Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,12,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(17.6718931529\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} + \cdots - 51\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-62.6325\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 65.6325 | 1.45029 | 0.725143 | − | 0.688598i | \(-0.241773\pi\) | ||||
0.725143 | + | 0.688598i | \(0.241773\pi\) | |||||||
\(3\) | 631.031 | 1.49928 | 0.749642 | − | 0.661843i | \(-0.230226\pi\) | ||||
0.749642 | + | 0.661843i | \(0.230226\pi\) | |||||||
\(4\) | 2259.62 | 1.10333 | ||||||||
\(5\) | 3124.13 | 0.447089 | 0.223545 | − | 0.974694i | \(-0.428237\pi\) | ||||
0.223545 | + | 0.974694i | \(0.428237\pi\) | |||||||
\(6\) | 41416.2 | 2.17439 | ||||||||
\(7\) | 7787.45 | 0.175128 | 0.0875641 | − | 0.996159i | \(-0.472092\pi\) | ||||
0.0875641 | + | 0.996159i | \(0.472092\pi\) | |||||||
\(8\) | 13889.4 | 0.149861 | ||||||||
\(9\) | 221053. | 1.24785 | ||||||||
\(10\) | 205044. | 0.648407 | ||||||||
\(11\) | 211691. | 0.396318 | 0.198159 | − | 0.980170i | \(-0.436504\pi\) | ||||
0.198159 | + | 0.980170i | \(0.436504\pi\) | |||||||
\(12\) | 1.42589e6 | 1.65421 | ||||||||
\(13\) | −351807. | −0.262794 | −0.131397 | − | 0.991330i | \(-0.541946\pi\) | ||||
−0.131397 | + | 0.991330i | \(0.541946\pi\) | |||||||
\(14\) | 511110. | 0.253986 | ||||||||
\(15\) | 1.97142e6 | 0.670314 | ||||||||
\(16\) | −3.71611e6 | −0.885991 | ||||||||
\(17\) | −4.23853e6 | −0.724012 | −0.362006 | − | 0.932176i | \(-0.617908\pi\) | ||||
−0.362006 | + | 0.932176i | \(0.617908\pi\) | |||||||
\(18\) | 1.45083e7 | 1.80974 | ||||||||
\(19\) | 2.23632e6 | 0.207200 | 0.103600 | − | 0.994619i | \(-0.466964\pi\) | ||||
0.103600 | + | 0.994619i | \(0.466964\pi\) | |||||||
\(20\) | 7.05936e6 | 0.493288 | ||||||||
\(21\) | 4.91413e6 | 0.262567 | ||||||||
\(22\) | 1.38938e7 | 0.574774 | ||||||||
\(23\) | −6.43634e6 | −0.208514 | ||||||||
\(24\) | 8.76464e6 | 0.224684 | ||||||||
\(25\) | −3.90679e7 | −0.800111 | ||||||||
\(26\) | −2.30900e7 | −0.381127 | ||||||||
\(27\) | 2.77063e7 | 0.371602 | ||||||||
\(28\) | 1.75967e7 | 0.193225 | ||||||||
\(29\) | 1.29485e8 | 1.17228 | 0.586140 | − | 0.810210i | \(-0.300647\pi\) | ||||
0.586140 | + | 0.810210i | \(0.300647\pi\) | |||||||
\(30\) | 1.29389e8 | 0.972147 | ||||||||
\(31\) | 2.61520e8 | 1.64065 | 0.820324 | − | 0.571899i | \(-0.193793\pi\) | ||||
0.820324 | + | 0.571899i | \(0.193793\pi\) | |||||||
\(32\) | −2.72343e8 | −1.43480 | ||||||||
\(33\) | 1.33584e8 | 0.594193 | ||||||||
\(34\) | −2.78185e8 | −1.05003 | ||||||||
\(35\) | 2.43290e7 | 0.0782980 | ||||||||
\(36\) | 4.99498e8 | 1.37680 | ||||||||
\(37\) | 3.25723e7 | 0.0772217 | 0.0386109 | − | 0.999254i | \(-0.487707\pi\) | ||||
0.0386109 | + | 0.999254i | \(0.487707\pi\) | |||||||
\(38\) | 1.46776e8 | 0.300500 | ||||||||
\(39\) | −2.22001e8 | −0.394004 | ||||||||
\(40\) | 4.33923e7 | 0.0670012 | ||||||||
\(41\) | −4.87104e8 | −0.656615 | −0.328307 | − | 0.944571i | \(-0.606478\pi\) | ||||
−0.328307 | + | 0.944571i | \(0.606478\pi\) | |||||||
\(42\) | 3.22526e8 | 0.380798 | ||||||||
\(43\) | −1.03801e9 | −1.07677 | −0.538386 | − | 0.842699i | \(-0.680966\pi\) | ||||
−0.538386 | + | 0.842699i | \(0.680966\pi\) | |||||||
\(44\) | 4.78343e8 | 0.437270 | ||||||||
\(45\) | 6.90600e8 | 0.557902 | ||||||||
\(46\) | −4.22433e8 | −0.302406 | ||||||||
\(47\) | −1.79020e9 | −1.13858 | −0.569289 | − | 0.822138i | \(-0.692781\pi\) | ||||
−0.569289 | + | 0.822138i | \(0.692781\pi\) | |||||||
\(48\) | −2.34498e9 | −1.32835 | ||||||||
\(49\) | −1.91668e9 | −0.969330 | ||||||||
\(50\) | −2.56413e9 | −1.16039 | ||||||||
\(51\) | −2.67464e9 | −1.08550 | ||||||||
\(52\) | −7.94952e8 | −0.289950 | ||||||||
\(53\) | −4.41673e8 | −0.145072 | −0.0725360 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725360 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(54\) | 1.81844e9 | 0.538930 | ||||||||
\(55\) | 6.61351e8 | 0.177189 | ||||||||
\(56\) | 1.08163e8 | 0.0262449 | ||||||||
\(57\) | 1.41119e9 | 0.310652 | ||||||||
\(58\) | 8.49844e9 | 1.70014 | ||||||||
\(59\) | −1.84548e9 | −0.336065 | −0.168033 | − | 0.985781i | \(-0.553741\pi\) | ||||
−0.168033 | + | 0.985781i | \(0.553741\pi\) | |||||||
\(60\) | 4.45468e9 | 0.739578 | ||||||||
\(61\) | 4.99566e9 | 0.757319 | 0.378660 | − | 0.925536i | \(-0.376385\pi\) | ||||
0.378660 | + | 0.925536i | \(0.376385\pi\) | |||||||
\(62\) | 1.71642e10 | 2.37941 | ||||||||
\(63\) | 1.72144e9 | 0.218534 | ||||||||
\(64\) | −1.02640e10 | −1.19488 | ||||||||
\(65\) | −1.09909e9 | −0.117493 | ||||||||
\(66\) | 8.76744e9 | 0.861750 | ||||||||
\(67\) | 1.53293e10 | 1.38711 | 0.693554 | − | 0.720405i | \(-0.256044\pi\) | ||||
0.693554 | + | 0.720405i | \(0.256044\pi\) | |||||||
\(68\) | −9.57748e9 | −0.798826 | ||||||||
\(69\) | −4.06153e9 | −0.312622 | ||||||||
\(70\) | 1.59677e9 | 0.113554 | ||||||||
\(71\) | −4.47622e9 | −0.294436 | −0.147218 | − | 0.989104i | \(-0.547032\pi\) | ||||
−0.147218 | + | 0.989104i | \(0.547032\pi\) | |||||||
\(72\) | 3.07030e9 | 0.187004 | ||||||||
\(73\) | −1.34861e10 | −0.761398 | −0.380699 | − | 0.924699i | \(-0.624317\pi\) | ||||
−0.380699 | + | 0.924699i | \(0.624317\pi\) | |||||||
\(74\) | 2.13780e9 | 0.111994 | ||||||||
\(75\) | −2.46531e10 | −1.19959 | ||||||||
\(76\) | 5.05325e9 | 0.228610 | ||||||||
\(77\) | 1.64854e9 | 0.0694064 | ||||||||
\(78\) | −1.45705e10 | −0.571418 | ||||||||
\(79\) | 2.89555e9 | 0.105872 | 0.0529360 | − | 0.998598i | \(-0.483142\pi\) | ||||
0.0529360 | + | 0.998598i | \(0.483142\pi\) | |||||||
\(80\) | −1.16096e10 | −0.396117 | ||||||||
\(81\) | −2.16754e10 | −0.690716 | ||||||||
\(82\) | −3.19698e10 | −0.952279 | ||||||||
\(83\) | 6.75213e10 | 1.88153 | 0.940765 | − | 0.339060i | \(-0.110109\pi\) | ||||
0.940765 | + | 0.339060i | \(0.110109\pi\) | |||||||
\(84\) | 1.11041e10 | 0.289699 | ||||||||
\(85\) | −1.32417e10 | −0.323698 | ||||||||
\(86\) | −6.81269e10 | −1.56163 | ||||||||
\(87\) | 8.17092e10 | 1.75758 | ||||||||
\(88\) | 2.94026e9 | 0.0593925 | ||||||||
\(89\) | 9.32766e10 | 1.77063 | 0.885315 | − | 0.464993i | \(-0.153943\pi\) | ||||
0.885315 | + | 0.464993i | \(0.153943\pi\) | |||||||
\(90\) | 4.53258e10 | 0.809117 | ||||||||
\(91\) | −2.73968e9 | −0.0460227 | ||||||||
\(92\) | −1.45437e10 | −0.230061 | ||||||||
\(93\) | 1.65027e11 | 2.45980 | ||||||||
\(94\) | −1.17495e11 | −1.65126 | ||||||||
\(95\) | 6.98657e9 | 0.0926369 | ||||||||
\(96\) | −1.71857e11 | −2.15118 | ||||||||
\(97\) | −8.00449e10 | −0.946432 | −0.473216 | − | 0.880947i | \(-0.656907\pi\) | ||||
−0.473216 | + | 0.880947i | \(0.656907\pi\) | |||||||
\(98\) | −1.25797e11 | −1.40581 | ||||||||
\(99\) | 4.67951e10 | 0.494546 | ||||||||
\(100\) | −8.82788e10 | −0.882788 | ||||||||
\(101\) | −7.80524e10 | −0.738956 | −0.369478 | − | 0.929239i | \(-0.620464\pi\) | ||||
−0.369478 | + | 0.929239i | \(0.620464\pi\) | |||||||
\(102\) | −1.75544e11 | −1.57429 | ||||||||
\(103\) | 4.31237e10 | 0.366532 | 0.183266 | − | 0.983063i | \(-0.441333\pi\) | ||||
0.183266 | + | 0.983063i | \(0.441333\pi\) | |||||||
\(104\) | −4.88639e9 | −0.0393826 | ||||||||
\(105\) | 1.53524e10 | 0.117391 | ||||||||
\(106\) | −2.89881e10 | −0.210396 | ||||||||
\(107\) | 2.31187e11 | 1.59351 | 0.796753 | − | 0.604306i | \(-0.206549\pi\) | ||||
0.796753 | + | 0.604306i | \(0.206549\pi\) | |||||||
\(108\) | 6.26059e10 | 0.410001 | ||||||||
\(109\) | −1.11970e11 | −0.697037 | −0.348518 | − | 0.937302i | \(-0.613315\pi\) | ||||
−0.348518 | + | 0.937302i | \(0.613315\pi\) | |||||||
\(110\) | 4.34061e10 | 0.256975 | ||||||||
\(111\) | 2.05542e10 | 0.115777 | ||||||||
\(112\) | −2.89391e10 | −0.155162 | ||||||||
\(113\) | 3.61946e11 | 1.84805 | 0.924023 | − | 0.382337i | \(-0.124881\pi\) | ||||
0.924023 | + | 0.382337i | \(0.124881\pi\) | |||||||
\(114\) | 9.26199e10 | 0.450534 | ||||||||
\(115\) | −2.01080e10 | −0.0932245 | ||||||||
\(116\) | 2.92588e11 | 1.29341 | ||||||||
\(117\) | −7.77682e10 | −0.327929 | ||||||||
\(118\) | −1.21124e11 | −0.487391 | ||||||||
\(119\) | −3.30073e10 | −0.126795 | ||||||||
\(120\) | 2.73819e10 | 0.100454 | ||||||||
\(121\) | −2.40498e11 | −0.842932 | ||||||||
\(122\) | 3.27878e11 | 1.09833 | ||||||||
\(123\) | −3.07378e11 | −0.984452 | ||||||||
\(124\) | 5.90936e11 | 1.81018 | ||||||||
\(125\) | −2.74599e11 | −0.804810 | ||||||||
\(126\) | 1.12983e11 | 0.316938 | ||||||||
\(127\) | 3.05442e11 | 0.820368 | 0.410184 | − | 0.912003i | \(-0.365465\pi\) | ||||
0.410184 | + | 0.912003i | \(0.365465\pi\) | |||||||
\(128\) | −1.15891e11 | −0.298122 | ||||||||
\(129\) | −6.55014e11 | −1.61439 | ||||||||
\(130\) | −7.21361e10 | −0.170398 | ||||||||
\(131\) | 1.58005e11 | 0.357832 | 0.178916 | − | 0.983864i | \(-0.442741\pi\) | ||||
0.178916 | + | 0.983864i | \(0.442741\pi\) | |||||||
\(132\) | 3.01849e11 | 0.655592 | ||||||||
\(133\) | 1.74153e10 | 0.0362866 | ||||||||
\(134\) | 1.00610e12 | 2.01170 | ||||||||
\(135\) | 8.65582e10 | 0.166139 | ||||||||
\(136\) | −5.88706e10 | −0.108501 | ||||||||
\(137\) | 9.32644e11 | 1.65102 | 0.825510 | − | 0.564387i | \(-0.190887\pi\) | ||||
0.825510 | + | 0.564387i | \(0.190887\pi\) | |||||||
\(138\) | −2.66569e11 | −0.453392 | ||||||||
\(139\) | 2.56688e11 | 0.419590 | 0.209795 | − | 0.977745i | \(-0.432720\pi\) | ||||
0.209795 | + | 0.977745i | \(0.432720\pi\) | |||||||
\(140\) | 5.49744e10 | 0.0863886 | ||||||||
\(141\) | −1.12967e12 | −1.70705 | ||||||||
\(142\) | −2.93786e11 | −0.427017 | ||||||||
\(143\) | −7.44745e10 | −0.104150 | ||||||||
\(144\) | −8.21460e11 | −1.10559 | ||||||||
\(145\) | 4.04529e11 | 0.524113 | ||||||||
\(146\) | −8.85129e11 | −1.10425 | ||||||||
\(147\) | −1.20949e12 | −1.45330 | ||||||||
\(148\) | 7.36012e10 | 0.0852012 | ||||||||
\(149\) | −6.21251e11 | −0.693015 | −0.346507 | − | 0.938047i | \(-0.612632\pi\) | ||||
−0.346507 | + | 0.938047i | \(0.612632\pi\) | |||||||
\(150\) | −1.61804e12 | −1.73976 | ||||||||
\(151\) | 1.52696e12 | 1.58290 | 0.791451 | − | 0.611233i | \(-0.209326\pi\) | ||||
0.791451 | + | 0.611233i | \(0.209326\pi\) | |||||||
\(152\) | 3.10612e10 | 0.0310512 | ||||||||
\(153\) | −9.36941e11 | −0.903461 | ||||||||
\(154\) | 1.08198e11 | 0.100659 | ||||||||
\(155\) | 8.17022e11 | 0.733516 | ||||||||
\(156\) | −5.01639e11 | −0.434717 | ||||||||
\(157\) | −4.68531e11 | −0.392004 | −0.196002 | − | 0.980604i | \(-0.562796\pi\) | ||||
−0.196002 | + | 0.980604i | \(0.562796\pi\) | |||||||
\(158\) | 1.90042e11 | 0.153545 | ||||||||
\(159\) | −2.78710e11 | −0.217504 | ||||||||
\(160\) | −8.50836e11 | −0.641484 | ||||||||
\(161\) | −5.01227e10 | −0.0365168 | ||||||||
\(162\) | −1.42261e12 | −1.00174 | ||||||||
\(163\) | 2.50532e12 | 1.70542 | 0.852710 | − | 0.522385i | \(-0.174957\pi\) | ||||
0.852710 | + | 0.522385i | \(0.174957\pi\) | |||||||
\(164\) | −1.10067e12 | −0.724464 | ||||||||
\(165\) | 4.17333e11 | 0.265657 | ||||||||
\(166\) | 4.43159e12 | 2.72876 | ||||||||
\(167\) | −6.33000e11 | −0.377106 | −0.188553 | − | 0.982063i | \(-0.560380\pi\) | ||||
−0.188553 | + | 0.982063i | \(0.560380\pi\) | |||||||
\(168\) | 6.82542e10 | 0.0393485 | ||||||||
\(169\) | −1.66839e12 | −0.930939 | ||||||||
\(170\) | −8.69087e11 | −0.469455 | ||||||||
\(171\) | 4.94347e11 | 0.258555 | ||||||||
\(172\) | −2.34550e12 | −1.18804 | ||||||||
\(173\) | −1.80580e12 | −0.885962 | −0.442981 | − | 0.896531i | \(-0.646079\pi\) | ||||
−0.442981 | + | 0.896531i | \(0.646079\pi\) | |||||||
\(174\) | 5.36278e12 | 2.54900 | ||||||||
\(175\) | −3.04240e11 | −0.140122 | ||||||||
\(176\) | −7.86669e11 | −0.351134 | ||||||||
\(177\) | −1.16456e12 | −0.503857 | ||||||||
\(178\) | 6.12197e12 | 2.56792 | ||||||||
\(179\) | 1.01526e12 | 0.412938 | 0.206469 | − | 0.978453i | \(-0.433803\pi\) | ||||
0.206469 | + | 0.978453i | \(0.433803\pi\) | |||||||
\(180\) | 1.56050e12 | 0.615551 | ||||||||
\(181\) | 7.01470e11 | 0.268397 | 0.134198 | − | 0.990955i | \(-0.457154\pi\) | ||||
0.134198 | + | 0.990955i | \(0.457154\pi\) | |||||||
\(182\) | −1.79812e11 | −0.0667462 | ||||||||
\(183\) | 3.15242e12 | 1.13544 | ||||||||
\(184\) | −8.93969e10 | −0.0312481 | ||||||||
\(185\) | 1.01760e11 | 0.0345250 | ||||||||
\(186\) | 1.08311e13 | 3.56741 | ||||||||
\(187\) | −8.97260e11 | −0.286939 | ||||||||
\(188\) | −4.04517e12 | −1.25623 | ||||||||
\(189\) | 2.15762e11 | 0.0650781 | ||||||||
\(190\) | 4.58546e11 | 0.134350 | ||||||||
\(191\) | −4.84201e12 | −1.37830 | −0.689148 | − | 0.724621i | \(-0.742015\pi\) | ||||
−0.689148 | + | 0.724621i | \(0.742015\pi\) | |||||||
\(192\) | −6.47688e12 | −1.79147 | ||||||||
\(193\) | 3.09865e12 | 0.832927 | 0.416463 | − | 0.909152i | \(-0.363269\pi\) | ||||
0.416463 | + | 0.909152i | \(0.363269\pi\) | |||||||
\(194\) | −5.25355e12 | −1.37260 | ||||||||
\(195\) | −6.93561e11 | −0.176155 | ||||||||
\(196\) | −4.33098e12 | −1.06949 | ||||||||
\(197\) | −2.23378e12 | −0.536386 | −0.268193 | − | 0.963365i | \(-0.586426\pi\) | ||||
−0.268193 | + | 0.963365i | \(0.586426\pi\) | |||||||
\(198\) | 3.07128e12 | 0.717234 | ||||||||
\(199\) | −4.84925e12 | −1.10149 | −0.550747 | − | 0.834672i | \(-0.685657\pi\) | ||||
−0.550747 | + | 0.834672i | \(0.685657\pi\) | |||||||
\(200\) | −5.42630e11 | −0.119905 | ||||||||
\(201\) | 9.67325e12 | 2.07967 | ||||||||
\(202\) | −5.12278e12 | −1.07170 | ||||||||
\(203\) | 1.00836e12 | 0.205299 | ||||||||
\(204\) | −6.04369e12 | −1.19767 | ||||||||
\(205\) | −1.52178e12 | −0.293565 | ||||||||
\(206\) | 2.83032e12 | 0.531576 | ||||||||
\(207\) | −1.42278e12 | −0.260195 | ||||||||
\(208\) | 1.30736e12 | 0.232833 | ||||||||
\(209\) | 4.73410e11 | 0.0821170 | ||||||||
\(210\) | 1.00761e12 | 0.170250 | ||||||||
\(211\) | −1.09399e12 | −0.180078 | −0.0900392 | − | 0.995938i | \(-0.528699\pi\) | ||||
−0.0900392 | + | 0.995938i | \(0.528699\pi\) | |||||||
\(212\) | −9.98015e11 | −0.160063 | ||||||||
\(213\) | −2.82464e12 | −0.441443 | ||||||||
\(214\) | 1.51734e13 | 2.31104 | ||||||||
\(215\) | −3.24287e12 | −0.481413 | ||||||||
\(216\) | 3.84824e11 | 0.0556886 | ||||||||
\(217\) | 2.03657e12 | 0.287324 | ||||||||
\(218\) | −7.34886e12 | −1.01090 | ||||||||
\(219\) | −8.51018e12 | −1.14155 | ||||||||
\(220\) | 1.49441e12 | 0.195499 | ||||||||
\(221\) | 1.49114e12 | 0.190266 | ||||||||
\(222\) | 1.34902e12 | 0.167910 | ||||||||
\(223\) | −6.86430e12 | −0.833527 | −0.416764 | − | 0.909015i | \(-0.636836\pi\) | ||||
−0.416764 | + | 0.909015i | \(0.636836\pi\) | |||||||
\(224\) | −2.12086e12 | −0.251274 | ||||||||
\(225\) | −8.63610e12 | −0.998421 | ||||||||
\(226\) | 2.37554e13 | 2.68020 | ||||||||
\(227\) | −3.03775e12 | −0.334510 | −0.167255 | − | 0.985914i | \(-0.553490\pi\) | ||||
−0.167255 | + | 0.985914i | \(0.553490\pi\) | |||||||
\(228\) | 3.18876e12 | 0.342752 | ||||||||
\(229\) | 1.48440e13 | 1.55760 | 0.778798 | − | 0.627274i | \(-0.215830\pi\) | ||||
0.778798 | + | 0.627274i | \(0.215830\pi\) | |||||||
\(230\) | −1.31974e12 | −0.135202 | ||||||||
\(231\) | 1.04028e12 | 0.104060 | ||||||||
\(232\) | 1.79847e12 | 0.175679 | ||||||||
\(233\) | −1.01878e12 | −0.0971900 | −0.0485950 | − | 0.998819i | \(-0.515474\pi\) | ||||
−0.0485950 | + | 0.998819i | \(0.515474\pi\) | |||||||
\(234\) | −5.10412e12 | −0.475591 | ||||||||
\(235\) | −5.59281e12 | −0.509045 | ||||||||
\(236\) | −4.17009e12 | −0.370791 | ||||||||
\(237\) | 1.82718e12 | 0.158732 | ||||||||
\(238\) | −2.16635e12 | −0.183889 | ||||||||
\(239\) | 2.02747e12 | 0.168177 | 0.0840886 | − | 0.996458i | \(-0.473202\pi\) | ||||
0.0840886 | + | 0.996458i | \(0.473202\pi\) | |||||||
\(240\) | −7.32604e12 | −0.593892 | ||||||||
\(241\) | 7.37078e12 | 0.584010 | 0.292005 | − | 0.956417i | \(-0.405678\pi\) | ||||
0.292005 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(242\) | −1.57845e13 | −1.22249 | ||||||||
\(243\) | −1.85859e13 | −1.40718 | ||||||||
\(244\) | 1.12883e13 | 0.835574 | ||||||||
\(245\) | −5.98797e12 | −0.433377 | ||||||||
\(246\) | −2.01740e13 | −1.42774 | ||||||||
\(247\) | −7.86755e11 | −0.0544510 | ||||||||
\(248\) | 3.63235e12 | 0.245869 | ||||||||
\(249\) | 4.26080e13 | 2.82095 | ||||||||
\(250\) | −1.80226e13 | −1.16721 | ||||||||
\(251\) | −2.08015e12 | −0.131792 | −0.0658960 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658960 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(252\) | 3.88981e12 | 0.241116 | ||||||||
\(253\) | −1.36252e12 | −0.0826379 | ||||||||
\(254\) | 2.00469e13 | 1.18977 | ||||||||
\(255\) | −8.35594e12 | −0.485315 | ||||||||
\(256\) | 1.34144e13 | 0.762521 | ||||||||
\(257\) | −2.40233e13 | −1.33660 | −0.668298 | − | 0.743894i | \(-0.732977\pi\) | ||||
−0.668298 | + | 0.743894i | \(0.732977\pi\) | |||||||
\(258\) | −4.29902e13 | −2.34132 | ||||||||
\(259\) | 2.53656e11 | 0.0135237 | ||||||||
\(260\) | −2.48353e12 | −0.129633 | ||||||||
\(261\) | 2.86232e13 | 1.46283 | ||||||||
\(262\) | 1.03703e13 | 0.518959 | ||||||||
\(263\) | −1.11284e13 | −0.545352 | −0.272676 | − | 0.962106i | \(-0.587909\pi\) | ||||
−0.272676 | + | 0.962106i | \(0.587909\pi\) | |||||||
\(264\) | 1.85540e12 | 0.0890462 | ||||||||
\(265\) | −1.37984e12 | −0.0648601 | ||||||||
\(266\) | 1.14301e12 | 0.0526260 | ||||||||
\(267\) | 5.88604e13 | 2.65468 | ||||||||
\(268\) | 3.46384e13 | 1.53044 | ||||||||
\(269\) | 1.07133e13 | 0.463752 | 0.231876 | − | 0.972745i | \(-0.425514\pi\) | ||||
0.231876 | + | 0.972745i | \(0.425514\pi\) | |||||||
\(270\) | 5.68103e12 | 0.240950 | ||||||||
\(271\) | 3.65688e12 | 0.151978 | 0.0759889 | − | 0.997109i | \(-0.475789\pi\) | ||||
0.0759889 | + | 0.997109i | \(0.475789\pi\) | |||||||
\(272\) | 1.57509e13 | 0.641468 | ||||||||
\(273\) | −1.72883e12 | −0.0690012 | ||||||||
\(274\) | 6.12117e13 | 2.39445 | ||||||||
\(275\) | −8.27035e12 | −0.317098 | ||||||||
\(276\) | −9.17754e12 | −0.344926 | ||||||||
\(277\) | 4.09792e13 | 1.50982 | 0.754910 | − | 0.655829i | \(-0.227681\pi\) | ||||
0.754910 | + | 0.655829i | \(0.227681\pi\) | |||||||
\(278\) | 1.68471e13 | 0.608525 | ||||||||
\(279\) | 5.78099e13 | 2.04729 | ||||||||
\(280\) | 3.37915e11 | 0.0117338 | ||||||||
\(281\) | −3.21025e13 | −1.09308 | −0.546542 | − | 0.837432i | \(-0.684056\pi\) | ||||
−0.546542 | + | 0.837432i | \(0.684056\pi\) | |||||||
\(282\) | −7.41430e13 | −2.47571 | ||||||||
\(283\) | −5.54920e13 | −1.81721 | −0.908604 | − | 0.417658i | \(-0.862851\pi\) | ||||
−0.908604 | + | 0.417658i | \(0.862851\pi\) | |||||||
\(284\) | −1.01146e13 | −0.324861 | ||||||||
\(285\) | 4.40874e12 | 0.138889 | ||||||||
\(286\) | −4.88795e12 | −0.151048 | ||||||||
\(287\) | −3.79330e12 | −0.114992 | ||||||||
\(288\) | −6.02024e13 | −1.79042 | ||||||||
\(289\) | −1.63068e13 | −0.475806 | ||||||||
\(290\) | 2.65502e13 | 0.760115 | ||||||||
\(291\) | −5.05108e13 | −1.41897 | ||||||||
\(292\) | −3.04736e13 | −0.840075 | ||||||||
\(293\) | 1.93859e13 | 0.524461 | 0.262230 | − | 0.965005i | \(-0.415542\pi\) | ||||
0.262230 | + | 0.965005i | \(0.415542\pi\) | |||||||
\(294\) | −7.93816e13 | −2.10770 | ||||||||
\(295\) | −5.76552e12 | −0.150251 | ||||||||
\(296\) | 4.52410e11 | 0.0115725 | ||||||||
\(297\) | 5.86519e12 | 0.147273 | ||||||||
\(298\) | −4.07742e13 | −1.00507 | ||||||||
\(299\) | 2.26435e12 | 0.0547964 | ||||||||
\(300\) | −5.57067e13 | −1.32355 | ||||||||
\(301\) | −8.08343e12 | −0.188573 | ||||||||
\(302\) | 1.00218e14 | 2.29566 | ||||||||
\(303\) | −4.92535e13 | −1.10791 | ||||||||
\(304\) | −8.31043e12 | −0.183577 | ||||||||
\(305\) | 1.56071e13 | 0.338589 | ||||||||
\(306\) | −6.14938e13 | −1.31028 | ||||||||
\(307\) | 7.42246e13 | 1.55341 | 0.776706 | − | 0.629863i | \(-0.216889\pi\) | ||||
0.776706 | + | 0.629863i | \(0.216889\pi\) | |||||||
\(308\) | 3.72507e12 | 0.0765783 | ||||||||
\(309\) | 2.72124e13 | 0.549535 | ||||||||
\(310\) | 5.36232e13 | 1.06381 | ||||||||
\(311\) | −5.46873e13 | −1.06587 | −0.532935 | − | 0.846156i | \(-0.678911\pi\) | ||||
−0.532935 | + | 0.846156i | \(0.678911\pi\) | |||||||
\(312\) | −3.08346e12 | −0.0590457 | ||||||||
\(313\) | −3.81780e13 | −0.718322 | −0.359161 | − | 0.933276i | \(-0.616937\pi\) | ||||
−0.359161 | + | 0.933276i | \(0.616937\pi\) | |||||||
\(314\) | −3.07508e13 | −0.568518 | ||||||||
\(315\) | 5.37801e12 | 0.0977044 | ||||||||
\(316\) | 6.54285e12 | 0.116812 | ||||||||
\(317\) | 1.95246e13 | 0.342575 | 0.171287 | − | 0.985221i | \(-0.445207\pi\) | ||||
0.171287 | + | 0.985221i | \(0.445207\pi\) | |||||||
\(318\) | −1.82924e13 | −0.315443 | ||||||||
\(319\) | 2.74109e13 | 0.464595 | ||||||||
\(320\) | −3.20660e13 | −0.534219 | ||||||||
\(321\) | 1.45887e14 | 2.38912 | ||||||||
\(322\) | −3.28968e12 | −0.0529598 | ||||||||
\(323\) | −9.47872e12 | −0.150015 | ||||||||
\(324\) | −4.89782e13 | −0.762089 | ||||||||
\(325\) | 1.37444e13 | 0.210265 | ||||||||
\(326\) | 1.64430e14 | 2.47335 | ||||||||
\(327\) | −7.06565e13 | −1.04506 | ||||||||
\(328\) | −6.76558e12 | −0.0984008 | ||||||||
\(329\) | −1.39411e13 | −0.199397 | ||||||||
\(330\) | 2.73906e13 | 0.385279 | ||||||||
\(331\) | −8.92708e13 | −1.23497 | −0.617484 | − | 0.786584i | \(-0.711848\pi\) | ||||
−0.617484 | + | 0.786584i | \(0.711848\pi\) | |||||||
\(332\) | 1.52573e14 | 2.07595 | ||||||||
\(333\) | 7.20023e12 | 0.0963614 | ||||||||
\(334\) | −4.15454e13 | −0.546911 | ||||||||
\(335\) | 4.78907e13 | 0.620161 | ||||||||
\(336\) | −1.82615e13 | −0.232632 | ||||||||
\(337\) | −2.35212e13 | −0.294778 | −0.147389 | − | 0.989079i | \(-0.547087\pi\) | ||||
−0.147389 | + | 0.989079i | \(0.547087\pi\) | |||||||
\(338\) | −1.09501e14 | −1.35013 | ||||||||
\(339\) | 2.28399e14 | 2.77075 | ||||||||
\(340\) | −2.99213e13 | −0.357146 | ||||||||
\(341\) | 5.53615e13 | 0.650218 | ||||||||
\(342\) | 3.24452e13 | 0.374979 | ||||||||
\(343\) | −3.03244e13 | −0.344885 | ||||||||
\(344\) | −1.44173e13 | −0.161366 | ||||||||
\(345\) | −1.26888e13 | −0.139770 | ||||||||
\(346\) | −1.18519e14 | −1.28490 | ||||||||
\(347\) | 1.08486e13 | 0.115761 | 0.0578804 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578804 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(348\) | 1.84632e14 | 1.93919 | ||||||||
\(349\) | 4.75012e13 | 0.491094 | 0.245547 | − | 0.969385i | \(-0.421032\pi\) | ||||
0.245547 | + | 0.969385i | \(0.421032\pi\) | |||||||
\(350\) | −1.99680e13 | −0.203217 | ||||||||
\(351\) | −9.74729e12 | −0.0976550 | ||||||||
\(352\) | −5.76527e13 | −0.568637 | ||||||||
\(353\) | −4.65249e12 | −0.0451777 | −0.0225889 | − | 0.999745i | \(-0.507191\pi\) | ||||
−0.0225889 | + | 0.999745i | \(0.507191\pi\) | |||||||
\(354\) | −7.64327e13 | −0.730738 | ||||||||
\(355\) | −1.39843e13 | −0.131639 | ||||||||
\(356\) | 2.10770e14 | 1.95359 | ||||||||
\(357\) | −2.08287e13 | −0.190102 | ||||||||
\(358\) | 6.66339e13 | 0.598878 | ||||||||
\(359\) | −1.98229e14 | −1.75447 | −0.877237 | − | 0.480057i | \(-0.840616\pi\) | ||||
−0.877237 | + | 0.480057i | \(0.840616\pi\) | |||||||
\(360\) | 9.59201e12 | 0.0836076 | ||||||||
\(361\) | −1.11489e14 | −0.957068 | ||||||||
\(362\) | 4.60392e13 | 0.389252 | ||||||||
\(363\) | −1.51762e14 | −1.26380 | ||||||||
\(364\) | −6.19065e12 | −0.0507784 | ||||||||
\(365\) | −4.21325e13 | −0.340413 | ||||||||
\(366\) | 2.06901e14 | 1.64671 | ||||||||
\(367\) | 2.00670e14 | 1.57333 | 0.786665 | − | 0.617381i | \(-0.211806\pi\) | ||||
0.786665 | + | 0.617381i | \(0.211806\pi\) | |||||||
\(368\) | 2.39182e13 | 0.184742 | ||||||||
\(369\) | −1.07676e14 | −0.819358 | ||||||||
\(370\) | 6.67878e12 | 0.0500712 | ||||||||
\(371\) | −3.43951e12 | −0.0254062 | ||||||||
\(372\) | 3.72899e14 | 2.71397 | ||||||||
\(373\) | −2.31699e14 | −1.66160 | −0.830800 | − | 0.556571i | \(-0.812117\pi\) | ||||
−0.830800 | + | 0.556571i | \(0.812117\pi\) | |||||||
\(374\) | −5.88894e13 | −0.416144 | ||||||||
\(375\) | −1.73280e14 | −1.20664 | ||||||||
\(376\) | −2.48647e13 | −0.170628 | ||||||||
\(377\) | −4.55538e13 | −0.308069 | ||||||||
\(378\) | 1.41610e13 | 0.0943819 | ||||||||
\(379\) | 3.29073e13 | 0.216161 | 0.108080 | − | 0.994142i | \(-0.465530\pi\) | ||||
0.108080 | + | 0.994142i | \(0.465530\pi\) | |||||||
\(380\) | 1.57870e13 | 0.102209 | ||||||||
\(381\) | 1.92744e14 | 1.22996 | ||||||||
\(382\) | −3.17793e14 | −1.99892 | ||||||||
\(383\) | −2.64354e14 | −1.63905 | −0.819525 | − | 0.573044i | \(-0.805762\pi\) | ||||
−0.819525 | + | 0.573044i | \(0.805762\pi\) | |||||||
\(384\) | −7.31306e13 | −0.446969 | ||||||||
\(385\) | 5.15024e12 | 0.0310309 | ||||||||
\(386\) | 2.03372e14 | 1.20798 | ||||||||
\(387\) | −2.29455e14 | −1.34365 | ||||||||
\(388\) | −1.80871e14 | −1.04423 | ||||||||
\(389\) | −7.50535e13 | −0.427217 | −0.213608 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213608 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(390\) | −4.55201e13 | −0.255475 | ||||||||
\(391\) | 2.72806e13 | 0.150967 | ||||||||
\(392\) | −2.66215e13 | −0.145265 | ||||||||
\(393\) | 9.97062e13 | 0.536492 | ||||||||
\(394\) | −1.46609e14 | −0.777913 | ||||||||
\(395\) | 9.04606e12 | 0.0473343 | ||||||||
\(396\) | 1.05739e14 | 0.545649 | ||||||||
\(397\) | 4.56165e13 | 0.232153 | 0.116076 | − | 0.993240i | \(-0.462968\pi\) | ||||
0.116076 | + | 0.993240i | \(0.462968\pi\) | |||||||
\(398\) | −3.18268e14 | −1.59748 | ||||||||
\(399\) | 1.09896e13 | 0.0544039 | ||||||||
\(400\) | 1.45181e14 | 0.708891 | ||||||||
\(401\) | −3.08793e14 | −1.48722 | −0.743608 | − | 0.668616i | \(-0.766887\pi\) | ||||
−0.743608 | + | 0.668616i | \(0.766887\pi\) | |||||||
\(402\) | 6.34880e14 | 3.01612 | ||||||||
\(403\) | −9.20046e13 | −0.431153 | ||||||||
\(404\) | −1.76369e14 | −0.815314 | ||||||||
\(405\) | −6.77167e13 | −0.308811 | ||||||||
\(406\) | 6.61812e13 | 0.297743 | ||||||||
\(407\) | 6.89529e12 | 0.0306043 | ||||||||
\(408\) | −3.71492e13 | −0.162674 | ||||||||
\(409\) | 1.66809e14 | 0.720677 | 0.360338 | − | 0.932822i | \(-0.382661\pi\) | ||||
0.360338 | + | 0.932822i | \(0.382661\pi\) | |||||||
\(410\) | −9.98780e13 | −0.425754 | ||||||||
\(411\) | 5.88527e14 | 2.47535 | ||||||||
\(412\) | 9.74434e13 | 0.404406 | ||||||||
\(413\) | −1.43716e13 | −0.0588545 | ||||||||
\(414\) | −9.33803e13 | −0.377358 | ||||||||
\(415\) | 2.10945e14 | 0.841211 | ||||||||
\(416\) | 9.58123e13 | 0.377058 | ||||||||
\(417\) | 1.61978e14 | 0.629084 | ||||||||
\(418\) | 3.10711e13 | 0.119093 | ||||||||
\(419\) | 8.64443e13 | 0.327009 | 0.163504 | − | 0.986543i | \(-0.447720\pi\) | ||||
0.163504 | + | 0.986543i | \(0.447720\pi\) | |||||||
\(420\) | 3.46906e13 | 0.129521 | ||||||||
\(421\) | 3.12336e14 | 1.15099 | 0.575494 | − | 0.817806i | \(-0.304810\pi\) | ||||
0.575494 | + | 0.817806i | \(0.304810\pi\) | |||||||
\(422\) | −7.18016e13 | −0.261165 | ||||||||
\(423\) | −3.95729e14 | −1.42078 | ||||||||
\(424\) | −6.13457e12 | −0.0217406 | ||||||||
\(425\) | 1.65591e14 | 0.579291 | ||||||||
\(426\) | −1.85388e14 | −0.640219 | ||||||||
\(427\) | 3.89035e13 | 0.132628 | ||||||||
\(428\) | 5.22397e14 | 1.75817 | ||||||||
\(429\) | −4.69958e13 | −0.156151 | ||||||||
\(430\) | −2.12837e14 | −0.698186 | ||||||||
\(431\) | −5.74775e14 | −1.86154 | −0.930771 | − | 0.365603i | \(-0.880863\pi\) | ||||
−0.930771 | + | 0.365603i | \(0.880863\pi\) | |||||||
\(432\) | −1.02960e14 | −0.329236 | ||||||||
\(433\) | 2.05185e14 | 0.647831 | 0.323915 | − | 0.946086i | \(-0.395001\pi\) | ||||
0.323915 | + | 0.946086i | \(0.395001\pi\) | |||||||
\(434\) | 1.33665e14 | 0.416702 | ||||||||
\(435\) | 2.55270e14 | 0.785795 | ||||||||
\(436\) | −2.53010e14 | −0.769063 | ||||||||
\(437\) | −1.43937e13 | −0.0432042 | ||||||||
\(438\) | −5.58544e14 | −1.65558 | ||||||||
\(439\) | −3.80092e14 | −1.11259 | −0.556293 | − | 0.830986i | \(-0.687777\pi\) | ||||
−0.556293 | + | 0.830986i | \(0.687777\pi\) | |||||||
\(440\) | 9.18577e12 | 0.0265537 | ||||||||
\(441\) | −4.23689e14 | −1.20958 | ||||||||
\(442\) | 9.78675e13 | 0.275941 | ||||||||
\(443\) | 1.44902e14 | 0.403510 | 0.201755 | − | 0.979436i | \(-0.435335\pi\) | ||||
0.201755 | + | 0.979436i | \(0.435335\pi\) | |||||||
\(444\) | 4.64447e13 | 0.127741 | ||||||||
\(445\) | 2.91408e14 | 0.791629 | ||||||||
\(446\) | −4.50521e14 | −1.20885 | ||||||||
\(447\) | −3.92029e14 | −1.03903 | ||||||||
\(448\) | −7.99302e13 | −0.209258 | ||||||||
\(449\) | 7.06589e13 | 0.182731 | 0.0913654 | − | 0.995817i | \(-0.470877\pi\) | ||||
0.0913654 | + | 0.995817i | \(0.470877\pi\) | |||||||
\(450\) | −5.66809e14 | −1.44800 | ||||||||
\(451\) | −1.03116e14 | −0.260228 | ||||||||
\(452\) | 8.17863e14 | 2.03901 | ||||||||
\(453\) | 9.63559e14 | 2.37322 | ||||||||
\(454\) | −1.99375e14 | −0.485136 | ||||||||
\(455\) | −8.55912e12 | −0.0205763 | ||||||||
\(456\) | 1.96006e13 | 0.0465545 | ||||||||
\(457\) | 7.84592e14 | 1.84122 | 0.920609 | − | 0.390487i | \(-0.127693\pi\) | ||||
0.920609 | + | 0.390487i | \(0.127693\pi\) | |||||||
\(458\) | 9.74247e14 | 2.25896 | ||||||||
\(459\) | −1.17434e14 | −0.269045 | ||||||||
\(460\) | −4.54365e13 | −0.102858 | ||||||||
\(461\) | 4.18981e14 | 0.937216 | 0.468608 | − | 0.883406i | \(-0.344756\pi\) | ||||
0.468608 | + | 0.883406i | \(0.344756\pi\) | |||||||
\(462\) | 6.82761e13 | 0.150917 | ||||||||
\(463\) | −6.91249e13 | −0.150987 | −0.0754934 | − | 0.997146i | \(-0.524053\pi\) | ||||
−0.0754934 | + | 0.997146i | \(0.524053\pi\) | |||||||
\(464\) | −4.81182e14 | −1.03863 | ||||||||
\(465\) | 5.15566e14 | 1.09975 | ||||||||
\(466\) | −6.68649e13 | −0.140953 | ||||||||
\(467\) | 4.37356e14 | 0.911154 | 0.455577 | − | 0.890196i | \(-0.349433\pi\) | ||||
0.455577 | + | 0.890196i | \(0.349433\pi\) | |||||||
\(468\) | −1.75727e14 | −0.361814 | ||||||||
\(469\) | 1.19376e14 | 0.242922 | ||||||||
\(470\) | −3.67070e14 | −0.738262 | ||||||||
\(471\) | −2.95658e14 | −0.587725 | ||||||||
\(472\) | −2.56326e13 | −0.0503630 | ||||||||
\(473\) | −2.19737e14 | −0.426743 | ||||||||
\(474\) | 1.19922e14 | 0.230207 | ||||||||
\(475\) | −8.73686e13 | −0.165783 | ||||||||
\(476\) | −7.45842e13 | −0.139897 | ||||||||
\(477\) | −9.76334e13 | −0.181029 | ||||||||
\(478\) | 1.33068e14 | 0.243905 | ||||||||
\(479\) | 4.94438e14 | 0.895914 | 0.447957 | − | 0.894055i | \(-0.352152\pi\) | ||||
0.447957 | + | 0.894055i | \(0.352152\pi\) | |||||||
\(480\) | −5.36904e14 | −0.961767 | ||||||||
\(481\) | −1.14592e13 | −0.0202934 | ||||||||
\(482\) | 4.83763e14 | 0.846981 | ||||||||
\(483\) | −3.16290e13 | −0.0547490 | ||||||||
\(484\) | −5.43436e14 | −0.930034 | ||||||||
\(485\) | −2.50071e14 | −0.423139 | ||||||||
\(486\) | −1.21984e15 | −2.04082 | ||||||||
\(487\) | −1.82867e14 | −0.302501 | −0.151251 | − | 0.988495i | \(-0.548330\pi\) | ||||
−0.151251 | + | 0.988495i | \(0.548330\pi\) | |||||||
\(488\) | 6.93867e13 | 0.113493 | ||||||||
\(489\) | 1.58094e15 | 2.55691 | ||||||||
\(490\) | −3.93005e14 | −0.628521 | ||||||||
\(491\) | 4.83418e13 | 0.0764495 | 0.0382248 | − | 0.999269i | \(-0.487830\pi\) | ||||
0.0382248 | + | 0.999269i | \(0.487830\pi\) | |||||||
\(492\) | −6.94558e14 | −1.08618 | ||||||||
\(493\) | −5.48827e14 | −0.848745 | ||||||||
\(494\) | −5.16367e13 | −0.0789696 | ||||||||
\(495\) | 1.46194e14 | 0.221106 | ||||||||
\(496\) | −9.71838e14 | −1.45360 | ||||||||
\(497\) | −3.48584e13 | −0.0515641 | ||||||||
\(498\) | 2.79647e15 | 4.09118 | ||||||||
\(499\) | 4.47577e14 | 0.647612 | 0.323806 | − | 0.946123i | \(-0.395037\pi\) | ||||
0.323806 | + | 0.946123i | \(0.395037\pi\) | |||||||
\(500\) | −6.20490e14 | −0.887973 | ||||||||
\(501\) | −3.99443e14 | −0.565389 | ||||||||
\(502\) | −1.36525e14 | −0.191136 | ||||||||
\(503\) | −1.28069e15 | −1.77345 | −0.886725 | − | 0.462297i | \(-0.847025\pi\) | ||||
−0.886725 | + | 0.462297i | \(0.847025\pi\) | |||||||
\(504\) | 2.39098e13 | 0.0327498 | ||||||||
\(505\) | −2.43846e14 | −0.330379 | ||||||||
\(506\) | −8.94255e13 | −0.119849 | ||||||||
\(507\) | −1.05281e15 | −1.39574 | ||||||||
\(508\) | 6.90184e14 | 0.905138 | ||||||||
\(509\) | −1.67577e14 | −0.217404 | −0.108702 | − | 0.994074i | \(-0.534669\pi\) | ||||
−0.108702 | + | 0.994074i | \(0.534669\pi\) | |||||||
\(510\) | −5.48421e14 | −0.703847 | ||||||||
\(511\) | −1.05023e14 | −0.133342 | ||||||||
\(512\) | 1.11777e15 | 1.40400 | ||||||||
\(513\) | 6.19603e13 | 0.0769960 | ||||||||
\(514\) | −1.57671e15 | −1.93845 | ||||||||
\(515\) | 1.34724e14 | 0.163872 | ||||||||
\(516\) | −1.48009e15 | −1.78120 | ||||||||
\(517\) | −3.78969e14 | −0.451238 | ||||||||
\(518\) | 1.66481e13 | 0.0196133 | ||||||||
\(519\) | −1.13951e15 | −1.32831 | ||||||||
\(520\) | −1.52657e13 | −0.0176075 | ||||||||
\(521\) | 4.70966e14 | 0.537505 | 0.268753 | − | 0.963209i | \(-0.413389\pi\) | ||||
0.268753 | + | 0.963209i | \(0.413389\pi\) | |||||||
\(522\) | 1.87861e15 | 2.12153 | ||||||||
\(523\) | −6.32034e14 | −0.706287 | −0.353143 | − | 0.935569i | \(-0.614887\pi\) | ||||
−0.353143 | + | 0.935569i | \(0.614887\pi\) | |||||||
\(524\) | 3.57032e14 | 0.394808 | ||||||||
\(525\) | −1.91985e14 | −0.210083 | ||||||||
\(526\) | −7.30386e14 | −0.790917 | ||||||||
\(527\) | −1.10846e15 | −1.18785 | ||||||||
\(528\) | −4.96413e14 | −0.526449 | ||||||||
\(529\) | 4.14265e13 | 0.0434783 | ||||||||
\(530\) | −9.05626e13 | −0.0940658 | ||||||||
\(531\) | −4.07950e14 | −0.419360 | ||||||||
\(532\) | 3.93520e13 | 0.0400362 | ||||||||
\(533\) | 1.71367e14 | 0.172555 | ||||||||
\(534\) | 3.86316e15 | 3.85004 | ||||||||
\(535\) | 7.22260e14 | 0.712439 | ||||||||
\(536\) | 2.12914e14 | 0.207873 | ||||||||
\(537\) | 6.40659e14 | 0.619111 | ||||||||
\(538\) | 7.03141e14 | 0.672574 | ||||||||
\(539\) | −4.05745e14 | −0.384163 | ||||||||
\(540\) | 1.95589e14 | 0.183307 | ||||||||
\(541\) | −1.07949e15 | −1.00146 | −0.500730 | − | 0.865603i | \(-0.666935\pi\) | ||||
−0.500730 | + | 0.865603i | \(0.666935\pi\) | |||||||
\(542\) | 2.40010e14 | 0.220411 | ||||||||
\(543\) | 4.42649e14 | 0.402403 | ||||||||
\(544\) | 1.15433e15 | 1.03881 | ||||||||
\(545\) | −3.49809e14 | −0.311637 | ||||||||
\(546\) | −1.13467e14 | −0.100072 | ||||||||
\(547\) | 1.42629e15 | 1.24531 | 0.622655 | − | 0.782496i | \(-0.286054\pi\) | ||||
0.622655 | + | 0.782496i | \(0.286054\pi\) | |||||||
\(548\) | 2.10742e15 | 1.82162 | ||||||||
\(549\) | 1.10431e15 | 0.945023 | ||||||||
\(550\) | −5.42803e14 | −0.459883 | ||||||||
\(551\) | 2.89571e14 | 0.242896 | ||||||||
\(552\) | −5.64122e13 | −0.0468499 | ||||||||
\(553\) | 2.25489e13 | 0.0185412 | ||||||||
\(554\) | 2.68957e15 | 2.18967 | ||||||||
\(555\) | 6.42139e13 | 0.0517628 | ||||||||
\(556\) | 5.80019e14 | 0.462947 | ||||||||
\(557\) | 1.68524e15 | 1.33186 | 0.665931 | − | 0.746013i | \(-0.268034\pi\) | ||||
0.665931 | + | 0.746013i | \(0.268034\pi\) | |||||||
\(558\) | 3.79421e15 | 2.96915 | ||||||||
\(559\) | 3.65178e14 | 0.282969 | ||||||||
\(560\) | −9.04094e13 | −0.0693713 | ||||||||
\(561\) | −5.66199e14 | −0.430203 | ||||||||
\(562\) | −2.10696e15 | −1.58529 | ||||||||
\(563\) | −8.84001e14 | −0.658653 | −0.329326 | − | 0.944216i | \(-0.606822\pi\) | ||||
−0.329326 | + | 0.944216i | \(0.606822\pi\) | |||||||
\(564\) | −2.55263e15 | −1.88344 | ||||||||
\(565\) | 1.13077e15 | 0.826241 | ||||||||
\(566\) | −3.64208e15 | −2.63547 | ||||||||
\(567\) | −1.68796e14 | −0.120964 | ||||||||
\(568\) | −6.21720e13 | −0.0441244 | ||||||||
\(569\) | −5.53267e14 | −0.388882 | −0.194441 | − | 0.980914i | \(-0.562289\pi\) | ||||
−0.194441 | + | 0.980914i | \(0.562289\pi\) | |||||||
\(570\) | 2.89357e14 | 0.201429 | ||||||||
\(571\) | 9.37636e14 | 0.646451 | 0.323226 | − | 0.946322i | \(-0.395233\pi\) | ||||
0.323226 | + | 0.946322i | \(0.395233\pi\) | |||||||
\(572\) | −1.68284e14 | −0.114912 | ||||||||
\(573\) | −3.05546e15 | −2.06646 | ||||||||
\(574\) | −2.48964e14 | −0.166771 | ||||||||
\(575\) | 2.51455e14 | 0.166835 | ||||||||
\(576\) | −2.26889e15 | −1.49104 | ||||||||
\(577\) | 1.63506e15 | 1.06431 | 0.532155 | − | 0.846647i | \(-0.321382\pi\) | ||||
0.532155 | + | 0.846647i | \(0.321382\pi\) | |||||||
\(578\) | −1.07025e15 | −0.690055 | ||||||||
\(579\) | 1.95534e15 | 1.24879 | ||||||||
\(580\) | 9.14083e14 | 0.578271 | ||||||||
\(581\) | 5.25819e14 | 0.329509 | ||||||||
\(582\) | −3.31515e15 | −2.05791 | ||||||||
\(583\) | −9.34984e13 | −0.0574946 | ||||||||
\(584\) | −1.87314e14 | −0.114104 | ||||||||
\(585\) | −2.42958e14 | −0.146613 | ||||||||
\(586\) | 1.27234e15 | 0.760619 | ||||||||
\(587\) | −7.43553e14 | −0.440354 | −0.220177 | − | 0.975460i | \(-0.570664\pi\) | ||||
−0.220177 | + | 0.975460i | \(0.570664\pi\) | |||||||
\(588\) | −2.73298e15 | −1.60347 | ||||||||
\(589\) | 5.84843e14 | 0.339942 | ||||||||
\(590\) | −3.78406e14 | −0.217907 | ||||||||
\(591\) | −1.40959e15 | −0.804194 | ||||||||
\(592\) | −1.21043e14 | −0.0684177 | ||||||||
\(593\) | 2.19012e15 | 1.22650 | 0.613251 | − | 0.789888i | \(-0.289862\pi\) | ||||
0.613251 | + | 0.789888i | \(0.289862\pi\) | |||||||
\(594\) | 3.84947e14 | 0.213587 | ||||||||
\(595\) | −1.03119e14 | −0.0566887 | ||||||||
\(596\) | −1.40379e15 | −0.764625 | ||||||||
\(597\) | −3.06003e15 | −1.65145 | ||||||||
\(598\) | 1.48615e14 | 0.0794706 | ||||||||
\(599\) | −2.27584e15 | −1.20585 | −0.602926 | − | 0.797797i | \(-0.705999\pi\) | ||||
−0.602926 | + | 0.797797i | \(0.705999\pi\) | |||||||
\(600\) | −3.42416e14 | −0.179772 | ||||||||
\(601\) | −1.06505e15 | −0.554067 | −0.277033 | − | 0.960860i | \(-0.589351\pi\) | ||||
−0.277033 | + | 0.960860i | \(0.589351\pi\) | |||||||
\(602\) | −5.30535e14 | −0.273485 | ||||||||
\(603\) | 3.38859e15 | 1.73091 | ||||||||
\(604\) | 3.45035e15 | 1.74647 | ||||||||
\(605\) | −7.51348e14 | −0.376866 | ||||||||
\(606\) | −3.23263e15 | −1.60678 | ||||||||
\(607\) | −2.09430e15 | −1.03157 | −0.515787 | − | 0.856717i | \(-0.672500\pi\) | ||||
−0.515787 | + | 0.856717i | \(0.672500\pi\) | |||||||
\(608\) | −6.09048e14 | −0.297291 | ||||||||
\(609\) | 6.36307e14 | 0.307802 | ||||||||
\(610\) | 1.02433e15 | 0.491051 | ||||||||
\(611\) | 6.29804e14 | 0.299212 | ||||||||
\(612\) | −2.11713e15 | −0.996818 | ||||||||
\(613\) | 3.24171e15 | 1.51266 | 0.756331 | − | 0.654189i | \(-0.226990\pi\) | ||||
0.756331 | + | 0.654189i | \(0.226990\pi\) | |||||||
\(614\) | 4.87154e15 | 2.25289 | ||||||||
\(615\) | −9.60288e14 | −0.440138 | ||||||||
\(616\) | 2.28972e13 | 0.0104013 | ||||||||
\(617\) | −3.18934e15 | −1.43593 | −0.717965 | − | 0.696080i | \(-0.754926\pi\) | ||||
−0.717965 | + | 0.696080i | \(0.754926\pi\) | |||||||
\(618\) | 1.78602e15 | 0.796984 | ||||||||
\(619\) | 2.10151e15 | 0.929464 | 0.464732 | − | 0.885451i | \(-0.346151\pi\) | ||||
0.464732 | + | 0.885451i | \(0.346151\pi\) | |||||||
\(620\) | 1.84616e15 | 0.809311 | ||||||||
\(621\) | −1.78327e14 | −0.0774844 | ||||||||
\(622\) | −3.58926e15 | −1.54582 | ||||||||
\(623\) | 7.26387e14 | 0.310087 | ||||||||
\(624\) | 8.24982e14 | 0.349084 | ||||||||
\(625\) | 1.04973e15 | 0.440289 | ||||||||
\(626\) | −2.50572e15 | −1.04177 | ||||||||
\(627\) | 2.98737e14 | 0.123117 | ||||||||
\(628\) | −1.05870e15 | −0.432510 | ||||||||
\(629\) | −1.38059e14 | −0.0559095 | ||||||||
\(630\) | 3.52972e14 | 0.141699 | ||||||||
\(631\) | −1.64216e15 | −0.653514 | −0.326757 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326757 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(632\) | 4.02174e13 | 0.0158661 | ||||||||
\(633\) | −6.90345e14 | −0.269989 | ||||||||
\(634\) | 1.28145e15 | 0.496832 | ||||||||
\(635\) | 9.54241e14 | 0.366778 | ||||||||
\(636\) | −6.29779e14 | −0.239979 | ||||||||
\(637\) | 6.74303e14 | 0.254735 | ||||||||
\(638\) | 1.79905e15 | 0.673796 | ||||||||
\(639\) | −9.89485e14 | −0.367413 | ||||||||
\(640\) | −3.62057e14 | −0.133287 | ||||||||
\(641\) | −2.26488e15 | −0.826657 | −0.413329 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413329 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(642\) | 9.57490e15 | 3.46491 | ||||||||
\(643\) | 3.87115e15 | 1.38893 | 0.694463 | − | 0.719528i | \(-0.255642\pi\) | ||||
0.694463 | + | 0.719528i | \(0.255642\pi\) | |||||||
\(644\) | −1.13259e14 | −0.0402901 | ||||||||
\(645\) | −2.04635e15 | −0.721774 | ||||||||
\(646\) | −6.22112e14 | −0.217565 | ||||||||
\(647\) | 7.28389e13 | 0.0252575 | 0.0126287 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126287 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(648\) | −3.01058e14 | −0.103511 | ||||||||
\(649\) | −3.90672e14 | −0.133189 | ||||||||
\(650\) | 9.02078e14 | 0.304944 | ||||||||
\(651\) | 1.28514e15 | 0.430780 | ||||||||
\(652\) | 5.66108e15 | 1.88164 | ||||||||
\(653\) | −5.02905e15 | −1.65754 | −0.828768 | − | 0.559592i | \(-0.810958\pi\) | ||||
−0.828768 | + | 0.559592i | \(0.810958\pi\) | |||||||
\(654\) | −4.63736e15 | −1.51563 | ||||||||
\(655\) | 4.93629e14 | 0.159983 | ||||||||
\(656\) | 1.81013e15 | 0.581754 | ||||||||
\(657\) | −2.98116e15 | −0.950113 | ||||||||
\(658\) | −9.14987e14 | −0.289183 | ||||||||
\(659\) | 2.85379e15 | 0.894443 | 0.447222 | − | 0.894423i | \(-0.352414\pi\) | ||||
0.447222 | + | 0.894423i | \(0.352414\pi\) | |||||||
\(660\) | 9.43016e14 | 0.293108 | ||||||||
\(661\) | −3.43478e15 | −1.05875 | −0.529373 | − | 0.848389i | \(-0.677573\pi\) | ||||
−0.529373 | + | 0.848389i | \(0.677573\pi\) | |||||||
\(662\) | −5.85907e15 | −1.79106 | ||||||||
\(663\) | 9.40959e14 | 0.285264 | ||||||||
\(664\) | 9.37829e14 | 0.281968 | ||||||||
\(665\) | 5.44076e13 | 0.0162233 | ||||||||
\(666\) | 4.72569e14 | 0.139752 | ||||||||
\(667\) | −8.33411e14 | −0.244437 | ||||||||
\(668\) | −1.43034e15 | −0.416073 | ||||||||
\(669\) | −4.33159e15 | −1.24969 | ||||||||
\(670\) | 3.14318e15 | 0.899411 | ||||||||
\(671\) | 1.05754e15 | 0.300139 | ||||||||
\(672\) | −1.33833e15 | −0.376732 | ||||||||
\(673\) | −3.24334e15 | −0.905545 | −0.452772 | − | 0.891626i | \(-0.649565\pi\) | ||||
−0.452772 | + | 0.891626i | \(0.649565\pi\) | |||||||
\(674\) | −1.54376e15 | −0.427513 | ||||||||
\(675\) | −1.08243e15 | −0.297323 | ||||||||
\(676\) | −3.76994e15 | −1.02713 | ||||||||
\(677\) | 3.99549e15 | 1.07977 | 0.539887 | − | 0.841738i | \(-0.318467\pi\) | ||||
0.539887 | + | 0.841738i | \(0.318467\pi\) | |||||||
\(678\) | 1.49904e16 | 4.01838 | ||||||||
\(679\) | −6.23346e14 | −0.165747 | ||||||||
\(680\) | −1.83919e14 | −0.0485097 | ||||||||
\(681\) | −1.91691e15 | −0.501526 | ||||||||
\(682\) | 3.63351e15 | 0.943002 | ||||||||
\(683\) | −6.59707e15 | −1.69839 | −0.849195 | − | 0.528080i | \(-0.822912\pi\) | ||||
−0.849195 | + | 0.528080i | \(0.822912\pi\) | |||||||
\(684\) | 1.11704e15 | 0.285272 | ||||||||
\(685\) | 2.91370e15 | 0.738153 | ||||||||
\(686\) | −1.99027e15 | −0.500183 | ||||||||
\(687\) | 9.36701e15 | 2.33528 | ||||||||
\(688\) | 3.85735e15 | 0.954009 | ||||||||
\(689\) | 1.55384e14 | 0.0381241 | ||||||||
\(690\) | −8.32795e14 | −0.202707 | ||||||||
\(691\) | 5.64954e15 | 1.36422 | 0.682110 | − | 0.731250i | \(-0.261063\pi\) | ||||
0.682110 | + | 0.731250i | \(0.261063\pi\) | |||||||
\(692\) | −4.08042e15 | −0.977510 | ||||||||
\(693\) | 3.64415e14 | 0.0866090 | ||||||||
\(694\) | 7.12021e14 | 0.167886 | ||||||||
\(695\) | 8.01928e14 | 0.187594 | ||||||||
\(696\) | 1.13489e15 | 0.263392 | ||||||||
\(697\) | 2.06460e15 | 0.475397 | ||||||||
\(698\) | 3.11762e15 | 0.712228 | ||||||||
\(699\) | −6.42880e14 | −0.145715 | ||||||||
\(700\) | −6.87467e14 | −0.154601 | ||||||||
\(701\) | 3.30062e15 | 0.736455 | 0.368227 | − | 0.929736i | \(-0.379965\pi\) | ||||
0.368227 | + | 0.929736i | \(0.379965\pi\) | |||||||
\(702\) | −6.39739e14 | −0.141628 | ||||||||
\(703\) | 7.28423e13 | 0.0160003 | ||||||||
\(704\) | −2.17279e15 | −0.473553 | ||||||||
\(705\) | −3.52924e15 | −0.763204 | ||||||||
\(706\) | −3.05354e14 | −0.0655207 | ||||||||
\(707\) | −6.07830e14 | −0.129412 | ||||||||
\(708\) | −2.63146e15 | −0.555922 | ||||||||
\(709\) | −7.21671e15 | −1.51281 | −0.756405 | − | 0.654103i | \(-0.773046\pi\) | ||||
−0.756405 | + | 0.654103i | \(0.773046\pi\) | |||||||
\(710\) | −9.17825e14 | −0.190914 | ||||||||
\(711\) | 6.40070e14 | 0.132113 | ||||||||
\(712\) | 1.29555e15 | 0.265348 | ||||||||
\(713\) | −1.68323e15 | −0.342099 | ||||||||
\(714\) | −1.36704e15 | −0.275702 | ||||||||
\(715\) | −2.32668e14 | −0.0465644 | ||||||||
\(716\) | 2.29410e15 | 0.455607 | ||||||||
\(717\) | 1.27940e15 | 0.252145 | ||||||||
\(718\) | −1.30102e16 | −2.54449 | ||||||||
\(719\) | −6.40385e15 | −1.24289 | −0.621445 | − | 0.783458i | \(-0.713454\pi\) | ||||
−0.621445 | + | 0.783458i | \(0.713454\pi\) | |||||||
\(720\) | −2.56635e15 | −0.494296 | ||||||||
\(721\) | 3.35824e14 | 0.0641901 | ||||||||
\(722\) | −7.31731e15 | −1.38802 | ||||||||
\(723\) | 4.65119e15 | 0.875596 | ||||||||
\(724\) | 1.58506e15 | 0.296130 | ||||||||
\(725\) | −5.05872e15 | −0.937954 | ||||||||
\(726\) | −9.96052e15 | −1.83287 | ||||||||
\(727\) | 1.01638e16 | 1.85617 | 0.928086 | − | 0.372366i | \(-0.121454\pi\) | ||||
0.928086 | + | 0.372366i | \(0.121454\pi\) | |||||||
\(728\) | −3.80525e13 | −0.00689701 | ||||||||
\(729\) | −7.88858e15 | −1.41905 | ||||||||
\(730\) | −2.76526e15 | −0.493696 | ||||||||
\(731\) | 4.39962e15 | 0.779596 | ||||||||
\(732\) | 7.12328e15 | 1.25276 | ||||||||
\(733\) | 9.72534e15 | 1.69759 | 0.848796 | − | 0.528721i | \(-0.177328\pi\) | ||||
0.848796 | + | 0.528721i | \(0.177328\pi\) | |||||||
\(734\) | 1.31705e16 | 2.28178 | ||||||||
\(735\) | −3.77859e15 | −0.649755 | ||||||||
\(736\) | 1.75289e15 | 0.299177 | ||||||||
\(737\) | 3.24508e15 | 0.549735 | ||||||||
\(738\) | −7.06704e15 | −1.18830 | ||||||||
\(739\) | 3.38213e15 | 0.564476 | 0.282238 | − | 0.959344i | \(-0.408923\pi\) | ||||
0.282238 | + | 0.959344i | \(0.408923\pi\) | |||||||
\(740\) | 2.29940e14 | 0.0380925 | ||||||||
\(741\) | −4.96467e14 | −0.0816376 | ||||||||
\(742\) | −2.25744e14 | −0.0368463 | ||||||||
\(743\) | −1.33089e15 | −0.215628 | −0.107814 | − | 0.994171i | \(-0.534385\pi\) | ||||
−0.107814 | + | 0.994171i | \(0.534385\pi\) | |||||||
\(744\) | 2.29213e15 | 0.368627 | ||||||||
\(745\) | −1.94087e15 | −0.309839 | ||||||||
\(746\) | −1.52070e16 | −2.40980 | ||||||||
\(747\) | 1.49258e16 | 2.34787 | ||||||||
\(748\) | −2.02747e15 | −0.316589 | ||||||||
\(749\) | 1.80036e15 | 0.279068 | ||||||||
\(750\) | −1.13728e16 | −1.74997 | ||||||||
\(751\) | −1.42326e15 | −0.217403 | −0.108702 | − | 0.994074i | \(-0.534669\pi\) | ||||
−0.108702 | + | 0.994074i | \(0.534669\pi\) | |||||||
\(752\) | 6.65257e15 | 1.00877 | ||||||||
\(753\) | −1.31264e15 | −0.197594 | ||||||||
\(754\) | −2.98981e15 | −0.446788 | ||||||||
\(755\) | 4.77042e15 | 0.707698 | ||||||||
\(756\) | 4.87541e14 | 0.0718027 | ||||||||
\(757\) | 3.26050e15 | 0.476713 | 0.238357 | − | 0.971178i | \(-0.423391\pi\) | ||||
0.238357 | + | 0.971178i | \(0.423391\pi\) | |||||||
\(758\) | 2.15979e15 | 0.313495 | ||||||||
\(759\) | −8.59792e14 | −0.123898 | ||||||||
\(760\) | 9.70391e13 | 0.0138826 | ||||||||
\(761\) | 4.96565e15 | 0.705278 | 0.352639 | − | 0.935759i | \(-0.385284\pi\) | ||||
0.352639 | + | 0.935759i | \(0.385284\pi\) | |||||||
\(762\) | 1.26502e16 | 1.78380 | ||||||||
\(763\) | −8.71961e14 | −0.122071 | ||||||||
\(764\) | −1.09411e16 | −1.52072 | ||||||||
\(765\) | −2.92713e15 | −0.403928 | ||||||||
\(766\) | −1.73502e16 | −2.37709 | ||||||||
\(767\) | 6.49253e14 | 0.0883161 | ||||||||
\(768\) | 8.46491e15 | 1.14324 | ||||||||
\(769\) | 7.89343e15 | 1.05845 | 0.529226 | − | 0.848481i | \(-0.322482\pi\) | ||||
0.529226 | + | 0.848481i | \(0.322482\pi\) | |||||||
\(770\) | 3.38023e14 | 0.0450036 | ||||||||
\(771\) | −1.51594e16 | −2.00394 | ||||||||
\(772\) | 7.00178e15 | 0.918995 | ||||||||
\(773\) | 5.05981e15 | 0.659397 | 0.329698 | − | 0.944086i | \(-0.393053\pi\) | ||||
0.329698 | + | 0.944086i | \(0.393053\pi\) | |||||||
\(774\) | −1.50597e16 | −1.94868 | ||||||||
\(775\) | −1.02170e16 | −1.31270 | ||||||||
\(776\) | −1.11178e15 | −0.141833 | ||||||||
\(777\) | 1.60065e14 | 0.0202759 | ||||||||
\(778\) | −4.92595e15 | −0.619586 | ||||||||
\(779\) | −1.08932e15 | −0.136051 | ||||||||
\(780\) | −1.56719e15 | −0.194357 | ||||||||
\(781\) | −9.47578e14 | −0.116690 | ||||||||
\(782\) | 1.79050e15 | 0.218946 | ||||||||
\(783\) | 3.58756e15 | 0.435622 | ||||||||
\(784\) | 7.12261e15 | 0.858817 | ||||||||
\(785\) | −1.46375e15 | −0.175261 | ||||||||
\(786\) | 6.54397e15 | 0.778067 | ||||||||
\(787\) | −1.07706e15 | −0.127168 | −0.0635841 | − | 0.997976i | \(-0.520253\pi\) | ||||
−0.0635841 | + | 0.997976i | \(0.520253\pi\) | |||||||
\(788\) | −5.04751e15 | −0.591811 | ||||||||
\(789\) | −7.02238e15 | −0.817638 | ||||||||
\(790\) | 5.93716e14 | 0.0686483 | ||||||||
\(791\) | 2.81864e15 | 0.323645 | ||||||||
\(792\) | 6.49955e14 | 0.0741131 | ||||||||
\(793\) | −1.75751e15 | −0.199019 | ||||||||
\(794\) | 2.99392e15 | 0.336688 | ||||||||
\(795\) | −8.70725e14 | −0.0972438 | ||||||||
\(796\) | −1.09575e16 | −1.21531 | ||||||||
\(797\) | 8.67469e15 | 0.955505 | 0.477753 | − | 0.878494i | \(-0.341452\pi\) | ||||
0.477753 | + | 0.878494i | \(0.341452\pi\) | |||||||
\(798\) | 7.21274e14 | 0.0789013 | ||||||||
\(799\) | 7.58780e15 | 0.824344 | ||||||||
\(800\) | 1.06399e16 | 1.14800 | ||||||||
\(801\) | 2.06191e16 | 2.20949 | ||||||||
\(802\) | −2.02669e16 | −2.15689 | ||||||||
\(803\) | −2.85490e15 | −0.301756 | ||||||||
\(804\) | 2.18579e16 | 2.29457 | ||||||||
\(805\) | −1.56590e14 | −0.0163263 | ||||||||
\(806\) | −6.03849e15 | −0.625296 | ||||||||
\(807\) | 6.76043e15 | 0.695296 | ||||||||
\(808\) | −1.08410e15 | −0.110741 | ||||||||
\(809\) | 1.03496e16 | 1.05004 | 0.525020 | − | 0.851090i | \(-0.324058\pi\) | ||||
0.525020 | + | 0.851090i | \(0.324058\pi\) | |||||||
\(810\) | −4.44442e15 | −0.447865 | ||||||||
\(811\) | −6.40587e15 | −0.641156 | −0.320578 | − | 0.947222i | \(-0.603877\pi\) | ||||
−0.320578 | + | 0.947222i | \(0.603877\pi\) | |||||||
\(812\) | 2.27851e15 | 0.226513 | ||||||||
\(813\) | 2.30761e15 | 0.227858 | ||||||||
\(814\) | 4.52555e14 | 0.0443851 | ||||||||
\(815\) | 7.82695e15 | 0.762475 | ||||||||
\(816\) | 9.93928e15 | 0.961743 | ||||||||
\(817\) | −2.32132e15 | −0.223107 | ||||||||
\(818\) | 1.09481e16 | 1.04519 | ||||||||
\(819\) | −6.05616e14 | −0.0574296 | ||||||||
\(820\) | −3.43864e15 | −0.323900 | ||||||||
\(821\) | −1.18787e16 | −1.11143 | −0.555716 | − | 0.831372i | \(-0.687556\pi\) | ||||
−0.555716 | + | 0.831372i | \(0.687556\pi\) | |||||||
\(822\) | 3.86265e16 | 3.58997 | ||||||||
\(823\) | −1.15406e16 | −1.06544 | −0.532721 | − | 0.846291i | \(-0.678831\pi\) | ||||
−0.532721 | + | 0.846291i | \(0.678831\pi\) | |||||||
\(824\) | 5.98962e14 | 0.0549288 | ||||||||
\(825\) | −5.21885e15 | −0.475420 | ||||||||
\(826\) | −9.43244e14 | −0.0853559 | ||||||||
\(827\) | 3.57014e14 | 0.0320926 | 0.0160463 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160463 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(828\) | −3.21494e15 | −0.287082 | ||||||||
\(829\) | −1.87404e16 | −1.66237 | −0.831187 | − | 0.555993i | \(-0.812338\pi\) | ||||
−0.831187 | + | 0.555993i | \(0.812338\pi\) | |||||||
\(830\) | 1.38449e16 | 1.22000 | ||||||||
\(831\) | 2.58592e16 | 2.26365 | ||||||||
\(832\) | 3.61094e15 | 0.314009 | ||||||||
\(833\) | 8.12391e15 | 0.701807 | ||||||||
\(834\) | 1.06310e16 | 0.912352 | ||||||||
\(835\) | −1.97757e15 | −0.168600 | ||||||||
\(836\) | 1.06973e15 | 0.0906024 | ||||||||
\(837\) | 7.24576e15 | 0.609668 | ||||||||
\(838\) | 5.67355e15 | 0.474256 | ||||||||
\(839\) | −2.05506e16 | −1.70661 | −0.853304 | − | 0.521414i | \(-0.825405\pi\) | ||||
−0.853304 | + | 0.521414i | \(0.825405\pi\) | |||||||
\(840\) | 2.13235e14 | 0.0175923 | ||||||||
\(841\) | 4.56591e15 | 0.374239 | ||||||||
\(842\) | 2.04994e16 | 1.66926 | ||||||||
\(843\) | −2.02577e16 | −1.63884 | ||||||||
\(844\) | −2.47202e15 | −0.198686 | ||||||||
\(845\) | −5.21227e15 | −0.416213 | ||||||||
\(846\) | −2.59727e16 | −2.06053 | ||||||||
\(847\) | −1.87287e15 | −0.147621 | ||||||||
\(848\) | 1.64131e15 | 0.128532 | ||||||||
\(849\) | −3.50172e16 | −2.72451 | ||||||||
\(850\) | 1.08681e16 | 0.840138 | ||||||||
\(851\) | −2.09647e14 | −0.0161018 | ||||||||
\(852\) | −6.38262e15 | −0.487058 | ||||||||
\(853\) | −1.25187e16 | −0.949163 | −0.474581 | − | 0.880212i | \(-0.657401\pi\) | ||||
−0.474581 | + | 0.880212i | \(0.657401\pi\) | |||||||
\(854\) | 2.55333e15 | 0.192349 | ||||||||
\(855\) | 1.54440e15 | 0.115597 | ||||||||
\(856\) | 3.21105e15 | 0.238804 | ||||||||
\(857\) | 7.50578e15 | 0.554627 | 0.277314 | − | 0.960779i | \(-0.410556\pi\) | ||||
0.277314 | + | 0.960779i | \(0.410556\pi\) | |||||||
\(858\) | −3.08445e15 | −0.226463 | ||||||||
\(859\) | 1.42159e16 | 1.03708 | 0.518541 | − | 0.855053i | \(-0.326475\pi\) | ||||
0.518541 | + | 0.855053i | \(0.326475\pi\) | |||||||
\(860\) | −7.32766e15 | −0.531158 | ||||||||
\(861\) | −2.39369e15 | −0.172405 | ||||||||
\(862\) | −3.77239e16 | −2.69977 | ||||||||
\(863\) | −2.41818e16 | −1.71961 | −0.859803 | − | 0.510626i | \(-0.829414\pi\) | ||||
−0.859803 | + | 0.510626i | \(0.829414\pi\) | |||||||
\(864\) | −7.54564e15 | −0.533176 | ||||||||
\(865\) | −5.64154e15 | −0.396104 | ||||||||
\(866\) | 1.34668e16 | 0.939540 | ||||||||
\(867\) | −1.02901e16 | −0.713368 | ||||||||
\(868\) | 4.60189e15 | 0.317014 | ||||||||
\(869\) | 6.12962e14 | 0.0419590 | ||||||||
\(870\) | 1.67540e16 | 1.13963 | ||||||||
\(871\) | −5.39295e15 | −0.364524 | ||||||||
\(872\) | −1.55519e15 | −0.104458 | ||||||||
\(873\) | −1.76942e16 | −1.18101 | ||||||||
\(874\) | −9.44697e14 | −0.0626585 | ||||||||
\(875\) | −2.13843e15 | −0.140945 | ||||||||
\(876\) | −1.92298e16 | −1.25951 | ||||||||
\(877\) | 2.28486e15 | 0.148717 | 0.0743587 | − | 0.997232i | \(-0.476309\pi\) | ||||
0.0743587 | + | 0.997232i | \(0.476309\pi\) | |||||||
\(878\) | −2.49464e16 | −1.61357 | ||||||||
\(879\) | 1.22331e16 | 0.786316 | ||||||||
\(880\) | −2.45766e15 | −0.156988 | ||||||||
\(881\) | 1.67582e16 | 1.06380 | 0.531900 | − | 0.846807i | \(-0.321478\pi\) | ||||
0.531900 | + | 0.846807i | \(0.321478\pi\) | |||||||
\(882\) | −2.78078e16 | −1.75424 | ||||||||
\(883\) | −2.41720e16 | −1.51540 | −0.757702 | − | 0.652601i | \(-0.773678\pi\) | ||||
−0.757702 | + | 0.652601i | \(0.773678\pi\) | |||||||
\(884\) | 3.36943e15 | 0.209927 | ||||||||
\(885\) | −3.63823e15 | −0.225269 | ||||||||
\(886\) | 9.51030e15 | 0.585206 | ||||||||
\(887\) | 2.01345e16 | 1.23129 | 0.615646 | − | 0.788023i | \(-0.288895\pi\) | ||||
0.615646 | + | 0.788023i | \(0.288895\pi\) | |||||||
\(888\) | 2.85485e14 | 0.0173505 | ||||||||
\(889\) | 2.37862e15 | 0.143670 | ||||||||
\(890\) | 1.91258e16 | 1.14809 | ||||||||
\(891\) | −4.58849e15 | −0.273743 | ||||||||
\(892\) | −1.55107e16 | −0.919657 | ||||||||
\(893\) | −4.00346e15 | −0.235913 | ||||||||
\(894\) | −2.57298e16 | −1.50689 | ||||||||
\(895\) | 3.17180e15 | 0.184620 | ||||||||
\(896\) | −9.02493e14 | −0.0522095 | ||||||||
\(897\) | 1.42888e15 | 0.0821554 | ||||||||
\(898\) | 4.63752e15 | 0.265012 | ||||||||
\(899\) | 3.38630e16 | 1.92330 | ||||||||
\(900\) | −1.95143e16 | −1.10159 | ||||||||
\(901\) | 1.87204e15 | 0.105034 | ||||||||
\(902\) | −6.76774e15 | −0.377405 | ||||||||
\(903\) | −5.10089e15 | −0.282725 | ||||||||
\(904\) | 5.02721e15 | 0.276950 | ||||||||
\(905\) | 2.19148e15 | 0.119997 | ||||||||
\(906\) | 6.32407e16 | 3.44185 | ||||||||
\(907\) | −2.67779e14 | −0.0144856 | −0.00724279 | − | 0.999974i | \(-0.502305\pi\) | ||||
−0.00724279 | + | 0.999974i | \(0.502305\pi\) | |||||||
\(908\) | −6.86417e15 | −0.369076 | ||||||||
\(909\) | −1.72538e16 | −0.922109 | ||||||||
\(910\) | −5.61757e14 | −0.0298415 | ||||||||
\(911\) | 2.11521e16 | 1.11687 | 0.558436 | − | 0.829548i | \(-0.311402\pi\) | ||||
0.558436 | + | 0.829548i | \(0.311402\pi\) | |||||||
\(912\) | −5.24414e15 | −0.275235 | ||||||||
\(913\) | 1.42937e16 | 0.745683 | ||||||||
\(914\) | 5.14948e16 | 2.67029 | ||||||||
\(915\) | 9.84857e15 | 0.507641 | ||||||||
\(916\) | 3.35418e16 | 1.71855 | ||||||||
\(917\) | 1.23046e15 | 0.0626665 | ||||||||
\(918\) | −7.70749e15 | −0.390192 | ||||||||
\(919\) | −2.21346e15 | −0.111388 | −0.0556938 | − | 0.998448i | \(-0.517737\pi\) | ||||
−0.0556938 | + | 0.998448i | \(0.517737\pi\) | |||||||
\(920\) | −2.79287e14 | −0.0139707 | ||||||||
\(921\) | 4.68380e16 | 2.32901 | ||||||||
\(922\) | 2.74988e16 | 1.35923 | ||||||||
\(923\) | 1.57477e15 | 0.0773761 | ||||||||
\(924\) | 2.35064e15 | 0.114813 | ||||||||
\(925\) | −1.27253e15 | −0.0617860 | ||||||||
\(926\) | −4.53684e15 | −0.218974 | ||||||||
\(927\) | 9.53265e15 | 0.457378 | ||||||||
\(928\) | −3.52644e16 | −1.68199 | ||||||||
\(929\) | −1.10071e16 | −0.521900 | −0.260950 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260950 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(930\) | 3.38379e16 | 1.59495 | ||||||||
\(931\) | −4.28632e15 | −0.200845 | ||||||||
\(932\) | −2.30205e15 | −0.107233 | ||||||||
\(933\) | −3.45094e16 | −1.59804 | ||||||||
\(934\) | 2.87047e16 | 1.32144 | ||||||||
\(935\) | −2.80316e15 | −0.128287 | ||||||||
\(936\) | −1.08015e15 | −0.0491437 | ||||||||
\(937\) | −2.39029e16 | −1.08114 | −0.540571 | − | 0.841299i | \(-0.681792\pi\) | ||||
−0.540571 | + | 0.841299i | \(0.681792\pi\) | |||||||
\(938\) | 7.83495e15 | 0.352306 | ||||||||
\(939\) | −2.40915e16 | −1.07697 | ||||||||
\(940\) | −1.26376e16 | −0.561646 | ||||||||
\(941\) | 3.04569e15 | 0.134568 | 0.0672841 | − | 0.997734i | \(-0.478567\pi\) | ||||
0.0672841 | + | 0.997734i | \(0.478567\pi\) | |||||||
\(942\) | −1.94047e16 | −0.852369 | ||||||||
\(943\) | 3.13517e15 | 0.136914 | ||||||||
\(944\) | 6.85802e15 | 0.297751 | ||||||||
\(945\) | 6.74068e14 | 0.0290957 | ||||||||
\(946\) | −1.44219e16 | −0.618900 | ||||||||
\(947\) | −4.48147e16 | −1.91203 | −0.956017 | − | 0.293313i | \(-0.905242\pi\) | ||||
−0.956017 | + | 0.293313i | \(0.905242\pi\) | |||||||
\(948\) | 4.12874e15 | 0.175134 | ||||||||
\(949\) | 4.74452e15 | 0.200091 | ||||||||
\(950\) | −5.73422e15 | −0.240433 | ||||||||
\(951\) | 1.23206e16 | 0.513617 | ||||||||
\(952\) | −4.58452e14 | −0.0190016 | ||||||||
\(953\) | −4.37899e16 | −1.80453 | −0.902263 | − | 0.431187i | \(-0.858095\pi\) | ||||
−0.902263 | + | 0.431187i | \(0.858095\pi\) | |||||||
\(954\) | −6.40792e15 | −0.262543 | ||||||||
\(955\) | −1.51271e16 | −0.616221 | ||||||||
\(956\) | 4.58133e15 | 0.185555 | ||||||||
\(957\) | 1.72971e16 | 0.696560 | ||||||||
\(958\) | 3.24512e16 | 1.29933 | ||||||||
\(959\) | 7.26292e15 | 0.289140 | ||||||||
\(960\) | −2.02346e16 | −0.800946 | ||||||||
\(961\) | 4.29842e16 | 1.69172 | ||||||||
\(962\) | −7.52095e14 | −0.0294313 | ||||||||
\(963\) | 5.11048e16 | 1.98846 | ||||||||
\(964\) | 1.66552e16 | 0.644356 | ||||||||
\(965\) | 9.68058e15 | 0.372393 | ||||||||
\(966\) | −2.07589e15 | −0.0794018 | ||||||||
\(967\) | 3.51227e16 | 1.33580 | 0.667902 | − | 0.744250i | \(-0.267193\pi\) | ||||
0.667902 | + | 0.744250i | \(0.267193\pi\) | |||||||
\(968\) | −3.34038e15 | −0.126323 | ||||||||
\(969\) | −5.98137e15 | −0.224916 | ||||||||
\(970\) | −1.64128e16 | −0.613673 | ||||||||
\(971\) | −2.39866e16 | −0.891789 | −0.445895 | − | 0.895086i | \(-0.647114\pi\) | ||||
−0.445895 | + | 0.895086i | \(0.647114\pi\) | |||||||
\(972\) | −4.19972e16 | −1.55259 | ||||||||
\(973\) | 1.99895e15 | 0.0734820 | ||||||||
\(974\) | −1.20020e16 | −0.438713 | ||||||||
\(975\) | 8.67313e15 | 0.315247 | ||||||||
\(976\) | −1.85645e16 | −0.670978 | ||||||||
\(977\) | −4.60047e16 | −1.65342 | −0.826708 | − | 0.562631i | \(-0.809789\pi\) | ||||
−0.826708 | + | 0.562631i | \(0.809789\pi\) | |||||||
\(978\) | 1.03761e17 | 3.70825 | ||||||||
\(979\) | 1.97458e16 | 0.701732 | ||||||||
\(980\) | −1.35305e16 | −0.478159 | ||||||||
\(981\) | −2.47513e16 | −0.869799 | ||||||||
\(982\) | 3.17279e15 | 0.110874 | ||||||||
\(983\) | −2.69580e16 | −0.936791 | −0.468396 | − | 0.883519i | \(-0.655168\pi\) | ||||
−0.468396 | + | 0.883519i | \(0.655168\pi\) | |||||||
\(984\) | −4.26929e15 | −0.147531 | ||||||||
\(985\) | −6.97863e15 | −0.239812 | ||||||||
\(986\) | −3.60209e16 | −1.23092 | ||||||||
\(987\) | −8.79725e15 | −0.298953 | ||||||||
\(988\) | −1.77777e15 | −0.0600776 | ||||||||
\(989\) | 6.68096e15 | 0.224522 | ||||||||
\(990\) | 9.59508e15 | 0.320667 | ||||||||
\(991\) | −2.65968e15 | −0.0883945 | −0.0441972 | − | 0.999023i | \(-0.514073\pi\) | ||||
−0.0441972 | + | 0.999023i | \(0.514073\pi\) | |||||||
\(992\) | −7.12232e16 | −2.35400 | ||||||||
\(993\) | −5.63327e16 | −1.85157 | ||||||||
\(994\) | −2.28784e15 | −0.0747827 | ||||||||
\(995\) | −1.51497e16 | −0.492466 | ||||||||
\(996\) | 9.62781e16 | 3.11244 | ||||||||
\(997\) | 3.33774e16 | 1.07307 | 0.536537 | − | 0.843877i | \(-0.319732\pi\) | ||||
0.536537 | + | 0.843877i | \(0.319732\pi\) | |||||||
\(998\) | 2.93756e16 | 0.939224 | ||||||||
\(999\) | 9.02460e14 | 0.0286958 |
(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 | 23.12.a.b.1.10 | ✓ | 11 | |
3.2 | odd | 2 | 207.12.a.d.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.12.a.b.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
207.12.a.d.1.2 | 11 | 3.2 | odd | 2 |