Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,12,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(16.1352067918\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.176777 | 0.0883883 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883883 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1984.00 | −0.968750 | ||||||||
\(5\) | 4390.00 | 0.628246 | 0.314123 | − | 0.949382i | \(-0.398290\pi\) | ||||
0.314123 | + | 0.949382i | \(0.398290\pi\) | |||||||
\(6\) | 1944.00 | 0.102062 | ||||||||
\(7\) | −16807.0 | −0.377964 | ||||||||
\(8\) | −32256.0 | −0.348029 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 35120.0 | 0.111059 | ||||||||
\(11\) | −804836. | −1.50677 | −0.753386 | − | 0.657578i | \(-0.771581\pi\) | ||||
−0.753386 | + | 0.657578i | \(0.771581\pi\) | |||||||
\(12\) | −482112. | −0.559308 | ||||||||
\(13\) | 358294. | 0.267640 | 0.133820 | − | 0.991006i | \(-0.457276\pi\) | ||||
0.133820 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(14\) | −134456. | −0.0668153 | ||||||||
\(15\) | 1.06677e6 | 0.362718 | ||||||||
\(16\) | 3.80518e6 | 0.907227 | ||||||||
\(17\) | −5.65786e6 | −0.966459 | −0.483229 | − | 0.875494i | \(-0.660536\pi\) | ||||
−0.483229 | + | 0.875494i | \(0.660536\pi\) | |||||||
\(18\) | 472392. | 0.0589256 | ||||||||
\(19\) | −1.46020e7 | −1.35291 | −0.676453 | − | 0.736486i | \(-0.736484\pi\) | ||||
−0.676453 | + | 0.736486i | \(0.736484\pi\) | |||||||
\(20\) | −8.70976e6 | −0.608613 | ||||||||
\(21\) | −4.08410e6 | −0.218218 | ||||||||
\(22\) | −6.43869e6 | −0.266362 | ||||||||
\(23\) | −3.67248e7 | −1.18975 | −0.594876 | − | 0.803818i | \(-0.702799\pi\) | ||||
−0.594876 | + | 0.803818i | \(0.702799\pi\) | |||||||
\(24\) | −7.83821e6 | −0.200935 | ||||||||
\(25\) | −2.95560e7 | −0.605307 | ||||||||
\(26\) | 2.86635e6 | 0.0473125 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 3.33451e7 | 0.366153 | ||||||||
\(29\) | 5.11270e7 | 0.462872 | 0.231436 | − | 0.972850i | \(-0.425658\pi\) | ||||
0.231436 | + | 0.972850i | \(0.425658\pi\) | |||||||
\(30\) | 8.53416e6 | 0.0641201 | ||||||||
\(31\) | −2.08102e8 | −1.30553 | −0.652765 | − | 0.757560i | \(-0.726391\pi\) | ||||
−0.652765 | + | 0.757560i | \(0.726391\pi\) | |||||||
\(32\) | 9.65018e7 | 0.508406 | ||||||||
\(33\) | −1.95575e8 | −0.869935 | ||||||||
\(34\) | −4.52629e7 | −0.170847 | ||||||||
\(35\) | −7.37827e7 | −0.237455 | ||||||||
\(36\) | −1.17153e8 | −0.322917 | ||||||||
\(37\) | 6.52146e8 | 1.54609 | 0.773046 | − | 0.634350i | \(-0.218732\pi\) | ||||
0.773046 | + | 0.634350i | \(0.218732\pi\) | |||||||
\(38\) | −1.16816e8 | −0.239162 | ||||||||
\(39\) | 8.70654e7 | 0.154522 | ||||||||
\(40\) | −1.41604e8 | −0.218648 | ||||||||
\(41\) | 9.51188e8 | 1.28220 | 0.641099 | − | 0.767458i | \(-0.278479\pi\) | ||||
0.641099 | + | 0.767458i | \(0.278479\pi\) | |||||||
\(42\) | −3.26728e7 | −0.0385758 | ||||||||
\(43\) | 8.58608e8 | 0.890673 | 0.445337 | − | 0.895363i | \(-0.353084\pi\) | ||||
0.445337 | + | 0.895363i | \(0.353084\pi\) | |||||||
\(44\) | 1.59679e9 | 1.45969 | ||||||||
\(45\) | 2.59225e8 | 0.209415 | ||||||||
\(46\) | −2.93798e8 | −0.210320 | ||||||||
\(47\) | −1.33655e9 | −0.850058 | −0.425029 | − | 0.905180i | \(-0.639736\pi\) | ||||
−0.425029 | + | 0.905180i | \(0.639736\pi\) | |||||||
\(48\) | 9.24660e8 | 0.523788 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | −2.36448e8 | −0.107004 | ||||||||
\(51\) | −1.37486e9 | −0.557985 | ||||||||
\(52\) | −7.10855e8 | −0.259276 | ||||||||
\(53\) | 1.49760e9 | 0.491901 | 0.245950 | − | 0.969282i | \(-0.420900\pi\) | ||||
0.245950 | + | 0.969282i | \(0.420900\pi\) | |||||||
\(54\) | 1.14791e8 | 0.0340207 | ||||||||
\(55\) | −3.53323e9 | −0.946623 | ||||||||
\(56\) | 5.42127e8 | 0.131543 | ||||||||
\(57\) | −3.54829e9 | −0.781101 | ||||||||
\(58\) | 4.09016e8 | 0.0818250 | ||||||||
\(59\) | 7.06794e9 | 1.28708 | 0.643542 | − | 0.765411i | \(-0.277464\pi\) | ||||
0.643542 | + | 0.765411i | \(0.277464\pi\) | |||||||
\(60\) | −2.11647e9 | −0.351383 | ||||||||
\(61\) | −7.64393e9 | −1.15878 | −0.579392 | − | 0.815049i | \(-0.696710\pi\) | ||||
−0.579392 | + | 0.815049i | \(0.696710\pi\) | |||||||
\(62\) | −1.66482e9 | −0.230787 | ||||||||
\(63\) | −9.92437e8 | −0.125988 | ||||||||
\(64\) | −7.02100e9 | −0.817352 | ||||||||
\(65\) | 1.57291e9 | 0.168144 | ||||||||
\(66\) | −1.56460e9 | −0.153784 | ||||||||
\(67\) | −5.08676e9 | −0.460288 | −0.230144 | − | 0.973157i | \(-0.573920\pi\) | ||||
−0.230144 | + | 0.973157i | \(0.573920\pi\) | |||||||
\(68\) | 1.12252e10 | 0.936257 | ||||||||
\(69\) | −8.92413e9 | −0.686903 | ||||||||
\(70\) | −5.90262e8 | −0.0419764 | ||||||||
\(71\) | 2.80141e9 | 0.184271 | 0.0921353 | − | 0.995746i | \(-0.470631\pi\) | ||||
0.0921353 | + | 0.995746i | \(0.470631\pi\) | |||||||
\(72\) | −1.90468e9 | −0.116010 | ||||||||
\(73\) | −7.84428e9 | −0.442871 | −0.221436 | − | 0.975175i | \(-0.571074\pi\) | ||||
−0.221436 | + | 0.975175i | \(0.571074\pi\) | |||||||
\(74\) | 5.21717e9 | 0.273313 | ||||||||
\(75\) | −7.18211e9 | −0.349474 | ||||||||
\(76\) | 2.89704e10 | 1.31063 | ||||||||
\(77\) | 1.35269e10 | 0.569506 | ||||||||
\(78\) | 6.96524e8 | 0.0273159 | ||||||||
\(79\) | −2.11567e10 | −0.773567 | −0.386784 | − | 0.922170i | \(-0.626414\pi\) | ||||
−0.386784 | + | 0.922170i | \(0.626414\pi\) | |||||||
\(80\) | 1.67048e10 | 0.569961 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 7.60951e9 | 0.226663 | ||||||||
\(83\) | −1.08949e10 | −0.303596 | −0.151798 | − | 0.988412i | \(-0.548506\pi\) | ||||
−0.151798 | + | 0.988412i | \(0.548506\pi\) | |||||||
\(84\) | 8.10286e9 | 0.211399 | ||||||||
\(85\) | −2.48380e10 | −0.607173 | ||||||||
\(86\) | 6.86886e9 | 0.157450 | ||||||||
\(87\) | 1.24239e10 | 0.267239 | ||||||||
\(88\) | 2.59608e10 | 0.524401 | ||||||||
\(89\) | 7.07888e10 | 1.34375 | 0.671876 | − | 0.740663i | \(-0.265489\pi\) | ||||
0.671876 | + | 0.740663i | \(0.265489\pi\) | |||||||
\(90\) | 2.07380e9 | 0.0370197 | ||||||||
\(91\) | −6.02185e9 | −0.101158 | ||||||||
\(92\) | 7.28620e10 | 1.15257 | ||||||||
\(93\) | −5.05688e10 | −0.753749 | ||||||||
\(94\) | −1.06924e10 | −0.150270 | ||||||||
\(95\) | −6.41028e10 | −0.849957 | ||||||||
\(96\) | 2.34499e10 | 0.293528 | ||||||||
\(97\) | 8.22238e10 | 0.972194 | 0.486097 | − | 0.873905i | \(-0.338420\pi\) | ||||
0.486097 | + | 0.873905i | \(0.338420\pi\) | |||||||
\(98\) | 2.25980e9 | 0.0252538 | ||||||||
\(99\) | −4.75248e10 | −0.502257 | ||||||||
\(100\) | 5.86392e10 | 0.586392 | ||||||||
\(101\) | −1.38046e11 | −1.30694 | −0.653472 | − | 0.756950i | \(-0.726688\pi\) | ||||
−0.653472 | + | 0.756950i | \(0.726688\pi\) | |||||||
\(102\) | −1.09989e10 | −0.0986388 | ||||||||
\(103\) | −6.01027e10 | −0.510845 | −0.255422 | − | 0.966830i | \(-0.582215\pi\) | ||||
−0.255422 | + | 0.966830i | \(0.582215\pi\) | |||||||
\(104\) | −1.15571e10 | −0.0931465 | ||||||||
\(105\) | −1.79292e10 | −0.137094 | ||||||||
\(106\) | 1.19808e10 | 0.0869566 | ||||||||
\(107\) | 1.33576e11 | 0.920702 | 0.460351 | − | 0.887737i | \(-0.347724\pi\) | ||||
0.460351 | + | 0.887737i | \(0.347724\pi\) | |||||||
\(108\) | −2.84682e10 | −0.186436 | ||||||||
\(109\) | −2.16913e11 | −1.35033 | −0.675164 | − | 0.737668i | \(-0.735927\pi\) | ||||
−0.675164 | + | 0.737668i | \(0.735927\pi\) | |||||||
\(110\) | −2.82658e10 | −0.167341 | ||||||||
\(111\) | 1.58471e11 | 0.892637 | ||||||||
\(112\) | −6.39537e10 | −0.342899 | ||||||||
\(113\) | −3.52345e11 | −1.79902 | −0.899512 | − | 0.436896i | \(-0.856078\pi\) | ||||
−0.899512 | + | 0.436896i | \(0.856078\pi\) | |||||||
\(114\) | −2.83863e10 | −0.138080 | ||||||||
\(115\) | −1.61222e11 | −0.747456 | ||||||||
\(116\) | −1.01436e11 | −0.448408 | ||||||||
\(117\) | 2.11569e10 | 0.0892133 | ||||||||
\(118\) | 5.65436e10 | 0.227527 | ||||||||
\(119\) | 9.50917e10 | 0.365287 | ||||||||
\(120\) | −3.44097e10 | −0.126236 | ||||||||
\(121\) | 3.62449e11 | 1.27036 | ||||||||
\(122\) | −6.11514e10 | −0.204846 | ||||||||
\(123\) | 2.31139e11 | 0.740278 | ||||||||
\(124\) | 4.12875e11 | 1.26473 | ||||||||
\(125\) | −3.44106e11 | −1.00853 | ||||||||
\(126\) | −7.93949e9 | −0.0222718 | ||||||||
\(127\) | −3.23741e11 | −0.869514 | −0.434757 | − | 0.900548i | \(-0.643166\pi\) | ||||
−0.434757 | + | 0.900548i | \(0.643166\pi\) | |||||||
\(128\) | −2.53804e11 | −0.652894 | ||||||||
\(129\) | 2.08642e11 | 0.514230 | ||||||||
\(130\) | 1.25833e10 | 0.0297239 | ||||||||
\(131\) | 2.68716e11 | 0.608557 | 0.304278 | − | 0.952583i | \(-0.401585\pi\) | ||||
0.304278 | + | 0.952583i | \(0.401585\pi\) | |||||||
\(132\) | 3.88021e11 | 0.842750 | ||||||||
\(133\) | 2.45416e11 | 0.511350 | ||||||||
\(134\) | −4.06941e10 | −0.0813682 | ||||||||
\(135\) | 6.29917e10 | 0.120906 | ||||||||
\(136\) | 1.82500e11 | 0.336356 | ||||||||
\(137\) | −3.76903e11 | −0.667215 | −0.333608 | − | 0.942712i | \(-0.608266\pi\) | ||||
−0.333608 | + | 0.942712i | \(0.608266\pi\) | |||||||
\(138\) | −7.13930e10 | −0.121429 | ||||||||
\(139\) | 6.81630e11 | 1.11421 | 0.557105 | − | 0.830442i | \(-0.311912\pi\) | ||||
0.557105 | + | 0.830442i | \(0.311912\pi\) | |||||||
\(140\) | 1.46385e11 | 0.230034 | ||||||||
\(141\) | −3.24783e11 | −0.490781 | ||||||||
\(142\) | 2.24113e10 | 0.0325747 | ||||||||
\(143\) | −2.88368e11 | −0.403273 | ||||||||
\(144\) | 2.24692e11 | 0.302409 | ||||||||
\(145\) | 2.24447e11 | 0.290797 | ||||||||
\(146\) | −6.27542e10 | −0.0782893 | ||||||||
\(147\) | 6.86415e10 | 0.0824786 | ||||||||
\(148\) | −1.29386e12 | −1.49778 | ||||||||
\(149\) | 1.38806e12 | 1.54840 | 0.774201 | − | 0.632940i | \(-0.218152\pi\) | ||||
0.774201 | + | 0.632940i | \(0.218152\pi\) | |||||||
\(150\) | −5.74569e10 | −0.0617789 | ||||||||
\(151\) | 1.53008e12 | 1.58614 | 0.793068 | − | 0.609133i | \(-0.208482\pi\) | ||||
0.793068 | + | 0.609133i | \(0.208482\pi\) | |||||||
\(152\) | 4.71002e11 | 0.470851 | ||||||||
\(153\) | −3.34091e11 | −0.322153 | ||||||||
\(154\) | 1.08215e11 | 0.100675 | ||||||||
\(155\) | −9.13568e11 | −0.820194 | ||||||||
\(156\) | −1.72738e11 | −0.149693 | ||||||||
\(157\) | −8.76928e11 | −0.733696 | −0.366848 | − | 0.930281i | \(-0.619563\pi\) | ||||
−0.366848 | + | 0.930281i | \(0.619563\pi\) | |||||||
\(158\) | −1.69253e11 | −0.136749 | ||||||||
\(159\) | 3.63916e11 | 0.283999 | ||||||||
\(160\) | 4.23643e11 | 0.319404 | ||||||||
\(161\) | 6.17234e11 | 0.449684 | ||||||||
\(162\) | 2.78943e10 | 0.0196419 | ||||||||
\(163\) | −2.02497e12 | −1.37844 | −0.689220 | − | 0.724552i | \(-0.742047\pi\) | ||||
−0.689220 | + | 0.724552i | \(0.742047\pi\) | |||||||
\(164\) | −1.88716e12 | −1.24213 | ||||||||
\(165\) | −8.58575e11 | −0.546533 | ||||||||
\(166\) | −8.71596e10 | −0.0536687 | ||||||||
\(167\) | 3.19750e11 | 0.190489 | 0.0952444 | − | 0.995454i | \(-0.469637\pi\) | ||||
0.0952444 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(168\) | 1.31737e11 | 0.0759462 | ||||||||
\(169\) | −1.66379e12 | −0.928369 | ||||||||
\(170\) | −1.98704e11 | −0.107334 | ||||||||
\(171\) | −8.62234e11 | −0.450969 | ||||||||
\(172\) | −1.70348e12 | −0.862839 | ||||||||
\(173\) | 1.53948e12 | 0.755301 | 0.377650 | − | 0.925948i | \(-0.376732\pi\) | ||||
0.377650 | + | 0.925948i | \(0.376732\pi\) | |||||||
\(174\) | 9.93909e10 | 0.0472417 | ||||||||
\(175\) | 4.96748e11 | 0.228785 | ||||||||
\(176\) | −3.06255e12 | −1.36698 | ||||||||
\(177\) | 1.71751e12 | 0.743099 | ||||||||
\(178\) | 5.66310e11 | 0.237544 | ||||||||
\(179\) | 1.81701e10 | 0.00739036 | 0.00369518 | − | 0.999993i | \(-0.498824\pi\) | ||||
0.00369518 | + | 0.999993i | \(0.498824\pi\) | |||||||
\(180\) | −5.14303e11 | −0.202871 | ||||||||
\(181\) | 1.75588e12 | 0.671834 | 0.335917 | − | 0.941892i | \(-0.390954\pi\) | ||||
0.335917 | + | 0.941892i | \(0.390954\pi\) | |||||||
\(182\) | −4.81748e10 | −0.0178825 | ||||||||
\(183\) | −1.85747e12 | −0.669024 | ||||||||
\(184\) | 1.18460e12 | 0.414068 | ||||||||
\(185\) | 2.86292e12 | 0.971326 | ||||||||
\(186\) | −4.04550e11 | −0.133245 | ||||||||
\(187\) | 4.55365e12 | 1.45623 | ||||||||
\(188\) | 2.65172e12 | 0.823494 | ||||||||
\(189\) | −2.41162e11 | −0.0727393 | ||||||||
\(190\) | −5.12822e11 | −0.150253 | ||||||||
\(191\) | 5.77511e12 | 1.64390 | 0.821952 | − | 0.569556i | \(-0.192885\pi\) | ||||
0.821952 | + | 0.569556i | \(0.192885\pi\) | |||||||
\(192\) | −1.70610e12 | −0.471899 | ||||||||
\(193\) | −4.14036e12 | −1.11294 | −0.556471 | − | 0.830867i | \(-0.687845\pi\) | ||||
−0.556471 | + | 0.830867i | \(0.687845\pi\) | |||||||
\(194\) | 6.57790e11 | 0.171861 | ||||||||
\(195\) | 3.82217e11 | 0.0970778 | ||||||||
\(196\) | −5.60431e11 | −0.138393 | ||||||||
\(197\) | 6.91145e11 | 0.165961 | 0.0829803 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829803 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(198\) | −3.80198e11 | −0.0887874 | ||||||||
\(199\) | −7.42261e12 | −1.68603 | −0.843014 | − | 0.537891i | \(-0.819221\pi\) | ||||
−0.843014 | + | 0.537891i | \(0.819221\pi\) | |||||||
\(200\) | 9.53359e11 | 0.210665 | ||||||||
\(201\) | −1.23608e12 | −0.265747 | ||||||||
\(202\) | −1.10437e12 | −0.231037 | ||||||||
\(203\) | −8.59291e11 | −0.174949 | ||||||||
\(204\) | 2.72772e12 | 0.540548 | ||||||||
\(205\) | 4.17572e12 | 0.805536 | ||||||||
\(206\) | −4.80821e11 | −0.0903055 | ||||||||
\(207\) | −2.16856e12 | −0.396584 | ||||||||
\(208\) | 1.36337e12 | 0.242810 | ||||||||
\(209\) | 1.17522e13 | 2.03852 | ||||||||
\(210\) | −1.43434e11 | −0.0242351 | ||||||||
\(211\) | −6.43036e11 | −0.105848 | −0.0529239 | − | 0.998599i | \(-0.516854\pi\) | ||||
−0.0529239 | + | 0.998599i | \(0.516854\pi\) | |||||||
\(212\) | −2.97123e12 | −0.476529 | ||||||||
\(213\) | 6.80743e11 | 0.106389 | ||||||||
\(214\) | 1.06861e12 | 0.162759 | ||||||||
\(215\) | 3.76929e12 | 0.559561 | ||||||||
\(216\) | −4.62838e11 | −0.0669782 | ||||||||
\(217\) | 3.49757e12 | 0.493444 | ||||||||
\(218\) | −1.73530e12 | −0.238706 | ||||||||
\(219\) | −1.90616e12 | −0.255692 | ||||||||
\(220\) | 7.00993e12 | 0.917041 | ||||||||
\(221\) | −2.02718e12 | −0.258663 | ||||||||
\(222\) | 1.26777e12 | 0.157797 | ||||||||
\(223\) | −1.22383e13 | −1.48609 | −0.743045 | − | 0.669242i | \(-0.766619\pi\) | ||||
−0.743045 | + | 0.669242i | \(0.766619\pi\) | |||||||
\(224\) | −1.62191e12 | −0.192159 | ||||||||
\(225\) | −1.74525e12 | −0.201769 | ||||||||
\(226\) | −2.81876e12 | −0.318026 | ||||||||
\(227\) | −1.05402e12 | −0.116067 | −0.0580334 | − | 0.998315i | \(-0.518483\pi\) | ||||
−0.0580334 | + | 0.998315i | \(0.518483\pi\) | |||||||
\(228\) | 7.03980e12 | 0.756691 | ||||||||
\(229\) | 3.31679e12 | 0.348035 | 0.174018 | − | 0.984743i | \(-0.444325\pi\) | ||||
0.174018 | + | 0.984743i | \(0.444325\pi\) | |||||||
\(230\) | −1.28977e12 | −0.132133 | ||||||||
\(231\) | 3.28703e12 | 0.328805 | ||||||||
\(232\) | −1.64915e12 | −0.161093 | ||||||||
\(233\) | −1.63955e13 | −1.56410 | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||||
−0.782052 | + | 0.623213i | \(0.785827\pi\) | |||||||
\(234\) | 1.69255e11 | 0.0157708 | ||||||||
\(235\) | −5.86748e12 | −0.534045 | ||||||||
\(236\) | −1.40228e13 | −1.24686 | ||||||||
\(237\) | −5.14107e12 | −0.446619 | ||||||||
\(238\) | 7.60733e11 | 0.0645742 | ||||||||
