | 7.46716e7 | 0.565775 | ||||||||
\(210\) | −3.11850e7 | −0.232369 | ||||||||
\(211\) | −1.69917e8 | −1.24523 | −0.622613 | − | 0.782530i | \(-0.713929\pi\) | ||||
−0.622613 | + | 0.782530i | \(0.713929\pi\) | |||||||
\(212\) | 1.78673e8 | 1.28790 | ||||||||
\(213\) | 4.08465e7 | 0.289618 | ||||||||
\(214\) | 2.53875e8 | 1.77081 | ||||||||
\(215\) | 2.39350e6 | 0.0164248 | ||||||||
\(216\) | −9.87299e7 | −0.666593 | ||||||||
\(217\) | 8.46720e7 | 0.562511 | ||||||||
\(218\) | 3.45795e7 | 0.226058 | ||||||||
\(219\) | −4.11186e7 | −0.264535 | ||||||||
\(220\) | 1.31008e8 | 0.829504 | ||||||||
\(221\) | 1.82105e8 | 1.13488 | ||||||||
\(222\) | −7.15948e7 | −0.439184 | ||||||||
\(223\) | 1.48129e8 | 0.894484 | 0.447242 | − | 0.894413i | \(-0.352406\pi\) | ||||
0.447242 | + | 0.894413i | \(0.352406\pi\) | |||||||
\(224\) | 3.28944e8 | 1.95548 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | 5.54509e8 | 3.19543 | ||||||||
\(227\) | −3.96127e7 | −0.224773 | −0.112387 | − | 0.993665i | \(-0.535849\pi\) | ||||
−0.112387 | + | 0.993665i | \(0.535849\pi\) | |||||||
\(228\) | −2.43799e8 | −1.36226 | ||||||||
\(229\) | −3.71816e7 | −0.204599 | −0.102300 | − | 0.994754i | \(-0.532620\pi\) | ||||
−0.102300 | + | 0.994754i | \(0.532620\pi\) | |||||||
\(230\) | −1.61700e7 | −0.0876320 | ||||||||
\(231\) | 3.33850e7 | 0.178201 | ||||||||
\(232\) | −8.17819e8 | −4.29981 | ||||||||
\(233\) | −1.79591e8 | −0.930122 | −0.465061 | − | 0.885279i | \(-0.653968\pi\) | ||||
−0.465061 | + | 0.885279i | \(0.653968\pi\) | |||||||
\(234\) | 1.76514e8 | 0.900584 | ||||||||
\(235\) | −1.05127e8 | −0.528417 | ||||||||
\(236\) | −5.64679e8 | −2.79646 | ||||||||
\(237\) | 1.14262e8 | 0.557548 | ||||||||
\(238\) | −1.52885e8 | −0.735099 | ||||||||
\(239\) | −3.73328e8 | −1.76888 | −0.884439 | − | 0.466655i | \(-0.845459\pi\) | ||||
−0.884439 | + | 0.466655i | \(0.845459\pi\) | |||||||
\(240\) | −2.18646e8 | −1.02094 | ||||||||
\(241\) | −2.57022e8 | −1.18280 | −0.591398 | − | 0.806380i | \(-0.701424\pi\) | ||||
−0.591398 | + | 0.806380i | \(0.701424\pi\) | |||||||
\(242\) | 2.38041e8 | 1.07969 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −1.32774e8 | −0.585127 | ||||||||
\(245\) | 8.08929e7 | 0.351422 | ||||||||
\(246\) | 6.88505e7 | 0.294873 | ||||||||
\(247\) | 2.79156e8 | 1.17871 | ||||||||
\(248\) | 1.01123e9 | 4.20986 | ||||||||
\(249\) | −5.00635e7 | −0.205506 | ||||||||
\(250\) | 4.29688e7 | 0.173925 | ||||||||
\(251\) | −1.27344e8 | −0.508302 | −0.254151 | − | 0.967165i | \(-0.581796\pi\) | ||||
−0.254151 | + | 0.967165i | \(0.581796\pi\) | |||||||
\(252\) | −1.09000e8 | −0.429067 | ||||||||
\(253\) | 1.73107e7 | 0.0672037 | ||||||||
\(254\) | −8.66976e8 | −3.31963 | ||||||||
\(255\) | 5.58427e7 | 0.210900 | ||||||||
\(256\) | 9.76454e8 | 3.63757 | ||||||||
\(257\) | 1.30682e8 | 0.480230 | 0.240115 | − | 0.970744i | \(-0.422815\pi\) | ||||
0.240115 | + | 0.970744i | \(0.422815\pi\) | |||||||
\(258\) | 1.13739e7 | 0.0412326 | ||||||||
\(259\) | −5.06226e7 | −0.181049 | ||||||||
\(260\) | 4.89767e8 | 1.72816 | ||||||||
\(261\) | 1.18858e8 | 0.413795 | ||||||||
\(262\) | −3.10381e8 | −1.06620 | ||||||||
\(263\) | −2.67747e8 | −0.907568 | −0.453784 | − | 0.891112i | \(-0.649926\pi\) | ||||
−0.453784 | + | 0.891112i | \(0.649926\pi\) | |||||||
\(264\) | 3.98712e8 | 1.33366 | ||||||||
\(265\) | −6.27363e7 | −0.207089 | ||||||||
\(266\) | −2.34363e8 | −0.763491 | ||||||||
\(267\) | −1.85981e8 | −0.597969 | ||||||||
\(268\) | 1.62373e9 | 5.15279 | ||||||||
\(269\) | 1.49432e8 | 0.468070 | 0.234035 | − | 0.972228i | \(-0.424807\pi\) | ||||
0.234035 | + | 0.972228i | \(0.424807\pi\) | |||||||
\(270\) | 5.41282e7 | 0.167360 | ||||||||
\(271\) | −1.53185e8 | −0.467545 | −0.233773 | − | 0.972291i | \(-0.575107\pi\) | ||||
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(272\) | −1.07192e9 | −3.22976 | ||||||||
\(273\) | 1.24808e8 | 0.371256 | ||||||||
\(274\) | 1.76113e8 | 0.517206 | ||||||||
\(275\) | −4.60000e7 | −0.133381 | ||||||||
\(276\) | −5.65186e7 | −0.161811 | ||||||||
\(277\) | 6.54462e8 | 1.85014 | 0.925072 | − | 0.379792i | \(-0.124004\pi\) | ||||
0.925072 | + | 0.379792i | \(0.124004\pi\) | |||||||
\(278\) | −1.01358e9 | −2.82943 | ||||||||
\(279\) | −1.46966e8 | −0.405138 | ||||||||
\(280\) | −2.63340e8 | −0.716908 | ||||||||
\(281\) | 5.51493e8 | 1.48275 | 0.741375 | − | 0.671091i | \(-0.234174\pi\) | ||||
0.741375 | + | 0.671091i | \(0.234174\pi\) | |||||||
\(282\) | −4.99564e8 | −1.32654 | ||||||||
\(283\) | −2.10200e8 | −0.551291 | −0.275646 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275646 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(284\) | 5.38568e8 | 1.39517 | ||||||||
\(285\) | 8.56035e7 | 0.219046 | ||||||||
\(286\) | −7.12837e8 | −1.80181 | ||||||||
\(287\) | 4.86822e7 | 0.121558 | ||||||||
\(288\) | −5.70953e8 | −1.40840 | ||||||||
\(289\) | −1.36569e8 | −0.332819 | ||||||||
\(290\) | 4.48366e8 | 1.07954 | ||||||||
\(291\) | 9.99009e7 | 0.237653 | ||||||||
\(292\) | −5.42156e8 | −1.27434 | ||||||||
\(293\) | 5.42402e8 | 1.25975 | 0.629875 | − | 0.776697i | \(-0.283106\pi\) | ||||
0.629875 | + | 0.776697i | \(0.283106\pi\) | |||||||
\(294\) | 3.84403e8 | 0.882208 | ||||||||
\(295\) | 1.98272e8 | 0.449660 | ||||||||
\(296\) | −6.04578e8 | −1.35498 | ||||||||
\(297\) | −5.79468e7 | −0.128346 | ||||||||
\(298\) | −1.59175e9 | −3.48433 | ||||||||
\(299\) | 6.47153e7 | 0.140010 | ||||||||
\(300\) | 1.50188e8 | 0.321151 | ||||||||
\(301\) | 8.04216e6 | 0.0169977 | ||||||||
\(302\) | 8.14137e8 | 1.70088 | ||||||||
\(303\) | −4.86066e8 | −1.00380 | ||||||||
\(304\) | −1.64318e9 | −3.35450 | ||||||||
\(305\) | 4.66202e7 | 0.0940860 | ||||||||
\(306\) | 2.65365e8 | 0.529442 | ||||||||
\(307\) | 9.26477e8 | 1.82747 | 0.913736 | − | 0.406310i | \(-0.133185\pi\) | ||||
0.913736 | + | 0.406310i | \(0.133185\pi\) | |||||||
