Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(0\) |
Dimension: | \(138\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24651 | −1.58852 | −0.794262 | − | 0.607575i | \(-0.792142\pi\) | ||||
−0.794262 | + | 0.607575i | \(0.792142\pi\) | |||||||
\(3\) | −2.33680 | −1.34915 | −0.674577 | − | 0.738204i | \(-0.735674\pi\) | ||||
−0.674577 | + | 0.738204i | \(0.735674\pi\) | |||||||
\(4\) | 3.04682 | 1.52341 | ||||||||
\(5\) | 3.03120 | 1.35559 | 0.677796 | − | 0.735250i | \(-0.262935\pi\) | ||||
0.677796 | + | 0.735250i | \(0.262935\pi\) | |||||||
\(6\) | 5.24966 | 2.14316 | ||||||||
\(7\) | −0.990135 | −0.374236 | −0.187118 | − | 0.982337i | \(-0.559915\pi\) | ||||
−0.187118 | + | 0.982337i | \(0.559915\pi\) | |||||||
\(8\) | −2.35169 | −0.831448 | ||||||||
\(9\) | 2.46065 | 0.820218 | ||||||||
\(10\) | −6.80962 | −2.15339 | ||||||||
\(11\) | −4.71761 | −1.42241 | −0.711206 | − | 0.702984i | \(-0.751851\pi\) | ||||
−0.711206 | + | 0.702984i | \(0.751851\pi\) | |||||||
\(12\) | −7.11982 | −2.05531 | ||||||||
\(13\) | 0.982347 | 0.272454 | 0.136227 | − | 0.990678i | \(-0.456502\pi\) | ||||
0.136227 | + | 0.990678i | \(0.456502\pi\) | |||||||
\(14\) | 2.22435 | 0.594483 | ||||||||
\(15\) | −7.08331 | −1.82890 | ||||||||
\(16\) | −0.810536 | −0.202634 | ||||||||
\(17\) | 1.95999 | 0.475368 | 0.237684 | − | 0.971343i | \(-0.423612\pi\) | ||||
0.237684 | + | 0.971343i | \(0.423612\pi\) | |||||||
\(18\) | −5.52789 | −1.30294 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 9.23550 | 2.06512 | ||||||||
\(21\) | 2.31375 | 0.504902 | ||||||||
\(22\) | 10.5982 | 2.25954 | ||||||||
\(23\) | −7.14721 | −1.49030 | −0.745149 | − | 0.666898i | \(-0.767621\pi\) | ||||
−0.745149 | + | 0.666898i | \(0.767621\pi\) | |||||||
\(24\) | 5.49544 | 1.12175 | ||||||||
\(25\) | 4.18814 | 0.837629 | ||||||||
\(26\) | −2.20685 | −0.432800 | ||||||||
\(27\) | 1.26035 | 0.242554 | ||||||||
\(28\) | −3.01676 | −0.570114 | ||||||||
\(29\) | 4.75205 | 0.882433 | 0.441216 | − | 0.897401i | \(-0.354547\pi\) | ||||
0.441216 | + | 0.897401i | \(0.354547\pi\) | |||||||
\(30\) | 15.9127 | 2.90526 | ||||||||
\(31\) | −9.35401 | −1.68003 | −0.840015 | − | 0.542563i | \(-0.817454\pi\) | ||||
−0.840015 | + | 0.542563i | \(0.817454\pi\) | |||||||
\(32\) | 6.52426 | 1.15334 | ||||||||
\(33\) | 11.0241 | 1.91905 | ||||||||
\(34\) | −4.40314 | −0.755133 | ||||||||
\(35\) | −3.00129 | −0.507311 | ||||||||
\(36\) | 7.49716 | 1.24953 | ||||||||
\(37\) | −10.7647 | −1.76970 | −0.884851 | − | 0.465873i | \(-0.845740\pi\) | ||||
−0.884851 | + | 0.465873i | \(0.845740\pi\) | |||||||
\(38\) | −2.24651 | −0.364432 | ||||||||
\(39\) | −2.29555 | −0.367582 | ||||||||
\(40\) | −7.12843 | −1.12710 | ||||||||
\(41\) | −7.04437 | −1.10015 | −0.550073 | − | 0.835116i | \(-0.685400\pi\) | ||||
−0.550073 | + | 0.835116i | \(0.685400\pi\) | |||||||
\(42\) | −5.19787 | −0.802049 | ||||||||
\(43\) | −5.79369 | −0.883529 | −0.441765 | − | 0.897131i | \(-0.645647\pi\) | ||||
−0.441765 | + | 0.897131i | \(0.645647\pi\) | |||||||
\(44\) | −14.3737 | −2.16692 | ||||||||
\(45\) | 7.45872 | 1.11188 | ||||||||
\(46\) | 16.0563 | 2.36737 | ||||||||
\(47\) | −5.58364 | −0.814457 | −0.407229 | − | 0.913326i | \(-0.633505\pi\) | ||||
−0.407229 | + | 0.913326i | \(0.633505\pi\) | |||||||
\(48\) | 1.89406 | 0.273385 | ||||||||
\(49\) | −6.01963 | −0.859948 | ||||||||
\(50\) | −9.40872 | −1.33059 | ||||||||
\(51\) | −4.58012 | −0.641344 | ||||||||
\(52\) | 2.99303 | 0.415059 | ||||||||
\(53\) | 1.96479 | 0.269884 | 0.134942 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134942 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(54\) | −2.83139 | −0.385303 | ||||||||
\(55\) | −14.3000 | −1.92821 | ||||||||
\(56\) | 2.32849 | 0.311158 | ||||||||
\(57\) | −2.33680 | −0.309517 | ||||||||
\(58\) | −10.6755 | −1.40177 | ||||||||
\(59\) | 6.40016 | 0.833230 | 0.416615 | − | 0.909083i | \(-0.363216\pi\) | ||||
0.416615 | + | 0.909083i | \(0.363216\pi\) | |||||||
\(60\) | −21.5816 | −2.78617 | ||||||||
\(61\) | 13.2076 | 1.69106 | 0.845528 | − | 0.533931i | \(-0.179286\pi\) | ||||
0.845528 | + | 0.533931i | \(0.179286\pi\) | |||||||
\(62\) | 21.0139 | 2.66877 | ||||||||
\(63\) | −2.43638 | −0.306955 | ||||||||
\(64\) | −13.0358 | −1.62947 | ||||||||
\(65\) | 2.97768 | 0.369336 | ||||||||
\(66\) | −24.7658 | −3.04846 | ||||||||
\(67\) | 11.2308 | 1.37206 | 0.686030 | − | 0.727573i | \(-0.259352\pi\) | ||||
0.686030 | + | 0.727573i | \(0.259352\pi\) | |||||||
\(68\) | 5.97174 | 0.724179 | ||||||||
\(69\) | 16.7016 | 2.01064 | ||||||||
\(70\) | 6.74244 | 0.805876 | ||||||||
\(71\) | −6.38919 | −0.758257 | −0.379129 | − | 0.925344i | \(-0.623776\pi\) | ||||
−0.379129 | + | 0.925344i | \(0.623776\pi\) | |||||||
\(72\) | −5.78669 | −0.681968 | ||||||||
\(73\) | 4.18724 | 0.490079 | 0.245040 | − | 0.969513i | \(-0.421199\pi\) | ||||
0.245040 | + | 0.969513i | \(0.421199\pi\) | |||||||
\(74\) | 24.1830 | 2.81122 | ||||||||
\(75\) | −9.78687 | −1.13009 | ||||||||
\(76\) | 3.04682 | 0.349494 | ||||||||
\(77\) | 4.67107 | 0.532318 | ||||||||
\(78\) | 5.15698 | 0.583914 | ||||||||
\(79\) | −4.55325 | −0.512281 | −0.256140 | − | 0.966640i | \(-0.582451\pi\) | ||||
−0.256140 | + | 0.966640i | \(0.582451\pi\) | |||||||
\(80\) | −2.45689 | −0.274689 | ||||||||
\(81\) | −10.3271 | −1.14746 | ||||||||
\(82\) | 15.8253 | 1.74761 | ||||||||
\(83\) | −9.02474 | −0.990594 | −0.495297 | − | 0.868724i | \(-0.664941\pi\) | ||||
−0.495297 | + | 0.868724i | \(0.664941\pi\) | |||||||
\(84\) | 7.04958 | 0.769172 | ||||||||
\(85\) | 5.94112 | 0.644405 | ||||||||
\(86\) | 13.0156 | 1.40351 | ||||||||
\(87\) | −11.1046 | −1.19054 | ||||||||
\(88\) | 11.0943 | 1.18266 | ||||||||
\(89\) | −14.5015 | −1.53716 | −0.768579 | − | 0.639755i | \(-0.779036\pi\) | ||||
−0.768579 | + | 0.639755i | \(0.779036\pi\) | |||||||
\(90\) | −16.7561 | −1.76625 | ||||||||
\(91\) | −0.972656 | −0.101962 | ||||||||
\(92\) | −21.7763 | −2.27033 | ||||||||
\(93\) | 21.8585 | 2.26662 | ||||||||
\(94\) | 12.5437 | 1.29378 | ||||||||
\(95\) | 3.03120 | 0.310994 | ||||||||
\(96\) | −15.2459 | −1.55603 | ||||||||
\(97\) | 0.636067 | 0.0645828 | 0.0322914 | − | 0.999478i | \(-0.489720\pi\) | ||||
0.0322914 | + | 0.999478i | \(0.489720\pi\) | |||||||
\(98\) | 13.5232 | 1.36605 | ||||||||
\(99\) | −11.6084 | −1.16669 | ||||||||
\(100\) | 12.7605 | 1.27605 | ||||||||
\(101\) | 18.0618 | 1.79721 | 0.898607 | − | 0.438755i | \(-0.144581\pi\) | ||||
0.898607 | + | 0.438755i | \(0.144581\pi\) | |||||||
\(102\) | 10.2893 | 1.01879 | ||||||||
\(103\) | 10.9746 | 1.08136 | 0.540681 | − | 0.841228i | \(-0.318167\pi\) | ||||
0.540681 | + | 0.841228i | \(0.318167\pi\) | |||||||
\(104\) | −2.31017 | −0.226531 | ||||||||
\(105\) | 7.01343 | 0.684441 | ||||||||
\(106\) | −4.41392 | −0.428718 | ||||||||
\(107\) | 20.0448 | 1.93781 | 0.968903 | − | 0.247442i | \(-0.0795901\pi\) | ||||
0.968903 | + | 0.247442i | \(0.0795901\pi\) | |||||||
\(108\) | 3.84005 | 0.369509 | ||||||||
\(109\) | 16.6461 | 1.59441 | 0.797206 | − | 0.603708i | \(-0.206311\pi\) | ||||
0.797206 | + | 0.603708i | \(0.206311\pi\) | |||||||
