Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,88,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 88, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 88);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 88 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(95.8667262922\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11473904362186221800312196301729x - 156905659743614387346100645850205598702591560 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{9}\cdot 5^{3}\cdot 7\cdot 11\cdot 29 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.38046e15\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.79609e12 | 0.707107 | ||||||||
\(3\) | 1.94339e18 | 0.00341810 | 0.00170905 | − | 0.999999i | \(-0.499456\pi\) | ||||
0.00170905 | + | 0.999999i | \(0.499456\pi\) | |||||||
\(4\) | 7.73713e25 | 0.500000 | ||||||||
\(5\) | −1.48628e30 | −0.584665 | −0.292332 | − | 0.956317i | \(-0.594431\pi\) | ||||
−0.292332 | + | 0.956317i | \(0.594431\pi\) | |||||||
\(6\) | 1.70942e31 | 0.00241696 | ||||||||
\(7\) | 3.06439e35 | 0.0530370 | 0.0265185 | − | 0.999648i | \(-0.491558\pi\) | ||||
0.0265185 | + | 0.999648i | \(0.491558\pi\) | |||||||
\(8\) | 6.80565e38 | 0.353553 | ||||||||
\(9\) | −3.23254e41 | −0.999988 | ||||||||
\(10\) | −1.30735e43 | −0.413420 | ||||||||
\(11\) | 3.31652e45 | 1.65997 | 0.829986 | − | 0.557785i | \(-0.188348\pi\) | ||||
0.829986 | + | 0.557785i | \(0.188348\pi\) | |||||||
\(12\) | 1.50363e44 | 0.00170905 | ||||||||
\(13\) | −2.23868e48 | −0.782448 | −0.391224 | − | 0.920296i | \(-0.627948\pi\) | ||||
−0.391224 | + | 0.920296i | \(0.627948\pi\) | |||||||
\(14\) | 2.69547e48 | 0.0375028 | ||||||||
\(15\) | −2.88843e48 | −0.00199844 | ||||||||
\(16\) | 5.98631e51 | 0.250000 | ||||||||
\(17\) | 5.17291e52 | 0.154599 | 0.0772996 | − | 0.997008i | \(-0.475370\pi\) | ||||
0.0772996 | + | 0.997008i | \(0.475370\pi\) | |||||||
\(18\) | −2.84337e54 | −0.707099 | ||||||||
\(19\) | 5.90527e55 | 1.39784 | 0.698920 | − | 0.715199i | \(-0.253664\pi\) | ||||
0.698920 | + | 0.715199i | \(0.253664\pi\) | |||||||
\(20\) | −1.14996e56 | −0.292332 | ||||||||
\(21\) | 5.95530e53 | 0.000181286 0 | ||||||||
\(22\) | 2.91724e58 | 1.17378 | ||||||||
\(23\) | −1.78385e59 | −1.03800 | −0.519001 | − | 0.854773i | \(-0.673696\pi\) | ||||
−0.519001 | + | 0.854773i | \(0.673696\pi\) | |||||||
\(24\) | 1.32260e57 | 0.00120848 | ||||||||
\(25\) | −4.25331e60 | −0.658167 | ||||||||
\(26\) | −1.96916e61 | −0.553274 | ||||||||
\(27\) | −1.25642e60 | −0.00683617 | ||||||||
\(28\) | 2.37096e61 | 0.0265185 | ||||||||
\(29\) | 7.16217e62 | 0.174073 | 0.0870365 | − | 0.996205i | \(-0.472260\pi\) | ||||
0.0870365 | + | 0.996205i | \(0.472260\pi\) | |||||||
\(30\) | −2.54069e61 | −0.00141311 | ||||||||
\(31\) | 3.20860e63 | 0.0428630 | 0.0214315 | − | 0.999770i | \(-0.493178\pi\) | ||||
0.0214315 | + | 0.999770i | \(0.493178\pi\) | |||||||
\(32\) | 5.26561e64 | 0.176777 | ||||||||
\(33\) | 6.44529e63 | 0.00567396 | ||||||||
\(34\) | 4.55014e65 | 0.109318 | ||||||||
\(35\) | −4.55455e65 | −0.0310089 | ||||||||
\(36\) | −2.50106e67 | −0.499994 | ||||||||
\(37\) | −7.99266e67 | −0.485195 | −0.242598 | − | 0.970127i | \(-0.577999\pi\) | ||||
−0.242598 | + | 0.970127i | \(0.577999\pi\) | |||||||
\(38\) | 5.19433e68 | 0.988423 | ||||||||
\(39\) | −4.35062e66 | −0.00267449 | ||||||||
\(40\) | −1.01151e69 | −0.206710 | ||||||||
\(41\) | 2.83063e69 | 0.197599 | 0.0987996 | − | 0.995107i | \(-0.468500\pi\) | ||||
0.0987996 | + | 0.995107i | \(0.468500\pi\) | |||||||
\(42\) | 5.23834e66 | 0.000128189 0 | ||||||||
\(43\) | −1.74847e71 | −1.53738 | −0.768689 | − | 0.639623i | \(-0.779090\pi\) | ||||
−0.768689 | + | 0.639623i | \(0.779090\pi\) | |||||||
\(44\) | 2.56603e71 | 0.829986 | ||||||||
\(45\) | 4.80448e71 | 0.584658 | ||||||||
\(46\) | −1.56909e72 | −0.733979 | ||||||||
\(47\) | −1.86943e72 | −0.343125 | −0.171563 | − | 0.985173i | \(-0.554882\pi\) | ||||
−0.171563 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(48\) | 1.16337e70 | 0.000854526 0 | ||||||||
\(49\) | −3.32894e73 | −0.997187 | ||||||||
\(50\) | −3.74125e73 | −0.465395 | ||||||||
\(51\) | 1.00530e71 | 0.000528436 0 | ||||||||
\(52\) | −1.73209e74 | −0.391224 | ||||||||
\(53\) | −7.26699e74 | −0.716728 | −0.358364 | − | 0.933582i | \(-0.616665\pi\) | ||||
−0.358364 | + | 0.933582i | \(0.616665\pi\) | |||||||
\(54\) | −1.10516e73 | −0.00483390 | ||||||||
\(55\) | −4.92929e75 | −0.970527 | ||||||||
\(56\) | 2.08552e74 | 0.0187514 | ||||||||
\(57\) | 1.14762e74 | 0.00477797 | ||||||||
\(58\) | 6.29991e75 | 0.123088 | ||||||||
\(59\) | −1.25975e76 | −0.117010 | −0.0585050 | − | 0.998287i | \(-0.518633\pi\) | ||||
−0.0585050 | + | 0.998287i | \(0.518633\pi\) | |||||||
\(60\) | −2.23481e74 | −0.000999222 0 | ||||||||
\(61\) | 6.16865e77 | 1.34382 | 0.671912 | − | 0.740631i | \(-0.265473\pi\) | ||||
0.671912 | + | 0.740631i | \(0.265473\pi\) | |||||||
\(62\) | 2.82232e76 | 0.0303087 | ||||||||
\(63\) | −9.90576e76 | −0.0530364 | ||||||||
\(64\) | 4.63168e77 | 0.125000 | ||||||||
\(65\) | 3.32731e78 | 0.457469 | ||||||||
\(66\) | 5.66934e76 | 0.00401209 | ||||||||
\(67\) | −1.22223e79 | −0.449676 | −0.224838 | − | 0.974396i | \(-0.572185\pi\) | ||||
−0.224838 | + | 0.974396i | \(0.572185\pi\) | |||||||
\(68\) | 4.00235e78 | 0.0772996 | ||||||||
\(69\) | −3.46672e77 | −0.00354800 | ||||||||
\(70\) | −4.00623e78 | −0.0219266 | ||||||||
\(71\) | −5.46609e80 | −1.61413 | −0.807065 | − | 0.590463i | \(-0.798945\pi\) | ||||
−0.807065 | + | 0.590463i | \(0.798945\pi\) | |||||||
\(72\) | −2.19995e80 | −0.353549 | ||||||||
\(73\) | 1.44460e81 | 1.27410 | 0.637051 | − | 0.770821i | \(-0.280154\pi\) | ||||
0.637051 | + | 0.770821i | \(0.280154\pi\) | |||||||
\(74\) | −7.03042e80 | −0.343085 | ||||||||
\(75\) | −8.26583e78 | −0.00224968 | ||||||||
\(76\) | 4.56898e81 | 0.698920 | ||||||||
\(77\) | 1.01631e81 | 0.0880400 | ||||||||
\(78\) | −3.82685e79 | −0.00189115 | ||||||||
\(79\) | −6.33613e81 | −0.179906 | −0.0899530 | − | 0.995946i | \(-0.528672\pi\) | ||||
−0.0899530 | + | 0.995946i | \(0.528672\pi\) | |||||||
\(80\) | −8.89736e81 | −0.146166 | ||||||||
\(81\) | 1.04492e83 | 0.999965 | ||||||||
\(82\) | 2.48985e82 | 0.139724 | ||||||||
\(83\) | −4.56399e83 | −1.51164 | −0.755820 | − | 0.654780i | \(-0.772761\pi\) | ||||
−0.755820 | + | 0.654780i | \(0.772761\pi\) | |||||||
\(84\) | 4.60769e79 | 9.06430e−5 0 | ||||||||
\(85\) | −7.68842e82 | −0.0903886 | ||||||||
\(86\) | −1.53797e84 | −1.08709 | ||||||||
\(87\) | 1.39189e81 | 0.000595000 0 | ||||||||
\(88\) | 2.25711e84 | 0.586889 | ||||||||
\(89\) | −3.23071e84 | −0.513845 | −0.256923 | − | 0.966432i | \(-0.582709\pi\) | ||||
−0.256923 | + | 0.966432i | \(0.582709\pi\) | |||||||
\(90\) | 4.22606e84 | 0.413415 | ||||||||
\(91\) | −6.86017e83 | −0.0414987 | ||||||||
\(92\) | −1.38019e85 | −0.519001 | ||||||||
\(93\) | 6.23557e81 | 0.000146510 0 | ||||||||
\(94\) | −1.64437e85 | −0.242626 | ||||||||
\(95\) | −8.77690e85 | −0.817268 | ||||||||
\(96\) | 1.02331e83 | 0.000604241 0 | ||||||||
\(97\) | −1.98116e86 | −0.745331 | −0.372665 | − | 0.927966i | \(-0.621556\pi\) | ||||
−0.372665 | + | 0.927966i | \(0.621556\pi\) | |||||||
\(98\) | −2.92817e86 | −0.705118 | ||||||||
\(99\) | −1.07208e87 | −1.65995 | ||||||||
\(100\) | −3.29084e86 | −0.329084 | ||||||||
\(101\) | −8.39486e86 | −0.544545 | −0.272272 | − | 0.962220i | \(-0.587775\pi\) | ||||
−0.272272 | + | 0.962220i | \(0.587775\pi\) | |||||||
\(102\) | 8.84270e83 | 0.000373661 0 | ||||||||
\(103\) | −5.87568e87 | −1.62420 | −0.812098 | − | 0.583520i | \(-0.801675\pi\) | ||||
−0.812098 | + | 0.583520i | \(0.801675\pi\) | |||||||
\(104\) | −1.52356e87 | −0.276637 | ||||||||
\(105\) | −8.85127e83 | −0.000105992 0 | ||||||||
\(106\) | −6.39211e87 | −0.506803 | ||||||||
\(107\) | −7.14100e87 | −0.376326 | −0.188163 | − | 0.982138i | \(-0.560253\pi\) | ||||
