Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{95351}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 95351 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(308.790\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4096.00 | 0.707107 | ||||||||
\(3\) | 618439. | 0.671864 | 0.335932 | − | 0.941886i | \(-0.390949\pi\) | ||||
0.335932 | + | 0.941886i | \(0.390949\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | −2.44141e8 | −0.447214 | ||||||||
\(6\) | 2.53313e9 | 0.475080 | ||||||||
\(7\) | 4.78762e10 | 1.30736 | 0.653678 | − | 0.756773i | \(-0.273225\pi\) | ||||
0.653678 | + | 0.756773i | \(0.273225\pi\) | |||||||
\(8\) | 6.87195e10 | 0.353553 | ||||||||
\(9\) | −4.64821e11 | −0.548598 | ||||||||
\(10\) | −1.00000e12 | −0.316228 | ||||||||
\(11\) | 3.58198e11 | 0.0344124 | 0.0172062 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172062 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(12\) | 1.03757e13 | 0.335932 | ||||||||
\(13\) | 7.76408e13 | 0.924269 | 0.462134 | − | 0.886810i | \(-0.347084\pi\) | ||||
0.462134 | + | 0.886810i | \(0.347084\pi\) | |||||||
\(14\) | 1.96101e14 | 0.924440 | ||||||||
\(15\) | −1.50986e14 | −0.300467 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.50624e15 | 0.627023 | 0.313511 | − | 0.949584i | \(-0.398495\pi\) | ||||
0.313511 | + | 0.949584i | \(0.398495\pi\) | |||||||
\(18\) | −1.90391e15 | −0.387918 | ||||||||
\(19\) | 4.83611e15 | 0.501276 | 0.250638 | − | 0.968081i | \(-0.419360\pi\) | ||||
0.250638 | + | 0.968081i | \(0.419360\pi\) | |||||||
\(20\) | −4.09600e15 | −0.223607 | ||||||||
\(21\) | 2.96085e16 | 0.878366 | ||||||||
\(22\) | 1.46718e15 | 0.0243332 | ||||||||
\(23\) | 2.59330e16 | 0.246749 | 0.123374 | − | 0.992360i | \(-0.460628\pi\) | ||||
0.123374 | + | 0.992360i | \(0.460628\pi\) | |||||||
\(24\) | 4.24988e16 | 0.237540 | ||||||||
\(25\) | 5.96046e16 | 0.200000 | ||||||||
\(26\) | 3.18017e17 | 0.653557 | ||||||||
\(27\) | −8.11461e17 | −1.04045 | ||||||||
\(28\) | 8.03229e17 | 0.653678 | ||||||||
\(29\) | 9.30223e17 | 0.488216 | 0.244108 | − | 0.969748i | \(-0.421505\pi\) | ||||
0.244108 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(30\) | −6.18439e17 | −0.212462 | ||||||||
\(31\) | 3.10982e18 | 0.709110 | 0.354555 | − | 0.935035i | \(-0.384632\pi\) | ||||
0.354555 | + | 0.935035i | \(0.384632\pi\) | |||||||
\(32\) | 1.15292e18 | 0.176777 | ||||||||
\(33\) | 2.21524e17 | 0.0231205 | ||||||||
\(34\) | 6.16957e18 | 0.443372 | ||||||||
\(35\) | −1.16885e19 | −0.584667 | ||||||||
\(36\) | −7.79841e18 | −0.274299 | ||||||||
\(37\) | −4.54619e19 | −1.13534 | −0.567670 | − | 0.823256i | \(-0.692155\pi\) | ||||
−0.567670 | + | 0.823256i | \(0.692155\pi\) | |||||||
\(38\) | 1.98087e19 | 0.354455 | ||||||||
\(39\) | 4.80162e19 | 0.620983 | ||||||||
\(40\) | −1.67772e19 | −0.158114 | ||||||||
\(41\) | 1.02459e20 | 0.709172 | 0.354586 | − | 0.935023i | \(-0.384622\pi\) | ||||
0.354586 | + | 0.935023i | \(0.384622\pi\) | |||||||
\(42\) | 1.21276e20 | 0.621098 | ||||||||
\(43\) | 4.58049e20 | 1.74806 | 0.874029 | − | 0.485874i | \(-0.161498\pi\) | ||||
0.874029 | + | 0.485874i | \(0.161498\pi\) | |||||||
\(44\) | 6.00957e18 | 0.0172062 | ||||||||
\(45\) | 1.13482e20 | 0.245341 | ||||||||
\(46\) | 1.06222e20 | 0.174478 | ||||||||
\(47\) | 1.51063e21 | 1.89642 | 0.948210 | − | 0.317644i | \(-0.102892\pi\) | ||||
0.948210 | + | 0.317644i | \(0.102892\pi\) | |||||||
\(48\) | 1.74075e20 | 0.167966 | ||||||||
\(49\) | 9.51058e20 | 0.709179 | ||||||||
\(50\) | 2.44141e20 | 0.141421 | ||||||||
\(51\) | 9.31520e20 | 0.421274 | ||||||||
\(52\) | 1.30260e21 | 0.462134 | ||||||||
\(53\) | −2.00272e21 | −0.559980 | −0.279990 | − | 0.960003i | \(-0.590331\pi\) | ||||
−0.279990 | + | 0.960003i | \(0.590331\pi\) | |||||||
\(54\) | −3.32374e21 | −0.735708 | ||||||||
\(55\) | −8.74507e19 | −0.0153897 | ||||||||
\(56\) | 3.29002e21 | 0.462220 | ||||||||
\(57\) | 2.99084e21 | 0.336789 | ||||||||
\(58\) | 3.81019e21 | 0.345221 | ||||||||
\(59\) | 2.00362e22 | 1.46611 | 0.733053 | − | 0.680171i | \(-0.238095\pi\) | ||||
0.733053 | + | 0.680171i | \(0.238095\pi\) | |||||||
\(60\) | −2.53313e21 | −0.150233 | ||||||||
\(61\) | −2.40289e22 | −1.15908 | −0.579538 | − | 0.814945i | \(-0.696767\pi\) | ||||
−0.579538 | + | 0.814945i | \(0.696767\pi\) | |||||||
\(62\) | 1.27378e22 | 0.501417 | ||||||||
\(63\) | −2.22539e22 | −0.717213 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | −1.89553e22 | −0.413346 | ||||||||
\(66\) | 9.07362e20 | 0.0163486 | ||||||||
\(67\) | −5.68406e22 | −0.848640 | −0.424320 | − | 0.905512i | \(-0.639487\pi\) | ||||
−0.424320 | + | 0.905512i | \(0.639487\pi\) | |||||||
\(68\) | 2.52706e22 | 0.313511 | ||||||||
\(69\) | 1.60380e22 | 0.165782 | ||||||||
\(70\) | −4.78762e22 | −0.413422 | ||||||||
\(71\) | 2.06619e22 | 0.149431 | 0.0747156 | − | 0.997205i | \(-0.476195\pi\) | ||||
0.0747156 | + | 0.997205i | \(0.476195\pi\) | |||||||
\(72\) | −3.19423e22 | −0.193959 | ||||||||
\(73\) | −3.20846e23 | −1.63969 | −0.819843 | − | 0.572588i | \(-0.805939\pi\) | ||||
−0.819843 | + | 0.572588i | \(0.805939\pi\) | |||||||
\(74\) | −1.86212e23 | −0.802806 | ||||||||
\(75\) | 3.68619e22 | 0.134373 | ||||||||
\(76\) | 8.11365e22 | 0.250638 | ||||||||
\(77\) | 1.71492e22 | 0.0449892 | ||||||||
\(78\) | 1.96674e23 | 0.439101 | ||||||||
\(79\) | −4.28561e23 | −0.815969 | −0.407985 | − | 0.912989i | \(-0.633768\pi\) | ||||
−0.407985 | + | 0.912989i | \(0.633768\pi\) | |||||||
\(80\) | −6.87195e22 | −0.111803 | ||||||||
\(81\) | −1.08001e23 | −0.150441 | ||||||||
\(82\) | 4.19671e23 | 0.501460 | ||||||||
\(83\) | −1.11807e24 | −1.14814 | −0.574069 | − | 0.818807i | \(-0.694636\pi\) | ||||
−0.574069 | + | 0.818807i | \(0.694636\pi\) | |||||||
\(84\) | 4.96748e23 | 0.439183 | ||||||||
\(85\) | −3.67735e23 | −0.280413 | ||||||||
\(86\) | 1.87617e24 | 1.23606 | ||||||||
\(87\) | 5.75287e23 | 0.328015 | ||||||||
\(88\) | 2.46152e22 | 0.0121666 | ||||||||
\(89\) | 1.75157e24 | 0.751712 | 0.375856 | − | 0.926678i | \(-0.377349\pi\) | ||||
0.375856 | + | 0.926678i | \(0.377349\pi\) | |||||||
\(90\) | 4.64821e23 | 0.173482 | ||||||||
\(91\) | 3.71714e24 | 1.20835 | ||||||||
\(92\) | 4.35084e23 | 0.123374 | ||||||||
\(93\) | 1.92323e24 | 0.476426 | ||||||||
\(94\) | 6.18754e24 | 1.34097 | ||||||||
\(95\) | −1.18069e24 | −0.224177 | ||||||||
\(96\) | 7.13012e23 | 0.118770 | ||||||||
\(97\) | −1.28690e25 | −1.88320 | −0.941601 | − | 0.336729i | \(-0.890679\pi\) | ||||
−0.941601 | + | 0.336729i | \(0.890679\pi\) | |||||||
\(98\) | 3.89553e24 | 0.501466 | ||||||||
\(99\) | −1.66498e23 | −0.0188786 | ||||||||
\(100\) | 1.00000e24 | 0.100000 | ||||||||
\(101\) | −3.20176e24 | −0.282730 | −0.141365 | − | 0.989958i | \(-0.545149\pi\) | ||||
−0.141365 | + | 0.989958i | \(0.545149\pi\) | |||||||
\(102\) | 3.81551e24 | 0.297886 | ||||||||
\(103\) | −5.43797e23 | −0.0375813 | −0.0187906 | − | 0.999823i | \(-0.505982\pi\) | ||||
−0.0187906 | + | 0.999823i | \(0.505982\pi\) | |||||||
\(104\) | 5.33544e24 | 0.326778 | ||||||||
\(105\) | −7.22864e24 | −0.392817 | ||||||||
\(106\) | −8.20316e24 | −0.395966 | ||||||||
\(107\) | −1.45562e25 | −0.624816 | −0.312408 | − | 0.949948i | \(-0.601136\pi\) | ||||
−0.312408 | + | 0.949948i | \(0.601136\pi\) | |||||||
\(108\) | −1.36140e25 | −0.520224 | ||||||||
\(109\) | −3.33253e25 | −1.13486 | −0.567431 | − | 0.823421i | \(-0.692063\pi\) | ||||
−0.567431 | + | 0.823421i | \(0.692063\pi\) | |||||||
\(110\) | −3.58198e23 | −0.0108822 | ||||||||
\(111\) | −2.81154e25 | −0.762794 | ||||||||
\(112\) | 1.34759e25 | 0.326839 | ||||||||
