Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,8,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(32.8004276758\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.176777 | −0.0883883 | − | 0.996086i | \(-0.528172\pi\) | ||||
−0.0883883 | + | 0.996086i | \(0.528172\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −124.000 | −0.968750 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 54.0000 | 0.102062 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 504.000 | 0.348029 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 250.000 | 0.0790569 | ||||||||
\(11\) | 2724.00 | 0.617068 | 0.308534 | − | 0.951213i | \(-0.400162\pi\) | ||||
0.308534 | + | 0.951213i | \(0.400162\pi\) | |||||||
\(12\) | 3348.00 | 0.559308 | ||||||||
\(13\) | 2874.00 | 0.362815 | 0.181407 | − | 0.983408i | \(-0.441935\pi\) | ||||
0.181407 | + | 0.983408i | \(0.441935\pi\) | |||||||
\(14\) | −686.000 | −0.0668153 | ||||||||
\(15\) | 3375.00 | 0.258199 | ||||||||
\(16\) | 14864.0 | 0.907227 | ||||||||
\(17\) | 9278.00 | 0.458019 | 0.229009 | − | 0.973424i | \(-0.426451\pi\) | ||||
0.229009 | + | 0.973424i | \(0.426451\pi\) | |||||||
\(18\) | −1458.00 | −0.0589256 | ||||||||
\(19\) | −4304.00 | −0.143958 | −0.0719788 | − | 0.997406i | \(-0.522931\pi\) | ||||
−0.0719788 | + | 0.997406i | \(0.522931\pi\) | |||||||
\(20\) | 15500.0 | 0.433238 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | −5448.00 | −0.109083 | ||||||||
\(23\) | −41500.0 | −0.711215 | −0.355607 | − | 0.934635i | \(-0.615726\pi\) | ||||
−0.355607 | + | 0.934635i | \(0.615726\pi\) | |||||||
\(24\) | −13608.0 | −0.200935 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −5748.00 | −0.0641372 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −42532.0 | −0.366153 | ||||||||
\(29\) | −35498.0 | −0.270278 | −0.135139 | − | 0.990827i | \(-0.543148\pi\) | ||||
−0.135139 | + | 0.990827i | \(0.543148\pi\) | |||||||
\(30\) | −6750.00 | −0.0456435 | ||||||||
\(31\) | −52940.0 | −0.319167 | −0.159584 | − | 0.987184i | \(-0.551015\pi\) | ||||
−0.159584 | + | 0.987184i | \(0.551015\pi\) | |||||||
\(32\) | −94240.0 | −0.508406 | ||||||||
\(33\) | −73548.0 | −0.356264 | ||||||||
\(34\) | −18556.0 | −0.0809670 | ||||||||
\(35\) | −42875.0 | −0.169031 | ||||||||
\(36\) | −90396.0 | −0.322917 | ||||||||
\(37\) | −84098.0 | −0.272948 | −0.136474 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136474 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(38\) | 8608.00 | 0.0254484 | ||||||||
\(39\) | −77598.0 | −0.209471 | ||||||||
\(40\) | −63000.0 | −0.155643 | ||||||||
\(41\) | 180342. | 0.408652 | 0.204326 | − | 0.978903i | \(-0.434500\pi\) | ||||
0.204326 | + | 0.978903i | \(0.434500\pi\) | |||||||
\(42\) | 18522.0 | 0.0385758 | ||||||||
\(43\) | −33452.0 | −0.0641627 | −0.0320813 | − | 0.999485i | \(-0.510214\pi\) | ||||
−0.0320813 | + | 0.999485i | \(0.510214\pi\) | |||||||
\(44\) | −337776. | −0.597784 | ||||||||
\(45\) | −91125.0 | −0.149071 | ||||||||
\(46\) | 83000.0 | 0.125726 | ||||||||
\(47\) | −136120. | −0.191240 | −0.0956202 | − | 0.995418i | \(-0.530483\pi\) | ||||
−0.0956202 | + | 0.995418i | \(0.530483\pi\) | |||||||
\(48\) | −401328. | −0.523788 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −31250.0 | −0.0353553 | ||||||||
\(51\) | −250506. | −0.264437 | ||||||||
\(52\) | −356376. | −0.351477 | ||||||||
\(53\) | −1.27062e6 | −1.17233 | −0.586166 | − | 0.810191i | \(-0.699363\pi\) | ||||
−0.586166 | + | 0.810191i | \(0.699363\pi\) | |||||||
\(54\) | 39366.0 | 0.0340207 | ||||||||
\(55\) | −340500. | −0.275961 | ||||||||
\(56\) | 172872. | 0.131543 | ||||||||
\(57\) | 116208. | 0.0831140 | ||||||||
\(58\) | 70996.0 | 0.0477789 | ||||||||
\(59\) | −1.55325e6 | −0.984600 | −0.492300 | − | 0.870426i | \(-0.663844\pi\) | ||||
−0.492300 | + | 0.870426i | \(0.663844\pi\) | |||||||
\(60\) | −418500. | −0.250130 | ||||||||
\(61\) | 213598. | 0.120488 | 0.0602439 | − | 0.998184i | \(-0.480812\pi\) | ||||
0.0602439 | + | 0.998184i | \(0.480812\pi\) | |||||||
\(62\) | 105880. | 0.0564213 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | −1.71411e6 | −0.817352 | ||||||||
\(65\) | −359250. | −0.162256 | ||||||||
\(66\) | 147096. | 0.0629792 | ||||||||
\(67\) | 487228. | 0.197911 | 0.0989556 | − | 0.995092i | \(-0.468450\pi\) | ||||
0.0989556 | + | 0.995092i | \(0.468450\pi\) | |||||||
\(68\) | −1.15047e6 | −0.443706 | ||||||||
\(69\) | 1.12050e6 | 0.410620 | ||||||||
\(70\) | 85750.0 | 0.0298807 | ||||||||
\(71\) | 1.08600e6 | 0.360102 | 0.180051 | − | 0.983657i | \(-0.442374\pi\) | ||||
0.180051 | + | 0.983657i | \(0.442374\pi\) | |||||||
\(72\) | 367416. | 0.116010 | ||||||||
\(73\) | −5.92198e6 | −1.78171 | −0.890855 | − | 0.454289i | \(-0.849893\pi\) | ||||
−0.890855 | + | 0.454289i | \(0.849893\pi\) | |||||||
\(74\) | 168196. | 0.0482508 | ||||||||
\(75\) | −421875. | −0.115470 | ||||||||
\(76\) | 533696. | 0.139459 | ||||||||
\(77\) | 934332. | 0.233230 | ||||||||
\(78\) | 155196. | 0.0370296 | ||||||||
\(79\) | −5.42982e6 | −1.23906 | −0.619528 | − | 0.784975i | \(-0.712676\pi\) | ||||
−0.619528 | + | 0.784975i | \(0.712676\pi\) | |||||||
\(80\) | −1.85800e6 | −0.405724 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −360684. | −0.0722401 | ||||||||
\(83\) | 6.93340e6 | 1.33099 | 0.665493 | − | 0.746405i | \(-0.268222\pi\) | ||||
0.665493 | + | 0.746405i | \(0.268222\pi\) | |||||||
\(84\) | 1.14836e6 | 0.211399 | ||||||||
\(85\) | −1.15975e6 | −0.204832 | ||||||||
\(86\) | 66904.0 | 0.0113425 | ||||||||
\(87\) | 958446. | 0.156045 | ||||||||
\(88\) | 1.37290e6 | 0.214757 | ||||||||
\(89\) | 262614. | 0.0394869 | 0.0197434 | − | 0.999805i | \(-0.493715\pi\) | ||||
0.0197434 | + | 0.999805i | \(0.493715\pi\) | |||||||
\(90\) | 182250. | 0.0263523 | ||||||||
\(91\) | 985782. | 0.137131 | ||||||||
\(92\) | 5.14600e6 | 0.688989 | ||||||||
\(93\) | 1.42938e6 | 0.184271 | ||||||||
\(94\) | 272240. | 0.0338068 | ||||||||
\(95\) | 538000. | 0.0643798 | ||||||||
\(96\) | 2.54448e6 | 0.293528 | ||||||||
\(97\) | −522234. | −0.0580984 | −0.0290492 | − | 0.999578i | \(-0.509248\pi\) | ||||
−0.0290492 | + | 0.999578i | \(0.509248\pi\) | |||||||
\(98\) | −235298. | −0.0252538 | ||||||||
\(99\) | 1.98580e6 | 0.205689 | ||||||||
\(100\) | −1.93750e6 | −0.193750 | ||||||||
\(101\) | −1.63961e6 | −0.158349 | −0.0791744 | − | 0.996861i | \(-0.525228\pi\) | ||||
−0.0791744 | + | 0.996861i | \(0.525228\pi\) | |||||||
\(102\) | 501012. | 0.0467463 | ||||||||
\(103\) | −6.57506e6 | −0.592883 | −0.296442 | − | 0.955051i | \(-0.595800\pi\) | ||||
−0.296442 | + | 0.955051i | \(0.595800\pi\) | |||||||
\(104\) | 1.44850e6 | 0.126270 | ||||||||
\(105\) | 1.15762e6 | 0.0975900 | ||||||||
\(106\) | 2.54124e6 | 0.207241 | ||||||||
\(107\) | 1.21480e7 | 0.958654 | 0.479327 | − | 0.877636i | \(-0.340881\pi\) | ||||
0.479327 | + | 0.877636i | \(0.340881\pi\) | |||||||
\(108\) | 2.44069e6 | 0.186436 | ||||||||
\(109\) | −9.68452e6 | −0.716284 | −0.358142 | − | 0.933667i | \(-0.616590\pi\) | ||||
−0.358142 | + | 0.933667i | \(0.616590\pi\) | |||||||
\(110\) | 681000. | 0.0487835 | ||||||||
\(111\) | 2.27065e6 | 0.157586 | ||||||||
\(112\) | 5.09835e6 | 0.342899 | ||||||||
\(113\) | 2.50296e7 | 1.63184 | 0.815922 | − | 0.578162i | \(-0.196230\pi\) | ||||
0.815922 | + | 0.578162i | \(0.196230\pi\) | |||||||
\(114\) | −232416. | −0.0146926 | ||||||||
\(115\) | 5.18750e6 | 0.318065 | ||||||||
\(116\) | 4.40175e6 | 0.261832 | ||||||||
\(117\) | 2.09515e6 | 0.120938 | ||||||||
