Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.667457 | −0.471963 | −0.235982 | − | 0.971758i | \(-0.575831\pi\) | ||||
−0.235982 | + | 0.971758i | \(0.575831\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.55450 | −0.777251 | ||||||||
\(5\) | −3.08787 | −1.38094 | −0.690469 | − | 0.723362i | \(-0.742596\pi\) | ||||
−0.690469 | + | 0.723362i | \(0.742596\pi\) | |||||||
\(6\) | −0.667457 | −0.272488 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.37248 | 0.838797 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.06102 | 0.651752 | ||||||||
\(11\) | 3.38261 | 1.01990 | 0.509948 | − | 0.860205i | \(-0.329665\pi\) | ||||
0.509948 | + | 0.860205i | \(0.329665\pi\) | |||||||
\(12\) | −1.55450 | −0.448746 | ||||||||
\(13\) | 5.44801 | 1.51101 | 0.755503 | − | 0.655145i | \(-0.227392\pi\) | ||||
0.755503 | + | 0.655145i | \(0.227392\pi\) | |||||||
\(14\) | −0.667457 | −0.178385 | ||||||||
\(15\) | −3.08787 | −0.797285 | ||||||||
\(16\) | 1.52548 | 0.381370 | ||||||||
\(17\) | 3.25641 | 0.789794 | 0.394897 | − | 0.918725i | \(-0.370780\pi\) | ||||
0.394897 | + | 0.918725i | \(0.370780\pi\) | |||||||
\(18\) | −0.667457 | −0.157321 | ||||||||
\(19\) | −2.41947 | −0.555063 | −0.277532 | − | 0.960716i | \(-0.589516\pi\) | ||||
−0.277532 | + | 0.960716i | \(0.589516\pi\) | |||||||
\(20\) | 4.80010 | 1.07334 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.25775 | −0.481353 | ||||||||
\(23\) | 3.81625 | 0.795743 | 0.397871 | − | 0.917441i | \(-0.369749\pi\) | ||||
0.397871 | + | 0.917441i | \(0.369749\pi\) | |||||||
\(24\) | 2.37248 | 0.484280 | ||||||||
\(25\) | 4.53495 | 0.906990 | ||||||||
\(26\) | −3.63631 | −0.713140 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.55450 | −0.293773 | ||||||||
\(29\) | −2.74166 | −0.509114 | −0.254557 | − | 0.967058i | \(-0.581930\pi\) | ||||
−0.254557 | + | 0.967058i | \(0.581930\pi\) | |||||||
\(30\) | 2.06102 | 0.376289 | ||||||||
\(31\) | −2.56542 | −0.460763 | −0.230382 | − | 0.973100i | \(-0.573997\pi\) | ||||
−0.230382 | + | 0.973100i | \(0.573997\pi\) | |||||||
\(32\) | −5.76314 | −1.01879 | ||||||||
\(33\) | 3.38261 | 0.588837 | ||||||||
\(34\) | −2.17351 | −0.372754 | ||||||||
\(35\) | −3.08787 | −0.521945 | ||||||||
\(36\) | −1.55450 | −0.259084 | ||||||||
\(37\) | −2.44039 | −0.401198 | −0.200599 | − | 0.979673i | \(-0.564289\pi\) | ||||
−0.200599 | + | 0.979673i | \(0.564289\pi\) | |||||||
\(38\) | 1.61489 | 0.261969 | ||||||||
\(39\) | 5.44801 | 0.872380 | ||||||||
\(40\) | −7.32590 | −1.15833 | ||||||||
\(41\) | 7.88451 | 1.23135 | 0.615677 | − | 0.787999i | \(-0.288883\pi\) | ||||
0.615677 | + | 0.787999i | \(0.288883\pi\) | |||||||
\(42\) | −0.667457 | −0.102991 | ||||||||
\(43\) | −5.47513 | −0.834949 | −0.417475 | − | 0.908689i | \(-0.637085\pi\) | ||||
−0.417475 | + | 0.908689i | \(0.637085\pi\) | |||||||
\(44\) | −5.25828 | −0.792715 | ||||||||
\(45\) | −3.08787 | −0.460313 | ||||||||
\(46\) | −2.54718 | −0.375561 | ||||||||
\(47\) | −7.99578 | −1.16630 | −0.583152 | − | 0.812363i | \(-0.698181\pi\) | ||||
−0.583152 | + | 0.812363i | \(0.698181\pi\) | |||||||
\(48\) | 1.52548 | 0.220184 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.02688 | −0.428066 | ||||||||
\(51\) | 3.25641 | 0.455988 | ||||||||
\(52\) | −8.46894 | −1.17443 | ||||||||
\(53\) | 4.78771 | 0.657643 | 0.328822 | − | 0.944392i | \(-0.393349\pi\) | ||||
0.328822 | + | 0.944392i | \(0.393349\pi\) | |||||||
\(54\) | −0.667457 | −0.0908294 | ||||||||
\(55\) | −10.4451 | −1.40841 | ||||||||
\(56\) | 2.37248 | 0.317035 | ||||||||
\(57\) | −2.41947 | −0.320466 | ||||||||
\(58\) | 1.82994 | 0.240283 | ||||||||
\(59\) | −7.18848 | −0.935860 | −0.467930 | − | 0.883766i | \(-0.655000\pi\) | ||||
−0.467930 | + | 0.883766i | \(0.655000\pi\) | |||||||
\(60\) | 4.80010 | 0.619690 | ||||||||
\(61\) | 11.6380 | 1.49009 | 0.745045 | − | 0.667014i | \(-0.232428\pi\) | ||||
0.745045 | + | 0.667014i | \(0.232428\pi\) | |||||||
\(62\) | 1.71231 | 0.217463 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0.795692 | 0.0994615 | ||||||||
\(65\) | −16.8228 | −2.08661 | ||||||||
\(66\) | −2.25775 | −0.277909 | ||||||||
\(67\) | −6.11569 | −0.747150 | −0.373575 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373575 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(68\) | −5.06209 | −0.613868 | ||||||||
\(69\) | 3.81625 | 0.459422 | ||||||||
\(70\) | 2.06102 | 0.246339 | ||||||||
\(71\) | 15.4248 | 1.83058 | 0.915291 | − | 0.402794i | \(-0.131961\pi\) | ||||
0.915291 | + | 0.402794i | \(0.131961\pi\) | |||||||
\(72\) | 2.37248 | 0.279599 | ||||||||
\(73\) | −0.602919 | −0.0705663 | −0.0352831 | − | 0.999377i | \(-0.511233\pi\) | ||||
−0.0352831 | + | 0.999377i | \(0.511233\pi\) | |||||||
\(74\) | 1.62885 | 0.189350 | ||||||||
\(75\) | 4.53495 | 0.523651 | ||||||||
\(76\) | 3.76106 | 0.431423 | ||||||||
\(77\) | 3.38261 | 0.385484 | ||||||||
\(78\) | −3.63631 | −0.411731 | ||||||||
\(79\) | −5.66920 | −0.637834 | −0.318917 | − | 0.947783i | \(-0.603319\pi\) | ||||
−0.318917 | + | 0.947783i | \(0.603319\pi\) | |||||||
\(80\) | −4.71048 | −0.526648 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.26257 | −0.581153 | ||||||||
\(83\) | 4.60337 | 0.505285 | 0.252643 | − | 0.967560i | \(-0.418700\pi\) | ||||
0.252643 | + | 0.967560i | \(0.418700\pi\) | |||||||
\(84\) | −1.55450 | −0.169610 | ||||||||
\(85\) | −10.0554 | −1.09066 | ||||||||
\(86\) | 3.65441 | 0.394065 | ||||||||
\(87\) | −2.74166 | −0.293937 | ||||||||
\(88\) | 8.02517 | 0.855486 | ||||||||
\(89\) | 0.152886 | 0.0162059 | 0.00810293 | − | 0.999967i | \(-0.497421\pi\) | ||||
0.00810293 | + | 0.999967i | \(0.497421\pi\) | |||||||
\(90\) | 2.06102 | 0.217251 | ||||||||
\(91\) | 5.44801 | 0.571107 | ||||||||
\(92\) | −5.93236 | −0.618492 | ||||||||
\(93\) | −2.56542 | −0.266022 | ||||||||
\(94\) | 5.33684 | 0.550453 | ||||||||
\(95\) | 7.47100 | 0.766508 | ||||||||
\(96\) | −5.76314 | −0.588198 | ||||||||
\(97\) | 4.77136 | 0.484459 | 0.242229 | − | 0.970219i | \(-0.422121\pi\) | ||||
0.242229 | + | 0.970219i | \(0.422121\pi\) | |||||||
\(98\) | −0.667457 | −0.0674233 | ||||||||
\(99\) | 3.38261 | 0.339965 | ||||||||
\(100\) | −7.04958 | −0.704958 | ||||||||
\(101\) | 14.5572 | 1.44850 | 0.724248 | − | 0.689540i | \(-0.242187\pi\) | ||||
0.724248 | + | 0.689540i | \(0.242187\pi\) | |||||||
\(102\) | −2.17351 | −0.215210 | ||||||||
\(103\) | −17.7347 | −1.74745 | −0.873726 | − | 0.486419i | \(-0.838303\pi\) | ||||
−0.873726 | + | 0.486419i | \(0.838303\pi\) | |||||||
\(104\) | 12.9253 | 1.26743 | ||||||||
\(105\) | −3.08787 | −0.301345 | ||||||||
\(106\) | −3.19559 | −0.310383 | ||||||||
\(107\) | 2.98071 | 0.288156 | 0.144078 | − | 0.989566i | \(-0.453978\pi\) | ||||
0.144078 | + | 0.989566i | \(0.453978\pi\) | |||||||
\(108\) | −1.55450 | −0.149582 | ||||||||
\(109\) | 10.0142 | 0.959189 | 0.479594 | − | 0.877490i | \(-0.340784\pi\) | ||||
0.479594 | + | 0.877490i | \(0.340784\pi\) | |||||||
\(110\) | 6.97163 | 0.664719 | ||||||||
\(111\) | −2.44039 | −0.231632 | ||||||||
\(112\) | 1.52548 | 0.144144 | ||||||||
\(113\) | 4.26465 | 0.401185 | 0.200592 | − | 0.979675i | \(-0.435713\pi\) | ||||
0.200592 | + | 0.979675i | \(0.435713\pi\) | |||||||
\(114\) | 1.61489 | 0.151248 | ||||||||
\(115\) | −11.7841 | −1.09887 | ||||||||
\(116\) | 4.26192 | 0.395709 | ||||||||
\(117\) | 5.44801 | 0.503669 | ||||||||
\(118\) | 4.79800 | 0.441691 | ||||||||
\(119\) | 3.25641 | 0.298514 | ||||||||
\(120\) | −7.32590 | −0.668760 | ||||||||
\(121\) | 0.442066 | 0.0401878 | ||||||||
\(122\) | −7.76784 | −0.703267 | ||||||||
\(123\) | 7.88451 | 0.710922 | ||||||||
\(124\) | 3.98795 | 0.358128 | ||||||||
\(125\) | 1.43602 | 0.128442 | ||||||||
\(126\) | −0.667457 | −0.0594618 | ||||||||
\(127\) | −4.08207 | −0.362225 | −0.181112 | − | 0.983462i | \(-0.557970\pi\) | ||||
−0.181112 | + | 0.983462i | \(0.557970\pi\) | |||||||
\(128\) | 10.9952 | 0.971847 | ||||||||
\(129\) | −5.47513 | −0.482058 | ||||||||
\(130\) | 11.2285 | 0.984802 | ||||||||
\(131\) | −5.40654 | −0.472372 | −0.236186 | − | 0.971708i | \(-0.575897\pi\) | ||||
−0.236186 | + | 0.971708i | \(0.575897\pi\) | |||||||
\(132\) | −5.25828 | −0.457674 | ||||||||
\(133\) | −2.41947 | −0.209794 | ||||||||
\(134\) | 4.08196 | 0.352627 | ||||||||
\(135\) | −3.08787 | −0.265762 | ||||||||
\(136\) | 7.72574 | 0.662477 | ||||||||
\(137\) | 3.15025 | 0.269144 | 0.134572 | − | 0.990904i | \(-0.457034\pi\) | ||||
0.134572 | + | 0.990904i | \(0.457034\pi\) | |||||||
\(138\) | −2.54718 | −0.216830 | ||||||||
\(139\) | −0.517691 | −0.0439100 | −0.0219550 | − | 0.999759i | \(-0.506989\pi\) | ||||
−0.0219550 | + | 0.999759i | \(0.506989\pi\) | |||||||
\(140\) | 4.80010 | 0.405683 | ||||||||
\(141\) | −7.99578 | −0.673366 | ||||||||
\(142\) | −10.2954 | −0.863967 | ||||||||
\(143\) | 18.4285 | 1.54107 | ||||||||
\(144\) | 1.52548 | 0.127123 | ||||||||
\(145\) | 8.46590 | 0.703054 | ||||||||
\(146\) | 0.402422 | 0.0333047 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 3.79359 | 0.311831 | ||||||||
\(149\) | −14.3198 | −1.17312 | −0.586562 | − | 0.809904i | \(-0.699519\pi\) | ||||
−0.586562 | + | 0.809904i | \(0.699519\pi\) | |||||||
\(150\) | −3.02688 | −0.247144 | ||||||||
\(151\) | −4.69987 | −0.382470 | −0.191235 | − | 0.981544i | \(-0.561249\pi\) | ||||
−0.191235 | + | 0.981544i | \(0.561249\pi\) | |||||||
\(152\) | −5.74012 | −0.465585 | ||||||||
\(153\) | 3.25641 | 0.263265 | ||||||||
\(154\) | −2.25775 | −0.181934 | ||||||||
\(155\) | 7.92169 | 0.636285 | ||||||||
\(156\) | −8.46894 | −0.678058 | ||||||||
\(157\) | 13.9878 | 1.11635 | 0.558175 | − | 0.829724i | \(-0.311502\pi\) | ||||
0.558175 | + | 0.829724i | \(0.311502\pi\) | |||||||
\(158\) | 3.78394 | 0.301034 | ||||||||
\(159\) | 4.78771 | 0.379690 | ||||||||
\(160\) | 17.7958 | 1.40688 | ||||||||
\(161\) | 3.81625 | 0.300763 | ||||||||
\(162\) | −0.667457 | −0.0524404 | ||||||||
\(163\) | 9.64387 | 0.755366 | 0.377683 | − | 0.925935i | \(-0.376721\pi\) | ||||
0.377683 | + | 0.925935i | \(0.376721\pi\) | |||||||
\(164\) | −12.2565 | −0.957070 | ||||||||
\(165\) | −10.4451 | −0.813148 | ||||||||
\(166\) | −3.07255 | −0.238476 | ||||||||
\(167\) | 7.61005 | 0.588883 | 0.294442 | − | 0.955670i | \(-0.404866\pi\) | ||||
0.294442 | + | 0.955670i | \(0.404866\pi\) | |||||||
\(168\) | 2.37248 | 0.183040 | ||||||||
\(169\) | 16.6808 | 1.28314 | ||||||||
\(170\) | 6.71152 | 0.514750 | ||||||||
\(171\) | −2.41947 | −0.185021 | ||||||||
\(172\) | 8.51109 | 0.648965 | ||||||||
\(173\) | 11.3520 | 0.863079 | 0.431539 | − | 0.902094i | \(-0.357971\pi\) | ||||
0.431539 | + | 0.902094i | \(0.357971\pi\) | |||||||
\(174\) | 1.82994 | 0.138727 | ||||||||
\(175\) | 4.53495 | 0.342810 | ||||||||
\(176\) | 5.16010 | 0.388957 | ||||||||
\(177\) | −7.18848 | −0.540319 | ||||||||
\(178\) | −0.102045 | −0.00764857 | ||||||||
\(179\) | −3.53608 | −0.264299 | −0.132150 | − | 0.991230i | \(-0.542188\pi\) | ||||
−0.132150 | + | 0.991230i | \(0.542188\pi\) | |||||||
\(180\) | 4.80010 | 0.357778 | ||||||||
\(181\) | −5.12094 | −0.380636 | −0.190318 | − | 0.981722i | \(-0.560952\pi\) | ||||
−0.190318 | + | 0.981722i | \(0.560952\pi\) | |||||||
\(182\) | −3.63631 | −0.269541 | ||||||||
\(183\) | 11.6380 | 0.860304 | ||||||||
\(184\) | 9.05396 | 0.667467 | ||||||||
\(185\) | 7.53561 | 0.554029 | ||||||||
\(186\) | 1.71231 | 0.125552 | ||||||||
\(187\) | 11.0152 | 0.805508 | ||||||||
\(188\) | 12.4295 | 0.906511 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −4.98657 | −0.361764 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 0.795692 | 0.0574241 | ||||||||
\(193\) | 9.36730 | 0.674273 | 0.337136 | − | 0.941456i | \(-0.390542\pi\) | ||||
0.337136 | + | 0.941456i | \(0.390542\pi\) | |||||||
\(194\) | −3.18468 | −0.228647 | ||||||||
\(195\) | −16.8228 | −1.20470 | ||||||||
\(196\) | −1.55450 | −0.111036 | ||||||||
\(197\) | 21.2008 | 1.51049 | 0.755247 | − | 0.655441i | \(-0.227517\pi\) | ||||
0.755247 | + | 0.655441i | \(0.227517\pi\) | |||||||
\(198\) | −2.25775 | −0.160451 | ||||||||
\(199\) | −8.78524 | −0.622769 | −0.311385 | − | 0.950284i | \(-0.600793\pi\) | ||||
−0.311385 | + | 0.950284i | \(0.600793\pi\) | |||||||
\(200\) | 10.7591 | 0.760780 | ||||||||
\(201\) | −6.11569 | −0.431367 | ||||||||
\(202\) | −9.71630 | −0.683637 | ||||||||
\(203\) | −2.74166 | −0.192427 | ||||||||
\(204\) | −5.06209 | −0.354417 | ||||||||
\(205\) | −24.3463 | −1.70042 | ||||||||
\(206\) | 11.8371 | 0.824733 | ||||||||
\(207\) | 3.81625 | 0.265248 | ||||||||
\(208\) | 8.31082 | 0.576252 | ||||||||
\(209\) | −8.18411 | −0.566107 | ||||||||
\(210\) | 2.06102 | 0.142224 | ||||||||
\(211\) | 2.26025 | 0.155602 | 0.0778012 | − | 0.996969i | \(-0.475210\pi\) | ||||
0.0778012 | + | 0.996969i | \(0.475210\pi\) | |||||||
\(212\) | −7.44251 | −0.511154 | ||||||||
\(213\) | 15.4248 | 1.05689 | ||||||||
\(214\) | −1.98949 | −0.135999 | ||||||||
\(215\) | 16.9065 | 1.15301 | ||||||||
\(216\) | 2.37248 | 0.161427 | ||||||||
\(217\) | −2.56542 | −0.174152 | ||||||||
\(218\) | −6.68406 | −0.452702 | ||||||||
\(219\) | −0.602919 | −0.0407415 | ||||||||
\(220\) | 16.2369 | 1.09469 | ||||||||
\(221\) | 17.7409 | 1.19338 | ||||||||
\(222\) | 1.62885 | 0.109322 | ||||||||
\(223\) | 10.8614 | 0.727336 | 0.363668 | − | 0.931529i | \(-0.381524\pi\) | ||||
0.363668 | + | 0.931529i | \(0.381524\pi\) | |||||||
\(224\) | −5.76314 | −0.385066 | ||||||||
\(225\) | 4.53495 | 0.302330 | ||||||||
\(226\) | −2.84647 | −0.189344 | ||||||||
\(227\) | 15.5064 | 1.02919 | 0.514597 | − | 0.857432i | \(-0.327942\pi\) | ||||
0.514597 | + | 0.857432i | \(0.327942\pi\) | |||||||
\(228\) | 3.76106 | 0.249082 | ||||||||
\(229\) | −10.2988 | −0.680562 | −0.340281 | − | 0.940324i | \(-0.610522\pi\) | ||||
−0.340281 | + | 0.940324i | \(0.610522\pi\) | |||||||
\(230\) | 7.86537 | 0.518627 | ||||||||
\(231\) | 3.38261 | 0.222560 | ||||||||
\(232\) | −6.50453 | −0.427043 | ||||||||
\(233\) | −15.9728 | −1.04641 | −0.523206 | − | 0.852206i | \(-0.675264\pi\) | ||||
−0.523206 | + | 0.852206i | \(0.675264\pi\) | |||||||
\(234\) | −3.63631 | −0.237713 | ||||||||
\(235\) | 24.6899 | 1.61059 | ||||||||
\(236\) | 11.1745 | 0.727398 | ||||||||
\(237\) | −5.66920 | −0.368254 | ||||||||
\(238\) | −2.17351 | −0.140888 | ||||||||
\(239\) | −9.28681 | −0.600714 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(240\) | −4.71048 | −0.304060 | ||||||||
\(241\) | 28.5878 | 1.84150 | 0.920752 | − | 0.390149i | \(-0.127577\pi\) | ||||
0.920752 | + | 0.390149i | \(0.127577\pi\) | |||||||
\(242\) | −0.295060 | −0.0189672 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −18.0912 | −1.15817 | ||||||||
\(245\) | −3.08787 | −0.197277 | ||||||||
\(246\) | −5.26257 | −0.335529 | ||||||||
\(247\) | −13.1813 | −0.838705 | ||||||||
\(248\) | −6.08640 | −0.386487 | ||||||||
\(249\) | 4.60337 | 0.291726 | ||||||||
\(250\) | −0.958482 | −0.0606197 | ||||||||
\(251\) | −10.2397 | −0.646322 | −0.323161 | − | 0.946344i | \(-0.604746\pi\) | ||||
−0.323161 | + | 0.946344i | \(0.604746\pi\) | |||||||
\(252\) | −1.55450 | −0.0979244 | ||||||||
\(253\) | 12.9089 | 0.811575 | ||||||||
\(254\) | 2.72460 | 0.170957 | ||||||||
\(255\) | −10.0554 | −0.629691 | ||||||||
\(256\) | −8.93020 | −0.558138 | ||||||||
\(257\) | 23.6781 | 1.47700 | 0.738500 | − | 0.674254i | \(-0.235535\pi\) | ||||
0.738500 | + | 0.674254i | \(0.235535\pi\) | |||||||
\(258\) | 3.65441 | 0.227514 | ||||||||
\(259\) | −2.44039 | −0.151638 | ||||||||
\(260\) | 26.1510 | 1.62182 | ||||||||
\(261\) | −2.74166 | −0.169705 | ||||||||
\(262\) | 3.60863 | 0.222942 | ||||||||
\(263\) | 22.9556 | 1.41551 | 0.707753 | − | 0.706460i | \(-0.249709\pi\) | ||||
0.707753 | + | 0.706460i | \(0.249709\pi\) | |||||||
\(264\) | 8.02517 | 0.493915 | ||||||||
\(265\) | −14.7838 | −0.908164 | ||||||||
\(266\) | 1.61489 | 0.0990151 | ||||||||
\(267\) | 0.152886 | 0.00935645 | ||||||||
\(268\) | 9.50684 | 0.580723 | ||||||||
\(269\) | 27.0414 | 1.64874 | 0.824370 | − | 0.566051i | \(-0.191529\pi\) | ||||
0.824370 | + | 0.566051i | \(0.191529\pi\) | |||||||
\(270\) | 2.06102 | 0.125430 | ||||||||
\(271\) | 3.95819 | 0.240443 | 0.120222 | − | 0.992747i | \(-0.461640\pi\) | ||||
0.120222 | + | 0.992747i | \(0.461640\pi\) | |||||||
\(272\) | 4.96758 | 0.301204 | ||||||||
\(273\) | 5.44801 | 0.329729 | ||||||||
\(274\) | −2.10266 | −0.127026 | ||||||||
\(275\) | 15.3400 | 0.925035 | ||||||||
\(276\) | −5.93236 | −0.357086 | ||||||||
\(277\) | 1.44990 | 0.0871160 | 0.0435580 | − | 0.999051i | \(-0.486131\pi\) | ||||
0.0435580 | + | 0.999051i | \(0.486131\pi\) | |||||||
\(278\) | 0.345537 | 0.0207239 | ||||||||
\(279\) | −2.56542 | −0.153588 | ||||||||
\(280\) | −7.32590 | −0.437806 | ||||||||
\(281\) | −18.6067 | −1.10998 | −0.554991 | − | 0.831856i | \(-0.687278\pi\) | ||||
−0.554991 | + | 0.831856i | \(0.687278\pi\) | |||||||
\(282\) | 5.33684 | 0.317804 | ||||||||
\(283\) | −28.3029 | −1.68243 | −0.841215 | − | 0.540701i | \(-0.818159\pi\) | ||||
−0.841215 | + | 0.540701i | \(0.818159\pi\) | |||||||
\(284\) | −23.9778 | −1.42282 | ||||||||
\(285\) | 7.47100 | 0.442544 | ||||||||
\(286\) | −12.3002 | −0.727328 | ||||||||
\(287\) | 7.88451 | 0.465408 | ||||||||
\(288\) | −5.76314 | −0.339596 | ||||||||
\(289\) | −6.39582 | −0.376225 | ||||||||
\(290\) | −5.65062 | −0.331816 | ||||||||
\(291\) | 4.77136 | 0.279702 | ||||||||
\(292\) | 0.937238 | 0.0548477 | ||||||||
\(293\) | 9.35124 | 0.546305 | 0.273153 | − | 0.961971i | \(-0.411934\pi\) | ||||
0.273153 | + | 0.961971i | \(0.411934\pi\) | |||||||
\(294\) | −0.667457 | −0.0389269 | ||||||||
\(295\) | 22.1971 | 1.29236 | ||||||||
\(296\) | −5.78977 | −0.336523 | ||||||||
\(297\) | 3.38261 | 0.196279 | ||||||||
\(298\) | 9.55785 | 0.553672 | ||||||||
\(299\) | 20.7910 | 1.20237 | ||||||||
\(300\) | −7.04958 | −0.407008 | ||||||||
\(301\) | −5.47513 | −0.315581 | ||||||||
\(302\) | 3.13696 | 0.180512 | ||||||||
\(303\) | 14.5572 | 0.836290 | ||||||||
\(304\) | −3.69084 | −0.211684 | ||||||||
\(305\) | −35.9366 | −2.05772 | ||||||||
\(306\) | −2.17351 | −0.124251 | ||||||||
\(307\) | −0.546078 | −0.0311663 | −0.0155832 | − | 0.999879i | \(-0.504960\pi\) | ||||
−0.0155832 | + | 0.999879i | \(0.504960\pi\) | |||||||
\(308\) | −5.25828 | −0.299618 | ||||||||
\(309\) | −17.7347 | −1.00889 | ||||||||
\(310\) | −5.28738 | −0.300303 | ||||||||
\(311\) | 11.3455 | 0.643343 | 0.321672 | − | 0.946851i | \(-0.395755\pi\) | ||||
0.321672 | + | 0.946851i | \(0.395755\pi\) | |||||||
\(312\) | 12.9253 | 0.731750 | ||||||||
\(313\) | 23.5566 | 1.33150 | 0.665749 | − | 0.746176i | \(-0.268112\pi\) | ||||
0.665749 | + | 0.746176i | \(0.268112\pi\) | |||||||
\(314\) | −9.33626 | −0.526876 | ||||||||
\(315\) | −3.08787 | −0.173982 | ||||||||
\(316\) | 8.81277 | 0.495757 | ||||||||
\(317\) | −9.58214 | −0.538186 | −0.269093 | − | 0.963114i | \(-0.586724\pi\) | ||||
−0.269093 | + | 0.963114i | \(0.586724\pi\) | |||||||
\(318\) | −3.19559 | −0.179200 | ||||||||
\(319\) | −9.27398 | −0.519243 | ||||||||
\(320\) | −2.45699 | −0.137350 | ||||||||
\(321\) | 2.98071 | 0.166367 | ||||||||
\(322\) | −2.54718 | −0.141949 | ||||||||
\(323\) | −7.87876 | −0.438386 | ||||||||
\(324\) | −1.55450 | −0.0863612 | ||||||||
\(325\) | 24.7065 | 1.37047 | ||||||||
\(326\) | −6.43687 | −0.356505 | ||||||||
\(327\) | 10.0142 | 0.553788 | ||||||||
\(328\) | 18.7058 | 1.03286 | ||||||||
\(329\) | −7.99578 | −0.440822 | ||||||||
\(330\) | 6.97163 | 0.383776 | ||||||||
\(331\) | −3.58708 | −0.197164 | −0.0985818 | − | 0.995129i | \(-0.531431\pi\) | ||||
−0.0985818 | + | 0.995129i | \(0.531431\pi\) | |||||||
\(332\) | −7.15594 | −0.392733 | ||||||||
\(333\) | −2.44039 | −0.133733 | ||||||||
\(334\) | −5.07938 | −0.277931 | ||||||||
\(335\) | 18.8845 | 1.03177 | ||||||||
\(336\) | 1.52548 | 0.0832216 | ||||||||
\(337\) | −4.45757 | −0.242819 | −0.121410 | − | 0.992602i | \(-0.538741\pi\) | ||||
−0.121410 | + | 0.992602i | \(0.538741\pi\) | |||||||
\(338\) | −11.1337 | −0.605596 | ||||||||
\(339\) | 4.26465 | 0.231624 | ||||||||
\(340\) | 15.6311 | 0.847714 | ||||||||
\(341\) | −8.67782 | −0.469930 | ||||||||
\(342\) | 1.61489 | 0.0873232 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.9896 | −0.700353 | ||||||||
\(345\) | −11.7841 | −0.634434 | ||||||||
\(346\) | −7.57699 | −0.407341 | ||||||||
\(347\) | 8.25148 | 0.442963 | 0.221481 | − | 0.975165i | \(-0.428911\pi\) | ||||
0.221481 | + | 0.975165i | \(0.428911\pi\) | |||||||
\(348\) | 4.26192 | 0.228463 | ||||||||
\(349\) | −13.8205 | −0.739793 | −0.369896 | − | 0.929073i | \(-0.620607\pi\) | ||||
−0.369896 | + | 0.929073i | \(0.620607\pi\) | |||||||
\(350\) | −3.02688 | −0.161794 | ||||||||
\(351\) | 5.44801 | 0.290793 | ||||||||
\(352\) | −19.4945 | −1.03906 | ||||||||
\(353\) | −8.82099 | −0.469494 | −0.234747 | − | 0.972057i | \(-0.575426\pi\) | ||||
−0.234747 | + | 0.972057i | \(0.575426\pi\) | |||||||
\(354\) | 4.79800 | 0.255011 | ||||||||
\(355\) | −47.6297 | −2.52792 | ||||||||
\(356\) | −0.237661 | −0.0125960 | ||||||||
\(357\) | 3.25641 | 0.172347 | ||||||||
\(358\) | 2.36018 | 0.124740 | ||||||||
\(359\) | −19.4495 | −1.02651 | −0.513253 | − | 0.858238i | \(-0.671560\pi\) | ||||
−0.513253 | + | 0.858238i | \(0.671560\pi\) | |||||||
\(360\) | −7.32590 | −0.386109 | ||||||||
\(361\) | −13.1462 | −0.691905 | ||||||||
\(362\) | 3.41800 | 0.179646 | ||||||||
\(363\) | 0.442066 | 0.0232024 | ||||||||
\(364\) | −8.46894 | −0.443893 | ||||||||
\(365\) | 1.86174 | 0.0974477 | ||||||||
\(366\) | −7.76784 | −0.406032 | ||||||||
\(367\) | 0.638828 | 0.0333466 | 0.0166733 | − | 0.999861i | \(-0.494692\pi\) | ||||
0.0166733 | + | 0.999861i | \(0.494692\pi\) | |||||||
\(368\) | 5.82160 | 0.303472 | ||||||||
\(369\) | 7.88451 | 0.410451 | ||||||||
\(370\) | −5.02969 | −0.261481 | ||||||||
\(371\) | 4.78771 | 0.248566 | ||||||||
\(372\) | 3.98795 | 0.206766 | ||||||||
\(373\) | −10.5405 | −0.545766 | −0.272883 | − | 0.962047i | \(-0.587977\pi\) | ||||
−0.272883 | + | 0.962047i | \(0.587977\pi\) | |||||||
\(374\) | −7.35214 | −0.380170 | ||||||||
\(375\) | 1.43602 | 0.0741558 | ||||||||
\(376\) | −18.9698 | −0.978293 | ||||||||
\(377\) | −14.9366 | −0.769274 | ||||||||
\(378\) | −0.667457 | −0.0343303 | ||||||||
\(379\) | 5.64807 | 0.290122 | 0.145061 | − | 0.989423i | \(-0.453662\pi\) | ||||
0.145061 | + | 0.989423i | \(0.453662\pi\) | |||||||
\(380\) | −11.6137 | −0.595769 | ||||||||
\(381\) | −4.08207 | −0.209131 | ||||||||
\(382\) | −0.667457 | −0.0341501 | ||||||||
\(383\) | −6.62269 | −0.338404 | −0.169202 | − | 0.985581i | \(-0.554119\pi\) | ||||
−0.169202 | + | 0.985581i | \(0.554119\pi\) | |||||||
\(384\) | 10.9952 | 0.561096 | ||||||||
\(385\) | −10.4451 | −0.532330 | ||||||||
\(386\) | −6.25226 | −0.318232 | ||||||||
\(387\) | −5.47513 | −0.278316 | ||||||||
\(388\) | −7.41709 | −0.376546 | ||||||||
\(389\) | −12.8099 | −0.649488 | −0.324744 | − | 0.945802i | \(-0.605278\pi\) | ||||
−0.324744 | + | 0.945802i | \(0.605278\pi\) | |||||||
\(390\) | 11.2285 | 0.568575 | ||||||||
\(391\) | 12.4273 | 0.628473 | ||||||||
\(392\) | 2.37248 | 0.119828 | ||||||||
\(393\) | −5.40654 | −0.272724 | ||||||||
\(394\) | −14.1506 | −0.712897 | ||||||||
\(395\) | 17.5057 | 0.880810 | ||||||||
\(396\) | −5.25828 | −0.264238 | ||||||||
\(397\) | −8.72778 | −0.438035 | −0.219017 | − | 0.975721i | \(-0.570285\pi\) | ||||
−0.219017 | + | 0.975721i | \(0.570285\pi\) | |||||||
\(398\) | 5.86377 | 0.293924 | ||||||||
\(399\) | −2.41947 | −0.121125 | ||||||||
\(400\) | 6.91796 | 0.345898 | ||||||||
\(401\) | 25.0406 | 1.25047 | 0.625234 | − | 0.780437i | \(-0.285004\pi\) | ||||
0.625234 | + | 0.780437i | \(0.285004\pi\) | |||||||
\(402\) | 4.08196 | 0.203589 | ||||||||
\(403\) | −13.9764 | −0.696216 | ||||||||
\(404\) | −22.6292 | −1.12584 | ||||||||
\(405\) | −3.08787 | −0.153438 | ||||||||
\(406\) | 1.82994 | 0.0908184 | ||||||||
\(407\) | −8.25489 | −0.409180 | ||||||||
\(408\) | 7.72574 | 0.382481 | ||||||||
\(409\) | −5.72950 | −0.283305 | −0.141653 | − | 0.989916i | \(-0.545242\pi\) | ||||
−0.141653 | + | 0.989916i | \(0.545242\pi\) | |||||||
\(410\) | 16.2501 | 0.802537 | ||||||||
\(411\) | 3.15025 | 0.155390 | ||||||||
\(412\) | 27.5686 | 1.35821 | ||||||||
\(413\) | −7.18848 | −0.353722 | ||||||||
\(414\) | −2.54718 | −0.125187 | ||||||||
\(415\) | −14.2146 | −0.697767 | ||||||||
\(416\) | −31.3977 | −1.53940 | ||||||||
\(417\) | −0.517691 | −0.0253514 | ||||||||
\(418\) | 5.46254 | 0.267182 | ||||||||
\(419\) | 6.07304 | 0.296687 | 0.148344 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148344 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(420\) | 4.80010 | 0.234221 | ||||||||
\(421\) | 8.67038 | 0.422568 | 0.211284 | − | 0.977425i | \(-0.432235\pi\) | ||||
0.211284 | + | 0.977425i | \(0.432235\pi\) | |||||||
\(422\) | −1.50862 | −0.0734386 | ||||||||
\(423\) | −7.99578 | −0.388768 | ||||||||
\(424\) | 11.3587 | 0.551629 | ||||||||
\(425\) | 14.7676 | 0.716335 | ||||||||
\(426\) | −10.2954 | −0.498812 | ||||||||
\(427\) | 11.6380 | 0.563201 | ||||||||
\(428\) | −4.63351 | −0.223969 | ||||||||
\(429\) | 18.4285 | 0.889737 | ||||||||
\(430\) | −11.2843 | −0.544180 | ||||||||
\(431\) | −3.52565 | −0.169824 | −0.0849122 | − | 0.996388i | \(-0.527061\pi\) | ||||
−0.0849122 | + | 0.996388i | \(0.527061\pi\) | |||||||
\(432\) | 1.52548 | 0.0733946 | ||||||||
\(433\) | −28.4726 | −1.36831 | −0.684153 | − | 0.729338i | \(-0.739828\pi\) | ||||
−0.684153 | + | 0.729338i | \(0.739828\pi\) | |||||||
\(434\) | 1.71231 | 0.0821934 | ||||||||
\(435\) | 8.46590 | 0.405909 | ||||||||
\(436\) | −15.5671 | −0.745530 | ||||||||
\(437\) | −9.23328 | −0.441688 | ||||||||
\(438\) | 0.402422 | 0.0192285 | ||||||||
\(439\) | −21.7932 | −1.04013 | −0.520066 | − | 0.854126i | \(-0.674093\pi\) | ||||
−0.520066 | + | 0.854126i | \(0.674093\pi\) | |||||||
\(440\) | −24.7807 | −1.18137 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −11.8413 | −0.563234 | ||||||||
\(443\) | −28.8685 | −1.37159 | −0.685793 | − | 0.727797i | \(-0.740544\pi\) | ||||
−0.685793 | + | 0.727797i | \(0.740544\pi\) | |||||||
\(444\) | 3.79359 | 0.180036 | ||||||||
\(445\) | −0.472091 | −0.0223793 | ||||||||
\(446\) | −7.24955 | −0.343276 | ||||||||
\(447\) | −14.3198 | −0.677304 | ||||||||
\(448\) | 0.795692 | 0.0375929 | ||||||||
\(449\) | 3.56074 | 0.168042 | 0.0840208 | − | 0.996464i | \(-0.473224\pi\) | ||||
0.0840208 | + | 0.996464i | \(0.473224\pi\) | |||||||
\(450\) | −3.02688 | −0.142689 | ||||||||
\(451\) | 26.6702 | 1.25585 | ||||||||
\(452\) | −6.62941 | −0.311821 | ||||||||
\(453\) | −4.69987 | −0.220819 | ||||||||
\(454\) | −10.3498 | −0.485742 | ||||||||
\(455\) | −16.8228 | −0.788663 | ||||||||
\(456\) | −5.74012 | −0.268806 | ||||||||
\(457\) | 21.6075 | 1.01076 | 0.505378 | − | 0.862898i | \(-0.331353\pi\) | ||||
0.505378 | + | 0.862898i | \(0.331353\pi\) | |||||||
\(458\) | 6.87399 | 0.321200 | ||||||||
\(459\) | 3.25641 | 0.151996 | ||||||||
\(460\) | 18.3184 | 0.854099 | ||||||||
\(461\) | 21.4463 | 0.998854 | 0.499427 | − | 0.866356i | \(-0.333544\pi\) | ||||
0.499427 | + | 0.866356i | \(0.333544\pi\) | |||||||
\(462\) | −2.25775 | −0.105040 | ||||||||
\(463\) | −16.2899 | −0.757057 | −0.378529 | − | 0.925590i | \(-0.623570\pi\) | ||||
−0.378529 | + | 0.925590i | \(0.623570\pi\) | |||||||
\(464\) | −4.18234 | −0.194160 | ||||||||
\(465\) | 7.92169 | 0.367359 | ||||||||
\(466\) | 10.6611 | 0.493868 | ||||||||
\(467\) | 20.1213 | 0.931105 | 0.465552 | − | 0.885020i | \(-0.345856\pi\) | ||||
0.465552 | + | 0.885020i | \(0.345856\pi\) | |||||||
\(468\) | −8.46894 | −0.391477 | ||||||||
\(469\) | −6.11569 | −0.282396 | ||||||||
\(470\) | −16.4795 | −0.760141 | ||||||||
\(471\) | 13.9878 | 0.644524 | ||||||||
\(472\) | −17.0545 | −0.784996 | ||||||||
\(473\) | −18.5202 | −0.851561 | ||||||||
\(474\) | 3.78394 | 0.173802 | ||||||||
\(475\) | −10.9721 | −0.503437 | ||||||||
\(476\) | −5.06209 | −0.232020 | ||||||||
\(477\) | 4.78771 | 0.219214 | ||||||||
\(478\) | 6.19855 | 0.283515 | ||||||||
\(479\) | −6.59382 | −0.301279 | −0.150640 | − | 0.988589i | \(-0.548133\pi\) | ||||
−0.150640 | + | 0.988589i | \(0.548133\pi\) | |||||||
\(480\) | 17.7958 | 0.812265 | ||||||||
\(481\) | −13.2953 | −0.606212 | ||||||||
\(482\) | −19.0811 | −0.869122 | ||||||||
\(483\) | 3.81625 | 0.173645 | ||||||||
\(484\) | −0.687192 | −0.0312360 | ||||||||
\(485\) | −14.7334 | −0.669007 | ||||||||
\(486\) | −0.667457 | −0.0302765 | ||||||||
\(487\) | 40.4016 | 1.83077 | 0.915385 | − | 0.402578i | \(-0.131886\pi\) | ||||
0.915385 | + | 0.402578i | \(0.131886\pi\) | |||||||
\(488\) | 27.6108 | 1.24988 | ||||||||
\(489\) | 9.64387 | 0.436111 | ||||||||
\(490\) | 2.06102 | 0.0931074 | ||||||||
\(491\) | 6.34604 | 0.286393 | 0.143196 | − | 0.989694i | \(-0.454262\pi\) | ||||
0.143196 | + | 0.989694i | \(0.454262\pi\) | |||||||
\(492\) | −12.2565 | −0.552565 | ||||||||
\(493\) | −8.92796 | −0.402095 | ||||||||
\(494\) | 8.79793 | 0.395838 | ||||||||
\(495\) | −10.4451 | −0.469471 | ||||||||
\(496\) | −3.91349 | −0.175721 | ||||||||
\(497\) | 15.4248 | 0.691895 | ||||||||
\(498\) | −3.07255 | −0.137684 | ||||||||
\(499\) | 10.8364 | 0.485102 | 0.242551 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242551 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(500\) | −2.23230 | −0.0998313 | ||||||||
\(501\) | 7.61005 | 0.339992 | ||||||||
\(502\) | 6.83454 | 0.305040 | ||||||||
\(503\) | 32.9473 | 1.46905 | 0.734523 | − | 0.678584i | \(-0.237406\pi\) | ||||
0.734523 | + | 0.678584i | \(0.237406\pi\) | |||||||
\(504\) | 2.37248 | 0.105678 | ||||||||
\(505\) | −44.9508 | −2.00028 | ||||||||
\(506\) | −8.61613 | −0.383034 | ||||||||
\(507\) | 16.6808 | 0.740822 | ||||||||
\(508\) | 6.34558 | 0.281540 | ||||||||
\(509\) | 23.6706 | 1.04918 | 0.524590 | − | 0.851355i | \(-0.324219\pi\) | ||||
0.524590 | + | 0.851355i | \(0.324219\pi\) | |||||||
\(510\) | 6.71152 | 0.297191 | ||||||||
\(511\) | −0.602919 | −0.0266716 | ||||||||
\(512\) | −16.0299 | −0.708427 | ||||||||
\(513\) | −2.41947 | −0.106822 | ||||||||
\(514\) | −15.8041 | −0.697089 | ||||||||
\(515\) | 54.7624 | 2.41312 | ||||||||
\(516\) | 8.51109 | 0.374680 | ||||||||
\(517\) | −27.0466 | −1.18951 | ||||||||
\(518\) | 1.62885 | 0.0715678 | ||||||||
\(519\) | 11.3520 | 0.498299 | ||||||||
\(520\) | −39.9116 | −1.75024 | ||||||||
\(521\) | −11.0945 | −0.486061 | −0.243030 | − | 0.970019i | \(-0.578141\pi\) | ||||
−0.243030 | + | 0.970019i | \(0.578141\pi\) | |||||||
\(522\) | 1.82994 | 0.0800943 | ||||||||
\(523\) | 22.1200 | 0.967238 | 0.483619 | − | 0.875279i | \(-0.339322\pi\) | ||||
0.483619 | + | 0.875279i | \(0.339322\pi\) | |||||||
\(524\) | 8.40448 | 0.367151 | ||||||||
\(525\) | 4.53495 | 0.197921 | ||||||||
\(526\) | −15.3219 | −0.668067 | ||||||||
\(527\) | −8.35405 | −0.363908 | ||||||||
\(528\) | 5.16010 | 0.224565 | ||||||||
\(529\) | −8.43624 | −0.366793 | ||||||||
\(530\) | 9.86758 | 0.428620 | ||||||||
\(531\) | −7.18848 | −0.311953 | ||||||||
\(532\) | 3.76106 | 0.163063 | ||||||||
\(533\) | 42.9549 | 1.86058 | ||||||||
\(534\) | −0.102045 | −0.00441590 | ||||||||
\(535\) | −9.20404 | −0.397925 | ||||||||
\(536\) | −14.5093 | −0.626707 | ||||||||
\(537\) | −3.53608 | −0.152593 | ||||||||
\(538\) | −18.0489 | −0.778145 | ||||||||
\(539\) | 3.38261 | 0.145699 | ||||||||
\(540\) | 4.80010 | 0.206563 | ||||||||
\(541\) | 19.2252 | 0.826554 | 0.413277 | − | 0.910605i | \(-0.364384\pi\) | ||||
0.413277 | + | 0.910605i | \(0.364384\pi\) | |||||||
\(542\) | −2.64192 | −0.113480 | ||||||||
\(543\) | −5.12094 | −0.219760 | ||||||||
\(544\) | −18.7671 | −0.804634 | ||||||||
\(545\) | −30.9226 | −1.32458 | ||||||||
\(546\) | −3.63631 | −0.155620 | ||||||||
\(547\) | −2.34687 | −0.100345 | −0.0501725 | − | 0.998741i | \(-0.515977\pi\) | ||||
−0.0501725 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(548\) | −4.89707 | −0.209192 | ||||||||
\(549\) | 11.6380 | 0.496697 | ||||||||
\(550\) | −10.2388 | −0.436582 | ||||||||
\(551\) | 6.63335 | 0.282590 | ||||||||
\(552\) | 9.05396 | 0.385362 | ||||||||
\(553\) | −5.66920 | −0.241079 | ||||||||
\(554\) | −0.967745 | −0.0411156 | ||||||||
\(555\) | 7.53561 | 0.319869 | ||||||||
\(556\) | 0.804752 | 0.0341291 | ||||||||
\(557\) | 10.0338 | 0.425147 | 0.212573 | − | 0.977145i | \(-0.431816\pi\) | ||||
0.212573 | + | 0.977145i | \(0.431816\pi\) | |||||||
\(558\) | 1.71231 | 0.0724877 | ||||||||
\(559\) | −29.8286 | −1.26161 | ||||||||
\(560\) | −4.71048 | −0.199054 | ||||||||
\(561\) | 11.0152 | 0.465060 | ||||||||
\(562\) | 12.4192 | 0.523871 | ||||||||
\(563\) | 23.3001 | 0.981983 | 0.490992 | − | 0.871164i | \(-0.336635\pi\) | ||||
0.490992 | + | 0.871164i | \(0.336635\pi\) | |||||||
\(564\) | 12.4295 | 0.523374 | ||||||||
\(565\) | −13.1687 | −0.554011 | ||||||||
\(566\) | 18.8909 | 0.794045 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 36.5949 | 1.53549 | ||||||||
\(569\) | 13.8704 | 0.581477 | 0.290738 | − | 0.956803i | \(-0.406099\pi\) | ||||
0.290738 | + | 0.956803i | \(0.406099\pi\) | |||||||
\(570\) | −4.98657 | −0.208864 | ||||||||
\(571\) | −3.38015 | −0.141455 | −0.0707275 | − | 0.997496i | \(-0.522532\pi\) | ||||
−0.0707275 | + | 0.997496i | \(0.522532\pi\) | |||||||
\(572\) | −28.6472 | −1.19780 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −5.26257 | −0.219655 | ||||||||
\(575\) | 17.3065 | 0.721731 | ||||||||
\(576\) | 0.795692 | 0.0331538 | ||||||||
\(577\) | 1.31753 | 0.0548496 | 0.0274248 | − | 0.999624i | \(-0.491269\pi\) | ||||
0.0274248 | + | 0.999624i | \(0.491269\pi\) | |||||||
\(578\) | 4.26893 | 0.177564 | ||||||||
\(579\) | 9.36730 | 0.389292 | ||||||||
\(580\) | −13.1602 | −0.546450 | ||||||||
\(581\) | 4.60337 | 0.190980 | ||||||||
\(582\) | −3.18468 | −0.132009 | ||||||||
\(583\) | 16.1950 | 0.670728 | ||||||||
\(584\) | −1.43041 | −0.0591908 | ||||||||
\(585\) | −16.8228 | −0.695536 | ||||||||
\(586\) | −6.24155 | −0.257836 | ||||||||
\(587\) | 19.2731 | 0.795487 | 0.397744 | − | 0.917497i | \(-0.369793\pi\) | ||||
0.397744 | + | 0.917497i | \(0.369793\pi\) | |||||||
\(588\) | −1.55450 | −0.0641066 | ||||||||
\(589\) | 6.20694 | 0.255753 | ||||||||
\(590\) | −14.8156 | −0.609948 | ||||||||
\(591\) | 21.2008 | 0.872084 | ||||||||
\(592\) | −3.72276 | −0.153005 | ||||||||
\(593\) | 17.8721 | 0.733920 | 0.366960 | − | 0.930237i | \(-0.380399\pi\) | ||||
0.366960 | + | 0.930237i | \(0.380399\pi\) | |||||||
\(594\) | −2.25775 | −0.0926365 | ||||||||
\(595\) | −10.0554 | −0.412230 | ||||||||
\(596\) | 22.2602 | 0.911812 | ||||||||
\(597\) | −8.78524 | −0.359556 | ||||||||
\(598\) | −13.8771 | −0.567476 | ||||||||
\(599\) | 14.1308 | 0.577370 | 0.288685 | − | 0.957424i | \(-0.406782\pi\) | ||||
0.288685 | + | 0.957424i | \(0.406782\pi\) | |||||||
\(600\) | 10.7591 | 0.439237 | ||||||||
\(601\) | 11.9782 | 0.488601 | 0.244301 | − | 0.969700i | \(-0.421442\pi\) | ||||
0.244301 | + | 0.969700i | \(0.421442\pi\) | |||||||
\(602\) | 3.65441 | 0.148943 | ||||||||
\(603\) | −6.11569 | −0.249050 | ||||||||
\(604\) | 7.30596 | 0.297275 | ||||||||
\(605\) | −1.36504 | −0.0554968 | ||||||||
\(606\) | −9.71630 | −0.394698 | ||||||||
\(607\) | −20.7704 | −0.843043 | −0.421522 | − | 0.906818i | \(-0.638504\pi\) | ||||
−0.421522 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(608\) | 13.9437 | 0.565493 | ||||||||
\(609\) | −2.74166 | −0.111098 | ||||||||
\(610\) | 23.9861 | 0.971169 | ||||||||
\(611\) | −43.5611 | −1.76229 | ||||||||
\(612\) | −5.06209 | −0.204623 | ||||||||
\(613\) | 11.9465 | 0.482514 | 0.241257 | − | 0.970461i | \(-0.422440\pi\) | ||||
0.241257 | + | 0.970461i | \(0.422440\pi\) | |||||||
\(614\) | 0.364484 | 0.0147094 | ||||||||
\(615\) | −24.3463 | −0.981739 | ||||||||
\(616\) | 8.02517 | 0.323343 | ||||||||
\(617\) | −21.9687 | −0.884425 | −0.442213 | − | 0.896910i | \(-0.645806\pi\) | ||||
−0.442213 | + | 0.896910i | \(0.645806\pi\) | |||||||
\(618\) | 11.8371 | 0.476160 | ||||||||
\(619\) | 44.9141 | 1.80525 | 0.902625 | − | 0.430428i | \(-0.141638\pi\) | ||||
0.902625 | + | 0.430428i | \(0.141638\pi\) | |||||||
\(620\) | −12.3143 | −0.494553 | ||||||||
\(621\) | 3.81625 | 0.153141 | ||||||||
\(622\) | −7.57262 | −0.303634 | ||||||||
\(623\) | 0.152886 | 0.00612524 | ||||||||
\(624\) | 8.31082 | 0.332699 | ||||||||
\(625\) | −27.1090 | −1.08436 | ||||||||
\(626\) | −15.7230 | −0.628418 | ||||||||
\(627\) | −8.18411 | −0.326842 | ||||||||
\(628\) | −21.7441 | −0.867683 | ||||||||
\(629\) | −7.94690 | −0.316864 | ||||||||
\(630\) | 2.06102 | 0.0821130 | ||||||||
\(631\) | 2.72164 | 0.108347 | 0.0541734 | − | 0.998532i | \(-0.482748\pi\) | ||||
0.0541734 | + | 0.998532i | \(0.482748\pi\) | |||||||
\(632\) | −13.4500 | −0.535013 | ||||||||
\(633\) | 2.26025 | 0.0898370 | ||||||||
\(634\) | 6.39566 | 0.254004 | ||||||||
\(635\) | 12.6049 | 0.500210 | ||||||||
\(636\) | −7.44251 | −0.295115 | ||||||||
\(637\) | 5.44801 | 0.215858 | ||||||||
\(638\) | 6.18998 | 0.245064 | ||||||||
\(639\) | 15.4248 | 0.610194 | ||||||||
\(640\) | −33.9517 | −1.34206 | ||||||||
\(641\) | −21.3447 | −0.843067 | −0.421533 | − | 0.906813i | \(-0.638508\pi\) | ||||
−0.421533 | + | 0.906813i | \(0.638508\pi\) | |||||||
\(642\) | −1.98949 | −0.0785190 | ||||||||
\(643\) | −32.7446 | −1.29132 | −0.645660 | − | 0.763625i | \(-0.723418\pi\) | ||||
−0.645660 | + | 0.763625i | \(0.723418\pi\) | |||||||
\(644\) | −5.93236 | −0.233768 | ||||||||
\(645\) | 16.9065 | 0.665692 | ||||||||
\(646\) | 5.25873 | 0.206902 | ||||||||
\(647\) | −25.0467 | −0.984689 | −0.492344 | − | 0.870401i | \(-0.663860\pi\) | ||||
−0.492344 | + | 0.870401i | \(0.663860\pi\) | |||||||
\(648\) | 2.37248 | 0.0931997 | ||||||||
\(649\) | −24.3158 | −0.954480 | ||||||||
\(650\) | −16.4905 | −0.646810 | ||||||||
\(651\) | −2.56542 | −0.100547 | ||||||||
\(652\) | −14.9914 | −0.587109 | ||||||||
\(653\) | −21.0387 | −0.823309 | −0.411655 | − | 0.911340i | \(-0.635049\pi\) | ||||
−0.411655 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(654\) | −6.68406 | −0.261368 | ||||||||
\(655\) | 16.6947 | 0.652316 | ||||||||
\(656\) | 12.0276 | 0.469600 | ||||||||
\(657\) | −0.602919 | −0.0235221 | ||||||||
\(658\) | 5.33684 | 0.208052 | ||||||||
\(659\) | 42.1066 | 1.64024 | 0.820121 | − | 0.572190i | \(-0.193906\pi\) | ||||
0.820121 | + | 0.572190i | \(0.193906\pi\) | |||||||
\(660\) | 16.2369 | 0.632020 | ||||||||
\(661\) | −15.7775 | −0.613672 | −0.306836 | − | 0.951762i | \(-0.599270\pi\) | ||||
−0.306836 | + | 0.951762i | \(0.599270\pi\) | |||||||
\(662\) | 2.39422 | 0.0930540 | ||||||||
\(663\) | 17.7409 | 0.689001 | ||||||||
\(664\) | 10.9214 | 0.423832 | ||||||||
\(665\) | 7.47100 | 0.289713 | ||||||||
\(666\) | 1.62885 | 0.0631168 | ||||||||
\(667\) | −10.4629 | −0.405124 | ||||||||
\(668\) | −11.8298 | −0.457710 | ||||||||
\(669\) | 10.8614 | 0.419928 | ||||||||
\(670\) | −12.6046 | −0.486956 | ||||||||
\(671\) | 39.3667 | 1.51974 | ||||||||
\(672\) | −5.76314 | −0.222318 | ||||||||
\(673\) | −28.9199 | −1.11478 | −0.557391 | − | 0.830250i | \(-0.688197\pi\) | ||||
−0.557391 | + | 0.830250i | \(0.688197\pi\) | |||||||
\(674\) | 2.97524 | 0.114602 | ||||||||
\(675\) | 4.53495 | 0.174550 | ||||||||
\(676\) | −25.9304 | −0.997323 | ||||||||
\(677\) | 44.9752 | 1.72854 | 0.864268 | − | 0.503031i | \(-0.167782\pi\) | ||||
0.864268 | + | 0.503031i | \(0.167782\pi\) | |||||||
\(678\) | −2.84647 | −0.109318 | ||||||||
\(679\) | 4.77136 | 0.183108 | ||||||||
\(680\) | −23.8561 | −0.914840 | ||||||||
\(681\) | 15.5064 | 0.594205 | ||||||||
\(682\) | 5.79207 | 0.221790 | ||||||||
\(683\) | −41.4891 | −1.58754 | −0.793768 | − | 0.608220i | \(-0.791884\pi\) | ||||
−0.793768 | + | 0.608220i | \(0.791884\pi\) | |||||||
\(684\) | 3.76106 | 0.143808 | ||||||||
\(685\) | −9.72757 | −0.371671 | ||||||||
\(686\) | −0.667457 | −0.0254836 | ||||||||
\(687\) | −10.2988 | −0.392923 | ||||||||
\(688\) | −8.35219 | −0.318424 | ||||||||
\(689\) | 26.0835 | 0.993703 | ||||||||
\(690\) | 7.86537 | 0.299429 | ||||||||
\(691\) | 10.2203 | 0.388798 | 0.194399 | − | 0.980923i | \(-0.437724\pi\) | ||||
0.194399 | + | 0.980923i | \(0.437724\pi\) | |||||||
\(692\) | −17.6467 | −0.670828 | ||||||||
\(693\) | 3.38261 | 0.128495 | ||||||||
\(694\) | −5.50751 | −0.209062 | ||||||||
\(695\) | 1.59856 | 0.0606370 | ||||||||
\(696\) | −6.50453 | −0.246553 | ||||||||
\(697\) | 25.6752 | 0.972516 | ||||||||
\(698\) | 9.22457 | 0.349155 | ||||||||
\(699\) | −15.9728 | −0.604146 | ||||||||
\(700\) | −7.04958 | −0.266449 | ||||||||
\(701\) | −0.664532 | −0.0250990 | −0.0125495 | − | 0.999921i | \(-0.503995\pi\) | ||||
−0.0125495 | + | 0.999921i | \(0.503995\pi\) | |||||||
\(702\) | −3.63631 | −0.137244 | ||||||||
\(703\) | 5.90444 | 0.222690 | ||||||||
\(704\) | 2.69152 | 0.101440 | ||||||||
\(705\) | 24.6899 | 0.929877 | ||||||||
\(706\) | 5.88763 | 0.221584 | ||||||||
\(707\) | 14.5572 | 0.547480 | ||||||||
\(708\) | 11.1745 | 0.419963 | ||||||||
\(709\) | 32.1354 | 1.20687 | 0.603435 | − | 0.797412i | \(-0.293798\pi\) | ||||
0.603435 | + | 0.797412i | \(0.293798\pi\) | |||||||
\(710\) | 31.7907 | 1.19308 | ||||||||
\(711\) | −5.66920 | −0.212611 | ||||||||
\(712\) | 0.362718 | 0.0135934 | ||||||||
\(713\) | −9.79028 | −0.366649 | ||||||||
\(714\) | −2.17351 | −0.0813416 | ||||||||
\(715\) | −56.9049 | −2.12812 | ||||||||
\(716\) | 5.49685 | 0.205427 | ||||||||
\(717\) | −9.28681 | −0.346822 | ||||||||
\(718\) | 12.9817 | 0.484473 | ||||||||
\(719\) | 27.6666 | 1.03179 | 0.515895 | − | 0.856652i | \(-0.327460\pi\) | ||||
0.515895 | + | 0.856652i | \(0.327460\pi\) | |||||||
\(720\) | −4.71048 | −0.175549 | ||||||||
\(721\) | −17.7347 | −0.660474 | ||||||||
\(722\) | 8.77451 | 0.326554 | ||||||||
\(723\) | 28.5878 | 1.06319 | ||||||||
\(724\) | 7.96050 | 0.295850 | ||||||||
\(725\) | −12.4333 | −0.461761 | ||||||||
\(726\) | −0.295060 | −0.0109507 | ||||||||
\(727\) | −4.97543 | −0.184529 | −0.0922643 | − | 0.995735i | \(-0.529410\pi\) | ||||
−0.0922643 | + | 0.995735i | \(0.529410\pi\) | |||||||
\(728\) | 12.9253 | 0.479043 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.24263 | −0.0459917 | ||||||||
\(731\) | −17.8292 | −0.659438 | ||||||||
\(732\) | −18.0912 | −0.668672 | ||||||||
\(733\) | 31.6841 | 1.17028 | 0.585140 | − | 0.810932i | \(-0.301040\pi\) | ||||
0.585140 | + | 0.810932i | \(0.301040\pi\) | |||||||
\(734\) | −0.426390 | −0.0157384 | ||||||||
\(735\) | −3.08787 | −0.113898 | ||||||||
\(736\) | −21.9936 | −0.810694 | ||||||||
\(737\) | −20.6870 | −0.762015 | ||||||||
\(738\) | −5.26257 | −0.193718 | ||||||||
\(739\) | −13.4057 | −0.493138 | −0.246569 | − | 0.969125i | \(-0.579303\pi\) | ||||
−0.246569 | + | 0.969125i | \(0.579303\pi\) | |||||||
\(740\) | −11.7141 | −0.430619 | ||||||||
\(741\) | −13.1813 | −0.484226 | ||||||||
\(742\) | −3.19559 | −0.117314 | ||||||||
\(743\) | 52.4454 | 1.92403 | 0.962017 | − | 0.272990i | \(-0.0880126\pi\) | ||||
0.962017 | + | 0.272990i | \(0.0880126\pi\) | |||||||
\(744\) | −6.08640 | −0.223138 | ||||||||
\(745\) | 44.2177 | 1.62001 | ||||||||
\(746\) | 7.03532 | 0.257581 | ||||||||
\(747\) | 4.60337 | 0.168428 | ||||||||
\(748\) | −17.1231 | −0.626082 | ||||||||
\(749\) | 2.98071 | 0.108913 | ||||||||
\(750\) | −0.958482 | −0.0349988 | ||||||||
\(751\) | 39.7434 | 1.45026 | 0.725129 | − | 0.688613i | \(-0.241780\pi\) | ||||
0.725129 | + | 0.688613i | \(0.241780\pi\) | |||||||
\(752\) | −12.1974 | −0.444793 | ||||||||
\(753\) | −10.2397 | −0.373154 | ||||||||
\(754\) | 9.96954 | 0.363069 | ||||||||
\(755\) | 14.5126 | 0.528168 | ||||||||
\(756\) | −1.55450 | −0.0565367 | ||||||||
\(757\) | −34.7249 | −1.26210 | −0.631049 | − | 0.775743i | \(-0.717375\pi\) | ||||
−0.631049 | + | 0.775743i | \(0.717375\pi\) | |||||||
\(758\) | −3.76984 | −0.136927 | ||||||||
\(759\) | 12.9089 | 0.468563 | ||||||||
\(760\) | 17.7248 | 0.642945 | ||||||||
\(761\) | −42.6721 | −1.54686 | −0.773430 | − | 0.633881i | \(-0.781461\pi\) | ||||
−0.773430 | + | 0.633881i | \(0.781461\pi\) | |||||||
\(762\) | 2.72460 | 0.0987020 | ||||||||
\(763\) | 10.0142 | 0.362539 | ||||||||
\(764\) | −1.55450 | −0.0562399 | ||||||||
\(765\) | −10.0554 | −0.363552 | ||||||||
\(766\) | 4.42036 | 0.159714 | ||||||||
\(767\) | −39.1629 | −1.41409 | ||||||||
\(768\) | −8.93020 | −0.322241 | ||||||||
\(769\) | 27.9809 | 1.00902 | 0.504509 | − | 0.863406i | \(-0.331673\pi\) | ||||
0.504509 | + | 0.863406i | \(0.331673\pi\) | |||||||
\(770\) | 6.97163 | 0.251240 | ||||||||
\(771\) | 23.6781 | 0.852746 | ||||||||
\(772\) | −14.5615 | −0.524079 | ||||||||
\(773\) | 24.4508 | 0.879433 | 0.439716 | − | 0.898137i | \(-0.355079\pi\) | ||||
0.439716 | + | 0.898137i | \(0.355079\pi\) | |||||||
\(774\) | 3.65441 | 0.131355 | ||||||||
\(775\) | −11.6340 | −0.417907 | ||||||||
\(776\) | 11.3199 | 0.406362 | ||||||||
\(777\) | −2.44039 | −0.0875485 | ||||||||
\(778\) | 8.55005 | 0.306534 | ||||||||
\(779\) | −19.0763 | −0.683479 | ||||||||
\(780\) | 26.1510 | 0.936356 | ||||||||
\(781\) | 52.1760 | 1.86700 | ||||||||
\(782\) | −8.29466 | −0.296616 | ||||||||
\(783\) | −2.74166 | −0.0979790 | ||||||||
\(784\) | 1.52548 | 0.0544814 | ||||||||
\(785\) | −43.1926 | −1.54161 | ||||||||
\(786\) | 3.60863 | 0.128716 | ||||||||
\(787\) | −0.895713 | −0.0319287 | −0.0159644 | − | 0.999873i | \(-0.505082\pi\) | ||||
−0.0159644 | + | 0.999873i | \(0.505082\pi\) | |||||||
\(788\) | −32.9567 | −1.17403 | ||||||||
\(789\) | 22.9556 | 0.817243 | ||||||||
\(790\) | −11.6843 | −0.415710 | ||||||||
\(791\) | 4.26465 | 0.151634 | ||||||||
\(792\) | 8.02517 | 0.285162 | ||||||||
\(793\) | 63.4038 | 2.25154 | ||||||||
\(794\) | 5.82542 | 0.206736 | ||||||||
\(795\) | −14.7838 | −0.524329 | ||||||||
\(796\) | 13.6567 | 0.484048 | ||||||||
\(797\) | 41.4695 | 1.46893 | 0.734463 | − | 0.678649i | \(-0.237434\pi\) | ||||
0.734463 | + | 0.678649i | \(0.237434\pi\) | |||||||
\(798\) | 1.61489 | 0.0571664 | ||||||||
\(799\) | −26.0375 | −0.921141 | ||||||||
\(800\) | −26.1356 | −0.924031 | ||||||||
\(801\) | 0.152886 | 0.00540195 | ||||||||
\(802\) | −16.7135 | −0.590175 | ||||||||
\(803\) | −2.03944 | −0.0719703 | ||||||||
\(804\) | 9.50684 | 0.335281 | ||||||||
\(805\) | −11.7841 | −0.415334 | ||||||||
\(806\) | 9.32867 | 0.328588 | ||||||||
\(807\) | 27.0414 | 0.951901 | ||||||||
\(808\) | 34.5366 | 1.21499 | ||||||||
\(809\) | 34.5365 | 1.21424 | 0.607120 | − | 0.794610i | \(-0.292325\pi\) | ||||
0.607120 | + | 0.794610i | \(0.292325\pi\) | |||||||
\(810\) | 2.06102 | 0.0724169 | ||||||||
\(811\) | −53.1637 | −1.86683 | −0.933414 | − | 0.358801i | \(-0.883186\pi\) | ||||
−0.933414 | + | 0.358801i | \(0.883186\pi\) | |||||||
\(812\) | 4.26192 | 0.149564 | ||||||||
\(813\) | 3.95819 | 0.138820 | ||||||||
\(814\) | 5.50978 | 0.193118 | ||||||||
\(815\) | −29.7790 | −1.04311 | ||||||||
\(816\) | 4.96758 | 0.173900 | ||||||||
\(817\) | 13.2469 | 0.463450 | ||||||||
\(818\) | 3.82419 | 0.133710 | ||||||||
\(819\) | 5.44801 | 0.190369 | ||||||||
\(820\) | 37.8464 | 1.32165 | ||||||||
\(821\) | −15.2289 | −0.531491 | −0.265745 | − | 0.964043i | \(-0.585618\pi\) | ||||
−0.265745 | + | 0.964043i | \(0.585618\pi\) | |||||||
\(822\) | −2.10266 | −0.0733385 | ||||||||
\(823\) | 51.5387 | 1.79653 | 0.898264 | − | 0.439457i | \(-0.144829\pi\) | ||||
0.898264 | + | 0.439457i | \(0.144829\pi\) | |||||||
\(824\) | −42.0751 | −1.46576 | ||||||||
\(825\) | 15.3400 | 0.534069 | ||||||||
\(826\) | 4.79800 | 0.166944 | ||||||||
\(827\) | 7.11862 | 0.247539 | 0.123769 | − | 0.992311i | \(-0.460502\pi\) | ||||
0.123769 | + | 0.992311i | \(0.460502\pi\) | |||||||
\(828\) | −5.93236 | −0.206164 | ||||||||
\(829\) | 1.66078 | 0.0576813 | 0.0288406 | − | 0.999584i | \(-0.490818\pi\) | ||||
0.0288406 | + | 0.999584i | \(0.490818\pi\) | |||||||
\(830\) | 9.48763 | 0.329320 | ||||||||
\(831\) | 1.44990 | 0.0502965 | ||||||||
\(832\) | 4.33494 | 0.150287 | ||||||||
\(833\) | 3.25641 | 0.112828 | ||||||||
\(834\) | 0.345537 | 0.0119650 | ||||||||
\(835\) | −23.4988 | −0.813211 | ||||||||
\(836\) | 12.7222 | 0.440007 | ||||||||
\(837\) | −2.56542 | −0.0886739 | ||||||||
\(838\) | −4.05349 | −0.140026 | ||||||||
\(839\) | −2.24558 | −0.0775260 | −0.0387630 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387630 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(840\) | −7.32590 | −0.252768 | ||||||||
\(841\) | −21.4833 | −0.740803 | ||||||||
\(842\) | −5.78710 | −0.199437 | ||||||||
\(843\) | −18.6067 | −0.640849 | ||||||||
\(844\) | −3.51357 | −0.120942 | ||||||||
\(845\) | −51.5083 | −1.77194 | ||||||||
\(846\) | 5.33684 | 0.183484 | ||||||||
\(847\) | 0.442066 | 0.0151896 | ||||||||
\(848\) | 7.30355 | 0.250805 | ||||||||
\(849\) | −28.3029 | −0.971352 | ||||||||
\(850\) | −9.85675 | −0.338084 | ||||||||
\(851\) | −9.31313 | −0.319250 | ||||||||
\(852\) | −23.9778 | −0.821466 | ||||||||
\(853\) | 52.9448 | 1.81280 | 0.906398 | − | 0.422425i | \(-0.138821\pi\) | ||||
0.906398 | + | 0.422425i | \(0.138821\pi\) | |||||||
\(854\) | −7.76784 | −0.265810 | ||||||||
\(855\) | 7.47100 | 0.255503 | ||||||||
\(856\) | 7.07166 | 0.241704 | ||||||||
\(857\) | −32.5834 | −1.11303 | −0.556514 | − | 0.830838i | \(-0.687861\pi\) | ||||
−0.556514 | + | 0.830838i | \(0.687861\pi\) | |||||||
\(858\) | −12.3002 | −0.419923 | ||||||||
\(859\) | −40.1398 | −1.36955 | −0.684776 | − | 0.728754i | \(-0.740100\pi\) | ||||
−0.684776 | + | 0.728754i | \(0.740100\pi\) | |||||||
\(860\) | −26.2812 | −0.896180 | ||||||||
\(861\) | 7.88451 | 0.268703 | ||||||||
\(862\) | 2.35322 | 0.0801509 | ||||||||
\(863\) | −2.78104 | −0.0946679 | −0.0473339 | − | 0.998879i | \(-0.515072\pi\) | ||||
−0.0473339 | + | 0.998879i | \(0.515072\pi\) | |||||||
\(864\) | −5.76314 | −0.196066 | ||||||||
\(865\) | −35.0536 | −1.19186 | ||||||||
\(866\) | 19.0042 | 0.645790 | ||||||||
\(867\) | −6.39582 | −0.217213 | ||||||||
\(868\) | 3.98795 | 0.135360 | ||||||||
\(869\) | −19.1767 | −0.650525 | ||||||||
\(870\) | −5.65062 | −0.191574 | ||||||||
\(871\) | −33.3183 | −1.12895 | ||||||||
\(872\) | 23.7585 | 0.804565 | ||||||||
\(873\) | 4.77136 | 0.161486 | ||||||||
\(874\) | 6.16282 | 0.208460 | ||||||||
\(875\) | 1.43602 | 0.0485464 | ||||||||
\(876\) | 0.937238 | 0.0316663 | ||||||||
\(877\) | −11.7384 | −0.396378 | −0.198189 | − | 0.980164i | \(-0.563506\pi\) | ||||
−0.198189 | + | 0.980164i | \(0.563506\pi\) | |||||||
\(878\) | 14.5460 | 0.490904 | ||||||||
\(879\) | 9.35124 | 0.315409 | ||||||||
\(880\) | −15.9337 | −0.537126 | ||||||||
\(881\) | −44.2002 | −1.48914 | −0.744571 | − | 0.667543i | \(-0.767346\pi\) | ||||
−0.744571 | + | 0.667543i | \(0.767346\pi\) | |||||||
\(882\) | −0.667457 | −0.0224744 | ||||||||
\(883\) | −58.0283 | −1.95281 | −0.976404 | − | 0.215951i | \(-0.930715\pi\) | ||||
−0.976404 | + | 0.215951i | \(0.930715\pi\) | |||||||
\(884\) | −27.5783 | −0.927559 | ||||||||
\(885\) | 22.1971 | 0.746147 | ||||||||
\(886\) | 19.2685 | 0.647338 | ||||||||
\(887\) | −42.0717 | −1.41263 | −0.706314 | − | 0.707899i | \(-0.749643\pi\) | ||||
−0.706314 | + | 0.707899i | \(0.749643\pi\) | |||||||
\(888\) | −5.78977 | −0.194292 | ||||||||
\(889\) | −4.08207 | −0.136908 | ||||||||
\(890\) | 0.315101 | 0.0105622 | ||||||||
\(891\) | 3.38261 | 0.113322 | ||||||||
\(892\) | −16.8841 | −0.565323 | ||||||||
\(893\) | 19.3455 | 0.647373 | ||||||||
\(894\) | 9.55785 | 0.319662 | ||||||||
\(895\) | 10.9190 | 0.364981 | ||||||||
\(896\) | 10.9952 | 0.367324 | ||||||||
\(897\) | 20.7910 | 0.694190 | ||||||||
\(898\) | −2.37664 | −0.0793095 | ||||||||
\(899\) | 7.03351 | 0.234581 | ||||||||
\(900\) | −7.04958 | −0.234986 | ||||||||
\(901\) | 15.5907 | 0.519403 | ||||||||
\(902\) | −17.8012 | −0.592716 | ||||||||
\(903\) | −5.47513 | −0.182201 | ||||||||
\(904\) | 10.1178 | 0.336512 | ||||||||
\(905\) | 15.8128 | 0.525635 | ||||||||
\(906\) | 3.13696 | 0.104219 | ||||||||
\(907\) | 44.1502 | 1.46598 | 0.732992 | − | 0.680237i | \(-0.238123\pi\) | ||||
0.732992 | + | 0.680237i | \(0.238123\pi\) | |||||||
\(908\) | −24.1047 | −0.799942 | ||||||||
\(909\) | 14.5572 | 0.482832 | ||||||||
\(910\) | 11.2285 | 0.372220 | ||||||||
\(911\) | 49.6877 | 1.64623 | 0.823113 | − | 0.567878i | \(-0.192235\pi\) | ||||
0.823113 | + | 0.567878i | \(0.192235\pi\) | |||||||
\(912\) | −3.69084 | −0.122216 | ||||||||
\(913\) | 15.5714 | 0.515338 | ||||||||
\(914\) | −14.4221 | −0.477040 | ||||||||
\(915\) | −35.9366 | −1.18803 | ||||||||
\(916\) | 16.0095 | 0.528967 | ||||||||
\(917\) | −5.40654 | −0.178540 | ||||||||
\(918\) | −2.17351 | −0.0717365 | ||||||||
\(919\) | 26.5819 | 0.876856 | 0.438428 | − | 0.898766i | \(-0.355535\pi\) | ||||
0.438428 | + | 0.898766i | \(0.355535\pi\) | |||||||
\(920\) | −27.9575 | −0.921730 | ||||||||
\(921\) | −0.546078 | −0.0179939 | ||||||||
\(922\) | −14.3145 | −0.471422 | ||||||||
\(923\) | 84.0343 | 2.76602 | ||||||||
\(924\) | −5.25828 | −0.172985 | ||||||||
\(925\) | −11.0670 | −0.363882 | ||||||||
\(926\) | 10.8728 | 0.357303 | ||||||||
\(927\) | −17.7347 | −0.582484 | ||||||||
\(928\) | 15.8006 | 0.518680 | ||||||||
\(929\) | −52.1297 | −1.71032 | −0.855160 | − | 0.518365i | \(-0.826541\pi\) | ||||
−0.855160 | + | 0.518365i | \(0.826541\pi\) | |||||||
\(930\) | −5.28738 | −0.173380 | ||||||||
\(931\) | −2.41947 | −0.0792948 | ||||||||
\(932\) | 24.8297 | 0.813324 | ||||||||
\(933\) | 11.3455 | 0.371434 | ||||||||
\(934\) | −13.4301 | −0.439447 | ||||||||
\(935\) | −34.0134 | −1.11236 | ||||||||
\(936\) | 12.9253 | 0.422476 | ||||||||
\(937\) | −36.5170 | −1.19296 | −0.596479 | − | 0.802629i | \(-0.703434\pi\) | ||||
−0.596479 | + | 0.802629i | \(0.703434\pi\) | |||||||
\(938\) | 4.08196 | 0.133281 | ||||||||
\(939\) | 23.5566 | 0.768740 | ||||||||
\(940\) | −38.3805 | −1.25184 | ||||||||
\(941\) | −38.4973 | −1.25498 | −0.627488 | − | 0.778626i | \(-0.715917\pi\) | ||||
−0.627488 | + | 0.778626i | \(0.715917\pi\) | |||||||
\(942\) | −9.33626 | −0.304192 | ||||||||
\(943\) | 30.0892 | 0.979840 | ||||||||
\(944\) | −10.9659 | −0.356908 | ||||||||
\(945\) | −3.08787 | −0.100448 | ||||||||
\(946\) | 12.3615 | 0.401906 | ||||||||
\(947\) | 48.1836 | 1.56576 | 0.782879 | − | 0.622174i | \(-0.213751\pi\) | ||||
0.782879 | + | 0.622174i | \(0.213751\pi\) | |||||||
\(948\) | 8.81277 | 0.286226 | ||||||||
\(949\) | −3.28471 | −0.106626 | ||||||||
\(950\) | 7.32343 | 0.237604 | ||||||||
\(951\) | −9.58214 | −0.310722 | ||||||||
\(952\) | 7.72574 | 0.250393 | ||||||||
\(953\) | −31.7010 | −1.02690 | −0.513448 | − | 0.858121i | \(-0.671632\pi\) | ||||
−0.513448 | + | 0.858121i | \(0.671632\pi\) | |||||||
\(954\) | −3.19559 | −0.103461 | ||||||||
\(955\) | −3.08787 | −0.0999212 | ||||||||
\(956\) | 14.4364 | 0.466905 | ||||||||
\(957\) | −9.27398 | −0.299785 | ||||||||
\(958\) | 4.40109 | 0.142193 | ||||||||
\(959\) | 3.15025 | 0.101727 | ||||||||
\(960\) | −2.45699 | −0.0792992 | ||||||||
\(961\) | −24.4186 | −0.787697 | ||||||||
\(962\) | 8.87402 | 0.286110 | ||||||||
\(963\) | 2.98071 | 0.0960519 | ||||||||
\(964\) | −44.4398 | −1.43131 | ||||||||
\(965\) | −28.9250 | −0.931129 | ||||||||
\(966\) | −2.54718 | −0.0819542 | ||||||||
\(967\) | 18.0366 | 0.580019 | 0.290009 | − | 0.957024i | \(-0.406342\pi\) | ||||
0.290009 | + | 0.957024i | \(0.406342\pi\) | |||||||
\(968\) | 1.04879 | 0.0337094 | ||||||||
\(969\) | −7.87876 | −0.253102 | ||||||||
\(970\) | 9.83388 | 0.315747 | ||||||||
\(971\) | 22.3712 | 0.717925 | 0.358963 | − | 0.933352i | \(-0.383131\pi\) | ||||
0.358963 | + | 0.933352i | \(0.383131\pi\) | |||||||
\(972\) | −1.55450 | −0.0498607 | ||||||||
\(973\) | −0.517691 | −0.0165964 | ||||||||
\(974\) | −26.9663 | −0.864056 | ||||||||
\(975\) | 24.7065 | 0.791240 | ||||||||
\(976\) | 17.7535 | 0.568275 | ||||||||
\(977\) | 16.6502 | 0.532688 | 0.266344 | − | 0.963878i | \(-0.414184\pi\) | ||||
0.266344 | + | 0.963878i | \(0.414184\pi\) | |||||||
\(978\) | −6.43687 | −0.205828 | ||||||||
\(979\) | 0.517153 | 0.0165283 | ||||||||
\(980\) | 4.80010 | 0.153334 | ||||||||
\(981\) | 10.0142 | 0.319730 | ||||||||
\(982\) | −4.23571 | −0.135167 | ||||||||
\(983\) | 11.1289 | 0.354958 | 0.177479 | − | 0.984125i | \(-0.443206\pi\) | ||||
0.177479 | + | 0.984125i | \(0.443206\pi\) | |||||||
\(984\) | 18.7058 | 0.596319 | ||||||||
\(985\) | −65.4653 | −2.08590 | ||||||||
\(986\) | 5.95903 | 0.189774 | ||||||||
\(987\) | −7.99578 | −0.254509 | ||||||||
\(988\) | 20.4903 | 0.651884 | ||||||||
\(989\) | −20.8945 | −0.664405 | ||||||||
\(990\) | 6.97163 | 0.221573 | ||||||||
\(991\) | −29.1450 | −0.925822 | −0.462911 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462911 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(992\) | 14.7849 | 0.469420 | ||||||||
\(993\) | −3.58708 | −0.113832 | ||||||||
\(994\) | −10.2954 | −0.326549 | ||||||||
\(995\) | 27.1277 | 0.860006 | ||||||||
\(996\) | −7.15594 | −0.226745 | ||||||||
\(997\) | 38.2625 | 1.21179 | 0.605893 | − | 0.795546i | \(-0.292816\pi\) | ||||
0.605893 | + | 0.795546i | \(0.292816\pi\) | |||||||
\(998\) | −7.23280 | −0.228950 | ||||||||
\(999\) | −2.44039 | −0.0772105 |
(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 | 4011.2.a.k.1.10 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.k.1.10 | ✓ | 27 | 1.1 | even | 1 | trivial |