−0.188163 | + | 0.982138i | \(0.560253\pi\) | |||||||
\(108\) | −9.72112e85 | −0.00341808 | ||||||||
\(109\) | −6.97198e88 | −1.64174 | −0.820869 | − | 0.571117i | \(-0.806510\pi\) | ||||
−0.820869 | + | 0.571117i | \(0.806510\pi\) | |||||||
\(110\) | −4.33585e88 | −0.686266 | ||||||||
\(111\) | −1.55329e86 | −0.00165845 | ||||||||
\(112\) | 1.83444e87 | 0.0132593 | ||||||||
\(113\) | −3.90703e89 | −1.91838 | −0.959188 | − | 0.282768i | \(-0.908747\pi\) | ||||
−0.959188 | + | 0.282768i | \(0.908747\pi\) | |||||||
\(114\) | 1.00946e87 | 0.00337853 | ||||||||
\(115\) | 2.65131e89 | 0.606883 | ||||||||
\(116\) | 5.54146e88 | 0.0870365 | ||||||||
\(117\) | 7.23661e89 | 0.782439 | ||||||||
\(118\) | −1.10809e89 | −0.0827385 | ||||||||
\(119\) | 1.58518e88 | 0.00819948 | ||||||||
\(120\) | −1.96576e87 | −0.000706557 0 | ||||||||
\(121\) | 7.00754e90 | 1.75551 | ||||||||
\(122\) | 5.42600e90 | 0.950227 | ||||||||
\(123\) | 5.50102e87 | 0.000675415 0 | ||||||||
\(124\) | 2.48254e89 | 0.0214315 | ||||||||
\(125\) | 1.59265e91 | 0.969472 | ||||||||
\(126\) | −8.71320e89 | −0.0375024 | ||||||||
\(127\) | −2.77596e90 | −0.0847132 | −0.0423566 | − | 0.999103i | \(-0.513487\pi\) | ||||
−0.0423566 | + | 0.999103i | \(0.513487\pi\) | |||||||
\(128\) | 4.07407e90 | 0.0883883 | ||||||||
\(129\) | −3.39796e89 | −0.00525492 | ||||||||
\(130\) | 2.92673e91 | 0.323480 | ||||||||
\(131\) | 1.41138e92 | 1.11774 | 0.558870 | − | 0.829255i | \(-0.311235\pi\) | ||||
0.558870 | + | 0.829255i | \(0.311235\pi\) | |||||||
\(132\) | 4.98680e89 | 0.00283698 | ||||||||
\(133\) | 1.80960e91 | 0.0741373 | ||||||||
\(134\) | −1.07509e92 | −0.317969 | ||||||||
\(135\) | 1.86740e90 | 0.00399687 | ||||||||
\(136\) | 3.52050e91 | 0.0546590 | ||||||||
\(137\) | −1.38903e93 | −1.56808 | −0.784038 | − | 0.620713i | \(-0.786843\pi\) | ||||
−0.784038 | + | 0.620713i | \(0.786843\pi\) | |||||||
\(138\) | −3.04936e90 | −0.00250882 | ||||||||
\(139\) | −1.25618e93 | −0.754933 | −0.377466 | − | 0.926023i | \(-0.623205\pi\) | ||||
−0.377466 | + | 0.926023i | \(0.623205\pi\) | |||||||
\(140\) | −3.52392e91 | −0.0155044 | ||||||||
\(141\) | −3.63303e90 | −0.00117284 | ||||||||
\(142\) | −4.80802e93 | −1.14136 | ||||||||
\(143\) | −7.42461e93 | −1.29884 | ||||||||
\(144\) | −1.93510e93 | −0.249997 | ||||||||
\(145\) | −1.06450e93 | −0.101774 | ||||||||
\(146\) | 1.27069e94 | 0.900926 | ||||||||
\(147\) | −6.46943e91 | −0.00340849 | ||||||||
\(148\) | −6.18402e93 | −0.242598 | ||||||||
\(149\) | 3.42541e94 | 1.00256 | 0.501280 | − | 0.865285i | \(-0.332863\pi\) | ||||
0.501280 | + | 0.865285i | \(0.332863\pi\) | |||||||
\(150\) | −7.27070e91 | −0.00159077 | ||||||||
\(151\) | 5.08705e94 | 0.833622 | 0.416811 | − | 0.908993i | \(-0.363148\pi\) | ||||
0.416811 | + | 0.908993i | \(0.363148\pi\) | |||||||
\(152\) | 4.01892e94 | 0.494211 | ||||||||
\(153\) | −1.67217e94 | −0.154597 | ||||||||
\(154\) | 8.93956e93 | 0.0622537 | ||||||||
\(155\) | −4.76890e93 | −0.0250605 | ||||||||
\(156\) | −3.36613e92 | −0.00133724 | ||||||||
\(157\) | 4.78956e95 | 1.44099 | 0.720495 | − | 0.693460i | \(-0.243915\pi\) | ||||
0.720495 | + | 0.693460i | \(0.243915\pi\) | |||||||
\(158\) | −5.57332e94 | −0.127213 | ||||||||
\(159\) | −1.41226e93 | −0.00244985 | ||||||||
\(160\) | −7.82620e94 | −0.103355 | ||||||||
\(161\) | −5.46642e94 | −0.0550526 | ||||||||
\(162\) | 9.19121e95 | 0.707082 | ||||||||
\(163\) | −1.20910e95 | −0.0711710 | −0.0355855 | − | 0.999367i | \(-0.511330\pi\) | ||||
−0.0355855 | + | 0.999367i | \(0.511330\pi\) | |||||||
\(164\) | 2.19009e95 | 0.0987996 | ||||||||
\(165\) | −9.57953e93 | −0.00331736 | ||||||||
\(166\) | −4.01453e96 | −1.06889 | ||||||||
\(167\) | −2.77875e96 | −0.569749 | −0.284875 | − | 0.958565i | \(-0.591952\pi\) | ||||
−0.284875 | + | 0.958565i | \(0.591952\pi\) | |||||||
\(168\) | 4.05297e92 | 6.40943e−5 0 | ||||||||
\(169\) | −3.17433e96 | −0.387776 | ||||||||
\(170\) | −6.76280e95 | −0.0639144 | ||||||||
\(171\) | −1.90890e97 | −1.39782 | ||||||||
\(172\) | −1.35281e97 | −0.768689 | ||||||||
\(173\) | 5.66922e96 | 0.250333 | 0.125166 | − | 0.992136i | \(-0.460053\pi\) | ||||
0.125166 | + | 0.992136i | \(0.460053\pi\) | |||||||
\(174\) | 1.22432e94 | 0.000420728 0 | ||||||||
\(175\) | −1.30338e96 | −0.0349072 | ||||||||
\(176\) | 1.98537e97 | 0.414993 | ||||||||
\(177\) | −2.44819e94 | −0.000399952 0 | ||||||||
\(178\) | −2.84176e97 | −0.363343 | ||||||||
\(179\) | 1.18026e98 | 1.18269 | 0.591345 | − | 0.806419i | \(-0.298597\pi\) | ||||
0.591345 | + | 0.806419i | \(0.298597\pi\) | |||||||
\(180\) | 3.71728e97 | 0.292329 | ||||||||
\(181\) | 2.82565e98 | 1.74623 | 0.873113 | − | 0.487518i | \(-0.162098\pi\) | ||||
0.873113 | + | 0.487518i | \(0.162098\pi\) | |||||||
\(182\) | −6.03427e96 | −0.0293440 | ||||||||
\(183\) | 1.19881e96 | 0.00459333 | ||||||||
\(184\) | −1.21403e98 | −0.366989 | ||||||||
\(185\) | 1.18794e98 | 0.283676 | ||||||||
\(186\) | 5.48486e94 | 0.000103598 0 | ||||||||
\(187\) | 1.71561e98 | 0.256630 | ||||||||
\(188\) | −1.44640e98 | −0.171563 | ||||||||
\(189\) | −3.85017e95 | −0.000362570 0 | ||||||||
\(190\) | −7.72025e98 | −0.577896 | ||||||||
\(191\) | 1.84740e99 | 1.10055 | 0.550276 | − | 0.834983i | \(-0.314523\pi\) | ||||
0.550276 | + | 0.834983i | \(0.314523\pi\) | |||||||
\(192\) | 9.00117e95 | 0.000427263 0 | ||||||||
\(193\) | −2.04418e99 | −0.774064 | −0.387032 | − | 0.922066i | \(-0.626500\pi\) | ||||
−0.387032 | + | 0.922066i | \(0.626500\pi\) | |||||||
\(194\) | −1.74265e99 | −0.527028 | ||||||||
\(195\) | 6.46626e96 | 0.00156368 | ||||||||
\(196\) | −2.57564e99 | −0.498594 | ||||||||
\(197\) | 2.67935e99 | 0.415670 | 0.207835 | − | 0.978164i | \(-0.433358\pi\) | ||||
0.207835 | + | 0.978164i | \(0.433358\pi\) | |||||||
\(198\) | −9.43010e99 | −1.17376 | ||||||||
\(199\) | 3.20765e98 | 0.0320685 | 0.0160343 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160343 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(200\) | −2.89465e99 | −0.232697 | ||||||||
\(201\) | −2.37527e97 | −0.00153704 | ||||||||
\(202\) | −7.38419e99 | −0.385051 | ||||||||
\(203\) | 2.19477e98 | 0.00923232 | ||||||||
\(204\) | 7.77812e96 | 0.000264218 0 | ||||||||
\(205\) | −4.20712e99 | −0.115529 | ||||||||
\(206\) | −5.16830e100 | −1.14848 | ||||||||
\(207\) | 5.76638e100 | 1.03799 | ||||||||
\(208\) | −1.34014e100 | −0.195612 | ||||||||
\(209\) | 1.95849e101 | 2.32038 | ||||||||
\(210\) | −7.78566e96 | −7.49473e−5 0 | ||||||||
\(211\) | 1.81411e101 | 1.42029 | 0.710145 | − | 0.704056i | \(-0.248629\pi\) | ||||
0.710145 | + | 0.704056i | \(0.248629\pi\) | |||||||
\(212\) | −5.62256e100 | −0.358364 | ||||||||
\(213\) | −1.06227e99 | −0.00551726 | ||||||||
\(214\) | −6.28129e100 | −0.266103 | ||||||||
\(215\) | 2.59872e101 | 0.898850 | ||||||||
\(216\) | −8.55078e98 | −0.00241695 | ||||||||
\(217\) | 9.83241e98 | 0.00227332 | ||||||||
\(218\) | −6.13262e101 | −1.16088 | ||||||||
\(219\) | 2.80743e99 | 0.00435502 | ||||||||
\(220\) | −3.81385e101 | −0.485263 | ||||||||
\(221\) | −1.15805e101 | −0.120966 | ||||||||
\(222\) | −1.36628e99 | −0.00117270 | ||||||||
\(223\) | −1.07759e102 | −0.760663 | −0.380331 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380331 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(224\) | 1.61359e100 | 0.00937571 | ||||||||
\(225\) | 1.37490e102 | 0.658160 | ||||||||
\(226\) | −3.43666e102 | −1.35650 | ||||||||
\(227\) | −3.09841e102 | −1.00928 | −0.504642 | − | 0.863329i | \(-0.668376\pi\) | ||||
−0.504642 | + | 0.863329i | \(0.668376\pi\) | |||||||
\(228\) | 8.87930e99 | 0.00238898 | ||||||||
\(229\) | 4.98158e102 | 1.10796 | 0.553979 | − | 0.832530i | \(-0.313109\pi\) | ||||
0.553979 | + | 0.832530i | \(0.313109\pi\) | |||||||
\(230\) | 2.33212e102 | 0.429131 | ||||||||
\(231\) | 1.97509e99 | 0.000300930 0 | ||||||||
\(232\) | 4.87432e101 | 0.0615441 | ||||||||
\(233\) | −8.46223e102 | −0.886139 | −0.443070 | − | 0.896487i | \(-0.646111\pi\) | ||||
−0.443070 | + | 0.896487i | \(0.646111\pi\) | |||||||
\(234\) | 6.36539e102 | 0.553268 | ||||||||
\(235\) | 2.77851e102 | 0.200613 | ||||||||
\(236\) | −9.74686e101 | −0.0585050 | ||||||||
\(237\) | −1.23136e100 | −0.000614937 0 | ||||||||
\(238\) | 1.39434e101 | 0.00579791 | ||||||||
\(239\) | 4.32752e103 | 1.49945 | 0.749723 | − | 0.661752i | \(-0.230187\pi\) | ||||
0.749723 | + | 0.661752i | \(0.230187\pi\) | |||||||
\(240\) | −1.72910e100 | −0.000499611 0 | ||||||||
\(241\) | −4.24378e103 | −1.02332 | −0.511660 | − | 0.859188i | \(-0.670969\pi\) | ||||
−0.511660 | + | 0.859188i | \(0.670969\pi\) | |||||||
\(242\) | 6.16390e103 | 1.24133 | ||||||||
\(243\) | 6.09218e101 | 0.0102542 | ||||||||
\(244\) | 4.77276e103 | 0.671912 | ||||||||
\(245\) | 4.94775e103 | 0.583020 | ||||||||
\(246\) | 4.83875e100 | 0.000477591 0 | ||||||||
\(247\) | −1.32200e104 | −1.09374 | ||||||||
\(248\) | 2.18366e102 | 0.0151543 | ||||||||
\(249\) | −8.86962e101 | −0.00516694 | ||||||||
\(250\) | 1.40091e104 | 0.685520 | ||||||||
\(251\) | −3.77631e104 | −1.55332 | −0.776659 | − | 0.629921i | \(-0.783087\pi\) | ||||
−0.776659 | + | 0.629921i | \(0.783087\pi\) | |||||||
\(252\) | −7.66421e102 | −0.0265182 | ||||||||
\(253\) | −5.91619e104 | −1.72305 | ||||||||
\(254\) | −2.44176e103 | −0.0599013 | ||||||||
\(255\) | −1.49416e101 | −0.000308958 0 | ||||||||
\(256\) | 3.58359e103 | 0.0625000 | ||||||||
\(257\) | −2.83536e104 | −0.417366 | −0.208683 | − | 0.977983i | \(-0.566918\pi\) | ||||
−0.208683 | + | 0.977983i | \(0.566918\pi\) | |||||||
\(258\) | −2.98888e102 | −0.00371579 | ||||||||
\(259\) | −2.44926e103 | −0.0257333 | ||||||||
\(260\) | 2.57438e104 | 0.228735 | ||||||||
\(261\) | −2.31520e104 | −0.174071 | ||||||||
\(262\) | 1.24146e105 | 0.790362 | ||||||||
\(263\) | 1.67842e105 | 0.905367 | 0.452683 | − | 0.891671i | \(-0.350467\pi\) | ||||
0.452683 | + | 0.891671i | \(0.350467\pi\) | |||||||
\(264\) | 4.38644e102 | 0.00200605 | ||||||||
\(265\) | 1.08008e105 | 0.419045 | ||||||||
\(266\) | 1.59174e104 | 0.0524230 | ||||||||
\(267\) | −6.27852e102 | −0.00175638 | ||||||||
\(268\) | −9.45655e104 | −0.224838 | ||||||||
\(269\) | 6.23031e105 | 1.25975 | 0.629876 | − | 0.776695i | \(-0.283106\pi\) | ||||
0.629876 | + | 0.776695i | \(0.283106\pi\) | |||||||
\(270\) | 1.64259e103 | 0.00282621 | ||||||||
\(271\) | 3.19394e105 | 0.467910 | 0.233955 | − | 0.972247i | \(-0.424833\pi\) | ||||
0.233955 | + | 0.972247i | \(0.424833\pi\) | |||||||
\(272\) | 3.09667e104 | 0.0386498 | ||||||||
\(273\) | −1.33320e102 | −0.000141847 0 | ||||||||
\(274\) | −1.22180e106 | −1.10880 | ||||||||
\(275\) | −1.41062e106 | −1.09254 | ||||||||
\(276\) | −2.68225e103 | −0.00177400 | ||||||||
\(277\) | 2.49419e106 | 1.40948 | 0.704741 | − | 0.709464i | \(-0.251063\pi\) | ||||
0.704741 | + | 0.709464i | \(0.251063\pi\) | |||||||
\(278\) | −1.10495e106 | −0.533818 | ||||||||
\(279\) | −1.03719e105 | −0.0428625 | ||||||||
\(280\) | −3.09967e104 | −0.0109633 | ||||||||
\(281\) | −3.89839e106 | −1.18076 | −0.590378 | − | 0.807127i | \(-0.701021\pi\) | ||||
−0.590378 | + | 0.807127i | \(0.701021\pi\) | |||||||
\(282\) | −3.19565e103 | −0.000829321 0 | ||||||||
\(283\) | 5.81694e106 | 1.29415 | 0.647075 | − | 0.762426i | \(-0.275992\pi\) | ||||
0.647075 | + | 0.762426i | \(0.275992\pi\) | |||||||
\(284\) | −4.22918e106 | −0.807065 | ||||||||
\(285\) | −1.70569e104 | −0.00279351 | ||||||||
\(286\) | −6.53076e106 | −0.918419 | ||||||||
\(287\) | 8.67415e104 | 0.0104801 | ||||||||
\(288\) | −1.70213e106 | −0.176775 | ||||||||
\(289\) | −1.09282e107 | −0.976099 | ||||||||
\(290\) | −9.36346e105 | −0.0719653 | ||||||||
\(291\) | −3.85016e104 | −0.00254762 | ||||||||
\(292\) | 1.11771e107 | 0.637051 | ||||||||
\(293\) | 3.43154e107 | 1.68557 | 0.842786 | − | 0.538249i | \(-0.180914\pi\) | ||||
0.842786 | + | 0.538249i | \(0.180914\pi\) | |||||||
\(294\) | −5.69057e104 | −0.00241017 | ||||||||
\(295\) | 1.87235e106 | 0.0684116 | ||||||||
\(296\) | −5.43952e106 | −0.171542 | ||||||||
\(297\) | −4.16696e105 | −0.0113478 | ||||||||
\(298\) | 3.01303e107 | 0.708917 | ||||||||
\(299\) | 3.99347e107 | 0.812183 | ||||||||
\(300\) | −6.39538e104 | −0.00112484 | ||||||||
\(301\) | −5.35799e106 | −0.0815379 | ||||||||
\(302\) | 4.47462e107 | 0.589460 | ||||||||
\(303\) | −1.63145e105 | −0.00186131 | ||||||||
\(304\) | 3.53508e107 | 0.349460 | ||||||||
\(305\) | −9.16837e107 | −0.785686 | ||||||||
\(306\) | −1.47085e107 | −0.109317 | ||||||||
\(307\) | −1.02262e108 | −0.659470 | −0.329735 | − | 0.944074i | \(-0.606959\pi\) | ||||
−0.329735 | + | 0.944074i | \(0.606959\pi\) | |||||||
\(308\) | 7.86332e106 | 0.0440200 | ||||||||
\(309\) | −1.14187e106 | −0.00555167 | ||||||||
\(310\) | −4.19477e106 | −0.0177204 | ||||||||
\(311\) | −5.27827e108 | −1.93827 | −0.969136 | − | 0.246526i | \(-0.920711\pi\) | ||||
−0.969136 | + | 0.246526i | \(0.920711\pi\) | |||||||
\(312\) | −2.96088e105 | −0.000945574 0 | ||||||||
\(313\) | −6.02896e108 | −1.67519 | −0.837594 | − | 0.546293i | \(-0.816039\pi\) | ||||
−0.837594 | + | 0.546293i | \(0.816039\pi\) | |||||||
\(314\) | 4.21294e108 | 1.01893 | ||||||||
\(315\) | 1.47228e107 | 0.0310085 | ||||||||
\(316\) | −4.90234e107 | −0.0899530 | ||||||||
\(317\) | 6.55434e108 | 1.04822 | 0.524108 | − | 0.851652i | \(-0.324399\pi\) | ||||
0.524108 | + | 0.851652i | \(0.324399\pi\) | |||||||
\(318\) | −1.24224e106 | −0.00173231 | ||||||||
\(319\) | 2.37535e108 | 0.288956 | ||||||||
\(320\) | −6.88400e107 | −0.0730831 | ||||||||
\(321\) | −1.38777e106 | −0.00128632 | ||||||||
\(322\) | −4.80832e107 | −0.0389280 | ||||||||
\(323\) | 3.05474e108 | 0.216105 | ||||||||
\(324\) | 8.08468e108 | 0.499982 | ||||||||
\(325\) | 9.52177e108 | 0.514982 | ||||||||
\(326\) | −1.06354e108 | −0.0503255 | ||||||||
\(327\) | −1.35493e107 | −0.00561163 | ||||||||
\(328\) | 1.92643e108 | 0.0698619 | ||||||||
\(329\) | −5.72866e107 | −0.0181983 | ||||||||
\(330\) | −8.42625e106 | −0.00234573 | ||||||||
\(331\) | 4.06789e109 | 0.992776 | 0.496388 | − | 0.868101i | \(-0.334659\pi\) | ||||
0.496388 | + | 0.868101i | \(0.334659\pi\) | |||||||
\(332\) | −3.53122e109 | −0.755820 | ||||||||
\(333\) | 2.58366e109 | 0.485190 | ||||||||
\(334\) | −2.44422e109 | −0.402873 | ||||||||
\(335\) | 1.81658e109 | 0.262909 | ||||||||
\(336\) | 3.56503e105 | 4.53215e−5 0 | ||||||||
\(337\) | −1.61026e109 | −0.179885 | −0.0899425 | − | 0.995947i | \(-0.528668\pi\) | ||||
−0.0899425 | + | 0.995947i | \(0.528668\pi\) | |||||||
\(338\) | −2.79217e109 | −0.274199 | ||||||||
\(339\) | −7.59287e107 | −0.00655721 | ||||||||
\(340\) | −5.94863e108 | −0.0451943 | ||||||||
\(341\) | 1.06414e109 | 0.0711513 | ||||||||
\(342\) | −1.67909e110 | −0.988411 | ||||||||
\(343\) | −2.04311e109 | −0.105925 | ||||||||
\(344\) | −1.18995e110 | −0.543545 | ||||||||
\(345\) | 5.15254e107 | 0.00207439 | ||||||||
\(346\) | 4.98670e109 | 0.177012 | ||||||||
\(347\) | −7.65989e109 | −0.239823 | −0.119911 | − | 0.992785i | \(-0.538261\pi\) | ||||
−0.119911 | + | 0.992785i | \(0.538261\pi\) | |||||||
\(348\) | 1.07692e107 | 0.000297500 0 | ||||||||
\(349\) | −4.97256e110 | −1.21248 | −0.606240 | − | 0.795282i | \(-0.707323\pi\) | ||||
−0.606240 | + | 0.795282i | \(0.707323\pi\) | |||||||
\(350\) | −1.14646e109 | −0.0246831 | ||||||||
\(351\) | 2.81273e108 | 0.00534894 | ||||||||
\(352\) | 1.74635e110 | 0.293444 | ||||||||
\(353\) | 8.25147e110 | 1.22555 | 0.612776 | − | 0.790257i | \(-0.290053\pi\) | ||||
0.612776 | + | 0.790257i | \(0.290053\pi\) | |||||||
\(354\) | −2.15345e107 | −0.000282809 0 | ||||||||
\(355\) | 8.12416e110 | 0.943724 | ||||||||
\(356\) | −2.49964e110 | −0.256923 | ||||||||
\(357\) | 3.08063e106 | 2.80267e−5 0 | ||||||||
