Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,8,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, 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("29.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(9.05916573904\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 1101 x^{8} - 1540 x^{7} + 405148 x^{6} + 870160 x^{5} - 54569376 x^{4} - 87078400 x^{3} + \cdots - 9372051456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(22.0686\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.0686 | −1.95061 | −0.975303 | − | 0.220869i | \(-0.929111\pi\) | ||||
−0.975303 | + | 0.220869i | \(0.929111\pi\) | |||||||
\(3\) | 73.8979 | 1.58018 | 0.790092 | − | 0.612988i | \(-0.210033\pi\) | ||||
0.790092 | + | 0.612988i | \(0.210033\pi\) | |||||||
\(4\) | 359.023 | 2.80487 | ||||||||
\(5\) | 376.792 | 1.34805 | 0.674025 | − | 0.738708i | \(-0.264564\pi\) | ||||
0.674025 | + | 0.738708i | \(0.264564\pi\) | |||||||
\(6\) | −1630.82 | −3.08232 | ||||||||
\(7\) | 647.379 | 0.713371 | 0.356685 | − | 0.934225i | \(-0.383907\pi\) | ||||
0.356685 | + | 0.934225i | \(0.383907\pi\) | |||||||
\(8\) | −5098.36 | −3.52059 | ||||||||
\(9\) | 3273.90 | 1.49698 | ||||||||
\(10\) | −8315.26 | −2.62952 | ||||||||
\(11\) | −917.032 | −0.207735 | −0.103868 | − | 0.994591i | \(-0.533122\pi\) | ||||
−0.103868 | + | 0.994591i | \(0.533122\pi\) | |||||||
\(12\) | 26531.1 | 4.43221 | ||||||||
\(13\) | 5439.90 | 0.686735 | 0.343367 | − | 0.939201i | \(-0.388432\pi\) | ||||
0.343367 | + | 0.939201i | \(0.388432\pi\) | |||||||
\(14\) | −14286.7 | −1.39151 | ||||||||
\(15\) | 27844.1 | 2.13017 | ||||||||
\(16\) | 66558.6 | 4.06241 | ||||||||
\(17\) | −23747.6 | −1.17233 | −0.586163 | − | 0.810193i | \(-0.699362\pi\) | ||||
−0.586163 | + | 0.810193i | \(0.699362\pi\) | |||||||
\(18\) | −72250.4 | −2.92002 | ||||||||
\(19\) | −29878.0 | −0.999340 | −0.499670 | − | 0.866216i | \(-0.666545\pi\) | ||||
−0.499670 | + | 0.866216i | \(0.666545\pi\) | |||||||
\(20\) | 135277. | 3.78110 | ||||||||
\(21\) | 47840.0 | 1.12726 | ||||||||
\(22\) | 20237.6 | 0.405210 | ||||||||
\(23\) | 34152.9 | 0.585302 | 0.292651 | − | 0.956219i | \(-0.405463\pi\) | ||||
0.292651 | + | 0.956219i | \(0.405463\pi\) | |||||||
\(24\) | −376758. | −5.56318 | ||||||||
\(25\) | 63846.9 | 0.817241 | ||||||||
\(26\) | −120051. | −1.33955 | ||||||||
\(27\) | 80319.7 | 0.785324 | ||||||||
\(28\) | 232424. | 2.00091 | ||||||||
\(29\) | −24389.0 | −0.185695 | ||||||||
\(30\) | −614481. | −4.15512 | ||||||||
\(31\) | 215829. | 1.30120 | 0.650598 | − | 0.759422i | \(-0.274518\pi\) | ||||
0.650598 | + | 0.759422i | \(0.274518\pi\) | |||||||
\(32\) | −816266. | −4.40359 | ||||||||
\(33\) | −67766.7 | −0.328260 | ||||||||
\(34\) | 524076. | 2.28675 | ||||||||
\(35\) | 243927. | 0.961660 | ||||||||
\(36\) | 1.17541e6 | 4.19884 | ||||||||
\(37\) | 61163.9 | 0.198513 | 0.0992565 | − | 0.995062i | \(-0.468354\pi\) | ||||
0.0992565 | + | 0.995062i | \(0.468354\pi\) | |||||||
\(38\) | 659365. | 1.94932 | ||||||||
\(39\) | 401997. | 1.08517 | ||||||||
\(40\) | −1.92102e6 | −4.74593 | ||||||||
\(41\) | −202987. | −0.459964 | −0.229982 | − | 0.973195i | \(-0.573867\pi\) | ||||
−0.229982 | + | 0.973195i | \(0.573867\pi\) | |||||||
\(42\) | −1.05576e6 | −2.19884 | ||||||||
\(43\) | 436213. | 0.836679 | 0.418339 | − | 0.908291i | \(-0.362612\pi\) | ||||
0.418339 | + | 0.908291i | \(0.362612\pi\) | |||||||
\(44\) | −329236. | −0.582670 | ||||||||
\(45\) | 1.23358e6 | 2.01801 | ||||||||
\(46\) | −753706. | −1.14169 | ||||||||
\(47\) | −1.14899e6 | −1.61426 | −0.807131 | − | 0.590372i | \(-0.798981\pi\) | ||||
−0.807131 | + | 0.590372i | \(0.798981\pi\) | |||||||
\(48\) | 4.91854e6 | 6.41936 | ||||||||
\(49\) | −404443. | −0.491102 | ||||||||
\(50\) | −1.40901e6 | −1.59412 | ||||||||
\(51\) | −1.75490e6 | −1.85249 | ||||||||
\(52\) | 1.95305e6 | 1.92620 | ||||||||
\(53\) | 237602. | 0.219222 | 0.109611 | − | 0.993975i | \(-0.465040\pi\) | ||||
0.109611 | + | 0.993975i | \(0.465040\pi\) | |||||||
\(54\) | −1.77254e6 | −1.53186 | ||||||||
\(55\) | −345530. | −0.280038 | ||||||||
\(56\) | −3.30057e6 | −2.51148 | ||||||||
\(57\) | −2.20792e6 | −1.57914 | ||||||||
\(58\) | 538231. | 0.362219 | ||||||||
\(59\) | −1.56197e6 | −0.990126 | −0.495063 | − | 0.868857i | \(-0.664855\pi\) | ||||
−0.495063 | + | 0.868857i | \(0.664855\pi\) | |||||||
\(60\) | 9.99668e6 | 5.97484 | ||||||||
\(61\) | 2.82667e6 | 1.59449 | 0.797243 | − | 0.603659i | \(-0.206291\pi\) | ||||
0.797243 | + | 0.603659i | \(0.206291\pi\) | |||||||
\(62\) | −4.76303e6 | −2.53812 | ||||||||
\(63\) | 2.11945e6 | 1.06790 | ||||||||
\(64\) | 9.49434e6 | 4.52725 | ||||||||
\(65\) | 2.04971e6 | 0.925753 | ||||||||
\(66\) | 1.49552e6 | 0.640306 | ||||||||
\(67\) | −1.28367e6 | −0.521424 | −0.260712 | − | 0.965417i | \(-0.583957\pi\) | ||||
−0.260712 | + | 0.965417i | \(0.583957\pi\) | |||||||
\(68\) | −8.52593e6 | −3.28822 | ||||||||
\(69\) | 2.52383e6 | 0.924884 | ||||||||
\(70\) | −5.38313e6 | −1.87582 | ||||||||
\(71\) | 3.48686e6 | 1.15619 | 0.578096 | − | 0.815969i | \(-0.303796\pi\) | ||||
0.578096 | + | 0.815969i | \(0.303796\pi\) | |||||||
\(72\) | −1.66915e7 | −5.27026 | ||||||||
\(73\) | 68118.2 | 0.0204943 | 0.0102472 | − | 0.999947i | \(-0.496738\pi\) | ||||
0.0102472 | + | 0.999947i | \(0.496738\pi\) | |||||||
\(74\) | −1.34980e6 | −0.387221 | ||||||||
\(75\) | 4.71816e6 | 1.29139 | ||||||||
\(76\) | −1.07269e7 | −2.80302 | ||||||||
\(77\) | −593667. | −0.148192 | ||||||||
\(78\) | −8.87151e6 | −2.11673 | ||||||||
\(79\) | −770647. | −0.175857 | −0.0879287 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879287 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(80\) | 2.50787e7 | 5.47634 | ||||||||
\(81\) | −1.22456e6 | −0.256026 | ||||||||
\(82\) | 4.47963e6 | 0.897209 | ||||||||
\(83\) | −3.66552e6 | −0.703658 | −0.351829 | − | 0.936064i | \(-0.614440\pi\) | ||||
−0.351829 | + | 0.936064i | \(0.614440\pi\) | |||||||
\(84\) | 1.71756e7 | 3.16181 | ||||||||
\(85\) | −8.94789e6 | −1.58035 | ||||||||
\(86\) | −9.62660e6 | −1.63203 | ||||||||
\(87\) | −1.80230e6 | −0.293433 | ||||||||
\(88\) | 4.67535e6 | 0.731350 | ||||||||
\(89\) | −322570. | −0.0485019 | −0.0242509 | − | 0.999706i | \(-0.507720\pi\) | ||||
−0.0242509 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(90\) | −2.72233e7 | −3.93634 | ||||||||
\(91\) | 3.52167e6 | 0.489897 | ||||||||
\(92\) | 1.22617e7 | 1.64169 | ||||||||
\(93\) | 1.59493e7 | 2.05613 | ||||||||
\(94\) | 2.53566e7 | 3.14879 | ||||||||
\(95\) | −1.12578e7 | −1.34716 | ||||||||
\(96\) | −6.03203e7 | −6.95848 | ||||||||
\(97\) | −2.17987e6 | −0.242510 | −0.121255 | − | 0.992621i | \(-0.538692\pi\) | ||||
−0.121255 | + | 0.992621i | \(0.538692\pi\) | |||||||
\(98\) | 8.92550e6 | 0.957947 | ||||||||
\(99\) | −3.00227e6 | −0.310976 | ||||||||
\(100\) | 2.29225e7 | 2.29225 | ||||||||
\(101\) | 1.90852e7 | 1.84320 | 0.921598 | − | 0.388147i | \(-0.126885\pi\) | ||||
0.921598 | + | 0.388147i | \(0.126885\pi\) | |||||||
\(102\) | 3.87281e7 | 3.61348 | ||||||||
\(103\) | −1.33432e7 | −1.20317 | −0.601587 | − | 0.798808i | \(-0.705465\pi\) | ||||
−0.601587 | + | 0.798808i | \(0.705465\pi\) | |||||||
\(104\) | −2.77345e7 | −2.41771 | ||||||||
\(105\) | 1.80257e7 | 1.51960 | ||||||||
\(106\) | −5.24354e6 | −0.427616 | ||||||||
\(107\) | −6.92372e6 | −0.546382 | −0.273191 | − | 0.961960i | \(-0.588079\pi\) | ||||
−0.273191 | + | 0.961960i | \(0.588079\pi\) | |||||||
\(108\) | 2.88366e7 | 2.20273 | ||||||||