\(118\) | 3.10650e6 | 0.174054 | ||||||||
\(119\) | 3.18235e6 | 0.173115 | ||||||||
\(120\) | 1.70100e6 | 0.0898607 | ||||||||
\(121\) | −1.20670e7 | −0.619228 | ||||||||
\(122\) | −427196. | −0.0212994 | ||||||||
\(123\) | −4.86923e6 | −0.235935 | ||||||||
\(124\) | 6.56456e6 | 0.309193 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | −500094. | −0.0222718 | ||||||||
\(127\) | 3.05960e6 | 0.132541 | 0.0662707 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662707 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(128\) | 1.54909e7 | 0.652894 | ||||||||
\(129\) | 903204. | 0.0370443 | ||||||||
\(130\) | 718500. | 0.0286830 | ||||||||
\(131\) | −3.56912e6 | −0.138711 | −0.0693555 | − | 0.997592i | \(-0.522094\pi\) | ||||
−0.0693555 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(132\) | 9.11995e6 | 0.345131 | ||||||||
\(133\) | −1.47627e6 | −0.0544109 | ||||||||
\(134\) | −974456. | −0.0349861 | ||||||||
\(135\) | 2.46038e6 | 0.0860663 | ||||||||
\(136\) | 4.67611e6 | 0.159404 | ||||||||
\(137\) | 4.83736e6 | 0.160726 | 0.0803630 | − | 0.996766i | \(-0.474392\pi\) | ||||
0.0803630 | + | 0.996766i | \(0.474392\pi\) | |||||||
\(138\) | −2.24100e6 | −0.0725880 | ||||||||
\(139\) | 2.48573e6 | 0.0785058 | 0.0392529 | − | 0.999229i | \(-0.487502\pi\) | ||||
0.0392529 | + | 0.999229i | \(0.487502\pi\) | |||||||
\(140\) | 5.31650e6 | 0.163749 | ||||||||
\(141\) | 3.67524e6 | 0.110413 | ||||||||
\(142\) | −2.17200e6 | −0.0636577 | ||||||||
\(143\) | 7.82878e6 | 0.223881 | ||||||||
\(144\) | 1.08359e7 | 0.302409 | ||||||||
\(145\) | 4.43725e6 | 0.120872 | ||||||||
\(146\) | 1.18440e7 | 0.314965 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | 1.04282e7 | 0.264418 | ||||||||
\(149\) | −3.99895e7 | −0.990362 | −0.495181 | − | 0.868790i | \(-0.664898\pi\) | ||||
−0.495181 | + | 0.868790i | \(0.664898\pi\) | |||||||
\(150\) | 843750. | 0.0204124 | ||||||||
\(151\) | −5.37919e7 | −1.27145 | −0.635723 | − | 0.771918i | \(-0.719298\pi\) | ||||
−0.635723 | + | 0.771918i | \(0.719298\pi\) | |||||||
\(152\) | −2.16922e6 | −0.0501014 | ||||||||
\(153\) | 6.76366e6 | 0.152673 | ||||||||
\(154\) | −1.86866e6 | −0.0412296 | ||||||||
\(155\) | 6.61750e6 | 0.142736 | ||||||||
\(156\) | 9.62215e6 | 0.202925 | ||||||||
\(157\) | 9.64019e6 | 0.198809 | 0.0994046 | − | 0.995047i | \(-0.468306\pi\) | ||||
0.0994046 | + | 0.995047i | \(0.468306\pi\) | |||||||
\(158\) | 1.08596e7 | 0.219036 | ||||||||
\(159\) | 3.43068e7 | 0.676847 | ||||||||
\(160\) | 1.17800e7 | 0.227366 | ||||||||
\(161\) | −1.42345e7 | −0.268814 | ||||||||
\(162\) | −1.06288e6 | −0.0196419 | ||||||||
\(163\) | −7.67343e7 | −1.38782 | −0.693910 | − | 0.720062i | \(-0.744113\pi\) | ||||
−0.693910 | + | 0.720062i | \(0.744113\pi\) | |||||||
\(164\) | −2.23624e7 | −0.395881 | ||||||||
\(165\) | 9.19350e6 | 0.159326 | ||||||||
\(166\) | −1.38668e7 | −0.235287 | ||||||||
\(167\) | 1.03856e7 | 0.172554 | 0.0862770 | − | 0.996271i | \(-0.472503\pi\) | ||||
0.0862770 | + | 0.996271i | \(0.472503\pi\) | |||||||
\(168\) | −4.66754e6 | −0.0759462 | ||||||||
\(169\) | −5.44886e7 | −0.868365 | ||||||||
\(170\) | 2.31950e6 | 0.0362096 | ||||||||
\(171\) | −3.13762e6 | −0.0479859 | ||||||||
\(172\) | 4.14805e6 | 0.0621576 | ||||||||
\(173\) | −5.64927e6 | −0.0829528 | −0.0414764 | − | 0.999139i | \(-0.513206\pi\) | ||||
−0.0414764 | + | 0.999139i | \(0.513206\pi\) | |||||||
\(174\) | −1.91689e6 | −0.0275851 | ||||||||
\(175\) | 5.35938e6 | 0.0755929 | ||||||||
\(176\) | 4.04895e7 | 0.559820 | ||||||||
\(177\) | 4.19378e7 | 0.568459 | ||||||||
\(178\) | −525228. | −0.00698036 | ||||||||
\(179\) | −1.04373e8 | −1.36020 | −0.680098 | − | 0.733121i | \(-0.738063\pi\) | ||||
−0.680098 | + | 0.733121i | \(0.738063\pi\) | |||||||
\(180\) | 1.12995e7 | 0.144413 | ||||||||
\(181\) | −1.42262e8 | −1.78326 | −0.891628 | − | 0.452769i | \(-0.850436\pi\) | ||||
−0.891628 | + | 0.452769i | \(0.850436\pi\) | |||||||
\(182\) | −1.97156e6 | −0.0242416 | ||||||||
\(183\) | −5.76715e6 | −0.0695636 | ||||||||
\(184\) | −2.09160e7 | −0.247523 | ||||||||
\(185\) | 1.05122e7 | 0.122066 | ||||||||
\(186\) | −2.85876e6 | −0.0325748 | ||||||||
\(187\) | 2.52733e7 | 0.282628 | ||||||||
\(188\) | 1.68789e7 | 0.185264 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | −1.07600e6 | −0.0113808 | ||||||||
\(191\) | −3.35533e7 | −0.348433 | −0.174216 | − | 0.984707i | \(-0.555739\pi\) | ||||
−0.174216 | + | 0.984707i | \(0.555739\pi\) | |||||||
\(192\) | 4.62810e7 | 0.471899 | ||||||||
\(193\) | −1.70599e8 | −1.70815 | −0.854073 | − | 0.520153i | \(-0.825875\pi\) | ||||
−0.854073 | + | 0.520153i | \(0.825875\pi\) | |||||||
\(194\) | 1.04447e6 | 0.0102704 | ||||||||
\(195\) | 9.69975e6 | 0.0936784 | ||||||||
\(196\) | −1.45885e7 | −0.138393 | ||||||||
\(197\) | 6.92904e7 | 0.645716 | 0.322858 | − | 0.946447i | \(-0.395356\pi\) | ||||
0.322858 | + | 0.946447i | \(0.395356\pi\) | |||||||
\(198\) | −3.97159e6 | −0.0363611 | ||||||||
\(199\) | −6.71910e7 | −0.604401 | −0.302201 | − | 0.953244i | \(-0.597721\pi\) | ||||
−0.302201 | + | 0.953244i | \(0.597721\pi\) | |||||||
\(200\) | 7.87500e6 | 0.0696058 | ||||||||
\(201\) | −1.31552e7 | −0.114264 | ||||||||
\(202\) | 3.27921e6 | 0.0279924 | ||||||||
\(203\) | −1.21758e7 | −0.102156 | ||||||||
\(204\) | 3.10627e7 | 0.256174 | ||||||||
\(205\) | −2.25428e7 | −0.182755 | ||||||||
\(206\) | 1.31501e7 | 0.104808 | ||||||||
\(207\) | −3.02535e7 | −0.237072 | ||||||||
\(208\) | 4.27191e7 | 0.329155 | ||||||||
\(209\) | −1.17241e7 | −0.0888316 | ||||||||
\(210\) | −2.31525e6 | −0.0172516 | ||||||||
\(211\) | −5.14714e7 | −0.377205 | −0.188602 | − | 0.982054i | \(-0.560396\pi\) | ||||
−0.188602 | + | 0.982054i | \(0.560396\pi\) | |||||||
\(212\) | 1.57557e8 | 1.13570 | ||||||||
\(213\) | −2.93220e7 | −0.207905 | ||||||||
\(214\) | −2.42960e7 | −0.169468 | ||||||||
\(215\) | 4.18150e6 | 0.0286944 | ||||||||
\(216\) | −9.92023e6 | −0.0669782 | ||||||||
\(217\) | −1.81584e7 | −0.120634 | ||||||||
\(218\) | 1.93690e7 | 0.126622 | ||||||||
\(219\) | 1.59893e8 | 1.02867 | ||||||||
\(220\) | 4.22220e7 | 0.267337 | ||||||||
\(221\) | 2.66650e7 | 0.166176 | ||||||||
\(222\) | −4.54129e6 | −0.0278576 | ||||||||
\(223\) | −2.49372e8 | −1.50585 | −0.752923 | − | 0.658109i | \(-0.771357\pi\) | ||||
−0.752923 | + | 0.658109i | \(0.771357\pi\) | |||||||
\(224\) | −3.23243e7 | −0.192159 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | −5.00591e7 | −0.288472 | ||||||||
\(227\) | 3.93928e7 | 0.223525 | 0.111762 | − | 0.993735i | \(-0.464350\pi\) | ||||
0.111762 | + | 0.993735i | \(0.464350\pi\) | |||||||
\(228\) | −1.44098e7 | −0.0805167 | ||||||||
\(229\) | 1.25945e8 | 0.693035 | 0.346517 | − | 0.938044i | \(-0.387364\pi\) | ||||
0.346517 | + | 0.938044i | \(0.387364\pi\) | |||||||
\(230\) | −1.03750e7 | −0.0562265 | ||||||||
\(231\) | −2.52270e7 | −0.134655 | ||||||||
\(232\) | −1.78910e7 | −0.0940647 | ||||||||
\(233\) | −1.55290e8 | −0.804265 | −0.402132 | − | 0.915582i | \(-0.631731\pi\) | ||||
−0.402132 | + | 0.915582i | \(0.631731\pi\) | |||||||
\(234\) | −4.19029e6 | −0.0213791 | ||||||||
\(235\) | 1.70150e7 | 0.0855253 | ||||||||
\(236\) | 1.92603e8 | 0.953831 | ||||||||
\(237\) | 1.46605e8 | 0.715369 | ||||||||
\(238\) | −6.36471e6 | −0.0306027 | ||||||||
\(239\) | −1.53561e8 | −0.727593 | −0.363797 | − | 0.931478i | \(-0.618520\pi\) | ||||
−0.363797 | + | 0.931478i | \(0.618520\pi\) | |||||||
\(240\) | 5.01660e7 | 0.234245 | ||||||||
