Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.69202 | −0.639524 | −0.319762 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319762 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −4.55496 | −1.37337 | −0.686686 | − | 0.726954i | \(-0.740935\pi\) | ||||
−0.686686 | + | 0.726954i | \(0.740935\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.69202 | −0.452212 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.35690 | 0.571631 | 0.285816 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285816 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.51573 | −1.49481 | −0.747405 | − | 0.664368i | \(-0.768701\pi\) | ||||
−0.747405 | + | 0.664368i | \(0.768701\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.69202 | 0.369229 | ||||||||
\(22\) | −4.55496 | −0.971120 | ||||||||
\(23\) | 8.94869 | 1.86593 | 0.932965 | − | 0.359966i | \(-0.117212\pi\) | ||||
0.932965 | + | 0.359966i | \(0.117212\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.69202 | −0.319762 | ||||||||
\(29\) | 9.07606 | 1.68538 | 0.842691 | − | 0.538397i | \(-0.180970\pi\) | ||||
0.842691 | + | 0.538397i | \(0.180970\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −10.6528 | −1.91330 | −0.956649 | − | 0.291243i | \(-0.905931\pi\) | ||||
−0.956649 | + | 0.291243i | \(0.905931\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.55496 | 0.792916 | ||||||||
\(34\) | 2.35690 | 0.404204 | ||||||||
\(35\) | −1.69202 | −0.286004 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.18598 | 1.01697 | 0.508484 | − | 0.861071i | \(-0.330206\pi\) | ||||
0.508484 | + | 0.861071i | \(0.330206\pi\) | |||||||
\(38\) | −6.51573 | −1.05699 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.00969 | 0.470034 | 0.235017 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235017 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(42\) | 1.69202 | 0.261085 | ||||||||
\(43\) | −4.93900 | −0.753191 | −0.376595 | − | 0.926378i | \(-0.622905\pi\) | ||||
−0.376595 | + | 0.926378i | \(0.622905\pi\) | |||||||
\(44\) | −4.55496 | −0.686686 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 8.94869 | 1.31941 | ||||||||
\(47\) | −4.28621 | −0.625208 | −0.312604 | − | 0.949884i | \(-0.601201\pi\) | ||||
−0.312604 | + | 0.949884i | \(0.601201\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.13706 | −0.591009 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.35690 | −0.330031 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.40581 | −0.467824 | −0.233912 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233912 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.55496 | −0.614190 | ||||||||
\(56\) | −1.69202 | −0.226106 | ||||||||
\(57\) | 6.51573 | 0.863029 | ||||||||
\(58\) | 9.07606 | 1.19175 | ||||||||
\(59\) | 4.32304 | 0.562812 | 0.281406 | − | 0.959589i | \(-0.409199\pi\) | ||||
0.281406 | + | 0.959589i | \(0.409199\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −14.3666 | −1.83945 | −0.919726 | − | 0.392560i | \(-0.871589\pi\) | ||||
−0.919726 | + | 0.392560i | \(0.871589\pi\) | |||||||
\(62\) | −10.6528 | −1.35291 | ||||||||
\(63\) | −1.69202 | −0.213175 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.55496 | 0.560677 | ||||||||
\(67\) | −3.24698 | −0.396682 | −0.198341 | − | 0.980133i | \(-0.563555\pi\) | ||||
−0.198341 | + | 0.980133i | \(0.563555\pi\) | |||||||
\(68\) | 2.35690 | 0.285816 | ||||||||
\(69\) | −8.94869 | −1.07730 | ||||||||
\(70\) | −1.69202 | −0.202235 | ||||||||
\(71\) | −14.9487 | −1.77408 | −0.887042 | − | 0.461690i | \(-0.847243\pi\) | ||||
−0.887042 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.72886 | −0.787553 | −0.393777 | − | 0.919206i | \(-0.628832\pi\) | ||||
−0.393777 | + | 0.919206i | \(0.628832\pi\) | |||||||
\(74\) | 6.18598 | 0.719106 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −6.51573 | −0.747405 | ||||||||
\(77\) | 7.70709 | 0.878304 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.67994 | 0.639043 | 0.319522 | − | 0.947579i | \(-0.396478\pi\) | ||||
0.319522 | + | 0.947579i | \(0.396478\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.00969 | 0.332365 | ||||||||
\(83\) | −7.71917 | −0.847289 | −0.423644 | − | 0.905829i | \(-0.639249\pi\) | ||||
−0.423644 | + | 0.905829i | \(0.639249\pi\) | |||||||
\(84\) | 1.69202 | 0.184615 | ||||||||
\(85\) | 2.35690 | 0.255641 | ||||||||
\(86\) | −4.93900 | −0.532586 | ||||||||
\(87\) | −9.07606 | −0.973056 | ||||||||
\(88\) | −4.55496 | −0.485560 | ||||||||
\(89\) | −9.12498 | −0.967246 | −0.483623 | − | 0.875276i | \(-0.660679\pi\) | ||||
−0.483623 | + | 0.875276i | \(0.660679\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.94869 | 0.932965 | ||||||||
\(93\) | 10.6528 | 1.10464 | ||||||||
\(94\) | −4.28621 | −0.442089 | ||||||||
\(95\) | −6.51573 | −0.668500 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.40581 | −0.447343 | −0.223671 | − | 0.974665i | \(-0.571804\pi\) | ||||
−0.223671 | + | 0.974665i | \(0.571804\pi\) | |||||||
\(98\) | −4.13706 | −0.417907 | ||||||||
\(99\) | −4.55496 | −0.457791 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.31767 | 0.230617 | 0.115308 | − | 0.993330i | \(-0.463214\pi\) | ||||
0.115308 | + | 0.993330i | \(0.463214\pi\) | |||||||
\(102\) | −2.35690 | −0.233367 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69202 | 0.165124 | ||||||||
\(106\) | −3.40581 | −0.330802 | ||||||||
\(107\) | −3.06100 | −0.295918 | −0.147959 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147959 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.45473 | 0.714034 | 0.357017 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357017 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(110\) | −4.55496 | −0.434298 | ||||||||
\(111\) | −6.18598 | −0.587147 | ||||||||
\(112\) | −1.69202 | −0.159881 | ||||||||
\(113\) | −19.9812 | −1.87967 | −0.939837 | − | 0.341623i | \(-0.889024\pi\) | ||||
−0.939837 | + | 0.341623i | \(0.889024\pi\) | |||||||
\(114\) | 6.51573 | 0.610254 | ||||||||
\(115\) | 8.94869 | 0.834470 | ||||||||
\(116\) | 9.07606 | 0.842691 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.32304 | 0.397968 | ||||||||
\(119\) | −3.98792 | −0.365572 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 9.74764 | 0.886149 | ||||||||
\(122\) | −14.3666 | −1.30069 | ||||||||
\(123\) | −3.00969 | −0.271374 | ||||||||
\(124\) | −10.6528 | −0.956649 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.69202 | −0.150737 | ||||||||
\(127\) | −3.14244 | −0.278846 | −0.139423 | − | 0.990233i | \(-0.544525\pi\) | ||||
−0.139423 | + | 0.990233i | \(0.544525\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.93900 | 0.434855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.77479 | −0.329805 | −0.164902 | − | 0.986310i | \(-0.552731\pi\) | ||||
−0.164902 | + | 0.986310i | \(0.552731\pi\) | |||||||
\(132\) | 4.55496 | 0.396458 | ||||||||
\(133\) | 11.0248 | 0.955967 | ||||||||
\(134\) | −3.24698 | −0.280496 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 2.35690 | 0.202102 | ||||||||
\(137\) | 14.5894 | 1.24646 | 0.623228 | − | 0.782040i | \(-0.285821\pi\) | ||||
0.623228 | + | 0.782040i | \(0.285821\pi\) | |||||||
\(138\) | −8.94869 | −0.761763 | ||||||||
\(139\) | −14.3599 | −1.21799 | −0.608995 | − | 0.793174i | \(-0.708427\pi\) | ||||
−0.608995 | + | 0.793174i | \(0.708427\pi\) | |||||||
\(140\) | −1.69202 | −0.143002 | ||||||||
\(141\) | 4.28621 | 0.360964 | ||||||||
\(142\) | −14.9487 | −1.25447 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.07606 | 0.753726 | ||||||||
\(146\) | −6.72886 | −0.556884 | ||||||||
\(147\) | 4.13706 | 0.341219 | ||||||||
\(148\) | 6.18598 | 0.508484 | ||||||||
\(149\) | 0.252356 | 0.0206738 | 0.0103369 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103369 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 11.0804 | 0.901708 | 0.450854 | − | 0.892598i | \(-0.351119\pi\) | ||||
0.450854 | + | 0.892598i | \(0.351119\pi\) | |||||||
\(152\) | −6.51573 | −0.528495 | ||||||||
\(153\) | 2.35690 | 0.190544 | ||||||||
\(154\) | 7.70709 | 0.621055 | ||||||||
\(155\) | −10.6528 | −0.855653 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.03923 | 0.402174 | 0.201087 | − | 0.979573i | \(-0.435553\pi\) | ||||
0.201087 | + | 0.979573i | \(0.435553\pi\) | |||||||
\(158\) | 5.67994 | 0.451872 | ||||||||
\(159\) | 3.40581 | 0.270099 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −15.1414 | −1.19331 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 20.9825 | 1.64348 | 0.821740 | − | 0.569863i | \(-0.193004\pi\) | ||||
0.821740 | + | 0.569863i | \(0.193004\pi\) | |||||||
\(164\) | 3.00969 | 0.235017 | ||||||||
\(165\) | 4.55496 | 0.354603 | ||||||||
\(166\) | −7.71917 | −0.599124 | ||||||||
\(167\) | −22.2325 | −1.72040 | −0.860201 | − | 0.509954i | \(-0.829662\pi\) | ||||
−0.860201 | + | 0.509954i | \(0.829662\pi\) | |||||||
\(168\) | 1.69202 | 0.130542 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.35690 | 0.180766 | ||||||||
\(171\) | −6.51573 | −0.498270 | ||||||||
\(172\) | −4.93900 | −0.376595 | ||||||||
\(173\) | −11.6286 | −0.884108 | −0.442054 | − | 0.896988i | \(-0.645750\pi\) | ||||
−0.442054 | + | 0.896988i | \(0.645750\pi\) | |||||||
\(174\) | −9.07606 | −0.688055 | ||||||||
\(175\) | −1.69202 | −0.127905 | ||||||||
\(176\) | −4.55496 | −0.343343 | ||||||||
\(177\) | −4.32304 | −0.324940 | ||||||||
\(178\) | −9.12498 | −0.683946 | ||||||||
\(179\) | −15.7875 | −1.18001 | −0.590005 | − | 0.807399i | \(-0.700874\pi\) | ||||
−0.590005 | + | 0.807399i | \(0.700874\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −1.91185 | −0.142107 | −0.0710535 | − | 0.997473i | \(-0.522636\pi\) | ||||
−0.0710535 | + | 0.997473i | \(0.522636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3666 | 1.06201 | ||||||||
\(184\) | 8.94869 | 0.659706 | ||||||||
\(185\) | 6.18598 | 0.454802 | ||||||||
\(186\) | 10.6528 | 0.781101 | ||||||||
\(187\) | −10.7356 | −0.785062 | ||||||||
\(188\) | −4.28621 | −0.312604 | ||||||||
\(189\) | 1.69202 | 0.123076 | ||||||||
\(190\) | −6.51573 | −0.472701 | ||||||||
\(191\) | 24.3260 | 1.76017 | 0.880085 | − | 0.474817i | \(-0.157486\pi\) | ||||
0.880085 | + | 0.474817i | \(0.157486\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.521106 | −0.0375101 | −0.0187550 | − | 0.999824i | \(-0.505970\pi\) | ||||
−0.0187550 | + | 0.999824i | \(0.505970\pi\) | |||||||
\(194\) | −4.40581 | −0.316319 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.13706 | −0.295505 | ||||||||
\(197\) | −4.87502 | −0.347331 | −0.173665 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173665 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(198\) | −4.55496 | −0.323707 | ||||||||
\(199\) | −18.4983 | −1.31131 | −0.655654 | − | 0.755062i | \(-0.727607\pi\) | ||||
−0.655654 | + | 0.755062i | \(0.727607\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 3.24698 | 0.229024 | ||||||||
\(202\) | 2.31767 | 0.163070 | ||||||||
\(203\) | −15.3569 | −1.07784 | ||||||||
\(204\) | −2.35690 | −0.165016 | ||||||||
\(205\) | 3.00969 | 0.210206 | ||||||||
\(206\) | −9.00000 | −0.627060 | ||||||||
\(207\) | 8.94869 | 0.621977 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.6789 | 2.05293 | ||||||||
\(210\) | 1.69202 | 0.116761 | ||||||||
\(211\) | 18.2500 | 1.25638 | 0.628190 | − | 0.778060i | \(-0.283796\pi\) | ||||
0.628190 | + | 0.778060i | \(0.283796\pi\) | |||||||
\(212\) | −3.40581 | −0.233912 | ||||||||
\(213\) | 14.9487 | 1.02427 | ||||||||
\(214\) | −3.06100 | −0.209246 | ||||||||
\(215\) | −4.93900 | −0.336837 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 18.0248 | 1.22360 | ||||||||
\(218\) | 7.45473 | 0.504898 | ||||||||
\(219\) | 6.72886 | 0.454694 | ||||||||
\(220\) | −4.55496 | −0.307095 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.18598 | −0.415176 | ||||||||
\(223\) | 8.54048 | 0.571913 | 0.285957 | − | 0.958243i | \(-0.407689\pi\) | ||||
0.285957 | + | 0.958243i | \(0.407689\pi\) | |||||||
\(224\) | −1.69202 | −0.113053 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −19.9812 | −1.32913 | ||||||||
\(227\) | −9.61596 | −0.638233 | −0.319117 | − | 0.947715i | \(-0.603386\pi\) | ||||
−0.319117 | + | 0.947715i | \(0.603386\pi\) | |||||||
\(228\) | 6.51573 | 0.431515 | ||||||||
\(229\) | −13.4058 | −0.885881 | −0.442941 | − | 0.896551i | \(-0.646065\pi\) | ||||
−0.442941 | + | 0.896551i | \(0.646065\pi\) | |||||||
\(230\) | 8.94869 | 0.590059 | ||||||||
\(231\) | −7.70709 | −0.507089 | ||||||||
\(232\) | 9.07606 | 0.595873 | ||||||||
\(233\) | −0.153457 | −0.0100533 | −0.00502664 | − | 0.999987i | \(-0.501600\pi\) | ||||
−0.00502664 | + | 0.999987i | \(0.501600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.28621 | −0.279601 | ||||||||
\(236\) | 4.32304 | 0.281406 | ||||||||
\(237\) | −5.67994 | −0.368952 | ||||||||
\(238\) | −3.98792 | −0.258498 | ||||||||
\(239\) | 14.5851 | 0.943431 | 0.471715 | − | 0.881751i | \(-0.343635\pi\) | ||||
0.471715 | + | 0.881751i | \(0.343635\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 3.40044 | 0.219041 | 0.109521 | − | 0.993985i | \(-0.465068\pi\) | ||||
0.109521 | + | 0.993985i | \(0.465068\pi\) | |||||||
\(242\) | 9.74764 | 0.626602 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.3666 | −0.919726 | ||||||||
\(245\) | −4.13706 | −0.264307 | ||||||||
\(246\) | −3.00969 | −0.191891 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.6528 | −0.676453 | ||||||||
\(249\) | 7.71917 | 0.489182 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 1.80864 | 0.114161 | 0.0570803 | − | 0.998370i | \(-0.481821\pi\) | ||||
0.0570803 | + | 0.998370i | \(0.481821\pi\) | |||||||
\(252\) | −1.69202 | −0.106587 | ||||||||
\(253\) | −40.7609 | −2.56262 | ||||||||
\(254\) | −3.14244 | −0.197174 | ||||||||
\(255\) | −2.35690 | −0.147595 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.2664 | −1.38894 | −0.694469 | − | 0.719523i | \(-0.744360\pi\) | ||||
−0.694469 | + | 0.719523i | \(0.744360\pi\) | |||||||
\(258\) | 4.93900 | 0.307489 | ||||||||
\(259\) | −10.4668 | −0.650376 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.07606 | 0.561794 | ||||||||
\(262\) | −3.77479 | −0.233207 | ||||||||
\(263\) | 8.08815 | 0.498736 | 0.249368 | − | 0.968409i | \(-0.419777\pi\) | ||||
0.249368 | + | 0.968409i | \(0.419777\pi\) | |||||||
\(264\) | 4.55496 | 0.280338 | ||||||||
\(265\) | −3.40581 | −0.209217 | ||||||||
\(266\) | 11.0248 | 0.675971 | ||||||||
\(267\) | 9.12498 | 0.558440 | ||||||||
\(268\) | −3.24698 | −0.198341 | ||||||||
\(269\) | 16.6843 | 1.01726 | 0.508628 | − | 0.860986i | \(-0.330153\pi\) | ||||
0.508628 | + | 0.860986i | \(0.330153\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 27.4077 | 1.66490 | 0.832451 | − | 0.554099i | \(-0.186937\pi\) | ||||
0.832451 | + | 0.554099i | \(0.186937\pi\) | |||||||
\(272\) | 2.35690 | 0.142908 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5894 | 0.881378 | ||||||||
\(275\) | −4.55496 | −0.274674 | ||||||||
\(276\) | −8.94869 | −0.538648 | ||||||||
\(277\) | −16.0411 | −0.963819 | −0.481910 | − | 0.876221i | \(-0.660057\pi\) | ||||
−0.481910 | + | 0.876221i | \(0.660057\pi\) | |||||||
\(278\) | −14.3599 | −0.861248 | ||||||||
\(279\) | −10.6528 | −0.637766 | ||||||||
\(280\) | −1.69202 | −0.101118 | ||||||||
\(281\) | −10.0935 | −0.602129 | −0.301065 | − | 0.953604i | \(-0.597342\pi\) | ||||
−0.301065 | + | 0.953604i | \(0.597342\pi\) | |||||||
\(282\) | 4.28621 | 0.255240 | ||||||||
\(283\) | 12.1021 | 0.719398 | 0.359699 | − | 0.933068i | \(-0.382879\pi\) | ||||
0.359699 | + | 0.933068i | \(0.382879\pi\) | |||||||
\(284\) | −14.9487 | −0.887042 | ||||||||
\(285\) | 6.51573 | 0.385959 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.09246 | −0.300598 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.4450 | −0.673238 | ||||||||
\(290\) | 9.07606 | 0.532965 | ||||||||
\(291\) | 4.40581 | 0.258273 | ||||||||
\(292\) | −6.72886 | −0.393777 | ||||||||
\(293\) | 4.01075 | 0.234311 | 0.117155 | − | 0.993114i | \(-0.462622\pi\) | ||||
0.117155 | + | 0.993114i | \(0.462622\pi\) | |||||||
\(294\) | 4.13706 | 0.241278 | ||||||||
\(295\) | 4.32304 | 0.251697 | ||||||||
\(296\) | 6.18598 | 0.359553 | ||||||||
\(297\) | 4.55496 | 0.264305 | ||||||||
\(298\) | 0.252356 | 0.0146186 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 8.35690 | 0.481683 | ||||||||
\(302\) | 11.0804 | 0.637604 | ||||||||
\(303\) | −2.31767 | −0.133147 | ||||||||
\(304\) | −6.51573 | −0.373703 | ||||||||
\(305\) | −14.3666 | −0.822628 | ||||||||
\(306\) | 2.35690 | 0.134735 | ||||||||
\(307\) | −15.2784 | −0.871987 | −0.435993 | − | 0.899950i | \(-0.643603\pi\) | ||||
−0.435993 | + | 0.899950i | \(0.643603\pi\) | |||||||
\(308\) | 7.70709 | 0.439152 | ||||||||
\(309\) | 9.00000 | 0.511992 | ||||||||
\(310\) | −10.6528 | −0.605038 | ||||||||
\(311\) | 25.4330 | 1.44217 | 0.721085 | − | 0.692846i | \(-0.243644\pi\) | ||||
0.721085 | + | 0.692846i | \(0.243644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.1226 | −1.08087 | −0.540436 | − | 0.841385i | \(-0.681741\pi\) | ||||
−0.540436 | + | 0.841385i | \(0.681741\pi\) | |||||||
\(314\) | 5.03923 | 0.284380 | ||||||||
\(315\) | −1.69202 | −0.0953346 | ||||||||
\(316\) | 5.67994 | 0.319522 | ||||||||
\(317\) | −20.3230 | −1.14146 | −0.570728 | − | 0.821139i | \(-0.693339\pi\) | ||||
−0.570728 | + | 0.821139i | \(0.693339\pi\) | |||||||
\(318\) | 3.40581 | 0.190989 | ||||||||
\(319\) | −41.3411 | −2.31466 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 3.06100 | 0.170848 | ||||||||
\(322\) | −15.1414 | −0.843796 | ||||||||
\(323\) | −15.3569 | −0.854481 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.9825 | 1.16212 | ||||||||
\(327\) | −7.45473 | −0.412248 | ||||||||
\(328\) | 3.00969 | 0.166182 | ||||||||
\(329\) | 7.25236 | 0.399835 | ||||||||
\(330\) | 4.55496 | 0.250742 | ||||||||
\(331\) | −22.3588 | −1.22895 | −0.614476 | − | 0.788936i | \(-0.710632\pi\) | ||||
−0.614476 | + | 0.788936i | \(0.710632\pi\) | |||||||
\(332\) | −7.71917 | −0.423644 | ||||||||
\(333\) | 6.18598 | 0.338990 | ||||||||
\(334\) | −22.2325 | −1.21651 | ||||||||
\(335\) | −3.24698 | −0.177401 | ||||||||
\(336\) | 1.69202 | 0.0923073 | ||||||||
\(337\) | −3.67025 | −0.199931 | −0.0999657 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999657 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.9812 | 1.08523 | ||||||||
\(340\) | 2.35690 | 0.127821 | ||||||||
\(341\) | 48.5230 | 2.62767 | ||||||||
\(342\) | −6.51573 | −0.352330 | ||||||||
\(343\) | 18.8442 | 1.01749 | ||||||||
\(344\) | −4.93900 | −0.266293 | ||||||||
\(345\) | −8.94869 | −0.481781 | ||||||||
\(346\) | −11.6286 | −0.625159 | ||||||||
\(347\) | −21.7832 | −1.16938 | −0.584690 | − | 0.811257i | \(-0.698784\pi\) | ||||
−0.584690 | + | 0.811257i | \(0.698784\pi\) | |||||||
\(348\) | −9.07606 | −0.486528 | ||||||||
\(349\) | −1.74333 | −0.0933184 | −0.0466592 | − | 0.998911i | \(-0.514857\pi\) | ||||
−0.0466592 | + | 0.998911i | \(0.514857\pi\) | |||||||
\(350\) | −1.69202 | −0.0904424 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.55496 | −0.242780 | ||||||||
\(353\) | 6.09544 | 0.324428 | 0.162214 | − | 0.986756i | \(-0.448137\pi\) | ||||
0.162214 | + | 0.986756i | \(0.448137\pi\) | |||||||
\(354\) | −4.32304 | −0.229767 | ||||||||
\(355\) | −14.9487 | −0.793394 | ||||||||
\(356\) | −9.12498 | −0.483623 | ||||||||
\(357\) | 3.98792 | 0.211063 | ||||||||
\(358\) | −15.7875 | −0.834393 | ||||||||
\(359\) | 25.9627 | 1.37026 | 0.685129 | − | 0.728422i | \(-0.259746\pi\) | ||||
0.685129 | + | 0.728422i | \(0.259746\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 23.4547 | 1.23446 | ||||||||
\(362\) | −1.91185 | −0.100485 | ||||||||
\(363\) | −9.74764 | −0.511619 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.72886 | −0.352204 | ||||||||
\(366\) | 14.3666 | 0.750953 | ||||||||
\(367\) | 27.8799 | 1.45532 | 0.727660 | − | 0.685938i | \(-0.240608\pi\) | ||||
0.727660 | + | 0.685938i | \(0.240608\pi\) | |||||||
\(368\) | 8.94869 | 0.466483 | ||||||||
\(369\) | 3.00969 | 0.156678 | ||||||||
\(370\) | 6.18598 | 0.321594 | ||||||||
\(371\) | 5.76271 | 0.299185 | ||||||||
\(372\) | 10.6528 | 0.552322 | ||||||||
\(373\) | −25.1400 | −1.30170 | −0.650851 | − | 0.759205i | \(-0.725588\pi\) | ||||
−0.650851 | + | 0.759205i | \(0.725588\pi\) | |||||||
\(374\) | −10.7356 | −0.555123 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −4.28621 | −0.221044 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.69202 | 0.0870282 | ||||||||
\(379\) | −15.7463 | −0.808834 | −0.404417 | − | 0.914575i | \(-0.632526\pi\) | ||||
−0.404417 | + | 0.914575i | \(0.632526\pi\) | |||||||
\(380\) | −6.51573 | −0.334250 | ||||||||
\(381\) | 3.14244 | 0.160992 | ||||||||
\(382\) | 24.3260 | 1.24463 | ||||||||
\(383\) | 11.8183 | 0.603889 | 0.301944 | − | 0.953326i | \(-0.402364\pi\) | ||||
0.301944 | + | 0.953326i | \(0.402364\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 7.70709 | 0.392790 | ||||||||
\(386\) | −0.521106 | −0.0265236 | ||||||||
\(387\) | −4.93900 | −0.251064 | ||||||||
\(388\) | −4.40581 | −0.223671 | ||||||||
\(389\) | −6.14675 | −0.311653 | −0.155826 | − | 0.987784i | \(-0.549804\pi\) | ||||
−0.155826 | + | 0.987784i | \(0.549804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0911 | 1.06662 | ||||||||
\(392\) | −4.13706 | −0.208953 | ||||||||
\(393\) | 3.77479 | 0.190413 | ||||||||
\(394\) | −4.87502 | −0.245600 | ||||||||
\(395\) | 5.67994 | 0.285789 | ||||||||
\(396\) | −4.55496 | −0.228895 | ||||||||
\(397\) | −5.92825 | −0.297530 | −0.148765 | − | 0.988873i | \(-0.547530\pi\) | ||||
−0.148765 | + | 0.988873i | \(0.547530\pi\) | |||||||
\(398\) | −18.4983 | −0.927235 | ||||||||
\(399\) | −11.0248 | −0.551928 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.49934 | 0.474374 | 0.237187 | − | 0.971464i | \(-0.423775\pi\) | ||||
0.237187 | + | 0.971464i | \(0.423775\pi\) | |||||||
\(402\) | 3.24698 | 0.161945 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.31767 | 0.115308 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −15.3569 | −0.762150 | ||||||||
\(407\) | −28.1769 | −1.39668 | ||||||||
\(408\) | −2.35690 | −0.116684 | ||||||||
\(409\) | −9.00000 | −0.445021 | −0.222511 | − | 0.974930i | \(-0.571425\pi\) | ||||
−0.222511 | + | 0.974930i | \(0.571425\pi\) | |||||||
\(410\) | 3.00969 | 0.148638 | ||||||||
\(411\) | −14.5894 | −0.719642 | ||||||||
\(412\) | −9.00000 | −0.443398 | ||||||||
\(413\) | −7.31468 | −0.359932 | ||||||||
\(414\) | 8.94869 | 0.439804 | ||||||||
\(415\) | −7.71917 | −0.378919 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3599 | 0.703206 | ||||||||
\(418\) | 29.6789 | 1.45164 | ||||||||
\(419\) | 30.6450 | 1.49711 | 0.748554 | − | 0.663074i | \(-0.230749\pi\) | ||||
0.748554 | + | 0.663074i | \(0.230749\pi\) | |||||||
\(420\) | 1.69202 | 0.0825622 | ||||||||
\(421\) | 4.03252 | 0.196533 | 0.0982666 | − | 0.995160i | \(-0.468670\pi\) | ||||
0.0982666 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(422\) | 18.2500 | 0.888394 | ||||||||
\(423\) | −4.28621 | −0.208403 | ||||||||
\(424\) | −3.40581 | −0.165401 | ||||||||
\(425\) | 2.35690 | 0.114326 | ||||||||
\(426\) | 14.9487 | 0.724266 | ||||||||
\(427\) | 24.3086 | 1.17637 | ||||||||
\(428\) | −3.06100 | −0.147959 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.93900 | −0.238180 | ||||||||
\(431\) | −27.6179 | −1.33031 | −0.665153 | − | 0.746707i | \(-0.731634\pi\) | ||||
−0.665153 | + | 0.746707i | \(0.731634\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 10.6756 | 0.513038 | 0.256519 | − | 0.966539i | \(-0.417424\pi\) | ||||
0.256519 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(434\) | 18.0248 | 0.865216 | ||||||||
\(435\) | −9.07606 | −0.435164 | ||||||||
\(436\) | 7.45473 | 0.357017 | ||||||||
\(437\) | −58.3072 | −2.78921 | ||||||||
\(438\) | 6.72886 | 0.321517 | ||||||||
\(439\) | 25.9299 | 1.23757 | 0.618783 | − | 0.785562i | \(-0.287626\pi\) | ||||
0.618783 | + | 0.785562i | \(0.287626\pi\) | |||||||
\(440\) | −4.55496 | −0.217149 | ||||||||
\(441\) | −4.13706 | −0.197003 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3749 | −1.68071 | −0.840357 | − | 0.542033i | \(-0.817655\pi\) | ||||
−0.840357 | + | 0.542033i | \(0.817655\pi\) | |||||||
\(444\) | −6.18598 | −0.293574 | ||||||||
\(445\) | −9.12498 | −0.432566 | ||||||||
\(446\) | 8.54048 | 0.404404 | ||||||||
\(447\) | −0.252356 | −0.0119360 | ||||||||
\(448\) | −1.69202 | −0.0799405 | ||||||||
\(449\) | −6.24698 | −0.294813 | −0.147407 | − | 0.989076i | \(-0.547093\pi\) | ||||
−0.147407 | + | 0.989076i | \(0.547093\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −13.7090 | −0.645532 | ||||||||
\(452\) | −19.9812 | −0.939837 | ||||||||
\(453\) | −11.0804 | −0.520601 | ||||||||
\(454\) | −9.61596 | −0.451299 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.51573 | 0.305127 | ||||||||
\(457\) | −29.6383 | −1.38642 | −0.693211 | − | 0.720735i | \(-0.743805\pi\) | ||||
−0.693211 | + | 0.720735i | \(0.743805\pi\) | |||||||
\(458\) | −13.4058 | −0.626413 | ||||||||
\(459\) | −2.35690 | −0.110010 | ||||||||
\(460\) | 8.94869 | 0.417235 | ||||||||
\(461\) | 34.2911 | 1.59710 | 0.798548 | − | 0.601931i | \(-0.205602\pi\) | ||||
0.798548 | + | 0.601931i | \(0.205602\pi\) | |||||||
\(462\) | −7.70709 | −0.358566 | ||||||||
\(463\) | 24.1769 | 1.12360 | 0.561798 | − | 0.827275i | \(-0.310110\pi\) | ||||
0.561798 | + | 0.827275i | \(0.310110\pi\) | |||||||
\(464\) | 9.07606 | 0.421346 | ||||||||
\(465\) | 10.6528 | 0.494011 | ||||||||
\(466\) | −0.153457 | −0.00710875 | ||||||||
\(467\) | −0.521106 | −0.0241139 | −0.0120570 | − | 0.999927i | \(-0.503838\pi\) | ||||
−0.0120570 | + | 0.999927i | \(0.503838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.49396 | 0.253687 | ||||||||
\(470\) | −4.28621 | −0.197708 | ||||||||
\(471\) | −5.03923 | −0.232195 | ||||||||
\(472\) | 4.32304 | 0.198984 | ||||||||
\(473\) | 22.4969 | 1.03441 | ||||||||
\(474\) | −5.67994 | −0.260888 | ||||||||
\(475\) | −6.51573 | −0.298962 | ||||||||
\(476\) | −3.98792 | −0.182786 | ||||||||
\(477\) | −3.40581 | −0.155941 | ||||||||
\(478\) | 14.5851 | 0.667106 | ||||||||
\(479\) | 10.4168 | 0.475957 | 0.237979 | − | 0.971270i | \(-0.423515\pi\) | ||||
0.237979 | + | 0.971270i | \(0.423515\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.40044 | 0.154886 | ||||||||
\(483\) | 15.1414 | 0.688956 | ||||||||
\(484\) | 9.74764 | 0.443075 | ||||||||
\(485\) | −4.40581 | −0.200058 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 30.2349 | 1.37007 | 0.685037 | − | 0.728508i | \(-0.259786\pi\) | ||||
0.685037 | + | 0.728508i | \(0.259786\pi\) | |||||||
\(488\) | −14.3666 | −0.650345 | ||||||||
\(489\) | −20.9825 | −0.948863 | ||||||||
\(490\) | −4.13706 | −0.186893 | ||||||||
\(491\) | −31.5883 | −1.42556 | −0.712781 | − | 0.701387i | \(-0.752565\pi\) | ||||
−0.712781 | + | 0.701387i | \(0.752565\pi\) | |||||||
\(492\) | −3.00969 | −0.135687 | ||||||||
\(493\) | 21.3913 | 0.963417 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.55496 | −0.204730 | ||||||||
\(496\) | −10.6528 | −0.478325 | ||||||||
\(497\) | 25.2935 | 1.13457 | ||||||||
\(498\) | 7.71917 | 0.345904 | ||||||||
\(499\) | −27.2862 | −1.22150 | −0.610749 | − | 0.791824i | \(-0.709132\pi\) | ||||
−0.610749 | + | 0.791824i | \(0.709132\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 22.2325 | 0.993275 | ||||||||
\(502\) | 1.80864 | 0.0807237 | ||||||||
\(503\) | 29.6752 | 1.32315 | 0.661575 | − | 0.749879i | \(-0.269888\pi\) | ||||
0.661575 | + | 0.749879i | \(0.269888\pi\) | |||||||
\(504\) | −1.69202 | −0.0753686 | ||||||||
\(505\) | 2.31767 | 0.103135 | ||||||||
\(506\) | −40.7609 | −1.81204 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.14244 | −0.139423 | ||||||||
\(509\) | −44.1661 | −1.95763 | −0.978815 | − | 0.204748i | \(-0.934362\pi\) | ||||
−0.978815 | + | 0.204748i | \(0.934362\pi\) | |||||||
\(510\) | −2.35690 | −0.104365 | ||||||||
\(511\) | 11.3854 | 0.503659 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.51573 | 0.287676 | ||||||||
\(514\) | −22.2664 | −0.982127 | ||||||||
\(515\) | −9.00000 | −0.396587 | ||||||||
\(516\) | 4.93900 | 0.217427 | ||||||||
\(517\) | 19.5235 | 0.858643 | ||||||||
\(518\) | −10.4668 | −0.459885 | ||||||||
\(519\) | 11.6286 | 0.510440 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1153 | 0.881267 | 0.440633 | − | 0.897687i | \(-0.354754\pi\) | ||||
0.440633 | + | 0.897687i | \(0.354754\pi\) | |||||||
\(522\) | 9.07606 | 0.397249 | ||||||||
\(523\) | 6.46117 | 0.282527 | 0.141264 | − | 0.989972i | \(-0.454883\pi\) | ||||
0.141264 | + | 0.989972i | \(0.454883\pi\) | |||||||
\(524\) | −3.77479 | −0.164902 | ||||||||
\(525\) | 1.69202 | 0.0738459 | ||||||||
\(526\) | 8.08815 | 0.352660 | ||||||||
\(527\) | −25.1075 | −1.09370 | ||||||||
\(528\) | 4.55496 | 0.198229 | ||||||||
\(529\) | 57.0790 | 2.48170 | ||||||||
\(530\) | −3.40581 | −0.147939 | ||||||||
\(531\) | 4.32304 | 0.187604 | ||||||||
\(532\) | 11.0248 | 0.477984 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.12498 | 0.394877 | ||||||||
\(535\) | −3.06100 | −0.132339 | ||||||||
\(536\) | −3.24698 | −0.140248 | ||||||||
\(537\) | 15.7875 | 0.681279 | ||||||||
\(538\) | 16.6843 | 0.719309 | ||||||||
\(539\) | 18.8442 | 0.811675 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 34.0097 | 1.46219 | 0.731095 | − | 0.682275i | \(-0.239009\pi\) | ||||
0.731095 | + | 0.682275i | \(0.239009\pi\) | |||||||
\(542\) | 27.4077 | 1.17726 | ||||||||
\(543\) | 1.91185 | 0.0820455 | ||||||||
\(544\) | 2.35690 | 0.101051 | ||||||||
\(545\) | 7.45473 | 0.319326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6907 | 0.628129 | 0.314064 | − | 0.949402i | \(-0.398309\pi\) | ||||
0.314064 | + | 0.949402i | \(0.398309\pi\) | |||||||
\(548\) | 14.5894 | 0.623228 | ||||||||
\(549\) | −14.3666 | −0.613151 | ||||||||
\(550\) | −4.55496 | −0.194224 | ||||||||
\(551\) | −59.1372 | −2.51933 | ||||||||
\(552\) | −8.94869 | −0.380882 | ||||||||
\(553\) | −9.61058 | −0.408683 | ||||||||
\(554\) | −16.0411 | −0.681523 | ||||||||
\(555\) | −6.18598 | −0.262580 | ||||||||
\(556\) | −14.3599 | −0.608995 | ||||||||
\(557\) | 7.00969 | 0.297010 | 0.148505 | − | 0.988912i | \(-0.452554\pi\) | ||||
0.148505 | + | 0.988912i | \(0.452554\pi\) | |||||||
\(558\) | −10.6528 | −0.450969 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | 10.7356 | 0.453256 | ||||||||
\(562\) | −10.0935 | −0.425770 | ||||||||
\(563\) | −30.2131 | −1.27333 | −0.636666 | − | 0.771140i | \(-0.719687\pi\) | ||||
−0.636666 | + | 0.771140i | \(0.719687\pi\) | |||||||
\(564\) | 4.28621 | 0.180482 | ||||||||
\(565\) | −19.9812 | −0.840616 | ||||||||
\(566\) | 12.1021 | 0.508691 | ||||||||
\(567\) | −1.69202 | −0.0710582 | ||||||||
\(568\) | −14.9487 | −0.627233 | ||||||||
\(569\) | 14.8436 | 0.622274 | 0.311137 | − | 0.950365i | \(-0.399290\pi\) | ||||
0.311137 | + | 0.950365i | \(0.399290\pi\) | |||||||
\(570\) | 6.51573 | 0.272914 | ||||||||
\(571\) | 0.965557 | 0.0404073 | 0.0202037 | − | 0.999796i | \(-0.493569\pi\) | ||||
0.0202037 | + | 0.999796i | \(0.493569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.3260 | −1.01623 | ||||||||
\(574\) | −5.09246 | −0.212555 | ||||||||
\(575\) | 8.94869 | 0.373186 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 27.8431 | 1.15912 | 0.579561 | − | 0.814929i | \(-0.303224\pi\) | ||||
0.579561 | + | 0.814929i | \(0.303224\pi\) | |||||||
\(578\) | −11.4450 | −0.476051 | ||||||||
\(579\) | 0.521106 | 0.0216564 | ||||||||
\(580\) | 9.07606 | 0.376863 | ||||||||
\(581\) | 13.0610 | 0.541862 | ||||||||
\(582\) | 4.40581 | 0.182627 | ||||||||
\(583\) | 15.5133 | 0.642497 | ||||||||
\(584\) | −6.72886 | −0.278442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.01075 | 0.165683 | ||||||||
\(587\) | −1.47889 | −0.0610405 | −0.0305202 | − | 0.999534i | \(-0.509716\pi\) | ||||
−0.0305202 | + | 0.999534i | \(0.509716\pi\) | |||||||
\(588\) | 4.13706 | 0.170610 | ||||||||
\(589\) | 69.4107 | 2.86002 | ||||||||
\(590\) | 4.32304 | 0.177977 | ||||||||
\(591\) | 4.87502 | 0.200531 | ||||||||
\(592\) | 6.18598 | 0.254242 | ||||||||
\(593\) | −16.8552 | −0.692159 | −0.346079 | − | 0.938205i | \(-0.612487\pi\) | ||||
−0.346079 | + | 0.938205i | \(0.612487\pi\) | |||||||
\(594\) | 4.55496 | 0.186892 | ||||||||
\(595\) | −3.98792 | −0.163489 | ||||||||
\(596\) | 0.252356 | 0.0103369 | ||||||||
\(597\) | 18.4983 | 0.757084 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.4862 | −1.00048 | −0.500239 | − | 0.865887i | \(-0.666755\pi\) | ||||
−0.500239 | + | 0.865887i | \(0.666755\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −9.97344 | −0.406825 | −0.203413 | − | 0.979093i | \(-0.565203\pi\) | ||||
−0.203413 | + | 0.979093i | \(0.565203\pi\) | |||||||
\(602\) | 8.35690 | 0.340602 | ||||||||
\(603\) | −3.24698 | −0.132227 | ||||||||
\(604\) | 11.0804 | 0.450854 | ||||||||
\(605\) | 9.74764 | 0.396298 | ||||||||
\(606\) | −2.31767 | −0.0941488 | ||||||||
\(607\) | −35.4476 | −1.43877 | −0.719386 | − | 0.694611i | \(-0.755577\pi\) | ||||
−0.719386 | + | 0.694611i | \(0.755577\pi\) | |||||||
\(608\) | −6.51573 | −0.264248 | ||||||||
\(609\) | 15.3569 | 0.622293 | ||||||||
\(610\) | −14.3666 | −0.581686 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.35690 | 0.0952719 | ||||||||
\(613\) | 16.1782 | 0.653432 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(614\) | −15.2784 | −0.616588 | ||||||||
\(615\) | −3.00969 | −0.121362 | ||||||||
\(616\) | 7.70709 | 0.310527 | ||||||||
\(617\) | −17.6920 | −0.712254 | −0.356127 | − | 0.934438i | \(-0.615903\pi\) | ||||
−0.356127 | + | 0.934438i | \(0.615903\pi\) | |||||||
\(618\) | 9.00000 | 0.362033 | ||||||||
\(619\) | 1.23968 | 0.0498271 | 0.0249136 | − | 0.999690i | \(-0.492069\pi\) | ||||
0.0249136 | + | 0.999690i | \(0.492069\pi\) | |||||||
\(620\) | −10.6528 | −0.427826 | ||||||||
\(621\) | −8.94869 | −0.359099 | ||||||||
\(622\) | 25.4330 | 1.01977 | ||||||||
\(623\) | 15.4397 | 0.618577 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.1226 | −0.764292 | ||||||||
\(627\) | −29.6789 | −1.18526 | ||||||||
\(628\) | 5.03923 | 0.201087 | ||||||||
\(629\) | 14.5797 | 0.581331 | ||||||||
\(630\) | −1.69202 | −0.0674117 | ||||||||
\(631\) | 33.7845 | 1.34494 | 0.672469 | − | 0.740125i | \(-0.265234\pi\) | ||||
0.672469 | + | 0.740125i | \(0.265234\pi\) | |||||||
\(632\) | 5.67994 | 0.225936 | ||||||||
\(633\) | −18.2500 | −0.725371 | ||||||||
\(634\) | −20.3230 | −0.807131 | ||||||||
\(635\) | −3.14244 | −0.124704 | ||||||||
\(636\) | 3.40581 | 0.135049 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −41.3411 | −1.63671 | ||||||||
\(639\) | −14.9487 | −0.591361 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 12.0785 | 0.477070 | 0.238535 | − | 0.971134i | \(-0.423333\pi\) | ||||
0.238535 | + | 0.971134i | \(0.423333\pi\) | |||||||
\(642\) | 3.06100 | 0.120808 | ||||||||
\(643\) | −41.1377 | −1.62231 | −0.811155 | − | 0.584831i | \(-0.801161\pi\) | ||||
−0.811155 | + | 0.584831i | \(0.801161\pi\) | |||||||
\(644\) | −15.1414 | −0.596654 | ||||||||
\(645\) | 4.93900 | 0.194473 | ||||||||
\(646\) | −15.3569 | −0.604209 | ||||||||
\(647\) | 23.2054 | 0.912297 | 0.456148 | − | 0.889904i | \(-0.349229\pi\) | ||||
0.456148 | + | 0.889904i | \(0.349229\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −19.6913 | −0.772951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0248 | −0.706446 | ||||||||
\(652\) | 20.9825 | 0.821740 | ||||||||
\(653\) | 7.77538 | 0.304274 | 0.152137 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152137 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(654\) | −7.45473 | −0.291503 | ||||||||
\(655\) | −3.77479 | −0.147493 | ||||||||
\(656\) | 3.00969 | 0.117509 | ||||||||
\(657\) | −6.72886 | −0.262518 | ||||||||
\(658\) | 7.25236 | 0.282726 | ||||||||
\(659\) | −0.349600 | −0.0136185 | −0.00680924 | − | 0.999977i | \(-0.502167\pi\) | ||||
−0.00680924 | + | 0.999977i | \(0.502167\pi\) | |||||||
\(660\) | 4.55496 | 0.177302 | ||||||||
\(661\) | 19.7855 | 0.769568 | 0.384784 | − | 0.923007i | \(-0.374276\pi\) | ||||
0.384784 | + | 0.923007i | \(0.374276\pi\) | |||||||
\(662\) | −22.3588 | −0.869000 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.71917 | −0.299562 | ||||||||
\(665\) | 11.0248 | 0.427522 | ||||||||
\(666\) | 6.18598 | 0.239702 | ||||||||
\(667\) | 81.2189 | 3.14481 | ||||||||
\(668\) | −22.2325 | −0.860201 | ||||||||
\(669\) | −8.54048 | −0.330194 | ||||||||
\(670\) | −3.24698 | −0.125442 | ||||||||
\(671\) | 65.4392 | 2.52625 | ||||||||
\(672\) | 1.69202 | 0.0652711 | ||||||||
\(673\) | −16.6146 | −0.640447 | −0.320223 | − | 0.947342i | \(-0.603758\pi\) | ||||
−0.320223 | + | 0.947342i | \(0.603758\pi\) | |||||||
\(674\) | −3.67025 | −0.141373 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.85517 | −0.225032 | −0.112516 | − | 0.993650i | \(-0.535891\pi\) | ||||
−0.112516 | + | 0.993650i | \(0.535891\pi\) | |||||||
\(678\) | 19.9812 | 0.767374 | ||||||||
\(679\) | 7.45473 | 0.286086 | ||||||||
\(680\) | 2.35690 | 0.0903828 | ||||||||
\(681\) | 9.61596 | 0.368484 | ||||||||
\(682\) | 48.5230 | 1.85804 | ||||||||
\(683\) | −2.19029 | −0.0838092 | −0.0419046 | − | 0.999122i | \(-0.513343\pi\) | ||||
−0.0419046 | + | 0.999122i | \(0.513343\pi\) | |||||||
\(684\) | −6.51573 | −0.249135 | ||||||||
\(685\) | 14.5894 | 0.557432 | ||||||||
\(686\) | 18.8442 | 0.719473 | ||||||||
\(687\) | 13.4058 | 0.511464 | ||||||||
\(688\) | −4.93900 | −0.188298 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.94869 | −0.340671 | ||||||||
\(691\) | 11.8576 | 0.451083 | 0.225541 | − | 0.974234i | \(-0.427585\pi\) | ||||
0.225541 | + | 0.974234i | \(0.427585\pi\) | |||||||
\(692\) | −11.6286 | −0.442054 | ||||||||
\(693\) | 7.70709 | 0.292768 | ||||||||
\(694\) | −21.7832 | −0.826877 | ||||||||
\(695\) | −14.3599 | −0.544701 | ||||||||
\(696\) | −9.07606 | −0.344027 | ||||||||
\(697\) | 7.09352 | 0.268686 | ||||||||
\(698\) | −1.74333 | −0.0659861 | ||||||||
\(699\) | 0.153457 | 0.00580427 | ||||||||
\(700\) | −1.69202 | −0.0639524 | ||||||||
\(701\) | 22.7627 | 0.859736 | 0.429868 | − | 0.902892i | \(-0.358560\pi\) | ||||
0.429868 | + | 0.902892i | \(0.358560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.3062 | −1.52018 | ||||||||
\(704\) | −4.55496 | −0.171671 | ||||||||
\(705\) | 4.28621 | 0.161428 | ||||||||
\(706\) | 6.09544 | 0.229405 | ||||||||
\(707\) | −3.92154 | −0.147485 | ||||||||
\(708\) | −4.32304 | −0.162470 | ||||||||
\(709\) | 18.5854 | 0.697988 | 0.348994 | − | 0.937125i | \(-0.386523\pi\) | ||||
0.348994 | + | 0.937125i | \(0.386523\pi\) | |||||||
\(710\) | −14.9487 | −0.561014 | ||||||||
\(711\) | 5.67994 | 0.213014 | ||||||||
\(712\) | −9.12498 | −0.341973 | ||||||||
\(713\) | −95.3285 | −3.57008 | ||||||||
\(714\) | 3.98792 | 0.149244 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.7875 | −0.590005 | ||||||||
\(717\) | −14.5851 | −0.544690 | ||||||||
\(718\) | 25.9627 | 0.968919 | ||||||||
\(719\) | −36.1575 | −1.34845 | −0.674224 | − | 0.738527i | \(-0.735522\pi\) | ||||
−0.674224 | + | 0.738527i | \(0.735522\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 15.2282 | 0.567128 | ||||||||
\(722\) | 23.4547 | 0.872895 | ||||||||
\(723\) | −3.40044 | −0.126464 | ||||||||
\(724\) | −1.91185 | −0.0710535 | ||||||||
\(725\) | 9.07606 | 0.337077 | ||||||||
\(726\) | −9.74764 | −0.361769 | ||||||||
\(727\) | 19.0164 | 0.705279 | 0.352639 | − | 0.935759i | \(-0.385284\pi\) | ||||
0.352639 | + | 0.935759i | \(0.385284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.72886 | −0.249046 | ||||||||
\(731\) | −11.6407 | −0.430547 | ||||||||
\(732\) | 14.3666 | 0.531004 | ||||||||
\(733\) | 8.89248 | 0.328451 | 0.164226 | − | 0.986423i | \(-0.447488\pi\) | ||||
0.164226 | + | 0.986423i | \(0.447488\pi\) | |||||||
\(734\) | 27.8799 | 1.02907 | ||||||||
\(735\) | 4.13706 | 0.152598 | ||||||||
\(736\) | 8.94869 | 0.329853 | ||||||||
\(737\) | 14.7899 | 0.544791 | ||||||||
\(738\) | 3.00969 | 0.110788 | ||||||||
\(739\) | −30.8595 | −1.13518 | −0.567592 | − | 0.823310i | \(-0.692125\pi\) | ||||
−0.567592 | + | 0.823310i | \(0.692125\pi\) | |||||||
\(740\) | 6.18598 | 0.227401 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.76271 | 0.211556 | ||||||||
\(743\) | 18.6300 | 0.683467 | 0.341733 | − | 0.939797i | \(-0.388986\pi\) | ||||
0.341733 | + | 0.939797i | \(0.388986\pi\) | |||||||
\(744\) | 10.6528 | 0.390550 | ||||||||
\(745\) | 0.252356 | 0.00924562 | ||||||||
\(746\) | −25.1400 | −0.920443 | ||||||||
\(747\) | −7.71917 | −0.282430 | ||||||||
\(748\) | −10.7356 | −0.392531 | ||||||||
\(749\) | 5.17928 | 0.189247 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 12.5147 | 0.456667 | 0.228333 | − | 0.973583i | \(-0.426672\pi\) | ||||
0.228333 | + | 0.973583i | \(0.426672\pi\) | |||||||
\(752\) | −4.28621 | −0.156302 | ||||||||
\(753\) | −1.80864 | −0.0659106 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.0804 | 0.403256 | ||||||||
\(756\) | 1.69202 | 0.0615382 | ||||||||
\(757\) | −4.75494 | −0.172821 | −0.0864106 | − | 0.996260i | \(-0.527540\pi\) | ||||
−0.0864106 | + | 0.996260i | \(0.527540\pi\) | |||||||
\(758\) | −15.7463 | −0.571932 | ||||||||
\(759\) | 40.7609 | 1.47953 | ||||||||
\(760\) | −6.51573 | −0.236350 | ||||||||
\(761\) | −21.7748 | −0.789336 | −0.394668 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394668 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(762\) | 3.14244 | 0.113839 | ||||||||
\(763\) | −12.6136 | −0.456642 | ||||||||
\(764\) | 24.3260 | 0.880085 | ||||||||
\(765\) | 2.35690 | 0.0852137 | ||||||||
\(766\) | 11.8183 | 0.427014 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 11.4045 | 0.411256 | 0.205628 | − | 0.978630i | \(-0.434076\pi\) | ||||
0.205628 | + | 0.978630i | \(0.434076\pi\) | |||||||
\(770\) | 7.70709 | 0.277744 | ||||||||
\(771\) | 22.2664 | 0.801903 | ||||||||
\(772\) | −0.521106 | −0.0187550 | ||||||||
\(773\) | 49.6118 | 1.78441 | 0.892206 | − | 0.451630i | \(-0.149157\pi\) | ||||
0.892206 | + | 0.451630i | \(0.149157\pi\) | |||||||
\(774\) | −4.93900 | −0.177529 | ||||||||
\(775\) | −10.6528 | −0.382660 | ||||||||
\(776\) | −4.40581 | −0.158159 | ||||||||
\(777\) | 10.4668 | 0.375495 | ||||||||
\(778\) | −6.14675 | −0.220372 | ||||||||
\(779\) | −19.6103 | −0.702613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 68.0907 | 2.43648 | ||||||||
\(782\) | 21.0911 | 0.754217 | ||||||||
\(783\) | −9.07606 | −0.324352 | ||||||||
\(784\) | −4.13706 | −0.147752 | ||||||||
\(785\) | 5.03923 | 0.179858 | ||||||||
\(786\) | 3.77479 | 0.134642 | ||||||||
\(787\) | 26.5532 | 0.946518 | 0.473259 | − | 0.880923i | \(-0.343078\pi\) | ||||
0.473259 | + | 0.880923i | \(0.343078\pi\) | |||||||
\(788\) | −4.87502 | −0.173665 | ||||||||
\(789\) | −8.08815 | −0.287946 | ||||||||
\(790\) | 5.67994 | 0.202083 | ||||||||
\(791\) | 33.8086 | 1.20210 | ||||||||
\(792\) | −4.55496 | −0.161853 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.92825 | −0.210386 | ||||||||
\(795\) | 3.40581 | 0.120792 | ||||||||
\(796\) | −18.4983 | −0.655654 | ||||||||
\(797\) | 9.44803 | 0.334666 | 0.167333 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167333 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(798\) | −11.0248 | −0.390272 | ||||||||
\(799\) | −10.1021 | −0.357388 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −9.12498 | −0.322415 | ||||||||
\(802\) | 9.49934 | 0.335433 | ||||||||
\(803\) | 30.6497 | 1.08160 | ||||||||
\(804\) | 3.24698 | 0.114512 | ||||||||
\(805\) | −15.1414 | −0.533663 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.6843 | −0.587313 | ||||||||
\(808\) | 2.31767 | 0.0815352 | ||||||||
\(809\) | −27.3376 | −0.961140 | −0.480570 | − | 0.876956i | \(-0.659570\pi\) | ||||
−0.480570 | + | 0.876956i | \(0.659570\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −2.86592 | −0.100636 | −0.0503180 | − | 0.998733i | \(-0.516023\pi\) | ||||
−0.0503180 | + | 0.998733i | \(0.516023\pi\) | |||||||
\(812\) | −15.3569 | −0.538921 | ||||||||
\(813\) | −27.4077 | −0.961231 | ||||||||
\(814\) | −28.1769 | −0.987599 | ||||||||
\(815\) | 20.9825 | 0.734986 | ||||||||
\(816\) | −2.35690 | −0.0825079 | ||||||||
\(817\) | 32.1812 | 1.12588 | ||||||||
\(818\) | −9.00000 | −0.314678 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.00969 | 0.105103 | ||||||||
\(821\) | 16.9739 | 0.592394 | 0.296197 | − | 0.955127i | \(-0.404282\pi\) | ||||
0.296197 | + | 0.955127i | \(0.404282\pi\) | |||||||
\(822\) | −14.5894 | −0.508864 | ||||||||
\(823\) | −22.2083 | −0.774134 | −0.387067 | − | 0.922052i | \(-0.626512\pi\) | ||||
−0.387067 | + | 0.922052i | \(0.626512\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 4.55496 | 0.158583 | ||||||||
\(826\) | −7.31468 | −0.254510 | ||||||||
\(827\) | 36.3618 | 1.26442 | 0.632212 | − | 0.774796i | \(-0.282147\pi\) | ||||
0.632212 | + | 0.774796i | \(0.282147\pi\) | |||||||
\(828\) | 8.94869 | 0.310988 | ||||||||
\(829\) | −26.5478 | −0.922042 | −0.461021 | − | 0.887389i | \(-0.652517\pi\) | ||||
−0.461021 | + | 0.887389i | \(0.652517\pi\) | |||||||
\(830\) | −7.71917 | −0.267936 | ||||||||
\(831\) | 16.0411 | 0.556461 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.75063 | −0.337839 | ||||||||
\(834\) | 14.3599 | 0.497242 | ||||||||
\(835\) | −22.2325 | −0.769388 | ||||||||
\(836\) | 29.6789 | 1.02647 | ||||||||
\(837\) | 10.6528 | 0.368214 | ||||||||
\(838\) | 30.6450 | 1.05861 | ||||||||
\(839\) | 26.7668 | 0.924091 | 0.462046 | − | 0.886856i | \(-0.347116\pi\) | ||||
0.462046 | + | 0.886856i | \(0.347116\pi\) | |||||||
\(840\) | 1.69202 | 0.0583803 | ||||||||
\(841\) | 53.3749 | 1.84052 | ||||||||
\(842\) | 4.03252 | 0.138970 | ||||||||
\(843\) | 10.0935 | 0.347639 | ||||||||
\(844\) | 18.2500 | 0.628190 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.28621 | −0.147363 | ||||||||
\(847\) | −16.4932 | −0.566714 | ||||||||
\(848\) | −3.40581 | −0.116956 | ||||||||
\(849\) | −12.1021 | −0.415345 | ||||||||
\(850\) | 2.35690 | 0.0808409 | ||||||||
\(851\) | 55.3564 | 1.89759 | ||||||||
\(852\) | 14.9487 | 0.512134 | ||||||||
\(853\) | −50.3967 | −1.72555 | −0.862775 | − | 0.505587i | \(-0.831276\pi\) | ||||
−0.862775 | + | 0.505587i | \(0.831276\pi\) | |||||||
\(854\) | 24.3086 | 0.831822 | ||||||||
\(855\) | −6.51573 | −0.222833 | ||||||||
\(856\) | −3.06100 | −0.104623 | ||||||||
\(857\) | 27.5114 | 0.939772 | 0.469886 | − | 0.882727i | \(-0.344295\pi\) | ||||
0.469886 | + | 0.882727i | \(0.344295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.26098 | 0.0771436 | 0.0385718 | − | 0.999256i | \(-0.487719\pi\) | ||||
0.0385718 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(860\) | −4.93900 | −0.168419 | ||||||||
\(861\) | 5.09246 | 0.173550 | ||||||||
\(862\) | −27.6179 | −0.940669 | ||||||||
\(863\) | 2.18406 | 0.0743463 | 0.0371732 | − | 0.999309i | \(-0.488165\pi\) | ||||
0.0371732 | + | 0.999309i | \(0.488165\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −11.6286 | −0.395385 | ||||||||
\(866\) | 10.6756 | 0.362773 | ||||||||
\(867\) | 11.4450 | 0.388694 | ||||||||
\(868\) | 18.0248 | 0.611800 | ||||||||
\(869\) | −25.8719 | −0.877644 | ||||||||
\(870\) | −9.07606 | −0.307707 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7.45473 | 0.252449 | ||||||||
\(873\) | −4.40581 | −0.149114 | ||||||||
\(874\) | −58.3072 | −1.97227 | ||||||||
\(875\) | −1.69202 | −0.0572008 | ||||||||
\(876\) | 6.72886 | 0.227347 | ||||||||
\(877\) | 19.9815 | 0.674727 | 0.337363 | − | 0.941375i | \(-0.390465\pi\) | ||||
0.337363 | + | 0.941375i | \(0.390465\pi\) | |||||||
\(878\) | 25.9299 | 0.875092 | ||||||||
\(879\) | −4.01075 | −0.135279 | ||||||||
\(880\) | −4.55496 | −0.153548 | ||||||||
\(881\) | −38.4801 | −1.29643 | −0.648213 | − | 0.761459i | \(-0.724484\pi\) | ||||
−0.648213 | + | 0.761459i | \(0.724484\pi\) | |||||||
\(882\) | −4.13706 | −0.139302 | ||||||||
\(883\) | −37.5512 | −1.26370 | −0.631850 | − | 0.775091i | \(-0.717704\pi\) | ||||
−0.631850 | + | 0.775091i | \(0.717704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.32304 | −0.145318 | ||||||||
\(886\) | −35.3749 | −1.18844 | ||||||||
\(887\) | 18.5676 | 0.623440 | 0.311720 | − | 0.950174i | \(-0.399095\pi\) | ||||
0.311720 | + | 0.950174i | \(0.399095\pi\) | |||||||
\(888\) | −6.18598 | −0.207588 | ||||||||
\(889\) | 5.31708 | 0.178329 | ||||||||
\(890\) | −9.12498 | −0.305870 | ||||||||
\(891\) | −4.55496 | −0.152597 | ||||||||
\(892\) | 8.54048 | 0.285957 | ||||||||
\(893\) | 27.9278 | 0.934567 | ||||||||
\(894\) | −0.252356 | −0.00844006 | ||||||||
\(895\) | −15.7875 | −0.527717 | ||||||||
\(896\) | −1.69202 | −0.0565265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.24698 | −0.208464 | ||||||||
\(899\) | −96.6854 | −3.22464 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −8.02715 | −0.267423 | ||||||||
\(902\) | −13.7090 | −0.456460 | ||||||||
\(903\) | −8.35690 | −0.278100 | ||||||||
\(904\) | −19.9812 | −0.664565 | ||||||||
\(905\) | −1.91185 | −0.0635522 | ||||||||
\(906\) | −11.0804 | −0.368121 | ||||||||
\(907\) | 60.1648 | 1.99774 | 0.998870 | − | 0.0475319i | \(-0.0151356\pi\) | ||||
0.998870 | + | 0.0475319i | \(0.0151356\pi\) | |||||||
\(908\) | −9.61596 | −0.319117 | ||||||||
\(909\) | 2.31767 | 0.0768722 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.0737 | −1.22831 | −0.614153 | − | 0.789187i | \(-0.710502\pi\) | ||||
−0.614153 | + | 0.789187i | \(0.710502\pi\) | |||||||
\(912\) | 6.51573 | 0.215757 | ||||||||
\(913\) | 35.1605 | 1.16364 | ||||||||
\(914\) | −29.6383 | −0.980348 | ||||||||
\(915\) | 14.3666 | 0.474945 | ||||||||
\(916\) | −13.4058 | −0.442941 | ||||||||
\(917\) | 6.38703 | 0.210918 | ||||||||
\(918\) | −2.35690 | −0.0777892 | ||||||||
\(919\) | −50.5526 | −1.66758 | −0.833788 | − | 0.552085i | \(-0.813832\pi\) | ||||
−0.833788 | + | 0.552085i | \(0.813832\pi\) | |||||||
\(920\) | 8.94869 | 0.295030 | ||||||||
\(921\) | 15.2784 | 0.503442 | ||||||||
\(922\) | 34.2911 | 1.12932 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.70709 | −0.253545 | ||||||||
\(925\) | 6.18598 | 0.203394 | ||||||||
\(926\) | 24.1769 | 0.794502 | ||||||||
\(927\) | −9.00000 | −0.295599 | ||||||||
\(928\) | 9.07606 | 0.297936 | ||||||||
\(929\) | −12.7269 | −0.417557 | −0.208779 | − | 0.977963i | \(-0.566949\pi\) | ||||
−0.208779 | + | 0.977963i | \(0.566949\pi\) | |||||||
\(930\) | 10.6528 | 0.349319 | ||||||||
\(931\) | 26.9560 | 0.883447 | ||||||||
\(932\) | −0.153457 | −0.00502664 | ||||||||
\(933\) | −25.4330 | −0.832638 | ||||||||
\(934\) | −0.521106 | −0.0170511 | ||||||||
\(935\) | −10.7356 | −0.351090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.3279 | −1.15411 | −0.577057 | − | 0.816704i | \(-0.695799\pi\) | ||||
−0.577057 | + | 0.816704i | \(0.695799\pi\) | |||||||
\(938\) | 5.49396 | 0.179384 | ||||||||
\(939\) | 19.1226 | 0.624042 | ||||||||
\(940\) | −4.28621 | −0.139801 | ||||||||
\(941\) | 42.0267 | 1.37003 | 0.685015 | − | 0.728529i | \(-0.259796\pi\) | ||||
0.685015 | + | 0.728529i | \(0.259796\pi\) | |||||||
\(942\) | −5.03923 | −0.164187 | ||||||||
\(943\) | 26.9328 | 0.877052 | ||||||||
\(944\) | 4.32304 | 0.140703 | ||||||||
\(945\) | 1.69202 | 0.0550415 | ||||||||
\(946\) | 22.4969 | 0.731439 | ||||||||
\(947\) | 4.63640 | 0.150663 | 0.0753314 | − | 0.997159i | \(-0.475999\pi\) | ||||
0.0753314 | + | 0.997159i | \(0.475999\pi\) | |||||||
\(948\) | −5.67994 | −0.184476 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.51573 | −0.211398 | ||||||||
\(951\) | 20.3230 | 0.659020 | ||||||||
\(952\) | −3.98792 | −0.129249 | ||||||||
\(953\) | −41.8998 | −1.35727 | −0.678633 | − | 0.734477i | \(-0.737427\pi\) | ||||
−0.678633 | + | 0.734477i | \(0.737427\pi\) | |||||||
\(954\) | −3.40581 | −0.110267 | ||||||||
\(955\) | 24.3260 | 0.787172 | ||||||||
\(956\) | 14.5851 | 0.471715 | ||||||||
\(957\) | 41.3411 | 1.33637 | ||||||||
\(958\) | 10.4168 | 0.336552 | ||||||||
\(959\) | −24.6856 | −0.797139 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 82.4820 | 2.66071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.06100 | −0.0986393 | ||||||||
\(964\) | 3.40044 | 0.109521 | ||||||||
\(965\) | −0.521106 | −0.0167750 | ||||||||
\(966\) | 15.1414 | 0.487166 | ||||||||
\(967\) | −48.3545 | −1.55498 | −0.777488 | − | 0.628898i | \(-0.783506\pi\) | ||||
−0.777488 | + | 0.628898i | \(0.783506\pi\) | |||||||
\(968\) | 9.74764 | 0.313301 | ||||||||
\(969\) | 15.3569 | 0.493335 | ||||||||
\(970\) | −4.40581 | −0.141462 | ||||||||
\(971\) | −18.9326 | −0.607575 | −0.303787 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303787 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 24.2972 | 0.778933 | ||||||||
\(974\) | 30.2349 | 0.968789 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.3666 | −0.459863 | ||||||||
\(977\) | −54.7972 | −1.75312 | −0.876558 | − | 0.481296i | \(-0.840166\pi\) | ||||
−0.876558 | + | 0.481296i | \(0.840166\pi\) | |||||||
\(978\) | −20.9825 | −0.670948 | ||||||||
\(979\) | 41.5639 | 1.32839 | ||||||||
\(980\) | −4.13706 | −0.132154 | ||||||||
\(981\) | 7.45473 | 0.238011 | ||||||||
\(982\) | −31.5883 | −1.00802 | ||||||||
\(983\) | 24.6431 | 0.785993 | 0.392996 | − | 0.919540i | \(-0.371438\pi\) | ||||
0.392996 | + | 0.919540i | \(0.371438\pi\) | |||||||
\(984\) | −3.00969 | −0.0959454 | ||||||||
\(985\) | −4.87502 | −0.155331 | ||||||||
\(986\) | 21.3913 | 0.681239 | ||||||||
\(987\) | −7.25236 | −0.230845 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.1976 | −1.40540 | ||||||||
\(990\) | −4.55496 | −0.144766 | ||||||||
\(991\) | 23.1612 | 0.735741 | 0.367870 | − | 0.929877i | \(-0.380087\pi\) | ||||
0.367870 | + | 0.929877i | \(0.380087\pi\) | |||||||
\(992\) | −10.6528 | −0.338227 | ||||||||
\(993\) | 22.3588 | 0.709536 | ||||||||
\(994\) | 25.2935 | 0.802261 | ||||||||
\(995\) | −18.4983 | −0.586435 | ||||||||
\(996\) | 7.71917 | 0.244591 | ||||||||
\(997\) | −11.5700 | −0.366426 | −0.183213 | − | 0.983073i | \(-0.558650\pi\) | ||||
−0.183213 | + | 0.983073i | \(0.558650\pi\) | |||||||
\(998\) | −27.2862 | −0.863730 | ||||||||
\(999\) | −6.18598 | −0.195716 |
(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 | 5070.2.a.bt.1.1 | yes | 3 | |
13.5 | odd | 4 | 5070.2.b.s.1351.1 | 6 | |||
13.8 | odd | 4 | 5070.2.b.s.1351.6 | 6 | |||
13.12 | even | 2 | 5070.2.a.bk.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bk.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
5070.2.a.bt.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
5070.2.b.s.1351.1 | 6 | 13.5 | odd | 4 | |||
5070.2.b.s.1351.6 | 6 | 13.8 | odd | 4 |