Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,80,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, 80, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 80);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 80 \) |
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: | \(39.5237048722\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 76\!\cdots\!88 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{54}\cdot 3^{24}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.49960e10\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.42585e11 | −1.08375 | −0.541874 | − | 0.840459i | \(-0.682285\pi\) | ||||
−0.541874 | + | 0.840459i | \(0.682285\pi\) | |||||||
\(3\) | 1.18388e19 | 1.68663 | 0.843314 | − | 0.537422i | \(-0.180602\pi\) | ||||
0.843314 | + | 0.537422i | \(0.180602\pi\) | |||||||
\(4\) | 1.05486e23 | 0.174512 | ||||||||
\(5\) | 5.37236e27 | 1.32084 | 0.660419 | − | 0.750897i | \(-0.270379\pi\) | ||||
0.660419 | + | 0.750897i | \(0.270379\pi\) | |||||||
\(6\) | −9.97521e30 | −1.82788 | ||||||||
\(7\) | −2.88361e33 | −1.19829 | −0.599147 | − | 0.800639i | \(-0.704494\pi\) | ||||
−0.599147 | + | 0.800639i | \(0.704494\pi\) | |||||||
\(8\) | 4.20430e35 | 0.894622 | ||||||||
\(9\) | 9.08882e37 | 1.84471 | ||||||||
\(10\) | −4.52667e39 | −1.43146 | ||||||||
\(11\) | 1.27714e41 | 0.935892 | 0.467946 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467946 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(12\) | 1.24883e42 | 0.294336 | ||||||||
\(13\) | 8.81976e43 | 0.880429 | 0.440214 | − | 0.897893i | \(-0.354902\pi\) | ||||
0.440214 | + | 0.897893i | \(0.354902\pi\) | |||||||
\(14\) | 2.42968e45 | 1.29865 | ||||||||
\(15\) | 6.36024e46 | 2.22776 | ||||||||
\(16\) | −4.18010e47 | −1.14406 | ||||||||
\(17\) | −2.88942e47 | −0.0721238 | −0.0360619 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360619 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(18\) | −7.65810e49 | −1.99920 | ||||||||
\(19\) | 2.48242e50 | 0.765789 | 0.382894 | − | 0.923792i | \(-0.374927\pi\) | ||||
0.382894 | + | 0.923792i | \(0.374927\pi\) | |||||||
\(20\) | 5.66707e50 | 0.230502 | ||||||||
\(21\) | −3.41385e52 | −2.02108 | ||||||||
\(22\) | −1.07609e53 | −1.01427 | ||||||||
\(23\) | −9.54744e53 | −1.55467 | −0.777334 | − | 0.629088i | \(-0.783428\pi\) | ||||
−0.777334 | + | 0.629088i | \(0.783428\pi\) | |||||||
\(24\) | 4.97740e54 | 1.50889 | ||||||||
\(25\) | 1.23186e55 | 0.744615 | ||||||||
\(26\) | −7.43139e55 | −0.954164 | ||||||||
\(27\) | 4.92715e56 | 1.42471 | ||||||||
\(28\) | −3.04179e56 | −0.209116 | ||||||||
\(29\) | 2.62380e57 | 0.451034 | 0.225517 | − | 0.974239i | \(-0.427593\pi\) | ||||
0.225517 | + | 0.974239i | \(0.427593\pi\) | |||||||
\(30\) | −5.35904e58 | −2.41433 | ||||||||
\(31\) | 5.35966e58 | 0.661226 | 0.330613 | − | 0.943766i | \(-0.392744\pi\) | ||||
0.330613 | + | 0.943766i | \(0.392744\pi\) | |||||||
\(32\) | 9.80745e58 | 0.345249 | ||||||||
\(33\) | 1.51198e60 | 1.57850 | ||||||||
\(34\) | 2.43458e59 | 0.0781641 | ||||||||
\(35\) | −1.54918e61 | −1.58275 | ||||||||
\(36\) | 9.58741e60 | 0.321923 | ||||||||
\(37\) | 1.24508e62 | 1.41654 | 0.708268 | − | 0.705944i | \(-0.249477\pi\) | ||||
0.708268 | + | 0.705944i | \(0.249477\pi\) | |||||||
\(38\) | −2.09165e62 | −0.829922 | ||||||||
\(39\) | 1.04416e63 | 1.48496 | ||||||||
\(40\) | 2.25870e63 | 1.18165 | ||||||||
\(41\) | 4.32605e62 | 0.0853355 | 0.0426677 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426677 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(42\) | 2.87646e64 | 2.19034 | ||||||||
\(43\) | −2.59673e64 | −0.780590 | −0.390295 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390295 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(44\) | 1.34720e64 | 0.163324 | ||||||||
\(45\) | 4.88284e65 | 2.43657 | ||||||||
\(46\) | 8.04453e65 | 1.68487 | ||||||||
\(47\) | 1.81584e65 | 0.162634 | 0.0813170 | − | 0.996688i | \(-0.474087\pi\) | ||||
0.0813170 | + | 0.996688i | \(0.474087\pi\) | |||||||
\(48\) | −4.94875e66 | −1.92960 | ||||||||
\(49\) | 2.52430e66 | 0.435909 | ||||||||
\(50\) | −1.03795e67 | −0.806976 | ||||||||
\(51\) | −3.42074e66 | −0.121646 | ||||||||
\(52\) | 9.30359e66 | 0.153645 | ||||||||
\(53\) | −1.64629e68 | −1.28117 | −0.640587 | − | 0.767885i | \(-0.721309\pi\) | ||||
−0.640587 | + | 0.767885i | \(0.721309\pi\) | |||||||
\(54\) | −4.15154e68 | −1.54403 | ||||||||
\(55\) | 6.86123e68 | 1.23616 | ||||||||
\(56\) | −1.21236e69 | −1.07202 | ||||||||
\(57\) | 2.93890e69 | 1.29160 | ||||||||
\(58\) | −2.21077e69 | −0.488808 | ||||||||
\(59\) | 1.72621e70 | 1.94285 | 0.971424 | − | 0.237352i | \(-0.0762795\pi\) | ||||
0.971424 | + | 0.237352i | \(0.0762795\pi\) | |||||||
\(60\) | 6.70915e69 | 0.388770 | ||||||||
\(61\) | 3.55854e70 | 1.07335 | 0.536677 | − | 0.843788i | \(-0.319679\pi\) | ||||
0.536677 | + | 0.843788i | \(0.319679\pi\) | |||||||
\(62\) | −4.51596e70 | −0.716603 | ||||||||
\(63\) | −2.62086e71 | −2.21051 | ||||||||
\(64\) | 1.70036e71 | 0.769895 | ||||||||
\(65\) | 4.73829e71 | 1.16290 | ||||||||
\(66\) | −1.27397e72 | −1.71070 | ||||||||
\(67\) | 1.15292e71 | 0.0854762 | 0.0427381 | − | 0.999086i | \(-0.486392\pi\) | ||||
0.0427381 | + | 0.999086i | \(0.486392\pi\) | |||||||
\(68\) | −3.04793e70 | −0.0125864 | ||||||||
\(69\) | −1.13031e73 | −2.62214 | ||||||||
\(70\) | 1.30531e73 | 1.71531 | ||||||||
\(71\) | 1.64661e73 | 1.23562 | 0.617812 | − | 0.786326i | \(-0.288019\pi\) | ||||
0.617812 | + | 0.786326i | \(0.288019\pi\) | |||||||
\(72\) | 3.82122e73 | 1.65032 | ||||||||
\(73\) | −2.56980e72 | −0.0643645 | −0.0321822 | − | 0.999482i | \(-0.510246\pi\) | ||||
−0.0321822 | + | 0.999482i | \(0.510246\pi\) | |||||||
\(74\) | −1.04908e74 | −1.53517 | ||||||||
\(75\) | 1.45838e74 | 1.25589 | ||||||||
\(76\) | 2.61860e73 | 0.133639 | ||||||||
\(77\) | −3.68276e74 | −1.12147 | ||||||||
\(78\) | −8.79790e74 | −1.60932 | ||||||||
\(79\) | 1.45007e75 | 1.60369 | 0.801844 | − | 0.597533i | \(-0.203852\pi\) | ||||
0.801844 | + | 0.597533i | \(0.203852\pi\) | |||||||
\(80\) | −2.24570e75 | −1.51112 | ||||||||
\(81\) | 1.35514e75 | 0.558247 | ||||||||
\(82\) | −3.64507e74 | −0.0924822 | ||||||||
\(83\) | 5.44189e75 | 0.855391 | 0.427696 | − | 0.903923i | \(-0.359326\pi\) | ||||
0.427696 | + | 0.903923i | \(0.359326\pi\) | |||||||
\(84\) | −3.60113e75 | −0.352701 | ||||||||
\(85\) | −1.55230e75 | −0.0952639 | ||||||||
\(86\) | 2.18797e76 | 0.845964 | ||||||||
\(87\) | 3.10627e76 | 0.760726 | ||||||||
\(88\) | 5.36947e76 | 0.837270 | ||||||||
\(89\) | 1.18618e76 | 0.118371 | 0.0591856 | − | 0.998247i | \(-0.481150\pi\) | ||||
0.0591856 | + | 0.998247i | \(0.481150\pi\) | |||||||
\(90\) | −4.11420e77 | −2.64063 | ||||||||
\(91\) | −2.54327e77 | −1.05501 | ||||||||
\(92\) | −1.00712e77 | −0.271307 | ||||||||
\(93\) | 6.34521e77 | 1.11524 | ||||||||
\(94\) | −1.53000e77 | −0.176254 | ||||||||
\(95\) | 1.33365e78 | 1.01148 | ||||||||
\(96\) | 1.16109e78 | 0.582306 | ||||||||
\(97\) | −2.81055e78 | −0.936068 | −0.468034 | − | 0.883711i | \(-0.655037\pi\) | ||||
−0.468034 | + | 0.883711i | \(0.655037\pi\) | |||||||
\(98\) | −2.12694e78 | −0.472416 | ||||||||
\(99\) | 1.16077e79 | 1.72645 | ||||||||
\(100\) | 1.29944e78 | 0.129944 | ||||||||
\(101\) | −5.67731e78 | −0.383220 | −0.191610 | − | 0.981471i | \(-0.561371\pi\) | ||||
−0.191610 | + | 0.981471i | \(0.561371\pi\) | |||||||
\(102\) | 2.88226e78 | 0.131834 | ||||||||
\(103\) | −3.45707e79 | −1.07557 | −0.537784 | − | 0.843082i | \(-0.680739\pi\) | ||||
−0.537784 | + | 0.843082i | \(0.680739\pi\) | |||||||
\(104\) | 3.70810e79 | 0.787651 | ||||||||
\(105\) | −1.83404e80 | −2.66951 | ||||||||
\(106\) | 1.38713e80 | 1.38847 | ||||||||
\(107\) | −3.03063e79 | −0.209350 | −0.104675 | − | 0.994506i | \(-0.533380\pi\) | ||||
−0.104675 | + | 0.994506i | \(0.533380\pi\) | |||||||
\(108\) | 5.19744e79 | 0.248629 | ||||||||
\(109\) | 1.29743e80 | 0.431259 | 0.215629 | − | 0.976475i | \(-0.430820\pi\) | ||||
0.215629 | + | 0.976475i | \(0.430820\pi\) | |||||||
\(110\) | −5.78116e80 | −1.33969 | ||||||||
\(111\) | 1.47402e81 | 2.38917 | ||||||||
\(112\) | 1.20538e81 | 1.37092 | ||||||||
\(113\) | 1.61408e80 | 0.129219 | 0.0646094 | − | 0.997911i | \(-0.479420\pi\) | ||||
0.0646094 | + | 0.997911i | \(0.479420\pi\) | |||||||
\(114\) | −2.47627e81 | −1.39977 | ||||||||
\(115\) | −5.12923e81 | −2.05347 | ||||||||
\(116\) | 2.76773e80 | 0.0787106 | ||||||||
\(117\) | 8.01612e81 | 1.62414 | ||||||||
\(118\) | −1.45448e82 | −2.10556 | ||||||||
\(119\) | 8.33196e80 | 0.0864256 | ||||||||
\(120\) | 2.67404e82 | 1.99301 | ||||||||
\(121\) | −2.31107e81 | −0.124106 | ||||||||
\(122\) | −2.99837e82 | −1.16325 | ||||||||
\(123\) | 5.12154e81 | 0.143929 | ||||||||
\(124\) | 5.65368e81 | 0.115392 | ||||||||
\(125\) | −2.26982e82 | −0.337322 | ||||||||
\(126\) | 2.20829e83 | 2.39563 | ||||||||
\(127\) | 1.29381e83 | 1.02713 | 0.513564 | − | 0.858051i | \(-0.328325\pi\) | ||||
0.513564 | + | 0.858051i | \(0.328325\pi\) | |||||||
\(128\) | −2.02552e83 | −1.17962 | ||||||||
\(129\) | −3.07423e83 | −1.31656 | ||||||||
\(130\) | −3.99241e83 | −1.26030 | ||||||||
\(131\) | 1.27969e83 | 0.298461 | 0.149230 | − | 0.988802i | \(-0.452320\pi\) | ||||
0.149230 | + | 0.988802i | \(0.452320\pi\) | |||||||
\(132\) | 1.59492e83 | 0.275467 | ||||||||
\(133\) | −7.15834e83 | −0.917640 | ||||||||
\(134\) | −9.71434e82 | −0.0926347 | ||||||||
\(135\) | 2.64704e84 | 1.88181 | ||||||||
\(136\) | −1.21480e83 | −0.0645236 | ||||||||
\(137\) | −3.69646e84 | −1.47002 | −0.735010 | − | 0.678056i | \(-0.762823\pi\) | ||||
−0.735010 | + | 0.678056i | \(0.762823\pi\) | |||||||
\(138\) | 9.52378e84 | 2.84175 | ||||||||
\(139\) | −1.99076e84 | −0.446615 | −0.223307 | − | 0.974748i | \(-0.571685\pi\) | ||||
−0.223307 | + | 0.974748i | \(0.571685\pi\) | |||||||
\(140\) | −1.63416e84 | −0.276209 | ||||||||
\(141\) | 2.14974e84 | 0.274303 | ||||||||
\(142\) | −1.38741e85 | −1.33911 | ||||||||
\(143\) | 1.12640e85 | 0.823987 | ||||||||
\(144\) | −3.79922e85 | −2.11045 | ||||||||
\(145\) | 1.40960e85 | 0.595743 | ||||||||
\(146\) | 2.16527e84 | 0.0697549 | ||||||||
\(147\) | 2.98848e85 | 0.735216 | ||||||||
\(148\) | 1.31338e85 | 0.247202 | ||||||||
\(149\) | −1.34763e85 | −0.194408 | −0.0972041 | − | 0.995264i | \(-0.530990\pi\) | ||||
−0.0972041 | + | 0.995264i | \(0.530990\pi\) | |||||||
\(150\) | −1.22881e86 | −1.36107 | ||||||||
\(151\) | 7.89611e85 | 0.672704 | 0.336352 | − | 0.941736i | \(-0.390807\pi\) | ||||
0.336352 | + | 0.941736i | \(0.390807\pi\) | |||||||
\(152\) | 1.04369e86 | 0.685091 | ||||||||
\(153\) | −2.62614e85 | −0.133048 | ||||||||
\(154\) | 3.10303e86 | 1.21540 | ||||||||
\(155\) | 2.87940e86 | 0.873373 | ||||||||
\(156\) | 1.10144e86 | 0.259142 | ||||||||
\(157\) | −4.59639e86 | −0.840196 | −0.420098 | − | 0.907479i | \(-0.638004\pi\) | ||||
−0.420098 | + | 0.907479i | \(0.638004\pi\) | |||||||
\(158\) | −1.22181e87 | −1.73800 | ||||||||
\(159\) | −1.94901e87 | −2.16086 | ||||||||
\(160\) | 5.26891e86 | 0.456018 | ||||||||
\(161\) | 2.75311e87 | 1.86295 | ||||||||
\(162\) | −1.14182e87 | −0.605000 | ||||||||
\(163\) | 4.82420e84 | 0.00200454 | 0.00100227 | − | 0.999999i | \(-0.499681\pi\) | ||||
0.00100227 | + | 0.999999i | \(0.499681\pi\) | |||||||
\(164\) | 4.56337e85 | 0.0148920 | ||||||||
\(165\) | 8.12289e87 | 2.08495 | ||||||||
\(166\) | −4.58525e87 | −0.927029 | ||||||||
\(167\) | 8.96603e87 | 1.42988 | 0.714940 | − | 0.699186i | \(-0.246454\pi\) | ||||
0.714940 | + | 0.699186i | \(0.246454\pi\) | |||||||
\(168\) | −1.43529e88 | −1.80810 | ||||||||
\(169\) | −2.25636e87 | −0.224845 | ||||||||
\(170\) | 1.30795e87 | 0.103242 | ||||||||
\(171\) | 2.25623e88 | 1.41266 | ||||||||
\(172\) | −2.73918e87 | −0.136222 | ||||||||
\(173\) | −2.37720e88 | −0.940255 | −0.470127 | − | 0.882599i | \(-0.655792\pi\) | ||||
−0.470127 | + | 0.882599i | \(0.655792\pi\) | |||||||
\(174\) | −2.61729e88 | −0.824436 | ||||||||
\(175\) | −3.55221e88 | −0.892268 | ||||||||
\(176\) | −5.33856e88 | −1.07071 | ||||||||
\(177\) | 2.04363e89 | 3.27686 | ||||||||
\(178\) | −9.99459e87 | −0.128285 | ||||||||
\(179\) | −1.10473e89 | −1.13648 | −0.568241 | − | 0.822862i | \(-0.692376\pi\) | ||||
−0.568241 | + | 0.822862i | \(0.692376\pi\) | |||||||
\(180\) | 5.15070e88 | 0.425209 | ||||||||
\(181\) | −1.73036e89 | −1.14771 | −0.573856 | − | 0.818956i | \(-0.694553\pi\) | ||||
−0.573856 | + | 0.818956i | \(0.694553\pi\) | |||||||
\(182\) | 2.14292e89 | 1.14337 | ||||||||
\(183\) | 4.21289e89 | 1.81035 | ||||||||
\(184\) | −4.01404e89 | −1.39084 | ||||||||
\(185\) | 6.68899e89 | 1.87102 | ||||||||
\(186\) | −5.34637e89 | −1.20864 | ||||||||
\(187\) | −3.69018e88 | −0.0675001 | ||||||||
\(188\) | 1.91545e88 | 0.0283815 | ||||||||
\(189\) | −1.42080e90 | −1.70722 | ||||||||
\(190\) | −1.12371e90 | −1.09619 | ||||||||
\(191\) | −5.36614e89 | −0.425445 | −0.212723 | − | 0.977113i | \(-0.568233\pi\) | ||||
−0.212723 | + | 0.977113i | \(0.568233\pi\) | |||||||
\(192\) | 2.01302e90 | 1.29852 | ||||||||
\(193\) | −1.08896e90 | −0.572134 | −0.286067 | − | 0.958210i | \(-0.592348\pi\) | ||||
−0.286067 | + | 0.958210i | \(0.592348\pi\) | |||||||
\(194\) | 2.36812e90 | 1.01446 | ||||||||
\(195\) | 5.60958e90 | 1.96139 | ||||||||
\(196\) | 2.66278e89 | 0.0760712 | ||||||||
\(197\) | 2.43944e90 | 0.569999 | 0.285000 | − | 0.958528i | \(-0.408007\pi\) | ||||
0.285000 | + | 0.958528i | \(0.408007\pi\) | |||||||
\(198\) | −9.78043e90 | −1.87104 | ||||||||
\(199\) | −4.75368e90 | −0.745304 | −0.372652 | − | 0.927971i | \(-0.621551\pi\) | ||||
−0.372652 | + | 0.927971i | \(0.621551\pi\) | |||||||
\(200\) | 5.17912e90 | 0.666149 | ||||||||
\(201\) | 1.36492e90 | 0.144166 | ||||||||
\(202\) | 4.78362e90 | 0.415315 | ||||||||
\(203\) | −7.56600e90 | −0.540472 | ||||||||
\(204\) | −3.60839e89 | −0.0212286 | ||||||||
\(205\) | 2.32411e90 | 0.112714 | ||||||||
\(206\) | 2.91288e91 | 1.16565 | ||||||||
\(207\) | −8.67750e91 | −2.86791 | ||||||||
\(208\) | −3.68675e91 | −1.00726 | ||||||||
\(209\) | 3.17039e91 | 0.716696 | ||||||||
\(210\) | 1.54534e92 | 2.89308 | ||||||||
\(211\) | −1.15316e92 | −1.78950 | −0.894750 | − | 0.446568i | \(-0.852646\pi\) | ||||
−0.894750 | + | 0.446568i | \(0.852646\pi\) | |||||||
\(212\) | −1.73660e91 | −0.223580 | ||||||||
\(213\) | 1.94939e92 | 2.08404 | ||||||||
\(214\) | 2.55356e91 | 0.226883 | ||||||||
\(215\) | −1.39506e92 | −1.03103 | ||||||||
\(216\) | 2.07152e92 | 1.27458 | ||||||||
\(217\) | −1.54551e92 | −0.792344 | ||||||||
\(218\) | −1.09320e92 | −0.467376 | ||||||||
\(219\) | −3.04234e91 | −0.108559 | ||||||||
\(220\) | 7.23762e91 | 0.215725 | ||||||||
\(221\) | −2.54840e91 | −0.0634999 | ||||||||
\(222\) | −1.24199e93 | −2.58926 | ||||||||
\(223\) | 5.04592e92 | 0.880843 | 0.440421 | − | 0.897791i | \(-0.354829\pi\) | ||||
0.440421 | + | 0.897791i | \(0.354829\pi\) | |||||||
\(224\) | −2.82808e92 | −0.413709 | ||||||||
\(225\) | 1.11962e93 | 1.37360 | ||||||||
\(226\) | −1.36000e92 | −0.140041 | ||||||||
\(227\) | −6.12932e92 | −0.530141 | −0.265070 | − | 0.964229i | \(-0.585395\pi\) | ||||
−0.265070 | + | 0.964229i | \(0.585395\pi\) | |||||||
\(228\) | 3.10012e92 | 0.225399 | ||||||||
\(229\) | 3.04419e93 | 1.86196 | 0.930979 | − | 0.365074i | \(-0.118956\pi\) | ||||
0.930979 | + | 0.365074i | \(0.118956\pi\) | |||||||
\(230\) | 4.32181e93 | 2.22544 | ||||||||
\(231\) | −4.35995e93 | −1.89151 | ||||||||
\(232\) | 1.10312e93 | 0.403505 | ||||||||
\(233\) | −5.71081e93 | −1.76254 | −0.881270 | − | 0.472613i | \(-0.843311\pi\) | ||||
−0.881270 | + | 0.472613i | \(0.843311\pi\) | |||||||
\(234\) | −6.75426e93 | −1.76016 | ||||||||
\(235\) | 9.75532e92 | 0.214813 | ||||||||
\(236\) | 1.82090e93 | 0.339049 | ||||||||
\(237\) | 1.71672e94 | 2.70482 | ||||||||
\(238\) | −7.02038e92 | −0.0936636 | ||||||||
\(239\) | −7.27019e93 | −0.821919 | −0.410959 | − | 0.911654i | \(-0.634806\pi\) | ||||
−0.410959 | + | 0.911654i | \(0.634806\pi\) | |||||||
\(240\) | −2.65865e94 | −2.54869 | ||||||||
\(241\) | 1.42766e94 | 1.16132 | 0.580660 | − | 0.814146i | \(-0.302795\pi\) | ||||
0.580660 | + | 0.814146i | \(0.302795\pi\) | |||||||
\(242\) | 1.94728e93 | 0.134499 | ||||||||
\(243\) | −8.23259e93 | −0.483157 | ||||||||
\(244\) | 3.75375e93 | 0.187313 | ||||||||
\(245\) | 1.35615e94 | 0.575766 | ||||||||
\(246\) | −4.31533e93 | −0.155983 | ||||||||
\(247\) | 2.18944e94 | 0.674222 | ||||||||
\(248\) | 2.25336e94 | 0.591548 | ||||||||
\(249\) | 6.44255e94 | 1.44273 | ||||||||
\(250\) | 1.91251e94 | 0.365573 | ||||||||
\(251\) | −7.23508e94 | −1.18122 | −0.590611 | − | 0.806957i | \(-0.701113\pi\) | ||||
−0.590611 | + | 0.806957i | \(0.701113\pi\) | |||||||
\(252\) | −2.76463e94 | −0.385759 | ||||||||
\(253\) | −1.21934e95 | −1.45500 | ||||||||
\(254\) | −1.09015e95 | −1.11315 | ||||||||
\(255\) | −1.83774e94 | −0.160675 | ||||||||
\(256\) | 6.78868e94 | 0.508518 | ||||||||
\(257\) | 4.59411e94 | 0.295014 | 0.147507 | − | 0.989061i | \(-0.452875\pi\) | ||||
0.147507 | + | 0.989061i | \(0.452875\pi\) | |||||||
\(258\) | 2.59030e95 | 1.42683 | ||||||||
\(259\) | −3.59031e95 | −1.69743 | ||||||||
\(260\) | 4.99822e94 | 0.202940 | ||||||||
\(261\) | 2.38472e95 | 0.832027 | ||||||||
\(262\) | −1.07824e95 | −0.323456 | ||||||||
\(263\) | 3.48081e95 | 0.898313 | 0.449157 | − | 0.893453i | \(-0.351725\pi\) | ||||
0.449157 | + | 0.893453i | \(0.351725\pi\) | |||||||
\(264\) | 6.35682e95 | 1.41216 | ||||||||
\(265\) | −8.84444e95 | −1.69223 | ||||||||
\(266\) | 6.03150e95 | 0.994491 | ||||||||
\(267\) | 1.40430e95 | 0.199648 | ||||||||
\(268\) | 1.21617e94 | 0.0149166 | ||||||||
\(269\) | −6.17619e95 | −0.653891 | −0.326946 | − | 0.945043i | \(-0.606019\pi\) | ||||
−0.326946 | + | 0.945043i | \(0.606019\pi\) | |||||||
\(270\) | −2.23036e96 | −2.03941 | ||||||||
\(271\) | 1.31525e96 | 1.03925 | 0.519626 | − | 0.854394i | \(-0.326071\pi\) | ||||
0.519626 | + | 0.854394i | \(0.326071\pi\) | |||||||
\(272\) | 1.20781e95 | 0.0825138 | ||||||||
\(273\) | −3.01094e96 | −1.77941 | ||||||||
\(274\) | 3.11458e96 | 1.59313 | ||||||||
\(275\) | 1.57325e96 | 0.696879 | ||||||||
\(276\) | −1.19231e96 | −0.457595 | ||||||||
\(277\) | −2.08593e96 | −0.693982 | −0.346991 | − | 0.937868i | \(-0.612797\pi\) | ||||
−0.346991 | + | 0.937868i | \(0.612797\pi\) | |||||||
\(278\) | 1.67738e96 | 0.484018 | ||||||||
\(279\) | 4.87130e96 | 1.21977 | ||||||||
\(280\) | −6.51321e96 | −1.41597 | ||||||||
\(281\) | −8.38622e95 | −0.158368 | −0.0791838 | − | 0.996860i | \(-0.525231\pi\) | ||||
−0.0791838 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(282\) | −1.81134e96 | −0.297275 | ||||||||
\(283\) | 9.06369e96 | 1.29342 | 0.646712 | − | 0.762734i | \(-0.276144\pi\) | ||||
0.646712 | + | 0.762734i | \(0.276144\pi\) | |||||||
\(284\) | 1.73694e96 | 0.215631 | ||||||||
\(285\) | 1.57888e97 | 1.70599 | ||||||||
\(286\) | −9.49089e96 | −0.892995 | ||||||||
\(287\) | −1.24746e96 | −0.102257 | ||||||||
\(288\) | 8.91381e96 | 0.636884 | ||||||||
\(289\) | −1.59661e97 | −0.994798 | ||||||||
\(290\) | −1.18771e97 | −0.645636 | ||||||||
\(291\) | −3.32736e97 | −1.57880 | ||||||||
\(292\) | −2.71077e95 | −0.0112323 | ||||||||
\(293\) | −4.12037e97 | −1.49164 | −0.745821 | − | 0.666146i | \(-0.767943\pi\) | ||||
−0.745821 | + | 0.666146i | \(0.767943\pi\) | |||||||
\(294\) | −2.51804e97 | −0.796790 | ||||||||
\(295\) | 9.27381e97 | 2.56619 | ||||||||
\(296\) | 5.23467e97 | 1.26726 | ||||||||
\(297\) | 6.29264e97 | 1.33338 | ||||||||
\(298\) | 1.13550e97 | 0.210690 | ||||||||
\(299\) | −8.42062e97 | −1.36877 | ||||||||
\(300\) | 1.53838e97 | 0.219167 | ||||||||
\(301\) | 7.48795e97 | 0.935377 | ||||||||
\(302\) | −6.65314e97 | −0.729042 | ||||||||
\(303\) | −6.72127e97 | −0.646350 | ||||||||
\(304\) | −1.03768e98 | −0.876106 | ||||||||
\(305\) | 1.91177e98 | 1.41773 | ||||||||
\(306\) | 2.21275e97 | 0.144190 | ||||||||
\(307\) | 2.87152e97 | 0.164492 | 0.0822462 | − | 0.996612i | \(-0.473791\pi\) | ||||
0.0822462 | + | 0.996612i | \(0.473791\pi\) | |||||||
\(308\) | −3.88478e97 | −0.195710 | ||||||||
\(309\) | −4.09277e98 | −1.81408 | ||||||||
\(310\) | −2.42614e98 | −0.946517 | ||||||||
\(311\) | 1.34411e98 | 0.461741 | 0.230870 | − | 0.972985i | \(-0.425843\pi\) | ||||
0.230870 | + | 0.972985i | \(0.425843\pi\) | |||||||
\(312\) | 4.38995e98 | 1.32847 | ||||||||
\(313\) | 1.81703e98 | 0.484574 | 0.242287 | − | 0.970205i | \(-0.422102\pi\) | ||||
0.242287 | + | 0.970205i | \(0.422102\pi\) | |||||||
\(314\) | 3.87285e98 | 0.910561 | ||||||||
\(315\) | −1.40802e99 | −2.91972 | ||||||||
\(316\) | 1.52962e98 | 0.279862 | ||||||||
\(317\) | −1.07040e98 | −0.172864 | −0.0864319 | − | 0.996258i | \(-0.527546\pi\) | ||||
−0.0864319 | + | 0.996258i | \(0.527546\pi\) | |||||||
\(318\) | 1.64220e99 | 2.34183 | ||||||||
\(319\) | 3.35094e98 | 0.422119 | ||||||||
\(320\) | 9.13493e98 | 1.01691 | ||||||||
\(321\) | −3.58791e98 | −0.353096 | ||||||||
\(322\) | −2.31973e99 | −2.01897 | ||||||||
\(323\) | −7.17278e97 | −0.0552316 | ||||||||
\(324\) | 1.42948e98 | 0.0974206 | ||||||||
\(325\) | 1.08647e99 | 0.655581 | ||||||||
\(326\) | −4.06480e96 | −0.00217242 | ||||||||
\(327\) | 1.53601e99 | 0.727373 | ||||||||
\(328\) | 1.81880e98 | 0.0763430 | ||||||||
\(329\) | −5.23616e98 | −0.194883 | ||||||||
\(330\) | −6.84422e99 | −2.25956 | ||||||||
\(331\) | −6.59239e99 | −1.93124 | −0.965622 | − | 0.259951i | \(-0.916294\pi\) | ||||
−0.965622 | + | 0.259951i | \(0.916294\pi\) | |||||||
\(332\) | 5.74042e98 | 0.149276 | ||||||||
\(333\) | 1.13163e100 | 2.61310 | ||||||||
\(334\) | −7.55464e99 | −1.54963 | ||||||||
\(335\) | 6.19391e98 | 0.112900 | ||||||||
\(336\) | 1.42703e100 | 2.31223 | ||||||||
\(337\) | 4.54396e99 | 0.654716 | 0.327358 | − | 0.944900i | \(-0.393842\pi\) | ||||
0.327358 | + | 0.944900i | \(0.393842\pi\) | |||||||
\(338\) | 1.90117e99 | 0.243675 | ||||||||
\(339\) | 1.91088e99 | 0.217944 | ||||||||
\(340\) | −1.63746e98 | −0.0166247 | ||||||||
\(341\) | 6.84501e99 | 0.618837 | ||||||||
\(342\) | −1.90107e100 | −1.53097 | ||||||||
\(343\) | 9.41955e99 | 0.675947 | ||||||||
\(344\) | −1.09175e100 | −0.698333 | ||||||||
\(345\) | −6.07240e100 | −3.46343 | ||||||||
\(346\) | 2.00300e100 | 1.01900 | ||||||||
\(347\) | 3.55374e100 | 1.61314 | 0.806569 | − | 0.591140i | \(-0.201322\pi\) | ||||
0.806569 | + | 0.591140i | \(0.201322\pi\) | |||||||
\(348\) | 3.27667e99 | 0.132756 | ||||||||
\(349\) | −4.60202e100 | −1.66473 | −0.832366 | − | 0.554227i | \(-0.813014\pi\) | ||||
−0.832366 | + | 0.554227i | \(0.813014\pi\) | |||||||
\(350\) | 2.99303e100 | 0.966994 | ||||||||
\(351\) | 4.34563e100 | 1.25436 | ||||||||
\(352\) | 1.25254e100 | 0.323115 | ||||||||
\(353\) | 1.55847e100 | 0.359416 | 0.179708 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179708 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(354\) | −1.72193e101 | −3.55129 | ||||||||
\(355\) | 8.84618e100 | 1.63206 | ||||||||
\(356\) | 1.25125e99 | 0.0206571 | ||||||||
\(357\) | 9.86406e99 | 0.145768 | ||||||||
\(358\) | 9.30831e100 | 1.23166 | ||||||||
\(359\) | −1.48242e101 | −1.75687 | −0.878436 | − | 0.477859i | \(-0.841413\pi\) | ||||
−0.878436 | + | 0.477859i | \(0.841413\pi\) | |||||||
\(360\) | 2.05289e101 | 2.17981 | ||||||||
\(361\) | −4.34592e100 | −0.413568 | ||||||||
\(362\) | 1.45798e101 | 1.24383 | ||||||||
\(363\) | −2.73604e100 | −0.209320 | ||||||||
\(364\) | −2.68279e100 | −0.184112 | ||||||||
\(365\) | −1.38059e100 | −0.0850151 | ||||||||
\(366\) | −3.54972e101 | −1.96196 | ||||||||
\(367\) | −3.28023e101 | −1.62777 | −0.813887 | − | 0.581023i | \(-0.802653\pi\) | ||||
−0.813887 | + | 0.581023i | \(0.802653\pi\) | |||||||
\(368\) | 3.99093e101 | 1.77863 | ||||||||
\(369\) | 3.93187e100 | 0.157419 | ||||||||
\(370\) | −5.63604e101 | −2.02771 | ||||||||
\(371\) | 4.74724e101 | 1.53522 | ||||||||
\(372\) | 6.69329e100 | 0.194623 | ||||||||
\(373\) | −4.44406e100 | −0.116220 | −0.0581100 | − | 0.998310i | \(-0.518507\pi\) | ||||
−0.0581100 | + | 0.998310i | \(0.518507\pi\) | |||||||
\(374\) | 3.10929e100 | 0.0731532 | ||||||||
\(375\) | −2.68720e101 | −0.568937 | ||||||||
\(376\) | 7.63433e100 | 0.145496 | ||||||||
\(377\) | 2.31413e101 | 0.397103 | ||||||||
\(378\) | 1.19714e102 | 1.85020 | ||||||||
\(379\) | −8.31944e101 | −1.15836 | −0.579182 | − | 0.815198i | \(-0.696628\pi\) | ||||
−0.579182 | + | 0.815198i | \(0.696628\pi\) | |||||||
\(380\) | 1.40681e101 | 0.176515 | ||||||||
\(381\) | 1.53172e102 | 1.73238 | ||||||||
\(382\) | 4.52143e101 | 0.461076 | ||||||||
\(383\) | 3.50121e101 | 0.322008 | 0.161004 | − | 0.986954i | \(-0.448527\pi\) | ||||
0.161004 | + | 0.986954i | \(0.448527\pi\) | |||||||
\(384\) | −2.39798e102 | −1.98958 | ||||||||
\(385\) | −1.97851e102 | −1.48129 | ||||||||
\(386\) | 9.17539e101 | 0.620049 | ||||||||
\(387\) | −2.36012e102 | −1.43996 | ||||||||
\(388\) | −2.96473e101 | −0.163355 | ||||||||
\(389\) | 3.91980e102 | 1.95099 | 0.975495 | − | 0.220020i | \(-0.0706123\pi\) | ||||
0.975495 | + | 0.220020i | \(0.0706123\pi\) | |||||||
\(390\) | −4.72655e102 | −2.12565 | ||||||||
\(391\) | 2.75866e101 | 0.112129 | ||||||||
\(392\) | 1.06129e102 | 0.389974 | ||||||||
\(393\) | 1.51500e102 | 0.503392 | ||||||||
\(394\) | −2.05543e102 | −0.617736 | ||||||||
\(395\) | 7.79032e102 | 2.11821 | ||||||||
\(396\) | 1.22444e102 | 0.301286 | ||||||||
\(397\) | 9.85040e101 | 0.219396 | 0.109698 | − | 0.993965i | \(-0.465012\pi\) | ||||
0.109698 | + | 0.993965i | \(0.465012\pi\) | |||||||
\(398\) | 4.00537e102 | 0.807722 | ||||||||
\(399\) | −8.47463e102 | −1.54772 | ||||||||
\(400\) | −5.14931e102 | −0.851882 | ||||||||
\(401\) | −1.90633e102 | −0.285757 | −0.142878 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142878 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(402\) | −1.15006e102 | −0.156240 | ||||||||
\(403\) | 4.72709e102 | 0.582163 | ||||||||
\(404\) | −5.98876e101 | −0.0668764 | ||||||||
\(405\) | 7.28031e102 | 0.737354 | ||||||||
\(406\) | 6.37499e102 | 0.585735 | ||||||||
\(407\) | 1.59013e103 | 1.32572 | ||||||||
\(408\) | −1.43818e102 | −0.108827 | ||||||||
\(409\) | −2.16826e103 | −1.48950 | −0.744751 | − | 0.667342i | \(-0.767432\pi\) | ||||
−0.744751 | + | 0.667342i | \(0.767432\pi\) | |||||||
\(410\) | −1.95826e102 | −0.122154 | ||||||||
\(411\) | −4.37617e103 | −2.47938 | ||||||||
\(412\) | −3.64672e102 | −0.187699 | ||||||||
\(413\) | −4.97771e103 | −2.32810 | ||||||||
\(414\) | 7.31153e103 | 3.10810 | ||||||||
\(415\) | 2.92358e103 | 1.12983 | ||||||||
\(416\) | 8.64993e102 | 0.303967 | ||||||||
\(417\) | −2.35682e103 | −0.753273 | ||||||||
\(418\) | −2.67132e103 | −0.776718 | ||||||||
\(419\) | 4.16825e103 | 1.10281 | 0.551404 | − | 0.834238i | \(-0.314092\pi\) | ||||
0.551404 | + | 0.834238i | \(0.314092\pi\) | |||||||
\(420\) | −1.93465e103 | −0.465861 | ||||||||
\(421\) | 7.48726e103 | 1.64127 | 0.820635 | − | 0.571452i | \(-0.193620\pi\) | ||||
0.820635 | + | 0.571452i | \(0.193620\pi\) | |||||||
\(422\) | 9.71632e103 | 1.93937 | ||||||||
\(423\) | 1.65038e103 | 0.300013 | ||||||||
\(424\) | −6.92149e103 | −1.14617 | ||||||||
\(425\) | −3.55937e102 | −0.0537045 | ||||||||
\(426\) | −1.64253e104 | −2.25857 | ||||||||
\(427\) | −1.02614e104 | −1.28619 | ||||||||
\(428\) | −3.19688e102 | −0.0365341 | ||||||||
\(429\) | 1.33353e104 | 1.38976 | ||||||||
\(430\) | 1.17545e104 | 1.11738 | ||||||||
\(431\) | 5.01983e102 | 0.0435348 | 0.0217674 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217674 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(432\) | −2.05960e104 | −1.62995 | ||||||||
\(433\) | −2.28973e104 | −1.65391 | −0.826957 | − | 0.562265i | \(-0.809930\pi\) | ||||
−0.826957 | + | 0.562265i | \(0.809930\pi\) | |||||||
\(434\) | 1.30223e104 | 0.858702 | ||||||||
\(435\) | 1.66880e104 | 1.00480 | ||||||||
\(436\) | 1.36861e103 | 0.0752596 | ||||||||
\(437\) | −2.37008e104 | −1.19055 | ||||||||
\(438\) | 2.56343e103 | 0.117651 | ||||||||
\(439\) | 1.98050e104 | 0.830664 | 0.415332 | − | 0.909670i | \(-0.363665\pi\) | ||||
0.415332 | + | 0.909670i | \(0.363665\pi\) | |||||||
\(440\) | 2.88467e104 | 1.10590 | ||||||||
\(441\) | 2.29429e104 | 0.804126 | ||||||||
\(442\) | 2.14724e103 | 0.0688180 | ||||||||
\(443\) | −1.06558e104 | −0.312347 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(444\) | 1.55488e104 | 0.416937 | ||||||||
\(445\) | 6.37259e103 | 0.156349 | ||||||||
\(446\) | −4.25161e104 | −0.954612 | ||||||||
\(447\) | −1.59544e104 | −0.327894 | ||||||||
\(448\) | −4.90316e104 | −0.922560 | ||||||||
\(449\) | 6.69918e104 | 1.15423 | 0.577113 | − | 0.816664i | \(-0.304179\pi\) | ||||
0.577113 | + | 0.816664i | \(0.304179\pi\) | |||||||
\(450\) | −9.43372e104 | −1.48864 | ||||||||
\(451\) | 5.52496e103 | 0.0798648 | ||||||||
\(452\) | 1.70262e103 | 0.0225502 | ||||||||
\(453\) | 9.34807e104 | 1.13460 | ||||||||
\(454\) | 5.16447e104 | 0.574540 | ||||||||
\(455\) | −1.36634e105 | −1.39350 | ||||||||
\(456\) | 1.23560e105 | 1.15549 | ||||||||
\(457\) | 1.78653e104 | 0.153222 | 0.0766108 | − | 0.997061i | \(-0.475590\pi\) | ||||
0.0766108 | + | 0.997061i | \(0.475590\pi\) | |||||||
\(458\) | −2.56498e105 | −2.01789 | ||||||||
\(459\) | −1.42366e104 | −0.102756 | ||||||||
\(460\) | −5.41061e104 | −0.358353 | ||||||||
\(461\) | −1.12025e105 | −0.680971 | −0.340486 | − | 0.940250i | \(-0.610591\pi\) | ||||
−0.340486 | + | 0.940250i | \(0.610591\pi\) | |||||||
\(462\) | 3.67363e105 | 2.04992 | ||||||||
\(463\) | −8.78634e104 | −0.450152 | −0.225076 | − | 0.974341i | \(-0.572263\pi\) | ||||
−0.225076 | + | 0.974341i | \(0.572263\pi\) | |||||||
\(464\) | −1.09677e105 | −0.516009 | ||||||||
\(465\) | 3.40887e105 | 1.47306 | ||||||||
\(466\) | 4.81184e105 | 1.91015 | ||||||||
\(467\) | −7.04870e104 | −0.257094 | −0.128547 | − | 0.991703i | \(-0.541031\pi\) | ||||
−0.128547 | + | 0.991703i | \(0.541031\pi\) | |||||||
\(468\) | 8.45586e104 | 0.283431 | ||||||||
\(469\) | −3.32457e104 | −0.102426 | ||||||||
\(470\) | −8.21969e104 | −0.232804 | ||||||||
\(471\) | −5.44158e105 | −1.41710 | ||||||||
\(472\) | 7.25750e105 | 1.73811 | ||||||||
\(473\) | −3.31638e105 | −0.730548 | ||||||||
\(474\) | −1.44648e106 | −2.93135 | ||||||||
\(475\) | 3.05801e105 | 0.570218 | ||||||||
\(476\) | 8.78903e103 | 0.0150823 | ||||||||
\(477\) | −1.49628e106 | −2.36340 | ||||||||
\(478\) | 6.12575e105 | 0.890753 | ||||||||
\(479\) | 2.95510e105 | 0.395658 | 0.197829 | − | 0.980237i | \(-0.436611\pi\) | ||||
0.197829 | + | 0.980237i | \(0.436611\pi\) | |||||||
\(480\) | 6.23777e105 | 0.769132 | ||||||||
\(481\) | 1.09813e106 | 1.24716 | ||||||||
\(482\) | −1.20292e106 | −1.25858 | ||||||||
\(483\) | 3.25936e106 | 3.14210 | ||||||||
\(484\) | −2.43785e104 | −0.0216579 | ||||||||
\(485\) | −1.50993e106 | −1.23639 | ||||||||
\(486\) | 6.93665e105 | 0.523621 | ||||||||
\(487\) | −2.60640e106 | −1.81404 | −0.907020 | − | 0.421087i | \(-0.861649\pi\) | ||||
−0.907020 | + | 0.421087i | \(0.861649\pi\) | |||||||
\(488\) | 1.49612e106 | 0.960246 | ||||||||
\(489\) | 5.71129e103 | 0.00338092 | ||||||||
\(490\) | −1.14267e106 | −0.623985 | ||||||||
\(491\) | 2.32180e106 | 1.16979 | 0.584893 | − | 0.811111i | \(-0.301137\pi\) | ||||
0.584893 | + | 0.811111i | \(0.301137\pi\) | |||||||
\(492\) | 5.40249e104 | 0.0251173 | ||||||||
\(493\) | −7.58126e104 | −0.0325303 | ||||||||
\(494\) | −1.84479e106 | −0.730688 | ||||||||
\(495\) | 6.23605e106 | 2.28036 | ||||||||
\(496\) | −2.24039e106 | −0.756481 | ||||||||
\(497\) | −4.74818e106 | −1.48064 | ||||||||
\(498\) | −5.42840e106 | −1.56355 | ||||||||
\(499\) | −4.48706e106 | −1.19396 | −0.596981 | − | 0.802256i | \(-0.703633\pi\) | ||||
−0.596981 | + | 0.802256i | \(0.703633\pi\) | |||||||
\(500\) | −2.39433e105 | −0.0588667 | ||||||||
\(501\) | 1.06147e107 | 2.41167 | ||||||||
\(502\) | 6.09617e106 | 1.28015 | ||||||||
\(503\) | −1.36594e106 | −0.265152 | −0.132576 | − | 0.991173i | \(-0.542325\pi\) | ||||
−0.132576 | + | 0.991173i | \(0.542325\pi\) | |||||||
\(504\) | −1.10189e107 | −1.97757 | ||||||||
\(505\) | −3.05006e106 | −0.506172 | ||||||||
\(506\) | 1.02740e107 | 1.57686 | ||||||||
\(507\) | −2.67126e106 | −0.379229 | ||||||||
\(508\) | 1.36479e106 | 0.179246 | ||||||||
\(509\) | 1.91849e106 | 0.233135 | 0.116568 | − | 0.993183i | \(-0.462811\pi\) | ||||
0.116568 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(510\) | 1.54845e106 | 0.174131 | ||||||||
\(511\) | 7.41029e105 | 0.0771276 | ||||||||
\(512\) | 6.52347e106 | 0.628515 | ||||||||
\(513\) | 1.22313e107 | 1.09103 | ||||||||
\(514\) | −3.87092e106 | −0.319721 | ||||||||
\(515\) | −1.85726e107 | −1.42065 | ||||||||
\(516\) | −3.24287e106 | −0.229756 | ||||||||
\(517\) | 2.31907e106 | 0.152208 | ||||||||
\(518\) | 3.02514e107 | 1.83958 | ||||||||
\(519\) | −2.81433e107 | −1.58586 | ||||||||
\(520\) | 1.99212e107 | 1.04036 | ||||||||
\(521\) | 3.81999e106 | 0.184915 | 0.0924575 | − | 0.995717i | \(-0.470528\pi\) | ||||
0.0924575 | + | 0.995717i | \(0.470528\pi\) | |||||||
\(522\) | −2.00933e107 | −0.901709 | ||||||||
\(523\) | −2.09703e107 | −0.872546 | −0.436273 | − | 0.899814i | \(-0.643702\pi\) | ||||
−0.436273 | + | 0.899814i | \(0.643702\pi\) | |||||||
\(524\) | 1.34989e106 | 0.0520848 | ||||||||
\(525\) | −4.20540e107 | −1.50492 | ||||||||
\(526\) | −2.93287e107 | −0.973546 | ||||||||
\(527\) | −1.54863e106 | −0.0476902 | ||||||||
\(528\) | −6.32023e107 | −1.80590 | ||||||||
\(529\) | 5.34400e107 | 1.41699 | ||||||||
\(530\) | 7.45219e107 | 1.83395 | ||||||||
\(531\) | 1.56892e108 | 3.58399 | ||||||||
\(532\) | −7.55103e106 | −0.160139 | ||||||||
\(533\) | 3.81548e106 | 0.0751318 | ||||||||
\(534\) | −1.18324e107 | −0.216368 | ||||||||
\(535\) | −1.62816e107 | −0.276518 | ||||||||
\(536\) | 4.84723e106 | 0.0764689 | ||||||||
\(537\) | −1.30787e108 | −1.91682 | ||||||||
\(538\) | 5.20396e107 | 0.708654 | ||||||||
\(539\) | 3.22387e107 | 0.407964 | ||||||||
\(540\) | 2.79225e107 | 0.328398 | ||||||||
\(541\) | −2.74852e107 | −0.300475 | −0.150237 | − | 0.988650i | \(-0.548004\pi\) | ||||
−0.150237 | + | 0.988650i | \(0.548004\pi\) | |||||||
\(542\) | −1.10821e108 | −1.12629 | ||||||||
\(543\) | −2.04855e108 | −1.93576 | ||||||||
\(544\) | −2.83379e106 | −0.0249006 | ||||||||
\(545\) | 6.97027e107 | 0.569623 | ||||||||
\(546\) | 2.53697e108 | 1.92844 | ||||||||
\(547\) | −1.01588e108 | −0.718363 | −0.359181 | − | 0.933268i | \(-0.616944\pi\) | ||||
−0.359181 | + | 0.933268i | \(0.616944\pi\) | |||||||
\(548\) | −3.89924e107 | −0.256535 | ||||||||
\(549\) | 3.23429e108 | 1.98003 | ||||||||
\(550\) | −1.32560e108 | −0.755242 | ||||||||
\(551\) | 6.51338e107 | 0.345397 | ||||||||
\(552\) | −4.75215e108 | −2.34583 | ||||||||
\(553\) | −4.18144e108 | −1.92169 | ||||||||
\(554\) | 1.75757e108 | 0.752103 | ||||||||
\(555\) | 7.91898e108 | 3.15570 | ||||||||
\(556\) | −2.09996e107 | −0.0779395 | ||||||||
\(557\) | 6.78169e107 | 0.234454 | 0.117227 | − | 0.993105i | \(-0.462599\pi\) | ||||
0.117227 | + | 0.993105i | \(0.462599\pi\) | |||||||
\(558\) | −4.10448e108 | −1.32193 | ||||||||
\(559\) | −2.29026e108 | −0.687254 | ||||||||
\(560\) | 6.47572e108 | 1.81076 | ||||||||
\(561\) | −4.36874e107 | −0.113848 | ||||||||
\(562\) | 7.06610e107 | 0.171631 | ||||||||
\(563\) | 6.00806e108 | 1.36036 | 0.680178 | − | 0.733047i | \(-0.261903\pi\) | ||||
0.680178 | + | 0.733047i | \(0.261903\pi\) | |||||||
\(564\) | 2.26767e107 | 0.0478690 | ||||||||
\(565\) | 8.67140e107 | 0.170677 | ||||||||
\(566\) | −7.63692e108 | −1.40175 | ||||||||
\(567\) | −3.90770e108 | −0.668944 | ||||||||
\(568\) | 6.92285e108 | 1.10542 | ||||||||
\(569\) | −1.02026e109 | −1.51976 | −0.759881 | − | 0.650062i | \(-0.774743\pi\) | ||||
−0.759881 | + | 0.650062i | \(0.774743\pi\) | |||||||
\(570\) | −1.33034e109 | −1.84887 | ||||||||
\(571\) | 1.13551e109 | 1.47253 | 0.736264 | − | 0.676694i | \(-0.236588\pi\) | ||||
0.736264 | + | 0.676694i | \(0.236588\pi\) | |||||||
\(572\) | 1.18819e108 | 0.143795 | ||||||||
\(573\) | −6.35288e108 | −0.717568 | ||||||||
\(574\) | 1.05109e108 | 0.110821 | ||||||||
\(575\) | −1.17611e109 | −1.15763 | ||||||||
\(576\) | 1.54542e109 | 1.42023 | ||||||||
\(577\) | 2.13763e108 | 0.183438 | 0.0917189 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917189 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(578\) | 1.34528e109 | 1.07811 | ||||||||
\(579\) | −1.28920e109 | −0.964976 | ||||||||
\(580\) | 1.48692e108 | 0.103964 | ||||||||
\(581\) | −1.56923e109 | −1.02501 | ||||||||
\(582\) | 2.80358e109 | 1.71102 | ||||||||
\(583\) | −2.10253e109 | −1.19904 | ||||||||
\(584\) | −1.08042e108 | −0.0575819 | ||||||||
\(585\) | 4.30655e109 | 2.14522 | ||||||||
\(586\) | 3.47176e109 | 1.61657 | ||||||||
\(587\) | −4.78489e108 | −0.208289 | −0.104145 | − | 0.994562i | \(-0.533211\pi\) | ||||
−0.104145 | + | 0.994562i | \(0.533211\pi\) | |||||||
\(588\) | 3.15242e108 | 0.128304 | ||||||||
\(589\) | 1.33049e109 | 0.506360 | ||||||||
\(590\) | −7.81397e109 | −2.78110 | ||||||||
\(591\) | 2.88801e109 | 0.961376 | ||||||||
\(592\) | −5.20454e109 | −1.62060 | ||||||||
\(593\) | −1.37706e108 | −0.0401137 | −0.0200568 | − | 0.999799i | \(-0.506385\pi\) | ||||
−0.0200568 | + | 0.999799i | \(0.506385\pi\) | |||||||
\(594\) | −5.30208e109 | −1.44505 | ||||||||
\(595\) | 4.47623e108 | 0.114154 | ||||||||
\(596\) | −1.42156e108 | −0.0339265 | ||||||||
\(597\) | −5.62780e109 | −1.25705 | ||||||||
\(598\) | 7.09508e109 | 1.48341 | ||||||||
\(599\) | 1.69678e108 | 0.0332097 | 0.0166049 | − | 0.999862i | \(-0.494714\pi\) | ||||
0.0166049 | + | 0.999862i | \(0.494714\pi\) | |||||||
\(600\) | 6.13147e109 | 1.12355 | ||||||||
\(601\) | 5.53355e109 | 0.949428 | 0.474714 | − | 0.880140i | \(-0.342551\pi\) | ||||
0.474714 | + | 0.880140i | \(0.342551\pi\) | |||||||
\(602\) | −6.30923e109 | −1.01371 | ||||||||
\(603\) | 1.04787e109 | 0.157679 | ||||||||
\(604\) | 8.32928e108 | 0.117395 | ||||||||
\(605\) | −1.24159e109 | −0.163924 | ||||||||
\(606\) | 5.66324e109 | 0.700481 | ||||||||
\(607\) | 8.72796e109 | 1.01148 | 0.505742 | − | 0.862684i | \(-0.331219\pi\) | ||||
0.505742 | + | 0.862684i | \(0.331219\pi\) | |||||||
\(608\) | 2.43463e109 | 0.264387 | ||||||||
\(609\) | −8.95725e109 | −0.911574 | ||||||||
\(610\) | −1.61083e110 | −1.53646 | ||||||||
\(611\) | 1.60152e109 | 0.143188 | ||||||||
\(612\) | −2.77021e108 | −0.0232183 | ||||||||
\(613\) | 9.62870e109 | 0.756622 | 0.378311 | − | 0.925679i | \(-0.376505\pi\) | ||||
0.378311 | + | 0.925679i | \(0.376505\pi\) | |||||||
\(614\) | −2.41950e109 | −0.178269 | ||||||||
\(615\) | 2.75147e109 | 0.190107 | ||||||||
\(616\) | −1.54834e110 | −1.00330 | ||||||||
\(617\) | 1.93190e110 | 1.17414 | 0.587071 | − | 0.809536i | \(-0.300281\pi\) | ||||
0.587071 | + | 0.809536i | \(0.300281\pi\) | |||||||
\(618\) | 3.44850e110 | 1.96601 | ||||||||
\(619\) | 4.62898e109 | 0.247574 | 0.123787 | − | 0.992309i | \(-0.460496\pi\) | ||||
0.123787 | + | 0.992309i | \(0.460496\pi\) | |||||||
\(620\) | 3.03736e109 | 0.152414 | ||||||||
\(621\) | −4.70417e110 | −2.21495 | ||||||||
\(622\) | −1.13252e110 | −0.500411 | ||||||||
\(623\) | −3.42048e109 | −0.141844 | ||||||||
\(624\) | −4.36468e110 | −1.69887 | ||||||||
\(625\) | −3.25737e110 | −1.19016 | ||||||||
\(626\) | −1.53100e110 | −0.525157 | ||||||||
\(627\) | 3.75337e110 | 1.20880 | ||||||||
\(628\) | −4.84853e109 | −0.146624 | ||||||||
\(629\) | −3.59755e109 | −0.102166 | ||||||||
\(630\) | 1.18637e111 | 3.16425 | ||||||||
\(631\) | 2.31441e110 | 0.579804 | 0.289902 | − | 0.957056i | \(-0.406377\pi\) | ||||
0.289902 | + | 0.957056i | \(0.406377\pi\) | |||||||
\(632\) | 6.09655e110 | 1.43470 | ||||||||
\(633\) | −1.36520e111 | −3.01822 | ||||||||
\(634\) | 9.01900e109 | 0.187341 | ||||||||
\(635\) | 6.95083e110 | 1.35667 | ||||||||
\(636\) | −2.05593e110 | −0.377096 | ||||||||
\(637\) | 2.22637e110 | 0.383787 | ||||||||
\(638\) | −2.82345e110 | −0.457471 | ||||||||
\(639\) | 1.49657e111 | 2.27937 | ||||||||
\(640\) | −1.08818e111 | −1.55809 | ||||||||
\(641\) | −3.59419e110 | −0.483848 | −0.241924 | − | 0.970295i | \(-0.577778\pi\) | ||||
−0.241924 | + | 0.970295i | \(0.577778\pi\) | |||||||
\(642\) | 3.02312e110 | 0.382668 | ||||||||
\(643\) | −8.26218e110 | −0.983470 | −0.491735 | − | 0.870745i | \(-0.663637\pi\) | ||||
−0.491735 | + | 0.870745i | \(0.663637\pi\) | |||||||
\(644\) | 2.90414e110 | 0.325106 | ||||||||
\(645\) | −1.65158e111 | −1.73897 | ||||||||
\(646\) | 6.04367e109 | 0.0598572 | ||||||||
\(647\) | −1.00058e111 | −0.932253 | −0.466127 | − | 0.884718i | \(-0.654351\pi\) | ||||
−0.466127 | + | 0.884718i | \(0.654351\pi\) | |||||||
\(648\) | 5.69743e110 | 0.499420 | ||||||||
\(649\) | 2.20460e111 | 1.81830 | ||||||||
\(650\) | −9.15445e110 | −0.710485 | ||||||||
\(651\) | −1.82971e111 | −1.33639 | ||||||||
\(652\) | 5.08885e107 | 0.000349816 0 | ||||||||
\(653\) | 2.19401e111 | 1.41961 | 0.709803 | − | 0.704400i | \(-0.248784\pi\) | ||||
0.709803 | + | 0.704400i | \(0.248784\pi\) | |||||||
\(654\) | −1.29422e111 | −0.788289 | ||||||||
\(655\) | 6.87493e110 | 0.394218 | ||||||||
\(656\) | −1.80834e110 | −0.0976287 | ||||||||
\(657\) | −2.33564e110 | −0.118734 | ||||||||
\(658\) | 4.41191e110 | 0.211205 | ||||||||
\(659\) | 2.97784e111 | 1.34254 | 0.671271 | − | 0.741212i | \(-0.265749\pi\) | ||||
0.671271 | + | 0.741212i | \(0.265749\pi\) | |||||||
\(660\) | 8.56849e110 | 0.363847 | ||||||||
\(661\) | −1.56534e111 | −0.626110 | −0.313055 | − | 0.949735i | \(-0.601352\pi\) | ||||
−0.313055 | + | 0.949735i | \(0.601352\pi\) | |||||||
\(662\) | 5.55464e111 | 2.09298 | ||||||||
\(663\) | −3.01701e110 | −0.107101 | ||||||||
\(664\) | 2.28793e111 | 0.765252 | ||||||||
\(665\) | −3.84572e111 | −1.21205 | ||||||||
\(666\) | −9.53491e111 | −2.83194 | ||||||||
\(667\) | −2.50506e111 | −0.701208 | ||||||||
\(668\) | 9.45788e110 | 0.249531 | ||||||||
\(669\) | 5.97378e111 | 1.48565 | ||||||||
\(670\) | −5.21889e110 | −0.122356 | ||||||||
\(671\) | 4.54473e111 | 1.00454 | ||||||||
\(672\) | −3.34812e111 | −0.697773 | ||||||||
\(673\) | −5.99621e111 | −1.17837 | −0.589185 | − | 0.807998i | \(-0.700551\pi\) | ||||
−0.589185 | + | 0.807998i | \(0.700551\pi\) | |||||||
\(674\) | −3.82867e111 | −0.709548 | ||||||||
\(675\) | 6.06957e111 | 1.06086 | ||||||||
\(676\) | −2.38013e110 | −0.0392380 | ||||||||
\(677\) | 3.39075e111 | 0.527282 | 0.263641 | − | 0.964621i | \(-0.415077\pi\) | ||||
0.263641 | + | 0.964621i | \(0.415077\pi\) | |||||||
\(678\) | −1.61008e111 | −0.236197 | ||||||||
\(679\) | 8.10451e111 | 1.12168 | ||||||||
\(680\) | −6.52635e110 | −0.0852252 | ||||||||
\(681\) | −7.25640e111 | −0.894150 | ||||||||
\(682\) | −5.76750e111 | −0.670663 | ||||||||
\(683\) | −5.01990e111 | −0.550905 | −0.275453 | − | 0.961315i | \(-0.588828\pi\) | ||||
−0.275453 | + | 0.961315i | \(0.588828\pi\) | |||||||
\(684\) | 2.38000e111 | 0.246525 | ||||||||
\(685\) | −1.98587e112 | −1.94166 | ||||||||
\(686\) | −7.93677e111 | −0.732557 | ||||||||
\(687\) | 3.60396e112 | 3.14043 | ||||||||
\(688\) | 1.08546e112 | 0.893040 | ||||||||
\(689\) | −1.45198e112 | −1.12798 | ||||||||
\(690\) | 5.11651e112 | 3.75349 | ||||||||
\(691\) | 2.42401e112 | 1.67939 | 0.839696 | − | 0.543057i | \(-0.182733\pi\) | ||||
0.839696 | + | 0.543057i | \(0.182733\pi\) | |||||||
\(692\) | −2.50761e111 | −0.164085 | ||||||||
\(693\) | −3.34719e112 | −2.06880 | ||||||||
\(694\) | −2.99433e112 | −1.74824 | ||||||||
\(695\) | −1.06951e112 | −0.589906 | ||||||||
\(696\) | 1.30597e112 | 0.680563 | ||||||||
\(697\) | −1.24998e110 | −0.00615472 | ||||||||
\(698\) | 3.87759e112 | 1.80415 | ||||||||
\(699\) | −6.76093e112 | −2.97275 | ||||||||
\(700\) | −3.74707e111 | −0.155711 | ||||||||
\(701\) | −3.79533e112 | −1.49069 | −0.745346 | − | 0.666678i | \(-0.767716\pi\) | ||||
−0.745346 | + | 0.666678i | \(0.767716\pi\) | |||||||
\(702\) | −3.66156e112 | −1.35941 | ||||||||
\(703\) | 3.09081e112 | 1.08477 | ||||||||
\(704\) | 2.17159e112 | 0.720538 | ||||||||
\(705\) | 1.15492e112 | 0.362310 | ||||||||
\(706\) | −1.31314e112 | −0.389517 | ||||||||
\(707\) | 1.63711e112 | 0.459211 | ||||||||
\(708\) | 2.15574e112 | 0.571850 | ||||||||
\(709\) | 4.39351e112 | 1.10226 | 0.551131 | − | 0.834419i | \(-0.314196\pi\) | ||||
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(710\) | −7.45366e112 | −1.76874 | ||||||||
\(711\) | 1.31795e113 | 2.95834 | ||||||||
\(712\) | 4.98707e111 | 0.105898 | ||||||||
\(713\) | −5.11710e112 | −1.02799 | ||||||||
\(714\) | −8.31131e111 | −0.157976 | ||||||||
\(715\) | 6.05144e112 | 1.08835 | ||||||||
\(716\) | −1.16534e112 | −0.198329 | ||||||||
\(717\) | −8.60706e112 | −1.38627 | ||||||||
\(718\) | 1.24906e113 | 1.90401 | ||||||||
\(719\) | −8.57228e112 | −1.23682 | −0.618408 | − | 0.785857i | \(-0.712222\pi\) | ||||
−0.618408 | + | 0.785857i | \(0.712222\pi\) | |||||||
\(720\) | −2.04108e113 | −2.78757 | ||||||||
\(721\) | 9.96884e112 | 1.28885 | ||||||||
\(722\) | 3.66180e112 | 0.448204 | ||||||||
\(723\) | 1.69018e113 | 1.95871 | ||||||||
\(724\) | −1.82529e112 | −0.200289 | ||||||||
\(725\) | 3.23216e112 | 0.335847 | ||||||||
\(726\) | 2.30535e112 | 0.226850 | ||||||||
\(727\) | −1.80771e113 | −1.68469 | −0.842344 | − | 0.538940i | \(-0.818825\pi\) | ||||
−0.842344 | + | 0.538940i | \(0.818825\pi\) | |||||||
\(728\) | −1.06927e113 | −0.943838 | ||||||||
\(729\) | −1.64231e113 | −1.37315 | ||||||||
\(730\) | 1.16326e112 | 0.0921350 | ||||||||
\(731\) | 7.50306e111 | 0.0562992 | ||||||||
\(732\) | 4.44400e112 | 0.315927 | ||||||||
\(733\) | −1.18515e113 | −0.798300 | −0.399150 | − | 0.916886i | \(-0.630695\pi\) | ||||
−0.399150 | + | 0.916886i | \(0.630695\pi\) | |||||||
\(734\) | 2.76387e113 | 1.76410 | ||||||||
\(735\) | 1.60552e113 | 0.971102 | ||||||||
\(736\) | −9.36361e112 | −0.536747 | ||||||||
\(737\) | 1.47244e112 | 0.0799965 | ||||||||
\(738\) | −3.31293e112 | −0.170603 | ||||||||
\(739\) | 1.08752e113 | 0.530865 | 0.265432 | − | 0.964130i | \(-0.414485\pi\) | ||||
0.265432 | + | 0.964130i | \(0.414485\pi\) | |||||||
\(740\) | 7.05593e112 | 0.326514 | ||||||||
\(741\) | 2.59204e113 | 1.13716 | ||||||||
\(742\) | −3.99995e113 | −1.66380 | ||||||||
\(743\) | −3.36935e113 | −1.32889 | −0.664443 | − | 0.747339i | \(-0.731331\pi\) | ||||
−0.664443 | + | 0.747339i | \(0.731331\pi\) | |||||||
\(744\) | 2.66772e113 | 0.997720 | ||||||||
\(745\) | −7.23998e112 | −0.256782 | ||||||||
\(746\) | 3.74449e112 | 0.125953 | ||||||||
\(747\) | 4.94603e113 | 1.57795 | ||||||||
\(748\) | −3.89262e111 | −0.0117796 | ||||||||
\(749\) | 8.73915e112 | 0.250863 | ||||||||
\(750\) | 2.26419e113 | 0.616585 | ||||||||
\(751\) | −1.70764e112 | −0.0441184 | −0.0220592 | − | 0.999757i | \(-0.507022\pi\) | ||||
−0.0220592 | + | 0.999757i | \(0.507022\pi\) | |||||||
\(752\) | −7.59039e112 | −0.186063 | ||||||||
\(753\) | −8.56549e113 | −1.99228 | ||||||||
\(754\) | −1.94985e113 | −0.430360 | ||||||||
\(755\) | 4.24208e113 | 0.888533 | ||||||||
\(756\) | −1.49874e113 | −0.297930 | ||||||||
\(757\) | −3.22054e113 | −0.607634 | −0.303817 | − | 0.952730i | \(-0.598261\pi\) | ||||
−0.303817 | + | 0.952730i | \(0.598261\pi\) | |||||||
\(758\) | 7.00983e113 | 1.25538 | ||||||||
\(759\) | −1.44355e114 | −2.45404 | ||||||||
\(760\) | 5.60706e113 | 0.904895 | ||||||||
\(761\) | 5.35481e113 | 0.820446 | 0.410223 | − | 0.911985i | \(-0.365451\pi\) | ||||
0.410223 | + | 0.911985i | \(0.365451\pi\) | |||||||
\(762\) | −1.29061e114 | −1.87747 | ||||||||
\(763\) | −3.74128e113 | −0.516775 | ||||||||
\(764\) | −5.66051e112 | −0.0742451 | ||||||||
\(765\) | −1.41086e113 | −0.175734 | ||||||||
\(766\) | −2.95007e113 | −0.348976 | ||||||||
\(767\) | 1.52247e114 | 1.71054 | ||||||||
\(768\) | 8.03700e113 | 0.857681 | ||||||||
\(769\) | 1.38510e114 | 1.40408 | 0.702039 | − | 0.712138i | \(-0.252273\pi\) | ||||
0.702039 | + | 0.712138i | \(0.252273\pi\) | |||||||
\(770\) | 1.66706e114 | 1.60534 | ||||||||
\(771\) | 5.43888e113 | 0.497579 | ||||||||
\(772\) | −1.14870e113 | −0.0998439 | ||||||||
\(773\) | −1.39183e114 | −1.14947 | −0.574733 | − | 0.818341i | \(-0.694894\pi\) | ||||
−0.574733 | + | 0.818341i | \(0.694894\pi\) | |||||||
\(774\) | 1.98860e114 | 1.56056 | ||||||||
\(775\) | 6.60236e113 | 0.492359 | ||||||||
\(776\) | −1.18164e114 | −0.837427 | ||||||||
\(777\) | −4.25050e114 | −2.86293 | ||||||||
\(778\) | −3.30277e114 | −2.11438 | ||||||||
\(779\) | 1.07391e113 | 0.0653489 | ||||||||
\(780\) | 5.91731e113 | 0.342285 | ||||||||
\(781\) | 2.10294e114 | 1.15641 | ||||||||
\(782\) | −2.32440e113 | −0.121519 | ||||||||
\(783\) | 1.29278e114 | 0.642594 | ||||||||
\(784\) | −1.05518e114 | −0.498705 | ||||||||
\(785\) | −2.46934e114 | −1.10976 | ||||||||
\(786\) | −1.27651e114 | −0.545550 | ||||||||
\(787\) | 4.36246e114 | 1.77308 | 0.886542 | − | 0.462649i | \(-0.153101\pi\) | ||||
0.886542 | + | 0.462649i | \(0.153101\pi\) | |||||||
\(788\) | 2.57326e113 | 0.0994715 | ||||||||
\(789\) | 4.12087e114 | 1.51512 | ||||||||
\(790\) | −6.56400e114 | −2.29561 | ||||||||
\(791\) | −4.65436e113 | −0.154842 | ||||||||
\(792\) | 4.88021e114 | 1.54452 | ||||||||
\(793\) | 3.13854e114 | 0.945012 | ||||||||
\(794\) | −8.29980e113 | −0.237770 | ||||||||
\(795\) | −1.04708e115 | −2.85415 | ||||||||
\(796\) | −5.01445e113 | −0.130064 | ||||||||
\(797\) | 4.51588e113 | 0.111465 | 0.0557325 | − | 0.998446i | \(-0.482251\pi\) | ||||
0.0557325 | + | 0.998446i | \(0.482251\pi\) | |||||||
\(798\) | 7.14059e114 | 1.67734 | ||||||||
\(799\) | −5.24672e112 | −0.0117298 | ||||||||
\(800\) | 1.20814e114 | 0.257077 | ||||||||
\(801\) | 1.07810e114 | 0.218361 | ||||||||
\(802\) | 1.60625e114 | 0.309688 | ||||||||
\(803\) | −3.28198e113 | −0.0602382 | ||||||||
\(804\) | 1.43980e113 | 0.0251587 | ||||||||
\(805\) | 1.47907e115 | 2.46066 | ||||||||
\(806\) | −3.98297e114 | −0.630918 | ||||||||
\(807\) | −7.31188e114 | −1.10287 | ||||||||
\(808\) | −2.38692e114 | −0.342838 | ||||||||
\(809\) | −1.13305e114 | −0.154982 | −0.0774911 | − | 0.996993i | \(-0.524691\pi\) | ||||
−0.0774911 | + | 0.996993i | \(0.524691\pi\) | |||||||
\(810\) | −6.13427e114 | −0.799107 | ||||||||
\(811\) | −8.23822e114 | −1.02214 | −0.511069 | − | 0.859540i | \(-0.670750\pi\) | ||||
−0.511069 | + | 0.859540i | \(0.670750\pi\) | |||||||
\(812\) | −7.98105e113 | −0.0943185 | ||||||||
\(813\) | 1.55710e115 | 1.75283 | ||||||||
\(814\) | −1.33982e115 | −1.43675 | ||||||||
\(815\) | 2.59174e112 | 0.00264768 | ||||||||
\(816\) | 1.42990e114 | 0.139170 | ||||||||
\(817\) | −6.44619e114 | −0.597767 | ||||||||
\(818\) | 1.82694e115 | 1.61425 | ||||||||
\(819\) | −2.31153e115 | −1.94619 | ||||||||
\(820\) | 2.45161e113 | 0.0196700 | ||||||||
\(821\) | −1.83306e115 | −1.40159 | −0.700795 | − | 0.713362i | \(-0.747171\pi\) | ||||
−0.700795 | + | 0.713362i | \(0.747171\pi\) | |||||||
\(822\) | 3.68729e115 | 2.68702 | ||||||||
\(823\) | −1.77225e115 | −1.23093 | −0.615463 | − | 0.788166i | \(-0.711031\pi\) | ||||
−0.615463 | + | 0.788166i | \(0.711031\pi\) | |||||||
\(824\) | −1.45346e115 | −0.962228 | ||||||||
\(825\) | 1.86255e115 | 1.17538 | ||||||||
\(826\) | 4.19414e115 | 2.52308 | ||||||||
\(827\) | 9.78862e114 | 0.561376 | 0.280688 | − | 0.959799i | \(-0.409437\pi\) | ||||
0.280688 | + | 0.959799i | \(0.409437\pi\) | |||||||
\(828\) | −9.15352e114 | −0.500484 | ||||||||
\(829\) | 4.01341e114 | 0.209223 | 0.104612 | − | 0.994513i | \(-0.466640\pi\) | ||||
0.104612 | + | 0.994513i | \(0.466640\pi\) | |||||||
\(830\) | −2.46336e115 | −1.22446 | ||||||||
\(831\) | −2.46949e115 | −1.17049 | ||||||||
\(832\) | 1.49967e115 | 0.677837 | ||||||||
\(833\) | −7.29377e113 | −0.0314394 | ||||||||
\(834\) | 1.98582e115 | 0.816359 | ||||||||
\(835\) | 4.81687e115 | 1.88864 | ||||||||
\(836\) | 3.34431e114 | 0.125072 | ||||||||
\(837\) | 2.64078e115 | 0.942057 | ||||||||
\(838\) | −3.51210e115 | −1.19517 | ||||||||
\(839\) | 1.59510e115 | 0.517834 | 0.258917 | − | 0.965900i | \(-0.416634\pi\) | ||||
0.258917 | + | 0.965900i | \(0.416634\pi\) | |||||||
\(840\) | −7.71088e115 | −2.38821 | ||||||||
\(841\) | −2.69566e115 | −0.796568 | ||||||||
\(842\) | −6.30865e115 | −1.77873 | ||||||||
\(843\) | −9.92830e114 | −0.267107 | ||||||||
\(844\) | −1.21642e115 | −0.312288 | ||||||||
\(845\) | −1.21220e115 | −0.296984 | ||||||||
\(846\) | −1.39059e115 | −0.325138 | ||||||||
\(847\) | 6.66423e114 | 0.148715 | ||||||||
\(848\) | 6.88165e115 | 1.46574 | ||||||||
\(849\) | 1.07303e116 | 2.18152 | ||||||||
\(850\) | 2.99907e114 | 0.0582022 | ||||||||
\(851\) | −1.18873e116 | −2.20224 | ||||||||
\(852\) | 2.05633e115 | 0.363688 | ||||||||
\(853\) | 5.81489e115 | 0.981871 | 0.490936 | − | 0.871196i | \(-0.336655\pi\) | ||||
0.490936 | + | 0.871196i | \(0.336655\pi\) | |||||||
\(854\) | 8.64611e115 | 1.39391 | ||||||||
\(855\) | 1.21213e116 | 1.86589 | ||||||||
\(856\) | −1.27417e115 | −0.187290 | ||||||||
\(857\) | −8.63740e115 | −1.21239 | −0.606193 | − | 0.795318i | \(-0.707304\pi\) | ||||
−0.606193 | + | 0.795318i | \(0.707304\pi\) | |||||||
\(858\) | −1.12361e116 | −1.50615 | ||||||||
\(859\) | −8.23961e114 | −0.105482 | −0.0527408 | − | 0.998608i | \(-0.516796\pi\) | ||||
−0.0527408 | + | 0.998608i | \(0.516796\pi\) | |||||||
\(860\) | −1.47159e115 | −0.179927 | ||||||||
\(861\) | −1.47685e115 | −0.172469 | ||||||||
\(862\) | −4.22963e114 | −0.0471808 | ||||||||
\(863\) | 7.93638e115 | 0.845661 | 0.422830 | − | 0.906209i | \(-0.361037\pi\) | ||||
0.422830 | + | 0.906209i | \(0.361037\pi\) | |||||||
\(864\) | 4.83228e115 | 0.491880 | ||||||||
\(865\) | −1.27712e116 | −1.24192 | ||||||||
\(866\) | 1.92929e116 | 1.79243 | ||||||||
\(867\) | −1.89020e116 | −1.67785 | ||||||||
\(868\) | −1.63030e115 | −0.138273 | ||||||||
\(869\) | 1.85194e116 | 1.50088 | ||||||||
\(870\) | −1.40610e116 | −1.08895 | ||||||||
\(871\) | 1.01685e115 | 0.0752557 | ||||||||
\(872\) | 5.45480e115 | 0.385814 | ||||||||
\(873\) | −2.55445e116 | −1.72677 | ||||||||
\(874\) | 1.99699e116 | 1.29025 | ||||||||
\(875\) | 6.54526e115 | 0.404212 | ||||||||
\(876\) | −3.20924e114 | −0.0189448 | ||||||||
\(877\) | 2.93010e116 | 1.65348 | 0.826740 | − | 0.562584i | \(-0.190193\pi\) | ||||
0.826740 | + | 0.562584i | \(0.190193\pi\) | |||||||
\(878\) | −1.66874e116 | −0.900232 | ||||||||
\(879\) | −4.87803e116 | −2.51584 | ||||||||
\(880\) | −2.86806e116 | −1.41424 | ||||||||
\(881\) | 1.12747e116 | 0.531565 | 0.265783 | − | 0.964033i | \(-0.414370\pi\) | ||||
0.265783 | + | 0.964033i | \(0.414370\pi\) | |||||||
\(882\) | −1.93313e116 | −0.871471 | ||||||||
\(883\) | −3.56610e116 | −1.53726 | −0.768628 | − | 0.639696i | \(-0.779060\pi\) | ||||
−0.768628 | + | 0.639696i | \(0.779060\pi\) | |||||||
\(884\) | −2.68820e114 | −0.0110815 | ||||||||
\(885\) | 1.09791e117 | 4.32820 | ||||||||
\(886\) | 8.97838e115 | 0.338506 | ||||||||
\(887\) | 1.58042e116 | 0.569889 | 0.284944 | − | 0.958544i | \(-0.408025\pi\) | ||||
0.284944 | + | 0.958544i | \(0.408025\pi\) | |||||||
\(888\) | 6.19724e116 | 2.13740 | ||||||||
\(889\) | −3.73085e116 | −1.23080 | ||||||||
\(890\) | −5.36945e115 | −0.169443 | ||||||||
\(891\) | 1.73070e116 | 0.522459 | ||||||||
\(892\) | 5.32273e115 | 0.153717 | ||||||||
\(893\) | 4.50768e115 | 0.124543 | ||||||||
\(894\) | 1.34429e116 | 0.355355 | ||||||||
\(895\) | −5.93502e116 | −1.50111 | ||||||||
\(896\) | 5.84080e116 | 1.41353 | ||||||||
\(897\) | −9.96902e116 | −2.30861 | ||||||||
\(898\) | −5.64462e116 | −1.25089 | ||||||||
\(899\) | 1.40627e116 | 0.298236 | ||||||||
\(900\) | 1.18104e116 | 0.239709 | ||||||||
\(901\) | 4.75682e115 | 0.0924032 | ||||||||
\(902\) | −4.65524e115 | −0.0865534 | ||||||||
\(903\) | 8.86486e116 | 1.57763 | ||||||||
\(904\) | 6.78607e115 | 0.115602 | ||||||||
\(905\) | −9.29612e116 | −1.51594 | ||||||||
\(906\) | −7.87654e116 | −1.22962 | ||||||||
\(907\) | −8.05017e115 | −0.120314 | −0.0601571 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601571 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(908\) | −6.46556e115 | −0.0925157 | ||||||||
\(909\) | −5.16001e116 | −0.706931 | ||||||||
\(910\) | 1.15125e117 | 1.51021 | ||||||||
\(911\) | 1.78870e116 | 0.224679 | 0.112339 | − | 0.993670i | \(-0.464166\pi\) | ||||
0.112339 | + | 0.993670i | \(0.464166\pi\) | |||||||
\(912\) | −1.22849e117 | −1.47766 | ||||||||
\(913\) | 6.95003e116 | 0.800554 | ||||||||
\(914\) | −1.50530e116 | −0.166054 | ||||||||
\(915\) | 2.26332e117 | 2.39118 | ||||||||
\(916\) | 3.21118e116 | 0.324933 | ||||||||
\(917\) | −3.69011e116 | −0.357644 | ||||||||
\(918\) | 1.19956e116 | 0.111361 | ||||||||
\(919\) | 9.52514e116 | 0.847049 | 0.423525 | − | 0.905885i | \(-0.360793\pi\) | ||||
0.423525 | + | 0.905885i | \(0.360793\pi\) | |||||||
\(920\) | −2.15648e117 | −1.83708 | ||||||||
\(921\) | 3.39954e116 | 0.277437 | ||||||||
\(922\) | 9.43906e116 | 0.738002 | ||||||||
\(923\) | 1.45227e117 | 1.08788 | ||||||||
\(924\) | −4.59913e116 | −0.330090 | ||||||||
\(925\) | 1.53376e117 | 1.05477 | ||||||||
\(926\) | 7.40323e116 | 0.487851 | ||||||||
\(927\) | −3.14207e117 | −1.98411 | ||||||||
\(928\) | 2.57328e116 | 0.155719 | ||||||||
\(929\) | −2.85231e117 | −1.65415 | −0.827077 | − | 0.562088i | \(-0.809998\pi\) | ||||
−0.827077 | + | 0.562088i | \(0.809998\pi\) | |||||||
\(930\) | −2.87226e117 | −1.59642 | ||||||||
\(931\) | 6.26639e116 | 0.333814 | ||||||||
\(932\) | −6.02409e116 | −0.307584 | ||||||||
\(933\) | 1.59126e117 | 0.778784 | ||||||||
\(934\) | 5.93912e116 | 0.278625 | ||||||||
\(935\) | −1.98250e116 | −0.0891568 | ||||||||
\(936\) | 3.37022e117 | 1.45299 | ||||||||
\(937\) | −4.69296e117 | −1.93969 | −0.969847 | − | 0.243714i | \(-0.921634\pi\) | ||||
−0.969847 | + | 0.243714i | \(0.921634\pi\) | |||||||
\(938\) | 2.80123e116 | 0.111004 | ||||||||
\(939\) | 2.15115e117 | 0.817296 | ||||||||
\(940\) | 1.02905e116 | 0.0374874 | ||||||||
\(941\) | 2.18384e117 | 0.762835 | 0.381418 | − | 0.924403i | \(-0.375436\pi\) | ||||
0.381418 | + | 0.924403i | \(0.375436\pi\) | |||||||
\(942\) | 4.58499e117 | 1.53578 | ||||||||
\(943\) | −4.13028e116 | −0.132668 | ||||||||
\(944\) | −7.21573e117 | −2.22273 | ||||||||
\(945\) | −7.63303e117 | −2.25497 | ||||||||
\(946\) | 2.79433e117 | 0.791731 | ||||||||
\(947\) | 6.61338e117 | 1.79721 | 0.898606 | − | 0.438757i | \(-0.144581\pi\) | ||||
0.898606 | + | 0.438757i | \(0.144581\pi\) | |||||||
\(948\) | 1.81089e117 | 0.472023 | ||||||||
\(949\) | −2.26650e116 | −0.0566684 | ||||||||
\(950\) | −2.57663e117 | −0.617973 | ||||||||
\(951\) | −1.26722e117 | −0.291557 | ||||||||
\(952\) | 3.50301e116 | 0.0773182 | ||||||||
\(953\) | −4.39619e117 | −0.930908 | −0.465454 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465454 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(954\) | 1.26074e118 | 2.56133 | ||||||||
\(955\) | −2.88288e117 | −0.561945 | ||||||||
\(956\) | −7.66902e116 | −0.143434 | ||||||||
\(957\) | 3.96712e117 | 0.711958 | ||||||||
\(958\) | −2.48992e117 | −0.428793 | ||||||||
\(959\) | 1.06591e118 | 1.76152 | ||||||||
\(960\) | 1.08147e118 | 1.71514 | ||||||||
\(961\) | −3.69753e117 | −0.562780 | ||||||||
\(962\) | −9.25264e117 | −1.35161 | ||||||||
\(963\) | −2.75449e117 | −0.386191 | ||||||||
\(964\) | 1.50598e117 | 0.202664 | ||||||||
\(965\) | −5.85027e117 | −0.755696 | ||||||||
\(966\) | −2.74628e118 | −3.40525 | ||||||||
\(967\) | −8.20710e117 | −0.976886 | −0.488443 | − | 0.872596i | \(-0.662435\pi\) | ||||
−0.488443 | + | 0.872596i | \(0.662435\pi\) | |||||||
\(968\) | −9.71646e116 | −0.111028 | ||||||||
\(969\) | −8.49172e116 | −0.0931551 | ||||||||
\(970\) | 1.27224e118 | 1.33994 | ||||||||
\(971\) | −9.66918e117 | −0.977755 | −0.488877 | − | 0.872353i | \(-0.662593\pi\) | ||||
−0.488877 | + | 0.872353i | \(0.662593\pi\) | |||||||
\(972\) | −8.68421e116 | −0.0843165 | ||||||||
\(973\) | 5.74056e117 | 0.535176 | ||||||||
\(974\) | 2.19611e118 | 1.96596 | ||||||||
\(975\) | 1.28626e118 | 1.10572 | ||||||||
\(976\) | −1.48751e118 | −1.22798 | ||||||||
\(977\) | 1.35219e118 | 1.07202 | 0.536008 | − | 0.844213i | \(-0.319932\pi\) | ||||
0.536008 | + | 0.844213i | \(0.319932\pi\) | |||||||
\(978\) | −4.81225e115 | −0.00366406 | ||||||||
\(979\) | 1.51491e117 | 0.110783 | ||||||||
\(980\) | 1.43054e117 | 0.100478 | ||||||||
\(981\) | 1.17921e118 | 0.795548 | ||||||||
\(982\) | −1.95631e118 | −1.26775 | ||||||||
\(983\) | 1.23625e118 | 0.769559 | 0.384780 | − | 0.923008i | \(-0.374277\pi\) | ||||
0.384780 | + | 0.923008i | \(0.374277\pi\) | |||||||
\(984\) | 2.15325e117 | 0.128762 | ||||||||
\(985\) | 1.31055e118 | 0.752877 | ||||||||
\(986\) | 6.38785e116 | 0.0352547 | ||||||||
\(987\) | −6.19900e117 | −0.328696 | ||||||||
\(988\) | 2.30955e117 | 0.117660 | ||||||||
\(989\) | 2.47922e118 | 1.21356 | ||||||||
\(990\) | −5.25440e118 | −2.47134 | ||||||||
\(991\) | 5.32564e117 | 0.240692 | 0.120346 | − | 0.992732i | \(-0.461600\pi\) | ||||
0.120346 | + | 0.992732i | \(0.461600\pi\) | |||||||
\(992\) | 5.25646e117 | 0.228287 | ||||||||
\(993\) | −7.80461e118 | −3.25729 | ||||||||
\(994\) | 4.00074e118 | 1.60464 | ||||||||
\(995\) | −2.55385e118 | −0.984426 | ||||||||
\(996\) | 6.79598e117 | 0.251772 | ||||||||
\(997\) | 1.22747e118 | 0.437071 | 0.218535 | − | 0.975829i | \(-0.429872\pi\) | ||||
0.218535 | + | 0.975829i | \(0.429872\pi\) | |||||||
\(998\) | 3.78073e118 | 1.29395 | ||||||||
\(999\) | 6.13467e118 | 2.01816 |
(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 | 1.80.a.a.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 9.80.a.b.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.80.a.a.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.80.a.b.1.5 | 6 | 3.2 | odd | 2 |