\(241\) | 1.67184e8 | 0.769369 | 0.384685 | − | 0.923048i | \(-0.374310\pi\) | ||||
0.384685 | + | 0.923048i | \(0.374310\pi\) | |||||||
\(242\) | 2.41340e7 | 0.109465 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −2.64862e7 | −0.116722 | ||||||||
\(245\) | −1.47061e7 | −0.0638877 | ||||||||
\(246\) | 9.73847e6 | 0.0417078 | ||||||||
\(247\) | −1.23697e7 | −0.0522300 | ||||||||
\(248\) | −2.66818e7 | −0.111079 | ||||||||
\(249\) | −1.87202e8 | −0.768445 | ||||||||
\(250\) | 3.90625e6 | 0.0158114 | ||||||||
\(251\) | −4.29028e7 | −0.171249 | −0.0856245 | − | 0.996327i | \(-0.527289\pi\) | ||||
−0.0856245 | + | 0.996327i | \(0.527289\pi\) | |||||||
\(252\) | −3.10058e7 | −0.122051 | ||||||||
\(253\) | −1.13046e8 | −0.438867 | ||||||||
\(254\) | −6.11920e6 | −0.0234302 | ||||||||
\(255\) | 3.13132e7 | 0.118260 | ||||||||
\(256\) | 1.88424e8 | 0.701936 | ||||||||
\(257\) | 4.70837e8 | 1.73023 | 0.865116 | − | 0.501571i | \(-0.167245\pi\) | ||||
0.865116 | + | 0.501571i | \(0.167245\pi\) | |||||||
\(258\) | −1.80641e6 | −0.00654858 | ||||||||
\(259\) | −2.88456e7 | −0.103165 | ||||||||
\(260\) | 4.45470e7 | 0.157185 | ||||||||
\(261\) | −2.58780e7 | −0.0900927 | ||||||||
\(262\) | 7.13823e6 | 0.0245209 | ||||||||
\(263\) | −1.02607e8 | −0.347802 | −0.173901 | − | 0.984763i | \(-0.555637\pi\) | ||||
−0.173901 | + | 0.984763i | \(0.555637\pi\) | |||||||
\(264\) | −3.70682e7 | −0.123990 | ||||||||
\(265\) | 1.58828e8 | 0.524283 | ||||||||
\(266\) | 2.95254e6 | 0.00961857 | ||||||||
\(267\) | −7.09058e6 | −0.0227978 | ||||||||
\(268\) | −6.04163e7 | −0.191727 | ||||||||
\(269\) | −5.49478e8 | −1.72114 | −0.860571 | − | 0.509330i | \(-0.829893\pi\) | ||||
−0.860571 | + | 0.509330i | \(0.829893\pi\) | |||||||
\(270\) | −4.92075e6 | −0.0152145 | ||||||||
\(271\) | 3.38205e8 | 1.03225 | 0.516127 | − | 0.856512i | \(-0.327373\pi\) | ||||
0.516127 | + | 0.856512i | \(0.327373\pi\) | |||||||
\(272\) | 1.37908e8 | 0.415527 | ||||||||
\(273\) | −2.66161e7 | −0.0791727 | ||||||||
\(274\) | −9.67472e6 | −0.0284126 | ||||||||
\(275\) | 4.25625e7 | 0.123414 | ||||||||
\(276\) | −1.38942e8 | −0.397788 | ||||||||
\(277\) | 3.85029e8 | 1.08846 | 0.544232 | − | 0.838934i | \(-0.316821\pi\) | ||||
0.544232 | + | 0.838934i | \(0.316821\pi\) | |||||||
\(278\) | −4.97146e6 | −0.0138780 | ||||||||
\(279\) | −3.85933e7 | −0.106389 | ||||||||
\(280\) | −2.16090e7 | −0.0588277 | ||||||||
\(281\) | 3.58731e8 | 0.964488 | 0.482244 | − | 0.876037i | \(-0.339822\pi\) | ||||
0.482244 | + | 0.876037i | \(0.339822\pi\) | |||||||
\(282\) | −7.35048e6 | −0.0195184 | ||||||||
\(283\) | 5.81811e7 | 0.152591 | 0.0762955 | − | 0.997085i | \(-0.475691\pi\) | ||||
0.0762955 | + | 0.997085i | \(0.475691\pi\) | |||||||
\(284\) | −1.34664e8 | −0.348849 | ||||||||
\(285\) | −1.45260e7 | −0.0371697 | ||||||||
\(286\) | −1.56576e7 | −0.0395770 | ||||||||
\(287\) | 6.18573e7 | 0.154456 | ||||||||
\(288\) | −6.87010e7 | −0.169469 | ||||||||
\(289\) | −3.24257e8 | −0.790219 | ||||||||
\(290\) | −8.87450e6 | −0.0213674 | ||||||||
\(291\) | 1.41003e7 | 0.0335431 | ||||||||
\(292\) | 7.34325e8 | 1.72603 | ||||||||
\(293\) | 5.57054e8 | 1.29378 | 0.646890 | − | 0.762583i | \(-0.276069\pi\) | ||||
0.646890 | + | 0.762583i | \(0.276069\pi\) | |||||||
\(294\) | 6.35305e6 | 0.0145803 | ||||||||
\(295\) | 1.94156e8 | 0.440327 | ||||||||
\(296\) | −4.23854e7 | −0.0949938 | ||||||||
\(297\) | −5.36165e7 | −0.118755 | ||||||||
\(298\) | 7.99790e7 | 0.175073 | ||||||||
\(299\) | −1.19271e8 | −0.258039 | ||||||||
\(300\) | 5.23125e7 | 0.111862 | ||||||||
\(301\) | −1.14740e7 | −0.0242512 | ||||||||
\(302\) | 1.07584e8 | 0.224762 | ||||||||
\(303\) | 4.42694e7 | 0.0914227 | ||||||||
\(304\) | −6.39747e7 | −0.130602 | ||||||||
\(305\) | −2.66998e7 | −0.0538837 | ||||||||
\(306\) | −1.35273e7 | −0.0269890 | ||||||||
\(307\) | 5.19798e8 | 1.02530 | 0.512649 | − | 0.858598i | \(-0.328664\pi\) | ||||
0.512649 | + | 0.858598i | \(0.328664\pi\) | |||||||
\(308\) | −1.15857e8 | −0.225941 | ||||||||
\(309\) | 1.77527e8 | 0.342301 | ||||||||
\(310\) | −1.32350e7 | −0.0252324 | ||||||||
\(311\) | −3.93391e8 | −0.741589 | −0.370794 | − | 0.928715i | \(-0.620915\pi\) | ||||
−0.370794 | + | 0.928715i | \(0.620915\pi\) | |||||||
\(312\) | −3.91094e7 | −0.0729021 | ||||||||
\(313\) | 7.46643e8 | 1.37628 | 0.688142 | − | 0.725576i | \(-0.258427\pi\) | ||||
0.688142 | + | 0.725576i | \(0.258427\pi\) | |||||||
\(314\) | −1.92804e7 | −0.0351448 | ||||||||
\(315\) | −3.12559e7 | −0.0563436 | ||||||||
\(316\) | 6.73298e8 | 1.20034 | ||||||||
\(317\) | 1.90220e8 | 0.335389 | 0.167694 | − | 0.985839i | \(-0.446368\pi\) | ||||
0.167694 | + | 0.985839i | \(0.446368\pi\) | |||||||
\(318\) | −6.86136e7 | −0.119651 | ||||||||
\(319\) | −9.66966e7 | −0.166780 | ||||||||
\(320\) | 2.14264e8 | 0.365531 | ||||||||
\(321\) | −3.27996e8 | −0.553479 | ||||||||
\(322\) | 2.84690e7 | 0.0475200 | ||||||||
\(323\) | −3.99325e7 | −0.0659353 | ||||||||
\(324\) | −6.58987e7 | −0.107639 | ||||||||
\(325\) | 4.49063e7 | 0.0725630 | ||||||||
\(326\) | 1.53469e8 | 0.245334 | ||||||||
\(327\) | 2.61482e8 | 0.413547 | ||||||||
\(328\) | 9.08924e7 | 0.142223 | ||||||||
\(329\) | −4.66892e7 | −0.0722820 | ||||||||
\(330\) | −1.83870e7 | −0.0281652 | ||||||||
\(331\) | −1.09993e9 | −1.66712 | −0.833559 | − | 0.552430i | \(-0.813701\pi\) | ||||
−0.833559 | + | 0.552430i | \(0.813701\pi\) | |||||||
\(332\) | −8.59742e8 | −1.28939 | ||||||||
\(333\) | −6.13074e7 | −0.0909826 | ||||||||
\(334\) | −2.07712e7 | −0.0305035 | ||||||||
\(335\) | −6.09035e7 | −0.0885086 | ||||||||
\(336\) | −1.37656e8 | −0.197973 | ||||||||
\(337\) | 4.94657e8 | 0.704043 | 0.352022 | − | 0.935992i | \(-0.385494\pi\) | ||||
0.352022 | + | 0.935992i | \(0.385494\pi\) | |||||||
\(338\) | 1.08977e8 | 0.153507 | ||||||||
\(339\) | −6.75798e8 | −0.942146 | ||||||||
\(340\) | 1.43809e8 | 0.198431 | ||||||||
\(341\) | −1.44209e8 | −0.196948 | ||||||||
\(342\) | 6.27523e6 | 0.00848278 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | −1.68598e7 | −0.0223305 | ||||||||
\(345\) | −1.40062e8 | −0.183635 | ||||||||
\(346\) | 1.12985e7 | 0.0146641 | ||||||||
\(347\) | −9.31091e8 | −1.19630 | −0.598148 | − | 0.801385i | \(-0.704097\pi\) | ||||
−0.598148 | + | 0.801385i | \(0.704097\pi\) | |||||||
\(348\) | −1.18847e8 | −0.151169 | ||||||||
\(349\) | −4.56646e8 | −0.575031 | −0.287515 | − | 0.957776i | \(-0.592829\pi\) | ||||
−0.287515 | + | 0.957776i | \(0.592829\pi\) | |||||||
\(350\) | −1.07188e7 | −0.0133631 | ||||||||
\(351\) | −5.65689e7 | −0.0698237 | ||||||||
\(352\) | −2.56710e8 | −0.313721 | ||||||||
\(353\) | −5.02682e8 | −0.608250 | −0.304125 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304125 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(354\) | −8.38756e7 | −0.100490 | ||||||||
\(355\) | −1.35750e8 | −0.161043 | ||||||||
\(356\) | −3.25641e7 | −0.0382529 | ||||||||
\(357\) | −8.59236e7 | −0.0999479 | ||||||||
\(358\) | 2.08746e8 | 0.240451 | ||||||||
\(359\) | −1.39665e9 | −1.59316 | −0.796578 | − | 0.604536i | \(-0.793359\pi\) | ||||
−0.796578 | + | 0.604536i | \(0.793359\pi\) | |||||||
\(360\) | −4.59270e7 | −0.0518811 | ||||||||
\(361\) | −8.75347e8 | −0.979276 | ||||||||
\(362\) | 2.84524e8 | 0.315238 | ||||||||
\(363\) | 3.25809e8 | 0.357511 | ||||||||
\(364\) | −1.22237e8 | −0.132846 | ||||||||
\(365\) | 7.40247e8 | 0.796804 | ||||||||
\(366\) | 1.15343e7 | 0.0122972 | ||||||||
\(367\) | −2.70500e8 | −0.285651 | −0.142826 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142826 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(368\) | −6.16856e8 | −0.645233 | ||||||||
\(369\) | 1.31469e8 | 0.136217 | ||||||||
\(370\) | −2.10245e7 | −0.0215784 | ||||||||
\(371\) | −4.35823e8 | −0.443100 | ||||||||
\(372\) | −1.77243e8 | −0.178513 | ||||||||
\(373\) | −1.06422e9 | −1.06182 | −0.530912 | − | 0.847427i | \(-0.678150\pi\) | ||||
−0.530912 | + | 0.847427i | \(0.678150\pi\) | |||||||
\(374\) | −5.05465e7 | −0.0499621 | ||||||||
\(375\) | 5.27344e7 | 0.0516398 | ||||||||
\(376\) | −6.86045e7 | −0.0665572 | ||||||||
\(377\) | −1.02021e8 | −0.0980609 | ||||||||
\(378\) | 1.35025e7 | 0.0128586 | ||||||||
\(379\) | −3.95456e8 | −0.373131 | −0.186565 | − | 0.982443i | \(-0.559736\pi\) | ||||
−0.186565 | + | 0.982443i | \(0.559736\pi\) | |||||||
\(380\) | −6.67120e7 | −0.0623679 | ||||||||
\(381\) | −8.26092e7 | −0.0765228 | ||||||||
\(382\) | 6.71067e7 | 0.0615948 | ||||||||
\(383\) | 1.64793e8 | 0.149880 | 0.0749400 | − | 0.997188i | \(-0.476123\pi\) | ||||
0.0749400 | + | 0.997188i | \(0.476123\pi\) | |||||||
\(384\) | −4.18255e8 | −0.376949 | ||||||||
\(385\) | −1.16792e8 | −0.104303 | ||||||||
\(386\) | 3.41197e8 | 0.301960 | ||||||||
\(387\) | −2.43865e7 | −0.0213876 | ||||||||
\(388\) | 6.47570e7 | 0.0562828 | ||||||||
\(389\) | −1.71125e8 | −0.147398 | −0.0736989 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736989 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(390\) | −1.93995e7 | −0.0165602 | ||||||||
\(391\) | −3.85037e8 | −0.325750 | ||||||||
\(392\) | 5.92951e7 | 0.0497184 | ||||||||
\(393\) | 9.63661e7 | 0.0800849 | ||||||||
\(394\) | −1.38581e8 | −0.114147 | ||||||||
\(395\) | 6.78728e8 | 0.554123 | ||||||||
\(396\) | −2.46239e8 | −0.199261 | ||||||||
\(397\) | 1.73552e9 | 1.39207 | 0.696037 | − | 0.718006i | \(-0.254945\pi\) | ||||
0.696037 | + | 0.718006i | \(0.254945\pi\) | |||||||
\(398\) | 1.34382e8 | 0.106844 | ||||||||
\(399\) | 3.98593e7 | 0.0314141 | ||||||||
\(400\) | 2.32250e8 | 0.181445 | ||||||||
\(401\) | 2.26343e8 | 0.175292 | 0.0876458 | − | 0.996152i | \(-0.472066\pi\) | ||||
0.0876458 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(402\) | 2.63103e7 | 0.0201992 | ||||||||
\(403\) | −1.52150e8 | −0.115799 | ||||||||
\(404\) | 2.03311e8 | 0.153400 | ||||||||
\(405\) | −6.64301e7 | −0.0496904 | ||||||||
\(406\) | 2.43516e7 | 0.0180587 | ||||||||
\(407\) | −2.29083e8 | −0.168427 | ||||||||
\(408\) | −1.26255e8 | −0.0920318 | ||||||||
\(409\) | 1.14869e9 | 0.830176 | 0.415088 | − | 0.909781i | \(-0.363751\pi\) | ||||
0.415088 | + | 0.909781i | \(0.363751\pi\) | |||||||
\(410\) | 4.50855e7 | 0.0323068 | ||||||||
\(411\) | −1.30609e8 | −0.0927952 | ||||||||
\(412\) | 8.15307e8 | 0.574356 | ||||||||
\(413\) | −5.32765e8 | −0.372144 | ||||||||
\(414\) | 6.05070e7 | 0.0419087 | ||||||||
\(415\) | −8.66676e8 | −0.595235 | ||||||||
\(416\) | −2.70846e8 | −0.184457 | ||||||||
\(417\) | −6.71147e7 | −0.0453254 | ||||||||
\(418\) | 2.34482e7 | 0.0157034 | ||||||||
\(419\) | 1.98365e9 | 1.31740 | 0.658699 | − | 0.752407i | \(-0.271107\pi\) | ||||
0.658699 | + | 0.752407i | \(0.271107\pi\) | |||||||
\(420\) | −1.43546e8 | −0.0945403 | ||||||||
\(421\) | 2.66045e9 | 1.73767 | 0.868835 | − | 0.495103i | \(-0.164870\pi\) | ||||
0.868835 | + | 0.495103i | \(0.164870\pi\) | |||||||
\(422\) | 1.02943e8 | 0.0666810 | ||||||||
\(423\) | −9.92315e7 | −0.0637468 | ||||||||
\(424\) | −6.40393e8 | −0.408006 | ||||||||
\(425\) | 1.44969e8 | 0.0916037 | ||||||||
\(426\) | 5.86440e7 | 0.0367528 | ||||||||
\(427\) | 7.32641e7 | 0.0455401 | ||||||||
\(428\) | −1.50635e9 | −0.928696 | ||||||||
\(429\) | −2.11377e8 | −0.129258 | ||||||||
\(430\) | −8.36300e6 | −0.00507251 | ||||||||
\(431\) | −1.50478e9 | −0.905322 | −0.452661 | − | 0.891683i | \(-0.649525\pi\) | ||||
−0.452661 | + | 0.891683i | \(0.649525\pi\) | |||||||
\(432\) | −2.92568e8 | −0.174596 | ||||||||
\(433\) | 1.37803e9 | 0.815738 | 0.407869 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407869 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(434\) | 3.63168e7 | 0.0213252 | ||||||||
\(435\) | −1.19806e8 | −0.0697855 | ||||||||
\(436\) | 1.20088e9 | 0.693900 | ||||||||
\(437\) | 1.78616e8 | 0.102385 | ||||||||
\(438\) | −3.19787e8 | −0.181845 | ||||||||
\(439\) | 2.15016e9 | 1.21296 | 0.606478 | − | 0.795100i | \(-0.292582\pi\) | ||||
0.606478 | + | 0.795100i | \(0.292582\pi\) | |||||||
\(440\) | −1.71612e8 | −0.0960425 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −5.33299e7 | −0.0293760 | ||||||||
\(443\) | −1.01094e9 | −0.552474 | −0.276237 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276237 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(444\) | −2.81560e8 | −0.152662 | ||||||||
\(445\) | −3.28268e7 | −0.0176591 | ||||||||
\(446\) | 4.98744e8 | 0.266198 | ||||||||
\(447\) | 1.07972e9 | 0.571786 | ||||||||
\(448\) | −5.87940e8 | −0.308930 | ||||||||
\(449\) | 1.82648e8 | 0.0952256 | 0.0476128 | − | 0.998866i | \(-0.484839\pi\) | ||||
0.0476128 | + | 0.998866i | \(0.484839\pi\) | |||||||
\(450\) | −2.27812e7 | −0.0117851 | ||||||||
\(451\) | 4.91252e8 | 0.252166 | ||||||||
\(452\) | −3.10367e9 | −1.58085 | ||||||||
\(453\) | 1.45238e9 | 0.734069 | ||||||||
\(454\) | −7.87855e7 | −0.0395140 | ||||||||
\(455\) | −1.23223e8 | −0.0613269 | ||||||||
\(456\) | 5.85688e7 | 0.0289261 | ||||||||
\(457\) | −1.51611e6 | −0.000743060 0 | −0.000371530 | − | 1.00000i | \(-0.500118\pi\) | ||||
−0.000371530 | 1.00000i | \(0.500118\pi\) | ||||||||
\(458\) | −2.51889e8 | −0.122512 | ||||||||
\(459\) | −1.82619e8 | −0.0881457 | ||||||||
\(460\) | −6.43250e8 | −0.308125 | ||||||||
\(461\) | −4.79940e8 | −0.228157 | −0.114079 | − | 0.993472i | \(-0.536392\pi\) | ||||
−0.114079 | + | 0.993472i | \(0.536392\pi\) | |||||||
\(462\) | 5.04539e7 | 0.0238039 | ||||||||
\(463\) | −6.86812e8 | −0.321591 | −0.160796 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160796 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(464\) | −5.27642e8 | −0.245203 | ||||||||
\(465\) | −1.78672e8 | −0.0824086 | ||||||||
\(466\) | 3.10581e8 | 0.142175 | ||||||||
\(467\) | 1.69004e9 | 0.767869 | 0.383934 | − | 0.923360i | \(-0.374569\pi\) | ||||
0.383934 | + | 0.923360i | \(0.374569\pi\) | |||||||
\(468\) | −2.59798e8 | −0.117159 | ||||||||
\(469\) | 1.67119e8 | 0.0748034 | ||||||||
\(470\) | −3.40300e7 | −0.0151189 | ||||||||
\(471\) | −2.60285e8 | −0.114783 | ||||||||
\(472\) | −7.82839e8 | −0.342670 | ||||||||
\(473\) | −9.11232e7 | −0.0395927 | ||||||||
\(474\) | −2.93210e8 | −0.126461 | ||||||||
\(475\) | −6.72500e7 | −0.0287915 | ||||||||
\(476\) | −3.94612e8 | −0.167705 | ||||||||
\(477\) | −9.26283e8 | −0.390778 | ||||||||
\(478\) | 3.07122e8 | 0.128622 | ||||||||
\(479\) | 2.39843e9 | 0.997132 | 0.498566 | − | 0.866852i | \(-0.333860\pi\) | ||||
0.498566 | + | 0.866852i | \(0.333860\pi\) | |||||||
\(480\) | −3.18060e8 | −0.131270 | ||||||||
\(481\) | −2.41698e8 | −0.0990295 | ||||||||
\(482\) | −3.34368e8 | −0.136007 | ||||||||
\(483\) | 3.84332e8 | 0.155200 | ||||||||
\(484\) | 1.49631e9 | 0.599877 | ||||||||
\(485\) | 6.52792e7 | 0.0259824 | ||||||||
\(486\) | 2.86978e7 | 0.0113402 | ||||||||
\(487\) | −6.76814e8 | −0.265533 | −0.132766 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132766 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(488\) | 1.07653e8 | 0.0419332 | ||||||||
\(489\) | 2.07183e9 | 0.801258 | ||||||||
\(490\) | 2.94122e7 | 0.0112938 | ||||||||
\(491\) | 3.97038e9 | 1.51372 | 0.756862 | − | 0.653574i | \(-0.226731\pi\) | ||||
0.756862 | + | 0.653574i | \(0.226731\pi\) | |||||||
\(492\) | 6.03785e8 | 0.228562 | ||||||||
\(493\) | −3.29350e8 | −0.123792 | ||||||||
\(494\) | 2.47394e7 | 0.00923304 | ||||||||
\(495\) | −2.48224e8 | −0.0919870 | ||||||||
\(496\) | −7.86900e8 | −0.289557 | ||||||||
\(497\) | 3.72498e8 | 0.136106 | ||||||||
\(498\) | 3.74404e8 | 0.135843 | ||||||||
\(499\) | 1.59757e9 | 0.575584 | 0.287792 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287792 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(500\) | 2.42188e8 | 0.0866476 | ||||||||
\(501\) | −2.80412e8 | −0.0996241 | ||||||||
\(502\) | 8.58056e7 | 0.0302728 | ||||||||
\(503\) | 1.72479e9 | 0.604295 | 0.302148 | − | 0.953261i | \(-0.402296\pi\) | ||||
0.302148 | + | 0.953261i | \(0.402296\pi\) | |||||||
\(504\) | 1.26024e8 | 0.0438475 | ||||||||
\(505\) | 2.04951e8 | 0.0708157 | ||||||||
\(506\) | 2.26092e8 | 0.0775815 | ||||||||
\(507\) | 1.47119e9 | 0.501351 | ||||||||
\(508\) | −3.79390e8 | −0.128400 | ||||||||
\(509\) | 5.83626e9 | 1.96165 | 0.980827 | − | 0.194880i | \(-0.0624316\pi\) | ||||
0.980827 | + | 0.194880i | \(0.0624316\pi\) | |||||||
\(510\) | −6.26265e7 | −0.0209056 | ||||||||
\(511\) | −2.03124e9 | −0.673423 | ||||||||
\(512\) | −2.35969e9 | −0.776980 | ||||||||
\(513\) | 8.47156e7 | 0.0277047 | ||||||||
\(514\) | −9.41674e8 | −0.305865 | ||||||||
\(515\) | 8.21882e8 | 0.265145 | ||||||||
\(516\) | −1.11997e8 | −0.0358867 | ||||||||
\(517\) | −3.70791e8 | −0.118008 | ||||||||
\(518\) | 5.76912e7 | 0.0182371 | ||||||||
\(519\) | 1.52530e8 | 0.0478928 | ||||||||
\(520\) | −1.81062e8 | −0.0564697 | ||||||||
\(521\) | 4.99457e9 | 1.54727 | 0.773634 | − | 0.633632i | \(-0.218437\pi\) | ||||
0.773634 | + | 0.633632i | \(0.218437\pi\) | |||||||
\(522\) | 5.17561e7 | 0.0159263 | ||||||||
\(523\) | 1.03723e9 | 0.317045 | 0.158522 | − | 0.987355i | \(-0.449327\pi\) | ||||
0.158522 | + | 0.987355i | \(0.449327\pi\) | |||||||
\(524\) | 4.42570e8 | 0.134376 | ||||||||
\(525\) | −1.44703e8 | −0.0436436 | ||||||||
\(526\) | 2.05214e8 | 0.0614834 | ||||||||
\(527\) | −4.91177e8 | −0.146184 | ||||||||
\(528\) | −1.09322e9 | −0.323212 | ||||||||
\(529\) | −1.68258e9 | −0.494174 | ||||||||
\(530\) | −3.17655e8 | −0.0926810 | ||||||||
\(531\) | −1.13232e9 | −0.328200 | ||||||||
\(532\) | 1.83058e8 | 0.0527105 | ||||||||
\(533\) | 5.18303e8 | 0.148265 | ||||||||
\(534\) | 1.41812e7 | 0.00403011 | ||||||||
\(535\) | −1.51850e9 | −0.428723 | ||||||||
\(536\) | 2.45563e8 | 0.0688789 | ||||||||
\(537\) | 2.81807e9 | 0.785310 | ||||||||
\(538\) | 1.09896e9 | 0.304258 | ||||||||
\(539\) | 3.20476e8 | 0.0881525 | ||||||||
\(540\) | −3.05086e8 | −0.0833767 | ||||||||
\(541\) | −2.48336e9 | −0.674295 | −0.337147 | − | 0.941452i | \(-0.609462\pi\) | ||||
−0.337147 | + | 0.941452i | \(0.609462\pi\) | |||||||
\(542\) | −6.76409e8 | −0.182479 | ||||||||
\(543\) | 3.84107e9 | 1.02956 | ||||||||
\(544\) | −8.74359e8 | −0.232859 | ||||||||
\(545\) | 1.21057e9 | 0.320332 | ||||||||
\(546\) | 5.32322e7 | 0.0139959 | ||||||||
\(547\) | −3.74874e9 | −0.979331 | −0.489665 | − | 0.871910i | \(-0.662881\pi\) | ||||
−0.489665 | + | 0.871910i | \(0.662881\pi\) | |||||||
\(548\) | −5.99832e8 | −0.155703 | ||||||||
\(549\) | 1.55713e8 | 0.0401626 | ||||||||
\(550\) | −8.51250e7 | −0.0218166 | ||||||||
\(551\) | 1.52783e8 | 0.0389086 | ||||||||
\(552\) | 5.64732e8 | 0.142908 | ||||||||
\(553\) | −1.86243e9 | −0.468319 | ||||||||
\(554\) | −7.70058e8 | −0.192415 | ||||||||
\(555\) | −2.83831e8 | −0.0704748 | ||||||||
\(556\) | −3.08230e8 | −0.0760525 | ||||||||
\(557\) | −2.18032e9 | −0.534596 | −0.267298 | − | 0.963614i | \(-0.586131\pi\) | ||||
−0.267298 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(558\) | 7.71865e7 | 0.0188071 | ||||||||
\(559\) | −9.61410e7 | −0.0232792 | ||||||||
\(560\) | −6.37294e8 | −0.153349 | ||||||||
\(561\) | −6.82378e8 | −0.163176 | ||||||||
\(562\) | −7.17462e8 | −0.170499 | ||||||||
\(563\) | 2.56548e9 | 0.605883 | 0.302941 | − | 0.953009i | \(-0.402031\pi\) | ||||
0.302941 | + | 0.953009i | \(0.402031\pi\) | |||||||
\(564\) | −4.55730e8 | −0.106962 | ||||||||
\(565\) | −3.12869e9 | −0.729783 | ||||||||
\(566\) | −1.16362e8 | −0.0269745 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 5.47344e8 | 0.125326 | ||||||||
\(569\) | 1.65916e8 | 0.0377568 | 0.0188784 | − | 0.999822i | \(-0.493990\pi\) | ||||
0.0188784 | + | 0.999822i | \(0.493990\pi\) | |||||||
\(570\) | 2.90520e7 | 0.00657074 | ||||||||
\(571\) | −5.11928e9 | −1.15075 | −0.575377 | − | 0.817888i | \(-0.695145\pi\) | ||||
−0.575377 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(572\) | −9.70768e8 | −0.216885 | ||||||||
\(573\) | 9.05940e8 | 0.201168 | ||||||||
\(574\) | −1.23715e8 | −0.0273042 | ||||||||
\(575\) | −6.48438e8 | −0.142243 | ||||||||
\(576\) | −1.24959e9 | −0.272451 | ||||||||
\(577\) | −6.90669e9 | −1.49677 | −0.748384 | − | 0.663265i | \(-0.769170\pi\) | ||||
−0.748384 | + | 0.663265i | \(0.769170\pi\) | |||||||
\(578\) | 6.48515e8 | 0.139692 | ||||||||
\(579\) | 4.60616e9 | 0.986199 | ||||||||
\(580\) | −5.50219e8 | −0.117095 | ||||||||
\(581\) | 2.37816e9 | 0.503065 | ||||||||
\(582\) | −2.82006e7 | −0.00592964 | ||||||||
\(583\) | −3.46117e9 | −0.723408 | ||||||||
\(584\) | −2.98468e9 | −0.620087 | ||||||||
\(585\) | −2.61893e8 | −0.0540852 | ||||||||
\(586\) | −1.11411e9 | −0.228710 | ||||||||
\(587\) | −4.92686e9 | −1.00540 | −0.502698 | − | 0.864462i | \(-0.667659\pi\) | ||||
−0.502698 | + | 0.864462i | \(0.667659\pi\) | |||||||
\(588\) | 3.93889e8 | 0.0799012 | ||||||||
\(589\) | 2.27854e8 | 0.0459465 | ||||||||
\(590\) | −3.88313e8 | −0.0778395 | ||||||||
\(591\) | −1.87084e9 | −0.372804 | ||||||||
\(592\) | −1.25003e9 | −0.247626 | ||||||||
\(593\) | 2.48990e9 | 0.490332 | 0.245166 | − | 0.969481i | \(-0.421158\pi\) | ||||
0.245166 | + | 0.969481i | \(0.421158\pi\) | |||||||
\(594\) | 1.07233e8 | 0.0209931 | ||||||||
\(595\) | −3.97794e8 | −0.0774193 | ||||||||
\(596\) | 4.95870e9 | 0.959413 | ||||||||
\(597\) | 1.81416e9 | 0.348951 | ||||||||
\(598\) | 2.38542e8 | 0.0456153 | ||||||||
\(599\) | −1.79975e9 | −0.342151 | −0.171076 | − | 0.985258i | \(-0.554724\pi\) | ||||
−0.171076 | + | 0.985258i | \(0.554724\pi\) | |||||||
\(600\) | −2.12625e8 | −0.0401869 | ||||||||
\(601\) | −9.64250e9 | −1.81188 | −0.905939 | − | 0.423409i | \(-0.860834\pi\) | ||||
−0.905939 | + | 0.423409i | \(0.860834\pi\) | |||||||
\(602\) | 2.29481e7 | 0.00428705 | ||||||||
\(603\) | 3.55189e8 | 0.0659704 | ||||||||
\(604\) | 6.67020e9 | 1.23171 | ||||||||
\(605\) | 1.50837e9 | 0.276927 | ||||||||
\(606\) | −8.85387e7 | −0.0161614 | ||||||||
\(607\) | −7.59240e9 | −1.37790 | −0.688951 | − | 0.724808i | \(-0.741929\pi\) | ||||
−0.688951 | + | 0.724808i | \(0.741929\pi\) | |||||||
\(608\) | 4.05609e8 | 0.0731889 | ||||||||
\(609\) | 3.28747e8 | 0.0589795 | ||||||||
\(610\) | 5.33995e7 | 0.00952539 | ||||||||
\(611\) | −3.91209e8 | −0.0693848 | ||||||||
\(612\) | −8.38694e8 | −0.147902 | ||||||||
\(613\) | 6.21966e9 | 1.09057 | 0.545287 | − | 0.838249i | \(-0.316421\pi\) | ||||
0.545287 | + | 0.838249i | \(0.316421\pi\) | |||||||
\(614\) | −1.03960e9 | −0.181249 | ||||||||
\(615\) | 6.08654e8 | 0.105513 | ||||||||
\(616\) | 4.70903e8 | 0.0811707 | ||||||||
\(617\) | −1.01931e10 | −1.74706 | −0.873529 | − | 0.486772i | \(-0.838174\pi\) | ||||
