Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,70,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, 70, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 70);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 70 \) |
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: | \(30.1514953292\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 94\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.52577e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.75433e10 | −1.95684 | −0.978418 | − | 0.206634i | \(-0.933749\pi\) | ||||
−0.978418 | + | 0.206634i | \(0.933749\pi\) | |||||||
\(3\) | −9.70523e15 | −0.335987 | −0.167994 | − | 0.985788i | \(-0.553729\pi\) | ||||
−0.167994 | + | 0.985788i | \(0.553729\pi\) | |||||||
\(4\) | 1.67007e21 | 2.82921 | ||||||||
\(5\) | −1.40726e24 | −1.08121 | −0.540603 | − | 0.841278i | \(-0.681804\pi\) | ||||
−0.540603 | + | 0.841278i | \(0.681804\pi\) | |||||||
\(6\) | 4.61419e26 | 0.657472 | ||||||||
\(7\) | −1.18429e27 | −0.00827136 | −0.00413568 | − | 0.999991i | \(-0.501316\pi\) | ||||
−0.00413568 | + | 0.999991i | \(0.501316\pi\) | |||||||
\(8\) | −5.13361e31 | −3.57946 | ||||||||
\(9\) | −7.40194e32 | −0.887113 | ||||||||
\(10\) | 6.69057e34 | 2.11574 | ||||||||
\(11\) | 2.72474e34 | 0.0321572 | 0.0160786 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160786 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(12\) | −1.62084e37 | −0.950578 | ||||||||
\(13\) | 4.14237e38 | 1.53533 | 0.767667 | − | 0.640849i | \(-0.221418\pi\) | ||||
0.767667 | + | 0.640849i | \(0.221418\pi\) | |||||||
\(14\) | 5.63052e37 | 0.0161857 | ||||||||
\(15\) | 1.36578e40 | 0.363271 | ||||||||
\(16\) | 1.45485e42 | 4.17522 | ||||||||
\(17\) | −7.81618e41 | −0.277017 | −0.138509 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138509 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(18\) | 3.51913e43 | 1.73593 | ||||||||
\(19\) | 6.36441e43 | 0.486137 | 0.243069 | − | 0.970009i | \(-0.421846\pi\) | ||||
0.243069 | + | 0.970009i | \(0.421846\pi\) | |||||||
\(20\) | −2.35022e45 | −3.05896 | ||||||||
\(21\) | 1.14938e43 | 0.00277907 | ||||||||
\(22\) | −1.29543e45 | −0.0629263 | ||||||||
\(23\) | 8.76109e46 | 0.918222 | 0.459111 | − | 0.888379i | \(-0.348168\pi\) | ||||
0.459111 | + | 0.888379i | \(0.348168\pi\) | |||||||
\(24\) | 4.98228e47 | 1.20265 | ||||||||
\(25\) | 2.86308e47 | 0.169006 | ||||||||
\(26\) | −1.96942e49 | −3.00440 | ||||||||
\(27\) | 1.52816e49 | 0.634045 | ||||||||
\(28\) | −1.97785e48 | −0.0234014 | ||||||||
\(29\) | 5.98090e49 | 0.210880 | 0.105440 | − | 0.994426i | \(-0.466375\pi\) | ||||
0.105440 | + | 0.994426i | \(0.466375\pi\) | |||||||
\(30\) | −6.49335e50 | −0.710862 | ||||||||
\(31\) | 1.30933e51 | 0.462455 | 0.231228 | − | 0.972900i | \(-0.425726\pi\) | ||||
0.231228 | + | 0.972900i | \(0.425726\pi\) | |||||||
\(32\) | −3.88650e52 | −4.59075 | ||||||||
\(33\) | −2.64442e50 | −0.0108044 | ||||||||
\(34\) | 3.71607e52 | 0.542077 | ||||||||
\(35\) | 1.66661e51 | 0.00894304 | ||||||||
\(36\) | −1.23618e54 | −2.50983 | ||||||||
\(37\) | 1.23271e54 | 0.972528 | 0.486264 | − | 0.873812i | \(-0.338359\pi\) | ||||
0.486264 | + | 0.873812i | \(0.338359\pi\) | |||||||
\(38\) | −3.02585e54 | −0.951291 | ||||||||
\(39\) | −4.02026e54 | −0.515852 | ||||||||
\(40\) | 7.22431e55 | 3.87014 | ||||||||
\(41\) | 1.03929e55 | 0.237516 | 0.118758 | − | 0.992923i | \(-0.462109\pi\) | ||||
0.118758 | + | 0.992923i | \(0.462109\pi\) | |||||||
\(42\) | −5.46455e53 | −0.00543819 | ||||||||
\(43\) | −2.30147e56 | −1.01705 | −0.508525 | − | 0.861047i | \(-0.669809\pi\) | ||||
−0.508525 | + | 0.861047i | \(0.669809\pi\) | |||||||
\(44\) | 4.55051e55 | 0.0909793 | ||||||||
\(45\) | 1.04164e57 | 0.959152 | ||||||||
\(46\) | −4.16531e57 | −1.79681 | ||||||||
\(47\) | 5.31802e57 | 1.09238 | 0.546190 | − | 0.837662i | \(-0.316078\pi\) | ||||
0.546190 | + | 0.837662i | \(0.316078\pi\) | |||||||
\(48\) | −1.41197e58 | −1.40282 | ||||||||
\(49\) | −2.04991e58 | −0.999932 | ||||||||
\(50\) | −1.36120e58 | −0.330718 | ||||||||
\(51\) | 7.58578e57 | 0.0930742 | ||||||||
\(52\) | 6.91804e59 | 4.34378 | ||||||||
\(53\) | −2.46445e59 | −0.802051 | −0.401026 | − | 0.916067i | \(-0.631346\pi\) | ||||
−0.401026 | + | 0.916067i | \(0.631346\pi\) | |||||||
\(54\) | −7.26540e59 | −1.24072 | ||||||||
\(55\) | −3.83441e58 | −0.0347685 | ||||||||
\(56\) | 6.07970e58 | 0.0296070 | ||||||||
\(57\) | −6.17680e59 | −0.163336 | ||||||||
\(58\) | −2.84352e60 | −0.412658 | ||||||||
\(59\) | −7.33567e60 | −0.590263 | −0.295132 | − | 0.955457i | \(-0.595363\pi\) | ||||
−0.295132 | + | 0.955457i | \(0.595363\pi\) | |||||||
\(60\) | 2.28094e61 | 1.02777 | ||||||||
\(61\) | −4.55049e61 | −1.15926 | −0.579628 | − | 0.814881i | \(-0.696802\pi\) | ||||
−0.579628 | + | 0.814881i | \(0.696802\pi\) | |||||||
\(62\) | −6.22497e61 | −0.904949 | ||||||||
\(63\) | 8.76606e59 | 0.00733763 | ||||||||
\(64\) | 9.88976e62 | 4.80814 | ||||||||
\(65\) | −5.82938e62 | −1.66001 | ||||||||
\(66\) | 1.25725e61 | 0.0211424 | ||||||||
\(67\) | −9.77457e62 | −0.978401 | −0.489201 | − | 0.872171i | \(-0.662711\pi\) | ||||
−0.489201 | + | 0.872171i | \(0.662711\pi\) | |||||||
\(68\) | −1.30536e63 | −0.783740 | ||||||||
\(69\) | −8.50284e62 | −0.308511 | ||||||||
\(70\) | −7.92359e61 | −0.0175001 | ||||||||
\(71\) | −1.10646e64 | −1.49804 | −0.749018 | − | 0.662550i | \(-0.769474\pi\) | ||||
−0.749018 | + | 0.662550i | \(0.769474\pi\) | |||||||
\(72\) | 3.79986e64 | 3.17539 | ||||||||
\(73\) | 3.21128e63 | 0.166740 | 0.0833699 | − | 0.996519i | \(-0.473432\pi\) | ||||
0.0833699 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(74\) | −5.86072e64 | −1.90308 | ||||||||
\(75\) | −2.77868e63 | −0.0567839 | ||||||||
\(76\) | 1.06290e65 | 1.37538 | ||||||||
\(77\) | −3.22689e61 | −0.000265983 0 | ||||||||
\(78\) | 1.91137e65 | 1.00944 | ||||||||
\(79\) | 3.60745e65 | 1.22762 | 0.613812 | − | 0.789453i | \(-0.289635\pi\) | ||||
0.613812 | + | 0.789453i | \(0.289635\pi\) | |||||||
\(80\) | −2.04735e66 | −4.51427 | ||||||||
\(81\) | 4.69295e65 | 0.674082 | ||||||||
\(82\) | −4.94112e65 | −0.464780 | ||||||||
\(83\) | 1.23807e66 | 0.766569 | 0.383285 | − | 0.923630i | \(-0.374793\pi\) | ||||
0.383285 | + | 0.923630i | \(0.374793\pi\) | |||||||
\(84\) | 1.91955e64 | 0.00786257 | ||||||||
\(85\) | 1.09994e66 | 0.299513 | ||||||||
\(86\) | 1.09419e67 | 1.99020 | ||||||||
\(87\) | −5.80460e65 | −0.0708530 | ||||||||
\(88\) | −1.39877e66 | −0.115105 | ||||||||
\(89\) | −1.50302e67 | −0.837545 | −0.418773 | − | 0.908091i | \(-0.637540\pi\) | ||||
−0.418773 | + | 0.908091i | \(0.637540\pi\) | |||||||
\(90\) | −4.95232e67 | −1.87690 | ||||||||
\(91\) | −4.90578e65 | −0.0126993 | ||||||||
\(92\) | 1.46316e68 | 2.59784 | ||||||||
\(93\) | −1.27073e67 | −0.155379 | ||||||||
\(94\) | −2.52836e68 | −2.13761 | ||||||||
\(95\) | −8.95636e67 | −0.525614 | ||||||||
\(96\) | 3.77193e68 | 1.54243 | ||||||||
\(97\) | −4.11315e68 | −1.17639 | −0.588194 | − | 0.808720i | \(-0.700161\pi\) | ||||
−0.588194 | + | 0.808720i | \(0.700161\pi\) | |||||||
\(98\) | 9.74596e68 | 1.95670 | ||||||||
\(99\) | −2.01684e67 | −0.0285270 | ||||||||
\(100\) | 4.78154e68 | 0.478154 | ||||||||
\(101\) | −1.18761e68 | −0.0842530 | −0.0421265 | − | 0.999112i | \(-0.513413\pi\) | ||||
−0.0421265 | + | 0.999112i | \(0.513413\pi\) | |||||||
\(102\) | −3.60653e68 | −0.182131 | ||||||||
\(103\) | 4.66232e69 | 1.68158 | 0.840791 | − | 0.541360i | \(-0.182090\pi\) | ||||
0.840791 | + | 0.541360i | \(0.182090\pi\) | |||||||
\(104\) | −2.12653e70 | −5.49567 | ||||||||
\(105\) | −1.61748e67 | −0.00300475 | ||||||||
\(106\) | 1.17168e70 | 1.56948 | ||||||||
\(107\) | 1.24749e70 | 1.20864 | 0.604318 | − | 0.796743i | \(-0.293446\pi\) | ||||
0.604318 | + | 0.796743i | \(0.293446\pi\) | |||||||
\(108\) | 2.55214e70 | 1.79385 | ||||||||
\(109\) | −2.39650e70 | −1.22564 | −0.612820 | − | 0.790222i | \(-0.709965\pi\) | ||||
−0.612820 | + | 0.790222i | \(0.709965\pi\) | |||||||
\(110\) | 1.82301e69 | 0.0680363 | ||||||||
\(111\) | −1.19637e70 | −0.326757 | ||||||||
\(112\) | −1.72297e69 | −0.0345347 | ||||||||
\(113\) | 1.93197e70 | 0.284966 | 0.142483 | − | 0.989797i | \(-0.454491\pi\) | ||||
0.142483 | + | 0.989797i | \(0.454491\pi\) | |||||||
\(114\) | 2.93666e70 | 0.319621 | ||||||||
\(115\) | −1.23291e71 | −0.992787 | ||||||||
\(116\) | 9.98852e70 | 0.596624 | ||||||||
\(117\) | −3.06615e71 | −1.36201 | ||||||||
\(118\) | 3.48762e71 | 1.15505 | ||||||||
\(119\) | 9.25665e68 | 0.00229131 | ||||||||
\(120\) | −7.01135e71 | −1.30032 | ||||||||
\(121\) | −7.17209e71 | −0.998966 | ||||||||
\(122\) | 2.16346e72 | 2.26847 | ||||||||
\(123\) | −1.00865e71 | −0.0798023 | ||||||||
\(124\) | 2.18667e72 | 1.30838 | ||||||||
\(125\) | 1.98108e72 | 0.898475 | ||||||||
\(126\) | −4.16768e70 | −0.0143585 | ||||||||
\(127\) | −1.49058e72 | −0.390956 | −0.195478 | − | 0.980708i | \(-0.562626\pi\) | ||||
−0.195478 | + | 0.980708i | \(0.562626\pi\) | |||||||
\(128\) | −2.40774e73 | −4.81799 | ||||||||
\(129\) | 2.23362e72 | 0.341716 | ||||||||
\(130\) | 2.77148e73 | 3.24837 | ||||||||
\(131\) | −1.53034e73 | −1.37698 | −0.688492 | − | 0.725244i | \(-0.741727\pi\) | ||||
−0.688492 | + | 0.725244i | \(0.741727\pi\) | |||||||
\(132\) | −4.41637e71 | −0.0305679 | ||||||||
\(133\) | −7.53733e70 | −0.00402102 | ||||||||
\(134\) | 4.64716e73 | 1.91457 | ||||||||
\(135\) | −2.15052e73 | −0.685534 | ||||||||
\(136\) | 4.01252e73 | 0.991573 | ||||||||
\(137\) | −6.90072e73 | −1.32445 | −0.662223 | − | 0.749306i | \(-0.730387\pi\) | ||||
−0.662223 | + | 0.749306i | \(0.730387\pi\) | |||||||
\(138\) | 4.04253e73 | 0.603705 | ||||||||
\(139\) | −1.02770e74 | −1.19634 | −0.598169 | − | 0.801370i | \(-0.704105\pi\) | ||||
−0.598169 | + | 0.801370i | \(0.704105\pi\) | |||||||
\(140\) | 2.78335e72 | 0.0253017 | ||||||||
\(141\) | −5.16126e73 | −0.367025 | ||||||||
\(142\) | 5.26047e74 | 2.93141 | ||||||||
\(143\) | 1.12869e73 | 0.0493720 | ||||||||
\(144\) | −1.07687e75 | −3.70389 | ||||||||
\(145\) | −8.41667e73 | −0.228005 | ||||||||
\(146\) | −1.52675e74 | −0.326283 | ||||||||
\(147\) | 1.98949e74 | 0.335964 | ||||||||
\(148\) | 2.05871e75 | 2.75148 | ||||||||
\(149\) | −1.83242e74 | −0.194133 | −0.0970663 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970663 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(150\) | 1.32108e74 | 0.111117 | ||||||||
\(151\) | 1.98978e75 | 1.33076 | 0.665382 | − | 0.746503i | \(-0.268269\pi\) | ||||
0.665382 | + | 0.746503i | \(0.268269\pi\) | |||||||
\(152\) | −3.26724e75 | −1.74011 | ||||||||
\(153\) | 5.78549e74 | 0.245746 | ||||||||
\(154\) | 1.53417e72 | 0.000520486 0 | ||||||||
\(155\) | −1.84256e75 | −0.500009 | ||||||||
\(156\) | −6.71412e75 | −1.45945 | ||||||||
\(157\) | 3.13434e75 | 0.546523 | 0.273261 | − | 0.961940i | \(-0.411898\pi\) | ||||
0.273261 | + | 0.961940i | \(0.411898\pi\) | |||||||
\(158\) | −1.71510e76 | −2.40226 | ||||||||
\(159\) | 2.39180e75 | 0.269479 | ||||||||
\(160\) | 5.46930e76 | 4.96355 | ||||||||
\(161\) | −1.03757e74 | −0.00759495 | ||||||||
\(162\) | −2.23118e76 | −1.31907 | ||||||||
\(163\) | −2.16359e76 | −1.03444 | −0.517218 | − | 0.855854i | \(-0.673032\pi\) | ||||
−0.517218 | + | 0.855854i | \(0.673032\pi\) | |||||||
\(164\) | 1.73568e76 | 0.671983 | ||||||||
\(165\) | 3.72139e74 | 0.0116818 | ||||||||
\(166\) | −5.88620e76 | −1.50005 | ||||||||
\(167\) | 5.73499e76 | 1.18799 | 0.593997 | − | 0.804467i | \(-0.297549\pi\) | ||||
0.593997 | + | 0.804467i | \(0.297549\pi\) | |||||||
\(168\) | −5.90048e74 | −0.00994758 | ||||||||
\(169\) | 9.87987e76 | 1.35725 | ||||||||
\(170\) | −5.22947e76 | −0.586097 | ||||||||
\(171\) | −4.71090e76 | −0.431258 | ||||||||
\(172\) | −3.84361e77 | −2.87745 | ||||||||
\(173\) | 2.41165e77 | 1.47817 | 0.739085 | − | 0.673613i | \(-0.235258\pi\) | ||||
0.739085 | + | 0.673613i | \(0.235258\pi\) | |||||||
\(174\) | 2.75970e76 | 0.138648 | ||||||||
\(175\) | −3.39072e74 | −0.00139791 | ||||||||
\(176\) | 3.96409e76 | 0.134263 | ||||||||
\(177\) | 7.11944e76 | 0.198321 | ||||||||
\(178\) | 7.14584e77 | 1.63894 | ||||||||
\(179\) | −5.78963e77 | −1.09451 | −0.547257 | − | 0.836965i | \(-0.684328\pi\) | ||||
−0.547257 | + | 0.836965i | \(0.684328\pi\) | |||||||
\(180\) | 1.73962e78 | 2.71364 | ||||||||
\(181\) | −1.16858e78 | −1.50573 | −0.752863 | − | 0.658177i | \(-0.771328\pi\) | ||||
−0.752863 | + | 0.658177i | \(0.771328\pi\) | |||||||
\(182\) | 2.33237e76 | 0.0248505 | ||||||||
\(183\) | 4.41636e77 | 0.389495 | ||||||||
\(184\) | −4.49760e78 | −3.28674 | ||||||||
\(185\) | −1.73474e78 | −1.05150 | ||||||||
\(186\) | 6.04148e77 | 0.304051 | ||||||||
\(187\) | −2.12971e76 | −0.00890809 | ||||||||
\(188\) | 8.88146e78 | 3.09057 | ||||||||
\(189\) | −1.80980e76 | −0.00524442 | ||||||||
\(190\) | 4.25815e78 | 1.02854 | ||||||||
\(191\) | −5.94585e78 | −1.19829 | −0.599146 | − | 0.800640i | \(-0.704493\pi\) | ||||
−0.599146 | + | 0.800640i | \(0.704493\pi\) | |||||||
\(192\) | −9.59824e78 | −1.61547 | ||||||||
\(193\) | 1.93367e78 | 0.272055 | 0.136027 | − | 0.990705i | \(-0.456567\pi\) | ||||
0.136027 | + | 0.990705i | \(0.456567\pi\) | |||||||
\(194\) | 1.95553e79 | 2.30200 | ||||||||
\(195\) | 5.65754e78 | 0.557742 | ||||||||
\(196\) | −3.42350e79 | −2.82902 | ||||||||
\(197\) | 9.34495e78 | 0.647877 | 0.323938 | − | 0.946078i | \(-0.394993\pi\) | ||||
0.323938 | + | 0.946078i | \(0.394993\pi\) | |||||||
\(198\) | 9.58871e77 | 0.0558227 | ||||||||
\(199\) | 2.69839e78 | 0.132030 | 0.0660152 | − | 0.997819i | \(-0.478971\pi\) | ||||
0.0660152 | + | 0.997819i | \(0.478971\pi\) | |||||||
\(200\) | −1.46979e79 | −0.604952 | ||||||||
\(201\) | 9.48645e78 | 0.328730 | ||||||||
\(202\) | 5.64627e78 | 0.164869 | ||||||||
\(203\) | −7.08314e76 | −0.00174427 | ||||||||
\(204\) | 1.26688e79 | 0.263326 | ||||||||
\(205\) | −1.46255e79 | −0.256804 | ||||||||
\(206\) | −2.21662e80 | −3.29058 | ||||||||
\(207\) | −6.48490e79 | −0.814567 | ||||||||
\(208\) | 6.02652e80 | 6.41035 | ||||||||
\(209\) | 1.73414e78 | 0.0156328 | ||||||||
\(210\) | 7.69003e77 | 0.00587980 | ||||||||
\(211\) | 7.71421e79 | 0.500665 | 0.250332 | − | 0.968160i | \(-0.419460\pi\) | ||||
0.250332 | + | 0.968160i | \(0.419460\pi\) | |||||||
\(212\) | −4.11580e80 | −2.26917 | ||||||||
\(213\) | 1.07384e80 | 0.503321 | ||||||||
\(214\) | −5.93096e80 | −2.36510 | ||||||||
\(215\) | 3.23875e80 | 1.09964 | ||||||||
\(216\) | −7.84500e80 | −2.26954 | ||||||||
\(217\) | −1.55063e78 | −0.00382513 | ||||||||
\(218\) | 1.13937e81 | 2.39838 | ||||||||
\(219\) | −3.11662e79 | −0.0560224 | ||||||||
\(220\) | −6.40374e79 | −0.0983674 | ||||||||
\(221\) | −3.23775e80 | −0.425314 | ||||||||
\(222\) | 5.68796e80 | 0.639409 | ||||||||
\(223\) | 1.62026e81 | 1.55980 | 0.779898 | − | 0.625907i | \(-0.215271\pi\) | ||||
0.779898 | + | 0.625907i | \(0.215271\pi\) | |||||||
\(224\) | 4.60275e79 | 0.0379718 | ||||||||
\(225\) | −2.11923e80 | −0.149928 | ||||||||
\(226\) | −9.18520e80 | −0.557632 | ||||||||
\(227\) | −2.43804e81 | −1.27101 | −0.635505 | − | 0.772097i | \(-0.719208\pi\) | ||||
−0.635505 | + | 0.772097i | \(0.719208\pi\) | |||||||
\(228\) | −1.03157e81 | −0.462111 | ||||||||
\(229\) | −1.14930e81 | −0.442701 | −0.221351 | − | 0.975194i | \(-0.571047\pi\) | ||||
−0.221351 | + | 0.975194i | \(0.571047\pi\) | |||||||
\(230\) | 5.86167e81 | 1.94272 | ||||||||
\(231\) | 3.13177e77 | 8.93670e−5 0 | ||||||||
\(232\) | −3.07036e81 | −0.754838 | ||||||||
\(233\) | −4.64743e81 | −0.984994 | −0.492497 | − | 0.870314i | \(-0.663916\pi\) | ||||
−0.492497 | + | 0.870314i | \(0.663916\pi\) | |||||||
\(234\) | 1.45775e82 | 2.66524 | ||||||||
\(235\) | −7.48382e81 | −1.18109 | ||||||||
\(236\) | −1.22511e82 | −1.66998 | ||||||||
\(237\) | −3.50111e81 | −0.412465 | ||||||||
\(238\) | −4.40092e79 | −0.00448372 | ||||||||
\(239\) | 1.79106e81 | 0.157900 | 0.0789500 | − | 0.996879i | \(-0.474843\pi\) | ||||
0.0789500 | + | 0.996879i | \(0.474843\pi\) | |||||||
\(240\) | 1.98700e82 | 1.51674 | ||||||||
\(241\) | 2.19407e82 | 1.45098 | 0.725490 | − | 0.688232i | \(-0.241613\pi\) | ||||
0.725490 | + | 0.688232i | \(0.241613\pi\) | |||||||
\(242\) | 3.40985e82 | 1.95481 | ||||||||
\(243\) | −1.73054e82 | −0.860528 | ||||||||
\(244\) | −7.59965e82 | −3.27978 | ||||||||
\(245\) | 2.88475e82 | 1.08113 | ||||||||
\(246\) | 4.79547e81 | 0.156160 | ||||||||
\(247\) | 2.63637e82 | 0.746383 | ||||||||
\(248\) | −6.72157e82 | −1.65534 | ||||||||
\(249\) | −1.20158e82 | −0.257557 | ||||||||
\(250\) | −9.41870e82 | −1.75817 | ||||||||
\(251\) | 5.39936e82 | 0.878211 | 0.439105 | − | 0.898436i | \(-0.355295\pi\) | ||||
0.439105 | + | 0.898436i | \(0.355295\pi\) | |||||||
\(252\) | 1.46399e81 | 0.0207597 | ||||||||
\(253\) | 2.38717e81 | 0.0295274 | ||||||||
\(254\) | 7.08673e82 | 0.765038 | ||||||||
\(255\) | −1.06751e82 | −0.100632 | ||||||||
\(256\) | 5.60930e83 | 4.61987 | ||||||||
\(257\) | −1.14417e83 | −0.823752 | −0.411876 | − | 0.911240i | \(-0.635126\pi\) | ||||
−0.411876 | + | 0.911240i | \(0.635126\pi\) | |||||||
\(258\) | −1.06194e83 | −0.668682 | ||||||||
\(259\) | −1.45989e81 | −0.00804413 | ||||||||
\(260\) | −9.73547e83 | −4.69652 | ||||||||
\(261\) | −4.42702e82 | −0.187074 | ||||||||
\(262\) | 7.27575e83 | 2.69453 | ||||||||
\(263\) | −7.65214e82 | −0.248490 | −0.124245 | − | 0.992252i | \(-0.539651\pi\) | ||||
−0.124245 | + | 0.992252i | \(0.539651\pi\) | |||||||
\(264\) | 1.35754e82 | 0.0386739 | ||||||||
\(265\) | 3.46811e83 | 0.867182 | ||||||||
\(266\) | 3.58349e81 | 0.00786847 | ||||||||
\(267\) | 1.45871e83 | 0.281404 | ||||||||
\(268\) | −1.63242e84 | −2.76810 | ||||||||
\(269\) | 2.43965e83 | 0.363810 | 0.181905 | − | 0.983316i | \(-0.441774\pi\) | ||||
0.181905 | + | 0.983316i | \(0.441774\pi\) | |||||||
\(270\) | 1.02243e84 | 1.34148 | ||||||||
\(271\) | −9.89400e82 | −0.114270 | −0.0571349 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571349 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(272\) | −1.13714e84 | −1.15661 | ||||||||
\(273\) | 4.76117e81 | 0.00426680 | ||||||||
\(274\) | 3.28083e84 | 2.59173 | ||||||||
\(275\) | 7.80114e81 | 0.00543476 | ||||||||
\(276\) | −1.42003e84 | −0.872842 | ||||||||
\(277\) | −2.18243e84 | −1.18410 | −0.592050 | − | 0.805901i | \(-0.701681\pi\) | ||||
−0.592050 | + | 0.805901i | \(0.701681\pi\) | |||||||
\(278\) | 4.88600e84 | 2.34104 | ||||||||
\(279\) | −9.69155e83 | −0.410250 | ||||||||
\(280\) | −8.55570e82 | −0.0320113 | ||||||||
\(281\) | 2.98947e81 | 0.000989067 0 | 0.000494533 | − | 1.00000i | \(-0.499843\pi\) | ||||
0.000494533 | 1.00000i | \(0.499843\pi\) | ||||||||
\(282\) | 2.45383e84 | 0.718209 | ||||||||
\(283\) | −2.71964e84 | −0.704498 | −0.352249 | − | 0.935906i | \(-0.614583\pi\) | ||||
−0.352249 | + | 0.935906i | \(0.614583\pi\) | |||||||
\(284\) | −1.84786e85 | −4.23826 | ||||||||
\(285\) | 8.69235e83 | 0.176600 | ||||||||
\(286\) | −5.36615e83 | −0.0966129 | ||||||||
\(287\) | −1.23082e82 | −0.00196458 | ||||||||
\(288\) | 2.87676e85 | 4.07252 | ||||||||
\(289\) | −7.35022e84 | −0.923261 | ||||||||
\(290\) | 4.00156e84 | 0.446168 | ||||||||
\(291\) | 3.99191e84 | 0.395251 | ||||||||
\(292\) | 5.36306e84 | 0.471742 | ||||||||
\(293\) | 9.86994e84 | 0.771581 | 0.385791 | − | 0.922586i | \(-0.373929\pi\) | ||||
0.385791 | + | 0.922586i | \(0.373929\pi\) | |||||||
\(294\) | −9.45867e84 | −0.657427 | ||||||||
\(295\) | 1.03232e85 | 0.638196 | ||||||||
\(296\) | −6.32825e85 | −3.48113 | ||||||||
\(297\) | 4.16385e83 | 0.0203891 | ||||||||
\(298\) | 8.71193e84 | 0.379886 | ||||||||
\(299\) | 3.62916e85 | 1.40978 | ||||||||
\(300\) | −4.64060e84 | −0.160654 | ||||||||
\(301\) | 2.72561e83 | 0.00841239 | ||||||||
\(302\) | −9.46008e85 | −2.60409 | ||||||||
\(303\) | 1.15260e84 | 0.0283079 | ||||||||
\(304\) | 9.25927e85 | 2.02973 | ||||||||
\(305\) | 6.40372e85 | 1.25339 | ||||||||
\(306\) | −2.75061e85 | −0.480884 | ||||||||
\(307\) | −3.27318e85 | −0.511324 | −0.255662 | − | 0.966766i | \(-0.582293\pi\) | ||||
−0.255662 | + | 0.966766i | \(0.582293\pi\) | |||||||
\(308\) | −5.38914e82 | −0.000752523 0 | ||||||||
\(309\) | −4.52489e85 | −0.564990 | ||||||||
\(310\) | 8.76014e85 | 0.978436 | ||||||||
\(311\) | −1.76892e86 | −1.76797 | −0.883986 | − | 0.467513i | \(-0.845150\pi\) | ||||
−0.883986 | + | 0.467513i | \(0.845150\pi\) | |||||||
\(312\) | 2.06384e86 | 1.84647 | ||||||||
\(313\) | −3.41545e85 | −0.273633 | −0.136816 | − | 0.990596i | \(-0.543687\pi\) | ||||
−0.136816 | + | 0.990596i | \(0.543687\pi\) | |||||||
\(314\) | −1.49017e86 | −1.06946 | ||||||||
\(315\) | −1.23361e84 | −0.00793349 | ||||||||
\(316\) | 6.02469e86 | 3.47320 | ||||||||
\(317\) | 7.71691e85 | 0.398932 | 0.199466 | − | 0.979905i | \(-0.436079\pi\) | ||||
0.199466 | + | 0.979905i | \(0.436079\pi\) | |||||||
\(318\) | −1.13714e86 | −0.527326 | ||||||||
\(319\) | 1.62964e84 | 0.00678130 | ||||||||
\(320\) | −1.39174e87 | −5.19859 | ||||||||
\(321\) | −1.21071e86 | −0.406086 | ||||||||
\(322\) | 4.93295e84 | 0.0148621 | ||||||||
\(323\) | −4.97454e85 | −0.134668 | ||||||||
\(324\) | 7.83755e86 | 1.90712 | ||||||||
\(325\) | 1.18599e86 | 0.259481 | ||||||||
\(326\) | 1.02864e87 | 2.02422 | ||||||||
\(327\) | 2.32586e86 | 0.411799 | ||||||||
\(328\) | −5.33530e86 | −0.850180 | ||||||||
\(329\) | −6.29809e84 | −0.00903546 | ||||||||
\(330\) | −1.76927e85 | −0.0228593 | ||||||||
\(331\) | −1.76756e83 | −0.000205735 0 | −0.000102867 | − | 1.00000i | \(-0.500033\pi\) | ||||
−0.000102867 | 1.00000i | \(0.500033\pi\) | ||||||||
\(332\) | 2.06767e87 | 2.16879 | ||||||||
\(333\) | −9.12445e86 | −0.862742 | ||||||||
\(334\) | −2.72660e87 | −2.32471 | ||||||||
\(335\) | 1.37553e87 | 1.05785 | ||||||||
\(336\) | 1.67218e85 | 0.0116032 | ||||||||
\(337\) | −5.65069e86 | −0.353891 | −0.176946 | − | 0.984221i | \(-0.556622\pi\) | ||||
−0.176946 | + | 0.984221i | \(0.556622\pi\) | |||||||
\(338\) | −4.69722e87 | −2.65592 | ||||||||
\(339\) | −1.87502e86 | −0.0957449 | ||||||||
\(340\) | 1.83697e87 | 0.847384 | ||||||||
\(341\) | 3.56758e85 | 0.0148712 | ||||||||
\(342\) | 2.23972e87 | 0.843902 | ||||||||
\(343\) | 4.85556e85 | 0.0165422 | ||||||||
\(344\) | 1.18148e88 | 3.64050 | ||||||||
\(345\) | 1.19657e87 | 0.333564 | ||||||||
\(346\) | −1.14658e88 | −2.89254 | ||||||||
\(347\) | −6.30525e87 | −1.43991 | −0.719955 | − | 0.694021i | \(-0.755838\pi\) | ||||
−0.719955 | + | 0.694021i | \(0.755838\pi\) | |||||||
\(348\) | −9.69409e86 | −0.200458 | ||||||||
\(349\) | 4.26563e87 | 0.798925 | 0.399463 | − | 0.916750i | \(-0.369197\pi\) | ||||
0.399463 | + | 0.916750i | \(0.369197\pi\) | |||||||
\(350\) | 1.61206e85 | 0.00273548 | ||||||||
\(351\) | 6.33022e87 | 0.973471 | ||||||||
\(352\) | −1.05897e87 | −0.147626 | ||||||||
\(353\) | 5.91830e87 | 0.748117 | 0.374058 | − | 0.927405i | \(-0.377966\pi\) | ||||
0.374058 | + | 0.927405i | \(0.377966\pi\) | |||||||
\(354\) | −3.38482e87 | −0.388081 | ||||||||
\(355\) | 1.55707e88 | 1.61968 | ||||||||
\(356\) | −2.51014e88 | −2.36959 | ||||||||
\(357\) | −8.98379e84 | −0.000769850 0 | ||||||||
\(358\) | 2.75258e88 | 2.14179 | ||||||||
\(359\) | −1.96053e88 | −1.38553 | −0.692764 | − | 0.721164i | \(-0.743607\pi\) | ||||
−0.692764 | + | 0.721164i | \(0.743607\pi\) | |||||||
\(360\) | −5.34739e88 | −3.43325 | ||||||||
\(361\) | −1.30889e88 | −0.763671 | ||||||||
\(362\) | 5.55580e88 | 2.94646 | ||||||||
\(363\) | 6.96068e87 | 0.335640 | ||||||||
\(364\) | −8.19299e86 | −0.0359290 | ||||||||
\(365\) | −4.51910e87 | −0.180280 | ||||||||
\(366\) | −2.09968e88 | −0.762178 | ||||||||
\(367\) | −4.95070e88 | −1.63564 | −0.817819 | − | 0.575475i | \(-0.804817\pi\) | ||||
−0.817819 | + | 0.575475i | \(0.804817\pi\) | |||||||
\(368\) | 1.27461e89 | 3.83378 | ||||||||
\(369\) | −7.69275e87 | −0.210703 | ||||||||
\(370\) | 8.24754e88 | 2.05762 | ||||||||
\(371\) | 2.91863e86 | 0.00663405 | ||||||||
\(372\) | −2.12221e88 | −0.439599 | ||||||||
\(373\) | −3.78408e88 | −0.714505 | −0.357253 | − | 0.934008i | \(-0.616286\pi\) | ||||
−0.357253 | + | 0.934008i | \(0.616286\pi\) | |||||||
\(374\) | 1.01253e87 | 0.0174317 | ||||||||
\(375\) | −1.92268e88 | −0.301876 | ||||||||
\(376\) | −2.73006e89 | −3.91013 | ||||||||
\(377\) | 2.47751e88 | 0.323771 | ||||||||
\(378\) | 8.60437e86 | 0.0102625 | ||||||||
\(379\) | 1.13681e89 | 1.23776 | 0.618880 | − | 0.785485i | \(-0.287587\pi\) | ||||
0.618880 | + | 0.785485i | \(0.287587\pi\) | |||||||
\(380\) | −1.49578e89 | −1.48707 | ||||||||
\(381\) | 1.44665e88 | 0.131356 | ||||||||
\(382\) | 2.82685e89 | 2.34486 | ||||||||
\(383\) | −8.73915e87 | −0.0662387 | −0.0331193 | − | 0.999451i | \(-0.510544\pi\) | ||||
−0.0331193 | + | 0.999451i | \(0.510544\pi\) | |||||||
\(384\) | 2.33677e89 | 1.61878 | ||||||||
\(385\) | 4.54107e85 | 0.000287583 0 | ||||||||
\(386\) | −9.19332e88 | −0.532366 | ||||||||
\(387\) | 1.70353e89 | 0.902239 | ||||||||
\(388\) | −6.86926e89 | −3.32825 | ||||||||
\(389\) | 2.58092e89 | 1.14423 | 0.572115 | − | 0.820173i | \(-0.306123\pi\) | ||||
0.572115 | + | 0.820173i | \(0.306123\pi\) | |||||||
\(390\) | −2.68978e89 | −1.09141 | ||||||||
\(391\) | −6.84783e88 | −0.254363 | ||||||||
\(392\) | 1.05234e90 | 3.57922 | ||||||||
\(393\) | 1.48523e89 | 0.462649 | ||||||||
\(394\) | −4.44290e89 | −1.26779 | ||||||||
\(395\) | −5.07660e89 | −1.32731 | ||||||||
\(396\) | −3.36826e88 | −0.0807089 | ||||||||
\(397\) | −4.90688e88 | −0.107779 | −0.0538893 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538893 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(398\) | −1.28290e89 | −0.258362 | ||||||||
\(399\) | 7.31515e86 | 0.00135101 | ||||||||
\(400\) | 4.16535e89 | 0.705638 | ||||||||
\(401\) | −1.24261e89 | −0.193132 | −0.0965662 | − | 0.995327i | \(-0.530786\pi\) | ||||
−0.0965662 | + | 0.995327i | \(0.530786\pi\) | |||||||
\(402\) | −4.51017e89 | −0.643271 | ||||||||
\(403\) | 5.42371e89 | 0.710023 | ||||||||
\(404\) | −1.98339e89 | −0.238369 | ||||||||
\(405\) | −6.60419e89 | −0.728821 | ||||||||
\(406\) | 3.36756e87 | 0.00341324 | ||||||||
\(407\) | 3.35882e88 | 0.0312737 | ||||||||
\(408\) | −3.89424e89 | −0.333156 | ||||||||
\(409\) | −6.64009e89 | −0.522060 | −0.261030 | − | 0.965331i | \(-0.584062\pi\) | ||||
−0.261030 | + | 0.965331i | \(0.584062\pi\) | |||||||
\(410\) | 6.95343e89 | 0.502523 | ||||||||
\(411\) | 6.69730e89 | 0.444997 | ||||||||
\(412\) | 7.78641e90 | 4.75755 | ||||||||
\(413\) | 8.68759e87 | 0.00488228 | ||||||||
\(414\) | 3.08314e90 | 1.59397 | ||||||||
\(415\) | −1.74229e90 | −0.828819 | ||||||||
\(416\) | −1.60993e91 | −7.04834 | ||||||||
\(417\) | 9.97402e89 | 0.401954 | ||||||||
\(418\) | −8.24466e88 | −0.0305908 | ||||||||
\(419\) | 2.42519e90 | 0.828633 | 0.414317 | − | 0.910133i | \(-0.364021\pi\) | ||||
0.414317 | + | 0.910133i | \(0.364021\pi\) | |||||||
\(420\) | −2.70130e88 | −0.00850106 | ||||||||
\(421\) | 8.45515e89 | 0.245126 | 0.122563 | − | 0.992461i | \(-0.460889\pi\) | ||||
0.122563 | + | 0.992461i | \(0.460889\pi\) | |||||||
\(422\) | −3.66759e90 | −0.979719 | ||||||||
\(423\) | −3.93636e90 | −0.969064 | ||||||||
\(424\) | 1.26515e91 | 2.87091 | ||||||||
\(425\) | −2.23783e89 | −0.0468176 | ||||||||
\(426\) | −5.10541e90 | −0.984916 | ||||||||
\(427\) | 5.38912e88 | 0.00958862 | ||||||||
\(428\) | 2.08339e91 | 3.41948 | ||||||||
\(429\) | −1.09542e89 | −0.0165883 | ||||||||
\(430\) | −1.53981e91 | −2.15182 | ||||||||
\(431\) | −1.00762e91 | −1.29966 | −0.649832 | − | 0.760078i | \(-0.725161\pi\) | ||||
−0.649832 | + | 0.760078i | \(0.725161\pi\) | |||||||
\(432\) | 2.22325e91 | 2.64728 | ||||||||
\(433\) | 2.48563e90 | 0.273278 | 0.136639 | − | 0.990621i | \(-0.456370\pi\) | ||||
0.136639 | + | 0.990621i | \(0.456370\pi\) | |||||||
\(434\) | 7.37219e88 | 0.00748516 | ||||||||
\(435\) | 8.16857e89 | 0.0766067 | ||||||||
\(436\) | −4.00232e91 | −3.46759 | ||||||||
\(437\) | 5.57592e90 | 0.446382 | ||||||||
\(438\) | 1.48174e90 | 0.109627 | ||||||||
\(439\) | −7.87845e90 | −0.538784 | −0.269392 | − | 0.963031i | \(-0.586823\pi\) | ||||
−0.269392 | + | 0.963031i | \(0.586823\pi\) | |||||||
\(440\) | 1.96844e90 | 0.124453 | ||||||||
\(441\) | 1.51733e91 | 0.887052 | ||||||||
\(442\) | 1.53933e91 | 0.832270 | ||||||||
\(443\) | 2.92208e91 | 1.46138 | 0.730692 | − | 0.682708i | \(-0.239198\pi\) | ||||
0.730692 | + | 0.682708i | \(0.239198\pi\) | |||||||
\(444\) | −1.99803e91 | −0.924463 | ||||||||
\(445\) | 2.11513e91 | 0.905559 | ||||||||
\(446\) | −7.70327e91 | −3.05227 | ||||||||
\(447\) | 1.77840e90 | 0.0652260 | ||||||||
\(448\) | −1.17124e90 | −0.0397698 | ||||||||
\(449\) | −1.09047e91 | −0.342858 | −0.171429 | − | 0.985196i | \(-0.554838\pi\) | ||||
−0.171429 | + | 0.985196i | \(0.554838\pi\) | |||||||
\(450\) | 1.00755e91 | 0.293384 | ||||||||
\(451\) | 2.83179e89 | 0.00763784 | ||||||||
\(452\) | 3.22652e91 | 0.806228 | ||||||||
\(453\) | −1.93113e91 | −0.447119 | ||||||||
\(454\) | 1.15913e92 | 2.48716 | ||||||||
\(455\) | 6.90369e89 | 0.0137306 | ||||||||
\(456\) | 3.17093e91 | 0.584655 | ||||||||
\(457\) | −1.22143e91 | −0.208813 | −0.104407 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104407 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(458\) | 5.46417e91 | 0.866294 | ||||||||
\(459\) | −1.19444e91 | −0.175642 | ||||||||
\(460\) | −2.05905e92 | −2.80880 | ||||||||
\(461\) | −2.42324e91 | −0.306700 | −0.153350 | − | 0.988172i | \(-0.549006\pi\) | ||||
−0.153350 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(462\) | −1.48895e88 | −0.000174877 0 | ||||||||
\(463\) | −1.70450e92 | −1.85803 | −0.929015 | − | 0.370042i | \(-0.879343\pi\) | ||||
−0.929015 | + | 0.370042i | \(0.879343\pi\) | |||||||
\(464\) | 8.70132e91 | 0.880470 | ||||||||
\(465\) | 1.78825e91 | 0.167997 | ||||||||
\(466\) | 2.20954e92 | 1.92747 | ||||||||
\(467\) | −1.90134e91 | −0.154038 | −0.0770188 | − | 0.997030i | \(-0.524540\pi\) | ||||
−0.0770188 | + | 0.997030i | \(0.524540\pi\) | |||||||
\(468\) | −5.12069e92 | −3.85342 | ||||||||
\(469\) | 1.15760e90 | 0.00809271 | ||||||||
\(470\) | 3.55805e92 | 2.31119 | ||||||||
\(471\) | −3.04195e91 | −0.183625 | ||||||||
\(472\) | 3.76585e92 | 2.11283 | ||||||||
\(473\) | −6.27090e90 | −0.0327055 | ||||||||
\(474\) | 1.66454e92 | 0.807128 | ||||||||
\(475\) | 1.82218e91 | 0.0821602 | ||||||||
\(476\) | 1.54593e90 | 0.00648259 | ||||||||
\(477\) | 1.82417e92 | 0.711510 | ||||||||
\(478\) | −8.51528e91 | −0.308984 | ||||||||
\(479\) | −1.43905e92 | −0.485847 | −0.242923 | − | 0.970045i | \(-0.578106\pi\) | ||||
−0.242923 | + | 0.970045i | \(0.578106\pi\) | |||||||
\(480\) | −5.30808e92 | −1.66769 | ||||||||
\(481\) | 5.10634e92 | 1.49315 | ||||||||
\(482\) | −1.04313e93 | −2.83933 | ||||||||
\(483\) | 1.00699e90 | 0.00255180 | ||||||||
\(484\) | −1.19779e93 | −2.82628 | ||||||||
\(485\) | 5.78827e92 | 1.27192 | ||||||||
\(486\) | 8.22756e92 | 1.68391 | ||||||||
\(487\) | −5.62055e91 | −0.107159 | −0.0535796 | − | 0.998564i | \(-0.517063\pi\) | ||||
−0.0535796 | + | 0.998564i | \(0.517063\pi\) | |||||||
\(488\) | 2.33604e93 | 4.14951 | ||||||||
\(489\) | 2.09982e92 | 0.347557 | ||||||||
\(490\) | −1.37151e93 | −2.11560 | ||||||||
\(491\) | −9.59231e92 | −1.37915 | −0.689576 | − | 0.724214i | \(-0.742203\pi\) | ||||
−0.689576 | + | 0.724214i | \(0.742203\pi\) | |||||||
\(492\) | −1.68452e92 | −0.225777 | ||||||||
\(493\) | −4.67478e91 | −0.0584174 | ||||||||
\(494\) | −1.25342e93 | −1.46055 | ||||||||
\(495\) | 2.83821e91 | 0.0308436 | ||||||||
\(496\) | 1.90487e93 | 1.93085 | ||||||||
\(497\) | 1.31037e91 | 0.0123908 | ||||||||
\(498\) | 5.71269e92 | 0.503998 | ||||||||
\(499\) | −8.50645e92 | −0.700293 | −0.350146 | − | 0.936695i | \(-0.613868\pi\) | ||||
−0.350146 | + | 0.936695i | \(0.613868\pi\) | |||||||
\(500\) | 3.30854e93 | 2.54198 | ||||||||
\(501\) | −5.56594e92 | −0.399151 | ||||||||
\(502\) | −2.56703e93 | −1.71852 | ||||||||
\(503\) | 9.92271e92 | 0.620204 | 0.310102 | − | 0.950703i | \(-0.399637\pi\) | ||||
0.310102 | + | 0.950703i | \(0.399637\pi\) | |||||||
\(504\) | −4.50015e91 | −0.0262648 | ||||||||
\(505\) | 1.67127e92 | 0.0910948 | ||||||||
\(506\) | −1.13494e92 | −0.0577803 | ||||||||
\(507\) | −9.58864e92 | −0.456018 | ||||||||
\(508\) | −2.48938e93 | −1.10610 | ||||||||
\(509\) | 4.21070e93 | 1.74820 | 0.874099 | − | 0.485747i | \(-0.161452\pi\) | ||||
0.874099 | + | 0.485747i | \(0.161452\pi\) | |||||||
\(510\) | 5.07532e92 | 0.196921 | ||||||||
\(511\) | −3.80310e90 | −0.00137916 | ||||||||
\(512\) | −1.24557e94 | −4.22235 | ||||||||
\(513\) | 9.72587e92 | 0.308233 | ||||||||
\(514\) | 5.43974e93 | 1.61195 | ||||||||
\(515\) | −6.56109e93 | −1.81814 | ||||||||
\(516\) | 3.73031e93 | 0.966786 | ||||||||
\(517\) | 1.44902e92 | 0.0351278 | ||||||||
\(518\) | 6.94081e91 | 0.0157410 | ||||||||
\(519\) | −2.34056e93 | −0.496646 | ||||||||
\(520\) | 2.99257e94 | 5.94195 | ||||||||
\(521\) | 7.50601e93 | 1.39479 | 0.697393 | − | 0.716689i | \(-0.254343\pi\) | ||||
0.697393 | + | 0.716689i | \(0.254343\pi\) | |||||||
\(522\) | 2.10475e93 | 0.366074 | ||||||||
\(523\) | −9.56209e93 | −1.55684 | −0.778421 | − | 0.627742i | \(-0.783979\pi\) | ||||
−0.778421 | + | 0.627742i | \(0.783979\pi\) | |||||||
\(524\) | −2.55578e94 | −3.89578 | ||||||||
\(525\) | 3.29078e90 | 0.000469680 0 | ||||||||
\(526\) | 3.63808e93 | 0.486255 | ||||||||
\(527\) | −1.02339e93 | −0.128108 | ||||||||
\(528\) | −3.84724e92 | −0.0451107 | ||||||||
\(529\) | −1.42809e93 | −0.156868 | ||||||||
\(530\) | −1.64886e94 | −1.69693 | ||||||||
\(531\) | 5.42982e93 | 0.523630 | ||||||||
\(532\) | −1.25879e92 | −0.0113763 | ||||||||
\(533\) | 4.30511e93 | 0.364666 | ||||||||
\(534\) | −6.93520e93 | −0.550662 | ||||||||
\(535\) | −1.75553e94 | −1.30678 | ||||||||
\(536\) | 5.01788e94 | 3.50215 | ||||||||
\(537\) | 5.61897e93 | 0.367743 | ||||||||
\(538\) | −1.15989e94 | −0.711917 | ||||||||
\(539\) | −5.58548e92 | −0.0321550 | ||||||||
\(540\) | −3.59152e94 | −1.93952 | ||||||||
\(541\) | 1.58147e94 | 0.801226 | 0.400613 | − | 0.916247i | \(-0.368797\pi\) | ||||
0.400613 | + | 0.916247i | \(0.368797\pi\) | |||||||
\(542\) | 4.70393e93 | 0.223607 | ||||||||
\(543\) | 1.13413e94 | 0.505905 | ||||||||
\(544\) | 3.03776e94 | 1.27172 | ||||||||
\(545\) | 3.37249e94 | 1.32517 | ||||||||
\(546\) | −2.26362e92 | −0.00834943 | ||||||||
\(547\) | −2.71305e94 | −0.939495 | −0.469748 | − | 0.882801i | \(-0.655655\pi\) | ||||
−0.469748 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(548\) | −1.15247e95 | −3.74714 | ||||||||
\(549\) | 3.36825e94 | 1.02839 | ||||||||
\(550\) | −3.70892e92 | −0.0106349 | ||||||||
\(551\) | 3.80649e93 | 0.102517 | ||||||||
\(552\) | 4.36502e94 | 1.10430 | ||||||||
\(553\) | −4.27227e92 | −0.0101541 | ||||||||
\(554\) | 1.03760e95 | 2.31709 | ||||||||
\(555\) | 1.68361e94 | 0.353291 | ||||||||
\(556\) | −1.71632e95 | −3.38469 | ||||||||
\(557\) | 3.94686e94 | 0.731555 | 0.365777 | − | 0.930702i | \(-0.380803\pi\) | ||||
0.365777 | + | 0.930702i | \(0.380803\pi\) | |||||||
\(558\) | 4.60768e94 | 0.802792 | ||||||||
\(559\) | −9.53351e94 | −1.56151 | ||||||||
\(560\) | 2.42466e93 | 0.0373391 | ||||||||
\(561\) | 2.06693e92 | 0.00299300 | ||||||||
\(562\) | −1.42129e92 | −0.00193544 | ||||||||
\(563\) | −1.43702e95 | −1.84044 | −0.920222 | − | 0.391396i | \(-0.871992\pi\) | ||||
−0.920222 | + | 0.391396i | \(0.871992\pi\) | |||||||
\(564\) | −8.61966e94 | −1.03839 | ||||||||
\(565\) | −2.71877e94 | −0.308107 | ||||||||
\(566\) | 1.29301e95 | 1.37859 | ||||||||
\(567\) | −5.55783e92 | −0.00557557 | ||||||||
\(568\) | 5.68012e95 | 5.36216 | ||||||||
\(569\) | 6.44138e94 | 0.572276 | 0.286138 | − | 0.958188i | \(-0.407628\pi\) | ||||
0.286138 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(570\) | −4.13263e94 | −0.345577 | ||||||||
\(571\) | −1.65144e95 | −1.29992 | −0.649959 | − | 0.759969i | \(-0.725214\pi\) | ||||
−0.649959 | + | 0.759969i | \(0.725214\pi\) | |||||||
\(572\) | 1.88499e94 | 0.139684 | ||||||||
\(573\) | 5.77058e94 | 0.402611 | ||||||||
\(574\) | 5.85174e92 | 0.00384436 | ||||||||
\(575\) | 2.50837e94 | 0.155185 | ||||||||
\(576\) | −7.32034e95 | −4.26536 | ||||||||
\(577\) | −3.57373e94 | −0.196136 | −0.0980678 | − | 0.995180i | \(-0.531266\pi\) | ||||
−0.0980678 | + | 0.995180i | \(0.531266\pi\) | |||||||
\(578\) | 3.49454e95 | 1.80667 | ||||||||
\(579\) | −1.87667e94 | −0.0914068 | ||||||||
\(580\) | −1.40564e95 | −0.645073 | ||||||||
\(581\) | −1.46624e93 | −0.00634057 | ||||||||
\(582\) | −1.89789e95 | −0.773441 | ||||||||
\(583\) | −6.71498e93 | −0.0257917 | ||||||||
\(584\) | −1.64854e95 | −0.596839 | ||||||||
\(585\) | 4.31487e95 | 1.47262 | ||||||||
\(586\) | −4.69250e95 | −1.50986 | ||||||||
\(587\) | 5.28696e95 | 1.60395 | 0.801976 | − | 0.597356i | \(-0.203782\pi\) | ||||
0.801976 | + | 0.597356i | \(0.203782\pi\) | |||||||
\(588\) | 3.32258e95 | 0.950513 | ||||||||
\(589\) | 8.33309e94 | 0.224817 | ||||||||
\(590\) | −4.90798e95 | −1.24885 | ||||||||
\(591\) | −9.06949e94 | −0.217678 | ||||||||
\(592\) | 1.79341e96 | 4.06051 | ||||||||
\(593\) | −4.37868e95 | −0.935312 | −0.467656 | − | 0.883910i | \(-0.654901\pi\) | ||||
−0.467656 | + | 0.883910i | \(0.654901\pi\) | |||||||
\(594\) | −1.97963e94 | −0.0398981 | ||||||||
\(595\) | −1.30265e93 | −0.00247738 | ||||||||
\(596\) | −3.06027e95 | −0.549242 | ||||||||
\(597\) | −2.61885e94 | −0.0443605 | ||||||||
\(598\) | −1.72542e96 | −2.75870 | ||||||||
\(599\) | −3.20966e95 | −0.484433 | −0.242217 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242217 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(600\) | 1.42647e95 | 0.203256 | ||||||||
\(601\) | −5.87229e95 | −0.790020 | −0.395010 | − | 0.918677i | \(-0.629259\pi\) | ||||
−0.395010 | + | 0.918677i | \(0.629259\pi\) | |||||||
\(602\) | −1.29585e94 | −0.0164617 | ||||||||
\(603\) | 7.23508e95 | 0.867952 | ||||||||
\(604\) | 3.32308e96 | 3.76501 | ||||||||
\(605\) | 1.00930e96 | 1.08009 | ||||||||
\(606\) | −5.47984e94 | −0.0553939 | ||||||||
\(607\) | −1.99576e96 | −1.90589 | −0.952944 | − | 0.303145i | \(-0.901963\pi\) | ||||
−0.952944 | + | 0.303145i | \(0.901963\pi\) | |||||||
\(608\) | −2.47352e96 | −2.23174 | ||||||||
\(609\) | 6.87435e92 | 0.000586050 0 | ||||||||
\(610\) | −3.04454e96 | −2.45269 | ||||||||
\(611\) | 2.20292e96 | 1.67717 | ||||||||
\(612\) | 9.66217e95 | 0.695266 | ||||||||
\(613\) | −1.69286e96 | −1.15142 | −0.575711 | − | 0.817653i | \(-0.695275\pi\) | ||||
−0.575711 | + | 0.817653i | \(0.695275\pi\) | |||||||
\(614\) | 1.55618e96 | 1.00058 | ||||||||
\(615\) | 1.41943e95 | 0.0862827 | ||||||||
\(616\) | 1.65656e93 | 0.000952078 0 | ||||||||
\(617\) | 2.01970e96 | 1.09761 | 0.548807 | − | 0.835949i | \(-0.315082\pi\) | ||||
0.548807 | + | 0.835949i | \(0.315082\pi\) | |||||||
\(618\) | 2.15128e96 | 1.10559 | ||||||||
\(619\) | −1.55484e96 | −0.755713 | −0.377857 | − | 0.925864i | \(-0.623339\pi\) | ||||
−0.377857 | + | 0.925864i | \(0.623339\pi\) | |||||||
\(620\) | −3.07720e96 | −1.41463 | ||||||||
\(621\) | 1.33884e96 | 0.582195 | ||||||||
\(622\) | 8.41005e96 | 3.45963 | ||||||||
\(623\) | 1.78001e94 | 0.00692764 | ||||||||
\(624\) | −5.84888e96 | −2.15379 | ||||||||
\(625\) | −3.27291e96 | −1.14044 | ||||||||
\(626\) | 1.62382e96 | 0.535454 | ||||||||
\(627\) | −1.68302e94 | −0.00525241 | ||||||||
\(628\) | 5.23457e96 | 1.54623 | ||||||||
\(629\) | −9.63509e95 | −0.269407 | ||||||||
\(630\) | 5.86499e94 | 0.0155245 | ||||||||
\(631\) | 1.41840e96 | 0.355456 | 0.177728 | − | 0.984080i | \(-0.443125\pi\) | ||||
0.177728 | + | 0.984080i | \(0.443125\pi\) | |||||||
\(632\) | −1.85192e97 | −4.39423 | ||||||||
\(633\) | −7.48682e95 | −0.168217 | ||||||||
\(634\) | −3.66887e96 | −0.780645 | ||||||||
\(635\) | 2.09764e96 | 0.422704 | ||||||||
\(636\) | 3.99448e96 | 0.762412 | ||||||||
\(637\) | −8.49148e96 | −1.53523 | ||||||||
\(638\) | −7.74785e94 | −0.0132699 | ||||||||
\(639\) | 8.18994e96 | 1.32893 | ||||||||
\(640\) | 3.38831e97 | 5.20923 | ||||||||
\(641\) | −1.09579e97 | −1.59635 | −0.798173 | − | 0.602429i | \(-0.794200\pi\) | ||||
−0.798173 | + | 0.602429i | \(0.794200\pi\) | |||||||
\(642\) | 5.75614e96 | 0.794644 | ||||||||
\(643\) | 1.16589e96 | 0.152539 | 0.0762693 | − | 0.997087i | \(-0.475699\pi\) | ||||
0.0762693 | + | 0.997087i | \(0.475699\pi\) | |||||||
\(644\) | −1.73282e95 | −0.0214877 | ||||||||
\(645\) | −3.14329e96 | −0.369465 | ||||||||
\(646\) | 2.36506e96 | 0.263524 | ||||||||
\(647\) | 7.27773e96 | 0.768773 | 0.384387 | − | 0.923172i | \(-0.374413\pi\) | ||||
0.384387 | + | 0.923172i | \(0.374413\pi\) | |||||||
\(648\) | −2.40917e97 | −2.41285 | ||||||||
\(649\) | −1.99878e95 | −0.0189812 | ||||||||
\(650\) | −5.63860e96 | −0.507762 | ||||||||
\(651\) | 1.50492e94 | 0.00128519 | ||||||||
\(652\) | −3.61336e97 | −2.92664 | ||||||||
\(653\) | 2.36544e97 | 1.81722 | 0.908611 | − | 0.417644i | \(-0.137144\pi\) | ||||
0.908611 | + | 0.417644i | \(0.137144\pi\) | |||||||
\(654\) | −1.10579e97 | −0.805824 | ||||||||
\(655\) | 2.15359e97 | 1.48880 | ||||||||
\(656\) | 1.51201e97 | 0.991681 | ||||||||
\(657\) | −2.37697e96 | −0.147917 | ||||||||
\(658\) | 2.99432e95 | 0.0176809 | ||||||||
\(659\) | 4.12773e96 | 0.231294 | 0.115647 | − | 0.993290i | \(-0.463106\pi\) | ||||
0.115647 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(660\) | 6.21498e95 | 0.0330502 | ||||||||
\(661\) | −1.44124e97 | −0.727422 | −0.363711 | − | 0.931512i | \(-0.618490\pi\) | ||||
−0.363711 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(662\) | 8.40356e93 | 0.000402590 0 | ||||||||
\(663\) | 3.14231e96 | 0.142900 | ||||||||
\(664\) | −6.35577e97 | −2.74391 | ||||||||
\(665\) | 1.06070e95 | 0.00434755 | ||||||||
\(666\) | 4.33807e97 | 1.68824 | ||||||||
\(667\) | 5.23992e96 | 0.193635 | ||||||||
\(668\) | 9.57784e97 | 3.36109 | ||||||||
\(669\) | −1.57250e97 | −0.524071 | ||||||||
\(670\) | −6.53974e97 | −2.07005 | ||||||||
\(671\) | −1.23989e96 | −0.0372784 | ||||||||
\(672\) | −4.46708e95 | −0.0127580 | ||||||||
\(673\) | −5.38065e97 | −1.45987 | −0.729936 | − | 0.683516i | \(-0.760450\pi\) | ||||
−0.729936 | + | 0.683516i | \(0.760450\pi\) | |||||||
\(674\) | 2.68652e97 | 0.692507 | ||||||||
\(675\) | 4.37525e96 | 0.107158 | ||||||||
\(676\) | 1.65001e98 | 3.83994 | ||||||||
\(677\) | −7.23414e97 | −1.59984 | −0.799922 | − | 0.600104i | \(-0.795126\pi\) | ||||
−0.799922 | + | 0.600104i | \(0.795126\pi\) | |||||||
\(678\) | 8.91445e96 | 0.187357 | ||||||||
\(679\) | 4.87118e95 | 0.00973032 | ||||||||
\(680\) | −5.64665e97 | −1.07209 | ||||||||
\(681\) | 2.36617e97 | 0.427043 | ||||||||
\(682\) | −1.69614e96 | −0.0291006 | ||||||||
\(683\) | −2.87542e97 | −0.469015 | −0.234507 | − | 0.972114i | \(-0.575348\pi\) | ||||
−0.234507 | + | 0.972114i | \(0.575348\pi\) | |||||||
\(684\) | −7.86753e97 | −1.22012 | ||||||||
\(685\) | 9.71108e97 | 1.43200 | ||||||||
\(686\) | −2.30849e96 | −0.0323703 | ||||||||
\(687\) | 1.11543e97 | 0.148742 | ||||||||
\(688\) | −3.34829e98 | −4.24641 | ||||||||
\(689\) | −1.02086e98 | −1.23142 | ||||||||
\(690\) | −5.68888e97 | −0.652730 | ||||||||
\(691\) | −2.09622e97 | −0.228794 | −0.114397 | − | 0.993435i | \(-0.536494\pi\) | ||||
−0.114397 | + | 0.993435i | \(0.536494\pi\) | |||||||
\(692\) | 4.02763e98 | 4.18205 | ||||||||
\(693\) | 2.38853e94 | 0.000235957 0 | ||||||||
\(694\) | 2.99772e98 | 2.81767 | ||||||||
\(695\) | 1.44623e98 | 1.29349 | ||||||||
\(696\) | 2.97985e97 | 0.253616 | ||||||||
\(697\) | −8.12326e96 | −0.0657960 | ||||||||
\(698\) | −2.02802e98 | −1.56337 | ||||||||
\(699\) | 4.51044e97 | 0.330945 | ||||||||
\(700\) | −5.66275e95 | −0.00395498 | ||||||||
\(701\) | 1.95600e97 | 0.130046 | 0.0650231 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650231 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(702\) | −3.00960e98 | −1.90492 | ||||||||
\(703\) | 7.84548e97 | 0.472782 | ||||||||
\(704\) | 2.69470e97 | 0.154616 | ||||||||
\(705\) | 7.26322e97 | 0.396830 | ||||||||
\(706\) | −2.81375e98 | −1.46394 | ||||||||
\(707\) | 1.40647e95 | 0.000696887 0 | ||||||||
\(708\) | 1.18900e98 | 0.561091 | ||||||||
\(709\) | 1.46385e98 | 0.657962 | 0.328981 | − | 0.944337i | \(-0.393295\pi\) | ||||
0.328981 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(710\) | −7.40284e98 | −3.16946 | ||||||||
\(711\) | −2.67021e98 | −1.08904 | ||||||||
\(712\) | 7.71589e98 | 2.99796 | ||||||||
\(713\) | 1.14711e98 | 0.424636 | ||||||||
\(714\) | 4.27119e95 | 0.00150647 | ||||||||
\(715\) | −1.58835e97 | −0.0533813 | ||||||||
\(716\) | −9.66909e98 | −3.09661 | ||||||||
\(717\) | −1.73826e97 | −0.0530523 | ||||||||
\(718\) | 9.32102e98 | 2.71125 | ||||||||
\(719\) | −2.66577e98 | −0.739054 | −0.369527 | − | 0.929220i | \(-0.620480\pi\) | ||||
−0.369527 | + | 0.929220i | \(0.620480\pi\) | |||||||
\(720\) | 1.51544e99 | 4.00467 | ||||||||
\(721\) | −5.52156e96 | −0.0139090 | ||||||||
\(722\) | 6.22292e98 | 1.49438 | ||||||||
\(723\) | −2.12939e98 | −0.487511 | ||||||||
\(724\) | −1.95160e99 | −4.26002 | ||||||||
\(725\) | 1.71238e97 | 0.0356401 | ||||||||
\(726\) | −3.30934e98 | −0.656792 | ||||||||
\(727\) | −9.09844e97 | −0.172199 | −0.0860993 | − | 0.996287i | \(-0.527440\pi\) | ||||
−0.0860993 | + | 0.996287i | \(0.527440\pi\) | |||||||
\(728\) | 2.51843e97 | 0.0454567 | ||||||||
\(729\) | −2.23620e98 | −0.384955 | ||||||||
\(730\) | 2.14853e98 | 0.352779 | ||||||||
\(731\) | 1.79887e98 | 0.281741 | ||||||||
\(732\) | 7.37563e98 | 1.10196 | ||||||||
\(733\) | 1.09199e99 | 1.55644 | 0.778222 | − | 0.627989i | \(-0.216122\pi\) | ||||
0.778222 | + | 0.627989i | \(0.216122\pi\) | |||||||
\(734\) | 2.35373e99 | 3.20068 | ||||||||
\(735\) | −2.79972e98 | −0.363246 | ||||||||
\(736\) | −3.40499e99 | −4.21533 | ||||||||
\(737\) | −2.66332e97 | −0.0314626 | ||||||||
\(738\) | 3.65739e98 | 0.412312 | ||||||||
\(739\) | 1.00500e99 | 1.08127 | 0.540634 | − | 0.841258i | \(-0.318185\pi\) | ||||
0.540634 | + | 0.841258i | \(0.318185\pi\) | |||||||
\(740\) | −2.89714e99 | −2.97492 | ||||||||
\(741\) | −2.55866e98 | −0.250775 | ||||||||
\(742\) | −1.38761e97 | −0.0129818 | ||||||||
\(743\) | −1.61438e99 | −1.44175 | −0.720876 | − | 0.693064i | \(-0.756260\pi\) | ||||
−0.720876 | + | 0.693064i | \(0.756260\pi\) | |||||||
\(744\) | 6.52343e98 | 0.556173 | ||||||||
\(745\) | 2.57869e98 | 0.209897 | ||||||||
\(746\) | 1.79908e99 | 1.39817 | ||||||||
\(747\) | −9.16413e98 | −0.680034 | ||||||||
\(748\) | −3.55676e97 | −0.0252028 | ||||||||
\(749\) | −1.47739e97 | −0.00999706 | ||||||||
\(750\) | 9.14107e98 | 0.590722 | ||||||||
\(751\) | −1.42488e98 | −0.0879427 | −0.0439714 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439714 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(752\) | 7.73692e99 | 4.56092 | ||||||||
\(753\) | −5.24020e98 | −0.295067 | ||||||||
\(754\) | −1.17789e99 | −0.633568 | ||||||||
\(755\) | −2.80014e99 | −1.43883 | ||||||||
\(756\) | −3.02249e97 | −0.0148376 | ||||||||
\(757\) | 2.24957e99 | 1.05510 | 0.527548 | − | 0.849525i | \(-0.323112\pi\) | ||||
0.527548 | + | 0.849525i | \(0.323112\pi\) | |||||||
\(758\) | −5.40479e99 | −2.42209 | ||||||||
\(759\) | −2.31680e97 | −0.00992083 | ||||||||
\(760\) | 4.59784e99 | 1.88142 | ||||||||
\(761\) | 2.11733e99 | 0.827977 | 0.413989 | − | 0.910282i | \(-0.364135\pi\) | ||||
0.413989 | + | 0.910282i | \(0.364135\pi\) | |||||||
\(762\) | −6.87784e98 | −0.257043 | ||||||||
\(763\) | 2.83816e97 | 0.0101377 | ||||||||
\(764\) | −9.92999e99 | −3.39022 | ||||||||
\(765\) | −8.14167e98 | −0.265701 | ||||||||
\(766\) | 4.15488e98 | 0.129618 | ||||||||
\(767\) | −3.03870e99 | −0.906251 | ||||||||
\(768\) | −5.44396e99 | −1.55222 | ||||||||
\(769\) | 5.07951e99 | 1.38472 | 0.692362 | − | 0.721550i | \(-0.256570\pi\) | ||||
0.692362 | + | 0.721550i | \(0.256570\pi\) | |||||||
\(770\) | −2.15897e96 | −0.000562753 0 | ||||||||
\(771\) | 1.11044e99 | 0.276770 | ||||||||
\(772\) | 3.22937e99 | 0.769699 | ||||||||
\(773\) | 7.19171e99 | 1.63923 | 0.819614 | − | 0.572916i | \(-0.194188\pi\) | ||||
0.819614 | + | 0.572916i | \(0.194188\pi\) | |||||||
\(774\) | −8.09915e99 | −1.76553 | ||||||||
\(775\) | 3.74870e98 | 0.0781578 | ||||||||
\(776\) | 2.11153e100 | 4.21084 | ||||||||
\(777\) | 1.41686e97 | 0.00270272 | ||||||||
\(778\) | −1.22705e100 | −2.23907 | ||||||||
\(779\) | 6.61445e98 | 0.115465 | ||||||||
\(780\) | 9.44850e99 | 1.57797 | ||||||||
\(781\) | −3.01481e98 | −0.0481726 | ||||||||
\(782\) | 3.25568e99 | 0.497748 | ||||||||
\(783\) | 9.13980e98 | 0.133708 | ||||||||
\(784\) | −2.98231e100 | −4.17493 | ||||||||
\(785\) | −4.41083e99 | −0.590904 | ||||||||
\(786\) | −7.06128e99 | −0.905328 | ||||||||
\(787\) | 2.21935e99 | 0.272331 | 0.136166 | − | 0.990686i | \(-0.456522\pi\) | ||||
0.136166 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(788\) | 1.56067e100 | 1.83298 | ||||||||
\(789\) | 7.42657e98 | 0.0834895 | ||||||||
\(790\) | 2.41359e100 | 2.59734 | ||||||||
\(791\) | −2.28801e97 | −0.00235706 | ||||||||
\(792\) | 1.03536e99 | 0.102111 | ||||||||
\(793\) | −1.88498e100 | −1.77984 | ||||||||
\(794\) | 2.33289e99 | 0.210905 | ||||||||
\(795\) | −3.36588e99 | −0.291362 | ||||||||
\(796\) | 4.50650e99 | 0.373542 | ||||||||
\(797\) | −1.80947e100 | −1.43628 | −0.718139 | − | 0.695899i | \(-0.755006\pi\) | ||||
−0.718139 | + | 0.695899i | \(0.755006\pi\) | |||||||
\(798\) | −3.47786e97 | −0.00264370 | ||||||||
\(799\) | −4.15666e99 | −0.302608 | ||||||||
\(800\) | −1.11273e100 | −0.775866 | ||||||||
\(801\) | 1.11252e100 | 0.742997 | ||||||||
\(802\) | 5.90779e99 | 0.377928 | ||||||||
\(803\) | 8.74990e97 | 0.00536188 | ||||||||
\(804\) | 1.58430e100 | 0.930047 | ||||||||
\(805\) | 1.46013e98 | 0.00821170 | ||||||||
\(806\) | −2.57861e100 | −1.38940 | ||||||||
\(807\) | −2.36774e99 | −0.122235 | ||||||||
\(808\) | 6.09670e99 | 0.301580 | ||||||||
\(809\) | 1.24685e100 | 0.591004 | 0.295502 | − | 0.955342i | \(-0.404513\pi\) | ||||
0.295502 | + | 0.955342i | \(0.404513\pi\) | |||||||
\(810\) | 3.13985e100 | 1.42618 | ||||||||
\(811\) | −9.08873e99 | −0.395625 | −0.197813 | − | 0.980240i | \(-0.563384\pi\) | ||||
−0.197813 | + | 0.980240i | \(0.563384\pi\) | |||||||
\(812\) | −1.18293e98 | −0.00493489 | ||||||||
\(813\) | 9.60235e98 | 0.0383932 | ||||||||
\(814\) | −1.59689e99 | −0.0611976 | ||||||||
\(815\) | 3.04473e100 | 1.11844 | ||||||||
\(816\) | 1.10362e100 | 0.388605 | ||||||||
\(817\) | −1.46475e100 | −0.494426 | ||||||||
\(818\) | 3.15692e100 | 1.02159 | ||||||||
\(819\) | 3.63122e98 | 0.0112657 | ||||||||
\(820\) | −2.44255e100 | −0.726552 | ||||||||
\(821\) | 1.37155e100 | 0.391176 | 0.195588 | − | 0.980686i | \(-0.437338\pi\) | ||||
0.195588 | + | 0.980686i | \(0.437338\pi\) | |||||||
\(822\) | −3.18412e100 | −0.870786 | ||||||||
\(823\) | 5.47295e100 | 1.43525 | 0.717624 | − | 0.696430i | \(-0.245229\pi\) | ||||
0.717624 | + | 0.696430i | \(0.245229\pi\) | |||||||
\(824\) | −2.39345e101 | −6.01916 | ||||||||
\(825\) | −7.57119e97 | −0.00182601 | ||||||||
\(826\) | −4.13037e98 | −0.00955382 | ||||||||
\(827\) | 1.68367e100 | 0.373523 | 0.186761 | − | 0.982405i | \(-0.440201\pi\) | ||||
0.186761 | + | 0.982405i | \(0.440201\pi\) | |||||||
\(828\) | −1.08302e101 | −2.30458 | ||||||||
\(829\) | −3.72126e100 | −0.759554 | −0.379777 | − | 0.925078i | \(-0.623999\pi\) | ||||
−0.379777 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(830\) | 8.28340e100 | 1.62186 | ||||||||
\(831\) | 2.11810e100 | 0.397842 | ||||||||
\(832\) | 4.09670e101 | 7.38209 | ||||||||
\(833\) | 1.60225e100 | 0.276998 | ||||||||
\(834\) | −4.74198e100 | −0.786558 | ||||||||
\(835\) | −8.07061e100 | −1.28447 | ||||||||
\(836\) | 2.89613e99 | 0.0442284 | ||||||||
\(837\) | 2.00087e100 | 0.293217 | ||||||||
\(838\) | −1.15302e101 | −1.62150 | ||||||||
\(839\) | 6.67827e100 | 0.901314 | 0.450657 | − | 0.892697i | \(-0.351190\pi\) | ||||
0.450657 | + | 0.892697i | \(0.351190\pi\) | |||||||
\(840\) | 8.30350e98 | 0.0107554 | ||||||||
\(841\) | −7.68610e100 | −0.955530 | ||||||||
\(842\) | −4.01986e100 | −0.479671 | ||||||||
\(843\) | −2.90135e97 | −0.000332314 0 | ||||||||
\(844\) | 1.28833e101 | 1.41648 | ||||||||
\(845\) | −1.39035e101 | −1.46747 | ||||||||
\(846\) | 1.87148e101 | 1.89630 | ||||||||
\(847\) | 8.49386e98 | 0.00826281 | ||||||||
\(848\) | −3.58540e101 | −3.34874 | ||||||||
\(849\) | 2.63947e100 | 0.236702 | ||||||||
\(850\) | 1.06394e100 | 0.0916145 | ||||||||
\(851\) | 1.07999e101 | 0.892996 | ||||||||
\(852\) | 1.79339e101 | 1.42400 | ||||||||
\(853\) | −6.96534e100 | −0.531130 | −0.265565 | − | 0.964093i | \(-0.585558\pi\) | ||||
−0.265565 | + | 0.964093i | \(0.585558\pi\) | |||||||
\(854\) | −2.56217e99 | −0.0187634 | ||||||||
\(855\) | 6.62944e100 | 0.466279 | ||||||||
\(856\) | −6.40410e101 | −4.32627 | ||||||||
\(857\) | −7.62224e99 | −0.0494589 | −0.0247294 | − | 0.999694i | \(-0.507872\pi\) | ||||
−0.0247294 | + | 0.999694i | \(0.507872\pi\) | |||||||
\(858\) | 5.20798e99 | 0.0324607 | ||||||||
\(859\) | 2.50764e101 | 1.50142 | 0.750708 | − | 0.660634i | \(-0.229713\pi\) | ||||
0.750708 | + | 0.660634i | \(0.229713\pi\) | |||||||
\(860\) | 5.40895e101 | 3.11112 | ||||||||
\(861\) | 1.19454e98 | 0.000660074 0 | ||||||||
\(862\) | 4.79056e101 | 2.54323 | ||||||||
\(863\) | −6.09184e100 | −0.310725 | −0.155362 | − | 0.987858i | \(-0.549655\pi\) | ||||
−0.155362 | + | 0.987858i | \(0.549655\pi\) | |||||||
\(864\) | −5.93921e101 | −2.91075 | ||||||||
\(865\) | −3.39382e101 | −1.59821 | ||||||||
\(866\) | −1.18175e101 | −0.534760 | ||||||||
\(867\) | 7.13356e100 | 0.310204 | ||||||||
\(868\) | −2.58966e99 | −0.0108221 | ||||||||
\(869\) | 9.82935e99 | 0.0394769 | ||||||||
\(870\) | −3.88361e100 | −0.149907 | ||||||||
\(871\) | −4.04899e101 | −1.50217 | ||||||||
\(872\) | 1.23027e102 | 4.38714 | ||||||||
\(873\) | 3.04453e101 | 1.04359 | ||||||||
\(874\) | −2.65097e101 | −0.873497 | ||||||||
\(875\) | −2.34618e99 | −0.00743161 | ||||||||
\(876\) | −5.20497e100 | −0.158499 | ||||||||
\(877\) | −2.02770e101 | −0.593633 | −0.296817 | − | 0.954934i | \(-0.595925\pi\) | ||||
−0.296817 | + | 0.954934i | \(0.595925\pi\) | |||||||
\(878\) | 3.74567e101 | 1.05431 | ||||||||
\(879\) | −9.57900e100 | −0.259241 | ||||||||
\(880\) | −5.57850e100 | −0.145166 | ||||||||
\(881\) | 2.95221e101 | 0.738717 | 0.369359 | − | 0.929287i | \(-0.379577\pi\) | ||||
0.369359 | + | 0.929287i | \(0.379577\pi\) | |||||||
\(882\) | −7.21390e101 | −1.73582 | ||||||||
\(883\) | 3.63350e101 | 0.840778 | 0.420389 | − | 0.907344i | \(-0.361894\pi\) | ||||
0.420389 | + | 0.907344i | \(0.361894\pi\) | |||||||
\(884\) | −5.40727e101 | −1.20330 | ||||||||
\(885\) | −1.00189e101 | −0.214426 | ||||||||
\(886\) | −1.38926e102 | −2.85969 | ||||||||
\(887\) | −5.78176e101 | −1.14471 | −0.572355 | − | 0.820006i | \(-0.693970\pi\) | ||||
−0.572355 | + | 0.820006i | \(0.693970\pi\) | |||||||
\(888\) | 6.14172e101 | 1.16961 | ||||||||
\(889\) | 1.76529e99 | 0.00323374 | ||||||||
\(890\) | −1.00560e102 | −1.77203 | ||||||||
\(891\) | 1.27871e100 | 0.0216765 | ||||||||
\(892\) | 2.70595e102 | 4.41299 | ||||||||
\(893\) | 3.38460e101 | 0.531046 | ||||||||
\(894\) | −8.45513e100 | −0.127637 | ||||||||
\(895\) | 8.14750e101 | 1.18340 | ||||||||
\(896\) | 2.85147e100 | 0.0398513 | ||||||||
\(897\) | −3.52219e101 | −0.473667 | ||||||||
\(898\) | 5.18445e101 | 0.670917 | ||||||||
\(899\) | 7.83095e100 | 0.0975226 | ||||||||
\(900\) | −3.53927e101 | −0.424177 | ||||||||
\(901\) | 1.92626e101 | 0.222182 | ||||||||
\(902\) | −1.34633e100 | −0.0149460 | ||||||||
\(903\) | −2.64527e99 | −0.00282646 | ||||||||
\(904\) | −9.91795e101 | −1.02003 | ||||||||
\(905\) | 1.64449e102 | 1.62800 | ||||||||
\(906\) | 9.18123e101 | 0.874939 | ||||||||
\(907\) | −8.87640e100 | −0.0814302 | −0.0407151 | − | 0.999171i | \(-0.512964\pi\) | ||||
−0.0407151 | + | 0.999171i | \(0.512964\pi\) | |||||||
\(908\) | −4.07170e102 | −3.59595 | ||||||||
\(909\) | 8.79059e100 | 0.0747419 | ||||||||
\(910\) | −3.28224e100 | −0.0268685 | ||||||||
\(911\) | −4.55318e101 | −0.358864 | −0.179432 | − | 0.983770i | \(-0.557426\pi\) | ||||
−0.179432 | + | 0.983770i | \(0.557426\pi\) | |||||||
\(912\) | −8.98633e101 | −0.681962 | ||||||||
\(913\) | 3.37342e100 | 0.0246507 | ||||||||
\(914\) | 5.80707e101 | 0.408614 | ||||||||
\(915\) | −6.21495e101 | −0.421124 | ||||||||
\(916\) | −1.91942e102 | −1.25249 | ||||||||
\(917\) | 1.81237e100 | 0.0113895 | ||||||||
\(918\) | 5.67877e101 | 0.343702 | ||||||||
\(919\) | 8.86482e101 | 0.516755 | 0.258378 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258378 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(920\) | 6.32928e102 | 3.55365 | ||||||||
\(921\) | 3.17670e101 | 0.171798 | ||||||||
\(922\) | 1.15209e102 | 0.600163 | ||||||||
\(923\) | −4.58336e102 | −2.29998 | ||||||||
\(924\) | 5.23028e98 | 0.000252838 0 | ||||||||
\(925\) | 3.52935e101 | 0.164363 | ||||||||
\(926\) | 8.10375e102 | 3.63586 | ||||||||
\(927\) | −3.45102e102 | −1.49175 | ||||||||
\(928\) | −2.32447e102 | −0.968098 | ||||||||
\(929\) | −3.08187e102 | −1.23672 | −0.618362 | − | 0.785894i | \(-0.712203\pi\) | ||||
−0.618362 | + | 0.785894i | \(0.712203\pi\) | |||||||
\(930\) | −8.50191e101 | −0.328742 | ||||||||
\(931\) | −1.30465e102 | −0.486104 | ||||||||
\(932\) | −7.76153e102 | −2.78675 | ||||||||
\(933\) | 1.71678e102 | 0.594016 | ||||||||
\(934\) | 9.03959e101 | 0.301427 | ||||||||
\(935\) | 2.99705e100 | 0.00963148 | ||||||||
\(936\) | 1.57404e103 | 4.87528 | ||||||||
\(937\) | 5.42024e102 | 1.61809 | 0.809044 | − | 0.587748i | \(-0.199985\pi\) | ||||
0.809044 | + | 0.587748i | \(0.199985\pi\) | |||||||
\(938\) | −5.50360e100 | −0.0158361 | ||||||||
\(939\) | 3.31477e101 | 0.0919370 | ||||||||
\(940\) | −1.24985e103 | −3.34154 | ||||||||
\(941\) | 1.40089e102 | 0.361045 | 0.180522 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180522 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(942\) | 1.44624e102 | 0.359323 | ||||||||
\(943\) | 9.10530e101 | 0.218092 | ||||||||
\(944\) | −1.06723e103 | −2.46448 | ||||||||
\(945\) | 2.54685e100 | 0.00567030 | ||||||||
\(946\) | 2.98139e101 | 0.0639992 | ||||||||
\(947\) | 1.40868e102 | 0.291566 | 0.145783 | − | 0.989317i | \(-0.453430\pi\) | ||||
0.145783 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(948\) | −5.84710e102 | −1.16695 | ||||||||
\(949\) | 1.33023e102 | 0.256001 | ||||||||
\(950\) | −8.66324e101 | −0.160774 | ||||||||
\(951\) | −7.48944e101 | −0.134036 | ||||||||
\(952\) | −4.75200e100 | −0.00820166 | ||||||||
\(953\) | 5.24667e102 | 0.873331 | 0.436666 | − | 0.899624i | \(-0.356159\pi\) | ||||
0.436666 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(954\) | −8.67270e102 | −1.39231 | ||||||||
\(955\) | 8.36734e102 | 1.29560 | ||||||||
\(956\) | 2.99119e102 | 0.446732 | ||||||||
\(957\) | −1.58160e100 | −0.00227843 | ||||||||
\(958\) | 6.84170e102 | 0.950723 | ||||||||
\(959\) | 8.17247e100 | 0.0109550 | ||||||||
\(960\) | 1.35072e103 | 1.74666 | ||||||||
\(961\) | −6.30165e102 | −0.786135 | ||||||||
\(962\) | −2.42772e103 | −2.92186 | ||||||||
\(963\) | −9.23381e102 | −1.07220 | ||||||||
\(964\) | 3.66424e103 | 4.10513 | ||||||||
\(965\) | −2.72118e102 | −0.294147 | ||||||||
\(966\) | −4.78754e100 | −0.00499346 | ||||||||
\(967\) | 7.85802e102 | 0.790860 | 0.395430 | − | 0.918496i | \(-0.370596\pi\) | ||||
0.395430 | + | 0.918496i | \(0.370596\pi\) | |||||||
\(968\) | 3.68187e103 | 3.57576 | ||||||||
\(969\) | 4.82790e101 | 0.0452468 | ||||||||
\(970\) | −2.75193e103 | −2.48893 | ||||||||
\(971\) | −8.53716e102 | −0.745161 | −0.372580 | − | 0.928000i | \(-0.621527\pi\) | ||||
−0.372580 | + | 0.928000i | \(0.621527\pi\) | |||||||
\(972\) | −2.89012e103 | −2.43461 | ||||||||
\(973\) | 1.21709e101 | 0.00989534 | ||||||||
\(974\) | 2.67220e102 | 0.209693 | ||||||||
\(975\) | −1.15103e102 | −0.0871823 | ||||||||
\(976\) | −6.62029e103 | −4.84014 | ||||||||
\(977\) | −1.72478e102 | −0.121722 | −0.0608611 | − | 0.998146i | \(-0.519385\pi\) | ||||
−0.0608611 | + | 0.998146i | \(0.519385\pi\) | |||||||
\(978\) | −9.98323e102 | −0.680112 | ||||||||
\(979\) | −4.09533e101 | −0.0269331 | ||||||||
\(980\) | 4.81774e103 | 3.05875 | ||||||||
\(981\) | 1.77387e103 | 1.08728 | ||||||||
\(982\) | 4.56050e103 | 2.69877 | ||||||||
\(983\) | −1.14304e103 | −0.653078 | −0.326539 | − | 0.945184i | \(-0.605882\pi\) | ||||
−0.326539 | + | 0.945184i | \(0.605882\pi\) | |||||||
\(984\) | 5.17803e102 | 0.285649 | ||||||||
\(985\) | −1.31508e103 | −0.700488 | ||||||||
\(986\) | 2.22254e102 | 0.114313 | ||||||||
\(987\) | 6.11244e100 | 0.00303580 | ||||||||
\(988\) | 4.40293e103 | 2.11167 | ||||||||
\(989\) | −2.01633e103 | −0.933879 | ||||||||
\(990\) | −1.34938e102 | −0.0603559 | ||||||||
\(991\) | 2.50288e103 | 1.08118 | 0.540591 | − | 0.841286i | \(-0.318201\pi\) | ||||
0.540591 | + | 0.841286i | \(0.318201\pi\) | |||||||
\(992\) | −5.08869e103 | −2.12302 | ||||||||
\(993\) | 1.71546e99 | 6.91243e−5 0 | ||||||||
\(994\) | −6.22994e101 | −0.0242468 | ||||||||
\(995\) | −3.79733e102 | −0.142752 | ||||||||
\(996\) | −2.00672e103 | −0.728684 | ||||||||
\(997\) | 1.06606e103 | 0.373937 | 0.186969 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(998\) | 4.04425e103 | 1.37036 | ||||||||
\(999\) | 1.88379e103 | 0.616627 |
(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 | 1.70.a.a.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 9.70.a.b.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.70.a.a.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.70.a.b.1.5 | 5 | 3.2 | odd | 2 |