\(308\) | 4.40187e8 | 0.858439 | ||||||||
\(309\) | −1.45046e8 | −0.279673 | ||||||||
\(310\) | −5.54400e8 | −1.05696 | ||||||||
\(311\) | −2.12976e8 | −0.401485 | −0.200743 | − | 0.979644i | \(-0.564335\pi\) | ||||
−0.200743 | + | 0.979644i | \(0.564335\pi\) | |||||||
\(312\) | 1.49056e9 | 2.77850 | ||||||||
\(313\) | 3.63896e8 | 0.670768 | 0.335384 | − | 0.942081i | \(-0.391134\pi\) | ||||
0.335384 | + | 0.942081i | \(0.391134\pi\) | |||||||
\(314\) | 1.72718e9 | 3.14835 | ||||||||
\(315\) | 3.82725e7 | 0.0689922 | ||||||||
\(316\) | 1.50656e9 | 2.68586 | ||||||||
\(317\) | −3.17049e8 | −0.559009 | −0.279505 | − | 0.960144i | \(-0.590170\pi\) | ||||
−0.279505 | + | 0.960144i | \(0.590170\pi\) | |||||||
\(318\) | −2.98123e8 | −0.519876 | ||||||||
\(319\) | −4.79996e8 | −0.827885 | ||||||||
\(320\) | −1.11726e9 | −1.90602 | ||||||||
\(321\) | −3.11574e8 | −0.525767 | ||||||||
\(322\) | −5.43312e7 | −0.0906888 | ||||||||
\(323\) | 4.19673e8 | 0.692950 | ||||||||
\(324\) | 1.89193e8 | 0.309028 | ||||||||
\(325\) | −1.71969e8 | −0.277880 | ||||||||
\(326\) | 1.03001e9 | 1.64656 | ||||||||
\(327\) | −4.24384e7 | −0.0671185 | ||||||||
\(328\) | 5.81405e8 | 0.909746 | ||||||||
\(329\) | −3.53227e8 | −0.546850 | ||||||||
\(330\) | −2.18592e8 | −0.334839 | ||||||||
\(331\) | 2.24556e8 | 0.340351 | 0.170176 | − | 0.985414i | \(-0.445566\pi\) | ||||
0.170176 | + | 0.985414i | \(0.445566\pi\) | |||||||
\(332\) | −6.60097e8 | −0.989975 | ||||||||
\(333\) | 8.78664e7 | 0.130397 | ||||||||
\(334\) | 5.50094e8 | 0.807838 | ||||||||
\(335\) | −5.70130e8 | −0.828548 | ||||||||
\(336\) | −7.34651e8 | −1.05656 | ||||||||
\(337\) | −1.23886e9 | −1.76327 | −0.881633 | − | 0.471935i | \(-0.843556\pi\) | ||||
−0.881633 | + | 0.471935i | \(0.843556\pi\) | |||||||
\(338\) | −1.28444e9 | −1.80927 | ||||||||
\(339\) | −6.80534e8 | −0.948748 | ||||||||
\(340\) | 7.36297e8 | 1.01596 | ||||||||
\(341\) | 5.93510e8 | 0.810565 | ||||||||
\(342\) | 4.06788e8 | 0.549891 | ||||||||
\(343\) | 6.17688e8 | 0.826494 | ||||||||
\(344\) | 9.60464e7 | 0.127212 | ||||||||
\(345\) | 1.98450e7 | 0.0260186 | ||||||||
\(346\) | −1.16748e9 | −1.51524 | ||||||||
\(347\) | −5.83643e8 | −0.749884 | −0.374942 | − | 0.927048i | \(-0.622337\pi\) | ||||
−0.374942 | + | 0.927048i | \(0.622337\pi\) | |||||||
\(348\) | 1.56716e9 | 1.99336 | ||||||||
\(349\) | −4.69471e8 | −0.591180 | −0.295590 | − | 0.955315i | \(-0.595516\pi\) | ||||
−0.295590 | + | 0.955315i | \(0.595516\pi\) | |||||||
\(350\) | 1.44375e8 | 0.179992 | ||||||||
\(351\) | −2.16631e8 | −0.267390 | ||||||||
\(352\) | 2.30574e9 | 2.81781 | ||||||||
\(353\) | 6.18559e7 | 0.0748461 | 0.0374231 | − | 0.999300i | \(-0.488085\pi\) | ||||
0.0374231 | + | 0.999300i | \(0.488085\pi\) | |||||||
\(354\) | 9.42189e8 | 1.12882 | ||||||||
\(355\) | −1.89104e8 | −0.224337 | ||||||||
\(356\) | −2.45219e9 | −2.88057 | ||||||||
\(357\) | 1.87632e8 | 0.218257 | ||||||||
\(358\) | −9.28519e8 | −1.06955 | ||||||||
\(359\) | −1.23537e7 | −0.0140918 | −0.00704592 | − | 0.999975i | \(-0.502243\pi\) | ||||
−0.00704592 | + | 0.999975i | \(0.502243\pi\) | |||||||
\(360\) | 4.57083e8 | 0.516341 | ||||||||
\(361\) | −2.50539e8 | −0.280285 | ||||||||
\(362\) | 2.20045e9 | 2.43799 | ||||||||
\(363\) | −2.92141e8 | −0.320567 | ||||||||
\(364\) | 1.64562e9 | 1.78844 | ||||||||
\(365\) | 1.90364e8 | 0.204908 | ||||||||
\(366\) | 2.21539e8 | 0.236193 | ||||||||
\(367\) | −1.25514e7 | −0.0132544 | −0.00662721 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662721 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(368\) | −3.80930e8 | −0.398454 | ||||||||
\(369\) | −8.44984e7 | −0.0875500 | ||||||||
\(370\) | 3.31458e8 | 0.340190 | ||||||||
\(371\) | −2.10794e8 | −0.214313 | ||||||||
\(372\) | −1.93778e9 | −1.95166 | ||||||||
\(373\) | −5.65994e8 | −0.564717 | −0.282359 | − | 0.959309i | \(-0.591117\pi\) | ||||
−0.282359 | + | 0.959309i | \(0.591117\pi\) | |||||||
\(374\) | −1.07165e9 | −1.05926 | ||||||||
\(375\) | −5.27344e7 | −0.0516398 | ||||||||
\(376\) | −4.21854e9 | −4.09265 | ||||||||
\(377\) | −1.79444e9 | −1.72478 | ||||||||
\(378\) | 1.81871e8 | 0.173198 | ||||||||
\(379\) | 1.77776e9 | 1.67740 | 0.838698 | − | 0.544597i | \(-0.183317\pi\) | ||||
0.838698 | + | 0.544597i | \(0.183317\pi\) | |||||||
\(380\) | 1.12870e9 | 1.05520 | ||||||||
\(381\) | 1.06402e9 | 0.985623 | ||||||||
\(382\) | −1.35874e9 | −1.24714 | ||||||||
\(383\) | 1.18195e9 | 1.07498 | 0.537492 | − | 0.843269i | \(-0.319372\pi\) | ||||
0.537492 | + | 0.843269i | \(0.319372\pi\) | |||||||
\(384\) | −2.60246e9 | −2.34544 | ||||||||
\(385\) | −1.54560e8 | −0.138034 | ||||||||
\(386\) | 1.68832e9 | 1.49417 | ||||||||
\(387\) | −1.39589e7 | −0.0122423 | ||||||||
\(388\) | 1.31721e9 | 1.14484 | ||||||||
\(389\) | 6.02482e8 | 0.518944 | 0.259472 | − | 0.965751i | \(-0.416451\pi\) | ||||
0.259472 | + | 0.965751i | \(0.416451\pi\) | |||||||
\(390\) | −8.17196e8 | −0.697589 | ||||||||
\(391\) | 9.72905e7 | 0.0823098 | ||||||||
\(392\) | 3.24607e9 | 2.72180 | ||||||||
\(393\) | 3.80922e8 | 0.316564 | ||||||||
\(394\) | 3.98270e9 | 3.28051 | ||||||||
\(395\) | −5.28990e8 | −0.431875 | ||||||||
\(396\) | −7.64039e8 | −0.618276 | ||||||||
\(397\) | −1.86765e8 | −0.149806 | −0.0749029 | − | 0.997191i | \(-0.523865\pi\) | ||||
−0.0749029 | + | 0.997191i | \(0.523865\pi\) | |||||||
\(398\) | −1.35539e9 | −1.07764 | ||||||||
\(399\) | 2.87628e8 | 0.226687 | ||||||||
\(400\) | 1.01225e9 | 0.790820 | ||||||||
\(401\) | −9.96333e8 | −0.771613 | −0.385806 | − | 0.922580i | \(-0.626077\pi\) | ||||
−0.385806 | + | 0.922580i | \(0.626077\pi\) | |||||||
\(402\) | −2.70926e9 | −2.07998 | ||||||||
\(403\) | 2.21881e9 | 1.68870 | ||||||||
\(404\) | −6.40887e9 | −4.83556 | ||||||||
\(405\) | −6.64301e7 | −0.0496904 | ||||||||
\(406\) | 1.50651e9 | 1.11720 | ||||||||
\(407\) | −3.54840e8 | −0.260887 | ||||||||