\(109\) | −2.41593e7 | −1.78686 | −0.893432 | − | 0.449199i | \(-0.851710\pi\) | ||||
−0.893432 | + | 0.449199i | \(0.851710\pi\) | |||||||
\(110\) | 7.62536e6 | 0.546243 | ||||||||
\(111\) | 4.51988e6 | 0.313687 | ||||||||
\(112\) | 4.30886e7 | 2.89801 | ||||||||
\(113\) | 5.03277e6 | 0.328120 | 0.164060 | − | 0.986450i | \(-0.447541\pi\) | ||||
0.164060 | + | 0.986450i | \(0.447541\pi\) | |||||||
\(114\) | 4.87257e7 | 3.08029 | ||||||||
\(115\) | 1.28685e7 | 0.789016 | ||||||||
\(116\) | −8.75621e6 | −0.520851 | ||||||||
\(117\) | 1.78097e7 | 1.02803 | ||||||||
\(118\) | 3.44705e7 | 1.93135 | ||||||||
\(119\) | −1.53737e7 | −0.836303 | ||||||||
\(120\) | −1.41959e8 | −7.49945 | ||||||||
\(121\) | −1.86462e7 | −0.956846 | ||||||||
\(122\) | −6.23806e7 | −3.11021 | ||||||||
\(123\) | −1.50003e7 | −0.726828 | ||||||||
\(124\) | 7.74874e7 | 3.64968 | ||||||||
\(125\) | −5.37985e6 | −0.246368 | ||||||||
\(126\) | −4.67734e7 | −2.08306 | ||||||||
\(127\) | −2.20593e7 | −0.955605 | −0.477803 | − | 0.878467i | \(-0.658567\pi\) | ||||
−0.477803 | + | 0.878467i | \(0.658567\pi\) | |||||||
\(128\) | −1.05045e8 | −4.42730 | ||||||||
\(129\) | 3.22352e7 | 1.32211 | ||||||||
\(130\) | −4.52342e7 | −1.80578 | ||||||||
\(131\) | 4.21270e7 | 1.63723 | 0.818617 | − | 0.574340i | \(-0.194741\pi\) | ||||
0.818617 | + | 0.574340i | \(0.194741\pi\) | |||||||
\(132\) | −2.43298e7 | −0.920726 | ||||||||
\(133\) | −1.93424e7 | −0.712900 | ||||||||
\(134\) | 2.83288e7 | 1.01709 | ||||||||
\(135\) | 3.02638e7 | 1.05866 | ||||||||
\(136\) | 1.21074e8 | 4.12727 | ||||||||
\(137\) | −1.07382e6 | −0.0356789 | −0.0178394 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178394 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(138\) | −5.56973e7 | −1.80409 | ||||||||
\(139\) | 7.04746e6 | 0.222577 | 0.111289 | − | 0.993788i | \(-0.464502\pi\) | ||||
0.111289 | + | 0.993788i | \(0.464502\pi\) | |||||||
\(140\) | 8.75754e7 | 2.69733 | ||||||||
\(141\) | −8.49080e7 | −2.55083 | ||||||||
\(142\) | −7.69501e7 | −2.25528 | ||||||||
\(143\) | −4.98856e6 | −0.142659 | ||||||||
\(144\) | 2.17906e8 | 6.08136 | ||||||||
\(145\) | −9.18957e6 | −0.250327 | ||||||||
\(146\) | −1.50327e6 | −0.0399763 | ||||||||
\(147\) | −2.98875e7 | −0.776031 | ||||||||
\(148\) | 2.19592e7 | 0.556803 | ||||||||
\(149\) | 2.10846e6 | 0.0522173 | 0.0261086 | − | 0.999659i | \(-0.491688\pi\) | ||||
0.0261086 | + | 0.999659i | \(0.491688\pi\) | |||||||
\(150\) | −1.04123e8 | −2.51900 | ||||||||
\(151\) | 3.04554e7 | 0.719854 | 0.359927 | − | 0.932980i | \(-0.382802\pi\) | ||||
0.359927 | + | 0.932980i | \(0.382802\pi\) | |||||||
\(152\) | 1.52328e8 | 3.51827 | ||||||||
\(153\) | −7.77472e7 | −1.75495 | ||||||||
\(154\) | 1.31014e7 | 0.289065 | ||||||||
\(155\) | 8.13224e7 | 1.75408 | ||||||||
\(156\) | 1.44326e8 | 3.04375 | ||||||||
\(157\) | −4.33834e7 | −0.894694 | −0.447347 | − | 0.894360i | \(-0.647631\pi\) | ||||
−0.447347 | + | 0.894360i | \(0.647631\pi\) | |||||||
\(158\) | 1.70071e7 | 0.343029 | ||||||||
\(159\) | 1.75583e7 | 0.346411 | ||||||||
\(160\) | −3.07562e8 | −5.93626 | ||||||||
\(161\) | 2.21098e7 | 0.417537 | ||||||||
\(162\) | 2.70244e7 | 0.499406 | ||||||||
\(163\) | −6.67032e7 | −1.20640 | −0.603198 | − | 0.797591i | \(-0.706107\pi\) | ||||
−0.603198 | + | 0.797591i | \(0.706107\pi\) | |||||||
\(164\) | −7.28769e7 | −1.29014 | ||||||||
\(165\) | −2.55339e7 | −0.442511 | ||||||||
\(166\) | 8.08928e7 | 1.37256 | ||||||||
\(167\) | 6.05087e7 | 1.00533 | 0.502667 | − | 0.864480i | \(-0.332352\pi\) | ||||
0.502667 | + | 0.864480i | \(0.332352\pi\) | |||||||
\(168\) | −2.43905e8 | −3.96861 | ||||||||
\(169\) | −3.31560e7 | −0.528396 | ||||||||
\(170\) | 1.97467e8 | 3.08265 | ||||||||
\(171\) | −9.78175e7 | −1.49600 | ||||||||
\(172\) | 1.56610e8 | 2.34677 | ||||||||
\(173\) | −1.01700e8 | −1.49335 | −0.746675 | − | 0.665189i | \(-0.768351\pi\) | ||||
−0.746675 | + | 0.665189i | \(0.768351\pi\) | |||||||
\(174\) | 3.97741e7 | 0.572372 | ||||||||
\(175\) | 4.13332e7 | 0.582996 | ||||||||
\(176\) | −6.10364e7 | −0.843907 | ||||||||
\(177\) | −1.15426e8 | −1.56458 | ||||||||
\(178\) | 7.11866e6 | 0.0946081 | ||||||||
\(179\) | 3.98101e7 | 0.518809 | 0.259405 | − | 0.965769i | \(-0.416474\pi\) | ||||
0.259405 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(180\) | 4.42883e8 | 5.66025 | ||||||||
\(181\) | 5.63538e7 | 0.706396 | 0.353198 | − | 0.935549i | \(-0.385094\pi\) | ||||
0.353198 | + | 0.935549i | \(0.385094\pi\) | |||||||
\(182\) | −7.77184e7 | −0.955596 | ||||||||
\(183\) | 2.08885e8 | 2.51958 | ||||||||
\(184\) | −1.74123e8 | −2.06061 | ||||||||
\(185\) | 2.30460e7 | 0.267606 | ||||||||
\(186\) | −3.51978e8 | −4.01070 | ||||||||
\(187\) | 2.17773e7 | 0.243533 | ||||||||
\(188\) | −4.12514e8 | −4.52779 | ||||||||
\(189\) | 5.19973e7 | 0.560227 | ||||||||
\(190\) | 2.48443e8 | 2.62778 | ||||||||
\(191\) | 1.79471e7 | 0.186370 | 0.0931851 | − | 0.995649i | \(-0.470295\pi\) | ||||
0.0931851 | + | 0.995649i | \(0.470295\pi\) | |||||||
\(192\) | 7.01612e8 | 7.15389 | ||||||||
\(193\) | −8.66641e7 | −0.867738 | −0.433869 | − | 0.900976i | \(-0.642852\pi\) | ||||
−0.433869 | + | 0.900976i | \(0.642852\pi\) | |||||||
\(194\) | 4.81068e7 | 0.473042 | ||||||||
\(195\) | 1.51469e8 | 1.46286 | ||||||||
\(196\) | −1.45205e8 | −1.37748 | ||||||||
\(197\) | −1.48231e8 | −1.38136 | −0.690681 | − | 0.723159i | \(-0.742689\pi\) | ||||
−0.690681 | + | 0.723159i | \(0.742689\pi\) | |||||||
\(198\) | 6.62559e7 | 0.606592 | ||||||||
\(199\) | 1.80493e8 | 1.62358 | 0.811791 | − | 0.583948i | \(-0.198493\pi\) | ||||
0.811791 | + | 0.583948i | \(0.198493\pi\) | |||||||
\(200\) | −3.25514e8 | −2.87717 | ||||||||
\(201\) | −9.48604e7 | −0.823946 | ||||||||
\(202\) | −4.21183e8 | −3.59535 | ||||||||
\(203\) | −1.57889e7 | −0.132470 | ||||||||
\(204\) | −6.30048e8 | −5.19599 | ||||||||
\(205\) | −7.64837e7 | −0.620055 | ||||||||
\(206\) | 2.94465e8 | 2.34692 | ||||||||
\(207\) | 1.11813e8 | 0.876186 | ||||||||
\(208\) | 3.62072e8 | 2.78980 | ||||||||
\(209\) | 2.73991e7 | 0.207598 | ||||||||
\(210\) | −3.97802e8 | −2.96414 | ||||||||
\(211\) | 1.01529e8 | 0.744049 | 0.372024 | − | 0.928223i | \(-0.378664\pi\) | ||||
0.372024 | + | 0.928223i | \(0.378664\pi\) | |||||||
\(212\) | 8.53045e7 | 0.614888 | ||||||||
\(213\) | 2.57672e8 | 1.82700 | ||||||||
\(214\) | 1.52797e8 | 1.06578 | ||||||||
\(215\) | 1.64361e8 | 1.12789 | ||||||||
\(216\) | −4.09498e8 | −2.76480 | ||||||||
\(217\) | 1.39723e8 | 0.928236 | ||||||||
\(218\) | 5.33162e8 | 3.48547 | ||||||||
\(219\) | 5.03379e6 | 0.0323848 | ||||||||
\(220\) | −1.24053e8 | −0.785468 | ||||||||
\(221\) | −1.29184e8 | −0.805077 | ||||||||
\(222\) | −9.97475e7 | −0.611880 | ||||||||
\(223\) | 9.90258e7 | 0.597973 | 0.298986 | − | 0.954257i | \(-0.403351\pi\) | ||||
0.298986 | + | 0.954257i | \(0.403351\pi\) | |||||||
\(224\) | −5.28433e8 | −3.14139 | ||||||||
\(225\) | 2.09029e8 | 1.22340 | ||||||||
\(226\) | −1.11066e8 | −0.640033 | ||||||||
\(227\) | −7.06827e7 | −0.401072 | −0.200536 | − | 0.979686i | \(-0.564268\pi\) | ||||
−0.200536 | + | 0.979686i | \(0.564268\pi\) | |||||||
\(228\) | −7.92694e8 | −4.42928 | ||||||||
\(229\) | 7.97463e7 | 0.438820 | 0.219410 | − | 0.975633i | \(-0.429587\pi\) | ||||
0.219410 | + | 0.975633i | \(0.429587\pi\) | |||||||
\(230\) | −2.83990e8 | −1.53906 | ||||||||
\(231\) | −4.38708e7 | −0.234171 | ||||||||
\(232\) | 1.24344e8 | 0.653757 | ||||||||
\(233\) | 2.78555e8 | 1.44266 | 0.721332 | − | 0.692590i | \(-0.243530\pi\) | ||||
0.721332 | + | 0.692590i | \(0.243530\pi\) | |||||||
\(234\) | −3.93035e8 | −2.00528 | ||||||||
\(235\) | −4.32930e8 | −2.17611 | ||||||||
\(236\) | −5.60783e8 | −2.77717 | ||||||||
\(237\) | −5.69492e7 | −0.277887 | ||||||||
\(238\) | 3.39276e8 | 1.63130 | ||||||||
\(239\) | 3.03984e8 | 1.44032 | 0.720159 | − | 0.693809i | \(-0.244069\pi\) | ||||
0.720159 | + | 0.693809i | \(0.244069\pi\) | |||||||
\(240\) | 1.85327e9 | 8.65363 | ||||||||
\(241\) | 1.62667e8 | 0.748581 | 0.374291 | − | 0.927311i | \(-0.377886\pi\) | ||||
0.374291 | + | 0.927311i | \(0.377886\pi\) | |||||||
\(242\) | 4.11496e8 | 1.86643 | ||||||||
\(243\) | −2.66152e8 | −1.18989 | ||||||||
\(244\) | 1.01484e9 | 4.47232 | ||||||||
\(245\) | −1.52391e8 | −0.662030 | ||||||||
\(246\) | 3.31035e8 | 1.41776 | ||||||||
\(247\) | −1.62533e8 | −0.686282 | ||||||||
\(248\) | −1.10037e9 | −4.58098 | ||||||||
\(249\) | −2.70874e8 | −1.11191 | ||||||||
\(250\) | 1.18726e8 | 0.480568 | ||||||||
\(251\) | −9.86866e7 | −0.393913 | −0.196956 | − | 0.980412i | \(-0.563106\pi\) | ||||
−0.196956 | + | 0.980412i | \(0.563106\pi\) | |||||||
\(252\) | 7.60933e8 | 2.99533 | ||||||||
\(253\) | −3.13193e7 | −0.121588 | ||||||||
\(254\) | 4.86818e8 | 1.86401 | ||||||||
\(255\) | −6.61230e8 | −2.49725 | ||||||||
\(256\) | 1.10291e9 | 4.10868 | ||||||||
\(257\) | 1.41643e8 | 0.520509 | 0.260254 | − | 0.965540i | \(-0.416194\pi\) | ||||
0.260254 | + | 0.965540i | \(0.416194\pi\) | |||||||
\(258\) | −7.11386e8 | −2.57891 | ||||||||
\(259\) | 3.95962e7 | 0.141613 | ||||||||
\(260\) | 7.35892e8 | 2.59662 | ||||||||
\(261\) | −7.98472e7 | −0.277983 | ||||||||
\(262\) | −9.29683e8 | −3.19360 | ||||||||
\(263\) | 1.80962e8 | 0.613396 | 0.306698 | − | 0.951807i | \(-0.400776\pi\) | ||||
0.306698 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(264\) | 3.45499e8 | 1.15567 | ||||||||
\(265\) | 8.95263e7 | 0.295522 | ||||||||
\(266\) | 4.26859e8 | 1.39059 | ||||||||
\(267\) | −2.38372e7 | −0.0766419 | ||||||||
\(268\) | −4.60866e8 | −1.46252 | ||||||||
\(269\) | −2.27845e8 | −0.713684 | −0.356842 | − | 0.934165i | \(-0.616146\pi\) | ||||
−0.356842 | + | 0.934165i | \(0.616146\pi\) | |||||||
\(270\) | −6.67880e8 | −2.06502 | ||||||||
\(271\) | −6.01958e8 | −1.83727 | −0.918636 | − | 0.395104i | \(-0.870709\pi\) | ||||
−0.918636 | + | 0.395104i | \(0.870709\pi\) | |||||||
\(272\) | −1.58061e9 | −4.76247 | ||||||||
\(273\) | 2.60244e8 | 0.774127 | ||||||||
\(274\) | 2.36978e7 | 0.0695954 | ||||||||
\(275\) | −5.85497e7 | −0.169770 | ||||||||
\(276\) | 9.06112e8 | 2.59418 | ||||||||
\(277\) | −1.98459e8 | −0.561036 | −0.280518 | − | 0.959849i | \(-0.590506\pi\) | ||||
−0.280518 | + | 0.959849i | \(0.590506\pi\) | |||||||
\(278\) | −1.55528e8 | −0.434161 | ||||||||
\(279\) | 7.06601e8 | 1.94787 | ||||||||
\(280\) | −1.24363e9 | −3.38561 | ||||||||
\(281\) | −3.68152e8 | −0.989818 | −0.494909 | − | 0.868945i | \(-0.664799\pi\) | ||||
−0.494909 | + | 0.868945i | \(0.664799\pi\) | |||||||
\(282\) | 1.87380e9 | 4.97567 | ||||||||
\(283\) | 2.58445e8 | 0.677821 | 0.338910 | − | 0.940819i | \(-0.389942\pi\) | ||||
0.338910 | + | 0.940819i | \(0.389942\pi\) | |||||||
\(284\) | 1.25186e9 | 3.24297 | ||||||||
\(285\) | −8.31926e8 | −2.12876 | ||||||||
\(286\) | 1.10091e8 | 0.278272 | ||||||||
\(287\) | −1.31409e8 | −0.328125 | ||||||||
\(288\) | −2.67237e9 | −6.59209 | ||||||||
\(289\) | 1.53609e8 | 0.374347 | ||||||||
\(290\) | 2.02801e8 | 0.488289 | ||||||||
\(291\) | −1.61088e8 | −0.383211 | ||||||||
\(292\) | 2.44560e7 | 0.0574838 | ||||||||
\(293\) | −4.91702e8 | −1.14200 | −0.570999 | − | 0.820951i | \(-0.693444\pi\) | ||||
−0.570999 | + | 0.820951i | \(0.693444\pi\) | |||||||
\(294\) | 6.59576e8 | 1.51373 | ||||||||
\(295\) | −5.88537e8 | −1.33474 | ||||||||
\(296\) | −3.11835e8 | −0.698882 | ||||||||
\(297\) | −7.36557e7 | −0.163139 | ||||||||
\(298\) | −4.65308e7 | −0.101855 | ||||||||
\(299\) | 1.85788e8 | 0.401947 | ||||||||
\(300\) | 1.69393e9 | 3.62218 | ||||||||
\(301\) | 2.82395e8 | 0.596862 | ||||||||
\(302\) | −6.72107e8 | −1.40415 | ||||||||
\(303\) | 1.41035e9 | 2.91259 | ||||||||
\(304\) | −1.98864e9 | −4.05973 | ||||||||
\(305\) | 1.06507e9 | 2.14945 | ||||||||
\(306\) | 1.71577e9 | 3.42322 | ||||||||
\(307\) | −4.21676e8 | −0.831754 | −0.415877 | − | 0.909421i | \(-0.636525\pi\) | ||||
−0.415877 | + | 0.909421i | \(0.636525\pi\) | |||||||
\(308\) | −2.13140e8 | −0.415660 | ||||||||
\(309\) | −9.86031e8 | −1.90124 | ||||||||
\(310\) | −1.79467e9 | −3.42152 | ||||||||
\(311\) | 8.55447e8 | 1.61262 | 0.806310 | − | 0.591494i | \(-0.201461\pi\) | ||||
0.806310 | + | 0.591494i | \(0.201461\pi\) | |||||||
\(312\) | −2.04952e9 | −3.82043 | ||||||||
\(313\) | −417650. | −0.000769853 0 | −0.000384926 | − | 1.00000i | \(-0.500123\pi\) | ||||
−0.000384926 | 1.00000i | \(0.500123\pi\) | ||||||||
\(314\) | 9.57410e8 | 1.74520 | ||||||||
\(315\) | 7.98593e8 | 1.43959 | ||||||||
\(316\) | −2.76680e8 | −0.493257 | ||||||||
\(317\) | −3.50781e8 | −0.618484 | −0.309242 | − | 0.950983i | \(-0.600075\pi\) | ||||
−0.309242 | + | 0.950983i | \(0.600075\pi\) | |||||||
\(318\) | −3.87486e8 | −0.675712 | ||||||||
\(319\) | 2.23655e7 | 0.0385755 | ||||||||
\(320\) | 3.57739e9 | 6.10297 | ||||||||
\(321\) | −5.11649e8 | −0.863385 | ||||||||
\(322\) | −4.87933e8 | −0.814451 | ||||||||
\(323\) | 7.09530e8 | 1.17155 | ||||||||
\(324\) | −4.39646e8 | −0.718118 | ||||||||
\(325\) | 3.47321e8 | 0.561228 | ||||||||
\(326\) | 1.47205e9 | 2.35321 | ||||||||
\(327\) | −1.78532e9 | −2.82357 | ||||||||
\(328\) | 1.03490e9 | 1.61934 | ||||||||
\(329\) | −7.43832e8 | −1.15157 | ||||||||
\(330\) | 5.63498e8 | 0.863165 | ||||||||
\(331\) | 4.95807e8 | 0.751475 | 0.375738 | − | 0.926726i | \(-0.377389\pi\) | ||||
0.375738 | + | 0.926726i | \(0.377389\pi\) | |||||||
\(332\) | −1.31601e9 | −1.97367 | ||||||||
\(333\) | 2.00244e8 | 0.297170 | ||||||||
\(334\) | −1.33534e9 | −1.96101 | ||||||||
\(335\) | −4.83675e8 | −0.702906 | ||||||||
\(336\) | 3.18416e9 | 4.57939 | ||||||||
\(337\) | 9.54347e8 | 1.35832 | 0.679159 | − | 0.733991i | \(-0.262345\pi\) | ||||
0.679159 | + | 0.733991i | \(0.262345\pi\) | |||||||
\(338\) | 7.31707e8 | 1.03069 | ||||||||
\(339\) | 3.71911e8 | 0.518490 | ||||||||
\(340\) | −3.21250e9 | −4.43268 | ||||||||
\(341\) | −1.97922e8 | −0.270304 | ||||||||
\(342\) | 2.15870e9 | 2.91810 | ||||||||
\(343\) | −7.94973e8 | −1.06371 | ||||||||
\(344\) | −2.22397e9 | −2.94560 | ||||||||
\(345\) | 9.50956e8 | 1.24679 | ||||||||
\(346\) | 2.24439e9 | 2.91294 | ||||||||
\(347\) | −1.49821e8 | −0.192495 | −0.0962474 | − | 0.995357i | \(-0.530684\pi\) | ||||
−0.0962474 | + | 0.995357i | \(0.530684\pi\) | |||||||
\(348\) | −6.47066e8 | −0.823040 | ||||||||
\(349\) | −9.98391e8 | −1.25722 | −0.628611 | − | 0.777720i | \(-0.716376\pi\) | ||||
−0.628611 | + | 0.777720i | \(0.716376\pi\) | |||||||
\(350\) | −9.12165e8 | −1.13720 | ||||||||
\(351\) | 4.36931e8 | 0.539309 | ||||||||
\(352\) | 7.48542e8 | 0.914780 | ||||||||
\(353\) | 1.40557e9 | 1.70075 | 0.850373 | − | 0.526180i | \(-0.176376\pi\) | ||||
0.850373 | + | 0.526180i | \(0.176376\pi\) | |||||||
\(354\) | 2.54730e9 | 3.05188 | ||||||||
\(355\) | 1.31382e9 | 1.55861 | ||||||||
\(356\) | −1.15810e8 | −0.136041 | ||||||||
\(357\) | −1.13608e9 | −1.32151 | ||||||||
\(358\) | −8.78553e8 | −1.01199 | ||||||||
\(359\) | 1.30123e9 | 1.48431 | 0.742155 | − | 0.670228i | \(-0.233804\pi\) | ||||
0.742155 | + | 0.670228i | \(0.233804\pi\) | |||||||
\(360\) | −6.28922e9 | −7.10458 | ||||||||
\(361\) | −1.17891e6 | −0.00131888 | ||||||||
\(362\) | −1.24365e9 | −1.37790 | ||||||||
\(363\) | −1.37792e9 | −1.51199 | ||||||||
\(364\) | 1.26436e9 | 1.37410 | ||||||||
\(365\) | 2.56664e7 | 0.0276274 | ||||||||
\(366\) | −4.60980e9 | −4.91471 | ||||||||
\(367\) | 8.12443e8 | 0.857950 | 0.428975 | − | 0.903316i | \(-0.358875\pi\) | ||||
0.428975 | + | 0.903316i | \(0.358875\pi\) | |||||||
\(368\) | 2.27317e9 | 2.37774 | ||||||||
\(369\) | −6.64558e8 | −0.688558 | ||||||||
\(370\) | −5.08594e8 | −0.521993 | ||||||||
\(371\) | 1.53818e8 | 0.156387 | ||||||||
\(372\) | 5.72616e9 | 5.76717 | ||||||||
\(373\) | 1.29059e9 | 1.28767 | 0.643837 | − | 0.765163i | \(-0.277342\pi\) | ||||
0.643837 | + | 0.765163i | \(0.277342\pi\) | |||||||
\(374\) | −4.80594e8 | −0.475038 | ||||||||
\(375\) | −3.97560e8 | −0.389308 | ||||||||
\(376\) | 5.85796e9 | 5.68315 | ||||||||
\(377\) | −1.32674e8 | −0.127523 | ||||||||
\(378\) | −1.14751e9 | −1.09278 | ||||||||
\(379\) | 4.40462e7 | 0.0415596 | 0.0207798 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207798 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(380\) | −4.04180e9 | −3.77861 | ||||||||
\(381\) | −1.63014e9 | −1.51003 | ||||||||
\(382\) | −3.96066e8 | −0.363535 | ||||||||
\(383\) | −1.42034e9 | −1.29180 | −0.645902 | − | 0.763421i | \(-0.723518\pi\) | ||||
−0.645902 | + | 0.763421i | \(0.723518\pi\) | |||||||
\(384\) | −7.76259e9 | −6.99596 | ||||||||
\(385\) | −2.23689e8 | −0.199771 | ||||||||
\(386\) | 1.91256e9 | 1.69262 | ||||||||
\(387\) | 1.42812e9 | 1.25249 | ||||||||
\(388\) | −7.82625e8 | −0.680209 | ||||||||
\(389\) | 8.67673e8 | 0.747365 | 0.373682 | − | 0.927557i | \(-0.378095\pi\) | ||||
0.373682 | + | 0.927557i | \(0.378095\pi\) | |||||||
\(390\) | −3.34271e9 | −2.85347 | ||||||||
\(391\) | −8.11048e8 | −0.686164 | ||||||||
\(392\) | 2.06200e9 | 1.72897 | ||||||||
\(393\) | 3.11309e9 | 2.58713 | ||||||||
\(394\) | 3.27125e9 | 2.69450 | ||||||||
\(395\) | −2.90373e8 | −0.237065 | ||||||||
\(396\) | −1.07788e9 | −0.872246 | ||||||||
\(397\) | 1.11899e7 | 0.00897550 | 0.00448775 | − | 0.999990i | \(-0.498571\pi\) | ||||
0.00448775 | + | 0.999990i | \(0.498571\pi\) | |||||||
\(398\) | −3.98322e9 | −3.16697 | ||||||||
\(399\) | −1.42936e9 | −1.12651 | ||||||||
\(400\) | 4.24956e9 | 3.31997 | ||||||||
\(401\) | −1.18782e9 | −0.919906 | −0.459953 | − | 0.887943i | \(-0.652134\pi\) | ||||
−0.459953 | + | 0.887943i | \(0.652134\pi\) | |||||||
\(402\) | 2.09344e9 | 1.60719 | ||||||||
\(403\) | 1.17409e9 | 0.893577 | ||||||||
\(404\) | 6.85202e9 | 5.16992 | ||||||||
\(405\) | −4.61405e8 | −0.345136 | ||||||||
\(406\) | 3.48439e8 | 0.258396 | ||||||||
\(407\) | −5.60892e7 | −0.0412381 | ||||||||
\(408\) | 8.94709e9 | 6.52185 | ||||||||
\(409\) | −1.10619e9 | −0.799462 | −0.399731 | − | 0.916632i | \(-0.630896\pi\) | ||||
−0.399731 | + | 0.916632i | \(0.630896\pi\) | |||||||
\(410\) | 1.68789e9 | 1.20948 | ||||||||
\(411\) | −7.93533e7 | −0.0563792 | ||||||||
\(412\) | −4.79050e9 | −3.37474 | ||||||||
\(413\) | −1.01119e9 | −0.706327 | ||||||||
\(414\) | −2.46756e9 | −1.70910 | ||||||||
\(415\) | −1.38114e9 | −0.948567 | ||||||||
\(416\) | −4.44040e9 | −3.02410 | ||||||||
\(417\) | 5.20792e8 | 0.351713 | ||||||||
\(418\) | −6.04659e8 | −0.404942 | ||||||||
\(419\) | 2.88674e9 | 1.91716 | 0.958581 | − | 0.284819i | \(-0.0919336\pi\) | ||||
0.958581 | + | 0.284819i | \(0.0919336\pi\) | |||||||
\(420\) | 6.47164e9 | 4.26228 | ||||||||
\(421\) | 9.42877e8 | 0.615840 | 0.307920 | − | 0.951412i | \(-0.400367\pi\) | ||||
0.307920 | + | 0.951412i | \(0.400367\pi\) | |||||||
\(422\) | −2.24060e9 | −1.45135 | ||||||||
\(423\) | −3.76168e9 | −2.41652 | ||||||||
\(424\) | −1.21138e9 | −0.771790 | ||||||||
\(425\) | −1.51621e9 | −0.958072 | ||||||||
\(426\) | −5.68645e9 | −3.56375 | ||||||||
\(427\) | 1.82993e9 | 1.13746 | ||||||||
\(428\) | −2.48578e9 | −1.53253 | ||||||||
\(429\) | −3.68644e8 | −0.225427 | ||||||||
\(430\) | −3.62722e9 | −2.20006 | ||||||||
\(431\) | 4.00016e8 | 0.240662 | 0.120331 | − | 0.992734i | \(-0.461604\pi\) | ||||
0.120331 | + | 0.992734i | \(0.461604\pi\) | |||||||
\(432\) | 5.34597e9 | 3.19031 | ||||||||
\(433\) | −2.34094e9 | −1.38575 | −0.692873 | − | 0.721060i | \(-0.743655\pi\) | ||||
−0.692873 | + | 0.721060i | \(0.743655\pi\) | |||||||
\(434\) | −3.08349e9 | −1.81062 | ||||||||
\(435\) | −6.79090e8 | −0.395562 | ||||||||
\(436\) | −8.67374e9 | −5.01192 | ||||||||
\(437\) | −1.02042e9 | −0.584916 | ||||||||
\(438\) | −1.11089e8 | −0.0631700 | ||||||||
\(439\) | −7.14577e8 | −0.403110 | −0.201555 | − | 0.979477i | \(-0.564599\pi\) | ||||
−0.201555 | + | 0.979477i | \(0.564599\pi\) | |||||||
\(440\) | 1.76163e9 | 0.985897 | ||||||||
\(441\) | −1.32411e9 | −0.735171 | ||||||||
\(442\) | 2.85092e9 | 1.57039 | ||||||||
\(443\) | 2.19239e9 | 1.19813 | 0.599066 | − | 0.800699i | \(-0.295539\pi\) | ||||
0.599066 | + | 0.800699i | \(0.295539\pi\) | |||||||
\(444\) | 1.62274e9 | 0.879851 | ||||||||
\(445\) | −1.21542e8 | −0.0653830 | ||||||||
\(446\) | −2.18536e9 | −1.16641 | ||||||||
\(447\) | 1.55811e8 | 0.0825129 | ||||||||
\(448\) | 6.14643e9 | 3.22961 | ||||||||
\(449\) | 5.35068e8 | 0.278963 | 0.139482 | − | 0.990225i | \(-0.455456\pi\) | ||||
0.139482 | + | 0.990225i | \(0.455456\pi\) | |||||||
\(450\) | −4.61297e9 | −2.38636 | ||||||||
\(451\) | 1.86145e8 | 0.0955507 | ||||||||
\(452\) | 1.80688e9 | 0.920333 | ||||||||
\(453\) | 2.25059e9 | 1.13750 | ||||||||
\(454\) | 1.55987e9 | 0.782335 | ||||||||
\(455\) | 1.32694e9 | 0.660405 | ||||||||
\(456\) | 1.12568e10 | 5.55951 | ||||||||
\(457\) | 3.18626e9 | 1.56162 | 0.780808 | − | 0.624771i | \(-0.214808\pi\) | ||||
0.780808 | + | 0.624771i | \(0.214808\pi\) | |||||||
\(458\) | −1.75989e9 | −0.855965 | ||||||||
\(459\) | −1.90740e9 | −0.920655 | ||||||||
\(460\) | 4.62009e9 | 2.21309 | ||||||||
\(461\) | 3.12207e9 | 1.48419 | 0.742094 | − | 0.670296i | \(-0.233833\pi\) | ||||
0.742094 | + | 0.670296i | \(0.233833\pi\) | |||||||
\(462\) | 9.68166e8 | 0.456776 | ||||||||
\(463\) | 3.15215e9 | 1.47595 | 0.737977 | − | 0.674825i | \(-0.235781\pi\) | ||||
0.737977 | + | 0.674825i | \(0.235781\pi\) | |||||||
\(464\) | −1.62330e9 | −0.754371 | ||||||||
\(465\) | 6.00956e9 | 2.77177 | ||||||||
\(466\) | −6.14732e9 | −2.81407 | ||||||||
\(467\) | 7.68753e8 | 0.349283 | 0.174642 | − | 0.984632i | \(-0.444123\pi\) | ||||
0.174642 | + | 0.984632i | \(0.444123\pi\) | |||||||
\(468\) | 6.39409e9 | 2.88349 | ||||||||
\(469\) | −8.31020e8 | −0.371969 | ||||||||
\(470\) | 9.55416e9 | 4.24473 | ||||||||
\(471\) | −3.20594e9 | −1.41378 | ||||||||
\(472\) | 7.96347e9 | 3.48582 | ||||||||
\(473\) | −4.00021e8 | −0.173808 | ||||||||
\(474\) | 1.25679e9 | 0.542048 | ||||||||
\(475\) | −1.90762e9 | −0.816702 | ||||||||
\(476\) | −5.51951e9 | −2.34572 | ||||||||
\(477\) | 7.77884e8 | 0.328171 | ||||||||
\(478\) | −6.70850e9 | −2.80949 | ||||||||
\(479\) | 1.41643e9 | 0.588873 | 0.294436 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294436 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(480\) | −2.27282e10 | −9.38038 | ||||||||
\(481\) | 3.32725e8 | 0.136326 | ||||||||
\(482\) | −3.58983e9 | −1.46019 | ||||||||
\(483\) | 1.63387e9 | 0.659786 | ||||||||
\(484\) | −6.69442e9 | −2.68383 | ||||||||
\(485\) | −8.21358e8 | −0.326916 | ||||||||
\(486\) | 5.87360e9 | 2.32101 | ||||||||
\(487\) | 3.54792e9 | 1.39195 | 0.695974 | − | 0.718067i | \(-0.254973\pi\) | ||||
0.695974 | + | 0.718067i | \(0.254973\pi\) | |||||||
\(488\) | −1.44114e10 | −5.61353 | ||||||||
\(489\) | −4.92923e9 | −1.90633 | ||||||||
\(490\) | 3.36305e9 | 1.29136 | ||||||||
\(491\) | −4.84906e8 | −0.184872 | −0.0924362 | − | 0.995719i | \(-0.529465\pi\) | ||||
−0.0924362 | + | 0.995719i | \(0.529465\pi\) | |||||||
\(492\) | −5.38545e9 | −2.03866 | ||||||||
\(493\) | 5.79180e8 | 0.217695 | ||||||||
\(494\) | 3.58688e9 | 1.33867 | ||||||||
\(495\) | −1.13123e9 | −0.419211 | ||||||||
\(496\) | 1.43652e10 | 5.28600 | ||||||||
\(497\) | 2.25732e9 | 0.824794 | ||||||||
\(498\) | 5.97781e9 | 2.16890 | ||||||||
\(499\) | −4.20411e9 | −1.51468 | −0.757342 | − | 0.653018i | \(-0.773503\pi\) | ||||
−0.757342 | + | 0.653018i | \(0.773503\pi\) | |||||||
\(500\) | −1.93149e9 | −0.691031 | ||||||||
\(501\) | 4.47147e9 | 1.58861 | ||||||||
\(502\) | 2.17787e9 | 0.768369 | ||||||||
\(503\) | −6.03464e8 | −0.211428 | −0.105714 | − | 0.994397i | \(-0.533713\pi\) | ||||
−0.105714 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(504\) | −1.08057e10 | −3.75965 | ||||||||
\(505\) | 7.19114e9 | 2.48472 | ||||||||
\(506\) | 6.91172e8 | 0.237170 | ||||||||
\(507\) | −2.45016e9 | −0.834962 | ||||||||
\(508\) | −7.91979e9 | −2.68035 | ||||||||
\(509\) | −3.03471e9 | −1.02001 | −0.510006 | − | 0.860171i | \(-0.670357\pi\) | ||||
−0.510006 | + | 0.860171i | \(0.670357\pi\) | |||||||
\(510\) | 1.45924e10 | 4.87116 | ||||||||
\(511\) | 4.40983e7 | 0.0146200 | ||||||||
\(512\) | −1.08941e10 | −3.58711 | ||||||||
\(513\) | −2.39979e9 | −0.784806 | ||||||||
\(514\) | −3.12585e9 | −1.01531 | ||||||||
\(515\) | −5.02759e9 | −1.62194 | ||||||||
\(516\) | 1.15732e10 | 3.70833 | ||||||||
\(517\) | 1.05366e9 | 0.335339 | ||||||||
\(518\) | −8.73833e8 | −0.276232 | ||||||||
\(519\) | −7.51545e9 | −2.35977 | ||||||||
\(520\) | −1.04501e10 | −3.25919 | ||||||||
\(521\) | −4.88230e9 | −1.51249 | −0.756245 | − | 0.654289i | \(-0.772968\pi\) | ||||
−0.756245 | + | 0.654289i | \(0.772968\pi\) | |||||||
\(522\) | 1.76212e9 | 0.542235 | ||||||||
\(523\) | 4.28368e9 | 1.30936 | 0.654682 | − | 0.755904i | \(-0.272802\pi\) | ||||
0.654682 | + | 0.755904i | \(0.272802\pi\) | |||||||
\(524\) | 1.51246e10 | 4.59222 | ||||||||
\(525\) | 3.05443e9 | 0.921241 | ||||||||
\(526\) | −3.99357e9 | −1.19650 | ||||||||
\(527\) | −5.12541e9 | −1.52543 | ||||||||
\(528\) | −4.51046e9 | −1.33353 | ||||||||
\(529\) | −2.23841e9 | −0.657422 | ||||||||
\(530\) | −1.97572e9 | −0.576448 | ||||||||
\(531\) | −5.11373e9 | −1.48220 | ||||||||
\(532\) | −6.94436e9 | −1.99959 | ||||||||
\(533\) | −1.10423e9 | −0.315873 | ||||||||
\(534\) | 5.26054e8 | 0.149498 | ||||||||
\(535\) | −2.60880e9 | −0.736551 | ||||||||
\(536\) | 6.54459e9 | 1.83572 | ||||||||
\(537\) | 2.94188e9 | 0.819814 | ||||||||
\(538\) | 5.02821e9 | 1.39212 | ||||||||
\(539\) | 3.70888e8 | 0.102019 | ||||||||
\(540\) | 1.08654e10 | 2.96939 | ||||||||
\(541\) | 9.58437e8 | 0.260239 | 0.130120 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130120 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(542\) | 1.32844e10 | 3.58380 | ||||||||
\(543\) | 4.16443e9 | 1.11624 | ||||||||
\(544\) | 1.93843e10 | 5.16244 | ||||||||
\(545\) | −9.10302e9 | −2.40878 | ||||||||
\(546\) | −5.74323e9 | −1.51002 | ||||||||
\(547\) | −1.14779e9 | −0.299851 | −0.149926 | − | 0.988697i | \(-0.547903\pi\) | ||||
−0.149926 | + | 0.988697i | \(0.547903\pi\) | |||||||
\(548\) | −3.85527e8 | −0.100074 | ||||||||
\(549\) | 9.25424e9 | 2.38692 | ||||||||
\(550\) | 1.29211e9 | 0.331154 | ||||||||
\(551\) | 7.28694e8 | 0.185573 | ||||||||
\(552\) | −1.28674e10 | −3.25614 | ||||||||
\(553\) | −4.98900e8 | −0.125452 | ||||||||
\(554\) | 4.37970e9 | 1.09436 | ||||||||
\(555\) | 1.70305e9 | 0.422866 | ||||||||
\(556\) | 2.53020e9 | 0.624300 | ||||||||
\(557\) | −5.96397e9 | −1.46232 | −0.731159 | − | 0.682207i | \(-0.761020\pi\) | ||||
−0.731159 | + | 0.682207i | \(0.761020\pi\) | |||||||
\(558\) | −1.55937e10 | −3.79953 | ||||||||
\(559\) | 2.37295e9 | 0.574576 | ||||||||
\(560\) | 1.62354e10 | 3.90666 | ||||||||
\(561\) | 1.60930e9 | 0.384827 | ||||||||
\(562\) | 8.12461e9 | 1.93075 | ||||||||
\(563\) | −2.86789e9 | −0.677302 | −0.338651 | − | 0.940912i | \(-0.609971\pi\) | ||||
−0.338651 | + | 0.940912i | \(0.609971\pi\) | |||||||
\(564\) | −3.04839e10 | −7.15474 | ||||||||
\(565\) | 1.89631e9 | 0.442322 | ||||||||
\(566\) | −5.70351e9 | −1.32216 | ||||||||
\(567\) | −7.92756e8 | −0.182641 | ||||||||
\(568\) | −1.77772e10 | −4.07048 | ||||||||
\(569\) | −5.88781e8 | −0.133986 | −0.0669932 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669932 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(570\) | 1.83594e10 | 4.15238 | ||||||||
\(571\) | 6.81053e9 | 1.53093 | 0.765463 | − | 0.643479i | \(-0.222510\pi\) | ||||
0.765463 | + | 0.643479i | \(0.222510\pi\) | |||||||
\(572\) | −1.79101e9 | −0.400139 | ||||||||
\(573\) | 1.32625e9 | 0.294499 | ||||||||
\(574\) | 2.90002e9 | 0.640043 | ||||||||
\(575\) | 2.18056e9 | 0.478332 | ||||||||
\(576\) | 3.10835e10 | 6.77722 | ||||||||
\(577\) | 6.57528e9 | 1.42495 | 0.712474 | − | 0.701698i | \(-0.247575\pi\) | ||||
0.712474 | + | 0.701698i | \(0.247575\pi\) | |||||||
\(578\) | −3.38994e9 | −0.730204 | ||||||||
\(579\) | −6.40430e9 | −1.37119 | ||||||||
\(580\) | −3.29927e9 | −0.702133 | ||||||||
\(581\) | −2.37298e9 | −0.501970 | ||||||||
\(582\) | 3.55499e9 | 0.747494 | ||||||||
\(583\) | −2.17888e8 | −0.0455401 | ||||||||
\(584\) | −3.47291e8 | −0.0721520 | ||||||||
\(585\) | 6.71054e9 | 1.38584 | ||||||||
\(586\) | 1.08512e10 | 2.22759 | ||||||||
\(587\) | 3.22998e9 | 0.659123 | 0.329561 | − | 0.944134i | \(-0.393099\pi\) | ||||
0.329561 | + | 0.944134i | \(0.393099\pi\) | |||||||
\(588\) | −1.07303e10 | −2.17667 | ||||||||
\(589\) | −6.44852e9 | −1.30034 | ||||||||
\(590\) | 1.29882e10 | 2.60355 | ||||||||
\(591\) | −1.09540e10 | −2.18281 | ||||||||
\(592\) | 4.07098e9 | 0.806442 | ||||||||
\(593\) | 1.64704e9 | 0.324350 | 0.162175 | − | 0.986762i | \(-0.448149\pi\) | ||||
0.162175 | + | 0.986762i | \(0.448149\pi\) | |||||||
\(594\) | 1.62548e9 | 0.318221 | ||||||||
\(595\) | −5.79268e9 | −1.12738 | ||||||||
\(596\) | 7.56987e8 | 0.146463 | ||||||||
\(597\) | 1.33380e10 | 2.56556 | ||||||||
\(598\) | −4.10008e9 | −0.784040 | ||||||||
\(599\) | −2.22562e9 | −0.423114 | −0.211557 | − | 0.977366i | \(-0.567853\pi\) | ||||
−0.211557 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(600\) | −2.40548e10 | −4.54646 | ||||||||
\(601\) | −3.05479e9 | −0.574012 | −0.287006 | − | 0.957929i | \(-0.592660\pi\) | ||||
−0.287006 | + | 0.957929i | \(0.592660\pi\) | |||||||
\(602\) | −6.23206e9 | −1.16424 | ||||||||
\(603\) | −4.20260e9 | −0.780562 | ||||||||
\(604\) | 1.09342e10 | 2.01910 | ||||||||
\(605\) | −7.02574e9 | −1.28988 | ||||||||
\(606\) | −3.11246e10 | −5.68132 | ||||||||
\(607\) | 6.32843e9 | 1.14851 | 0.574256 | − | 0.818676i | \(-0.305292\pi\) | ||||
0.574256 | + | 0.818676i | \(0.305292\pi\) | |||||||
\(608\) | 2.43884e10 | 4.40068 | ||||||||
\(609\) | −1.16677e9 | −0.209326 | ||||||||
\(610\) | −2.35045e10 | −4.19273 | ||||||||
\(611\) | −6.25039e9 | −1.10857 | ||||||||
\(612\) | −2.79131e10 | −4.92240 | ||||||||
\(613\) | −4.08769e9 | −0.716747 | −0.358373 | − | 0.933578i | \(-0.616669\pi\) | ||||
−0.358373 | + | 0.933578i | \(0.616669\pi\) | |||||||
\(614\) | 9.30580e9 | 1.62242 | ||||||||
\(615\) | −5.65198e9 | −0.979801 | ||||||||
\(616\) | 3.02673e9 | 0.521724 | ||||||||
\(617\) | 5.74557e9 | 0.984771 | 0.492385 | − | 0.870377i | \(-0.336125\pi\) | ||||
0.492385 | + | 0.870377i | \(0.336125\pi\) | |||||||
\(618\) | 2.17603e10 | 3.70856 | ||||||||
\(619\) | 7.82745e9 | 1.32649 | 0.663244 | − | 0.748404i | \(-0.269179\pi\) | ||||
0.663244 | + | 0.748404i | \(0.269179\pi\) | |||||||
\(620\) | 2.91966e10 | 4.91996 | ||||||||
\(621\) | 2.74315e9 | 0.459651 | ||||||||
\(622\) | −1.88785e10 | −3.14559 | ||||||||
\(623\) | −2.08825e8 | −0.0345998 | ||||||||
\(624\) | 2.67564e10 | 4.40840 | ||||||||
\(625\) | −7.01513e9 | −1.14936 | ||||||||
\(626\) | 9.21696e6 | 0.00150168 | ||||||||
\(627\) | 2.02473e9 | 0.328043 | ||||||||
\(628\) | −1.55756e10 | −2.50950 | ||||||||
\(629\) | −1.45249e9 | −0.232722 | ||||||||
\(630\) | −1.76238e10 | −2.80807 | ||||||||
\(631\) | −8.67471e9 | −1.37452 | −0.687262 | − | 0.726410i | \(-0.741188\pi\) | ||||
−0.687262 | + | 0.726410i | \(0.741188\pi\) | |||||||
\(632\) | 3.92903e9 | 0.619121 | ||||||||
\(633\) | 7.50278e9 | 1.17573 | ||||||||
\(634\) | 7.74124e9 | 1.20642 | ||||||||
\(635\) | −8.31176e9 | −1.28820 | ||||||||
\(636\) | 6.30382e9 | 0.971637 | ||||||||
\(637\) | −2.20013e9 | −0.337257 | ||||||||
\(638\) | −4.93575e8 | −0.0752456 | ||||||||
\(639\) | 1.14156e10 | 1.73080 | ||||||||
\(640\) | −3.95800e10 | −5.96823 | ||||||||
\(641\) | −2.90390e8 | −0.0435490 | −0.0217745 | − | 0.999763i | \(-0.506932\pi\) | ||||
−0.0217745 | + | 0.999763i | \(0.506932\pi\) | |||||||
\(642\) | 1.12914e10 | 1.68412 | ||||||||
\(643\) | 7.73663e9 | 1.14766 | 0.573830 | − | 0.818974i | \(-0.305457\pi\) | ||||
0.573830 | + | 0.818974i | \(0.305457\pi\) | |||||||
\(644\) | 7.93794e9 | 1.17114 | ||||||||
\(645\) | 1.21460e10 | 1.78227 | ||||||||
\(646\) | −1.56583e10 | −2.28524 | ||||||||
\(647\) | 2.11912e9 | 0.307604 | 0.153802 | − | 0.988102i | \(-0.450848\pi\) | ||||
0.153802 | + | 0.988102i | \(0.450848\pi\) | |||||||
\(648\) | 6.24326e9 | 0.901361 | ||||||||
\(649\) | 1.43238e9 | 0.205684 | ||||||||
\(650\) | −7.66488e9 | −1.09473 | ||||||||
\(651\) | 1.03252e10 | 1.46678 | ||||||||
\(652\) | −2.39480e10 | −3.38378 | ||||||||
\(653\) | −6.36948e9 | −0.895174 | −0.447587 | − | 0.894240i | \(-0.647717\pi\) | ||||
−0.447587 | + | 0.894240i | \(0.647717\pi\) | |||||||
\(654\) | 3.93995e10 | 5.50768 | ||||||||
\(655\) | 1.58731e10 | 2.20707 | ||||||||
\(656\) | −1.35105e10 | −1.86856 | ||||||||
\(657\) | 2.23012e8 | 0.0306796 | ||||||||
\(658\) | 1.64153e10 | 2.24626 | ||||||||
\(659\) | −3.59109e9 | −0.488796 | −0.244398 | − | 0.969675i | \(-0.578590\pi\) | ||||
−0.244398 | + | 0.969675i | \(0.578590\pi\) | |||||||
\(660\) | −9.16727e9 | −1.24118 | ||||||||
\(661\) | 5.83457e9 | 0.785786 | 0.392893 | − | 0.919584i | \(-0.371474\pi\) | ||||
0.392893 | + | 0.919584i | \(0.371474\pi\) | |||||||
\(662\) | −1.09418e10 | −1.46583 | ||||||||
\(663\) | −9.54646e9 | −1.27217 | ||||||||
\(664\) | 1.86881e10 | 2.47729 | ||||||||
\(665\) | −7.28804e9 | −0.961026 | ||||||||
\(666\) | −4.41911e9 | −0.579663 | ||||||||
\(667\) | −8.32954e8 | −0.108688 | ||||||||
\(668\) | 2.17240e10 | 2.81983 | ||||||||
\(669\) | 7.31780e9 | 0.944907 | ||||||||
\(670\) | 1.06740e10 | 1.37109 | ||||||||
\(671\) | −2.59215e9 | −0.331231 | ||||||||
\(672\) | −3.90501e10 | −4.96398 | ||||||||
\(673\) | −4.35317e9 | −0.550494 | −0.275247 | − | 0.961374i | \(-0.588760\pi\) | ||||
−0.275247 | + | 0.961374i | \(0.588760\pi\) | |||||||
\(674\) | −2.10611e10 | −2.64955 | ||||||||
\(675\) | 5.12817e9 | 0.641799 | ||||||||
\(676\) | −1.19038e10 | −1.48208 | ||||||||
\(677\) | 1.40182e9 | 0.173632 | 0.0868162 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868162 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(678\) | −8.20756e9 | −1.01137 | ||||||||
\(679\) | −1.41120e9 | −0.173000 | ||||||||
\(680\) | 4.56195e10 | 5.56378 | ||||||||
\(681\) | −5.22331e9 | −0.633768 | ||||||||
\(682\) | 4.36785e9 | 0.527258 | ||||||||
\(683\) | −2.09063e9 | −0.251076 | −0.125538 | − | 0.992089i | \(-0.540066\pi\) | ||||
−0.125538 | + | 0.992089i | \(0.540066\pi\) | |||||||
\(684\) | −3.51187e10 | −4.19607 | ||||||||
\(685\) | −4.04608e8 | −0.0480969 | ||||||||
\(686\) | 1.75439e10 | 2.07488 | ||||||||
\(687\) | 5.89308e9 | 0.693416 | ||||||||
\(688\) | 2.90337e10 | 3.39894 | ||||||||
\(689\) | 1.29253e9 | 0.150547 | ||||||||
\(690\) | −2.09863e10 | −2.43200 | ||||||||
\(691\) | 4.31774e9 | 0.497833 | 0.248916 | − | 0.968525i | \(-0.419926\pi\) | ||||
0.248916 | + | 0.968525i | \(0.419926\pi\) | |||||||
\(692\) | −3.65128e10 | −4.18865 | ||||||||
\(693\) | −1.94361e9 | −0.221841 | ||||||||
\(694\) | 3.30633e9 | 0.375482 | ||||||||
\(695\) | 2.65542e9 | 0.300045 | ||||||||
\(696\) | 9.18875e9 | 1.03306 | ||||||||
\(697\) | 4.82044e9 | 0.539228 | ||||||||
\(698\) | 2.20331e10 | 2.45234 | ||||||||
\(699\) | 2.05846e10 | 2.27967 | ||||||||
\(700\) | 1.48396e10 | 1.63523 | ||||||||
\(701\) | 1.20285e10 | 1.31886 | 0.659428 | − | 0.751768i | \(-0.270799\pi\) | ||||
0.659428 | + | 0.751768i | \(0.270799\pi\) | |||||||
\(702\) | −9.64245e9 | −1.05198 | ||||||||
\(703\) | −1.82745e9 | −0.198382 | ||||||||
\(704\) | −8.70661e9 | −0.940470 | ||||||||
\(705\) | −3.19926e10 | −3.43865 | ||||||||
\(706\) | −3.10189e10 | −3.31749 | ||||||||
\(707\) | 1.23553e10 | 1.31488 | ||||||||
\(708\) | −4.14407e10 | −4.38844 | ||||||||
\(709\) | 4.69177e9 | 0.494396 | 0.247198 | − | 0.968965i | \(-0.420490\pi\) | ||||
0.247198 | + | 0.968965i | \(0.420490\pi\) | |||||||
\(710\) | −2.89942e10 | −3.04023 | ||||||||
\(711\) | −2.52302e9 | −0.263255 | ||||||||
\(712\) | 1.64457e9 | 0.170755 | ||||||||
\(713\) | 7.37116e9 | 0.761593 | ||||||||
\(714\) | 2.50718e10 | 2.57775 | ||||||||
\(715\) | −1.87965e9 | −0.192312 | ||||||||
\(716\) | 1.42927e10 | 1.45519 | ||||||||
\(717\) | 2.24638e10 | 2.27597 | ||||||||
\(718\) | −2.87164e10 | −2.89531 | ||||||||
\(719\) | −1.45057e9 | −0.145542 | −0.0727708 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727708 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(720\) | 8.21053e10 | 8.19799 | ||||||||
\(721\) | −8.63808e9 | −0.858309 | ||||||||
\(722\) | 2.60169e7 | 0.00257262 | ||||||||
\(723\) | 1.20207e10 | 1.18290 | ||||||||
\(724\) | 2.02323e10 | 1.98135 | ||||||||
\(725\) | −1.55716e9 | −0.151758 | ||||||||
\(726\) | 3.04087e10 | 2.94930 | ||||||||
\(727\) | −1.50239e10 | −1.45015 | −0.725073 | − | 0.688672i | \(-0.758194\pi\) | ||||
−0.725073 | + | 0.688672i | \(0.758194\pi\) | |||||||
\(728\) | −1.79547e10 | −1.72472 | ||||||||
\(729\) | −1.69899e10 | −1.62422 | ||||||||
\(730\) | −5.66421e8 | −0.0538901 | ||||||||
\(731\) | −1.03590e10 | −0.980860 | ||||||||
\(732\) | 7.49945e10 | 7.06709 | ||||||||
\(733\) | 1.07112e10 | 1.00456 | 0.502280 | − | 0.864705i | \(-0.332495\pi\) | ||||
0.502280 | + | 0.864705i | \(0.332495\pi\) | |||||||
\(734\) | −1.79295e10 | −1.67352 | ||||||||
\(735\) | −1.12614e10 | −1.04613 | ||||||||
\(736\) | −2.78778e10 | −2.57743 | ||||||||
\(737\) | 1.17716e9 | 0.108318 | ||||||||
\(738\) | 1.46659e10 | 1.34311 | ||||||||
\(739\) | 1.14070e10 | 1.03972 | 0.519859 | − | 0.854252i | \(-0.325984\pi\) | ||||
0.519859 | + | 0.854252i | \(0.325984\pi\) | |||||||
\(740\) | 8.27406e9 | 0.750598 | ||||||||
\(741\) | −1.20109e10 | −1.08445 | ||||||||
\(742\) | −3.39455e9 | −0.305049 | ||||||||
\(743\) | 1.77671e10 | 1.58912 | 0.794559 | − | 0.607187i | \(-0.207702\pi\) | ||||
0.794559 | + | 0.607187i | \(0.207702\pi\) | |||||||
\(744\) | −8.13151e10 | −7.23879 | ||||||||
\(745\) | 7.94452e8 | 0.0703916 | ||||||||
\(746\) | −2.84814e10 | −2.51175 | ||||||||
\(747\) | −1.20005e10 | −1.05336 | ||||||||
\(748\) | 7.81855e9 | 0.683079 | ||||||||
\(749\) | −4.48227e9 | −0.389773 | ||||||||
\(750\) | 8.77359e9 | 0.759386 | ||||||||
\(751\) | −1.00842e9 | −0.0868765 | −0.0434382 | − | 0.999056i | \(-0.513831\pi\) | ||||
−0.0434382 | + | 0.999056i | \(0.513831\pi\) | |||||||
\(752\) | −7.64752e10 | −6.55780 | ||||||||
\(753\) | −7.29273e9 | −0.622455 | ||||||||
\(754\) | 2.92792e9 | 0.248748 | ||||||||
\(755\) | 1.14753e10 | 0.970400 | ||||||||
\(756\) | 1.86682e10 | 1.57136 | ||||||||
\(757\) | −1.41694e10 | −1.18718 | −0.593591 | − | 0.804767i | \(-0.702290\pi\) | ||||
−0.593591 | + | 0.804767i | \(0.702290\pi\) | |||||||
\(758\) | −9.72039e8 | −0.0810665 | ||||||||
\(759\) | −2.31443e9 | −0.192131 | ||||||||
\(760\) | 5.73961e10 | 4.74280 | ||||||||
\(761\) | −1.23239e10 | −1.01368 | −0.506842 | − | 0.862039i | \(-0.669187\pi\) | ||||
−0.506842 | + | 0.862039i | \(0.669187\pi\) | |||||||
\(762\) | 3.59748e10 | 2.94548 | ||||||||
\(763\) | −1.56402e10 | −1.27470 | ||||||||
\(764\) | 6.44340e9 | 0.522744 | ||||||||
\(765\) | −2.92945e10 | −2.36576 | ||||||||
\(766\) | 3.13449e10 | 2.51980 | ||||||||
\(767\) | −8.49695e9 | −0.679954 | ||||||||
\(768\) | 8.15031e10 | 6.49247 | ||||||||
\(769\) | −7.92692e9 | −0.628583 | −0.314291 | − | 0.949327i | \(-0.601767\pi\) | ||||
−0.314291 | + | 0.949327i | \(0.601767\pi\) | |||||||
\(770\) | 4.93650e9 | 0.389674 | ||||||||
\(771\) | 1.04671e10 | 0.822500 | ||||||||
\(772\) | −3.11144e10 | −2.43389 | ||||||||
\(773\) | 1.76622e10 | 1.37536 | 0.687679 | − | 0.726015i | \(-0.258630\pi\) | ||||
0.687679 | + | 0.726015i | \(0.258630\pi\) | |||||||
\(774\) | −3.15165e10 | −2.44312 | ||||||||
\(775\) | 1.37800e10 | 1.06339 | ||||||||
\(776\) | 1.11138e10 | 0.853779 | ||||||||
\(777\) | 2.92608e9 | 0.223775 | ||||||||
\(778\) | −1.91483e10 | −1.45781 | ||||||||
\(779\) | 6.06483e9 | 0.459661 | ||||||||
\(780\) | 5.43809e10 | 4.10313 | ||||||||
\(781\) | −3.19756e9 | −0.240182 | ||||||||
\(782\) | 1.78987e10 | 1.33844 | ||||||||
\(783\) | −1.95892e9 | −0.145831 | ||||||||
\(784\) | −2.69192e10 | −1.99506 | ||||||||
\(785\) | −1.63465e10 | −1.20609 | ||||||||
\(786\) | −6.87016e10 | −5.04648 | ||||||||
\(787\) | 2.48767e9 | 0.181920 | 0.0909601 | − | 0.995855i | \(-0.471006\pi\) | ||||
0.0909601 | + | 0.995855i | \(0.471006\pi\) | |||||||
\(788\) | −5.32184e10 | −3.87454 | ||||||||
\(789\) | 1.33727e10 | 0.969279 | ||||||||
\(790\) | 6.40813e9 | 0.462420 | ||||||||
\(791\) | 3.25811e9 | 0.234071 | ||||||||
\(792\) | 1.53066e10 | 1.09482 | ||||||||
\(793\) | 1.53768e10 | 1.09499 | ||||||||
\(794\) | −2.46945e8 | −0.0175077 | ||||||||
\(795\) | 6.61581e9 | 0.466980 | ||||||||
\(796\) | 6.48011e10 | 4.55393 | ||||||||
\(797\) | −1.94471e10 | −1.36066 | −0.680332 | − | 0.732904i | \(-0.738165\pi\) | ||||
−0.680332 | + | 0.732904i | \(0.738165\pi\) | |||||||
\(798\) | 3.15440e10 | 2.19739 | ||||||||
\(799\) | 2.72858e10 | 1.89244 | ||||||||
\(800\) | −5.21161e10 | −3.59879 | ||||||||
\(801\) | −1.05606e9 | −0.0726065 | ||||||||
\(802\) | 2.62134e10 | 1.79438 | ||||||||
\(803\) | −6.24666e7 | −0.00425739 | ||||||||
\(804\) | −3.40571e10 | −2.31106 | ||||||||
\(805\) | 8.33081e9 | 0.562861 | ||||||||
\(806\) | −2.59104e10 | −1.74302 | ||||||||
\(807\) | −1.68372e10 | −1.12775 | ||||||||
\(808\) | −9.73030e10 | −6.48913 | ||||||||
\(809\) | 1.91310e10 | 1.27033 | 0.635167 | − | 0.772375i | \(-0.280931\pi\) | ||||
0.635167 | + | 0.772375i | \(0.280931\pi\) | |||||||
\(810\) | 1.01826e10 | 0.673224 | ||||||||
\(811\) | 1.21261e9 | 0.0798266 | 0.0399133 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399133 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(812\) | −5.66859e9 | −0.371560 | ||||||||
\(813\) | −4.44834e10 | −2.90323 | ||||||||
\(814\) | 1.23781e9 | 0.0804394 | ||||||||
\(815\) | −2.51332e10 | −1.62628 | ||||||||
\(816\) | −1.16803e11 | −7.52558 | ||||||||
\(817\) | −1.30331e10 | −0.836127 | ||||||||
\(818\) | 2.44120e10 | 1.55944 | ||||||||
\(819\) | 1.15296e10 | 0.733367 | ||||||||
\(820\) | −2.74594e10 | −1.73917 | ||||||||
\(821\) | 1.93729e9 | 0.122178 | 0.0610890 | − | 0.998132i | \(-0.480543\pi\) | ||||
0.0610890 | + | 0.998132i | \(0.480543\pi\) | |||||||
\(822\) | 1.75122e9 | 0.109974 | ||||||||
\(823\) | 9.15703e9 | 0.572605 | 0.286302 | − | 0.958139i | \(-0.407574\pi\) | ||||
0.286302 | + | 0.958139i | \(0.407574\pi\) | |||||||
\(824\) | 6.80281e10 | 4.23588 | ||||||||
\(825\) | −4.32670e9 | −0.268267 | ||||||||
\(826\) | 2.23155e10 | 1.37777 | ||||||||
\(827\) | 2.73124e10 | 1.67916 | 0.839578 | − | 0.543239i | \(-0.182802\pi\) | ||||
0.839578 | + | 0.543239i | \(0.182802\pi\) | |||||||
\(828\) | 4.01435e10 | 2.45759 | ||||||||
\(829\) | −9.35892e9 | −0.570538 | −0.285269 | − | 0.958447i | \(-0.592083\pi\) | ||||
−0.285269 | + | 0.958447i | \(0.592083\pi\) | |||||||
\(830\) | 3.04797e10 | 1.85028 | ||||||||
\(831\) | −1.46657e10 | −0.886540 | ||||||||
\(832\) | 5.16482e10 | 3.10902 | ||||||||
\(833\) | 9.60456e9 | 0.575731 | ||||||||
\(834\) | −1.14932e10 | −0.686054 | ||||||||
\(835\) | 2.27992e10 | 1.35524 | ||||||||
\(836\) | 9.83689e9 | 0.582285 | ||||||||
\(837\) | 1.73353e10 | 1.02186 | ||||||||
\(838\) | −6.37064e10 | −3.73963 | ||||||||
\(839\) | 9.38707e9 | 0.548735 | 0.274368 | − | 0.961625i | \(-0.411531\pi\) | ||||
0.274368 | + | 0.961625i | \(0.411531\pi\) | |||||||
\(840\) | −9.19014e10 | −5.34989 | ||||||||
\(841\) | 5.94823e8 | 0.0344828 | ||||||||
\(842\) | −2.08080e10 | −1.20126 | ||||||||
\(843\) | −2.72057e10 | −1.56410 | ||||||||
\(844\) | 3.64513e10 | 2.08696 | ||||||||
\(845\) | −1.24929e10 | −0.712304 | ||||||||
\(846\) | 8.30150e10 | 4.71368 | ||||||||
\(847\) | −1.20712e10 | −0.682586 | ||||||||
\(848\) | 1.58144e10 | 0.890570 | ||||||||
\(849\) | 1.90985e10 | 1.07108 | ||||||||
\(850\) | 3.34606e10 | 1.86882 | ||||||||
\(851\) | 2.08892e9 | 0.116190 | ||||||||
\(852\) | 9.25100e10 | 5.12449 | ||||||||
\(853\) | −1.00111e10 | −0.552280 | −0.276140 | − | 0.961117i | \(-0.589055\pi\) | ||||
−0.276140 | + | 0.961117i | \(0.589055\pi\) | |||||||
\(854\) | −4.03839e10 | −2.21874 | ||||||||
\(855\) | −3.68568e10 | −2.01668 | ||||||||
\(856\) | 3.52996e10 | 1.92359 | ||||||||
\(857\) | 1.11853e10 | 0.607036 | 0.303518 | − | 0.952826i | \(-0.401839\pi\) | ||||
0.303518 | + | 0.952826i | \(0.401839\pi\) | |||||||
\(858\) | 8.13546e9 | 0.439720 | ||||||||
\(859\) | −1.06684e10 | −0.574282 | −0.287141 | − | 0.957888i | \(-0.592705\pi\) | ||||
−0.287141 | + | 0.957888i | \(0.592705\pi\) | |||||||
\(860\) | 5.90095e10 | 3.16357 | ||||||||
\(861\) | −9.71087e9 | −0.518498 | ||||||||
\(862\) | −8.82780e9 | −0.469436 | ||||||||
\(863\) | 1.41277e10 | 0.748229 | 0.374114 | − | 0.927383i | \(-0.377947\pi\) | ||||
0.374114 | + | 0.927383i | \(0.377947\pi\) | |||||||
\(864\) | −6.55622e10 | −3.45824 | ||||||||
\(865\) | −3.83199e10 | −2.01311 | ||||||||
\(866\) | 5.16614e10 | 2.70305 | ||||||||
\(867\) | 1.13514e10 | 0.591537 | ||||||||
\(868\) | 5.01637e10 | 2.60358 | ||||||||
\(869\) | 7.06708e8 | 0.0365318 | ||||||||
\(870\) | 1.49866e10 | 0.771587 | ||||||||
\(871\) | −6.98302e9 | −0.358080 | ||||||||
\(872\) | 1.23173e11 | 6.29081 | ||||||||
\(873\) | −7.13669e9 | −0.363034 | ||||||||
\(874\) | 2.25192e10 | 1.14094 | ||||||||
\(875\) | −3.48280e9 | −0.175752 | ||||||||
\(876\) | 1.80725e9 | 0.0908350 | ||||||||
\(877\) | 4.77476e9 | 0.239030 | 0.119515 | − | 0.992832i | \(-0.461866\pi\) | ||||
0.119515 | + | 0.992832i | \(0.461866\pi\) | |||||||
\(878\) | 1.57697e10 | 0.786309 | ||||||||
\(879\) | −3.63357e10 | −1.80457 | ||||||||
\(880\) | −2.29980e10 | −1.13763 | ||||||||
\(881\) | −1.54995e10 | −0.763664 | −0.381832 | − | 0.924232i | \(-0.624707\pi\) | ||||
−0.381832 | + | 0.924232i | \(0.624707\pi\) | |||||||
\(882\) | 2.92212e10 | 1.43403 | ||||||||
\(883\) | −1.16646e10 | −0.570173 | −0.285086 | − | 0.958502i | \(-0.592022\pi\) | ||||
−0.285086 | + | 0.958502i | \(0.592022\pi\) | |||||||
\(884\) | −4.63802e10 | −2.25813 | ||||||||
\(885\) | −4.34916e10 | −2.10913 | ||||||||
\(886\) | −4.83830e10 | −2.33709 | ||||||||
\(887\) | −7.82168e9 | −0.376329 | −0.188164 | − | 0.982138i | \(-0.560254\pi\) | ||||
−0.188164 | + | 0.982138i | \(0.560254\pi\) | |||||||
\(888\) | −2.30440e10 | −1.10436 | ||||||||
\(889\) | −1.42807e10 | −0.681701 | ||||||||
\(890\) | 2.68225e9 | 0.127537 | ||||||||
\(891\) | 1.12296e9 | 0.0531856 | ||||||||
\(892\) | 3.55526e10 | 1.67723 | ||||||||
\(893\) | 3.43295e10 | 1.61320 | ||||||||
\(894\) | −3.43853e9 | −0.160950 | ||||||||
\(895\) | 1.50001e10 | 0.699381 | ||||||||
\(896\) | −6.80038e10 | −3.15831 | ||||||||
\(897\) | 1.37294e10 | 0.635150 | ||||||||
\(898\) | −1.18082e10 | −0.544148 | ||||||||
\(899\) | −5.26384e9 | −0.241626 | ||||||||
\(900\) | 7.50461e10 | 3.43146 | ||||||||
\(901\) | −5.64246e9 | −0.256999 | ||||||||
\(902\) | −4.10796e9 | −0.186382 | ||||||||
\(903\) | 2.08684e10 | 0.943152 | ||||||||
\(904\) | −2.56589e10 | −1.15517 | ||||||||
\(905\) | 2.12336e10 | 0.952258 | ||||||||
\(906\) | −4.96673e10 | −2.21882 | ||||||||
\(907\) | 9.52932e9 | 0.424069 | 0.212034 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212034 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(908\) | −2.53767e10 | −1.12496 | ||||||||
\(909\) | 6.24830e10 | 2.75923 | ||||||||
\(910\) | −2.92837e10 | −1.28819 | ||||||||
\(911\) | 2.59809e9 | 0.113852 | 0.0569260 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569260 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(912\) | −1.46956e11 | −6.41513 | ||||||||
\(913\) | 3.36140e9 | 0.146175 | ||||||||
\(914\) | −7.03162e10 | −3.04610 | ||||||||
\(915\) | 7.87061e10 | 3.39652 | ||||||||
\(916\) | 2.86307e10 | 1.23083 | ||||||||
\(917\) | 2.72721e10 | 1.16796 | ||||||||
\(918\) | 4.20936e10 | 1.79584 | ||||||||
\(919\) | 8.94350e9 | 0.380105 | 0.190052 | − | 0.981774i | \(-0.439134\pi\) | ||||
0.190052 | + | 0.981774i | \(0.439134\pi\) | |||||||
\(920\) | −6.56083e10 | −2.77780 | ||||||||
\(921\) | −3.11610e10 | −1.31432 | ||||||||
\(922\) | −6.88997e10 | −2.89507 | ||||||||
\(923\) | 1.89682e10 | 0.793997 | ||||||||
\(924\) | −1.57506e10 | −0.656819 | ||||||||
\(925\) | 3.90513e9 | 0.162233 | ||||||||
\(926\) | −6.95635e10 | −2.87901 | ||||||||
\(927\) | −4.36842e10 | −1.80113 | ||||||||
\(928\) | 1.99079e10 | 0.817726 | ||||||||
\(929\) | 2.88780e10 | 1.18171 | 0.590856 | − | 0.806777i | \(-0.298790\pi\) | ||||
0.590856 | + | 0.806777i | \(0.298790\pi\) | |||||||
\(930\) | −1.32622e11 | −5.40663 | ||||||||
\(931\) | 1.20839e10 | 0.490778 | ||||||||
\(932\) | 1.00008e11 | 4.04648 | ||||||||
\(933\) | 6.32158e10 | 2.54824 | ||||||||
\(934\) | −1.69653e10 | −0.681314 | ||||||||
\(935\) | 8.20550e9 | 0.328295 | ||||||||
\(936\) | −9.08001e10 | −3.61927 | ||||||||
\(937\) | 2.86074e10 | 1.13603 | 0.568016 | − | 0.823018i | \(-0.307711\pi\) | ||||
0.568016 | + | 0.823018i | \(0.307711\pi\) | |||||||
\(938\) | 1.83394e10 | 0.725565 | ||||||||
\(939\) | −3.08635e7 | −0.00121651 | ||||||||
\(940\) | −1.55432e11 | −6.10369 | ||||||||
\(941\) | 4.92468e10 | 1.92670 | 0.963351 | − | 0.268246i | \(-0.0864438\pi\) | ||||
0.963351 | + | 0.268246i | \(0.0864438\pi\) | |||||||
\(942\) | 7.07506e10 | 2.75773 | ||||||||
\(943\) | −6.93258e9 | −0.269218 | ||||||||
\(944\) | −1.03962e11 | −4.02230 | ||||||||
\(945\) | 1.95921e10 | 0.755215 | ||||||||
\(946\) | 8.82790e9 | 0.339030 | ||||||||
\(947\) | −4.35016e10 | −1.66449 | −0.832244 | − | 0.554410i | \(-0.812944\pi\) | ||||
−0.832244 | + | 0.554410i | \(0.812944\pi\) | |||||||
\(948\) | −2.04461e10 | −0.779436 | ||||||||
\(949\) | 3.70556e8 | 0.0140742 | ||||||||
\(950\) | 4.20984e10 | 1.59306 | ||||||||
\(951\) | −2.59220e10 | −0.977318 | ||||||||
\(952\) | 7.83805e10 | 2.94428 | ||||||||
\(953\) | 1.40959e10 | 0.527556 | 0.263778 | − | 0.964583i | \(-0.415031\pi\) | ||||
0.263778 | + | 0.964583i | \(0.415031\pi\) | |||||||
\(954\) | −1.71668e10 | −0.640133 | ||||||||
\(955\) | 6.76230e9 | 0.251236 | ||||||||
\(956\) | 1.09137e11 | 4.03990 | ||||||||
\(957\) | 1.65276e9 | 0.0609563 | ||||||||
\(958\) | −3.12587e10 | −1.14866 | ||||||||
\(959\) | −6.95171e8 | −0.0254523 | ||||||||
\(960\) | 2.64361e11 | 9.64381 | ||||||||
\(961\) | 1.90694e10 | 0.693113 | ||||||||
\(962\) | −7.34278e9 | −0.265918 | ||||||||
\(963\) | −2.26676e10 | −0.817925 | ||||||||
\(964\) | 5.84011e10 | 2.09967 | ||||||||
\(965\) | −3.26543e10 | −1.16975 | ||||||||
\(966\) | −3.60573e10 | −1.28698 | ||||||||
\(967\) | −4.02387e9 | −0.143104 | −0.0715519 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715519 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(968\) | 9.50651e10 | 3.36866 | ||||||||
\(969\) | 5.24327e10 | 1.85127 | ||||||||
\(970\) | 1.81262e10 | 0.637685 | ||||||||
\(971\) | −3.56517e10 | −1.24972 | −0.624861 | − | 0.780736i | \(-0.714844\pi\) | ||||
−0.624861 | + | 0.780736i | \(0.714844\pi\) | |||||||
\(972\) | −9.55546e10 | −3.33749 | ||||||||
\(973\) | 4.56238e9 | 0.158780 | ||||||||
\(974\) | −7.82977e10 | −2.71514 | ||||||||
\(975\) | 2.56663e10 | 0.886843 | ||||||||
\(976\) | 1.88139e11 | 6.47746 | ||||||||
\(977\) | −3.79562e10 | −1.30212 | −0.651060 | − | 0.759026i | \(-0.725676\pi\) | ||||
−0.651060 | + | 0.759026i | \(0.725676\pi\) | |||||||
\(978\) | 1.08781e11 | 3.71850 | ||||||||
\(979\) | 2.95807e8 | 0.0100755 | ||||||||
\(980\) | −5.47119e10 | −1.85691 | ||||||||
\(981\) | −7.90951e10 | −2.67490 | ||||||||
\(982\) | 1.07012e10 | 0.360613 | ||||||||
\(983\) | −3.53123e10 | −1.18574 | −0.592868 | − | 0.805299i | \(-0.702005\pi\) | ||||
−0.592868 | + | 0.805299i | \(0.702005\pi\) | |||||||
\(984\) | 7.64768e10 | 2.55886 | ||||||||
\(985\) | −5.58523e10 | −1.86215 | ||||||||
\(986\) | −1.27817e10 | −0.424638 | ||||||||
\(987\) | −5.49677e10 | −1.81969 | ||||||||
\(988\) | −5.83531e10 | −1.92493 | ||||||||
\(989\) | 1.48979e10 | 0.489709 | ||||||||
\(990\) | 2.49647e10 | 0.817717 | ||||||||
\(991\) | 1.92381e10 | 0.627920 | 0.313960 | − | 0.949436i | \(-0.398344\pi\) | ||||
0.313960 | + | 0.949436i | \(0.398344\pi\) | |||||||
\(992\) | −1.76173e11 | −5.72993 | ||||||||
\(993\) | 3.66391e10 | 1.18747 | ||||||||
\(994\) | −4.98159e10 | −1.60885 | ||||||||
\(995\) | 6.80082e10 | 2.18867 | ||||||||
\(996\) | −9.72500e10 | −3.11876 | ||||||||
\(997\) | −1.85218e10 | −0.591901 | −0.295951 | − | 0.955203i | \(-0.595636\pi\) | ||||
−0.295951 | + | 0.955203i | \(0.595636\pi\) | |||||||
\(998\) | 9.27788e10 | 2.95455 | ||||||||
\(999\) | 4.91266e9 | 0.155897 |
(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 | 29.8.a.b.1.1 | ✓ | 10 | |
3.2 | odd | 2 | 261.8.a.f.1.10 | 10 | |||
4.3 | odd | 2 | 464.8.a.g.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.8.a.b.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
261.8.a.f.1.10 | 10 | 3.2 | odd | 2 | |||
464.8.a.g.1.2 | 10 | 4.3 | odd | 2 |