−0.873529 | + | 0.486772i | \(0.838174\pi\) | |||||||
\(618\) | −3.55053e8 | −0.0605109 | ||||||||
\(619\) | −1.86525e9 | −0.316097 | −0.158048 | − | 0.987431i | \(-0.550520\pi\) | ||||
−0.158048 | + | 0.987431i | \(0.550520\pi\) | |||||||
\(620\) | −8.20570e8 | −0.138275 | ||||||||
\(621\) | 8.16844e8 | 0.136873 | ||||||||
\(622\) | 7.86782e8 | 0.131096 | ||||||||
\(623\) | 9.00766e7 | 0.0149246 | ||||||||
\(624\) | −1.15342e9 | −0.190038 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −1.49329e9 | −0.243295 | ||||||||
\(627\) | 3.16551e8 | 0.0512869 | ||||||||
\(628\) | −1.19538e9 | −0.192596 | ||||||||
\(629\) | −7.80261e8 | −0.125015 | ||||||||
\(630\) | 6.25118e7 | 0.00996024 | ||||||||
\(631\) | 3.03048e9 | 0.480185 | 0.240092 | − | 0.970750i | \(-0.422822\pi\) | ||||
0.240092 | + | 0.970750i | \(0.422822\pi\) | |||||||
\(632\) | −2.73663e9 | −0.431228 | ||||||||
\(633\) | 1.38973e9 | 0.217779 | ||||||||
\(634\) | −3.80440e8 | −0.0592889 | ||||||||
\(635\) | −3.82450e8 | −0.0592743 | ||||||||
\(636\) | −4.25404e9 | −0.655695 | ||||||||
\(637\) | 3.38123e8 | 0.0518307 | ||||||||
\(638\) | 1.93393e8 | 0.0294828 | ||||||||
\(639\) | 7.91694e8 | 0.120034 | ||||||||
\(640\) | −1.93637e9 | −0.291983 | ||||||||
\(641\) | 1.08550e10 | 1.62789 | 0.813945 | − | 0.580942i | \(-0.197316\pi\) | ||||
0.813945 | + | 0.580942i | \(0.197316\pi\) | |||||||
\(642\) | 6.55992e8 | 0.0978422 | ||||||||
\(643\) | 9.35593e8 | 0.138787 | 0.0693934 | − | 0.997589i | \(-0.477894\pi\) | ||||
0.0693934 | + | 0.997589i | \(0.477894\pi\) | |||||||
\(644\) | 1.76508e9 | 0.260413 | ||||||||
\(645\) | −1.12900e8 | −0.0165667 | ||||||||
\(646\) | 7.98650e7 | 0.0116558 | ||||||||
\(647\) | −8.82519e9 | −1.28103 | −0.640514 | − | 0.767946i | \(-0.721279\pi\) | ||||
−0.640514 | + | 0.767946i | \(0.721279\pi\) | |||||||
\(648\) | 2.67846e8 | 0.0386699 | ||||||||
\(649\) | −4.23106e9 | −0.607565 | ||||||||
\(650\) | −8.98125e7 | −0.0128274 | ||||||||
\(651\) | 4.90277e8 | 0.0696480 | ||||||||
\(652\) | 9.51506e9 | 1.34445 | ||||||||
\(653\) | 2.99850e9 | 0.421413 | 0.210707 | − | 0.977549i | \(-0.432424\pi\) | ||||
0.210707 | + | 0.977549i | \(0.432424\pi\) | |||||||
\(654\) | −5.22964e8 | −0.0731055 | ||||||||
\(655\) | 4.46140e8 | 0.0620335 | ||||||||
\(656\) | 2.68060e9 | 0.370740 | ||||||||
\(657\) | −4.31712e9 | −0.593903 | ||||||||
\(658\) | 9.33783e7 | 0.0127778 | ||||||||
\(659\) | −3.93595e9 | −0.535736 | −0.267868 | − | 0.963456i | \(-0.586319\pi\) | ||||
−0.267868 | + | 0.963456i | \(0.586319\pi\) | |||||||
\(660\) | −1.13999e9 | −0.154347 | ||||||||
\(661\) | −6.26839e8 | −0.0844211 | −0.0422106 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422106 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(662\) | 2.19986e9 | 0.294708 | ||||||||
\(663\) | −7.19954e8 | −0.0959417 | ||||||||
\(664\) | 3.49444e9 | 0.463222 | ||||||||
\(665\) | 1.84534e8 | 0.0243333 | ||||||||
\(666\) | 1.22615e8 | 0.0160836 | ||||||||
\(667\) | 1.47317e9 | 0.192226 | ||||||||
\(668\) | −1.28782e9 | −0.167162 | ||||||||
\(669\) | 6.73304e9 | 0.869400 | ||||||||
\(670\) | 1.21807e8 | 0.0156463 | ||||||||
\(671\) | 5.81841e8 | 0.0743491 | ||||||||
\(672\) | 8.72757e8 | 0.110943 | ||||||||
\(673\) | 4.74113e9 | 0.599555 | 0.299777 | − | 0.954009i | \(-0.403088\pi\) | ||||
0.299777 | + | 0.954009i | \(0.403088\pi\) | |||||||
\(674\) | −9.89313e8 | −0.124458 | ||||||||
\(675\) | −3.07547e8 | −0.0384900 | ||||||||
\(676\) | 6.75659e9 | 0.841229 | ||||||||
\(677\) | −8.34660e9 | −1.03383 | −0.516915 | − | 0.856037i | \(-0.672920\pi\) | ||||
−0.516915 | + | 0.856037i | \(0.672920\pi\) | |||||||
\(678\) | 1.35160e9 | 0.166549 | ||||||||
\(679\) | −1.79126e8 | −0.0219591 | ||||||||
\(680\) | −5.84514e8 | −0.0712876 | ||||||||
\(681\) | −1.06360e9 | −0.129052 | ||||||||
\(682\) | 2.88417e8 | 0.0348157 | ||||||||
\(683\) | 1.00158e10 | 1.20286 | 0.601428 | − | 0.798927i | \(-0.294599\pi\) | ||||
0.601428 | + | 0.798927i | \(0.294599\pi\) | |||||||
\(684\) | 3.89064e8 | 0.0464863 | ||||||||
\(685\) | −6.04670e8 | −0.0718789 | ||||||||
\(686\) | −8.07072e7 | −0.00954504 | ||||||||
\(687\) | −3.40050e9 | −0.400124 | ||||||||
\(688\) | −4.97231e8 | −0.0582101 | ||||||||
\(689\) | −3.65177e9 | −0.425340 | ||||||||
\(690\) | 2.80125e8 | 0.0324624 | ||||||||
\(691\) | −1.16744e10 | −1.34605 | −0.673024 | − | 0.739621i | \(-0.735005\pi\) | ||||
−0.673024 | + | 0.739621i | \(0.735005\pi\) | |||||||
\(692\) | 7.00509e8 | 0.0803605 | ||||||||
\(693\) | 6.81128e8 | 0.0777432 | ||||||||
\(694\) | 1.86218e9 | 0.211477 | ||||||||
\(695\) | −3.10716e8 | −0.0351089 | ||||||||
\(696\) | 4.83057e8 | 0.0543083 | ||||||||
\(697\) | 1.67321e9 | 0.187170 | ||||||||
\(698\) | 9.13293e8 | 0.101652 | ||||||||
\(699\) | 4.19284e9 | 0.464342 | ||||||||
\(700\) | −6.64562e8 | −0.0732306 | ||||||||
\(701\) | 7.05584e9 | 0.773634 | 0.386817 | − | 0.922157i | \(-0.373575\pi\) | ||||
0.386817 | + | 0.922157i | \(0.373575\pi\) | |||||||
\(702\) | 1.13138e8 | 0.0123432 | ||||||||
\(703\) | 3.61958e8 | 0.0392929 | ||||||||
\(704\) | −4.66924e9 | −0.504362 | ||||||||
\(705\) | −4.59405e8 | −0.0493780 | ||||||||
\(706\) | 1.00536e9 | 0.107524 | ||||||||
\(707\) | −5.62385e8 | −0.0598502 | ||||||||
\(708\) | −5.20029e9 | −0.550695 | ||||||||
\(709\) | 1.96477e8 | 0.0207038 | 0.0103519 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103519 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(710\) | 2.71500e8 | 0.0284686 | ||||||||
\(711\) | −3.95834e9 | −0.413019 | ||||||||
\(712\) | 1.32357e8 | 0.0137426 | ||||||||
\(713\) | 2.19701e9 | 0.226996 | ||||||||
\(714\) | 1.71847e8 | 0.0176685 | ||||||||
\(715\) | −9.78597e8 | −0.100123 | ||||||||
\(716\) | 1.29422e10 | 1.31769 | ||||||||
\(717\) | 4.14615e9 | 0.420076 | ||||||||
\(718\) | 2.79331e9 | 0.281633 | ||||||||
\(719\) | −8.96572e9 | −0.899569 | −0.449784 | − | 0.893137i | \(-0.648499\pi\) | ||||
−0.449784 | + | 0.893137i | \(0.648499\pi\) | |||||||
\(720\) | −1.35448e9 | −0.135241 | ||||||||
\(721\) | −2.25524e9 | −0.224089 | ||||||||
\(722\) | 1.75069e9 | 0.173113 | ||||||||
\(723\) | −4.51397e9 | −0.444196 | ||||||||
\(724\) | 1.76405e10 | 1.72753 | ||||||||
\(725\) | −5.54656e8 | −0.0540556 | ||||||||
\(726\) | −6.51618e8 | −0.0631997 | ||||||||
\(727\) | −4.44082e9 | −0.428640 | −0.214320 | − | 0.976763i | \(-0.568754\pi\) | ||||
−0.214320 | + | 0.976763i | \(0.568754\pi\) | |||||||
\(728\) | 4.96834e8 | 0.0477256 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.48049e9 | −0.140856 | ||||||||
\(731\) | −3.10368e8 | −0.0293877 | ||||||||
\(732\) | 7.15126e8 | 0.0673898 | ||||||||
\(733\) | −8.97113e9 | −0.841363 | −0.420681 | − | 0.907208i | \(-0.638209\pi\) | ||||
−0.420681 | + | 0.907208i | \(0.638209\pi\) | |||||||
\(734\) | 5.41000e8 | 0.0504965 | ||||||||
\(735\) | 3.97065e8 | 0.0368856 | ||||||||
\(736\) | 3.91096e9 | 0.361586 | ||||||||
\(737\) | 1.32721e9 | 0.122125 | ||||||||
\(738\) | −2.62939e8 | −0.0240800 | ||||||||
\(739\) | 1.27011e10 | 1.15767 | 0.578835 | − | 0.815445i | \(-0.303508\pi\) | ||||
0.578835 | + | 0.815445i | \(0.303508\pi\) | |||||||
\(740\) | −1.30352e9 | −0.118251 | ||||||||
\(741\) | 3.33982e8 | 0.0301550 | ||||||||
\(742\) | 8.71647e8 | 0.0783298 | ||||||||
\(743\) | −1.54200e10 | −1.37919 | −0.689593 | − | 0.724197i | \(-0.742211\pi\) | ||||
−0.689593 | + | 0.724197i | \(0.742211\pi\) | |||||||
\(744\) | 7.20408e8 | 0.0641317 | ||||||||
\(745\) | 4.99869e9 | 0.442903 | ||||||||
