Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 302081x^{4} - 2628147x^{3} + 19116974952x^{2} - 78725393748x - 5138711063280 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-445.917\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 438.917 | 1.57032 | 0.785158 | − | 0.619295i | \(-0.212582\pi\) | ||||
0.785158 | + | 0.619295i | \(0.212582\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −3511.33 | −1.11038 | ||||||||
\(11\) | −613.237 | −0.138917 | −0.0694583 | − | 0.997585i | \(-0.522127\pi\) | ||||
−0.0694583 | + | 0.997585i | \(0.522127\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 11850.8 | 0.906622 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 16657.1 | 0.822298 | 0.411149 | − | 0.911568i | \(-0.365128\pi\) | ||||
0.411149 | + | 0.911568i | \(0.365128\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | 1693.74 | 0.0566513 | 0.0283256 | − | 0.999599i | \(-0.490982\pi\) | ||||
0.0283256 | + | 0.999599i | \(0.490982\pi\) | |||||||
\(20\) | 28090.7 | 0.785158 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | 4905.90 | 0.0982289 | ||||||||
\(23\) | −59980.0 | −1.02792 | −0.513960 | − | 0.857814i | \(-0.671822\pi\) | ||||
−0.513960 | + | 0.857814i | \(0.671822\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 114523. | 1.46589 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −134472. | −1.02385 | −0.511927 | − | 0.859029i | \(-0.671068\pi\) | ||||
−0.511927 | + | 0.859029i | \(0.671068\pi\) | |||||||
\(30\) | −94806.0 | −0.641079 | ||||||||
\(31\) | −246211. | −1.48437 | −0.742184 | − | 0.670196i | \(-0.766210\pi\) | ||||
−0.742184 | + | 0.670196i | \(0.766210\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | −16557.4 | −0.0802036 | ||||||||
\(34\) | −133257. | −0.581453 | ||||||||
\(35\) | 150548. | 0.593524 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −2910.28 | −0.00944558 | −0.00472279 | − | 0.999989i | \(-0.501503\pi\) | ||||
−0.00472279 | + | 0.999989i | \(0.501503\pi\) | |||||||
\(38\) | −13549.9 | −0.0400585 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | −224725. | −0.555191 | ||||||||
\(41\) | 487387. | 1.10441 | 0.552205 | − | 0.833708i | \(-0.313787\pi\) | ||||
0.552205 | + | 0.833708i | \(0.313787\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | 854728. | 1.63941 | 0.819707 | − | 0.572784i | \(-0.194136\pi\) | ||||
0.819707 | + | 0.572784i | \(0.194136\pi\) | |||||||
\(44\) | −39247.2 | −0.0694583 | ||||||||
\(45\) | 319970. | 0.523439 | ||||||||
\(46\) | 479840. | 0.726849 | ||||||||
\(47\) | 1.10441e6 | 1.55163 | 0.775817 | − | 0.630957i | \(-0.217338\pi\) | ||||
0.775817 | + | 0.630957i | \(0.217338\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −916183. | −1.03654 | ||||||||
\(51\) | 449743. | 0.474754 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | 824971. | 0.761155 | 0.380577 | − | 0.924749i | \(-0.375725\pi\) | ||||
0.380577 | + | 0.924749i | \(0.375725\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −269160. | −0.218143 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | 45731.0 | 0.0327076 | ||||||||
\(58\) | 1.07577e6 | 0.723975 | ||||||||
\(59\) | −445602. | −0.282465 | −0.141233 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141233 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(60\) | 758448. | 0.453311 | ||||||||
\(61\) | 481991. | 0.271884 | 0.135942 | − | 0.990717i | \(-0.456594\pi\) | ||||
0.135942 | + | 0.990717i | \(0.456594\pi\) | |||||||
\(62\) | 1.96969e6 | 1.04961 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −964300. | −0.435527 | ||||||||
\(66\) | 132459. | 0.0567125 | ||||||||
\(67\) | 4.20932e6 | 1.70982 | 0.854909 | − | 0.518777i | \(-0.173613\pi\) | ||||
0.854909 | + | 0.518777i | \(0.173613\pi\) | |||||||
\(68\) | 1.06606e6 | 0.411149 | ||||||||
\(69\) | −1.61946e6 | −0.593469 | ||||||||
\(70\) | −1.20439e6 | −0.419685 | ||||||||
\(71\) | −2.08192e6 | −0.690335 | −0.345167 | − | 0.938541i | \(-0.612178\pi\) | ||||
−0.345167 | + | 0.938541i | \(0.612178\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | 4.93459e6 | 1.48464 | 0.742320 | − | 0.670046i | \(-0.233726\pi\) | ||||
0.742320 | + | 0.670046i | \(0.233726\pi\) | |||||||
\(74\) | 23282.2 | 0.00667903 | ||||||||
\(75\) | 3.09212e6 | 0.846333 | ||||||||
\(76\) | 108400. | 0.0283256 | ||||||||
\(77\) | −210340. | −0.0525056 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | 2.23377e6 | 0.509735 | 0.254867 | − | 0.966976i | \(-0.417968\pi\) | ||||
0.254867 | + | 0.966976i | \(0.417968\pi\) | |||||||
\(80\) | 1.79780e6 | 0.392579 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −3.89909e6 | −0.780936 | ||||||||
\(83\) | 8.38110e6 | 1.60889 | 0.804447 | − | 0.594024i | \(-0.202462\pi\) | ||||
0.804447 | + | 0.594024i | \(0.202462\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 7.31110e6 | 1.29127 | ||||||||
\(86\) | −6.83783e6 | −1.15924 | ||||||||
\(87\) | −3.63074e6 | −0.591123 | ||||||||
\(88\) | 313978. | 0.0491144 | ||||||||
\(89\) | −8.66671e6 | −1.30313 | −0.651567 | − | 0.758591i | \(-0.725888\pi\) | ||||
−0.651567 | + | 0.758591i | \(0.725888\pi\) | |||||||
\(90\) | −2.55976e6 | −0.370127 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | −3.83872e6 | −0.513960 | ||||||||
\(93\) | −6.64770e6 | −0.857000 | ||||||||
\(94\) | −8.83531e6 | −1.09717 | ||||||||
\(95\) | 743412. | 0.0889604 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −2.82328e6 | −0.314089 | −0.157045 | − | 0.987592i | \(-0.550197\pi\) | ||||
−0.157045 | + | 0.987592i | \(0.550197\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | −447050. | −0.0463055 | ||||||||
\(100\) | 7.32946e6 | 0.732946 | ||||||||
\(101\) | 7.84523e6 | 0.757671 | 0.378835 | − | 0.925464i | \(-0.376325\pi\) | ||||
0.378835 | + | 0.925464i | \(0.376325\pi\) | |||||||
\(102\) | −3.59794e6 | −0.335702 | ||||||||
\(103\) | 1.20435e7 | 1.08599 | 0.542993 | − | 0.839737i | \(-0.317291\pi\) | ||||
0.542993 | + | 0.839737i | \(0.317291\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | 4.06481e6 | 0.342671 | ||||||||
\(106\) | −6.59977e6 | −0.538218 | ||||||||
\(107\) | 6.39831e6 | 0.504919 | 0.252460 | − | 0.967607i | \(-0.418761\pi\) | ||||
0.252460 | + | 0.967607i | \(0.418761\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −2.95465e6 | −0.218531 | −0.109266 | − | 0.994013i | \(-0.534850\pi\) | ||||
−0.109266 | + | 0.994013i | \(0.534850\pi\) | |||||||
\(110\) | 2.15328e6 | 0.154250 | ||||||||
\(111\) | −78577.5 | −0.00545341 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −1.06356e7 | −0.693406 | −0.346703 | − | 0.937975i | \(-0.612699\pi\) | ||||
−0.346703 | + | 0.937975i | \(0.612699\pi\) | |||||||
\(114\) | −365848. | −0.0231278 | ||||||||
\(115\) | −2.63262e7 | −1.61416 | ||||||||
\(116\) | −8.60620e6 | −0.511927 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | 3.56482e6 | 0.199733 | ||||||||
\(119\) | 5.71340e6 | 0.310800 | ||||||||
\(120\) | −6.06758e6 | −0.320539 | ||||||||
\(121\) | −1.91111e7 | −0.980702 | ||||||||
\(122\) | −3.85593e6 | −0.192251 | ||||||||
\(123\) | 1.31594e7 | 0.637631 | ||||||||
\(124\) | −1.57575e7 | −0.742184 | ||||||||
\(125\) | 1.59756e7 | 0.731598 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | 3.02472e7 | 1.31030 | 0.655152 | − | 0.755497i | \(-0.272604\pi\) | ||||
0.655152 | + | 0.755497i | \(0.272604\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 2.30777e7 | 0.946516 | ||||||||
\(130\) | 7.71440e6 | 0.307964 | ||||||||
\(131\) | 2.42926e7 | 0.944114 | 0.472057 | − | 0.881568i | \(-0.343512\pi\) | ||||
0.472057 | + | 0.881568i | \(0.343512\pi\) | |||||||
\(132\) | −1.05967e6 | −0.0401018 | ||||||||
\(133\) | 580954. | 0.0214122 | ||||||||
\(134\) | −3.36746e7 | −1.20902 | ||||||||
\(135\) | 8.63920e6 | 0.302207 | ||||||||
\(136\) | −8.52846e6 | −0.290726 | ||||||||
\(137\) | −3.75416e7 | −1.24736 | −0.623679 | − | 0.781681i | \(-0.714363\pi\) | ||||
−0.623679 | + | 0.781681i | \(0.714363\pi\) | |||||||
\(138\) | 1.29557e7 | 0.419646 | ||||||||
\(139\) | −4.94601e7 | −1.56208 | −0.781039 | − | 0.624482i | \(-0.785310\pi\) | ||||
−0.781039 | + | 0.624482i | \(0.785310\pi\) | |||||||
\(140\) | 9.63510e6 | 0.296762 | ||||||||
\(141\) | 2.98192e7 | 0.895837 | ||||||||
\(142\) | 1.66554e7 | 0.488140 | ||||||||
\(143\) | 1.34728e6 | 0.0385285 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −5.90219e7 | −1.60778 | ||||||||
\(146\) | −3.94767e7 | −1.04980 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | −186258. | −0.00472279 | ||||||||
\(149\) | 4.51637e7 | 1.11850 | 0.559251 | − | 0.828998i | \(-0.311089\pi\) | ||||
0.559251 | + | 0.828998i | \(0.311089\pi\) | |||||||
\(150\) | −2.47369e7 | −0.598448 | ||||||||
\(151\) | −2.20766e7 | −0.521811 | −0.260906 | − | 0.965364i | \(-0.584021\pi\) | ||||
−0.260906 | + | 0.965364i | \(0.584021\pi\) | |||||||
\(152\) | −867196. | −0.0200293 | ||||||||
\(153\) | 1.21431e7 | 0.274099 | ||||||||
\(154\) | 1.68272e6 | 0.0371270 | ||||||||
\(155\) | −1.08066e8 | −2.33093 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | 3.45895e7 | 0.713338 | 0.356669 | − | 0.934231i | \(-0.383912\pi\) | ||||
0.356669 | + | 0.934231i | \(0.383912\pi\) | |||||||
\(158\) | −1.78702e7 | −0.360437 | ||||||||
\(159\) | 2.22742e7 | 0.439453 | ||||||||
\(160\) | −1.43824e7 | −0.277595 | ||||||||
\(161\) | −2.05731e7 | −0.388517 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | 9.40073e7 | 1.70022 | 0.850110 | − | 0.526605i | \(-0.176535\pi\) | ||||
0.850110 | + | 0.526605i | \(0.176535\pi\) | |||||||
\(164\) | 3.11928e7 | 0.552205 | ||||||||
\(165\) | −7.26732e6 | −0.125945 | ||||||||
\(166\) | −6.70488e7 | −1.13766 | ||||||||
\(167\) | −3.56325e7 | −0.592023 | −0.296012 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296012 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −5.84888e7 | −0.913065 | ||||||||
\(171\) | 1.23474e6 | 0.0188838 | ||||||||
\(172\) | 5.47026e7 | 0.819707 | ||||||||
\(173\) | −1.14790e7 | −0.168555 | −0.0842777 | − | 0.996442i | \(-0.526858\pi\) | ||||
−0.0842777 | + | 0.996442i | \(0.526858\pi\) | |||||||
\(174\) | 2.90459e7 | 0.417987 | ||||||||
\(175\) | 3.92813e7 | 0.554055 | ||||||||
\(176\) | −2.51182e6 | −0.0347292 | ||||||||
\(177\) | −1.20313e7 | −0.163081 | ||||||||
\(178\) | 6.93337e7 | 0.921455 | ||||||||
\(179\) | 3.18719e7 | 0.415357 | 0.207679 | − | 0.978197i | \(-0.433409\pi\) | ||||
0.207679 | + | 0.978197i | \(0.433409\pi\) | |||||||
\(180\) | 2.04781e7 | 0.261719 | ||||||||
\(181\) | 1.56681e7 | 0.196400 | 0.0981999 | − | 0.995167i | \(-0.468692\pi\) | ||||
0.0981999 | + | 0.995167i | \(0.468692\pi\) | |||||||
\(182\) | 6.02857e6 | 0.0741249 | ||||||||
\(183\) | 1.30138e7 | 0.156973 | ||||||||
\(184\) | 3.07098e7 | 0.363424 | ||||||||
\(185\) | −1.27737e6 | −0.0148325 | ||||||||
\(186\) | 5.31816e7 | 0.605991 | ||||||||
\(187\) | −1.02148e7 | −0.114231 | ||||||||
\(188\) | 7.06825e7 | 0.775817 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | −5.94729e6 | −0.0629045 | ||||||||
\(191\) | 3.16069e6 | 0.0328220 | 0.0164110 | − | 0.999865i | \(-0.494776\pi\) | ||||
0.0164110 | + | 0.999865i | \(0.494776\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −1.93300e7 | −0.193545 | −0.0967724 | − | 0.995307i | \(-0.530852\pi\) | ||||
−0.0967724 | + | 0.995307i | \(0.530852\pi\) | |||||||
\(194\) | 2.25862e7 | 0.222095 | ||||||||
\(195\) | −2.60361e7 | −0.251452 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 6.07765e7 | 0.566375 | 0.283187 | − | 0.959065i | \(-0.408608\pi\) | ||||
0.283187 | + | 0.959065i | \(0.408608\pi\) | |||||||
\(198\) | 3.57640e6 | 0.0327430 | ||||||||
\(199\) | −1.34769e8 | −1.21228 | −0.606141 | − | 0.795357i | \(-0.707283\pi\) | ||||
−0.606141 | + | 0.795357i | \(0.707283\pi\) | |||||||
\(200\) | −5.86357e7 | −0.518271 | ||||||||
\(201\) | 1.13652e8 | 0.987164 | ||||||||
\(202\) | −6.27618e7 | −0.535754 | ||||||||
\(203\) | −4.61238e7 | −0.386981 | ||||||||
\(204\) | 2.87836e7 | 0.237377 | ||||||||
\(205\) | 2.13922e8 | 1.73427 | ||||||||
\(206\) | −9.63484e7 | −0.767908 | ||||||||
\(207\) | −4.37254e7 | −0.342640 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | −1.03867e6 | −0.00786981 | ||||||||
\(210\) | −3.25185e7 | −0.242305 | ||||||||
\(211\) | −2.09419e8 | −1.53472 | −0.767358 | − | 0.641219i | \(-0.778429\pi\) | ||||
−0.767358 | + | 0.641219i | \(0.778429\pi\) | |||||||
\(212\) | 5.27981e7 | 0.380577 | ||||||||
\(213\) | −5.62118e7 | −0.398565 | ||||||||
\(214\) | −5.11865e7 | −0.357032 | ||||||||
\(215\) | 3.75154e8 | 2.57440 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −8.44504e7 | −0.561038 | ||||||||
\(218\) | 2.36372e7 | 0.154525 | ||||||||
\(219\) | 1.33234e8 | 0.857157 | ||||||||
\(220\) | −1.72262e7 | −0.109072 | ||||||||
\(221\) | −3.65958e7 | −0.228065 | ||||||||
\(222\) | 628620. | 0.00385614 | ||||||||
\(223\) | −1.32856e8 | −0.802257 | −0.401128 | − | 0.916022i | \(-0.631382\pi\) | ||||
−0.401128 | + | 0.916022i | \(0.631382\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 8.34872e7 | 0.488631 | ||||||||
\(226\) | 8.50848e7 | 0.490312 | ||||||||
\(227\) | −2.43707e8 | −1.38286 | −0.691429 | − | 0.722445i | \(-0.743018\pi\) | ||||
−0.691429 | + | 0.722445i | \(0.743018\pi\) | |||||||
\(228\) | 2.92679e6 | 0.0163538 | ||||||||
\(229\) | 2.06423e8 | 1.13589 | 0.567943 | − | 0.823068i | \(-0.307740\pi\) | ||||
0.567943 | + | 0.823068i | \(0.307740\pi\) | |||||||
\(230\) | 2.10610e8 | 1.14138 | ||||||||
\(231\) | −5.67919e6 | −0.0303141 | ||||||||
\(232\) | 6.88496e7 | 0.361987 | ||||||||
\(233\) | 3.44118e7 | 0.178222 | 0.0891111 | − | 0.996022i | \(-0.471597\pi\) | ||||
0.0891111 | + | 0.996022i | \(0.471597\pi\) | |||||||
\(234\) | 1.28129e7 | 0.0653720 | ||||||||
\(235\) | 4.84746e8 | 2.43656 | ||||||||
\(236\) | −2.85185e7 | −0.141233 | ||||||||
\(237\) | 6.03119e7 | 0.294295 | ||||||||
\(238\) | −4.57072e7 | −0.219768 | ||||||||
\(239\) | 2.90139e8 | 1.37472 | 0.687358 | − | 0.726319i | \(-0.258770\pi\) | ||||
0.687358 | + | 0.726319i | \(0.258770\pi\) | |||||||
\(240\) | 4.85407e7 | 0.226656 | ||||||||
\(241\) | −1.56531e8 | −0.720343 | −0.360172 | − | 0.932886i | \(-0.617282\pi\) | ||||
−0.360172 | + | 0.932886i | \(0.617282\pi\) | |||||||
\(242\) | 1.52889e8 | 0.693461 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 3.08474e7 | 0.135942 | ||||||||
\(245\) | 5.16381e7 | 0.224331 | ||||||||
\(246\) | −1.05276e8 | −0.450873 | ||||||||
\(247\) | −3.72115e6 | −0.0157122 | ||||||||
\(248\) | 1.26060e8 | 0.524803 | ||||||||
\(249\) | 2.26290e8 | 0.928896 | ||||||||
\(250\) | −1.27805e8 | −0.517318 | ||||||||
\(251\) | 3.39741e8 | 1.35609 | 0.678046 | − | 0.735019i | \(-0.262827\pi\) | ||||
0.678046 | + | 0.735019i | \(0.262827\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 3.67820e7 | 0.142795 | ||||||||
\(254\) | −2.41978e8 | −0.926525 | ||||||||
\(255\) | 1.97400e8 | 0.745514 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 1.78281e8 | 0.655147 | 0.327574 | − | 0.944826i | \(-0.393769\pi\) | ||||
0.327574 | + | 0.944826i | \(0.393769\pi\) | |||||||
\(258\) | −1.84621e8 | −0.669288 | ||||||||
\(259\) | −998225. | −0.00357009 | ||||||||
\(260\) | −6.17152e7 | −0.217764 | ||||||||
\(261\) | −9.80300e7 | −0.341285 | ||||||||
\(262\) | −1.94341e8 | −0.667590 | ||||||||
\(263\) | 1.06970e8 | 0.362591 | 0.181296 | − | 0.983429i | \(-0.441971\pi\) | ||||
0.181296 | + | 0.983429i | \(0.441971\pi\) | |||||||
\(264\) | 8.47739e6 | 0.0283562 | ||||||||
\(265\) | 3.62093e8 | 1.19525 | ||||||||
\(266\) | −4.64763e6 | −0.0151407 | ||||||||
\(267\) | −2.34001e8 | −0.752365 | ||||||||
\(268\) | 2.69396e8 | 0.854909 | ||||||||
\(269\) | −4.33449e8 | −1.35770 | −0.678852 | − | 0.734275i | \(-0.737522\pi\) | ||||
−0.678852 | + | 0.734275i | \(0.737522\pi\) | |||||||
\(270\) | −6.91136e7 | −0.213693 | ||||||||
\(271\) | 5.07880e8 | 1.55013 | 0.775066 | − | 0.631880i | \(-0.217717\pi\) | ||||
0.775066 | + | 0.631880i | \(0.217717\pi\) | |||||||
\(272\) | 6.82277e7 | 0.205575 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | 3.00333e8 | 0.882015 | ||||||||
\(275\) | −7.02297e7 | −0.203637 | ||||||||
\(276\) | −1.03645e8 | −0.296735 | ||||||||
\(277\) | −1.24580e8 | −0.352183 | −0.176092 | − | 0.984374i | \(-0.556346\pi\) | ||||
−0.176092 | + | 0.984374i | \(0.556346\pi\) | |||||||
\(278\) | 3.95680e8 | 1.10456 | ||||||||
\(279\) | −1.79488e8 | −0.494789 | ||||||||
\(280\) | −7.70808e7 | −0.209842 | ||||||||
\(281\) | −3.46435e8 | −0.931427 | −0.465714 | − | 0.884935i | \(-0.654202\pi\) | ||||
−0.465714 | + | 0.884935i | \(0.654202\pi\) | |||||||
\(282\) | −2.38553e8 | −0.633452 | ||||||||
\(283\) | −4.34781e8 | −1.14030 | −0.570148 | − | 0.821542i | \(-0.693114\pi\) | ||||
−0.570148 | + | 0.821542i | \(0.693114\pi\) | |||||||
\(284\) | −1.33243e8 | −0.345167 | ||||||||
\(285\) | 2.00721e7 | 0.0513613 | ||||||||
\(286\) | −1.07783e7 | −0.0272438 | ||||||||
\(287\) | 1.67174e8 | 0.417428 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | −1.32878e8 | −0.323825 | ||||||||
\(290\) | 4.72175e8 | 1.13687 | ||||||||
\(291\) | −7.62286e7 | −0.181339 | ||||||||
\(292\) | 3.15814e8 | 0.742320 | ||||||||
\(293\) | 4.82394e8 | 1.12038 | 0.560190 | − | 0.828364i | \(-0.310728\pi\) | ||||
0.560190 | + | 0.828364i | \(0.310728\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −1.95582e8 | −0.443560 | ||||||||
\(296\) | 1.49006e6 | 0.00333952 | ||||||||
\(297\) | −1.20704e7 | −0.0267345 | ||||||||
\(298\) | −3.61309e8 | −0.790901 | ||||||||
\(299\) | 1.31776e8 | 0.285093 | ||||||||
\(300\) | 1.97895e8 | 0.423167 | ||||||||
\(301\) | 2.93172e8 | 0.619640 | ||||||||
\(302\) | 1.76613e8 | 0.368976 | ||||||||
\(303\) | 2.11821e8 | 0.437441 | ||||||||
\(304\) | 6.93757e6 | 0.0141628 | ||||||||
\(305\) | 2.11554e8 | 0.426944 | ||||||||
\(306\) | −9.71445e7 | −0.193818 | ||||||||
\(307\) | 9.44305e8 | 1.86264 | 0.931318 | − | 0.364206i | \(-0.118660\pi\) | ||||
0.931318 | + | 0.364206i | \(0.118660\pi\) | |||||||
\(308\) | −1.34618e7 | −0.0262528 | ||||||||
\(309\) | 3.25176e8 | 0.626994 | ||||||||
\(310\) | 8.64529e8 | 1.64821 | ||||||||
\(311\) | 2.26285e8 | 0.426573 | 0.213287 | − | 0.976990i | \(-0.431583\pi\) | ||||
0.213287 | + | 0.976990i | \(0.431583\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | −3.80424e8 | −0.701233 | −0.350616 | − | 0.936519i | \(-0.614028\pi\) | ||||
−0.350616 | + | 0.936519i | \(0.614028\pi\) | |||||||
\(314\) | −2.76716e8 | −0.504406 | ||||||||
\(315\) | 1.09750e8 | 0.197841 | ||||||||
\(316\) | 1.42961e8 | 0.254867 | ||||||||
\(317\) | −3.24262e8 | −0.571726 | −0.285863 | − | 0.958270i | \(-0.592280\pi\) | ||||
−0.285863 | + | 0.958270i | \(0.592280\pi\) | |||||||
\(318\) | −1.78194e8 | −0.310740 | ||||||||
\(319\) | 8.24632e7 | 0.142230 | ||||||||
\(320\) | 1.15059e8 | 0.196290 | ||||||||
\(321\) | 1.72754e8 | 0.291515 | ||||||||
\(322\) | 1.64585e8 | 0.274723 | ||||||||
\(323\) | 2.82129e7 | 0.0465843 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −2.51607e8 | −0.406565 | ||||||||
\(326\) | −7.52059e8 | −1.20224 | ||||||||
\(327\) | −7.97756e7 | −0.126169 | ||||||||
\(328\) | −2.49542e8 | −0.390468 | ||||||||
\(329\) | 3.78814e8 | 0.586463 | ||||||||
\(330\) | 5.81386e7 | 0.0890565 | ||||||||
\(331\) | −1.30516e8 | −0.197818 | −0.0989092 | − | 0.995096i | \(-0.531535\pi\) | ||||
−0.0989092 | + | 0.995096i | \(0.531535\pi\) | |||||||
\(332\) | 5.36390e8 | 0.804447 | ||||||||
\(333\) | −2.12159e6 | −0.00314853 | ||||||||
\(334\) | 2.85060e8 | 0.418624 | ||||||||
\(335\) | 1.84754e9 | 2.68496 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | −1.12353e9 | −1.59912 | −0.799561 | − | 0.600584i | \(-0.794935\pi\) | ||||
−0.799561 | + | 0.600584i | \(0.794935\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | −2.87161e8 | −0.400338 | ||||||||
\(340\) | 4.67910e8 | 0.645634 | ||||||||
\(341\) | 1.50986e8 | 0.206203 | ||||||||
\(342\) | −9.87790e6 | −0.0133528 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −4.37621e8 | −0.579620 | ||||||||
\(345\) | −7.10808e8 | −0.931935 | ||||||||
\(346\) | 9.18320e7 | 0.119187 | ||||||||
\(347\) | 9.67690e8 | 1.24332 | 0.621660 | − | 0.783287i | \(-0.286458\pi\) | ||||
0.621660 | + | 0.783287i | \(0.286458\pi\) | |||||||
\(348\) | −2.32367e8 | −0.295561 | ||||||||
\(349\) | 4.64555e8 | 0.584990 | 0.292495 | − | 0.956267i | \(-0.405515\pi\) | ||||
0.292495 | + | 0.956267i | \(0.405515\pi\) | |||||||
\(350\) | −3.14251e8 | −0.391776 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | 2.00946e7 | 0.0245572 | ||||||||
\(353\) | 4.19259e8 | 0.507307 | 0.253653 | − | 0.967295i | \(-0.418368\pi\) | ||||
0.253653 | + | 0.967295i | \(0.418368\pi\) | |||||||
\(354\) | 9.62501e7 | 0.115316 | ||||||||
\(355\) | −9.13789e8 | −1.08404 | ||||||||
\(356\) | −5.54669e8 | −0.651567 | ||||||||
\(357\) | 1.54262e8 | 0.179440 | ||||||||
\(358\) | −2.54975e8 | −0.293702 | ||||||||
\(359\) | 1.33446e9 | 1.52221 | 0.761105 | − | 0.648628i | \(-0.224657\pi\) | ||||
0.761105 | + | 0.648628i | \(0.224657\pi\) | |||||||
\(360\) | −1.63825e8 | −0.185064 | ||||||||
\(361\) | −8.91003e8 | −0.996791 | ||||||||
\(362\) | −1.25345e8 | −0.138876 | ||||||||
\(363\) | −5.16000e8 | −0.566209 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | 2.16587e9 | 2.33135 | ||||||||
\(366\) | −1.04110e8 | −0.110996 | ||||||||
\(367\) | 1.50489e9 | 1.58919 | 0.794593 | − | 0.607142i | \(-0.207684\pi\) | ||||
0.794593 | + | 0.607142i | \(0.207684\pi\) | |||||||
\(368\) | −2.45678e8 | −0.256980 | ||||||||
\(369\) | 3.55305e8 | 0.368137 | ||||||||
\(370\) | 1.02190e7 | 0.0104882 | ||||||||
\(371\) | 2.82965e8 | 0.287690 | ||||||||
\(372\) | −4.25453e8 | −0.428500 | ||||||||
\(373\) | −8.19165e8 | −0.817317 | −0.408658 | − | 0.912687i | \(-0.634003\pi\) | ||||
−0.408658 | + | 0.912687i | \(0.634003\pi\) | |||||||
\(374\) | 8.17183e7 | 0.0807735 | ||||||||
\(375\) | 4.31342e8 | 0.422388 | ||||||||
\(376\) | −5.65460e8 | −0.548586 | ||||||||
\(377\) | 2.95435e8 | 0.283966 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | −8.69668e8 | −0.820571 | −0.410286 | − | 0.911957i | \(-0.634571\pi\) | ||||
−0.410286 | + | 0.911957i | \(0.634571\pi\) | |||||||
\(380\) | 4.75783e7 | 0.0444802 | ||||||||
\(381\) | 8.16674e8 | 0.756505 | ||||||||
\(382\) | −2.52855e7 | −0.0232086 | ||||||||
\(383\) | 9.21258e8 | 0.837888 | 0.418944 | − | 0.908012i | \(-0.362400\pi\) | ||||
0.418944 | + | 0.908012i | \(0.362400\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −9.23219e7 | −0.0824503 | ||||||||
\(386\) | 1.54640e8 | 0.136857 | ||||||||
\(387\) | 6.23097e8 | 0.546471 | ||||||||
\(388\) | −1.80690e8 | −0.157045 | ||||||||
\(389\) | 1.44157e9 | 1.24169 | 0.620843 | − | 0.783935i | \(-0.286791\pi\) | ||||
0.620843 | + | 0.783935i | \(0.286791\pi\) | |||||||
\(390\) | 2.08289e8 | 0.177803 | ||||||||
\(391\) | −9.99096e8 | −0.845256 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | 6.55900e8 | 0.545085 | ||||||||
\(394\) | −4.86212e8 | −0.400487 | ||||||||
\(395\) | 9.80440e8 | 0.800444 | ||||||||
\(396\) | −2.86112e7 | −0.0231528 | ||||||||
\(397\) | 1.08851e9 | 0.873100 | 0.436550 | − | 0.899680i | \(-0.356200\pi\) | ||||
0.436550 | + | 0.899680i | \(0.356200\pi\) | |||||||
\(398\) | 1.07815e9 | 0.857212 | ||||||||
\(399\) | 1.56857e7 | 0.0123623 | ||||||||
\(400\) | 4.69086e8 | 0.366473 | ||||||||
\(401\) | 4.45951e8 | 0.345368 | 0.172684 | − | 0.984977i | \(-0.444756\pi\) | ||||
0.172684 | + | 0.984977i | \(0.444756\pi\) | |||||||
\(402\) | −9.09213e8 | −0.698031 | ||||||||
\(403\) | 5.40926e8 | 0.411690 | ||||||||
\(404\) | 5.02094e8 | 0.378835 | ||||||||
\(405\) | 2.33258e8 | 0.174480 | ||||||||
\(406\) | 3.68991e8 | 0.273637 | ||||||||
\(407\) | 1.78469e6 | 0.00131215 | ||||||||
\(408\) | −2.30268e8 | −0.167851 | ||||||||
\(409\) | 3.99616e8 | 0.288809 | 0.144405 | − | 0.989519i | \(-0.453873\pi\) | ||||
0.144405 | + | 0.989519i | \(0.453873\pi\) | |||||||
\(410\) | −1.71138e9 | −1.22632 | ||||||||
\(411\) | −1.01362e9 | −0.720163 | ||||||||
\(412\) | 7.70787e8 | 0.542993 | ||||||||
\(413\) | −1.52842e8 | −0.106762 | ||||||||
\(414\) | 3.49803e8 | 0.242283 | ||||||||
\(415\) | 3.67860e9 | 2.52647 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | −1.33542e9 | −0.901866 | ||||||||
\(418\) | 8.30933e6 | 0.00556479 | ||||||||
\(419\) | 2.54419e9 | 1.68966 | 0.844832 | − | 0.535032i | \(-0.179701\pi\) | ||||
0.844832 | + | 0.535032i | \(0.179701\pi\) | |||||||
\(420\) | 2.60148e8 | 0.171336 | ||||||||
\(421\) | −1.96882e9 | −1.28594 | −0.642968 | − | 0.765893i | \(-0.722297\pi\) | ||||
−0.642968 | + | 0.765893i | \(0.722297\pi\) | |||||||
\(422\) | 1.67535e9 | 1.08521 | ||||||||
\(423\) | 8.05118e8 | 0.517212 | ||||||||
\(424\) | −4.22385e8 | −0.269109 | ||||||||
\(425\) | 1.90762e9 | 1.20540 | ||||||||
\(426\) | 4.49695e8 | 0.281828 | ||||||||
\(427\) | 1.65323e8 | 0.102763 | ||||||||
\(428\) | 4.09492e8 | 0.252460 | ||||||||
\(429\) | 3.63766e7 | 0.0222445 | ||||||||
\(430\) | −3.00124e9 | −1.82037 | ||||||||
\(431\) | −2.97818e9 | −1.79176 | −0.895882 | − | 0.444291i | \(-0.853455\pi\) | ||||
−0.895882 | + | 0.444291i | \(0.853455\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | −1.47714e9 | −0.874408 | −0.437204 | − | 0.899362i | \(-0.644031\pi\) | ||||
−0.437204 | + | 0.899362i | \(0.644031\pi\) | |||||||
\(434\) | 6.75603e8 | 0.396714 | ||||||||
\(435\) | −1.59359e9 | −0.928249 | ||||||||
\(436\) | −1.89098e8 | −0.109266 | ||||||||
\(437\) | −1.01591e8 | −0.0582329 | ||||||||
\(438\) | −1.06587e9 | −0.606102 | ||||||||
\(439\) | −8.70468e8 | −0.491051 | −0.245526 | − | 0.969390i | \(-0.578961\pi\) | ||||
−0.245526 | + | 0.969390i | \(0.578961\pi\) | |||||||
\(440\) | 1.37810e8 | 0.0771252 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 2.92766e8 | 0.161266 | ||||||||
\(443\) | 1.46819e9 | 0.802361 | 0.401180 | − | 0.915999i | \(-0.368600\pi\) | ||||
0.401180 | + | 0.915999i | \(0.368600\pi\) | |||||||
\(444\) | −5.02896e6 | −0.00272670 | ||||||||
\(445\) | −3.80396e9 | −2.04633 | ||||||||
\(446\) | 1.06285e9 | 0.567281 | ||||||||
\(447\) | 1.21942e9 | 0.645768 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 2.67108e8 | 0.139260 | 0.0696298 | − | 0.997573i | \(-0.477818\pi\) | ||||
0.0696298 | + | 0.997573i | \(0.477818\pi\) | |||||||
\(450\) | −6.67897e8 | −0.345514 | ||||||||
\(451\) | −2.98884e8 | −0.153421 | ||||||||
\(452\) | −6.80679e8 | −0.346703 | ||||||||
\(453\) | −5.96069e8 | −0.301268 | ||||||||
\(454\) | 1.94966e9 | 0.977828 | ||||||||
\(455\) | −3.30755e8 | −0.164614 | ||||||||
\(456\) | −2.34143e7 | −0.0115639 | ||||||||
\(457\) | −3.53476e9 | −1.73242 | −0.866210 | − | 0.499679i | \(-0.833451\pi\) | ||||
−0.866210 | + | 0.499679i | \(0.833451\pi\) | |||||||
\(458\) | −1.65139e9 | −0.803192 | ||||||||
\(459\) | 3.27863e8 | 0.158251 | ||||||||
\(460\) | −1.68488e9 | −0.807079 | ||||||||
\(461\) | 2.38295e9 | 1.13282 | 0.566411 | − | 0.824123i | \(-0.308332\pi\) | ||||
0.566411 | + | 0.824123i | \(0.308332\pi\) | |||||||
\(462\) | 4.54335e7 | 0.0214353 | ||||||||
\(463\) | 7.25473e7 | 0.0339694 | 0.0169847 | − | 0.999856i | \(-0.494593\pi\) | ||||
0.0169847 | + | 0.999856i | \(0.494593\pi\) | |||||||
\(464\) | −5.50797e8 | −0.255964 | ||||||||
\(465\) | −2.91779e9 | −1.34576 | ||||||||
\(466\) | −2.75295e8 | −0.126022 | ||||||||
\(467\) | −2.33898e9 | −1.06272 | −0.531359 | − | 0.847147i | \(-0.678318\pi\) | ||||
−0.531359 | + | 0.847147i | \(0.678318\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | 1.44380e9 | 0.646251 | ||||||||
\(470\) | −3.87797e9 | −1.72291 | ||||||||
\(471\) | 9.33916e8 | 0.411846 | ||||||||
\(472\) | 2.28148e8 | 0.0998666 | ||||||||
\(473\) | −5.24151e8 | −0.227742 | ||||||||
\(474\) | −4.82495e8 | −0.208098 | ||||||||
\(475\) | 1.93972e8 | 0.0830447 | ||||||||
\(476\) | 3.65658e8 | 0.155400 | ||||||||
\(477\) | 6.01404e8 | 0.253718 | ||||||||
\(478\) | −2.32111e9 | −0.972071 | ||||||||
\(479\) | −3.13204e9 | −1.30213 | −0.651063 | − | 0.759024i | \(-0.725677\pi\) | ||||
−0.651063 | + | 0.759024i | \(0.725677\pi\) | |||||||
\(480\) | −3.88325e8 | −0.160270 | ||||||||
\(481\) | 6.39388e6 | 0.00261973 | ||||||||
\(482\) | 1.25224e9 | 0.509360 | ||||||||
\(483\) | −5.55475e8 | −0.224310 | ||||||||
\(484\) | −1.22311e9 | −0.490351 | ||||||||
\(485\) | −1.23918e9 | −0.493219 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 2.96988e9 | 1.16516 | 0.582582 | − | 0.812772i | \(-0.302042\pi\) | ||||
0.582582 | + | 0.812772i | \(0.302042\pi\) | |||||||
\(488\) | −2.46779e8 | −0.0961257 | ||||||||
\(489\) | 2.53820e9 | 0.981622 | ||||||||
\(490\) | −4.13105e8 | −0.158626 | ||||||||
\(491\) | −4.25451e9 | −1.62205 | −0.811025 | − | 0.585012i | \(-0.801090\pi\) | ||||
−0.811025 | + | 0.585012i | \(0.801090\pi\) | |||||||
\(492\) | 8.42204e8 | 0.318816 | ||||||||
\(493\) | −2.23992e9 | −0.841914 | ||||||||
\(494\) | 2.97692e7 | 0.0111102 | ||||||||
\(495\) | −1.96218e8 | −0.0727143 | ||||||||
\(496\) | −1.00848e9 | −0.371092 | ||||||||
\(497\) | −7.14098e8 | −0.260922 | ||||||||
\(498\) | −1.81032e9 | −0.656828 | ||||||||
\(499\) | −1.93730e9 | −0.697984 | −0.348992 | − | 0.937126i | \(-0.613476\pi\) | ||||
−0.348992 | + | 0.937126i | \(0.613476\pi\) | |||||||
\(500\) | 1.02244e9 | 0.365799 | ||||||||
\(501\) | −9.62077e8 | −0.341805 | ||||||||
\(502\) | −2.71793e9 | −0.958903 | ||||||||
\(503\) | −2.02364e9 | −0.708998 | −0.354499 | − | 0.935056i | \(-0.615349\pi\) | ||||
−0.354499 | + | 0.935056i | \(0.615349\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 3.44340e9 | 1.18978 | ||||||||
\(506\) | −2.94256e8 | −0.100971 | ||||||||
\(507\) | 1.30324e8 | 0.0444116 | ||||||||
\(508\) | 1.93582e9 | 0.655152 | ||||||||
\(509\) | −1.24256e9 | −0.417641 | −0.208821 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208821 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(510\) | −1.57920e9 | −0.527158 | ||||||||
\(511\) | 1.69256e9 | 0.561141 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 3.33379e7 | 0.0109025 | ||||||||
\(514\) | −1.42625e9 | −0.463259 | ||||||||
\(515\) | 5.28611e9 | 1.70534 | ||||||||
\(516\) | 1.47697e9 | 0.473258 | ||||||||
\(517\) | −6.77268e8 | −0.215548 | ||||||||
\(518\) | 7.98580e6 | 0.00252444 | ||||||||
\(519\) | −3.09933e8 | −0.0973155 | ||||||||
\(520\) | 4.93722e8 | 0.153982 | ||||||||
\(521\) | 3.23123e9 | 1.00100 | 0.500501 | − | 0.865736i | \(-0.333149\pi\) | ||||
0.500501 | + | 0.865736i | \(0.333149\pi\) | |||||||
\(522\) | 7.84240e8 | 0.241325 | ||||||||
\(523\) | −5.06922e9 | −1.54948 | −0.774738 | − | 0.632282i | \(-0.782118\pi\) | ||||
−0.774738 | + | 0.632282i | \(0.782118\pi\) | |||||||
\(524\) | 1.55473e9 | 0.472057 | ||||||||
\(525\) | 1.06060e9 | 0.319884 | ||||||||
\(526\) | −8.55761e8 | −0.256391 | ||||||||
\(527\) | −4.10117e9 | −1.22059 | ||||||||
\(528\) | −6.78192e7 | −0.0200509 | ||||||||
\(529\) | 1.92774e8 | 0.0566179 | ||||||||
\(530\) | −2.89675e9 | −0.845172 | ||||||||
\(531\) | −3.24844e8 | −0.0941551 | ||||||||
\(532\) | 3.71810e7 | 0.0107061 | ||||||||
\(533\) | −1.07079e9 | −0.306308 | ||||||||
\(534\) | 1.87201e9 | 0.532002 | ||||||||
\(535\) | 2.80832e9 | 0.792883 | ||||||||
\(536\) | −2.15517e9 | −0.604512 | ||||||||
\(537\) | 8.60540e8 | 0.239807 | ||||||||
\(538\) | 3.46759e9 | 0.960042 | ||||||||
\(539\) | −7.21468e7 | −0.0198452 | ||||||||
\(540\) | 5.52909e8 | 0.151104 | ||||||||
\(541\) | −2.40143e9 | −0.652047 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(542\) | −4.06304e9 | −1.09611 | ||||||||
\(543\) | 4.23039e8 | 0.113392 | ||||||||
\(544\) | −5.45821e8 | −0.145363 | ||||||||
\(545\) | −1.29685e9 | −0.343163 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | −3.71482e9 | −0.970470 | −0.485235 | − | 0.874384i | \(-0.661266\pi\) | ||||
−0.485235 | + | 0.874384i | \(0.661266\pi\) | |||||||
\(548\) | −2.40266e9 | −0.623679 | ||||||||
\(549\) | 3.51371e8 | 0.0906281 | ||||||||
\(550\) | 5.61838e8 | 0.143993 | ||||||||
\(551\) | −2.27761e8 | −0.0580027 | ||||||||
\(552\) | 8.29163e8 | 0.209823 | ||||||||
\(553\) | 7.66184e8 | 0.192662 | ||||||||
\(554\) | 9.96640e8 | 0.249031 | ||||||||
\(555\) | −3.44890e7 | −0.00856357 | ||||||||
\(556\) | −3.16544e9 | −0.781039 | ||||||||
\(557\) | −3.24801e9 | −0.796388 | −0.398194 | − | 0.917301i | \(-0.630363\pi\) | ||||
−0.398194 | + | 0.917301i | \(0.630363\pi\) | |||||||
\(558\) | 1.43590e9 | 0.349869 | ||||||||
\(559\) | −1.87784e9 | −0.454691 | ||||||||
\(560\) | 6.16646e8 | 0.148381 | ||||||||
\(561\) | −2.75799e8 | −0.0659513 | ||||||||
\(562\) | 2.77148e9 | 0.658619 | ||||||||
\(563\) | 5.28287e9 | 1.24764 | 0.623822 | − | 0.781566i | \(-0.285579\pi\) | ||||
0.623822 | + | 0.781566i | \(0.285579\pi\) | |||||||
\(564\) | 1.90843e9 | 0.447918 | ||||||||
\(565\) | −4.66814e9 | −1.08887 | ||||||||
\(566\) | 3.47825e9 | 0.806311 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 1.06594e9 | 0.244070 | ||||||||
\(569\) | 9.03192e8 | 0.205536 | 0.102768 | − | 0.994705i | \(-0.467230\pi\) | ||||
0.102768 | + | 0.994705i | \(0.467230\pi\) | |||||||
\(570\) | −1.60577e8 | −0.0363179 | ||||||||
\(571\) | −5.41402e9 | −1.21701 | −0.608504 | − | 0.793551i | \(-0.708230\pi\) | ||||
−0.608504 | + | 0.793551i | \(0.708230\pi\) | |||||||
\(572\) | 8.62261e7 | 0.0192643 | ||||||||
\(573\) | 8.53385e7 | 0.0189498 | ||||||||
\(574\) | −1.33739e9 | −0.295166 | ||||||||
\(575\) | −6.86908e9 | −1.50682 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 4.61481e8 | 0.100009 | 0.0500044 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500044 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(578\) | 1.06302e9 | 0.228979 | ||||||||
\(579\) | −5.21910e8 | −0.111743 | ||||||||
\(580\) | −3.77740e9 | −0.803888 | ||||||||
\(581\) | 2.87472e9 | 0.608105 | ||||||||
\(582\) | 6.09829e8 | 0.128226 | ||||||||
\(583\) | −5.05903e8 | −0.105737 | ||||||||
\(584\) | −2.52651e9 | −0.524899 | ||||||||
\(585\) | −7.02975e8 | −0.145176 | ||||||||
\(586\) | −3.85915e9 | −0.792228 | ||||||||
\(587\) | −8.26817e9 | −1.68724 | −0.843618 | − | 0.536944i | \(-0.819579\pi\) | ||||
−0.843618 | + | 0.536944i | \(0.819579\pi\) | |||||||
\(588\) | 2.03297e8 | 0.0412393 | ||||||||
\(589\) | −4.17018e8 | −0.0840913 | ||||||||
\(590\) | 1.56466e9 | 0.313644 | ||||||||
\(591\) | 1.64096e9 | 0.326996 | ||||||||
\(592\) | −1.19205e7 | −0.00236139 | ||||||||
\(593\) | 2.54940e9 | 0.502049 | 0.251024 | − | 0.967981i | \(-0.419233\pi\) | ||||
0.251024 | + | 0.967981i | \(0.419233\pi\) | |||||||
\(594\) | 9.65628e7 | 0.0189042 | ||||||||
\(595\) | 2.50771e9 | 0.488054 | ||||||||
\(596\) | 2.89047e9 | 0.559251 | ||||||||
\(597\) | −3.63876e9 | −0.699911 | ||||||||
\(598\) | −1.05421e9 | −0.201592 | ||||||||
\(599\) | 1.70985e9 | 0.325060 | 0.162530 | − | 0.986704i | \(-0.448035\pi\) | ||||
0.162530 | + | 0.986704i | \(0.448035\pi\) | |||||||
\(600\) | −1.58316e9 | −0.299224 | ||||||||
\(601\) | 9.49145e9 | 1.78350 | 0.891748 | − | 0.452533i | \(-0.149479\pi\) | ||||
0.891748 | + | 0.452533i | \(0.149479\pi\) | |||||||
\(602\) | −2.34537e9 | −0.438152 | ||||||||
\(603\) | 3.06859e9 | 0.569940 | ||||||||
\(604\) | −1.41290e9 | −0.260906 | ||||||||
\(605\) | −8.38819e9 | −1.54001 | ||||||||
\(606\) | −1.69457e9 | −0.309318 | ||||||||
\(607\) | 5.68060e9 | 1.03094 | 0.515470 | − | 0.856907i | \(-0.327617\pi\) | ||||
0.515470 | + | 0.856907i | \(0.327617\pi\) | |||||||
\(608\) | −5.55005e7 | −0.0100146 | ||||||||
\(609\) | −1.24534e9 | −0.223423 | ||||||||
\(610\) | −1.69243e9 | −0.301895 | ||||||||
\(611\) | −2.42640e9 | −0.430346 | ||||||||
\(612\) | 7.77156e8 | 0.137050 | ||||||||
\(613\) | −1.95983e9 | −0.343642 | −0.171821 | − | 0.985128i | \(-0.554965\pi\) | ||||
−0.171821 | + | 0.985128i | \(0.554965\pi\) | |||||||
\(614\) | −7.55444e9 | −1.31708 | ||||||||
\(615\) | 5.77590e9 | 1.00128 | ||||||||
\(616\) | 1.07694e8 | 0.0185635 | ||||||||
\(617\) | 2.58071e9 | 0.442325 | 0.221163 | − | 0.975237i | \(-0.429015\pi\) | ||||
0.221163 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(618\) | −2.60141e9 | −0.443352 | ||||||||
\(619\) | 1.43435e9 | 0.243073 | 0.121537 | − | 0.992587i | \(-0.461218\pi\) | ||||
0.121537 | + | 0.992587i | \(0.461218\pi\) | |||||||
\(620\) | −6.91623e9 | −1.16546 | ||||||||
\(621\) | −1.18059e9 | −0.197823 | ||||||||
\(622\) | −1.81028e9 | −0.301633 | ||||||||
\(623\) | −2.97268e9 | −0.492538 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | −1.93513e9 | −0.317052 | ||||||||
\(626\) | 3.04339e9 | 0.495846 | ||||||||
\(627\) | −2.80440e7 | −0.00454363 | ||||||||
\(628\) | 2.21373e9 | 0.356669 | ||||||||
\(629\) | −4.84769e7 | −0.00776708 | ||||||||
\(630\) | −8.77998e8 | −0.139895 | ||||||||
\(631\) | −8.72934e9 | −1.38318 | −0.691590 | − | 0.722290i | \(-0.743089\pi\) | ||||
−0.691590 | + | 0.722290i | \(0.743089\pi\) | |||||||
\(632\) | −1.14369e9 | −0.180218 | ||||||||
\(633\) | −5.65432e9 | −0.886068 | ||||||||
\(634\) | 2.59409e9 | 0.404271 | ||||||||
\(635\) | 1.32760e10 | 2.05759 | ||||||||
\(636\) | 1.42555e9 | 0.219726 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −6.59705e8 | −0.100572 | ||||||||
\(639\) | −1.51772e9 | −0.230112 | ||||||||
\(640\) | −9.20475e8 | −0.138798 | ||||||||
\(641\) | 1.04731e10 | 1.57062 | 0.785312 | − | 0.619100i | \(-0.212502\pi\) | ||||
0.785312 | + | 0.619100i | \(0.212502\pi\) | |||||||
\(642\) | −1.38203e9 | −0.206132 | ||||||||
\(643\) | 9.70622e9 | 1.43983 | 0.719916 | − | 0.694061i | \(-0.244180\pi\) | ||||
0.719916 | + | 0.694061i | \(0.244180\pi\) | |||||||
\(644\) | −1.31668e9 | −0.194258 | ||||||||
\(645\) | 1.01292e10 | 1.48633 | ||||||||
\(646\) | −2.25703e8 | −0.0329400 | ||||||||
\(647\) | 1.96219e9 | 0.284823 | 0.142412 | − | 0.989808i | \(-0.454514\pi\) | ||||
0.142412 | + | 0.989808i | \(0.454514\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | 2.73260e8 | 0.0392391 | ||||||||
\(650\) | 2.01285e9 | 0.287485 | ||||||||
\(651\) | −2.28016e9 | −0.323916 | ||||||||
\(652\) | 6.01647e9 | 0.850110 | ||||||||
\(653\) | 5.22739e9 | 0.734664 | 0.367332 | − | 0.930090i | \(-0.380271\pi\) | ||||
0.367332 | + | 0.930090i | \(0.380271\pi\) | |||||||
\(654\) | 6.38205e8 | 0.0892150 | ||||||||
\(655\) | 1.06624e10 | 1.48256 | ||||||||
\(656\) | 1.99634e9 | 0.276102 | ||||||||
\(657\) | 3.59732e9 | 0.494880 | ||||||||
\(658\) | −3.03051e9 | −0.414692 | ||||||||
\(659\) | 5.16442e9 | 0.702947 | 0.351474 | − | 0.936198i | \(-0.385681\pi\) | ||||
0.351474 | + | 0.936198i | \(0.385681\pi\) | |||||||
\(660\) | −4.65109e8 | −0.0629725 | ||||||||
\(661\) | 1.33212e9 | 0.179406 | 0.0897030 | − | 0.995969i | \(-0.471408\pi\) | ||||
0.0897030 | + | 0.995969i | \(0.471408\pi\) | |||||||
\(662\) | 1.04413e9 | 0.139879 | ||||||||
\(663\) | −9.88085e8 | −0.131673 | ||||||||
\(664\) | −4.29112e9 | −0.568830 | ||||||||
\(665\) | 2.54990e8 | 0.0336239 | ||||||||
\(666\) | 1.69727e7 | 0.00222634 | ||||||||
\(667\) | 8.06562e9 | 1.05244 | ||||||||
\(668\) | −2.28048e9 | −0.296012 | ||||||||
\(669\) | −3.58711e9 | −0.463183 | ||||||||
\(670\) | −1.47803e10 | −1.89855 | ||||||||
\(671\) | −2.95575e8 | −0.0377693 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −1.19480e10 | −1.51093 | −0.755463 | − | 0.655192i | \(-0.772588\pi\) | ||||
−0.755463 | + | 0.655192i | \(0.772588\pi\) | |||||||
\(674\) | 8.98828e9 | 1.13075 | ||||||||
\(675\) | 2.25415e9 | 0.282111 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 3.91347e9 | 0.484732 | 0.242366 | − | 0.970185i | \(-0.422077\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422077\pi\) | |||||||
\(678\) | 2.29729e9 | 0.283082 | ||||||||
\(679\) | −9.68385e8 | −0.118715 | ||||||||
\(680\) | −3.74328e9 | −0.456532 | ||||||||
\(681\) | −6.58009e9 | −0.798393 | ||||||||
\(682\) | −1.20789e9 | −0.145808 | ||||||||
\(683\) | 2.60024e9 | 0.312277 | 0.156139 | − | 0.987735i | \(-0.450095\pi\) | ||||
0.156139 | + | 0.987735i | \(0.450095\pi\) | |||||||
\(684\) | 7.90232e7 | 0.00944188 | ||||||||
\(685\) | −1.64776e10 | −1.95875 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | 5.57343e9 | 0.655804 | ||||||||
\(688\) | 3.50097e9 | 0.409853 | ||||||||
\(689\) | −1.81246e9 | −0.211106 | ||||||||
\(690\) | 5.68646e9 | 0.658977 | ||||||||
\(691\) | 2.54480e9 | 0.293414 | 0.146707 | − | 0.989180i | \(-0.453133\pi\) | ||||
0.146707 | + | 0.989180i | \(0.453133\pi\) | |||||||
\(692\) | −7.34656e8 | −0.0842777 | ||||||||
\(693\) | −1.53338e8 | −0.0175019 | ||||||||
\(694\) | −7.74152e9 | −0.879161 | ||||||||
\(695\) | −2.17088e10 | −2.45296 | ||||||||
\(696\) | 1.85894e9 | 0.208993 | ||||||||
\(697\) | 8.11847e9 | 0.908154 | ||||||||
\(698\) | −3.71644e9 | −0.413650 | ||||||||
\(699\) | 9.29119e8 | 0.102897 | ||||||||
\(700\) | 2.51401e9 | 0.277028 | ||||||||
\(701\) | −6.53781e9 | −0.716835 | −0.358418 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358418 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | −4.92926e6 | −0.000535104 0 | ||||||||
\(704\) | −1.60757e8 | −0.0173646 | ||||||||
\(705\) | 1.30881e10 | 1.40675 | ||||||||
\(706\) | −3.35407e9 | −0.358720 | ||||||||
\(707\) | 2.69091e9 | 0.286373 | ||||||||
\(708\) | −7.70001e8 | −0.0815407 | ||||||||
\(709\) | 2.52199e9 | 0.265755 | 0.132877 | − | 0.991132i | \(-0.457578\pi\) | ||||
0.132877 | + | 0.991132i | \(0.457578\pi\) | |||||||
\(710\) | 7.31031e9 | 0.766535 | ||||||||
\(711\) | 1.62842e9 | 0.169912 | ||||||||
\(712\) | 4.43735e9 | 0.460727 | ||||||||
\(713\) | 1.47677e10 | 1.52581 | ||||||||
\(714\) | −1.23409e9 | −0.126883 | ||||||||
\(715\) | 5.91345e8 | 0.0605020 | ||||||||
\(716\) | 2.03980e9 | 0.207679 | ||||||||
\(717\) | 7.83375e9 | 0.793693 | ||||||||
\(718\) | −1.06757e10 | −1.07637 | ||||||||
\(719\) | 1.27204e10 | 1.27629 | 0.638143 | − | 0.769918i | \(-0.279703\pi\) | ||||
0.638143 | + | 0.769918i | \(0.279703\pi\) | |||||||
\(720\) | 1.31060e9 | 0.130860 | ||||||||
\(721\) | 4.13094e9 | 0.410464 | ||||||||
\(722\) | 7.12802e9 | 0.704837 | ||||||||
\(723\) | −4.22633e9 | −0.415890 | ||||||||
\(724\) | 1.00276e9 | 0.0981999 | ||||||||
\(725\) | −1.54001e10 | −1.50086 | ||||||||
\(726\) | 4.12800e9 | 0.400370 | ||||||||
\(727\) | 5.70658e9 | 0.550815 | 0.275407 | − | 0.961328i | \(-0.411187\pi\) | ||||
0.275407 | + | 0.961328i | \(0.411187\pi\) | |||||||
\(728\) | 3.85828e8 | 0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.73270e10 | −1.64852 | ||||||||
\(731\) | 1.42373e10 | 1.34809 | ||||||||
\(732\) | 8.32880e8 | 0.0784863 | ||||||||
\(733\) | −1.61419e10 | −1.51387 | −0.756937 | − | 0.653488i | \(-0.773305\pi\) | ||||
−0.756937 | + | 0.653488i | \(0.773305\pi\) | |||||||
\(734\) | −1.20392e10 | −1.12372 | ||||||||
\(735\) | 1.39423e9 | 0.129517 | ||||||||
\(736\) | 1.96542e9 | 0.181712 | ||||||||
\(737\) | −2.58131e9 | −0.237522 | ||||||||
\(738\) | −2.84244e9 | −0.260312 | ||||||||
\(739\) | −4.00265e9 | −0.364831 | −0.182416 | − | 0.983222i | \(-0.558392\pi\) | ||||
−0.182416 | + | 0.983222i | \(0.558392\pi\) | |||||||
\(740\) | −8.17516e7 | −0.00741627 | ||||||||
\(741\) | −1.00471e8 | −0.00907146 | ||||||||
\(742\) | −2.26372e9 | −0.203427 | ||||||||
\(743\) | −4.09597e9 | −0.366350 | −0.183175 | − | 0.983080i | \(-0.558637\pi\) | ||||
−0.183175 | + | 0.983080i | \(0.558637\pi\) | |||||||
\(744\) | 3.40362e9 | 0.302995 | ||||||||
\(745\) | 1.98231e10 | 1.75640 | ||||||||
\(746\) | 6.55332e9 | 0.577930 | ||||||||
\(747\) | 6.10982e9 | 0.536298 | ||||||||
\(748\) | −6.53746e8 | −0.0571155 | ||||||||
\(749\) | 2.19462e9 | 0.190841 | ||||||||
\(750\) | −3.45073e9 | −0.298674 | ||||||||
\(751\) | −1.36616e10 | −1.17696 | −0.588481 | − | 0.808511i | \(-0.700274\pi\) | ||||
−0.588481 | + | 0.808511i | \(0.700274\pi\) | |||||||
\(752\) | 4.52368e9 | 0.387909 | ||||||||
\(753\) | 9.17300e9 | 0.782941 | ||||||||
\(754\) | −2.36348e9 | −0.200794 | ||||||||
\(755\) | −9.68980e9 | −0.819408 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | 5.79115e9 | 0.485210 | 0.242605 | − | 0.970125i | \(-0.421998\pi\) | ||||
0.242605 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(758\) | 6.95735e9 | 0.580232 | ||||||||
\(759\) | 9.93113e8 | 0.0824428 | ||||||||
\(760\) | −3.80627e8 | −0.0314523 | ||||||||
\(761\) | −1.57699e10 | −1.29713 | −0.648564 | − | 0.761160i | \(-0.724630\pi\) | ||||
−0.648564 | + | 0.761160i | \(0.724630\pi\) | |||||||
\(762\) | −6.53340e9 | −0.534930 | ||||||||
\(763\) | −1.01345e9 | −0.0825970 | ||||||||
\(764\) | 2.02284e8 | 0.0164110 | ||||||||
\(765\) | 5.32979e9 | 0.430423 | ||||||||
\(766\) | −7.37007e9 | −0.592476 | ||||||||
\(767\) | 9.78988e8 | 0.0783418 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | −1.39801e10 | −1.10858 | −0.554292 | − | 0.832322i | \(-0.687011\pi\) | ||||
−0.554292 | + | 0.832322i | \(0.687011\pi\) | |||||||
\(770\) | 7.38575e8 | 0.0583012 | ||||||||
\(771\) | 4.81359e9 | 0.378250 | ||||||||
\(772\) | −1.23712e9 | −0.0967724 | ||||||||
\(773\) | 1.10317e10 | 0.859040 | 0.429520 | − | 0.903057i | \(-0.358683\pi\) | ||||
0.429520 | + | 0.903057i | \(0.358683\pi\) | |||||||
\(774\) | −4.98478e9 | −0.386413 | ||||||||
\(775\) | −2.81968e10 | −2.17592 | ||||||||
\(776\) | 1.44552e9 | 0.111047 | ||||||||
\(777\) | −2.69521e7 | −0.00206119 | ||||||||
\(778\) | −1.15325e10 | −0.878004 | ||||||||
\(779\) | 8.25508e8 | 0.0625662 | ||||||||
\(780\) | −1.66631e9 | −0.125726 | ||||||||
\(781\) | 1.27671e9 | 0.0958990 | ||||||||
\(782\) | 7.99277e9 | 0.597686 | ||||||||
\(783\) | −2.64681e9 | −0.197041 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | 1.51819e10 | 1.12017 | ||||||||
\(786\) | −5.24720e9 | −0.385433 | ||||||||
\(787\) | −1.59771e10 | −1.16838 | −0.584192 | − | 0.811615i | \(-0.698589\pi\) | ||||
−0.584192 | + | 0.811615i | \(0.698589\pi\) | |||||||
\(788\) | 3.88969e9 | 0.283187 | ||||||||
\(789\) | 2.88819e9 | 0.209342 | ||||||||
\(790\) | −7.84352e9 | −0.566000 | ||||||||
\(791\) | −3.64801e9 | −0.262083 | ||||||||
\(792\) | 2.28890e8 | 0.0163715 | ||||||||
\(793\) | −1.05893e9 | −0.0754072 | ||||||||
\(794\) | −8.70805e9 | −0.617375 | ||||||||
\(795\) | 9.77652e9 | 0.690080 | ||||||||
\(796\) | −8.62520e9 | −0.606141 | ||||||||
\(797\) | 1.94142e9 | 0.135836 | 0.0679180 | − | 0.997691i | \(-0.478364\pi\) | ||||
0.0679180 | + | 0.997691i | \(0.478364\pi\) | |||||||
\(798\) | −1.25486e8 | −0.00874148 | ||||||||
\(799\) | 1.83964e10 | 1.27591 | ||||||||
\(800\) | −3.75268e9 | −0.259136 | ||||||||
\(801\) | −6.31803e9 | −0.434378 | ||||||||
\(802\) | −3.56761e9 | −0.244212 | ||||||||
\(803\) | −3.02607e9 | −0.206241 | ||||||||
\(804\) | 7.27370e9 | 0.493582 | ||||||||
\(805\) | −9.02989e9 | −0.610094 | ||||||||
\(806\) | −4.32740e9 | −0.291108 | ||||||||
\(807\) | −1.17031e10 | −0.783871 | ||||||||
\(808\) | −4.01676e9 | −0.267877 | ||||||||
\(809\) | −7.76568e9 | −0.515655 | −0.257828 | − | 0.966191i | \(-0.583007\pi\) | ||||
−0.257828 | + | 0.966191i | \(0.583007\pi\) | |||||||
\(810\) | −1.86607e9 | −0.123376 | ||||||||
\(811\) | −9.86945e9 | −0.649711 | −0.324855 | − | 0.945764i | \(-0.605316\pi\) | ||||
−0.324855 | + | 0.945764i | \(0.605316\pi\) | |||||||
\(812\) | −2.95193e9 | −0.193490 | ||||||||
\(813\) | 1.37128e10 | 0.894969 | ||||||||
\(814\) | −1.42775e7 | −0.000927829 0 | ||||||||
\(815\) | 4.12614e10 | 2.66988 | ||||||||
\(816\) | 1.84215e9 | 0.118689 | ||||||||
\(817\) | 1.44769e9 | 0.0928749 | ||||||||
\(818\) | −3.19692e9 | −0.204219 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | 1.36910e10 | 0.867136 | ||||||||
\(821\) | 1.07418e10 | 0.677445 | 0.338722 | − | 0.940886i | \(-0.390005\pi\) | ||||
0.338722 | + | 0.940886i | \(0.390005\pi\) | |||||||
\(822\) | 8.10899e9 | 0.509232 | ||||||||
\(823\) | 1.14068e10 | 0.713289 | 0.356645 | − | 0.934240i | \(-0.383921\pi\) | ||||
0.356645 | + | 0.934240i | \(0.383921\pi\) | |||||||
\(824\) | −6.16630e9 | −0.383954 | ||||||||
\(825\) | −1.89620e9 | −0.117570 | ||||||||
\(826\) | 1.22273e9 | 0.0754921 | ||||||||
\(827\) | −2.63229e10 | −1.61832 | −0.809161 | − | 0.587587i | \(-0.800078\pi\) | ||||
−0.809161 | + | 0.587587i | \(0.800078\pi\) | |||||||
\(828\) | −2.79843e9 | −0.171320 | ||||||||
\(829\) | 8.82574e9 | 0.538035 | 0.269017 | − | 0.963135i | \(-0.413301\pi\) | ||||
0.269017 | + | 0.963135i | \(0.413301\pi\) | |||||||
\(830\) | −2.94288e10 | −1.78649 | ||||||||
\(831\) | −3.36366e9 | −0.203333 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | 1.95970e9 | 0.117471 | ||||||||
\(834\) | 1.06834e10 | 0.637716 | ||||||||
\(835\) | −1.56397e10 | −0.929663 | ||||||||
\(836\) | −6.64746e7 | −0.00393490 | ||||||||
\(837\) | −4.84617e9 | −0.285667 | ||||||||
\(838\) | −2.03535e10 | −1.19477 | ||||||||
\(839\) | 3.61230e9 | 0.211162 | 0.105581 | − | 0.994411i | \(-0.466330\pi\) | ||||
0.105581 | + | 0.994411i | \(0.466330\pi\) | |||||||
\(840\) | −2.08118e9 | −0.121153 | ||||||||
\(841\) | 8.32794e8 | 0.0482782 | ||||||||
\(842\) | 1.57506e10 | 0.909293 | ||||||||
\(843\) | −9.35373e9 | −0.537760 | ||||||||
\(844\) | −1.34028e10 | −0.767358 | ||||||||
\(845\) | 2.11857e9 | 0.120794 | ||||||||
\(846\) | −6.44094e9 | −0.365724 | ||||||||
\(847\) | −6.55511e9 | −0.370671 | ||||||||
\(848\) | 3.37908e9 | 0.190289 | ||||||||
\(849\) | −1.17391e10 | −0.658351 | ||||||||
\(850\) | −1.52610e10 | −0.852347 | ||||||||
\(851\) | 1.74558e8 | 0.00970929 | ||||||||
\(852\) | −3.59756e9 | −0.199282 | ||||||||
\(853\) | 3.42387e10 | 1.88884 | 0.944421 | − | 0.328739i | \(-0.106624\pi\) | ||||
0.944421 | + | 0.328739i | \(0.106624\pi\) | |||||||
\(854\) | −1.32258e9 | −0.0726642 | ||||||||
\(855\) | 5.41947e8 | 0.0296535 | ||||||||
\(856\) | −3.27593e9 | −0.178516 | ||||||||
\(857\) | 7.73043e9 | 0.419537 | 0.209769 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209769 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(858\) | −2.91013e8 | −0.0157292 | ||||||||
\(859\) | −2.16322e10 | −1.16446 | −0.582231 | − | 0.813024i | \(-0.697820\pi\) | ||||
−0.582231 | + | 0.813024i | \(0.697820\pi\) | |||||||
\(860\) | 2.40099e10 | 1.28720 | ||||||||
\(861\) | 4.51369e9 | 0.241002 | ||||||||
\(862\) | 2.38255e10 | 1.26697 | ||||||||
\(863\) | −7.81992e9 | −0.414157 | −0.207078 | − | 0.978324i | \(-0.566396\pi\) | ||||
−0.207078 | + | 0.978324i | \(0.566396\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −5.03832e9 | −0.264685 | ||||||||
\(866\) | 1.18171e10 | 0.618300 | ||||||||
\(867\) | −3.58771e9 | −0.186961 | ||||||||
\(868\) | −5.40482e9 | −0.280519 | ||||||||
\(869\) | −1.36983e9 | −0.0708106 | ||||||||
\(870\) | 1.27487e10 | 0.656372 | ||||||||
\(871\) | −9.24788e9 | −0.474218 | ||||||||
\(872\) | 1.51278e9 | 0.0772625 | ||||||||
\(873\) | −2.05817e9 | −0.104696 | ||||||||
\(874\) | 8.12725e8 | 0.0411769 | ||||||||
\(875\) | 5.47964e9 | 0.276518 | ||||||||
\(876\) | 8.52697e9 | 0.428578 | ||||||||
\(877\) | −2.90504e10 | −1.45430 | −0.727150 | − | 0.686479i | \(-0.759156\pi\) | ||||
−0.727150 | + | 0.686479i | \(0.759156\pi\) | |||||||
\(878\) | 6.96374e9 | 0.347226 | ||||||||
\(879\) | 1.30246e10 | 0.646852 | ||||||||
\(880\) | −1.10248e9 | −0.0545358 | ||||||||
\(881\) | −1.62576e10 | −0.801016 | −0.400508 | − | 0.916293i | \(-0.631166\pi\) | ||||
−0.400508 | + | 0.916293i | \(0.631166\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | 1.52535e9 | 0.0745603 | 0.0372802 | − | 0.999305i | \(-0.488131\pi\) | ||||
0.0372802 | + | 0.999305i | \(0.488131\pi\) | |||||||
\(884\) | −2.34213e9 | −0.114032 | ||||||||
\(885\) | −5.28072e9 | −0.256089 | ||||||||
\(886\) | −1.17455e10 | −0.567355 | ||||||||
\(887\) | −1.92252e9 | −0.0924991 | −0.0462496 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462496 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(888\) | 4.02317e7 | 0.00192807 | ||||||||
\(889\) | 1.03748e10 | 0.495249 | ||||||||
\(890\) | 3.04317e10 | 1.44698 | ||||||||
\(891\) | −3.25900e8 | −0.0154352 | ||||||||
\(892\) | −8.50277e9 | −0.401128 | ||||||||
\(893\) | 1.87059e9 | 0.0879021 | ||||||||
\(894\) | −9.75535e9 | −0.456627 | ||||||||
\(895\) | 1.39891e10 | 0.652242 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | 3.55795e9 | 0.164599 | ||||||||
\(898\) | −2.13687e9 | −0.0984715 | ||||||||
\(899\) | 3.31084e10 | 1.51978 | ||||||||
\(900\) | 5.34318e9 | 0.244315 | ||||||||
\(901\) | 1.37417e10 | 0.625896 | ||||||||
\(902\) | 2.39107e9 | 0.108485 | ||||||||
\(903\) | 7.91564e9 | 0.357749 | ||||||||
\(904\) | 5.44543e9 | 0.245156 | ||||||||
\(905\) | 6.87699e9 | 0.308410 | ||||||||
\(906\) | 4.76855e9 | 0.213028 | ||||||||
\(907\) | 3.62031e10 | 1.61109 | 0.805546 | − | 0.592534i | \(-0.201872\pi\) | ||||
0.805546 | + | 0.592534i | \(0.201872\pi\) | |||||||
\(908\) | −1.55972e10 | −0.691429 | ||||||||
\(909\) | 5.71917e9 | 0.252557 | ||||||||
\(910\) | 2.64604e9 | 0.116400 | ||||||||
\(911\) | 8.19212e9 | 0.358990 | 0.179495 | − | 0.983759i | \(-0.442554\pi\) | ||||
0.179495 | + | 0.983759i | \(0.442554\pi\) | |||||||
\(912\) | 1.87314e8 | 0.00817691 | ||||||||
\(913\) | −5.13960e9 | −0.223502 | ||||||||
\(914\) | 2.82781e10 | 1.22501 | ||||||||
\(915\) | 5.71195e9 | 0.246497 | ||||||||
\(916\) | 1.32111e10 | 0.567943 | ||||||||
\(917\) | 8.33236e9 | 0.356842 | ||||||||
\(918\) | −2.62290e9 | −0.111901 | ||||||||
\(919\) | −1.64307e10 | −0.698317 | −0.349159 | − | 0.937064i | \(-0.613533\pi\) | ||||
−0.349159 | + | 0.937064i | \(0.613533\pi\) | |||||||
\(920\) | 1.34790e10 | 0.570691 | ||||||||
\(921\) | 2.54962e10 | 1.07539 | ||||||||
\(922\) | −1.90636e10 | −0.801026 | ||||||||
\(923\) | 4.57398e9 | 0.191464 | ||||||||
\(924\) | −3.63468e8 | −0.0151570 | ||||||||
\(925\) | −3.33293e8 | −0.0138462 | ||||||||
\(926\) | −5.80379e8 | −0.0240200 | ||||||||
\(927\) | 8.77975e9 | 0.361995 | ||||||||
\(928\) | 4.40637e9 | 0.180994 | ||||||||
\(929\) | −1.47398e10 | −0.603167 | −0.301583 | − | 0.953440i | \(-0.597515\pi\) | ||||
−0.301583 | + | 0.953440i | \(0.597515\pi\) | |||||||
\(930\) | 2.33423e10 | 0.951597 | ||||||||
\(931\) | 1.99267e8 | 0.00809304 | ||||||||
\(932\) | 2.20236e9 | 0.0891111 | ||||||||
\(933\) | 6.10968e9 | 0.246282 | ||||||||
\(934\) | 1.87119e10 | 0.751455 | ||||||||
\(935\) | −4.48344e9 | −0.179379 | ||||||||
\(936\) | 8.20026e8 | 0.0326860 | ||||||||
\(937\) | 1.81420e10 | 0.720440 | 0.360220 | − | 0.932867i | \(-0.382702\pi\) | ||||
0.360220 | + | 0.932867i | \(0.382702\pi\) | |||||||
\(938\) | −1.15504e10 | −0.456968 | ||||||||
\(939\) | −1.02714e10 | −0.404857 | ||||||||
\(940\) | 3.10237e10 | 1.21828 | ||||||||
\(941\) | 3.42264e10 | 1.33905 | 0.669526 | − | 0.742789i | \(-0.266497\pi\) | ||||
0.669526 | + | 0.742789i | \(0.266497\pi\) | |||||||
\(942\) | −7.47133e9 | −0.291219 | ||||||||
\(943\) | −2.92335e10 | −1.13524 | ||||||||
\(944\) | −1.82519e9 | −0.0706164 | ||||||||
\(945\) | 2.96324e9 | 0.114224 | ||||||||
\(946\) | 4.19321e9 | 0.161038 | ||||||||
\(947\) | 3.63418e10 | 1.39053 | 0.695267 | − | 0.718752i | \(-0.255286\pi\) | ||||
0.695267 | + | 0.718752i | \(0.255286\pi\) | |||||||
\(948\) | 3.85996e9 | 0.147148 | ||||||||
\(949\) | −1.08413e10 | −0.411765 | ||||||||
\(950\) | −1.55178e9 | −0.0587215 | ||||||||
\(951\) | −8.75506e9 | −0.330086 | ||||||||
\(952\) | −2.92526e9 | −0.109884 | ||||||||
\(953\) | −1.65036e10 | −0.617665 | −0.308832 | − | 0.951116i | \(-0.599938\pi\) | ||||
−0.308832 | + | 0.951116i | \(0.599938\pi\) | |||||||
\(954\) | −4.81123e9 | −0.179406 | ||||||||
\(955\) | 1.38728e9 | 0.0515409 | ||||||||
\(956\) | 1.85689e10 | 0.687358 | ||||||||
\(957\) | 2.22651e9 | 0.0821168 | ||||||||
\(958\) | 2.50563e10 | 0.920742 | ||||||||
\(959\) | −1.28768e10 | −0.471457 | ||||||||
\(960\) | 3.10660e9 | 0.113328 | ||||||||
\(961\) | 3.31073e10 | 1.20335 | ||||||||
\(962\) | −5.11510e7 | −0.00185243 | ||||||||
\(963\) | 4.66437e9 | 0.168306 | ||||||||
\(964\) | −1.00180e10 | −0.360172 | ||||||||
\(965\) | −8.48426e9 | −0.303926 | ||||||||
\(966\) | 4.44380e9 | 0.158611 | ||||||||
\(967\) | 3.80596e10 | 1.35354 | 0.676770 | − | 0.736194i | \(-0.263379\pi\) | ||||
0.676770 | + | 0.736194i | \(0.263379\pi\) | |||||||
\(968\) | 9.78489e9 | 0.346731 | ||||||||
\(969\) | 7.61749e8 | 0.0268954 | ||||||||
\(970\) | 9.91348e9 | 0.348759 | ||||||||
\(971\) | −2.09923e10 | −0.735855 | −0.367928 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367928 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −1.69648e10 | −0.590410 | ||||||||
\(974\) | −2.37590e10 | −0.823896 | ||||||||
\(975\) | −6.79338e9 | −0.234731 | ||||||||
\(976\) | 1.97423e9 | 0.0679711 | ||||||||
\(977\) | −1.01782e10 | −0.349172 | −0.174586 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174586 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(978\) | −2.03056e10 | −0.694112 | ||||||||
\(979\) | 5.31475e9 | 0.181027 | ||||||||
\(980\) | 3.30484e9 | 0.112165 | ||||||||
\(981\) | −2.15394e9 | −0.0728437 | ||||||||
\(982\) | 3.40361e10 | 1.14696 | ||||||||
\(983\) | −8.08833e9 | −0.271595 | −0.135797 | − | 0.990737i | \(-0.543360\pi\) | ||||
−0.135797 | + | 0.990737i | \(0.543360\pi\) | |||||||
\(984\) | −6.73763e9 | −0.225437 | ||||||||
\(985\) | 2.66758e10 | 0.889387 | ||||||||
\(986\) | 1.79193e10 | 0.595323 | ||||||||
\(987\) | 1.02280e10 | 0.338594 | ||||||||
\(988\) | −2.38154e8 | −0.00785612 | ||||||||
\(989\) | −5.12666e10 | −1.68518 | ||||||||
\(990\) | 1.56974e9 | 0.0514168 | ||||||||
\(991\) | −4.00185e10 | −1.30618 | −0.653090 | − | 0.757281i | \(-0.726527\pi\) | ||||
−0.653090 | + | 0.757281i | \(0.726527\pi\) | |||||||
\(992\) | 8.06784e9 | 0.262402 | ||||||||
\(993\) | −3.52394e9 | −0.114210 | ||||||||
\(994\) | 5.71279e9 | 0.184500 | ||||||||
\(995\) | −5.91522e10 | −1.90366 | ||||||||
\(996\) | 1.44825e10 | 0.464448 | ||||||||
\(997\) | −4.41698e10 | −1.41154 | −0.705769 | − | 0.708442i | \(-0.749398\pi\) | ||||
−0.705769 | + | 0.708442i | \(0.749398\pi\) | |||||||
\(998\) | 1.54984e10 | 0.493549 | ||||||||
\(999\) | −5.72830e7 | −0.00181780 |
(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 | 546.8.a.p.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.p.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial |