Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,10,Mod(1,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, 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("7.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(3.60525085315\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.8924 | 0.481383 | 0.240691 | − | 0.970602i | \(-0.422626\pi\) | ||||
0.240691 | + | 0.970602i | \(0.422626\pi\) | |||||||
\(3\) | −195.817 | −1.39574 | −0.697870 | − | 0.716225i | \(-0.745869\pi\) | ||||
−0.697870 | + | 0.716225i | \(0.745869\pi\) | |||||||
\(4\) | −393.355 | −0.768271 | ||||||||
\(5\) | 200.782 | 0.143668 | 0.0718340 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718340 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(6\) | −2132.92 | −0.671885 | ||||||||
\(7\) | −2401.00 | −0.377964 | ||||||||
\(8\) | −9861.52 | −0.851215 | ||||||||
\(9\) | 18661.3 | 0.948090 | ||||||||
\(10\) | 2187.01 | 0.0691593 | ||||||||
\(11\) | 63864.3 | 1.31520 | 0.657599 | − | 0.753369i | \(-0.271572\pi\) | ||||
0.657599 | + | 0.753369i | \(0.271572\pi\) | |||||||
\(12\) | 77025.5 | 1.07231 | ||||||||
\(13\) | −164679. | −1.59916 | −0.799581 | − | 0.600558i | \(-0.794945\pi\) | ||||
−0.799581 | + | 0.600558i | \(0.794945\pi\) | |||||||
\(14\) | −26152.8 | −0.181946 | ||||||||
\(15\) | −39316.5 | −0.200523 | ||||||||
\(16\) | 93981.5 | 0.358511 | ||||||||
\(17\) | −362910. | −1.05385 | −0.526925 | − | 0.849912i | \(-0.676655\pi\) | ||||
−0.526925 | + | 0.849912i | \(0.676655\pi\) | |||||||
\(18\) | 203267. | 0.456394 | ||||||||
\(19\) | −436498. | −0.768406 | −0.384203 | − | 0.923249i | \(-0.625524\pi\) | ||||
−0.384203 | + | 0.923249i | \(0.625524\pi\) | |||||||
\(20\) | −78978.6 | −0.110376 | ||||||||
\(21\) | 470156. | 0.527540 | ||||||||
\(22\) | 695638. | 0.633113 | ||||||||
\(23\) | 918199. | 0.684166 | 0.342083 | − | 0.939670i | \(-0.388868\pi\) | ||||
0.342083 | + | 0.939670i | \(0.388868\pi\) | |||||||
\(24\) | 1.93105e6 | 1.18807 | ||||||||
\(25\) | −1.91281e6 | −0.979359 | ||||||||
\(26\) | −1.79375e6 | −0.769809 | ||||||||
\(27\) | 200076. | 0.0724531 | ||||||||
\(28\) | 944445. | 0.290379 | ||||||||
\(29\) | −3.68643e6 | −0.967865 | −0.483932 | − | 0.875105i | \(-0.660792\pi\) | ||||
−0.483932 | + | 0.875105i | \(0.660792\pi\) | |||||||
\(30\) | −428253. | −0.0965284 | ||||||||
\(31\) | 3.47629e6 | 0.676064 | 0.338032 | − | 0.941135i | \(-0.390239\pi\) | ||||
0.338032 | + | 0.941135i | \(0.390239\pi\) | |||||||
\(32\) | 6.07279e6 | 1.02380 | ||||||||
\(33\) | −1.25057e7 | −1.83567 | ||||||||
\(34\) | −3.95298e6 | −0.507305 | ||||||||
\(35\) | −482078. | −0.0543014 | ||||||||
\(36\) | −7.34049e6 | −0.728390 | ||||||||
\(37\) | 1.88149e7 | 1.65042 | 0.825210 | − | 0.564826i | \(-0.191057\pi\) | ||||
0.825210 | + | 0.564826i | \(0.191057\pi\) | |||||||
\(38\) | −4.75453e6 | −0.369897 | ||||||||
\(39\) | 3.22469e7 | 2.23201 | ||||||||
\(40\) | −1.98002e6 | −0.122292 | ||||||||
\(41\) | 2.40714e6 | 0.133038 | 0.0665188 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665188 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(42\) | 5.12115e6 | 0.253949 | ||||||||
\(43\) | −1.25306e7 | −0.558938 | −0.279469 | − | 0.960155i | \(-0.590158\pi\) | ||||
−0.279469 | + | 0.960155i | \(0.590158\pi\) | |||||||
\(44\) | −2.51213e7 | −1.01043 | ||||||||
\(45\) | 3.74685e6 | 0.136210 | ||||||||
\(46\) | 1.00014e7 | 0.329346 | ||||||||
\(47\) | −5.54509e7 | −1.65756 | −0.828779 | − | 0.559577i | \(-0.810964\pi\) | ||||
−0.828779 | + | 0.559577i | \(0.810964\pi\) | |||||||
\(48\) | −1.84032e7 | −0.500388 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −2.08352e7 | −0.471447 | ||||||||
\(51\) | 7.10639e7 | 1.47090 | ||||||||
\(52\) | 6.47772e7 | 1.22859 | ||||||||
\(53\) | −9.26889e7 | −1.61356 | −0.806782 | − | 0.590849i | \(-0.798793\pi\) | ||||
−0.806782 | + | 0.590849i | \(0.798793\pi\) | |||||||
\(54\) | 2.17931e6 | 0.0348777 | ||||||||
\(55\) | 1.28228e7 | 0.188952 | ||||||||
\(56\) | 2.36775e7 | 0.321729 | ||||||||
\(57\) | 8.54737e7 | 1.07250 | ||||||||
\(58\) | −4.01542e7 | −0.465913 | ||||||||
\(59\) | −2.52600e7 | −0.271393 | −0.135696 | − | 0.990750i | \(-0.543327\pi\) | ||||
−0.135696 | + | 0.990750i | \(0.543327\pi\) | |||||||
\(60\) | 1.54653e7 | 0.154056 | ||||||||
\(61\) | 6.93275e7 | 0.641093 | 0.320547 | − | 0.947233i | \(-0.396133\pi\) | ||||
0.320547 | + | 0.947233i | \(0.396133\pi\) | |||||||
\(62\) | 3.78653e7 | 0.325446 | ||||||||
\(63\) | −4.48057e7 | −0.358344 | ||||||||
\(64\) | 1.80290e7 | 0.134326 | ||||||||
\(65\) | −3.30646e7 | −0.229748 | ||||||||
\(66\) | −1.36218e8 | −0.883661 | ||||||||
\(67\) | −2.33494e7 | −0.141559 | −0.0707796 | − | 0.997492i | \(-0.522549\pi\) | ||||
−0.0707796 | + | 0.997492i | \(0.522549\pi\) | |||||||
\(68\) | 1.42752e8 | 0.809643 | ||||||||
\(69\) | −1.79799e8 | −0.954918 | ||||||||
\(70\) | −5.25101e6 | −0.0261398 | ||||||||
\(71\) | −1.06194e8 | −0.495950 | −0.247975 | − | 0.968766i | \(-0.579765\pi\) | ||||
−0.247975 | + | 0.968766i | \(0.579765\pi\) | |||||||
\(72\) | −1.84028e8 | −0.807028 | ||||||||
\(73\) | −2.10115e8 | −0.865974 | −0.432987 | − | 0.901400i | \(-0.642540\pi\) | ||||
−0.432987 | + | 0.901400i | \(0.642540\pi\) | |||||||
\(74\) | 2.04940e8 | 0.794483 | ||||||||
\(75\) | 3.74561e8 | 1.36693 | ||||||||
\(76\) | 1.71699e8 | 0.590344 | ||||||||
\(77\) | −1.53338e8 | −0.497098 | ||||||||
\(78\) | 3.51247e8 | 1.07445 | ||||||||
\(79\) | −149606. | −0.000432144 0 | −0.000216072 | − | 1.00000i | \(-0.500069\pi\) | ||||
−0.000216072 | 1.00000i | \(0.500069\pi\) | ||||||||
\(80\) | 1.88698e7 | 0.0515066 | ||||||||
\(81\) | −4.06488e8 | −1.04922 | ||||||||
\(82\) | 2.62197e7 | 0.0640420 | ||||||||
\(83\) | 5.21565e8 | 1.20630 | 0.603152 | − | 0.797626i | \(-0.293911\pi\) | ||||
0.603152 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(84\) | −1.84938e8 | −0.405294 | ||||||||
\(85\) | −7.28659e7 | −0.151405 | ||||||||
\(86\) | −1.36489e8 | −0.269063 | ||||||||
\(87\) | 7.21865e8 | 1.35089 | ||||||||
\(88\) | −6.29799e8 | −1.11952 | ||||||||
\(89\) | 2.98587e8 | 0.504448 | 0.252224 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252224 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(90\) | 4.08123e7 | 0.0655692 | ||||||||
\(91\) | 3.95394e8 | 0.604426 | ||||||||
\(92\) | −3.61178e8 | −0.525625 | ||||||||
\(93\) | −6.80716e8 | −0.943610 | ||||||||
\(94\) | −6.03996e8 | −0.797919 | ||||||||
\(95\) | −8.76410e7 | −0.110395 | ||||||||
\(96\) | −1.18915e9 | −1.42895 | ||||||||
\(97\) | −8.95983e8 | −1.02761 | −0.513803 | − | 0.857908i | \(-0.671764\pi\) | ||||
−0.513803 | + | 0.857908i | \(0.671764\pi\) | |||||||
\(98\) | 6.27928e7 | 0.0687689 | ||||||||
\(99\) | 1.19179e9 | 1.24693 | ||||||||
\(100\) | 7.52413e8 | 0.752413 | ||||||||
\(101\) | −4.13043e7 | −0.0394956 | −0.0197478 | − | 0.999805i | \(-0.506286\pi\) | ||||
−0.0197478 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(102\) | 7.74060e8 | 0.708066 | ||||||||
\(103\) | 4.29472e8 | 0.375982 | 0.187991 | − | 0.982171i | \(-0.439802\pi\) | ||||
0.187991 | + | 0.982171i | \(0.439802\pi\) | |||||||
\(104\) | 1.62398e9 | 1.36123 | ||||||||
\(105\) | 9.43990e7 | 0.0757906 | ||||||||
\(106\) | −1.00961e9 | −0.776742 | ||||||||
\(107\) | 1.23287e9 | 0.909265 | 0.454632 | − | 0.890679i | \(-0.349771\pi\) | ||||
0.454632 | + | 0.890679i | \(0.349771\pi\) | |||||||
\(108\) | −7.87006e7 | −0.0556636 | ||||||||
\(109\) | 1.69619e9 | 1.15095 | 0.575475 | − | 0.817820i | \(-0.304817\pi\) | ||||
0.575475 | + | 0.817820i | \(0.304817\pi\) | |||||||
\(110\) | 1.39672e8 | 0.0909581 | ||||||||
\(111\) | −3.68428e9 | −2.30356 | ||||||||
\(112\) | −2.25650e8 | −0.135504 | ||||||||
\(113\) | −1.42449e9 | −0.821878 | −0.410939 | − | 0.911663i | \(-0.634799\pi\) | ||||
−0.410939 | + | 0.911663i | \(0.634799\pi\) | |||||||
\(114\) | 9.31017e8 | 0.516281 | ||||||||
\(115\) | 1.84358e8 | 0.0982928 | ||||||||
\(116\) | 1.45007e9 | 0.743582 | ||||||||
\(117\) | −3.07311e9 | −1.51615 | ||||||||
\(118\) | −2.75143e8 | −0.130644 | ||||||||
\(119\) | 8.71347e8 | 0.398318 | ||||||||
\(120\) | 3.87721e8 | 0.170688 | ||||||||
\(121\) | 1.72070e9 | 0.729744 | ||||||||
\(122\) | 7.55146e8 | 0.308611 | ||||||||
\(123\) | −4.71359e8 | −0.185686 | ||||||||
\(124\) | −1.36741e9 | −0.519401 | ||||||||
\(125\) | −7.76211e8 | −0.284371 | ||||||||
\(126\) | −4.88043e8 | −0.172501 | ||||||||
\(127\) | −3.12858e9 | −1.06716 | −0.533581 | − | 0.845749i | \(-0.679154\pi\) | ||||
−0.533581 | + | 0.845749i | \(0.679154\pi\) | |||||||
\(128\) | −2.91289e9 | −0.959133 | ||||||||
\(129\) | 2.45370e9 | 0.780132 | ||||||||
\(130\) | −3.60154e8 | −0.110597 | ||||||||
\(131\) | 7.03123e8 | 0.208598 | 0.104299 | − | 0.994546i | \(-0.466740\pi\) | ||||
0.104299 | + | 0.994546i | \(0.466740\pi\) | |||||||
\(132\) | 4.91918e9 | 1.41029 | ||||||||
\(133\) | 1.04803e9 | 0.290430 | ||||||||
\(134\) | −2.54332e8 | −0.0681442 | ||||||||
\(135\) | 4.01716e7 | 0.0104092 | ||||||||
\(136\) | 3.57885e9 | 0.897053 | ||||||||
\(137\) | −3.07310e9 | −0.745306 | −0.372653 | − | 0.927971i | \(-0.621552\pi\) | ||||
−0.372653 | + | 0.927971i | \(0.621552\pi\) | |||||||
\(138\) | −1.95845e9 | −0.459681 | ||||||||
\(139\) | 5.07806e9 | 1.15380 | 0.576901 | − | 0.816814i | \(-0.304262\pi\) | ||||
0.576901 | + | 0.816814i | \(0.304262\pi\) | |||||||
\(140\) | 1.89628e8 | 0.0417182 | ||||||||
\(141\) | 1.08582e10 | 2.31352 | ||||||||
\(142\) | −1.15671e9 | −0.238742 | ||||||||
\(143\) | −1.05171e10 | −2.10321 | ||||||||
\(144\) | 1.75381e9 | 0.339901 | ||||||||
\(145\) | −7.40169e8 | −0.139051 | ||||||||
\(146\) | −2.28867e9 | −0.416865 | ||||||||
\(147\) | −1.12885e9 | −0.199391 | ||||||||
\(148\) | −7.40093e9 | −1.26797 | ||||||||
\(149\) | 2.13455e9 | 0.354788 | 0.177394 | − | 0.984140i | \(-0.443233\pi\) | ||||
0.177394 | + | 0.984140i | \(0.443233\pi\) | |||||||
\(150\) | 4.07988e9 | 0.658017 | ||||||||
\(151\) | −2.35298e9 | −0.368318 | −0.184159 | − | 0.982897i | \(-0.558956\pi\) | ||||
−0.184159 | + | 0.982897i | \(0.558956\pi\) | |||||||
\(152\) | 4.30454e9 | 0.654079 | ||||||||
\(153\) | −6.77236e9 | −0.999145 | ||||||||
\(154\) | −1.67023e9 | −0.239294 | ||||||||
\(155\) | 6.97977e8 | 0.0971288 | ||||||||
\(156\) | −1.26845e10 | −1.71479 | ||||||||
\(157\) | −2.98482e9 | −0.392075 | −0.196038 | − | 0.980596i | \(-0.562807\pi\) | ||||
−0.196038 | + | 0.980596i | \(0.562807\pi\) | |||||||
\(158\) | −1.62958e6 | −0.000208027 0 | ||||||||
\(159\) | 1.81501e10 | 2.25212 | ||||||||
\(160\) | 1.21931e9 | 0.147087 | ||||||||
\(161\) | −2.20460e9 | −0.258591 | ||||||||
\(162\) | −4.42764e9 | −0.505074 | ||||||||
\(163\) | 9.20745e9 | 1.02163 | 0.510817 | − | 0.859690i | \(-0.329343\pi\) | ||||
0.510817 | + | 0.859690i | \(0.329343\pi\) | |||||||
\(164\) | −9.46860e8 | −0.102209 | ||||||||
\(165\) | −2.51092e9 | −0.263728 | ||||||||
\(166\) | 5.68111e9 | 0.580694 | ||||||||
\(167\) | −4.95501e9 | −0.492970 | −0.246485 | − | 0.969147i | \(-0.579276\pi\) | ||||
−0.246485 | + | 0.969147i | \(0.579276\pi\) | |||||||
\(168\) | −4.63646e9 | −0.449050 | ||||||||
\(169\) | 1.65146e10 | 1.55732 | ||||||||
\(170\) | −7.93688e8 | −0.0728835 | ||||||||
\(171\) | −8.14560e9 | −0.728518 | ||||||||
\(172\) | 4.92897e9 | 0.429416 | ||||||||
\(173\) | 3.77546e9 | 0.320452 | 0.160226 | − | 0.987080i | \(-0.448778\pi\) | ||||
0.160226 | + | 0.987080i | \(0.448778\pi\) | |||||||
\(174\) | 7.86287e9 | 0.650294 | ||||||||
\(175\) | 4.59266e9 | 0.370163 | ||||||||
\(176\) | 6.00206e9 | 0.471513 | ||||||||
\(177\) | 4.94633e9 | 0.378794 | ||||||||
\(178\) | 3.25235e9 | 0.242833 | ||||||||
\(179\) | −1.94362e10 | −1.41505 | −0.707526 | − | 0.706687i | \(-0.750189\pi\) | ||||
−0.707526 | + | 0.706687i | \(0.750189\pi\) | |||||||
\(180\) | −1.47384e9 | −0.104646 | ||||||||
\(181\) | −9.81530e9 | −0.679751 | −0.339875 | − | 0.940470i | \(-0.610385\pi\) | ||||
−0.339875 | + | 0.940470i | \(0.610385\pi\) | |||||||
\(182\) | 4.30680e9 | 0.290960 | ||||||||
\(183\) | −1.35755e10 | −0.894799 | ||||||||
\(184\) | −9.05485e9 | −0.582373 | ||||||||
\(185\) | 3.77770e9 | 0.237113 | ||||||||
\(186\) | −7.41466e9 | −0.454237 | ||||||||
\(187\) | −2.31770e10 | −1.38602 | ||||||||
\(188\) | 2.18119e10 | 1.27345 | ||||||||
\(189\) | −4.80381e8 | −0.0273847 | ||||||||
\(190\) | −9.54625e8 | −0.0531424 | ||||||||
\(191\) | −1.84579e10 | −1.00354 | −0.501768 | − | 0.865002i | \(-0.667317\pi\) | ||||
−0.501768 | + | 0.865002i | \(0.667317\pi\) | |||||||
\(192\) | −3.53038e9 | −0.187485 | ||||||||
\(193\) | 4.83605e9 | 0.250890 | 0.125445 | − | 0.992101i | \(-0.459964\pi\) | ||||
0.125445 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(194\) | −9.75944e9 | −0.494672 | ||||||||
\(195\) | 6.47460e9 | 0.320669 | ||||||||
\(196\) | −2.26761e9 | −0.109753 | ||||||||
\(197\) | 2.70242e10 | 1.27836 | 0.639182 | − | 0.769056i | \(-0.279273\pi\) | ||||
0.639182 | + | 0.769056i | \(0.279273\pi\) | |||||||
\(198\) | 1.29815e10 | 0.600248 | ||||||||
\(199\) | 1.65772e10 | 0.749330 | 0.374665 | − | 0.927160i | \(-0.377758\pi\) | ||||
0.374665 | + | 0.927160i | \(0.377758\pi\) | |||||||
\(200\) | 1.88632e10 | 0.833645 | ||||||||
\(201\) | 4.57220e9 | 0.197580 | ||||||||
\(202\) | −4.49904e8 | −0.0190125 | ||||||||
\(203\) | 8.85111e9 | 0.365819 | ||||||||
\(204\) | −2.79533e10 | −1.13005 | ||||||||
\(205\) | 4.83311e8 | 0.0191132 | ||||||||
\(206\) | 4.67800e9 | 0.180991 | ||||||||
\(207\) | 1.71348e10 | 0.648651 | ||||||||
\(208\) | −1.54768e10 | −0.573317 | ||||||||
\(209\) | −2.78766e10 | −1.01061 | ||||||||
\(210\) | 1.02824e9 | 0.0364843 | ||||||||
\(211\) | −5.44866e10 | −1.89243 | −0.946213 | − | 0.323544i | \(-0.895126\pi\) | ||||
−0.946213 | + | 0.323544i | \(0.895126\pi\) | |||||||
\(212\) | 3.64596e10 | 1.23965 | ||||||||
\(213\) | 2.07946e10 | 0.692218 | ||||||||
\(214\) | 1.34290e10 | 0.437704 | ||||||||
\(215\) | −2.51592e9 | −0.0803015 | ||||||||
\(216\) | −1.97305e9 | −0.0616731 | ||||||||
\(217\) | −8.34657e9 | −0.255528 | ||||||||
\(218\) | 1.84757e10 | 0.554047 | ||||||||
\(219\) | 4.11441e10 | 1.20867 | ||||||||
\(220\) | −5.04391e9 | −0.145166 | ||||||||
\(221\) | 5.97636e10 | 1.68528 | ||||||||
\(222\) | −4.01308e10 | −1.10889 | ||||||||
\(223\) | −2.05500e10 | −0.556468 | −0.278234 | − | 0.960513i | \(-0.589749\pi\) | ||||
−0.278234 | + | 0.960513i | \(0.589749\pi\) | |||||||
\(224\) | −1.45808e10 | −0.386958 | ||||||||
\(225\) | −3.56955e10 | −0.928521 | ||||||||
\(226\) | −1.55162e10 | −0.395638 | ||||||||
\(227\) | −3.94058e10 | −0.985017 | −0.492509 | − | 0.870307i | \(-0.663920\pi\) | ||||
−0.492509 | + | 0.870307i | \(0.663920\pi\) | |||||||
\(228\) | −3.36215e10 | −0.823967 | ||||||||
\(229\) | −1.82516e10 | −0.438572 | −0.219286 | − | 0.975661i | \(-0.570373\pi\) | ||||
−0.219286 | + | 0.975661i | \(0.570373\pi\) | |||||||
\(230\) | 2.00811e9 | 0.0473165 | ||||||||
\(231\) | 3.00262e10 | 0.693819 | ||||||||
\(232\) | 3.63538e10 | 0.823861 | ||||||||
\(233\) | −5.08161e10 | −1.12953 | −0.564767 | − | 0.825250i | \(-0.691034\pi\) | ||||
−0.564767 | + | 0.825250i | \(0.691034\pi\) | |||||||
\(234\) | −3.34737e10 | −0.729848 | ||||||||
\(235\) | −1.11336e10 | −0.238138 | ||||||||
\(236\) | 9.93612e9 | 0.208503 | ||||||||
\(237\) | 2.92955e7 | 0.000603160 0 | ||||||||
\(238\) | 9.49110e9 | 0.191743 | ||||||||
\(239\) | 3.80447e10 | 0.754230 | 0.377115 | − | 0.926166i | \(-0.376916\pi\) | ||||
0.377115 | + | 0.926166i | \(0.376916\pi\) | |||||||
\(240\) | −3.69503e9 | −0.0718898 | ||||||||
\(241\) | 9.80077e10 | 1.87147 | 0.935737 | − | 0.352699i | \(-0.114736\pi\) | ||||
0.935737 | + | 0.352699i | \(0.114736\pi\) | |||||||
\(242\) | 1.87426e10 | 0.351286 | ||||||||
\(243\) | 7.56590e10 | 1.39198 | ||||||||
\(244\) | −2.72703e10 | −0.492533 | ||||||||
\(245\) | 1.15747e9 | 0.0205240 | ||||||||
\(246\) | −5.13425e9 | −0.0893859 | ||||||||
\(247\) | 7.18819e10 | 1.22881 | ||||||||
\(248\) | −3.42815e10 | −0.575476 | ||||||||
\(249\) | −1.02131e11 | −1.68369 | ||||||||
\(250\) | −8.45484e9 | −0.136891 | ||||||||
\(251\) | 7.75125e10 | 1.23265 | 0.616325 | − | 0.787492i | \(-0.288621\pi\) | ||||
0.616325 | + | 0.787492i | \(0.288621\pi\) | |||||||
\(252\) | 1.76245e10 | 0.275305 | ||||||||
\(253\) | 5.86401e10 | 0.899814 | ||||||||
\(254\) | −3.40778e10 | −0.513713 | ||||||||
\(255\) | 1.42684e10 | 0.211321 | ||||||||
\(256\) | −4.09593e10 | −0.596036 | ||||||||
\(257\) | −1.07589e11 | −1.53840 | −0.769199 | − | 0.639009i | \(-0.779345\pi\) | ||||
−0.769199 | + | 0.639009i | \(0.779345\pi\) | |||||||
\(258\) | 2.67268e10 | 0.375542 | ||||||||
\(259\) | −4.51746e10 | −0.623800 | ||||||||
\(260\) | 1.30061e10 | 0.176509 | ||||||||
\(261\) | −6.87934e10 | −0.917623 | ||||||||
\(262\) | 7.65873e9 | 0.100416 | ||||||||
\(263\) | −1.21615e10 | −0.156742 | −0.0783708 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783708 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(264\) | 1.23325e11 | 1.56255 | ||||||||
\(265\) | −1.86103e10 | −0.231818 | ||||||||
\(266\) | 1.14156e10 | 0.139808 | ||||||||
\(267\) | −5.84685e10 | −0.704078 | ||||||||
\(268\) | 9.18458e9 | 0.108756 | ||||||||
\(269\) | −1.23517e11 | −1.43827 | −0.719134 | − | 0.694872i | \(-0.755461\pi\) | ||||
−0.719134 | + | 0.694872i | \(0.755461\pi\) | |||||||
\(270\) | 4.37567e8 | 0.00501080 | ||||||||
\(271\) | 1.34305e11 | 1.51263 | 0.756313 | − | 0.654210i | \(-0.226999\pi\) | ||||
0.756313 | + | 0.654210i | \(0.226999\pi\) | |||||||
\(272\) | −3.41068e10 | −0.377817 | ||||||||
\(273\) | −7.74248e10 | −0.843622 | ||||||||
\(274\) | −3.34736e10 | −0.358777 | ||||||||
\(275\) | −1.22160e11 | −1.28805 | ||||||||
\(276\) | 7.07248e10 | 0.733636 | ||||||||
\(277\) | −2.16684e10 | −0.221140 | −0.110570 | − | 0.993868i | \(-0.535268\pi\) | ||||
−0.110570 | + | 0.993868i | \(0.535268\pi\) | |||||||
\(278\) | 5.53125e10 | 0.555420 | ||||||||
\(279\) | 6.48719e10 | 0.640970 | ||||||||
\(280\) | 4.75402e9 | 0.0462222 | ||||||||
\(281\) | 7.73283e9 | 0.0739878 | 0.0369939 | − | 0.999315i | \(-0.488222\pi\) | ||||
0.0369939 | + | 0.999315i | \(0.488222\pi\) | |||||||
\(282\) | 1.18273e11 | 1.11369 | ||||||||
\(283\) | −7.19601e10 | −0.666888 | −0.333444 | − | 0.942770i | \(-0.608211\pi\) | ||||
−0.333444 | + | 0.942770i | \(0.608211\pi\) | |||||||
\(284\) | 4.17720e10 | 0.381024 | ||||||||
\(285\) | 1.71616e10 | 0.154083 | ||||||||
\(286\) | −1.14557e11 | −1.01245 | ||||||||
\(287\) | −5.77955e9 | −0.0502835 | ||||||||
\(288\) | 1.13326e11 | 0.970650 | ||||||||
\(289\) | 1.31159e10 | 0.110601 | ||||||||
\(290\) | −8.06225e9 | −0.0669368 | ||||||||
\(291\) | 1.75449e11 | 1.43427 | ||||||||
\(292\) | 8.26498e10 | 0.665303 | ||||||||
\(293\) | 1.73674e11 | 1.37667 | 0.688335 | − | 0.725393i | \(-0.258342\pi\) | ||||
0.688335 | + | 0.725393i | \(0.258342\pi\) | |||||||
\(294\) | −1.22959e10 | −0.0959835 | ||||||||
\(295\) | −5.07175e9 | −0.0389905 | ||||||||
\(296\) | −1.85544e11 | −1.40486 | ||||||||
\(297\) | 1.27777e10 | 0.0952901 | ||||||||
\(298\) | 2.32505e10 | 0.170789 | ||||||||
\(299\) | −1.51208e11 | −1.09409 | ||||||||
\(300\) | −1.47335e11 | −1.05017 | ||||||||
\(301\) | 3.00860e10 | 0.211259 | ||||||||
\(302\) | −2.56297e10 | −0.177302 | ||||||||
\(303\) | 8.08807e9 | 0.0551256 | ||||||||
\(304\) | −4.10227e10 | −0.275482 | ||||||||
\(305\) | 1.39197e10 | 0.0921046 | ||||||||
\(306\) | −7.37675e10 | −0.480971 | ||||||||
\(307\) | 2.27108e11 | 1.45918 | 0.729591 | − | 0.683884i | \(-0.239710\pi\) | ||||
0.729591 | + | 0.683884i | \(0.239710\pi\) | |||||||
\(308\) | 6.03163e10 | 0.381906 | ||||||||
\(309\) | −8.40978e10 | −0.524773 | ||||||||
\(310\) | 7.60267e9 | 0.0467561 | ||||||||
\(311\) | −8.68962e10 | −0.526719 | −0.263360 | − | 0.964698i | \(-0.584831\pi\) | ||||
−0.263360 | + | 0.964698i | \(0.584831\pi\) | |||||||
\(312\) | −3.18003e11 | −1.89992 | ||||||||
\(313\) | −5.25289e10 | −0.309349 | −0.154674 | − | 0.987965i | \(-0.549433\pi\) | ||||
−0.154674 | + | 0.987965i | \(0.549433\pi\) | |||||||
\(314\) | −3.25120e10 | −0.188738 | ||||||||
\(315\) | −8.99618e9 | −0.0514826 | ||||||||
\(316\) | 5.88484e7 | 0.000332004 0 | ||||||||
\(317\) | 2.63784e11 | 1.46718 | 0.733588 | − | 0.679595i | \(-0.237844\pi\) | ||||
0.733588 | + | 0.679595i | \(0.237844\pi\) | |||||||
\(318\) | 1.97698e11 | 1.08413 | ||||||||
\(319\) | −2.35431e11 | −1.27293 | ||||||||
\(320\) | 3.61990e9 | 0.0192984 | ||||||||
\(321\) | −2.41417e11 | −1.26910 | ||||||||
\(322\) | −2.40134e10 | −0.124481 | ||||||||
\(323\) | 1.58410e11 | 0.809786 | ||||||||
\(324\) | 1.59894e11 | 0.806082 | ||||||||
\(325\) | 3.14999e11 | 1.56615 | ||||||||
\(326\) | 1.00292e11 | 0.491797 | ||||||||
\(327\) | −3.32143e11 | −1.60643 | ||||||||
\(328\) | −2.37381e10 | −0.113244 | ||||||||
\(329\) | 1.33138e11 | 0.626498 | ||||||||
\(330\) | −2.73501e10 | −0.126954 | ||||||||
\(331\) | −2.11350e11 | −0.967780 | −0.483890 | − | 0.875129i | \(-0.660776\pi\) | ||||
−0.483890 | + | 0.875129i | \(0.660776\pi\) | |||||||
\(332\) | −2.05160e11 | −0.926768 | ||||||||
\(333\) | 3.51110e11 | 1.56475 | ||||||||
\(334\) | −5.39722e10 | −0.237307 | ||||||||
\(335\) | −4.68813e9 | −0.0203375 | ||||||||
\(336\) | 4.41860e10 | 0.189129 | ||||||||
\(337\) | −3.67482e11 | −1.55203 | −0.776017 | − | 0.630712i | \(-0.782763\pi\) | ||||
−0.776017 | + | 0.630712i | \(0.782763\pi\) | |||||||
\(338\) | 1.79884e11 | 0.749666 | ||||||||
\(339\) | 2.78940e11 | 1.14713 | ||||||||
\(340\) | 2.86621e10 | 0.116320 | ||||||||
\(341\) | 2.22011e11 | 0.889158 | ||||||||
\(342\) | −8.87255e10 | −0.350696 | ||||||||
\(343\) | −1.38413e10 | −0.0539949 | ||||||||
\(344\) | 1.23571e11 | 0.475776 | ||||||||
\(345\) | −3.61004e10 | −0.137191 | ||||||||
\(346\) | 4.11240e10 | 0.154260 | ||||||||
\(347\) | 4.33866e11 | 1.60647 | 0.803235 | − | 0.595662i | \(-0.203110\pi\) | ||||
0.803235 | + | 0.595662i | \(0.203110\pi\) | |||||||
\(348\) | −2.83949e11 | −1.03785 | ||||||||
\(349\) | 1.04086e11 | 0.375559 | 0.187780 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187780 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(350\) | 5.00253e10 | 0.178190 | ||||||||
\(351\) | −3.29482e10 | −0.115864 | ||||||||
\(352\) | 3.87834e11 | 1.34649 | ||||||||
\(353\) | −4.46890e11 | −1.53184 | −0.765922 | − | 0.642934i | \(-0.777717\pi\) | ||||
−0.765922 | + | 0.642934i | \(0.777717\pi\) | |||||||
\(354\) | 5.38776e10 | 0.182345 | ||||||||
\(355\) | −2.13219e10 | −0.0712522 | ||||||||
\(356\) | −1.17451e11 | −0.387553 | ||||||||
\(357\) | −1.70625e11 | −0.555948 | ||||||||
\(358\) | −2.11708e11 | −0.681182 | ||||||||
\(359\) | −1.96551e11 | −0.624526 | −0.312263 | − | 0.949996i | \(-0.601087\pi\) | ||||
−0.312263 | + | 0.949996i | \(0.601087\pi\) | |||||||
\(360\) | −3.69496e10 | −0.115944 | ||||||||
\(361\) | −1.32157e11 | −0.409551 | ||||||||
\(362\) | −1.06913e11 | −0.327220 | ||||||||
\(363\) | −3.36942e11 | −1.01853 | ||||||||
\(364\) | −1.55530e11 | −0.464363 | ||||||||
\(365\) | −4.21874e10 | −0.124413 | ||||||||
\(366\) | −1.47870e11 | −0.430741 | ||||||||
\(367\) | −2.25518e11 | −0.648908 | −0.324454 | − | 0.945901i | \(-0.605181\pi\) | ||||
−0.324454 | + | 0.945901i | \(0.605181\pi\) | |||||||
\(368\) | 8.62937e10 | 0.245281 | ||||||||
\(369\) | 4.49203e10 | 0.126132 | ||||||||
\(370\) | 4.11484e10 | 0.114142 | ||||||||
\(371\) | 2.22546e11 | 0.609870 | ||||||||
\(372\) | 2.67763e11 | 0.724948 | ||||||||
\(373\) | −2.04414e11 | −0.546791 | −0.273395 | − | 0.961902i | \(-0.588147\pi\) | ||||
−0.273395 | + | 0.961902i | \(0.588147\pi\) | |||||||
\(374\) | −2.52454e11 | −0.667206 | ||||||||
\(375\) | 1.51995e11 | 0.396908 | ||||||||
\(376\) | 5.46831e11 | 1.41094 | ||||||||
\(377\) | 6.07076e11 | 1.54777 | ||||||||
\(378\) | −5.23253e9 | −0.0131825 | ||||||||
\(379\) | 4.03306e10 | 0.100406 | 0.0502029 | − | 0.998739i | \(-0.484013\pi\) | ||||
0.0502029 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(380\) | 3.44740e10 | 0.0848136 | ||||||||
\(381\) | 6.12628e11 | 1.48948 | ||||||||
\(382\) | −2.01052e11 | −0.483084 | ||||||||
\(383\) | −3.98325e11 | −0.945895 | −0.472947 | − | 0.881091i | \(-0.656810\pi\) | ||||
−0.472947 | + | 0.881091i | \(0.656810\pi\) | |||||||
\(384\) | 5.70393e11 | 1.33870 | ||||||||
\(385\) | −3.07876e10 | −0.0714171 | ||||||||
\(386\) | 5.26764e10 | 0.120774 | ||||||||
\(387\) | −2.33837e11 | −0.529923 | ||||||||
\(388\) | 3.52439e11 | 0.789480 | ||||||||
\(389\) | −4.22504e11 | −0.935531 | −0.467765 | − | 0.883853i | \(-0.654941\pi\) | ||||
−0.467765 | + | 0.883853i | \(0.654941\pi\) | |||||||
\(390\) | 7.05242e10 | 0.154365 | ||||||||
\(391\) | −3.33224e11 | −0.721009 | ||||||||
\(392\) | −5.68497e10 | −0.121602 | ||||||||
\(393\) | −1.37683e11 | −0.291149 | ||||||||
\(394\) | 2.94359e11 | 0.615382 | ||||||||
\(395\) | −3.00383e7 | −6.20853e−5 0 | ||||||||
\(396\) | −4.68795e11 | −0.957976 | ||||||||
\(397\) | 6.50999e11 | 1.31529 | 0.657647 | − | 0.753326i | \(-0.271552\pi\) | ||||
0.657647 | + | 0.753326i | \(0.271552\pi\) | |||||||
\(398\) | 1.80567e11 | 0.360714 | ||||||||
\(399\) | −2.05222e11 | −0.405365 | ||||||||
\(400\) | −1.79769e11 | −0.351111 | ||||||||
\(401\) | −3.10509e11 | −0.599687 | −0.299843 | − | 0.953988i | \(-0.596934\pi\) | ||||
−0.299843 | + | 0.953988i | \(0.596934\pi\) | |||||||
\(402\) | 4.98024e10 | 0.0951115 | ||||||||
\(403\) | −5.72471e11 | −1.08114 | ||||||||
\(404\) | 1.62472e10 | 0.0303433 | ||||||||
\(405\) | −8.16155e10 | −0.150739 | ||||||||
\(406\) | 9.64102e10 | 0.176099 | ||||||||
\(407\) | 1.20160e12 | 2.17063 | ||||||||
\(408\) | −7.00799e11 | −1.25205 | ||||||||
\(409\) | 2.99519e11 | 0.529261 | 0.264630 | − | 0.964350i | \(-0.414750\pi\) | ||||
0.264630 | + | 0.964350i | \(0.414750\pi\) | |||||||
\(410\) | 5.26444e9 | 0.00920078 | ||||||||
\(411\) | 6.01766e11 | 1.04025 | ||||||||
\(412\) | −1.68935e11 | −0.288856 | ||||||||
\(413\) | 6.06492e10 | 0.102577 | ||||||||
\(414\) | 1.86639e11 | 0.312249 | ||||||||
\(415\) | 1.04721e11 | 0.173307 | ||||||||
\(416\) | −1.00006e12 | −1.63722 | ||||||||
\(417\) | −9.94370e11 | −1.61041 | ||||||||
\(418\) | −3.03645e11 | −0.486488 | ||||||||
\(419\) | −4.35217e11 | −0.689832 | −0.344916 | − | 0.938634i | \(-0.612093\pi\) | ||||
−0.344916 | + | 0.938634i | \(0.612093\pi\) | |||||||
\(420\) | −3.71323e10 | −0.0582277 | ||||||||
\(421\) | −2.07600e11 | −0.322076 | −0.161038 | − | 0.986948i | \(-0.551484\pi\) | ||||
−0.161038 | + | 0.986948i | \(0.551484\pi\) | |||||||
\(422\) | −5.93493e11 | −0.910981 | ||||||||
\(423\) | −1.03478e12 | −1.57151 | ||||||||
\(424\) | 9.14054e11 | 1.37349 | ||||||||
\(425\) | 6.94179e11 | 1.03210 | ||||||||
\(426\) | 2.26504e11 | 0.333222 | ||||||||
\(427\) | −1.66455e11 | −0.242310 | ||||||||
\(428\) | −4.84955e11 | −0.698562 | ||||||||
\(429\) | 2.05942e12 | 2.93554 | ||||||||
\(430\) | −2.74045e10 | −0.0386557 | ||||||||
\(431\) | 8.61584e11 | 1.20268 | 0.601340 | − | 0.798993i | \(-0.294634\pi\) | ||||
0.601340 | + | 0.798993i | \(0.294634\pi\) | |||||||
\(432\) | 1.88034e10 | 0.0259752 | ||||||||
\(433\) | 1.45840e11 | 0.199379 | 0.0996896 | − | 0.995019i | \(-0.468215\pi\) | ||||
0.0996896 | + | 0.995019i | \(0.468215\pi\) | |||||||
\(434\) | −9.09145e10 | −0.123007 | ||||||||
\(435\) | 1.44938e11 | 0.194079 | ||||||||
\(436\) | −6.67206e11 | −0.884241 | ||||||||
\(437\) | −4.00792e11 | −0.525718 | ||||||||
\(438\) | 4.48160e11 | 0.581835 | ||||||||
\(439\) | −1.07131e11 | −0.137665 | −0.0688324 | − | 0.997628i | \(-0.521927\pi\) | ||||
−0.0688324 | + | 0.997628i | \(0.521927\pi\) | |||||||
\(440\) | −1.26452e11 | −0.160839 | ||||||||
\(441\) | 1.07578e11 | 0.135441 | ||||||||
\(442\) | 6.50972e11 | 0.811263 | ||||||||
\(443\) | −1.36838e11 | −0.168806 | −0.0844031 | − | 0.996432i | \(-0.526898\pi\) | ||||
−0.0844031 | + | 0.996432i | \(0.526898\pi\) | |||||||
\(444\) | 1.44923e12 | 1.76976 | ||||||||
\(445\) | 5.99510e10 | 0.0724731 | ||||||||
\(446\) | −2.23840e11 | −0.267874 | ||||||||
\(447\) | −4.17981e11 | −0.495191 | ||||||||
\(448\) | −4.32876e10 | −0.0507706 | ||||||||
\(449\) | −7.65671e11 | −0.889065 | −0.444532 | − | 0.895763i | \(-0.646630\pi\) | ||||
−0.444532 | + | 0.895763i | \(0.646630\pi\) | |||||||
\(450\) | −3.88811e11 | −0.446974 | ||||||||
\(451\) | 1.53730e11 | 0.174971 | ||||||||
\(452\) | 5.60331e11 | 0.631425 | ||||||||
\(453\) | 4.60754e11 | 0.514076 | ||||||||
\(454\) | −4.29226e11 | −0.474170 | ||||||||
\(455\) | 7.93880e10 | 0.0868368 | ||||||||
\(456\) | −8.42901e11 | −0.912924 | ||||||||
\(457\) | 5.41842e11 | 0.581099 | 0.290549 | − | 0.956860i | \(-0.406162\pi\) | ||||
0.290549 | + | 0.956860i | \(0.406162\pi\) | |||||||
\(458\) | −1.98805e11 | −0.211121 | ||||||||
\(459\) | −7.26094e10 | −0.0763547 | ||||||||
\(460\) | −7.25181e10 | −0.0755155 | ||||||||
\(461\) | −7.10838e11 | −0.733021 | −0.366510 | − | 0.930414i | \(-0.619448\pi\) | ||||
−0.366510 | + | 0.930414i | \(0.619448\pi\) | |||||||
\(462\) | 3.27059e11 | 0.333992 | ||||||||
\(463\) | 7.96272e11 | 0.805280 | 0.402640 | − | 0.915358i | \(-0.368093\pi\) | ||||
0.402640 | + | 0.915358i | \(0.368093\pi\) | |||||||
\(464\) | −3.46456e11 | −0.346990 | ||||||||
\(465\) | −1.36676e11 | −0.135567 | ||||||||
\(466\) | −5.53511e11 | −0.543738 | ||||||||
\(467\) | −1.67673e12 | −1.63132 | −0.815658 | − | 0.578535i | \(-0.803625\pi\) | ||||
−0.815658 | + | 0.578535i | \(0.803625\pi\) | |||||||
\(468\) | 1.20882e12 | 1.16481 | ||||||||
\(469\) | 5.60618e10 | 0.0535044 | ||||||||
\(470\) | −1.21272e11 | −0.114635 | ||||||||
\(471\) | 5.84478e11 | 0.547235 | ||||||||
\(472\) | 2.49102e11 | 0.231014 | ||||||||
\(473\) | −8.00257e11 | −0.735114 | ||||||||
\(474\) | 3.19099e8 | 0.000290351 0 | ||||||||
\(475\) | 8.34938e11 | 0.752546 | ||||||||
\(476\) | −3.42749e11 | −0.306016 | ||||||||
\(477\) | −1.72969e12 | −1.52980 | ||||||||
\(478\) | 4.14400e11 | 0.363073 | ||||||||
\(479\) | 1.17129e12 | 1.01661 | 0.508305 | − | 0.861177i | \(-0.330272\pi\) | ||||
0.508305 | + | 0.861177i | \(0.330272\pi\) | |||||||
\(480\) | −2.38761e11 | −0.205295 | ||||||||
\(481\) | −3.09842e12 | −2.63929 | ||||||||
\(482\) | 1.06754e12 | 0.900895 | ||||||||
\(483\) | 4.31697e11 | 0.360925 | ||||||||
\(484\) | −6.76844e11 | −0.560641 | ||||||||
\(485\) | −1.79897e11 | −0.147634 | ||||||||
\(486\) | 8.24112e11 | 0.670074 | ||||||||
\(487\) | 4.49797e11 | 0.362357 | 0.181178 | − | 0.983450i | \(-0.442009\pi\) | ||||
0.181178 | + | 0.983450i | \(0.442009\pi\) | |||||||
\(488\) | −6.83675e11 | −0.545708 | ||||||||
\(489\) | −1.80297e12 | −1.42594 | ||||||||
\(490\) | 1.26077e10 | 0.00987990 | ||||||||
\(491\) | 2.25034e12 | 1.74735 | 0.873677 | − | 0.486506i | \(-0.161729\pi\) | ||||
0.873677 | + | 0.486506i | \(0.161729\pi\) | |||||||
\(492\) | 1.85411e11 | 0.142657 | ||||||||
\(493\) | 1.33784e12 | 1.01998 | ||||||||
\(494\) | 7.82970e11 | 0.591526 | ||||||||
\(495\) | 2.39290e11 | 0.179143 | ||||||||
\(496\) | 3.26707e11 | 0.242376 | ||||||||
\(497\) | 2.54972e11 | 0.187452 | ||||||||
\(498\) | −1.11246e12 | −0.810497 | ||||||||
\(499\) | 1.59712e10 | 0.0115315 | 0.00576574 | − | 0.999983i | \(-0.498165\pi\) | ||||
0.00576574 | + | 0.999983i | \(0.498165\pi\) | |||||||
\(500\) | 3.05326e11 | 0.218474 | ||||||||
\(501\) | 9.70275e11 | 0.688058 | ||||||||
\(502\) | 8.44300e11 | 0.593376 | ||||||||
\(503\) | 1.73375e12 | 1.20762 | 0.603811 | − | 0.797127i | \(-0.293648\pi\) | ||||
0.603811 | + | 0.797127i | \(0.293648\pi\) | |||||||
\(504\) | 4.41852e11 | 0.305028 | ||||||||
\(505\) | −8.29316e9 | −0.00567425 | ||||||||
\(506\) | 6.38734e11 | 0.433155 | ||||||||
\(507\) | −3.23384e12 | −2.17361 | ||||||||
\(508\) | 1.23064e12 | 0.819869 | ||||||||
\(509\) | 9.77460e11 | 0.645460 | 0.322730 | − | 0.946491i | \(-0.395399\pi\) | ||||
0.322730 | + | 0.946491i | \(0.395399\pi\) | |||||||
\(510\) | 1.55417e11 | 0.101726 | ||||||||
\(511\) | 5.04487e11 | 0.327307 | ||||||||
\(512\) | 1.04525e12 | 0.672212 | ||||||||
\(513\) | −8.73326e10 | −0.0556734 | ||||||||
\(514\) | −1.17191e12 | −0.740558 | ||||||||
\(515\) | 8.62303e10 | 0.0540166 | ||||||||
\(516\) | −9.65175e11 | −0.599353 | ||||||||
\(517\) | −3.54133e12 | −2.18001 | ||||||||
\(518\) | −4.92062e11 | −0.300286 | ||||||||
\(519\) | −7.39300e11 | −0.447268 | ||||||||
\(520\) | 3.26067e11 | 0.195565 | ||||||||
\(521\) | 5.89223e11 | 0.350356 | 0.175178 | − | 0.984537i | \(-0.443950\pi\) | ||||
0.175178 | + | 0.984537i | \(0.443950\pi\) | |||||||
\(522\) | −7.49328e11 | −0.441728 | ||||||||
\(523\) | 1.43218e12 | 0.837027 | 0.418513 | − | 0.908211i | \(-0.362551\pi\) | ||||
0.418513 | + | 0.908211i | \(0.362551\pi\) | |||||||
\(524\) | −2.76577e11 | −0.160260 | ||||||||
\(525\) | −8.99320e11 | −0.516651 | ||||||||
\(526\) | −1.32468e11 | −0.0754527 | ||||||||
\(527\) | −1.26158e12 | −0.712471 | ||||||||
\(528\) | −1.17530e12 | −0.658109 | ||||||||
\(529\) | −9.58063e11 | −0.531916 | ||||||||
\(530\) | −2.02711e11 | −0.111593 | ||||||||
\(531\) | −4.71382e11 | −0.257305 | ||||||||
\(532\) | −4.12248e11 | −0.223129 | ||||||||
\(533\) | −3.96405e11 | −0.212749 | ||||||||
\(534\) | −6.36865e11 | −0.338931 | ||||||||
\(535\) | 2.47538e11 | 0.130632 | ||||||||
\(536\) | 2.30260e11 | 0.120497 | ||||||||
\(537\) | 3.80594e12 | 1.97505 | ||||||||
\(538\) | −1.34540e12 | −0.692357 | ||||||||
\(539\) | 3.68165e11 | 0.187885 | ||||||||
\(540\) | −1.58017e10 | −0.00799708 | ||||||||
\(541\) | 1.17323e12 | 0.588839 | 0.294419 | − | 0.955676i | \(-0.404874\pi\) | ||||
0.294419 | + | 0.955676i | \(0.404874\pi\) | |||||||
\(542\) | 1.46291e12 | 0.728152 | ||||||||
\(543\) | 1.92200e12 | 0.948755 | ||||||||
\(544\) | −2.20388e12 | −1.07893 | ||||||||
\(545\) | 3.40565e11 | 0.165355 | ||||||||
\(546\) | −8.43345e11 | −0.406105 | ||||||||
\(547\) | 2.59515e11 | 0.123942 | 0.0619712 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619712 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(548\) | 1.20882e12 | 0.572597 | ||||||||
\(549\) | 1.29374e12 | 0.607814 | ||||||||
\(550\) | −1.33062e12 | −0.620045 | ||||||||
\(551\) | 1.60912e12 | 0.743714 | ||||||||
\(552\) | 1.77309e12 | 0.812841 | ||||||||
\(553\) | 3.59205e8 | 0.000163335 0 | ||||||||
\(554\) | −2.36022e11 | −0.106453 | ||||||||
\(555\) | −7.39737e11 | −0.330947 | ||||||||
\(556\) | −1.99748e12 | −0.886432 | ||||||||
\(557\) | −2.36651e12 | −1.04174 | −0.520871 | − | 0.853635i | \(-0.674393\pi\) | ||||
−0.520871 | + | 0.853635i | \(0.674393\pi\) | |||||||
\(558\) | 7.06613e11 | 0.308552 | ||||||||
\(559\) | 2.06352e12 | 0.893832 | ||||||||
\(560\) | −4.53064e10 | −0.0194676 | ||||||||
\(561\) | 4.53845e12 | 1.93453 | ||||||||
\(562\) | 8.42294e10 | 0.0356164 | ||||||||
\(563\) | −2.42400e12 | −1.01682 | −0.508410 | − | 0.861115i | \(-0.669767\pi\) | ||||
−0.508410 | + | 0.861115i | \(0.669767\pi\) | |||||||
\(564\) | −4.27113e12 | −1.77741 | ||||||||
\(565\) | −2.86013e11 | −0.118078 | ||||||||
\(566\) | −7.83821e11 | −0.321028 | ||||||||
\(567\) | 9.75977e11 | 0.396566 | ||||||||
\(568\) | 1.04724e12 | 0.422160 | ||||||||
\(569\) | −2.11854e12 | −0.847290 | −0.423645 | − | 0.905828i | \(-0.639250\pi\) | ||||
−0.423645 | + | 0.905828i | \(0.639250\pi\) | |||||||
\(570\) | 1.86932e11 | 0.0741730 | ||||||||
\(571\) | −7.50992e11 | −0.295646 | −0.147823 | − | 0.989014i | \(-0.547227\pi\) | ||||
−0.147823 | + | 0.989014i | \(0.547227\pi\) | |||||||
\(572\) | 4.13695e12 | 1.61584 | ||||||||
\(573\) | 3.61437e12 | 1.40067 | ||||||||
\(574\) | −6.29534e10 | −0.0242056 | ||||||||
\(575\) | −1.75634e12 | −0.670045 | ||||||||
\(576\) | 3.36444e11 | 0.127354 | ||||||||
\(577\) | 4.35951e12 | 1.63737 | 0.818685 | − | 0.574243i | \(-0.194704\pi\) | ||||
0.818685 | + | 0.574243i | \(0.194704\pi\) | |||||||
\(578\) | 1.42864e11 | 0.0532413 | ||||||||
\(579\) | −9.46981e11 | −0.350177 | ||||||||
\(580\) | 2.91149e11 | 0.106829 | ||||||||
\(581\) | −1.25228e12 | −0.455940 | ||||||||
\(582\) | 1.91106e12 | 0.690433 | ||||||||
\(583\) | −5.91951e12 | −2.12216 | ||||||||
\(584\) | 2.07206e12 | 0.737130 | ||||||||
\(585\) | −6.17026e11 | −0.217822 | ||||||||
\(586\) | 1.89173e12 | 0.662704 | ||||||||
\(587\) | −2.20056e12 | −0.765002 | −0.382501 | − | 0.923955i | \(-0.624937\pi\) | ||||
−0.382501 | + | 0.923955i | \(0.624937\pi\) | |||||||
\(588\) | 4.44037e11 | 0.153187 | ||||||||
\(589\) | −1.51739e12 | −0.519492 | ||||||||
\(590\) | −5.52438e10 | −0.0187693 | ||||||||
\(591\) | −5.29179e12 | −1.78426 | ||||||||
\(592\) | 1.76825e12 | 0.591693 | ||||||||
\(593\) | −2.83604e12 | −0.941815 | −0.470907 | − | 0.882183i | \(-0.656073\pi\) | ||||
−0.470907 | + | 0.882183i | \(0.656073\pi\) | |||||||
\(594\) | 1.39180e11 | 0.0458710 | ||||||||
\(595\) | 1.74951e11 | 0.0572256 | ||||||||
\(596\) | −8.39636e11 | −0.272573 | ||||||||
\(597\) | −3.24610e12 | −1.04587 | ||||||||
\(598\) | −1.64702e12 | −0.526677 | ||||||||
\(599\) | −8.29286e11 | −0.263199 | −0.131599 | − | 0.991303i | \(-0.542011\pi\) | ||||
−0.131599 | + | 0.991303i | \(0.542011\pi\) | |||||||
\(600\) | −3.69374e12 | −1.16355 | ||||||||
\(601\) | 5.62459e12 | 1.75855 | 0.879277 | − | 0.476311i | \(-0.158026\pi\) | ||||
0.879277 | + | 0.476311i | \(0.158026\pi\) | |||||||
\(602\) | 3.27710e11 | 0.101696 | ||||||||
\(603\) | −4.35728e11 | −0.134211 | ||||||||
\(604\) | 9.25557e11 | 0.282968 | ||||||||
\(605\) | 3.45485e11 | 0.104841 | ||||||||
\(606\) | 8.80989e10 | 0.0265365 | ||||||||
\(607\) | −4.68777e11 | −0.140158 | −0.0700789 | − | 0.997541i | \(-0.522325\pi\) | ||||
−0.0700789 | + | 0.997541i | \(0.522325\pi\) | |||||||
\(608\) | −2.65076e12 | −0.786691 | ||||||||
\(609\) | −1.73320e12 | −0.510588 | ||||||||
\(610\) | 1.51620e11 | 0.0443375 | ||||||||
\(611\) | 9.13159e12 | 2.65070 | ||||||||
\(612\) | 2.66394e12 | 0.767614 | ||||||||
\(613\) | 5.58394e12 | 1.59723 | 0.798617 | − | 0.601840i | \(-0.205566\pi\) | ||||
0.798617 | + | 0.601840i | \(0.205566\pi\) | |||||||
\(614\) | 2.47376e12 | 0.702425 | ||||||||
\(615\) | −9.46405e10 | −0.0266771 | ||||||||
\(616\) | 1.51215e12 | 0.423137 | ||||||||
\(617\) | −3.36717e12 | −0.935367 | −0.467683 | − | 0.883896i | \(-0.654911\pi\) | ||||
−0.467683 | + | 0.883896i | \(0.654911\pi\) | |||||||
\(618\) | −9.16031e11 | −0.252617 | ||||||||
\(619\) | −5.66928e12 | −1.55210 | −0.776051 | − | 0.630671i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630671i | \(0.782780\pi\) | |||||||
\(620\) | −2.74552e11 | −0.0746212 | ||||||||
\(621\) | 1.83709e11 | 0.0495700 | ||||||||
\(622\) | −9.46512e11 | −0.253553 | ||||||||
\(623\) | −7.16909e11 | −0.190663 | ||||||||
\(624\) | 3.03061e12 | 0.800201 | ||||||||
\(625\) | 3.58011e12 | 0.938505 | ||||||||
\(626\) | −5.72168e11 | −0.148915 | ||||||||
\(627\) | 5.45871e12 | 1.41054 | ||||||||
\(628\) | 1.17409e12 | 0.301220 | ||||||||
\(629\) | −6.82812e12 | −1.73930 | ||||||||
\(630\) | −9.79904e10 | −0.0247828 | ||||||||
\(631\) | −1.06685e12 | −0.267899 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(632\) | 1.47535e9 | 0.000367847 0 | ||||||||
\(633\) | 1.06694e13 | 2.64133 | ||||||||
\(634\) | 2.87325e12 | 0.706273 | ||||||||
\(635\) | −6.28163e11 | −0.153317 | ||||||||
\(636\) | −7.13941e12 | −1.73024 | ||||||||
\(637\) | −9.49340e11 | −0.228452 | ||||||||
\(638\) | −2.56442e12 | −0.612768 | ||||||||
\(639\) | −1.98172e12 | −0.470205 | ||||||||
\(640\) | −5.84856e11 | −0.137797 | ||||||||
\(641\) | −7.83632e12 | −1.83337 | −0.916686 | − | 0.399607i | \(-0.869147\pi\) | ||||
−0.916686 | + | 0.399607i | \(0.869147\pi\) | |||||||
\(642\) | −2.62962e12 | −0.610921 | ||||||||
\(643\) | 7.05971e12 | 1.62869 | 0.814343 | − | 0.580383i | \(-0.197097\pi\) | ||||
0.814343 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(644\) | 8.67188e11 | 0.198668 | ||||||||
\(645\) | 4.92660e11 | 0.112080 | ||||||||
\(646\) | 1.72547e12 | 0.389817 | ||||||||
\(647\) | 2.77314e12 | 0.622161 | 0.311081 | − | 0.950384i | \(-0.399309\pi\) | ||||
0.311081 | + | 0.950384i | \(0.399309\pi\) | |||||||
\(648\) | 4.00859e12 | 0.893108 | ||||||||
\(649\) | −1.61321e12 | −0.356935 | ||||||||
\(650\) | 3.43111e12 | 0.753919 | ||||||||
\(651\) | 1.63440e12 | 0.356651 | ||||||||
\(652\) | −3.62179e12 | −0.784891 | ||||||||
\(653\) | 3.09564e12 | 0.666257 | 0.333128 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333128 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(654\) | −3.61785e12 | −0.773305 | ||||||||
\(655\) | 1.41175e11 | 0.0299689 | ||||||||
\(656\) | 2.26227e11 | 0.0476954 | ||||||||
\(657\) | −3.92102e12 | −0.821021 | ||||||||
\(658\) | 1.45019e12 | 0.301585 | ||||||||
\(659\) | −4.80261e12 | −0.991958 | −0.495979 | − | 0.868335i | \(-0.665191\pi\) | ||||
−0.495979 | + | 0.868335i | \(0.665191\pi\) | |||||||
\(660\) | 9.87683e11 | 0.202614 | ||||||||
\(661\) | −5.13389e12 | −1.04602 | −0.523010 | − | 0.852327i | \(-0.675191\pi\) | ||||
−0.523010 | + | 0.852327i | \(0.675191\pi\) | |||||||
\(662\) | −2.30212e12 | −0.465872 | ||||||||
\(663\) | −1.17027e13 | −2.35221 | ||||||||
\(664\) | −5.14342e12 | −1.02682 | ||||||||
\(665\) | 2.10426e11 | 0.0417256 | ||||||||
\(666\) | 3.82444e12 | 0.753241 | ||||||||
\(667\) | −3.38488e12 | −0.662181 | ||||||||
\(668\) | 1.94908e12 | 0.378735 | ||||||||
\(669\) | 4.02404e12 | 0.776685 | ||||||||
\(670\) | −5.10652e10 | −0.00979014 | ||||||||
\(671\) | 4.42755e12 | 0.843164 | ||||||||
\(672\) | 2.85516e12 | 0.540093 | ||||||||
\(673\) | 4.43802e12 | 0.833915 | 0.416957 | − | 0.908926i | \(-0.363096\pi\) | ||||
0.416957 | + | 0.908926i | \(0.363096\pi\) | |||||||
\(674\) | −4.00277e12 | −0.747122 | ||||||||
\(675\) | −3.82707e11 | −0.0709576 | ||||||||
\(676\) | −6.49609e12 | −1.19644 | ||||||||
\(677\) | −4.70675e12 | −0.861136 | −0.430568 | − | 0.902558i | \(-0.641687\pi\) | ||||
−0.430568 | + | 0.902558i | \(0.641687\pi\) | |||||||
\(678\) | 3.03834e12 | 0.552207 | ||||||||
\(679\) | 2.15126e12 | 0.388399 | ||||||||
\(680\) | 7.18569e11 | 0.128878 | ||||||||
\(681\) | 7.71632e12 | 1.37483 | ||||||||
\(682\) | 2.41824e12 | 0.428025 | ||||||||
\(683\) | 6.12667e11 | 0.107729 | 0.0538644 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538644 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(684\) | 3.20411e12 | 0.559699 | ||||||||
\(685\) | −6.17025e11 | −0.107077 | ||||||||
\(686\) | −1.50765e11 | −0.0259922 | ||||||||
\(687\) | 3.57397e12 | 0.612133 | ||||||||
\(688\) | −1.17764e12 | −0.200385 | ||||||||
\(689\) | 1.52639e13 | 2.58035 | ||||||||
\(690\) | −3.93222e11 | −0.0660415 | ||||||||
\(691\) | 2.69919e12 | 0.450383 | 0.225191 | − | 0.974315i | \(-0.427699\pi\) | ||||
0.225191 | + | 0.974315i | \(0.427699\pi\) | |||||||
\(692\) | −1.48510e12 | −0.246194 | ||||||||
\(693\) | −2.86148e12 | −0.471293 | ||||||||
\(694\) | 4.72586e12 | 0.773327 | ||||||||
\(695\) | 1.01958e12 | 0.165764 | ||||||||
\(696\) | −7.11869e12 | −1.14990 | ||||||||
\(697\) | −8.73576e11 | −0.140202 | ||||||||
\(698\) | 1.13375e12 | 0.180788 | ||||||||
\(699\) | 9.95064e12 | 1.57654 | ||||||||
\(700\) | −1.80654e12 | −0.284386 | ||||||||
\(701\) | −5.78506e12 | −0.904850 | −0.452425 | − | 0.891802i | \(-0.649441\pi\) | ||||
−0.452425 | + | 0.891802i | \(0.649441\pi\) | |||||||
\(702\) | −3.58886e11 | −0.0557750 | ||||||||
\(703\) | −8.21267e12 | −1.26819 | ||||||||
\(704\) | 1.15141e12 | 0.176666 | ||||||||
\(705\) | 2.18014e12 | 0.332379 | ||||||||
\(706\) | −4.86772e12 | −0.737403 | ||||||||
\(707\) | 9.91715e10 | 0.0149279 | ||||||||
\(708\) | −1.94566e12 | −0.291016 | ||||||||
\(709\) | −3.72656e12 | −0.553860 | −0.276930 | − | 0.960890i | \(-0.589317\pi\) | ||||
−0.276930 | + | 0.960890i | \(0.589317\pi\) | |||||||
\(710\) | −2.32248e11 | −0.0342996 | ||||||||
\(711\) | −2.79184e9 | −0.000409711 0 | ||||||||
\(712\) | −2.94453e12 | −0.429394 | ||||||||
\(713\) | 3.19192e12 | 0.462541 | ||||||||
\(714\) | −1.85852e12 | −0.267624 | ||||||||
\(715\) | −2.11164e12 | −0.302165 | ||||||||
\(716\) | 7.64532e12 | 1.08714 | ||||||||
\(717\) | −7.44980e12 | −1.05271 | ||||||||
\(718\) | −2.14092e12 | −0.300636 | ||||||||
\(719\) | 1.33255e13 | 1.85953 | 0.929765 | − | 0.368154i | \(-0.120010\pi\) | ||||
0.929765 | + | 0.368154i | \(0.120010\pi\) | |||||||
\(720\) | 3.52134e11 | 0.0488328 | ||||||||
\(721\) | −1.03116e12 | −0.142108 | ||||||||
\(722\) | −1.43952e12 | −0.197151 | ||||||||
\(723\) | −1.91916e13 | −2.61209 | ||||||||
\(724\) | 3.86089e12 | 0.522233 | ||||||||
\(725\) | 7.05144e12 | 0.947888 | ||||||||
\(726\) | −3.67012e12 | −0.490304 | ||||||||
\(727\) | −2.39852e12 | −0.318448 | −0.159224 | − | 0.987242i | \(-0.550899\pi\) | ||||
−0.159224 | + | 0.987242i | \(0.550899\pi\) | |||||||
\(728\) | −3.89918e12 | −0.514497 | ||||||||
\(729\) | −6.81442e12 | −0.893625 | ||||||||
\(730\) | −4.59524e11 | −0.0598901 | ||||||||
\(731\) | 4.54748e12 | 0.589037 | ||||||||
\(732\) | 5.33998e12 | 0.687448 | ||||||||
\(733\) | 7.93815e12 | 1.01567 | 0.507834 | − | 0.861455i | \(-0.330446\pi\) | ||||
0.507834 | + | 0.861455i | \(0.330446\pi\) | |||||||
\(734\) | −2.45644e12 | −0.312373 | ||||||||
\(735\) | −2.26652e11 | −0.0286462 | ||||||||
\(736\) | 5.57603e12 | 0.700447 | ||||||||
\(737\) | −1.49119e12 | −0.186178 | ||||||||
\(738\) | 4.89292e11 | 0.0607175 | ||||||||
\(739\) | −2.20371e12 | −0.271803 | −0.135902 | − | 0.990722i | \(-0.543393\pi\) | ||||
−0.135902 | + | 0.990722i | \(0.543393\pi\) | |||||||
\(740\) | −1.48598e12 | −0.182167 | ||||||||
\(741\) | −1.40757e13 | −1.71509 | ||||||||
\(742\) | 2.42407e12 | 0.293581 | ||||||||
\(743\) | −1.09079e12 | −0.131308 | −0.0656540 | − | 0.997842i | \(-0.520913\pi\) | ||||
−0.0656540 | + | 0.997842i | \(0.520913\pi\) | |||||||
\(744\) | 6.71290e12 | 0.803215 | ||||||||
\(745\) | 4.28580e11 | 0.0509716 | ||||||||
\(746\) | −2.22657e12 | −0.263215 | ||||||||
\(747\) | 9.73305e12 | 1.14368 | ||||||||
\(748\) | 9.11678e12 | 1.06484 | ||||||||
\(749\) | −2.96012e12 | −0.343670 | ||||||||
\(750\) | 1.65560e12 | 0.191064 | ||||||||
\(751\) | −3.09647e11 | −0.0355212 | −0.0177606 | − | 0.999842i | \(-0.505654\pi\) | ||||
−0.0177606 | + | 0.999842i | \(0.505654\pi\) | |||||||
\(752\) | −5.21136e12 | −0.594252 | ||||||||
\(753\) | −1.51783e13 | −1.72046 | ||||||||
\(754\) | 6.61254e12 | 0.745071 | ||||||||
\(755\) | −4.72437e11 | −0.0529155 | ||||||||
\(756\) | 1.88960e11 | 0.0210389 | ||||||||
\(757\) | 1.44340e12 | 0.159755 | 0.0798777 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798777 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(758\) | 4.39299e11 | 0.0483336 | ||||||||
\(759\) | −1.14827e13 | −1.25591 | ||||||||
\(760\) | 8.64274e11 | 0.0939702 | ||||||||
\(761\) | −2.27862e12 | −0.246287 | −0.123143 | − | 0.992389i | \(-0.539297\pi\) | ||||
−0.123143 | + | 0.992389i | \(0.539297\pi\) | |||||||
\(762\) | 6.67302e12 | 0.717010 | ||||||||
\(763\) | −4.07256e12 | −0.435018 | ||||||||
\(764\) | 7.26051e12 | 0.770987 | ||||||||
\(765\) | −1.35977e12 | −0.143545 | ||||||||
\(766\) | −4.33873e12 | −0.455337 | ||||||||
\(767\) | 4.15978e12 | 0.434001 | ||||||||
\(768\) | 8.02053e12 | 0.831912 | ||||||||
\(769\) | 1.09547e13 | 1.12962 | 0.564809 | − | 0.825221i | \(-0.308950\pi\) | ||||
0.564809 | + | 0.825221i | \(0.308950\pi\) | |||||||
\(770\) | −3.35352e11 | −0.0343789 | ||||||||
\(771\) | 2.10677e13 | 2.14720 | ||||||||
\(772\) | −1.90228e12 | −0.192751 | ||||||||
\(773\) | 7.52114e12 | 0.757663 | 0.378831 | − | 0.925466i | \(-0.376326\pi\) | ||||
0.378831 | + | 0.925466i | \(0.376326\pi\) | |||||||
\(774\) | −2.54705e12 | −0.255096 | ||||||||
\(775\) | −6.64948e12 | −0.662110 | ||||||||
\(776\) | 8.83576e12 | 0.874714 | ||||||||
\(777\) | 8.84595e12 | 0.870662 | ||||||||
\(778\) | −4.60211e12 | −0.450348 | ||||||||
\(779\) | −1.05071e12 | −0.102227 | ||||||||
\(780\) | −2.54681e12 | −0.246361 | ||||||||
\(781\) | −6.78201e12 | −0.652272 | ||||||||
\(782\) | −3.62962e12 | −0.347081 | ||||||||
\(783\) | −7.37564e11 | −0.0701248 | ||||||||
\(784\) | 5.41785e11 | 0.0512158 | ||||||||
\(785\) | −5.99298e11 | −0.0563287 | ||||||||
\(786\) | −1.49971e12 | −0.140154 | ||||||||
\(787\) | 1.85303e12 | 0.172185 | 0.0860926 | − | 0.996287i | \(-0.472562\pi\) | ||||
0.0860926 | + | 0.996287i | \(0.472562\pi\) | |||||||
\(788\) | −1.06301e13 | −0.982129 | ||||||||
\(789\) | 2.38142e12 | 0.218771 | ||||||||
\(790\) | −3.27191e8 | −2.98868e−5 0 | ||||||||
\(791\) | 3.42021e12 | 0.310641 | ||||||||
\(792\) | −1.17528e13 | −1.06140 | ||||||||
\(793\) | −1.14168e13 | −1.02521 | ||||||||
\(794\) | 7.09097e12 | 0.633159 | ||||||||
\(795\) | 3.64421e12 | 0.323557 | ||||||||
\(796\) | −6.52073e12 | −0.575688 | ||||||||
\(797\) | −1.84378e13 | −1.61863 | −0.809314 | − | 0.587377i | \(-0.800161\pi\) | ||||
−0.809314 | + | 0.587377i | \(0.800161\pi\) | |||||||
\(798\) | −2.23537e12 | −0.195136 | ||||||||
\(799\) | 2.01237e13 | 1.74682 | ||||||||
\(800\) | −1.16161e13 | −1.00266 | ||||||||
\(801\) | 5.57202e12 | 0.478262 | ||||||||
\(802\) | −3.38220e12 | −0.288679 | ||||||||
\(803\) | −1.34189e13 | −1.13893 | ||||||||
\(804\) | −1.79850e12 | −0.151795 | ||||||||
\(805\) | −4.42644e11 | −0.0371512 | ||||||||
\(806\) | −6.23560e12 | −0.520440 | ||||||||
\(807\) | 2.41866e13 | 2.00745 | ||||||||
\(808\) | 4.07323e11 | 0.0336192 | ||||||||
\(809\) | −1.03419e13 | −0.848856 | −0.424428 | − | 0.905462i | \(-0.639525\pi\) | ||||
−0.424428 | + | 0.905462i | \(0.639525\pi\) | |||||||
\(810\) | −8.88992e11 | −0.0725630 | ||||||||
\(811\) | −2.31795e13 | −1.88153 | −0.940764 | − | 0.339062i | \(-0.889890\pi\) | ||||
−0.940764 | + | 0.339062i | \(0.889890\pi\) | |||||||
\(812\) | −3.48163e12 | −0.281048 | ||||||||
\(813\) | −2.62993e13 | −2.11123 | ||||||||
\(814\) | 1.30884e13 | 1.04490 | ||||||||
\(815\) | 1.84869e12 | 0.146776 | ||||||||
\(816\) | 6.67869e12 | 0.527334 | ||||||||
\(817\) | 5.46958e12 | 0.429492 | ||||||||
\(818\) | 3.26250e12 | 0.254777 | ||||||||
\(819\) | 7.37854e12 | 0.573051 | ||||||||
\(820\) | −1.90113e11 | −0.0146842 | ||||||||
\(821\) | 1.10059e13 | 0.845436 | 0.422718 | − | 0.906261i | \(-0.361076\pi\) | ||||
0.422718 | + | 0.906261i | \(0.361076\pi\) | |||||||
\(822\) | 6.55470e12 | 0.500760 | ||||||||
\(823\) | 2.30119e13 | 1.74845 | 0.874224 | − | 0.485523i | \(-0.161371\pi\) | ||||
0.874224 | + | 0.485523i | \(0.161371\pi\) | |||||||
\(824\) | −4.23525e12 | −0.320041 | ||||||||
\(825\) | 2.39211e13 | 1.79778 | ||||||||
\(826\) | 6.60618e11 | 0.0493787 | ||||||||
\(827\) | 6.58898e12 | 0.489827 | 0.244914 | − | 0.969545i | \(-0.421240\pi\) | ||||
0.244914 | + | 0.969545i | \(0.421240\pi\) | |||||||
\(828\) | −6.74003e12 | −0.498340 | ||||||||
\(829\) | −1.32427e13 | −0.973829 | −0.486915 | − | 0.873450i | \(-0.661878\pi\) | ||||
−0.486915 | + | 0.873450i | \(0.661878\pi\) | |||||||
\(830\) | 1.14067e12 | 0.0834271 | ||||||||
\(831\) | 4.24304e12 | 0.308654 | ||||||||
\(832\) | −2.96899e12 | −0.214810 | ||||||||
\(833\) | −2.09210e12 | −0.150550 | ||||||||
\(834\) | −1.08311e13 | −0.775222 | ||||||||
\(835\) | −9.94878e11 | −0.0708240 | ||||||||
\(836\) | 1.09654e13 | 0.776419 | ||||||||
\(837\) | 6.95520e11 | 0.0489830 | ||||||||
\(838\) | −4.74058e12 | −0.332073 | ||||||||
\(839\) | −5.05558e12 | −0.352243 | −0.176122 | − | 0.984368i | \(-0.556355\pi\) | ||||
−0.176122 | + | 0.984368i | \(0.556355\pi\) | |||||||
\(840\) | −9.30918e11 | −0.0645141 | ||||||||
\(841\) | −9.17397e11 | −0.0632376 | ||||||||
\(842\) | −2.26127e12 | −0.155042 | ||||||||
\(843\) | −1.51422e12 | −0.103268 | ||||||||
\(844\) | 2.14326e13 | 1.45390 | ||||||||
\(845\) | 3.31584e12 | 0.223737 | ||||||||
\(846\) | −1.12713e13 | −0.756499 | ||||||||
\(847\) | −4.13139e12 | −0.275817 | ||||||||
\(848\) | −8.71104e12 | −0.578480 | ||||||||
\(849\) | 1.40910e13 | 0.930802 | ||||||||
\(850\) | 7.56130e12 | 0.496834 | ||||||||
\(851\) | 1.72758e13 | 1.12916 | ||||||||
\(852\) | −8.17966e12 | −0.531811 | ||||||||
\(853\) | 1.03049e13 | 0.666456 | 0.333228 | − | 0.942846i | \(-0.391862\pi\) | ||||
0.333228 | + | 0.942846i | \(0.391862\pi\) | |||||||
\(854\) | −1.81310e12 | −0.116644 | ||||||||
\(855\) | −1.63549e12 | −0.104665 | ||||||||
\(856\) | −1.21580e13 | −0.773979 | ||||||||
\(857\) | −1.66788e13 | −1.05621 | −0.528105 | − | 0.849179i | \(-0.677097\pi\) | ||||
−0.528105 | + | 0.849179i | \(0.677097\pi\) | |||||||
\(858\) | 2.24322e13 | 1.41312 | ||||||||
\(859\) | −2.36677e13 | −1.48316 | −0.741579 | − | 0.670865i | \(-0.765923\pi\) | ||||
−0.741579 | + | 0.670865i | \(0.765923\pi\) | |||||||
\(860\) | 9.89649e11 | 0.0616933 | ||||||||
\(861\) | 1.13173e12 | 0.0701827 | ||||||||
\(862\) | 9.38476e12 | 0.578949 | ||||||||
\(863\) | 1.26428e13 | 0.775880 | 0.387940 | − | 0.921685i | \(-0.373187\pi\) | ||||
0.387940 | + | 0.921685i | \(0.373187\pi\) | |||||||
\(864\) | 1.21502e12 | 0.0741772 | ||||||||
\(865\) | 7.58046e11 | 0.0460387 | ||||||||
\(866\) | 1.58855e12 | 0.0959776 | ||||||||
\(867\) | −2.56832e12 | −0.154370 | ||||||||
\(868\) | 3.28316e12 | 0.196315 | ||||||||
\(869\) | −9.55450e9 | −0.000568354 0 | ||||||||
\(870\) | 1.57872e12 | 0.0934264 | ||||||||
\(871\) | 3.84514e12 | 0.226376 | ||||||||
\(872\) | −1.67271e13 | −0.979705 | ||||||||
\(873\) | −1.67202e13 | −0.974264 | ||||||||
\(874\) | −4.36561e12 | −0.253071 | ||||||||
\(875\) | 1.86368e12 | 0.107482 | ||||||||
\(876\) | −1.61842e13 | −0.928589 | ||||||||
\(877\) | 2.21629e13 | 1.26511 | 0.632555 | − | 0.774515i | \(-0.282006\pi\) | ||||
0.632555 | + | 0.774515i | \(0.282006\pi\) | |||||||
\(878\) | −1.16691e12 | −0.0662695 | ||||||||
\(879\) | −3.40082e13 | −1.92147 | ||||||||
\(880\) | 1.20511e12 | 0.0677413 | ||||||||
\(881\) | −1.87132e13 | −1.04654 | −0.523272 | − | 0.852166i | \(-0.675289\pi\) | ||||
−0.523272 | + | 0.852166i | \(0.675289\pi\) | |||||||
\(882\) | 1.17179e12 | 0.0651991 | ||||||||
\(883\) | −1.66483e13 | −0.921611 | −0.460805 | − | 0.887501i | \(-0.652439\pi\) | ||||
−0.460805 | + | 0.887501i | \(0.652439\pi\) | |||||||
\(884\) | −2.35083e13 | −1.29475 | ||||||||
\(885\) | 9.93134e11 | 0.0544206 | ||||||||
\(886\) | −1.49050e12 | −0.0812604 | ||||||||
\(887\) | −1.58859e13 | −0.861698 | −0.430849 | − | 0.902424i | \(-0.641786\pi\) | ||||
−0.430849 | + | 0.902424i | \(0.641786\pi\) | |||||||
\(888\) | 3.63326e13 | 1.96082 | ||||||||
\(889\) | 7.51171e12 | 0.403349 | ||||||||
\(890\) | 6.53013e11 | 0.0348873 | ||||||||
\(891\) | −2.59600e13 | −1.37993 | ||||||||
\(892\) | 8.08344e12 | 0.427518 | ||||||||
\(893\) | 2.42042e13 | 1.27368 | ||||||||
\(894\) | −4.55284e12 | −0.238376 | ||||||||
\(895\) | −3.90244e12 | −0.203298 | ||||||||
\(896\) | 6.99384e12 | 0.362518 | ||||||||
\(897\) | 2.96091e13 | 1.52707 | ||||||||
\(898\) | −8.34003e12 | −0.427980 | ||||||||
\(899\) | −1.28151e13 | −0.654339 | ||||||||
\(900\) | 1.40410e13 | 0.713355 | ||||||||
\(901\) | 3.36377e13 | 1.70046 | ||||||||
\(902\) | 1.67450e12 | 0.0842278 | ||||||||
\(903\) | −5.89134e12 | −0.294862 | ||||||||
\(904\) | 1.40477e13 | 0.699595 | ||||||||
\(905\) | −1.97074e12 | −0.0976585 | ||||||||
\(906\) | 5.01873e12 | 0.247467 | ||||||||
\(907\) | −3.65370e13 | −1.79267 | −0.896333 | − | 0.443381i | \(-0.853779\pi\) | ||||
−0.896333 | + | 0.443381i | \(0.853779\pi\) | |||||||
\(908\) | 1.55005e13 | 0.756760 | ||||||||
\(909\) | −7.70789e11 | −0.0374454 | ||||||||
\(910\) | 8.64729e11 | 0.0418017 | ||||||||
\(911\) | 2.09138e13 | 1.00600 | 0.503002 | − | 0.864286i | \(-0.332229\pi\) | ||||
0.503002 | + | 0.864286i | \(0.332229\pi\) | |||||||
\(912\) | 8.03294e12 | 0.384501 | ||||||||
\(913\) | 3.33093e13 | 1.58653 | ||||||||
\(914\) | 5.90199e12 | 0.279731 | ||||||||
\(915\) | −2.72572e12 | −0.128554 | ||||||||
\(916\) | 7.17935e12 | 0.336942 | ||||||||
\(917\) | −1.68820e12 | −0.0788427 | ||||||||
\(918\) | −7.90894e11 | −0.0367558 | ||||||||
\(919\) | −1.22511e12 | −0.0566571 | −0.0283286 | − | 0.999599i | \(-0.509018\pi\) | ||||
−0.0283286 | + | 0.999599i | \(0.509018\pi\) | |||||||
\(920\) | −1.81805e12 | −0.0836683 | ||||||||
\(921\) | −4.44716e13 | −2.03664 | ||||||||
\(922\) | −7.74276e12 | −0.352863 | ||||||||
\(923\) | 1.74879e13 | 0.793105 | ||||||||
\(924\) | −1.18109e13 | −0.533041 | ||||||||
\(925\) | −3.59894e13 | −1.61635 | ||||||||
\(926\) | 8.67335e12 | 0.387648 | ||||||||
\(927\) | 8.01448e12 | 0.356465 | ||||||||
\(928\) | −2.23869e13 | −0.990896 | ||||||||
\(929\) | 9.53162e12 | 0.419852 | 0.209926 | − | 0.977717i | \(-0.432678\pi\) | ||||
0.209926 | + | 0.977717i | \(0.432678\pi\) | |||||||
\(930\) | −1.48873e12 | −0.0652594 | ||||||||
\(931\) | −2.51632e12 | −0.109772 | ||||||||
\(932\) | 1.99887e13 | 0.867788 | ||||||||
\(933\) | 1.70157e13 | 0.735163 | ||||||||
\(934\) | −1.82637e13 | −0.785287 | ||||||||
\(935\) | −4.65353e12 | −0.199127 | ||||||||
\(936\) | 3.03056e13 | 1.29057 | ||||||||
\(937\) | −9.70345e12 | −0.411242 | −0.205621 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205621 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(938\) | 6.10650e11 | 0.0257561 | ||||||||
\(939\) | 1.02860e13 | 0.431770 | ||||||||
\(940\) | 4.37944e12 | 0.182954 | ||||||||
\(941\) | −2.29625e13 | −0.954698 | −0.477349 | − | 0.878714i | \(-0.658402\pi\) | ||||
−0.477349 | + | 0.878714i | \(0.658402\pi\) | |||||||
\(942\) | 6.36639e12 | 0.263429 | ||||||||
\(943\) | 2.21024e12 | 0.0910198 | ||||||||
\(944\) | −2.37397e12 | −0.0972973 | ||||||||
\(945\) | −9.64520e10 | −0.00393431 | ||||||||
\(946\) | −8.71676e12 | −0.353871 | ||||||||
\(947\) | 1.40763e13 | 0.568738 | 0.284369 | − | 0.958715i | \(-0.408216\pi\) | ||||
0.284369 | + | 0.958715i | \(0.408216\pi\) | |||||||
\(948\) | −1.15235e10 | −0.000463391 0 | ||||||||
\(949\) | 3.46015e13 | 1.38483 | ||||||||
\(950\) | 9.09452e12 | 0.362263 | ||||||||
\(951\) | −5.16534e13 | −2.04780 | ||||||||
\(952\) | −8.59281e12 | −0.339054 | ||||||||
\(953\) | 9.86435e12 | 0.387392 | 0.193696 | − | 0.981062i | \(-0.437953\pi\) | ||||
0.193696 | + | 0.981062i | \(0.437953\pi\) | |||||||
\(954\) | −1.88406e13 | −0.736421 | ||||||||
\(955\) | −3.70602e12 | −0.144176 | ||||||||
\(956\) | −1.49651e13 | −0.579453 | ||||||||
\(957\) | 4.61014e13 | 1.77668 | ||||||||
\(958\) | 1.27582e13 | 0.489378 | ||||||||
\(959\) | 7.37852e12 | 0.281699 | ||||||||
\(960\) | −7.08838e11 | −0.0269356 | ||||||||
\(961\) | −1.43550e13 | −0.542937 | ||||||||
\(962\) | −3.37493e13 | −1.27051 | ||||||||
\(963\) | 2.30069e13 | 0.862065 | ||||||||
\(964\) | −3.85518e13 | −1.43780 | ||||||||
\(965\) | 9.70993e11 | 0.0360449 | ||||||||
\(966\) | 4.70224e12 | 0.173743 | ||||||||
\(967\) | −2.37375e12 | −0.0873002 | −0.0436501 | − | 0.999047i | \(-0.513899\pi\) | ||||
−0.0436501 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(968\) | −1.69687e13 | −0.621168 | ||||||||
\(969\) | −3.10193e13 | −1.13025 | ||||||||
\(970\) | −1.95952e12 | −0.0710686 | ||||||||
\(971\) | 4.45895e13 | 1.60970 | 0.804852 | − | 0.593476i | \(-0.202245\pi\) | ||||
0.804852 | + | 0.593476i | \(0.202245\pi\) | |||||||
\(972\) | −2.97608e13 | −1.06942 | ||||||||
\(973\) | −1.21924e13 | −0.436096 | ||||||||
\(974\) | 4.89939e12 | 0.174432 | ||||||||
\(975\) | −6.16822e13 | −2.18594 | ||||||||
\(976\) | 6.51550e12 | 0.229839 | ||||||||
\(977\) | 8.90599e11 | 0.0312721 | 0.0156360 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156360 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(978\) | −1.96388e13 | −0.686420 | ||||||||
\(979\) | 1.90691e13 | 0.663449 | ||||||||
\(980\) | −4.55296e11 | −0.0157680 | ||||||||
\(981\) | 3.16531e13 | 1.09120 | ||||||||
\(982\) | 2.45117e13 | 0.841146 | ||||||||
\(983\) | 8.23794e12 | 0.281402 | 0.140701 | − | 0.990052i | \(-0.455064\pi\) | ||||
0.140701 | + | 0.990052i | \(0.455064\pi\) | |||||||
\(984\) | 4.64832e12 | 0.158059 | ||||||||
\(985\) | 5.42597e12 | 0.183660 | ||||||||
\(986\) | 1.45724e13 | 0.491003 | ||||||||
\(987\) | −2.60706e13 | −0.874428 | ||||||||
\(988\) | −2.82751e13 | −0.944056 | ||||||||
\(989\) | −1.15056e13 | −0.382407 | ||||||||
\(990\) | 2.60645e12 | 0.0862364 | ||||||||
\(991\) | 8.90224e12 | 0.293203 | 0.146601 | − | 0.989196i | \(-0.453167\pi\) | ||||
0.146601 | + | 0.989196i | \(0.453167\pi\) | |||||||
\(992\) | 2.11108e13 | 0.692152 | ||||||||
\(993\) | 4.13859e13 | 1.35077 | ||||||||
\(994\) | 2.77727e12 | 0.0902359 | ||||||||
\(995\) | 3.32841e12 | 0.107655 | ||||||||
\(996\) | 4.01738e13 | 1.29353 | ||||||||
\(997\) | 1.45450e13 | 0.466216 | 0.233108 | − | 0.972451i | \(-0.425110\pi\) | ||||
0.233108 | + | 0.972451i | \(0.425110\pi\) | |||||||
\(998\) | 1.73965e11 | 0.00555106 | ||||||||
\(999\) | 3.76440e12 | 0.119578 |
(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 | 7.10.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 63.10.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 112.10.a.e.1.2 | 2 | |||
5.2 | odd | 4 | 175.10.b.b.99.3 | 4 | |||
5.3 | odd | 4 | 175.10.b.b.99.2 | 4 | |||
5.4 | even | 2 | 175.10.a.b.1.1 | 2 | |||
7.2 | even | 3 | 49.10.c.c.18.1 | 4 | |||
7.3 | odd | 6 | 49.10.c.b.30.1 | 4 | |||
7.4 | even | 3 | 49.10.c.c.30.1 | 4 | |||
7.5 | odd | 6 | 49.10.c.b.18.1 | 4 | |||
7.6 | odd | 2 | 49.10.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
49.10.a.b.1.2 | 2 | 7.6 | odd | 2 | |||
49.10.c.b.18.1 | 4 | 7.5 | odd | 6 | |||
49.10.c.b.30.1 | 4 | 7.3 | odd | 6 | |||
49.10.c.c.18.1 | 4 | 7.2 | even | 3 | |||
49.10.c.c.30.1 | 4 | 7.4 | even | 3 | |||
63.10.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
112.10.a.e.1.2 | 2 | 4.3 | odd | 2 | |||
175.10.a.b.1.1 | 2 | 5.4 | even | 2 | |||
175.10.b.b.99.2 | 4 | 5.3 | odd | 4 | |||
175.10.b.b.99.3 | 4 | 5.2 | odd | 4 |