Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, 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("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(197.998389976\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 25534923283x^{3} - 31863478542482x^{2} + 141941149085067124800x + 2515032055818200956928000 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{5}\cdot 5^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-18822.3\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 | ||||||||
\(3\) | 43423.8 | 0.0471750 | 0.0235875 | − | 0.999722i | \(-0.492491\pi\) | ||||
0.0235875 | + | 0.999722i | \(0.492491\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.77864e8 | −0.0333578 | ||||||||
\(7\) | 1.17021e10 | 0.319549 | 0.159774 | − | 0.987154i | \(-0.448923\pi\) | ||||
0.159774 | + | 0.987154i | \(0.448923\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | −8.45403e11 | −0.997775 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64780e13 | 1.58305 | 0.791525 | − | 0.611137i | \(-0.209287\pi\) | ||||
0.791525 | + | 0.611137i | \(0.209287\pi\) | |||||||
\(12\) | 7.28531e11 | 0.0235875 | ||||||||
\(13\) | −1.00150e14 | −1.19222 | −0.596112 | − | 0.802901i | \(-0.703289\pi\) | ||||
−0.596112 | + | 0.802901i | \(0.703289\pi\) | |||||||
\(14\) | −4.79317e13 | −0.225955 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −4.09920e15 | −1.70643 | −0.853214 | − | 0.521561i | \(-0.825350\pi\) | ||||
−0.853214 | + | 0.521561i | \(0.825350\pi\) | |||||||
\(18\) | 3.46277e15 | 0.705533 | ||||||||
\(19\) | 6.47386e15 | 0.671032 | 0.335516 | − | 0.942035i | \(-0.391089\pi\) | ||||
0.335516 | + | 0.942035i | \(0.391089\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.08149e14 | 0.0150747 | ||||||||
\(22\) | −6.74937e16 | −1.11939 | ||||||||
\(23\) | 1.11414e17 | 1.06009 | 0.530043 | − | 0.847971i | \(-0.322176\pi\) | ||||
0.530043 | + | 0.847971i | \(0.322176\pi\) | |||||||
\(24\) | −2.98406e15 | −0.0166789 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.10213e17 | 0.843030 | ||||||||
\(27\) | −7.35031e16 | −0.0942451 | ||||||||
\(28\) | 1.96328e17 | 0.159774 | ||||||||
\(29\) | −2.49627e18 | −1.31014 | −0.655070 | − | 0.755569i | \(-0.727361\pi\) | ||||
−0.655070 | + | 0.755569i | \(0.727361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.13708e18 | −1.62742 | −0.813710 | − | 0.581271i | \(-0.802556\pi\) | ||||
−0.813710 | + | 0.581271i | \(0.802556\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 7.15536e17 | 0.0746805 | ||||||||
\(34\) | 1.67903e19 | 1.20663 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.41835e19 | −0.498887 | ||||||||
\(37\) | 1.51372e19 | 0.378027 | 0.189013 | − | 0.981974i | \(-0.439471\pi\) | ||||
0.189013 | + | 0.981974i | \(0.439471\pi\) | |||||||
\(38\) | −2.65169e19 | −0.474491 | ||||||||
\(39\) | −4.34889e18 | −0.0562432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.55381e20 | 1.76762 | 0.883811 | − | 0.467843i | \(-0.154969\pi\) | ||||
0.883811 | + | 0.467843i | \(0.154969\pi\) | |||||||
\(42\) | −2.08138e18 | −0.0106594 | ||||||||
\(43\) | 1.31517e20 | 0.501911 | 0.250955 | − | 0.967999i | \(-0.419255\pi\) | ||||
0.250955 | + | 0.967999i | \(0.419255\pi\) | |||||||
\(44\) | 2.76454e20 | 0.791525 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.56351e20 | −0.749594 | ||||||||
\(47\) | 5.62025e20 | 0.705557 | 0.352778 | − | 0.935707i | \(-0.385237\pi\) | ||||
0.352778 | + | 0.935707i | \(0.385237\pi\) | |||||||
\(48\) | 1.22227e19 | 0.0117938 | ||||||||
\(49\) | −1.20413e21 | −0.897889 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.78003e20 | −0.0805008 | ||||||||
\(52\) | −1.68023e21 | −0.596112 | ||||||||
\(53\) | −5.11971e21 | −1.43152 | −0.715759 | − | 0.698348i | \(-0.753919\pi\) | ||||
−0.715759 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(54\) | 3.01069e20 | 0.0666413 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.04160e20 | −0.112978 | ||||||||
\(57\) | 2.81120e20 | 0.0316560 | ||||||||
\(58\) | 1.02247e22 | 0.926408 | ||||||||
\(59\) | 1.95274e22 | 1.42888 | 0.714438 | − | 0.699699i | \(-0.246682\pi\) | ||||
0.714438 | + | 0.699699i | \(0.246682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40784e22 | 1.16146 | 0.580731 | − | 0.814096i | \(-0.302767\pi\) | ||||
0.580731 | + | 0.814096i | \(0.302767\pi\) | |||||||
\(62\) | 2.92335e22 | 1.15076 | ||||||||
\(63\) | −9.89297e21 | −0.318838 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.93083e21 | −0.0528071 | ||||||||
\(67\) | −3.73512e22 | −0.557660 | −0.278830 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278830 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(68\) | −6.87732e22 | −0.853214 | ||||||||
\(69\) | 4.83801e21 | 0.0500096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.22452e23 | −0.885601 | −0.442800 | − | 0.896620i | \(-0.646015\pi\) | ||||
−0.442800 | + | 0.896620i | \(0.646015\pi\) | |||||||
\(72\) | 5.80957e22 | 0.352767 | ||||||||
\(73\) | 1.02009e23 | 0.521316 | 0.260658 | − | 0.965431i | \(-0.416060\pi\) | ||||
0.260658 | + | 0.965431i | \(0.416060\pi\) | |||||||
\(74\) | −6.20018e22 | −0.267305 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.08613e23 | 0.335516 | ||||||||
\(77\) | 1.92826e23 | 0.505862 | ||||||||
\(78\) | 1.78130e22 | 0.0397700 | ||||||||
\(79\) | −3.06262e23 | −0.583115 | −0.291558 | − | 0.956553i | \(-0.594173\pi\) | ||||
−0.291558 | + | 0.956553i | \(0.594173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.13109e23 | 0.993328 | ||||||||
\(82\) | −1.04604e24 | −1.24990 | ||||||||
\(83\) | −1.24177e23 | −0.127516 | −0.0637581 | − | 0.997965i | \(-0.520309\pi\) | ||||
−0.0637581 | + | 0.997965i | \(0.520309\pi\) | |||||||
\(84\) | 8.52532e21 | 0.00753736 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.38694e23 | −0.354905 | ||||||||
\(87\) | −1.08398e23 | −0.0618059 | ||||||||
\(88\) | −1.13236e24 | −0.559693 | ||||||||
\(89\) | 6.70415e23 | 0.287719 | 0.143859 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143859 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17196e24 | −0.380974 | ||||||||
\(92\) | 1.86921e24 | 0.530043 | ||||||||
\(93\) | −3.09919e23 | −0.0767736 | ||||||||
\(94\) | −2.30205e24 | −0.498904 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.00642e22 | −0.00833945 | ||||||||
\(97\) | −2.48231e24 | −0.363253 | −0.181626 | − | 0.983368i | \(-0.558136\pi\) | ||||
−0.181626 | + | 0.983368i | \(0.558136\pi\) | |||||||
\(98\) | 4.93212e24 | 0.634903 | ||||||||
\(99\) | −1.39305e25 | −1.57953 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.99639e24 | 0.529508 | 0.264754 | − | 0.964316i | \(-0.414709\pi\) | ||||
0.264754 | + | 0.964316i | \(0.414709\pi\) | |||||||
\(102\) | 7.29100e23 | 0.0569227 | ||||||||
\(103\) | −1.43755e25 | −0.993474 | −0.496737 | − | 0.867901i | \(-0.665469\pi\) | ||||
−0.496737 | + | 0.867901i | \(0.665469\pi\) | |||||||
\(104\) | 6.88224e24 | 0.421515 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.09703e25 | 1.01224 | ||||||||
\(107\) | −2.52288e25 | −1.08293 | −0.541463 | − | 0.840725i | \(-0.682129\pi\) | ||||
−0.541463 | + | 0.840725i | \(0.682129\pi\) | |||||||
\(108\) | −1.23318e24 | −0.0471225 | ||||||||
\(109\) | 1.90602e25 | 0.649078 | 0.324539 | − | 0.945872i | \(-0.394791\pi\) | ||||
