Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,64,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, 64, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 64);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 64 \) |
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: | \(25.1360966918\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2 x^{4} + \cdots - 35\!\cdots\!34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{37}\cdot 3^{17}\cdot 5^{3}\cdot 7^{2}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.39250e7\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54406e9 | 0.837690 | 0.418845 | − | 0.908058i | \(-0.362435\pi\) | ||||
0.418845 | + | 0.908058i | \(0.362435\pi\) | |||||||
\(3\) | −9.84533e14 | −0.920260 | −0.460130 | − | 0.887851i | \(-0.652197\pi\) | ||||
−0.460130 | + | 0.887851i | \(0.652197\pi\) | |||||||
\(4\) | −2.75111e18 | −0.298276 | ||||||||
\(5\) | −1.69176e22 | −1.62474 | −0.812371 | − | 0.583141i | \(-0.801824\pi\) | ||||
−0.812371 | + | 0.583141i | \(0.801824\pi\) | |||||||
\(6\) | −2.50471e24 | −0.770893 | ||||||||
\(7\) | 1.59356e26 | 0.381752 | 0.190876 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190876 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(8\) | −3.04638e28 | −1.08755 | ||||||||
\(9\) | −1.75256e29 | −0.153121 | ||||||||
\(10\) | −4.30395e31 | −1.36103 | ||||||||
\(11\) | 8.86905e32 | 1.39318 | 0.696591 | − | 0.717469i | \(-0.254699\pi\) | ||||
0.696591 | + | 0.717469i | \(0.254699\pi\) | |||||||
\(12\) | 2.70856e33 | 0.274492 | ||||||||
\(13\) | 7.82830e34 | 0.637458 | 0.318729 | − | 0.947846i | \(-0.396744\pi\) | ||||
0.318729 | + | 0.947846i | \(0.396744\pi\) | |||||||
\(14\) | 4.05413e35 | 0.319790 | ||||||||
\(15\) | 1.66560e37 | 1.49519 | ||||||||
\(16\) | −5.21275e37 | −0.612755 | ||||||||
\(17\) | −5.03105e38 | −0.876028 | −0.438014 | − | 0.898968i | \(-0.644318\pi\) | ||||
−0.438014 | + | 0.898968i | \(0.644318\pi\) | |||||||
\(18\) | −4.45863e38 | −0.128268 | ||||||||
\(19\) | 8.03315e39 | 0.420870 | 0.210435 | − | 0.977608i | \(-0.432512\pi\) | ||||
0.210435 | + | 0.977608i | \(0.432512\pi\) | |||||||
\(20\) | 4.65423e40 | 0.484622 | ||||||||
\(21\) | −1.56892e41 | −0.351311 | ||||||||
\(22\) | 2.25634e42 | 1.16705 | ||||||||
\(23\) | −1.14581e43 | −1.46112 | −0.730559 | − | 0.682850i | \(-0.760740\pi\) | ||||
−0.730559 | + | 0.682850i | \(0.760740\pi\) | |||||||
\(24\) | 2.99927e43 | 1.00083 | ||||||||
\(25\) | 1.77786e44 | 1.63979 | ||||||||
\(26\) | 1.99157e44 | 0.533992 | ||||||||
\(27\) | 1.29940e45 | 1.06117 | ||||||||
\(28\) | −4.38407e44 | −0.113868 | ||||||||
\(29\) | 2.15529e46 | 1.85340 | 0.926701 | − | 0.375800i | \(-0.122632\pi\) | ||||
0.926701 | + | 0.375800i | \(0.122632\pi\) | |||||||
\(30\) | 4.23738e46 | 1.25250 | ||||||||
\(31\) | −6.36423e46 | −0.669657 | −0.334828 | − | 0.942279i | \(-0.608678\pi\) | ||||
−0.334828 | + | 0.942279i | \(0.608678\pi\) | |||||||
\(32\) | 1.48364e47 | 0.574254 | ||||||||
\(33\) | −8.73187e47 | −1.28209 | ||||||||
\(34\) | −1.27993e48 | −0.733840 | ||||||||
\(35\) | −2.69593e48 | −0.620249 | ||||||||
\(36\) | 4.82150e47 | 0.0456723 | ||||||||
\(37\) | −1.05964e49 | −0.423451 | −0.211725 | − | 0.977329i | \(-0.567908\pi\) | ||||
−0.211725 | + | 0.977329i | \(0.567908\pi\) | |||||||
\(38\) | 2.04368e49 | 0.352558 | ||||||||
\(39\) | −7.70722e49 | −0.586628 | ||||||||
\(40\) | 5.15376e50 | 1.76699 | ||||||||
\(41\) | 8.54270e50 | 1.34556 | 0.672781 | − | 0.739842i | \(-0.265100\pi\) | ||||
0.672781 | + | 0.739842i | \(0.265100\pi\) | |||||||
\(42\) | −3.99142e50 | −0.294290 | ||||||||
\(43\) | −3.25759e51 | −1.14456 | −0.572282 | − | 0.820057i | \(-0.693942\pi\) | ||||
−0.572282 | + | 0.820057i | \(0.693942\pi\) | |||||||
\(44\) | −2.43998e51 | −0.415553 | ||||||||
\(45\) | 2.96492e51 | 0.248782 | ||||||||
\(46\) | −2.91501e52 | −1.22396 | ||||||||
\(47\) | 1.11016e52 | 0.236757 | 0.118379 | − | 0.992969i | \(-0.462230\pi\) | ||||
0.118379 | + | 0.992969i | \(0.462230\pi\) | |||||||
\(48\) | 5.13212e52 | 0.563894 | ||||||||
\(49\) | −1.48857e53 | −0.854265 | ||||||||
\(50\) | 4.52300e53 | 1.37363 | ||||||||
\(51\) | 4.95324e53 | 0.806174 | ||||||||
\(52\) | −2.15365e53 | −0.190139 | ||||||||
\(53\) | −5.90596e53 | −0.286155 | −0.143077 | − | 0.989712i | \(-0.545700\pi\) | ||||
−0.143077 | + | 0.989712i | \(0.545700\pi\) | |||||||
\(54\) | 3.30577e54 | 0.888932 | ||||||||
\(55\) | −1.50043e55 | −2.26356 | ||||||||
\(56\) | −4.85461e54 | −0.415175 | ||||||||
\(57\) | −7.90890e54 | −0.387310 | ||||||||
\(58\) | 5.48320e55 | 1.55258 | ||||||||
\(59\) | 2.16563e55 | 0.357887 | 0.178944 | − | 0.983859i | \(-0.442732\pi\) | ||||
0.178944 | + | 0.983859i | \(0.442732\pi\) | |||||||
\(60\) | −4.58224e55 | −0.445978 | ||||||||
\(61\) | 1.72006e56 | 0.994612 | 0.497306 | − | 0.867575i | \(-0.334323\pi\) | ||||
0.497306 | + | 0.867575i | \(0.334323\pi\) | |||||||
\(62\) | −1.61910e56 | −0.560965 | ||||||||
\(63\) | −2.79282e55 | −0.0584543 | ||||||||
\(64\) | 8.58238e56 | 1.09380 | ||||||||
\(65\) | −1.32436e57 | −1.03571 | ||||||||
\(66\) | −2.22144e57 | −1.07399 | ||||||||
\(67\) | −2.22054e57 | −0.668501 | −0.334251 | − | 0.942484i | \(-0.608483\pi\) | ||||
−0.334251 | + | 0.942484i | \(0.608483\pi\) | |||||||
\(68\) | 1.38410e57 | 0.261298 | ||||||||
\(69\) | 1.12809e58 | 1.34461 | ||||||||
\(70\) | −6.85863e57 | −0.519576 | ||||||||
\(71\) | 2.30418e58 | 1.11655 | 0.558276 | − | 0.829656i | \(-0.311463\pi\) | ||||
0.558276 | + | 0.829656i | \(0.311463\pi\) | |||||||
\(72\) | 5.33898e57 | 0.166527 | ||||||||
\(73\) | 1.23249e58 | 0.248951 | 0.124475 | − | 0.992223i | \(-0.460275\pi\) | ||||
0.124475 | + | 0.992223i | \(0.460275\pi\) | |||||||
\(74\) | −2.69579e58 | −0.354720 | ||||||||
\(75\) | −1.75036e59 | −1.50903 | ||||||||
\(76\) | −2.21001e58 | −0.125535 | ||||||||
\(77\) | 1.41334e59 | 0.531850 | ||||||||
\(78\) | −1.96077e59 | −0.491412 | ||||||||
\(79\) | 8.71843e58 | 0.146280 | 0.0731400 | − | 0.997322i | \(-0.476698\pi\) | ||||
0.0731400 | + | 0.997322i | \(0.476698\pi\) | |||||||
\(80\) | 8.81873e59 | 0.995570 | ||||||||
\(81\) | −1.07871e60 | −0.823433 | ||||||||
\(82\) | 2.17332e60 | 1.12716 | ||||||||
\(83\) | −1.10737e60 | −0.392041 | −0.196021 | − | 0.980600i | \(-0.562802\pi\) | ||||
−0.196021 | + | 0.980600i | \(0.562802\pi\) | |||||||
\(84\) | 4.31626e59 | 0.104788 | ||||||||
\(85\) | 8.51136e60 | 1.42332 | ||||||||
\(86\) | −8.28752e60 | −0.958789 | ||||||||
\(87\) | −2.12196e61 | −1.70561 | ||||||||
\(88\) | −2.70185e61 | −1.51516 | ||||||||
\(89\) | 4.52990e61 | 1.77952 | 0.889762 | − | 0.456425i | \(-0.150870\pi\) | ||||
0.889762 | + | 0.456425i | \(0.150870\pi\) | |||||||
\(90\) | 7.54295e60 | 0.208402 | ||||||||
\(91\) | 1.24749e61 | 0.243351 | ||||||||
\(92\) | 3.15225e61 | 0.435816 | ||||||||
\(93\) | 6.26579e61 | 0.616259 | ||||||||
\(94\) | 2.82432e61 | 0.198329 | ||||||||
\(95\) | −1.35902e62 | −0.683805 | ||||||||
\(96\) | −1.46069e62 | −0.528463 | ||||||||
\(97\) | 2.14118e62 | 0.558913 | 0.279456 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279456 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(98\) | −3.78702e62 | −0.715609 | ||||||||
\(99\) | −1.55436e62 | −0.213325 | ||||||||
\(100\) | −4.89110e62 | −0.489110 | ||||||||
\(101\) | 5.59834e61 | 0.0409200 | 0.0204600 | − | 0.999791i | \(-0.493487\pi\) | ||||
0.0204600 | + | 0.999791i | \(0.493487\pi\) | |||||||
\(102\) | 1.26014e63 | 0.675323 | ||||||||
\(103\) | 1.88637e63 | 0.743454 | 0.371727 | − | 0.928342i | \(-0.378766\pi\) | ||||
0.371727 | + | 0.928342i | \(0.378766\pi\) | |||||||
\(104\) | −2.38480e63 | −0.693269 | ||||||||
\(105\) | 2.65424e63 | 0.570790 | ||||||||
\(106\) | −1.50252e63 | −0.239709 | ||||||||
\(107\) | 1.23542e64 | 1.46631 | 0.733154 | − | 0.680063i | \(-0.238047\pi\) | ||||
0.733154 | + | 0.680063i | \(0.238047\pi\) | |||||||
\(108\) | −3.57480e63 | −0.316522 | ||||||||
\(109\) | −1.18914e64 | −0.787587 | −0.393793 | − | 0.919199i | \(-0.628837\pi\) | ||||
−0.393793 | + | 0.919199i | \(0.628837\pi\) | |||||||
\(110\) | −3.81720e64 | −1.89616 | ||||||||
\(111\) | 1.04325e64 | 0.389685 | ||||||||
\(112\) | −8.30685e63 | −0.233921 | ||||||||
\(113\) | 2.40110e64 | 0.511022 | 0.255511 | − | 0.966806i | \(-0.417756\pi\) | ||||
0.255511 | + | 0.966806i | \(0.417756\pi\) | |||||||
\(114\) | −2.01207e64 | −0.324445 | ||||||||
\(115\) | 1.93844e65 | 2.37394 | ||||||||
\(116\) | −5.92945e64 | −0.552825 | ||||||||
\(117\) | −1.37196e64 | −0.0976083 | ||||||||
\(118\) | 5.50950e64 | 0.299798 | ||||||||
\(119\) | −8.01731e64 | −0.334426 | ||||||||
\(120\) | −5.07405e65 | −1.62609 | ||||||||
\(121\) | 3.81336e65 | 0.940954 | ||||||||
\(122\) | 4.37594e65 | 0.833177 | ||||||||
\(123\) | −8.41057e65 | −1.23827 | ||||||||
\(124\) | 1.75087e65 | 0.199743 | ||||||||
\(125\) | −1.17351e66 | −1.03949 | ||||||||
\(126\) | −7.10512e64 | −0.0489665 | ||||||||
\(127\) | 2.34022e66 | 1.25730 | 0.628651 | − | 0.777687i | \(-0.283607\pi\) | ||||
0.628651 | + | 0.777687i | \(0.283607\pi\) | |||||||
\(128\) | 8.14997e65 | 0.342013 | ||||||||
\(129\) | 3.20720e66 | 1.05330 | ||||||||
\(130\) | −3.36926e66 | −0.867600 | ||||||||
\(131\) | 2.18093e64 | 0.00441159 | 0.00220579 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220579 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(132\) | 2.40224e66 | 0.382417 | ||||||||
\(133\) | 1.28013e66 | 0.160668 | ||||||||
\(134\) | −5.64919e66 | −0.559997 | ||||||||
\(135\) | −2.19828e67 | −1.72413 | ||||||||
\(136\) | 1.53265e67 | 0.952726 | ||||||||
\(137\) | −3.44835e67 | −1.70182 | −0.850909 | − | 0.525312i | \(-0.823948\pi\) | ||||
−0.850909 | + | 0.525312i | \(0.823948\pi\) | |||||||
\(138\) | 2.86992e67 | 1.12636 | ||||||||
\(139\) | 2.95724e67 | 0.924528 | 0.462264 | − | 0.886742i | \(-0.347037\pi\) | ||||
0.462264 | + | 0.886742i | \(0.347037\pi\) | |||||||
\(140\) | 7.41682e66 | 0.185005 | ||||||||
\(141\) | −1.09299e67 | −0.217878 | ||||||||
\(142\) | 5.86198e67 | 0.935323 | ||||||||
\(143\) | 6.94296e67 | 0.888095 | ||||||||
\(144\) | 9.13567e66 | 0.0938257 | ||||||||
\(145\) | −3.64625e68 | −3.01130 | ||||||||
\(146\) | 3.13553e67 | 0.208544 | ||||||||
\(147\) | 1.46555e68 | 0.786147 | ||||||||
\(148\) | 2.91518e67 | 0.126305 | ||||||||
\(149\) | 1.45208e68 | 0.508889 | 0.254444 | − | 0.967087i | \(-0.418107\pi\) | ||||
0.254444 | + | 0.967087i | \(0.418107\pi\) | |||||||
\(150\) | −4.45304e68 | −1.26410 | ||||||||
\(151\) | 1.10687e68 | 0.254872 | 0.127436 | − | 0.991847i | \(-0.459325\pi\) | ||||
0.127436 | + | 0.991847i | \(0.459325\pi\) | |||||||
\(152\) | −2.44721e68 | −0.457718 | ||||||||
\(153\) | 8.81724e67 | 0.134138 | ||||||||
\(154\) | 3.59563e68 | 0.445525 | ||||||||
\(155\) | 1.07668e69 | 1.08802 | ||||||||
\(156\) | 2.12034e68 | 0.174977 | ||||||||
\(157\) | 1.88317e66 | 0.00127072 | 0.000635360 | − | 1.00000i | \(-0.499798\pi\) | ||||
0.000635360 | 1.00000i | \(0.499798\pi\) | ||||||||
\(158\) | 2.21802e68 | 0.122537 | ||||||||
\(159\) | 5.81462e68 | 0.263337 | ||||||||
\(160\) | −2.50997e69 | −0.933014 | ||||||||
\(161\) | −1.82592e69 | −0.557785 | ||||||||
\(162\) | −2.74432e69 | −0.689781 | ||||||||
\(163\) | −3.00371e69 | −0.621941 | −0.310970 | − | 0.950420i | \(-0.600654\pi\) | ||||
−0.310970 | + | 0.950420i | \(0.600654\pi\) | |||||||
\(164\) | −2.35019e69 | −0.401349 | ||||||||
\(165\) | 1.47723e70 | 2.08307 | ||||||||
\(166\) | −2.81721e69 | −0.328409 | ||||||||
\(167\) | 2.97039e69 | 0.286579 | 0.143290 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143290 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(168\) | 4.77952e69 | 0.382069 | ||||||||
\(169\) | −8.95281e69 | −0.593647 | ||||||||
\(170\) | 2.16534e70 | 1.19230 | ||||||||
\(171\) | −1.40786e69 | −0.0644440 | ||||||||
\(172\) | 8.96199e69 | 0.341396 | ||||||||
\(173\) | −2.38452e70 | −0.756743 | −0.378371 | − | 0.925654i | \(-0.623516\pi\) | ||||
−0.378371 | + | 0.925654i | \(0.623516\pi\) | |||||||
\(174\) | −5.39839e70 | −1.42877 | ||||||||
\(175\) | 2.83314e70 | 0.625993 | ||||||||
\(176\) | −4.62321e70 | −0.853679 | ||||||||
\(177\) | −2.13213e70 | −0.329349 | ||||||||
\(178\) | 1.15244e71 | 1.49069 | ||||||||
\(179\) | −7.15882e69 | −0.0776195 | −0.0388097 | − | 0.999247i | \(-0.512357\pi\) | ||||
−0.0388097 | + | 0.999247i | \(0.512357\pi\) | |||||||
\(180\) | −8.15683e69 | −0.0742058 | ||||||||
\(181\) | −4.39429e70 | −0.335748 | −0.167874 | − | 0.985808i | \(-0.553690\pi\) | ||||
−0.167874 | + | 0.985808i | \(0.553690\pi\) | |||||||
\(182\) | 3.17369e70 | 0.203853 | ||||||||
\(183\) | −1.69346e71 | −0.915302 | ||||||||
\(184\) | 3.49057e71 | 1.58904 | ||||||||
\(185\) | 1.79266e71 | 0.687999 | ||||||||
\(186\) | 1.59406e71 | 0.516234 | ||||||||
\(187\) | −4.46207e71 | −1.22047 | ||||||||
\(188\) | −3.05417e70 | −0.0706190 | ||||||||
\(189\) | 2.07068e71 | 0.405104 | ||||||||
\(190\) | −3.45743e71 | −0.572816 | ||||||||
\(191\) | −7.65031e71 | −1.07431 | −0.537153 | − | 0.843485i | \(-0.680500\pi\) | ||||
−0.537153 | + | 0.843485i | \(0.680500\pi\) | |||||||
\(192\) | −8.44964e71 | −1.00658 | ||||||||
\(193\) | 2.52559e70 | 0.0255451 | 0.0127726 | − | 0.999918i | \(-0.495934\pi\) | ||||
0.0127726 | + | 0.999918i | \(0.495934\pi\) | |||||||
\(194\) | 5.44731e71 | 0.468196 | ||||||||
\(195\) | 1.30388e72 | 0.953119 | ||||||||
\(196\) | 4.09522e71 | 0.254807 | ||||||||
\(197\) | 3.17310e72 | 1.68189 | 0.840945 | − | 0.541120i | \(-0.182000\pi\) | ||||
0.840945 | + | 0.541120i | \(0.182000\pi\) | |||||||
\(198\) | −3.95439e71 | −0.178700 | ||||||||
\(199\) | 8.06783e70 | 0.0311089 | 0.0155545 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155545 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(200\) | −5.41605e72 | −1.78336 | ||||||||
\(201\) | 2.18619e72 | 0.615195 | ||||||||
\(202\) | 1.42425e71 | 0.0342783 | ||||||||
\(203\) | 3.43460e72 | 0.707540 | ||||||||
\(204\) | −1.36269e72 | −0.240462 | ||||||||
\(205\) | −1.44522e73 | −2.18619 | ||||||||
\(206\) | 4.79904e72 | 0.622783 | ||||||||
\(207\) | 2.00810e72 | 0.223728 | ||||||||
\(208\) | −4.08069e72 | −0.390606 | ||||||||
\(209\) | 7.12464e72 | 0.586348 | ||||||||
\(210\) | 6.75255e72 | 0.478145 | ||||||||
\(211\) | −1.70718e72 | −0.104084 | −0.0520418 | − | 0.998645i | \(-0.516573\pi\) | ||||
−0.0520418 | + | 0.998645i | \(0.516573\pi\) | |||||||
\(212\) | 1.62480e72 | 0.0853531 | ||||||||
\(213\) | −2.26854e73 | −1.02752 | ||||||||
\(214\) | 3.14298e73 | 1.22831 | ||||||||
\(215\) | 5.51107e73 | 1.85962 | ||||||||
\(216\) | −3.95848e73 | −1.15408 | ||||||||
\(217\) | −1.01418e73 | −0.255643 | ||||||||
\(218\) | −3.02525e73 | −0.659753 | ||||||||
\(219\) | −1.21343e73 | −0.229100 | ||||||||
\(220\) | 4.12786e73 | 0.675166 | ||||||||
\(221\) | −3.93846e73 | −0.558431 | ||||||||
\(222\) | 2.65409e73 | 0.326435 | ||||||||
\(223\) | −1.54395e74 | −1.64827 | −0.824136 | − | 0.566391i | \(-0.808339\pi\) | ||||
−0.824136 | + | 0.566391i | \(0.808339\pi\) | |||||||
\(224\) | 2.36427e73 | 0.219223 | ||||||||
\(225\) | −3.11582e73 | −0.251086 | ||||||||
\(226\) | 6.10855e73 | 0.428078 | ||||||||
\(227\) | 2.89225e73 | 0.176369 | 0.0881843 | − | 0.996104i | \(-0.471894\pi\) | ||||
0.0881843 | + | 0.996104i | \(0.471894\pi\) | |||||||
\(228\) | 2.17583e73 | 0.115525 | ||||||||
\(229\) | 3.67482e74 | 1.69988 | 0.849940 | − | 0.526879i | \(-0.176638\pi\) | ||||
0.849940 | + | 0.526879i | \(0.176638\pi\) | |||||||
\(230\) | 4.93151e74 | 1.98862 | ||||||||
\(231\) | −1.39148e74 | −0.489440 | ||||||||
\(232\) | −6.56585e74 | −2.01567 | ||||||||
\(233\) | −1.84654e74 | −0.495047 | −0.247523 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247523 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(234\) | −3.49035e73 | −0.0817654 | ||||||||
\(235\) | −1.87813e74 | −0.384670 | ||||||||
\(236\) | −5.95789e73 | −0.106749 | ||||||||
\(237\) | −8.58358e73 | −0.134616 | ||||||||
\(238\) | −2.03965e74 | −0.280145 | ||||||||
\(239\) | 9.41567e74 | 1.13323 | 0.566614 | − | 0.823983i | \(-0.308253\pi\) | ||||
0.566614 | + | 0.823983i | \(0.308253\pi\) | |||||||
\(240\) | −8.68233e74 | −0.916183 | ||||||||
\(241\) | 1.39238e74 | 0.128890 | 0.0644451 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644451 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(242\) | 9.70143e74 | 0.788228 | ||||||||
\(243\) | −4.25218e74 | −0.303399 | ||||||||
\(244\) | −4.73208e74 | −0.296669 | ||||||||
\(245\) | 2.51831e75 | 1.38796 | ||||||||
\(246\) | −2.13970e75 | −1.03728 | ||||||||
\(247\) | 6.28859e74 | 0.268287 | ||||||||
\(248\) | 1.93879e75 | 0.728287 | ||||||||
\(249\) | 1.09024e75 | 0.360780 | ||||||||
\(250\) | −2.98548e75 | −0.870771 | ||||||||
\(251\) | 2.56608e75 | 0.660007 | 0.330003 | − | 0.943980i | \(-0.392950\pi\) | ||||
0.330003 | + | 0.943980i | \(0.392950\pi\) | |||||||
\(252\) | 7.68337e73 | 0.0174355 | ||||||||
\(253\) | −1.01622e76 | −2.03560 | ||||||||
\(254\) | 5.95367e75 | 1.05323 | ||||||||
\(255\) | −8.37971e75 | −1.30983 | ||||||||
\(256\) | −5.84244e75 | −0.807301 | ||||||||
\(257\) | 8.56043e75 | 1.04617 | 0.523085 | − | 0.852281i | \(-0.324781\pi\) | ||||
0.523085 | + | 0.852281i | \(0.324781\pi\) | |||||||
\(258\) | 8.15933e75 | 0.882336 | ||||||||
\(259\) | −1.68860e75 | −0.161653 | ||||||||
\(260\) | 3.64347e75 | 0.308926 | ||||||||
\(261\) | −3.77729e75 | −0.283795 | ||||||||
\(262\) | 5.54841e73 | 0.00369554 | ||||||||
\(263\) | 6.11957e75 | 0.361506 | 0.180753 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180753 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(264\) | 2.66006e76 | 1.39434 | ||||||||
\(265\) | 9.99150e75 | 0.464928 | ||||||||
\(266\) | 3.25674e75 | 0.134590 | ||||||||
\(267\) | −4.45984e76 | −1.63762 | ||||||||
\(268\) | 6.10895e75 | 0.199398 | ||||||||
\(269\) | −3.88727e76 | −1.12836 | −0.564180 | − | 0.825652i | \(-0.690808\pi\) | ||||
−0.564180 | + | 0.825652i | \(0.690808\pi\) | |||||||
\(270\) | −5.59258e76 | −1.44429 | ||||||||
\(271\) | 3.99908e76 | 0.919237 | 0.459618 | − | 0.888116i | \(-0.347986\pi\) | ||||
0.459618 | + | 0.888116i | \(0.347986\pi\) | |||||||
\(272\) | 2.62256e76 | 0.536791 | ||||||||
\(273\) | −1.22819e76 | −0.223946 | ||||||||
\(274\) | −8.77282e76 | −1.42560 | ||||||||
\(275\) | 1.57680e77 | 2.28452 | ||||||||
\(276\) | −3.10349e76 | −0.401065 | ||||||||
\(277\) | 8.95270e75 | 0.103238 | 0.0516192 | − | 0.998667i | \(-0.483562\pi\) | ||||
0.0516192 | + | 0.998667i | \(0.483562\pi\) | |||||||
\(278\) | 7.52340e76 | 0.774467 | ||||||||
\(279\) | 1.11537e76 | 0.102539 | ||||||||
\(280\) | 8.21285e76 | 0.674553 | ||||||||
\(281\) | −1.02715e77 | −0.754021 | −0.377010 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377010 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(282\) | −2.78063e76 | −0.182514 | ||||||||
\(283\) | −1.44978e77 | −0.851195 | −0.425597 | − | 0.904913i | \(-0.639936\pi\) | ||||
−0.425597 | + | 0.904913i | \(0.639936\pi\) | |||||||
\(284\) | −6.33906e76 | −0.333040 | ||||||||
\(285\) | 1.33800e77 | 0.629278 | ||||||||
\(286\) | 1.76633e77 | 0.743948 | ||||||||
\(287\) | 1.36133e77 | 0.513671 | ||||||||
\(288\) | −2.60017e76 | −0.0879303 | ||||||||
\(289\) | −7.67087e76 | −0.232575 | ||||||||
\(290\) | −9.27629e77 | −2.52253 | ||||||||
\(291\) | −2.10806e77 | −0.514345 | ||||||||
\(292\) | −3.39072e76 | −0.0742561 | ||||||||
\(293\) | 7.30204e77 | 1.43587 | 0.717934 | − | 0.696112i | \(-0.245088\pi\) | ||||
0.717934 | + | 0.696112i | \(0.245088\pi\) | |||||||
\(294\) | 3.72844e77 | 0.658547 | ||||||||
\(295\) | −3.66374e77 | −0.581474 | ||||||||
\(296\) | 3.22806e77 | 0.460525 | ||||||||
\(297\) | 1.15245e78 | 1.47840 | ||||||||
\(298\) | 3.69418e77 | 0.426291 | ||||||||
\(299\) | −8.96973e77 | −0.931401 | ||||||||
\(300\) | 4.81545e77 | 0.450108 | ||||||||
\(301\) | −5.19118e77 | −0.436940 | ||||||||
\(302\) | 2.81594e77 | 0.213504 | ||||||||
\(303\) | −5.51175e76 | −0.0376571 | ||||||||
\(304\) | −4.18748e77 | −0.257890 | ||||||||
\(305\) | −2.90994e78 | −1.61599 | ||||||||
\(306\) | 2.24316e77 | 0.112366 | ||||||||
\(307\) | 1.16301e77 | 0.0525685 | 0.0262842 | − | 0.999655i | \(-0.491633\pi\) | ||||
0.0262842 | + | 0.999655i | \(0.491633\pi\) | |||||||
\(308\) | −3.88826e77 | −0.158638 | ||||||||
\(309\) | −1.85719e78 | −0.684171 | ||||||||
\(310\) | 2.73913e78 | 0.911423 | ||||||||
\(311\) | −1.09750e78 | −0.329953 | −0.164977 | − | 0.986297i | \(-0.552755\pi\) | ||||
−0.164977 | + | 0.986297i | \(0.552755\pi\) | |||||||
\(312\) | 2.34792e78 | 0.637988 | ||||||||
\(313\) | 4.21242e78 | 1.03487 | 0.517434 | − | 0.855723i | \(-0.326887\pi\) | ||||
0.517434 | + | 0.855723i | \(0.326887\pi\) | |||||||
\(314\) | 4.79090e75 | 0.00106447 | ||||||||
\(315\) | 4.72480e77 | 0.0949731 | ||||||||
\(316\) | −2.39854e77 | −0.0436318 | ||||||||
\(317\) | −3.47405e78 | −0.572096 | −0.286048 | − | 0.958215i | \(-0.592342\pi\) | ||||
−0.286048 | + | 0.958215i | \(0.592342\pi\) | |||||||
\(318\) | 1.47928e78 | 0.220595 | ||||||||
\(319\) | 1.91154e79 | 2.58212 | ||||||||
\(320\) | −1.45194e79 | −1.77715 | ||||||||
\(321\) | −1.21631e79 | −1.34938 | ||||||||
\(322\) | −4.64526e78 | −0.467250 | ||||||||
\(323\) | −4.04152e78 | −0.368694 | ||||||||
\(324\) | 2.96766e78 | 0.245610 | ||||||||
\(325\) | 1.39176e79 | 1.04530 | ||||||||
\(326\) | −7.64164e78 | −0.520993 | ||||||||
\(327\) | 1.17075e79 | 0.724785 | ||||||||
\(328\) | −2.60244e79 | −1.46337 | ||||||||
\(329\) | 1.76911e78 | 0.0903825 | ||||||||
\(330\) | 3.75816e79 | 1.74496 | ||||||||
\(331\) | −4.43371e79 | −1.87148 | −0.935741 | − | 0.352687i | \(-0.885268\pi\) | ||||
−0.935741 | + | 0.352687i | \(0.885268\pi\) | |||||||
\(332\) | 3.04649e78 | 0.116937 | ||||||||
\(333\) | 1.85708e78 | 0.0648392 | ||||||||
\(334\) | 7.55686e78 | 0.240064 | ||||||||
\(335\) | 3.75663e79 | 1.08614 | ||||||||
\(336\) | 8.17836e78 | 0.215268 | ||||||||
\(337\) | 7.26234e79 | 1.74074 | 0.870372 | − | 0.492396i | \(-0.163879\pi\) | ||||
0.870372 | + | 0.492396i | \(0.163879\pi\) | |||||||
\(338\) | −2.27765e79 | −0.497292 | ||||||||
\(339\) | −2.36396e79 | −0.470273 | ||||||||
\(340\) | −2.34157e79 | −0.424542 | ||||||||
\(341\) | −5.64447e79 | −0.932954 | ||||||||
\(342\) | −3.58169e78 | −0.0539840 | ||||||||
\(343\) | −5.14894e79 | −0.707870 | ||||||||
\(344\) | 9.92387e79 | 1.24477 | ||||||||
\(345\) | −1.90845e80 | −2.18464 | ||||||||
\(346\) | −6.06637e79 | −0.633916 | ||||||||
\(347\) | 4.96199e79 | 0.473454 | 0.236727 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236727 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(348\) | 5.83774e79 | 0.508743 | ||||||||
\(349\) | 4.97595e79 | 0.396164 | 0.198082 | − | 0.980185i | \(-0.436529\pi\) | ||||
0.198082 | + | 0.980185i | \(0.436529\pi\) | |||||||
\(350\) | 7.20768e79 | 0.524388 | ||||||||
\(351\) | 1.01721e80 | 0.676453 | ||||||||
\(352\) | 1.31585e80 | 0.800040 | ||||||||
\(353\) | 1.92495e80 | 1.07033 | 0.535163 | − | 0.844749i | \(-0.320250\pi\) | ||||
0.535163 | + | 0.844749i | \(0.320250\pi\) | |||||||
\(354\) | −5.42429e79 | −0.275892 | ||||||||
\(355\) | −3.89813e80 | −1.81411 | ||||||||
\(356\) | −1.24623e80 | −0.530789 | ||||||||
\(357\) | 7.89331e79 | 0.307759 | ||||||||
\(358\) | −1.82125e79 | −0.0650210 | ||||||||
\(359\) | 5.20149e80 | 1.70080 | 0.850398 | − | 0.526140i | \(-0.176361\pi\) | ||||
0.850398 | + | 0.526140i | \(0.176361\pi\) | |||||||
\(360\) | −9.03230e79 | −0.270564 | ||||||||
\(361\) | −2.99783e80 | −0.822869 | ||||||||
\(362\) | −1.11794e80 | −0.281253 | ||||||||
\(363\) | −3.75438e80 | −0.865923 | ||||||||
\(364\) | −3.43198e79 | −0.0725858 | ||||||||
\(365\) | −2.08508e80 | −0.404481 | ||||||||
\(366\) | −4.30826e80 | −0.766739 | ||||||||
\(367\) | 6.58558e80 | 1.07551 | 0.537753 | − | 0.843103i | \(-0.319273\pi\) | ||||
0.537753 | + | 0.843103i | \(0.319273\pi\) | |||||||
\(368\) | 5.97281e80 | 0.895307 | ||||||||
\(369\) | −1.49716e80 | −0.206034 | ||||||||
\(370\) | 4.56063e80 | 0.576329 | ||||||||
\(371\) | −9.41153e79 | −0.109240 | ||||||||
\(372\) | −1.72379e80 | −0.183815 | ||||||||
\(373\) | 3.59988e80 | 0.352744 | 0.176372 | − | 0.984324i | \(-0.443564\pi\) | ||||
0.176372 | + | 0.984324i | \(0.443564\pi\) | |||||||
\(374\) | −1.13518e81 | −1.02237 | ||||||||
\(375\) | 1.15536e81 | 0.956603 | ||||||||
\(376\) | −3.38198e80 | −0.257486 | ||||||||
\(377\) | 1.68723e81 | 1.18147 | ||||||||
\(378\) | 5.26795e80 | 0.339352 | ||||||||
\(379\) | −8.36060e80 | −0.495567 | −0.247784 | − | 0.968815i | \(-0.579702\pi\) | ||||
−0.247784 | + | 0.968815i | \(0.579702\pi\) | |||||||
\(380\) | 3.73881e80 | 0.203963 | ||||||||
\(381\) | −2.30403e81 | −1.15705 | ||||||||
\(382\) | −1.94629e81 | −0.899935 | ||||||||
\(383\) | 1.93079e81 | 0.822193 | 0.411097 | − | 0.911592i | \(-0.365146\pi\) | ||||
0.411097 | + | 0.911592i | \(0.365146\pi\) | |||||||
\(384\) | −8.02392e80 | −0.314741 | ||||||||
\(385\) | −2.39104e81 | −0.864119 | ||||||||
\(386\) | 6.42527e79 | 0.0213989 | ||||||||
\(387\) | 5.70913e80 | 0.175257 | ||||||||
\(388\) | −5.89063e80 | −0.166710 | ||||||||
\(389\) | −5.18176e81 | −1.35227 | −0.676137 | − | 0.736776i | \(-0.736347\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(390\) | 3.31715e81 | 0.798418 | ||||||||
\(391\) | 5.76462e81 | 1.27998 | ||||||||
\(392\) | 4.53476e81 | 0.929058 | ||||||||
\(393\) | −2.14719e79 | −0.00405981 | ||||||||
\(394\) | 8.07257e81 | 1.40890 | ||||||||
\(395\) | −1.47495e81 | −0.237667 | ||||||||
\(396\) | 4.27621e80 | 0.0636298 | ||||||||
\(397\) | −4.30808e81 | −0.592083 | −0.296041 | − | 0.955175i | \(-0.595667\pi\) | ||||
−0.296041 | + | 0.955175i | \(0.595667\pi\) | |||||||
\(398\) | 2.05251e80 | 0.0260596 | ||||||||
\(399\) | −1.26033e81 | −0.147856 | ||||||||
\(400\) | −9.26754e81 | −1.00479 | ||||||||
\(401\) | −1.60082e82 | −1.60434 | −0.802168 | − | 0.597098i | \(-0.796320\pi\) | ||||
−0.802168 | + | 0.597098i | \(0.796320\pi\) | |||||||
\(402\) | 5.56182e81 | 0.515343 | ||||||||
\(403\) | −4.98211e81 | −0.426878 | ||||||||
\(404\) | −1.54017e80 | −0.0122055 | ||||||||
\(405\) | 1.82493e82 | 1.33787 | ||||||||
\(406\) | 8.73784e81 | 0.592699 | ||||||||
\(407\) | −9.39798e81 | −0.589944 | ||||||||
\(408\) | −1.50895e82 | −0.876756 | ||||||||
\(409\) | 2.24771e82 | 1.20908 | 0.604541 | − | 0.796574i | \(-0.293357\pi\) | ||||
0.604541 | + | 0.796574i | \(0.293357\pi\) | |||||||
\(410\) | −3.67674e82 | −1.83135 | ||||||||
\(411\) | 3.39501e82 | 1.56612 | ||||||||
\(412\) | −5.18961e81 | −0.221754 | ||||||||
\(413\) | 3.45107e81 | 0.136624 | ||||||||
\(414\) | 5.10874e81 | 0.187414 | ||||||||
\(415\) | 1.87340e82 | 0.636966 | ||||||||
\(416\) | 1.16144e82 | 0.366063 | ||||||||
\(417\) | −2.91150e82 | −0.850806 | ||||||||
\(418\) | 1.81255e82 | 0.491177 | ||||||||
\(419\) | 1.12509e82 | 0.282779 | 0.141389 | − | 0.989954i | \(-0.454843\pi\) | ||||
0.141389 | + | 0.989954i | \(0.454843\pi\) | |||||||
\(420\) | −7.30210e81 | −0.170253 | ||||||||
\(421\) | −8.89409e81 | −0.192405 | −0.0962023 | − | 0.995362i | \(-0.530670\pi\) | ||||
−0.0962023 | + | 0.995362i | \(0.530670\pi\) | |||||||
\(422\) | −4.34318e81 | −0.0871897 | ||||||||
\(423\) | −1.94563e81 | −0.0362525 | ||||||||
\(424\) | 1.79918e82 | 0.311208 | ||||||||
\(425\) | −8.94452e82 | −1.43650 | ||||||||
\(426\) | −5.77132e82 | −0.860741 | ||||||||
\(427\) | 2.74103e82 | 0.379695 | ||||||||
\(428\) | −3.39877e82 | −0.437365 | ||||||||
\(429\) | −6.83557e82 | −0.817279 | ||||||||
\(430\) | 1.40205e83 | 1.55779 | ||||||||
\(431\) | 1.55724e83 | 1.60813 | 0.804063 | − | 0.594544i | \(-0.202667\pi\) | ||||
0.804063 | + | 0.594544i | \(0.202667\pi\) | |||||||
\(432\) | −6.77346e82 | −0.650238 | ||||||||
\(433\) | −1.61378e83 | −1.44037 | −0.720185 | − | 0.693782i | \(-0.755943\pi\) | ||||
−0.720185 | + | 0.693782i | \(0.755943\pi\) | |||||||
\(434\) | −2.58014e82 | −0.214149 | ||||||||
\(435\) | 3.58985e83 | 2.77118 | ||||||||
\(436\) | 3.27146e82 | 0.234918 | ||||||||
\(437\) | −9.20445e82 | −0.614940 | ||||||||
\(438\) | −3.08704e82 | −0.191914 | ||||||||
\(439\) | −2.41284e83 | −1.39603 | −0.698016 | − | 0.716082i | \(-0.745934\pi\) | ||||
−0.698016 | + | 0.716082i | \(0.745934\pi\) | |||||||
\(440\) | 4.57090e83 | 2.46174 | ||||||||
\(441\) | 2.60881e82 | 0.130806 | ||||||||
\(442\) | −1.00197e83 | −0.467792 | ||||||||
\(443\) | 1.04534e83 | 0.454506 | 0.227253 | − | 0.973836i | \(-0.427025\pi\) | ||||
0.227253 | + | 0.973836i | \(0.427025\pi\) | |||||||
\(444\) | −2.87009e82 | −0.116234 | ||||||||
\(445\) | −7.66353e83 | −2.89127 | ||||||||
\(446\) | −3.92790e83 | −1.38074 | ||||||||
\(447\) | −1.42962e83 | −0.468310 | ||||||||
\(448\) | 1.36766e83 | 0.417561 | ||||||||
\(449\) | 4.96606e83 | 1.41336 | 0.706678 | − | 0.707535i | \(-0.250193\pi\) | ||||
0.706678 | + | 0.707535i | \(0.250193\pi\) | |||||||
\(450\) | −7.92684e82 | −0.210332 | ||||||||
\(451\) | 7.57657e83 | 1.87461 | ||||||||
\(452\) | −6.60569e82 | −0.152426 | ||||||||
\(453\) | −1.08975e83 | −0.234549 | ||||||||
\(454\) | 7.35807e82 | 0.147742 | ||||||||
\(455\) | −2.11046e83 | −0.395383 | ||||||||
\(456\) | 2.40936e83 | 0.421219 | ||||||||
\(457\) | −1.18034e83 | −0.192596 | −0.0962979 | − | 0.995353i | \(-0.530700\pi\) | ||||
−0.0962979 | + | 0.995353i | \(0.530700\pi\) | |||||||
\(458\) | 9.34897e83 | 1.42397 | ||||||||
\(459\) | −6.53737e83 | −0.929616 | ||||||||
\(460\) | −5.33286e83 | −0.708089 | ||||||||
\(461\) | 7.43360e83 | 0.921764 | 0.460882 | − | 0.887461i | \(-0.347533\pi\) | ||||
0.460882 | + | 0.887461i | \(0.347533\pi\) | |||||||
\(462\) | −3.54001e83 | −0.409999 | ||||||||
\(463\) | 8.96271e83 | 0.969701 | 0.484851 | − | 0.874597i | \(-0.338874\pi\) | ||||
0.484851 | + | 0.874597i | \(0.338874\pi\) | |||||||
\(464\) | −1.12350e84 | −1.13568 | ||||||||
\(465\) | −1.06002e84 | −1.00126 | ||||||||
\(466\) | −4.69771e83 | −0.414696 | ||||||||
\(467\) | 2.08627e84 | 1.72143 | 0.860714 | − | 0.509090i | \(-0.170018\pi\) | ||||
0.860714 | + | 0.509090i | \(0.170018\pi\) | |||||||
\(468\) | 3.77441e82 | 0.0291142 | ||||||||
\(469\) | −3.53857e83 | −0.255202 | ||||||||
\(470\) | −4.77808e83 | −0.322234 | ||||||||
\(471\) | −1.85404e81 | −0.00116939 | ||||||||
\(472\) | −6.59734e83 | −0.389221 | ||||||||
\(473\) | −2.88917e84 | −1.59459 | ||||||||
\(474\) | −2.18372e83 | −0.112766 | ||||||||
\(475\) | 1.42818e84 | 0.690137 | ||||||||
\(476\) | 2.20565e83 | 0.0997511 | ||||||||
\(477\) | 1.03506e83 | 0.0438163 | ||||||||
\(478\) | 2.39541e84 | 0.949293 | ||||||||
\(479\) | 2.82456e84 | 1.04805 | 0.524026 | − | 0.851702i | \(-0.324430\pi\) | ||||
0.524026 | + | 0.851702i | \(0.324430\pi\) | |||||||
\(480\) | 2.47114e84 | 0.858616 | ||||||||
\(481\) | −8.29516e83 | −0.269932 | ||||||||
\(482\) | 3.54229e83 | 0.107970 | ||||||||
\(483\) | 1.79768e84 | 0.513307 | ||||||||
\(484\) | −1.04910e84 | −0.280664 | ||||||||
\(485\) | −3.62238e84 | −0.908090 | ||||||||
\(486\) | −1.08178e84 | −0.254154 | ||||||||
\(487\) | −1.40116e84 | −0.308550 | −0.154275 | − | 0.988028i | \(-0.549304\pi\) | ||||
−0.154275 | + | 0.988028i | \(0.549304\pi\) | |||||||
\(488\) | −5.23997e84 | −1.08169 | ||||||||
\(489\) | 2.95726e84 | 0.572347 | ||||||||
\(490\) | 6.40674e84 | 1.16268 | ||||||||
\(491\) | −9.53280e84 | −1.62238 | −0.811192 | − | 0.584780i | \(-0.801181\pi\) | ||||
−0.811192 | + | 0.584780i | \(0.801181\pi\) | |||||||
\(492\) | 2.31384e84 | 0.369346 | ||||||||
\(493\) | −1.08434e85 | −1.62363 | ||||||||
\(494\) | 1.59986e84 | 0.224741 | ||||||||
\(495\) | 2.62961e84 | 0.346599 | ||||||||
\(496\) | 3.31751e84 | 0.410336 | ||||||||
\(497\) | 3.67186e84 | 0.426246 | ||||||||
\(498\) | 2.77364e84 | 0.302222 | ||||||||
\(499\) | 9.33185e83 | 0.0954554 | 0.0477277 | − | 0.998860i | \(-0.484802\pi\) | ||||
0.0477277 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(500\) | 3.22845e84 | 0.310056 | ||||||||
\(501\) | −2.92445e84 | −0.263727 | ||||||||
\(502\) | 6.52828e84 | 0.552881 | ||||||||
\(503\) | 1.86028e85 | 1.47975 | 0.739873 | − | 0.672747i | \(-0.234886\pi\) | ||||
0.739873 | + | 0.672747i | \(0.234886\pi\) | |||||||
\(504\) | 8.50801e83 | 0.0635721 | ||||||||
\(505\) | −9.47107e83 | −0.0664845 | ||||||||
\(506\) | −2.58534e85 | −1.70520 | ||||||||
\(507\) | 8.81434e84 | 0.546310 | ||||||||
\(508\) | −6.43821e84 | −0.375023 | ||||||||
\(509\) | 1.08331e85 | 0.593119 | 0.296559 | − | 0.955014i | \(-0.404161\pi\) | ||||
0.296559 | + | 0.955014i | \(0.404161\pi\) | |||||||
\(510\) | −2.13185e85 | −1.09723 | ||||||||
\(511\) | 1.96405e84 | 0.0950375 | ||||||||
\(512\) | −2.23806e85 | −1.01828 | ||||||||
\(513\) | 1.04383e85 | 0.446615 | ||||||||
\(514\) | 2.17783e85 | 0.876366 | ||||||||
\(515\) | −3.19129e85 | −1.20792 | ||||||||
\(516\) | −8.82338e84 | −0.314173 | ||||||||
\(517\) | 9.84607e84 | 0.329846 | ||||||||
\(518\) | −4.29591e84 | −0.135415 | ||||||||
\(519\) | 2.34764e85 | 0.696400 | ||||||||
\(520\) | 4.03452e85 | 1.12638 | ||||||||
\(521\) | −1.60719e84 | −0.0422356 | −0.0211178 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211178 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(522\) | −9.60966e84 | −0.237732 | ||||||||
\(523\) | −4.89922e85 | −1.14110 | −0.570550 | − | 0.821263i | \(-0.693270\pi\) | ||||
−0.570550 | + | 0.821263i | \(0.693270\pi\) | |||||||
\(524\) | −5.99997e82 | −0.00131587 | ||||||||
\(525\) | −2.78932e85 | −0.576076 | ||||||||
\(526\) | 1.55686e85 | 0.302829 | ||||||||
\(527\) | 3.20188e85 | 0.586638 | ||||||||
\(528\) | 4.55170e85 | 0.785607 | ||||||||
\(529\) | 6.97907e85 | 1.13486 | ||||||||
\(530\) | 2.54190e85 | 0.389465 | ||||||||
\(531\) | −3.79541e84 | −0.0548000 | ||||||||
\(532\) | −3.52179e84 | −0.0479234 | ||||||||
\(533\) | 6.68748e85 | 0.857740 | ||||||||
\(534\) | −1.13461e86 | −1.37182 | ||||||||
\(535\) | −2.09004e86 | −2.38237 | ||||||||
\(536\) | 6.76462e85 | 0.727030 | ||||||||
\(537\) | 7.04809e84 | 0.0714301 | ||||||||
\(538\) | −9.88946e85 | −0.945216 | ||||||||
\(539\) | −1.32022e86 | −1.19015 | ||||||||
\(540\) | 6.04772e85 | 0.514267 | ||||||||
\(541\) | 1.88800e85 | 0.151457 | 0.0757284 | − | 0.997128i | \(-0.475872\pi\) | ||||
0.0757284 | + | 0.997128i | \(0.475872\pi\) | |||||||
\(542\) | 1.01739e86 | 0.770035 | ||||||||
\(543\) | 4.32632e85 | 0.308976 | ||||||||
\(544\) | −7.46427e85 | −0.503062 | ||||||||
\(545\) | 2.01174e86 | 1.27963 | ||||||||
\(546\) | −3.12461e85 | −0.187597 | ||||||||
\(547\) | −5.20458e85 | −0.294975 | −0.147487 | − | 0.989064i | \(-0.547119\pi\) | ||||
−0.147487 | + | 0.989064i | \(0.547119\pi\) | |||||||
\(548\) | 9.48679e85 | 0.507612 | ||||||||
\(549\) | −3.01452e85 | −0.152296 | ||||||||
\(550\) | 4.01147e86 | 1.91372 | ||||||||
\(551\) | 1.73138e86 | 0.780040 | ||||||||
\(552\) | −3.43658e86 | −1.46233 | ||||||||
\(553\) | 1.38934e85 | 0.0558427 | ||||||||
\(554\) | 2.27762e85 | 0.0864817 | ||||||||
\(555\) | −1.76493e86 | −0.633138 | ||||||||
\(556\) | −8.13569e85 | −0.275764 | ||||||||
\(557\) | −3.49609e86 | −1.11981 | −0.559905 | − | 0.828557i | \(-0.689162\pi\) | ||||
−0.559905 | + | 0.828557i | \(0.689162\pi\) | |||||||
\(558\) | 2.83758e85 | 0.0858955 | ||||||||
\(559\) | −2.55014e86 | −0.729612 | ||||||||
\(560\) | 1.40532e86 | 0.380061 | ||||||||
\(561\) | 4.39305e86 | 1.12315 | ||||||||
\(562\) | −2.61313e86 | −0.631635 | ||||||||
\(563\) | 3.12313e86 | 0.713799 | 0.356899 | − | 0.934143i | \(-0.383834\pi\) | ||||
0.356899 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(564\) | 3.00694e85 | 0.0649879 | ||||||||
\(565\) | −4.06209e86 | −0.830279 | ||||||||
\(566\) | −3.68833e86 | −0.713037 | ||||||||
\(567\) | −1.71900e86 | −0.314347 | ||||||||
\(568\) | −7.01942e86 | −1.21431 | ||||||||
\(569\) | 9.57453e86 | 1.56704 | 0.783522 | − | 0.621365i | \(-0.213421\pi\) | ||||
0.783522 | + | 0.621365i | \(0.213421\pi\) | |||||||
\(570\) | 3.40396e86 | 0.527140 | ||||||||
\(571\) | 1.18863e87 | 1.74184 | 0.870922 | − | 0.491421i | \(-0.163522\pi\) | ||||
0.870922 | + | 0.491421i | \(0.163522\pi\) | |||||||
\(572\) | −1.91009e86 | −0.264898 | ||||||||
\(573\) | 7.53199e86 | 0.988642 | ||||||||
\(574\) | 3.46332e86 | 0.430297 | ||||||||
\(575\) | −2.03709e87 | −2.39592 | ||||||||
\(576\) | −1.50412e86 | −0.167484 | ||||||||
\(577\) | 6.90737e86 | 0.728240 | 0.364120 | − | 0.931352i | \(-0.381370\pi\) | ||||
0.364120 | + | 0.931352i | \(0.381370\pi\) | |||||||
\(578\) | −1.95152e86 | −0.194825 | ||||||||
\(579\) | −2.48653e85 | −0.0235082 | ||||||||
\(580\) | 1.00312e87 | 0.898199 | ||||||||
\(581\) | −1.76466e86 | −0.149663 | ||||||||
\(582\) | −5.36305e86 | −0.430862 | ||||||||
\(583\) | −5.23803e86 | −0.398665 | ||||||||
\(584\) | −3.75464e86 | −0.270747 | ||||||||
\(585\) | 2.32103e86 | 0.158588 | ||||||||
\(586\) | 1.85769e87 | 1.20281 | ||||||||
\(587\) | −2.29584e87 | −1.40878 | −0.704388 | − | 0.709815i | \(-0.748779\pi\) | ||||
−0.704388 | + | 0.709815i | \(0.748779\pi\) | |||||||
\(588\) | −4.03188e86 | −0.234489 | ||||||||
\(589\) | −5.11248e86 | −0.281838 | ||||||||
\(590\) | −9.32078e86 | −0.487095 | ||||||||
\(591\) | −3.12402e87 | −1.54778 | ||||||||
\(592\) | 5.52362e86 | 0.259472 | ||||||||
\(593\) | 1.89673e87 | 0.844856 | 0.422428 | − | 0.906396i | \(-0.361178\pi\) | ||||
0.422428 | + | 0.906396i | \(0.361178\pi\) | |||||||
\(594\) | 2.93190e87 | 1.23844 | ||||||||
\(595\) | 1.35634e87 | 0.543355 | ||||||||
\(596\) | −3.99483e86 | −0.151789 | ||||||||
\(597\) | −7.94305e85 | −0.0286283 | ||||||||
\(598\) | −2.28196e87 | −0.780225 | ||||||||
\(599\) | 3.88204e87 | 1.25926 | 0.629630 | − | 0.776895i | \(-0.283206\pi\) | ||||
0.629630 | + | 0.776895i | \(0.283206\pi\) | |||||||
\(600\) | 5.33228e87 | 1.64115 | ||||||||
\(601\) | 1.33959e87 | 0.391225 | 0.195613 | − | 0.980681i | \(-0.437330\pi\) | ||||
0.195613 | + | 0.980681i | \(0.437330\pi\) | |||||||
\(602\) | −1.32067e87 | −0.366020 | ||||||||
\(603\) | 3.89164e86 | 0.102362 | ||||||||
\(604\) | −3.04512e86 | −0.0760222 | ||||||||
\(605\) | −6.45130e87 | −1.52881 | ||||||||
\(606\) | −1.40222e86 | −0.0315450 | ||||||||
\(607\) | −3.65491e87 | −0.780608 | −0.390304 | − | 0.920686i | \(-0.627630\pi\) | ||||
−0.390304 | + | 0.920686i | \(0.627630\pi\) | |||||||
\(608\) | 1.19183e87 | 0.241686 | ||||||||
\(609\) | −3.38148e87 | −0.651121 | ||||||||
\(610\) | −7.40306e87 | −1.35370 | ||||||||
\(611\) | 8.69067e86 | 0.150923 | ||||||||
\(612\) | −2.42572e86 | −0.0400102 | ||||||||
\(613\) | 9.00256e86 | 0.141046 | 0.0705231 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705231 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(614\) | 2.95878e86 | 0.0440361 | ||||||||
\(615\) | 1.42287e88 | 2.01187 | ||||||||
\(616\) | −4.30558e87 | −0.578415 | ||||||||
\(617\) | 1.99271e87 | 0.254368 | 0.127184 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127184 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(618\) | −4.72481e87 | −0.573123 | ||||||||
\(619\) | 1.64027e88 | 1.89087 | 0.945433 | − | 0.325818i | \(-0.105640\pi\) | ||||
0.945433 | + | 0.325818i | \(0.105640\pi\) | |||||||
\(620\) | −2.96206e87 | −0.324530 | ||||||||
\(621\) | −1.48887e88 | −1.55050 | ||||||||
\(622\) | −2.79211e87 | −0.276399 | ||||||||
\(623\) | 7.21869e87 | 0.679337 | ||||||||
\(624\) | 4.01758e87 | 0.359459 | ||||||||
\(625\) | 5.77379e86 | 0.0491180 | ||||||||
\(626\) | 1.07167e88 | 0.866898 | ||||||||
\(627\) | −7.01445e87 | −0.539592 | ||||||||
\(628\) | −5.18081e84 | −0.000379026 0 | ||||||||
\(629\) | 5.33109e87 | 0.370955 | ||||||||
\(630\) | 1.20202e87 | 0.0795580 | ||||||||
\(631\) | 2.29325e87 | 0.144387 | 0.0721934 | − | 0.997391i | \(-0.477000\pi\) | ||||
0.0721934 | + | 0.997391i | \(0.477000\pi\) | |||||||
\(632\) | −2.65597e87 | −0.159087 | ||||||||
\(633\) | 1.68078e87 | 0.0957840 | ||||||||
\(634\) | −8.83819e87 | −0.479239 | ||||||||
\(635\) | −3.95910e88 | −2.04279 | ||||||||
\(636\) | −1.59967e87 | −0.0785471 | ||||||||
\(637\) | −1.16530e88 | −0.544559 | ||||||||
\(638\) | 4.86308e88 | 2.16302 | ||||||||
\(639\) | −4.03822e87 | −0.170967 | ||||||||
\(640\) | −1.37878e88 | −0.555682 | ||||||||
\(641\) | 1.08867e88 | 0.417706 | 0.208853 | − | 0.977947i | \(-0.433027\pi\) | ||||
0.208853 | + | 0.977947i | \(0.433027\pi\) | |||||||
\(642\) | −3.09437e88 | −1.13037 | ||||||||
\(643\) | 2.35352e88 | 0.818600 | 0.409300 | − | 0.912400i | \(-0.365773\pi\) | ||||
0.409300 | + | 0.912400i | \(0.365773\pi\) | |||||||
\(644\) | 5.02331e87 | 0.166374 | ||||||||
\(645\) | −5.42583e88 | −1.71134 | ||||||||
\(646\) | −1.02819e88 | −0.308851 | ||||||||
\(647\) | 5.67683e88 | 1.62413 | 0.812065 | − | 0.583567i | \(-0.198343\pi\) | ||||
0.812065 | + | 0.583567i | \(0.198343\pi\) | |||||||
\(648\) | 3.28618e88 | 0.895527 | ||||||||
\(649\) | 1.92071e88 | 0.498602 | ||||||||
\(650\) | 3.54074e88 | 0.875634 | ||||||||
\(651\) | 9.98494e87 | 0.235258 | ||||||||
\(652\) | 8.26355e87 | 0.185510 | ||||||||
\(653\) | −6.10331e88 | −1.30557 | −0.652785 | − | 0.757543i | \(-0.726400\pi\) | ||||
−0.652785 | + | 0.757543i | \(0.726400\pi\) | |||||||
\(654\) | 2.97846e88 | 0.607145 | ||||||||
\(655\) | −3.68961e86 | −0.00716770 | ||||||||
\(656\) | −4.45309e88 | −0.824500 | ||||||||
\(657\) | −2.16002e87 | −0.0381196 | ||||||||
\(658\) | 4.50073e87 | 0.0757125 | ||||||||
\(659\) | 4.53598e88 | 0.727413 | 0.363706 | − | 0.931514i | \(-0.381511\pi\) | ||||
0.363706 | + | 0.931514i | \(0.381511\pi\) | |||||||
\(660\) | −4.06402e88 | −0.621329 | ||||||||
\(661\) | −2.88478e88 | −0.420501 | −0.210251 | − | 0.977648i | \(-0.567428\pi\) | ||||
−0.210251 | + | 0.977648i | \(0.567428\pi\) | |||||||
\(662\) | −1.12797e89 | −1.56772 | ||||||||
\(663\) | 3.87754e88 | 0.513902 | ||||||||
\(664\) | 3.37347e88 | 0.426366 | ||||||||
\(665\) | −2.16568e88 | −0.261044 | ||||||||
\(666\) | 4.72454e87 | 0.0543151 | ||||||||
\(667\) | −2.46955e89 | −2.70804 | ||||||||
\(668\) | −8.17187e87 | −0.0854797 | ||||||||
\(669\) | 1.52007e89 | 1.51684 | ||||||||
\(670\) | 9.55710e88 | 0.909850 | ||||||||
\(671\) | 1.52553e89 | 1.38568 | ||||||||
\(672\) | −2.32770e88 | −0.201742 | ||||||||
\(673\) | −4.58578e88 | −0.379261 | −0.189631 | − | 0.981856i | \(-0.560729\pi\) | ||||
−0.189631 | + | 0.981856i | \(0.560729\pi\) | |||||||
\(674\) | 1.84759e89 | 1.45820 | ||||||||
\(675\) | 2.31016e89 | 1.74010 | ||||||||
\(676\) | 2.46302e88 | 0.177071 | ||||||||
\(677\) | −2.36254e89 | −1.62120 | −0.810600 | − | 0.585600i | \(-0.800859\pi\) | ||||
−0.810600 | + | 0.585600i | \(0.800859\pi\) | |||||||
\(678\) | −6.01407e88 | −0.393943 | ||||||||
\(679\) | 3.41211e88 | 0.213366 | ||||||||
\(680\) | −2.59289e89 | −1.54794 | ||||||||
\(681\) | −2.84751e88 | −0.162305 | ||||||||
\(682\) | −1.43599e89 | −0.781526 | ||||||||
\(683\) | 2.85240e88 | 0.148238 | 0.0741188 | − | 0.997249i | \(-0.476386\pi\) | ||||
0.0741188 | + | 0.997249i | \(0.476386\pi\) | |||||||
\(684\) | 3.87318e87 | 0.0192221 | ||||||||
\(685\) | 5.83379e89 | 2.76502 | ||||||||
\(686\) | −1.30992e89 | −0.592975 | ||||||||
\(687\) | −3.61798e89 | −1.56433 | ||||||||
\(688\) | 1.69810e89 | 0.701338 | ||||||||
\(689\) | −4.62337e88 | −0.182412 | ||||||||
\(690\) | −4.85523e89 | −1.83005 | ||||||||
\(691\) | 2.68324e89 | 0.966276 | 0.483138 | − | 0.875544i | \(-0.339497\pi\) | ||||
0.483138 | + | 0.875544i | \(0.339497\pi\) | |||||||
\(692\) | 6.56007e88 | 0.225718 | ||||||||
\(693\) | −2.47697e88 | −0.0814374 | ||||||||
\(694\) | 1.26236e89 | 0.396608 | ||||||||
\(695\) | −5.00295e89 | −1.50212 | ||||||||
\(696\) | 6.46430e89 | 1.85494 | ||||||||
\(697\) | −4.29788e89 | −1.17875 | ||||||||
\(698\) | 1.26591e89 | 0.331862 | ||||||||
\(699\) | 1.81798e89 | 0.455572 | ||||||||
\(700\) | −7.79428e88 | −0.186719 | ||||||||
\(701\) | −3.19036e89 | −0.730672 | −0.365336 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365336 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(702\) | 2.58785e89 | 0.566657 | ||||||||
\(703\) | −8.51223e88 | −0.178218 | ||||||||
\(704\) | 7.61176e89 | 1.52386 | ||||||||
\(705\) | 1.84908e89 | 0.353996 | ||||||||
\(706\) | 4.89720e89 | 0.896601 | ||||||||
\(707\) | 8.92132e87 | 0.0156213 | ||||||||
\(708\) | 5.86574e88 | 0.0982370 | ||||||||
\(709\) | 2.81601e89 | 0.451106 | 0.225553 | − | 0.974231i | \(-0.427581\pi\) | ||||
0.225553 | + | 0.974231i | \(0.427581\pi\) | |||||||
\(710\) | −9.91709e89 | −1.51966 | ||||||||
\(711\) | −1.52796e88 | −0.0223985 | ||||||||
\(712\) | −1.37998e90 | −1.93532 | ||||||||
\(713\) | 7.29218e89 | 0.978447 | ||||||||
\(714\) | 2.00811e89 | 0.257806 | ||||||||
\(715\) | −1.17458e90 | −1.44293 | ||||||||
\(716\) | 1.96947e88 | 0.0231520 | ||||||||
\(717\) | −9.27003e89 | −1.04286 | ||||||||
\(718\) | 1.32329e90 | 1.42474 | ||||||||
\(719\) | −3.41292e89 | −0.351695 | −0.175847 | − | 0.984417i | \(-0.556267\pi\) | ||||
−0.175847 | + | 0.984417i | \(0.556267\pi\) | |||||||
\(720\) | −1.54554e89 | −0.152443 | ||||||||
\(721\) | 3.00605e89 | 0.283815 | ||||||||
\(722\) | −7.62668e89 | −0.689309 | ||||||||
\(723\) | −1.37084e89 | −0.118612 | ||||||||
\(724\) | 1.20892e89 | 0.100146 | ||||||||
\(725\) | 3.83181e90 | 3.03919 | ||||||||
\(726\) | −9.55138e89 | −0.725375 | ||||||||
\(727\) | −1.71525e90 | −1.24737 | −0.623683 | − | 0.781678i | \(-0.714364\pi\) | ||||
−0.623683 | + | 0.781678i | \(0.714364\pi\) | |||||||
\(728\) | −3.80033e89 | −0.264657 | ||||||||
\(729\) | 1.65330e90 | 1.10264 | ||||||||
\(730\) | −5.30458e89 | −0.338830 | ||||||||
\(731\) | 1.63891e90 | 1.00267 | ||||||||
\(732\) | 4.65889e89 | 0.273013 | ||||||||
\(733\) | 2.18440e90 | 1.22618 | 0.613092 | − | 0.790011i | \(-0.289925\pi\) | ||||
0.613092 | + | 0.790011i | \(0.289925\pi\) | |||||||
\(734\) | 1.67541e90 | 0.900940 | ||||||||
\(735\) | −2.47936e90 | −1.27729 | ||||||||
\(736\) | −1.69997e90 | −0.839052 | ||||||||
\(737\) | −1.96941e90 | −0.931343 | ||||||||
\(738\) | −3.80888e89 | −0.172592 | ||||||||
\(739\) | −1.54735e90 | −0.671875 | −0.335938 | − | 0.941884i | \(-0.609053\pi\) | ||||
−0.335938 | + | 0.941884i | \(0.609053\pi\) | |||||||
\(740\) | −4.93180e89 | −0.205214 | ||||||||
