Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,22,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(27.9477344287\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{474529}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 118632 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(344.930\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1024.00 | −0.707107 | ||||||||
\(3\) | −94506.7 | −0.924037 | −0.462019 | − | 0.886870i | \(-0.652875\pi\) | ||||
−0.462019 | + | 0.886870i | \(0.652875\pi\) | |||||||
\(4\) | 1.04858e6 | 0.500000 | ||||||||
\(5\) | 9.76562e6 | 0.447214 | ||||||||
\(6\) | 9.67749e7 | 0.653393 | ||||||||
\(7\) | 3.65434e8 | 0.488967 | 0.244483 | − | 0.969653i | \(-0.421382\pi\) | ||||
0.244483 | + | 0.969653i | \(0.421382\pi\) | |||||||
\(8\) | −1.07374e9 | −0.353553 | ||||||||
\(9\) | −1.52883e9 | −0.146155 | ||||||||
\(10\) | −1.00000e10 | −0.316228 | ||||||||
\(11\) | −3.92190e10 | −0.455904 | −0.227952 | − | 0.973672i | \(-0.573203\pi\) | ||||
−0.227952 | + | 0.973672i | \(0.573203\pi\) | |||||||
\(12\) | −9.90975e10 | −0.462019 | ||||||||
\(13\) | −4.64598e11 | −0.934701 | −0.467350 | − | 0.884072i | \(-0.654791\pi\) | ||||
−0.467350 | + | 0.884072i | \(0.654791\pi\) | |||||||
\(14\) | −3.74204e11 | −0.345752 | ||||||||
\(15\) | −9.22917e11 | −0.413242 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | 2.43124e11 | 0.0292492 | 0.0146246 | − | 0.999893i | \(-0.495345\pi\) | ||||
0.0146246 | + | 0.999893i | \(0.495345\pi\) | |||||||
\(18\) | 1.56552e12 | 0.103347 | ||||||||
\(19\) | −6.74889e12 | −0.252534 | −0.126267 | − | 0.991996i | \(-0.540300\pi\) | ||||
−0.126267 | + | 0.991996i | \(0.540300\pi\) | |||||||
\(20\) | 1.02400e13 | 0.223607 | ||||||||
\(21\) | −3.45360e13 | −0.451824 | ||||||||
\(22\) | 4.01602e13 | 0.322373 | ||||||||
\(23\) | −1.66102e14 | −0.836052 | −0.418026 | − | 0.908435i | \(-0.637278\pi\) | ||||
−0.418026 | + | 0.908435i | \(0.637278\pi\) | |||||||
\(24\) | 1.01476e14 | 0.326697 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | 4.75749e14 | 0.660933 | ||||||||
\(27\) | 1.13306e15 | 1.05909 | ||||||||
\(28\) | 3.83185e14 | 0.244483 | ||||||||
\(29\) | 2.85150e15 | 1.25862 | 0.629310 | − | 0.777155i | \(-0.283338\pi\) | ||||
0.629310 | + | 0.777155i | \(0.283338\pi\) | |||||||
\(30\) | 9.45067e14 | 0.292206 | ||||||||
\(31\) | 3.48202e15 | 0.763017 | 0.381508 | − | 0.924365i | \(-0.375405\pi\) | ||||
0.381508 | + | 0.924365i | \(0.375405\pi\) | |||||||
\(32\) | −1.12590e15 | −0.176777 | ||||||||
\(33\) | 3.70646e15 | 0.421272 | ||||||||
\(34\) | −2.48959e14 | −0.0206823 | ||||||||
\(35\) | 3.56869e15 | 0.218673 | ||||||||
\(36\) | −1.60309e15 | −0.0730774 | ||||||||
\(37\) | 3.87028e15 | 0.132320 | 0.0661598 | − | 0.997809i | \(-0.478925\pi\) | ||||
0.0661598 | + | 0.997809i | \(0.478925\pi\) | |||||||
\(38\) | 6.91086e15 | 0.178568 | ||||||||
\(39\) | 4.39077e16 | 0.863698 | ||||||||
\(40\) | −1.04858e16 | −0.158114 | ||||||||
\(41\) | 1.53913e17 | 1.79079 | 0.895396 | − | 0.445272i | \(-0.146893\pi\) | ||||
0.895396 | + | 0.445272i | \(0.146893\pi\) | |||||||
\(42\) | 3.53648e16 | 0.319488 | ||||||||
\(43\) | −6.75910e15 | −0.0476947 | −0.0238473 | − | 0.999716i | \(-0.507592\pi\) | ||||
−0.0238473 | + | 0.999716i | \(0.507592\pi\) | |||||||
\(44\) | −4.11241e16 | −0.227952 | ||||||||
\(45\) | −1.49300e16 | −0.0653624 | ||||||||
\(46\) | 1.70089e17 | 0.591178 | ||||||||
\(47\) | −1.11128e17 | −0.308174 | −0.154087 | − | 0.988057i | \(-0.549244\pi\) | ||||
−0.154087 | + | 0.988057i | \(0.549244\pi\) | |||||||
\(48\) | −1.03911e17 | −0.231009 | ||||||||
\(49\) | −4.25004e17 | −0.760911 | ||||||||
\(50\) | −9.76562e16 | −0.141421 | ||||||||
\(51\) | −2.29769e16 | −0.0270274 | ||||||||
\(52\) | −4.87167e17 | −0.467350 | ||||||||
\(53\) | −2.06153e18 | −1.61917 | −0.809584 | − | 0.587003i | \(-0.800307\pi\) | ||||
−0.809584 | + | 0.587003i | \(0.800307\pi\) | |||||||
\(54\) | −1.16025e18 | −0.748890 | ||||||||
\(55\) | −3.82998e17 | −0.203886 | ||||||||
\(56\) | −3.92382e17 | −0.172876 | ||||||||
\(57\) | 6.37815e17 | 0.233351 | ||||||||
\(58\) | −2.91994e18 | −0.889978 | ||||||||
\(59\) | 5.84178e18 | 1.48799 | 0.743993 | − | 0.668188i | \(-0.232930\pi\) | ||||
0.743993 | + | 0.668188i | \(0.232930\pi\) | |||||||
\(60\) | −9.67749e17 | −0.206621 | ||||||||
\(61\) | 4.90762e18 | 0.880861 | 0.440431 | − | 0.897787i | \(-0.354826\pi\) | ||||
0.440431 | + | 0.897787i | \(0.354826\pi\) | |||||||
\(62\) | −3.56559e18 | −0.539534 | ||||||||
\(63\) | −5.58686e17 | −0.0714648 | ||||||||
\(64\) | 1.15292e18 | 0.125000 | ||||||||
\(65\) | −4.53709e18 | −0.418011 | ||||||||
\(66\) | −3.79541e18 | −0.297884 | ||||||||
\(67\) | 1.35893e19 | 0.910776 | 0.455388 | − | 0.890293i | \(-0.349500\pi\) | ||||
0.455388 | + | 0.890293i | \(0.349500\pi\) | |||||||
\(68\) | 2.54934e17 | 0.0146246 | ||||||||
\(69\) | 1.56978e19 | 0.772543 | ||||||||
\(70\) | −3.65434e18 | −0.154625 | ||||||||
\(71\) | 3.28855e19 | 1.19893 | 0.599463 | − | 0.800403i | \(-0.295381\pi\) | ||||
0.599463 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(72\) | 1.64157e18 | 0.0516735 | ||||||||
\(73\) | 3.25004e19 | 0.885112 | 0.442556 | − | 0.896741i | \(-0.354072\pi\) | ||||
0.442556 | + | 0.896741i | \(0.354072\pi\) | |||||||
\(74\) | −3.96317e18 | −0.0935641 | ||||||||
\(75\) | −9.01286e18 | −0.184807 | ||||||||
\(76\) | −7.07672e18 | −0.126267 | ||||||||
\(77\) | −1.43319e19 | −0.222922 | ||||||||
\(78\) | −4.49615e19 | −0.610727 | ||||||||
\(79\) | 5.11527e19 | 0.607832 | 0.303916 | − | 0.952699i | \(-0.401706\pi\) | ||||
0.303916 | + | 0.952699i | \(0.401706\pi\) | |||||||
\(80\) | 1.07374e19 | 0.111803 | ||||||||
\(81\) | −9.10896e19 | −0.832484 | ||||||||
\(82\) | −1.57607e20 | −1.26628 | ||||||||
\(83\) | 2.02190e20 | 1.43034 | 0.715171 | − | 0.698949i | \(-0.246349\pi\) | ||||
0.715171 | + | 0.698949i | \(0.246349\pi\) | |||||||
\(84\) | −3.62136e19 | −0.225912 | ||||||||
\(85\) | 2.37426e18 | 0.0130807 | ||||||||
\(86\) | 6.92131e18 | 0.0337252 | ||||||||
\(87\) | −2.69486e20 | −1.16301 | ||||||||
\(88\) | 4.21111e19 | 0.161186 | ||||||||
\(89\) | 2.17189e20 | 0.738316 | 0.369158 | − | 0.929367i | \(-0.379646\pi\) | ||||
0.369158 | + | 0.929367i | \(0.379646\pi\) | |||||||
\(90\) | 1.52883e19 | 0.0462182 | ||||||||
\(91\) | −1.69780e20 | −0.457038 | ||||||||
\(92\) | −1.74171e20 | −0.418026 | ||||||||
\(93\) | −3.29075e20 | −0.705056 | ||||||||
\(94\) | 1.13795e20 | 0.217912 | ||||||||
\(95\) | −6.59071e19 | −0.112937 | ||||||||
\(96\) | 1.06405e20 | 0.163348 | ||||||||
\(97\) | −1.03286e21 | −1.42213 | −0.711063 | − | 0.703129i | \(-0.751786\pi\) | ||||
−0.711063 | + | 0.703129i | \(0.751786\pi\) | |||||||
\(98\) | 4.35204e20 | 0.538046 | ||||||||
\(99\) | 5.99592e19 | 0.0666325 | ||||||||
\(100\) | 1.00000e20 | 0.100000 | ||||||||
\(101\) | −9.83683e20 | −0.886096 | −0.443048 | − | 0.896498i | \(-0.646103\pi\) | ||||
−0.443048 | + | 0.896498i | \(0.646103\pi\) | |||||||
\(102\) | 2.35283e19 | 0.0191113 | ||||||||
\(103\) | 1.00540e21 | 0.737140 | 0.368570 | − | 0.929600i | \(-0.379848\pi\) | ||||
0.368570 | + | 0.929600i | \(0.379848\pi\) | |||||||
\(104\) | 4.98859e20 | 0.330467 | ||||||||
\(105\) | −3.37265e20 | −0.202062 | ||||||||
\(106\) | 2.11100e21 | 1.14493 | ||||||||
\(107\) | 3.28755e21 | 1.61563 | 0.807817 | − | 0.589433i | \(-0.200649\pi\) | ||||
0.807817 | + | 0.589433i | \(0.200649\pi\) | |||||||
\(108\) | 1.18810e21 | 0.529545 | ||||||||
\(109\) | 2.52264e21 | 1.02065 | 0.510324 | − | 0.859982i | \(-0.329525\pi\) | ||||
0.510324 | + | 0.859982i | \(0.329525\pi\) | |||||||
\(110\) | 3.92190e20 | 0.144169 | ||||||||
\(111\) | −3.65767e20 | −0.122268 | ||||||||
\(112\) | 4.01799e20 | 0.122242 | ||||||||
\(113\) | −2.85082e21 | −0.790034 | −0.395017 | − | 0.918674i | \(-0.629261\pi\) | ||||
−0.395017 | + | 0.918674i | \(0.629261\pi\) | |||||||
\(114\) | −6.53123e20 | −0.165004 | ||||||||
\(115\) | −1.62209e21 | −0.373894 | ||||||||
\(116\) | 2.99001e21 | 0.629310 | ||||||||
\(117\) | 7.10292e20 | 0.136611 | ||||||||
\(118\) | −5.98198e21 | −1.05216 | ||||||||
\(119\) | 8.88458e19 | 0.0143019 | ||||||||
\(120\) | 9.90975e20 | 0.146103 | ||||||||
\(121\) | −5.86212e21 | −0.792152 | ||||||||
\(122\) | −5.02540e21 | −0.622863 | ||||||||
\(123\) | −1.45458e22 | −1.65476 | ||||||||
\(124\) | 3.65117e21 | 0.381508 | ||||||||
\(125\) | 9.31323e20 | 0.0894427 | ||||||||
\(126\) | 5.72095e20 | 0.0505332 | ||||||||
\(127\) | 1.38451e21 | 0.112553 | 0.0562764 | − | 0.998415i | \(-0.482077\pi\) | ||||
0.0562764 | + | 0.998415i | \(0.482077\pi\) | |||||||
\(128\) | −1.18059e21 | −0.0883883 | ||||||||
\(129\) | 6.38780e20 | 0.0440717 | ||||||||
\(130\) | 4.64598e21 | 0.295578 | ||||||||
\(131\) | −6.11455e21 | −0.358935 | −0.179468 | − | 0.983764i | \(-0.557438\pi\) | ||||
−0.179468 | + | 0.983764i | \(0.557438\pi\) | |||||||
\(132\) | 3.88650e21 | 0.210636 | ||||||||
\(133\) | −2.46627e21 | −0.123481 | ||||||||
\(134\) | −1.39154e22 | −0.644016 | ||||||||
\(135\) | 1.10650e22 | 0.473639 | ||||||||
\(136\) | −2.61053e20 | −0.0103412 | ||||||||
\(137\) | 3.06697e22 | 1.12498 | 0.562488 | − | 0.826806i | \(-0.309844\pi\) | ||||
0.562488 | + | 0.826806i | \(0.309844\pi\) | |||||||
\(138\) | −1.60745e22 | −0.546271 | ||||||||
\(139\) | 2.77909e21 | 0.0875483 | 0.0437742 | − | 0.999041i | \(-0.486062\pi\) | ||||
0.0437742 | + | 0.999041i | \(0.486062\pi\) | |||||||
\(140\) | 3.74204e21 | 0.109336 | ||||||||
\(141\) | 1.05024e22 | 0.284765 | ||||||||
\(142\) | −3.36748e22 | −0.847768 | ||||||||
\(143\) | 1.82211e22 | 0.426134 | ||||||||
\(144\) | −1.68097e21 | −0.0365387 | ||||||||
\(145\) | 2.78467e22 | 0.562872 | ||||||||
\(146\) | −3.32804e22 | −0.625868 | ||||||||
\(147\) | 4.01657e22 | 0.703111 | ||||||||
\(148\) | 4.05828e21 | 0.0661598 | ||||||||
\(149\) | 1.15060e23 | 1.74771 | 0.873854 | − | 0.486188i | \(-0.161613\pi\) | ||||
0.873854 | + | 0.486188i | \(0.161613\pi\) | |||||||
\(150\) | 9.22917e21 | 0.130679 | ||||||||
\(151\) | −9.22398e22 | −1.21804 | −0.609019 | − | 0.793156i | \(-0.708437\pi\) | ||||
−0.609019 | + | 0.793156i | \(0.708437\pi\) | |||||||
\(152\) | 7.24656e21 | 0.0892842 | ||||||||
\(153\) | −3.71696e20 | −0.00427491 | ||||||||
\(154\) | 1.46759e22 | 0.157630 | ||||||||
\(155\) | 3.40041e22 | 0.341231 | ||||||||
\(156\) | 4.60405e22 | 0.431849 | ||||||||
\(157\) | −9.83630e22 | −0.862751 | −0.431375 | − | 0.902173i | \(-0.641971\pi\) | ||||
−0.431375 | + | 0.902173i | \(0.641971\pi\) | |||||||
\(158\) | −5.23803e22 | −0.429802 | ||||||||
\(159\) | 1.94828e23 | 1.49617 | ||||||||
\(160\) | −1.09951e22 | −0.0790569 | ||||||||
\(161\) | −6.06994e22 | −0.408802 | ||||||||
\(162\) | 9.32757e22 | 0.588655 | ||||||||
\(163\) | −2.88242e23 | −1.70525 | −0.852623 | − | 0.522526i | \(-0.824990\pi\) | ||||
−0.852623 | + | 0.522526i | \(0.824990\pi\) | |||||||
\(164\) | 1.61390e23 | 0.895396 | ||||||||
\(165\) | 3.61959e22 | 0.188399 | ||||||||
\(166\) | −2.07043e23 | −1.01140 | ||||||||
\(167\) | −1.80201e23 | −0.826484 | −0.413242 | − | 0.910621i | \(-0.635604\pi\) | ||||
−0.413242 | + | 0.910621i | \(0.635604\pi\) | |||||||
\(168\) | 3.70827e22 | 0.159744 | ||||||||
\(169\) | −3.12128e22 | −0.126335 | ||||||||
\(170\) | −2.43124e21 | −0.00924942 | ||||||||
\(171\) | 1.03179e22 | 0.0369090 | ||||||||
\(172\) | −7.08743e21 | −0.0238473 | ||||||||
\(173\) | −4.53364e23 | −1.43537 | −0.717683 | − | 0.696370i | \(-0.754797\pi\) | ||||
−0.717683 | + | 0.696370i | \(0.754797\pi\) | |||||||
\(174\) | 2.75954e23 | 0.822373 | ||||||||
\(175\) | 3.48505e22 | 0.0977934 | ||||||||
\(176\) | −4.31217e22 | −0.113976 | ||||||||
\(177\) | −5.52087e23 | −1.37495 | ||||||||
\(178\) | −2.22401e23 | −0.522068 | ||||||||
\(179\) | 6.58352e23 | 1.45714 | 0.728570 | − | 0.684971i | \(-0.240185\pi\) | ||||
0.728570 | + | 0.684971i | \(0.240185\pi\) | |||||||
\(180\) | −1.56552e22 | −0.0326812 | ||||||||
\(181\) | 1.55219e23 | 0.305717 | 0.152858 | − | 0.988248i | \(-0.451152\pi\) | ||||
0.152858 | + | 0.988248i | \(0.451152\pi\) | |||||||
\(182\) | 1.73855e23 | 0.323174 | ||||||||
\(183\) | −4.63803e23 | −0.813949 | ||||||||
\(184\) | 1.78351e23 | 0.295589 | ||||||||
\(185\) | 3.77957e22 | 0.0591751 | ||||||||
\(186\) | 3.36973e23 | 0.498550 | ||||||||
\(187\) | −9.53509e21 | −0.0133348 | ||||||||
\(188\) | −1.16526e23 | −0.154087 | ||||||||
\(189\) | 4.14058e23 | 0.517860 | ||||||||
\(190\) | 6.74889e22 | 0.0798582 | ||||||||
\(191\) | 6.36717e23 | 0.713010 | 0.356505 | − | 0.934293i | \(-0.383968\pi\) | ||||
0.356505 | + | 0.934293i | \(0.383968\pi\) | |||||||
\(192\) | −1.08959e23 | −0.115505 | ||||||||
\(193\) | −4.28896e23 | −0.430527 | −0.215263 | − | 0.976556i | \(-0.569061\pi\) | ||||
−0.215263 | + | 0.976556i | \(0.569061\pi\) | |||||||
\(194\) | 1.05765e24 | 1.00559 | ||||||||
\(195\) | 4.28786e23 | 0.386258 | ||||||||
\(196\) | −4.45649e23 | −0.380456 | ||||||||
\(197\) | −2.72735e23 | −0.220722 | −0.110361 | − | 0.993892i | \(-0.535201\pi\) | ||||
−0.110361 | + | 0.993892i | \(0.535201\pi\) | |||||||
\(198\) | −6.13982e22 | −0.0471163 | ||||||||
\(199\) | 2.24441e24 | 1.63360 | 0.816799 | − | 0.576923i | \(-0.195747\pi\) | ||||
0.816799 | + | 0.576923i | \(0.195747\pi\) | |||||||
\(200\) | −1.02400e23 | −0.0707107 | ||||||||
\(201\) | −1.28428e24 | −0.841591 | ||||||||
\(202\) | 1.00729e24 | 0.626565 | ||||||||
\(203\) | 1.04203e24 | 0.615423 | ||||||||
\(204\) | −2.40930e22 | −0.0135137 | ||||||||
\(205\) | 1.50306e24 | 0.800866 | ||||||||
\(206\) | −1.02953e24 | −0.521236 | ||||||||
\(207\) | 2.53942e23 | 0.122193 | ||||||||
\(208\) | −5.10831e23 | −0.233675 | ||||||||
\(209\) | 2.64685e23 | 0.115131 | ||||||||
\(210\) | 3.45360e23 | 0.142879 | ||||||||
\(211\) | −3.61254e24 | −1.42183 | −0.710913 | − | 0.703280i | \(-0.751718\pi\) | ||||
−0.710913 | + | 0.703280i | \(0.751718\pi\) | |||||||
\(212\) | −2.16167e24 | −0.809584 | ||||||||
\(213\) | −3.10790e24 | −1.10785 | ||||||||
\(214\) | −3.36646e24 | −1.14243 | ||||||||
\(215\) | −6.60068e22 | −0.0213297 | ||||||||
\(216\) | −1.21661e24 | −0.374445 | ||||||||
\(217\) | 1.27245e24 | 0.373090 | ||||||||
\(218\) | −2.58318e24 | −0.721708 | ||||||||
\(219\) | −3.07150e24 | −0.817876 | ||||||||
\(220\) | −4.01602e23 | −0.101943 | ||||||||
\(221\) | −1.12955e23 | −0.0273393 | ||||||||
\(222\) | 3.74546e23 | 0.0864567 | ||||||||
\(223\) | 4.19001e24 | 0.922600 | 0.461300 | − | 0.887244i | \(-0.347383\pi\) | ||||
0.461300 | + | 0.887244i | \(0.347383\pi\) | |||||||
\(224\) | −4.11442e23 | −0.0864379 | ||||||||
\(225\) | −1.45801e23 | −0.0292309 | ||||||||
\(226\) | 2.91924e24 | 0.558638 | ||||||||
\(227\) | 7.86051e24 | 1.43608 | 0.718041 | − | 0.696001i | \(-0.245039\pi\) | ||||
0.718041 | + | 0.696001i | \(0.245039\pi\) | |||||||
\(228\) | 6.68798e23 | 0.116675 | ||||||||
\(229\) | 3.29155e23 | 0.0548439 | 0.0274220 | − | 0.999624i | \(-0.491270\pi\) | ||||
0.0274220 | + | 0.999624i | \(0.491270\pi\) | |||||||
\(230\) | 1.66102e24 | 0.264383 | ||||||||
\(231\) | 1.35447e24 | 0.205988 | ||||||||
\(232\) | −3.06177e24 | −0.444989 | ||||||||
\(233\) | 3.62417e24 | 0.503468 | 0.251734 | − | 0.967796i | \(-0.418999\pi\) | ||||
0.251734 | + | 0.967796i | \(0.418999\pi\) | |||||||
\(234\) | −7.27339e23 | −0.0965985 | ||||||||
\(235\) | −1.08524e24 | −0.137820 | ||||||||
\(236\) | 6.12555e24 | 0.743993 | ||||||||
\(237\) | −4.83427e24 | −0.561660 | ||||||||
\(238\) | −9.09781e22 | −0.0101130 | ||||||||
\(239\) | −5.27026e23 | −0.0560601 | −0.0280301 | − | 0.999607i | \(-0.508923\pi\) | ||||
−0.0280301 | + | 0.999607i | \(0.508923\pi\) | |||||||
\(240\) | −1.01476e24 | −0.103311 | ||||||||
\(241\) | −3.17826e24 | −0.309749 | −0.154874 | − | 0.987934i | \(-0.549497\pi\) | ||||
−0.154874 | + | 0.987934i | \(0.549497\pi\) | |||||||
\(242\) | 6.00281e24 | 0.560136 | ||||||||
\(243\) | −3.24361e24 | −0.289843 | ||||||||
\(244\) | 5.14601e24 | 0.440431 | ||||||||
\(245\) | −4.15043e24 | −0.340290 | ||||||||
\(246\) | 1.48949e25 | 1.17009 | ||||||||
\(247\) | 3.13552e24 | 0.236043 | ||||||||
\(248\) | −3.73880e24 | −0.269767 | ||||||||
\(249\) | −1.91083e25 | −1.32169 | ||||||||
\(250\) | −9.53674e23 | −0.0632456 | ||||||||
\(251\) | 1.26683e25 | 0.805649 | 0.402824 | − | 0.915277i | \(-0.368029\pi\) | ||||
0.402824 | + | 0.915277i | \(0.368029\pi\) | |||||||
\(252\) | −5.85825e23 | −0.0357324 | ||||||||
\(253\) | 6.51436e24 | 0.381159 | ||||||||
\(254\) | −1.41774e24 | −0.0795868 | ||||||||
\(255\) | −2.24384e23 | −0.0120870 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | −1.86982e24 | −0.0927902 | −0.0463951 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463951 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(258\) | −6.54111e23 | −0.0311634 | ||||||||
\(259\) | 1.41433e24 | 0.0646999 | ||||||||
\(260\) | −4.75749e24 | −0.209005 | ||||||||
\(261\) | −4.35946e24 | −0.183953 | ||||||||
\(262\) | 6.26130e24 | 0.253806 | ||||||||
\(263\) | 4.09180e25 | 1.59360 | 0.796800 | − | 0.604243i | \(-0.206524\pi\) | ||||
0.796800 | + | 0.604243i | \(0.206524\pi\) | |||||||
\(264\) | −3.97978e24 | −0.148942 | ||||||||
\(265\) | −2.01321e25 | −0.724114 | ||||||||
\(266\) | 2.52546e24 | 0.0873140 | ||||||||
\(267\) | −2.05258e25 | −0.682232 | ||||||||
\(268\) | 1.42494e25 | 0.455388 | ||||||||
\(269\) | −3.93628e25 | −1.20973 | −0.604864 | − | 0.796329i | \(-0.706772\pi\) | ||||
−0.604864 | + | 0.796329i | \(0.706772\pi\) | |||||||
\(270\) | −1.13306e25 | −0.334914 | ||||||||
\(271\) | −2.31984e25 | −0.659600 | −0.329800 | − | 0.944051i | \(-0.606981\pi\) | ||||
−0.329800 | + | 0.944051i | \(0.606981\pi\) | |||||||
\(272\) | 2.67318e23 | 0.00731231 | ||||||||
\(273\) | 1.60454e25 | 0.422320 | ||||||||
\(274\) | −3.14057e25 | −0.795478 | ||||||||
\(275\) | −3.74021e24 | −0.0911808 | ||||||||
\(276\) | 1.64603e25 | 0.386272 | ||||||||
\(277\) | −6.39590e25 | −1.44499 | −0.722494 | − | 0.691378i | \(-0.757004\pi\) | ||||
−0.722494 | + | 0.691378i | \(0.757004\pi\) | |||||||
\(278\) | −2.84579e24 | −0.0619060 | ||||||||
\(279\) | −5.32342e24 | −0.111518 | ||||||||
\(280\) | −3.83185e24 | −0.0773124 | ||||||||
\(281\) | −4.18321e25 | −0.813005 | −0.406503 | − | 0.913650i | \(-0.633252\pi\) | ||||
−0.406503 | + | 0.913650i | \(0.633252\pi\) | |||||||
\(282\) | −1.07544e25 | −0.201359 | ||||||||
\(283\) | 7.89427e25 | 1.42415 | 0.712073 | − | 0.702106i | \(-0.247757\pi\) | ||||
0.712073 | + | 0.702106i | \(0.247757\pi\) | |||||||
\(284\) | 3.44830e25 | 0.599463 | ||||||||
\(285\) | 6.22867e24 | 0.104358 | ||||||||
\(286\) | −1.86584e25 | −0.301322 | ||||||||
\(287\) | 5.62450e25 | 0.875638 | ||||||||
\(288\) | 1.72131e24 | 0.0258367 | ||||||||
\(289\) | −6.90328e25 | −0.999144 | ||||||||
\(290\) | −2.85150e25 | −0.398010 | ||||||||
\(291\) | 9.76121e25 | 1.31410 | ||||||||
\(292\) | 3.40791e25 | 0.442556 | ||||||||
\(293\) | 1.30571e26 | 1.63583 | 0.817913 | − | 0.575343i | \(-0.195131\pi\) | ||||
0.817913 | + | 0.575343i | \(0.195131\pi\) | |||||||
\(294\) | −4.11297e25 | −0.497174 | ||||||||
\(295\) | 5.70486e25 | 0.665447 | ||||||||
\(296\) | −4.15568e24 | −0.0467820 | ||||||||
\(297\) | −4.44374e25 | −0.482843 | ||||||||
\(298\) | −1.17822e26 | −1.23582 | ||||||||
\(299\) | 7.71709e25 | 0.781458 | ||||||||
\(300\) | −9.45067e24 | −0.0924037 | ||||||||
\(301\) | −2.47000e24 | −0.0233211 | ||||||||
\(302\) | 9.44536e25 | 0.861282 | ||||||||
\(303\) | 9.29647e25 | 0.818786 | ||||||||
\(304\) | −7.42048e24 | −0.0631334 | ||||||||
\(305\) | 4.79259e25 | 0.393933 | ||||||||
\(306\) | 3.80616e23 | 0.00302282 | ||||||||
\(307\) | 3.70803e25 | 0.284571 | 0.142285 | − | 0.989826i | \(-0.454555\pi\) | ||||
0.142285 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(308\) | −1.50281e25 | −0.111461 | ||||||||
\(309\) | −9.50175e25 | −0.681145 | ||||||||
\(310\) | −3.48202e25 | −0.241287 | ||||||||
\(311\) | 1.83082e26 | 1.22648 | 0.613242 | − | 0.789895i | \(-0.289865\pi\) | ||||
0.613242 | + | 0.789895i | \(0.289865\pi\) | |||||||
\(312\) | −4.71455e25 | −0.305363 | ||||||||
\(313\) | −2.37945e26 | −1.49026 | −0.745129 | − | 0.666921i | \(-0.767612\pi\) | ||||
−0.745129 | + | 0.666921i | \(0.767612\pi\) | |||||||
\(314\) | 1.00724e26 | 0.610057 | ||||||||
\(315\) | −5.45592e24 | −0.0319600 | ||||||||
\(316\) | 5.36375e25 | 0.303916 | ||||||||
\(317\) | 1.60193e26 | 0.878055 | 0.439027 | − | 0.898474i | \(-0.355323\pi\) | ||||
0.439027 | + | 0.898474i | \(0.355323\pi\) | |||||||
\(318\) | −1.99504e26 | −1.05795 | ||||||||
\(319\) | −1.11833e26 | −0.573809 | ||||||||
\(320\) | 1.12590e25 | 0.0559017 | ||||||||
\(321\) | −3.10696e26 | −1.49291 | ||||||||
\(322\) | 6.21562e25 | 0.289066 | ||||||||
\(323\) | −1.64082e24 | −0.00738642 | ||||||||
\(324\) | −9.55143e25 | −0.416242 | ||||||||
\(325\) | −4.43076e25 | −0.186940 | ||||||||
\(326\) | 2.95160e26 | 1.20579 | ||||||||
\(327\) | −2.38406e26 | −0.943118 | ||||||||
\(328\) | −1.65263e26 | −0.633140 | ||||||||
\(329\) | −4.06100e25 | −0.150687 | ||||||||
\(330\) | −3.70646e25 | −0.133218 | ||||||||
\(331\) | −5.15992e26 | −1.79659 | −0.898295 | − | 0.439393i | \(-0.855193\pi\) | ||||
−0.898295 | + | 0.439393i | \(0.855193\pi\) | |||||||
\(332\) | 2.12012e26 | 0.715171 | ||||||||
\(333\) | −5.91700e24 | −0.0193391 | ||||||||
\(334\) | 1.84526e26 | 0.584413 | ||||||||
\(335\) | 1.32708e26 | 0.407312 | ||||||||
\(336\) | −3.79727e25 | −0.112956 | ||||||||
\(337\) | −2.13485e26 | −0.615535 | −0.307768 | − | 0.951462i | \(-0.599582\pi\) | ||||
−0.307768 | + | 0.951462i | \(0.599582\pi\) | |||||||
\(338\) | 3.19620e25 | 0.0893322 | ||||||||
\(339\) | 2.69421e26 | 0.730021 | ||||||||
\(340\) | 2.48959e24 | 0.00654033 | ||||||||
\(341\) | −1.36561e26 | −0.347862 | ||||||||
\(342\) | −1.05655e25 | −0.0260986 | ||||||||
\(343\) | −3.59422e26 | −0.861027 | ||||||||
\(344\) | 7.25752e24 | 0.0168626 | ||||||||
\(345\) | 1.53299e26 | 0.345492 | ||||||||
\(346\) | 4.64244e26 | 1.01496 | ||||||||
\(347\) | 2.02825e26 | 0.430191 | 0.215095 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215095 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(348\) | −2.82577e26 | −0.581506 | ||||||||
\(349\) | 7.65093e26 | 1.52773 | 0.763866 | − | 0.645375i | \(-0.223299\pi\) | ||||
0.763866 | + | 0.645375i | \(0.223299\pi\) | |||||||
\(350\) | −3.56869e25 | −0.0691504 | ||||||||
\(351\) | −5.26417e26 | −0.989932 | ||||||||
\(352\) | 4.41567e25 | 0.0805932 | ||||||||
\(353\) | 5.36101e26 | 0.949756 | 0.474878 | − | 0.880052i | \(-0.342492\pi\) | ||||
0.474878 | + | 0.880052i | \(0.342492\pi\) | |||||||
\(354\) | 5.65337e26 | 0.972240 | ||||||||
\(355\) | 3.21148e26 | 0.536176 | ||||||||
\(356\) | 2.27739e26 | 0.369158 | ||||||||
\(357\) | −8.39653e24 | −0.0132155 | ||||||||
\(358\) | −6.74153e26 | −1.03035 | ||||||||
\(359\) | 9.97471e26 | 1.48050 | 0.740250 | − | 0.672332i | \(-0.234707\pi\) | ||||
0.740250 | + | 0.672332i | \(0.234707\pi\) | |||||||
\(360\) | 1.60309e25 | 0.0231091 | ||||||||
\(361\) | −6.68662e26 | −0.936227 | ||||||||
\(362\) | −1.58944e26 | −0.216175 | ||||||||
\(363\) | 5.54010e26 | 0.731978 | ||||||||
\(364\) | −1.78027e26 | −0.228519 | ||||||||
\(365\) | 3.17386e26 | 0.395834 | ||||||||
\(366\) | 4.74934e26 | 0.575549 | ||||||||
\(367\) | −7.27262e26 | −0.856441 | −0.428220 | − | 0.903674i | \(-0.640859\pi\) | ||||
−0.428220 | + | 0.903674i | \(0.640859\pi\) | |||||||
\(368\) | −1.82631e26 | −0.209013 | ||||||||
\(369\) | −2.35307e26 | −0.261733 | ||||||||
\(370\) | −3.87028e25 | −0.0418431 | ||||||||
\(371\) | −7.53351e26 | −0.791720 | ||||||||
\(372\) | −3.45060e26 | −0.352528 | ||||||||
\(373\) | 8.47344e26 | 0.841622 | 0.420811 | − | 0.907148i | \(-0.361746\pi\) | ||||
0.420811 | + | 0.907148i | \(0.361746\pi\) | |||||||
\(374\) | 9.76393e24 | 0.00942915 | ||||||||
\(375\) | −8.80163e25 | −0.0826484 | ||||||||
\(376\) | 1.19323e26 | 0.108956 | ||||||||
\(377\) | −1.32480e27 | −1.17643 | ||||||||
\(378\) | −4.23995e26 | −0.366182 | ||||||||
\(379\) | 9.08041e26 | 0.762771 | 0.381385 | − | 0.924416i | \(-0.375447\pi\) | ||||
0.381385 | + | 0.924416i | \(0.375447\pi\) | |||||||
\(380\) | −6.91086e25 | −0.0564683 | ||||||||
\(381\) | −1.30845e26 | −0.104003 | ||||||||
\(382\) | −6.51998e26 | −0.504175 | ||||||||
\(383\) | −3.75246e25 | −0.0282312 | −0.0141156 | − | 0.999900i | \(-0.504493\pi\) | ||||
−0.0141156 | + | 0.999900i | \(0.504493\pi\) | |||||||
\(384\) | 1.11574e26 | 0.0816741 | ||||||||
\(385\) | −1.39960e26 | −0.0996937 | ||||||||
\(386\) | 4.39189e26 | 0.304428 | ||||||||
\(387\) | 1.03335e25 | 0.00697080 | ||||||||
\(388\) | −1.08303e27 | −0.711063 | ||||||||
\(389\) | −5.30842e26 | −0.339230 | −0.169615 | − | 0.985510i | \(-0.554252\pi\) | ||||
−0.169615 | + | 0.985510i | \(0.554252\pi\) | |||||||
\(390\) | −4.39077e26 | −0.273125 | ||||||||
\(391\) | −4.03835e25 | −0.0244539 | ||||||||
\(392\) | 4.56344e26 | 0.269023 | ||||||||
\(393\) | 5.77867e26 | 0.331670 | ||||||||
\(394\) | 2.79281e26 | 0.156074 | ||||||||
\(395\) | 4.99538e26 | 0.271831 | ||||||||
\(396\) | 6.28717e25 | 0.0333162 | ||||||||
\(397\) | 1.80269e27 | 0.930297 | 0.465149 | − | 0.885233i | \(-0.346001\pi\) | ||||
0.465149 | + | 0.885233i | \(0.346001\pi\) | |||||||
\(398\) | −2.29828e27 | −1.15513 | ||||||||
\(399\) | 2.33079e26 | 0.114101 | ||||||||
\(400\) | 1.04858e26 | 0.0500000 | ||||||||
\(401\) | 1.75068e27 | 0.813187 | 0.406594 | − | 0.913609i | \(-0.366717\pi\) | ||||
0.406594 | + | 0.913609i | \(0.366717\pi\) | |||||||
\(402\) | 1.31510e27 | 0.595095 | ||||||||
\(403\) | −1.61774e27 | −0.713192 | ||||||||
\(404\) | −1.03147e27 | −0.443048 | ||||||||
\(405\) | −8.89547e26 | −0.372298 | ||||||||
\(406\) | −1.06704e27 | −0.435170 | ||||||||
\(407\) | −1.51788e26 | −0.0603250 | ||||||||
\(408\) | 2.46712e25 | 0.00955563 | ||||||||
\(409\) | −1.99836e27 | −0.754362 | −0.377181 | − | 0.926140i | \(-0.623107\pi\) | ||||
−0.377181 | + | 0.926140i | \(0.623107\pi\) | |||||||
\(410\) | −1.53913e27 | −0.566298 | ||||||||
\(411\) | −2.89849e27 | −1.03952 | ||||||||
\(412\) | 1.05424e27 | 0.368570 | ||||||||
\(413\) | 2.13478e27 | 0.727576 | ||||||||
\(414\) | −2.60037e26 | −0.0864035 | ||||||||
\(415\) | 1.97451e27 | 0.639669 | ||||||||
\(416\) | 5.23091e26 | 0.165233 | ||||||||
\(417\) | −2.62643e26 | −0.0808979 | ||||||||
\(418\) | −2.71037e26 | −0.0814100 | ||||||||
\(419\) | −2.81050e27 | −0.823259 | −0.411630 | − | 0.911351i | \(-0.635040\pi\) | ||||
−0.411630 | + | 0.911351i | \(0.635040\pi\) | |||||||
\(420\) | −3.53648e26 | −0.101031 | ||||||||
\(421\) | 4.66949e27 | 1.30109 | 0.650546 | − | 0.759467i | \(-0.274540\pi\) | ||||
0.650546 | + | 0.759467i | \(0.274540\pi\) | |||||||
\(422\) | 3.69924e27 | 1.00538 | ||||||||
\(423\) | 1.69896e26 | 0.0450411 | ||||||||
\(424\) | 2.21355e27 | 0.572463 | ||||||||
\(425\) | 2.31861e25 | 0.00584985 | ||||||||
\(426\) | 3.18249e27 | 0.783370 | ||||||||
\(427\) | 1.79341e27 | 0.430712 | ||||||||
\(428\) | 3.44725e27 | 0.807817 | ||||||||
\(429\) | −1.72201e27 | −0.393763 | ||||||||
\(430\) | 6.75910e25 | 0.0150824 | ||||||||
\(431\) | −6.66126e26 | −0.145059 | −0.0725296 | − | 0.997366i | \(-0.523107\pi\) | ||||
−0.0725296 | + | 0.997366i | \(0.523107\pi\) | |||||||
\(432\) | 1.24581e27 | 0.264772 | ||||||||
\(433\) | 8.02347e27 | 1.66433 | 0.832165 | − | 0.554528i | \(-0.187101\pi\) | ||||
0.832165 | + | 0.554528i | \(0.187101\pi\) | |||||||
\(434\) | −1.30299e27 | −0.263814 | ||||||||
\(435\) | −2.63170e27 | −0.520115 | ||||||||
\(436\) | 2.64518e27 | 0.510324 | ||||||||
\(437\) | 1.12101e27 | 0.211131 | ||||||||
\(438\) | 3.14522e27 | 0.578326 | ||||||||
\(439\) | −6.00429e27 | −1.07791 | −0.538957 | − | 0.842333i | \(-0.681182\pi\) | ||||
−0.538957 | + | 0.842333i | \(0.681182\pi\) | |||||||
\(440\) | 4.11241e26 | 0.0720847 | ||||||||
\(441\) | 6.49759e26 | 0.111211 | ||||||||
\(442\) | 1.15666e26 | 0.0193318 | ||||||||
\(443\) | −2.47404e27 | −0.403802 | −0.201901 | − | 0.979406i | \(-0.564712\pi\) | ||||
−0.201901 | + | 0.979406i | \(0.564712\pi\) | |||||||
\(444\) | −3.83535e26 | −0.0611341 | ||||||||
\(445\) | 2.12098e27 | 0.330185 | ||||||||
\(446\) | −4.29057e27 | −0.652377 | ||||||||
\(447\) | −1.08740e28 | −1.61495 | ||||||||
\(448\) | 4.21317e26 | 0.0611209 | ||||||||
\(449\) | −1.39880e28 | −1.98230 | −0.991151 | − | 0.132738i | \(-0.957623\pi\) | ||||
−0.991151 | + | 0.132738i | \(0.957623\pi\) | |||||||
\(450\) | 1.49300e26 | 0.0206694 | ||||||||
\(451\) | −6.03631e27 | −0.816429 | ||||||||
\(452\) | −2.98930e27 | −0.395017 | ||||||||
\(453\) | 8.71729e27 | 1.12551 | ||||||||
\(454\) | −8.04916e27 | −1.01546 | ||||||||
\(455\) | −1.65801e27 | −0.204393 | ||||||||
\(456\) | −6.84849e26 | −0.0825019 | ||||||||
\(457\) | 5.38517e27 | 0.633985 | 0.316993 | − | 0.948428i | \(-0.397327\pi\) | ||||
0.316993 | + | 0.948428i | \(0.397327\pi\) | |||||||
\(458\) | −3.37055e26 | −0.0387805 | ||||||||
\(459\) | 2.75474e26 | 0.0309776 | ||||||||
\(460\) | −1.70089e27 | −0.186947 | ||||||||
\(461\) | 4.10176e27 | 0.440667 | 0.220334 | − | 0.975425i | \(-0.429285\pi\) | ||||
0.220334 | + | 0.975425i | \(0.429285\pi\) | |||||||
\(462\) | −1.38697e27 | −0.145656 | ||||||||
\(463\) | −1.59610e27 | −0.163855 | −0.0819276 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819276 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(464\) | 3.13526e27 | 0.314655 | ||||||||
\(465\) | −3.21362e27 | −0.315311 | ||||||||
\(466\) | −3.71115e27 | −0.356006 | ||||||||
\(467\) | −5.00681e27 | −0.469607 | −0.234803 | − | 0.972043i | \(-0.575445\pi\) | ||||
−0.234803 | + | 0.972043i | \(0.575445\pi\) | |||||||
\(468\) | 7.44795e26 | 0.0683054 | ||||||||
\(469\) | 4.96599e27 | 0.445339 | ||||||||
\(470\) | 1.11128e27 | 0.0974532 | ||||||||
\(471\) | 9.29596e27 | 0.797214 | ||||||||
\(472\) | −6.27256e27 | −0.526082 | ||||||||
\(473\) | 2.65085e26 | 0.0217442 | ||||||||
\(474\) | 4.95029e27 | 0.397153 | ||||||||
\(475\) | −6.43624e26 | −0.0505067 | ||||||||
\(476\) | 9.31616e25 | 0.00715095 | ||||||||
\(477\) | 3.15172e27 | 0.236649 | ||||||||
\(478\) | 5.39674e26 | 0.0396405 | ||||||||
\(479\) | 4.44191e27 | 0.319188 | 0.159594 | − | 0.987183i | \(-0.448981\pi\) | ||||
0.159594 | + | 0.987183i | \(0.448981\pi\) | |||||||
\(480\) | 1.03911e27 | 0.0730516 | ||||||||
\(481\) | −1.79813e27 | −0.123679 | ||||||||
\(482\) | 3.25453e27 | 0.219026 | ||||||||
\(483\) | 5.73650e27 | 0.377748 | ||||||||
\(484\) | −6.14688e27 | −0.396076 | ||||||||
\(485\) | −1.00865e28 | −0.635994 | ||||||||
\(486\) | 3.32146e27 | 0.204950 | ||||||||
\(487\) | 1.46905e28 | 0.887119 | 0.443559 | − | 0.896245i | \(-0.353716\pi\) | ||||
0.443559 | + | 0.896245i | \(0.353716\pi\) | |||||||
\(488\) | −5.26951e27 | −0.311431 | ||||||||
\(489\) | 2.72408e28 | 1.57571 | ||||||||
\(490\) | 4.25004e27 | 0.240621 | ||||||||
\(491\) | −2.20895e27 | −0.122414 | −0.0612069 | − | 0.998125i | \(-0.519495\pi\) | ||||
−0.0612069 | + | 0.998125i | \(0.519495\pi\) | |||||||
\(492\) | −1.52524e28 | −0.827379 | ||||||||
\(493\) | 6.93269e26 | 0.0368137 | ||||||||
\(494\) | −3.21078e27 | −0.166908 | ||||||||
\(495\) | 5.85539e26 | 0.0297990 | ||||||||
\(496\) | 3.82853e27 | 0.190754 | ||||||||
\(497\) | 1.20175e28 | 0.586235 | ||||||||
\(498\) | 1.95669e28 | 0.934576 | ||||||||
\(499\) | 3.64836e28 | 1.70625 | 0.853125 | − | 0.521707i | \(-0.174705\pi\) | ||||
0.853125 | + | 0.521707i | \(0.174705\pi\) | |||||||
\(500\) | 9.76563e26 | 0.0447214 | ||||||||
\(501\) | 1.70302e28 | 0.763702 | ||||||||
\(502\) | −1.29724e28 | −0.569680 | ||||||||
\(503\) | −4.00705e28 | −1.72330 | −0.861651 | − | 0.507502i | \(-0.830569\pi\) | ||||
−0.861651 | + | 0.507502i | \(0.830569\pi\) | |||||||
\(504\) | 5.99885e26 | 0.0252666 | ||||||||
\(505\) | −9.60628e27 | −0.396274 | ||||||||
\(506\) | −6.67071e27 | −0.269520 | ||||||||
\(507\) | 2.94982e27 | 0.116738 | ||||||||
\(508\) | 1.45176e27 | 0.0562764 | ||||||||
\(509\) | −4.63213e28 | −1.75891 | −0.879456 | − | 0.475979i | \(-0.842094\pi\) | ||||
−0.879456 | + | 0.475979i | \(0.842094\pi\) | |||||||
\(510\) | 2.29769e26 | 0.00854681 | ||||||||
\(511\) | 1.18767e28 | 0.432790 | ||||||||
\(512\) | −1.23794e27 | −0.0441942 | ||||||||
\(513\) | −7.64689e27 | −0.267456 | ||||||||
\(514\) | 1.91470e27 | 0.0656126 | ||||||||
\(515\) | 9.81840e27 | 0.329659 | ||||||||
\(516\) | 6.69810e26 | 0.0220358 | ||||||||
\(517\) | 4.35833e27 | 0.140498 | ||||||||
\(518\) | −1.44828e27 | −0.0457497 | ||||||||
\(519\) | 4.28459e28 | 1.32633 | ||||||||
\(520\) | 4.87167e27 | 0.147789 | ||||||||
\(521\) | −1.41568e28 | −0.420891 | −0.210445 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210445 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(522\) | 4.46409e27 | 0.130075 | ||||||||
\(523\) | −5.46471e28 | −1.56063 | −0.780314 | − | 0.625388i | \(-0.784941\pi\) | ||||
−0.780314 | + | 0.625388i | \(0.784941\pi\) | |||||||
\(524\) | −6.41158e27 | −0.179468 | ||||||||
\(525\) | −3.29361e27 | −0.0903647 | ||||||||
\(526\) | −4.19001e28 | −1.12685 | ||||||||
\(527\) | 8.46564e26 | 0.0223177 | ||||||||
\(528\) | 4.07529e27 | 0.105318 | ||||||||
\(529\) | −1.18816e28 | −0.301017 | ||||||||
\(530\) | 2.06153e28 | 0.512026 | ||||||||
\(531\) | −8.93108e27 | −0.217476 | ||||||||
\(532\) | −2.58607e27 | −0.0617403 | ||||||||
\(533\) | −7.15078e28 | −1.67385 | ||||||||
\(534\) | 2.10184e28 | 0.482411 | ||||||||
\(535\) | 3.21050e28 | 0.722534 | ||||||||
\(536\) | −1.45914e28 | −0.322008 | ||||||||
\(537\) | −6.22187e28 | −1.34645 | ||||||||
\(538\) | 4.03076e28 | 0.855406 | ||||||||
\(539\) | 1.66682e28 | 0.346902 | ||||||||
\(540\) | 1.16025e28 | 0.236820 | ||||||||
\(541\) | −1.97332e28 | −0.395026 | −0.197513 | − | 0.980300i | \(-0.563286\pi\) | ||||
−0.197513 | + | 0.980300i | \(0.563286\pi\) | |||||||
\(542\) | 2.37552e28 | 0.466408 | ||||||||
\(543\) | −1.46692e28 | −0.282494 | ||||||||
\(544\) | −2.73734e26 | −0.00517058 | ||||||||
\(545\) | 2.46351e28 | 0.456448 | ||||||||
\(546\) | −1.64304e28 | −0.298625 | ||||||||
\(547\) | 4.31761e28 | 0.769797 | 0.384899 | − | 0.922959i | \(-0.374236\pi\) | ||||
0.384899 | + | 0.922959i | \(0.374236\pi\) | |||||||
\(548\) | 3.21595e28 | 0.562488 | ||||||||
\(549\) | −7.50291e27 | −0.128742 | ||||||||
\(550\) | 3.82998e27 | 0.0644745 | ||||||||
\(551\) | −1.92445e28 | −0.317844 | ||||||||
\(552\) | −1.68554e28 | −0.273135 | ||||||||
\(553\) | 1.86929e28 | 0.297210 | ||||||||
\(554\) | 6.54940e28 | 1.02176 | ||||||||
\(555\) | −3.57195e27 | −0.0546800 | ||||||||
\(556\) | 2.91409e27 | 0.0437742 | ||||||||
\(557\) | 3.91712e27 | 0.0577414 | 0.0288707 | − | 0.999583i | \(-0.490809\pi\) | ||||
0.0288707 | + | 0.999583i | \(0.490809\pi\) | |||||||
\(558\) | 5.45119e27 | 0.0788555 | ||||||||
\(559\) | 3.14027e27 | 0.0445802 | ||||||||
\(560\) | 3.92382e27 | 0.0546682 | ||||||||
\(561\) | 9.01130e26 | 0.0123219 | ||||||||
\(562\) | 4.28361e28 | 0.574881 | ||||||||
\(563\) | −2.70683e28 | −0.356551 | −0.178276 | − | 0.983981i | \(-0.557052\pi\) | ||||
−0.178276 | + | 0.983981i | \(0.557052\pi\) | |||||||
\(564\) | 1.10125e28 | 0.142382 | ||||||||
\(565\) | −2.78400e28 | −0.353314 | ||||||||
\(566\) | −8.08373e28 | −1.00702 | ||||||||
\(567\) | −3.32872e28 | −0.407057 | ||||||||
\(568\) | −3.53106e28 | −0.423884 | ||||||||
\(569\) | 4.56161e28 | 0.537575 | 0.268788 | − | 0.963199i | \(-0.413377\pi\) | ||||
0.268788 | + | 0.963199i | \(0.413377\pi\) | |||||||
\(570\) | −6.37815e27 | −0.0737920 | ||||||||
\(571\) | 1.31174e29 | 1.48994 | 0.744968 | − | 0.667100i | \(-0.232465\pi\) | ||||
0.744968 | + | 0.667100i | \(0.232465\pi\) | |||||||
\(572\) | 1.91062e28 | 0.213067 | ||||||||
\(573\) | −6.01740e28 | −0.658848 | ||||||||
\(574\) | −5.75949e28 | −0.619169 | ||||||||
\(575\) | −1.58407e28 | −0.167210 | ||||||||
\(576\) | −1.76262e27 | −0.0182693 | ||||||||
\(577\) | 1.42017e29 | 1.44542 | 0.722710 | − | 0.691151i | \(-0.242896\pi\) | ||||
0.722710 | + | 0.691151i | \(0.242896\pi\) | |||||||
\(578\) | 7.06896e28 | 0.706502 | ||||||||
\(579\) | 4.05336e28 | 0.397823 | ||||||||
\(580\) | 2.91994e28 | 0.281436 | ||||||||
\(581\) | 7.38871e28 | 0.699390 | ||||||||
\(582\) | −9.99548e28 | −0.929207 | ||||||||
\(583\) | 8.08510e28 | 0.738185 | ||||||||
\(584\) | −3.48970e28 | −0.312934 | ||||||||
\(585\) | 6.93644e27 | 0.0610942 | ||||||||
\(586\) | −1.33705e29 | −1.15670 | ||||||||
\(587\) | 9.99241e28 | 0.849122 | 0.424561 | − | 0.905399i | \(-0.360428\pi\) | ||||
0.424561 | + | 0.905399i | \(0.360428\pi\) | |||||||
\(588\) | 4.21168e28 | 0.351555 | ||||||||
\(589\) | −2.34998e28 | −0.192687 | ||||||||
\(590\) | −5.84178e28 | −0.470542 | ||||||||
\(591\) | 2.57753e28 | 0.203955 | ||||||||
\(592\) | 4.25542e27 | 0.0330799 | ||||||||
\(593\) | −1.01433e29 | −0.774647 | −0.387323 | − | 0.921944i | \(-0.626600\pi\) | ||||
−0.387323 | + | 0.921944i | \(0.626600\pi\) | |||||||
\(594\) | 4.55039e28 | 0.341422 | ||||||||
\(595\) | 8.67635e26 | 0.00639601 | ||||||||
\(596\) | 1.20649e29 | 0.873854 | ||||||||
\(597\) | −2.12112e29 | −1.50950 | ||||||||
\(598\) | −7.90230e28 | −0.552574 | ||||||||
\(599\) | 5.05093e28 | 0.347048 | 0.173524 | − | 0.984830i | \(-0.444485\pi\) | ||||
0.173524 | + | 0.984830i | \(0.444485\pi\) | |||||||
\(600\) | 9.67749e27 | 0.0653393 | ||||||||
\(601\) | 1.29341e29 | 0.858130 | 0.429065 | − | 0.903274i | \(-0.358843\pi\) | ||||
0.429065 | + | 0.903274i | \(0.358843\pi\) | |||||||
\(602\) | 2.52928e27 | 0.0164905 | ||||||||
\(603\) | −2.07757e28 | −0.133114 | ||||||||
\(604\) | −9.67205e28 | −0.609019 | ||||||||
\(605\) | −5.72473e28 | −0.354261 | ||||||||
\(606\) | −9.51958e28 | −0.578969 | ||||||||
\(607\) | −8.14047e28 | −0.486596 | −0.243298 | − | 0.969952i | \(-0.578229\pi\) | ||||
−0.243298 | + | 0.969952i | \(0.578229\pi\) | |||||||
\(608\) | 7.59857e27 | 0.0446421 | ||||||||
\(609\) | −9.84793e28 | −0.568674 | ||||||||
\(610\) | −4.90762e28 | −0.278553 | ||||||||
\(611\) | 5.16299e28 | 0.288051 | ||||||||
\(612\) | −3.89751e26 | −0.00213746 | ||||||||
\(613\) | 2.20870e28 | 0.119070 | 0.0595349 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595349 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(614\) | −3.79702e28 | −0.201222 | ||||||||
\(615\) | −1.42049e29 | −0.740030 | ||||||||
\(616\) | 1.53888e28 | 0.0788148 | ||||||||
\(617\) | −1.09793e29 | −0.552818 | −0.276409 | − | 0.961040i | \(-0.589144\pi\) | ||||
−0.276409 | + | 0.961040i | \(0.589144\pi\) | |||||||
\(618\) | 9.72979e28 | 0.481642 | ||||||||
\(619\) | −1.54602e29 | −0.752424 | −0.376212 | − | 0.926534i | \(-0.622774\pi\) | ||||
−0.376212 | + | 0.926534i | \(0.622774\pi\) | |||||||
\(620\) | 3.56559e28 | 0.170616 | ||||||||
\(621\) | −1.88204e29 | −0.885454 | ||||||||
\(622\) | −1.87476e29 | −0.867255 | ||||||||
\(623\) | 7.93682e28 | 0.361012 | ||||||||
\(624\) | 4.82770e28 | 0.215925 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | 2.43656e29 | 1.05377 | ||||||||
\(627\) | −2.50145e28 | −0.106385 | ||||||||
\(628\) | −1.03141e29 | −0.431375 | ||||||||
\(629\) | 9.40958e26 | 0.00387025 | ||||||||
\(630\) | 5.58686e27 | 0.0225992 | ||||||||
\(631\) | −1.10811e29 | −0.440832 | −0.220416 | − | 0.975406i | \(-0.570742\pi\) | ||||
−0.220416 | + | 0.975406i | \(0.570742\pi\) | |||||||
\(632\) | −5.49248e28 | −0.214901 | ||||||||
\(633\) | 3.41409e29 | 1.31382 | ||||||||
\(634\) | −1.64038e29 | −0.620878 | ||||||||
\(635\) | 1.35206e28 | 0.0503351 | ||||||||
\(636\) | 2.04292e29 | 0.748086 | ||||||||
\(637\) | 1.97456e29 | 0.711224 | ||||||||
\(638\) | 1.14517e29 | 0.405744 | ||||||||
\(639\) | −5.02764e28 | −0.175229 | ||||||||
\(640\) | −1.15292e28 | −0.0395285 | ||||||||
\(641\) | 1.41424e29 | 0.476995 | 0.238497 | − | 0.971143i | \(-0.423345\pi\) | ||||
0.238497 | + | 0.971143i | \(0.423345\pi\) | |||||||
\(642\) | 3.18153e29 | 1.05564 | ||||||||
\(643\) | 5.97065e29 | 1.94897 | 0.974487 | − | 0.224442i | \(-0.0720559\pi\) | ||||
0.974487 | + | 0.224442i | \(0.0720559\pi\) | |||||||
\(644\) | −6.36479e28 | −0.204401 | ||||||||
\(645\) | 6.23809e27 | 0.0197094 | ||||||||
\(646\) | 1.68020e27 | 0.00522299 | ||||||||
\(647\) | 4.89100e29 | 1.49590 | 0.747951 | − | 0.663754i | \(-0.231038\pi\) | ||||
0.747951 | + | 0.663754i | \(0.231038\pi\) | |||||||
\(648\) | 9.78067e28 | 0.294328 | ||||||||
\(649\) | −2.29109e29 | −0.678378 | ||||||||
\(650\) | 4.53709e28 | 0.132187 | ||||||||
\(651\) | −1.20255e29 | −0.344749 | ||||||||
\(652\) | −3.02244e29 | −0.852623 | ||||||||
\(653\) | 2.34337e29 | 0.650508 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(654\) | 2.44128e29 | 0.666885 | ||||||||
\(655\) | −5.97124e28 | −0.160521 | ||||||||
\(656\) | 1.69229e29 | 0.447698 | ||||||||
\(657\) | −4.96875e28 | −0.129363 | ||||||||
\(658\) | 4.15846e28 | 0.106552 | ||||||||
\(659\) | −4.06286e29 | −1.02455 | −0.512277 | − | 0.858820i | \(-0.671198\pi\) | ||||
−0.512277 | + | 0.858820i | \(0.671198\pi\) | |||||||
\(660\) | 3.79541e28 | 0.0941993 | ||||||||
\(661\) | −3.10306e29 | −0.758009 | −0.379005 | − | 0.925395i | \(-0.623734\pi\) | ||||
−0.379005 | + | 0.925395i | \(0.623734\pi\) | |||||||
\(662\) | 5.28376e29 | 1.27038 | ||||||||
\(663\) | 1.06750e28 | 0.0252625 | ||||||||
\(664\) | −2.17100e29 | −0.505702 | ||||||||
\(665\) | −2.40847e28 | −0.0552222 | ||||||||
\(666\) | 6.05901e27 | 0.0136748 | ||||||||
\(667\) | −4.73641e29 | −1.05227 | ||||||||
\(668\) | −1.88955e29 | −0.413242 | ||||||||
\(669\) | −3.95984e29 | −0.852517 | ||||||||
\(670\) | −1.35893e29 | −0.288013 | ||||||||
\(671\) | −1.92472e29 | −0.401588 | ||||||||
\(672\) | 3.88840e28 | 0.0798719 | ||||||||
\(673\) | −1.94077e29 | −0.392478 | −0.196239 | − | 0.980556i | \(-0.562873\pi\) | ||||
−0.196239 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(674\) | 2.18608e29 | 0.435249 | ||||||||
\(675\) | 1.08057e29 | 0.211818 | ||||||||
\(676\) | −3.27290e28 | −0.0631674 | ||||||||
\(677\) | 2.34383e29 | 0.445395 | 0.222697 | − | 0.974888i | \(-0.428514\pi\) | ||||
0.222697 | + | 0.974888i | \(0.428514\pi\) | |||||||
\(678\) | −2.75887e29 | −0.516203 | ||||||||
\(679\) | −3.77442e29 | −0.695372 | ||||||||
\(680\) | −2.54934e27 | −0.00462471 | ||||||||
\(681\) | −7.42871e29 | −1.32699 | ||||||||
\(682\) | 1.39839e29 | 0.245976 | ||||||||
\(683\) | −3.67410e29 | −0.636405 | −0.318202 | − | 0.948023i | \(-0.603079\pi\) | ||||
−0.318202 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(684\) | 1.08191e28 | 0.0184545 | ||||||||
\(685\) | 2.99508e29 | 0.503104 | ||||||||
\(686\) | 3.68049e29 | 0.608838 | ||||||||
\(687\) | −3.11074e28 | −0.0506778 | ||||||||
\(688\) | −7.43171e27 | −0.0119237 | ||||||||
\(689\) | 9.57782e29 | 1.51344 | ||||||||
\(690\) | −1.56978e29 | −0.244300 | ||||||||
\(691\) | 9.60338e27 | 0.0147199 | 0.00735994 | − | 0.999973i | \(-0.497657\pi\) | ||||
0.00735994 | + | 0.999973i | \(0.497657\pi\) | |||||||
\(692\) | −4.75386e29 | −0.717683 | ||||||||
\(693\) | 2.19111e28 | 0.0325811 | ||||||||
\(694\) | −2.07692e29 | −0.304191 | ||||||||
\(695\) | 2.71396e28 | 0.0391528 | ||||||||
\(696\) | 2.89358e29 | 0.411187 | ||||||||
\(697\) | 3.74200e28 | 0.0523793 | ||||||||
\(698\) | −7.83455e29 | −1.08027 | ||||||||
\(699\) | −3.42509e29 | −0.465223 | ||||||||
\(700\) | 3.65434e28 | 0.0488967 | ||||||||
\(701\) | 9.60216e29 | 1.26570 | 0.632849 | − | 0.774276i | \(-0.281886\pi\) | ||||
0.632849 | + | 0.774276i | \(0.281886\pi\) | |||||||
\(702\) | 5.39051e29 | 0.699988 | ||||||||
\(703\) | −2.61201e28 | −0.0334152 | ||||||||
\(704\) | −4.52164e28 | −0.0569880 | ||||||||
\(705\) | 1.02562e29 | 0.127351 | ||||||||
\(706\) | −5.48967e29 | −0.671579 | ||||||||
\(707\) | −3.59471e29 | −0.433272 | ||||||||
\(708\) | −5.78905e29 | −0.687477 | ||||||||
\(709\) | 1.47754e30 | 1.72884 | 0.864418 | − | 0.502775i | \(-0.167687\pi\) | ||||
0.864418 | + | 0.502775i | \(0.167687\pi\) | |||||||
\(710\) | −3.28855e29 | −0.379133 | ||||||||
\(711\) | −7.82037e28 | −0.0888376 | ||||||||
\(712\) | −2.33205e29 | −0.261034 | ||||||||
\(713\) | −5.78372e29 | −0.637922 | ||||||||
\(714\) | 8.59805e27 | 0.00934477 | ||||||||
\(715\) | 1.77940e29 | 0.190573 | ||||||||
\(716\) | 6.90332e29 | 0.728570 | ||||||||
\(717\) | 4.98075e28 | 0.0518016 | ||||||||
\(718\) | −1.02141e30 | −1.04687 | ||||||||
\(719\) | −5.91742e29 | −0.597695 | −0.298847 | − | 0.954301i | \(-0.596602\pi\) | ||||
−0.298847 | + | 0.954301i | \(0.596602\pi\) | |||||||
\(720\) | −1.64157e28 | −0.0163406 | ||||||||
\(721\) | 3.67409e29 | 0.360437 | ||||||||
\(722\) | 6.84710e29 | 0.662012 | ||||||||
\(723\) | 3.00367e29 | 0.286220 | ||||||||
\(724\) | 1.62759e29 | 0.152858 | ||||||||
\(725\) | 2.71940e29 | 0.251724 | ||||||||
\(726\) | −5.67306e29 | −0.517587 | ||||||||
\(727\) | −6.05957e29 | −0.544917 | −0.272459 | − | 0.962168i | \(-0.587837\pi\) | ||||
−0.272459 | + | 0.962168i | \(0.587837\pi\) | |||||||
\(728\) | 1.82300e29 | 0.161587 | ||||||||
\(729\) | 1.25937e30 | 1.10031 | ||||||||
\(730\) | −3.25004e29 | −0.279897 | ||||||||
\(731\) | −1.64330e27 | −0.00139503 | ||||||||
\(732\) | −4.86333e29 | −0.406974 | ||||||||
\(733\) | 2.10206e30 | 1.73402 | 0.867010 | − | 0.498291i | \(-0.166039\pi\) | ||||
0.867010 | + | 0.498291i | \(0.166039\pi\) | |||||||
\(734\) | 7.44717e29 | 0.605595 | ||||||||
\(735\) | 3.92243e29 | 0.314441 | ||||||||
\(736\) | 1.87015e29 | 0.147795 | ||||||||
\(737\) | −5.32959e29 | −0.415226 | ||||||||
\(738\) | 2.40954e29 | 0.185073 | ||||||||
\(739\) | 9.22542e29 | 0.698585 | 0.349293 | − | 0.937014i | \(-0.386422\pi\) | ||||
0.349293 | + | 0.937014i | \(0.386422\pi\) | |||||||
\(740\) | 3.96317e28 | 0.0295876 | ||||||||
\(741\) | −2.96328e29 | −0.218113 | ||||||||
\(742\) | 7.71432e29 | 0.559831 | ||||||||
\(743\) | −6.11017e29 | −0.437191 | −0.218595 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218595 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(744\) | 3.53341e29 | 0.249275 | ||||||||
\(745\) | 1.12363e30 | 0.781599 | ||||||||
\(746\) | −8.67680e29 | −0.595116 | ||||||||
\(747\) | −3.09114e29 | −0.209051 | ||||||||
\(748\) | −9.99826e27 | −0.00666742 | ||||||||
\(749\) | 1.20138e30 | 0.789992 | ||||||||
\(750\) | 9.01286e28 | 0.0584413 | ||||||||
\(751\) | −1.36857e30 | −0.875078 | −0.437539 | − | 0.899199i | \(-0.644150\pi\) | ||||
−0.437539 | + | 0.899199i | \(0.644150\pi\) | |||||||
\(752\) | −1.22187e29 | −0.0770436 | ||||||||
\(753\) | −1.19724e30 | −0.744450 | ||||||||
\(754\) | 1.35660e30 | 0.831863 | ||||||||
\(755\) | −9.00780e29 | −0.544723 | ||||||||
\(756\) | 4.34171e29 | 0.258930 | ||||||||
\(757\) | −5.97591e29 | −0.351477 | −0.175739 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175739 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(758\) | −9.29834e29 | −0.539360 | ||||||||
\(759\) | −6.15651e29 | −0.352205 | ||||||||
\(760\) | 7.07672e28 | 0.0399291 | ||||||||
\(761\) | −2.76098e30 | −1.53647 | −0.768236 | − | 0.640166i | \(-0.778865\pi\) | ||||
−0.768236 | + | 0.640166i | \(0.778865\pi\) | |||||||
\(762\) | 1.33986e29 | 0.0735412 | ||||||||
\(763\) | 9.21857e29 | 0.499064 | ||||||||
\(764\) | 6.67646e29 | 0.356505 | ||||||||
\(765\) | −3.62984e27 | −0.00191180 | ||||||||
\(766\) | 3.84252e28 | 0.0199625 | ||||||||
\(767\) | −2.71408e30 | −1.39082 | ||||||||
\(768\) | −1.14252e29 | −0.0577523 | ||||||||
\(769\) | 2.46811e30 | 1.23066 | 0.615330 | − | 0.788269i | \(-0.289023\pi\) | ||||
0.615330 | + | 0.788269i | \(0.289023\pi\) | |||||||
\(770\) | 1.43319e29 | 0.0704941 | ||||||||
\(771\) | 1.76711e29 | 0.0857416 | ||||||||
\(772\) | −4.49730e29 | −0.215263 | ||||||||
\(773\) | −2.37027e30 | −1.11921 | −0.559606 | − | 0.828759i | \(-0.689048\pi\) | ||||
−0.559606 | + | 0.828759i | \(0.689048\pi\) | |||||||
\(774\) | −1.05815e28 | −0.00492910 | ||||||||
\(775\) | 3.32072e29 | 0.152603 | ||||||||
\(776\) | 1.10902e30 | 0.502797 | ||||||||
\(777\) | −1.33664e29 | −0.0597851 | ||||||||
\(778\) | 5.43582e29 | 0.239872 | ||||||||
\(779\) | −1.03874e30 | −0.452235 | ||||||||
\(780\) | 4.49615e29 | 0.193129 | ||||||||
\(781\) | −1.28974e30 | −0.546595 | ||||||||
\(782\) | 4.13527e28 | 0.0172915 | ||||||||
\(783\) | 3.23092e30 | 1.33299 | ||||||||
\(784\) | −4.67297e29 | −0.190228 | ||||||||
\(785\) | −9.60576e29 | −0.385834 | ||||||||
\(786\) | −5.91735e29 | −0.234526 | ||||||||
\(787\) | 2.43834e30 | 0.953585 | 0.476792 | − | 0.879016i | \(-0.341799\pi\) | ||||
0.476792 | + | 0.879016i | \(0.341799\pi\) | |||||||
\(788\) | −2.85983e29 | −0.110361 | ||||||||
\(789\) | −3.86703e30 | −1.47255 | ||||||||
\(790\) | −5.11527e29 | −0.192213 | ||||||||
\(791\) | −1.04178e30 | −0.386300 | ||||||||
\(792\) | −6.43807e28 | −0.0235581 | ||||||||
\(793\) | −2.28007e30 | −0.823341 | ||||||||
\(794\) | −1.84596e30 | −0.657820 | ||||||||
\(795\) | 1.90262e30 | 0.669109 | ||||||||
\(796\) | 2.35343e30 | 0.816799 | ||||||||
\(797\) | −1.54506e29 | −0.0529215 | −0.0264608 | − | 0.999650i | \(-0.508424\pi\) | ||||
−0.0264608 | + | 0.999650i | \(0.508424\pi\) | |||||||
\(798\) | −2.38673e29 | −0.0806814 | ||||||||
\(799\) | −2.70179e28 | −0.00901386 | ||||||||
\(800\) | −1.07374e29 | −0.0353553 | ||||||||
\(801\) | −3.32045e29 | −0.107908 | ||||||||
\(802\) | −1.79269e30 | −0.575010 | ||||||||
\(803\) | −1.27463e30 | −0.403526 | ||||||||
\(804\) | −1.34667e30 | −0.420796 | ||||||||
\(805\) | −5.92768e29 | −0.182822 | ||||||||
\(806\) | 1.65657e30 | 0.504303 | ||||||||
\(807\) | 3.72005e30 | 1.11783 | ||||||||
\(808\) | 1.05622e30 | 0.313282 | ||||||||
\(809\) | −2.18140e30 | −0.638668 | −0.319334 | − | 0.947642i | \(-0.603459\pi\) | ||||
−0.319334 | + | 0.947642i | \(0.603459\pi\) | |||||||
\(810\) | 9.10896e29 | 0.263255 | ||||||||
\(811\) | 2.64431e30 | 0.754387 | 0.377193 | − | 0.926134i | \(-0.376889\pi\) | ||||
0.377193 | + | 0.926134i | \(0.376889\pi\) | |||||||
\(812\) | 1.09265e30 | 0.307712 | ||||||||
\(813\) | 2.19241e30 | 0.609495 | ||||||||
\(814\) | 1.55431e29 | 0.0426562 | ||||||||
\(815\) | −2.81486e30 | −0.762610 | ||||||||
\(816\) | −2.52633e28 | −0.00675685 | ||||||||
\(817\) | 4.56164e28 | 0.0120445 | ||||||||
\(818\) | 2.04632e30 | 0.533414 | ||||||||
\(819\) | 2.59565e29 | 0.0667982 | ||||||||
\(820\) | 1.57607e30 | 0.400433 | ||||||||
\(821\) | 4.66260e30 | 1.16957 | 0.584784 | − | 0.811189i | \(-0.301179\pi\) | ||||
0.584784 | + | 0.811189i | \(0.301179\pi\) | |||||||
\(822\) | 2.96805e30 | 0.735051 | ||||||||
\(823\) | −2.92987e30 | −0.716392 | −0.358196 | − | 0.933646i | \(-0.616608\pi\) | ||||
−0.358196 | + | 0.933646i | \(0.616608\pi\) | |||||||
\(824\) | −1.07954e30 | −0.260618 | ||||||||
\(825\) | 3.53475e29 | 0.0842544 | ||||||||
\(826\) | −2.18602e30 | −0.514474 | ||||||||
\(827\) | 5.72515e30 | 1.33039 | 0.665195 | − | 0.746669i | \(-0.268348\pi\) | ||||
0.665195 | + | 0.746669i | \(0.268348\pi\) | |||||||
\(828\) | 2.66278e29 | 0.0610965 | ||||||||
\(829\) | −7.48372e29 | −0.169549 | −0.0847745 | − | 0.996400i | \(-0.527017\pi\) | ||||
−0.0847745 | + | 0.996400i | \(0.527017\pi\) | |||||||
\(830\) | −2.02190e30 | −0.452314 | ||||||||
\(831\) | 6.04456e30 | 1.33522 | ||||||||
\(832\) | −5.35645e29 | −0.116838 | ||||||||
\(833\) | −1.03329e29 | −0.0222561 | ||||||||
\(834\) | 2.68947e29 | 0.0572035 | ||||||||
\(835\) | −1.75978e30 | −0.369615 | ||||||||
\(836\) | 2.77542e29 | 0.0575655 | ||||||||
\(837\) | 3.94534e30 | 0.808103 | ||||||||
\(838\) | 2.87795e30 | 0.582132 | ||||||||
\(839\) | 2.16889e30 | 0.433249 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(840\) | 3.62136e29 | 0.0714396 | ||||||||
\(841\) | 2.99821e30 | 0.584123 | ||||||||
\(842\) | −4.78156e30 | −0.920010 | ||||||||
\(843\) | 3.95342e30 | 0.751247 | ||||||||
\(844\) | −3.78802e30 | −0.710913 | ||||||||
\(845\) | −3.04813e29 | −0.0564986 | ||||||||
\(846\) | −1.73973e29 | −0.0318489 | ||||||||
\(847\) | −2.14222e30 | −0.387336 | ||||||||
\(848\) | −2.26667e30 | −0.404792 | ||||||||
\(849\) | −7.46062e30 | −1.31596 | ||||||||
\(850\) | −2.37426e28 | −0.00413647 | ||||||||
\(851\) | −6.42862e29 | −0.110626 | ||||||||
\(852\) | −3.25887e30 | −0.553926 | ||||||||
\(853\) | 4.43176e30 | 0.744065 | 0.372033 | − | 0.928220i | \(-0.378661\pi\) | ||||
0.372033 | + | 0.928220i | \(0.378661\pi\) | |||||||
\(854\) | −1.83645e30 | −0.304559 | ||||||||
\(855\) | 1.00761e29 | 0.0165062 | ||||||||
\(856\) | −3.52998e30 | −0.571213 | ||||||||
\(857\) | −1.50790e30 | −0.241031 | −0.120515 | − | 0.992711i | \(-0.538455\pi\) | ||||
−0.120515 | + | 0.992711i | \(0.538455\pi\) | |||||||
\(858\) | 1.76334e30 | 0.278433 | ||||||||
\(859\) | 1.77910e30 | 0.277506 | 0.138753 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138753 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(860\) | −6.92131e28 | −0.0106649 | ||||||||
\(861\) | −5.31554e30 | −0.809122 | ||||||||
\(862\) | 6.82113e29 | 0.102572 | ||||||||
\(863\) | −5.78269e30 | −0.859047 | −0.429523 | − | 0.903056i | \(-0.641318\pi\) | ||||
−0.429523 | + | 0.903056i | \(0.641318\pi\) | |||||||
\(864\) | −1.27571e30 | −0.187222 | ||||||||
\(865\) | −4.42738e30 | −0.641915 | ||||||||
\(866\) | −8.21604e30 | −1.17686 | ||||||||
\(867\) | 6.52407e30 | 0.923247 | ||||||||
\(868\) | 1.33426e30 | 0.186545 | ||||||||
\(869\) | −2.00616e30 | −0.277113 | ||||||||
\(870\) | 2.69486e30 | 0.367777 | ||||||||
\(871\) | −6.31357e30 | −0.851303 | ||||||||
\(872\) | −2.70866e30 | −0.360854 | ||||||||
\(873\) | 1.57907e30 | 0.207850 | ||||||||
\(874\) | −1.14791e30 | −0.149292 | ||||||||
\(875\) | 3.40337e29 | 0.0437345 | ||||||||
\(876\) | −3.22070e30 | −0.408938 | ||||||||
\(877\) | −1.01800e31 | −1.27718 | −0.638589 | − | 0.769548i | \(-0.720482\pi\) | ||||
−0.638589 | + | 0.769548i | \(0.720482\pi\) | |||||||
\(878\) | 6.14839e30 | 0.762201 | ||||||||
\(879\) | −1.23398e31 | −1.51156 | ||||||||
\(880\) | −4.21111e29 | −0.0509716 | ||||||||
\(881\) | 1.30842e31 | 1.56495 | 0.782473 | − | 0.622685i | \(-0.213958\pi\) | ||||
0.782473 | + | 0.622685i | \(0.213958\pi\) | |||||||
\(882\) | −6.65353e29 | −0.0786379 | ||||||||
\(883\) | 6.52955e30 | 0.762598 | 0.381299 | − | 0.924452i | \(-0.375477\pi\) | ||||
0.381299 | + | 0.924452i | \(0.375477\pi\) | |||||||
\(884\) | −1.18442e29 | −0.0136696 | ||||||||
\(885\) | −5.39148e30 | −0.614898 | ||||||||
\(886\) | 2.53342e30 | 0.285531 | ||||||||
\(887\) | −1.68400e30 | −0.187562 | −0.0937810 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937810 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(888\) | 3.92740e29 | 0.0432284 | ||||||||
\(889\) | 5.05946e29 | 0.0550346 | ||||||||
\(890\) | −2.17189e30 | −0.233476 | ||||||||
\(891\) | 3.57244e30 | 0.379533 | ||||||||
\(892\) | 4.39354e30 | 0.461300 | ||||||||
\(893\) | 7.49991e29 | 0.0778244 | ||||||||
\(894\) | 1.11349e31 | 1.14194 | ||||||||
\(895\) | 6.42922e30 | 0.651653 | ||||||||
\(896\) | −4.31428e29 | −0.0432190 | ||||||||
\(897\) | −7.29317e30 | −0.722097 | ||||||||
\(898\) | 1.43237e31 | 1.40170 | ||||||||
\(899\) | 9.92899e30 | 0.960348 | ||||||||
\(900\) | −1.52883e29 | −0.0146155 | ||||||||
\(901\) | −5.01207e29 | −0.0473594 | ||||||||
\(902\) | 6.18119e30 | 0.577302 | ||||||||
\(903\) | 2.33432e29 | 0.0215496 | ||||||||
\(904\) | 3.06104e30 | 0.279319 | ||||||||
\(905\) | 1.51581e30 | 0.136721 | ||||||||
\(906\) | −8.92650e30 | −0.795857 | ||||||||
\(907\) | −6.67368e30 | −0.588151 | −0.294076 | − | 0.955782i | \(-0.595012\pi\) | ||||
−0.294076 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(908\) | 8.24234e30 | 0.718041 | ||||||||
\(909\) | 1.50388e30 | 0.129507 | ||||||||
\(910\) | 1.69780e30 | 0.144528 | ||||||||
\(911\) | 1.76568e31 | 1.48583 | 0.742915 | − | 0.669385i | \(-0.233442\pi\) | ||||
0.742915 | + | 0.669385i | \(0.233442\pi\) | |||||||
\(912\) | 7.01285e29 | 0.0583377 | ||||||||
\(913\) | −7.92969e30 | −0.652098 | ||||||||
\(914\) | −5.51441e30 | −0.448295 | ||||||||
\(915\) | −4.52932e30 | −0.364009 | ||||||||
\(916\) | 3.45144e29 | 0.0274220 | ||||||||
\(917\) | −2.23447e30 | −0.175507 | ||||||||
\(918\) | −2.82085e29 | −0.0219044 | ||||||||
\(919\) | −2.65243e30 | −0.203625 | −0.101812 | − | 0.994804i | \(-0.532464\pi\) | ||||
−0.101812 | + | 0.994804i | \(0.532464\pi\) | |||||||
\(920\) | 1.74171e30 | 0.132191 | ||||||||
\(921\) | −3.50434e30 | −0.262954 | ||||||||
\(922\) | −4.20020e30 | −0.311599 | ||||||||
\(923\) | −1.52786e31 | −1.12064 | ||||||||
\(924\) | 1.42026e30 | 0.102994 | ||||||||
\(925\) | 3.69099e29 | 0.0264639 | ||||||||
\(926\) | 1.63441e30 | 0.115863 | ||||||||
\(927\) | −1.53709e30 | −0.107736 | ||||||||
\(928\) | −3.21050e30 | −0.222495 | ||||||||
\(929\) | 1.93439e31 | 1.32550 | 0.662748 | − | 0.748842i | \(-0.269390\pi\) | ||||
0.662748 | + | 0.748842i | \(0.269390\pi\) | |||||||
\(930\) | 3.29075e30 | 0.222958 | ||||||||
\(931\) | 2.86830e30 | 0.192156 | ||||||||
\(932\) | 3.80022e30 | 0.251734 | ||||||||
\(933\) | −1.73025e31 | −1.13332 | ||||||||
\(934\) | 5.12698e30 | 0.332062 | ||||||||
\(935\) | −9.31161e28 | −0.00596352 | ||||||||
\(936\) | −7.62670e29 | −0.0482992 | ||||||||
\(937\) | 5.66629e30 | 0.354841 | 0.177420 | − | 0.984135i | \(-0.443225\pi\) | ||||
0.177420 | + | 0.984135i | \(0.443225\pi\) | |||||||
\(938\) | −5.08518e30 | −0.314903 | ||||||||
\(939\) | 2.24874e31 | 1.37705 | ||||||||
\(940\) | −1.13795e30 | −0.0689098 | ||||||||
\(941\) | 5.09478e30 | 0.305095 | 0.152547 | − | 0.988296i | \(-0.451252\pi\) | ||||
0.152547 | + | 0.988296i | \(0.451252\pi\) | |||||||
\(942\) | −9.51907e30 | −0.563715 | ||||||||
\(943\) | −2.55653e31 | −1.49719 | ||||||||
\(944\) | 6.42310e30 | 0.371996 | ||||||||
\(945\) | 4.04354e30 | 0.231594 | ||||||||
\(946\) | −2.71447e29 | −0.0153755 | ||||||||
\(947\) | 1.88265e31 | 1.05462 | 0.527310 | − | 0.849673i | \(-0.323201\pi\) | ||||
0.527310 | + | 0.849673i | \(0.323201\pi\) | |||||||
\(948\) | −5.06910e30 | −0.280830 | ||||||||
\(949\) | −1.50996e31 | −0.827314 | ||||||||
\(950\) | 6.59071e29 | 0.0357137 | ||||||||
\(951\) | −1.51393e31 | −0.811355 | ||||||||
\(952\) | −9.53975e28 | −0.00505649 | ||||||||
\(953\) | −1.70882e29 | −0.00895823 | −0.00447911 | − | 0.999990i | \(-0.501426\pi\) | ||||
−0.00447911 | + | 0.999990i | \(0.501426\pi\) | |||||||
\(954\) | −3.22736e30 | −0.167336 | ||||||||
\(955\) | 6.21794e30 | 0.318868 | ||||||||
\(956\) | −5.52627e29 | −0.0280301 | ||||||||
\(957\) | 1.05690e31 | 0.530221 | ||||||||
\(958\) | −4.54852e30 | −0.225700 | ||||||||
\(959\) | 1.12077e31 | 0.550076 | ||||||||
\(960\) | −1.06405e30 | −0.0516553 | ||||||||
\(961\) | −8.70101e30 | −0.417806 | ||||||||
\(962\) | 1.84128e30 | 0.0874544 | ||||||||
\(963\) | −5.02611e30 | −0.236133 | ||||||||
\(964\) | −3.33264e30 | −0.154874 | ||||||||
\(965\) | −4.18844e30 | −0.192537 | ||||||||
\(966\) | −5.87418e30 | −0.267108 | ||||||||
\(967\) | −4.87103e30 | −0.219100 | −0.109550 | − | 0.993981i | \(-0.534941\pi\) | ||||
−0.109550 | + | 0.993981i | \(0.534941\pi\) | |||||||
\(968\) | 6.29440e30 | 0.280068 | ||||||||
\(969\) | 1.55068e29 | 0.00682533 | ||||||||
\(970\) | 1.03286e31 | 0.449715 | ||||||||
\(971\) | −1.12704e31 | −0.485443 | −0.242722 | − | 0.970096i | \(-0.578040\pi\) | ||||
−0.242722 | + | 0.970096i | \(0.578040\pi\) | |||||||
\(972\) | −3.40118e30 | −0.144922 | ||||||||
\(973\) | 1.01558e30 | 0.0428082 | ||||||||
\(974\) | −1.50430e31 | −0.627288 | ||||||||
\(975\) | 4.18736e30 | 0.172740 | ||||||||
\(976\) | 5.39598e30 | 0.220215 | ||||||||
\(977\) | 1.66556e31 | 0.672462 | 0.336231 | − | 0.941780i | \(-0.390848\pi\) | ||||
0.336231 | + | 0.941780i | \(0.390848\pi\) | |||||||
\(978\) | −2.78946e31 | −1.11420 | ||||||||
\(979\) | −8.51793e30 | −0.336601 | ||||||||
\(980\) | −4.35204e30 | −0.170145 | ||||||||
\(981\) | −3.85668e30 | −0.149173 | ||||||||
\(982\) | 2.26196e30 | 0.0865596 | ||||||||
\(983\) | −3.01316e31 | −1.14080 | −0.570402 | − | 0.821366i | \(-0.693213\pi\) | ||||
−0.570402 | + | 0.821366i | \(0.693213\pi\) | |||||||
\(984\) | 1.56185e31 | 0.585045 | ||||||||
\(985\) | −2.66343e30 | −0.0987098 | ||||||||
\(986\) | −7.09907e29 | −0.0260312 | ||||||||
\(987\) | 3.83792e30 | 0.139240 | ||||||||
\(988\) | 3.28783e30 | 0.118022 | ||||||||
\(989\) | 1.12270e30 | 0.0398752 | ||||||||
\(990\) | −5.99592e29 | −0.0210710 | ||||||||
\(991\) | −3.83614e31 | −1.33389 | −0.666946 | − | 0.745106i | \(-0.732399\pi\) | ||||
−0.666946 | + | 0.745106i | \(0.732399\pi\) | |||||||
\(992\) | −3.92041e30 | −0.134884 | ||||||||
\(993\) | 4.87647e31 | 1.66012 | ||||||||
\(994\) | −1.23059e31 | −0.414531 | ||||||||
\(995\) | 2.19181e31 | 0.730567 | ||||||||
\(996\) | −2.00365e31 | −0.660845 | ||||||||
\(997\) | −9.24504e30 | −0.301724 | −0.150862 | − | 0.988555i | \(-0.548205\pi\) | ||||
−0.150862 | + | 0.988555i | \(0.548205\pi\) | |||||||
\(998\) | −3.73592e31 | −1.20650 | ||||||||
\(999\) | 4.38525e30 | 0.140138 |
(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 | 10.22.a.c.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 80.22.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 50.22.b.d.49.2 | 4 | |||
5.3 | odd | 4 | 50.22.b.d.49.3 | 4 | |||
5.4 | even | 2 | 50.22.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.22.a.e.1.2 | 2 | 5.4 | even | 2 | |||
50.22.b.d.49.2 | 4 | 5.2 | odd | 4 | |||
50.22.b.d.49.3 | 4 | 5.3 | odd | 4 | |||
80.22.a.b.1.2 | 2 | 4.3 | odd | 2 |