0.324539 | + | 0.945872i | \(0.394791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.57313e23 | 0.0178334 | ||||||||
\(112\) | 3.29384e24 | 0.0798872 | ||||||||
\(113\) | −7.00404e25 | −1.52009 | −0.760043 | − | 0.649873i | \(-0.774822\pi\) | ||||
−0.760043 | + | 0.649873i | \(0.774822\pi\) | |||||||
\(114\) | −1.15147e24 | −0.0223841 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.18805e25 | −0.655070 | ||||||||
\(117\) | 8.46669e25 | 1.18957 | ||||||||
\(118\) | −7.99843e25 | −1.01037 | ||||||||
\(119\) | −4.79692e25 | −0.545287 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.63176e26 | 1.50605 | ||||||||
\(122\) | −9.86252e25 | −0.821277 | ||||||||
\(123\) | 1.10896e25 | 0.0833877 | ||||||||
\(124\) | −1.19740e26 | −0.813710 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.05216e25 | 0.225452 | ||||||||
\(127\) | −1.37993e26 | −0.695519 | −0.347759 | − | 0.937584i | \(-0.613057\pi\) | ||||
−0.347759 | + | 0.937584i | \(0.613057\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 5.71097e24 | 0.0236777 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.92280e25 | −0.202598 | −0.101299 | − | 0.994856i | \(-0.532300\pi\) | ||||
−0.101299 | + | 0.994856i | \(0.532300\pi\) | |||||||
\(132\) | 1.20047e25 | 0.0373402 | ||||||||
\(133\) | 7.57576e25 | 0.214427 | ||||||||
\(134\) | 1.52991e26 | 0.394325 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.81695e26 | 0.603313 | ||||||||
\(137\) | −4.40818e26 | −0.861494 | −0.430747 | − | 0.902473i | \(-0.641750\pi\) | ||||
−0.430747 | + | 0.902473i | \(0.641750\pi\) | |||||||
\(138\) | −1.98165e25 | −0.0353621 | ||||||||
\(139\) | −8.03278e26 | −1.30973 | −0.654863 | − | 0.755747i | \(-0.727274\pi\) | ||||
−0.654863 | + | 0.755747i | \(0.727274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.44053e25 | 0.0332847 | ||||||||
\(142\) | 5.01565e26 | 0.626214 | ||||||||
\(143\) | −1.65026e27 | −1.88735 | ||||||||
\(144\) | −2.37960e26 | −0.249444 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.17828e26 | −0.368626 | ||||||||
\(147\) | −5.22879e25 | −0.0423579 | ||||||||
\(148\) | 2.53959e26 | 0.189013 | ||||||||
\(149\) | 1.20493e27 | 0.824393 | 0.412197 | − | 0.911095i | \(-0.364762\pi\) | ||||
0.412197 | + | 0.911095i | \(0.364762\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.12194e27 | 0.649767 | 0.324884 | − | 0.945754i | \(-0.394675\pi\) | ||||
0.324884 | + | 0.945754i | \(0.394675\pi\) | |||||||
\(152\) | −4.44880e26 | −0.237246 | ||||||||
\(153\) | 3.46548e27 | 1.70263 | ||||||||
\(154\) | −7.89816e26 | −0.357698 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.29622e25 | −0.0281216 | ||||||||
\(157\) | −7.34635e26 | −0.261412 | −0.130706 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130706 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(158\) | 1.25445e27 | 0.412325 | ||||||||
\(159\) | −2.22317e26 | −0.0675319 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.30377e27 | 0.338749 | ||||||||
\(162\) | −2.92089e27 | −0.702389 | ||||||||
\(163\) | −3.30397e27 | −0.735683 | −0.367841 | − | 0.929889i | \(-0.619903\pi\) | ||||
−0.367841 | + | 0.929889i | \(0.619903\pi\) | |||||||
\(164\) | 4.28457e27 | 0.883811 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.08629e26 | 0.0901676 | ||||||||
\(167\) | 8.04476e27 | 1.32299 | 0.661496 | − | 0.749949i | \(-0.269922\pi\) | ||||
0.661496 | + | 0.749949i | \(0.269922\pi\) | |||||||
\(168\) | −3.49197e25 | −0.00532972 | ||||||||
\(169\) | 2.97357e27 | 0.421399 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.47302e27 | −0.669539 | ||||||||
\(172\) | 2.20649e27 | 0.250955 | ||||||||
\(173\) | 1.78239e28 | 1.88550 | 0.942749 | − | 0.333504i | \(-0.108231\pi\) | ||||
0.942749 | + | 0.333504i | \(0.108231\pi\) | |||||||
\(174\) | 4.43997e26 | 0.0437033 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.63813e27 | 0.395763 | ||||||||
\(177\) | 8.47955e26 | 0.0674073 | ||||||||
\(178\) | −2.74602e27 | −0.203448 | ||||||||
\(179\) | 2.18421e28 | 1.50880 | 0.754399 | − | 0.656416i | \(-0.227928\pi\) | ||||
0.754399 | + | 0.656416i | \(0.227928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.17113e27 | 0.190648 | 0.0953238 | − | 0.995446i | \(-0.469611\pi\) | ||||
0.0953238 | + | 0.995446i | \(0.469611\pi\) | |||||||
\(182\) | 4.80035e27 | 0.269389 | ||||||||
\(183\) | 1.04558e27 | 0.0547920 | ||||||||
\(184\) | −7.65630e27 | −0.374797 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.26943e27 | 0.0542871 | ||||||||
\(187\) | −6.75465e28 | −2.70136 | ||||||||
\(188\) | 9.42921e27 | 0.352778 | ||||||||
\(189\) | −8.60139e26 | −0.0301159 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.72320e28 | 1.14288 | 0.571439 | − | 0.820645i | \(-0.306385\pi\) | ||||
0.571439 | + | 0.820645i | \(0.306385\pi\) | |||||||
\(192\) | 2.05063e26 | 0.00589688 | ||||||||
\(193\) | 5.76046e28 | 1.55235 | 0.776176 | − | 0.630516i | \(-0.217157\pi\) | ||||
0.776176 | + | 0.630516i | \(0.217157\pi\) | |||||||
\(194\) | 1.01675e28 | 0.256859 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.02020e28 | −0.448944 | ||||||||
\(197\) | 7.70781e28 | 1.60732 | 0.803662 | − | 0.595086i | \(-0.202882\pi\) | ||||
0.803662 | + | 0.595086i | \(0.202882\pi\) | |||||||
\(198\) | 5.70594e28 | 1.11689 | ||||||||
\(199\) | −3.56814e28 | −0.655811 | −0.327906 | − | 0.944711i | \(-0.606343\pi\) | ||||
−0.327906 | + | 0.944711i | \(0.606343\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.62193e27 | −0.0263076 | ||||||||
\(202\) | −2.45612e28 | −0.374419 | ||||||||
\(203\) | −2.92116e28 | −0.418653 | ||||||||
\(204\) | −2.98640e27 | −0.0402504 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.88819e28 | 0.702492 | ||||||||
\(207\) | −9.41896e28 | −1.05773 | ||||||||
\(208\) | −2.81897e28 | −0.298056 | ||||||||
\(209\) | 1.06676e29 | 1.06228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.75441e29 | 1.55096 | 0.775480 | − | 0.631373i | \(-0.217508\pi\) | ||||
0.775480 | + | 0.631373i | \(0.217508\pi\) | |||||||
\(212\) | −8.58944e28 | −0.715759 | ||||||||
\(213\) | −5.31735e27 | −0.0417783 | ||||||||
\(214\) | 1.03337e29 | 0.765744 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.05110e27 | 0.0333207 | ||||||||
\(217\) | −8.35187e28 | −0.520040 | ||||||||
\(218\) | −7.80707e28 | −0.458968 | ||||||||
\(219\) | 4.42961e27 | 0.0245931 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.10534e29 | 2.03445 | ||||||||
\(222\) | −2.69235e27 | −0.0126101 | ||||||||
\(223\) | 3.77614e29 | 1.67200 | 0.836001 | − | 0.548728i | \(-0.184888\pi\) | ||||
0.836001 | + | 0.548728i | \(0.184888\pi\) | |||||||
\(224\) | −1.34916e28 | −0.0564888 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.86886e29 | 1.07486 | ||||||||
\(227\) | −4.12672e29 | −1.46312 | −0.731562 | − | 0.681774i | \(-0.761209\pi\) | ||||
−0.731562 | + | 0.681774i | \(0.761209\pi\) | |||||||
\(228\) | 4.71641e27 | 0.0158280 | ||||||||
\(229\) | −1.29184e29 | −0.410454 | −0.205227 | − | 0.978714i | \(-0.565793\pi\) | ||||
−0.205227 | + | 0.978714i | \(0.565793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.37325e27 | 0.0238641 | ||||||||
\(232\) | 1.71543e29 | 0.463204 | ||||||||
\(233\) | −4.29301e29 | −1.09853 | −0.549266 | − | 0.835648i | \(-0.685093\pi\) | ||||
−0.549266 | + | 0.835648i | \(0.685093\pi\) | |||||||
\(234\) | −3.46796e29 | −0.841154 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.27616e29 | 0.714438 | ||||||||
\(237\) | −1.32991e28 | −0.0275085 | ||||||||
\(238\) | 1.96482e29 | 0.385576 | ||||||||
\(239\) | 6.70528e29 | 1.24866 | 0.624329 | − | 0.781162i | \(-0.285373\pi\) | ||||
0.624329 | + | 0.781162i | \(0.285373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.94387e29 | 1.50076 | 0.750382 | − | 0.661004i | \(-0.229870\pi\) | ||||
0.750382 | + | 0.661004i | \(0.229870\pi\) | |||||||
\(242\) | −6.68368e29 | −1.06494 | ||||||||
\(243\) | 9.32443e28 | 0.141105 | ||||||||
\(244\) | 4.03969e29 | 0.580731 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.54230e28 | −0.0589640 | ||||||||
\(247\) | −6.48356e29 | −0.800021 | ||||||||
\(248\) | 4.90457e29 | 0.575380 | ||||||||
\(249\) | −5.39224e27 | −0.00601558 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.46535e30 | 1.47917 | 0.739587 | − | 0.673061i | \(-0.235021\pi\) | ||||
0.739587 | + | 0.673061i | \(0.235021\pi\) | |||||||
\(252\) | −1.65976e29 | −0.159419 | ||||||||
\(253\) | 1.83587e30 | 1.67817 | ||||||||
\(254\) | 5.65217e29 | 0.491806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −1.69807e30 | −1.27582 | −0.637912 | − | 0.770110i | \(-0.720201\pi\) | ||||
−0.637912 | + | 0.770110i | \(0.720201\pi\) | |||||||
\(258\) | −2.33922e28 | −0.0167426 | ||||||||
\(259\) | 1.77136e29 | 0.120798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.11036e30 | 1.30722 | ||||||||
\(262\) | 2.42598e29 | 0.143259 | ||||||||
\(263\) | 2.11180e30 | 1.18907 | 0.594534 | − | 0.804070i | \(-0.297336\pi\) | ||||
0.594534 | + | 0.804070i | \(0.297336\pi\) | |||||||
\(264\) | −4.91712e28 | −0.0264035 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.10303e29 | −0.151623 | ||||||||
\(267\) | 2.91120e28 | 0.0135731 | ||||||||
\(268\) | −6.26649e29 | −0.278830 | ||||||||
\(269\) | −1.68743e30 | −0.716676 | −0.358338 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358338 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00044e30 | −0.387324 | −0.193662 | − | 0.981068i | \(-0.562036\pi\) | ||||
−0.193662 | + | 0.981068i | \(0.562036\pi\) | |||||||
\(272\) | −1.15382e30 | −0.426607 | ||||||||
\(273\) | −5.08910e28 | −0.0179725 | ||||||||
\(274\) | 1.80559e30 | 0.609168 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.11684e28 | 0.0250048 | ||||||||
\(277\) | −7.83715e29 | −0.230760 | −0.115380 | − | 0.993321i | \(-0.536809\pi\) | ||||
−0.115380 | + | 0.993321i | \(0.536809\pi\) | |||||||
\(278\) | 3.29023e30 | 0.926117 | ||||||||
\(279\) | 6.03371e30 | 1.62380 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80627e30 | 0.444584 | 0.222292 | − | 0.974980i | \(-0.428646\pi\) | ||||
0.222292 | + | 0.974980i | \(0.428646\pi\) | |||||||
\(282\) | −9.99639e28 | −0.0235358 | ||||||||
\(283\) | 4.85439e30 | 1.09346 | 0.546732 | − | 0.837308i | \(-0.315872\pi\) | ||||
0.546732 | + | 0.837308i | \(0.315872\pi\) | |||||||
\(284\) | −2.05441e30 | −0.442800 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.75948e30 | 1.33456 | ||||||||
\(287\) | 2.98848e30 | 0.564842 | ||||||||
\(288\) | 9.74683e29 | 0.176383 | ||||||||
\(289\) | 1.10328e31 | 1.91190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07791e29 | −0.0171365 | ||||||||
\(292\) | 1.71142e30 | 0.260658 | ||||||||
\(293\) | 1.46069e30 | 0.213163 | 0.106582 | − | 0.994304i | \(-0.466009\pi\) | ||||
0.106582 | + | 0.994304i | \(0.466009\pi\) | |||||||
\(294\) | 2.14171e29 | 0.0299516 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.04022e30 | −0.133653 | ||||||||
\(297\) | −1.21118e30 | −0.149195 | ||||||||
\(298\) | −4.93541e30 | −0.582934 | ||||||||
\(299\) | −1.11581e31 | −1.26386 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53902e30 | 0.160385 | ||||||||
\(302\) | −4.59547e30 | −0.459455 | ||||||||
\(303\) | 2.60386e29 | 0.0249796 | ||||||||
\(304\) | 1.82223e30 | 0.167758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.41946e31 | −1.20394 | ||||||||
\(307\) | 1.83807e30 | 0.149669 | 0.0748345 | − | 0.997196i | \(-0.476157\pi\) | ||||
0.0748345 | + | 0.997196i | \(0.476157\pi\) | |||||||
\(308\) | 3.23509e30 | 0.252931 | ||||||||
\(309\) | −6.24238e29 | −0.0468672 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.33152e30 | −0.230748 | −0.115374 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115374 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(312\) | 2.98853e29 | 0.0198850 | ||||||||
\(313\) | −3.48183e30 | −0.222589 | −0.111294 | − | 0.993787i | \(-0.535500\pi\) | ||||
−0.111294 | + | 0.993787i | \(0.535500\pi\) | |||||||
\(314\) | 3.00907e30 | 0.184846 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.13822e30 | −0.291558 | ||||||||
\(317\) | 3.11024e30 | 0.169650 | 0.0848249 | − | 0.996396i | \(-0.472967\pi\) | ||||
0.0848249 | + | 0.996396i | \(0.472967\pi\) | |||||||
\(318\) | 9.10611e29 | 0.0477523 | ||||||||
\(319\) | −4.11335e31 | −2.07402 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.09553e30 | −0.0510871 | ||||||||
\(322\) | −5.34025e30 | −0.239532 | ||||||||
\(323\) | −2.65377e31 | −1.14507 | ||||||||
\(324\) | 1.19640e31 | 0.496664 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.35330e31 | 0.520206 | ||||||||
\(327\) | 8.27668e29 | 0.0306203 | ||||||||
\(328\) | −1.75496e31 | −0.624949 | ||||||||
\(329\) | 6.57685e30 | 0.225460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.69668e31 | 0.856998 | 0.428499 | − | 0.903542i | \(-0.359043\pi\) | ||||
0.428499 | + | 0.903542i | \(0.359043\pi\) | |||||||
\(332\) | −2.08335e30 | −0.0637581 | ||||||||
\(333\) | −1.27970e31 | −0.377186 | ||||||||
\(334\) | −3.29513e31 | −0.935497 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.43031e29 | 0.00376868 | ||||||||
\(337\) | 4.07016e31 | 1.03333 | 0.516664 | − | 0.856188i | \(-0.327174\pi\) | ||||
0.516664 | + | 0.856188i | \(0.327174\pi\) | |||||||
\(338\) | −1.21797e31 | −0.297974 | ||||||||
\(339\) | −3.04142e30 | −0.0717101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17605e32 | −2.57629 | ||||||||
\(342\) | 2.24175e31 | 0.473435 | ||||||||
\(343\) | −2.97841e31 | −0.606468 | ||||||||
\(344\) | −9.03779e30 | −0.177452 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.30066e31 | −1.33325 | ||||||||
\(347\) | 1.58471e31 | 0.279145 | 0.139573 | − | 0.990212i | \(-0.455427\pi\) | ||||
0.139573 | + | 0.990212i | \(0.455427\pi\) | |||||||
\(348\) | −1.81861e30 | −0.0309029 | ||||||||
\(349\) | −2.28191e30 | −0.0374094 | −0.0187047 | − | 0.999825i | \(-0.505954\pi\) | ||||
−0.0187047 | + | 0.999825i | \(0.505954\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.36132e30 | 0.112361 | ||||||||
\(352\) | −1.89978e31 | −0.279846 | ||||||||
\(353\) | −8.46470e31 | −1.20345 | −0.601725 | − | 0.798704i | \(-0.705520\pi\) | ||||
−0.601725 | + | 0.798704i | \(0.705520\pi\) | |||||||
\(354\) | −3.47322e30 | −0.0476642 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.12477e31 | 0.143859 | ||||||||
\(357\) | −2.08300e30 | −0.0257239 | ||||||||
\(358\) | −8.94652e31 | −1.06688 | ||||||||
\(359\) | −2.47468e31 | −0.284996 | −0.142498 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142498 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.11656e31 | −0.549716 | ||||||||
