Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,106,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, 106, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 106);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 106 \) |
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: | \(69.8187388595\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-5.83850e13\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.55432e15 | −1.50012 | −0.750058 | − | 0.661372i | \(-0.769974\pi\) | ||||
−0.750058 | + | 0.661372i | \(0.769974\pi\) | |||||||
\(3\) | −1.37857e25 | −1.23186 | −0.615932 | − | 0.787799i | \(-0.711220\pi\) | ||||
−0.615932 | + | 0.787799i | \(0.711220\pi\) | |||||||
\(4\) | 5.07201e31 | 1.25035 | ||||||||
\(5\) | −2.80039e36 | −0.564018 | −0.282009 | − | 0.959412i | \(-0.591001\pi\) | ||||
−0.282009 | + | 0.959412i | \(0.591001\pi\) | |||||||
\(6\) | 1.31713e41 | 1.84794 | ||||||||
\(7\) | −2.78207e44 | −1.19322 | −0.596610 | − | 0.802531i | \(-0.703486\pi\) | ||||
−0.596610 | + | 0.802531i | \(0.703486\pi\) | |||||||
\(8\) | −9.70270e46 | −0.375551 | ||||||||
\(9\) | 6.48087e49 | 0.517490 | ||||||||
\(10\) | 2.67558e52 | 0.846093 | ||||||||
\(11\) | 6.08520e53 | 0.129169 | 0.0645846 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645846 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(12\) | −6.99212e56 | −1.54026 | ||||||||
\(13\) | −5.49066e58 | −1.80967 | −0.904834 | − | 0.425764i | \(-0.860005\pi\) | ||||
−0.904834 | + | 0.425764i | \(0.860005\pi\) | |||||||
\(14\) | 2.65807e60 | 1.78997 | ||||||||
\(15\) | 3.86053e61 | 0.694794 | ||||||||
\(16\) | −1.13043e63 | −0.686978 | ||||||||
\(17\) | −2.90311e64 | −0.731636 | −0.365818 | − | 0.930686i | \(-0.619211\pi\) | ||||
−0.365818 | + | 0.930686i | \(0.619211\pi\) | |||||||
\(18\) | −6.19203e65 | −0.776295 | ||||||||
\(19\) | −1.56027e67 | −1.14455 | −0.572277 | − | 0.820061i | \(-0.693940\pi\) | ||||
−0.572277 | + | 0.820061i | \(0.693940\pi\) | |||||||
\(20\) | −1.42036e68 | −0.705219 | ||||||||
\(21\) | 3.83527e69 | 1.46988 | ||||||||
\(22\) | −5.81399e69 | −0.193769 | ||||||||
\(23\) | 5.72406e71 | 1.84924 | 0.924620 | − | 0.380892i | \(-0.124383\pi\) | ||||
0.924620 | + | 0.380892i | \(0.124383\pi\) | |||||||
\(24\) | 1.33759e72 | 0.462627 | ||||||||
\(25\) | −1.68097e73 | −0.681883 | ||||||||
\(26\) | 5.24595e74 | 2.71471 | ||||||||
\(27\) | 8.33042e74 | 0.594387 | ||||||||
\(28\) | −1.41107e76 | −1.49194 | ||||||||
\(29\) | −1.76595e76 | −0.295857 | −0.147929 | − | 0.988998i | \(-0.547261\pi\) | ||||
−0.147929 | + | 0.988998i | \(0.547261\pi\) | |||||||
\(30\) | −3.68848e77 | −1.04227 | ||||||||
\(31\) | 1.61443e78 | 0.815700 | 0.407850 | − | 0.913049i | \(-0.366279\pi\) | ||||
0.407850 | + | 0.913049i | \(0.366279\pi\) | |||||||
\(32\) | 1.47363e79 | 1.40610 | ||||||||
\(33\) | −8.38888e78 | −0.159119 | ||||||||
\(34\) | 2.77372e80 | 1.09754 | ||||||||
\(35\) | 7.79087e80 | 0.672998 | ||||||||
\(36\) | 3.28711e81 | 0.647042 | ||||||||
\(37\) | 1.96604e82 | 0.918335 | 0.459168 | − | 0.888350i | \(-0.348148\pi\) | ||||
0.459168 | + | 0.888350i | \(0.348148\pi\) | |||||||
\(38\) | 1.49073e83 | 1.71696 | ||||||||
\(39\) | 7.56926e83 | 2.22927 | ||||||||
\(40\) | 2.71714e83 | 0.211817 | ||||||||
\(41\) | 1.17183e83 | 0.0249870 | 0.0124935 | − | 0.999922i | \(-0.496023\pi\) | ||||
0.0124935 | + | 0.999922i | \(0.496023\pi\) | |||||||
\(42\) | −3.66434e85 | −2.20500 | ||||||||
\(43\) | 1.98821e84 | 0.0347831 | 0.0173915 | − | 0.999849i | \(-0.494464\pi\) | ||||
0.0173915 | + | 0.999849i | \(0.494464\pi\) | |||||||
\(44\) | 3.08642e85 | 0.161506 | ||||||||
\(45\) | −1.81490e86 | −0.291874 | ||||||||
\(46\) | −5.46895e87 | −2.77407 | ||||||||
\(47\) | 1.10467e88 | 1.81173 | 0.905866 | − | 0.423564i | \(-0.139221\pi\) | ||||
0.905866 | + | 0.423564i | \(0.139221\pi\) | |||||||
\(48\) | 1.55837e88 | 0.846264 | ||||||||
\(49\) | 2.30371e88 | 0.423773 | ||||||||
\(50\) | 1.60605e89 | 1.02290 | ||||||||
\(51\) | 4.00214e89 | 0.901276 | ||||||||
\(52\) | −2.78487e90 | −2.26271 | ||||||||
\(53\) | −7.34914e89 | −0.219661 | −0.109831 | − | 0.993950i | \(-0.535031\pi\) | ||||
−0.109831 | + | 0.993950i | \(0.535031\pi\) | |||||||
\(54\) | −7.95915e90 | −0.891650 | ||||||||
\(55\) | −1.70409e90 | −0.0728538 | ||||||||
\(56\) | 2.69936e91 | 0.448114 | ||||||||
\(57\) | 2.15094e92 | 1.40993 | ||||||||
\(58\) | 1.68724e92 | 0.443820 | ||||||||
\(59\) | −1.37917e93 | −1.47872 | −0.739360 | − | 0.673310i | \(-0.764872\pi\) | ||||
−0.739360 | + | 0.673310i | \(0.764872\pi\) | |||||||
\(60\) | 1.95807e93 | 0.868734 | ||||||||
\(61\) | 1.74942e93 | 0.325894 | 0.162947 | − | 0.986635i | \(-0.447900\pi\) | ||||
0.162947 | + | 0.986635i | \(0.447900\pi\) | |||||||
\(62\) | −1.54248e94 | −1.22365 | ||||||||
\(63\) | −1.80302e94 | −0.617479 | ||||||||
\(64\) | −9.49400e94 | −1.42233 | ||||||||
\(65\) | 1.53760e95 | 1.02069 | ||||||||
\(66\) | 8.01500e94 | 0.238697 | ||||||||
\(67\) | 1.25972e96 | 1.70352 | 0.851762 | − | 0.523929i | \(-0.175534\pi\) | ||||
0.851762 | + | 0.523929i | \(0.175534\pi\) | |||||||
\(68\) | −1.47246e96 | −0.914799 | ||||||||
\(69\) | −7.89102e96 | −2.27801 | ||||||||
\(70\) | −7.44364e96 | −1.00957 | ||||||||
\(71\) | −1.81563e97 | −1.16940 | −0.584702 | − | 0.811248i | \(-0.698788\pi\) | ||||
−0.584702 | + | 0.811248i | \(0.698788\pi\) | |||||||
\(72\) | −6.28820e96 | −0.194344 | ||||||||
\(73\) | −2.37938e97 | −0.356462 | −0.178231 | − | 0.983989i | \(-0.557037\pi\) | ||||
−0.178231 | + | 0.983989i | \(0.557037\pi\) | |||||||
\(74\) | −1.87841e98 | −1.37761 | ||||||||
\(75\) | 2.31734e98 | 0.839988 | ||||||||
\(76\) | −7.91371e98 | −1.43109 | ||||||||
\(77\) | −1.69294e98 | −0.154127 | ||||||||
\(78\) | −7.23191e99 | −3.34416 | ||||||||
\(79\) | 8.68206e98 | 0.205684 | 0.102842 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102842 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(80\) | 3.16563e99 | 0.387468 | ||||||||
\(81\) | −1.96005e100 | −1.24969 | ||||||||
\(82\) | −1.11961e99 | −0.0374834 | ||||||||
\(83\) | 2.69773e100 | 0.477968 | 0.238984 | − | 0.971023i | \(-0.423186\pi\) | ||||
0.238984 | + | 0.971023i | \(0.423186\pi\) | |||||||
\(84\) | 1.94526e101 | 1.83787 | ||||||||
\(85\) | 8.12984e100 | 0.412656 | ||||||||
\(86\) | −1.89960e100 | −0.0521787 | ||||||||
\(87\) | 2.43448e101 | 0.364456 | ||||||||
\(88\) | −5.90429e100 | −0.0485096 | ||||||||
\(89\) | −5.78519e101 | −0.262629 | −0.131314 | − | 0.991341i | \(-0.541920\pi\) | ||||
−0.131314 | + | 0.991341i | \(0.541920\pi\) | |||||||
\(90\) | 1.73401e102 | 0.437845 | ||||||||
\(91\) | 1.52754e103 | 2.15933 | ||||||||
\(92\) | 2.90325e103 | 2.31219 | ||||||||
\(93\) | −2.22561e103 | −1.00483 | ||||||||
\(94\) | −1.05543e104 | −2.71781 | ||||||||
\(95\) | 4.36937e103 | 0.645549 | ||||||||
\(96\) | −2.03151e104 | −1.73212 | ||||||||
\(97\) | 1.53726e103 | 0.0760730 | 0.0380365 | − | 0.999276i | \(-0.487890\pi\) | ||||
0.0380365 | + | 0.999276i | \(0.487890\pi\) | |||||||
\(98\) | −2.20103e104 | −0.635708 | ||||||||
\(99\) | 3.94374e103 | 0.0668438 | ||||||||
\(100\) | −8.52591e104 | −0.852591 | ||||||||
\(101\) | 2.28689e105 | 1.35635 | 0.678177 | − | 0.734898i | \(-0.262770\pi\) | ||||
0.678177 | + | 0.734898i | \(0.262770\pi\) | |||||||
\(102\) | −3.82377e105 | −1.35202 | ||||||||
\(103\) | 3.42402e105 | 0.725408 | 0.362704 | − | 0.931904i | \(-0.381854\pi\) | ||||
0.362704 | + | 0.931904i | \(0.381854\pi\) | |||||||
\(104\) | 5.32743e105 | 0.679622 | ||||||||
\(105\) | −1.07403e106 | −0.829042 | ||||||||
\(106\) | 7.02160e105 | 0.329517 | ||||||||
\(107\) | 2.13857e106 | 0.613020 | 0.306510 | − | 0.951867i | \(-0.400839\pi\) | ||||
0.306510 | + | 0.951867i | \(0.400839\pi\) | |||||||