\(239\) | −1.28637e13 | −1.06703 | −0.533516 | − | 0.845790i | \(-0.679130\pi\) | ||||
−0.533516 | + | 0.845790i | \(0.679130\pi\) | |||||||
\(240\) | 4.05926e12 | 0.329067 | ||||||||
\(241\) | −5.00644e12 | −0.396675 | −0.198338 | − | 0.980134i | \(-0.563554\pi\) | ||||
−0.198338 | + | 0.980134i | \(0.563554\pi\) | |||||||
\(242\) | 2.89959e12 | 0.224571 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.51656e13 | 1.12257 | ||||||||
\(245\) | 1.24007e12 | 0.0897494 | ||||||||
\(246\) | 1.84911e12 | 0.130864 | ||||||||
\(247\) | −5.23181e12 | −0.362092 | ||||||||
\(248\) | 6.71254e12 | 0.454363 | ||||||||
\(249\) | −2.64747e12 | −0.175281 | ||||||||
\(250\) | −2.75285e12 | −0.178284 | ||||||||
\(251\) | −1.74289e13 | −1.10424 | −0.552121 | − | 0.833764i | \(-0.686182\pi\) | ||||
−0.552121 | + | 0.833764i | \(0.686182\pi\) | |||||||
\(252\) | 1.96899e12 | 0.122051 | ||||||||
\(253\) | 2.95574e13 | 1.79268 | ||||||||
\(254\) | −2.58993e12 | −0.153710 | ||||||||
\(255\) | −6.03564e12 | −0.350552 | ||||||||
\(256\) | 1.23486e13 | 0.701936 | ||||||||
\(257\) | −1.01846e13 | −0.566644 | −0.283322 | − | 0.959025i | \(-0.591436\pi\) | ||||
−0.283322 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(258\) | 1.66913e12 | 0.0909039 | ||||||||
\(259\) | −1.09606e13 | −0.584368 | ||||||||
\(260\) | −3.12065e12 | −0.162889 | ||||||||
\(261\) | 3.01900e12 | 0.154291 | ||||||||
\(262\) | 2.14973e12 | 0.107579 | ||||||||
\(263\) | 6.78972e12 | 0.332733 | 0.166366 | − | 0.986064i | \(-0.446797\pi\) | ||||
0.166366 | + | 0.986064i | \(0.446797\pi\) | |||||||
\(264\) | 6.30847e12 | 0.302763 | ||||||||
\(265\) | 6.57445e12 | 0.309034 | ||||||||
\(266\) | 1.96333e12 | 0.0903948 | ||||||||
\(267\) | 1.72017e13 | 0.775816 | ||||||||
\(268\) | 1.00921e13 | 0.445904 | ||||||||
\(269\) | 2.94099e13 | 1.27308 | 0.636540 | − | 0.771244i | \(-0.280365\pi\) | ||||
0.636540 | + | 0.771244i | \(0.280365\pi\) | |||||||
\(270\) | 5.03934e11 | 0.0213734 | ||||||||
\(271\) | −3.10163e13 | −1.28902 | −0.644509 | − | 0.764596i | \(-0.722938\pi\) | ||||
−0.644509 | + | 0.764596i | \(0.722938\pi\) | |||||||
\(272\) | −2.15292e13 | −0.876797 | ||||||||
\(273\) | −1.46331e12 | −0.0584038 | ||||||||
\(274\) | −3.01522e12 | −0.117948 | ||||||||
\(275\) | 2.37878e13 | 0.912060 | ||||||||
\(276\) | 1.77055e13 | 0.665438 | ||||||||
\(277\) | 1.12341e13 | 0.413903 | 0.206952 | − | 0.978351i | \(-0.433646\pi\) | ||||
0.206952 | + | 0.978351i | \(0.433646\pi\) | |||||||
\(278\) | 5.45304e12 | 0.196966 | ||||||||
\(279\) | −1.22882e13 | −0.435177 | ||||||||
\(280\) | 2.37994e12 | 0.0826411 | ||||||||
\(281\) | 2.65890e13 | 0.905351 | 0.452676 | − | 0.891675i | \(-0.350470\pi\) | ||||
0.452676 | + | 0.891675i | \(0.350470\pi\) | |||||||
\(282\) | −2.59826e12 | −0.0867587 | ||||||||
\(283\) | 1.78795e13 | 0.585503 | 0.292751 | − | 0.956189i | \(-0.405429\pi\) | ||||
0.292751 | + | 0.956189i | \(0.405429\pi\) | |||||||
\(284\) | −5.55800e12 | −0.178512 | ||||||||
\(285\) | −1.55770e13 | −0.490723 | ||||||||
\(286\) | −2.30694e12 | −0.0712892 | ||||||||
\(287\) | −1.59866e13 | −0.484626 | ||||||||
\(288\) | 5.69833e12 | 0.169469 | ||||||||
\(289\) | −2.26049e12 | −0.0659577 | ||||||||
\(290\) | 1.79558e12 | 0.0514062 | ||||||||
\(291\) | 1.99804e13 | 0.561297 | ||||||||
\(292\) | 1.55631e13 | 0.429031 | ||||||||
\(293\) | −1.90224e13 | −0.514627 | −0.257314 | − | 0.966328i | \(-0.582837\pi\) | ||||
−0.257314 | + | 0.966328i | \(0.582837\pi\) | |||||||
\(294\) | 5.49132e11 | 0.0145803 | ||||||||
\(295\) | 3.10283e13 | 0.808605 | ||||||||
\(296\) | −2.10356e13 | −0.538085 | ||||||||
\(297\) | −1.15485e13 | −0.289978 | ||||||||
\(298\) | 1.11045e13 | 0.273721 | ||||||||
\(299\) | −1.31583e13 | −0.318425 | ||||||||
\(300\) | 1.42493e13 | 0.338553 | ||||||||
\(301\) | −1.44306e13 | −0.336643 | ||||||||
\(302\) | 1.22406e13 | 0.280392 | ||||||||
\(303\) | −3.35453e13 | −0.754565 | ||||||||
\(304\) | −5.55633e13 | −1.22739 | ||||||||
\(305\) | −3.35568e13 | −0.728001 | ||||||||
\(306\) | −2.67273e12 | −0.0569491 | ||||||||
\(307\) | −2.84379e13 | −0.595164 | −0.297582 | − | 0.954696i | \(-0.596180\pi\) | ||||
−0.297582 | + | 0.954696i | \(0.596180\pi\) | |||||||
\(308\) | −2.68373e13 | −0.551709 | ||||||||
\(309\) | −1.46049e13 | −0.294936 | ||||||||
\(310\) | −7.30855e12 | −0.144991 | ||||||||
\(311\) | 2.74409e13 | 0.534831 | 0.267416 | − | 0.963581i | \(-0.413830\pi\) | ||||
0.267416 | + | 0.963581i | \(0.413830\pi\) | |||||||
\(312\) | −2.80838e12 | −0.0537782 | ||||||||
\(313\) | −4.29785e13 | −0.808643 | −0.404322 | − | 0.914617i | \(-0.632492\pi\) | ||||
−0.404322 | + | 0.914617i | \(0.632492\pi\) | |||||||
\(314\) | −7.01543e12 | −0.129700 | ||||||||
\(315\) | −4.35680e12 | −0.0791515 | ||||||||
\(316\) | 4.19748e13 | 0.749393 | ||||||||
\(317\) | 6.59529e13 | 1.15720 | 0.578600 | − | 0.815612i | \(-0.303599\pi\) | ||||
0.578600 | + | 0.815612i | \(0.303599\pi\) | |||||||
\(318\) | 2.91133e12 | 0.0502044 | ||||||||
\(319\) | −4.11488e13 | −0.697443 | ||||||||
\(320\) | −3.08222e13 | −0.513498 | ||||||||
\(321\) | 3.24591e13 | 0.531568 | ||||||||
\(322\) | 4.93787e12 | 0.0794936 | ||||||||
\(323\) | 8.26161e13 | 1.30753 | ||||||||
\(324\) | −6.91778e12 | −0.107639 | ||||||||
\(325\) | −1.05897e13 | −0.162004 | ||||||||
\(326\) | −1.61998e13 | −0.243676 | ||||||||
\(327\) | −5.27098e13 | −0.779612 | ||||||||
\(328\) | −3.06815e13 | −0.446242 | ||||||||
\(329\) | 2.24635e13 | 0.321292 | ||||||||
\(330\) | −6.86860e12 | −0.0966143 | ||||||||
\(331\) | −1.19488e14 | −1.65299 | −0.826495 | − | 0.562944i | \(-0.809669\pi\) | ||||
−0.826495 | + | 0.562944i | \(0.809669\pi\) | |||||||
\(332\) | 2.16156e13 | 0.294108 | ||||||||
\(333\) | 3.85086e13 | 0.515364 | ||||||||
\(334\) | 2.55800e12 | 0.0336740 | ||||||||
\(335\) | −2.23309e13 | −0.289174 | ||||||||
\(336\) | −1.55408e13 | −0.197973 | ||||||||
\(337\) | 6.39053e13 | 0.800890 | 0.400445 | − | 0.916321i | \(-0.368856\pi\) | ||||
0.400445 | + | 0.916321i | \(0.368856\pi\) | |||||||
\(338\) | −1.33103e13 | −0.164114 | ||||||||
\(339\) | −8.56199e13 | −1.03867 | ||||||||
\(340\) | 4.92786e13 | 0.588199 | ||||||||
\(341\) | 1.67488e14 | 1.96714 | ||||||||
\(342\) | −6.89787e12 | −0.0797208 | ||||||||
\(343\) | −4.74756e12 | −0.0539949 | ||||||||
\(344\) | −2.76953e13 | −0.309980 | ||||||||
\(345\) | −3.91769e13 | −0.431544 | ||||||||
\(346\) | 1.23158e13 | 0.133520 | ||||||||
\(347\) | 9.53921e13 | 1.01789 | 0.508944 | − | 0.860800i | \(-0.330036\pi\) | ||||
0.508944 | + | 0.860800i | \(0.330036\pi\) | |||||||
\(348\) | −2.46489e13 | −0.258888 | ||||||||
\(349\) | 1.14672e13 | 0.118554 | 0.0592772 | − | 0.998242i | \(-0.481120\pi\) | ||||
0.0592772 | + | 0.998242i | \(0.481120\pi\) | |||||||
\(350\) | 3.97398e12 | 0.0404438 | ||||||||
\(351\) | 5.14113e12 | 0.0515074 | ||||||||
\(352\) | −7.76681e13 | −0.766052 | ||||||||
\(353\) | 1.96672e14 | 1.90977 | 0.954886 | − | 0.296971i | \(-0.0959765\pi\) | ||||
0.954886 | + | 0.296971i | \(0.0959765\pi\) | |||||||
\(354\) | 1.37401e13 | 0.131363 | ||||||||
\(355\) | 1.22982e13 | 0.115767 | ||||||||
\(356\) | −1.40445e14 | −1.30176 | ||||||||
\(357\) | 2.31073e13 | 0.210899 | ||||||||
\(358\) | 1.45361e11 | 0.00130644 | ||||||||
\(359\) | 3.53266e13 | 0.312668 | 0.156334 | − | 0.987704i | \(-0.450032\pi\) | ||||
0.156334 | + | 0.987704i | \(0.450032\pi\) | |||||||
\(360\) | −8.36157e12 | −0.0728826 | ||||||||
\(361\) | 9.67283e13 | 0.830355 | ||||||||
\(362\) | 1.40470e13 | 0.118765 | ||||||||
\(363\) | 8.80752e13 | 0.733444 | ||||||||
\(364\) | 1.19473e13 | 0.0979972 | ||||||||
