Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,10,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(12.8758959041\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 652x + 4000 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.48955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.2014 | −0.892785 | −0.446393 | − | 0.894837i | \(-0.647291\pi\) | ||||
−0.446393 | + | 0.894837i | \(0.647291\pi\) | |||||||
\(3\) | 30.5073 | 0.217449 | 0.108725 | − | 0.994072i | \(-0.465323\pi\) | ||||
0.108725 | + | 0.994072i | \(0.465323\pi\) | |||||||
\(4\) | −103.903 | −0.202935 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −616.291 | −0.194136 | ||||||||
\(7\) | −4010.25 | −0.631292 | −0.315646 | − | 0.948877i | \(-0.602221\pi\) | ||||
−0.315646 | + | 0.948877i | \(0.602221\pi\) | |||||||
\(8\) | 12442.1 | 1.07396 | ||||||||
\(9\) | −18752.3 | −0.952716 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42110.0 | −0.867198 | −0.433599 | − | 0.901106i | \(-0.642757\pi\) | ||||
−0.433599 | + | 0.901106i | \(0.642757\pi\) | |||||||
\(12\) | −3169.79 | −0.0441281 | ||||||||
\(13\) | 123743. | 1.20165 | 0.600824 | − | 0.799382i | \(-0.294839\pi\) | ||||
0.600824 | + | 0.799382i | \(0.294839\pi\) | |||||||
\(14\) | 81012.8 | 0.563608 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −198150. | −0.755883 | ||||||||
\(17\) | 319945. | 0.929085 | 0.464543 | − | 0.885551i | \(-0.346219\pi\) | ||||
0.464543 | + | 0.885551i | \(0.346219\pi\) | |||||||
\(18\) | 378823. | 0.850570 | ||||||||
\(19\) | 1.08733e6 | 1.91412 | 0.957059 | − | 0.289893i | \(-0.0936197\pi\) | ||||
0.957059 | + | 0.289893i | \(0.0936197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −122342. | −0.137274 | ||||||||
\(22\) | 850682. | 0.774221 | ||||||||
\(23\) | 1.50672e6 | 1.12268 | 0.561341 | − | 0.827585i | \(-0.310286\pi\) | ||||
0.561341 | + | 0.827585i | \(0.310286\pi\) | |||||||
\(24\) | 379575. | 0.233532 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.49979e6 | −1.07281 | ||||||||
\(27\) | −1.17256e6 | −0.424617 | ||||||||
\(28\) | 416676. | 0.128111 | ||||||||
\(29\) | −2.62160e6 | −0.688295 | −0.344148 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344148 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27023e6 | 0.635991 | 0.317996 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317996 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(32\) | −2.36745e6 | −0.399122 | ||||||||
\(33\) | −1.28466e6 | −0.188572 | ||||||||
\(34\) | −6.46335e6 | −0.829473 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94841e6 | 0.193339 | ||||||||
\(37\) | −2.51034e6 | −0.220204 | −0.110102 | − | 0.993920i | \(-0.535118\pi\) | ||||
−0.110102 | + | 0.993920i | \(0.535118\pi\) | |||||||
\(38\) | −2.19655e7 | −1.70890 | ||||||||
\(39\) | 3.77508e6 | 0.261297 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.95349e7 | 1.63233 | 0.816165 | − | 0.577819i | \(-0.196096\pi\) | ||||
0.816165 | + | 0.577819i | \(0.196096\pi\) | |||||||
\(42\) | 2.47148e6 | 0.122556 | ||||||||
\(43\) | −1.42413e7 | −0.635244 | −0.317622 | − | 0.948217i | \(-0.602884\pi\) | ||||
−0.317622 | + | 0.948217i | \(0.602884\pi\) | |||||||
\(44\) | 4.37534e6 | 0.175985 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.04378e7 | −1.00231 | ||||||||
\(47\) | 1.35318e6 | 0.0404496 | 0.0202248 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202248 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(48\) | −6.04503e6 | −0.164366 | ||||||||
\(49\) | −2.42715e7 | −0.601470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.76067e6 | 0.202029 | ||||||||
\(52\) | −1.28573e7 | −0.243856 | ||||||||
\(53\) | 9.73342e7 | 1.69443 | 0.847216 | − | 0.531249i | \(-0.178277\pi\) | ||||
0.847216 | + | 0.531249i | \(0.178277\pi\) | |||||||
\(54\) | 2.36873e7 | 0.379092 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.98960e7 | −0.677984 | ||||||||
\(57\) | 3.31714e7 | 0.416224 | ||||||||
\(58\) | 5.29599e7 | 0.614500 | ||||||||
\(59\) | −7.48924e6 | −0.0804644 | −0.0402322 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402322 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.11752e7 | −0.843126 | −0.421563 | − | 0.906799i | \(-0.638518\pi\) | ||||
−0.421563 | + | 0.906799i | \(0.638518\pi\) | |||||||
\(62\) | −6.60633e7 | −0.567803 | ||||||||
\(63\) | 7.52015e7 | 0.601442 | ||||||||
\(64\) | 1.49279e8 | 1.11221 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.59520e7 | 0.168354 | ||||||||
\(67\) | 2.94376e8 | 1.78470 | 0.892350 | − | 0.451344i | \(-0.149055\pi\) | ||||
0.892350 | + | 0.451344i | \(0.149055\pi\) | |||||||
\(68\) | −3.32432e7 | −0.188544 | ||||||||
\(69\) | 4.59659e7 | 0.244127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.56193e8 | 0.729455 | 0.364728 | − | 0.931114i | \(-0.381162\pi\) | ||||
0.364728 | + | 0.931114i | \(0.381162\pi\) | |||||||
\(72\) | −2.33318e8 | −1.02318 | ||||||||
\(73\) | −2.82539e8 | −1.16446 | −0.582232 | − | 0.813023i | \(-0.697820\pi\) | ||||
−0.582232 | + | 0.813023i | \(0.697820\pi\) | |||||||
\(74\) | 5.07124e7 | 0.196594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12976e8 | −0.388441 | ||||||||
\(77\) | 1.68872e8 | 0.547455 | ||||||||
\(78\) | −7.62619e7 | −0.233282 | ||||||||
\(79\) | −5.55294e8 | −1.60399 | −0.801994 | − | 0.597332i | \(-0.796228\pi\) | ||||
−0.801994 | + | 0.597332i | \(0.796228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.33330e8 | 0.860383 | ||||||||
\(82\) | −5.96647e8 | −1.45732 | ||||||||
\(83\) | 6.48378e6 | 0.0149960 | 0.00749802 | − | 0.999972i | \(-0.497613\pi\) | ||||
0.00749802 | + | 0.999972i | \(0.497613\pi\) | |||||||
\(84\) | 1.27117e7 | 0.0278577 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.87694e8 | 0.567137 | ||||||||
\(87\) | −7.99778e7 | −0.149669 | ||||||||
\(88\) | −5.23937e8 | −0.931338 | ||||||||
\(89\) | −5.99001e8 | −1.01198 | −0.505990 | − | 0.862539i | \(-0.668873\pi\) | ||||
−0.505990 | + | 0.862539i | \(0.668873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.96242e8 | −0.758591 | ||||||||
\(92\) | −1.56552e8 | −0.227831 | ||||||||
\(93\) | 9.97660e7 | 0.138296 | ||||||||
\(94\) | −2.73361e7 | −0.0361128 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.22244e7 | −0.0867887 | ||||||||
\(97\) | 9.25317e8 | 1.06125 | 0.530625 | − | 0.847606i | \(-0.321957\pi\) | ||||
0.530625 | + | 0.847606i | \(0.321957\pi\) | |||||||
\(98\) | 4.90319e8 | 0.536984 | ||||||||
\(99\) | 7.89660e8 | 0.826193 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.58959e8 | 0.916967 | 0.458483 | − | 0.888703i | \(-0.348393\pi\) | ||||
0.458483 | + | 0.888703i | \(0.348393\pi\) | |||||||
\(102\) | −1.97179e8 | −0.180368 | ||||||||
\(103\) | 1.60441e8 | 0.140458 | 0.0702292 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702292 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(104\) | 1.53963e9 | 1.29052 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.96629e9 | −1.51276 | ||||||||
\(107\) | 9.60457e8 | 0.708355 | 0.354178 | − | 0.935178i | \(-0.384761\pi\) | ||||
0.354178 | + | 0.935178i | \(0.384761\pi\) | |||||||
\(108\) | 1.21832e8 | 0.0861696 | ||||||||
\(109\) | 9.98912e8 | 0.677810 | 0.338905 | − | 0.940821i | \(-0.389943\pi\) | ||||
0.338905 | + | 0.940821i | \(0.389943\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.65836e7 | −0.0478831 | ||||||||
\(112\) | 7.94632e8 | 0.477183 | ||||||||
\(113\) | 2.50705e9 | 1.44647 | 0.723236 | − | 0.690601i | \(-0.242654\pi\) | ||||
0.723236 | + | 0.690601i | \(0.242654\pi\) | |||||||
\(114\) | −6.70109e8 | −0.371598 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.72391e8 | 0.139679 | ||||||||
\(117\) | −2.32047e9 | −1.14483 | ||||||||
\(118\) | 1.51293e8 | 0.0718374 | ||||||||
\(119\) | −1.28306e9 | −0.586524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.84695e8 | −0.247968 | ||||||||
\(122\) | 1.84187e9 | 0.752730 | ||||||||
\(123\) | 9.01030e8 | 0.354949 | ||||||||
\(124\) | −3.39786e8 | −0.129065 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.51918e9 | −0.536958 | ||||||||
\(127\) | −2.47541e9 | −0.844364 | −0.422182 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422182 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(128\) | −1.80351e9 | −0.593845 | ||||||||
\(129\) | −4.34463e8 | −0.138134 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.92402e9 | 0.570808 | 0.285404 | − | 0.958407i | \(-0.407872\pi\) | ||||
0.285404 | + | 0.958407i | \(0.407872\pi\) | |||||||
\(132\) | 1.33480e8 | 0.0382678 | ||||||||
\(133\) | −4.36045e9 | −1.20837 | ||||||||
\(134\) | −5.94680e9 | −1.59335 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.98079e9 | 0.997802 | ||||||||
\(137\) | 4.48594e8 | 0.108796 | 0.0543978 | − | 0.998519i | \(-0.482676\pi\) | ||||
0.0543978 | + | 0.998519i | \(0.482676\pi\) | |||||||
\(138\) | −9.28577e8 | −0.217953 | ||||||||
\(139\) | 4.48415e9 | 1.01886 | 0.509429 | − | 0.860513i | \(-0.329857\pi\) | ||||
0.509429 | + | 0.860513i | \(0.329857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.12818e7 | 0.00879575 | ||||||||
\(142\) | −3.15532e9 | −0.651247 | ||||||||
\(143\) | −5.21084e9 | −1.04207 | ||||||||
\(144\) | 3.71577e9 | 0.720141 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.70769e9 | 1.03962 | ||||||||
\(147\) | −7.40458e8 | −0.130789 | ||||||||
\(148\) | 2.60831e8 | 0.0446870 | ||||||||
\(149\) | −2.20480e9 | −0.366463 | −0.183232 | − | 0.983070i | \(-0.558656\pi\) | ||||
−0.183232 | + | 0.983070i | \(0.558656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.21248e9 | −0.502857 | −0.251428 | − | 0.967876i | \(-0.580900\pi\) | ||||
−0.251428 | + | 0.967876i | \(0.580900\pi\) | |||||||
\(152\) | 1.35286e10 | 2.05569 | ||||||||
\(153\) | −5.99971e9 | −0.885154 | ||||||||
\(154\) | −3.41145e9 | −0.488760 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.92241e8 | −0.0530264 | ||||||||
\(157\) | −1.08870e10 | −1.43007 | −0.715036 | − | 0.699088i | \(-0.753590\pi\) | ||||
−0.715036 | + | 0.699088i | \(0.753590\pi\) | |||||||
\(158\) | 1.12177e10 | 1.43202 | ||||||||
\(159\) | 2.96940e9 | 0.368453 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.04232e9 | −0.708740 | ||||||||
\(162\) | −6.73374e9 | −0.768137 | ||||||||
\(163\) | 1.19994e10 | 1.33142 | 0.665708 | − | 0.746212i | \(-0.268130\pi\) | ||||
0.665708 | + | 0.746212i | \(0.268130\pi\) | |||||||
\(164\) | −3.06875e9 | −0.331257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.30982e8 | −0.0133882 | ||||||||
\(167\) | 9.68608e9 | 0.963660 | 0.481830 | − | 0.876265i | \(-0.339972\pi\) | ||||
0.481830 | + | 0.876265i | \(0.339972\pi\) | |||||||
\(168\) | −1.52219e9 | −0.147427 | ||||||||
\(169\) | 4.70793e9 | 0.443956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.03899e10 | −1.82361 | ||||||||
\(172\) | 1.47971e9 | 0.128913 | ||||||||
\(173\) | 7.35665e9 | 0.624414 | 0.312207 | − | 0.950014i | \(-0.398932\pi\) | ||||
0.312207 | + | 0.950014i | \(0.398932\pi\) | |||||||
\(174\) | 1.61567e9 | 0.133623 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.34410e9 | 0.655500 | ||||||||
\(177\) | −2.28477e8 | −0.0174969 | ||||||||
\(178\) | 1.21007e10 | 0.903481 | ||||||||
\(179\) | −2.00351e9 | −0.145866 | −0.0729329 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729329 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.63414e9 | 0.390188 | 0.195094 | − | 0.980785i | \(-0.437499\pi\) | ||||
0.195094 | + | 0.980785i | \(0.437499\pi\) | |||||||
\(182\) | 1.00248e10 | 0.677258 | ||||||||
\(183\) | −2.78151e9 | −0.183337 | ||||||||
\(184\) | 1.87467e10 | 1.20572 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.01541e9 | −0.123469 | ||||||||
\(187\) | −1.34729e10 | −0.805701 | ||||||||
\(188\) | −1.40599e8 | −0.00820864 | ||||||||
\(189\) | 4.70225e9 | 0.268057 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.16925e9 | 0.498521 | 0.249261 | − | 0.968436i | \(-0.419812\pi\) | ||||
0.249261 | + | 0.968436i | \(0.419812\pi\) | |||||||
\(192\) | 4.55409e9 | 0.241850 | ||||||||
\(193\) | −3.16327e10 | −1.64107 | −0.820536 | − | 0.571594i | \(-0.806325\pi\) | ||||
−0.820536 | + | 0.571594i | \(0.806325\pi\) | |||||||
\(194\) | −1.86927e10 | −0.947469 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.52187e9 | 0.122059 | ||||||||
\(197\) | 2.59858e10 | 1.22924 | 0.614621 | − | 0.788822i | \(-0.289309\pi\) | ||||
0.614621 | + | 0.788822i | \(0.289309\pi\) | |||||||
\(198\) | −1.59522e10 | −0.737613 | ||||||||
\(199\) | 1.05766e10 | 0.478088 | 0.239044 | − | 0.971009i | \(-0.423166\pi\) | ||||
0.239044 | + | 0.971009i | \(0.423166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.98061e9 | 0.388082 | ||||||||
\(202\) | −1.93723e10 | −0.818654 | ||||||||
\(203\) | 1.05133e10 | 0.434515 | ||||||||
\(204\) | −1.01416e9 | −0.0409987 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.24113e9 | −0.125399 | ||||||||
\(207\) | −2.82544e10 | −1.06960 | ||||||||
\(208\) | −2.45198e10 | −0.908304 | ||||||||
\(209\) | −4.57873e10 | −1.65992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.80228e10 | 0.625965 | 0.312983 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312983 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(212\) | −1.01133e10 | −0.343859 | ||||||||
\(213\) | 4.76502e9 | 0.158620 | ||||||||
\(214\) | −1.94026e10 | −0.632409 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.45891e10 | −0.456023 | ||||||||
\(217\) | −1.31145e10 | −0.401496 | ||||||||
\(218\) | −2.01794e10 | −0.605139 | ||||||||
\(219\) | −8.61951e9 | −0.253212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.95911e10 | 1.11643 | ||||||||
\(222\) | 1.54710e9 | 0.0427493 | ||||||||
\(223\) | 4.44522e10 | 1.20371 | 0.601855 | − | 0.798606i | \(-0.294429\pi\) | ||||
0.601855 | + | 0.798606i | \(0.294429\pi\) | |||||||
\(224\) | 9.49405e9 | 0.251962 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.06460e10 | −1.29139 | ||||||||
\(227\) | 5.59677e10 | 1.39901 | 0.699505 | − | 0.714627i | \(-0.253404\pi\) | ||||
0.699505 | + | 0.714627i | \(0.253404\pi\) | |||||||
\(228\) | −3.44660e9 | −0.0844663 | ||||||||
\(229\) | −1.47705e9 | −0.0354923 | −0.0177462 | − | 0.999843i | \(-0.505649\pi\) | ||||
−0.0177462 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.15182e9 | 0.119044 | ||||||||
\(232\) | −3.26182e10 | −0.739203 | ||||||||
\(233\) | −7.83279e9 | −0.174106 | −0.0870532 | − | 0.996204i | \(-0.527745\pi\) | ||||
−0.0870532 | + | 0.996204i | \(0.527745\pi\) | |||||||
\(234\) | 4.68769e10 | 1.02209 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.78152e8 | 0.0163290 | ||||||||
\(237\) | −1.69405e10 | −0.348786 | ||||||||
\(238\) | 2.59197e10 | 0.523640 | ||||||||
\(239\) | 5.56371e10 | 1.10300 | 0.551498 | − | 0.834176i | \(-0.314057\pi\) | ||||
0.551498 | + | 0.834176i | \(0.314057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.16053e10 | −0.221606 | −0.110803 | − | 0.993842i | \(-0.535342\pi\) | ||||
−0.110803 | + | 0.993842i | \(0.535342\pi\) | |||||||
\(242\) | 1.18117e10 | 0.221382 | ||||||||
\(243\) | 3.32485e10 | 0.611707 | ||||||||
\(244\) | 9.47334e9 | 0.171100 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.82021e10 | −0.316893 | ||||||||
\(247\) | 1.34549e11 | 2.30009 | ||||||||
\(248\) | 4.06886e10 | 0.683030 | ||||||||
\(249\) | 1.97803e8 | 0.00326088 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.45974e10 | −0.550189 | −0.275094 | − | 0.961417i | \(-0.588709\pi\) | ||||
−0.275094 | + | 0.961417i | \(0.588709\pi\) | |||||||
\(252\) | −7.81363e9 | −0.122054 | ||||||||
\(253\) | −6.34479e10 | −0.973587 | ||||||||
\(254\) | 5.00067e10 | 0.753836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.99972e10 | −0.582036 | ||||||||
\(257\) | −3.67735e10 | −0.525818 | −0.262909 | − | 0.964821i | \(-0.584682\pi\) | ||||
−0.262909 | + | 0.964821i | \(0.584682\pi\) | |||||||
\(258\) | 8.77677e9 | 0.123324 | ||||||||
\(259\) | 1.00671e10 | 0.139013 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.91609e10 | 0.655750 | ||||||||
\(262\) | −3.88680e10 | −0.509609 | ||||||||
\(263\) | 1.33758e11 | 1.72392 | 0.861962 | − | 0.506974i | \(-0.169236\pi\) | ||||
0.861962 | + | 0.506974i | \(0.169236\pi\) | |||||||
\(264\) | −1.59839e10 | −0.202519 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.80873e10 | 1.07881 | ||||||||
\(267\) | −1.82739e10 | −0.220055 | ||||||||
\(268\) | −3.05864e10 | −0.362178 | ||||||||
\(269\) | −1.42461e11 | −1.65886 | −0.829429 | − | 0.558612i | \(-0.811334\pi\) | ||||
−0.829429 | + | 0.558612i | \(0.811334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.11046e11 | −1.25067 | −0.625333 | − | 0.780358i | \(-0.715037\pi\) | ||||
−0.625333 | + | 0.780358i | \(0.715037\pi\) | |||||||
\(272\) | −6.33972e10 | −0.702279 | ||||||||
\(273\) | −1.51390e10 | −0.164955 | ||||||||
\(274\) | −9.06224e9 | −0.0971310 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.77598e9 | −0.0495418 | ||||||||
\(277\) | 2.80726e10 | 0.286500 | 0.143250 | − | 0.989687i | \(-0.454245\pi\) | ||||
0.143250 | + | 0.989687i | \(0.454245\pi\) | |||||||
\(278\) | −9.05861e10 | −0.909620 | ||||||||
\(279\) | −6.13244e10 | −0.605919 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.47143e10 | 0.523507 | 0.261753 | − | 0.965135i | \(-0.415699\pi\) | ||||
0.261753 | + | 0.965135i | \(0.415699\pi\) | |||||||
\(282\) | −8.33951e8 | −0.00785271 | ||||||||
\(283\) | −1.09950e11 | −1.01895 | −0.509477 | − | 0.860484i | \(-0.670161\pi\) | ||||
−0.509477 | + | 0.860484i | \(0.670161\pi\) | |||||||
\(284\) | −1.62288e10 | −0.148032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05266e11 | 0.930341 | ||||||||
\(287\) | −1.18442e11 | −1.03048 | ||||||||
\(288\) | 4.43951e10 | 0.380249 | ||||||||
\(289\) | −1.62229e10 | −0.136801 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82289e10 | 0.230768 | ||||||||
\(292\) | 2.93566e10 | 0.236310 | ||||||||
\(293\) | −2.30453e11 | −1.82675 | −0.913373 | − | 0.407124i | \(-0.866532\pi\) | ||||
−0.913373 | + | 0.407124i | \(0.866532\pi\) | |||||||
\(294\) | 1.49583e10 | 0.116767 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.12339e10 | −0.236490 | ||||||||
\(297\) | 4.93764e10 | 0.368227 | ||||||||
\(298\) | 4.45400e10 | 0.327173 | ||||||||
\(299\) | 1.86446e11 | 1.34907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.71111e10 | 0.401025 | ||||||||
\(302\) | 6.48966e10 | 0.448943 | ||||||||
\(303\) | 2.92552e10 | 0.199394 | ||||||||
\(304\) | −2.15454e11 | −1.44685 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.21203e11 | 0.790252 | ||||||||
\(307\) | 6.85036e10 | 0.440140 | 0.220070 | − | 0.975484i | \(-0.429371\pi\) | ||||
0.220070 | + | 0.975484i | \(0.429371\pi\) | |||||||
\(308\) | −1.75462e10 | −0.111098 | ||||||||
\(309\) | 4.89462e9 | 0.0305426 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.98797e11 | −1.20500 | −0.602502 | − | 0.798118i | \(-0.705829\pi\) | ||||
−0.602502 | + | 0.798118i | \(0.705829\pi\) | |||||||
\(312\) | 4.69699e10 | 0.280624 | ||||||||
\(313\) | −6.15202e10 | −0.362300 | −0.181150 | − | 0.983455i | \(-0.557982\pi\) | ||||
−0.181150 | + | 0.983455i | \(0.557982\pi\) | |||||||
\(314\) | 2.19932e11 | 1.27675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.76965e10 | 0.325505 | ||||||||
\(317\) | −2.25932e11 | −1.25664 | −0.628320 | − | 0.777955i | \(-0.716257\pi\) | ||||
−0.628320 | + | 0.777955i | \(0.716257\pi\) | |||||||
\(318\) | −5.99862e10 | −0.328950 | ||||||||
\(319\) | 1.10395e11 | 0.596888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.93010e10 | 0.154031 | ||||||||
\(322\) | 1.22063e11 | 0.632753 | ||||||||
\(323\) | 3.47885e11 | 1.77838 | ||||||||
\(324\) | −3.46339e10 | −0.174602 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.42404e11 | −1.18867 | ||||||||
\(327\) | 3.04741e10 | 0.147389 | ||||||||
\(328\) | 3.67476e11 | 1.75306 | ||||||||
\(329\) | −5.42658e9 | −0.0255355 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.38825e10 | −0.384101 | −0.192050 | − | 0.981385i | \(-0.561514\pi\) | ||||
−0.192050 | + | 0.981385i | \(0.561514\pi\) | |||||||
\(332\) | −6.73682e8 | −0.00304322 | ||||||||
\(333\) | 4.70746e10 | 0.209791 | ||||||||
\(334\) | −1.95673e11 | −0.860341 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.42421e10 | 0.103763 | ||||||||
\(337\) | −2.19457e11 | −0.926862 | −0.463431 | − | 0.886133i | \(-0.653382\pi\) | ||||
−0.463431 | + | 0.886133i | \(0.653382\pi\) | |||||||
\(338\) | −9.51069e10 | −0.396357 | ||||||||
\(339\) | 7.64834e10 | 0.314535 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.37710e11 | −0.551530 | ||||||||
\(342\) | 4.11904e11 | 1.62809 | ||||||||
\(343\) | 2.59163e11 | 1.01100 | ||||||||
\(344\) | −1.77191e11 | −0.682228 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.48615e11 | −0.557467 | ||||||||
\(347\) | −1.85960e11 | −0.688551 | −0.344276 | − | 0.938869i | \(-0.611875\pi\) | ||||
−0.344276 | + | 0.938869i | \(0.611875\pi\) | |||||||
\(348\) | 8.30990e9 | 0.0303731 | ||||||||
\(349\) | 2.73237e11 | 0.985881 | 0.492940 | − | 0.870063i | \(-0.335922\pi\) | ||||
0.492940 | + | 0.870063i | \(0.335922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.45096e11 | −0.510240 | ||||||||
\(352\) | 9.96932e10 | 0.346117 | ||||||||
\(353\) | −3.02861e11 | −1.03814 | −0.519072 | − | 0.854731i | \(-0.673722\pi\) | ||||
−0.519072 | + | 0.854731i | \(0.673722\pi\) | |||||||
\(354\) | 4.61555e9 | 0.0156210 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.22378e10 | 0.205366 | ||||||||
\(357\) | −3.91427e10 | −0.127539 | ||||||||
\(358\) | 4.04738e10 | 0.130227 | ||||||||
\(359\) | 2.47660e11 | 0.786919 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.59591e11 | 2.66385 | ||||||||
\(362\) | −1.13818e11 | −0.348354 | ||||||||
\(363\) | −1.78375e10 | −0.0539205 | ||||||||
\(364\) | 5.15609e10 | 0.153944 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.61904e10 | 0.163681 | ||||||||
\(367\) | 2.66354e11 | 0.766412 | 0.383206 | − | 0.923663i | \(-0.374820\pi\) | ||||
0.383206 | + | 0.923663i | \(0.374820\pi\) | |||||||
\(368\) | −2.98556e11 | −0.848616 | ||||||||
\(369\) | −5.53847e11 | −1.55515 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.90335e11 | −1.06968 | ||||||||
\(372\) | −1.03660e10 | −0.0280651 | ||||||||
\(373\) | −5.20850e11 | −1.39323 | −0.696616 | − | 0.717445i | \(-0.745312\pi\) | ||||
−0.696616 | + | 0.717445i | \(0.745312\pi\) | |||||||
\(374\) | 2.72172e11 | 0.719318 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.68364e10 | 0.0434414 | ||||||||
\(377\) | −3.24405e11 | −0.827088 | ||||||||
\(378\) | −9.49921e10 | −0.239318 | ||||||||
\(379\) | 3.28308e10 | 0.0817344 | 0.0408672 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408672 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.55180e10 | −0.183607 | ||||||||
\(382\) | −1.85232e11 | −0.445072 | ||||||||
\(383\) | −7.15293e10 | −0.169859 | −0.0849297 | − | 0.996387i | \(-0.527067\pi\) | ||||
−0.0849297 | + | 0.996387i | \(0.527067\pi\) | |||||||
\(384\) | −5.50202e10 | −0.129131 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.39025e11 | 1.46513 | ||||||||
\(387\) | 2.67057e11 | 0.605207 | ||||||||
\(388\) | −9.61429e10 | −0.215365 | ||||||||
\(389\) | −2.02681e11 | −0.448787 | −0.224394 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224394 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82067e11 | 1.04307 | ||||||||
\(392\) | −3.01989e11 | −0.645956 | ||||||||
\(393\) | 5.86968e10 | 0.124122 | ||||||||
\(394\) | −5.24949e11 | −1.09745 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.20477e10 | −0.167663 | ||||||||
\(397\) | 1.63266e10 | 0.0329867 | 0.0164934 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164934 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(398\) | −2.13663e11 | −0.426830 | ||||||||
\(399\) | −1.33026e11 | −0.262759 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.20766e11 | −1.58515 | −0.792574 | − | 0.609776i | \(-0.791259\pi\) | ||||
−0.792574 | + | 0.609776i | \(0.791259\pi\) | |||||||
\(402\) | −1.81421e11 | −0.346474 | ||||||||
\(403\) | 4.04670e11 | 0.764237 | ||||||||
\(404\) | −9.96383e10 | −0.186085 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.12383e11 | −0.387929 | ||||||||
\(407\) | 1.05710e11 | 0.190960 | ||||||||
\(408\) | 1.21443e11 | 0.216972 | ||||||||
\(409\) | −4.24628e11 | −0.750332 | −0.375166 | − | 0.926958i | \(-0.622414\pi\) | ||||
−0.375166 | + | 0.926958i | \(0.622414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.36854e10 | 0.0236575 | ||||||||
\(412\) | −1.66702e10 | −0.0285039 | ||||||||
\(413\) | 3.00337e10 | 0.0507966 | ||||||||
\(414\) | 5.70780e11 | 0.954920 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.92956e11 | −0.479603 | ||||||||
\(417\) | 1.36799e11 | 0.221550 | ||||||||
\(418\) | 9.24969e11 | 1.48195 | ||||||||
\(419\) | −1.26375e10 | −0.0200308 | −0.0100154 | − | 0.999950i | \(-0.503188\pi\) | ||||
−0.0100154 | + | 0.999950i | \(0.503188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.04545e10 | −0.0472479 | −0.0236240 | − | 0.999721i | \(-0.507520\pi\) | ||||
−0.0236240 | + | 0.999721i | \(0.507520\pi\) | |||||||
\(422\) | −3.64085e11 | −0.558853 | ||||||||
\(423\) | −2.53752e10 | −0.0385370 | ||||||||
\(424\) | 1.21104e12 | 1.81976 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.62602e10 | −0.141613 | ||||||||
\(427\) | 3.65635e11 | 0.532259 | ||||||||
\(428\) | −9.97940e10 | −0.143750 | ||||||||
\(429\) | −1.58969e11 | −0.226597 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.05830e11 | 0.566495 | 0.283248 | − | 0.959047i | \(-0.408588\pi\) | ||||
0.283248 | + | 0.959047i | \(0.408588\pi\) | |||||||
\(432\) | 2.32342e11 | 0.320961 | ||||||||
\(433\) | 1.36978e11 | 0.187265 | 0.0936324 | − | 0.995607i | \(-0.470152\pi\) | ||||
0.0936324 | + | 0.995607i | \(0.470152\pi\) | |||||||
\(434\) | 2.64931e11 | 0.358450 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.03790e11 | −0.137551 | ||||||||
\(437\) | 1.63829e12 | 2.14895 | ||||||||
\(438\) | 1.74126e11 | 0.226064 | ||||||||
\(439\) | 7.84981e11 | 1.00872 | 0.504358 | − | 0.863495i | \(-0.331729\pi\) | ||||
0.504358 | + | 0.863495i | \(0.331729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.55146e11 | 0.573030 | ||||||||
\(442\) | −7.99797e11 | −0.996734 | ||||||||
\(443\) | 8.87799e11 | 1.09521 | 0.547605 | − | 0.836737i | \(-0.315540\pi\) | ||||
0.547605 | + | 0.836737i | \(0.315540\pi\) | |||||||
\(444\) | 7.95724e9 | 0.00971716 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.97998e11 | −1.07465 | ||||||||
\(447\) | −6.72624e10 | −0.0796872 | ||||||||
\(448\) | −5.98645e11 | −0.702131 | ||||||||
\(449\) | 8.35477e11 | 0.970122 | 0.485061 | − | 0.874480i | \(-0.338797\pi\) | ||||
0.485061 | + | 0.874480i | \(0.338797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.24371e12 | −1.41555 | ||||||||
\(452\) | −2.60489e11 | −0.293540 | ||||||||
\(453\) | −9.80041e10 | −0.109346 | ||||||||
\(454\) | −1.13063e12 | −1.24902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.12722e11 | 0.447009 | ||||||||
\(457\) | 6.01172e11 | 0.644727 | 0.322364 | − | 0.946616i | \(-0.395523\pi\) | ||||
0.322364 | + | 0.946616i | \(0.395523\pi\) | |||||||
\(458\) | 2.98384e10 | 0.0316870 | ||||||||
\(459\) | −3.75154e11 | −0.394505 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52807e12 | 1.57576 | 0.787879 | − | 0.615829i | \(-0.211179\pi\) | ||||
0.787879 | + | 0.615829i | \(0.211179\pi\) | |||||||
\(462\) | −1.04074e11 | −0.106281 | ||||||||
\(463\) | −7.80402e11 | −0.789231 | −0.394615 | − | 0.918846i | \(-0.629122\pi\) | ||||
−0.394615 | + | 0.918846i | \(0.629122\pi\) | |||||||
\(464\) | 5.19469e11 | 0.520270 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.58234e11 | 0.155440 | ||||||||
\(467\) | −4.04751e11 | −0.393788 | −0.196894 | − | 0.980425i | \(-0.563085\pi\) | ||||
−0.196894 | + | 0.980425i | \(0.563085\pi\) | |||||||
\(468\) | 2.41103e11 | 0.232326 | ||||||||
\(469\) | −1.18052e12 | −1.12667 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.32132e11 | −0.310968 | ||||||||
\(472\) | −9.31820e10 | −0.0864158 | ||||||||
\(473\) | 5.99700e11 | 0.550883 | ||||||||
\(474\) | 3.42223e11 | 0.311391 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.33313e11 | 0.119026 | ||||||||
\(477\) | −1.82524e12 | −1.61431 | ||||||||
\(478\) | −1.12395e12 | −0.984738 | ||||||||
\(479\) | −2.06972e12 | −1.79640 | −0.898199 | − | 0.439588i | \(-0.855124\pi\) | ||||
−0.898199 | + | 0.439588i | \(0.855124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.10638e11 | −0.264607 | ||||||||
\(482\) | 2.34444e11 | 0.197846 | ||||||||
\(483\) | −1.84335e11 | −0.154115 | ||||||||
\(484\) | 6.07514e10 | 0.0503213 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.71666e11 | −0.546123 | ||||||||
\(487\) | −2.41184e11 | −0.194298 | −0.0971490 | − | 0.995270i | \(-0.530972\pi\) | ||||
−0.0971490 | + | 0.995270i | \(0.530972\pi\) | |||||||
\(488\) | −1.13441e12 | −0.905485 | ||||||||
\(489\) | 3.66068e11 | 0.289516 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.27883e12 | 1.76948 | 0.884739 | − | 0.466088i | \(-0.154337\pi\) | ||||
0.884739 | + | 0.466088i | \(0.154337\pi\) | |||||||
\(492\) | −9.36194e10 | −0.0720316 | ||||||||
\(493\) | −8.38767e11 | −0.639485 | ||||||||
\(494\) | −2.71809e12 | −2.05349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.47997e11 | −0.480735 | ||||||||
\(497\) | −6.26373e11 | −0.460499 | ||||||||
\(498\) | −3.99589e9 | −0.00291127 | ||||||||
\(499\) | 9.88752e11 | 0.713896 | 0.356948 | − | 0.934124i | \(-0.383817\pi\) | ||||
0.356948 | + | 0.934124i | \(0.383817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.95496e11 | 0.209547 | ||||||||
\(502\) | 6.98916e11 | 0.491200 | ||||||||
\(503\) | 1.22385e12 | 0.852455 | 0.426228 | − | 0.904616i | \(-0.359842\pi\) | ||||
0.426228 | + | 0.904616i | \(0.359842\pi\) | |||||||
\(504\) | 9.35665e11 | 0.645926 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.28174e12 | 0.869204 | ||||||||
\(507\) | 1.43626e11 | 0.0965380 | ||||||||
\(508\) | 2.57201e11 | 0.171351 | ||||||||
\(509\) | 1.58447e12 | 1.04629 | 0.523146 | − | 0.852243i | \(-0.324758\pi\) | ||||
0.523146 | + | 0.852243i | \(0.324758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13305e12 | 0.735117 | ||||||||
\(512\) | 1.73140e12 | 1.11348 | ||||||||
\(513\) | −1.27495e12 | −0.812767 | ||||||||
\(514\) | 7.42877e11 | 0.469443 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.51418e10 | 0.0280321 | ||||||||
\(517\) | −5.69823e10 | −0.0350778 | ||||||||
\(518\) | −2.03369e11 | −0.124109 | ||||||||
\(519\) | 2.24432e11 | 0.135778 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.71561e12 | −1.61472 | −0.807362 | − | 0.590057i | \(-0.799105\pi\) | ||||
−0.807362 | + | 0.590057i | \(0.799105\pi\) | |||||||
\(522\) | −9.93121e11 | −0.585443 | ||||||||
\(523\) | −2.16171e12 | −1.26340 | −0.631698 | − | 0.775214i | \(-0.717642\pi\) | ||||
−0.631698 | + | 0.775214i | \(0.717642\pi\) | |||||||
\(524\) | −1.99911e11 | −0.115837 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.70210e12 | −1.53909 | ||||||||
\(527\) | 1.04630e12 | 0.590890 | ||||||||
\(528\) | 2.54556e11 | 0.142538 | ||||||||
\(529\) | 4.69046e11 | 0.260415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.40441e11 | 0.0766597 | ||||||||
\(532\) | 4.53062e11 | 0.245220 | ||||||||
\(533\) | 3.65475e12 | 1.96149 | ||||||||
\(534\) | 3.69159e11 | 0.196462 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.66265e12 | 1.91670 | ||||||||
\(537\) | −6.11217e10 | −0.0317184 | ||||||||
\(538\) | 2.87791e12 | 1.48100 | ||||||||
\(539\) | 1.02207e12 | 0.521594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29090e12 | −1.14979 | −0.574895 | − | 0.818227i | \(-0.694957\pi\) | ||||
−0.574895 | + | 0.818227i | \(0.694957\pi\) | |||||||
\(542\) | 2.24329e12 | 1.11658 | ||||||||
\(543\) | 1.71882e11 | 0.0848462 | ||||||||
\(544\) | −7.57453e11 | −0.370818 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.05830e11 | 0.147269 | ||||||||
\(547\) | −3.39447e12 | −1.62117 | −0.810586 | − | 0.585620i | \(-0.800851\pi\) | ||||
−0.810586 | + | 0.585620i | \(0.800851\pi\) | |||||||
\(548\) | −4.66101e10 | −0.0220784 | ||||||||
\(549\) | 1.70974e12 | 0.803259 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.85053e12 | −1.31748 | ||||||||
\(552\) | 5.71913e11 | 0.262183 | ||||||||
\(553\) | 2.22687e12 | 1.01259 | ||||||||
\(554\) | −5.67107e11 | −0.255783 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.65915e11 | −0.206762 | ||||||||
\(557\) | 1.74706e12 | 0.769060 | 0.384530 | − | 0.923113i | \(-0.374364\pi\) | ||||
0.384530 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(558\) | 1.23884e12 | 0.540955 | ||||||||
\(559\) | −1.76226e12 | −0.763340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.11022e11 | −0.175199 | ||||||||
\(562\) | −1.10531e12 | −0.467379 | ||||||||
\(563\) | −2.58864e12 | −1.08588 | −0.542942 | − | 0.839770i | \(-0.682690\pi\) | ||||
−0.542942 | + | 0.839770i | \(0.682690\pi\) | |||||||
\(564\) | −4.28929e9 | −0.00178496 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.22114e12 | 0.909707 | ||||||||
\(567\) | −1.33674e12 | −0.543153 | ||||||||
\(568\) | 1.94337e12 | 0.783407 | ||||||||
\(569\) | −1.99294e12 | −0.797055 | −0.398527 | − | 0.917156i | \(-0.630479\pi\) | ||||
−0.398527 | + | 0.917156i | \(0.630479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50761e10 | 0.0138086 | 0.00690428 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690428 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(572\) | 5.41420e11 | 0.211471 | ||||||||
\(573\) | 2.79729e11 | 0.108403 | ||||||||
\(574\) | 2.39270e12 | 0.919995 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.79932e12 | −1.05962 | ||||||||
\(577\) | −7.75900e11 | −0.291417 | −0.145708 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145708 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 3.27726e11 | 0.122134 | ||||||||
\(579\) | −9.65027e11 | −0.356850 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.60016e10 | −0.00946689 | ||||||||
\(582\) | −5.70265e11 | −0.206027 | ||||||||
\(583\) | −4.09874e12 | −1.46941 | ||||||||
\(584\) | −3.51538e12 | −1.25059 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.65548e12 | 1.63089 | ||||||||
\(587\) | 1.24477e12 | 0.432730 | 0.216365 | − | 0.976313i | \(-0.430580\pi\) | ||||
0.216365 | + | 0.976313i | \(0.430580\pi\) | |||||||
\(588\) | 7.69355e10 | 0.0265417 | ||||||||
\(589\) | 3.55581e12 | 1.21736 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.92756e11 | 0.267298 | ||||||||
\(592\) | 4.97424e11 | 0.166448 | ||||||||
\(593\) | −2.57794e11 | −0.0856103 | −0.0428052 | − | 0.999083i | \(-0.513629\pi\) | ||||
−0.0428052 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(594\) | −9.97474e11 | −0.328747 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.29084e11 | 0.0743681 | ||||||||
\(597\) | 3.22664e11 | 0.103960 | ||||||||
\(598\) | −3.76648e12 | −1.20443 | ||||||||
\(599\) | 2.32089e12 | 0.736604 | 0.368302 | − | 0.929706i | \(-0.379939\pi\) | ||||
0.368302 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78665e12 | 0.558605 | 0.279302 | − | 0.960203i | \(-0.409897\pi\) | ||||
0.279302 | + | 0.960203i | \(0.409897\pi\) | |||||||
\(602\) | −1.15373e12 | −0.358029 | ||||||||
\(603\) | −5.52022e12 | −1.70031 | ||||||||
\(604\) | 3.33785e11 | 0.102047 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.90997e11 | −0.178016 | ||||||||
\(607\) | −1.45787e12 | −0.435883 | −0.217941 | − | 0.975962i | \(-0.569934\pi\) | ||||
−0.217941 | + | 0.975962i | \(0.569934\pi\) | |||||||
\(608\) | −2.57419e12 | −0.763966 | ||||||||
\(609\) | 3.20731e11 | 0.0944851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.67447e11 | 0.0486062 | ||||||||
\(612\) | 6.23386e11 | 0.179629 | ||||||||
\(613\) | 1.42075e12 | 0.406394 | 0.203197 | − | 0.979138i | \(-0.434867\pi\) | ||||
0.203197 | + | 0.979138i | \(0.434867\pi\) | |||||||
\(614\) | −1.38387e12 | −0.392950 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.10112e12 | 0.587946 | ||||||||
\(617\) | 1.20441e12 | 0.334573 | 0.167286 | − | 0.985908i | \(-0.446500\pi\) | ||||
0.167286 | + | 0.985908i | \(0.446500\pi\) | |||||||
\(618\) | −9.88782e10 | −0.0272680 | ||||||||
\(619\) | −4.91349e12 | −1.34519 | −0.672593 | − | 0.740013i | \(-0.734819\pi\) | ||||
−0.672593 | + | 0.740013i | \(0.734819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.76671e12 | −0.476710 | ||||||||
\(622\) | 4.01598e12 | 1.07581 | ||||||||
\(623\) | 2.40214e12 | 0.638856 | ||||||||
\(624\) | −7.48032e11 | −0.197510 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.24280e12 | 0.323456 | ||||||||
\(627\) | −1.39685e12 | −0.360948 | ||||||||
\(628\) | 1.13118e12 | 0.290211 | ||||||||
\(629\) | −8.03171e11 | −0.204588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.58663e12 | 1.15176 | 0.575879 | − | 0.817535i | \(-0.304660\pi\) | ||||
0.575879 | + | 0.817535i | \(0.304660\pi\) | |||||||
\(632\) | −6.90903e12 | −1.72262 | ||||||||
\(633\) | 5.49826e11 | 0.136116 | ||||||||
\(634\) | 4.56414e12 | 1.12191 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.08529e11 | −0.0747720 | ||||||||
\(637\) | −3.00344e12 | −0.722755 | ||||||||
\(638\) | −2.23014e12 | −0.532893 | ||||||||
\(639\) | −2.92898e12 | −0.694963 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.30636e12 | −0.539593 | −0.269796 | − | 0.962917i | \(-0.586956\pi\) | ||||
−0.269796 | + | 0.962917i | \(0.586956\pi\) | |||||||
\(642\) | −5.91921e11 | −0.137517 | ||||||||
\(643\) | 2.59493e12 | 0.598654 | 0.299327 | − | 0.954151i | \(-0.403238\pi\) | ||||
0.299327 | + | 0.954151i | \(0.403238\pi\) | |||||||
\(644\) | 6.27813e11 | 0.143828 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.02777e12 | −1.58771 | ||||||||
\(647\) | 5.14811e12 | 1.15499 | 0.577495 | − | 0.816394i | \(-0.304030\pi\) | ||||
0.577495 | + | 0.816394i | \(0.304030\pi\) | |||||||
\(648\) | 4.14733e12 | 0.924019 | ||||||||
\(649\) | 3.15372e11 | 0.0697786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00087e11 | −0.0873051 | ||||||||
\(652\) | −1.24676e12 | −0.270191 | ||||||||
\(653\) | 4.42559e12 | 0.952492 | 0.476246 | − | 0.879312i | \(-0.341997\pi\) | ||||
0.476246 | + | 0.879312i | \(0.341997\pi\) | |||||||
\(654\) | −6.15621e11 | −0.131587 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.85234e12 | −1.23385 | ||||||||
\(657\) | 5.29826e12 | 1.10940 | ||||||||
\(658\) | 1.09625e11 | 0.0227977 | ||||||||
\(659\) | 1.09827e12 | 0.226842 | 0.113421 | − | 0.993547i | \(-0.463819\pi\) | ||||
0.113421 | + | 0.993547i | \(0.463819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.99232e11 | 0.162842 | 0.0814209 | − | 0.996680i | \(-0.474054\pi\) | ||||
0.0814209 | + | 0.996680i | \(0.474054\pi\) | |||||||
\(662\) | 1.69455e12 | 0.342919 | ||||||||
\(663\) | 1.20782e12 | 0.242768 | ||||||||
\(664\) | 8.06719e10 | 0.0161052 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.50974e11 | −0.187299 | ||||||||
\(667\) | −3.95000e12 | −0.772736 | ||||||||
\(668\) | −1.00641e12 | −0.195560 | ||||||||
\(669\) | 1.35612e12 | 0.261746 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.83939e12 | 0.731157 | ||||||||
\(672\) | 2.89638e11 | 0.0547891 | ||||||||
\(673\) | 7.68445e12 | 1.44393 | 0.721963 | − | 0.691931i | \(-0.243240\pi\) | ||||
0.721963 | + | 0.691931i | \(0.243240\pi\) | |||||||
\(674\) | 4.43334e12 | 0.827488 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.89167e11 | −0.0900942 | ||||||||
\(677\) | 1.28854e12 | 0.235749 | 0.117874 | − | 0.993029i | \(-0.462392\pi\) | ||||
0.117874 | + | 0.993029i | \(0.462392\pi\) | |||||||
\(678\) | −1.54507e12 | −0.280812 | ||||||||
\(679\) | −3.71076e12 | −0.669959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.70742e12 | 0.304214 | ||||||||
\(682\) | 2.78193e12 | 0.492398 | ||||||||
\(683\) | −8.11444e11 | −0.142681 | −0.0713404 | − | 0.997452i | \(-0.522728\pi\) | ||||
−0.0713404 | + | 0.997452i | \(0.522728\pi\) | |||||||
\(684\) | 2.11856e12 | 0.370074 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.23546e12 | −0.902602 | ||||||||
\(687\) | −4.50607e10 | −0.00771778 | ||||||||
\(688\) | 2.82191e12 | 0.480170 | ||||||||
\(689\) | 1.20445e13 | 2.03611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.26741e12 | 0.378338 | 0.189169 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189169 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(692\) | −7.64375e11 | −0.126715 | ||||||||
\(693\) | −3.16673e12 | −0.521569 | ||||||||
\(694\) | 3.75665e12 | 0.614728 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.95093e11 | −0.160739 | ||||||||
\(697\) | 9.44955e12 | 1.51657 | ||||||||
\(698\) | −5.51977e12 | −0.880180 | ||||||||
\(699\) | −2.38957e11 | −0.0378594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.92113e12 | −0.769721 | −0.384861 | − | 0.922975i | \(-0.625751\pi\) | ||||
−0.384861 | + | 0.922975i | \(0.625751\pi\) | |||||||
\(702\) | 2.93115e12 | 0.455534 | ||||||||
\(703\) | −2.72956e12 | −0.421496 | ||||||||
\(704\) | −6.28612e12 | −0.964508 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.11822e12 | 0.926839 | ||||||||
\(707\) | −3.84566e12 | −0.578874 | ||||||||
\(708\) | 2.37393e10 | 0.00355074 | ||||||||
\(709\) | −6.12354e12 | −0.910112 | −0.455056 | − | 0.890463i | \(-0.650381\pi\) | ||||
−0.455056 | + | 0.890463i | \(0.650381\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.04130e13 | 1.52815 | ||||||||
\(712\) | −7.45283e12 | −1.08683 | ||||||||
\(713\) | 4.92732e12 | 0.714016 | ||||||||
\(714\) | 7.90739e11 | 0.113865 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08170e11 | 0.0296012 | ||||||||
\(717\) | 1.69734e12 | 0.239846 | ||||||||
\(718\) | −5.00307e12 | −0.702550 | ||||||||
\(719\) | −2.30376e11 | −0.0321483 | −0.0160741 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160741 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.43408e11 | −0.0886702 | ||||||||
\(722\) | −1.73650e13 | −2.37824 | ||||||||
\(723\) | −3.54048e11 | −0.0481880 | ||||||||
\(724\) | −5.85402e11 | −0.0791827 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.60342e11 | 0.0481394 | ||||||||
\(727\) | 9.25894e12 | 1.22930 | 0.614648 | − | 0.788801i | \(-0.289298\pi\) | ||||
0.614648 | + | 0.788801i | \(0.289298\pi\) | |||||||
\(728\) | −6.17430e12 | −0.814698 | ||||||||
\(729\) | −5.54661e12 | −0.727368 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.55643e12 | −0.590196 | ||||||||
\(732\) | 2.89006e11 | 0.0372055 | ||||||||
\(733\) | −7.22531e12 | −0.924461 | −0.462231 | − | 0.886760i | \(-0.652951\pi\) | ||||
−0.462231 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(734\) | −5.38074e12 | −0.684241 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.56707e12 | −0.448086 | ||||||||
\(737\) | −1.23962e13 | −1.54769 | ||||||||
\(738\) | 1.11885e13 | 1.38841 | ||||||||
\(739\) | −1.24725e13 | −1.53834 | −0.769170 | − | 0.639044i | \(-0.779330\pi\) | ||||
−0.769170 | + | 0.639044i | \(0.779330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.10474e12 | 0.500154 | ||||||||
\(742\) | 7.88531e12 | 0.954996 | ||||||||
\(743\) | −1.15645e13 | −1.39212 | −0.696058 | − | 0.717986i | \(-0.745064\pi\) | ||||
−0.696058 | + | 0.717986i | \(0.745064\pi\) | |||||||
\(744\) | 1.24130e12 | 0.148525 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.05219e13 | 1.24386 | ||||||||
\(747\) | −1.21586e11 | −0.0142870 | ||||||||
\(748\) | 1.39987e12 | 0.163505 | ||||||||
\(749\) | −3.85167e12 | −0.447179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.70732e12 | −0.425285 | −0.212642 | − | 0.977130i | \(-0.568207\pi\) | ||||
−0.212642 | + | 0.977130i | \(0.568207\pi\) | |||||||
\(752\) | −2.68132e11 | −0.0305752 | ||||||||
\(753\) | −1.05547e12 | −0.119638 | ||||||||
\(754\) | 6.55344e12 | 0.738412 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.88576e11 | −0.0543982 | ||||||||
\(757\) | −4.86635e11 | −0.0538607 | −0.0269303 | − | 0.999637i | \(-0.508573\pi\) | ||||
−0.0269303 | + | 0.999637i | \(0.508573\pi\) | |||||||
\(758\) | −6.63228e11 | −0.0729712 | ||||||||
\(759\) | −1.93562e12 | −0.211706 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.28395e12 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(762\) | 1.52557e12 | 0.163921 | ||||||||
\(763\) | −4.00589e12 | −0.427896 | ||||||||
\(764\) | −9.52709e11 | −0.101167 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.44499e12 | 0.151648 | ||||||||
\(767\) | −9.26745e11 | −0.0966899 | ||||||||
\(768\) | −1.22021e12 | −0.126563 | ||||||||
\(769\) | −4.03625e12 | −0.416207 | −0.208103 | − | 0.978107i | \(-0.566729\pi\) | ||||
−0.208103 | + | 0.978107i | \(0.566729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.12186e12 | −0.114339 | ||||||||
\(772\) | 3.28672e12 | 0.333031 | ||||||||
\(773\) | 1.21916e13 | 1.22815 | 0.614076 | − | 0.789247i | \(-0.289529\pi\) | ||||
0.614076 | + | 0.789247i | \(0.289529\pi\) | |||||||
\(774\) | −5.39492e12 | −0.540320 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.15129e13 | 1.13974 | ||||||||
\(777\) | 3.07120e11 | 0.0302282 | ||||||||
\(778\) | 4.09445e12 | 0.400671 | ||||||||
\(779\) | 3.21141e13 | 3.12447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.57728e12 | −0.632582 | ||||||||
\(782\) | −9.73844e12 | −0.931235 | ||||||||
\(783\) | 3.07397e12 | 0.292262 | ||||||||
\(784\) | 4.80940e12 | 0.454641 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.18576e12 | −0.110814 | ||||||||
\(787\) | −1.20299e12 | −0.111783 | −0.0558913 | − | 0.998437i | \(-0.517800\pi\) | ||||
−0.0558913 | + | 0.998437i | \(0.517800\pi\) | |||||||
\(788\) | −2.69999e12 | −0.249456 | ||||||||
\(789\) | 4.08059e12 | 0.374866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.00539e13 | −0.913147 | ||||||||
\(792\) | 9.82503e12 | 0.887300 | ||||||||
\(793\) | −1.12823e13 | −1.01314 | ||||||||
\(794\) | −3.29821e11 | −0.0294501 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.09894e12 | −0.0970208 | ||||||||
\(797\) | 1.72611e13 | 1.51533 | 0.757663 | − | 0.652646i | \(-0.226341\pi\) | ||||
0.757663 | + | 0.652646i | \(0.226341\pi\) | |||||||
\(798\) | 2.68731e12 | 0.234587 | ||||||||
\(799\) | 4.32943e11 | 0.0375811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.12326e13 | 0.964130 | ||||||||
\(802\) | 1.65806e13 | 1.41520 | ||||||||
\(803\) | 1.18977e13 | 1.00982 | ||||||||
\(804\) | −9.33109e11 | −0.0787553 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.17490e12 | −0.682299 | ||||||||
\(807\) | −4.34609e12 | −0.360718 | ||||||||
\(808\) | 1.19315e13 | 0.984788 | ||||||||
\(809\) | 7.44408e12 | 0.611002 | 0.305501 | − | 0.952192i | \(-0.401176\pi\) | ||||
0.305501 | + | 0.952192i | \(0.401176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.59955e12 | −0.779214 | −0.389607 | − | 0.920981i | \(-0.627389\pi\) | ||||
−0.389607 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(812\) | −1.09235e12 | −0.0881783 | ||||||||
\(813\) | −3.38772e12 | −0.271957 | ||||||||
\(814\) | −2.13550e12 | −0.170486 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.93408e12 | −0.152710 | ||||||||
\(817\) | −1.54849e13 | −1.21593 | ||||||||
\(818\) | 8.57808e12 | 0.669885 | ||||||||
\(819\) | 9.30568e12 | 0.722721 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.04043e12 | −0.387189 | −0.193595 | − | 0.981082i | \(-0.562015\pi\) | ||||
−0.193595 | + | 0.981082i | \(0.562015\pi\) | |||||||
\(822\) | −2.76464e11 | −0.0211211 | ||||||||
\(823\) | 1.62323e13 | 1.23333 | 0.616666 | − | 0.787225i | \(-0.288483\pi\) | ||||
0.616666 | + | 0.787225i | \(0.288483\pi\) | |||||||
\(824\) | 1.99622e12 | 0.150847 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.06724e11 | −0.0453504 | ||||||||
\(827\) | −1.74898e13 | −1.30020 | −0.650099 | − | 0.759850i | \(-0.725273\pi\) | ||||
−0.650099 | + | 0.759850i | \(0.725273\pi\) | |||||||
\(828\) | 2.93571e12 | 0.217058 | ||||||||
\(829\) | −1.04102e13 | −0.765535 | −0.382768 | − | 0.923845i | \(-0.625029\pi\) | ||||
−0.382768 | + | 0.923845i | \(0.625029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.56420e11 | 0.0622992 | ||||||||
\(832\) | 1.84722e13 | 1.33649 | ||||||||
\(833\) | −7.76555e12 | −0.558817 | ||||||||
\(834\) | −2.76354e12 | −0.197796 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.75742e12 | 0.336855 | ||||||||
\(837\) | −3.83454e12 | −0.270053 | ||||||||
\(838\) | 2.55296e11 | 0.0178832 | ||||||||
\(839\) | −2.66219e13 | −1.85485 | −0.927426 | − | 0.374006i | \(-0.877984\pi\) | ||||
−0.927426 | + | 0.374006i | \(0.877984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.63439e12 | −0.526250 | ||||||||
\(842\) | 6.15225e11 | 0.0421822 | ||||||||
\(843\) | 1.66919e12 | 0.113836 | ||||||||
\(844\) | −1.87261e12 | −0.127030 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.12615e11 | 0.0344052 | ||||||||
\(847\) | 2.34477e12 | 0.156540 | ||||||||
\(848\) | −1.92868e13 | −1.28079 | ||||||||
\(849\) | −3.35427e12 | −0.221571 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.78237e12 | −0.247219 | ||||||||
\(852\) | −4.95098e11 | −0.0321894 | ||||||||
\(853\) | −7.30064e12 | −0.472161 | −0.236080 | − | 0.971734i | \(-0.575863\pi\) | ||||
−0.236080 | + | 0.971734i | \(0.575863\pi\) | |||||||
\(854\) | −7.38635e12 | −0.475192 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.19501e13 | 0.760747 | ||||||||
\(857\) | −1.18598e13 | −0.751041 | −0.375520 | − | 0.926814i | \(-0.622536\pi\) | ||||
−0.375520 | + | 0.926814i | \(0.622536\pi\) | |||||||
\(858\) | 3.21139e12 | 0.202302 | ||||||||
\(859\) | 1.67692e13 | 1.05085 | 0.525427 | − | 0.850839i | \(-0.323906\pi\) | ||||
0.525427 | + | 0.850839i | \(0.323906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.61336e12 | −0.224077 | ||||||||
\(862\) | −8.19834e12 | −0.505759 | ||||||||
\(863\) | 6.71596e12 | 0.412154 | 0.206077 | − | 0.978536i | \(-0.433930\pi\) | ||||
0.206077 | + | 0.978536i | \(0.433930\pi\) | |||||||
\(864\) | 2.77597e12 | 0.169474 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.76716e12 | −0.167187 | ||||||||
\(867\) | −4.94917e11 | −0.0297472 | ||||||||
\(868\) | 1.36263e12 | 0.0814776 | ||||||||
\(869\) | 2.33834e13 | 1.39098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.64270e13 | 2.14458 | ||||||||
\(872\) | 1.24286e13 | 0.727943 | ||||||||
\(873\) | −1.73518e13 | −1.01107 | ||||||||
\(874\) | −3.30959e13 | −1.91855 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.95590e11 | 0.0513855 | ||||||||
\(877\) | −2.79757e13 | −1.59692 | −0.798458 | − | 0.602051i | \(-0.794351\pi\) | ||||
−0.798458 | + | 0.602051i | \(0.794351\pi\) | |||||||
\(878\) | −1.58577e13 | −0.900566 | ||||||||
\(879\) | −7.03050e12 | −0.397225 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.06225e13 | 1.15332 | 0.576660 | − | 0.816984i | \(-0.304356\pi\) | ||||
0.576660 | + | 0.816984i | \(0.304356\pi\) | |||||||
\(882\) | −9.19460e12 | −0.511593 | ||||||||
\(883\) | −2.02048e13 | −1.11849 | −0.559244 | − | 0.829003i | \(-0.688909\pi\) | ||||
−0.559244 | + | 0.829003i | \(0.688909\pi\) | |||||||
\(884\) | −4.11362e12 | −0.226563 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.79348e13 | −0.977788 | ||||||||
\(887\) | 3.19954e13 | 1.73553 | 0.867763 | − | 0.496978i | \(-0.165557\pi\) | ||||
0.867763 | + | 0.496978i | \(0.165557\pi\) | |||||||
\(888\) | −9.52862e11 | −0.0514247 | ||||||||
\(889\) | 9.92701e12 | 0.533041 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.40365e13 | −0.746122 | ||||||||
\(892\) | −4.61870e12 | −0.244275 | ||||||||
\(893\) | 1.47135e12 | 0.0774254 | ||||||||
\(894\) | 1.35880e12 | 0.0711436 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.23252e12 | 0.374890 | ||||||||
\(897\) | 5.68798e12 | 0.293354 | ||||||||
\(898\) | −1.68778e13 | −0.866110 | ||||||||
\(899\) | −8.57323e12 | −0.437750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.11416e13 | 1.57427 | ||||||||
\(902\) | 2.51248e13 | 1.26378 | ||||||||
\(903\) | 1.74231e12 | 0.0872026 | ||||||||
\(904\) | 3.11930e13 | 1.55346 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.97982e12 | 0.0976223 | ||||||||
\(907\) | 2.40537e12 | 0.118018 | 0.0590091 | − | 0.998257i | \(-0.481206\pi\) | ||||
0.0590091 | + | 0.998257i | \(0.481206\pi\) | |||||||
\(908\) | −5.81519e12 | −0.283908 | ||||||||
\(909\) | −1.79827e13 | −0.873609 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.11773e13 | −1.49970 | −0.749852 | − | 0.661606i | \(-0.769875\pi\) | ||||
−0.749852 | + | 0.661606i | \(0.769875\pi\) | |||||||
\(912\) | −6.57292e12 | −0.314616 | ||||||||
\(913\) | −2.73032e11 | −0.0130045 | ||||||||
\(914\) | −1.21445e13 | −0.575603 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.53469e11 | 0.00720263 | ||||||||
\(917\) | −7.71582e12 | −0.360346 | ||||||||
\(918\) | 7.57865e12 | 0.352208 | ||||||||
\(919\) | 3.42677e13 | 1.58477 | 0.792383 | − | 0.610024i | \(-0.208840\pi\) | ||||
0.792383 | + | 0.610024i | \(0.208840\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.08986e12 | 0.0957082 | ||||||||
\(922\) | −3.08692e13 | −1.40681 | ||||||||
\(923\) | 1.93278e13 | 0.876548 | ||||||||
\(924\) | −5.35288e11 | −0.0241581 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.57652e13 | 0.704614 | ||||||||
\(927\) | −3.00864e12 | −0.133817 | ||||||||
\(928\) | 6.20648e12 | 0.274713 | ||||||||
\(929\) | −2.52782e13 | −1.11346 | −0.556730 | − | 0.830693i | \(-0.687944\pi\) | ||||
−0.556730 | + | 0.830693i | \(0.687944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.63910e13 | −1.15129 | ||||||||
\(932\) | 8.13848e11 | 0.0353323 | ||||||||
\(933\) | −6.06476e12 | −0.262027 | ||||||||
\(934\) | 8.17655e12 | 0.351568 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.88716e13 | −1.22950 | ||||||||
\(937\) | 2.72636e13 | 1.15546 | 0.577731 | − | 0.816227i | \(-0.303938\pi\) | ||||
0.577731 | + | 0.816227i | \(0.303938\pi\) | |||||||
\(938\) | 2.38482e13 | 1.00587 | ||||||||
\(939\) | −1.87682e12 | −0.0787819 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.57383e13 | 0.654340 | 0.327170 | − | 0.944966i | \(-0.393905\pi\) | ||||
0.327170 | + | 0.944966i | \(0.393905\pi\) | |||||||
\(942\) | 6.70953e12 | 0.277628 | ||||||||
\(943\) | 4.45008e13 | 1.83259 | ||||||||
\(944\) | 1.48399e12 | 0.0608217 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.21148e13 | −0.491820 | ||||||||
\(947\) | −9.71128e12 | −0.392375 | −0.196188 | − | 0.980566i | \(-0.562856\pi\) | ||||
−0.196188 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(948\) | 1.76017e12 | 0.0707809 | ||||||||
\(949\) | −3.49624e13 | −1.39927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.89257e12 | −0.273256 | ||||||||
\(952\) | −1.59640e13 | −0.629905 | ||||||||
\(953\) | 4.15385e12 | 0.163130 | 0.0815648 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815648 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(954\) | 3.68725e13 | 1.44123 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.78084e12 | −0.223836 | ||||||||
\(957\) | 3.36787e12 | 0.129793 | ||||||||
\(958\) | 4.18114e13 | 1.60380 | ||||||||
\(959\) | −1.79897e12 | −0.0686818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57452e13 | −0.595515 | ||||||||
\(962\) | 6.27532e12 | 0.236237 | ||||||||
\(963\) | −1.80108e13 | −0.674861 | ||||||||
\(964\) | 1.20582e12 | 0.0449715 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.72383e12 | 0.137592 | ||||||||
\(967\) | 1.84544e13 | 0.678706 | 0.339353 | − | 0.940659i | \(-0.389792\pi\) | ||||
0.339353 | + | 0.940659i | \(0.389792\pi\) | |||||||
\(968\) | −7.27484e12 | −0.266308 | ||||||||
\(969\) | 1.06130e13 | 0.386707 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.95973e12 | −0.106848 | −0.0534238 | − | 0.998572i | \(-0.517013\pi\) | ||||
−0.0534238 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(972\) | −3.45460e12 | −0.124137 | ||||||||
\(973\) | −1.79826e13 | −0.643197 | ||||||||
\(974\) | 4.87226e12 | 0.173466 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.80664e13 | 0.637304 | ||||||||
\(977\) | 4.44178e13 | 1.55967 | 0.779833 | − | 0.625988i | \(-0.215304\pi\) | ||||
0.779833 | + | 0.625988i | \(0.215304\pi\) | |||||||
\(978\) | −7.39509e12 | −0.258475 | ||||||||
\(979\) | 2.52239e13 | 0.877588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.87319e13 | −0.645761 | ||||||||
\(982\) | −4.60356e13 | −1.57976 | ||||||||
\(983\) | 4.57558e13 | 1.56299 | 0.781493 | − | 0.623914i | \(-0.214459\pi\) | ||||
0.781493 | + | 0.623914i | \(0.214459\pi\) | |||||||
\(984\) | 1.12107e13 | 0.381202 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.69443e13 | 0.570922 | ||||||||
\(987\) | −1.65550e11 | −0.00555269 | ||||||||
\(988\) | −1.39800e13 | −0.466769 | ||||||||
\(989\) | −2.14576e13 | −0.713177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30469e13 | 0.429710 | 0.214855 | − | 0.976646i | \(-0.431072\pi\) | ||||
0.214855 | + | 0.976646i | \(0.431072\pi\) | |||||||
\(992\) | −7.74210e12 | −0.253838 | ||||||||
\(993\) | −2.55903e12 | −0.0835225 | ||||||||
\(994\) | 1.26536e13 | 0.411127 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.05522e10 | −0.000661747 0 | ||||||||
\(997\) | −5.07578e12 | −0.162695 | −0.0813476 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813476 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(998\) | −1.99742e13 | −0.637356 | ||||||||
\(999\) | 2.94352e12 | 0.0935022 |
(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 | 25.10.a.d.1.1 | yes | 3 | |
3.2 | odd | 2 | 225.10.a.m.1.3 | 3 | |||
4.3 | odd | 2 | 400.10.a.u.1.2 | 3 | |||
5.2 | odd | 4 | 25.10.b.c.24.3 | 6 | |||
5.3 | odd | 4 | 25.10.b.c.24.4 | 6 | |||
5.4 | even | 2 | 25.10.a.c.1.3 | ✓ | 3 | ||
15.2 | even | 4 | 225.10.b.m.199.4 | 6 | |||
15.8 | even | 4 | 225.10.b.m.199.3 | 6 | |||
15.14 | odd | 2 | 225.10.a.p.1.1 | 3 | |||
20.3 | even | 4 | 400.10.c.q.49.3 | 6 | |||
20.7 | even | 4 | 400.10.c.q.49.4 | 6 | |||
20.19 | odd | 2 | 400.10.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
25.10.a.d.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
25.10.b.c.24.3 | 6 | 5.2 | odd | 4 | |||
25.10.b.c.24.4 | 6 | 5.3 | odd | 4 | |||
225.10.a.m.1.3 | 3 | 3.2 | odd | 2 | |||
225.10.a.p.1.1 | 3 | 15.14 | odd | 2 | |||
225.10.b.m.199.3 | 6 | 15.8 | even | 4 | |||
225.10.b.m.199.4 | 6 | 15.2 | even | 4 | |||
400.10.a.u.1.2 | 3 | 4.3 | odd | 2 | |||
400.10.a.y.1.2 | 3 | 20.19 | odd | 2 | |||
400.10.c.q.49.3 | 6 | 20.3 | even | 4 | |||
400.10.c.q.49.4 | 6 | 20.7 | even | 4 |