Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.524728 | 0.302952 | 0.151476 | − | 0.988461i | \(-0.451597\pi\) | ||||
0.151476 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.579848 | 0.259316 | 0.129658 | − | 0.991559i | \(-0.458612\pi\) | ||||
0.129658 | + | 0.991559i | \(0.458612\pi\) | |||||||
\(6\) | 0.524728 | 0.214219 | ||||||||
\(7\) | 1.74824 | 0.660771 | 0.330386 | − | 0.943846i | \(-0.392821\pi\) | ||||
0.330386 | + | 0.943846i | \(0.392821\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.72466 | −0.908220 | ||||||||
\(10\) | 0.579848 | 0.183364 | ||||||||
\(11\) | −4.24317 | −1.27936 | −0.639682 | − | 0.768640i | \(-0.720934\pi\) | ||||
−0.639682 | + | 0.768640i | \(0.720934\pi\) | |||||||
\(12\) | 0.524728 | 0.151476 | ||||||||
\(13\) | −1.10363 | −0.306092 | −0.153046 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153046 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(14\) | 1.74824 | 0.467236 | ||||||||
\(15\) | 0.304262 | 0.0785602 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.907928 | 0.220205 | 0.110102 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110102 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(18\) | −2.72466 | −0.642209 | ||||||||
\(19\) | −4.36173 | −1.00065 | −0.500325 | − | 0.865838i | \(-0.666786\pi\) | ||||
−0.500325 | + | 0.865838i | \(0.666786\pi\) | |||||||
\(20\) | 0.579848 | 0.129658 | ||||||||
\(21\) | 0.917349 | 0.200182 | ||||||||
\(22\) | −4.24317 | −0.904646 | ||||||||
\(23\) | −5.04037 | −1.05099 | −0.525494 | − | 0.850797i | \(-0.676120\pi\) | ||||
−0.525494 | + | 0.850797i | \(0.676120\pi\) | |||||||
\(24\) | 0.524728 | 0.107110 | ||||||||
\(25\) | −4.66378 | −0.932755 | ||||||||
\(26\) | −1.10363 | −0.216440 | ||||||||
\(27\) | −3.00389 | −0.578099 | ||||||||
\(28\) | 1.74824 | 0.330386 | ||||||||
\(29\) | −10.2412 | −1.90174 | −0.950868 | − | 0.309597i | \(-0.899806\pi\) | ||||
−0.950868 | + | 0.309597i | \(0.899806\pi\) | |||||||
\(30\) | 0.304262 | 0.0555505 | ||||||||
\(31\) | 7.70378 | 1.38364 | 0.691820 | − | 0.722070i | \(-0.256809\pi\) | ||||
0.691820 | + | 0.722070i | \(0.256809\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.22651 | −0.387586 | ||||||||
\(34\) | 0.907928 | 0.155708 | ||||||||
\(35\) | 1.01371 | 0.171348 | ||||||||
\(36\) | −2.72466 | −0.454110 | ||||||||
\(37\) | 1.16291 | 0.191181 | 0.0955905 | − | 0.995421i | \(-0.469526\pi\) | ||||
0.0955905 | + | 0.995421i | \(0.469526\pi\) | |||||||
\(38\) | −4.36173 | −0.707566 | ||||||||
\(39\) | −0.579106 | −0.0927311 | ||||||||
\(40\) | 0.579848 | 0.0916820 | ||||||||
\(41\) | −7.50439 | −1.17199 | −0.585994 | − | 0.810315i | \(-0.699296\pi\) | ||||
−0.585994 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(42\) | 0.917349 | 0.141550 | ||||||||
\(43\) | −7.75223 | −1.18220 | −0.591102 | − | 0.806597i | \(-0.701307\pi\) | ||||
−0.591102 | + | 0.806597i | \(0.701307\pi\) | |||||||
\(44\) | −4.24317 | −0.639682 | ||||||||
\(45\) | −1.57989 | −0.235516 | ||||||||
\(46\) | −5.04037 | −0.743161 | ||||||||
\(47\) | 2.42807 | 0.354170 | 0.177085 | − | 0.984196i | \(-0.443333\pi\) | ||||
0.177085 | + | 0.984196i | \(0.443333\pi\) | |||||||
\(48\) | 0.524728 | 0.0757380 | ||||||||
\(49\) | −3.94367 | −0.563381 | ||||||||
\(50\) | −4.66378 | −0.659558 | ||||||||
\(51\) | 0.476416 | 0.0667115 | ||||||||
\(52\) | −1.10363 | −0.153046 | ||||||||
\(53\) | 10.0991 | 1.38721 | 0.693607 | − | 0.720353i | \(-0.256020\pi\) | ||||
0.693607 | + | 0.720353i | \(0.256020\pi\) | |||||||
\(54\) | −3.00389 | −0.408778 | ||||||||
\(55\) | −2.46039 | −0.331759 | ||||||||
\(56\) | 1.74824 | 0.233618 | ||||||||
\(57\) | −2.28872 | −0.303149 | ||||||||
\(58\) | −10.2412 | −1.34473 | ||||||||
\(59\) | 9.25914 | 1.20544 | 0.602718 | − | 0.797954i | \(-0.294084\pi\) | ||||
0.602718 | + | 0.797954i | \(0.294084\pi\) | |||||||
\(60\) | 0.304262 | 0.0392801 | ||||||||
\(61\) | −3.81983 | −0.489078 | −0.244539 | − | 0.969639i | \(-0.578637\pi\) | ||||
−0.244539 | + | 0.969639i | \(0.578637\pi\) | |||||||
\(62\) | 7.70378 | 0.978381 | ||||||||
\(63\) | −4.76335 | −0.600126 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.639937 | −0.0793744 | ||||||||
\(66\) | −2.22651 | −0.274064 | ||||||||
\(67\) | 5.50662 | 0.672741 | 0.336370 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336370 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(68\) | 0.907928 | 0.110102 | ||||||||
\(69\) | −2.64482 | −0.318399 | ||||||||
\(70\) | 1.01371 | 0.121162 | ||||||||
\(71\) | −4.13901 | −0.491210 | −0.245605 | − | 0.969370i | \(-0.578987\pi\) | ||||
−0.245605 | + | 0.969370i | \(0.578987\pi\) | |||||||
\(72\) | −2.72466 | −0.321104 | ||||||||
\(73\) | 2.16475 | 0.253364 | 0.126682 | − | 0.991943i | \(-0.459567\pi\) | ||||
0.126682 | + | 0.991943i | \(0.459567\pi\) | |||||||
\(74\) | 1.16291 | 0.135185 | ||||||||
\(75\) | −2.44722 | −0.282580 | ||||||||
\(76\) | −4.36173 | −0.500325 | ||||||||
\(77\) | −7.41806 | −0.845367 | ||||||||
\(78\) | −0.579106 | −0.0655708 | ||||||||
\(79\) | −3.49154 | −0.392829 | −0.196415 | − | 0.980521i | \(-0.562930\pi\) | ||||
−0.196415 | + | 0.980521i | \(0.562930\pi\) | |||||||
\(80\) | 0.579848 | 0.0648289 | ||||||||
\(81\) | 6.59775 | 0.733084 | ||||||||
\(82\) | −7.50439 | −0.828721 | ||||||||
\(83\) | −2.19884 | −0.241355 | −0.120677 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120677 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(84\) | 0.917349 | 0.100091 | ||||||||
\(85\) | 0.526460 | 0.0571026 | ||||||||
\(86\) | −7.75223 | −0.835944 | ||||||||
\(87\) | −5.37383 | −0.576135 | ||||||||
\(88\) | −4.24317 | −0.452323 | ||||||||
\(89\) | 15.2655 | 1.61814 | 0.809071 | − | 0.587711i | \(-0.199971\pi\) | ||||
0.809071 | + | 0.587711i | \(0.199971\pi\) | |||||||
\(90\) | −1.57989 | −0.166535 | ||||||||
\(91\) | −1.92941 | −0.202257 | ||||||||
\(92\) | −5.04037 | −0.525494 | ||||||||
\(93\) | 4.04239 | 0.419176 | ||||||||
\(94\) | 2.42807 | 0.250436 | ||||||||
\(95\) | −2.52914 | −0.259484 | ||||||||
\(96\) | 0.524728 | 0.0535549 | ||||||||
\(97\) | −6.83419 | −0.693906 | −0.346953 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346953 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(98\) | −3.94367 | −0.398371 | ||||||||
\(99\) | 11.5612 | 1.16194 | ||||||||
\(100\) | −4.66378 | −0.466378 | ||||||||
\(101\) | 11.5078 | 1.14507 | 0.572536 | − | 0.819880i | \(-0.305960\pi\) | ||||
0.572536 | + | 0.819880i | \(0.305960\pi\) | |||||||
\(102\) | 0.476416 | 0.0471722 | ||||||||
\(103\) | −13.5504 | −1.33516 | −0.667578 | − | 0.744540i | \(-0.732669\pi\) | ||||
−0.667578 | + | 0.744540i | \(0.732669\pi\) | |||||||
\(104\) | −1.10363 | −0.108220 | ||||||||
\(105\) | 0.531923 | 0.0519104 | ||||||||
\(106\) | 10.0991 | 0.980909 | ||||||||
\(107\) | 1.45069 | 0.140244 | 0.0701218 | − | 0.997538i | \(-0.477661\pi\) | ||||
0.0701218 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(108\) | −3.00389 | −0.289050 | ||||||||
\(109\) | −16.7867 | −1.60787 | −0.803936 | − | 0.594716i | \(-0.797265\pi\) | ||||
−0.803936 | + | 0.594716i | \(0.797265\pi\) | |||||||
\(110\) | −2.46039 | −0.234589 | ||||||||
\(111\) | 0.610211 | 0.0579187 | ||||||||
\(112\) | 1.74824 | 0.165193 | ||||||||
\(113\) | −3.36677 | −0.316719 | −0.158360 | − | 0.987382i | \(-0.550621\pi\) | ||||
−0.158360 | + | 0.987382i | \(0.550621\pi\) | |||||||
\(114\) | −2.28872 | −0.214359 | ||||||||
\(115\) | −2.92264 | −0.272538 | ||||||||
\(116\) | −10.2412 | −0.950868 | ||||||||
\(117\) | 3.00702 | 0.277999 | ||||||||
\(118\) | 9.25914 | 0.852373 | ||||||||
\(119\) | 1.58727 | 0.145505 | ||||||||
\(120\) | 0.304262 | 0.0277752 | ||||||||
\(121\) | 7.00447 | 0.636770 | ||||||||
\(122\) | −3.81983 | −0.345831 | ||||||||
\(123\) | −3.93776 | −0.355056 | ||||||||
\(124\) | 7.70378 | 0.691820 | ||||||||
\(125\) | −5.60352 | −0.501194 | ||||||||
\(126\) | −4.76335 | −0.424353 | ||||||||
\(127\) | 8.42595 | 0.747682 | 0.373841 | − | 0.927493i | \(-0.378041\pi\) | ||||
0.373841 | + | 0.927493i | \(0.378041\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.06781 | −0.358151 | ||||||||
\(130\) | −0.639937 | −0.0561262 | ||||||||
\(131\) | 10.6228 | 0.928116 | 0.464058 | − | 0.885805i | \(-0.346393\pi\) | ||||
0.464058 | + | 0.885805i | \(0.346393\pi\) | |||||||
\(132\) | −2.22651 | −0.193793 | ||||||||
\(133\) | −7.62534 | −0.661201 | ||||||||
\(134\) | 5.50662 | 0.475699 | ||||||||
\(135\) | −1.74180 | −0.149910 | ||||||||
\(136\) | 0.907928 | 0.0778542 | ||||||||
\(137\) | 11.4425 | 0.977602 | 0.488801 | − | 0.872395i | \(-0.337434\pi\) | ||||
0.488801 | + | 0.872395i | \(0.337434\pi\) | |||||||
\(138\) | −2.64482 | −0.225142 | ||||||||
\(139\) | 3.11849 | 0.264507 | 0.132254 | − | 0.991216i | \(-0.457779\pi\) | ||||
0.132254 | + | 0.991216i | \(0.457779\pi\) | |||||||
\(140\) | 1.01371 | 0.0856742 | ||||||||
\(141\) | 1.27408 | 0.107297 | ||||||||
\(142\) | −4.13901 | −0.347338 | ||||||||
\(143\) | 4.68288 | 0.391602 | ||||||||
\(144\) | −2.72466 | −0.227055 | ||||||||
\(145\) | −5.93831 | −0.493150 | ||||||||
\(146\) | 2.16475 | 0.179156 | ||||||||
\(147\) | −2.06935 | −0.170677 | ||||||||
\(148\) | 1.16291 | 0.0955905 | ||||||||
\(149\) | −7.52927 | −0.616822 | −0.308411 | − | 0.951253i | \(-0.599797\pi\) | ||||
−0.308411 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(150\) | −2.44722 | −0.199814 | ||||||||
\(151\) | 2.25758 | 0.183719 | 0.0918596 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918596 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(152\) | −4.36173 | −0.353783 | ||||||||
\(153\) | −2.47380 | −0.199995 | ||||||||
\(154\) | −7.41806 | −0.597764 | ||||||||
\(155\) | 4.46702 | 0.358800 | ||||||||
\(156\) | −0.579106 | −0.0463656 | ||||||||
\(157\) | 14.6282 | 1.16746 | 0.583729 | − | 0.811949i | \(-0.301593\pi\) | ||||
0.583729 | + | 0.811949i | \(0.301593\pi\) | |||||||
\(158\) | −3.49154 | −0.277772 | ||||||||
\(159\) | 5.29927 | 0.420259 | ||||||||
\(160\) | 0.579848 | 0.0458410 | ||||||||
\(161\) | −8.81175 | −0.694463 | ||||||||
\(162\) | 6.59775 | 0.518369 | ||||||||
\(163\) | −19.0197 | −1.48974 | −0.744868 | − | 0.667212i | \(-0.767488\pi\) | ||||
−0.744868 | + | 0.667212i | \(0.767488\pi\) | |||||||
\(164\) | −7.50439 | −0.585994 | ||||||||
\(165\) | −1.29104 | −0.100507 | ||||||||
\(166\) | −2.19884 | −0.170663 | ||||||||
\(167\) | −1.30550 | −0.101023 | −0.0505113 | − | 0.998723i | \(-0.516085\pi\) | ||||
−0.0505113 | + | 0.998723i | \(0.516085\pi\) | |||||||
\(168\) | 0.917349 | 0.0707750 | ||||||||
\(169\) | −11.7820 | −0.906308 | ||||||||
\(170\) | 0.526460 | 0.0403776 | ||||||||
\(171\) | 11.8842 | 0.908811 | ||||||||
\(172\) | −7.75223 | −0.591102 | ||||||||
\(173\) | 17.7649 | 1.35064 | 0.675320 | − | 0.737525i | \(-0.264005\pi\) | ||||
0.675320 | + | 0.737525i | \(0.264005\pi\) | |||||||
\(174\) | −5.37383 | −0.407389 | ||||||||
\(175\) | −8.15339 | −0.616338 | ||||||||
\(176\) | −4.24317 | −0.319841 | ||||||||
\(177\) | 4.85853 | 0.365190 | ||||||||
\(178\) | 15.2655 | 1.14420 | ||||||||
\(179\) | 10.1556 | 0.759062 | 0.379531 | − | 0.925179i | \(-0.376085\pi\) | ||||
0.379531 | + | 0.925179i | \(0.376085\pi\) | |||||||
\(180\) | −1.57989 | −0.117758 | ||||||||
\(181\) | −8.62692 | −0.641234 | −0.320617 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320617 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(182\) | −1.92941 | −0.143017 | ||||||||
\(183\) | −2.00437 | −0.148167 | ||||||||
\(184\) | −5.04037 | −0.371581 | ||||||||
\(185\) | 0.674310 | 0.0495763 | ||||||||
\(186\) | 4.04239 | 0.296402 | ||||||||
\(187\) | −3.85249 | −0.281722 | ||||||||
\(188\) | 2.42807 | 0.177085 | ||||||||
\(189\) | −5.25151 | −0.381991 | ||||||||
\(190\) | −2.52914 | −0.183483 | ||||||||
\(191\) | −19.8025 | −1.43286 | −0.716429 | − | 0.697660i | \(-0.754224\pi\) | ||||
−0.716429 | + | 0.697660i | \(0.754224\pi\) | |||||||
\(192\) | 0.524728 | 0.0378690 | ||||||||
\(193\) | 26.9778 | 1.94191 | 0.970953 | − | 0.239270i | \(-0.0769082\pi\) | ||||
0.970953 | + | 0.239270i | \(0.0769082\pi\) | |||||||
\(194\) | −6.83419 | −0.490666 | ||||||||
\(195\) | −0.335793 | −0.0240466 | ||||||||
\(196\) | −3.94367 | −0.281691 | ||||||||
\(197\) | −0.737518 | −0.0525460 | −0.0262730 | − | 0.999655i | \(-0.508364\pi\) | ||||
−0.0262730 | + | 0.999655i | \(0.508364\pi\) | |||||||
\(198\) | 11.5612 | 0.821618 | ||||||||
\(199\) | −12.4212 | −0.880518 | −0.440259 | − | 0.897871i | \(-0.645113\pi\) | ||||
−0.440259 | + | 0.897871i | \(0.645113\pi\) | |||||||
\(200\) | −4.66378 | −0.329779 | ||||||||
\(201\) | 2.88948 | 0.203808 | ||||||||
\(202\) | 11.5078 | 0.809688 | ||||||||
\(203\) | −17.9040 | −1.25661 | ||||||||
\(204\) | 0.476416 | 0.0333558 | ||||||||
\(205\) | −4.35140 | −0.303915 | ||||||||
\(206\) | −13.5504 | −0.944098 | ||||||||
\(207\) | 13.7333 | 0.954529 | ||||||||
\(208\) | −1.10363 | −0.0765229 | ||||||||
\(209\) | 18.5076 | 1.28019 | ||||||||
\(210\) | 0.531923 | 0.0367062 | ||||||||
\(211\) | −23.5187 | −1.61909 | −0.809546 | − | 0.587056i | \(-0.800287\pi\) | ||||
−0.809546 | + | 0.587056i | \(0.800287\pi\) | |||||||
\(212\) | 10.0991 | 0.693607 | ||||||||
\(213\) | −2.17186 | −0.148813 | ||||||||
\(214\) | 1.45069 | 0.0991672 | ||||||||
\(215\) | −4.49511 | −0.306564 | ||||||||
\(216\) | −3.00389 | −0.204389 | ||||||||
\(217\) | 13.4680 | 0.914269 | ||||||||
\(218\) | −16.7867 | −1.13694 | ||||||||
\(219\) | 1.13590 | 0.0767573 | ||||||||
\(220\) | −2.46039 | −0.165879 | ||||||||
\(221\) | −1.00202 | −0.0674029 | ||||||||
\(222\) | 0.610211 | 0.0409547 | ||||||||
\(223\) | −7.88310 | −0.527892 | −0.263946 | − | 0.964538i | \(-0.585024\pi\) | ||||
−0.263946 | + | 0.964538i | \(0.585024\pi\) | |||||||
\(224\) | 1.74824 | 0.116809 | ||||||||
\(225\) | 12.7072 | 0.847147 | ||||||||
\(226\) | −3.36677 | −0.223954 | ||||||||
\(227\) | 23.0428 | 1.52941 | 0.764704 | − | 0.644382i | \(-0.222885\pi\) | ||||
0.764704 | + | 0.644382i | \(0.222885\pi\) | |||||||
\(228\) | −2.28872 | −0.151574 | ||||||||
\(229\) | 15.7163 | 1.03856 | 0.519280 | − | 0.854604i | \(-0.326200\pi\) | ||||
0.519280 | + | 0.854604i | \(0.326200\pi\) | |||||||
\(230\) | −2.92264 | −0.192713 | ||||||||
\(231\) | −3.89247 | −0.256106 | ||||||||
\(232\) | −10.2412 | −0.672365 | ||||||||
\(233\) | −15.8094 | −1.03571 | −0.517853 | − | 0.855469i | \(-0.673269\pi\) | ||||
−0.517853 | + | 0.855469i | \(0.673269\pi\) | |||||||
\(234\) | 3.00702 | 0.196575 | ||||||||
\(235\) | 1.40791 | 0.0918420 | ||||||||
\(236\) | 9.25914 | 0.602718 | ||||||||
\(237\) | −1.83211 | −0.119008 | ||||||||
\(238\) | 1.58727 | 0.102888 | ||||||||
\(239\) | −19.2990 | −1.24835 | −0.624173 | − | 0.781286i | \(-0.714564\pi\) | ||||
−0.624173 | + | 0.781286i | \(0.714564\pi\) | |||||||
\(240\) | 0.304262 | 0.0196401 | ||||||||
\(241\) | 11.0444 | 0.711431 | 0.355715 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355715 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(242\) | 7.00447 | 0.450264 | ||||||||
\(243\) | 12.4737 | 0.800188 | ||||||||
\(244\) | −3.81983 | −0.244539 | ||||||||
\(245\) | −2.28673 | −0.146094 | ||||||||
\(246\) | −3.93776 | −0.251063 | ||||||||
\(247\) | 4.81374 | 0.306291 | ||||||||
\(248\) | 7.70378 | 0.489190 | ||||||||
\(249\) | −1.15380 | −0.0731188 | ||||||||
\(250\) | −5.60352 | −0.354398 | ||||||||
\(251\) | 0.443319 | 0.0279820 | 0.0139910 | − | 0.999902i | \(-0.495546\pi\) | ||||
0.0139910 | + | 0.999902i | \(0.495546\pi\) | |||||||
\(252\) | −4.76335 | −0.300063 | ||||||||
\(253\) | 21.3871 | 1.34460 | ||||||||
\(254\) | 8.42595 | 0.528691 | ||||||||
\(255\) | 0.276248 | 0.0172993 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.2469 | 1.69961 | 0.849807 | − | 0.527094i | \(-0.176718\pi\) | ||||
0.849807 | + | 0.527094i | \(0.176718\pi\) | |||||||
\(258\) | −4.06781 | −0.253251 | ||||||||
\(259\) | 2.03304 | 0.126327 | ||||||||
\(260\) | −0.639937 | −0.0396872 | ||||||||
\(261\) | 27.9037 | 1.72719 | ||||||||
\(262\) | 10.6228 | 0.656277 | ||||||||
\(263\) | 10.8589 | 0.669591 | 0.334795 | − | 0.942291i | \(-0.391333\pi\) | ||||
0.334795 | + | 0.942291i | \(0.391333\pi\) | |||||||
\(264\) | −2.22651 | −0.137032 | ||||||||
\(265\) | 5.85592 | 0.359727 | ||||||||
\(266\) | −7.62534 | −0.467540 | ||||||||
\(267\) | 8.01025 | 0.490220 | ||||||||
\(268\) | 5.50662 | 0.336370 | ||||||||
\(269\) | −12.9728 | −0.790966 | −0.395483 | − | 0.918473i | \(-0.629423\pi\) | ||||
−0.395483 | + | 0.918473i | \(0.629423\pi\) | |||||||
\(270\) | −1.74180 | −0.106003 | ||||||||
\(271\) | 13.0312 | 0.791590 | 0.395795 | − | 0.918339i | \(-0.370469\pi\) | ||||
0.395795 | + | 0.918339i | \(0.370469\pi\) | |||||||
\(272\) | 0.907928 | 0.0550512 | ||||||||
\(273\) | −1.01241 | −0.0612741 | ||||||||
\(274\) | 11.4425 | 0.691269 | ||||||||
\(275\) | 19.7892 | 1.19333 | ||||||||
\(276\) | −2.64482 | −0.159200 | ||||||||
\(277\) | −9.85960 | −0.592406 | −0.296203 | − | 0.955125i | \(-0.595720\pi\) | ||||
−0.296203 | + | 0.955125i | \(0.595720\pi\) | |||||||
\(278\) | 3.11849 | 0.187035 | ||||||||
\(279\) | −20.9902 | −1.25665 | ||||||||
\(280\) | 1.01371 | 0.0605808 | ||||||||
\(281\) | −27.0146 | −1.61156 | −0.805779 | − | 0.592217i | \(-0.798253\pi\) | ||||
−0.805779 | + | 0.592217i | \(0.798253\pi\) | |||||||
\(282\) | 1.27408 | 0.0758702 | ||||||||
\(283\) | 5.04576 | 0.299939 | 0.149970 | − | 0.988691i | \(-0.452082\pi\) | ||||
0.149970 | + | 0.988691i | \(0.452082\pi\) | |||||||
\(284\) | −4.13901 | −0.245605 | ||||||||
\(285\) | −1.32711 | −0.0786113 | ||||||||
\(286\) | 4.68288 | 0.276905 | ||||||||
\(287\) | −13.1194 | −0.774416 | ||||||||
\(288\) | −2.72466 | −0.160552 | ||||||||
\(289\) | −16.1757 | −0.951510 | ||||||||
\(290\) | −5.93831 | −0.348710 | ||||||||
\(291\) | −3.58609 | −0.210220 | ||||||||
\(292\) | 2.16475 | 0.126682 | ||||||||
\(293\) | 13.5863 | 0.793721 | 0.396860 | − | 0.917879i | \(-0.370100\pi\) | ||||
0.396860 | + | 0.917879i | \(0.370100\pi\) | |||||||
\(294\) | −2.06935 | −0.120687 | ||||||||
\(295\) | 5.36889 | 0.312589 | ||||||||
\(296\) | 1.16291 | 0.0675927 | ||||||||
\(297\) | 12.7460 | 0.739599 | ||||||||
\(298\) | −7.52927 | −0.436159 | ||||||||
\(299\) | 5.56270 | 0.321699 | ||||||||
\(300\) | −2.44722 | −0.141290 | ||||||||
\(301\) | −13.5527 | −0.781167 | ||||||||
\(302\) | 2.25758 | 0.129909 | ||||||||
\(303\) | 6.03848 | 0.346902 | ||||||||
\(304\) | −4.36173 | −0.250163 | ||||||||
\(305\) | −2.21492 | −0.126826 | ||||||||
\(306\) | −2.47380 | −0.141417 | ||||||||
\(307\) | 29.5812 | 1.68829 | 0.844144 | − | 0.536116i | \(-0.180109\pi\) | ||||
0.844144 | + | 0.536116i | \(0.180109\pi\) | |||||||
\(308\) | −7.41806 | −0.422683 | ||||||||
\(309\) | −7.11025 | −0.404488 | ||||||||
\(310\) | 4.46702 | 0.253710 | ||||||||
\(311\) | −14.3306 | −0.812613 | −0.406306 | − | 0.913737i | \(-0.633183\pi\) | ||||
−0.406306 | + | 0.913737i | \(0.633183\pi\) | |||||||
\(312\) | −0.579106 | −0.0327854 | ||||||||
\(313\) | −24.3489 | −1.37628 | −0.688140 | − | 0.725578i | \(-0.741572\pi\) | ||||
−0.688140 | + | 0.725578i | \(0.741572\pi\) | |||||||
\(314\) | 14.6282 | 0.825517 | ||||||||
\(315\) | −2.76202 | −0.155622 | ||||||||
\(316\) | −3.49154 | −0.196415 | ||||||||
\(317\) | −31.4001 | −1.76360 | −0.881802 | − | 0.471620i | \(-0.843669\pi\) | ||||
−0.881802 | + | 0.471620i | \(0.843669\pi\) | |||||||
\(318\) | 5.29927 | 0.297168 | ||||||||
\(319\) | 43.4550 | 2.43301 | ||||||||
\(320\) | 0.579848 | 0.0324145 | ||||||||
\(321\) | 0.761219 | 0.0424871 | ||||||||
\(322\) | −8.81175 | −0.491060 | ||||||||
\(323\) | −3.96014 | −0.220348 | ||||||||
\(324\) | 6.59775 | 0.366542 | ||||||||
\(325\) | 5.14708 | 0.285509 | ||||||||
\(326\) | −19.0197 | −1.05340 | ||||||||
\(327\) | −8.80845 | −0.487108 | ||||||||
\(328\) | −7.50439 | −0.414360 | ||||||||
\(329\) | 4.24484 | 0.234026 | ||||||||
\(330\) | −1.29104 | −0.0710692 | ||||||||
\(331\) | −18.1365 | −0.996874 | −0.498437 | − | 0.866926i | \(-0.666093\pi\) | ||||
−0.498437 | + | 0.866926i | \(0.666093\pi\) | |||||||
\(332\) | −2.19884 | −0.120677 | ||||||||
\(333\) | −3.16853 | −0.173634 | ||||||||
\(334\) | −1.30550 | −0.0714337 | ||||||||
\(335\) | 3.19300 | 0.174452 | ||||||||
\(336\) | 0.917349 | 0.0500455 | ||||||||
\(337\) | −19.2491 | −1.04856 | −0.524282 | − | 0.851545i | \(-0.675666\pi\) | ||||
−0.524282 | + | 0.851545i | \(0.675666\pi\) | |||||||
\(338\) | −11.7820 | −0.640856 | ||||||||
\(339\) | −1.76664 | −0.0959507 | ||||||||
\(340\) | 0.526460 | 0.0285513 | ||||||||
\(341\) | −32.6884 | −1.77018 | ||||||||
\(342\) | 11.8842 | 0.642626 | ||||||||
\(343\) | −19.1321 | −1.03304 | ||||||||
\(344\) | −7.75223 | −0.417972 | ||||||||
\(345\) | −1.53359 | −0.0825659 | ||||||||
\(346\) | 17.7649 | 0.955047 | ||||||||
\(347\) | 28.1876 | 1.51319 | 0.756595 | − | 0.653884i | \(-0.226862\pi\) | ||||
0.756595 | + | 0.653884i | \(0.226862\pi\) | |||||||
\(348\) | −5.37383 | −0.288067 | ||||||||
\(349\) | −16.6189 | −0.889588 | −0.444794 | − | 0.895633i | \(-0.646723\pi\) | ||||
−0.444794 | + | 0.895633i | \(0.646723\pi\) | |||||||
\(350\) | −8.15339 | −0.435817 | ||||||||
\(351\) | 3.31518 | 0.176951 | ||||||||
\(352\) | −4.24317 | −0.226162 | ||||||||
\(353\) | −21.8164 | −1.16117 | −0.580585 | − | 0.814199i | \(-0.697176\pi\) | ||||
−0.580585 | + | 0.814199i | \(0.697176\pi\) | |||||||
\(354\) | 4.85853 | 0.258228 | ||||||||
\(355\) | −2.40000 | −0.127379 | ||||||||
\(356\) | 15.2655 | 0.809071 | ||||||||
\(357\) | 0.832887 | 0.0440811 | ||||||||
\(358\) | 10.1556 | 0.536738 | ||||||||
\(359\) | −11.8039 | −0.622985 | −0.311493 | − | 0.950249i | \(-0.600829\pi\) | ||||
−0.311493 | + | 0.950249i | \(0.600829\pi\) | |||||||
\(360\) | −1.57989 | −0.0832674 | ||||||||
\(361\) | 0.0247128 | 0.00130068 | ||||||||
\(362\) | −8.62692 | −0.453421 | ||||||||
\(363\) | 3.67544 | 0.192911 | ||||||||
\(364\) | −1.92941 | −0.101128 | ||||||||
\(365\) | 1.25522 | 0.0657014 | ||||||||
\(366\) | −2.00437 | −0.104770 | ||||||||
\(367\) | −37.7917 | −1.97271 | −0.986354 | − | 0.164638i | \(-0.947354\pi\) | ||||
−0.986354 | + | 0.164638i | \(0.947354\pi\) | |||||||
\(368\) | −5.04037 | −0.262747 | ||||||||
\(369\) | 20.4469 | 1.06442 | ||||||||
\(370\) | 0.674310 | 0.0350557 | ||||||||
\(371\) | 17.6556 | 0.916632 | ||||||||
\(372\) | 4.04239 | 0.209588 | ||||||||
\(373\) | 9.93160 | 0.514239 | 0.257119 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257119 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(374\) | −3.85249 | −0.199208 | ||||||||
\(375\) | −2.94032 | −0.151838 | ||||||||
\(376\) | 2.42807 | 0.125218 | ||||||||
\(377\) | 11.3024 | 0.582106 | ||||||||
\(378\) | −5.25151 | −0.270109 | ||||||||
\(379\) | −2.08125 | −0.106907 | −0.0534534 | − | 0.998570i | \(-0.517023\pi\) | ||||
−0.0534534 | + | 0.998570i | \(0.517023\pi\) | |||||||
\(380\) | −2.52914 | −0.129742 | ||||||||
\(381\) | 4.42133 | 0.226512 | ||||||||
\(382\) | −19.8025 | −1.01318 | ||||||||
\(383\) | −3.37711 | −0.172562 | −0.0862810 | − | 0.996271i | \(-0.527498\pi\) | ||||
−0.0862810 | + | 0.996271i | \(0.527498\pi\) | |||||||
\(384\) | 0.524728 | 0.0267774 | ||||||||
\(385\) | −4.30135 | −0.219217 | ||||||||
\(386\) | 26.9778 | 1.37313 | ||||||||
\(387\) | 21.1222 | 1.07370 | ||||||||
\(388\) | −6.83419 | −0.346953 | ||||||||
\(389\) | 0.435883 | 0.0221002 | 0.0110501 | − | 0.999939i | \(-0.496483\pi\) | ||||
0.0110501 | + | 0.999939i | \(0.496483\pi\) | |||||||
\(390\) | −0.335793 | −0.0170035 | ||||||||
\(391\) | −4.57629 | −0.231433 | ||||||||
\(392\) | −3.94367 | −0.199185 | ||||||||
\(393\) | 5.57407 | 0.281175 | ||||||||
\(394\) | −0.737518 | −0.0371556 | ||||||||
\(395\) | −2.02456 | −0.101867 | ||||||||
\(396\) | 11.5612 | 0.580972 | ||||||||
\(397\) | −7.38433 | −0.370609 | −0.185305 | − | 0.982681i | \(-0.559327\pi\) | ||||
−0.185305 | + | 0.982681i | \(0.559327\pi\) | |||||||
\(398\) | −12.4212 | −0.622620 | ||||||||
\(399\) | −4.00123 | −0.200312 | ||||||||
\(400\) | −4.66378 | −0.233189 | ||||||||
\(401\) | −30.0393 | −1.50009 | −0.750045 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750045 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(402\) | 2.88948 | 0.144114 | ||||||||
\(403\) | −8.50212 | −0.423521 | ||||||||
\(404\) | 11.5078 | 0.572536 | ||||||||
\(405\) | 3.82569 | 0.190100 | ||||||||
\(406\) | −17.9040 | −0.888559 | ||||||||
\(407\) | −4.93442 | −0.244590 | ||||||||
\(408\) | 0.476416 | 0.0235861 | ||||||||
\(409\) | −25.0098 | −1.23666 | −0.618329 | − | 0.785920i | \(-0.712190\pi\) | ||||
−0.618329 | + | 0.785920i | \(0.712190\pi\) | |||||||
\(410\) | −4.35140 | −0.214900 | ||||||||
\(411\) | 6.00423 | 0.296167 | ||||||||
\(412\) | −13.5504 | −0.667578 | ||||||||
\(413\) | 16.1872 | 0.796518 | ||||||||
\(414\) | 13.7333 | 0.674954 | ||||||||
\(415\) | −1.27499 | −0.0625870 | ||||||||
\(416\) | −1.10363 | −0.0541099 | ||||||||
\(417\) | 1.63636 | 0.0801330 | ||||||||
\(418\) | 18.5076 | 0.905234 | ||||||||
\(419\) | 35.4484 | 1.73177 | 0.865885 | − | 0.500244i | \(-0.166756\pi\) | ||||
0.865885 | + | 0.500244i | \(0.166756\pi\) | |||||||
\(420\) | 0.531923 | 0.0259552 | ||||||||
\(421\) | 4.49450 | 0.219049 | 0.109524 | − | 0.993984i | \(-0.465067\pi\) | ||||
0.109524 | + | 0.993984i | \(0.465067\pi\) | |||||||
\(422\) | −23.5187 | −1.14487 | ||||||||
\(423\) | −6.61567 | −0.321665 | ||||||||
\(424\) | 10.0991 | 0.490454 | ||||||||
\(425\) | −4.23437 | −0.205397 | ||||||||
\(426\) | −2.17186 | −0.105227 | ||||||||
\(427\) | −6.67796 | −0.323169 | ||||||||
\(428\) | 1.45069 | 0.0701218 | ||||||||
\(429\) | 2.45724 | 0.118637 | ||||||||
\(430\) | −4.49511 | −0.216774 | ||||||||
\(431\) | −16.5094 | −0.795231 | −0.397615 | − | 0.917552i | \(-0.630162\pi\) | ||||
−0.397615 | + | 0.917552i | \(0.630162\pi\) | |||||||
\(432\) | −3.00389 | −0.144525 | ||||||||
\(433\) | 3.74448 | 0.179948 | 0.0899741 | − | 0.995944i | \(-0.471322\pi\) | ||||
0.0899741 | + | 0.995944i | \(0.471322\pi\) | |||||||
\(434\) | 13.4680 | 0.646486 | ||||||||
\(435\) | −3.11600 | −0.149401 | ||||||||
\(436\) | −16.7867 | −0.803936 | ||||||||
\(437\) | 21.9847 | 1.05167 | ||||||||
\(438\) | 1.13590 | 0.0542756 | ||||||||
\(439\) | −23.9564 | −1.14338 | −0.571688 | − | 0.820471i | \(-0.693711\pi\) | ||||
−0.571688 | + | 0.820471i | \(0.693711\pi\) | |||||||
\(440\) | −2.46039 | −0.117295 | ||||||||
\(441\) | 10.7452 | 0.511674 | ||||||||
\(442\) | −1.00202 | −0.0476610 | ||||||||
\(443\) | −38.5346 | −1.83083 | −0.915416 | − | 0.402509i | \(-0.868138\pi\) | ||||
−0.915416 | + | 0.402509i | \(0.868138\pi\) | |||||||
\(444\) | 0.610211 | 0.0289593 | ||||||||
\(445\) | 8.85168 | 0.419610 | ||||||||
\(446\) | −7.88310 | −0.373276 | ||||||||
\(447\) | −3.95082 | −0.186867 | ||||||||
\(448\) | 1.74824 | 0.0825964 | ||||||||
\(449\) | −5.34299 | −0.252151 | −0.126076 | − | 0.992021i | \(-0.540238\pi\) | ||||
−0.126076 | + | 0.992021i | \(0.540238\pi\) | |||||||
\(450\) | 12.7072 | 0.599023 | ||||||||
\(451\) | 31.8424 | 1.49940 | ||||||||
\(452\) | −3.36677 | −0.158360 | ||||||||
\(453\) | 1.18462 | 0.0556581 | ||||||||
\(454\) | 23.0428 | 1.08145 | ||||||||
\(455\) | −1.11876 | −0.0524483 | ||||||||
\(456\) | −2.28872 | −0.107179 | ||||||||
\(457\) | 9.37871 | 0.438717 | 0.219359 | − | 0.975644i | \(-0.429603\pi\) | ||||
0.219359 | + | 0.975644i | \(0.429603\pi\) | |||||||
\(458\) | 15.7163 | 0.734372 | ||||||||
\(459\) | −2.72732 | −0.127300 | ||||||||
\(460\) | −2.92264 | −0.136269 | ||||||||
\(461\) | 26.6068 | 1.23920 | 0.619601 | − | 0.784917i | \(-0.287295\pi\) | ||||
0.619601 | + | 0.784917i | \(0.287295\pi\) | |||||||
\(462\) | −3.89247 | −0.181094 | ||||||||
\(463\) | 25.3046 | 1.17600 | 0.588002 | − | 0.808859i | \(-0.299915\pi\) | ||||
0.588002 | + | 0.808859i | \(0.299915\pi\) | |||||||
\(464\) | −10.2412 | −0.475434 | ||||||||
\(465\) | 2.34397 | 0.108699 | ||||||||
\(466\) | −15.8094 | −0.732355 | ||||||||
\(467\) | 38.7351 | 1.79245 | 0.896224 | − | 0.443602i | \(-0.146299\pi\) | ||||
0.896224 | + | 0.443602i | \(0.146299\pi\) | |||||||
\(468\) | 3.00702 | 0.138999 | ||||||||
\(469\) | 9.62687 | 0.444528 | ||||||||
\(470\) | 1.40791 | 0.0649421 | ||||||||
\(471\) | 7.67583 | 0.353684 | ||||||||
\(472\) | 9.25914 | 0.426186 | ||||||||
\(473\) | 32.8940 | 1.51247 | ||||||||
\(474\) | −1.83211 | −0.0841517 | ||||||||
\(475\) | 20.3421 | 0.933362 | ||||||||
\(476\) | 1.58727 | 0.0727526 | ||||||||
\(477\) | −27.5165 | −1.25990 | ||||||||
\(478\) | −19.2990 | −0.882714 | ||||||||
\(479\) | 7.26758 | 0.332064 | 0.166032 | − | 0.986120i | \(-0.446904\pi\) | ||||
0.166032 | + | 0.986120i | \(0.446904\pi\) | |||||||
\(480\) | 0.304262 | 0.0138876 | ||||||||
\(481\) | −1.28342 | −0.0585189 | ||||||||
\(482\) | 11.0444 | 0.503058 | ||||||||
\(483\) | −4.62378 | −0.210389 | ||||||||
\(484\) | 7.00447 | 0.318385 | ||||||||
\(485\) | −3.96279 | −0.179941 | ||||||||
\(486\) | 12.4737 | 0.565819 | ||||||||
\(487\) | 4.61766 | 0.209246 | 0.104623 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104623 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(488\) | −3.81983 | −0.172915 | ||||||||
\(489\) | −9.98016 | −0.451319 | ||||||||
\(490\) | −2.28673 | −0.103304 | ||||||||
\(491\) | 6.30455 | 0.284520 | 0.142260 | − | 0.989829i | \(-0.454563\pi\) | ||||
0.142260 | + | 0.989829i | \(0.454563\pi\) | |||||||
\(492\) | −3.93776 | −0.177528 | ||||||||
\(493\) | −9.29824 | −0.418772 | ||||||||
\(494\) | 4.81374 | 0.216580 | ||||||||
\(495\) | 6.70373 | 0.301310 | ||||||||
\(496\) | 7.70378 | 0.345910 | ||||||||
\(497\) | −7.23597 | −0.324578 | ||||||||
\(498\) | −1.15380 | −0.0517028 | ||||||||
\(499\) | −24.2705 | −1.08650 | −0.543249 | − | 0.839571i | \(-0.682806\pi\) | ||||
−0.543249 | + | 0.839571i | \(0.682806\pi\) | |||||||
\(500\) | −5.60352 | −0.250597 | ||||||||
\(501\) | −0.685032 | −0.0306050 | ||||||||
\(502\) | 0.443319 | 0.0197863 | ||||||||
\(503\) | 2.43140 | 0.108411 | 0.0542054 | − | 0.998530i | \(-0.482737\pi\) | ||||
0.0542054 | + | 0.998530i | \(0.482737\pi\) | |||||||
\(504\) | −4.76335 | −0.212177 | ||||||||
\(505\) | 6.67279 | 0.296935 | ||||||||
\(506\) | 21.3871 | 0.950773 | ||||||||
\(507\) | −6.18235 | −0.274568 | ||||||||
\(508\) | 8.42595 | 0.373841 | ||||||||
\(509\) | −12.8200 | −0.568237 | −0.284119 | − | 0.958789i | \(-0.591701\pi\) | ||||
−0.284119 | + | 0.958789i | \(0.591701\pi\) | |||||||
\(510\) | 0.276248 | 0.0122325 | ||||||||
\(511\) | 3.78449 | 0.167416 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 13.1022 | 0.578475 | ||||||||
\(514\) | 27.2469 | 1.20181 | ||||||||
\(515\) | −7.85714 | −0.346227 | ||||||||
\(516\) | −4.06781 | −0.179076 | ||||||||
\(517\) | −10.3027 | −0.453113 | ||||||||
\(518\) | 2.03304 | 0.0893267 | ||||||||
\(519\) | 9.32174 | 0.409179 | ||||||||
\(520\) | −0.639937 | −0.0280631 | ||||||||
\(521\) | 9.40642 | 0.412103 | 0.206051 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206051 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(522\) | 27.9037 | 1.22131 | ||||||||
\(523\) | −7.01366 | −0.306686 | −0.153343 | − | 0.988173i | \(-0.549004\pi\) | ||||
−0.153343 | + | 0.988173i | \(0.549004\pi\) | |||||||
\(524\) | 10.6228 | 0.464058 | ||||||||
\(525\) | −4.27831 | −0.186721 | ||||||||
\(526\) | 10.8589 | 0.473472 | ||||||||
\(527\) | 6.99448 | 0.304684 | ||||||||
\(528\) | −2.22651 | −0.0968964 | ||||||||
\(529\) | 2.40528 | 0.104578 | ||||||||
\(530\) | 5.85592 | 0.254365 | ||||||||
\(531\) | −25.2280 | −1.09480 | ||||||||
\(532\) | −7.62534 | −0.330601 | ||||||||
\(533\) | 8.28206 | 0.358736 | ||||||||
\(534\) | 8.01025 | 0.346638 | ||||||||
\(535\) | 0.841180 | 0.0363674 | ||||||||
\(536\) | 5.50662 | 0.237850 | ||||||||
\(537\) | 5.32891 | 0.229959 | ||||||||
\(538\) | −12.9728 | −0.559298 | ||||||||
\(539\) | 16.7336 | 0.720769 | ||||||||
\(540\) | −1.74180 | −0.0749551 | ||||||||
\(541\) | 14.2576 | 0.612984 | 0.306492 | − | 0.951873i | \(-0.400845\pi\) | ||||
0.306492 | + | 0.951873i | \(0.400845\pi\) | |||||||
\(542\) | 13.0312 | 0.559738 | ||||||||
\(543\) | −4.52679 | −0.194263 | ||||||||
\(544\) | 0.907928 | 0.0389271 | ||||||||
\(545\) | −9.73372 | −0.416947 | ||||||||
\(546\) | −1.01241 | −0.0433273 | ||||||||
\(547\) | −27.1789 | −1.16209 | −0.581043 | − | 0.813873i | \(-0.697355\pi\) | ||||
−0.581043 | + | 0.813873i | \(0.697355\pi\) | |||||||
\(548\) | 11.4425 | 0.488801 | ||||||||
\(549\) | 10.4077 | 0.444191 | ||||||||
\(550\) | 19.7892 | 0.843814 | ||||||||
\(551\) | 44.6692 | 1.90297 | ||||||||
\(552\) | −2.64482 | −0.112571 | ||||||||
\(553\) | −6.10404 | −0.259570 | ||||||||
\(554\) | −9.85960 | −0.418894 | ||||||||
\(555\) | 0.353830 | 0.0150192 | ||||||||
\(556\) | 3.11849 | 0.132254 | ||||||||
\(557\) | 11.9344 | 0.505675 | 0.252838 | − | 0.967509i | \(-0.418636\pi\) | ||||
0.252838 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(558\) | −20.9902 | −0.888585 | ||||||||
\(559\) | 8.55559 | 0.361863 | ||||||||
\(560\) | 1.01371 | 0.0428371 | ||||||||
\(561\) | −2.02151 | −0.0853482 | ||||||||
\(562\) | −27.0146 | −1.13954 | ||||||||
\(563\) | 14.4444 | 0.608761 | 0.304380 | − | 0.952551i | \(-0.401551\pi\) | ||||
0.304380 | + | 0.952551i | \(0.401551\pi\) | |||||||
\(564\) | 1.27408 | 0.0536483 | ||||||||
\(565\) | −1.95221 | −0.0821303 | ||||||||
\(566\) | 5.04576 | 0.212089 | ||||||||
\(567\) | 11.5344 | 0.484401 | ||||||||
\(568\) | −4.13901 | −0.173669 | ||||||||
\(569\) | 25.9706 | 1.08874 | 0.544372 | − | 0.838844i | \(-0.316768\pi\) | ||||
0.544372 | + | 0.838844i | \(0.316768\pi\) | |||||||
\(570\) | −1.32711 | −0.0555866 | ||||||||
\(571\) | −17.3276 | −0.725138 | −0.362569 | − | 0.931957i | \(-0.618100\pi\) | ||||
−0.362569 | + | 0.931957i | \(0.618100\pi\) | |||||||
\(572\) | 4.68288 | 0.195801 | ||||||||
\(573\) | −10.3909 | −0.434087 | ||||||||
\(574\) | −13.1194 | −0.547595 | ||||||||
\(575\) | 23.5071 | 0.980315 | ||||||||
\(576\) | −2.72466 | −0.113528 | ||||||||
\(577\) | 33.3026 | 1.38641 | 0.693203 | − | 0.720742i | \(-0.256199\pi\) | ||||
0.693203 | + | 0.720742i | \(0.256199\pi\) | |||||||
\(578\) | −16.1757 | −0.672819 | ||||||||
\(579\) | 14.1560 | 0.588304 | ||||||||
\(580\) | −5.93831 | −0.246575 | ||||||||
\(581\) | −3.84410 | −0.159480 | ||||||||
\(582\) | −3.58609 | −0.148648 | ||||||||
\(583\) | −42.8521 | −1.77475 | ||||||||
\(584\) | 2.16475 | 0.0895779 | ||||||||
\(585\) | 1.74361 | 0.0720894 | ||||||||
\(586\) | 13.5863 | 0.561245 | ||||||||
\(587\) | −12.7872 | −0.527782 | −0.263891 | − | 0.964552i | \(-0.585006\pi\) | ||||
−0.263891 | + | 0.964552i | \(0.585006\pi\) | |||||||
\(588\) | −2.06935 | −0.0853387 | ||||||||
\(589\) | −33.6018 | −1.38454 | ||||||||
\(590\) | 5.36889 | 0.221034 | ||||||||
\(591\) | −0.386997 | −0.0159189 | ||||||||
\(592\) | 1.16291 | 0.0477953 | ||||||||
\(593\) | 37.7716 | 1.55109 | 0.775546 | − | 0.631291i | \(-0.217474\pi\) | ||||
0.775546 | + | 0.631291i | \(0.217474\pi\) | |||||||
\(594\) | 12.7460 | 0.522975 | ||||||||
\(595\) | 0.920377 | 0.0377318 | ||||||||
\(596\) | −7.52927 | −0.308411 | ||||||||
\(597\) | −6.51777 | −0.266755 | ||||||||
\(598\) | 5.56270 | 0.227476 | ||||||||
\(599\) | −39.3724 | −1.60871 | −0.804357 | − | 0.594146i | \(-0.797490\pi\) | ||||
−0.804357 | + | 0.594146i | \(0.797490\pi\) | |||||||
\(600\) | −2.44722 | −0.0999072 | ||||||||
\(601\) | −27.3220 | −1.11449 | −0.557244 | − | 0.830349i | \(-0.688141\pi\) | ||||
−0.557244 | + | 0.830349i | \(0.688141\pi\) | |||||||
\(602\) | −13.5527 | −0.552368 | ||||||||
\(603\) | −15.0037 | −0.610996 | ||||||||
\(604\) | 2.25758 | 0.0918596 | ||||||||
\(605\) | 4.06152 | 0.165124 | ||||||||
\(606\) | 6.03848 | 0.245297 | ||||||||
\(607\) | −18.1635 | −0.737234 | −0.368617 | − | 0.929581i | \(-0.620169\pi\) | ||||
−0.368617 | + | 0.929581i | \(0.620169\pi\) | |||||||
\(608\) | −4.36173 | −0.176892 | ||||||||
\(609\) | −9.39472 | −0.380693 | ||||||||
\(610\) | −2.21492 | −0.0896794 | ||||||||
\(611\) | −2.67969 | −0.108409 | ||||||||
\(612\) | −2.47380 | −0.0999973 | ||||||||
\(613\) | 23.4303 | 0.946341 | 0.473171 | − | 0.880971i | \(-0.343109\pi\) | ||||
0.473171 | + | 0.880971i | \(0.343109\pi\) | |||||||
\(614\) | 29.5812 | 1.19380 | ||||||||
\(615\) | −2.28330 | −0.0920717 | ||||||||
\(616\) | −7.41806 | −0.298882 | ||||||||
\(617\) | 32.1152 | 1.29291 | 0.646454 | − | 0.762953i | \(-0.276251\pi\) | ||||
0.646454 | + | 0.762953i | \(0.276251\pi\) | |||||||
\(618\) | −7.11025 | −0.286016 | ||||||||
\(619\) | 17.0924 | 0.687002 | 0.343501 | − | 0.939152i | \(-0.388387\pi\) | ||||
0.343501 | + | 0.939152i | \(0.388387\pi\) | |||||||
\(620\) | 4.46702 | 0.179400 | ||||||||
\(621\) | 15.1407 | 0.607576 | ||||||||
\(622\) | −14.3306 | −0.574604 | ||||||||
\(623\) | 26.6878 | 1.06922 | ||||||||
\(624\) | −0.579106 | −0.0231828 | ||||||||
\(625\) | 20.0697 | 0.802788 | ||||||||
\(626\) | −24.3489 | −0.973176 | ||||||||
\(627\) | 9.71144 | 0.387838 | ||||||||
\(628\) | 14.6282 | 0.583729 | ||||||||
\(629\) | 1.05584 | 0.0420990 | ||||||||
\(630\) | −2.76202 | −0.110041 | ||||||||
\(631\) | 44.1562 | 1.75783 | 0.878915 | − | 0.476978i | \(-0.158268\pi\) | ||||
0.878915 | + | 0.476978i | \(0.158268\pi\) | |||||||
\(632\) | −3.49154 | −0.138886 | ||||||||
\(633\) | −12.3409 | −0.490507 | ||||||||
\(634\) | −31.4001 | −1.24706 | ||||||||
\(635\) | 4.88577 | 0.193886 | ||||||||
\(636\) | 5.29927 | 0.210130 | ||||||||
\(637\) | 4.35235 | 0.172446 | ||||||||
\(638\) | 43.4550 | 1.72040 | ||||||||
\(639\) | 11.2774 | 0.446127 | ||||||||
\(640\) | 0.579848 | 0.0229205 | ||||||||
\(641\) | −14.1301 | −0.558104 | −0.279052 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279052 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(642\) | 0.761219 | 0.0300429 | ||||||||
\(643\) | 37.3366 | 1.47241 | 0.736205 | − | 0.676758i | \(-0.236616\pi\) | ||||
0.736205 | + | 0.676758i | \(0.236616\pi\) | |||||||
\(644\) | −8.81175 | −0.347232 | ||||||||
\(645\) | −2.35871 | −0.0928742 | ||||||||
\(646\) | −3.96014 | −0.155810 | ||||||||
\(647\) | −33.3606 | −1.31154 | −0.655770 | − | 0.754961i | \(-0.727656\pi\) | ||||
−0.655770 | + | 0.754961i | \(0.727656\pi\) | |||||||
\(648\) | 6.59775 | 0.259184 | ||||||||
\(649\) | −39.2881 | −1.54219 | ||||||||
\(650\) | 5.14708 | 0.201885 | ||||||||
\(651\) | 7.06706 | 0.276980 | ||||||||
\(652\) | −19.0197 | −0.744868 | ||||||||
\(653\) | 10.4815 | 0.410174 | 0.205087 | − | 0.978744i | \(-0.434252\pi\) | ||||
0.205087 | + | 0.978744i | \(0.434252\pi\) | |||||||
\(654\) | −8.80845 | −0.344437 | ||||||||
\(655\) | 6.15959 | 0.240675 | ||||||||
\(656\) | −7.50439 | −0.292997 | ||||||||
\(657\) | −5.89820 | −0.230111 | ||||||||
\(658\) | 4.24484 | 0.165481 | ||||||||
\(659\) | −16.4501 | −0.640805 | −0.320403 | − | 0.947281i | \(-0.603818\pi\) | ||||
−0.320403 | + | 0.947281i | \(0.603818\pi\) | |||||||
\(660\) | −1.29104 | −0.0502535 | ||||||||
\(661\) | 33.3664 | 1.29780 | 0.648901 | − | 0.760872i | \(-0.275229\pi\) | ||||
0.648901 | + | 0.760872i | \(0.275229\pi\) | |||||||
\(662\) | −18.1365 | −0.704897 | ||||||||
\(663\) | −0.525786 | −0.0204198 | ||||||||
\(664\) | −2.19884 | −0.0853317 | ||||||||
\(665\) | −4.42154 | −0.171460 | ||||||||
\(666\) | −3.16853 | −0.122778 | ||||||||
\(667\) | 51.6192 | 1.99870 | ||||||||
\(668\) | −1.30550 | −0.0505113 | ||||||||
\(669\) | −4.13649 | −0.159926 | ||||||||
\(670\) | 3.19300 | 0.123356 | ||||||||
\(671\) | 16.2082 | 0.625709 | ||||||||
\(672\) | 0.917349 | 0.0353875 | ||||||||
\(673\) | 34.1976 | 1.31822 | 0.659110 | − | 0.752046i | \(-0.270933\pi\) | ||||
0.659110 | + | 0.752046i | \(0.270933\pi\) | |||||||
\(674\) | −19.2491 | −0.741447 | ||||||||
\(675\) | 14.0095 | 0.539225 | ||||||||
\(676\) | −11.7820 | −0.453154 | ||||||||
\(677\) | 42.4697 | 1.63224 | 0.816121 | − | 0.577881i | \(-0.196120\pi\) | ||||
0.816121 | + | 0.577881i | \(0.196120\pi\) | |||||||
\(678\) | −1.76664 | −0.0678474 | ||||||||
\(679\) | −11.9478 | −0.458514 | ||||||||
\(680\) | 0.526460 | 0.0201888 | ||||||||
\(681\) | 12.0912 | 0.463337 | ||||||||
\(682\) | −32.6884 | −1.25170 | ||||||||
\(683\) | −22.2549 | −0.851560 | −0.425780 | − | 0.904827i | \(-0.640000\pi\) | ||||
−0.425780 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(684\) | 11.8842 | 0.454405 | ||||||||
\(685\) | 6.63493 | 0.253508 | ||||||||
\(686\) | −19.1321 | −0.730468 | ||||||||
\(687\) | 8.24676 | 0.314634 | ||||||||
\(688\) | −7.75223 | −0.295551 | ||||||||
\(689\) | −11.1456 | −0.424615 | ||||||||
\(690\) | −1.53359 | −0.0583829 | ||||||||
\(691\) | 4.39965 | 0.167371 | 0.0836853 | − | 0.996492i | \(-0.473331\pi\) | ||||
0.0836853 | + | 0.996492i | \(0.473331\pi\) | |||||||
\(692\) | 17.7649 | 0.675320 | ||||||||
\(693\) | 20.2117 | 0.767779 | ||||||||
\(694\) | 28.1876 | 1.06999 | ||||||||
\(695\) | 1.80825 | 0.0685909 | ||||||||
\(696\) | −5.37383 | −0.203694 | ||||||||
\(697\) | −6.81344 | −0.258078 | ||||||||
\(698\) | −16.6189 | −0.629034 | ||||||||
\(699\) | −8.29563 | −0.313769 | ||||||||
\(700\) | −8.15339 | −0.308169 | ||||||||
\(701\) | 12.6008 | 0.475925 | 0.237963 | − | 0.971274i | \(-0.423520\pi\) | ||||
0.237963 | + | 0.971274i | \(0.423520\pi\) | |||||||
\(702\) | 3.31518 | 0.125124 | ||||||||
\(703\) | −5.07230 | −0.191305 | ||||||||
\(704\) | −4.24317 | −0.159920 | ||||||||
\(705\) | 0.738771 | 0.0278237 | ||||||||
\(706\) | −21.8164 | −0.821072 | ||||||||
\(707\) | 20.1184 | 0.756631 | ||||||||
\(708\) | 4.85853 | 0.182595 | ||||||||
\(709\) | 22.9615 | 0.862339 | 0.431169 | − | 0.902271i | \(-0.358101\pi\) | ||||
0.431169 | + | 0.902271i | \(0.358101\pi\) | |||||||
\(710\) | −2.40000 | −0.0900703 | ||||||||
\(711\) | 9.51327 | 0.356775 | ||||||||
\(712\) | 15.2655 | 0.572100 | ||||||||
\(713\) | −38.8299 | −1.45419 | ||||||||
\(714\) | 0.832887 | 0.0311700 | ||||||||
\(715\) | 2.71536 | 0.101549 | ||||||||
\(716\) | 10.1556 | 0.379531 | ||||||||
\(717\) | −10.1267 | −0.378189 | ||||||||
\(718\) | −11.8039 | −0.440517 | ||||||||
\(719\) | 14.2247 | 0.530490 | 0.265245 | − | 0.964181i | \(-0.414547\pi\) | ||||
0.265245 | + | 0.964181i | \(0.414547\pi\) | |||||||
\(720\) | −1.57989 | −0.0588789 | ||||||||
\(721\) | −23.6892 | −0.882233 | ||||||||
\(722\) | 0.0247128 | 0.000919717 0 | ||||||||
\(723\) | 5.79530 | 0.215529 | ||||||||
\(724\) | −8.62692 | −0.320617 | ||||||||
\(725\) | 47.7625 | 1.77385 | ||||||||
\(726\) | 3.67544 | 0.136408 | ||||||||
\(727\) | −0.451032 | −0.0167278 | −0.00836392 | − | 0.999965i | \(-0.502662\pi\) | ||||
−0.00836392 | + | 0.999965i | \(0.502662\pi\) | |||||||
\(728\) | −1.92941 | −0.0715085 | ||||||||
\(729\) | −13.2480 | −0.490665 | ||||||||
\(730\) | 1.25522 | 0.0464579 | ||||||||
\(731\) | −7.03847 | −0.260327 | ||||||||
\(732\) | −2.00437 | −0.0740837 | ||||||||
\(733\) | 49.6160 | 1.83261 | 0.916304 | − | 0.400483i | \(-0.131158\pi\) | ||||
0.916304 | + | 0.400483i | \(0.131158\pi\) | |||||||
\(734\) | −37.7917 | −1.39492 | ||||||||
\(735\) | −1.19991 | −0.0442593 | ||||||||
\(736\) | −5.04037 | −0.185790 | ||||||||
\(737\) | −23.3655 | −0.860679 | ||||||||
\(738\) | 20.4469 | 0.752661 | ||||||||
\(739\) | −26.6773 | −0.981339 | −0.490669 | − | 0.871346i | \(-0.663248\pi\) | ||||
−0.490669 | + | 0.871346i | \(0.663248\pi\) | |||||||
\(740\) | 0.674310 | 0.0247881 | ||||||||
\(741\) | 2.52590 | 0.0927914 | ||||||||
\(742\) | 17.6556 | 0.648156 | ||||||||
\(743\) | 2.06939 | 0.0759185 | 0.0379592 | − | 0.999279i | \(-0.487914\pi\) | ||||
0.0379592 | + | 0.999279i | \(0.487914\pi\) | |||||||
\(744\) | 4.04239 | 0.148201 | ||||||||
\(745\) | −4.36583 | −0.159952 | ||||||||
\(746\) | 9.93160 | 0.363622 | ||||||||
\(747\) | 5.99110 | 0.219203 | ||||||||
\(748\) | −3.85249 | −0.140861 | ||||||||
\(749\) | 2.53615 | 0.0926690 | ||||||||
\(750\) | −2.94032 | −0.107365 | ||||||||
\(751\) | −6.73841 | −0.245888 | −0.122944 | − | 0.992414i | \(-0.539234\pi\) | ||||
−0.122944 | + | 0.992414i | \(0.539234\pi\) | |||||||
\(752\) | 2.42807 | 0.0885426 | ||||||||
\(753\) | 0.232622 | 0.00847721 | ||||||||
\(754\) | 11.3024 | 0.411611 | ||||||||
\(755\) | 1.30905 | 0.0476413 | ||||||||
\(756\) | −5.25151 | −0.190996 | ||||||||
\(757\) | −36.2973 | −1.31925 | −0.659623 | − | 0.751596i | \(-0.729284\pi\) | ||||
−0.659623 | + | 0.751596i | \(0.729284\pi\) | |||||||
\(758\) | −2.08125 | −0.0755945 | ||||||||
\(759\) | 11.2224 | 0.407348 | ||||||||
\(760\) | −2.52914 | −0.0917416 | ||||||||
\(761\) | 54.1522 | 1.96301 | 0.981507 | − | 0.191425i | \(-0.0613107\pi\) | ||||
0.981507 | + | 0.191425i | \(0.0613107\pi\) | |||||||
\(762\) | 4.42133 | 0.160168 | ||||||||
\(763\) | −29.3471 | −1.06244 | ||||||||
\(764\) | −19.8025 | −0.716429 | ||||||||
\(765\) | −1.43442 | −0.0518617 | ||||||||
\(766\) | −3.37711 | −0.122020 | ||||||||
\(767\) | −10.2187 | −0.368974 | ||||||||
\(768\) | 0.524728 | 0.0189345 | ||||||||
\(769\) | −4.21453 | −0.151980 | −0.0759899 | − | 0.997109i | \(-0.524212\pi\) | ||||
−0.0759899 | + | 0.997109i | \(0.524212\pi\) | |||||||
\(770\) | −4.30135 | −0.155010 | ||||||||
\(771\) | 14.2972 | 0.514902 | ||||||||
\(772\) | 26.9778 | 0.970953 | ||||||||
\(773\) | 1.84907 | 0.0665064 | 0.0332532 | − | 0.999447i | \(-0.489413\pi\) | ||||
0.0332532 | + | 0.999447i | \(0.489413\pi\) | |||||||
\(774\) | 21.1222 | 0.759222 | ||||||||
\(775\) | −35.9287 | −1.29060 | ||||||||
\(776\) | −6.83419 | −0.245333 | ||||||||
\(777\) | 1.06679 | 0.0382710 | ||||||||
\(778\) | 0.435883 | 0.0156272 | ||||||||
\(779\) | 32.7321 | 1.17275 | ||||||||
\(780\) | −0.335793 | −0.0120233 | ||||||||
\(781\) | 17.5625 | 0.628436 | ||||||||
\(782\) | −4.57629 | −0.163648 | ||||||||
\(783\) | 30.7633 | 1.09939 | ||||||||
\(784\) | −3.94367 | −0.140845 | ||||||||
\(785\) | 8.48213 | 0.302740 | ||||||||
\(786\) | 5.57407 | 0.198820 | ||||||||
\(787\) | −13.5333 | −0.482408 | −0.241204 | − | 0.970474i | \(-0.577542\pi\) | ||||
−0.241204 | + | 0.970474i | \(0.577542\pi\) | |||||||
\(788\) | −0.737518 | −0.0262730 | ||||||||
\(789\) | 5.69799 | 0.202854 | ||||||||
\(790\) | −2.02456 | −0.0720307 | ||||||||
\(791\) | −5.88591 | −0.209279 | ||||||||
\(792\) | 11.5612 | 0.410809 | ||||||||
\(793\) | 4.21567 | 0.149703 | ||||||||
\(794\) | −7.38433 | −0.262060 | ||||||||
\(795\) | 3.07277 | 0.108980 | ||||||||
\(796\) | −12.4212 | −0.440259 | ||||||||
\(797\) | 14.1358 | 0.500716 | 0.250358 | − | 0.968153i | \(-0.419452\pi\) | ||||
0.250358 | + | 0.968153i | \(0.419452\pi\) | |||||||
\(798\) | −4.00123 | −0.141642 | ||||||||
\(799\) | 2.20451 | 0.0779901 | ||||||||
\(800\) | −4.66378 | −0.164889 | ||||||||
\(801\) | −41.5934 | −1.46963 | ||||||||
\(802\) | −30.0393 | −1.06072 | ||||||||
\(803\) | −9.18538 | −0.324145 | ||||||||
\(804\) | 2.88948 | 0.101904 | ||||||||
\(805\) | −5.10947 | −0.180085 | ||||||||
\(806\) | −8.50212 | −0.299474 | ||||||||
\(807\) | −6.80720 | −0.239625 | ||||||||
\(808\) | 11.5078 | 0.404844 | ||||||||
\(809\) | −33.1148 | −1.16426 | −0.582128 | − | 0.813097i | \(-0.697780\pi\) | ||||
−0.582128 | + | 0.813097i | \(0.697780\pi\) | |||||||
\(810\) | 3.82569 | 0.134421 | ||||||||
\(811\) | −24.6147 | −0.864338 | −0.432169 | − | 0.901793i | \(-0.642252\pi\) | ||||
−0.432169 | + | 0.901793i | \(0.642252\pi\) | |||||||
\(812\) | −17.9040 | −0.628306 | ||||||||
\(813\) | 6.83785 | 0.239814 | ||||||||
\(814\) | −4.93442 | −0.172951 | ||||||||
\(815\) | −11.0285 | −0.386312 | ||||||||
\(816\) | 0.476416 | 0.0166779 | ||||||||
\(817\) | 33.8132 | 1.18297 | ||||||||
\(818\) | −25.0098 | −0.874449 | ||||||||
\(819\) | 5.25698 | 0.183694 | ||||||||
\(820\) | −4.35140 | −0.151957 | ||||||||
\(821\) | 0.918011 | 0.0320388 | 0.0160194 | − | 0.999872i | \(-0.494901\pi\) | ||||
0.0160194 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(822\) | 6.00423 | 0.209421 | ||||||||
\(823\) | −30.2958 | −1.05605 | −0.528023 | − | 0.849230i | \(-0.677067\pi\) | ||||
−0.528023 | + | 0.849230i | \(0.677067\pi\) | |||||||
\(824\) | −13.5504 | −0.472049 | ||||||||
\(825\) | 10.3839 | 0.361523 | ||||||||
\(826\) | 16.1872 | 0.563224 | ||||||||
\(827\) | −3.77313 | −0.131204 | −0.0656022 | − | 0.997846i | \(-0.520897\pi\) | ||||
−0.0656022 | + | 0.997846i | \(0.520897\pi\) | |||||||
\(828\) | 13.7333 | 0.477265 | ||||||||
\(829\) | −45.0545 | −1.56481 | −0.782403 | − | 0.622772i | \(-0.786006\pi\) | ||||
−0.782403 | + | 0.622772i | \(0.786006\pi\) | |||||||
\(830\) | −1.27499 | −0.0442557 | ||||||||
\(831\) | −5.17361 | −0.179471 | ||||||||
\(832\) | −1.10363 | −0.0382615 | ||||||||
\(833\) | −3.58057 | −0.124059 | ||||||||
\(834\) | 1.63636 | 0.0566626 | ||||||||
\(835\) | −0.756991 | −0.0261967 | ||||||||
\(836\) | 18.5076 | 0.640097 | ||||||||
\(837\) | −23.1413 | −0.799881 | ||||||||
\(838\) | 35.4484 | 1.22455 | ||||||||
\(839\) | −22.1547 | −0.764864 | −0.382432 | − | 0.923984i | \(-0.624913\pi\) | ||||
−0.382432 | + | 0.923984i | \(0.624913\pi\) | |||||||
\(840\) | 0.531923 | 0.0183531 | ||||||||
\(841\) | 75.8814 | 2.61660 | ||||||||
\(842\) | 4.49450 | 0.154891 | ||||||||
\(843\) | −14.1753 | −0.488225 | ||||||||
\(844\) | −23.5187 | −0.809546 | ||||||||
\(845\) | −6.83177 | −0.235020 | ||||||||
\(846\) | −6.61567 | −0.227451 | ||||||||
\(847\) | 12.2455 | 0.420759 | ||||||||
\(848\) | 10.0991 | 0.346804 | ||||||||
\(849\) | 2.64765 | 0.0908672 | ||||||||
\(850\) | −4.23437 | −0.145238 | ||||||||
\(851\) | −5.86149 | −0.200929 | ||||||||
\(852\) | −2.17186 | −0.0744066 | ||||||||
\(853\) | 12.8890 | 0.441311 | 0.220655 | − | 0.975352i | \(-0.429180\pi\) | ||||
0.220655 | + | 0.975352i | \(0.429180\pi\) | |||||||
\(854\) | −6.67796 | −0.228515 | ||||||||
\(855\) | 6.89105 | 0.235669 | ||||||||
\(856\) | 1.45069 | 0.0495836 | ||||||||
\(857\) | 31.3615 | 1.07129 | 0.535644 | − | 0.844444i | \(-0.320069\pi\) | ||||
0.535644 | + | 0.844444i | \(0.320069\pi\) | |||||||
\(858\) | 2.45724 | 0.0838889 | ||||||||
\(859\) | −12.7738 | −0.435837 | −0.217919 | − | 0.975967i | \(-0.569927\pi\) | ||||
−0.217919 | + | 0.975967i | \(0.569927\pi\) | |||||||
\(860\) | −4.49511 | −0.153282 | ||||||||
\(861\) | −6.88414 | −0.234611 | ||||||||
\(862\) | −16.5094 | −0.562313 | ||||||||
\(863\) | 57.3228 | 1.95129 | 0.975646 | − | 0.219352i | \(-0.0703944\pi\) | ||||
0.975646 | + | 0.219352i | \(0.0703944\pi\) | |||||||
\(864\) | −3.00389 | −0.102194 | ||||||||
\(865\) | 10.3009 | 0.350242 | ||||||||
\(866\) | 3.74448 | 0.127243 | ||||||||
\(867\) | −8.48783 | −0.288262 | ||||||||
\(868\) | 13.4680 | 0.457135 | ||||||||
\(869\) | 14.8152 | 0.502571 | ||||||||
\(870\) | −3.11600 | −0.105642 | ||||||||
\(871\) | −6.07727 | −0.205920 | ||||||||
\(872\) | −16.7867 | −0.568469 | ||||||||
\(873\) | 18.6208 | 0.630220 | ||||||||
\(874\) | 21.9847 | 0.743645 | ||||||||
\(875\) | −9.79628 | −0.331175 | ||||||||
\(876\) | 1.13590 | 0.0383786 | ||||||||
\(877\) | −1.00474 | −0.0339276 | −0.0169638 | − | 0.999856i | \(-0.505400\pi\) | ||||
−0.0169638 | + | 0.999856i | \(0.505400\pi\) | |||||||
\(878\) | −23.9564 | −0.808489 | ||||||||
\(879\) | 7.12912 | 0.240459 | ||||||||
\(880\) | −2.46039 | −0.0829397 | ||||||||
\(881\) | −43.3265 | −1.45971 | −0.729853 | − | 0.683604i | \(-0.760412\pi\) | ||||
−0.729853 | + | 0.683604i | \(0.760412\pi\) | |||||||
\(882\) | 10.7452 | 0.361808 | ||||||||
\(883\) | −27.9397 | −0.940245 | −0.470123 | − | 0.882601i | \(-0.655790\pi\) | ||||
−0.470123 | + | 0.882601i | \(0.655790\pi\) | |||||||
\(884\) | −1.00202 | −0.0337015 | ||||||||
\(885\) | 2.81721 | 0.0946994 | ||||||||
\(886\) | −38.5346 | −1.29459 | ||||||||
\(887\) | −29.1669 | −0.979330 | −0.489665 | − | 0.871911i | \(-0.662881\pi\) | ||||
−0.489665 | + | 0.871911i | \(0.662881\pi\) | |||||||
\(888\) | 0.610211 | 0.0204773 | ||||||||
\(889\) | 14.7306 | 0.494047 | ||||||||
\(890\) | 8.85168 | 0.296709 | ||||||||
\(891\) | −27.9954 | −0.937880 | ||||||||
\(892\) | −7.88310 | −0.263946 | ||||||||
\(893\) | −10.5906 | −0.354401 | ||||||||
\(894\) | −3.95082 | −0.132135 | ||||||||
\(895\) | 5.88868 | 0.196837 | ||||||||
\(896\) | 1.74824 | 0.0584045 | ||||||||
\(897\) | 2.91890 | 0.0974594 | ||||||||
\(898\) | −5.34299 | −0.178298 | ||||||||
\(899\) | −78.8956 | −2.63132 | ||||||||
\(900\) | 12.7072 | 0.423574 | ||||||||
\(901\) | 9.16923 | 0.305471 | ||||||||
\(902\) | 31.8424 | 1.06023 | ||||||||
\(903\) | −7.11150 | −0.236656 | ||||||||
\(904\) | −3.36677 | −0.111977 | ||||||||
\(905\) | −5.00230 | −0.166282 | ||||||||
\(906\) | 1.18462 | 0.0393562 | ||||||||
\(907\) | −37.2353 | −1.23638 | −0.618188 | − | 0.786030i | \(-0.712133\pi\) | ||||
−0.618188 | + | 0.786030i | \(0.712133\pi\) | |||||||
\(908\) | 23.0428 | 0.764704 | ||||||||
\(909\) | −31.3549 | −1.03998 | ||||||||
\(910\) | −1.11876 | −0.0370866 | ||||||||
\(911\) | −19.0463 | −0.631034 | −0.315517 | − | 0.948920i | \(-0.602178\pi\) | ||||
−0.315517 | + | 0.948920i | \(0.602178\pi\) | |||||||
\(912\) | −2.28872 | −0.0757872 | ||||||||
\(913\) | 9.33007 | 0.308780 | ||||||||
\(914\) | 9.37871 | 0.310220 | ||||||||
\(915\) | −1.16223 | −0.0384221 | ||||||||
\(916\) | 15.7163 | 0.519280 | ||||||||
\(917\) | 18.5711 | 0.613272 | ||||||||
\(918\) | −2.72732 | −0.0900149 | ||||||||
\(919\) | 5.88448 | 0.194111 | 0.0970556 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970556 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(920\) | −2.92264 | −0.0963567 | ||||||||
\(921\) | 15.5221 | 0.511470 | ||||||||
\(922\) | 26.6068 | 0.876248 | ||||||||
\(923\) | 4.56794 | 0.150355 | ||||||||
\(924\) | −3.89247 | −0.128053 | ||||||||
\(925\) | −5.42355 | −0.178325 | ||||||||
\(926\) | 25.3046 | 0.831561 | ||||||||
\(927\) | 36.9201 | 1.21262 | ||||||||
\(928\) | −10.2412 | −0.336183 | ||||||||
\(929\) | 1.84754 | 0.0606159 | 0.0303080 | − | 0.999541i | \(-0.490351\pi\) | ||||
0.0303080 | + | 0.999541i | \(0.490351\pi\) | |||||||
\(930\) | 2.34397 | 0.0768618 | ||||||||
\(931\) | 17.2012 | 0.563747 | ||||||||
\(932\) | −15.8094 | −0.517853 | ||||||||
\(933\) | −7.51966 | −0.246183 | ||||||||
\(934\) | 38.7351 | 1.26745 | ||||||||
\(935\) | −2.23386 | −0.0730550 | ||||||||
\(936\) | 3.00702 | 0.0982874 | ||||||||
\(937\) | −34.6431 | −1.13174 | −0.565870 | − | 0.824494i | \(-0.691460\pi\) | ||||
−0.565870 | + | 0.824494i | \(0.691460\pi\) | |||||||
\(938\) | 9.62687 | 0.314329 | ||||||||
\(939\) | −12.7765 | −0.416947 | ||||||||
\(940\) | 1.40791 | 0.0459210 | ||||||||
\(941\) | −54.7222 | −1.78389 | −0.891947 | − | 0.452140i | \(-0.850661\pi\) | ||||
−0.891947 | + | 0.452140i | \(0.850661\pi\) | |||||||
\(942\) | 7.67583 | 0.250092 | ||||||||
\(943\) | 37.8248 | 1.23175 | ||||||||
\(944\) | 9.25914 | 0.301359 | ||||||||
\(945\) | −3.04508 | −0.0990564 | ||||||||
\(946\) | 32.8940 | 1.06948 | ||||||||
\(947\) | −18.6067 | −0.604637 | −0.302319 | − | 0.953207i | \(-0.597761\pi\) | ||||
−0.302319 | + | 0.953207i | \(0.597761\pi\) | |||||||
\(948\) | −1.83211 | −0.0595042 | ||||||||
\(949\) | −2.38908 | −0.0775528 | ||||||||
\(950\) | 20.3421 | 0.659986 | ||||||||
\(951\) | −16.4765 | −0.534287 | ||||||||
\(952\) | 1.58727 | 0.0514438 | ||||||||
\(953\) | 7.53800 | 0.244180 | 0.122090 | − | 0.992519i | \(-0.461040\pi\) | ||||
0.122090 | + | 0.992519i | \(0.461040\pi\) | |||||||
\(954\) | −27.5165 | −0.890881 | ||||||||
\(955\) | −11.4824 | −0.371562 | ||||||||
\(956\) | −19.2990 | −0.624173 | ||||||||
\(957\) | 22.8020 | 0.737086 | ||||||||
\(958\) | 7.26758 | 0.234805 | ||||||||
\(959\) | 20.0043 | 0.645972 | ||||||||
\(960\) | 0.304262 | 0.00982003 | ||||||||
\(961\) | 28.3482 | 0.914458 | ||||||||
\(962\) | −1.28342 | −0.0413791 | ||||||||
\(963\) | −3.95264 | −0.127372 | ||||||||
\(964\) | 11.0444 | 0.355715 | ||||||||
\(965\) | 15.6430 | 0.503567 | ||||||||
\(966\) | −4.62378 | −0.148768 | ||||||||
\(967\) | 54.2198 | 1.74359 | 0.871796 | − | 0.489869i | \(-0.162955\pi\) | ||||
0.871796 | + | 0.489869i | \(0.162955\pi\) | |||||||
\(968\) | 7.00447 | 0.225132 | ||||||||
\(969\) | −2.07800 | −0.0667549 | ||||||||
\(970\) | −3.96279 | −0.127237 | ||||||||
\(971\) | −34.6730 | −1.11271 | −0.556355 | − | 0.830945i | \(-0.687801\pi\) | ||||
−0.556355 | + | 0.830945i | \(0.687801\pi\) | |||||||
\(972\) | 12.4737 | 0.400094 | ||||||||
\(973\) | 5.45187 | 0.174779 | ||||||||
\(974\) | 4.61766 | 0.147959 | ||||||||
\(975\) | 2.70082 | 0.0864954 | ||||||||
\(976\) | −3.81983 | −0.122270 | ||||||||
\(977\) | 9.32413 | 0.298305 | 0.149153 | − | 0.988814i | \(-0.452345\pi\) | ||||
0.149153 | + | 0.988814i | \(0.452345\pi\) | |||||||
\(978\) | −9.98016 | −0.319130 | ||||||||
\(979\) | −64.7742 | −2.07019 | ||||||||
\(980\) | −2.28673 | −0.0730468 | ||||||||
\(981\) | 45.7380 | 1.46030 | ||||||||
\(982\) | 6.30455 | 0.201186 | ||||||||
\(983\) | −32.7800 | −1.04552 | −0.522759 | − | 0.852480i | \(-0.675097\pi\) | ||||
−0.522759 | + | 0.852480i | \(0.675097\pi\) | |||||||
\(984\) | −3.93776 | −0.125531 | ||||||||
\(985\) | −0.427648 | −0.0136260 | ||||||||
\(986\) | −9.29824 | −0.296116 | ||||||||
\(987\) | 2.22739 | 0.0708986 | ||||||||
\(988\) | 4.81374 | 0.153145 | ||||||||
\(989\) | 39.0741 | 1.24248 | ||||||||
\(990\) | 6.70373 | 0.213058 | ||||||||
\(991\) | 21.9102 | 0.696000 | 0.348000 | − | 0.937495i | \(-0.386861\pi\) | ||||
0.348000 | + | 0.937495i | \(0.386861\pi\) | |||||||
\(992\) | 7.70378 | 0.244595 | ||||||||
\(993\) | −9.51676 | −0.302005 | ||||||||
\(994\) | −7.23597 | −0.229511 | ||||||||
\(995\) | −7.20242 | −0.228332 | ||||||||
\(996\) | −1.15380 | −0.0365594 | ||||||||
\(997\) | 37.0735 | 1.17413 | 0.587065 | − | 0.809540i | \(-0.300283\pi\) | ||||
0.587065 | + | 0.809540i | \(0.300283\pi\) | |||||||
\(998\) | −24.2705 | −0.768270 | ||||||||
\(999\) | −3.49325 | −0.110522 |
(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 | 4022.2.a.c.1.19 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.c.1.19 | ✓ | 31 | 1.1 | even | 1 | trivial |