\(108\) | 4.22520e106 | 0.743191 | ||||||||
\(109\) | 1.63899e107 | 1.77699 | 0.888495 | − | 0.458886i | \(-0.151751\pi\) | ||||
0.888495 | + | 0.458886i | \(0.151751\pi\) | |||||||
\(110\) | 1.62815e106 | 0.109289 | ||||||||
\(111\) | −2.71032e107 | −1.13126 | ||||||||
\(112\) | 3.14492e107 | 0.819716 | ||||||||
\(113\) | −1.62565e107 | −0.265711 | −0.132855 | − | 0.991135i | \(-0.542415\pi\) | ||||
−0.132855 | + | 0.991135i | \(0.542415\pi\) | |||||||
\(114\) | −2.05508e108 | −2.11506 | ||||||||
\(115\) | −1.60296e108 | −1.04301 | ||||||||
\(116\) | −8.95690e107 | −0.369924 | ||||||||
\(117\) | −3.55843e108 | −0.936485 | ||||||||
\(118\) | 1.31770e109 | 2.21825 | ||||||||
\(119\) | 8.07664e108 | 0.873002 | ||||||||
\(120\) | −3.74576e108 | −0.260930 | ||||||||
\(121\) | −2.18235e109 | −0.983315 | ||||||||
\(122\) | −1.67145e109 | −0.488879 | ||||||||
\(123\) | −1.61546e108 | −0.0307806 | ||||||||
\(124\) | 8.18842e109 | 1.01991 | ||||||||
\(125\) | 1.16109e110 | 0.948613 | ||||||||
\(126\) | 1.72266e110 | 0.926290 | ||||||||
\(127\) | −3.88074e109 | −0.137790 | −0.0688952 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688952 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(128\) | 3.09310e110 | 0.727564 | ||||||||
\(129\) | −2.74088e109 | −0.0428480 | ||||||||
\(130\) | −1.46907e111 | −1.53115 | ||||||||
\(131\) | −1.57108e111 | −1.09510 | −0.547552 | − | 0.836772i | \(-0.684440\pi\) | ||||
−0.547552 | + | 0.836772i | \(0.684440\pi\) | |||||||
\(132\) | −4.25485e110 | −0.198954 | ||||||||
\(133\) | 4.34078e111 | 1.36570 | ||||||||
\(134\) | −1.20358e112 | −2.55548 | ||||||||
\(135\) | −2.33284e111 | −0.335245 | ||||||||
\(136\) | 2.81680e111 | 0.274766 | ||||||||
\(137\) | −1.76329e111 | −0.117083 | −0.0585416 | − | 0.998285i | \(-0.518645\pi\) | ||||
−0.0585416 | + | 0.998285i | \(0.518645\pi\) | |||||||
\(138\) | 7.53933e112 | 3.41728 | ||||||||
\(139\) | −2.53726e112 | −0.787207 | −0.393603 | − | 0.919280i | \(-0.628772\pi\) | ||||
−0.393603 | + | 0.919280i | \(0.628772\pi\) | |||||||
\(140\) | 3.95154e112 | 0.841481 | ||||||||
\(141\) | −1.52286e113 | −2.23181 | ||||||||
\(142\) | 1.73471e113 | 1.75424 | ||||||||
\(143\) | −3.34118e112 | −0.233753 | ||||||||
\(144\) | −7.32615e112 | −0.355504 | ||||||||
\(145\) | 4.94534e112 | 0.166869 | ||||||||
\(146\) | 2.27333e113 | 0.534734 | ||||||||
\(147\) | −3.17582e113 | −0.522031 | ||||||||
\(148\) | 9.97177e113 | 1.14824 | ||||||||
\(149\) | −8.32260e113 | −0.672945 | −0.336473 | − | 0.941693i | \(-0.609234\pi\) | ||||
−0.336473 | + | 0.941693i | \(0.609234\pi\) | |||||||
\(150\) | −2.21406e114 | −1.26008 | ||||||||
\(151\) | −4.51522e114 | −1.81296 | −0.906482 | − | 0.422245i | \(-0.861242\pi\) | ||||
−0.906482 | + | 0.422245i | \(0.861242\pi\) | |||||||
\(152\) | 1.51388e114 | 0.429838 | ||||||||
\(153\) | −1.88147e114 | −0.378614 | ||||||||
\(154\) | 1.61749e114 | 0.231209 | ||||||||
\(155\) | −4.52104e114 | −0.460070 | ||||||||
\(156\) | 3.83914e115 | 2.78736 | ||||||||
\(157\) | 2.88320e115 | 1.49673 | 0.748364 | − | 0.663288i | \(-0.230839\pi\) | ||||
0.748364 | + | 0.663288i | \(0.230839\pi\) | |||||||
\(158\) | −8.29511e114 | −0.308550 | ||||||||
\(159\) | 1.01313e115 | 0.270593 | ||||||||
\(160\) | −4.12675e115 | −0.793065 | ||||||||
\(161\) | −1.59247e116 | −2.20655 | ||||||||
\(162\) | 1.87269e116 | 1.87469 | ||||||||
\(163\) | −5.49862e115 | −0.398478 | −0.199239 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199239 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(164\) | 5.94356e114 | 0.0312424 | ||||||||
\(165\) | 2.34921e115 | 0.0897460 | ||||||||
\(166\) | −2.57750e116 | −0.717008 | ||||||||
\(167\) | −6.07691e116 | −1.23330 | −0.616649 | − | 0.787238i | \(-0.711510\pi\) | ||||
−0.616649 | + | 0.787238i | \(0.711510\pi\) | |||||||
\(168\) | −3.72125e116 | −0.552016 | ||||||||
\(169\) | 2.09418e117 | 2.27490 | ||||||||
\(170\) | −7.76751e116 | −0.619032 | ||||||||
\(171\) | −1.01119e117 | −0.592295 | ||||||||
\(172\) | 1.00842e116 | 0.0434909 | ||||||||
\(173\) | 1.52150e117 | 0.484006 | 0.242003 | − | 0.970275i | \(-0.422196\pi\) | ||||
0.242003 | + | 0.970275i | \(0.422196\pi\) | |||||||
\(174\) | −2.32598e117 | −0.546726 | ||||||||
\(175\) | 4.67657e117 | 0.813636 | ||||||||
\(176\) | −6.87887e116 | −0.0887365 | ||||||||
\(177\) | 1.90128e118 | 1.82158 | ||||||||
\(178\) | 5.52735e117 | 0.393973 | ||||||||
\(179\) | −1.41887e117 | −0.0753629 | −0.0376814 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376814 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(180\) | −9.20518e117 | −0.364944 | ||||||||
\(181\) | 2.12802e118 | 0.630741 | 0.315370 | − | 0.948969i | \(-0.397871\pi\) | ||||
0.315370 | + | 0.948969i | \(0.397871\pi\) | |||||||
\(182\) | −1.45946e119 | −3.23925 | ||||||||
\(183\) | −2.41169e118 | −0.401458 | ||||||||
\(184\) | −5.55389e118 | −0.694483 | ||||||||
\(185\) | −5.50567e118 | −0.517958 | ||||||||
\(186\) | 2.12641e119 | 1.50736 | ||||||||
\(187\) | −1.76660e118 | −0.0945049 | ||||||||
\(188\) | 5.60289e119 | 2.26530 | ||||||||
\(189\) | −2.31758e119 | −0.709234 | ||||||||
\(190\) | −4.17463e119 | −0.968399 | ||||||||
\(191\) | 3.26522e119 | 0.574991 | 0.287495 | − | 0.957782i | \(-0.407177\pi\) | ||||
0.287495 | + | 0.957782i | \(0.407177\pi\) | |||||||
\(192\) | 1.30881e120 | 1.75212 | ||||||||
\(193\) | −1.01008e120 | −1.02943 | −0.514713 | − | 0.857362i | \(-0.672102\pi\) | ||||
−0.514713 | + | 0.857362i | \(0.672102\pi\) | |||||||
\(194\) | −1.46874e119 | −0.114118 | ||||||||
\(195\) | −2.11969e120 | −1.25735 | ||||||||
\(196\) | 1.16844e120 | 0.529863 | ||||||||
\(197\) | 3.20363e120 | 1.11215 | 0.556077 | − | 0.831130i | \(-0.312306\pi\) | ||||
0.556077 | + | 0.831130i | \(0.312306\pi\) | |||||||
\(198\) | −3.76798e119 | −0.100273 | ||||||||
\(199\) | 3.54060e120 | 0.723253 | 0.361627 | − | 0.932323i | \(-0.382221\pi\) | ||||
0.361627 | + | 0.932323i | \(0.382221\pi\) | |||||||
\(200\) | 1.63100e120 | 0.256082 | ||||||||
\(201\) | −1.73662e121 | −2.09851 | ||||||||
\(202\) | −2.18497e121 | −2.03469 | ||||||||
\(203\) | 4.91298e120 | 0.353023 | ||||||||
\(204\) | 2.02989e121 | 1.12691 | ||||||||
\(205\) | −3.28159e119 | −0.0140931 | ||||||||
\(206\) | −3.27142e121 | −1.08820 | ||||||||
\(207\) | 3.70969e121 | 0.956962 | ||||||||
\(208\) | 6.20679e121 | 1.24320 | ||||||||
\(209\) | −9.49457e120 | −0.147841 | ||||||||
\(210\) | 1.02616e122 | 1.24366 | ||||||||
\(211\) | −3.74411e121 | −0.353606 | −0.176803 | − | 0.984246i | \(-0.556576\pi\) | ||||
−0.176803 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(212\) | −3.72750e121 | −0.274653 | ||||||||
\(213\) | 2.50297e122 | 1.44055 | ||||||||
\(214\) | −2.04325e122 | −0.919601 | ||||||||
\(215\) | −5.56776e120 | −0.0196183 | ||||||||
\(216\) | −8.08276e121 | −0.223222 | ||||||||
\(217\) | −4.49145e122 | −0.973310 | ||||||||
\(218\) | −1.56594e123 | −2.66569 | ||||||||
\(219\) | 3.28014e122 | 0.439112 | ||||||||
\(220\) | −8.64319e121 | −0.0910926 | ||||||||
\(221\) | 1.59400e123 | 1.32402 | ||||||||
\(222\) | 2.58952e123 | 1.69703 | ||||||||
\(223\) | 1.59180e123 | 0.823918 | 0.411959 | − | 0.911202i | \(-0.364845\pi\) | ||||
0.411959 | + | 0.911202i | \(0.364845\pi\) | |||||||
\(224\) | −4.09974e123 | −1.67778 | ||||||||
\(225\) | −1.08942e123 | −0.352868 | ||||||||
\(226\) | 1.55320e123 | 0.398597 | ||||||||
\(227\) | −6.30732e123 | −1.28377 | −0.641885 | − | 0.766801i | \(-0.721847\pi\) | ||||
−0.641885 | + | 0.766801i | \(0.721847\pi\) | |||||||
\(228\) | 1.09096e124 | 1.76291 | ||||||||
\(229\) | −8.73627e123 | −1.12192 | −0.560962 | − | 0.827842i | \(-0.689569\pi\) | ||||
−0.560962 | + | 0.827842i | \(0.689569\pi\) | |||||||
\(230\) | 1.53152e124 | 1.56463 | ||||||||
\(231\) | 2.33384e123 | 0.189864 | ||||||||
\(232\) | 1.71344e123 | 0.111109 | ||||||||
\(233\) | −2.69610e123 | −0.139492 | −0.0697461 | − | 0.997565i | \(-0.522219\pi\) | ||||
−0.0697461 | + | 0.997565i | \(0.522219\pi\) | |||||||
\(234\) | 3.39984e124 | 1.40484 | ||||||||
\(235\) | −3.09350e124 | −1.02185 | ||||||||
\(236\) | −6.99515e124 | −1.84891 | ||||||||
\(237\) | −1.19688e124 | −0.253375 | ||||||||
\(238\) | −7.71668e124 | −1.30960 | ||||||||
\(239\) | 4.10469e124 | 0.558972 | 0.279486 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279486 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(240\) | −4.36405e124 | −0.477309 | ||||||||
\(241\) | −4.83839e124 | −0.425409 | −0.212704 | − | 0.977117i | \(-0.568227\pi\) | ||||
−0.212704 | + | 0.977117i | \(0.568227\pi\) | |||||||
\(242\) | 2.08509e125 | 1.47509 | ||||||||
\(243\) | 1.65879e125 | 0.945066 | ||||||||
\(244\) | 8.87306e124 | 0.407481 | ||||||||
\(245\) | −6.45128e124 | −0.239016 | ||||||||
\(246\) | 1.54346e124 | 0.0461744 | ||||||||
\(247\) | 8.56693e125 | 2.07126 | ||||||||
\(248\) | −1.56643e125 | −0.306337 | ||||||||
\(249\) | −3.71901e125 | −0.588792 | ||||||||
\(250\) | −1.10934e126 | −1.42303 | ||||||||
\(251\) | 2.38736e125 | 0.248341 | 0.124170 | − | 0.992261i | \(-0.460373\pi\) | ||||
0.124170 | + | 0.992261i | \(0.460373\pi\) | |||||||
\(252\) | −9.14495e125 | −0.772063 | ||||||||
\(253\) | 3.48321e125 | 0.238865 | ||||||||
\(254\) | 3.70778e125 | 0.206701 | ||||||||
\(255\) | −1.12076e126 | −0.508337 | ||||||||
\(256\) | 8.95976e125 | 0.330901 | ||||||||
\(257\) | −1.73877e126 | −0.523302 | −0.261651 | − | 0.965163i | \(-0.584267\pi\) | ||||
−0.261651 | + | 0.965163i | \(0.584267\pi\) | |||||||
\(258\) | 2.61873e125 | 0.0642770 | ||||||||
\(259\) | −5.46965e126 | −1.09578 | ||||||||
\(260\) | 7.79873e126 | 1.27621 | ||||||||
\(261\) | −1.14449e126 | −0.153103 | ||||||||
\(262\) | 1.50106e127 | 1.64278 | ||||||||
\(263\) | −8.47350e126 | −0.759252 | −0.379626 | − | 0.925140i | \(-0.623947\pi\) | ||||
−0.379626 | + | 0.925140i | \(0.623947\pi\) | |||||||
\(264\) | 8.13948e125 | 0.0597572 | ||||||||
\(265\) | 2.05805e126 | 0.123893 | ||||||||
\(266\) | −4.14732e127 | −2.04871 | ||||||||
\(267\) | 7.97529e126 | 0.323523 | ||||||||
\(268\) | 6.38934e127 | 2.13000 | ||||||||
\(269\) | 5.38318e127 | 1.47586 | 0.737928 | − | 0.674880i | \(-0.235805\pi\) | ||||
0.737928 | + | 0.674880i | \(0.235805\pi\) | |||||||
\(270\) | 2.22887e127 | 0.502907 | ||||||||
\(271\) | −6.18683e127 | −1.14969 | −0.574845 | − | 0.818263i | \(-0.694937\pi\) | ||||
−0.574845 | + | 0.818263i | \(0.694937\pi\) | |||||||
\(272\) | 3.28175e127 | 0.502618 | ||||||||
\(273\) | −2.10582e128 | −2.66000 | ||||||||
\(274\) | 1.68470e127 | 0.175638 | ||||||||
\(275\) | −1.02291e127 | −0.0880783 | ||||||||
\(276\) | −4.00234e128 | −2.84831 | ||||||||
\(277\) | 5.28238e127 | 0.310915 | 0.155458 | − | 0.987843i | \(-0.450315\pi\) | ||||
0.155458 | + | 0.987843i | \(0.450315\pi\) | |||||||
\(278\) | 2.42418e128 | 1.18090 | ||||||||
\(279\) | 1.04629e128 | 0.422117 | ||||||||
\(280\) | −7.55925e127 | −0.252745 | ||||||||
\(281\) | 4.88641e128 | 1.35490 | 0.677451 | − | 0.735568i | \(-0.263085\pi\) | ||||
0.677451 | + | 0.735568i | \(0.263085\pi\) | |||||||
\(282\) | 1.45499e129 | 3.34797 | ||||||||
\(283\) | −4.29397e128 | −0.820486 | −0.410243 | − | 0.911976i | \(-0.634556\pi\) | ||||
−0.410243 | + | 0.911976i | \(0.634556\pi\) | |||||||
\(284\) | −9.20891e128 | −1.46216 | ||||||||
\(285\) | −6.02348e128 | −0.795229 | ||||||||
\(286\) | 3.19227e128 | 0.350657 | ||||||||
\(287\) | −3.26012e127 | −0.0298149 | ||||||||
\(288\) | 9.55043e128 | 0.727641 | ||||||||
\(289\) | −7.31674e128 | −0.464709 | ||||||||
\(290\) | −4.72493e128 | −0.250323 | ||||||||
\(291\) | −2.11922e128 | −0.0937116 | ||||||||
\(292\) | −1.20682e129 | −0.445701 | ||||||||
\(293\) | −4.25875e129 | −1.31441 | −0.657207 | − | 0.753710i | \(-0.728262\pi\) | ||||
−0.657207 | + | 0.753710i | \(0.728262\pi\) | |||||||
\(294\) | 3.03428e129 | 0.783106 | ||||||||
\(295\) | 3.86220e129 | 0.834026 | ||||||||
\(296\) | −1.90759e129 | −0.344881 | ||||||||
\(297\) | 5.06923e128 | 0.0767765 | ||||||||
\(298\) | 7.95167e129 | 1.00950 | ||||||||
\(299\) | −3.14289e130 | −3.34651 | ||||||||
\(300\) | 1.17536e130 | 1.05028 | ||||||||
\(301\) | −5.53133e128 | −0.0415039 | ||||||||
\(302\) | 4.31398e130 | 2.71966 | ||||||||
\(303\) | −3.15264e130 | −1.67084 | ||||||||
\(304\) | 1.76377e130 | 0.786283 | ||||||||
\(305\) | −4.89905e129 | −0.183810 | ||||||||
\(306\) | 1.79761e130 | 0.567965 | ||||||||
\(307\) | 3.47475e130 | 0.925036 | 0.462518 | − | 0.886610i | \(-0.346946\pi\) | ||||
0.462518 | + | 0.886610i | \(0.346946\pi\) | |||||||
\(308\) | −8.58663e129 | −0.192713 | ||||||||
\(309\) | −4.72026e130 | −0.893605 | ||||||||
\(310\) | 4.31954e130 | 0.690158 | ||||||||
\(311\) | 4.08993e130 | 0.551817 | 0.275908 | − | 0.961184i | \(-0.411021\pi\) | ||||
0.275908 | + | 0.961184i | \(0.411021\pi\) | |||||||
\(312\) | −7.34423e130 | −0.837202 | ||||||||
\(313\) | −1.00853e131 | −0.971873 | −0.485937 | − | 0.873994i | \(-0.661521\pi\) | ||||
−0.485937 | + | 0.873994i | \(0.661521\pi\) | |||||||
\(314\) | −2.75470e131 | −2.24527 | ||||||||
\(315\) | 5.04916e130 | 0.348270 | ||||||||
\(316\) | 4.40355e130 | 0.257176 | ||||||||
\(317\) | 7.79846e130 | 0.385832 | 0.192916 | − | 0.981215i | \(-0.438206\pi\) | ||||
0.192916 | + | 0.981215i | \(0.438206\pi\) | |||||||
\(318\) | −9.67977e130 | −0.405921 | ||||||||
\(319\) | −1.07461e130 | −0.0382157 | ||||||||
\(320\) | 2.65869e131 | 0.802221 | ||||||||
\(321\) | −2.94816e131 | −0.755157 | ||||||||
\(322\) | 1.52150e132 | 3.31008 | ||||||||
\(323\) | 4.52964e131 | 0.837396 | ||||||||
\(324\) | −9.94140e131 | −1.56255 | ||||||||
\(325\) | 9.22965e131 | 1.23398 | ||||||||
\(326\) | 5.25355e131 | 0.597763 | ||||||||
\(327\) | −2.25946e132 | −2.18901 | ||||||||
\(328\) | −1.13700e130 | −0.00938387 | ||||||||
\(329\) | −3.07326e132 | −2.16179 | ||||||||
\(330\) | −2.24451e131 | −0.134629 | ||||||||
\(331\) | 1.33736e132 | 0.684353 | 0.342176 | − | 0.939636i | \(-0.388836\pi\) | ||||
0.342176 | + | 0.939636i | \(0.388836\pi\) | |||||||
\(332\) | 1.36829e132 | 0.597627 | ||||||||
\(333\) | 1.27416e132 | 0.475229 | ||||||||
\(334\) | 5.80608e132 | 1.85009 | ||||||||
\(335\) | −3.52772e132 | −0.960819 | ||||||||
\(336\) | −4.33549e132 | −1.00978 | ||||||||
\(337\) | 5.42067e132 | 1.08015 | 0.540074 | − | 0.841618i | \(-0.318396\pi\) | ||||
0.540074 | + | 0.841618i | \(0.318396\pi\) | |||||||
\(338\) | −2.00085e133 | −3.41261 | ||||||||
\(339\) | 2.24108e132 | 0.327320 | ||||||||
\(340\) | 4.12347e132 | 0.515964 | ||||||||
\(341\) | 9.82414e131 | 0.105363 | ||||||||
\(342\) | 9.66125e132 | 0.888511 | ||||||||
\(343\) | 8.71476e132 | 0.687566 | ||||||||
\(344\) | −1.92910e131 | −0.0130628 | ||||||||
\(345\) | 2.20979e133 | 1.28484 | ||||||||
\(346\) | −1.45369e133 | −0.726066 | ||||||||
\(347\) | 1.25222e132 | 0.0537506 | 0.0268753 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268753 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(348\) | 1.23477e133 | 0.455697 | ||||||||
\(349\) | 4.47790e133 | 1.42148 | 0.710738 | − | 0.703457i | \(-0.248361\pi\) | ||||
0.710738 | + | 0.703457i | \(0.248361\pi\) | |||||||
\(350\) | −4.46815e133 | −1.22055 | ||||||||
\(351\) | −4.57396e133 | −1.07564 | ||||||||
\(352\) | 8.96736e132 | 0.181625 | ||||||||
\(353\) | 5.25259e133 | 0.916645 | 0.458323 | − | 0.888786i | \(-0.348450\pi\) | ||||
0.458323 | + | 0.888786i | \(0.348450\pi\) | |||||||
\(354\) | −1.81654e134 | −2.73259 | ||||||||
\(355\) | 5.08448e133 | 0.659565 | ||||||||
\(356\) | −2.93425e133 | −0.328377 | ||||||||
