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: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 | ||||||||
\(3\) | −1.96616 | −1.13516 | −0.567582 | − | 0.823317i | \(-0.692121\pi\) | ||||
−0.567582 | + | 0.823317i | \(0.692121\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.21238 | −0.542193 | −0.271097 | − | 0.962552i | \(-0.587386\pi\) | ||||
−0.271097 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(6\) | 1.96616 | 0.802682 | ||||||||
\(7\) | −3.03603 | −1.14751 | −0.573756 | − | 0.819026i | \(-0.694514\pi\) | ||||
−0.573756 | + | 0.819026i | \(0.694514\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.865786 | 0.288595 | ||||||||
\(10\) | 1.21238 | 0.383388 | ||||||||
\(11\) | −3.99510 | −1.20457 | −0.602284 | − | 0.798282i | \(-0.705743\pi\) | ||||
−0.602284 | + | 0.798282i | \(0.705743\pi\) | |||||||
\(12\) | −1.96616 | −0.567582 | ||||||||
\(13\) | −2.32483 | −0.644792 | −0.322396 | − | 0.946605i | \(-0.604488\pi\) | ||||
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(14\) | 3.03603 | 0.811414 | ||||||||
\(15\) | 2.38374 | 0.615478 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.92751 | −0.467489 | −0.233744 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233744 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(18\) | −0.865786 | −0.204068 | ||||||||
\(19\) | 0.125430 | 0.0287755 | 0.0143878 | − | 0.999896i | \(-0.495420\pi\) | ||||
0.0143878 | + | 0.999896i | \(0.495420\pi\) | |||||||
\(20\) | −1.21238 | −0.271097 | ||||||||
\(21\) | 5.96933 | 1.30261 | ||||||||
\(22\) | 3.99510 | 0.851758 | ||||||||
\(23\) | 8.03653 | 1.67573 | 0.837866 | − | 0.545876i | \(-0.183803\pi\) | ||||
0.837866 | + | 0.545876i | \(0.183803\pi\) | |||||||
\(24\) | 1.96616 | 0.401341 | ||||||||
\(25\) | −3.53013 | −0.706027 | ||||||||
\(26\) | 2.32483 | 0.455937 | ||||||||
\(27\) | 4.19621 | 0.807560 | ||||||||
\(28\) | −3.03603 | −0.573756 | ||||||||
\(29\) | 8.61158 | 1.59913 | 0.799565 | − | 0.600580i | \(-0.205063\pi\) | ||||
0.799565 | + | 0.600580i | \(0.205063\pi\) | |||||||
\(30\) | −2.38374 | −0.435208 | ||||||||
\(31\) | 5.02585 | 0.902669 | 0.451334 | − | 0.892355i | \(-0.350948\pi\) | ||||
0.451334 | + | 0.892355i | \(0.350948\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.85501 | 1.36738 | ||||||||
\(34\) | 1.92751 | 0.330564 | ||||||||
\(35\) | 3.68083 | 0.622173 | ||||||||
\(36\) | 0.865786 | 0.144298 | ||||||||
\(37\) | 4.76131 | 0.782755 | 0.391377 | − | 0.920230i | \(-0.371999\pi\) | ||||
0.391377 | + | 0.920230i | \(0.371999\pi\) | |||||||
\(38\) | −0.125430 | −0.0203474 | ||||||||
\(39\) | 4.57099 | 0.731945 | ||||||||
\(40\) | 1.21238 | 0.191694 | ||||||||
\(41\) | 0.478489 | 0.0747274 | 0.0373637 | − | 0.999302i | \(-0.488104\pi\) | ||||
0.0373637 | + | 0.999302i | \(0.488104\pi\) | |||||||
\(42\) | −5.96933 | −0.921087 | ||||||||
\(43\) | 6.52334 | 0.994801 | 0.497400 | − | 0.867521i | \(-0.334288\pi\) | ||||
0.497400 | + | 0.867521i | \(0.334288\pi\) | |||||||
\(44\) | −3.99510 | −0.602284 | ||||||||
\(45\) | −1.04966 | −0.156474 | ||||||||
\(46\) | −8.03653 | −1.18492 | ||||||||
\(47\) | −2.89425 | −0.422169 | −0.211085 | − | 0.977468i | \(-0.567700\pi\) | ||||
−0.211085 | + | 0.977468i | \(0.567700\pi\) | |||||||
\(48\) | −1.96616 | −0.283791 | ||||||||
\(49\) | 2.21749 | 0.316784 | ||||||||
\(50\) | 3.53013 | 0.499236 | ||||||||
\(51\) | 3.78978 | 0.530676 | ||||||||
\(52\) | −2.32483 | −0.322396 | ||||||||
\(53\) | −2.52743 | −0.347169 | −0.173585 | − | 0.984819i | \(-0.555535\pi\) | ||||
−0.173585 | + | 0.984819i | \(0.555535\pi\) | |||||||
\(54\) | −4.19621 | −0.571031 | ||||||||
\(55\) | 4.84358 | 0.653109 | ||||||||
\(56\) | 3.03603 | 0.405707 | ||||||||
\(57\) | −0.246615 | −0.0326649 | ||||||||
\(58\) | −8.61158 | −1.13076 | ||||||||
\(59\) | −7.53375 | −0.980811 | −0.490405 | − | 0.871494i | \(-0.663151\pi\) | ||||
−0.490405 | + | 0.871494i | \(0.663151\pi\) | |||||||
\(60\) | 2.38374 | 0.307739 | ||||||||
\(61\) | −2.67530 | −0.342537 | −0.171269 | − | 0.985224i | \(-0.554787\pi\) | ||||
−0.171269 | + | 0.985224i | \(0.554787\pi\) | |||||||
\(62\) | −5.02585 | −0.638283 | ||||||||
\(63\) | −2.62856 | −0.331167 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.81858 | 0.349602 | ||||||||
\(66\) | −7.85501 | −0.966885 | ||||||||
\(67\) | −10.2963 | −1.25789 | −0.628946 | − | 0.777449i | \(-0.716513\pi\) | ||||
−0.628946 | + | 0.777449i | \(0.716513\pi\) | |||||||
\(68\) | −1.92751 | −0.233744 | ||||||||
\(69\) | −15.8011 | −1.90223 | ||||||||
\(70\) | −3.68083 | −0.439943 | ||||||||
\(71\) | 5.48123 | 0.650503 | 0.325251 | − | 0.945628i | \(-0.394551\pi\) | ||||
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(72\) | −0.865786 | −0.102034 | ||||||||
\(73\) | 8.94590 | 1.04704 | 0.523519 | − | 0.852014i | \(-0.324619\pi\) | ||||
0.523519 | + | 0.852014i | \(0.324619\pi\) | |||||||
\(74\) | −4.76131 | −0.553491 | ||||||||
\(75\) | 6.94081 | 0.801455 | ||||||||
\(76\) | 0.125430 | 0.0143878 | ||||||||
\(77\) | 12.1293 | 1.38226 | ||||||||
\(78\) | −4.57099 | −0.517563 | ||||||||
\(79\) | 13.5038 | 1.51930 | 0.759651 | − | 0.650331i | \(-0.225370\pi\) | ||||
0.759651 | + | 0.650331i | \(0.225370\pi\) | |||||||
\(80\) | −1.21238 | −0.135548 | ||||||||
\(81\) | −10.8478 | −1.20531 | ||||||||
\(82\) | −0.478489 | −0.0528402 | ||||||||
\(83\) | −9.03972 | −0.992238 | −0.496119 | − | 0.868254i | \(-0.665242\pi\) | ||||
−0.496119 | + | 0.868254i | \(0.665242\pi\) | |||||||
\(84\) | 5.96933 | 0.651307 | ||||||||
\(85\) | 2.33687 | 0.253469 | ||||||||
\(86\) | −6.52334 | −0.703430 | ||||||||
\(87\) | −16.9317 | −1.81527 | ||||||||
\(88\) | 3.99510 | 0.425879 | ||||||||
\(89\) | −1.30467 | −0.138295 | −0.0691476 | − | 0.997606i | \(-0.522028\pi\) | ||||
−0.0691476 | + | 0.997606i | \(0.522028\pi\) | |||||||
\(90\) | 1.04966 | 0.110644 | ||||||||
\(91\) | 7.05826 | 0.739907 | ||||||||
\(92\) | 8.03653 | 0.837866 | ||||||||
\(93\) | −9.88162 | −1.02468 | ||||||||
\(94\) | 2.89425 | 0.298519 | ||||||||
\(95\) | −0.152069 | −0.0156019 | ||||||||
\(96\) | 1.96616 | 0.200670 | ||||||||
\(97\) | −15.2284 | −1.54621 | −0.773104 | − | 0.634280i | \(-0.781297\pi\) | ||||
−0.773104 | + | 0.634280i | \(0.781297\pi\) | |||||||
\(98\) | −2.21749 | −0.224000 | ||||||||
\(99\) | −3.45890 | −0.347633 | ||||||||
\(100\) | −3.53013 | −0.353013 | ||||||||
\(101\) | 0.891029 | 0.0886607 | 0.0443303 | − | 0.999017i | \(-0.485885\pi\) | ||||
0.0443303 | + | 0.999017i | \(0.485885\pi\) | |||||||
\(102\) | −3.78978 | −0.375245 | ||||||||
\(103\) | 5.20638 | 0.513000 | 0.256500 | − | 0.966544i | \(-0.417431\pi\) | ||||
0.256500 | + | 0.966544i | \(0.417431\pi\) | |||||||
\(104\) | 2.32483 | 0.227969 | ||||||||
\(105\) | −7.23710 | −0.706268 | ||||||||
\(106\) | 2.52743 | 0.245486 | ||||||||
\(107\) | 8.28823 | 0.801254 | 0.400627 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400627 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(108\) | 4.19621 | 0.403780 | ||||||||
\(109\) | 1.01086 | 0.0968233 | 0.0484116 | − | 0.998827i | \(-0.484584\pi\) | ||||
0.0484116 | + | 0.998827i | \(0.484584\pi\) | |||||||
\(110\) | −4.84358 | −0.461818 | ||||||||