\(365\) | −3.44364e13 | −0.278232 | ||||||||
\(366\) | −1.48598e13 | −0.118268 | ||||||||
\(367\) | 1.65633e14 | 1.29862 | 0.649311 | − | 0.760523i | \(-0.275057\pi\) | ||||
0.649311 | + | 0.760523i | \(0.275057\pi\) | |||||||
\(368\) | −1.39745e14 | −1.07937 | ||||||||
\(369\) | 5.61667e13 | 0.427400 | ||||||||
\(370\) | 2.29034e13 | 0.171708 | ||||||||
\(371\) | −2.51701e13 | −0.185921 | ||||||||
\(372\) | 1.00329e14 | 0.730194 | ||||||||
\(373\) | 6.00067e13 | 0.430330 | 0.215165 | − | 0.976578i | \(-0.430971\pi\) | ||||
0.215165 | + | 0.976578i | \(0.430971\pi\) | |||||||
\(374\) | 3.64292e13 | 0.257428 | ||||||||
\(375\) | −8.36179e13 | −0.582274 | ||||||||
\(376\) | 4.31119e13 | 0.295845 | ||||||||
\(377\) | 1.83185e13 | 0.123883 | ||||||||
\(378\) | −1.92930e12 | −0.0128586 | ||||||||
\(379\) | −2.02889e14 | −1.33273 | −0.666367 | − | 0.745624i | \(-0.732152\pi\) | ||||
−0.666367 | + | 0.745624i | \(0.732152\pi\) | |||||||
\(380\) | 1.27180e14 | 0.823396 | ||||||||
\(381\) | −7.86690e13 | −0.502014 | ||||||||
\(382\) | 4.62009e13 | 0.290604 | ||||||||
\(383\) | −2.99017e14 | −1.85397 | −0.926985 | − | 0.375099i | \(-0.877609\pi\) | ||||
−0.926985 | + | 0.375099i | \(0.877609\pi\) | |||||||
\(384\) | −6.16743e13 | −0.376949 | ||||||||
\(385\) | 5.93830e13 | 0.357790 | ||||||||
\(386\) | −3.31229e13 | −0.196742 | ||||||||
\(387\) | 5.06999e13 | 0.296891 | ||||||||
\(388\) | −1.63132e14 | −0.941813 | ||||||||
\(389\) | −2.48539e14 | −1.41472 | −0.707362 | − | 0.706852i | \(-0.750115\pi\) | ||||
−0.707362 | + | 0.706852i | \(0.750115\pi\) | |||||||
\(390\) | 3.05774e12 | 0.0171611 | ||||||||
\(391\) | 2.07784e14 | 1.14985 | ||||||||
\(392\) | −9.11152e12 | −0.0497184 | ||||||||
\(393\) | 6.52980e13 | 0.351350 | ||||||||
\(394\) | 5.52916e12 | 0.0293380 | ||||||||
\(395\) | −9.28777e13 | −0.485990 | ||||||||
\(396\) | 9.42891e13 | 0.486562 | ||||||||
\(397\) | −1.74060e14 | −0.885833 | −0.442917 | − | 0.896563i | \(-0.646056\pi\) | ||||
−0.442917 | + | 0.896563i | \(0.646056\pi\) | |||||||
\(398\) | −5.93809e13 | −0.298051 | ||||||||
\(399\) | 5.96361e13 | 0.295228 | ||||||||
\(400\) | −1.12466e14 | −0.549151 | ||||||||
\(401\) | 2.15357e14 | 1.03720 | 0.518602 | − | 0.855016i | \(-0.326453\pi\) | ||||
0.518602 | + | 0.855016i | \(0.326453\pi\) | |||||||
\(402\) | −9.88866e12 | −0.0469779 | ||||||||
\(403\) | −7.45617e13 | −0.349412 | ||||||||
\(404\) | 2.73884e14 | 1.26610 | ||||||||
\(405\) | 1.53070e13 | 0.0698051 | ||||||||
\(406\) | −6.87433e12 | −0.0309270 | ||||||||
\(407\) | −5.24871e14 | −2.32961 | ||||||||
\(408\) | 4.43475e13 | 0.194195 | ||||||||
\(409\) | −2.90910e14 | −1.25684 | −0.628422 | − | 0.777873i | \(-0.716299\pi\) | ||||
−0.628422 | + | 0.777873i | \(0.716299\pi\) | |||||||
\(410\) | 3.34057e13 | 0.142400 | ||||||||
\(411\) | −9.15873e13 | −0.385217 | ||||||||
\(412\) | 1.19244e14 | 0.494881 | ||||||||
\(413\) | −1.18791e14 | −0.486472 | ||||||||
\(414\) | −1.73485e13 | −0.0701068 | ||||||||
\(415\) | −4.78288e13 | −0.190733 | ||||||||
\(416\) | 3.45760e13 | 0.136070 | ||||||||
\(417\) | 1.65636e14 | 0.643290 | ||||||||
\(418\) | 9.40177e13 | 0.360363 | ||||||||
\(419\) | 1.64921e14 | 0.623875 | 0.311938 | − | 0.950103i | \(-0.399022\pi\) | ||||
0.311938 | + | 0.950103i | \(0.399022\pi\) | |||||||
\(420\) | 3.55715e13 | 0.132810 | ||||||||
\(421\) | 2.67118e14 | 0.984353 | 0.492177 | − | 0.870495i | \(-0.336201\pi\) | ||||
0.492177 | + | 0.870495i | \(0.336201\pi\) | |||||||
\(422\) | −5.14429e12 | −0.0187114 | ||||||||
\(423\) | −7.89222e13 | −0.283353 | ||||||||
\(424\) | −4.83065e13 | −0.171196 | ||||||||
\(425\) | 1.67224e14 | 0.585005 | ||||||||
\(426\) | 5.44594e12 | 0.0188070 | ||||||||
\(427\) | 1.28471e14 | 0.437979 | ||||||||
\(428\) | −2.65016e14 | −0.891930 | ||||||||
\(429\) | −7.00734e13 | −0.232830 | ||||||||
\(430\) | 3.01543e13 | 0.0989174 | ||||||||
\(431\) | −5.64399e14 | −1.82794 | −0.913968 | − | 0.405787i | \(-0.866998\pi\) | ||||
−0.913968 | + | 0.405787i | \(0.866998\pi\) | |||||||
\(432\) | 5.46002e13 | 0.174596 | ||||||||
\(433\) | −1.37266e14 | −0.433390 | −0.216695 | − | 0.976239i | \(-0.569528\pi\) | ||||
−0.216695 | + | 0.976239i | \(0.569528\pi\) | |||||||
\(434\) | 2.79806e13 | 0.0872294 | ||||||||
\(435\) | 5.45407e13 | 0.167892 | ||||||||
\(436\) | 4.30355e14 | 1.30813 | ||||||||
\(437\) | 5.36256e14 | 1.60962 | ||||||||
\(438\) | −1.52493e13 | −0.0452003 | ||||||||
\(439\) | 8.97819e12 | 0.0262805 | 0.0131403 | − | 0.999914i | \(-0.495817\pi\) | ||||
0.0131403 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(440\) | 1.13968e14 | 0.329452 | ||||||||
\(441\) | 1.66799e13 | 0.0476190 | ||||||||
\(442\) | −1.62174e13 | −0.0457256 | ||||||||
\(443\) | −4.04100e14 | −1.12530 | −0.562650 | − | 0.826696i | \(-0.690218\pi\) | ||||
−0.562650 | + | 0.826696i | \(0.690218\pi\) | |||||||
\(444\) | −3.14407e14 | −0.864742 | ||||||||
\(445\) | 3.10763e14 | 0.844207 | ||||||||
\(446\) | −9.79065e13 | −0.262706 | ||||||||
\(447\) | 3.37299e14 | 0.893971 | ||||||||
\(448\) | 1.18002e14 | 0.308930 | ||||||||
\(449\) | −6.27613e14 | −1.62307 | −0.811534 | − | 0.584305i | \(-0.801367\pi\) | ||||
−0.811534 | + | 0.584305i | \(0.801367\pi\) | |||||||
\(450\) | −1.39620e13 | −0.0356681 | ||||||||
\(451\) | −7.65551e14 | −1.93198 | ||||||||
\(452\) | 6.99053e14 | 1.74280 | ||||||||
\(453\) | 3.71809e14 | 0.915756 | ||||||||
\(454\) | −8.43219e12 | −0.0205179 | ||||||||
\(455\) | −2.64359e13 | −0.0635523 | ||||||||
\(456\) | 1.14454e14 | 0.271846 | ||||||||
\(457\) | 3.01238e14 | 0.706921 | 0.353460 | − | 0.935449i | \(-0.385005\pi\) | ||||
0.353460 | + | 0.935449i | \(0.385005\pi\) | |||||||
\(458\) | 2.65343e13 | 0.0615245 | ||||||||
\(459\) | −8.11841e13 | −0.185995 | ||||||||
\(460\) | 3.19864e14 | 0.724098 | ||||||||
\(461\) | 3.50379e14 | 0.783759 | 0.391880 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391880 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(462\) | 2.62963e13 | 0.0581250 | ||||||||
\(463\) | 4.90390e14 | 1.07114 | 0.535569 | − | 0.844491i | \(-0.320097\pi\) | ||||
0.535569 | + | 0.844491i | \(0.320097\pi\) | |||||||
\(464\) | 1.94548e14 | 0.419930 | ||||||||
\(465\) | −2.21997e14 | −0.473539 | ||||||||
\(466\) | −1.31164e14 | −0.276497 | ||||||||
\(467\) | 6.80842e14 | 1.41842 | 0.709208 | − | 0.704999i | \(-0.249053\pi\) | ||||
0.709208 | + | 0.704999i | \(0.249053\pi\) | |||||||
\(468\) | −4.19753e13 | −0.0864254 | ||||||||
\(469\) | 8.54931e13 | 0.173972 | ||||||||
\(470\) | −4.69398e13 | −0.0944067 | ||||||||
\(471\) | −2.13094e14 | −0.423600 | ||||||||
\(472\) | −2.27984e14 | −0.447943 | ||||||||
\(473\) | −6.91038e14 | −1.34204 | ||||||||
\(474\) | −4.11285e13 | −0.0789519 | ||||||||
\(475\) | 4.31577e14 | 0.818924 | ||||||||
\(476\) | −1.88662e14 | −0.353872 | ||||||||
\(477\) | 8.84315e13 | 0.163967 | ||||||||
\(478\) | −1.02910e14 | −0.188626 | ||||||||
\(479\) | 7.91988e14 | 1.43507 | 0.717535 | − | 0.696523i | \(-0.245270\pi\) | ||||
0.717535 | + | 0.696523i | \(0.245270\pi\) | |||||||
\(480\) | 1.02945e14 | 0.184408 | ||||||||
\(481\) | 2.33660e14 | 0.413796 | ||||||||
\(482\) | −4.00515e13 | −0.0701229 | ||||||||
\(483\) | 1.49988e14 | 0.259625 | ||||||||
\(484\) | −7.19099e14 | −1.23066 | ||||||||
\(485\) | 3.60962e14 | 0.610777 | ||||||||
\(486\) | 6.77831e12 | 0.0113402 | ||||||||
\(487\) | −4.92313e14 | −0.814388 | −0.407194 | − | 0.913342i | \(-0.633493\pi\) | ||||
−0.407194 | + | 0.913342i | \(0.633493\pi\) | |||||||
\(488\) | 2.46562e14 | 0.403290 | ||||||||
\(489\) | −4.92069e14 | −0.795842 | ||||||||
\(490\) | 9.92053e12 | 0.0158656 | ||||||||
\(491\) | −1.07948e15 | −1.70713 | −0.853564 | − | 0.520989i | \(-0.825563\pi\) | ||||
−0.853564 | + | 0.520989i | \(0.825563\pi\) | |||||||
\(492\) | −4.58579e14 | −0.717144 | ||||||||
\(493\) | −2.89269e14 | −0.447347 | ||||||||
\(494\) | −4.18545e13 | −0.0640094 | ||||||||
\(495\) | −2.08634e14 | −0.315541 | ||||||||
\(496\) | −7.91867e14 | −1.18441 | ||||||||
\(497\) | −4.70833e13 | −0.0696477 | ||||||||
\(498\) | −2.11798e13 | −0.0309856 | ||||||||
\(499\) | −1.04552e15 | −1.51280 | −0.756400 | − | 0.654110i | \(-0.773044\pi\) | ||||
−0.756400 | + | 0.654110i | \(0.773044\pi\) | |||||||
\(500\) | 6.82707e14 | 0.977011 | ||||||||
\(501\) | 7.76992e13 | 0.109979 | ||||||||
\(502\) | −1.39431e14 | −0.195204 | ||||||||
\(503\) | −4.47866e14 | −0.620189 | −0.310094 | − | 0.950706i | \(-0.600361\pi\) | ||||
−0.310094 | + | 0.950706i | \(0.600361\pi\) | |||||||
\(504\) | 3.20120e13 | 0.0438475 | ||||||||
\(505\) | −6.06023e14 | −0.821082 | ||||||||
\(506\) | 2.36460e14 | 0.316905 | ||||||||
\(507\) | −4.04300e14 | −0.535994 | ||||||||
\(508\) | 6.42301e14 | 0.842342 | ||||||||
\(509\) | 4.18511e14 | 0.542949 | 0.271475 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271475 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(510\) | −4.82851e13 | −0.0619694 | ||||||||
\(511\) | 1.31839e14 | 0.167390 | ||||||||
\(512\) | 6.18579e14 | 0.776980 | ||||||||
\(513\) | −2.09523e14 | −0.260367 | ||||||||
\(514\) | −8.14765e13 | −0.100169 | ||||||||
\(515\) | −2.63851e14 | −0.320936 | ||||||||
\(516\) | −4.13945e14 | −0.498161 | ||||||||
\(517\) | 1.07571e15 | 1.28084 | ||||||||
\(518\) | −8.76849e13 | −0.103303 | ||||||||
\(519\) | 3.74093e14 | 0.436073 | ||||||||
\(520\) | −5.07358e13 | −0.0585189 | ||||||||
\(521\) | 7.11671e14 | 0.812216 | 0.406108 | − | 0.913825i | \(-0.366886\pi\) | ||||
0.406108 | + | 0.913825i | \(0.366886\pi\) | |||||||
\(522\) | 2.41520e13 | 0.0272750 | ||||||||
\(523\) | −9.56769e14 | −1.06917 | −0.534586 | − | 0.845114i | \(-0.679533\pi\) | ||||
−0.534586 | + | 0.845114i | \(0.679533\pi\) | |||||||
\(524\) | −5.33132e14 | −0.589539 | ||||||||
\(525\) | 1.20710e14 | 0.132089 | ||||||||
\(526\) | 5.43178e13 | 0.0588194 | ||||||||
\(527\) | 1.17741e15 | 1.26174 | ||||||||
\(528\) | −7.44199e14 | −0.789228 | ||||||||
\(529\) | 3.95901e14 | 0.415509 | ||||||||
\(530\) | 5.25956e13 | 0.0546301 | ||||||||
\(531\) | 4.17355e14 | 0.429028 | ||||||||
\(532\) | −4.86905e14 | −0.495371 | ||||||||
\(533\) | 3.40805e14 | 0.343168 | ||||||||
\(534\) | 1.37613e14 | 0.137146 | ||||||||
\(535\) | 5.86401e14 | 0.578427 | ||||||||
\(536\) | 1.64078e14 | 0.160194 | ||||||||
\(537\) | 4.41533e12 | 0.00426683 | ||||||||
\(538\) | 2.35279e14 | 0.225051 | ||||||||
\(539\) | −2.27346e14 | −0.215253 | ||||||||
\(540\) | −1.24976e14 | −0.117128 | ||||||||
\(541\) | 2.13753e14 | 0.198302 | 0.0991509 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991509 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(542\) | −2.48131e14 | −0.227868 | ||||||||
\(543\) | 4.26678e14 | 0.387884 | ||||||||
\(544\) | −5.45994e14 | −0.491353 | ||||||||
\(545\) | −9.52247e14 | −0.848338 | ||||||||
\(546\) | −1.17065e13 | −0.0103244 | ||||||||
\(547\) | 1.98142e15 | 1.73000 | 0.865001 | − | 0.501771i | \(-0.167318\pi\) | ||||
0.865001 | + | 0.501771i | \(0.167318\pi\) | |||||||
\(548\) | 7.47775e14 | 0.646365 | ||||||||
\(549\) | −4.51366e14 | −0.386261 | ||||||||
\(550\) | 1.90302e14 | 0.161231 | ||||||||
\(551\) | −7.46556e14 | −0.626223 | ||||||||
\(552\) | 2.87857e14 | 0.239062 | ||||||||
\(553\) | 3.55580e14 | 0.292381 | ||||||||
\(554\) | 8.98726e13 | 0.0731684 | ||||||||
\(555\) | 6.95690e14 | 0.560795 | ||||||||
\(556\) | −1.35235e15 | −1.07939 | ||||||||
\(557\) | −1.45121e15 | −1.14691 | −0.573453 | − | 0.819238i | \(-0.694397\pi\) | ||||
−0.573453 | + | 0.819238i | \(0.694397\pi\) | |||||||
\(558\) | −9.83058e13 | −0.0769291 | ||||||||
\(559\) | 3.07634e14 | 0.238380 | ||||||||
\(560\) | −2.80757e14 | −0.215425 | ||||||||
\(561\) | 1.10654e15 | 0.840757 | ||||||||
\(562\) | 2.12712e14 | 0.160045 | ||||||||
\(563\) | 1.69873e15 | 1.26569 | 0.632846 | − | 0.774278i | \(-0.281887\pi\) | ||||
0.632846 | + | 0.774278i | \(0.281887\pi\) | |||||||
\(564\) | 6.44369e14 | 0.475444 | ||||||||
\(565\) | −1.54680e15 | −1.13023 | ||||||||
\(566\) | 1.43036e14 | 0.103503 | ||||||||
\(567\) | −5.86024e13 | −0.0419961 | ||||||||
\(568\) | −9.03623e13 | −0.0641315 | ||||||||
\(569\) | −1.69686e14 | −0.119270 | −0.0596348 | − | 0.998220i | \(-0.518994\pi\) | ||||
−0.0596348 | + | 0.998220i | \(0.518994\pi\) | |||||||
\(570\) | −1.24616e14 | −0.0867484 | ||||||||
\(571\) | 1.03308e15 | 0.712254 | 0.356127 | − | 0.934438i | \(-0.384097\pi\) | ||||
0.356127 | + | 0.934438i | \(0.384097\pi\) | |||||||
\(572\) | 5.72122e14 | 0.390670 | ||||||||
\(573\) | 1.40335e15 | 0.949109 | ||||||||
\(574\) | −1.27893e14 | −0.0856705 | ||||||||
\(575\) | 1.08544e15 | 0.720166 | ||||||||
\(576\) | −4.14583e14 | −0.272451 | ||||||||
\(577\) | 1.45083e15 | 0.944384 | 0.472192 | − | 0.881496i | \(-0.343463\pi\) | ||||
0.472192 | + | 0.881496i | \(0.343463\pi\) | |||||||
\(578\) | −1.80840e13 | −0.0116598 | ||||||||
\(579\) | −1.00611e15 | −0.642557 | ||||||||
\(580\) | −4.45304e14 | −0.281710 | ||||||||
\(581\) | 1.83111e14 | 0.114748 | ||||||||
\(582\) | 1.59843e14 | 0.0992241 | ||||||||
\(583\) | −1.20532e15 | −0.741182 | ||||||||
\(584\) | 2.53025e14 | 0.154132 | ||||||||
\(585\) | 9.28788e13 | 0.0560479 | ||||||||
\(586\) | −1.52179e14 | −0.0909741 | ||||||||
\(587\) | −1.76163e15 | −1.04329 | −0.521646 | − | 0.853162i | \(-0.674682\pi\) | ||||
−0.521646 | + | 0.853162i | \(0.674682\pi\) | |||||||
\(588\) | −1.36185e14 | −0.0799012 | ||||||||
\(589\) | 3.03871e15 | 1.76626 | ||||||||
\(590\) | 2.48226e14 | 0.142943 | ||||||||
\(591\) | 1.67948e14 | 0.0958174 | ||||||||
\(592\) | 2.48154e15 | 1.40266 | ||||||||
\(593\) | −2.51119e15 | −1.40630 | −0.703151 | − | 0.711041i | \(-0.748224\pi\) | ||||
−0.703151 | + | 0.711041i | \(0.748224\pi\) | |||||||
\(594\) | −9.23881e13 | −0.0512614 | ||||||||
\(595\) | 4.17453e14 | 0.229490 | ||||||||
\(596\) | −2.75391e15 | −1.50001 | ||||||||
\(597\) | −1.80370e15 | −0.973429 | ||||||||
\(598\) | −1.05266e14 | −0.0562902 | ||||||||
\(599\) | −2.36908e15 | −1.25525 | −0.627627 | − | 0.778514i | \(-0.715974\pi\) | ||||
−0.627627 | + | 0.778514i | \(0.715974\pi\) | |||||||
\(600\) | 2.31666e14 | 0.121627 | ||||||||
\(601\) | −2.51626e15 | −1.30902 | −0.654509 | − | 0.756054i | \(-0.727125\pi\) | ||||
−0.654509 | + | 0.756054i | \(0.727125\pi\) | |||||||
\(602\) | −1.15445e14 | −0.0595106 | ||||||||
\(603\) | −3.00368e14 | −0.153429 | ||||||||
\(604\) | −3.03568e15 | −1.53657 | ||||||||
\(605\) | 1.59115e15 | 0.798100 | ||||||||
\(606\) | −2.68362e14 | −0.133390 | ||||||||
\(607\) | 3.45512e15 | 1.70186 | 0.850932 | − | 0.525276i | \(-0.176038\pi\) | ||||
0.850932 | + | 0.525276i | \(0.176038\pi\) | |||||||
\(608\) | −1.40912e15 | −0.687825 | ||||||||
\(609\) | −2.08808e14 | −0.101007 | ||||||||
\(610\) | −2.68455e14 | −0.128694 | ||||||||
\(611\) | −4.78880e14 | −0.227510 | ||||||||
\(612\) | 6.62837e14 | 0.312086 | ||||||||
\(613\) | −3.60688e15 | −1.68306 | −0.841529 | − | 0.540212i | \(-0.818344\pi\) | ||||
−0.841529 | + | 0.540212i | \(0.818344\pi\) | |||||||
\(614\) | −2.27503e14 | −0.105211 | ||||||||
\(615\) | 1.01470e15 | 0.465076 | ||||||||
\(616\) | −4.36323e14 | −0.198205 | ||||||||
\(617\) | 2.66149e15 | 1.19827 | 0.599137 | − | 0.800646i | \(-0.295510\pi\) | ||||
0.599137 | + | 0.800646i | \(0.295510\pi\) | |||||||
\(618\) | −1.16840e14 | −0.0521379 | ||||||||
\(619\) | −1.02858e14 | −0.0454925 | −0.0227463 | − | 0.999741i | \(-0.507241\pi\) | ||||
−0.0227463 | + | 0.999741i | \(0.507241\pi\) | |||||||
\(620\) | 1.81252e15 | 0.794563 | ||||||||
\(621\) | −5.26961e14 | −0.228968 | ||||||||
\(622\) | 2.19527e14 | 0.0945457 | ||||||||
\(623\) | −1.18975e15 | −0.507891 | ||||||||
\(624\) | 3.31300e14 | 0.140187 | ||||||||
\(625\) | −6.74619e13 | −0.0282956 | ||||||||
\(626\) | −3.43828e14 | −0.142949 | ||||||||
\(627\) | 2.85579e15 | 1.17694 | ||||||||
\(628\) | 1.73983e15 | 0.710768 | ||||||||
\(629\) | −3.68975e15 | −1.49423 | ||||||||
\(630\) | −3.48544e13 | −0.0139921 | ||||||||
\(631\) | 2.00659e14 | 0.0798541 | 0.0399270 | − | 0.999203i | \(-0.487287\pi\) | ||||
0.0399270 | + | 0.999203i | \(0.487287\pi\) | |||||||
\(632\) | 6.82429e14 | 0.269224 | ||||||||
\(633\) | −1.56258e14 | −0.0611112 | ||||||||
\(634\) | 5.27623e14 | 0.204566 | ||||||||
\(635\) | −1.42122e15 | −0.546269 | ||||||||
\(636\) | −7.22009e14 | −0.275124 | ||||||||
\(637\) | 1.01209e14 | 0.0382343 | ||||||||
\(638\) | −3.29191e14 | −0.123292 | ||||||||
\(639\) | 1.65421e14 | 0.0614235 | ||||||||
\(640\) | −1.11420e15 | −0.410178 | ||||||||
\(641\) | −2.24823e15 | −0.820581 | −0.410291 | − | 0.911955i | \(-0.634573\pi\) | ||||
−0.410291 | + | 0.911955i | \(0.634573\pi\) | |||||||
\(642\) | 2.59673e14 | 0.0939688 | ||||||||
\(643\) | 2.81606e15 | 1.01037 | 0.505187 | − | 0.863010i | \(-0.331424\pi\) | ||||
0.505187 | + | 0.863010i | \(0.331424\pi\) | |||||||
\(644\) | −1.22459e15 | −0.435631 | ||||||||
\(645\) | 9.15937e14 | 0.323063 | ||||||||
\(646\) | 6.60929e14 | 0.231140 | ||||||||
\(647\) | 3.23571e15 | 1.12201 | 0.561004 | − | 0.827813i | \(-0.310415\pi\) | ||||
0.561004 | + | 0.827813i | \(0.310415\pi\) | |||||||
\(648\) | −1.12470e14 | −0.0386699 | ||||||||
\(649\) | −5.68854e15 | −1.93934 | ||||||||
\(650\) | −8.47180e13 | −0.0286386 | ||||||||
\(651\) | 8.49910e14 | 0.284890 | ||||||||
\(652\) | 4.01755e15 | 1.33536 | ||||||||
\(653\) | −3.14088e15 | −1.03521 | −0.517606 | − | 0.855619i | \(-0.673177\pi\) | ||||
−0.517606 | + | 0.855619i | \(0.673177\pi\) | |||||||
\(654\) | −4.21678e14 | −0.137817 | ||||||||
\(655\) | 1.17966e15 | 0.382323 | ||||||||
\(656\) | 3.61945e15 | 1.16324 | ||||||||
\(657\) | −4.63197e14 | −0.147624 | ||||||||
\(658\) | 1.79708e14 | 0.0567969 | ||||||||
\(659\) | 8.48017e14 | 0.265788 | 0.132894 | − | 0.991130i | \(-0.457573\pi\) | ||||
0.132894 | + | 0.991130i | \(0.457573\pi\) | |||||||
\(660\) | 1.70341e15 | 0.529454 | ||||||||
\(661\) | 2.31505e15 | 0.713596 | 0.356798 | − | 0.934182i | \(-0.383868\pi\) | ||||
0.356798 | + | 0.934182i | \(0.383868\pi\) | |||||||
\(662\) | −9.55904e14 | −0.292210 | ||||||||
\(663\) | −4.92604e14 | −0.149339 | ||||||||
\(664\) | 3.51427e14 | 0.105660 | ||||||||
\(665\) | 1.07738e15 | 0.321254 | ||||||||
\(666\) | 3.08069e14 | 0.0911043 | ||||||||
\(667\) | −1.87763e15 | −0.550703 | ||||||||
\(668\) | −6.34384e14 | −0.184536 | ||||||||
\(669\) | −2.97391e15 | −0.857994 | ||||||||
\(670\) | −1.78647e14 | −0.0511192 | ||||||||
\(671\) | 6.15211e15 | 1.74602 | ||||||||
\(672\) | −3.94123e14 | −0.110943 | ||||||||
\(673\) | −3.64280e15 | −1.01707 | −0.508536 | − | 0.861041i | \(-0.669813\pi\) | ||||
−0.508536 | + | 0.861041i | \(0.669813\pi\) | |||||||
\(674\) | 5.11243e14 | 0.141579 | ||||||||
\(675\) | −4.24097e14 | −0.116491 | ||||||||
\(676\) | 3.30095e15 | 0.899357 | ||||||||
\(677\) | 4.64522e15 | 1.25536 | 0.627681 | − | 0.778471i | \(-0.284004\pi\) | ||||
0.627681 | + | 0.778471i | \(0.284004\pi\) | |||||||
\(678\) | −6.84959e14 | −0.183612 | ||||||||
\(679\) | −1.38194e15 | −0.367455 | ||||||||
\(680\) | 8.01175e14 | 0.211314 | ||||||||
\(681\) | −2.56128e14 | −0.0670113 | ||||||||
\(682\) | 1.33990e15 | 0.347744 | ||||||||
\(683\) | 3.94390e15 | 1.01534 | 0.507671 | − | 0.861551i | \(-0.330507\pi\) | ||||
0.507671 | + | 0.861551i | \(0.330507\pi\) | |||||||
\(684\) | 1.71067e15 | 0.436876 | ||||||||
\(685\) | −1.65460e15 | −0.419175 | ||||||||
\(686\) | −3.79805e13 | −0.00954504 | ||||||||
\(687\) | 8.05980e14 | 0.200938 | ||||||||
\(688\) | 3.26716e15 | 0.808042 | ||||||||
\(689\) | 5.36580e14 | 0.131652 | ||||||||
\(690\) | −3.13415e14 | −0.0762869 | ||||||||
\(691\) | 1.73361e15 | 0.418621 | 0.209310 | − | 0.977849i | \(-0.432878\pi\) | ||||
0.209310 | + | 0.977849i | \(0.432878\pi\) | |||||||
\(692\) | −3.05433e15 | −0.731698 | ||||||||
\(693\) | 7.98749e14 | 0.189835 | ||||||||
\(694\) | 7.63136e14 | 0.179939 | ||||||||
\(695\) | 2.99236e15 | 0.699998 | ||||||||
\(696\) | −4.00744e14 | −0.0930071 | ||||||||
\(697\) | −5.38169e15 | −1.23919 | ||||||||
\(698\) | 9.17377e13 | 0.0209577 | ||||||||
\(699\) | −3.98410e15 | −0.903036 | ||||||||
\(700\) | −9.85548e14 | −0.221635 | ||||||||
\(701\) | −4.34481e15 | −0.969441 | −0.484720 | − | 0.874669i | \(-0.661079\pi\) | ||||
−0.484720 | + | 0.874669i | \(0.661079\pi\) | |||||||
\(702\) | 4.11290e13 | 0.00910530 | ||||||||
\(703\) | −9.52264e15 | −2.09172 | ||||||||
\(704\) | 5.65076e15 | 1.23156 | ||||||||
\(705\) | −1.42580e15 | −0.308331 | ||||||||
\(706\) | 1.57338e15 | 0.337603 | ||||||||
\(707\) | 2.32014e15 | 0.493979 | ||||||||
\(708\) | −3.40754e15 | −0.719877 | ||||||||
\(709\) | 3.46868e15 | 0.727126 | 0.363563 | − | 0.931570i | \(-0.381560\pi\) | ||||
0.363563 | + | 0.931570i | \(0.381560\pi\) | |||||||
\(710\) | 9.83856e13 | 0.0204649 | ||||||||
\(711\) | −1.24928e15 | −0.257856 | ||||||||
\(712\) | −2.28336e15 | −0.467665 | ||||||||
\(713\) | 7.64251e15 | 1.55326 | ||||||||
\(714\) | 1.84858e14 | 0.0372820 | ||||||||
\(715\) | −1.26594e15 | −0.253354 | ||||||||
\(716\) | −3.60495e13 | −0.00715941 | ||||||||
\(717\) | −3.12588e15 | −0.616051 | ||||||||
\(718\) | 2.82613e14 | 0.0552723 | ||||||||
\(719\) | −8.98716e15 | −1.74427 | −0.872134 | − | 0.489266i | \(-0.837265\pi\) | ||||
−0.872134 | + | 0.489266i | \(0.837265\pi\) | |||||||
\(720\) | 9.86399e14 | 0.189987 | ||||||||
\(721\) | 1.01015e15 | 0.193081 | ||||||||
\(722\) | 7.73826e14 | 0.146787 | ||||||||
\(723\) | −1.21656e15 | −0.229021 | ||||||||
\(724\) | −3.48366e15 | −0.650839 | ||||||||
\(725\) | −1.51111e15 | −0.280180 | ||||||||
\(726\) | 7.04601e14 | 0.129656 | ||||||||
\(727\) | 2.99194e15 | 0.546404 | 0.273202 | − | 0.961957i | \(-0.411917\pi\) | ||||
0.273202 | + | 0.961957i | \(0.411917\pi\) | |||||||
\(728\) | 1.94241e14 | 0.0352061 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −2.75491e14 | −0.0491849 | ||||||||
\(731\) | −4.85788e15 | −0.860799 | ||||||||
\(732\) | 3.68523e15 | 0.648117 | ||||||||
\(733\) | 4.15129e15 | 0.724622 | 0.362311 | − | 0.932057i | \(-0.381988\pi\) | ||||
0.362311 | + | 0.932057i | \(0.381988\pi\) | |||||||
\(734\) | 1.32506e15 | 0.229566 | ||||||||
\(735\) | 3.01336e14 | 0.0518168 | ||||||||
\(736\) | −3.54401e15 | −0.604876 | ||||||||
\(737\) | 4.09401e15 | 0.693549 | ||||||||
\(738\) | 4.49334e14 | 0.0755543 | ||||||||
\(739\) | −7.42523e15 | −1.23927 | −0.619635 | − | 0.784890i | \(-0.712719\pi\) | ||||
−0.619635 | + | 0.784890i | \(0.712719\pi\) | |||||||
\(740\) | −5.68003e15 | −0.940972 | ||||||||
\(741\) | −1.27133e15 | −0.209054 | ||||||||
\(742\) | −2.01361e14 | −0.0328665 | ||||||||
\(743\) | 6.33952e14 | 0.102711 | 0.0513556 | − | 0.998680i | \(-0.483646\pi\) | ||||
0.0513556 | + | 0.998680i | \(0.483646\pi\) | |||||||
\(744\) | 1.63115e15 | 0.262326 | ||||||||
\(745\) | 6.09358e15 | 0.972777 | ||||||||
\(746\) | 4.80054e14 | 0.0760723 | ||||||||
\(747\) | −6.43336e14 | −0.101199 | ||||||||
\(748\) | −9.03444e15 | −1.41073 | ||||||||
\(749\) | −2.24502e15 | −0.347993 | ||||||||
\(750\) | −6.68943e14 | −0.102932 | ||||||||
\(751\) | 3.55460e15 | 0.542964 | 0.271482 | − | 0.962444i | \(-0.412486\pi\) | ||||
0.271482 | + | 0.962444i | \(0.412486\pi\) | |||||||
\(752\) | −5.08584e15 | −0.771195 | ||||||||
\(753\) | −4.23522e15 | −0.637535 | ||||||||
\(754\) | 1.46548e14 | 0.0218997 | ||||||||
\(755\) | 6.71704e15 | 0.996483 | ||||||||
\(756\) | 4.78466e14 | 0.0704662 | ||||||||
\(757\) | −8.89494e15 | −1.30052 | −0.650258 | − | 0.759713i | \(-0.725339\pi\) | ||||
−0.650258 | + | 0.759713i | \(0.725339\pi\) | |||||||
\(758\) | −1.62311e15 | −0.235596 | ||||||||
\(759\) | 7.18246e15 | 1.03501 | ||||||||
\(760\) | 2.06770e15 | 0.295810 | ||||||||
\(761\) | 1.04253e16 | 1.48072 | 0.740360 | − | 0.672210i | \(-0.234655\pi\) | ||||
0.740360 | + | 0.672210i | \(0.234655\pi\) | |||||||
\(762\) | −6.29352e14 | −0.0887444 | ||||||||
\(763\) | 3.64565e15 | 0.510376 | ||||||||
\(764\) | −1.14578e16 | −1.59253 | ||||||||
\(765\) | −1.46666e15 | −0.202391 | ||||||||
\(766\) | −2.39214e15 | −0.327739 | ||||||||
\(767\) | 2.53240e15 | 0.344475 | ||||||||
\(768\) | 3.00071e15 | 0.405263 | ||||||||
\(769\) | 9.07977e14 | 0.121753 | 0.0608765 | − | 0.998145i | \(-0.480610\pi\) | ||||
0.0608765 | + | 0.998145i | \(0.480610\pi\) | |||||||
\(770\) | 4.75064e14 | 0.0632489 | ||||||||
\(771\) | −2.47485e15 | −0.327152 | ||||||||
\(772\) | 8.21447e15 | 1.07816 | ||||||||
\(773\) | 2.88244e15 | 0.375641 | 0.187820 | − | 0.982203i | \(-0.439858\pi\) | ||||
0.187820 | + | 0.982203i | \(0.439858\pi\) | |||||||
\(774\) | 4.05599e14 | 0.0524834 | ||||||||
\(775\) | 6.15067e15 | 0.790247 | ||||||||
\(776\) | −2.65221e15 | −0.338352 | ||||||||
\(777\) | −2.66343e15 | −0.337385 | ||||||||
\(778\) | −1.98831e15 | −0.250090 | ||||||||
\(779\) | −1.38893e16 | −1.73469 | ||||||||
\(780\) | −7.58319e14 | −0.0940441 | ||||||||
\(781\) | −2.25468e15 | −0.277654 | ||||||||
\(782\) | 1.66227e15 | 0.203266 | ||||||||
\(783\) | 7.33616e14 | 0.0890798 | ||||||||
\(784\) | 1.07487e15 | 0.129604 | ||||||||
\(785\) | −3.84972e15 | −0.460941 | ||||||||
\(786\) | 5.22384e14 | 0.0621106 | ||||||||
\(787\) | 9.61839e15 | 1.13564 | 0.567821 | − | 0.823152i | \(-0.307787\pi\) | ||||
0.567821 | + | 0.823152i | \(0.307787\pi\) | |||||||
\(788\) | −1.37123e15 | −0.160774 | ||||||||
\(789\) | 1.64990e15 | 0.192103 | ||||||||
\(790\) | −7.43022e14 | −0.0859118 | ||||||||
\(791\) | 5.92187e15 | 0.679967 | ||||||||
\(792\) | 1.53296e15 | 0.174800 | ||||||||
\(793\) | −2.73877e15 | −0.310137 | ||||||||
\(794\) | −1.39248e15 | −0.156595 | ||||||||
\(795\) | 1.59759e15 | 0.178421 | ||||||||
\(796\) | 1.47265e16 | 1.63334 | ||||||||
\(797\) | 1.07318e16 | 1.18209 | 0.591046 | − | 0.806638i | \(-0.298715\pi\) | ||||
0.591046 | + | 0.806638i | \(0.298715\pi\) | |||||||
\(798\) | 4.77088e14 | 0.0521895 | ||||||||
\(799\) | 7.56204e15 | 0.821546 | ||||||||
\(800\) | −2.85221e15 | −0.307742 | ||||||||
\(801\) | 4.18001e15 | 0.447918 | ||||||||
\(802\) | 1.72285e15 | 0.183353 | ||||||||
\(803\) | 6.31336e15 | 0.667306 | ||||||||
\(804\) | 2.45239e15 | 0.257443 | ||||||||
\(805\) | 2.70966e15 | 0.282512 | ||||||||
\(806\) | −5.96494e14 | −0.0617680 | ||||||||
\(807\) | 7.14660e15 | 0.735013 | ||||||||
\(808\) | 4.45282e15 | 0.454855 | ||||||||
\(809\) | 3.94794e15 | 0.400547 | 0.200273 | − | 0.979740i | \(-0.435817\pi\) | ||||
0.200273 | + | 0.979740i | \(0.435817\pi\) | |||||||
\(810\) | 1.22456e14 | 0.0123399 | ||||||||
\(811\) | 7.55537e15 | 0.756207 | 0.378104 | − | 0.925763i | \(-0.376576\pi\) | ||||
0.378104 | + | 0.925763i | \(0.376576\pi\) | |||||||
\(812\) | 1.70483e15 | 0.169482 | ||||||||
\(813\) | −7.53697e15 | −0.744215 | ||||||||
\(814\) | −4.19896e15 | −0.411821 | ||||||||
\(815\) | −8.88964e15 | −0.865999 | ||||||||
\(816\) | −5.23160e15 | −0.506219 | ||||||||
\(817\) | −1.25374e16 | −1.20500 | ||||||||
\(818\) | −2.32728e15 | −0.222181 | ||||||||
\(819\) | −3.55584e14 | −0.0337195 | ||||||||
\(820\) | −8.28462e15 | −0.780363 | ||||||||
\(821\) | 9.48454e14 | 0.0887420 | 0.0443710 | − | 0.999015i | \(-0.485872\pi\) | ||||
0.0443710 | + | 0.999015i | \(0.485872\pi\) | |||||||
\(822\) | −7.32699e14 | −0.0680974 | ||||||||
\(823\) | −2.39832e15 | −0.221416 | −0.110708 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110708 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(824\) | 1.93867e15 | 0.177789 | ||||||||
\(825\) | 5.78042e15 | 0.526578 | ||||||||
\(826\) | −9.50327e14 | −0.0859969 | ||||||||
\(827\) | 1.20594e16 | 1.08404 | 0.542019 | − | 0.840366i | \(-0.317660\pi\) | ||||
0.542019 | + | 0.840366i | \(0.317660\pi\) | |||||||
\(828\) | 4.30243e15 | 0.384191 | ||||||||
\(829\) | −3.00246e15 | −0.266334 | −0.133167 | − | 0.991094i | \(-0.542515\pi\) | ||||
−0.133167 | + | 0.991094i | \(0.542515\pi\) | |||||||
\(830\) | −3.82631e14 | −0.0337171 | ||||||||
\(831\) | 2.72988e15 | 0.238967 | ||||||||
\(832\) | −2.51558e15 | −0.218756 | ||||||||
\(833\) | −1.59821e15 | −0.138066 | ||||||||
\(834\) | 1.32509e15 | 0.113719 | ||||||||
\(835\) | 1.40370e15 | 0.119674 | ||||||||
\(836\) | −2.33164e16 | −1.97482 | ||||||||
\(837\) | −2.98604e15 | −0.251250 | ||||||||
\(838\) | 1.31936e15 | 0.110287 | ||||||||
\(839\) | −7.55751e15 | −0.627607 | −0.313804 | − | 0.949488i | \(-0.601603\pi\) | ||||
−0.313804 | + | 0.949488i | \(0.601603\pi\) | |||||||
\(840\) | 5.78324e14 | 0.0477129 | ||||||||
\(841\) | −9.58654e15 | −0.785749 | ||||||||
\(842\) | 2.13694e15 | 0.174011 | ||||||||
\(843\) | 6.46112e15 | 0.522705 | ||||||||
\(844\) | 1.27578e15 | 0.102540 | ||||||||
\(845\) | −7.30402e15 | −0.583244 | ||||||||
\(846\) | −6.31378e14 | −0.0500901 | ||||||||
\(847\) | −6.09169e15 | −0.480152 | ||||||||
\(848\) | 5.69863e15 | 0.446265 | ||||||||
\(849\) | 4.34471e15 | 0.338040 | ||||||||
\(850\) | 1.33779e15 | 0.103415 | ||||||||
\(851\) | −2.39499e16 | −1.83947 | ||||||||
\(852\) | −1.35059e15 | −0.103064 | ||||||||
\(853\) | 1.04461e16 | 0.792015 | 0.396008 | − | 0.918247i | \(-0.370395\pi\) | ||||
0.396008 | + | 0.918247i | \(0.370395\pi\) | |||||||
\(854\) | 1.02777e15 | 0.0774245 | ||||||||
\(855\) | −3.78521e15 | −0.283319 | ||||||||
\(856\) | −4.30864e15 | −0.320431 | ||||||||
\(857\) | −2.13498e16 | −1.57761 | −0.788804 | − | 0.614645i | \(-0.789299\pi\) | ||||
−0.788804 | + | 0.614645i | \(0.789299\pi\) | |||||||
\(858\) | −5.60587e14 | −0.0411588 | ||||||||
\(859\) | 1.22807e16 | 0.895905 | 0.447952 | − | 0.894057i | \(-0.352153\pi\) | ||||
0.447952 | + | 0.894057i | \(0.352153\pi\) | |||||||
\(860\) | −7.47827e15 | −0.542075 | ||||||||
\(861\) | −3.88475e15 | −0.279799 | ||||||||
\(862\) | −4.51519e15 | −0.323136 | ||||||||
\(863\) | 1.68658e15 | 0.119935 | 0.0599676 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599676 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(864\) | 1.38469e15 | 0.0978427 | ||||||||
\(865\) | 6.75831e15 | 0.474515 | ||||||||
\(866\) | −1.09813e15 | −0.0766133 | ||||||||
\(867\) | −5.49300e14 | −0.0380807 | ||||||||
\(868\) | −6.93918e15 | −0.478024 | ||||||||
\(869\) | 1.70276e16 | 1.16559 | ||||||||
\(870\) | 4.36326e14 | 0.0296794 | ||||||||
\(871\) | −1.82255e15 | −0.123191 | ||||||||
\(872\) | 6.99674e15 | 0.469953 | ||||||||
\(873\) | 4.85523e15 | 0.324065 | ||||||||
\(874\) | 4.29005e15 | 0.284544 | ||||||||
\(875\) | 5.78340e15 | 0.381188 | ||||||||
\(876\) | 3.78182e15 | 0.247701 | ||||||||
\(877\) | −1.36349e16 | −0.887470 | −0.443735 | − | 0.896158i | \(-0.646347\pi\) | ||||
−0.443735 | + | 0.896158i | \(0.646347\pi\) | |||||||
\(878\) | 7.18255e13 | 0.00464578 | ||||||||
\(879\) | −4.62244e15 | −0.297120 | ||||||||
\(880\) | −1.34446e16 | −0.858802 | ||||||||
\(881\) | 4.78019e15 | 0.303443 | 0.151722 | − | 0.988423i | \(-0.451518\pi\) | ||||
0.151722 | + | 0.988423i | \(0.451518\pi\) | |||||||
\(882\) | 1.33439e14 | 0.00841794 | ||||||||
\(883\) | 2.35034e15 | 0.147349 | 0.0736743 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736743 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(884\) | 4.02192e15 | 0.250580 | ||||||||
\(885\) | 7.53987e15 | 0.466848 | ||||||||
\(886\) | −3.23280e15 | −0.198927 | ||||||||
\(887\) | −2.80378e16 | −1.71461 | −0.857304 | − | 0.514811i | \(-0.827862\pi\) | ||||
−0.857304 | + | 0.514811i | \(0.827862\pi\) | |||||||
\(888\) | −5.11166e15 | −0.310664 | ||||||||
\(889\) | 5.44111e15 | 0.328646 | ||||||||
\(890\) | 2.48610e15 | 0.149236 | ||||||||
\(891\) | −2.80629e15 | −0.167419 | ||||||||
\(892\) | 2.42808e16 | 1.43965 | ||||||||
\(893\) | 1.95164e16 | 1.15005 | ||||||||
\(894\) | 2.69839e15 | 0.158033 | ||||||||
\(895\) | 7.97667e13 | 0.00464296 | ||||||||
\(896\) | 4.26568e15 | 0.246771 | ||||||||
\(897\) | −3.19746e15 | −0.183843 | ||||||||
\(898\) | −5.02090e15 | −0.286921 | ||||||||
\(899\) | −1.06396e16 | −0.604294 | ||||||||
\(900\) | 3.46258e15 | 0.195464 | ||||||||
\(901\) | −8.47319e15 | −0.475402 | ||||||||
\(902\) | −6.12441e15 | −0.341529 | ||||||||
\(903\) | −3.50664e15 | −0.194361 | ||||||||
\(904\) | 1.13652e16 | 0.626113 | ||||||||
\(905\) | 7.70830e15 | 0.422077 | ||||||||
\(906\) | 2.97447e15 | 0.161884 | ||||||||
\(907\) | −7.92531e15 | −0.428723 | −0.214361 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214361 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(908\) | 2.09118e15 | 0.112440 | ||||||||
\(909\) | −8.15150e15 | −0.435648 | ||||||||
\(910\) | −2.11487e14 | −0.0112346 | ||||||||
\(911\) | 1.57528e16 | 0.831777 | 0.415888 | − | 0.909416i | \(-0.363471\pi\) | ||||
0.415888 | + | 0.909416i | \(0.363471\pi\) | |||||||
\(912\) | −1.35019e16 | −0.708635 | ||||||||
\(913\) | 8.76865e15 | 0.457450 | ||||||||
\(914\) | 2.40990e15 | 0.124967 | ||||||||
\(915\) | −8.15431e15 | −0.420312 | ||||||||
\(916\) | −6.58051e15 | −0.337159 | ||||||||
\(917\) | −4.51631e15 | −0.230013 | ||||||||
\(918\) | −6.49473e14 | −0.0328796 | ||||||||
\(919\) | 2.85627e16 | 1.43735 | 0.718677 | − | 0.695344i | \(-0.244748\pi\) | ||||
0.718677 | + | 0.695344i | \(0.244748\pi\) | |||||||
\(920\) | 5.20037e15 | 0.260137 | ||||||||
\(921\) | −6.91042e15 | −0.343618 | ||||||||
\(922\) | 2.80303e15 | 0.138550 | ||||||||
\(923\) | 1.00373e15 | 0.0493182 | ||||||||
\(924\) | −6.52147e15 | −0.318530 | ||||||||
\(925\) | −1.92748e16 | −0.935861 | ||||||||
\(926\) | 3.92312e15 | 0.189352 | ||||||||
\(927\) | −3.54900e15 | −0.170282 | ||||||||
\(928\) | 4.93384e15 | 0.235327 | ||||||||
\(929\) | 2.08352e16 | 0.987897 | 0.493949 | − | 0.869491i | \(-0.335553\pi\) | ||||
0.493949 | + | 0.869491i | \(0.335553\pi\) | |||||||
\(930\) | −1.77598e15 | −0.0837107 | ||||||||
\(931\) | −4.12470e15 | −0.193272 | ||||||||
\(932\) | 3.25286e16 | 1.51523 | ||||||||
\(933\) | 6.66815e15 | 0.308785 | ||||||||
\(934\) | 5.44674e15 | 0.250743 | ||||||||
\(935\) | 1.99905e16 | 0.914872 | ||||||||
\(936\) | −6.82437e14 | −0.0310488 | ||||||||
\(937\) | −3.63422e16 | −1.64378 | −0.821889 | − | 0.569648i | \(-0.807080\pi\) | ||||
−0.821889 | + | 0.569648i | \(0.807080\pi\) | |||||||
\(938\) | 6.83945e14 | 0.0307543 | ||||||||
\(939\) | −1.04438e16 | −0.466870 | ||||||||
\(940\) | 1.16411e16 | 0.517356 | ||||||||
\(941\) | 1.70015e16 | 0.751180 | 0.375590 | − | 0.926786i | \(-0.377440\pi\) | ||||
0.375590 | + | 0.926786i | \(0.377440\pi\) | |||||||
\(942\) | −1.70475e15 | −0.0748825 | ||||||||
\(943\) | −3.49322e16 | −1.52550 | ||||||||
\(944\) | 2.68948e16 | 1.16768 | ||||||||
\(945\) | −1.05870e15 | −0.0456981 | ||||||||
\(946\) | −5.52831e15 | −0.237242 | ||||||||
\(947\) | −3.90585e16 | −1.66644 | −0.833222 | − | 0.552938i | \(-0.813507\pi\) | ||||
−0.833222 | + | 0.552938i | \(0.813507\pi\) | |||||||
\(948\) | 1.01999e16 | 0.432662 | ||||||||
\(949\) | −2.81056e15 | −0.118530 | ||||||||
\(950\) | 3.45262e15 | 0.144767 | ||||||||
\(951\) | 1.60266e16 | 0.668109 | ||||||||
\(952\) | −3.06728e15 | −0.127131 | ||||||||
\(953\) | 3.25047e16 | 1.33948 | 0.669739 | − | 0.742596i | \(-0.266406\pi\) | ||||
0.669739 | + | 0.742596i | \(0.266406\pi\) | |||||||
\(954\) | 7.07452e14 | 0.0289855 | ||||||||
\(955\) | 2.53527e16 | 1.03278 | ||||||||
\(956\) | 2.55216e16 | 1.03369 | ||||||||
\(957\) | −9.99917e15 | −0.402669 | ||||||||
\(958\) | 6.33590e15 | 0.253687 | ||||||||
\(959\) | 6.33460e15 | 0.252184 | ||||||||
\(960\) | −7.48980e15 | −0.296468 | ||||||||
\(961\) | 1.78980e16 | 0.704411 | ||||||||
\(962\) | 1.86928e15 | 0.0731495 | ||||||||
\(963\) | 7.88756e15 | 0.306901 | ||||||||
\(964\) | 9.93277e15 | 0.384279 | ||||||||
\(965\) | −1.81762e16 | −0.699201 | ||||||||
\(966\) | 1.19990e15 | 0.0458957 | ||||||||
\(967\) | 2.41922e16 | 0.920090 | 0.460045 | − | 0.887896i | \(-0.347833\pi\) | ||||
0.460045 | + | 0.887896i | \(0.347833\pi\) | |||||||
\(968\) | −1.16912e16 | −0.442123 | ||||||||
\(969\) | 2.00757e16 | 0.754902 | ||||||||
\(970\) | 2.88770e15 | 0.107971 | ||||||||
\(971\) | −4.32072e15 | −0.160639 | −0.0803193 | − | 0.996769i | \(-0.525594\pi\) | ||||
−0.0803193 | + | 0.996769i | \(0.525594\pi\) | |||||||
\(972\) | −1.68102e15 | −0.0621453 | ||||||||
\(973\) | −1.14562e16 | −0.421132 | ||||||||
\(974\) | −3.93850e15 | −0.143965 | ||||||||
\(975\) | −2.57331e15 | −0.0935333 | ||||||||
\(976\) | −2.90865e16 | −1.05128 | ||||||||
\(977\) | 2.18589e16 | 0.785614 | 0.392807 | − | 0.919621i | \(-0.371504\pi\) | ||||
0.392807 | + | 0.919621i | \(0.371504\pi\) | |||||||
\(978\) | −3.93655e15 | −0.140686 | ||||||||
\(979\) | −5.69734e16 | −2.02473 | ||||||||
\(980\) | −2.46029e15 | −0.0869447 | ||||||||
\(981\) | −1.28085e16 | −0.450109 | ||||||||
\(982\) | −8.63583e15 | −0.301780 | ||||||||
\(983\) | −4.03990e16 | −1.40387 | −0.701934 | − | 0.712242i | \(-0.747680\pi\) | ||||
−0.701934 | + | 0.712242i | \(0.747680\pi\) | |||||||
\(984\) | −7.45561e15 | −0.257638 | ||||||||
\(985\) | 3.03413e15 | 0.104264 | ||||||||
\(986\) | −2.31416e15 | −0.0790805 | ||||||||
\(987\) | 5.45862e15 | 0.185498 | ||||||||
\(988\) | 1.03799e16 | 0.350776 | ||||||||
\(989\) | −3.15322e16 | −1.05968 | ||||||||
\(990\) | −1.66907e15 | −0.0557803 | ||||||||
\(991\) | 9.82831e15 | 0.326643 | 0.163322 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163322 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(992\) | −2.00822e16 | −0.663739 | ||||||||
\(993\) | −2.90356e16 | −0.954355 | ||||||||
\(994\) | −3.76667e14 | −0.0123121 | ||||||||
\(995\) | −3.25853e16 | −1.05924 | ||||||||
\(996\) | 5.25259e15 | 0.169804 | ||||||||
\(997\) | 4.40587e16 | 1.41647 | 0.708236 | − | 0.705976i | \(-0.249491\pi\) | ||||
0.708236 | + | 0.705976i | \(0.249491\pi\) | |||||||
\(998\) | −8.36420e15 | −0.267428 | ||||||||
\(999\) | 9.35758e15 | 0.297546 |
(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 | 21.12.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.12.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 147.12.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.12.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
63.12.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
147.12.a.b.1.1 | 1 | 7.6 | odd | 2 |