\(746\) | 2.12845e9 | 0.187706 | ||||||||
\(747\) | 5.05445e9 | 0.443662 | ||||||||
\(748\) | −3.13389e9 | −0.273796 | ||||||||
\(749\) | 4.16677e9 | 0.362337 | ||||||||
\(750\) | −1.05469e8 | −0.00912871 | ||||||||
\(751\) | 4.99561e9 | 0.430376 | 0.215188 | − | 0.976573i | \(-0.430964\pi\) | ||||
0.215188 | + | 0.976573i | \(0.430964\pi\) | |||||||
\(752\) | −2.02329e9 | −0.173498 | ||||||||
\(753\) | 1.15838e9 | 0.0988706 | ||||||||
\(754\) | 2.04043e8 | 0.0173349 | ||||||||
\(755\) | 6.72399e9 | 0.568608 | ||||||||
\(756\) | 8.37157e8 | 0.0704662 | ||||||||
\(757\) | 1.13781e10 | 0.953313 | 0.476657 | − | 0.879090i | \(-0.341848\pi\) | ||||
0.476657 | + | 0.879090i | \(0.341848\pi\) | |||||||
\(758\) | 7.90912e8 | 0.0659608 | ||||||||
\(759\) | 3.05224e9 | 0.253380 | ||||||||
\(760\) | 2.71152e8 | 0.0224060 | ||||||||
\(761\) | 9.31372e9 | 0.766084 | 0.383042 | − | 0.923731i | \(-0.374876\pi\) | ||||
0.383042 | + | 0.923731i | \(0.374876\pi\) | |||||||
\(762\) | 1.65218e8 | 0.0135275 | ||||||||
\(763\) | −3.32179e9 | −0.270730 | ||||||||
\(764\) | 4.16061e9 | 0.337544 | ||||||||
\(765\) | −8.45458e8 | −0.0682774 | ||||||||
\(766\) | −3.29586e8 | −0.0264953 | ||||||||
\(767\) | −4.46405e9 | −0.357228 | ||||||||
\(768\) | −5.08746e9 | −0.405263 | ||||||||
\(769\) | −5.75726e9 | −0.456535 | −0.228267 | − | 0.973598i | \(-0.573306\pi\) | ||||
−0.228267 | + | 0.973598i | \(0.573306\pi\) | |||||||
\(770\) | 2.33583e8 | 0.0184384 | ||||||||
\(771\) | −1.27126e10 | −0.998950 | ||||||||
\(772\) | 2.11542e10 | 1.65477 | ||||||||
\(773\) | 1.45658e10 | 1.13424 | 0.567121 | − | 0.823634i | \(-0.308057\pi\) | ||||
0.567121 | + | 0.823634i | \(0.308057\pi\) | |||||||
\(774\) | 4.87730e7 | 0.00378082 | ||||||||
\(775\) | −8.27188e8 | −0.0638334 | ||||||||
\(776\) | −2.63206e8 | −0.0202199 | ||||||||
\(777\) | 7.78832e8 | 0.0595621 | ||||||||
\(778\) | 3.42251e8 | 0.0260565 | ||||||||
\(779\) | −7.76192e8 | −0.0588285 | ||||||||
\(780\) | −1.20277e9 | −0.0907509 | ||||||||
\(781\) | 2.95826e9 | 0.222207 | ||||||||
\(782\) | 7.70074e8 | 0.0575849 | ||||||||
\(783\) | 6.98707e8 | 0.0520150 | ||||||||
\(784\) | 1.74873e9 | 0.129604 | ||||||||
\(785\) | −1.20502e9 | −0.0889102 | ||||||||
\(786\) | −1.92732e8 | −0.0141571 | ||||||||
\(787\) | 7.81273e9 | 0.571336 | 0.285668 | − | 0.958329i | \(-0.407785\pi\) | ||||
0.285668 | + | 0.958329i | \(0.407785\pi\) | |||||||
\(788\) | −8.59201e9 | −0.625537 | ||||||||
\(789\) | 2.77039e9 | 0.200804 | ||||||||
\(790\) | −1.35746e9 | −0.0979560 | ||||||||
\(791\) | 8.58514e9 | 0.616779 | ||||||||
\(792\) | 1.00084e9 | 0.0715858 | ||||||||
\(793\) | 6.13881e8 | 0.0437147 | ||||||||
\(794\) | −3.47103e9 | −0.246086 | ||||||||
\(795\) | −4.28835e9 | −0.302695 | ||||||||
\(796\) | 8.33168e9 | 0.585514 | ||||||||
\(797\) | 5.72212e9 | 0.400362 | 0.200181 | − | 0.979759i | \(-0.435847\pi\) | ||||
0.200181 | + | 0.979759i | \(0.435847\pi\) | |||||||
\(798\) | −7.97187e7 | −0.00555329 | ||||||||
\(799\) | −1.26292e9 | −0.0875916 | ||||||||
\(800\) | −1.47250e9 | −0.101681 | ||||||||
\(801\) | 1.91446e8 | 0.0131623 | ||||||||
\(802\) | −4.52685e8 | −0.0309875 | ||||||||
\(803\) | −1.61315e10 | −1.09943 | ||||||||
\(804\) | 1.63124e9 | 0.110693 | ||||||||
\(805\) | 1.77931e9 | 0.120217 | ||||||||
\(806\) | 3.04299e8 | 0.0204705 | ||||||||
\(807\) | 1.48359e10 | 0.993702 | ||||||||
\(808\) | −8.26361e8 | −0.0551100 | ||||||||
\(809\) | −9.16070e9 | −0.608287 | −0.304144 | − | 0.952626i | \(-0.598370\pi\) | ||||
−0.304144 | + | 0.952626i | \(0.598370\pi\) | |||||||
\(810\) | 1.32860e8 | 0.00878410 | ||||||||
\(811\) | −2.04091e10 | −1.34354 | −0.671771 | − | 0.740759i | \(-0.734466\pi\) | ||||
−0.671771 | + | 0.740759i | \(0.734466\pi\) | |||||||
\(812\) | 1.50980e9 | 0.0989632 | ||||||||
\(813\) | −9.13152e9 | −0.595973 | ||||||||
\(814\) | 4.58166e8 | 0.0297740 | ||||||||
\(815\) | 9.59179e9 | 0.620652 | ||||||||
\(816\) | −3.72352e9 | −0.239904 | ||||||||
\(817\) | 1.43977e8 | 0.00923671 | ||||||||
\(818\) | −2.29738e9 | −0.146756 | ||||||||
\(819\) | 7.18635e8 | 0.0457104 | ||||||||
\(820\) | 2.79530e9 | 0.177044 | ||||||||
\(821\) | 6.26680e9 | 0.395225 | 0.197613 | − | 0.980280i | \(-0.436681\pi\) | ||||
0.197613 | + | 0.980280i | \(0.436681\pi\) | |||||||
\(822\) | 2.61217e8 | 0.0164040 | ||||||||
\(823\) | 4.37792e9 | 0.273759 | 0.136879 | − | 0.990588i | \(-0.456293\pi\) | ||||
0.136879 | + | 0.990588i | \(0.456293\pi\) | |||||||
\(824\) | −3.31383e9 | −0.206341 | ||||||||
\(825\) | −1.14919e9 | −0.0712528 | ||||||||
\(826\) | 1.06553e9 | 0.0657864 | ||||||||
\(827\) | −1.61665e10 | −0.993912 | −0.496956 | − | 0.867776i | \(-0.665549\pi\) | ||||
−0.496956 | + | 0.867776i | \(0.665549\pi\) | |||||||
\(828\) | 3.75143e9 | 0.229663 | ||||||||
\(829\) | 2.76523e10 | 1.68574 | 0.842868 | − | 0.538120i | \(-0.180865\pi\) | ||||
0.842868 | + | 0.538120i | \(0.180865\pi\) | |||||||
\(830\) | 1.73335e9 | 0.105224 | ||||||||
\(831\) | −1.03958e10 | −0.628425 | ||||||||
\(832\) | −4.92636e9 | −0.296548 | ||||||||
\(833\) | 1.09155e9 | 0.0654312 | ||||||||
\(834\) | 1.34229e8 | 0.00801247 | ||||||||
\(835\) | −1.29820e9 | −0.0771685 | ||||||||
\(836\) | 1.45379e9 | 0.0860556 | ||||||||
\(837\) | 1.04202e9 | 0.0614237 | ||||||||
\(838\) | −3.96731e9 | −0.232885 | ||||||||
\(839\) | −1.72137e10 | −1.00625 | −0.503126 | − | 0.864213i | \(-0.667817\pi\) | ||||
−0.503126 | + | 0.864213i | \(0.667817\pi\) | |||||||
\(840\) | 5.83443e8 | 0.0339642 | ||||||||
\(841\) | −1.59898e10 | −0.926950 | ||||||||
\(842\) | −5.32089e9 | −0.307179 | ||||||||
\(843\) | −9.68574e9 | −0.556847 | ||||||||
\(844\) | 6.38245e9 | 0.365417 | ||||||||
\(845\) | 6.81108e9 | 0.388345 | ||||||||
\(846\) | 1.98463e8 | 0.0112689 | ||||||||
\(847\) | −4.13898e9 | −0.234046 | ||||||||
\(848\) | −1.88865e10 | −1.06357 | ||||||||
\(849\) | −1.57089e9 | −0.0880985 | ||||||||
\(850\) | −2.89938e8 | −0.0161934 | ||||||||
\(851\) | 3.49007e9 | 0.194124 | ||||||||
\(852\) | 3.63593e9 | 0.201408 | ||||||||
\(853\) | 6.71439e9 | 0.370412 | 0.185206 | − | 0.982700i | \(-0.440705\pi\) | ||||
0.185206 | + | 0.982700i | \(0.440705\pi\) | |||||||
\(854\) | −1.46528e8 | −0.00805042 | ||||||||
\(855\) | 3.92202e8 | 0.0214599 | ||||||||
\(856\) | 6.12260e9 | 0.333639 | ||||||||
\(857\) | −9.89153e9 | −0.536822 | −0.268411 | − | 0.963304i | \(-0.586499\pi\) | ||||
−0.268411 | + | 0.963304i | \(0.586499\pi\) | |||||||
\(858\) | 4.22754e8 | 0.0228498 | ||||||||
\(859\) | −3.35625e10 | −1.80667 | −0.903335 | − | 0.428937i | \(-0.858888\pi\) | ||||
−0.903335 | + | 0.428937i | \(0.858888\pi\) | |||||||
\(860\) | −5.18506e8 | −0.0277977 | ||||||||
\(861\) | −1.67015e9 | −0.0891751 | ||||||||
\(862\) | 3.00956e9 | 0.160040 | ||||||||
\(863\) | 9.99427e9 | 0.529314 | 0.264657 | − | 0.964343i | \(-0.414741\pi\) | ||||
0.264657 | + | 0.964343i | \(0.414741\pi\) | |||||||
\(864\) | 1.85493e9 | 0.0978427 | ||||||||
\(865\) | 7.06159e8 | 0.0370976 | ||||||||
\(866\) | −2.75606e9 | −0.144203 | ||||||||
\(867\) | 8.75495e9 | 0.456233 | ||||||||
\(868\) | 2.25164e9 | 0.116864 | ||||||||
\(869\) | −1.47908e10 | −0.764581 | ||||||||
\(870\) | 2.39611e8 | 0.0123365 | ||||||||
\(871\) | 1.40029e9 | 0.0718051 | ||||||||
\(872\) | −4.88100e9 | −0.249288 | ||||||||
\(873\) | −3.80709e8 | −0.0193661 | ||||||||
\(874\) | −3.57232e8 | −0.0180992 | ||||||||
\(875\) | −6.69922e8 | −0.0338062 | ||||||||
\(876\) | −1.98268e10 | −0.996524 | ||||||||