\(113\) | 1.71253e25 | 0.371670 | 0.185835 | − | 0.982581i | \(-0.440501\pi\) | ||||
0.185835 | + | 0.982581i | \(0.440501\pi\) | |||||||
\(114\) | 1.22505e25 | 0.238146 | ||||||||
\(115\) | −6.33130e24 | −0.110349 | ||||||||
\(116\) | 1.56066e25 | 0.244108 | ||||||||
\(117\) | −3.60891e25 | −0.507052 | ||||||||
\(118\) | 8.20683e25 | 1.03669 | ||||||||
\(119\) | 7.21131e25 | 0.819742 | ||||||||
\(120\) | −1.03757e25 | −0.106231 | ||||||||
\(121\) | −1.08219e26 | −0.998816 | ||||||||
\(122\) | −9.84225e25 | −0.819590 | ||||||||
\(123\) | 6.33646e25 | 0.476467 | ||||||||
\(124\) | 5.21741e25 | 0.354555 | ||||||||
\(125\) | −1.45519e25 | −0.0894427 | ||||||||
\(126\) | −9.11518e25 | −0.507146 | ||||||||
\(127\) | −2.80916e26 | −1.41589 | −0.707947 | − | 0.706266i | \(-0.750378\pi\) | ||||
−0.707947 | + | 0.706266i | \(0.750378\pi\) | |||||||
\(128\) | 1.93428e25 | 0.0883883 | ||||||||
\(129\) | 2.83275e26 | 1.17446 | ||||||||
\(130\) | −7.76408e25 | −0.292279 | ||||||||
\(131\) | 3.91683e26 | 1.33981 | 0.669906 | − | 0.742446i | \(-0.266334\pi\) | ||||
0.669906 | + | 0.742446i | \(0.266334\pi\) | |||||||
\(132\) | 3.71655e24 | 0.0115602 | ||||||||
\(133\) | 2.31535e26 | 0.655346 | ||||||||
\(134\) | −2.32819e26 | −0.600079 | ||||||||
\(135\) | 1.98110e26 | 0.465302 | ||||||||
\(136\) | 1.03508e26 | 0.221686 | ||||||||
\(137\) | 7.30593e24 | 0.0142780 | 0.00713902 | − | 0.999975i | \(-0.497728\pi\) | ||||
0.00713902 | + | 0.999975i | \(0.497728\pi\) | |||||||
\(138\) | 6.56916e25 | 0.117225 | ||||||||
\(139\) | 9.32000e26 | 1.51961 | 0.759803 | − | 0.650154i | \(-0.225295\pi\) | ||||
0.759803 | + | 0.650154i | \(0.225295\pi\) | |||||||
\(140\) | −1.96101e26 | −0.292334 | ||||||||
\(141\) | 9.34233e26 | 1.27414 | ||||||||
\(142\) | 8.46313e25 | 0.105664 | ||||||||
\(143\) | 2.78108e25 | 0.0318063 | ||||||||
\(144\) | −1.30836e26 | −0.137150 | ||||||||
\(145\) | −2.27105e26 | −0.218337 | ||||||||
\(146\) | −1.31419e27 | −1.15943 | ||||||||
\(147\) | 5.88172e26 | 0.476472 | ||||||||
\(148\) | −7.62723e26 | −0.567670 | ||||||||
\(149\) | −2.86893e27 | −1.96287 | −0.981434 | − | 0.191800i | \(-0.938567\pi\) | ||||
−0.981434 | + | 0.191800i | \(0.938567\pi\) | |||||||
\(150\) | 1.50986e26 | 0.0950160 | ||||||||
\(151\) | 6.35122e26 | 0.367828 | 0.183914 | − | 0.982942i | \(-0.441123\pi\) | ||||
0.183914 | + | 0.982942i | \(0.441123\pi\) | |||||||
\(152\) | 3.32335e26 | 0.177228 | ||||||||
\(153\) | −7.00134e26 | −0.343984 | ||||||||
\(154\) | 7.02429e25 | 0.0318122 | ||||||||
\(155\) | −7.59233e26 | −0.317124 | ||||||||
\(156\) | 8.05577e26 | 0.310492 | ||||||||
\(157\) | −2.51786e27 | −0.895954 | −0.447977 | − | 0.894045i | \(-0.647855\pi\) | ||||
−0.447977 | + | 0.894045i | \(0.647855\pi\) | |||||||
\(158\) | −1.75538e27 | −0.576977 | ||||||||
\(159\) | −1.23856e27 | −0.376231 | ||||||||
\(160\) | −2.81475e26 | −0.0790569 | ||||||||
\(161\) | 1.24157e27 | 0.322588 | ||||||||
\(162\) | −4.42374e26 | −0.106378 | ||||||||
\(163\) | −4.89494e26 | −0.108994 | −0.0544970 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544970 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(164\) | 1.71897e27 | 0.354586 | ||||||||
\(165\) | −5.40830e25 | −0.0103398 | ||||||||
\(166\) | −4.57963e27 | −0.811856 | ||||||||
\(167\) | 2.73255e27 | 0.449378 | 0.224689 | − | 0.974430i | \(-0.427863\pi\) | ||||
0.224689 | + | 0.974430i | \(0.427863\pi\) | |||||||
\(168\) | 2.03468e27 | 0.310549 | ||||||||
\(169\) | −1.02831e27 | −0.145727 | ||||||||
\(170\) | −1.50624e27 | −0.198282 | ||||||||
\(171\) | −2.24793e27 | −0.274999 | ||||||||
\(172\) | 7.68478e27 | 0.874029 | ||||||||
\(173\) | 8.64082e27 | 0.914069 | 0.457034 | − | 0.889449i | \(-0.348912\pi\) | ||||
0.457034 | + | 0.889449i | \(0.348912\pi\) | |||||||
\(174\) | 2.35637e27 | 0.231942 | ||||||||
\(175\) | 2.85364e27 | 0.261471 | ||||||||
\(176\) | 1.00824e26 | 0.00860310 | ||||||||
\(177\) | 1.23912e28 | 0.985025 | ||||||||
\(178\) | 7.17441e27 | 0.531540 | ||||||||
\(179\) | −2.03598e28 | −1.40640 | −0.703201 | − | 0.710991i | \(-0.748247\pi\) | ||||
−0.703201 | + | 0.710991i | \(0.748247\pi\) | |||||||
\(180\) | 1.90391e27 | 0.122670 | ||||||||
\(181\) | 1.34351e28 | 0.807718 | 0.403859 | − | 0.914821i | \(-0.367669\pi\) | ||||
0.403859 | + | 0.914821i | \(0.367669\pi\) | |||||||
\(182\) | 1.52254e28 | 0.854431 | ||||||||
\(183\) | −1.48604e28 | −0.778741 | ||||||||
\(184\) | 1.78210e27 | 0.0872388 | ||||||||
\(185\) | 1.10991e28 | 0.507739 | ||||||||
\(186\) | 7.87757e27 | 0.336884 | ||||||||
\(187\) | 5.39533e26 | 0.0215774 | ||||||||
\(188\) | 2.53441e28 | 0.948210 | ||||||||
\(189\) | −3.88496e28 | −1.36024 | ||||||||
\(190\) | −4.83611e27 | −0.158517 | ||||||||
\(191\) | −1.46283e28 | −0.449030 | −0.224515 | − | 0.974471i | \(-0.572080\pi\) | ||||
−0.224515 | + | 0.974471i | \(0.572080\pi\) | |||||||
\(192\) | 2.92050e27 | 0.0839830 | ||||||||
\(193\) | 3.37927e28 | 0.910659 | 0.455330 | − | 0.890323i | \(-0.349521\pi\) | ||||
0.455330 | + | 0.890323i | \(0.349521\pi\) | |||||||
\(194\) | −5.27113e28 | −1.33163 | ||||||||
\(195\) | −1.17227e28 | −0.277712 | ||||||||
\(196\) | 1.59561e28 | 0.354590 | ||||||||
\(197\) | −5.93119e28 | −1.23684 | −0.618420 | − | 0.785847i | \(-0.712227\pi\) | ||||
−0.618420 | + | 0.785847i | \(0.712227\pi\) | |||||||
\(198\) | −6.81976e26 | −0.0133492 | ||||||||
\(199\) | −1.85919e28 | −0.341712 | −0.170856 | − | 0.985296i | \(-0.554653\pi\) | ||||
−0.170856 | + | 0.985296i | \(0.554653\pi\) | |||||||
\(200\) | 4.09600e27 | 0.0707107 | ||||||||
\(201\) | −3.51525e28 | −0.570171 | ||||||||
\(202\) | −1.31144e28 | −0.199920 | ||||||||
\(203\) | 4.45355e28 | 0.638272 | ||||||||
\(204\) | 1.56283e28 | 0.210637 | ||||||||
\(205\) | −2.50144e28 | −0.317151 | ||||||||
\(206\) | −2.22739e27 | −0.0265740 | ||||||||
\(207\) | −1.20542e28 | −0.135366 | ||||||||
\(208\) | 2.18540e28 | 0.231067 | ||||||||
\(209\) | 1.73229e27 | 0.0172501 | ||||||||
\(210\) | −2.96085e28 | −0.277764 | ||||||||
\(211\) | 1.59544e29 | 1.41042 | 0.705212 | − | 0.708996i | \(-0.250852\pi\) | ||||
0.705212 | + | 0.708996i | \(0.250852\pi\) | |||||||
\(212\) | −3.36001e28 | −0.279990 | ||||||||
\(213\) | 1.27782e28 | 0.100398 | ||||||||
\(214\) | −5.96224e28 | −0.441812 | ||||||||
\(215\) | −1.11828e29 | −0.781755 | ||||||||
\(216\) | −5.57631e28 | −0.367854 | ||||||||
\(217\) | 1.48886e29 | 0.927060 | ||||||||
\(218\) | −1.36501e29 | −0.802469 | ||||||||
\(219\) | −1.98424e29 | −1.10165 | ||||||||
\(220\) | −1.46718e27 | −0.00769484 | ||||||||
\(221\) | 1.16946e29 | 0.579538 | ||||||||
\(222\) | −1.15161e29 | −0.539377 | ||||||||
\(223\) | 2.93272e29 | 1.29855 | 0.649277 | − | 0.760552i | \(-0.275072\pi\) | ||||
0.649277 | + | 0.760552i | \(0.275072\pi\) | |||||||
\(224\) | 5.51975e28 | 0.231110 | ||||||||
\(225\) | −2.77055e28 | −0.109720 | ||||||||
\(226\) | 7.01452e28 | 0.262810 | ||||||||
\(227\) | 2.86033e29 | 1.01413 | 0.507065 | − | 0.861908i | \(-0.330730\pi\) | ||||
0.507065 | + | 0.861908i | \(0.330730\pi\) | |||||||
\(228\) | 5.01780e28 | 0.168395 | ||||||||
\(229\) | −2.27815e29 | −0.723833 | −0.361916 | − | 0.932211i | \(-0.617877\pi\) | ||||
−0.361916 | + | 0.932211i | \(0.617877\pi\) | |||||||
\(230\) | −2.59330e28 | −0.0780288 | ||||||||
\(231\) | 1.06057e28 | 0.0302267 | ||||||||
\(232\) | 6.39244e28 | 0.172610 | ||||||||
\(233\) | 6.95835e29 | 1.78056 | 0.890281 | − | 0.455411i | \(-0.150508\pi\) | ||||
0.890281 | + | 0.455411i | \(0.150508\pi\) | |||||||
\(234\) | −1.47821e29 | −0.358540 | ||||||||
\(235\) | −3.68806e29 | −0.848105 | ||||||||
\(236\) | 3.36152e29 | 0.733053 | ||||||||
\(237\) | −2.65039e29 | −0.548220 | ||||||||
\(238\) | 2.95375e29 | 0.579645 | ||||||||
\(239\) | 1.46812e29 | 0.273393 | 0.136696 | − | 0.990613i | \(-0.456352\pi\) | ||||
0.136696 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(240\) | −4.24988e28 | −0.0751167 | ||||||||
\(241\) | 7.86832e29 | 1.32029 | 0.660144 | − | 0.751139i | \(-0.270495\pi\) | ||||
0.660144 | + | 0.751139i | \(0.270495\pi\) | |||||||
\(242\) | −4.43264e29 | −0.706269 | ||||||||
\(243\) | 6.20749e29 | 0.939372 | ||||||||
\(244\) | −4.03139e29 | −0.579538 | ||||||||
\(245\) | −2.32192e29 | −0.317155 | ||||||||
\(246\) | 2.59541e29 | 0.336913 | ||||||||
\(247\) | 3.75480e29 | 0.463313 | ||||||||
\(248\) | 2.13705e29 | 0.250708 | ||||||||
\(249\) | −6.91461e29 | −0.771393 | ||||||||
\(250\) | −5.96046e28 | −0.0632456 | ||||||||
\(251\) | −1.30352e30 | −1.31582 | −0.657910 | − | 0.753097i | \(-0.728559\pi\) | ||||
−0.657910 | + | 0.753097i | \(0.728559\pi\) | |||||||
\(252\) | −3.73358e29 | −0.358607 | ||||||||
\(253\) | 9.28916e27 | 0.00849121 | ||||||||
\(254\) | −1.15063e30 | −1.00119 | ||||||||
\(255\) | −2.27422e29 | −0.188400 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −2.21600e30 | −1.66496 | −0.832482 | − | 0.554052i | \(-0.813081\pi\) | ||||
−0.832482 | + | 0.554052i | \(0.813081\pi\) | |||||||
\(258\) | 1.16030e30 | 0.830467 | ||||||||
\(259\) | −2.17654e30 | −1.48429 | ||||||||
\(260\) | −3.18017e29 | −0.206673 | ||||||||
\(261\) | −4.32387e29 | −0.267835 | ||||||||
\(262\) | 1.60433e30 | 0.947390 | ||||||||
\(263\) | 3.37258e29 | 0.189896 | 0.0949479 | − | 0.995482i | \(-0.469732\pi\) | ||||
0.0949479 | + | 0.995482i | \(0.469732\pi\) | |||||||
\(264\) | 1.52230e28 | 0.00817431 | ||||||||
\(265\) | 4.88946e29 | 0.250431 | ||||||||
\(266\) | 9.48366e29 | 0.463399 | ||||||||
\(267\) | 1.08324e30 | 0.505048 | ||||||||
\(268\) | −9.53627e29 | −0.424320 | ||||||||
\(269\) | −4.13865e30 | −1.75774 | −0.878871 | − | 0.477059i | \(-0.841703\pi\) | ||||
−0.878871 | + | 0.477059i | \(0.841703\pi\) | |||||||
\(270\) | 8.11461e29 | 0.329019 | ||||||||
\(271\) | 2.28080e29 | 0.0883021 | 0.0441511 | − | 0.999025i | \(-0.485942\pi\) | ||||
0.0441511 | + | 0.999025i | \(0.485942\pi\) | |||||||
\(272\) | 4.23970e29 | 0.156756 | ||||||||
\(273\) | 2.29883e30 | 0.811846 | ||||||||
\(274\) | 2.99251e28 | 0.0100961 | ||||||||
\(275\) | 2.13503e28 | 0.00688248 | ||||||||
\(276\) | 2.69073e29 | 0.0828908 | ||||||||
\(277\) | 3.78637e30 | 1.11487 | 0.557437 | − | 0.830219i | \(-0.311785\pi\) | ||||
0.557437 | + | 0.830219i | \(0.311785\pi\) | |||||||
\(278\) | 3.81747e30 | 1.07452 | ||||||||
\(279\) | −1.44551e30 | −0.389017 | ||||||||
\(280\) | −8.03229e29 | −0.206711 | ||||||||
\(281\) | 4.87412e30 | 1.19969 | 0.599843 | − | 0.800118i | \(-0.295230\pi\) | ||||
0.599843 | + | 0.800118i | \(0.295230\pi\) | |||||||
\(282\) | 3.82662e30 | 0.900951 | ||||||||
\(283\) | −7.79414e29 | −0.175565 | −0.0877825 | − | 0.996140i | \(-0.527978\pi\) | ||||
−0.0877825 | + | 0.996140i | \(0.527978\pi\) | |||||||
\(284\) | 3.46650e29 | 0.0747156 | ||||||||
\(285\) | −7.30186e29 | −0.150617 | ||||||||
\(286\) | 1.13913e29 | 0.0224904 | ||||||||
\(287\) | 4.90534e30 | 0.927140 | ||||||||
\(288\) | −5.35902e29 | −0.0969794 | ||||||||
\(289\) | −3.50186e30 | −0.606842 | ||||||||
\(290\) | −9.30223e29 | −0.154387 | ||||||||
\(291\) | −7.95868e30 | −1.26526 | ||||||||
\(292\) | −5.38290e30 | −0.819843 | ||||||||
\(293\) | 8.97738e30 | 1.31010 | 0.655050 | − | 0.755586i | \(-0.272648\pi\) | ||||
0.655050 | + | 0.755586i | \(0.272648\pi\) | |||||||
\(294\) | 2.40915e30 | 0.336917 | ||||||||
\(295\) | −4.89165e30 | −0.655663 | ||||||||
\(296\) | −3.12412e30 | −0.401403 | ||||||||
\(297\) | −2.90664e29 | −0.0358043 | ||||||||
\(298\) | −1.17511e31 | −1.38796 | ||||||||
\(299\) | 2.01346e30 | 0.228062 | ||||||||
\(300\) | 6.18439e29 | 0.0671864 | ||||||||
\(301\) | 2.19296e31 | 2.28533 | ||||||||
\(302\) | 2.60146e30 | 0.260094 | ||||||||
\(303\) | −1.98009e30 | −0.189956 | ||||||||
\(304\) | 1.36125e30 | 0.125319 | ||||||||
\(305\) | 5.86644e30 | 0.518354 | ||||||||
\(306\) | −2.86775e30 | −0.243233 | ||||||||
\(307\) | −1.03718e31 | −0.844547 | −0.422274 | − | 0.906468i | \(-0.638768\pi\) | ||||
−0.422274 | + | 0.906468i | \(0.638768\pi\) | |||||||
\(308\) | 2.87715e29 | 0.0224946 | ||||||||
\(309\) | −3.36306e29 | −0.0252495 | ||||||||
\(310\) | −3.10982e30 | −0.224240 | ||||||||
\(311\) | −3.85228e30 | −0.266817 | −0.133408 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133408 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(312\) | 3.29965e30 | 0.219551 | ||||||||
\(313\) | −2.63756e31 | −1.68616 | −0.843079 | − | 0.537789i | \(-0.819260\pi\) | ||||
−0.843079 | + | 0.537789i | \(0.819260\pi\) | |||||||
\(314\) | −1.03132e31 | −0.633535 | ||||||||
\(315\) | 5.43307e30 | 0.320748 | ||||||||
\(316\) | −7.19006e30 | −0.407985 | ||||||||
\(317\) | −3.65330e30 | −0.199271 | −0.0996355 | − | 0.995024i | \(-0.531768\pi\) | ||||
−0.0996355 | + | 0.995024i | \(0.531768\pi\) | |||||||
\(318\) | −5.07316e30 | −0.266035 | ||||||||
\(319\) | 3.33204e29 | 0.0168007 | ||||||||
\(320\) | −1.15292e30 | −0.0559017 | ||||||||
\(321\) | −9.00216e30 | −0.419792 | ||||||||
\(322\) | 5.08548e30 | 0.228104 | ||||||||
\(323\) | 7.28436e30 | 0.314311 | ||||||||
\(324\) | −1.81196e30 | −0.0752206 | ||||||||
\(325\) | 4.62775e30 | 0.184854 | ||||||||
\(326\) | −2.00497e30 | −0.0770703 | ||||||||
\(327\) | −2.06097e31 | −0.762474 | ||||||||
\(328\) | 7.04092e30 | 0.250730 | ||||||||
\(329\) | 7.23231e31 | 2.47930 | ||||||||
\(330\) | −2.21524e29 | −0.00731133 | ||||||||
\(331\) | −2.52293e31 | −0.801781 | −0.400890 | − | 0.916126i | \(-0.631299\pi\) | ||||
−0.400890 | + | 0.916126i | \(0.631299\pi\) | |||||||
\(332\) | −1.87582e31 | −0.574069 | ||||||||
\(333\) | 2.11316e31 | 0.622845 | ||||||||
\(334\) | 1.11925e31 | 0.317759 | ||||||||
\(335\) | 1.38771e31 | 0.379523 | ||||||||
\(336\) | 8.33405e30 | 0.219591 | ||||||||
\(337\) | −2.57479e31 | −0.653684 | −0.326842 | − | 0.945079i | \(-0.605985\pi\) | ||||
−0.326842 | + | 0.945079i | \(0.605985\pi\) | |||||||
\(338\) | −4.21196e30 | −0.103045 | ||||||||
\(339\) | 1.05910e31 | 0.249712 | ||||||||
\(340\) | −6.16957e30 | −0.140207 | ||||||||
\(341\) | 1.11393e30 | 0.0244022 | ||||||||
\(342\) | −9.20751e30 | −0.194454 | ||||||||
\(343\) | −1.86722e31 | −0.380206 | ||||||||
\(344\) | 3.14769e31 | 0.618032 | ||||||||
\(345\) | −3.91553e30 | −0.0741398 | ||||||||
\(346\) | 3.53928e31 | 0.646344 | ||||||||
\(347\) | −1.71059e31 | −0.301319 | −0.150660 | − | 0.988586i | \(-0.548140\pi\) | ||||
−0.150660 | + | 0.988586i | \(0.548140\pi\) | |||||||
\(348\) | 9.65171e30 | 0.164007 | ||||||||
\(349\) | 6.93560e31 | 1.13702 | 0.568508 | − | 0.822678i | \(-0.307521\pi\) | ||||
0.568508 | + | 0.822678i | \(0.307521\pi\) | |||||||
\(350\) | 1.16885e31 | 0.184888 | ||||||||
\(351\) | −6.30025e31 | −0.961653 | ||||||||
\(352\) | 4.12974e29 | 0.00608331 | ||||||||
\(353\) | 1.22234e31 | 0.173783 | 0.0868914 | − | 0.996218i | \(-0.472307\pi\) | ||||
0.0868914 | + | 0.996218i | \(0.472307\pi\) | |||||||
\(354\) | 5.07543e31 | 0.696518 | ||||||||
\(355\) | −5.04442e30 | −0.0668277 | ||||||||
\(356\) | 2.93864e31 | 0.375856 | ||||||||
\(357\) | 4.45976e31 | 0.550755 | ||||||||
\(358\) | −8.33936e31 | −0.994477 | ||||||||
\(359\) | 5.26279e31 | 0.606087 | 0.303044 | − | 0.952977i | \(-0.401997\pi\) | ||||
0.303044 | + | 0.952977i | \(0.401997\pi\) | |||||||
\(360\) | 7.79841e30 | 0.0867410 | ||||||||
\(361\) | −6.96885e31 | −0.748723 | ||||||||
\(362\) | 5.50303e31 | 0.571143 | ||||||||
\(363\) | −6.69267e31 | −0.671069 | ||||||||
\(364\) | 6.23633e31 | 0.604174 | ||||||||
\(365\) | 7.83315e31 | 0.733290 | ||||||||
\(366\) | −6.08684e31 | −0.550653 | ||||||||
\(367\) | −1.04735e31 | −0.0915729 | −0.0457864 | − | 0.998951i | \(-0.514579\pi\) | ||||
−0.0457864 | + | 0.998951i | \(0.514579\pi\) | |||||||
\(368\) | 7.29949e30 | 0.0616872 | ||||||||
\(369\) | −4.76250e31 | −0.389050 | ||||||||
\(370\) | 4.54619e31 | 0.359026 | ||||||||
\(371\) | −9.58828e31 | −0.732094 | ||||||||
\(372\) | 3.22665e31 | 0.238213 | ||||||||
\(373\) | −1.24978e32 | −0.892221 | −0.446111 | − | 0.894978i | \(-0.647191\pi\) | ||||
−0.446111 | + | 0.894978i | \(0.647191\pi\) | |||||||
\(374\) | 2.20993e30 | 0.0152575 | ||||||||
\(375\) | −8.99948e30 | −0.0600934 | ||||||||
\(376\) | 1.03810e32 | 0.670486 | ||||||||
\(377\) | 7.22233e31 | 0.451243 | ||||||||
\(378\) | −1.59128e32 | −0.961832 | ||||||||
\(379\) | −1.71176e32 | −1.00104 | −0.500522 | − | 0.865724i | \(-0.666859\pi\) | ||||
−0.500522 | + | 0.865724i | \(0.666859\pi\) | |||||||
\(380\) | −1.98087e31 | −0.112089 | ||||||||
\(381\) | −1.73730e32 | −0.951288 | ||||||||
\(382\) | −5.99173e31 | −0.317512 | ||||||||
\(383\) | −2.63626e32 | −1.35209 | −0.676043 | − | 0.736862i | \(-0.736307\pi\) | ||||
−0.676043 | + | 0.736862i | \(0.736307\pi\) | |||||||
\(384\) | 1.19624e31 | 0.0593850 | ||||||||
\(385\) | −4.18680e30 | −0.0201198 | ||||||||
\(386\) | 1.38415e32 | 0.643933 | ||||||||
\(387\) | −2.12911e32 | −0.958982 | ||||||||
\(388\) | −2.15905e32 | −0.941601 | ||||||||
\(389\) | 3.01567e32 | 1.27354 | 0.636772 | − | 0.771052i | \(-0.280269\pi\) | ||||
0.636772 | + | 0.771052i | \(0.280269\pi\) | |||||||
\(390\) | −4.80162e31 | −0.196372 | ||||||||
\(391\) | 3.90614e31 | 0.154717 | ||||||||
\(392\) | 6.53562e31 | 0.250733 | ||||||||
\(393\) | 2.42232e32 | 0.900172 | ||||||||
\(394\) | −2.42941e32 | −0.874578 | ||||||||
\(395\) | 1.04629e32 | 0.364912 | ||||||||
\(396\) | −2.79337e30 | −0.00943929 | ||||||||
\(397\) | 3.60886e32 | 1.18165 | 0.590824 | − | 0.806800i | \(-0.298803\pi\) | ||||
0.590824 | + | 0.806800i | \(0.298803\pi\) | |||||||
\(398\) | −7.61523e31 | −0.241627 | ||||||||
\(399\) | 1.43190e32 | 0.440303 | ||||||||
\(400\) | 1.67772e31 | 0.0500000 | ||||||||
\(401\) | 3.40848e32 | 0.984591 | 0.492295 | − | 0.870428i | \(-0.336158\pi\) | ||||
0.492295 | + | 0.870428i | \(0.336158\pi\) | |||||||
\(402\) | −1.43985e32 | −0.403172 | ||||||||
\(403\) | 2.41449e32 | 0.655409 | ||||||||
\(404\) | −5.37166e31 | −0.141365 | ||||||||
\(405\) | 2.63676e31 | 0.0672794 | ||||||||
\(406\) | 1.82417e32 | 0.451327 | ||||||||
\(407\) | −1.62844e31 | −0.0390697 | ||||||||
\(408\) | 6.40136e31 | 0.148943 | ||||||||
\(409\) | 1.88820e32 | 0.426095 | 0.213048 | − | 0.977042i | \(-0.431661\pi\) | ||||
0.213048 | + | 0.977042i | \(0.431661\pi\) | |||||||
\(410\) | −1.02459e32 | −0.224260 | ||||||||
\(411\) | 4.51827e30 | 0.00959290 | ||||||||
\(412\) | −9.12340e30 | −0.0187906 | ||||||||
\(413\) | 9.59257e32 | 1.91672 | ||||||||
\(414\) | −4.93741e31 | −0.0957182 | ||||||||
\(415\) | 2.72967e32 | 0.513463 | ||||||||
\(416\) | 8.95138e31 | 0.163389 | ||||||||
\(417\) | 5.76386e32 | 1.02097 | ||||||||
\(418\) | 7.09545e30 | 0.0121977 | ||||||||
\(419\) | −6.53498e32 | −1.09036 | −0.545179 | − | 0.838320i | \(-0.683538\pi\) | ||||
−0.545179 | + | 0.838320i | \(0.683538\pi\) | |||||||
\(420\) | −1.21276e32 | −0.196409 | ||||||||
\(421\) | −8.06557e32 | −1.26797 | −0.633985 | − | 0.773345i | \(-0.718582\pi\) | ||||
−0.633985 | + | 0.773345i | \(0.718582\pi\) | |||||||
\(422\) | 6.53492e32 | 0.997321 | ||||||||
\(423\) | −7.02172e32 | −1.04037 | ||||||||
\(424\) | −1.37626e32 | −0.197983 | ||||||||
\(425\) | 8.97791e31 | 0.125405 | ||||||||
\(426\) | 5.23393e31 | 0.0709918 | ||||||||
\(427\) | −1.15041e33 | −1.51532 | ||||||||
\(428\) | −2.44213e32 | −0.312408 | ||||||||
\(429\) | 1.71993e31 | 0.0213695 | ||||||||
\(430\) | −4.58049e32 | −0.552785 | ||||||||
\(431\) | −1.89617e32 | −0.222285 | −0.111143 | − | 0.993804i | \(-0.535451\pi\) | ||||
−0.111143 | + | 0.993804i | \(0.535451\pi\) | |||||||
\(432\) | −2.28406e32 | −0.260112 | ||||||||
\(433\) | 1.55976e33 | 1.72567 | 0.862835 | − | 0.505485i | \(-0.168687\pi\) | ||||
0.862835 | + | 0.505485i | \(0.168687\pi\) | |||||||
\(434\) | 6.09838e32 | 0.655530 | ||||||||
\(435\) | −1.40451e32 | −0.146693 | ||||||||
\(436\) | −5.59106e32 | −0.567431 | ||||||||
\(437\) | 1.25415e32 | 0.123689 | ||||||||
\(438\) | −8.12744e32 | −0.778982 | ||||||||
\(439\) | −1.73749e33 | −1.61851 | −0.809254 | − | 0.587460i | \(-0.800128\pi\) | ||||
−0.809254 | + | 0.587460i | \(0.800128\pi\) | |||||||
\(440\) | −6.00957e30 | −0.00544108 | ||||||||
\(441\) | −4.42072e32 | −0.389055 | ||||||||
\(442\) | 4.79011e32 | 0.409795 | ||||||||
\(443\) | 2.09110e33 | 1.73912 | 0.869559 | − | 0.493830i | \(-0.164403\pi\) | ||||
0.869559 | + | 0.493830i | \(0.164403\pi\) | |||||||
\(444\) | −4.71698e32 | −0.381397 | ||||||||
\(445\) | −4.27628e32 | −0.336176 | ||||||||
\(446\) | 1.20124e33 | 0.918216 | ||||||||
\(447\) | −1.77426e33 | −1.31878 | ||||||||
\(448\) | 2.26089e32 | 0.163419 | ||||||||
\(449\) | −2.57391e32 | −0.180932 | −0.0904659 | − | 0.995900i | \(-0.528836\pi\) | ||||
−0.0904659 | + | 0.995900i | \(0.528836\pi\) | |||||||
\(450\) | −1.13482e32 | −0.0775835 | ||||||||
\(451\) | 3.67006e31 | 0.0244043 | ||||||||
\(452\) | 2.87315e32 | 0.185835 | ||||||||
\(453\) | 3.92785e32 | 0.247131 | ||||||||
\(454\) | 1.17159e33 | 0.717098 | ||||||||
\(455\) | −9.07506e32 | −0.540390 | ||||||||
\(456\) | 2.05529e32 | 0.119073 | ||||||||
\(457\) | −3.29162e33 | −1.85548 | −0.927742 | − | 0.373222i | \(-0.878253\pi\) | ||||
−0.927742 | + | 0.373222i | \(0.878253\pi\) | |||||||
\(458\) | −9.33129e32 | −0.511827 | ||||||||
\(459\) | −1.22226e33 | −0.652385 | ||||||||
\(460\) | −1.06222e32 | −0.0551747 | ||||||||
\(461\) | 2.82594e33 | 1.42857 | 0.714286 | − | 0.699854i | \(-0.246752\pi\) | ||||
0.714286 | + | 0.699854i | \(0.246752\pi\) | |||||||
\(462\) | 4.34410e31 | 0.0213735 | ||||||||
\(463\) | 3.15530e33 | 1.51105 | 0.755523 | − | 0.655122i | \(-0.227383\pi\) | ||||
0.755523 | + | 0.655122i | \(0.227383\pi\) | |||||||
\(464\) | 2.61834e32 | 0.122054 | ||||||||
\(465\) | −4.69540e32 | −0.213064 | ||||||||
\(466\) | 2.85014e33 | 1.25905 | ||||||||
\(467\) | 1.46352e33 | 0.629417 | 0.314709 | − | 0.949188i | \(-0.398093\pi\) | ||||
0.314709 | + | 0.949188i | \(0.398093\pi\) | |||||||
\(468\) | −6.05475e32 | −0.253526 | ||||||||
\(469\) | −2.72131e33 | −1.10947 | ||||||||
\(470\) | −1.51063e33 | −0.599701 | ||||||||
\(471\) | −1.55714e33 | −0.601960 | ||||||||
\(472\) | 1.37688e33 | 0.518347 | ||||||||
\(473\) | 1.64072e32 | 0.0601549 | ||||||||
\(474\) | −1.08560e33 | −0.387650 | ||||||||
\(475\) | 2.88255e32 | 0.100255 | ||||||||
\(476\) | 1.20986e33 | 0.409871 | ||||||||
\(477\) | 9.30909e32 | 0.307204 | ||||||||
\(478\) | 6.01341e32 | 0.193318 | ||||||||
\(479\) | −9.44658e31 | −0.0295856 | −0.0147928 | − | 0.999891i | \(-0.504709\pi\) | ||||
−0.0147928 | + | 0.999891i | \(0.504709\pi\) | |||||||
\(480\) | −1.74075e32 | −0.0531155 | ||||||||
\(481\) | −3.52970e33 | −1.04936 | ||||||||
\(482\) | 3.22286e33 | 0.933585 | ||||||||
\(483\) | 7.67838e32 | 0.216736 | ||||||||
\(484\) | −1.81561e33 | −0.499408 | ||||||||
\(485\) | 3.14184e33 | 0.842194 | ||||||||
\(486\) | 2.54259e33 | 0.664236 | ||||||||
\(487\) | 2.95578e33 | 0.752593 | 0.376296 | − | 0.926499i | \(-0.377197\pi\) | ||||
0.376296 | + | 0.926499i | \(0.377197\pi\) | |||||||
\(488\) | −1.65126e33 | −0.409795 | ||||||||
\(489\) | −3.02722e32 | −0.0732291 | ||||||||
\(490\) | −9.51058e32 | −0.224262 | ||||||||
\(491\) | 3.19357e33 | 0.734103 | 0.367052 | − | 0.930201i | \(-0.380367\pi\) | ||||
0.367052 | + | 0.930201i | \(0.380367\pi\) | |||||||
\(492\) | 1.06308e33 | 0.238233 | ||||||||
\(493\) | 1.40114e33 | 0.306123 | ||||||||
\(494\) | 1.53797e33 | 0.327612 | ||||||||
\(495\) | 4.06490e31 | 0.00844276 | ||||||||
\(496\) | 8.75336e32 | 0.177278 | ||||||||
\(497\) | 9.89214e32 | 0.195360 | ||||||||
\(498\) | −2.83222e33 | −0.545457 | ||||||||
\(499\) | −3.38640e33 | −0.636036 | −0.318018 | − | 0.948085i | \(-0.603017\pi\) | ||||
−0.318018 | + | 0.948085i | \(0.603017\pi\) | |||||||
\(500\) | −2.44141e32 | −0.0447214 | ||||||||
\(501\) | 1.68992e33 | 0.301921 | ||||||||
\(502\) | −5.33922e33 | −0.930425 | ||||||||
\(503\) | 6.76442e33 | 1.14982 | 0.574911 | − | 0.818216i | \(-0.305037\pi\) | ||||
0.574911 | + | 0.818216i | \(0.305037\pi\) | |||||||
\(504\) | −1.52927e33 | −0.253573 | ||||||||
\(505\) | 7.81679e32 | 0.126441 | ||||||||
\(506\) | 3.80484e31 | 0.00600419 | ||||||||
\(507\) | −6.35948e32 | −0.0979089 | ||||||||
\(508\) | −4.71299e33 | −0.707947 | ||||||||
\(509\) | 6.69189e33 | 0.980791 | 0.490395 | − | 0.871500i | \(-0.336852\pi\) | ||||
0.490395 | + | 0.871500i | \(0.336852\pi\) | |||||||
\(510\) | −9.31520e32 | −0.133219 | ||||||||
\(511\) | −1.53609e34 | −2.14365 | ||||||||
\(512\) | 3.24519e32 | 0.0441942 | ||||||||
\(513\) | −3.92432e33 | −0.521551 | ||||||||
\(514\) | −9.07672e33 | −1.17731 | ||||||||
\(515\) | 1.32763e32 | 0.0168069 | ||||||||
\(516\) | 4.75257e33 | 0.587229 | ||||||||
\(517\) | 5.41105e32 | 0.0652603 | ||||||||
\(518\) | −8.91511e33 | −1.04955 | ||||||||
\(519\) | 5.34383e33 | 0.614130 | ||||||||
\(520\) | −1.30260e33 | −0.146140 | ||||||||
\(521\) | −1.12229e34 | −1.22923 | −0.614616 | − | 0.788826i | \(-0.710689\pi\) | ||||
−0.614616 | + | 0.788826i | \(0.710689\pi\) | |||||||
\(522\) | −1.77106e33 | −0.189388 | ||||||||
\(523\) | 7.35349e33 | 0.767754 | 0.383877 | − | 0.923384i | \(-0.374589\pi\) | ||||
0.383877 | + | 0.923384i | \(0.374589\pi\) | |||||||
\(524\) | 6.57136e33 | 0.669906 | ||||||||
\(525\) | 1.76480e33 | 0.175673 | ||||||||
\(526\) | 1.38141e33 | 0.134277 | ||||||||
\(527\) | 4.68414e33 | 0.444628 | ||||||||
\(528\) | 6.23534e31 | 0.00578011 | ||||||||
\(529\) | −1.03732e34 | −0.939115 | ||||||||
\(530\) | 2.00272e33 | 0.177081 | ||||||||
\(531\) | −9.31326e33 | −0.804304 | ||||||||
\(532\) | 3.88451e33 | 0.327673 | ||||||||
\(533\) | 7.95499e33 | 0.655465 | ||||||||
\(534\) | 4.43694e33 | 0.357123 | ||||||||
\(535\) | 3.55377e33 | 0.279426 | ||||||||
\(536\) | −3.90606e33 | −0.300040 | ||||||||
\(537\) | −1.25913e34 | −0.944912 | ||||||||
\(538\) | −1.69519e34 | −1.24291 | ||||||||
\(539\) | 3.40667e32 | 0.0244046 | ||||||||
\(540\) | 3.32374e33 | 0.232651 | ||||||||
\(541\) | 6.91384e32 | 0.0472883 | 0.0236441 | − | 0.999720i | \(-0.492473\pi\) | ||||
0.0236441 | + | 0.999720i | \(0.492473\pi\) | |||||||
\(542\) | 9.34216e32 | 0.0624390 | ||||||||
\(543\) | 8.30881e33 | 0.542677 | ||||||||
\(544\) | 1.73658e33 | 0.110843 | ||||||||
\(545\) | 8.13607e33 | 0.507526 | ||||||||
\(546\) | 9.41600e33 | 0.574062 | ||||||||
\(547\) | 1.40577e34 | 0.837672 | 0.418836 | − | 0.908062i | \(-0.362438\pi\) | ||||
0.418836 | + | 0.908062i | \(0.362438\pi\) | |||||||
\(548\) | 1.22573e32 | 0.00713902 | ||||||||
\(549\) | 1.11692e34 | 0.635867 | ||||||||
\(550\) | 8.74507e31 | 0.00486665 | ||||||||
\(551\) | 4.49866e33 | 0.244731 | ||||||||
\(552\) | 1.10212e33 | 0.0586127 | ||||||||
\(553\) | −2.05178e34 | −1.06676 | ||||||||
\(554\) | 1.55090e34 | 0.788335 | ||||||||
\(555\) | 6.86411e33 | 0.341132 | ||||||||
\(556\) | 1.56364e34 | 0.759803 | ||||||||
\(557\) | −2.49292e34 | −1.18445 | −0.592227 | − | 0.805771i | \(-0.701751\pi\) | ||||
−0.592227 | + | 0.805771i | \(0.701751\pi\) | |||||||
\(558\) | −5.92081e33 | −0.275076 | ||||||||
\(559\) | 3.55633e34 | 1.61568 | ||||||||
\(560\) | −3.29002e33 | −0.146167 | ||||||||
\(561\) | 3.33669e32 | 0.0144971 | ||||||||
\(562\) | 1.99644e34 | 0.848306 | ||||||||
\(563\) | −1.70240e34 | −0.707466 | −0.353733 | − | 0.935346i | \(-0.615088\pi\) | ||||
−0.353733 | + | 0.935346i | \(0.615088\pi\) | |||||||
\(564\) | 1.56738e34 | 0.637068 | ||||||||
\(565\) | −4.18098e33 | −0.166216 | ||||||||
\(566\) | −3.19248e33 | −0.124143 | ||||||||
\(567\) | −5.17070e33 | −0.196680 | ||||||||
\(568\) | 1.41988e33 | 0.0528319 | ||||||||
\(569\) | 1.90307e34 | 0.692709 | 0.346355 | − | 0.938104i | \(-0.387419\pi\) | ||||
0.346355 | + | 0.938104i | \(0.387419\pi\) | |||||||
\(570\) | −2.99084e33 | −0.106502 | ||||||||
\(571\) | 2.13655e34 | 0.744323 | 0.372162 | − | 0.928168i | \(-0.378617\pi\) | ||||
0.372162 | + | 0.928168i | \(0.378617\pi\) | |||||||
\(572\) | 4.66588e32 | 0.0159031 | ||||||||
\(573\) | −9.04669e33 | −0.301687 | ||||||||
\(574\) | 2.00923e34 | 0.655587 | ||||||||
\(575\) | 1.54573e33 | 0.0493497 | ||||||||
\(576\) | −2.19506e33 | −0.0685748 | ||||||||
\(577\) | −2.06745e34 | −0.632030 | −0.316015 | − | 0.948754i | \(-0.602345\pi\) | ||||
−0.316015 | + | 0.948754i | \(0.602345\pi\) | |||||||
\(578\) | −1.43436e34 | −0.429102 | ||||||||
\(579\) | 2.08987e34 | 0.611839 | ||||||||
\(580\) | −3.81019e33 | −0.109168 | ||||||||
\(581\) | −5.35291e34 | −1.50103 | ||||||||
\(582\) | −3.25988e34 | −0.894672 | ||||||||
\(583\) | −7.17372e32 | −0.0192703 | ||||||||
\(584\) | −2.20484e34 | −0.579717 | ||||||||
\(585\) | 8.81082e33 | 0.226761 | ||||||||
\(586\) | 3.67713e34 | 0.926380 | ||||||||
\(587\) | −5.55725e34 | −1.37052 | −0.685258 | − | 0.728301i | \(-0.740310\pi\) | ||||
−0.685258 | + | 0.728301i | \(0.740310\pi\) | |||||||
\(588\) | 9.86789e33 | 0.238236 | ||||||||
\(589\) | 1.50394e34 | 0.355460 | ||||||||
\(590\) | −2.00362e34 | −0.463624 | ||||||||
\(591\) | −3.66808e34 | −0.830989 | ||||||||
\(592\) | −1.27964e34 | −0.283835 | ||||||||
\(593\) | −6.93628e34 | −1.50641 | −0.753204 | − | 0.657787i | \(-0.771493\pi\) | ||||
−0.753204 | + | 0.657787i | \(0.771493\pi\) | |||||||
\(594\) | −1.19056e33 | −0.0253175 | ||||||||
\(595\) | −1.76057e34 | −0.366600 | ||||||||
\(596\) | −4.81326e34 | −0.981434 | ||||||||
\(597\) | −1.14979e34 | −0.229584 | ||||||||
\(598\) | 8.24713e33 | 0.161264 | ||||||||
\(599\) | −3.28492e34 | −0.629056 | −0.314528 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314528 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(600\) | 2.53313e33 | 0.0475080 | ||||||||
\(601\) | −2.89648e34 | −0.532034 | −0.266017 | − | 0.963968i | \(-0.585708\pi\) | ||||
−0.266017 | + | 0.963968i | \(0.585708\pi\) | |||||||
\(602\) | 8.98237e34 | 1.61598 | ||||||||
\(603\) | 2.64207e34 | 0.465563 | ||||||||
\(604\) | 1.06556e34 | 0.183914 | ||||||||
\(605\) | 2.64206e34 | 0.446684 | ||||||||
\(606\) | −8.11046e33 | −0.134319 | ||||||||
\(607\) | 8.42327e34 | 1.36654 | 0.683270 | − | 0.730166i | \(-0.260557\pi\) | ||||
0.683270 | + | 0.730166i | \(0.260557\pi\) | |||||||
\(608\) | 5.57566e33 | 0.0886138 | ||||||||
\(609\) | 2.75425e34 | 0.428832 | ||||||||
\(610\) | 2.40289e34 | 0.366532 | ||||||||
\(611\) | 1.17286e35 | 1.75280 | ||||||||
\(612\) | −1.17463e34 | −0.171992 | ||||||||
\(613\) | 1.08389e34 | 0.155499 | 0.0777496 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777496 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(614\) | −4.24829e34 | −0.597185 | ||||||||
\(615\) | −1.54699e34 | −0.213083 | ||||||||
\(616\) | 1.17848e33 | 0.0159061 | ||||||||
\(617\) | 7.99721e33 | 0.105773 | 0.0528864 | − | 0.998601i | \(-0.483158\pi\) | ||||
