Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.9818 | 0.706305 | 0.353152 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353152 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −256.580 | −0.501134 | ||||||||
\(5\) | 61.0966 | 0.0437172 | 0.0218586 | − | 0.999761i | \(-0.493042\pi\) | ||||
0.0218586 | + | 0.999761i | \(0.493042\pi\) | |||||||
\(6\) | 1294.53 | 0.407785 | ||||||||
\(7\) | 4757.03 | 0.748850 | 0.374425 | − | 0.927257i | \(-0.377840\pi\) | ||||
0.374425 | + | 0.927257i | \(0.377840\pi\) | |||||||
\(8\) | −12283.3 | −1.06026 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 976.437 | 0.0308776 | ||||||||
\(11\) | 5603.63 | 0.115399 | 0.0576996 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0576996 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(12\) | −20783.0 | −0.289330 | ||||||||
\(13\) | −73495.1 | −0.713696 | −0.356848 | − | 0.934162i | \(-0.616149\pi\) | ||||
−0.356848 | + | 0.934162i | \(0.616149\pi\) | |||||||
\(14\) | 76026.1 | 0.528916 | ||||||||
\(15\) | 4948.83 | 0.0252401 | ||||||||
\(16\) | −64941.2 | −0.247731 | ||||||||
\(17\) | 430505. | 1.25014 | 0.625069 | − | 0.780569i | \(-0.285071\pi\) | ||||
0.625069 | + | 0.780569i | \(0.285071\pi\) | |||||||
\(18\) | 104857. | 0.235435 | ||||||||
\(19\) | −718411. | −1.26468 | −0.632341 | − | 0.774690i | \(-0.717906\pi\) | ||||
−0.632341 | + | 0.774690i | \(0.717906\pi\) | |||||||
\(20\) | −15676.2 | −0.0219082 | ||||||||
\(21\) | 385319. | 0.432348 | ||||||||
\(22\) | 89556.4 | 0.0815070 | ||||||||
\(23\) | 3945.26 | 0.00293968 | 0.00146984 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00146984 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(24\) | −994950. | −0.612140 | ||||||||
\(25\) | −1.94939e6 | −0.998089 | ||||||||
\(26\) | −1.17459e6 | −0.504087 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −1.22056e6 | −0.375274 | ||||||||
\(29\) | 627200. | 0.164670 | 0.0823351 | − | 0.996605i | \(-0.473762\pi\) | ||||
0.0823351 | + | 0.996605i | \(0.473762\pi\) | |||||||
\(30\) | 79091.4 | 0.0178272 | ||||||||
\(31\) | 1.02481e6 | 0.199304 | 0.0996518 | − | 0.995022i | \(-0.468227\pi\) | ||||
0.0996518 | + | 0.995022i | \(0.468227\pi\) | |||||||
\(32\) | 5.25119e6 | 0.885284 | ||||||||
\(33\) | 453894. | 0.0666257 | ||||||||
\(34\) | 6.88027e6 | 0.882978 | ||||||||
\(35\) | 290638. | 0.0327376 | ||||||||
\(36\) | −1.68342e6 | −0.167045 | ||||||||
\(37\) | −1.31994e7 | −1.15783 | −0.578917 | − | 0.815386i | \(-0.696525\pi\) | ||||
−0.578917 | + | 0.815386i | \(0.696525\pi\) | |||||||
\(38\) | −1.14815e7 | −0.893251 | ||||||||
\(39\) | −5.95311e6 | −0.412053 | ||||||||
\(40\) | −750470. | −0.0463515 | ||||||||
\(41\) | −7.00235e6 | −0.387005 | −0.193503 | − | 0.981100i | \(-0.561985\pi\) | ||||
−0.193503 | + | 0.981100i | \(0.561985\pi\) | |||||||
\(42\) | 6.15811e6 | 0.305370 | ||||||||
\(43\) | 3.11873e7 | 1.39113 | 0.695567 | − | 0.718461i | \(-0.255153\pi\) | ||||
0.695567 | + | 0.718461i | \(0.255153\pi\) | |||||||
\(44\) | −1.43778e6 | −0.0578304 | ||||||||
\(45\) | 400855. | 0.0145724 | ||||||||
\(46\) | 63052.5 | 0.00207631 | ||||||||
\(47\) | −7.14985e6 | −0.213726 | −0.106863 | − | 0.994274i | \(-0.534081\pi\) | ||||
−0.106863 | + | 0.994274i | \(0.534081\pi\) | |||||||
\(48\) | −5.26024e6 | −0.143028 | ||||||||
\(49\) | −1.77243e7 | −0.439224 | ||||||||
\(50\) | −3.11549e7 | −0.704955 | ||||||||
\(51\) | 3.48709e7 | 0.721768 | ||||||||
\(52\) | 1.88574e7 | 0.357657 | ||||||||
\(53\) | −1.00893e8 | −1.75639 | −0.878195 | − | 0.478303i | \(-0.841252\pi\) | ||||
−0.878195 | + | 0.478303i | \(0.841252\pi\) | |||||||
\(54\) | 8.49341e6 | 0.135928 | ||||||||
\(55\) | 342363. | 0.00504493 | ||||||||
\(56\) | −5.84322e7 | −0.793973 | ||||||||
\(57\) | −5.81913e7 | −0.730165 | ||||||||
\(58\) | 1.00238e7 | 0.116307 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −1.26977e6 | −0.0126487 | ||||||||
\(61\) | −4.94621e7 | −0.457391 | −0.228696 | − | 0.973498i | \(-0.573446\pi\) | ||||
−0.228696 | + | 0.973498i | \(0.573446\pi\) | |||||||
\(62\) | 1.63783e7 | 0.140769 | ||||||||
\(63\) | 3.12109e7 | 0.249617 | ||||||||
\(64\) | 1.17174e8 | 0.873011 | ||||||||
\(65\) | −4.49030e6 | −0.0312008 | ||||||||
\(66\) | 7.25407e6 | 0.0470581 | ||||||||
\(67\) | −2.76538e8 | −1.67656 | −0.838280 | − | 0.545240i | \(-0.816438\pi\) | ||||
−0.838280 | + | 0.545240i | \(0.816438\pi\) | |||||||
\(68\) | −1.10459e8 | −0.626486 | ||||||||
\(69\) | 319566. | 0.00169723 | ||||||||
\(70\) | 4.64494e6 | 0.0231227 | ||||||||
\(71\) | −2.12153e8 | −0.990799 | −0.495400 | − | 0.868665i | \(-0.664978\pi\) | ||||
−0.495400 | + | 0.868665i | \(0.664978\pi\) | |||||||
\(72\) | −8.05910e7 | −0.353419 | ||||||||
\(73\) | −1.63627e8 | −0.674377 | −0.337189 | − | 0.941437i | \(-0.609476\pi\) | ||||
−0.337189 | + | 0.941437i | \(0.609476\pi\) | |||||||
\(74\) | −2.10951e8 | −0.817784 | ||||||||
\(75\) | −1.57901e8 | −0.576247 | ||||||||
\(76\) | 1.84330e8 | 0.633775 | ||||||||
\(77\) | 2.66566e7 | 0.0864166 | ||||||||
\(78\) | −9.51416e7 | −0.291035 | ||||||||
\(79\) | −5.43394e8 | −1.56961 | −0.784807 | − | 0.619741i | \(-0.787238\pi\) | ||||
−0.784807 | + | 0.619741i | \(0.787238\pi\) | |||||||
\(80\) | −3.96769e6 | −0.0108301 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.11911e8 | −0.273344 | ||||||||
\(83\) | 5.64040e8 | 1.30454 | 0.652272 | − | 0.757985i | \(-0.273816\pi\) | ||||
0.652272 | + | 0.757985i | \(0.273816\pi\) | |||||||
\(84\) | −9.88654e7 | −0.216664 | ||||||||
\(85\) | 2.63024e7 | 0.0546525 | ||||||||
\(86\) | 4.98430e8 | 0.982565 | ||||||||
\(87\) | 5.08032e7 | 0.0950724 | ||||||||
\(88\) | −6.88313e7 | −0.122353 | ||||||||
\(89\) | −3.74114e8 | −0.632047 | −0.316023 | − | 0.948751i | \(-0.602348\pi\) | ||||
−0.316023 | + | 0.948751i | \(0.602348\pi\) | |||||||
\(90\) | 6.40640e6 | 0.0102925 | ||||||||
\(91\) | −3.49618e8 | −0.534451 | ||||||||
\(92\) | −1.01228e6 | −0.00147317 | ||||||||
\(93\) | 8.30095e7 | 0.115068 | ||||||||
\(94\) | −1.14268e8 | −0.150955 | ||||||||
\(95\) | −4.38925e7 | −0.0552884 | ||||||||
\(96\) | 4.25346e8 | 0.511119 | ||||||||
\(97\) | 1.37988e9 | 1.58259 | 0.791296 | − | 0.611433i | \(-0.209407\pi\) | ||||
0.791296 | + | 0.611433i | \(0.209407\pi\) | |||||||
\(98\) | −2.83267e8 | −0.310226 | ||||||||
\(99\) | 3.67654e7 | 0.0384664 | ||||||||
\(100\) | 5.00176e8 | 0.500176 | ||||||||
\(101\) | 7.62944e8 | 0.729536 | 0.364768 | − | 0.931099i | \(-0.381148\pi\) | ||||
0.364768 | + | 0.931099i | \(0.381148\pi\) | |||||||
\(102\) | 5.57301e8 | 0.509788 | ||||||||
\(103\) | −1.73748e9 | −1.52108 | −0.760538 | − | 0.649293i | \(-0.775065\pi\) | ||||
−0.760538 | + | 0.649293i | \(0.775065\pi\) | |||||||
\(104\) | 9.02765e8 | 0.756702 | ||||||||
\(105\) | 2.35417e7 | 0.0189011 | ||||||||
\(106\) | −1.61246e9 | −1.24055 | ||||||||
\(107\) | −9.32433e8 | −0.687687 | −0.343843 | − | 0.939027i | \(-0.611729\pi\) | ||||
−0.343843 | + | 0.939027i | \(0.611729\pi\) | |||||||
\(108\) | −1.36357e8 | −0.0964432 | ||||||||
\(109\) | −1.28116e9 | −0.869331 | −0.434665 | − | 0.900592i | \(-0.643133\pi\) | ||||
−0.434665 | + | 0.900592i | \(0.643133\pi\) | |||||||
\(110\) | 5.47159e6 | 0.00356325 | ||||||||
\(111\) | −1.06915e9 | −0.668476 | ||||||||
\(112\) | −3.08927e8 | −0.185513 | ||||||||
\(113\) | 2.83825e8 | 0.163756 | 0.0818782 | − | 0.996642i | \(-0.473908\pi\) | ||||
0.0818782 | + | 0.996642i | \(0.473908\pi\) | |||||||
\(114\) | −9.30004e8 | −0.515719 | ||||||||
\(115\) | 241042. | 0.000128515 0 | ||||||||
\(116\) | −1.60927e8 | −0.0825218 | ||||||||
\(117\) | −4.82202e8 | −0.237899 | ||||||||
\(118\) | 1.93658e8 | 0.0919530 | ||||||||
\(119\) | 2.04792e9 | 0.936165 | ||||||||
\(120\) | −6.07881e7 | −0.0267610 | ||||||||
\(121\) | −2.32655e9 | −0.986683 | ||||||||
\(122\) | −7.90495e8 | −0.323058 | ||||||||
\(123\) | −5.67191e8 | −0.223438 | ||||||||
\(124\) | −2.62946e8 | −0.0998778 | ||||||||
\(125\) | −2.38431e8 | −0.0873508 | ||||||||
\(126\) | 4.98807e8 | 0.176305 | ||||||||
\(127\) | 1.68868e9 | 0.576012 | 0.288006 | − | 0.957629i | \(-0.407008\pi\) | ||||
0.288006 | + | 0.957629i | \(0.407008\pi\) | |||||||
\(128\) | −8.15957e8 | −0.268672 | ||||||||
\(129\) | 2.52617e9 | 0.803172 | ||||||||
\(130\) | −7.17634e7 | −0.0220373 | ||||||||
\(131\) | −3.62798e9 | −1.07633 | −0.538164 | − | 0.842840i | \(-0.680882\pi\) | ||||
−0.538164 | + | 0.842840i | \(0.680882\pi\) | |||||||
\(132\) | −1.16460e8 | −0.0333884 | ||||||||
\(133\) | −3.41750e9 | −0.947057 | ||||||||
\(134\) | −4.41960e9 | −1.18416 | ||||||||
\(135\) | 3.24692e7 | 0.00841337 | ||||||||
\(136\) | −5.28804e9 | −1.32547 | ||||||||
\(137\) | 5.88802e9 | 1.42800 | 0.713998 | − | 0.700148i | \(-0.246883\pi\) | ||||
0.713998 | + | 0.700148i | \(0.246883\pi\) | |||||||
\(138\) | 5.10725e6 | 0.00119876 | ||||||||
\(139\) | −2.41235e9 | −0.548117 | −0.274058 | − | 0.961713i | \(-0.588366\pi\) | ||||
−0.274058 | + | 0.961713i | \(0.588366\pi\) | |||||||
\(140\) | −7.45721e7 | −0.0164059 | ||||||||
\(141\) | −5.79138e8 | −0.123395 | ||||||||
\(142\) | −3.39059e9 | −0.699806 | ||||||||
\(143\) | −4.11840e8 | −0.0823600 | ||||||||
\(144\) | −4.26080e8 | −0.0825771 | ||||||||
\(145\) | 3.83198e7 | 0.00719892 | ||||||||
\(146\) | −2.61507e9 | −0.476316 | ||||||||
\(147\) | −1.43567e9 | −0.253586 | ||||||||
\(148\) | 3.38671e9 | 0.580230 | ||||||||
\(149\) | −2.91781e9 | −0.484975 | −0.242487 | − | 0.970155i | \(-0.577963\pi\) | ||||
−0.242487 | + | 0.970155i | \(0.577963\pi\) | |||||||
\(150\) | −2.52355e9 | −0.407006 | ||||||||
\(151\) | 8.01296e9 | 1.25429 | 0.627144 | − | 0.778904i | \(-0.284224\pi\) | ||||
0.627144 | + | 0.778904i | \(0.284224\pi\) | |||||||
\(152\) | 8.82448e9 | 1.34089 | ||||||||
\(153\) | 2.82454e9 | 0.416713 | ||||||||
\(154\) | 4.26022e8 | 0.0610365 | ||||||||
\(155\) | 6.26123e7 | 0.00871299 | ||||||||
\(156\) | 1.52745e9 | 0.206494 | ||||||||
\(157\) | −4.74620e9 | −0.623444 | −0.311722 | − | 0.950173i | \(-0.600906\pi\) | ||||
−0.311722 | + | 0.950173i | \(0.600906\pi\) | |||||||
\(158\) | −8.68444e9 | −1.10863 | ||||||||
\(159\) | −8.17236e9 | −1.01405 | ||||||||
\(160\) | 3.20830e8 | 0.0387021 | ||||||||
\(161\) | 1.87677e7 | 0.00220138 | ||||||||
\(162\) | 6.87966e8 | 0.0784783 | ||||||||
\(163\) | 7.60267e9 | 0.843571 | 0.421786 | − | 0.906696i | \(-0.361403\pi\) | ||||
0.421786 | + | 0.906696i | \(0.361403\pi\) | |||||||
\(164\) | 1.79667e9 | 0.193941 | ||||||||
\(165\) | 2.77314e7 | 0.00291269 | ||||||||
\(166\) | 9.01440e9 | 0.921405 | ||||||||
\(167\) | −7.86896e9 | −0.782876 | −0.391438 | − | 0.920204i | \(-0.628022\pi\) | ||||
−0.391438 | + | 0.920204i | \(0.628022\pi\) | |||||||
\(168\) | −4.73301e9 | −0.458401 | ||||||||
\(169\) | −5.20297e9 | −0.490638 | ||||||||
\(170\) | 4.20361e8 | 0.0386013 | ||||||||
\(171\) | −4.71349e9 | −0.421561 | ||||||||
\(172\) | −8.00204e9 | −0.697145 | ||||||||
\(173\) | −1.07654e10 | −0.913741 | −0.456871 | − | 0.889533i | \(-0.651030\pi\) | ||||
−0.456871 | + | 0.889533i | \(0.651030\pi\) | |||||||
\(174\) | 8.11929e8 | 0.0671501 | ||||||||
\(175\) | −9.27331e9 | −0.747418 | ||||||||
\(176\) | −3.63907e8 | −0.0285880 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −5.97904e9 | −0.446417 | ||||||||
\(179\) | −4.69084e9 | −0.341517 | −0.170758 | − | 0.985313i | \(-0.554622\pi\) | ||||
−0.170758 | + | 0.985313i | \(0.554622\pi\) | |||||||
\(180\) | −1.02852e8 | −0.00730272 | ||||||||
\(181\) | 6.97407e9 | 0.482984 | 0.241492 | − | 0.970403i | \(-0.422363\pi\) | ||||
0.241492 | + | 0.970403i | \(0.422363\pi\) | |||||||
\(182\) | −5.58755e9 | −0.377485 | ||||||||
\(183\) | −4.00643e9 | −0.264075 | ||||||||
\(184\) | −4.84609e7 | −0.00311682 | ||||||||
\(185\) | −8.06439e8 | −0.0506173 | ||||||||
\(186\) | 1.32665e9 | 0.0812731 | ||||||||
\(187\) | 2.41239e9 | 0.144265 | ||||||||
\(188\) | 1.83451e9 | 0.107105 | ||||||||
\(189\) | 2.52808e9 | 0.144116 | ||||||||
\(190\) | −7.01483e8 | −0.0390504 | ||||||||
\(191\) | −1.76966e10 | −0.962142 | −0.481071 | − | 0.876682i | \(-0.659752\pi\) | ||||
−0.481071 | + | 0.876682i | \(0.659752\pi\) | |||||||
\(192\) | 9.49106e9 | 0.504033 | ||||||||
\(193\) | −1.86734e10 | −0.968761 | −0.484380 | − | 0.874858i | \(-0.660955\pi\) | ||||
−0.484380 | + | 0.874858i | \(0.660955\pi\) | |||||||
\(194\) | 2.20531e10 | 1.11779 | ||||||||
\(195\) | −3.63715e8 | −0.0180138 | ||||||||
\(196\) | 4.54771e9 | 0.220110 | ||||||||
\(197\) | 3.63127e10 | 1.71775 | 0.858875 | − | 0.512185i | \(-0.171164\pi\) | ||||
0.858875 | + | 0.512185i | \(0.171164\pi\) | |||||||
\(198\) | 5.87580e8 | 0.0271690 | ||||||||
\(199\) | −5.95324e9 | −0.269100 | −0.134550 | − | 0.990907i | \(-0.542959\pi\) | ||||
−0.134550 | + | 0.990907i | \(0.542959\pi\) | |||||||
\(200\) | 2.39450e10 | 1.05823 | ||||||||
\(201\) | −2.23996e10 | −0.967962 | ||||||||
\(202\) | 1.21933e10 | 0.515274 | ||||||||
\(203\) | 2.98361e9 | 0.123313 | ||||||||
\(204\) | −8.94719e9 | −0.361702 | ||||||||
\(205\) | −4.27820e8 | −0.0169188 | ||||||||
\(206\) | −2.77681e10 | −1.07434 | ||||||||
\(207\) | 2.58848e7 | 0.000979894 0 | ||||||||
\(208\) | 4.77287e9 | 0.176805 | ||||||||
\(209\) | −4.02571e9 | −0.145943 | ||||||||
\(210\) | 3.76240e8 | 0.0133499 | ||||||||
\(211\) | 3.77367e10 | 1.31067 | 0.655334 | − | 0.755340i | \(-0.272528\pi\) | ||||
0.655334 | + | 0.755340i | \(0.272528\pi\) | |||||||
\(212\) | 2.58873e10 | 0.880186 | ||||||||
\(213\) | −1.71844e10 | −0.572038 | ||||||||
\(214\) | −1.49020e10 | −0.485716 | ||||||||
\(215\) | 1.90544e9 | 0.0608165 | ||||||||
\(216\) | −6.52787e9 | −0.204047 | ||||||||
\(217\) | 4.87504e9 | 0.149248 | ||||||||
\(218\) | −2.04754e10 | −0.614012 | ||||||||
\(219\) | −1.32538e10 | −0.389352 | ||||||||
\(220\) | −8.78437e7 | −0.00252818 | ||||||||
\(221\) | −3.16400e10 | −0.892219 | ||||||||
\(222\) | −1.70870e10 | −0.472148 | ||||||||
\(223\) | 1.69256e10 | 0.458324 | 0.229162 | − | 0.973388i | \(-0.426401\pi\) | ||||
0.229162 | + | 0.973388i | \(0.426401\pi\) | |||||||
\(224\) | 2.49800e10 | 0.662945 | ||||||||
\(225\) | −1.27900e10 | −0.332696 | ||||||||
\(226\) | 4.53605e9 | 0.115662 | ||||||||
\(227\) | 7.85769e10 | 1.96417 | 0.982084 | − | 0.188442i | \(-0.0603437\pi\) | ||||
0.982084 | + | 0.188442i | \(0.0603437\pi\) | |||||||
\(228\) | 1.49307e10 | 0.365910 | ||||||||
\(229\) | −4.19589e10 | −1.00824 | −0.504121 | − | 0.863633i | \(-0.668183\pi\) | ||||
−0.504121 | + | 0.863633i | \(0.668183\pi\) | |||||||
\(230\) | 3.85230e6 | 9.07704e−5 0 | ||||||||
\(231\) | 2.15919e9 | 0.0498927 | ||||||||
\(232\) | −7.70411e9 | −0.174593 | ||||||||
\(233\) | −3.02106e10 | −0.671519 | −0.335759 | − | 0.941948i | \(-0.608993\pi\) | ||||
−0.335759 | + | 0.941948i | \(0.608993\pi\) | |||||||
\(234\) | −7.70647e9 | −0.168029 | ||||||||
\(235\) | −4.36832e8 | −0.00934348 | ||||||||
\(236\) | −3.10908e9 | −0.0652421 | ||||||||
\(237\) | −4.40149e10 | −0.906217 | ||||||||
\(238\) | 3.27296e10 | 0.661218 | ||||||||
\(239\) | 6.22144e10 | 1.23339 | 0.616695 | − | 0.787202i | \(-0.288471\pi\) | ||||
0.616695 | + | 0.787202i | \(0.288471\pi\) | |||||||
\(240\) | −3.21383e8 | −0.00625277 | ||||||||
\(241\) | 1.51274e10 | 0.288861 | 0.144430 | − | 0.989515i | \(-0.453865\pi\) | ||||
0.144430 | + | 0.989515i | \(0.453865\pi\) | |||||||
\(242\) | −3.71825e10 | −0.696899 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 1.26910e10 | 0.229214 | ||||||||
\(245\) | −1.08289e9 | −0.0192017 | ||||||||
\(246\) | −9.06476e9 | −0.157815 | ||||||||
\(247\) | 5.27997e10 | 0.902599 | ||||||||
\(248\) | −1.25881e10 | −0.211313 | ||||||||
\(249\) | 4.56872e10 | 0.753178 | ||||||||
\(250\) | −3.81056e9 | −0.0616963 | ||||||||
\(251\) | 2.58692e10 | 0.411387 | 0.205694 | − | 0.978616i | \(-0.434055\pi\) | ||||
0.205694 | + | 0.978616i | \(0.434055\pi\) | |||||||
\(252\) | −8.00810e9 | −0.125091 | ||||||||
\(253\) | 2.21078e7 | 0.000339237 0 | ||||||||
\(254\) | 2.69883e10 | 0.406840 | ||||||||
\(255\) | 2.13049e9 | 0.0315536 | ||||||||
\(256\) | −7.30334e10 | −1.06278 | ||||||||
\(257\) | 3.89821e10 | 0.557399 | 0.278699 | − | 0.960378i | \(-0.410097\pi\) | ||||
0.278699 | + | 0.960378i | \(0.410097\pi\) | |||||||
\(258\) | 4.03728e10 | 0.567284 | ||||||||
\(259\) | −6.27900e10 | −0.867044 | ||||||||
\(260\) | 1.15212e9 | 0.0156358 | ||||||||
\(261\) | 4.11506e9 | 0.0548901 | ||||||||
\(262\) | −5.79819e10 | −0.760215 | ||||||||
\(263\) | −5.55292e10 | −0.715682 | −0.357841 | − | 0.933783i | \(-0.616487\pi\) | ||||
−0.357841 | + | 0.933783i | \(0.616487\pi\) | |||||||
\(264\) | −5.57534e9 | −0.0706405 | ||||||||
\(265\) | −6.16424e9 | −0.0767844 | ||||||||
\(266\) | −5.46180e10 | −0.668911 | ||||||||
\(267\) | −3.03032e10 | −0.364912 | ||||||||
\(268\) | 7.09544e10 | 0.840181 | ||||||||
\(269\) | −1.80216e10 | −0.209849 | −0.104925 | − | 0.994480i | \(-0.533460\pi\) | ||||
−0.104925 | + | 0.994480i | \(0.533460\pi\) | |||||||
\(270\) | 5.18919e8 | 0.00594241 | ||||||||
\(271\) | 1.52363e11 | 1.71600 | 0.858001 | − | 0.513648i | \(-0.171706\pi\) | ||||
0.858001 | + | 0.513648i | \(0.171706\pi\) | |||||||
\(272\) | −2.79575e10 | −0.309698 | ||||||||
\(273\) | −2.83191e10 | −0.308566 | ||||||||
\(274\) | 9.41015e10 | 1.00860 | ||||||||
\(275\) | −1.09237e10 | −0.115179 | ||||||||
\(276\) | −8.19944e7 | −0.000850537 0 | ||||||||
\(277\) | −4.45229e8 | −0.00454386 | −0.00227193 | − | 0.999997i | \(-0.500723\pi\) | ||||
−0.00227193 | + | 0.999997i | \(0.500723\pi\) | |||||||
\(278\) | −3.85538e10 | −0.387138 | ||||||||
\(279\) | 6.72377e9 | 0.0664345 | ||||||||
\(280\) | −3.57001e9 | −0.0347103 | ||||||||
\(281\) | 1.75664e11 | 1.68075 | 0.840377 | − | 0.542002i | \(-0.182334\pi\) | ||||
0.840377 | + | 0.542002i | \(0.182334\pi\) | |||||||
\(282\) | −9.25569e9 | −0.0871541 | ||||||||
\(283\) | −3.05315e10 | −0.282950 | −0.141475 | − | 0.989942i | \(-0.545184\pi\) | ||||
−0.141475 | + | 0.989942i | \(0.545184\pi\) | |||||||
\(284\) | 5.44342e10 | 0.496523 | ||||||||
\(285\) | −3.55529e9 | −0.0319207 | ||||||||
\(286\) | −6.58196e9 | −0.0581712 | ||||||||
\(287\) | −3.33104e10 | −0.289809 | ||||||||
\(288\) | 3.44530e10 | 0.295095 | ||||||||
\(289\) | 6.67466e10 | 0.562845 | ||||||||
\(290\) | 6.12421e8 | 0.00508463 | ||||||||
\(291\) | 1.11770e11 | 0.913710 | ||||||||
\(292\) | 4.19836e10 | 0.337953 | ||||||||
\(293\) | 1.77930e11 | 1.41041 | 0.705205 | − | 0.709003i | \(-0.250855\pi\) | ||||
0.705205 | + | 0.709003i | \(0.250855\pi\) | |||||||
\(294\) | −2.29446e10 | −0.179109 | ||||||||
\(295\) | 7.40330e8 | 0.00569149 | ||||||||
\(296\) | 1.62133e11 | 1.22760 | ||||||||
\(297\) | 2.97800e9 | 0.0222086 | ||||||||
\(298\) | −4.66320e10 | −0.342540 | ||||||||
\(299\) | −2.89957e8 | −0.00209804 | ||||||||
\(300\) | 4.05143e10 | 0.288777 | ||||||||
\(301\) | 1.48359e11 | 1.04175 | ||||||||
\(302\) | 1.28062e11 | 0.885909 | ||||||||
\(303\) | 6.17985e10 | 0.421198 | ||||||||
\(304\) | 4.66545e10 | 0.313301 | ||||||||
\(305\) | −3.02196e9 | −0.0199959 | ||||||||
\(306\) | 4.51414e10 | 0.294326 | ||||||||
\(307\) | 2.97466e11 | 1.91124 | 0.955620 | − | 0.294602i | \(-0.0951870\pi\) | ||||
0.955620 | + | 0.294602i | \(0.0951870\pi\) | |||||||
\(308\) | −6.83957e9 | −0.0433063 | ||||||||
\(309\) | −1.40735e11 | −0.878194 | ||||||||
\(310\) | 1.00066e9 | 0.00615403 | ||||||||
\(311\) | 1.82887e11 | 1.10856 | 0.554282 | − | 0.832329i | \(-0.312993\pi\) | ||||
0.554282 | + | 0.832329i | \(0.312993\pi\) | |||||||
\(312\) | 7.31240e10 | 0.436882 | ||||||||
\(313\) | 8.49405e10 | 0.500225 | 0.250112 | − | 0.968217i | \(-0.419532\pi\) | ||||
0.250112 | + | 0.968217i | \(0.419532\pi\) | |||||||
\(314\) | −7.58530e10 | −0.440341 | ||||||||
\(315\) | 1.90688e9 | 0.0109125 | ||||||||
\(316\) | 1.39424e11 | 0.786586 | ||||||||
\(317\) | −2.29248e11 | −1.27509 | −0.637543 | − | 0.770415i | \(-0.720049\pi\) | ||||
−0.637543 | + | 0.770415i | \(0.720049\pi\) | |||||||
\(318\) | −1.30609e11 | −0.716230 | ||||||||
\(319\) | 3.51460e9 | 0.0190028 | ||||||||
\(320\) | 7.15891e9 | 0.0381656 | ||||||||
\(321\) | −7.55271e10 | −0.397036 | ||||||||
\(322\) | 2.99943e8 | 0.00155484 | ||||||||
\(323\) | −3.09279e11 | −1.58103 | ||||||||
\(324\) | −1.10449e10 | −0.0556815 | ||||||||
\(325\) | 1.43271e11 | 0.712332 | ||||||||
\(326\) | 1.21505e11 | 0.595818 | ||||||||
\(327\) | −1.03774e11 | −0.501908 | ||||||||
\(328\) | 8.60123e10 | 0.410325 | ||||||||
\(329\) | −3.40120e10 | −0.160048 | ||||||||
\(330\) | 4.43199e8 | 0.00205725 | ||||||||
\(331\) | 3.80256e11 | 1.74121 | 0.870603 | − | 0.491986i | \(-0.163729\pi\) | ||||
0.870603 | + | 0.491986i | \(0.163729\pi\) | |||||||
\(332\) | −1.44722e11 | −0.653751 | ||||||||
\(333\) | −8.66013e10 | −0.385945 | ||||||||
\(334\) | −1.25760e11 | −0.552949 | ||||||||
\(335\) | −1.68956e10 | −0.0732944 | ||||||||
\(336\) | −2.50231e10 | −0.107106 | ||||||||
\(337\) | −2.10397e11 | −0.888599 | −0.444299 | − | 0.895878i | \(-0.646547\pi\) | ||||
−0.444299 | + | 0.895878i | \(0.646547\pi\) | |||||||
\(338\) | −8.31530e10 | −0.346540 | ||||||||
\(339\) | 2.29899e10 | 0.0945448 | ||||||||
\(340\) | −6.74868e9 | −0.0273882 | ||||||||
\(341\) | 5.74265e9 | 0.0229995 | ||||||||
\(342\) | −7.53303e10 | −0.297750 | ||||||||
\(343\) | −2.76278e11 | −1.07776 | ||||||||
\(344\) | −3.83084e11 | −1.47496 | ||||||||
\(345\) | 1.95244e7 | 7.41979e−5 0 | ||||||||
\(346\) | −1.72051e11 | −0.645380 | ||||||||
\(347\) | −1.31135e10 | −0.0485552 | −0.0242776 | − | 0.999705i | \(-0.507729\pi\) | ||||
−0.0242776 | + | 0.999705i | \(0.507729\pi\) | |||||||
\(348\) | −1.30351e10 | −0.0476440 | ||||||||
\(349\) | 4.66318e11 | 1.68255 | 0.841275 | − | 0.540608i | \(-0.181806\pi\) | ||||
0.841275 | + | 0.540608i | \(0.181806\pi\) | |||||||
\(350\) | −1.48205e11 | −0.527905 | ||||||||
\(351\) | −3.90583e10 | −0.137351 | ||||||||
\(352\) | 2.94257e10 | 0.102161 | ||||||||
\(353\) | −8.93581e10 | −0.306301 | −0.153150 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153150 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(354\) | 1.56863e10 | 0.0530891 | ||||||||
\(355\) | −1.29618e10 | −0.0433150 | ||||||||
\(356\) | 9.59904e10 | 0.316740 | ||||||||
\(357\) | 1.65882e11 | 0.540495 | ||||||||
\(358\) | −7.49683e10 | −0.241215 | ||||||||
\(359\) | 3.45879e11 | 1.09900 | 0.549502 | − | 0.835492i | \(-0.314817\pi\) | ||||
0.549502 | + | 0.835492i | \(0.314817\pi\) | |||||||
\(360\) | −4.92384e9 | −0.0154505 | ||||||||
\(361\) | 1.93426e11 | 0.599422 | ||||||||
\(362\) | 1.11458e11 | 0.341134 | ||||||||
\(363\) | −1.88450e11 | −0.569662 | ||||||||
\(364\) | 8.97053e10 | 0.267832 | ||||||||
\(365\) | −9.99708e9 | −0.0294819 | ||||||||
\(366\) | −6.40301e10 | −0.186517 | ||||||||
\(367\) | 7.78994e10 | 0.224149 | 0.112074 | − | 0.993700i | \(-0.464250\pi\) | ||||
0.112074 | + | 0.993700i | \(0.464250\pi\) | |||||||
\(368\) | −2.56210e8 | −0.000728251 0 | ||||||||
\(369\) | −4.59425e10 | −0.129002 | ||||||||
\(370\) | −1.28884e10 | −0.0357512 | ||||||||
\(371\) | −4.79952e11 | −1.31527 | ||||||||
\(372\) | −2.12986e10 | −0.0576645 | ||||||||
\(373\) | 3.52486e11 | 0.942870 | 0.471435 | − | 0.881901i | \(-0.343736\pi\) | ||||
0.471435 | + | 0.881901i | \(0.343736\pi\) | |||||||
\(374\) | 3.85545e10 | 0.101895 | ||||||||
\(375\) | −1.93129e10 | −0.0504320 | ||||||||
\(376\) | 8.78240e10 | 0.226604 | ||||||||
\(377\) | −4.60962e10 | −0.117525 | ||||||||
\(378\) | 4.04034e10 | 0.101790 | ||||||||
\(379\) | −7.71787e11 | −1.92142 | −0.960708 | − | 0.277562i | \(-0.910473\pi\) | ||||
−0.960708 | + | 0.277562i | \(0.910473\pi\) | |||||||
\(380\) | 1.12619e10 | 0.0277069 | ||||||||
\(381\) | 1.36783e11 | 0.332561 | ||||||||
\(382\) | −2.82824e11 | −0.679566 | ||||||||
\(383\) | −5.61364e11 | −1.33306 | −0.666530 | − | 0.745478i | \(-0.732221\pi\) | ||||
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(384\) | −6.60925e10 | −0.155118 | ||||||||
\(385\) | 1.62863e9 | 0.00377789 | ||||||||
\(386\) | −2.98436e11 | −0.684240 | ||||||||
\(387\) | 2.04620e11 | 0.463712 | ||||||||
\(388\) | −3.54051e11 | −0.793091 | ||||||||
\(389\) | −1.29451e10 | −0.0286636 | −0.0143318 | − | 0.999897i | \(-0.504562\pi\) | ||||
−0.0143318 | + | 0.999897i | \(0.504562\pi\) | |||||||
\(390\) | −5.81283e9 | −0.0127232 | ||||||||
\(391\) | 1.69845e9 | 0.00367501 | ||||||||
\(392\) | 2.17713e11 | 0.465691 | ||||||||
\(393\) | −2.93867e11 | −0.621418 | ||||||||
\(394\) | 5.80344e11 | 1.21326 | ||||||||
\(395\) | −3.31995e10 | −0.0686191 | ||||||||
\(396\) | −9.43329e9 | −0.0192768 | ||||||||
\(397\) | −4.55778e11 | −0.920866 | −0.460433 | − | 0.887695i | \(-0.652306\pi\) | ||||
−0.460433 | + | 0.887695i | \(0.652306\pi\) | |||||||
\(398\) | −9.51438e10 | −0.190067 | ||||||||
\(399\) | −2.76817e11 | −0.546784 | ||||||||
\(400\) | 1.26596e11 | 0.247258 | ||||||||
\(401\) | −7.04177e11 | −1.35998 | −0.679989 | − | 0.733222i | \(-0.738016\pi\) | ||||
−0.679989 | + | 0.733222i | \(0.738016\pi\) | |||||||
\(402\) | −3.57987e11 | −0.683676 | ||||||||
\(403\) | −7.53184e10 | −0.142242 | ||||||||
\(404\) | −1.95757e11 | −0.365595 | ||||||||
\(405\) | 2.63001e9 | 0.00485746 | ||||||||
\(406\) | 4.76836e10 | 0.0870967 | ||||||||
\(407\) | −7.39646e10 | −0.133613 | ||||||||
\(408\) | −4.28331e11 | −0.765260 | ||||||||
\(409\) | −3.04678e11 | −0.538376 | −0.269188 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269188 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(410\) | −6.83736e9 | −0.0119498 | ||||||||
\(411\) | 4.76930e11 | 0.824454 | ||||||||
\(412\) | 4.45802e11 | 0.762263 | ||||||||
\(413\) | 5.76426e10 | 0.0974919 | ||||||||
\(414\) | 4.13688e8 | 0.000692103 0 | ||||||||
\(415\) | 3.44609e10 | 0.0570310 | ||||||||
\(416\) | −3.85937e11 | −0.631824 | ||||||||
\(417\) | −1.95400e11 | −0.316455 | ||||||||
\(418\) | −6.43383e10 | −0.103080 | ||||||||
\(419\) | −1.10294e12 | −1.74818 | −0.874092 | − | 0.485760i | \(-0.838543\pi\) | ||||
−0.874092 | + | 0.485760i | \(0.838543\pi\) | |||||||
\(420\) | −6.04034e9 | −0.00947196 | ||||||||
\(421\) | 3.72442e11 | 0.577815 | 0.288908 | − | 0.957357i | \(-0.406708\pi\) | ||||
0.288908 | + | 0.957357i | \(0.406708\pi\) | |||||||
\(422\) | 6.03102e11 | 0.925730 | ||||||||
\(423\) | −4.69102e10 | −0.0712419 | ||||||||
\(424\) | 1.23931e12 | 1.86223 | ||||||||
\(425\) | −8.39223e11 | −1.24775 | ||||||||
\(426\) | −2.74638e11 | −0.404033 | ||||||||
\(427\) | −2.35292e11 | −0.342517 | ||||||||
\(428\) | 2.39244e11 | 0.344623 | ||||||||
\(429\) | −3.33590e10 | −0.0475505 | ||||||||
\(430\) | 3.04524e10 | 0.0429550 | ||||||||
\(431\) | −8.30400e11 | −1.15915 | −0.579575 | − | 0.814919i | \(-0.696782\pi\) | ||||
−0.579575 | + | 0.814919i | \(0.696782\pi\) | |||||||
\(432\) | −3.45124e10 | −0.0476759 | ||||||||
\(433\) | −1.15753e12 | −1.58248 | −0.791238 | − | 0.611508i | \(-0.790563\pi\) | ||||
−0.791238 | + | 0.611508i | \(0.790563\pi\) | |||||||
\(434\) | 7.79122e10 | 0.105415 | ||||||||
\(435\) | 3.10390e9 | 0.00415630 | ||||||||
\(436\) | 3.28721e11 | 0.435651 | ||||||||
\(437\) | −2.83432e9 | −0.00371776 | ||||||||
\(438\) | −2.11820e11 | −0.275001 | ||||||||
\(439\) | 4.39794e11 | 0.565144 | 0.282572 | − | 0.959246i | \(-0.408812\pi\) | ||||
0.282572 | + | 0.959246i | \(0.408812\pi\) | |||||||
\(440\) | −4.20536e9 | −0.00534892 | ||||||||
\(441\) | −1.16289e11 | −0.146408 | ||||||||
\(442\) | −5.05666e11 | −0.630178 | ||||||||
\(443\) | −7.14220e11 | −0.881080 | −0.440540 | − | 0.897733i | \(-0.645213\pi\) | ||||
−0.440540 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(444\) | 2.74324e11 | 0.334996 | ||||||||
\(445\) | −2.28571e10 | −0.0276313 | ||||||||
\(446\) | 2.70503e11 | 0.323717 | ||||||||
\(447\) | −2.36343e11 | −0.280000 | ||||||||
\(448\) | 5.57398e11 | 0.653754 | ||||||||
\(449\) | −1.44352e12 | −1.67616 | −0.838078 | − | 0.545551i | \(-0.816320\pi\) | ||||
−0.838078 | + | 0.545551i | \(0.816320\pi\) | |||||||
\(450\) | −2.04407e11 | −0.234985 | ||||||||
\(451\) | −3.92386e10 | −0.0446601 | ||||||||
\(452\) | −7.28241e10 | −0.0820639 | ||||||||
\(453\) | 6.49050e11 | 0.724163 | ||||||||
\(454\) | 1.25580e12 | 1.38730 | ||||||||
\(455\) | −2.13605e10 | −0.0233647 | ||||||||
\(456\) | 7.14783e11 | 0.774163 | ||||||||
\(457\) | 9.30712e11 | 0.998142 | 0.499071 | − | 0.866561i | \(-0.333675\pi\) | ||||
0.499071 | + | 0.866561i | \(0.333675\pi\) | |||||||
\(458\) | −6.70581e11 | −0.712126 | ||||||||
\(459\) | 2.28788e11 | 0.240589 | ||||||||
\(460\) | −6.18467e7 | −6.44030e−5 0 | ||||||||
\(461\) | −4.17109e11 | −0.430125 | −0.215063 | − | 0.976600i | \(-0.568996\pi\) | ||||
−0.215063 | + | 0.976600i | \(0.568996\pi\) | |||||||
\(462\) | 3.45078e10 | 0.0352394 | ||||||||
\(463\) | 6.97753e11 | 0.705646 | 0.352823 | − | 0.935690i | \(-0.385222\pi\) | ||||
0.352823 | + | 0.935690i | \(0.385222\pi\) | |||||||
\(464\) | −4.07312e10 | −0.0407940 | ||||||||
\(465\) | 5.07160e9 | 0.00503045 | ||||||||
\(466\) | −4.82822e11 | −0.474297 | ||||||||
\(467\) | 1.07830e12 | 1.04909 | 0.524545 | − | 0.851383i | \(-0.324235\pi\) | ||||
0.524545 | + | 0.851383i | \(0.324235\pi\) | |||||||
\(468\) | 1.23724e11 | 0.119219 | ||||||||
\(469\) | −1.31550e12 | −1.25549 | ||||||||
\(470\) | −6.98138e9 | −0.00659934 | ||||||||
\(471\) | −3.84442e11 | −0.359945 | ||||||||
\(472\) | −1.48842e11 | −0.138034 | ||||||||
\(473\) | 1.74762e11 | 0.160536 | ||||||||
\(474\) | −7.03439e11 | −0.640065 | ||||||||
\(475\) | 1.40046e12 | 1.26227 | ||||||||
\(476\) | −5.25457e11 | −0.469144 | ||||||||
\(477\) | −6.61961e11 | −0.585463 | ||||||||
\(478\) | 9.94302e11 | 0.871150 | ||||||||
\(479\) | −2.23813e11 | −0.194257 | −0.0971283 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971283 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(480\) | 2.59872e10 | 0.0223447 | ||||||||
\(481\) | 9.70092e11 | 0.826343 | ||||||||
\(482\) | 2.41764e11 | 0.204024 | ||||||||
\(483\) | 1.52018e9 | 0.00127097 | ||||||||
\(484\) | 5.96947e11 | 0.494460 | ||||||||
\(485\) | 8.43061e10 | 0.0691865 | ||||||||
\(486\) | 5.57253e10 | 0.0453095 | ||||||||
\(487\) | 7.00426e11 | 0.564264 | 0.282132 | − | 0.959376i | \(-0.408958\pi\) | ||||
0.282132 | + | 0.959376i | \(0.408958\pi\) | |||||||
\(488\) | 6.07559e11 | 0.484953 | ||||||||
\(489\) | 6.15816e11 | 0.487036 | ||||||||
\(490\) | −1.73066e10 | −0.0135622 | ||||||||
\(491\) | 7.68487e11 | 0.596719 | 0.298359 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298359 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(492\) | 1.45530e11 | 0.111972 | ||||||||
\(493\) | 2.70013e11 | 0.205861 | ||||||||
\(494\) | 8.43837e11 | 0.637510 | ||||||||
\(495\) | 2.24624e9 | 0.00168164 | ||||||||
\(496\) | −6.65523e10 | −0.0493737 | ||||||||
\(497\) | −1.00922e12 | −0.741960 | ||||||||
\(498\) | 7.30167e11 | 0.531973 | ||||||||
\(499\) | 2.27431e12 | 1.64209 | 0.821044 | − | 0.570865i | \(-0.193392\pi\) | ||||
0.821044 | + | 0.570865i | \(0.193392\pi\) | |||||||
\(500\) | 6.11766e10 | 0.0437744 | ||||||||
\(501\) | −6.37385e11 | −0.451994 | ||||||||
\(502\) | 4.13437e11 | 0.290565 | ||||||||
\(503\) | −1.50660e11 | −0.104940 | −0.0524700 | − | 0.998623i | \(-0.516709\pi\) | ||||
−0.0524700 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(504\) | −3.83374e11 | −0.264658 | ||||||||
\(505\) | 4.66133e10 | 0.0318932 | ||||||||
\(506\) | 3.53323e8 | 0.000239604 0 | ||||||||
\(507\) | −4.21440e11 | −0.283270 | ||||||||
\(508\) | −4.33283e11 | −0.288659 | ||||||||
\(509\) | 6.47058e11 | 0.427281 | 0.213640 | − | 0.976912i | \(-0.431468\pi\) | ||||
0.213640 | + | 0.976912i | \(0.431468\pi\) | |||||||
\(510\) | 3.40492e10 | 0.0222865 | ||||||||
\(511\) | −7.78380e11 | −0.505007 | ||||||||
\(512\) | −7.49439e11 | −0.481971 | ||||||||
\(513\) | −3.81793e11 | −0.243388 | ||||||||
\(514\) | 6.23006e11 | 0.393693 | ||||||||
\(515\) | −1.06154e11 | −0.0664972 | ||||||||
\(516\) | −6.48165e11 | −0.402497 | ||||||||
\(517\) | −4.00651e10 | −0.0246638 | ||||||||
\(518\) | −1.00350e12 | −0.612397 | ||||||||
\(519\) | −8.71999e11 | −0.527549 | ||||||||
\(520\) | 5.51559e10 | 0.0330809 | ||||||||
\(521\) | −1.54003e12 | −0.915713 | −0.457857 | − | 0.889026i | \(-0.651383\pi\) | ||||
−0.457857 | + | 0.889026i | \(0.651383\pi\) | |||||||
\(522\) | 6.57663e10 | 0.0387691 | ||||||||
\(523\) | 2.04280e12 | 1.19390 | 0.596949 | − | 0.802279i | \(-0.296379\pi\) | ||||
0.596949 | + | 0.802279i | \(0.296379\pi\) | |||||||
\(524\) | 9.30870e11 | 0.539384 | ||||||||
\(525\) | −7.51138e11 | −0.431522 | ||||||||
\(526\) | −8.87459e11 | −0.505490 | ||||||||
\(527\) | 4.41185e11 | 0.249157 | ||||||||
\(528\) | −2.94765e10 | −0.0165053 | ||||||||
\(529\) | −1.80114e12 | −0.999991 | ||||||||
\(530\) | −9.85160e10 | −0.0542332 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 8.76864e11 | 0.474602 | ||||||||
\(533\) | 5.14639e11 | 0.276204 | ||||||||
\(534\) | −4.84302e11 | −0.257739 | ||||||||
\(535\) | −5.69685e10 | −0.0300637 | ||||||||
\(536\) | 3.39682e12 | 1.77759 | ||||||||
\(537\) | −3.79958e11 | −0.197175 | ||||||||
\(538\) | −2.88018e11 | −0.148217 | ||||||||
\(539\) | −9.93204e10 | −0.0506861 | ||||||||
\(540\) | −8.33097e9 | −0.00421623 | ||||||||
\(541\) | −3.00028e12 | −1.50582 | −0.752912 | − | 0.658121i | \(-0.771352\pi\) | ||||
−0.752912 | + | 0.658121i | \(0.771352\pi\) | |||||||
\(542\) | 2.43504e12 | 1.21202 | ||||||||
\(543\) | 5.64899e11 | 0.278851 | ||||||||
\(544\) | 2.26066e12 | 1.10673 | ||||||||
\(545\) | −7.82747e10 | −0.0380047 | ||||||||
\(546\) | −4.52591e11 | −0.217941 | ||||||||
\(547\) | 2.43565e12 | 1.16325 | 0.581625 | − | 0.813457i | \(-0.302417\pi\) | ||||
0.581625 | + | 0.813457i | \(0.302417\pi\) | |||||||
\(548\) | −1.51075e12 | −0.715617 | ||||||||
\(549\) | −3.24521e11 | −0.152464 | ||||||||
\(550\) | −1.74581e11 | −0.0813512 | ||||||||
\(551\) | −4.50587e11 | −0.208256 | ||||||||
\(552\) | −3.92534e9 | −0.00179950 | ||||||||
\(553\) | −2.58494e12 | −1.17540 | ||||||||
\(554\) | −7.11559e9 | −0.00320935 | ||||||||
\(555\) | −6.53216e10 | −0.0292239 | ||||||||
\(556\) | 6.18961e11 | 0.274680 | ||||||||
\(557\) | 1.08394e12 | 0.477151 | 0.238575 | − | 0.971124i | \(-0.423320\pi\) | ||||
0.238575 | + | 0.971124i | \(0.423320\pi\) | |||||||
\(558\) | 1.07458e11 | 0.0469230 | ||||||||
\(559\) | −2.29211e12 | −0.992848 | ||||||||
\(560\) | −1.88744e10 | −0.00811012 | ||||||||
\(561\) | 1.95404e11 | 0.0832914 | ||||||||
\(562\) | 2.80743e12 | 1.18712 | ||||||||
\(563\) | −3.18803e12 | −1.33732 | −0.668659 | − | 0.743569i | \(-0.733131\pi\) | ||||
−0.668659 | + | 0.743569i | \(0.733131\pi\) | |||||||
\(564\) | 1.48595e11 | 0.0618372 | ||||||||
\(565\) | 1.73408e10 | 0.00715897 | ||||||||
\(566\) | −4.87950e11 | −0.199849 | ||||||||
\(567\) | 2.04774e11 | 0.0832055 | ||||||||
\(568\) | 2.60594e12 | 1.05050 | ||||||||
\(569\) | 2.82225e12 | 1.12873 | 0.564366 | − | 0.825525i | \(-0.309121\pi\) | ||||
0.564366 | + | 0.825525i | \(0.309121\pi\) | |||||||
\(570\) | −5.68201e10 | −0.0225458 | ||||||||
\(571\) | −3.48287e12 | −1.37112 | −0.685559 | − | 0.728017i | \(-0.740442\pi\) | ||||
−0.685559 | + | 0.728017i | \(0.740442\pi\) | |||||||
\(572\) | 1.05670e11 | 0.0412734 | ||||||||
\(573\) | −1.43342e12 | −0.555493 | ||||||||
\(574\) | −5.32362e11 | −0.204693 | ||||||||
\(575\) | −7.69086e9 | −0.00293406 | ||||||||
\(576\) | 7.68776e11 | 0.291004 | ||||||||
\(577\) | 8.09796e11 | 0.304148 | 0.152074 | − | 0.988369i | \(-0.451405\pi\) | ||||
0.152074 | + | 0.988369i | \(0.451405\pi\) | |||||||
\(578\) | 1.06673e12 | 0.397540 | ||||||||
\(579\) | −1.51255e12 | −0.559314 | ||||||||
\(580\) | −9.83211e9 | −0.00360762 | ||||||||
\(581\) | 2.68315e12 | 0.976907 | ||||||||
\(582\) | 1.78630e12 | 0.645358 | ||||||||
\(583\) | −5.65369e11 | −0.202686 | ||||||||
\(584\) | 2.00989e12 | 0.715014 | ||||||||
\(585\) | −2.94609e10 | −0.0104003 | ||||||||
\(586\) | 2.84365e12 | 0.996179 | ||||||||
\(587\) | 2.65276e12 | 0.922203 | 0.461101 | − | 0.887348i | \(-0.347454\pi\) | ||||
0.461101 | + | 0.887348i | \(0.347454\pi\) | |||||||
\(588\) | 3.68364e11 | 0.127081 | ||||||||
\(589\) | −7.36233e11 | −0.252056 | ||||||||
\(590\) | 1.18318e10 | 0.00401993 | ||||||||
\(591\) | 2.94133e12 | 0.991744 | ||||||||
\(592\) | 8.57186e11 | 0.286832 | ||||||||
\(593\) | −1.08368e12 | −0.359879 | −0.179940 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179940 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(594\) | 4.75940e10 | 0.0156860 | ||||||||
\(595\) | 1.25121e11 | 0.0409265 | ||||||||
\(596\) | 7.48654e11 | 0.243037 | ||||||||
\(597\) | −4.82212e11 | −0.155365 | ||||||||
\(598\) | −4.63405e9 | −0.00148186 | ||||||||
\(599\) | −1.57285e12 | −0.499191 | −0.249595 | − | 0.968350i | \(-0.580298\pi\) | ||||
−0.249595 | + | 0.968350i | \(0.580298\pi\) | |||||||
\(600\) | 1.93955e12 | 0.610970 | ||||||||
\(601\) | 8.26489e10 | 0.0258406 | 0.0129203 | − | 0.999917i | \(-0.495887\pi\) | ||||
0.0129203 | + | 0.999917i | \(0.495887\pi\) | |||||||
\(602\) | 2.37105e12 | 0.735793 | ||||||||
\(603\) | −1.81437e12 | −0.558853 | ||||||||
\(604\) | −2.05597e12 | −0.628566 | ||||||||
\(605\) | −1.42144e11 | −0.0431350 | ||||||||
\(606\) | 9.87654e11 | 0.297494 | ||||||||
\(607\) | −1.82660e12 | −0.546127 | −0.273063 | − | 0.961996i | \(-0.588037\pi\) | ||||
−0.273063 | + | 0.961996i | \(0.588037\pi\) | |||||||
\(608\) | −3.77251e12 | −1.11960 | ||||||||
\(609\) | 2.41672e11 | 0.0711949 | ||||||||
\(610\) | −4.82966e10 | −0.0141232 | ||||||||
\(611\) | 5.25479e11 | 0.152535 | ||||||||
\(612\) | −7.24723e11 | −0.208829 | ||||||||
\(613\) | −8.02251e11 | −0.229476 | −0.114738 | − | 0.993396i | \(-0.536603\pi\) | ||||
−0.114738 | + | 0.993396i | \(0.536603\pi\) | |||||||
\(614\) | 4.75406e12 | 1.34992 | ||||||||
\(615\) | −3.46534e10 | −0.00976806 | ||||||||
\(616\) | −3.27433e11 | −0.0916239 | ||||||||
\(617\) | 1.88160e11 | 0.0522691 | 0.0261345 | − | 0.999658i | \(-0.491680\pi\) | ||||
0.0261345 | + | 0.999658i | \(0.491680\pi\) | |||||||
\(618\) | −2.24921e12 | −0.620272 | ||||||||
\(619\) | 3.64562e12 | 0.998076 | 0.499038 | − | 0.866580i | \(-0.333687\pi\) | ||||
0.499038 | + | 0.866580i | \(0.333687\pi\) | |||||||
\(620\) | −1.60651e10 | −0.00436637 | ||||||||
\(621\) | 2.09667e9 | 0.000565742 0 | ||||||||
\(622\) | 2.92287e12 | 0.782984 | ||||||||
\(623\) | −1.77967e12 | −0.473308 | ||||||||
\(624\) | 3.86602e11 | 0.102078 | ||||||||
\(625\) | 3.79284e12 | 0.994270 | ||||||||
\(626\) | 1.35751e12 | 0.353311 | ||||||||
\(627\) | −3.26083e11 | −0.0842604 | ||||||||
\(628\) | 1.21778e12 | 0.312429 | ||||||||
\(629\) | −5.68241e12 | −1.44745 | ||||||||
\(630\) | 3.04754e10 | 0.00770757 | ||||||||
\(631\) | −6.95665e12 | −1.74690 | −0.873450 | − | 0.486914i | \(-0.838123\pi\) | ||||
−0.873450 | + | 0.486914i | \(0.838123\pi\) | |||||||
\(632\) | 6.67469e12 | 1.66419 | ||||||||
\(633\) | 3.05667e12 | 0.756714 | ||||||||
\(634\) | −3.66381e12 | −0.900599 | ||||||||
\(635\) | 1.03173e11 | 0.0251816 | ||||||||
\(636\) | 2.09687e12 | 0.508176 | ||||||||
\(637\) | 1.30265e12 | 0.313473 | ||||||||
\(638\) | 5.61698e10 | 0.0134218 | ||||||||
\(639\) | −1.39193e12 | −0.330266 | ||||||||
\(640\) | −4.98522e10 | −0.0117456 | ||||||||
\(641\) | −6.18919e12 | −1.44801 | −0.724007 | − | 0.689792i | \(-0.757702\pi\) | ||||
−0.724007 | + | 0.689792i | \(0.757702\pi\) | |||||||
\(642\) | −1.20706e12 | −0.280428 | ||||||||
\(643\) | 2.77548e11 | 0.0640307 | 0.0320154 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320154 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(644\) | −4.81543e9 | −0.00110319 | ||||||||
\(645\) | 1.54340e11 | 0.0351124 | ||||||||
\(646\) | −4.94286e12 | −1.11669 | ||||||||
\(647\) | −6.51803e12 | −1.46234 | −0.731168 | − | 0.682197i | \(-0.761024\pi\) | ||||
−0.731168 | + | 0.682197i | \(0.761024\pi\) | |||||||
\(648\) | −5.28757e11 | −0.117806 | ||||||||
\(649\) | 6.79013e10 | 0.0150237 | ||||||||
\(650\) | 2.28973e12 | 0.503124 | ||||||||
\(651\) | 3.94879e11 | 0.0861686 | ||||||||
\(652\) | −1.95070e12 | −0.422742 | ||||||||
\(653\) | 7.85123e12 | 1.68977 | 0.844887 | − | 0.534945i | \(-0.179668\pi\) | ||||
0.844887 | + | 0.534945i | \(0.179668\pi\) | |||||||
\(654\) | −1.65850e12 | −0.354500 | ||||||||
\(655\) | −2.21658e11 | −0.0470540 | ||||||||
\(656\) | 4.54742e11 | 0.0958732 | ||||||||
\(657\) | −1.07356e12 | −0.224792 | ||||||||
\(658\) | −5.43575e11 | −0.113043 | ||||||||
\(659\) | 3.89784e11 | 0.0805081 | 0.0402540 | − | 0.999189i | \(-0.487183\pi\) | ||||
0.0402540 | + | 0.999189i | \(0.487183\pi\) | |||||||
\(660\) | −7.11534e9 | −0.00145965 | ||||||||
\(661\) | 1.65637e12 | 0.337482 | 0.168741 | − | 0.985660i | \(-0.446030\pi\) | ||||
0.168741 | + | 0.985660i | \(0.446030\pi\) | |||||||
\(662\) | 6.07720e12 | 1.22982 | ||||||||
\(663\) | −2.56284e12 | −0.515123 | ||||||||
\(664\) | −6.92829e12 | −1.38315 | ||||||||
\(665\) | −2.08798e11 | −0.0414027 | ||||||||
\(666\) | −1.38405e12 | −0.272595 | ||||||||
\(667\) | 2.47447e9 | 0.000484078 0 | ||||||||
\(668\) | 2.01902e12 | 0.392326 | ||||||||
\(669\) | 1.37098e12 | 0.264614 | ||||||||
\(670\) | −2.70022e11 | −0.0517682 | ||||||||
\(671\) | −2.77167e11 | −0.0527826 | ||||||||
\(672\) | 2.02338e12 | 0.382751 | ||||||||
\(673\) | 8.32730e11 | 0.156472 | 0.0782360 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782360 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(674\) | −3.36254e12 | −0.627622 | ||||||||
\(675\) | −1.03599e12 | −0.192082 | ||||||||
\(676\) | 1.33498e12 | 0.245875 | ||||||||
\(677\) | −1.03042e13 | −1.88524 | −0.942620 | − | 0.333868i | \(-0.891646\pi\) | ||||
−0.942620 | + | 0.333868i | \(0.891646\pi\) | |||||||
\(678\) | 3.67420e11 | 0.0667774 | ||||||||
\(679\) | 6.56414e12 | 1.18512 | ||||||||
\(680\) | −3.23081e11 | −0.0579457 | ||||||||
\(681\) | 6.36473e12 | 1.13401 | ||||||||
\(682\) | 9.17782e10 | 0.0162446 | ||||||||
\(683\) | 3.22944e12 | 0.567850 | 0.283925 | − | 0.958847i | \(-0.408363\pi\) | ||||
0.283925 | + | 0.958847i | \(0.408363\pi\) | |||||||
\(684\) | 1.20939e12 | 0.211258 | ||||||||
\(685\) | 3.59738e11 | 0.0624279 | ||||||||
\(686\) | −4.41544e12 | −0.761229 | ||||||||
\(687\) | −3.39867e12 | −0.582108 | ||||||||
\(688\) | −2.02534e12 | −0.344627 | ||||||||
\(689\) | 7.41517e12 | 1.25353 | ||||||||
\(690\) | 3.12036e8 | 5.24063e−5 0 | ||||||||
\(691\) | −6.35783e12 | −1.06086 | −0.530430 | − | 0.847729i | \(-0.677969\pi\) | ||||
−0.530430 | + | 0.847729i | \(0.677969\pi\) | |||||||
\(692\) | 2.76220e12 | 0.457907 | ||||||||
\(693\) | 1.74894e11 | 0.0288055 | ||||||||
\(694\) | −2.09578e11 | −0.0342948 | ||||||||
\(695\) | −1.47386e11 | −0.0239621 | ||||||||
\(696\) | −6.24033e11 | −0.100801 | ||||||||
\(697\) | −3.01455e12 | −0.483810 | ||||||||
\(698\) | 7.45263e12 | 1.18839 | ||||||||
\(699\) | −2.44706e12 | −0.387702 | ||||||||
\(700\) | 2.37935e12 | 0.374557 | ||||||||
\(701\) | −6.24586e11 | −0.0976925 | −0.0488463 | − | 0.998806i | \(-0.515554\pi\) | ||||
−0.0488463 | + | 0.998806i | \(0.515554\pi\) | |||||||
\(702\) | −6.24224e11 | −0.0970116 | ||||||||
\(703\) | 9.48259e12 | 1.46429 | ||||||||
\(704\) | 6.56598e11 | 0.100745 | ||||||||
\(705\) | −3.53834e10 | −0.00539446 | ||||||||
\(706\) | −1.42811e12 | −0.216342 | ||||||||
\(707\) | 3.62935e12 | 0.546312 | ||||||||
\(708\) | −2.51835e11 | −0.0376675 | ||||||||
\(709\) | −5.99601e12 | −0.891157 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(710\) | −2.07154e11 | −0.0305936 | ||||||||
\(711\) | −3.56521e12 | −0.523204 | ||||||||
\(712\) | 4.59537e12 | 0.670132 | ||||||||
\(713\) | 4.04314e9 | 0.000585889 0 | ||||||||
\(714\) | 2.65110e12 | 0.381754 | ||||||||
\(715\) | −2.51620e10 | −0.00360054 | ||||||||
\(716\) | 1.20358e12 | 0.171146 | ||||||||
\(717\) | 5.03937e12 | 0.712099 | ||||||||
\(718\) | 5.52779e12 | 0.776232 | ||||||||
\(719\) | −5.44093e12 | −0.759265 | −0.379632 | − | 0.925137i | \(-0.623949\pi\) | ||||
−0.379632 | + | 0.925137i | \(0.623949\pi\) | |||||||
\(720\) | −2.60320e10 | −0.00361004 | ||||||||
\(721\) | −8.26522e12 | −1.13906 | ||||||||
\(722\) | 3.09131e12 | 0.423375 | ||||||||
\(723\) | 1.22532e12 | 0.166774 | ||||||||
\(724\) | −1.78941e12 | −0.242039 | ||||||||
\(725\) | −1.22266e12 | −0.164356 | ||||||||
\(726\) | −3.01178e12 | −0.402355 | ||||||||
\(727\) | 3.33589e11 | 0.0442902 | 0.0221451 | − | 0.999755i | \(-0.492950\pi\) | ||||
0.0221451 | + | 0.999755i | \(0.492950\pi\) | |||||||
\(728\) | 4.29448e12 | 0.566656 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.59772e11 | −0.0208232 | ||||||||
\(731\) | 1.34263e13 | 1.73911 | ||||||||
\(732\) | 1.02797e12 | 0.132337 | ||||||||
\(733\) | 6.61739e12 | 0.846680 | 0.423340 | − | 0.905971i | \(-0.360858\pi\) | ||||
0.423340 | + | 0.905971i | \(0.360858\pi\) | |||||||
\(734\) | 1.24498e12 | 0.158317 | ||||||||
\(735\) | −8.77144e10 | −0.0110861 | ||||||||
\(736\) | 2.07173e10 | 0.00260245 | ||||||||
\(737\) | −1.54962e12 | −0.193474 | ||||||||
\(738\) | −7.34245e11 | −0.0911145 | ||||||||
\(739\) | −5.63499e12 | −0.695014 | −0.347507 | − | 0.937677i | \(-0.612972\pi\) | ||||
−0.347507 | + | 0.937677i | \(0.612972\pi\) | |||||||
\(740\) | 2.06917e11 | 0.0253660 | ||||||||
\(741\) | 4.27677e12 | 0.521116 | ||||||||
\(742\) | −7.67053e12 | −0.928983 | ||||||||
\(743\) | −1.64104e13 | −1.97547 | −0.987735 | − | 0.156140i | \(-0.950095\pi\) | ||||
−0.987735 | + | 0.156140i | \(0.950095\pi\) | |||||||
\(744\) | −1.01963e12 | −0.122002 | ||||||||
\(745\) | −1.78268e11 | −0.0212017 | ||||||||
\(746\) | 5.63337e12 | 0.665953 | ||||||||
\(747\) | 3.70067e12 | 0.434848 | ||||||||
\(748\) | −6.18973e11 | −0.0722960 | ||||||||
\(749\) | −4.43561e12 | −0.514974 | ||||||||
\(750\) | −3.08655e11 | −0.0356204 | ||||||||
\(751\) | 4.91387e10 | 0.00563694 | 0.00281847 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281847 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(752\) | 4.64320e11 | 0.0529465 | ||||||||
\(753\) | 2.09540e12 | 0.237515 | ||||||||
\(754\) | −7.36702e11 | −0.0830081 | ||||||||
\(755\) | 4.89565e11 | 0.0548339 | ||||||||
\(756\) | −6.48656e11 | −0.0722215 | ||||||||
\(757\) | −4.10791e12 | −0.454663 | −0.227332 | − | 0.973817i | \(-0.573000\pi\) | ||||
−0.227332 | + | 0.973817i | \(0.573000\pi\) | |||||||
\(758\) | −1.23346e13 | −1.35710 | ||||||||
\(759\) | 1.79073e9 | 0.000195858 0 | ||||||||
\(760\) | 5.39146e11 | 0.0586199 | ||||||||
\(761\) | −3.72963e12 | −0.403121 | −0.201560 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201560 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(762\) | 2.18605e12 | 0.234889 | ||||||||
\(763\) | −6.09453e12 | −0.650998 | ||||||||
\(764\) | 4.54060e12 | 0.482162 | ||||||||
\(765\) | 1.72570e11 | 0.0182175 | ||||||||
\(766\) | −8.97163e12 | −0.941547 | ||||||||
\(767\) | −8.90567e11 | −0.0929153 | ||||||||
\(768\) | −5.91570e12 | −0.613594 | ||||||||
\(769\) | −5.30984e12 | −0.547537 | −0.273768 | − | 0.961796i | \(-0.588270\pi\) | ||||
−0.273768 | + | 0.961796i | \(0.588270\pi\) | |||||||
\(770\) | 2.60285e10 | 0.00266834 | ||||||||
\(771\) | 3.15755e12 | 0.321814 | ||||||||
\(772\) | 4.79124e12 | 0.485479 | ||||||||
\(773\) | 1.53805e13 | 1.54940 | 0.774700 | − | 0.632329i | \(-0.217901\pi\) | ||||
0.774700 | + | 0.632329i | \(0.217901\pi\) | |||||||
\(774\) | 3.27020e12 | 0.327522 | ||||||||
\(775\) | −1.99775e12 | −0.198923 | ||||||||
\(776\) | −1.69496e13 | −1.67796 | ||||||||
\(777\) | −5.08599e12 | −0.500588 | ||||||||
\(778\) | −2.06886e11 | −0.0202453 | ||||||||
\(779\) | 5.03057e12 | 0.489439 | ||||||||
\(780\) | 9.33221e10 | 0.00902732 | ||||||||
\(781\) | −1.18883e12 | −0.114337 | ||||||||
\(782\) | 2.71444e10 | 0.00259567 | ||||||||
\(783\) | 3.33320e11 | 0.0316908 | ||||||||
\(784\) | 1.15104e12 | 0.108810 | ||||||||
\(785\) | −2.89977e11 | −0.0272552 | ||||||||
\(786\) | −4.69653e12 | −0.438910 | ||||||||
\(787\) | 2.05993e12 | 0.191410 | 0.0957052 | − | 0.995410i | \(-0.469489\pi\) | ||||
0.0957052 | + | 0.995410i | \(0.469489\pi\) | |||||||
\(788\) | −9.31712e12 | −0.860823 | ||||||||
\(789\) | −4.49786e12 | −0.413199 | ||||||||
\(790\) | −5.30590e11 | −0.0484660 | ||||||||
\(791\) | 1.35017e12 | 0.122629 | ||||||||
\(792\) | −4.51602e11 | −0.0407843 | ||||||||
\(793\) | 3.63522e12 | 0.326439 | ||||||||
\(794\) | −7.28418e12 | −0.650412 | ||||||||
\(795\) | −4.99303e11 | −0.0443315 | ||||||||
\(796\) | 1.52748e12 | 0.134855 | ||||||||
\(797\) | −6.13048e12 | −0.538186 | −0.269093 | − | 0.963114i | \(-0.586724\pi\) | ||||
−0.269093 | + | 0.963114i | \(0.586724\pi\) | |||||||
\(798\) | −4.42406e12 | −0.386196 | ||||||||
\(799\) | −3.07805e12 | −0.267187 | ||||||||
\(800\) | −1.02366e13 | −0.883592 | ||||||||
\(801\) | −2.45456e12 | −0.210682 | ||||||||
\(802\) | −1.12540e13 | −0.960559 | ||||||||
\(803\) | −9.16908e11 | −0.0778226 | ||||||||
\(804\) | 5.74730e12 | 0.485078 | ||||||||
\(805\) | 1.14664e9 | 9.62381e−5 0 | ||||||||
\(806\) | −1.20373e12 | −0.100466 | ||||||||
\(807\) | −1.45975e12 | −0.121156 | ||||||||
\(808\) | −9.37150e12 | −0.773496 | ||||||||
\(809\) | 1.02968e13 | 0.845147 | 0.422574 | − | 0.906329i | \(-0.361127\pi\) | ||||
0.422574 | + | 0.906329i | \(0.361127\pi\) | |||||||
\(810\) | 4.20324e10 | 0.00343085 | ||||||||
\(811\) | 1.95327e13 | 1.58551 | 0.792754 | − | 0.609541i | \(-0.208646\pi\) | ||||
0.792754 | + | 0.609541i | \(0.208646\pi\) | |||||||
\(812\) | −7.65536e11 | −0.0617964 | ||||||||
\(813\) | 1.23414e13 | 0.990734 | ||||||||
\(814\) | −1.18209e12 | −0.0943716 | ||||||||
\(815\) | 4.64497e11 | 0.0368786 | ||||||||
\(816\) | −2.26456e12 | −0.178804 | ||||||||
\(817\) | −2.24053e13 | −1.75934 | ||||||||
\(818\) | −4.86931e12 | −0.380258 | ||||||||
\(819\) | −2.29385e12 | −0.178150 | ||||||||
\(820\) | 1.09770e11 | 0.00847857 | ||||||||
\(821\) | −4.94835e12 | −0.380116 | −0.190058 | − | 0.981773i | \(-0.560868\pi\) | ||||
−0.190058 | + | 0.981773i | \(0.560868\pi\) | |||||||
\(822\) | 7.62222e12 | 0.582315 | ||||||||
\(823\) | −7.29946e12 | −0.554615 | −0.277308 | − | 0.960781i | \(-0.589442\pi\) | ||||
−0.277308 | + | 0.960781i | \(0.589442\pi\) | |||||||
\(824\) | 2.13420e13 | 1.61273 | ||||||||
\(825\) | −8.84818e11 | −0.0664984 | ||||||||
\(826\) | 9.21236e11 | 0.0688590 | ||||||||
\(827\) | −6.55140e12 | −0.487034 | −0.243517 | − | 0.969897i | \(-0.578301\pi\) | ||||
−0.243517 | + | 0.969897i | \(0.578301\pi\) | |||||||
\(828\) | −6.64155e9 | −0.000491058 0 | ||||||||
\(829\) | 6.85363e12 | 0.503994 | 0.251997 | − | 0.967728i | \(-0.418913\pi\) | ||||
0.251997 | + | 0.967728i | \(0.418913\pi\) | |||||||
\(830\) | 5.50749e11 | 0.0402812 | ||||||||
\(831\) | −3.60636e10 | −0.00262340 | ||||||||
\(832\) | −8.61169e12 | −0.623065 | ||||||||
\(833\) | −7.63039e12 | −0.549091 | ||||||||
\(834\) | −3.12286e12 | −0.223514 | ||||||||
\(835\) | −4.80767e11 | −0.0342251 | ||||||||
\(836\) | 1.03292e12 | 0.0731371 | ||||||||
\(837\) | 5.44625e11 | 0.0383560 | ||||||||
\(838\) | −1.76270e13 | −1.23475 | ||||||||
\(839\) | −1.69365e12 | −0.118003 | −0.0590017 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590017 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(840\) | −2.89171e11 | −0.0200400 | ||||||||
\(841\) | −1.41138e13 | −0.972884 | ||||||||
\(842\) | 5.95231e12 | 0.408114 | ||||||||
\(843\) | 1.42288e13 | 0.970384 | ||||||||
\(844\) | −9.68249e12 | −0.656820 | ||||||||
\(845\) | −3.17884e11 | −0.0214493 | ||||||||
\(846\) | −7.49711e11 | −0.0503185 | ||||||||
\(847\) | −1.10674e13 | −0.738877 | ||||||||
\(848\) | 6.55214e12 | 0.435113 | ||||||||
\(849\) | −2.47305e12 | −0.163361 | ||||||||
\(850\) | −1.34123e13 | −0.881291 | ||||||||
\(851\) | −5.20751e10 | −0.00340367 | ||||||||
\(852\) | 4.40917e12 | 0.286668 | ||||||||
\(853\) | 5.29571e12 | 0.342495 | 0.171247 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171247 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(854\) | −3.76041e12 | −0.241922 | ||||||||
\(855\) | −2.87978e11 | −0.0184295 | ||||||||
\(856\) | 1.14534e13 | 0.729125 | ||||||||
\(857\) | 1.96625e12 | 0.124516 | 0.0622579 | − | 0.998060i | \(-0.480170\pi\) | ||||
0.0622579 | + | 0.998060i | \(0.480170\pi\) | |||||||
\(858\) | −5.33139e11 | −0.0335852 | ||||||||
\(859\) | 9.30080e12 | 0.582842 | 0.291421 | − | 0.956595i | \(-0.405872\pi\) | ||||
0.291421 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(860\) | −4.88898e11 | −0.0304772 | ||||||||
\(861\) | −2.69814e12 | −0.167321 | ||||||||
\(862\) | −1.32713e13 | −0.818713 | ||||||||
\(863\) | 1.38352e13 | 0.849059 | 0.424530 | − | 0.905414i | \(-0.360439\pi\) | ||||
0.424530 | + | 0.905414i | \(0.360439\pi\) | |||||||
\(864\) | 2.79070e12 | 0.170373 | ||||||||
\(865\) | −6.57730e11 | −0.0399462 | ||||||||
\(866\) | −1.84995e13 | −1.11771 | ||||||||
\(867\) | 5.40648e12 | 0.324959 | ||||||||
\(868\) | −1.25084e12 | −0.0747934 | ||||||||
\(869\) | −3.04498e12 | −0.181132 | ||||||||
\(870\) | 4.96061e10 | 0.00293561 | ||||||||
\(871\) | 2.03242e13 | 1.19655 | ||||||||
\(872\) | 1.57370e13 | 0.921715 | ||||||||
\(873\) | 9.05340e12 | 0.527531 | ||||||||
\(874\) | −4.52976e10 | −0.00262587 | ||||||||
\(875\) | −1.13422e12 | −0.0654126 | ||||||||
\(876\) | 3.40067e12 | 0.195117 | ||||||||
\(877\) | −5.14801e11 | −0.0293860 | −0.0146930 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146930 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(878\) | 7.02872e12 | 0.399164 | ||||||||
\(879\) | 1.44123e13 | 0.814301 | ||||||||
\(880\) | −2.22335e10 | −0.00124979 | ||||||||
\(881\) | −1.48523e13 | −0.830621 | −0.415310 | − | 0.909680i | \(-0.636327\pi\) | ||||
−0.415310 | + | 0.909680i | \(0.636327\pi\) | |||||||
\(882\) | −1.85851e12 | −0.103409 | ||||||||
\(883\) | 7.61722e12 | 0.421671 | 0.210835 | − | 0.977522i | \(-0.432382\pi\) | ||||
0.210835 | + | 0.977522i | \(0.432382\pi\) | |||||||
\(884\) | 8.11821e12 | 0.447121 | ||||||||
\(885\) | 5.99667e10 | 0.00328598 | ||||||||
\(886\) | −1.14146e13 | −0.622311 | ||||||||
\(887\) | −1.19196e13 | −0.646556 | −0.323278 | − | 0.946304i | \(-0.604785\pi\) | ||||
−0.323278 | + | 0.946304i | \(0.604785\pi\) | |||||||
\(888\) | 1.31328e13 | 0.708757 | ||||||||
\(889\) | 8.03311e12 | 0.431346 | ||||||||
\(890\) | −3.65299e11 | −0.0195161 | ||||||||
\(891\) | 2.41218e11 | 0.0128221 | ||||||||
\(892\) | −4.34279e12 | −0.229682 | ||||||||
\(893\) | 5.13653e12 | 0.270295 | ||||||||
\(894\) | −3.77719e12 | −0.197765 | ||||||||
\(895\) | −2.86595e11 | −0.0149302 | ||||||||
\(896\) | −3.88153e12 | −0.201195 | ||||||||
\(897\) | −2.34865e10 | −0.00121130 | ||||||||
\(898\) | −2.30701e13 | −1.18388 | ||||||||
\(899\) | 6.42760e11 | 0.0328194 | ||||||||
\(900\) | 3.28165e12 | 0.166725 | ||||||||
\(901\) | −4.34351e13 | −2.19573 | ||||||||
\(902\) | −6.27106e11 | −0.0315436 | ||||||||
\(903\) | 1.20171e13 | 0.601455 | ||||||||
\(904\) | −3.48632e12 | −0.173624 | ||||||||
\(905\) | 4.26092e11 | 0.0211147 | ||||||||
\(906\) | 1.03730e13 | 0.511480 | ||||||||
\(907\) | 8.17267e12 | 0.400988 | 0.200494 | − | 0.979695i | \(-0.435745\pi\) | ||||
0.200494 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(908\) | −2.01613e13 | −0.984311 | ||||||||
\(909\) | 5.00568e12 | 0.243179 | ||||||||
\(910\) | −3.41380e11 | −0.0165026 | ||||||||
\(911\) | −3.55337e12 | −0.170926 | −0.0854630 | − | 0.996341i | \(-0.527237\pi\) | ||||
−0.0854630 | + | 0.996341i | \(0.527237\pi\) | |||||||
\(912\) | 3.77901e12 | 0.180885 | ||||||||
\(913\) | 3.16067e12 | 0.150543 | ||||||||
\(914\) | 1.48745e13 | 0.704992 | ||||||||
\(915\) | −2.44779e11 | −0.0115446 | ||||||||
\(916\) | 1.07658e13 | 0.505264 | ||||||||
\(917\) | −1.72584e13 | −0.806007 | ||||||||
\(918\) | 3.65645e12 | 0.169929 | ||||||||
\(919\) | −2.00027e12 | −0.0925060 | −0.0462530 | − | 0.998930i | \(-0.514728\pi\) | ||||
−0.0462530 | + | 0.998930i | \(0.514728\pi\) | |||||||
\(920\) | −2.96080e9 | −0.000136259 0 | ||||||||
\(921\) | 2.40948e13 | 1.10346 | ||||||||
\(922\) | −6.66617e12 | −0.303799 | ||||||||
\(923\) | 1.55922e13 | 0.707130 | ||||||||
\(924\) | −5.54006e11 | −0.0250029 | ||||||||
\(925\) | 2.57308e13 | 1.15562 | ||||||||
\(926\) | 1.11514e13 | 0.498401 | ||||||||
\(927\) | −1.13996e13 | −0.507026 | ||||||||
\(928\) | 3.29355e12 | 0.145780 | ||||||||
\(929\) | 1.77193e13 | 0.780507 | 0.390253 | − | 0.920707i | \(-0.372387\pi\) | ||||
0.390253 | + | 0.920707i | \(0.372387\pi\) | |||||||
\(930\) | 8.10535e10 | 0.00355303 | ||||||||
\(931\) | 1.27333e13 | 0.555479 | ||||||||
\(932\) | 7.75146e12 | 0.336521 | ||||||||
\(933\) | 1.48138e13 | 0.640030 | ||||||||
\(934\) | 1.72332e13 | 0.740977 | ||||||||
\(935\) | 1.47389e11 | 0.00630685 | ||||||||
\(936\) | 5.92304e12 | 0.252234 | ||||||||
\(937\) | 2.49060e13 | 1.05554 | 0.527771 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527771 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(938\) | −2.10241e13 | −0.886759 | ||||||||
\(939\) | 6.88018e12 | 0.288805 | ||||||||
\(940\) | 1.12082e11 | 0.00468233 | ||||||||
\(941\) | −3.15204e13 | −1.31050 | −0.655252 | − | 0.755410i | \(-0.727438\pi\) | ||||
−0.655252 | + | 0.755410i | \(0.727438\pi\) | |||||||
\(942\) | −6.14409e12 | −0.254231 | ||||||||
\(943\) | −2.76261e10 | −0.00113767 | ||||||||
\(944\) | −7.86917e11 | −0.0322519 | ||||||||
\(945\) | 1.54457e11 | 0.00630035 | ||||||||
\(946\) | 2.79302e12 | 0.113387 | ||||||||
\(947\) | −3.38266e13 | −1.36673 | −0.683367 | − | 0.730075i | \(-0.739485\pi\) | ||||
−0.683367 | + | 0.730075i | \(0.739485\pi\) | |||||||
\(948\) | 1.12934e13 | 0.454136 | ||||||||
\(949\) | 1.20258e13 | 0.481301 | ||||||||
\(950\) | 2.23820e13 | 0.891544 | ||||||||
\(951\) | −1.85691e13 | −0.736171 | ||||||||
\(952\) | −2.51553e13 | −0.992577 | ||||||||
\(953\) | 1.17005e13 | 0.459503 | 0.229751 | − | 0.973249i | \(-0.426209\pi\) | ||||
0.229751 | + | 0.973249i | \(0.426209\pi\) | |||||||
\(954\) | −1.05794e13 | −0.413515 | ||||||||
\(955\) | −1.08120e12 | −0.0420621 | ||||||||
\(956\) | −1.59630e13 | −0.618094 | ||||||||
\(957\) | 2.84683e11 | 0.0109713 | ||||||||
\(958\) | −3.57695e12 | −0.137204 | ||||||||
\(959\) | 2.80095e13 | 1.06935 | ||||||||
\(960\) | 5.79872e11 | 0.0220349 | ||||||||
\(961\) | −2.53894e13 | −0.960278 | ||||||||
\(962\) | 1.55039e13 | 0.583650 | ||||||||
\(963\) | −6.11769e12 | −0.229229 | ||||||||
\(964\) | −3.88140e12 | −0.144758 | ||||||||
\(965\) | −1.14088e12 | −0.0423515 | ||||||||
\(966\) | 2.42954e10 | 0.000897690 0 | ||||||||
\(967\) | 5.41005e13 | 1.98968 | 0.994838 | − | 0.101475i | \(-0.0323563\pi\) | ||||
0.994838 | + | 0.101475i | \(0.0323563\pi\) | |||||||
\(968\) | 2.85778e13 | 1.04614 | ||||||||
\(969\) | −2.50516e13 | −0.912807 | ||||||||
\(970\) | 1.34737e12 | 0.0488667 | ||||||||
\(971\) | 1.68712e12 | 0.0609059 | 0.0304529 | − | 0.999536i | \(-0.490305\pi\) | ||||
0.0304529 | + | 0.999536i | \(0.490305\pi\) | |||||||
\(972\) | −8.94641e11 | −0.0321477 | ||||||||
\(973\) | −1.14756e13 | −0.410457 | ||||||||
\(974\) | 1.11941e13 | 0.398542 | ||||||||
\(975\) | 1.16049e13 | 0.411265 | ||||||||
\(976\) | 3.21213e12 | 0.113310 | ||||||||
\(977\) | −9.67341e12 | −0.339668 | −0.169834 | − | 0.985473i | \(-0.554323\pi\) | ||||
−0.169834 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(978\) | 9.84188e12 | 0.343996 | ||||||||
\(979\) | −2.09640e12 | −0.0729376 | ||||||||
\(980\) | 2.77849e11 | 0.00962260 | ||||||||
\(981\) | −8.40571e12 | −0.289777 | ||||||||
\(982\) | 1.22818e13 | 0.421465 | ||||||||
\(983\) | 3.21482e13 | 1.09816 | 0.549080 | − | 0.835770i | \(-0.314978\pi\) | ||||
0.549080 | + | 0.835770i | \(0.314978\pi\) | |||||||
\(984\) | 6.96700e12 | 0.236901 | ||||||||
\(985\) | 2.21858e12 | 0.0750952 | ||||||||
\(986\) | 4.31530e12 | 0.145400 | ||||||||
\(987\) | −2.75498e12 | −0.0924039 | ||||||||
\(988\) | −1.35474e13 | −0.452323 | ||||||||
\(989\) | 1.23042e11 | 0.00408949 | ||||||||
\(990\) | 3.58991e10 | 0.00118775 | ||||||||
\(991\) | −3.41521e13 | −1.12483 | −0.562413 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562413 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(992\) | 5.38146e12 | 0.176440 | ||||||||
\(993\) | 3.08007e13 | 1.00529 | ||||||||
\(994\) | −1.61291e13 | −0.524050 | ||||||||
\(995\) | −3.63723e11 | −0.0117643 | ||||||||
\(996\) | −1.17225e13 | −0.377443 | ||||||||
\(997\) | 3.99927e13 | 1.28190 | 0.640948 | − | 0.767584i | \(-0.278541\pi\) | ||||
0.640948 | + | 0.767584i | \(0.278541\pi\) | |||||||
\(998\) | 3.63476e13 | 1.15981 | ||||||||
\(999\) | −7.01471e12 | −0.222825 |
(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 | 177.10.a.a.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.15 | ✓ | 21 | 1.1 | even | 1 | trivial |