\(111\) | −9.36150 | −0.888554 | ||||||||
\(112\) | −3.03603 | −0.286878 | ||||||||
\(113\) | 8.04213 | 0.756540 | 0.378270 | − | 0.925695i | \(-0.376519\pi\) | ||||
0.378270 | + | 0.925695i | \(0.376519\pi\) | |||||||
\(114\) | 0.246615 | 0.0230976 | ||||||||
\(115\) | −9.74333 | −0.908570 | ||||||||
\(116\) | 8.61158 | 0.799565 | ||||||||
\(117\) | −2.01281 | −0.186084 | ||||||||
\(118\) | 7.53375 | 0.693538 | ||||||||
\(119\) | 5.85197 | 0.536449 | ||||||||
\(120\) | −2.38374 | −0.217604 | ||||||||
\(121\) | 4.96083 | 0.450985 | ||||||||
\(122\) | 2.67530 | 0.242211 | ||||||||
\(123\) | −0.940785 | −0.0848278 | ||||||||
\(124\) | 5.02585 | 0.451334 | ||||||||
\(125\) | 10.3418 | 0.924996 | ||||||||
\(126\) | 2.62856 | 0.234170 | ||||||||
\(127\) | 3.89597 | 0.345711 | 0.172856 | − | 0.984947i | \(-0.444701\pi\) | ||||
0.172856 | + | 0.984947i | \(0.444701\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.8259 | −1.12926 | ||||||||
\(130\) | −2.81858 | −0.247206 | ||||||||
\(131\) | 9.83007 | 0.858857 | 0.429428 | − | 0.903101i | \(-0.358715\pi\) | ||||
0.429428 | + | 0.903101i | \(0.358715\pi\) | |||||||
\(132\) | 7.85501 | 0.683691 | ||||||||
\(133\) | −0.380809 | −0.0330203 | ||||||||
\(134\) | 10.2963 | 0.889464 | ||||||||
\(135\) | −5.08740 | −0.437854 | ||||||||
\(136\) | 1.92751 | 0.165282 | ||||||||
\(137\) | −7.02100 | −0.599844 | −0.299922 | − | 0.953964i | \(-0.596961\pi\) | ||||
−0.299922 | + | 0.953964i | \(0.596961\pi\) | |||||||
\(138\) | 15.8011 | 1.34508 | ||||||||
\(139\) | −3.72284 | −0.315767 | −0.157884 | − | 0.987458i | \(-0.550467\pi\) | ||||
−0.157884 | + | 0.987458i | \(0.550467\pi\) | |||||||
\(140\) | 3.68083 | 0.311087 | ||||||||
\(141\) | 5.69055 | 0.479231 | ||||||||
\(142\) | −5.48123 | −0.459975 | ||||||||
\(143\) | 9.28794 | 0.776696 | ||||||||
\(144\) | 0.865786 | 0.0721489 | ||||||||
\(145\) | −10.4405 | −0.867037 | ||||||||
\(146\) | −8.94590 | −0.740368 | ||||||||
\(147\) | −4.35994 | −0.359602 | ||||||||
\(148\) | 4.76131 | 0.391377 | ||||||||
\(149\) | 1.69160 | 0.138581 | 0.0692907 | − | 0.997597i | \(-0.477926\pi\) | ||||
0.0692907 | + | 0.997597i | \(0.477926\pi\) | |||||||
\(150\) | −6.94081 | −0.566714 | ||||||||
\(151\) | −14.4311 | −1.17439 | −0.587193 | − | 0.809447i | \(-0.699767\pi\) | ||||
−0.587193 | + | 0.809447i | \(0.699767\pi\) | |||||||
\(152\) | −0.125430 | −0.0101737 | ||||||||
\(153\) | −1.66881 | −0.134915 | ||||||||
\(154\) | −12.1293 | −0.977403 | ||||||||
\(155\) | −6.09324 | −0.489421 | ||||||||
\(156\) | 4.57099 | 0.365972 | ||||||||
\(157\) | −12.9000 | −1.02953 | −0.514767 | − | 0.857330i | \(-0.672122\pi\) | ||||
−0.514767 | + | 0.857330i | \(0.672122\pi\) | |||||||
\(158\) | −13.5038 | −1.07431 | ||||||||
\(159\) | 4.96934 | 0.394094 | ||||||||
\(160\) | 1.21238 | 0.0958471 | ||||||||
\(161\) | −24.3992 | −1.92292 | ||||||||
\(162\) | 10.8478 | 0.852282 | ||||||||
\(163\) | −2.06249 | −0.161547 | −0.0807733 | − | 0.996733i | \(-0.525739\pi\) | ||||
−0.0807733 | + | 0.996733i | \(0.525739\pi\) | |||||||
\(164\) | 0.478489 | 0.0373637 | ||||||||
\(165\) | −9.52326 | −0.741385 | ||||||||
\(166\) | 9.03972 | 0.701619 | ||||||||
\(167\) | −13.6412 | −1.05559 | −0.527794 | − | 0.849373i | \(-0.676981\pi\) | ||||
−0.527794 | + | 0.849373i | \(0.676981\pi\) | |||||||
\(168\) | −5.96933 | −0.460543 | ||||||||
\(169\) | −7.59516 | −0.584243 | ||||||||
\(170\) | −2.33687 | −0.179230 | ||||||||
\(171\) | 0.108595 | 0.00830449 | ||||||||
\(172\) | 6.52334 | 0.497400 | ||||||||
\(173\) | −2.88871 | −0.219625 | −0.109812 | − | 0.993952i | \(-0.535025\pi\) | ||||
−0.109812 | + | 0.993952i | \(0.535025\pi\) | |||||||
\(174\) | 16.9317 | 1.28359 | ||||||||
\(175\) | 10.7176 | 0.810174 | ||||||||
\(176\) | −3.99510 | −0.301142 | ||||||||
\(177\) | 14.8126 | 1.11338 | ||||||||
\(178\) | 1.30467 | 0.0977895 | ||||||||
\(179\) | 13.2390 | 0.989528 | 0.494764 | − | 0.869027i | \(-0.335255\pi\) | ||||
0.494764 | + | 0.869027i | \(0.335255\pi\) | |||||||
\(180\) | −1.04966 | −0.0782372 | ||||||||
\(181\) | 15.2572 | 1.13406 | 0.567030 | − | 0.823697i | \(-0.308092\pi\) | ||||
0.567030 | + | 0.823697i | \(0.308092\pi\) | |||||||
\(182\) | −7.05826 | −0.523193 | ||||||||
\(183\) | 5.26007 | 0.388836 | ||||||||
\(184\) | −8.03653 | −0.592461 | ||||||||
\(185\) | −5.77252 | −0.424404 | ||||||||
\(186\) | 9.88162 | 0.724556 | ||||||||
\(187\) | 7.70058 | 0.563122 | ||||||||
\(188\) | −2.89425 | −0.211085 | ||||||||
\(189\) | −12.7398 | −0.926685 | ||||||||
\(190\) | 0.152069 | 0.0110322 | ||||||||
\(191\) | 17.8264 | 1.28988 | 0.644938 | − | 0.764235i | \(-0.276883\pi\) | ||||
0.644938 | + | 0.764235i | \(0.276883\pi\) | |||||||
\(192\) | −1.96616 | −0.141895 | ||||||||
\(193\) | −20.0035 | −1.43988 | −0.719941 | − | 0.694035i | \(-0.755831\pi\) | ||||
−0.719941 | + | 0.694035i | \(0.755831\pi\) | |||||||
\(194\) | 15.2284 | 1.09333 | ||||||||
\(195\) | −5.54178 | −0.396855 | ||||||||
\(196\) | 2.21749 | 0.158392 | ||||||||
\(197\) | −2.56418 | −0.182690 | −0.0913450 | − | 0.995819i | \(-0.529117\pi\) | ||||
−0.0913450 | + | 0.995819i | \(0.529117\pi\) | |||||||
\(198\) | 3.45890 | 0.245814 | ||||||||
\(199\) | 23.4744 | 1.66406 | 0.832028 | − | 0.554734i | \(-0.187180\pi\) | ||||
0.832028 | + | 0.554734i | \(0.187180\pi\) | |||||||
\(200\) | 3.53013 | 0.249618 | ||||||||
\(201\) | 20.2442 | 1.42791 | ||||||||
\(202\) | −0.891029 | −0.0626926 | ||||||||
\(203\) | −26.1450 | −1.83502 | ||||||||
\(204\) | 3.78978 | 0.265338 | ||||||||
\(205\) | −0.580111 | −0.0405167 | ||||||||
\(206\) | −5.20638 | −0.362746 | ||||||||
\(207\) | 6.95791 | 0.483608 | ||||||||
\(208\) | −2.32483 | −0.161198 | ||||||||
\(209\) | −0.501104 | −0.0346621 | ||||||||
\(210\) | 7.23710 | 0.499407 | ||||||||
\(211\) | 6.59096 | 0.453740 | 0.226870 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226870 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(212\) | −2.52743 | −0.173585 | ||||||||
\(213\) | −10.7770 | −0.738427 | ||||||||
\(214\) | −8.28823 | −0.566572 | ||||||||
\(215\) | −7.90878 | −0.539374 | ||||||||
\(216\) | −4.19621 | −0.285516 | ||||||||
\(217\) | −15.2586 | −1.03582 | ||||||||
\(218\) | −1.01086 | −0.0684644 | ||||||||
\(219\) | −17.5891 | −1.18856 | ||||||||
\(220\) | 4.84358 | 0.326554 | ||||||||
\(221\) | 4.48113 | 0.301433 | ||||||||
\(222\) | 9.36150 | 0.628303 | ||||||||
\(223\) | −8.00322 | −0.535935 | −0.267968 | − | 0.963428i | \(-0.586352\pi\) | ||||
−0.267968 | + | 0.963428i | \(0.586352\pi\) | |||||||
\(224\) | 3.03603 | 0.202853 | ||||||||
\(225\) | −3.05634 | −0.203756 | ||||||||
\(226\) | −8.04213 | −0.534954 | ||||||||
\(227\) | −12.9737 | −0.861097 | −0.430549 | − | 0.902567i | \(-0.641680\pi\) | ||||
−0.430549 | + | 0.902567i | \(0.641680\pi\) | |||||||
\(228\) | −0.246615 | −0.0163325 | ||||||||
\(229\) | −18.9837 | −1.25448 | −0.627238 | − | 0.778827i | \(-0.715815\pi\) | ||||
−0.627238 | + | 0.778827i | \(0.715815\pi\) | |||||||
\(230\) | 9.74333 | 0.642456 | ||||||||
\(231\) | −23.8481 | −1.56909 | ||||||||
\(232\) | −8.61158 | −0.565378 | ||||||||
\(233\) | −2.29063 | −0.150064 | −0.0750321 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750321 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(234\) | 2.01281 | 0.131581 | ||||||||
\(235\) | 3.50893 | 0.228897 | ||||||||
\(236\) | −7.53375 | −0.490405 | ||||||||
\(237\) | −26.5507 | −1.72465 | ||||||||
\(238\) | −5.85197 | −0.379327 | ||||||||
\(239\) | 26.1796 | 1.69342 | 0.846708 | − | 0.532058i | \(-0.178581\pi\) | ||||
0.846708 | + | 0.532058i | \(0.178581\pi\) | |||||||
\(240\) | 2.38374 | 0.153869 | ||||||||
\(241\) | 19.2456 | 1.23972 | 0.619860 | − | 0.784713i | \(-0.287189\pi\) | ||||
0.619860 | + | 0.784713i | \(0.287189\pi\) | |||||||
\(242\) | −4.96083 | −0.318895 | ||||||||
\(243\) | 8.73984 | 0.560661 | ||||||||
\(244\) | −2.67530 | −0.171269 | ||||||||
\(245\) | −2.68844 | −0.171758 | ||||||||
\(246\) | 0.940785 | 0.0599823 | ||||||||
\(247\) | −0.291603 | −0.0185542 | ||||||||
\(248\) | −5.02585 | −0.319142 | ||||||||
\(249\) | 17.7735 | 1.12635 | ||||||||
\(250\) | −10.3418 | −0.654071 | ||||||||
\(251\) | 16.3253 | 1.03044 | 0.515221 | − | 0.857058i | \(-0.327710\pi\) | ||||
0.515221 | + | 0.857058i | \(0.327710\pi\) | |||||||
\(252\) | −2.62856 | −0.165583 | ||||||||
\(253\) | −32.1067 | −2.01853 | ||||||||
\(254\) | −3.89597 | −0.244455 | ||||||||
\(255\) | −4.59466 | −0.287729 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.7039 | 0.667692 | 0.333846 | − | 0.942628i | \(-0.391653\pi\) | ||||
0.333846 | + | 0.942628i | \(0.391653\pi\) | |||||||
\(258\) | 12.8259 | 0.798508 | ||||||||
\(259\) | −14.4555 | −0.898221 | ||||||||
\(260\) | 2.81858 | 0.174801 | ||||||||
\(261\) | 7.45579 | 0.461502 | ||||||||
\(262\) | −9.83007 | −0.607304 | ||||||||
\(263\) | 7.66329 | 0.472539 | 0.236269 | − | 0.971688i | \(-0.424075\pi\) | ||||
0.236269 | + | 0.971688i | \(0.424075\pi\) | |||||||
\(264\) | −7.85501 | −0.483442 | ||||||||
\(265\) | 3.06421 | 0.188233 | ||||||||
\(266\) | 0.380809 | 0.0233489 | ||||||||
\(267\) | 2.56520 | 0.156988 | ||||||||
\(268\) | −10.2963 | −0.628946 | ||||||||
\(269\) | 14.6744 | 0.894715 | 0.447358 | − | 0.894355i | \(-0.352365\pi\) | ||||
0.447358 | + | 0.894355i | \(0.352365\pi\) | |||||||
\(270\) | 5.08740 | 0.309609 | ||||||||
\(271\) | −11.2820 | −0.685332 | −0.342666 | − | 0.939457i | \(-0.611330\pi\) | ||||
−0.342666 | + | 0.939457i | \(0.611330\pi\) | |||||||
\(272\) | −1.92751 | −0.116872 | ||||||||
\(273\) | −13.8777 | −0.839915 | ||||||||
\(274\) | 7.02100 | 0.424154 | ||||||||
\(275\) | 14.1032 | 0.850457 | ||||||||
\(276\) | −15.8011 | −0.951114 | ||||||||
\(277\) | −18.5157 | −1.11250 | −0.556252 | − | 0.831014i | \(-0.687761\pi\) | ||||
−0.556252 | + | 0.831014i | \(0.687761\pi\) | |||||||
\(278\) | 3.72284 | 0.223281 | ||||||||
\(279\) | 4.35131 | 0.260506 | ||||||||
\(280\) | −3.68083 | −0.219971 | ||||||||
\(281\) | 30.6557 | 1.82877 | 0.914384 | − | 0.404848i | \(-0.132676\pi\) | ||||
0.914384 | + | 0.404848i | \(0.132676\pi\) | |||||||
\(282\) | −5.69055 | −0.338868 | ||||||||
\(283\) | −15.8667 | −0.943179 | −0.471589 | − | 0.881818i | \(-0.656320\pi\) | ||||
−0.471589 | + | 0.881818i | \(0.656320\pi\) | |||||||
\(284\) | 5.48123 | 0.325251 | ||||||||
\(285\) | 0.298991 | 0.0177107 | ||||||||
\(286\) | −9.28794 | −0.549207 | ||||||||
\(287\) | −1.45271 | −0.0857506 | ||||||||
\(288\) | −0.865786 | −0.0510169 | ||||||||
\(289\) | −13.2847 | −0.781454 | ||||||||
\(290\) | 10.4405 | 0.613088 | ||||||||
\(291\) | 29.9414 | 1.75520 | ||||||||
\(292\) | 8.94590 | 0.523519 | ||||||||
\(293\) | −31.3370 | −1.83073 | −0.915363 | − | 0.402631i | \(-0.868096\pi\) | ||||
−0.915363 | + | 0.402631i | \(0.868096\pi\) | |||||||
\(294\) | 4.35994 | 0.254277 | ||||||||
\(295\) | 9.13377 | 0.531789 | ||||||||
\(296\) | −4.76131 | −0.276746 | ||||||||
\(297\) | −16.7643 | −0.972762 | ||||||||
\(298\) | −1.69160 | −0.0979919 | ||||||||
\(299\) | −18.6836 | −1.08050 | ||||||||
\(300\) | 6.94081 | 0.400728 | ||||||||
\(301\) | −19.8051 | −1.14155 | ||||||||
\(302\) | 14.4311 | 0.830417 | ||||||||
\(303\) | −1.75191 | −0.100644 | ||||||||
\(304\) | 0.125430 | 0.00719389 | ||||||||
\(305\) | 3.24349 | 0.185721 | ||||||||
\(306\) | 1.66881 | 0.0953994 | ||||||||
\(307\) | −20.1214 | −1.14839 | −0.574194 | − | 0.818719i | \(-0.694684\pi\) | ||||
−0.574194 | + | 0.818719i | \(0.694684\pi\) | |||||||
\(308\) | 12.1293 | 0.691128 | ||||||||
\(309\) | −10.2366 | −0.582338 | ||||||||
\(310\) | 6.09324 | 0.346073 | ||||||||
\(311\) | −8.16659 | −0.463085 | −0.231543 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231543 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(312\) | −4.57099 | −0.258781 | ||||||||
\(313\) | 2.35668 | 0.133208 | 0.0666038 | − | 0.997780i | \(-0.478784\pi\) | ||||
0.0666038 | + | 0.997780i | \(0.478784\pi\) | |||||||
\(314\) | 12.9000 | 0.727991 | ||||||||
\(315\) | 3.18681 | 0.179556 | ||||||||
\(316\) | 13.5038 | 0.759651 | ||||||||
\(317\) | −12.4194 | −0.697544 | −0.348772 | − | 0.937208i | \(-0.613401\pi\) | ||||
−0.348772 | + | 0.937208i | \(0.613401\pi\) | |||||||
\(318\) | −4.96934 | −0.278667 | ||||||||
\(319\) | −34.4041 | −1.92626 | ||||||||
\(320\) | −1.21238 | −0.0677742 | ||||||||
\(321\) | −16.2960 | −0.909554 | ||||||||
\(322\) | 24.3992 | 1.35971 | ||||||||
\(323\) | −0.241766 | −0.0134522 | ||||||||
\(324\) | −10.8478 | −0.602654 | ||||||||
\(325\) | 8.20696 | 0.455240 | ||||||||
\(326\) | 2.06249 | 0.114231 | ||||||||
\(327\) | −1.98752 | −0.109910 | ||||||||
\(328\) | −0.478489 | −0.0264201 | ||||||||
\(329\) | 8.78703 | 0.484445 | ||||||||
\(330\) | 9.52326 | 0.524238 | ||||||||
\(331\) | −7.38483 | −0.405907 | −0.202953 | − | 0.979188i | \(-0.565054\pi\) | ||||
−0.202953 | + | 0.979188i | \(0.565054\pi\) | |||||||
\(332\) | −9.03972 | −0.496119 | ||||||||
\(333\) | 4.12228 | 0.225899 | ||||||||
\(334\) | 13.6412 | 0.746413 | ||||||||
\(335\) | 12.4830 | 0.682021 | ||||||||
\(336\) | 5.96933 | 0.325653 | ||||||||
\(337\) | −26.7158 | −1.45530 | −0.727651 | − | 0.685948i | \(-0.759388\pi\) | ||||
−0.727651 | + | 0.685948i | \(0.759388\pi\) | |||||||
\(338\) | 7.59516 | 0.413122 | ||||||||
\(339\) | −15.8121 | −0.858796 | ||||||||
\(340\) | 2.33687 | 0.126735 | ||||||||
\(341\) | −20.0788 | −1.08733 | ||||||||
\(342\) | −0.108595 | −0.00587216 | ||||||||
\(343\) | 14.5199 | 0.783998 | ||||||||
\(344\) | −6.52334 | −0.351715 | ||||||||
\(345\) | 19.1569 | 1.03138 | ||||||||
\(346\) | 2.88871 | 0.155298 | ||||||||
\(347\) | 12.8400 | 0.689288 | 0.344644 | − | 0.938733i | \(-0.388000\pi\) | ||||
0.344644 | + | 0.938733i | \(0.388000\pi\) | |||||||
\(348\) | −16.9317 | −0.907637 | ||||||||
\(349\) | −6.78309 | −0.363090 | −0.181545 | − | 0.983383i | \(-0.558110\pi\) | ||||
−0.181545 | + | 0.983383i | \(0.558110\pi\) | |||||||
\(350\) | −10.7176 | −0.572880 | ||||||||
\(351\) | −9.75547 | −0.520709 | ||||||||
\(352\) | 3.99510 | 0.212940 | ||||||||
\(353\) | −7.54677 | −0.401674 | −0.200837 | − | 0.979625i | \(-0.564366\pi\) | ||||
−0.200837 | + | 0.979625i | \(0.564366\pi\) | |||||||
\(354\) | −14.8126 | −0.787279 | ||||||||
\(355\) | −6.64534 | −0.352698 | ||||||||
\(356\) | −1.30467 | −0.0691476 | ||||||||
\(357\) | −11.5059 | −0.608957 | ||||||||
\(358\) | −13.2390 | −0.699702 | ||||||||
\(359\) | 31.9699 | 1.68731 | 0.843653 | − | 0.536888i | \(-0.180400\pi\) | ||||
0.843653 | + | 0.536888i | \(0.180400\pi\) | |||||||
\(360\) | 1.04966 | 0.0553221 | ||||||||
\(361\) | −18.9843 | −0.999172 | ||||||||
\(362\) | −15.2572 | −0.801902 | ||||||||
\(363\) | −9.75380 | −0.511942 | ||||||||
\(364\) | 7.05826 | 0.369954 | ||||||||
\(365\) | −10.8458 | −0.567697 | ||||||||
\(366\) | −5.26007 | −0.274948 | ||||||||
\(367\) | 18.9373 | 0.988518 | 0.494259 | − | 0.869315i | \(-0.335439\pi\) | ||||
0.494259 | + | 0.869315i | \(0.335439\pi\) | |||||||
\(368\) | 8.03653 | 0.418933 | ||||||||
\(369\) | 0.414269 | 0.0215660 | ||||||||
\(370\) | 5.77252 | 0.300099 | ||||||||
\(371\) | 7.67336 | 0.398381 | ||||||||
\(372\) | −9.88162 | −0.512338 | ||||||||
\(373\) | 14.5719 | 0.754504 | 0.377252 | − | 0.926111i | \(-0.376869\pi\) | ||||
0.377252 | + | 0.926111i | \(0.376869\pi\) | |||||||
\(374\) | −7.70058 | −0.398187 | ||||||||
\(375\) | −20.3336 | −1.05002 | ||||||||
\(376\) | 2.89425 | 0.149259 | ||||||||
\(377\) | −20.0205 | −1.03111 | ||||||||
\(378\) | 12.7398 | 0.655265 | ||||||||
\(379\) | −5.07720 | −0.260798 | −0.130399 | − | 0.991462i | \(-0.541626\pi\) | ||||
−0.130399 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(380\) | −0.152069 | −0.00780095 | ||||||||
\(381\) | −7.66009 | −0.392438 | ||||||||
\(382\) | −17.8264 | −0.912080 | ||||||||
\(383\) | 34.2654 | 1.75088 | 0.875440 | − | 0.483327i | \(-0.160572\pi\) | ||||
0.875440 | + | 0.483327i | \(0.160572\pi\) | |||||||
\(384\) | 1.96616 | 0.100335 | ||||||||
\(385\) | −14.7053 | −0.749450 | ||||||||
\(386\) | 20.0035 | 1.01815 | ||||||||
\(387\) | 5.64782 | 0.287095 | ||||||||
\(388\) | −15.2284 | −0.773104 | ||||||||
\(389\) | 14.6450 | 0.742533 | 0.371267 | − | 0.928526i | \(-0.378924\pi\) | ||||
0.371267 | + | 0.928526i | \(0.378924\pi\) | |||||||
\(390\) | 5.54178 | 0.280619 | ||||||||
\(391\) | −15.4904 | −0.783386 | ||||||||
\(392\) | −2.21749 | −0.112000 | ||||||||
\(393\) | −19.3275 | −0.974943 | ||||||||
\(394\) | 2.56418 | 0.129181 | ||||||||
\(395\) | −16.3718 | −0.823755 | ||||||||
\(396\) | −3.45890 | −0.173816 | ||||||||
\(397\) | 25.7608 | 1.29290 | 0.646449 | − | 0.762958i | \(-0.276254\pi\) | ||||
0.646449 | + | 0.762958i | \(0.276254\pi\) | |||||||
\(398\) | −23.4744 | −1.17667 | ||||||||
\(399\) | 0.748731 | 0.0374834 | ||||||||
\(400\) | −3.53013 | −0.176507 | ||||||||
\(401\) | −19.5958 | −0.978568 | −0.489284 | − | 0.872125i | \(-0.662742\pi\) | ||||
−0.489284 | + | 0.872125i | \(0.662742\pi\) | |||||||
\(402\) | −20.2442 | −1.00969 | ||||||||
\(403\) | −11.6843 | −0.582034 | ||||||||
\(404\) | 0.891029 | 0.0443303 | ||||||||
\(405\) | 13.1516 | 0.653510 | ||||||||
\(406\) | 26.1450 | 1.29756 | ||||||||
\(407\) | −19.0219 | −0.942882 | ||||||||
\(408\) | −3.78978 | −0.187622 | ||||||||
\(409\) | −35.6758 | −1.76405 | −0.882027 | − | 0.471199i | \(-0.843821\pi\) | ||||
−0.882027 | + | 0.471199i | \(0.843821\pi\) | |||||||
\(410\) | 0.580111 | 0.0286496 | ||||||||
\(411\) | 13.8044 | 0.680921 | ||||||||
\(412\) | 5.20638 | 0.256500 | ||||||||
\(413\) | 22.8727 | 1.12549 | ||||||||
\(414\) | −6.95791 | −0.341963 | ||||||||
\(415\) | 10.9596 | 0.537985 | ||||||||
\(416\) | 2.32483 | 0.113984 | ||||||||
\(417\) | 7.31970 | 0.358447 | ||||||||
\(418\) | 0.501104 | 0.0245098 | ||||||||
\(419\) | 3.31570 | 0.161983 | 0.0809913 | − | 0.996715i | \(-0.474191\pi\) | ||||
0.0809913 | + | 0.996715i | \(0.474191\pi\) | |||||||
\(420\) | −7.23710 | −0.353134 | ||||||||
\(421\) | 9.67605 | 0.471582 | 0.235791 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235791 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(422\) | −6.59096 | −0.320843 | ||||||||
\(423\) | −2.50580 | −0.121836 | ||||||||
\(424\) | 2.52743 | 0.122743 | ||||||||
\(425\) | 6.80435 | 0.330059 | ||||||||
\(426\) | 10.7770 | 0.522147 | ||||||||
\(427\) | 8.12231 | 0.393066 | ||||||||
\(428\) | 8.28823 | 0.400627 | ||||||||
\(429\) | −18.2616 | −0.881677 | ||||||||
\(430\) | 7.90878 | 0.381395 | ||||||||
\(431\) | −21.4587 | −1.03363 | −0.516816 | − | 0.856097i | \(-0.672883\pi\) | ||||
−0.516816 | + | 0.856097i | \(0.672883\pi\) | |||||||
\(432\) | 4.19621 | 0.201890 | ||||||||
\(433\) | −20.2969 | −0.975409 | −0.487705 | − | 0.873009i | \(-0.662166\pi\) | ||||
−0.487705 | + | 0.873009i | \(0.662166\pi\) | |||||||
\(434\) | 15.2586 | 0.732438 | ||||||||
\(435\) | 20.5277 | 0.984229 | ||||||||
\(436\) | 1.01086 | 0.0484116 | ||||||||
\(437\) | 1.00802 | 0.0482201 | ||||||||
\(438\) | 17.5891 | 0.840439 | ||||||||
\(439\) | 26.0058 | 1.24119 | 0.620593 | − | 0.784133i | \(-0.286892\pi\) | ||||
0.620593 | + | 0.784133i | \(0.286892\pi\) | |||||||
\(440\) | −4.84358 | −0.230909 | ||||||||
\(441\) | 1.91987 | 0.0914225 | ||||||||
\(442\) | −4.48113 | −0.213145 | ||||||||
\(443\) | −1.33689 | −0.0635178 | −0.0317589 | − | 0.999496i | \(-0.510111\pi\) | ||||
−0.0317589 | + | 0.999496i | \(0.510111\pi\) | |||||||
\(444\) | −9.36150 | −0.444277 | ||||||||
\(445\) | 1.58176 | 0.0749827 | ||||||||
\(446\) | 8.00322 | 0.378964 | ||||||||
\(447\) | −3.32596 | −0.157313 | ||||||||
\(448\) | −3.03603 | −0.143439 | ||||||||
\(449\) | −20.7627 | −0.979853 | −0.489926 | − | 0.871764i | \(-0.662976\pi\) | ||||
−0.489926 | + | 0.871764i | \(0.662976\pi\) | |||||||
\(450\) | 3.05634 | 0.144077 | ||||||||
\(451\) | −1.91161 | −0.0900142 | ||||||||
\(452\) | 8.04213 | 0.378270 | ||||||||
\(453\) | 28.3739 | 1.33312 | ||||||||
\(454\) | 12.9737 | 0.608888 | ||||||||
\(455\) | −8.55730 | −0.401173 | ||||||||
\(456\) | 0.246615 | 0.0115488 | ||||||||
\(457\) | −24.6091 | −1.15117 | −0.575583 | − | 0.817743i | \(-0.695225\pi\) | ||||
−0.575583 | + | 0.817743i | \(0.695225\pi\) | |||||||
\(458\) | 18.9837 | 0.887049 | ||||||||
\(459\) | −8.08821 | −0.377525 | ||||||||
\(460\) | −9.74333 | −0.454285 | ||||||||
\(461\) | −5.21566 | −0.242918 | −0.121459 | − | 0.992596i | \(-0.538757\pi\) | ||||
−0.121459 | + | 0.992596i | \(0.538757\pi\) | |||||||
\(462\) | 23.8481 | 1.10951 | ||||||||
\(463\) | 17.1556 | 0.797290 | 0.398645 | − | 0.917105i | \(-0.369480\pi\) | ||||
0.398645 | + | 0.917105i | \(0.369480\pi\) | |||||||
\(464\) | 8.61158 | 0.399782 | ||||||||
\(465\) | 11.9803 | 0.555573 | ||||||||
\(466\) | 2.29063 | 0.106111 | ||||||||
\(467\) | −22.2729 | −1.03067 | −0.515333 | − | 0.856990i | \(-0.672332\pi\) | ||||
−0.515333 | + | 0.856990i | \(0.672332\pi\) | |||||||
\(468\) | −2.01281 | −0.0930421 | ||||||||
\(469\) | 31.2599 | 1.44345 | ||||||||
\(470\) | −3.50893 | −0.161855 | ||||||||
\(471\) | 25.3635 | 1.16869 | ||||||||
\(472\) | 7.53375 | 0.346769 | ||||||||
\(473\) | −26.0614 | −1.19831 | ||||||||
\(474\) | 26.5507 | 1.21952 | ||||||||
\(475\) | −0.442783 | −0.0203163 | ||||||||
\(476\) | 5.85197 | 0.268225 | ||||||||
\(477\) | −2.18822 | −0.100192 | ||||||||
\(478\) | −26.1796 | −1.19743 | ||||||||
\(479\) | 4.87943 | 0.222947 | 0.111473 | − | 0.993767i | \(-0.464443\pi\) | ||||
0.111473 | + | 0.993767i | \(0.464443\pi\) | |||||||
\(480\) | −2.38374 | −0.108802 | ||||||||
\(481\) | −11.0692 | −0.504714 | ||||||||
\(482\) | −19.2456 | −0.876614 | ||||||||
\(483\) | 47.9726 | 2.18283 | ||||||||
\(484\) | 4.96083 | 0.225492 | ||||||||
\(485\) | 18.4626 | 0.838343 | ||||||||
\(486\) | −8.73984 | −0.396447 | ||||||||
\(487\) | 13.4611 | 0.609979 | 0.304990 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304990 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(488\) | 2.67530 | 0.121105 | ||||||||
\(489\) | 4.05518 | 0.183382 | ||||||||
\(490\) | 2.68844 | 0.121451 | ||||||||
\(491\) | −28.9472 | −1.30637 | −0.653183 | − | 0.757200i | \(-0.726567\pi\) | ||||
−0.653183 | + | 0.757200i | \(0.726567\pi\) | |||||||
\(492\) | −0.940785 | −0.0424139 | ||||||||
\(493\) | −16.5989 | −0.747575 | ||||||||
\(494\) | 0.291603 | 0.0131198 | ||||||||
\(495\) | 4.19351 | 0.188484 | ||||||||
\(496\) | 5.02585 | 0.225667 | ||||||||
\(497\) | −16.6412 | −0.746460 | ||||||||
\(498\) | −17.7735 | −0.796452 | ||||||||
\(499\) | −27.7545 | −1.24246 | −0.621231 | − | 0.783627i | \(-0.713367\pi\) | ||||
−0.621231 | + | 0.783627i | \(0.713367\pi\) | |||||||
\(500\) | 10.3418 | 0.462498 | ||||||||
\(501\) | 26.8208 | 1.19826 | ||||||||
\(502\) | −16.3253 | −0.728632 | ||||||||
\(503\) | 1.89185 | 0.0843532 | 0.0421766 | − | 0.999110i | \(-0.486571\pi\) | ||||
0.0421766 | + | 0.999110i | \(0.486571\pi\) | |||||||
\(504\) | 2.62856 | 0.117085 | ||||||||
\(505\) | −1.08027 | −0.0480712 | ||||||||
\(506\) | 32.1067 | 1.42732 | ||||||||
\(507\) | 14.9333 | 0.663211 | ||||||||
\(508\) | 3.89597 | 0.172856 | ||||||||
\(509\) | −36.4667 | −1.61636 | −0.808179 | − | 0.588937i | \(-0.799547\pi\) | ||||
−0.808179 | + | 0.588937i | \(0.799547\pi\) | |||||||
\(510\) | 4.59466 | 0.203455 | ||||||||
\(511\) | −27.1601 | −1.20149 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.526329 | 0.0232380 | ||||||||
\(514\) | −10.7039 | −0.472130 | ||||||||
\(515\) | −6.31211 | −0.278145 | ||||||||
\(516\) | −12.8259 | −0.564631 | ||||||||
\(517\) | 11.5628 | 0.508532 | ||||||||
\(518\) | 14.4555 | 0.635138 | ||||||||
\(519\) | 5.67967 | 0.249310 | ||||||||
\(520\) | −2.81858 | −0.123603 | ||||||||
\(521\) | 4.31284 | 0.188949 | 0.0944745 | − | 0.995527i | \(-0.469883\pi\) | ||||
0.0944745 | + | 0.995527i | \(0.469883\pi\) | |||||||
\(522\) | −7.45579 | −0.326331 | ||||||||
\(523\) | −38.2053 | −1.67060 | −0.835301 | − | 0.549793i | \(-0.814707\pi\) | ||||
−0.835301 | + | 0.549793i | \(0.814707\pi\) | |||||||
\(524\) | 9.83007 | 0.429428 | ||||||||
\(525\) | −21.0725 | −0.919680 | ||||||||
\(526\) | −7.66329 | −0.334135 | ||||||||
\(527\) | −9.68735 | −0.421988 | ||||||||
\(528\) | 7.85501 | 0.341845 | ||||||||
\(529\) | 41.5858 | 1.80808 | ||||||||
\(530\) | −3.06421 | −0.133101 | ||||||||
\(531\) | −6.52262 | −0.283057 | ||||||||
\(532\) | −0.380809 | −0.0165101 | ||||||||
\(533\) | −1.11241 | −0.0481836 | ||||||||
\(534\) | −2.56520 | −0.111007 | ||||||||
\(535\) | −10.0485 | −0.434434 | ||||||||
\(536\) | 10.2963 | 0.444732 | ||||||||
\(537\) | −26.0300 | −1.12328 | ||||||||
\(538\) | −14.6744 | −0.632659 | ||||||||
\(539\) | −8.85910 | −0.381588 | ||||||||
\(540\) | −5.08740 | −0.218927 | ||||||||
\(541\) | 10.5835 | 0.455021 | 0.227510 | − | 0.973776i | \(-0.426941\pi\) | ||||
0.227510 | + | 0.973776i | \(0.426941\pi\) | |||||||
\(542\) | 11.2820 | 0.484603 | ||||||||
\(543\) | −29.9982 | −1.28734 | ||||||||
\(544\) | 1.92751 | 0.0826411 | ||||||||
\(545\) | −1.22555 | −0.0524969 | ||||||||
\(546\) | 13.8777 | 0.593910 | ||||||||
\(547\) | −3.51632 | −0.150347 | −0.0751735 | − | 0.997170i | \(-0.523951\pi\) | ||||
−0.0751735 | + | 0.997170i | \(0.523951\pi\) | |||||||
\(548\) | −7.02100 | −0.299922 | ||||||||
\(549\) | −2.31624 | −0.0988547 | ||||||||
\(550\) | −14.1032 | −0.601364 | ||||||||
\(551\) | 1.08015 | 0.0460158 | ||||||||
\(552\) | 15.8011 | 0.672539 | ||||||||
\(553\) | −40.9981 | −1.74342 | ||||||||
\(554\) | 18.5157 | 0.786659 | ||||||||
\(555\) | 11.3497 | 0.481768 | ||||||||
\(556\) | −3.72284 | −0.157884 | ||||||||
\(557\) | 2.12170 | 0.0898992 | 0.0449496 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449496 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(558\) | −4.35131 | −0.184206 | ||||||||
\(559\) | −15.1657 | −0.641440 | ||||||||
\(560\) | 3.68083 | 0.155543 | ||||||||
\(561\) | −15.1406 | −0.639235 | ||||||||
\(562\) | −30.6557 | −1.29313 | ||||||||
\(563\) | 17.4414 | 0.735069 | 0.367535 | − | 0.930010i | \(-0.380202\pi\) | ||||
0.367535 | + | 0.930010i | \(0.380202\pi\) | |||||||
\(564\) | 5.69055 | 0.239616 | ||||||||
\(565\) | −9.75012 | −0.410191 | ||||||||
\(566\) | 15.8667 | 0.666928 | ||||||||
\(567\) | 32.9342 | 1.38311 | ||||||||
\(568\) | −5.48123 | −0.229988 | ||||||||
\(569\) | −1.58951 | −0.0666358 | −0.0333179 | − | 0.999445i | \(-0.510607\pi\) | ||||
−0.0333179 | + | 0.999445i | \(0.510607\pi\) | |||||||
\(570\) | −0.298991 | −0.0125234 | ||||||||
\(571\) | −14.7370 | −0.616723 | −0.308361 | − | 0.951269i | \(-0.599781\pi\) | ||||
−0.308361 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(572\) | 9.28794 | 0.388348 | ||||||||
\(573\) | −35.0496 | −1.46422 | ||||||||
\(574\) | 1.45271 | 0.0606348 | ||||||||
\(575\) | −28.3700 | −1.18311 | ||||||||
\(576\) | 0.865786 | 0.0360744 | ||||||||
\(577\) | 14.9053 | 0.620516 | 0.310258 | − | 0.950652i | \(-0.399585\pi\) | ||||
0.310258 | + | 0.950652i | \(0.399585\pi\) | |||||||
\(578\) | 13.2847 | 0.552572 | ||||||||
\(579\) | 39.3300 | 1.63450 | ||||||||
\(580\) | −10.4405 | −0.433519 | ||||||||
\(581\) | 27.4449 | 1.13861 | ||||||||
\(582\) | −29.9414 | −1.24111 | ||||||||
\(583\) | 10.0973 | 0.418189 | ||||||||
\(584\) | −8.94590 | −0.370184 | ||||||||
\(585\) | 2.44029 | 0.100894 | ||||||||
\(586\) | 31.3370 | 1.29452 | ||||||||
\(587\) | 38.2985 | 1.58075 | 0.790374 | − | 0.612625i | \(-0.209886\pi\) | ||||
0.790374 | + | 0.612625i | \(0.209886\pi\) | |||||||
\(588\) | −4.35994 | −0.179801 | ||||||||
\(589\) | 0.630390 | 0.0259748 | ||||||||
\(590\) | −9.13377 | −0.376031 | ||||||||
\(591\) | 5.04158 | 0.207383 | ||||||||
\(592\) | 4.76131 | 0.195689 | ||||||||
\(593\) | 43.5909 | 1.79006 | 0.895031 | − | 0.446004i | \(-0.147153\pi\) | ||||
0.895031 | + | 0.446004i | \(0.147153\pi\) | |||||||
\(594\) | 16.7643 | 0.687846 | ||||||||
\(595\) | −7.09481 | −0.290859 | ||||||||
\(596\) | 1.69160 | 0.0692907 | ||||||||
\(597\) | −46.1544 | −1.88898 | ||||||||
\(598\) | 18.6836 | 0.764028 | ||||||||
\(599\) | 23.3674 | 0.954765 | 0.477383 | − | 0.878696i | \(-0.341586\pi\) | ||||
0.477383 | + | 0.878696i | \(0.341586\pi\) | |||||||
\(600\) | −6.94081 | −0.283357 | ||||||||
\(601\) | 12.6980 | 0.517964 | 0.258982 | − | 0.965882i | \(-0.416613\pi\) | ||||
0.258982 | + | 0.965882i | \(0.416613\pi\) | |||||||
\(602\) | 19.8051 | 0.807195 | ||||||||
\(603\) | −8.91439 | −0.363022 | ||||||||
\(604\) | −14.4311 | −0.587193 | ||||||||
\(605\) | −6.01442 | −0.244521 | ||||||||
\(606\) | 1.75191 | 0.0711663 | ||||||||
\(607\) | −36.0635 | −1.46377 | −0.731886 | − | 0.681427i | \(-0.761360\pi\) | ||||
−0.731886 | + | 0.681427i | \(0.761360\pi\) | |||||||
\(608\) | −0.125430 | −0.00508685 | ||||||||
\(609\) | 51.4053 | 2.08305 | ||||||||
\(610\) | −3.24349 | −0.131325 | ||||||||
\(611\) | 6.72864 | 0.272212 | ||||||||
\(612\) | −1.66881 | −0.0674576 | ||||||||
\(613\) | −32.1028 | −1.29662 | −0.648310 | − | 0.761377i | \(-0.724524\pi\) | ||||
−0.648310 | + | 0.761377i | \(0.724524\pi\) | |||||||
\(614\) | 20.1214 | 0.812033 | ||||||||
\(615\) | 1.14059 | 0.0459930 | ||||||||
\(616\) | −12.1293 | −0.488702 | ||||||||
\(617\) | 2.39790 | 0.0965359 | 0.0482680 | − | 0.998834i | \(-0.484630\pi\) | ||||
0.0482680 | + | 0.998834i | \(0.484630\pi\) | |||||||
\(618\) | 10.2366 | 0.411775 | ||||||||
\(619\) | −16.7314 | −0.672491 | −0.336246 | − | 0.941774i | \(-0.609157\pi\) | ||||
−0.336246 | + | 0.941774i | \(0.609157\pi\) | |||||||
\(620\) | −6.09324 | −0.244710 | ||||||||
\(621\) | 33.7229 | 1.35325 | ||||||||
\(622\) | 8.16659 | 0.327451 | ||||||||
\(623\) | 3.96103 | 0.158695 | ||||||||
\(624\) | 4.57099 | 0.182986 | ||||||||
\(625\) | 5.11250 | 0.204500 | ||||||||
\(626\) | −2.35668 | −0.0941919 | ||||||||
\(627\) | 0.985251 | 0.0393471 | ||||||||
\(628\) | −12.9000 | −0.514767 | ||||||||
\(629\) | −9.17745 | −0.365929 | ||||||||
\(630\) | −3.18681 | −0.126966 | ||||||||
\(631\) | 29.8096 | 1.18670 | 0.593351 | − | 0.804944i | \(-0.297805\pi\) | ||||
0.593351 | + | 0.804944i | \(0.297805\pi\) | |||||||
\(632\) | −13.5038 | −0.537154 | ||||||||
\(633\) | −12.9589 | −0.515069 | ||||||||
\(634\) | 12.4194 | 0.493238 | ||||||||
\(635\) | −4.72339 | −0.187442 | ||||||||
\(636\) | 4.96934 | 0.197047 | ||||||||
\(637\) | −5.15529 | −0.204260 | ||||||||
\(638\) | 34.4041 | 1.36207 | ||||||||
\(639\) | 4.74558 | 0.187732 | ||||||||
\(640\) | 1.21238 | 0.0479236 | ||||||||
\(641\) | −3.18129 | −0.125654 | −0.0628268 | − | 0.998024i | \(-0.520012\pi\) | ||||
−0.0628268 | + | 0.998024i | \(0.520012\pi\) | |||||||
\(642\) | 16.2960 | 0.643152 | ||||||||
\(643\) | 12.9328 | 0.510018 | 0.255009 | − | 0.966939i | \(-0.417921\pi\) | ||||
0.255009 | + | 0.966939i | \(0.417921\pi\) | |||||||
\(644\) | −24.3992 | −0.961461 | ||||||||
\(645\) | 15.5499 | 0.612278 | ||||||||
\(646\) | 0.241766 | 0.00951217 | ||||||||
\(647\) | −6.44584 | −0.253412 | −0.126706 | − | 0.991940i | \(-0.540441\pi\) | ||||
−0.126706 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(648\) | 10.8478 | 0.426141 | ||||||||
\(649\) | 30.0981 | 1.18145 | ||||||||
\(650\) | −8.20696 | −0.321904 | ||||||||
\(651\) | 30.0009 | 1.17583 | ||||||||
\(652\) | −2.06249 | −0.0807733 | ||||||||
\(653\) | −20.8830 | −0.817216 | −0.408608 | − | 0.912710i | \(-0.633986\pi\) | ||||
−0.408608 | + | 0.912710i | \(0.633986\pi\) | |||||||
\(654\) | 1.98752 | 0.0777182 | ||||||||
\(655\) | −11.9178 | −0.465666 | ||||||||
\(656\) | 0.478489 | 0.0186818 | ||||||||
\(657\) | 7.74524 | 0.302171 | ||||||||
\(658\) | −8.78703 | −0.342554 | ||||||||
\(659\) | −31.5599 | −1.22940 | −0.614699 | − | 0.788762i | \(-0.710723\pi\) | ||||
−0.614699 | + | 0.788762i | \(0.710723\pi\) | |||||||
\(660\) | −9.52326 | −0.370693 | ||||||||
\(661\) | 20.7960 | 0.808870 | 0.404435 | − | 0.914567i | \(-0.367468\pi\) | ||||
0.404435 | + | 0.914567i | \(0.367468\pi\) | |||||||
\(662\) | 7.38483 | 0.287020 | ||||||||
\(663\) | −8.81061 | −0.342176 | ||||||||
\(664\) | 9.03972 | 0.350809 | ||||||||
\(665\) | 0.461685 | 0.0179034 | ||||||||
\(666\) | −4.12228 | −0.159735 | ||||||||
\(667\) | 69.2072 | 2.67971 | ||||||||
\(668\) | −13.6412 | −0.527794 | ||||||||
\(669\) | 15.7356 | 0.608374 | ||||||||
\(670\) | −12.4830 | −0.482261 | ||||||||
\(671\) | 10.6881 | 0.412610 | ||||||||
\(672\) | −5.96933 | −0.230272 | ||||||||
\(673\) | 15.9172 | 0.613563 | 0.306782 | − | 0.951780i | \(-0.400748\pi\) | ||||
0.306782 | + | 0.951780i | \(0.400748\pi\) | |||||||
\(674\) | 26.7158 | 1.02905 | ||||||||
\(675\) | −14.8132 | −0.570159 | ||||||||
\(676\) | −7.59516 | −0.292121 | ||||||||
\(677\) | −10.5731 | −0.406357 | −0.203178 | − | 0.979142i | \(-0.565127\pi\) | ||||
−0.203178 | + | 0.979142i | \(0.565127\pi\) | |||||||
\(678\) | 15.8121 | 0.607261 | ||||||||
\(679\) | 46.2338 | 1.77429 | ||||||||
\(680\) | −2.33687 | −0.0896149 | ||||||||
\(681\) | 25.5084 | 0.977486 | ||||||||
\(682\) | 20.0788 | 0.768856 | ||||||||
\(683\) | 7.93608 | 0.303666 | 0.151833 | − | 0.988406i | \(-0.451482\pi\) | ||||
0.151833 | + | 0.988406i | \(0.451482\pi\) | |||||||
\(684\) | 0.108595 | 0.00415225 | ||||||||
\(685\) | 8.51212 | 0.325232 | ||||||||
\(686\) | −14.5199 | −0.554371 | ||||||||
\(687\) | 37.3249 | 1.42404 | ||||||||
\(688\) | 6.52334 | 0.248700 | ||||||||
\(689\) | 5.87585 | 0.223852 | ||||||||
\(690\) | −19.1569 | −0.729293 | ||||||||
\(691\) | 46.8791 | 1.78336 | 0.891682 | − | 0.452663i | \(-0.149526\pi\) | ||||
0.891682 | + | 0.452663i | \(0.149526\pi\) | |||||||
\(692\) | −2.88871 | −0.109812 | ||||||||
\(693\) | 10.5013 | 0.398913 | ||||||||
\(694\) | −12.8400 | −0.487400 | ||||||||
\(695\) | 4.51350 | 0.171207 | ||||||||
\(696\) | 16.9317 | 0.641796 | ||||||||
\(697\) | −0.922289 | −0.0349342 | ||||||||
\(698\) | 6.78309 | 0.256744 | ||||||||
\(699\) | 4.50375 | 0.170347 | ||||||||
\(700\) | 10.7176 | 0.405087 | ||||||||
\(701\) | 11.6287 | 0.439211 | 0.219606 | − | 0.975589i | \(-0.429523\pi\) | ||||
0.219606 | + | 0.975589i | \(0.429523\pi\) | |||||||
\(702\) | 9.75547 | 0.368197 | ||||||||
\(703\) | 0.597210 | 0.0225242 | ||||||||
\(704\) | −3.99510 | −0.150571 | ||||||||
\(705\) | −6.89912 | −0.259836 | ||||||||
\(706\) | 7.54677 | 0.284026 | ||||||||
\(707\) | −2.70519 | −0.101739 | ||||||||
\(708\) | 14.8126 | 0.556690 | ||||||||
\(709\) | −15.1422 | −0.568675 | −0.284338 | − | 0.958724i | \(-0.591774\pi\) | ||||
−0.284338 | + | 0.958724i | \(0.591774\pi\) | |||||||
\(710\) | 6.64534 | 0.249395 | ||||||||
\(711\) | 11.6914 | 0.438463 | ||||||||
\(712\) | 1.30467 | 0.0488948 | ||||||||
\(713\) | 40.3904 | 1.51263 | ||||||||
\(714\) | 11.5059 | 0.430598 | ||||||||
\(715\) | −11.2605 | −0.421120 | ||||||||
\(716\) | 13.2390 | 0.494764 | ||||||||
\(717\) | −51.4732 | −1.92230 | ||||||||
\(718\) | −31.9699 | −1.19311 | ||||||||
\(719\) | −17.3155 | −0.645761 | −0.322880 | − | 0.946440i | \(-0.604651\pi\) | ||||
−0.322880 | + | 0.946440i | \(0.604651\pi\) | |||||||
\(720\) | −1.04966 | −0.0391186 | ||||||||
\(721\) | −15.8067 | −0.588674 | ||||||||
\(722\) | 18.9843 | 0.706521 | ||||||||
\(723\) | −37.8400 | −1.40728 | ||||||||
\(724\) | 15.2572 | 0.567030 | ||||||||
\(725\) | −30.4000 | −1.12903 | ||||||||
\(726\) | 9.75380 | 0.361997 | ||||||||
\(727\) | −46.3764 | −1.72000 | −0.860002 | − | 0.510291i | \(-0.829538\pi\) | ||||
−0.860002 | + | 0.510291i | \(0.829538\pi\) | |||||||
\(728\) | −7.05826 | −0.261597 | ||||||||
\(729\) | 15.3594 | 0.568866 | ||||||||
\(730\) | 10.8458 | 0.401423 | ||||||||
\(731\) | −12.5738 | −0.465058 | ||||||||
\(732\) | 5.26007 | 0.194418 | ||||||||
\(733\) | −15.7861 | −0.583074 | −0.291537 | − | 0.956560i | \(-0.594167\pi\) | ||||
−0.291537 | + | 0.956560i | \(0.594167\pi\) | |||||||
\(734\) | −18.9373 | −0.698988 | ||||||||
\(735\) | 5.28591 | 0.194974 | ||||||||
\(736\) | −8.03653 | −0.296230 | ||||||||
\(737\) | 41.1347 | 1.51522 | ||||||||
\(738\) | −0.414269 | −0.0152495 | ||||||||
\(739\) | 36.7794 | 1.35295 | 0.676475 | − | 0.736465i | \(-0.263507\pi\) | ||||
0.676475 | + | 0.736465i | \(0.263507\pi\) | |||||||
\(740\) | −5.77252 | −0.212202 | ||||||||
\(741\) | 0.573338 | 0.0210621 | ||||||||
\(742\) | −7.67336 | −0.281698 | ||||||||
\(743\) | −8.59866 | −0.315454 | −0.157727 | − | 0.987483i | \(-0.550417\pi\) | ||||
−0.157727 | + | 0.987483i | \(0.550417\pi\) | |||||||
\(744\) | 9.88162 | 0.362278 | ||||||||
\(745\) | −2.05087 | −0.0751379 | ||||||||
\(746\) | −14.5719 | −0.533515 | ||||||||
\(747\) | −7.82647 | −0.286356 | ||||||||
\(748\) | 7.70058 | 0.281561 | ||||||||
\(749\) | −25.1633 | −0.919449 | ||||||||
\(750\) | 20.3336 | 0.742477 | ||||||||
\(751\) | −8.82635 | −0.322078 | −0.161039 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161039 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(752\) | −2.89425 | −0.105542 | ||||||||
\(753\) | −32.0981 | −1.16972 | ||||||||
\(754\) | 20.0205 | 0.729102 | ||||||||
\(755\) | 17.4960 | 0.636744 | ||||||||
\(756\) | −12.7398 | −0.463343 | ||||||||
\(757\) | −16.2358 | −0.590101 | −0.295051 | − | 0.955482i | \(-0.595336\pi\) | ||||
−0.295051 | + | 0.955482i | \(0.595336\pi\) | |||||||
\(758\) | 5.07720 | 0.184412 | ||||||||
\(759\) | 63.1270 | 2.29136 | ||||||||
\(760\) | 0.152069 | 0.00551611 | ||||||||
\(761\) | 18.5682 | 0.673095 | 0.336548 | − | 0.941666i | \(-0.390741\pi\) | ||||
0.336548 | + | 0.941666i | \(0.390741\pi\) | |||||||
\(762\) | 7.66009 | 0.277496 | ||||||||
\(763\) | −3.06902 | −0.111106 | ||||||||
\(764\) | 17.8264 | 0.644938 | ||||||||
\(765\) | 2.02323 | 0.0731501 | ||||||||
\(766\) | −34.2654 | −1.23806 | ||||||||
\(767\) | 17.5147 | 0.632419 | ||||||||
\(768\) | −1.96616 | −0.0709477 | ||||||||
\(769\) | −19.2383 | −0.693751 | −0.346875 | − | 0.937911i | \(-0.612757\pi\) | ||||
−0.346875 | + | 0.937911i | \(0.612757\pi\) | |||||||
\(770\) | 14.7053 | 0.529941 | ||||||||
\(771\) | −21.0456 | −0.757940 | ||||||||
\(772\) | −20.0035 | −0.719941 | ||||||||
\(773\) | −16.7102 | −0.601023 | −0.300511 | − | 0.953778i | \(-0.597157\pi\) | ||||
−0.300511 | + | 0.953778i | \(0.597157\pi\) | |||||||
\(774\) | −5.64782 | −0.203007 | ||||||||
\(775\) | −17.7419 | −0.637308 | ||||||||
\(776\) | 15.2284 | 0.546667 | ||||||||
\(777\) | 28.4218 | 1.01963 | ||||||||
\(778\) | −14.6450 | −0.525050 | ||||||||
\(779\) | 0.0600167 | 0.00215032 | ||||||||
\(780\) | −5.54178 | −0.198428 | ||||||||
\(781\) | −21.8981 | −0.783575 | ||||||||
\(782\) | 15.4904 | 0.553937 | ||||||||
\(783\) | 36.1360 | 1.29139 | ||||||||
\(784\) | 2.21749 | 0.0791961 | ||||||||
\(785\) | 15.6398 | 0.558207 | ||||||||
\(786\) | 19.3275 | 0.689389 | ||||||||
\(787\) | −22.6255 | −0.806512 | −0.403256 | − | 0.915087i | \(-0.632122\pi\) | ||||
−0.403256 | + | 0.915087i | \(0.632122\pi\) | |||||||
\(788\) | −2.56418 | −0.0913450 | ||||||||
\(789\) | −15.0673 | −0.536409 | ||||||||
\(790\) | 16.3718 | 0.582483 | ||||||||
\(791\) | −24.4162 | −0.868139 | ||||||||
\(792\) | 3.45890 | 0.122907 | ||||||||
\(793\) | 6.21963 | 0.220866 | ||||||||
\(794\) | −25.7608 | −0.914216 | ||||||||
\(795\) | −6.02473 | −0.213675 | ||||||||
\(796\) | 23.4744 | 0.832028 | ||||||||
\(797\) | 4.03878 | 0.143061 | 0.0715305 | − | 0.997438i | \(-0.477212\pi\) | ||||
0.0715305 | + | 0.997438i | \(0.477212\pi\) | |||||||
\(798\) | −0.748731 | −0.0265048 | ||||||||
\(799\) | 5.57868 | 0.197359 | ||||||||
\(800\) | 3.53013 | 0.124809 | ||||||||
\(801\) | −1.12957 | −0.0399114 | ||||||||
\(802\) | 19.5958 | 0.691952 | ||||||||
\(803\) | −35.7398 | −1.26123 | ||||||||
\(804\) | 20.2442 | 0.713957 | ||||||||
\(805\) | 29.5811 | 1.04260 | ||||||||
\(806\) | 11.6843 | 0.411560 | ||||||||
\(807\) | −28.8523 | −1.01565 | ||||||||
\(808\) | −0.891029 | −0.0313463 | ||||||||
\(809\) | −24.8416 | −0.873384 | −0.436692 | − | 0.899611i | \(-0.643850\pi\) | ||||
−0.436692 | + | 0.899611i | \(0.643850\pi\) | |||||||
\(810\) | −13.1516 | −0.462101 | ||||||||
\(811\) | 7.79868 | 0.273849 | 0.136924 | − | 0.990581i | \(-0.456278\pi\) | ||||
0.136924 | + | 0.990581i | \(0.456278\pi\) | |||||||
\(812\) | −26.1450 | −0.917511 | ||||||||
\(813\) | 22.1822 | 0.777964 | ||||||||
\(814\) | 19.0219 | 0.666718 | ||||||||
\(815\) | 2.50052 | 0.0875894 | ||||||||
\(816\) | 3.78978 | 0.132669 | ||||||||
\(817\) | 0.818221 | 0.0286259 | ||||||||
\(818\) | 35.6758 | 1.24737 | ||||||||
\(819\) | 6.11095 | 0.213534 | ||||||||
\(820\) | −0.580111 | −0.0202583 | ||||||||
\(821\) | −10.2558 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(822\) | −13.8044 | −0.481484 | ||||||||
\(823\) | −3.57707 | −0.124689 | −0.0623444 | − | 0.998055i | \(-0.519858\pi\) | ||||
−0.0623444 | + | 0.998055i | \(0.519858\pi\) | |||||||
\(824\) | −5.20638 | −0.181373 | ||||||||
\(825\) | −27.7292 | −0.965408 | ||||||||
\(826\) | −22.8727 | −0.795843 | ||||||||
\(827\) | 51.9404 | 1.80615 | 0.903073 | − | 0.429487i | \(-0.141306\pi\) | ||||
0.903073 | + | 0.429487i | \(0.141306\pi\) | |||||||
\(828\) | 6.95791 | 0.241804 | ||||||||
\(829\) | 52.6136 | 1.82735 | 0.913673 | − | 0.406451i | \(-0.133234\pi\) | ||||
0.913673 | + | 0.406451i | \(0.133234\pi\) | |||||||
\(830\) | −10.9596 | −0.380413 | ||||||||
\(831\) | 36.4049 | 1.26287 | ||||||||
\(832\) | −2.32483 | −0.0805990 | ||||||||
\(833\) | −4.27423 | −0.148093 | ||||||||
\(834\) | −7.31970 | −0.253460 | ||||||||
\(835\) | 16.5383 | 0.572332 | ||||||||
\(836\) | −0.501104 | −0.0173311 | ||||||||
\(837\) | 21.0895 | 0.728960 | ||||||||
\(838\) | −3.31570 | −0.114539 | ||||||||
\(839\) | −13.9353 | −0.481100 | −0.240550 | − | 0.970637i | \(-0.577328\pi\) | ||||
−0.240550 | + | 0.970637i | \(0.577328\pi\) | |||||||
\(840\) | 7.23710 | 0.249704 | ||||||||
\(841\) | 45.1593 | 1.55722 | ||||||||
\(842\) | −9.67605 | −0.333459 | ||||||||
\(843\) | −60.2741 | −2.07595 | ||||||||
\(844\) | 6.59096 | 0.226870 | ||||||||
\(845\) | 9.20822 | 0.316773 | ||||||||
\(846\) | 2.50580 | 0.0861512 | ||||||||
\(847\) | −15.0613 | −0.517511 | ||||||||
\(848\) | −2.52743 | −0.0867924 | ||||||||
\(849\) | 31.1965 | 1.07066 | ||||||||
\(850\) | −6.80435 | −0.233387 | ||||||||
\(851\) | 38.2644 | 1.31169 | ||||||||
\(852\) | −10.7770 | −0.369213 | ||||||||
\(853\) | 27.0644 | 0.926668 | 0.463334 | − | 0.886184i | \(-0.346653\pi\) | ||||
0.463334 | + | 0.886184i | \(0.346653\pi\) | |||||||
\(854\) | −8.12231 | −0.277940 | ||||||||
\(855\) | −0.131659 | −0.00450264 | ||||||||
\(856\) | −8.28823 | −0.283286 | ||||||||
\(857\) | 30.3400 | 1.03639 | 0.518197 | − | 0.855261i | \(-0.326603\pi\) | ||||
0.518197 | + | 0.855261i | \(0.326603\pi\) | |||||||
\(858\) | 18.2616 | 0.623440 | ||||||||
\(859\) | −21.9453 | −0.748763 | −0.374381 | − | 0.927275i | \(-0.622145\pi\) | ||||
−0.374381 | + | 0.927275i | \(0.622145\pi\) | |||||||
\(860\) | −7.90878 | −0.269687 | ||||||||
\(861\) | 2.85625 | 0.0973409 | ||||||||
\(862\) | 21.4587 | 0.730888 | ||||||||
\(863\) | 16.3614 | 0.556950 | 0.278475 | − | 0.960443i | \(-0.410171\pi\) | ||||
0.278475 | + | 0.960443i | \(0.410171\pi\) | |||||||
\(864\) | −4.19621 | −0.142758 | ||||||||
\(865\) | 3.50222 | 0.119079 | ||||||||
\(866\) | 20.2969 | 0.689718 | ||||||||
\(867\) | 26.1199 | 0.887078 | ||||||||
\(868\) | −15.2586 | −0.517912 | ||||||||
\(869\) | −53.9492 | −1.83010 | ||||||||
\(870\) | −20.5277 | −0.695955 | ||||||||
\(871\) | 23.9372 | 0.811079 | ||||||||
\(872\) | −1.01086 | −0.0342322 | ||||||||
\(873\) | −13.1845 | −0.446228 | ||||||||
\(874\) | −1.00802 | −0.0340967 | ||||||||
\(875\) | −31.3979 | −1.06144 | ||||||||
\(876\) | −17.5891 | −0.594280 | ||||||||
\(877\) | −11.9984 | −0.405157 | −0.202578 | − | 0.979266i | \(-0.564932\pi\) | ||||
−0.202578 | + | 0.979266i | \(0.564932\pi\) | |||||||
\(878\) | −26.0058 | −0.877652 | ||||||||
\(879\) | 61.6135 | 2.07817 | ||||||||
\(880\) | 4.84358 | 0.163277 | ||||||||
\(881\) | −38.1499 | −1.28530 | −0.642652 | − | 0.766158i | \(-0.722166\pi\) | ||||
−0.642652 | + | 0.766158i | \(0.722166\pi\) | |||||||
\(882\) | −1.91987 | −0.0646455 | ||||||||
\(883\) | −28.1150 | −0.946146 | −0.473073 | − | 0.881023i | \(-0.656855\pi\) | ||||
−0.473073 | + | 0.881023i | \(0.656855\pi\) | |||||||
\(884\) | 4.48113 | 0.150717 | ||||||||
\(885\) | −17.9585 | −0.603667 | ||||||||
\(886\) | 1.33689 | 0.0449139 | ||||||||
\(887\) | 3.41377 | 0.114623 | 0.0573116 | − | 0.998356i | \(-0.481747\pi\) | ||||
0.0573116 | + | 0.998356i | \(0.481747\pi\) | |||||||
\(888\) | 9.36150 | 0.314151 | ||||||||
\(889\) | −11.8283 | −0.396708 | ||||||||
\(890\) | −1.58176 | −0.0530208 | ||||||||
\(891\) | 43.3380 | 1.45188 | ||||||||
\(892\) | −8.00322 | −0.267968 | ||||||||
\(893\) | −0.363025 | −0.0121482 | ||||||||
\(894\) | 3.32596 | 0.111237 | ||||||||
\(895\) | −16.0507 | −0.536515 | ||||||||
\(896\) | 3.03603 | 0.101427 | ||||||||
\(897\) | 36.7349 | 1.22654 | ||||||||
\(898\) | 20.7627 | 0.692861 | ||||||||
\(899\) | 43.2805 | 1.44348 | ||||||||
\(900\) | −3.05634 | −0.101878 | ||||||||
\(901\) | 4.87164 | 0.162298 | ||||||||
\(902\) | 1.91161 | 0.0636497 | ||||||||
\(903\) | 38.9400 | 1.29584 | ||||||||
\(904\) | −8.04213 | −0.267477 | ||||||||
\(905\) | −18.4976 | −0.614880 | ||||||||
\(906\) | −28.3739 | −0.942658 | ||||||||
\(907\) | −15.0853 | −0.500900 | −0.250450 | − | 0.968130i | \(-0.580579\pi\) | ||||
−0.250450 | + | 0.968130i | \(0.580579\pi\) | |||||||
\(908\) | −12.9737 | −0.430549 | ||||||||
\(909\) | 0.771441 | 0.0255871 | ||||||||
\(910\) | 8.55730 | 0.283672 | ||||||||
\(911\) | 1.49008 | 0.0493686 | 0.0246843 | − | 0.999695i | \(-0.492142\pi\) | ||||
0.0246843 | + | 0.999695i | \(0.492142\pi\) | |||||||
\(912\) | −0.246615 | −0.00816623 | ||||||||
\(913\) | 36.1146 | 1.19522 | ||||||||
\(914\) | 24.6091 | 0.813997 | ||||||||
\(915\) | −6.37721 | −0.210824 | ||||||||
\(916\) | −18.9837 | −0.627238 | ||||||||
\(917\) | −29.8444 | −0.985549 | ||||||||
\(918\) | 8.08821 | 0.266951 | ||||||||
\(919\) | −45.7417 | −1.50888 | −0.754440 | − | 0.656369i | \(-0.772091\pi\) | ||||
−0.754440 | + | 0.656369i | \(0.772091\pi\) | |||||||
\(920\) | 9.74333 | 0.321228 | ||||||||
\(921\) | 39.5618 | 1.30361 | ||||||||
\(922\) | 5.21566 | 0.171769 | ||||||||
\(923\) | −12.7429 | −0.419439 | ||||||||
\(924\) | −23.8481 | −0.784544 | ||||||||
\(925\) | −16.8081 | −0.552646 | ||||||||
\(926\) | −17.1556 | −0.563769 | ||||||||
\(927\) | 4.50761 | 0.148049 | ||||||||
\(928\) | −8.61158 | −0.282689 | ||||||||
\(929\) | 34.6357 | 1.13636 | 0.568180 | − | 0.822904i | \(-0.307648\pi\) | ||||
0.568180 | + | 0.822904i | \(0.307648\pi\) | |||||||
\(930\) | −11.9803 | −0.392849 | ||||||||
\(931\) | 0.278139 | 0.00911564 | ||||||||
\(932\) | −2.29063 | −0.0750321 | ||||||||
\(933\) | 16.0568 | 0.525677 | ||||||||
\(934\) | 22.2729 | 0.728792 | ||||||||
\(935\) | −9.33603 | −0.305321 | ||||||||
\(936\) | 2.01281 | 0.0657907 | ||||||||
\(937\) | 22.6066 | 0.738526 | 0.369263 | − | 0.929325i | \(-0.379610\pi\) | ||||
0.369263 | + | 0.929325i | \(0.379610\pi\) | |||||||
\(938\) | −31.2599 | −1.02067 | ||||||||
\(939\) | −4.63361 | −0.151212 | ||||||||
\(940\) | 3.50893 | 0.114449 | ||||||||
\(941\) | −2.54897 | −0.0830940 | −0.0415470 | − | 0.999137i | \(-0.513229\pi\) | ||||
−0.0415470 | + | 0.999137i | \(0.513229\pi\) | |||||||
\(942\) | −25.3635 | −0.826389 | ||||||||
\(943\) | 3.84539 | 0.125223 | ||||||||
\(944\) | −7.53375 | −0.245203 | ||||||||
\(945\) | 15.4455 | 0.502442 | ||||||||
\(946\) | 26.0614 | 0.847330 | ||||||||
\(947\) | 15.8261 | 0.514280 | 0.257140 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(948\) | −26.5507 | −0.862327 | ||||||||
\(949\) | −20.7977 | −0.675123 | ||||||||
\(950\) | 0.442783 | 0.0143658 | ||||||||
\(951\) | 24.4186 | 0.791827 | ||||||||
\(952\) | −5.85197 | −0.189663 | ||||||||
\(953\) | 39.9285 | 1.29341 | 0.646705 | − | 0.762740i | \(-0.276146\pi\) | ||||
0.646705 | + | 0.762740i | \(0.276146\pi\) | |||||||
\(954\) | 2.18822 | 0.0708461 | ||||||||
\(955\) | −21.6124 | −0.699362 | ||||||||
\(956\) | 26.1796 | 0.846708 | ||||||||
\(957\) | 67.6440 | 2.18662 | ||||||||
\(958\) | −4.87943 | −0.157647 | ||||||||
\(959\) | 21.3160 | 0.688329 | ||||||||
\(960\) | 2.38374 | 0.0769347 | ||||||||
\(961\) | −5.74085 | −0.185189 | ||||||||
\(962\) | 11.0692 | 0.356887 | ||||||||
\(963\) | 7.17584 | 0.231238 | ||||||||
\(964\) | 19.2456 | 0.619860 | ||||||||
\(965\) | 24.2518 | 0.780694 | ||||||||
\(966\) | −47.9726 | −1.54349 | ||||||||
\(967\) | 9.68040 | 0.311301 | 0.155650 | − | 0.987812i | \(-0.450253\pi\) | ||||
0.155650 | + | 0.987812i | \(0.450253\pi\) | |||||||
\(968\) | −4.96083 | −0.159447 | ||||||||
\(969\) | 0.475351 | 0.0152705 | ||||||||
\(970\) | −18.4626 | −0.592798 | ||||||||
\(971\) | −11.0553 | −0.354782 | −0.177391 | − | 0.984140i | \(-0.556766\pi\) | ||||
−0.177391 | + | 0.984140i | \(0.556766\pi\) | |||||||
\(972\) | 8.73984 | 0.280331 | ||||||||
\(973\) | 11.3027 | 0.362347 | ||||||||
\(974\) | −13.4611 | −0.431320 | ||||||||
\(975\) | −16.1362 | −0.516772 | ||||||||
\(976\) | −2.67530 | −0.0856344 | ||||||||
\(977\) | 20.7390 | 0.663500 | 0.331750 | − | 0.943367i | \(-0.392361\pi\) | ||||
0.331750 | + | 0.943367i | \(0.392361\pi\) | |||||||
\(978\) | −4.05518 | −0.129670 | ||||||||
\(979\) | 5.21231 | 0.166586 | ||||||||
\(980\) | −2.68844 | −0.0858792 | ||||||||
\(981\) | 0.875193 | 0.0279427 | ||||||||
\(982\) | 28.9472 | 0.923741 | ||||||||
\(983\) | −48.7892 | −1.55613 | −0.778067 | − | 0.628181i | \(-0.783800\pi\) | ||||
−0.778067 | + | 0.628181i | \(0.783800\pi\) | |||||||
\(984\) | 0.940785 | 0.0299911 | ||||||||
\(985\) | 3.10876 | 0.0990533 | ||||||||
\(986\) | 16.5989 | 0.528615 | ||||||||
\(987\) | −17.2767 | −0.549924 | ||||||||
\(988\) | −0.291603 | −0.00927712 | ||||||||
\(989\) | 52.4250 | 1.66702 | ||||||||
\(990\) | −4.19351 | −0.133278 | ||||||||
\(991\) | 1.29093 | 0.0410077 | 0.0205038 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205038 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(992\) | −5.02585 | −0.159571 | ||||||||
\(993\) | 14.5198 | 0.460771 | ||||||||
\(994\) | 16.6412 | 0.527827 | ||||||||
\(995\) | −28.4599 | −0.902240 | ||||||||
\(996\) | 17.7735 | 0.563176 | ||||||||
\(997\) | −17.8459 | −0.565184 | −0.282592 | − | 0.959240i | \(-0.591194\pi\) | ||||
−0.282592 | + | 0.959240i | \(0.591194\pi\) | |||||||
\(998\) | 27.7545 | 0.878554 | ||||||||
\(999\) | 19.9794 | 0.632122 |
(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.d.1.8 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.8 | ✓ | 37 | 1.1 | even | 1 | trivial |