Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.47 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.71867 | 1.21528 | 0.607642 | − | 0.794211i | \(-0.292116\pi\) | ||||
0.607642 | + | 0.794211i | \(0.292116\pi\) | |||||||
\(3\) | 2.98867 | 1.72551 | 0.862756 | − | 0.505621i | \(-0.168736\pi\) | ||||
0.862756 | + | 0.505621i | \(0.168736\pi\) | |||||||
\(4\) | 0.953829 | 0.476915 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 5.13655 | 2.09699 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.79802 | −0.635697 | ||||||||
\(9\) | 5.93217 | 1.97739 | ||||||||
\(10\) | −1.71867 | −0.543491 | ||||||||
\(11\) | −2.58842 | −0.780439 | −0.390220 | − | 0.920722i | \(-0.627601\pi\) | ||||
−0.390220 | + | 0.920722i | \(0.627601\pi\) | |||||||
\(12\) | 2.85068 | 0.822922 | ||||||||
\(13\) | 2.49362 | 0.691605 | 0.345802 | − | 0.938307i | \(-0.387607\pi\) | ||||
0.345802 | + | 0.938307i | \(0.387607\pi\) | |||||||
\(14\) | −1.71867 | −0.459334 | ||||||||
\(15\) | −2.98867 | −0.771672 | ||||||||
\(16\) | −4.99787 | −1.24947 | ||||||||
\(17\) | −1.60527 | −0.389335 | −0.194667 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194667 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(18\) | 10.1955 | 2.40309 | ||||||||
\(19\) | 4.99210 | 1.14527 | 0.572633 | − | 0.819812i | \(-0.305922\pi\) | ||||
0.572633 | + | 0.819812i | \(0.305922\pi\) | |||||||
\(20\) | −0.953829 | −0.213283 | ||||||||
\(21\) | −2.98867 | −0.652182 | ||||||||
\(22\) | −4.44865 | −0.948455 | ||||||||
\(23\) | 6.92222 | 1.44338 | 0.721691 | − | 0.692215i | \(-0.243365\pi\) | ||||
0.721691 | + | 0.692215i | \(0.243365\pi\) | |||||||
\(24\) | −5.37371 | −1.09690 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.28570 | 0.840496 | ||||||||
\(27\) | 8.76331 | 1.68650 | ||||||||
\(28\) | −0.953829 | −0.180257 | ||||||||
\(29\) | 10.2434 | 1.90216 | 0.951079 | − | 0.308949i | \(-0.0999772\pi\) | ||||
0.951079 | + | 0.308949i | \(0.0999772\pi\) | |||||||
\(30\) | −5.13655 | −0.937801 | ||||||||
\(31\) | 8.48682 | 1.52428 | 0.762139 | − | 0.647413i | \(-0.224149\pi\) | ||||
0.762139 | + | 0.647413i | \(0.224149\pi\) | |||||||
\(32\) | −4.99364 | −0.882760 | ||||||||
\(33\) | −7.73596 | −1.34666 | ||||||||
\(34\) | −2.75893 | −0.473152 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 5.65828 | 0.943046 | ||||||||
\(37\) | −7.50564 | −1.23392 | −0.616960 | − | 0.786995i | \(-0.711636\pi\) | ||||
−0.616960 | + | 0.786995i | \(0.711636\pi\) | |||||||
\(38\) | 8.57978 | 1.39182 | ||||||||
\(39\) | 7.45261 | 1.19337 | ||||||||
\(40\) | 1.79802 | 0.284292 | ||||||||
\(41\) | 0.0621418 | 0.00970492 | 0.00485246 | − | 0.999988i | \(-0.498455\pi\) | ||||
0.00485246 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(42\) | −5.13655 | −0.792586 | ||||||||
\(43\) | −4.94818 | −0.754590 | −0.377295 | − | 0.926093i | \(-0.623146\pi\) | ||||
−0.377295 | + | 0.926093i | \(0.623146\pi\) | |||||||
\(44\) | −2.46892 | −0.372203 | ||||||||
\(45\) | −5.93217 | −0.884316 | ||||||||
\(46\) | 11.8970 | 1.75412 | ||||||||
\(47\) | 2.50251 | 0.365028 | 0.182514 | − | 0.983203i | \(-0.441576\pi\) | ||||
0.182514 | + | 0.983203i | \(0.441576\pi\) | |||||||
\(48\) | −14.9370 | −2.15597 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.71867 | 0.243057 | ||||||||
\(51\) | −4.79762 | −0.671802 | ||||||||
\(52\) | 2.37848 | 0.329836 | ||||||||
\(53\) | 10.4911 | 1.44107 | 0.720534 | − | 0.693419i | \(-0.243897\pi\) | ||||
0.720534 | + | 0.693419i | \(0.243897\pi\) | |||||||
\(54\) | 15.0612 | 2.04958 | ||||||||
\(55\) | 2.58842 | 0.349023 | ||||||||
\(56\) | 1.79802 | 0.240271 | ||||||||
\(57\) | 14.9198 | 1.97617 | ||||||||
\(58\) | 17.6051 | 2.31166 | ||||||||
\(59\) | −10.9191 | −1.42154 | −0.710770 | − | 0.703424i | \(-0.751653\pi\) | ||||
−0.710770 | + | 0.703424i | \(0.751653\pi\) | |||||||
\(60\) | −2.85068 | −0.368022 | ||||||||
\(61\) | 2.59765 | 0.332594 | 0.166297 | − | 0.986076i | \(-0.446819\pi\) | ||||
0.166297 | + | 0.986076i | \(0.446819\pi\) | |||||||
\(62\) | 14.5861 | 1.85243 | ||||||||
\(63\) | −5.93217 | −0.747383 | ||||||||
\(64\) | 1.41331 | 0.176663 | ||||||||
\(65\) | −2.49362 | −0.309295 | ||||||||
\(66\) | −13.2956 | −1.63657 | ||||||||
\(67\) | −2.10858 | −0.257604 | −0.128802 | − | 0.991670i | \(-0.541113\pi\) | ||||
−0.128802 | + | 0.991670i | \(0.541113\pi\) | |||||||
\(68\) | −1.53115 | −0.185679 | ||||||||
\(69\) | 20.6882 | 2.49057 | ||||||||
\(70\) | 1.71867 | 0.205420 | ||||||||
\(71\) | 13.1283 | 1.55805 | 0.779023 | − | 0.626995i | \(-0.215715\pi\) | ||||
0.779023 | + | 0.626995i | \(0.215715\pi\) | |||||||
\(72\) | −10.6662 | −1.25702 | ||||||||
\(73\) | 12.0683 | 1.41249 | 0.706244 | − | 0.707969i | \(-0.250388\pi\) | ||||
0.706244 | + | 0.707969i | \(0.250388\pi\) | |||||||
\(74\) | −12.8997 | −1.49956 | ||||||||
\(75\) | 2.98867 | 0.345102 | ||||||||
\(76\) | 4.76161 | 0.546194 | ||||||||
\(77\) | 2.58842 | 0.294978 | ||||||||
\(78\) | 12.8086 | 1.45029 | ||||||||
\(79\) | −14.0565 | −1.58148 | −0.790741 | − | 0.612151i | \(-0.790304\pi\) | ||||
−0.790741 | + | 0.612151i | \(0.790304\pi\) | |||||||
\(80\) | 4.99787 | 0.558779 | ||||||||
\(81\) | 8.39415 | 0.932684 | ||||||||
\(82\) | 0.106801 | 0.0117942 | ||||||||
\(83\) | 6.55734 | 0.719761 | 0.359881 | − | 0.932998i | \(-0.382817\pi\) | ||||
0.359881 | + | 0.932998i | \(0.382817\pi\) | |||||||
\(84\) | −2.85068 | −0.311035 | ||||||||
\(85\) | 1.60527 | 0.174116 | ||||||||
\(86\) | −8.50429 | −0.917041 | ||||||||
\(87\) | 30.6143 | 3.28219 | ||||||||
\(88\) | 4.65405 | 0.496123 | ||||||||
\(89\) | −0.754527 | −0.0799797 | −0.0399898 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399898 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(90\) | −10.1955 | −1.07469 | ||||||||
\(91\) | −2.49362 | −0.261402 | ||||||||
\(92\) | 6.60261 | 0.688370 | ||||||||
\(93\) | 25.3644 | 2.63016 | ||||||||
\(94\) | 4.30099 | 0.443613 | ||||||||
\(95\) | −4.99210 | −0.512179 | ||||||||
\(96\) | −14.9244 | −1.52321 | ||||||||
\(97\) | −14.2332 | −1.44517 | −0.722583 | − | 0.691284i | \(-0.757045\pi\) | ||||
−0.722583 | + | 0.691284i | \(0.757045\pi\) | |||||||
\(98\) | 1.71867 | 0.173612 | ||||||||
\(99\) | −15.3550 | −1.54323 | ||||||||
\(100\) | 0.953829 | 0.0953829 | ||||||||
\(101\) | −2.88454 | −0.287023 | −0.143511 | − | 0.989649i | \(-0.545839\pi\) | ||||
−0.143511 | + | 0.989649i | \(0.545839\pi\) | |||||||
\(102\) | −8.24554 | −0.816430 | ||||||||
\(103\) | −9.54503 | −0.940500 | −0.470250 | − | 0.882533i | \(-0.655836\pi\) | ||||
−0.470250 | + | 0.882533i | \(0.655836\pi\) | |||||||
\(104\) | −4.48358 | −0.439651 | ||||||||
\(105\) | 2.98867 | 0.291665 | ||||||||
\(106\) | 18.0308 | 1.75131 | ||||||||
\(107\) | −13.8210 | −1.33613 | −0.668063 | − | 0.744105i | \(-0.732876\pi\) | ||||
−0.668063 | + | 0.744105i | \(0.732876\pi\) | |||||||
\(108\) | 8.35870 | 0.804316 | ||||||||
\(109\) | 17.3847 | 1.66515 | 0.832575 | − | 0.553912i | \(-0.186866\pi\) | ||||
0.832575 | + | 0.553912i | \(0.186866\pi\) | |||||||
\(110\) | 4.44865 | 0.424162 | ||||||||
\(111\) | −22.4319 | −2.12914 | ||||||||
\(112\) | 4.99787 | 0.472254 | ||||||||
\(113\) | 15.5005 | 1.45816 | 0.729082 | − | 0.684426i | \(-0.239947\pi\) | ||||
0.729082 | + | 0.684426i | \(0.239947\pi\) | |||||||
\(114\) | 25.6422 | 2.40161 | ||||||||
\(115\) | −6.92222 | −0.645500 | ||||||||
\(116\) | 9.77048 | 0.907167 | ||||||||
\(117\) | 14.7926 | 1.36757 | ||||||||
\(118\) | −18.7663 | −1.72757 | ||||||||
\(119\) | 1.60527 | 0.147155 | ||||||||
\(120\) | 5.37371 | 0.490550 | ||||||||
\(121\) | −4.30006 | −0.390914 | ||||||||
\(122\) | 4.46450 | 0.404197 | ||||||||
\(123\) | 0.185722 | 0.0167460 | ||||||||
\(124\) | 8.09498 | 0.726951 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −10.1955 | −0.908283 | ||||||||
\(127\) | −6.28392 | −0.557608 | −0.278804 | − | 0.960348i | \(-0.589938\pi\) | ||||
−0.278804 | + | 0.960348i | \(0.589938\pi\) | |||||||
\(128\) | 12.4163 | 1.09746 | ||||||||
\(129\) | −14.7885 | −1.30205 | ||||||||
\(130\) | −4.28570 | −0.375881 | ||||||||
\(131\) | 10.4308 | 0.911344 | 0.455672 | − | 0.890148i | \(-0.349399\pi\) | ||||
0.455672 | + | 0.890148i | \(0.349399\pi\) | |||||||
\(132\) | −7.37878 | −0.642241 | ||||||||
\(133\) | −4.99210 | −0.432870 | ||||||||
\(134\) | −3.62395 | −0.313061 | ||||||||
\(135\) | −8.76331 | −0.754225 | ||||||||
\(136\) | 2.88631 | 0.247499 | ||||||||
\(137\) | −4.31594 | −0.368736 | −0.184368 | − | 0.982857i | \(-0.559024\pi\) | ||||
−0.184368 | + | 0.982857i | \(0.559024\pi\) | |||||||
\(138\) | 35.5563 | 3.02675 | ||||||||
\(139\) | 10.4798 | 0.888887 | 0.444443 | − | 0.895807i | \(-0.353401\pi\) | ||||
0.444443 | + | 0.895807i | \(0.353401\pi\) | |||||||
\(140\) | 0.953829 | 0.0806133 | ||||||||
\(141\) | 7.47918 | 0.629860 | ||||||||
\(142\) | 22.5633 | 1.89347 | ||||||||
\(143\) | −6.45454 | −0.539756 | ||||||||
\(144\) | −29.6482 | −2.47068 | ||||||||
\(145\) | −10.2434 | −0.850671 | ||||||||
\(146\) | 20.7414 | 1.71657 | ||||||||
\(147\) | 2.98867 | 0.246502 | ||||||||
\(148\) | −7.15910 | −0.588474 | ||||||||
\(149\) | 16.7860 | 1.37516 | 0.687581 | − | 0.726108i | \(-0.258673\pi\) | ||||
0.687581 | + | 0.726108i | \(0.258673\pi\) | |||||||
\(150\) | 5.13655 | 0.419397 | ||||||||
\(151\) | 5.26242 | 0.428250 | 0.214125 | − | 0.976806i | \(-0.431310\pi\) | ||||
0.214125 | + | 0.976806i | \(0.431310\pi\) | |||||||
\(152\) | −8.97591 | −0.728043 | ||||||||
\(153\) | −9.52273 | −0.769867 | ||||||||
\(154\) | 4.44865 | 0.358482 | ||||||||
\(155\) | −8.48682 | −0.681678 | ||||||||
\(156\) | 7.10851 | 0.569136 | ||||||||
\(157\) | 8.32402 | 0.664329 | 0.332165 | − | 0.943221i | \(-0.392221\pi\) | ||||
0.332165 | + | 0.943221i | \(0.392221\pi\) | |||||||
\(158\) | −24.1585 | −1.92195 | ||||||||
\(159\) | 31.3546 | 2.48658 | ||||||||
\(160\) | 4.99364 | 0.394782 | ||||||||
\(161\) | −6.92222 | −0.545547 | ||||||||
\(162\) | 14.4268 | 1.13348 | ||||||||
\(163\) | 19.9541 | 1.56292 | 0.781462 | − | 0.623953i | \(-0.214474\pi\) | ||||
0.781462 | + | 0.623953i | \(0.214474\pi\) | |||||||
\(164\) | 0.0592727 | 0.00462842 | ||||||||
\(165\) | 7.73596 | 0.602244 | ||||||||
\(166\) | 11.2699 | 0.874714 | ||||||||
\(167\) | −4.07611 | −0.315419 | −0.157709 | − | 0.987486i | \(-0.550411\pi\) | ||||
−0.157709 | + | 0.987486i | \(0.550411\pi\) | |||||||
\(168\) | 5.37371 | 0.414590 | ||||||||
\(169\) | −6.78188 | −0.521683 | ||||||||
\(170\) | 2.75893 | 0.211600 | ||||||||
\(171\) | 29.6140 | 2.26464 | ||||||||
\(172\) | −4.71972 | −0.359875 | ||||||||
\(173\) | 23.9651 | 1.82203 | 0.911016 | − | 0.412371i | \(-0.135299\pi\) | ||||
0.911016 | + | 0.412371i | \(0.135299\pi\) | |||||||
\(174\) | 52.6159 | 3.98880 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 12.9366 | 0.975133 | ||||||||
\(177\) | −32.6335 | −2.45288 | ||||||||
\(178\) | −1.29678 | −0.0971980 | ||||||||
\(179\) | 2.12699 | 0.158979 | 0.0794894 | − | 0.996836i | \(-0.474671\pi\) | ||||
0.0794894 | + | 0.996836i | \(0.474671\pi\) | |||||||
\(180\) | −5.65828 | −0.421743 | ||||||||
\(181\) | −25.3090 | −1.88120 | −0.940600 | − | 0.339517i | \(-0.889736\pi\) | ||||
−0.940600 | + | 0.339517i | \(0.889736\pi\) | |||||||
\(182\) | −4.28570 | −0.317678 | ||||||||
\(183\) | 7.76352 | 0.573896 | ||||||||
\(184\) | −12.4463 | −0.917554 | ||||||||
\(185\) | 7.50564 | 0.551825 | ||||||||
\(186\) | 43.5930 | 3.19639 | ||||||||
\(187\) | 4.15512 | 0.303852 | ||||||||
\(188\) | 2.38696 | 0.174087 | ||||||||
\(189\) | −8.76331 | −0.637437 | ||||||||
\(190\) | −8.57978 | −0.622443 | ||||||||
\(191\) | −18.7581 | −1.35729 | −0.678644 | − | 0.734468i | \(-0.737432\pi\) | ||||
−0.678644 | + | 0.734468i | \(0.737432\pi\) | |||||||
\(192\) | 4.22392 | 0.304835 | ||||||||
\(193\) | −1.09742 | −0.0789943 | −0.0394971 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394971 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(194\) | −24.4622 | −1.75629 | ||||||||
\(195\) | −7.45261 | −0.533692 | ||||||||
\(196\) | 0.953829 | 0.0681307 | ||||||||
\(197\) | 12.6261 | 0.899574 | 0.449787 | − | 0.893136i | \(-0.351500\pi\) | ||||
0.449787 | + | 0.893136i | \(0.351500\pi\) | |||||||
\(198\) | −26.3902 | −1.87547 | ||||||||
\(199\) | −3.79252 | −0.268845 | −0.134422 | − | 0.990924i | \(-0.542918\pi\) | ||||
−0.134422 | + | 0.990924i | \(0.542918\pi\) | |||||||
\(200\) | −1.79802 | −0.127139 | ||||||||
\(201\) | −6.30185 | −0.444498 | ||||||||
\(202\) | −4.95758 | −0.348814 | ||||||||
\(203\) | −10.2434 | −0.718948 | ||||||||
\(204\) | −4.57611 | −0.320392 | ||||||||
\(205\) | −0.0621418 | −0.00434017 | ||||||||
\(206\) | −16.4048 | −1.14297 | ||||||||
\(207\) | 41.0638 | 2.85413 | ||||||||
\(208\) | −12.4628 | −0.864137 | ||||||||
\(209\) | −12.9217 | −0.893811 | ||||||||
\(210\) | 5.13655 | 0.354455 | ||||||||
\(211\) | 18.1869 | 1.25204 | 0.626019 | − | 0.779808i | \(-0.284683\pi\) | ||||
0.626019 | + | 0.779808i | \(0.284683\pi\) | |||||||
\(212\) | 10.0068 | 0.687267 | ||||||||
\(213\) | 39.2363 | 2.68843 | ||||||||
\(214\) | −23.7537 | −1.62377 | ||||||||
\(215\) | 4.94818 | 0.337463 | ||||||||
\(216\) | −15.7566 | −1.07210 | ||||||||
\(217\) | −8.48682 | −0.576123 | ||||||||
\(218\) | 29.8785 | 2.02363 | ||||||||
\(219\) | 36.0682 | 2.43726 | ||||||||
\(220\) | 2.46892 | 0.166454 | ||||||||
\(221\) | −4.00292 | −0.269266 | ||||||||
\(222\) | −38.5531 | −2.58751 | ||||||||
\(223\) | −11.3104 | −0.757399 | −0.378699 | − | 0.925520i | \(-0.623629\pi\) | ||||
−0.378699 | + | 0.925520i | \(0.623629\pi\) | |||||||
\(224\) | 4.99364 | 0.333652 | ||||||||
\(225\) | 5.93217 | 0.395478 | ||||||||
\(226\) | 26.6402 | 1.77208 | ||||||||
\(227\) | 2.46590 | 0.163668 | 0.0818338 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818338 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(228\) | 14.2309 | 0.942465 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −11.8970 | −0.784466 | ||||||||
\(231\) | 7.73596 | 0.508989 | ||||||||
\(232\) | −18.4179 | −1.20920 | ||||||||
\(233\) | 15.4443 | 1.01179 | 0.505894 | − | 0.862595i | \(-0.331163\pi\) | ||||
0.505894 | + | 0.862595i | \(0.331163\pi\) | |||||||
\(234\) | 25.4235 | 1.66199 | ||||||||
\(235\) | −2.50251 | −0.163246 | ||||||||
\(236\) | −10.4149 | −0.677953 | ||||||||
\(237\) | −42.0104 | −2.72887 | ||||||||
\(238\) | 2.75893 | 0.178835 | ||||||||
\(239\) | 4.73569 | 0.306326 | 0.153163 | − | 0.988201i | \(-0.451054\pi\) | ||||
0.153163 | + | 0.988201i | \(0.451054\pi\) | |||||||
\(240\) | 14.9370 | 0.964179 | ||||||||
\(241\) | −0.223275 | −0.0143824 | −0.00719120 | − | 0.999974i | \(-0.502289\pi\) | ||||
−0.00719120 | + | 0.999974i | \(0.502289\pi\) | |||||||
\(242\) | −7.39038 | −0.475072 | ||||||||
\(243\) | −1.20253 | −0.0771426 | ||||||||
\(244\) | 2.47771 | 0.158619 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0.319194 | 0.0203511 | ||||||||
\(247\) | 12.4484 | 0.792072 | ||||||||
\(248\) | −15.2595 | −0.968980 | ||||||||
\(249\) | 19.5977 | 1.24196 | ||||||||
\(250\) | −1.71867 | −0.108698 | ||||||||
\(251\) | 6.73357 | 0.425019 | 0.212510 | − | 0.977159i | \(-0.431836\pi\) | ||||
0.212510 | + | 0.977159i | \(0.431836\pi\) | |||||||
\(252\) | −5.65828 | −0.356438 | ||||||||
\(253\) | −17.9176 | −1.12647 | ||||||||
\(254\) | −10.8000 | −0.677652 | ||||||||
\(255\) | 4.79762 | 0.300439 | ||||||||
\(256\) | 18.5129 | 1.15706 | ||||||||
\(257\) | −7.76249 | −0.484211 | −0.242105 | − | 0.970250i | \(-0.577838\pi\) | ||||
−0.242105 | + | 0.970250i | \(0.577838\pi\) | |||||||
\(258\) | −25.4166 | −1.58237 | ||||||||
\(259\) | 7.50564 | 0.466378 | ||||||||
\(260\) | −2.37848 | −0.147507 | ||||||||
\(261\) | 60.7658 | 3.76131 | ||||||||
\(262\) | 17.9271 | 1.10754 | ||||||||
\(263\) | −26.6773 | −1.64500 | −0.822498 | − | 0.568769i | \(-0.807420\pi\) | ||||
−0.822498 | + | 0.568769i | \(0.807420\pi\) | |||||||
\(264\) | 13.9094 | 0.856066 | ||||||||
\(265\) | −10.4911 | −0.644466 | ||||||||
\(266\) | −8.57978 | −0.526060 | ||||||||
\(267\) | −2.25503 | −0.138006 | ||||||||
\(268\) | −2.01122 | −0.122855 | ||||||||
\(269\) | −22.1004 | −1.34749 | −0.673743 | − | 0.738965i | \(-0.735315\pi\) | ||||
−0.673743 | + | 0.738965i | \(0.735315\pi\) | |||||||
\(270\) | −15.0612 | −0.916598 | ||||||||
\(271\) | −15.1357 | −0.919427 | −0.459714 | − | 0.888067i | \(-0.652048\pi\) | ||||
−0.459714 | + | 0.888067i | \(0.652048\pi\) | |||||||
\(272\) | 8.02292 | 0.486461 | ||||||||
\(273\) | −7.45261 | −0.451052 | ||||||||
\(274\) | −7.41768 | −0.448119 | ||||||||
\(275\) | −2.58842 | −0.156088 | ||||||||
\(276\) | 19.7331 | 1.18779 | ||||||||
\(277\) | −27.1869 | −1.63350 | −0.816752 | − | 0.576989i | \(-0.804228\pi\) | ||||
−0.816752 | + | 0.576989i | \(0.804228\pi\) | |||||||
\(278\) | 18.0114 | 1.08025 | ||||||||
\(279\) | 50.3453 | 3.01409 | ||||||||
\(280\) | −1.79802 | −0.107452 | ||||||||
\(281\) | −31.3042 | −1.86745 | −0.933725 | − | 0.357991i | \(-0.883462\pi\) | ||||
−0.933725 | + | 0.357991i | \(0.883462\pi\) | |||||||
\(282\) | 12.8542 | 0.765459 | ||||||||
\(283\) | 8.05205 | 0.478645 | 0.239322 | − | 0.970940i | \(-0.423075\pi\) | ||||
0.239322 | + | 0.970940i | \(0.423075\pi\) | |||||||
\(284\) | 12.5222 | 0.743055 | ||||||||
\(285\) | −14.9198 | −0.883771 | ||||||||
\(286\) | −11.0932 | −0.655956 | ||||||||
\(287\) | −0.0621418 | −0.00366812 | ||||||||
\(288\) | −29.6232 | −1.74556 | ||||||||
\(289\) | −14.4231 | −0.848418 | ||||||||
\(290\) | −17.6051 | −1.03381 | ||||||||
\(291\) | −42.5385 | −2.49365 | ||||||||
\(292\) | 11.5111 | 0.673636 | ||||||||
\(293\) | −29.2879 | −1.71102 | −0.855508 | − | 0.517790i | \(-0.826755\pi\) | ||||
−0.855508 | + | 0.517790i | \(0.826755\pi\) | |||||||
\(294\) | 5.13655 | 0.299569 | ||||||||
\(295\) | 10.9191 | 0.635732 | ||||||||
\(296\) | 13.4953 | 0.784399 | ||||||||
\(297\) | −22.6832 | −1.31621 | ||||||||
\(298\) | 28.8496 | 1.67121 | ||||||||
\(299\) | 17.2613 | 0.998249 | ||||||||
\(300\) | 2.85068 | 0.164584 | ||||||||
\(301\) | 4.94818 | 0.285208 | ||||||||
\(302\) | 9.04436 | 0.520445 | ||||||||
\(303\) | −8.62096 | −0.495261 | ||||||||
\(304\) | −24.9499 | −1.43097 | ||||||||
\(305\) | −2.59765 | −0.148741 | ||||||||
\(306\) | −16.3664 | −0.935607 | ||||||||
\(307\) | −13.6449 | −0.778758 | −0.389379 | − | 0.921078i | \(-0.627310\pi\) | ||||
−0.389379 | + | 0.921078i | \(0.627310\pi\) | |||||||
\(308\) | 2.46892 | 0.140679 | ||||||||
\(309\) | −28.5270 | −1.62284 | ||||||||
\(310\) | −14.5861 | −0.828432 | ||||||||
\(311\) | −21.2834 | −1.20687 | −0.603434 | − | 0.797413i | \(-0.706201\pi\) | ||||
−0.603434 | + | 0.797413i | \(0.706201\pi\) | |||||||
\(312\) | −13.4000 | −0.758623 | ||||||||
\(313\) | −6.96416 | −0.393637 | −0.196819 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(314\) | 14.3063 | 0.807349 | ||||||||
\(315\) | 5.93217 | 0.334240 | ||||||||
\(316\) | −13.4075 | −0.754232 | ||||||||
\(317\) | 15.3647 | 0.862970 | 0.431485 | − | 0.902120i | \(-0.357990\pi\) | ||||
0.431485 | + | 0.902120i | \(0.357990\pi\) | |||||||
\(318\) | 53.8882 | 3.02190 | ||||||||
\(319\) | −26.5144 | −1.48452 | ||||||||
\(320\) | −1.41331 | −0.0790063 | ||||||||
\(321\) | −41.3064 | −2.30550 | ||||||||
\(322\) | −11.8970 | −0.662994 | ||||||||
\(323\) | −8.01366 | −0.445892 | ||||||||
\(324\) | 8.00659 | 0.444810 | ||||||||
\(325\) | 2.49362 | 0.138321 | ||||||||
\(326\) | 34.2945 | 1.89940 | ||||||||
\(327\) | 51.9572 | 2.87324 | ||||||||
\(328\) | −0.111732 | −0.00616939 | ||||||||
\(329\) | −2.50251 | −0.137968 | ||||||||
\(330\) | 13.2956 | 0.731897 | ||||||||
\(331\) | −6.25879 | −0.344014 | −0.172007 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172007 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(332\) | 6.25458 | 0.343265 | ||||||||
\(333\) | −44.5247 | −2.43994 | ||||||||
\(334\) | −7.00549 | −0.383323 | ||||||||
\(335\) | 2.10858 | 0.115204 | ||||||||
\(336\) | 14.9370 | 0.814880 | ||||||||
\(337\) | 6.33726 | 0.345213 | 0.172606 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172606 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(338\) | −11.6558 | −0.633993 | ||||||||
\(339\) | 46.3259 | 2.51608 | ||||||||
\(340\) | 1.53115 | 0.0830384 | ||||||||
\(341\) | −21.9675 | −1.18961 | ||||||||
\(342\) | 50.8967 | 2.75218 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.89694 | 0.479691 | ||||||||
\(345\) | −20.6882 | −1.11382 | ||||||||
\(346\) | 41.1881 | 2.21429 | ||||||||
\(347\) | 29.2180 | 1.56850 | 0.784252 | − | 0.620443i | \(-0.213047\pi\) | ||||
0.784252 | + | 0.620443i | \(0.213047\pi\) | |||||||
\(348\) | 29.2008 | 1.56533 | ||||||||
\(349\) | 14.8977 | 0.797458 | 0.398729 | − | 0.917069i | \(-0.369451\pi\) | ||||
0.398729 | + | 0.917069i | \(0.369451\pi\) | |||||||
\(350\) | −1.71867 | −0.0918668 | ||||||||
\(351\) | 21.8523 | 1.16639 | ||||||||
\(352\) | 12.9257 | 0.688941 | ||||||||
\(353\) | 5.29554 | 0.281853 | 0.140927 | − | 0.990020i | \(-0.454992\pi\) | ||||
0.140927 | + | 0.990020i | \(0.454992\pi\) | |||||||
\(354\) | −56.0862 | −2.98095 | ||||||||
\(355\) | −13.1283 | −0.696780 | ||||||||
\(356\) | −0.719690 | −0.0381435 | ||||||||
\(357\) | 4.79762 | 0.253917 | ||||||||
\(358\) | 3.65560 | 0.193204 | ||||||||
\(359\) | −36.4601 | −1.92429 | −0.962145 | − | 0.272538i | \(-0.912137\pi\) | ||||
−0.962145 | + | 0.272538i | \(0.912137\pi\) | |||||||
\(360\) | 10.6662 | 0.562157 | ||||||||
\(361\) | 5.92107 | 0.311636 | ||||||||
\(362\) | −43.4978 | −2.28619 | ||||||||
\(363\) | −12.8515 | −0.674527 | ||||||||
\(364\) | −2.37848 | −0.124666 | ||||||||
\(365\) | −12.0683 | −0.631683 | ||||||||
\(366\) | 13.3429 | 0.697446 | ||||||||
\(367\) | 12.0061 | 0.626714 | 0.313357 | − | 0.949635i | \(-0.398546\pi\) | ||||
0.313357 | + | 0.949635i | \(0.398546\pi\) | |||||||
\(368\) | −34.5963 | −1.80346 | ||||||||
\(369\) | 0.368636 | 0.0191904 | ||||||||
\(370\) | 12.8997 | 0.670624 | ||||||||
\(371\) | −10.4911 | −0.544673 | ||||||||
\(372\) | 24.1933 | 1.25436 | ||||||||
\(373\) | −0.947578 | −0.0490637 | −0.0245319 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245319 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(374\) | 7.14128 | 0.369267 | ||||||||
\(375\) | −2.98867 | −0.154334 | ||||||||
\(376\) | −4.49957 | −0.232047 | ||||||||
\(377\) | 25.5432 | 1.31554 | ||||||||
\(378\) | −15.0612 | −0.774667 | ||||||||
\(379\) | 12.0547 | 0.619208 | 0.309604 | − | 0.950866i | \(-0.399804\pi\) | ||||
0.309604 | + | 0.950866i | \(0.399804\pi\) | |||||||
\(380\) | −4.76161 | −0.244266 | ||||||||
\(381\) | −18.7806 | −0.962159 | ||||||||
\(382\) | −32.2390 | −1.64949 | ||||||||
\(383\) | −9.57640 | −0.489331 | −0.244666 | − | 0.969608i | \(-0.578678\pi\) | ||||
−0.244666 | + | 0.969608i | \(0.578678\pi\) | |||||||
\(384\) | 37.1083 | 1.89367 | ||||||||
\(385\) | −2.58842 | −0.131918 | ||||||||
\(386\) | −1.88611 | −0.0960005 | ||||||||
\(387\) | −29.3535 | −1.49212 | ||||||||
\(388\) | −13.5761 | −0.689221 | ||||||||
\(389\) | −13.1398 | −0.666217 | −0.333108 | − | 0.942889i | \(-0.608097\pi\) | ||||
−0.333108 | + | 0.942889i | \(0.608097\pi\) | |||||||
\(390\) | −12.8086 | −0.648587 | ||||||||
\(391\) | −11.1120 | −0.561959 | ||||||||
\(392\) | −1.79802 | −0.0908139 | ||||||||
\(393\) | 31.1743 | 1.57253 | ||||||||
\(394\) | 21.7002 | 1.09324 | ||||||||
\(395\) | 14.0565 | 0.707260 | ||||||||
\(396\) | −14.6460 | −0.735991 | ||||||||
\(397\) | 25.8115 | 1.29544 | 0.647722 | − | 0.761877i | \(-0.275722\pi\) | ||||
0.647722 | + | 0.761877i | \(0.275722\pi\) | |||||||
\(398\) | −6.51809 | −0.326722 | ||||||||
\(399\) | −14.9198 | −0.746922 | ||||||||
\(400\) | −4.99787 | −0.249893 | ||||||||
\(401\) | −0.267879 | −0.0133772 | −0.00668862 | − | 0.999978i | \(-0.502129\pi\) | ||||
−0.00668862 | + | 0.999978i | \(0.502129\pi\) | |||||||
\(402\) | −10.8308 | −0.540191 | ||||||||
\(403\) | 21.1629 | 1.05420 | ||||||||
\(404\) | −2.75136 | −0.136885 | ||||||||
\(405\) | −8.39415 | −0.417109 | ||||||||
\(406\) | −17.6051 | −0.873726 | ||||||||
\(407\) | 19.4278 | 0.962999 | ||||||||
\(408\) | 8.62624 | 0.427062 | ||||||||
\(409\) | 6.83566 | 0.338002 | 0.169001 | − | 0.985616i | \(-0.445946\pi\) | ||||
0.169001 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(410\) | −0.106801 | −0.00527454 | ||||||||
\(411\) | −12.8989 | −0.636258 | ||||||||
\(412\) | −9.10433 | −0.448538 | ||||||||
\(413\) | 10.9191 | 0.537292 | ||||||||
\(414\) | 70.5751 | 3.46858 | ||||||||
\(415\) | −6.55734 | −0.321887 | ||||||||
\(416\) | −12.4522 | −0.610521 | ||||||||
\(417\) | 31.3208 | 1.53378 | ||||||||
\(418\) | −22.2081 | −1.08623 | ||||||||
\(419\) | −29.1855 | −1.42580 | −0.712901 | − | 0.701264i | \(-0.752619\pi\) | ||||
−0.712901 | + | 0.701264i | \(0.752619\pi\) | |||||||
\(420\) | 2.85068 | 0.139099 | ||||||||
\(421\) | 8.75521 | 0.426703 | 0.213351 | − | 0.976976i | \(-0.431562\pi\) | ||||
0.213351 | + | 0.976976i | \(0.431562\pi\) | |||||||
\(422\) | 31.2573 | 1.52158 | ||||||||
\(423\) | 14.8453 | 0.721803 | ||||||||
\(424\) | −18.8633 | −0.916083 | ||||||||
\(425\) | −1.60527 | −0.0778669 | ||||||||
\(426\) | 67.4343 | 3.26720 | ||||||||
\(427\) | −2.59765 | −0.125709 | ||||||||
\(428\) | −13.1829 | −0.637218 | ||||||||
\(429\) | −19.2905 | −0.931355 | ||||||||
\(430\) | 8.50429 | 0.410113 | ||||||||
\(431\) | −12.8117 | −0.617119 | −0.308560 | − | 0.951205i | \(-0.599847\pi\) | ||||
−0.308560 | + | 0.951205i | \(0.599847\pi\) | |||||||
\(432\) | −43.7979 | −2.10723 | ||||||||
\(433\) | −28.9383 | −1.39068 | −0.695342 | − | 0.718679i | \(-0.744747\pi\) | ||||
−0.695342 | + | 0.718679i | \(0.744747\pi\) | |||||||
\(434\) | −14.5861 | −0.700153 | ||||||||
\(435\) | −30.6143 | −1.46784 | ||||||||
\(436\) | 16.5820 | 0.794135 | ||||||||
\(437\) | 34.5564 | 1.65306 | ||||||||
\(438\) | 61.9894 | 2.96197 | ||||||||
\(439\) | −17.4275 | −0.831771 | −0.415885 | − | 0.909417i | \(-0.636528\pi\) | ||||
−0.415885 | + | 0.909417i | \(0.636528\pi\) | |||||||
\(440\) | −4.65405 | −0.221873 | ||||||||
\(441\) | 5.93217 | 0.282484 | ||||||||
\(442\) | −6.87971 | −0.327234 | ||||||||
\(443\) | −31.1315 | −1.47910 | −0.739552 | − | 0.673100i | \(-0.764962\pi\) | ||||
−0.739552 | + | 0.673100i | \(0.764962\pi\) | |||||||
\(444\) | −21.3962 | −1.01542 | ||||||||
\(445\) | 0.754527 | 0.0357680 | ||||||||
\(446\) | −19.4388 | −0.920454 | ||||||||
\(447\) | 50.1678 | 2.37286 | ||||||||
\(448\) | −1.41331 | −0.0667725 | ||||||||
\(449\) | −8.20023 | −0.386993 | −0.193496 | − | 0.981101i | \(-0.561983\pi\) | ||||
−0.193496 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(450\) | 10.1955 | 0.480618 | ||||||||
\(451\) | −0.160849 | −0.00757410 | ||||||||
\(452\) | 14.7848 | 0.695420 | ||||||||
\(453\) | 15.7277 | 0.738950 | ||||||||
\(454\) | 4.23807 | 0.198903 | ||||||||
\(455\) | 2.49362 | 0.116903 | ||||||||
\(456\) | −26.8261 | −1.25625 | ||||||||
\(457\) | 8.96593 | 0.419408 | 0.209704 | − | 0.977765i | \(-0.432750\pi\) | ||||
0.209704 | + | 0.977765i | \(0.432750\pi\) | |||||||
\(458\) | 1.71867 | 0.0803082 | ||||||||
\(459\) | −14.0675 | −0.656613 | ||||||||
\(460\) | −6.60261 | −0.307848 | ||||||||
\(461\) | −27.8648 | −1.29779 | −0.648896 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648896 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(462\) | 13.2956 | 0.618566 | ||||||||
\(463\) | 10.9177 | 0.507386 | 0.253693 | − | 0.967285i | \(-0.418355\pi\) | ||||
0.253693 | + | 0.967285i | \(0.418355\pi\) | |||||||
\(464\) | −51.1953 | −2.37668 | ||||||||
\(465\) | −25.3644 | −1.17624 | ||||||||
\(466\) | 26.5436 | 1.22961 | ||||||||
\(467\) | 16.6236 | 0.769250 | 0.384625 | − | 0.923073i | \(-0.374331\pi\) | ||||
0.384625 | + | 0.923073i | \(0.374331\pi\) | |||||||
\(468\) | 14.1096 | 0.652215 | ||||||||
\(469\) | 2.10858 | 0.0973650 | ||||||||
\(470\) | −4.30099 | −0.198390 | ||||||||
\(471\) | 24.8778 | 1.14631 | ||||||||
\(472\) | 19.6327 | 0.903669 | ||||||||
\(473\) | 12.8080 | 0.588912 | ||||||||
\(474\) | −72.2020 | −3.31635 | ||||||||
\(475\) | 4.99210 | 0.229053 | ||||||||
\(476\) | 1.53115 | 0.0701802 | ||||||||
\(477\) | 62.2353 | 2.84956 | ||||||||
\(478\) | 8.13908 | 0.372273 | ||||||||
\(479\) | −2.33393 | −0.106640 | −0.0533200 | − | 0.998577i | \(-0.516980\pi\) | ||||
−0.0533200 | + | 0.998577i | \(0.516980\pi\) | |||||||
\(480\) | 14.9244 | 0.681201 | ||||||||
\(481\) | −18.7162 | −0.853384 | ||||||||
\(482\) | −0.383736 | −0.0174787 | ||||||||
\(483\) | −20.6882 | −0.941348 | ||||||||
\(484\) | −4.10152 | −0.186433 | ||||||||
\(485\) | 14.2332 | 0.646298 | ||||||||
\(486\) | −2.06676 | −0.0937502 | ||||||||
\(487\) | 6.53717 | 0.296228 | 0.148114 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148114 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(488\) | −4.67063 | −0.211429 | ||||||||
\(489\) | 59.6363 | 2.69684 | ||||||||
\(490\) | −1.71867 | −0.0776416 | ||||||||
\(491\) | −23.9084 | −1.07897 | −0.539486 | − | 0.841995i | \(-0.681381\pi\) | ||||
−0.539486 | + | 0.841995i | \(0.681381\pi\) | |||||||
\(492\) | 0.177147 | 0.00798639 | ||||||||
\(493\) | −16.4435 | −0.740576 | ||||||||
\(494\) | 21.3947 | 0.962592 | ||||||||
\(495\) | 15.3550 | 0.690155 | ||||||||
\(496\) | −42.4160 | −1.90454 | ||||||||
\(497\) | −13.1283 | −0.588886 | ||||||||
\(498\) | 33.6821 | 1.50933 | ||||||||
\(499\) | 26.4920 | 1.18594 | 0.592972 | − | 0.805223i | \(-0.297955\pi\) | ||||
0.592972 | + | 0.805223i | \(0.297955\pi\) | |||||||
\(500\) | −0.953829 | −0.0426565 | ||||||||
\(501\) | −12.1822 | −0.544259 | ||||||||
\(502\) | 11.5728 | 0.516519 | ||||||||
\(503\) | 11.1418 | 0.496788 | 0.248394 | − | 0.968659i | \(-0.420097\pi\) | ||||
0.248394 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(504\) | 10.6662 | 0.475110 | ||||||||
\(505\) | 2.88454 | 0.128361 | ||||||||
\(506\) | −30.7945 | −1.36898 | ||||||||
\(507\) | −20.2688 | −0.900170 | ||||||||
\(508\) | −5.99379 | −0.265931 | ||||||||
\(509\) | −33.1254 | −1.46826 | −0.734129 | − | 0.679010i | \(-0.762409\pi\) | ||||
−0.734129 | + | 0.679010i | \(0.762409\pi\) | |||||||
\(510\) | 8.24554 | 0.365118 | ||||||||
\(511\) | −12.0683 | −0.533870 | ||||||||
\(512\) | 6.98500 | 0.308697 | ||||||||
\(513\) | 43.7473 | 1.93149 | ||||||||
\(514\) | −13.3412 | −0.588453 | ||||||||
\(515\) | 9.54503 | 0.420604 | ||||||||
\(516\) | −14.1057 | −0.620969 | ||||||||
\(517\) | −6.47755 | −0.284882 | ||||||||
\(518\) | 12.8997 | 0.566781 | ||||||||
\(519\) | 71.6238 | 3.14394 | ||||||||
\(520\) | 4.48358 | 0.196618 | ||||||||
\(521\) | −2.66617 | −0.116807 | −0.0584035 | − | 0.998293i | \(-0.518601\pi\) | ||||
−0.0584035 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(522\) | 104.436 | 4.57106 | ||||||||
\(523\) | 36.4560 | 1.59411 | 0.797055 | − | 0.603907i | \(-0.206390\pi\) | ||||
0.797055 | + | 0.603907i | \(0.206390\pi\) | |||||||
\(524\) | 9.94921 | 0.434633 | ||||||||
\(525\) | −2.98867 | −0.130436 | ||||||||
\(526\) | −45.8496 | −1.99914 | ||||||||
\(527\) | −13.6236 | −0.593455 | ||||||||
\(528\) | 38.6633 | 1.68260 | ||||||||
\(529\) | 24.9171 | 1.08335 | ||||||||
\(530\) | −18.0308 | −0.783209 | ||||||||
\(531\) | −64.7737 | −2.81094 | ||||||||
\(532\) | −4.76161 | −0.206442 | ||||||||
\(533\) | 0.154958 | 0.00671197 | ||||||||
\(534\) | −3.87566 | −0.167716 | ||||||||
\(535\) | 13.8210 | 0.597534 | ||||||||
\(536\) | 3.79127 | 0.163758 | ||||||||
\(537\) | 6.35688 | 0.274320 | ||||||||
\(538\) | −37.9834 | −1.63758 | ||||||||
\(539\) | −2.58842 | −0.111491 | ||||||||
\(540\) | −8.35870 | −0.359701 | ||||||||
\(541\) | 1.85396 | 0.0797080 | 0.0398540 | − | 0.999206i | \(-0.487311\pi\) | ||||
0.0398540 | + | 0.999206i | \(0.487311\pi\) | |||||||
\(542\) | −26.0133 | −1.11737 | ||||||||
\(543\) | −75.6402 | −3.24603 | ||||||||
\(544\) | 8.01614 | 0.343689 | ||||||||
\(545\) | −17.3847 | −0.744678 | ||||||||
\(546\) | −12.8086 | −0.548156 | ||||||||
\(547\) | 3.47960 | 0.148777 | 0.0743884 | − | 0.997229i | \(-0.476300\pi\) | ||||
0.0743884 | + | 0.997229i | \(0.476300\pi\) | |||||||
\(548\) | −4.11667 | −0.175855 | ||||||||
\(549\) | 15.4097 | 0.657669 | ||||||||
\(550\) | −4.44865 | −0.189691 | ||||||||
\(551\) | 51.1362 | 2.17848 | ||||||||
\(552\) | −37.1979 | −1.58325 | ||||||||
\(553\) | 14.0565 | 0.597744 | ||||||||
\(554\) | −46.7254 | −1.98517 | ||||||||
\(555\) | 22.4319 | 0.952181 | ||||||||
\(556\) | 9.99596 | 0.423923 | ||||||||
\(557\) | −3.77795 | −0.160077 | −0.0800384 | − | 0.996792i | \(-0.525504\pi\) | ||||
−0.0800384 | + | 0.996792i | \(0.525504\pi\) | |||||||
\(558\) | 86.5270 | 3.66298 | ||||||||
\(559\) | −12.3389 | −0.521878 | ||||||||
\(560\) | −4.99787 | −0.211198 | ||||||||
\(561\) | 12.4183 | 0.524301 | ||||||||
\(562\) | −53.8015 | −2.26948 | ||||||||
\(563\) | −26.5422 | −1.11862 | −0.559310 | − | 0.828958i | \(-0.688934\pi\) | ||||
−0.559310 | + | 0.828958i | \(0.688934\pi\) | |||||||
\(564\) | 7.13386 | 0.300390 | ||||||||
\(565\) | −15.5005 | −0.652111 | ||||||||
\(566\) | 13.8388 | 0.581689 | ||||||||
\(567\) | −8.39415 | −0.352521 | ||||||||
\(568\) | −23.6051 | −0.990446 | ||||||||
\(569\) | −15.3193 | −0.642220 | −0.321110 | − | 0.947042i | \(-0.604056\pi\) | ||||
−0.321110 | + | 0.947042i | \(0.604056\pi\) | |||||||
\(570\) | −25.6422 | −1.07403 | ||||||||
\(571\) | −24.2824 | −1.01619 | −0.508094 | − | 0.861302i | \(-0.669650\pi\) | ||||
−0.508094 | + | 0.861302i | \(0.669650\pi\) | |||||||
\(572\) | −6.15653 | −0.257417 | ||||||||
\(573\) | −56.0618 | −2.34202 | ||||||||
\(574\) | −0.106801 | −0.00445780 | ||||||||
\(575\) | 6.92222 | 0.288676 | ||||||||
\(576\) | 8.38399 | 0.349333 | ||||||||
\(577\) | 37.3321 | 1.55415 | 0.777077 | − | 0.629405i | \(-0.216702\pi\) | ||||
0.777077 | + | 0.629405i | \(0.216702\pi\) | |||||||
\(578\) | −24.7886 | −1.03107 | ||||||||
\(579\) | −3.27984 | −0.136306 | ||||||||
\(580\) | −9.77048 | −0.405697 | ||||||||
\(581\) | −6.55734 | −0.272044 | ||||||||
\(582\) | −73.1097 | −3.03049 | ||||||||
\(583\) | −27.1555 | −1.12467 | ||||||||
\(584\) | −21.6991 | −0.897914 | ||||||||
\(585\) | −14.7926 | −0.611597 | ||||||||
\(586\) | −50.3362 | −2.07937 | ||||||||
\(587\) | −38.0015 | −1.56849 | −0.784245 | − | 0.620451i | \(-0.786949\pi\) | ||||
−0.784245 | + | 0.620451i | \(0.786949\pi\) | |||||||
\(588\) | 2.85068 | 0.117560 | ||||||||
\(589\) | 42.3671 | 1.74571 | ||||||||
\(590\) | 18.7663 | 0.772595 | ||||||||
\(591\) | 37.7354 | 1.55223 | ||||||||
\(592\) | 37.5122 | 1.54174 | ||||||||
\(593\) | −24.7386 | −1.01589 | −0.507945 | − | 0.861389i | \(-0.669595\pi\) | ||||
−0.507945 | + | 0.861389i | \(0.669595\pi\) | |||||||
\(594\) | −38.9849 | −1.59957 | ||||||||
\(595\) | −1.60527 | −0.0658096 | ||||||||
\(596\) | 16.0110 | 0.655835 | ||||||||
\(597\) | −11.3346 | −0.463894 | ||||||||
\(598\) | 29.6666 | 1.21316 | ||||||||
\(599\) | −22.1218 | −0.903872 | −0.451936 | − | 0.892050i | \(-0.649266\pi\) | ||||
−0.451936 | + | 0.892050i | \(0.649266\pi\) | |||||||
\(600\) | −5.37371 | −0.219381 | ||||||||
\(601\) | −1.07752 | −0.0439532 | −0.0219766 | − | 0.999758i | \(-0.506996\pi\) | ||||
−0.0219766 | + | 0.999758i | \(0.506996\pi\) | |||||||
\(602\) | 8.50429 | 0.346609 | ||||||||
\(603\) | −12.5084 | −0.509383 | ||||||||
\(604\) | 5.01945 | 0.204238 | ||||||||
\(605\) | 4.30006 | 0.174822 | ||||||||
\(606\) | −14.8166 | −0.601883 | ||||||||
\(607\) | 20.5327 | 0.833395 | 0.416697 | − | 0.909045i | \(-0.363188\pi\) | ||||
0.416697 | + | 0.909045i | \(0.363188\pi\) | |||||||
\(608\) | −24.9288 | −1.01100 | ||||||||
\(609\) | −30.6143 | −1.24055 | ||||||||
\(610\) | −4.46450 | −0.180762 | ||||||||
\(611\) | 6.24029 | 0.252455 | ||||||||
\(612\) | −9.08306 | −0.367161 | ||||||||
\(613\) | 19.6185 | 0.792383 | 0.396191 | − | 0.918168i | \(-0.370332\pi\) | ||||
0.396191 | + | 0.918168i | \(0.370332\pi\) | |||||||
\(614\) | −23.4512 | −0.946412 | ||||||||
\(615\) | −0.185722 | −0.00748902 | ||||||||
\(616\) | −4.65405 | −0.187517 | ||||||||
\(617\) | 15.1976 | 0.611831 | 0.305915 | − | 0.952059i | \(-0.401038\pi\) | ||||
0.305915 | + | 0.952059i | \(0.401038\pi\) | |||||||
\(618\) | −49.0285 | −1.97221 | ||||||||
\(619\) | 16.2629 | 0.653662 | 0.326831 | − | 0.945083i | \(-0.394019\pi\) | ||||
0.326831 | + | 0.945083i | \(0.394019\pi\) | |||||||
\(620\) | −8.09498 | −0.325102 | ||||||||
\(621\) | 60.6615 | 2.43426 | ||||||||
\(622\) | −36.5791 | −1.46669 | ||||||||
\(623\) | 0.754527 | 0.0302295 | ||||||||
\(624\) | −37.2471 | −1.49108 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.9691 | −0.478381 | ||||||||
\(627\) | −38.6187 | −1.54228 | ||||||||
\(628\) | 7.93969 | 0.316828 | ||||||||
\(629\) | 12.0486 | 0.480408 | ||||||||
\(630\) | 10.1955 | 0.406197 | ||||||||
\(631\) | −0.867869 | −0.0345493 | −0.0172747 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172747 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(632\) | 25.2739 | 1.00534 | ||||||||
\(633\) | 54.3547 | 2.16040 | ||||||||
\(634\) | 26.4069 | 1.04875 | ||||||||
\(635\) | 6.28392 | 0.249370 | ||||||||
\(636\) | 29.9069 | 1.18589 | ||||||||
\(637\) | 2.49362 | 0.0988007 | ||||||||
\(638\) | −45.5694 | −1.80411 | ||||||||
\(639\) | 77.8795 | 3.08087 | ||||||||
\(640\) | −12.4163 | −0.490797 | ||||||||
\(641\) | 31.3984 | 1.24016 | 0.620082 | − | 0.784537i | \(-0.287100\pi\) | ||||
0.620082 | + | 0.784537i | \(0.287100\pi\) | |||||||
\(642\) | −70.9922 | −2.80184 | ||||||||
\(643\) | 6.49828 | 0.256267 | 0.128134 | − | 0.991757i | \(-0.459101\pi\) | ||||
0.128134 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(644\) | −6.60261 | −0.260179 | ||||||||
\(645\) | 14.7885 | 0.582296 | ||||||||
\(646\) | −13.7728 | −0.541885 | ||||||||
\(647\) | 16.3970 | 0.644633 | 0.322316 | − | 0.946632i | \(-0.395538\pi\) | ||||
0.322316 | + | 0.946632i | \(0.395538\pi\) | |||||||
\(648\) | −15.0929 | −0.592904 | ||||||||
\(649\) | 28.2632 | 1.10943 | ||||||||
\(650\) | 4.28570 | 0.168099 | ||||||||
\(651\) | −25.3644 | −0.994107 | ||||||||
\(652\) | 19.0328 | 0.745381 | ||||||||
\(653\) | −7.00912 | −0.274288 | −0.137144 | − | 0.990551i | \(-0.543792\pi\) | ||||
−0.137144 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(654\) | 89.2972 | 3.49180 | ||||||||
\(655\) | −10.4308 | −0.407565 | ||||||||
\(656\) | −0.310577 | −0.0121260 | ||||||||
\(657\) | 71.5912 | 2.79304 | ||||||||
\(658\) | −4.30099 | −0.167670 | ||||||||
\(659\) | −8.28207 | −0.322624 | −0.161312 | − | 0.986903i | \(-0.551572\pi\) | ||||
−0.161312 | + | 0.986903i | \(0.551572\pi\) | |||||||
\(660\) | 7.37878 | 0.287219 | ||||||||
\(661\) | 29.9745 | 1.16587 | 0.582937 | − | 0.812517i | \(-0.301903\pi\) | ||||
0.582937 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(662\) | −10.7568 | −0.418075 | ||||||||
\(663\) | −11.9634 | −0.464621 | ||||||||
\(664\) | −11.7902 | −0.457550 | ||||||||
\(665\) | 4.99210 | 0.193585 | ||||||||
\(666\) | −76.5234 | −2.96522 | ||||||||
\(667\) | 70.9072 | 2.74554 | ||||||||
\(668\) | −3.88791 | −0.150428 | ||||||||
\(669\) | −33.8030 | −1.30690 | ||||||||
\(670\) | 3.62395 | 0.140005 | ||||||||
\(671\) | −6.72381 | −0.259570 | ||||||||
\(672\) | 14.9244 | 0.575720 | ||||||||
\(673\) | −26.1184 | −1.00679 | −0.503395 | − | 0.864057i | \(-0.667916\pi\) | ||||
−0.503395 | + | 0.864057i | \(0.667916\pi\) | |||||||
\(674\) | 10.8917 | 0.419531 | ||||||||
\(675\) | 8.76331 | 0.337300 | ||||||||
\(676\) | −6.46875 | −0.248798 | ||||||||
\(677\) | −32.4814 | −1.24836 | −0.624180 | − | 0.781280i | \(-0.714567\pi\) | ||||
−0.624180 | + | 0.781280i | \(0.714567\pi\) | |||||||
\(678\) | 79.6190 | 3.05775 | ||||||||
\(679\) | 14.2332 | 0.546222 | ||||||||
\(680\) | −2.88631 | −0.110685 | ||||||||
\(681\) | 7.36978 | 0.282410 | ||||||||
\(682\) | −37.7549 | −1.44571 | ||||||||
\(683\) | −31.6652 | −1.21163 | −0.605817 | − | 0.795604i | \(-0.707154\pi\) | ||||
−0.605817 | + | 0.795604i | \(0.707154\pi\) | |||||||
\(684\) | 28.2467 | 1.08004 | ||||||||
\(685\) | 4.31594 | 0.164904 | ||||||||
\(686\) | −1.71867 | −0.0656192 | ||||||||
\(687\) | 2.98867 | 0.114025 | ||||||||
\(688\) | 24.7303 | 0.942836 | ||||||||
\(689\) | 26.1609 | 0.996650 | ||||||||
\(690\) | −35.5563 | −1.35360 | ||||||||
\(691\) | −40.1525 | −1.52747 | −0.763736 | − | 0.645529i | \(-0.776637\pi\) | ||||
−0.763736 | + | 0.645529i | \(0.776637\pi\) | |||||||
\(692\) | 22.8586 | 0.868954 | ||||||||
\(693\) | 15.3550 | 0.583288 | ||||||||
\(694\) | 50.2161 | 1.90618 | ||||||||
\(695\) | −10.4798 | −0.397522 | ||||||||
\(696\) | −55.0452 | −2.08648 | ||||||||
\(697\) | −0.0997543 | −0.00377846 | ||||||||
\(698\) | 25.6043 | 0.969138 | ||||||||
\(699\) | 46.1579 | 1.74585 | ||||||||
\(700\) | −0.953829 | −0.0360514 | ||||||||
\(701\) | −36.3265 | −1.37203 | −0.686016 | − | 0.727586i | \(-0.740642\pi\) | ||||
−0.686016 | + | 0.727586i | \(0.740642\pi\) | |||||||
\(702\) | 37.5570 | 1.41750 | ||||||||
\(703\) | −37.4689 | −1.41317 | ||||||||
\(704\) | −3.65824 | −0.137875 | ||||||||
\(705\) | −7.47918 | −0.281682 | ||||||||
\(706\) | 9.10129 | 0.342532 | ||||||||
\(707\) | 2.88454 | 0.108484 | ||||||||
\(708\) | −31.1268 | −1.16982 | ||||||||
\(709\) | −25.7268 | −0.966189 | −0.483094 | − | 0.875568i | \(-0.660487\pi\) | ||||
−0.483094 | + | 0.875568i | \(0.660487\pi\) | |||||||
\(710\) | −22.5633 | −0.846785 | ||||||||
\(711\) | −83.3857 | −3.12721 | ||||||||
\(712\) | 1.35666 | 0.0508429 | ||||||||
\(713\) | 58.7476 | 2.20012 | ||||||||
\(714\) | 8.24554 | 0.308581 | ||||||||
\(715\) | 6.45454 | 0.241386 | ||||||||
\(716\) | 2.02879 | 0.0758193 | ||||||||
\(717\) | 14.1534 | 0.528569 | ||||||||
\(718\) | −62.6629 | −2.33856 | ||||||||
\(719\) | 30.1001 | 1.12254 | 0.561272 | − | 0.827632i | \(-0.310312\pi\) | ||||
0.561272 | + | 0.827632i | \(0.310312\pi\) | |||||||
\(720\) | 29.6482 | 1.10492 | ||||||||
\(721\) | 9.54503 | 0.355475 | ||||||||
\(722\) | 10.1764 | 0.378726 | ||||||||
\(723\) | −0.667296 | −0.0248170 | ||||||||
\(724\) | −24.1404 | −0.897172 | ||||||||
\(725\) | 10.2434 | 0.380431 | ||||||||
\(726\) | −22.0874 | −0.819742 | ||||||||
\(727\) | 7.97316 | 0.295708 | 0.147854 | − | 0.989009i | \(-0.452763\pi\) | ||||
0.147854 | + | 0.989009i | \(0.452763\pi\) | |||||||
\(728\) | 4.48358 | 0.166173 | ||||||||
\(729\) | −28.7764 | −1.06579 | ||||||||
\(730\) | −20.7414 | −0.767675 | ||||||||
\(731\) | 7.94316 | 0.293788 | ||||||||
\(732\) | 7.40507 | 0.273699 | ||||||||
\(733\) | 25.5651 | 0.944267 | 0.472134 | − | 0.881527i | \(-0.343484\pi\) | ||||
0.472134 | + | 0.881527i | \(0.343484\pi\) | |||||||
\(734\) | 20.6345 | 0.761635 | ||||||||
\(735\) | −2.98867 | −0.110239 | ||||||||
\(736\) | −34.5671 | −1.27416 | ||||||||
\(737\) | 5.45789 | 0.201044 | ||||||||
\(738\) | 0.633564 | 0.0233218 | ||||||||
\(739\) | 35.6717 | 1.31220 | 0.656102 | − | 0.754672i | \(-0.272204\pi\) | ||||
0.656102 | + | 0.754672i | \(0.272204\pi\) | |||||||
\(740\) | 7.15910 | 0.263174 | ||||||||
\(741\) | 37.2042 | 1.36673 | ||||||||
\(742\) | −18.0308 | −0.661932 | ||||||||
\(743\) | −37.9824 | −1.39344 | −0.696719 | − | 0.717344i | \(-0.745358\pi\) | ||||
−0.696719 | + | 0.717344i | \(0.745358\pi\) | |||||||
\(744\) | −45.6057 | −1.67199 | ||||||||
\(745\) | −16.7860 | −0.614991 | ||||||||
\(746\) | −1.62857 | −0.0596263 | ||||||||
\(747\) | 38.8993 | 1.42325 | ||||||||
\(748\) | 3.96327 | 0.144912 | ||||||||
\(749\) | 13.8210 | 0.505008 | ||||||||
\(750\) | −5.13655 | −0.187560 | ||||||||
\(751\) | 10.7851 | 0.393553 | 0.196776 | − | 0.980448i | \(-0.436953\pi\) | ||||
0.196776 | + | 0.980448i | \(0.436953\pi\) | |||||||
\(752\) | −12.5072 | −0.456091 | ||||||||
\(753\) | 20.1244 | 0.733376 | ||||||||
\(754\) | 43.9003 | 1.59876 | ||||||||
\(755\) | −5.26242 | −0.191519 | ||||||||
\(756\) | −8.35870 | −0.304003 | ||||||||
\(757\) | −11.0028 | −0.399903 | −0.199951 | − | 0.979806i | \(-0.564078\pi\) | ||||
−0.199951 | + | 0.979806i | \(0.564078\pi\) | |||||||
\(758\) | 20.7180 | 0.752513 | ||||||||
\(759\) | −53.5500 | −1.94374 | ||||||||
\(760\) | 8.97591 | 0.325591 | ||||||||
\(761\) | 36.8820 | 1.33697 | 0.668486 | − | 0.743724i | \(-0.266942\pi\) | ||||
0.668486 | + | 0.743724i | \(0.266942\pi\) | |||||||
\(762\) | −32.2777 | −1.16930 | ||||||||
\(763\) | −17.3847 | −0.629368 | ||||||||
\(764\) | −17.8920 | −0.647310 | ||||||||
\(765\) | 9.52273 | 0.344295 | ||||||||
\(766\) | −16.4587 | −0.594676 | ||||||||
\(767\) | −27.2279 | −0.983144 | ||||||||
\(768\) | 55.3291 | 1.99652 | ||||||||
\(769\) | 26.1789 | 0.944036 | 0.472018 | − | 0.881589i | \(-0.343526\pi\) | ||||
0.472018 | + | 0.881589i | \(0.343526\pi\) | |||||||
\(770\) | −4.44865 | −0.160318 | ||||||||
\(771\) | −23.1995 | −0.835511 | ||||||||
\(772\) | −1.04675 | −0.0376735 | ||||||||
\(773\) | 37.3901 | 1.34483 | 0.672415 | − | 0.740175i | \(-0.265257\pi\) | ||||
0.672415 | + | 0.740175i | \(0.265257\pi\) | |||||||
\(774\) | −50.4489 | −1.81335 | ||||||||
\(775\) | 8.48682 | 0.304856 | ||||||||
\(776\) | 25.5917 | 0.918688 | ||||||||
\(777\) | 22.4319 | 0.804740 | ||||||||
\(778\) | −22.5831 | −0.809642 | ||||||||
\(779\) | 0.310218 | 0.0111147 | ||||||||
\(780\) | −7.10851 | −0.254526 | ||||||||
\(781\) | −33.9817 | −1.21596 | ||||||||
\(782\) | −19.0979 | −0.682939 | ||||||||
\(783\) | 89.7663 | 3.20799 | ||||||||
\(784\) | −4.99787 | −0.178495 | ||||||||
\(785\) | −8.32402 | −0.297097 | ||||||||
\(786\) | 53.5783 | 1.91108 | ||||||||
\(787\) | −13.0730 | −0.466004 | −0.233002 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233002 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(788\) | 12.0432 | 0.429020 | ||||||||
\(789\) | −79.7299 | −2.83846 | ||||||||
\(790\) | 24.1585 | 0.859522 | ||||||||
\(791\) | −15.5005 | −0.551134 | ||||||||
\(792\) | 27.6086 | 0.981029 | ||||||||
\(793\) | 6.47753 | 0.230024 | ||||||||
\(794\) | 44.3616 | 1.57433 | ||||||||
\(795\) | −31.3546 | −1.11203 | ||||||||
\(796\) | −3.61742 | −0.128216 | ||||||||
\(797\) | −28.4984 | −1.00947 | −0.504733 | − | 0.863275i | \(-0.668409\pi\) | ||||
−0.504733 | + | 0.863275i | \(0.668409\pi\) | |||||||
\(798\) | −25.6422 | −0.907723 | ||||||||
\(799\) | −4.01719 | −0.142118 | ||||||||
\(800\) | −4.99364 | −0.176552 | ||||||||
\(801\) | −4.47598 | −0.158151 | ||||||||
\(802\) | −0.460396 | −0.0162572 | ||||||||
\(803\) | −31.2379 | −1.10236 | ||||||||
\(804\) | −6.01088 | −0.211988 | ||||||||
\(805\) | 6.92222 | 0.243976 | ||||||||
\(806\) | 36.3720 | 1.28115 | ||||||||
\(807\) | −66.0510 | −2.32510 | ||||||||
\(808\) | 5.18648 | 0.182460 | ||||||||
\(809\) | 4.98266 | 0.175181 | 0.0875906 | − | 0.996157i | \(-0.472083\pi\) | ||||
0.0875906 | + | 0.996157i | \(0.472083\pi\) | |||||||
\(810\) | −14.4268 | −0.506906 | ||||||||
\(811\) | 43.1869 | 1.51650 | 0.758248 | − | 0.651966i | \(-0.226055\pi\) | ||||
0.758248 | + | 0.651966i | \(0.226055\pi\) | |||||||
\(812\) | −9.77048 | −0.342877 | ||||||||
\(813\) | −45.2356 | −1.58648 | ||||||||
\(814\) | 33.3900 | 1.17032 | ||||||||
\(815\) | −19.9541 | −0.698961 | ||||||||
\(816\) | 23.9779 | 0.839394 | ||||||||
\(817\) | −24.7018 | −0.864207 | ||||||||
\(818\) | 11.7482 | 0.410768 | ||||||||
\(819\) | −14.7926 | −0.516894 | ||||||||
\(820\) | −0.0592727 | −0.00206989 | ||||||||
\(821\) | −49.5240 | −1.72840 | −0.864200 | − | 0.503149i | \(-0.832175\pi\) | ||||
−0.864200 | + | 0.503149i | \(0.832175\pi\) | |||||||
\(822\) | −22.1690 | −0.773234 | ||||||||
\(823\) | 11.9212 | 0.415548 | 0.207774 | − | 0.978177i | \(-0.433378\pi\) | ||||
0.207774 | + | 0.978177i | \(0.433378\pi\) | |||||||
\(824\) | 17.1622 | 0.597873 | ||||||||
\(825\) | −7.73596 | −0.269331 | ||||||||
\(826\) | 18.7663 | 0.652962 | ||||||||
\(827\) | 3.74076 | 0.130079 | 0.0650395 | − | 0.997883i | \(-0.479283\pi\) | ||||
0.0650395 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(828\) | 39.1678 | 1.36118 | ||||||||
\(829\) | −29.5750 | −1.02718 | −0.513591 | − | 0.858035i | \(-0.671685\pi\) | ||||
−0.513591 | + | 0.858035i | \(0.671685\pi\) | |||||||
\(830\) | −11.2699 | −0.391184 | ||||||||
\(831\) | −81.2529 | −2.81863 | ||||||||
\(832\) | 3.52425 | 0.122181 | ||||||||
\(833\) | −1.60527 | −0.0556192 | ||||||||
\(834\) | 53.8301 | 1.86398 | ||||||||
\(835\) | 4.07611 | 0.141060 | ||||||||
\(836\) | −12.3251 | −0.426272 | ||||||||
\(837\) | 74.3727 | 2.57070 | ||||||||
\(838\) | −50.1602 | −1.73275 | ||||||||
\(839\) | 36.2034 | 1.24988 | 0.624939 | − | 0.780673i | \(-0.285124\pi\) | ||||
0.624939 | + | 0.780673i | \(0.285124\pi\) | |||||||
\(840\) | −5.37371 | −0.185410 | ||||||||
\(841\) | 75.9279 | 2.61820 | ||||||||
\(842\) | 15.0473 | 0.518565 | ||||||||
\(843\) | −93.5579 | −3.22231 | ||||||||
\(844\) | 17.3472 | 0.597115 | ||||||||
\(845\) | 6.78188 | 0.233304 | ||||||||
\(846\) | 25.5142 | 0.877196 | ||||||||
\(847\) | 4.30006 | 0.147752 | ||||||||
\(848\) | −52.4333 | −1.80057 | ||||||||
\(849\) | 24.0650 | 0.825907 | ||||||||
\(850\) | −2.75893 | −0.0946304 | ||||||||
\(851\) | −51.9556 | −1.78102 | ||||||||
\(852\) | 37.4247 | 1.28215 | ||||||||
\(853\) | 33.0461 | 1.13148 | 0.565738 | − | 0.824585i | \(-0.308591\pi\) | ||||
0.565738 | + | 0.824585i | \(0.308591\pi\) | |||||||
\(854\) | −4.46450 | −0.152772 | ||||||||
\(855\) | −29.6140 | −1.01278 | ||||||||
\(856\) | 24.8505 | 0.849371 | ||||||||
\(857\) | −22.4301 | −0.766198 | −0.383099 | − | 0.923707i | \(-0.625143\pi\) | ||||
−0.383099 | + | 0.923707i | \(0.625143\pi\) | |||||||
\(858\) | −33.1540 | −1.13186 | ||||||||
\(859\) | −46.5415 | −1.58798 | −0.793988 | − | 0.607933i | \(-0.791999\pi\) | ||||
−0.793988 | + | 0.607933i | \(0.791999\pi\) | |||||||
\(860\) | 4.71972 | 0.160941 | ||||||||
\(861\) | −0.185722 | −0.00632938 | ||||||||
\(862\) | −22.0191 | −0.749975 | ||||||||
\(863\) | −51.4066 | −1.74990 | −0.874950 | − | 0.484213i | \(-0.839106\pi\) | ||||
−0.874950 | + | 0.484213i | \(0.839106\pi\) | |||||||
\(864\) | −43.7608 | −1.48877 | ||||||||
\(865\) | −23.9651 | −0.814838 | ||||||||
\(866\) | −49.7354 | −1.69008 | ||||||||
\(867\) | −43.1060 | −1.46396 | ||||||||
\(868\) | −8.09498 | −0.274762 | ||||||||
\(869\) | 36.3842 | 1.23425 | ||||||||
\(870\) | −52.6159 | −1.78384 | ||||||||
\(871\) | −5.25798 | −0.178160 | ||||||||
\(872\) | −31.2581 | −1.05853 | ||||||||
\(873\) | −84.4340 | −2.85766 | ||||||||
\(874\) | 59.3911 | 2.00893 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 34.4029 | 1.16237 | ||||||||
\(877\) | 41.6264 | 1.40562 | 0.702812 | − | 0.711375i | \(-0.251927\pi\) | ||||
0.702812 | + | 0.711375i | \(0.251927\pi\) | |||||||
\(878\) | −29.9522 | −1.01084 | ||||||||
\(879\) | −87.5319 | −2.95238 | ||||||||
\(880\) | −12.9366 | −0.436093 | ||||||||
\(881\) | 5.40727 | 0.182175 | 0.0910877 | − | 0.995843i | \(-0.470966\pi\) | ||||
0.0910877 | + | 0.995843i | \(0.470966\pi\) | |||||||
\(882\) | 10.1955 | 0.343299 | ||||||||
\(883\) | 50.3899 | 1.69576 | 0.847878 | − | 0.530192i | \(-0.177880\pi\) | ||||
0.847878 | + | 0.530192i | \(0.177880\pi\) | |||||||
\(884\) | −3.81810 | −0.128417 | ||||||||
\(885\) | 32.6335 | 1.09696 | ||||||||
\(886\) | −53.5048 | −1.79753 | ||||||||
\(887\) | −16.2276 | −0.544870 | −0.272435 | − | 0.962174i | \(-0.587829\pi\) | ||||
−0.272435 | + | 0.962174i | \(0.587829\pi\) | |||||||
\(888\) | 40.3331 | 1.35349 | ||||||||
\(889\) | 6.28392 | 0.210756 | ||||||||
\(890\) | 1.29678 | 0.0434683 | ||||||||
\(891\) | −21.7276 | −0.727903 | ||||||||
\(892\) | −10.7882 | −0.361215 | ||||||||
\(893\) | 12.4928 | 0.418055 | ||||||||
\(894\) | 86.2220 | 2.88370 | ||||||||
\(895\) | −2.12699 | −0.0710974 | ||||||||
\(896\) | −12.4163 | −0.414799 | ||||||||
\(897\) | 51.5885 | 1.72249 | ||||||||
\(898\) | −14.0935 | −0.470306 | ||||||||
\(899\) | 86.9342 | 2.89942 | ||||||||
\(900\) | 5.65828 | 0.188609 | ||||||||
\(901\) | −16.8411 | −0.561058 | ||||||||
\(902\) | −0.276447 | −0.00920469 | ||||||||
\(903\) | 14.7885 | 0.492130 | ||||||||
\(904\) | −27.8703 | −0.926951 | ||||||||
\(905\) | 25.3090 | 0.841298 | ||||||||
\(906\) | 27.0307 | 0.898033 | ||||||||
\(907\) | −54.3644 | −1.80514 | −0.902570 | − | 0.430543i | \(-0.858322\pi\) | ||||
−0.902570 | + | 0.430543i | \(0.858322\pi\) | |||||||
\(908\) | 2.35205 | 0.0780555 | ||||||||
\(909\) | −17.1116 | −0.567556 | ||||||||
\(910\) | 4.28570 | 0.142070 | ||||||||
\(911\) | 43.6526 | 1.44628 | 0.723138 | − | 0.690704i | \(-0.242699\pi\) | ||||
0.723138 | + | 0.690704i | \(0.242699\pi\) | |||||||
\(912\) | −74.5670 | −2.46916 | ||||||||
\(913\) | −16.9732 | −0.561730 | ||||||||
\(914\) | 15.4095 | 0.509700 | ||||||||
\(915\) | −7.76352 | −0.256654 | ||||||||
\(916\) | 0.953829 | 0.0315154 | ||||||||
\(917\) | −10.4308 | −0.344456 | ||||||||
\(918\) | −24.1773 | −0.797971 | ||||||||
\(919\) | 48.9151 | 1.61356 | 0.806779 | − | 0.590853i | \(-0.201209\pi\) | ||||
0.806779 | + | 0.590853i | \(0.201209\pi\) | |||||||
\(920\) | 12.4463 | 0.410343 | ||||||||
\(921\) | −40.7803 | −1.34376 | ||||||||
\(922\) | −47.8904 | −1.57719 | ||||||||
\(923\) | 32.7370 | 1.07755 | ||||||||
\(924\) | 7.37878 | 0.242744 | ||||||||
\(925\) | −7.50564 | −0.246784 | ||||||||
\(926\) | 18.7638 | 0.616618 | ||||||||
\(927\) | −56.6228 | −1.85974 | ||||||||
\(928\) | −51.1520 | −1.67915 | ||||||||
\(929\) | 6.69369 | 0.219613 | 0.109806 | − | 0.993953i | \(-0.464977\pi\) | ||||
0.109806 | + | 0.993953i | \(0.464977\pi\) | |||||||
\(930\) | −43.5930 | −1.42947 | ||||||||
\(931\) | 4.99210 | 0.163610 | ||||||||
\(932\) | 14.7312 | 0.482537 | ||||||||
\(933\) | −63.6090 | −2.08247 | ||||||||
\(934\) | 28.5706 | 0.934857 | ||||||||
\(935\) | −4.15512 | −0.135887 | ||||||||
\(936\) | −26.5974 | −0.869362 | ||||||||
\(937\) | 36.3051 | 1.18604 | 0.593018 | − | 0.805189i | \(-0.297936\pi\) | ||||
0.593018 | + | 0.805189i | \(0.297936\pi\) | |||||||
\(938\) | 3.62395 | 0.118326 | ||||||||
\(939\) | −20.8136 | −0.679226 | ||||||||
\(940\) | −2.38696 | −0.0778542 | ||||||||
\(941\) | −45.3421 | −1.47811 | −0.739055 | − | 0.673645i | \(-0.764728\pi\) | ||||
−0.739055 | + | 0.673645i | \(0.764728\pi\) | |||||||
\(942\) | 42.7567 | 1.39309 | ||||||||
\(943\) | 0.430159 | 0.0140079 | ||||||||
\(944\) | 54.5720 | 1.77617 | ||||||||
\(945\) | 8.76331 | 0.285070 | ||||||||
\(946\) | 22.0127 | 0.715695 | ||||||||
\(947\) | −42.6472 | −1.38585 | −0.692923 | − | 0.721011i | \(-0.743678\pi\) | ||||
−0.692923 | + | 0.721011i | \(0.743678\pi\) | |||||||
\(948\) | −40.0707 | −1.30144 | ||||||||
\(949\) | 30.0937 | 0.976883 | ||||||||
\(950\) | 8.57978 | 0.278365 | ||||||||
\(951\) | 45.9202 | 1.48906 | ||||||||
\(952\) | −2.88631 | −0.0935458 | ||||||||
\(953\) | −2.52634 | −0.0818360 | −0.0409180 | − | 0.999163i | \(-0.513028\pi\) | ||||
−0.0409180 | + | 0.999163i | \(0.513028\pi\) | |||||||
\(954\) | 106.962 | 3.46302 | ||||||||
\(955\) | 18.7581 | 0.606997 | ||||||||
\(956\) | 4.51703 | 0.146091 | ||||||||
\(957\) | −79.2428 | −2.56155 | ||||||||
\(958\) | −4.01126 | −0.129598 | ||||||||
\(959\) | 4.31594 | 0.139369 | ||||||||
\(960\) | −4.22392 | −0.136326 | ||||||||
\(961\) | 41.0262 | 1.32343 | ||||||||
\(962\) | −32.1669 | −1.03710 | ||||||||
\(963\) | −81.9885 | −2.64204 | ||||||||
\(964\) | −0.212966 | −0.00685918 | ||||||||
\(965\) | 1.09742 | 0.0353273 | ||||||||
\(966\) | −35.5563 | −1.14400 | ||||||||
\(967\) | −8.86804 | −0.285177 | −0.142588 | − | 0.989782i | \(-0.545543\pi\) | ||||
−0.142588 | + | 0.989782i | \(0.545543\pi\) | |||||||
\(968\) | 7.73160 | 0.248503 | ||||||||
\(969\) | −23.9502 | −0.769392 | ||||||||
\(970\) | 24.4622 | 0.785436 | ||||||||
\(971\) | 36.2224 | 1.16243 | 0.581216 | − | 0.813749i | \(-0.302577\pi\) | ||||
0.581216 | + | 0.813749i | \(0.302577\pi\) | |||||||
\(972\) | −1.14701 | −0.0367904 | ||||||||
\(973\) | −10.4798 | −0.335968 | ||||||||
\(974\) | 11.2352 | 0.360001 | ||||||||
\(975\) | 7.45261 | 0.238674 | ||||||||
\(976\) | −12.9827 | −0.415566 | ||||||||
\(977\) | 48.0417 | 1.53699 | 0.768495 | − | 0.639856i | \(-0.221006\pi\) | ||||
0.768495 | + | 0.639856i | \(0.221006\pi\) | |||||||
\(978\) | 102.495 | 3.27743 | ||||||||
\(979\) | 1.95304 | 0.0624193 | ||||||||
\(980\) | −0.953829 | −0.0304690 | ||||||||
\(981\) | 103.129 | 3.29265 | ||||||||
\(982\) | −41.0907 | −1.31126 | ||||||||
\(983\) | 5.54888 | 0.176982 | 0.0884910 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884910 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(984\) | −0.333932 | −0.0106454 | ||||||||
\(985\) | −12.6261 | −0.402302 | ||||||||
\(986\) | −28.2609 | −0.900010 | ||||||||
\(987\) | −7.47918 | −0.238065 | ||||||||
\(988\) | 11.8736 | 0.377751 | ||||||||
\(989\) | −34.2524 | −1.08916 | ||||||||
\(990\) | 26.3902 | 0.838734 | ||||||||
\(991\) | 15.1140 | 0.480111 | 0.240055 | − | 0.970759i | \(-0.422834\pi\) | ||||
0.240055 | + | 0.970759i | \(0.422834\pi\) | |||||||
\(992\) | −42.3802 | −1.34557 | ||||||||
\(993\) | −18.7055 | −0.593601 | ||||||||
\(994\) | −22.5633 | −0.715664 | ||||||||
\(995\) | 3.79252 | 0.120231 | ||||||||
\(996\) | 18.6929 | 0.592307 | ||||||||
\(997\) | 11.3090 | 0.358161 | 0.179080 | − | 0.983834i | \(-0.442688\pi\) | ||||
0.179080 | + | 0.983834i | \(0.442688\pi\) | |||||||
\(998\) | 45.5310 | 1.44126 | ||||||||
\(999\) | −65.7742 | −2.08100 |
(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 | 8015.2.a.l.1.47 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.47 | ✓ | 62 | 1.1 | even | 1 | trivial |