\(110\) | 32.1251 | 3.06301 | ||||||||
\(111\) | 25.1550 | 2.38760 | ||||||||
\(112\) | 0.802540 | 0.0758329 | ||||||||
\(113\) | −6.70393 | −0.630653 | −0.315326 | − | 0.948983i | \(-0.602114\pi\) | ||||
−0.315326 | + | 0.948983i | \(0.602114\pi\) | |||||||
\(114\) | 5.24966 | 0.491676 | ||||||||
\(115\) | −21.6646 | −2.02023 | ||||||||
\(116\) | 14.4786 | 1.34431 | ||||||||
\(117\) | 2.41721 | 0.223472 | ||||||||
\(118\) | −14.3780 | −1.32361 | ||||||||
\(119\) | −1.94066 | −0.177900 | ||||||||
\(120\) | 16.6577 | 1.52064 | ||||||||
\(121\) | 11.2558 | 1.02326 | ||||||||
\(122\) | −29.6710 | −2.68628 | ||||||||
\(123\) | 16.4613 | 1.48427 | ||||||||
\(124\) | −28.5000 | −2.55937 | ||||||||
\(125\) | −2.46089 | −0.220109 | ||||||||
\(126\) | 5.47335 | 0.487605 | ||||||||
\(127\) | 15.8629 | 1.40761 | 0.703803 | − | 0.710396i | \(-0.251484\pi\) | ||||
0.703803 | + | 0.710396i | \(0.251484\pi\) | |||||||
\(128\) | 16.2365 | 1.43511 | ||||||||
\(129\) | 13.5387 | 1.19202 | ||||||||
\(130\) | −6.68940 | −0.586700 | ||||||||
\(131\) | −0.984306 | −0.0859993 | −0.0429996 | − | 0.999075i | \(-0.513691\pi\) | ||||
−0.0429996 | + | 0.999075i | \(0.513691\pi\) | |||||||
\(132\) | 33.5885 | 2.92350 | ||||||||
\(133\) | −0.990135 | −0.0858556 | ||||||||
\(134\) | −25.2301 | −2.17955 | ||||||||
\(135\) | 3.82036 | 0.328804 | ||||||||
\(136\) | −4.60929 | −0.395243 | ||||||||
\(137\) | −9.80107 | −0.837362 | −0.418681 | − | 0.908133i | \(-0.637507\pi\) | ||||
−0.418681 | + | 0.908133i | \(0.637507\pi\) | |||||||
\(138\) | −37.5204 | −3.19395 | ||||||||
\(139\) | −1.48104 | −0.125620 | −0.0628099 | − | 0.998026i | \(-0.520006\pi\) | ||||
−0.0628099 | + | 0.998026i | \(0.520006\pi\) | |||||||
\(140\) | −9.14439 | −0.772842 | ||||||||
\(141\) | 13.0479 | 1.09883 | ||||||||
\(142\) | 14.3534 | 1.20451 | ||||||||
\(143\) | −4.63433 | −0.387542 | ||||||||
\(144\) | −1.99445 | −0.166204 | ||||||||
\(145\) | 14.4044 | 1.19622 | ||||||||
\(146\) | −9.40669 | −0.778503 | ||||||||
\(147\) | 14.0667 | 1.16020 | ||||||||
\(148\) | −32.7980 | −2.69598 | ||||||||
\(149\) | 9.30290 | 0.762123 | 0.381062 | − | 0.924550i | \(-0.375559\pi\) | ||||
0.381062 | + | 0.924550i | \(0.375559\pi\) | |||||||
\(150\) | 21.9863 | 1.79518 | ||||||||
\(151\) | −5.24037 | −0.426456 | −0.213228 | − | 0.977003i | \(-0.568398\pi\) | ||||
−0.213228 | + | 0.977003i | \(0.568398\pi\) | |||||||
\(152\) | −2.35169 | −0.190747 | ||||||||
\(153\) | 4.82286 | 0.389905 | ||||||||
\(154\) | −10.4936 | −0.845599 | ||||||||
\(155\) | −28.3538 | −2.27743 | ||||||||
\(156\) | −6.99413 | −0.559978 | ||||||||
\(157\) | −6.98762 | −0.557673 | −0.278836 | − | 0.960339i | \(-0.589949\pi\) | ||||
−0.278836 | + | 0.960339i | \(0.589949\pi\) | |||||||
\(158\) | 10.2289 | 0.813770 | ||||||||
\(159\) | −4.59132 | −0.364116 | ||||||||
\(160\) | 19.7763 | 1.56345 | ||||||||
\(161\) | 7.07671 | 0.557723 | ||||||||
\(162\) | 23.2001 | 1.82277 | ||||||||
\(163\) | −14.9708 | −1.17260 | −0.586300 | − | 0.810094i | \(-0.699416\pi\) | ||||
−0.586300 | + | 0.810094i | \(0.699416\pi\) | |||||||
\(164\) | −21.4629 | −1.67597 | ||||||||
\(165\) | 33.4163 | 2.60145 | ||||||||
\(166\) | 20.2742 | 1.57358 | ||||||||
\(167\) | −0.920748 | −0.0712496 | −0.0356248 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356248 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(168\) | −5.44123 | −0.419800 | ||||||||
\(169\) | −12.0350 | −0.925769 | ||||||||
\(170\) | −13.3468 | −1.02365 | ||||||||
\(171\) | 2.46065 | 0.188171 | ||||||||
\(172\) | −17.6523 | −1.34598 | ||||||||
\(173\) | 20.2945 | 1.54296 | 0.771481 | − | 0.636252i | \(-0.219516\pi\) | ||||
0.771481 | + | 0.636252i | \(0.219516\pi\) | |||||||
\(174\) | 24.9466 | 1.89120 | ||||||||
\(175\) | −4.14683 | −0.313471 | ||||||||
\(176\) | 3.82379 | 0.288229 | ||||||||
\(177\) | −14.9559 | −1.12416 | ||||||||
\(178\) | 32.5778 | 2.44181 | ||||||||
\(179\) | −21.7633 | −1.62666 | −0.813332 | − | 0.581799i | \(-0.802349\pi\) | ||||
−0.813332 | + | 0.581799i | \(0.802349\pi\) | |||||||
\(180\) | 22.7254 | 1.69385 | ||||||||
\(181\) | 20.3646 | 1.51369 | 0.756845 | − | 0.653594i | \(-0.226740\pi\) | ||||
0.756845 | + | 0.653594i | \(0.226740\pi\) | |||||||
\(182\) | 2.18508 | 0.161969 | ||||||||
\(183\) | −30.8635 | −2.28150 | ||||||||
\(184\) | 16.8080 | 1.23910 | ||||||||
\(185\) | −32.6299 | −2.39899 | ||||||||
\(186\) | −49.1054 | −3.60058 | ||||||||
\(187\) | −9.24647 | −0.676169 | ||||||||
\(188\) | −17.0123 | −1.24075 | ||||||||
\(189\) | −1.24791 | −0.0907724 | ||||||||
\(190\) | −6.80962 | −0.494022 | ||||||||
\(191\) | −1.88675 | −0.136520 | −0.0682601 | − | 0.997668i | \(-0.521745\pi\) | ||||
−0.0682601 | + | 0.997668i | \(0.521745\pi\) | |||||||
\(192\) | 30.4620 | 2.19841 | ||||||||
\(193\) | −10.4251 | −0.750415 | −0.375207 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375207 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(194\) | −1.42893 | −0.102591 | ||||||||
\(195\) | −6.95826 | −0.498292 | ||||||||
\(196\) | −18.3407 | −1.31005 | ||||||||
\(197\) | 4.85938 | 0.346217 | 0.173108 | − | 0.984903i | \(-0.444619\pi\) | ||||
0.173108 | + | 0.984903i | \(0.444619\pi\) | |||||||
\(198\) | 26.0784 | 1.85331 | ||||||||
\(199\) | 7.32918 | 0.519552 | 0.259776 | − | 0.965669i | \(-0.416351\pi\) | ||||
0.259776 | + | 0.965669i | \(0.416351\pi\) | |||||||
\(200\) | −9.84922 | −0.696445 | ||||||||
\(201\) | −26.2442 | −1.85112 | ||||||||
\(202\) | −40.5760 | −2.85492 | ||||||||
\(203\) | −4.70517 | −0.330238 | ||||||||
\(204\) | −13.9548 | −0.977030 | ||||||||
\(205\) | −21.3529 | −1.49135 | ||||||||
\(206\) | −24.6546 | −1.71777 | ||||||||
\(207\) | −17.5868 | −1.22237 | ||||||||
\(208\) | −0.796227 | −0.0552084 | ||||||||
\(209\) | −4.71761 | −0.326324 | ||||||||
\(210\) | −15.7558 | −1.08725 | ||||||||
\(211\) | 1.68065 | 0.115701 | 0.0578503 | − | 0.998325i | \(-0.481575\pi\) | ||||
0.0578503 | + | 0.998325i | \(0.481575\pi\) | |||||||
\(212\) | 5.98635 | 0.411144 | ||||||||
\(213\) | 14.9303 | 1.02301 | ||||||||
\(214\) | −45.0309 | −3.07825 | ||||||||
\(215\) | −17.5618 | −1.19771 | ||||||||
\(216\) | −2.96395 | −0.201671 | ||||||||
\(217\) | 9.26173 | 0.628727 | ||||||||
\(218\) | −37.3958 | −2.53276 | ||||||||
\(219\) | −9.78476 | −0.661193 | ||||||||
\(220\) | −43.5695 | −2.93745 | ||||||||
\(221\) | 1.92539 | 0.129516 | ||||||||
\(222\) | −56.5109 | −3.79276 | ||||||||
\(223\) | 7.20359 | 0.482388 | 0.241194 | − | 0.970477i | \(-0.422461\pi\) | ||||
0.241194 | + | 0.970477i | \(0.422461\pi\) | |||||||
\(224\) | −6.45990 | −0.431620 | ||||||||
\(225\) | 10.3056 | 0.687038 | ||||||||
\(226\) | 15.0605 | 1.00181 | ||||||||
\(227\) | 26.9962 | 1.79180 | 0.895901 | − | 0.444255i | \(-0.146531\pi\) | ||||
0.895901 | + | 0.444255i | \(0.146531\pi\) | |||||||
\(228\) | −7.11982 | −0.471521 | ||||||||
\(229\) | −19.5521 | −1.29204 | −0.646019 | − | 0.763321i | \(-0.723567\pi\) | ||||
−0.646019 | + | 0.763321i | \(0.723567\pi\) | |||||||
\(230\) | 48.6698 | 3.20919 | ||||||||
\(231\) | −10.9154 | −0.718179 | ||||||||
\(232\) | −11.1753 | −0.733697 | ||||||||
\(233\) | −5.06179 | −0.331609 | −0.165805 | − | 0.986159i | \(-0.553022\pi\) | ||||
−0.165805 | + | 0.986159i | \(0.553022\pi\) | |||||||
\(234\) | −5.43030 | −0.354990 | ||||||||
\(235\) | −16.9251 | −1.10407 | ||||||||
\(236\) | 19.5001 | 1.26935 | ||||||||
\(237\) | 10.6401 | 0.691146 | ||||||||
\(238\) | 4.35971 | 0.282598 | ||||||||
\(239\) | −7.81353 | −0.505415 | −0.252708 | − | 0.967543i | \(-0.581321\pi\) | ||||
−0.252708 | + | 0.967543i | \(0.581321\pi\) | |||||||
\(240\) | 5.74128 | 0.370598 | ||||||||
\(241\) | −7.68831 | −0.495248 | −0.247624 | − | 0.968856i | \(-0.579650\pi\) | ||||
−0.247624 | + | 0.968856i | \(0.579650\pi\) | |||||||
\(242\) | −25.2863 | −1.62547 | ||||||||
\(243\) | 20.3515 | 1.30555 | ||||||||
\(244\) | 40.2411 | 2.57617 | ||||||||
\(245\) | −18.2467 | −1.16574 | ||||||||
\(246\) | −36.9806 | −2.35779 | ||||||||
\(247\) | 0.982347 | 0.0625052 | ||||||||
\(248\) | 21.9977 | 1.39686 | ||||||||
\(249\) | 21.0891 | 1.33646 | ||||||||
\(250\) | 5.52843 | 0.349649 | ||||||||
\(251\) | 12.0524 | 0.760741 | 0.380370 | − | 0.924834i | \(-0.375797\pi\) | ||||
0.380370 | + | 0.924834i | \(0.375797\pi\) | |||||||
\(252\) | −7.42320 | −0.467618 | ||||||||
\(253\) | 33.7177 | 2.11982 | ||||||||
\(254\) | −35.6362 | −2.23601 | ||||||||
\(255\) | −13.8832 | −0.869401 | ||||||||
\(256\) | −10.4039 | −0.650245 | ||||||||
\(257\) | 1.62358 | 0.101276 | 0.0506379 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506379 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(258\) | −30.4149 | −1.89355 | ||||||||
\(259\) | 10.6585 | 0.662286 | ||||||||
\(260\) | 9.07246 | 0.562650 | ||||||||
\(261\) | 11.6931 | 0.723787 | ||||||||
\(262\) | 2.21126 | 0.136612 | ||||||||
\(263\) | −3.59961 | −0.221961 | −0.110981 | − | 0.993823i | \(-0.535399\pi\) | ||||
−0.110981 | + | 0.993823i | \(0.535399\pi\) | |||||||
\(264\) | −25.9253 | −1.59559 | ||||||||
\(265\) | 5.95566 | 0.365853 | ||||||||
\(266\) | 2.22435 | 0.136384 | ||||||||
\(267\) | 33.8872 | 2.07386 | ||||||||
\(268\) | 34.2182 | 2.09021 | ||||||||
\(269\) | 12.3974 | 0.755882 | 0.377941 | − | 0.925830i | \(-0.376632\pi\) | ||||
0.377941 | + | 0.925830i | \(0.376632\pi\) | |||||||
\(270\) | −8.58249 | −0.522313 | ||||||||
\(271\) | −20.7277 | −1.25912 | −0.629558 | − | 0.776953i | \(-0.716764\pi\) | ||||
−0.629558 | + | 0.776953i | \(0.716764\pi\) | |||||||
\(272\) | −1.58864 | −0.0963256 | ||||||||
\(273\) | 2.27291 | 0.137563 | ||||||||
\(274\) | 22.0182 | 1.33017 | ||||||||
\(275\) | −19.7580 | −1.19145 | ||||||||
\(276\) | 50.8869 | 3.06303 | ||||||||
\(277\) | 16.4598 | 0.988973 | 0.494486 | − | 0.869185i | \(-0.335356\pi\) | ||||
0.494486 | + | 0.869185i | \(0.335356\pi\) | |||||||
\(278\) | 3.32717 | 0.199550 | ||||||||
\(279\) | −23.0170 | −1.37799 | ||||||||
\(280\) | 7.05811 | 0.421803 | ||||||||
\(281\) | −23.7608 | −1.41745 | −0.708725 | − | 0.705485i | \(-0.750729\pi\) | ||||
−0.708725 | + | 0.705485i | \(0.750729\pi\) | |||||||
\(282\) | −29.3122 | −1.74552 | ||||||||
\(283\) | −27.1330 | −1.61289 | −0.806444 | − | 0.591310i | \(-0.798611\pi\) | ||||
−0.806444 | + | 0.591310i | \(0.798611\pi\) | |||||||
\(284\) | −19.4667 | −1.15514 | ||||||||
\(285\) | −7.08331 | −0.419579 | ||||||||
\(286\) | 10.4111 | 0.615619 | ||||||||
\(287\) | 6.97488 | 0.411714 | ||||||||
\(288\) | 16.0539 | 0.945987 | ||||||||
\(289\) | −13.1584 | −0.774026 | ||||||||
\(290\) | −32.3596 | −1.90022 | ||||||||
\(291\) | −1.48636 | −0.0871321 | ||||||||
\(292\) | 12.7578 | 0.746591 | ||||||||
\(293\) | 10.4635 | 0.611287 | 0.305644 | − | 0.952146i | \(-0.401128\pi\) | ||||
0.305644 | + | 0.952146i | \(0.401128\pi\) | |||||||
\(294\) | −31.6010 | −1.84301 | ||||||||
\(295\) | 19.4001 | 1.12952 | ||||||||
\(296\) | 25.3152 | 1.47142 | ||||||||
\(297\) | −5.94583 | −0.345012 | ||||||||
\(298\) | −20.8991 | −1.21065 | ||||||||
\(299\) | −7.02104 | −0.406037 | ||||||||
\(300\) | −29.8188 | −1.72159 | ||||||||
\(301\) | 5.73653 | 0.330648 | ||||||||
\(302\) | 11.7726 | 0.677435 | ||||||||
\(303\) | −42.2068 | −2.42472 | ||||||||
\(304\) | −0.810536 | −0.0464874 | ||||||||
\(305\) | 40.0347 | 2.29238 | ||||||||
\(306\) | −10.8346 | −0.619374 | ||||||||
\(307\) | 21.2390 | 1.21217 | 0.606087 | − | 0.795398i | \(-0.292738\pi\) | ||||
0.606087 | + | 0.795398i | \(0.292738\pi\) | |||||||
\(308\) | 14.2319 | 0.810937 | ||||||||
\(309\) | −25.6455 | −1.45892 | ||||||||
\(310\) | 63.6972 | 3.61776 | ||||||||
\(311\) | −8.08881 | −0.458674 | −0.229337 | − | 0.973347i | \(-0.573656\pi\) | ||||
−0.229337 | + | 0.973347i | \(0.573656\pi\) | |||||||
\(312\) | 5.39842 | 0.305626 | ||||||||
\(313\) | 25.2086 | 1.42487 | 0.712436 | − | 0.701737i | \(-0.247592\pi\) | ||||
0.712436 | + | 0.701737i | \(0.247592\pi\) | |||||||
\(314\) | 15.6978 | 0.885877 | ||||||||
\(315\) | −7.38514 | −0.416105 | ||||||||
\(316\) | −13.8729 | −0.780413 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | 10.3145 | 0.578407 | ||||||||
\(319\) | −22.4183 | −1.25518 | ||||||||
\(320\) | −39.5139 | −2.20890 | ||||||||
\(321\) | −46.8408 | −2.61440 | ||||||||
\(322\) | −15.8979 | −0.885956 | ||||||||
\(323\) | 1.95999 | 0.109057 | ||||||||
\(324\) | −31.4649 | −1.74805 | ||||||||
\(325\) | 4.11421 | 0.228215 | ||||||||
\(326\) | 33.6320 | 1.86270 | ||||||||
\(327\) | −38.8988 | −2.15111 | ||||||||
\(328\) | 16.5662 | 0.914714 | ||||||||
\(329\) | 5.52855 | 0.304799 | ||||||||
\(330\) | −75.0701 | −4.13247 | ||||||||
\(331\) | −9.98492 | −0.548821 | −0.274410 | − | 0.961613i | \(-0.588483\pi\) | ||||
−0.274410 | + | 0.961613i | \(0.588483\pi\) | |||||||
\(332\) | −27.4968 | −1.50908 | ||||||||
\(333\) | −26.4882 | −1.45154 | ||||||||
\(334\) | 2.06847 | 0.113182 | ||||||||
\(335\) | 34.0428 | 1.85995 | ||||||||
\(336\) | −1.87538 | −0.102310 | ||||||||
\(337\) | 35.6075 | 1.93966 | 0.969832 | − | 0.243772i | \(-0.0783850\pi\) | ||||
0.969832 | + | 0.243772i | \(0.0783850\pi\) | |||||||
\(338\) | 27.0368 | 1.47061 | ||||||||
\(339\) | 15.6658 | 0.850848 | ||||||||
\(340\) | 18.1015 | 0.981692 | ||||||||
\(341\) | 44.1286 | 2.38970 | ||||||||
\(342\) | −5.52789 | −0.298914 | ||||||||
\(343\) | 12.8912 | 0.696059 | ||||||||
\(344\) | 13.6250 | 0.734609 | ||||||||
\(345\) | 50.6259 | 2.72561 | ||||||||
\(346\) | −45.5918 | −2.45103 | ||||||||
\(347\) | 16.7055 | 0.896801 | 0.448400 | − | 0.893833i | \(-0.351994\pi\) | ||||
0.448400 | + | 0.893833i | \(0.351994\pi\) | |||||||
\(348\) | −33.8337 | −1.81368 | ||||||||
\(349\) | 12.3832 | 0.662856 | 0.331428 | − | 0.943481i | \(-0.392470\pi\) | ||||
0.331428 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(350\) | 9.31590 | 0.497956 | ||||||||
\(351\) | 1.23810 | 0.0660848 | ||||||||
\(352\) | −30.7789 | −1.64052 | ||||||||
\(353\) | −18.9665 | −1.00948 | −0.504742 | − | 0.863270i | \(-0.668412\pi\) | ||||
−0.504742 | + | 0.863270i | \(0.668412\pi\) | |||||||
\(354\) | 33.5987 | 1.78575 | ||||||||
\(355\) | −19.3669 | −1.02789 | ||||||||
\(356\) | −44.1835 | −2.34172 | ||||||||
\(357\) | 4.53493 | 0.240014 | ||||||||
\(358\) | 48.8915 | 2.58400 | ||||||||
\(359\) | −1.90194 | −0.100380 | −0.0501902 | − | 0.998740i | \(-0.515983\pi\) | ||||
−0.0501902 | + | 0.998740i | \(0.515983\pi\) | |||||||
\(360\) | −17.5406 | −0.924471 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −45.7494 | −2.40453 | ||||||||
\(363\) | −26.3026 | −1.38053 | ||||||||
\(364\) | −2.96350 | −0.155330 | ||||||||
\(365\) | 12.6923 | 0.664348 | ||||||||
\(366\) | 69.3353 | 3.62421 | ||||||||
\(367\) | 26.7059 | 1.39404 | 0.697018 | − | 0.717053i | \(-0.254510\pi\) | ||||
0.697018 | + | 0.717053i | \(0.254510\pi\) | |||||||
\(368\) | 5.79307 | 0.301985 | ||||||||
\(369\) | −17.3338 | −0.902360 | ||||||||
\(370\) | 73.3034 | 3.81086 | ||||||||
\(371\) | −1.94541 | −0.101000 | ||||||||
\(372\) | 66.5989 | 3.45299 | ||||||||
\(373\) | −12.0084 | −0.621770 | −0.310885 | − | 0.950448i | \(-0.600625\pi\) | ||||
−0.310885 | + | 0.950448i | \(0.600625\pi\) | |||||||
\(374\) | 20.7723 | 1.07411 | ||||||||
\(375\) | 5.75063 | 0.296961 | ||||||||
\(376\) | 13.1310 | 0.677179 | ||||||||
\(377\) | 4.66816 | 0.240422 | ||||||||
\(378\) | 2.80345 | 0.144194 | ||||||||
\(379\) | 7.11223 | 0.365331 | 0.182665 | − | 0.983175i | \(-0.441528\pi\) | ||||
0.182665 | + | 0.983175i | \(0.441528\pi\) | |||||||
\(380\) | 9.23550 | 0.473771 | ||||||||
\(381\) | −37.0685 | −1.89908 | ||||||||
\(382\) | 4.23860 | 0.216865 | ||||||||
\(383\) | 0.255783 | 0.0130699 | 0.00653496 | − | 0.999979i | \(-0.497920\pi\) | ||||
0.00653496 | + | 0.999979i | \(0.497920\pi\) | |||||||
\(384\) | −37.9415 | −1.93619 | ||||||||
\(385\) | 14.1589 | 0.721605 | ||||||||
\(386\) | 23.4201 | 1.19205 | ||||||||
\(387\) | −14.2563 | −0.724687 | ||||||||
\(388\) | 1.93798 | 0.0983860 | ||||||||
\(389\) | −17.1331 | −0.868682 | −0.434341 | − | 0.900749i | \(-0.643019\pi\) | ||||
−0.434341 | + | 0.900749i | \(0.643019\pi\) | |||||||
\(390\) | 15.6318 | 0.791548 | ||||||||
\(391\) | −14.0085 | −0.708439 | ||||||||
\(392\) | 14.1563 | 0.715002 | ||||||||
\(393\) | 2.30013 | 0.116026 | ||||||||
\(394\) | −10.9167 | −0.549974 | ||||||||
\(395\) | −13.8018 | −0.694443 | ||||||||
\(396\) | −35.3687 | −1.77734 | ||||||||
\(397\) | −24.5938 | −1.23433 | −0.617163 | − | 0.786836i | \(-0.711718\pi\) | ||||
−0.617163 | + | 0.786836i | \(0.711718\pi\) | |||||||
\(398\) | −16.4651 | −0.825320 | ||||||||
\(399\) | 2.31375 | 0.115832 | ||||||||
\(400\) | −3.39464 | −0.169732 | ||||||||
\(401\) | −16.7524 | −0.836573 | −0.418286 | − | 0.908315i | \(-0.637369\pi\) | ||||
−0.418286 | + | 0.908315i | \(0.637369\pi\) | |||||||
\(402\) | 58.9579 | 2.94055 | ||||||||
\(403\) | −9.18888 | −0.457731 | ||||||||
\(404\) | 55.0309 | 2.73789 | ||||||||
\(405\) | −31.3036 | −1.55549 | ||||||||
\(406\) | 10.5702 | 0.524591 | ||||||||
\(407\) | 50.7835 | 2.51725 | ||||||||
\(408\) | 10.7710 | 0.533245 | ||||||||
\(409\) | −13.2782 | −0.656564 | −0.328282 | − | 0.944580i | \(-0.606470\pi\) | ||||
−0.328282 | + | 0.944580i | \(0.606470\pi\) | |||||||
\(410\) | 47.9695 | 2.36904 | ||||||||
\(411\) | 22.9032 | 1.12973 | ||||||||
\(412\) | 33.4377 | 1.64736 | ||||||||
\(413\) | −6.33703 | −0.311825 | ||||||||
\(414\) | 39.5090 | 1.94176 | ||||||||
\(415\) | −27.3558 | −1.34284 | ||||||||
\(416\) | 6.40908 | 0.314231 | ||||||||
\(417\) | 3.46089 | 0.169481 | ||||||||
\(418\) | 10.5982 | 0.518373 | ||||||||
\(419\) | −29.0375 | −1.41858 | −0.709288 | − | 0.704919i | \(-0.750983\pi\) | ||||
−0.709288 | + | 0.704919i | \(0.750983\pi\) | |||||||
\(420\) | 21.3687 | 1.04268 | ||||||||
\(421\) | 11.5283 | 0.561856 | 0.280928 | − | 0.959729i | \(-0.409358\pi\) | ||||
0.280928 | + | 0.959729i | \(0.409358\pi\) | |||||||
\(422\) | −3.77559 | −0.183793 | ||||||||
\(423\) | −13.7394 | −0.668032 | ||||||||
\(424\) | −4.62057 | −0.224395 | ||||||||
\(425\) | 8.20873 | 0.398182 | ||||||||
\(426\) | −33.5411 | −1.62507 | ||||||||
\(427\) | −13.0773 | −0.632854 | ||||||||
\(428\) | 61.0729 | 2.95207 | ||||||||
\(429\) | 10.8295 | 0.522854 | ||||||||
\(430\) | 39.4528 | 1.90258 | ||||||||
\(431\) | 3.13143 | 0.150836 | 0.0754179 | − | 0.997152i | \(-0.475971\pi\) | ||||
0.0754179 | + | 0.997152i | \(0.475971\pi\) | |||||||
\(432\) | −1.02156 | −0.0491497 | ||||||||
\(433\) | 19.1899 | 0.922210 | 0.461105 | − | 0.887346i | \(-0.347453\pi\) | ||||
0.461105 | + | 0.887346i | \(0.347453\pi\) | |||||||
\(434\) | −20.8066 | −0.998749 | ||||||||
\(435\) | −33.6602 | −1.61388 | ||||||||
\(436\) | 50.7178 | 2.42894 | ||||||||
\(437\) | −7.14721 | −0.341898 | ||||||||
\(438\) | 21.9816 | 1.05032 | ||||||||
\(439\) | 24.2367 | 1.15675 | 0.578377 | − | 0.815770i | \(-0.303686\pi\) | ||||
0.578377 | + | 0.815770i | \(0.303686\pi\) | |||||||
\(440\) | 33.6291 | 1.60321 | ||||||||
\(441\) | −14.8122 | −0.705344 | ||||||||
\(442\) | −4.32541 | −0.205739 | ||||||||
\(443\) | −15.9253 | −0.756636 | −0.378318 | − | 0.925676i | \(-0.623497\pi\) | ||||
−0.378318 | + | 0.925676i | \(0.623497\pi\) | |||||||
\(444\) | 76.6426 | 3.63730 | ||||||||
\(445\) | −43.9569 | −2.08376 | ||||||||
\(446\) | −16.1830 | −0.766285 | ||||||||
\(447\) | −21.7391 | −1.02822 | ||||||||
\(448\) | 12.9072 | 0.609806 | ||||||||
\(449\) | −23.4097 | −1.10477 | −0.552387 | − | 0.833588i | \(-0.686283\pi\) | ||||
−0.552387 | + | 0.833588i | \(0.686283\pi\) | |||||||
\(450\) | −23.1516 | −1.09138 | ||||||||
\(451\) | 33.2326 | 1.56486 | ||||||||
\(452\) | −20.4257 | −0.960742 | ||||||||
\(453\) | 12.2457 | 0.575354 | ||||||||
\(454\) | −60.6473 | −2.84632 | ||||||||
\(455\) | −2.94831 | −0.138219 | ||||||||
\(456\) | 5.49544 | 0.257347 | ||||||||
\(457\) | 25.3983 | 1.18808 | 0.594042 | − | 0.804434i | \(-0.297531\pi\) | ||||
0.594042 | + | 0.804434i | \(0.297531\pi\) | |||||||
\(458\) | 43.9240 | 2.05243 | ||||||||
\(459\) | 2.47027 | 0.115302 | ||||||||
\(460\) | −66.0081 | −3.07764 | ||||||||
\(461\) | 6.71653 | 0.312820 | 0.156410 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156410 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(462\) | 24.5215 | 1.14084 | ||||||||
\(463\) | 30.3913 | 1.41240 | 0.706201 | − | 0.708011i | \(-0.250407\pi\) | ||||
0.706201 | + | 0.708011i | \(0.250407\pi\) | |||||||
\(464\) | −3.85170 | −0.178811 | ||||||||
\(465\) | 66.2574 | 3.07261 | ||||||||
\(466\) | 11.3714 | 0.526769 | ||||||||
\(467\) | 36.8354 | 1.70454 | 0.852269 | − | 0.523104i | \(-0.175226\pi\) | ||||
0.852269 | + | 0.523104i | \(0.175226\pi\) | |||||||
\(468\) | 7.36481 | 0.340439 | ||||||||
\(469\) | −11.1200 | −0.513474 | ||||||||
\(470\) | 38.0224 | 1.75384 | ||||||||
\(471\) | 16.3287 | 0.752387 | ||||||||
\(472\) | −15.0512 | −0.692788 | ||||||||
\(473\) | 27.3324 | 1.25674 | ||||||||
\(474\) | −23.9030 | −1.09790 | ||||||||
\(475\) | 4.18814 | 0.192165 | ||||||||
\(476\) | −5.91283 | −0.271014 | ||||||||
\(477\) | 4.83466 | 0.221364 | ||||||||
\(478\) | 17.5532 | 0.802865 | ||||||||
\(479\) | −40.7121 | −1.86018 | −0.930091 | − | 0.367330i | \(-0.880272\pi\) | ||||
−0.930091 | + | 0.367330i | \(0.880272\pi\) | |||||||
\(480\) | −46.2133 | −2.10934 | ||||||||
\(481\) | −10.5746 | −0.482163 | ||||||||
\(482\) | 17.2719 | 0.786713 | ||||||||
\(483\) | −16.5369 | −0.752454 | ||||||||
\(484\) | 34.2944 | 1.55884 | ||||||||
\(485\) | 1.92804 | 0.0875479 | ||||||||
\(486\) | −45.7198 | −2.07389 | ||||||||
\(487\) | 32.9772 | 1.49434 | 0.747171 | − | 0.664632i | \(-0.231412\pi\) | ||||
0.747171 | + | 0.664632i | \(0.231412\pi\) | |||||||
\(488\) | −31.0601 | −1.40603 | ||||||||
\(489\) | 34.9837 | 1.58202 | ||||||||
\(490\) | 40.9914 | 1.85180 | ||||||||
\(491\) | 1.05286 | 0.0475149 | 0.0237574 | − | 0.999718i | \(-0.492437\pi\) | ||||
0.0237574 | + | 0.999718i | \(0.492437\pi\) | |||||||
\(492\) | 50.1547 | 2.26115 | ||||||||
\(493\) | 9.31397 | 0.419480 | ||||||||
\(494\) | −2.20685 | −0.0992910 | ||||||||
\(495\) | −35.1873 | −1.58155 | ||||||||
\(496\) | 7.58176 | 0.340431 | ||||||||
\(497\) | 6.32616 | 0.283767 | ||||||||
\(498\) | −47.3768 | −2.12301 | ||||||||
\(499\) | −5.20928 | −0.233199 | −0.116600 | − | 0.993179i | \(-0.537199\pi\) | ||||
−0.116600 | + | 0.993179i | \(0.537199\pi\) | |||||||
\(500\) | −7.49790 | −0.335316 | ||||||||
\(501\) | 2.15161 | 0.0961268 | ||||||||
\(502\) | −27.0759 | −1.20845 | ||||||||
\(503\) | −19.0458 | −0.849209 | −0.424605 | − | 0.905379i | \(-0.639587\pi\) | ||||
−0.424605 | + | 0.905379i | \(0.639587\pi\) | |||||||
\(504\) | 5.72961 | 0.255217 | ||||||||
\(505\) | 54.7487 | 2.43629 | ||||||||
\(506\) | −75.7473 | −3.36738 | ||||||||
\(507\) | 28.1234 | 1.24901 | ||||||||
\(508\) | 48.3314 | 2.14436 | ||||||||
\(509\) | −42.2038 | −1.87065 | −0.935324 | − | 0.353791i | \(-0.884892\pi\) | ||||
−0.935324 | + | 0.353791i | \(0.884892\pi\) | |||||||
\(510\) | 31.1888 | 1.38106 | ||||||||
\(511\) | −4.14593 | −0.183405 | ||||||||
\(512\) | −9.10040 | −0.402185 | ||||||||
\(513\) | 1.26035 | 0.0556457 | ||||||||
\(514\) | −3.64738 | −0.160879 | ||||||||
\(515\) | 33.2662 | 1.46588 | ||||||||
\(516\) | 41.2500 | 1.81593 | ||||||||
\(517\) | 26.3414 | 1.15849 | ||||||||
\(518\) | −23.9444 | −1.05206 | ||||||||
\(519\) | −47.4243 | −2.08169 | ||||||||
\(520\) | −7.00259 | −0.307084 | ||||||||
\(521\) | 32.9852 | 1.44511 | 0.722553 | − | 0.691315i | \(-0.242968\pi\) | ||||
0.722553 | + | 0.691315i | \(0.242968\pi\) | |||||||
\(522\) | −26.2688 | −1.14975 | ||||||||
\(523\) | 8.45407 | 0.369671 | 0.184835 | − | 0.982770i | \(-0.440825\pi\) | ||||
0.184835 | + | 0.982770i | \(0.440825\pi\) | |||||||
\(524\) | −2.99900 | −0.131012 | ||||||||
\(525\) | 9.69032 | 0.422920 | ||||||||
\(526\) | 8.08657 | 0.352591 | ||||||||
\(527\) | −18.3338 | −0.798632 | ||||||||
\(528\) | −8.93545 | −0.388865 | ||||||||
\(529\) | 28.0827 | 1.22099 | ||||||||
\(530\) | −13.3795 | −0.581166 | ||||||||
\(531\) | 15.7486 | 0.683430 | ||||||||
\(532\) | −3.01676 | −0.130793 | ||||||||
\(533\) | −6.92002 | −0.299739 | ||||||||
\(534\) | −76.1280 | −3.29438 | ||||||||
\(535\) | 60.7597 | 2.62687 | ||||||||
\(536\) | −26.4114 | −1.14080 | ||||||||
\(537\) | 50.8565 | 2.19462 | ||||||||
\(538\) | −27.8509 | −1.20074 | ||||||||
\(539\) | 28.3983 | 1.22320 | ||||||||
\(540\) | 11.6399 | 0.500903 | ||||||||
\(541\) | −6.78617 | −0.291760 | −0.145880 | − | 0.989302i | \(-0.546601\pi\) | ||||
−0.145880 | + | 0.989302i | \(0.546601\pi\) | |||||||
\(542\) | 46.5650 | 2.00014 | ||||||||
\(543\) | −47.5881 | −2.04220 | ||||||||
\(544\) | 12.7875 | 0.548259 | ||||||||
\(545\) | 50.4577 | 2.16137 | ||||||||
\(546\) | −5.10611 | −0.218521 | ||||||||
\(547\) | −13.1790 | −0.563492 | −0.281746 | − | 0.959489i | \(-0.590913\pi\) | ||||
−0.281746 | + | 0.959489i | \(0.590913\pi\) | |||||||
\(548\) | −29.8621 | −1.27564 | ||||||||
\(549\) | 32.4993 | 1.38703 | ||||||||
\(550\) | 44.3866 | 1.89265 | ||||||||
\(551\) | 4.75205 | 0.202444 | ||||||||
\(552\) | −39.2771 | −1.67174 | ||||||||
\(553\) | 4.50833 | 0.191714 | ||||||||
\(554\) | −36.9771 | −1.57101 | ||||||||
\(555\) | 76.2496 | 3.23661 | ||||||||
\(556\) | −4.51245 | −0.191370 | ||||||||
\(557\) | 24.2300 | 1.02666 | 0.513329 | − | 0.858192i | \(-0.328412\pi\) | ||||
0.513329 | + | 0.858192i | \(0.328412\pi\) | |||||||
\(558\) | 51.7079 | 2.18897 | ||||||||
\(559\) | −5.69141 | −0.240721 | ||||||||
\(560\) | 2.43265 | 0.102798 | ||||||||
\(561\) | 21.6072 | 0.912256 | ||||||||
\(562\) | 53.3789 | 2.25165 | ||||||||
\(563\) | 10.2851 | 0.433466 | 0.216733 | − | 0.976231i | \(-0.430460\pi\) | ||||
0.216733 | + | 0.976231i | \(0.430460\pi\) | |||||||
\(564\) | 39.7545 | 1.67397 | ||||||||
\(565\) | −20.3209 | −0.854908 | ||||||||
\(566\) | 60.9546 | 2.56211 | ||||||||
\(567\) | 10.2253 | 0.429421 | ||||||||
\(568\) | 15.0254 | 0.630451 | ||||||||
\(569\) | 43.1473 | 1.80883 | 0.904415 | − | 0.426653i | \(-0.140308\pi\) | ||||
0.904415 | + | 0.426653i | \(0.140308\pi\) | |||||||
\(570\) | 15.9127 | 0.666511 | ||||||||
\(571\) | −12.2971 | −0.514619 | −0.257309 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257309 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(572\) | −14.1199 | −0.590385 | ||||||||
\(573\) | 4.40895 | 0.184187 | ||||||||
\(574\) | −15.6692 | −0.654018 | ||||||||
\(575\) | −29.9336 | −1.24832 | ||||||||
\(576\) | −32.0765 | −1.33652 | ||||||||
\(577\) | −1.92496 | −0.0801371 | −0.0400686 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400686 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(578\) | 29.5606 | 1.22956 | ||||||||
\(579\) | 24.3614 | 1.01243 | ||||||||
\(580\) | 43.8875 | 1.82233 | ||||||||
\(581\) | 8.93571 | 0.370716 | ||||||||
\(582\) | 3.33913 | 0.138411 | ||||||||
\(583\) | −9.26910 | −0.383887 | ||||||||
\(584\) | −9.84709 | −0.407475 | ||||||||
\(585\) | 7.32705 | 0.302936 | ||||||||
\(586\) | −23.5065 | −0.971044 | ||||||||
\(587\) | 26.8410 | 1.10785 | 0.553923 | − | 0.832568i | \(-0.313130\pi\) | ||||
0.553923 | + | 0.832568i | \(0.313130\pi\) | |||||||
\(588\) | 42.8587 | 1.76746 | ||||||||
\(589\) | −9.35401 | −0.385425 | ||||||||
\(590\) | −43.5827 | −1.79427 | ||||||||
\(591\) | −11.3554 | −0.467100 | ||||||||
\(592\) | 8.72516 | 0.358602 | ||||||||
\(593\) | −27.4962 | −1.12913 | −0.564567 | − | 0.825387i | \(-0.690957\pi\) | ||||
−0.564567 | + | 0.825387i | \(0.690957\pi\) | |||||||
\(594\) | 13.3574 | 0.548060 | ||||||||
\(595\) | −5.88251 | −0.241159 | ||||||||
\(596\) | 28.3442 | 1.16103 | ||||||||
\(597\) | −17.1269 | −0.700955 | ||||||||
\(598\) | 15.7729 | 0.645000 | ||||||||
\(599\) | −7.47771 | −0.305531 | −0.152765 | − | 0.988262i | \(-0.548818\pi\) | ||||
−0.152765 | + | 0.988262i | \(0.548818\pi\) | |||||||
\(600\) | 23.0157 | 0.939611 | ||||||||
\(601\) | 37.1015 | 1.51340 | 0.756701 | − | 0.653761i | \(-0.226810\pi\) | ||||
0.756701 | + | 0.653761i | \(0.226810\pi\) | |||||||
\(602\) | −12.8872 | −0.525243 | ||||||||
\(603\) | 27.6351 | 1.12539 | ||||||||
\(604\) | −15.9665 | −0.649666 | ||||||||
\(605\) | 34.1186 | 1.38712 | ||||||||
\(606\) | 94.8181 | 3.85172 | ||||||||
\(607\) | −36.8264 | −1.49474 | −0.747369 | − | 0.664409i | \(-0.768683\pi\) | ||||
−0.747369 | + | 0.664409i | \(0.768683\pi\) | |||||||
\(608\) | 6.52426 | 0.264594 | ||||||||
\(609\) | 10.9951 | 0.445542 | ||||||||
\(610\) | −89.9385 | −3.64150 | ||||||||
\(611\) | −5.48507 | −0.221902 | ||||||||
\(612\) | 14.6944 | 0.593985 | ||||||||
\(613\) | 41.2218 | 1.66493 | 0.832466 | − | 0.554077i | \(-0.186929\pi\) | ||||
0.832466 | + | 0.554077i | \(0.186929\pi\) | |||||||
\(614\) | −47.7137 | −1.92557 | ||||||||
\(615\) | 49.8975 | 2.01206 | ||||||||
\(616\) | −10.9849 | −0.442594 | ||||||||
\(617\) | −19.9554 | −0.803374 | −0.401687 | − | 0.915777i | \(-0.631576\pi\) | ||||
−0.401687 | + | 0.915777i | \(0.631576\pi\) | |||||||
\(618\) | 57.6130 | 2.31753 | ||||||||
\(619\) | −3.77795 | −0.151849 | −0.0759243 | − | 0.997114i | \(-0.524191\pi\) | ||||
−0.0759243 | + | 0.997114i | \(0.524191\pi\) | |||||||
\(620\) | −86.3890 | −3.46947 | ||||||||
\(621\) | −9.00797 | −0.361478 | ||||||||
\(622\) | 18.1716 | 0.728615 | ||||||||
\(623\) | 14.3585 | 0.575260 | ||||||||
\(624\) | 1.86063 | 0.0744847 | ||||||||
\(625\) | −28.4002 | −1.13601 | ||||||||
\(626\) | −56.6314 | −2.26344 | ||||||||
\(627\) | 11.0241 | 0.440261 | ||||||||
\(628\) | −21.2900 | −0.849564 | ||||||||
\(629\) | −21.0987 | −0.841260 | ||||||||
\(630\) | 16.5908 | 0.660994 | ||||||||
\(631\) | 22.8127 | 0.908159 | 0.454080 | − | 0.890961i | \(-0.349968\pi\) | ||||
0.454080 | + | 0.890961i | \(0.349968\pi\) | |||||||
\(632\) | 10.7078 | 0.425935 | ||||||||
\(633\) | −3.92734 | −0.156098 | ||||||||
\(634\) | 2.24651 | 0.0892204 | ||||||||
\(635\) | 48.0836 | 1.90814 | ||||||||
\(636\) | −13.9889 | −0.554697 | ||||||||
\(637\) | −5.91337 | −0.234296 | ||||||||
\(638\) | 50.3630 | 1.99389 | ||||||||
\(639\) | −15.7216 | −0.621936 | ||||||||
\(640\) | 49.2159 | 1.94543 | ||||||||
\(641\) | −3.41041 | −0.134703 | −0.0673515 | − | 0.997729i | \(-0.521455\pi\) | ||||
−0.0673515 | + | 0.997729i | \(0.521455\pi\) | |||||||
\(642\) | 105.228 | 4.15304 | ||||||||
\(643\) | 36.0005 | 1.41972 | 0.709861 | − | 0.704342i | \(-0.248758\pi\) | ||||
0.709861 | + | 0.704342i | \(0.248758\pi\) | |||||||
\(644\) | 21.5614 | 0.849640 | ||||||||
\(645\) | 41.0385 | 1.61589 | ||||||||
\(646\) | −4.40314 | −0.173239 | ||||||||
\(647\) | 37.1509 | 1.46055 | 0.730277 | − | 0.683152i | \(-0.239391\pi\) | ||||
0.730277 | + | 0.683152i | \(0.239391\pi\) | |||||||
\(648\) | 24.2862 | 0.954054 | ||||||||
\(649\) | −30.1935 | −1.18520 | ||||||||
\(650\) | −9.24262 | −0.362525 | ||||||||
\(651\) | −21.6429 | −0.848250 | ||||||||
\(652\) | −45.6132 | −1.78635 | ||||||||
\(653\) | 0.196865 | 0.00770392 | 0.00385196 | − | 0.999993i | \(-0.498774\pi\) | ||||
0.00385196 | + | 0.999993i | \(0.498774\pi\) | |||||||
\(654\) | 87.3866 | 3.41708 | ||||||||
\(655\) | −2.98362 | −0.116580 | ||||||||
\(656\) | 5.70972 | 0.222927 | ||||||||
\(657\) | 10.3033 | 0.401972 | ||||||||
\(658\) | −12.4200 | −0.484181 | ||||||||
\(659\) | −43.5634 | −1.69699 | −0.848494 | − | 0.529206i | \(-0.822490\pi\) | ||||
−0.848494 | + | 0.529206i | \(0.822490\pi\) | |||||||
\(660\) | 101.813 | 3.96308 | ||||||||
\(661\) | −20.0380 | −0.779389 | −0.389694 | − | 0.920944i | \(-0.627419\pi\) | ||||
−0.389694 | + | 0.920944i | \(0.627419\pi\) | |||||||
\(662\) | 22.4313 | 0.871815 | ||||||||
\(663\) | −4.49926 | −0.174737 | ||||||||
\(664\) | 21.2234 | 0.823628 | ||||||||
\(665\) | −3.00129 | −0.116385 | ||||||||
\(666\) | 59.5060 | 2.30581 | ||||||||
\(667\) | −33.9639 | −1.31509 | ||||||||
\(668\) | −2.80535 | −0.108542 | ||||||||
\(669\) | −16.8334 | −0.650816 | ||||||||
\(670\) | −76.4775 | −2.95458 | ||||||||
\(671\) | −62.3082 | −2.40538 | ||||||||
\(672\) | 15.0955 | 0.582322 | ||||||||
\(673\) | −7.27714 | −0.280513 | −0.140257 | − | 0.990115i | \(-0.544793\pi\) | ||||
−0.140257 | + | 0.990115i | \(0.544793\pi\) | |||||||
\(674\) | −79.9927 | −3.08120 | ||||||||
\(675\) | 5.27852 | 0.203170 | ||||||||
\(676\) | −36.6684 | −1.41032 | ||||||||
\(677\) | 48.7398 | 1.87322 | 0.936611 | − | 0.350371i | \(-0.113945\pi\) | ||||
0.936611 | + | 0.350371i | \(0.113945\pi\) | |||||||
\(678\) | −35.1934 | −1.35159 | ||||||||
\(679\) | −0.629792 | −0.0241692 | ||||||||
\(680\) | −13.9717 | −0.535789 | ||||||||
\(681\) | −63.0848 | −2.41742 | ||||||||
\(682\) | −99.1354 | −3.79609 | ||||||||
\(683\) | −27.8611 | −1.06608 | −0.533038 | − | 0.846091i | \(-0.678950\pi\) | ||||
−0.533038 | + | 0.846091i | \(0.678950\pi\) | |||||||
\(684\) | 7.49716 | 0.286661 | ||||||||
\(685\) | −29.7090 | −1.13512 | ||||||||
\(686\) | −28.9602 | −1.10571 | ||||||||
\(687\) | 45.6894 | 1.74316 | ||||||||
\(688\) | 4.69599 | 0.179033 | ||||||||
\(689\) | 1.93010 | 0.0735311 | ||||||||
\(690\) | −113.732 | −4.32969 | ||||||||
\(691\) | 10.2521 | 0.390008 | 0.195004 | − | 0.980802i | \(-0.437528\pi\) | ||||
0.195004 | + | 0.980802i | \(0.437528\pi\) | |||||||
\(692\) | 61.8336 | 2.35056 | ||||||||
\(693\) | 11.4939 | 0.436616 | ||||||||
\(694\) | −37.5292 | −1.42459 | ||||||||
\(695\) | −4.48931 | −0.170289 | ||||||||
\(696\) | 26.1146 | 0.989870 | ||||||||
\(697\) | −13.8069 | −0.522974 | ||||||||
\(698\) | −27.8189 | −1.05296 | ||||||||
\(699\) | 11.8284 | 0.447392 | ||||||||
\(700\) | −12.6346 | −0.477544 | ||||||||
\(701\) | −35.6918 | −1.34806 | −0.674030 | − | 0.738704i | \(-0.735438\pi\) | ||||
−0.674030 | + | 0.738704i | \(0.735438\pi\) | |||||||
\(702\) | −2.78140 | −0.104977 | ||||||||
\(703\) | −10.7647 | −0.405998 | ||||||||
\(704\) | 61.4976 | 2.31778 | ||||||||
\(705\) | 39.5506 | 1.48956 | ||||||||
\(706\) | 42.6084 | 1.60359 | ||||||||
\(707\) | −17.8836 | −0.672582 | ||||||||
\(708\) | −45.5680 | −1.71255 | ||||||||
\(709\) | 7.35713 | 0.276303 | 0.138151 | − | 0.990411i | \(-0.455884\pi\) | ||||
0.138151 | + | 0.990411i | \(0.455884\pi\) | |||||||
\(710\) | 43.5079 | 1.63282 | ||||||||
\(711\) | −11.2040 | −0.420182 | ||||||||
\(712\) | 34.1031 | 1.27807 | ||||||||
\(713\) | 66.8551 | 2.50374 | ||||||||
\(714\) | −10.1878 | −0.381268 | ||||||||
\(715\) | −14.0475 | −0.525348 | ||||||||
\(716\) | −66.3088 | −2.47808 | ||||||||
\(717\) | 18.2587 | 0.681884 | ||||||||
\(718\) | 4.27273 | 0.159457 | ||||||||
\(719\) | 47.4234 | 1.76860 | 0.884298 | − | 0.466923i | \(-0.154638\pi\) | ||||
0.884298 | + | 0.466923i | \(0.154638\pi\) | |||||||
\(720\) | −6.04556 | −0.225305 | ||||||||
\(721\) | −10.8664 | −0.404684 | ||||||||
\(722\) | −2.24651 | −0.0836065 | ||||||||
\(723\) | 17.9661 | 0.668166 | ||||||||
\(724\) | 62.0473 | 2.30597 | ||||||||
\(725\) | 19.9022 | 0.739151 | ||||||||
\(726\) | 59.0892 | 2.19301 | ||||||||
\(727\) | 41.7898 | 1.54990 | 0.774948 | − | 0.632024i | \(-0.217776\pi\) | ||||
0.774948 | + | 0.632024i | \(0.217776\pi\) | |||||||
\(728\) | 2.28738 | 0.0847761 | ||||||||
\(729\) | −16.5760 | −0.613925 | ||||||||
\(730\) | −28.5135 | −1.05533 | ||||||||
\(731\) | −11.3556 | −0.420001 | ||||||||
\(732\) | −94.0355 | −3.47565 | ||||||||
\(733\) | 11.3085 | 0.417690 | 0.208845 | − | 0.977949i | \(-0.433030\pi\) | ||||
0.208845 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(734\) | −59.9952 | −2.21446 | ||||||||
\(735\) | 42.6389 | 1.57276 | ||||||||
\(736\) | −46.6303 | −1.71881 | ||||||||
\(737\) | −52.9825 | −1.95164 | ||||||||
\(738\) | 38.9405 | 1.43342 | ||||||||
\(739\) | 32.7113 | 1.20330 | 0.601652 | − | 0.798759i | \(-0.294510\pi\) | ||||
0.601652 | + | 0.798759i | \(0.294510\pi\) | |||||||
\(740\) | −99.4172 | −3.65465 | ||||||||
\(741\) | −2.29555 | −0.0843292 | ||||||||
\(742\) | 4.37038 | 0.160442 | ||||||||
\(743\) | −30.1176 | −1.10491 | −0.552454 | − | 0.833543i | \(-0.686309\pi\) | ||||
−0.552454 | + | 0.833543i | \(0.686309\pi\) | |||||||
\(744\) | −51.4044 | −1.88458 | ||||||||
\(745\) | 28.1989 | 1.03313 | ||||||||
\(746\) | 26.9769 | 0.987696 | ||||||||
\(747\) | −22.2068 | −0.812503 | ||||||||
\(748\) | −28.1723 | −1.03008 | ||||||||
\(749\) | −19.8471 | −0.725196 | ||||||||
\(750\) | −12.9189 | −0.471730 | ||||||||
\(751\) | 41.3929 | 1.51045 | 0.755223 | − | 0.655468i | \(-0.227528\pi\) | ||||
0.755223 | + | 0.655468i | \(0.227528\pi\) | |||||||
\(752\) | 4.52574 | 0.165037 | ||||||||
\(753\) | −28.1641 | −1.02636 | ||||||||
\(754\) | −10.4871 | −0.381917 | ||||||||
\(755\) | −15.8846 | −0.578100 | ||||||||
\(756\) | −3.80217 | −0.138284 | ||||||||
\(757\) | 23.5140 | 0.854632 | 0.427316 | − | 0.904102i | \(-0.359459\pi\) | ||||
0.427316 | + | 0.904102i | \(0.359459\pi\) | |||||||
\(758\) | −15.9777 | −0.580336 | ||||||||
\(759\) | −78.7918 | −2.85996 | ||||||||
\(760\) | −7.12843 | −0.258575 | ||||||||
\(761\) | −33.0173 | −1.19688 | −0.598438 | − | 0.801169i | \(-0.704212\pi\) | ||||
−0.598438 | + | 0.801169i | \(0.704212\pi\) | |||||||
\(762\) | 83.2748 | 3.01673 | ||||||||
\(763\) | −16.4819 | −0.596686 | ||||||||
\(764\) | −5.74857 | −0.207976 | ||||||||
\(765\) | 14.6190 | 0.528552 | ||||||||
\(766\) | −0.574620 | −0.0207619 | ||||||||
\(767\) | 6.28718 | 0.227017 | ||||||||
\(768\) | 24.3119 | 0.877281 | ||||||||
\(769\) | 31.2121 | 1.12554 | 0.562769 | − | 0.826614i | \(-0.309736\pi\) | ||||
0.562769 | + | 0.826614i | \(0.309736\pi\) | |||||||
\(770\) | −31.8082 | −1.14629 | ||||||||
\(771\) | −3.79398 | −0.136637 | ||||||||
\(772\) | −31.7634 | −1.14319 | ||||||||
\(773\) | 49.9478 | 1.79650 | 0.898248 | − | 0.439488i | \(-0.144840\pi\) | ||||
0.898248 | + | 0.439488i | \(0.144840\pi\) | |||||||
\(774\) | 32.0269 | 1.15118 | ||||||||
\(775\) | −39.1760 | −1.40724 | ||||||||
\(776\) | −1.49583 | −0.0536972 | ||||||||
\(777\) | −24.9068 | −0.893526 | ||||||||
\(778\) | 38.4897 | 1.37992 | ||||||||
\(779\) | −7.04437 | −0.252391 | ||||||||
\(780\) | −21.2006 | −0.759102 | ||||||||
\(781\) | 30.1417 | 1.07855 | ||||||||
\(782\) | 31.4702 | 1.12537 | ||||||||
\(783\) | 5.98923 | 0.214038 | ||||||||
\(784\) | 4.87913 | 0.174255 | ||||||||
\(785\) | −21.1808 | −0.755977 | ||||||||
\(786\) | −5.16727 | −0.184311 | ||||||||
\(787\) | 26.2294 | 0.934975 | 0.467488 | − | 0.884000i | \(-0.345159\pi\) | ||||
0.467488 | + | 0.884000i | \(0.345159\pi\) | |||||||
\(788\) | 14.8057 | 0.527430 | ||||||||
\(789\) | 8.41158 | 0.299460 | ||||||||
\(790\) | 31.0059 | 1.10314 | ||||||||
\(791\) | 6.63780 | 0.236013 | ||||||||
\(792\) | 27.2993 | 0.970040 | ||||||||
\(793\) | 12.9744 | 0.460735 | ||||||||
\(794\) | 55.2502 | 1.96076 | ||||||||
\(795\) | −13.9172 | −0.493592 | ||||||||
\(796\) | 22.3307 | 0.791490 | ||||||||
\(797\) | −5.66490 | −0.200661 | −0.100331 | − | 0.994954i | \(-0.531990\pi\) | ||||
−0.100331 | + | 0.994954i | \(0.531990\pi\) | |||||||
\(798\) | −5.19787 | −0.184003 | ||||||||
\(799\) | −10.9439 | −0.387167 | ||||||||
\(800\) | 27.3245 | 0.966068 | ||||||||
\(801\) | −35.6832 | −1.26080 | ||||||||
\(802\) | 37.6344 | 1.32892 | ||||||||
\(803\) | −19.7538 | −0.697095 | ||||||||
\(804\) | −79.9613 | −2.82002 | ||||||||
\(805\) | 21.4509 | 0.756044 | ||||||||
\(806\) | 20.6429 | 0.727116 | ||||||||
\(807\) | −28.9703 | −1.01980 | ||||||||
\(808\) | −42.4757 | −1.49429 | ||||||||
\(809\) | 41.5516 | 1.46088 | 0.730438 | − | 0.682979i | \(-0.239316\pi\) | ||||
0.730438 | + | 0.682979i | \(0.239316\pi\) | |||||||
\(810\) | 70.3239 | 2.47093 | ||||||||
\(811\) | 18.2169 | 0.639680 | 0.319840 | − | 0.947472i | \(-0.396371\pi\) | ||||
0.319840 | + | 0.947472i | \(0.396371\pi\) | |||||||
\(812\) | −14.3358 | −0.503087 | ||||||||
\(813\) | 48.4365 | 1.69874 | ||||||||
\(814\) | −114.086 | −3.99871 | ||||||||
\(815\) | −45.3793 | −1.58957 | ||||||||
\(816\) | 3.71235 | 0.129958 | ||||||||
\(817\) | −5.79369 | −0.202696 | ||||||||
\(818\) | 29.8296 | 1.04297 | ||||||||
\(819\) | −2.39337 | −0.0836311 | ||||||||
\(820\) | −65.0583 | −2.27194 | ||||||||
\(821\) | −37.8805 | −1.32204 | −0.661019 | − | 0.750369i | \(-0.729876\pi\) | ||||
−0.661019 | + | 0.750369i | \(0.729876\pi\) | |||||||
\(822\) | −51.4523 | −1.79460 | ||||||||
\(823\) | 11.7544 | 0.409732 | 0.204866 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204866 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(824\) | −25.8089 | −0.899095 | ||||||||
\(825\) | 46.1706 | 1.60745 | ||||||||
\(826\) | 14.2362 | 0.495341 | ||||||||
\(827\) | −49.7491 | −1.72994 | −0.864972 | − | 0.501819i | \(-0.832664\pi\) | ||||
−0.864972 | + | 0.501819i | \(0.832664\pi\) | |||||||
\(828\) | −53.5838 | −1.86217 | ||||||||
\(829\) | 9.21493 | 0.320048 | 0.160024 | − | 0.987113i | \(-0.448843\pi\) | ||||
0.160024 | + | 0.987113i | \(0.448843\pi\) | |||||||
\(830\) | 61.4551 | 2.13314 | ||||||||
\(831\) | −38.4633 | −1.33428 | ||||||||
\(832\) | −12.8056 | −0.443955 | ||||||||
\(833\) | −11.7984 | −0.408791 | ||||||||
\(834\) | −7.77494 | −0.269224 | ||||||||
\(835\) | −2.79097 | −0.0965854 | ||||||||
\(836\) | −14.3737 | −0.497125 | ||||||||
\(837\) | −11.7893 | −0.407498 | ||||||||
\(838\) | 65.2332 | 2.25344 | ||||||||
\(839\) | 53.7185 | 1.85457 | 0.927284 | − | 0.374358i | \(-0.122137\pi\) | ||||
0.927284 | + | 0.374358i | \(0.122137\pi\) | |||||||
\(840\) | −16.4934 | −0.569077 | ||||||||
\(841\) | −6.41807 | −0.221313 | ||||||||
\(842\) | −25.8985 | −0.892522 | ||||||||
\(843\) | 55.5243 | 1.91236 | ||||||||
\(844\) | 5.12063 | 0.176259 | ||||||||
\(845\) | −36.4804 | −1.25496 | ||||||||
\(846\) | 30.8657 | 1.06119 | ||||||||
\(847\) | −11.1448 | −0.382939 | ||||||||
\(848\) | −1.59253 | −0.0546877 | ||||||||
\(849\) | 63.4044 | 2.17604 | ||||||||
\(850\) | −18.4410 | −0.632521 | ||||||||
\(851\) | 76.9375 | 2.63738 | ||||||||
\(852\) | 45.4898 | 1.55846 | ||||||||
\(853\) | 18.6109 | 0.637225 | 0.318612 | − | 0.947885i | \(-0.396783\pi\) | ||||
0.318612 | + | 0.947885i | \(0.396783\pi\) | |||||||
\(854\) | 29.3783 | 1.00530 | ||||||||
\(855\) | 7.45872 | 0.255083 | ||||||||
\(856\) | −47.1392 | −1.61118 | ||||||||
\(857\) | −39.2833 | −1.34189 | −0.670946 | − | 0.741506i | \(-0.734112\pi\) | ||||
−0.670946 | + | 0.741506i | \(0.734112\pi\) | |||||||
\(858\) | −24.3286 | −0.830566 | ||||||||
\(859\) | 26.4755 | 0.903332 | 0.451666 | − | 0.892187i | \(-0.350830\pi\) | ||||
0.451666 | + | 0.892187i | \(0.350830\pi\) | |||||||
\(860\) | −53.5076 | −1.82459 | ||||||||
\(861\) | −16.2989 | −0.555466 | ||||||||
\(862\) | −7.03481 | −0.239606 | ||||||||
\(863\) | −45.5458 | −1.55040 | −0.775198 | − | 0.631719i | \(-0.782350\pi\) | ||||
−0.775198 | + | 0.631719i | \(0.782350\pi\) | |||||||
\(864\) | 8.22283 | 0.279746 | ||||||||
\(865\) | 61.5166 | 2.09163 | ||||||||
\(866\) | −43.1104 | −1.46495 | ||||||||
\(867\) | 30.7487 | 1.04428 | ||||||||
\(868\) | 28.2188 | 0.957809 | ||||||||
\(869\) | 21.4804 | 0.728674 | ||||||||
\(870\) | 75.6181 | 2.56369 | ||||||||
\(871\) | 11.0325 | 0.373823 | ||||||||
\(872\) | −39.1466 | −1.32567 | ||||||||
\(873\) | 1.56514 | 0.0529719 | ||||||||
\(874\) | 16.0563 | 0.543113 | ||||||||
\(875\) | 2.43662 | 0.0823727 | ||||||||
\(876\) | −29.8124 | −1.00727 | ||||||||
\(877\) | −35.4241 | −1.19619 | −0.598093 | − | 0.801427i | \(-0.704075\pi\) | ||||
−0.598093 | + | 0.801427i | \(0.704075\pi\) | |||||||
\(878\) | −54.4480 | −1.83753 | ||||||||
\(879\) | −24.4513 | −0.824721 | ||||||||
\(880\) | 11.5907 | 0.390721 | ||||||||
\(881\) | −30.6880 | −1.03390 | −0.516952 | − | 0.856014i | \(-0.672933\pi\) | ||||
−0.516952 | + | 0.856014i | \(0.672933\pi\) | |||||||
\(882\) | 33.2759 | 1.12046 | ||||||||
\(883\) | −27.2736 | −0.917830 | −0.458915 | − | 0.888480i | \(-0.651762\pi\) | ||||
−0.458915 | + | 0.888480i | \(0.651762\pi\) | |||||||
\(884\) | 5.86632 | 0.197306 | ||||||||
\(885\) | −45.3343 | −1.52390 | ||||||||
\(886\) | 35.7765 | 1.20193 | ||||||||
\(887\) | −43.1044 | −1.44730 | −0.723652 | − | 0.690165i | \(-0.757538\pi\) | ||||
−0.723652 | + | 0.690165i | \(0.757538\pi\) | |||||||
\(888\) | −59.1566 | −1.98517 | ||||||||
\(889\) | −15.7064 | −0.526776 | ||||||||
\(890\) | 98.7498 | 3.31010 | ||||||||
\(891\) | 48.7194 | 1.63216 | ||||||||
\(892\) | 21.9480 | 0.734874 | ||||||||
\(893\) | −5.58364 | −0.186849 | ||||||||
\(894\) | 48.8371 | 1.63336 | ||||||||
\(895\) | −65.9688 | −2.20509 | ||||||||
\(896\) | −16.0763 | −0.537071 | ||||||||
\(897\) | 16.4068 | 0.547807 | ||||||||
\(898\) | 52.5903 | 1.75496 | ||||||||
\(899\) | −44.4507 | −1.48251 | ||||||||
\(900\) | 31.3992 | 1.04664 | ||||||||
\(901\) | 3.85097 | 0.128294 | ||||||||
\(902\) | −74.6574 | −2.48582 | ||||||||
\(903\) | −13.4052 | −0.446096 | ||||||||
\(904\) | 15.7656 | 0.524355 | ||||||||
\(905\) | 61.7291 | 2.05195 | ||||||||
\(906\) | −27.5102 | −0.913964 | ||||||||
\(907\) | 13.3421 | 0.443019 | 0.221509 | − | 0.975158i | \(-0.428902\pi\) | ||||
0.221509 | + | 0.975158i | \(0.428902\pi\) | |||||||
\(908\) | 82.2525 | 2.72965 | ||||||||
\(909\) | 44.4437 | 1.47411 | ||||||||
\(910\) | 6.62341 | 0.219564 | ||||||||
\(911\) | 11.3142 | 0.374855 | 0.187427 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187427 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(912\) | 1.89406 | 0.0627187 | ||||||||
\(913\) | 42.5752 | 1.40903 | ||||||||
\(914\) | −57.0577 | −1.88730 | ||||||||
\(915\) | −93.5533 | −3.09278 | ||||||||
\(916\) | −59.5717 | −1.96830 | ||||||||
\(917\) | 0.974596 | 0.0321840 | ||||||||
\(918\) | −5.54949 | −0.183161 | ||||||||
\(919\) | −5.07988 | −0.167570 | −0.0837848 | − | 0.996484i | \(-0.526701\pi\) | ||||
−0.0837848 | + | 0.996484i | \(0.526701\pi\) | |||||||
\(920\) | 50.9484 | 1.67972 | ||||||||
\(921\) | −49.6314 | −1.63541 | ||||||||
\(922\) | −15.0888 | −0.496922 | ||||||||
\(923\) | −6.27640 | −0.206590 | ||||||||
\(924\) | −33.2571 | −1.09408 | ||||||||
\(925\) | −45.0840 | −1.48235 | ||||||||
\(926\) | −68.2744 | −2.24364 | ||||||||
\(927\) | 27.0047 | 0.886952 | ||||||||
\(928\) | 31.0036 | 1.01774 | ||||||||
\(929\) | 18.3022 | 0.600475 | 0.300238 | − | 0.953864i | \(-0.402934\pi\) | ||||
0.300238 | + | 0.953864i | \(0.402934\pi\) | |||||||
\(930\) | −148.848 | −4.88092 | ||||||||
\(931\) | −6.01963 | −0.197285 | ||||||||
\(932\) | −15.4224 | −0.505176 | ||||||||
\(933\) | 18.9020 | 0.618823 | ||||||||
\(934\) | −82.7511 | −2.70770 | ||||||||
\(935\) | −28.0279 | −0.916609 | ||||||||
\(936\) | −5.68454 | −0.185805 | ||||||||
\(937\) | 18.6708 | 0.609947 | 0.304974 | − | 0.952361i | \(-0.401352\pi\) | ||||
0.304974 | + | 0.952361i | \(0.401352\pi\) | |||||||
\(938\) | 24.9812 | 0.815666 | ||||||||
\(939\) | −58.9075 | −1.92237 | ||||||||
\(940\) | −51.5677 | −1.68195 | ||||||||
\(941\) | −1.26325 | −0.0411807 | −0.0205903 | − | 0.999788i | \(-0.506555\pi\) | ||||
−0.0205903 | + | 0.999788i | \(0.506555\pi\) | |||||||
\(942\) | −36.6826 | −1.19518 | ||||||||
\(943\) | 50.3477 | 1.63955 | ||||||||
\(944\) | −5.18756 | −0.168841 | ||||||||
\(945\) | −3.78267 | −0.123050 | ||||||||
\(946\) | −61.4025 | −1.99637 | ||||||||
\(947\) | −56.6561 | −1.84108 | −0.920538 | − | 0.390653i | \(-0.872249\pi\) | ||||
−0.920538 | + | 0.390653i | \(0.872249\pi\) | |||||||
\(948\) | 32.4183 | 1.05290 | ||||||||
\(949\) | 4.11332 | 0.133524 | ||||||||
\(950\) | −9.40872 | −0.305259 | ||||||||
\(951\) | 2.33680 | 0.0757761 | ||||||||
\(952\) | 4.56382 | 0.147914 | ||||||||
\(953\) | 14.9498 | 0.484271 | 0.242136 | − | 0.970242i | \(-0.422152\pi\) | ||||
0.242136 | + | 0.970242i | \(0.422152\pi\) | |||||||
\(954\) | −10.8611 | −0.351642 | ||||||||
\(955\) | −5.71909 | −0.185066 | ||||||||
\(956\) | −23.8064 | −0.769954 | ||||||||
\(957\) | 52.3871 | 1.69344 | ||||||||
\(958\) | 91.4601 | 2.95494 | ||||||||
\(959\) | 9.70438 | 0.313371 | ||||||||
\(960\) | 92.3363 | 2.98014 | ||||||||
\(961\) | 56.4975 | 1.82250 | ||||||||
\(962\) | 23.7561 | 0.765927 | ||||||||
\(963\) | 49.3233 | 1.58942 | ||||||||
\(964\) | −23.4249 | −0.754465 | ||||||||
\(965\) | −31.6005 | −1.01726 | ||||||||
\(966\) | 37.1503 | 1.19529 | ||||||||
\(967\) | 41.5686 | 1.33676 | 0.668379 | − | 0.743821i | \(-0.266989\pi\) | ||||
0.668379 | + | 0.743821i | \(0.266989\pi\) | |||||||
\(968\) | −26.4702 | −0.850784 | ||||||||
\(969\) | −4.58012 | −0.147135 | ||||||||
\(970\) | −4.33137 | −0.139072 | ||||||||
\(971\) | 61.2844 | 1.96671 | 0.983355 | − | 0.181693i | \(-0.0581576\pi\) | ||||
0.983355 | + | 0.181693i | \(0.0581576\pi\) | |||||||
\(972\) | 62.0072 | 1.98888 | ||||||||
\(973\) | 1.46643 | 0.0470115 | ||||||||
\(974\) | −74.0838 | −2.37380 | ||||||||
\(975\) | −9.61410 | −0.307898 | ||||||||
\(976\) | −10.7052 | −0.342666 | ||||||||
\(977\) | 24.1750 | 0.773428 | 0.386714 | − | 0.922200i | \(-0.373610\pi\) | ||||
0.386714 | + | 0.922200i | \(0.373610\pi\) | |||||||
\(978\) | −78.5914 | −2.51308 | ||||||||
\(979\) | 68.4125 | 2.18647 | ||||||||
\(980\) | −55.5943 | −1.77590 | ||||||||
\(981\) | 40.9604 | 1.30776 | ||||||||
\(982\) | −2.36526 | −0.0754785 | ||||||||
\(983\) | 13.1607 | 0.419761 | 0.209881 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209881 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(984\) | −38.7119 | −1.23409 | ||||||||
\(985\) | 14.7297 | 0.469329 | ||||||||
\(986\) | −20.9239 | −0.666354 | ||||||||
\(987\) | −12.9191 | −0.411221 | ||||||||
\(988\) | 2.99303 | 0.0952210 | ||||||||
\(989\) | 41.4087 | 1.31672 | ||||||||
\(990\) | 79.0487 | 2.51233 | ||||||||
\(991\) | −19.9981 | −0.635261 | −0.317631 | − | 0.948215i | \(-0.602887\pi\) | ||||
−0.317631 | + | 0.948215i | \(0.602887\pi\) | |||||||
\(992\) | −61.0280 | −1.93764 | ||||||||
\(993\) | 23.3328 | 0.740444 | ||||||||
\(994\) | −14.2118 | −0.450771 | ||||||||
\(995\) | 22.2162 | 0.704300 | ||||||||
\(996\) | 64.2545 | 2.03598 | ||||||||
\(997\) | 21.4858 | 0.680461 | 0.340230 | − | 0.940342i | \(-0.389495\pi\) | ||||
0.340230 | + | 0.940342i | \(0.389495\pi\) | |||||||
\(998\) | 11.7027 | 0.370443 | ||||||||
\(999\) | −13.5672 | −0.429249 |
(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 | 6023.2.a.c.1.17 | ✓ | 138 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.c.1.17 | ✓ | 138 | 1.1 | even | 1 | trivial |