\(362\) | −1.29889e31 | −0.134808 | ||||||||
\(363\) | 7.08572e30 | 0.0710479 | ||||||||
\(364\) | −1.96622e31 | −0.190487 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.28268e30 | −0.0387438 | ||||||||
\(367\) | 2.15791e32 | 1.88672 | 0.943359 | − | 0.331773i | \(-0.107647\pi\) | ||||
0.943359 | + | 0.331773i | \(0.107647\pi\) | |||||||
\(368\) | 3.13602e31 | 0.265022 | ||||||||
\(369\) | −2.15899e32 | −1.76369 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.99112e31 | −0.457440 | ||||||||
\(372\) | −5.19958e30 | −0.0383868 | ||||||||
\(373\) | 1.43569e32 | 1.02494 | 0.512471 | − | 0.858705i | \(-0.328730\pi\) | ||||
0.512471 | + | 0.858705i | \(0.328730\pi\) | |||||||
\(374\) | 2.76670e32 | 1.91015 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.86220e31 | −0.249452 | ||||||||
\(377\) | 2.50001e32 | 1.56198 | ||||||||
\(378\) | 3.52313e30 | 0.0212952 | ||||||||
\(379\) | 1.53691e32 | 0.898791 | 0.449396 | − | 0.893333i | \(-0.351639\pi\) | ||||
0.449396 | + | 0.893333i | \(0.351639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.99216e30 | −0.0328111 | ||||||||
\(382\) | −1.52502e32 | −0.808137 | ||||||||
\(383\) | −2.05714e32 | −1.05506 | −0.527532 | − | 0.849535i | \(-0.676882\pi\) | ||||
−0.527532 | + | 0.849535i | \(0.676882\pi\) | |||||||
\(384\) | −8.39939e29 | −0.00416972 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.35948e32 | −1.09768 | ||||||||
\(387\) | −1.11185e32 | −0.500794 | ||||||||
\(388\) | −4.16462e31 | −0.181626 | ||||||||
\(389\) | −1.97058e32 | −0.832192 | −0.416096 | − | 0.909321i | \(-0.636602\pi\) | ||||
−0.416096 | + | 0.909321i | \(0.636602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.56708e32 | −1.80896 | ||||||||
\(392\) | 8.27472e31 | 0.317452 | ||||||||
\(393\) | −2.57191e30 | −0.00955759 | ||||||||
\(394\) | −3.15712e32 | −1.13655 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.33715e32 | −0.789764 | ||||||||
\(397\) | 2.04618e31 | 0.0669980 | 0.0334990 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334990 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(398\) | 1.46151e32 | 0.463728 | ||||||||
\(399\) | 3.28968e30 | 0.0101156 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.79432e32 | 1.38491 | 0.692456 | − | 0.721460i | \(-0.256529\pi\) | ||||
0.692456 | + | 0.721460i | \(0.256529\pi\) | |||||||
\(402\) | 6.64343e30 | 0.0186023 | ||||||||
\(403\) | 7.14777e32 | 1.94025 | ||||||||
\(404\) | 1.00603e32 | 0.264754 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.19651e32 | 0.296033 | ||||||||
\(407\) | 2.49429e32 | 0.598436 | ||||||||
\(408\) | 1.22323e31 | 0.0284613 | ||||||||
\(409\) | 2.61432e32 | 0.589952 | 0.294976 | − | 0.955505i | \(-0.404688\pi\) | ||||
0.294976 | + | 0.955505i | \(0.404688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.91420e31 | −0.0406410 | ||||||||
\(412\) | −2.41180e32 | −0.496737 | ||||||||
\(413\) | 2.28511e32 | 0.456596 | ||||||||
\(414\) | 3.85801e32 | 0.747926 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.15465e32 | 0.210758 | ||||||||
\(417\) | −3.48814e31 | −0.0617864 | ||||||||
\(418\) | −4.36945e32 | −0.751144 | ||||||||
\(419\) | −2.37687e32 | −0.396579 | −0.198290 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198290 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.17539e32 | 1.12803 | 0.564013 | − | 0.825766i | \(-0.309257\pi\) | ||||
0.564013 | + | 0.825766i | \(0.309257\pi\) | |||||||
\(422\) | −7.18606e32 | −1.09669 | ||||||||
\(423\) | −4.75137e32 | −0.703987 | ||||||||
\(424\) | 3.51824e32 | 0.506118 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.17799e31 | 0.0295417 | ||||||||
\(427\) | 2.81767e32 | 0.371144 | ||||||||
\(428\) | −4.23269e32 | −0.541463 | ||||||||
\(429\) | −7.16607e31 | −0.0890359 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.94839e32 | 0.580094 | 0.290047 | − | 0.957012i | \(-0.406329\pi\) | ||||
0.290047 | + | 0.957012i | \(0.406329\pi\) | |||||||
\(432\) | −2.06893e31 | −0.0235613 | ||||||||
\(433\) | −1.87459e32 | −0.207399 | −0.103700 | − | 0.994609i | \(-0.533068\pi\) | ||||
−0.103700 | + | 0.994609i | \(0.533068\pi\) | |||||||
\(434\) | 3.42092e32 | 0.367724 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.19778e32 | 0.324539 | ||||||||
\(437\) | 7.21278e32 | 0.711352 | ||||||||
\(438\) | −1.81437e31 | −0.0173900 | ||||||||
\(439\) | −2.54653e32 | −0.237215 | −0.118607 | − | 0.992941i | \(-0.537843\pi\) | ||||
−0.118607 | + | 0.992941i | \(0.537843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.01798e33 | 0.895890 | ||||||||
\(442\) | −1.68155e33 | −1.43857 | ||||||||
\(443\) | 1.63920e33 | 1.36328 | 0.681642 | − | 0.731685i | \(-0.261266\pi\) | ||||
0.681642 | + | 0.731685i | \(0.261266\pi\) | |||||||
\(444\) | 1.10279e31 | 0.00891672 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.54671e33 | −1.18228 | ||||||||
\(447\) | 5.23228e31 | 0.0388908 | ||||||||
\(448\) | 5.52615e31 | 0.0399436 | ||||||||
\(449\) | −1.07131e33 | −0.753068 | −0.376534 | − | 0.926403i | \(-0.622884\pi\) | ||||
−0.376534 | + | 0.926403i | \(0.622884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.20815e33 | 2.79824 | ||||||||
\(452\) | −1.17508e33 | −0.760043 | ||||||||
\(453\) | 4.87189e31 | 0.0306528 | ||||||||
\(454\) | 1.69030e33 | 1.03459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.93184e31 | −0.0111921 | ||||||||
\(457\) | −1.92628e33 | −1.08584 | −0.542921 | − | 0.839784i | \(-0.682682\pi\) | ||||
−0.542921 | + | 0.839784i | \(0.682682\pi\) | |||||||
\(458\) | 5.29137e32 | 0.290235 | ||||||||
\(459\) | 3.01304e32 | 0.160822 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.76482e33 | 0.892152 | 0.446076 | − | 0.894995i | \(-0.352821\pi\) | ||||
0.446076 | + | 0.894995i | \(0.352821\pi\) | |||||||
\(462\) | −3.42968e31 | −0.0168744 | ||||||||
\(463\) | −6.39982e32 | −0.306482 | −0.153241 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153241 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(464\) | −7.02639e32 | −0.327535 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.75842e33 | 0.776779 | ||||||||
\(467\) | −1.87926e33 | −0.808213 | −0.404106 | − | 0.914712i | \(-0.632417\pi\) | ||||
−0.404106 | + | 0.914712i | \(0.632417\pi\) | |||||||
\(468\) | 1.42048e33 | 0.594786 | ||||||||
\(469\) | −4.37087e32 | −0.178200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.19007e31 | −0.0123321 | ||||||||
\(472\) | −1.34191e33 | −0.505184 | ||||||||
\(473\) | 2.16713e33 | 0.794550 | ||||||||
\(474\) | 5.44729e31 | 0.0194514 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.04789e32 | −0.272643 | ||||||||
\(477\) | 4.32821e33 | 1.42833 | ||||||||
\(478\) | −2.74648e33 | −0.882934 | ||||||||
\(479\) | −4.49267e32 | −0.140705 | −0.0703527 | − | 0.997522i | \(-0.522412\pi\) | ||||
−0.0703527 | + | 0.997522i | \(0.522412\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.51598e33 | −0.450693 | ||||||||
\(482\) | −3.66341e33 | −1.06120 | ||||||||
\(483\) | 5.66148e31 | 0.0159805 | ||||||||
\(484\) | 2.73764e33 | 0.753024 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.81928e32 | −0.0997766 | ||||||||
\(487\) | 4.38487e33 | 1.11646 | 0.558232 | − | 0.829685i | \(-0.311480\pi\) | ||||