\(408\) | 2.24086e9 | 1.63344 | ||||||||
\(409\) | −2.38644e9 | −1.72472 | −0.862362 | − | 0.506293i | \(-0.831015\pi\) | ||||
−0.862362 | + | 0.506293i | \(0.831015\pi\) | |||||||
\(410\) | −3.18752e8 | −0.228407 | ||||||||
\(411\) | −2.16138e8 | −0.153563 | ||||||||
\(412\) | −1.91246e9 | −1.34726 | ||||||||
\(413\) | 6.66194e8 | 0.465345 | ||||||||
\(414\) | 9.43034e7 | 0.0653170 | ||||||||
\(415\) | 2.31775e8 | 0.159184 | ||||||||
\(416\) | 8.61990e9 | 5.87051 | ||||||||
\(417\) | 1.24393e9 | 0.840081 | ||||||||
\(418\) | −1.64278e9 | −1.10017 | ||||||||
\(419\) | 2.59644e9 | 1.72437 | 0.862183 | − | 0.506597i | \(-0.169097\pi\) | ||||
0.862183 | + | 0.506597i | \(0.169097\pi\) | |||||||
\(420\) | 5.04630e8 | 0.332354 | ||||||||
\(421\) | 2.83850e9 | 1.85396 | 0.926981 | − | 0.375108i | \(-0.122394\pi\) | ||||
0.926981 | + | 0.375108i | \(0.122394\pi\) | |||||||
\(422\) | 3.73817e9 | 2.42139 | ||||||||
\(423\) | 6.13101e8 | 0.393859 | ||||||||
\(424\) | −2.51748e9 | −1.60393 | ||||||||
\(425\) | −2.58531e8 | −0.163362 | ||||||||
\(426\) | −8.98622e8 | −0.563175 | ||||||||
\(427\) | 1.56644e8 | 0.0973680 | ||||||||
\(428\) | −4.10816e9 | −2.53276 | ||||||||
\(429\) | 8.74845e8 | 0.534971 | ||||||||
\(430\) | −5.26570e7 | −0.0319386 | ||||||||
\(431\) | −1.52808e9 | −0.919342 | −0.459671 | − | 0.888089i | \(-0.652033\pi\) | ||||
−0.459671 | + | 0.888089i | \(0.652033\pi\) | |||||||
\(432\) | 1.27514e9 | 0.760967 | ||||||||
\(433\) | −2.66061e9 | −1.57498 | −0.787488 | − | 0.616330i | \(-0.788619\pi\) | ||||
−0.787488 | + | 0.616330i | \(0.788619\pi\) | |||||||
\(434\) | −1.86278e9 | −1.09383 | ||||||||
\(435\) | −5.50267e8 | −0.320524 | ||||||||
\(436\) | −5.59559e8 | −0.323328 | ||||||||
\(437\) | 1.49140e8 | 0.0854890 | ||||||||
\(438\) | 9.04609e8 | 0.514400 | ||||||||
\(439\) | 2.29222e9 | 1.29310 | 0.646549 | − | 0.762873i | \(-0.276212\pi\) | ||||
0.646549 | + | 0.762873i | \(0.276212\pi\) | |||||||
\(440\) | −1.84589e9 | −1.03305 | ||||||||
\(441\) | −4.71767e8 | −0.261935 | ||||||||
\(442\) | −4.00632e9 | −2.20682 | ||||||||
\(443\) | −9.34043e8 | −0.510451 | −0.255225 | − | 0.966882i | \(-0.582150\pi\) | ||||
−0.255225 | + | 0.966882i | \(0.582150\pi\) | |||||||
\(444\) | 1.15853e9 | 0.628157 | ||||||||
\(445\) | 8.61022e8 | 0.463185 | ||||||||
\(446\) | −3.25884e9 | −1.73936 | ||||||||
\(447\) | 1.95352e9 | 1.03452 | ||||||||
\(448\) | −3.75398e9 | −1.97251 | ||||||||
\(449\) | −8.85012e7 | −0.0461410 | −0.0230705 | − | 0.999734i | \(-0.507344\pi\) | ||||
−0.0230705 | + | 0.999734i | \(0.507344\pi\) | |||||||
\(450\) | −2.50594e8 | −0.129636 | ||||||||
\(451\) | 3.41239e8 | 0.175162 | ||||||||
\(452\) | −8.97296e9 | −4.57037 | ||||||||
\(453\) | −9.99168e8 | −0.505004 | ||||||||
\(454\) | 8.71480e8 | 0.437081 | ||||||||
\(455\) | −5.77815e8 | −0.287574 | ||||||||
\(456\) | 3.43510e9 | 1.69653 | ||||||||
\(457\) | −1.21064e9 | −0.593347 | −0.296674 | − | 0.954979i | \(-0.595877\pi\) | ||||
−0.296674 | + | 0.954979i | \(0.595877\pi\) | |||||||
\(458\) | 8.17995e8 | 0.397852 | ||||||||
\(459\) | −3.25675e8 | −0.157195 | ||||||||
\(460\) | 2.61660e8 | 0.125339 | ||||||||
\(461\) | 8.57428e8 | 0.407610 | 0.203805 | − | 0.979012i | \(-0.434669\pi\) | ||||
0.203805 | + | 0.979012i | \(0.434669\pi\) | |||||||
\(462\) | −7.34469e8 | −0.346519 | ||||||||
\(463\) | −1.94662e9 | −0.911481 | −0.455741 | − | 0.890113i | \(-0.650625\pi\) | ||||
−0.455741 | + | 0.890113i | \(0.650625\pi\) | |||||||
\(464\) | 1.05625e10 | 4.90856 | ||||||||
\(465\) | 6.80400e8 | 0.313819 | ||||||||
\(466\) | 3.95101e9 | 1.80866 | ||||||||
\(467\) | −9.59955e8 | −0.436156 | −0.218078 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218078 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(468\) | −2.85632e9 | −1.28809 | ||||||||
\(469\) | −1.91564e9 | −0.857450 | ||||||||
\(470\) | 2.31279e9 | 1.02753 | ||||||||
\(471\) | −2.11972e9 | −0.934769 | ||||||||
\(472\) | 7.95626e9 | 3.48267 | ||||||||
\(473\) | 5.63717e7 | 0.0244933 | ||||||||
\(474\) | −2.51376e9 | −1.08418 | ||||||||
\(475\) | −3.96312e8 | −0.169672 | ||||||||
\(476\) | 2.47396e9 | 1.05140 | ||||||||
\(477\) | 3.65878e8 | 0.154355 | ||||||||
\(478\) | 8.21322e9 | 3.43966 | ||||||||
\(479\) | 3.03579e8 | 0.126211 | 0.0631054 | − | 0.998007i | \(-0.479900\pi\) | ||||
0.0631054 | + | 0.998007i | \(0.479900\pi\) | |||||||
\(480\) | 2.64330e9 | 1.09094 | ||||||||
\(481\) | −1.32655e9 | −0.543522 | ||||||||
\(482\) | 5.65447e9 | 2.30000 | ||||||||
\(483\) | 6.66792e7 | 0.0269262 | ||||||||
\(484\) | −3.85193e9 | −1.54426 | ||||||||
\(485\) | −4.62504e8 | −0.184086 | ||||||||
\(486\) | −3.15676e8 | −0.124743 | ||||||||
\(487\) | 4.36059e8 | 0.171078 | 0.0855389 | − | 0.996335i | \(-0.472739\pi\) | ||||
0.0855389 | + | 0.996335i | \(0.472739\pi\) | |||||||
\(488\) | 1.87078e9 | 0.728707 | ||||||||
\(489\) | −1.26410e9 | −0.488877 | ||||||||
\(490\) | −1.77964e9 | −0.683355 | ||||||||
\(491\) | 8.34813e8 | 0.318276 | 0.159138 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159138 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(492\) | −1.11413e9 | −0.421752 | ||||||||
\(493\) | −2.69769e9 | −1.01398 | ||||||||
\(494\) | −6.14144e9 | −2.29206 | ||||||||
\(495\) | 2.68272e8 | 0.0994162 | ||||||||
\(496\) | −1.30605e10 | −4.80587 | ||||||||
\(497\) | −6.35389e8 | −0.232163 | ||||||||
\(498\) | 1.10140e9 | 0.399615 | ||||||||
\(499\) | −4.50230e9 | −1.62212 | −0.811059 | − | 0.584964i | \(-0.801109\pi\) | ||||
−0.811059 | + | 0.584964i | \(0.801109\pi\) | |||||||
\(500\) | −6.95312e8 | −0.248763 | ||||||||
\(501\) | −6.75116e8 | −0.239854 | ||||||||
\(502\) | 2.80158e9 | 0.988416 | ||||||||
\(503\) | 2.41700e9 | 0.846815 | 0.423407 | − | 0.905939i | \(-0.360834\pi\) | ||||
0.423407 | + | 0.905939i | \(0.360834\pi\) | |||||||
\(504\) | 1.53580e9 | 0.534352 | ||||||||
\(505\) | 2.25031e9 | 0.777538 | ||||||||
\(506\) | −3.80836e8 | −0.130681 | ||||||||
\(507\) | 1.57636e9 | 0.537188 | ||||||||
\(508\) | 1.40292e10 | 4.74801 | ||||||||
\(509\) | 3.51209e9 | 1.18047 | 0.590233 | − | 0.807233i | \(-0.299036\pi\) | ||||
0.590233 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(510\) | −1.22854e9 | −0.410104 | ||||||||
\(511\) | 6.39622e8 | 0.212056 | ||||||||
\(512\) | −9.14439e9 | −3.01099 | ||||||||
\(513\) | −4.99240e8 | −0.163267 | ||||||||
\(514\) | −2.87500e9 | −0.933829 | ||||||||
\(515\) | 6.71508e8 | 0.216634 | ||||||||
\(516\) | −1.84051e8 | −0.0589744 | ||||||||
\(517\) | −2.47595e9 | −0.787998 | ||||||||
\(518\) | 1.11370e9 | 0.352057 | ||||||||
\(519\) | 1.43281e9 | 0.449887 | ||||||||
\(520\) | −6.90076e9 | −2.15221 | ||||||||
\(521\) | 9.90013e8 | 0.306697 | 0.153348 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153348 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(522\) | −2.61487e9 | −0.804642 | ||||||||
\(523\) | 4.45926e8 | 0.136303 | 0.0681517 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681517 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(524\) | 5.02252e9 | 1.52497 | ||||||||
\(525\) | −1.77188e8 | −0.0534411 | ||||||||
\(526\) | 5.89043e9 | 1.76481 | ||||||||
\(527\) | 3.33567e9 | 0.992765 | ||||||||
\(528\) | −5.14955e9 | −1.52248 | ||||||||
\(529\) | −3.37025e9 | −0.989845 | ||||||||
\(530\) | 1.38020e9 | 0.402694 | ||||||||
\(531\) | −1.15632e9 | −0.335157 | ||||||||
\(532\) | 3.79243e9 | 1.09201 | ||||||||
\(533\) | 1.27571e9 | 0.364926 | ||||||||
\(534\) | 4.09158e9 | 1.16278 | ||||||||
\(535\) | 1.44247e9 | 0.407257 | ||||||||
\(536\) | −2.28782e10 | −6.41719 | ||||||||
\(537\) | 1.13955e9 | 0.317557 | ||||||||
\(538\) | −3.28751e9 | −0.910183 | ||||||||
\(539\) | 1.90519e9 | 0.524056 | ||||||||
\(540\) | −8.75893e8 | −0.239372 | ||||||||
\(541\) | 2.84753e9 | 0.773175 | 0.386588 | − | 0.922253i | \(-0.373654\pi\) | ||||
0.386588 | + | 0.922253i | \(0.373654\pi\) | |||||||
\(542\) | 3.37007e9 | 0.909162 | ||||||||
\(543\) | −2.70055e9 | −0.723858 | ||||||||
\(544\) | 1.29588e10 | 3.45120 | ||||||||
\(545\) | 1.96474e8 | 0.0519898 | ||||||||
\(546\) | −2.74578e9 | −0.721923 | ||||||||
\(547\) | 4.34116e9 | 1.13410 | 0.567048 | − | 0.823684i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823684i | \(0.308085\pi\) | |||||||
\(548\) | −2.84982e9 | −0.739752 | ||||||||
\(549\) | −2.71889e8 | −0.0701276 | ||||||||
\(550\) | 1.01200e9 | 0.259365 | ||||||||
\(551\) | −4.13540e9 | −1.05314 | ||||||||
\(552\) | 7.96340e8 | 0.201517 | ||||||||
\(553\) | −1.77741e9 | −0.446940 | ||||||||
\(554\) | −1.43982e10 | −3.59769 | ||||||||
\(555\) | −4.06789e8 | −0.101005 | ||||||||
\(556\) | 1.64015e10 | 4.04690 | ||||||||
\(557\) | 3.00124e9 | 0.735880 | 0.367940 | − | 0.929849i | \(-0.380063\pi\) | ||||
0.367940 | + | 0.929849i | \(0.380063\pi\) | |||||||
\(558\) | 3.23326e9 | 0.787809 | ||||||||
\(559\) | 2.10743e8 | 0.0510284 | ||||||||
\(560\) | 3.40116e9 | 0.818406 | ||||||||
\(561\) | 1.31521e9 | 0.314503 | ||||||||
\(562\) | −1.21328e10 | −2.88327 | ||||||||
\(563\) | −7.43886e9 | −1.75682 | −0.878409 | − | 0.477909i | \(-0.841395\pi\) | ||||
−0.878409 | + | 0.477909i | \(0.841395\pi\) | |||||||
\(564\) | 8.08385e9 | 1.89732 | ||||||||
\(565\) | 3.15062e9 | 0.734897 | ||||||||
\(566\) | 4.62441e9 | 1.07201 | ||||||||
\(567\) | −2.23205e8 | −0.0514237 | ||||||||
\(568\) | −7.58837e9 | −1.73752 | ||||||||
\(569\) | −7.20171e8 | −0.163886 | −0.0819431 | − | 0.996637i | \(-0.526113\pi\) | ||||
−0.0819431 | + | 0.996637i | \(0.526113\pi\) | |||||||
\(570\) | −1.88328e9 | −0.425944 | ||||||||
\(571\) | −2.30186e9 | −0.517431 | −0.258716 | − | 0.965954i | \(-0.583299\pi\) | ||||
−0.258716 | + | 0.965954i | \(0.583299\pi\) | |||||||
\(572\) | 1.15350e10 | 2.57710 | ||||||||
\(573\) | 1.66755e9 | 0.370286 | ||||||||
\(574\) | −1.07101e9 | −0.236375 | ||||||||
\(575\) | −9.18750e7 | −0.0201539 | ||||||||
\(576\) | 6.51584e9 | 1.42066 | ||||||||
\(577\) | −7.37257e9 | −1.59773 | −0.798865 | − | 0.601511i | \(-0.794566\pi\) | ||||
−0.798865 | + | 0.601511i | \(0.794566\pi\) | |||||||
\(578\) | 3.00451e9 | 0.647181 | ||||||||
\(579\) | −2.07203e9 | −0.443630 | ||||||||
\(580\) | −7.25537e9 | −1.54405 | ||||||||
\(581\) | 7.78766e8 | 0.164737 | ||||||||
\(582\) | −2.19782e9 | −0.462127 | ||||||||
\(583\) | −1.47756e9 | −0.308821 | ||||||||
\(584\) | 7.63892e9 | 1.58704 | ||||||||
\(585\) | 1.00292e9 | 0.207120 | ||||||||
\(586\) | −1.19328e10 | −2.44964 | ||||||||
\(587\) | 7.36500e8 | 0.150293 | 0.0751467 | − | 0.997172i | \(-0.476058\pi\) | ||||
0.0751467 | + | 0.997172i | \(0.476058\pi\) | |||||||
\(588\) | −6.22034e9 | −1.26181 | ||||||||
\(589\) | 5.11338e9 | 1.03111 | ||||||||
\(590\) | −4.36198e9 | −0.874384 | ||||||||
\(591\) | −4.88786e9 | −0.974008 | ||||||||
\(592\) | 7.80842e9 | 1.54681 | ||||||||
\(593\) | −5.08539e9 | −1.00146 | −0.500729 | − | 0.865604i | \(-0.666935\pi\) | ||||
−0.500729 | + | 0.865604i | \(0.666935\pi\) | |||||||
\(594\) | 1.27483e9 | 0.249574 | ||||||||
\(595\) | −8.68665e8 | −0.169061 | ||||||||
\(596\) | 2.57575e10 | 4.98358 | ||||||||
\(597\) | 1.66343e9 | 0.319959 | ||||||||
\(598\) | −1.42374e9 | −0.272255 | ||||||||
\(599\) | 4.86023e9 | 0.923980 | 0.461990 | − | 0.886885i | \(-0.347136\pi\) | ||||
0.461990 | + | 0.886885i | \(0.347136\pi\) | |||||||
\(600\) | −2.11613e9 | −0.399956 | ||||||||
\(601\) | 6.78466e9 | 1.27488 | 0.637438 | − | 0.770502i | \(-0.279994\pi\) | ||||
0.637438 | + | 0.770502i | \(0.279994\pi\) | |||||||
\(602\) | −1.76928e8 | −0.0330528 | ||||||||
\(603\) | 3.32500e9 | 0.617563 | ||||||||
\(604\) | −1.31742e10 | −2.43274 | ||||||||
\(605\) | 1.35250e9 | 0.248310 | ||||||||
\(606\) | 1.06935e10 | 1.95193 | ||||||||
\(607\) | 2.85250e9 | 0.517685 | 0.258842 | − | 0.965920i | \(-0.416659\pi\) | ||||
0.258842 | + | 0.965920i | \(0.416659\pi\) | |||||||
\(608\) | 1.98651e10 | 3.58449 | ||||||||
\(609\) | −1.84890e9 | −0.331705 | ||||||||
\(610\) | −1.02565e9 | −0.182954 | ||||||||
\(611\) | −9.25622e9 | −1.64168 | ||||||||
\(612\) | −4.29408e9 | −0.757252 | ||||||||
\(613\) | 7.75467e9 | 1.35973 | 0.679864 | − | 0.733339i | \(-0.262039\pi\) | ||||
0.679864 | + | 0.733339i | \(0.262039\pi\) | |||||||
\(614\) | −2.03825e10 | −3.55360 | ||||||||
\(615\) | 3.91196e8 | 0.0678159 | ||||||||
\(616\) | −6.20218e9 | −1.06908 | ||||||||
\(617\) | −6.34097e9 | −1.08682 | −0.543410 | − | 0.839468i | \(-0.682867\pi\) | ||||
−0.543410 | + | 0.839468i | \(0.682867\pi\) | |||||||
\(618\) | 3.19101e9 | 0.543836 | ||||||||
\(619\) | 3.19831e9 | 0.542005 | 0.271003 | − | 0.962579i | \(-0.412645\pi\) | ||||
0.271003 | + | 0.962579i | \(0.412645\pi\) | |||||||
\(620\) | 8.97120e9 | 1.51175 | ||||||||
\(621\) | −1.15736e8 | −0.0193931 | ||||||||
\(622\) | 4.68548e9 | 0.780706 | ||||||||
\(623\) | 2.89303e9 | 0.479342 | ||||||||
\(624\) | −1.92513e10 | −3.17187 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −8.00572e9 | −1.30434 | ||||||||
\(627\) | 2.01613e9 | 0.326650 | ||||||||
\(628\) | −2.79488e10 | −4.50303 | ||||||||
\(629\) | −1.99429e9 | −0.319529 | ||||||||
\(630\) | −8.41995e8 | −0.134158 | ||||||||
\(631\) | −3.79459e9 | −0.601260 | −0.300630 | − | 0.953741i | \(-0.597197\pi\) | ||||
−0.300630 | + | 0.953741i | \(0.597197\pi\) | |||||||
\(632\) | −2.12273e10 | −3.34492 | ||||||||
\(633\) | −4.58776e9 | −0.718931 | ||||||||
\(634\) | 6.97508e9 | 1.08702 | ||||||||
\(635\) | −4.92600e9 | −0.763460 | ||||||||
\(636\) | 4.82417e9 | 0.743571 | ||||||||
\(637\) | 7.12246e9 | 1.09180 | ||||||||
\(638\) | 1.05599e10 | 1.60986 | ||||||||
\(639\) | 1.10285e9 | 0.167211 | ||||||||
\(640\) | 1.20484e10 | 1.81677 | ||||||||
\(641\) | 6.77964e9 | 1.01672 | 0.508362 | − | 0.861143i | \(-0.330251\pi\) | ||||
0.508362 | + | 0.861143i | \(0.330251\pi\) | |||||||
\(642\) | 6.85462e9 | 1.02238 | ||||||||
\(643\) | −1.13203e9 | −0.167927 | −0.0839635 | − | 0.996469i | \(-0.526758\pi\) | ||||
−0.0839635 | + | 0.996469i | \(0.526758\pi\) | |||||||
\(644\) | 8.79178e8 | 0.129711 | ||||||||
\(645\) | 6.46245e7 | 0.00948284 | ||||||||
\(646\) | −9.23280e9 | −1.34747 | ||||||||
\(647\) | −5.54265e9 | −0.804549 | −0.402274 | − | 0.915519i | \(-0.631780\pi\) | ||||
−0.402274 | + | 0.915519i | \(0.631780\pi\) | |||||||
\(648\) | −2.66571e9 | −0.384858 | ||||||||
\(649\) | 4.66970e9 | 0.670552 | ||||||||
\(650\) | 3.78331e9 | 0.540350 | ||||||||
\(651\) | 2.28614e9 | 0.324766 | ||||||||
\(652\) | −1.66674e10 | −2.35505 | ||||||||
\(653\) | 9.41765e9 | 1.32357 | 0.661784 | − | 0.749695i | \(-0.269800\pi\) | ||||
0.661784 | + | 0.749695i | \(0.269800\pi\) | |||||||
\(654\) | 9.33646e8 | 0.130515 | ||||||||
\(655\) | −1.76353e9 | −0.245210 | ||||||||
\(656\) | −7.50911e9 | −1.03854 | ||||||||
\(657\) | −1.11020e9 | −0.152730 | ||||||||
\(658\) | 7.77099e9 | 1.06337 | ||||||||
\(659\) | 7.46390e9 | 1.01594 | 0.507969 | − | 0.861376i | \(-0.330397\pi\) | ||||
0.507969 | + | 0.861376i | \(0.330397\pi\) | |||||||
\(660\) | 3.53722e9 | 0.478914 | ||||||||
\(661\) | 5.58309e9 | 0.751917 | 0.375958 | − | 0.926637i | \(-0.377314\pi\) | ||||
0.375958 | + | 0.926637i | \(0.377314\pi\) | |||||||
\(662\) | −4.94024e9 | −0.661828 | ||||||||
\(663\) | 4.91684e9 | 0.655223 | ||||||||
\(664\) | 9.30069e9 | 1.23290 | ||||||||
\(665\) | −1.33161e9 | −0.175591 | ||||||||
\(666\) | −1.93306e9 | −0.253563 | ||||||||
\(667\) | −9.58687e8 | −0.125094 | ||||||||
\(668\) | −8.90152e9 | −1.15544 | ||||||||
\(669\) | 3.99948e9 | 0.516431 | ||||||||
\(670\) | 1.25429e10 | 1.61115 | ||||||||
\(671\) | 1.09800e9 | 0.140305 | ||||||||
\(672\) | 8.88149e9 | 1.12900 | ||||||||
\(673\) | 3.39933e9 | 0.429873 | 0.214936 | − | 0.976628i | \(-0.431046\pi\) | ||||
0.214936 | + | 0.976628i | \(0.431046\pi\) | |||||||
\(674\) | 2.72549e10 | 3.42875 | ||||||||
\(675\) | 3.07547e8 | 0.0384900 | ||||||||
\(676\) | 2.07845e10 | 2.58778 | ||||||||
\(677\) | −1.38930e10 | −1.72082 | −0.860409 | − | 0.509604i | \(-0.829792\pi\) | ||||
−0.860409 | + | 0.509604i | \(0.829792\pi\) | |||||||
\(678\) | 1.49717e10 | 1.84488 | ||||||||
\(679\) | −1.55401e9 | −0.190507 | ||||||||
\(680\) | −1.03743e10 | −1.26526 | ||||||||
\(681\) | −1.06954e9 | −0.129773 | ||||||||
\(682\) | −1.30572e10 | −1.57618 | ||||||||
\(683\) | −7.22576e9 | −0.867782 | −0.433891 | − | 0.900965i | \(-0.642860\pi\) | ||||
−0.433891 | + | 0.900965i | \(0.642860\pi\) | |||||||
\(684\) | −6.58257e9 | −0.786500 | ||||||||
\(685\) | 1.00064e9 | 0.118949 | ||||||||
\(686\) | −1.35891e10 | −1.60715 | ||||||||
\(687\) | −1.00390e9 | −0.118125 | ||||||||
\(688\) | −1.24048e9 | −0.145222 | ||||||||
\(689\) | −5.52380e9 | −0.643385 | ||||||||
\(690\) | −4.36590e8 | −0.0505943 | ||||||||
\(691\) | −5.83386e9 | −0.672641 | −0.336320 | − | 0.941748i | \(-0.609182\pi\) | ||||
−0.336320 | + | 0.941748i | \(0.609182\pi\) | |||||||
\(692\) | 1.88919e10 | 2.16722 | ||||||||
\(693\) | 9.01394e8 | 0.102884 | ||||||||
\(694\) | 1.28401e10 | 1.45818 | ||||||||
\(695\) | −5.75896e9 | −0.650724 | ||||||||
\(696\) | −2.20811e10 | −2.48250 | ||||||||
\(697\) | 1.91785e9 | 0.214536 | ||||||||
\(698\) | 1.03284e10 | 1.14958 | ||||||||
\(699\) | −4.84897e9 | −0.537006 | ||||||||
\(700\) | −2.33625e9 | −0.257440 | ||||||||
\(701\) | 4.37486e9 | 0.479680 | 0.239840 | − | 0.970812i | \(-0.422905\pi\) | ||||
0.239840 | + | 0.970812i | \(0.422905\pi\) | |||||||
\(702\) | 4.76588e9 | 0.519952 | ||||||||
\(703\) | −3.05712e9 | −0.331871 | ||||||||
\(704\) | −2.63136e10 | −2.84234 | ||||||||
\(705\) | −2.83843e9 | −0.305082 | ||||||||
\(706\) | −1.36083e9 | −0.145542 | ||||||||
\(707\) | 7.56103e9 | 0.804661 | ||||||||
\(708\) | −1.52463e10 | −1.61454 | ||||||||
\(709\) | −3.54685e9 | −0.373750 | −0.186875 | − | 0.982384i | \(-0.559836\pi\) | ||||
−0.186875 | + | 0.982384i | \(0.559836\pi\) | |||||||
\(710\) | 4.16029e9 | 0.436234 | ||||||||
\(711\) | 3.08507e9 | 0.321900 | ||||||||
\(712\) | 3.45511e10 | 3.58742 | ||||||||
\(713\) | 1.18541e9 | 0.122477 | ||||||||
\(714\) | −4.12790e9 | −0.424409 | ||||||||
\(715\) | −4.05021e9 | −0.414387 | ||||||||
\(716\) | 1.50251e10 | 1.52976 | ||||||||
\(717\) | −1.00799e10 | −1.02126 | ||||||||
\(718\) | 2.71782e8 | 0.0274022 | ||||||||
\(719\) | −1.06545e10 | −1.06901 | −0.534507 | − | 0.845164i | \(-0.679503\pi\) | ||||
−0.534507 | + | 0.845164i | \(0.679503\pi\) | |||||||
\(720\) | −5.90344e9 | −0.589443 | ||||||||
\(721\) | 2.25627e9 | 0.224191 | ||||||||
\(722\) | 5.51186e9 | 0.545027 | ||||||||
\(723\) | −6.93958e9 | −0.682888 | ||||||||
\(724\) | −3.56073e10 | −3.48702 | ||||||||
\(725\) | 2.54753e9 | 0.248277 | ||||||||
\(726\) | 6.42710e9 | 0.623357 | ||||||||
\(727\) | −9.21169e9 | −0.889138 | −0.444569 | − | 0.895745i | \(-0.646643\pi\) | ||||
−0.444569 | + | 0.895745i | \(0.646643\pi\) | |||||||
\(728\) | −2.31866e10 | −2.22729 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −4.18800e9 | −0.398453 | ||||||||
\(731\) | 3.16823e8 | 0.0299989 | ||||||||
\(732\) | −3.58491e9 | −0.337823 | ||||||||
\(733\) | −5.81770e8 | −0.0545616 | −0.0272808 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272808 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(734\) | 2.76131e8 | 0.0257738 | ||||||||
\(735\) | 2.18411e9 | 0.202894 | ||||||||
\(736\) | 4.60522e9 | 0.425773 | ||||||||
\(737\) | −1.34277e10 | −1.23557 | ||||||||
\(738\) | 1.85896e9 | 0.170245 | ||||||||
\(739\) | 1.43208e8 | 0.0130531 | 0.00652654 | − | 0.999979i | \(-0.497923\pi\) | ||||
0.00652654 | + | 0.999979i | \(0.497923\pi\) | |||||||
\(740\) | −5.36358e9 | −0.486569 | ||||||||
\(741\) | 7.53722e9 | 0.680530 | ||||||||
\(742\) | 4.63746e9 | 0.416742 | ||||||||
\(743\) | 1.76012e10 | 1.57428 | 0.787139 | − | 0.616775i | \(-0.211561\pi\) | ||||
0.787139 | + | 0.616775i | \(0.211561\pi\) | |||||||
\(744\) | 2.73031e10 | 2.43056 | ||||||||
\(745\) | −9.04406e9 | −0.801340 | ||||||||
\(746\) | 1.24519e10 | 1.09812 | ||||||||
\(747\) | −1.35171e9 | −0.118649 | ||||||||
\(748\) | 1.73413e10 | 1.51504 | ||||||||
\(749\) | 4.84670e9 | 0.421463 | ||||||||
\(750\) | 1.16016e9 | 0.100416 | ||||||||
\(751\) | −2.10398e10 | −1.81260 | −0.906299 | − | 0.422636i | \(-0.861105\pi\) | ||||
−0.906299 | + | 0.422636i | \(0.861105\pi\) | |||||||
\(752\) | 5.44844e10 | 4.67207 | ||||||||
\(753\) | −3.43830e9 | −0.293468 | ||||||||
\(754\) | 3.94777e10 | 3.35391 | ||||||||
\(755\) | 4.62578e9 | 0.391174 | ||||||||
\(756\) | −2.94300e9 | −0.247722 | ||||||||
\(757\) | −3.91015e9 | −0.327610 | −0.163805 | − | 0.986493i | \(-0.552377\pi\) | ||||
−0.163805 | + | 0.986493i | \(0.552377\pi\) | |||||||
\(758\) | −3.91107e10 | −3.26177 | ||||||||
\(759\) | 4.67389e8 | 0.0388001 | ||||||||
\(760\) | −1.59032e10 | −1.31413 | ||||||||
\(761\) | 1.20242e10 | 0.989032 | 0.494516 | − | 0.869169i | \(-0.335345\pi\) | ||||
0.494516 | + | 0.869169i | \(0.335345\pi\) | |||||||
\(762\) | −2.34084e10 | −1.91659 | ||||||||
\(763\) | 6.60153e8 | 0.0538033 | ||||||||
\(764\) | 2.19869e10 | 1.78377 | ||||||||
\(765\) | 1.50775e9 | 0.121763 | ||||||||
\(766\) | −2.60028e10 | −2.09035 | ||||||||
\(767\) | 1.74575e10 | 1.39700 | ||||||||
\(768\) | 2.63643e10 | 2.10015 | ||||||||
\(769\) | 1.18948e10 | 0.943223 | 0.471611 | − | 0.881807i | \(-0.343673\pi\) | ||||
0.471611 | + | 0.881807i | \(0.343673\pi\) | |||||||
\(770\) | 3.40032e9 | 0.268412 | ||||||||
\(771\) | 3.52841e9 | 0.277261 | ||||||||
\(772\) | −2.73201e10 | −2.13709 | ||||||||
\(773\) | −7.77614e9 | −0.605531 | −0.302765 | − | 0.953065i | \(-0.597910\pi\) | ||||
−0.302765 | + | 0.953065i | \(0.597910\pi\) | |||||||
\(774\) | 3.07096e8 | 0.0238057 | ||||||||
\(775\) | −3.15000e9 | −0.243083 | ||||||||
\(776\) | −1.85594e10 | −1.42576 | ||||||||
\(777\) | −1.36681e9 | −0.104528 | ||||||||
\(778\) | −1.32546e10 | −1.00911 | ||||||||
\(779\) | 2.93994e9 | 0.222822 | ||||||||
\(780\) | 1.32237e10 | 0.997751 | ||||||||
\(781\) | −4.45378e9 | −0.334541 | ||||||||
\(782\) | −2.14039e9 | −0.160055 | ||||||||
\(783\) | 3.20916e9 | 0.238905 | ||||||||
\(784\) | −4.19245e10 | −3.10715 | ||||||||
\(785\) | 9.81350e9 | 0.724069 | ||||||||
\(786\) | −8.38028e9 | −0.615573 | ||||||||
\(787\) | 2.44365e10 | 1.78701 | 0.893507 | − | 0.449050i | \(-0.148237\pi\) | ||||
0.893507 | + | 0.449050i | \(0.148237\pi\) | |||||||
\(788\) | −6.44473e10 | −4.69206 | ||||||||
\(789\) | −7.22916e9 | −0.523985 | ||||||||
\(790\) | 1.16378e10 | 0.839799 | ||||||||
\(791\) | 1.05861e10 | 0.760532 | ||||||||
\(792\) | 1.07652e10 | 0.769989 | ||||||||
\(793\) | 4.10482e9 | 0.292306 | ||||||||
\(794\) | 4.10883e9 | 0.291304 | ||||||||
\(795\) | −1.69388e9 | −0.119563 | ||||||||
\(796\) | 2.19326e10 | 1.54133 | ||||||||
\(797\) | −2.26970e9 | −0.158805 | −0.0794024 | − | 0.996843i | \(-0.525301\pi\) | ||||
−0.0794024 | + | 0.996843i | \(0.525301\pi\) | |||||||
\(798\) | −6.32781e9 | −0.440802 | ||||||||
\(799\) | −1.39155e10 | −0.965125 | ||||||||
\(800\) | −1.22375e10 | −0.845041 | ||||||||
\(801\) | −5.02148e9 | −0.345237 | ||||||||
\(802\) | 2.19193e10 | 1.50043 | ||||||||
\(803\) | 4.48345e9 | 0.305568 | ||||||||
\(804\) | 4.38408e10 | 2.97496 | ||||||||
\(805\) | −3.08700e8 | −0.0208570 | ||||||||
\(806\) | −4.88138e10 | −3.28375 | ||||||||
\(807\) | 4.03467e9 | 0.270240 | ||||||||
\(808\) | 9.03003e10 | 6.02212 | ||||||||
\(809\) | −1.63200e10 | −1.08368 | −0.541838 | − | 0.840483i | \(-0.682271\pi\) | ||||
−0.541838 | + | 0.840483i | \(0.682271\pi\) | |||||||
\(810\) | 1.46146e9 | 0.0966252 | ||||||||
\(811\) | 6.99393e9 | 0.460414 | 0.230207 | − | 0.973142i | \(-0.426060\pi\) | ||||
0.230207 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(812\) | −2.43780e10 | −1.59791 | ||||||||
\(813\) | −4.13599e9 | −0.269937 | ||||||||
\(814\) | 7.80649e9 | 0.507306 | ||||||||
\(815\) | 5.85230e9 | 0.378682 | ||||||||
\(816\) | −2.89417e10 | −1.86470 | ||||||||
\(817\) | 4.85670e8 | 0.0311576 | ||||||||
\(818\) | 5.25017e10 | 3.35380 | ||||||||
\(819\) | 3.36982e9 | 0.214345 | ||||||||
\(820\) | 5.15800e9 | 0.326687 | ||||||||
\(821\) | 4.00949e9 | 0.252865 | 0.126432 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126432 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(822\) | 4.75504e9 | 0.298609 | ||||||||
\(823\) | 1.88572e10 | 1.17917 | 0.589586 | − | 0.807706i | \(-0.299291\pi\) | ||||
0.589586 | + | 0.807706i | \(0.299291\pi\) | |||||||
\(824\) | 2.69463e10 | 1.67785 | ||||||||
\(825\) | −1.24200e9 | −0.0770075 | ||||||||
\(826\) | −1.46563e10 | −0.904885 | ||||||||
\(827\) | 1.66386e10 | 1.02293 | 0.511466 | − | 0.859304i | \(-0.329103\pi\) | ||||
0.511466 | + | 0.859304i | \(0.329103\pi\) | |||||||
\(828\) | −1.52600e9 | −0.0934219 | ||||||||
\(829\) | −1.37224e10 | −0.836547 | −0.418274 | − | 0.908321i | \(-0.637365\pi\) | ||||
−0.418274 | + | 0.908321i | \(0.637365\pi\) | |||||||
\(830\) | −5.09906e9 | −0.309540 | ||||||||
\(831\) | 1.76705e10 | 1.06818 | ||||||||
\(832\) | −9.83722e10 | −5.92162 | ||||||||
\(833\) | 1.07076e10 | 0.641853 | ||||||||
\(834\) | −2.73666e10 | −1.63357 | ||||||||
\(835\) | 3.12554e9 | 0.185790 | ||||||||
\(836\) | 2.65831e10 | 1.57356 | ||||||||
\(837\) | −3.96809e9 | −0.233907 | ||||||||
\(838\) | −5.71217e10 | −3.35311 | ||||||||
\(839\) | −6.56954e8 | −0.0384033 | −0.0192016 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192016 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(840\) | −7.11018e9 | −0.413907 | ||||||||
\(841\) | 9.33282e9 | 0.541037 | ||||||||
\(842\) | −6.24469e10 | −3.60511 | ||||||||
\(843\) | 1.48903e10 | 0.856066 | ||||||||
\(844\) | −6.04904e10 | −3.46328 | ||||||||
\(845\) | −7.29794e9 | −0.416104 | ||||||||
\(846\) | −1.34882e10 | −0.765876 | ||||||||
\(847\) | 4.54441e9 | 0.256972 | ||||||||
\(848\) | 3.25144e10 | 1.83101 | ||||||||
\(849\) | −5.67541e9 | −0.318288 | ||||||||
\(850\) | 5.68769e9 | 0.317665 | ||||||||
\(851\) | −7.08716e8 | −0.0394202 | ||||||||
\(852\) | 1.45413e10 | 0.805501 | ||||||||
\(853\) | −8.70997e9 | −0.480502 | −0.240251 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240251 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(854\) | −3.44617e9 | −0.189336 | ||||||||
\(855\) | 2.31129e9 | 0.126466 | ||||||||
\(856\) | 5.78835e10 | 3.15425 | ||||||||
\(857\) | 1.93825e9 | 0.105190 | 0.0525952 | − | 0.998616i | \(-0.483251\pi\) | ||||
0.0525952 | + | 0.998616i | \(0.483251\pi\) | |||||||
\(858\) | −1.92466e10 | −1.04028 | ||||||||
\(859\) | −7.95332e8 | −0.0428127 | −0.0214063 | − | 0.999771i | \(-0.506814\pi\) | ||||
−0.0214063 | + | 0.999771i | \(0.506814\pi\) | |||||||
\(860\) | 8.52086e8 | 0.0456813 | ||||||||
\(861\) | 1.31442e9 | 0.0701815 | ||||||||
\(862\) | 3.36179e10 | 1.78770 | ||||||||
\(863\) | 2.24172e9 | 0.118725 | 0.0593626 | − | 0.998236i | \(-0.481093\pi\) | ||||
0.0593626 | + | 0.998236i | \(0.481093\pi\) | |||||||
\(864\) | −1.54157e10 | −0.813141 | ||||||||
\(865\) | −6.63338e9 | −0.348481 | ||||||||
\(866\) | 5.85335e10 | 3.06261 | ||||||||
\(867\) | −3.68735e9 | −0.192153 | ||||||||
\(868\) | 3.01432e10 | 1.56448 | ||||||||
\(869\) | −1.24588e10 | −0.644030 | ||||||||
\(870\) | 1.21059e10 | 0.623273 | ||||||||
\(871\) | −5.01989e10 | −2.57413 | ||||||||
\(872\) | 7.88412e9 | 0.402666 | ||||||||
\(873\) | 2.69732e9 | 0.137209 | ||||||||
\(874\) | −3.28109e9 | −0.166237 | ||||||||
\(875\) | 8.20312e8 | 0.0413953 | ||||||||
\(876\) | −1.46382e10 | −0.735739 | ||||||||
\(877\) | 1.99169e10 | 0.997062 | 0.498531 | − | 0.866872i | \(-0.333873\pi\) | ||||
0.498531 | + | 0.866872i | \(0.333873\pi\) | |||||||
\(878\) | −5.04289e10 | −2.51449 | ||||||||
\(879\) | 1.46448e10 | 0.727317 | ||||||||
\(880\) | 2.38405e10 | 1.17931 | ||||||||
\(881\) | −2.76906e10 | −1.36432 | −0.682161 | − | 0.731202i | \(-0.738960\pi\) | ||||
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(882\) | 1.03789e10 | 0.509343 | ||||||||
\(883\) | −1.65616e10 | −0.809544 | −0.404772 | − | 0.914418i | \(-0.632649\pi\) | ||||
−0.404772 | + | 0.914418i | \(0.632649\pi\) | |||||||
\(884\) | 6.48295e10 | 3.15638 | ||||||||
\(885\) | 5.35334e9 | 0.259611 | ||||||||
\(886\) | 2.05489e10 | 0.992593 | ||||||||
\(887\) | 6.69904e9 | 0.322314 | 0.161157 | − | 0.986929i | \(-0.448477\pi\) | ||||
0.161157 | + | 0.986929i | \(0.448477\pi\) | |||||||
\(888\) | −1.63236e10 | −0.782296 | ||||||||
\(889\) | −1.65514e10 | −0.790092 | ||||||||
\(890\) | −1.89425e10 | −0.900683 | ||||||||
\(891\) | −1.56456e9 | −0.0741005 | ||||||||
\(892\) | 5.27339e10 | 2.48778 | ||||||||
\(893\) | −2.13315e10 | −1.00240 | ||||||||
\(894\) | −4.29774e10 | −2.01168 | ||||||||
\(895\) | −5.27568e9 | −0.245979 | ||||||||
\(896\) | 4.04827e10 | 1.88015 | ||||||||
\(897\) | 1.74731e9 | 0.0808346 | ||||||||
\(898\) | 1.94703e9 | 0.0897232 | ||||||||
\(899\) | −3.28693e10 | −1.50880 | ||||||||
\(900\) | 4.05506e9 | 0.185417 | ||||||||
\(901\) | −8.30427e9 | −0.378238 | ||||||||
\(902\) | −7.50726e9 | −0.340611 | ||||||||
\(903\) | 2.17138e8 | 0.00981362 | ||||||||
\(904\) | 1.26428e11 | 5.69186 | ||||||||
\(905\) | 1.25026e10 | 0.560698 | ||||||||
\(906\) | 2.19817e10 | 0.982002 | ||||||||
\(907\) | 3.87814e9 | 0.172583 | 0.0862916 | − | 0.996270i | \(-0.472498\pi\) | ||||
0.0862916 | + | 0.996270i | \(0.472498\pi\) | |||||||
\(908\) | −1.41021e10 | −0.625150 | ||||||||
\(909\) | −1.31238e10 | −0.579543 | ||||||||
\(910\) | 1.27119e10 | 0.559199 | ||||||||
\(911\) | −7.15870e9 | −0.313704 | −0.156852 | − | 0.987622i | \(-0.550135\pi\) | ||||
−0.156852 | + | 0.987622i | \(0.550135\pi\) | |||||||
\(912\) | −4.43659e10 | −1.93672 | ||||||||
\(913\) | 5.45878e9 | 0.237382 | ||||||||
\(914\) | 2.66341e10 | 1.15379 | ||||||||
\(915\) | 1.25875e9 | 0.0543206 | ||||||||
\(916\) | −1.32366e10 | −0.569041 | ||||||||
\(917\) | −5.92545e9 | −0.253763 | ||||||||
\(918\) | 7.16485e9 | 0.305673 | ||||||||
\(919\) | 2.54160e10 | 1.08020 | 0.540098 | − | 0.841602i | \(-0.318387\pi\) | ||||
0.540098 | + | 0.841602i | \(0.318387\pi\) | |||||||
\(920\) | −3.68676e9 | −0.156094 | ||||||||
\(921\) | 2.50149e10 | 1.05509 | ||||||||
\(922\) | −1.88634e10 | −0.792615 | ||||||||
\(923\) | −1.66502e10 | −0.696970 | ||||||||
\(924\) | 1.18850e10 | 0.495620 | ||||||||
\(925\) | 1.88328e9 | 0.0782382 | ||||||||
\(926\) | 4.28256e10 | 1.77241 | ||||||||
\(927\) | −3.91624e9 | −0.161469 | ||||||||
\(928\) | −1.27694e11 | −5.24511 | ||||||||
\(929\) | −2.34566e10 | −0.959865 | −0.479932 | − | 0.877306i | \(-0.659339\pi\) | ||||
−0.479932 | + | 0.877306i | \(0.659339\pi\) | |||||||
\(930\) | −1.49688e10 | −0.610234 | ||||||||
\(931\) | 1.64141e10 | 0.666644 | ||||||||
\(932\) | −6.39345e10 | −2.58690 | ||||||||
\(933\) | −5.75036e9 | −0.231798 | ||||||||
\(934\) | 2.11190e10 | 0.848124 | ||||||||
\(935\) | −6.08893e9 | −0.243613 | ||||||||
\(936\) | 4.02452e10 | 1.60417 | ||||||||
\(937\) | 9.30070e9 | 0.369341 | 0.184670 | − | 0.982801i | \(-0.440878\pi\) | ||||
0.184670 | + | 0.982801i | \(0.440878\pi\) | |||||||
\(938\) | 4.21440e10 | 1.66735 | ||||||||
\(939\) | 9.82520e9 | 0.387268 | ||||||||
\(940\) | −3.74252e10 | −1.46966 | ||||||||
\(941\) | −1.13117e10 | −0.442553 | −0.221276 | − | 0.975211i | \(-0.571022\pi\) | ||||
−0.221276 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(942\) | 4.66337e10 | 1.81770 | ||||||||
\(943\) | 6.81551e8 | 0.0264672 | ||||||||
\(944\) | −1.02759e11 | −3.97573 | ||||||||
\(945\) | 1.03336e9 | 0.0398327 | ||||||||
\(946\) | −1.24018e9 | −0.0476283 | ||||||||
\(947\) | 4.46270e9 | 0.170755 | 0.0853774 | − | 0.996349i | \(-0.472790\pi\) | ||||
0.0853774 | + | 0.996349i | \(0.472790\pi\) | |||||||
\(948\) | 4.06772e10 | 1.55068 | ||||||||
\(949\) | 1.67611e10 | 0.636608 | ||||||||
\(950\) | 8.71888e9 | 0.329935 | ||||||||
\(951\) | −8.56032e9 | −0.322744 | ||||||||
\(952\) | −3.48578e10 | −1.30939 | ||||||||
\(953\) | 1.90872e10 | 0.714359 | 0.357179 | − | 0.934036i | \(-0.383739\pi\) | ||||
0.357179 | + | 0.934036i | \(0.383739\pi\) | |||||||
\(954\) | −8.04931e9 | −0.300151 | ||||||||
\(955\) | −7.72013e9 | −0.286822 | ||||||||
\(956\) | −1.32905e11 | −4.91969 | ||||||||
\(957\) | −1.29599e10 | −0.477980 | ||||||||
\(958\) | −6.67873e9 | −0.245423 | ||||||||
\(959\) | 3.36215e9 | 0.123098 | ||||||||
\(960\) | −3.01659e10 | −1.10044 | ||||||||
\(961\) | 1.31299e10 | 0.477234 | ||||||||
\(962\) | 2.91842e10 | 1.05690 | ||||||||
\(963\) | −8.41249e9 | −0.303552 | ||||||||
\(964\) | −9.14997e10 | −3.28965 | ||||||||
\(965\) | 9.59274e9 | 0.343635 | ||||||||
\(966\) | −1.46694e9 | −0.0523592 | ||||||||
\(967\) | −1.34102e10 | −0.476916 | −0.238458 | − | 0.971153i | \(-0.576642\pi\) | ||||
−0.238458 | + | 0.971153i | \(0.576642\pi\) | |||||||
\(968\) | 5.42733e10 | 1.92319 | ||||||||
\(969\) | 1.13312e10 | 0.400075 | ||||||||
\(970\) | 1.01751e10 | 0.357962 | ||||||||
\(971\) | 4.64191e10 | 1.62716 | 0.813579 | − | 0.581455i | \(-0.197516\pi\) | ||||
0.813579 | + | 0.581455i | \(0.197516\pi\) | |||||||
\(972\) | 5.10821e9 | 0.178417 | ||||||||
\(973\) | −1.93501e10 | −0.673423 | ||||||||
\(974\) | −9.59329e9 | −0.332668 | ||||||||
\(975\) | −4.64316e9 | −0.160434 | ||||||||
\(976\) | −2.41620e10 | −0.831875 | ||||||||
\(977\) | 3.92972e10 | 1.34813 | 0.674064 | − | 0.738673i | \(-0.264547\pi\) | ||||
0.674064 | + | 0.738673i | \(0.264547\pi\) | |||||||
\(978\) | 2.78101e10 | 0.950642 | ||||||||
\(979\) | 2.02788e10 | 0.690721 | ||||||||
\(980\) | 2.87979e10 | 0.977393 | ||||||||
\(981\) | −1.14584e9 | −0.0387509 | ||||||||
\(982\) | −1.83659e10 | −0.618902 | ||||||||
\(983\) | −3.69370e10 | −1.24029 | −0.620146 | − | 0.784486i | \(-0.712927\pi\) | ||||
−0.620146 | + | 0.784486i | \(0.712927\pi\) | |||||||
\(984\) | 1.56979e10 | 0.525242 | ||||||||
\(985\) | 2.26290e10 | 0.754463 | ||||||||
\(986\) | 5.93492e10 | 1.97172 | ||||||||
\(987\) | −9.53712e9 | −0.315724 | ||||||||
\(988\) | 9.93796e10 | 3.27829 | ||||||||
\(989\) | 1.12590e8 | 0.00370095 | ||||||||
\(990\) | −5.90198e9 | −0.193319 | ||||||||
\(991\) | −1.02868e10 | −0.335753 | −0.167877 | − | 0.985808i | \(-0.553691\pi\) | ||||
−0.167877 | + | 0.985808i | \(0.553691\pi\) | |||||||
\(992\) | 1.57893e11 | 5.13538 | ||||||||
\(993\) | 6.06302e9 | 0.196502 | ||||||||
\(994\) | 1.39786e10 | 0.451451 | ||||||||
\(995\) | −7.70106e9 | −0.247839 | ||||||||
\(996\) | −1.78226e10 | −0.571562 | ||||||||
\(997\) | −3.24439e10 | −1.03681 | −0.518407 | − | 0.855134i | \(-0.673475\pi\) | ||||
−0.518407 | + | 0.855134i | \(0.673475\pi\) | |||||||
\(998\) | 9.90506e10 | 3.15428 | ||||||||
\(999\) | 2.37239e9 | 0.0752848 |
(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 | 15.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 45.8.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 240.8.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 75.8.b.a.49.1 | 2 | |||
5.3 | odd | 4 | 75.8.b.a.49.2 | 2 | |||
5.4 | even | 2 | 75.8.a.c.1.1 | 1 | |||
15.2 | even | 4 | 225.8.b.a.199.2 | 2 | |||
15.8 | even | 4 | 225.8.b.a.199.1 | 2 | |||
15.14 | odd | 2 | 225.8.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
45.8.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
75.8.a.c.1.1 | 1 | 5.4 | even | 2 | |||
75.8.b.a.49.1 | 2 | 5.2 | odd | 4 | |||
75.8.b.a.49.2 | 2 | 5.3 | odd | 4 | |||
225.8.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
225.8.b.a.199.1 | 2 | 15.8 | even | 4 | |||
225.8.b.a.199.2 | 2 | 15.2 | even | 4 | |||
240.8.a.c.1.1 | 1 | 4.3 | odd | 2 |