Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36345 | −1.67121 | −0.835607 | − | 0.549328i | \(-0.814884\pi\) | ||||
−0.835607 | + | 0.549328i | \(0.814884\pi\) | |||||||
\(3\) | 0.649215 | 0.374825 | 0.187412 | − | 0.982281i | \(-0.439990\pi\) | ||||
0.187412 | + | 0.982281i | \(0.439990\pi\) | |||||||
\(4\) | 3.58591 | 1.79295 | ||||||||
\(5\) | −0.526324 | −0.235379 | −0.117690 | − | 0.993050i | \(-0.537549\pi\) | ||||
−0.117690 | + | 0.993050i | \(0.537549\pi\) | |||||||
\(6\) | −1.53439 | −0.626412 | ||||||||
\(7\) | 1.65204 | 0.624414 | 0.312207 | − | 0.950014i | \(-0.398932\pi\) | ||||
0.312207 | + | 0.950014i | \(0.398932\pi\) | |||||||
\(8\) | −3.74822 | −1.32519 | ||||||||
\(9\) | −2.57852 | −0.859506 | ||||||||
\(10\) | 1.24394 | 0.393369 | ||||||||
\(11\) | −0.633045 | −0.190870 | −0.0954352 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954352 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(12\) | 2.32803 | 0.672043 | ||||||||
\(13\) | −4.08101 | −1.13187 | −0.565934 | − | 0.824450i | \(-0.691484\pi\) | ||||
−0.565934 | + | 0.824450i | \(0.691484\pi\) | |||||||
\(14\) | −3.90453 | −1.04353 | ||||||||
\(15\) | −0.341697 | −0.0882259 | ||||||||
\(16\) | 1.68692 | 0.421729 | ||||||||
\(17\) | −1.27562 | −0.309383 | −0.154692 | − | 0.987963i | \(-0.549438\pi\) | ||||
−0.154692 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(18\) | 6.09421 | 1.43642 | ||||||||
\(19\) | −0.310985 | −0.0713448 | −0.0356724 | − | 0.999364i | \(-0.511357\pi\) | ||||
−0.0356724 | + | 0.999364i | \(0.511357\pi\) | |||||||
\(20\) | −1.88735 | −0.422024 | ||||||||
\(21\) | 1.07253 | 0.234046 | ||||||||
\(22\) | 1.49617 | 0.318985 | ||||||||
\(23\) | −3.61411 | −0.753593 | −0.376797 | − | 0.926296i | \(-0.622974\pi\) | ||||
−0.376797 | + | 0.926296i | \(0.622974\pi\) | |||||||
\(24\) | −2.43340 | −0.496716 | ||||||||
\(25\) | −4.72298 | −0.944597 | ||||||||
\(26\) | 9.64527 | 1.89159 | ||||||||
\(27\) | −3.62166 | −0.696989 | ||||||||
\(28\) | 5.92408 | 1.11955 | ||||||||
\(29\) | −2.51840 | −0.467655 | −0.233828 | − | 0.972278i | \(-0.575125\pi\) | ||||
−0.233828 | + | 0.972278i | \(0.575125\pi\) | |||||||
\(30\) | 0.807585 | 0.147444 | ||||||||
\(31\) | −1.97607 | −0.354913 | −0.177456 | − | 0.984129i | \(-0.556787\pi\) | ||||
−0.177456 | + | 0.984129i | \(0.556787\pi\) | |||||||
\(32\) | 3.50948 | 0.620395 | ||||||||
\(33\) | −0.410983 | −0.0715429 | ||||||||
\(34\) | 3.01487 | 0.517046 | ||||||||
\(35\) | −0.869510 | −0.146974 | ||||||||
\(36\) | −9.24633 | −1.54106 | ||||||||
\(37\) | 4.86204 | 0.799314 | 0.399657 | − | 0.916665i | \(-0.369129\pi\) | ||||
0.399657 | + | 0.916665i | \(0.369129\pi\) | |||||||
\(38\) | 0.734997 | 0.119232 | ||||||||
\(39\) | −2.64945 | −0.424252 | ||||||||
\(40\) | 1.97278 | 0.311923 | ||||||||
\(41\) | 2.89719 | 0.452465 | 0.226233 | − | 0.974073i | \(-0.427359\pi\) | ||||
0.226233 | + | 0.974073i | \(0.427359\pi\) | |||||||
\(42\) | −2.53488 | −0.391140 | ||||||||
\(43\) | −10.7661 | −1.64181 | −0.820905 | − | 0.571064i | \(-0.806531\pi\) | ||||
−0.820905 | + | 0.571064i | \(0.806531\pi\) | |||||||
\(44\) | −2.27004 | −0.342222 | ||||||||
\(45\) | 1.35714 | 0.202310 | ||||||||
\(46\) | 8.54177 | 1.25942 | ||||||||
\(47\) | 8.11626 | 1.18388 | 0.591939 | − | 0.805983i | \(-0.298363\pi\) | ||||
0.591939 | + | 0.805983i | \(0.298363\pi\) | |||||||
\(48\) | 1.09517 | 0.158075 | ||||||||
\(49\) | −4.27075 | −0.610107 | ||||||||
\(50\) | 11.1625 | 1.57862 | ||||||||
\(51\) | −0.828153 | −0.115965 | ||||||||
\(52\) | −14.6341 | −2.02939 | ||||||||
\(53\) | 5.26987 | 0.723873 | 0.361936 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361936 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(54\) | 8.55962 | 1.16482 | ||||||||
\(55\) | 0.333187 | 0.0449269 | ||||||||
\(56\) | −6.19222 | −0.827470 | ||||||||
\(57\) | −0.201896 | −0.0267418 | ||||||||
\(58\) | 5.95212 | 0.781552 | ||||||||
\(59\) | 5.54935 | 0.722464 | 0.361232 | − | 0.932476i | \(-0.382356\pi\) | ||||
0.361232 | + | 0.932476i | \(0.382356\pi\) | |||||||
\(60\) | −1.22530 | −0.158185 | ||||||||
\(61\) | 4.30300 | 0.550942 | 0.275471 | − | 0.961309i | \(-0.411166\pi\) | ||||
0.275471 | + | 0.961309i | \(0.411166\pi\) | |||||||
\(62\) | 4.67035 | 0.593135 | ||||||||
\(63\) | −4.25983 | −0.536688 | ||||||||
\(64\) | −11.6683 | −1.45854 | ||||||||
\(65\) | 2.14793 | 0.266418 | ||||||||
\(66\) | 0.971338 | 0.119563 | ||||||||
\(67\) | −3.11613 | −0.380695 | −0.190348 | − | 0.981717i | \(-0.560962\pi\) | ||||
−0.190348 | + | 0.981717i | \(0.560962\pi\) | |||||||
\(68\) | −4.57426 | −0.554710 | ||||||||
\(69\) | −2.34633 | −0.282465 | ||||||||
\(70\) | 2.05504 | 0.245625 | ||||||||
\(71\) | 6.57046 | 0.779771 | 0.389885 | − | 0.920863i | \(-0.372515\pi\) | ||||
0.389885 | + | 0.920863i | \(0.372515\pi\) | |||||||
\(72\) | 9.66485 | 1.13901 | ||||||||
\(73\) | 0.973762 | 0.113970 | 0.0569851 | − | 0.998375i | \(-0.481851\pi\) | ||||
0.0569851 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(74\) | −11.4912 | −1.33582 | ||||||||
\(75\) | −3.06623 | −0.354058 | ||||||||
\(76\) | −1.11516 | −0.127918 | ||||||||
\(77\) | −1.04582 | −0.119182 | ||||||||
\(78\) | 6.26186 | 0.709016 | ||||||||
\(79\) | 4.86469 | 0.547320 | 0.273660 | − | 0.961826i | \(-0.411766\pi\) | ||||
0.273660 | + | 0.961826i | \(0.411766\pi\) | |||||||
\(80\) | −0.887864 | −0.0992663 | ||||||||
\(81\) | 5.38432 | 0.598258 | ||||||||
\(82\) | −6.84738 | −0.756166 | ||||||||
\(83\) | 12.8455 | 1.40997 | 0.704986 | − | 0.709221i | \(-0.250953\pi\) | ||||
0.704986 | + | 0.709221i | \(0.250953\pi\) | |||||||
\(84\) | 3.84600 | 0.419633 | ||||||||
\(85\) | 0.671389 | 0.0728224 | ||||||||
\(86\) | 25.4451 | 2.74382 | ||||||||
\(87\) | −1.63498 | −0.175289 | ||||||||
\(88\) | 2.37279 | 0.252940 | ||||||||
\(89\) | 15.0161 | 1.59170 | 0.795851 | − | 0.605492i | \(-0.207024\pi\) | ||||
0.795851 | + | 0.605492i | \(0.207024\pi\) | |||||||
\(90\) | −3.20753 | −0.338103 | ||||||||
\(91\) | −6.74200 | −0.706754 | ||||||||
\(92\) | −12.9599 | −1.35116 | ||||||||
\(93\) | −1.28290 | −0.133030 | ||||||||
\(94\) | −19.1824 | −1.97851 | ||||||||
\(95\) | 0.163679 | 0.0167931 | ||||||||
\(96\) | 2.27841 | 0.232539 | ||||||||
\(97\) | 11.4793 | 1.16555 | 0.582774 | − | 0.812635i | \(-0.301967\pi\) | ||||
0.582774 | + | 0.812635i | \(0.301967\pi\) | |||||||
\(98\) | 10.0937 | 1.01962 | ||||||||
\(99\) | 1.63232 | 0.164054 | ||||||||
\(100\) | −16.9362 | −1.69362 | ||||||||
\(101\) | 5.98989 | 0.596016 | 0.298008 | − | 0.954563i | \(-0.403678\pi\) | ||||
0.298008 | + | 0.954563i | \(0.403678\pi\) | |||||||
\(102\) | 1.95730 | 0.193801 | ||||||||
\(103\) | −4.94804 | −0.487545 | −0.243772 | − | 0.969832i | \(-0.578385\pi\) | ||||
−0.243772 | + | 0.969832i | \(0.578385\pi\) | |||||||
\(104\) | 15.2965 | 1.49995 | ||||||||
\(105\) | −0.564499 | −0.0550895 | ||||||||
\(106\) | −12.4551 | −1.20975 | ||||||||
\(107\) | 8.12729 | 0.785695 | 0.392847 | − | 0.919604i | \(-0.371490\pi\) | ||||
0.392847 | + | 0.919604i | \(0.371490\pi\) | |||||||
\(108\) | −12.9869 | −1.24967 | ||||||||
\(109\) | −7.64157 | −0.731930 | −0.365965 | − | 0.930629i | \(-0.619261\pi\) | ||||
−0.365965 | + | 0.930629i | \(0.619261\pi\) | |||||||
\(110\) | −0.787471 | −0.0750824 | ||||||||
\(111\) | 3.15651 | 0.299603 | ||||||||
\(112\) | 2.78686 | 0.263334 | ||||||||
\(113\) | 7.67191 | 0.721712 | 0.360856 | − | 0.932621i | \(-0.382485\pi\) | ||||
0.360856 | + | 0.932621i | \(0.382485\pi\) | |||||||
\(114\) | 0.477172 | 0.0446912 | ||||||||
\(115\) | 1.90219 | 0.177380 | ||||||||
\(116\) | −9.03075 | −0.838484 | ||||||||
\(117\) | 10.5230 | 0.972848 | ||||||||
\(118\) | −13.1156 | −1.20739 | ||||||||
\(119\) | −2.10738 | −0.193183 | ||||||||
\(120\) | 1.28076 | 0.116916 | ||||||||
\(121\) | −10.5993 | −0.963569 | ||||||||
\(122\) | −10.1699 | −0.920742 | ||||||||
\(123\) | 1.88090 | 0.169595 | ||||||||
\(124\) | −7.08601 | −0.636342 | ||||||||
\(125\) | 5.11744 | 0.457717 | ||||||||
\(126\) | 10.0679 | 0.896920 | ||||||||
\(127\) | 14.5359 | 1.28985 | 0.644927 | − | 0.764244i | \(-0.276888\pi\) | ||||
0.644927 | + | 0.764244i | \(0.276888\pi\) | |||||||
\(128\) | 20.5586 | 1.81714 | ||||||||
\(129\) | −6.98950 | −0.615391 | ||||||||
\(130\) | −5.07653 | −0.445241 | ||||||||
\(131\) | −4.14418 | −0.362078 | −0.181039 | − | 0.983476i | \(-0.557946\pi\) | ||||
−0.181039 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(132\) | −1.47375 | −0.128273 | ||||||||
\(133\) | −0.513760 | −0.0445487 | ||||||||
\(134\) | 7.36482 | 0.636223 | ||||||||
\(135\) | 1.90617 | 0.164057 | ||||||||
\(136\) | 4.78130 | 0.409993 | ||||||||
\(137\) | −10.3901 | −0.887686 | −0.443843 | − | 0.896105i | \(-0.646385\pi\) | ||||
−0.443843 | + | 0.896105i | \(0.646385\pi\) | |||||||
\(138\) | 5.54545 | 0.472060 | ||||||||
\(139\) | 14.5831 | 1.23692 | 0.618459 | − | 0.785817i | \(-0.287757\pi\) | ||||
0.618459 | + | 0.785817i | \(0.287757\pi\) | |||||||
\(140\) | −3.11798 | −0.263517 | ||||||||
\(141\) | 5.26920 | 0.443747 | ||||||||
\(142\) | −15.5290 | −1.30316 | ||||||||
\(143\) | 2.58346 | 0.216040 | ||||||||
\(144\) | −4.34975 | −0.362479 | ||||||||
\(145\) | 1.32549 | 0.110076 | ||||||||
\(146\) | −2.30144 | −0.190468 | ||||||||
\(147\) | −2.77264 | −0.228683 | ||||||||
\(148\) | 17.4348 | 1.43313 | ||||||||
\(149\) | −0.869103 | −0.0711997 | −0.0355998 | − | 0.999366i | \(-0.511334\pi\) | ||||
−0.0355998 | + | 0.999366i | \(0.511334\pi\) | |||||||
\(150\) | 7.24690 | 0.591707 | ||||||||
\(151\) | 8.95417 | 0.728680 | 0.364340 | − | 0.931266i | \(-0.381295\pi\) | ||||
0.364340 | + | 0.931266i | \(0.381295\pi\) | |||||||
\(152\) | 1.16564 | 0.0945457 | ||||||||
\(153\) | 3.28921 | 0.265917 | ||||||||
\(154\) | 2.47174 | 0.199179 | ||||||||
\(155\) | 1.04005 | 0.0835390 | ||||||||
\(156\) | −9.50069 | −0.760664 | ||||||||
\(157\) | −13.5009 | −1.07749 | −0.538744 | − | 0.842470i | \(-0.681101\pi\) | ||||
−0.538744 | + | 0.842470i | \(0.681101\pi\) | |||||||
\(158\) | −11.4975 | −0.914689 | ||||||||
\(159\) | 3.42128 | 0.271325 | ||||||||
\(160\) | −1.84712 | −0.146028 | ||||||||
\(161\) | −5.97066 | −0.470554 | ||||||||
\(162\) | −12.7256 | −0.999817 | ||||||||
\(163\) | 17.3353 | 1.35781 | 0.678903 | − | 0.734228i | \(-0.262456\pi\) | ||||
0.678903 | + | 0.734228i | \(0.262456\pi\) | |||||||
\(164\) | 10.3891 | 0.811250 | ||||||||
\(165\) | 0.216310 | 0.0168397 | ||||||||
\(166\) | −30.3596 | −2.35636 | ||||||||
\(167\) | −4.66788 | −0.361212 | −0.180606 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180606 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(168\) | −4.02008 | −0.310156 | ||||||||
\(169\) | 3.65463 | 0.281126 | ||||||||
\(170\) | −1.58680 | −0.121702 | ||||||||
\(171\) | 0.801880 | 0.0613213 | ||||||||
\(172\) | −38.6061 | −2.94369 | ||||||||
\(173\) | −9.99524 | −0.759924 | −0.379962 | − | 0.925002i | \(-0.624063\pi\) | ||||
−0.379962 | + | 0.925002i | \(0.624063\pi\) | |||||||
\(174\) | 3.86421 | 0.292945 | ||||||||
\(175\) | −7.80257 | −0.589819 | ||||||||
\(176\) | −1.06790 | −0.0804956 | ||||||||
\(177\) | 3.60273 | 0.270797 | ||||||||
\(178\) | −35.4898 | −2.66007 | ||||||||
\(179\) | 16.4105 | 1.22658 | 0.613291 | − | 0.789857i | \(-0.289845\pi\) | ||||
0.613291 | + | 0.789857i | \(0.289845\pi\) | |||||||
\(180\) | 4.86656 | 0.362732 | ||||||||
\(181\) | 8.86149 | 0.658670 | 0.329335 | − | 0.944213i | \(-0.393176\pi\) | ||||
0.329335 | + | 0.944213i | \(0.393176\pi\) | |||||||
\(182\) | 15.9344 | 1.18114 | ||||||||
\(183\) | 2.79357 | 0.206507 | ||||||||
\(184\) | 13.5465 | 0.998658 | ||||||||
\(185\) | −2.55900 | −0.188142 | ||||||||
\(186\) | 3.03206 | 0.222322 | ||||||||
\(187\) | 0.807526 | 0.0590521 | ||||||||
\(188\) | 29.1042 | 2.12264 | ||||||||
\(189\) | −5.98314 | −0.435209 | ||||||||
\(190\) | −0.386846 | −0.0280648 | ||||||||
\(191\) | −11.6906 | −0.845900 | −0.422950 | − | 0.906153i | \(-0.639005\pi\) | ||||
−0.422950 | + | 0.906153i | \(0.639005\pi\) | |||||||
\(192\) | −7.57526 | −0.546697 | ||||||||
\(193\) | 9.31426 | 0.670455 | 0.335227 | − | 0.942137i | \(-0.391187\pi\) | ||||
0.335227 | + | 0.942137i | \(0.391187\pi\) | |||||||
\(194\) | −27.1308 | −1.94788 | ||||||||
\(195\) | 1.39447 | 0.0998601 | ||||||||
\(196\) | −15.3145 | −1.09389 | ||||||||
\(197\) | −15.1413 | −1.07877 | −0.539385 | − | 0.842059i | \(-0.681343\pi\) | ||||
−0.539385 | + | 0.842059i | \(0.681343\pi\) | |||||||
\(198\) | −3.85791 | −0.274170 | ||||||||
\(199\) | −19.1608 | −1.35827 | −0.679136 | − | 0.734012i | \(-0.737646\pi\) | ||||
−0.679136 | + | 0.734012i | \(0.737646\pi\) | |||||||
\(200\) | 17.7028 | 1.25177 | ||||||||
\(201\) | −2.02304 | −0.142694 | ||||||||
\(202\) | −14.1568 | −0.996070 | ||||||||
\(203\) | −4.16051 | −0.292010 | ||||||||
\(204\) | −2.96968 | −0.207919 | ||||||||
\(205\) | −1.52486 | −0.106501 | ||||||||
\(206\) | 11.6945 | 0.814791 | ||||||||
\(207\) | 9.31904 | 0.647718 | ||||||||
\(208\) | −6.88432 | −0.477342 | ||||||||
\(209\) | 0.196867 | 0.0136176 | ||||||||
\(210\) | 1.33417 | 0.0920662 | ||||||||
\(211\) | 12.8339 | 0.883522 | 0.441761 | − | 0.897133i | \(-0.354354\pi\) | ||||
0.441761 | + | 0.897133i | \(0.354354\pi\) | |||||||
\(212\) | 18.8973 | 1.29787 | ||||||||
\(213\) | 4.26565 | 0.292277 | ||||||||
\(214\) | −19.2085 | −1.31306 | ||||||||
\(215\) | 5.66644 | 0.386448 | ||||||||
\(216\) | 13.5748 | 0.923646 | ||||||||
\(217\) | −3.26456 | −0.221612 | ||||||||
\(218\) | 18.0605 | 1.22321 | ||||||||
\(219\) | 0.632181 | 0.0427188 | ||||||||
\(220\) | 1.19478 | 0.0805518 | ||||||||
\(221\) | 5.20582 | 0.350181 | ||||||||
\(222\) | −7.46026 | −0.500700 | ||||||||
\(223\) | 21.8682 | 1.46441 | 0.732203 | − | 0.681087i | \(-0.238492\pi\) | ||||
0.732203 | + | 0.681087i | \(0.238492\pi\) | |||||||
\(224\) | 5.79782 | 0.387383 | ||||||||
\(225\) | 12.1783 | 0.811887 | ||||||||
\(226\) | −18.1322 | −1.20614 | ||||||||
\(227\) | 3.50310 | 0.232509 | 0.116254 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116254 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(228\) | −0.723980 | −0.0479468 | ||||||||
\(229\) | −17.5497 | −1.15972 | −0.579860 | − | 0.814716i | \(-0.696893\pi\) | ||||
−0.579860 | + | 0.814716i | \(0.696893\pi\) | |||||||
\(230\) | −4.49573 | −0.296440 | ||||||||
\(231\) | −0.678961 | −0.0446724 | ||||||||
\(232\) | 9.43951 | 0.619734 | ||||||||
\(233\) | −3.93239 | −0.257620 | −0.128810 | − | 0.991669i | \(-0.541116\pi\) | ||||
−0.128810 | + | 0.991669i | \(0.541116\pi\) | |||||||
\(234\) | −24.8705 | −1.62584 | ||||||||
\(235\) | −4.27178 | −0.278660 | ||||||||
\(236\) | 19.8995 | 1.29535 | ||||||||
\(237\) | 3.15823 | 0.205149 | ||||||||
\(238\) | 4.98070 | 0.322851 | ||||||||
\(239\) | −23.6035 | −1.52678 | −0.763392 | − | 0.645936i | \(-0.776467\pi\) | ||||
−0.763392 | + | 0.645936i | \(0.776467\pi\) | |||||||
\(240\) | −0.576415 | −0.0372074 | ||||||||
\(241\) | 3.80978 | 0.245410 | 0.122705 | − | 0.992443i | \(-0.460843\pi\) | ||||
0.122705 | + | 0.992443i | \(0.460843\pi\) | |||||||
\(242\) | 25.0508 | 1.61033 | ||||||||
\(243\) | 14.3606 | 0.921231 | ||||||||
\(244\) | 15.4301 | 0.987814 | ||||||||
\(245\) | 2.24780 | 0.143607 | ||||||||
\(246\) | −4.44542 | −0.283430 | ||||||||
\(247\) | 1.26913 | 0.0807529 | ||||||||
\(248\) | 7.40674 | 0.470329 | ||||||||
\(249\) | 8.33947 | 0.528492 | ||||||||
\(250\) | −12.0948 | −0.764943 | ||||||||
\(251\) | 15.0718 | 0.951322 | 0.475661 | − | 0.879629i | \(-0.342209\pi\) | ||||
0.475661 | + | 0.879629i | \(0.342209\pi\) | |||||||
\(252\) | −15.2753 | −0.962256 | ||||||||
\(253\) | 2.28789 | 0.143839 | ||||||||
\(254\) | −34.3549 | −2.15562 | ||||||||
\(255\) | 0.435876 | 0.0272956 | ||||||||
\(256\) | −25.2526 | −1.57829 | ||||||||
\(257\) | −31.1104 | −1.94061 | −0.970306 | − | 0.241882i | \(-0.922235\pi\) | ||||
−0.970306 | + | 0.241882i | \(0.922235\pi\) | |||||||
\(258\) | 16.5193 | 1.02845 | ||||||||
\(259\) | 8.03230 | 0.499103 | ||||||||
\(260\) | 7.70228 | 0.477675 | ||||||||
\(261\) | 6.49375 | 0.401953 | ||||||||
\(262\) | 9.79456 | 0.605110 | ||||||||
\(263\) | −8.72424 | −0.537960 | −0.268980 | − | 0.963146i | \(-0.586686\pi\) | ||||
−0.268980 | + | 0.963146i | \(0.586686\pi\) | |||||||
\(264\) | 1.54045 | 0.0948083 | ||||||||
\(265\) | −2.77366 | −0.170384 | ||||||||
\(266\) | 1.21425 | 0.0744503 | ||||||||
\(267\) | 9.74867 | 0.596609 | ||||||||
\(268\) | −11.1741 | −0.682569 | ||||||||
\(269\) | −31.0441 | −1.89279 | −0.946396 | − | 0.323010i | \(-0.895305\pi\) | ||||
−0.946396 | + | 0.323010i | \(0.895305\pi\) | |||||||
\(270\) | −4.50513 | −0.274174 | ||||||||
\(271\) | 8.71066 | 0.529135 | 0.264567 | − | 0.964367i | \(-0.414771\pi\) | ||||
0.264567 | + | 0.964367i | \(0.414771\pi\) | |||||||
\(272\) | −2.15187 | −0.130476 | ||||||||
\(273\) | −4.37701 | −0.264909 | ||||||||
\(274\) | 24.5565 | 1.48351 | ||||||||
\(275\) | 2.98986 | 0.180296 | ||||||||
\(276\) | −8.41373 | −0.506447 | ||||||||
\(277\) | 30.9394 | 1.85897 | 0.929484 | − | 0.368861i | \(-0.120252\pi\) | ||||
0.929484 | + | 0.368861i | \(0.120252\pi\) | |||||||
\(278\) | −34.4663 | −2.06715 | ||||||||
\(279\) | 5.09534 | 0.305050 | ||||||||
\(280\) | 3.25911 | 0.194769 | ||||||||
\(281\) | 32.1693 | 1.91906 | 0.959530 | − | 0.281607i | \(-0.0908673\pi\) | ||||
0.959530 | + | 0.281607i | \(0.0908673\pi\) | |||||||
\(282\) | −12.4535 | −0.741595 | ||||||||
\(283\) | −11.3371 | −0.673919 | −0.336960 | − | 0.941519i | \(-0.609399\pi\) | ||||
−0.336960 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(284\) | 23.5611 | 1.39809 | ||||||||
\(285\) | 0.106263 | 0.00629445 | ||||||||
\(286\) | −6.10589 | −0.361049 | ||||||||
\(287\) | 4.78629 | 0.282526 | ||||||||
\(288\) | −9.04927 | −0.533234 | ||||||||
\(289\) | −15.3728 | −0.904282 | ||||||||
\(290\) | −3.13274 | −0.183961 | ||||||||
\(291\) | 7.45254 | 0.436876 | ||||||||
\(292\) | 3.49182 | 0.204343 | ||||||||
\(293\) | 5.05427 | 0.295274 | 0.147637 | − | 0.989042i | \(-0.452833\pi\) | ||||
0.147637 | + | 0.989042i | \(0.452833\pi\) | |||||||
\(294\) | 6.55300 | 0.382179 | ||||||||
\(295\) | −2.92076 | −0.170053 | ||||||||
\(296\) | −18.2240 | −1.05925 | ||||||||
\(297\) | 2.29268 | 0.133035 | ||||||||
\(298\) | 2.05408 | 0.118990 | ||||||||
\(299\) | 14.7492 | 0.852968 | ||||||||
\(300\) | −10.9952 | −0.634810 | ||||||||
\(301\) | −17.7860 | −1.02517 | ||||||||
\(302\) | −21.1628 | −1.21778 | ||||||||
\(303\) | 3.88873 | 0.223402 | ||||||||
\(304\) | −0.524605 | −0.0300882 | ||||||||
\(305\) | −2.26477 | −0.129680 | ||||||||
\(306\) | −7.77390 | −0.444404 | ||||||||
\(307\) | −18.1759 | −1.03735 | −0.518677 | − | 0.854970i | \(-0.673575\pi\) | ||||
−0.518677 | + | 0.854970i | \(0.673575\pi\) | |||||||
\(308\) | −3.75021 | −0.213688 | ||||||||
\(309\) | −3.21234 | −0.182744 | ||||||||
\(310\) | −2.45812 | −0.139612 | ||||||||
\(311\) | 5.07837 | 0.287968 | 0.143984 | − | 0.989580i | \(-0.454009\pi\) | ||||
0.143984 | + | 0.989580i | \(0.454009\pi\) | |||||||
\(312\) | 9.93073 | 0.562217 | ||||||||
\(313\) | −27.1417 | −1.53414 | −0.767071 | − | 0.641563i | \(-0.778286\pi\) | ||||
−0.767071 | + | 0.641563i | \(0.778286\pi\) | |||||||
\(314\) | 31.9087 | 1.80071 | ||||||||
\(315\) | 2.24205 | 0.126325 | ||||||||
\(316\) | 17.4443 | 0.981320 | ||||||||
\(317\) | 19.0628 | 1.07067 | 0.535337 | − | 0.844638i | \(-0.320185\pi\) | ||||
0.535337 | + | 0.844638i | \(0.320185\pi\) | |||||||
\(318\) | −8.08604 | −0.453442 | ||||||||
\(319\) | 1.59426 | 0.0892615 | ||||||||
\(320\) | 6.14132 | 0.343310 | ||||||||
\(321\) | 5.27636 | 0.294498 | ||||||||
\(322\) | 14.1114 | 0.786396 | ||||||||
\(323\) | 0.396698 | 0.0220729 | ||||||||
\(324\) | 19.3077 | 1.07265 | ||||||||
\(325\) | 19.2745 | 1.06916 | ||||||||
\(326\) | −40.9712 | −2.26918 | ||||||||
\(327\) | −4.96103 | −0.274345 | ||||||||
\(328\) | −10.8593 | −0.599605 | ||||||||
\(329\) | 13.4084 | 0.739230 | ||||||||
\(330\) | −0.511238 | −0.0281427 | ||||||||
\(331\) | −9.27026 | −0.509540 | −0.254770 | − | 0.967002i | \(-0.582000\pi\) | ||||
−0.254770 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(332\) | 46.0626 | 2.52802 | ||||||||
\(333\) | −12.5369 | −0.687015 | ||||||||
\(334\) | 11.0323 | 0.603662 | ||||||||
\(335\) | 1.64009 | 0.0896077 | ||||||||
\(336\) | 1.80927 | 0.0987039 | ||||||||
\(337\) | −19.9624 | −1.08742 | −0.543710 | − | 0.839273i | \(-0.682981\pi\) | ||||
−0.543710 | + | 0.839273i | \(0.682981\pi\) | |||||||
\(338\) | −8.63755 | −0.469821 | ||||||||
\(339\) | 4.98072 | 0.270516 | ||||||||
\(340\) | 2.40754 | 0.130567 | ||||||||
\(341\) | 1.25094 | 0.0677423 | ||||||||
\(342\) | −1.89521 | −0.102481 | ||||||||
\(343\) | −18.6198 | −1.00537 | ||||||||
\(344\) | 40.3536 | 2.17572 | ||||||||
\(345\) | 1.23493 | 0.0664864 | ||||||||
\(346\) | 23.6233 | 1.27000 | ||||||||
\(347\) | 23.2231 | 1.24668 | 0.623340 | − | 0.781951i | \(-0.285775\pi\) | ||||
0.623340 | + | 0.781951i | \(0.285775\pi\) | |||||||
\(348\) | −5.86290 | −0.314285 | ||||||||
\(349\) | −19.9715 | −1.06905 | −0.534524 | − | 0.845153i | \(-0.679509\pi\) | ||||
−0.534524 | + | 0.845153i | \(0.679509\pi\) | |||||||
\(350\) | 18.4410 | 0.985714 | ||||||||
\(351\) | 14.7800 | 0.788899 | ||||||||
\(352\) | −2.22166 | −0.118415 | ||||||||
\(353\) | 6.19470 | 0.329711 | 0.164855 | − | 0.986318i | \(-0.447284\pi\) | ||||
0.164855 | + | 0.986318i | \(0.447284\pi\) | |||||||
\(354\) | −8.51487 | −0.452560 | ||||||||
\(355\) | −3.45819 | −0.183542 | ||||||||
\(356\) | 53.8463 | 2.85385 | ||||||||
\(357\) | −1.36814 | −0.0724099 | ||||||||
\(358\) | −38.7855 | −2.04988 | ||||||||
\(359\) | 27.9578 | 1.47556 | 0.737778 | − | 0.675044i | \(-0.235875\pi\) | ||||
0.737778 | + | 0.675044i | \(0.235875\pi\) | |||||||
\(360\) | −5.08684 | −0.268100 | ||||||||
\(361\) | −18.9033 | −0.994910 | ||||||||
\(362\) | −20.9437 | −1.10078 | ||||||||
\(363\) | −6.88120 | −0.361169 | ||||||||
\(364\) | −24.1762 | −1.26718 | ||||||||
\(365\) | −0.512514 | −0.0268262 | ||||||||
\(366\) | −6.60247 | −0.345117 | ||||||||
\(367\) | 7.43665 | 0.388190 | 0.194095 | − | 0.980983i | \(-0.437823\pi\) | ||||
0.194095 | + | 0.980983i | \(0.437823\pi\) | |||||||
\(368\) | −6.09670 | −0.317812 | ||||||||
\(369\) | −7.47047 | −0.388897 | ||||||||
\(370\) | 6.04809 | 0.314425 | ||||||||
\(371\) | 8.70606 | 0.451996 | ||||||||
\(372\) | −4.60034 | −0.238517 | ||||||||
\(373\) | 6.51575 | 0.337373 | 0.168686 | − | 0.985670i | \(-0.446048\pi\) | ||||
0.168686 | + | 0.985670i | \(0.446048\pi\) | |||||||
\(374\) | −1.90855 | −0.0986887 | ||||||||
\(375\) | 3.32232 | 0.171564 | ||||||||
\(376\) | −30.4215 | −1.56887 | ||||||||
\(377\) | 10.2776 | 0.529324 | ||||||||
\(378\) | 14.1409 | 0.727328 | ||||||||
\(379\) | 9.91005 | 0.509045 | 0.254523 | − | 0.967067i | \(-0.418082\pi\) | ||||
0.254523 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(380\) | 0.586936 | 0.0301092 | ||||||||
\(381\) | 9.43694 | 0.483469 | ||||||||
\(382\) | 27.6301 | 1.41368 | ||||||||
\(383\) | −0.632507 | −0.0323196 | −0.0161598 | − | 0.999869i | \(-0.505144\pi\) | ||||
−0.0161598 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(384\) | 13.3469 | 0.681109 | ||||||||
\(385\) | 0.550439 | 0.0280530 | ||||||||
\(386\) | −22.0138 | −1.12047 | ||||||||
\(387\) | 27.7605 | 1.41115 | ||||||||
\(388\) | 41.1637 | 2.08977 | ||||||||
\(389\) | −6.18092 | −0.313385 | −0.156693 | − | 0.987647i | \(-0.550083\pi\) | ||||
−0.156693 | + | 0.987647i | \(0.550083\pi\) | |||||||
\(390\) | −3.29576 | −0.166887 | ||||||||
\(391\) | 4.61023 | 0.233149 | ||||||||
\(392\) | 16.0077 | 0.808511 | ||||||||
\(393\) | −2.69046 | −0.135716 | ||||||||
\(394\) | 35.7857 | 1.80286 | ||||||||
\(395\) | −2.56040 | −0.128828 | ||||||||
\(396\) | 5.85335 | 0.294142 | ||||||||
\(397\) | 15.1784 | 0.761782 | 0.380891 | − | 0.924620i | \(-0.375617\pi\) | ||||
0.380891 | + | 0.924620i | \(0.375617\pi\) | |||||||
\(398\) | 45.2856 | 2.26996 | ||||||||
\(399\) | −0.333541 | −0.0166979 | ||||||||
\(400\) | −7.96728 | −0.398364 | ||||||||
\(401\) | 33.4282 | 1.66932 | 0.834662 | − | 0.550762i | \(-0.185663\pi\) | ||||
0.834662 | + | 0.550762i | \(0.185663\pi\) | |||||||
\(402\) | 4.78135 | 0.238472 | ||||||||
\(403\) | 8.06436 | 0.401715 | ||||||||
\(404\) | 21.4792 | 1.06863 | ||||||||
\(405\) | −2.83390 | −0.140817 | ||||||||
\(406\) | 9.83316 | 0.488012 | ||||||||
\(407\) | −3.07789 | −0.152565 | ||||||||
\(408\) | 3.10410 | 0.153676 | ||||||||
\(409\) | 0.408352 | 0.0201917 | 0.0100959 | − | 0.999949i | \(-0.496786\pi\) | ||||
0.0100959 | + | 0.999949i | \(0.496786\pi\) | |||||||
\(410\) | 3.60394 | 0.177986 | ||||||||
\(411\) | −6.74541 | −0.332726 | ||||||||
\(412\) | −17.7432 | −0.874145 | ||||||||
\(413\) | 9.16778 | 0.451117 | ||||||||
\(414\) | −22.0251 | −1.08248 | ||||||||
\(415\) | −6.76087 | −0.331878 | ||||||||
\(416\) | −14.3222 | −0.702205 | ||||||||
\(417\) | 9.46754 | 0.463627 | ||||||||
\(418\) | −0.465287 | −0.0227579 | ||||||||
\(419\) | −24.8485 | −1.21393 | −0.606964 | − | 0.794729i | \(-0.707613\pi\) | ||||
−0.606964 | + | 0.794729i | \(0.707613\pi\) | |||||||
\(420\) | −2.02424 | −0.0987728 | ||||||||
\(421\) | −6.48342 | −0.315983 | −0.157991 | − | 0.987441i | \(-0.550502\pi\) | ||||
−0.157991 | + | 0.987441i | \(0.550502\pi\) | |||||||
\(422\) | −30.3323 | −1.47655 | ||||||||
\(423\) | −20.9279 | −1.01755 | ||||||||
\(424\) | −19.7526 | −0.959272 | ||||||||
\(425\) | 6.02474 | 0.292243 | ||||||||
\(426\) | −10.0817 | −0.488458 | ||||||||
\(427\) | 7.10874 | 0.344016 | ||||||||
\(428\) | 29.1437 | 1.40871 | ||||||||
\(429\) | 1.67722 | 0.0809771 | ||||||||
\(430\) | −13.3924 | −0.645837 | ||||||||
\(431\) | 3.48121 | 0.167684 | 0.0838421 | − | 0.996479i | \(-0.473281\pi\) | ||||
0.0838421 | + | 0.996479i | \(0.473281\pi\) | |||||||
\(432\) | −6.10944 | −0.293941 | ||||||||
\(433\) | 16.8220 | 0.808413 | 0.404206 | − | 0.914668i | \(-0.367548\pi\) | ||||
0.404206 | + | 0.914668i | \(0.367548\pi\) | |||||||
\(434\) | 7.71562 | 0.370362 | ||||||||
\(435\) | 0.860531 | 0.0412593 | ||||||||
\(436\) | −27.4020 | −1.31232 | ||||||||
\(437\) | 1.12393 | 0.0537649 | ||||||||
\(438\) | −1.49413 | −0.0713923 | ||||||||
\(439\) | −28.9313 | −1.38082 | −0.690408 | − | 0.723420i | \(-0.742569\pi\) | ||||
−0.690408 | + | 0.723420i | \(0.742569\pi\) | |||||||
\(440\) | −1.24886 | −0.0595369 | ||||||||
\(441\) | 11.0122 | 0.524391 | ||||||||
\(442\) | −12.3037 | −0.585228 | ||||||||
\(443\) | 14.6616 | 0.696592 | 0.348296 | − | 0.937385i | \(-0.386760\pi\) | ||||
0.348296 | + | 0.937385i | \(0.386760\pi\) | |||||||
\(444\) | 11.3189 | 0.537173 | ||||||||
\(445\) | −7.90332 | −0.374653 | ||||||||
\(446\) | −51.6845 | −2.44733 | ||||||||
\(447\) | −0.564235 | −0.0266874 | ||||||||
\(448\) | −19.2766 | −0.910734 | ||||||||
\(449\) | 22.4037 | 1.05730 | 0.528649 | − | 0.848841i | \(-0.322699\pi\) | ||||
0.528649 | + | 0.848841i | \(0.322699\pi\) | |||||||
\(450\) | −28.7828 | −1.35684 | ||||||||
\(451\) | −1.83405 | −0.0863622 | ||||||||
\(452\) | 27.5108 | 1.29400 | ||||||||
\(453\) | 5.81318 | 0.273127 | ||||||||
\(454\) | −8.27941 | −0.388572 | ||||||||
\(455\) | 3.54848 | 0.166355 | ||||||||
\(456\) | 0.756750 | 0.0354381 | ||||||||
\(457\) | 32.9272 | 1.54027 | 0.770135 | − | 0.637881i | \(-0.220189\pi\) | ||||
0.770135 | + | 0.637881i | \(0.220189\pi\) | |||||||
\(458\) | 41.4780 | 1.93814 | ||||||||
\(459\) | 4.61987 | 0.215637 | ||||||||
\(460\) | 6.82108 | 0.318034 | ||||||||
\(461\) | 12.2143 | 0.568876 | 0.284438 | − | 0.958695i | \(-0.408193\pi\) | ||||
0.284438 | + | 0.958695i | \(0.408193\pi\) | |||||||
\(462\) | 1.60469 | 0.0746571 | ||||||||
\(463\) | 40.6005 | 1.88686 | 0.943432 | − | 0.331567i | \(-0.107577\pi\) | ||||
0.943432 | + | 0.331567i | \(0.107577\pi\) | |||||||
\(464\) | −4.24833 | −0.197224 | ||||||||
\(465\) | 0.675218 | 0.0313125 | ||||||||
\(466\) | 9.29402 | 0.430537 | ||||||||
\(467\) | 31.2808 | 1.44750 | 0.723751 | − | 0.690061i | \(-0.242416\pi\) | ||||
0.723751 | + | 0.690061i | \(0.242416\pi\) | |||||||
\(468\) | 37.7344 | 1.74427 | ||||||||
\(469\) | −5.14798 | −0.237711 | ||||||||
\(470\) | 10.0961 | 0.465700 | ||||||||
\(471\) | −8.76498 | −0.403869 | ||||||||
\(472\) | −20.8002 | −0.957406 | ||||||||
\(473\) | 6.81541 | 0.313373 | ||||||||
\(474\) | −7.46433 | −0.342848 | ||||||||
\(475\) | 1.46878 | 0.0673920 | ||||||||
\(476\) | −7.55687 | −0.346369 | ||||||||
\(477\) | −13.5885 | −0.622173 | ||||||||
\(478\) | 55.7857 | 2.55158 | ||||||||
\(479\) | 20.1463 | 0.920509 | 0.460255 | − | 0.887787i | \(-0.347758\pi\) | ||||
0.460255 | + | 0.887787i | \(0.347758\pi\) | |||||||
\(480\) | −1.19918 | −0.0547349 | ||||||||
\(481\) | −19.8420 | −0.904718 | ||||||||
\(482\) | −9.00423 | −0.410132 | ||||||||
\(483\) | −3.87624 | −0.176375 | ||||||||
\(484\) | −38.0079 | −1.72763 | ||||||||
\(485\) | −6.04183 | −0.274345 | ||||||||
\(486\) | −33.9405 | −1.53957 | ||||||||
\(487\) | −6.32709 | −0.286708 | −0.143354 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143354 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(488\) | −16.1286 | −0.730106 | ||||||||
\(489\) | 11.2543 | 0.508939 | ||||||||
\(490\) | −5.31256 | −0.239997 | ||||||||
\(491\) | −38.6544 | −1.74445 | −0.872223 | − | 0.489108i | \(-0.837322\pi\) | ||||
−0.872223 | + | 0.489108i | \(0.837322\pi\) | |||||||
\(492\) | 6.74474 | 0.304076 | ||||||||
\(493\) | 3.21252 | 0.144685 | ||||||||
\(494\) | −2.99953 | −0.134955 | ||||||||
\(495\) | −0.859128 | −0.0386150 | ||||||||
\(496\) | −3.33347 | −0.149677 | ||||||||
\(497\) | 10.8547 | 0.486900 | ||||||||
\(498\) | −19.7099 | −0.883224 | ||||||||
\(499\) | 38.0515 | 1.70342 | 0.851709 | − | 0.524014i | \(-0.175566\pi\) | ||||
0.851709 | + | 0.524014i | \(0.175566\pi\) | |||||||
\(500\) | 18.3507 | 0.820666 | ||||||||
\(501\) | −3.03046 | −0.135391 | ||||||||
\(502\) | −35.6214 | −1.58986 | ||||||||
\(503\) | 25.1828 | 1.12285 | 0.561423 | − | 0.827529i | \(-0.310254\pi\) | ||||
0.561423 | + | 0.827529i | \(0.310254\pi\) | |||||||
\(504\) | 15.9668 | 0.711216 | ||||||||
\(505\) | −3.15262 | −0.140290 | ||||||||
\(506\) | −5.40733 | −0.240385 | ||||||||
\(507\) | 2.37264 | 0.105373 | ||||||||
\(508\) | 52.1244 | 2.31265 | ||||||||
\(509\) | 17.0270 | 0.754709 | 0.377355 | − | 0.926069i | \(-0.376834\pi\) | ||||
0.377355 | + | 0.926069i | \(0.376834\pi\) | |||||||
\(510\) | −1.03017 | −0.0456168 | ||||||||
\(511\) | 1.60870 | 0.0711646 | ||||||||
\(512\) | 18.5661 | 0.820512 | ||||||||
\(513\) | 1.12628 | 0.0497265 | ||||||||
\(514\) | 73.5279 | 3.24318 | ||||||||
\(515\) | 2.60427 | 0.114758 | ||||||||
\(516\) | −25.0637 | −1.10337 | ||||||||
\(517\) | −5.13796 | −0.225967 | ||||||||
\(518\) | −18.9839 | −0.834107 | ||||||||
\(519\) | −6.48906 | −0.284838 | ||||||||
\(520\) | −8.05091 | −0.353056 | ||||||||
\(521\) | 21.3881 | 0.937029 | 0.468515 | − | 0.883456i | \(-0.344789\pi\) | ||||
0.468515 | + | 0.883456i | \(0.344789\pi\) | |||||||
\(522\) | −15.3477 | −0.671749 | ||||||||
\(523\) | 1.55238 | 0.0678810 | 0.0339405 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339405 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(524\) | −14.8606 | −0.649190 | ||||||||
\(525\) | −5.06555 | −0.221079 | ||||||||
\(526\) | 20.6193 | 0.899045 | ||||||||
\(527\) | 2.52072 | 0.109804 | ||||||||
\(528\) | −0.693294 | −0.0301717 | ||||||||
\(529\) | −9.93824 | −0.432097 | ||||||||
\(530\) | 6.55541 | 0.284749 | ||||||||
\(531\) | −14.3091 | −0.620963 | ||||||||
\(532\) | −1.84230 | −0.0798737 | ||||||||
\(533\) | −11.8235 | −0.512131 | ||||||||
\(534\) | −23.0405 | −0.997061 | ||||||||
\(535\) | −4.27759 | −0.184936 | ||||||||
\(536\) | 11.6799 | 0.504496 | ||||||||
\(537\) | 10.6540 | 0.459753 | ||||||||
\(538\) | 73.3712 | 3.16326 | ||||||||
\(539\) | 2.70358 | 0.116451 | ||||||||
\(540\) | 6.83533 | 0.294146 | ||||||||
\(541\) | 0.480736 | 0.0206684 | 0.0103342 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103342 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(542\) | −20.5872 | −0.884297 | ||||||||
\(543\) | 5.75302 | 0.246886 | ||||||||
\(544\) | −4.47677 | −0.191940 | ||||||||
\(545\) | 4.02194 | 0.172281 | ||||||||
\(546\) | 10.3449 | 0.442719 | ||||||||
\(547\) | 16.5777 | 0.708810 | 0.354405 | − | 0.935092i | \(-0.384683\pi\) | ||||
0.354405 | + | 0.935092i | \(0.384683\pi\) | |||||||
\(548\) | −37.2579 | −1.59158 | ||||||||
\(549\) | −11.0954 | −0.473538 | ||||||||
\(550\) | −7.06640 | −0.301312 | ||||||||
\(551\) | 0.783184 | 0.0333648 | ||||||||
\(552\) | 8.79457 | 0.374322 | ||||||||
\(553\) | 8.03668 | 0.341754 | ||||||||
\(554\) | −73.1238 | −3.10673 | ||||||||
\(555\) | −1.66134 | −0.0705202 | ||||||||
\(556\) | 52.2935 | 2.21774 | ||||||||
\(557\) | −25.3169 | −1.07271 | −0.536356 | − | 0.843992i | \(-0.680200\pi\) | ||||
−0.536356 | + | 0.843992i | \(0.680200\pi\) | |||||||
\(558\) | −12.0426 | −0.509803 | ||||||||
\(559\) | 43.9364 | 1.85831 | ||||||||
\(560\) | −1.46679 | −0.0619832 | ||||||||
\(561\) | 0.524258 | 0.0221342 | ||||||||
\(562\) | −76.0306 | −3.20716 | ||||||||
\(563\) | −24.4573 | −1.03075 | −0.515376 | − | 0.856964i | \(-0.672348\pi\) | ||||
−0.515376 | + | 0.856964i | \(0.672348\pi\) | |||||||
\(564\) | 18.8949 | 0.795617 | ||||||||
\(565\) | −4.03791 | −0.169876 | ||||||||
\(566\) | 26.7946 | 1.12626 | ||||||||
\(567\) | 8.89513 | 0.373560 | ||||||||
\(568\) | −24.6275 | −1.03335 | ||||||||
\(569\) | −22.3472 | −0.936841 | −0.468421 | − | 0.883506i | \(-0.655177\pi\) | ||||
−0.468421 | + | 0.883506i | \(0.655177\pi\) | |||||||
\(570\) | −0.251147 | −0.0105194 | ||||||||
\(571\) | 25.1290 | 1.05162 | 0.525808 | − | 0.850603i | \(-0.323763\pi\) | ||||
0.525808 | + | 0.850603i | \(0.323763\pi\) | |||||||
\(572\) | 9.26406 | 0.387350 | ||||||||
\(573\) | −7.58970 | −0.317064 | ||||||||
\(574\) | −11.3122 | −0.472161 | ||||||||
\(575\) | 17.0694 | 0.711842 | ||||||||
\(576\) | 30.0870 | 1.25363 | ||||||||
\(577\) | 5.14159 | 0.214047 | 0.107024 | − | 0.994256i | \(-0.465868\pi\) | ||||
0.107024 | + | 0.994256i | \(0.465868\pi\) | |||||||
\(578\) | 36.3329 | 1.51125 | ||||||||
\(579\) | 6.04696 | 0.251303 | ||||||||
\(580\) | 4.75310 | 0.197362 | ||||||||
\(581\) | 21.2213 | 0.880406 | ||||||||
\(582\) | −17.6137 | −0.730113 | ||||||||
\(583\) | −3.33607 | −0.138166 | ||||||||
\(584\) | −3.64987 | −0.151033 | ||||||||
\(585\) | −5.53848 | −0.228988 | ||||||||
\(586\) | −11.9455 | −0.493465 | ||||||||
\(587\) | 27.8853 | 1.15095 | 0.575474 | − | 0.817820i | \(-0.304817\pi\) | ||||
0.575474 | + | 0.817820i | \(0.304817\pi\) | |||||||
\(588\) | −9.94242 | −0.410019 | ||||||||
\(589\) | 0.614528 | 0.0253212 | ||||||||
\(590\) | 6.90307 | 0.284195 | ||||||||
\(591\) | −9.82995 | −0.404350 | ||||||||
\(592\) | 8.20185 | 0.337094 | ||||||||
\(593\) | −47.1304 | −1.93541 | −0.967706 | − | 0.252080i | \(-0.918885\pi\) | ||||
−0.967706 | + | 0.252080i | \(0.918885\pi\) | |||||||
\(594\) | −5.41863 | −0.222329 | ||||||||
\(595\) | 1.10916 | 0.0454713 | ||||||||
\(596\) | −3.11652 | −0.127658 | ||||||||
\(597\) | −12.4395 | −0.509114 | ||||||||
\(598\) | −34.8590 | −1.42549 | ||||||||
\(599\) | 13.1755 | 0.538337 | 0.269169 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269169 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(600\) | 11.4929 | 0.469196 | ||||||||
\(601\) | −11.7942 | −0.481096 | −0.240548 | − | 0.970637i | \(-0.577327\pi\) | ||||
−0.240548 | + | 0.970637i | \(0.577327\pi\) | |||||||
\(602\) | 42.0364 | 1.71328 | ||||||||
\(603\) | 8.03499 | 0.327210 | ||||||||
\(604\) | 32.1088 | 1.30649 | ||||||||
\(605\) | 5.57864 | 0.226804 | ||||||||
\(606\) | −9.19082 | −0.373352 | ||||||||
\(607\) | 28.4747 | 1.15575 | 0.577877 | − | 0.816124i | \(-0.303881\pi\) | ||||
0.577877 | + | 0.816124i | \(0.303881\pi\) | |||||||
\(608\) | −1.09140 | −0.0442619 | ||||||||
\(609\) | −2.70107 | −0.109453 | ||||||||
\(610\) | 5.35267 | 0.216723 | ||||||||
\(611\) | −33.1225 | −1.33999 | ||||||||
\(612\) | 11.7948 | 0.476777 | ||||||||
\(613\) | 25.2323 | 1.01912 | 0.509562 | − | 0.860434i | \(-0.329808\pi\) | ||||
0.509562 | + | 0.860434i | \(0.329808\pi\) | |||||||
\(614\) | 42.9579 | 1.73364 | ||||||||
\(615\) | −0.989963 | −0.0399192 | ||||||||
\(616\) | 3.91995 | 0.157939 | ||||||||
\(617\) | 32.1226 | 1.29321 | 0.646603 | − | 0.762827i | \(-0.276189\pi\) | ||||
0.646603 | + | 0.762827i | \(0.276189\pi\) | |||||||
\(618\) | 7.59222 | 0.305404 | ||||||||
\(619\) | −10.0797 | −0.405138 | −0.202569 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202569 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(620\) | 3.72953 | 0.149782 | ||||||||
\(621\) | 13.0891 | 0.525246 | ||||||||
\(622\) | −12.0025 | −0.481256 | ||||||||
\(623\) | 24.8072 | 0.993881 | ||||||||
\(624\) | −4.46941 | −0.178920 | ||||||||
\(625\) | 20.9215 | 0.836860 | ||||||||
\(626\) | 64.1482 | 2.56388 | ||||||||
\(627\) | 0.127809 | 0.00510421 | ||||||||
\(628\) | −48.4129 | −1.93188 | ||||||||
\(629\) | −6.20211 | −0.247295 | ||||||||
\(630\) | −5.29897 | −0.211116 | ||||||||
\(631\) | −16.1451 | −0.642726 | −0.321363 | − | 0.946956i | \(-0.604141\pi\) | ||||
−0.321363 | + | 0.946956i | \(0.604141\pi\) | |||||||
\(632\) | −18.2339 | −0.725306 | ||||||||
\(633\) | 8.33196 | 0.331166 | ||||||||
\(634\) | −45.0541 | −1.78933 | ||||||||
\(635\) | −7.65059 | −0.303605 | ||||||||
\(636\) | 12.2684 | 0.486474 | ||||||||
\(637\) | 17.4290 | 0.690561 | ||||||||
\(638\) | −3.76796 | −0.149175 | ||||||||
\(639\) | −16.9421 | −0.670218 | ||||||||
\(640\) | −10.8205 | −0.427717 | ||||||||
\(641\) | 11.1707 | 0.441217 | 0.220608 | − | 0.975362i | \(-0.429196\pi\) | ||||
0.220608 | + | 0.975362i | \(0.429196\pi\) | |||||||
\(642\) | −12.4704 | −0.492169 | ||||||||
\(643\) | −41.0142 | −1.61744 | −0.808722 | − | 0.588191i | \(-0.799840\pi\) | ||||
−0.808722 | + | 0.588191i | \(0.799840\pi\) | |||||||
\(644\) | −21.4102 | −0.843682 | ||||||||
\(645\) | 3.67874 | 0.144850 | ||||||||
\(646\) | −0.937578 | −0.0368885 | ||||||||
\(647\) | −2.94961 | −0.115961 | −0.0579806 | − | 0.998318i | \(-0.518466\pi\) | ||||
−0.0579806 | + | 0.998318i | \(0.518466\pi\) | |||||||
\(648\) | −20.1816 | −0.792808 | ||||||||
\(649\) | −3.51299 | −0.137897 | ||||||||
\(650\) | −45.5545 | −1.78679 | ||||||||
\(651\) | −2.11940 | −0.0830658 | ||||||||
\(652\) | 62.1628 | 2.43448 | ||||||||
\(653\) | 18.7782 | 0.734847 | 0.367424 | − | 0.930054i | \(-0.380240\pi\) | ||||
0.367424 | + | 0.930054i | \(0.380240\pi\) | |||||||
\(654\) | 11.7252 | 0.458490 | ||||||||
\(655\) | 2.18118 | 0.0852256 | ||||||||
\(656\) | 4.88732 | 0.190818 | ||||||||
\(657\) | −2.51086 | −0.0979581 | ||||||||
\(658\) | −31.6901 | −1.23541 | ||||||||
\(659\) | 33.6369 | 1.31031 | 0.655153 | − | 0.755496i | \(-0.272604\pi\) | ||||
0.655153 | + | 0.755496i | \(0.272604\pi\) | |||||||
\(660\) | 0.775667 | 0.0301928 | ||||||||
\(661\) | −13.3413 | −0.518915 | −0.259457 | − | 0.965755i | \(-0.583544\pi\) | ||||
−0.259457 | + | 0.965755i | \(0.583544\pi\) | |||||||
\(662\) | 21.9098 | 0.851549 | ||||||||
\(663\) | 3.37970 | 0.131257 | ||||||||
\(664\) | −48.1476 | −1.86849 | ||||||||
\(665\) | 0.270404 | 0.0104858 | ||||||||
\(666\) | 29.6303 | 1.14815 | ||||||||
\(667\) | 9.10177 | 0.352422 | ||||||||
\(668\) | −16.7386 | −0.647636 | ||||||||
\(669\) | 14.1972 | 0.548895 | ||||||||
\(670\) | −3.87628 | −0.149754 | ||||||||
\(671\) | −2.72399 | −0.105159 | ||||||||
\(672\) | 3.76403 | 0.145201 | ||||||||
\(673\) | −0.197926 | −0.00762950 | −0.00381475 | − | 0.999993i | \(-0.501214\pi\) | ||||
−0.00381475 | + | 0.999993i | \(0.501214\pi\) | |||||||
\(674\) | 47.1801 | 1.81731 | ||||||||
\(675\) | 17.1050 | 0.658373 | ||||||||
\(676\) | 13.1052 | 0.504045 | ||||||||
\(677\) | 10.9735 | 0.421745 | 0.210872 | − | 0.977514i | \(-0.432370\pi\) | ||||
0.210872 | + | 0.977514i | \(0.432370\pi\) | |||||||
\(678\) | −11.7717 | −0.452089 | ||||||||
\(679\) | 18.9643 | 0.727784 | ||||||||
\(680\) | −2.51651 | −0.0965039 | ||||||||
\(681\) | 2.27427 | 0.0871501 | ||||||||
\(682\) | −2.95654 | −0.113212 | ||||||||
\(683\) | 30.6641 | 1.17333 | 0.586664 | − | 0.809830i | \(-0.300441\pi\) | ||||
0.586664 | + | 0.809830i | \(0.300441\pi\) | |||||||
\(684\) | 2.87547 | 0.109946 | ||||||||
\(685\) | 5.46855 | 0.208943 | ||||||||
\(686\) | 44.0069 | 1.68019 | ||||||||
\(687\) | −11.3936 | −0.434691 | ||||||||
\(688\) | −18.1615 | −0.692400 | ||||||||
\(689\) | −21.5064 | −0.819328 | ||||||||
\(690\) | −2.91870 | −0.111113 | ||||||||
\(691\) | 18.6644 | 0.710026 | 0.355013 | − | 0.934861i | \(-0.384476\pi\) | ||||
0.355013 | + | 0.934861i | \(0.384476\pi\) | |||||||
\(692\) | −35.8420 | −1.36251 | ||||||||
\(693\) | 2.69666 | 0.102438 | ||||||||
\(694\) | −54.8866 | −2.08347 | ||||||||
\(695\) | −7.67540 | −0.291145 | ||||||||
\(696\) | 6.12828 | 0.232292 | ||||||||
\(697\) | −3.69572 | −0.139985 | ||||||||
\(698\) | 47.2016 | 1.78661 | ||||||||
\(699\) | −2.55297 | −0.0965622 | ||||||||
\(700\) | −27.9793 | −1.05752 | ||||||||
\(701\) | −14.2851 | −0.539541 | −0.269770 | − | 0.962925i | \(-0.586948\pi\) | ||||
−0.269770 | + | 0.962925i | \(0.586948\pi\) | |||||||
\(702\) | −34.9319 | −1.31842 | ||||||||
\(703\) | −1.51202 | −0.0570269 | ||||||||
\(704\) | 7.38659 | 0.278392 | ||||||||
\(705\) | −2.77330 | −0.104449 | ||||||||
\(706\) | −14.6409 | −0.551017 | ||||||||
\(707\) | 9.89556 | 0.372161 | ||||||||
\(708\) | 12.9190 | 0.485527 | ||||||||
\(709\) | 16.7757 | 0.630024 | 0.315012 | − | 0.949088i | \(-0.397992\pi\) | ||||
0.315012 | + | 0.949088i | \(0.397992\pi\) | |||||||
\(710\) | 8.17327 | 0.306737 | ||||||||
\(711\) | −12.5437 | −0.470425 | ||||||||
\(712\) | −56.2836 | −2.10932 | ||||||||
\(713\) | 7.14173 | 0.267460 | ||||||||
\(714\) | 3.23354 | 0.121012 | ||||||||
\(715\) | −1.35974 | −0.0508513 | ||||||||
\(716\) | 58.8467 | 2.19920 | ||||||||
\(717\) | −15.3238 | −0.572276 | ||||||||
\(718\) | −66.0769 | −2.46597 | ||||||||
\(719\) | −17.9755 | −0.670373 | −0.335187 | − | 0.942152i | \(-0.608799\pi\) | ||||
−0.335187 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(720\) | 2.28938 | 0.0853200 | ||||||||
\(721\) | −8.17437 | −0.304430 | ||||||||
\(722\) | 44.6770 | 1.66271 | ||||||||
\(723\) | 2.47337 | 0.0919855 | ||||||||
\(724\) | 31.7765 | 1.18096 | ||||||||
\(725\) | 11.8944 | 0.441746 | ||||||||
\(726\) | 16.2634 | 0.603591 | ||||||||
\(727\) | 12.5687 | 0.466146 | 0.233073 | − | 0.972459i | \(-0.425122\pi\) | ||||
0.233073 | + | 0.972459i | \(0.425122\pi\) | |||||||
\(728\) | 25.2705 | 0.936587 | ||||||||
\(729\) | −6.82987 | −0.252958 | ||||||||
\(730\) | 1.21130 | 0.0448323 | ||||||||
\(731\) | 13.7334 | 0.507949 | ||||||||
\(732\) | 10.0175 | 0.370257 | ||||||||
\(733\) | −15.9789 | −0.590194 | −0.295097 | − | 0.955467i | \(-0.595352\pi\) | ||||
−0.295097 | + | 0.955467i | \(0.595352\pi\) | |||||||
\(734\) | −17.5762 | −0.648748 | ||||||||
\(735\) | 1.45930 | 0.0538273 | ||||||||
\(736\) | −12.6837 | −0.467526 | ||||||||
\(737\) | 1.97265 | 0.0726635 | ||||||||
\(738\) | 17.6561 | 0.649930 | ||||||||
\(739\) | −39.0078 | −1.43493 | −0.717463 | − | 0.696596i | \(-0.754697\pi\) | ||||
−0.717463 | + | 0.696596i | \(0.754697\pi\) | |||||||
\(740\) | −9.17635 | −0.337329 | ||||||||
\(741\) | 0.823939 | 0.0302682 | ||||||||
\(742\) | −20.5764 | −0.755382 | ||||||||
\(743\) | 26.5753 | 0.974952 | 0.487476 | − | 0.873136i | \(-0.337918\pi\) | ||||
0.487476 | + | 0.873136i | \(0.337918\pi\) | |||||||
\(744\) | 4.80857 | 0.176291 | ||||||||
\(745\) | 0.457429 | 0.0167589 | ||||||||
\(746\) | −15.3997 | −0.563821 | ||||||||
\(747\) | −33.1223 | −1.21188 | ||||||||
\(748\) | 2.89571 | 0.105878 | ||||||||
\(749\) | 13.4266 | 0.490599 | ||||||||
\(750\) | −7.85214 | −0.286720 | ||||||||
\(751\) | −23.4259 | −0.854822 | −0.427411 | − | 0.904057i | \(-0.640574\pi\) | ||||
−0.427411 | + | 0.904057i | \(0.640574\pi\) | |||||||
\(752\) | 13.6915 | 0.499276 | ||||||||
\(753\) | 9.78483 | 0.356579 | ||||||||
\(754\) | −24.2907 | −0.884614 | ||||||||
\(755\) | −4.71279 | −0.171516 | ||||||||
\(756\) | −21.4550 | −0.780310 | ||||||||
\(757\) | 40.0411 | 1.45532 | 0.727659 | − | 0.685939i | \(-0.240608\pi\) | ||||
0.727659 | + | 0.685939i | \(0.240608\pi\) | |||||||
\(758\) | −23.4219 | −0.850723 | ||||||||
\(759\) | 1.48534 | 0.0539143 | ||||||||
\(760\) | −0.613503 | −0.0222541 | ||||||||
\(761\) | −16.7667 | −0.607792 | −0.303896 | − | 0.952705i | \(-0.598287\pi\) | ||||
−0.303896 | + | 0.952705i | \(0.598287\pi\) | |||||||
\(762\) | −22.3038 | −0.807980 | ||||||||
\(763\) | −12.6242 | −0.457027 | ||||||||
\(764\) | −41.9213 | −1.51666 | ||||||||
\(765\) | −1.73119 | −0.0625913 | ||||||||
\(766\) | 1.49490 | 0.0540129 | ||||||||
\(767\) | −22.6470 | −0.817734 | ||||||||
\(768\) | −16.3944 | −0.591580 | ||||||||
\(769\) | 30.6719 | 1.10606 | 0.553028 | − | 0.833163i | \(-0.313472\pi\) | ||||
0.553028 | + | 0.833163i | \(0.313472\pi\) | |||||||
\(770\) | −1.30094 | −0.0468825 | ||||||||
\(771\) | −20.1973 | −0.727389 | ||||||||
\(772\) | 33.4001 | 1.20209 | ||||||||
\(773\) | −16.3817 | −0.589210 | −0.294605 | − | 0.955619i | \(-0.595188\pi\) | ||||
−0.294605 | + | 0.955619i | \(0.595188\pi\) | |||||||
\(774\) | −65.6107 | −2.35833 | ||||||||
\(775\) | 9.33295 | 0.335249 | ||||||||
\(776\) | −43.0269 | −1.54458 | ||||||||
\(777\) | 5.21469 | 0.187076 | ||||||||
\(778\) | 14.6083 | 0.523733 | ||||||||
\(779\) | −0.900982 | −0.0322810 | ||||||||
\(780\) | 5.00044 | 0.179044 | ||||||||
\(781\) | −4.15940 | −0.148835 | ||||||||
\(782\) | −10.8961 | −0.389642 | ||||||||
\(783\) | 9.12079 | 0.325951 | ||||||||
\(784\) | −7.20441 | −0.257300 | ||||||||
\(785\) | 7.10583 | 0.253618 | ||||||||
\(786\) | 6.35878 | 0.226810 | ||||||||
\(787\) | −30.2666 | −1.07889 | −0.539444 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539444 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(788\) | −54.2952 | −1.93419 | ||||||||
\(789\) | −5.66391 | −0.201640 | ||||||||
\(790\) | 6.05139 | 0.215299 | ||||||||
\(791\) | 12.6743 | 0.450647 | ||||||||
\(792\) | −6.11829 | −0.217404 | ||||||||
\(793\) | −17.5606 | −0.623594 | ||||||||
\(794\) | −35.8734 | −1.27310 | ||||||||
\(795\) | −1.80070 | −0.0638643 | ||||||||
\(796\) | −68.7088 | −2.43532 | ||||||||
\(797\) | 31.5290 | 1.11681 | 0.558406 | − | 0.829567i | \(-0.311413\pi\) | ||||
0.558406 | + | 0.829567i | \(0.311413\pi\) | |||||||
\(798\) | 0.788308 | 0.0279058 | ||||||||
\(799\) | −10.3533 | −0.366272 | ||||||||
\(800\) | −16.5752 | −0.586023 | ||||||||
\(801\) | −38.7193 | −1.36808 | ||||||||
\(802\) | −79.0059 | −2.78980 | ||||||||
\(803\) | −0.616435 | −0.0217535 | ||||||||
\(804\) | −7.25442 | −0.255844 | ||||||||
\(805\) | 3.14250 | 0.110759 | ||||||||
\(806\) | −19.0597 | −0.671351 | ||||||||
\(807\) | −20.1543 | −0.709465 | ||||||||
\(808\) | −22.4514 | −0.789838 | ||||||||
\(809\) | 10.0219 | 0.352352 | 0.176176 | − | 0.984359i | \(-0.443627\pi\) | ||||
0.176176 | + | 0.984359i | \(0.443627\pi\) | |||||||
\(810\) | 6.69778 | 0.235336 | ||||||||
\(811\) | −28.8994 | −1.01479 | −0.507397 | − | 0.861712i | \(-0.669392\pi\) | ||||
−0.507397 | + | 0.861712i | \(0.669392\pi\) | |||||||
\(812\) | −14.9192 | −0.523561 | ||||||||
\(813\) | 5.65509 | 0.198333 | ||||||||
\(814\) | 7.27445 | 0.254969 | ||||||||
\(815\) | −9.12398 | −0.319599 | ||||||||
\(816\) | −1.39702 | −0.0489057 | ||||||||
\(817\) | 3.34808 | 0.117135 | ||||||||
\(818\) | −0.965121 | −0.0337447 | ||||||||
\(819\) | 17.3844 | 0.607460 | ||||||||
\(820\) | −5.46801 | −0.190951 | ||||||||
\(821\) | −48.9801 | −1.70942 | −0.854709 | − | 0.519107i | \(-0.826265\pi\) | ||||
−0.854709 | + | 0.519107i | \(0.826265\pi\) | |||||||
\(822\) | 15.9424 | 0.556057 | ||||||||
\(823\) | −2.10161 | −0.0732576 | −0.0366288 | − | 0.999329i | \(-0.511662\pi\) | ||||
−0.0366288 | + | 0.999329i | \(0.511662\pi\) | |||||||
\(824\) | 18.5463 | 0.646092 | ||||||||
\(825\) | 1.94106 | 0.0675792 | ||||||||
\(826\) | −21.6676 | −0.753912 | ||||||||
\(827\) | 8.59211 | 0.298777 | 0.149388 | − | 0.988779i | \(-0.452269\pi\) | ||||
0.149388 | + | 0.988779i | \(0.452269\pi\) | |||||||
\(828\) | 33.4172 | 1.16133 | ||||||||
\(829\) | 6.46277 | 0.224461 | 0.112231 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112231 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(830\) | 15.9790 | 0.554639 | ||||||||
\(831\) | 20.0863 | 0.696787 | ||||||||
\(832\) | 47.6186 | 1.65088 | ||||||||
\(833\) | 5.44786 | 0.188757 | ||||||||
\(834\) | −22.3761 | −0.774820 | ||||||||
\(835\) | 2.45682 | 0.0850217 | ||||||||
\(836\) | 0.705948 | 0.0244157 | ||||||||
\(837\) | 7.15666 | 0.247370 | ||||||||
\(838\) | 58.7282 | 2.02873 | ||||||||
\(839\) | −28.6908 | −0.990515 | −0.495257 | − | 0.868746i | \(-0.664926\pi\) | ||||
−0.495257 | + | 0.868746i | \(0.664926\pi\) | |||||||
\(840\) | 2.11586 | 0.0730043 | ||||||||
\(841\) | −22.6577 | −0.781298 | ||||||||
\(842\) | 15.3233 | 0.528074 | ||||||||
\(843\) | 20.8848 | 0.719311 | ||||||||
\(844\) | 46.0212 | 1.58411 | ||||||||
\(845\) | −1.92352 | −0.0661711 | ||||||||
\(846\) | 49.4622 | 1.70054 | ||||||||
\(847\) | −17.5104 | −0.601665 | ||||||||
\(848\) | 8.88984 | 0.305278 | ||||||||
\(849\) | −7.36020 | −0.252601 | ||||||||
\(850\) | −14.2392 | −0.488400 | ||||||||
\(851\) | −17.5719 | −0.602358 | ||||||||
\(852\) | 15.2962 | 0.524040 | ||||||||
\(853\) | 23.8723 | 0.817371 | 0.408686 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408686 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(854\) | −16.8012 | −0.574924 | ||||||||
\(855\) | −0.422048 | −0.0144337 | ||||||||
\(856\) | −30.4629 | −1.04120 | ||||||||
\(857\) | −37.1228 | −1.26809 | −0.634045 | − | 0.773296i | \(-0.718607\pi\) | ||||
−0.634045 | + | 0.773296i | \(0.718607\pi\) | |||||||
\(858\) | −3.96404 | −0.135330 | ||||||||
\(859\) | −20.2360 | −0.690442 | −0.345221 | − | 0.938521i | \(-0.612196\pi\) | ||||
−0.345221 | + | 0.938521i | \(0.612196\pi\) | |||||||
\(860\) | 20.3193 | 0.692883 | ||||||||
\(861\) | 3.10733 | 0.105898 | ||||||||
\(862\) | −8.22769 | −0.280236 | ||||||||
\(863\) | −31.4426 | −1.07032 | −0.535159 | − | 0.844751i | \(-0.679748\pi\) | ||||
−0.535159 | + | 0.844751i | \(0.679748\pi\) | |||||||
\(864\) | −12.7102 | −0.432408 | ||||||||
\(865\) | 5.26073 | 0.178870 | ||||||||
\(866\) | −39.7579 | −1.35103 | ||||||||
\(867\) | −9.98025 | −0.338947 | ||||||||
\(868\) | −11.7064 | −0.397341 | ||||||||
\(869\) | −3.07957 | −0.104467 | ||||||||
\(870\) | −2.03382 | −0.0689531 | ||||||||
\(871\) | 12.7169 | 0.430897 | ||||||||
\(872\) | 28.6423 | 0.969950 | ||||||||
\(873\) | −29.5996 | −1.00180 | ||||||||
\(874\) | −2.65636 | −0.0898527 | ||||||||
\(875\) | 8.45423 | 0.285805 | ||||||||
\(876\) | 2.26694 | 0.0765929 | ||||||||
\(877\) | −42.6242 | −1.43932 | −0.719659 | − | 0.694328i | \(-0.755702\pi\) | ||||
−0.719659 | + | 0.694328i | \(0.755702\pi\) | |||||||
\(878\) | 68.3778 | 2.30764 | ||||||||
\(879\) | 3.28131 | 0.110676 | ||||||||
\(880\) | 0.562059 | 0.0189470 | ||||||||
\(881\) | −26.2582 | −0.884661 | −0.442330 | − | 0.896852i | \(-0.645848\pi\) | ||||
−0.442330 | + | 0.896852i | \(0.645848\pi\) | |||||||
\(882\) | −26.0269 | −0.876370 | ||||||||
\(883\) | −30.4910 | −1.02610 | −0.513052 | − | 0.858357i | \(-0.671485\pi\) | ||||
−0.513052 | + | 0.858357i | \(0.671485\pi\) | |||||||
\(884\) | 18.6676 | 0.627859 | ||||||||
\(885\) | −1.89620 | −0.0637401 | ||||||||
\(886\) | −34.6519 | −1.16415 | ||||||||
\(887\) | −19.5268 | −0.655644 | −0.327822 | − | 0.944739i | \(-0.606315\pi\) | ||||
−0.327822 | + | 0.944739i | \(0.606315\pi\) | |||||||
\(888\) | −11.8313 | −0.397032 | ||||||||
\(889\) | 24.0140 | 0.805402 | ||||||||
\(890\) | 18.6791 | 0.626126 | ||||||||
\(891\) | −3.40852 | −0.114190 | ||||||||
\(892\) | 78.4175 | 2.62561 | ||||||||
\(893\) | −2.52403 | −0.0844635 | ||||||||
\(894\) | 1.33354 | 0.0446003 | ||||||||
\(895\) | −8.63726 | −0.288712 | ||||||||
\(896\) | 33.9637 | 1.13465 | ||||||||
\(897\) | 9.57541 | 0.319713 | ||||||||
\(898\) | −52.9502 | −1.76697 | ||||||||
\(899\) | 4.97654 | 0.165977 | ||||||||
\(900\) | 43.6703 | 1.45568 | ||||||||
\(901\) | −6.72236 | −0.223954 | ||||||||
\(902\) | 4.33470 | 0.144330 | ||||||||
\(903\) | −11.5470 | −0.384259 | ||||||||
\(904\) | −28.7560 | −0.956410 | ||||||||
\(905\) | −4.66401 | −0.155037 | ||||||||
\(906\) | −13.7392 | −0.456454 | ||||||||
\(907\) | 24.1460 | 0.801756 | 0.400878 | − | 0.916131i | \(-0.368705\pi\) | ||||
0.400878 | + | 0.916131i | \(0.368705\pi\) | |||||||
\(908\) | 12.5618 | 0.416878 | ||||||||
\(909\) | −15.4450 | −0.512280 | ||||||||
\(910\) | −8.38665 | −0.278015 | ||||||||
\(911\) | −28.5199 | −0.944907 | −0.472453 | − | 0.881356i | \(-0.656631\pi\) | ||||
−0.472453 | + | 0.881356i | \(0.656631\pi\) | |||||||
\(912\) | −0.340582 | −0.0112778 | ||||||||
\(913\) | −8.13176 | −0.269122 | ||||||||
\(914\) | −77.8219 | −2.57412 | ||||||||
\(915\) | −1.47032 | −0.0486074 | ||||||||
\(916\) | −62.9317 | −2.07932 | ||||||||
\(917\) | −6.84636 | −0.226087 | ||||||||
\(918\) | −10.9188 | −0.360375 | ||||||||
\(919\) | −38.8303 | −1.28089 | −0.640446 | − | 0.768003i | \(-0.721251\pi\) | ||||
−0.640446 | + | 0.768003i | \(0.721251\pi\) | |||||||
\(920\) | −7.12982 | −0.235063 | ||||||||
\(921\) | −11.8001 | −0.388826 | ||||||||
\(922\) | −28.8679 | −0.950712 | ||||||||
\(923\) | −26.8141 | −0.882598 | ||||||||
\(924\) | −2.43469 | −0.0800955 | ||||||||
\(925\) | −22.9633 | −0.755029 | ||||||||
\(926\) | −95.9572 | −3.15335 | ||||||||
\(927\) | 12.7586 | 0.419048 | ||||||||
\(928\) | −8.83829 | −0.290131 | ||||||||
\(929\) | −13.3814 | −0.439029 | −0.219514 | − | 0.975609i | \(-0.570447\pi\) | ||||
−0.219514 | + | 0.975609i | \(0.570447\pi\) | |||||||
\(930\) | −1.59585 | −0.0523299 | ||||||||
\(931\) | 1.32814 | 0.0435280 | ||||||||
\(932\) | −14.1012 | −0.461900 | ||||||||
\(933\) | 3.29696 | 0.107938 | ||||||||
\(934\) | −73.9307 | −2.41909 | ||||||||
\(935\) | −0.425020 | −0.0138996 | ||||||||
\(936\) | −39.4423 | −1.28921 | ||||||||
\(937\) | 33.2360 | 1.08577 | 0.542887 | − | 0.839806i | \(-0.317331\pi\) | ||||
0.542887 | + | 0.839806i | \(0.317331\pi\) | |||||||
\(938\) | 12.1670 | 0.397267 | ||||||||
\(939\) | −17.6208 | −0.575034 | ||||||||
\(940\) | −15.3182 | −0.499625 | ||||||||
\(941\) | 16.6981 | 0.544344 | 0.272172 | − | 0.962249i | \(-0.412258\pi\) | ||||
0.272172 | + | 0.962249i | \(0.412258\pi\) | |||||||
\(942\) | 20.7156 | 0.674951 | ||||||||
\(943\) | −10.4708 | −0.340975 | ||||||||
\(944\) | 9.36130 | 0.304684 | ||||||||
\(945\) | 3.14907 | 0.102439 | ||||||||
\(946\) | −16.1079 | −0.523713 | ||||||||
\(947\) | −41.6671 | −1.35400 | −0.676999 | − | 0.735984i | \(-0.736720\pi\) | ||||
−0.676999 | + | 0.735984i | \(0.736720\pi\) | |||||||
\(948\) | 11.3251 | 0.367823 | ||||||||
\(949\) | −3.97393 | −0.128999 | ||||||||
\(950\) | −3.47138 | −0.112626 | ||||||||
\(951\) | 12.3759 | 0.401315 | ||||||||
\(952\) | 7.89892 | 0.256006 | ||||||||
\(953\) | −0.601559 | −0.0194864 | −0.00974321 | − | 0.999953i | \(-0.503101\pi\) | ||||
−0.00974321 | + | 0.999953i | \(0.503101\pi\) | |||||||
\(954\) | 32.1157 | 1.03978 | ||||||||
\(955\) | 6.15302 | 0.199107 | ||||||||
\(956\) | −84.6400 | −2.73745 | ||||||||
\(957\) | 1.03502 | 0.0334574 | ||||||||
\(958\) | −47.6149 | −1.53837 | ||||||||
\(959\) | −17.1649 | −0.554283 | ||||||||
\(960\) | 3.98704 | 0.128681 | ||||||||
\(961\) | −27.0951 | −0.874037 | ||||||||
\(962\) | 46.8957 | 1.51198 | ||||||||
\(963\) | −20.9564 | −0.675310 | ||||||||
\(964\) | 13.6615 | 0.440008 | ||||||||
\(965\) | −4.90231 | −0.157811 | ||||||||
\(966\) | 9.16132 | 0.294761 | ||||||||
\(967\) | 42.4904 | 1.36640 | 0.683199 | − | 0.730232i | \(-0.260588\pi\) | ||||
0.683199 | + | 0.730232i | \(0.260588\pi\) | |||||||
\(968\) | 39.7283 | 1.27692 | ||||||||
\(969\) | 0.257543 | 0.00827346 | ||||||||
\(970\) | 14.2796 | 0.458490 | ||||||||
\(971\) | −53.6985 | −1.72327 | −0.861633 | − | 0.507531i | \(-0.830558\pi\) | ||||
−0.861633 | + | 0.507531i | \(0.830558\pi\) | |||||||
\(972\) | 51.4957 | 1.65172 | ||||||||
\(973\) | 24.0918 | 0.772349 | ||||||||
\(974\) | 14.9538 | 0.479150 | ||||||||
\(975\) | 12.5133 | 0.400747 | ||||||||
\(976\) | 7.25880 | 0.232349 | ||||||||
\(977\) | 52.4695 | 1.67865 | 0.839324 | − | 0.543632i | \(-0.182951\pi\) | ||||
0.839324 | + | 0.543632i | \(0.182951\pi\) | |||||||
\(978\) | −26.5991 | −0.850546 | ||||||||
\(979\) | −9.50587 | −0.303809 | ||||||||
\(980\) | 8.06039 | 0.257480 | ||||||||
\(981\) | 19.7039 | 0.629099 | ||||||||
\(982\) | 91.3577 | 2.91534 | ||||||||
\(983\) | 21.0306 | 0.670772 | 0.335386 | − | 0.942081i | \(-0.391133\pi\) | ||||
0.335386 | + | 0.942081i | \(0.391133\pi\) | |||||||
\(984\) | −7.05003 | −0.224747 | ||||||||
\(985\) | 7.96921 | 0.253920 | ||||||||
\(986\) | −7.59265 | −0.241799 | ||||||||
\(987\) | 8.70495 | 0.277082 | ||||||||
\(988\) | 4.55099 | 0.144786 | ||||||||
\(989\) | 38.9097 | 1.23726 | ||||||||
\(990\) | 2.03051 | 0.0645338 | ||||||||
\(991\) | −13.7116 | −0.435563 | −0.217782 | − | 0.975998i | \(-0.569882\pi\) | ||||
−0.217782 | + | 0.975998i | \(0.569882\pi\) | |||||||
\(992\) | −6.93499 | −0.220186 | ||||||||
\(993\) | −6.01840 | −0.190988 | ||||||||
\(994\) | −25.6546 | −0.813713 | ||||||||
\(995\) | 10.0848 | 0.319709 | ||||||||
\(996\) | 29.9046 | 0.947562 | ||||||||
\(997\) | 23.1884 | 0.734385 | 0.367192 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367192 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(998\) | −89.9329 | −2.84678 | ||||||||
\(999\) | −17.6086 | −0.557113 |
(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 | 4027.2.a.c.1.18 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.18 | ✓ | 174 | 1.1 | even | 1 | trivial |