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: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 | ||||||||
\(3\) | −1.60405 | −0.926096 | −0.463048 | − | 0.886333i | \(-0.653244\pi\) | ||||
−0.463048 | + | 0.886333i | \(0.653244\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.46390 | 0.654678 | 0.327339 | − | 0.944907i | \(-0.393848\pi\) | ||||
0.327339 | + | 0.944907i | \(0.393848\pi\) | |||||||
\(6\) | −1.60405 | −0.654849 | ||||||||
\(7\) | 4.50208 | 1.70163 | 0.850813 | − | 0.525468i | \(-0.176110\pi\) | ||||
0.850813 | + | 0.525468i | \(0.176110\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.427040 | −0.142347 | ||||||||
\(10\) | 1.46390 | 0.462927 | ||||||||
\(11\) | 0.640800 | 0.193209 | 0.0966043 | − | 0.995323i | \(-0.469202\pi\) | ||||
0.0966043 | + | 0.995323i | \(0.469202\pi\) | |||||||
\(12\) | −1.60405 | −0.463048 | ||||||||
\(13\) | −0.795145 | −0.220533 | −0.110267 | − | 0.993902i | \(-0.535171\pi\) | ||||
−0.110267 | + | 0.993902i | \(0.535171\pi\) | |||||||
\(14\) | 4.50208 | 1.20323 | ||||||||
\(15\) | −2.34817 | −0.606294 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.01845 | 0.732083 | 0.366041 | − | 0.930599i | \(-0.380713\pi\) | ||||
0.366041 | + | 0.930599i | \(0.380713\pi\) | |||||||
\(18\) | −0.427040 | −0.100654 | ||||||||
\(19\) | −4.80731 | −1.10287 | −0.551436 | − | 0.834217i | \(-0.685920\pi\) | ||||
−0.551436 | + | 0.834217i | \(0.685920\pi\) | |||||||
\(20\) | 1.46390 | 0.327339 | ||||||||
\(21\) | −7.22154 | −1.57587 | ||||||||
\(22\) | 0.640800 | 0.136619 | ||||||||
\(23\) | 4.47690 | 0.933498 | 0.466749 | − | 0.884390i | \(-0.345425\pi\) | ||||
0.466749 | + | 0.884390i | \(0.345425\pi\) | |||||||
\(24\) | −1.60405 | −0.327424 | ||||||||
\(25\) | −2.85699 | −0.571397 | ||||||||
\(26\) | −0.795145 | −0.155941 | ||||||||
\(27\) | 5.49713 | 1.05792 | ||||||||
\(28\) | 4.50208 | 0.850813 | ||||||||
\(29\) | 4.51886 | 0.839131 | 0.419565 | − | 0.907725i | \(-0.362183\pi\) | ||||
0.419565 | + | 0.907725i | \(0.362183\pi\) | |||||||
\(30\) | −2.34817 | −0.428715 | ||||||||
\(31\) | 3.84587 | 0.690738 | 0.345369 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345369 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.02787 | −0.178930 | ||||||||
\(34\) | 3.01845 | 0.517661 | ||||||||
\(35\) | 6.59061 | 1.11402 | ||||||||
\(36\) | −0.427040 | −0.0711733 | ||||||||
\(37\) | 10.3793 | 1.70635 | 0.853177 | − | 0.521622i | \(-0.174673\pi\) | ||||
0.853177 | + | 0.521622i | \(0.174673\pi\) | |||||||
\(38\) | −4.80731 | −0.779849 | ||||||||
\(39\) | 1.27545 | 0.204235 | ||||||||
\(40\) | 1.46390 | 0.231464 | ||||||||
\(41\) | 4.31664 | 0.674146 | 0.337073 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337073 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(42\) | −7.22154 | −1.11431 | ||||||||
\(43\) | −5.08727 | −0.775802 | −0.387901 | − | 0.921701i | \(-0.626800\pi\) | ||||
−0.387901 | + | 0.921701i | \(0.626800\pi\) | |||||||
\(44\) | 0.640800 | 0.0966043 | ||||||||
\(45\) | −0.625145 | −0.0931911 | ||||||||
\(46\) | 4.47690 | 0.660083 | ||||||||
\(47\) | −9.95370 | −1.45190 | −0.725948 | − | 0.687750i | \(-0.758599\pi\) | ||||
−0.725948 | + | 0.687750i | \(0.758599\pi\) | |||||||
\(48\) | −1.60405 | −0.231524 | ||||||||
\(49\) | 13.2687 | 1.89553 | ||||||||
\(50\) | −2.85699 | −0.404039 | ||||||||
\(51\) | −4.84174 | −0.677979 | ||||||||
\(52\) | −0.795145 | −0.110267 | ||||||||
\(53\) | −11.6932 | −1.60618 | −0.803092 | − | 0.595855i | \(-0.796813\pi\) | ||||
−0.803092 | + | 0.595855i | \(0.796813\pi\) | |||||||
\(54\) | 5.49713 | 0.748064 | ||||||||
\(55\) | 0.938070 | 0.126489 | ||||||||
\(56\) | 4.50208 | 0.601616 | ||||||||
\(57\) | 7.71114 | 1.02137 | ||||||||
\(58\) | 4.51886 | 0.593355 | ||||||||
\(59\) | 0.0329516 | 0.00428994 | 0.00214497 | − | 0.999998i | \(-0.499317\pi\) | ||||
0.00214497 | + | 0.999998i | \(0.499317\pi\) | |||||||
\(60\) | −2.34817 | −0.303147 | ||||||||
\(61\) | −10.2099 | −1.30724 | −0.653620 | − | 0.756823i | \(-0.726750\pi\) | ||||
−0.653620 | + | 0.756823i | \(0.726750\pi\) | |||||||
\(62\) | 3.84587 | 0.488426 | ||||||||
\(63\) | −1.92257 | −0.242221 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.16402 | −0.144378 | ||||||||
\(66\) | −1.02787 | −0.126522 | ||||||||
\(67\) | 13.1604 | 1.60780 | 0.803899 | − | 0.594765i | \(-0.202755\pi\) | ||||
0.803899 | + | 0.594765i | \(0.202755\pi\) | |||||||
\(68\) | 3.01845 | 0.366041 | ||||||||
\(69\) | −7.18115 | −0.864508 | ||||||||
\(70\) | 6.59061 | 0.787729 | ||||||||
\(71\) | −7.70461 | −0.914368 | −0.457184 | − | 0.889372i | \(-0.651142\pi\) | ||||
−0.457184 | + | 0.889372i | \(0.651142\pi\) | |||||||
\(72\) | −0.427040 | −0.0503271 | ||||||||
\(73\) | 12.6960 | 1.48595 | 0.742975 | − | 0.669319i | \(-0.233414\pi\) | ||||
0.742975 | + | 0.669319i | \(0.233414\pi\) | |||||||
\(74\) | 10.3793 | 1.20657 | ||||||||
\(75\) | 4.58273 | 0.529168 | ||||||||
\(76\) | −4.80731 | −0.551436 | ||||||||
\(77\) | 2.88493 | 0.328769 | ||||||||
\(78\) | 1.27545 | 0.144416 | ||||||||
\(79\) | 14.2214 | 1.60004 | 0.800019 | − | 0.599975i | \(-0.204823\pi\) | ||||
0.800019 | + | 0.599975i | \(0.204823\pi\) | |||||||
\(80\) | 1.46390 | 0.163669 | ||||||||
\(81\) | −7.53652 | −0.837391 | ||||||||
\(82\) | 4.31664 | 0.476693 | ||||||||
\(83\) | 14.5419 | 1.59618 | 0.798089 | − | 0.602540i | \(-0.205845\pi\) | ||||
0.798089 | + | 0.602540i | \(0.205845\pi\) | |||||||
\(84\) | −7.22154 | −0.787935 | ||||||||
\(85\) | 4.41873 | 0.479278 | ||||||||
\(86\) | −5.08727 | −0.548575 | ||||||||
\(87\) | −7.24845 | −0.777115 | ||||||||
\(88\) | 0.640800 | 0.0683095 | ||||||||
\(89\) | 6.30123 | 0.667929 | 0.333965 | − | 0.942586i | \(-0.391613\pi\) | ||||
0.333965 | + | 0.942586i | \(0.391613\pi\) | |||||||
\(90\) | −0.625145 | −0.0658961 | ||||||||
\(91\) | −3.57981 | −0.375266 | ||||||||
\(92\) | 4.47690 | 0.466749 | ||||||||
\(93\) | −6.16895 | −0.639690 | ||||||||
\(94\) | −9.95370 | −1.02665 | ||||||||
\(95\) | −7.03744 | −0.722026 | ||||||||
\(96\) | −1.60405 | −0.163712 | ||||||||
\(97\) | −7.18050 | −0.729069 | −0.364535 | − | 0.931190i | \(-0.618772\pi\) | ||||
−0.364535 | + | 0.931190i | \(0.618772\pi\) | |||||||
\(98\) | 13.2687 | 1.34034 | ||||||||
\(99\) | −0.273647 | −0.0275026 | ||||||||
\(100\) | −2.85699 | −0.285699 | ||||||||
\(101\) | 11.0254 | 1.09707 | 0.548534 | − | 0.836128i | \(-0.315186\pi\) | ||||
0.548534 | + | 0.836128i | \(0.315186\pi\) | |||||||
\(102\) | −4.84174 | −0.479403 | ||||||||
\(103\) | −7.91711 | −0.780096 | −0.390048 | − | 0.920795i | \(-0.627542\pi\) | ||||
−0.390048 | + | 0.920795i | \(0.627542\pi\) | |||||||
\(104\) | −0.795145 | −0.0779703 | ||||||||
\(105\) | −10.5716 | −1.03169 | ||||||||
\(106\) | −11.6932 | −1.13574 | ||||||||
\(107\) | −12.0099 | −1.16104 | −0.580520 | − | 0.814246i | \(-0.697151\pi\) | ||||
−0.580520 | + | 0.814246i | \(0.697151\pi\) | |||||||
\(108\) | 5.49713 | 0.528961 | ||||||||
\(109\) | −9.78046 | −0.936798 | −0.468399 | − | 0.883517i | \(-0.655169\pi\) | ||||
−0.468399 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(110\) | 0.938070 | 0.0894415 | ||||||||
\(111\) | −16.6489 | −1.58025 | ||||||||
\(112\) | 4.50208 | 0.425407 | ||||||||
