Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.288385.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 2x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.35681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35681 | −0.959407 | −0.479703 | − | 0.877431i | \(-0.659256\pi\) | ||||
−0.479703 | + | 0.877431i | \(0.659256\pi\) | |||||||
\(3\) | −0.242974 | −0.140281 | −0.0701406 | − | 0.997537i | \(-0.522345\pi\) | ||||
−0.0701406 | + | 0.997537i | \(0.522345\pi\) | |||||||
\(4\) | −0.159077 | −0.0795386 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.329669 | 0.134587 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.92945 | 1.03572 | ||||||||
\(9\) | −2.94096 | −0.980321 | ||||||||
\(10\) | −1.35681 | −0.429060 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.0386517 | 0.0111578 | ||||||||
\(13\) | −2.34529 | −0.650467 | −0.325233 | − | 0.945634i | \(-0.605443\pi\) | ||||
−0.325233 | + | 0.945634i | \(0.605443\pi\) | |||||||
\(14\) | 1.35681 | 0.362622 | ||||||||
\(15\) | −0.242974 | −0.0627357 | ||||||||
\(16\) | −3.65654 | −0.914135 | ||||||||
\(17\) | −0.927617 | −0.224980 | −0.112490 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112490 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(18\) | 3.99032 | 0.940527 | ||||||||
\(19\) | 1.95659 | 0.448872 | 0.224436 | − | 0.974489i | \(-0.427946\pi\) | ||||
0.224436 | + | 0.974489i | \(0.427946\pi\) | |||||||
\(20\) | −0.159077 | −0.0355707 | ||||||||
\(21\) | 0.242974 | 0.0530213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.68368 | 0.559585 | 0.279793 | − | 0.960060i | \(-0.409734\pi\) | ||||
0.279793 | + | 0.960060i | \(0.409734\pi\) | |||||||
\(24\) | −0.711781 | −0.145292 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.18211 | 0.624062 | ||||||||
\(27\) | 1.44350 | 0.277802 | ||||||||
\(28\) | 0.159077 | 0.0300628 | ||||||||
\(29\) | 0.245772 | 0.0456387 | 0.0228193 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228193 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(30\) | 0.329669 | 0.0601890 | ||||||||
\(31\) | 2.99032 | 0.537077 | 0.268538 | − | 0.963269i | \(-0.413459\pi\) | ||||
0.268538 | + | 0.963269i | \(0.413459\pi\) | |||||||
\(32\) | −0.897683 | −0.158689 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.25860 | 0.215848 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0.467840 | 0.0779734 | ||||||||
\(37\) | 6.23609 | 1.02521 | 0.512603 | − | 0.858626i | \(-0.328681\pi\) | ||||
0.512603 | + | 0.858626i | \(0.328681\pi\) | |||||||
\(38\) | −2.65471 | −0.430651 | ||||||||
\(39\) | 0.569845 | 0.0912483 | ||||||||
\(40\) | 2.92945 | 0.463187 | ||||||||
\(41\) | 6.05663 | 0.945886 | 0.472943 | − | 0.881093i | \(-0.343192\pi\) | ||||
0.472943 | + | 0.881093i | \(0.343192\pi\) | |||||||
\(42\) | −0.329669 | −0.0508690 | ||||||||
\(43\) | −9.64965 | −1.47156 | −0.735779 | − | 0.677221i | \(-0.763184\pi\) | ||||
−0.735779 | + | 0.677221i | \(0.763184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.94096 | −0.438413 | ||||||||
\(46\) | −3.64123 | −0.536870 | ||||||||
\(47\) | 5.84459 | 0.852521 | 0.426260 | − | 0.904601i | \(-0.359831\pi\) | ||||
0.426260 | + | 0.904601i | \(0.359831\pi\) | |||||||
\(48\) | 0.888445 | 0.128236 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.35681 | −0.191881 | ||||||||
\(51\) | 0.225387 | 0.0315605 | ||||||||
\(52\) | 0.373082 | 0.0517372 | ||||||||
\(53\) | −4.58827 | −0.630247 | −0.315123 | − | 0.949051i | \(-0.602046\pi\) | ||||
−0.315123 | + | 0.949051i | \(0.602046\pi\) | |||||||
\(54\) | −1.95855 | −0.266525 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.92945 | −0.391464 | ||||||||
\(57\) | −0.475400 | −0.0629683 | ||||||||
\(58\) | −0.333465 | −0.0437861 | ||||||||
\(59\) | −9.66792 | −1.25866 | −0.629328 | − | 0.777140i | \(-0.716670\pi\) | ||||
−0.629328 | + | 0.777140i | \(0.716670\pi\) | |||||||
\(60\) | 0.0386517 | 0.00498991 | ||||||||
\(61\) | −2.82941 | −0.362269 | −0.181134 | − | 0.983458i | \(-0.557977\pi\) | ||||
−0.181134 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(62\) | −4.05728 | −0.515275 | ||||||||
\(63\) | 2.94096 | 0.370527 | ||||||||
\(64\) | 8.53106 | 1.06638 | ||||||||
\(65\) | −2.34529 | −0.290898 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0109 | 1.83388 | 0.916939 | − | 0.399028i | \(-0.130652\pi\) | ||||
0.916939 | + | 0.399028i | \(0.130652\pi\) | |||||||
\(68\) | 0.147563 | 0.0178946 | ||||||||
\(69\) | −0.652064 | −0.0784993 | ||||||||
\(70\) | 1.35681 | 0.162169 | ||||||||
\(71\) | −2.21995 | −0.263459 | −0.131730 | − | 0.991286i | \(-0.542053\pi\) | ||||
−0.131730 | + | 0.991286i | \(0.542053\pi\) | |||||||
\(72\) | −8.61540 | −1.01533 | ||||||||
\(73\) | −0.100173 | −0.0117244 | −0.00586220 | − | 0.999983i | \(-0.501866\pi\) | ||||
−0.00586220 | + | 0.999983i | \(0.501866\pi\) | |||||||
\(74\) | −8.46116 | −0.983590 | ||||||||
\(75\) | −0.242974 | −0.0280562 | ||||||||
\(76\) | −0.311248 | −0.0357026 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.773170 | −0.0875442 | ||||||||
\(79\) | −6.31847 | −0.710883 | −0.355442 | − | 0.934699i | \(-0.615669\pi\) | ||||
−0.355442 | + | 0.934699i | \(0.615669\pi\) | |||||||
\(80\) | −3.65654 | −0.408814 | ||||||||
\(81\) | 8.47216 | 0.941351 | ||||||||
\(82\) | −8.21767 | −0.907490 | ||||||||
\(83\) | −16.4112 | −1.80136 | −0.900679 | − | 0.434485i | \(-0.856931\pi\) | ||||
−0.900679 | + | 0.434485i | \(0.856931\pi\) | |||||||
\(84\) | −0.0386517 | −0.00421724 | ||||||||
\(85\) | −0.927617 | −0.100614 | ||||||||
\(86\) | 13.0927 | 1.41182 | ||||||||
\(87\) | −0.0597162 | −0.00640225 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.73384 | 0.289787 | 0.144893 | − | 0.989447i | \(-0.453716\pi\) | ||||
0.144893 | + | 0.989447i | \(0.453716\pi\) | |||||||
\(90\) | 3.99032 | 0.420616 | ||||||||
\(91\) | 2.34529 | 0.245853 | ||||||||
\(92\) | −0.426912 | −0.0445086 | ||||||||
\(93\) | −0.726570 | −0.0753418 | ||||||||
\(94\) | −7.92997 | −0.817914 | ||||||||
\(95\) | 1.95659 | 0.200742 | ||||||||
\(96\) | 0.218114 | 0.0222611 | ||||||||
\(97\) | 3.11103 | 0.315878 | 0.157939 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157939 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(98\) | −1.35681 | −0.137058 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.159077 | −0.0159077 | ||||||||
\(101\) | −14.9247 | −1.48506 | −0.742531 | − | 0.669812i | \(-0.766375\pi\) | ||||
−0.742531 | + | 0.669812i | \(0.766375\pi\) | |||||||
\(102\) | −0.305807 | −0.0302794 | ||||||||
\(103\) | 0.991937 | 0.0977384 | 0.0488692 | − | 0.998805i | \(-0.484438\pi\) | ||||
0.0488692 | + | 0.998805i | \(0.484438\pi\) | |||||||
\(104\) | −6.87041 | −0.673699 | ||||||||
\(105\) | 0.242974 | 0.0237119 | ||||||||
\(106\) | 6.22539 | 0.604663 | ||||||||
\(107\) | 3.31075 | 0.320062 | 0.160031 | − | 0.987112i | \(-0.448841\pi\) | ||||
0.160031 | + | 0.987112i | \(0.448841\pi\) | |||||||
\(108\) | −0.229628 | −0.0220960 | ||||||||
\(109\) | 6.08363 | 0.582706 | 0.291353 | − | 0.956616i | \(-0.405895\pi\) | ||||
0.291353 | + | 0.956616i | \(0.405895\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.51521 | −0.143817 | ||||||||
\(112\) | 3.65654 | 0.345511 | ||||||||
\(113\) | −9.54323 | −0.897751 | −0.448876 | − | 0.893594i | \(-0.648175\pi\) | ||||
−0.448876 | + | 0.893594i | \(0.648175\pi\) | |||||||
\(114\) | 0.645026 | 0.0604122 | ||||||||
\(115\) | 2.68368 | 0.250254 | ||||||||
\(116\) | −0.0390967 | −0.00363004 | ||||||||
\(117\) | 6.89742 | 0.637666 | ||||||||
\(118\) | 13.1175 | 1.20756 | ||||||||
\(119\) | 0.927617 | 0.0850346 | ||||||||
\(120\) | −0.711781 | −0.0649764 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.83896 | 0.347563 | ||||||||
\(123\) | −1.47160 | −0.132690 | ||||||||
\(124\) | −0.475691 | −0.0427183 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.99032 | −0.355486 | ||||||||
\(127\) | −10.1792 | −0.903256 | −0.451628 | − | 0.892206i | \(-0.649157\pi\) | ||||
−0.451628 | + | 0.892206i | \(0.649157\pi\) | |||||||
\(128\) | −9.77963 | −0.864405 | ||||||||
\(129\) | 2.34462 | 0.206432 | ||||||||
\(130\) | 3.18211 | 0.279089 | ||||||||
\(131\) | 12.4893 | 1.09119 | 0.545596 | − | 0.838048i | \(-0.316303\pi\) | ||||
0.545596 | + | 0.838048i | \(0.316303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.95659 | −0.169658 | ||||||||
\(134\) | −20.3669 | −1.75943 | ||||||||
\(135\) | 1.44350 | 0.124237 | ||||||||
\(136\) | −2.71741 | −0.233016 | ||||||||
\(137\) | 16.6161 | 1.41961 | 0.709805 | − | 0.704398i | \(-0.248783\pi\) | ||||
0.709805 | + | 0.704398i | \(0.248783\pi\) | |||||||
\(138\) | 0.884725 | 0.0753128 | ||||||||
\(139\) | −0.420472 | −0.0356640 | −0.0178320 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178320 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(140\) | 0.159077 | 0.0134445 | ||||||||
\(141\) | −1.42008 | −0.119593 | ||||||||
\(142\) | 3.01204 | 0.252764 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.7538 | 0.896146 | ||||||||
\(145\) | 0.245772 | 0.0204102 | ||||||||
\(146\) | 0.135916 | 0.0112485 | ||||||||
\(147\) | −0.242974 | −0.0200402 | ||||||||
\(148\) | −0.992020 | −0.0815435 | ||||||||
\(149\) | −10.1747 | −0.833544 | −0.416772 | − | 0.909011i | \(-0.636839\pi\) | ||||
−0.416772 | + | 0.909011i | \(0.636839\pi\) | |||||||
\(150\) | 0.329669 | 0.0269173 | ||||||||
\(151\) | 5.10643 | 0.415555 | 0.207778 | − | 0.978176i | \(-0.433377\pi\) | ||||
0.207778 | + | 0.978176i | \(0.433377\pi\) | |||||||
\(152\) | 5.73172 | 0.464904 | ||||||||
\(153\) | 2.72809 | 0.220553 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.99032 | 0.240188 | ||||||||
\(156\) | −0.0906494 | −0.00725776 | ||||||||
\(157\) | 3.85612 | 0.307752 | 0.153876 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153876 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(158\) | 8.57293 | 0.682026 | ||||||||
\(159\) | 1.11483 | 0.0884118 | ||||||||
\(160\) | −0.897683 | −0.0709680 | ||||||||
\(161\) | −2.68368 | −0.211503 | ||||||||
\(162\) | −11.4951 | −0.903138 | ||||||||
\(163\) | −8.98048 | −0.703406 | −0.351703 | − | 0.936112i | \(-0.614397\pi\) | ||||
−0.351703 | + | 0.936112i | \(0.614397\pi\) | |||||||
\(164\) | −0.963471 | −0.0752345 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.2668 | 1.72824 | ||||||||
\(167\) | 0.0644782 | 0.00498947 | 0.00249474 | − | 0.999997i | \(-0.499206\pi\) | ||||
0.00249474 | + | 0.999997i | \(0.499206\pi\) | |||||||
\(168\) | 0.711781 | 0.0549151 | ||||||||
\(169\) | −7.49961 | −0.576893 | ||||||||
\(170\) | 1.25860 | 0.0965300 | ||||||||
\(171\) | −5.75425 | −0.440038 | ||||||||
\(172\) | 1.53504 | 0.117046 | ||||||||
\(173\) | 17.2202 | 1.30923 | 0.654613 | − | 0.755964i | \(-0.272832\pi\) | ||||
0.654613 | + | 0.755964i | \(0.272832\pi\) | |||||||
\(174\) | 0.0810233 | 0.00614236 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.34906 | 0.176566 | ||||||||
\(178\) | −3.70930 | −0.278023 | ||||||||
\(179\) | −18.2017 | −1.36046 | −0.680230 | − | 0.732999i | \(-0.738120\pi\) | ||||
−0.680230 | + | 0.732999i | \(0.738120\pi\) | |||||||
\(180\) | 0.467840 | 0.0348708 | ||||||||
\(181\) | −9.54258 | −0.709294 | −0.354647 | − | 0.935000i | \(-0.615399\pi\) | ||||
−0.354647 | + | 0.935000i | \(0.615399\pi\) | |||||||
\(182\) | −3.18211 | −0.235873 | ||||||||
\(183\) | 0.687473 | 0.0508195 | ||||||||
\(184\) | 7.86170 | 0.579572 | ||||||||
\(185\) | 6.23609 | 0.458486 | ||||||||
\(186\) | 0.985814 | 0.0722834 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.929741 | −0.0678083 | ||||||||
\(189\) | −1.44350 | −0.104999 | ||||||||
\(190\) | −2.65471 | −0.192593 | ||||||||
\(191\) | 10.0070 | 0.724078 | 0.362039 | − | 0.932163i | \(-0.382081\pi\) | ||||
0.362039 | + | 0.932163i | \(0.382081\pi\) | |||||||
\(192\) | −2.07283 | −0.149593 | ||||||||
\(193\) | −13.5332 | −0.974141 | −0.487071 | − | 0.873363i | \(-0.661935\pi\) | ||||
−0.487071 | + | 0.873363i | \(0.661935\pi\) | |||||||
\(194\) | −4.22107 | −0.303055 | ||||||||
\(195\) | 0.569845 | 0.0408075 | ||||||||
\(196\) | −0.159077 | −0.0113627 | ||||||||
\(197\) | −22.2486 | −1.58515 | −0.792575 | − | 0.609774i | \(-0.791260\pi\) | ||||
−0.792575 | + | 0.609774i | \(0.791260\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.44551 | −0.669575 | −0.334787 | − | 0.942294i | \(-0.608664\pi\) | ||||
−0.334787 | + | 0.942294i | \(0.608664\pi\) | |||||||
\(200\) | 2.92945 | 0.207143 | ||||||||
\(201\) | −3.64727 | −0.257259 | ||||||||
\(202\) | 20.2499 | 1.42478 | ||||||||
\(203\) | −0.245772 | −0.0172498 | ||||||||
\(204\) | −0.0358540 | −0.00251028 | ||||||||
\(205\) | 6.05663 | 0.423013 | ||||||||
\(206\) | −1.34587 | −0.0937709 | ||||||||
\(207\) | −7.89260 | −0.548573 | ||||||||
\(208\) | 8.57565 | 0.594615 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.329669 | −0.0227493 | ||||||||
\(211\) | −4.75884 | −0.327612 | −0.163806 | − | 0.986493i | \(-0.552377\pi\) | ||||
−0.163806 | + | 0.986493i | \(0.552377\pi\) | |||||||
\(212\) | 0.729889 | 0.0501290 | ||||||||
\(213\) | 0.539389 | 0.0369584 | ||||||||
\(214\) | −4.49204 | −0.307070 | ||||||||
\(215\) | −9.64965 | −0.658101 | ||||||||
\(216\) | 4.22866 | 0.287724 | ||||||||
\(217\) | −2.99032 | −0.202996 | ||||||||
\(218\) | −8.25431 | −0.559052 | ||||||||
\(219\) | 0.0243395 | 0.00164471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17553 | 0.146342 | ||||||||
\(222\) | 2.05584 | 0.137979 | ||||||||
\(223\) | 19.6049 | 1.31284 | 0.656422 | − | 0.754394i | \(-0.272069\pi\) | ||||
0.656422 | + | 0.754394i | \(0.272069\pi\) | |||||||
\(224\) | 0.897683 | 0.0599789 | ||||||||
\(225\) | −2.94096 | −0.196064 | ||||||||
\(226\) | 12.9483 | 0.861309 | ||||||||
\(227\) | −8.13362 | −0.539847 | −0.269924 | − | 0.962882i | \(-0.586998\pi\) | ||||
−0.269924 | + | 0.962882i | \(0.586998\pi\) | |||||||
\(228\) | 0.0756253 | 0.00500841 | ||||||||
\(229\) | 12.5891 | 0.831910 | 0.415955 | − | 0.909385i | \(-0.363447\pi\) | ||||
0.415955 | + | 0.909385i | \(0.363447\pi\) | |||||||
\(230\) | −3.64123 | −0.240096 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.719976 | 0.0472688 | ||||||||
\(233\) | −2.77199 | −0.181599 | −0.0907996 | − | 0.995869i | \(-0.528942\pi\) | ||||
−0.0907996 | + | 0.995869i | \(0.528942\pi\) | |||||||
\(234\) | −9.35846 | −0.611782 | ||||||||
\(235\) | 5.84459 | 0.381259 | ||||||||
\(236\) | 1.53795 | 0.100112 | ||||||||
\(237\) | 1.53522 | 0.0997235 | ||||||||
\(238\) | −1.25860 | −0.0815827 | ||||||||
\(239\) | 1.04527 | 0.0676130 | 0.0338065 | − | 0.999428i | \(-0.489237\pi\) | ||||
0.0338065 | + | 0.999428i | \(0.489237\pi\) | |||||||
\(240\) | 0.888445 | 0.0573489 | ||||||||
\(241\) | −24.2918 | −1.56477 | −0.782385 | − | 0.622796i | \(-0.785997\pi\) | ||||
−0.782385 | + | 0.622796i | \(0.785997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.38902 | −0.409856 | ||||||||
\(244\) | 0.450094 | 0.0288143 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 1.99668 | 0.127304 | ||||||||
\(247\) | −4.58877 | −0.291976 | ||||||||
\(248\) | 8.75998 | 0.556259 | ||||||||
\(249\) | 3.98749 | 0.252697 | ||||||||
\(250\) | −1.35681 | −0.0858120 | ||||||||
\(251\) | −15.7101 | −0.991610 | −0.495805 | − | 0.868434i | \(-0.665127\pi\) | ||||
−0.495805 | + | 0.868434i | \(0.665127\pi\) | |||||||
\(252\) | −0.467840 | −0.0294712 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 13.8112 | 0.866590 | ||||||||
\(255\) | 0.225387 | 0.0141143 | ||||||||
\(256\) | −3.79306 | −0.237066 | ||||||||
\(257\) | 24.4875 | 1.52749 | 0.763745 | − | 0.645519i | \(-0.223359\pi\) | ||||
0.763745 | + | 0.645519i | \(0.223359\pi\) | |||||||
\(258\) | −3.18119 | −0.198052 | ||||||||
\(259\) | −6.23609 | −0.387492 | ||||||||
\(260\) | 0.373082 | 0.0231376 | ||||||||
\(261\) | −0.722806 | −0.0447406 | ||||||||
\(262\) | −16.9455 | −1.04690 | ||||||||
\(263\) | 21.7093 | 1.33865 | 0.669325 | − | 0.742969i | \(-0.266583\pi\) | ||||
0.669325 | + | 0.742969i | \(0.266583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.58827 | −0.281855 | ||||||||
\(266\) | 2.65471 | 0.162771 | ||||||||
\(267\) | −0.664253 | −0.0406516 | ||||||||
\(268\) | −2.38790 | −0.145864 | ||||||||
\(269\) | −10.5726 | −0.644621 | −0.322310 | − | 0.946634i | \(-0.604459\pi\) | ||||
−0.322310 | + | 0.946634i | \(0.604459\pi\) | |||||||
\(270\) | −1.95855 | −0.119194 | ||||||||
\(271\) | −23.8119 | −1.44647 | −0.723235 | − | 0.690602i | \(-0.757346\pi\) | ||||
−0.723235 | + | 0.690602i | \(0.757346\pi\) | |||||||
\(272\) | 3.39187 | 0.205662 | ||||||||
\(273\) | −0.569845 | −0.0344886 | ||||||||
\(274\) | −22.5448 | −1.36198 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.103729 | 0.00624373 | ||||||||
\(277\) | 0.357431 | 0.0214759 | 0.0107380 | − | 0.999942i | \(-0.496582\pi\) | ||||
0.0107380 | + | 0.999942i | \(0.496582\pi\) | |||||||
\(278\) | 0.570499 | 0.0342162 | ||||||||
\(279\) | −8.79441 | −0.526508 | ||||||||
\(280\) | −2.92945 | −0.175068 | ||||||||
\(281\) | 6.93387 | 0.413640 | 0.206820 | − | 0.978379i | \(-0.433689\pi\) | ||||
0.206820 | + | 0.978379i | \(0.433689\pi\) | |||||||
\(282\) | 1.92678 | 0.114738 | ||||||||
\(283\) | 12.2813 | 0.730050 | 0.365025 | − | 0.930998i | \(-0.381061\pi\) | ||||
0.365025 | + | 0.930998i | \(0.381061\pi\) | |||||||
\(284\) | 0.353143 | 0.0209552 | ||||||||
\(285\) | −0.475400 | −0.0281603 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.05663 | −0.357511 | ||||||||
\(288\) | 2.64005 | 0.155567 | ||||||||
\(289\) | −16.1395 | −0.949384 | ||||||||
\(290\) | −0.333465 | −0.0195817 | ||||||||
\(291\) | −0.755901 | −0.0443117 | ||||||||
\(292\) | 0.0159353 | 0.000932543 0 | ||||||||
\(293\) | −18.4314 | −1.07678 | −0.538388 | − | 0.842697i | \(-0.680966\pi\) | ||||
−0.538388 | + | 0.842697i | \(0.680966\pi\) | |||||||
\(294\) | 0.329669 | 0.0192267 | ||||||||
\(295\) | −9.66792 | −0.562888 | ||||||||
\(296\) | 18.2683 | 1.06182 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.8051 | 0.799708 | ||||||||
\(299\) | −6.29401 | −0.363992 | ||||||||
\(300\) | 0.0386517 | 0.00223155 | ||||||||
\(301\) | 9.64965 | 0.556197 | ||||||||
\(302\) | −6.92843 | −0.398686 | ||||||||
\(303\) | 3.62631 | 0.208326 | ||||||||
\(304\) | −7.15434 | −0.410329 | ||||||||
\(305\) | −2.82941 | −0.162011 | ||||||||
\(306\) | −3.70149 | −0.211600 | ||||||||
\(307\) | −27.8266 | −1.58815 | −0.794074 | − | 0.607821i | \(-0.792044\pi\) | ||||
−0.794074 | + | 0.607821i | \(0.792044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.241015 | −0.0137109 | ||||||||
\(310\) | −4.05728 | −0.230438 | ||||||||
\(311\) | −18.5140 | −1.04983 | −0.524916 | − | 0.851154i | \(-0.675903\pi\) | ||||
−0.524916 | + | 0.851154i | \(0.675903\pi\) | |||||||
\(312\) | 1.66933 | 0.0945074 | ||||||||
\(313\) | −9.40487 | −0.531595 | −0.265797 | − | 0.964029i | \(-0.585635\pi\) | ||||
−0.265797 | + | 0.964029i | \(0.585635\pi\) | |||||||
\(314\) | −5.23201 | −0.295259 | ||||||||
\(315\) | 2.94096 | 0.165705 | ||||||||
\(316\) | 1.00512 | 0.0565427 | ||||||||
\(317\) | −14.1532 | −0.794924 | −0.397462 | − | 0.917619i | \(-0.630109\pi\) | ||||
−0.397462 | + | 0.917619i | \(0.630109\pi\) | |||||||
\(318\) | −1.51261 | −0.0848229 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.53106 | 0.476901 | ||||||||
\(321\) | −0.804426 | −0.0448987 | ||||||||
\(322\) | 3.64123 | 0.202918 | ||||||||
\(323\) | −1.81496 | −0.100987 | ||||||||
\(324\) | −1.34773 | −0.0748737 | ||||||||
\(325\) | −2.34529 | −0.130093 | ||||||||
\(326\) | 12.1848 | 0.674852 | ||||||||
\(327\) | −1.47817 | −0.0817427 | ||||||||
\(328\) | 17.7426 | 0.979670 | ||||||||
\(329\) | −5.84459 | −0.322222 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4577 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(332\) | 2.61064 | 0.143278 | ||||||||
\(333\) | −18.3401 | −1.00503 | ||||||||
\(334\) | −0.0874844 | −0.00478693 | ||||||||
\(335\) | 15.0109 | 0.820135 | ||||||||
\(336\) | −0.888445 | −0.0484686 | ||||||||
\(337\) | 23.7769 | 1.29521 | 0.647605 | − | 0.761976i | \(-0.275771\pi\) | ||||
0.647605 | + | 0.761976i | \(0.275771\pi\) | |||||||
\(338\) | 10.1755 | 0.553475 | ||||||||
\(339\) | 2.31876 | 0.125938 | ||||||||
\(340\) | 0.147563 | 0.00800272 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.80740 | 0.422176 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −28.2682 | −1.52412 | ||||||||
\(345\) | −0.652064 | −0.0351060 | ||||||||
\(346\) | −23.3644 | −1.25608 | ||||||||
\(347\) | 2.31154 | 0.124090 | 0.0620450 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620450 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(348\) | 0.00949949 | 0.000509226 0 | ||||||||
\(349\) | −36.2674 | −1.94135 | −0.970675 | − | 0.240395i | \(-0.922723\pi\) | ||||
−0.970675 | + | 0.240395i | \(0.922723\pi\) | |||||||
\(350\) | 1.35681 | 0.0725243 | ||||||||
\(351\) | −3.38543 | −0.180701 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6567 | −0.567200 | −0.283600 | − | 0.958943i | \(-0.591529\pi\) | ||||
−0.283600 | + | 0.958943i | \(0.591529\pi\) | |||||||
\(354\) | −3.18721 | −0.169398 | ||||||||
\(355\) | −2.21995 | −0.117822 | ||||||||
\(356\) | −0.434892 | −0.0230492 | ||||||||
\(357\) | −0.225387 | −0.0119287 | ||||||||
\(358\) | 24.6962 | 1.30523 | ||||||||
\(359\) | −22.4588 | −1.18533 | −0.592664 | − | 0.805450i | \(-0.701924\pi\) | ||||
−0.592664 | + | 0.805450i | \(0.701924\pi\) | |||||||
\(360\) | −8.61540 | −0.454072 | ||||||||
\(361\) | −15.1718 | −0.798514 | ||||||||
\(362\) | 12.9474 | 0.680502 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.373082 | −0.0195548 | ||||||||
\(365\) | −0.100173 | −0.00524331 | ||||||||
\(366\) | −0.932768 | −0.0487566 | ||||||||
\(367\) | 15.1093 | 0.788698 | 0.394349 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394349 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(368\) | −9.81297 | −0.511537 | ||||||||
\(369\) | −17.8123 | −0.927272 | ||||||||
\(370\) | −8.46116 | −0.439875 | ||||||||
\(371\) | 4.58827 | 0.238211 | ||||||||
\(372\) | 0.115581 | 0.00599258 | ||||||||
\(373\) | 22.7153 | 1.17616 | 0.588078 | − | 0.808804i | \(-0.299885\pi\) | ||||
0.588078 | + | 0.808804i | \(0.299885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.242974 | −0.0125471 | ||||||||
\(376\) | 17.1214 | 0.882970 | ||||||||
\(377\) | −0.576407 | −0.0296865 | ||||||||
\(378\) | 1.95855 | 0.100737 | ||||||||
\(379\) | −1.50696 | −0.0774072 | −0.0387036 | − | 0.999251i | \(-0.512323\pi\) | ||||
−0.0387036 | + | 0.999251i | \(0.512323\pi\) | |||||||
\(380\) | −0.311248 | −0.0159667 | ||||||||
\(381\) | 2.47328 | 0.126710 | ||||||||
\(382\) | −13.5775 | −0.694686 | ||||||||
\(383\) | −14.8062 | −0.756564 | −0.378282 | − | 0.925690i | \(-0.623485\pi\) | ||||
−0.378282 | + | 0.925690i | \(0.623485\pi\) | |||||||
\(384\) | 2.37620 | 0.121260 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.3619 | 0.934598 | ||||||||
\(387\) | 28.3793 | 1.44260 | ||||||||
\(388\) | −0.494895 | −0.0251245 | ||||||||
\(389\) | −33.6017 | −1.70368 | −0.851838 | − | 0.523806i | \(-0.824512\pi\) | ||||
−0.851838 | + | 0.523806i | \(0.824512\pi\) | |||||||
\(390\) | −0.773170 | −0.0391510 | ||||||||
\(391\) | −2.48943 | −0.125896 | ||||||||
\(392\) | 2.92945 | 0.147960 | ||||||||
\(393\) | −3.03457 | −0.153074 | ||||||||
\(394\) | 30.1871 | 1.52080 | ||||||||
\(395\) | −6.31847 | −0.317917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7402 | −1.19149 | −0.595744 | − | 0.803174i | \(-0.703143\pi\) | ||||
−0.595744 | + | 0.803174i | \(0.703143\pi\) | |||||||
\(398\) | 12.8157 | 0.642394 | ||||||||
\(399\) | 0.475400 | 0.0237998 | ||||||||
\(400\) | −3.65654 | −0.182827 | ||||||||
\(401\) | 25.6299 | 1.27990 | 0.639949 | − | 0.768417i | \(-0.278955\pi\) | ||||
0.639949 | + | 0.768417i | \(0.278955\pi\) | |||||||
\(402\) | 4.94864 | 0.246816 | ||||||||
\(403\) | −7.01317 | −0.349351 | ||||||||
\(404\) | 2.37418 | 0.118120 | ||||||||
\(405\) | 8.47216 | 0.420985 | ||||||||
\(406\) | 0.333465 | 0.0165496 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.660260 | 0.0326877 | ||||||||
\(409\) | −26.5551 | −1.31306 | −0.656532 | − | 0.754299i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754299i | \(0.727977\pi\) | |||||||
\(410\) | −8.21767 | −0.405842 | ||||||||
\(411\) | −4.03728 | −0.199145 | ||||||||
\(412\) | −0.157795 | −0.00777398 | ||||||||
\(413\) | 9.66792 | 0.475727 | ||||||||
\(414\) | 10.7087 | 0.526305 | ||||||||
\(415\) | −16.4112 | −0.805592 | ||||||||
\(416\) | 2.10533 | 0.103222 | ||||||||
\(417\) | 0.102164 | 0.00500298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.6824 | −1.69435 | −0.847174 | − | 0.531316i | \(-0.821698\pi\) | ||||
−0.847174 | + | 0.531316i | \(0.821698\pi\) | |||||||
\(420\) | −0.0386517 | −0.00188601 | ||||||||
\(421\) | 24.7907 | 1.20823 | 0.604113 | − | 0.796899i | \(-0.293527\pi\) | ||||
0.604113 | + | 0.796899i | \(0.293527\pi\) | |||||||
\(422\) | 6.45682 | 0.314313 | ||||||||
\(423\) | −17.1887 | −0.835744 | ||||||||
\(424\) | −13.4411 | −0.652757 | ||||||||
\(425\) | −0.927617 | −0.0449961 | ||||||||
\(426\) | −0.731847 | −0.0354581 | ||||||||
\(427\) | 2.82941 | 0.136925 | ||||||||
\(428\) | −0.526665 | −0.0254573 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.0927 | 0.631387 | ||||||||
\(431\) | 6.59999 | 0.317910 | 0.158955 | − | 0.987286i | \(-0.449187\pi\) | ||||
0.158955 | + | 0.987286i | \(0.449187\pi\) | |||||||
\(432\) | −5.27822 | −0.253948 | ||||||||
\(433\) | 20.0200 | 0.962101 | 0.481050 | − | 0.876693i | \(-0.340255\pi\) | ||||
0.481050 | + | 0.876693i | \(0.340255\pi\) | |||||||
\(434\) | 4.05728 | 0.194756 | ||||||||
\(435\) | −0.0597162 | −0.00286317 | ||||||||
\(436\) | −0.967767 | −0.0463476 | ||||||||
\(437\) | 5.25085 | 0.251182 | ||||||||
\(438\) | −0.0330240 | −0.00157795 | ||||||||
\(439\) | 26.6216 | 1.27058 | 0.635290 | − | 0.772274i | \(-0.280881\pi\) | ||||
0.635290 | + | 0.772274i | \(0.280881\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.94096 | −0.140046 | ||||||||
\(442\) | −2.95178 | −0.140402 | ||||||||
\(443\) | 7.35380 | 0.349389 | 0.174695 | − | 0.984623i | \(-0.444106\pi\) | ||||
0.174695 | + | 0.984623i | \(0.444106\pi\) | |||||||
\(444\) | 0.241035 | 0.0114390 | ||||||||
\(445\) | 2.73384 | 0.129597 | ||||||||
\(446\) | −26.6001 | −1.25955 | ||||||||
\(447\) | 2.47219 | 0.116931 | ||||||||
\(448\) | −8.53106 | −0.403055 | ||||||||
\(449\) | 1.75184 | 0.0826744 | 0.0413372 | − | 0.999145i | \(-0.486838\pi\) | ||||
0.0413372 | + | 0.999145i | \(0.486838\pi\) | |||||||
\(450\) | 3.99032 | 0.188105 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.51811 | 0.0714059 | ||||||||
\(453\) | −1.24073 | −0.0582946 | ||||||||
\(454\) | 11.0357 | 0.517933 | ||||||||
\(455\) | 2.34529 | 0.109949 | ||||||||
\(456\) | −1.39266 | −0.0652173 | ||||||||
\(457\) | −17.7181 | −0.828817 | −0.414409 | − | 0.910091i | \(-0.636012\pi\) | ||||
−0.414409 | + | 0.910091i | \(0.636012\pi\) | |||||||
\(458\) | −17.0809 | −0.798140 | ||||||||
\(459\) | −1.33902 | −0.0624999 | ||||||||
\(460\) | −0.426912 | −0.0199049 | ||||||||
\(461\) | −20.6171 | −0.960235 | −0.480118 | − | 0.877204i | \(-0.659406\pi\) | ||||
−0.480118 | + | 0.877204i | \(0.659406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1323 | −0.610309 | −0.305154 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305154 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(464\) | −0.898675 | −0.0417199 | ||||||||
\(465\) | −0.726570 | −0.0336939 | ||||||||
\(466\) | 3.76105 | 0.174228 | ||||||||
\(467\) | 30.8738 | 1.42867 | 0.714334 | − | 0.699805i | \(-0.246730\pi\) | ||||
0.714334 | + | 0.699805i | \(0.246730\pi\) | |||||||
\(468\) | −1.09722 | −0.0507191 | ||||||||
\(469\) | −15.0109 | −0.693141 | ||||||||
\(470\) | −7.92997 | −0.365782 | ||||||||
\(471\) | −0.936938 | −0.0431718 | ||||||||
\(472\) | −28.3217 | −1.30361 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.08300 | −0.0956754 | ||||||||
\(475\) | 1.95659 | 0.0897743 | ||||||||
\(476\) | −0.147563 | −0.00676353 | ||||||||
\(477\) | 13.4939 | 0.617844 | ||||||||
\(478\) | −1.41823 | −0.0648684 | ||||||||
\(479\) | 36.4945 | 1.66748 | 0.833739 | − | 0.552159i | \(-0.186196\pi\) | ||||
0.833739 | + | 0.552159i | \(0.186196\pi\) | |||||||
\(480\) | 0.218114 | 0.00995548 | ||||||||
\(481\) | −14.6254 | −0.666863 | ||||||||
\(482\) | 32.9592 | 1.50125 | ||||||||
\(483\) | 0.652064 | 0.0296700 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.11103 | 0.141265 | ||||||||
\(486\) | 8.66866 | 0.393218 | ||||||||
\(487\) | −29.0277 | −1.31537 | −0.657685 | − | 0.753293i | \(-0.728464\pi\) | ||||
−0.657685 | + | 0.753293i | \(0.728464\pi\) | |||||||
\(488\) | −8.28861 | −0.375208 | ||||||||
\(489\) | 2.18203 | 0.0986746 | ||||||||
\(490\) | −1.35681 | −0.0612943 | ||||||||
\(491\) | −28.1964 | −1.27249 | −0.636244 | − | 0.771488i | \(-0.719513\pi\) | ||||
−0.636244 | + | 0.771488i | \(0.719513\pi\) | |||||||
\(492\) | 0.234099 | 0.0105540 | ||||||||
\(493\) | −0.227982 | −0.0102678 | ||||||||
\(494\) | 6.22607 | 0.280124 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.9342 | −0.490961 | ||||||||
\(497\) | 2.21995 | 0.0995782 | ||||||||
\(498\) | −5.41025 | −0.242439 | ||||||||
\(499\) | −12.1817 | −0.545326 | −0.272663 | − | 0.962110i | \(-0.587904\pi\) | ||||
−0.272663 | + | 0.962110i | \(0.587904\pi\) | |||||||
\(500\) | −0.159077 | −0.00711415 | ||||||||
\(501\) | −0.0156665 | −0.000699929 0 | ||||||||
\(502\) | 21.3155 | 0.951357 | ||||||||
\(503\) | −9.57390 | −0.426879 | −0.213439 | − | 0.976956i | \(-0.568467\pi\) | ||||
−0.213439 | + | 0.976956i | \(0.568467\pi\) | |||||||
\(504\) | 8.61540 | 0.383761 | ||||||||
\(505\) | −14.9247 | −0.664140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.82221 | 0.0809272 | ||||||||
\(508\) | 1.61927 | 0.0718437 | ||||||||
\(509\) | −28.2988 | −1.25432 | −0.627161 | − | 0.778889i | \(-0.715783\pi\) | ||||
−0.627161 | + | 0.778889i | \(0.715783\pi\) | |||||||
\(510\) | −0.305807 | −0.0135413 | ||||||||
\(511\) | 0.100173 | 0.00443141 | ||||||||
\(512\) | 24.7057 | 1.09185 | ||||||||
\(513\) | 2.82433 | 0.124697 | ||||||||
\(514\) | −33.2248 | −1.46548 | ||||||||
\(515\) | 0.991937 | 0.0437100 | ||||||||
\(516\) | −0.372975 | −0.0164193 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.46116 | 0.371762 | ||||||||
\(519\) | −4.18406 | −0.183660 | ||||||||
\(520\) | −6.87041 | −0.301288 | ||||||||
\(521\) | −6.04860 | −0.264994 | −0.132497 | − | 0.991183i | \(-0.542299\pi\) | ||||
−0.132497 | + | 0.991183i | \(0.542299\pi\) | |||||||
\(522\) | 0.980708 | 0.0429244 | ||||||||
\(523\) | −15.3496 | −0.671192 | −0.335596 | − | 0.942006i | \(-0.608938\pi\) | ||||
−0.335596 | + | 0.942006i | \(0.608938\pi\) | |||||||
\(524\) | −1.98676 | −0.0867919 | ||||||||
\(525\) | 0.242974 | 0.0106043 | ||||||||
\(526\) | −29.4553 | −1.28431 | ||||||||
\(527\) | −2.77387 | −0.120832 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7979 | −0.686864 | ||||||||
\(530\) | 6.22539 | 0.270414 | ||||||||
\(531\) | 28.4330 | 1.23389 | ||||||||
\(532\) | 0.311248 | 0.0134943 | ||||||||
\(533\) | −14.2046 | −0.615268 | ||||||||
\(534\) | 0.901263 | 0.0390015 | ||||||||
\(535\) | 3.31075 | 0.143136 | ||||||||
\(536\) | 43.9738 | 1.89938 | ||||||||
\(537\) | 4.42254 | 0.190847 | ||||||||
\(538\) | 14.3449 | 0.618453 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.229628 | −0.00988162 | ||||||||
\(541\) | 31.1468 | 1.33911 | 0.669553 | − | 0.742765i | \(-0.266486\pi\) | ||||
0.669553 | + | 0.742765i | \(0.266486\pi\) | |||||||
\(542\) | 32.3081 | 1.38775 | ||||||||
\(543\) | 2.31860 | 0.0995006 | ||||||||
\(544\) | 0.832706 | 0.0357020 | ||||||||
\(545\) | 6.08363 | 0.260594 | ||||||||
\(546\) | 0.773170 | 0.0330886 | ||||||||
\(547\) | −2.82444 | −0.120764 | −0.0603821 | − | 0.998175i | \(-0.519232\pi\) | ||||
−0.0603821 | + | 0.998175i | \(0.519232\pi\) | |||||||
\(548\) | −2.64324 | −0.112914 | ||||||||
\(549\) | 8.32119 | 0.355140 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.480874 | 0.0204859 | ||||||||
\(552\) | −1.91019 | −0.0813030 | ||||||||
\(553\) | 6.31847 | 0.268689 | ||||||||
\(554\) | −0.484965 | −0.0206042 | ||||||||
\(555\) | −1.51521 | −0.0643170 | ||||||||
\(556\) | 0.0668875 | 0.00283666 | ||||||||
\(557\) | −5.32104 | −0.225460 | −0.112730 | − | 0.993626i | \(-0.535959\pi\) | ||||
−0.112730 | + | 0.993626i | \(0.535959\pi\) | |||||||
\(558\) | 11.9323 | 0.505135 | ||||||||
\(559\) | 22.6313 | 0.957200 | ||||||||
\(560\) | 3.65654 | 0.154517 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.40792 | −0.396849 | ||||||||
\(563\) | −1.88609 | −0.0794893 | −0.0397447 | − | 0.999210i | \(-0.512654\pi\) | ||||
−0.0397447 | + | 0.999210i | \(0.512654\pi\) | |||||||
\(564\) | 0.225903 | 0.00951223 | ||||||||
\(565\) | −9.54323 | −0.401487 | ||||||||
\(566\) | −16.6634 | −0.700415 | ||||||||
\(567\) | −8.47216 | −0.355797 | ||||||||
\(568\) | −6.50322 | −0.272869 | ||||||||
\(569\) | −4.30097 | −0.180306 | −0.0901529 | − | 0.995928i | \(-0.528736\pi\) | ||||
−0.0901529 | + | 0.995928i | \(0.528736\pi\) | |||||||
\(570\) | 0.645026 | 0.0270171 | ||||||||
\(571\) | 10.5416 | 0.441153 | 0.220577 | − | 0.975370i | \(-0.429206\pi\) | ||||
0.220577 | + | 0.975370i | \(0.429206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.43143 | −0.101575 | ||||||||
\(574\) | 8.21767 | 0.342999 | ||||||||
\(575\) | 2.68368 | 0.111917 | ||||||||
\(576\) | −25.0895 | −1.04540 | ||||||||
\(577\) | −2.05286 | −0.0854618 | −0.0427309 | − | 0.999087i | \(-0.513606\pi\) | ||||
−0.0427309 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(578\) | 21.8982 | 0.910845 | ||||||||
\(579\) | 3.28822 | 0.136654 | ||||||||
\(580\) | −0.0390967 | −0.00162340 | ||||||||
\(581\) | 16.4112 | 0.680849 | ||||||||
\(582\) | 1.02561 | 0.0425129 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.293453 | −0.0121432 | ||||||||
\(585\) | 6.89742 | 0.285173 | ||||||||
\(586\) | 25.0079 | 1.03307 | ||||||||
\(587\) | 25.9972 | 1.07302 | 0.536510 | − | 0.843894i | \(-0.319742\pi\) | ||||
0.536510 | + | 0.843894i | \(0.319742\pi\) | |||||||
\(588\) | 0.0386517 | 0.00159397 | ||||||||
\(589\) | 5.85081 | 0.241079 | ||||||||
\(590\) | 13.1175 | 0.540039 | ||||||||
\(591\) | 5.40585 | 0.222367 | ||||||||
\(592\) | −22.8025 | −0.937177 | ||||||||
\(593\) | 11.1931 | 0.459645 | 0.229823 | − | 0.973233i | \(-0.426185\pi\) | ||||
0.229823 | + | 0.973233i | \(0.426185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.927617 | 0.0380286 | ||||||||
\(596\) | 1.61856 | 0.0662989 | ||||||||
\(597\) | 2.29502 | 0.0939287 | ||||||||
\(598\) | 8.53975 | 0.349216 | ||||||||
\(599\) | 33.8637 | 1.38363 | 0.691817 | − | 0.722073i | \(-0.256811\pi\) | ||||
0.691817 | + | 0.722073i | \(0.256811\pi\) | |||||||
\(600\) | −0.711781 | −0.0290583 | ||||||||
\(601\) | −42.1489 | −1.71929 | −0.859645 | − | 0.510892i | \(-0.829315\pi\) | ||||
−0.859645 | + | 0.510892i | \(0.829315\pi\) | |||||||
\(602\) | −13.0927 | −0.533619 | ||||||||
\(603\) | −44.1466 | −1.79779 | ||||||||
\(604\) | −0.812316 | −0.0330527 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.92020 | −0.199870 | ||||||||
\(607\) | 22.4797 | 0.912422 | 0.456211 | − | 0.889872i | \(-0.349206\pi\) | ||||
0.456211 | + | 0.889872i | \(0.349206\pi\) | |||||||
\(608\) | −1.75639 | −0.0712312 | ||||||||
\(609\) | 0.0597162 | 0.00241982 | ||||||||
\(610\) | 3.83896 | 0.155435 | ||||||||
\(611\) | −13.7073 | −0.554536 | ||||||||
\(612\) | −0.433977 | −0.0175425 | ||||||||
\(613\) | 8.61975 | 0.348148 | 0.174074 | − | 0.984733i | \(-0.444307\pi\) | ||||
0.174074 | + | 0.984733i | \(0.444307\pi\) | |||||||
\(614\) | 37.7553 | 1.52368 | ||||||||
\(615\) | −1.47160 | −0.0593408 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.79131 | −0.0721154 | −0.0360577 | − | 0.999350i | \(-0.511480\pi\) | ||||
−0.0360577 | + | 0.999350i | \(0.511480\pi\) | |||||||
\(618\) | 0.327011 | 0.0131543 | ||||||||
\(619\) | 12.4154 | 0.499016 | 0.249508 | − | 0.968373i | \(-0.419731\pi\) | ||||
0.249508 | + | 0.968373i | \(0.419731\pi\) | |||||||
\(620\) | −0.475691 | −0.0191042 | ||||||||
\(621\) | 3.87389 | 0.155454 | ||||||||
\(622\) | 25.1199 | 1.00722 | ||||||||
\(623\) | −2.73384 | −0.109529 | ||||||||
\(624\) | −2.08366 | −0.0834132 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.7606 | 0.510016 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.613421 | −0.0244782 | ||||||||
\(629\) | −5.78471 | −0.230651 | ||||||||
\(630\) | −3.99032 | −0.158978 | ||||||||
\(631\) | −6.81348 | −0.271240 | −0.135620 | − | 0.990761i | \(-0.543303\pi\) | ||||
−0.135620 | + | 0.990761i | \(0.543303\pi\) | |||||||
\(632\) | −18.5096 | −0.736273 | ||||||||
\(633\) | 1.15627 | 0.0459578 | ||||||||
\(634\) | 19.2032 | 0.762655 | ||||||||
\(635\) | −10.1792 | −0.403948 | ||||||||
\(636\) | −0.177344 | −0.00703215 | ||||||||
\(637\) | −2.34529 | −0.0929238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.52878 | 0.258274 | ||||||||
\(640\) | −9.77963 | −0.386574 | ||||||||
\(641\) | −48.3163 | −1.90838 | −0.954190 | − | 0.299202i | \(-0.903280\pi\) | ||||
−0.954190 | + | 0.299202i | \(0.903280\pi\) | |||||||
\(642\) | 1.09145 | 0.0430761 | ||||||||
\(643\) | −45.7624 | −1.80469 | −0.902346 | − | 0.431012i | \(-0.858157\pi\) | ||||
−0.902346 | + | 0.431012i | \(0.858157\pi\) | |||||||
\(644\) | 0.426912 | 0.0168227 | ||||||||
\(645\) | 2.34462 | 0.0923192 | ||||||||
\(646\) | 2.46255 | 0.0968879 | ||||||||
\(647\) | −14.5828 | −0.573310 | −0.286655 | − | 0.958034i | \(-0.592543\pi\) | ||||
−0.286655 | + | 0.958034i | \(0.592543\pi\) | |||||||
\(648\) | 24.8188 | 0.974973 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.18211 | 0.124812 | ||||||||
\(651\) | 0.726570 | 0.0284765 | ||||||||
\(652\) | 1.42859 | 0.0559479 | ||||||||
\(653\) | 17.5533 | 0.686913 | 0.343456 | − | 0.939169i | \(-0.388402\pi\) | ||||
0.343456 | + | 0.939169i | \(0.388402\pi\) | |||||||
\(654\) | 2.00558 | 0.0784245 | ||||||||
\(655\) | 12.4893 | 0.487996 | ||||||||
\(656\) | −22.1463 | −0.864668 | ||||||||
\(657\) | 0.294606 | 0.0114937 | ||||||||
\(658\) | 7.92997 | 0.309142 | ||||||||
\(659\) | −15.1180 | −0.588915 | −0.294458 | − | 0.955665i | \(-0.595139\pi\) | ||||
−0.294458 | + | 0.955665i | \(0.595139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.6231 | −1.50226 | −0.751132 | − | 0.660152i | \(-0.770492\pi\) | ||||
−0.751132 | + | 0.660152i | \(0.770492\pi\) | |||||||
\(662\) | 33.1844 | 1.28975 | ||||||||
\(663\) | −0.528598 | −0.0205291 | ||||||||
\(664\) | −48.0756 | −1.86570 | ||||||||
\(665\) | −1.95659 | −0.0758732 | ||||||||
\(666\) | 24.8840 | 0.964234 | ||||||||
\(667\) | 0.659572 | 0.0255387 | ||||||||
\(668\) | −0.0102570 | −0.000396856 0 | ||||||||
\(669\) | −4.76349 | −0.184167 | ||||||||
\(670\) | −20.3669 | −0.786843 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.218114 | −0.00841392 | ||||||||
\(673\) | −41.8975 | −1.61503 | −0.807515 | − | 0.589847i | \(-0.799188\pi\) | ||||
−0.807515 | + | 0.589847i | \(0.799188\pi\) | |||||||
\(674\) | −32.2606 | −1.24263 | ||||||||
\(675\) | 1.44350 | 0.0555604 | ||||||||
\(676\) | 1.19302 | 0.0458853 | ||||||||
\(677\) | 15.8363 | 0.608637 | 0.304318 | − | 0.952570i | \(-0.401571\pi\) | ||||
0.304318 | + | 0.952570i | \(0.401571\pi\) | |||||||
\(678\) | −3.14611 | −0.120825 | ||||||||
\(679\) | −3.11103 | −0.119391 | ||||||||
\(680\) | −2.71741 | −0.104208 | ||||||||
\(681\) | 1.97626 | 0.0757304 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7634 | 0.641434 | 0.320717 | − | 0.947175i | \(-0.396076\pi\) | ||||
0.320717 | + | 0.947175i | \(0.396076\pi\) | |||||||
\(684\) | 0.915370 | 0.0350000 | ||||||||
\(685\) | 16.6161 | 0.634869 | ||||||||
\(686\) | 1.35681 | 0.0518031 | ||||||||
\(687\) | −3.05882 | −0.116701 | ||||||||
\(688\) | 35.2843 | 1.34520 | ||||||||
\(689\) | 10.7608 | 0.409955 | ||||||||
\(690\) | 0.884725 | 0.0336809 | ||||||||
\(691\) | −0.259485 | −0.00987129 | −0.00493564 | − | 0.999988i | \(-0.501571\pi\) | ||||
−0.00493564 | + | 0.999988i | \(0.501571\pi\) | |||||||
\(692\) | −2.73934 | −0.104134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.13631 | −0.119053 | ||||||||
\(695\) | −0.420472 | −0.0159494 | ||||||||
\(696\) | −0.174936 | −0.00663092 | ||||||||
\(697\) | −5.61823 | −0.212806 | ||||||||
\(698\) | 49.2079 | 1.86254 | ||||||||
\(699\) | 0.673522 | 0.0254750 | ||||||||
\(700\) | 0.159077 | 0.00601255 | ||||||||
\(701\) | 14.0986 | 0.532498 | 0.266249 | − | 0.963904i | \(-0.414216\pi\) | ||||
0.266249 | + | 0.963904i | \(0.414216\pi\) | |||||||
\(702\) | 4.59337 | 0.173366 | ||||||||
\(703\) | 12.2014 | 0.460186 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.42008 | −0.0534834 | ||||||||
\(706\) | 14.4591 | 0.544176 | ||||||||
\(707\) | 14.9247 | 0.561301 | ||||||||
\(708\) | −0.373681 | −0.0140438 | ||||||||
\(709\) | 18.0034 | 0.676131 | 0.338065 | − | 0.941123i | \(-0.390227\pi\) | ||||
0.338065 | + | 0.941123i | \(0.390227\pi\) | |||||||
\(710\) | 3.01204 | 0.113040 | ||||||||
\(711\) | 18.5824 | 0.696894 | ||||||||
\(712\) | 8.00865 | 0.300137 | ||||||||
\(713\) | 8.02505 | 0.300540 | ||||||||
\(714\) | 0.305807 | 0.0114445 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.89548 | 0.108209 | ||||||||
\(717\) | −0.253974 | −0.00948483 | ||||||||
\(718\) | 30.4722 | 1.13721 | ||||||||
\(719\) | −20.5769 | −0.767387 | −0.383694 | − | 0.923460i | \(-0.625348\pi\) | ||||
−0.383694 | + | 0.923460i | \(0.625348\pi\) | |||||||
\(720\) | 10.7538 | 0.400769 | ||||||||
\(721\) | −0.991937 | −0.0369417 | ||||||||
\(722\) | 20.5851 | 0.766100 | ||||||||
\(723\) | 5.90227 | 0.219508 | ||||||||
\(724\) | 1.51801 | 0.0564163 | ||||||||
\(725\) | 0.245772 | 0.00912774 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.37912 | −0.0882368 | −0.0441184 | − | 0.999026i | \(-0.514048\pi\) | ||||
−0.0441184 | + | 0.999026i | \(0.514048\pi\) | |||||||
\(728\) | 6.87041 | 0.254634 | ||||||||
\(729\) | −23.8641 | −0.883856 | ||||||||
\(730\) | 0.135916 | 0.00503047 | ||||||||
\(731\) | 8.95119 | 0.331072 | ||||||||
\(732\) | −0.109361 | −0.00404211 | ||||||||
\(733\) | 9.09774 | 0.336033 | 0.168016 | − | 0.985784i | \(-0.446264\pi\) | ||||
0.168016 | + | 0.985784i | \(0.446264\pi\) | |||||||
\(734\) | −20.5004 | −0.756682 | ||||||||
\(735\) | −0.242974 | −0.00896224 | ||||||||
\(736\) | −2.40909 | −0.0888002 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 24.1679 | 0.889631 | ||||||||
\(739\) | 12.3131 | 0.452944 | 0.226472 | − | 0.974018i | \(-0.427281\pi\) | ||||
0.226472 | + | 0.974018i | \(0.427281\pi\) | |||||||
\(740\) | −0.992020 | −0.0364674 | ||||||||
\(741\) | 1.11495 | 0.0409588 | ||||||||
\(742\) | −6.22539 | −0.228541 | ||||||||
\(743\) | 51.7175 | 1.89733 | 0.948666 | − | 0.316279i | \(-0.102434\pi\) | ||||
0.948666 | + | 0.316279i | \(0.102434\pi\) | |||||||
\(744\) | −2.12845 | −0.0780327 | ||||||||
\(745\) | −10.1747 | −0.372772 | ||||||||
\(746\) | −30.8203 | −1.12841 | ||||||||
\(747\) | 48.2646 | 1.76591 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.31075 | −0.120972 | ||||||||
\(750\) | 0.329669 | 0.0120378 | ||||||||
\(751\) | 13.7321 | 0.501093 | 0.250546 | − | 0.968105i | \(-0.419390\pi\) | ||||
0.250546 | + | 0.968105i | \(0.419390\pi\) | |||||||
\(752\) | −21.3710 | −0.779319 | ||||||||
\(753\) | 3.81714 | 0.139104 | ||||||||
\(754\) | 0.782072 | 0.0284814 | ||||||||
\(755\) | 5.10643 | 0.185842 | ||||||||
\(756\) | 0.229628 | 0.00835149 | ||||||||
\(757\) | −49.2807 | −1.79114 | −0.895568 | − | 0.444924i | \(-0.853231\pi\) | ||||
−0.895568 | + | 0.444924i | \(0.853231\pi\) | |||||||
\(758\) | 2.04465 | 0.0742650 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.73172 | 0.207911 | ||||||||
\(761\) | −12.4590 | −0.451637 | −0.225818 | − | 0.974169i | \(-0.572506\pi\) | ||||
−0.225818 | + | 0.974169i | \(0.572506\pi\) | |||||||
\(762\) | −3.35576 | −0.121566 | ||||||||
\(763\) | −6.08363 | −0.220242 | ||||||||
\(764\) | −1.59188 | −0.0575922 | ||||||||
\(765\) | 2.72809 | 0.0986343 | ||||||||
\(766\) | 20.0892 | 0.725853 | ||||||||
\(767\) | 22.6741 | 0.818714 | ||||||||
\(768\) | 0.921616 | 0.0332559 | ||||||||
\(769\) | 21.9501 | 0.791540 | 0.395770 | − | 0.918350i | \(-0.370478\pi\) | ||||
0.395770 | + | 0.918350i | \(0.370478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.94983 | −0.214278 | ||||||||
\(772\) | 2.15282 | 0.0774819 | ||||||||
\(773\) | 23.0657 | 0.829617 | 0.414808 | − | 0.909909i | \(-0.363849\pi\) | ||||
0.414808 | + | 0.909909i | \(0.363849\pi\) | |||||||
\(774\) | −38.5052 | −1.38404 | ||||||||
\(775\) | 2.99032 | 0.107415 | ||||||||
\(776\) | 9.11362 | 0.327160 | ||||||||
\(777\) | 1.51521 | 0.0543578 | ||||||||
\(778\) | 45.5910 | 1.63452 | ||||||||
\(779\) | 11.8503 | 0.424582 | ||||||||
\(780\) | −0.0906494 | −0.00324577 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.37767 | 0.120785 | ||||||||
\(783\) | 0.354772 | 0.0126785 | ||||||||
\(784\) | −3.65654 | −0.130591 | ||||||||
\(785\) | 3.85612 | 0.137631 | ||||||||
\(786\) | 4.11732 | 0.146860 | ||||||||
\(787\) | 46.7274 | 1.66565 | 0.832826 | − | 0.553534i | \(-0.186721\pi\) | ||||
0.832826 | + | 0.553534i | \(0.186721\pi\) | |||||||
\(788\) | 3.53925 | 0.126081 | ||||||||
\(789\) | −5.27479 | −0.187788 | ||||||||
\(790\) | 8.57293 | 0.305011 | ||||||||
\(791\) | 9.54323 | 0.339318 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.63579 | 0.235644 | ||||||||
\(794\) | 32.2109 | 1.14312 | ||||||||
\(795\) | 1.11483 | 0.0395390 | ||||||||
\(796\) | 1.50257 | 0.0532570 | ||||||||
\(797\) | 49.0362 | 1.73695 | 0.868475 | − | 0.495732i | \(-0.165100\pi\) | ||||
0.868475 | + | 0.495732i | \(0.165100\pi\) | |||||||
\(798\) | −0.645026 | −0.0228337 | ||||||||
\(799\) | −5.42154 | −0.191800 | ||||||||
\(800\) | −0.897683 | −0.0317379 | ||||||||
\(801\) | −8.04013 | −0.284084 | ||||||||
\(802\) | −34.7749 | −1.22794 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.580198 | 0.0204620 | ||||||||
\(805\) | −2.68368 | −0.0945872 | ||||||||
\(806\) | 9.51551 | 0.335169 | ||||||||
\(807\) | 2.56886 | 0.0904282 | ||||||||
\(808\) | −43.7211 | −1.53810 | ||||||||
\(809\) | 9.38528 | 0.329969 | 0.164984 | − | 0.986296i | \(-0.447243\pi\) | ||||
0.164984 | + | 0.986296i | \(0.447243\pi\) | |||||||
\(810\) | −11.4951 | −0.403896 | ||||||||
\(811\) | −9.21722 | −0.323660 | −0.161830 | − | 0.986819i | \(-0.551740\pi\) | ||||
−0.161830 | + | 0.986819i | \(0.551740\pi\) | |||||||
\(812\) | 0.0390967 | 0.00137203 | ||||||||
\(813\) | 5.78568 | 0.202913 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.98048 | −0.314573 | ||||||||
\(816\) | −0.824137 | −0.0288506 | ||||||||
\(817\) | −18.8804 | −0.660541 | ||||||||
\(818\) | 36.0301 | 1.25976 | ||||||||
\(819\) | −6.89742 | −0.241015 | ||||||||
\(820\) | −0.963471 | −0.0336459 | ||||||||
\(821\) | 17.3336 | 0.604946 | 0.302473 | − | 0.953158i | \(-0.402188\pi\) | ||||
0.302473 | + | 0.953158i | \(0.402188\pi\) | |||||||
\(822\) | 5.47781 | 0.191061 | ||||||||
\(823\) | −42.7706 | −1.49089 | −0.745445 | − | 0.666567i | \(-0.767763\pi\) | ||||
−0.745445 | + | 0.666567i | \(0.767763\pi\) | |||||||
\(824\) | 2.90583 | 0.101229 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.1175 | −0.456416 | ||||||||
\(827\) | −19.0832 | −0.663589 | −0.331794 | − | 0.943352i | \(-0.607654\pi\) | ||||
−0.331794 | + | 0.943352i | \(0.607654\pi\) | |||||||
\(828\) | 1.25553 | 0.0436328 | ||||||||
\(829\) | −40.8201 | −1.41774 | −0.708870 | − | 0.705340i | \(-0.750795\pi\) | ||||
−0.708870 | + | 0.705340i | \(0.750795\pi\) | |||||||
\(830\) | 22.2668 | 0.772890 | ||||||||
\(831\) | −0.0868465 | −0.00301267 | ||||||||
\(832\) | −20.0078 | −0.693647 | ||||||||
\(833\) | −0.927617 | −0.0321400 | ||||||||
\(834\) | −0.138617 | −0.00479990 | ||||||||
\(835\) | 0.0644782 | 0.00223136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.31653 | 0.149201 | ||||||||
\(838\) | 47.0573 | 1.62557 | ||||||||
\(839\) | 33.0074 | 1.13954 | 0.569771 | − | 0.821804i | \(-0.307032\pi\) | ||||
0.569771 | + | 0.821804i | \(0.307032\pi\) | |||||||
\(840\) | 0.711781 | 0.0245588 | ||||||||
\(841\) | −28.9396 | −0.997917 | ||||||||
\(842\) | −33.6362 | −1.15918 | ||||||||
\(843\) | −1.68475 | −0.0580259 | ||||||||
\(844\) | 0.757022 | 0.0260578 | ||||||||
\(845\) | −7.49961 | −0.257994 | ||||||||
\(846\) | 23.3218 | 0.801818 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.7772 | 0.576131 | ||||||||
\(849\) | −2.98405 | −0.102412 | ||||||||
\(850\) | 1.25860 | 0.0431695 | ||||||||
\(851\) | 16.7357 | 0.573691 | ||||||||
\(852\) | −0.0858046 | −0.00293962 | ||||||||
\(853\) | −48.6092 | −1.66435 | −0.832173 | − | 0.554516i | \(-0.812903\pi\) | ||||
−0.832173 | + | 0.554516i | \(0.812903\pi\) | |||||||
\(854\) | −3.83896 | −0.131366 | ||||||||
\(855\) | −5.75425 | −0.196791 | ||||||||
\(856\) | 9.69867 | 0.331494 | ||||||||
\(857\) | −18.1003 | −0.618294 | −0.309147 | − | 0.951014i | \(-0.600043\pi\) | ||||
−0.309147 | + | 0.951014i | \(0.600043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.23154 | −0.246737 | −0.123368 | − | 0.992361i | \(-0.539370\pi\) | ||||
−0.123368 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(860\) | 1.53504 | 0.0523444 | ||||||||
\(861\) | 1.47160 | 0.0501521 | ||||||||
\(862\) | −8.95491 | −0.305005 | ||||||||
\(863\) | 30.3494 | 1.03310 | 0.516552 | − | 0.856256i | \(-0.327215\pi\) | ||||
0.516552 | + | 0.856256i | \(0.327215\pi\) | |||||||
\(864\) | −1.29581 | −0.0440842 | ||||||||
\(865\) | 17.2202 | 0.585504 | ||||||||
\(866\) | −27.1633 | −0.923046 | ||||||||
\(867\) | 3.92149 | 0.133181 | ||||||||
\(868\) | 0.475691 | 0.0161460 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.0810233 | 0.00274695 | ||||||||
\(871\) | −35.2050 | −1.19288 | ||||||||
\(872\) | 17.8217 | 0.603519 | ||||||||
\(873\) | −9.14944 | −0.309662 | ||||||||
\(874\) | −7.12438 | −0.240986 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.00387187 | −0.000130818 0 | ||||||||
\(877\) | −32.3026 | −1.09078 | −0.545391 | − | 0.838182i | \(-0.683619\pi\) | ||||
−0.545391 | + | 0.838182i | \(0.683619\pi\) | |||||||
\(878\) | −36.1203 | −1.21900 | ||||||||
\(879\) | 4.47836 | 0.151051 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.1158 | 0.778792 | 0.389396 | − | 0.921070i | \(-0.372684\pi\) | ||||
0.389396 | + | 0.921070i | \(0.372684\pi\) | |||||||
\(882\) | 3.99032 | 0.134361 | ||||||||
\(883\) | 47.4436 | 1.59661 | 0.798303 | − | 0.602257i | \(-0.205732\pi\) | ||||
0.798303 | + | 0.602257i | \(0.205732\pi\) | |||||||
\(884\) | −0.346078 | −0.0116399 | ||||||||
\(885\) | 2.34906 | 0.0789626 | ||||||||
\(886\) | −9.97768 | −0.335207 | ||||||||
\(887\) | 49.3267 | 1.65623 | 0.828114 | − | 0.560560i | \(-0.189414\pi\) | ||||
0.828114 | + | 0.560560i | \(0.189414\pi\) | |||||||
\(888\) | −4.43873 | −0.148954 | ||||||||
\(889\) | 10.1792 | 0.341399 | ||||||||
\(890\) | −3.70930 | −0.124336 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.11870 | −0.104422 | ||||||||
\(893\) | 11.4354 | 0.382672 | ||||||||
\(894\) | −3.35428 | −0.112184 | ||||||||
\(895\) | −18.2017 | −0.608416 | ||||||||
\(896\) | 9.77963 | 0.326715 | ||||||||
\(897\) | 1.52928 | 0.0510612 | ||||||||
\(898\) | −2.37691 | −0.0793184 | ||||||||
\(899\) | 0.734936 | 0.0245115 | ||||||||
\(900\) | 0.467840 | 0.0155947 | ||||||||
\(901\) | 4.25616 | 0.141793 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.34462 | −0.0780240 | ||||||||
\(904\) | −27.9564 | −0.929816 | ||||||||
\(905\) | −9.54258 | −0.317206 | ||||||||
\(906\) | 1.68343 | 0.0559282 | ||||||||
\(907\) | 32.7141 | 1.08625 | 0.543126 | − | 0.839651i | \(-0.317240\pi\) | ||||
0.543126 | + | 0.839651i | \(0.317240\pi\) | |||||||
\(908\) | 1.29387 | 0.0429387 | ||||||||
\(909\) | 43.8930 | 1.45584 | ||||||||
\(910\) | −3.18211 | −0.105486 | ||||||||
\(911\) | −15.9930 | −0.529870 | −0.264935 | − | 0.964266i | \(-0.585351\pi\) | ||||
−0.264935 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(912\) | 1.73832 | 0.0575615 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.0400 | 0.795173 | ||||||||
\(915\) | 0.687473 | 0.0227272 | ||||||||
\(916\) | −2.00264 | −0.0661689 | ||||||||
\(917\) | −12.4893 | −0.412432 | ||||||||
\(918\) | 1.81679 | 0.0599629 | ||||||||
\(919\) | −47.6485 | −1.57178 | −0.785890 | − | 0.618366i | \(-0.787795\pi\) | ||||
−0.785890 | + | 0.618366i | \(0.787795\pi\) | |||||||
\(920\) | 7.86170 | 0.259192 | ||||||||
\(921\) | 6.76115 | 0.222787 | ||||||||
\(922\) | 27.9734 | 0.921256 | ||||||||
\(923\) | 5.20642 | 0.171371 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.23609 | 0.205041 | ||||||||
\(926\) | 17.8179 | 0.585534 | ||||||||
\(927\) | −2.91725 | −0.0958151 | ||||||||
\(928\) | −0.220625 | −0.00724237 | ||||||||
\(929\) | 53.3770 | 1.75124 | 0.875622 | − | 0.482998i | \(-0.160452\pi\) | ||||
0.875622 | + | 0.482998i | \(0.160452\pi\) | |||||||
\(930\) | 0.985814 | 0.0323261 | ||||||||
\(931\) | 1.95659 | 0.0641245 | ||||||||
\(932\) | 0.440961 | 0.0144441 | ||||||||
\(933\) | 4.49842 | 0.147272 | ||||||||
\(934\) | −41.8897 | −1.37067 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.2056 | 0.660442 | ||||||||
\(937\) | −13.0806 | −0.427326 | −0.213663 | − | 0.976907i | \(-0.568539\pi\) | ||||
−0.213663 | + | 0.976907i | \(0.568539\pi\) | |||||||
\(938\) | 20.3669 | 0.665004 | ||||||||
\(939\) | 2.28514 | 0.0745727 | ||||||||
\(940\) | −0.929741 | −0.0303248 | ||||||||
\(941\) | 40.1799 | 1.30983 | 0.654913 | − | 0.755704i | \(-0.272705\pi\) | ||||
0.654913 | + | 0.755704i | \(0.272705\pi\) | |||||||
\(942\) | 1.27124 | 0.0414193 | ||||||||
\(943\) | 16.2540 | 0.529304 | ||||||||
\(944\) | 35.3511 | 1.15058 | ||||||||
\(945\) | −1.44350 | −0.0469571 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.1138 | 0.686105 | 0.343053 | − | 0.939316i | \(-0.388539\pi\) | ||||
0.343053 | + | 0.939316i | \(0.388539\pi\) | |||||||
\(948\) | −0.244219 | −0.00793187 | ||||||||
\(949\) | 0.234936 | 0.00762634 | ||||||||
\(950\) | −2.65471 | −0.0861301 | ||||||||
\(951\) | 3.43887 | 0.111513 | ||||||||
\(952\) | 2.71741 | 0.0880717 | ||||||||
\(953\) | 36.3562 | 1.17769 | 0.588846 | − | 0.808245i | \(-0.299582\pi\) | ||||
0.588846 | + | 0.808245i | \(0.299582\pi\) | |||||||
\(954\) | −18.3086 | −0.592764 | ||||||||
\(955\) | 10.0070 | 0.323818 | ||||||||
\(956\) | −0.166279 | −0.00537784 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −49.5160 | −1.59979 | ||||||||
\(959\) | −16.6161 | −0.536562 | ||||||||
\(960\) | −2.07283 | −0.0669002 | ||||||||
\(961\) | −22.0580 | −0.711548 | ||||||||
\(962\) | 19.8439 | 0.639793 | ||||||||
\(963\) | −9.73679 | −0.313764 | ||||||||
\(964\) | 3.86426 | 0.124460 | ||||||||
\(965\) | −13.5332 | −0.435649 | ||||||||
\(966\) | −0.884725 | −0.0284656 | ||||||||
\(967\) | 3.01730 | 0.0970299 | 0.0485149 | − | 0.998822i | \(-0.484551\pi\) | ||||
0.0485149 | + | 0.998822i | \(0.484551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.440989 | 0.0141666 | ||||||||
\(970\) | −4.22107 | −0.135530 | ||||||||
\(971\) | 49.6294 | 1.59268 | 0.796341 | − | 0.604847i | \(-0.206766\pi\) | ||||
0.796341 | + | 0.604847i | \(0.206766\pi\) | |||||||
\(972\) | 1.01635 | 0.0325994 | ||||||||
\(973\) | 0.420472 | 0.0134797 | ||||||||
\(974\) | 39.3849 | 1.26197 | ||||||||
\(975\) | 0.569845 | 0.0182497 | ||||||||
\(976\) | 10.3458 | 0.331162 | ||||||||
\(977\) | −11.0956 | −0.354979 | −0.177490 | − | 0.984123i | \(-0.556798\pi\) | ||||
−0.177490 | + | 0.984123i | \(0.556798\pi\) | |||||||
\(978\) | −2.96058 | −0.0946691 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.159077 | −0.00508154 | ||||||||
\(981\) | −17.8917 | −0.571239 | ||||||||
\(982\) | 38.2571 | 1.22083 | ||||||||
\(983\) | 16.2497 | 0.518283 | 0.259142 | − | 0.965839i | \(-0.416560\pi\) | ||||
0.259142 | + | 0.965839i | \(0.416560\pi\) | |||||||
\(984\) | −4.31099 | −0.137429 | ||||||||
\(985\) | −22.2486 | −0.708901 | ||||||||
\(986\) | 0.309328 | 0.00985100 | ||||||||
\(987\) | 1.42008 | 0.0452018 | ||||||||
\(988\) | 0.729968 | 0.0232234 | ||||||||
\(989\) | −25.8966 | −0.823463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8831 | −1.01280 | −0.506400 | − | 0.862299i | \(-0.669024\pi\) | ||||
−0.506400 | + | 0.862299i | \(0.669024\pi\) | |||||||
\(992\) | −2.68436 | −0.0852284 | ||||||||
\(993\) | 5.94259 | 0.188582 | ||||||||
\(994\) | −3.01204 | −0.0955360 | ||||||||
\(995\) | −9.44551 | −0.299443 | ||||||||
\(996\) | −0.634318 | −0.0200991 | ||||||||
\(997\) | 10.3751 | 0.328584 | 0.164292 | − | 0.986412i | \(-0.447466\pi\) | ||||
0.164292 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(998\) | 16.5282 | 0.523190 | ||||||||
\(999\) | 9.00180 | 0.284804 |
(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 | 4235.2.a.bc.1.2 | ✓ | 5 | |
11.10 | odd | 2 | 4235.2.a.bd.1.4 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.bc.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4235.2.a.bd.1.4 | yes | 5 | 11.10 | odd | 2 |