\(357\) | −1.11342e134 | −1.07542 | ||||||||
\(358\) | 1.35563e133 | 0.113053 | ||||||||
\(359\) | 1.00745e134 | 0.725712 | 0.362856 | − | 0.931845i | \(-0.381802\pi\) | ||||
0.362856 | + | 0.931845i | \(0.381802\pi\) | |||||||
\(360\) | 1.76094e133 | 0.109613 | ||||||||
\(361\) | 5.76093e133 | 0.310002 | ||||||||
\(362\) | −2.03318e134 | −0.946185 | ||||||||
\(363\) | 3.00852e134 | 1.21131 | ||||||||
\(364\) | 7.74770e134 | 2.69991 | ||||||||
\(365\) | 6.66318e133 | 0.201051 | ||||||||
\(366\) | 2.30421e134 | 0.602233 | ||||||||
\(367\) | −8.02021e134 | −1.81643 | −0.908213 | − | 0.418509i | \(-0.862553\pi\) | ||||
−0.908213 | + | 0.418509i | \(0.862553\pi\) | |||||||
\(368\) | −6.47063e134 | −1.27039 | ||||||||
\(369\) | 7.59451e132 | 0.0129305 | ||||||||
\(370\) | 5.26029e134 | 0.776997 | ||||||||
\(371\) | 2.04458e134 | 0.262104 | ||||||||
\(372\) | −1.12883e135 | −1.25639 | ||||||||
\(373\) | 4.43980e134 | 0.429190 | 0.214595 | − | 0.976703i | \(-0.431157\pi\) | ||||
0.214595 | + | 0.976703i | \(0.431157\pi\) | |||||||
\(374\) | 1.68787e134 | 0.141768 | ||||||||
\(375\) | −1.60064e135 | −1.16856 | ||||||||
\(376\) | −1.07183e135 | −0.680397 | ||||||||
\(377\) | 9.69621e134 | 0.535404 | ||||||||
\(378\) | 2.21429e135 | 1.06393 | ||||||||
\(379\) | −6.75431e133 | −0.0282502 | −0.0141251 | − | 0.999900i | \(-0.504496\pi\) | ||||
−0.0141251 | + | 0.999900i | \(0.504496\pi\) | |||||||
\(380\) | 2.21615e135 | 0.807161 | ||||||||
\(381\) | 5.34987e134 | 0.169739 | ||||||||
\(382\) | −3.11970e135 | −0.862553 | ||||||||
\(383\) | −5.34001e135 | −1.28708 | −0.643541 | − | 0.765412i | \(-0.722535\pi\) | ||||
−0.643541 | + | 0.765412i | \(0.722535\pi\) | |||||||
\(384\) | −4.26406e135 | −0.896260 | ||||||||
\(385\) | 4.74090e134 | 0.0869306 | ||||||||
\(386\) | 9.65059e135 | 1.54426 | ||||||||
\(387\) | 1.28853e134 | 0.0179999 | ||||||||
\(388\) | 7.79699e134 | 0.0951177 | ||||||||
\(389\) | 1.35889e136 | 1.44820 | 0.724102 | − | 0.689693i | \(-0.242254\pi\) | ||||
0.724102 | + | 0.689693i | \(0.242254\pi\) | |||||||
\(390\) | 2.02522e136 | 1.88617 | ||||||||
\(391\) | −1.66176e136 | −1.35297 | ||||||||
\(392\) | −2.23522e135 | −0.159148 | ||||||||
\(393\) | 2.16584e136 | 1.34902 | ||||||||
\(394\) | −3.06085e136 | −1.66836 | ||||||||
\(395\) | −2.43131e135 | −0.116010 | ||||||||
\(396\) | 2.00027e135 | 0.0835779 | ||||||||
\(397\) | −4.74251e136 | −1.73583 | −0.867914 | − | 0.496715i | \(-0.834539\pi\) | ||||
−0.867914 | + | 0.496715i | \(0.834539\pi\) | |||||||
\(398\) | −3.38280e136 | −1.08496 | ||||||||
\(399\) | −5.98406e136 | −1.68236 | ||||||||
\(400\) | 1.90021e136 | 0.468439 | ||||||||
\(401\) | −1.79524e135 | −0.0388189 | −0.0194094 | − | 0.999812i | \(-0.506179\pi\) | ||||
−0.0194094 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(402\) | 1.65922e137 | 3.14801 | ||||||||
\(403\) | −8.86430e136 | −1.47615 | ||||||||
\(404\) | 1.15991e137 | 1.69591 | ||||||||
\(405\) | 5.48891e136 | 0.704851 | ||||||||
\(406\) | −4.69401e136 | −0.529575 | ||||||||
\(407\) | 1.19637e136 | 0.118621 | ||||||||
\(408\) | −3.88316e136 | −0.338475 | ||||||||
\(409\) | −3.15143e136 | −0.241565 | −0.120783 | − | 0.992679i | \(-0.538540\pi\) | ||||
−0.120783 | + | 0.992679i | \(0.538540\pi\) | |||||||
\(410\) | 3.13534e135 | 0.0211413 | ||||||||
\(411\) | 2.43082e136 | 0.144231 | ||||||||
\(412\) | 1.73667e137 | 0.907013 | ||||||||
\(413\) | 3.83693e137 | 1.76444 | ||||||||
\(414\) | −3.54436e137 | −1.43555 | ||||||||
\(415\) | −7.55470e136 | −0.269583 | ||||||||
\(416\) | −8.09123e137 | −2.54457 | ||||||||
\(417\) | 3.49780e137 | 0.969732 | ||||||||
\(418\) | 9.07141e136 | 0.221779 | ||||||||
\(419\) | −4.51580e137 | −0.973864 | −0.486932 | − | 0.873440i | \(-0.661884\pi\) | ||||
−0.486932 | + | 0.873440i | \(0.661884\pi\) | |||||||
\(420\) | −5.44747e137 | −1.03659 | ||||||||
\(421\) | 6.83262e137 | 1.14757 | 0.573783 | − | 0.819008i | \(-0.305475\pi\) | ||||
0.573783 | + | 0.819008i | \(0.305475\pi\) | |||||||
\(422\) | 3.57724e137 | 0.530450 | ||||||||
\(423\) | 7.15921e137 | 0.937553 | ||||||||
\(424\) | 7.13066e136 | 0.0824939 | ||||||||
\(425\) | 4.88005e137 | 0.498890 | ||||||||
\(426\) | −2.39142e138 | −2.16099 | ||||||||
\(427\) | −4.86699e137 | −0.388863 | ||||||||
\(428\) | 1.08468e138 | 0.766488 | ||||||||
\(429\) | 4.60605e137 | 0.287953 | ||||||||
\(430\) | 5.31961e136 | 0.0294297 | ||||||||
\(431\) | 1.34945e137 | 0.0660846 | 0.0330423 | − | 0.999454i | \(-0.489480\pi\) | ||||
0.0330423 | + | 0.999454i | \(0.489480\pi\) | |||||||
\(432\) | −9.41693e137 | −0.408331 | ||||||||
\(433\) | 1.24017e138 | 0.476286 | 0.238143 | − | 0.971230i | \(-0.423461\pi\) | ||||
0.238143 | + | 0.971230i | \(0.423461\pi\) | |||||||
\(434\) | 4.29128e138 | 1.46008 | ||||||||
\(435\) | −6.81749e137 | −0.205560 | ||||||||
\(436\) | 8.31298e138 | 2.22186 | ||||||||
\(437\) | −8.93109e138 | −2.11655 | ||||||||
\(438\) | −3.13394e138 | −0.658720 | ||||||||
\(439\) | 6.09549e138 | 1.13664 | 0.568318 | − | 0.822809i | \(-0.307594\pi\) | ||||
0.568318 | + | 0.822809i | \(0.307594\pi\) | |||||||
\(440\) | 1.65343e137 | 0.0273603 | ||||||||
\(441\) | 1.49300e138 | 0.219298 | ||||||||
\(442\) | −1.52296e139 | −1.98618 | ||||||||
\(443\) | −6.29540e138 | −0.729168 | −0.364584 | − | 0.931171i | \(-0.618789\pi\) | ||||
−0.364584 | + | 0.931171i | \(0.618789\pi\) | |||||||
\(444\) | −1.37468e139 | −1.41447 | ||||||||
\(445\) | 1.62008e138 | 0.148127 | ||||||||
\(446\) | −1.52086e139 | −1.23597 | ||||||||
\(447\) | 1.14733e139 | 0.828977 | ||||||||
\(448\) | 2.64129e139 | 1.69715 | ||||||||
\(449\) | −3.53370e137 | −0.0201975 | −0.0100987 | − | 0.999949i | \(-0.503215\pi\) | ||||
−0.0100987 | + | 0.999949i | \(0.503215\pi\) | |||||||
\(450\) | 1.04086e139 | 0.529342 | ||||||||
\(451\) | 7.13085e136 | 0.00322755 | ||||||||
\(452\) | −8.24533e138 | −0.332231 | ||||||||
\(453\) | 6.22454e139 | 2.23333 | ||||||||
\(454\) | 6.02621e139 | 1.92580 | ||||||||
\(455\) | −4.27771e139 | −1.21790 | ||||||||
\(456\) | −2.08700e139 | −0.529502 | ||||||||
\(457\) | −7.29371e139 | −1.64948 | −0.824742 | − | 0.565510i | \(-0.808679\pi\) | ||||
−0.824742 | + | 0.565510i | \(0.808679\pi\) | |||||||
\(458\) | 8.34691e139 | 1.68302 | ||||||||
\(459\) | −2.41841e139 | −0.434875 | ||||||||
\(460\) | −8.13024e139 | −1.30412 | ||||||||
\(461\) | −1.26835e140 | −1.81526 | −0.907632 | − | 0.419768i | \(-0.862112\pi\) | ||||
−0.907632 | + | 0.419768i | \(0.862112\pi\) | |||||||
\(462\) | −2.22983e139 | −0.284818 | ||||||||
\(463\) | 1.37630e140 | 1.56932 | 0.784660 | − | 0.619927i | \(-0.212838\pi\) | ||||
0.784660 | + | 0.619927i | \(0.212838\pi\) | |||||||
\(464\) | 1.99627e139 | 0.203248 | ||||||||
\(465\) | 6.23257e139 | 0.566744 | ||||||||
\(466\) | 2.57594e139 | 0.209254 | ||||||||
\(467\) | 1.53938e140 | 1.11740 | 0.558700 | − | 0.829370i | \(-0.311300\pi\) | ||||
0.558700 | + | 0.829370i | \(0.311300\pi\) | |||||||
\(468\) | −1.80484e140 | −1.17093 | ||||||||
\(469\) | −3.50464e140 | −2.03268 | ||||||||
\(470\) | 2.95563e140 | 1.53289 | ||||||||
\(471\) | −3.97469e140 | −1.84377 | ||||||||
\(472\) | 1.33816e140 | 0.555334 | ||||||||
\(473\) | 1.20987e138 | 0.00449290 | ||||||||
\(474\) | 1.14354e140 | 0.380091 | ||||||||
\(475\) | 2.62277e140 | 0.780452 | ||||||||
\(476\) | 4.09648e140 | 1.09156 | ||||||||
\(477\) | −4.76289e139 | −0.113673 | ||||||||
\(478\) | −3.92175e140 | −0.838523 | ||||||||
\(479\) | 1.64056e140 | 0.314323 | 0.157162 | − | 0.987573i | \(-0.449766\pi\) | ||||
0.157162 | + | 0.987573i | \(0.449766\pi\) | |||||||
\(480\) | 5.68901e140 | 0.976949 | ||||||||
\(481\) | −1.07949e141 | −1.66188 | ||||||||
\(482\) | 4.62276e140 | 0.638163 | ||||||||
\(483\) | 2.19533e141 | 2.71817 | ||||||||
