Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.32 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.615474 | 0.435206 | 0.217603 | − | 0.976037i | \(-0.430176\pi\) | ||||
0.217603 | + | 0.976037i | \(0.430176\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.62119 | −0.810596 | ||||||||
\(5\) | −1.47525 | −0.659752 | −0.329876 | − | 0.944024i | \(-0.607007\pi\) | ||||
−0.329876 | + | 0.944024i | \(0.607007\pi\) | |||||||
\(6\) | −0.615474 | −0.251266 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.22875 | −0.787982 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.907978 | −0.287128 | ||||||||
\(11\) | 2.65989 | 0.801988 | 0.400994 | − | 0.916081i | \(-0.368665\pi\) | ||||
0.400994 | + | 0.916081i | \(0.368665\pi\) | |||||||
\(12\) | 1.62119 | 0.467998 | ||||||||
\(13\) | 3.14729 | 0.872901 | 0.436451 | − | 0.899728i | \(-0.356235\pi\) | ||||
0.436451 | + | 0.899728i | \(0.356235\pi\) | |||||||
\(14\) | 0.615474 | 0.164492 | ||||||||
\(15\) | 1.47525 | 0.380908 | ||||||||
\(16\) | 1.87064 | 0.467661 | ||||||||
\(17\) | 6.74505 | 1.63591 | 0.817957 | − | 0.575279i | \(-0.195106\pi\) | ||||
0.817957 | + | 0.575279i | \(0.195106\pi\) | |||||||
\(18\) | 0.615474 | 0.145069 | ||||||||
\(19\) | 5.14394 | 1.18010 | 0.590050 | − | 0.807367i | \(-0.299108\pi\) | ||||
0.590050 | + | 0.807367i | \(0.299108\pi\) | |||||||
\(20\) | 2.39166 | 0.534792 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.63710 | 0.349030 | ||||||||
\(23\) | 7.40766 | 1.54460 | 0.772301 | − | 0.635256i | \(-0.219106\pi\) | ||||
0.772301 | + | 0.635256i | \(0.219106\pi\) | |||||||
\(24\) | 2.22875 | 0.454942 | ||||||||
\(25\) | −2.82364 | −0.564728 | ||||||||
\(26\) | 1.93708 | 0.379892 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.62119 | −0.306376 | ||||||||
\(29\) | −2.09296 | −0.388652 | −0.194326 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194326 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(30\) | 0.907978 | 0.165773 | ||||||||
\(31\) | −0.306892 | −0.0551193 | −0.0275597 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275597 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(32\) | 5.60883 | 0.991511 | ||||||||
\(33\) | −2.65989 | −0.463028 | ||||||||
\(34\) | 4.15140 | 0.711960 | ||||||||
\(35\) | −1.47525 | −0.249363 | ||||||||
\(36\) | −1.62119 | −0.270199 | ||||||||
\(37\) | −7.93979 | −1.30529 | −0.652647 | − | 0.757662i | \(-0.726341\pi\) | ||||
−0.652647 | + | 0.757662i | \(0.726341\pi\) | |||||||
\(38\) | 3.16596 | 0.513587 | ||||||||
\(39\) | −3.14729 | −0.503970 | ||||||||
\(40\) | 3.28796 | 0.519873 | ||||||||
\(41\) | −1.15383 | −0.180197 | −0.0900986 | − | 0.995933i | \(-0.528718\pi\) | ||||
−0.0900986 | + | 0.995933i | \(0.528718\pi\) | |||||||
\(42\) | −0.615474 | −0.0949698 | ||||||||
\(43\) | 8.15649 | 1.24385 | 0.621927 | − | 0.783075i | \(-0.286350\pi\) | ||||
0.621927 | + | 0.783075i | \(0.286350\pi\) | |||||||
\(44\) | −4.31220 | −0.650088 | ||||||||
\(45\) | −1.47525 | −0.219917 | ||||||||
\(46\) | 4.55922 | 0.672221 | ||||||||
\(47\) | 4.92668 | 0.718631 | 0.359315 | − | 0.933216i | \(-0.383010\pi\) | ||||
0.359315 | + | 0.933216i | \(0.383010\pi\) | |||||||
\(48\) | −1.87064 | −0.270004 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.73788 | −0.245773 | ||||||||
\(51\) | −6.74505 | −0.944496 | ||||||||
\(52\) | −5.10236 | −0.707570 | ||||||||
\(53\) | 1.35908 | 0.186684 | 0.0933418 | − | 0.995634i | \(-0.470245\pi\) | ||||
0.0933418 | + | 0.995634i | \(0.470245\pi\) | |||||||
\(54\) | −0.615474 | −0.0837555 | ||||||||
\(55\) | −3.92401 | −0.529113 | ||||||||
\(56\) | −2.22875 | −0.297829 | ||||||||
\(57\) | −5.14394 | −0.681331 | ||||||||
\(58\) | −1.28816 | −0.169144 | ||||||||
\(59\) | 5.14225 | 0.669464 | 0.334732 | − | 0.942313i | \(-0.391354\pi\) | ||||
0.334732 | + | 0.942313i | \(0.391354\pi\) | |||||||
\(60\) | −2.39166 | −0.308762 | ||||||||
\(61\) | −3.38440 | −0.433328 | −0.216664 | − | 0.976246i | \(-0.569518\pi\) | ||||
−0.216664 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(62\) | −0.188884 | −0.0239883 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −0.289193 | −0.0361492 | ||||||||
\(65\) | −4.64304 | −0.575898 | ||||||||
\(66\) | −1.63710 | −0.201513 | ||||||||
\(67\) | −11.8164 | −1.44360 | −0.721801 | − | 0.692101i | \(-0.756685\pi\) | ||||
−0.721801 | + | 0.692101i | \(0.756685\pi\) | |||||||
\(68\) | −10.9350 | −1.32607 | ||||||||
\(69\) | −7.40766 | −0.891777 | ||||||||
\(70\) | −0.907978 | −0.108524 | ||||||||
\(71\) | 8.99642 | 1.06768 | 0.533839 | − | 0.845586i | \(-0.320749\pi\) | ||||
0.533839 | + | 0.845586i | \(0.320749\pi\) | |||||||
\(72\) | −2.22875 | −0.262661 | ||||||||
\(73\) | −11.9414 | −1.39763 | −0.698815 | − | 0.715303i | \(-0.746289\pi\) | ||||
−0.698815 | + | 0.715303i | \(0.746289\pi\) | |||||||
\(74\) | −4.88674 | −0.568072 | ||||||||
\(75\) | 2.82364 | 0.326046 | ||||||||
\(76\) | −8.33931 | −0.956584 | ||||||||
\(77\) | 2.65989 | 0.303123 | ||||||||
\(78\) | −1.93708 | −0.219331 | ||||||||
\(79\) | 3.67334 | 0.413283 | 0.206642 | − | 0.978417i | \(-0.433747\pi\) | ||||
0.206642 | + | 0.978417i | \(0.433747\pi\) | |||||||
\(80\) | −2.75967 | −0.308540 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.710150 | −0.0784230 | ||||||||
\(83\) | −7.07921 | −0.777044 | −0.388522 | − | 0.921439i | \(-0.627014\pi\) | ||||
−0.388522 | + | 0.921439i | \(0.627014\pi\) | |||||||
\(84\) | 1.62119 | 0.176886 | ||||||||
\(85\) | −9.95063 | −1.07930 | ||||||||
\(86\) | 5.02011 | 0.541333 | ||||||||
\(87\) | 2.09296 | 0.224388 | ||||||||
\(88\) | −5.92824 | −0.631953 | ||||||||
\(89\) | −15.1570 | −1.60664 | −0.803321 | − | 0.595547i | \(-0.796936\pi\) | ||||
−0.803321 | + | 0.595547i | \(0.796936\pi\) | |||||||
\(90\) | −0.907978 | −0.0957093 | ||||||||
\(91\) | 3.14729 | 0.329926 | ||||||||
\(92\) | −12.0092 | −1.25205 | ||||||||
\(93\) | 0.306892 | 0.0318232 | ||||||||
\(94\) | 3.03225 | 0.312752 | ||||||||
\(95\) | −7.58859 | −0.778573 | ||||||||
\(96\) | −5.60883 | −0.572449 | ||||||||
\(97\) | 16.8992 | 1.71585 | 0.857926 | − | 0.513773i | \(-0.171753\pi\) | ||||
0.857926 | + | 0.513773i | \(0.171753\pi\) | |||||||
\(98\) | 0.615474 | 0.0621723 | ||||||||
\(99\) | 2.65989 | 0.267329 | ||||||||
\(100\) | 4.57766 | 0.457766 | ||||||||
\(101\) | 7.70641 | 0.766816 | 0.383408 | − | 0.923579i | \(-0.374750\pi\) | ||||
0.383408 | + | 0.923579i | \(0.374750\pi\) | |||||||
\(102\) | −4.15140 | −0.411050 | ||||||||
\(103\) | 13.1014 | 1.29092 | 0.645462 | − | 0.763792i | \(-0.276665\pi\) | ||||
0.645462 | + | 0.763792i | \(0.276665\pi\) | |||||||
\(104\) | −7.01452 | −0.687831 | ||||||||
\(105\) | 1.47525 | 0.143970 | ||||||||
\(106\) | 0.836477 | 0.0812459 | ||||||||
\(107\) | 11.4290 | 1.10488 | 0.552442 | − | 0.833551i | \(-0.313696\pi\) | ||||
0.552442 | + | 0.833551i | \(0.313696\pi\) | |||||||
\(108\) | 1.62119 | 0.155999 | ||||||||
\(109\) | 8.24223 | 0.789463 | 0.394731 | − | 0.918797i | \(-0.370838\pi\) | ||||
0.394731 | + | 0.918797i | \(0.370838\pi\) | |||||||
\(110\) | −2.41513 | −0.230273 | ||||||||
\(111\) | 7.93979 | 0.753612 | ||||||||
\(112\) | 1.87064 | 0.176759 | ||||||||
\(113\) | −8.02930 | −0.755333 | −0.377667 | − | 0.925942i | \(-0.623273\pi\) | ||||
−0.377667 | + | 0.925942i | \(0.623273\pi\) | |||||||
\(114\) | −3.16596 | −0.296519 | ||||||||
\(115\) | −10.9281 | −1.01905 | ||||||||
\(116\) | 3.39308 | 0.315040 | ||||||||
\(117\) | 3.14729 | 0.290967 | ||||||||
\(118\) | 3.16492 | 0.291355 | ||||||||
\(119\) | 6.74505 | 0.618318 | ||||||||
\(120\) | −3.28796 | −0.300149 | ||||||||
\(121\) | −3.92496 | −0.356815 | ||||||||
\(122\) | −2.08301 | −0.188587 | ||||||||
\(123\) | 1.15383 | 0.104037 | ||||||||
\(124\) | 0.497530 | 0.0446795 | ||||||||
\(125\) | 11.5418 | 1.03233 | ||||||||
\(126\) | 0.615474 | 0.0548308 | ||||||||
\(127\) | 1.41454 | 0.125520 | 0.0627600 | − | 0.998029i | \(-0.480010\pi\) | ||||
0.0627600 | + | 0.998029i | \(0.480010\pi\) | |||||||
\(128\) | −11.3957 | −1.00724 | ||||||||
\(129\) | −8.15649 | −0.718139 | ||||||||
\(130\) | −2.85767 | −0.250634 | ||||||||
\(131\) | −0.675981 | −0.0590608 | −0.0295304 | − | 0.999564i | \(-0.509401\pi\) | ||||
−0.0295304 | + | 0.999564i | \(0.509401\pi\) | |||||||
\(132\) | 4.31220 | 0.375329 | ||||||||
\(133\) | 5.14394 | 0.446036 | ||||||||
\(134\) | −7.27268 | −0.628264 | ||||||||
\(135\) | 1.47525 | 0.126969 | ||||||||
\(136\) | −15.0330 | −1.28907 | ||||||||
\(137\) | −21.5180 | −1.83841 | −0.919205 | − | 0.393780i | \(-0.871167\pi\) | ||||
−0.919205 | + | 0.393780i | \(0.871167\pi\) | |||||||
\(138\) | −4.55922 | −0.388107 | ||||||||
\(139\) | 8.19044 | 0.694704 | 0.347352 | − | 0.937735i | \(-0.387081\pi\) | ||||
0.347352 | + | 0.937735i | \(0.387081\pi\) | |||||||
\(140\) | 2.39166 | 0.202132 | ||||||||
\(141\) | −4.92668 | −0.414902 | ||||||||
\(142\) | 5.53706 | 0.464660 | ||||||||
\(143\) | 8.37146 | 0.700057 | ||||||||
\(144\) | 1.87064 | 0.155887 | ||||||||
\(145\) | 3.08763 | 0.256414 | ||||||||
\(146\) | −7.34960 | −0.608257 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 12.8719 | 1.05807 | ||||||||
\(149\) | −9.02378 | −0.739257 | −0.369629 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369629 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(150\) | 1.73788 | 0.141897 | ||||||||
\(151\) | −1.10308 | −0.0897674 | −0.0448837 | − | 0.998992i | \(-0.514292\pi\) | ||||
−0.0448837 | + | 0.998992i | \(0.514292\pi\) | |||||||
\(152\) | −11.4646 | −0.929898 | ||||||||
\(153\) | 6.74505 | 0.545305 | ||||||||
\(154\) | 1.63710 | 0.131921 | ||||||||
\(155\) | 0.452742 | 0.0363651 | ||||||||
\(156\) | 5.10236 | 0.408516 | ||||||||
\(157\) | −13.5279 | −1.07964 | −0.539821 | − | 0.841780i | \(-0.681508\pi\) | ||||
−0.539821 | + | 0.841780i | \(0.681508\pi\) | |||||||
\(158\) | 2.26085 | 0.179863 | ||||||||
\(159\) | −1.35908 | −0.107782 | ||||||||
\(160\) | −8.27443 | −0.654151 | ||||||||
\(161\) | 7.40766 | 0.583805 | ||||||||
\(162\) | 0.615474 | 0.0483562 | ||||||||
\(163\) | 19.5088 | 1.52804 | 0.764022 | − | 0.645190i | \(-0.223222\pi\) | ||||
0.764022 | + | 0.645190i | \(0.223222\pi\) | |||||||
\(164\) | 1.87057 | 0.146067 | ||||||||
\(165\) | 3.92401 | 0.305484 | ||||||||
\(166\) | −4.35707 | −0.338174 | ||||||||
\(167\) | −11.5436 | −0.893271 | −0.446635 | − | 0.894716i | \(-0.647378\pi\) | ||||
−0.446635 | + | 0.894716i | \(0.647378\pi\) | |||||||
\(168\) | 2.22875 | 0.171952 | ||||||||
\(169\) | −3.09457 | −0.238044 | ||||||||
\(170\) | −6.12436 | −0.469717 | ||||||||
\(171\) | 5.14394 | 0.393367 | ||||||||
\(172\) | −13.2232 | −1.00826 | ||||||||
\(173\) | 5.54915 | 0.421894 | 0.210947 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210947 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(174\) | 1.28816 | 0.0976552 | ||||||||
\(175\) | −2.82364 | −0.213447 | ||||||||
\(176\) | 4.97571 | 0.375059 | ||||||||
\(177\) | −5.14225 | −0.386515 | ||||||||
\(178\) | −9.32876 | −0.699220 | ||||||||
\(179\) | 10.1298 | 0.757140 | 0.378570 | − | 0.925573i | \(-0.376416\pi\) | ||||
0.378570 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(180\) | 2.39166 | 0.178264 | ||||||||
\(181\) | −14.0856 | −1.04698 | −0.523489 | − | 0.852032i | \(-0.675370\pi\) | ||||
−0.523489 | + | 0.852032i | \(0.675370\pi\) | |||||||
\(182\) | 1.93708 | 0.143586 | ||||||||
\(183\) | 3.38440 | 0.250182 | ||||||||
\(184\) | −16.5098 | −1.21712 | ||||||||
\(185\) | 11.7132 | 0.861170 | ||||||||
\(186\) | 0.188884 | 0.0138496 | ||||||||
\(187\) | 17.9411 | 1.31198 | ||||||||
\(188\) | −7.98710 | −0.582519 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −4.67058 | −0.338840 | ||||||||
\(191\) | −7.70439 | −0.557470 | −0.278735 | − | 0.960368i | \(-0.589915\pi\) | ||||
−0.278735 | + | 0.960368i | \(0.589915\pi\) | |||||||
\(192\) | 0.289193 | 0.0208707 | ||||||||
\(193\) | 12.7262 | 0.916053 | 0.458027 | − | 0.888939i | \(-0.348556\pi\) | ||||
0.458027 | + | 0.888939i | \(0.348556\pi\) | |||||||
\(194\) | 10.4010 | 0.746749 | ||||||||
\(195\) | 4.64304 | 0.332495 | ||||||||
\(196\) | −1.62119 | −0.115799 | ||||||||
\(197\) | 14.4855 | 1.03205 | 0.516026 | − | 0.856573i | \(-0.327411\pi\) | ||||
0.516026 | + | 0.856573i | \(0.327411\pi\) | |||||||
\(198\) | 1.63710 | 0.116343 | ||||||||
\(199\) | 13.5022 | 0.957145 | 0.478573 | − | 0.878048i | \(-0.341154\pi\) | ||||
0.478573 | + | 0.878048i | \(0.341154\pi\) | |||||||
\(200\) | 6.29319 | 0.444996 | ||||||||
\(201\) | 11.8164 | 0.833464 | ||||||||
\(202\) | 4.74310 | 0.333723 | ||||||||
\(203\) | −2.09296 | −0.146897 | ||||||||
\(204\) | 10.9350 | 0.765604 | ||||||||
\(205\) | 1.70218 | 0.118885 | ||||||||
\(206\) | 8.06361 | 0.561818 | ||||||||
\(207\) | 7.40766 | 0.514868 | ||||||||
\(208\) | 5.88746 | 0.408222 | ||||||||
\(209\) | 13.6823 | 0.946427 | ||||||||
\(210\) | 0.907978 | 0.0626565 | ||||||||
\(211\) | −2.24176 | −0.154329 | −0.0771647 | − | 0.997018i | \(-0.524587\pi\) | ||||
−0.0771647 | + | 0.997018i | \(0.524587\pi\) | |||||||
\(212\) | −2.20332 | −0.151325 | ||||||||
\(213\) | −8.99642 | −0.616424 | ||||||||
\(214\) | 7.03427 | 0.480853 | ||||||||
\(215\) | −12.0329 | −0.820634 | ||||||||
\(216\) | 2.22875 | 0.151647 | ||||||||
\(217\) | −0.306892 | −0.0208332 | ||||||||
\(218\) | 5.07288 | 0.343579 | ||||||||
\(219\) | 11.9414 | 0.806922 | ||||||||
\(220\) | 6.36157 | 0.428897 | ||||||||
\(221\) | 21.2286 | 1.42799 | ||||||||
\(222\) | 4.88674 | 0.327976 | ||||||||
\(223\) | −21.3518 | −1.42982 | −0.714910 | − | 0.699216i | \(-0.753532\pi\) | ||||
−0.714910 | + | 0.699216i | \(0.753532\pi\) | |||||||
\(224\) | 5.60883 | 0.374756 | ||||||||
\(225\) | −2.82364 | −0.188243 | ||||||||
\(226\) | −4.94183 | −0.328726 | ||||||||
\(227\) | 24.1739 | 1.60448 | 0.802238 | − | 0.597004i | \(-0.203642\pi\) | ||||
0.802238 | + | 0.597004i | \(0.203642\pi\) | |||||||
\(228\) | 8.33931 | 0.552284 | ||||||||
\(229\) | 26.4007 | 1.74461 | 0.872303 | − | 0.488967i | \(-0.162626\pi\) | ||||
0.872303 | + | 0.488967i | \(0.162626\pi\) | |||||||
\(230\) | −6.72599 | −0.443499 | ||||||||
\(231\) | −2.65989 | −0.175008 | ||||||||
\(232\) | 4.66468 | 0.306251 | ||||||||
\(233\) | −0.670690 | −0.0439383 | −0.0219692 | − | 0.999759i | \(-0.506994\pi\) | ||||
−0.0219692 | + | 0.999759i | \(0.506994\pi\) | |||||||
\(234\) | 1.93708 | 0.126631 | ||||||||
\(235\) | −7.26809 | −0.474118 | ||||||||
\(236\) | −8.33657 | −0.542664 | ||||||||
\(237\) | −3.67334 | −0.238609 | ||||||||
\(238\) | 4.15140 | 0.269096 | ||||||||
\(239\) | 14.6314 | 0.946425 | 0.473212 | − | 0.880948i | \(-0.343094\pi\) | ||||
0.473212 | + | 0.880948i | \(0.343094\pi\) | |||||||
\(240\) | 2.75967 | 0.178136 | ||||||||
\(241\) | 22.1570 | 1.42726 | 0.713629 | − | 0.700524i | \(-0.247050\pi\) | ||||
0.713629 | + | 0.700524i | \(0.247050\pi\) | |||||||
\(242\) | −2.41571 | −0.155288 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.48675 | 0.351253 | ||||||||
\(245\) | −1.47525 | −0.0942502 | ||||||||
\(246\) | 0.710150 | 0.0452775 | ||||||||
\(247\) | 16.1895 | 1.03011 | ||||||||
\(248\) | 0.683985 | 0.0434331 | ||||||||
\(249\) | 7.07921 | 0.448627 | ||||||||
\(250\) | 7.10369 | 0.449277 | ||||||||
\(251\) | −29.0040 | −1.83071 | −0.915357 | − | 0.402642i | \(-0.868092\pi\) | ||||
−0.915357 | + | 0.402642i | \(0.868092\pi\) | |||||||
\(252\) | −1.62119 | −0.102125 | ||||||||
\(253\) | 19.7036 | 1.23875 | ||||||||
\(254\) | 0.870612 | 0.0546271 | ||||||||
\(255\) | 9.95063 | 0.623133 | ||||||||
\(256\) | −6.43535 | −0.402209 | ||||||||
\(257\) | 29.6195 | 1.84761 | 0.923807 | − | 0.382858i | \(-0.125060\pi\) | ||||
0.923807 | + | 0.382858i | \(0.125060\pi\) | |||||||
\(258\) | −5.02011 | −0.312539 | ||||||||
\(259\) | −7.93979 | −0.493355 | ||||||||
\(260\) | 7.52725 | 0.466820 | ||||||||
\(261\) | −2.09296 | −0.129551 | ||||||||
\(262\) | −0.416049 | −0.0257036 | ||||||||
\(263\) | −21.2369 | −1.30952 | −0.654761 | − | 0.755836i | \(-0.727231\pi\) | ||||
−0.654761 | + | 0.755836i | \(0.727231\pi\) | |||||||
\(264\) | 5.92824 | 0.364858 | ||||||||
\(265\) | −2.00498 | −0.123165 | ||||||||
\(266\) | 3.16596 | 0.194118 | ||||||||
\(267\) | 15.1570 | 0.927595 | ||||||||
\(268\) | 19.1566 | 1.17018 | ||||||||
\(269\) | −18.5699 | −1.13223 | −0.566113 | − | 0.824327i | \(-0.691554\pi\) | ||||
−0.566113 | + | 0.824327i | \(0.691554\pi\) | |||||||
\(270\) | 0.907978 | 0.0552578 | ||||||||
\(271\) | 16.9097 | 1.02719 | 0.513595 | − | 0.858033i | \(-0.328313\pi\) | ||||
0.513595 | + | 0.858033i | \(0.328313\pi\) | |||||||
\(272\) | 12.6176 | 0.765053 | ||||||||
\(273\) | −3.14729 | −0.190483 | ||||||||
\(274\) | −13.2438 | −0.800087 | ||||||||
\(275\) | −7.51058 | −0.452905 | ||||||||
\(276\) | 12.0092 | 0.722870 | ||||||||
\(277\) | 25.6380 | 1.54044 | 0.770218 | − | 0.637781i | \(-0.220148\pi\) | ||||
0.770218 | + | 0.637781i | \(0.220148\pi\) | |||||||
\(278\) | 5.04100 | 0.302339 | ||||||||
\(279\) | −0.306892 | −0.0183731 | ||||||||
\(280\) | 3.28796 | 0.196493 | ||||||||
\(281\) | −2.88827 | −0.172300 | −0.0861499 | − | 0.996282i | \(-0.527456\pi\) | ||||
−0.0861499 | + | 0.996282i | \(0.527456\pi\) | |||||||
\(282\) | −3.03225 | −0.180568 | ||||||||
\(283\) | 12.7424 | 0.757460 | 0.378730 | − | 0.925507i | \(-0.376361\pi\) | ||||
0.378730 | + | 0.925507i | \(0.376361\pi\) | |||||||
\(284\) | −14.5849 | −0.865455 | ||||||||
\(285\) | 7.58859 | 0.449509 | ||||||||
\(286\) | 5.15242 | 0.304669 | ||||||||
\(287\) | −1.15383 | −0.0681082 | ||||||||
\(288\) | 5.60883 | 0.330504 | ||||||||
\(289\) | 28.4957 | 1.67622 | ||||||||
\(290\) | 1.90036 | 0.111593 | ||||||||
\(291\) | −16.8992 | −0.990647 | ||||||||
\(292\) | 19.3592 | 1.13291 | ||||||||
\(293\) | −27.3377 | −1.59708 | −0.798542 | − | 0.601940i | \(-0.794395\pi\) | ||||
−0.798542 | + | 0.601940i | \(0.794395\pi\) | |||||||
\(294\) | −0.615474 | −0.0358952 | ||||||||
\(295\) | −7.58610 | −0.441680 | ||||||||
\(296\) | 17.6958 | 1.02855 | ||||||||
\(297\) | −2.65989 | −0.154343 | ||||||||
\(298\) | −5.55391 | −0.321729 | ||||||||
\(299\) | 23.3140 | 1.34829 | ||||||||
\(300\) | −4.57766 | −0.264291 | ||||||||
\(301\) | 8.15649 | 0.470132 | ||||||||
\(302\) | −0.678918 | −0.0390673 | ||||||||
\(303\) | −7.70641 | −0.442722 | ||||||||
\(304\) | 9.62247 | 0.551887 | ||||||||
\(305\) | 4.99283 | 0.285889 | ||||||||
\(306\) | 4.15140 | 0.237320 | ||||||||
\(307\) | −9.30967 | −0.531331 | −0.265665 | − | 0.964065i | \(-0.585592\pi\) | ||||
−0.265665 | + | 0.964065i | \(0.585592\pi\) | |||||||
\(308\) | −4.31220 | −0.245710 | ||||||||
\(309\) | −13.1014 | −0.745315 | ||||||||
\(310\) | 0.278651 | 0.0158263 | ||||||||
\(311\) | −4.29747 | −0.243687 | −0.121844 | − | 0.992549i | \(-0.538881\pi\) | ||||
−0.121844 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(312\) | 7.01452 | 0.397119 | ||||||||
\(313\) | −25.4078 | −1.43613 | −0.718067 | − | 0.695974i | \(-0.754973\pi\) | ||||
−0.718067 | + | 0.695974i | \(0.754973\pi\) | |||||||
\(314\) | −8.32606 | −0.469867 | ||||||||
\(315\) | −1.47525 | −0.0831209 | ||||||||
\(316\) | −5.95519 | −0.335006 | ||||||||
\(317\) | −0.0583539 | −0.00327748 | −0.00163874 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163874 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(318\) | −0.836477 | −0.0469073 | ||||||||
\(319\) | −5.56704 | −0.311695 | ||||||||
\(320\) | 0.426632 | 0.0238495 | ||||||||
\(321\) | −11.4290 | −0.637906 | ||||||||
\(322\) | 4.55922 | 0.254076 | ||||||||
\(323\) | 34.6961 | 1.93054 | ||||||||
\(324\) | −1.62119 | −0.0900662 | ||||||||
\(325\) | −8.88681 | −0.492952 | ||||||||
\(326\) | 12.0071 | 0.665014 | ||||||||
\(327\) | −8.24223 | −0.455797 | ||||||||
\(328\) | 2.57159 | 0.141992 | ||||||||
\(329\) | 4.92668 | 0.271617 | ||||||||
\(330\) | 2.41513 | 0.132948 | ||||||||
\(331\) | 13.5910 | 0.747027 | 0.373513 | − | 0.927625i | \(-0.378153\pi\) | ||||
0.373513 | + | 0.927625i | \(0.378153\pi\) | |||||||
\(332\) | 11.4767 | 0.629868 | ||||||||
\(333\) | −7.93979 | −0.435098 | ||||||||
\(334\) | −7.10479 | −0.388757 | ||||||||
\(335\) | 17.4321 | 0.952418 | ||||||||
\(336\) | −1.87064 | −0.102052 | ||||||||
\(337\) | 20.1155 | 1.09576 | 0.547880 | − | 0.836557i | \(-0.315435\pi\) | ||||
0.547880 | + | 0.836557i | \(0.315435\pi\) | |||||||
\(338\) | −1.90463 | −0.103598 | ||||||||
\(339\) | 8.02930 | 0.436092 | ||||||||
\(340\) | 16.1319 | 0.874874 | ||||||||
\(341\) | −0.816299 | −0.0442051 | ||||||||
\(342\) | 3.16596 | 0.171196 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −18.1788 | −0.980135 | ||||||||
\(345\) | 10.9281 | 0.588351 | ||||||||
\(346\) | 3.41536 | 0.183611 | ||||||||
\(347\) | −22.1518 | −1.18917 | −0.594584 | − | 0.804033i | \(-0.702683\pi\) | ||||
−0.594584 | + | 0.804033i | \(0.702683\pi\) | |||||||
\(348\) | −3.39308 | −0.181888 | ||||||||
\(349\) | −0.913744 | −0.0489116 | −0.0244558 | − | 0.999701i | \(-0.507785\pi\) | ||||
−0.0244558 | + | 0.999701i | \(0.507785\pi\) | |||||||
\(350\) | −1.73788 | −0.0928935 | ||||||||
\(351\) | −3.14729 | −0.167990 | ||||||||
\(352\) | 14.9189 | 0.795180 | ||||||||
\(353\) | −21.2068 | −1.12873 | −0.564363 | − | 0.825527i | \(-0.690878\pi\) | ||||
−0.564363 | + | 0.825527i | \(0.690878\pi\) | |||||||
\(354\) | −3.16492 | −0.168214 | ||||||||
\(355\) | −13.2720 | −0.704402 | ||||||||
\(356\) | 24.5724 | 1.30234 | ||||||||
\(357\) | −6.74505 | −0.356986 | ||||||||
\(358\) | 6.23466 | 0.329512 | ||||||||
\(359\) | −19.2109 | −1.01391 | −0.506956 | − | 0.861972i | \(-0.669229\pi\) | ||||
−0.506956 | + | 0.861972i | \(0.669229\pi\) | |||||||
\(360\) | 3.28796 | 0.173291 | ||||||||
\(361\) | 7.46009 | 0.392636 | ||||||||
\(362\) | −8.66935 | −0.455651 | ||||||||
\(363\) | 3.92496 | 0.206007 | ||||||||
\(364\) | −5.10236 | −0.267436 | ||||||||
\(365\) | 17.6165 | 0.922088 | ||||||||
\(366\) | 2.08301 | 0.108881 | ||||||||
\(367\) | −23.6552 | −1.23479 | −0.617396 | − | 0.786653i | \(-0.711812\pi\) | ||||
−0.617396 | + | 0.786653i | \(0.711812\pi\) | |||||||
\(368\) | 13.8571 | 0.722350 | ||||||||
\(369\) | −1.15383 | −0.0600658 | ||||||||
\(370\) | 7.20916 | 0.374786 | ||||||||
\(371\) | 1.35908 | 0.0705598 | ||||||||
\(372\) | −0.497530 | −0.0257957 | ||||||||
\(373\) | −7.47377 | −0.386977 | −0.193488 | − | 0.981103i | \(-0.561980\pi\) | ||||
−0.193488 | + | 0.981103i | \(0.561980\pi\) | |||||||
\(374\) | 11.0423 | 0.570984 | ||||||||
\(375\) | −11.5418 | −0.596017 | ||||||||
\(376\) | −10.9803 | −0.566268 | ||||||||
\(377\) | −6.58714 | −0.339255 | ||||||||
\(378\) | −0.615474 | −0.0316566 | ||||||||
\(379\) | 22.8644 | 1.17446 | 0.587232 | − | 0.809419i | \(-0.300218\pi\) | ||||
0.587232 | + | 0.809419i | \(0.300218\pi\) | |||||||
\(380\) | 12.3026 | 0.631108 | ||||||||
\(381\) | −1.41454 | −0.0724690 | ||||||||
\(382\) | −4.74186 | −0.242615 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 11.3957 | 0.581532 | ||||||||
\(385\) | −3.92401 | −0.199986 | ||||||||
\(386\) | 7.83266 | 0.398672 | ||||||||
\(387\) | 8.15649 | 0.414618 | ||||||||
\(388\) | −27.3968 | −1.39086 | ||||||||
\(389\) | 9.48152 | 0.480732 | 0.240366 | − | 0.970682i | \(-0.422733\pi\) | ||||
0.240366 | + | 0.970682i | \(0.422733\pi\) | |||||||
\(390\) | 2.85767 | 0.144704 | ||||||||
\(391\) | 49.9650 | 2.52684 | ||||||||
\(392\) | −2.22875 | −0.112569 | ||||||||
\(393\) | 0.675981 | 0.0340987 | ||||||||
\(394\) | 8.91547 | 0.449155 | ||||||||
\(395\) | −5.41910 | −0.272664 | ||||||||
\(396\) | −4.31220 | −0.216696 | ||||||||
\(397\) | −3.05615 | −0.153384 | −0.0766919 | − | 0.997055i | \(-0.524436\pi\) | ||||
−0.0766919 | + | 0.997055i | \(0.524436\pi\) | |||||||
\(398\) | 8.31026 | 0.416555 | ||||||||
\(399\) | −5.14394 | −0.257519 | ||||||||
\(400\) | −5.28202 | −0.264101 | ||||||||
\(401\) | 32.1996 | 1.60797 | 0.803985 | − | 0.594650i | \(-0.202709\pi\) | ||||
0.803985 | + | 0.594650i | \(0.202709\pi\) | |||||||
\(402\) | 7.27268 | 0.362729 | ||||||||
\(403\) | −0.965877 | −0.0481137 | ||||||||
\(404\) | −12.4936 | −0.621578 | ||||||||
\(405\) | −1.47525 | −0.0733057 | ||||||||
\(406\) | −1.28816 | −0.0639304 | ||||||||
\(407\) | −21.1190 | −1.04683 | ||||||||
\(408\) | 15.0330 | 0.744246 | ||||||||
\(409\) | 22.2879 | 1.10206 | 0.551032 | − | 0.834484i | \(-0.314234\pi\) | ||||
0.551032 | + | 0.834484i | \(0.314234\pi\) | |||||||
\(410\) | 1.04765 | 0.0517397 | ||||||||
\(411\) | 21.5180 | 1.06141 | ||||||||
\(412\) | −21.2400 | −1.04642 | ||||||||
\(413\) | 5.14225 | 0.253033 | ||||||||
\(414\) | 4.55922 | 0.224074 | ||||||||
\(415\) | 10.4436 | 0.512656 | ||||||||
\(416\) | 17.6526 | 0.865491 | ||||||||
\(417\) | −8.19044 | −0.401087 | ||||||||
\(418\) | 8.42112 | 0.411891 | ||||||||
\(419\) | −32.6032 | −1.59277 | −0.796385 | − | 0.604790i | \(-0.793257\pi\) | ||||
−0.796385 | + | 0.604790i | \(0.793257\pi\) | |||||||
\(420\) | −2.39166 | −0.116701 | ||||||||
\(421\) | 0.957212 | 0.0466517 | 0.0233258 | − | 0.999728i | \(-0.492574\pi\) | ||||
0.0233258 | + | 0.999728i | \(0.492574\pi\) | |||||||
\(422\) | −1.37975 | −0.0671651 | ||||||||
\(423\) | 4.92668 | 0.239544 | ||||||||
\(424\) | −3.02904 | −0.147103 | ||||||||
\(425\) | −19.0456 | −0.923847 | ||||||||
\(426\) | −5.53706 | −0.268272 | ||||||||
\(427\) | −3.38440 | −0.163782 | ||||||||
\(428\) | −18.5286 | −0.895615 | ||||||||
\(429\) | −8.37146 | −0.404178 | ||||||||
\(430\) | −7.40592 | −0.357145 | ||||||||
\(431\) | 14.5142 | 0.699122 | 0.349561 | − | 0.936914i | \(-0.386331\pi\) | ||||
0.349561 | + | 0.936914i | \(0.386331\pi\) | |||||||
\(432\) | −1.87064 | −0.0900014 | ||||||||
\(433\) | −20.1370 | −0.967721 | −0.483860 | − | 0.875145i | \(-0.660766\pi\) | ||||
−0.483860 | + | 0.875145i | \(0.660766\pi\) | |||||||
\(434\) | −0.188884 | −0.00906672 | ||||||||
\(435\) | −3.08763 | −0.148041 | ||||||||
\(436\) | −13.3622 | −0.639935 | ||||||||
\(437\) | 38.1045 | 1.82279 | ||||||||
\(438\) | 7.34960 | 0.351177 | ||||||||
\(439\) | −36.8477 | −1.75865 | −0.879323 | − | 0.476226i | \(-0.842004\pi\) | ||||
−0.879323 | + | 0.476226i | \(0.842004\pi\) | |||||||
\(440\) | 8.74563 | 0.416932 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 13.0657 | 0.621471 | ||||||||
\(443\) | −10.6354 | −0.505304 | −0.252652 | − | 0.967557i | \(-0.581303\pi\) | ||||
−0.252652 | + | 0.967557i | \(0.581303\pi\) | |||||||
\(444\) | −12.8719 | −0.610874 | ||||||||
\(445\) | 22.3604 | 1.05998 | ||||||||
\(446\) | −13.1415 | −0.622266 | ||||||||
\(447\) | 9.02378 | 0.426810 | ||||||||
\(448\) | −0.289193 | −0.0136631 | ||||||||
\(449\) | −27.7051 | −1.30749 | −0.653743 | − | 0.756716i | \(-0.726802\pi\) | ||||
−0.653743 | + | 0.756716i | \(0.726802\pi\) | |||||||
\(450\) | −1.73788 | −0.0819243 | ||||||||
\(451\) | −3.06905 | −0.144516 | ||||||||
\(452\) | 13.0170 | 0.612270 | ||||||||
\(453\) | 1.10308 | 0.0518272 | ||||||||
\(454\) | 14.8784 | 0.698278 | ||||||||
\(455\) | −4.64304 | −0.217669 | ||||||||
\(456\) | 11.4646 | 0.536877 | ||||||||
\(457\) | −7.54514 | −0.352947 | −0.176473 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176473 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(458\) | 16.2489 | 0.759263 | ||||||||
\(459\) | −6.74505 | −0.314832 | ||||||||
\(460\) | 17.7166 | 0.826041 | ||||||||
\(461\) | −36.0370 | −1.67841 | −0.839204 | − | 0.543816i | \(-0.816979\pi\) | ||||
−0.839204 | + | 0.543816i | \(0.816979\pi\) | |||||||
\(462\) | −1.63710 | −0.0761646 | ||||||||
\(463\) | 12.5248 | 0.582078 | 0.291039 | − | 0.956711i | \(-0.405999\pi\) | ||||
0.291039 | + | 0.956711i | \(0.405999\pi\) | |||||||
\(464\) | −3.91518 | −0.181757 | ||||||||
\(465\) | −0.452742 | −0.0209954 | ||||||||
\(466\) | −0.412792 | −0.0191222 | ||||||||
\(467\) | 11.0137 | 0.509651 | 0.254826 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254826 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(468\) | −5.10236 | −0.235857 | ||||||||
\(469\) | −11.8164 | −0.545630 | ||||||||
\(470\) | −4.47332 | −0.206339 | ||||||||
\(471\) | 13.5279 | 0.623332 | ||||||||
\(472\) | −11.4608 | −0.527525 | ||||||||
\(473\) | 21.6954 | 0.997556 | ||||||||
\(474\) | −2.26085 | −0.103844 | ||||||||
\(475\) | −14.5246 | −0.666435 | ||||||||
\(476\) | −10.9350 | −0.501206 | ||||||||
\(477\) | 1.35908 | 0.0622279 | ||||||||
\(478\) | 9.00524 | 0.411890 | ||||||||
\(479\) | 7.73058 | 0.353219 | 0.176610 | − | 0.984281i | \(-0.443487\pi\) | ||||
0.176610 | + | 0.984281i | \(0.443487\pi\) | |||||||
\(480\) | 8.27443 | 0.377674 | ||||||||
\(481\) | −24.9888 | −1.13939 | ||||||||
\(482\) | 13.6371 | 0.621151 | ||||||||
\(483\) | −7.40766 | −0.337060 | ||||||||
\(484\) | 6.36311 | 0.289232 | ||||||||
\(485\) | −24.9305 | −1.13204 | ||||||||
\(486\) | −0.615474 | −0.0279185 | ||||||||
\(487\) | 10.6857 | 0.484217 | 0.242108 | − | 0.970249i | \(-0.422161\pi\) | ||||
0.242108 | + | 0.970249i | \(0.422161\pi\) | |||||||
\(488\) | 7.54298 | 0.341454 | ||||||||
\(489\) | −19.5088 | −0.882217 | ||||||||
\(490\) | −0.907978 | −0.0410183 | ||||||||
\(491\) | 32.4946 | 1.46646 | 0.733230 | − | 0.679981i | \(-0.238012\pi\) | ||||
0.733230 | + | 0.679981i | \(0.238012\pi\) | |||||||
\(492\) | −1.87057 | −0.0843319 | ||||||||
\(493\) | −14.1171 | −0.635802 | ||||||||
\(494\) | 9.96420 | 0.448311 | ||||||||
\(495\) | −3.92401 | −0.176371 | ||||||||
\(496\) | −0.574085 | −0.0257772 | ||||||||
\(497\) | 8.99642 | 0.403544 | ||||||||
\(498\) | 4.35707 | 0.195245 | ||||||||
\(499\) | −5.90323 | −0.264265 | −0.132133 | − | 0.991232i | \(-0.542182\pi\) | ||||
−0.132133 | + | 0.991232i | \(0.542182\pi\) | |||||||
\(500\) | −18.7115 | −0.836804 | ||||||||
\(501\) | 11.5436 | 0.515730 | ||||||||
\(502\) | −17.8512 | −0.796738 | ||||||||
\(503\) | −5.10199 | −0.227486 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(504\) | −2.22875 | −0.0992764 | ||||||||
\(505\) | −11.3689 | −0.505908 | ||||||||
\(506\) | 12.1270 | 0.539113 | ||||||||
\(507\) | 3.09457 | 0.137434 | ||||||||
\(508\) | −2.29324 | −0.101746 | ||||||||
\(509\) | −6.50365 | −0.288269 | −0.144135 | − | 0.989558i | \(-0.546040\pi\) | ||||
−0.144135 | + | 0.989558i | \(0.546040\pi\) | |||||||
\(510\) | 6.12436 | 0.271191 | ||||||||
\(511\) | −11.9414 | −0.528254 | ||||||||
\(512\) | 18.8305 | 0.832200 | ||||||||
\(513\) | −5.14394 | −0.227110 | ||||||||
\(514\) | 18.2301 | 0.804093 | ||||||||
\(515\) | −19.3279 | −0.851689 | ||||||||
\(516\) | 13.2232 | 0.582120 | ||||||||
\(517\) | 13.1045 | 0.576333 | ||||||||
\(518\) | −4.88674 | −0.214711 | ||||||||
\(519\) | −5.54915 | −0.243581 | ||||||||
\(520\) | 10.3482 | 0.453797 | ||||||||
\(521\) | 10.9167 | 0.478268 | 0.239134 | − | 0.970987i | \(-0.423137\pi\) | ||||
0.239134 | + | 0.970987i | \(0.423137\pi\) | |||||||
\(522\) | −1.28816 | −0.0563813 | ||||||||
\(523\) | 19.0752 | 0.834101 | 0.417050 | − | 0.908883i | \(-0.363064\pi\) | ||||
0.417050 | + | 0.908883i | \(0.363064\pi\) | |||||||
\(524\) | 1.09589 | 0.0478744 | ||||||||
\(525\) | 2.82364 | 0.123234 | ||||||||
\(526\) | −13.0708 | −0.569912 | ||||||||
\(527\) | −2.07000 | −0.0901705 | ||||||||
\(528\) | −4.97571 | −0.216540 | ||||||||
\(529\) | 31.8734 | 1.38580 | ||||||||
\(530\) | −1.23401 | −0.0536021 | ||||||||
\(531\) | 5.14225 | 0.223155 | ||||||||
\(532\) | −8.33931 | −0.361555 | ||||||||
\(533\) | −3.63142 | −0.157294 | ||||||||
\(534\) | 9.32876 | 0.403695 | ||||||||
\(535\) | −16.8607 | −0.728950 | ||||||||
\(536\) | 26.3358 | 1.13753 | ||||||||
\(537\) | −10.1298 | −0.437135 | ||||||||
\(538\) | −11.4293 | −0.492752 | ||||||||
\(539\) | 2.65989 | 0.114570 | ||||||||
\(540\) | −2.39166 | −0.102921 | ||||||||
\(541\) | 32.5536 | 1.39959 | 0.699794 | − | 0.714345i | \(-0.253275\pi\) | ||||
0.699794 | + | 0.714345i | \(0.253275\pi\) | |||||||
\(542\) | 10.4075 | 0.447039 | ||||||||
\(543\) | 14.0856 | 0.604473 | ||||||||
\(544\) | 37.8319 | 1.62203 | ||||||||
\(545\) | −12.1594 | −0.520849 | ||||||||
\(546\) | −1.93708 | −0.0828992 | ||||||||
\(547\) | −26.9108 | −1.15062 | −0.575312 | − | 0.817934i | \(-0.695119\pi\) | ||||
−0.575312 | + | 0.817934i | \(0.695119\pi\) | |||||||
\(548\) | 34.8849 | 1.49021 | ||||||||
\(549\) | −3.38440 | −0.144443 | ||||||||
\(550\) | −4.62257 | −0.197107 | ||||||||
\(551\) | −10.7660 | −0.458649 | ||||||||
\(552\) | 16.5098 | 0.702704 | ||||||||
\(553\) | 3.67334 | 0.156206 | ||||||||
\(554\) | 15.7795 | 0.670407 | ||||||||
\(555\) | −11.7132 | −0.497196 | ||||||||
\(556\) | −13.2783 | −0.563124 | ||||||||
\(557\) | 42.8815 | 1.81695 | 0.908475 | − | 0.417940i | \(-0.137248\pi\) | ||||
0.908475 | + | 0.417940i | \(0.137248\pi\) | |||||||
\(558\) | −0.188884 | −0.00799609 | ||||||||
\(559\) | 25.6708 | 1.08576 | ||||||||
\(560\) | −2.75967 | −0.116617 | ||||||||
\(561\) | −17.9411 | −0.757475 | ||||||||
\(562\) | −1.77766 | −0.0749859 | ||||||||
\(563\) | 40.4360 | 1.70418 | 0.852088 | − | 0.523399i | \(-0.175336\pi\) | ||||
0.852088 | + | 0.523399i | \(0.175336\pi\) | |||||||
\(564\) | 7.98710 | 0.336317 | ||||||||
\(565\) | 11.8452 | 0.498332 | ||||||||
\(566\) | 7.84265 | 0.329651 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −20.0508 | −0.841312 | ||||||||
\(569\) | 33.2826 | 1.39528 | 0.697641 | − | 0.716448i | \(-0.254233\pi\) | ||||
0.697641 | + | 0.716448i | \(0.254233\pi\) | |||||||
\(570\) | 4.67058 | 0.195629 | ||||||||
\(571\) | 9.69896 | 0.405889 | 0.202945 | − | 0.979190i | \(-0.434949\pi\) | ||||
0.202945 | + | 0.979190i | \(0.434949\pi\) | |||||||
\(572\) | −13.5717 | −0.567463 | ||||||||
\(573\) | 7.70439 | 0.321856 | ||||||||
\(574\) | −0.710150 | −0.0296411 | ||||||||
\(575\) | −20.9165 | −0.872280 | ||||||||
\(576\) | −0.289193 | −0.0120497 | ||||||||
\(577\) | −45.1111 | −1.87800 | −0.939000 | − | 0.343918i | \(-0.888246\pi\) | ||||
−0.939000 | + | 0.343918i | \(0.888246\pi\) | |||||||
\(578\) | 17.5384 | 0.729500 | ||||||||
\(579\) | −12.7262 | −0.528884 | ||||||||
\(580\) | −5.00564 | −0.207848 | ||||||||
\(581\) | −7.07921 | −0.293695 | ||||||||
\(582\) | −10.4010 | −0.431136 | ||||||||
\(583\) | 3.61500 | 0.149718 | ||||||||
\(584\) | 26.6143 | 1.10131 | ||||||||
\(585\) | −4.64304 | −0.191966 | ||||||||
\(586\) | −16.8256 | −0.695060 | ||||||||
\(587\) | 38.7428 | 1.59909 | 0.799543 | − | 0.600609i | \(-0.205075\pi\) | ||||
0.799543 | + | 0.600609i | \(0.205075\pi\) | |||||||
\(588\) | 1.62119 | 0.0668568 | ||||||||
\(589\) | −1.57863 | −0.0650463 | ||||||||
\(590\) | −4.66905 | −0.192222 | ||||||||
\(591\) | −14.4855 | −0.595855 | ||||||||
\(592\) | −14.8525 | −0.610435 | ||||||||
\(593\) | −16.0695 | −0.659897 | −0.329949 | − | 0.943999i | \(-0.607031\pi\) | ||||
−0.329949 | + | 0.943999i | \(0.607031\pi\) | |||||||
\(594\) | −1.63710 | −0.0671709 | ||||||||
\(595\) | −9.95063 | −0.407936 | ||||||||
\(596\) | 14.6293 | 0.599239 | ||||||||
\(597\) | −13.5022 | −0.552608 | ||||||||
\(598\) | 14.3492 | 0.586782 | ||||||||
\(599\) | −29.1502 | −1.19104 | −0.595522 | − | 0.803339i | \(-0.703055\pi\) | ||||
−0.595522 | + | 0.803339i | \(0.703055\pi\) | |||||||
\(600\) | −6.29319 | −0.256918 | ||||||||
\(601\) | −10.1442 | −0.413790 | −0.206895 | − | 0.978363i | \(-0.566336\pi\) | ||||
−0.206895 | + | 0.978363i | \(0.566336\pi\) | |||||||
\(602\) | 5.02011 | 0.204605 | ||||||||
\(603\) | −11.8164 | −0.481201 | ||||||||
\(604\) | 1.78830 | 0.0727651 | ||||||||
\(605\) | 5.79030 | 0.235409 | ||||||||
\(606\) | −4.74310 | −0.192675 | ||||||||
\(607\) | −0.0952989 | −0.00386806 | −0.00193403 | − | 0.999998i | \(-0.500616\pi\) | ||||
−0.00193403 | + | 0.999998i | \(0.500616\pi\) | |||||||
\(608\) | 28.8515 | 1.17008 | ||||||||
\(609\) | 2.09296 | 0.0848109 | ||||||||
\(610\) | 3.07296 | 0.124420 | ||||||||
\(611\) | 15.5057 | 0.627294 | ||||||||
\(612\) | −10.9350 | −0.442022 | ||||||||
\(613\) | −22.4925 | −0.908464 | −0.454232 | − | 0.890883i | \(-0.650086\pi\) | ||||
−0.454232 | + | 0.890883i | \(0.650086\pi\) | |||||||
\(614\) | −5.72986 | −0.231238 | ||||||||
\(615\) | −1.70218 | −0.0686385 | ||||||||
\(616\) | −5.92824 | −0.238856 | ||||||||
\(617\) | 27.0522 | 1.08908 | 0.544541 | − | 0.838734i | \(-0.316704\pi\) | ||||
0.544541 | + | 0.838734i | \(0.316704\pi\) | |||||||
\(618\) | −8.06361 | −0.324366 | ||||||||
\(619\) | 16.6874 | 0.670724 | 0.335362 | − | 0.942089i | \(-0.391141\pi\) | ||||
0.335362 | + | 0.942089i | \(0.391141\pi\) | |||||||
\(620\) | −0.733981 | −0.0294774 | ||||||||
\(621\) | −7.40766 | −0.297259 | ||||||||
\(622\) | −2.64498 | −0.106054 | ||||||||
\(623\) | −15.1570 | −0.607253 | ||||||||
\(624\) | −5.88746 | −0.235687 | ||||||||
\(625\) | −2.90887 | −0.116355 | ||||||||
\(626\) | −15.6379 | −0.625014 | ||||||||
\(627\) | −13.6823 | −0.546420 | ||||||||
\(628\) | 21.9313 | 0.875153 | ||||||||
\(629\) | −53.5543 | −2.13535 | ||||||||
\(630\) | −0.907978 | −0.0361747 | ||||||||
\(631\) | 8.82839 | 0.351453 | 0.175726 | − | 0.984439i | \(-0.443773\pi\) | ||||
0.175726 | + | 0.984439i | \(0.443773\pi\) | |||||||
\(632\) | −8.18696 | −0.325660 | ||||||||
\(633\) | 2.24176 | 0.0891021 | ||||||||
\(634\) | −0.0359153 | −0.00142638 | ||||||||
\(635\) | −2.08680 | −0.0828120 | ||||||||
\(636\) | 2.20332 | 0.0873675 | ||||||||
\(637\) | 3.14729 | 0.124700 | ||||||||
\(638\) | −3.42637 | −0.135651 | ||||||||
\(639\) | 8.99642 | 0.355893 | ||||||||
\(640\) | 16.8114 | 0.664531 | ||||||||
\(641\) | 46.9449 | 1.85421 | 0.927107 | − | 0.374797i | \(-0.122288\pi\) | ||||
0.927107 | + | 0.374797i | \(0.122288\pi\) | |||||||
\(642\) | −7.03427 | −0.277620 | ||||||||
\(643\) | −5.38462 | −0.212349 | −0.106174 | − | 0.994348i | \(-0.533860\pi\) | ||||
−0.106174 | + | 0.994348i | \(0.533860\pi\) | |||||||
\(644\) | −12.0092 | −0.473230 | ||||||||
\(645\) | 12.0329 | 0.473793 | ||||||||
\(646\) | 21.3546 | 0.840184 | ||||||||
\(647\) | −25.8377 | −1.01579 | −0.507893 | − | 0.861420i | \(-0.669575\pi\) | ||||
−0.507893 | + | 0.861420i | \(0.669575\pi\) | |||||||
\(648\) | −2.22875 | −0.0875536 | ||||||||
\(649\) | 13.6778 | 0.536902 | ||||||||
\(650\) | −5.46960 | −0.214536 | ||||||||
\(651\) | 0.306892 | 0.0120280 | ||||||||
\(652\) | −31.6274 | −1.23863 | ||||||||
\(653\) | −16.0924 | −0.629745 | −0.314872 | − | 0.949134i | \(-0.601962\pi\) | ||||
−0.314872 | + | 0.949134i | \(0.601962\pi\) | |||||||
\(654\) | −5.07288 | −0.198365 | ||||||||
\(655\) | 0.997241 | 0.0389654 | ||||||||
\(656\) | −2.15840 | −0.0842712 | ||||||||
\(657\) | −11.9414 | −0.465877 | ||||||||
\(658\) | 3.03225 | 0.118209 | ||||||||
\(659\) | −15.9445 | −0.621108 | −0.310554 | − | 0.950556i | \(-0.600515\pi\) | ||||
−0.310554 | + | 0.950556i | \(0.600515\pi\) | |||||||
\(660\) | −6.36157 | −0.247624 | ||||||||
\(661\) | 20.9683 | 0.815573 | 0.407787 | − | 0.913077i | \(-0.366301\pi\) | ||||
0.407787 | + | 0.913077i | \(0.366301\pi\) | |||||||
\(662\) | 8.36489 | 0.325111 | ||||||||
\(663\) | −21.2286 | −0.824451 | ||||||||
\(664\) | 15.7778 | 0.612297 | ||||||||
\(665\) | −7.58859 | −0.294273 | ||||||||
\(666\) | −4.88674 | −0.189357 | ||||||||
\(667\) | −15.5039 | −0.600313 | ||||||||
\(668\) | 18.7144 | 0.724082 | ||||||||
\(669\) | 21.3518 | 0.825507 | ||||||||
\(670\) | 10.7290 | 0.414498 | ||||||||
\(671\) | −9.00214 | −0.347524 | ||||||||
\(672\) | −5.60883 | −0.216365 | ||||||||
\(673\) | −0.301084 | −0.0116059 | −0.00580297 | − | 0.999983i | \(-0.501847\pi\) | ||||
−0.00580297 | + | 0.999983i | \(0.501847\pi\) | |||||||
\(674\) | 12.3806 | 0.476881 | ||||||||
\(675\) | 2.82364 | 0.108682 | ||||||||
\(676\) | 5.01688 | 0.192957 | ||||||||
\(677\) | −2.71893 | −0.104497 | −0.0522484 | − | 0.998634i | \(-0.516639\pi\) | ||||
−0.0522484 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(678\) | 4.94183 | 0.189790 | ||||||||
\(679\) | 16.8992 | 0.648531 | ||||||||
\(680\) | 22.1775 | 0.850467 | ||||||||
\(681\) | −24.1739 | −0.926345 | ||||||||
\(682\) | −0.502411 | −0.0192383 | ||||||||
\(683\) | 4.24150 | 0.162297 | 0.0811483 | − | 0.996702i | \(-0.474141\pi\) | ||||
0.0811483 | + | 0.996702i | \(0.474141\pi\) | |||||||
\(684\) | −8.33931 | −0.318861 | ||||||||
\(685\) | 31.7445 | 1.21289 | ||||||||
\(686\) | 0.615474 | 0.0234989 | ||||||||
\(687\) | −26.4007 | −1.00725 | ||||||||
\(688\) | 15.2579 | 0.581702 | ||||||||
\(689\) | 4.27741 | 0.162956 | ||||||||
\(690\) | 6.72599 | 0.256054 | ||||||||
\(691\) | 25.6308 | 0.975042 | 0.487521 | − | 0.873111i | \(-0.337901\pi\) | ||||
0.487521 | + | 0.873111i | \(0.337901\pi\) | |||||||
\(692\) | −8.99623 | −0.341985 | ||||||||
\(693\) | 2.65989 | 0.101041 | ||||||||
\(694\) | −13.6338 | −0.517534 | ||||||||
\(695\) | −12.0829 | −0.458332 | ||||||||
\(696\) | −4.66468 | −0.176814 | ||||||||
\(697\) | −7.78261 | −0.294787 | ||||||||
\(698\) | −0.562386 | −0.0212866 | ||||||||
\(699\) | 0.670690 | 0.0253678 | ||||||||
\(700\) | 4.57766 | 0.173019 | ||||||||
\(701\) | −27.4453 | −1.03659 | −0.518297 | − | 0.855201i | \(-0.673434\pi\) | ||||
−0.518297 | + | 0.855201i | \(0.673434\pi\) | |||||||
\(702\) | −1.93708 | −0.0731102 | ||||||||
\(703\) | −40.8418 | −1.54038 | ||||||||
\(704\) | −0.769224 | −0.0289912 | ||||||||
\(705\) | 7.26809 | 0.273732 | ||||||||
\(706\) | −13.0523 | −0.491228 | ||||||||
\(707\) | 7.70641 | 0.289829 | ||||||||
\(708\) | 8.33657 | 0.313307 | ||||||||
\(709\) | −26.7447 | −1.00442 | −0.502209 | − | 0.864746i | \(-0.667479\pi\) | ||||
−0.502209 | + | 0.864746i | \(0.667479\pi\) | |||||||
\(710\) | −8.16855 | −0.306560 | ||||||||
\(711\) | 3.67334 | 0.137761 | ||||||||
\(712\) | 33.7812 | 1.26601 | ||||||||
\(713\) | −2.27335 | −0.0851375 | ||||||||
\(714\) | −4.15140 | −0.155362 | ||||||||
\(715\) | −12.3500 | −0.461863 | ||||||||
\(716\) | −16.4224 | −0.613734 | ||||||||
\(717\) | −14.6314 | −0.546419 | ||||||||
\(718\) | −11.8238 | −0.441261 | ||||||||
\(719\) | 20.0846 | 0.749028 | 0.374514 | − | 0.927221i | \(-0.377810\pi\) | ||||
0.374514 | + | 0.927221i | \(0.377810\pi\) | |||||||
\(720\) | −2.75967 | −0.102847 | ||||||||
\(721\) | 13.1014 | 0.487923 | ||||||||
\(722\) | 4.59149 | 0.170878 | ||||||||
\(723\) | −22.1570 | −0.824028 | ||||||||
\(724\) | 22.8355 | 0.848676 | ||||||||
\(725\) | 5.90975 | 0.219483 | ||||||||
\(726\) | 2.41571 | 0.0896555 | ||||||||
\(727\) | −6.01031 | −0.222910 | −0.111455 | − | 0.993769i | \(-0.535551\pi\) | ||||
−0.111455 | + | 0.993769i | \(0.535551\pi\) | |||||||
\(728\) | −7.01452 | −0.259976 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.8425 | 0.401298 | ||||||||
\(731\) | 55.0159 | 2.03484 | ||||||||
\(732\) | −5.48675 | −0.202796 | ||||||||
\(733\) | −38.0210 | −1.40434 | −0.702169 | − | 0.712010i | \(-0.747785\pi\) | ||||
−0.702169 | + | 0.712010i | \(0.747785\pi\) | |||||||
\(734\) | −14.5592 | −0.537389 | ||||||||
\(735\) | 1.47525 | 0.0544154 | ||||||||
\(736\) | 41.5483 | 1.53149 | ||||||||
\(737\) | −31.4303 | −1.15775 | ||||||||
\(738\) | −0.710150 | −0.0261410 | ||||||||
\(739\) | −2.83293 | −0.104211 | −0.0521056 | − | 0.998642i | \(-0.516593\pi\) | ||||
−0.0521056 | + | 0.998642i | \(0.516593\pi\) | |||||||
\(740\) | −18.9893 | −0.698060 | ||||||||
\(741\) | −16.1895 | −0.594735 | ||||||||
\(742\) | 0.836477 | 0.0307080 | ||||||||
\(743\) | −32.7158 | −1.20023 | −0.600114 | − | 0.799915i | \(-0.704878\pi\) | ||||
−0.600114 | + | 0.799915i | \(0.704878\pi\) | |||||||
\(744\) | −0.683985 | −0.0250761 | ||||||||
\(745\) | 13.3123 | 0.487726 | ||||||||
\(746\) | −4.59991 | −0.168415 | ||||||||
\(747\) | −7.07921 | −0.259015 | ||||||||
\(748\) | −29.0860 | −1.06349 | ||||||||
\(749\) | 11.4290 | 0.417607 | ||||||||
\(750\) | −7.10369 | −0.259390 | ||||||||
\(751\) | 41.5043 | 1.51451 | 0.757256 | − | 0.653118i | \(-0.226539\pi\) | ||||
0.757256 | + | 0.653118i | \(0.226539\pi\) | |||||||
\(752\) | 9.21607 | 0.336075 | ||||||||
\(753\) | 29.0040 | 1.05696 | ||||||||
\(754\) | −4.05422 | −0.147646 | ||||||||
\(755\) | 1.62732 | 0.0592242 | ||||||||
\(756\) | 1.62119 | 0.0589622 | ||||||||
\(757\) | 45.4278 | 1.65110 | 0.825551 | − | 0.564327i | \(-0.190864\pi\) | ||||
0.825551 | + | 0.564327i | \(0.190864\pi\) | |||||||
\(758\) | 14.0724 | 0.511134 | ||||||||
\(759\) | −19.7036 | −0.715195 | ||||||||
\(760\) | 16.9131 | 0.613502 | ||||||||
\(761\) | −16.5363 | −0.599439 | −0.299720 | − | 0.954027i | \(-0.596893\pi\) | ||||
−0.299720 | + | 0.954027i | \(0.596893\pi\) | |||||||
\(762\) | −0.870612 | −0.0315389 | ||||||||
\(763\) | 8.24223 | 0.298389 | ||||||||
\(764\) | 12.4903 | 0.451883 | ||||||||
\(765\) | −9.95063 | −0.359766 | ||||||||
\(766\) | −0.615474 | −0.0222380 | ||||||||
\(767\) | 16.1841 | 0.584376 | ||||||||
\(768\) | 6.43535 | 0.232216 | ||||||||
\(769\) | 26.2505 | 0.946618 | 0.473309 | − | 0.880897i | \(-0.343059\pi\) | ||||
0.473309 | + | 0.880897i | \(0.343059\pi\) | |||||||
\(770\) | −2.41513 | −0.0870351 | ||||||||
\(771\) | −29.6195 | −1.06672 | ||||||||
\(772\) | −20.6316 | −0.742549 | ||||||||
\(773\) | 25.5123 | 0.917612 | 0.458806 | − | 0.888536i | \(-0.348277\pi\) | ||||
0.458806 | + | 0.888536i | \(0.348277\pi\) | |||||||
\(774\) | 5.02011 | 0.180444 | ||||||||
\(775\) | 0.866551 | 0.0311274 | ||||||||
\(776\) | −37.6641 | −1.35206 | ||||||||
\(777\) | 7.93979 | 0.284838 | ||||||||
\(778\) | 5.83563 | 0.209217 | ||||||||
\(779\) | −5.93521 | −0.212651 | ||||||||
\(780\) | −7.52725 | −0.269519 | ||||||||
\(781\) | 23.9295 | 0.856266 | ||||||||
\(782\) | 30.7522 | 1.09970 | ||||||||
\(783\) | 2.09296 | 0.0747962 | ||||||||
\(784\) | 1.87064 | 0.0668087 | ||||||||
\(785\) | 19.9570 | 0.712296 | ||||||||
\(786\) | 0.416049 | 0.0148400 | ||||||||
\(787\) | −16.1606 | −0.576062 | −0.288031 | − | 0.957621i | \(-0.593001\pi\) | ||||
−0.288031 | + | 0.957621i | \(0.593001\pi\) | |||||||
\(788\) | −23.4838 | −0.836576 | ||||||||
\(789\) | 21.2369 | 0.756053 | ||||||||
\(790\) | −3.33531 | −0.118665 | ||||||||
\(791\) | −8.02930 | −0.285489 | ||||||||
\(792\) | −5.92824 | −0.210651 | ||||||||
\(793\) | −10.6517 | −0.378252 | ||||||||
\(794\) | −1.88098 | −0.0667536 | ||||||||
\(795\) | 2.00498 | 0.0711092 | ||||||||
\(796\) | −21.8896 | −0.775858 | ||||||||
\(797\) | 36.2983 | 1.28575 | 0.642876 | − | 0.765971i | \(-0.277741\pi\) | ||||
0.642876 | + | 0.765971i | \(0.277741\pi\) | |||||||
\(798\) | −3.16596 | −0.112074 | ||||||||
\(799\) | 33.2307 | 1.17562 | ||||||||
\(800\) | −15.8373 | −0.559934 | ||||||||
\(801\) | −15.1570 | −0.535547 | ||||||||
\(802\) | 19.8180 | 0.699798 | ||||||||
\(803\) | −31.7627 | −1.12088 | ||||||||
\(804\) | −19.1566 | −0.675602 | ||||||||
\(805\) | −10.9281 | −0.385166 | ||||||||
\(806\) | −0.594472 | −0.0209394 | ||||||||
\(807\) | 18.5699 | 0.653691 | ||||||||
\(808\) | −17.1757 | −0.604238 | ||||||||
\(809\) | −13.1186 | −0.461225 | −0.230613 | − | 0.973046i | \(-0.574073\pi\) | ||||
−0.230613 | + | 0.973046i | \(0.574073\pi\) | |||||||
\(810\) | −0.907978 | −0.0319031 | ||||||||
\(811\) | −2.48481 | −0.0872533 | −0.0436267 | − | 0.999048i | \(-0.513891\pi\) | ||||
−0.0436267 | + | 0.999048i | \(0.513891\pi\) | |||||||
\(812\) | 3.39308 | 0.119074 | ||||||||
\(813\) | −16.9097 | −0.593048 | ||||||||
\(814\) | −12.9982 | −0.455587 | ||||||||
\(815\) | −28.7803 | −1.00813 | ||||||||
\(816\) | −12.6176 | −0.441704 | ||||||||
\(817\) | 41.9565 | 1.46787 | ||||||||
\(818\) | 13.7176 | 0.479625 | ||||||||
\(819\) | 3.14729 | 0.109975 | ||||||||
\(820\) | −2.75956 | −0.0963680 | ||||||||
\(821\) | −6.05824 | −0.211434 | −0.105717 | − | 0.994396i | \(-0.533714\pi\) | ||||
−0.105717 | + | 0.994396i | \(0.533714\pi\) | |||||||
\(822\) | 13.2438 | 0.461931 | ||||||||
\(823\) | 37.7463 | 1.31575 | 0.657876 | − | 0.753126i | \(-0.271455\pi\) | ||||
0.657876 | + | 0.753126i | \(0.271455\pi\) | |||||||
\(824\) | −29.1999 | −1.01723 | ||||||||
\(825\) | 7.51058 | 0.261485 | ||||||||
\(826\) | 3.16492 | 0.110122 | ||||||||
\(827\) | −35.4685 | −1.23336 | −0.616680 | − | 0.787214i | \(-0.711523\pi\) | ||||
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(828\) | −12.0092 | −0.417349 | ||||||||
\(829\) | 48.9929 | 1.70159 | 0.850797 | − | 0.525495i | \(-0.176120\pi\) | ||||
0.850797 | + | 0.525495i | \(0.176120\pi\) | |||||||
\(830\) | 6.42777 | 0.223111 | ||||||||
\(831\) | −25.6380 | −0.889371 | ||||||||
\(832\) | −0.910175 | −0.0315546 | ||||||||
\(833\) | 6.74505 | 0.233702 | ||||||||
\(834\) | −5.04100 | −0.174556 | ||||||||
\(835\) | 17.0297 | 0.589337 | ||||||||
\(836\) | −22.1817 | −0.767169 | ||||||||
\(837\) | 0.306892 | 0.0106077 | ||||||||
\(838\) | −20.0664 | −0.693183 | ||||||||
\(839\) | −6.83910 | −0.236112 | −0.118056 | − | 0.993007i | \(-0.537666\pi\) | ||||
−0.118056 | + | 0.993007i | \(0.537666\pi\) | |||||||
\(840\) | −3.28796 | −0.113445 | ||||||||
\(841\) | −24.6195 | −0.848949 | ||||||||
\(842\) | 0.589140 | 0.0203031 | ||||||||
\(843\) | 2.88827 | 0.0994773 | ||||||||
\(844\) | 3.63433 | 0.125099 | ||||||||
\(845\) | 4.56526 | 0.157050 | ||||||||
\(846\) | 3.03225 | 0.104251 | ||||||||
\(847\) | −3.92496 | −0.134863 | ||||||||
\(848\) | 2.54235 | 0.0873046 | ||||||||
\(849\) | −12.7424 | −0.437320 | ||||||||
\(850\) | −11.7221 | −0.402064 | ||||||||
\(851\) | −58.8152 | −2.01616 | ||||||||
\(852\) | 14.5849 | 0.499671 | ||||||||
\(853\) | 9.49202 | 0.325001 | 0.162500 | − | 0.986708i | \(-0.448044\pi\) | ||||
0.162500 | + | 0.986708i | \(0.448044\pi\) | |||||||
\(854\) | −2.08301 | −0.0712791 | ||||||||
\(855\) | −7.58859 | −0.259524 | ||||||||
\(856\) | −25.4724 | −0.870630 | ||||||||
\(857\) | −1.40803 | −0.0480972 | −0.0240486 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240486 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(858\) | −5.15242 | −0.175901 | ||||||||
\(859\) | −46.5823 | −1.58937 | −0.794683 | − | 0.607024i | \(-0.792363\pi\) | ||||
−0.794683 | + | 0.607024i | \(0.792363\pi\) | |||||||
\(860\) | 19.5076 | 0.665203 | ||||||||
\(861\) | 1.15383 | 0.0393223 | ||||||||
\(862\) | 8.93309 | 0.304262 | ||||||||
\(863\) | 20.4439 | 0.695918 | 0.347959 | − | 0.937510i | \(-0.386875\pi\) | ||||
0.347959 | + | 0.937510i | \(0.386875\pi\) | |||||||
\(864\) | −5.60883 | −0.190816 | ||||||||
\(865\) | −8.18638 | −0.278345 | ||||||||
\(866\) | −12.3938 | −0.421158 | ||||||||
\(867\) | −28.4957 | −0.967764 | ||||||||
\(868\) | 0.497530 | 0.0168873 | ||||||||
\(869\) | 9.77070 | 0.331448 | ||||||||
\(870\) | −1.90036 | −0.0644282 | ||||||||
\(871\) | −37.1896 | −1.26012 | ||||||||
\(872\) | −18.3699 | −0.622083 | ||||||||
\(873\) | 16.8992 | 0.571951 | ||||||||
\(874\) | 23.4524 | 0.793288 | ||||||||
\(875\) | 11.5418 | 0.390185 | ||||||||
\(876\) | −19.3592 | −0.654087 | ||||||||
\(877\) | 49.0726 | 1.65707 | 0.828533 | − | 0.559941i | \(-0.189176\pi\) | ||||
0.828533 | + | 0.559941i | \(0.189176\pi\) | |||||||
\(878\) | −22.6788 | −0.765373 | ||||||||
\(879\) | 27.3377 | 0.922076 | ||||||||
\(880\) | −7.34042 | −0.247446 | ||||||||
\(881\) | −13.7137 | −0.462026 | −0.231013 | − | 0.972951i | \(-0.574204\pi\) | ||||
−0.231013 | + | 0.972951i | \(0.574204\pi\) | |||||||
\(882\) | 0.615474 | 0.0207241 | ||||||||
\(883\) | 12.0308 | 0.404869 | 0.202435 | − | 0.979296i | \(-0.435115\pi\) | ||||
0.202435 | + | 0.979296i | \(0.435115\pi\) | |||||||
\(884\) | −34.4157 | −1.15752 | ||||||||
\(885\) | 7.58610 | 0.255004 | ||||||||
\(886\) | −6.54583 | −0.219912 | ||||||||
\(887\) | 39.6259 | 1.33051 | 0.665253 | − | 0.746618i | \(-0.268324\pi\) | ||||
0.665253 | + | 0.746618i | \(0.268324\pi\) | |||||||
\(888\) | −17.6958 | −0.593833 | ||||||||
\(889\) | 1.41454 | 0.0474421 | ||||||||
\(890\) | 13.7623 | 0.461312 | ||||||||
\(891\) | 2.65989 | 0.0891098 | ||||||||
\(892\) | 34.6153 | 1.15901 | ||||||||
\(893\) | 25.3425 | 0.848056 | ||||||||
\(894\) | 5.55391 | 0.185750 | ||||||||
\(895\) | −14.9440 | −0.499524 | ||||||||
\(896\) | −11.3957 | −0.380702 | ||||||||
\(897\) | −23.3140 | −0.778433 | ||||||||
\(898\) | −17.0518 | −0.569026 | ||||||||
\(899\) | 0.642311 | 0.0214223 | ||||||||
\(900\) | 4.57766 | 0.152589 | ||||||||
\(901\) | 9.16704 | 0.305398 | ||||||||
\(902\) | −1.88892 | −0.0628943 | ||||||||
\(903\) | −8.15649 | −0.271431 | ||||||||
\(904\) | 17.8953 | 0.595189 | ||||||||
\(905\) | 20.7798 | 0.690745 | ||||||||
\(906\) | 0.678918 | 0.0225555 | ||||||||
\(907\) | 3.14956 | 0.104579 | 0.0522897 | − | 0.998632i | \(-0.483348\pi\) | ||||
0.0522897 | + | 0.998632i | \(0.483348\pi\) | |||||||
\(908\) | −39.1905 | −1.30058 | ||||||||
\(909\) | 7.70641 | 0.255605 | ||||||||
\(910\) | −2.85767 | −0.0947309 | ||||||||
\(911\) | 14.0435 | 0.465281 | 0.232641 | − | 0.972563i | \(-0.425263\pi\) | ||||
0.232641 | + | 0.972563i | \(0.425263\pi\) | |||||||
\(912\) | −9.62247 | −0.318632 | ||||||||
\(913\) | −18.8299 | −0.623180 | ||||||||
\(914\) | −4.64384 | −0.153605 | ||||||||
\(915\) | −4.99283 | −0.165058 | ||||||||
\(916\) | −42.8005 | −1.41417 | ||||||||
\(917\) | −0.675981 | −0.0223229 | ||||||||
\(918\) | −4.15140 | −0.137017 | ||||||||
\(919\) | 45.4700 | 1.49992 | 0.749959 | − | 0.661485i | \(-0.230073\pi\) | ||||
0.749959 | + | 0.661485i | \(0.230073\pi\) | |||||||
\(920\) | 24.3561 | 0.802997 | ||||||||
\(921\) | 9.30967 | 0.306764 | ||||||||
\(922\) | −22.1798 | −0.730454 | ||||||||
\(923\) | 28.3143 | 0.931978 | ||||||||
\(924\) | 4.31220 | 0.141861 | ||||||||
\(925\) | 22.4191 | 0.737136 | ||||||||
\(926\) | 7.70872 | 0.253324 | ||||||||
\(927\) | 13.1014 | 0.430308 | ||||||||
\(928\) | −11.7390 | −0.385353 | ||||||||
\(929\) | 6.63884 | 0.217813 | 0.108907 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108907 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(930\) | −0.278651 | −0.00913732 | ||||||||
\(931\) | 5.14394 | 0.168586 | ||||||||
\(932\) | 1.08732 | 0.0356162 | ||||||||
\(933\) | 4.29747 | 0.140693 | ||||||||
\(934\) | 6.77862 | 0.221803 | ||||||||
\(935\) | −26.4676 | −0.865584 | ||||||||
\(936\) | −7.01452 | −0.229277 | ||||||||
\(937\) | 31.9585 | 1.04404 | 0.522020 | − | 0.852933i | \(-0.325179\pi\) | ||||
0.522020 | + | 0.852933i | \(0.325179\pi\) | |||||||
\(938\) | −7.27268 | −0.237462 | ||||||||
\(939\) | 25.4078 | 0.829152 | ||||||||
\(940\) | 11.7830 | 0.384318 | ||||||||
\(941\) | −16.6734 | −0.543537 | −0.271769 | − | 0.962363i | \(-0.587609\pi\) | ||||
−0.271769 | + | 0.962363i | \(0.587609\pi\) | |||||||
\(942\) | 8.32606 | 0.271278 | ||||||||
\(943\) | −8.54714 | −0.278333 | ||||||||
\(944\) | 9.61931 | 0.313082 | ||||||||
\(945\) | 1.47525 | 0.0479899 | ||||||||
\(946\) | 13.3530 | 0.434142 | ||||||||
\(947\) | 3.91223 | 0.127130 | 0.0635651 | − | 0.997978i | \(-0.479753\pi\) | ||||
0.0635651 | + | 0.997978i | \(0.479753\pi\) | |||||||
\(948\) | 5.95519 | 0.193416 | ||||||||
\(949\) | −37.5829 | −1.21999 | ||||||||
\(950\) | −8.93953 | −0.290037 | ||||||||
\(951\) | 0.0583539 | 0.00189225 | ||||||||
\(952\) | −15.0330 | −0.487223 | ||||||||
\(953\) | −27.6278 | −0.894952 | −0.447476 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447476 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(954\) | 0.836477 | 0.0270820 | ||||||||
\(955\) | 11.3659 | 0.367792 | ||||||||
\(956\) | −23.7203 | −0.767168 | ||||||||
\(957\) | 5.56704 | 0.179957 | ||||||||
\(958\) | 4.75797 | 0.153723 | ||||||||
\(959\) | −21.5180 | −0.694854 | ||||||||
\(960\) | −0.426632 | −0.0137695 | ||||||||
\(961\) | −30.9058 | −0.996962 | ||||||||
\(962\) | −15.3800 | −0.495871 | ||||||||
\(963\) | 11.4290 | 0.368295 | ||||||||
\(964\) | −35.9207 | −1.15693 | ||||||||
\(965\) | −18.7743 | −0.604367 | ||||||||
\(966\) | −4.55922 | −0.146691 | ||||||||
\(967\) | −16.6158 | −0.534329 | −0.267164 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267164 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(968\) | 8.74776 | 0.281164 | ||||||||
\(969\) | −34.6961 | −1.11460 | ||||||||
\(970\) | −15.3441 | −0.492669 | ||||||||
\(971\) | 50.4062 | 1.61761 | 0.808806 | − | 0.588076i | \(-0.200114\pi\) | ||||
0.808806 | + | 0.588076i | \(0.200114\pi\) | |||||||
\(972\) | 1.62119 | 0.0519997 | ||||||||
\(973\) | 8.19044 | 0.262573 | ||||||||
\(974\) | 6.57680 | 0.210734 | ||||||||
\(975\) | 8.88681 | 0.284606 | ||||||||
\(976\) | −6.33100 | −0.202650 | ||||||||
\(977\) | −20.5800 | −0.658413 | −0.329207 | − | 0.944258i | \(-0.606781\pi\) | ||||
−0.329207 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(978\) | −12.0071 | −0.383946 | ||||||||
\(979\) | −40.3161 | −1.28851 | ||||||||
\(980\) | 2.39166 | 0.0763988 | ||||||||
\(981\) | 8.24223 | 0.263154 | ||||||||
\(982\) | 19.9996 | 0.638212 | ||||||||
\(983\) | −15.4553 | −0.492946 | −0.246473 | − | 0.969150i | \(-0.579272\pi\) | ||||
−0.246473 | + | 0.969150i | \(0.579272\pi\) | |||||||
\(984\) | −2.57159 | −0.0819793 | ||||||||
\(985\) | −21.3698 | −0.680898 | ||||||||
\(986\) | −8.68871 | −0.276705 | ||||||||
\(987\) | −4.92668 | −0.156818 | ||||||||
\(988\) | −26.2462 | −0.835003 | ||||||||
\(989\) | 60.4205 | 1.92126 | ||||||||
\(990\) | −2.41513 | −0.0767578 | ||||||||
\(991\) | −11.6290 | −0.369407 | −0.184704 | − | 0.982794i | \(-0.559133\pi\) | ||||
−0.184704 | + | 0.982794i | \(0.559133\pi\) | |||||||
\(992\) | −1.72130 | −0.0546515 | ||||||||
\(993\) | −13.5910 | −0.431296 | ||||||||
\(994\) | 5.53706 | 0.175625 | ||||||||
\(995\) | −19.9191 | −0.631478 | ||||||||
\(996\) | −11.4767 | −0.363655 | ||||||||
\(997\) | 47.2683 | 1.49700 | 0.748501 | − | 0.663133i | \(-0.230774\pi\) | ||||
0.748501 | + | 0.663133i | \(0.230774\pi\) | |||||||
\(998\) | −3.63329 | −0.115010 | ||||||||
\(999\) | 7.93979 | 0.251204 |
(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 | 8043.2.a.t.1.32 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.32 | ✓ | 52 | 1.1 | even | 1 | trivial |