0.0528864 | + | 0.998601i | \(0.483158\pi\) | |||||||
\(618\) | −1.37751e33 | −0.0178541 | ||||||||
\(619\) | −6.34272e34 | −0.805643 | −0.402822 | − | 0.915279i | \(-0.631970\pi\) | ||||
−0.402822 | + | 0.915279i | \(0.631970\pi\) | |||||||
\(620\) | −1.27378e34 | −0.158562 | ||||||||
\(621\) | −2.10436e34 | −0.256729 | ||||||||
\(622\) | −1.57789e34 | −0.188668 | ||||||||
\(623\) | 8.38582e34 | 0.982755 | ||||||||
\(624\) | 1.35153e34 | 0.155246 | ||||||||
\(625\) | 3.55271e33 | 0.0400000 | ||||||||
\(626\) | −1.08035e35 | −1.19229 | ||||||||
\(627\) | 1.07131e33 | 0.0115897 | ||||||||
\(628\) | −4.22427e34 | −0.447977 | ||||||||
\(629\) | −6.84766e34 | −0.711884 | ||||||||
\(630\) | 2.22539e34 | 0.226803 | ||||||||
\(631\) | 1.41569e35 | 1.41449 | 0.707245 | − | 0.706968i | \(-0.249938\pi\) | ||||
0.707245 | + | 0.706968i | \(0.249938\pi\) | |||||||
\(632\) | −2.94505e34 | −0.288489 | ||||||||
\(633\) | 9.86683e34 | 0.947614 | ||||||||
\(634\) | −1.49639e34 | −0.140906 | ||||||||
\(635\) | 6.85831e34 | 0.633207 | ||||||||
\(636\) | −2.07797e34 | −0.188115 | ||||||||
\(637\) | 7.38409e34 | 0.655472 | ||||||||
\(638\) | 1.36480e33 | 0.0118799 | ||||||||
\(639\) | −9.60410e33 | −0.0819778 | ||||||||
\(640\) | −4.72237e33 | −0.0395285 | ||||||||
\(641\) | −4.50631e34 | −0.369910 | −0.184955 | − | 0.982747i | \(-0.559214\pi\) | ||||
−0.184955 | + | 0.982747i | \(0.559214\pi\) | |||||||
\(642\) | −3.68728e34 | −0.296837 | ||||||||
\(643\) | 1.18877e35 | 0.938561 | 0.469280 | − | 0.883049i | \(-0.344513\pi\) | ||||
0.469280 | + | 0.883049i | \(0.344513\pi\) | |||||||
\(644\) | 2.08301e34 | 0.161294 | ||||||||
\(645\) | −6.91590e34 | −0.525233 | ||||||||
\(646\) | 2.98367e34 | 0.222252 | ||||||||
\(647\) | 1.85298e34 | 0.135384 | 0.0676921 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676921 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(648\) | −7.42181e33 | −0.0531890 | ||||||||
\(649\) | 7.17694e33 | 0.0504522 | ||||||||
\(650\) | 1.89553e34 | 0.130711 | ||||||||
\(651\) | 9.20771e34 | 0.622858 | ||||||||
\(652\) | −8.21234e33 | −0.0544970 | ||||||||
\(653\) | −1.84607e35 | −1.20180 | −0.600902 | − | 0.799323i | \(-0.705192\pi\) | ||||
−0.600902 | + | 0.799323i | \(0.705192\pi\) | |||||||
\(654\) | −8.44173e34 | −0.539150 | ||||||||
\(655\) | −9.56258e34 | −0.599182 | ||||||||
\(656\) | 2.88396e34 | 0.177293 | ||||||||
\(657\) | 1.49136e35 | 0.899530 | ||||||||
\(658\) | 2.96235e35 | 1.75313 | ||||||||
\(659\) | −3.04390e35 | −1.76752 | −0.883758 | − | 0.467944i | \(-0.844995\pi\) | ||||
−0.883758 | + | 0.467944i | \(0.844995\pi\) | |||||||
\(660\) | −9.07362e32 | −0.00516989 | ||||||||
\(661\) | 2.88465e34 | 0.161278 | 0.0806389 | − | 0.996743i | \(-0.474304\pi\) | ||||
0.0806389 | + | 0.996743i | \(0.474304\pi\) | |||||||
\(662\) | −1.03339e35 | −0.566945 | ||||||||
\(663\) | 7.23240e34 | 0.389371 | ||||||||
\(664\) | −7.68334e34 | −0.405928 | ||||||||
\(665\) | −5.65270e34 | −0.293079 | ||||||||
\(666\) | 8.65552e34 | 0.440418 | ||||||||
\(667\) | 2.41235e34 | 0.120467 | ||||||||
\(668\) | 4.58446e34 | 0.224689 | ||||||||
\(669\) | 1.81371e35 | 0.872452 | ||||||||
\(670\) | 5.68406e34 | 0.268364 | ||||||||
\(671\) | −8.60712e33 | −0.0398865 | ||||||||
\(672\) | 3.41363e34 | 0.155275 | ||||||||
\(673\) | −6.39436e34 | −0.285502 | −0.142751 | − | 0.989759i | \(-0.545595\pi\) | ||||
−0.142751 | + | 0.989759i | \(0.545595\pi\) | |||||||
\(674\) | −1.05463e35 | −0.462225 | ||||||||
\(675\) | −4.83668e34 | −0.208090 | ||||||||
\(676\) | −1.72522e34 | −0.0728636 | ||||||||
\(677\) | 6.00220e34 | 0.248858 | 0.124429 | − | 0.992229i | \(-0.460290\pi\) | ||||
0.124429 | + | 0.992229i | \(0.460290\pi\) | |||||||
\(678\) | 4.33806e34 | 0.176573 | ||||||||
\(679\) | −6.16117e35 | −2.46202 | ||||||||
\(680\) | −2.52706e34 | −0.0991410 | ||||||||
\(681\) | 1.76894e35 | 0.681358 | ||||||||
\(682\) | 4.56266e33 | 0.0172549 | ||||||||
\(683\) | −3.76829e35 | −1.39922 | −0.699610 | − | 0.714525i | \(-0.746643\pi\) | ||||
−0.699610 | + | 0.714525i | \(0.746643\pi\) | |||||||
\(684\) | −3.77140e34 | −0.137499 | ||||||||
\(685\) | −1.78367e33 | −0.00638533 | ||||||||
\(686\) | −7.64813e34 | −0.268846 | ||||||||
\(687\) | −1.40890e35 | −0.486317 | ||||||||
\(688\) | 1.28929e35 | 0.437015 | ||||||||
\(689\) | −1.55493e35 | −0.517572 | ||||||||
\(690\) | −1.60380e34 | −0.0524248 | ||||||||
\(691\) | −3.26709e35 | −1.04878 | −0.524392 | − | 0.851477i | \(-0.675707\pi\) | ||||
−0.524392 | + | 0.851477i | \(0.675707\pi\) | |||||||
\(692\) | 1.44969e35 | 0.457034 | ||||||||
\(693\) | −7.97129e33 | −0.0246810 | ||||||||
\(694\) | −7.00657e34 | −0.213065 | ||||||||
\(695\) | −2.27539e35 | −0.679588 | ||||||||
\(696\) | 3.95334e34 | 0.115971 | ||||||||
\(697\) | 1.54328e35 | 0.444667 | ||||||||
\(698\) | 2.84082e35 | 0.803991 | ||||||||
\(699\) | 4.30332e35 | 1.19630 | ||||||||
\(700\) | 4.78762e34 | 0.130736 | ||||||||
\(701\) | 3.88741e35 | 1.04276 | 0.521381 | − | 0.853324i | \(-0.325417\pi\) | ||||
0.521381 | + | 0.853324i | \(0.325417\pi\) | |||||||
\(702\) | −2.58058e35 | −0.679992 | ||||||||
\(703\) | −2.19859e35 | −0.569118 | ||||||||
\(704\) | 1.69154e33 | 0.00430155 | ||||||||
\(705\) | −2.28084e35 | −0.569811 | ||||||||
\(706\) | 5.00669e34 | 0.122883 | ||||||||
\(707\) | −1.53288e35 | −0.369628 | ||||||||
\(708\) | 2.07890e35 | 0.492512 | ||||||||
\(709\) | 4.23533e35 | 0.985848 | 0.492924 | − | 0.870072i | \(-0.335928\pi\) | ||||
0.492924 | + | 0.870072i | \(0.335928\pi\) | |||||||
\(710\) | −2.06619e34 | −0.0472543 | ||||||||
\(711\) | 1.99204e35 | 0.447639 | ||||||||
\(712\) | 1.20367e35 | 0.265770 | ||||||||
\(713\) | 8.06469e34 | 0.174972 | ||||||||
\(714\) | 1.82672e35 | 0.389443 | ||||||||
\(715\) | −6.78975e33 | −0.0142242 | ||||||||
\(716\) | −3.41580e35 | −0.703201 | ||||||||
\(717\) | 9.07941e34 | 0.183683 | ||||||||
\(718\) | 2.15564e35 | 0.428568 | ||||||||
\(719\) | 6.21554e35 | 1.21442 | 0.607208 | − | 0.794543i | \(-0.292289\pi\) | ||||
0.607208 | + | 0.794543i | \(0.292289\pi\) | |||||||
\(720\) | 3.19423e34 | 0.0613352 | ||||||||
\(721\) | −2.60349e34 | −0.0491321 | ||||||||
\(722\) | −2.85444e35 | −0.529427 | ||||||||
\(723\) | 4.86608e35 | 0.887055 | ||||||||
\(724\) | 2.25404e35 | 0.403859 | ||||||||
\(725\) | 5.54456e34 | 0.0976432 | ||||||||
\(726\) | −2.74132e35 | −0.474517 | ||||||||
\(727\) | −4.24475e35 | −0.722225 | −0.361112 | − | 0.932522i | \(-0.617603\pi\) | ||||
−0.361112 | + | 0.932522i | \(0.617603\pi\) | |||||||
\(728\) | 2.55440e35 | 0.427216 | ||||||||
\(729\) | 4.75404e35 | 0.781572 | ||||||||
\(730\) | 3.20846e35 | 0.518514 | ||||||||
\(731\) | 6.89932e35 | 1.09607 | ||||||||
\(732\) | −2.49317e35 | −0.389371 | ||||||||
\(733\) | 7.04925e34 | 0.108229 | 0.0541145 | − | 0.998535i | \(-0.482766\pi\) | ||||
0.0541145 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(734\) | −4.28995e34 | −0.0647518 | ||||||||
\(735\) | −1.43597e35 | −0.213085 | ||||||||
\(736\) | 2.98987e34 | 0.0436194 | ||||||||
\(737\) | −2.03602e34 | −0.0292037 | ||||||||
\(738\) | −1.95072e35 | −0.275100 | ||||||||
\(739\) | −9.55082e35 | −1.32430 | −0.662148 | − | 0.749373i | \(-0.730355\pi\) | ||||
−0.662148 | + | 0.749373i | \(0.730355\pi\) | |||||||
\(740\) | 1.86212e35 | 0.253870 | ||||||||
\(741\) | 2.32212e35 | 0.311284 | ||||||||
\(742\) | −3.92736e35 | −0.517668 | ||||||||
\(743\) | −1.29129e35 | −0.167364 | −0.0836820 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836820 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(744\) | 1.32164e35 | 0.168442 | ||||||||
\(745\) | 7.00422e35 | 0.877821 | ||||||||
\(746\) | −5.11909e35 | −0.630896 | ||||||||
\(747\) | 5.19704e35 | 0.629867 | ||||||||
\(748\) | 9.05187e33 | 0.0107887 | ||||||||
\(749\) | −6.96897e35 | −0.816857 | ||||||||
\(750\) | −3.68619e34 | −0.0424924 | ||||||||
\(751\) | −1.00002e36 | −1.13373 | −0.566864 | − | 0.823812i | \(-0.691843\pi\) | ||||
−0.566864 | + | 0.823812i | \(0.691843\pi\) | |||||||
\(752\) | 4.25204e35 | 0.474105 | ||||||||
\(753\) | −8.06149e35 | −0.884052 | ||||||||
\(754\) | 2.95827e35 | 0.319077 | ||||||||
\(755\) | −1.55059e35 | −0.164498 | ||||||||
\(756\) | −6.51788e35 | −0.680118 | ||||||||
\(757\) | −4.62323e35 | −0.474511 | −0.237256 | − | 0.971447i | \(-0.576248\pi\) | ||||
−0.237256 | + | 0.971447i | \(0.576248\pi\) | |||||||
\(758\) | −7.01138e35 | −0.707846 | ||||||||
\(759\) | 5.74478e33 | 0.00570494 | ||||||||
\(760\) | −8.11365e34 | −0.0792586 | ||||||||
\(761\) | 1.71968e36 | 1.65249 | 0.826247 | − | 0.563308i | \(-0.190471\pi\) | ||||
0.826247 | + | 0.563308i | \(0.190471\pi\) | |||||||
\(762\) | −7.11597e35 | −0.672662 | ||||||||
\(763\) | −1.59549e36 | −1.48367 | ||||||||
\(764\) | −2.45421e35 | −0.224515 | ||||||||
\(765\) | 1.70931e35 | 0.153834 | ||||||||
\(766\) | −1.07981e36 | −0.956069 | ||||||||
\(767\) | 1.55563e36 | 1.35508 | ||||||||
\(768\) | 4.89978e34 | 0.0419915 | ||||||||
\(769\) | 1.91462e36 | 1.61437 | 0.807184 | − | 0.590299i | \(-0.200990\pi\) | ||||
0.807184 | + | 0.590299i | \(0.200990\pi\) | |||||||
\(770\) | −1.71492e34 | −0.0142268 | ||||||||
\(771\) | −1.37046e36 | −1.11863 | ||||||||
\(772\) | 5.66947e35 | 0.455330 | ||||||||
\(773\) | −9.08398e35 | −0.717848 | −0.358924 | − | 0.933367i | \(-0.616856\pi\) | ||||
−0.358924 | + | 0.933367i | \(0.616856\pi\) | |||||||
\(774\) | −8.72082e35 | −0.678103 | ||||||||
\(775\) | 1.85360e35 | 0.141822 | ||||||||
\(776\) | −8.84349e35 | −0.665813 | ||||||||
\(777\) | −1.34606e36 | −0.997243 | ||||||||
\(778\) | 1.23522e36 | 0.900532 | ||||||||
\(779\) | 4.95503e35 | 0.355490 | ||||||||
\(780\) | −1.96674e35 | −0.138856 | ||||||||
\(781\) | 7.40106e33 | 0.00514229 | ||||||||
\(782\) | 1.59995e35 | 0.109402 | ||||||||
\(783\) | −7.54839e35 | −0.507963 | ||||||||
\(784\) | 2.67699e35 | 0.177295 | ||||||||
\(785\) | 6.14712e35 | 0.400683 | ||||||||
\(786\) | 9.92184e35 | 0.636518 | ||||||||
\(787\) | 5.77613e35 | 0.364714 | 0.182357 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182357 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(788\) | −9.95088e35 | −0.618420 | ||||||||
\(789\) | 2.08574e35 | 0.127584 | ||||||||
\(790\) | 4.28561e35 | 0.258032 | ||||||||
\(791\) | 8.19893e35 | 0.485905 | ||||||||
\(792\) | −1.14417e34 | −0.00667459 | ||||||||
\(793\) | −1.86563e36 | −1.07130 | ||||||||
\(794\) | 1.47819e36 | 0.835552 | ||||||||
\(795\) | 3.02384e35 | 0.168256 | ||||||||
\(796\) | −3.11920e35 | −0.170856 | ||||||||
\(797\) | 1.37116e36 | 0.739364 | 0.369682 | − | 0.929158i | \(-0.379467\pi\) | ||||
0.369682 | + | 0.929158i | \(0.379467\pi\) | |||||||
\(798\) | 5.86507e35 | 0.311341 | ||||||||
\(799\) | 2.27537e36 | 1.18910 | ||||||||
\(800\) | 6.87195e34 | 0.0353553 | ||||||||
\(801\) | −8.14165e35 | −0.412388 | ||||||||
\(802\) | 1.39611e36 | 0.696211 | ||||||||
\(803\) | −1.14926e35 | −0.0564255 | ||||||||
\(804\) | −5.89761e35 | −0.285085 | ||||||||
\(805\) | −3.03118e35 | −0.144266 | ||||||||
\(806\) | 9.88975e35 | 0.463444 | ||||||||
\(807\) | −2.55951e36 | −1.18096 | ||||||||
\(808\) | −2.20023e35 | −0.0999600 | ||||||||
\(809\) | 3.58962e36 | 1.60580 | 0.802902 | − | 0.596111i | \(-0.203288\pi\) | ||||
0.802902 | + | 0.596111i | \(0.203288\pi\) | |||||||
\(810\) | 1.08001e35 | 0.0475737 | ||||||||
\(811\) | 1.03429e35 | 0.0448624 | 0.0224312 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224312 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(812\) | 7.47182e35 | 0.319136 | ||||||||
\(813\) | 1.41054e35 | 0.0593270 | ||||||||
\(814\) | −6.67007e34 | −0.0276265 | ||||||||
\(815\) | 1.19505e35 | 0.0487436 | ||||||||
\(816\) | 2.62200e35 | 0.105319 | ||||||||
\(817\) | 2.21518e36 | 0.876259 | ||||||||
\(818\) | 7.73407e35 | 0.301295 | ||||||||
\(819\) | −1.72781e36 | −0.662898 | ||||||||
\(820\) | −4.19671e35 | −0.158576 | ||||||||
\(821\) | −2.70025e36 | −1.00488 | −0.502439 | − | 0.864612i | \(-0.667564\pi\) | ||||
−0.502439 | + | 0.864612i | \(0.667564\pi\) | |||||||
\(822\) | 1.85069e34 | 0.00678320 | ||||||||
\(823\) | −2.53917e36 | −0.916630 | −0.458315 | − | 0.888790i | \(-0.651547\pi\) | ||||
−0.458315 | + | 0.888790i | \(0.651547\pi\) | |||||||
\(824\) | −3.73695e34 | −0.0132870 | ||||||||
\(825\) | 1.32039e34 | 0.00462409 | ||||||||
\(826\) | 3.92912e36 | 1.35533 | ||||||||
\(827\) | 2.67322e36 | 0.908270 | 0.454135 | − | 0.890933i | \(-0.349948\pi\) | ||||
0.454135 | + | 0.890933i | \(0.349948\pi\) | |||||||
\(828\) | −2.02236e35 | −0.0676830 | ||||||||
\(829\) | −5.79155e36 | −1.90925 | −0.954626 | − | 0.297806i | \(-0.903745\pi\) | ||||
−0.954626 | + | 0.297806i | \(0.903745\pi\) | |||||||
\(830\) | 1.11807e36 | 0.363073 | ||||||||
\(831\) | 2.34164e36 | 0.749044 | ||||||||
\(832\) | 3.66648e35 | 0.115534 | ||||||||
\(833\) | 1.43252e36 | 0.444672 | ||||||||
\(834\) | 2.36088e36 | 0.721934 | ||||||||
\(835\) | −6.67126e35 | −0.200968 | ||||||||
\(836\) | 2.90630e34 | 0.00862504 | ||||||||
\(837\) | −2.52349e36 | −0.737792 | ||||||||
\(838\) | −2.67673e36 | −0.770999 | ||||||||
\(839\) | −2.27845e36 | −0.646568 | −0.323284 | − | 0.946302i | \(-0.604787\pi\) | ||||
−0.323284 | + | 0.946302i | \(0.604787\pi\) | |||||||
\(840\) | −4.96748e35 | −0.138882 | ||||||||
\(841\) | −2.76505e36 | −0.761645 | ||||||||
\(842\) | −3.30366e36 | −0.896590 | ||||||||
\(843\) | 3.01435e36 | 0.806026 | ||||||||
\(844\) | 2.67671e36 | 0.705212 | ||||||||
\(845\) | 2.51053e35 | 0.0651712 | ||||||||
\(846\) | −2.87610e36 | −0.735655 | ||||||||
\(847\) | −5.18110e36 | −1.30581 | ||||||||
\(848\) | −5.63717e35 | −0.139995 | ||||||||
\(849\) | −4.82020e35 | −0.117956 | ||||||||
\(850\) | 3.67735e35 | 0.0886744 | ||||||||
\(851\) | −1.17896e36 | −0.280144 | ||||||||
\(852\) | 2.14382e35 | 0.0501988 | ||||||||
\(853\) | 3.72321e36 | 0.859122 | 0.429561 | − | 0.903038i | \(-0.358668\pi\) | ||||
0.429561 | + | 0.903038i | \(0.358668\pi\) | |||||||
\(854\) | −4.71209e36 | −1.07150 | ||||||||
\(855\) | 5.48811e35 | 0.122983 | ||||||||
\(856\) | −1.00030e36 | −0.220906 | ||||||||
\(857\) | 1.02353e36 | 0.222761 | 0.111381 | − | 0.993778i | \(-0.464473\pi\) | ||||
0.111381 | + | 0.993778i | \(0.464473\pi\) | |||||||
\(858\) | 7.04483e34 | 0.0151105 | ||||||||
\(859\) | 1.85947e36 | 0.393074 | 0.196537 | − | 0.980496i | \(-0.437030\pi\) | ||||
0.196537 | + | 0.980496i | \(0.437030\pi\) | |||||||
\(860\) | −1.87617e36 | −0.390878 | ||||||||
\(861\) | 3.03365e36 | 0.622912 | ||||||||
\(862\) | −7.76670e35 | −0.157180 | ||||||||
\(863\) | 8.67106e36 | 1.72957 | 0.864783 | − | 0.502146i | \(-0.167456\pi\) | ||||
0.864783 | + | 0.502146i | \(0.167456\pi\) | |||||||
\(864\) | −9.35550e35 | −0.183927 | ||||||||
\(865\) | −2.10958e36 | −0.408784 | ||||||||
\(866\) | 6.38876e36 | 1.22023 | ||||||||
\(867\) | −2.16569e36 | −0.407716 | ||||||||
\(868\) | 2.49790e36 | 0.463530 | ||||||||
\(869\) | −1.53510e35 | −0.0280794 | ||||||||
\(870\) | −5.75287e35 | −0.103727 | ||||||||
\(871\) | −4.41315e36 | −0.784372 | ||||||||
\(872\) | −2.29010e36 | −0.401235 | ||||||||
\(873\) | 5.98177e36 | 1.03312 | ||||||||
\(874\) | 5.13700e35 | 0.0874614 | ||||||||
\(875\) | −6.96690e35 | −0.116933 | ||||||||
\(876\) | −3.32900e36 | −0.550823 | ||||||||
\(877\) | −7.14177e36 | −1.16496 | −0.582480 | − | 0.812845i | \(-0.697918\pi\) | ||||
−0.582480 | + | 0.812845i | \(0.697918\pi\) | |||||||
\(878\) | −7.11674e36 | −1.14446 | ||||||||
\(879\) | 5.55196e36 | 0.880209 | ||||||||
\(880\) | −2.46152e34 | −0.00384742 | ||||||||
\(881\) | −3.00182e36 | −0.462579 | −0.231290 | − | 0.972885i | \(-0.574294\pi\) | ||||
−0.231290 | + | 0.972885i | \(0.574294\pi\) | |||||||
\(882\) | −1.81073e36 | −0.275103 | ||||||||
\(883\) | −2.65767e36 | −0.398100 | −0.199050 | − | 0.979989i | \(-0.563786\pi\) | ||||
−0.199050 | + | 0.979989i | \(0.563786\pi\) | |||||||
\(884\) | 1.96203e36 | 0.289769 | ||||||||
\(885\) | −3.02519e36 | −0.440516 | ||||||||
\(886\) | 8.56516e36 | 1.22974 | ||||||||
\(887\) | 2.39194e36 | 0.338613 | 0.169307 | − | 0.985563i | \(-0.445847\pi\) | ||||
0.169307 | + | 0.985563i | \(0.445847\pi\) | |||||||
\(888\) | −1.93208e36 | −0.269688 | ||||||||
\(889\) | −1.34492e37 | −1.85108 | ||||||||
\(890\) | −1.75157e36 | −0.237712 | ||||||||
\(891\) | −3.86859e34 | −0.00517704 | ||||||||
\(892\) | 4.92029e36 | 0.649277 | ||||||||
\(893\) | 7.30557e36 | 0.950629 | ||||||||
\(894\) | −7.26736e36 | −0.932519 | ||||||||
\(895\) | 4.97064e36 | 0.628962 | ||||||||
\(896\) | 9.26060e35 | 0.115555 | ||||||||
\(897\) | 1.24520e36 | 0.153227 | ||||||||
\(898\) | −1.05428e36 | −0.127938 | ||||||||
\(899\) | 2.89282e36 | 0.346199 | ||||||||
\(900\) | −4.64821e35 | −0.0548598 | ||||||||
\(901\) | −3.01659e36 | −0.351121 | ||||||||
\(902\) | 1.50326e35 | 0.0172564 | ||||||||
\(903\) | 1.35621e37 | 1.53543 | ||||||||
\(904\) | 1.17684e36 | 0.131405 | ||||||||
\(905\) | −3.28006e36 | −0.361222 | ||||||||
\(906\) | 1.60885e36 | 0.174748 | ||||||||
\(907\) | 1.27834e37 | 1.36948 | 0.684741 | − | 0.728787i | \(-0.259915\pi\) | ||||
0.684741 | + | 0.728787i | \(0.259915\pi\) | |||||||
\(908\) | 4.79885e36 | 0.507065 | ||||||||
\(909\) | 1.48824e36 | 0.155105 | ||||||||
\(910\) | −3.71714e36 | −0.382113 | ||||||||
\(911\) | 1.51675e37 | 1.53792 | 0.768961 | − | 0.639296i | \(-0.220774\pi\) | ||||
0.768961 | + | 0.639296i | \(0.220774\pi\) | |||||||
\(912\) | 8.41848e35 | 0.0841973 | ||||||||
\(913\) | −4.00492e35 | −0.0395102 | ||||||||
\(914\) | −1.34825e37 | −1.31203 | ||||||||
\(915\) | 3.62804e36 | 0.348264 | ||||||||
\(916\) | −3.82210e36 | −0.361916 | ||||||||
\(917\) | 1.87523e37 | 1.75161 | ||||||||
\(918\) | −5.00636e36 | −0.461306 | ||||||||
\(919\) | −1.63543e36 | −0.148658 | −0.0743292 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743292 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(920\) | −4.35084e35 | −0.0390144 | ||||||||
\(921\) | −6.41432e36 | −0.567421 | ||||||||
\(922\) | 1.15751e37 | 1.01015 | ||||||||
\(923\) | 1.60421e36 | 0.138115 | ||||||||
\(924\) | 1.77934e35 | 0.0151133 | ||||||||
\(925\) | −2.70974e36 | −0.227068 | ||||||||
\(926\) | 1.29241e37 | 1.06847 | ||||||||
\(927\) | 2.52769e35 | 0.0206170 | ||||||||
\(928\) | 1.07247e36 | 0.0863052 | ||||||||
\(929\) | −7.47115e36 | −0.593186 | −0.296593 | − | 0.955004i | \(-0.595850\pi\) | ||||
−0.296593 | + | 0.955004i | \(0.595850\pi\) | |||||||
\(930\) | −1.92323e36 | −0.150659 | ||||||||
\(931\) | 4.59943e36 | 0.355494 | ||||||||
\(932\) | 1.16742e37 | 0.890281 | ||||||||
\(933\) | −2.38240e36 | −0.179265 | ||||||||
\(934\) | 5.99459e36 | 0.445065 | ||||||||
\(935\) | −1.31722e35 | −0.00964969 | ||||||||
\(936\) | −2.48002e36 | −0.179270 | ||||||||
\(937\) | −2.45447e37 | −1.75070 | −0.875351 | − | 0.483488i | \(-0.839370\pi\) | ||||
−0.875351 | + | 0.483488i | \(0.839370\pi\) | |||||||
\(938\) | −1.11465e37 | −0.784517 | ||||||||
\(939\) | −1.63117e37 | −1.13287 | ||||||||
\(940\) | −6.18754e36 | −0.424052 | ||||||||
\(941\) | −1.35589e36 | −0.0916968 | −0.0458484 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458484 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(942\) | −6.37806e36 | −0.425650 | ||||||||
\(943\) | 2.65707e36 | 0.174987 | ||||||||
\(944\) | 5.63969e36 | 0.366527 | ||||||||
\(945\) | 9.48477e36 | 0.608316 | ||||||||
\(946\) | 6.72040e35 | 0.0425359 | ||||||||
\(947\) | −2.07354e37 | −1.29520 | −0.647601 | − | 0.761980i | \(-0.724227\pi\) | ||||
−0.647601 | + | 0.761980i | \(0.724227\pi\) | |||||||
\(948\) | −4.44661e36 | −0.274110 | ||||||||
\(949\) | −2.49107e37 | −1.51551 | ||||||||
\(950\) | 1.18069e36 | 0.0708911 | ||||||||
\(951\) | −2.25934e36 | −0.133883 | ||||||||
\(952\) | 4.95558e36 | 0.289823 | ||||||||
\(953\) | −2.04124e37 | −1.17823 | −0.589117 | − | 0.808048i | \(-0.700524\pi\) | ||||
−0.589117 | + | 0.808048i | \(0.700524\pi\) | |||||||
\(954\) | 3.81300e36 | 0.217226 | ||||||||
\(955\) | 3.57135e36 | 0.200812 | ||||||||
\(956\) | 2.46309e36 | 0.136696 | ||||||||
\(957\) | 2.06067e35 | 0.0112878 | ||||||||
\(958\) | −3.86932e35 | −0.0209202 | ||||||||
\(959\) | 3.49780e35 | 0.0186665 | ||||||||
\(960\) | −7.13012e35 | −0.0375584 | ||||||||
\(961\) | −9.56182e36 | −0.497163 | ||||||||
\(962\) | −1.44576e37 | −0.742009 | ||||||||
\(963\) | 6.76605e36 | 0.342773 | ||||||||
\(964\) | 1.32008e37 | 0.660144 | ||||||||
\(965\) | −8.25016e36 | −0.407259 | ||||||||
\(966\) | 3.14506e36 | 0.153255 | ||||||||
\(967\) | −1.88209e37 | −0.905333 | −0.452666 | − | 0.891680i | \(-0.649527\pi\) | ||||
−0.452666 | + | 0.891680i | \(0.649527\pi\) | |||||||
\(968\) | −7.43674e36 | −0.353135 | ||||||||
\(969\) | 4.50494e36 | 0.211174 | ||||||||
\(970\) | 1.28690e37 | 0.595521 | ||||||||
\(971\) | −2.62810e37 | −1.20061 | −0.600305 | − | 0.799771i | \(-0.704954\pi\) | ||||
−0.600305 | + | 0.799771i | \(0.704954\pi\) | |||||||
\(972\) | 1.04144e37 | 0.469686 | ||||||||
\(973\) | 4.46206e37 | 1.98667 | ||||||||
\(974\) | 1.21069e37 | 0.532163 | ||||||||
\(975\) | 2.86199e36 | 0.124197 | ||||||||
\(976\) | −6.76354e36 | −0.289769 | ||||||||
\(977\) | 6.14194e36 | 0.259791 | 0.129895 | − | 0.991528i | \(-0.458536\pi\) | ||||
0.129895 | + | 0.991528i | \(0.458536\pi\) | |||||||
\(978\) | −1.23995e36 | −0.0517808 | ||||||||
\(979\) | 6.27407e35 | 0.0258682 | ||||||||
\(980\) | −3.89553e36 | −0.158577 | ||||||||
\(981\) | 1.54903e37 | 0.622584 | ||||||||
\(982\) | 1.30808e37 | 0.519089 | ||||||||
\(983\) | −5.02851e37 | −1.97025 | −0.985123 | − | 0.171849i | \(-0.945026\pi\) | ||||
−0.985123 | + | 0.171849i | \(0.945026\pi\) | |||||||
\(984\) | 4.35438e36 | 0.168457 | ||||||||
\(985\) | 1.44804e37 | 0.553132 | ||||||||
\(986\) | 5.73908e36 | 0.216461 | ||||||||
\(987\) | 4.47275e37 | 1.66575 | ||||||||
\(988\) | 6.29951e36 | 0.231657 | ||||||||
\(989\) | 1.18786e37 | 0.431331 | ||||||||
\(990\) | 1.66498e35 | 0.00596993 | ||||||||
\(991\) | −2.22624e37 | −0.788226 | −0.394113 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394113 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(992\) | 3.58538e36 | 0.125354 | ||||||||
\(993\) | −1.56028e37 | −0.538688 | ||||||||
\(994\) | 4.05182e36 | 0.138140 | ||||||||
\(995\) | 4.53903e36 | 0.152818 | ||||||||
\(996\) | −1.16008e37 | −0.385697 | ||||||||
\(997\) | −7.44693e36 | −0.244505 | −0.122253 | − | 0.992499i | \(-0.539012\pi\) | ||||
−0.122253 | + | 0.992499i | \(0.539012\pi\) | |||||||
\(998\) | −1.38707e37 | −0.449745 | ||||||||
\(999\) | 3.68905e37 | 1.18126 |
(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 | 10.26.a.d.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.26.b.d.49.3 | 4 | |||
5.3 | odd | 4 | 50.26.b.d.49.2 | 4 | |||
5.4 | even | 2 | 50.26.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.26.a.d.1.1 | 2 | 5.4 | even | 2 | |||
50.26.b.d.49.2 | 4 | 5.3 | odd | 4 | |||
50.26.b.d.49.3 | 4 | 5.2 | odd | 4 |