0.558232 | + | 0.829685i | \(0.311480\pi\) | |||||||
\(488\) | −1.65466e33 | −0.410639 | ||||||||
\(489\) | −1.43471e32 | −0.0347059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.31613e33 | 1.91162 | 0.955812 | − | 0.293978i | \(-0.0949794\pi\) | ||||
0.955812 | + | 0.293978i | \(0.0949794\pi\) | |||||||
\(492\) | 1.86053e32 | 0.0416938 | ||||||||
\(493\) | 1.02327e34 | 2.23566 | ||||||||
\(494\) | 2.65566e33 | 0.565700 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00891e33 | −0.406855 | ||||||||
\(497\) | −1.43295e33 | −0.282993 | ||||||||
\(498\) | 2.20866e31 | 0.00425366 | ||||||||
\(499\) | −5.09164e33 | −0.956315 | −0.478158 | − | 0.878274i | \(-0.658695\pi\) | ||||
−0.478158 | + | 0.878274i | \(0.658695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.49334e32 | 0.0624122 | ||||||||
\(502\) | −6.00207e33 | −1.04593 | ||||||||
\(503\) | 1.81699e33 | 0.308853 | 0.154427 | − | 0.988004i | \(-0.450647\pi\) | ||||
0.154427 | + | 0.988004i | \(0.450647\pi\) | |||||||
\(504\) | 6.79839e32 | 0.112726 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.51973e33 | −1.18665 | ||||||||
\(507\) | 1.29124e32 | 0.0198795 | ||||||||
\(508\) | −2.31513e33 | −0.347759 | ||||||||
\(509\) | 5.80999e33 | 0.851537 | 0.425768 | − | 0.904832i | \(-0.360004\pi\) | ||||
0.425768 | + | 0.904832i | \(0.360004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19371e33 | 0.166586 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | −4.75849e32 | −0.0632415 | ||||||||
\(514\) | 6.95528e33 | 0.902143 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.58143e31 | 0.0118388 | ||||||||
\(517\) | 9.26101e33 | 1.11693 | ||||||||
\(518\) | −7.25549e32 | −0.0854171 | ||||||||
\(519\) | 7.73981e32 | 0.0889484 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.31585e33 | −0.582238 | −0.291119 | − | 0.956687i | \(-0.594028\pi\) | ||||
−0.291119 | + | 0.956687i | \(0.594028\pi\) | |||||||
\(522\) | −8.64403e33 | −0.924347 | ||||||||
\(523\) | 6.52606e33 | 0.681365 | 0.340682 | − | 0.940178i | \(-0.389342\pi\) | ||||
0.340682 | + | 0.940178i | \(0.389342\pi\) | |||||||
\(524\) | −9.93681e32 | −0.101299 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.64995e33 | −0.840798 | ||||||||
\(527\) | 2.92564e34 | 2.77707 | ||||||||
\(528\) | 2.01405e32 | 0.0186701 | ||||||||
\(529\) | 1.36728e33 | 0.123783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.65085e34 | −1.42570 | ||||||||
\(532\) | 1.27100e33 | 0.107214 | ||||||||
\(533\) | −2.55763e34 | −2.10740 | ||||||||
\(534\) | −1.19243e32 | −0.00959767 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.56676e33 | 0.197163 | ||||||||
\(537\) | 9.48467e32 | 0.0711776 | ||||||||
\(538\) | 6.91172e33 | 0.506766 | ||||||||
\(539\) | −1.98416e34 | −1.42140 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.24335e34 | 0.850410 | 0.425205 | − | 0.905097i | \(-0.360202\pi\) | ||||
0.425205 | + | 0.905097i | \(0.360202\pi\) | |||||||
\(542\) | 4.09779e33 | 0.273879 | ||||||||
\(543\) | 1.37702e32 | 0.00899381 | ||||||||
\(544\) | 4.72606e33 | 0.301657 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.08449e32 | 0.0127084 | ||||||||
\(547\) | −1.77086e34 | −1.05522 | −0.527610 | − | 0.849487i | \(-0.676912\pi\) | ||||
−0.527610 | + | 0.849487i | \(0.676912\pi\) | |||||||
\(548\) | −7.39570e33 | −0.430747 | ||||||||
\(549\) | −2.03560e34 | −1.15888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.61605e34 | −0.879145 | ||||||||
\(552\) | −3.32466e32 | −0.0176811 | ||||||||
\(553\) | −3.58390e33 | −0.186334 | ||||||||
\(554\) | 3.21010e33 | 0.163172 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.34768e34 | −0.654863 | ||||||||
\(557\) | 8.12072e33 | 0.385838 | 0.192919 | − | 0.981215i | \(-0.438205\pi\) | ||||
0.192919 | + | 0.981215i | \(0.438205\pi\) | |||||||
\(558\) | −2.47141e34 | −1.14820 | ||||||||
\(559\) | −1.31714e34 | −0.598390 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.93313e33 | −0.127437 | ||||||||
\(562\) | −7.39849e33 | −0.314369 | ||||||||
\(563\) | 1.21025e34 | 0.502946 | 0.251473 | − | 0.967864i | \(-0.419085\pi\) | ||||
0.251473 | + | 0.967864i | \(0.419085\pi\) | |||||||
\(564\) | 4.09452e32 | 0.0166423 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.98836e34 | −0.773195 | ||||||||
\(567\) | 8.34485e33 | 0.317417 | ||||||||
\(568\) | 8.41487e33 | 0.313107 | ||||||||
\(569\) | −9.61211e33 | −0.349877 | −0.174938 | − | 0.984579i | \(-0.555973\pi\) | ||||
−0.174938 | + | 0.984579i | \(0.555973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.48318e34 | −0.516704 | −0.258352 | − | 0.966051i | \(-0.583179\pi\) | ||||
−0.258352 | + | 0.966051i | \(0.583179\pi\) | |||||||
\(572\) | −2.76868e34 | −0.943676 | ||||||||
\(573\) | 1.61676e33 | 0.0539153 | ||||||||
\(574\) | −1.22408e34 | −0.399403 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.99230e33 | −0.124722 | ||||||||
\(577\) | 4.94604e34 | 1.51203 | 0.756014 | − | 0.654556i | \(-0.227144\pi\) | ||||
0.756014 | + | 0.654556i | \(0.227144\pi\) | |||||||
\(578\) | −4.51905e34 | −1.35191 | ||||||||
\(579\) | 2.50141e33 | 0.0732323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.45313e33 | −0.0407477 | ||||||||
\(582\) | 4.41513e32 | 0.0121173 | ||||||||
\(583\) | −8.43623e34 | −2.26616 | ||||||||
\(584\) | −7.00998e33 | −0.184313 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.98297e33 | −0.150729 | ||||||||
\(587\) | 5.81688e34 | 1.43454 | 0.717272 | − | 0.696793i | \(-0.245390\pi\) | ||||
0.717272 | + | 0.696793i | \(0.245390\pi\) | |||||||
\(588\) | −8.77246e32 | −0.0211790 | ||||||||
\(589\) | −4.62045e34 | −1.09205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.34703e33 | 0.0758256 | ||||||||
\(592\) | 4.26073e33 | 0.0945067 | ||||||||
\(593\) | −1.10616e34 | −0.240234 | −0.120117 | − | 0.992760i | \(-0.538327\pi\) | ||||
−0.120117 | + | 0.992760i | \(0.538327\pi\) | |||||||
\(594\) | 4.96100e33 | 0.105497 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.02154e34 | 0.412197 | ||||||||
\(597\) | −1.54942e33 | −0.0309379 | ||||||||
\(598\) | 4.57035e34 | 0.893685 | ||||||||
\(599\) | 7.59828e34 | 1.45506 | 0.727529 | − | 0.686077i | \(-0.240669\pi\) | ||||
0.727529 | + | 0.686077i | \(0.240669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.55188e34 | 0.652421 | 0.326210 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326210 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(602\) | −6.30384e33 | −0.113409 | ||||||||
\(603\) | 3.15768e34 | 0.556419 | ||||||||
\(604\) | 1.88230e34 | 0.324884 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.06654e33 | −0.0176632 | ||||||||
\(607\) | −7.28541e34 | −1.18194 | −0.590970 | − | 0.806694i | \(-0.701255\pi\) | ||||
−0.590970 | + | 0.806694i | \(0.701255\pi\) | |||||||
\(608\) | −7.46385e33 | −0.118623 | ||||||||
\(609\) | −1.26848e33 | −0.0197500 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.62866e34 | −0.841182 | ||||||||
\(612\) | 5.81411e34 | 0.851315 | ||||||||
\(613\) | 1.55275e34 | 0.222765 | 0.111382 | − | 0.993778i | \(-0.464472\pi\) | ||||
0.111382 | + | 0.993778i | \(0.464472\pi\) | |||||||
\(614\) | −7.52872e33 | −0.105832 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.32509e34 | −0.178849 | ||||||||
\(617\) | −1.18825e35 | −1.57160 | −0.785800 | − | 0.618481i | \(-0.787748\pi\) | ||||
−0.785800 | + | 0.618481i | \(0.787748\pi\) | |||||||
\(618\) | 2.55688e33 | 0.0331401 | ||||||||
\(619\) | −1.31383e34 | −0.166881 | −0.0834406 | − | 0.996513i | \(-0.526591\pi\) | ||||
−0.0834406 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.18927e33 | −0.0999079 | ||||||||
\(622\) | 1.36459e34 | 0.163163 | ||||||||
\(623\) | 7.84524e33 | 0.0919402 | ||||||||
\(624\) | −1.22410e33 | −0.0140608 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.42616e34 | 0.157394 | ||||||||
\(627\) | 4.63228e33 | 0.0501130 | ||||||||
\(628\) | −1.23251e34 | −0.130706 | ||||||||
\(629\) | −6.20503e34 | −0.645076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.62969e35 | 1.62831 | 0.814154 | − | 0.580649i | \(-0.197201\pi\) | ||||
0.814154 | + | 0.580649i | \(0.197201\pi\) | |||||||
\(632\) | 2.10462e34 | 0.206162 | ||||||||
\(633\) | 7.61832e33 | 0.0731666 | ||||||||
\(634\) | −1.27395e34 | −0.119961 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.72986e33 | −0.0337659 | ||||||||
\(637\) | 1.20593e35 | 1.07048 | ||||||||
\(638\) | 1.68483e35 | 1.46655 | ||||||||
\(639\) | 1.03522e35 | 0.883630 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.15302e35 | −1.76735 | −0.883675 | − | 0.468100i | \(-0.844939\pi\) | ||||
−0.883675 | + | 0.468100i | \(0.844939\pi\) | |||||||
\(642\) | 4.48729e33 | 0.0361240 | ||||||||
\(643\) | 9.81888e34 | 0.775220 | 0.387610 | − | 0.921823i | \(-0.373301\pi\) | ||||
0.387610 | + | 0.921823i | \(0.373301\pi\) | |||||||
\(644\) | 2.18737e34 | 0.169375 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.08698e35 | 0.809685 | ||||||||
\(647\) | −9.66650e34 | −0.706262 | −0.353131 | − | 0.935574i | \(-0.614883\pi\) | ||||
−0.353131 | + | 0.935574i | \(0.614883\pi\) | |||||||
\(648\) | −4.90044e34 | −0.351195 | ||||||||
\(649\) | 3.21772e35 | 2.26198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.62670e33 | −0.0245329 | ||||||||
\(652\) | −5.54314e34 | −0.367841 | ||||||||
\(653\) | 2.65692e35 | 1.72967 | 0.864835 | − | 0.502056i | \(-0.167423\pi\) | ||||
0.864835 | + | 0.502056i | \(0.167423\pi\) | |||||||
\(654\) | −3.39013e33 | −0.0216518 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.18832e34 | 0.441906 | ||||||||
\(657\) | −8.62384e34 | −0.520156 | ||||||||
\(658\) | −2.69388e34 | −0.159424 | ||||||||
\(659\) | −1.12403e35 | −0.652697 | −0.326348 | − | 0.945250i | \(-0.605818\pi\) | ||||
−0.326348 | + | 0.945250i | \(0.605818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.74137e35 | 0.973582 | 0.486791 | − | 0.873518i | \(-0.338167\pi\) | ||||
0.486791 | + | 0.873518i | \(0.338167\pi\) | |||||||
\(662\) | −1.10456e35 | −0.605989 | ||||||||
\(663\) | 1.78270e34 | 0.0959750 | ||||||||
\(664\) | 8.53339e33 | 0.0450838 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.24165e34 | 0.266711 | ||||||||
\(667\) | −2.78120e35 | −1.38886 | ||||||||
\(668\) | 1.34969e35 | 0.661496 | ||||||||
\(669\) | 1.63974e34 | 0.0788768 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.96763e35 | 1.83865 | ||||||||
\(672\) | −5.85855e32 | −0.00266486 | ||||||||
\(673\) | 7.64859e34 | 0.341502 | 0.170751 | − | 0.985314i | \(-0.445381\pi\) | ||||
0.170751 | + | 0.985314i | \(0.445381\pi\) | |||||||
\(674\) | −1.66714e35 | −0.730673 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.98882e34 | 0.210700 | ||||||||
\(677\) | −3.11236e34 | −0.129042 | −0.0645211 | − | 0.997916i | \(-0.520552\pi\) | ||||
−0.0645211 | + | 0.997916i | \(0.520552\pi\) | |||||||
\(678\) | 1.24577e34 | 0.0507067 | ||||||||
\(679\) | −2.90481e34 | −0.116077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.79198e34 | −0.0690230 | ||||||||
\(682\) | 4.81708e35 | 1.82171 | ||||||||
\(683\) | −1.85231e35 | −0.687790 | −0.343895 | − | 0.939008i | \(-0.611746\pi\) | ||||
−0.343895 | + | 0.939008i | \(0.611746\pi\) | |||||||
\(684\) | −9.18220e34 | −0.334769 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.21996e35 | 0.428838 | ||||||||
\(687\) | −5.60966e33 | −0.0193632 | ||||||||
\(688\) | 3.70188e34 | 0.125478 | ||||||||
\(689\) | 5.12737e35 | 1.70669 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.90286e35 | −1.57389 | −0.786944 | − | 0.617024i | \(-0.788338\pi\) | ||||
−0.786944 | + | 0.617024i | \(0.788338\pi\) | |||||||
\(692\) | 2.99035e35 | 0.942749 | ||||||||
\(693\) | −1.63016e35 | −0.504736 | ||||||||
\(694\) | −6.49096e34 | −0.197386 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.44904e33 | 0.0218517 | ||||||||
\(697\) | −1.04686e36 | −3.01632 | ||||||||
\(698\) | 9.34669e33 | 0.0264524 | ||||||||
\(699\) | −1.86419e34 | −0.0518233 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.65445e35 | 1.24851 | 0.624257 | − | 0.781219i | \(-0.285402\pi\) | ||||
0.624257 | + | 0.781219i | \(0.285402\pi\) | |||||||
\(702\) | −3.01520e34 | −0.0794514 | ||||||||
\(703\) | 9.79958e34 | 0.253668 | ||||||||
\(704\) | 7.78149e34 | 0.197881 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.46714e35 | 0.850967 | ||||||||
\(707\) | 7.01702e34 | 0.169204 | ||||||||
\(708\) | 1.42263e34 | 0.0337036 | ||||||||
\(709\) | −1.61968e35 | −0.377009 | −0.188504 | − | 0.982072i | \(-0.560364\pi\) | ||||
−0.188504 | + | 0.982072i | \(0.560364\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.58915e35 | 0.581817 | ||||||||
\(712\) | −4.60705e34 | −0.101724 | ||||||||
\(713\) | −7.95170e35 | −1.72521 | ||||||||
\(714\) | 8.53198e33 | 0.0181896 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.66449e35 | 0.754399 | ||||||||
\(717\) | 2.91169e34 | 0.0589055 | ||||||||
\(718\) | 1.01363e35 | 0.201523 | ||||||||
\(719\) | 3.86289e35 | 0.754747 | 0.377374 | − | 0.926061i | \(-0.376827\pi\) | ||||
0.377374 | + | 0.926061i | \(0.376827\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.68223e35 | −0.317464 | ||||||||
\(722\) | 2.09574e35 | 0.388708 | ||||||||
\(723\) | 3.88377e34 | 0.0707986 | ||||||||
\(724\) | 5.32027e34 | 0.0953238 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.90231e34 | −0.0502384 | ||||||||
\(727\) | 3.11776e35 | 0.530471 | 0.265236 | − | 0.964184i | \(-0.414550\pi\) | ||||
0.265236 | + | 0.964184i | \(0.414550\pi\) | |||||||
\(728\) | 8.05365e34 | 0.134695 | ||||||||
\(729\) | −6.00160e35 | −0.986672 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.39115e35 | −0.856474 | ||||||||
\(732\) | 1.75419e34 | 0.0273960 | ||||||||
\(733\) | 2.23983e35 | 0.343886 | 0.171943 | − | 0.985107i | \(-0.444995\pi\) | ||||
0.171943 | + | 0.985107i | \(0.444995\pi\) | |||||||
\(734\) | −8.83879e35 | −1.33411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.28451e35 | −0.187399 | ||||||||
\(737\) | −6.15471e35 | −0.882804 | ||||||||
\(738\) | 8.84324e35 | 1.24712 | ||||||||
\(739\) | 5.23044e34 | 0.0725241 | 0.0362621 | − | 0.999342i | \(-0.488455\pi\) | ||||
0.0362621 | + | 0.999342i | \(0.488455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.81541e34 | −0.0377410 | ||||||||
\(742\) | 2.45396e35 | 0.323459 | ||||||||
\(743\) | −7.47724e35 | −0.969127 | −0.484564 | − | 0.874756i | \(-0.661022\pi\) | ||||
−0.484564 | + | 0.874756i | \(0.661022\pi\) | |||||||
\(744\) | 2.12975e34 | 0.0271436 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.88057e35 | −0.724743 | ||||||||
\(747\) | 1.04980e35 | 0.127232 | ||||||||
\(748\) | −1.13324e36 | −1.35068 | ||||||||
\(749\) | −2.95229e35 | −0.346048 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.40867e36 | −1.59702 | −0.798510 | − | 0.601982i | \(-0.794378\pi\) | ||||
−0.798510 | + | 0.601982i | \(0.794378\pi\) | |||||||
\(752\) | 1.58196e35 | 0.176389 | ||||||||
\(753\) | 6.36310e34 | 0.0697801 | ||||||||
\(754\) | −1.02401e36 | −1.10449 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.44307e34 | −0.0150580 | ||||||||
\(757\) | 1.39455e36 | 1.43132 | 0.715658 | − | 0.698451i | \(-0.246127\pi\) | ||||
0.715658 | + | 0.698451i | \(0.246127\pi\) | |||||||
\(758\) | −6.29519e35 | −0.635541 | ||||||||
\(759\) | 7.97206e34 | 0.0791677 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.19222e36 | −1.14564 | −0.572818 | − | 0.819682i | \(-0.694150\pi\) | ||||
−0.572818 | + | 0.819682i | \(0.694150\pi\) | |||||||
\(762\) | 2.45439e34 | 0.0232010 | ||||||||
\(763\) | 2.23044e35 | 0.207412 | ||||||||
\(764\) | 6.24650e35 | 0.571439 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.42603e35 | 0.746042 | ||||||||
\(767\) | −1.95567e36 | −1.70354 | ||||||||
\(768\) | 3.44039e33 | 0.00294844 | ||||||||
\(769\) | 4.70446e35 | 0.396671 | 0.198336 | − | 0.980134i | \(-0.436446\pi\) | ||||
0.198336 | + | 0.980134i | \(0.436446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.37365e34 | −0.0601870 | ||||||||
\(772\) | 9.66444e35 | 0.776176 | ||||||||
\(773\) | −4.82216e35 | −0.381064 | −0.190532 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190532 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(774\) | 4.55414e35 | 0.354115 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.70583e35 | 0.128429 | ||||||||
\(777\) | 7.69192e33 | 0.00569865 | ||||||||
\(778\) | 8.07148e35 | 0.588448 | ||||||||
\(779\) | 1.65330e36 | 1.18613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.01777e36 | −1.40195 | ||||||||
\(782\) | 1.87068e36 | 1.27913 | ||||||||
\(783\) | 1.83484e35 | 0.123474 | ||||||||
\(784\) | −3.38933e35 | −0.224472 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.05345e34 | 0.00675824 | ||||||||
\(787\) | 1.69806e36 | 1.07219 | 0.536093 | − | 0.844159i | \(-0.319900\pi\) | ||||
0.536093 | + | 0.844159i | \(0.319900\pi\) | |||||||
\(788\) | 1.29316e36 | 0.803662 | ||||||||
\(789\) | 9.17026e34 | 0.0560944 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.19618e35 | −0.485742 | ||||||||
\(792\) | 9.57297e35 | 0.558447 | ||||||||
\(793\) | −2.41145e36 | −1.38472 | ||||||||
\(794\) | −8.38114e34 | −0.0473747 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.98635e35 | −0.327906 | ||||||||
\(797\) | 2.41463e36 | 1.30203 | 0.651017 | − | 0.759063i | \(-0.274343\pi\) | ||||
0.651017 | + | 0.759063i | \(0.274343\pi\) | |||||||
\(798\) | −1.34745e34 | −0.00715283 | ||||||||
\(799\) | −2.30385e36 | −1.20398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.66770e35 | −0.287079 | ||||||||
\(802\) | −1.96375e36 | −0.979281 | ||||||||
\(803\) | 1.68089e36 | 0.825270 | ||||||||
\(804\) | −2.72115e34 | −0.0131538 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.92773e36 | −1.37196 | ||||||||
\(807\) | −7.32747e34 | −0.0338092 | ||||||||
\(808\) | −4.12069e35 | −0.187209 | ||||||||
\(809\) | −4.34243e35 | −0.194257 | −0.0971283 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971283 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.52344e35 | −0.0660792 | −0.0330396 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330396 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(812\) | −4.90089e35 | −0.209327 | ||||||||
\(813\) | −4.34428e34 | −0.0182720 | ||||||||
\(814\) | −1.02166e36 | −0.423158 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.01034e34 | −0.0201252 | ||||||||
\(817\) | 8.51423e35 | 0.336798 | ||||||||
\(818\) | −1.07082e36 | −0.417159 | ||||||||
\(819\) | 9.90778e35 | 0.380126 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.12855e36 | 0.419983 | 0.209992 | − | 0.977703i | \(-0.432656\pi\) | ||||
0.209992 | + | 0.977703i | \(0.432656\pi\) | |||||||
\(822\) | 7.84056e34 | 0.0287375 | ||||||||
\(823\) | −3.43120e36 | −1.23865 | −0.619325 | − | 0.785135i | \(-0.712594\pi\) | ||||
−0.619325 | + | 0.785135i | \(0.712594\pi\) | |||||||
\(824\) | 9.87875e35 | 0.351246 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.35982e35 | −0.322862 | ||||||||
\(827\) | −2.18743e36 | −0.743216 | −0.371608 | − | 0.928390i | \(-0.621193\pi\) | ||||
−0.371608 | + | 0.928390i | \(0.621193\pi\) | |||||||
\(828\) | −1.58024e36 | −0.528864 | ||||||||
\(829\) | 2.16830e36 | 0.714804 | 0.357402 | − | 0.933951i | \(-0.383663\pi\) | ||||
0.357402 | + | 0.933951i | \(0.383663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.40319e34 | −0.0108861 | ||||||||
\(832\) | −4.72944e35 | −0.149028 | ||||||||
\(833\) | 4.93597e36 | 1.53218 | ||||||||
\(834\) | 1.42874e35 | 0.0436896 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.78973e36 | 0.531139 | ||||||||
\(837\) | 5.24598e35 | 0.153376 | ||||||||
\(838\) | 9.73566e35 | 0.280424 | ||||||||
\(839\) | −6.23659e36 | −1.76980 | −0.884898 | − | 0.465786i | \(-0.845772\pi\) | ||||
−0.884898 | + | 0.465786i | \(0.845772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.60103e36 | 0.716465 | ||||||||
\(842\) | −2.93904e36 | −0.797635 | ||||||||
\(843\) | 7.84352e34 | 0.0209733 | ||||||||
\(844\) | 2.94341e36 | 0.775480 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.94616e36 | 0.497794 | ||||||||
\(847\) | 1.90950e36 | 0.481256 | ||||||||
\(848\) | −1.44107e36 | −0.357879 | ||||||||
\(849\) | 2.10796e35 | 0.0515842 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.68649e36 | 0.400741 | ||||||||
\(852\) | −8.92103e34 | −0.0208891 | ||||||||
\(853\) | 1.57022e36 | 0.362325 | 0.181163 | − | 0.983453i | \(-0.442014\pi\) | ||||
0.181163 | + | 0.983453i | \(0.442014\pi\) | |||||||
\(854\) | −1.15412e36 | −0.262438 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.73371e36 | 0.382872 | ||||||||
\(857\) | −1.90353e36 | −0.414284 | −0.207142 | − | 0.978311i | \(-0.566416\pi\) | ||||
−0.207142 | + | 0.978311i | \(0.566416\pi\) | |||||||
\(858\) | 2.93522e35 | 0.0629579 | ||||||||
\(859\) | 1.49712e36 | 0.316476 | 0.158238 | − | 0.987401i | \(-0.449419\pi\) | ||||
0.158238 | + | 0.987401i | \(0.449419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.29771e35 | 0.0266464 | ||||||||
\(862\) | −2.02686e36 | −0.410188 | ||||||||
\(863\) | −6.49700e36 | −1.29592 | −0.647960 | − | 0.761675i | \(-0.724378\pi\) | ||||
−0.647960 | + | 0.761675i | \(0.724378\pi\) | |||||||
\(864\) | 8.47433e34 | 0.0166603 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.67830e35 | 0.146653 | ||||||||
\(867\) | 4.79088e35 | 0.0901937 | ||||||||
\(868\) | −1.40121e36 | −0.260020 | ||||||||
\(869\) | −5.04657e36 | −0.923101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.74072e36 | 0.664856 | ||||||||
\(872\) | −1.30981e36 | −0.229484 | ||||||||
\(873\) | 2.09855e36 | 0.362444 | ||||||||
\(874\) | −2.95435e36 | −0.503002 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.43165e34 | 0.0122966 | ||||||||
\(877\) | −4.25958e36 | −0.694819 | −0.347410 | − | 0.937713i | \(-0.612939\pi\) | ||||
−0.347410 | + | 0.937713i | \(0.612939\pi\) | |||||||
\(878\) | 1.04306e36 | 0.167736 | ||||||||
\(879\) | 6.34286e34 | 0.0100560 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.17230e36 | 0.180652 | 0.0903258 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903258 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(882\) | −4.16963e36 | −0.633490 | ||||||||
\(883\) | 8.13959e36 | 1.21925 | 0.609626 | − | 0.792689i | \(-0.291320\pi\) | ||||
0.609626 | + | 0.792689i | \(0.291320\pi\) | |||||||
\(884\) | 6.88762e36 | 1.01722 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.71418e36 | −0.963988 | ||||||||
\(887\) | −3.20938e36 | −0.454335 | −0.227168 | − | 0.973856i | \(-0.572947\pi\) | ||||
−0.227168 | + | 0.973856i | \(0.572947\pi\) | |||||||
\(888\) | −4.51702e34 | −0.00630507 | ||||||||
\(889\) | −1.61480e36 | −0.222252 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.17506e37 | 1.57249 | ||||||||
\(892\) | 6.33530e36 | 0.836001 | ||||||||
\(893\) | 3.63847e36 | 0.473451 | ||||||||
\(894\) | −2.14314e35 | −0.0274999 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.26351e35 | −0.0282444 | ||||||||
\(897\) | −4.84526e35 | −0.0596227 | ||||||||
\(898\) | 4.38807e36 | 0.532499 | ||||||||
\(899\) | 1.78161e37 | 2.13215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.09867e37 | 2.44278 | ||||||||
\(902\) | −1.72366e37 | −1.97865 | ||||||||
\(903\) | 6.68302e34 | 0.00756617 | ||||||||
\(904\) | 4.81314e36 | 0.537432 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.99553e35 | −0.0216748 | ||||||||
\(907\) | 1.37794e37 | 1.47618 | 0.738091 | − | 0.674702i | \(-0.235728\pi\) | ||||
0.738091 | + | 0.674702i | \(0.235728\pi\) | |||||||
\(908\) | −6.92348e36 | −0.731562 | ||||||||
\(909\) | −5.06937e36 | −0.528330 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.00864e37 | 1.02272 | 0.511359 | − | 0.859367i | \(-0.329142\pi\) | ||||
0.511359 | + | 0.859367i | \(0.329142\pi\) | |||||||
\(912\) | 7.91282e34 | 0.00791399 | ||||||||
\(913\) | −2.04618e36 | −0.201865 | ||||||||
\(914\) | 7.89003e36 | 0.767806 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.16735e36 | −0.205227 | ||||||||
\(917\) | −6.93090e35 | −0.0647401 | ||||||||
\(918\) | −1.23414e36 | −0.113719 | ||||||||
\(919\) | −1.70873e37 | −1.55321 | −0.776603 | − | 0.629991i | \(-0.783059\pi\) | ||||
−0.776603 | + | 0.629991i | \(0.783059\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.98159e34 | 0.00706064 | ||||||||
\(922\) | −7.22870e36 | −0.630846 | ||||||||
\(923\) | 1.22636e37 | 1.05584 | ||||||||
\(924\) | 1.40480e35 | 0.0119320 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.62137e36 | 0.216716 | ||||||||
\(927\) | 1.21531e37 | 0.991263 | ||||||||
\(928\) | 2.87801e36 | 0.231602 | ||||||||
\(929\) | 1.39851e37 | 1.11037 | 0.555185 | − | 0.831727i | \(-0.312647\pi\) | ||||
0.555185 | + | 0.831727i | \(0.312647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.79537e36 | −0.602512 | ||||||||
\(932\) | −7.20247e36 | −0.549266 | ||||||||
\(933\) | −1.44667e35 | −0.0108855 | ||||||||
\(934\) | 7.69744e36 | 0.571493 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.81827e36 | −0.420577 | ||||||||
\(937\) | −5.96148e36 | −0.425216 | −0.212608 | − | 0.977138i | \(-0.568196\pi\) | ||||
−0.212608 | + | 0.977138i | \(0.568196\pi\) | |||||||
\(938\) | 1.79031e36 | 0.126006 | ||||||||
\(939\) | −1.51194e35 | −0.0105006 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.77897e37 | −1.87937 | −0.939686 | − | 0.342038i | \(-0.888883\pi\) | ||||
−0.939686 | + | 0.342038i | \(0.888883\pi\) | |||||||
\(942\) | 1.30665e35 | 0.00872014 | ||||||||
\(943\) | 2.84529e37 | 1.87383 | ||||||||
\(944\) | 5.49648e36 | 0.357219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.87658e36 | −0.561832 | ||||||||
\(947\) | 3.29072e36 | 0.205549 | 0.102775 | − | 0.994705i | \(-0.467228\pi\) | ||||
0.102775 | + | 0.994705i | \(0.467228\pi\) | |||||||
\(948\) | −2.23121e35 | −0.0137542 | ||||||||
\(949\) | −1.02161e37 | −0.621526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.35059e35 | 0.00800324 | ||||||||
\(952\) | 3.29642e36 | 0.192788 | ||||||||
\(953\) | −3.30322e36 | −0.190667 | −0.0953337 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953337 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(954\) | −1.77284e37 | −1.00998 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.12496e37 | 0.624329 | ||||||||
\(957\) | −1.78617e36 | −0.0978418 | ||||||||
\(958\) | 1.84020e36 | 0.0994938 | ||||||||
\(959\) | −5.15848e36 | −0.275289 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.17052e37 | 1.64850 | ||||||||
\(962\) | 6.20947e36 | 0.318688 | ||||||||
\(963\) | 2.13285e37 | 1.08052 | ||||||||
\(964\) | 1.50053e37 | 0.750382 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.31894e35 | −0.0112999 | ||||||||
\(967\) | −1.07284e37 | −0.516064 | −0.258032 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258032 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(968\) | −1.12134e37 | −0.532468 | ||||||||
\(969\) | −1.15237e36 | −0.0540186 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.81170e36 | −0.174132 | −0.0870659 | − | 0.996203i | \(-0.527749\pi\) | ||||
−0.0870659 | + | 0.996203i | \(0.527749\pi\) | |||||||
\(972\) | 1.56438e36 | 0.0705527 | ||||||||
\(973\) | −9.40001e36 | −0.418522 | ||||||||
\(974\) | −1.79604e37 | −0.789459 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.77747e36 | 0.290365 | ||||||||
\(977\) | 4.24334e37 | 1.79484 | 0.897420 | − | 0.441178i | \(-0.145439\pi\) | ||||
0.897420 | + | 0.441178i | \(0.145439\pi\) | |||||||
\(978\) | 5.87657e35 | 0.0245408 | ||||||||
\(979\) | 1.10471e37 | 0.455473 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.61136e37 | −0.647634 | ||||||||
\(982\) | −3.40629e37 | −1.35172 | ||||||||
\(983\) | −2.83202e37 | −1.10963 | −0.554814 | − | 0.831974i | \(-0.687211\pi\) | ||||
−0.554814 | + | 0.831974i | \(0.687211\pi\) | |||||||
\(984\) | −7.62071e35 | −0.0294820 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.19133e37 | −1.58085 | ||||||||
\(987\) | 2.85592e35 | 0.0106361 | ||||||||
\(988\) | −1.08776e37 | −0.400010 | ||||||||
\(989\) | 1.46528e37 | 0.532069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.64697e37 | −0.937193 | −0.468596 | − | 0.883412i | \(-0.655240\pi\) | ||||
−0.468596 | + | 0.883412i | \(0.655240\pi\) | |||||||
\(992\) | 8.22850e36 | 0.287690 | ||||||||
\(993\) | 1.17100e36 | 0.0404289 | ||||||||
\(994\) | 5.86935e36 | 0.200106 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.04668e34 | −0.00300779 | ||||||||
\(997\) | 2.72983e37 | 0.896287 | 0.448143 | − | 0.893962i | \(-0.352085\pi\) | ||||
0.448143 | + | 0.893962i | \(0.352085\pi\) | |||||||
\(998\) | 2.08554e37 | 0.676217 | ||||||||
\(999\) | −1.11263e36 | −0.0356272 |
(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 | 50.26.a.i.1.3 | ✓ | 5 | |
5.2 | odd | 4 | 50.26.b.h.49.3 | 10 | |||
5.3 | odd | 4 | 50.26.b.h.49.8 | 10 | |||
5.4 | even | 2 | 50.26.a.j.1.3 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.26.a.i.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
50.26.a.j.1.3 | yes | 5 | 5.4 | even | 2 | ||
50.26.b.h.49.3 | 10 | 5.2 | odd | 4 | |||
50.26.b.h.49.8 | 10 | 5.3 | odd | 4 |