\(484\) | −1.10689e141 | −1.22949 | ||||||||
\(485\) | −4.30492e139 | −0.0429066 | ||||||||
\(486\) | −1.58486e141 | −1.41771 | ||||||||
\(487\) | −6.86441e140 | −0.551230 | −0.275615 | − | 0.961268i | \(-0.588881\pi\) | ||||
−0.275615 | + | 0.961268i | \(0.588881\pi\) | |||||||
\(488\) | −1.69741e140 | −0.122390 | ||||||||
\(489\) | 7.58023e140 | 0.490871 | ||||||||
\(490\) | 6.16376e140 | 0.358551 | ||||||||
\(491\) | −1.07369e141 | −0.561176 | −0.280588 | − | 0.959828i | \(-0.590529\pi\) | ||||
−0.280588 | + | 0.959828i | \(0.590529\pi\) | |||||||
\(492\) | −8.19361e139 | −0.0384864 | ||||||||
\(493\) | 5.12673e140 | 0.216460 | ||||||||
\(494\) | −8.18511e141 | −3.10713 | ||||||||
\(495\) | −1.10440e140 | −0.0377011 | ||||||||
\(496\) | −1.82500e141 | −0.560368 | ||||||||
\(497\) | 5.05121e141 | 1.39536 | ||||||||
\(498\) | 3.55326e141 | 0.883256 | ||||||||
\(499\) | 7.22628e141 | 1.61673 | 0.808363 | − | 0.588685i | \(-0.200354\pi\) | ||||
0.808363 | + | 0.588685i | \(0.200354\pi\) | |||||||
\(500\) | 5.88905e141 | 1.18610 | ||||||||
\(501\) | 8.37745e141 | 1.51926 | ||||||||
\(502\) | −2.28096e141 | −0.372540 | ||||||||
\(503\) | −2.57863e140 | −0.0379376 | −0.0189688 | − | 0.999820i | \(-0.506038\pi\) | ||||
−0.0189688 | + | 0.999820i | \(0.506038\pi\) | |||||||
\(504\) | 1.74942e141 | 0.231895 | ||||||||
\(505\) | −6.40419e141 | −0.765009 | ||||||||
\(506\) | −3.32797e141 | −0.358325 | ||||||||
\(507\) | −2.88697e142 | −2.80237 | ||||||||
\(508\) | −1.96831e141 | −0.172286 | ||||||||
\(509\) | 8.55017e141 | 0.674981 | 0.337490 | − | 0.941329i | \(-0.390422\pi\) | ||||
0.337490 | + | 0.941329i | \(0.390422\pi\) | |||||||
\(510\) | 1.07080e142 | 0.762564 | ||||||||
\(511\) | 6.61958e141 | 0.425337 | ||||||||
\(512\) | −2.11076e142 | −1.22395 | ||||||||
\(513\) | −1.29977e142 | −0.680308 | ||||||||
\(514\) | 1.66127e142 | 0.785013 | ||||||||
\(515\) | −9.58861e141 | −0.409144 | ||||||||
\(516\) | −1.39018e141 | −0.0535749 | ||||||||
\(517\) | 6.72213e141 | 0.234020 | ||||||||
\(518\) | 5.22587e142 | 1.64379 | ||||||||
\(519\) | −2.09749e142 | −0.596230 | ||||||||
\(520\) | −1.49189e142 | −0.383319 | ||||||||
\(521\) | −2.86534e141 | −0.0665572 | −0.0332786 | − | 0.999446i | \(-0.510595\pi\) | ||||
−0.0332786 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(522\) | 1.09348e142 | 0.229672 | ||||||||
\(523\) | 4.48660e142 | 0.852272 | 0.426136 | − | 0.904659i | \(-0.359874\pi\) | ||||
0.426136 | + | 0.904659i | \(0.359874\pi\) | |||||||
\(524\) | −7.96854e142 | −1.36926 | ||||||||
\(525\) | −6.44698e142 | −1.00229 | ||||||||
\(526\) | 8.09585e142 | 1.13897 | ||||||||
\(527\) | −4.68687e142 | −0.596796 | ||||||||
\(528\) | 9.48300e141 | 0.109311 | ||||||||
\(529\) | 2.31836e143 | 2.41969 | ||||||||
\(530\) | −1.96632e142 | −0.185854 | ||||||||
\(531\) | −8.93820e142 | −0.765223 | ||||||||
\(532\) | 2.20165e143 | 1.70760 | ||||||||
\(533\) | −6.43415e141 | −0.0452181 | ||||||||
\(534\) | −7.61984e142 | −0.485322 | ||||||||
\(535\) | −5.98882e142 | −0.345754 | ||||||||
\(536\) | −1.22227e143 | −0.639759 | ||||||||
\(537\) | 1.95601e142 | 0.0928368 | ||||||||
\(538\) | −5.14326e143 | −2.21395 | ||||||||
\(539\) | 1.40185e142 | 0.0547384 | ||||||||
\(540\) | −1.18322e143 | −0.419173 | ||||||||
\(541\) | −1.97481e143 | −0.634847 | −0.317424 | − | 0.948284i | \(-0.602818\pi\) | ||||
−0.317424 | + | 0.948284i | \(0.602818\pi\) | |||||||
\(542\) | 5.91109e143 | 1.72467 | ||||||||
\(543\) | −2.93363e143 | −0.776987 | ||||||||
\(544\) | −4.27812e143 | −1.02875 | ||||||||
\(545\) | −4.58981e143 | −1.00226 | ||||||||
\(546\) | 2.01197e144 | 3.99031 | ||||||||
\(547\) | −1.18448e143 | −0.213399 | −0.106700 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106700 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(548\) | −8.94344e142 | −0.146395 | ||||||||
\(549\) | 1.13377e143 | 0.168647 | ||||||||
\(550\) | 9.77316e142 | 0.132128 | ||||||||
\(551\) | 2.75535e143 | 0.338624 | ||||||||
\(552\) | 7.65642e143 | 0.855509 | ||||||||
\(553\) | −2.41541e143 | −0.245426 | ||||||||
\(554\) | −5.04695e143 | −0.466409 | ||||||||
\(555\) | 7.58995e143 | 0.638054 | ||||||||
\(556\) | −1.28690e144 | −0.984282 | ||||||||
\(557\) | 1.54722e144 | 1.07685 | 0.538423 | − | 0.842675i | \(-0.319020\pi\) | ||||
0.538423 | + | 0.842675i | \(0.319020\pi\) | |||||||
\(558\) | −9.99661e143 | −0.633224 | ||||||||
\(559\) | −1.09166e143 | −0.0629458 | ||||||||
\(560\) | −8.80700e143 | −0.462335 | ||||||||
\(561\) | 2.43538e143 | 0.116417 | ||||||||
\(562\) | −4.66863e144 | −2.03251 | ||||||||
\(563\) | 1.70654e144 | 0.676748 | 0.338374 | − | 0.941012i | \(-0.390123\pi\) | ||||
0.338374 | + | 0.941012i | \(0.390123\pi\) | |||||||
\(564\) | −7.72397e144 | −2.79054 | ||||||||
\(565\) | 4.55246e143 | 0.149866 | ||||||||
\(566\) | 4.10260e144 | 1.23082 | ||||||||
\(567\) | 5.45299e144 | 1.49116 | ||||||||
\(568\) | 1.76165e144 | 0.439170 | ||||||||
\(569\) | −2.55776e144 | −0.581388 | −0.290694 | − | 0.956816i | \(-0.593886\pi\) | ||||
−0.290694 | + | 0.956816i | \(0.593886\pi\) | |||||||
\(570\) | 5.75502e144 | 1.19294 | ||||||||
\(571\) | 7.49648e144 | 1.41730 | 0.708650 | − | 0.705561i | \(-0.249305\pi\) | ||||
0.708650 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(572\) | −1.69465e144 | −0.292273 | ||||||||
\(573\) | −4.50134e144 | −0.708311 | ||||||||
\(574\) | 3.11482e143 | 0.0447259 | ||||||||
\(575\) | −9.62199e144 | −1.26097 | ||||||||
\(576\) | −6.15294e144 | −0.736042 | ||||||||
\(577\) | −2.51068e144 | −0.274196 | −0.137098 | − | 0.990557i | \(-0.543778\pi\) | ||||
−0.137098 | + | 0.990557i | \(0.543778\pi\) | |||||||
\(578\) | 6.99064e144 | 0.697117 | ||||||||
\(579\) | 1.39246e145 | 1.26811 | ||||||||
\(580\) | 2.50828e144 | 0.208644 | ||||||||
\(581\) | −7.50527e144 | −0.570321 | ||||||||
\(582\) | 2.02477e144 | 0.140578 | ||||||||
\(583\) | −4.47210e143 | −0.0283735 | ||||||||
\(584\) | 2.30864e144 | 0.133869 | ||||||||
\(585\) | 9.96499e144 | 0.528195 | ||||||||
\(586\) | 4.06895e145 | 1.97177 | ||||||||
\(587\) | −1.70386e145 | −0.754978 | −0.377489 | − | 0.926014i | \(-0.623212\pi\) | ||||
−0.377489 | + | 0.926014i | \(0.623212\pi\) | |||||||
\(588\) | −1.61078e145 | −0.652720 | ||||||||
\(589\) | −2.51895e145 | −0.933612 | ||||||||
\(590\) | −3.69007e145 | −1.25114 | ||||||||
\(591\) | −4.41643e145 | −1.37002 | ||||||||
\(592\) | −2.22246e145 | −0.630876 | ||||||||
\(593\) | 3.57082e145 | 0.927675 | 0.463838 | − | 0.885920i | \(-0.346472\pi\) | ||||
0.463838 | + | 0.885920i | \(0.346472\pi\) | |||||||
\(594\) | −4.84330e144 | −0.115174 | ||||||||
\(595\) | −2.26178e145 | −0.492389 | ||||||||
\(596\) | −4.22123e145 | −0.841415 | ||||||||
\(597\) | −4.88097e145 | −0.890950 | ||||||||
\(598\) | 3.00282e146 | 5.02015 | ||||||||
\(599\) | 4.04087e145 | 0.618823 | 0.309412 | − | 0.950928i | \(-0.399868\pi\) | ||||
0.309412 | + | 0.950928i | \(0.399868\pi\) | |||||||
\(600\) | −2.24844e145 | −0.315458 | ||||||||
\(601\) | −4.23700e145 | −0.544689 | −0.272345 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272345 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(602\) | 5.28481e144 | 0.0622606 | ||||||||
\(603\) | 8.16411e145 | 0.881556 | ||||||||
\(604\) | −2.29012e146 | −2.26683 | ||||||||
\(605\) | 6.11144e145 | 0.554608 | ||||||||
\(606\) | 3.01213e146 | 2.50646 | ||||||||
\(607\) | 1.81602e146 | 1.38584 | 0.692920 | − | 0.721014i | \(-0.256324\pi\) | ||||
0.692920 | + | 0.721014i | \(0.256324\pi\) | |||||||
\(608\) | −2.29927e146 | −1.60935 | ||||||||
\(609\) | −6.77288e145 | −0.434876 | ||||||||
\(610\) | 4.68070e145 | 0.275737 | ||||||||
\(611\) | −6.06536e146 | −3.27863 | ||||||||
\(612\) | −9.54283e145 | −0.473399 | ||||||||