\(741\) | −6.19132e89 | −0.246894 | ||||||||
\(742\) | −2.39435e89 | −0.0915093 | ||||||||
\(743\) | 2.46406e90 | 0.902617 | 0.451309 | − | 0.892368i | \(-0.350957\pi\) | ||||
0.451309 | + | 0.892368i | \(0.350957\pi\) | |||||||
\(744\) | −1.90880e90 | −0.670214 | ||||||||
\(745\) | −2.45658e90 | −0.826813 | ||||||||
\(746\) | 9.15831e89 | 0.295490 | ||||||||
\(747\) | 1.94073e89 | 0.0600298 | ||||||||
\(748\) | 1.22756e90 | 0.364036 | ||||||||
\(749\) | 1.96872e90 | 0.559766 | ||||||||
\(750\) | 2.93931e90 | 0.801336 | ||||||||
\(751\) | −1.27632e90 | −0.333657 | −0.166829 | − | 0.985986i | \(-0.553353\pi\) | ||||
−0.166829 | + | 0.985986i | \(0.553353\pi\) | |||||||
\(752\) | −5.78698e89 | −0.145074 | ||||||||
\(753\) | −2.52639e90 | −0.607378 | ||||||||
\(754\) | 4.29242e90 | 0.989702 | ||||||||
\(755\) | −1.87256e90 | −0.414101 | ||||||||
\(756\) | −5.69668e89 | −0.120833 | ||||||||
\(757\) | 1.74981e90 | 0.356016 | 0.178008 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178008 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(758\) | −2.12699e90 | −0.415131 | ||||||||
\(759\) | 1.00051e91 | 1.87328 | ||||||||
\(760\) | 4.14010e90 | 0.743673 | ||||||||
\(761\) | −8.36501e90 | −1.44162 | −0.720809 | − | 0.693134i | \(-0.756229\pi\) | ||||
−0.720809 | + | 0.693134i | \(0.756229\pi\) | |||||||
\(762\) | −5.86159e90 | −0.969245 | ||||||||
\(763\) | −1.89497e90 | −0.300663 | ||||||||
\(764\) | 2.10469e90 | 0.320440 | ||||||||
\(765\) | −1.49167e90 | −0.217940 | ||||||||
\(766\) | 4.91206e90 | 0.688743 | ||||||||
\(767\) | 1.69532e90 | 0.228138 | ||||||||
\(768\) | 5.75208e90 | 0.742927 | ||||||||
\(769\) | 5.02702e90 | 0.623205 | 0.311602 | − | 0.950213i | \(-0.399134\pi\) | ||||
0.311602 | + | 0.950213i | \(0.399134\pi\) | |||||||
\(770\) | −6.08295e90 | −0.723864 | ||||||||
\(771\) | −8.42803e90 | −0.962749 | ||||||||
\(772\) | −6.94818e88 | −0.00761950 | ||||||||
\(773\) | −9.31255e90 | −0.980425 | −0.490213 | − | 0.871603i | \(-0.663081\pi\) | ||||
−0.490213 | + | 0.871603i | \(0.663081\pi\) | |||||||
\(774\) | 1.45244e90 | 0.146811 | ||||||||
\(775\) | −1.13147e91 | −1.09810 | ||||||||
\(776\) | −6.52287e90 | −0.607847 | ||||||||
\(777\) | 1.66248e90 | 0.148763 | ||||||||
\(778\) | −1.31827e91 | −1.13279 | ||||||||
\(779\) | 6.86248e90 | 0.566306 | ||||||||
\(780\) | −3.58712e90 | −0.284293 | ||||||||
\(781\) | 2.04359e91 | 1.55556 | ||||||||
\(782\) | 1.46656e91 | 1.07223 | ||||||||
\(783\) | 2.80060e91 | 1.96678 | ||||||||
\(784\) | 7.75954e90 | 0.523456 | ||||||||
\(785\) | −3.18588e88 | −0.00206459 | ||||||||
\(786\) | −5.46259e88 | −0.00340086 | ||||||||
\(787\) | −1.11647e91 | −0.667793 | −0.333896 | − | 0.942610i | \(-0.608364\pi\) | ||||
−0.333896 | + | 0.942610i | \(0.608364\pi\) | |||||||
\(788\) | −8.72955e90 | −0.501668 | ||||||||
\(789\) | −6.02492e90 | −0.332679 | ||||||||
\(790\) | −3.75237e90 | −0.199091 | ||||||||
\(791\) | 3.82631e90 | 0.195084 | ||||||||
\(792\) | 4.73517e90 | 0.232002 | ||||||||
\(793\) | 1.34651e91 | 0.634024 | ||||||||
\(794\) | −1.09600e91 | −0.495982 | ||||||||
\(795\) | −9.83696e90 | −0.427855 | ||||||||
\(796\) | −2.21955e89 | −0.00927905 | ||||||||
\(797\) | −3.74336e91 | −1.50427 | −0.752133 | − | 0.659011i | \(-0.770975\pi\) | ||||
−0.752133 | + | 0.659011i | \(0.770975\pi\) | |||||||
\(798\) | −3.20637e90 | −0.123858 | ||||||||
\(799\) | −5.58528e90 | −0.207406 | ||||||||
\(800\) | 2.63771e91 | 0.941655 | ||||||||
\(801\) | −7.93894e90 | −0.272482 | ||||||||
\(802\) | −4.07259e91 | −1.34394 | ||||||||
\(803\) | 1.09310e91 | 0.346834 | ||||||||
\(804\) | −6.01446e90 | −0.183498 | ||||||||
\(805\) | 3.08902e91 | 0.906256 | ||||||||
\(806\) | −1.26748e91 | −0.357592 | ||||||||
\(807\) | 3.82714e91 | 1.03839 | ||||||||
\(808\) | −1.70547e90 | −0.0445027 | ||||||||
\(809\) | −4.60359e91 | −1.15536 | −0.577682 | − | 0.816262i | \(-0.696042\pi\) | ||||
−0.577682 | + | 0.816262i | \(0.696042\pi\) | |||||||
\(810\) | 4.64274e91 | 1.12072 | ||||||||
\(811\) | 6.97054e91 | 1.61849 | 0.809244 | − | 0.587473i | \(-0.199877\pi\) | ||||
0.809244 | + | 0.587473i | \(0.199877\pi\) | |||||||
\(812\) | −9.44896e90 | −0.211042 | ||||||||
\(813\) | −3.93723e91 | −0.845937 | ||||||||
\(814\) | −2.39091e91 | −0.494190 | ||||||||
\(815\) | 5.08157e91 | 1.01049 | ||||||||
\(816\) | −2.58200e91 | −0.493987 | ||||||||
\(817\) | −2.61687e91 | −0.481712 | ||||||||
\(818\) | 5.71831e91 | 1.01283 | ||||||||
\(819\) | −2.18631e90 | −0.0372622 | ||||||||
\(820\) | 3.97597e91 | 0.652089 | ||||||||
\(821\) | 2.40187e90 | 0.0379088 | 0.0189544 | − | 0.999820i | \(-0.493966\pi\) | ||||
0.0189544 | + | 0.999820i | \(0.493966\pi\) | |||||||
\(822\) | 8.63713e91 | 1.31192 | ||||||||
\(823\) | −1.25656e92 | −1.83691 | −0.918456 | − | 0.395523i | \(-0.870563\pi\) | ||||
−0.918456 | + | 0.395523i | \(0.870563\pi\) | |||||||
\(824\) | −5.74660e91 | −0.808545 | ||||||||
\(825\) | −1.55241e92 | −2.10236 | ||||||||
\(826\) | 8.77975e90 | 0.114449 | ||||||||
\(827\) | 1.21276e92 | 1.52178 | 0.760891 | − | 0.648880i | \(-0.224762\pi\) | ||||
0.760891 | + | 0.648880i | \(0.224762\pi\) | |||||||
\(828\) | −5.52451e90 | −0.0667326 | ||||||||
\(829\) | −6.65548e91 | −0.773948 | −0.386974 | − | 0.922091i | \(-0.626480\pi\) | ||||
−0.386974 | + | 0.922091i | \(0.626480\pi\) | |||||||
\(830\) | 4.76606e91 | 0.533580 | ||||||||
\(831\) | −8.81423e90 | −0.0950062 | ||||||||
\(832\) | 6.71854e91 | 0.697253 | ||||||||
\(833\) | 7.48908e91 | 0.748360 | ||||||||
\(834\) | −7.40703e91 | −0.712711 | ||||||||
\(835\) | −5.02520e91 | −0.465617 | ||||||||
\(836\) | −1.96007e91 | −0.174893 | ||||||||
\(837\) | −8.26970e91 | −0.710621 | ||||||||
\(838\) | 2.86231e91 | 0.236881 | ||||||||
\(839\) | −1.35743e92 | −1.08197 | −0.540984 | − | 0.841033i | \(-0.681948\pi\) | ||||
−0.540984 | + | 0.841033i | \(0.681948\pi\) | |||||||
\(840\) | −8.08583e91 | −0.620764 | ||||||||
\(841\) | 3.29299e92 | 2.43510 | ||||||||
\(842\) | −2.26271e91 | −0.161175 | ||||||||
\(843\) | 1.01126e92 | 0.693895 | ||||||||
\(844\) | 4.69664e90 | 0.0310456 | ||||||||
\(845\) | 1.51460e92 | 0.964523 | ||||||||
\(846\) | −4.94980e90 | −0.0303683 | ||||||||
\(847\) | 6.07683e91 | 0.359211 | ||||||||
\(848\) | 3.07863e91 | 0.175343 | ||||||||
\(849\) | 1.42735e92 | 0.783321 | ||||||||
\(850\) | −2.27554e92 | −1.20334 | ||||||||
\(851\) | 1.21414e92 | 0.618711 | ||||||||
\(852\) | 6.24101e91 | 0.306484 | ||||||||
\(853\) | −3.81968e92 | −1.80773 | −0.903864 | − | 0.427821i | \(-0.859281\pi\) | ||||
−0.903864 | + | 0.427821i | \(0.859281\pi\) | |||||||
\(854\) | 6.97335e91 | 0.318067 | ||||||||
\(855\) | 2.38177e91 | 0.104705 | ||||||||
\(856\) | −3.76356e92 | −1.59469 | ||||||||
\(857\) | 1.69651e92 | 0.692883 | 0.346441 | − | 0.938072i | \(-0.387390\pi\) | ||||
0.346441 | + | 0.938072i | \(0.387390\pi\) | |||||||
\(858\) | −1.73901e92 | −0.684626 | ||||||||
\(859\) | −2.92816e92 | −1.11125 | −0.555623 | − | 0.831434i | \(-0.687520\pi\) | ||||
−0.555623 | + | 0.831434i | \(0.687520\pi\) | |||||||
\(860\) | −1.51616e92 | −0.554681 | ||||||||
\(861\) | −1.34028e92 | −0.472711 | ||||||||
\(862\) | 3.96171e92 | 1.34711 | ||||||||
\(863\) | −1.14708e92 | −0.376058 | −0.188029 | − | 0.982163i | \(-0.560210\pi\) | ||||
−0.188029 | + | 0.982163i | \(0.560210\pi\) | |||||||
\(864\) | 1.92785e92 | 0.609382 | ||||||||
\(865\) | 4.03404e92 | 1.22951 | ||||||||
\(866\) | −4.10555e92 | −1.20658 | ||||||||
\(867\) | 7.55222e91 | 0.214029 | ||||||||
\(868\) | 2.79012e91 | 0.0762522 | ||||||||
\(869\) | 7.73242e91 | 0.203795 | ||||||||
\(870\) | 9.13281e92 | 2.32139 | ||||||||
\(871\) | −1.73830e92 | −0.426142 | ||||||||
\(872\) | 3.62258e92 | 0.856542 | ||||||||
\(873\) | −3.75256e91 | −0.0855813 | ||||||||
\(874\) | −2.34167e92 | −0.515129 | ||||||||
\(875\) | −1.87006e92 | −0.396828 | ||||||||
\(876\) | 3.33827e91 | 0.0683349 | ||||||||
\(877\) | 3.77068e92 | 0.744615 | 0.372308 | − | 0.928109i | \(-0.378567\pi\) | ||||
0.372308 | + | 0.928109i | \(0.378567\pi\) | |||||||
\(878\) | −6.13841e92 | −1.16944 | ||||||||
\(879\) | −7.18910e92 | −1.32137 | ||||||||
\(880\) | 7.82138e92 | 1.38701 | ||||||||
\(881\) | −7.07985e92 | −1.21139 | −0.605694 | − | 0.795698i | \(-0.707104\pi\) | ||||
−0.605694 | + | 0.795698i | \(0.707104\pi\) | |||||||
\(882\) | 6.63699e91 | 0.109575 | ||||||||
\(883\) | −1.04734e92 | −0.166850 | −0.0834251 | − | 0.996514i | \(-0.526586\pi\) | ||||
−0.0834251 | + | 0.996514i | \(0.526586\pi\) | |||||||
\(884\) | 1.08351e92 | 0.166567 | ||||||||
\(885\) | 3.60707e92 | 0.535108 | ||||||||
\(886\) | 2.65941e92 | 0.380735 | ||||||||
\(887\) | 7.01851e92 | 0.969730 | 0.484865 | − | 0.874589i | \(-0.338869\pi\) | ||||
0.484865 | + | 0.874589i | \(0.338869\pi\) | |||||||
\(888\) | −3.17813e92 | −0.423803 | ||||||||
\(889\) | 3.72930e92 | 0.479978 | ||||||||
\(890\) | −1.94965e93 | −2.42198 | ||||||||
\(891\) | −9.56717e92 | −1.14719 | ||||||||
\(892\) | 4.24757e92 | 0.491640 | ||||||||
\(893\) | 8.91809e91 | 0.0996439 | ||||||||
\(894\) | −3.63704e92 | −0.392299 | ||||||||
\(895\) | 1.21110e92 | 0.126112 | ||||||||
\(896\) | 1.29875e92 | 0.130564 | ||||||||
\(897\) | 8.83099e92 | 0.857132 | ||||||||
\(898\) | 1.26340e93 | 1.18395 | ||||||||
\(899\) | −1.37168e93 | −1.24114 | ||||||||
\(900\) | 8.57196e91 | 0.0748930 | ||||||||
\(901\) | 2.97132e92 | 0.250680 | ||||||||
\(902\) | 1.92753e93 | 1.57034 | ||||||||
\(903\) | 5.11089e92 | 0.402098 | ||||||||
\(904\) | −7.31468e92 | −0.555763 | ||||||||
\(905\) | 7.43410e92 | 0.545504 | ||||||||
\(906\) | −2.77239e92 | −0.196479 | ||||||||
\(907\) | −1.65121e93 | −1.13024 | −0.565122 | − | 0.825007i | \(-0.691171\pi\) | ||||
−0.565122 | + | 0.825007i | \(0.691171\pi\) | |||||||
\(908\) | −7.95690e91 | −0.0526065 | ||||||||
\(909\) | −9.81145e90 | −0.00626572 | ||||||||
\(910\) | −5.36914e92 | −0.331208 | ||||||||
\(911\) | 2.13707e93 | 1.27347 | 0.636735 | − | 0.771082i | \(-0.280284\pi\) | ||||
0.636735 | + | 0.771082i | \(0.280284\pi\) | |||||||
\(912\) | 4.12271e92 | 0.237326 | ||||||||
\(913\) | −9.82130e92 | −0.546185 | ||||||||
\(914\) | −3.00286e92 | −0.161336 | ||||||||
\(915\) | 2.86493e93 | 1.48713 | ||||||||
\(916\) | −1.01098e93 | −0.507034 | ||||||||
\(917\) | 3.47545e90 | 0.00168413 | ||||||||
\(918\) | −1.66315e93 | −0.778730 | ||||||||
\(919\) | −2.31977e93 | −1.04956 | −0.524779 | − | 0.851238i | \(-0.675852\pi\) | ||||
−0.524779 | + | 0.851238i | \(0.675852\pi\) | |||||||
\(920\) | −5.90522e93 | −2.58178 | ||||||||
\(921\) | −1.14502e92 | −0.0483767 | ||||||||
\(922\) | 1.89115e93 | 0.772152 | ||||||||
\(923\) | 1.80378e93 | 0.711755 | ||||||||
\(924\) | 3.82812e92 | 0.145988 | ||||||||
\(925\) | −1.88389e93 | −0.694370 | ||||||||
\(926\) | 2.28017e93 | 0.812309 | ||||||||
\(927\) | −3.30598e92 | −0.113838 | ||||||||
\(928\) | 3.19768e93 | 1.06432 | ||||||||
\(929\) | 7.42194e92 | 0.238794 | 0.119397 | − | 0.992847i | \(-0.461904\pi\) | ||||
0.119397 | + | 0.992847i | \(0.461904\pi\) | |||||||
\(930\) | −2.69677e93 | −0.838747 | ||||||||
\(931\) | −1.19579e93 | −0.359534 | ||||||||
\(932\) | 5.08003e92 | 0.147661 | ||||||||
\(933\) | 1.08053e93 | 0.303643 | ||||||||
\(934\) | 5.30760e93 | 1.44202 | ||||||||
\(935\) | 7.54877e93 | 1.98294 | ||||||||
\(936\) | 4.17952e92 | 0.106154 | ||||||||
\(937\) | −3.23775e93 | −0.795144 | −0.397572 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397572 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(938\) | −9.00235e92 | −0.213780 | ||||||||
\(939\) | −4.14727e93 | −0.952348 | ||||||||
\(940\) | 5.16694e92 | 0.114738 | ||||||||
\(941\) | 8.51382e93 | 1.82832 | 0.914158 | − | 0.405357i | \(-0.132853\pi\) | ||||
0.914158 | + | 0.405357i | \(0.132853\pi\) | |||||||
\(942\) | −4.71680e90 | −0.000979589 0 | ||||||||
\(943\) | −9.78830e93 | −1.96602 | ||||||||
\(944\) | −1.12889e93 | −0.219297 | ||||||||
\(945\) | −3.50311e93 | −0.658190 | ||||||||
\(946\) | −7.35024e93 | −1.33577 | ||||||||
\(947\) | −6.01031e93 | −1.05651 | −0.528254 | − | 0.849087i | \(-0.677153\pi\) | ||||
−0.528254 | + | 0.849087i | \(0.677153\pi\) | |||||||
\(948\) | 2.36144e92 | 0.0401526 | ||||||||
\(949\) | 9.64831e92 | 0.158696 | ||||||||
\(950\) | 3.63339e93 | 0.578121 | ||||||||
\(951\) | 3.42031e93 | 0.526477 | ||||||||
\(952\) | 2.44238e93 | 0.363705 | ||||||||
\(953\) | 2.35944e93 | 0.339924 | 0.169962 | − | 0.985451i | \(-0.445636\pi\) | ||||
0.169962 | + | 0.985451i | \(0.445636\pi\) | |||||||
\(954\) | 2.63325e92 | 0.0367045 | ||||||||
\(955\) | 1.29425e94 | 1.74547 | ||||||||
\(956\) | −2.59035e93 | −0.338015 | ||||||||
\(957\) | −1.88197e94 | −2.37623 | ||||||||
\(958\) | 7.18587e93 | 0.877942 | ||||||||
\(959\) | −5.49517e93 | −0.649673 | ||||||||
\(960\) | 1.42948e94 | 1.63544 | ||||||||
\(961\) | −4.98172e93 | −0.551560 | ||||||||
\(962\) | −2.11034e93 | −0.226119 | ||||||||
\(963\) | −2.16515e93 | −0.224523 | ||||||||
\(964\) | −3.83058e92 | −0.0384448 | ||||||||
\(965\) | −4.27270e92 | −0.0415042 | ||||||||
\(966\) | 4.57341e93 | 0.429992 | ||||||||
\(967\) | 1.61123e94 | 1.46630 | 0.733150 | − | 0.680067i | \(-0.238049\pi\) | ||||
0.733150 | + | 0.680067i | \(0.238049\pi\) | |||||||
\(968\) | −1.16170e94 | −1.02334 | ||||||||
\(969\) | 3.97901e93 | 0.339294 | ||||||||
\(970\) | −9.21555e93 | −0.760697 | ||||||||
\(971\) | 2.23086e94 | 1.78265 | 0.891326 | − | 0.453363i | \(-0.149776\pi\) | ||||
0.891326 | + | 0.453363i | \(0.149776\pi\) | |||||||
\(972\) | 1.16982e93 | 0.0904966 | ||||||||
\(973\) | 4.71255e93 | 0.352940 | ||||||||
\(974\) | −3.56464e93 | −0.258469 | ||||||||
\(975\) | −1.37024e94 | −0.961945 | ||||||||
\(976\) | −8.96624e93 | −0.609454 | ||||||||
\(977\) | −2.74680e94 | −1.80779 | −0.903895 | − | 0.427755i | \(-0.859305\pi\) | ||||
−0.903895 | + | 0.427755i | \(0.859305\pi\) | |||||||
\(978\) | 7.52345e93 | 0.479450 | ||||||||
\(979\) | 4.01759e94 | 2.47920 | ||||||||
\(980\) | −6.92815e93 | −0.413996 | ||||||||
\(981\) | 2.08404e93 | 0.120596 | ||||||||
\(982\) | −2.42521e94 | −1.35905 | ||||||||
\(983\) | −3.40980e93 | −0.185052 | −0.0925259 | − | 0.995710i | \(-0.529494\pi\) | ||||
−0.0925259 | + | 0.995710i | \(0.529494\pi\) | |||||||
\(984\) | 2.56218e94 | 1.34668 | ||||||||
\(985\) | −5.36814e94 | −2.73264 | ||||||||
\(986\) | −2.75863e94 | −1.36010 | ||||||||
\(987\) | −1.74175e93 | −0.0831755 | ||||||||
\(988\) | −1.73006e93 | −0.0800235 | ||||||||
\(989\) | 3.73257e94 | 1.67234 | ||||||||
\(990\) | 6.68989e93 | 0.290342 | ||||||||
\(991\) | 1.50057e94 | 0.630865 | 0.315432 | − | 0.948948i | \(-0.397850\pi\) | ||||
0.315432 | + | 0.948948i | \(0.397850\pi\) | |||||||
\(992\) | −9.44221e93 | −0.384553 | ||||||||
\(993\) | 4.36514e94 | 1.72225 | ||||||||
\(994\) | 9.34145e93 | 0.357062 | ||||||||
\(995\) | −1.36489e93 | −0.0505440 | ||||||||
\(996\) | −2.99937e93 | −0.107612 | ||||||||
\(997\) | −3.28573e93 | −0.114218 | −0.0571090 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571090 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(998\) | 2.37408e93 | 0.0799620 | ||||||||
\(999\) | −1.37690e94 | −0.449354 |
(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 | 1.64.a.a.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 9.64.a.c.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.64.a.a.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.64.a.c.1.2 | 5 | 3.2 | odd | 2 |