Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, 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("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42574 | −1.71526 | −0.857630 | − | 0.514267i | \(-0.828064\pi\) | ||||
−0.857630 | + | 0.514267i | \(0.828064\pi\) | |||||||
\(3\) | −1.56213 | −0.901897 | −0.450948 | − | 0.892550i | \(-0.648914\pi\) | ||||
−0.450948 | + | 0.892550i | \(0.648914\pi\) | |||||||
\(4\) | 3.88424 | 1.94212 | ||||||||
\(5\) | 2.05918 | 0.920892 | 0.460446 | − | 0.887688i | \(-0.347689\pi\) | ||||
0.460446 | + | 0.887688i | \(0.347689\pi\) | |||||||
\(6\) | 3.78933 | 1.54699 | ||||||||
\(7\) | −2.28895 | −0.865141 | −0.432571 | − | 0.901600i | \(-0.642393\pi\) | ||||
−0.432571 | + | 0.901600i | \(0.642393\pi\) | |||||||
\(8\) | −4.57068 | −1.61598 | ||||||||
\(9\) | −0.559747 | −0.186582 | ||||||||
\(10\) | −4.99504 | −1.57957 | ||||||||
\(11\) | −5.80011 | −1.74880 | −0.874400 | − | 0.485206i | \(-0.838745\pi\) | ||||
−0.874400 | + | 0.485206i | \(0.838745\pi\) | |||||||
\(12\) | −6.06769 | −1.75159 | ||||||||
\(13\) | −4.60944 | −1.27843 | −0.639215 | − | 0.769028i | \(-0.720740\pi\) | ||||
−0.639215 | + | 0.769028i | \(0.720740\pi\) | |||||||
\(14\) | 5.55240 | 1.48394 | ||||||||
\(15\) | −3.21671 | −0.830550 | ||||||||
\(16\) | 3.31883 | 0.829706 | ||||||||
\(17\) | 6.41164 | 1.55505 | 0.777526 | − | 0.628851i | \(-0.216475\pi\) | ||||
0.777526 | + | 0.628851i | \(0.216475\pi\) | |||||||
\(18\) | 1.35780 | 0.320037 | ||||||||
\(19\) | 6.83128 | 1.56720 | 0.783601 | − | 0.621264i | \(-0.213380\pi\) | ||||
0.783601 | + | 0.621264i | \(0.213380\pi\) | |||||||
\(20\) | 7.99834 | 1.78848 | ||||||||
\(21\) | 3.57564 | 0.780268 | ||||||||
\(22\) | 14.0696 | 2.99965 | ||||||||
\(23\) | −2.96482 | −0.618208 | −0.309104 | − | 0.951028i | \(-0.600029\pi\) | ||||
−0.309104 | + | 0.951028i | \(0.600029\pi\) | |||||||
\(24\) | 7.14000 | 1.45745 | ||||||||
\(25\) | −0.759787 | −0.151957 | ||||||||
\(26\) | 11.1813 | 2.19284 | ||||||||
\(27\) | 5.56079 | 1.07017 | ||||||||
\(28\) | −8.89082 | −1.68021 | ||||||||
\(29\) | −8.95853 | −1.66356 | −0.831778 | − | 0.555108i | \(-0.812677\pi\) | ||||
−0.831778 | + | 0.555108i | \(0.812677\pi\) | |||||||
\(30\) | 7.80291 | 1.42461 | ||||||||
\(31\) | −0.0443456 | −0.00796470 | −0.00398235 | − | 0.999992i | \(-0.501268\pi\) | ||||
−0.00398235 | + | 0.999992i | \(0.501268\pi\) | |||||||
\(32\) | 1.09073 | 0.192816 | ||||||||
\(33\) | 9.06053 | 1.57724 | ||||||||
\(34\) | −15.5530 | −2.66732 | ||||||||
\(35\) | −4.71335 | −0.796702 | ||||||||
\(36\) | −2.17419 | −0.362365 | ||||||||
\(37\) | −3.78168 | −0.621705 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(38\) | −16.5709 | −2.68816 | ||||||||
\(39\) | 7.20055 | 1.15301 | ||||||||
\(40\) | −9.41184 | −1.48814 | ||||||||
\(41\) | −2.12203 | −0.331405 | −0.165702 | − | 0.986176i | \(-0.552989\pi\) | ||||
−0.165702 | + | 0.986176i | \(0.552989\pi\) | |||||||
\(42\) | −8.67358 | −1.33836 | ||||||||
\(43\) | 0.112527 | 0.0171602 | 0.00858012 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00858012 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(44\) | −22.5290 | −3.39638 | ||||||||
\(45\) | −1.15262 | −0.171822 | ||||||||
\(46\) | 7.19190 | 1.06039 | ||||||||
\(47\) | −0.270503 | −0.0394569 | −0.0197285 | − | 0.999805i | \(-0.506280\pi\) | ||||
−0.0197285 | + | 0.999805i | \(0.506280\pi\) | |||||||
\(48\) | −5.18444 | −0.748309 | ||||||||
\(49\) | −1.76071 | −0.251531 | ||||||||
\(50\) | 1.84305 | 0.260647 | ||||||||
\(51\) | −10.0158 | −1.40250 | ||||||||
\(52\) | −17.9042 | −2.48286 | ||||||||
\(53\) | −3.37618 | −0.463754 | −0.231877 | − | 0.972745i | \(-0.574487\pi\) | ||||
−0.231877 | + | 0.972745i | \(0.574487\pi\) | |||||||
\(54\) | −13.4891 | −1.83563 | ||||||||
\(55\) | −11.9435 | −1.61046 | ||||||||
\(56\) | 10.4620 | 1.39805 | ||||||||
\(57\) | −10.6714 | −1.41346 | ||||||||
\(58\) | 21.7311 | 2.85343 | ||||||||
\(59\) | 1.96851 | 0.256278 | 0.128139 | − | 0.991756i | \(-0.459100\pi\) | ||||
0.128139 | + | 0.991756i | \(0.459100\pi\) | |||||||
\(60\) | −12.4944 | −1.61303 | ||||||||
\(61\) | 3.04149 | 0.389423 | 0.194712 | − | 0.980861i | \(-0.437623\pi\) | ||||
0.194712 | + | 0.980861i | \(0.437623\pi\) | |||||||
\(62\) | 0.107571 | 0.0136615 | ||||||||
\(63\) | 1.28123 | 0.161420 | ||||||||
\(64\) | −9.28349 | −1.16044 | ||||||||
\(65\) | −9.49166 | −1.17730 | ||||||||
\(66\) | −21.9785 | −2.70537 | ||||||||
\(67\) | −8.25273 | −1.00823 | −0.504115 | − | 0.863636i | \(-0.668181\pi\) | ||||
−0.504115 | + | 0.863636i | \(0.668181\pi\) | |||||||
\(68\) | 24.9043 | 3.02009 | ||||||||
\(69\) | 4.63144 | 0.557560 | ||||||||
\(70\) | 11.4334 | 1.36655 | ||||||||
\(71\) | −3.54466 | −0.420674 | −0.210337 | − | 0.977629i | \(-0.567456\pi\) | ||||
−0.210337 | + | 0.977629i | \(0.567456\pi\) | |||||||
\(72\) | 2.55842 | 0.301513 | ||||||||
\(73\) | −9.18737 | −1.07530 | −0.537650 | − | 0.843168i | \(-0.680688\pi\) | ||||
−0.537650 | + | 0.843168i | \(0.680688\pi\) | |||||||
\(74\) | 9.17340 | 1.06639 | ||||||||
\(75\) | 1.18689 | 0.137050 | ||||||||
\(76\) | 26.5343 | 3.04369 | ||||||||
\(77\) | 13.2762 | 1.51296 | ||||||||
\(78\) | −17.4667 | −1.97771 | ||||||||
\(79\) | −13.7295 | −1.54469 | −0.772347 | − | 0.635201i | \(-0.780917\pi\) | ||||
−0.772347 | + | 0.635201i | \(0.780917\pi\) | |||||||
\(80\) | 6.83405 | 0.764070 | ||||||||
\(81\) | −7.00744 | −0.778605 | ||||||||
\(82\) | 5.14750 | 0.568446 | ||||||||
\(83\) | 9.68690 | 1.06327 | 0.531637 | − | 0.846972i | \(-0.321577\pi\) | ||||
0.531637 | + | 0.846972i | \(0.321577\pi\) | |||||||
\(84\) | 13.8886 | 1.51537 | ||||||||
\(85\) | 13.2027 | 1.43203 | ||||||||
\(86\) | −0.272962 | −0.0294343 | ||||||||
\(87\) | 13.9944 | 1.50036 | ||||||||
\(88\) | 26.5104 | 2.82602 | ||||||||
\(89\) | −2.01602 | −0.213698 | −0.106849 | − | 0.994275i | \(-0.534076\pi\) | ||||
−0.106849 | + | 0.994275i | \(0.534076\pi\) | |||||||
\(90\) | 2.79596 | 0.294720 | ||||||||
\(91\) | 10.5508 | 1.10602 | ||||||||
\(92\) | −11.5161 | −1.20063 | ||||||||
\(93\) | 0.0692736 | 0.00718334 | ||||||||
\(94\) | 0.656171 | 0.0676789 | ||||||||
\(95\) | 14.0668 | 1.44323 | ||||||||
\(96\) | −1.70387 | −0.173901 | ||||||||
\(97\) | −5.72428 | −0.581213 | −0.290606 | − | 0.956843i | \(-0.593857\pi\) | ||||
−0.290606 | + | 0.956843i | \(0.593857\pi\) | |||||||
\(98\) | 4.27104 | 0.431441 | ||||||||
\(99\) | 3.24660 | 0.326295 | ||||||||
\(100\) | −2.95119 | −0.295119 | ||||||||
\(101\) | −20.0427 | −1.99432 | −0.997162 | − | 0.0752845i | \(-0.976013\pi\) | ||||
−0.997162 | + | 0.0752845i | \(0.976013\pi\) | |||||||
\(102\) | 24.2958 | 2.40565 | ||||||||
\(103\) | 11.9064 | 1.17318 | 0.586588 | − | 0.809886i | \(-0.300471\pi\) | ||||
0.586588 | + | 0.809886i | \(0.300471\pi\) | |||||||
\(104\) | 21.0683 | 2.06592 | ||||||||
\(105\) | 7.36287 | 0.718543 | ||||||||
\(106\) | 8.18976 | 0.795459 | ||||||||
\(107\) | 4.58073 | 0.442836 | 0.221418 | − | 0.975179i | \(-0.428931\pi\) | ||||
0.221418 | + | 0.975179i | \(0.428931\pi\) | |||||||
\(108\) | 21.5994 | 2.07841 | ||||||||
\(109\) | 8.04979 | 0.771030 | 0.385515 | − | 0.922702i | \(-0.374024\pi\) | ||||
0.385515 | + | 0.922702i | \(0.374024\pi\) | |||||||
\(110\) | 28.9718 | 2.76235 | ||||||||
\(111\) | 5.90748 | 0.560713 | ||||||||
\(112\) | −7.59662 | −0.717813 | ||||||||
\(113\) | −4.43589 | −0.417294 | −0.208647 | − | 0.977991i | \(-0.566906\pi\) | ||||
−0.208647 | + | 0.977991i | \(0.566906\pi\) | |||||||
\(114\) | 25.8860 | 2.42444 | ||||||||
\(115\) | −6.10510 | −0.569303 | ||||||||
\(116\) | −34.7970 | −3.23082 | ||||||||
\(117\) | 2.58012 | 0.238532 | ||||||||
\(118\) | −4.77510 | −0.439583 | ||||||||
\(119\) | −14.6759 | −1.34534 | ||||||||
\(120\) | 14.7025 | 1.34215 | ||||||||
\(121\) | 22.6413 | 2.05830 | ||||||||
\(122\) | −7.37789 | −0.667963 | ||||||||
\(123\) | 3.31488 | 0.298893 | ||||||||
\(124\) | −0.172249 | −0.0154684 | ||||||||
\(125\) | −11.8604 | −1.06083 | ||||||||
\(126\) | −3.10794 | −0.276878 | ||||||||
\(127\) | −1.41651 | −0.125695 | −0.0628476 | − | 0.998023i | \(-0.520018\pi\) | ||||
−0.0628476 | + | 0.998023i | \(0.520018\pi\) | |||||||
\(128\) | 20.3379 | 1.79764 | ||||||||
\(129\) | −0.175782 | −0.0154768 | ||||||||
\(130\) | 23.0243 | 2.01937 | ||||||||
\(131\) | 4.69318 | 0.410045 | 0.205023 | − | 0.978757i | \(-0.434273\pi\) | ||||
0.205023 | + | 0.978757i | \(0.434273\pi\) | |||||||
\(132\) | 35.1933 | 3.06318 | ||||||||
\(133\) | −15.6364 | −1.35585 | ||||||||
\(134\) | 20.0190 | 1.72938 | ||||||||
\(135\) | 11.4507 | 0.985516 | ||||||||
\(136\) | −29.3056 | −2.51293 | ||||||||
\(137\) | −9.23756 | −0.789218 | −0.394609 | − | 0.918849i | \(-0.629120\pi\) | ||||
−0.394609 | + | 0.918849i | \(0.629120\pi\) | |||||||
\(138\) | −11.2347 | −0.956360 | ||||||||
\(139\) | −2.92337 | −0.247957 | −0.123978 | − | 0.992285i | \(-0.539565\pi\) | ||||
−0.123978 | + | 0.992285i | \(0.539565\pi\) | |||||||
\(140\) | −18.3078 | −1.54729 | ||||||||
\(141\) | 0.422561 | 0.0355861 | ||||||||
\(142\) | 8.59845 | 0.721566 | ||||||||
\(143\) | 26.7353 | 2.23572 | ||||||||
\(144\) | −1.85770 | −0.154809 | ||||||||
\(145\) | −18.4472 | −1.53196 | ||||||||
\(146\) | 22.2862 | 1.84442 | ||||||||
\(147\) | 2.75047 | 0.226855 | ||||||||
\(148\) | −14.6890 | −1.20742 | ||||||||
\(149\) | 7.39579 | 0.605886 | 0.302943 | − | 0.953009i | \(-0.402031\pi\) | ||||
0.302943 | + | 0.953009i | \(0.402031\pi\) | |||||||
\(150\) | −2.87908 | −0.235076 | ||||||||
\(151\) | −0.0268784 | −0.00218733 | −0.00109367 | − | 0.999999i | \(-0.500348\pi\) | ||||
−0.00109367 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(152\) | −31.2236 | −2.53257 | ||||||||
\(153\) | −3.58890 | −0.290145 | ||||||||
\(154\) | −32.2046 | −2.59512 | ||||||||
\(155\) | −0.0913154 | −0.00733463 | ||||||||
\(156\) | 27.9687 | 2.23928 | ||||||||
\(157\) | −5.07212 | −0.404799 | −0.202399 | − | 0.979303i | \(-0.564874\pi\) | ||||
−0.202399 | + | 0.979303i | \(0.564874\pi\) | |||||||
\(158\) | 33.3044 | 2.64955 | ||||||||
\(159\) | 5.27404 | 0.418258 | ||||||||
\(160\) | 2.24602 | 0.177563 | ||||||||
\(161\) | 6.78632 | 0.534837 | ||||||||
\(162\) | 16.9983 | 1.33551 | ||||||||
\(163\) | −11.8124 | −0.925217 | −0.462609 | − | 0.886563i | \(-0.653086\pi\) | ||||
−0.462609 | + | 0.886563i | \(0.653086\pi\) | |||||||
\(164\) | −8.24246 | −0.643628 | ||||||||
\(165\) | 18.6572 | 1.45246 | ||||||||
\(166\) | −23.4979 | −1.82379 | ||||||||
\(167\) | 18.5164 | 1.43284 | 0.716421 | − | 0.697668i | \(-0.245779\pi\) | ||||
0.716421 | + | 0.697668i | \(0.245779\pi\) | |||||||
\(168\) | −16.3431 | −1.26090 | ||||||||
\(169\) | 8.24696 | 0.634382 | ||||||||
\(170\) | −32.0264 | −2.45631 | ||||||||
\(171\) | −3.82379 | −0.292412 | ||||||||
\(172\) | 0.437082 | 0.0333272 | ||||||||
\(173\) | 3.96285 | 0.301290 | 0.150645 | − | 0.988588i | \(-0.451865\pi\) | ||||
0.150645 | + | 0.988588i | \(0.451865\pi\) | |||||||
\(174\) | −33.9468 | −2.57350 | ||||||||
\(175\) | 1.73911 | 0.131465 | ||||||||
\(176\) | −19.2496 | −1.45099 | ||||||||
\(177\) | −3.07507 | −0.231136 | ||||||||
\(178\) | 4.89035 | 0.366547 | ||||||||
\(179\) | −20.9482 | −1.56574 | −0.782872 | − | 0.622183i | \(-0.786246\pi\) | ||||
−0.782872 | + | 0.622183i | \(0.786246\pi\) | |||||||
\(180\) | −4.47705 | −0.333699 | ||||||||
\(181\) | 2.23679 | 0.166259 | 0.0831296 | − | 0.996539i | \(-0.473508\pi\) | ||||
0.0831296 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(182\) | −25.5935 | −1.89712 | ||||||||
\(183\) | −4.75121 | −0.351220 | ||||||||
\(184\) | 13.5512 | 0.999011 | ||||||||
\(185\) | −7.78716 | −0.572523 | ||||||||
\(186\) | −0.168040 | −0.0123213 | ||||||||
\(187\) | −37.1882 | −2.71947 | ||||||||
\(188\) | −1.05070 | −0.0766300 | ||||||||
\(189\) | −12.7284 | −0.925852 | ||||||||
\(190\) | −34.1225 | −2.47551 | ||||||||
\(191\) | 10.4705 | 0.757620 | 0.378810 | − | 0.925475i | \(-0.376333\pi\) | ||||
0.378810 | + | 0.925475i | \(0.376333\pi\) | |||||||
\(192\) | 14.5020 | 1.04659 | ||||||||
\(193\) | 16.2046 | 1.16643 | 0.583217 | − | 0.812317i | \(-0.301794\pi\) | ||||
0.583217 | + | 0.812317i | \(0.301794\pi\) | |||||||
\(194\) | 13.8856 | 0.996931 | ||||||||
\(195\) | 14.8272 | 1.06180 | ||||||||
\(196\) | −6.83903 | −0.488502 | ||||||||
\(197\) | −10.9169 | −0.777798 | −0.388899 | − | 0.921280i | \(-0.627144\pi\) | ||||
−0.388899 | + | 0.921280i | \(0.627144\pi\) | |||||||
\(198\) | −7.87541 | −0.559681 | ||||||||
\(199\) | −11.3412 | −0.803959 | −0.401979 | − | 0.915649i | \(-0.631678\pi\) | ||||
−0.401979 | + | 0.915649i | \(0.631678\pi\) | |||||||
\(200\) | 3.47274 | 0.245560 | ||||||||
\(201\) | 12.8918 | 0.909320 | ||||||||
\(202\) | 48.6185 | 3.42079 | ||||||||
\(203\) | 20.5056 | 1.43921 | ||||||||
\(204\) | −38.9038 | −2.72381 | ||||||||
\(205\) | −4.36963 | −0.305188 | ||||||||
\(206\) | −28.8820 | −2.01230 | ||||||||
\(207\) | 1.65955 | 0.115347 | ||||||||
\(208\) | −15.2979 | −1.06072 | ||||||||
\(209\) | −39.6222 | −2.74072 | ||||||||
\(210\) | −17.8604 | −1.23249 | ||||||||
\(211\) | 7.13087 | 0.490910 | 0.245455 | − | 0.969408i | \(-0.421063\pi\) | ||||
0.245455 | + | 0.969408i | \(0.421063\pi\) | |||||||
\(212\) | −13.1139 | −0.900666 | ||||||||
\(213\) | 5.53723 | 0.379405 | ||||||||
\(214\) | −11.1117 | −0.759580 | ||||||||
\(215\) | 0.231713 | 0.0158027 | ||||||||
\(216\) | −25.4166 | −1.72938 | ||||||||
\(217\) | 0.101505 | 0.00689059 | ||||||||
\(218\) | −19.5267 | −1.32252 | ||||||||
\(219\) | 14.3519 | 0.969809 | ||||||||
\(220\) | −46.3912 | −3.12770 | ||||||||
\(221\) | −29.5541 | −1.98802 | ||||||||
\(222\) | −14.3300 | −0.961770 | ||||||||
\(223\) | 14.6473 | 0.980853 | 0.490427 | − | 0.871482i | \(-0.336841\pi\) | ||||
0.490427 | + | 0.871482i | \(0.336841\pi\) | |||||||
\(224\) | −2.49664 | −0.166813 | ||||||||
\(225\) | 0.425289 | 0.0283526 | ||||||||
\(226\) | 10.7603 | 0.715767 | ||||||||
\(227\) | 2.60750 | 0.173066 | 0.0865330 | − | 0.996249i | \(-0.472421\pi\) | ||||
0.0865330 | + | 0.996249i | \(0.472421\pi\) | |||||||
\(228\) | −41.4501 | −2.74510 | ||||||||
\(229\) | −27.6328 | −1.82603 | −0.913013 | − | 0.407930i | \(-0.866251\pi\) | ||||
−0.913013 | + | 0.407930i | \(0.866251\pi\) | |||||||
\(230\) | 14.8094 | 0.976503 | ||||||||
\(231\) | −20.7391 | −1.36453 | ||||||||
\(232\) | 40.9465 | 2.68827 | ||||||||
\(233\) | 4.36316 | 0.285840 | 0.142920 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142920 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(234\) | −6.25872 | −0.409145 | ||||||||
\(235\) | −0.557014 | −0.0363356 | ||||||||
\(236\) | 7.64615 | 0.497722 | ||||||||
\(237\) | 21.4473 | 1.39315 | ||||||||
\(238\) | 35.6000 | 2.30761 | ||||||||
\(239\) | −13.9622 | −0.903137 | −0.451568 | − | 0.892236i | \(-0.649135\pi\) | ||||
−0.451568 | + | 0.892236i | \(0.649135\pi\) | |||||||
\(240\) | −10.6757 | −0.689112 | ||||||||
\(241\) | −18.1453 | −1.16884 | −0.584420 | − | 0.811452i | \(-0.698678\pi\) | ||||
−0.584420 | + | 0.811452i | \(0.698678\pi\) | |||||||
\(242\) | −54.9220 | −3.53052 | ||||||||
\(243\) | −5.73583 | −0.367954 | ||||||||
\(244\) | 11.8139 | 0.756306 | ||||||||
\(245\) | −3.62562 | −0.231633 | ||||||||
\(246\) | −8.04106 | −0.512679 | ||||||||
\(247\) | −31.4884 | −2.00356 | ||||||||
\(248\) | 0.202689 | 0.0128708 | ||||||||
\(249\) | −15.1322 | −0.958964 | ||||||||
\(250\) | 28.7704 | 1.81960 | ||||||||
\(251\) | 13.5816 | 0.857264 | 0.428632 | − | 0.903479i | \(-0.358996\pi\) | ||||
0.428632 | + | 0.903479i | \(0.358996\pi\) | |||||||
\(252\) | 4.97661 | 0.313497 | ||||||||
\(253\) | 17.1963 | 1.08112 | ||||||||
\(254\) | 3.43610 | 0.215600 | ||||||||
\(255\) | −20.6244 | −1.29155 | ||||||||
\(256\) | −30.7676 | −1.92298 | ||||||||
\(257\) | 27.0662 | 1.68834 | 0.844171 | − | 0.536075i | \(-0.180093\pi\) | ||||
0.844171 | + | 0.536075i | \(0.180093\pi\) | |||||||
\(258\) | 0.426403 | 0.0265467 | ||||||||
\(259\) | 8.65608 | 0.537862 | ||||||||
\(260\) | −36.8679 | −2.28645 | ||||||||
\(261\) | 5.01451 | 0.310390 | ||||||||
\(262\) | −11.3845 | −0.703334 | ||||||||
\(263\) | 21.0277 | 1.29662 | 0.648312 | − | 0.761374i | \(-0.275475\pi\) | ||||
0.648312 | + | 0.761374i | \(0.275475\pi\) | |||||||
\(264\) | −41.4128 | −2.54878 | ||||||||
\(265\) | −6.95216 | −0.427068 | ||||||||
\(266\) | 37.9300 | 2.32564 | ||||||||
\(267\) | 3.14929 | 0.192733 | ||||||||
\(268\) | −32.0555 | −1.95810 | ||||||||
\(269\) | 14.3612 | 0.875616 | 0.437808 | − | 0.899068i | \(-0.355755\pi\) | ||||
0.437808 | + | 0.899068i | \(0.355755\pi\) | |||||||
\(270\) | −27.7764 | −1.69042 | ||||||||
\(271\) | −16.5621 | −1.00607 | −0.503037 | − | 0.864265i | \(-0.667784\pi\) | ||||
−0.503037 | + | 0.864265i | \(0.667784\pi\) | |||||||
\(272\) | 21.2791 | 1.29024 | ||||||||
\(273\) | −16.4817 | −0.997518 | ||||||||
\(274\) | 22.4080 | 1.35371 | ||||||||
\(275\) | 4.40685 | 0.265743 | ||||||||
\(276\) | 17.9896 | 1.08285 | ||||||||
\(277\) | −28.9776 | −1.74109 | −0.870547 | − | 0.492086i | \(-0.836235\pi\) | ||||
−0.870547 | + | 0.492086i | \(0.836235\pi\) | |||||||
\(278\) | 7.09135 | 0.425311 | ||||||||
\(279\) | 0.0248223 | 0.00148607 | ||||||||
\(280\) | 21.5432 | 1.28745 | ||||||||
\(281\) | −15.6451 | −0.933307 | −0.466653 | − | 0.884440i | \(-0.654540\pi\) | ||||
−0.466653 | + | 0.884440i | \(0.654540\pi\) | |||||||
\(282\) | −1.02503 | −0.0610394 | ||||||||
\(283\) | 25.8810 | 1.53847 | 0.769233 | − | 0.638969i | \(-0.220639\pi\) | ||||
0.769233 | + | 0.638969i | \(0.220639\pi\) | |||||||
\(284\) | −13.7683 | −0.816999 | ||||||||
\(285\) | −21.9742 | −1.30164 | ||||||||
\(286\) | −64.8530 | −3.83484 | ||||||||
\(287\) | 4.85721 | 0.286712 | ||||||||
\(288\) | −0.610536 | −0.0359762 | ||||||||
\(289\) | 24.1091 | 1.41818 | ||||||||
\(290\) | 44.7482 | 2.62770 | ||||||||
\(291\) | 8.94208 | 0.524194 | ||||||||
\(292\) | −35.6859 | −2.08836 | ||||||||
\(293\) | 8.89669 | 0.519750 | 0.259875 | − | 0.965642i | \(-0.416319\pi\) | ||||
0.259875 | + | 0.965642i | \(0.416319\pi\) | |||||||
\(294\) | −6.67193 | −0.389115 | ||||||||
\(295\) | 4.05351 | 0.236004 | ||||||||
\(296\) | 17.2849 | 1.00466 | ||||||||
\(297\) | −32.2532 | −1.87152 | ||||||||
\(298\) | −17.9403 | −1.03925 | ||||||||
\(299\) | 13.6662 | 0.790335 | ||||||||
\(300\) | 4.61015 | 0.266167 | ||||||||
\(301\) | −0.257569 | −0.0148460 | ||||||||
\(302\) | 0.0652001 | 0.00375184 | ||||||||
\(303\) | 31.3093 | 1.79867 | ||||||||
\(304\) | 22.6718 | 1.30032 | ||||||||
\(305\) | 6.26298 | 0.358617 | ||||||||
\(306\) | 8.70575 | 0.497675 | ||||||||
\(307\) | −16.2746 | −0.928840 | −0.464420 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464420 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(308\) | 51.5677 | 2.93835 | ||||||||
\(309\) | −18.5994 | −1.05808 | ||||||||
\(310\) | 0.221508 | 0.0125808 | ||||||||
\(311\) | 28.8159 | 1.63400 | 0.816999 | − | 0.576639i | \(-0.195636\pi\) | ||||
0.816999 | + | 0.576639i | \(0.195636\pi\) | |||||||
\(312\) | −32.9114 | −1.86324 | ||||||||
\(313\) | 16.3485 | 0.924074 | 0.462037 | − | 0.886861i | \(-0.347119\pi\) | ||||
0.462037 | + | 0.886861i | \(0.347119\pi\) | |||||||
\(314\) | 12.3037 | 0.694336 | ||||||||
\(315\) | 2.63829 | 0.148651 | ||||||||
\(316\) | −53.3288 | −2.99998 | ||||||||
\(317\) | 29.2646 | 1.64366 | 0.821832 | − | 0.569730i | \(-0.192952\pi\) | ||||
0.821832 | + | 0.569730i | \(0.192952\pi\) | |||||||
\(318\) | −12.7935 | −0.717422 | ||||||||
\(319\) | 51.9605 | 2.90923 | ||||||||
\(320\) | −19.1164 | −1.06864 | ||||||||
\(321\) | −7.15571 | −0.399393 | ||||||||
\(322\) | −16.4619 | −0.917385 | ||||||||
\(323\) | 43.7997 | 2.43708 | ||||||||
\(324\) | −27.2186 | −1.51214 | ||||||||
\(325\) | 3.50219 | 0.194267 | ||||||||
\(326\) | 28.6538 | 1.58699 | ||||||||
\(327\) | −12.5748 | −0.695389 | ||||||||
\(328\) | 9.69911 | 0.535544 | ||||||||
\(329\) | 0.619167 | 0.0341358 | ||||||||
\(330\) | −45.2577 | −2.49136 | ||||||||
\(331\) | 11.5934 | 0.637229 | 0.318615 | − | 0.947884i | \(-0.396782\pi\) | ||||
0.318615 | + | 0.947884i | \(0.396782\pi\) | |||||||
\(332\) | 37.6262 | 2.06501 | ||||||||
\(333\) | 2.11679 | 0.115999 | ||||||||
\(334\) | −44.9161 | −2.45770 | ||||||||
\(335\) | −16.9938 | −0.928472 | ||||||||
\(336\) | 11.8669 | 0.647393 | ||||||||
\(337\) | 0.140612 | 0.00765963 | 0.00382981 | − | 0.999993i | \(-0.498781\pi\) | ||||
0.00382981 | + | 0.999993i | \(0.498781\pi\) | |||||||
\(338\) | −20.0050 | −1.08813 | ||||||||
\(339\) | 6.92944 | 0.376356 | ||||||||
\(340\) | 51.2825 | 2.78118 | ||||||||
\(341\) | 0.257209 | 0.0139287 | ||||||||
\(342\) | 9.27554 | 0.501564 | ||||||||
\(343\) | 20.0528 | 1.08275 | ||||||||
\(344\) | −0.514326 | −0.0277306 | ||||||||
\(345\) | 9.53696 | 0.513453 | ||||||||
\(346\) | −9.61287 | −0.516791 | ||||||||
\(347\) | 19.5651 | 1.05031 | 0.525154 | − | 0.851007i | \(-0.324008\pi\) | ||||
0.525154 | + | 0.851007i | \(0.324008\pi\) | |||||||
\(348\) | 54.3575 | 2.91387 | ||||||||
\(349\) | 9.75644 | 0.522250 | 0.261125 | − | 0.965305i | \(-0.415906\pi\) | ||||
0.261125 | + | 0.965305i | \(0.415906\pi\) | |||||||
\(350\) | −4.21864 | −0.225496 | ||||||||
\(351\) | −25.6321 | −1.36814 | ||||||||
\(352\) | −6.32638 | −0.337197 | ||||||||
\(353\) | 7.66210 | 0.407812 | 0.203906 | − | 0.978990i | \(-0.434636\pi\) | ||||
0.203906 | + | 0.978990i | \(0.434636\pi\) | |||||||
\(354\) | 7.45933 | 0.396459 | ||||||||
\(355\) | −7.29909 | −0.387396 | ||||||||
\(356\) | −7.83071 | −0.415027 | ||||||||
\(357\) | 22.9257 | 1.21336 | ||||||||
\(358\) | 50.8151 | 2.68566 | ||||||||
\(359\) | −28.9320 | −1.52698 | −0.763488 | − | 0.645823i | \(-0.776515\pi\) | ||||
−0.763488 | + | 0.645823i | \(0.776515\pi\) | |||||||
\(360\) | 5.26825 | 0.277661 | ||||||||
\(361\) | 27.6664 | 1.45612 | ||||||||
\(362\) | −5.42588 | −0.285178 | ||||||||
\(363\) | −35.3687 | −1.85637 | ||||||||
\(364\) | 40.9817 | 2.14803 | ||||||||
\(365\) | −18.9184 | −0.990235 | ||||||||
\(366\) | 11.5252 | 0.602433 | ||||||||
\(367\) | −26.9298 | −1.40572 | −0.702861 | − | 0.711327i | \(-0.748094\pi\) | ||||
−0.702861 | + | 0.711327i | \(0.748094\pi\) | |||||||
\(368\) | −9.83973 | −0.512931 | ||||||||
\(369\) | 1.18780 | 0.0618343 | ||||||||
\(370\) | 18.8897 | 0.982026 | ||||||||
\(371\) | 7.72791 | 0.401213 | ||||||||
\(372\) | 0.269075 | 0.0139509 | ||||||||
\(373\) | 2.12880 | 0.110225 | 0.0551125 | − | 0.998480i | \(-0.482448\pi\) | ||||
0.0551125 | + | 0.998480i | \(0.482448\pi\) | |||||||
\(374\) | 90.2092 | 4.66460 | ||||||||
\(375\) | 18.5275 | 0.956758 | ||||||||
\(376\) | 1.23638 | 0.0637615 | ||||||||
\(377\) | 41.2938 | 2.12674 | ||||||||
\(378\) | 30.8758 | 1.58808 | ||||||||
\(379\) | 12.8192 | 0.658477 | 0.329238 | − | 0.944247i | \(-0.393208\pi\) | ||||
0.329238 | + | 0.944247i | \(0.393208\pi\) | |||||||
\(380\) | 54.6389 | 2.80291 | ||||||||
\(381\) | 2.21278 | 0.113364 | ||||||||
\(382\) | −25.3988 | −1.29951 | ||||||||
\(383\) | −0.850467 | −0.0434569 | −0.0217284 | − | 0.999764i | \(-0.506917\pi\) | ||||
−0.0217284 | + | 0.999764i | \(0.506917\pi\) | |||||||
\(384\) | −31.7705 | −1.62128 | ||||||||
\(385\) | 27.3380 | 1.39327 | ||||||||
\(386\) | −39.3083 | −2.00074 | ||||||||
\(387\) | −0.0629868 | −0.00320180 | ||||||||
\(388\) | −22.2345 | −1.12878 | ||||||||
\(389\) | 38.4592 | 1.94996 | 0.974979 | − | 0.222297i | \(-0.0713554\pi\) | ||||
0.974979 | + | 0.222297i | \(0.0713554\pi\) | |||||||
\(390\) | −35.9670 | −1.82126 | ||||||||
\(391\) | −19.0094 | −0.961345 | ||||||||
\(392\) | 8.04766 | 0.406468 | ||||||||
\(393\) | −7.33136 | −0.369818 | ||||||||
\(394\) | 26.4816 | 1.33413 | ||||||||
\(395\) | −28.2716 | −1.42250 | ||||||||
\(396\) | 12.6106 | 0.633704 | ||||||||
\(397\) | 13.9730 | 0.701286 | 0.350643 | − | 0.936509i | \(-0.385963\pi\) | ||||
0.350643 | + | 0.936509i | \(0.385963\pi\) | |||||||
\(398\) | 27.5109 | 1.37900 | ||||||||
\(399\) | 24.4262 | 1.22284 | ||||||||
\(400\) | −2.52160 | −0.126080 | ||||||||
\(401\) | −36.5357 | −1.82451 | −0.912254 | − | 0.409626i | \(-0.865659\pi\) | ||||
−0.912254 | + | 0.409626i | \(0.865659\pi\) | |||||||
\(402\) | −31.2723 | −1.55972 | ||||||||
\(403\) | 0.204408 | 0.0101823 | ||||||||
\(404\) | −77.8506 | −3.87321 | ||||||||
\(405\) | −14.4296 | −0.717011 | ||||||||
\(406\) | −49.7414 | −2.46862 | ||||||||
\(407\) | 21.9342 | 1.08724 | ||||||||
\(408\) | 45.7791 | 2.26640 | ||||||||
\(409\) | −12.8893 | −0.637337 | −0.318668 | − | 0.947866i | \(-0.603236\pi\) | ||||
−0.318668 | + | 0.947866i | \(0.603236\pi\) | |||||||
\(410\) | 10.5996 | 0.523477 | ||||||||
\(411\) | 14.4303 | 0.711793 | ||||||||
\(412\) | 46.2474 | 2.27845 | ||||||||
\(413\) | −4.50581 | −0.221717 | ||||||||
\(414\) | −4.02565 | −0.197850 | ||||||||
\(415\) | 19.9470 | 0.979162 | ||||||||
\(416\) | −5.02768 | −0.246502 | ||||||||
\(417\) | 4.56668 | 0.223631 | ||||||||
\(418\) | 96.1133 | 4.70106 | ||||||||
\(419\) | −12.4117 | −0.606350 | −0.303175 | − | 0.952935i | \(-0.598047\pi\) | ||||
−0.303175 | + | 0.952935i | \(0.598047\pi\) | |||||||
\(420\) | 28.5991 | 1.39550 | ||||||||
\(421\) | −0.317345 | −0.0154664 | −0.00773322 | − | 0.999970i | \(-0.502462\pi\) | ||||
−0.00773322 | + | 0.999970i | \(0.502462\pi\) | |||||||
\(422\) | −17.2977 | −0.842038 | ||||||||
\(423\) | 0.151413 | 0.00736196 | ||||||||
\(424\) | 15.4314 | 0.749417 | ||||||||
\(425\) | −4.87148 | −0.236302 | ||||||||
\(426\) | −13.4319 | −0.650778 | ||||||||
\(427\) | −6.96182 | −0.336906 | ||||||||
\(428\) | 17.7927 | 0.860041 | ||||||||
\(429\) | −41.7640 | −2.01639 | ||||||||
\(430\) | −0.562078 | −0.0271058 | ||||||||
\(431\) | 37.8615 | 1.82372 | 0.911861 | − | 0.410499i | \(-0.134645\pi\) | ||||
0.911861 | + | 0.410499i | \(0.134645\pi\) | |||||||
\(432\) | 18.4553 | 0.887931 | ||||||||
\(433\) | −32.8172 | −1.57709 | −0.788547 | − | 0.614974i | \(-0.789166\pi\) | ||||
−0.788547 | + | 0.614974i | \(0.789166\pi\) | |||||||
\(434\) | −0.246225 | −0.0118192 | ||||||||
\(435\) | 28.8169 | 1.38167 | ||||||||
\(436\) | 31.2673 | 1.49743 | ||||||||
\(437\) | −20.2535 | −0.968858 | ||||||||
\(438\) | −34.8140 | −1.66348 | ||||||||
\(439\) | −37.5346 | −1.79143 | −0.895715 | − | 0.444628i | \(-0.853336\pi\) | ||||
−0.895715 | + | 0.444628i | \(0.853336\pi\) | |||||||
\(440\) | 54.5897 | 2.60246 | ||||||||
\(441\) | 0.985555 | 0.0469312 | ||||||||
\(442\) | 71.6907 | 3.40998 | ||||||||
\(443\) | −2.54505 | −0.120919 | −0.0604594 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604594 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(444\) | 22.9461 | 1.08897 | ||||||||
\(445\) | −4.15135 | −0.196793 | ||||||||
\(446\) | −35.5305 | −1.68242 | ||||||||
\(447\) | −11.5532 | −0.546447 | ||||||||
\(448\) | 21.2494 | 1.00394 | ||||||||
\(449\) | 30.7052 | 1.44907 | 0.724534 | − | 0.689239i | \(-0.242055\pi\) | ||||
0.724534 | + | 0.689239i | \(0.242055\pi\) | |||||||
\(450\) | −1.03164 | −0.0486320 | ||||||||
\(451\) | 12.3080 | 0.579561 | ||||||||
\(452\) | −17.2301 | −0.810434 | ||||||||
\(453\) | 0.0419875 | 0.00197275 | ||||||||
\(454\) | −6.32513 | −0.296853 | ||||||||
\(455\) | 21.7259 | 1.01853 | ||||||||
\(456\) | 48.7753 | 2.28411 | ||||||||
\(457\) | −5.09754 | −0.238453 | −0.119226 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119226 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(458\) | 67.0301 | 3.13211 | ||||||||
\(459\) | 35.6538 | 1.66418 | ||||||||
\(460\) | −23.7136 | −1.10565 | ||||||||
\(461\) | 18.1124 | 0.843581 | 0.421790 | − | 0.906693i | \(-0.361402\pi\) | ||||
0.421790 | + | 0.906693i | \(0.361402\pi\) | |||||||
\(462\) | 50.3078 | 2.34053 | ||||||||
\(463\) | 3.83657 | 0.178300 | 0.0891502 | − | 0.996018i | \(-0.471585\pi\) | ||||
0.0891502 | + | 0.996018i | \(0.471585\pi\) | |||||||
\(464\) | −29.7318 | −1.38026 | ||||||||
\(465\) | 0.142647 | 0.00661508 | ||||||||
\(466\) | −10.5839 | −0.490290 | ||||||||
\(467\) | 35.4850 | 1.64205 | 0.821026 | − | 0.570891i | \(-0.193402\pi\) | ||||
0.821026 | + | 0.570891i | \(0.193402\pi\) | |||||||
\(468\) | 10.0218 | 0.463258 | ||||||||
\(469\) | 18.8901 | 0.872262 | ||||||||
\(470\) | 1.35117 | 0.0623250 | ||||||||
\(471\) | 7.92331 | 0.365087 | ||||||||
\(472\) | −8.99742 | −0.414140 | ||||||||
\(473\) | −0.652670 | −0.0300098 | ||||||||
\(474\) | −52.0258 | −2.38962 | ||||||||
\(475\) | −5.19032 | −0.238148 | ||||||||
\(476\) | −57.0047 | −2.61281 | ||||||||
\(477\) | 1.88981 | 0.0865284 | ||||||||
\(478\) | 33.8686 | 1.54912 | ||||||||
\(479\) | −24.2725 | −1.10904 | −0.554519 | − | 0.832171i | \(-0.687098\pi\) | ||||
−0.554519 | + | 0.832171i | \(0.687098\pi\) | |||||||
\(480\) | −3.50857 | −0.160144 | ||||||||
\(481\) | 17.4314 | 0.794806 | ||||||||
\(482\) | 44.0158 | 2.00486 | ||||||||
\(483\) | −10.6011 | −0.482368 | ||||||||
\(484\) | 87.9442 | 3.99746 | ||||||||
\(485\) | −11.7873 | −0.535234 | ||||||||
\(486\) | 13.9137 | 0.631137 | ||||||||
\(487\) | 14.9614 | 0.677968 | 0.338984 | − | 0.940792i | \(-0.389917\pi\) | ||||
0.338984 | + | 0.940792i | \(0.389917\pi\) | |||||||
\(488\) | −13.9017 | −0.629300 | ||||||||
\(489\) | 18.4525 | 0.834450 | ||||||||
\(490\) | 8.79484 | 0.397310 | ||||||||
\(491\) | −28.6489 | −1.29291 | −0.646454 | − | 0.762953i | \(-0.723749\pi\) | ||||
−0.646454 | + | 0.762953i | \(0.723749\pi\) | |||||||
\(492\) | 12.8758 | 0.580486 | ||||||||
\(493\) | −57.4389 | −2.58692 | ||||||||
\(494\) | 76.3828 | 3.43662 | ||||||||
\(495\) | 6.68532 | 0.300483 | ||||||||
\(496\) | −0.147175 | −0.00660836 | ||||||||
\(497\) | 8.11356 | 0.363943 | ||||||||
\(498\) | 36.7069 | 1.64487 | ||||||||
\(499\) | 31.2043 | 1.39690 | 0.698448 | − | 0.715661i | \(-0.253874\pi\) | ||||
0.698448 | + | 0.715661i | \(0.253874\pi\) | |||||||
\(500\) | −46.0687 | −2.06026 | ||||||||
\(501\) | −28.9251 | −1.29228 | ||||||||
\(502\) | −32.9455 | −1.47043 | ||||||||
\(503\) | −27.4422 | −1.22359 | −0.611794 | − | 0.791017i | \(-0.709552\pi\) | ||||
−0.611794 | + | 0.791017i | \(0.709552\pi\) | |||||||
\(504\) | −5.85610 | −0.260852 | ||||||||
\(505\) | −41.2715 | −1.83656 | ||||||||
\(506\) | −41.7138 | −1.85441 | ||||||||
\(507\) | −12.8828 | −0.572147 | ||||||||
\(508\) | −5.50207 | −0.244115 | ||||||||
\(509\) | 5.56861 | 0.246824 | 0.123412 | − | 0.992355i | \(-0.460616\pi\) | ||||
0.123412 | + | 0.992355i | \(0.460616\pi\) | |||||||
\(510\) | 50.0294 | 2.21534 | ||||||||
\(511\) | 21.0294 | 0.930286 | ||||||||
\(512\) | 33.9585 | 1.50077 | ||||||||
\(513\) | 37.9873 | 1.67718 | ||||||||
\(514\) | −65.6556 | −2.89594 | ||||||||
\(515\) | 24.5175 | 1.08037 | ||||||||
\(516\) | −0.682780 | −0.0300577 | ||||||||
\(517\) | 1.56895 | 0.0690022 | ||||||||
\(518\) | −20.9974 | −0.922574 | ||||||||
\(519\) | −6.19049 | −0.271733 | ||||||||
\(520\) | 43.3833 | 1.90249 | ||||||||
\(521\) | −13.3389 | −0.584389 | −0.292195 | − | 0.956359i | \(-0.594385\pi\) | ||||
−0.292195 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(522\) | −12.1639 | −0.532400 | ||||||||
\(523\) | 25.2134 | 1.10250 | 0.551251 | − | 0.834339i | \(-0.314150\pi\) | ||||
0.551251 | + | 0.834339i | \(0.314150\pi\) | |||||||
\(524\) | 18.2294 | 0.796356 | ||||||||
\(525\) | −2.71672 | −0.118567 | ||||||||
\(526\) | −51.0079 | −2.22405 | ||||||||
\(527\) | −0.284328 | −0.0123855 | ||||||||
\(528\) | 30.0703 | 1.30864 | ||||||||
\(529\) | −14.2098 | −0.617819 | ||||||||
\(530\) | 16.8642 | 0.732533 | ||||||||
\(531\) | −1.10187 | −0.0478170 | ||||||||
\(532\) | −60.7357 | −2.63323 | ||||||||
\(533\) | 9.78136 | 0.423678 | ||||||||
\(534\) | −7.63937 | −0.330588 | ||||||||
\(535\) | 9.43255 | 0.407805 | ||||||||
\(536\) | 37.7206 | 1.62928 | ||||||||
\(537\) | 32.7239 | 1.41214 | ||||||||
\(538\) | −34.8365 | −1.50191 | ||||||||
\(539\) | 10.2123 | 0.439877 | ||||||||
\(540\) | 44.4771 | 1.91399 | ||||||||
\(541\) | 5.94819 | 0.255733 | 0.127866 | − | 0.991791i | \(-0.459187\pi\) | ||||
0.127866 | + | 0.991791i | \(0.459187\pi\) | |||||||
\(542\) | 40.1754 | 1.72568 | ||||||||
\(543\) | −3.49416 | −0.149949 | ||||||||
\(544\) | 6.99340 | 0.299839 | ||||||||
\(545\) | 16.5759 | 0.710036 | ||||||||
\(546\) | 39.9804 | 1.71100 | ||||||||
\(547\) | 3.05965 | 0.130821 | 0.0654106 | − | 0.997858i | \(-0.479164\pi\) | ||||
0.0654106 | + | 0.997858i | \(0.479164\pi\) | |||||||
\(548\) | −35.8809 | −1.53275 | ||||||||
\(549\) | −1.70247 | −0.0726595 | ||||||||
\(550\) | −10.6899 | −0.455819 | ||||||||
\(551\) | −61.1982 | −2.60713 | ||||||||
\(552\) | −21.1688 | −0.901005 | ||||||||
\(553\) | 31.4262 | 1.33638 | ||||||||
\(554\) | 70.2922 | 2.98643 | ||||||||
\(555\) | 12.1646 | 0.516357 | ||||||||
\(556\) | −11.3551 | −0.481562 | ||||||||
\(557\) | −28.8557 | −1.22266 | −0.611329 | − | 0.791377i | \(-0.709365\pi\) | ||||
−0.611329 | + | 0.791377i | \(0.709365\pi\) | |||||||
\(558\) | −0.0602126 | −0.00254900 | ||||||||
\(559\) | −0.518688 | −0.0219381 | ||||||||
\(560\) | −15.6428 | −0.661029 | ||||||||
\(561\) | 58.0929 | 2.45268 | ||||||||
\(562\) | 37.9510 | 1.60086 | ||||||||
\(563\) | 17.2038 | 0.725055 | 0.362527 | − | 0.931973i | \(-0.381914\pi\) | ||||
0.362527 | + | 0.931973i | \(0.381914\pi\) | |||||||
\(564\) | 1.64133 | 0.0691123 | ||||||||
\(565\) | −9.13429 | −0.384282 | ||||||||
\(566\) | −62.7807 | −2.63887 | ||||||||
\(567\) | 16.0397 | 0.673603 | ||||||||
\(568\) | 16.2015 | 0.679801 | ||||||||
\(569\) | −44.1835 | −1.85227 | −0.926134 | − | 0.377195i | \(-0.876889\pi\) | ||||
−0.926134 | + | 0.377195i | \(0.876889\pi\) | |||||||
\(570\) | 53.3038 | 2.23265 | ||||||||
\(571\) | −40.4540 | −1.69295 | −0.846473 | − | 0.532431i | \(-0.821279\pi\) | ||||
−0.846473 | + | 0.532431i | \(0.821279\pi\) | |||||||
\(572\) | 103.846 | 4.34203 | ||||||||
\(573\) | −16.3563 | −0.683295 | ||||||||
\(574\) | −11.7824 | −0.491786 | ||||||||
\(575\) | 2.25263 | 0.0939413 | ||||||||
\(576\) | 5.19641 | 0.216517 | ||||||||
\(577\) | −25.5282 | −1.06275 | −0.531377 | − | 0.847136i | \(-0.678325\pi\) | ||||
−0.531377 | + | 0.847136i | \(0.678325\pi\) | |||||||
\(578\) | −58.4826 | −2.43256 | ||||||||
\(579\) | −25.3137 | −1.05200 | ||||||||
\(580\) | −71.6533 | −2.97524 | ||||||||
\(581\) | −22.1728 | −0.919883 | ||||||||
\(582\) | −21.6912 | −0.899129 | ||||||||
\(583\) | 19.5822 | 0.811013 | ||||||||
\(584\) | 41.9925 | 1.73766 | ||||||||
\(585\) | 5.31293 | 0.219663 | ||||||||
\(586\) | −21.5811 | −0.891507 | ||||||||
\(587\) | 35.8989 | 1.48171 | 0.740853 | − | 0.671667i | \(-0.234421\pi\) | ||||
0.740853 | + | 0.671667i | \(0.234421\pi\) | |||||||
\(588\) | 10.6835 | 0.440579 | ||||||||
\(589\) | −0.302937 | −0.0124823 | ||||||||
\(590\) | −9.83278 | −0.404809 | ||||||||
\(591\) | 17.0536 | 0.701493 | ||||||||
\(592\) | −12.5507 | −0.515832 | ||||||||
\(593\) | 42.7221 | 1.75439 | 0.877194 | − | 0.480137i | \(-0.159413\pi\) | ||||
0.877194 | + | 0.480137i | \(0.159413\pi\) | |||||||
\(594\) | 78.2381 | 3.21015 | ||||||||
\(595\) | −30.2203 | −1.23891 | ||||||||
\(596\) | 28.7270 | 1.17670 | ||||||||
\(597\) | 17.7165 | 0.725088 | ||||||||
\(598\) | −33.1507 | −1.35563 | ||||||||
\(599\) | 13.4305 | 0.548755 | 0.274378 | − | 0.961622i | \(-0.411528\pi\) | ||||
0.274378 | + | 0.961622i | \(0.411528\pi\) | |||||||
\(600\) | −5.42488 | −0.221470 | ||||||||
\(601\) | −2.26638 | −0.0924474 | −0.0462237 | − | 0.998931i | \(-0.514719\pi\) | ||||
−0.0462237 | + | 0.998931i | \(0.514719\pi\) | |||||||
\(602\) | 0.624797 | 0.0254648 | ||||||||
\(603\) | 4.61944 | 0.188118 | ||||||||
\(604\) | −0.104402 | −0.00424806 | ||||||||
\(605\) | 46.6225 | 1.89547 | ||||||||
\(606\) | −75.9485 | −3.08520 | ||||||||
\(607\) | 34.4150 | 1.39686 | 0.698430 | − | 0.715678i | \(-0.253882\pi\) | ||||
0.698430 | + | 0.715678i | \(0.253882\pi\) | |||||||
\(608\) | 7.45111 | 0.302182 | ||||||||
\(609\) | −32.0324 | −1.29802 | ||||||||
\(610\) | −15.1924 | −0.615122 | ||||||||
\(611\) | 1.24687 | 0.0504429 | ||||||||
\(612\) | −13.9401 | −0.563496 | ||||||||
\(613\) | −24.0650 | −0.971977 | −0.485989 | − | 0.873965i | \(-0.661540\pi\) | ||||
−0.485989 | + | 0.873965i | \(0.661540\pi\) | |||||||
\(614\) | 39.4780 | 1.59320 | ||||||||
\(615\) | 6.82594 | 0.275248 | ||||||||
\(616\) | −60.6811 | −2.44491 | ||||||||
\(617\) | 23.6360 | 0.951552 | 0.475776 | − | 0.879567i | \(-0.342167\pi\) | ||||
0.475776 | + | 0.879567i | \(0.342167\pi\) | |||||||
\(618\) | 45.1174 | 1.81489 | ||||||||
\(619\) | −17.1471 | −0.689202 | −0.344601 | − | 0.938749i | \(-0.611986\pi\) | ||||
−0.344601 | + | 0.938749i | \(0.611986\pi\) | |||||||
\(620\) | −0.354691 | −0.0142447 | ||||||||
\(621\) | −16.4868 | −0.661591 | ||||||||
\(622\) | −69.9000 | −2.80273 | ||||||||
\(623\) | 4.61457 | 0.184879 | ||||||||
\(624\) | 23.8974 | 0.956661 | ||||||||
\(625\) | −20.6238 | −0.824952 | ||||||||
\(626\) | −39.6574 | −1.58503 | ||||||||
\(627\) | 61.8950 | 2.47185 | ||||||||
\(628\) | −19.7013 | −0.786168 | ||||||||
\(629\) | −24.2468 | −0.966783 | ||||||||
\(630\) | −6.39981 | −0.254974 | ||||||||
\(631\) | −9.06466 | −0.360859 | −0.180429 | − | 0.983588i | \(-0.557749\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557749\pi\) | |||||||
\(632\) | 62.7533 | 2.49619 | ||||||||
\(633\) | −11.1394 | −0.442750 | ||||||||
\(634\) | −70.9885 | −2.81931 | ||||||||
\(635\) | −2.91685 | −0.115752 | ||||||||
\(636\) | 20.4856 | 0.812308 | ||||||||
\(637\) | 8.11591 | 0.321564 | ||||||||
\(638\) | −126.043 | −4.99008 | ||||||||
\(639\) | 1.98412 | 0.0784904 | ||||||||
\(640\) | 41.8794 | 1.65543 | ||||||||
\(641\) | 40.4480 | 1.59760 | 0.798801 | − | 0.601596i | \(-0.205468\pi\) | ||||
0.798801 | + | 0.601596i | \(0.205468\pi\) | |||||||
\(642\) | 17.3579 | 0.685062 | ||||||||
\(643\) | 7.64870 | 0.301635 | 0.150818 | − | 0.988562i | \(-0.451809\pi\) | ||||
0.150818 | + | 0.988562i | \(0.451809\pi\) | |||||||
\(644\) | 26.3597 | 1.03872 | ||||||||
\(645\) | −0.361967 | −0.0142524 | ||||||||
\(646\) | −106.247 | −4.18023 | ||||||||
\(647\) | 41.7733 | 1.64228 | 0.821139 | − | 0.570728i | \(-0.193339\pi\) | ||||
0.821139 | + | 0.570728i | \(0.193339\pi\) | |||||||
\(648\) | 32.0288 | 1.25821 | ||||||||
\(649\) | −11.4176 | −0.448179 | ||||||||
\(650\) | −8.49543 | −0.333218 | ||||||||
\(651\) | −0.158564 | −0.00621460 | ||||||||
\(652\) | −45.8821 | −1.79688 | ||||||||
\(653\) | 18.7320 | 0.733039 | 0.366520 | − | 0.930410i | \(-0.380549\pi\) | ||||
0.366520 | + | 0.930410i | \(0.380549\pi\) | |||||||
\(654\) | 30.5033 | 1.19277 | ||||||||
\(655\) | 9.66409 | 0.377607 | ||||||||
\(656\) | −7.04264 | −0.274969 | ||||||||
\(657\) | 5.14260 | 0.200632 | ||||||||
\(658\) | −1.50194 | −0.0585518 | ||||||||
\(659\) | 38.2256 | 1.48906 | 0.744529 | − | 0.667590i | \(-0.232674\pi\) | ||||
0.744529 | + | 0.667590i | \(0.232674\pi\) | |||||||
\(660\) | 72.4692 | 2.82086 | ||||||||
\(661\) | −13.4050 | −0.521393 | −0.260697 | − | 0.965421i | \(-0.583952\pi\) | ||||
−0.260697 | + | 0.965421i | \(0.583952\pi\) | |||||||
\(662\) | −28.1225 | −1.09301 | ||||||||
\(663\) | 46.1674 | 1.79299 | ||||||||
\(664\) | −44.2757 | −1.71823 | ||||||||
\(665\) | −32.1982 | −1.24859 | ||||||||
\(666\) | −5.13478 | −0.198969 | ||||||||
\(667\) | 26.5604 | 1.02842 | ||||||||
\(668\) | 71.9221 | 2.78275 | ||||||||
\(669\) | −22.8809 | −0.884628 | ||||||||
\(670\) | 41.2227 | 1.59257 | ||||||||
\(671\) | −17.6410 | −0.681023 | ||||||||
\(672\) | 3.90007 | 0.150449 | ||||||||
\(673\) | −8.36526 | −0.322457 | −0.161229 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161229 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(674\) | −0.341089 | −0.0131383 | ||||||||
\(675\) | −4.22502 | −0.162621 | ||||||||
\(676\) | 32.0332 | 1.23204 | ||||||||
\(677\) | −4.25412 | −0.163499 | −0.0817496 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817496 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(678\) | −16.8091 | −0.645548 | ||||||||
\(679\) | 13.1026 | 0.502831 | ||||||||
\(680\) | −60.3453 | −2.31414 | ||||||||
\(681\) | −4.07326 | −0.156088 | ||||||||
\(682\) | −0.623924 | −0.0238913 | ||||||||
\(683\) | 36.0456 | 1.37925 | 0.689624 | − | 0.724168i | \(-0.257776\pi\) | ||||
0.689624 | + | 0.724168i | \(0.257776\pi\) | |||||||
\(684\) | −14.8525 | −0.567900 | ||||||||
\(685\) | −19.0218 | −0.726784 | ||||||||
\(686\) | −48.6430 | −1.85720 | ||||||||
\(687\) | 43.1660 | 1.64689 | ||||||||
\(688\) | 0.373458 | 0.0142380 | ||||||||
\(689\) | 15.5623 | 0.592877 | ||||||||
\(690\) | −23.1342 | −0.880705 | ||||||||
\(691\) | 51.1452 | 1.94565 | 0.972827 | − | 0.231532i | \(-0.0743738\pi\) | ||||
0.972827 | + | 0.231532i | \(0.0743738\pi\) | |||||||
\(692\) | 15.3927 | 0.585141 | ||||||||
\(693\) | −7.43129 | −0.282291 | ||||||||
\(694\) | −47.4599 | −1.80155 | ||||||||
\(695\) | −6.01974 | −0.228342 | ||||||||
\(696\) | −63.9639 | −2.42454 | ||||||||
\(697\) | −13.6057 | −0.515352 | ||||||||
\(698\) | −23.6666 | −0.895796 | ||||||||
\(699\) | −6.81582 | −0.257798 | ||||||||
\(700\) | 6.75513 | 0.255320 | ||||||||
\(701\) | 24.3917 | 0.921262 | 0.460631 | − | 0.887592i | \(-0.347623\pi\) | ||||
0.460631 | + | 0.887592i | \(0.347623\pi\) | |||||||
\(702\) | 62.1770 | 2.34672 | ||||||||
\(703\) | −25.8337 | −0.974337 | ||||||||
\(704\) | 53.8453 | 2.02937 | ||||||||
\(705\) | 0.870128 | 0.0327709 | ||||||||
\(706\) | −18.5863 | −0.699504 | ||||||||
\(707\) | 45.8767 | 1.72537 | ||||||||
\(708\) | −11.9443 | −0.448894 | ||||||||
\(709\) | −33.6884 | −1.26519 | −0.632597 | − | 0.774481i | \(-0.718011\pi\) | ||||
−0.632597 | + | 0.774481i | \(0.718011\pi\) | |||||||
\(710\) | 17.7057 | 0.664485 | ||||||||
\(711\) | 7.68507 | 0.288213 | ||||||||
\(712\) | 9.21459 | 0.345331 | ||||||||
\(713\) | 0.131477 | 0.00492384 | ||||||||
\(714\) | −55.6119 | −2.08122 | ||||||||
\(715\) | 55.0527 | 2.05885 | ||||||||
\(716\) | −81.3679 | −3.04086 | ||||||||
\(717\) | 21.8107 | 0.814536 | ||||||||
\(718\) | 70.1818 | 2.61916 | ||||||||
\(719\) | 48.9834 | 1.82677 | 0.913385 | − | 0.407096i | \(-0.133459\pi\) | ||||
0.913385 | + | 0.407096i | \(0.133459\pi\) | |||||||
\(720\) | −3.82534 | −0.142562 | ||||||||
\(721\) | −27.2532 | −1.01496 | ||||||||
\(722\) | −67.1116 | −2.49763 | ||||||||
\(723\) | 28.3453 | 1.05417 | ||||||||
\(724\) | 8.68822 | 0.322895 | ||||||||
\(725\) | 6.80657 | 0.252790 | ||||||||
\(726\) | 85.7954 | 3.18416 | ||||||||
\(727\) | −3.58508 | −0.132963 | −0.0664816 | − | 0.997788i | \(-0.521177\pi\) | ||||
−0.0664816 | + | 0.997788i | \(0.521177\pi\) | |||||||
\(728\) | −48.2242 | −1.78731 | ||||||||
\(729\) | 29.9824 | 1.11046 | ||||||||
\(730\) | 45.8913 | 1.69851 | ||||||||
\(731\) | 0.721484 | 0.0266850 | ||||||||
\(732\) | −18.4548 | −0.682110 | ||||||||
\(733\) | −15.5288 | −0.573569 | −0.286784 | − | 0.957995i | \(-0.592586\pi\) | ||||
−0.286784 | + | 0.957995i | \(0.592586\pi\) | |||||||
\(734\) | 65.3247 | 2.41118 | ||||||||
\(735\) | 5.66370 | 0.208909 | ||||||||
\(736\) | −3.23383 | −0.119201 | ||||||||
\(737\) | 47.8667 | 1.76319 | ||||||||
\(738\) | −2.88130 | −0.106062 | ||||||||
\(739\) | 25.0152 | 0.920198 | 0.460099 | − | 0.887868i | \(-0.347814\pi\) | ||||
0.460099 | + | 0.887868i | \(0.347814\pi\) | |||||||
\(740\) | −30.2472 | −1.11191 | ||||||||
\(741\) | 49.1890 | 1.80700 | ||||||||
\(742\) | −18.7459 | −0.688185 | ||||||||
\(743\) | −22.4347 | −0.823051 | −0.411526 | − | 0.911398i | \(-0.635004\pi\) | ||||
−0.411526 | + | 0.911398i | \(0.635004\pi\) | |||||||
\(744\) | −0.316627 | −0.0116081 | ||||||||
\(745\) | 15.2292 | 0.557956 | ||||||||
\(746\) | −5.16392 | −0.189065 | ||||||||
\(747\) | −5.42221 | −0.198388 | ||||||||
\(748\) | −144.448 | −5.28154 | ||||||||
\(749\) | −10.4851 | −0.383116 | ||||||||
\(750\) | −44.9431 | −1.64109 | ||||||||
\(751\) | 1.74911 | 0.0638259 | 0.0319130 | − | 0.999491i | \(-0.489840\pi\) | ||||
0.0319130 | + | 0.999491i | \(0.489840\pi\) | |||||||
\(752\) | −0.897752 | −0.0327376 | ||||||||
\(753\) | −21.2163 | −0.773164 | ||||||||
\(754\) | −100.168 | −3.64791 | ||||||||
\(755\) | −0.0553473 | −0.00201430 | ||||||||
\(756\) | −49.4400 | −1.79811 | ||||||||
\(757\) | −15.7128 | −0.571090 | −0.285545 | − | 0.958365i | \(-0.592175\pi\) | ||||
−0.285545 | + | 0.958365i | \(0.592175\pi\) | |||||||
\(758\) | −31.0961 | −1.12946 | ||||||||
\(759\) | −26.8629 | −0.975060 | ||||||||
\(760\) | −64.2949 | −2.33222 | ||||||||
\(761\) | −25.3025 | −0.917216 | −0.458608 | − | 0.888639i | \(-0.651652\pi\) | ||||
−0.458608 | + | 0.888639i | \(0.651652\pi\) | |||||||
\(762\) | −5.36764 | −0.194449 | ||||||||
\(763\) | −18.4256 | −0.667050 | ||||||||
\(764\) | 40.6699 | 1.47139 | ||||||||
\(765\) | −7.39018 | −0.267192 | ||||||||
\(766\) | 2.06302 | 0.0745398 | ||||||||
\(767\) | −9.07373 | −0.327633 | ||||||||
\(768\) | 48.0630 | 1.73433 | ||||||||
\(769\) | −50.2908 | −1.81353 | −0.906766 | − | 0.421634i | \(-0.861457\pi\) | ||||
−0.906766 | + | 0.421634i | \(0.861457\pi\) | |||||||
\(770\) | −66.3149 | −2.38982 | ||||||||
\(771\) | −42.2809 | −1.52271 | ||||||||
\(772\) | 62.9426 | 2.26535 | ||||||||
\(773\) | −2.41580 | −0.0868903 | −0.0434451 | − | 0.999056i | \(-0.513833\pi\) | ||||
−0.0434451 | + | 0.999056i | \(0.513833\pi\) | |||||||
\(774\) | 0.152790 | 0.00549192 | ||||||||
\(775\) | 0.0336932 | 0.00121030 | ||||||||
\(776\) | 26.1639 | 0.939228 | ||||||||
\(777\) | −13.5219 | −0.485096 | ||||||||
\(778\) | −93.2922 | −3.34469 | ||||||||
\(779\) | −14.4962 | −0.519379 | ||||||||
\(780\) | 57.5924 | 2.06214 | ||||||||
\(781\) | 20.5595 | 0.735675 | ||||||||
\(782\) | 46.1119 | 1.64896 | ||||||||
\(783\) | −49.8165 | −1.78030 | ||||||||
\(784\) | −5.84350 | −0.208697 | ||||||||
\(785\) | −10.4444 | −0.372776 | ||||||||
\(786\) | 17.7840 | 0.634335 | ||||||||
\(787\) | −18.1082 | −0.645489 | −0.322744 | − | 0.946486i | \(-0.604605\pi\) | ||||
−0.322744 | + | 0.946486i | \(0.604605\pi\) | |||||||
\(788\) | −42.4039 | −1.51058 | ||||||||
\(789\) | −32.8481 | −1.16942 | ||||||||
\(790\) | 68.5796 | 2.43995 | ||||||||
\(791\) | 10.1535 | 0.361018 | ||||||||
\(792\) | −14.8391 | −0.527286 | ||||||||
\(793\) | −14.0196 | −0.497850 | ||||||||
\(794\) | −33.8950 | −1.20289 | ||||||||
\(795\) | 10.8602 | 0.385171 | ||||||||
\(796\) | −44.0520 | −1.56138 | ||||||||
\(797\) | −34.3957 | −1.21836 | −0.609178 | − | 0.793033i | \(-0.708501\pi\) | ||||
−0.609178 | + | 0.793033i | \(0.708501\pi\) | |||||||
\(798\) | −59.2517 | −2.09749 | ||||||||
\(799\) | −1.73437 | −0.0613575 | ||||||||
\(800\) | −0.828726 | −0.0292999 | ||||||||
\(801\) | 1.12846 | 0.0398723 | ||||||||
\(802\) | 88.6264 | 3.12951 | ||||||||
\(803\) | 53.2878 | 1.88048 | ||||||||
\(804\) | 50.0750 | 1.76601 | ||||||||
\(805\) | 13.9742 | 0.492528 | ||||||||
\(806\) | −0.495843 | −0.0174653 | ||||||||
\(807\) | −22.4340 | −0.789715 | ||||||||
\(808\) | 91.6088 | 3.22279 | ||||||||
\(809\) | 47.5598 | 1.67211 | 0.836056 | − | 0.548644i | \(-0.184856\pi\) | ||||
0.836056 | + | 0.548644i | \(0.184856\pi\) | |||||||
\(810\) | 35.0024 | 1.22986 | ||||||||
\(811\) | 31.9953 | 1.12351 | 0.561754 | − | 0.827305i | \(-0.310127\pi\) | ||||
0.561754 | + | 0.827305i | \(0.310127\pi\) | |||||||
\(812\) | 79.6486 | 2.79512 | ||||||||
\(813\) | 25.8721 | 0.907376 | ||||||||
\(814\) | −53.2067 | −1.86489 | ||||||||
\(815\) | −24.3238 | −0.852026 | ||||||||
\(816\) | −33.2408 | −1.16366 | ||||||||
\(817\) | 0.768705 | 0.0268936 | ||||||||
\(818\) | 31.2662 | 1.09320 | ||||||||
\(819\) | −5.90577 | −0.206364 | ||||||||
\(820\) | −16.9727 | −0.592712 | ||||||||
\(821\) | −6.66881 | −0.232743 | −0.116372 | − | 0.993206i | \(-0.537126\pi\) | ||||
−0.116372 | + | 0.993206i | \(0.537126\pi\) | |||||||
\(822\) | −35.0042 | −1.22091 | ||||||||
\(823\) | 34.1861 | 1.19165 | 0.595827 | − | 0.803113i | \(-0.296824\pi\) | ||||
0.595827 | + | 0.803113i | \(0.296824\pi\) | |||||||
\(824\) | −54.4205 | −1.89583 | ||||||||
\(825\) | −6.88408 | −0.239673 | ||||||||
\(826\) | 10.9300 | 0.380302 | ||||||||
\(827\) | −29.0965 | −1.01178 | −0.505892 | − | 0.862597i | \(-0.668837\pi\) | ||||
−0.505892 | + | 0.862597i | \(0.668837\pi\) | |||||||
\(828\) | 6.44609 | 0.224017 | ||||||||
\(829\) | 39.7742 | 1.38141 | 0.690707 | − | 0.723135i | \(-0.257300\pi\) | ||||
0.690707 | + | 0.723135i | \(0.257300\pi\) | |||||||
\(830\) | −48.3864 | −1.67952 | ||||||||
\(831\) | 45.2668 | 1.57029 | ||||||||
\(832\) | 42.7917 | 1.48354 | ||||||||
\(833\) | −11.2891 | −0.391143 | ||||||||
\(834\) | −11.0776 | −0.383586 | ||||||||
\(835\) | 38.1286 | 1.31949 | ||||||||
\(836\) | −153.902 | −5.32281 | ||||||||
\(837\) | −0.246596 | −0.00852362 | ||||||||
\(838\) | 30.1075 | 1.04005 | ||||||||
\(839\) | −36.0138 | −1.24333 | −0.621667 | − | 0.783281i | \(-0.713544\pi\) | ||||
−0.621667 | + | 0.783281i | \(0.713544\pi\) | |||||||
\(840\) | −33.6533 | −1.16115 | ||||||||
\(841\) | 51.2552 | 1.76742 | ||||||||
\(842\) | 0.769798 | 0.0265290 | ||||||||
\(843\) | 24.4397 | 0.841746 | ||||||||
\(844\) | 27.6980 | 0.953405 | ||||||||
\(845\) | 16.9820 | 0.584197 | ||||||||
\(846\) | −0.367290 | −0.0126277 | ||||||||
\(847\) | −51.8248 | −1.78072 | ||||||||
\(848\) | −11.2050 | −0.384780 | ||||||||
\(849\) | −40.4295 | −1.38754 | ||||||||
\(850\) | 11.8170 | 0.405319 | ||||||||
\(851\) | 11.2120 | 0.384343 | ||||||||
\(852\) | 21.5079 | 0.736849 | ||||||||
\(853\) | 48.1008 | 1.64694 | 0.823469 | − | 0.567361i | \(-0.192036\pi\) | ||||
0.823469 | + | 0.567361i | \(0.192036\pi\) | |||||||
\(854\) | 16.8876 | 0.577882 | ||||||||
\(855\) | −7.87386 | −0.269280 | ||||||||
\(856\) | −20.9371 | −0.715614 | ||||||||
\(857\) | 12.0261 | 0.410805 | 0.205402 | − | 0.978678i | \(-0.434150\pi\) | ||||
0.205402 | + | 0.978678i | \(0.434150\pi\) | |||||||
\(858\) | 101.309 | 3.45863 | ||||||||
\(859\) | 8.89951 | 0.303647 | 0.151824 | − | 0.988408i | \(-0.451485\pi\) | ||||
0.151824 | + | 0.988408i | \(0.451485\pi\) | |||||||
\(860\) | 0.900030 | 0.0306908 | ||||||||
\(861\) | −7.58760 | −0.258585 | ||||||||
\(862\) | −91.8422 | −3.12816 | ||||||||
\(863\) | 7.65175 | 0.260469 | 0.130234 | − | 0.991483i | \(-0.458427\pi\) | ||||
0.130234 | + | 0.991483i | \(0.458427\pi\) | |||||||
\(864\) | 6.06535 | 0.206347 | ||||||||
\(865\) | 8.16022 | 0.277456 | ||||||||
\(866\) | 79.6062 | 2.70513 | ||||||||
\(867\) | −37.6616 | −1.27906 | ||||||||
\(868\) | 0.394269 | 0.0133823 | ||||||||
\(869\) | 79.6328 | 2.70136 | ||||||||
\(870\) | −69.9025 | −2.36992 | ||||||||
\(871\) | 38.0405 | 1.28895 | ||||||||
\(872\) | −36.7930 | −1.24597 | ||||||||
\(873\) | 3.20415 | 0.108444 | ||||||||
\(874\) | 49.1299 | 1.66184 | ||||||||
\(875\) | 27.1479 | 0.917767 | ||||||||
\(876\) | 55.7461 | 1.88348 | ||||||||
\(877\) | 0.0219545 | 0.000741352 0 | 0.000370676 | − | 1.00000i | \(-0.499882\pi\) | ||||
0.000370676 | 1.00000i | \(0.499882\pi\) | ||||||||
\(878\) | 91.0495 | 3.07277 | ||||||||
\(879\) | −13.8978 | −0.468761 | ||||||||
\(880\) | −39.6383 | −1.33621 | ||||||||
\(881\) | 31.8051 | 1.07154 | 0.535771 | − | 0.844363i | \(-0.320021\pi\) | ||||
0.535771 | + | 0.844363i | \(0.320021\pi\) | |||||||
\(882\) | −2.39070 | −0.0804992 | ||||||||
\(883\) | −24.8895 | −0.837599 | −0.418800 | − | 0.908079i | \(-0.637549\pi\) | ||||
−0.418800 | + | 0.908079i | \(0.637549\pi\) | |||||||
\(884\) | −114.795 | −3.86098 | ||||||||
\(885\) | −6.33211 | −0.212852 | ||||||||
\(886\) | 6.17364 | 0.207407 | ||||||||
\(887\) | 9.02867 | 0.303153 | 0.151577 | − | 0.988446i | \(-0.451565\pi\) | ||||
0.151577 | + | 0.988446i | \(0.451565\pi\) | |||||||
\(888\) | −27.0012 | −0.906101 | ||||||||
\(889\) | 3.24233 | 0.108744 | ||||||||
\(890\) | 10.0701 | 0.337551 | ||||||||
\(891\) | 40.6439 | 1.36162 | ||||||||
\(892\) | 56.8935 | 1.90493 | ||||||||
\(893\) | −1.84788 | −0.0618370 | ||||||||
\(894\) | 28.0251 | 0.937299 | ||||||||
\(895\) | −43.1361 | −1.44188 | ||||||||
\(896\) | −46.5524 | −1.55521 | ||||||||
\(897\) | −21.3484 | −0.712801 | ||||||||
\(898\) | −74.4830 | −2.48553 | ||||||||
\(899\) | 0.397271 | 0.0132497 | ||||||||
\(900\) | 1.65192 | 0.0550641 | ||||||||
\(901\) | −21.6469 | −0.721162 | ||||||||
\(902\) | −29.8561 | −0.994098 | ||||||||
\(903\) | 0.402356 | 0.0133896 | ||||||||
\(904\) | 20.2750 | 0.674338 | ||||||||
\(905\) | 4.60595 | 0.153107 | ||||||||
\(906\) | −0.101851 | −0.00338377 | ||||||||
\(907\) | 1.00343 | 0.0333185 | 0.0166592 | − | 0.999861i | \(-0.494697\pi\) | ||||
0.0166592 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(908\) | 10.1282 | 0.336115 | ||||||||
\(909\) | 11.2188 | 0.372106 | ||||||||
\(910\) | −52.7015 | −1.74704 | ||||||||
\(911\) | 3.10353 | 0.102825 | 0.0514123 | − | 0.998678i | \(-0.483628\pi\) | ||||
0.0514123 | + | 0.998678i | \(0.483628\pi\) | |||||||
\(912\) | −35.4164 | −1.17275 | ||||||||
\(913\) | −56.1851 | −1.85945 | ||||||||
\(914\) | 12.3653 | 0.409009 | ||||||||
\(915\) | −9.78359 | −0.323435 | ||||||||
\(916\) | −107.332 | −3.54636 | ||||||||
\(917\) | −10.7424 | −0.354747 | ||||||||
\(918\) | −86.4870 | −2.85450 | ||||||||
\(919\) | −33.0360 | −1.08976 | −0.544878 | − | 0.838515i | \(-0.683424\pi\) | ||||
−0.544878 | + | 0.838515i | \(0.683424\pi\) | |||||||
\(920\) | 27.9044 | 0.919982 | ||||||||
\(921\) | 25.4230 | 0.837718 | ||||||||
\(922\) | −43.9362 | −1.44696 | ||||||||
\(923\) | 16.3389 | 0.537802 | ||||||||
\(924\) | −80.5556 | −2.65008 | ||||||||
\(925\) | 2.87327 | 0.0944726 | ||||||||
\(926\) | −9.30653 | −0.305832 | ||||||||
\(927\) | −6.66459 | −0.218894 | ||||||||
\(928\) | −9.77137 | −0.320761 | ||||||||
\(929\) | 25.3858 | 0.832880 | 0.416440 | − | 0.909163i | \(-0.363278\pi\) | ||||
0.416440 | + | 0.909163i | \(0.363278\pi\) | |||||||
\(930\) | −0.346024 | −0.0113466 | ||||||||
\(931\) | −12.0279 | −0.394200 | ||||||||
\(932\) | 16.9475 | 0.555135 | ||||||||
\(933\) | −45.0142 | −1.47370 | ||||||||
\(934\) | −86.0777 | −2.81655 | ||||||||
\(935\) | −76.5772 | −2.50434 | ||||||||
\(936\) | −11.7929 | −0.385463 | ||||||||
\(937\) | 32.1424 | 1.05005 | 0.525024 | − | 0.851088i | \(-0.324057\pi\) | ||||
0.525024 | + | 0.851088i | \(0.324057\pi\) | |||||||
\(938\) | −45.8225 | −1.49616 | ||||||||
\(939\) | −25.5385 | −0.833419 | ||||||||
\(940\) | −2.16357 | −0.0705680 | ||||||||
\(941\) | −13.9674 | −0.455325 | −0.227662 | − | 0.973740i | \(-0.573108\pi\) | ||||
−0.227662 | + | 0.973740i | \(0.573108\pi\) | |||||||
\(942\) | −19.2199 | −0.626219 | ||||||||
\(943\) | 6.29143 | 0.204877 | ||||||||
\(944\) | 6.53314 | 0.212635 | ||||||||
\(945\) | −26.2100 | −0.852610 | ||||||||
\(946\) | 1.58321 | 0.0514746 | ||||||||
\(947\) | 48.8909 | 1.58874 | 0.794370 | − | 0.607434i | \(-0.207801\pi\) | ||||
0.794370 | + | 0.607434i | \(0.207801\pi\) | |||||||
\(948\) | 83.3065 | 2.70567 | ||||||||
\(949\) | 42.3486 | 1.37469 | ||||||||
\(950\) | 12.5904 | 0.408486 | ||||||||
\(951\) | −45.7151 | −1.48241 | ||||||||
\(952\) | 67.0789 | 2.17404 | ||||||||
\(953\) | 52.2428 | 1.69231 | 0.846155 | − | 0.532937i | \(-0.178912\pi\) | ||||
0.846155 | + | 0.532937i | \(0.178912\pi\) | |||||||
\(954\) | −4.58419 | −0.148419 | ||||||||
\(955\) | 21.5606 | 0.697686 | ||||||||
\(956\) | −54.2323 | −1.75400 | ||||||||
\(957\) | −81.1690 | −2.62382 | ||||||||
\(958\) | 58.8788 | 1.90229 | ||||||||
\(959\) | 21.1443 | 0.682785 | ||||||||
\(960\) | 29.8623 | 0.963800 | ||||||||
\(961\) | −30.9980 | −0.999937 | ||||||||
\(962\) | −42.2842 | −1.36330 | ||||||||
\(963\) | −2.56405 | −0.0826255 | ||||||||
\(964\) | −70.4805 | −2.27002 | ||||||||
\(965\) | 33.3682 | 1.07416 | ||||||||
\(966\) | 25.7156 | 0.827387 | ||||||||
\(967\) | −29.1713 | −0.938087 | −0.469043 | − | 0.883175i | \(-0.655401\pi\) | ||||
−0.469043 | + | 0.883175i | \(0.655401\pi\) | |||||||
\(968\) | −103.486 | −3.32617 | ||||||||
\(969\) | −68.4209 | −2.19800 | ||||||||
\(970\) | 28.5930 | 0.918066 | ||||||||
\(971\) | −20.8016 | −0.667557 | −0.333778 | − | 0.942652i | \(-0.608324\pi\) | ||||
−0.333778 | + | 0.942652i | \(0.608324\pi\) | |||||||
\(972\) | −22.2793 | −0.714610 | ||||||||
\(973\) | 6.69144 | 0.214518 | ||||||||
\(974\) | −36.2926 | −1.16289 | ||||||||
\(975\) | −5.47089 | −0.175209 | ||||||||
\(976\) | 10.0942 | 0.323107 | ||||||||
\(977\) | 33.6083 | 1.07523 | 0.537613 | − | 0.843192i | \(-0.319326\pi\) | ||||
0.537613 | + | 0.843192i | \(0.319326\pi\) | |||||||
\(978\) | −44.7610 | −1.43130 | ||||||||
\(979\) | 11.6932 | 0.373715 | ||||||||
\(980\) | −14.0828 | −0.449858 | ||||||||
\(981\) | −4.50585 | −0.143861 | ||||||||
\(982\) | 69.4950 | 2.21768 | ||||||||
\(983\) | −24.6901 | −0.787492 | −0.393746 | − | 0.919219i | \(-0.628821\pi\) | ||||
−0.393746 | + | 0.919219i | \(0.628821\pi\) | |||||||
\(984\) | −15.1513 | −0.483005 | ||||||||
\(985\) | −22.4799 | −0.716268 | ||||||||
\(986\) | 139.332 | 4.43723 | ||||||||
\(987\) | −0.967220 | −0.0307870 | ||||||||
\(988\) | −122.308 | −3.89115 | ||||||||
\(989\) | −0.333623 | −0.0106086 | ||||||||
\(990\) | −16.2169 | −0.515406 | ||||||||
\(991\) | 46.5567 | 1.47892 | 0.739461 | − | 0.673199i | \(-0.235080\pi\) | ||||
0.739461 | + | 0.673199i | \(0.235080\pi\) | |||||||
\(992\) | −0.0483693 | −0.00153573 | ||||||||
\(993\) | −18.1104 | −0.574715 | ||||||||
\(994\) | −19.6814 | −0.624257 | ||||||||
\(995\) | −23.3536 | −0.740359 | ||||||||
\(996\) | −58.7771 | −1.86242 | ||||||||
\(997\) | −55.2891 | −1.75102 | −0.875511 | − | 0.483198i | \(-0.839475\pi\) | ||||
−0.875511 | + | 0.483198i | \(0.839475\pi\) | |||||||
\(998\) | −75.6937 | −2.39604 | ||||||||
\(999\) | −21.0291 | −0.665333 |
(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 | 5077.2.a.c.1.19 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.19 | ✓ | 216 | 1.1 | even | 1 | trivial |