\(877\) | 1.24239e8 | 0.00621953 | 0.00310977 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00310977 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(878\) | −4.30032e9 | −0.214422 | ||||||||
\(879\) | −1.50405e10 | −0.746964 | ||||||||
\(880\) | −5.06119e9 | −0.250359 | ||||||||
\(881\) | 2.45438e10 | 1.20928 | 0.604640 | − | 0.796499i | \(-0.293317\pi\) | ||||
0.604640 | + | 0.796499i | \(0.293317\pi\) | |||||||
\(882\) | −1.71532e8 | −0.00841794 | ||||||||
\(883\) | 9.35492e9 | 0.457275 | 0.228638 | − | 0.973512i | \(-0.426573\pi\) | ||||
0.228638 | + | 0.973512i | \(0.426573\pi\) | |||||||
\(884\) | −3.30646e9 | −0.160983 | ||||||||
\(885\) | −5.24223e9 | −0.254223 | ||||||||
\(886\) | 2.02188e9 | 0.0976646 | ||||||||
\(887\) | −3.18320e10 | −1.53155 | −0.765776 | − | 0.643107i | \(-0.777645\pi\) | ||||
−0.765776 | + | 0.643107i | \(0.777645\pi\) | |||||||
\(888\) | 1.14441e9 | 0.0548447 | ||||||||
\(889\) | 1.04944e9 | 0.0500959 | ||||||||
\(890\) | 6.56535e7 | 0.00312171 | ||||||||
\(891\) | 1.44765e9 | 0.0685631 | ||||||||
\(892\) | 3.09221e10 | 1.45879 | ||||||||
\(893\) | 5.85860e8 | 0.0275305 | ||||||||
\(894\) | −2.15943e9 | −0.101078 | ||||||||
\(895\) | 1.30466e10 | 0.608298 | ||||||||
\(896\) | 5.31339e9 | 0.246771 | ||||||||
\(897\) | 3.22032e9 | 0.148979 | ||||||||
\(898\) | −3.65297e8 | −0.0168337 | ||||||||
\(899\) | 1.87926e9 | 0.0862639 | ||||||||
\(900\) | −1.41244e9 | −0.0645833 | ||||||||
\(901\) | −1.17888e10 | −0.536950 | ||||||||
\(902\) | −9.82503e8 | −0.0445770 | ||||||||
\(903\) | 3.09799e8 | 0.0140014 | ||||||||
\(904\) | 1.26149e10 | 0.567929 | ||||||||
\(905\) | 1.77827e10 | 0.797496 | ||||||||
\(906\) | −2.90476e9 | −0.129766 | ||||||||
\(907\) | 2.00342e10 | 0.891552 | 0.445776 | − | 0.895144i | \(-0.352928\pi\) | ||||
0.445776 | + | 0.895144i | \(0.352928\pi\) | |||||||
\(908\) | −4.88470e9 | −0.216540 | ||||||||
\(909\) | −1.19527e9 | −0.0527829 | ||||||||
\(910\) | 2.46446e8 | 0.0108412 | ||||||||
\(911\) | −2.82239e10 | −1.23681 | −0.618405 | − | 0.785859i | \(-0.712221\pi\) | ||||
−0.618405 | + | 0.785859i | \(0.712221\pi\) | |||||||
\(912\) | 1.72732e9 | 0.0754032 | ||||||||
\(913\) | 1.88866e10 | 0.821308 | ||||||||
\(914\) | 3.03222e6 | 0.000131356 0 | ||||||||
\(915\) | 7.20893e8 | 0.0311098 | ||||||||
\(916\) | −1.56171e10 | −0.671377 | ||||||||
\(917\) | −1.22421e9 | −0.0524279 | ||||||||
\(918\) | 3.65238e8 | 0.0155821 | ||||||||
\(919\) | −3.40984e10 | −1.44921 | −0.724603 | − | 0.689167i | \(-0.757977\pi\) | ||||
−0.724603 | + | 0.689167i | \(0.757977\pi\) | |||||||
\(920\) | 2.61450e9 | 0.110696 | ||||||||
\(921\) | −1.40345e10 | −0.591956 | ||||||||
\(922\) | 9.59881e8 | 0.0403329 | ||||||||
\(923\) | 3.12116e9 | 0.130650 | ||||||||
\(924\) | 3.12814e9 | 0.130447 | ||||||||
\(925\) | −1.31403e9 | −0.0545896 | ||||||||
\(926\) | 1.37362e9 | 0.0568499 | ||||||||
\(927\) | −4.79322e9 | −0.197628 | ||||||||
\(928\) | 3.34533e9 | 0.137411 | ||||||||
\(929\) | −2.18397e10 | −0.893698 | −0.446849 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446849 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(930\) | 3.57345e8 | 0.0145679 | ||||||||
\(931\) | −5.06361e8 | −0.0205654 | ||||||||
\(932\) | 1.92560e10 | 0.779131 | ||||||||
\(933\) | 1.06216e10 | 0.428157 | ||||||||
\(934\) | −3.38007e9 | −0.135741 | ||||||||
\(935\) | −3.15916e9 | −0.126395 | ||||||||
\(936\) | 1.05595e9 | 0.0420900 | ||||||||
\(937\) | −1.29359e10 | −0.513699 | −0.256849 | − | 0.966451i | \(-0.582684\pi\) | ||||
−0.256849 | + | 0.966451i | \(0.582684\pi\) | |||||||
\(938\) | −3.34238e8 | −0.0132235 | ||||||||
\(939\) | −2.01594e10 | −0.794598 | ||||||||
\(940\) | −2.10986e9 | −0.0828526 | ||||||||
\(941\) | −1.70996e10 | −0.668995 | −0.334497 | − | 0.942397i | \(-0.608567\pi\) | ||||
−0.334497 | + | 0.942397i | \(0.608567\pi\) | |||||||
\(942\) | 5.20570e8 | 0.0202909 | ||||||||
\(943\) | −7.48419e9 | −0.290639 | ||||||||
\(944\) | −2.30875e10 | −0.893255 | ||||||||
\(945\) | 8.43909e8 | 0.0325300 | ||||||||
\(946\) | 1.82246e8 | 0.00699907 | ||||||||
\(947\) | −1.95022e8 | −0.00746207 | −0.00373104 | − | 0.999993i | \(-0.501188\pi\) | ||||
−0.00373104 | + | 0.999993i | \(0.501188\pi\) | |||||||
\(948\) | −1.81791e10 | −0.693014 | ||||||||
\(949\) | −1.70198e10 | −0.646430 | ||||||||
\(950\) | 1.34500e8 | 0.00508967 | ||||||||
\(951\) | −5.13594e9 | −0.193637 | ||||||||
\(952\) | 1.60391e9 | 0.0602490 | ||||||||
\(953\) | −1.97958e10 | −0.740878 | −0.370439 | − | 0.928857i | \(-0.620793\pi\) | ||||
−0.370439 | + | 0.928857i | \(0.620793\pi\) | |||||||
\(954\) | 1.85257e9 | 0.0690804 | ||||||||
\(955\) | 4.19417e9 | 0.155824 | ||||||||
\(956\) | 1.90416e10 | 0.704856 | ||||||||
\(957\) | 2.61081e9 | 0.0962904 | ||||||||
\(958\) | −4.79686e9 | −0.176270 | ||||||||
\(959\) | 1.65921e9 | 0.0607487 | ||||||||
\(960\) | −5.78513e9 | −0.211039 | ||||||||
\(961\) | −2.47100e10 | −0.898132 | ||||||||
\(962\) | 4.83395e8 | 0.0175061 | ||||||||
\(963\) | 8.85590e9 | 0.319551 | ||||||||
\(964\) | −2.07308e10 | −0.745327 | ||||||||
\(965\) | 2.13248e10 | 0.763906 | ||||||||
\(966\) | −7.68663e8 | −0.0274357 | ||||||||
\(967\) | 4.18825e10 | 1.48950 | 0.744748 | − | 0.667346i | \(-0.232570\pi\) | ||||
0.744748 | + | 0.667346i | \(0.232570\pi\) | |||||||
\(968\) | −6.08177e9 | −0.215509 | ||||||||
\(969\) | 1.07818e9 | 0.0380677 | ||||||||
\(970\) | −1.30559e8 | −0.00459308 | ||||||||
\(971\) | −1.82766e9 | −0.0640661 | −0.0320331 | − | 0.999487i | \(-0.510198\pi\) | ||||
−0.0320331 | + | 0.999487i | \(0.510198\pi\) | |||||||
\(972\) | 1.77926e9 | 0.0621453 | ||||||||
\(973\) | 8.52605e8 | 0.0296724 | ||||||||
\(974\) | 1.35363e9 | 0.0469400 | ||||||||
\(975\) | −1.21247e9 | −0.0418942 | ||||||||
\(976\) | 3.17492e9 | 0.109310 | ||||||||
\(977\) | 4.04873e10 | 1.38895 | 0.694477 | − | 0.719515i | \(-0.255636\pi\) | ||||
0.694477 | + | 0.719515i | \(0.255636\pi\) | |||||||
\(978\) | −4.14365e9 | −0.141644 | ||||||||
\(979\) | 7.15361e8 | 0.0243661 | ||||||||
\(980\) | 1.82356e9 | 0.0618912 | ||||||||
\(981\) | −7.06002e9 | −0.238761 | ||||||||
\(982\) | −7.94076e9 | −0.267591 | ||||||||
\(983\) | 1.79913e9 | 0.0604124 | 0.0302062 | − | 0.999544i | \(-0.490384\pi\) | ||||
0.0302062 | + | 0.999544i | \(0.490384\pi\) | |||||||
\(984\) | −2.45409e9 | −0.0821123 | ||||||||
\(985\) | −8.66130e9 | −0.288773 | ||||||||
\(986\) | 6.58701e8 | 0.0218836 | ||||||||
\(987\) | 1.26061e9 | 0.0417321 | ||||||||
\(988\) | 1.53384e9 | 0.0505978 | ||||||||
\(989\) | 1.38826e9 | 0.0456334 | ||||||||
\(990\) | 4.96449e8 | 0.0162612 | ||||||||
\(991\) | −1.80926e10 | −0.590532 | −0.295266 | − | 0.955415i | \(-0.595408\pi\) | ||||
−0.295266 | + | 0.955415i | \(0.595408\pi\) | |||||||
\(992\) | 4.98907e9 | 0.162266 | ||||||||
\(993\) | 2.96981e10 | 0.962511 | ||||||||
\(994\) | −7.44996e8 | −0.0240603 | ||||||||
\(995\) | 8.39888e9 | 0.270296 | ||||||||
\(996\) | 2.32130e10 | 0.744431 | ||||||||
\(997\) | 4.79210e10 | 1.53141 | 0.765707 | − | 0.643189i | \(-0.222389\pi\) | ||||
0.765707 | + | 0.643189i | \(0.222389\pi\) | |||||||
\(998\) | −3.19514e9 | −0.101750 | ||||||||
\(999\) | 1.65530e9 | 0.0525288 |
(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 | 105.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 315.8.a.b.1.1 | 1 | |||
5.4 | even | 2 | 525.8.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
315.8.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
525.8.a.c.1.1 | 1 | 5.4 | even | 2 |