\(358\) | 1.03817e111 | 0.836288 | ||||||||
\(359\) | −5.82269e110 | −0.415447 | −0.207723 | − | 0.978188i | \(-0.566605\pi\) | ||||
−0.207723 | + | 0.978188i | \(0.566605\pi\) | |||||||
\(360\) | 3.26976e110 | 0.206708 | ||||||||
\(361\) | 1.70252e111 | 0.953959 | ||||||||
\(362\) | 2.48547e111 | 1.23477 | ||||||||
\(363\) | 1.36184e109 | 0.00600050 | ||||||||
\(364\) | −5.30780e109 | −0.0207493 | ||||||||
\(365\) | −2.14709e111 | −0.744922 | ||||||||
\(366\) | 1.05448e109 | 0.00324798 | ||||||||
\(367\) | −6.51905e111 | −1.78324 | −0.891621 | − | 0.452782i | \(-0.850432\pi\) | ||||
−0.891621 | + | 0.452782i | \(0.850432\pi\) | |||||||
\(368\) | −1.06787e111 | −0.259501 | ||||||||
\(369\) | −9.15013e110 | −0.197597 | ||||||||
\(370\) | 1.04492e111 | 0.200590 | ||||||||
\(371\) | −2.22689e110 | −0.0380131 | ||||||||
\(372\) | 4.82454e107 | 7.32551e−5 0 | ||||||||
\(373\) | −9.32477e111 | −1.25981 | −0.629903 | − | 0.776674i | \(-0.716905\pi\) | ||||
−0.629903 | + | 0.776674i | \(0.716905\pi\) | |||||||
\(374\) | 1.50906e111 | 0.181465 | ||||||||
\(375\) | 3.09514e109 | 0.00331376 | ||||||||
\(376\) | −1.27227e111 | −0.121313 | ||||||||
\(377\) | −1.60338e111 | −0.136203 | ||||||||
\(378\) | −3.38665e108 | −0.000256376 0 | ||||||||
\(379\) | 1.11106e112 | 0.749777 | 0.374889 | − | 0.927070i | \(-0.377681\pi\) | ||||
0.374889 | + | 0.927070i | \(0.377681\pi\) | |||||||
\(380\) | −6.79080e111 | −0.408634 | ||||||||
\(381\) | −5.39477e108 | −0.000289559 0 | ||||||||
\(382\) | 1.62499e112 | 0.778207 | ||||||||
\(383\) | −1.11409e112 | −0.476183 | −0.238092 | − | 0.971243i | \(-0.576522\pi\) | ||||
−0.238092 | + | 0.971243i | \(0.576522\pi\) | |||||||
\(384\) | 7.91751e108 | 0.000302121 0 | ||||||||
\(385\) | −1.51053e111 | −0.0514738 | ||||||||
\(386\) | −1.79808e112 | −0.547346 | ||||||||
\(387\) | 5.65200e112 | 1.53736 | ||||||||
\(388\) | −1.53285e112 | −0.372665 | ||||||||
\(389\) | 6.31321e112 | 1.37228 | 0.686140 | − | 0.727470i | \(-0.259304\pi\) | ||||
0.686140 | + | 0.727470i | \(0.259304\pi\) | |||||||
\(390\) | 5.68778e109 | 0.00110569 | ||||||||
\(391\) | −9.22772e111 | −0.160474 | ||||||||
\(392\) | −2.26556e112 | −0.352559 | ||||||||
\(393\) | 2.74285e110 | 0.00382055 | ||||||||
\(394\) | 2.35678e112 | 0.293923 | ||||||||
\(395\) | 9.41729e111 | 0.105185 | ||||||||
\(396\) | −8.29480e112 | −0.829976 | ||||||||
\(397\) | 7.56626e112 | 0.678413 | 0.339207 | − | 0.940712i | \(-0.389841\pi\) | ||||
0.339207 | + | 0.940712i | \(0.389841\pi\) | |||||||
\(398\) | 2.82148e111 | 0.0226759 | ||||||||
\(399\) | 3.51676e109 | 0.000253409 0 | ||||||||
\(400\) | −2.54616e112 | −0.164542 | ||||||||
\(401\) | 7.08912e112 | 0.410972 | 0.205486 | − | 0.978660i | \(-0.434123\pi\) | ||||
0.205486 | + | 0.978660i | \(0.434123\pi\) | |||||||
\(402\) | −2.08931e110 | −0.00108685 | ||||||||
\(403\) | −7.18302e111 | −0.0335380 | ||||||||
\(404\) | −6.49521e112 | −0.272272 | ||||||||
\(405\) | −1.55305e113 | −0.584644 | ||||||||
\(406\) | 1.93054e111 | 0.00652823 | ||||||||
\(407\) | −2.65078e113 | −0.805410 | ||||||||
\(408\) | 6.84171e109 | 0.000186830 0 | ||||||||
\(409\) | −5.19837e113 | −1.27615 | −0.638077 | − | 0.769973i | \(-0.720270\pi\) | ||||
−0.638077 | + | 0.769973i | \(0.720270\pi\) | |||||||
\(410\) | −3.70062e112 | −0.0816916 | ||||||||
\(411\) | −2.69943e111 | −0.00535985 | ||||||||
\(412\) | −4.54609e113 | −0.812098 | ||||||||
\(413\) | −3.86037e111 | −0.00620586 | ||||||||
\(414\) | 5.07216e113 | 0.733970 | ||||||||
\(415\) | 6.78339e113 | 0.883802 | ||||||||
\(416\) | −1.17880e113 | −0.138319 | ||||||||
\(417\) | −2.44125e111 | −0.00258044 | ||||||||
\(418\) | 1.72271e114 | 1.64075 | ||||||||
\(419\) | −1.54329e114 | −1.32476 | −0.662381 | − | 0.749167i | \(-0.730454\pi\) | ||||
−0.662381 | + | 0.749167i | \(0.730454\pi\) | |||||||
\(420\) | −6.84834e109 | −5.29958e−5 0 | ||||||||
\(421\) | 1.84834e114 | 1.28977 | 0.644884 | − | 0.764281i | \(-0.276906\pi\) | ||||
0.644884 | + | 0.764281i | \(0.276906\pi\) | |||||||
\(422\) | 1.59571e114 | 1.00430 | ||||||||
\(423\) | 6.04301e113 | 0.343121 | ||||||||
\(424\) | −4.94566e113 | −0.253401 | ||||||||
\(425\) | −2.20020e113 | −0.101752 | ||||||||
\(426\) | −9.34386e111 | −0.00390129 | ||||||||
\(427\) | 1.89031e113 | 0.0712724 | ||||||||
\(428\) | −5.52508e113 | −0.188163 | ||||||||
\(429\) | −1.44289e112 | −0.00443957 | ||||||||
\(430\) | 2.28586e114 | 0.635583 | ||||||||
\(431\) | 4.82943e112 | 0.0121376 | 0.00606882 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00606882 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(432\) | −7.52135e111 | −0.00170904 | ||||||||
\(433\) | −6.57000e114 | −1.35003 | −0.675013 | − | 0.737806i | \(-0.735862\pi\) | ||||
−0.675013 | + | 0.737806i | \(0.735862\pi\) | |||||||
\(434\) | 8.64868e111 | 0.00160748 | ||||||||
\(435\) | −2.06874e111 | −0.000347875 0 | ||||||||
\(436\) | −5.39431e114 | −0.820869 | ||||||||
\(437\) | −1.05341e115 | −1.45096 | ||||||||
\(438\) | 2.46944e112 | 0.00307946 | ||||||||
\(439\) | 4.37173e114 | 0.493681 | 0.246840 | − | 0.969056i | \(-0.420608\pi\) | ||||
0.246840 | + | 0.969056i | \(0.420608\pi\) | |||||||
\(440\) | −3.35470e114 | −0.343133 | ||||||||
\(441\) | 1.07609e115 | 0.997175 | ||||||||
\(442\) | −1.01863e114 | −0.0855357 | ||||||||
\(443\) | −7.45834e114 | −0.567650 | −0.283825 | − | 0.958876i | \(-0.591603\pi\) | ||||
−0.283825 | + | 0.958876i | \(0.591603\pi\) | |||||||
\(444\) | −1.20180e112 | −0.000829224 0 | ||||||||
\(445\) | 4.80175e114 | 0.300427 | ||||||||
\(446\) | −9.47859e114 | −0.537870 | ||||||||
\(447\) | 6.65691e112 | 0.00342685 | ||||||||
\(448\) | 1.41933e113 | 0.00662963 | ||||||||
\(449\) | 3.45732e115 | 1.46563 | 0.732814 | − | 0.680429i | \(-0.238206\pi\) | ||||
0.732814 | + | 0.680429i | \(0.238206\pi\) | |||||||
\(450\) | 1.20937e115 | 0.465389 | ||||||||
\(451\) | 9.38784e114 | 0.328009 | ||||||||
\(452\) | −3.02291e115 | −0.959188 | ||||||||
\(453\) | 9.88613e112 | 0.00284941 | ||||||||
\(454\) | −2.72539e115 | −0.713672 | ||||||||
\(455\) | 1.01962e114 | 0.0242628 | ||||||||
\(456\) | 7.81032e112 | 0.00168927 | ||||||||
\(457\) | 7.12074e115 | 1.40014 | 0.700069 | − | 0.714076i | \(-0.253153\pi\) | ||||
0.700069 | + | 0.714076i | \(0.253153\pi\) | |||||||
\(458\) | 4.38184e115 | 0.783445 | ||||||||
\(459\) | −6.49938e112 | −0.00105687 | ||||||||
\(460\) | 2.05136e115 | 0.303442 | ||||||||
\(461\) | −8.55299e115 | −1.15114 | −0.575569 | − | 0.817753i | \(-0.695220\pi\) | ||||
−0.575569 | + | 0.817753i | \(0.695220\pi\) | |||||||
\(462\) | 1.73731e112 | 0.000212789 0 | ||||||||
\(463\) | 7.10573e115 | 0.792201 | 0.396100 | − | 0.918207i | \(-0.370363\pi\) | ||||
0.396100 | + | 0.918207i | \(0.370363\pi\) | |||||||
\(464\) | 4.28750e114 | 0.0435183 | ||||||||
\(465\) | −9.26782e111 | −8.56593e−5 0 | ||||||||
\(466\) | −7.44345e115 | −0.626595 | ||||||||
\(467\) | 1.50144e115 | 0.115139 | 0.0575696 | − | 0.998341i | \(-0.481665\pi\) | ||||
0.0575696 | + | 0.998341i | \(0.481665\pi\) | |||||||
\(468\) | 5.59906e115 | 0.391219 | ||||||||
\(469\) | −3.74539e114 | −0.0238495 | ||||||||
\(470\) | 2.44400e115 | 0.141855 | ||||||||
\(471\) | 9.30798e113 | 0.00492545 | ||||||||
\(472\) | −8.57343e114 | −0.0413693 | ||||||||
\(473\) | −5.79883e116 | −2.55200 | ||||||||
\(474\) | −1.08311e113 | −0.000434826 0 | ||||||||
\(475\) | −2.51169e116 | −0.920013 | ||||||||
\(476\) | 1.22647e114 | 0.00409974 | ||||||||
\(477\) | 2.34908e116 | 0.716719 | ||||||||
\(478\) | 3.80653e116 | 1.06027 | ||||||||
\(479\) | −5.55082e116 | −1.41177 | −0.705883 | − | 0.708329i | \(-0.749449\pi\) | ||||
−0.705883 | + | 0.708329i | \(0.749449\pi\) | |||||||
\(480\) | −1.52094e113 | −0.000353278 0 | ||||||||
\(481\) | 1.78930e116 | 0.379640 | ||||||||
\(482\) | −3.73287e116 | −0.723596 | ||||||||
\(483\) | −1.06234e113 | −0.000188175 0 | ||||||||
\(484\) | 5.42182e116 | 0.877753 | ||||||||
\(485\) | 2.94457e116 | 0.435768 | ||||||||
\(486\) | 5.35874e114 | 0.00725078 | ||||||||
\(487\) | 4.01646e116 | 0.496974 | 0.248487 | − | 0.968635i | \(-0.420067\pi\) | ||||
0.248487 | + | 0.968635i | \(0.420067\pi\) | |||||||
\(488\) | 4.19817e116 | 0.475114 | ||||||||
\(489\) | −2.34976e113 | −0.000243270 0 | ||||||||
\(490\) | 4.35209e116 | 0.412257 | ||||||||
\(491\) | 1.23510e117 | 1.07067 | 0.535336 | − | 0.844639i | \(-0.320185\pi\) | ||||
0.535336 | + | 0.844639i | \(0.320185\pi\) | |||||||
\(492\) | 4.25621e113 | 0.000337708 0 | ||||||||
\(493\) | 3.70493e115 | 0.0269115 | ||||||||
\(494\) | −1.16284e117 | −0.773389 | ||||||||
\(495\) | 1.59341e117 | 0.970515 | ||||||||
\(496\) | 1.92077e115 | 0.0107157 | ||||||||
\(497\) | −1.67502e116 | −0.0856086 | ||||||||
\(498\) | −7.80180e114 | −0.00365358 | ||||||||
\(499\) | −4.83344e116 | −0.207435 | −0.103718 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103718 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(500\) | 1.23225e117 | 0.484736 | ||||||||
\(501\) | −5.40020e114 | −0.00194746 | ||||||||
\(502\) | −3.32167e117 | −1.09836 | ||||||||
\(503\) | −5.52289e117 | −1.67479 | −0.837393 | − | 0.546602i | \(-0.815921\pi\) | ||||
−0.837393 | + | 0.546602i | \(0.815921\pi\) | |||||||
\(504\) | −6.74151e115 | −0.0187512 | ||||||||
\(505\) | 1.24771e117 | 0.318376 | ||||||||
\(506\) | −5.20393e117 | −1.21838 | ||||||||
\(507\) | −6.16896e114 | −0.00132546 | ||||||||
\(508\) | −2.14779e116 | −0.0423566 | ||||||||
\(509\) | 3.82676e117 | 0.692801 | 0.346400 | − | 0.938087i | \(-0.387404\pi\) | ||||
0.346400 | + | 0.938087i | \(0.387404\pi\) | |||||||
\(510\) | −1.31428e114 | −0.000218466 0 | ||||||||
\(511\) | 4.42683e116 | 0.0675746 | ||||||||
\(512\) | 3.15216e116 | 0.0441942 | ||||||||
\(513\) | −7.41952e115 | −0.00955588 | ||||||||
\(514\) | −2.49401e117 | −0.295122 | ||||||||
\(515\) | 8.73293e117 | 0.949610 | ||||||||
\(516\) | −2.62904e115 | −0.00262746 | ||||||||
\(517\) | −6.20000e117 | −0.569578 | ||||||||
\(518\) | −2.15439e116 | −0.0181962 | ||||||||
\(519\) | 1.10175e115 | 0.000855664 0 | ||||||||
\(520\) | 2.26445e117 | 0.161740 | ||||||||
\(521\) | −1.08580e117 | −0.0713359 | −0.0356680 | − | 0.999364i | \(-0.511356\pi\) | ||||
−0.0356680 | + | 0.999364i | \(0.511356\pi\) | |||||||
\(522\) | −2.03647e117 | −0.123087 | ||||||||
\(523\) | 6.58601e117 | 0.366268 | 0.183134 | − | 0.983088i | \(-0.441376\pi\) | ||||
0.183134 | + | 0.983088i | \(0.441376\pi\) | |||||||
\(524\) | 1.09200e118 | 0.558870 | ||||||||
\(525\) | −2.53297e114 | −0.000119317 0 | ||||||||
\(526\) | 1.47635e118 | 0.640191 | ||||||||
\(527\) | 1.65978e116 | 0.00662658 | ||||||||
\(528\) | 3.85835e115 | 0.00141849 | ||||||||
\(529\) | 2.28739e117 | 0.0774494 | ||||||||
\(530\) | 9.50050e117 | 0.296310 | ||||||||
\(531\) | 4.07220e117 | 0.117009 | ||||||||
\(532\) | 1.40011e117 | 0.0370687 | ||||||||
\(533\) | −6.33686e117 | −0.154611 | ||||||||
\(534\) | −5.52265e115 | −0.00124195 | ||||||||
\(535\) | 1.06136e118 | 0.220025 | ||||||||
\(536\) | −8.31807e117 | −0.158984 | ||||||||
\(537\) | 2.29371e116 | 0.00404256 | ||||||||
\(538\) | 5.48024e118 | 0.890780 | ||||||||
\(539\) | −1.10405e119 | −1.65530 | ||||||||
\(540\) | 1.44483e116 | 0.00199843 | ||||||||
\(541\) | −7.73190e118 | −0.986746 | −0.493373 | − | 0.869818i | \(-0.664236\pi\) | ||||
−0.493373 | + | 0.869818i | \(0.664236\pi\) | |||||||
\(542\) | 2.80942e118 | 0.330862 | ||||||||
\(543\) | 5.49134e116 | 0.00596878 | ||||||||
\(544\) | 2.72386e117 | 0.0273295 | ||||||||
\(545\) | 1.03623e119 | 0.959866 | ||||||||
\(546\) | −1.17269e115 | −0.000100301 0 | ||||||||
\(547\) | −9.37680e118 | −0.740638 | −0.370319 | − | 0.928905i | \(-0.620752\pi\) | ||||
−0.370319 | + | 0.928905i | \(0.620752\pi\) | |||||||
\(548\) | −1.07471e119 | −0.784038 | ||||||||
\(549\) | −1.99404e119 | −1.34381 | ||||||||
\(550\) | −1.24079e119 | −0.772542 | ||||||||
\(551\) | 4.22945e118 | 0.243326 | ||||||||
\(552\) | −2.35933e116 | −0.00125441 | ||||||||
\(553\) | −1.94164e117 | −0.00954168 | ||||||||
\(554\) | 2.19391e119 | 0.996655 | ||||||||
\(555\) | 2.30862e116 | 0.000969636 0 | ||||||||
\(556\) | −9.71923e118 | −0.377466 | ||||||||
\(557\) | 4.73467e119 | 1.70055 | 0.850273 | − | 0.526342i | \(-0.176437\pi\) | ||||
0.850273 | + | 0.526342i | \(0.176437\pi\) | |||||||
\(558\) | −9.12326e117 | −0.0303083 | ||||||||
\(559\) | 3.91426e119 | 1.20292 | ||||||||
\(560\) | −2.72650e117 | −0.00775222 | ||||||||
\(561\) | 3.33409e116 | 0.000877189 0 | ||||||||
\(562\) | −3.42906e119 | −0.834921 | ||||||||
\(563\) | 3.60938e119 | 0.813425 | 0.406713 | − | 0.913556i | \(-0.366675\pi\) | ||||
0.406713 | + | 0.913556i | \(0.366675\pi\) | |||||||
\(564\) | −2.81092e116 | −0.000586419 0 | ||||||||
\(565\) | 5.80695e119 | 1.12161 | ||||||||
\(566\) | 5.11664e119 | 0.915103 | ||||||||
\(567\) | 3.20204e118 | 0.0530352 | ||||||||
\(568\) | −3.72003e119 | −0.570681 | ||||||||
\(569\) | −5.05559e119 | −0.718437 | −0.359218 | − | 0.933254i | \(-0.616957\pi\) | ||||
−0.359218 | + | 0.933254i | \(0.616957\pi\) | |||||||
\(570\) | −1.50034e117 | −0.00197531 | ||||||||
\(571\) | −4.86735e119 | −0.593775 | −0.296887 | − | 0.954913i | \(-0.595949\pi\) | ||||
−0.296887 | + | 0.954913i | \(0.595949\pi\) | |||||||
\(572\) | −5.74451e119 | −0.649420 | ||||||||
\(573\) | 3.59022e117 | 0.00376180 | ||||||||
\(574\) | 7.62987e117 | 0.00741053 | ||||||||
\(575\) | 7.58728e119 | 0.683179 | ||||||||
\(576\) | −1.49721e119 | −0.124999 | ||||||||
\(577\) | −1.27003e120 | −0.983257 | −0.491629 | − | 0.870805i | \(-0.663598\pi\) | ||||
−0.491629 | + | 0.870805i | \(0.663598\pi\) | |||||||
\(578\) | −9.61258e119 | −0.690206 | ||||||||
\(579\) | −3.97264e117 | −0.00264583 | ||||||||
\(580\) | −8.23618e118 | −0.0508872 | ||||||||
\(581\) | −1.39859e119 | −0.0801728 | ||||||||
\(582\) | −3.38664e117 | −0.00180144 | ||||||||
\(583\) | −2.41011e120 | −1.18975 | ||||||||
\(584\) | 9.83146e119 | 0.450463 | ||||||||
\(585\) | −1.07557e120 | −0.457464 | ||||||||
\(586\) | 3.01841e120 | 1.19188 | ||||||||
\(587\) | −3.67749e118 | −0.0134833 | −0.00674163 | − | 0.999977i | \(-0.502146\pi\) | ||||
−0.00674163 | + | 0.999977i | \(0.502146\pi\) | |||||||
\(588\) | −5.00548e117 | −0.00170424 | ||||||||
\(589\) | 1.89477e119 | 0.0599156 | ||||||||
\(590\) | 1.64694e119 | 0.0483743 | ||||||||
\(591\) | 5.20702e117 | 0.00142080 | ||||||||
\(592\) | −4.78466e119 | −0.121299 | ||||||||
\(593\) | 2.80937e120 | 0.661805 | 0.330902 | − | 0.943665i | \(-0.392647\pi\) | ||||
0.330902 | + | 0.943665i | \(0.392647\pi\) | |||||||
\(594\) | −3.66529e118 | −0.00802414 | ||||||||
\(595\) | −2.35603e118 | −0.00479394 | ||||||||
\(596\) | 2.65029e120 | 0.501280 | ||||||||
\(597\) | 6.23372e116 | 0.000109614 0 | ||||||||
\(598\) | 3.51269e120 | 0.574300 | ||||||||
\(599\) | −5.73088e120 | −0.871274 | −0.435637 | − | 0.900122i | \(-0.643477\pi\) | ||||
−0.435637 | + | 0.900122i | \(0.643477\pi\) | |||||||
\(600\) | −5.62543e117 | −0.000795384 0 | ||||||||
\(601\) | 5.51773e120 | 0.725640 | 0.362820 | − | 0.931859i | \(-0.381814\pi\) | ||||
0.362820 | + | 0.931859i | \(0.381814\pi\) | |||||||
\(602\) | −4.71294e119 | −0.0576560 | ||||||||
\(603\) | 3.95091e120 | 0.449670 | ||||||||
\(604\) | 3.93592e120 | 0.416811 | ||||||||
\(605\) | −1.04152e121 | −1.02638 | ||||||||
\(606\) | −1.43504e118 | −0.00131615 | ||||||||
\(607\) | 8.85493e120 | 0.755922 | 0.377961 | − | 0.925822i | \(-0.376625\pi\) | ||||
0.377961 | + | 0.925822i | \(0.376625\pi\) | |||||||
\(608\) | 3.10949e120 | 0.247106 | ||||||||
\(609\) | 4.26529e116 | 3.15570e−5 0 | ||||||||
\(610\) | −8.06458e120 | −0.555564 | ||||||||
\(611\) | 4.18505e120 | 0.268477 | ||||||||
\(612\) | −1.29378e120 | −0.0772987 | ||||||||
\(613\) | −3.73288e120 | −0.207737 | −0.103868 | − | 0.994591i | \(-0.533122\pi\) | ||||
−0.103868 | + | 0.994591i | \(0.533122\pi\) | |||||||
\(614\) | −8.99506e120 | −0.466316 | ||||||||
\(615\) | −8.17608e117 | −0.000394891 0 | ||||||||
\(616\) | 6.91665e119 | 0.0311268 | ||||||||
\(617\) | 6.91361e120 | 0.289935 | 0.144967 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144967 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(618\) | −1.00440e119 | −0.00392563 | ||||||||
\(619\) | −2.47069e121 | −0.900067 | −0.450034 | − | 0.893012i | \(-0.648588\pi\) | ||||
−0.450034 | + | 0.893012i | \(0.648588\pi\) | |||||||
\(620\) | −3.68975e119 | −0.0125302 | ||||||||
\(621\) | 2.24128e119 | 0.00709596 | ||||||||
\(622\) | −4.64282e121 | −1.37057 | ||||||||
\(623\) | −9.90014e119 | −0.0272528 | ||||||||
\(624\) | −2.60442e118 | −0.000668622 0 | ||||||||
\(625\) | 3.81502e120 | 0.0913517 | ||||||||
\(626\) | −5.30313e121 | −1.18454 | ||||||||
\(627\) | 3.80611e119 | 0.00793129 | ||||||||
\(628\) | 3.70574e121 | 0.720495 | ||||||||
\(629\) | −4.13453e120 | −0.0750108 | ||||||||
\(630\) | 1.29503e120 | 0.0219263 | ||||||||
\(631\) | 6.86619e121 | 1.08502 | 0.542511 | − | 0.840049i | \(-0.317474\pi\) | ||||
0.542511 | + | 0.840049i | \(0.317474\pi\) | |||||||
\(632\) | −4.31215e120 | −0.0636064 | ||||||||
\(633\) | 3.52552e119 | 0.00485470 | ||||||||
\(634\) | 5.76526e121 | 0.741201 | ||||||||
\(635\) | 4.12587e120 | 0.0495288 | ||||||||
\(636\) | −1.09268e119 | −0.00122492 | ||||||||
\(637\) | 7.45242e121 | 0.780247 | ||||||||
\(638\) | 2.08938e121 | 0.204323 | ||||||||
\(639\) | 1.76694e122 | 1.61411 | ||||||||
\(640\) | −6.05523e120 | −0.0516775 | ||||||||
\(641\) | −2.09794e120 | −0.0167289 | −0.00836447 | − | 0.999965i | \(-0.502663\pi\) | ||||
−0.00836447 | + | 0.999965i | \(0.502663\pi\) | |||||||
\(642\) | −1.22070e119 | −0.000909568 0 | ||||||||
\(643\) | −1.49365e122 | −1.04009 | −0.520045 | − | 0.854139i | \(-0.674085\pi\) | ||||
−0.520045 | + | 0.854139i | \(0.674085\pi\) | |||||||
\(644\) | −4.22944e120 | −0.0275263 | ||||||||
\(645\) | 5.05033e119 | 0.00307236 | ||||||||
\(646\) | 2.68698e121 | 0.152809 | ||||||||
\(647\) | −1.18107e122 | −0.627972 | −0.313986 | − | 0.949428i | \(-0.601665\pi\) | ||||
−0.313986 | + | 0.949428i | \(0.601665\pi\) | |||||||
\(648\) | 7.11136e121 | 0.353541 | ||||||||
\(649\) | −4.17799e121 | −0.194233 | ||||||||
\(650\) | 8.37544e121 | 0.364147 | ||||||||
\(651\) | 1.91082e117 | 7.77046e−6 0 | ||||||||
\(652\) | −9.35499e120 | −0.0355855 | ||||||||
\(653\) | −2.90684e122 | −1.03442 | −0.517211 | − | 0.855858i | \(-0.673030\pi\) | ||||
−0.517211 | + | 0.855858i | \(0.673030\pi\) | |||||||
\(654\) | −1.19181e120 | −0.00396802 | ||||||||
\(655\) | −2.09770e122 | −0.653503 | ||||||||
\(656\) | 1.69450e121 | 0.0493998 | ||||||||
\(657\) | −4.66974e122 | −1.27409 | ||||||||
\(658\) | −5.03898e120 | −0.0128682 | ||||||||
\(659\) | −5.14132e122 | −1.22902 | −0.614510 | − | 0.788909i | \(-0.710646\pi\) | ||||
−0.614510 | + | 0.788909i | \(0.710646\pi\) | |||||||
\(660\) | −7.41180e119 | −0.00165868 | ||||||||
\(661\) | 6.77533e122 | 1.41960 | 0.709801 | − | 0.704402i | \(-0.248785\pi\) | ||||
0.709801 | + | 0.704402i | \(0.248785\pi\) | |||||||
\(662\) | 3.57815e122 | 0.701998 | ||||||||
\(663\) | −2.25054e119 | −0.000413473 0 | ||||||||
\(664\) | −3.10609e122 | −0.534445 | ||||||||
\(665\) | −2.68958e121 | −0.0433455 | ||||||||
\(666\) | 2.27261e122 | 0.343081 | ||||||||
\(667\) | −1.27763e122 | −0.180688 | ||||||||
\(668\) | −2.14996e122 | −0.284875 | ||||||||
\(669\) | −2.09418e120 | −0.00260003 | ||||||||
\(670\) | 1.59788e122 | 0.185905 | ||||||||
\(671\) | 2.04584e123 | 2.23071 | ||||||||
\(672\) | 3.13583e118 | 3.20472e−5 0 | ||||||||
\(673\) | 3.96945e122 | 0.380255 | 0.190127 | − | 0.981759i | \(-0.439110\pi\) | ||||
0.190127 | + | 0.981759i | \(0.439110\pi\) | |||||||
\(674\) | −1.41640e122 | −0.127198 | ||||||||
\(675\) | 5.34396e120 | 0.00449934 | ||||||||
\(676\) | −2.45602e122 | −0.193888 | ||||||||
\(677\) | −1.73245e123 | −1.28249 | −0.641245 | − | 0.767337i | \(-0.721582\pi\) | ||||
−0.641245 | + | 0.767337i | \(0.721582\pi\) | |||||||
\(678\) | −6.67876e120 | −0.00463665 | ||||||||
\(679\) | −6.07104e121 | −0.0395301 | ||||||||
\(680\) | −5.23247e121 | −0.0319572 | ||||||||
\(681\) | −6.02141e120 | −0.00344984 | ||||||||
\(682\) | 9.36027e121 | 0.0503116 | ||||||||
\(683\) | 3.73381e123 | 1.88301 | 0.941503 | − | 0.337005i | \(-0.109414\pi\) | ||||
0.941503 | + | 0.337005i | \(0.109414\pi\) | |||||||
\(684\) | −1.47694e123 | −0.698912 | ||||||||
\(685\) | 2.06449e123 | 0.916799 | ||||||||
\(686\) | −1.79714e122 | −0.0749002 | ||||||||
\(687\) | 9.68115e120 | 0.00378712 | ||||||||
\(688\) | −1.04669e123 | −0.384344 | ||||||||
\(689\) | 1.62684e123 | 0.560802 | ||||||||
\(690\) | 4.53222e120 | 0.00146682 | ||||||||
\(691\) | −6.17382e123 | −1.87611 | −0.938057 | − | 0.346481i | \(-0.887376\pi\) | ||||
−0.938057 | + | 0.346481i | \(0.887376\pi\) | |||||||
\(692\) | 4.38635e122 | 0.125166 | ||||||||
\(693\) | −3.28527e122 | −0.0880389 | ||||||||
\(694\) | −6.73771e122 | −0.169580 | ||||||||
\(695\) | 1.86704e123 | 0.441382 | ||||||||
\(696\) | 9.47270e119 | 0.000210364 0 | ||||||||
\(697\) | 1.46426e122 | 0.0305487 | ||||||||
\(698\) | −4.37391e123 | −0.857352 | ||||||||
\(699\) | −1.64454e121 | −0.00302892 | ||||||||
\(700\) | −1.00844e122 | −0.0174536 | ||||||||
\(701\) | −6.53861e123 | −1.06353 | −0.531767 | − | 0.846891i | \(-0.678472\pi\) | ||||
−0.531767 | + | 0.846891i | \(0.678472\pi\) | |||||||
\(702\) | 2.47410e121 | 0.00378228 | ||||||||
\(703\) | −4.71988e123 | −0.678226 | ||||||||
\(704\) | 1.53611e123 | 0.207496 | ||||||||
\(705\) | 5.39972e120 | 0.000685716 0 | ||||||||
\(706\) | 7.25807e123 | 0.866596 | ||||||||
\(707\) | −2.57251e122 | −0.0288810 | ||||||||
\(708\) | −1.89420e120 | −0.000199976 0 | ||||||||
\(709\) | −5.30349e123 | −0.526563 | −0.263281 | − | 0.964719i | \(-0.584805\pi\) | ||||
−0.263281 | + | 0.964719i | \(0.584805\pi\) | |||||||
\(710\) | 7.14609e123 | 0.667314 | ||||||||
\(711\) | 2.04818e123 | 0.179904 | ||||||||
\(712\) | −2.19871e123 | −0.181672 | ||||||||
\(713\) | −5.72368e122 | −0.0444919 | ||||||||
\(714\) | 2.70975e119 | 1.98178e−5 0 | ||||||||
\(715\) | 1.10351e124 | 0.759386 | ||||||||
\(716\) | 9.13182e123 | 0.591345 | ||||||||
\(717\) | 8.41006e121 | 0.00512526 | ||||||||
\(718\) | −5.12169e123 | −0.293765 | ||||||||
\(719\) | 2.57142e124 | 1.38825 | 0.694124 | − | 0.719856i | \(-0.255792\pi\) | ||||
0.694124 | + | 0.719856i | \(0.255792\pi\) | |||||||
\(720\) | 2.87611e123 | 0.146164 | ||||||||
\(721\) | −1.80054e123 | −0.0861426 | ||||||||
\(722\) | 1.49756e124 | 0.674551 | ||||||||
\(723\) | −8.24732e121 | −0.00349781 | ||||||||
\(724\) | 2.18624e124 | 0.873113 | ||||||||
\(725\) | −3.04629e123 | −0.114569 | ||||||||
\(726\) | 1.19789e122 | 0.00424300 | ||||||||
\(727\) | −2.59022e124 | −0.864151 | −0.432076 | − | 0.901837i | \(-0.642219\pi\) | ||||
−0.432076 | + | 0.901837i | \(0.642219\pi\) | |||||||
\(728\) | −4.66879e122 | −0.0146720 | ||||||||
\(729\) | −3.37767e124 | −0.999930 | ||||||||
\(730\) | −1.88860e124 | −0.526740 | ||||||||
\(731\) | −9.04468e123 | −0.237677 | ||||||||
\(732\) | 9.27534e121 | 0.00229667 | ||||||||
\(733\) | 2.50373e124 | 0.584204 | 0.292102 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292102 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(734\) | −5.73421e124 | −1.26094 | ||||||||
\(735\) | 9.61541e121 | 0.00199282 | ||||||||
\(736\) | −9.39309e123 | −0.183495 | ||||||||
\(737\) | −4.05355e124 | −0.746449 | ||||||||
\(738\) | −8.04854e123 | −0.139722 | ||||||||
\(739\) | −1.01449e124 | −0.166040 | −0.0830202 | − | 0.996548i | \(-0.526457\pi\) | ||||
−0.0830202 | + | 0.996548i | \(0.526457\pi\) | |||||||
\(740\) | 9.19122e123 | 0.141838 | ||||||||
\(741\) | −2.56916e122 | −0.00373851 | ||||||||
\(742\) | −1.95879e123 | −0.0268793 | ||||||||
\(743\) | 2.59365e124 | 0.335659 | 0.167829 | − | 0.985816i | \(-0.446324\pi\) | ||||
0.167829 | + | 0.985816i | \(0.446324\pi\) | |||||||
\(744\) | 4.24371e120 | 5.17991e−5 0 | ||||||||
\(745\) | −5.09114e124 | −0.586161 | ||||||||
\(746\) | −8.20215e124 | −0.890817 | ||||||||
\(747\) | 1.47533e125 | 1.51162 | ||||||||
\(748\) | 1.32739e124 | 0.128315 | ||||||||
\(749\) | −2.18828e123 | −0.0199592 | ||||||||
\(750\) | 2.72252e122 | 0.00234318 | ||||||||
\(751\) | 2.28124e125 | 1.85282 | 0.926412 | − | 0.376510i | \(-0.122876\pi\) | ||||
0.926412 | + | 0.376510i | \(0.122876\pi\) | |||||||
\(752\) | −1.11910e124 | −0.0857813 | ||||||||
\(753\) | −7.33884e122 | −0.00530940 | ||||||||
\(754\) | −1.41034e124 | −0.0963101 | ||||||||
\(755\) | −7.56081e124 | −0.487389 | ||||||||
\(756\) | −2.97893e121 | −0.000181285 0 | ||||||||
\(757\) | 2.13261e124 | 0.122529 | 0.0612647 | − | 0.998122i | \(-0.480487\pi\) | ||||
0.0612647 | + | 0.998122i | \(0.480487\pi\) | |||||||
\(758\) | 9.77299e124 | 0.530172 | ||||||||
\(759\) | −1.14975e123 | −0.00588958 | ||||||||
\(760\) | −5.97325e124 | −0.288948 | ||||||||
\(761\) | 7.05135e124 | 0.322136 | 0.161068 | − | 0.986943i | \(-0.448506\pi\) | ||||
0.161068 | + | 0.986943i | \(0.448506\pi\) | |||||||
\(762\) | −4.74529e121 | −0.000204749 0 | ||||||||
\(763\) | −2.13649e124 | −0.0870729 | ||||||||
\(764\) | 1.42936e125 | 0.550276 | ||||||||
\(765\) | 2.48531e124 | 0.0903876 | ||||||||
\(766\) | −9.79965e124 | −0.336712 | ||||||||
\(767\) | 2.82018e124 | 0.0915542 | ||||||||
\(768\) | 6.96432e121 | 0.000213632 0 | ||||||||
\(769\) | 6.76050e124 | 0.195967 | 0.0979835 | − | 0.995188i | \(-0.468761\pi\) | ||||
0.0979835 | + | 0.995188i | \(0.468761\pi\) | |||||||
\(770\) | −1.32867e124 | −0.0363975 | ||||||||
\(771\) | −5.51020e122 | −0.00142660 | ||||||||
\(772\) | −1.58161e125 | −0.387032 | ||||||||
\(773\) | −6.77589e125 | −1.56732 | −0.783662 | − | 0.621188i | \(-0.786650\pi\) | ||||
−0.783662 | + | 0.621188i | \(0.786650\pi\) | |||||||
\(774\) | 4.97155e125 | 1.08708 | ||||||||
\(775\) | −1.36472e124 | −0.0282110 | ||||||||
\(776\) | −1.34831e125 | −0.263514 | ||||||||
\(777\) | −4.75987e121 | −8.79591e−5 0 | ||||||||
\(778\) | 5.55316e125 | 0.970348 | ||||||||
\(779\) | 1.67156e125 | 0.276212 | ||||||||
\(780\) | 5.00302e122 | 0.000781839 0 | ||||||||
\(781\) | −1.81284e126 | −2.67941 | ||||||||
\(782\) | −8.11679e124 | −0.113472 | ||||||||
\(783\) | −8.99872e122 | −0.00118999 | ||||||||
\(784\) | −1.99281e125 | −0.249297 | ||||||||
\(785\) | −7.11865e125 | −0.842496 | ||||||||
\(786\) | 2.41264e123 | 0.00270154 | ||||||||
\(787\) | 1.77603e126 | 1.88169 | 0.940846 | − | 0.338834i | \(-0.110033\pi\) | ||||
0.940846 | + | 0.338834i | \(0.110033\pi\) | |||||||
\(788\) | 2.07305e125 | 0.207835 | ||||||||
\(789\) | 3.26182e123 | 0.00309464 | ||||||||
\(790\) | 8.28354e124 | 0.0743768 | ||||||||
\(791\) | −1.19726e125 | −0.101745 | ||||||||
\(792\) | −7.29619e125 | −0.586882 | ||||||||
\(793\) | −1.38096e126 | −1.05147 | ||||||||
\(794\) | 6.65535e125 | 0.479711 | ||||||||
\(795\) | 2.09902e123 | 0.00143234 | ||||||||
\(796\) | 2.48180e124 | 0.0160343 | ||||||||
\(797\) | 1.82927e126 | 1.11903 | 0.559515 | − | 0.828820i | \(-0.310987\pi\) | ||||
0.559515 | + | 0.828820i | \(0.310987\pi\) | |||||||
\(798\) | 3.09338e122 | 0.000179187 0 | ||||||||
\(799\) | −9.67040e124 | −0.0530468 | ||||||||
\(800\) | −2.23963e125 | −0.116349 | ||||||||
\(801\) | 1.04434e126 | 0.513839 | ||||||||
\(802\) | 6.23565e125 | 0.290601 | ||||||||
\(803\) | 4.79106e126 | 2.11497 | ||||||||
\(804\) | −1.83778e123 | −0.000768519 0 | ||||||||
\(805\) | 8.12466e124 | 0.0321873 | ||||||||
\(806\) | −6.31825e124 | −0.0237150 | ||||||||
\(807\) | 1.21079e124 | 0.00430597 | ||||||||
\(808\) | −5.71324e125 | −0.192526 | ||||||||
\(809\) | −3.64974e125 | −0.116547 | −0.0582735 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582735 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(810\) | −1.36608e126 | −0.413406 | ||||||||
\(811\) | 2.92103e126 | 0.837779 | 0.418889 | − | 0.908037i | \(-0.362420\pi\) | ||||
0.418889 | + | 0.908037i | \(0.362420\pi\) | |||||||
\(812\) | 1.69812e124 | 0.00461616 | ||||||||
\(813\) | 6.20707e123 | 0.00159937 | ||||||||
\(814\) | −2.33165e126 | −0.569511 | ||||||||
\(815\) | 1.79707e125 | 0.0416112 | ||||||||
\(816\) | 6.01803e122 | 0.000132109 0 | ||||||||
\(817\) | −1.03252e127 | −2.14901 | ||||||||
\(818\) | −4.57253e126 | −0.902377 | ||||||||
\(819\) | 2.21758e125 | 0.0414982 | ||||||||
\(820\) | −3.25510e125 | −0.0577647 | ||||||||
\(821\) | −3.59144e126 | −0.604423 | −0.302212 | − | 0.953241i | \(-0.597725\pi\) | ||||
−0.302212 | + | 0.953241i | \(0.597725\pi\) | |||||||
\(822\) | −2.37444e124 | −0.00378999 | ||||||||
\(823\) | 5.32071e126 | 0.805521 | 0.402760 | − | 0.915305i | \(-0.368051\pi\) | ||||
0.402760 | + | 0.915305i | \(0.368051\pi\) | |||||||
\(824\) | −3.99878e126 | −0.574240 | ||||||||
\(825\) | −2.74138e124 | −0.00373441 | ||||||||
\(826\) | −3.39562e124 | −0.00438821 | ||||||||
\(827\) | 3.65757e126 | 0.448438 | 0.224219 | − | 0.974539i | \(-0.428017\pi\) | ||||
0.224219 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(828\) | 4.46152e126 | 0.518995 | ||||||||
\(829\) | −1.19598e127 | −1.32008 | −0.660041 | − | 0.751229i | \(-0.729461\pi\) | ||||
−0.660041 | + | 0.751229i | \(0.729461\pi\) | |||||||
\(830\) | 5.96674e126 | 0.624942 | ||||||||
\(831\) | 4.84719e124 | 0.00481776 | ||||||||
\(832\) | −1.03688e126 | −0.0978060 | ||||||||
\(833\) | −1.72203e126 | −0.154164 | ||||||||
\(834\) | −2.14735e124 | −0.00182465 | ||||||||
\(835\) | 4.13002e126 | 0.333112 | ||||||||
\(836\) | 1.51531e127 | 1.16019 | ||||||||
\(837\) | −4.03137e123 | −0.000293019 0 | ||||||||
\(838\) | −1.35749e127 | −0.936748 | ||||||||
\(839\) | 2.45050e127 | 1.60550 | 0.802749 | − | 0.596317i | \(-0.203370\pi\) | ||||
0.802749 | + | 0.596317i | \(0.203370\pi\) | |||||||
\(840\) | −6.02386e122 | −3.74737e−5 0 | ||||||||
\(841\) | −1.64158e127 | −0.969699 | ||||||||
\(842\) | 1.62582e127 | 0.912003 | ||||||||
\(843\) | −7.57609e124 | −0.00403595 | ||||||||
\(844\) | 1.40360e127 | 0.710145 | ||||||||
\(845\) | 4.71796e126 | 0.226719 | ||||||||
\(846\) | 5.31549e126 | 0.242623 | ||||||||
\(847\) | 2.14738e126 | 0.0931068 | ||||||||
\(848\) | −4.35025e126 | −0.179182 | ||||||||
\(849\) | 1.13046e125 | 0.00442354 | ||||||||
\(850\) | −1.93531e126 | −0.0719496 | ||||||||
\(851\) | 1.42577e127 | 0.503634 | ||||||||
\(852\) | −8.21895e124 | −0.00275863 | ||||||||
\(853\) | −5.97437e127 | −1.90550 | −0.952750 | − | 0.303756i | \(-0.901759\pi\) | ||||
−0.952750 | + | 0.303756i | \(0.901759\pi\) | |||||||
\(854\) | 1.66274e126 | 0.0503972 | ||||||||
\(855\) | 2.83717e127 | 0.817258 | ||||||||
\(856\) | −4.85991e126 | −0.133051 | ||||||||
\(857\) | −4.68393e127 | −1.21883 | −0.609417 | − | 0.792850i | \(-0.708596\pi\) | ||||
−0.609417 | + | 0.792850i | \(0.708596\pi\) | |||||||
\(858\) | −1.26918e125 | −0.00313925 | ||||||||
\(859\) | −3.88133e126 | −0.0912594 | −0.0456297 | − | 0.998958i | \(-0.514529\pi\) | ||||
−0.0456297 | + | 0.998958i | \(0.514529\pi\) | |||||||
\(860\) | 2.01067e127 | 0.449425 | ||||||||
\(861\) | 1.68573e123 | 3.58220e−5 0 | ||||||||
\(862\) | 4.24801e125 | 0.00858261 | ||||||||
\(863\) | 3.37776e127 | 0.648873 | 0.324436 | − | 0.945907i | \(-0.394825\pi\) | ||||
0.324436 | + | 0.945907i | \(0.394825\pi\) | |||||||
\(864\) | −6.61585e124 | −0.00120848 | ||||||||
\(865\) | −8.42608e126 | −0.146361 | ||||||||
\(866\) | −5.77904e127 | −0.954613 | ||||||||
\(867\) | −2.12378e125 | −0.00333641 | ||||||||
\(868\) | 7.60746e124 | 0.00113666 | ||||||||
\(869\) | −2.10139e127 | −0.298639 | ||||||||
\(870\) | −1.81968e124 | −0.000245985 0 | ||||||||
\(871\) | 2.73618e127 | 0.351848 | ||||||||
\(872\) | −4.74489e127 | −0.580442 | ||||||||
\(873\) | 6.40418e127 | 0.745322 | ||||||||
\(874\) | −9.26592e127 | −1.02599 | ||||||||
\(875\) | 4.88050e126 | 0.0514179 | ||||||||
\(876\) | 2.17214e125 | 0.00217751 | ||||||||
\(877\) | −8.90445e127 | −0.849424 | −0.424712 | − | 0.905328i | \(-0.639625\pi\) | ||||
−0.424712 | + | 0.905328i | \(0.639625\pi\) | |||||||
\(878\) | 3.84541e127 | 0.349085 | ||||||||
\(879\) | 6.66882e125 | 0.00576146 | ||||||||
\(880\) | −2.95083e127 | −0.242632 | ||||||||
\(881\) | −1.67955e127 | −0.131444 | −0.0657221 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657221 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(882\) | 9.46542e127 | 0.705110 | ||||||||
\(883\) | 1.33044e128 | 0.943423 | 0.471711 | − | 0.881753i | \(-0.343636\pi\) | ||||
0.471711 | + | 0.881753i | \(0.343636\pi\) | |||||||
\(884\) | −8.95996e126 | −0.0604829 | ||||||||
\(885\) | 3.63871e124 | 0.000233838 0 | ||||||||
\(886\) | −6.56043e127 | −0.401389 | ||||||||
\(887\) | 2.54669e128 | 1.48354 | 0.741769 | − | 0.670655i | \(-0.233987\pi\) | ||||
0.741769 | + | 0.670655i | \(0.233987\pi\) | |||||||
\(888\) | −1.05711e125 | −0.000586350 0 | ||||||||
\(889\) | −8.50662e125 | −0.00449294 | ||||||||
\(890\) | 4.22366e127 | 0.212434 | ||||||||
\(891\) | 3.46550e128 | 1.65991 | ||||||||
\(892\) | −8.33745e127 | −0.380331 | ||||||||
\(893\) | −1.10395e128 | −0.479634 | ||||||||
\(894\) | 5.85548e125 | 0.00242315 | ||||||||
\(895\) | −1.75420e128 | −0.691477 | ||||||||
\(896\) | 1.24845e126 | 0.00468786 | ||||||||
\(897\) | 7.76087e125 | 0.00277613 | ||||||||
\(898\) | 3.04109e128 | 1.03636 | ||||||||
\(899\) | 2.29805e126 | 0.00746129 | ||||||||
\(900\) | 1.06378e128 | 0.329080 | ||||||||
\(901\) | −3.75915e127 | −0.110805 | ||||||||
\(902\) | 8.25763e127 | 0.231938 | ||||||||
\(903\) | −1.04127e125 | −0.000278705 0 | ||||||||
\(904\) | −2.65898e128 | −0.678249 | ||||||||
\(905\) | −4.19972e128 | −1.02096 | ||||||||
\(906\) | 8.69593e125 | 0.00201483 | ||||||||
\(907\) | −8.51106e128 | −1.87961 | −0.939803 | − | 0.341717i | \(-0.888992\pi\) | ||||
−0.939803 | + | 0.341717i | \(0.888992\pi\) | |||||||
\(908\) | −2.39728e128 | −0.504642 | ||||||||
\(909\) | 2.71367e128 | 0.544538 | ||||||||
\(910\) | 8.96864e126 | 0.0171564 | ||||||||
\(911\) | 4.32834e128 | 0.789354 | 0.394677 | − | 0.918820i | \(-0.370857\pi\) | ||||
0.394677 | + | 0.918820i | \(0.370857\pi\) | |||||||
\(912\) | 6.87003e125 | 0.00119449 | ||||||||
\(913\) | −1.51366e129 | −2.50928 | ||||||||
\(914\) | 6.26347e128 | 0.990047 | ||||||||
\(915\) | −1.78177e126 | −0.00268556 | ||||||||
\(916\) | 3.85431e128 | 0.553979 | ||||||||
\(917\) | 4.32500e127 | 0.0592816 | ||||||||
\(918\) | −5.71691e125 | −0.000747317 0 | ||||||||
\(919\) | −9.82778e128 | −1.22527 | −0.612633 | − | 0.790367i | \(-0.709890\pi\) | ||||
−0.612633 | + | 0.790367i | \(0.709890\pi\) | |||||||
\(920\) | 1.80439e128 | 0.214566 | ||||||||
\(921\) | −1.98735e126 | −0.00225414 | ||||||||
\(922\) | −7.52329e128 | −0.813978 | ||||||||
\(923\) | 1.22368e129 | 1.26297 | ||||||||
\(924\) | 1.52815e125 | 0.000150465 0 | ||||||||
\(925\) | 3.39952e128 | 0.319340 | ||||||||
\(926\) | 6.25026e128 | 0.560171 | ||||||||
\(927\) | 1.89934e129 | 1.62418 | ||||||||
\(928\) | 3.77132e127 | 0.0307721 | ||||||||
\(929\) | 2.05228e129 | 1.59791 | 0.798955 | − | 0.601390i | \(-0.205386\pi\) | ||||
0.798955 | + | 0.601390i | \(0.205386\pi\) | |||||||
\(930\) | −8.15206e124 | −6.05702e−5 0 | ||||||||
\(931\) | −1.96583e129 | −1.39391 | ||||||||
\(932\) | −6.54733e128 | −0.443070 | ||||||||
\(933\) | −1.02577e127 | −0.00662522 | ||||||||
\(934\) | 1.32068e128 | 0.0814158 | ||||||||
\(935\) | −2.54988e128 | −0.150043 | ||||||||
\(936\) | 4.92498e128 | 0.276634 | ||||||||
\(937\) | 1.97964e129 | 1.06149 | 0.530743 | − | 0.847533i | \(-0.321913\pi\) | ||||
0.530743 | + | 0.847533i | \(0.321913\pi\) | |||||||
\(938\) | −3.29448e127 | −0.0168641 | ||||||||
\(939\) | −1.17166e127 | −0.00572597 | ||||||||
\(940\) | 2.14976e128 | 0.100307 | ||||||||
\(941\) | 2.92123e128 | 0.130142 | 0.0650709 | − | 0.997881i | \(-0.479273\pi\) | ||||
0.0650709 | + | 0.997881i | \(0.479273\pi\) | |||||||
\(942\) | 8.18739e126 | 0.00348282 | ||||||||
\(943\) | −5.04943e128 | −0.205109 | ||||||||
\(944\) | −7.54127e127 | −0.0292525 | ||||||||
\(945\) | 5.72245e125 | 0.000211982 0 | ||||||||
\(946\) | −5.10071e129 | −1.80454 | ||||||||
\(947\) | 6.44723e128 | 0.217846 | 0.108923 | − | 0.994050i | \(-0.465260\pi\) | ||||
0.108923 | + | 0.994050i | \(0.465260\pi\) | |||||||
\(948\) | −9.52716e125 | −0.000307469 0 | ||||||||
\(949\) | −3.23400e129 | −0.996918 | ||||||||
\(950\) | −2.20931e129 | −0.650548 | ||||||||
\(951\) | 1.27376e127 | 0.00358291 | ||||||||
\(952\) | 1.07882e127 | 0.00289895 | ||||||||
\(953\) | 5.84421e129 | 1.50032 | 0.750161 | − | 0.661255i | \(-0.229976\pi\) | ||||
0.750161 | + | 0.661255i | \(0.229976\pi\) | |||||||
\(954\) | 2.06628e129 | 0.506797 | ||||||||
\(955\) | −2.74577e129 | −0.643453 | ||||||||
\(956\) | 3.34826e129 | 0.749723 | ||||||||
\(957\) | 4.61622e126 | 0.000987683 0 | ||||||||
\(958\) | −4.88255e129 | −0.998269 | ||||||||
\(959\) | −4.25653e128 | −0.0831661 | ||||||||
\(960\) | −1.33783e126 | −0.000249806 0 | ||||||||
\(961\) | −5.59331e129 | −0.998163 | ||||||||
\(962\) | 1.57388e129 | 0.268446 | ||||||||
\(963\) | 2.30836e129 | 0.376322 | ||||||||
\(964\) | −3.28346e129 | −0.511660 | ||||||||
\(965\) | 3.03824e129 | 0.452568 | ||||||||
\(966\) | −9.34443e125 | −0.000133060 0 | ||||||||
\(967\) | −7.02214e129 | −0.955912 | −0.477956 | − | 0.878384i | \(-0.658622\pi\) | ||||
−0.477956 | + | 0.878384i | \(0.658622\pi\) | |||||||
\(968\) | 4.76909e129 | 0.620665 | ||||||||
\(969\) | 5.93655e126 | 0.000738669 0 | ||||||||
\(970\) | 2.59007e129 | 0.308135 | ||||||||
\(971\) | −2.95416e129 | −0.336045 | −0.168023 | − | 0.985783i | \(-0.553738\pi\) | ||||
−0.168023 | + | 0.985783i | \(0.553738\pi\) | |||||||
\(972\) | 4.71360e127 | 0.00512708 | ||||||||
\(973\) | −3.84943e128 | −0.0400394 | ||||||||
\(974\) | 3.53291e129 | 0.351413 | ||||||||
\(975\) | 1.85045e127 | 0.00176026 | ||||||||
\(976\) | 3.69275e129 | 0.335956 | ||||||||
\(977\) | 9.86052e129 | 0.857998 | 0.428999 | − | 0.903305i | \(-0.358866\pi\) | ||||
0.428999 | + | 0.903305i | \(0.358866\pi\) | |||||||
\(978\) | −2.06687e126 | −0.000172018 0 | ||||||||
\(979\) | −1.07147e130 | −0.852969 | ||||||||
\(980\) | 3.82814e129 | 0.291510 | ||||||||
\(981\) | 2.25372e130 | 1.64172 | ||||||||
\(982\) | 1.08640e130 | 0.757079 | ||||||||
\(983\) | −1.04802e130 | −0.698704 | −0.349352 | − | 0.936992i | \(-0.613598\pi\) | ||||
−0.349352 | + | 0.936992i | \(0.613598\pi\) | |||||||
\(984\) | 3.74380e126 | 0.000238795 0 | ||||||||
\(985\) | −3.98227e129 | −0.243027 | ||||||||
\(986\) | 3.25889e128 | 0.0190293 | ||||||||
\(987\) | −1.11330e126 | −6.22038e−5 0 | ||||||||
\(988\) | −1.02285e130 | −0.546869 | ||||||||
\(989\) | 3.11902e130 | 1.59580 | ||||||||
\(990\) | 1.40158e130 | 0.686258 | ||||||||
\(991\) | −3.40775e130 | −1.59685 | −0.798425 | − | 0.602094i | \(-0.794333\pi\) | ||||
−0.798425 | + | 0.602094i | \(0.794333\pi\) | |||||||
\(992\) | 1.68953e128 | 0.00757717 | ||||||||
\(993\) | 7.90549e127 | 0.00339341 | ||||||||
\(994\) | −1.47336e129 | −0.0605344 | ||||||||
\(995\) | −4.76749e128 | −0.0187493 | ||||||||
\(996\) | −6.86254e127 | −0.00258347 | ||||||||
\(997\) | −2.57728e130 | −0.928799 | −0.464400 | − | 0.885626i | \(-0.653730\pi\) | ||||
−0.464400 | + | 0.885626i | \(0.653730\pi\) | |||||||
\(998\) | −4.25154e129 | −0.146679 | ||||||||
\(999\) | 1.00422e128 | 0.00331688 |
(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 | 2.88.a.a.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.88.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |