Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,98,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 98, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 98);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 98 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(59.5852992940\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots - 60\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.21527e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.80945e14 | 1.45942 | 0.729709 | − | 0.683757i | \(-0.239655\pi\) | ||||
0.729709 | + | 0.683757i | \(0.239655\pi\) | |||||||
\(3\) | 1.62851e23 | 1.17872 | 0.589360 | − | 0.807871i | \(-0.299380\pi\) | ||||
0.589360 | + | 0.807871i | \(0.299380\pi\) | |||||||
\(4\) | 1.79040e29 | 1.12990 | ||||||||
\(5\) | −5.19758e33 | −0.654269 | −0.327134 | − | 0.944978i | \(-0.606083\pi\) | ||||
−0.327134 | + | 0.944978i | \(0.606083\pi\) | |||||||
\(6\) | 9.46076e37 | 1.72025 | ||||||||
\(7\) | −7.14729e40 | −0.736015 | −0.368007 | − | 0.929823i | \(-0.619960\pi\) | ||||
−0.368007 | + | 0.929823i | \(0.619960\pi\) | |||||||
\(8\) | 1.19582e43 | 0.189583 | ||||||||
\(9\) | 7.43249e45 | 0.389379 | ||||||||
\(10\) | −3.01951e48 | −0.954852 | ||||||||
\(11\) | −5.76894e50 | −1.79288 | −0.896440 | − | 0.443166i | \(-0.853855\pi\) | ||||
−0.896440 | + | 0.443166i | \(0.853855\pi\) | |||||||
\(12\) | 2.91569e52 | 1.33184 | ||||||||
\(13\) | 1.05855e54 | 0.996454 | 0.498227 | − | 0.867047i | \(-0.333985\pi\) | ||||
0.498227 | + | 0.867047i | \(0.333985\pi\) | |||||||
\(14\) | −4.15218e55 | −1.07415 | ||||||||
\(15\) | −8.46433e56 | −0.771199 | ||||||||
\(16\) | −2.14230e58 | −0.853222 | ||||||||
\(17\) | −4.74193e59 | −0.998120 | −0.499060 | − | 0.866567i | \(-0.666321\pi\) | ||||
−0.499060 | + | 0.866567i | \(0.666321\pi\) | |||||||
\(18\) | 4.31787e60 | 0.568267 | ||||||||
\(19\) | −1.19343e61 | −0.114090 | −0.0570448 | − | 0.998372i | \(-0.518168\pi\) | ||||
−0.0570448 | + | 0.998372i | \(0.518168\pi\) | |||||||
\(20\) | −9.30577e62 | −0.739260 | ||||||||
\(21\) | −1.16395e64 | −0.867555 | ||||||||
\(22\) | −3.35144e65 | −2.61656 | ||||||||
\(23\) | 1.47380e66 | 1.33241 | 0.666207 | − | 0.745767i | \(-0.267917\pi\) | ||||
0.666207 | + | 0.745767i | \(0.267917\pi\) | |||||||
\(24\) | 1.94740e66 | 0.223465 | ||||||||
\(25\) | −3.60940e67 | −0.571932 | ||||||||
\(26\) | 6.14957e68 | 1.45424 | ||||||||
\(27\) | −1.89812e69 | −0.719751 | ||||||||
\(28\) | −1.27965e70 | −0.831626 | ||||||||
\(29\) | −1.17673e71 | −1.39436 | −0.697180 | − | 0.716896i | \(-0.745562\pi\) | ||||
−0.697180 | + | 0.716896i | \(0.745562\pi\) | |||||||
\(30\) | −4.91731e71 | −1.12550 | ||||||||
\(31\) | 9.54912e71 | 0.445575 | 0.222788 | − | 0.974867i | \(-0.428484\pi\) | ||||
0.222788 | + | 0.974867i | \(0.428484\pi\) | |||||||
\(32\) | −1.43404e73 | −1.43479 | ||||||||
\(33\) | −9.39480e73 | −2.11330 | ||||||||
\(34\) | −2.75480e74 | −1.45668 | ||||||||
\(35\) | 3.71486e74 | 0.481552 | ||||||||
\(36\) | 1.33072e75 | 0.439961 | ||||||||
\(37\) | 1.79614e76 | 1.57238 | 0.786188 | − | 0.617988i | \(-0.212052\pi\) | ||||
0.786188 | + | 0.617988i | \(0.212052\pi\) | |||||||
\(38\) | −6.93314e75 | −0.166504 | ||||||||
\(39\) | 1.72386e77 | 1.17454 | ||||||||
\(40\) | −6.21535e76 | −0.124038 | ||||||||
\(41\) | −5.94728e77 | −0.358345 | −0.179172 | − | 0.983818i | \(-0.557342\pi\) | ||||
−0.179172 | + | 0.983818i | \(0.557342\pi\) | |||||||
\(42\) | −6.76188e78 | −1.26613 | ||||||||
\(43\) | 1.56674e79 | 0.937080 | 0.468540 | − | 0.883442i | \(-0.344780\pi\) | ||||
0.468540 | + | 0.883442i | \(0.344780\pi\) | |||||||
\(44\) | −1.03287e80 | −2.02578 | ||||||||
\(45\) | −3.86310e79 | −0.254759 | ||||||||
\(46\) | 8.56198e80 | 1.94455 | ||||||||
\(47\) | 2.24254e81 | 1.79471 | 0.897355 | − | 0.441310i | \(-0.145486\pi\) | ||||
0.897355 | + | 0.441310i | \(0.145486\pi\) | |||||||
\(48\) | −3.48877e81 | −1.00571 | ||||||||
\(49\) | −4.32158e81 | −0.458282 | ||||||||
\(50\) | −2.09686e82 | −0.834689 | ||||||||
\(51\) | −7.72230e82 | −1.17650 | ||||||||
\(52\) | 1.89523e83 | 1.12590 | ||||||||
\(53\) | 1.09991e83 | 0.259404 | 0.129702 | − | 0.991553i | \(-0.458598\pi\) | ||||
0.129702 | + | 0.991553i | \(0.458598\pi\) | |||||||
\(54\) | −1.10270e84 | −1.05042 | ||||||||
\(55\) | 2.99846e84 | 1.17303 | ||||||||
\(56\) | −8.54684e83 | −0.139536 | ||||||||
\(57\) | −1.94351e84 | −0.134480 | ||||||||
\(58\) | −6.83616e85 | −2.03495 | ||||||||
\(59\) | −4.65431e85 | −0.604690 | −0.302345 | − | 0.953199i | \(-0.597769\pi\) | ||||
−0.302345 | + | 0.953199i | \(0.597769\pi\) | |||||||
\(60\) | −1.51546e86 | −0.871381 | ||||||||
\(61\) | −3.66482e86 | −0.945270 | −0.472635 | − | 0.881258i | \(-0.656697\pi\) | ||||
−0.472635 | + | 0.881258i | \(0.656697\pi\) | |||||||
\(62\) | 5.54751e86 | 0.650281 | ||||||||
\(63\) | −5.31222e86 | −0.286589 | ||||||||
\(64\) | −4.93639e87 | −1.24074 | ||||||||
\(65\) | −5.50188e87 | −0.651949 | ||||||||
\(66\) | −5.45786e88 | −3.08419 | ||||||||
\(67\) | −1.40795e88 | −0.383672 | −0.191836 | − | 0.981427i | \(-0.561444\pi\) | ||||
−0.191836 | + | 0.981427i | \(0.561444\pi\) | |||||||
\(68\) | −8.48997e88 | −1.12778 | ||||||||
\(69\) | 2.40011e89 | 1.57054 | ||||||||
\(70\) | 2.15813e89 | 0.702785 | ||||||||
\(71\) | −7.30927e89 | −1.19631 | −0.598156 | − | 0.801380i | \(-0.704100\pi\) | ||||
−0.598156 | + | 0.801380i | \(0.704100\pi\) | |||||||
\(72\) | 8.88789e88 | 0.0738197 | ||||||||
\(73\) | −7.23237e89 | −0.307696 | −0.153848 | − | 0.988095i | \(-0.549167\pi\) | ||||
−0.153848 | + | 0.988095i | \(0.549167\pi\) | |||||||
\(74\) | 1.04346e91 | 2.29475 | ||||||||
\(75\) | −5.87796e90 | −0.674148 | ||||||||
\(76\) | −2.13671e90 | −0.128910 | ||||||||
\(77\) | 4.12323e91 | 1.31959 | ||||||||
\(78\) | 1.00147e92 | 1.71415 | ||||||||
\(79\) | 2.50159e91 | 0.230835 | 0.115418 | − | 0.993317i | \(-0.463179\pi\) | ||||
0.115418 | + | 0.993317i | \(0.463179\pi\) | |||||||
\(80\) | 1.11348e92 | 0.558237 | ||||||||
\(81\) | −4.50984e92 | −1.23776 | ||||||||
\(82\) | −3.45504e92 | −0.522975 | ||||||||
\(83\) | −1.80342e93 | −1.51638 | −0.758190 | − | 0.652033i | \(-0.773916\pi\) | ||||
−0.758190 | + | 0.652033i | \(0.773916\pi\) | |||||||
\(84\) | −2.08393e93 | −0.980253 | ||||||||
\(85\) | 2.46466e93 | 0.653039 | ||||||||
\(86\) | 9.10189e93 | 1.36759 | ||||||||
\(87\) | −1.91632e94 | −1.64356 | ||||||||
\(88\) | −6.89859e93 | −0.339900 | ||||||||
\(89\) | 4.69345e93 | 0.133683 | 0.0668417 | − | 0.997764i | \(-0.478708\pi\) | ||||
0.0668417 | + | 0.997764i | \(0.478708\pi\) | |||||||
\(90\) | −2.24425e94 | −0.371800 | ||||||||
\(91\) | −7.56574e94 | −0.733405 | ||||||||
\(92\) | 2.63870e95 | 1.50550 | ||||||||
\(93\) | 1.55509e95 | 0.525208 | ||||||||
\(94\) | 1.30279e96 | 2.61923 | ||||||||
\(95\) | 6.20293e94 | 0.0746452 | ||||||||
\(96\) | −2.33536e96 | −1.69122 | ||||||||
\(97\) | 1.90672e96 | 0.835329 | 0.417664 | − | 0.908601i | \(-0.362849\pi\) | ||||
0.417664 | + | 0.908601i | \(0.362849\pi\) | |||||||
\(98\) | −2.51060e96 | −0.668826 | ||||||||
\(99\) | −4.28776e96 | −0.698110 | ||||||||
\(100\) | −6.46228e96 | −0.646228 | ||||||||
\(101\) | 7.76230e96 | 0.479075 | 0.239538 | − | 0.970887i | \(-0.423004\pi\) | ||||
0.239538 | + | 0.970887i | \(0.423004\pi\) | |||||||
\(102\) | −4.48623e97 | −1.71701 | ||||||||
\(103\) | 2.20969e97 | 0.526897 | 0.263448 | − | 0.964673i | \(-0.415140\pi\) | ||||
0.263448 | + | 0.964673i | \(0.415140\pi\) | |||||||
\(104\) | 1.26583e97 | 0.188911 | ||||||||
\(105\) | 6.04971e97 | 0.567614 | ||||||||
\(106\) | 6.38984e97 | 0.378578 | ||||||||
\(107\) | −1.94773e98 | −0.731841 | −0.365920 | − | 0.930646i | \(-0.619246\pi\) | ||||
−0.365920 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(108\) | −3.39841e98 | −0.813249 | ||||||||
\(109\) | 2.04416e98 | 0.312845 | 0.156422 | − | 0.987690i | \(-0.450004\pi\) | ||||
0.156422 | + | 0.987690i | \(0.450004\pi\) | |||||||
\(110\) | 1.74194e99 | 1.71193 | ||||||||
\(111\) | 2.92504e99 | 1.85339 | ||||||||
\(112\) | 1.53117e99 | 0.627984 | ||||||||
\(113\) | −6.20044e99 | −1.65241 | −0.826205 | − | 0.563370i | \(-0.809505\pi\) | ||||
−0.826205 | + | 0.563370i | \(0.809505\pi\) | |||||||
\(114\) | −1.12907e99 | −0.196262 | ||||||||
\(115\) | −7.66021e99 | −0.871757 | ||||||||
\(116\) | −2.10683e100 | −1.57549 | ||||||||
\(117\) | 7.86764e99 | 0.387999 | ||||||||
\(118\) | −2.70390e100 | −0.882496 | ||||||||
\(119\) | 3.38920e100 | 0.734631 | ||||||||
\(120\) | −1.01218e100 | −0.146206 | ||||||||
\(121\) | 2.29271e101 | 2.21442 | ||||||||
\(122\) | −2.12906e101 | −1.37954 | ||||||||
\(123\) | −9.68522e100 | −0.422388 | ||||||||
\(124\) | 1.70968e101 | 0.503457 | ||||||||
\(125\) | 5.15615e101 | 1.02847 | ||||||||
\(126\) | −3.08610e101 | −0.418253 | ||||||||
\(127\) | 7.55132e101 | 0.697497 | 0.348749 | − | 0.937216i | \(-0.386607\pi\) | ||||
0.348749 | + | 0.937216i | \(0.386607\pi\) | |||||||
\(128\) | −5.95434e101 | −0.375967 | ||||||||
\(129\) | 2.55146e102 | 1.10455 | ||||||||
\(130\) | −3.19629e102 | −0.951467 | ||||||||
\(131\) | 3.29245e102 | 0.675867 | 0.337933 | − | 0.941170i | \(-0.390272\pi\) | ||||
0.337933 | + | 0.941170i | \(0.390272\pi\) | |||||||
\(132\) | −1.68205e103 | −2.38783 | ||||||||
\(133\) | 8.52977e101 | 0.0839716 | ||||||||
\(134\) | −8.17941e102 | −0.559937 | ||||||||
\(135\) | 9.86566e102 | 0.470910 | ||||||||
\(136\) | −5.67048e102 | −0.189227 | ||||||||
\(137\) | −7.54798e103 | −1.76556 | −0.882781 | − | 0.469784i | \(-0.844332\pi\) | ||||
−0.882781 | + | 0.469784i | \(0.844332\pi\) | |||||||
\(138\) | 1.39433e104 | 2.29208 | ||||||||
\(139\) | 1.04374e104 | 1.20886 | 0.604429 | − | 0.796659i | \(-0.293401\pi\) | ||||
0.604429 | + | 0.796659i | \(0.293401\pi\) | |||||||
\(140\) | 6.65110e103 | 0.544107 | ||||||||
\(141\) | 3.65201e104 | 2.11546 | ||||||||
\(142\) | −4.24628e104 | −1.74592 | ||||||||
\(143\) | −6.10670e104 | −1.78652 | ||||||||
\(144\) | −1.59227e104 | −0.332227 | ||||||||
\(145\) | 6.11616e104 | 0.912286 | ||||||||
\(146\) | −4.20161e104 | −0.449057 | ||||||||
\(147\) | −7.03775e104 | −0.540186 | ||||||||
\(148\) | 3.21581e105 | 1.77663 | ||||||||
\(149\) | −1.15832e105 | −0.461629 | −0.230815 | − | 0.972998i | \(-0.574139\pi\) | ||||
−0.230815 | + | 0.972998i | \(0.574139\pi\) | |||||||
\(150\) | −3.41477e105 | −0.983864 | ||||||||
\(151\) | −6.18810e105 | −1.29174 | −0.645870 | − | 0.763447i | \(-0.723505\pi\) | ||||
−0.645870 | + | 0.763447i | \(0.723505\pi\) | |||||||
\(152\) | −1.42712e104 | −0.0216295 | ||||||||
\(153\) | −3.52444e105 | −0.388647 | ||||||||
\(154\) | 2.39537e106 | 1.92583 | ||||||||
\(155\) | −4.96323e105 | −0.291526 | ||||||||
\(156\) | 3.08640e106 | 1.32712 | ||||||||
\(157\) | −4.62201e105 | −0.145780 | −0.0728900 | − | 0.997340i | \(-0.523222\pi\) | ||||
−0.0728900 | + | 0.997340i | \(0.523222\pi\) | |||||||
\(158\) | 1.45329e106 | 0.336885 | ||||||||
\(159\) | 1.79121e106 | 0.305764 | ||||||||
\(160\) | 7.45357e106 | 0.938739 | ||||||||
\(161\) | −1.05337e107 | −0.980677 | ||||||||
\(162\) | −2.61997e107 | −1.80641 | ||||||||
\(163\) | −1.23935e107 | −0.634010 | −0.317005 | − | 0.948424i | \(-0.602677\pi\) | ||||
−0.317005 | + | 0.948424i | \(0.602677\pi\) | |||||||
\(164\) | −1.06480e107 | −0.404895 | ||||||||
\(165\) | 4.88303e107 | 1.38267 | ||||||||
\(166\) | −1.04768e108 | −2.21303 | ||||||||
\(167\) | 1.14523e108 | 1.80777 | 0.903884 | − | 0.427777i | \(-0.140703\pi\) | ||||
0.903884 | + | 0.427777i | \(0.140703\pi\) | |||||||
\(168\) | −1.39186e107 | −0.164474 | ||||||||
\(169\) | −7.98835e105 | −0.00707867 | ||||||||
\(170\) | 1.43183e108 | 0.953057 | ||||||||
\(171\) | −8.87013e106 | −0.0444241 | ||||||||
\(172\) | 2.80510e108 | 1.05881 | ||||||||
\(173\) | 9.59378e107 | 0.273372 | 0.136686 | − | 0.990614i | \(-0.456355\pi\) | ||||
0.136686 | + | 0.990614i | \(0.456355\pi\) | |||||||
\(174\) | −1.11328e109 | −2.39864 | ||||||||
\(175\) | 2.57974e108 | 0.420951 | ||||||||
\(176\) | 1.23588e109 | 1.52972 | ||||||||
\(177\) | −7.57960e108 | −0.712759 | ||||||||
\(178\) | 2.72664e108 | 0.195100 | ||||||||
\(179\) | 5.91656e108 | 0.322625 | 0.161312 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161312 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(180\) | −6.91650e108 | −0.287853 | ||||||||
\(181\) | −1.14400e109 | −0.363929 | −0.181965 | − | 0.983305i | \(-0.558246\pi\) | ||||
−0.181965 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(182\) | −4.39528e109 | −1.07035 | ||||||||
\(183\) | −5.96821e109 | −1.11421 | ||||||||
\(184\) | 1.76240e109 | 0.252603 | ||||||||
\(185\) | −9.33558e109 | −1.02876 | ||||||||
\(186\) | 9.03419e109 | 0.766499 | ||||||||
\(187\) | 2.73559e110 | 1.78951 | ||||||||
\(188\) | 4.01505e110 | 2.02785 | ||||||||
\(189\) | 1.35664e110 | 0.529747 | ||||||||
\(190\) | 3.60356e109 | 0.108939 | ||||||||
\(191\) | −6.34699e110 | −1.48748 | −0.743738 | − | 0.668471i | \(-0.766949\pi\) | ||||
−0.743738 | + | 0.668471i | \(0.766949\pi\) | |||||||
\(192\) | −8.03897e110 | −1.46248 | ||||||||
\(193\) | 6.48750e109 | 0.0917377 | 0.0458689 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458689 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(194\) | 1.10770e111 | 1.21909 | ||||||||
\(195\) | −8.95989e110 | −0.768465 | ||||||||
\(196\) | −7.73737e110 | −0.517814 | ||||||||
\(197\) | −4.96074e110 | −0.259379 | −0.129689 | − | 0.991555i | \(-0.541398\pi\) | ||||
−0.129689 | + | 0.991555i | \(0.541398\pi\) | |||||||
\(198\) | −2.49095e111 | −1.01883 | ||||||||
\(199\) | 3.90550e111 | 1.25113 | 0.625565 | − | 0.780172i | \(-0.284869\pi\) | ||||
0.625565 | + | 0.780172i | \(0.284869\pi\) | |||||||
\(200\) | −4.31618e110 | −0.108429 | ||||||||
\(201\) | −2.29287e111 | −0.452241 | ||||||||
\(202\) | 4.50947e111 | 0.699171 | ||||||||
\(203\) | 8.41045e111 | 1.02627 | ||||||||
\(204\) | −1.38260e112 | −1.32934 | ||||||||
\(205\) | 3.09115e111 | 0.234454 | ||||||||
\(206\) | 1.28371e112 | 0.768963 | ||||||||
\(207\) | 1.09540e112 | 0.518815 | ||||||||
\(208\) | −2.26773e112 | −0.850197 | ||||||||
\(209\) | 6.88481e111 | 0.204549 | ||||||||
\(210\) | 3.51454e112 | 0.828387 | ||||||||
\(211\) | 1.93935e112 | 0.363041 | 0.181521 | − | 0.983387i | \(-0.441898\pi\) | ||||
0.181521 | + | 0.983387i | \(0.441898\pi\) | |||||||
\(212\) | 1.96928e112 | 0.293101 | ||||||||
\(213\) | −1.19032e113 | −1.41011 | ||||||||
\(214\) | −1.13153e113 | −1.06806 | ||||||||
\(215\) | −8.14326e112 | −0.613102 | ||||||||
\(216\) | −2.26981e112 | −0.136453 | ||||||||
\(217\) | −6.82503e112 | −0.327950 | ||||||||
\(218\) | 1.18754e113 | 0.456572 | ||||||||
\(219\) | −1.17780e113 | −0.362687 | ||||||||
\(220\) | 5.36845e113 | 1.32540 | ||||||||
\(221\) | −5.01956e113 | −0.994581 | ||||||||
\(222\) | 1.69928e114 | 2.70487 | ||||||||
\(223\) | 3.72463e113 | 0.476758 | 0.238379 | − | 0.971172i | \(-0.423384\pi\) | ||||
0.238379 | + | 0.971172i | \(0.423384\pi\) | |||||||
\(224\) | 1.02495e114 | 1.05603 | ||||||||
\(225\) | −2.68268e113 | −0.222698 | ||||||||
\(226\) | −3.60211e114 | −2.41156 | ||||||||
\(227\) | −1.86629e114 | −1.00861 | −0.504307 | − | 0.863524i | \(-0.668252\pi\) | ||||
−0.504307 | + | 0.863524i | \(0.668252\pi\) | |||||||
\(228\) | −3.47967e113 | −0.151949 | ||||||||
\(229\) | 2.25589e114 | 0.796705 | 0.398353 | − | 0.917232i | \(-0.369582\pi\) | ||||
0.398353 | + | 0.917232i | \(0.369582\pi\) | |||||||
\(230\) | −4.45016e114 | −1.27226 | ||||||||
\(231\) | 6.71474e114 | 1.55542 | ||||||||
\(232\) | −1.40715e114 | −0.264347 | ||||||||
\(233\) | 3.48285e113 | 0.0531096 | 0.0265548 | − | 0.999647i | \(-0.491546\pi\) | ||||
0.0265548 | + | 0.999647i | \(0.491546\pi\) | |||||||
\(234\) | 4.57066e114 | 0.566252 | ||||||||
\(235\) | −1.16558e115 | −1.17422 | ||||||||
\(236\) | −8.33309e114 | −0.683241 | ||||||||
\(237\) | 4.07387e114 | 0.272090 | ||||||||
\(238\) | 1.96894e115 | 1.07213 | ||||||||
\(239\) | −2.83338e115 | −1.25895 | −0.629473 | − | 0.777023i | \(-0.716729\pi\) | ||||
−0.629473 | + | 0.777023i | \(0.716729\pi\) | |||||||
\(240\) | 1.81332e115 | 0.658004 | ||||||||
\(241\) | 9.69225e112 | 0.00287474 | 0.00143737 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00143737 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(242\) | 1.33194e116 | 3.23176 | ||||||||
\(243\) | −3.72118e115 | −0.739225 | ||||||||
\(244\) | −6.56151e115 | −1.06806 | ||||||||
\(245\) | 2.24618e115 | 0.299840 | ||||||||
\(246\) | −5.62658e115 | −0.616441 | ||||||||
\(247\) | −1.26330e115 | −0.113685 | ||||||||
\(248\) | 1.14190e115 | 0.0844736 | ||||||||
\(249\) | −2.93689e116 | −1.78739 | ||||||||
\(250\) | 2.99544e116 | 1.50096 | ||||||||
\(251\) | −1.66692e116 | −0.688238 | −0.344119 | − | 0.938926i | \(-0.611822\pi\) | ||||
−0.344119 | + | 0.938926i | \(0.611822\pi\) | |||||||
\(252\) | −9.51101e115 | −0.323818 | ||||||||
\(253\) | −8.50229e116 | −2.38886 | ||||||||
\(254\) | 4.38690e116 | 1.01794 | ||||||||
\(255\) | 4.01373e116 | 0.769750 | ||||||||
\(256\) | 4.36288e116 | 0.692046 | ||||||||
\(257\) | 1.50051e117 | 1.97008 | 0.985038 | − | 0.172337i | \(-0.0551317\pi\) | ||||
0.985038 | + | 0.172337i | \(0.0551317\pi\) | |||||||
\(258\) | 1.48225e117 | 1.61201 | ||||||||
\(259\) | −1.28375e117 | −1.15729 | ||||||||
\(260\) | −9.85059e116 | −0.736639 | ||||||||
\(261\) | −8.74605e116 | −0.542935 | ||||||||
\(262\) | 1.91273e117 | 0.986373 | ||||||||
\(263\) | −3.21862e117 | −1.37980 | −0.689899 | − | 0.723905i | \(-0.742345\pi\) | ||||
−0.689899 | + | 0.723905i | \(0.742345\pi\) | |||||||
\(264\) | −1.12344e117 | −0.400646 | ||||||||
\(265\) | −5.71685e116 | −0.169720 | ||||||||
\(266\) | 4.95532e116 | 0.122550 | ||||||||
\(267\) | 7.64335e116 | 0.157575 | ||||||||
\(268\) | −2.52080e117 | −0.433512 | ||||||||
\(269\) | −9.90826e116 | −0.142237 | −0.0711184 | − | 0.997468i | \(-0.522657\pi\) | ||||
−0.0711184 | + | 0.997468i | \(0.522657\pi\) | |||||||
\(270\) | 5.73140e117 | 0.687255 | ||||||||
\(271\) | 1.88089e117 | 0.188518 | 0.0942590 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942590 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(272\) | 1.01587e118 | 0.851618 | ||||||||
\(273\) | −1.23209e118 | −0.864479 | ||||||||
\(274\) | −4.38496e118 | −2.57669 | ||||||||
\(275\) | 2.08224e118 | 1.02541 | ||||||||
\(276\) | 4.29716e118 | 1.77456 | ||||||||
\(277\) | −3.82013e118 | −1.32376 | −0.661880 | − | 0.749610i | \(-0.730241\pi\) | ||||
−0.661880 | + | 0.749610i | \(0.730241\pi\) | |||||||
\(278\) | 6.06356e118 | 1.76423 | ||||||||
\(279\) | 7.09737e117 | 0.173498 | ||||||||
\(280\) | 4.44229e117 | 0.0912941 | ||||||||
\(281\) | −1.43114e118 | −0.247415 | −0.123707 | − | 0.992319i | \(-0.539478\pi\) | ||||
−0.123707 | + | 0.992319i | \(0.539478\pi\) | |||||||
\(282\) | 2.12161e119 | 3.08734 | ||||||||
\(283\) | −1.55838e119 | −1.90999 | −0.954995 | − | 0.296621i | \(-0.904140\pi\) | ||||
−0.954995 | + | 0.296621i | \(0.904140\pi\) | |||||||
\(284\) | −1.30865e119 | −1.35172 | ||||||||
\(285\) | 1.01016e118 | 0.0879858 | ||||||||
\(286\) | −3.54765e119 | −2.60728 | ||||||||
\(287\) | 4.25069e118 | 0.263747 | ||||||||
\(288\) | −1.06585e119 | −0.558678 | ||||||||
\(289\) | −8.47790e116 | −0.00375615 | ||||||||
\(290\) | 3.55315e119 | 1.33141 | ||||||||
\(291\) | 3.10512e119 | 0.984618 | ||||||||
\(292\) | −1.29489e119 | −0.347667 | ||||||||
\(293\) | 2.93290e119 | 0.667142 | 0.333571 | − | 0.942725i | \(-0.391746\pi\) | ||||
0.333571 | + | 0.942725i | \(0.391746\pi\) | |||||||
\(294\) | −4.08854e119 | −0.788358 | ||||||||
\(295\) | 2.41912e119 | 0.395630 | ||||||||
\(296\) | 2.14785e119 | 0.298096 | ||||||||
\(297\) | 1.09502e120 | 1.29043 | ||||||||
\(298\) | −6.72918e119 | −0.673710 | ||||||||
\(299\) | 1.56009e120 | 1.32769 | ||||||||
\(300\) | −1.05239e120 | −0.761722 | ||||||||
\(301\) | −1.11979e120 | −0.689705 | ||||||||
\(302\) | −3.59494e120 | −1.88519 | ||||||||
\(303\) | 1.26410e120 | 0.564695 | ||||||||
\(304\) | 2.55668e119 | 0.0973437 | ||||||||
\(305\) | 1.90482e120 | 0.618461 | ||||||||
\(306\) | −2.04750e120 | −0.567199 | ||||||||
\(307\) | −6.57031e120 | −1.55373 | −0.776863 | − | 0.629669i | \(-0.783190\pi\) | ||||
−0.776863 | + | 0.629669i | \(0.783190\pi\) | |||||||
\(308\) | 7.38225e120 | 1.49100 | ||||||||
\(309\) | 3.59851e120 | 0.621063 | ||||||||
\(310\) | −2.88336e120 | −0.425459 | ||||||||
\(311\) | 4.96160e120 | 0.626244 | 0.313122 | − | 0.949713i | \(-0.398625\pi\) | ||||
0.313122 | + | 0.949713i | \(0.398625\pi\) | |||||||
\(312\) | 2.06142e120 | 0.222673 | ||||||||
\(313\) | −1.65467e121 | −1.53042 | −0.765212 | − | 0.643779i | \(-0.777366\pi\) | ||||
−0.765212 | + | 0.643779i | \(0.777366\pi\) | |||||||
\(314\) | −2.68513e120 | −0.212754 | ||||||||
\(315\) | 2.76107e120 | 0.187506 | ||||||||
\(316\) | 4.47885e120 | 0.260822 | ||||||||
\(317\) | 4.69666e120 | 0.234647 | 0.117323 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117323 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(318\) | 1.04059e121 | 0.446238 | ||||||||
\(319\) | 6.78850e121 | 2.49992 | ||||||||
\(320\) | 2.56573e121 | 0.811777 | ||||||||
\(321\) | −3.17191e121 | −0.862635 | ||||||||
\(322\) | −6.11950e121 | −1.43122 | ||||||||
\(323\) | 5.65915e120 | 0.113875 | ||||||||
\(324\) | −8.07443e121 | −1.39855 | ||||||||
\(325\) | −3.82072e121 | −0.569904 | ||||||||
\(326\) | −7.19995e121 | −0.925286 | ||||||||
\(327\) | 3.32894e121 | 0.368756 | ||||||||
\(328\) | −7.11185e120 | −0.0679362 | ||||||||
\(329\) | −1.60281e122 | −1.32093 | ||||||||
\(330\) | 2.83677e122 | 2.01789 | ||||||||
\(331\) | 1.43264e122 | 0.879994 | 0.439997 | − | 0.897999i | \(-0.354979\pi\) | ||||
0.439997 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(332\) | −3.22884e122 | −1.71336 | ||||||||
\(333\) | 1.33498e122 | 0.612250 | ||||||||
\(334\) | 6.65314e122 | 2.63829 | ||||||||
\(335\) | 7.31794e121 | 0.251024 | ||||||||
\(336\) | 2.49353e122 | 0.740217 | ||||||||
\(337\) | −4.66879e122 | −1.19993 | −0.599963 | − | 0.800028i | \(-0.704818\pi\) | ||||
−0.599963 | + | 0.800028i | \(0.704818\pi\) | |||||||
\(338\) | −4.64079e120 | −0.0103308 | ||||||||
\(339\) | −1.00975e123 | −1.94773 | ||||||||
\(340\) | 4.41273e122 | 0.737871 | ||||||||
\(341\) | −5.50883e122 | −0.798863 | ||||||||
\(342\) | −5.15305e121 | −0.0648334 | ||||||||
\(343\) | 9.82863e122 | 1.07332 | ||||||||
\(344\) | 1.87353e122 | 0.177655 | ||||||||
\(345\) | −1.24748e123 | −1.02756 | ||||||||
\(346\) | 5.57346e122 | 0.398964 | ||||||||
\(347\) | 1.52298e123 | 0.947794 | 0.473897 | − | 0.880580i | \(-0.342847\pi\) | ||||
0.473897 | + | 0.880580i | \(0.342847\pi\) | |||||||
\(348\) | −3.43099e123 | −1.85706 | ||||||||
\(349\) | −1.39112e123 | −0.655136 | −0.327568 | − | 0.944828i | \(-0.606229\pi\) | ||||
−0.327568 | + | 0.944828i | \(0.606229\pi\) | |||||||
\(350\) | 1.49869e123 | 0.614343 | ||||||||
\(351\) | −2.00925e123 | −0.717199 | ||||||||
\(352\) | 8.27292e123 | 2.57241 | ||||||||
\(353\) | −3.28231e123 | −0.889418 | −0.444709 | − | 0.895675i | \(-0.646693\pi\) | ||||
−0.444709 | + | 0.895675i | \(0.646693\pi\) | |||||||
\(354\) | −4.40333e123 | −1.04021 | ||||||||
\(355\) | 3.79905e123 | 0.782709 | ||||||||
\(356\) | 8.40317e122 | 0.151049 | ||||||||
\(357\) | 5.51935e123 | 0.865924 | ||||||||
\(358\) | 3.43720e123 | 0.470844 | ||||||||
\(359\) | −3.45698e122 | −0.0413634 | −0.0206817 | − | 0.999786i | \(-0.506584\pi\) | ||||
−0.0206817 | + | 0.999786i | \(0.506584\pi\) | |||||||
\(360\) | −4.61955e122 | −0.0482980 | ||||||||
\(361\) | −1.07996e124 | −0.986984 | ||||||||
\(362\) | −6.64603e123 | −0.531125 | ||||||||
\(363\) | 3.73371e124 | 2.61017 | ||||||||
\(364\) | −1.35457e124 | −0.828677 | ||||||||
\(365\) | 3.75908e123 | 0.201316 | ||||||||
\(366\) | −3.46720e124 | −1.62610 | ||||||||
\(367\) | −3.96529e123 | −0.162919 | −0.0814593 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814593 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(368\) | −3.15734e124 | −1.13685 | ||||||||
\(369\) | −4.42031e123 | −0.139532 | ||||||||
\(370\) | −5.42345e124 | −1.50139 | ||||||||
\(371\) | −7.86135e123 | −0.190925 | ||||||||
\(372\) | 2.78423e124 | 0.593434 | ||||||||
\(373\) | 4.73757e124 | 0.886498 | 0.443249 | − | 0.896399i | \(-0.353826\pi\) | ||||
0.443249 | + | 0.896399i | \(0.353826\pi\) | |||||||
\(374\) | 1.58923e125 | 2.61164 | ||||||||
\(375\) | 8.39686e124 | 1.21227 | ||||||||
\(376\) | 2.68166e124 | 0.340247 | ||||||||
\(377\) | −1.24563e125 | −1.38942 | ||||||||
\(378\) | 7.88135e124 | 0.773123 | ||||||||
\(379\) | −1.09064e125 | −0.941193 | −0.470596 | − | 0.882349i | \(-0.655961\pi\) | ||||
−0.470596 | + | 0.882349i | \(0.655961\pi\) | |||||||
\(380\) | 1.11057e124 | 0.0843419 | ||||||||
\(381\) | 1.22974e125 | 0.822153 | ||||||||
\(382\) | −3.68725e125 | −2.17085 | ||||||||
\(383\) | 6.19469e124 | 0.321277 | 0.160638 | − | 0.987013i | \(-0.448645\pi\) | ||||
0.160638 | + | 0.987013i | \(0.448645\pi\) | |||||||
\(384\) | −9.69672e124 | −0.443160 | ||||||||
\(385\) | −2.14308e125 | −0.863364 | ||||||||
\(386\) | 3.76888e124 | 0.133884 | ||||||||
\(387\) | 1.16448e125 | 0.364880 | ||||||||
\(388\) | 3.41380e125 | 0.943841 | ||||||||
\(389\) | 5.76337e125 | 1.40644 | 0.703220 | − | 0.710972i | \(-0.251745\pi\) | ||||
0.703220 | + | 0.710972i | \(0.251745\pi\) | |||||||
\(390\) | −5.20520e125 | −1.12151 | ||||||||
\(391\) | −6.98868e125 | −1.32991 | ||||||||
\(392\) | −5.16782e124 | −0.0868826 | ||||||||
\(393\) | 5.36180e125 | 0.796657 | ||||||||
\(394\) | −2.88191e125 | −0.378542 | ||||||||
\(395\) | −1.30022e125 | −0.151028 | ||||||||
\(396\) | −7.67682e125 | −0.788796 | ||||||||
\(397\) | 5.08950e125 | 0.462738 | 0.231369 | − | 0.972866i | \(-0.425679\pi\) | ||||
0.231369 | + | 0.972866i | \(0.425679\pi\) | |||||||
\(398\) | 2.26888e126 | 1.82592 | ||||||||
\(399\) | 1.38908e125 | 0.0989790 | ||||||||
\(400\) | 7.73243e125 | 0.487985 | ||||||||
\(401\) | −1.13668e126 | −0.635533 | −0.317766 | − | 0.948169i | \(-0.602933\pi\) | ||||
−0.317766 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(402\) | −1.33203e126 | −0.660009 | ||||||||
\(403\) | 1.01082e126 | 0.443995 | ||||||||
\(404\) | 1.38976e126 | 0.541309 | ||||||||
\(405\) | 2.34403e126 | 0.809830 | ||||||||
\(406\) | 4.88601e126 | 1.49776 | ||||||||
\(407\) | −1.03618e127 | −2.81908 | ||||||||
\(408\) | −9.23445e125 | −0.223045 | ||||||||
\(409\) | −6.20420e126 | −1.33078 | −0.665389 | − | 0.746497i | \(-0.731734\pi\) | ||||
−0.665389 | + | 0.746497i | \(0.731734\pi\) | |||||||
\(410\) | 1.79579e126 | 0.342166 | ||||||||
\(411\) | −1.22920e127 | −2.08110 | ||||||||
\(412\) | 3.95623e126 | 0.595342 | ||||||||
\(413\) | 3.32657e126 | 0.445061 | ||||||||
\(414\) | 6.36368e126 | 0.757168 | ||||||||
\(415\) | 9.37340e126 | 0.992121 | ||||||||
\(416\) | −1.51800e127 | −1.42970 | ||||||||
\(417\) | 1.69975e127 | 1.42490 | ||||||||
\(418\) | 3.99969e126 | 0.298522 | ||||||||
\(419\) | −6.36234e126 | −0.422899 | −0.211450 | − | 0.977389i | \(-0.567818\pi\) | ||||
−0.211450 | + | 0.977389i | \(0.567818\pi\) | |||||||
\(420\) | 1.08314e127 | 0.641349 | ||||||||
\(421\) | 4.23408e126 | 0.223397 | 0.111698 | − | 0.993742i | \(-0.464371\pi\) | ||||
0.111698 | + | 0.993742i | \(0.464371\pi\) | |||||||
\(422\) | 1.12665e127 | 0.529830 | ||||||||
\(423\) | 1.66677e127 | 0.698822 | ||||||||
\(424\) | 1.31528e126 | 0.0491785 | ||||||||
\(425\) | 1.71155e127 | 0.570857 | ||||||||
\(426\) | −6.91512e127 | −2.05795 | ||||||||
\(427\) | 2.61936e127 | 0.695733 | ||||||||
\(428\) | −3.48723e127 | −0.826909 | ||||||||
\(429\) | −9.94483e127 | −2.10581 | ||||||||
\(430\) | −4.73078e127 | −0.894773 | ||||||||
\(431\) | 2.86163e127 | 0.483577 | 0.241788 | − | 0.970329i | \(-0.422266\pi\) | ||||
0.241788 | + | 0.970329i | \(0.422266\pi\) | |||||||
\(432\) | 4.06636e127 | 0.614107 | ||||||||
\(433\) | 9.31655e127 | 1.25774 | 0.628872 | − | 0.777509i | \(-0.283517\pi\) | ||||
0.628872 | + | 0.777509i | \(0.283517\pi\) | |||||||
\(434\) | −3.96497e127 | −0.478616 | ||||||||
\(435\) | 9.96025e127 | 1.07533 | ||||||||
\(436\) | 3.65987e127 | 0.353485 | ||||||||
\(437\) | −1.75888e127 | −0.152015 | ||||||||
\(438\) | −6.84237e127 | −0.529313 | ||||||||
\(439\) | 4.77870e126 | 0.0330964 | 0.0165482 | − | 0.999863i | \(-0.494732\pi\) | ||||
0.0165482 | + | 0.999863i | \(0.494732\pi\) | |||||||
\(440\) | 3.58560e127 | 0.222386 | ||||||||
\(441\) | −3.21201e127 | −0.178445 | ||||||||
\(442\) | −2.91609e128 | −1.45151 | ||||||||
\(443\) | −1.23338e128 | −0.550196 | −0.275098 | − | 0.961416i | \(-0.588710\pi\) | ||||
−0.275098 | + | 0.961416i | \(0.588710\pi\) | |||||||
\(444\) | 5.23699e128 | 2.09415 | ||||||||
\(445\) | −2.43946e127 | −0.0874648 | ||||||||
\(446\) | 2.16381e128 | 0.695789 | ||||||||
\(447\) | −1.88633e128 | −0.544131 | ||||||||
\(448\) | 3.52818e128 | 0.913203 | ||||||||
\(449\) | 6.26534e128 | 1.45545 | 0.727725 | − | 0.685869i | \(-0.240578\pi\) | ||||
0.727725 | + | 0.685869i | \(0.240578\pi\) | |||||||
\(450\) | −1.55849e128 | −0.325010 | ||||||||
\(451\) | 3.43095e128 | 0.642469 | ||||||||
\(452\) | −1.11013e129 | −1.86706 | ||||||||
\(453\) | −1.00774e129 | −1.52260 | ||||||||
\(454\) | −1.08421e129 | −1.47199 | ||||||||
\(455\) | 3.93236e128 | 0.479844 | ||||||||
\(456\) | −2.32408e127 | −0.0254951 | ||||||||
\(457\) | −1.07131e129 | −1.05677 | −0.528386 | − | 0.849004i | \(-0.677203\pi\) | ||||
−0.528386 | + | 0.849004i | \(0.677203\pi\) | |||||||
\(458\) | 1.31055e129 | 1.16273 | ||||||||
\(459\) | 9.00078e128 | 0.718398 | ||||||||
\(460\) | −1.37149e129 | −0.985002 | ||||||||
\(461\) | −3.95142e128 | −0.255422 | −0.127711 | − | 0.991811i | \(-0.540763\pi\) | ||||
−0.127711 | + | 0.991811i | \(0.540763\pi\) | |||||||
\(462\) | 3.90089e129 | 2.27001 | ||||||||
\(463\) | −1.49616e129 | −0.783969 | −0.391984 | − | 0.919972i | \(-0.628211\pi\) | ||||
−0.391984 | + | 0.919972i | \(0.628211\pi\) | |||||||
\(464\) | 2.52092e129 | 1.18970 | ||||||||
\(465\) | −8.08269e128 | −0.343627 | ||||||||
\(466\) | 2.02335e128 | 0.0775092 | ||||||||
\(467\) | 4.11978e129 | 1.42235 | 0.711174 | − | 0.703017i | \(-0.248164\pi\) | ||||
0.711174 | + | 0.703017i | \(0.248164\pi\) | |||||||
\(468\) | 1.40862e129 | 0.438401 | ||||||||
\(469\) | 1.00630e129 | 0.282388 | ||||||||
\(470\) | −6.77137e129 | −1.71368 | ||||||||
\(471\) | −7.52700e128 | −0.171834 | ||||||||
\(472\) | −5.56569e128 | −0.114639 | ||||||||
\(473\) | −9.03843e129 | −1.68007 | ||||||||
\(474\) | 2.36669e129 | 0.397093 | ||||||||
\(475\) | 4.30755e128 | 0.0652515 | ||||||||
\(476\) | 6.06803e129 | 0.830062 | ||||||||
\(477\) | 8.17504e128 | 0.101006 | ||||||||
\(478\) | −1.64604e130 | −1.83733 | ||||||||
\(479\) | −1.35340e130 | −1.36506 | −0.682532 | − | 0.730856i | \(-0.739121\pi\) | ||||
−0.682532 | + | 0.730856i | \(0.739121\pi\) | |||||||
\(480\) | 1.21382e130 | 1.10651 | ||||||||
\(481\) | 1.90130e130 | 1.56680 | ||||||||
\(482\) | 5.63066e127 | 0.00419544 | ||||||||
\(483\) | −1.71543e130 | −1.15594 | ||||||||
\(484\) | 4.10488e130 | 2.50208 | ||||||||
\(485\) | −9.91033e129 | −0.546530 | ||||||||
\(486\) | −2.16180e130 | −1.07884 | ||||||||
\(487\) | 2.48775e130 | 1.12370 | 0.561852 | − | 0.827238i | \(-0.310089\pi\) | ||||
0.561852 | + | 0.827238i | \(0.310089\pi\) | |||||||
\(488\) | −4.38245e129 | −0.179207 | ||||||||
\(489\) | −2.01830e130 | −0.747320 | ||||||||
\(490\) | 1.30491e130 | 0.437592 | ||||||||
\(491\) | −4.38925e129 | −0.133333 | −0.0666665 | − | 0.997775i | \(-0.521236\pi\) | ||||
−0.0666665 | + | 0.997775i | \(0.521236\pi\) | |||||||
\(492\) | −1.73404e130 | −0.477258 | ||||||||
\(493\) | 5.57999e130 | 1.39174 | ||||||||
\(494\) | −7.33906e129 | −0.165914 | ||||||||
\(495\) | 2.22860e130 | 0.456751 | ||||||||
\(496\) | −2.04571e130 | −0.380175 | ||||||||
\(497\) | 5.22415e130 | 0.880503 | ||||||||
\(498\) | −1.70617e131 | −2.60855 | ||||||||
\(499\) | −3.55420e130 | −0.493021 | −0.246510 | − | 0.969140i | \(-0.579284\pi\) | ||||
−0.246510 | + | 0.969140i | \(0.579284\pi\) | |||||||
\(500\) | 9.23159e130 | 1.16207 | ||||||||
\(501\) | 1.86502e131 | 2.13085 | ||||||||
\(502\) | −9.68387e130 | −1.00443 | ||||||||
\(503\) | −8.92475e130 | −0.840521 | −0.420261 | − | 0.907403i | \(-0.638061\pi\) | ||||
−0.420261 | + | 0.907403i | \(0.638061\pi\) | |||||||
\(504\) | −6.35243e129 | −0.0543324 | ||||||||
\(505\) | −4.03452e130 | −0.313444 | ||||||||
\(506\) | −4.93936e131 | −3.48635 | ||||||||
\(507\) | −1.30091e129 | −0.00834377 | ||||||||
\(508\) | 1.35199e131 | 0.788104 | ||||||||
\(509\) | 1.97808e131 | 1.04817 | 0.524085 | − | 0.851666i | \(-0.324407\pi\) | ||||
0.524085 | + | 0.851666i | \(0.324407\pi\) | |||||||
\(510\) | 2.33176e131 | 1.12339 | ||||||||
\(511\) | 5.16919e130 | 0.226469 | ||||||||
\(512\) | 3.47809e131 | 1.38595 | ||||||||
\(513\) | 2.26527e130 | 0.0821160 | ||||||||
\(514\) | 8.71714e131 | 2.87517 | ||||||||
\(515\) | −1.14850e131 | −0.344732 | ||||||||
\(516\) | 4.56814e131 | 1.24804 | ||||||||
\(517\) | −1.29371e132 | −3.21770 | ||||||||
\(518\) | −7.45789e131 | −1.68897 | ||||||||
\(519\) | 1.56236e131 | 0.322229 | ||||||||
\(520\) | −6.57924e130 | −0.123599 | ||||||||
\(521\) | −3.34022e131 | −0.571670 | −0.285835 | − | 0.958279i | \(-0.592271\pi\) | ||||
−0.285835 | + | 0.958279i | \(0.592271\pi\) | |||||||
\(522\) | −5.08097e131 | −0.792369 | ||||||||
\(523\) | 1.61863e131 | 0.230046 | 0.115023 | − | 0.993363i | \(-0.463306\pi\) | ||||
0.115023 | + | 0.993363i | \(0.463306\pi\) | |||||||
\(524\) | 5.89481e131 | 0.763664 | ||||||||
\(525\) | 4.20115e131 | 0.496183 | ||||||||
\(526\) | −1.86984e132 | −2.01370 | ||||||||
\(527\) | −4.52813e131 | −0.444738 | ||||||||
\(528\) | 2.01265e132 | 1.80312 | ||||||||
\(529\) | 9.48607e131 | 0.775329 | ||||||||
\(530\) | −3.32117e131 | −0.247692 | ||||||||
\(531\) | −3.45931e131 | −0.235454 | ||||||||
\(532\) | 1.52717e131 | 0.0948798 | ||||||||
\(533\) | −6.29547e131 | −0.357074 | ||||||||
\(534\) | 4.44036e131 | 0.229968 | ||||||||
\(535\) | 1.01235e132 | 0.478821 | ||||||||
\(536\) | −1.68365e131 | −0.0727377 | ||||||||
\(537\) | 9.63520e131 | 0.380284 | ||||||||
\(538\) | −5.75615e131 | −0.207583 | ||||||||
\(539\) | 2.49310e132 | 0.821644 | ||||||||
\(540\) | 1.76635e132 | 0.532083 | ||||||||
\(541\) | −5.87111e132 | −1.61679 | −0.808394 | − | 0.588641i | \(-0.799663\pi\) | ||||
−0.808394 | + | 0.588641i | \(0.799663\pi\) | |||||||
\(542\) | 1.09269e132 | 0.275127 | ||||||||
\(543\) | −1.86303e132 | −0.428970 | ||||||||
\(544\) | 6.80015e132 | 1.43209 | ||||||||
\(545\) | −1.06247e132 | −0.204685 | ||||||||
\(546\) | −7.15777e132 | −1.26164 | ||||||||
\(547\) | 7.80647e132 | 1.25913 | 0.629563 | − | 0.776949i | \(-0.283234\pi\) | ||||
0.629563 | + | 0.776949i | \(0.283234\pi\) | |||||||
\(548\) | −1.35139e133 | −1.99491 | ||||||||
\(549\) | −2.72388e132 | −0.368068 | ||||||||
\(550\) | 1.20967e133 | 1.49650 | ||||||||
\(551\) | 1.40434e132 | 0.159082 | ||||||||
\(552\) | 2.87009e132 | 0.297749 | ||||||||
\(553\) | −1.78796e132 | −0.169898 | ||||||||
\(554\) | −2.21928e133 | −1.93192 | ||||||||
\(555\) | −1.52031e133 | −1.21261 | ||||||||
\(556\) | 1.86872e133 | 1.36589 | ||||||||
\(557\) | −1.08981e133 | −0.730088 | −0.365044 | − | 0.930990i | \(-0.618946\pi\) | ||||
−0.365044 | + | 0.930990i | \(0.618946\pi\) | |||||||
\(558\) | 4.12318e132 | 0.253206 | ||||||||
\(559\) | 1.65847e133 | 0.933758 | ||||||||
\(560\) | −7.95837e132 | −0.410870 | ||||||||
\(561\) | 4.45495e133 | 2.10933 | ||||||||
\(562\) | −8.31413e132 | −0.361082 | ||||||||
\(563\) | −1.63334e133 | −0.650758 | −0.325379 | − | 0.945584i | \(-0.605492\pi\) | ||||
−0.325379 | + | 0.945584i | \(0.605492\pi\) | |||||||
\(564\) | 6.53856e133 | 2.39026 | ||||||||
\(565\) | 3.22273e133 | 1.08112 | ||||||||
\(566\) | −9.05332e133 | −2.78748 | ||||||||
\(567\) | 3.22331e133 | 0.911012 | ||||||||
\(568\) | −8.74054e132 | −0.226800 | ||||||||
\(569\) | 2.54954e133 | 0.607459 | 0.303730 | − | 0.952758i | \(-0.401768\pi\) | ||||
0.303730 | + | 0.952758i | \(0.401768\pi\) | |||||||
\(570\) | 5.86844e132 | 0.128408 | ||||||||
\(571\) | 3.10057e132 | 0.0623146 | 0.0311573 | − | 0.999514i | \(-0.490081\pi\) | ||||
0.0311573 | + | 0.999514i | \(0.490081\pi\) | |||||||
\(572\) | −1.09334e134 | −2.01860 | ||||||||
\(573\) | −1.03362e134 | −1.75332 | ||||||||
\(574\) | 2.46942e133 | 0.384918 | ||||||||
\(575\) | −5.31955e133 | −0.762051 | ||||||||
\(576\) | −3.66897e133 | −0.483118 | ||||||||
\(577\) | 2.35450e133 | 0.285018 | 0.142509 | − | 0.989794i | \(-0.454483\pi\) | ||||
0.142509 | + | 0.989794i | \(0.454483\pi\) | |||||||
\(578\) | −4.92519e131 | −0.00548179 | ||||||||
\(579\) | 1.05650e133 | 0.108133 | ||||||||
\(580\) | 1.09504e134 | 1.03079 | ||||||||
\(581\) | 1.28895e134 | 1.11608 | ||||||||
\(582\) | 1.80390e134 | 1.43697 | ||||||||
\(583\) | −6.34530e133 | −0.465079 | ||||||||
\(584\) | −8.64858e132 | −0.0583340 | ||||||||
\(585\) | −4.08927e133 | −0.253855 | ||||||||
\(586\) | 1.70385e134 | 0.973639 | ||||||||
\(587\) | −8.16435e133 | −0.429511 | −0.214755 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214755 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(588\) | −1.26004e134 | −0.610358 | ||||||||
\(589\) | −1.13962e133 | −0.0508355 | ||||||||
\(590\) | 1.40537e134 | 0.577389 | ||||||||
\(591\) | −8.07863e133 | −0.305735 | ||||||||
\(592\) | −3.84788e134 | −1.34159 | ||||||||
\(593\) | −3.69984e134 | −1.18858 | −0.594292 | − | 0.804249i | \(-0.702568\pi\) | ||||
−0.594292 | + | 0.804249i | \(0.702568\pi\) | |||||||
\(594\) | 6.36144e134 | 1.88327 | ||||||||
\(595\) | −1.76156e134 | −0.480646 | ||||||||
\(596\) | −2.07385e134 | −0.521596 | ||||||||
\(597\) | 6.36016e134 | 1.47473 | ||||||||
\(598\) | 9.06326e134 | 1.93766 | ||||||||
\(599\) | −5.58734e134 | −1.10155 | −0.550775 | − | 0.834654i | \(-0.685668\pi\) | ||||
−0.550775 | + | 0.834654i | \(0.685668\pi\) | |||||||
\(600\) | −7.02895e133 | −0.127807 | ||||||||
\(601\) | −2.81713e134 | −0.472493 | −0.236247 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236247 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(602\) | −6.50539e134 | −1.00657 | ||||||||
\(603\) | −1.04646e134 | −0.149394 | ||||||||
\(604\) | −1.10792e135 | −1.45954 | ||||||||
\(605\) | −1.19166e135 | −1.44882 | ||||||||
\(606\) | 7.34372e134 | 0.824127 | ||||||||
\(607\) | 2.09397e134 | 0.216929 | 0.108465 | − | 0.994100i | \(-0.465407\pi\) | ||||
0.108465 | + | 0.994100i | \(0.465407\pi\) | |||||||
\(608\) | 1.71143e134 | 0.163695 | ||||||||
\(609\) | 1.36965e135 | 1.20968 | ||||||||
\(610\) | 1.10660e135 | 0.902593 | ||||||||
\(611\) | 2.37383e135 | 1.78835 | ||||||||
\(612\) | −6.31016e134 | −0.439134 | ||||||||
\(613\) | 2.80652e134 | 0.180441 | 0.0902204 | − | 0.995922i | \(-0.471243\pi\) | ||||
0.0902204 | + | 0.995922i | \(0.471243\pi\) | |||||||
\(614\) | −3.81698e135 | −2.26754 | ||||||||
\(615\) | 5.03397e134 | 0.276355 | ||||||||
\(616\) | 4.93063e134 | 0.250171 | ||||||||
\(617\) | 2.41135e135 | 1.13092 | 0.565458 | − | 0.824777i | \(-0.308700\pi\) | ||||
0.565458 | + | 0.824777i | \(0.308700\pi\) | |||||||
\(618\) | 2.09053e135 | 0.906392 | ||||||||
\(619\) | 3.55769e134 | 0.142617 | 0.0713087 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713087 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(620\) | −8.88619e134 | −0.329396 | ||||||||
\(621\) | −2.79746e135 | −0.959006 | ||||||||
\(622\) | 2.88242e135 | 0.913952 | ||||||||
\(623\) | −3.35455e134 | −0.0983929 | ||||||||
\(624\) | −3.69303e135 | −1.00214 | ||||||||
\(625\) | −4.02101e134 | −0.100961 | ||||||||
\(626\) | −9.61273e135 | −2.23353 | ||||||||
\(627\) | 1.12120e135 | 0.241106 | ||||||||
\(628\) | −8.27526e134 | −0.164717 | ||||||||
\(629\) | −8.51717e135 | −1.56942 | ||||||||
\(630\) | 1.60403e135 | 0.273650 | ||||||||
\(631\) | 1.14878e136 | 1.81473 | 0.907367 | − | 0.420338i | \(-0.138089\pi\) | ||||
0.907367 | + | 0.420338i | \(0.138089\pi\) | |||||||
\(632\) | 2.99144e134 | 0.0437625 | ||||||||
\(633\) | 3.15825e135 | 0.427924 | ||||||||
\(634\) | 2.72850e135 | 0.342448 | ||||||||
\(635\) | −3.92486e135 | −0.456351 | ||||||||
\(636\) | 3.20699e135 | 0.345484 | ||||||||
\(637\) | −4.57460e135 | −0.456657 | ||||||||
\(638\) | 3.94374e136 | 3.64843 | ||||||||
\(639\) | −5.43261e135 | −0.465819 | ||||||||
\(640\) | 3.09482e135 | 0.245984 | ||||||||
\(641\) | −4.34208e135 | −0.319951 | −0.159976 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159976 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(642\) | −1.84270e136 | −1.25895 | ||||||||
\(643\) | 9.80684e135 | 0.621294 | 0.310647 | − | 0.950525i | \(-0.399454\pi\) | ||||
0.310647 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(644\) | −1.88596e136 | −1.10807 | ||||||||
\(645\) | −1.32614e136 | −0.722676 | ||||||||
\(646\) | 3.28765e135 | 0.166191 | ||||||||
\(647\) | −9.88248e135 | −0.463456 | −0.231728 | − | 0.972781i | \(-0.574438\pi\) | ||||
−0.231728 | + | 0.972781i | \(0.574438\pi\) | |||||||
\(648\) | −5.39293e135 | −0.234659 | ||||||||
\(649\) | 2.68504e136 | 1.08414 | ||||||||
\(650\) | −2.21963e136 | −0.831729 | ||||||||
\(651\) | −1.11147e136 | −0.386561 | ||||||||
\(652\) | −2.21894e136 | −0.716370 | ||||||||
\(653\) | 6.46443e136 | 1.93750 | 0.968748 | − | 0.248049i | \(-0.0797893\pi\) | ||||
0.968748 | + | 0.248049i | \(0.0797893\pi\) | |||||||
\(654\) | 1.93393e136 | 0.538170 | ||||||||
\(655\) | −1.71128e136 | −0.442199 | ||||||||
\(656\) | 1.27409e136 | 0.305748 | ||||||||
\(657\) | −5.37545e135 | −0.119810 | ||||||||
\(658\) | −9.31143e136 | −1.92779 | ||||||||
\(659\) | −2.78484e136 | −0.535621 | −0.267811 | − | 0.963472i | \(-0.586300\pi\) | ||||
−0.267811 | + | 0.963472i | \(0.586300\pi\) | |||||||
\(660\) | 8.74258e136 | 1.56228 | ||||||||
\(661\) | −3.15747e136 | −0.524285 | −0.262143 | − | 0.965029i | \(-0.584429\pi\) | ||||
−0.262143 | + | 0.965029i | \(0.584429\pi\) | |||||||
\(662\) | 8.32285e136 | 1.28428 | ||||||||
\(663\) | −8.17442e136 | −1.17233 | ||||||||
\(664\) | −2.15655e136 | −0.287480 | ||||||||
\(665\) | −4.43342e135 | −0.0549400 | ||||||||
\(666\) | 7.75548e136 | 0.893529 | ||||||||
\(667\) | −1.73427e137 | −1.85787 | ||||||||
\(668\) | 2.05042e137 | 2.04260 | ||||||||
\(669\) | 6.06561e136 | 0.561963 | ||||||||
\(670\) | 4.25132e136 | 0.366350 | ||||||||
\(671\) | 2.11422e137 | 1.69476 | ||||||||
\(672\) | 1.66915e137 | 1.24476 | ||||||||
\(673\) | −1.55040e137 | −1.07575 | −0.537876 | − | 0.843024i | \(-0.680773\pi\) | ||||
−0.537876 | + | 0.843024i | \(0.680773\pi\) | |||||||
\(674\) | −2.71231e137 | −1.75119 | ||||||||
\(675\) | 6.85109e136 | 0.411649 | ||||||||
\(676\) | −1.43024e135 | −0.00799822 | ||||||||
\(677\) | 1.63602e137 | 0.851604 | 0.425802 | − | 0.904816i | \(-0.359992\pi\) | ||||
0.425802 | + | 0.904816i | \(0.359992\pi\) | |||||||
\(678\) | −5.86608e137 | −2.84255 | ||||||||
\(679\) | −1.36279e137 | −0.614815 | ||||||||
\(680\) | 2.94728e136 | 0.123805 | ||||||||
\(681\) | −3.03928e137 | −1.18887 | ||||||||
\(682\) | −3.20033e137 | −1.16588 | ||||||||
\(683\) | 1.68242e137 | 0.570859 | 0.285430 | − | 0.958400i | \(-0.407864\pi\) | ||||
0.285430 | + | 0.958400i | \(0.407864\pi\) | |||||||
\(684\) | −1.58811e136 | −0.0501949 | ||||||||
\(685\) | 3.92312e137 | 1.15515 | ||||||||
\(686\) | 5.70989e137 | 1.56642 | ||||||||
\(687\) | 3.67375e137 | 0.939092 | ||||||||
\(688\) | −3.35643e137 | −0.799538 | ||||||||
\(689\) | 1.16430e137 | 0.258484 | ||||||||
\(690\) | −7.24714e137 | −1.49964 | ||||||||
\(691\) | 6.99090e137 | 1.34849 | 0.674245 | − | 0.738508i | \(-0.264469\pi\) | ||||
0.674245 | + | 0.738508i | \(0.264469\pi\) | |||||||
\(692\) | 1.71767e137 | 0.308884 | ||||||||
\(693\) | 3.06459e137 | 0.513819 | ||||||||
\(694\) | 8.84766e137 | 1.38323 | ||||||||
\(695\) | −5.42493e137 | −0.790918 | ||||||||
\(696\) | −2.29157e137 | −0.311591 | ||||||||
\(697\) | 2.82016e137 | 0.357671 | ||||||||
\(698\) | −8.08163e137 | −0.956117 | ||||||||
\(699\) | 5.67187e136 | 0.0626013 | ||||||||
\(700\) | 4.61878e137 | 0.475634 | ||||||||
\(701\) | −2.94894e137 | −0.283363 | −0.141681 | − | 0.989912i | \(-0.545251\pi\) | ||||
−0.141681 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(702\) | −1.16726e138 | −1.04669 | ||||||||
\(703\) | −2.14356e137 | −0.179392 | ||||||||
\(704\) | 2.84777e138 | 2.22450 | ||||||||
\(705\) | −1.89816e138 | −1.38408 | ||||||||
\(706\) | −1.90684e138 | −1.29803 | ||||||||
\(707\) | −5.54794e137 | −0.352606 | ||||||||
\(708\) | −1.35705e138 | −0.805349 | ||||||||
\(709\) | −1.16348e138 | −0.644788 | −0.322394 | − | 0.946606i | \(-0.604488\pi\) | ||||
−0.322394 | + | 0.946606i | \(0.604488\pi\) | |||||||
\(710\) | 2.20704e138 | 1.14230 | ||||||||
\(711\) | 1.85930e137 | 0.0898824 | ||||||||
\(712\) | 5.61251e136 | 0.0253441 | ||||||||
\(713\) | 1.40735e138 | 0.593691 | ||||||||
\(714\) | 3.20644e138 | 1.26375 | ||||||||
\(715\) | 3.17401e138 | 1.16887 | ||||||||
\(716\) | 1.05930e138 | 0.364535 | ||||||||
\(717\) | −4.61420e138 | −1.48394 | ||||||||
\(718\) | −2.00831e137 | −0.0603665 | ||||||||
\(719\) | −1.87813e138 | −0.527684 | −0.263842 | − | 0.964566i | \(-0.584990\pi\) | ||||
−0.263842 | + | 0.964566i | \(0.584990\pi\) | |||||||
\(720\) | 8.27593e137 | 0.217366 | ||||||||
\(721\) | −1.57933e138 | −0.387804 | ||||||||
\(722\) | −6.27399e138 | −1.44042 | ||||||||
\(723\) | 1.57840e136 | 0.00338851 | ||||||||
\(724\) | −2.04823e138 | −0.411205 | ||||||||
\(725\) | 4.24730e138 | 0.797479 | ||||||||
\(726\) | 2.16908e139 | 3.80934 | ||||||||
\(727\) | −2.39883e138 | −0.394077 | −0.197039 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197039 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(728\) | −9.04723e137 | −0.139041 | ||||||||
\(729\) | 2.54841e138 | 0.366425 | ||||||||
\(730\) | 2.18382e138 | 0.293804 | ||||||||
\(731\) | −7.42938e138 | −0.935319 | ||||||||
\(732\) | −1.06855e139 | −1.25895 | ||||||||
\(733\) | −4.36487e137 | −0.0481314 | −0.0240657 | − | 0.999710i | \(-0.507661\pi\) | ||||
−0.0240657 | + | 0.999710i | \(0.507661\pi\) | |||||||
\(734\) | −2.30361e138 | −0.237766 | ||||||||
\(735\) | 3.65793e138 | 0.353427 | ||||||||
\(736\) | −2.11350e139 | −1.91174 | ||||||||
\(737\) | 8.12239e138 | 0.687877 | ||||||||
\(738\) | −2.56795e138 | −0.203636 | ||||||||
\(739\) | −6.08027e137 | −0.0451510 | −0.0225755 | − | 0.999745i | \(-0.507187\pi\) | ||||
−0.0225755 | + | 0.999745i | \(0.507187\pi\) | |||||||
\(740\) | −1.67145e139 | −1.16239 | ||||||||
\(741\) | −2.05730e138 | −0.134003 | ||||||||
\(742\) | −4.56701e138 | −0.278639 | ||||||||
\(743\) | 4.71092e138 | 0.269245 | 0.134623 | − | 0.990897i | \(-0.457018\pi\) | ||||
0.134623 | + | 0.990897i | \(0.457018\pi\) | |||||||
\(744\) | 1.85960e138 | 0.0995706 | ||||||||
\(745\) | 6.02045e138 | 0.302030 | ||||||||
\(746\) | 2.75227e139 | 1.29377 | ||||||||
\(747\) | −1.34039e139 | −0.590447 | ||||||||
\(748\) | 4.89782e139 | 2.02197 | ||||||||
\(749\) | 1.39210e139 | 0.538646 | ||||||||
\(750\) | 4.87811e139 | 1.76921 | ||||||||
\(751\) | 3.47103e139 | 1.18011 | 0.590054 | − | 0.807364i | \(-0.299107\pi\) | ||||
0.590054 | + | 0.807364i | \(0.299107\pi\) | |||||||
\(752\) | −4.80420e139 | −1.53129 | ||||||||
\(753\) | −2.71460e139 | −0.811239 | ||||||||
\(754\) | −7.23640e139 | −2.02774 | ||||||||
\(755\) | 3.21631e139 | 0.845145 | ||||||||
\(756\) | 2.42894e139 | 0.598563 | ||||||||
\(757\) | 3.25016e139 | 0.751198 | 0.375599 | − | 0.926782i | \(-0.377437\pi\) | ||||
0.375599 | + | 0.926782i | \(0.377437\pi\) | |||||||
\(758\) | −6.33600e139 | −1.37359 | ||||||||
\(759\) | −1.38461e140 | −2.81579 | ||||||||
\(760\) | 7.41756e137 | 0.0141515 | ||||||||
\(761\) | 5.29421e139 | 0.947644 | 0.473822 | − | 0.880621i | \(-0.342874\pi\) | ||||
0.473822 | + | 0.880621i | \(0.342874\pi\) | |||||||
\(762\) | 7.14412e139 | 1.19987 | ||||||||
\(763\) | −1.46102e139 | −0.230259 | ||||||||
\(764\) | −1.13637e140 | −1.68070 | ||||||||
\(765\) | 1.83186e139 | 0.254280 | ||||||||
\(766\) | 3.59877e139 | 0.468877 | ||||||||
\(767\) | −4.92680e139 | −0.602546 | ||||||||
\(768\) | 7.10501e139 | 0.815728 | ||||||||
\(769\) | 9.09061e139 | 0.979864 | 0.489932 | − | 0.871761i | \(-0.337022\pi\) | ||||
0.489932 | + | 0.871761i | \(0.337022\pi\) | |||||||
\(770\) | −1.24501e140 | −1.26001 | ||||||||
\(771\) | 2.44360e140 | 2.32217 | ||||||||
\(772\) | 1.16152e139 | 0.103655 | ||||||||
\(773\) | −2.36440e140 | −1.98160 | −0.990799 | − | 0.135342i | \(-0.956787\pi\) | ||||
−0.990799 | + | 0.135342i | \(0.956787\pi\) | |||||||
\(774\) | 6.76497e139 | 0.532512 | ||||||||
\(775\) | −3.44666e139 | −0.254839 | ||||||||
\(776\) | 2.28008e139 | 0.158364 | ||||||||
\(777\) | −2.09061e140 | −1.36412 | ||||||||
\(778\) | 3.34820e140 | 2.05258 | ||||||||
\(779\) | 7.09764e138 | 0.0408834 | ||||||||
\(780\) | −1.60418e140 | −0.868291 | ||||||||
\(781\) | 4.21668e140 | 2.14484 | ||||||||
\(782\) | −4.06003e140 | −1.94090 | ||||||||
\(783\) | 2.23358e140 | 1.00359 | ||||||||
\(784\) | 9.25814e139 | 0.391016 | ||||||||
\(785\) | 2.40233e139 | 0.0953793 | ||||||||
\(786\) | 3.11491e140 | 1.16266 | ||||||||
\(787\) | −3.96482e140 | −1.39139 | −0.695695 | − | 0.718337i | \(-0.744904\pi\) | ||||
−0.695695 | + | 0.718337i | \(0.744904\pi\) | |||||||
\(788\) | −8.88172e139 | −0.293073 | ||||||||
\(789\) | −5.24156e140 | −1.62640 | ||||||||
\(790\) | −7.55357e139 | −0.220414 | ||||||||
\(791\) | 4.43163e140 | 1.21620 | ||||||||
\(792\) | −5.12737e139 | −0.132350 | ||||||||
\(793\) | −3.87939e140 | −0.941919 | ||||||||
\(794\) | 2.95672e140 | 0.675329 | ||||||||
\(795\) | −9.30997e139 | −0.200052 | ||||||||
\(796\) | 6.99242e140 | 1.41366 | ||||||||
\(797\) | −6.88825e140 | −1.31033 | −0.655165 | − | 0.755486i | \(-0.727401\pi\) | ||||
−0.655165 | + | 0.755486i | \(0.727401\pi\) | |||||||
\(798\) | 8.06981e139 | 0.144452 | ||||||||
\(799\) | −1.06340e141 | −1.79134 | ||||||||
\(800\) | 5.17604e140 | 0.820603 | ||||||||
\(801\) | 3.48841e139 | 0.0520535 | ||||||||
\(802\) | −6.60351e140 | −0.927508 | ||||||||
\(803\) | 4.17231e140 | 0.551662 | ||||||||
\(804\) | −4.10516e140 | −0.510989 | ||||||||
\(805\) | 5.47498e140 | 0.641626 | ||||||||
\(806\) | 5.87230e140 | 0.647975 | ||||||||
\(807\) | −1.61357e140 | −0.167657 | ||||||||
\(808\) | 9.28228e139 | 0.0908246 | ||||||||
\(809\) | 1.41935e141 | 1.30793 | 0.653967 | − | 0.756523i | \(-0.273104\pi\) | ||||
0.653967 | + | 0.756523i | \(0.273104\pi\) | |||||||
\(810\) | 1.36175e141 | 1.18188 | ||||||||
\(811\) | 2.06491e141 | 1.68806 | 0.844032 | − | 0.536293i | \(-0.180176\pi\) | ||||
0.844032 | + | 0.536293i | \(0.180176\pi\) | |||||||
\(812\) | 1.50581e141 | 1.15959 | ||||||||
\(813\) | 3.06305e140 | 0.222210 | ||||||||
\(814\) | −6.01964e141 | −4.11422 | ||||||||
\(815\) | 6.44164e140 | 0.414813 | ||||||||
\(816\) | 1.65435e141 | 1.00382 | ||||||||
\(817\) | −1.86979e140 | −0.106911 | ||||||||
\(818\) | −3.60430e141 | −1.94216 | ||||||||
\(819\) | −5.62323e140 | −0.285573 | ||||||||
\(820\) | 5.53440e140 | 0.264910 | ||||||||
\(821\) | −1.50810e141 | −0.680434 | −0.340217 | − | 0.940347i | \(-0.610501\pi\) | ||||
−0.340217 | + | 0.940347i | \(0.610501\pi\) | |||||||
\(822\) | −7.14096e141 | −3.03720 | ||||||||
\(823\) | −1.16847e140 | −0.0468517 | −0.0234258 | − | 0.999726i | \(-0.507457\pi\) | ||||
−0.0234258 | + | 0.999726i | \(0.507457\pi\) | |||||||
\(824\) | 2.64238e140 | 0.0998908 | ||||||||
\(825\) | 3.39096e141 | 1.20867 | ||||||||
\(826\) | 1.93255e141 | 0.649530 | ||||||||
\(827\) | 1.96275e141 | 0.622081 | 0.311040 | − | 0.950397i | \(-0.399323\pi\) | ||||
0.311040 | + | 0.950397i | \(0.399323\pi\) | |||||||
\(828\) | 1.96121e141 | 0.586210 | ||||||||
\(829\) | 4.38312e141 | 1.23563 | 0.617816 | − | 0.786323i | \(-0.288018\pi\) | ||||
0.617816 | + | 0.786323i | \(0.288018\pi\) | |||||||
\(830\) | 5.44543e141 | 1.44792 | ||||||||
\(831\) | −6.22113e141 | −1.56034 | ||||||||
\(832\) | −5.22540e141 | −1.23634 | ||||||||
\(833\) | 2.04927e141 | 0.457421 | ||||||||
\(834\) | 9.87459e141 | 2.07953 | ||||||||
\(835\) | −5.95241e141 | −1.18277 | ||||||||
\(836\) | 1.23266e141 | 0.231120 | ||||||||
\(837\) | −1.81254e141 | −0.320703 | ||||||||
\(838\) | −3.69617e141 | −0.617187 | ||||||||
\(839\) | −3.13805e141 | −0.494543 | −0.247272 | − | 0.968946i | \(-0.579534\pi\) | ||||
−0.247272 | + | 0.968946i | \(0.579534\pi\) | |||||||
\(840\) | 7.23433e140 | 0.107610 | ||||||||
\(841\) | 6.72493e141 | 0.944239 | ||||||||
\(842\) | 2.45977e141 | 0.326030 | ||||||||
\(843\) | −2.33063e141 | −0.291632 | ||||||||
\(844\) | 3.47221e141 | 0.410202 | ||||||||
\(845\) | 4.15201e139 | 0.00463136 | ||||||||
\(846\) | 9.68299e141 | 1.01987 | ||||||||
\(847\) | −1.63867e142 | −1.62984 | ||||||||
\(848\) | −2.35633e141 | −0.221329 | ||||||||
\(849\) | −2.53784e142 | −2.25134 | ||||||||
\(850\) | 9.94318e141 | 0.833120 | ||||||||
\(851\) | 2.64715e142 | 2.09506 | ||||||||
\(852\) | −2.13116e142 | −1.59329 | ||||||||
\(853\) | 2.04478e142 | 1.44417 | 0.722084 | − | 0.691805i | \(-0.243184\pi\) | ||||
0.722084 | + | 0.691805i | \(0.243184\pi\) | |||||||
\(854\) | 1.52170e142 | 1.01537 | ||||||||
\(855\) | 4.61032e140 | 0.0290653 | ||||||||
\(856\) | −2.32913e141 | −0.138745 | ||||||||
\(857\) | −2.81479e142 | −1.58444 | −0.792219 | − | 0.610236i | \(-0.791074\pi\) | ||||
−0.792219 | + | 0.610236i | \(0.791074\pi\) | |||||||
\(858\) | −5.77740e142 | −3.07326 | ||||||||
\(859\) | 1.42795e142 | 0.717868 | 0.358934 | − | 0.933363i | \(-0.383140\pi\) | ||||
0.358934 | + | 0.933363i | \(0.383140\pi\) | |||||||
\(860\) | −1.45797e142 | −0.692746 | ||||||||
\(861\) | 6.92231e141 | 0.310884 | ||||||||
\(862\) | 1.66245e142 | 0.705741 | ||||||||
\(863\) | 1.15899e142 | 0.465110 | 0.232555 | − | 0.972583i | \(-0.425291\pi\) | ||||
0.232555 | + | 0.972583i | \(0.425291\pi\) | |||||||
\(864\) | 2.72199e142 | 1.03269 | ||||||||
\(865\) | −4.98645e141 | −0.178859 | ||||||||
\(866\) | 5.41240e142 | 1.83557 | ||||||||
\(867\) | −1.38064e140 | −0.00442745 | ||||||||
\(868\) | −1.22196e142 | −0.370552 | ||||||||
\(869\) | −1.44315e142 | −0.413860 | ||||||||
\(870\) | 5.78636e142 | 1.56936 | ||||||||
\(871\) | −1.49038e142 | −0.382311 | ||||||||
\(872\) | 2.44444e141 | 0.0593101 | ||||||||
\(873\) | 1.41717e142 | 0.325260 | ||||||||
\(874\) | −1.02181e142 | −0.221853 | ||||||||
\(875\) | −3.68525e142 | −0.756966 | ||||||||
\(876\) | −2.10874e142 | −0.409802 | ||||||||
\(877\) | 2.04337e142 | 0.375721 | 0.187861 | − | 0.982196i | \(-0.439845\pi\) | ||||
0.187861 | + | 0.982196i | \(0.439845\pi\) | |||||||
\(878\) | 2.77616e141 | 0.0483014 | ||||||||
\(879\) | 4.77627e142 | 0.786373 | ||||||||
\(880\) | −6.42361e142 | −1.00085 | ||||||||
\(881\) | 7.94028e141 | 0.117086 | 0.0585429 | − | 0.998285i | \(-0.481355\pi\) | ||||
0.0585429 | + | 0.998285i | \(0.481355\pi\) | |||||||
\(882\) | −1.86600e142 | −0.260427 | ||||||||
\(883\) | −1.29445e143 | −1.70998 | −0.854989 | − | 0.518646i | \(-0.826436\pi\) | ||||
−0.854989 | + | 0.518646i | \(0.826436\pi\) | |||||||
\(884\) | −8.98703e142 | −1.12378 | ||||||||
\(885\) | 3.93956e142 | 0.466336 | ||||||||
\(886\) | −7.16527e142 | −0.802966 | ||||||||
\(887\) | 3.36952e142 | 0.357497 | 0.178748 | − | 0.983895i | \(-0.442795\pi\) | ||||
0.178748 | + | 0.983895i | \(0.442795\pi\) | |||||||
\(888\) | 3.49780e142 | 0.351371 | ||||||||
\(889\) | −5.39715e142 | −0.513368 | ||||||||
\(890\) | −1.41719e142 | −0.127648 | ||||||||
\(891\) | 2.60170e143 | 2.21916 | ||||||||
\(892\) | 6.66859e142 | 0.538690 | ||||||||
\(893\) | −2.67631e142 | −0.204758 | ||||||||
\(894\) | −1.09586e143 | −0.794115 | ||||||||
\(895\) | −3.07518e142 | −0.211083 | ||||||||
\(896\) | 4.25574e142 | 0.276717 | ||||||||
\(897\) | 2.54063e143 | 1.56497 | ||||||||
\(898\) | 3.63982e143 | 2.12411 | ||||||||
\(899\) | −1.12368e143 | −0.621292 | ||||||||
\(900\) | −4.80308e142 | −0.251628 | ||||||||
\(901\) | −5.21568e142 | −0.258916 | ||||||||
\(902\) | 1.99319e143 | 0.937632 | ||||||||
\(903\) | −1.82360e143 | −0.812969 | ||||||||
\(904\) | −7.41458e142 | −0.313269 | ||||||||
\(905\) | 5.94606e142 | 0.238107 | ||||||||
\(906\) | −5.85441e143 | −2.22211 | ||||||||
\(907\) | −2.14396e143 | −0.771372 | −0.385686 | − | 0.922630i | \(-0.626035\pi\) | ||||
−0.385686 | + | 0.922630i | \(0.626035\pi\) | |||||||
\(908\) | −3.34141e143 | −1.13964 | ||||||||
\(909\) | 5.76932e142 | 0.186542 | ||||||||
\(910\) | 2.28448e143 | 0.700294 | ||||||||
\(911\) | −1.63615e143 | −0.475534 | −0.237767 | − | 0.971322i | \(-0.576415\pi\) | ||||
−0.237767 | + | 0.971322i | \(0.576415\pi\) | |||||||
\(912\) | 4.16359e142 | 0.114741 | ||||||||
\(913\) | 1.04038e144 | 2.71869 | ||||||||
\(914\) | −6.22374e143 | −1.54227 | ||||||||
\(915\) | 3.10203e143 | 0.728992 | ||||||||
\(916\) | 4.03896e143 | 0.900200 | ||||||||
\(917\) | −2.35321e143 | −0.497448 | ||||||||
\(918\) | 5.22895e143 | 1.04844 | ||||||||
\(919\) | −2.84470e143 | −0.541046 | −0.270523 | − | 0.962714i | \(-0.587197\pi\) | ||||
−0.270523 | + | 0.962714i | \(0.587197\pi\) | |||||||
\(920\) | −9.16020e142 | −0.165271 | ||||||||
\(921\) | −1.06998e144 | −1.83141 | ||||||||
\(922\) | −2.29555e143 | −0.372767 | ||||||||
\(923\) | −7.73720e143 | −1.19207 | ||||||||
\(924\) | 1.20221e144 | 1.75748 | ||||||||
\(925\) | −6.48298e143 | −0.899292 | ||||||||
\(926\) | −8.69183e143 | −1.14414 | ||||||||
\(927\) | 1.64235e143 | 0.205163 | ||||||||
\(928\) | 1.68749e144 | 2.00062 | ||||||||
\(929\) | 8.93629e143 | 1.00553 | 0.502765 | − | 0.864423i | \(-0.332316\pi\) | ||||
0.502765 | + | 0.864423i | \(0.332316\pi\) | |||||||
\(930\) | −4.69559e143 | −0.501496 | ||||||||
\(931\) | 5.15749e142 | 0.0522852 | ||||||||
\(932\) | 6.23571e142 | 0.0600087 | ||||||||
\(933\) | 8.08004e143 | 0.738165 | ||||||||
\(934\) | 2.39337e144 | 2.07580 | ||||||||
\(935\) | −1.42185e144 | −1.17082 | ||||||||
\(936\) | 9.40824e142 | 0.0735580 | ||||||||
\(937\) | 1.50749e144 | 1.11914 | 0.559571 | − | 0.828783i | \(-0.310966\pi\) | ||||
0.559571 | + | 0.828783i | \(0.310966\pi\) | |||||||
\(938\) | 5.84607e143 | 0.412122 | ||||||||
\(939\) | −2.69466e144 | −1.80394 | ||||||||
\(940\) | −2.08686e144 | −1.32676 | ||||||||
\(941\) | 9.16279e143 | 0.553262 | 0.276631 | − | 0.960976i | \(-0.410782\pi\) | ||||
0.276631 | + | 0.960976i | \(0.410782\pi\) | |||||||
\(942\) | −4.37277e143 | −0.250777 | ||||||||
\(943\) | −8.76512e143 | −0.477464 | ||||||||
\(944\) | 9.97095e143 | 0.515935 | ||||||||
\(945\) | −7.05127e143 | −0.346597 | ||||||||
\(946\) | −5.25083e144 | −2.45193 | ||||||||
\(947\) | 6.11306e143 | 0.271197 | 0.135598 | − | 0.990764i | \(-0.456704\pi\) | ||||
0.135598 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(948\) | 7.29387e143 | 0.307435 | ||||||||
\(949\) | −7.65580e143 | −0.306605 | ||||||||
\(950\) | 2.50245e143 | 0.0952293 | ||||||||
\(951\) | 7.64857e143 | 0.276583 | ||||||||
\(952\) | 4.05286e143 | 0.139274 | ||||||||
\(953\) | −8.83941e143 | −0.288681 | −0.144340 | − | 0.989528i | \(-0.546106\pi\) | ||||
−0.144340 | + | 0.989528i | \(0.546106\pi\) | |||||||
\(954\) | 4.74925e143 | 0.147411 | ||||||||
\(955\) | 3.29890e144 | 0.973209 | ||||||||
\(956\) | −5.07289e144 | −1.42249 | ||||||||
\(957\) | 1.10552e145 | 2.94670 | ||||||||
\(958\) | −7.86249e144 | −1.99220 | ||||||||
\(959\) | 5.39476e144 | 1.29948 | ||||||||
\(960\) | 4.17832e144 | 0.956857 | ||||||||
\(961\) | −3.68102e144 | −0.801463 | ||||||||
\(962\) | 1.10455e145 | 2.28662 | ||||||||
\(963\) | −1.44765e144 | −0.284963 | ||||||||
\(964\) | 1.73530e142 | 0.00324817 | ||||||||
\(965\) | −3.37193e143 | −0.0600211 | ||||||||
\(966\) | −9.96568e144 | −1.68700 | ||||||||
\(967\) | 5.00806e144 | 0.806279 | 0.403139 | − | 0.915139i | \(-0.367919\pi\) | ||||
0.403139 | + | 0.915139i | \(0.367919\pi\) | |||||||
\(968\) | 2.74166e144 | 0.419816 | ||||||||
\(969\) | 9.21600e143 | 0.134227 | ||||||||
\(970\) | −5.75735e144 | −0.797616 | ||||||||
\(971\) | −1.17752e145 | −1.55180 | −0.775902 | − | 0.630853i | \(-0.782705\pi\) | ||||
−0.775902 | + | 0.630853i | \(0.782705\pi\) | |||||||
\(972\) | −6.66241e144 | −0.835252 | ||||||||
\(973\) | −7.45993e144 | −0.889737 | ||||||||
\(974\) | 1.44524e145 | 1.63995 | ||||||||
\(975\) | −6.22209e144 | −0.671757 | ||||||||
\(976\) | 7.85117e144 | 0.806525 | ||||||||
\(977\) | 6.85312e144 | 0.669888 | 0.334944 | − | 0.942238i | \(-0.391283\pi\) | ||||
0.334944 | + | 0.942238i | \(0.391283\pi\) | |||||||
\(978\) | −1.17252e145 | −1.09065 | ||||||||
\(979\) | −2.70763e144 | −0.239678 | ||||||||
\(980\) | 4.02156e144 | 0.338790 | ||||||||
\(981\) | 1.51932e144 | 0.121815 | ||||||||
\(982\) | −2.54991e144 | −0.194589 | ||||||||
\(983\) | −1.01485e145 | −0.737152 | −0.368576 | − | 0.929598i | \(-0.620155\pi\) | ||||
−0.368576 | + | 0.929598i | \(0.620155\pi\) | |||||||
\(984\) | −1.15817e144 | −0.0800777 | ||||||||
\(985\) | 2.57838e144 | 0.169703 | ||||||||
\(986\) | 3.24166e145 | 2.03113 | ||||||||
\(987\) | −2.61020e145 | −1.55701 | ||||||||
\(988\) | −2.26181e144 | −0.128453 | ||||||||
\(989\) | 2.30907e145 | 1.24858 | ||||||||
\(990\) | 1.29469e145 | 0.666592 | ||||||||
\(991\) | −9.22135e143 | −0.0452087 | −0.0226044 | − | 0.999744i | \(-0.507196\pi\) | ||||
−0.0226044 | + | 0.999744i | \(0.507196\pi\) | |||||||
\(992\) | −1.36939e145 | −0.639308 | ||||||||
\(993\) | 2.33308e145 | 1.03727 | ||||||||
\(994\) | 3.03494e145 | 1.28502 | ||||||||
\(995\) | −2.02992e145 | −0.818575 | ||||||||
\(996\) | −5.25821e145 | −2.01957 | ||||||||
\(997\) | −6.29694e144 | −0.230364 | −0.115182 | − | 0.993344i | \(-0.536745\pi\) | ||||
−0.115182 | + | 0.993344i | \(0.536745\pi\) | |||||||
\(998\) | −2.06479e145 | −0.719524 | ||||||||
\(999\) | −3.40929e145 | −1.13172 |
(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 | 1.98.a.a.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 9.98.a.a.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.98.a.a.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.98.a.a.1.1 | 7 | 3.2 | odd | 2 |