Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63657 | −1.86434 | −0.932170 | − | 0.362021i | \(-0.882087\pi\) | ||||
−0.932170 | + | 0.362021i | \(0.882087\pi\) | |||||||
\(3\) | 1.64340 | 0.948818 | 0.474409 | − | 0.880305i | \(-0.342662\pi\) | ||||
0.474409 | + | 0.880305i | \(0.342662\pi\) | |||||||
\(4\) | 4.95152 | 2.47576 | ||||||||
\(5\) | −0.607936 | −0.271877 | −0.135939 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135939 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(6\) | −4.33295 | −1.76892 | ||||||||
\(7\) | −1.90677 | −0.720693 | −0.360347 | − | 0.932819i | \(-0.617342\pi\) | ||||
−0.360347 | + | 0.932819i | \(0.617342\pi\) | |||||||
\(8\) | −7.78191 | −2.75132 | ||||||||
\(9\) | −0.299236 | −0.0997453 | ||||||||
\(10\) | 1.60287 | 0.506871 | ||||||||
\(11\) | −1.70915 | −0.515328 | −0.257664 | − | 0.966235i | \(-0.582953\pi\) | ||||
−0.257664 | + | 0.966235i | \(0.582953\pi\) | |||||||
\(12\) | 8.13733 | 2.34905 | ||||||||
\(13\) | 5.00785 | 1.38893 | 0.694464 | − | 0.719527i | \(-0.255641\pi\) | ||||
0.694464 | + | 0.719527i | \(0.255641\pi\) | |||||||
\(14\) | 5.02735 | 1.34362 | ||||||||
\(15\) | −0.999082 | −0.257962 | ||||||||
\(16\) | 10.6145 | 2.65363 | ||||||||
\(17\) | 4.32864 | 1.04985 | 0.524925 | − | 0.851149i | \(-0.324093\pi\) | ||||
0.524925 | + | 0.851149i | \(0.324093\pi\) | |||||||
\(18\) | 0.788958 | 0.185959 | ||||||||
\(19\) | 2.36317 | 0.542149 | 0.271075 | − | 0.962558i | \(-0.412621\pi\) | ||||
0.271075 | + | 0.962558i | \(0.412621\pi\) | |||||||
\(20\) | −3.01021 | −0.673103 | ||||||||
\(21\) | −3.13359 | −0.683806 | ||||||||
\(22\) | 4.50630 | 0.960747 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −12.7888 | −2.61050 | ||||||||
\(25\) | −4.63041 | −0.926083 | ||||||||
\(26\) | −13.2036 | −2.58943 | ||||||||
\(27\) | −5.42196 | −1.04346 | ||||||||
\(28\) | −9.44144 | −1.78426 | ||||||||
\(29\) | 9.97868 | 1.85300 | 0.926498 | − | 0.376301i | \(-0.122804\pi\) | ||||
0.926498 | + | 0.376301i | \(0.122804\pi\) | |||||||
\(30\) | 2.63415 | 0.480928 | ||||||||
\(31\) | 2.03651 | 0.365768 | 0.182884 | − | 0.983135i | \(-0.441457\pi\) | ||||
0.182884 | + | 0.983135i | \(0.441457\pi\) | |||||||
\(32\) | −12.4222 | −2.19595 | ||||||||
\(33\) | −2.80882 | −0.488952 | ||||||||
\(34\) | −11.4128 | −1.95728 | ||||||||
\(35\) | 1.15920 | 0.195940 | ||||||||
\(36\) | −1.48167 | −0.246946 | ||||||||
\(37\) | 6.33509 | 1.04148 | 0.520741 | − | 0.853715i | \(-0.325656\pi\) | ||||
0.520741 | + | 0.853715i | \(0.325656\pi\) | |||||||
\(38\) | −6.23068 | −1.01075 | ||||||||
\(39\) | 8.22991 | 1.31784 | ||||||||
\(40\) | 4.73090 | 0.748021 | ||||||||
\(41\) | −2.18062 | −0.340556 | −0.170278 | − | 0.985396i | \(-0.554467\pi\) | ||||
−0.170278 | + | 0.985396i | \(0.554467\pi\) | |||||||
\(42\) | 8.26195 | 1.27485 | ||||||||
\(43\) | 4.94696 | 0.754404 | 0.377202 | − | 0.926131i | \(-0.376886\pi\) | ||||
0.377202 | + | 0.926131i | \(0.376886\pi\) | |||||||
\(44\) | −8.46290 | −1.27583 | ||||||||
\(45\) | 0.181916 | 0.0271185 | ||||||||
\(46\) | −2.63657 | −0.388742 | ||||||||
\(47\) | −10.8495 | −1.58256 | −0.791282 | − | 0.611452i | \(-0.790586\pi\) | ||||
−0.791282 | + | 0.611452i | \(0.790586\pi\) | |||||||
\(48\) | 17.4439 | 2.51781 | ||||||||
\(49\) | −3.36421 | −0.480601 | ||||||||
\(50\) | 12.2084 | 1.72653 | ||||||||
\(51\) | 7.11369 | 0.996116 | ||||||||
\(52\) | 24.7965 | 3.43866 | ||||||||
\(53\) | −10.8360 | −1.48844 | −0.744218 | − | 0.667937i | \(-0.767178\pi\) | ||||
−0.744218 | + | 0.667937i | \(0.767178\pi\) | |||||||
\(54\) | 14.2954 | 1.94536 | ||||||||
\(55\) | 1.03905 | 0.140106 | ||||||||
\(56\) | 14.8384 | 1.98286 | ||||||||
\(57\) | 3.88364 | 0.514401 | ||||||||
\(58\) | −26.3095 | −3.45461 | ||||||||
\(59\) | −3.53380 | −0.460061 | −0.230031 | − | 0.973183i | \(-0.573883\pi\) | ||||
−0.230031 | + | 0.973183i | \(0.573883\pi\) | |||||||
\(60\) | −4.94698 | −0.638652 | ||||||||
\(61\) | 5.69234 | 0.728830 | 0.364415 | − | 0.931237i | \(-0.381269\pi\) | ||||
0.364415 | + | 0.931237i | \(0.381269\pi\) | |||||||
\(62\) | −5.36940 | −0.681915 | ||||||||
\(63\) | 0.570576 | 0.0718858 | ||||||||
\(64\) | 11.5230 | 1.44037 | ||||||||
\(65\) | −3.04445 | −0.377618 | ||||||||
\(66\) | 7.40566 | 0.911573 | ||||||||
\(67\) | 10.5950 | 1.29439 | 0.647194 | − | 0.762325i | \(-0.275942\pi\) | ||||
0.647194 | + | 0.762325i | \(0.275942\pi\) | |||||||
\(68\) | 21.4334 | 2.59918 | ||||||||
\(69\) | 1.64340 | 0.197842 | ||||||||
\(70\) | −3.05631 | −0.365299 | ||||||||
\(71\) | 9.59204 | 1.13837 | 0.569183 | − | 0.822211i | \(-0.307260\pi\) | ||||
0.569183 | + | 0.822211i | \(0.307260\pi\) | |||||||
\(72\) | 2.32863 | 0.274431 | ||||||||
\(73\) | 14.6035 | 1.70921 | 0.854606 | − | 0.519277i | \(-0.173799\pi\) | ||||
0.854606 | + | 0.519277i | \(0.173799\pi\) | |||||||
\(74\) | −16.7029 | −1.94168 | ||||||||
\(75\) | −7.60962 | −0.878684 | ||||||||
\(76\) | 11.7013 | 1.34223 | ||||||||
\(77\) | 3.25896 | 0.371394 | ||||||||
\(78\) | −21.6988 | −2.45690 | ||||||||
\(79\) | −13.0776 | −1.47135 | −0.735675 | − | 0.677335i | \(-0.763135\pi\) | ||||
−0.735675 | + | 0.677335i | \(0.763135\pi\) | |||||||
\(80\) | −6.45296 | −0.721462 | ||||||||
\(81\) | −8.01275 | −0.890306 | ||||||||
\(82\) | 5.74937 | 0.634911 | ||||||||
\(83\) | 10.5285 | 1.15565 | 0.577825 | − | 0.816161i | \(-0.303902\pi\) | ||||
0.577825 | + | 0.816161i | \(0.303902\pi\) | |||||||
\(84\) | −15.5161 | −1.69294 | ||||||||
\(85\) | −2.63154 | −0.285430 | ||||||||
\(86\) | −13.0430 | −1.40646 | ||||||||
\(87\) | 16.3990 | 1.75815 | ||||||||
\(88\) | 13.3005 | 1.41783 | ||||||||
\(89\) | 11.2687 | 1.19449 | 0.597243 | − | 0.802061i | \(-0.296263\pi\) | ||||
0.597243 | + | 0.802061i | \(0.296263\pi\) | |||||||
\(90\) | −0.479636 | −0.0505580 | ||||||||
\(91\) | −9.54885 | −1.00099 | ||||||||
\(92\) | 4.95152 | 0.516232 | ||||||||
\(93\) | 3.34680 | 0.347047 | ||||||||
\(94\) | 28.6055 | 2.95044 | ||||||||
\(95\) | −1.43666 | −0.147398 | ||||||||
\(96\) | −20.4146 | −2.08356 | ||||||||
\(97\) | −9.14110 | −0.928138 | −0.464069 | − | 0.885799i | \(-0.653611\pi\) | ||||
−0.464069 | + | 0.885799i | \(0.653611\pi\) | |||||||
\(98\) | 8.86999 | 0.896004 | ||||||||
\(99\) | 0.511439 | 0.0514016 | ||||||||
\(100\) | −22.9276 | −2.29276 | ||||||||
\(101\) | −8.84196 | −0.879808 | −0.439904 | − | 0.898045i | \(-0.644988\pi\) | ||||
−0.439904 | + | 0.898045i | \(0.644988\pi\) | |||||||
\(102\) | −18.7558 | −1.85710 | ||||||||
\(103\) | −1.70094 | −0.167599 | −0.0837993 | − | 0.996483i | \(-0.526705\pi\) | ||||
−0.0837993 | + | 0.996483i | \(0.526705\pi\) | |||||||
\(104\) | −38.9707 | −3.82139 | ||||||||
\(105\) | 1.90502 | 0.185911 | ||||||||
\(106\) | 28.5699 | 2.77495 | ||||||||
\(107\) | −11.4304 | −1.10502 | −0.552508 | − | 0.833508i | \(-0.686329\pi\) | ||||
−0.552508 | + | 0.833508i | \(0.686329\pi\) | |||||||
\(108\) | −26.8470 | −2.58335 | ||||||||
\(109\) | 9.49004 | 0.908981 | 0.454490 | − | 0.890752i | \(-0.349821\pi\) | ||||
0.454490 | + | 0.890752i | \(0.349821\pi\) | |||||||
\(110\) | −2.73954 | −0.261205 | ||||||||
\(111\) | 10.4111 | 0.988177 | ||||||||
\(112\) | −20.2395 | −1.91246 | ||||||||
\(113\) | −11.3169 | −1.06461 | −0.532304 | − | 0.846553i | \(-0.678674\pi\) | ||||
−0.532304 | + | 0.846553i | \(0.678674\pi\) | |||||||
\(114\) | −10.2395 | −0.959017 | ||||||||
\(115\) | −0.607936 | −0.0566903 | ||||||||
\(116\) | 49.4097 | 4.58757 | ||||||||
\(117\) | −1.49853 | −0.138539 | ||||||||
\(118\) | 9.31711 | 0.857710 | ||||||||
\(119\) | −8.25374 | −0.756619 | ||||||||
\(120\) | 7.77476 | 0.709736 | ||||||||
\(121\) | −8.07880 | −0.734437 | ||||||||
\(122\) | −15.0083 | −1.35879 | ||||||||
\(123\) | −3.58363 | −0.323125 | ||||||||
\(124\) | 10.0838 | 0.905553 | ||||||||
\(125\) | 5.85467 | 0.523658 | ||||||||
\(126\) | −1.50436 | −0.134019 | ||||||||
\(127\) | −10.8972 | −0.966968 | −0.483484 | − | 0.875353i | \(-0.660629\pi\) | ||||
−0.483484 | + | 0.875353i | \(0.660629\pi\) | |||||||
\(128\) | −5.53676 | −0.489385 | ||||||||
\(129\) | 8.12983 | 0.715791 | ||||||||
\(130\) | 8.02692 | 0.704008 | ||||||||
\(131\) | −2.15149 | −0.187977 | −0.0939885 | − | 0.995573i | \(-0.529962\pi\) | ||||
−0.0939885 | + | 0.995573i | \(0.529962\pi\) | |||||||
\(132\) | −13.9079 | −1.21053 | ||||||||
\(133\) | −4.50604 | −0.390723 | ||||||||
\(134\) | −27.9346 | −2.41318 | ||||||||
\(135\) | 3.29621 | 0.283692 | ||||||||
\(136\) | −33.6851 | −2.88847 | ||||||||
\(137\) | 0.344286 | 0.0294144 | 0.0147072 | − | 0.999892i | \(-0.495318\pi\) | ||||
0.0147072 | + | 0.999892i | \(0.495318\pi\) | |||||||
\(138\) | −4.33295 | −0.368845 | ||||||||
\(139\) | 20.2372 | 1.71650 | 0.858250 | − | 0.513232i | \(-0.171552\pi\) | ||||
0.858250 | + | 0.513232i | \(0.171552\pi\) | |||||||
\(140\) | 5.73979 | 0.485101 | ||||||||
\(141\) | −17.8301 | −1.50156 | ||||||||
\(142\) | −25.2901 | −2.12230 | ||||||||
\(143\) | −8.55917 | −0.715754 | ||||||||
\(144\) | −3.17625 | −0.264688 | ||||||||
\(145\) | −6.06640 | −0.503787 | ||||||||
\(146\) | −38.5032 | −3.18655 | ||||||||
\(147\) | −5.52874 | −0.456003 | ||||||||
\(148\) | 31.3683 | 2.57846 | ||||||||
\(149\) | −18.0257 | −1.47672 | −0.738361 | − | 0.674405i | \(-0.764400\pi\) | ||||
−0.738361 | + | 0.674405i | \(0.764400\pi\) | |||||||
\(150\) | 20.0633 | 1.63816 | ||||||||
\(151\) | −13.5923 | −1.10613 | −0.553064 | − | 0.833138i | \(-0.686542\pi\) | ||||
−0.553064 | + | 0.833138i | \(0.686542\pi\) | |||||||
\(152\) | −18.3900 | −1.49163 | ||||||||
\(153\) | −1.29528 | −0.104718 | ||||||||
\(154\) | −8.59250 | −0.692404 | ||||||||
\(155\) | −1.23807 | −0.0994438 | ||||||||
\(156\) | 40.7506 | 3.26266 | ||||||||
\(157\) | −14.7510 | −1.17726 | −0.588628 | − | 0.808404i | \(-0.700332\pi\) | ||||
−0.588628 | + | 0.808404i | \(0.700332\pi\) | |||||||
\(158\) | 34.4802 | 2.74310 | ||||||||
\(159\) | −17.8078 | −1.41225 | ||||||||
\(160\) | 7.55190 | 0.597030 | ||||||||
\(161\) | −1.90677 | −0.150275 | ||||||||
\(162\) | 21.1262 | 1.65983 | ||||||||
\(163\) | 2.47996 | 0.194246 | 0.0971228 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971228 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(164\) | −10.7974 | −0.843135 | ||||||||
\(165\) | 1.70758 | 0.132935 | ||||||||
\(166\) | −27.7591 | −2.15452 | ||||||||
\(167\) | −9.48227 | −0.733760 | −0.366880 | − | 0.930268i | \(-0.619574\pi\) | ||||
−0.366880 | + | 0.930268i | \(0.619574\pi\) | |||||||
\(168\) | 24.3853 | 1.88137 | ||||||||
\(169\) | 12.0786 | 0.929122 | ||||||||
\(170\) | 6.93824 | 0.532139 | ||||||||
\(171\) | −0.707146 | −0.0540768 | ||||||||
\(172\) | 24.4950 | 1.86772 | ||||||||
\(173\) | 19.6984 | 1.49764 | 0.748820 | − | 0.662774i | \(-0.230621\pi\) | ||||
0.748820 | + | 0.662774i | \(0.230621\pi\) | |||||||
\(174\) | −43.2371 | −3.27780 | ||||||||
\(175\) | 8.82916 | 0.667421 | ||||||||
\(176\) | −18.1418 | −1.36749 | ||||||||
\(177\) | −5.80744 | −0.436514 | ||||||||
\(178\) | −29.7109 | −2.22693 | ||||||||
\(179\) | −8.03467 | −0.600540 | −0.300270 | − | 0.953854i | \(-0.597077\pi\) | ||||
−0.300270 | + | 0.953854i | \(0.597077\pi\) | |||||||
\(180\) | 0.900762 | 0.0671389 | ||||||||
\(181\) | 12.8014 | 0.951524 | 0.475762 | − | 0.879574i | \(-0.342172\pi\) | ||||
0.475762 | + | 0.879574i | \(0.342172\pi\) | |||||||
\(182\) | 25.1762 | 1.86619 | ||||||||
\(183\) | 9.35479 | 0.691526 | ||||||||
\(184\) | −7.78191 | −0.573690 | ||||||||
\(185\) | −3.85133 | −0.283155 | ||||||||
\(186\) | −8.82408 | −0.647013 | ||||||||
\(187\) | −7.39830 | −0.541017 | ||||||||
\(188\) | −53.7216 | −3.91805 | ||||||||
\(189\) | 10.3385 | 0.752013 | ||||||||
\(190\) | 3.78785 | 0.274800 | ||||||||
\(191\) | 9.57623 | 0.692911 | 0.346456 | − | 0.938066i | \(-0.387385\pi\) | ||||
0.346456 | + | 0.938066i | \(0.387385\pi\) | |||||||
\(192\) | 18.9368 | 1.36665 | ||||||||
\(193\) | 20.3494 | 1.46478 | 0.732392 | − | 0.680884i | \(-0.238404\pi\) | ||||
0.732392 | + | 0.680884i | \(0.238404\pi\) | |||||||
\(194\) | 24.1012 | 1.73037 | ||||||||
\(195\) | −5.00325 | −0.358290 | ||||||||
\(196\) | −16.6580 | −1.18985 | ||||||||
\(197\) | −7.49801 | −0.534211 | −0.267106 | − | 0.963667i | \(-0.586067\pi\) | ||||
−0.267106 | + | 0.963667i | \(0.586067\pi\) | |||||||
\(198\) | −1.34845 | −0.0958300 | ||||||||
\(199\) | 7.63098 | 0.540946 | 0.270473 | − | 0.962728i | \(-0.412820\pi\) | ||||
0.270473 | + | 0.962728i | \(0.412820\pi\) | |||||||
\(200\) | 36.0335 | 2.54795 | ||||||||
\(201\) | 17.4119 | 1.22814 | ||||||||
\(202\) | 23.3125 | 1.64026 | ||||||||
\(203\) | −19.0271 | −1.33544 | ||||||||
\(204\) | 35.2236 | 2.46614 | ||||||||
\(205\) | 1.32568 | 0.0925893 | ||||||||
\(206\) | 4.48465 | 0.312461 | ||||||||
\(207\) | −0.299236 | −0.0207983 | ||||||||
\(208\) | 53.1560 | 3.68571 | ||||||||
\(209\) | −4.03902 | −0.279385 | ||||||||
\(210\) | −5.02274 | −0.346602 | ||||||||
\(211\) | 24.7488 | 1.70378 | 0.851890 | − | 0.523721i | \(-0.175457\pi\) | ||||
0.851890 | + | 0.523721i | \(0.175457\pi\) | |||||||
\(212\) | −53.6546 | −3.68501 | ||||||||
\(213\) | 15.7636 | 1.08010 | ||||||||
\(214\) | 30.1370 | 2.06012 | ||||||||
\(215\) | −3.00743 | −0.205105 | ||||||||
\(216\) | 42.1932 | 2.87089 | ||||||||
\(217\) | −3.88316 | −0.263606 | ||||||||
\(218\) | −25.0212 | −1.69465 | ||||||||
\(219\) | 23.9994 | 1.62173 | ||||||||
\(220\) | 5.14490 | 0.346869 | ||||||||
\(221\) | 21.6772 | 1.45817 | ||||||||
\(222\) | −27.4496 | −1.84230 | ||||||||
\(223\) | 29.5235 | 1.97704 | 0.988519 | − | 0.151100i | \(-0.0482815\pi\) | ||||
0.988519 | + | 0.151100i | \(0.0482815\pi\) | |||||||
\(224\) | 23.6863 | 1.58261 | ||||||||
\(225\) | 1.38559 | 0.0923724 | ||||||||
\(226\) | 29.8379 | 1.98479 | ||||||||
\(227\) | −18.0587 | −1.19860 | −0.599298 | − | 0.800526i | \(-0.704554\pi\) | ||||
−0.599298 | + | 0.800526i | \(0.704554\pi\) | |||||||
\(228\) | 19.2299 | 1.27353 | ||||||||
\(229\) | 22.8986 | 1.51318 | 0.756590 | − | 0.653889i | \(-0.226864\pi\) | ||||
0.756590 | + | 0.653889i | \(0.226864\pi\) | |||||||
\(230\) | 1.60287 | 0.105690 | ||||||||
\(231\) | 5.35578 | 0.352385 | ||||||||
\(232\) | −77.6532 | −5.09818 | ||||||||
\(233\) | 12.1725 | 0.797447 | 0.398724 | − | 0.917071i | \(-0.369453\pi\) | ||||
0.398724 | + | 0.917071i | \(0.369453\pi\) | |||||||
\(234\) | 3.95098 | 0.258284 | ||||||||
\(235\) | 6.59580 | 0.430263 | ||||||||
\(236\) | −17.4977 | −1.13900 | ||||||||
\(237\) | −21.4918 | −1.39604 | ||||||||
\(238\) | 21.7616 | 1.41060 | ||||||||
\(239\) | −0.105377 | −0.00681629 | −0.00340814 | − | 0.999994i | \(-0.501085\pi\) | ||||
−0.00340814 | + | 0.999994i | \(0.501085\pi\) | |||||||
\(240\) | −10.6048 | −0.684536 | ||||||||
\(241\) | −1.70718 | −0.109969 | −0.0549845 | − | 0.998487i | \(-0.517511\pi\) | ||||
−0.0549845 | + | 0.998487i | \(0.517511\pi\) | |||||||
\(242\) | 21.3004 | 1.36924 | ||||||||
\(243\) | 3.09774 | 0.198720 | ||||||||
\(244\) | 28.1858 | 1.80441 | ||||||||
\(245\) | 2.04522 | 0.130665 | ||||||||
\(246\) | 9.44851 | 0.602415 | ||||||||
\(247\) | 11.8344 | 0.753006 | ||||||||
\(248\) | −15.8479 | −1.00634 | ||||||||
\(249\) | 17.3025 | 1.09650 | ||||||||
\(250\) | −15.4363 | −0.976276 | ||||||||
\(251\) | −0.779810 | −0.0492211 | −0.0246106 | − | 0.999697i | \(-0.507835\pi\) | ||||
−0.0246106 | + | 0.999697i | \(0.507835\pi\) | |||||||
\(252\) | 2.82522 | 0.177972 | ||||||||
\(253\) | −1.70915 | −0.107453 | ||||||||
\(254\) | 28.7312 | 1.80276 | ||||||||
\(255\) | −4.32467 | −0.270821 | ||||||||
\(256\) | −8.44785 | −0.527991 | ||||||||
\(257\) | 9.04524 | 0.564227 | 0.282113 | − | 0.959381i | \(-0.408965\pi\) | ||||
0.282113 | + | 0.959381i | \(0.408965\pi\) | |||||||
\(258\) | −21.4349 | −1.33448 | ||||||||
\(259\) | −12.0796 | −0.750589 | ||||||||
\(260\) | −15.0747 | −0.934892 | ||||||||
\(261\) | −2.98598 | −0.184828 | ||||||||
\(262\) | 5.67258 | 0.350453 | ||||||||
\(263\) | 16.7032 | 1.02996 | 0.514981 | − | 0.857202i | \(-0.327799\pi\) | ||||
0.514981 | + | 0.857202i | \(0.327799\pi\) | |||||||
\(264\) | 21.8580 | 1.34527 | ||||||||
\(265\) | 6.58758 | 0.404672 | ||||||||
\(266\) | 11.8805 | 0.728440 | ||||||||
\(267\) | 18.5191 | 1.13335 | ||||||||
\(268\) | 52.4615 | 3.20460 | ||||||||
\(269\) | −15.9918 | −0.975038 | −0.487519 | − | 0.873112i | \(-0.662098\pi\) | ||||
−0.487519 | + | 0.873112i | \(0.662098\pi\) | |||||||
\(270\) | −8.69069 | −0.528899 | ||||||||
\(271\) | 11.5420 | 0.701129 | 0.350565 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350565 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(272\) | 45.9465 | 2.78592 | ||||||||
\(273\) | −15.6926 | −0.949758 | ||||||||
\(274\) | −0.907736 | −0.0548384 | ||||||||
\(275\) | 7.91407 | 0.477237 | ||||||||
\(276\) | 8.13733 | 0.489810 | ||||||||
\(277\) | 14.0530 | 0.844363 | 0.422181 | − | 0.906511i | \(-0.361265\pi\) | ||||
0.422181 | + | 0.906511i | \(0.361265\pi\) | |||||||
\(278\) | −53.3570 | −3.20014 | ||||||||
\(279\) | −0.609396 | −0.0364836 | ||||||||
\(280\) | −9.02076 | −0.539094 | ||||||||
\(281\) | 7.90708 | 0.471697 | 0.235848 | − | 0.971790i | \(-0.424213\pi\) | ||||
0.235848 | + | 0.971790i | \(0.424213\pi\) | |||||||
\(282\) | 47.0103 | 2.79942 | ||||||||
\(283\) | −15.5998 | −0.927314 | −0.463657 | − | 0.886015i | \(-0.653463\pi\) | ||||
−0.463657 | + | 0.886015i | \(0.653463\pi\) | |||||||
\(284\) | 47.4952 | 2.81832 | ||||||||
\(285\) | −2.36100 | −0.139854 | ||||||||
\(286\) | 22.5669 | 1.33441 | ||||||||
\(287\) | 4.15795 | 0.245436 | ||||||||
\(288\) | 3.71717 | 0.219036 | ||||||||
\(289\) | 1.73713 | 0.102184 | ||||||||
\(290\) | 15.9945 | 0.939230 | ||||||||
\(291\) | −15.0225 | −0.880634 | ||||||||
\(292\) | 72.3096 | 4.23160 | ||||||||
\(293\) | 5.63033 | 0.328927 | 0.164464 | − | 0.986383i | \(-0.447411\pi\) | ||||
0.164464 | + | 0.986383i | \(0.447411\pi\) | |||||||
\(294\) | 14.5769 | 0.850145 | ||||||||
\(295\) | 2.14832 | 0.125080 | ||||||||
\(296\) | −49.2991 | −2.86545 | ||||||||
\(297\) | 9.26695 | 0.537723 | ||||||||
\(298\) | 47.5261 | 2.75311 | ||||||||
\(299\) | 5.00785 | 0.289612 | ||||||||
\(300\) | −37.6792 | −2.17541 | ||||||||
\(301\) | −9.43273 | −0.543693 | ||||||||
\(302\) | 35.8372 | 2.06220 | ||||||||
\(303\) | −14.5309 | −0.834777 | ||||||||
\(304\) | 25.0840 | 1.43867 | ||||||||
\(305\) | −3.46058 | −0.198152 | ||||||||
\(306\) | 3.41511 | 0.195229 | ||||||||
\(307\) | 11.9256 | 0.680627 | 0.340314 | − | 0.940312i | \(-0.389467\pi\) | ||||
0.340314 | + | 0.940312i | \(0.389467\pi\) | |||||||
\(308\) | 16.1368 | 0.919482 | ||||||||
\(309\) | −2.79532 | −0.159020 | ||||||||
\(310\) | 3.26425 | 0.185397 | ||||||||
\(311\) | −1.29915 | −0.0736682 | −0.0368341 | − | 0.999321i | \(-0.511727\pi\) | ||||
−0.0368341 | + | 0.999321i | \(0.511727\pi\) | |||||||
\(312\) | −64.0444 | −3.62580 | ||||||||
\(313\) | 18.0288 | 1.01905 | 0.509525 | − | 0.860456i | \(-0.329821\pi\) | ||||
0.509525 | + | 0.860456i | \(0.329821\pi\) | |||||||
\(314\) | 38.8921 | 2.19481 | ||||||||
\(315\) | −0.346873 | −0.0195441 | ||||||||
\(316\) | −64.7543 | −3.64271 | ||||||||
\(317\) | 13.5054 | 0.758537 | 0.379268 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379268 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(318\) | 46.9517 | 2.63292 | ||||||||
\(319\) | −17.0551 | −0.954901 | ||||||||
\(320\) | −7.00522 | −0.391604 | ||||||||
\(321\) | −18.7847 | −1.04846 | ||||||||
\(322\) | 5.02735 | 0.280163 | ||||||||
\(323\) | 10.2293 | 0.569175 | ||||||||
\(324\) | −39.6753 | −2.20418 | ||||||||
\(325\) | −23.1884 | −1.28626 | ||||||||
\(326\) | −6.53861 | −0.362140 | ||||||||
\(327\) | 15.5959 | 0.862457 | ||||||||
\(328\) | 16.9694 | 0.936978 | ||||||||
\(329\) | 20.6876 | 1.14054 | ||||||||
\(330\) | −4.50216 | −0.247836 | ||||||||
\(331\) | −3.16347 | −0.173880 | −0.0869401 | − | 0.996214i | \(-0.527709\pi\) | ||||
−0.0869401 | + | 0.996214i | \(0.527709\pi\) | |||||||
\(332\) | 52.1320 | 2.86111 | ||||||||
\(333\) | −1.89569 | −0.103883 | ||||||||
\(334\) | 25.0007 | 1.36798 | ||||||||
\(335\) | −6.44109 | −0.351914 | ||||||||
\(336\) | −33.2616 | −1.81457 | ||||||||
\(337\) | −4.88725 | −0.266226 | −0.133113 | − | 0.991101i | \(-0.542497\pi\) | ||||
−0.133113 | + | 0.991101i | \(0.542497\pi\) | |||||||
\(338\) | −31.8461 | −1.73220 | ||||||||
\(339\) | −18.5982 | −1.01012 | ||||||||
\(340\) | −13.0301 | −0.706657 | ||||||||
\(341\) | −3.48070 | −0.188490 | ||||||||
\(342\) | 1.86444 | 0.100818 | ||||||||
\(343\) | 19.7622 | 1.06706 | ||||||||
\(344\) | −38.4968 | −2.07561 | ||||||||
\(345\) | −0.999082 | −0.0537887 | ||||||||
\(346\) | −51.9362 | −2.79211 | ||||||||
\(347\) | −13.6511 | −0.732829 | −0.366414 | − | 0.930452i | \(-0.619415\pi\) | ||||
−0.366414 | + | 0.930452i | \(0.619415\pi\) | |||||||
\(348\) | 81.1999 | 4.35277 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −23.2787 | −1.24430 | ||||||||
\(351\) | −27.1524 | −1.44929 | ||||||||
\(352\) | 21.2314 | 1.13164 | ||||||||
\(353\) | 8.13096 | 0.432768 | 0.216384 | − | 0.976308i | \(-0.430574\pi\) | ||||
0.216384 | + | 0.976308i | \(0.430574\pi\) | |||||||
\(354\) | 15.3117 | 0.813810 | ||||||||
\(355\) | −5.83134 | −0.309496 | ||||||||
\(356\) | 55.7975 | 2.95726 | ||||||||
\(357\) | −13.5642 | −0.717894 | ||||||||
\(358\) | 21.1840 | 1.11961 | ||||||||
\(359\) | −7.63110 | −0.402754 | −0.201377 | − | 0.979514i | \(-0.564542\pi\) | ||||
−0.201377 | + | 0.979514i | \(0.564542\pi\) | |||||||
\(360\) | −1.41566 | −0.0746116 | ||||||||
\(361\) | −13.4154 | −0.706074 | ||||||||
\(362\) | −33.7519 | −1.77396 | ||||||||
\(363\) | −13.2767 | −0.696846 | ||||||||
\(364\) | −47.2813 | −2.47822 | ||||||||
\(365\) | −8.87800 | −0.464696 | ||||||||
\(366\) | −24.6646 | −1.28924 | ||||||||
\(367\) | −24.4133 | −1.27436 | −0.637182 | − | 0.770713i | \(-0.719900\pi\) | ||||
−0.637182 | + | 0.770713i | \(0.719900\pi\) | |||||||
\(368\) | 10.6145 | 0.553321 | ||||||||
\(369\) | 0.652520 | 0.0339688 | ||||||||
\(370\) | 10.1543 | 0.527897 | ||||||||
\(371\) | 20.6618 | 1.07271 | ||||||||
\(372\) | 16.5717 | 0.859205 | ||||||||
\(373\) | 9.23433 | 0.478136 | 0.239068 | − | 0.971003i | \(-0.423158\pi\) | ||||
0.239068 | + | 0.971003i | \(0.423158\pi\) | |||||||
\(374\) | 19.5062 | 1.00864 | ||||||||
\(375\) | 9.62157 | 0.496856 | ||||||||
\(376\) | 84.4299 | 4.35414 | ||||||||
\(377\) | 49.9718 | 2.57368 | ||||||||
\(378\) | −27.2581 | −1.40201 | ||||||||
\(379\) | 17.6248 | 0.905324 | 0.452662 | − | 0.891682i | \(-0.350474\pi\) | ||||
0.452662 | + | 0.891682i | \(0.350474\pi\) | |||||||
\(380\) | −7.11364 | −0.364922 | ||||||||
\(381\) | −17.9084 | −0.917476 | ||||||||
\(382\) | −25.2484 | −1.29182 | ||||||||
\(383\) | 23.6066 | 1.20624 | 0.603121 | − | 0.797650i | \(-0.293924\pi\) | ||||
0.603121 | + | 0.797650i | \(0.293924\pi\) | |||||||
\(384\) | −9.09911 | −0.464337 | ||||||||
\(385\) | −1.98124 | −0.100973 | ||||||||
\(386\) | −53.6527 | −2.73085 | ||||||||
\(387\) | −1.48031 | −0.0752482 | ||||||||
\(388\) | −45.2624 | −2.29785 | ||||||||
\(389\) | 0.662173 | 0.0335735 | 0.0167867 | − | 0.999859i | \(-0.494656\pi\) | ||||
0.0167867 | + | 0.999859i | \(0.494656\pi\) | |||||||
\(390\) | 13.1914 | 0.667975 | ||||||||
\(391\) | 4.32864 | 0.218909 | ||||||||
\(392\) | 26.1800 | 1.32229 | ||||||||
\(393\) | −3.53577 | −0.178356 | ||||||||
\(394\) | 19.7691 | 0.995951 | ||||||||
\(395\) | 7.95037 | 0.400026 | ||||||||
\(396\) | 2.53240 | 0.127258 | ||||||||
\(397\) | −5.83901 | −0.293051 | −0.146526 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146526 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(398\) | −20.1197 | −1.00851 | ||||||||
\(399\) | −7.40522 | −0.370725 | ||||||||
\(400\) | −49.1497 | −2.45749 | ||||||||
\(401\) | 20.8106 | 1.03923 | 0.519615 | − | 0.854401i | \(-0.326075\pi\) | ||||
0.519615 | + | 0.854401i | \(0.326075\pi\) | |||||||
\(402\) | −45.9077 | −2.28967 | ||||||||
\(403\) | 10.1985 | 0.508025 | ||||||||
\(404\) | −43.7812 | −2.17819 | ||||||||
\(405\) | 4.87124 | 0.242054 | ||||||||
\(406\) | 50.1664 | 2.48971 | ||||||||
\(407\) | −10.8276 | −0.536705 | ||||||||
\(408\) | −55.3581 | −2.74063 | ||||||||
\(409\) | 19.9880 | 0.988341 | 0.494171 | − | 0.869365i | \(-0.335472\pi\) | ||||
0.494171 | + | 0.869365i | \(0.335472\pi\) | |||||||
\(410\) | −3.49525 | −0.172618 | ||||||||
\(411\) | 0.565800 | 0.0279089 | ||||||||
\(412\) | −8.42224 | −0.414934 | ||||||||
\(413\) | 6.73815 | 0.331563 | ||||||||
\(414\) | 0.788958 | 0.0387752 | ||||||||
\(415\) | −6.40063 | −0.314195 | ||||||||
\(416\) | −62.2085 | −3.05002 | ||||||||
\(417\) | 33.2579 | 1.62864 | ||||||||
\(418\) | 10.6492 | 0.520868 | ||||||||
\(419\) | −35.6823 | −1.74319 | −0.871597 | − | 0.490223i | \(-0.836915\pi\) | ||||
−0.871597 | + | 0.490223i | \(0.836915\pi\) | |||||||
\(420\) | 9.43277 | 0.460272 | ||||||||
\(421\) | 16.5533 | 0.806760 | 0.403380 | − | 0.915033i | \(-0.367835\pi\) | ||||
0.403380 | + | 0.915033i | \(0.367835\pi\) | |||||||
\(422\) | −65.2521 | −3.17642 | ||||||||
\(423\) | 3.24656 | 0.157853 | ||||||||
\(424\) | 84.3246 | 4.09516 | ||||||||
\(425\) | −20.0434 | −0.972248 | ||||||||
\(426\) | −41.5618 | −2.01368 | ||||||||
\(427\) | −10.8540 | −0.525262 | ||||||||
\(428\) | −56.5978 | −2.73576 | ||||||||
\(429\) | −14.0661 | −0.679120 | ||||||||
\(430\) | 7.92931 | 0.382385 | ||||||||
\(431\) | 1.66686 | 0.0802899 | 0.0401450 | − | 0.999194i | \(-0.487218\pi\) | ||||
0.0401450 | + | 0.999194i | \(0.487218\pi\) | |||||||
\(432\) | −57.5517 | −2.76896 | ||||||||
\(433\) | 30.4107 | 1.46144 | 0.730722 | − | 0.682675i | \(-0.239184\pi\) | ||||
0.730722 | + | 0.682675i | \(0.239184\pi\) | |||||||
\(434\) | 10.2382 | 0.491451 | ||||||||
\(435\) | −9.96952 | −0.478002 | ||||||||
\(436\) | 46.9902 | 2.25042 | ||||||||
\(437\) | 2.36317 | 0.113046 | ||||||||
\(438\) | −63.2762 | −3.02346 | ||||||||
\(439\) | −22.1759 | −1.05840 | −0.529198 | − | 0.848498i | \(-0.677507\pi\) | ||||
−0.529198 | + | 0.848498i | \(0.677507\pi\) | |||||||
\(440\) | −8.08582 | −0.385476 | ||||||||
\(441\) | 1.00669 | 0.0479377 | ||||||||
\(442\) | −57.1535 | −2.71852 | ||||||||
\(443\) | 18.7735 | 0.891956 | 0.445978 | − | 0.895044i | \(-0.352856\pi\) | ||||
0.445978 | + | 0.895044i | \(0.352856\pi\) | |||||||
\(444\) | 51.5507 | 2.44649 | ||||||||
\(445\) | −6.85068 | −0.324753 | ||||||||
\(446\) | −77.8408 | −3.68587 | ||||||||
\(447\) | −29.6234 | −1.40114 | ||||||||
\(448\) | −21.9717 | −1.03807 | ||||||||
\(449\) | 26.8482 | 1.26704 | 0.633522 | − | 0.773725i | \(-0.281609\pi\) | ||||
0.633522 | + | 0.773725i | \(0.281609\pi\) | |||||||
\(450\) | −3.65320 | −0.172214 | ||||||||
\(451\) | 3.72701 | 0.175498 | ||||||||
\(452\) | −56.0361 | −2.63571 | ||||||||
\(453\) | −22.3377 | −1.04951 | ||||||||
\(454\) | 47.6130 | 2.23459 | ||||||||
\(455\) | 5.80508 | 0.272147 | ||||||||
\(456\) | −30.2221 | −1.41528 | ||||||||
\(457\) | −15.3981 | −0.720291 | −0.360146 | − | 0.932896i | \(-0.617273\pi\) | ||||
−0.360146 | + | 0.932896i | \(0.617273\pi\) | |||||||
\(458\) | −60.3738 | −2.82108 | ||||||||
\(459\) | −23.4697 | −1.09547 | ||||||||
\(460\) | −3.01021 | −0.140352 | ||||||||
\(461\) | −4.94351 | −0.230242 | −0.115121 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115121 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(462\) | −14.1209 | −0.656965 | ||||||||
\(463\) | 20.7293 | 0.963374 | 0.481687 | − | 0.876343i | \(-0.340024\pi\) | ||||
0.481687 | + | 0.876343i | \(0.340024\pi\) | |||||||
\(464\) | 105.919 | 4.91717 | ||||||||
\(465\) | −2.03464 | −0.0943540 | ||||||||
\(466\) | −32.0937 | −1.48671 | ||||||||
\(467\) | 19.9019 | 0.920952 | 0.460476 | − | 0.887672i | \(-0.347679\pi\) | ||||
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(468\) | −7.42000 | −0.342990 | ||||||||
\(469\) | −20.2023 | −0.932857 | ||||||||
\(470\) | −17.3903 | −0.802156 | ||||||||
\(471\) | −24.2418 | −1.11700 | ||||||||
\(472\) | 27.4997 | 1.26578 | ||||||||
\(473\) | −8.45509 | −0.388765 | ||||||||
\(474\) | 56.6647 | 2.60270 | ||||||||
\(475\) | −10.9425 | −0.502075 | ||||||||
\(476\) | −40.8686 | −1.87321 | ||||||||
\(477\) | 3.24251 | 0.148465 | ||||||||
\(478\) | 0.277835 | 0.0127079 | ||||||||
\(479\) | −28.2127 | −1.28907 | −0.644536 | − | 0.764574i | \(-0.722949\pi\) | ||||
−0.644536 | + | 0.764574i | \(0.722949\pi\) | |||||||
\(480\) | 12.4108 | 0.566472 | ||||||||
\(481\) | 31.7252 | 1.44654 | ||||||||
\(482\) | 4.50110 | 0.205020 | ||||||||
\(483\) | −3.13359 | −0.142583 | ||||||||
\(484\) | −40.0024 | −1.81829 | ||||||||
\(485\) | 5.55720 | 0.252340 | ||||||||
\(486\) | −8.16742 | −0.370482 | ||||||||
\(487\) | 14.3970 | 0.652389 | 0.326195 | − | 0.945303i | \(-0.394234\pi\) | ||||
0.326195 | + | 0.945303i | \(0.394234\pi\) | |||||||
\(488\) | −44.2973 | −2.00524 | ||||||||
\(489\) | 4.07557 | 0.184304 | ||||||||
\(490\) | −5.39238 | −0.243603 | ||||||||
\(491\) | 8.47476 | 0.382461 | 0.191230 | − | 0.981545i | \(-0.438752\pi\) | ||||
0.191230 | + | 0.981545i | \(0.438752\pi\) | |||||||
\(492\) | −17.7444 | −0.799981 | ||||||||
\(493\) | 43.1941 | 1.94537 | ||||||||
\(494\) | −31.2023 | −1.40386 | ||||||||
\(495\) | −0.310922 | −0.0139749 | ||||||||
\(496\) | 21.6166 | 0.970613 | ||||||||
\(497\) | −18.2899 | −0.820412 | ||||||||
\(498\) | −45.6193 | −2.04425 | ||||||||
\(499\) | −23.9521 | −1.07224 | −0.536122 | − | 0.844141i | \(-0.680111\pi\) | ||||
−0.536122 | + | 0.844141i | \(0.680111\pi\) | |||||||
\(500\) | 28.9895 | 1.29645 | ||||||||
\(501\) | −15.5832 | −0.696205 | ||||||||
\(502\) | 2.05603 | 0.0917649 | ||||||||
\(503\) | 17.4413 | 0.777670 | 0.388835 | − | 0.921307i | \(-0.372878\pi\) | ||||
0.388835 | + | 0.921307i | \(0.372878\pi\) | |||||||
\(504\) | −4.44017 | −0.197781 | ||||||||
\(505\) | 5.37534 | 0.239200 | ||||||||
\(506\) | 4.50630 | 0.200330 | ||||||||
\(507\) | 19.8500 | 0.881567 | ||||||||
\(508\) | −53.9576 | −2.39398 | ||||||||
\(509\) | 19.9721 | 0.885250 | 0.442625 | − | 0.896707i | \(-0.354047\pi\) | ||||
0.442625 | + | 0.896707i | \(0.354047\pi\) | |||||||
\(510\) | 11.4023 | 0.504902 | ||||||||
\(511\) | −27.8456 | −1.23182 | ||||||||
\(512\) | 33.3469 | 1.47374 | ||||||||
\(513\) | −12.8130 | −0.565710 | ||||||||
\(514\) | −23.8484 | −1.05191 | ||||||||
\(515\) | 1.03406 | 0.0455662 | ||||||||
\(516\) | 40.2550 | 1.77213 | ||||||||
\(517\) | 18.5434 | 0.815540 | ||||||||
\(518\) | 31.8487 | 1.39935 | ||||||||
\(519\) | 32.3723 | 1.42099 | ||||||||
\(520\) | 23.6917 | 1.03895 | ||||||||
\(521\) | 23.4574 | 1.02769 | 0.513844 | − | 0.857884i | \(-0.328221\pi\) | ||||
0.513844 | + | 0.857884i | \(0.328221\pi\) | |||||||
\(522\) | 7.87276 | 0.344581 | ||||||||
\(523\) | −23.1124 | −1.01063 | −0.505317 | − | 0.862934i | \(-0.668625\pi\) | ||||
−0.505317 | + | 0.862934i | \(0.668625\pi\) | |||||||
\(524\) | −10.6532 | −0.465386 | ||||||||
\(525\) | 14.5098 | 0.633261 | ||||||||
\(526\) | −44.0392 | −1.92020 | ||||||||
\(527\) | 8.81531 | 0.384001 | ||||||||
\(528\) | −29.8143 | −1.29750 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −17.3686 | −0.754445 | ||||||||
\(531\) | 1.05744 | 0.0458889 | ||||||||
\(532\) | −22.3118 | −0.967337 | ||||||||
\(533\) | −10.9202 | −0.473008 | ||||||||
\(534\) | −48.8269 | −2.11295 | ||||||||
\(535\) | 6.94893 | 0.300429 | ||||||||
\(536\) | −82.4495 | −3.56128 | ||||||||
\(537\) | −13.2042 | −0.569803 | ||||||||
\(538\) | 42.1636 | 1.81780 | ||||||||
\(539\) | 5.74994 | 0.247668 | ||||||||
\(540\) | 16.3212 | 0.702354 | ||||||||
\(541\) | 12.6756 | 0.544965 | 0.272483 | − | 0.962161i | \(-0.412155\pi\) | ||||
0.272483 | + | 0.962161i | \(0.412155\pi\) | |||||||
\(542\) | −30.4315 | −1.30714 | ||||||||
\(543\) | 21.0379 | 0.902822 | ||||||||
\(544\) | −53.7712 | −2.30542 | ||||||||
\(545\) | −5.76933 | −0.247131 | ||||||||
\(546\) | 41.3746 | 1.77067 | ||||||||
\(547\) | −17.1411 | −0.732902 | −0.366451 | − | 0.930437i | \(-0.619427\pi\) | ||||
−0.366451 | + | 0.930437i | \(0.619427\pi\) | |||||||
\(548\) | 1.70474 | 0.0728230 | ||||||||
\(549\) | −1.70335 | −0.0726973 | ||||||||
\(550\) | −20.8660 | −0.889731 | ||||||||
\(551\) | 23.5814 | 1.00460 | ||||||||
\(552\) | −12.7888 | −0.544327 | ||||||||
\(553\) | 24.9361 | 1.06039 | ||||||||
\(554\) | −37.0518 | −1.57418 | ||||||||
\(555\) | −6.32927 | −0.268663 | ||||||||
\(556\) | 100.205 | 4.24964 | ||||||||
\(557\) | −32.7913 | −1.38941 | −0.694705 | − | 0.719294i | \(-0.744465\pi\) | ||||
−0.694705 | + | 0.719294i | \(0.744465\pi\) | |||||||
\(558\) | 1.60672 | 0.0680178 | ||||||||
\(559\) | 24.7736 | 1.04781 | ||||||||
\(560\) | 12.3043 | 0.519953 | ||||||||
\(561\) | −12.1584 | −0.513327 | ||||||||
\(562\) | −20.8476 | −0.879403 | ||||||||
\(563\) | −10.3633 | −0.436760 | −0.218380 | − | 0.975864i | \(-0.570077\pi\) | ||||
−0.218380 | + | 0.975864i | \(0.570077\pi\) | |||||||
\(564\) | −88.2861 | −3.71751 | ||||||||
\(565\) | 6.87997 | 0.289442 | ||||||||
\(566\) | 41.1301 | 1.72883 | ||||||||
\(567\) | 15.2785 | 0.641637 | ||||||||
\(568\) | −74.6444 | −3.13201 | ||||||||
\(569\) | −38.1386 | −1.59885 | −0.799426 | − | 0.600765i | \(-0.794863\pi\) | ||||
−0.799426 | + | 0.600765i | \(0.794863\pi\) | |||||||
\(570\) | 6.22496 | 0.260735 | ||||||||
\(571\) | 10.5721 | 0.442428 | 0.221214 | − | 0.975225i | \(-0.428998\pi\) | ||||
0.221214 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(572\) | −42.3809 | −1.77204 | ||||||||
\(573\) | 15.7376 | 0.657447 | ||||||||
\(574\) | −10.9627 | −0.457576 | ||||||||
\(575\) | −4.63041 | −0.193102 | ||||||||
\(576\) | −3.44809 | −0.143670 | ||||||||
\(577\) | 21.8011 | 0.907592 | 0.453796 | − | 0.891106i | \(-0.350070\pi\) | ||||
0.453796 | + | 0.891106i | \(0.350070\pi\) | |||||||
\(578\) | −4.58007 | −0.190506 | ||||||||
\(579\) | 33.4422 | 1.38981 | ||||||||
\(580\) | −30.0379 | −1.24726 | ||||||||
\(581\) | −20.0754 | −0.832869 | ||||||||
\(582\) | 39.6079 | 1.64180 | ||||||||
\(583\) | 18.5203 | 0.767033 | ||||||||
\(584\) | −113.643 | −4.70259 | ||||||||
\(585\) | 0.911010 | 0.0376656 | ||||||||
\(586\) | −14.8448 | −0.613232 | ||||||||
\(587\) | −16.4416 | −0.678617 | −0.339309 | − | 0.940675i | \(-0.610193\pi\) | ||||
−0.339309 | + | 0.940675i | \(0.610193\pi\) | |||||||
\(588\) | −27.3757 | −1.12896 | ||||||||
\(589\) | 4.81262 | 0.198301 | ||||||||
\(590\) | −5.66421 | −0.233192 | ||||||||
\(591\) | −12.3222 | −0.506869 | ||||||||
\(592\) | 67.2440 | 2.76371 | ||||||||
\(593\) | 18.7070 | 0.768203 | 0.384101 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384101 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(594\) | −24.4330 | −1.00250 | ||||||||
\(595\) | 5.01774 | 0.205707 | ||||||||
\(596\) | −89.2547 | −3.65601 | ||||||||
\(597\) | 12.5408 | 0.513259 | ||||||||
\(598\) | −13.2036 | −0.539934 | ||||||||
\(599\) | −10.8483 | −0.443248 | −0.221624 | − | 0.975132i | \(-0.571136\pi\) | ||||
−0.221624 | + | 0.975132i | \(0.571136\pi\) | |||||||
\(600\) | 59.2174 | 2.41754 | ||||||||
\(601\) | 2.36883 | 0.0966267 | 0.0483134 | − | 0.998832i | \(-0.484615\pi\) | ||||
0.0483134 | + | 0.998832i | \(0.484615\pi\) | |||||||
\(602\) | 24.8701 | 1.01363 | ||||||||
\(603\) | −3.17041 | −0.129109 | ||||||||
\(604\) | −67.3028 | −2.73851 | ||||||||
\(605\) | 4.91139 | 0.199677 | ||||||||
\(606\) | 38.3117 | 1.55631 | ||||||||
\(607\) | 20.9624 | 0.850838 | 0.425419 | − | 0.904996i | \(-0.360127\pi\) | ||||
0.425419 | + | 0.904996i | \(0.360127\pi\) | |||||||
\(608\) | −29.3558 | −1.19053 | ||||||||
\(609\) | −31.2691 | −1.26709 | ||||||||
\(610\) | 9.12407 | 0.369423 | ||||||||
\(611\) | −54.3327 | −2.19807 | ||||||||
\(612\) | −6.41363 | −0.259256 | ||||||||
\(613\) | −23.1952 | −0.936843 | −0.468422 | − | 0.883505i | \(-0.655177\pi\) | ||||
−0.468422 | + | 0.883505i | \(0.655177\pi\) | |||||||
\(614\) | −31.4426 | −1.26892 | ||||||||
\(615\) | 2.17862 | 0.0878504 | ||||||||
\(616\) | −25.3610 | −1.02182 | ||||||||
\(617\) | 30.6906 | 1.23556 | 0.617779 | − | 0.786352i | \(-0.288033\pi\) | ||||
0.617779 | + | 0.786352i | \(0.288033\pi\) | |||||||
\(618\) | 7.37008 | 0.296468 | ||||||||
\(619\) | 19.9187 | 0.800601 | 0.400301 | − | 0.916384i | \(-0.368906\pi\) | ||||
0.400301 | + | 0.916384i | \(0.368906\pi\) | |||||||
\(620\) | −6.13031 | −0.246199 | ||||||||
\(621\) | −5.42196 | −0.217576 | ||||||||
\(622\) | 3.42531 | 0.137342 | ||||||||
\(623\) | −21.4870 | −0.860857 | ||||||||
\(624\) | 87.3566 | 3.49706 | ||||||||
\(625\) | 19.5928 | 0.783712 | ||||||||
\(626\) | −47.5344 | −1.89985 | ||||||||
\(627\) | −6.63772 | −0.265085 | ||||||||
\(628\) | −73.0398 | −2.91461 | ||||||||
\(629\) | 27.4223 | 1.09340 | ||||||||
\(630\) | 0.914557 | 0.0364368 | ||||||||
\(631\) | 16.9341 | 0.674134 | 0.337067 | − | 0.941481i | \(-0.390565\pi\) | ||||
0.337067 | + | 0.941481i | \(0.390565\pi\) | |||||||
\(632\) | 101.769 | 4.04816 | ||||||||
\(633\) | 40.6722 | 1.61658 | ||||||||
\(634\) | −35.6079 | −1.41417 | ||||||||
\(635\) | 6.62478 | 0.262896 | ||||||||
\(636\) | −88.1760 | −3.49640 | ||||||||
\(637\) | −16.8475 | −0.667521 | ||||||||
\(638\) | 44.9670 | 1.78026 | ||||||||
\(639\) | −2.87028 | −0.113547 | ||||||||
\(640\) | 3.36599 | 0.133053 | ||||||||
\(641\) | −42.3221 | −1.67162 | −0.835811 | − | 0.549017i | \(-0.815002\pi\) | ||||
−0.835811 | + | 0.549017i | \(0.815002\pi\) | |||||||
\(642\) | 49.5272 | 1.95468 | ||||||||
\(643\) | 47.3934 | 1.86901 | 0.934507 | − | 0.355945i | \(-0.115841\pi\) | ||||
0.934507 | + | 0.355945i | \(0.115841\pi\) | |||||||
\(644\) | −9.44144 | −0.372045 | ||||||||
\(645\) | −4.94241 | −0.194607 | ||||||||
\(646\) | −26.9704 | −1.06114 | ||||||||
\(647\) | −22.9751 | −0.903245 | −0.451623 | − | 0.892209i | \(-0.649155\pi\) | ||||
−0.451623 | + | 0.892209i | \(0.649155\pi\) | |||||||
\(648\) | 62.3545 | 2.44952 | ||||||||
\(649\) | 6.03979 | 0.237082 | ||||||||
\(650\) | 61.1380 | 2.39803 | ||||||||
\(651\) | −6.38159 | −0.250114 | ||||||||
\(652\) | 12.2796 | 0.480906 | ||||||||
\(653\) | 30.0338 | 1.17531 | 0.587657 | − | 0.809110i | \(-0.300051\pi\) | ||||
0.587657 | + | 0.809110i | \(0.300051\pi\) | |||||||
\(654\) | −41.1198 | −1.60791 | ||||||||
\(655\) | 1.30797 | 0.0511066 | ||||||||
\(656\) | −23.1463 | −0.903710 | ||||||||
\(657\) | −4.36990 | −0.170486 | ||||||||
\(658\) | −54.5443 | −2.12636 | ||||||||
\(659\) | 31.2967 | 1.21914 | 0.609572 | − | 0.792730i | \(-0.291341\pi\) | ||||
0.609572 | + | 0.792730i | \(0.291341\pi\) | |||||||
\(660\) | 8.45513 | 0.329115 | ||||||||
\(661\) | 22.4784 | 0.874307 | 0.437154 | − | 0.899387i | \(-0.355987\pi\) | ||||
0.437154 | + | 0.899387i | \(0.355987\pi\) | |||||||
\(662\) | 8.34073 | 0.324172 | ||||||||
\(663\) | 35.6243 | 1.38353 | ||||||||
\(664\) | −81.9316 | −3.17956 | ||||||||
\(665\) | 2.73938 | 0.106229 | ||||||||
\(666\) | 4.99812 | 0.193673 | ||||||||
\(667\) | 9.97868 | 0.386376 | ||||||||
\(668\) | −46.9517 | −1.81662 | ||||||||
\(669\) | 48.5189 | 1.87585 | ||||||||
\(670\) | 16.9824 | 0.656088 | ||||||||
\(671\) | −9.72907 | −0.375586 | ||||||||
\(672\) | 38.9261 | 1.50161 | ||||||||
\(673\) | 0.599637 | 0.0231143 | 0.0115572 | − | 0.999933i | \(-0.496321\pi\) | ||||
0.0115572 | + | 0.999933i | \(0.496321\pi\) | |||||||
\(674\) | 12.8856 | 0.496335 | ||||||||
\(675\) | 25.1059 | 0.966328 | ||||||||
\(676\) | 59.8074 | 2.30028 | ||||||||
\(677\) | 45.6605 | 1.75487 | 0.877437 | − | 0.479691i | \(-0.159251\pi\) | ||||
0.877437 | + | 0.479691i | \(0.159251\pi\) | |||||||
\(678\) | 49.0357 | 1.88320 | ||||||||
\(679\) | 17.4300 | 0.668903 | ||||||||
\(680\) | 20.4784 | 0.785310 | ||||||||
\(681\) | −29.6776 | −1.13725 | ||||||||
\(682\) | 9.17712 | 0.351410 | ||||||||
\(683\) | 7.89455 | 0.302077 | 0.151038 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151038 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(684\) | −3.50145 | −0.133881 | ||||||||
\(685\) | −0.209304 | −0.00799709 | ||||||||
\(686\) | −52.1045 | −1.98936 | ||||||||
\(687\) | 37.6315 | 1.43573 | ||||||||
\(688\) | 52.5096 | 2.00191 | ||||||||
\(689\) | −54.2650 | −2.06733 | ||||||||
\(690\) | 2.63415 | 0.100280 | ||||||||
\(691\) | 11.2730 | 0.428847 | 0.214423 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214423 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(692\) | 97.5370 | 3.70780 | ||||||||
\(693\) | −0.975200 | −0.0370448 | ||||||||
\(694\) | 35.9921 | 1.36624 | ||||||||
\(695\) | −12.3029 | −0.466677 | ||||||||
\(696\) | −127.615 | −4.83725 | ||||||||
\(697\) | −9.43912 | −0.357532 | ||||||||
\(698\) | 2.63657 | 0.0997958 | ||||||||
\(699\) | 20.0043 | 0.756632 | ||||||||
\(700\) | 43.7178 | 1.65238 | ||||||||
\(701\) | 17.1738 | 0.648645 | 0.324322 | − | 0.945947i | \(-0.394864\pi\) | ||||
0.324322 | + | 0.945947i | \(0.394864\pi\) | |||||||
\(702\) | 71.5893 | 2.70196 | ||||||||
\(703\) | 14.9709 | 0.564639 | ||||||||
\(704\) | −19.6945 | −0.742264 | ||||||||
\(705\) | 10.8395 | 0.408241 | ||||||||
\(706\) | −21.4379 | −0.806826 | ||||||||
\(707\) | 16.8596 | 0.634071 | ||||||||
\(708\) | −28.7557 | −1.08070 | ||||||||
\(709\) | 3.12657 | 0.117421 | 0.0587104 | − | 0.998275i | \(-0.481301\pi\) | ||||
0.0587104 | + | 0.998275i | \(0.481301\pi\) | |||||||
\(710\) | 15.3748 | 0.577005 | ||||||||
\(711\) | 3.91330 | 0.146760 | ||||||||
\(712\) | −87.6924 | −3.28641 | ||||||||
\(713\) | 2.03651 | 0.0762678 | ||||||||
\(714\) | 35.7630 | 1.33840 | ||||||||
\(715\) | 5.20343 | 0.194597 | ||||||||
\(716\) | −39.7839 | −1.48679 | ||||||||
\(717\) | −0.173177 | −0.00646741 | ||||||||
\(718\) | 20.1200 | 0.750870 | ||||||||
\(719\) | 0.247381 | 0.00922577 | 0.00461288 | − | 0.999989i | \(-0.498532\pi\) | ||||
0.00461288 | + | 0.999989i | \(0.498532\pi\) | |||||||
\(720\) | 1.93096 | 0.0719625 | ||||||||
\(721\) | 3.24331 | 0.120787 | ||||||||
\(722\) | 35.3707 | 1.31636 | ||||||||
\(723\) | −2.80558 | −0.104341 | ||||||||
\(724\) | 63.3866 | 2.35575 | ||||||||
\(725\) | −46.2054 | −1.71603 | ||||||||
\(726\) | 35.0050 | 1.29916 | ||||||||
\(727\) | −1.34779 | −0.0499869 | −0.0249934 | − | 0.999688i | \(-0.507956\pi\) | ||||
−0.0249934 | + | 0.999688i | \(0.507956\pi\) | |||||||
\(728\) | 74.3083 | 2.75405 | ||||||||
\(729\) | 29.1291 | 1.07885 | ||||||||
\(730\) | 23.4075 | 0.866350 | ||||||||
\(731\) | 21.4136 | 0.792010 | ||||||||
\(732\) | 46.3205 | 1.71205 | ||||||||
\(733\) | −33.5556 | −1.23940 | −0.619702 | − | 0.784837i | \(-0.712747\pi\) | ||||
−0.619702 | + | 0.784837i | \(0.712747\pi\) | |||||||
\(734\) | 64.3675 | 2.37585 | ||||||||
\(735\) | 3.36112 | 0.123977 | ||||||||
\(736\) | −12.4222 | −0.457888 | ||||||||
\(737\) | −18.1085 | −0.667035 | ||||||||
\(738\) | −1.72042 | −0.0633295 | ||||||||
\(739\) | −24.4577 | −0.899690 | −0.449845 | − | 0.893107i | \(-0.648521\pi\) | ||||
−0.449845 | + | 0.893107i | \(0.648521\pi\) | |||||||
\(740\) | −19.0699 | −0.701025 | ||||||||
\(741\) | 19.4487 | 0.714465 | ||||||||
\(742\) | −54.4763 | −1.99989 | ||||||||
\(743\) | −5.00269 | −0.183531 | −0.0917655 | − | 0.995781i | \(-0.529251\pi\) | ||||
−0.0917655 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(744\) | −26.0445 | −0.954837 | ||||||||
\(745\) | 10.9585 | 0.401487 | ||||||||
\(746\) | −24.3470 | −0.891407 | ||||||||
\(747\) | −3.15050 | −0.115271 | ||||||||
\(748\) | −36.6328 | −1.33943 | ||||||||
\(749\) | 21.7951 | 0.796377 | ||||||||
\(750\) | −25.3680 | −0.926308 | ||||||||
\(751\) | 37.8714 | 1.38195 | 0.690974 | − | 0.722880i | \(-0.257182\pi\) | ||||
0.690974 | + | 0.722880i | \(0.257182\pi\) | |||||||
\(752\) | −115.163 | −4.19954 | ||||||||
\(753\) | −1.28154 | −0.0467019 | ||||||||
\(754\) | −131.754 | −4.79821 | ||||||||
\(755\) | 8.26327 | 0.300731 | ||||||||
\(756\) | 51.1912 | 1.86180 | ||||||||
\(757\) | 34.6620 | 1.25981 | 0.629907 | − | 0.776671i | \(-0.283093\pi\) | ||||
0.629907 | + | 0.776671i | \(0.283093\pi\) | |||||||
\(758\) | −46.4691 | −1.68783 | ||||||||
\(759\) | −2.80882 | −0.101954 | ||||||||
\(760\) | 11.1799 | 0.405539 | ||||||||
\(761\) | 47.1092 | 1.70771 | 0.853854 | − | 0.520513i | \(-0.174259\pi\) | ||||
0.853854 | + | 0.520513i | \(0.174259\pi\) | |||||||
\(762\) | 47.2169 | 1.71049 | ||||||||
\(763\) | −18.0954 | −0.655096 | ||||||||
\(764\) | 47.4169 | 1.71548 | ||||||||
\(765\) | 0.787450 | 0.0284703 | ||||||||
\(766\) | −62.2406 | −2.24884 | ||||||||
\(767\) | −17.6967 | −0.638992 | ||||||||
\(768\) | −13.8832 | −0.500967 | ||||||||
\(769\) | −22.3289 | −0.805201 | −0.402601 | − | 0.915376i | \(-0.631894\pi\) | ||||
−0.402601 | + | 0.915376i | \(0.631894\pi\) | |||||||
\(770\) | 5.22369 | 0.188249 | ||||||||
\(771\) | 14.8649 | 0.535348 | ||||||||
\(772\) | 100.761 | 3.62645 | ||||||||
\(773\) | 30.2420 | 1.08773 | 0.543865 | − | 0.839173i | \(-0.316961\pi\) | ||||
0.543865 | + | 0.839173i | \(0.316961\pi\) | |||||||
\(774\) | 3.90294 | 0.140288 | ||||||||
\(775\) | −9.42987 | −0.338731 | ||||||||
\(776\) | 71.1352 | 2.55361 | ||||||||
\(777\) | −19.8516 | −0.712172 | ||||||||
\(778\) | −1.74587 | −0.0625924 | ||||||||
\(779\) | −5.15318 | −0.184632 | ||||||||
\(780\) | −24.7737 | −0.887042 | ||||||||
\(781\) | −16.3942 | −0.586632 | ||||||||
\(782\) | −11.4128 | −0.408120 | ||||||||
\(783\) | −54.1041 | −1.93352 | ||||||||
\(784\) | −35.7095 | −1.27534 | ||||||||
\(785\) | 8.96765 | 0.320069 | ||||||||
\(786\) | 9.32231 | 0.332516 | ||||||||
\(787\) | −10.2073 | −0.363852 | −0.181926 | − | 0.983312i | \(-0.558233\pi\) | ||||
−0.181926 | + | 0.983312i | \(0.558233\pi\) | |||||||
\(788\) | −37.1266 | −1.32258 | ||||||||
\(789\) | 27.4500 | 0.977246 | ||||||||
\(790\) | −20.9617 | −0.745785 | ||||||||
\(791\) | 21.5788 | 0.767255 | ||||||||
\(792\) | −3.97997 | −0.141422 | ||||||||
\(793\) | 28.5064 | 1.01229 | ||||||||
\(794\) | 15.3950 | 0.546347 | ||||||||
\(795\) | 10.8260 | 0.383960 | ||||||||
\(796\) | 37.7850 | 1.33925 | ||||||||
\(797\) | −9.11218 | −0.322770 | −0.161385 | − | 0.986892i | \(-0.551596\pi\) | ||||
−0.161385 | + | 0.986892i | \(0.551596\pi\) | |||||||
\(798\) | 19.5244 | 0.691157 | ||||||||
\(799\) | −46.9636 | −1.66145 | ||||||||
\(800\) | 57.5199 | 2.03364 | ||||||||
\(801\) | −3.37202 | −0.119144 | ||||||||
\(802\) | −54.8686 | −1.93748 | ||||||||
\(803\) | −24.9596 | −0.880805 | ||||||||
\(804\) | 86.2152 | 3.04058 | ||||||||
\(805\) | 1.15920 | 0.0408563 | ||||||||
\(806\) | −26.8892 | −0.947131 | ||||||||
\(807\) | −26.2810 | −0.925133 | ||||||||
\(808\) | 68.8073 | 2.42063 | ||||||||
\(809\) | −21.6998 | −0.762923 | −0.381462 | − | 0.924385i | \(-0.624579\pi\) | ||||
−0.381462 | + | 0.924385i | \(0.624579\pi\) | |||||||
\(810\) | −12.8434 | −0.451270 | ||||||||
\(811\) | −34.7346 | −1.21970 | −0.609848 | − | 0.792518i | \(-0.708770\pi\) | ||||
−0.609848 | + | 0.792518i | \(0.708770\pi\) | |||||||
\(812\) | −94.2131 | −3.30623 | ||||||||
\(813\) | 18.9682 | 0.665244 | ||||||||
\(814\) | 28.5478 | 1.00060 | ||||||||
\(815\) | −1.50766 | −0.0528110 | ||||||||
\(816\) | 75.5085 | 2.64333 | ||||||||
\(817\) | 11.6905 | 0.408999 | ||||||||
\(818\) | −52.6998 | −1.84260 | ||||||||
\(819\) | 2.85736 | 0.0998442 | ||||||||
\(820\) | 6.56412 | 0.229229 | ||||||||
\(821\) | 26.5019 | 0.924924 | 0.462462 | − | 0.886639i | \(-0.346966\pi\) | ||||
0.462462 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(822\) | −1.49177 | −0.0520316 | ||||||||
\(823\) | −32.7115 | −1.14025 | −0.570125 | − | 0.821558i | \(-0.693105\pi\) | ||||
−0.570125 | + | 0.821558i | \(0.693105\pi\) | |||||||
\(824\) | 13.2366 | 0.461117 | ||||||||
\(825\) | 13.0060 | 0.452810 | ||||||||
\(826\) | −17.7656 | −0.618146 | ||||||||
\(827\) | −22.8742 | −0.795414 | −0.397707 | − | 0.917512i | \(-0.630194\pi\) | ||||
−0.397707 | + | 0.917512i | \(0.630194\pi\) | |||||||
\(828\) | −1.48167 | −0.0514917 | ||||||||
\(829\) | 15.6517 | 0.543607 | 0.271804 | − | 0.962353i | \(-0.412380\pi\) | ||||
0.271804 | + | 0.962353i | \(0.412380\pi\) | |||||||
\(830\) | 16.8757 | 0.585765 | ||||||||
\(831\) | 23.0947 | 0.801146 | ||||||||
\(832\) | 57.7053 | 2.00057 | ||||||||
\(833\) | −14.5625 | −0.504559 | ||||||||
\(834\) | −87.6868 | −3.03635 | ||||||||
\(835\) | 5.76461 | 0.199493 | ||||||||
\(836\) | −19.9993 | −0.691690 | ||||||||
\(837\) | −11.0419 | −0.381663 | ||||||||
\(838\) | 94.0790 | 3.24991 | ||||||||
\(839\) | −1.39286 | −0.0480867 | −0.0240434 | − | 0.999711i | \(-0.507654\pi\) | ||||
−0.0240434 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(840\) | −14.8247 | −0.511502 | ||||||||
\(841\) | 70.5741 | 2.43359 | ||||||||
\(842\) | −43.6441 | −1.50407 | ||||||||
\(843\) | 12.9945 | 0.447554 | ||||||||
\(844\) | 122.544 | 4.21815 | ||||||||
\(845\) | −7.34300 | −0.252607 | ||||||||
\(846\) | −8.55980 | −0.294292 | ||||||||
\(847\) | 15.4045 | 0.529304 | ||||||||
\(848\) | −115.019 | −3.94976 | ||||||||
\(849\) | −25.6368 | −0.879852 | ||||||||
\(850\) | 52.8459 | 1.81260 | ||||||||
\(851\) | 6.33509 | 0.217164 | ||||||||
\(852\) | 78.0537 | 2.67407 | ||||||||
\(853\) | −12.5718 | −0.430450 | −0.215225 | − | 0.976565i | \(-0.569048\pi\) | ||||
−0.215225 | + | 0.976565i | \(0.569048\pi\) | |||||||
\(854\) | 28.6174 | 0.979268 | ||||||||
\(855\) | 0.429900 | 0.0147023 | ||||||||
\(856\) | 88.9502 | 3.04025 | ||||||||
\(857\) | −5.87878 | −0.200815 | −0.100408 | − | 0.994946i | \(-0.532015\pi\) | ||||
−0.100408 | + | 0.994946i | \(0.532015\pi\) | |||||||
\(858\) | 37.0864 | 1.26611 | ||||||||
\(859\) | 48.9229 | 1.66923 | 0.834613 | − | 0.550837i | \(-0.185691\pi\) | ||||
0.834613 | + | 0.550837i | \(0.185691\pi\) | |||||||
\(860\) | −14.8914 | −0.507791 | ||||||||
\(861\) | 6.83318 | 0.232874 | ||||||||
\(862\) | −4.39481 | −0.149688 | ||||||||
\(863\) | 32.8555 | 1.11841 | 0.559207 | − | 0.829028i | \(-0.311106\pi\) | ||||
0.559207 | + | 0.829028i | \(0.311106\pi\) | |||||||
\(864\) | 67.3527 | 2.29139 | ||||||||
\(865\) | −11.9753 | −0.407174 | ||||||||
\(866\) | −80.1800 | −2.72463 | ||||||||
\(867\) | 2.85480 | 0.0969539 | ||||||||
\(868\) | −19.2276 | −0.652626 | ||||||||
\(869\) | 22.3517 | 0.758228 | ||||||||
\(870\) | 26.2854 | 0.891158 | ||||||||
\(871\) | 53.0583 | 1.79781 | ||||||||
\(872\) | −73.8506 | −2.50090 | ||||||||
\(873\) | 2.73535 | 0.0925775 | ||||||||
\(874\) | −6.23068 | −0.210756 | ||||||||
\(875\) | −11.1635 | −0.377397 | ||||||||
\(876\) | 118.834 | 4.01502 | ||||||||
\(877\) | 8.68321 | 0.293211 | 0.146606 | − | 0.989195i | \(-0.453165\pi\) | ||||
0.146606 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(878\) | 58.4683 | 1.97321 | ||||||||
\(879\) | 9.25288 | 0.312092 | ||||||||
\(880\) | 11.0291 | 0.371790 | ||||||||
\(881\) | −15.9274 | −0.536607 | −0.268304 | − | 0.963334i | \(-0.586463\pi\) | ||||
−0.268304 | + | 0.963334i | \(0.586463\pi\) | |||||||
\(882\) | −2.65422 | −0.0893722 | ||||||||
\(883\) | −19.6399 | −0.660935 | −0.330467 | − | 0.943817i | \(-0.607206\pi\) | ||||
−0.330467 | + | 0.943817i | \(0.607206\pi\) | |||||||
\(884\) | 107.335 | 3.61007 | ||||||||
\(885\) | 3.53055 | 0.118678 | ||||||||
\(886\) | −49.4977 | −1.66291 | ||||||||
\(887\) | −5.25326 | −0.176387 | −0.0881935 | − | 0.996103i | \(-0.528109\pi\) | ||||
−0.0881935 | + | 0.996103i | \(0.528109\pi\) | |||||||
\(888\) | −81.0181 | −2.71879 | ||||||||
\(889\) | 20.7784 | 0.696887 | ||||||||
\(890\) | 18.0623 | 0.605450 | ||||||||
\(891\) | 13.6950 | 0.458800 | ||||||||
\(892\) | 146.186 | 4.89467 | ||||||||
\(893\) | −25.6393 | −0.857985 | ||||||||
\(894\) | 78.1044 | 2.61220 | ||||||||
\(895\) | 4.88457 | 0.163273 | ||||||||
\(896\) | 10.5574 | 0.352696 | ||||||||
\(897\) | 8.22991 | 0.274789 | ||||||||
\(898\) | −70.7872 | −2.36220 | ||||||||
\(899\) | 20.3217 | 0.677766 | ||||||||
\(900\) | 6.86076 | 0.228692 | ||||||||
\(901\) | −46.9050 | −1.56263 | ||||||||
\(902\) | −9.82653 | −0.327188 | ||||||||
\(903\) | −15.5017 | −0.515866 | ||||||||
\(904\) | 88.0674 | 2.92908 | ||||||||
\(905\) | −7.78245 | −0.258697 | ||||||||
\(906\) | 58.8949 | 1.95665 | ||||||||
\(907\) | −25.8865 | −0.859547 | −0.429774 | − | 0.902937i | \(-0.641407\pi\) | ||||
−0.429774 | + | 0.902937i | \(0.641407\pi\) | |||||||
\(908\) | −89.4180 | −2.96744 | ||||||||
\(909\) | 2.64583 | 0.0877567 | ||||||||
\(910\) | −15.3055 | −0.507374 | ||||||||
\(911\) | −4.88285 | −0.161776 | −0.0808880 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808880 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(912\) | 41.2230 | 1.36503 | ||||||||
\(913\) | −17.9947 | −0.595539 | ||||||||
\(914\) | 40.5982 | 1.34287 | ||||||||
\(915\) | −5.68711 | −0.188010 | ||||||||
\(916\) | 113.383 | 3.74627 | ||||||||
\(917\) | 4.10242 | 0.135474 | ||||||||
\(918\) | 61.8797 | 2.04233 | ||||||||
\(919\) | 2.16483 | 0.0714111 | 0.0357056 | − | 0.999362i | \(-0.488632\pi\) | ||||
0.0357056 | + | 0.999362i | \(0.488632\pi\) | |||||||
\(920\) | 4.73090 | 0.155973 | ||||||||
\(921\) | 19.5985 | 0.645791 | ||||||||
\(922\) | 13.0339 | 0.429250 | ||||||||
\(923\) | 48.0355 | 1.58111 | ||||||||
\(924\) | 26.5193 | 0.872420 | ||||||||
\(925\) | −29.3341 | −0.964499 | ||||||||
\(926\) | −54.6544 | −1.79606 | ||||||||
\(927\) | 0.508982 | 0.0167172 | ||||||||
\(928\) | −123.957 | −4.06909 | ||||||||
\(929\) | 33.1333 | 1.08707 | 0.543534 | − | 0.839387i | \(-0.317086\pi\) | ||||
0.543534 | + | 0.839387i | \(0.317086\pi\) | |||||||
\(930\) | 5.36447 | 0.175908 | ||||||||
\(931\) | −7.95021 | −0.260558 | ||||||||
\(932\) | 60.2724 | 1.97429 | ||||||||
\(933\) | −2.13503 | −0.0698977 | ||||||||
\(934\) | −52.4729 | −1.71697 | ||||||||
\(935\) | 4.49769 | 0.147090 | ||||||||
\(936\) | 11.6614 | 0.381166 | ||||||||
\(937\) | 20.5124 | 0.670109 | 0.335055 | − | 0.942199i | \(-0.391245\pi\) | ||||
0.335055 | + | 0.942199i | \(0.391245\pi\) | |||||||
\(938\) | 53.2649 | 1.73916 | ||||||||
\(939\) | 29.6286 | 0.966892 | ||||||||
\(940\) | 32.6593 | 1.06523 | ||||||||
\(941\) | −38.6191 | −1.25895 | −0.629473 | − | 0.777022i | \(-0.716729\pi\) | ||||
−0.629473 | + | 0.777022i | \(0.716729\pi\) | |||||||
\(942\) | 63.9152 | 2.08247 | ||||||||
\(943\) | −2.18062 | −0.0710108 | ||||||||
\(944\) | −37.5096 | −1.22083 | ||||||||
\(945\) | −6.28512 | −0.204455 | ||||||||
\(946\) | 22.2925 | 0.724791 | ||||||||
\(947\) | −42.5206 | −1.38174 | −0.690868 | − | 0.722981i | \(-0.742771\pi\) | ||||
−0.690868 | + | 0.722981i | \(0.742771\pi\) | |||||||
\(948\) | −106.417 | −3.45627 | ||||||||
\(949\) | 73.1322 | 2.37397 | ||||||||
\(950\) | 28.8506 | 0.936038 | ||||||||
\(951\) | 22.1947 | 0.719713 | ||||||||
\(952\) | 64.2299 | 2.08170 | ||||||||
\(953\) | 39.8417 | 1.29060 | 0.645299 | − | 0.763930i | \(-0.276733\pi\) | ||||
0.645299 | + | 0.763930i | \(0.276733\pi\) | |||||||
\(954\) | −8.54913 | −0.276788 | ||||||||
\(955\) | −5.82173 | −0.188387 | ||||||||
\(956\) | −0.521778 | −0.0168755 | ||||||||
\(957\) | −28.0283 | −0.906027 | ||||||||
\(958\) | 74.3849 | 2.40327 | ||||||||
\(959\) | −0.656476 | −0.0211987 | ||||||||
\(960\) | −11.5124 | −0.371561 | ||||||||
\(961\) | −26.8526 | −0.866214 | ||||||||
\(962\) | −83.6458 | −2.69685 | ||||||||
\(963\) | 3.42038 | 0.110220 | ||||||||
\(964\) | −8.45313 | −0.272257 | ||||||||
\(965\) | −12.3711 | −0.398241 | ||||||||
\(966\) | 8.26195 | 0.265824 | ||||||||
\(967\) | 44.1313 | 1.41917 | 0.709584 | − | 0.704621i | \(-0.248883\pi\) | ||||
0.709584 | + | 0.704621i | \(0.248883\pi\) | |||||||
\(968\) | 62.8685 | 2.02067 | ||||||||
\(969\) | 16.8109 | 0.540043 | ||||||||
\(970\) | −14.6520 | −0.470447 | ||||||||
\(971\) | −33.5441 | −1.07648 | −0.538240 | − | 0.842791i | \(-0.680911\pi\) | ||||
−0.538240 | + | 0.842791i | \(0.680911\pi\) | |||||||
\(972\) | 15.3385 | 0.491984 | ||||||||
\(973\) | −38.5878 | −1.23707 | ||||||||
\(974\) | −37.9587 | −1.21628 | ||||||||
\(975\) | −38.1079 | −1.22043 | ||||||||
\(976\) | 60.4216 | 1.93405 | ||||||||
\(977\) | 15.5289 | 0.496815 | 0.248408 | − | 0.968656i | \(-0.420093\pi\) | ||||
0.248408 | + | 0.968656i | \(0.420093\pi\) | |||||||
\(978\) | −10.7455 | −0.343605 | ||||||||
\(979\) | −19.2600 | −0.615552 | ||||||||
\(980\) | 10.1270 | 0.323494 | ||||||||
\(981\) | −2.83976 | −0.0906666 | ||||||||
\(982\) | −22.3443 | −0.713037 | ||||||||
\(983\) | −32.0934 | −1.02362 | −0.511811 | − | 0.859098i | \(-0.671025\pi\) | ||||
−0.511811 | + | 0.859098i | \(0.671025\pi\) | |||||||
\(984\) | 27.8875 | 0.889021 | ||||||||
\(985\) | 4.55831 | 0.145240 | ||||||||
\(986\) | −113.885 | −3.62682 | ||||||||
\(987\) | 33.9980 | 1.08217 | ||||||||
\(988\) | 58.5984 | 1.86426 | ||||||||
\(989\) | 4.94696 | 0.157304 | ||||||||
\(990\) | 0.819769 | 0.0260540 | ||||||||
\(991\) | −0.298428 | −0.00947987 | −0.00473994 | − | 0.999989i | \(-0.501509\pi\) | ||||
−0.00473994 | + | 0.999989i | \(0.501509\pi\) | |||||||
\(992\) | −25.2979 | −0.803209 | ||||||||
\(993\) | −5.19885 | −0.164980 | ||||||||
\(994\) | 48.2226 | 1.52953 | ||||||||
\(995\) | −4.63915 | −0.147071 | ||||||||
\(996\) | 85.6737 | 2.71467 | ||||||||
\(997\) | −54.0188 | −1.71079 | −0.855396 | − | 0.517975i | \(-0.826686\pi\) | ||||
−0.855396 | + | 0.517975i | \(0.826686\pi\) | |||||||
\(998\) | 63.1515 | 1.99903 | ||||||||
\(999\) | −34.3486 | −1.08674 |
(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 | 8027.2.a.f.1.7 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.7 | ✓ | 176 | 1.1 | even | 1 | trivial |