\(113\) | 4.63963 | 0.436460 | 0.218230 | − | 0.975897i | \(-0.429972\pi\) | ||||
0.218230 | + | 0.975897i | \(0.429972\pi\) | |||||||
\(114\) | 7.71114 | 0.722215 | ||||||||
\(115\) | 6.55375 | 0.611140 | ||||||||
\(116\) | 4.51886 | 0.419565 | ||||||||
\(117\) | 0.339558 | 0.0313922 | ||||||||
\(118\) | 0.0329516 | 0.00303344 | ||||||||
\(119\) | 13.5893 | 1.24573 | ||||||||
\(120\) | −2.34817 | −0.214357 | ||||||||
\(121\) | −10.5894 | −0.962670 | ||||||||
\(122\) | −10.2099 | −0.924358 | ||||||||
\(123\) | −6.92409 | −0.624324 | ||||||||
\(124\) | 3.84587 | 0.345369 | ||||||||
\(125\) | −11.5019 | −1.02876 | ||||||||
\(126\) | −1.92257 | −0.171276 | ||||||||
\(127\) | −14.9796 | −1.32922 | −0.664612 | − | 0.747189i | \(-0.731403\pi\) | ||||
−0.664612 | + | 0.747189i | \(0.731403\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.16022 | 0.718467 | ||||||||
\(130\) | −1.16402 | −0.102091 | ||||||||
\(131\) | −2.72944 | −0.238472 | −0.119236 | − | 0.992866i | \(-0.538044\pi\) | ||||
−0.119236 | + | 0.992866i | \(0.538044\pi\) | |||||||
\(132\) | −1.02787 | −0.0894648 | ||||||||
\(133\) | −21.6429 | −1.87668 | ||||||||
\(134\) | 13.1604 | 1.13689 | ||||||||
\(135\) | 8.04726 | 0.692598 | ||||||||
\(136\) | 3.01845 | 0.258830 | ||||||||
\(137\) | −0.510043 | −0.0435759 | −0.0217880 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217880 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(138\) | −7.18115 | −0.611300 | ||||||||
\(139\) | 7.39069 | 0.626870 | 0.313435 | − | 0.949610i | \(-0.398520\pi\) | ||||
0.313435 | + | 0.949610i | \(0.398520\pi\) | |||||||
\(140\) | 6.59061 | 0.557008 | ||||||||
\(141\) | 15.9662 | 1.34459 | ||||||||
\(142\) | −7.70461 | −0.646556 | ||||||||
\(143\) | −0.509529 | −0.0426090 | ||||||||
\(144\) | −0.427040 | −0.0355866 | ||||||||
\(145\) | 6.61517 | 0.549360 | ||||||||
\(146\) | 12.6960 | 1.05073 | ||||||||
\(147\) | −21.2836 | −1.75544 | ||||||||
\(148\) | 10.3793 | 0.853177 | ||||||||
\(149\) | 14.0030 | 1.14717 | 0.573583 | − | 0.819147i | \(-0.305553\pi\) | ||||
0.573583 | + | 0.819147i | \(0.305553\pi\) | |||||||
\(150\) | 4.58273 | 0.374179 | ||||||||
\(151\) | 0.167706 | 0.0136477 | 0.00682387 | − | 0.999977i | \(-0.497828\pi\) | ||||
0.00682387 | + | 0.999977i | \(0.497828\pi\) | |||||||
\(152\) | −4.80731 | −0.389924 | ||||||||
\(153\) | −1.28900 | −0.104209 | ||||||||
\(154\) | 2.88493 | 0.232475 | ||||||||
\(155\) | 5.62998 | 0.452211 | ||||||||
\(156\) | 1.27545 | 0.102118 | ||||||||
\(157\) | −10.7916 | −0.861267 | −0.430634 | − | 0.902527i | \(-0.641710\pi\) | ||||
−0.430634 | + | 0.902527i | \(0.641710\pi\) | |||||||
\(158\) | 14.2214 | 1.13140 | ||||||||
\(159\) | 18.7564 | 1.48748 | ||||||||
\(160\) | 1.46390 | 0.115732 | ||||||||
\(161\) | 20.1554 | 1.58846 | ||||||||
\(162\) | −7.53652 | −0.592125 | ||||||||
\(163\) | −16.6289 | −1.30247 | −0.651237 | − | 0.758875i | \(-0.725749\pi\) | ||||
−0.651237 | + | 0.758875i | \(0.725749\pi\) | |||||||
\(164\) | 4.31664 | 0.337073 | ||||||||
\(165\) | −1.50471 | −0.117141 | ||||||||
\(166\) | 14.5419 | 1.12867 | ||||||||
\(167\) | 20.7414 | 1.60502 | 0.802510 | − | 0.596638i | \(-0.203497\pi\) | ||||
0.802510 | + | 0.596638i | \(0.203497\pi\) | |||||||
\(168\) | −7.22154 | −0.557154 | ||||||||
\(169\) | −12.3677 | −0.951365 | ||||||||
\(170\) | 4.41873 | 0.338901 | ||||||||
\(171\) | 2.05291 | 0.156990 | ||||||||
\(172\) | −5.08727 | −0.387901 | ||||||||
\(173\) | −0.856747 | −0.0651373 | −0.0325686 | − | 0.999470i | \(-0.510369\pi\) | ||||
−0.0325686 | + | 0.999470i | \(0.510369\pi\) | |||||||
\(174\) | −7.24845 | −0.549504 | ||||||||
\(175\) | −12.8624 | −0.972304 | ||||||||
\(176\) | 0.640800 | 0.0483021 | ||||||||
\(177\) | −0.0528559 | −0.00397289 | ||||||||
\(178\) | 6.30123 | 0.472297 | ||||||||
\(179\) | −3.22266 | −0.240873 | −0.120436 | − | 0.992721i | \(-0.538429\pi\) | ||||
−0.120436 | + | 0.992721i | \(0.538429\pi\) | |||||||
\(180\) | −0.625145 | −0.0465955 | ||||||||
\(181\) | 14.1885 | 1.05463 | 0.527313 | − | 0.849671i | \(-0.323199\pi\) | ||||
0.527313 | + | 0.849671i | \(0.323199\pi\) | |||||||
\(182\) | −3.57981 | −0.265353 | ||||||||
\(183\) | 16.3771 | 1.21063 | ||||||||
\(184\) | 4.47690 | 0.330041 | ||||||||
\(185\) | 15.1944 | 1.11711 | ||||||||
\(186\) | −6.16895 | −0.452329 | ||||||||
\(187\) | 1.93423 | 0.141445 | ||||||||
\(188\) | −9.95370 | −0.725948 | ||||||||
\(189\) | 24.7485 | 1.80019 | ||||||||
\(190\) | −7.03744 | −0.510550 | ||||||||
\(191\) | 14.2218 | 1.02906 | 0.514528 | − | 0.857473i | \(-0.327967\pi\) | ||||
0.514528 | + | 0.857473i | \(0.327967\pi\) | |||||||
\(192\) | −1.60405 | −0.115762 | ||||||||
\(193\) | 19.0874 | 1.37394 | 0.686971 | − | 0.726685i | \(-0.258940\pi\) | ||||
0.686971 | + | 0.726685i | \(0.258940\pi\) | |||||||
\(194\) | −7.18050 | −0.515530 | ||||||||
\(195\) | 1.86713 | 0.133708 | ||||||||
\(196\) | 13.2687 | 0.947766 | ||||||||
\(197\) | −21.5889 | −1.53815 | −0.769074 | − | 0.639159i | \(-0.779283\pi\) | ||||
−0.769074 | + | 0.639159i | \(0.779283\pi\) | |||||||
\(198\) | −0.273647 | −0.0194473 | ||||||||
\(199\) | 15.4251 | 1.09346 | 0.546728 | − | 0.837310i | \(-0.315873\pi\) | ||||
0.546728 | + | 0.837310i | \(0.315873\pi\) | |||||||
\(200\) | −2.85699 | −0.202019 | ||||||||
\(201\) | −21.1099 | −1.48898 | ||||||||
\(202\) | 11.0254 | 0.775745 | ||||||||
\(203\) | 20.3443 | 1.42789 | ||||||||
\(204\) | −4.84174 | −0.338989 | ||||||||
\(205\) | 6.31915 | 0.441348 | ||||||||
\(206\) | −7.91711 | −0.551611 | ||||||||
\(207\) | −1.91181 | −0.132880 | ||||||||
\(208\) | −0.795145 | −0.0551334 | ||||||||
\(209\) | −3.08053 | −0.213084 | ||||||||
\(210\) | −10.5716 | −0.729512 | ||||||||
\(211\) | 17.9469 | 1.23552 | 0.617758 | − | 0.786369i | \(-0.288041\pi\) | ||||
0.617758 | + | 0.786369i | \(0.288041\pi\) | |||||||
\(212\) | −11.6932 | −0.803092 | ||||||||
\(213\) | 12.3585 | 0.846793 | ||||||||
\(214\) | −12.0099 | −0.820980 | ||||||||
\(215\) | −7.44728 | −0.507900 | ||||||||
\(216\) | 5.49713 | 0.374032 | ||||||||
\(217\) | 17.3144 | 1.17538 | ||||||||
\(218\) | −9.78046 | −0.662416 | ||||||||
\(219\) | −20.3649 | −1.37613 | ||||||||
\(220\) | 0.938070 | 0.0632447 | ||||||||
\(221\) | −2.40011 | −0.161449 | ||||||||
\(222\) | −16.6489 | −1.11740 | ||||||||
\(223\) | 1.95762 | 0.131092 | 0.0655460 | − | 0.997850i | \(-0.479121\pi\) | ||||
0.0655460 | + | 0.997850i | \(0.479121\pi\) | |||||||
\(224\) | 4.50208 | 0.300808 | ||||||||
\(225\) | 1.22005 | 0.0813364 | ||||||||
\(226\) | 4.63963 | 0.308624 | ||||||||
\(227\) | 20.7135 | 1.37480 | 0.687401 | − | 0.726278i | \(-0.258752\pi\) | ||||
0.687401 | + | 0.726278i | \(0.258752\pi\) | |||||||
\(228\) | 7.71114 | 0.510683 | ||||||||
\(229\) | 14.1741 | 0.936650 | 0.468325 | − | 0.883556i | \(-0.344858\pi\) | ||||
0.468325 | + | 0.883556i | \(0.344858\pi\) | |||||||
\(230\) | 6.55375 | 0.432141 | ||||||||
\(231\) | −4.62757 | −0.304471 | ||||||||
\(232\) | 4.51886 | 0.296677 | ||||||||
\(233\) | 13.5610 | 0.888414 | 0.444207 | − | 0.895924i | \(-0.353485\pi\) | ||||
0.444207 | + | 0.895924i | \(0.353485\pi\) | |||||||
\(234\) | 0.339558 | 0.0221976 | ||||||||
\(235\) | −14.5713 | −0.950524 | ||||||||
\(236\) | 0.0329516 | 0.00214497 | ||||||||
\(237\) | −22.8118 | −1.48179 | ||||||||
\(238\) | 13.5893 | 0.880865 | ||||||||
\(239\) | 19.1300 | 1.23742 | 0.618708 | − | 0.785621i | \(-0.287656\pi\) | ||||
0.618708 | + | 0.785621i | \(0.287656\pi\) | |||||||
\(240\) | −2.34817 | −0.151574 | ||||||||
\(241\) | 8.68193 | 0.559252 | 0.279626 | − | 0.960109i | \(-0.409789\pi\) | ||||
0.279626 | + | 0.960109i | \(0.409789\pi\) | |||||||
\(242\) | −10.5894 | −0.680711 | ||||||||
\(243\) | −4.40246 | −0.282418 | ||||||||
\(244\) | −10.2099 | −0.653620 | ||||||||
\(245\) | 19.4241 | 1.24096 | ||||||||
\(246\) | −6.92409 | −0.441464 | ||||||||
\(247\) | 3.82251 | 0.243220 | ||||||||
\(248\) | 3.84587 | 0.244213 | ||||||||
\(249\) | −23.3258 | −1.47821 | ||||||||
\(250\) | −11.5019 | −0.727442 | ||||||||
\(251\) | −8.13314 | −0.513359 | −0.256680 | − | 0.966497i | \(-0.582629\pi\) | ||||
−0.256680 | + | 0.966497i | \(0.582629\pi\) | |||||||
\(252\) | −1.92257 | −0.121110 | ||||||||
\(253\) | 2.86880 | 0.180360 | ||||||||
\(254\) | −14.9796 | −0.939903 | ||||||||
\(255\) | −7.08784 | −0.443858 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.6400 | 0.913216 | 0.456608 | − | 0.889668i | \(-0.349064\pi\) | ||||
0.456608 | + | 0.889668i | \(0.349064\pi\) | |||||||
\(258\) | 8.16022 | 0.508033 | ||||||||
\(259\) | 46.7286 | 2.90358 | ||||||||
\(260\) | −1.16402 | −0.0721892 | ||||||||
\(261\) | −1.92973 | −0.119447 | ||||||||
\(262\) | −2.72944 | −0.168625 | ||||||||
\(263\) | 0.227959 | 0.0140566 | 0.00702829 | − | 0.999975i | \(-0.497763\pi\) | ||||
0.00702829 | + | 0.999975i | \(0.497763\pi\) | |||||||
\(264\) | −1.02787 | −0.0632612 | ||||||||
\(265\) | −17.1177 | −1.05153 | ||||||||
\(266\) | −21.6429 | −1.32701 | ||||||||
\(267\) | −10.1075 | −0.618566 | ||||||||
\(268\) | 13.1604 | 0.803899 | ||||||||
\(269\) | −8.67065 | −0.528659 | −0.264330 | − | 0.964432i | \(-0.585151\pi\) | ||||
−0.264330 | + | 0.964432i | \(0.585151\pi\) | |||||||
\(270\) | 8.04726 | 0.489741 | ||||||||
\(271\) | 2.31008 | 0.140327 | 0.0701636 | − | 0.997535i | \(-0.477648\pi\) | ||||
0.0701636 | + | 0.997535i | \(0.477648\pi\) | |||||||
\(272\) | 3.01845 | 0.183021 | ||||||||
\(273\) | 5.74217 | 0.347532 | ||||||||
\(274\) | −0.510043 | −0.0308128 | ||||||||
\(275\) | −1.83076 | −0.110399 | ||||||||
\(276\) | −7.18115 | −0.432254 | ||||||||
\(277\) | 0.538739 | 0.0323697 | 0.0161848 | − | 0.999869i | \(-0.494848\pi\) | ||||
0.0161848 | + | 0.999869i | \(0.494848\pi\) | |||||||
\(278\) | 7.39069 | 0.443264 | ||||||||
\(279\) | −1.64234 | −0.0983242 | ||||||||
\(280\) | 6.59061 | 0.393864 | ||||||||
\(281\) | −0.972148 | −0.0579935 | −0.0289967 | − | 0.999580i | \(-0.509231\pi\) | ||||
−0.0289967 | + | 0.999580i | \(0.509231\pi\) | |||||||
\(282\) | 15.9662 | 0.950772 | ||||||||
\(283\) | 1.76080 | 0.104669 | 0.0523344 | − | 0.998630i | \(-0.483334\pi\) | ||||
0.0523344 | + | 0.998630i | \(0.483334\pi\) | |||||||
\(284\) | −7.70461 | −0.457184 | ||||||||
\(285\) | 11.2884 | 0.668665 | ||||||||
\(286\) | −0.509529 | −0.0301291 | ||||||||
\(287\) | 19.4339 | 1.14714 | ||||||||
\(288\) | −0.427040 | −0.0251635 | ||||||||
\(289\) | −7.88893 | −0.464055 | ||||||||
\(290\) | 6.61517 | 0.388456 | ||||||||
\(291\) | 11.5178 | 0.675188 | ||||||||
\(292\) | 12.6960 | 0.742975 | ||||||||
\(293\) | −24.4340 | −1.42745 | −0.713724 | − | 0.700427i | \(-0.752993\pi\) | ||||
−0.713724 | + | 0.700427i | \(0.752993\pi\) | |||||||
\(294\) | −21.2836 | −1.24129 | ||||||||
\(295\) | 0.0482380 | 0.00280853 | ||||||||
\(296\) | 10.3793 | 0.603287 | ||||||||
\(297\) | 3.52256 | 0.204400 | ||||||||
\(298\) | 14.0030 | 0.811169 | ||||||||
\(299\) | −3.55978 | −0.205867 | ||||||||
\(300\) | 4.58273 | 0.264584 | ||||||||
\(301\) | −22.9033 | −1.32013 | ||||||||
\(302\) | 0.167706 | 0.00965041 | ||||||||
\(303\) | −17.6852 | −1.01599 | ||||||||
\(304\) | −4.80731 | −0.275718 | ||||||||
\(305\) | −14.9463 | −0.855820 | ||||||||
\(306\) | −1.28900 | −0.0736872 | ||||||||
\(307\) | −5.25863 | −0.300126 | −0.150063 | − | 0.988676i | \(-0.547948\pi\) | ||||
−0.150063 | + | 0.988676i | \(0.547948\pi\) | |||||||
\(308\) | 2.88493 | 0.164384 | ||||||||
\(309\) | 12.6994 | 0.722443 | ||||||||
\(310\) | 5.62998 | 0.319762 | ||||||||
\(311\) | −16.1067 | −0.913328 | −0.456664 | − | 0.889639i | \(-0.650956\pi\) | ||||
−0.456664 | + | 0.889639i | \(0.650956\pi\) | |||||||
\(312\) | 1.27545 | 0.0722080 | ||||||||
\(313\) | −21.9897 | −1.24293 | −0.621466 | − | 0.783441i | \(-0.713463\pi\) | ||||
−0.621466 | + | 0.783441i | \(0.713463\pi\) | |||||||
\(314\) | −10.7916 | −0.609008 | ||||||||
\(315\) | −2.81445 | −0.158576 | ||||||||
\(316\) | 14.2214 | 0.800019 | ||||||||
\(317\) | −17.3222 | −0.972911 | −0.486455 | − | 0.873705i | \(-0.661710\pi\) | ||||
−0.486455 | + | 0.873705i | \(0.661710\pi\) | |||||||
\(318\) | 18.7564 | 1.05181 | ||||||||
\(319\) | 2.89569 | 0.162127 | ||||||||
\(320\) | 1.46390 | 0.0818347 | ||||||||
\(321\) | 19.2644 | 1.07523 | ||||||||
\(322\) | 20.1554 | 1.12321 | ||||||||
\(323\) | −14.5106 | −0.807394 | ||||||||
\(324\) | −7.53652 | −0.418695 | ||||||||
\(325\) | 2.27172 | 0.126012 | ||||||||
\(326\) | −16.6289 | −0.920988 | ||||||||
\(327\) | 15.6883 | 0.867564 | ||||||||
\(328\) | 4.31664 | 0.238347 | ||||||||
\(329\) | −44.8123 | −2.47058 | ||||||||
\(330\) | −1.50471 | −0.0828314 | ||||||||
\(331\) | 27.3324 | 1.50233 | 0.751163 | − | 0.660117i | \(-0.229493\pi\) | ||||
0.751163 | + | 0.660117i | \(0.229493\pi\) | |||||||
\(332\) | 14.5419 | 0.798089 | ||||||||
\(333\) | −4.43239 | −0.242894 | ||||||||
\(334\) | 20.7414 | 1.13492 | ||||||||
\(335\) | 19.2656 | 1.05259 | ||||||||
\(336\) | −7.22154 | −0.393967 | ||||||||
\(337\) | 27.7097 | 1.50944 | 0.754722 | − | 0.656044i | \(-0.227772\pi\) | ||||
0.754722 | + | 0.656044i | \(0.227772\pi\) | |||||||
\(338\) | −12.3677 | −0.672717 | ||||||||
\(339\) | −7.44218 | −0.404204 | ||||||||
\(340\) | 4.41873 | 0.239639 | ||||||||
\(341\) | 2.46443 | 0.133457 | ||||||||
\(342\) | 2.05291 | 0.111009 | ||||||||
\(343\) | 28.2223 | 1.52386 | ||||||||
\(344\) | −5.08727 | −0.274287 | ||||||||
\(345\) | −10.5125 | −0.565974 | ||||||||
\(346\) | −0.856747 | −0.0460590 | ||||||||
\(347\) | −11.7509 | −0.630820 | −0.315410 | − | 0.948955i | \(-0.602142\pi\) | ||||
−0.315410 | + | 0.948955i | \(0.602142\pi\) | |||||||
\(348\) | −7.24845 | −0.388558 | ||||||||
\(349\) | 18.2275 | 0.975695 | 0.487847 | − | 0.872929i | \(-0.337782\pi\) | ||||
0.487847 | + | 0.872929i | \(0.337782\pi\) | |||||||
\(350\) | −12.8624 | −0.687523 | ||||||||
\(351\) | −4.37101 | −0.233307 | ||||||||
\(352\) | 0.640800 | 0.0341548 | ||||||||
\(353\) | 0.110514 | 0.00588207 | 0.00294103 | − | 0.999996i | \(-0.499064\pi\) | ||||
0.00294103 | + | 0.999996i | \(0.499064\pi\) | |||||||
\(354\) | −0.0528559 | −0.00280926 | ||||||||
\(355\) | −11.2788 | −0.598617 | ||||||||
\(356\) | 6.30123 | 0.333965 | ||||||||
\(357\) | −21.7979 | −1.15367 | ||||||||
\(358\) | −3.22266 | −0.170323 | ||||||||
\(359\) | −7.27872 | −0.384156 | −0.192078 | − | 0.981380i | \(-0.561523\pi\) | ||||
−0.192078 | + | 0.981380i | \(0.561523\pi\) | |||||||
\(360\) | −0.625145 | −0.0329480 | ||||||||
\(361\) | 4.11024 | 0.216328 | ||||||||
\(362\) | 14.1885 | 0.745733 | ||||||||
\(363\) | 16.9858 | 0.891525 | ||||||||
\(364\) | −3.57981 | −0.187633 | ||||||||
\(365\) | 18.5857 | 0.972819 | ||||||||
\(366\) | 16.3771 | 0.856044 | ||||||||
\(367\) | 34.8926 | 1.82138 | 0.910690 | − | 0.413090i | \(-0.135550\pi\) | ||||
0.910690 | + | 0.413090i | \(0.135550\pi\) | |||||||
\(368\) | 4.47690 | 0.233374 | ||||||||
\(369\) | −1.84338 | −0.0959624 | ||||||||
\(370\) | 15.1944 | 0.789917 | ||||||||
\(371\) | −52.6437 | −2.73313 | ||||||||
\(372\) | −6.16895 | −0.319845 | ||||||||
\(373\) | −14.7398 | −0.763197 | −0.381598 | − | 0.924328i | \(-0.624626\pi\) | ||||
−0.381598 | + | 0.924328i | \(0.624626\pi\) | |||||||
\(374\) | 1.93423 | 0.100016 | ||||||||
\(375\) | 18.4495 | 0.952729 | ||||||||
\(376\) | −9.95370 | −0.513323 | ||||||||
\(377\) | −3.59315 | −0.185056 | ||||||||
\(378\) | 24.7485 | 1.27293 | ||||||||
\(379\) | −5.57572 | −0.286405 | −0.143203 | − | 0.989693i | \(-0.545740\pi\) | ||||
−0.143203 | + | 0.989693i | \(0.545740\pi\) | |||||||
\(380\) | −7.03744 | −0.361013 | ||||||||
\(381\) | 24.0279 | 1.23099 | ||||||||
\(382\) | 14.2218 | 0.727653 | ||||||||
\(383\) | 19.9811 | 1.02099 | 0.510493 | − | 0.859882i | \(-0.329463\pi\) | ||||
0.510493 | + | 0.859882i | \(0.329463\pi\) | |||||||
\(384\) | −1.60405 | −0.0818561 | ||||||||
\(385\) | 4.22327 | 0.215238 | ||||||||
\(386\) | 19.0874 | 0.971523 | ||||||||
\(387\) | 2.17247 | 0.110433 | ||||||||
\(388\) | −7.18050 | −0.364535 | ||||||||
\(389\) | 19.3642 | 0.981803 | 0.490902 | − | 0.871215i | \(-0.336667\pi\) | ||||
0.490902 | + | 0.871215i | \(0.336667\pi\) | |||||||
\(390\) | 1.86713 | 0.0945460 | ||||||||
\(391\) | 13.5133 | 0.683397 | ||||||||
\(392\) | 13.2687 | 0.670172 | ||||||||
\(393\) | 4.37814 | 0.220848 | ||||||||
\(394\) | −21.5889 | −1.08764 | ||||||||
\(395\) | 20.8188 | 1.04751 | ||||||||
\(396\) | −0.273647 | −0.0137513 | ||||||||
\(397\) | −28.4011 | −1.42541 | −0.712706 | − | 0.701463i | \(-0.752530\pi\) | ||||
−0.712706 | + | 0.701463i | \(0.752530\pi\) | |||||||
\(398\) | 15.4251 | 0.773190 | ||||||||
\(399\) | 34.7162 | 1.73798 | ||||||||
\(400\) | −2.85699 | −0.142849 | ||||||||
\(401\) | −21.5763 | −1.07747 | −0.538734 | − | 0.842476i | \(-0.681097\pi\) | ||||
−0.538734 | + | 0.842476i | \(0.681097\pi\) | |||||||
\(402\) | −21.1099 | −1.05286 | ||||||||
\(403\) | −3.05802 | −0.152331 | ||||||||
\(404\) | 11.0254 | 0.548534 | ||||||||
\(405\) | −11.0327 | −0.548221 | ||||||||
\(406\) | 20.3443 | 1.00967 | ||||||||
\(407\) | 6.65109 | 0.329682 | ||||||||
\(408\) | −4.84174 | −0.239702 | ||||||||
\(409\) | −9.91465 | −0.490248 | −0.245124 | − | 0.969492i | \(-0.578829\pi\) | ||||
−0.245124 | + | 0.969492i | \(0.578829\pi\) | |||||||
\(410\) | 6.31915 | 0.312080 | ||||||||
\(411\) | 0.818132 | 0.0403555 | ||||||||
\(412\) | −7.91711 | −0.390048 | ||||||||
\(413\) | 0.148351 | 0.00729987 | ||||||||
\(414\) | −1.91181 | −0.0939605 | ||||||||
\(415\) | 21.2879 | 1.04498 | ||||||||
\(416\) | −0.795145 | −0.0389852 | ||||||||
\(417\) | −11.8550 | −0.580542 | ||||||||
\(418\) | −3.08053 | −0.150673 | ||||||||
\(419\) | −30.1952 | −1.47513 | −0.737567 | − | 0.675274i | \(-0.764026\pi\) | ||||
−0.737567 | + | 0.675274i | \(0.764026\pi\) | |||||||
\(420\) | −10.5716 | −0.515843 | ||||||||
\(421\) | −18.5652 | −0.904813 | −0.452407 | − | 0.891812i | \(-0.649434\pi\) | ||||
−0.452407 | + | 0.891812i | \(0.649434\pi\) | |||||||
\(422\) | 17.9469 | 0.873641 | ||||||||
\(423\) | 4.25062 | 0.206672 | ||||||||
\(424\) | −11.6932 | −0.567872 | ||||||||
\(425\) | −8.62368 | −0.418310 | ||||||||
\(426\) | 12.3585 | 0.598773 | ||||||||
\(427\) | −45.9656 | −2.22443 | ||||||||
\(428\) | −12.0099 | −0.580520 | ||||||||
\(429\) | 0.817307 | 0.0394600 | ||||||||
\(430\) | −7.44728 | −0.359140 | ||||||||
\(431\) | −29.5691 | −1.42429 | −0.712147 | − | 0.702030i | \(-0.752277\pi\) | ||||
−0.712147 | + | 0.702030i | \(0.752277\pi\) | |||||||
\(432\) | 5.49713 | 0.264481 | ||||||||
\(433\) | −37.6270 | −1.80824 | −0.904119 | − | 0.427280i | \(-0.859472\pi\) | ||||
−0.904119 | + | 0.427280i | \(0.859472\pi\) | |||||||
\(434\) | 17.3144 | 0.831118 | ||||||||
\(435\) | −10.6110 | −0.508760 | ||||||||
\(436\) | −9.78046 | −0.468399 | ||||||||
\(437\) | −21.5218 | −1.02953 | ||||||||
\(438\) | −20.3649 | −0.973073 | ||||||||
\(439\) | 22.4696 | 1.07242 | 0.536209 | − | 0.844085i | \(-0.319856\pi\) | ||||
0.536209 | + | 0.844085i | \(0.319856\pi\) | |||||||
\(440\) | 0.938070 | 0.0447207 | ||||||||
\(441\) | −5.66627 | −0.269823 | ||||||||
\(442\) | −2.40011 | −0.114161 | ||||||||
\(443\) | 36.7579 | 1.74642 | 0.873211 | − | 0.487342i | \(-0.162034\pi\) | ||||
0.873211 | + | 0.487342i | \(0.162034\pi\) | |||||||
\(444\) | −16.6489 | −0.790124 | ||||||||
\(445\) | 9.22440 | 0.437278 | ||||||||
\(446\) | 1.95762 | 0.0926961 | ||||||||
\(447\) | −22.4614 | −1.06239 | ||||||||
\(448\) | 4.50208 | 0.212703 | ||||||||
\(449\) | −4.29656 | −0.202767 | −0.101384 | − | 0.994847i | \(-0.532327\pi\) | ||||
−0.101384 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(450\) | 1.22005 | 0.0575135 | ||||||||
\(451\) | 2.76611 | 0.130251 | ||||||||
\(452\) | 4.63963 | 0.218230 | ||||||||
\(453\) | −0.269008 | −0.0126391 | ||||||||
\(454\) | 20.7135 | 0.972132 | ||||||||
\(455\) | −5.24049 | −0.245678 | ||||||||
\(456\) | 7.71114 | 0.361107 | ||||||||
\(457\) | −4.32456 | −0.202295 | −0.101147 | − | 0.994871i | \(-0.532251\pi\) | ||||
−0.101147 | + | 0.994871i | \(0.532251\pi\) | |||||||
\(458\) | 14.1741 | 0.662311 | ||||||||
\(459\) | 16.5928 | 0.774487 | ||||||||
\(460\) | 6.55375 | 0.305570 | ||||||||
\(461\) | −30.6666 | −1.42829 | −0.714143 | − | 0.700000i | \(-0.753183\pi\) | ||||
−0.714143 | + | 0.700000i | \(0.753183\pi\) | |||||||
\(462\) | −4.62757 | −0.215294 | ||||||||
\(463\) | 0.252334 | 0.0117270 | 0.00586349 | − | 0.999983i | \(-0.498134\pi\) | ||||
0.00586349 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(464\) | 4.51886 | 0.209783 | ||||||||
\(465\) | −9.03075 | −0.418791 | ||||||||
\(466\) | 13.5610 | 0.628203 | ||||||||
\(467\) | −11.7911 | −0.545628 | −0.272814 | − | 0.962067i | \(-0.587954\pi\) | ||||
−0.272814 | + | 0.962067i | \(0.587954\pi\) | |||||||
\(468\) | 0.339558 | 0.0156961 | ||||||||
\(469\) | 59.2492 | 2.73587 | ||||||||
\(470\) | −14.5713 | −0.672122 | ||||||||
\(471\) | 17.3103 | 0.797616 | ||||||||
\(472\) | 0.0329516 | 0.00151672 | ||||||||
\(473\) | −3.25993 | −0.149892 | ||||||||
\(474\) | −22.8118 | −1.04778 | ||||||||
\(475\) | 13.7344 | 0.630178 | ||||||||
\(476\) | 13.5893 | 0.622866 | ||||||||
\(477\) | 4.99346 | 0.228635 | ||||||||
\(478\) | 19.1300 | 0.874985 | ||||||||
\(479\) | 18.7333 | 0.855945 | 0.427973 | − | 0.903792i | \(-0.359228\pi\) | ||||
0.427973 | + | 0.903792i | \(0.359228\pi\) | |||||||
\(480\) | −2.34817 | −0.107179 | ||||||||
\(481\) | −8.25308 | −0.376308 | ||||||||
\(482\) | 8.68193 | 0.395451 | ||||||||
\(483\) | −32.3301 | −1.47107 | ||||||||
\(484\) | −10.5894 | −0.481335 | ||||||||
\(485\) | −10.5116 | −0.477306 | ||||||||
\(486\) | −4.40246 | −0.199700 | ||||||||
\(487\) | −35.2519 | −1.59742 | −0.798708 | − | 0.601719i | \(-0.794483\pi\) | ||||
−0.798708 | + | 0.601719i | \(0.794483\pi\) | |||||||
\(488\) | −10.2099 | −0.462179 | ||||||||
\(489\) | 26.6734 | 1.20621 | ||||||||
\(490\) | 19.4241 | 0.877493 | ||||||||
\(491\) | −40.3227 | −1.81974 | −0.909869 | − | 0.414895i | \(-0.863818\pi\) | ||||
−0.909869 | + | 0.414895i | \(0.863818\pi\) | |||||||
\(492\) | −6.92409 | −0.312162 | ||||||||
\(493\) | 13.6400 | 0.614313 | ||||||||
\(494\) | 3.82251 | 0.171983 | ||||||||
\(495\) | −0.400593 | −0.0180053 | ||||||||
\(496\) | 3.84587 | 0.172685 | ||||||||
\(497\) | −34.6868 | −1.55591 | ||||||||
\(498\) | −23.3258 | −1.04525 | ||||||||
\(499\) | −8.63150 | −0.386399 | −0.193199 | − | 0.981160i | \(-0.561886\pi\) | ||||
−0.193199 | + | 0.981160i | \(0.561886\pi\) | |||||||
\(500\) | −11.5019 | −0.514379 | ||||||||
\(501\) | −33.2702 | −1.48640 | ||||||||
\(502\) | −8.13314 | −0.363000 | ||||||||
\(503\) | 7.23331 | 0.322517 | 0.161259 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161259 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(504\) | −1.92257 | −0.0856379 | ||||||||
\(505\) | 16.1401 | 0.718226 | ||||||||
\(506\) | 2.86880 | 0.127534 | ||||||||
\(507\) | 19.8384 | 0.881055 | ||||||||
\(508\) | −14.9796 | −0.664612 | ||||||||
\(509\) | −42.0142 | −1.86225 | −0.931124 | − | 0.364704i | \(-0.881170\pi\) | ||||
−0.931124 | + | 0.364704i | \(0.881170\pi\) | |||||||
\(510\) | −7.08784 | −0.313855 | ||||||||
\(511\) | 57.1583 | 2.52853 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −26.4264 | −1.16675 | ||||||||
\(514\) | 14.6400 | 0.645741 | ||||||||
\(515\) | −11.5899 | −0.510711 | ||||||||
\(516\) | 8.16022 | 0.359233 | ||||||||
\(517\) | −6.37833 | −0.280519 | ||||||||
\(518\) | 46.7286 | 2.05314 | ||||||||
\(519\) | 1.37426 | 0.0603234 | ||||||||
\(520\) | −1.16402 | −0.0510454 | ||||||||
\(521\) | −25.1221 | −1.10062 | −0.550310 | − | 0.834960i | \(-0.685491\pi\) | ||||
−0.550310 | + | 0.834960i | \(0.685491\pi\) | |||||||
\(522\) | −1.92973 | −0.0844620 | ||||||||
\(523\) | −33.6186 | −1.47004 | −0.735018 | − | 0.678047i | \(-0.762826\pi\) | ||||
−0.735018 | + | 0.678047i | \(0.762826\pi\) | |||||||
\(524\) | −2.72944 | −0.119236 | ||||||||
\(525\) | 20.6318 | 0.900447 | ||||||||
\(526\) | 0.227959 | 0.00993950 | ||||||||
\(527\) | 11.6086 | 0.505678 | ||||||||
\(528\) | −1.02787 | −0.0447324 | ||||||||
\(529\) | −2.95739 | −0.128582 | ||||||||
\(530\) | −17.1177 | −0.743546 | ||||||||
\(531\) | −0.0140716 | −0.000610658 0 | ||||||||
\(532\) | −21.6429 | −0.938339 | ||||||||
\(533\) | −3.43235 | −0.148672 | ||||||||
\(534\) | −10.1075 | −0.437393 | ||||||||
\(535\) | −17.5813 | −0.760107 | ||||||||
\(536\) | 13.1604 | 0.568443 | ||||||||
\(537\) | 5.16929 | 0.223071 | ||||||||
\(538\) | −8.67065 | −0.373818 | ||||||||
\(539\) | 8.50261 | 0.366233 | ||||||||
\(540\) | 8.04726 | 0.346299 | ||||||||
\(541\) | −13.2826 | −0.571064 | −0.285532 | − | 0.958369i | \(-0.592170\pi\) | ||||
−0.285532 | + | 0.958369i | \(0.592170\pi\) | |||||||
\(542\) | 2.31008 | 0.0992263 | ||||||||
\(543\) | −22.7591 | −0.976685 | ||||||||
\(544\) | 3.01845 | 0.129415 | ||||||||
\(545\) | −14.3176 | −0.613301 | ||||||||
\(546\) | 5.74217 | 0.245742 | ||||||||
\(547\) | 7.91845 | 0.338569 | 0.169284 | − | 0.985567i | \(-0.445854\pi\) | ||||
0.169284 | + | 0.985567i | \(0.445854\pi\) | |||||||
\(548\) | −0.510043 | −0.0217880 | ||||||||
\(549\) | 4.36002 | 0.186081 | ||||||||
\(550\) | −1.83076 | −0.0780638 | ||||||||
\(551\) | −21.7235 | −0.925454 | ||||||||
\(552\) | −7.18115 | −0.305650 | ||||||||
\(553\) | 64.0261 | 2.72267 | ||||||||
\(554\) | 0.538739 | 0.0228888 | ||||||||
\(555\) | −24.3724 | −1.03455 | ||||||||
\(556\) | 7.39069 | 0.313435 | ||||||||
\(557\) | −11.0239 | −0.467099 | −0.233549 | − | 0.972345i | \(-0.575034\pi\) | ||||
−0.233549 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(558\) | −1.64234 | −0.0695257 | ||||||||
\(559\) | 4.04512 | 0.171090 | ||||||||
\(560\) | 6.59061 | 0.278504 | ||||||||
\(561\) | −3.10259 | −0.130991 | ||||||||
\(562\) | −0.972148 | −0.0410076 | ||||||||
\(563\) | −37.2641 | −1.57049 | −0.785247 | − | 0.619182i | \(-0.787464\pi\) | ||||
−0.785247 | + | 0.619182i | \(0.787464\pi\) | |||||||
\(564\) | 15.9662 | 0.672297 | ||||||||
\(565\) | 6.79198 | 0.285741 | ||||||||
\(566\) | 1.76080 | 0.0740120 | ||||||||
\(567\) | −33.9300 | −1.42493 | ||||||||
\(568\) | −7.70461 | −0.323278 | ||||||||
\(569\) | 10.0406 | 0.420926 | 0.210463 | − | 0.977602i | \(-0.432503\pi\) | ||||
0.210463 | + | 0.977602i | \(0.432503\pi\) | |||||||
\(570\) | 11.2884 | 0.472818 | ||||||||
\(571\) | 3.63429 | 0.152090 | 0.0760452 | − | 0.997104i | \(-0.475771\pi\) | ||||
0.0760452 | + | 0.997104i | \(0.475771\pi\) | |||||||
\(572\) | −0.509529 | −0.0213045 | ||||||||
\(573\) | −22.8125 | −0.953005 | ||||||||
\(574\) | 19.4339 | 0.811154 | ||||||||
\(575\) | −12.7904 | −0.533398 | ||||||||
\(576\) | −0.427040 | −0.0177933 | ||||||||
\(577\) | 0.717085 | 0.0298526 | 0.0149263 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149263 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(578\) | −7.88893 | −0.328136 | ||||||||
\(579\) | −30.6171 | −1.27240 | ||||||||
\(580\) | 6.61517 | 0.274680 | ||||||||
\(581\) | 65.4687 | 2.71610 | ||||||||
\(582\) | 11.5178 | 0.477430 | ||||||||
\(583\) | −7.49301 | −0.310329 | ||||||||
\(584\) | 12.6960 | 0.525363 | ||||||||
\(585\) | 0.497081 | 0.0205518 | ||||||||
\(586\) | −24.4340 | −1.00936 | ||||||||
\(587\) | −11.3283 | −0.467570 | −0.233785 | − | 0.972288i | \(-0.575111\pi\) | ||||
−0.233785 | + | 0.972288i | \(0.575111\pi\) | |||||||
\(588\) | −21.2836 | −0.877722 | ||||||||
\(589\) | −18.4883 | −0.761797 | ||||||||
\(590\) | 0.0482380 | 0.00198593 | ||||||||
\(591\) | 34.6296 | 1.42447 | ||||||||
\(592\) | 10.3793 | 0.426588 | ||||||||
\(593\) | −11.3351 | −0.465478 | −0.232739 | − | 0.972539i | \(-0.574769\pi\) | ||||
−0.232739 | + | 0.972539i | \(0.574769\pi\) | |||||||
\(594\) | 3.52256 | 0.144532 | ||||||||
\(595\) | 19.8935 | 0.815552 | ||||||||
\(596\) | 14.0030 | 0.573583 | ||||||||
\(597\) | −24.7425 | −1.01265 | ||||||||
\(598\) | −3.55978 | −0.145570 | ||||||||
\(599\) | 2.45449 | 0.100288 | 0.0501439 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501439 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(600\) | 4.58273 | 0.187089 | ||||||||
\(601\) | −18.2791 | −0.745621 | −0.372811 | − | 0.927907i | \(-0.621606\pi\) | ||||
−0.372811 | + | 0.927907i | \(0.621606\pi\) | |||||||
\(602\) | −22.9033 | −0.933469 | ||||||||
\(603\) | −5.62001 | −0.228865 | ||||||||
\(604\) | 0.167706 | 0.00682387 | ||||||||
\(605\) | −15.5018 | −0.630239 | ||||||||
\(606\) | −17.6852 | −0.718414 | ||||||||
\(607\) | 2.74297 | 0.111334 | 0.0556669 | − | 0.998449i | \(-0.482272\pi\) | ||||
0.0556669 | + | 0.998449i | \(0.482272\pi\) | |||||||
\(608\) | −4.80731 | −0.194962 | ||||||||
\(609\) | −32.6331 | −1.32236 | ||||||||
\(610\) | −14.9463 | −0.605156 | ||||||||
\(611\) | 7.91463 | 0.320192 | ||||||||
\(612\) | −1.28900 | −0.0521047 | ||||||||
\(613\) | −43.8834 | −1.77243 | −0.886217 | − | 0.463270i | \(-0.846676\pi\) | ||||
−0.886217 | + | 0.463270i | \(0.846676\pi\) | |||||||
\(614\) | −5.25863 | −0.212221 | ||||||||
\(615\) | −10.1362 | −0.408731 | ||||||||
\(616\) | 2.88493 | 0.116237 | ||||||||
\(617\) | 5.42811 | 0.218528 | 0.109264 | − | 0.994013i | \(-0.465151\pi\) | ||||
0.109264 | + | 0.994013i | \(0.465151\pi\) | |||||||
\(618\) | 12.6994 | 0.510845 | ||||||||
\(619\) | 34.3814 | 1.38191 | 0.690953 | − | 0.722899i | \(-0.257191\pi\) | ||||
0.690953 | + | 0.722899i | \(0.257191\pi\) | |||||||
\(620\) | 5.62998 | 0.226106 | ||||||||
\(621\) | 24.6101 | 0.987568 | ||||||||
\(622\) | −16.1067 | −0.645821 | ||||||||
\(623\) | 28.3687 | 1.13657 | ||||||||
\(624\) | 1.27545 | 0.0510588 | ||||||||
\(625\) | −2.55271 | −0.102108 | ||||||||
\(626\) | −21.9897 | −0.878886 | ||||||||
\(627\) | 4.94130 | 0.197337 | ||||||||
\(628\) | −10.7916 | −0.430634 | ||||||||
\(629\) | 31.3296 | 1.24919 | ||||||||
\(630\) | −2.81445 | −0.112130 | ||||||||
\(631\) | −30.5592 | −1.21654 | −0.608271 | − | 0.793730i | \(-0.708136\pi\) | ||||
−0.608271 | + | 0.793730i | \(0.708136\pi\) | |||||||
\(632\) | 14.2214 | 0.565699 | ||||||||
\(633\) | −28.7876 | −1.14421 | ||||||||
\(634\) | −17.3222 | −0.687952 | ||||||||
\(635\) | −21.9287 | −0.870213 | ||||||||
\(636\) | 18.7564 | 0.743740 | ||||||||
\(637\) | −10.5506 | −0.418028 | ||||||||
\(638\) | 2.89569 | 0.114641 | ||||||||
\(639\) | 3.29017 | 0.130157 | ||||||||
\(640\) | 1.46390 | 0.0578659 | ||||||||
\(641\) | −26.6530 | −1.05273 | −0.526364 | − | 0.850259i | \(-0.676445\pi\) | ||||
−0.526364 | + | 0.850259i | \(0.676445\pi\) | |||||||
\(642\) | 19.2644 | 0.760306 | ||||||||
\(643\) | −21.5247 | −0.848850 | −0.424425 | − | 0.905463i | \(-0.639524\pi\) | ||||
−0.424425 | + | 0.905463i | \(0.639524\pi\) | |||||||
\(644\) | 20.1554 | 0.794232 | ||||||||
\(645\) | 11.9458 | 0.470364 | ||||||||
\(646\) | −14.5106 | −0.570914 | ||||||||
\(647\) | −35.4030 | −1.39183 | −0.695917 | − | 0.718122i | \(-0.745002\pi\) | ||||
−0.695917 | + | 0.718122i | \(0.745002\pi\) | |||||||
\(648\) | −7.53652 | −0.296062 | ||||||||
\(649\) | 0.0211154 | 0.000828852 0 | ||||||||
\(650\) | 2.27172 | 0.0891041 | ||||||||
\(651\) | −27.7731 | −1.08851 | ||||||||
\(652\) | −16.6289 | −0.651237 | ||||||||
\(653\) | −6.97559 | −0.272976 | −0.136488 | − | 0.990642i | \(-0.543582\pi\) | ||||
−0.136488 | + | 0.990642i | \(0.543582\pi\) | |||||||
\(654\) | 15.6883 | 0.613461 | ||||||||
\(655\) | −3.99563 | −0.156122 | ||||||||
\(656\) | 4.31664 | 0.168537 | ||||||||
\(657\) | −5.42168 | −0.211520 | ||||||||
\(658\) | −44.8123 | −1.74697 | ||||||||
\(659\) | 29.9221 | 1.16560 | 0.582800 | − | 0.812616i | \(-0.301957\pi\) | ||||
0.582800 | + | 0.812616i | \(0.301957\pi\) | |||||||
\(660\) | −1.50471 | −0.0585706 | ||||||||
\(661\) | 39.0608 | 1.51929 | 0.759644 | − | 0.650339i | \(-0.225373\pi\) | ||||
0.759644 | + | 0.650339i | \(0.225373\pi\) | |||||||
\(662\) | 27.3324 | 1.06230 | ||||||||
\(663\) | 3.84988 | 0.149517 | ||||||||
\(664\) | 14.5419 | 0.564334 | ||||||||
\(665\) | −31.6831 | −1.22862 | ||||||||
\(666\) | −4.43239 | −0.171752 | ||||||||
\(667\) | 20.2305 | 0.783327 | ||||||||
\(668\) | 20.7414 | 0.802510 | ||||||||
\(669\) | −3.14011 | −0.121404 | ||||||||
\(670\) | 19.2656 | 0.744294 | ||||||||
\(671\) | −6.54248 | −0.252570 | ||||||||
\(672\) | −7.22154 | −0.278577 | ||||||||
\(673\) | 3.43410 | 0.132375 | 0.0661875 | − | 0.997807i | \(-0.478916\pi\) | ||||
0.0661875 | + | 0.997807i | \(0.478916\pi\) | |||||||
\(674\) | 27.7097 | 1.06734 | ||||||||
\(675\) | −15.7052 | −0.604494 | ||||||||
\(676\) | −12.3677 | −0.475682 | ||||||||
\(677\) | −12.5494 | −0.482315 | −0.241157 | − | 0.970486i | \(-0.577527\pi\) | ||||
−0.241157 | + | 0.970486i | \(0.577527\pi\) | |||||||
\(678\) | −7.44218 | −0.285815 | ||||||||
\(679\) | −32.3272 | −1.24060 | ||||||||
\(680\) | 4.41873 | 0.169450 | ||||||||
\(681\) | −33.2254 | −1.27320 | ||||||||
\(682\) | 2.46443 | 0.0943681 | ||||||||
\(683\) | −2.68799 | −0.102853 | −0.0514266 | − | 0.998677i | \(-0.516377\pi\) | ||||
−0.0514266 | + | 0.998677i | \(0.516377\pi\) | |||||||
\(684\) | 2.05291 | 0.0784951 | ||||||||
\(685\) | −0.746654 | −0.0285282 | ||||||||
\(686\) | 28.2223 | 1.07753 | ||||||||
\(687\) | −22.7359 | −0.867427 | ||||||||
\(688\) | −5.08727 | −0.193950 | ||||||||
\(689\) | 9.29778 | 0.354217 | ||||||||
\(690\) | −10.5125 | −0.400204 | ||||||||
\(691\) | 9.26446 | 0.352437 | 0.176218 | − | 0.984351i | \(-0.443614\pi\) | ||||
0.176218 | + | 0.984351i | \(0.443614\pi\) | |||||||
\(692\) | −0.856747 | −0.0325686 | ||||||||
\(693\) | −1.23198 | −0.0467991 | ||||||||
\(694\) | −11.7509 | −0.446057 | ||||||||
\(695\) | 10.8193 | 0.410398 | ||||||||
\(696\) | −7.24845 | −0.274752 | ||||||||
\(697\) | 13.0296 | 0.493531 | ||||||||
\(698\) | 18.2275 | 0.689921 | ||||||||
\(699\) | −21.7525 | −0.822756 | ||||||||
\(700\) | −12.8624 | −0.486152 | ||||||||
\(701\) | 31.7970 | 1.20096 | 0.600479 | − | 0.799641i | \(-0.294977\pi\) | ||||
0.600479 | + | 0.799641i | \(0.294977\pi\) | |||||||
\(702\) | −4.37101 | −0.164973 | ||||||||
\(703\) | −49.8967 | −1.88189 | ||||||||
\(704\) | 0.640800 | 0.0241511 | ||||||||
\(705\) | 23.3730 | 0.880276 | ||||||||
\(706\) | 0.110514 | 0.00415925 | ||||||||
\(707\) | 49.6373 | 1.86680 | ||||||||
\(708\) | −0.0528559 | −0.00198645 | ||||||||
\(709\) | −30.6649 | −1.15165 | −0.575823 | − | 0.817574i | \(-0.695318\pi\) | ||||
−0.575823 | + | 0.817574i | \(0.695318\pi\) | |||||||
\(710\) | −11.2788 | −0.423286 | ||||||||
\(711\) | −6.07312 | −0.227760 | ||||||||
\(712\) | 6.30123 | 0.236149 | ||||||||
\(713\) | 17.2176 | 0.644803 | ||||||||
\(714\) | −21.7979 | −0.815765 | ||||||||
\(715\) | −0.745901 | −0.0278951 | ||||||||
\(716\) | −3.22266 | −0.120436 | ||||||||
\(717\) | −30.6854 | −1.14597 | ||||||||
\(718\) | −7.27872 | −0.271640 | ||||||||
\(719\) | 21.1623 | 0.789222 | 0.394611 | − | 0.918848i | \(-0.370879\pi\) | ||||
0.394611 | + | 0.918848i | \(0.370879\pi\) | |||||||
\(720\) | −0.625145 | −0.0232978 | ||||||||
\(721\) | −35.6434 | −1.32743 | ||||||||
\(722\) | 4.11024 | 0.152967 | ||||||||
\(723\) | −13.9262 | −0.517921 | ||||||||
\(724\) | 14.1885 | 0.527313 | ||||||||
\(725\) | −12.9103 | −0.479477 | ||||||||
\(726\) | 16.9858 | 0.630403 | ||||||||
\(727\) | 15.0442 | 0.557960 | 0.278980 | − | 0.960297i | \(-0.410004\pi\) | ||||
0.278980 | + | 0.960297i | \(0.410004\pi\) | |||||||
\(728\) | −3.57981 | −0.132676 | ||||||||
\(729\) | 29.6713 | 1.09894 | ||||||||
\(730\) | 18.5857 | 0.687887 | ||||||||
\(731\) | −15.3557 | −0.567951 | ||||||||
\(732\) | 16.3771 | 0.605314 | ||||||||
\(733\) | 49.2290 | 1.81831 | 0.909157 | − | 0.416453i | \(-0.136727\pi\) | ||||
0.909157 | + | 0.416453i | \(0.136727\pi\) | |||||||
\(734\) | 34.8926 | 1.28791 | ||||||||
\(735\) | −31.1572 | −1.14925 | ||||||||
\(736\) | 4.47690 | 0.165021 | ||||||||
\(737\) | 8.43319 | 0.310641 | ||||||||
\(738\) | −1.84338 | −0.0678556 | ||||||||
\(739\) | 38.1345 | 1.40280 | 0.701400 | − | 0.712768i | \(-0.252559\pi\) | ||||
0.701400 | + | 0.712768i | \(0.252559\pi\) | |||||||
\(740\) | 15.1944 | 0.558556 | ||||||||
\(741\) | −6.13147 | −0.225245 | ||||||||
\(742\) | −52.6437 | −1.93261 | ||||||||
\(743\) | 31.7699 | 1.16552 | 0.582762 | − | 0.812643i | \(-0.301972\pi\) | ||||
0.582762 | + | 0.812643i | \(0.301972\pi\) | |||||||
\(744\) | −6.16895 | −0.226165 | ||||||||
\(745\) | 20.4990 | 0.751024 | ||||||||
\(746\) | −14.7398 | −0.539661 | ||||||||
\(747\) | −6.20995 | −0.227210 | ||||||||
\(748\) | 1.93423 | 0.0707223 | ||||||||
\(749\) | −54.0695 | −1.97566 | ||||||||
\(750\) | 18.4495 | 0.673681 | ||||||||
\(751\) | −13.1318 | −0.479187 | −0.239594 | − | 0.970873i | \(-0.577014\pi\) | ||||
−0.239594 | + | 0.970873i | \(0.577014\pi\) | |||||||
\(752\) | −9.95370 | −0.362974 | ||||||||
\(753\) | 13.0459 | 0.475420 | ||||||||
\(754\) | −3.59315 | −0.130855 | ||||||||
\(755\) | 0.245506 | 0.00893487 | ||||||||
\(756\) | 24.7485 | 0.900094 | ||||||||
\(757\) | 1.10834 | 0.0402833 | 0.0201416 | − | 0.999797i | \(-0.493588\pi\) | ||||
0.0201416 | + | 0.999797i | \(0.493588\pi\) | |||||||
\(758\) | −5.57572 | −0.202519 | ||||||||
\(759\) | −4.60168 | −0.167030 | ||||||||
\(760\) | −7.03744 | −0.255275 | ||||||||
\(761\) | 13.5311 | 0.490501 | 0.245251 | − | 0.969460i | \(-0.421130\pi\) | ||||
0.245251 | + | 0.969460i | \(0.421130\pi\) | |||||||
\(762\) | 24.0279 | 0.870441 | ||||||||
\(763\) | −44.0324 | −1.59408 | ||||||||
\(764\) | 14.2218 | 0.514528 | ||||||||
\(765\) | −1.88697 | −0.0682236 | ||||||||
\(766\) | 19.9811 | 0.721946 | ||||||||
\(767\) | −0.0262013 | −0.000946074 0 | ||||||||
\(768\) | −1.60405 | −0.0578810 | ||||||||
\(769\) | 32.4517 | 1.17024 | 0.585118 | − | 0.810948i | \(-0.301048\pi\) | ||||
0.585118 | + | 0.810948i | \(0.301048\pi\) | |||||||
\(770\) | 4.22327 | 0.152196 | ||||||||
\(771\) | −23.4832 | −0.845725 | ||||||||
\(772\) | 19.0874 | 0.686971 | ||||||||
\(773\) | −0.220654 | −0.00793639 | −0.00396819 | − | 0.999992i | \(-0.501263\pi\) | ||||
−0.00396819 | + | 0.999992i | \(0.501263\pi\) | |||||||
\(774\) | 2.17247 | 0.0780877 | ||||||||
\(775\) | −10.9876 | −0.394686 | ||||||||
\(776\) | −7.18050 | −0.257765 | ||||||||
\(777\) | −74.9548 | −2.68899 | ||||||||
\(778\) | 19.3642 | 0.694240 | ||||||||
\(779\) | −20.7514 | −0.743497 | ||||||||
\(780\) | 1.86713 | 0.0668541 | ||||||||
\(781\) | −4.93711 | −0.176664 | ||||||||
\(782\) | 13.5133 | 0.483235 | ||||||||
\(783\) | 24.8407 | 0.887735 | ||||||||
\(784\) | 13.2687 | 0.473883 | ||||||||
\(785\) | −15.7979 | −0.563852 | ||||||||
\(786\) | 4.37814 | 0.156163 | ||||||||
\(787\) | 42.3311 | 1.50894 | 0.754470 | − | 0.656335i | \(-0.227894\pi\) | ||||
0.754470 | + | 0.656335i | \(0.227894\pi\) | |||||||
\(788\) | −21.5889 | −0.769074 | ||||||||
\(789\) | −0.365657 | −0.0130177 | ||||||||
\(790\) | 20.8188 | 0.740701 | ||||||||
\(791\) | 20.8880 | 0.742692 | ||||||||
\(792\) | −0.273647 | −0.00972363 | ||||||||
\(793\) | 8.11832 | 0.288290 | ||||||||
\(794\) | −28.4011 | −1.00792 | ||||||||
\(795\) | 27.4576 | 0.973820 | ||||||||
\(796\) | 15.4251 | 0.546728 | ||||||||
\(797\) | −47.2639 | −1.67417 | −0.837086 | − | 0.547071i | \(-0.815743\pi\) | ||||
−0.837086 | + | 0.547071i | \(0.815743\pi\) | |||||||
\(798\) | 34.7162 | 1.22894 | ||||||||
\(799\) | −30.0448 | −1.06291 | ||||||||
\(800\) | −2.85699 | −0.101010 | ||||||||
\(801\) | −2.69088 | −0.0950774 | ||||||||
\(802\) | −21.5763 | −0.761886 | ||||||||
\(803\) | 8.13558 | 0.287098 | ||||||||
\(804\) | −21.1099 | −0.744488 | ||||||||
\(805\) | 29.5055 | 1.03993 | ||||||||
\(806\) | −3.05802 | −0.107714 | ||||||||
\(807\) | 13.9081 | 0.489589 | ||||||||
\(808\) | 11.0254 | 0.387872 | ||||||||
\(809\) | 31.5230 | 1.10829 | 0.554144 | − | 0.832421i | \(-0.313046\pi\) | ||||
0.554144 | + | 0.832421i | \(0.313046\pi\) | |||||||
\(810\) | −11.0327 | −0.387651 | ||||||||
\(811\) | 32.8236 | 1.15259 | 0.576296 | − | 0.817241i | \(-0.304498\pi\) | ||||
0.576296 | + | 0.817241i | \(0.304498\pi\) | |||||||
\(812\) | 20.3443 | 0.713943 | ||||||||
\(813\) | −3.70547 | −0.129956 | ||||||||
\(814\) | 6.65109 | 0.233120 | ||||||||
\(815\) | −24.3431 | −0.852700 | ||||||||
\(816\) | −4.84174 | −0.169495 | ||||||||
\(817\) | 24.4561 | 0.855611 | ||||||||
\(818\) | −9.91465 | −0.346658 | ||||||||
\(819\) | 1.52872 | 0.0534178 | ||||||||
\(820\) | 6.31915 | 0.220674 | ||||||||
\(821\) | −30.5298 | −1.06550 | −0.532749 | − | 0.846273i | \(-0.678841\pi\) | ||||
−0.532749 | + | 0.846273i | \(0.678841\pi\) | |||||||
\(822\) | 0.818132 | 0.0285356 | ||||||||
\(823\) | 31.5870 | 1.10106 | 0.550528 | − | 0.834817i | \(-0.314427\pi\) | ||||
0.550528 | + | 0.834817i | \(0.314427\pi\) | |||||||
\(824\) | −7.91711 | −0.275805 | ||||||||
\(825\) | 2.93662 | 0.102240 | ||||||||
\(826\) | 0.148351 | 0.00516179 | ||||||||
\(827\) | −35.1242 | −1.22139 | −0.610693 | − | 0.791867i | \(-0.709109\pi\) | ||||
−0.610693 | + | 0.791867i | \(0.709109\pi\) | |||||||
\(828\) | −1.91181 | −0.0664401 | ||||||||
\(829\) | −20.6724 | −0.717982 | −0.358991 | − | 0.933341i | \(-0.616879\pi\) | ||||
−0.358991 | + | 0.933341i | \(0.616879\pi\) | |||||||
\(830\) | 21.2879 | 0.738914 | ||||||||
\(831\) | −0.864161 | −0.0299774 | ||||||||
\(832\) | −0.795145 | −0.0275667 | ||||||||
\(833\) | 40.0511 | 1.38769 | ||||||||
\(834\) | −11.8550 | −0.410505 | ||||||||
\(835\) | 30.3635 | 1.05077 | ||||||||
\(836\) | −3.08053 | −0.106542 | ||||||||
\(837\) | 21.1412 | 0.730748 | ||||||||
\(838\) | −30.1952 | −1.04308 | ||||||||
\(839\) | −14.4932 | −0.500362 | −0.250181 | − | 0.968199i | \(-0.580490\pi\) | ||||
−0.250181 | + | 0.968199i | \(0.580490\pi\) | |||||||
\(840\) | −10.5716 | −0.364756 | ||||||||
\(841\) | −8.57993 | −0.295860 | ||||||||
\(842\) | −18.5652 | −0.639800 | ||||||||
\(843\) | 1.55937 | 0.0537075 | ||||||||
\(844\) | 17.9469 | 0.617758 | ||||||||
\(845\) | −18.1052 | −0.622837 | ||||||||
\(846\) | 4.25062 | 0.146139 | ||||||||
\(847\) | −47.6742 | −1.63811 | ||||||||
\(848\) | −11.6932 | −0.401546 | ||||||||
\(849\) | −2.82441 | −0.0969334 | ||||||||
\(850\) | −8.62368 | −0.295790 | ||||||||
\(851\) | 46.4673 | 1.59288 | ||||||||
\(852\) | 12.3585 | 0.423396 | ||||||||
\(853\) | 2.25368 | 0.0771645 | 0.0385823 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385823 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(854\) | −45.9656 | −1.57291 | ||||||||
\(855\) | 3.00527 | 0.102778 | ||||||||
\(856\) | −12.0099 | −0.410490 | ||||||||
\(857\) | −34.4017 | −1.17514 | −0.587570 | − | 0.809173i | \(-0.699916\pi\) | ||||
−0.587570 | + | 0.809173i | \(0.699916\pi\) | |||||||
\(858\) | 0.817307 | 0.0279024 | ||||||||
\(859\) | −0.744390 | −0.0253982 | −0.0126991 | − | 0.999919i | \(-0.504042\pi\) | ||||
−0.0126991 | + | 0.999919i | \(0.504042\pi\) | |||||||
\(860\) | −7.44728 | −0.253950 | ||||||||
\(861\) | −31.1728 | −1.06237 | ||||||||
\(862\) | −29.5691 | −1.00713 | ||||||||
\(863\) | 39.1580 | 1.33295 | 0.666476 | − | 0.745526i | \(-0.267802\pi\) | ||||
0.666476 | + | 0.745526i | \(0.267802\pi\) | |||||||
\(864\) | 5.49713 | 0.187016 | ||||||||
\(865\) | −1.25420 | −0.0426439 | ||||||||
\(866\) | −37.6270 | −1.27862 | ||||||||
\(867\) | 12.6542 | 0.429759 | ||||||||
\(868\) | 17.3144 | 0.587689 | ||||||||
\(869\) | 9.11311 | 0.309141 | ||||||||
\(870\) | −10.6110 | −0.359748 | ||||||||
\(871\) | −10.4644 | −0.354573 | ||||||||
\(872\) | −9.78046 | −0.331208 | ||||||||
\(873\) | 3.06636 | 0.103781 | ||||||||
\(874\) | −21.5218 | −0.727987 | ||||||||
\(875\) | −51.7824 | −1.75056 | ||||||||
\(876\) | −20.3649 | −0.688066 | ||||||||
\(877\) | −19.0938 | −0.644751 | −0.322376 | − | 0.946612i | \(-0.604481\pi\) | ||||
−0.322376 | + | 0.946612i | \(0.604481\pi\) | |||||||
\(878\) | 22.4696 | 0.758314 | ||||||||
\(879\) | 39.1932 | 1.32195 | ||||||||
\(880\) | 0.938070 | 0.0316223 | ||||||||
\(881\) | −1.04628 | −0.0352500 | −0.0176250 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176250 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(882\) | −5.66627 | −0.190793 | ||||||||
\(883\) | −26.0847 | −0.877820 | −0.438910 | − | 0.898531i | \(-0.644635\pi\) | ||||
−0.438910 | + | 0.898531i | \(0.644635\pi\) | |||||||
\(884\) | −2.40011 | −0.0807244 | ||||||||
\(885\) | −0.0773759 | −0.00260096 | ||||||||
\(886\) | 36.7579 | 1.23491 | ||||||||
\(887\) | −11.1024 | −0.372783 | −0.186392 | − | 0.982476i | \(-0.559679\pi\) | ||||
−0.186392 | + | 0.982476i | \(0.559679\pi\) | |||||||
\(888\) | −16.6489 | −0.558702 | ||||||||
\(889\) | −67.4394 | −2.26184 | ||||||||
\(890\) | 9.22440 | 0.309203 | ||||||||
\(891\) | −4.82940 | −0.161791 | ||||||||
\(892\) | 1.95762 | 0.0655460 | ||||||||
\(893\) | 47.8505 | 1.60126 | ||||||||
\(894\) | −22.4614 | −0.751220 | ||||||||
\(895\) | −4.71766 | −0.157694 | ||||||||
\(896\) | 4.50208 | 0.150404 | ||||||||
\(897\) | 5.71005 | 0.190653 | ||||||||
\(898\) | −4.29656 | −0.143378 | ||||||||
\(899\) | 17.3789 | 0.579620 | ||||||||
\(900\) | 1.22005 | 0.0406682 | ||||||||
\(901\) | −35.2954 | −1.17586 | ||||||||
\(902\) | 2.76611 | 0.0921012 | ||||||||
\(903\) | 36.7379 | 1.22256 | ||||||||
\(904\) | 4.63963 | 0.154312 | ||||||||
\(905\) | 20.7707 | 0.690440 | ||||||||
\(906\) | −0.269008 | −0.00893721 | ||||||||
\(907\) | 41.9498 | 1.39292 | 0.696460 | − | 0.717595i | \(-0.254757\pi\) | ||||
0.696460 | + | 0.717595i | \(0.254757\pi\) | |||||||
\(908\) | 20.7135 | 0.687401 | ||||||||
\(909\) | −4.70828 | −0.156164 | ||||||||
\(910\) | −5.24049 | −0.173721 | ||||||||
\(911\) | −42.8803 | −1.42069 | −0.710344 | − | 0.703855i | \(-0.751461\pi\) | ||||
−0.710344 | + | 0.703855i | \(0.751461\pi\) | |||||||
\(912\) | 7.71114 | 0.255341 | ||||||||
\(913\) | 9.31844 | 0.308395 | ||||||||
\(914\) | −4.32456 | −0.143044 | ||||||||
\(915\) | 23.9745 | 0.792572 | ||||||||
\(916\) | 14.1741 | 0.468325 | ||||||||
\(917\) | −12.2881 | −0.405790 | ||||||||
\(918\) | 16.5928 | 0.547645 | ||||||||
\(919\) | 5.70909 | 0.188325 | 0.0941627 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941627 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(920\) | 6.55375 | 0.216071 | ||||||||
\(921\) | 8.43508 | 0.277945 | ||||||||
\(922\) | −30.6666 | −1.00995 | ||||||||
\(923\) | 6.12628 | 0.201649 | ||||||||
\(924\) | −4.62757 | −0.152236 | ||||||||
\(925\) | −29.6536 | −0.975006 | ||||||||
\(926\) | 0.252334 | 0.00829222 | ||||||||
\(927\) | 3.38092 | 0.111044 | ||||||||
\(928\) | 4.51886 | 0.148339 | ||||||||
\(929\) | −19.3802 | −0.635844 | −0.317922 | − | 0.948117i | \(-0.602985\pi\) | ||||
−0.317922 | + | 0.948117i | \(0.602985\pi\) | |||||||
\(930\) | −9.03075 | −0.296130 | ||||||||
\(931\) | −63.7869 | −2.09053 | ||||||||
\(932\) | 13.5610 | 0.444207 | ||||||||
\(933\) | 25.8359 | 0.845830 | ||||||||
\(934\) | −11.7911 | −0.385817 | ||||||||
\(935\) | 2.83152 | 0.0926007 | ||||||||
\(936\) | 0.339558 | 0.0110988 | ||||||||
\(937\) | −36.1143 | −1.17980 | −0.589901 | − | 0.807475i | \(-0.700833\pi\) | ||||
−0.589901 | + | 0.807475i | \(0.700833\pi\) | |||||||
\(938\) | 59.2492 | 1.93455 | ||||||||
\(939\) | 35.2725 | 1.15107 | ||||||||
\(940\) | −14.5713 | −0.475262 | ||||||||
\(941\) | −30.1657 | −0.983374 | −0.491687 | − | 0.870772i | \(-0.663620\pi\) | ||||
−0.491687 | + | 0.870772i | \(0.663620\pi\) | |||||||
\(942\) | 17.3103 | 0.564000 | ||||||||
\(943\) | 19.3252 | 0.629314 | ||||||||
\(944\) | 0.0329516 | 0.00107248 | ||||||||
\(945\) | 36.2294 | 1.17854 | ||||||||
\(946\) | −3.25993 | −0.105989 | ||||||||
\(947\) | −5.83660 | −0.189664 | −0.0948319 | − | 0.995493i | \(-0.530231\pi\) | ||||
−0.0948319 | + | 0.995493i | \(0.530231\pi\) | |||||||
\(948\) | −22.8118 | −0.740894 | ||||||||
\(949\) | −10.0951 | −0.327702 | ||||||||
\(950\) | 13.7344 | 0.445603 | ||||||||
\(951\) | 27.7856 | 0.901009 | ||||||||
\(952\) | 13.5893 | 0.440433 | ||||||||
\(953\) | −42.4375 | −1.37469 | −0.687343 | − | 0.726333i | \(-0.741223\pi\) | ||||
−0.687343 | + | 0.726333i | \(0.741223\pi\) | |||||||
\(954\) | 4.99346 | 0.161669 | ||||||||
\(955\) | 20.8194 | 0.673700 | ||||||||
\(956\) | 19.1300 | 0.618708 | ||||||||
\(957\) | −4.64481 | −0.150145 | ||||||||
\(958\) | 18.7333 | 0.605245 | ||||||||
\(959\) | −2.29626 | −0.0741500 | ||||||||
\(960\) | −2.34817 | −0.0757868 | ||||||||
\(961\) | −16.2093 | −0.522880 | ||||||||
\(962\) | −8.25308 | −0.266090 | ||||||||
\(963\) | 5.12870 | 0.165270 | ||||||||
\(964\) | 8.68193 | 0.279626 | ||||||||
\(965\) | 27.9421 | 0.899489 | ||||||||
\(966\) | −32.3301 | −1.04020 | ||||||||
\(967\) | 34.3625 | 1.10502 | 0.552512 | − | 0.833505i | \(-0.313669\pi\) | ||||
0.552512 | + | 0.833505i | \(0.313669\pi\) | |||||||
\(968\) | −10.5894 | −0.340355 | ||||||||
\(969\) | 23.2757 | 0.747724 | ||||||||
\(970\) | −10.5116 | −0.337506 | ||||||||
\(971\) | −21.1595 | −0.679042 | −0.339521 | − | 0.940599i | \(-0.610265\pi\) | ||||
−0.339521 | + | 0.940599i | \(0.610265\pi\) | |||||||
\(972\) | −4.40246 | −0.141209 | ||||||||
\(973\) | 33.2735 | 1.06670 | ||||||||
\(974\) | −35.2519 | −1.12954 | ||||||||
\(975\) | −3.64394 | −0.116699 | ||||||||
\(976\) | −10.2099 | −0.326810 | ||||||||
\(977\) | −53.7924 | −1.72097 | −0.860486 | − | 0.509474i | \(-0.829840\pi\) | ||||
−0.860486 | + | 0.509474i | \(0.829840\pi\) | |||||||
\(978\) | 26.6734 | 0.852923 | ||||||||
\(979\) | 4.03783 | 0.129050 | ||||||||
\(980\) | 19.4241 | 0.620481 | ||||||||
\(981\) | 4.17664 | 0.133350 | ||||||||
\(982\) | −40.3227 | −1.28675 | ||||||||
\(983\) | 17.3371 | 0.552969 | 0.276484 | − | 0.961018i | \(-0.410831\pi\) | ||||
0.276484 | + | 0.961018i | \(0.410831\pi\) | |||||||
\(984\) | −6.92409 | −0.220732 | ||||||||
\(985\) | −31.6041 | −1.00699 | ||||||||
\(986\) | 13.6400 | 0.434385 | ||||||||
\(987\) | 71.8810 | 2.28800 | ||||||||
\(988\) | 3.82251 | 0.121610 | ||||||||
\(989\) | −22.7752 | −0.724209 | ||||||||
\(990\) | −0.400593 | −0.0127317 | ||||||||
\(991\) | −3.87627 | −0.123134 | −0.0615668 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615668 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(992\) | 3.84587 | 0.122106 | ||||||||
\(993\) | −43.8424 | −1.39130 | ||||||||
\(994\) | −34.6868 | −1.10020 | ||||||||
\(995\) | 22.5809 | 0.715861 | ||||||||
\(996\) | −23.3258 | −0.739107 | ||||||||
\(997\) | −53.5674 | −1.69650 | −0.848248 | − | 0.529600i | \(-0.822342\pi\) | ||||
−0.848248 | + | 0.529600i | \(0.822342\pi\) | |||||||
\(998\) | −8.63150 | −0.273225 | ||||||||
\(999\) | 57.0566 | 1.80519 |
(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.f.1.11 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.f.1.11 | ✓ | 50 | 1.1 | even | 1 | trivial |