Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,8,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(4.37339035678\) |
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 | \(\chi\) | \(=\) | 14.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −66.0000 | −1.41130 | −0.705650 | − | 0.708560i | \(-0.749345\pi\) | ||||
−0.705650 | + | 0.708560i | \(0.749345\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −400.000 | −1.43108 | −0.715542 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(6\) | −528.000 | −0.997940 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 2169.00 | 0.991770 | ||||||||
\(10\) | −3200.00 | −1.01193 | ||||||||
\(11\) | 40.0000 | 0.00906120 | 0.00453060 | − | 0.999990i | \(-0.498558\pi\) | ||||
0.00453060 | + | 0.999990i | \(0.498558\pi\) | |||||||
\(12\) | −4224.00 | −0.705650 | ||||||||
\(13\) | −4452.00 | −0.562022 | −0.281011 | − | 0.959705i | \(-0.590670\pi\) | ||||
−0.281011 | + | 0.959705i | \(0.590670\pi\) | |||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 26400.0 | 2.01969 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 36502.0 | 1.80196 | 0.900981 | − | 0.433859i | \(-0.142849\pi\) | ||||
0.900981 | + | 0.433859i | \(0.142849\pi\) | |||||||
\(18\) | 17352.0 | 0.701287 | ||||||||
\(19\) | −46222.0 | −1.54601 | −0.773003 | − | 0.634402i | \(-0.781246\pi\) | ||||
−0.773003 | + | 0.634402i | \(0.781246\pi\) | |||||||
\(20\) | −25600.0 | −0.715542 | ||||||||
\(21\) | 22638.0 | 0.533422 | ||||||||
\(22\) | 320.000 | 0.00640723 | ||||||||
\(23\) | −105200. | −1.80289 | −0.901443 | − | 0.432898i | \(-0.857491\pi\) | ||||
−0.901443 | + | 0.432898i | \(0.857491\pi\) | |||||||
\(24\) | −33792.0 | −0.498970 | ||||||||
\(25\) | 81875.0 | 1.04800 | ||||||||
\(26\) | −35616.0 | −0.397410 | ||||||||
\(27\) | 1188.00 | 0.0116156 | ||||||||
\(28\) | −21952.0 | −0.188982 | ||||||||
\(29\) | −126334. | −0.961894 | −0.480947 | − | 0.876750i | \(-0.659707\pi\) | ||||
−0.480947 | + | 0.876750i | \(0.659707\pi\) | |||||||
\(30\) | 211200. | 1.42814 | ||||||||
\(31\) | −170964. | −1.03072 | −0.515358 | − | 0.856975i | \(-0.672341\pi\) | ||||
−0.515358 | + | 0.856975i | \(0.672341\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −2640.00 | −0.0127881 | ||||||||
\(34\) | 292016. | 1.27418 | ||||||||
\(35\) | 137200. | 0.540899 | ||||||||
\(36\) | 138816. | 0.495885 | ||||||||
\(37\) | 20954.0 | 0.0680081 | 0.0340041 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340041 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(38\) | −369776. | −1.09319 | ||||||||
\(39\) | 293832. | 0.793182 | ||||||||
\(40\) | −204800. | −0.505964 | ||||||||
\(41\) | 318486. | 0.721684 | 0.360842 | − | 0.932627i | \(-0.382489\pi\) | ||||
0.360842 | + | 0.932627i | \(0.382489\pi\) | |||||||
\(42\) | 181104. | 0.377186 | ||||||||
\(43\) | 77744.0 | 0.149117 | 0.0745585 | − | 0.997217i | \(-0.476245\pi\) | ||||
0.0745585 | + | 0.997217i | \(0.476245\pi\) | |||||||
\(44\) | 2560.00 | 0.00453060 | ||||||||
\(45\) | −867600. | −1.41931 | ||||||||
\(46\) | −841600. | −1.27483 | ||||||||
\(47\) | 703716. | 0.988678 | 0.494339 | − | 0.869269i | \(-0.335410\pi\) | ||||
0.494339 | + | 0.869269i | \(0.335410\pi\) | |||||||
\(48\) | −270336. | −0.352825 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 655000. | 0.741048 | ||||||||
\(51\) | −2.40913e6 | −2.54311 | ||||||||
\(52\) | −284928. | −0.281011 | ||||||||
\(53\) | 1.60328e6 | 1.47926 | 0.739628 | − | 0.673016i | \(-0.235002\pi\) | ||||
0.739628 | + | 0.673016i | \(0.235002\pi\) | |||||||
\(54\) | 9504.00 | 0.00821350 | ||||||||
\(55\) | −16000.0 | −0.0129673 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | 3.05065e6 | 2.18188 | ||||||||
\(58\) | −1.01067e6 | −0.680162 | ||||||||
\(59\) | −1.17189e6 | −0.742859 | −0.371429 | − | 0.928461i | \(-0.621132\pi\) | ||||
−0.371429 | + | 0.928461i | \(0.621132\pi\) | |||||||
\(60\) | 1.68960e6 | 1.00984 | ||||||||
\(61\) | −2.06887e6 | −1.16702 | −0.583511 | − | 0.812105i | \(-0.698322\pi\) | ||||
−0.583511 | + | 0.812105i | \(0.698322\pi\) | |||||||
\(62\) | −1.36771e6 | −0.728826 | ||||||||
\(63\) | −743967. | −0.374854 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.78080e6 | 0.804301 | ||||||||
\(66\) | −21120.0 | −0.00904253 | ||||||||
\(67\) | −994268. | −0.403870 | −0.201935 | − | 0.979399i | \(-0.564723\pi\) | ||||
−0.201935 | + | 0.979399i | \(0.564723\pi\) | |||||||
\(68\) | 2.33613e6 | 0.900981 | ||||||||
\(69\) | 6.94320e6 | 2.54441 | ||||||||
\(70\) | 1.09760e6 | 0.382473 | ||||||||
\(71\) | 33280.0 | 0.0110352 | 0.00551759 | − | 0.999985i | \(-0.498244\pi\) | ||||
0.00551759 | + | 0.999985i | \(0.498244\pi\) | |||||||
\(72\) | 1.11053e6 | 0.350643 | ||||||||
\(73\) | −2.97145e6 | −0.894003 | −0.447002 | − | 0.894533i | \(-0.647508\pi\) | ||||
−0.447002 | + | 0.894533i | \(0.647508\pi\) | |||||||
\(74\) | 167632. | 0.0480890 | ||||||||
\(75\) | −5.40375e6 | −1.47904 | ||||||||
\(76\) | −2.95821e6 | −0.773003 | ||||||||
\(77\) | −13720.0 | −0.00342481 | ||||||||
\(78\) | 2.35066e6 | 0.560865 | ||||||||
\(79\) | −2.37617e6 | −0.542228 | −0.271114 | − | 0.962547i | \(-0.587392\pi\) | ||||
−0.271114 | + | 0.962547i | \(0.587392\pi\) | |||||||
\(80\) | −1.63840e6 | −0.357771 | ||||||||
\(81\) | −4.82201e6 | −1.00816 | ||||||||
\(82\) | 2.54789e6 | 0.510307 | ||||||||
\(83\) | −2.12236e6 | −0.407423 | −0.203711 | − | 0.979031i | \(-0.565300\pi\) | ||||
−0.203711 | + | 0.979031i | \(0.565300\pi\) | |||||||
\(84\) | 1.44883e6 | 0.266711 | ||||||||
\(85\) | −1.46008e7 | −2.57876 | ||||||||
\(86\) | 621952. | 0.105442 | ||||||||
\(87\) | 8.33804e6 | 1.35752 | ||||||||
\(88\) | 20480.0 | 0.00320362 | ||||||||
\(89\) | 6.92035e6 | 1.04055 | 0.520275 | − | 0.853999i | \(-0.325830\pi\) | ||||
0.520275 | + | 0.853999i | \(0.325830\pi\) | |||||||
\(90\) | −6.94080e6 | −1.00360 | ||||||||
\(91\) | 1.52704e6 | 0.212424 | ||||||||
\(92\) | −6.73280e6 | −0.901443 | ||||||||
\(93\) | 1.12836e7 | 1.45465 | ||||||||
\(94\) | 5.62973e6 | 0.699101 | ||||||||
\(95\) | 1.84888e7 | 2.21246 | ||||||||
\(96\) | −2.16269e6 | −0.249485 | ||||||||
\(97\) | 4.95271e6 | 0.550988 | 0.275494 | − | 0.961303i | \(-0.411159\pi\) | ||||
0.275494 | + | 0.961303i | \(0.411159\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | 86760.0 | 0.00898662 | ||||||||
\(100\) | 5.24000e6 | 0.524000 | ||||||||
\(101\) | 3.23000e6 | 0.311945 | 0.155972 | − | 0.987761i | \(-0.450149\pi\) | ||||
0.155972 | + | 0.987761i | \(0.450149\pi\) | |||||||
\(102\) | −1.92731e7 | −1.79825 | ||||||||
\(103\) | −1.79909e6 | −0.162227 | −0.0811135 | − | 0.996705i | \(-0.525848\pi\) | ||||
−0.0811135 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(104\) | −2.27942e6 | −0.198705 | ||||||||
\(105\) | −9.05520e6 | −0.763371 | ||||||||
\(106\) | 1.28262e7 | 1.04599 | ||||||||
\(107\) | −1.56429e7 | −1.23445 | −0.617225 | − | 0.786787i | \(-0.711743\pi\) | ||||
−0.617225 | + | 0.786787i | \(0.711743\pi\) | |||||||
\(108\) | 76032.0 | 0.00580782 | ||||||||
\(109\) | −6.31890e6 | −0.467357 | −0.233679 | − | 0.972314i | \(-0.575076\pi\) | ||||
−0.233679 | + | 0.972314i | \(0.575076\pi\) | |||||||
\(110\) | −128000. | −0.00916929 | ||||||||
\(111\) | −1.38296e6 | −0.0959799 | ||||||||
\(112\) | −1.40493e6 | −0.0944911 | ||||||||
\(113\) | −1.02288e7 | −0.666881 | −0.333441 | − | 0.942771i | \(-0.608210\pi\) | ||||
−0.333441 | + | 0.942771i | \(0.608210\pi\) | |||||||
\(114\) | 2.44052e7 | 1.54282 | ||||||||
\(115\) | 4.20800e7 | 2.58008 | ||||||||
\(116\) | −8.08538e6 | −0.480947 | ||||||||
\(117\) | −9.65639e6 | −0.557396 | ||||||||
\(118\) | −9.37515e6 | −0.525281 | ||||||||
\(119\) | −1.25202e7 | −0.681077 | ||||||||
\(120\) | 1.35168e7 | 0.714068 | ||||||||
\(121\) | −1.94856e7 | −0.999918 | ||||||||
\(122\) | −1.65510e7 | −0.825209 | ||||||||
\(123\) | −2.10201e7 | −1.01851 | ||||||||
\(124\) | −1.09417e7 | −0.515358 | ||||||||
\(125\) | −1.50000e6 | −0.0686920 | ||||||||
\(126\) | −5.95174e6 | −0.265062 | ||||||||
\(127\) | 6.00725e6 | 0.260233 | 0.130117 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130117 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −5.13110e6 | −0.210449 | ||||||||
\(130\) | 1.42464e7 | 0.568726 | ||||||||
\(131\) | 2.06396e7 | 0.802144 | 0.401072 | − | 0.916047i | \(-0.368638\pi\) | ||||
0.401072 | + | 0.916047i | \(0.368638\pi\) | |||||||
\(132\) | −168960. | −0.00639404 | ||||||||
\(133\) | 1.58541e7 | 0.584335 | ||||||||
\(134\) | −7.95414e6 | −0.285579 | ||||||||
\(135\) | −475200. | −0.0166230 | ||||||||
\(136\) | 1.86890e7 | 0.637089 | ||||||||
\(137\) | 4.76199e6 | 0.158222 | 0.0791109 | − | 0.996866i | \(-0.474792\pi\) | ||||
0.0791109 | + | 0.996866i | \(0.474792\pi\) | |||||||
\(138\) | 5.55456e7 | 1.79917 | ||||||||
\(139\) | −5.05723e6 | −0.159721 | −0.0798604 | − | 0.996806i | \(-0.525447\pi\) | ||||
−0.0798604 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(140\) | 8.78080e6 | 0.270449 | ||||||||
\(141\) | −4.64453e7 | −1.39532 | ||||||||
\(142\) | 266240. | 0.00780304 | ||||||||
\(143\) | −178080. | −0.00509259 | ||||||||
\(144\) | 8.88422e6 | 0.247942 | ||||||||
\(145\) | 5.05336e7 | 1.37655 | ||||||||
\(146\) | −2.37716e7 | −0.632156 | ||||||||
\(147\) | −7.76483e6 | −0.201614 | ||||||||
\(148\) | 1.34106e6 | 0.0340041 | ||||||||
\(149\) | −2.72736e7 | −0.675447 | −0.337723 | − | 0.941245i | \(-0.609657\pi\) | ||||
−0.337723 | + | 0.941245i | \(0.609657\pi\) | |||||||
\(150\) | −4.32300e7 | −1.04584 | ||||||||
\(151\) | 6.48921e6 | 0.153381 | 0.0766906 | − | 0.997055i | \(-0.475565\pi\) | ||||
0.0766906 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(152\) | −2.36657e7 | −0.546596 | ||||||||
\(153\) | 7.91728e7 | 1.78713 | ||||||||
\(154\) | −109760. | −0.00242171 | ||||||||
\(155\) | 6.83856e7 | 1.47504 | ||||||||
\(156\) | 1.88052e7 | 0.396591 | ||||||||
\(157\) | −6.30810e7 | −1.30092 | −0.650459 | − | 0.759541i | \(-0.725423\pi\) | ||||
−0.650459 | + | 0.759541i | \(0.725423\pi\) | |||||||
\(158\) | −1.90093e7 | −0.383413 | ||||||||
\(159\) | −1.05816e8 | −2.08767 | ||||||||
\(160\) | −1.31072e7 | −0.252982 | ||||||||
\(161\) | 3.60836e7 | 0.681427 | ||||||||
\(162\) | −3.85761e7 | −0.712879 | ||||||||
\(163\) | 8.32271e7 | 1.50525 | 0.752624 | − | 0.658450i | \(-0.228788\pi\) | ||||
0.752624 | + | 0.658450i | \(0.228788\pi\) | |||||||
\(164\) | 2.03831e7 | 0.360842 | ||||||||
\(165\) | 1.05600e6 | 0.0183008 | ||||||||
\(166\) | −1.69789e7 | −0.288091 | ||||||||
\(167\) | 3.06916e7 | 0.509931 | 0.254965 | − | 0.966950i | \(-0.417936\pi\) | ||||
0.254965 | + | 0.966950i | \(0.417936\pi\) | |||||||
\(168\) | 1.15907e7 | 0.188593 | ||||||||
\(169\) | −4.29282e7 | −0.684131 | ||||||||
\(170\) | −1.16806e8 | −1.82346 | ||||||||
\(171\) | −1.00256e8 | −1.53328 | ||||||||
\(172\) | 4.97562e6 | 0.0745585 | ||||||||
\(173\) | −5.27338e7 | −0.774333 | −0.387167 | − | 0.922010i | \(-0.626546\pi\) | ||||
−0.387167 | + | 0.922010i | \(0.626546\pi\) | |||||||
\(174\) | 6.67044e7 | 0.959913 | ||||||||
\(175\) | −2.80831e7 | −0.396107 | ||||||||
\(176\) | 163840. | 0.00226530 | ||||||||
\(177\) | 7.73450e7 | 1.04840 | ||||||||
\(178\) | 5.53628e7 | 0.735780 | ||||||||
\(179\) | 8.42739e7 | 1.09827 | 0.549133 | − | 0.835735i | \(-0.314958\pi\) | ||||
0.549133 | + | 0.835735i | \(0.314958\pi\) | |||||||
\(180\) | −5.55264e7 | −0.709653 | ||||||||
\(181\) | −1.03956e8 | −1.30309 | −0.651547 | − | 0.758608i | \(-0.725880\pi\) | ||||
−0.651547 | + | 0.758608i | \(0.725880\pi\) | |||||||
\(182\) | 1.22163e7 | 0.150207 | ||||||||
\(183\) | 1.36546e8 | 1.64702 | ||||||||
\(184\) | −5.38624e7 | −0.637417 | ||||||||
\(185\) | −8.38160e6 | −0.0973253 | ||||||||
\(186\) | 9.02690e7 | 1.02859 | ||||||||
\(187\) | 1.46008e6 | 0.0163279 | ||||||||
\(188\) | 4.50378e7 | 0.494339 | ||||||||
\(189\) | −407484. | −0.00439030 | ||||||||
\(190\) | 1.47910e8 | 1.56445 | ||||||||
\(191\) | −1.24775e8 | −1.29572 | −0.647861 | − | 0.761759i | \(-0.724336\pi\) | ||||
−0.647861 | + | 0.761759i | \(0.724336\pi\) | |||||||
\(192\) | −1.73015e7 | −0.176413 | ||||||||
\(193\) | 1.47589e8 | 1.47776 | 0.738878 | − | 0.673839i | \(-0.235356\pi\) | ||||
0.738878 | + | 0.673839i | \(0.235356\pi\) | |||||||
\(194\) | 3.96217e7 | 0.389607 | ||||||||
\(195\) | −1.17533e8 | −1.13511 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 1.55812e8 | 1.45200 | 0.726002 | − | 0.687692i | \(-0.241376\pi\) | ||||
0.726002 | + | 0.687692i | \(0.241376\pi\) | |||||||
\(198\) | 694080. | 0.00635450 | ||||||||
\(199\) | −1.33193e7 | −0.119810 | −0.0599052 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599052 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(200\) | 4.19200e7 | 0.370524 | ||||||||
\(201\) | 6.56217e7 | 0.569982 | ||||||||
\(202\) | 2.58400e7 | 0.220578 | ||||||||
\(203\) | 4.33326e7 | 0.363562 | ||||||||
\(204\) | −1.54184e8 | −1.27155 | ||||||||
\(205\) | −1.27394e8 | −1.03279 | ||||||||
\(206\) | −1.43927e7 | −0.114712 | ||||||||
\(207\) | −2.28179e8 | −1.78805 | ||||||||
\(208\) | −1.82354e7 | −0.140506 | ||||||||
\(209\) | −1.84888e6 | −0.0140087 | ||||||||
\(210\) | −7.24416e7 | −0.539785 | ||||||||
\(211\) | −2.04940e8 | −1.50189 | −0.750945 | − | 0.660365i | \(-0.770402\pi\) | ||||
−0.750945 | + | 0.660365i | \(0.770402\pi\) | |||||||
\(212\) | 1.02610e8 | 0.739628 | ||||||||
\(213\) | −2.19648e6 | −0.0155739 | ||||||||
\(214\) | −1.25143e8 | −0.872888 | ||||||||
\(215\) | −3.10976e7 | −0.213399 | ||||||||
\(216\) | 608256. | 0.00410675 | ||||||||
\(217\) | 5.86407e7 | 0.389574 | ||||||||
\(218\) | −5.05512e7 | −0.330471 | ||||||||
\(219\) | 1.96116e8 | 1.26171 | ||||||||
\(220\) | −1.02400e6 | −0.00648367 | ||||||||
\(221\) | −1.62507e8 | −1.01274 | ||||||||
\(222\) | −1.10637e7 | −0.0678681 | ||||||||
\(223\) | −6.84858e7 | −0.413555 | −0.206778 | − | 0.978388i | \(-0.566298\pi\) | ||||
−0.206778 | + | 0.978388i | \(0.566298\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.77587e8 | 1.03937 | ||||||||
\(226\) | −8.18301e7 | −0.471556 | ||||||||
\(227\) | −1.93627e7 | −0.109869 | −0.0549344 | − | 0.998490i | \(-0.517495\pi\) | ||||
−0.0549344 | + | 0.998490i | \(0.517495\pi\) | |||||||
\(228\) | 1.95242e8 | 1.09094 | ||||||||
\(229\) | 3.08157e8 | 1.69569 | 0.847847 | − | 0.530241i | \(-0.177898\pi\) | ||||
0.847847 | + | 0.530241i | \(0.177898\pi\) | |||||||
\(230\) | 3.36640e8 | 1.82439 | ||||||||
\(231\) | 905520. | 0.00483344 | ||||||||
\(232\) | −6.46830e7 | −0.340081 | ||||||||
\(233\) | 3.55797e7 | 0.184271 | 0.0921355 | − | 0.995746i | \(-0.470631\pi\) | ||||
0.0921355 | + | 0.995746i | \(0.470631\pi\) | |||||||
\(234\) | −7.72511e7 | −0.394139 | ||||||||
\(235\) | −2.81486e8 | −1.41488 | ||||||||
\(236\) | −7.50012e7 | −0.371429 | ||||||||
\(237\) | 1.56827e8 | 0.765247 | ||||||||
\(238\) | −1.00161e8 | −0.481594 | ||||||||
\(239\) | −2.30056e8 | −1.09004 | −0.545018 | − | 0.838424i | \(-0.683477\pi\) | ||||
−0.545018 | + | 0.838424i | \(0.683477\pi\) | |||||||
\(240\) | 1.08134e8 | 0.504922 | ||||||||
\(241\) | 5.03495e6 | 0.0231705 | 0.0115853 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115853 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(242\) | −1.55885e8 | −0.707049 | ||||||||
\(243\) | 3.15655e8 | 1.41121 | ||||||||
\(244\) | −1.32408e8 | −0.583511 | ||||||||
\(245\) | −4.70596e7 | −0.204441 | ||||||||
\(246\) | −1.68161e8 | −0.720197 | ||||||||
\(247\) | 2.05780e8 | 0.868890 | ||||||||
\(248\) | −8.75336e7 | −0.364413 | ||||||||
\(249\) | 1.40076e8 | 0.574996 | ||||||||
\(250\) | −1.20000e7 | −0.0485726 | ||||||||
\(251\) | −1.03283e8 | −0.412258 | −0.206129 | − | 0.978525i | \(-0.566087\pi\) | ||||
−0.206129 | + | 0.978525i | \(0.566087\pi\) | |||||||
\(252\) | −4.76139e7 | −0.187427 | ||||||||
\(253\) | −4.20800e6 | −0.0163363 | ||||||||
\(254\) | 4.80580e7 | 0.184013 | ||||||||
\(255\) | 9.63653e8 | 3.63940 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.32282e8 | −0.853592 | −0.426796 | − | 0.904348i | \(-0.640358\pi\) | ||||
−0.426796 | + | 0.904348i | \(0.640358\pi\) | |||||||
\(258\) | −4.10488e7 | −0.148810 | ||||||||
\(259\) | −7.18722e6 | −0.0257047 | ||||||||
\(260\) | 1.13971e8 | 0.402150 | ||||||||
\(261\) | −2.74018e8 | −0.953977 | ||||||||
\(262\) | 1.65117e8 | 0.567201 | ||||||||
\(263\) | 4.16749e8 | 1.41263 | 0.706317 | − | 0.707896i | \(-0.250356\pi\) | ||||
0.706317 | + | 0.707896i | \(0.250356\pi\) | |||||||
\(264\) | −1.35168e6 | −0.00452127 | ||||||||
\(265\) | −6.41311e8 | −2.11694 | ||||||||
\(266\) | 1.26833e8 | 0.413187 | ||||||||
\(267\) | −4.56743e8 | −1.46853 | ||||||||
\(268\) | −6.36332e7 | −0.201935 | ||||||||
\(269\) | −3.14679e8 | −0.985676 | −0.492838 | − | 0.870121i | \(-0.664041\pi\) | ||||
−0.492838 | + | 0.870121i | \(0.664041\pi\) | |||||||
\(270\) | −3.80160e6 | −0.0117542 | ||||||||
\(271\) | 1.92137e8 | 0.586433 | 0.293216 | − | 0.956046i | \(-0.405274\pi\) | ||||
0.293216 | + | 0.956046i | \(0.405274\pi\) | |||||||
\(272\) | 1.49512e8 | 0.450490 | ||||||||
\(273\) | −1.00784e8 | −0.299795 | ||||||||
\(274\) | 3.80959e7 | 0.111880 | ||||||||
\(275\) | 3.27500e6 | 0.00949613 | ||||||||
\(276\) | 4.44365e8 | 1.27221 | ||||||||
\(277\) | −4.40393e8 | −1.24498 | −0.622489 | − | 0.782629i | \(-0.713878\pi\) | ||||
−0.622489 | + | 0.782629i | \(0.713878\pi\) | |||||||
\(278\) | −4.04579e7 | −0.112940 | ||||||||
\(279\) | −3.70821e8 | −1.02223 | ||||||||
\(280\) | 7.02464e7 | 0.191237 | ||||||||
\(281\) | 3.59235e8 | 0.965842 | 0.482921 | − | 0.875664i | \(-0.339576\pi\) | ||||
0.482921 | + | 0.875664i | \(0.339576\pi\) | |||||||
\(282\) | −3.71562e8 | −0.986642 | ||||||||
\(283\) | −8.11467e7 | −0.212823 | −0.106411 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106411 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(284\) | 2.12992e6 | 0.00551759 | ||||||||
\(285\) | −1.22026e9 | −3.12245 | ||||||||
\(286\) | −1.42464e6 | −0.00360101 | ||||||||
\(287\) | −1.09241e8 | −0.272771 | ||||||||
\(288\) | 7.10738e7 | 0.175322 | ||||||||
\(289\) | 9.22057e8 | 2.24706 | ||||||||
\(290\) | 4.04269e8 | 0.973368 | ||||||||
\(291\) | −3.26879e8 | −0.777609 | ||||||||
\(292\) | −1.90173e8 | −0.447002 | ||||||||
\(293\) | 2.53416e8 | 0.588569 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(294\) | −6.21187e7 | −0.142563 | ||||||||
\(295\) | 4.68758e8 | 1.06309 | ||||||||
\(296\) | 1.07284e7 | 0.0240445 | ||||||||
\(297\) | 47520.0 | 0.000105252 0 | ||||||||
\(298\) | −2.18189e8 | −0.477613 | ||||||||
\(299\) | 4.68350e8 | 1.01326 | ||||||||
\(300\) | −3.45840e8 | −0.739522 | ||||||||
\(301\) | −2.66662e7 | −0.0563609 | ||||||||
\(302\) | 5.19137e7 | 0.108457 | ||||||||
\(303\) | −2.13180e8 | −0.440248 | ||||||||
\(304\) | −1.89325e8 | −0.386501 | ||||||||
\(305\) | 8.27549e8 | 1.67011 | ||||||||
\(306\) | 6.33383e8 | 1.26369 | ||||||||
\(307\) | 8.72706e8 | 1.72141 | 0.860703 | − | 0.509107i | \(-0.170024\pi\) | ||||
0.860703 | + | 0.509107i | \(0.170024\pi\) | |||||||
\(308\) | −878080. | −0.00171241 | ||||||||
\(309\) | 1.18740e8 | 0.228951 | ||||||||
\(310\) | 5.47085e8 | 1.04301 | ||||||||
\(311\) | −6.71611e8 | −1.26607 | −0.633033 | − | 0.774124i | \(-0.718190\pi\) | ||||
−0.633033 | + | 0.774124i | \(0.718190\pi\) | |||||||
\(312\) | 1.50442e8 | 0.280432 | ||||||||
\(313\) | −1.92216e8 | −0.354312 | −0.177156 | − | 0.984183i | \(-0.556690\pi\) | ||||
−0.177156 | + | 0.984183i | \(0.556690\pi\) | |||||||
\(314\) | −5.04648e8 | −0.919888 | ||||||||
\(315\) | 2.97587e8 | 0.536447 | ||||||||
\(316\) | −1.52075e8 | −0.271114 | ||||||||
\(317\) | −1.33837e8 | −0.235977 | −0.117988 | − | 0.993015i | \(-0.537645\pi\) | ||||
−0.117988 | + | 0.993015i | \(0.537645\pi\) | |||||||
\(318\) | −8.46531e8 | −1.47621 | ||||||||
\(319\) | −5.05336e6 | −0.00871591 | ||||||||
\(320\) | −1.04858e8 | −0.178885 | ||||||||
\(321\) | 1.03243e9 | 1.74218 | ||||||||
\(322\) | 2.88669e8 | 0.481842 | ||||||||
\(323\) | −1.68720e9 | −2.78584 | ||||||||
\(324\) | −3.08609e8 | −0.504081 | ||||||||
\(325\) | −3.64508e8 | −0.588999 | ||||||||
\(326\) | 6.65817e8 | 1.06437 | ||||||||
\(327\) | 4.17048e8 | 0.659581 | ||||||||
\(328\) | 1.63065e8 | 0.255154 | ||||||||
\(329\) | −2.41375e8 | −0.373685 | ||||||||
\(330\) | 8.44800e6 | 0.0129406 | ||||||||
\(331\) | 4.25298e8 | 0.644608 | 0.322304 | − | 0.946636i | \(-0.395543\pi\) | ||||
0.322304 | + | 0.946636i | \(0.395543\pi\) | |||||||
\(332\) | −1.35831e8 | −0.203711 | ||||||||
\(333\) | 4.54492e7 | 0.0674484 | ||||||||
\(334\) | 2.45532e8 | 0.360576 | ||||||||
\(335\) | 3.97707e8 | 0.577972 | ||||||||
\(336\) | 9.27252e7 | 0.133355 | ||||||||
\(337\) | 1.07703e9 | 1.53293 | 0.766463 | − | 0.642288i | \(-0.222015\pi\) | ||||
0.766463 | + | 0.642288i | \(0.222015\pi\) | |||||||
\(338\) | −3.43426e8 | −0.483754 | ||||||||
\(339\) | 6.75098e8 | 0.941170 | ||||||||
\(340\) | −9.34451e8 | −1.28938 | ||||||||
\(341\) | −6.83856e6 | −0.00933952 | ||||||||
\(342\) | −8.02044e8 | −1.08419 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 3.98049e7 | 0.0527208 | ||||||||
\(345\) | −2.77728e9 | −3.64127 | ||||||||
\(346\) | −4.21871e8 | −0.547536 | ||||||||
\(347\) | −7.23764e8 | −0.929916 | −0.464958 | − | 0.885333i | \(-0.653931\pi\) | ||||
−0.464958 | + | 0.885333i | \(0.653931\pi\) | |||||||
\(348\) | 5.33635e8 | 0.678761 | ||||||||
\(349\) | −4.48132e8 | −0.564310 | −0.282155 | − | 0.959369i | \(-0.591049\pi\) | ||||
−0.282155 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(350\) | −2.24665e8 | −0.280090 | ||||||||
\(351\) | −5.28898e6 | −0.00652825 | ||||||||
\(352\) | 1.31072e6 | 0.00160181 | ||||||||
\(353\) | −1.49946e9 | −1.81435 | −0.907177 | − | 0.420749i | \(-0.861767\pi\) | ||||
−0.907177 | + | 0.420749i | \(0.861767\pi\) | |||||||
\(354\) | 6.18760e8 | 0.741329 | ||||||||
\(355\) | −1.33120e7 | −0.0157923 | ||||||||
\(356\) | 4.42902e8 | 0.520275 | ||||||||
\(357\) | 8.26332e8 | 0.961205 | ||||||||
\(358\) | 6.74191e8 | 0.776591 | ||||||||
\(359\) | −2.56890e8 | −0.293033 | −0.146516 | − | 0.989208i | \(-0.546806\pi\) | ||||
−0.146516 | + | 0.989208i | \(0.546806\pi\) | |||||||
\(360\) | −4.44211e8 | −0.501800 | ||||||||
\(361\) | 1.24260e9 | 1.39013 | ||||||||
\(362\) | −8.31650e8 | −0.921427 | ||||||||
\(363\) | 1.28605e9 | 1.41118 | ||||||||
\(364\) | 9.77303e7 | 0.106212 | ||||||||
\(365\) | 1.18858e9 | 1.27939 | ||||||||
\(366\) | 1.09236e9 | 1.16462 | ||||||||
\(367\) | 6.50424e8 | 0.686856 | 0.343428 | − | 0.939179i | \(-0.388412\pi\) | ||||
0.343428 | + | 0.939179i | \(0.388412\pi\) | |||||||
\(368\) | −4.30899e8 | −0.450722 | ||||||||
\(369\) | 6.90796e8 | 0.715744 | ||||||||
\(370\) | −6.70528e7 | −0.0688194 | ||||||||
\(371\) | −5.49924e8 | −0.559106 | ||||||||
\(372\) | 7.22152e8 | 0.727325 | ||||||||
\(373\) | −4.66127e8 | −0.465076 | −0.232538 | − | 0.972587i | \(-0.574703\pi\) | ||||
−0.232538 | + | 0.972587i | \(0.574703\pi\) | |||||||
\(374\) | 1.16806e7 | 0.0115456 | ||||||||
\(375\) | 9.90000e7 | 0.0969451 | ||||||||
\(376\) | 3.60303e8 | 0.349551 | ||||||||
\(377\) | 5.62439e8 | 0.540606 | ||||||||
\(378\) | −3.25987e6 | −0.00310441 | ||||||||
\(379\) | 2.85860e8 | 0.269721 | 0.134861 | − | 0.990865i | \(-0.456941\pi\) | ||||
0.134861 | + | 0.990865i | \(0.456941\pi\) | |||||||
\(380\) | 1.18328e9 | 1.10623 | ||||||||
\(381\) | −3.96478e8 | −0.367267 | ||||||||
\(382\) | −9.98202e8 | −0.916213 | ||||||||
\(383\) | −1.65075e9 | −1.50136 | −0.750681 | − | 0.660665i | \(-0.770275\pi\) | ||||
−0.750681 | + | 0.660665i | \(0.770275\pi\) | |||||||
\(384\) | −1.38412e8 | −0.124743 | ||||||||
\(385\) | 5.48800e6 | 0.00490119 | ||||||||
\(386\) | 1.18071e9 | 1.04493 | ||||||||
\(387\) | 1.68627e8 | 0.147890 | ||||||||
\(388\) | 3.16973e8 | 0.275494 | ||||||||
\(389\) | 1.51304e9 | 1.30325 | 0.651624 | − | 0.758542i | \(-0.274088\pi\) | ||||
0.651624 | + | 0.758542i | \(0.274088\pi\) | |||||||
\(390\) | −9.40262e8 | −0.802644 | ||||||||
\(391\) | −3.84001e9 | −3.24873 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | −1.36221e9 | −1.13207 | ||||||||
\(394\) | 1.24649e9 | 1.02672 | ||||||||
\(395\) | 9.50467e8 | 0.775974 | ||||||||
\(396\) | 5.55264e6 | 0.00449331 | ||||||||
\(397\) | −8.63794e8 | −0.692857 | −0.346428 | − | 0.938076i | \(-0.612606\pi\) | ||||
−0.346428 | + | 0.938076i | \(0.612606\pi\) | |||||||
\(398\) | −1.06554e8 | −0.0847187 | ||||||||
\(399\) | −1.04637e9 | −0.824673 | ||||||||
\(400\) | 3.35360e8 | 0.262000 | ||||||||
\(401\) | 1.14042e8 | 0.0883199 | 0.0441599 | − | 0.999024i | \(-0.485939\pi\) | ||||
0.0441599 | + | 0.999024i | \(0.485939\pi\) | |||||||
\(402\) | 5.24974e8 | 0.403038 | ||||||||
\(403\) | 7.61132e8 | 0.579285 | ||||||||
\(404\) | 2.06720e8 | 0.155972 | ||||||||
\(405\) | 1.92880e9 | 1.44277 | ||||||||
\(406\) | 3.46660e8 | 0.257077 | ||||||||
\(407\) | 838160. | 0.000616235 0 | ||||||||
\(408\) | −1.23348e9 | −0.899125 | ||||||||
\(409\) | −1.18328e9 | −0.855176 | −0.427588 | − | 0.903974i | \(-0.640637\pi\) | ||||
−0.427588 | + | 0.903974i | \(0.640637\pi\) | |||||||
\(410\) | −1.01916e9 | −0.730292 | ||||||||
\(411\) | −3.14291e8 | −0.223298 | ||||||||
\(412\) | −1.15142e8 | −0.0811135 | ||||||||
\(413\) | 4.01960e8 | 0.280774 | ||||||||
\(414\) | −1.82543e9 | −1.26434 | ||||||||
\(415\) | 8.48943e8 | 0.583056 | ||||||||
\(416\) | −1.45883e8 | −0.0993524 | ||||||||
\(417\) | 3.33777e8 | 0.225414 | ||||||||
\(418\) | −1.47910e7 | −0.00990562 | ||||||||
\(419\) | 2.27959e8 | 0.151394 | 0.0756970 | − | 0.997131i | \(-0.475882\pi\) | ||||
0.0756970 | + | 0.997131i | \(0.475882\pi\) | |||||||
\(420\) | −5.79533e8 | −0.381685 | ||||||||
\(421\) | −3.90700e7 | −0.0255186 | −0.0127593 | − | 0.999919i | \(-0.504062\pi\) | ||||
−0.0127593 | + | 0.999919i | \(0.504062\pi\) | |||||||
\(422\) | −1.63952e9 | −1.06200 | ||||||||
\(423\) | 1.52636e9 | 0.980541 | ||||||||
\(424\) | 8.20878e8 | 0.522996 | ||||||||
\(425\) | 2.98860e9 | 1.88846 | ||||||||
\(426\) | −1.75718e7 | −0.0110124 | ||||||||
\(427\) | 7.09623e8 | 0.441093 | ||||||||
\(428\) | −1.00114e9 | −0.617225 | ||||||||
\(429\) | 1.17533e7 | 0.00718718 | ||||||||
\(430\) | −2.48781e8 | −0.150896 | ||||||||
\(431\) | −2.58620e9 | −1.55594 | −0.777968 | − | 0.628304i | \(-0.783749\pi\) | ||||
−0.777968 | + | 0.628304i | \(0.783749\pi\) | |||||||
\(432\) | 4.86605e6 | 0.00290391 | ||||||||
\(433\) | −1.78893e9 | −1.05897 | −0.529486 | − | 0.848318i | \(-0.677615\pi\) | ||||
−0.529486 | + | 0.848318i | \(0.677615\pi\) | |||||||
\(434\) | 4.69125e8 | 0.275470 | ||||||||
\(435\) | −3.33522e9 | −1.94273 | ||||||||
\(436\) | −4.04410e8 | −0.233679 | ||||||||
\(437\) | 4.86255e9 | 2.78727 | ||||||||
\(438\) | 1.56893e9 | 0.892162 | ||||||||
\(439\) | −4.58905e8 | −0.258879 | −0.129440 | − | 0.991587i | \(-0.541318\pi\) | ||||
−0.129440 | + | 0.991587i | \(0.541318\pi\) | |||||||
\(440\) | −8.19200e6 | −0.00458464 | ||||||||
\(441\) | 2.55181e8 | 0.141681 | ||||||||
\(442\) | −1.30006e9 | −0.716117 | ||||||||
\(443\) | 1.38459e9 | 0.756672 | 0.378336 | − | 0.925668i | \(-0.376496\pi\) | ||||
0.378336 | + | 0.925668i | \(0.376496\pi\) | |||||||
\(444\) | −8.85097e7 | −0.0479900 | ||||||||
\(445\) | −2.76814e9 | −1.48911 | ||||||||
\(446\) | −5.47887e8 | −0.292428 | ||||||||
\(447\) | 1.80006e9 | 0.953259 | ||||||||
\(448\) | −8.99154e7 | −0.0472456 | ||||||||
\(449\) | −2.73611e9 | −1.42650 | −0.713248 | − | 0.700911i | \(-0.752777\pi\) | ||||
−0.713248 | + | 0.700911i | \(0.752777\pi\) | |||||||
\(450\) | 1.42070e9 | 0.734949 | ||||||||
\(451\) | 1.27394e7 | 0.00653932 | ||||||||
\(452\) | −6.54641e8 | −0.333441 | ||||||||
\(453\) | −4.28288e8 | −0.216467 | ||||||||
\(454\) | −1.54901e8 | −0.0776890 | ||||||||
\(455\) | −6.10814e8 | −0.303997 | ||||||||
\(456\) | 1.56193e9 | 0.771411 | ||||||||
\(457\) | 2.43053e9 | 1.19123 | 0.595614 | − | 0.803271i | \(-0.296909\pi\) | ||||
0.595614 | + | 0.803271i | \(0.296909\pi\) | |||||||
\(458\) | 2.46525e9 | 1.19904 | ||||||||
\(459\) | 4.33644e7 | 0.0209309 | ||||||||
\(460\) | 2.69312e9 | 1.29004 | ||||||||
\(461\) | 3.94884e9 | 1.87723 | 0.938613 | − | 0.344971i | \(-0.112111\pi\) | ||||
0.938613 | + | 0.344971i | \(0.112111\pi\) | |||||||
\(462\) | 7.24416e6 | 0.00341776 | ||||||||
\(463\) | 2.57453e9 | 1.20549 | 0.602746 | − | 0.797933i | \(-0.294073\pi\) | ||||
0.602746 | + | 0.797933i | \(0.294073\pi\) | |||||||
\(464\) | −5.17464e8 | −0.240474 | ||||||||
\(465\) | −4.51345e9 | −2.08172 | ||||||||
\(466\) | 2.84638e8 | 0.130299 | ||||||||
\(467\) | 2.98482e8 | 0.135616 | 0.0678078 | − | 0.997698i | \(-0.478400\pi\) | ||||
0.0678078 | + | 0.997698i | \(0.478400\pi\) | |||||||
\(468\) | −6.18009e8 | −0.278698 | ||||||||
\(469\) | 3.41034e8 | 0.152649 | ||||||||
\(470\) | −2.25189e9 | −1.00047 | ||||||||
\(471\) | 4.16335e9 | 1.83599 | ||||||||
\(472\) | −6.00010e8 | −0.262640 | ||||||||
\(473\) | 3.10976e6 | 0.00135118 | ||||||||
\(474\) | 1.25462e9 | 0.541112 | ||||||||
\(475\) | −3.78443e9 | −1.62021 | ||||||||
\(476\) | −8.01292e8 | −0.340539 | ||||||||
\(477\) | 3.47751e9 | 1.46708 | ||||||||
\(478\) | −1.84045e9 | −0.770772 | ||||||||
\(479\) | 2.62000e9 | 1.08925 | 0.544625 | − | 0.838680i | \(-0.316672\pi\) | ||||
0.544625 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(480\) | 8.65075e8 | 0.357034 | ||||||||
\(481\) | −9.32872e7 | −0.0382221 | ||||||||
\(482\) | 4.02796e7 | 0.0163840 | ||||||||
\(483\) | −2.38152e9 | −0.961698 | ||||||||
\(484\) | −1.24708e9 | −0.499959 | ||||||||
\(485\) | −1.98108e9 | −0.788509 | ||||||||
\(486\) | 2.52524e9 | 0.997873 | ||||||||
\(487\) | −4.16662e9 | −1.63468 | −0.817339 | − | 0.576157i | \(-0.804552\pi\) | ||||
−0.817339 | + | 0.576157i | \(0.804552\pi\) | |||||||
\(488\) | −1.05926e9 | −0.412605 | ||||||||
\(489\) | −5.49299e9 | −2.12436 | ||||||||
\(490\) | −3.76477e8 | −0.144561 | ||||||||
\(491\) | 2.41300e9 | 0.919967 | 0.459983 | − | 0.887928i | \(-0.347855\pi\) | ||||
0.459983 | + | 0.887928i | \(0.347855\pi\) | |||||||
\(492\) | −1.34528e9 | −0.509256 | ||||||||
\(493\) | −4.61144e9 | −1.73330 | ||||||||
\(494\) | 1.64624e9 | 0.614398 | ||||||||
\(495\) | −3.47040e7 | −0.0128606 | ||||||||
\(496\) | −7.00269e8 | −0.257679 | ||||||||
\(497\) | −1.14150e7 | −0.00417090 | ||||||||
\(498\) | 1.12061e9 | 0.406584 | ||||||||
\(499\) | −1.04092e9 | −0.375029 | −0.187515 | − | 0.982262i | \(-0.560043\pi\) | ||||
−0.187515 | + | 0.982262i | \(0.560043\pi\) | |||||||
\(500\) | −9.60000e7 | −0.0343460 | ||||||||
\(501\) | −2.02564e9 | −0.719666 | ||||||||
\(502\) | −8.26261e8 | −0.291510 | ||||||||
\(503\) | −1.17273e9 | −0.410876 | −0.205438 | − | 0.978670i | \(-0.565862\pi\) | ||||
−0.205438 | + | 0.978670i | \(0.565862\pi\) | |||||||
\(504\) | −3.80911e8 | −0.132531 | ||||||||
\(505\) | −1.29200e9 | −0.446419 | ||||||||
\(506\) | −3.36640e7 | −0.0115515 | ||||||||
\(507\) | 2.83326e9 | 0.965515 | ||||||||
\(508\) | 3.84464e8 | 0.130117 | ||||||||
\(509\) | −8.13818e7 | −0.0273536 | −0.0136768 | − | 0.999906i | \(-0.504354\pi\) | ||||
−0.0136768 | + | 0.999906i | \(0.504354\pi\) | |||||||
\(510\) | 7.70922e9 | 2.57345 | ||||||||
\(511\) | 1.01921e9 | 0.337901 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −5.49117e7 | −0.0179579 | ||||||||
\(514\) | −1.85826e9 | −0.603580 | ||||||||
\(515\) | 7.19637e8 | 0.232160 | ||||||||
\(516\) | −3.28391e8 | −0.105224 | ||||||||
\(517\) | 2.81486e7 | 0.00895861 | ||||||||
\(518\) | −5.74978e7 | −0.0181759 | ||||||||
\(519\) | 3.48043e9 | 1.09282 | ||||||||
\(520\) | 9.11770e8 | 0.284363 | ||||||||
\(521\) | −2.77458e9 | −0.859540 | −0.429770 | − | 0.902939i | \(-0.641405\pi\) | ||||
−0.429770 | + | 0.902939i | \(0.641405\pi\) | |||||||
\(522\) | −2.19215e9 | −0.674564 | ||||||||
\(523\) | 4.99213e9 | 1.52591 | 0.762957 | − | 0.646449i | \(-0.223747\pi\) | ||||
0.762957 | + | 0.646449i | \(0.223747\pi\) | |||||||
\(524\) | 1.32094e9 | 0.401072 | ||||||||
\(525\) | 1.85349e9 | 0.559026 | ||||||||
\(526\) | 3.33399e9 | 0.998883 | ||||||||
\(527\) | −6.24053e9 | −1.85731 | ||||||||
\(528\) | −1.08134e7 | −0.00319702 | ||||||||
\(529\) | 7.66221e9 | 2.25040 | ||||||||
\(530\) | −5.13049e9 | −1.49690 | ||||||||
\(531\) | −2.54184e9 | −0.736745 | ||||||||
\(532\) | 1.01467e9 | 0.292168 | ||||||||
\(533\) | −1.41790e9 | −0.405602 | ||||||||
\(534\) | −3.65394e9 | −1.03841 | ||||||||
\(535\) | 6.25715e9 | 1.76660 | ||||||||
\(536\) | −5.09065e8 | −0.142790 | ||||||||
\(537\) | −5.56207e9 | −1.54998 | ||||||||
\(538\) | −2.51743e9 | −0.696978 | ||||||||
\(539\) | 4.70596e6 | 0.00129446 | ||||||||
\(540\) | −3.04128e7 | −0.00831148 | ||||||||
\(541\) | 1.63095e9 | 0.442844 | 0.221422 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221422 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(542\) | 1.53710e9 | 0.414671 | ||||||||
\(543\) | 6.86112e9 | 1.83906 | ||||||||
\(544\) | 1.19610e9 | 0.318545 | ||||||||
\(545\) | 2.52756e9 | 0.668827 | ||||||||
\(546\) | −8.06275e8 | −0.211987 | ||||||||
\(547\) | 2.00950e9 | 0.524967 | 0.262484 | − | 0.964936i | \(-0.415458\pi\) | ||||
0.262484 | + | 0.964936i | \(0.415458\pi\) | |||||||
\(548\) | 3.04767e8 | 0.0791109 | ||||||||
\(549\) | −4.48738e9 | −1.15742 | ||||||||
\(550\) | 2.62000e7 | 0.00671478 | ||||||||
\(551\) | 5.83941e9 | 1.48709 | ||||||||
\(552\) | 3.55492e9 | 0.899586 | ||||||||
\(553\) | 8.15026e8 | 0.204943 | ||||||||
\(554\) | −3.52315e9 | −0.880332 | ||||||||
\(555\) | 5.53186e8 | 0.137355 | ||||||||
\(556\) | −3.23663e8 | −0.0798604 | ||||||||
\(557\) | −4.47959e9 | −1.09836 | −0.549180 | − | 0.835704i | \(-0.685060\pi\) | ||||
−0.549180 | + | 0.835704i | \(0.685060\pi\) | |||||||
\(558\) | −2.96657e9 | −0.722827 | ||||||||
\(559\) | −3.46116e8 | −0.0838071 | ||||||||
\(560\) | 5.61971e8 | 0.135225 | ||||||||
\(561\) | −9.63653e7 | −0.0230436 | ||||||||
\(562\) | 2.87388e9 | 0.682954 | ||||||||
\(563\) | −1.50730e9 | −0.355976 | −0.177988 | − | 0.984033i | \(-0.556959\pi\) | ||||
−0.177988 | + | 0.984033i | \(0.556959\pi\) | |||||||
\(564\) | −2.97250e9 | −0.697661 | ||||||||
\(565\) | 4.09150e9 | 0.954363 | ||||||||
\(566\) | −6.49174e8 | −0.150489 | ||||||||
\(567\) | 1.65395e9 | 0.381050 | ||||||||
\(568\) | 1.70394e7 | 0.00390152 | ||||||||
\(569\) | 2.33088e9 | 0.530428 | 0.265214 | − | 0.964190i | \(-0.414557\pi\) | ||||
0.265214 | + | 0.964190i | \(0.414557\pi\) | |||||||
\(570\) | −9.76209e9 | −2.20791 | ||||||||
\(571\) | −2.91101e9 | −0.654362 | −0.327181 | − | 0.944962i | \(-0.606099\pi\) | ||||
−0.327181 | + | 0.944962i | \(0.606099\pi\) | |||||||
\(572\) | −1.13971e7 | −0.00254630 | ||||||||
\(573\) | 8.23517e9 | 1.82865 | ||||||||
\(574\) | −8.73926e8 | −0.192878 | ||||||||
\(575\) | −8.61325e9 | −1.88942 | ||||||||
\(576\) | 5.68590e8 | 0.123971 | ||||||||
\(577\) | −8.64805e9 | −1.87414 | −0.937072 | − | 0.349137i | \(-0.886475\pi\) | ||||
−0.937072 | + | 0.349137i | \(0.886475\pi\) | |||||||
\(578\) | 7.37646e9 | 1.58891 | ||||||||
\(579\) | −9.74086e9 | −2.08556 | ||||||||
\(580\) | 3.23415e9 | 0.688275 | ||||||||
\(581\) | 7.27969e8 | 0.153991 | ||||||||
\(582\) | −2.61503e9 | −0.549853 | ||||||||
\(583\) | 6.41311e7 | 0.0134038 | ||||||||
\(584\) | −1.52138e9 | −0.316078 | ||||||||
\(585\) | 3.86256e9 | 0.797681 | ||||||||
\(586\) | 2.02733e9 | 0.416181 | ||||||||
\(587\) | −6.33513e9 | −1.29277 | −0.646387 | − | 0.763010i | \(-0.723721\pi\) | ||||
−0.646387 | + | 0.763010i | \(0.723721\pi\) | |||||||
\(588\) | −4.96949e8 | −0.100807 | ||||||||
\(589\) | 7.90230e9 | 1.59349 | ||||||||
\(590\) | 3.75006e9 | 0.751720 | ||||||||
\(591\) | −1.02836e10 | −2.04921 | ||||||||
\(592\) | 8.58276e7 | 0.0170020 | ||||||||
\(593\) | −1.70162e9 | −0.335098 | −0.167549 | − | 0.985864i | \(-0.553585\pi\) | ||||
−0.167549 | + | 0.985864i | \(0.553585\pi\) | |||||||
\(594\) | 380160. | 7.44241e−5 0 | ||||||||
\(595\) | 5.00807e9 | 0.974679 | ||||||||
\(596\) | −1.74551e9 | −0.337723 | ||||||||
\(597\) | 8.79071e8 | 0.169088 | ||||||||
\(598\) | 3.74680e9 | 0.716484 | ||||||||
\(599\) | 3.01977e9 | 0.574090 | 0.287045 | − | 0.957917i | \(-0.407327\pi\) | ||||
0.287045 | + | 0.957917i | \(0.407327\pi\) | |||||||
\(600\) | −2.76672e9 | −0.522921 | ||||||||
\(601\) | −5.92708e9 | −1.11373 | −0.556865 | − | 0.830603i | \(-0.687996\pi\) | ||||
−0.556865 | + | 0.830603i | \(0.687996\pi\) | |||||||
\(602\) | −2.13330e8 | −0.0398532 | ||||||||
\(603\) | −2.15657e9 | −0.400546 | ||||||||
\(604\) | 4.15309e8 | 0.0766906 | ||||||||
\(605\) | 7.79423e9 | 1.43097 | ||||||||
\(606\) | −1.70544e9 | −0.311302 | ||||||||
\(607\) | −1.45649e9 | −0.264331 | −0.132165 | − | 0.991228i | \(-0.542193\pi\) | ||||
−0.132165 | + | 0.991228i | \(0.542193\pi\) | |||||||
\(608\) | −1.51460e9 | −0.273298 | ||||||||
\(609\) | −2.85995e9 | −0.513095 | ||||||||
\(610\) | 6.62039e9 | 1.18094 | ||||||||
\(611\) | −3.13294e9 | −0.555659 | ||||||||
\(612\) | 5.06706e9 | 0.893565 | ||||||||
\(613\) | −6.71607e9 | −1.17762 | −0.588808 | − | 0.808273i | \(-0.700403\pi\) | ||||
−0.588808 | + | 0.808273i | \(0.700403\pi\) | |||||||
\(614\) | 6.98164e9 | 1.21722 | ||||||||
\(615\) | 8.40803e9 | 1.45758 | ||||||||
\(616\) | −7.02464e6 | −0.00121085 | ||||||||
\(617\) | 7.02027e9 | 1.20325 | 0.601625 | − | 0.798779i | \(-0.294520\pi\) | ||||
0.601625 | + | 0.798779i | \(0.294520\pi\) | |||||||
\(618\) | 9.49921e8 | 0.161893 | ||||||||
\(619\) | 5.14352e9 | 0.871652 | 0.435826 | − | 0.900031i | \(-0.356456\pi\) | ||||
0.435826 | + | 0.900031i | \(0.356456\pi\) | |||||||
\(620\) | 4.37668e9 | 0.737520 | ||||||||
\(621\) | −1.24978e8 | −0.0209417 | ||||||||
\(622\) | −5.37289e9 | −0.895245 | ||||||||
\(623\) | −2.37368e9 | −0.393291 | ||||||||
\(624\) | 1.20354e9 | 0.198296 | ||||||||
\(625\) | −5.79648e9 | −0.949696 | ||||||||
\(626\) | −1.53773e9 | −0.250536 | ||||||||
\(627\) | 1.22026e8 | 0.0197704 | ||||||||
\(628\) | −4.03719e9 | −0.650459 | ||||||||
\(629\) | 7.64863e8 | 0.122548 | ||||||||
\(630\) | 2.38069e9 | 0.379325 | ||||||||
\(631\) | −4.41574e9 | −0.699681 | −0.349841 | − | 0.936809i | \(-0.613764\pi\) | ||||
−0.349841 | + | 0.936809i | \(0.613764\pi\) | |||||||
\(632\) | −1.21660e9 | −0.191707 | ||||||||
\(633\) | 1.35260e10 | 2.11962 | ||||||||
\(634\) | −1.07070e9 | −0.166861 | ||||||||
\(635\) | −2.40290e9 | −0.372415 | ||||||||
\(636\) | −6.77225e9 | −1.04384 | ||||||||
\(637\) | −5.23773e8 | −0.0802889 | ||||||||
\(638\) | −4.04269e7 | −0.00616308 | ||||||||
\(639\) | 7.21843e7 | 0.0109443 | ||||||||
\(640\) | −8.38861e8 | −0.126491 | ||||||||
\(641\) | 6.94176e8 | 0.104104 | 0.0520519 | − | 0.998644i | \(-0.483424\pi\) | ||||
0.0520519 | + | 0.998644i | \(0.483424\pi\) | |||||||
\(642\) | 8.25944e9 | 1.23191 | ||||||||
\(643\) | 9.50809e9 | 1.41044 | 0.705220 | − | 0.708988i | \(-0.250848\pi\) | ||||
0.705220 | + | 0.708988i | \(0.250848\pi\) | |||||||
\(644\) | 2.30935e9 | 0.340713 | ||||||||
\(645\) | 2.05244e9 | 0.301170 | ||||||||
\(646\) | −1.34976e10 | −1.96989 | ||||||||
\(647\) | −7.73215e9 | −1.12237 | −0.561184 | − | 0.827691i | \(-0.689654\pi\) | ||||
−0.561184 | + | 0.827691i | \(0.689654\pi\) | |||||||
\(648\) | −2.46887e9 | −0.356439 | ||||||||
\(649\) | −4.68758e7 | −0.00673119 | ||||||||
\(650\) | −2.91606e9 | −0.416485 | ||||||||
\(651\) | −3.87028e9 | −0.549806 | ||||||||
\(652\) | 5.32654e9 | 0.752624 | ||||||||
\(653\) | −5.06321e9 | −0.711590 | −0.355795 | − | 0.934564i | \(-0.615790\pi\) | ||||
−0.355795 | + | 0.934564i | \(0.615790\pi\) | |||||||
\(654\) | 3.33638e9 | 0.466395 | ||||||||
\(655\) | −8.25585e9 | −1.14793 | ||||||||
\(656\) | 1.30452e9 | 0.180421 | ||||||||
\(657\) | −6.44508e9 | −0.886645 | ||||||||
\(658\) | −1.93100e9 | −0.264235 | ||||||||
\(659\) | 8.08113e9 | 1.09995 | 0.549975 | − | 0.835181i | \(-0.314637\pi\) | ||||
0.549975 | + | 0.835181i | \(0.314637\pi\) | |||||||
\(660\) | 6.75840e7 | 0.00915040 | ||||||||
\(661\) | 6.30089e9 | 0.848588 | 0.424294 | − | 0.905524i | \(-0.360522\pi\) | ||||
0.424294 | + | 0.905524i | \(0.360522\pi\) | |||||||
\(662\) | 3.40239e9 | 0.455806 | ||||||||
\(663\) | 1.07255e10 | 1.42928 | ||||||||
\(664\) | −1.08665e9 | −0.144046 | ||||||||
\(665\) | −6.34166e9 | −0.836233 | ||||||||
\(666\) | 3.63594e8 | 0.0476932 | ||||||||
\(667\) | 1.32903e10 | 1.73419 | ||||||||
\(668\) | 1.96426e9 | 0.254965 | ||||||||
\(669\) | 4.52006e9 | 0.583651 | ||||||||
\(670\) | 3.18166e9 | 0.408688 | ||||||||
\(671\) | −8.27549e7 | −0.0105746 | ||||||||
\(672\) | 7.41802e8 | 0.0942965 | ||||||||
\(673\) | −9.62624e9 | −1.21732 | −0.608659 | − | 0.793432i | \(-0.708292\pi\) | ||||
−0.608659 | + | 0.793432i | \(0.708292\pi\) | |||||||
\(674\) | 8.61620e9 | 1.08394 | ||||||||
\(675\) | 9.72675e7 | 0.0121732 | ||||||||
\(676\) | −2.74741e9 | −0.342066 | ||||||||
\(677\) | −9.45429e9 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(678\) | 5.40079e9 | 0.665508 | ||||||||
\(679\) | −1.69878e9 | −0.208254 | ||||||||
\(680\) | −7.47561e9 | −0.911728 | ||||||||
\(681\) | 1.27794e9 | 0.155058 | ||||||||
\(682\) | −5.47085e7 | −0.00660403 | ||||||||
\(683\) | 2.48879e8 | 0.0298893 | 0.0149447 | − | 0.999888i | \(-0.495243\pi\) | ||||
0.0149447 | + | 0.999888i | \(0.495243\pi\) | |||||||
\(684\) | −6.41635e9 | −0.766641 | ||||||||
\(685\) | −1.90479e9 | −0.226429 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −2.03383e10 | −2.39313 | ||||||||
\(688\) | 3.18439e8 | 0.0372793 | ||||||||
\(689\) | −7.13779e9 | −0.831375 | ||||||||
\(690\) | −2.22182e10 | −2.57477 | ||||||||
\(691\) | −3.46412e9 | −0.399411 | −0.199705 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199705 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(692\) | −3.37497e9 | −0.387167 | ||||||||
\(693\) | −2.97587e7 | −0.00339662 | ||||||||
\(694\) | −5.79011e9 | −0.657550 | ||||||||
\(695\) | 2.02289e9 | 0.228574 | ||||||||
\(696\) | 4.26908e9 | 0.479956 | ||||||||
\(697\) | 1.16254e10 | 1.30045 | ||||||||
\(698\) | −3.58506e9 | −0.399027 | ||||||||
\(699\) | −2.34826e9 | −0.260062 | ||||||||
\(700\) | −1.79732e9 | −0.198053 | ||||||||
\(701\) | 5.56322e9 | 0.609976 | 0.304988 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304988 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(702\) | −4.23118e7 | −0.00461617 | ||||||||
\(703\) | −9.68536e8 | −0.105141 | ||||||||
\(704\) | 1.04858e7 | 0.00113265 | ||||||||
\(705\) | 1.85781e10 | 1.99682 | ||||||||
\(706\) | −1.19956e10 | −1.28294 | ||||||||
\(707\) | −1.10789e9 | −0.117904 | ||||||||
\(708\) | 4.95008e9 | 0.524199 | ||||||||
\(709\) | 8.23697e9 | 0.867971 | 0.433986 | − | 0.900920i | \(-0.357107\pi\) | ||||
0.433986 | + | 0.900920i | \(0.357107\pi\) | |||||||
\(710\) | −1.06496e8 | −0.0111668 | ||||||||
\(711\) | −5.15391e9 | −0.537766 | ||||||||
\(712\) | 3.54322e9 | 0.367890 | ||||||||
\(713\) | 1.79854e10 | 1.85826 | ||||||||
\(714\) | 6.61066e9 | 0.679674 | ||||||||
\(715\) | 7.12320e7 | 0.00728793 | ||||||||
\(716\) | 5.39353e9 | 0.549133 | ||||||||
\(717\) | 1.51837e10 | 1.53837 | ||||||||
\(718\) | −2.05512e9 | −0.207206 | ||||||||
\(719\) | 5.85212e9 | 0.587168 | 0.293584 | − | 0.955933i | \(-0.405152\pi\) | ||||
0.293584 | + | 0.955933i | \(0.405152\pi\) | |||||||
\(720\) | −3.55369e9 | −0.354826 | ||||||||
\(721\) | 6.17089e8 | 0.0613160 | ||||||||
\(722\) | 9.94081e9 | 0.982973 | ||||||||
\(723\) | −3.32307e8 | −0.0327005 | ||||||||
\(724\) | −6.65320e9 | −0.651547 | ||||||||
\(725\) | −1.03436e10 | −1.00807 | ||||||||
\(726\) | 1.02884e10 | 0.997858 | ||||||||
\(727\) | 1.51706e10 | 1.46431 | 0.732154 | − | 0.681139i | \(-0.238515\pi\) | ||||
0.732154 | + | 0.681139i | \(0.238515\pi\) | |||||||
\(728\) | 7.81842e8 | 0.0751034 | ||||||||
\(729\) | −1.02875e10 | −0.983472 | ||||||||
\(730\) | 9.50865e9 | 0.904667 | ||||||||
\(731\) | 2.83781e9 | 0.268703 | ||||||||
\(732\) | 8.73892e9 | 0.823510 | ||||||||
\(733\) | −1.55969e10 | −1.46277 | −0.731383 | − | 0.681967i | \(-0.761125\pi\) | ||||
−0.731383 | + | 0.681967i | \(0.761125\pi\) | |||||||
\(734\) | 5.20339e9 | 0.485680 | ||||||||
\(735\) | 3.10593e9 | 0.288527 | ||||||||
\(736\) | −3.44719e9 | −0.318708 | ||||||||
\(737\) | −3.97707e7 | −0.00365955 | ||||||||
\(738\) | 5.52637e9 | 0.506107 | ||||||||
\(739\) | −6.95573e9 | −0.633997 | −0.316998 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.316998 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(740\) | −5.36422e8 | −0.0486627 | ||||||||
\(741\) | −1.35815e10 | −1.22626 | ||||||||
\(742\) | −4.39939e9 | −0.395348 | ||||||||
\(743\) | −1.17803e10 | −1.05365 | −0.526824 | − | 0.849975i | \(-0.676617\pi\) | ||||
−0.526824 | + | 0.849975i | \(0.676617\pi\) | |||||||
\(744\) | 5.77722e9 | 0.514296 | ||||||||
\(745\) | 1.09095e10 | 0.966621 | ||||||||
\(746\) | −3.72902e9 | −0.328858 | ||||||||
\(747\) | −4.60339e9 | −0.404070 | ||||||||
\(748\) | 9.34451e7 | 0.00816396 | ||||||||
\(749\) | 5.36551e9 | 0.466578 | ||||||||
\(750\) | 7.92000e8 | 0.0685505 | ||||||||
\(751\) | −6.96200e9 | −0.599783 | −0.299892 | − | 0.953973i | \(-0.596951\pi\) | ||||
−0.299892 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(752\) | 2.88242e9 | 0.247170 | ||||||||
\(753\) | 6.81665e9 | 0.581820 | ||||||||
\(754\) | 4.49951e9 | 0.382266 | ||||||||
\(755\) | −2.59568e9 | −0.219501 | ||||||||
\(756\) | −2.60790e7 | −0.00219515 | ||||||||
\(757\) | −2.07114e10 | −1.73530 | −0.867648 | − | 0.497179i | \(-0.834369\pi\) | ||||
−0.867648 | + | 0.497179i | \(0.834369\pi\) | |||||||
\(758\) | 2.28688e9 | 0.190722 | ||||||||
\(759\) | 2.77728e8 | 0.0230554 | ||||||||
\(760\) | 9.46627e9 | 0.782224 | ||||||||
\(761\) | 1.65392e10 | 1.36041 | 0.680204 | − | 0.733023i | \(-0.261891\pi\) | ||||
0.680204 | + | 0.733023i | \(0.261891\pi\) | |||||||
\(762\) | −3.17183e9 | −0.259697 | ||||||||
\(763\) | 2.16738e9 | 0.176644 | ||||||||
\(764\) | −7.98562e9 | −0.647861 | ||||||||
\(765\) | −3.16691e10 | −2.55753 | ||||||||
\(766\) | −1.32060e10 | −1.06162 | ||||||||
\(767\) | 5.21727e9 | 0.417503 | ||||||||
\(768\) | −1.10730e9 | −0.0882063 | ||||||||
\(769\) | −2.33650e10 | −1.85278 | −0.926391 | − | 0.376562i | \(-0.877106\pi\) | ||||
−0.926391 | + | 0.376562i | \(0.877106\pi\) | |||||||
\(770\) | 4.39040e7 | 0.00346566 | ||||||||
\(771\) | 1.53306e10 | 1.20467 | ||||||||
\(772\) | 9.44568e9 | 0.738878 | ||||||||
\(773\) | 7.09263e9 | 0.552305 | 0.276152 | − | 0.961114i | \(-0.410941\pi\) | ||||
0.276152 | + | 0.961114i | \(0.410941\pi\) | |||||||
\(774\) | 1.34901e9 | 0.104574 | ||||||||
\(775\) | −1.39977e10 | −1.08019 | ||||||||
\(776\) | 2.53579e9 | 0.194804 | ||||||||
\(777\) | 4.74357e8 | 0.0362770 | ||||||||
\(778\) | 1.21043e10 | 0.921536 | ||||||||
\(779\) | −1.47211e10 | −1.11573 | ||||||||
\(780\) | −7.52210e9 | −0.567555 | ||||||||
\(781\) | 1.33120e6 | 9.99919e−5 0 | ||||||||
\(782\) | −3.07201e10 | −2.29720 | ||||||||
\(783\) | −1.50085e8 | −0.0111730 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 2.52324e10 | 1.86172 | ||||||||
\(786\) | −1.08977e10 | −0.800491 | ||||||||
\(787\) | −1.23030e10 | −0.899703 | −0.449851 | − | 0.893103i | \(-0.648523\pi\) | ||||
−0.449851 | + | 0.893103i | \(0.648523\pi\) | |||||||
\(788\) | 9.97194e9 | 0.726002 | ||||||||
\(789\) | −2.75054e10 | −1.99365 | ||||||||
\(790\) | 7.60374e9 | 0.548697 | ||||||||
\(791\) | 3.50847e9 | 0.252057 | ||||||||
\(792\) | 4.44211e7 | 0.00317725 | ||||||||
\(793\) | 9.21062e9 | 0.655892 | ||||||||
\(794\) | −6.91036e9 | −0.489924 | ||||||||
\(795\) | 4.23265e10 | 2.98764 | ||||||||
\(796\) | −8.52433e8 | −0.0599052 | ||||||||
\(797\) | −3.66650e9 | −0.256535 | −0.128268 | − | 0.991740i | \(-0.540942\pi\) | ||||
−0.128268 | + | 0.991740i | \(0.540942\pi\) | |||||||
\(798\) | −8.37099e9 | −0.583132 | ||||||||
\(799\) | 2.56870e10 | 1.78156 | ||||||||
\(800\) | 2.68288e9 | 0.185262 | ||||||||
\(801\) | 1.50102e10 | 1.03199 | ||||||||
\(802\) | 9.12334e8 | 0.0624516 | ||||||||
\(803\) | −1.18858e8 | −0.00810074 | ||||||||
\(804\) | 4.19979e9 | 0.284991 | ||||||||
\(805\) | −1.44334e10 | −0.975179 | ||||||||
\(806\) | 6.08905e9 | 0.409616 | ||||||||
\(807\) | 2.07688e10 | 1.39109 | ||||||||
\(808\) | 1.65376e9 | 0.110289 | ||||||||
\(809\) | −2.96609e10 | −1.96954 | −0.984770 | − | 0.173861i | \(-0.944376\pi\) | ||||
−0.984770 | + | 0.173861i | \(0.944376\pi\) | |||||||
\(810\) | 1.54304e10 | 1.02019 | ||||||||
\(811\) | 2.51278e10 | 1.65417 | 0.827087 | − | 0.562073i | \(-0.189996\pi\) | ||||
0.827087 | + | 0.562073i | \(0.189996\pi\) | |||||||
\(812\) | 2.77328e9 | 0.181781 | ||||||||
\(813\) | −1.26810e10 | −0.827633 | ||||||||
\(814\) | 6.70528e6 | 0.000435744 0 | ||||||||
\(815\) | −3.32908e10 | −2.15414 | ||||||||
\(816\) | −9.86780e9 | −0.635777 | ||||||||
\(817\) | −3.59348e9 | −0.230536 | ||||||||
\(818\) | −9.46623e9 | −0.604700 | ||||||||
\(819\) | 3.31214e9 | 0.210676 | ||||||||
\(820\) | −8.15324e9 | −0.516395 | ||||||||
\(821\) | 4.57772e9 | 0.288701 | 0.144350 | − | 0.989527i | \(-0.453891\pi\) | ||||
0.144350 | + | 0.989527i | \(0.453891\pi\) | |||||||
\(822\) | −2.51433e9 | −0.157896 | ||||||||
\(823\) | 1.93133e9 | 0.120769 | 0.0603846 | − | 0.998175i | \(-0.480767\pi\) | ||||
0.0603846 | + | 0.998175i | \(0.480767\pi\) | |||||||
\(824\) | −9.21135e8 | −0.0573559 | ||||||||
\(825\) | −2.16150e8 | −0.0134019 | ||||||||
\(826\) | 3.21568e9 | 0.198537 | ||||||||
\(827\) | 1.58094e10 | 0.971958 | 0.485979 | − | 0.873971i | \(-0.338463\pi\) | ||||
0.485979 | + | 0.873971i | \(0.338463\pi\) | |||||||
\(828\) | −1.46034e10 | −0.894024 | ||||||||
\(829\) | −2.46536e9 | −0.150293 | −0.0751465 | − | 0.997173i | \(-0.523942\pi\) | ||||
−0.0751465 | + | 0.997173i | \(0.523942\pi\) | |||||||
\(830\) | 6.79155e9 | 0.412283 | ||||||||
\(831\) | 2.90660e10 | 1.75704 | ||||||||
\(832\) | −1.16707e9 | −0.0702528 | ||||||||
\(833\) | 4.29442e9 | 0.257423 | ||||||||
\(834\) | 2.67022e9 | 0.159392 | ||||||||
\(835\) | −1.22766e10 | −0.729754 | ||||||||
\(836\) | −1.18328e8 | −0.00700433 | ||||||||
\(837\) | −2.03105e8 | −0.0119724 | ||||||||
\(838\) | 1.82368e9 | 0.107052 | ||||||||
\(839\) | 2.51861e10 | 1.47229 | 0.736147 | − | 0.676822i | \(-0.236643\pi\) | ||||
0.736147 | + | 0.676822i | \(0.236643\pi\) | |||||||
\(840\) | −4.63626e9 | −0.269892 | ||||||||
\(841\) | −1.28960e9 | −0.0747598 | ||||||||
\(842\) | −3.12560e8 | −0.0180444 | ||||||||
\(843\) | −2.37095e10 | −1.36309 | ||||||||
\(844\) | −1.31162e10 | −0.750945 | ||||||||
\(845\) | 1.71713e10 | 0.979049 | ||||||||
\(846\) | 1.22109e10 | 0.693347 | ||||||||
\(847\) | 6.68355e9 | 0.377933 | ||||||||
\(848\) | 6.56703e9 | 0.369814 | ||||||||
\(849\) | 5.35568e9 | 0.300357 | ||||||||
\(850\) | 2.39088e10 | 1.33534 | ||||||||
\(851\) | −2.20436e9 | −0.122611 | ||||||||
\(852\) | −1.40575e8 | −0.00778697 | ||||||||
\(853\) | 1.07306e10 | 0.591972 | 0.295986 | − | 0.955192i | \(-0.404352\pi\) | ||||
0.295986 | + | 0.955192i | \(0.404352\pi\) | |||||||
\(854\) | 5.67698e9 | 0.311900 | ||||||||
\(855\) | 4.01022e10 | 2.19425 | ||||||||
\(856\) | −8.00915e9 | −0.436444 | ||||||||
\(857\) | −2.79332e10 | −1.51596 | −0.757979 | − | 0.652279i | \(-0.773813\pi\) | ||||
−0.757979 | + | 0.652279i | \(0.773813\pi\) | |||||||
\(858\) | 9.40262e7 | 0.00508210 | ||||||||
\(859\) | −1.94983e10 | −1.04959 | −0.524795 | − | 0.851229i | \(-0.675858\pi\) | ||||
−0.524795 | + | 0.851229i | \(0.675858\pi\) | |||||||
\(860\) | −1.99025e9 | −0.106699 | ||||||||
\(861\) | 7.20989e9 | 0.384962 | ||||||||
\(862\) | −2.06896e10 | −1.10021 | ||||||||
\(863\) | −1.63551e10 | −0.866193 | −0.433096 | − | 0.901348i | \(-0.642579\pi\) | ||||
−0.433096 | + | 0.901348i | \(0.642579\pi\) | |||||||
\(864\) | 3.89284e7 | 0.00205338 | ||||||||
\(865\) | 2.10935e10 | 1.10814 | ||||||||
\(866\) | −1.43114e10 | −0.748807 | ||||||||
\(867\) | −6.08558e10 | −3.17128 | ||||||||
\(868\) | 3.75300e9 | 0.194787 | ||||||||
\(869\) | −9.50467e7 | −0.00491324 | ||||||||
\(870\) | −2.66817e10 | −1.37372 | ||||||||
\(871\) | 4.42648e9 | 0.226984 | ||||||||
\(872\) | −3.23528e9 | −0.165236 | ||||||||
\(873\) | 1.07424e10 | 0.546453 | ||||||||
\(874\) | 3.89004e10 | 1.97090 | ||||||||
\(875\) | 5.14500e8 | 0.0259631 | ||||||||
\(876\) | 1.25514e10 | 0.630854 | ||||||||
\(877\) | 2.68874e10 | 1.34601 | 0.673007 | − | 0.739636i | \(-0.265002\pi\) | ||||
0.673007 | + | 0.739636i | \(0.265002\pi\) | |||||||
\(878\) | −3.67124e9 | −0.183055 | ||||||||
\(879\) | −1.67255e10 | −0.830648 | ||||||||
\(880\) | −6.55360e7 | −0.00324183 | ||||||||
\(881\) | 1.08918e10 | 0.536644 | 0.268322 | − | 0.963329i | \(-0.413531\pi\) | ||||
0.268322 | + | 0.963329i | \(0.413531\pi\) | |||||||
\(882\) | 2.04145e9 | 0.100184 | ||||||||
\(883\) | −3.99542e10 | −1.95299 | −0.976495 | − | 0.215542i | \(-0.930848\pi\) | ||||
−0.976495 | + | 0.215542i | \(0.930848\pi\) | |||||||
\(884\) | −1.04004e10 | −0.506371 | ||||||||
\(885\) | −3.09380e10 | −1.50034 | ||||||||
\(886\) | 1.10767e10 | 0.535048 | ||||||||
\(887\) | 1.30306e10 | 0.626946 | 0.313473 | − | 0.949597i | \(-0.398507\pi\) | ||||
0.313473 | + | 0.949597i | \(0.398507\pi\) | |||||||
\(888\) | −7.08078e8 | −0.0339340 | ||||||||
\(889\) | −2.06049e9 | −0.0983589 | ||||||||
\(890\) | −2.21451e10 | −1.05296 | ||||||||
\(891\) | −1.92880e8 | −0.00913516 | ||||||||
\(892\) | −4.38309e9 | −0.206778 | ||||||||
\(893\) | −3.25272e10 | −1.52850 | ||||||||
\(894\) | 1.44005e10 | 0.674056 | ||||||||
\(895\) | −3.37095e10 | −1.57171 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −3.09111e10 | −1.43002 | ||||||||
\(898\) | −2.18889e10 | −1.00869 | ||||||||
\(899\) | 2.15986e10 | 0.991439 | ||||||||
\(900\) | 1.13656e10 | 0.519687 | ||||||||
\(901\) | 5.85229e10 | 2.66556 | ||||||||
\(902\) | 1.01916e8 | 0.00462400 | ||||||||
\(903\) | 1.75997e9 | 0.0795422 | ||||||||
\(904\) | −5.23713e9 | −0.235778 | ||||||||
\(905\) | 4.15825e10 | 1.86484 | ||||||||
\(906\) | −3.42630e9 | −0.153065 | ||||||||
\(907\) | 4.04015e10 | 1.79792 | 0.898962 | − | 0.438026i | \(-0.144322\pi\) | ||||
0.898962 | + | 0.438026i | \(0.144322\pi\) | |||||||
\(908\) | −1.23921e9 | −0.0549344 | ||||||||
\(909\) | 7.00587e9 | 0.309377 | ||||||||
\(910\) | −4.88652e9 | −0.214958 | ||||||||
\(911\) | 1.98919e10 | 0.871690 | 0.435845 | − | 0.900022i | \(-0.356450\pi\) | ||||
0.435845 | + | 0.900022i | \(0.356450\pi\) | |||||||
\(912\) | 1.24955e10 | 0.545470 | ||||||||
\(913\) | −8.48943e7 | −0.00369174 | ||||||||
\(914\) | 1.94443e10 | 0.842325 | ||||||||
\(915\) | −5.46182e10 | −2.35702 | ||||||||
\(916\) | 1.97220e10 | 0.847847 | ||||||||
\(917\) | −7.07939e9 | −0.303182 | ||||||||
\(918\) | 3.46915e8 | 0.0148004 | ||||||||
\(919\) | −4.10990e10 | −1.74674 | −0.873368 | − | 0.487061i | \(-0.838069\pi\) | ||||
−0.873368 | + | 0.487061i | \(0.838069\pi\) | |||||||
\(920\) | 2.15450e10 | 0.912196 | ||||||||
\(921\) | −5.75986e10 | −2.42942 | ||||||||
\(922\) | 3.15908e10 | 1.32740 | ||||||||
\(923\) | −1.48163e8 | −0.00620201 | ||||||||
\(924\) | 5.79533e7 | 0.00241672 | ||||||||
\(925\) | 1.71561e9 | 0.0712725 | ||||||||
\(926\) | 2.05962e10 | 0.852412 | ||||||||
\(927\) | −3.90223e9 | −0.160892 | ||||||||
\(928\) | −4.13971e9 | −0.170040 | ||||||||
\(929\) | −1.90374e10 | −0.779027 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(930\) | −3.61076e10 | −1.47200 | ||||||||
\(931\) | −5.43797e9 | −0.220858 | ||||||||
\(932\) | 2.27710e9 | 0.0921355 | ||||||||
\(933\) | 4.43264e10 | 1.78680 | ||||||||
\(934\) | 2.38786e9 | 0.0958947 | ||||||||
\(935\) | −5.84032e8 | −0.0233666 | ||||||||
\(936\) | −4.94407e9 | −0.197069 | ||||||||
\(937\) | 3.93830e10 | 1.56394 | 0.781971 | − | 0.623315i | \(-0.214214\pi\) | ||||
0.781971 | + | 0.623315i | \(0.214214\pi\) | |||||||
\(938\) | 2.72827e9 | 0.107939 | ||||||||
\(939\) | 1.26863e10 | 0.500040 | ||||||||
\(940\) | −1.80151e10 | −0.707440 | ||||||||
\(941\) | −1.59186e10 | −0.622791 | −0.311395 | − | 0.950280i | \(-0.600796\pi\) | ||||
−0.311395 | + | 0.950280i | \(0.600796\pi\) | |||||||
\(942\) | 3.33068e10 | 1.29824 | ||||||||
\(943\) | −3.35047e10 | −1.30111 | ||||||||
\(944\) | −4.80008e9 | −0.185715 | ||||||||
\(945\) | 1.62994e8 | 0.00628289 | ||||||||
\(946\) | 2.48781e7 | 0.000955428 0 | ||||||||
\(947\) | 3.57237e9 | 0.136688 | 0.0683442 | − | 0.997662i | \(-0.478228\pi\) | ||||
0.0683442 | + | 0.997662i | \(0.478228\pi\) | |||||||
\(948\) | 1.00369e10 | 0.382624 | ||||||||
\(949\) | 1.32289e10 | 0.502450 | ||||||||
\(950\) | −3.02754e10 | −1.14566 | ||||||||
\(951\) | 8.83326e9 | 0.333034 | ||||||||
\(952\) | −6.41034e9 | −0.240797 | ||||||||
\(953\) | 4.05101e9 | 0.151614 | 0.0758068 | − | 0.997123i | \(-0.475847\pi\) | ||||
0.0758068 | + | 0.997123i | \(0.475847\pi\) | |||||||
\(954\) | 2.78201e10 | 1.03738 | ||||||||
\(955\) | 4.99101e10 | 1.85429 | ||||||||
\(956\) | −1.47236e10 | −0.545018 | ||||||||
\(957\) | 3.33522e8 | 0.0123008 | ||||||||
\(958\) | 2.09600e10 | 0.770216 | ||||||||
\(959\) | −1.63336e9 | −0.0598022 | ||||||||
\(960\) | 6.92060e9 | 0.252461 | ||||||||
\(961\) | 1.71608e9 | 0.0623741 | ||||||||
\(962\) | −7.46298e8 | −0.0270271 | ||||||||
\(963\) | −3.39294e10 | −1.22429 | ||||||||
\(964\) | 3.22237e8 | 0.0115853 | ||||||||
\(965\) | −5.90355e10 | −2.11479 | ||||||||
\(966\) | −1.90521e10 | −0.680023 | ||||||||
\(967\) | 2.55791e10 | 0.909689 | 0.454844 | − | 0.890571i | \(-0.349695\pi\) | ||||
0.454844 | + | 0.890571i | \(0.349695\pi\) | |||||||
\(968\) | −9.97661e9 | −0.353524 | ||||||||
\(969\) | 1.11355e11 | 3.93166 | ||||||||
\(970\) | −1.58487e10 | −0.557560 | ||||||||
\(971\) | 4.10323e10 | 1.43833 | 0.719165 | − | 0.694840i | \(-0.244525\pi\) | ||||
0.719165 | + | 0.694840i | \(0.244525\pi\) | |||||||
\(972\) | 2.02019e10 | 0.705603 | ||||||||
\(973\) | 1.73463e9 | 0.0603688 | ||||||||
\(974\) | −3.33330e10 | −1.15589 | ||||||||
\(975\) | 2.40575e10 | 0.831255 | ||||||||
\(976\) | −8.47410e9 | −0.291756 | ||||||||
\(977\) | 4.87277e10 | 1.67165 | 0.835824 | − | 0.548998i | \(-0.184990\pi\) | ||||
0.835824 | + | 0.548998i | \(0.184990\pi\) | |||||||
\(978\) | −4.39439e10 | −1.50215 | ||||||||
\(979\) | 2.76814e8 | 0.00942863 | ||||||||
\(980\) | −3.01181e9 | −0.102220 | ||||||||
\(981\) | −1.37057e10 | −0.463511 | ||||||||
\(982\) | 1.93040e10 | 0.650515 | ||||||||
\(983\) | −6.94762e9 | −0.233291 | −0.116646 | − | 0.993174i | \(-0.537214\pi\) | ||||
−0.116646 | + | 0.993174i | \(0.537214\pi\) | |||||||
\(984\) | −1.07623e10 | −0.360099 | ||||||||
\(985\) | −6.23246e10 | −2.07794 | ||||||||
\(986\) | −3.68915e10 | −1.22563 | ||||||||
\(987\) | 1.59307e10 | 0.527382 | ||||||||
\(988\) | 1.31699e10 | 0.434445 | ||||||||
\(989\) | −8.17867e9 | −0.268841 | ||||||||
\(990\) | −2.77632e8 | −0.00909382 | ||||||||
\(991\) | −1.83565e10 | −0.599144 | −0.299572 | − | 0.954074i | \(-0.596844\pi\) | ||||
−0.299572 | + | 0.954074i | \(0.596844\pi\) | |||||||
\(992\) | −5.60215e9 | −0.182206 | ||||||||
\(993\) | −2.80697e10 | −0.909735 | ||||||||
\(994\) | −9.13203e7 | −0.00294927 | ||||||||
\(995\) | 5.32770e9 | 0.171459 | ||||||||
\(996\) | 8.96484e9 | 0.287498 | ||||||||
\(997\) | 3.44954e10 | 1.10237 | 0.551185 | − | 0.834383i | \(-0.314176\pi\) | ||||
0.551185 | + | 0.834383i | \(0.314176\pi\) | |||||||
\(998\) | −8.32735e9 | −0.265186 | ||||||||
\(999\) | 2.48934e7 | 0.000789958 0 |
(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 | 14.8.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 126.8.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 112.8.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 350.8.c.b.99.2 | 2 | |||
5.3 | odd | 4 | 350.8.c.b.99.1 | 2 | |||
5.4 | even | 2 | 350.8.a.d.1.1 | 1 | |||
7.2 | even | 3 | 98.8.c.b.67.1 | 2 | |||
7.3 | odd | 6 | 98.8.c.a.79.1 | 2 | |||
7.4 | even | 3 | 98.8.c.b.79.1 | 2 | |||
7.5 | odd | 6 | 98.8.c.a.67.1 | 2 | |||
7.6 | odd | 2 | 98.8.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 448.8.a.b.1.1 | 1 | |||
8.5 | even | 2 | 448.8.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
98.8.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
98.8.c.a.67.1 | 2 | 7.5 | odd | 6 | |||
98.8.c.a.79.1 | 2 | 7.3 | odd | 6 | |||
98.8.c.b.67.1 | 2 | 7.2 | even | 3 | |||
98.8.c.b.79.1 | 2 | 7.4 | even | 3 | |||
112.8.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
126.8.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
350.8.a.d.1.1 | 1 | 5.4 | even | 2 | |||
350.8.c.b.99.1 | 2 | 5.3 | odd | 4 | |||
350.8.c.b.99.2 | 2 | 5.2 | odd | 4 | |||
448.8.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
448.8.a.i.1.1 | 1 | 8.5 | even | 2 |