Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,38,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(8.67140381246\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 15934380 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3991.29\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 286012. | 0.771488 | 0.385744 | − | 0.922606i | \(-0.373945\pi\) | ||||
0.385744 | + | 0.922606i | \(0.373945\pi\) | |||||||
\(3\) | −2.05955e7 | −0.0306923 | −0.0153462 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153462 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(4\) | −5.56362e10 | −0.404807 | ||||||||
\(5\) | −8.29715e12 | −0.972711 | −0.486356 | − | 0.873761i | \(-0.661674\pi\) | ||||
−0.486356 | + | 0.873761i | \(0.661674\pi\) | |||||||
\(6\) | −5.89057e12 | −0.0236788 | ||||||||
\(7\) | 1.97377e15 | 0.458124 | 0.229062 | − | 0.973412i | \(-0.426434\pi\) | ||||
0.229062 | + | 0.973412i | \(0.426434\pi\) | |||||||
\(8\) | −5.52218e16 | −1.08379 | ||||||||
\(9\) | −4.49860e17 | −0.999058 | ||||||||
\(10\) | −2.37308e18 | −0.750435 | ||||||||
\(11\) | −2.57012e19 | −1.39376 | −0.696881 | − | 0.717187i | \(-0.745429\pi\) | ||||
−0.696881 | + | 0.717187i | \(0.745429\pi\) | |||||||
\(12\) | 1.14586e18 | 0.0124245 | ||||||||
\(13\) | 5.42906e20 | 1.33898 | 0.669488 | − | 0.742823i | \(-0.266514\pi\) | ||||
0.669488 | + | 0.742823i | \(0.266514\pi\) | |||||||
\(14\) | 5.64522e20 | 0.353437 | ||||||||
\(15\) | 1.70884e20 | 0.0298548 | ||||||||
\(16\) | −8.14749e21 | −0.431325 | ||||||||
\(17\) | −3.52797e22 | −0.608443 | −0.304221 | − | 0.952601i | \(-0.598396\pi\) | ||||
−0.304221 | + | 0.952601i | \(0.598396\pi\) | |||||||
\(18\) | −1.28665e23 | −0.770761 | ||||||||
\(19\) | 6.82122e23 | 1.50287 | 0.751433 | − | 0.659809i | \(-0.229363\pi\) | ||||
0.751433 | + | 0.659809i | \(0.229363\pi\) | |||||||
\(20\) | 4.61622e23 | 0.393760 | ||||||||
\(21\) | −4.06509e22 | −0.0140609 | ||||||||
\(22\) | −7.35084e24 | −1.07527 | ||||||||
\(23\) | −8.19547e22 | −0.00526755 | −0.00263378 | − | 0.999997i | \(-0.500838\pi\) | ||||
−0.00263378 | + | 0.999997i | \(0.500838\pi\) | |||||||
\(24\) | 1.13732e24 | 0.0332641 | ||||||||
\(25\) | −3.91685e24 | −0.0538328 | ||||||||
\(26\) | 1.55278e26 | 1.03300 | ||||||||
\(27\) | 1.85389e25 | 0.0613558 | ||||||||
\(28\) | −1.09813e26 | −0.185452 | ||||||||
\(29\) | −1.51991e27 | −1.34108 | −0.670541 | − | 0.741872i | \(-0.733938\pi\) | ||||
−0.670541 | + | 0.741872i | \(0.733938\pi\) | |||||||
\(30\) | 4.88749e25 | 0.0230326 | ||||||||
\(31\) | 2.60785e27 | 0.670025 | 0.335012 | − | 0.942214i | \(-0.391260\pi\) | ||||
0.335012 | + | 0.942214i | \(0.391260\pi\) | |||||||
\(32\) | 5.25934e27 | 0.751030 | ||||||||
\(33\) | 5.29330e26 | 0.0427778 | ||||||||
\(34\) | −1.00904e28 | −0.469406 | ||||||||
\(35\) | −1.63767e28 | −0.445623 | ||||||||
\(36\) | 2.50285e28 | 0.404426 | ||||||||
\(37\) | −1.30205e29 | −1.26734 | −0.633672 | − | 0.773602i | \(-0.718453\pi\) | ||||
−0.633672 | + | 0.773602i | \(0.718453\pi\) | |||||||
\(38\) | 1.95095e29 | 1.15944 | ||||||||
\(39\) | −1.11814e28 | −0.0410963 | ||||||||
\(40\) | 4.58183e29 | 1.05422 | ||||||||
\(41\) | −4.07079e29 | −0.593168 | −0.296584 | − | 0.955007i | \(-0.595847\pi\) | ||||
−0.296584 | + | 0.955007i | \(0.595847\pi\) | |||||||
\(42\) | −1.16266e28 | −0.0108478 | ||||||||
\(43\) | −2.92424e30 | −1.76541 | −0.882706 | − | 0.469926i | \(-0.844281\pi\) | ||||
−0.882706 | + | 0.469926i | \(0.844281\pi\) | |||||||
\(44\) | 1.42992e30 | 0.564204 | ||||||||
\(45\) | 3.73255e30 | 0.971795 | ||||||||
\(46\) | −2.34400e28 | −0.00406385 | ||||||||
\(47\) | 3.58323e30 | 0.417315 | 0.208658 | − | 0.977989i | \(-0.433091\pi\) | ||||
0.208658 | + | 0.977989i | \(0.433091\pi\) | |||||||
\(48\) | 1.67802e29 | 0.0132384 | ||||||||
\(49\) | −1.46663e31 | −0.790122 | ||||||||
\(50\) | −1.12027e30 | −0.0415313 | ||||||||
\(51\) | 7.26605e29 | 0.0186745 | ||||||||
\(52\) | −3.02052e31 | −0.542027 | ||||||||
\(53\) | 3.56714e31 | 0.450005 | 0.225002 | − | 0.974358i | \(-0.427761\pi\) | ||||
0.225002 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(54\) | 5.30236e30 | 0.0473352 | ||||||||
\(55\) | 2.13247e32 | 1.35573 | ||||||||
\(56\) | −1.08995e32 | −0.496511 | ||||||||
\(57\) | −1.40487e31 | −0.0461265 | ||||||||
\(58\) | −4.34713e32 | −1.03463 | ||||||||
\(59\) | −3.03666e32 | −0.526785 | −0.263393 | − | 0.964689i | \(-0.584841\pi\) | ||||
−0.263393 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(60\) | −9.50736e30 | −0.0120854 | ||||||||
\(61\) | 1.16214e33 | 1.08807 | 0.544034 | − | 0.839063i | \(-0.316896\pi\) | ||||
0.544034 | + | 0.839063i | \(0.316896\pi\) | |||||||
\(62\) | 7.45875e32 | 0.516916 | ||||||||
\(63\) | −8.87921e32 | −0.457693 | ||||||||
\(64\) | 2.62402e33 | 1.01073 | ||||||||
\(65\) | −4.50457e33 | −1.30244 | ||||||||
\(66\) | 1.51395e32 | 0.0330026 | ||||||||
\(67\) | −2.44324e33 | −0.403257 | −0.201628 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201628 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(68\) | 1.96283e33 | 0.246302 | ||||||||
\(69\) | 1.68790e30 | 0.000161673 0 | ||||||||
\(70\) | −4.68393e33 | −0.343792 | ||||||||
\(71\) | 6.30224e33 | 0.355808 | 0.177904 | − | 0.984048i | \(-0.443068\pi\) | ||||
0.177904 | + | 0.984048i | \(0.443068\pi\) | |||||||
\(72\) | 2.48421e34 | 1.08277 | ||||||||
\(73\) | 1.02725e34 | 0.346899 | 0.173450 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173450 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(74\) | −3.72400e34 | −0.977740 | ||||||||
\(75\) | 8.06697e31 | 0.00165226 | ||||||||
\(76\) | −3.79507e34 | −0.608371 | ||||||||
\(77\) | −5.07283e34 | −0.638516 | ||||||||
\(78\) | −3.19803e33 | −0.0317053 | ||||||||
\(79\) | 1.20547e35 | 0.944182 | 0.472091 | − | 0.881550i | \(-0.343499\pi\) | ||||
0.472091 | + | 0.881550i | \(0.343499\pi\) | |||||||
\(80\) | 6.76010e34 | 0.419554 | ||||||||
\(81\) | 2.02183e35 | 0.997175 | ||||||||
\(82\) | −1.16430e35 | −0.457622 | ||||||||
\(83\) | −3.26699e35 | −1.02613 | −0.513066 | − | 0.858349i | \(-0.671490\pi\) | ||||
−0.513066 | + | 0.858349i | \(0.671490\pi\) | |||||||
\(84\) | 2.26166e33 | 0.00569195 | ||||||||
\(85\) | 2.92721e35 | 0.591839 | ||||||||
\(86\) | −8.36366e35 | −1.36199 | ||||||||
\(87\) | 3.13034e34 | 0.0411610 | ||||||||
\(88\) | 1.41927e36 | 1.51055 | ||||||||
\(89\) | −1.56115e36 | −1.34812 | −0.674062 | − | 0.738674i | \(-0.735452\pi\) | ||||
−0.674062 | + | 0.738674i | \(0.735452\pi\) | |||||||
\(90\) | 1.06755e36 | 0.749728 | ||||||||
\(91\) | 1.07157e36 | 0.613418 | ||||||||
\(92\) | 4.55965e33 | 0.00213234 | ||||||||
\(93\) | −5.37100e34 | −0.0205646 | ||||||||
\(94\) | 1.02485e36 | 0.321954 | ||||||||
\(95\) | −5.65967e36 | −1.46186 | ||||||||
\(96\) | −1.08319e35 | −0.0230509 | ||||||||
\(97\) | −1.07155e36 | −0.188251 | −0.0941254 | − | 0.995560i | \(-0.530005\pi\) | ||||
−0.0941254 | + | 0.995560i | \(0.530005\pi\) | |||||||
\(98\) | −4.19474e36 | −0.609569 | ||||||||
\(99\) | 1.15619e37 | 1.39245 | ||||||||
\(100\) | 2.17919e35 | 0.0217919 | ||||||||
\(101\) | 1.29521e37 | 1.07744 | 0.538721 | − | 0.842484i | \(-0.318908\pi\) | ||||
0.538721 | + | 0.842484i | \(0.318908\pi\) | |||||||
\(102\) | 2.07817e35 | 0.0144072 | ||||||||
\(103\) | −3.39568e36 | −0.196534 | −0.0982672 | − | 0.995160i | \(-0.531330\pi\) | ||||
−0.0982672 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(104\) | −2.99802e37 | −1.45117 | ||||||||
\(105\) | 3.37287e35 | 0.0136772 | ||||||||
\(106\) | 1.02025e37 | 0.347173 | ||||||||
\(107\) | −1.58608e37 | −0.453653 | −0.226827 | − | 0.973935i | \(-0.572835\pi\) | ||||
−0.226827 | + | 0.973935i | \(0.572835\pi\) | |||||||
\(108\) | −1.03144e36 | −0.0248372 | ||||||||
\(109\) | −1.06858e36 | −0.0216978 | −0.0108489 | − | 0.999941i | \(-0.503453\pi\) | ||||
−0.0108489 | + | 0.999941i | \(0.503453\pi\) | |||||||
\(110\) | 6.09911e37 | 1.04593 | ||||||||
\(111\) | 2.68163e36 | 0.0388977 | ||||||||
\(112\) | −1.60813e37 | −0.197600 | ||||||||
\(113\) | 1.64170e37 | 0.171136 | 0.0855682 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855682 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(114\) | −4.01809e36 | −0.0355860 | ||||||||
\(115\) | 6.79990e35 | 0.00512381 | ||||||||
\(116\) | 8.45622e37 | 0.542879 | ||||||||
\(117\) | −2.44232e38 | −1.33771 | ||||||||
\(118\) | −8.68520e37 | −0.406408 | ||||||||
\(119\) | −6.96341e37 | −0.278743 | ||||||||
\(120\) | −9.43654e36 | −0.0323564 | ||||||||
\(121\) | 3.20512e38 | 0.942572 | ||||||||
\(122\) | 3.32386e38 | 0.839432 | ||||||||
\(123\) | 8.38402e36 | 0.0182057 | ||||||||
\(124\) | −1.45091e38 | −0.271231 | ||||||||
\(125\) | 6.36196e38 | 1.02508 | ||||||||
\(126\) | −2.53956e38 | −0.353104 | ||||||||
\(127\) | −1.42456e39 | −1.71124 | −0.855619 | − | 0.517606i | \(-0.826823\pi\) | ||||
−0.855619 | + | 0.517606i | \(0.826823\pi\) | |||||||
\(128\) | 2.76609e37 | 0.0287397 | ||||||||
\(129\) | 6.02262e37 | 0.0541846 | ||||||||
\(130\) | −1.28836e39 | −1.00481 | ||||||||
\(131\) | 2.12044e39 | 1.43518 | 0.717590 | − | 0.696466i | \(-0.245245\pi\) | ||||
0.717590 | + | 0.696466i | \(0.245245\pi\) | |||||||
\(132\) | −2.94499e37 | −0.0173168 | ||||||||
\(133\) | 1.34635e39 | 0.688500 | ||||||||
\(134\) | −6.98795e38 | −0.311108 | ||||||||
\(135\) | −1.53820e38 | −0.0596815 | ||||||||
\(136\) | 1.94821e39 | 0.659425 | ||||||||
\(137\) | −1.25855e39 | −0.371999 | −0.185999 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.185999 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(138\) | 4.82760e35 | 0.000124729 0 | ||||||||
\(139\) | −3.12966e39 | −0.707494 | −0.353747 | − | 0.935341i | \(-0.615093\pi\) | ||||
−0.353747 | + | 0.935341i | \(0.615093\pi\) | |||||||
\(140\) | 9.11138e38 | 0.180391 | ||||||||
\(141\) | −7.37986e37 | −0.0128084 | ||||||||
\(142\) | 1.80251e39 | 0.274501 | ||||||||
\(143\) | −1.39533e40 | −1.86621 | ||||||||
\(144\) | 3.66523e39 | 0.430918 | ||||||||
\(145\) | 1.26109e40 | 1.30449 | ||||||||
\(146\) | 2.93806e39 | 0.267628 | ||||||||
\(147\) | 3.02061e38 | 0.0242507 | ||||||||
\(148\) | 7.24409e39 | 0.513029 | ||||||||
\(149\) | 2.99066e39 | 0.186991 | 0.0934956 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934956 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(150\) | 2.30725e37 | 0.00127469 | ||||||||
\(151\) | −7.06984e39 | −0.345411 | −0.172706 | − | 0.984973i | \(-0.555251\pi\) | ||||
−0.172706 | + | 0.984973i | \(0.555251\pi\) | |||||||
\(152\) | −3.76680e40 | −1.62879 | ||||||||
\(153\) | 1.58709e40 | 0.607870 | ||||||||
\(154\) | −1.45089e40 | −0.492607 | ||||||||
\(155\) | −2.16377e40 | −0.651740 | ||||||||
\(156\) | 6.22094e38 | 0.0166361 | ||||||||
\(157\) | 7.04676e40 | 1.67435 | 0.837174 | − | 0.546937i | \(-0.184206\pi\) | ||||
0.837174 | + | 0.546937i | \(0.184206\pi\) | |||||||
\(158\) | 3.44779e40 | 0.728425 | ||||||||
\(159\) | −7.34673e38 | −0.0138117 | ||||||||
\(160\) | −4.36376e40 | −0.730535 | ||||||||
\(161\) | −1.61760e38 | −0.00241319 | ||||||||
\(162\) | 5.78267e40 | 0.769308 | ||||||||
\(163\) | −8.16698e40 | −0.969596 | −0.484798 | − | 0.874626i | \(-0.661107\pi\) | ||||
−0.484798 | + | 0.874626i | \(0.661107\pi\) | |||||||
\(164\) | 2.26484e40 | 0.240119 | ||||||||
\(165\) | −4.39193e39 | −0.0416105 | ||||||||
\(166\) | −9.34397e40 | −0.791648 | ||||||||
\(167\) | −3.94031e40 | −0.298728 | −0.149364 | − | 0.988782i | \(-0.547723\pi\) | ||||
−0.149364 | + | 0.988782i | \(0.547723\pi\) | |||||||
\(168\) | 2.24482e39 | 0.0152391 | ||||||||
\(169\) | 1.30346e41 | 0.792856 | ||||||||
\(170\) | 8.37216e40 | 0.456597 | ||||||||
\(171\) | −3.06859e41 | −1.50145 | ||||||||
\(172\) | 1.62693e41 | 0.714651 | ||||||||
\(173\) | 2.61566e41 | 1.03212 | 0.516058 | − | 0.856554i | \(-0.327399\pi\) | ||||
0.516058 | + | 0.856554i | \(0.327399\pi\) | |||||||
\(174\) | 8.95315e39 | 0.0317552 | ||||||||
\(175\) | −7.73098e39 | −0.0246621 | ||||||||
\(176\) | 2.09400e41 | 0.601164 | ||||||||
\(177\) | 6.25416e39 | 0.0161683 | ||||||||
\(178\) | −4.46508e41 | −1.04006 | ||||||||
\(179\) | −4.21879e41 | −0.885946 | −0.442973 | − | 0.896535i | \(-0.646076\pi\) | ||||
−0.442973 | + | 0.896535i | \(0.646076\pi\) | |||||||
\(180\) | −2.07665e41 | −0.393389 | ||||||||
\(181\) | −9.51260e40 | −0.162647 | −0.0813234 | − | 0.996688i | \(-0.525915\pi\) | ||||
−0.0813234 | + | 0.996688i | \(0.525915\pi\) | |||||||
\(182\) | 3.06483e41 | 0.473244 | ||||||||
\(183\) | −2.39349e40 | −0.0333954 | ||||||||
\(184\) | 4.52568e39 | 0.00570892 | ||||||||
\(185\) | 1.08033e42 | 1.23276 | ||||||||
\(186\) | −1.53617e40 | −0.0158654 | ||||||||
\(187\) | 9.06730e41 | 0.848024 | ||||||||
\(188\) | −1.99357e41 | −0.168932 | ||||||||
\(189\) | 3.65917e40 | 0.0281086 | ||||||||
\(190\) | −1.61873e42 | −1.12780 | ||||||||
\(191\) | −2.61439e41 | −0.165292 | −0.0826462 | − | 0.996579i | \(-0.526337\pi\) | ||||
−0.0826462 | + | 0.996579i | \(0.526337\pi\) | |||||||
\(192\) | −5.40431e40 | −0.0310218 | ||||||||
\(193\) | −6.27072e41 | −0.326969 | −0.163485 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163485 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(194\) | −3.06477e41 | −0.145233 | ||||||||
\(195\) | 9.27742e40 | 0.0399748 | ||||||||
\(196\) | 8.15980e41 | 0.319847 | ||||||||
\(197\) | −1.81081e42 | −0.646021 | −0.323010 | − | 0.946395i | \(-0.604695\pi\) | ||||
−0.323010 | + | 0.946395i | \(0.604695\pi\) | |||||||
\(198\) | 3.30685e42 | 1.07426 | ||||||||
\(199\) | −3.78123e41 | −0.111906 | −0.0559528 | − | 0.998433i | \(-0.517820\pi\) | ||||
−0.0559528 | + | 0.998433i | \(0.517820\pi\) | |||||||
\(200\) | 2.16295e41 | 0.0583435 | ||||||||
\(201\) | 5.03198e40 | 0.0123769 | ||||||||
\(202\) | 3.70445e42 | 0.831233 | ||||||||
\(203\) | −2.99996e42 | −0.614383 | ||||||||
\(204\) | −4.04255e40 | −0.00755958 | ||||||||
\(205\) | 3.37760e42 | 0.576981 | ||||||||
\(206\) | −9.71205e41 | −0.151624 | ||||||||
\(207\) | 3.68681e40 | 0.00526259 | ||||||||
\(208\) | −4.42332e42 | −0.577533 | ||||||||
\(209\) | −1.75313e43 | −2.09464 | ||||||||
\(210\) | 9.64680e40 | 0.0105518 | ||||||||
\(211\) | 1.66783e43 | 1.67081 | 0.835404 | − | 0.549637i | \(-0.185234\pi\) | ||||
0.835404 | + | 0.549637i | \(0.185234\pi\) | |||||||
\(212\) | −1.98462e42 | −0.182165 | ||||||||
\(213\) | −1.29798e41 | −0.0109206 | ||||||||
\(214\) | −4.53636e42 | −0.349988 | ||||||||
\(215\) | 2.42628e43 | 1.71724 | ||||||||
\(216\) | −1.02375e42 | −0.0664968 | ||||||||
\(217\) | 5.14730e42 | 0.306955 | ||||||||
\(218\) | −3.05626e41 | −0.0167396 | ||||||||
\(219\) | −2.11568e41 | −0.0106472 | ||||||||
\(220\) | −1.18642e43 | −0.548808 | ||||||||
\(221\) | −1.91536e43 | −0.814690 | ||||||||
\(222\) | 7.66979e41 | 0.0300091 | ||||||||
\(223\) | −3.60083e43 | −1.29647 | −0.648236 | − | 0.761439i | \(-0.724493\pi\) | ||||
−0.648236 | + | 0.761439i | \(0.724493\pi\) | |||||||
\(224\) | 1.03808e43 | 0.344065 | ||||||||
\(225\) | 1.76203e42 | 0.0537821 | ||||||||
\(226\) | 4.69546e42 | 0.132030 | ||||||||
\(227\) | 6.76307e43 | 1.75253 | 0.876265 | − | 0.481830i | \(-0.160028\pi\) | ||||
0.876265 | + | 0.481830i | \(0.160028\pi\) | |||||||
\(228\) | 7.81615e41 | 0.0186723 | ||||||||
\(229\) | −5.09302e43 | −1.12207 | −0.561033 | − | 0.827793i | \(-0.689596\pi\) | ||||
−0.561033 | + | 0.827793i | \(0.689596\pi\) | |||||||
\(230\) | 1.94485e41 | 0.00395295 | ||||||||
\(231\) | 1.04478e42 | 0.0195976 | ||||||||
\(232\) | 8.39322e43 | 1.45345 | ||||||||
\(233\) | 1.79375e43 | 0.286865 | 0.143432 | − | 0.989660i | \(-0.454186\pi\) | ||||
0.143432 | + | 0.989660i | \(0.454186\pi\) | |||||||
\(234\) | −6.98531e43 | −1.03203 | ||||||||
\(235\) | −2.97306e43 | −0.405927 | ||||||||
\(236\) | 1.68948e43 | 0.213246 | ||||||||
\(237\) | −2.48273e42 | −0.0289792 | ||||||||
\(238\) | −1.99162e43 | −0.215046 | ||||||||
\(239\) | −2.86950e43 | −0.286711 | −0.143356 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143356 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(240\) | −1.39228e42 | −0.0128771 | ||||||||
\(241\) | −1.12255e44 | −0.961372 | −0.480686 | − | 0.876893i | \(-0.659612\pi\) | ||||
−0.480686 | + | 0.876893i | \(0.659612\pi\) | |||||||
\(242\) | 9.16701e43 | 0.727182 | ||||||||
\(243\) | −1.25119e43 | −0.0919614 | ||||||||
\(244\) | −6.46571e43 | −0.440458 | ||||||||
\(245\) | 1.21689e44 | 0.768561 | ||||||||
\(246\) | 2.39793e42 | 0.0140455 | ||||||||
\(247\) | 3.70328e44 | 2.01230 | ||||||||
\(248\) | −1.44010e44 | −0.726167 | ||||||||
\(249\) | 6.72854e42 | 0.0314944 | ||||||||
\(250\) | 1.81960e44 | 0.790833 | ||||||||
\(251\) | −4.02278e44 | −1.62391 | −0.811955 | − | 0.583720i | \(-0.801597\pi\) | ||||
−0.811955 | + | 0.583720i | \(0.801597\pi\) | |||||||
\(252\) | 4.94006e43 | 0.185277 | ||||||||
\(253\) | 2.10633e42 | 0.00734171 | ||||||||
\(254\) | −4.07440e44 | −1.32020 | ||||||||
\(255\) | −6.02875e42 | −0.0181649 | ||||||||
\(256\) | −3.52731e44 | −0.988562 | ||||||||
\(257\) | 5.42969e44 | 1.41583 | 0.707917 | − | 0.706296i | \(-0.249635\pi\) | ||||
0.707917 | + | 0.706296i | \(0.249635\pi\) | |||||||
\(258\) | 1.72254e43 | 0.0418028 | ||||||||
\(259\) | −2.56994e44 | −0.580601 | ||||||||
\(260\) | 2.50618e44 | 0.527235 | ||||||||
\(261\) | 6.83747e44 | 1.33982 | ||||||||
\(262\) | 6.06470e44 | 1.10722 | ||||||||
\(263\) | −7.98181e44 | −1.35806 | −0.679031 | − | 0.734109i | \(-0.737600\pi\) | ||||
−0.679031 | + | 0.734109i | \(0.737600\pi\) | |||||||
\(264\) | −2.92305e43 | −0.0463622 | ||||||||
\(265\) | −2.95971e44 | −0.437725 | ||||||||
\(266\) | 3.85073e44 | 0.531169 | ||||||||
\(267\) | 3.21528e43 | 0.0413771 | ||||||||
\(268\) | 1.35933e44 | 0.163241 | ||||||||
\(269\) | −1.02189e45 | −1.14548 | −0.572739 | − | 0.819738i | \(-0.694119\pi\) | ||||
−0.572739 | + | 0.819738i | \(0.694119\pi\) | |||||||
\(270\) | −4.39945e43 | −0.0460435 | ||||||||
\(271\) | −2.63101e44 | −0.257152 | −0.128576 | − | 0.991700i | \(-0.541041\pi\) | ||||
−0.128576 | + | 0.991700i | \(0.541041\pi\) | |||||||
\(272\) | 2.87441e44 | 0.262436 | ||||||||
\(273\) | −2.20696e43 | −0.0188272 | ||||||||
\(274\) | −3.59961e44 | −0.286992 | ||||||||
\(275\) | 1.00668e44 | 0.0750301 | ||||||||
\(276\) | −9.39085e40 | −6.54465e−5 0 | ||||||||
\(277\) | 1.60882e45 | 1.04865 | 0.524327 | − | 0.851517i | \(-0.324317\pi\) | ||||
0.524327 | + | 0.851517i | \(0.324317\pi\) | |||||||
\(278\) | −8.95119e44 | −0.545823 | ||||||||
\(279\) | −1.17317e45 | −0.669393 | ||||||||
\(280\) | 9.04350e44 | 0.482962 | ||||||||
\(281\) | 2.86236e45 | 1.43106 | 0.715529 | − | 0.698583i | \(-0.246186\pi\) | ||||
0.715529 | + | 0.698583i | \(0.246186\pi\) | |||||||
\(282\) | −2.11073e43 | −0.00988151 | ||||||||
\(283\) | 7.97480e44 | 0.349680 | 0.174840 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174840 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(284\) | −3.50633e44 | −0.144033 | ||||||||
\(285\) | 1.16564e44 | 0.0448678 | ||||||||
\(286\) | −3.99082e45 | −1.43976 | ||||||||
\(287\) | −8.03482e44 | −0.271745 | ||||||||
\(288\) | −2.36597e45 | −0.750322 | ||||||||
\(289\) | −2.11744e45 | −0.629797 | ||||||||
\(290\) | 3.60688e45 | 1.00639 | ||||||||
\(291\) | 2.20692e43 | 0.00577786 | ||||||||
\(292\) | −5.71523e44 | −0.140427 | ||||||||
\(293\) | 5.17198e44 | 0.119290 | 0.0596452 | − | 0.998220i | \(-0.481003\pi\) | ||||
0.0596452 | + | 0.998220i | \(0.481003\pi\) | |||||||
\(294\) | 8.63931e43 | 0.0187091 | ||||||||
\(295\) | 2.51956e45 | 0.512410 | ||||||||
\(296\) | 7.19013e45 | 1.37354 | ||||||||
\(297\) | −4.76473e44 | −0.0855153 | ||||||||
\(298\) | 8.55364e44 | 0.144261 | ||||||||
\(299\) | −4.44937e43 | −0.00705312 | ||||||||
\(300\) | −4.48816e42 | −0.000668844 0 | ||||||||
\(301\) | −5.77178e45 | −0.808778 | ||||||||
\(302\) | −2.02206e45 | −0.266480 | ||||||||
\(303\) | −2.66755e44 | −0.0330692 | ||||||||
\(304\) | −5.55758e45 | −0.648223 | ||||||||
\(305\) | −9.64245e45 | −1.05838 | ||||||||
\(306\) | 4.53927e45 | 0.468964 | ||||||||
\(307\) | 9.59117e45 | 0.932850 | 0.466425 | − | 0.884561i | \(-0.345542\pi\) | ||||
0.466425 | + | 0.884561i | \(0.345542\pi\) | |||||||
\(308\) | 2.82233e45 | 0.258476 | ||||||||
\(309\) | 6.99360e43 | 0.00603210 | ||||||||
\(310\) | −6.18864e45 | −0.502810 | ||||||||
\(311\) | −5.05857e45 | −0.387222 | −0.193611 | − | 0.981078i | \(-0.562020\pi\) | ||||
−0.193611 | + | 0.981078i | \(0.562020\pi\) | |||||||
\(312\) | 6.17459e44 | 0.0445398 | ||||||||
\(313\) | 5.12462e45 | 0.348410 | 0.174205 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174205 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(314\) | 2.01546e46 | 1.29174 | ||||||||
\(315\) | 7.36722e45 | 0.445203 | ||||||||
\(316\) | −6.70679e45 | −0.382211 | ||||||||
\(317\) | −2.14514e46 | −1.15308 | −0.576541 | − | 0.817068i | \(-0.695598\pi\) | ||||
−0.576541 | + | 0.817068i | \(0.695598\pi\) | |||||||
\(318\) | −2.10125e44 | −0.0106556 | ||||||||
\(319\) | 3.90635e46 | 1.86915 | ||||||||
\(320\) | −2.17719e46 | −0.983153 | ||||||||
\(321\) | 3.26661e44 | 0.0139237 | ||||||||
\(322\) | −4.62652e43 | −0.00186175 | ||||||||
\(323\) | −2.40651e46 | −0.914408 | ||||||||
\(324\) | −1.12487e46 | −0.403663 | ||||||||
\(325\) | −2.12648e45 | −0.0720808 | ||||||||
\(326\) | −2.33585e46 | −0.748032 | ||||||||
\(327\) | 2.20080e43 | 0.000665958 0 | ||||||||
\(328\) | 2.24796e46 | 0.642870 | ||||||||
\(329\) | 7.07248e45 | 0.191182 | ||||||||
\(330\) | −1.25614e45 | −0.0321020 | ||||||||
\(331\) | 1.85276e46 | 0.447714 | 0.223857 | − | 0.974622i | \(-0.428135\pi\) | ||||
0.223857 | + | 0.974622i | \(0.428135\pi\) | |||||||
\(332\) | 1.81763e46 | 0.415385 | ||||||||
\(333\) | 5.85738e46 | 1.26615 | ||||||||
\(334\) | −1.12698e46 | −0.230465 | ||||||||
\(335\) | 2.02719e46 | 0.392253 | ||||||||
\(336\) | 3.31203e44 | 0.00606482 | ||||||||
\(337\) | −9.22947e46 | −1.59965 | −0.799823 | − | 0.600236i | \(-0.795073\pi\) | ||||
−0.799823 | + | 0.600236i | \(0.795073\pi\) | |||||||
\(338\) | 3.72805e46 | 0.611679 | ||||||||
\(339\) | −3.38117e44 | −0.00525258 | ||||||||
\(340\) | −1.62859e46 | −0.239581 | ||||||||
\(341\) | −6.70248e46 | −0.933855 | ||||||||
\(342\) | −8.77653e46 | −1.15835 | ||||||||
\(343\) | −6.55854e46 | −0.820099 | ||||||||
\(344\) | 1.61481e47 | 1.91334 | ||||||||
\(345\) | −1.40048e43 | −0.000157262 0 | ||||||||
\(346\) | 7.48110e46 | 0.796265 | ||||||||
\(347\) | −5.27249e46 | −0.532011 | −0.266005 | − | 0.963972i | \(-0.585704\pi\) | ||||
−0.266005 | + | 0.963972i | \(0.585704\pi\) | |||||||
\(348\) | −1.74160e45 | −0.0166622 | ||||||||
\(349\) | 9.71277e46 | 0.881196 | 0.440598 | − | 0.897704i | \(-0.354766\pi\) | ||||
0.440598 | + | 0.897704i | \(0.354766\pi\) | |||||||
\(350\) | −2.21115e45 | −0.0190265 | ||||||||
\(351\) | 1.00649e46 | 0.0821539 | ||||||||
\(352\) | −1.35171e47 | −1.04676 | ||||||||
\(353\) | 1.73375e47 | 1.27396 | 0.636979 | − | 0.770881i | \(-0.280184\pi\) | ||||
0.636979 | + | 0.770881i | \(0.280184\pi\) | |||||||
\(354\) | 1.78876e45 | 0.0124736 | ||||||||
\(355\) | −5.22906e46 | −0.346098 | ||||||||
\(356\) | 8.68566e46 | 0.545730 | ||||||||
\(357\) | 1.43415e45 | 0.00855526 | ||||||||
\(358\) | −1.20662e47 | −0.683497 | ||||||||
\(359\) | −1.13075e47 | −0.608301 | −0.304150 | − | 0.952624i | \(-0.598373\pi\) | ||||
−0.304150 | + | 0.952624i | \(0.598373\pi\) | |||||||
\(360\) | −2.06118e47 | −1.05322 | ||||||||
\(361\) | 2.59283e47 | 1.25861 | ||||||||
\(362\) | −2.72072e46 | −0.125480 | ||||||||
\(363\) | −6.60111e45 | −0.0289297 | ||||||||
\(364\) | −5.96183e46 | −0.248316 | ||||||||
\(365\) | −8.52325e46 | −0.337433 | ||||||||
\(366\) | −6.84566e45 | −0.0257641 | ||||||||
\(367\) | −8.74068e46 | −0.312768 | −0.156384 | − | 0.987696i | \(-0.549984\pi\) | ||||
−0.156384 | + | 0.987696i | \(0.549984\pi\) | |||||||
\(368\) | 6.67725e44 | 0.00227202 | ||||||||
\(369\) | 1.83129e47 | 0.592609 | ||||||||
\(370\) | 3.08986e47 | 0.951059 | ||||||||
\(371\) | 7.04073e46 | 0.206158 | ||||||||
\(372\) | 2.98822e45 | 0.00832470 | ||||||||
\(373\) | 2.70122e47 | 0.716056 | 0.358028 | − | 0.933711i | \(-0.383449\pi\) | ||||
0.358028 | + | 0.933711i | \(0.383449\pi\) | |||||||
\(374\) | 2.59335e47 | 0.654240 | ||||||||
\(375\) | −1.31028e46 | −0.0314620 | ||||||||
\(376\) | −1.97872e47 | −0.452283 | ||||||||
\(377\) | −8.25170e47 | −1.79568 | ||||||||
\(378\) | 1.04657e46 | 0.0216854 | ||||||||
\(379\) | −4.13508e47 | −0.815940 | −0.407970 | − | 0.912995i | \(-0.633763\pi\) | ||||
−0.407970 | + | 0.912995i | \(0.633763\pi\) | |||||||
\(380\) | 3.14883e47 | 0.591769 | ||||||||
\(381\) | 2.93395e46 | 0.0525219 | ||||||||
\(382\) | −7.47746e46 | −0.127521 | ||||||||
\(383\) | −6.64131e47 | −1.07914 | −0.539569 | − | 0.841942i | \(-0.681413\pi\) | ||||
−0.539569 | + | 0.841942i | \(0.681413\pi\) | |||||||
\(384\) | −5.69691e44 | −0.000882088 0 | ||||||||
\(385\) | 4.20901e47 | 0.621092 | ||||||||
\(386\) | −1.79350e47 | −0.252253 | ||||||||
\(387\) | 1.31550e48 | 1.76375 | ||||||||
\(388\) | 5.96172e46 | 0.0762052 | ||||||||
\(389\) | 4.74132e46 | 0.0577872 | 0.0288936 | − | 0.999582i | \(-0.490802\pi\) | ||||
0.0288936 | + | 0.999582i | \(0.490802\pi\) | |||||||
\(390\) | 2.65345e46 | 0.0308401 | ||||||||
\(391\) | 2.89134e45 | 0.00320500 | ||||||||
\(392\) | 8.09901e47 | 0.856327 | ||||||||
\(393\) | −4.36716e46 | −0.0440491 | ||||||||
\(394\) | −5.17912e47 | −0.498397 | ||||||||
\(395\) | −1.00020e48 | −0.918417 | ||||||||
\(396\) | −6.43262e47 | −0.563673 | ||||||||
\(397\) | 6.00594e47 | 0.502292 | 0.251146 | − | 0.967949i | \(-0.419193\pi\) | ||||
0.251146 | + | 0.967949i | \(0.419193\pi\) | |||||||
\(398\) | −1.08148e47 | −0.0863337 | ||||||||
\(399\) | −2.77289e46 | −0.0211317 | ||||||||
\(400\) | 3.19125e46 | 0.0232194 | ||||||||
\(401\) | −9.30169e47 | −0.646235 | −0.323118 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323118 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(402\) | 1.43921e46 | 0.00954863 | ||||||||
\(403\) | 1.41582e48 | 0.897147 | ||||||||
\(404\) | −7.20605e47 | −0.436156 | ||||||||
\(405\) | −1.67754e48 | −0.969963 | ||||||||
\(406\) | −8.58024e47 | −0.473989 | ||||||||
\(407\) | 3.34641e48 | 1.76637 | ||||||||
\(408\) | −4.01244e46 | −0.0202393 | ||||||||
\(409\) | −2.60436e47 | −0.125551 | −0.0627755 | − | 0.998028i | \(-0.519995\pi\) | ||||
−0.0627755 | + | 0.998028i | \(0.519995\pi\) | |||||||
\(410\) | 9.66033e47 | 0.445134 | ||||||||
\(411\) | 2.59206e46 | 0.0114175 | ||||||||
\(412\) | 1.88923e47 | 0.0795585 | ||||||||
\(413\) | −5.99367e47 | −0.241333 | ||||||||
\(414\) | 1.05447e46 | 0.00406002 | ||||||||
\(415\) | 2.71067e48 | 0.998130 | ||||||||
\(416\) | 2.85533e48 | 1.00561 | ||||||||
\(417\) | 6.44570e46 | 0.0217147 | ||||||||
\(418\) | −5.01417e48 | −1.61599 | ||||||||
\(419\) | −3.92255e48 | −1.20951 | −0.604755 | − | 0.796412i | \(-0.706729\pi\) | ||||
−0.604755 | + | 0.796412i | \(0.706729\pi\) | |||||||
\(420\) | −1.87654e46 | −0.00553663 | ||||||||
\(421\) | −3.86983e48 | −1.09263 | −0.546315 | − | 0.837580i | \(-0.683970\pi\) | ||||
−0.546315 | + | 0.837580i | \(0.683970\pi\) | |||||||
\(422\) | 4.77019e48 | 1.28901 | ||||||||
\(423\) | −1.61195e48 | −0.416922 | ||||||||
\(424\) | −1.96984e48 | −0.487711 | ||||||||
\(425\) | 1.38185e47 | 0.0327542 | ||||||||
\(426\) | −3.71238e46 | −0.00842509 | ||||||||
\(427\) | 2.29380e48 | 0.498471 | ||||||||
\(428\) | 8.82433e47 | 0.183642 | ||||||||
\(429\) | 2.87377e47 | 0.0572785 | ||||||||
\(430\) | 6.93945e48 | 1.32483 | ||||||||
\(431\) | 2.97992e48 | 0.544973 | 0.272487 | − | 0.962160i | \(-0.412154\pi\) | ||||
0.272487 | + | 0.962160i | \(0.412154\pi\) | |||||||
\(432\) | −1.51046e47 | −0.0264643 | ||||||||
\(433\) | −2.20884e48 | −0.370798 | −0.185399 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185399 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(434\) | 1.47219e48 | 0.236812 | ||||||||
\(435\) | −2.59729e47 | −0.0400377 | ||||||||
\(436\) | 5.94517e46 | 0.00878344 | ||||||||
\(437\) | −5.59031e46 | −0.00791643 | ||||||||
\(438\) | −6.05109e46 | −0.00821414 | ||||||||
\(439\) | −1.14225e49 | −1.48650 | −0.743252 | − | 0.669011i | \(-0.766718\pi\) | ||||
−0.743252 | + | 0.669011i | \(0.766718\pi\) | |||||||
\(440\) | −1.17759e49 | −1.46933 | ||||||||
\(441\) | 6.59779e48 | 0.789378 | ||||||||
\(442\) | −5.47814e48 | −0.628523 | ||||||||
\(443\) | 8.78568e48 | 0.966733 | 0.483366 | − | 0.875418i | \(-0.339414\pi\) | ||||
0.483366 | + | 0.875418i | \(0.339414\pi\) | |||||||
\(444\) | −1.49196e47 | −0.0157461 | ||||||||
\(445\) | 1.29531e49 | 1.31134 | ||||||||
\(446\) | −1.02988e49 | −1.00021 | ||||||||
\(447\) | −6.15943e46 | −0.00573920 | ||||||||
\(448\) | 5.17921e48 | 0.463042 | ||||||||
\(449\) | −8.94932e48 | −0.767773 | −0.383886 | − | 0.923380i | \(-0.625415\pi\) | ||||
−0.383886 | + | 0.923380i | \(0.625415\pi\) | |||||||
\(450\) | 5.03962e47 | 0.0414922 | ||||||||
\(451\) | 1.04624e49 | 0.826735 | ||||||||
\(452\) | −9.13380e47 | −0.0692772 | ||||||||
\(453\) | 1.45607e47 | 0.0106015 | ||||||||
\(454\) | 1.93432e49 | 1.35205 | ||||||||
\(455\) | −8.89101e48 | −0.596678 | ||||||||
\(456\) | 7.75793e47 | 0.0499915 | ||||||||
\(457\) | 3.77717e48 | 0.233731 | 0.116866 | − | 0.993148i | \(-0.462715\pi\) | ||||
0.116866 | + | 0.993148i | \(0.462715\pi\) | |||||||
\(458\) | −1.45666e49 | −0.865661 | ||||||||
\(459\) | −6.54048e47 | −0.0373315 | ||||||||
\(460\) | −3.78321e46 | −0.00207415 | ||||||||
\(461\) | 8.89831e48 | 0.468641 | 0.234320 | − | 0.972159i | \(-0.424714\pi\) | ||||
0.234320 | + | 0.972159i | \(0.424714\pi\) | |||||||
\(462\) | 2.98819e47 | 0.0151193 | ||||||||
\(463\) | −3.35423e49 | −1.63059 | −0.815294 | − | 0.579047i | \(-0.803425\pi\) | ||||
−0.815294 | + | 0.579047i | \(0.803425\pi\) | |||||||
\(464\) | 1.23835e49 | 0.578442 | ||||||||
\(465\) | 4.45640e47 | 0.0200034 | ||||||||
\(466\) | 5.13034e48 | 0.221313 | ||||||||
\(467\) | −3.67520e49 | −1.52377 | −0.761884 | − | 0.647714i | \(-0.775725\pi\) | ||||
−0.761884 | + | 0.647714i | \(0.775725\pi\) | |||||||
\(468\) | 1.35881e49 | 0.541516 | ||||||||
\(469\) | −4.82240e48 | −0.184742 | ||||||||
\(470\) | −8.50330e48 | −0.313168 | ||||||||
\(471\) | −1.45132e48 | −0.0513897 | ||||||||
\(472\) | 1.67690e49 | 0.570925 | ||||||||
\(473\) | 7.51563e49 | 2.46056 | ||||||||
\(474\) | −7.10091e47 | −0.0223571 | ||||||||
\(475\) | −2.67177e48 | −0.0809035 | ||||||||
\(476\) | 3.87418e48 | 0.112837 | ||||||||
\(477\) | −1.60471e49 | −0.449581 | ||||||||
\(478\) | −8.20711e48 | −0.221194 | ||||||||
\(479\) | 4.73384e49 | 1.22746 | 0.613730 | − | 0.789516i | \(-0.289669\pi\) | ||||
0.613730 | + | 0.789516i | \(0.289669\pi\) | |||||||
\(480\) | 8.98740e47 | 0.0224218 | ||||||||
\(481\) | −7.06889e49 | −1.69694 | ||||||||
\(482\) | −3.21063e49 | −0.741686 | ||||||||
\(483\) | 3.33153e45 | 7.40666e−5 0 | ||||||||
\(484\) | −1.78321e49 | −0.381560 | ||||||||
\(485\) | 8.89084e48 | 0.183114 | ||||||||
\(486\) | −3.57854e48 | −0.0709471 | ||||||||
\(487\) | 7.97298e48 | 0.152172 | 0.0760860 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760860 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(488\) | −6.41754e49 | −1.17924 | ||||||||
\(489\) | 1.68203e48 | 0.0297592 | ||||||||
\(490\) | 3.48044e49 | 0.592935 | ||||||||
\(491\) | 3.59851e49 | 0.590358 | 0.295179 | − | 0.955442i | \(-0.404621\pi\) | ||||
0.295179 | + | 0.955442i | \(0.404621\pi\) | |||||||
\(492\) | −4.66455e47 | −0.00736980 | ||||||||
\(493\) | 5.36220e49 | 0.815972 | ||||||||
\(494\) | 1.05918e50 | 1.55247 | ||||||||
\(495\) | −9.59311e49 | −1.35445 | ||||||||
\(496\) | −2.12474e49 | −0.288998 | ||||||||
\(497\) | 1.24392e49 | 0.163004 | ||||||||
\(498\) | 1.92444e48 | 0.0242975 | ||||||||
\(499\) | 7.98372e49 | 0.971282 | 0.485641 | − | 0.874158i | \(-0.338586\pi\) | ||||
0.485641 | + | 0.874158i | \(0.338586\pi\) | |||||||
\(500\) | −3.53955e49 | −0.414957 | ||||||||
\(501\) | 8.11529e47 | 0.00916866 | ||||||||
\(502\) | −1.15056e50 | −1.25283 | ||||||||
\(503\) | 6.32137e49 | 0.663443 | 0.331721 | − | 0.943377i | \(-0.392371\pi\) | ||||
0.331721 | + | 0.943377i | \(0.392371\pi\) | |||||||
\(504\) | 4.90326e49 | 0.496043 | ||||||||
\(505\) | −1.07465e50 | −1.04804 | ||||||||
\(506\) | 6.02436e47 | 0.00566404 | ||||||||
\(507\) | −2.68455e48 | −0.0243346 | ||||||||
\(508\) | 7.92569e49 | 0.692721 | ||||||||
\(509\) | −1.42477e50 | −1.20078 | −0.600392 | − | 0.799706i | \(-0.704989\pi\) | ||||
−0.600392 | + | 0.799706i | \(0.704989\pi\) | |||||||
\(510\) | −1.72429e48 | −0.0140140 | ||||||||
\(511\) | 2.02756e49 | 0.158923 | ||||||||
\(512\) | −1.04687e50 | −0.791403 | ||||||||
\(513\) | 1.26458e49 | 0.0922095 | ||||||||
\(514\) | 1.55295e50 | 1.09230 | ||||||||
\(515\) | 2.81745e49 | 0.191171 | ||||||||
\(516\) | −3.35076e48 | −0.0219343 | ||||||||
\(517\) | −9.20932e49 | −0.581638 | ||||||||
\(518\) | −7.35034e49 | −0.447927 | ||||||||
\(519\) | −5.38710e48 | −0.0316781 | ||||||||
\(520\) | 2.48751e50 | 1.41157 | ||||||||
\(521\) | 1.18735e50 | 0.650251 | 0.325125 | − | 0.945671i | \(-0.394593\pi\) | ||||
0.325125 | + | 0.945671i | \(0.394593\pi\) | |||||||
\(522\) | 1.95560e50 | 1.03365 | ||||||||
\(523\) | 6.66586e49 | 0.340075 | 0.170038 | − | 0.985438i | \(-0.445611\pi\) | ||||
0.170038 | + | 0.985438i | \(0.445611\pi\) | |||||||
\(524\) | −1.17973e50 | −0.580971 | ||||||||
\(525\) | 1.59224e47 | 0.000756938 0 | ||||||||
\(526\) | −2.28289e50 | −1.04773 | ||||||||
\(527\) | −9.20040e49 | −0.407672 | ||||||||
\(528\) | −4.31271e48 | −0.0184511 | ||||||||
\(529\) | −2.42057e50 | −0.999972 | ||||||||
\(530\) | −8.46513e49 | −0.337699 | ||||||||
\(531\) | 1.36607e50 | 0.526289 | ||||||||
\(532\) | −7.49061e49 | −0.278709 | ||||||||
\(533\) | −2.21006e50 | −0.794238 | ||||||||
\(534\) | 9.19607e48 | 0.0319219 | ||||||||
\(535\) | 1.31599e50 | 0.441274 | ||||||||
\(536\) | 1.34920e50 | 0.437046 | ||||||||
\(537\) | 8.68884e48 | 0.0271918 | ||||||||
\(538\) | −2.92272e50 | −0.883722 | ||||||||
\(539\) | 3.76942e50 | 1.10124 | ||||||||
\(540\) | 8.55799e48 | 0.0241595 | ||||||||
\(541\) | 7.31652e50 | 1.99597 | 0.997987 | − | 0.0634127i | \(-0.0201984\pi\) | ||||
0.997987 | + | 0.0634127i | \(0.0201984\pi\) | |||||||
\(542\) | −7.52499e49 | −0.198390 | ||||||||
\(543\) | 1.95917e48 | 0.00499201 | ||||||||
\(544\) | −1.85548e50 | −0.456959 | ||||||||
\(545\) | 8.86616e48 | 0.0211057 | ||||||||
\(546\) | −6.31218e48 | −0.0145250 | ||||||||
\(547\) | 1.90668e50 | 0.424143 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(548\) | 7.00212e49 | 0.150588 | ||||||||
\(549\) | −5.22800e50 | −1.08704 | ||||||||
\(550\) | 2.87922e49 | 0.0578848 | ||||||||
\(551\) | −1.03677e51 | −2.01547 | ||||||||
\(552\) | −9.32089e46 | −0.000175220 0 | ||||||||
\(553\) | 2.37933e50 | 0.432553 | ||||||||
\(554\) | 4.60142e50 | 0.809024 | ||||||||
\(555\) | −2.22499e49 | −0.0378363 | ||||||||
\(556\) | 1.74122e50 | 0.286399 | ||||||||
\(557\) | 6.78617e50 | 1.07970 | 0.539851 | − | 0.841761i | \(-0.318481\pi\) | ||||
0.539851 | + | 0.841761i | \(0.318481\pi\) | |||||||
\(558\) | −3.35539e50 | −0.516429 | ||||||||
\(559\) | −1.58759e51 | −2.36384 | ||||||||
\(560\) | 1.33429e50 | 0.192208 | ||||||||
\(561\) | −1.86746e49 | −0.0260279 | ||||||||
\(562\) | 8.18669e50 | 1.10404 | ||||||||
\(563\) | 6.45010e50 | 0.841708 | 0.420854 | − | 0.907128i | \(-0.361730\pi\) | ||||
0.420854 | + | 0.907128i | \(0.361730\pi\) | |||||||
\(564\) | 4.10587e48 | 0.00518492 | ||||||||
\(565\) | −1.36214e50 | −0.166466 | ||||||||
\(566\) | 2.28089e50 | 0.269774 | ||||||||
\(567\) | 3.99063e50 | 0.456830 | ||||||||
\(568\) | −3.48021e50 | −0.385621 | ||||||||
\(569\) | 2.68168e50 | 0.287627 | 0.143814 | − | 0.989605i | \(-0.454063\pi\) | ||||
0.143814 | + | 0.989605i | \(0.454063\pi\) | |||||||
\(570\) | 3.33387e49 | 0.0346149 | ||||||||
\(571\) | −3.44946e50 | −0.346724 | −0.173362 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173362 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(572\) | 7.76311e50 | 0.755456 | ||||||||
\(573\) | 5.38448e48 | 0.00507321 | ||||||||
\(574\) | −2.29805e50 | −0.209648 | ||||||||
\(575\) | 3.21004e47 | 0.000283567 0 | ||||||||
\(576\) | −1.18044e51 | −1.00978 | ||||||||
\(577\) | 2.52648e50 | 0.209297 | 0.104648 | − | 0.994509i | \(-0.466628\pi\) | ||||
0.104648 | + | 0.994509i | \(0.466628\pi\) | |||||||
\(578\) | −6.05612e50 | −0.485881 | ||||||||
\(579\) | 1.29149e49 | 0.0100355 | ||||||||
\(580\) | −7.01625e50 | −0.528065 | ||||||||
\(581\) | −6.44830e50 | −0.470096 | ||||||||
\(582\) | 6.31206e48 | 0.00445754 | ||||||||
\(583\) | −9.16799e50 | −0.627199 | ||||||||
\(584\) | −5.67266e50 | −0.375966 | ||||||||
\(585\) | 2.02643e51 | 1.30121 | ||||||||
\(586\) | 1.47925e50 | 0.0920311 | ||||||||
\(587\) | 1.13653e51 | 0.685134 | 0.342567 | − | 0.939493i | \(-0.388704\pi\) | ||||
0.342567 | + | 0.939493i | \(0.388704\pi\) | |||||||
\(588\) | −1.68055e49 | −0.00981685 | ||||||||
\(589\) | 1.77887e51 | 1.00696 | ||||||||
\(590\) | 7.20624e50 | 0.395318 | ||||||||
\(591\) | 3.72945e49 | 0.0198279 | ||||||||
\(592\) | 1.06084e51 | 0.546636 | ||||||||
\(593\) | −1.23614e51 | −0.617383 | −0.308692 | − | 0.951162i | \(-0.599891\pi\) | ||||
−0.308692 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(594\) | −1.36277e50 | −0.0659740 | ||||||||
\(595\) | 5.77765e50 | 0.271136 | ||||||||
\(596\) | −1.66389e50 | −0.0756954 | ||||||||
\(597\) | 7.78766e48 | 0.00343464 | ||||||||
\(598\) | −1.27257e49 | −0.00544140 | ||||||||
\(599\) | −4.59427e51 | −1.90467 | −0.952336 | − | 0.305052i | \(-0.901326\pi\) | ||||
−0.952336 | + | 0.305052i | \(0.901326\pi\) | |||||||
\(600\) | −4.45472e48 | −0.00179070 | ||||||||
\(601\) | −1.48401e49 | −0.00578442 | −0.00289221 | − | 0.999996i | \(-0.500921\pi\) | ||||
−0.00289221 | + | 0.999996i | \(0.500921\pi\) | |||||||
\(602\) | −1.65080e51 | −0.623962 | ||||||||
\(603\) | 1.09911e51 | 0.402877 | ||||||||
\(604\) | 3.93340e50 | 0.139825 | ||||||||
\(605\) | −2.65933e51 | −0.916850 | ||||||||
\(606\) | −7.62951e49 | −0.0255125 | ||||||||
\(607\) | 2.59968e51 | 0.843198 | 0.421599 | − | 0.906782i | \(-0.361469\pi\) | ||||
0.421599 | + | 0.906782i | \(0.361469\pi\) | |||||||
\(608\) | 3.58751e51 | 1.12870 | ||||||||
\(609\) | 6.17859e49 | 0.0188568 | ||||||||
\(610\) | −2.75785e51 | −0.816525 | ||||||||
\(611\) | 1.94536e51 | 0.558775 | ||||||||
\(612\) | −8.82998e50 | −0.246070 | ||||||||
\(613\) | 1.49376e50 | 0.0403890 | 0.0201945 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201945 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(614\) | 2.74319e51 | 0.719682 | ||||||||
\(615\) | −6.95635e49 | −0.0177089 | ||||||||
\(616\) | 2.80131e51 | 0.692018 | ||||||||
\(617\) | −6.30081e51 | −1.51050 | −0.755250 | − | 0.655437i | \(-0.772484\pi\) | ||||
−0.755250 | + | 0.655437i | \(0.772484\pi\) | |||||||
\(618\) | 2.00025e49 | 0.00465369 | ||||||||
\(619\) | 5.97852e51 | 1.34995 | 0.674974 | − | 0.737842i | \(-0.264155\pi\) | ||||
0.674974 | + | 0.737842i | \(0.264155\pi\) | |||||||
\(620\) | 1.20384e51 | 0.263829 | ||||||||
\(621\) | −1.51935e48 | −0.000323195 0 | ||||||||
\(622\) | −1.44681e51 | −0.298737 | ||||||||
\(623\) | −3.08136e51 | −0.617609 | ||||||||
\(624\) | 9.11007e49 | 0.0177258 | ||||||||
\(625\) | −4.99363e51 | −0.943269 | ||||||||
\(626\) | 1.46570e51 | 0.268794 | ||||||||
\(627\) | 3.61068e50 | 0.0642893 | ||||||||
\(628\) | −3.92055e51 | −0.677787 | ||||||||
\(629\) | 4.59358e51 | 0.771106 | ||||||||
\(630\) | 2.10711e51 | 0.343469 | ||||||||
\(631\) | −3.17011e51 | −0.501800 | −0.250900 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250900 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(632\) | −6.65683e51 | −1.02330 | ||||||||
\(633\) | −3.43499e50 | −0.0512810 | ||||||||
\(634\) | −6.13536e51 | −0.889588 | ||||||||
\(635\) | 1.18198e52 | 1.66454 | ||||||||
\(636\) | 4.08744e49 | 0.00559107 | ||||||||
\(637\) | −7.96244e51 | −1.05795 | ||||||||
\(638\) | 1.11726e52 | 1.44203 | ||||||||
\(639\) | −2.83512e51 | −0.355473 | ||||||||
\(640\) | −2.29507e50 | −0.0279554 | ||||||||
\(641\) | 1.15243e52 | 1.36377 | 0.681885 | − | 0.731459i | \(-0.261160\pi\) | ||||
0.681885 | + | 0.731459i | \(0.261160\pi\) | |||||||
\(642\) | 9.34289e49 | 0.0107420 | ||||||||
\(643\) | 1.66832e52 | 1.86370 | 0.931851 | − | 0.362842i | \(-0.118193\pi\) | ||||
0.931851 | + | 0.362842i | \(0.118193\pi\) | |||||||
\(644\) | 8.99971e48 | 0.000976877 0 | ||||||||
\(645\) | −4.99706e50 | −0.0527060 | ||||||||
\(646\) | −6.88289e51 | −0.705455 | ||||||||
\(647\) | −1.67531e52 | −1.66865 | −0.834327 | − | 0.551270i | \(-0.814144\pi\) | ||||
−0.834327 | + | 0.551270i | \(0.814144\pi\) | |||||||
\(648\) | −1.11649e52 | −1.08073 | ||||||||
\(649\) | 7.80457e51 | 0.734213 | ||||||||
\(650\) | −6.08199e50 | −0.0556095 | ||||||||
\(651\) | −1.06011e50 | −0.00942116 | ||||||||
\(652\) | 4.54380e51 | 0.392499 | ||||||||
\(653\) | −9.01096e51 | −0.756619 | −0.378309 | − | 0.925679i | \(-0.623494\pi\) | ||||
−0.378309 | + | 0.925679i | \(0.623494\pi\) | |||||||
\(654\) | 6.29454e48 | 0.000513778 0 | ||||||||
\(655\) | −1.75936e52 | −1.39602 | ||||||||
\(656\) | 3.31668e51 | 0.255848 | ||||||||
\(657\) | −4.62118e51 | −0.346572 | ||||||||
\(658\) | 2.02281e51 | 0.147495 | ||||||||
\(659\) | 1.92183e52 | 1.36249 | 0.681247 | − | 0.732054i | \(-0.261438\pi\) | ||||
0.681247 | + | 0.732054i | \(0.261438\pi\) | |||||||
\(660\) | 2.44351e50 | 0.0168442 | ||||||||
\(661\) | −1.12368e51 | −0.0753213 | −0.0376606 | − | 0.999291i | \(-0.511991\pi\) | ||||
−0.0376606 | + | 0.999291i | \(0.511991\pi\) | |||||||
\(662\) | 5.29910e51 | 0.345405 | ||||||||
\(663\) | 3.94478e50 | 0.0250048 | ||||||||
\(664\) | 1.80409e52 | 1.11211 | ||||||||
\(665\) | −1.11709e52 | −0.669712 | ||||||||
\(666\) | 1.67528e52 | 0.976819 | ||||||||
\(667\) | 1.24564e50 | 0.00706422 | ||||||||
\(668\) | 2.19224e51 | 0.120927 | ||||||||
\(669\) | 7.41611e50 | 0.0397918 | ||||||||
\(670\) | 5.79801e51 | 0.302618 | ||||||||
\(671\) | −2.98684e52 | −1.51651 | ||||||||
\(672\) | −2.13797e50 | −0.0105602 | ||||||||
\(673\) | 6.07438e51 | 0.291893 | 0.145946 | − | 0.989292i | \(-0.453377\pi\) | ||||
0.145946 | + | 0.989292i | \(0.453377\pi\) | |||||||
\(674\) | −2.63974e52 | −1.23411 | ||||||||
\(675\) | −7.26143e49 | −0.00330295 | ||||||||
\(676\) | −7.25197e51 | −0.320954 | ||||||||
\(677\) | 3.94010e52 | 1.69675 | 0.848373 | − | 0.529398i | \(-0.177582\pi\) | ||||
0.848373 | + | 0.529398i | \(0.177582\pi\) | |||||||
\(678\) | −9.67055e49 | −0.00405230 | ||||||||
\(679\) | −2.11500e51 | −0.0862423 | ||||||||
\(680\) | −1.61646e52 | −0.641430 | ||||||||
\(681\) | −1.39289e51 | −0.0537892 | ||||||||
\(682\) | −1.91699e52 | −0.720457 | ||||||||
\(683\) | −2.05041e52 | −0.749993 | −0.374996 | − | 0.927026i | \(-0.622356\pi\) | ||||
−0.374996 | + | 0.927026i | \(0.622356\pi\) | |||||||
\(684\) | 1.70725e52 | 0.607798 | ||||||||
\(685\) | 1.04424e52 | 0.361847 | ||||||||
\(686\) | −1.87582e52 | −0.632696 | ||||||||
\(687\) | 1.04893e51 | 0.0344389 | ||||||||
\(688\) | 2.38252e52 | 0.761465 | ||||||||
\(689\) | 1.93662e52 | 0.602545 | ||||||||
\(690\) | −4.00553e48 | −0.000121325 0 | ||||||||
\(691\) | 4.63109e51 | 0.136565 | 0.0682825 | − | 0.997666i | \(-0.478248\pi\) | ||||
0.0682825 | + | 0.997666i | \(0.478248\pi\) | |||||||
\(692\) | −1.45525e52 | −0.417808 | ||||||||
\(693\) | 2.28206e52 | 0.637915 | ||||||||
\(694\) | −1.50799e52 | −0.410440 | ||||||||
\(695\) | 2.59672e52 | 0.688188 | ||||||||
\(696\) | −1.72863e51 | −0.0446099 | ||||||||
\(697\) | 1.43616e52 | 0.360909 | ||||||||
\(698\) | 2.77797e52 | 0.679832 | ||||||||
\(699\) | −3.69433e50 | −0.00880456 | ||||||||
\(700\) | 4.30122e50 | 0.00998340 | ||||||||
\(701\) | −6.34322e51 | −0.143392 | −0.0716962 | − | 0.997427i | \(-0.522841\pi\) | ||||
−0.0716962 | + | 0.997427i | \(0.522841\pi\) | |||||||
\(702\) | 2.87868e51 | 0.0633807 | ||||||||
\(703\) | −8.88154e52 | −1.90465 | ||||||||
\(704\) | −6.74404e52 | −1.40872 | ||||||||
\(705\) | 6.12318e50 | 0.0124589 | ||||||||
\(706\) | 4.95873e52 | 0.982842 | ||||||||
\(707\) | 2.55645e52 | 0.493602 | ||||||||
\(708\) | −3.47958e50 | −0.00654503 | ||||||||
\(709\) | −7.70939e52 | −1.41275 | −0.706374 | − | 0.707839i | \(-0.749670\pi\) | ||||
−0.706374 | + | 0.707839i | \(0.749670\pi\) | |||||||
\(710\) | −1.49557e52 | −0.267010 | ||||||||
\(711\) | −5.42293e52 | −0.943293 | ||||||||
\(712\) | 8.62096e52 | 1.46109 | ||||||||
\(713\) | −2.13725e50 | −0.00352939 | ||||||||
\(714\) | 4.10184e50 | 0.00660028 | ||||||||
\(715\) | 1.15773e53 | 1.81529 | ||||||||
\(716\) | 2.34718e52 | 0.358637 | ||||||||
\(717\) | 5.90989e50 | 0.00879985 | ||||||||
\(718\) | −3.23407e52 | −0.469296 | ||||||||
\(719\) | 5.22428e52 | 0.738826 | 0.369413 | − | 0.929265i | \(-0.379559\pi\) | ||||
0.369413 | + | 0.929265i | \(0.379559\pi\) | |||||||
\(720\) | −3.04110e52 | −0.419159 | ||||||||
\(721\) | −6.70231e51 | −0.0900372 | ||||||||
\(722\) | 7.41579e52 | 0.971000 | ||||||||
\(723\) | 2.31196e51 | 0.0295068 | ||||||||
\(724\) | 5.29245e51 | 0.0658406 | ||||||||
\(725\) | 5.95327e51 | 0.0721942 | ||||||||
\(726\) | −1.88800e51 | −0.0223189 | ||||||||
\(727\) | −1.24495e53 | −1.43471 | −0.717354 | − | 0.696708i | \(-0.754647\pi\) | ||||
−0.717354 | + | 0.696708i | \(0.754647\pi\) | |||||||
\(728\) | −5.91742e52 | −0.664816 | ||||||||
\(729\) | −9.07820e52 | −0.994352 | ||||||||
\(730\) | −2.43775e52 | −0.260325 | ||||||||
\(731\) | 1.03166e53 | 1.07415 | ||||||||
\(732\) | 1.33165e51 | 0.0135187 | ||||||||
\(733\) | −1.12627e52 | −0.111485 | −0.0557427 | − | 0.998445i | \(-0.517753\pi\) | ||||
−0.0557427 | + | 0.998445i | \(0.517753\pi\) | |||||||
\(734\) | −2.49994e52 | −0.241297 | ||||||||
\(735\) | −2.50625e51 | −0.0235889 | ||||||||
\(736\) | −4.31028e50 | −0.00395609 | ||||||||
\(737\) | 6.27941e52 | 0.562044 | ||||||||
\(738\) | 5.23769e52 | 0.457191 | ||||||||
\(739\) | −2.92067e52 | −0.248634 | −0.124317 | − | 0.992243i | \(-0.539674\pi\) | ||||
−0.124317 | + | 0.992243i | \(0.539674\pi\) | |||||||
\(740\) | −6.01053e52 | −0.499029 | ||||||||
\(741\) | −7.62711e51 | −0.0617623 | ||||||||
\(742\) | 2.01373e52 | 0.159048 | ||||||||
\(743\) | 3.47917e52 | 0.268029 | 0.134015 | − | 0.990979i | \(-0.457213\pi\) | ||||
0.134015 | + | 0.990979i | \(0.457213\pi\) | |||||||
\(744\) | 2.96596e51 | 0.0222878 | ||||||||
\(745\) | −2.48140e52 | −0.181889 | ||||||||
\(746\) | 7.72582e52 | 0.552429 | ||||||||
\(747\) | 1.46969e53 | 1.02516 | ||||||||
\(748\) | −5.04470e52 | −0.343286 | ||||||||
\(749\) | −3.13055e52 | −0.207830 | ||||||||
\(750\) | −3.74756e51 | −0.0242725 | ||||||||
\(751\) | 1.55213e53 | 0.980818 | 0.490409 | − | 0.871492i | \(-0.336847\pi\) | ||||
0.490409 | + | 0.871492i | \(0.336847\pi\) | |||||||
\(752\) | −2.91943e52 | −0.179998 | ||||||||
\(753\) | 8.28513e51 | 0.0498416 | ||||||||
\(754\) | −2.36008e53 | −1.38534 | ||||||||
\(755\) | 5.86596e52 | 0.335985 | ||||||||
\(756\) | −2.03582e51 | −0.0113785 | ||||||||
\(757\) | −1.00018e51 | −0.00545510 | −0.00272755 | − | 0.999996i | \(-0.500868\pi\) | ||||
−0.00272755 | + | 0.999996i | \(0.500868\pi\) | |||||||
\(758\) | −1.18268e53 | −0.629488 | ||||||||
\(759\) | −4.33811e49 | −0.000225334 0 | ||||||||
\(760\) | 3.12537e53 | 1.58435 | ||||||||
\(761\) | −3.93324e53 | −1.94596 | −0.972981 | − | 0.230886i | \(-0.925838\pi\) | ||||
−0.972981 | + | 0.230886i | \(0.925838\pi\) | |||||||
\(762\) | 8.39144e51 | 0.0405200 | ||||||||
\(763\) | −2.10913e51 | −0.00994031 | ||||||||
\(764\) | 1.45455e52 | 0.0669115 | ||||||||
\(765\) | −1.31683e53 | −0.591282 | ||||||||
\(766\) | −1.89949e53 | −0.832541 | ||||||||
\(767\) | −1.64862e53 | −0.705353 | ||||||||
\(768\) | 7.26468e51 | 0.0303413 | ||||||||
\(769\) | 4.31322e53 | 1.75859 | 0.879295 | − | 0.476278i | \(-0.158015\pi\) | ||||
0.879295 | + | 0.476278i | \(0.158015\pi\) | |||||||
\(770\) | 1.20382e53 | 0.479165 | ||||||||
\(771\) | −1.11827e52 | −0.0434552 | ||||||||
\(772\) | 3.48879e52 | 0.132359 | ||||||||
\(773\) | 1.93734e53 | 0.717604 | 0.358802 | − | 0.933414i | \(-0.383185\pi\) | ||||
0.358802 | + | 0.933414i | \(0.383185\pi\) | |||||||
\(774\) | 3.76247e53 | 1.36071 | ||||||||
\(775\) | −1.02145e52 | −0.0360693 | ||||||||
\(776\) | 5.91731e52 | 0.204024 | ||||||||
\(777\) | 5.29294e51 | 0.0178200 | ||||||||
\(778\) | 1.35607e52 | 0.0445821 | ||||||||
\(779\) | −2.77678e53 | −0.891452 | ||||||||
\(780\) | −5.16160e51 | −0.0161821 | ||||||||
\(781\) | −1.61975e53 | −0.495911 | ||||||||
\(782\) | 8.26956e50 | 0.00247262 | ||||||||
\(783\) | −2.81776e52 | −0.0822832 | ||||||||
\(784\) | 1.19494e53 | 0.340799 | ||||||||
\(785\) | −5.84680e53 | −1.62866 | ||||||||
\(786\) | −1.24906e52 | −0.0339833 | ||||||||
\(787\) | −1.53439e52 | −0.0407759 | −0.0203880 | − | 0.999792i | \(-0.506490\pi\) | ||||
−0.0203880 | + | 0.999792i | \(0.506490\pi\) | |||||||
\(788\) | 1.00746e53 | 0.261514 | ||||||||
\(789\) | 1.64390e52 | 0.0416821 | ||||||||
\(790\) | −2.86068e53 | −0.708547 | ||||||||
\(791\) | 3.24034e52 | 0.0784018 | ||||||||
\(792\) | −6.38470e53 | −1.50912 | ||||||||
\(793\) | 6.30933e53 | 1.45690 | ||||||||
\(794\) | 1.71777e53 | 0.387512 | ||||||||
\(795\) | 6.09569e51 | 0.0134348 | ||||||||
\(796\) | 2.10374e52 | 0.0453001 | ||||||||
\(797\) | 5.82231e53 | 1.22494 | 0.612472 | − | 0.790493i | \(-0.290175\pi\) | ||||
0.612472 | + | 0.790493i | \(0.290175\pi\) | |||||||
\(798\) | −7.93079e51 | −0.0163028 | ||||||||
\(799\) | −1.26415e53 | −0.253912 | ||||||||
\(800\) | −2.06001e52 | −0.0404300 | ||||||||
\(801\) | 7.02299e53 | 1.34685 | ||||||||
\(802\) | −2.66039e53 | −0.498563 | ||||||||
\(803\) | −2.64015e53 | −0.483495 | ||||||||
\(804\) | −2.79960e51 | −0.00501025 | ||||||||
\(805\) | 1.34215e51 | 0.00234734 | ||||||||
\(806\) | 4.04940e53 | 0.692137 | ||||||||
\(807\) | 2.10464e52 | 0.0351574 | ||||||||
\(808\) | −7.15236e53 | −1.16772 | ||||||||
\(809\) | 7.29683e53 | 1.16436 | 0.582179 | − | 0.813061i | \(-0.302200\pi\) | ||||
0.582179 | + | 0.813061i | \(0.302200\pi\) | |||||||
\(810\) | −4.79796e53 | −0.748315 | ||||||||
\(811\) | −8.04109e53 | −1.22583 | −0.612914 | − | 0.790150i | \(-0.710003\pi\) | ||||
−0.612914 | + | 0.790150i | \(0.710003\pi\) | |||||||
\(812\) | 1.66907e53 | 0.248706 | ||||||||
\(813\) | 5.41870e51 | 0.00789261 | ||||||||
\(814\) | 9.57113e53 | 1.36274 | ||||||||
\(815\) | 6.77627e53 | 0.943137 | ||||||||
\(816\) | −5.92000e51 | −0.00805479 | ||||||||
\(817\) | −1.99469e54 | −2.65318 | ||||||||
\(818\) | −7.44878e52 | −0.0968611 | ||||||||
\(819\) | −4.82058e53 | −0.612840 | ||||||||
\(820\) | −1.87917e53 | −0.233566 | ||||||||
\(821\) | −1.06873e52 | −0.0129873 | −0.00649364 | − | 0.999979i | \(-0.502067\pi\) | ||||
−0.00649364 | + | 0.999979i | \(0.502067\pi\) | |||||||
\(822\) | 7.41360e51 | 0.00880847 | ||||||||
\(823\) | 1.55439e54 | 1.80578 | 0.902889 | − | 0.429874i | \(-0.141442\pi\) | ||||
0.902889 | + | 0.429874i | \(0.141442\pi\) | |||||||
\(824\) | 1.87516e53 | 0.213002 | ||||||||
\(825\) | −2.07331e51 | −0.00230285 | ||||||||
\(826\) | −1.71426e53 | −0.186186 | ||||||||
\(827\) | −1.52865e54 | −1.62352 | −0.811759 | − | 0.583992i | \(-0.801490\pi\) | ||||
−0.811759 | + | 0.583992i | \(0.801490\pi\) | |||||||
\(828\) | −2.05120e51 | −0.00213033 | ||||||||
\(829\) | 4.48559e53 | 0.455576 | 0.227788 | − | 0.973711i | \(-0.426851\pi\) | ||||
0.227788 | + | 0.973711i | \(0.426851\pi\) | |||||||
\(830\) | 7.75284e53 | 0.770045 | ||||||||
\(831\) | −3.31346e52 | −0.0321857 | ||||||||
\(832\) | 1.42459e54 | 1.35335 | ||||||||
\(833\) | 5.17424e53 | 0.480744 | ||||||||
\(834\) | 1.84355e52 | 0.0167526 | ||||||||
\(835\) | 3.26934e53 | 0.290576 | ||||||||
\(836\) | 9.75378e53 | 0.847924 | ||||||||
\(837\) | 4.83467e52 | 0.0411099 | ||||||||
\(838\) | −1.12190e54 | −0.933122 | ||||||||
\(839\) | −1.70786e54 | −1.38949 | −0.694747 | − | 0.719254i | \(-0.744484\pi\) | ||||
−0.694747 | + | 0.719254i | \(0.744484\pi\) | |||||||
\(840\) | −1.86256e52 | −0.0148232 | ||||||||
\(841\) | 1.02566e54 | 0.798502 | ||||||||
\(842\) | −1.10682e54 | −0.842950 | ||||||||
\(843\) | −5.89519e52 | −0.0439226 | ||||||||
\(844\) | −9.27918e53 | −0.676354 | ||||||||
\(845\) | −1.08150e54 | −0.771220 | ||||||||
\(846\) | −4.61037e53 | −0.321650 | ||||||||
\(847\) | 6.32617e53 | 0.431815 | ||||||||
\(848\) | −2.90633e53 | −0.194098 | ||||||||
\(849\) | −1.64245e52 | −0.0107325 | ||||||||
\(850\) | 3.95226e52 | 0.0252694 | ||||||||
\(851\) | 1.06709e52 | 0.00667580 | ||||||||
\(852\) | 7.22147e51 | 0.00442072 | ||||||||
\(853\) | −1.02278e54 | −0.612667 | −0.306334 | − | 0.951924i | \(-0.599102\pi\) | ||||
−0.306334 | + | 0.951924i | \(0.599102\pi\) | |||||||
\(854\) | 6.56054e53 | 0.384564 | ||||||||
\(855\) | 2.54606e54 | 1.46048 | ||||||||
\(856\) | 8.75859e53 | 0.491666 | ||||||||
\(857\) | 7.33586e52 | 0.0403001 | 0.0201500 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201500 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(858\) | 8.21931e52 | 0.0441896 | ||||||||
\(859\) | 1.46329e54 | 0.769938 | 0.384969 | − | 0.922929i | \(-0.374212\pi\) | ||||
0.384969 | + | 0.922929i | \(0.374212\pi\) | |||||||
\(860\) | −1.34989e54 | −0.695149 | ||||||||
\(861\) | 1.65482e52 | 0.00834049 | ||||||||
\(862\) | 8.52292e53 | 0.420440 | ||||||||
\(863\) | 2.49462e54 | 1.20449 | 0.602247 | − | 0.798310i | \(-0.294272\pi\) | ||||
0.602247 | + | 0.798310i | \(0.294272\pi\) | |||||||
\(864\) | 9.75027e52 | 0.0460800 | ||||||||
\(865\) | −2.17025e54 | −1.00395 | ||||||||
\(866\) | −6.31753e53 | −0.286066 | ||||||||
\(867\) | 4.36098e52 | 0.0193300 | ||||||||
\(868\) | −2.86376e53 | −0.124257 | ||||||||
\(869\) | −3.09821e54 | −1.31597 | ||||||||
\(870\) | −7.42856e52 | −0.0308886 | ||||||||
\(871\) | −1.32645e54 | −0.539951 | ||||||||
\(872\) | 5.90088e52 | 0.0235159 | ||||||||
\(873\) | 4.82049e53 | 0.188073 | ||||||||
\(874\) | −1.59889e52 | −0.00610742 | ||||||||
\(875\) | 1.25571e54 | 0.469612 | ||||||||
\(876\) | 1.17708e52 | 0.00431004 | ||||||||
\(877\) | 4.03070e54 | 1.44507 | 0.722534 | − | 0.691335i | \(-0.242977\pi\) | ||||
0.722534 | + | 0.691335i | \(0.242977\pi\) | |||||||
\(878\) | −3.26696e54 | −1.14682 | ||||||||
\(879\) | −1.06520e52 | −0.00366130 | ||||||||
\(880\) | −1.73743e54 | −0.584759 | ||||||||
\(881\) | −2.32935e54 | −0.767679 | −0.383840 | − | 0.923400i | \(-0.625398\pi\) | ||||
−0.383840 | + | 0.923400i | \(0.625398\pi\) | |||||||
\(882\) | 1.88705e54 | 0.608995 | ||||||||
\(883\) | −2.99176e54 | −0.945482 | −0.472741 | − | 0.881202i | \(-0.656735\pi\) | ||||
−0.472741 | + | 0.881202i | \(0.656735\pi\) | |||||||
\(884\) | 1.06563e54 | 0.329792 | ||||||||
\(885\) | −5.18917e52 | −0.0157271 | ||||||||
\(886\) | 2.51281e54 | 0.745822 | ||||||||
\(887\) | 5.34771e54 | 1.55447 | 0.777233 | − | 0.629213i | \(-0.216623\pi\) | ||||
0.777233 | + | 0.629213i | \(0.216623\pi\) | |||||||
\(888\) | −1.48085e53 | −0.0421570 | ||||||||
\(889\) | −2.81175e54 | −0.783960 | ||||||||
\(890\) | 3.70474e54 | 1.01168 | ||||||||
\(891\) | −5.19634e54 | −1.38982 | ||||||||
\(892\) | 2.00337e54 | 0.524821 | ||||||||
\(893\) | 2.44420e54 | 0.627169 | ||||||||
\(894\) | −1.76167e52 | −0.00442772 | ||||||||
\(895\) | 3.50040e54 | 0.861770 | ||||||||
\(896\) | 5.45963e52 | 0.0131663 | ||||||||
\(897\) | 9.16372e50 | 0.000216477 0 | ||||||||
\(898\) | −2.55961e54 | −0.592327 | ||||||||
\(899\) | −3.96370e54 | −0.898558 | ||||||||
\(900\) | −9.80329e52 | −0.0217714 | ||||||||
\(901\) | −1.25848e54 | −0.273802 | ||||||||
\(902\) | 2.99238e54 | 0.637816 | ||||||||
\(903\) | 1.18873e53 | 0.0248233 | ||||||||
\(904\) | −9.06576e53 | −0.185476 | ||||||||
\(905\) | 7.89275e53 | 0.158208 | ||||||||
\(906\) | 4.16454e52 | 0.00817891 | ||||||||
\(907\) | −6.45044e54 | −1.24124 | −0.620618 | − | 0.784113i | \(-0.713118\pi\) | ||||
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(908\) | −3.76271e54 | −0.709436 | ||||||||
\(909\) | −5.82662e54 | −1.07643 | ||||||||
\(910\) | −2.54293e54 | −0.460330 | ||||||||
\(911\) | 2.81261e54 | 0.498907 | 0.249453 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249453 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(912\) | 1.14461e53 | 0.0198955 | ||||||||
\(913\) | 8.39655e54 | 1.43018 | ||||||||
\(914\) | 1.08031e54 | 0.180321 | ||||||||
\(915\) | 1.98592e53 | 0.0324841 | ||||||||
\(916\) | 2.83356e54 | 0.454220 | ||||||||
\(917\) | 4.18526e54 | 0.657491 | ||||||||
\(918\) | −1.87066e53 | −0.0288008 | ||||||||
\(919\) | 5.50843e54 | 0.831171 | 0.415586 | − | 0.909554i | \(-0.363577\pi\) | ||||
0.415586 | + | 0.909554i | \(0.363577\pi\) | |||||||
\(920\) | −3.75503e52 | −0.00555314 | ||||||||
\(921\) | −1.97535e53 | −0.0286314 | ||||||||
\(922\) | 2.54502e54 | 0.361551 | ||||||||
\(923\) | 3.42152e54 | 0.476418 | ||||||||
\(924\) | −5.81275e52 | −0.00793323 | ||||||||
\(925\) | 5.09992e53 | 0.0682246 | ||||||||
\(926\) | −9.59349e54 | −1.25798 | ||||||||
\(927\) | 1.52758e54 | 0.196349 | ||||||||
\(928\) | −7.99374e54 | −1.00719 | ||||||||
\(929\) | 9.70568e54 | 1.19877 | 0.599384 | − | 0.800461i | \(-0.295412\pi\) | ||||
0.599384 | + | 0.800461i | \(0.295412\pi\) | |||||||
\(930\) | 1.27458e53 | 0.0154324 | ||||||||
\(931\) | −1.00042e55 | −1.18745 | ||||||||
\(932\) | −9.97975e53 | −0.116125 | ||||||||
\(933\) | 1.04184e53 | 0.0118848 | ||||||||
\(934\) | −1.05115e55 | −1.17557 | ||||||||
\(935\) | −7.52328e54 | −0.824883 | ||||||||
\(936\) | 1.34869e55 | 1.44980 | ||||||||
\(937\) | −4.05525e54 | −0.427401 | −0.213701 | − | 0.976899i | \(-0.568552\pi\) | ||||
−0.213701 | + | 0.976899i | \(0.568552\pi\) | |||||||
\(938\) | −1.37926e54 | −0.142526 | ||||||||
\(939\) | −1.05544e53 | −0.0106935 | ||||||||
\(940\) | 1.65410e54 | 0.164322 | ||||||||
\(941\) | 4.56539e54 | 0.444703 | 0.222351 | − | 0.974967i | \(-0.428627\pi\) | ||||
0.222351 | + | 0.974967i | \(0.428627\pi\) | |||||||
\(942\) | −4.15094e53 | −0.0396465 | ||||||||
\(943\) | 3.33621e52 | 0.00312454 | ||||||||
\(944\) | 2.47411e54 | 0.227215 | ||||||||
\(945\) | −3.03607e53 | −0.0273415 | ||||||||
\(946\) | 2.14956e55 | 1.89829 | ||||||||
\(947\) | −1.72468e55 | −1.49360 | −0.746798 | − | 0.665051i | \(-0.768410\pi\) | ||||
−0.746798 | + | 0.665051i | \(0.768410\pi\) | |||||||
\(948\) | 1.38130e53 | 0.0117310 | ||||||||
\(949\) | 5.57700e54 | 0.464490 | ||||||||
\(950\) | −7.64158e53 | −0.0624161 | ||||||||
\(951\) | 4.41804e53 | 0.0353908 | ||||||||
\(952\) | 3.84532e54 | 0.302099 | ||||||||
\(953\) | 6.30605e52 | 0.00485891 | 0.00242945 | − | 0.999997i | \(-0.499227\pi\) | ||||
0.00242945 | + | 0.999997i | \(0.499227\pi\) | |||||||
\(954\) | −4.58967e54 | −0.346846 | ||||||||
\(955\) | 2.16920e54 | 0.160782 | ||||||||
\(956\) | 1.59648e54 | 0.116063 | ||||||||
\(957\) | −8.04535e53 | −0.0573686 | ||||||||
\(958\) | 1.35394e55 | 0.946969 | ||||||||
\(959\) | −2.48410e54 | −0.170422 | ||||||||
\(960\) | 4.48403e53 | 0.0301753 | ||||||||
\(961\) | −8.34809e54 | −0.551067 | ||||||||
\(962\) | −2.02178e55 | −1.30917 | ||||||||
\(963\) | 7.13512e54 | 0.453226 | ||||||||
\(964\) | 6.24546e54 | 0.389170 | ||||||||
\(965\) | 5.20291e54 | 0.318047 | ||||||||
\(966\) | 9.52858e50 | 5.71415e−5 0 | ||||||||
\(967\) | −1.73337e55 | −1.01977 | −0.509883 | − | 0.860244i | \(-0.670311\pi\) | ||||
−0.509883 | + | 0.860244i | \(0.670311\pi\) | |||||||
\(968\) | −1.76992e55 | −1.02155 | ||||||||
\(969\) | 4.95633e53 | 0.0280653 | ||||||||
\(970\) | 2.54288e54 | 0.141270 | ||||||||
\(971\) | 1.04588e55 | 0.570067 | 0.285033 | − | 0.958518i | \(-0.407995\pi\) | ||||
0.285033 | + | 0.958518i | \(0.407995\pi\) | |||||||
\(972\) | 6.96112e53 | 0.0372266 | ||||||||
\(973\) | −6.17723e54 | −0.324121 | ||||||||
\(974\) | 2.28037e54 | 0.117399 | ||||||||
\(975\) | 4.37961e52 | 0.00221233 | ||||||||
\(976\) | −9.46852e54 | −0.469311 | ||||||||
\(977\) | −1.65065e55 | −0.802798 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(978\) | 4.81082e53 | 0.0229588 | ||||||||
\(979\) | 4.01235e55 | 1.87896 | ||||||||
\(980\) | −6.77031e54 | −0.311119 | ||||||||
\(981\) | 4.80711e53 | 0.0216774 | ||||||||
\(982\) | 1.02922e55 | 0.455454 | ||||||||
\(983\) | 3.82232e55 | 1.65992 | 0.829960 | − | 0.557823i | \(-0.188363\pi\) | ||||
0.829960 | + | 0.557823i | \(0.188363\pi\) | |||||||
\(984\) | −4.62981e53 | −0.0197312 | ||||||||
\(985\) | 1.50245e55 | 0.628392 | ||||||||
\(986\) | 1.53365e55 | 0.629512 | ||||||||
\(987\) | −1.45662e53 | −0.00586783 | ||||||||
\(988\) | −2.06037e55 | −0.814593 | ||||||||
\(989\) | 2.39655e53 | 0.00929939 | ||||||||
\(990\) | −2.74374e55 | −1.04494 | ||||||||
\(991\) | −4.27417e55 | −1.59768 | −0.798838 | − | 0.601546i | \(-0.794552\pi\) | ||||
−0.798838 | + | 0.601546i | \(0.794552\pi\) | |||||||
\(992\) | 1.37156e55 | 0.503208 | ||||||||
\(993\) | −3.81585e53 | −0.0137414 | ||||||||
\(994\) | 3.55775e54 | 0.125756 | ||||||||
\(995\) | 3.13735e54 | 0.108852 | ||||||||
\(996\) | −3.74351e53 | −0.0127491 | ||||||||
\(997\) | −3.39750e55 | −1.13579 | −0.567896 | − | 0.823100i | \(-0.692243\pi\) | ||||
−0.567896 | + | 0.823100i | \(0.692243\pi\) | |||||||
\(998\) | 2.28344e55 | 0.749332 | ||||||||
\(999\) | −2.41386e54 | −0.0777588 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.38.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.38.a.a.1.1 | 2 | |||
4.3 | odd | 2 | 16.38.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 25.38.b.a.24.3 | 4 | |||
5.3 | odd | 4 | 25.38.b.a.24.2 | 4 | |||
5.4 | even | 2 | 25.38.a.a.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.38.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.38.a.a.1.1 | 2 | 3.2 | odd | 2 | |||
16.38.a.b.1.2 | 2 | 4.3 | odd | 2 | |||
25.38.a.a.1.1 | 2 | 5.4 | even | 2 | |||
25.38.b.a.24.2 | 4 | 5.3 | odd | 4 | |||
25.38.b.a.24.3 | 4 | 5.2 | odd | 4 |