\(613\) | 1.35963e146 | 0.619079 | 0.309539 | − | 0.950887i | \(-0.399825\pi\) | ||||
0.309539 | + | 0.950887i | \(0.399825\pi\) | |||||||
\(614\) | −3.31988e146 | −1.38766 | ||||||||
\(615\) | 4.52390e144 | 0.0173608 | ||||||||
\(616\) | 1.64261e145 | 0.0578826 | ||||||||
\(617\) | 5.10995e146 | 1.65366 | 0.826829 | − | 0.562453i | \(-0.190142\pi\) | ||||
0.826829 | + | 0.562453i | \(0.190142\pi\) | |||||||
\(618\) | 4.50988e146 | 1.34051 | ||||||||
\(619\) | −2.66391e146 | −0.727378 | −0.363689 | − | 0.931520i | \(-0.618483\pi\) | ||||
−0.363689 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(620\) | −2.29308e146 | −0.575248 | ||||||||
\(621\) | 4.76839e146 | 1.09916 | ||||||||
\(622\) | −3.90764e146 | −0.827789 | ||||||||
\(623\) | 1.60948e146 | 0.313374 | ||||||||
\(624\) | −8.55649e146 | −1.53146 | ||||||||
\(625\) | 8.92418e145 | 0.146848 | ||||||||
\(626\) | 9.63578e146 | 1.45792 | ||||||||
\(627\) | 1.30889e146 | 0.182120 | ||||||||
\(628\) | 1.46236e147 | 1.87143 | ||||||||
\(629\) | −5.70762e146 | −0.671887 | ||||||||
\(630\) | −4.82413e146 | −0.522445 | ||||||||
\(631\) | −3.13753e146 | −0.312641 | −0.156321 | − | 0.987706i | \(-0.549963\pi\) | ||||
−0.156321 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(632\) | −8.42394e145 | −0.0772447 | ||||||||
\(633\) | 5.16152e146 | 0.435595 | ||||||||
\(634\) | −7.45090e146 | −0.578792 | ||||||||
\(635\) | 1.08676e146 | 0.0777163 | ||||||||
\(636\) | 5.13861e146 | 0.338335 | ||||||||
\(637\) | −1.26489e147 | −0.766888 | ||||||||
\(638\) | 1.02672e146 | 0.0573279 | ||||||||
\(639\) | −1.17669e147 | −0.605154 | ||||||||
\(640\) | −8.66190e146 | −0.410359 | ||||||||
\(641\) | 2.34806e147 | 1.02486 | 0.512428 | − | 0.858730i | \(-0.328746\pi\) | ||||
0.512428 | + | 0.858730i | \(0.328746\pi\) | |||||||
\(642\) | 2.81677e147 | 1.13282 | ||||||||
\(643\) | 2.81374e147 | 1.04282 | 0.521409 | − | 0.853307i | \(-0.325407\pi\) | ||||
0.521409 | + | 0.853307i | \(0.325407\pi\) | |||||||
\(644\) | −8.07704e147 | −2.75895 | ||||||||
\(645\) | 7.67555e145 | 0.0241671 | ||||||||
\(646\) | −4.32776e147 | −1.25619 | ||||||||
\(647\) | 2.99199e147 | 0.800728 | 0.400364 | − | 0.916356i | \(-0.368884\pi\) | ||||
0.400364 | + | 0.916356i | \(0.368884\pi\) | |||||||
\(648\) | 1.90178e147 | 0.469323 | ||||||||
\(649\) | −8.39251e146 | −0.191005 | ||||||||
\(650\) | −8.81830e147 | −1.85112 | ||||||||
\(651\) | 6.19178e147 | 1.19899 | ||||||||
\(652\) | −2.78891e147 | −0.498236 | ||||||||
\(653\) | −1.01216e148 | −1.66843 | −0.834214 | − | 0.551441i | \(-0.814078\pi\) | ||||
−0.834214 | + | 0.551441i | \(0.814078\pi\) | |||||||
\(654\) | 2.15876e148 | 3.28377 | ||||||||
\(655\) | 4.39964e147 | 0.617659 | ||||||||
\(656\) | −1.32467e146 | −0.0171655 | ||||||||
\(657\) | −1.54204e147 | −0.184465 | ||||||||
\(658\) | 2.93629e148 | 3.24294 | ||||||||
\(659\) | 3.85253e146 | 0.0392881 | 0.0196441 | − | 0.999807i | \(-0.493747\pi\) | ||||
0.0196441 | + | 0.999807i | \(0.493747\pi\) | |||||||
\(660\) | 1.19152e147 | 0.112214 | ||||||||
\(661\) | −2.48731e146 | −0.0216348 | −0.0108174 | − | 0.999941i | \(-0.503443\pi\) | ||||
−0.0108174 | + | 0.999941i | \(0.503443\pi\) | |||||||
\(662\) | −1.27776e148 | −1.02661 | ||||||||
\(663\) | −2.19744e148 | −1.63101 | ||||||||
\(664\) | −2.61753e147 | −0.179501 | ||||||||
\(665\) | −1.21559e148 | −0.770282 | ||||||||
\(666\) | −1.21738e148 | −0.712899 | ||||||||
\(667\) | −1.01084e148 | −0.547111 | ||||||||
\(668\) | −3.08222e148 | −1.54205 | ||||||||
\(669\) | −2.19441e148 | −1.01496 | ||||||||
\(670\) | 3.37049e148 | 1.44134 | ||||||||
\(671\) | 1.06456e147 | 0.0420955 | ||||||||
\(672\) | 5.65178e148 | 2.06680 | ||||||||
\(673\) | 3.07607e148 | 1.04041 | 0.520206 | − | 0.854041i | \(-0.325855\pi\) | ||||
0.520206 | + | 0.854041i | \(0.325855\pi\) | |||||||
\(674\) | −5.17908e148 | −1.62035 | ||||||||
\(675\) | −1.40032e148 | −0.405303 | ||||||||
\(676\) | 1.06217e149 | 2.84441 | ||||||||
\(677\) | −5.19092e148 | −1.28629 | −0.643146 | − | 0.765744i | \(-0.722371\pi\) | ||||
−0.643146 | + | 0.765744i | \(0.722371\pi\) | |||||||
\(678\) | −2.14119e148 | −0.491018 | ||||||||
\(679\) | −4.27675e147 | −0.0907718 | ||||||||
\(680\) | −7.88814e147 | −0.154973 | ||||||||
\(681\) | 8.69508e148 | 1.58143 | ||||||||
\(682\) | −9.38630e147 | −0.158057 | ||||||||
\(683\) | 1.89336e148 | 0.295221 | 0.147610 | − | 0.989046i | \(-0.452842\pi\) | ||||
0.147610 | + | 0.989046i | \(0.452842\pi\) | |||||||
\(684\) | −5.12878e148 | −0.740574 | ||||||||
\(685\) | 4.93791e147 | 0.0660371 | ||||||||
\(686\) | −8.32636e148 | −1.03143 | ||||||||
\(687\) | 1.20436e149 | 1.38206 | ||||||||
\(688\) | −2.24752e147 | −0.0238952 | ||||||||
\(689\) | 4.03517e148 | 0.397514 | ||||||||
\(690\) | −2.11131e149 | −1.92741 | ||||||||
\(691\) | 5.38718e148 | 0.455789 | 0.227894 | − | 0.973686i | \(-0.426816\pi\) | ||||
0.227894 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(692\) | 7.71706e148 | 0.605176 | ||||||||
\(693\) | −1.09718e148 | −0.0797593 | ||||||||
\(694\) | −1.19641e148 | −0.0806321 | ||||||||
\(695\) | 7.10533e148 | 0.443999 | ||||||||
\(696\) | −2.36210e148 | −0.136872 | ||||||||
\(697\) | −3.40196e147 | −0.0182814 | ||||||||
\(698\) | −4.27833e149 | −2.13238 | ||||||||
\(699\) | 3.71676e148 | 0.171835 | ||||||||
\(700\) | 2.37196e149 | 1.01733 | ||||||||
\(701\) | −2.86338e149 | −1.13942 | −0.569708 | − | 0.821847i | \(-0.692944\pi\) | ||||
−0.569708 | + | 0.821847i | \(0.692944\pi\) | |||||||
\(702\) | 4.37010e149 | 1.61359 | ||||||||
\(703\) | −3.06755e149 | −1.05108 | ||||||||
\(704\) | −5.77729e148 | −0.183721 | ||||||||
\(705\) | 4.26461e149 | 1.25878 | ||||||||
\(706\) | −5.01849e149 | −1.37507 | ||||||||
\(707\) | −6.36228e149 | −1.61843 | ||||||||
\(708\) | 9.64330e149 | 2.27761 | ||||||||
\(709\) | 4.90339e149 | 1.07540 | 0.537699 | − | 0.843137i | \(-0.319294\pi\) | ||||
0.537699 | + | 0.843137i | \(0.319294\pi\) | |||||||
\(710\) | −4.85787e149 | −0.989424 | ||||||||
\(711\) | 5.62673e148 | 0.106439 | ||||||||
\(712\) | 5.61320e148 | 0.0986303 | ||||||||
\(713\) | 9.24111e149 | 1.50843 | ||||||||
\(714\) | 1.06380e150 | 1.61326 | ||||||||
\(715\) | 9.35661e148 | 0.131841 | ||||||||
\(716\) | −7.19651e148 | −0.0942298 | ||||||||
\(717\) | −5.65860e149 | −0.688578 | ||||||||
\(718\) | −9.62548e149 | −1.08865 | ||||||||
\(719\) | −6.37999e149 | −0.670738 | −0.335369 | − | 0.942087i | \(-0.608861\pi\) | ||||
−0.335369 | + | 0.942087i | \(0.608861\pi\) | |||||||
\(720\) | 2.05161e149 | 0.200511 | ||||||||
\(721\) | −9.52586e149 | −0.865571 | ||||||||
\(722\) | −5.50418e149 | −0.465039 | ||||||||
\(723\) | 6.67007e149 | 0.524046 | ||||||||
\(724\) | 1.07934e150 | 0.788645 | ||||||||
\(725\) | 2.96850e149 | 0.201740 | ||||||||
\(726\) | −2.87444e150 | −1.81711 | ||||||||
\(727\) | −1.08800e150 | −0.639841 | −0.319921 | − | 0.947444i | \(-0.603656\pi\) | ||||
−0.319921 | + | 0.947444i | \(0.603656\pi\) | |||||||
\(728\) | −1.48213e150 | −0.810938 | ||||||||
\(729\) | 1.67944e149 | 0.0855004 | ||||||||
\(730\) | −6.36621e149 | −0.301600 | ||||||||
\(731\) | −5.77199e148 | −0.0254486 | ||||||||
\(732\) | −1.22321e150 | −0.501962 | ||||||||
\(733\) | 1.12535e150 | 0.429863 | 0.214932 | − | 0.976629i | \(-0.431047\pi\) | ||||
0.214932 | + | 0.976629i | \(0.431047\pi\) | |||||||
\(734\) | 7.66276e150 | 2.72485 | ||||||||
\(735\) | 8.89354e149 | 0.294435 | ||||||||
\(736\) | 8.43517e150 | 2.60021 | ||||||||
\(737\) | 7.66568e149 | 0.220043 | ||||||||
\(738\) | −7.25603e148 | −0.0193973 | ||||||||
\(739\) | 3.16267e150 | 0.787446 | 0.393723 | − | 0.919229i | \(-0.371187\pi\) | ||||
0.393723 | + | 0.919229i | \(0.371187\pi\) | |||||||
\(740\) | −2.79248e150 | −0.647628 | ||||||||
\(741\) | −1.18101e151 | −2.55151 | ||||||||
\(742\) | −1.95346e150 | −0.393187 | ||||||||
\(743\) | −6.22279e150 | −1.16701 | −0.583503 | − | 0.812111i | \(-0.698318\pi\) | ||||
−0.583503 | + | 0.812111i | \(0.698318\pi\) | |||||||
\(744\) | 2.15944e150 | 0.377365 | ||||||||
\(745\) | 2.33065e150 | 0.379554 | ||||||||
\(746\) | −4.24192e150 | −0.643834 | ||||||||
\(747\) | 1.74837e150 | 0.247344 | ||||||||
\(748\) | −8.96022e149 | −0.118164 | ||||||||
\(749\) | −5.94963e150 | −0.731467 | ||||||||
\(750\) | 1.52930e151 | 1.75298 | ||||||||
\(751\) | 1.24977e151 | 1.33577 | 0.667886 | − | 0.744264i | \(-0.267199\pi\) | ||||
0.667886 | + | 0.744264i | \(0.267199\pi\) | |||||||
\(752\) | −1.24874e151 | −1.24462 | ||||||||
\(753\) | −3.29115e150 | −0.305922 | ||||||||
\(754\) | −9.26407e150 | −0.803167 | ||||||||
\(755\) | 1.26444e151 | 1.02254 | ||||||||
\(756\) | −1.17548e151 | −0.886789 | ||||||||
\(757\) | 1.28207e151 | 0.902357 | 0.451178 | − | 0.892434i | \(-0.351004\pi\) | ||||
0.451178 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(758\) | 6.45328e149 | 0.0423786 | ||||||||
\(759\) | −4.80185e150 | −0.294249 | ||||||||
\(760\) | −4.23947e150 | −0.242436 | ||||||||
\(761\) | −1.91799e151 | −1.02365 | −0.511826 | − | 0.859089i | \(-0.671031\pi\) | ||||
−0.511826 | + | 0.859089i | \(0.671031\pi\) | |||||||
\(762\) | −5.11143e150 | −0.254628 | ||||||||
\(763\) | −4.55978e151 | −2.12034 | ||||||||
\(764\) | 1.65613e151 | 0.718939 | ||||||||
\(765\) | 5.26885e150 | 0.213545 | ||||||||
\(766\) | 5.10201e151 | 1.93077 | ||||||||
\(767\) | 7.57254e151 | 2.67599 | ||||||||
\(768\) | −1.23517e151 | −0.407625 | ||||||||
\(769\) | −4.55055e150 | −0.140259 | −0.0701296 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701296 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(770\) | −4.52961e150 | −0.130406 | ||||||||
\(771\) | 2.39701e151 | 0.644637 | ||||||||
\(772\) | −5.12312e151 | −1.28714 | ||||||||
\(773\) | 4.52563e151 | 1.06232 | 0.531160 | − | 0.847272i | \(-0.321756\pi\) | ||||
0.531160 | + | 0.847272i | \(0.321756\pi\) | |||||||
\(774\) | −1.23111e150 | −0.0270019 | ||||||||
\(775\) | −2.71381e151 | −0.556212 | ||||||||
\(776\) | −1.49156e150 | −0.0285693 | ||||||||
\(777\) | 7.54029e151 | 1.34985 | ||||||||
\(778\) | −1.29832e152 | −2.17247 | ||||||||
\(779\) | −1.82838e150 | −0.0285989 | ||||||||
\(780\) | −1.07511e152 | −1.57212 | ||||||||
\(781\) | −1.10485e151 | −0.151051 | ||||||||
\(782\) | 1.58770e152 | 2.02961 | ||||||||
\(783\) | −1.47111e151 | −0.175854 | ||||||||
\(784\) | −2.60417e151 | −0.291123 | ||||||||
\(785\) | −8.07409e151 | −0.844183 | ||||||||
\(786\) | −2.06931e152 | −2.02368 | ||||||||
\(787\) | −1.16926e152 | −1.06964 | −0.534819 | − | 0.844967i | \(-0.679620\pi\) | ||||
−0.534819 | + | 0.844967i | \(0.679620\pi\) | |||||||
\(788\) | 1.62488e152 | 1.39058 | ||||||||
\(789\) | 1.16813e152 | 0.935296 | ||||||||
\(790\) | 2.32295e151 | 0.174028 | ||||||||
\(791\) | 4.52267e151 | 0.317052 | ||||||||
\(792\) | −3.82650e150 | −0.0251032 | ||||||||
\(793\) | −9.60546e151 | −0.589761 | ||||||||
\(794\) | 4.53114e152 | 2.60394 | ||||||||
\(795\) | −2.83716e151 | −0.152619 | ||||||||
\(796\) | 1.79580e152 | 0.904318 | ||||||||
\(797\) | −1.15487e152 | −0.544468 | −0.272234 | − | 0.962231i | \(-0.587762\pi\) | ||||
−0.272234 | + | 0.962231i | \(0.587762\pi\) | |||||||
\(798\) | 5.71736e152 | 2.52374 | ||||||||
\(799\) | −3.20697e152 | −1.32553 | ||||||||
\(800\) | −2.47714e152 | −0.958794 | ||||||||
\(801\) | −3.74931e151 | −0.135908 | ||||||||
\(802\) | 1.71523e151 | 0.0582328 | ||||||||
\(803\) | −1.44790e151 | −0.0460439 | ||||||||
\(804\) | −8.80815e152 | −2.62387 | ||||||||
\(805\) | 4.45954e152 | 1.24453 | ||||||||
\(806\) | 8.46923e152 | 2.21439 | ||||||||
\(807\) | −7.42108e152 | −1.81805 | ||||||||
\(808\) | −2.21890e152 | −0.509380 | ||||||||
\(809\) | −4.63963e152 | −0.998127 | −0.499064 | − | 0.866565i | \(-0.666323\pi\) | ||||
−0.499064 | + | 0.866565i | \(0.666323\pi\) | |||||||
\(810\) | −5.24427e152 | −1.05736 | ||||||||
\(811\) | 8.65154e151 | 0.163493 | 0.0817464 | − | 0.996653i | \(-0.473950\pi\) | ||||
0.0817464 | + | 0.996653i | \(0.473950\pi\) | |||||||
\(812\) | 2.49187e152 | 0.441401 | ||||||||
\(813\) | 8.52898e152 | 1.41626 | ||||||||
\(814\) | −1.14305e152 | −0.177945 | ||||||||
\(815\) | 1.53983e152 | 0.224749 | ||||||||
\(816\) | −4.52412e152 | −0.619157 | ||||||||
\(817\) | −3.10214e151 | −0.0398111 | ||||||||
\(818\) | 3.01098e152 | 0.362376 | ||||||||
\(819\) | 9.89979e152 | 1.11743 | ||||||||
\(820\) | −1.66443e151 | −0.0176213 | ||||||||
\(821\) | −5.99650e152 | −0.595501 | −0.297750 | − | 0.954644i | \(-0.596236\pi\) | ||||
−0.297750 | + | 0.954644i | \(0.596236\pi\) | |||||||
\(822\) | −2.32248e152 | −0.216363 | ||||||||
\(823\) | 9.52116e152 | 0.832144 | 0.416072 | − | 0.909332i | \(-0.363406\pi\) | ||||
0.416072 | + | 0.909332i | \(0.363406\pi\) | |||||||
\(824\) | −3.32223e152 | −0.272428 | ||||||||
\(825\) | 1.41015e152 | 0.108501 | ||||||||
\(826\) | −3.66593e153 | −2.64686 | ||||||||
\(827\) | 1.42933e153 | 0.968488 | 0.484244 | − | 0.874933i | \(-0.339095\pi\) | ||||
0.484244 | + | 0.874933i | \(0.339095\pi\) | |||||||
\(828\) | 1.88156e153 | 1.19654 | ||||||||
\(829\) | −8.24532e152 | −0.492147 | −0.246073 | − | 0.969251i | \(-0.579140\pi\) | ||||
−0.246073 | + | 0.969251i | \(0.579140\pi\) | |||||||
\(830\) | 7.21800e152 | 0.404406 | ||||||||
\(831\) | −7.28213e152 | −0.383005 | ||||||||
\(832\) | 5.21284e153 | 2.57395 | ||||||||
\(833\) | −6.68791e152 | −0.310047 | ||||||||
\(834\) | −3.34190e153 | −1.45471 | ||||||||
\(835\) | 1.70177e153 | 0.695603 | ||||||||
\(836\) | −4.81566e152 | −0.184853 | ||||||||
\(837\) | 1.34489e153 | 0.484842 | ||||||||
\(838\) | 4.31453e153 | 1.46091 | ||||||||
\(839\) | −1.00004e153 | −0.318063 | −0.159031 | − | 0.987274i | \(-0.550837\pi\) | ||||
−0.159031 | + | 0.987274i | \(0.550837\pi\) | |||||||
\(840\) | 1.04210e153 | 0.311347 | ||||||||
\(841\) | −3.25093e153 | −0.912468 | ||||||||
\(842\) | −6.52810e153 | −1.72148 | ||||||||
\(843\) | −6.73625e153 | −1.66906 | ||||||||
\(844\) | −1.89902e153 | −0.442131 | ||||||||
\(845\) | −5.86452e153 | −1.28308 | ||||||||
\(846\) | −6.84014e153 | −1.40644 | ||||||||
\(847\) | 6.07145e153 | 1.17331 | ||||||||
\(848\) | 8.30766e152 | 0.150903 | ||||||||
\(849\) | 5.91954e153 | 1.01073 | ||||||||
\(850\) | −4.66255e153 | −0.748393 | ||||||||
\(851\) | 1.12537e154 | 1.69822 | ||||||||
\(852\) | 1.26951e154 | 1.80118 | ||||||||
\(853\) | 7.56898e153 | 1.00975 | 0.504874 | − | 0.863193i | \(-0.331539\pi\) | ||||
0.504874 | + | 0.863193i | \(0.331539\pi\) | |||||||
\(854\) | 4.65008e153 | 0.583340 | ||||||||
\(855\) | 2.83173e153 | 0.334065 | ||||||||
\(856\) | −2.07499e153 | −0.230220 | ||||||||
\(857\) | −2.02420e153 | −0.211232 | −0.105616 | − | 0.994407i | \(-0.533681\pi\) | ||||
−0.105616 | + | 0.994407i | \(0.533681\pi\) | |||||||
\(858\) | −4.40077e153 | −0.431962 | ||||||||
\(859\) | −1.23650e154 | −1.14171 | −0.570853 | − | 0.821053i | \(-0.693387\pi\) | ||||
−0.570853 | + | 0.821053i | \(0.693387\pi\) | |||||||
\(860\) | −2.82398e152 | −0.0245297 | ||||||||
\(861\) | 4.49430e152 | 0.0367280 | ||||||||
\(862\) | −1.28931e153 | −0.0991345 | ||||||||
\(863\) | 1.07223e154 | 0.775748 | 0.387874 | − | 0.921712i | \(-0.373210\pi\) | ||||
0.387874 | + | 0.921712i | \(0.373210\pi\) | |||||||
\(864\) | 1.22760e154 | 0.835766 | ||||||||
\(865\) | −4.26079e153 | −0.272989 | ||||||||
\(866\) | −1.18490e154 | −0.714484 | ||||||||
\(867\) | 1.00866e154 | 0.572458 | ||||||||
\(868\) | −2.27807e154 | −1.21698 | ||||||||
\(869\) | 5.28321e152 | 0.0265680 | ||||||||
\(870\) | 6.51364e153 | 0.308364 | ||||||||
\(871\) | −6.91672e154 | −3.08281 | ||||||||
\(872\) | −1.59026e154 | −0.667350 | ||||||||
\(873\) | 9.96277e152 | 0.0393670 | ||||||||
\(874\) | 8.53305e154 | 3.17507 | ||||||||
\(875\) | −3.23022e154 | −1.13190 | ||||||||
\(876\) | 1.66369e154 | 0.549043 | ||||||||
\(877\) | 1.27536e154 | 0.396420 | 0.198210 | − | 0.980160i | \(-0.436487\pi\) | ||||
0.198210 | + | 0.980160i | \(0.436487\pi\) | |||||||
\(878\) | −5.82382e154 | −1.70508 | ||||||||
\(879\) | 5.87099e154 | 1.61918 | ||||||||
\(880\) | 1.92635e153 | 0.0500490 | ||||||||
\(881\) | −1.17829e154 | −0.288414 | −0.144207 | − | 0.989548i | \(-0.546063\pi\) | ||||
−0.144207 | + | 0.989548i | \(0.546063\pi\) | |||||||
\(882\) | −1.42646e154 | −0.328973 | ||||||||
\(883\) | 1.02733e154 | 0.223241 | 0.111621 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111621 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(884\) | 8.08479e154 | 1.65548 | ||||||||
\(885\) | −5.32432e154 | −1.02741 | ||||||||
\(886\) | 6.01482e154 | 1.09384 | ||||||||
\(887\) | −3.44753e154 | −0.590906 | −0.295453 | − | 0.955357i | \(-0.595471\pi\) | ||||
−0.295453 | + | 0.955357i | \(0.595471\pi\) | |||||||
\(888\) | 2.62974e154 | 0.424847 | ||||||||
\(889\) | 1.07965e154 | 0.164414 | ||||||||
\(890\) | −1.54787e154 | −0.222208 | ||||||||
\(891\) | −1.19273e154 | −0.161422 | ||||||||
\(892\) | 8.07365e154 | 1.03018 | ||||||||
\(893\) | −1.72358e155 | −2.07362 | ||||||||
\(894\) | −1.09619e155 | −1.24356 | ||||||||
\(895\) | 3.97338e153 | 0.0425060 | ||||||||
\(896\) | −8.60522e154 | −0.868143 | ||||||||
\(897\) | 4.33270e155 | 4.12245 | ||||||||
\(898\) | 3.37621e153 | 0.0302985 | ||||||||
\(899\) | −2.85100e154 | −0.241331 | ||||||||
\(900\) | −5.52553e154 | −0.441207 | ||||||||
\(901\) | 2.13354e154 | 0.160712 | ||||||||
\(902\) | −6.81304e152 | −0.00484170 | ||||||||
\(903\) | 7.62532e153 | 0.0511271 | ||||||||
\(904\) | 1.57732e154 | 0.0997879 | ||||||||
\(905\) | −5.95929e154 | −0.355750 | ||||||||
\(906\) | −5.94713e155 | −3.35025 | ||||||||
\(907\) | 1.66663e155 | 0.886048 | 0.443024 | − | 0.896510i | \(-0.353906\pi\) | ||||
0.443024 | + | 0.896510i | \(0.353906\pi\) | |||||||
\(908\) | −3.19908e155 | −1.60516 | ||||||||
\(909\) | 1.48210e155 | 0.701900 | ||||||||
\(910\) | 4.08706e155 | 1.82700 | ||||||||
\(911\) | −3.43117e155 | −1.44786 | −0.723931 | − | 0.689873i | \(-0.757666\pi\) | ||||
−0.723931 | + | 0.689873i | \(0.757666\pi\) | |||||||
\(912\) | −2.43148e155 | −0.968594 | ||||||||
\(913\) | 1.64163e154 | 0.0617388 | ||||||||
\(914\) | 6.96864e155 | 2.47442 | ||||||||
\(915\) | 6.75368e154 | 0.226429 | ||||||||
\(916\) | −4.43105e155 | −1.40279 | ||||||||
\(917\) | 4.37085e155 | 1.30670 | ||||||||
\(918\) | 2.31063e155 | 0.652363 | ||||||||
\(919\) | −1.14534e155 | −0.305401 | −0.152700 | − | 0.988273i | \(-0.548797\pi\) | ||||
−0.152700 | + | 0.988273i | \(0.548797\pi\) | |||||||
\(920\) | 1.55531e155 | 0.391701 | ||||||||
\(921\) | −4.79018e155 | −1.13952 | ||||||||
\(922\) | 1.21182e156 | 2.72311 | ||||||||
\(923\) | 9.96902e155 | 2.11623 | ||||||||
\(924\) | 1.18373e155 | 0.237396 | ||||||||
\(925\) | −3.30485e155 | −0.626197 | ||||||||
\(926\) | −1.31496e156 | −2.35416 | ||||||||
\(927\) | 2.21907e155 | 0.375391 | ||||||||
\(928\) | −2.60235e155 | −0.416004 | ||||||||
\(929\) | −2.98166e155 | −0.450436 | −0.225218 | − | 0.974308i | \(-0.572309\pi\) | ||||
−0.225218 | + | 0.974308i | \(0.572309\pi\) | |||||||
\(930\) | −5.95479e155 | −0.850182 | ||||||||
\(931\) | −3.59441e155 | −0.485030 | ||||||||
\(932\) | −1.36746e155 | −0.174414 | ||||||||
\(933\) | −5.63825e155 | −0.679764 | ||||||||
\(934\) | −1.47077e156 | −1.67623 | ||||||||
\(935\) | 4.94717e154 | 0.0533025 | ||||||||
\(936\) | 3.45264e155 | 0.351697 | ||||||||
\(937\) | −1.80246e156 | −1.73595 | −0.867976 | − | 0.496605i | \(-0.834580\pi\) | ||||
−0.867976 | + | 0.496605i | \(0.834580\pi\) | |||||||
\(938\) | 3.34844e156 | 3.04925 | ||||||||
\(939\) | 1.39032e156 | 1.19722 | ||||||||
\(940\) | −1.56903e156 | −1.27767 | ||||||||
\(941\) | −1.52494e156 | −1.17435 | −0.587176 | − | 0.809460i | \(-0.699760\pi\) | ||||
−0.587176 | + | 0.809460i | \(0.699760\pi\) | |||||||
\(942\) | 3.79755e156 | 2.76586 | ||||||||
\(943\) | 6.70765e154 | 0.0462069 | ||||||||
\(944\) | 1.55905e156 | 1.01585 | ||||||||
\(945\) | 6.49012e155 | 0.400021 | ||||||||
\(946\) | −1.15594e154 | −0.00673988 | ||||||||
\(947\) | −2.42446e156 | −1.33734 | −0.668670 | − | 0.743559i | \(-0.733136\pi\) | ||||
−0.668670 | + | 0.743559i | \(0.733136\pi\) | |||||||
\(948\) | −6.07060e155 | −0.316806 | ||||||||
\(949\) | 1.30644e156 | 0.645077 | ||||||||
\(950\) | −2.50588e156 | −1.17077 | ||||||||
\(951\) | −1.07507e156 | −0.475292 | ||||||||
\(952\) | −7.83653e155 | −0.327857 | ||||||||
\(953\) | 4.23514e156 | 1.67683 | 0.838417 | − | 0.545029i | \(-0.183481\pi\) | ||||
0.838417 | + | 0.545029i | \(0.183481\pi\) | |||||||
\(954\) | 4.55061e155 | 0.170522 | ||||||||
\(955\) | −9.14390e155 | −0.324306 | ||||||||
\(956\) | 2.08190e156 | 0.698910 | ||||||||
\(957\) | 1.48143e155 | 0.0470765 | ||||||||
\(958\) | −1.56744e156 | −0.471521 | ||||||||
\(959\) | 4.90560e155 | 0.139706 | ||||||||
\(960\) | −3.66519e156 | −0.988227 | ||||||||
\(961\) | −1.31083e156 | −0.334633 | ||||||||
\(962\) | 1.03137e157 | 2.49302 | ||||||||
\(963\) | 1.38598e156 | 0.317231 | ||||||||
\(964\) | −2.45404e156 | −0.531909 | ||||||||
\(965\) | 2.82861e156 | 0.580616 | ||||||||
\(966\) | −2.09749e157 | −4.07757 | ||||||||
\(967\) | 2.95182e156 | 0.543500 | 0.271750 | − | 0.962368i | \(-0.412398\pi\) | ||||
0.271750 | + | 0.962368i | \(0.412398\pi\) | |||||||
\(968\) | 2.11747e156 | 0.369285 | ||||||||
\(969\) | −6.24442e156 | −1.03156 | ||||||||
\(970\) | 4.11306e155 | 0.0643648 | ||||||||
\(971\) | −2.93287e156 | −0.434794 | −0.217397 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217397 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(972\) | 8.41341e156 | 1.18166 | ||||||||
\(973\) | 7.05884e156 | 0.939310 | ||||||||
\(974\) | 6.55847e156 | 0.826909 | ||||||||
\(975\) | −1.27237e157 | −1.52010 | ||||||||
\(976\) | −1.97759e156 | −0.223882 | ||||||||
\(977\) | 1.11036e157 | 1.19123 | 0.595617 | − | 0.803268i | \(-0.296907\pi\) | ||||
0.595617 | + | 0.803268i | \(0.296907\pi\) | |||||||
\(978\) | −7.24239e156 | −0.736363 | ||||||||
\(979\) | −3.52040e155 | −0.0339235 | ||||||||
\(980\) | −3.27210e156 | −0.298853 | ||||||||
\(981\) | 1.06221e157 | 0.919574 | ||||||||
\(982\) | 1.02583e157 | 0.841829 | ||||||||
\(983\) | −2.45904e157 | −1.91296 | −0.956480 | − | 0.291799i | \(-0.905746\pi\) | ||||
−0.956480 | + | 0.291799i | \(0.905746\pi\) | |||||||
\(984\) | 1.56743e155 | 0.0115597 | ||||||||
\(985\) | −8.97141e156 | −0.627276 | ||||||||
\(986\) | −4.89824e156 | −0.324715 | ||||||||
\(987\) | 4.23670e157 | 2.66304 | ||||||||
\(988\) | 4.34516e157 | 2.58980 | ||||||||
\(989\) | 1.13806e156 | 0.0643222 | ||||||||
\(990\) | 1.05518e156 | 0.0565560 | ||||||||
\(991\) | −6.63369e156 | −0.337201 | −0.168600 | − | 0.985684i | \(-0.553925\pi\) | ||||
−0.168600 | + | 0.985684i | \(0.553925\pi\) | |||||||
\(992\) | 2.37908e157 | 1.14695 | ||||||||
\(993\) | −1.84365e157 | −0.843030 | ||||||||
\(994\) | −4.82608e157 | −2.09319 | ||||||||
\(995\) | −9.91506e156 | −0.407928 | ||||||||
\(996\) | −1.88629e157 | −0.736195 | ||||||||
\(997\) | 5.95950e156 | 0.220655 | 0.110328 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110328 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(998\) | −6.90422e157 | −2.42528 | ||||||||
\(999\) | 1.63779e157 | 0.545847 |
(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 | 1.106.a.a.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.106.a.a.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial |