Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 957 x^{8} + 1224 x^{7} + 310102 x^{6} - 241884 x^{5} - 40367312 x^{4} + 11067840 x^{3} + 1840757376 x^{2} + 541859072 x - 4516262912 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-20.0501\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.0501 | −1.94897 | −0.974487 | − | 0.224443i | \(-0.927944\pi\) | ||||
−0.974487 | + | 0.224443i | \(0.927944\pi\) | |||||||
\(3\) | −47.1151 | −1.00748 | −0.503739 | − | 0.863856i | \(-0.668043\pi\) | ||||
−0.503739 | + | 0.863856i | \(0.668043\pi\) | |||||||
\(4\) | 358.208 | 2.79850 | ||||||||
\(5\) | −467.623 | −1.67302 | −0.836509 | − | 0.547953i | \(-0.815407\pi\) | ||||
−0.836509 | + | 0.547953i | \(0.815407\pi\) | |||||||
\(6\) | 1038.89 | 1.96355 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −5076.12 | −3.50523 | ||||||||
\(9\) | 32.8291 | 0.0150110 | ||||||||
\(10\) | 10311.1 | 3.26067 | ||||||||
\(11\) | −4968.96 | −1.12562 | −0.562810 | − | 0.826587i | \(-0.690280\pi\) | ||||
−0.562810 | + | 0.826587i | \(0.690280\pi\) | |||||||
\(12\) | −16877.0 | −2.81943 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −7563.19 | −0.736643 | ||||||||
\(15\) | 22032.1 | 1.68553 | ||||||||
\(16\) | 66078.5 | 4.03311 | ||||||||
\(17\) | 20459.5 | 1.01001 | 0.505003 | − | 0.863118i | \(-0.331492\pi\) | ||||
0.505003 | + | 0.863118i | \(0.331492\pi\) | |||||||
\(18\) | −723.885 | −0.0292561 | ||||||||
\(19\) | 11244.3 | 0.376091 | 0.188046 | − | 0.982160i | \(-0.439785\pi\) | ||||
0.188046 | + | 0.982160i | \(0.439785\pi\) | |||||||
\(20\) | −167506. | −4.68194 | ||||||||
\(21\) | −16160.5 | −0.380791 | ||||||||
\(22\) | 109566. | 2.19380 | ||||||||
\(23\) | 62996.4 | 1.07961 | 0.539806 | − | 0.841789i | \(-0.318497\pi\) | ||||
0.539806 | + | 0.841789i | \(0.318497\pi\) | |||||||
\(24\) | 239162. | 3.53144 | ||||||||
\(25\) | 140546. | 1.79899 | ||||||||
\(26\) | 48444.1 | 0.540548 | ||||||||
\(27\) | 101494. | 0.992354 | ||||||||
\(28\) | 122865. | 1.05773 | ||||||||
\(29\) | −15545.6 | −0.118362 | −0.0591812 | − | 0.998247i | \(-0.518849\pi\) | ||||
−0.0591812 | + | 0.998247i | \(0.518849\pi\) | |||||||
\(30\) | −485810. | −3.28505 | ||||||||
\(31\) | 50810.4 | 0.306328 | 0.153164 | − | 0.988201i | \(-0.451054\pi\) | ||||
0.153164 | + | 0.988201i | \(0.451054\pi\) | |||||||
\(32\) | −807295. | −4.35519 | ||||||||
\(33\) | 234113. | 1.13404 | ||||||||
\(34\) | −451134. | −1.96847 | ||||||||
\(35\) | −160395. | −0.632341 | ||||||||
\(36\) | 11759.6 | 0.0420083 | ||||||||
\(37\) | 268555. | 0.871622 | 0.435811 | − | 0.900038i | \(-0.356462\pi\) | ||||
0.435811 | + | 0.900038i | \(0.356462\pi\) | |||||||
\(38\) | −247937. | −0.732992 | ||||||||
\(39\) | 103512. | 0.279424 | ||||||||
\(40\) | 2.37371e6 | 5.86432 | ||||||||
\(41\) | −524959. | −1.18955 | −0.594773 | − | 0.803893i | \(-0.702758\pi\) | ||||
−0.594773 | + | 0.803893i | \(0.702758\pi\) | |||||||
\(42\) | 356340. | 0.742151 | ||||||||
\(43\) | −1.02709e6 | −1.97000 | −0.985002 | − | 0.172542i | \(-0.944802\pi\) | ||||
−0.985002 | + | 0.172542i | \(0.944802\pi\) | |||||||
\(44\) | −1.77992e6 | −3.15005 | ||||||||
\(45\) | −15351.6 | −0.0251137 | ||||||||
\(46\) | −1.38908e6 | −2.10414 | ||||||||
\(47\) | 937764. | 1.31750 | 0.658751 | − | 0.752361i | \(-0.271085\pi\) | ||||
0.658751 | + | 0.752361i | \(0.271085\pi\) | |||||||
\(48\) | −3.11329e6 | −4.06327 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −3.09906e6 | −3.50618 | ||||||||
\(51\) | −963950. | −1.01756 | ||||||||
\(52\) | −786983. | −0.776165 | ||||||||
\(53\) | 1.65322e6 | 1.52533 | 0.762666 | − | 0.646793i | \(-0.223890\pi\) | ||||
0.762666 | + | 0.646793i | \(0.223890\pi\) | |||||||
\(54\) | −2.23795e6 | −1.93407 | ||||||||
\(55\) | 2.32360e6 | 1.88318 | ||||||||
\(56\) | −1.74111e6 | −1.32485 | ||||||||
\(57\) | −529774. | −0.378904 | ||||||||
\(58\) | 342782. | 0.230685 | ||||||||
\(59\) | −2.20262e6 | −1.39623 | −0.698116 | − | 0.715984i | \(-0.745978\pi\) | ||||
−0.698116 | + | 0.715984i | \(0.745978\pi\) | |||||||
\(60\) | 7.89207e6 | 4.71695 | ||||||||
\(61\) | 230413. | 0.129973 | 0.0649864 | − | 0.997886i | \(-0.479300\pi\) | ||||
0.0649864 | + | 0.997886i | \(0.479300\pi\) | |||||||
\(62\) | −1.12038e6 | −0.597025 | ||||||||
\(63\) | 11260.4 | 0.00567363 | ||||||||
\(64\) | 9.34292e6 | 4.45505 | ||||||||
\(65\) | 1.02737e6 | 0.464012 | ||||||||
\(66\) | −5.16222e6 | −2.21021 | ||||||||
\(67\) | 2.00255e6 | 0.813434 | 0.406717 | − | 0.913554i | \(-0.366674\pi\) | ||||
0.406717 | + | 0.913554i | \(0.366674\pi\) | |||||||
\(68\) | 7.32876e6 | 2.82650 | ||||||||
\(69\) | −2.96808e6 | −1.08769 | ||||||||
\(70\) | 3.53672e6 | 1.23242 | ||||||||
\(71\) | 2.93841e6 | 0.974335 | 0.487167 | − | 0.873309i | \(-0.338030\pi\) | ||||
0.487167 | + | 0.873309i | \(0.338030\pi\) | |||||||
\(72\) | −166644. | −0.0526171 | ||||||||
\(73\) | 1.33302e6 | 0.401057 | 0.200528 | − | 0.979688i | \(-0.435734\pi\) | ||||
0.200528 | + | 0.979688i | \(0.435734\pi\) | |||||||
\(74\) | −5.92168e6 | −1.69877 | ||||||||
\(75\) | −6.62183e6 | −1.81244 | ||||||||
\(76\) | 4.02779e6 | 1.05249 | ||||||||
\(77\) | −1.70435e6 | −0.425444 | ||||||||
\(78\) | −2.28245e6 | −0.544590 | ||||||||
\(79\) | −2.92073e6 | −0.666494 | −0.333247 | − | 0.942840i | \(-0.608144\pi\) | ||||
−0.333247 | + | 0.942840i | \(0.608144\pi\) | |||||||
\(80\) | −3.08998e7 | −6.74746 | ||||||||
\(81\) | −4.85369e6 | −1.01479 | ||||||||
\(82\) | 1.15754e7 | 2.31840 | ||||||||
\(83\) | −7.49486e6 | −1.43877 | −0.719383 | − | 0.694614i | \(-0.755575\pi\) | ||||
−0.719383 | + | 0.694614i | \(0.755575\pi\) | |||||||
\(84\) | −5.78881e6 | −1.06564 | ||||||||
\(85\) | −9.56732e6 | −1.68976 | ||||||||
\(86\) | 2.26474e7 | 3.83949 | ||||||||
\(87\) | 732431. | 0.119248 | ||||||||
\(88\) | 2.52231e7 | 3.94556 | ||||||||
\(89\) | −1.80466e6 | −0.271350 | −0.135675 | − | 0.990753i | \(-0.543320\pi\) | ||||
−0.135675 | + | 0.990753i | \(0.543320\pi\) | |||||||
\(90\) | 338505. | 0.0489459 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 2.25658e7 | 3.02130 | ||||||||
\(93\) | −2.39394e6 | −0.308619 | ||||||||
\(94\) | −2.06778e7 | −2.56778 | ||||||||
\(95\) | −5.25807e6 | −0.629207 | ||||||||
\(96\) | 3.80358e7 | 4.38776 | ||||||||
\(97\) | −5.26831e6 | −0.586098 | −0.293049 | − | 0.956097i | \(-0.594670\pi\) | ||||
−0.293049 | + | 0.956097i | \(0.594670\pi\) | |||||||
\(98\) | −2.59418e6 | −0.278425 | ||||||||
\(99\) | −163126. | −0.0168967 | ||||||||
\(100\) | 5.03447e7 | 5.03447 | ||||||||
\(101\) | 8.54858e6 | 0.825599 | 0.412799 | − | 0.910822i | \(-0.364551\pi\) | ||||
0.412799 | + | 0.910822i | \(0.364551\pi\) | |||||||
\(102\) | 2.12552e7 | 1.98319 | ||||||||
\(103\) | −1.48721e7 | −1.34104 | −0.670519 | − | 0.741893i | \(-0.733928\pi\) | ||||
−0.670519 | + | 0.741893i | \(0.733928\pi\) | |||||||
\(104\) | 1.11522e7 | 0.972177 | ||||||||
\(105\) | 7.55700e6 | 0.637070 | ||||||||
\(106\) | −3.64536e7 | −2.97283 | ||||||||
\(107\) | 1.38028e7 | 1.08924 | 0.544619 | − | 0.838684i | \(-0.316674\pi\) | ||||
0.544619 | + | 0.838684i | \(0.316674\pi\) | |||||||
\(108\) | 3.63559e7 | 2.77711 | ||||||||
\(109\) | −1.08168e7 | −0.800031 | −0.400016 | − | 0.916508i | \(-0.630995\pi\) | ||||
−0.400016 | + | 0.916508i | \(0.630995\pi\) | |||||||
\(110\) | −5.12357e7 | −3.67027 | ||||||||
\(111\) | −1.26530e7 | −0.878139 | ||||||||
\(112\) | 2.26649e7 | 1.52437 | ||||||||
\(113\) | 3.73413e6 | 0.243453 | 0.121726 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121726 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(114\) | 1.16816e7 | 0.738473 | ||||||||
\(115\) | −2.94585e7 | −1.80621 | ||||||||
\(116\) | −5.56856e6 | −0.331238 | ||||||||
\(117\) | −72125.5 | −0.00416330 | ||||||||
\(118\) | 4.85681e7 | 2.72122 | ||||||||
\(119\) | 7.01761e6 | 0.381746 | ||||||||
\(120\) | −1.11837e8 | −5.90817 | ||||||||
\(121\) | 5.20344e6 | 0.267018 | ||||||||
\(122\) | −5.08063e6 | −0.253313 | ||||||||
\(123\) | 2.47335e7 | 1.19844 | ||||||||
\(124\) | 1.82007e7 | 0.857259 | ||||||||
\(125\) | −2.91895e7 | −1.33672 | ||||||||
\(126\) | −248293. | −0.0110578 | ||||||||
\(127\) | 1.10183e7 | 0.477309 | 0.238655 | − | 0.971105i | \(-0.423294\pi\) | ||||
0.238655 | + | 0.971105i | \(0.423294\pi\) | |||||||
\(128\) | −1.02679e8 | −4.32759 | ||||||||
\(129\) | 4.83912e7 | 1.98474 | ||||||||
\(130\) | −2.26536e7 | −0.904347 | ||||||||
\(131\) | −9.49471e6 | −0.369005 | −0.184502 | − | 0.982832i | \(-0.559067\pi\) | ||||
−0.184502 | + | 0.982832i | \(0.559067\pi\) | |||||||
\(132\) | 8.38612e7 | 3.17360 | ||||||||
\(133\) | 3.85678e6 | 0.142149 | ||||||||
\(134\) | −4.41565e7 | −1.58536 | ||||||||
\(135\) | −4.74608e7 | −1.66023 | ||||||||
\(136\) | −1.03855e8 | −3.54030 | ||||||||
\(137\) | 3.15294e7 | 1.04759 | 0.523797 | − | 0.851843i | \(-0.324515\pi\) | ||||
0.523797 | + | 0.851843i | \(0.324515\pi\) | |||||||
\(138\) | 6.54465e7 | 2.11987 | ||||||||
\(139\) | −4.38808e7 | −1.38587 | −0.692936 | − | 0.720999i | \(-0.743683\pi\) | ||||
−0.692936 | + | 0.720999i | \(0.743683\pi\) | |||||||
\(140\) | −5.74547e7 | −1.76961 | ||||||||
\(141\) | −4.41828e7 | −1.32735 | ||||||||
\(142\) | −6.47923e7 | −1.89895 | ||||||||
\(143\) | 1.09168e7 | 0.312191 | ||||||||
\(144\) | 2.16929e6 | 0.0605410 | ||||||||
\(145\) | 7.26947e6 | 0.198023 | ||||||||
\(146\) | −2.93932e7 | −0.781650 | ||||||||
\(147\) | −5.54304e6 | −0.143925 | ||||||||
\(148\) | 9.61988e7 | 2.43923 | ||||||||
\(149\) | −2.35141e6 | −0.0582338 | −0.0291169 | − | 0.999576i | \(-0.509270\pi\) | ||||
−0.0291169 | + | 0.999576i | \(0.509270\pi\) | |||||||
\(150\) | 1.46012e8 | 3.53240 | ||||||||
\(151\) | 6.63014e7 | 1.56712 | 0.783562 | − | 0.621314i | \(-0.213401\pi\) | ||||
0.783562 | + | 0.621314i | \(0.213401\pi\) | |||||||
\(152\) | −5.70772e7 | −1.31829 | ||||||||
\(153\) | 671666. | 0.0151612 | ||||||||
\(154\) | 3.75812e7 | 0.829180 | ||||||||
\(155\) | −2.37601e7 | −0.512492 | ||||||||
\(156\) | 3.70788e7 | 0.781968 | ||||||||
\(157\) | −1.89167e7 | −0.390119 | −0.195059 | − | 0.980791i | \(-0.562490\pi\) | ||||
−0.195059 | + | 0.980791i | \(0.562490\pi\) | |||||||
\(158\) | 6.44024e7 | 1.29898 | ||||||||
\(159\) | −7.78914e7 | −1.53674 | ||||||||
\(160\) | 3.77510e8 | 7.28632 | ||||||||
\(161\) | 2.16078e7 | 0.408055 | ||||||||
\(162\) | 1.07024e8 | 1.97779 | ||||||||
\(163\) | −3.18530e7 | −0.576094 | −0.288047 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288047 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(164\) | −1.88044e8 | −3.32895 | ||||||||
\(165\) | −1.09477e8 | −1.89726 | ||||||||
\(166\) | 1.65263e8 | 2.80412 | ||||||||
\(167\) | −3.39660e7 | −0.564335 | −0.282167 | − | 0.959365i | \(-0.591053\pi\) | ||||
−0.282167 | + | 0.959365i | \(0.591053\pi\) | |||||||
\(168\) | 8.20325e7 | 1.33476 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 2.10961e8 | 3.29329 | ||||||||
\(171\) | 369139. | 0.00564551 | ||||||||
\(172\) | −3.67911e8 | −5.51306 | ||||||||
\(173\) | 8.91771e6 | 0.130946 | 0.0654730 | − | 0.997854i | \(-0.479144\pi\) | ||||
0.0654730 | + | 0.997854i | \(0.479144\pi\) | |||||||
\(174\) | −1.61502e7 | −0.232410 | ||||||||
\(175\) | 4.82073e7 | 0.679954 | ||||||||
\(176\) | −3.28342e8 | −4.53975 | ||||||||
\(177\) | 1.03777e8 | 1.40667 | ||||||||
\(178\) | 3.97929e7 | 0.528854 | ||||||||
\(179\) | −5.18357e7 | −0.675528 | −0.337764 | − | 0.941231i | \(-0.609671\pi\) | ||||
−0.337764 | + | 0.941231i | \(0.609671\pi\) | |||||||
\(180\) | −5.49908e6 | −0.0702807 | ||||||||
\(181\) | 7.62815e7 | 0.956190 | 0.478095 | − | 0.878308i | \(-0.341327\pi\) | ||||
0.478095 | + | 0.878308i | \(0.341327\pi\) | |||||||
\(182\) | 1.66163e7 | 0.204308 | ||||||||
\(183\) | −1.08559e7 | −0.130945 | ||||||||
\(184\) | −3.19777e8 | −3.78430 | ||||||||
\(185\) | −1.25583e8 | −1.45824 | ||||||||
\(186\) | 5.27866e7 | 0.601490 | ||||||||
\(187\) | −1.01662e8 | −1.13688 | ||||||||
\(188\) | 3.35915e8 | 3.68703 | ||||||||
\(189\) | 3.48124e7 | 0.375075 | ||||||||
\(190\) | 1.15941e8 | 1.22631 | ||||||||
\(191\) | 9.33400e7 | 0.969284 | 0.484642 | − | 0.874712i | \(-0.338950\pi\) | ||||
0.484642 | + | 0.874712i | \(0.338950\pi\) | |||||||
\(192\) | −4.40192e8 | −4.48836 | ||||||||
\(193\) | 1.59630e8 | 1.59832 | 0.799161 | − | 0.601117i | \(-0.205277\pi\) | ||||
0.799161 | + | 0.601117i | \(0.205277\pi\) | |||||||
\(194\) | 1.16167e8 | 1.14229 | ||||||||
\(195\) | −4.84045e7 | −0.467481 | ||||||||
\(196\) | 4.21428e7 | 0.399786 | ||||||||
\(197\) | −2.50462e7 | −0.233405 | −0.116702 | − | 0.993167i | \(-0.537232\pi\) | ||||
−0.116702 | + | 0.993167i | \(0.537232\pi\) | |||||||
\(198\) | 3.59696e6 | 0.0329312 | ||||||||
\(199\) | −8.14028e7 | −0.732240 | −0.366120 | − | 0.930568i | \(-0.619314\pi\) | ||||
−0.366120 | + | 0.930568i | \(0.619314\pi\) | |||||||
\(200\) | −7.13428e8 | −6.30587 | ||||||||
\(201\) | −9.43504e7 | −0.819516 | ||||||||
\(202\) | −1.88497e8 | −1.60907 | ||||||||
\(203\) | −5.33214e6 | −0.0447368 | ||||||||
\(204\) | −3.45295e8 | −2.84764 | ||||||||
\(205\) | 2.45483e8 | 1.99013 | ||||||||
\(206\) | 3.27931e8 | 2.61365 | ||||||||
\(207\) | 2.06811e6 | 0.0162061 | ||||||||
\(208\) | −1.45174e8 | −1.11858 | ||||||||
\(209\) | −5.58723e7 | −0.423336 | ||||||||
\(210\) | −1.66633e8 | −1.24163 | ||||||||
\(211\) | 2.41270e8 | 1.76813 | 0.884067 | − | 0.467361i | \(-0.154795\pi\) | ||||
0.884067 | + | 0.467361i | \(0.154795\pi\) | |||||||
\(212\) | 5.92196e8 | 4.26864 | ||||||||
\(213\) | −1.38443e8 | −0.981620 | ||||||||
\(214\) | −3.04353e8 | −2.12290 | ||||||||
\(215\) | 4.80289e8 | 3.29585 | ||||||||
\(216\) | −5.15195e8 | −3.47843 | ||||||||
\(217\) | 1.74280e7 | 0.115781 | ||||||||
\(218\) | 2.38512e8 | 1.55924 | ||||||||
\(219\) | −6.28052e7 | −0.404056 | ||||||||
\(220\) | 8.32333e8 | 5.27008 | ||||||||
\(221\) | −4.49495e7 | −0.280125 | ||||||||
\(222\) | 2.79000e8 | 1.71147 | ||||||||
\(223\) | 1.53450e8 | 0.926618 | 0.463309 | − | 0.886197i | \(-0.346662\pi\) | ||||
0.463309 | + | 0.886197i | \(0.346662\pi\) | |||||||
\(224\) | −2.76902e8 | −1.64611 | ||||||||
\(225\) | 4.61399e6 | 0.0270046 | ||||||||
\(226\) | −8.23380e7 | −0.474483 | ||||||||
\(227\) | −1.33687e7 | −0.0758575 | −0.0379288 | − | 0.999280i | \(-0.512076\pi\) | ||||
−0.0379288 | + | 0.999280i | \(0.512076\pi\) | |||||||
\(228\) | −1.89769e8 | −1.06036 | ||||||||
\(229\) | 3.89793e7 | 0.214492 | 0.107246 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107246 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(230\) | 6.49564e8 | 3.52026 | ||||||||
\(231\) | 8.03008e7 | 0.428625 | ||||||||
\(232\) | 7.89113e7 | 0.414888 | ||||||||
\(233\) | −2.83726e8 | −1.46945 | −0.734723 | − | 0.678367i | \(-0.762688\pi\) | ||||
−0.734723 | + | 0.678367i | \(0.762688\pi\) | |||||||
\(234\) | 1.59038e6 | 0.00811417 | ||||||||
\(235\) | −4.38520e8 | −2.20420 | ||||||||
\(236\) | −7.88997e8 | −3.90736 | ||||||||
\(237\) | 1.37610e8 | 0.671478 | ||||||||
\(238\) | −1.54739e8 | −0.744013 | ||||||||
\(239\) | 1.19229e8 | 0.564922 | 0.282461 | − | 0.959279i | \(-0.408849\pi\) | ||||
0.282461 | + | 0.959279i | \(0.408849\pi\) | |||||||
\(240\) | 1.45585e9 | 6.79792 | ||||||||
\(241\) | −3.04631e8 | −1.40189 | −0.700946 | − | 0.713215i | \(-0.747238\pi\) | ||||
−0.700946 | + | 0.713215i | \(0.747238\pi\) | |||||||
\(242\) | −1.14736e8 | −0.520412 | ||||||||
\(243\) | 6.71468e6 | 0.0300195 | ||||||||
\(244\) | 8.25357e7 | 0.363729 | ||||||||
\(245\) | −5.50153e7 | −0.239003 | ||||||||
\(246\) | −5.45376e8 | −2.33573 | ||||||||
\(247\) | −2.47036e7 | −0.104309 | ||||||||
\(248\) | −2.57920e8 | −1.07375 | ||||||||
\(249\) | 3.53121e8 | 1.44952 | ||||||||
\(250\) | 6.43631e8 | 2.60524 | ||||||||
\(251\) | 1.75280e8 | 0.699640 | 0.349820 | − | 0.936817i | \(-0.386243\pi\) | ||||
0.349820 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(252\) | 4.03356e6 | 0.0158777 | ||||||||
\(253\) | −3.13027e8 | −1.21523 | ||||||||
\(254\) | −2.42954e8 | −0.930264 | ||||||||
\(255\) | 4.50765e8 | 1.70239 | ||||||||
\(256\) | 1.06819e9 | 3.97931 | ||||||||
\(257\) | 2.16263e8 | 0.794724 | 0.397362 | − | 0.917662i | \(-0.369926\pi\) | ||||
0.397362 | + | 0.917662i | \(0.369926\pi\) | |||||||
\(258\) | −1.06703e9 | −3.86820 | ||||||||
\(259\) | 9.21145e7 | 0.329442 | ||||||||
\(260\) | 3.68011e8 | 1.29854 | ||||||||
\(261\) | −510347. | −0.00177674 | ||||||||
\(262\) | 2.09359e8 | 0.719181 | ||||||||
\(263\) | 5.74623e8 | 1.94777 | 0.973885 | − | 0.227040i | \(-0.0729049\pi\) | ||||
0.973885 | + | 0.227040i | \(0.0729049\pi\) | |||||||
\(264\) | −1.18839e9 | −3.97506 | ||||||||
\(265\) | −7.73082e8 | −2.55191 | ||||||||
\(266\) | −8.50425e7 | −0.277045 | ||||||||
\(267\) | 8.50265e7 | 0.273379 | ||||||||
\(268\) | 7.17331e8 | 2.27640 | ||||||||
\(269\) | −4.09722e8 | −1.28338 | −0.641692 | − | 0.766963i | \(-0.721767\pi\) | ||||
−0.641692 | + | 0.766963i | \(0.721767\pi\) | |||||||
\(270\) | 1.04652e9 | 3.23574 | ||||||||
\(271\) | −4.71283e8 | −1.43843 | −0.719215 | − | 0.694787i | \(-0.755498\pi\) | ||||
−0.719215 | + | 0.694787i | \(0.755498\pi\) | |||||||
\(272\) | 1.35193e9 | 4.07346 | ||||||||
\(273\) | 3.55045e7 | 0.105612 | ||||||||
\(274\) | −6.95226e8 | −2.04173 | ||||||||
\(275\) | −6.98368e8 | −2.02498 | ||||||||
\(276\) | −1.06319e9 | −3.04389 | ||||||||
\(277\) | −3.25552e8 | −0.920326 | −0.460163 | − | 0.887834i | \(-0.652209\pi\) | ||||
−0.460163 | + | 0.887834i | \(0.652209\pi\) | |||||||
\(278\) | 9.67578e8 | 2.70103 | ||||||||
\(279\) | 1.66806e6 | 0.00459829 | ||||||||
\(280\) | 8.14182e8 | 2.21650 | ||||||||
\(281\) | −2.59883e7 | −0.0698724 | −0.0349362 | − | 0.999390i | \(-0.511123\pi\) | ||||
−0.0349362 | + | 0.999390i | \(0.511123\pi\) | |||||||
\(282\) | 9.74237e8 | 2.58698 | ||||||||
\(283\) | 1.86622e8 | 0.489453 | 0.244727 | − | 0.969592i | \(-0.421302\pi\) | ||||
0.244727 | + | 0.969592i | \(0.421302\pi\) | |||||||
\(284\) | 1.05256e9 | 2.72668 | ||||||||
\(285\) | 2.47734e8 | 0.633912 | ||||||||
\(286\) | −2.40717e8 | −0.608451 | ||||||||
\(287\) | −1.80061e8 | −0.449606 | ||||||||
\(288\) | −2.65028e7 | −0.0653758 | ||||||||
\(289\) | 8.25224e6 | 0.0201108 | ||||||||
\(290\) | −1.60293e8 | −0.385941 | ||||||||
\(291\) | 2.48217e8 | 0.590481 | ||||||||
\(292\) | 4.77498e8 | 1.12236 | ||||||||
\(293\) | −7.58493e8 | −1.76163 | −0.880815 | − | 0.473460i | \(-0.843005\pi\) | ||||
−0.880815 | + | 0.473460i | \(0.843005\pi\) | |||||||
\(294\) | 1.22225e8 | 0.280507 | ||||||||
\(295\) | 1.03000e9 | 2.33592 | ||||||||
\(296\) | −1.36322e9 | −3.05524 | ||||||||
\(297\) | −5.04320e8 | −1.11701 | ||||||||
\(298\) | 5.18488e7 | 0.113496 | ||||||||
\(299\) | −1.38403e8 | −0.299431 | ||||||||
\(300\) | −2.37199e9 | −5.07212 | ||||||||
\(301\) | −3.52290e8 | −0.744592 | ||||||||
\(302\) | −1.46195e9 | −3.05428 | ||||||||
\(303\) | −4.02767e8 | −0.831772 | ||||||||
\(304\) | 7.43003e8 | 1.51682 | ||||||||
\(305\) | −1.07746e8 | −0.217447 | ||||||||
\(306\) | −1.48103e7 | −0.0295488 | ||||||||
\(307\) | 3.91537e8 | 0.772304 | 0.386152 | − | 0.922435i | \(-0.373804\pi\) | ||||
0.386152 | + | 0.922435i | \(0.373804\pi\) | |||||||
\(308\) | −6.10514e8 | −1.19061 | ||||||||
\(309\) | 7.00698e8 | 1.35106 | ||||||||
\(310\) | 5.23913e8 | 0.998834 | ||||||||
\(311\) | −3.63348e8 | −0.684955 | −0.342477 | − | 0.939526i | \(-0.611266\pi\) | ||||
−0.342477 | + | 0.939526i | \(0.611266\pi\) | |||||||
\(312\) | −5.25438e8 | −0.979446 | ||||||||
\(313\) | 5.35465e8 | 0.987020 | 0.493510 | − | 0.869740i | \(-0.335714\pi\) | ||||
0.493510 | + | 0.869740i | \(0.335714\pi\) | |||||||
\(314\) | 4.17116e8 | 0.760331 | ||||||||
\(315\) | −5.26561e6 | −0.00949208 | ||||||||
\(316\) | −1.04623e9 | −1.86518 | ||||||||
\(317\) | −3.64638e8 | −0.642917 | −0.321459 | − | 0.946924i | \(-0.604173\pi\) | ||||
−0.321459 | + | 0.946924i | \(0.604173\pi\) | |||||||
\(318\) | 1.71752e9 | 2.99506 | ||||||||
\(319\) | 7.72455e7 | 0.133231 | ||||||||
\(320\) | −4.36896e9 | −7.45338 | ||||||||
\(321\) | −6.50318e8 | −1.09738 | ||||||||
\(322\) | −4.76454e8 | −0.795289 | ||||||||
\(323\) | 2.30052e8 | 0.379854 | ||||||||
\(324\) | −1.73863e9 | −2.83988 | ||||||||
\(325\) | −3.08779e8 | −0.498950 | ||||||||
\(326\) | 7.02363e8 | 1.12279 | ||||||||
\(327\) | 5.09635e8 | 0.806014 | ||||||||
\(328\) | 2.66475e9 | 4.16964 | ||||||||
\(329\) | 3.21653e8 | 0.497969 | ||||||||
\(330\) | 2.41397e9 | 3.69772 | ||||||||
\(331\) | 6.19834e8 | 0.939458 | 0.469729 | − | 0.882811i | \(-0.344352\pi\) | ||||
0.469729 | + | 0.882811i | \(0.344352\pi\) | |||||||
\(332\) | −2.68472e9 | −4.02639 | ||||||||
\(333\) | 8.81643e6 | 0.0130839 | ||||||||
\(334\) | 7.48954e8 | 1.09987 | ||||||||
\(335\) | −9.36439e8 | −1.36089 | ||||||||
\(336\) | −1.06786e9 | −1.53577 | ||||||||
\(337\) | −6.79975e8 | −0.967806 | −0.483903 | − | 0.875122i | \(-0.660781\pi\) | ||||
−0.483903 | + | 0.875122i | \(0.660781\pi\) | |||||||
\(338\) | −1.06432e8 | −0.149921 | ||||||||
\(339\) | −1.75934e8 | −0.245273 | ||||||||
\(340\) | −3.42709e9 | −4.72879 | ||||||||
\(341\) | −2.52475e8 | −0.344809 | ||||||||
\(342\) | −8.13955e6 | −0.0110030 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 5.21361e9 | 6.90533 | ||||||||
\(345\) | 1.38794e9 | 1.81972 | ||||||||
\(346\) | −1.96637e8 | −0.255210 | ||||||||
\(347\) | 8.63591e8 | 1.10957 | 0.554785 | − | 0.831994i | \(-0.312800\pi\) | ||||
0.554785 | + | 0.831994i | \(0.312800\pi\) | |||||||
\(348\) | 2.62363e8 | 0.333714 | ||||||||
\(349\) | 2.13960e8 | 0.269429 | 0.134714 | − | 0.990884i | \(-0.456988\pi\) | ||||
0.134714 | + | 0.990884i | \(0.456988\pi\) | |||||||
\(350\) | −1.06298e9 | −1.32521 | ||||||||
\(351\) | −2.22982e8 | −0.275230 | ||||||||
\(352\) | 4.01142e9 | 4.90229 | ||||||||
\(353\) | −1.13948e9 | −1.37878 | −0.689389 | − | 0.724391i | \(-0.742121\pi\) | ||||
−0.689389 | + | 0.724391i | \(0.742121\pi\) | |||||||
\(354\) | −2.28829e9 | −2.74157 | ||||||||
\(355\) | −1.37407e9 | −1.63008 | ||||||||
\(356\) | −6.46443e8 | −0.759373 | ||||||||
\(357\) | −3.30635e8 | −0.384601 | ||||||||
\(358\) | 1.14298e9 | 1.31659 | ||||||||
\(359\) | −8.30408e8 | −0.947242 | −0.473621 | − | 0.880729i | \(-0.657053\pi\) | ||||
−0.473621 | + | 0.880729i | \(0.657053\pi\) | |||||||
\(360\) | 7.79267e7 | 0.0880293 | ||||||||
\(361\) | −7.67438e8 | −0.858555 | ||||||||
\(362\) | −1.68202e9 | −1.86359 | ||||||||
\(363\) | −2.45160e8 | −0.269015 | ||||||||
\(364\) | −2.69935e8 | −0.293363 | ||||||||
\(365\) | −6.23349e8 | −0.670975 | ||||||||
\(366\) | 2.39374e8 | 0.255208 | ||||||||
\(367\) | 9.59695e8 | 1.01345 | 0.506725 | − | 0.862108i | \(-0.330856\pi\) | ||||
0.506725 | + | 0.862108i | \(0.330856\pi\) | |||||||
\(368\) | 4.16270e9 | 4.35420 | ||||||||
\(369\) | −1.72339e7 | −0.0178563 | ||||||||
\(370\) | 2.76911e9 | 2.84207 | ||||||||
\(371\) | 5.67053e8 | 0.576521 | ||||||||
\(372\) | −8.57527e8 | −0.863670 | ||||||||
\(373\) | −1.25855e9 | −1.25571 | −0.627855 | − | 0.778330i | \(-0.716067\pi\) | ||||
−0.627855 | + | 0.778330i | \(0.716067\pi\) | |||||||
\(374\) | 2.24167e9 | 2.21575 | ||||||||
\(375\) | 1.37526e9 | 1.34672 | ||||||||
\(376\) | −4.76020e9 | −4.61815 | ||||||||
\(377\) | 3.41536e7 | 0.0328278 | ||||||||
\(378\) | −7.67618e8 | −0.731011 | ||||||||
\(379\) | −4.65618e8 | −0.439332 | −0.219666 | − | 0.975575i | \(-0.570497\pi\) | ||||
−0.219666 | + | 0.975575i | \(0.570497\pi\) | |||||||
\(380\) | −1.88348e9 | −1.76084 | ||||||||
\(381\) | −5.19126e8 | −0.480878 | ||||||||
\(382\) | −2.05816e9 | −1.88911 | ||||||||
\(383\) | −7.97037e8 | −0.724908 | −0.362454 | − | 0.932002i | \(-0.618061\pi\) | ||||
−0.362454 | + | 0.932002i | \(0.618061\pi\) | |||||||
\(384\) | 4.83772e9 | 4.35995 | ||||||||
\(385\) | 7.96995e8 | 0.711775 | ||||||||
\(386\) | −3.51987e9 | −3.11509 | ||||||||
\(387\) | −3.37183e7 | −0.0295718 | ||||||||
\(388\) | −1.88715e9 | −1.64020 | ||||||||
\(389\) | 1.01828e9 | 0.877092 | 0.438546 | − | 0.898709i | \(-0.355494\pi\) | ||||
0.438546 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(390\) | 1.06732e9 | 0.911109 | ||||||||
\(391\) | 1.28887e9 | 1.09041 | ||||||||
\(392\) | −5.97200e8 | −0.500748 | ||||||||
\(393\) | 4.47344e8 | 0.371764 | ||||||||
\(394\) | 5.52271e8 | 0.454900 | ||||||||
\(395\) | 1.36580e9 | 1.11506 | ||||||||
\(396\) | −5.84332e7 | −0.0472854 | ||||||||
\(397\) | 8.55854e8 | 0.686488 | 0.343244 | − | 0.939246i | \(-0.388474\pi\) | ||||
0.343244 | + | 0.939246i | \(0.388474\pi\) | |||||||
\(398\) | 1.79494e9 | 1.42712 | ||||||||
\(399\) | −1.81712e8 | −0.143212 | ||||||||
\(400\) | 9.28706e9 | 7.25552 | ||||||||
\(401\) | 5.97175e8 | 0.462483 | 0.231242 | − | 0.972896i | \(-0.425721\pi\) | ||||
0.231242 | + | 0.972896i | \(0.425721\pi\) | |||||||
\(402\) | 2.08044e9 | 1.59722 | ||||||||
\(403\) | −1.11630e8 | −0.0849601 | ||||||||
\(404\) | 3.06217e9 | 2.31044 | ||||||||
\(405\) | 2.26969e9 | 1.69775 | ||||||||
\(406\) | 1.17574e8 | 0.0871909 | ||||||||
\(407\) | −1.33444e9 | −0.981114 | ||||||||
\(408\) | 4.89313e9 | 3.56678 | ||||||||
\(409\) | 2.47188e9 | 1.78647 | 0.893234 | − | 0.449592i | \(-0.148431\pi\) | ||||
0.893234 | + | 0.449592i | \(0.148431\pi\) | |||||||
\(410\) | −5.41292e9 | −3.87872 | ||||||||
\(411\) | −1.48551e9 | −1.05543 | ||||||||
\(412\) | −5.32729e9 | −3.75289 | ||||||||
\(413\) | −7.55499e8 | −0.527726 | ||||||||
\(414\) | −4.56021e7 | −0.0315852 | ||||||||
\(415\) | 3.50477e9 | 2.40708 | ||||||||
\(416\) | 1.77363e9 | 1.20791 | ||||||||
\(417\) | 2.06745e9 | 1.39623 | ||||||||
\(418\) | 1.23199e9 | 0.825070 | ||||||||
\(419\) | 4.84975e7 | 0.0322085 | 0.0161042 | − | 0.999870i | \(-0.494874\pi\) | ||||
0.0161042 | + | 0.999870i | \(0.494874\pi\) | |||||||
\(420\) | 2.70698e9 | 1.78284 | ||||||||
\(421\) | −1.16612e9 | −0.761652 | −0.380826 | − | 0.924647i | \(-0.624360\pi\) | ||||
−0.380826 | + | 0.924647i | \(0.624360\pi\) | |||||||
\(422\) | −5.32004e9 | −3.44605 | ||||||||
\(423\) | 3.07859e7 | 0.0197770 | ||||||||
\(424\) | −8.39193e9 | −5.34664 | ||||||||
\(425\) | 2.87550e9 | 1.81699 | ||||||||
\(426\) | 3.05269e9 | 1.91315 | ||||||||
\(427\) | 7.90316e7 | 0.0491251 | ||||||||
\(428\) | 4.94426e9 | 3.04823 | ||||||||
\(429\) | −5.14346e8 | −0.314525 | ||||||||
\(430\) | −1.05904e10 | −6.42353 | ||||||||
\(431\) | 1.98606e8 | 0.119487 | 0.0597436 | − | 0.998214i | \(-0.480972\pi\) | ||||
0.0597436 | + | 0.998214i | \(0.480972\pi\) | |||||||
\(432\) | 6.70656e9 | 4.00227 | ||||||||
\(433\) | −1.72363e9 | −1.02032 | −0.510161 | − | 0.860079i | \(-0.670414\pi\) | ||||
−0.510161 | + | 0.860079i | \(0.670414\pi\) | |||||||
\(434\) | −3.84289e8 | −0.225654 | ||||||||
\(435\) | −3.42501e8 | −0.199503 | ||||||||
\(436\) | −3.87467e9 | −2.23889 | ||||||||
\(437\) | 7.08347e8 | 0.406033 | ||||||||
\(438\) | 1.38486e9 | 0.787495 | ||||||||
\(439\) | −8.39890e8 | −0.473801 | −0.236901 | − | 0.971534i | \(-0.576132\pi\) | ||||
−0.236901 | + | 0.971534i | \(0.576132\pi\) | |||||||
\(440\) | −1.17949e10 | −6.60099 | ||||||||
\(441\) | 3.86231e6 | 0.00214443 | ||||||||
\(442\) | 9.91142e8 | 0.545957 | ||||||||
\(443\) | −2.24667e8 | −0.122780 | −0.0613899 | − | 0.998114i | \(-0.519553\pi\) | ||||
−0.0613899 | + | 0.998114i | \(0.519553\pi\) | |||||||
\(444\) | −4.53241e9 | −2.45747 | ||||||||
\(445\) | 8.43898e8 | 0.453973 | ||||||||
\(446\) | −3.38360e9 | −1.80595 | ||||||||
\(447\) | 1.10787e8 | 0.0586693 | ||||||||
\(448\) | 3.20462e9 | 1.68385 | ||||||||
\(449\) | −1.76424e9 | −0.919805 | −0.459902 | − | 0.887970i | \(-0.652116\pi\) | ||||
−0.459902 | + | 0.887970i | \(0.652116\pi\) | |||||||
\(450\) | −1.01739e8 | −0.0526313 | ||||||||
\(451\) | 2.60850e9 | 1.33898 | ||||||||
\(452\) | 1.33760e9 | 0.681303 | ||||||||
\(453\) | −3.12379e9 | −1.57884 | ||||||||
\(454\) | 2.94782e8 | 0.147844 | ||||||||
\(455\) | 3.52387e8 | 0.175380 | ||||||||
\(456\) | 2.68920e9 | 1.32815 | ||||||||
\(457\) | −3.98300e9 | −1.95211 | −0.976054 | − | 0.217527i | \(-0.930201\pi\) | ||||
−0.976054 | + | 0.217527i | \(0.930201\pi\) | |||||||
\(458\) | −8.59499e8 | −0.418039 | ||||||||
\(459\) | 2.07651e9 | 1.00228 | ||||||||
\(460\) | −1.05523e10 | −5.05469 | ||||||||
\(461\) | −2.43458e9 | −1.15737 | −0.578684 | − | 0.815552i | \(-0.696434\pi\) | ||||
−0.578684 | + | 0.815552i | \(0.696434\pi\) | |||||||
\(462\) | −1.77064e9 | −0.835380 | ||||||||
\(463\) | 1.46969e8 | 0.0688166 | 0.0344083 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344083 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(464\) | −1.02723e9 | −0.477369 | ||||||||
\(465\) | 1.11946e9 | 0.516324 | ||||||||
\(466\) | 6.25620e9 | 2.86391 | ||||||||
\(467\) | 1.70476e9 | 0.774559 | 0.387280 | − | 0.921962i | \(-0.373415\pi\) | ||||
0.387280 | + | 0.921962i | \(0.373415\pi\) | |||||||
\(468\) | −2.58359e7 | −0.0116510 | ||||||||
\(469\) | 6.86875e8 | 0.307449 | ||||||||
\(470\) | 9.66942e9 | 4.29594 | ||||||||
\(471\) | 8.91262e8 | 0.393036 | ||||||||
\(472\) | 1.11808e10 | 4.89412 | ||||||||
\(473\) | 5.10355e9 | 2.21747 | ||||||||
\(474\) | −3.03432e9 | −1.30869 | ||||||||
\(475\) | 1.58034e9 | 0.676584 | ||||||||
\(476\) | 2.51376e9 | 1.06832 | ||||||||
\(477\) | 5.42736e7 | 0.0228968 | ||||||||
\(478\) | −2.62901e9 | −1.10102 | ||||||||
\(479\) | 1.54581e9 | 0.642660 | 0.321330 | − | 0.946967i | \(-0.395870\pi\) | ||||
0.321330 | + | 0.946967i | \(0.395870\pi\) | |||||||
\(480\) | −1.77864e10 | −7.34080 | ||||||||
\(481\) | −5.90016e8 | −0.241744 | ||||||||
\(482\) | 6.71715e9 | 2.73225 | ||||||||
\(483\) | −1.01805e9 | −0.411107 | ||||||||
\(484\) | 1.86391e9 | 0.747252 | ||||||||
\(485\) | 2.46358e9 | 0.980552 | ||||||||
\(486\) | −1.48060e8 | −0.0585072 | ||||||||
\(487\) | 1.57113e9 | 0.616396 | 0.308198 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308198 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(488\) | −1.16960e9 | −0.455585 | ||||||||
\(489\) | 1.50076e9 | 0.580402 | ||||||||
\(490\) | 1.21310e9 | 0.465810 | ||||||||
\(491\) | −4.44730e9 | −1.69555 | −0.847776 | − | 0.530354i | \(-0.822059\pi\) | ||||
−0.847776 | + | 0.530354i | \(0.822059\pi\) | |||||||
\(492\) | 8.85973e9 | 3.35384 | ||||||||
\(493\) | −3.18055e8 | −0.119547 | ||||||||
\(494\) | 5.44718e8 | 0.203295 | ||||||||
\(495\) | 7.62816e7 | 0.0282684 | ||||||||
\(496\) | 3.35747e9 | 1.23545 | ||||||||
\(497\) | 1.00787e9 | 0.368264 | ||||||||
\(498\) | −7.78636e9 | −2.82509 | ||||||||
\(499\) | 6.30533e7 | 0.0227173 | 0.0113586 | − | 0.999935i | \(-0.496384\pi\) | ||||
0.0113586 | + | 0.999935i | \(0.496384\pi\) | |||||||
\(500\) | −1.04559e10 | −3.74082 | ||||||||
\(501\) | 1.60031e9 | 0.568554 | ||||||||
\(502\) | −3.86495e9 | −1.36358 | ||||||||
\(503\) | −1.20044e9 | −0.420584 | −0.210292 | − | 0.977639i | \(-0.567441\pi\) | ||||
−0.210292 | + | 0.977639i | \(0.567441\pi\) | |||||||
\(504\) | −5.71590e7 | −0.0198874 | ||||||||
\(505\) | −3.99751e9 | −1.38124 | ||||||||
\(506\) | 6.90228e9 | 2.36846 | ||||||||
\(507\) | −2.27415e8 | −0.0774983 | ||||||||
\(508\) | 3.94683e9 | 1.33575 | ||||||||
\(509\) | −2.58483e9 | −0.868800 | −0.434400 | − | 0.900720i | \(-0.643040\pi\) | ||||
−0.434400 | + | 0.900720i | \(0.643040\pi\) | |||||||
\(510\) | −9.93943e9 | −3.31792 | ||||||||
\(511\) | 4.57225e8 | 0.151585 | ||||||||
\(512\) | −1.04108e10 | −3.42798 | ||||||||
\(513\) | 1.14122e9 | 0.373216 | ||||||||
\(514\) | −4.76863e9 | −1.54890 | ||||||||
\(515\) | 6.95451e9 | 2.24358 | ||||||||
\(516\) | 1.73341e10 | 5.55428 | ||||||||
\(517\) | −4.65972e9 | −1.48301 | ||||||||
\(518\) | −2.03114e9 | −0.642074 | ||||||||
\(519\) | −4.20159e8 | −0.131925 | ||||||||
\(520\) | −5.21504e9 | −1.62647 | ||||||||
\(521\) | 2.64704e9 | 0.820028 | 0.410014 | − | 0.912079i | \(-0.365524\pi\) | ||||
0.410014 | + | 0.912079i | \(0.365524\pi\) | |||||||
\(522\) | 1.12532e7 | 0.00346282 | ||||||||
\(523\) | 3.04754e9 | 0.931522 | 0.465761 | − | 0.884911i | \(-0.345781\pi\) | ||||
0.465761 | + | 0.884911i | \(0.345781\pi\) | |||||||
\(524\) | −3.40108e9 | −1.03266 | ||||||||
\(525\) | −2.27129e9 | −0.685038 | ||||||||
\(526\) | −1.26705e10 | −3.79616 | ||||||||
\(527\) | 1.03956e9 | 0.309393 | ||||||||
\(528\) | 1.54698e10 | 4.57369 | ||||||||
\(529\) | 5.63716e8 | 0.165564 | ||||||||
\(530\) | 1.70465e10 | 4.97360 | ||||||||
\(531\) | −7.23100e7 | −0.0209589 | ||||||||
\(532\) | 1.38153e9 | 0.397805 | ||||||||
\(533\) | 1.15333e9 | 0.329921 | ||||||||
\(534\) | −1.87485e9 | −0.532808 | ||||||||
\(535\) | −6.45448e9 | −1.82231 | ||||||||
\(536\) | −1.01652e10 | −2.85127 | ||||||||
\(537\) | 2.44224e9 | 0.680580 | ||||||||
\(538\) | 9.03442e9 | 2.50128 | ||||||||
\(539\) | −5.84594e8 | −0.160803 | ||||||||
\(540\) | −1.70009e10 | −4.64615 | ||||||||
\(541\) | 4.88226e9 | 1.32566 | 0.662828 | − | 0.748772i | \(-0.269356\pi\) | ||||
0.662828 | + | 0.748772i | \(0.269356\pi\) | |||||||
\(542\) | 1.03918e10 | 2.80346 | ||||||||
\(543\) | −3.59401e9 | −0.963340 | ||||||||
\(544\) | −1.65169e10 | −4.39877 | ||||||||
\(545\) | 5.05819e9 | 1.33847 | ||||||||
\(546\) | −7.82880e8 | −0.205836 | ||||||||
\(547\) | −5.03886e9 | −1.31637 | −0.658183 | − | 0.752858i | \(-0.728675\pi\) | ||||
−0.658183 | + | 0.752858i | \(0.728675\pi\) | |||||||
\(548\) | 1.12941e10 | 2.93169 | ||||||||
\(549\) | 7.56424e6 | 0.00195102 | ||||||||
\(550\) | 1.53991e10 | 3.94663 | ||||||||
\(551\) | −1.74799e8 | −0.0445151 | ||||||||
\(552\) | 1.50663e10 | 3.81259 | ||||||||
\(553\) | −1.00181e9 | −0.251911 | ||||||||
\(554\) | 7.17847e9 | 1.79369 | ||||||||
\(555\) | 5.91683e9 | 1.46914 | ||||||||
\(556\) | −1.57185e10 | −3.87836 | ||||||||
\(557\) | 4.09225e9 | 1.00339 | 0.501694 | − | 0.865045i | \(-0.332710\pi\) | ||||
0.501694 | + | 0.865045i | \(0.332710\pi\) | |||||||
\(558\) | −3.67809e7 | −0.00896195 | ||||||||
\(559\) | 2.25651e9 | 0.546381 | ||||||||
\(560\) | −1.05986e10 | −2.55030 | ||||||||
\(561\) | 4.78983e9 | 1.14538 | ||||||||
\(562\) | 5.73046e8 | 0.136180 | ||||||||
\(563\) | −2.85540e9 | −0.674353 | −0.337176 | − | 0.941442i | \(-0.609472\pi\) | ||||
−0.337176 | + | 0.941442i | \(0.609472\pi\) | |||||||
\(564\) | −1.58266e10 | −3.71460 | ||||||||
\(565\) | −1.74616e9 | −0.407301 | ||||||||
\(566\) | −4.11505e9 | −0.953932 | ||||||||
\(567\) | −1.66482e9 | −0.383553 | ||||||||
\(568\) | −1.49157e10 | −3.41527 | ||||||||
\(569\) | −2.69662e9 | −0.613659 | −0.306830 | − | 0.951764i | \(-0.599268\pi\) | ||||
−0.306830 | + | 0.951764i | \(0.599268\pi\) | |||||||
\(570\) | −5.46257e9 | −1.23548 | ||||||||
\(571\) | −5.34341e9 | −1.20114 | −0.600568 | − | 0.799574i | \(-0.705059\pi\) | ||||
−0.600568 | + | 0.799574i | \(0.705059\pi\) | |||||||
\(572\) | 3.91049e9 | 0.873666 | ||||||||
\(573\) | −4.39772e9 | −0.976532 | ||||||||
\(574\) | 3.97036e9 | 0.876271 | ||||||||
\(575\) | 8.85388e9 | 1.94221 | ||||||||
\(576\) | 3.06719e8 | 0.0668748 | ||||||||
\(577\) | 1.51880e9 | 0.329143 | 0.164571 | − | 0.986365i | \(-0.447376\pi\) | ||||
0.164571 | + | 0.986365i | \(0.447376\pi\) | |||||||
\(578\) | −1.81963e8 | −0.0391954 | ||||||||
\(579\) | −7.52098e9 | −1.61027 | ||||||||
\(580\) | 2.60398e9 | 0.554166 | ||||||||
\(581\) | −2.57074e9 | −0.543802 | ||||||||
\(582\) | −5.47321e9 | −1.15083 | ||||||||
\(583\) | −8.21477e9 | −1.71694 | ||||||||
\(584\) | −6.76656e9 | −1.40580 | ||||||||
\(585\) | 3.37275e7 | 0.00696528 | ||||||||
\(586\) | 1.67249e10 | 3.43337 | ||||||||
\(587\) | −4.06252e9 | −0.829014 | −0.414507 | − | 0.910046i | \(-0.636046\pi\) | ||||
−0.414507 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(588\) | −1.98556e9 | −0.402775 | ||||||||
\(589\) | 5.71325e8 | 0.115207 | ||||||||
\(590\) | −2.27115e10 | −4.55265 | ||||||||
\(591\) | 1.18005e9 | 0.235150 | ||||||||
\(592\) | 1.77457e10 | 3.51535 | ||||||||
\(593\) | −1.42420e9 | −0.280466 | −0.140233 | − | 0.990119i | \(-0.544785\pi\) | ||||
−0.140233 | + | 0.990119i | \(0.544785\pi\) | |||||||
\(594\) | 1.11203e10 | 2.17703 | ||||||||
\(595\) | −3.28159e9 | −0.638668 | ||||||||
\(596\) | −8.42293e8 | −0.162968 | ||||||||
\(597\) | 3.83530e9 | 0.737716 | ||||||||
\(598\) | 3.05180e9 | 0.583583 | ||||||||
\(599\) | −5.04245e8 | −0.0958623 | −0.0479312 | − | 0.998851i | \(-0.515263\pi\) | ||||
−0.0479312 | + | 0.998851i | \(0.515263\pi\) | |||||||
\(600\) | 3.36132e10 | 6.35303 | ||||||||
\(601\) | −3.01576e9 | −0.566678 | −0.283339 | − | 0.959020i | \(-0.591442\pi\) | ||||
−0.283339 | + | 0.959020i | \(0.591442\pi\) | |||||||
\(602\) | 7.76805e9 | 1.45119 | ||||||||
\(603\) | 6.57419e7 | 0.0122105 | ||||||||
\(604\) | 2.37497e10 | 4.38560 | ||||||||
\(605\) | −2.43324e9 | −0.446727 | ||||||||
\(606\) | 8.88106e9 | 1.62110 | ||||||||
\(607\) | −3.64713e9 | −0.661898 | −0.330949 | − | 0.943649i | \(-0.607369\pi\) | ||||
−0.330949 | + | 0.943649i | \(0.607369\pi\) | |||||||
\(608\) | −9.07744e9 | −1.63795 | ||||||||
\(609\) | 2.51224e8 | 0.0450713 | ||||||||
\(610\) | 2.37582e9 | 0.423798 | ||||||||
\(611\) | −2.06027e9 | −0.365409 | ||||||||
\(612\) | 2.40596e8 | 0.0424286 | ||||||||
\(613\) | −4.88911e9 | −0.857271 | −0.428635 | − | 0.903478i | \(-0.641005\pi\) | ||||
−0.428635 | + | 0.903478i | \(0.641005\pi\) | |||||||
\(614\) | −8.63344e9 | −1.50520 | ||||||||
\(615\) | −1.15659e10 | −2.00501 | ||||||||
\(616\) | 8.65151e9 | 1.49128 | ||||||||
\(617\) | −5.88695e8 | −0.100900 | −0.0504501 | − | 0.998727i | \(-0.516066\pi\) | ||||
−0.0504501 | + | 0.998727i | \(0.516066\pi\) | |||||||
\(618\) | −1.54505e10 | −2.63319 | ||||||||
\(619\) | −6.16760e9 | −1.04520 | −0.522600 | − | 0.852578i | \(-0.675038\pi\) | ||||
−0.522600 | + | 0.852578i | \(0.675038\pi\) | |||||||
\(620\) | −8.51106e9 | −1.43421 | ||||||||
\(621\) | 6.39375e9 | 1.07136 | ||||||||
\(622\) | 8.01188e9 | 1.33496 | ||||||||
\(623\) | −6.18997e8 | −0.102561 | ||||||||
\(624\) | 6.83990e9 | 1.12695 | ||||||||
\(625\) | 2.66950e9 | 0.437371 | ||||||||
\(626\) | −1.18071e10 | −1.92368 | ||||||||
\(627\) | 2.63243e9 | 0.426501 | ||||||||
\(628\) | −6.77612e9 | −1.09175 | ||||||||
\(629\) | 5.49451e9 | 0.880342 | ||||||||
\(630\) | 1.16107e8 | 0.0184998 | ||||||||
\(631\) | 1.00481e10 | 1.59213 | 0.796067 | − | 0.605209i | \(-0.206910\pi\) | ||||
0.796067 | + | 0.605209i | \(0.206910\pi\) | |||||||
\(632\) | 1.48260e10 | 2.33622 | ||||||||
\(633\) | −1.13675e10 | −1.78135 | ||||||||
\(634\) | 8.04032e9 | 1.25303 | ||||||||
\(635\) | −5.15239e9 | −0.798547 | ||||||||
\(636\) | −2.79013e10 | −4.30056 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −1.70327e9 | −0.259664 | ||||||||
\(639\) | 9.64653e7 | 0.0146257 | ||||||||
\(640\) | 4.80149e10 | 7.24013 | ||||||||
\(641\) | 8.25313e8 | 0.123770 | 0.0618850 | − | 0.998083i | \(-0.480289\pi\) | ||||
0.0618850 | + | 0.998083i | \(0.480289\pi\) | |||||||
\(642\) | 1.43396e10 | 2.13877 | ||||||||
\(643\) | −1.11163e10 | −1.64900 | −0.824502 | − | 0.565859i | \(-0.808545\pi\) | ||||
−0.824502 | + | 0.565859i | \(0.808545\pi\) | |||||||
\(644\) | 7.74007e9 | 1.14194 | ||||||||
\(645\) | −2.26288e10 | −3.32050 | ||||||||
\(646\) | −5.07267e9 | −0.740326 | ||||||||
\(647\) | 3.35721e9 | 0.487319 | 0.243659 | − | 0.969861i | \(-0.421652\pi\) | ||||
0.243659 | + | 0.969861i | \(0.421652\pi\) | |||||||
\(648\) | 2.46379e10 | 3.55706 | ||||||||
\(649\) | 1.09447e10 | 1.57163 | ||||||||
\(650\) | 6.80863e9 | 0.972440 | ||||||||
\(651\) | −8.21120e8 | −0.116647 | ||||||||
\(652\) | −1.14100e10 | −1.61220 | ||||||||
\(653\) | −3.12328e9 | −0.438949 | −0.219475 | − | 0.975618i | \(-0.570434\pi\) | ||||
−0.219475 | + | 0.975618i | \(0.570434\pi\) | |||||||
\(654\) | −1.12375e10 | −1.57090 | ||||||||
\(655\) | 4.43994e9 | 0.617351 | ||||||||
\(656\) | −3.46885e10 | −4.79757 | ||||||||
\(657\) | 4.37617e7 | 0.00602027 | ||||||||
\(658\) | −7.09249e9 | −0.970529 | ||||||||
\(659\) | −1.85958e8 | −0.0253113 | −0.0126557 | − | 0.999920i | \(-0.504029\pi\) | ||||
−0.0126557 | + | 0.999920i | \(0.504029\pi\) | |||||||
\(660\) | −3.92154e10 | −5.30949 | ||||||||
\(661\) | −7.98250e9 | −1.07506 | −0.537532 | − | 0.843244i | \(-0.680643\pi\) | ||||
−0.537532 | + | 0.843244i | \(0.680643\pi\) | |||||||
\(662\) | −1.36674e10 | −1.83098 | ||||||||
\(663\) | 2.11780e9 | 0.282220 | ||||||||
\(664\) | 3.80448e10 | 5.04321 | ||||||||
\(665\) | −1.80352e9 | −0.237818 | ||||||||
\(666\) | −1.94403e8 | −0.0255002 | ||||||||
\(667\) | −9.79315e8 | −0.127786 | ||||||||
\(668\) | −1.21669e10 | −1.57929 | ||||||||
\(669\) | −7.22982e9 | −0.933547 | ||||||||
\(670\) | 2.06486e10 | 2.65234 | ||||||||
\(671\) | −1.14491e9 | −0.146300 | ||||||||
\(672\) | 1.30463e10 | 1.65842 | ||||||||
\(673\) | −9.52399e9 | −1.20439 | −0.602194 | − | 0.798350i | \(-0.705706\pi\) | ||||
−0.602194 | + | 0.798350i | \(0.705706\pi\) | |||||||
\(674\) | 1.49935e10 | 1.88623 | ||||||||
\(675\) | 1.42646e10 | 1.78523 | ||||||||
\(676\) | 1.72900e9 | 0.215269 | ||||||||
\(677\) | −4.95260e9 | −0.613442 | −0.306721 | − | 0.951800i | \(-0.599232\pi\) | ||||
−0.306721 | + | 0.951800i | \(0.599232\pi\) | |||||||
\(678\) | 3.87936e9 | 0.478031 | ||||||||
\(679\) | −1.80703e9 | −0.221524 | ||||||||
\(680\) | 4.85649e10 | 5.92299 | ||||||||
\(681\) | 6.29867e8 | 0.0764247 | ||||||||
\(682\) | 5.56711e9 | 0.672023 | ||||||||
\(683\) | 1.44209e10 | 1.73189 | 0.865943 | − | 0.500142i | \(-0.166719\pi\) | ||||
0.865943 | + | 0.500142i | \(0.166719\pi\) | |||||||
\(684\) | 1.32228e8 | 0.0157990 | ||||||||
\(685\) | −1.47438e10 | −1.75264 | ||||||||
\(686\) | −8.89802e8 | −0.105235 | ||||||||
\(687\) | −1.83651e9 | −0.216095 | ||||||||
\(688\) | −6.78683e10 | −7.94524 | ||||||||
\(689\) | −3.63212e9 | −0.423051 | ||||||||
\(690\) | −3.06043e10 | −3.54658 | ||||||||
\(691\) | 1.55754e10 | 1.79584 | 0.897919 | − | 0.440161i | \(-0.145079\pi\) | ||||
0.897919 | + | 0.440161i | \(0.145079\pi\) | |||||||
\(692\) | 3.19440e9 | 0.366453 | ||||||||
\(693\) | −5.59524e7 | −0.00638634 | ||||||||
\(694\) | −1.90423e10 | −2.16252 | ||||||||
\(695\) | 2.05197e10 | 2.31859 | ||||||||
\(696\) | −3.71791e9 | −0.417990 | ||||||||
\(697\) | −1.07404e10 | −1.20145 | ||||||||
\(698\) | −4.71785e9 | −0.525110 | ||||||||
\(699\) | 1.33678e10 | 1.48043 | ||||||||
\(700\) | 1.72682e10 | 1.90285 | ||||||||
\(701\) | −3.18364e9 | −0.349069 | −0.174534 | − | 0.984651i | \(-0.555842\pi\) | ||||
−0.174534 | + | 0.984651i | \(0.555842\pi\) | |||||||
\(702\) | 4.91678e9 | 0.536415 | ||||||||
\(703\) | 3.01971e9 | 0.327809 | ||||||||
\(704\) | −4.64246e10 | −5.01469 | ||||||||
\(705\) | 2.06609e10 | 2.22069 | ||||||||
\(706\) | 2.51256e10 | 2.68720 | ||||||||
\(707\) | 2.93216e9 | 0.312047 | ||||||||
\(708\) | 3.71736e10 | 3.93658 | ||||||||
\(709\) | −9.62913e9 | −1.01467 | −0.507335 | − | 0.861749i | \(-0.669369\pi\) | ||||
−0.507335 | + | 0.861749i | \(0.669369\pi\) | |||||||
\(710\) | 3.02984e10 | 3.17698 | ||||||||
\(711\) | −9.58848e7 | −0.0100047 | ||||||||
\(712\) | 9.16066e9 | 0.951145 | ||||||||
\(713\) | 3.20087e9 | 0.330716 | ||||||||
\(714\) | 7.29054e9 | 0.749577 | ||||||||
\(715\) | −5.10495e9 | −0.522300 | ||||||||
\(716\) | −1.85680e10 | −1.89047 | ||||||||
\(717\) | −5.61747e9 | −0.569146 | ||||||||
\(718\) | 1.83106e10 | 1.84615 | ||||||||
\(719\) | −3.39050e8 | −0.0340183 | −0.0170092 | − | 0.999855i | \(-0.505414\pi\) | ||||
−0.0170092 | + | 0.999855i | \(0.505414\pi\) | |||||||
\(720\) | −1.01441e9 | −0.101286 | ||||||||
\(721\) | −5.10112e9 | −0.506864 | ||||||||
\(722\) | 1.69221e10 | 1.67330 | ||||||||
\(723\) | 1.43527e10 | 1.41237 | ||||||||
\(724\) | 2.73247e10 | 2.67590 | ||||||||
\(725\) | −2.18487e9 | −0.212933 | ||||||||
\(726\) | 5.40581e9 | 0.524304 | ||||||||
\(727\) | 9.26879e8 | 0.0894648 | 0.0447324 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447324 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(728\) | 3.82522e9 | 0.367448 | ||||||||
\(729\) | 1.02987e10 | 0.984542 | ||||||||
\(730\) | 1.37449e10 | 1.30771 | ||||||||
\(731\) | −2.10137e10 | −1.98971 | ||||||||
\(732\) | −3.88868e9 | −0.366449 | ||||||||
\(733\) | −6.82501e9 | −0.640088 | −0.320044 | − | 0.947403i | \(-0.603698\pi\) | ||||
−0.320044 | + | 0.947403i | \(0.603698\pi\) | |||||||
\(734\) | −2.11614e10 | −1.97519 | ||||||||
\(735\) | 2.59205e9 | 0.240790 | ||||||||
\(736\) | −5.08567e10 | −4.70192 | ||||||||
\(737\) | −9.95061e9 | −0.915616 | ||||||||
\(738\) | 3.80010e8 | 0.0348015 | ||||||||
\(739\) | 1.27514e10 | 1.16225 | 0.581127 | − | 0.813813i | \(-0.302612\pi\) | ||||
0.581127 | + | 0.813813i | \(0.302612\pi\) | |||||||
\(740\) | −4.49847e10 | −4.08088 | ||||||||
\(741\) | 1.16391e9 | 0.105089 | ||||||||
\(742\) | −1.25036e10 | −1.12362 | ||||||||
\(743\) | 8.91329e9 | 0.797218 | 0.398609 | − | 0.917121i | \(-0.369493\pi\) | ||||
0.398609 | + | 0.917121i | \(0.369493\pi\) | |||||||
\(744\) | 1.21519e10 | 1.08178 | ||||||||
\(745\) | 1.09957e9 | 0.0974263 | ||||||||
\(746\) | 2.77512e10 | 2.44735 | ||||||||
\(747\) | −2.46049e8 | −0.0215973 | ||||||||
\(748\) | −3.64163e10 | −3.18156 | ||||||||
\(749\) | 4.73435e9 | 0.411693 | ||||||||
\(750\) | −3.03247e10 | −2.62472 | ||||||||
\(751\) | −7.84865e9 | −0.676169 | −0.338084 | − | 0.941116i | \(-0.609779\pi\) | ||||
−0.338084 | + | 0.941116i | \(0.609779\pi\) | |||||||
\(752\) | 6.19660e10 | 5.31363 | ||||||||
\(753\) | −8.25834e9 | −0.704872 | ||||||||
\(754\) | −7.53092e8 | −0.0639806 | ||||||||
\(755\) | −3.10040e10 | −2.62183 | ||||||||
\(756\) | 1.24701e10 | 1.04965 | ||||||||
\(757\) | 1.18026e10 | 0.988873 | 0.494437 | − | 0.869214i | \(-0.335374\pi\) | ||||
0.494437 | + | 0.869214i | \(0.335374\pi\) | |||||||
\(758\) | 1.02669e10 | 0.856247 | ||||||||
\(759\) | 1.47483e10 | 1.22432 | ||||||||
\(760\) | 2.66906e10 | 2.20552 | ||||||||
\(761\) | 1.54333e10 | 1.26944 | 0.634718 | − | 0.772744i | \(-0.281116\pi\) | ||||
0.634718 | + | 0.772744i | \(0.281116\pi\) | |||||||
\(762\) | 1.14468e10 | 0.937220 | ||||||||
\(763\) | −3.71017e9 | −0.302383 | ||||||||
\(764\) | 3.34352e10 | 2.71254 | ||||||||
\(765\) | −3.14086e8 | −0.0253650 | ||||||||
\(766\) | 1.75748e10 | 1.41283 | ||||||||
\(767\) | 4.83916e9 | 0.387245 | ||||||||
\(768\) | −5.03277e10 | −4.00906 | ||||||||
\(769\) | −1.08288e10 | −0.858692 | −0.429346 | − | 0.903140i | \(-0.641256\pi\) | ||||
−0.429346 | + | 0.903140i | \(0.641256\pi\) | |||||||
\(770\) | −1.75738e10 | −1.38723 | ||||||||
\(771\) | −1.01892e10 | −0.800666 | ||||||||
\(772\) | 5.71808e10 | 4.47291 | ||||||||
\(773\) | −1.34170e10 | −1.04478 | −0.522392 | − | 0.852705i | \(-0.674960\pi\) | ||||
−0.522392 | + | 0.852705i | \(0.674960\pi\) | |||||||
\(774\) | 7.43492e8 | 0.0576346 | ||||||||
\(775\) | 7.14120e9 | 0.551080 | ||||||||
\(776\) | 2.67426e10 | 2.05441 | ||||||||
\(777\) | −4.33998e9 | −0.331905 | ||||||||
\(778\) | −2.24533e10 | −1.70943 | ||||||||
\(779\) | −5.90277e9 | −0.447378 | ||||||||
\(780\) | −1.73389e10 | −1.30825 | ||||||||
\(781\) | −1.46009e10 | −1.09673 | ||||||||
\(782\) | −2.84198e10 | −2.12519 | ||||||||
\(783\) | −1.57778e9 | −0.117458 | ||||||||
\(784\) | 7.77406e9 | 0.576158 | ||||||||
\(785\) | 8.84588e9 | 0.652675 | ||||||||
\(786\) | −9.86398e9 | −0.724559 | ||||||||
\(787\) | 1.38342e9 | 0.101168 | 0.0505840 | − | 0.998720i | \(-0.483892\pi\) | ||||
0.0505840 | + | 0.998720i | \(0.483892\pi\) | |||||||
\(788\) | −8.97174e9 | −0.653183 | ||||||||
\(789\) | −2.70734e10 | −1.96234 | ||||||||
\(790\) | −3.01160e10 | −2.17322 | ||||||||
\(791\) | 1.28081e9 | 0.0920165 | ||||||||
\(792\) | 8.28050e8 | 0.0592268 | ||||||||
\(793\) | −5.06217e8 | −0.0360479 | ||||||||
\(794\) | −1.88717e10 | −1.33795 | ||||||||
\(795\) | 3.64238e10 | 2.57099 | ||||||||
\(796\) | −2.91592e10 | −2.04918 | ||||||||
\(797\) | −7.26613e9 | −0.508392 | −0.254196 | − | 0.967153i | \(-0.581811\pi\) | ||||
−0.254196 | + | 0.967153i | \(0.581811\pi\) | |||||||
\(798\) | 4.00678e9 | 0.279117 | ||||||||
\(799\) | 1.91862e10 | 1.33068 | ||||||||
\(800\) | −1.13462e11 | −7.83494 | ||||||||
\(801\) | −5.92452e7 | −0.00407323 | ||||||||
\(802\) | −1.31678e10 | −0.901368 | ||||||||
\(803\) | −6.62372e9 | −0.451437 | ||||||||
\(804\) | −3.37971e10 | −2.29342 | ||||||||
\(805\) | −1.01043e10 | −0.682684 | ||||||||
\(806\) | 2.46147e9 | 0.165585 | ||||||||
\(807\) | 1.93041e10 | 1.29298 | ||||||||
\(808\) | −4.33936e10 | −2.89392 | ||||||||
\(809\) | −1.49759e10 | −0.994427 | −0.497213 | − | 0.867628i | \(-0.665643\pi\) | ||||
−0.497213 | + | 0.867628i | \(0.665643\pi\) | |||||||
\(810\) | −5.00471e10 | −3.30888 | ||||||||
\(811\) | −6.06531e9 | −0.399282 | −0.199641 | − | 0.979869i | \(-0.563978\pi\) | ||||
−0.199641 | + | 0.979869i | \(0.563978\pi\) | |||||||
\(812\) | −1.91001e9 | −0.125196 | ||||||||
\(813\) | 2.22045e10 | 1.44919 | ||||||||
\(814\) | 2.94246e10 | 1.91217 | ||||||||
\(815\) | 1.48952e10 | 0.963816 | ||||||||
\(816\) | −6.36964e10 | −4.10392 | ||||||||
\(817\) | −1.15488e10 | −0.740901 | ||||||||
\(818\) | −5.45052e10 | −3.48178 | ||||||||
\(819\) | −2.47390e7 | −0.00157358 | ||||||||
\(820\) | 8.79339e10 | 5.56939 | ||||||||
\(821\) | 3.43518e9 | 0.216645 | 0.108323 | − | 0.994116i | \(-0.465452\pi\) | ||||
0.108323 | + | 0.994116i | \(0.465452\pi\) | |||||||
\(822\) | 3.27556e10 | 2.05700 | ||||||||
\(823\) | −1.57126e8 | −0.00982537 | −0.00491269 | − | 0.999988i | \(-0.501564\pi\) | ||||
−0.00491269 | + | 0.999988i | \(0.501564\pi\) | |||||||
\(824\) | 7.54924e10 | 4.70065 | ||||||||
\(825\) | 3.29036e10 | 2.04012 | ||||||||
\(826\) | 1.66588e10 | 1.02852 | ||||||||
\(827\) | 2.08809e10 | 1.28375 | 0.641874 | − | 0.766810i | \(-0.278157\pi\) | ||||
0.641874 | + | 0.766810i | \(0.278157\pi\) | |||||||
\(828\) | 7.40815e8 | 0.0453527 | ||||||||
\(829\) | 2.58551e9 | 0.157618 | 0.0788088 | − | 0.996890i | \(-0.474888\pi\) | ||||
0.0788088 | + | 0.996890i | \(0.474888\pi\) | |||||||
\(830\) | −7.72805e10 | −4.69134 | ||||||||
\(831\) | 1.53384e10 | 0.927208 | ||||||||
\(832\) | −2.05264e10 | −1.23561 | ||||||||
\(833\) | 2.40704e9 | 0.144286 | ||||||||
\(834\) | −4.55875e10 | −2.72123 | ||||||||
\(835\) | 1.58833e10 | 0.944142 | ||||||||
\(836\) | −2.00139e10 | −1.18471 | ||||||||
\(837\) | 5.15695e9 | 0.303986 | ||||||||
\(838\) | −1.06938e9 | −0.0627735 | ||||||||
\(839\) | −7.67324e9 | −0.448551 | −0.224276 | − | 0.974526i | \(-0.572002\pi\) | ||||
−0.224276 | + | 0.974526i | \(0.572002\pi\) | |||||||
\(840\) | −3.83602e10 | −2.23308 | ||||||||
\(841\) | −1.70082e10 | −0.985990 | ||||||||
\(842\) | 2.57131e10 | 1.48444 | ||||||||
\(843\) | 1.22444e9 | 0.0703949 | ||||||||
\(844\) | 8.64249e10 | 4.94812 | ||||||||
\(845\) | −2.25713e9 | −0.128694 | ||||||||
\(846\) | −6.78834e8 | −0.0385449 | ||||||||
\(847\) | 1.78478e9 | 0.100924 | ||||||||
\(848\) | 1.09242e11 | 6.15183 | ||||||||
\(849\) | −8.79272e9 | −0.493113 | ||||||||
\(850\) | −6.34051e10 | −3.54126 | ||||||||
\(851\) | 1.69180e10 | 0.941014 | ||||||||
\(852\) | −4.95915e10 | −2.74707 | ||||||||
\(853\) | −2.43199e10 | −1.34165 | −0.670825 | − | 0.741616i | \(-0.734060\pi\) | ||||
−0.670825 | + | 0.741616i | \(0.734060\pi\) | |||||||
\(854\) | −1.74266e9 | −0.0957435 | ||||||||
\(855\) | −1.72618e8 | −0.00944504 | ||||||||
\(856\) | −7.00645e10 | −3.81803 | ||||||||
\(857\) | −1.57922e10 | −0.857055 | −0.428528 | − | 0.903529i | \(-0.640968\pi\) | ||||
−0.428528 | + | 0.903529i | \(0.640968\pi\) | |||||||
\(858\) | 1.13414e10 | 0.613001 | ||||||||
\(859\) | −1.62472e10 | −0.874588 | −0.437294 | − | 0.899319i | \(-0.644063\pi\) | ||||
−0.437294 | + | 0.899319i | \(0.644063\pi\) | |||||||
\(860\) | 1.72043e11 | 9.22345 | ||||||||
\(861\) | 8.48358e9 | 0.452968 | ||||||||
\(862\) | −4.37928e9 | −0.232877 | ||||||||
\(863\) | −1.85124e10 | −0.980449 | −0.490225 | − | 0.871596i | \(-0.663085\pi\) | ||||
−0.490225 | + | 0.871596i | \(0.663085\pi\) | |||||||
\(864\) | −8.19355e10 | −4.32189 | ||||||||
\(865\) | −4.17012e9 | −0.219075 | ||||||||
\(866\) | 3.80063e10 | 1.98858 | ||||||||
\(867\) | −3.88805e8 | −0.0202612 | ||||||||
\(868\) | 6.24284e9 | 0.324014 | ||||||||
\(869\) | 1.45130e10 | 0.750218 | ||||||||
\(870\) | 7.55220e9 | 0.388827 | ||||||||
\(871\) | −4.39961e9 | −0.225606 | ||||||||
\(872\) | 5.49075e10 | 2.80430 | ||||||||
\(873\) | −1.72954e8 | −0.00879792 | ||||||||
\(874\) | −1.56192e10 | −0.791348 | ||||||||
\(875\) | −1.00120e10 | −0.505233 | ||||||||
\(876\) | −2.24973e10 | −1.13075 | ||||||||
\(877\) | 1.60267e10 | 0.802314 | 0.401157 | − | 0.916009i | \(-0.368608\pi\) | ||||
0.401157 | + | 0.916009i | \(0.368608\pi\) | |||||||
\(878\) | 1.85197e10 | 0.923427 | ||||||||
\(879\) | 3.57364e10 | 1.77480 | ||||||||
\(880\) | 1.53540e11 | 7.59507 | ||||||||
\(881\) | 2.20272e10 | 1.08529 | 0.542643 | − | 0.839964i | \(-0.317424\pi\) | ||||
0.542643 | + | 0.839964i | \(0.317424\pi\) | |||||||
\(882\) | −8.51644e7 | −0.00417944 | ||||||||
\(883\) | −2.75424e10 | −1.34629 | −0.673146 | − | 0.739510i | \(-0.735057\pi\) | ||||
−0.673146 | + | 0.739510i | \(0.735057\pi\) | |||||||
\(884\) | −1.61013e10 | −0.783930 | ||||||||
\(885\) | −4.85283e10 | −2.35339 | ||||||||
\(886\) | 4.95394e9 | 0.239295 | ||||||||
\(887\) | 5.33447e9 | 0.256660 | 0.128330 | − | 0.991732i | \(-0.459038\pi\) | ||||
0.128330 | + | 0.991732i | \(0.459038\pi\) | |||||||
\(888\) | 6.42282e10 | 3.07808 | ||||||||
\(889\) | 3.77926e9 | 0.180406 | ||||||||
\(890\) | −1.86081e10 | −0.884782 | ||||||||
\(891\) | 2.41178e10 | 1.14226 | ||||||||
\(892\) | 5.49671e10 | 2.59314 | ||||||||
\(893\) | 1.05445e10 | 0.495501 | ||||||||
\(894\) | −2.44286e9 | −0.114345 | ||||||||
\(895\) | 2.42396e10 | 1.13017 | ||||||||
\(896\) | −3.52188e10 | −1.63567 | ||||||||
\(897\) | 6.52087e9 | 0.301670 | ||||||||
\(898\) | 3.89017e10 | 1.79268 | ||||||||
\(899\) | −7.89877e8 | −0.0362577 | ||||||||
\(900\) | 1.65277e9 | 0.0755725 | ||||||||
\(901\) | 3.38240e10 | 1.54059 | ||||||||
\(902\) | −5.75178e10 | −2.60963 | ||||||||
\(903\) | 1.65982e10 | 0.750159 | ||||||||
\(904\) | −1.89549e10 | −0.853359 | ||||||||
\(905\) | −3.56710e10 | −1.59972 | ||||||||
\(906\) | 6.88800e10 | 3.07712 | ||||||||
\(907\) | 1.78222e10 | 0.793115 | 0.396558 | − | 0.918010i | \(-0.370205\pi\) | ||||
0.396558 | + | 0.918010i | \(0.370205\pi\) | |||||||
\(908\) | −4.78878e9 | −0.212287 | ||||||||
\(909\) | 2.80642e8 | 0.0123931 | ||||||||
\(910\) | −7.77018e9 | −0.341811 | ||||||||
\(911\) | −1.58172e8 | −0.00693129 | −0.00346565 | − | 0.999994i | \(-0.501103\pi\) | ||||
−0.00346565 | + | 0.999994i | \(0.501103\pi\) | |||||||
\(912\) | −3.50066e10 | −1.52816 | ||||||||
\(913\) | 3.72417e10 | 1.61950 | ||||||||
\(914\) | 8.78257e10 | 3.80461 | ||||||||
\(915\) | 5.07647e9 | 0.219073 | ||||||||
\(916\) | 1.39627e10 | 0.600255 | ||||||||
\(917\) | −3.25668e9 | −0.139471 | ||||||||
\(918\) | −4.57874e10 | −1.95342 | ||||||||
\(919\) | 1.68755e10 | 0.717220 | 0.358610 | − | 0.933487i | \(-0.383251\pi\) | ||||
0.358610 | + | 0.933487i | \(0.383251\pi\) | |||||||
\(920\) | 1.49535e11 | 6.33119 | ||||||||
\(921\) | −1.84473e10 | −0.778079 | ||||||||
\(922\) | 5.36829e10 | 2.25568 | ||||||||
\(923\) | −6.45569e9 | −0.270232 | ||||||||
\(924\) | 2.87644e10 | 1.19951 | ||||||||
\(925\) | 3.77444e10 | 1.56804 | ||||||||
\(926\) | −3.24069e9 | −0.134122 | ||||||||
\(927\) | −4.88236e8 | −0.0201303 | ||||||||
\(928\) | 1.25499e10 | 0.515492 | ||||||||
\(929\) | 1.42088e10 | 0.581438 | 0.290719 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290719 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(930\) | −2.46842e10 | −1.00630 | ||||||||
\(931\) | 1.32288e9 | 0.0537273 | ||||||||
\(932\) | −1.01633e11 | −4.11225 | ||||||||
\(933\) | 1.71192e10 | 0.690076 | ||||||||
\(934\) | −3.75902e10 | −1.50960 | ||||||||
\(935\) | 4.75397e10 | 1.90202 | ||||||||
\(936\) | 3.66118e8 | 0.0145934 | ||||||||
\(937\) | −3.87897e10 | −1.54038 | −0.770189 | − | 0.637815i | \(-0.779838\pi\) | ||||
−0.770189 | + | 0.637815i | \(0.779838\pi\) | |||||||
\(938\) | −1.51457e10 | −0.599210 | ||||||||
\(939\) | −2.52285e10 | −0.994401 | ||||||||
\(940\) | −1.57081e11 | −6.16847 | ||||||||
\(941\) | 3.60809e10 | 1.41161 | 0.705804 | − | 0.708407i | \(-0.250586\pi\) | ||||
0.705804 | + | 0.708407i | \(0.250586\pi\) | |||||||
\(942\) | −1.96524e10 | −0.766017 | ||||||||
\(943\) | −3.30705e10 | −1.28425 | ||||||||
\(944\) | −1.45546e11 | −5.63116 | ||||||||
\(945\) | −1.62791e10 | −0.627507 | ||||||||
\(946\) | −1.12534e11 | −4.32180 | ||||||||
\(947\) | 2.13252e9 | 0.0815957 | 0.0407978 | − | 0.999167i | \(-0.487010\pi\) | ||||
0.0407978 | + | 0.999167i | \(0.487010\pi\) | |||||||
\(948\) | 4.92931e10 | 1.87913 | ||||||||
\(949\) | −2.92864e9 | −0.111233 | ||||||||
\(950\) | −3.48466e10 | −1.31864 | ||||||||
\(951\) | 1.71800e10 | 0.647724 | ||||||||
\(952\) | −3.56222e10 | −1.33811 | ||||||||
\(953\) | 3.44469e10 | 1.28922 | 0.644608 | − | 0.764514i | \(-0.277021\pi\) | ||||
0.644608 | + | 0.764514i | \(0.277021\pi\) | |||||||
\(954\) | −1.19674e9 | −0.0446252 | ||||||||
\(955\) | −4.36479e10 | −1.62163 | ||||||||
\(956\) | 4.27087e10 | 1.58093 | ||||||||
\(957\) | −3.63942e9 | −0.134227 | ||||||||
\(958\) | −3.40852e10 | −1.25253 | ||||||||
\(959\) | 1.08146e10 | 0.395953 | ||||||||
\(960\) | 2.05844e11 | 7.50911 | ||||||||
\(961\) | −2.49309e10 | −0.906163 | ||||||||
\(962\) | 1.30099e10 | 0.471154 | ||||||||
\(963\) | 4.53132e8 | 0.0163506 | ||||||||
\(964\) | −1.09121e11 | −3.92319 | ||||||||
\(965\) | −7.46467e10 | −2.67402 | ||||||||
\(966\) | 2.24481e10 | 0.801236 | ||||||||
\(967\) | −3.00671e10 | −1.06930 | −0.534650 | − | 0.845074i | \(-0.679556\pi\) | ||||
−0.534650 | + | 0.845074i | \(0.679556\pi\) | |||||||
\(968\) | −2.64133e10 | −0.935962 | ||||||||
\(969\) | −1.08389e10 | −0.382695 | ||||||||
\(970\) | −5.43223e10 | −1.91107 | ||||||||
\(971\) | −1.27577e10 | −0.447205 | −0.223602 | − | 0.974680i | \(-0.571782\pi\) | ||||
−0.223602 | + | 0.974680i | \(0.571782\pi\) | |||||||
\(972\) | 2.40525e9 | 0.0840096 | ||||||||
\(973\) | −1.50511e10 | −0.523810 | ||||||||
\(974\) | −3.46436e10 | −1.20134 | ||||||||
\(975\) | 1.45482e10 | 0.502680 | ||||||||
\(976\) | 1.52253e10 | 0.524194 | ||||||||
\(977\) | 6.08745e9 | 0.208835 | 0.104418 | − | 0.994534i | \(-0.466702\pi\) | ||||
0.104418 | + | 0.994534i | \(0.466702\pi\) | |||||||
\(978\) | −3.30919e10 | −1.13119 | ||||||||
\(979\) | 8.96728e9 | 0.305437 | ||||||||
\(980\) | −1.97069e10 | −0.668849 | ||||||||
\(981\) | −3.55106e8 | −0.0120093 | ||||||||
\(982\) | 9.80636e10 | 3.30459 | ||||||||
\(983\) | 2.52717e10 | 0.848589 | 0.424294 | − | 0.905524i | \(-0.360522\pi\) | ||||
0.424294 | + | 0.905524i | \(0.360522\pi\) | |||||||
\(984\) | −1.25550e11 | −4.20082 | ||||||||
\(985\) | 1.17122e10 | 0.390490 | ||||||||
\(986\) | 7.01315e9 | 0.232994 | ||||||||
\(987\) | −1.51547e10 | −0.501692 | ||||||||
\(988\) | −8.84905e9 | −0.291909 | ||||||||
\(989\) | −6.47027e10 | −2.12684 | ||||||||
\(990\) | −1.68202e9 | −0.0550945 | ||||||||
\(991\) | −1.17673e10 | −0.384079 | −0.192039 | − | 0.981387i | \(-0.561510\pi\) | ||||
−0.192039 | + | 0.981387i | \(0.561510\pi\) | |||||||
\(992\) | −4.10190e10 | −1.33412 | ||||||||
\(993\) | −2.92035e10 | −0.946483 | ||||||||
\(994\) | −2.22238e10 | −0.717737 | ||||||||
\(995\) | 3.80658e10 | 1.22505 | ||||||||
\(996\) | 1.26491e11 | 4.05650 | ||||||||
\(997\) | −3.40723e10 | −1.08885 | −0.544425 | − | 0.838810i | \(-0.683252\pi\) | ||||
−0.544425 | + | 0.838810i | \(0.683252\pi\) | |||||||
\(998\) | −1.39033e9 | −0.0442754 | ||||||||
\(999\) | 2.72567e10 | 0.864957 |
(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 | 91.8.a.c.1.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.c.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial |