Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,2,Mod(1,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.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: | \(2.69894358832\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.1 |
$q$-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 | ||||||||
\(3\) | −2.04892 | −1.18294 | −0.591471 | − | 0.806326i | \(-0.701453\pi\) | ||||
−0.591471 | + | 0.806326i | \(0.701453\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.60388 | 1.61170 | 0.805851 | − | 0.592118i | \(-0.201708\pi\) | ||||
0.805851 | + | 0.592118i | \(0.201708\pi\) | |||||||
\(6\) | −2.04892 | −0.836467 | ||||||||
\(7\) | −1.10992 | −0.419509 | −0.209754 | − | 0.977754i | \(-0.567266\pi\) | ||||
−0.209754 | + | 0.977754i | \(0.567266\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.19806 | 0.399354 | ||||||||
\(10\) | 3.60388 | 1.13965 | ||||||||
\(11\) | 2.35690 | 0.710631 | 0.355315 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355315 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(12\) | −2.04892 | −0.591471 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.10992 | −0.296638 | ||||||||
\(15\) | −7.38404 | −1.90655 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.96077 | 1.44570 | 0.722850 | − | 0.691005i | \(-0.242832\pi\) | ||||
0.722850 | + | 0.691005i | \(0.242832\pi\) | |||||||
\(18\) | 1.19806 | 0.282386 | ||||||||
\(19\) | −0.911854 | −0.209194 | −0.104597 | − | 0.994515i | \(-0.533355\pi\) | ||||
−0.104597 | + | 0.994515i | \(0.533355\pi\) | |||||||
\(20\) | 3.60388 | 0.805851 | ||||||||
\(21\) | 2.27413 | 0.496255 | ||||||||
\(22\) | 2.35690 | 0.502492 | ||||||||
\(23\) | 3.38404 | 0.705622 | 0.352811 | − | 0.935695i | \(-0.385226\pi\) | ||||
0.352811 | + | 0.935695i | \(0.385226\pi\) | |||||||
\(24\) | −2.04892 | −0.418234 | ||||||||
\(25\) | 7.98792 | 1.59758 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.69202 | 0.710530 | ||||||||
\(28\) | −1.10992 | −0.209754 | ||||||||
\(29\) | −3.78017 | −0.701959 | −0.350980 | − | 0.936383i | \(-0.614151\pi\) | ||||
−0.350980 | + | 0.936383i | \(0.614151\pi\) | |||||||
\(30\) | −7.38404 | −1.34814 | ||||||||
\(31\) | −8.49396 | −1.52556 | −0.762780 | − | 0.646658i | \(-0.776166\pi\) | ||||
−0.762780 | + | 0.646658i | \(0.776166\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.82908 | −0.840636 | ||||||||
\(34\) | 5.96077 | 1.02226 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 1.19806 | 0.199677 | ||||||||
\(37\) | −4.89008 | −0.803925 | −0.401962 | − | 0.915656i | \(-0.631672\pi\) | ||||
−0.401962 | + | 0.915656i | \(0.631672\pi\) | |||||||
\(38\) | −0.911854 | −0.147922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.60388 | 0.569823 | ||||||||
\(41\) | 7.18598 | 1.12226 | 0.561131 | − | 0.827727i | \(-0.310366\pi\) | ||||
0.561131 | + | 0.827727i | \(0.310366\pi\) | |||||||
\(42\) | 2.27413 | 0.350905 | ||||||||
\(43\) | −0.515729 | −0.0786480 | −0.0393240 | − | 0.999227i | \(-0.512520\pi\) | ||||
−0.0393240 | + | 0.999227i | \(0.512520\pi\) | |||||||
\(44\) | 2.35690 | 0.355315 | ||||||||
\(45\) | 4.31767 | 0.643640 | ||||||||
\(46\) | 3.38404 | 0.498950 | ||||||||
\(47\) | −6.98792 | −1.01929 | −0.509646 | − | 0.860384i | \(-0.670224\pi\) | ||||
−0.509646 | + | 0.860384i | \(0.670224\pi\) | |||||||
\(48\) | −2.04892 | −0.295736 | ||||||||
\(49\) | −5.76809 | −0.824012 | ||||||||
\(50\) | 7.98792 | 1.12966 | ||||||||
\(51\) | −12.2131 | −1.71018 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.38404 | −0.464834 | −0.232417 | − | 0.972616i | \(-0.574663\pi\) | ||||
−0.232417 | + | 0.972616i | \(0.574663\pi\) | |||||||
\(54\) | 3.69202 | 0.502420 | ||||||||
\(55\) | 8.49396 | 1.14533 | ||||||||
\(56\) | −1.10992 | −0.148319 | ||||||||
\(57\) | 1.86831 | 0.247464 | ||||||||
\(58\) | −3.78017 | −0.496360 | ||||||||
\(59\) | −10.1468 | −1.32099 | −0.660497 | − | 0.750828i | \(-0.729655\pi\) | ||||
−0.660497 | + | 0.750828i | \(0.729655\pi\) | |||||||
\(60\) | −7.38404 | −0.953276 | ||||||||
\(61\) | −0.439665 | −0.0562933 | −0.0281467 | − | 0.999604i | \(-0.508961\pi\) | ||||
−0.0281467 | + | 0.999604i | \(0.508961\pi\) | |||||||
\(62\) | −8.49396 | −1.07873 | ||||||||
\(63\) | −1.32975 | −0.167533 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.82908 | −0.594419 | ||||||||
\(67\) | −2.14675 | −0.262268 | −0.131134 | − | 0.991365i | \(-0.541862\pi\) | ||||
−0.131134 | + | 0.991365i | \(0.541862\pi\) | |||||||
\(68\) | 5.96077 | 0.722850 | ||||||||
\(69\) | −6.93362 | −0.834710 | ||||||||
\(70\) | −4.00000 | −0.478091 | ||||||||
\(71\) | −0.615957 | −0.0731007 | −0.0365503 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365503 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(72\) | 1.19806 | 0.141193 | ||||||||
\(73\) | −6.32304 | −0.740056 | −0.370028 | − | 0.929021i | \(-0.620652\pi\) | ||||
−0.370028 | + | 0.929021i | \(0.620652\pi\) | |||||||
\(74\) | −4.89008 | −0.568461 | ||||||||
\(75\) | −16.3666 | −1.88985 | ||||||||
\(76\) | −0.911854 | −0.104597 | ||||||||
\(77\) | −2.61596 | −0.298116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4819 | −1.74185 | −0.870924 | − | 0.491418i | \(-0.836479\pi\) | ||||
−0.870924 | + | 0.491418i | \(0.836479\pi\) | |||||||
\(80\) | 3.60388 | 0.402926 | ||||||||
\(81\) | −11.1588 | −1.23987 | ||||||||
\(82\) | 7.18598 | 0.793559 | ||||||||
\(83\) | 0.911854 | 0.100089 | 0.0500445 | − | 0.998747i | \(-0.484064\pi\) | ||||
0.0500445 | + | 0.998747i | \(0.484064\pi\) | |||||||
\(84\) | 2.27413 | 0.248128 | ||||||||
\(85\) | 21.4819 | 2.33004 | ||||||||
\(86\) | −0.515729 | −0.0556125 | ||||||||
\(87\) | 7.74525 | 0.830378 | ||||||||
\(88\) | 2.35690 | 0.251246 | ||||||||
\(89\) | −3.75063 | −0.397566 | −0.198783 | − | 0.980044i | \(-0.563699\pi\) | ||||
−0.198783 | + | 0.980044i | \(0.563699\pi\) | |||||||
\(90\) | 4.31767 | 0.455122 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.38404 | 0.352811 | ||||||||
\(93\) | 17.4034 | 1.80465 | ||||||||
\(94\) | −6.98792 | −0.720749 | ||||||||
\(95\) | −3.28621 | −0.337158 | ||||||||
\(96\) | −2.04892 | −0.209117 | ||||||||
\(97\) | 14.6746 | 1.48998 | 0.744988 | − | 0.667078i | \(-0.232455\pi\) | ||||
0.744988 | + | 0.667078i | \(0.232455\pi\) | |||||||
\(98\) | −5.76809 | −0.582665 | ||||||||
\(99\) | 2.82371 | 0.283793 | ||||||||
\(100\) | 7.98792 | 0.798792 | ||||||||
\(101\) | 8.76809 | 0.872457 | 0.436229 | − | 0.899836i | \(-0.356314\pi\) | ||||
0.436229 | + | 0.899836i | \(0.356314\pi\) | |||||||
\(102\) | −12.2131 | −1.20928 | ||||||||
\(103\) | 18.8116 | 1.85356 | 0.926782 | − | 0.375599i | \(-0.122563\pi\) | ||||
0.926782 | + | 0.375599i | \(0.122563\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.19567 | 0.799815 | ||||||||
\(106\) | −3.38404 | −0.328687 | ||||||||
\(107\) | 18.0519 | 1.74514 | 0.872572 | − | 0.488486i | \(-0.162451\pi\) | ||||
0.872572 | + | 0.488486i | \(0.162451\pi\) | |||||||
\(108\) | 3.69202 | 0.355265 | ||||||||
\(109\) | −6.09783 | −0.584067 | −0.292033 | − | 0.956408i | \(-0.594332\pi\) | ||||
−0.292033 | + | 0.956408i | \(0.594332\pi\) | |||||||
\(110\) | 8.49396 | 0.809867 | ||||||||
\(111\) | 10.0194 | 0.950997 | ||||||||
\(112\) | −1.10992 | −0.104877 | ||||||||
\(113\) | −12.2010 | −1.14778 | −0.573889 | − | 0.818933i | \(-0.694566\pi\) | ||||
−0.573889 | + | 0.818933i | \(0.694566\pi\) | |||||||
\(114\) | 1.86831 | 0.174984 | ||||||||
\(115\) | 12.1957 | 1.13725 | ||||||||
\(116\) | −3.78017 | −0.350980 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1468 | −0.934084 | ||||||||
\(119\) | −6.61596 | −0.606484 | ||||||||
\(120\) | −7.38404 | −0.674068 | ||||||||
\(121\) | −5.44504 | −0.495004 | ||||||||
\(122\) | −0.439665 | −0.0398054 | ||||||||
\(123\) | −14.7235 | −1.32757 | ||||||||
\(124\) | −8.49396 | −0.762780 | ||||||||
\(125\) | 10.7681 | 0.963127 | ||||||||
\(126\) | −1.32975 | −0.118463 | ||||||||
\(127\) | 11.4276 | 1.01403 | 0.507017 | − | 0.861936i | \(-0.330748\pi\) | ||||
0.507017 | + | 0.861936i | \(0.330748\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.05669 | 0.0930361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.29590 | 0.200593 | 0.100297 | − | 0.994958i | \(-0.468021\pi\) | ||||
0.100297 | + | 0.994958i | \(0.468021\pi\) | |||||||
\(132\) | −4.82908 | −0.420318 | ||||||||
\(133\) | 1.01208 | 0.0877586 | ||||||||
\(134\) | −2.14675 | −0.185451 | ||||||||
\(135\) | 13.3056 | 1.14516 | ||||||||
\(136\) | 5.96077 | 0.511132 | ||||||||
\(137\) | −9.08038 | −0.775789 | −0.387894 | − | 0.921704i | \(-0.626797\pi\) | ||||
−0.387894 | + | 0.921704i | \(0.626797\pi\) | |||||||
\(138\) | −6.93362 | −0.590229 | ||||||||
\(139\) | 18.9051 | 1.60351 | 0.801757 | − | 0.597650i | \(-0.203899\pi\) | ||||
0.801757 | + | 0.597650i | \(0.203899\pi\) | |||||||
\(140\) | −4.00000 | −0.338062 | ||||||||
\(141\) | 14.3177 | 1.20577 | ||||||||
\(142\) | −0.615957 | −0.0516900 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.19806 | 0.0998385 | ||||||||
\(145\) | −13.6233 | −1.13135 | ||||||||
\(146\) | −6.32304 | −0.523299 | ||||||||
\(147\) | 11.8183 | 0.974760 | ||||||||
\(148\) | −4.89008 | −0.401962 | ||||||||
\(149\) | −18.6896 | −1.53111 | −0.765557 | − | 0.643368i | \(-0.777537\pi\) | ||||
−0.765557 | + | 0.643368i | \(0.777537\pi\) | |||||||
\(150\) | −16.3666 | −1.33633 | ||||||||
\(151\) | 0.317667 | 0.0258514 | 0.0129257 | − | 0.999916i | \(-0.495886\pi\) | ||||
0.0129257 | + | 0.999916i | \(0.495886\pi\) | |||||||
\(152\) | −0.911854 | −0.0739611 | ||||||||
\(153\) | 7.14138 | 0.577346 | ||||||||
\(154\) | −2.61596 | −0.210800 | ||||||||
\(155\) | −30.6112 | −2.45875 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8901 | 1.50759 | 0.753796 | − | 0.657108i | \(-0.228220\pi\) | ||||
0.753796 | + | 0.657108i | \(0.228220\pi\) | |||||||
\(158\) | −15.4819 | −1.23167 | ||||||||
\(159\) | 6.93362 | 0.549872 | ||||||||
\(160\) | 3.60388 | 0.284911 | ||||||||
\(161\) | −3.75600 | −0.296015 | ||||||||
\(162\) | −11.1588 | −0.876721 | ||||||||
\(163\) | 4.33273 | 0.339366 | 0.169683 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169683 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(164\) | 7.18598 | 0.561131 | ||||||||
\(165\) | −17.4034 | −1.35485 | ||||||||
\(166\) | 0.911854 | 0.0707736 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 2.27413 | 0.175453 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 21.4819 | 1.64758 | ||||||||
\(171\) | −1.09246 | −0.0835423 | ||||||||
\(172\) | −0.515729 | −0.0393240 | ||||||||
\(173\) | −10.9879 | −0.835396 | −0.417698 | − | 0.908586i | \(-0.637163\pi\) | ||||
−0.417698 | + | 0.908586i | \(0.637163\pi\) | |||||||
\(174\) | 7.74525 | 0.587166 | ||||||||
\(175\) | −8.86592 | −0.670201 | ||||||||
\(176\) | 2.35690 | 0.177658 | ||||||||
\(177\) | 20.7899 | 1.56266 | ||||||||
\(178\) | −3.75063 | −0.281121 | ||||||||
\(179\) | 4.65519 | 0.347945 | 0.173972 | − | 0.984751i | \(-0.444340\pi\) | ||||
0.173972 | + | 0.984751i | \(0.444340\pi\) | |||||||
\(180\) | 4.31767 | 0.321820 | ||||||||
\(181\) | −1.06638 | −0.0792631 | −0.0396315 | − | 0.999214i | \(-0.512618\pi\) | ||||
−0.0396315 | + | 0.999214i | \(0.512618\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.900837 | 0.0665918 | ||||||||
\(184\) | 3.38404 | 0.249475 | ||||||||
\(185\) | −17.6233 | −1.29569 | ||||||||
\(186\) | 17.4034 | 1.27608 | ||||||||
\(187\) | 14.0489 | 1.02736 | ||||||||
\(188\) | −6.98792 | −0.509646 | ||||||||
\(189\) | −4.09783 | −0.298074 | ||||||||
\(190\) | −3.28621 | −0.238407 | ||||||||
\(191\) | 0.890084 | 0.0644042 | 0.0322021 | − | 0.999481i | \(-0.489748\pi\) | ||||
0.0322021 | + | 0.999481i | \(0.489748\pi\) | |||||||
\(192\) | −2.04892 | −0.147868 | ||||||||
\(193\) | −16.2174 | −1.16736 | −0.583678 | − | 0.811985i | \(-0.698387\pi\) | ||||
−0.583678 | + | 0.811985i | \(0.698387\pi\) | |||||||
\(194\) | 14.6746 | 1.05357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.76809 | −0.412006 | ||||||||
\(197\) | 11.4711 | 0.817284 | 0.408642 | − | 0.912695i | \(-0.366003\pi\) | ||||
0.408642 | + | 0.912695i | \(0.366003\pi\) | |||||||
\(198\) | 2.82371 | 0.200672 | ||||||||
\(199\) | −3.79954 | −0.269343 | −0.134671 | − | 0.990890i | \(-0.542998\pi\) | ||||
−0.134671 | + | 0.990890i | \(0.542998\pi\) | |||||||
\(200\) | 7.98792 | 0.564831 | ||||||||
\(201\) | 4.39852 | 0.310247 | ||||||||
\(202\) | 8.76809 | 0.616920 | ||||||||
\(203\) | 4.19567 | 0.294478 | ||||||||
\(204\) | −12.2131 | −0.855090 | ||||||||
\(205\) | 25.8974 | 1.80875 | ||||||||
\(206\) | 18.8116 | 1.31067 | ||||||||
\(207\) | 4.05429 | 0.281793 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.14914 | −0.148659 | ||||||||
\(210\) | 8.19567 | 0.565555 | ||||||||
\(211\) | −25.0465 | −1.72427 | −0.862137 | − | 0.506675i | \(-0.830874\pi\) | ||||
−0.862137 | + | 0.506675i | \(0.830874\pi\) | |||||||
\(212\) | −3.38404 | −0.232417 | ||||||||
\(213\) | 1.26205 | 0.0864739 | ||||||||
\(214\) | 18.0519 | 1.23400 | ||||||||
\(215\) | −1.85862 | −0.126757 | ||||||||
\(216\) | 3.69202 | 0.251210 | ||||||||
\(217\) | 9.42758 | 0.639986 | ||||||||
\(218\) | −6.09783 | −0.412997 | ||||||||
\(219\) | 12.9554 | 0.875444 | ||||||||
\(220\) | 8.49396 | 0.572663 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.0194 | 0.672457 | ||||||||
\(223\) | −12.9879 | −0.869735 | −0.434868 | − | 0.900494i | \(-0.643205\pi\) | ||||
−0.434868 | + | 0.900494i | \(0.643205\pi\) | |||||||
\(224\) | −1.10992 | −0.0741594 | ||||||||
\(225\) | 9.57002 | 0.638002 | ||||||||
\(226\) | −12.2010 | −0.811602 | ||||||||
\(227\) | 13.8049 | 0.916265 | 0.458132 | − | 0.888884i | \(-0.348519\pi\) | ||||
0.458132 | + | 0.888884i | \(0.348519\pi\) | |||||||
\(228\) | 1.86831 | 0.123732 | ||||||||
\(229\) | 11.5603 | 0.763928 | 0.381964 | − | 0.924177i | \(-0.375248\pi\) | ||||
0.381964 | + | 0.924177i | \(0.375248\pi\) | |||||||
\(230\) | 12.1957 | 0.804159 | ||||||||
\(231\) | 5.35988 | 0.352654 | ||||||||
\(232\) | −3.78017 | −0.248180 | ||||||||
\(233\) | 9.77479 | 0.640368 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.1836 | −1.64280 | ||||||||
\(236\) | −10.1468 | −0.660497 | ||||||||
\(237\) | 31.7211 | 2.06051 | ||||||||
\(238\) | −6.61596 | −0.428849 | ||||||||
\(239\) | 0.944378 | 0.0610867 | 0.0305434 | − | 0.999533i | \(-0.490276\pi\) | ||||
0.0305434 | + | 0.999533i | \(0.490276\pi\) | |||||||
\(240\) | −7.38404 | −0.476638 | ||||||||
\(241\) | 0.219833 | 0.0141607 | 0.00708033 | − | 0.999975i | \(-0.497746\pi\) | ||||
0.00708033 | + | 0.999975i | \(0.497746\pi\) | |||||||
\(242\) | −5.44504 | −0.350021 | ||||||||
\(243\) | 11.7875 | 0.756166 | ||||||||
\(244\) | −0.439665 | −0.0281467 | ||||||||
\(245\) | −20.7875 | −1.32806 | ||||||||
\(246\) | −14.7235 | −0.938735 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.49396 | −0.539367 | ||||||||
\(249\) | −1.86831 | −0.118400 | ||||||||
\(250\) | 10.7681 | 0.681034 | ||||||||
\(251\) | 16.2543 | 1.02596 | 0.512980 | − | 0.858400i | \(-0.328541\pi\) | ||||
0.512980 | + | 0.858400i | \(0.328541\pi\) | |||||||
\(252\) | −1.32975 | −0.0837663 | ||||||||
\(253\) | 7.97584 | 0.501437 | ||||||||
\(254\) | 11.4276 | 0.717030 | ||||||||
\(255\) | −44.0146 | −2.75630 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.4373 | −1.39960 | −0.699799 | − | 0.714340i | \(-0.746727\pi\) | ||||
−0.699799 | + | 0.714340i | \(0.746727\pi\) | |||||||
\(258\) | 1.05669 | 0.0657865 | ||||||||
\(259\) | 5.42758 | 0.337254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.52888 | −0.280330 | ||||||||
\(262\) | 2.29590 | 0.141841 | ||||||||
\(263\) | −10.4940 | −0.647085 | −0.323543 | − | 0.946214i | \(-0.604874\pi\) | ||||
−0.323543 | + | 0.946214i | \(0.604874\pi\) | |||||||
\(264\) | −4.82908 | −0.297210 | ||||||||
\(265\) | −12.1957 | −0.749174 | ||||||||
\(266\) | 1.01208 | 0.0620547 | ||||||||
\(267\) | 7.68473 | 0.470298 | ||||||||
\(268\) | −2.14675 | −0.131134 | ||||||||
\(269\) | 26.4155 | 1.61058 | 0.805291 | − | 0.592880i | \(-0.202009\pi\) | ||||
0.805291 | + | 0.592880i | \(0.202009\pi\) | |||||||
\(270\) | 13.3056 | 0.809752 | ||||||||
\(271\) | 22.0301 | 1.33824 | 0.669118 | − | 0.743157i | \(-0.266672\pi\) | ||||
0.669118 | + | 0.743157i | \(0.266672\pi\) | |||||||
\(272\) | 5.96077 | 0.361425 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.08038 | −0.548566 | ||||||||
\(275\) | 18.8267 | 1.13529 | ||||||||
\(276\) | −6.93362 | −0.417355 | ||||||||
\(277\) | 2.17629 | 0.130761 | 0.0653804 | − | 0.997860i | \(-0.479174\pi\) | ||||
0.0653804 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(278\) | 18.9051 | 1.13386 | ||||||||
\(279\) | −10.1763 | −0.609239 | ||||||||
\(280\) | −4.00000 | −0.239046 | ||||||||
\(281\) | −25.0030 | −1.49155 | −0.745776 | − | 0.666196i | \(-0.767921\pi\) | ||||
−0.745776 | + | 0.666196i | \(0.767921\pi\) | |||||||
\(282\) | 14.3177 | 0.852605 | ||||||||
\(283\) | −16.3153 | −0.969842 | −0.484921 | − | 0.874558i | \(-0.661152\pi\) | ||||
−0.484921 | + | 0.874558i | \(0.661152\pi\) | |||||||
\(284\) | −0.615957 | −0.0365503 | ||||||||
\(285\) | 6.73317 | 0.398839 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.97584 | −0.470799 | ||||||||
\(288\) | 1.19806 | 0.0705965 | ||||||||
\(289\) | 18.5308 | 1.09005 | ||||||||
\(290\) | −13.6233 | −0.799985 | ||||||||
\(291\) | −30.0670 | −1.76256 | ||||||||
\(292\) | −6.32304 | −0.370028 | ||||||||
\(293\) | 1.87800 | 0.109714 | 0.0548570 | − | 0.998494i | \(-0.482530\pi\) | ||||
0.0548570 | + | 0.998494i | \(0.482530\pi\) | |||||||
\(294\) | 11.8183 | 0.689259 | ||||||||
\(295\) | −36.5676 | −2.12905 | ||||||||
\(296\) | −4.89008 | −0.284230 | ||||||||
\(297\) | 8.70171 | 0.504924 | ||||||||
\(298\) | −18.6896 | −1.08266 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.3666 | −0.944925 | ||||||||
\(301\) | 0.572417 | 0.0329935 | ||||||||
\(302\) | 0.317667 | 0.0182797 | ||||||||
\(303\) | −17.9651 | −1.03207 | ||||||||
\(304\) | −0.911854 | −0.0522984 | ||||||||
\(305\) | −1.58450 | −0.0907281 | ||||||||
\(306\) | 7.14138 | 0.408245 | ||||||||
\(307\) | 23.9801 | 1.36862 | 0.684310 | − | 0.729192i | \(-0.260104\pi\) | ||||
0.684310 | + | 0.729192i | \(0.260104\pi\) | |||||||
\(308\) | −2.61596 | −0.149058 | ||||||||
\(309\) | −38.5435 | −2.19266 | ||||||||
\(310\) | −30.6112 | −1.73860 | ||||||||
\(311\) | −5.38404 | −0.305301 | −0.152651 | − | 0.988280i | \(-0.548781\pi\) | ||||
−0.152651 | + | 0.988280i | \(0.548781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.9487 | 1.07104 | 0.535522 | − | 0.844522i | \(-0.320115\pi\) | ||||
0.535522 | + | 0.844522i | \(0.320115\pi\) | |||||||
\(314\) | 18.8901 | 1.06603 | ||||||||
\(315\) | −4.79225 | −0.270013 | ||||||||
\(316\) | −15.4819 | −0.870924 | ||||||||
\(317\) | 11.5013 | 0.645975 | 0.322987 | − | 0.946403i | \(-0.395313\pi\) | ||||
0.322987 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(318\) | 6.93362 | 0.388818 | ||||||||
\(319\) | −8.90946 | −0.498834 | ||||||||
\(320\) | 3.60388 | 0.201463 | ||||||||
\(321\) | −36.9869 | −2.06440 | ||||||||
\(322\) | −3.75600 | −0.209314 | ||||||||
\(323\) | −5.43535 | −0.302431 | ||||||||
\(324\) | −11.1588 | −0.619935 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.33273 | 0.239968 | ||||||||
\(327\) | 12.4940 | 0.690918 | ||||||||
\(328\) | 7.18598 | 0.396779 | ||||||||
\(329\) | 7.75600 | 0.427602 | ||||||||
\(330\) | −17.4034 | −0.958027 | ||||||||
\(331\) | 34.6112 | 1.90240 | 0.951201 | − | 0.308572i | \(-0.0998511\pi\) | ||||
0.951201 | + | 0.308572i | \(0.0998511\pi\) | |||||||
\(332\) | 0.911854 | 0.0500445 | ||||||||
\(333\) | −5.85862 | −0.321051 | ||||||||
\(334\) | −14.0000 | −0.766046 | ||||||||
\(335\) | −7.73663 | −0.422697 | ||||||||
\(336\) | 2.27413 | 0.124064 | ||||||||
\(337\) | 1.95407 | 0.106445 | 0.0532224 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532224 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.9989 | 1.35776 | ||||||||
\(340\) | 21.4819 | 1.16502 | ||||||||
\(341\) | −20.0194 | −1.08411 | ||||||||
\(342\) | −1.09246 | −0.0590734 | ||||||||
\(343\) | 14.1715 | 0.765189 | ||||||||
\(344\) | −0.515729 | −0.0278063 | ||||||||
\(345\) | −24.9879 | −1.34530 | ||||||||
\(346\) | −10.9879 | −0.590714 | ||||||||
\(347\) | −6.41550 | −0.344402 | −0.172201 | − | 0.985062i | \(-0.555088\pi\) | ||||
−0.172201 | + | 0.985062i | \(0.555088\pi\) | |||||||
\(348\) | 7.74525 | 0.415189 | ||||||||
\(349\) | 1.08575 | 0.0581190 | 0.0290595 | − | 0.999578i | \(-0.490749\pi\) | ||||
0.0290595 | + | 0.999578i | \(0.490749\pi\) | |||||||
\(350\) | −8.86592 | −0.473903 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.35690 | 0.125623 | ||||||||
\(353\) | 4.28919 | 0.228291 | 0.114145 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114145 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(354\) | 20.7899 | 1.10497 | ||||||||
\(355\) | −2.21983 | −0.117816 | ||||||||
\(356\) | −3.75063 | −0.198783 | ||||||||
\(357\) | 13.5555 | 0.717436 | ||||||||
\(358\) | 4.65519 | 0.246034 | ||||||||
\(359\) | −15.5060 | −0.818378 | −0.409189 | − | 0.912450i | \(-0.634188\pi\) | ||||
−0.409189 | + | 0.912450i | \(0.634188\pi\) | |||||||
\(360\) | 4.31767 | 0.227561 | ||||||||
\(361\) | −18.1685 | −0.956238 | ||||||||
\(362\) | −1.06638 | −0.0560475 | ||||||||
\(363\) | 11.1564 | 0.585561 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.7875 | −1.19275 | ||||||||
\(366\) | 0.900837 | 0.0470875 | ||||||||
\(367\) | 17.4276 | 0.909712 | 0.454856 | − | 0.890565i | \(-0.349691\pi\) | ||||
0.454856 | + | 0.890565i | \(0.349691\pi\) | |||||||
\(368\) | 3.38404 | 0.176405 | ||||||||
\(369\) | 8.60925 | 0.448180 | ||||||||
\(370\) | −17.6233 | −0.916189 | ||||||||
\(371\) | 3.75600 | 0.195002 | ||||||||
\(372\) | 17.4034 | 0.902325 | ||||||||
\(373\) | 8.19567 | 0.424356 | 0.212178 | − | 0.977231i | \(-0.431944\pi\) | ||||
0.212178 | + | 0.977231i | \(0.431944\pi\) | |||||||
\(374\) | 14.0489 | 0.726452 | ||||||||
\(375\) | −22.0629 | −1.13932 | ||||||||
\(376\) | −6.98792 | −0.360374 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.09783 | −0.210770 | ||||||||
\(379\) | −15.0476 | −0.772943 | −0.386471 | − | 0.922301i | \(-0.626306\pi\) | ||||
−0.386471 | + | 0.922301i | \(0.626306\pi\) | |||||||
\(380\) | −3.28621 | −0.168579 | ||||||||
\(381\) | −23.4142 | −1.19954 | ||||||||
\(382\) | 0.890084 | 0.0455406 | ||||||||
\(383\) | −11.1207 | −0.568240 | −0.284120 | − | 0.958789i | \(-0.591701\pi\) | ||||
−0.284120 | + | 0.958789i | \(0.591701\pi\) | |||||||
\(384\) | −2.04892 | −0.104558 | ||||||||
\(385\) | −9.42758 | −0.480474 | ||||||||
\(386\) | −16.2174 | −0.825446 | ||||||||
\(387\) | −0.617876 | −0.0314084 | ||||||||
\(388\) | 14.6746 | 0.744988 | ||||||||
\(389\) | −8.04354 | −0.407824 | −0.203912 | − | 0.978989i | \(-0.565366\pi\) | ||||
−0.203912 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.1715 | 1.02012 | ||||||||
\(392\) | −5.76809 | −0.291332 | ||||||||
\(393\) | −4.70410 | −0.237291 | ||||||||
\(394\) | 11.4711 | 0.577907 | ||||||||
\(395\) | −55.7948 | −2.80734 | ||||||||
\(396\) | 2.82371 | 0.141897 | ||||||||
\(397\) | −21.9081 | −1.09954 | −0.549769 | − | 0.835317i | \(-0.685284\pi\) | ||||
−0.549769 | + | 0.835317i | \(0.685284\pi\) | |||||||
\(398\) | −3.79954 | −0.190454 | ||||||||
\(399\) | −2.07367 | −0.103813 | ||||||||
\(400\) | 7.98792 | 0.399396 | ||||||||
\(401\) | 17.4426 | 0.871044 | 0.435522 | − | 0.900178i | \(-0.356564\pi\) | ||||
0.435522 | + | 0.900178i | \(0.356564\pi\) | |||||||
\(402\) | 4.39852 | 0.219378 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.76809 | 0.436229 | ||||||||
\(405\) | −40.2150 | −1.99830 | ||||||||
\(406\) | 4.19567 | 0.208228 | ||||||||
\(407\) | −11.5254 | −0.571294 | ||||||||
\(408\) | −12.2131 | −0.604640 | ||||||||
\(409\) | −17.4330 | −0.862004 | −0.431002 | − | 0.902351i | \(-0.641840\pi\) | ||||
−0.431002 | + | 0.902351i | \(0.641840\pi\) | |||||||
\(410\) | 25.8974 | 1.27898 | ||||||||
\(411\) | 18.6049 | 0.917714 | ||||||||
\(412\) | 18.8116 | 0.926782 | ||||||||
\(413\) | 11.2620 | 0.554169 | ||||||||
\(414\) | 4.05429 | 0.199258 | ||||||||
\(415\) | 3.28621 | 0.161314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.7351 | −1.89687 | ||||||||
\(418\) | −2.14914 | −0.105118 | ||||||||
\(419\) | 9.97584 | 0.487352 | 0.243676 | − | 0.969857i | \(-0.421647\pi\) | ||||
0.243676 | + | 0.969857i | \(0.421647\pi\) | |||||||
\(420\) | 8.19567 | 0.399908 | ||||||||
\(421\) | 0.615957 | 0.0300199 | 0.0150100 | − | 0.999887i | \(-0.495222\pi\) | ||||
0.0150100 | + | 0.999887i | \(0.495222\pi\) | |||||||
\(422\) | −25.0465 | −1.21925 | ||||||||
\(423\) | −8.37196 | −0.407059 | ||||||||
\(424\) | −3.38404 | −0.164344 | ||||||||
\(425\) | 47.6142 | 2.30963 | ||||||||
\(426\) | 1.26205 | 0.0611463 | ||||||||
\(427\) | 0.487991 | 0.0236156 | ||||||||
\(428\) | 18.0519 | 0.872572 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.85862 | −0.0896308 | ||||||||
\(431\) | −14.7922 | −0.712518 | −0.356259 | − | 0.934387i | \(-0.615948\pi\) | ||||
−0.356259 | + | 0.934387i | \(0.615948\pi\) | |||||||
\(432\) | 3.69202 | 0.177632 | ||||||||
\(433\) | 16.5321 | 0.794483 | 0.397242 | − | 0.917714i | \(-0.369968\pi\) | ||||
0.397242 | + | 0.917714i | \(0.369968\pi\) | |||||||
\(434\) | 9.42758 | 0.452538 | ||||||||
\(435\) | 27.9129 | 1.33832 | ||||||||
\(436\) | −6.09783 | −0.292033 | ||||||||
\(437\) | −3.08575 | −0.147612 | ||||||||
\(438\) | 12.9554 | 0.619033 | ||||||||
\(439\) | 3.50125 | 0.167106 | 0.0835529 | − | 0.996503i | \(-0.473373\pi\) | ||||
0.0835529 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(440\) | 8.49396 | 0.404934 | ||||||||
\(441\) | −6.91053 | −0.329073 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4077 | 0.827066 | 0.413533 | − | 0.910489i | \(-0.364295\pi\) | ||||
0.413533 | + | 0.910489i | \(0.364295\pi\) | |||||||
\(444\) | 10.0194 | 0.475499 | ||||||||
\(445\) | −13.5168 | −0.640758 | ||||||||
\(446\) | −12.9879 | −0.614996 | ||||||||
\(447\) | 38.2935 | 1.81122 | ||||||||
\(448\) | −1.10992 | −0.0524386 | ||||||||
\(449\) | 34.1497 | 1.61163 | 0.805813 | − | 0.592170i | \(-0.201729\pi\) | ||||
0.805813 | + | 0.592170i | \(0.201729\pi\) | |||||||
\(450\) | 9.57002 | 0.451135 | ||||||||
\(451\) | 16.9366 | 0.797514 | ||||||||
\(452\) | −12.2010 | −0.573889 | ||||||||
\(453\) | −0.650874 | −0.0305807 | ||||||||
\(454\) | 13.8049 | 0.647897 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.86831 | 0.0874918 | ||||||||
\(457\) | 9.40342 | 0.439873 | 0.219937 | − | 0.975514i | \(-0.429415\pi\) | ||||
0.219937 | + | 0.975514i | \(0.429415\pi\) | |||||||
\(458\) | 11.5603 | 0.540179 | ||||||||
\(459\) | 22.0073 | 1.02721 | ||||||||
\(460\) | 12.1957 | 0.568626 | ||||||||
\(461\) | −0.733169 | −0.0341471 | −0.0170735 | − | 0.999854i | \(-0.505435\pi\) | ||||
−0.0170735 | + | 0.999854i | \(0.505435\pi\) | |||||||
\(462\) | 5.35988 | 0.249364 | ||||||||
\(463\) | 7.24267 | 0.336595 | 0.168298 | − | 0.985736i | \(-0.446173\pi\) | ||||
0.168298 | + | 0.985736i | \(0.446173\pi\) | |||||||
\(464\) | −3.78017 | −0.175490 | ||||||||
\(465\) | 62.7198 | 2.90856 | ||||||||
\(466\) | 9.77479 | 0.452808 | ||||||||
\(467\) | 30.2446 | 1.39955 | 0.699776 | − | 0.714362i | \(-0.253283\pi\) | ||||
0.699776 | + | 0.714362i | \(0.253283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.38271 | 0.110024 | ||||||||
\(470\) | −25.1836 | −1.16163 | ||||||||
\(471\) | −38.7042 | −1.78340 | ||||||||
\(472\) | −10.1468 | −0.467042 | ||||||||
\(473\) | −1.21552 | −0.0558897 | ||||||||
\(474\) | 31.7211 | 1.45700 | ||||||||
\(475\) | −7.28382 | −0.334204 | ||||||||
\(476\) | −6.61596 | −0.303242 | ||||||||
\(477\) | −4.05429 | −0.185633 | ||||||||
\(478\) | 0.944378 | 0.0431948 | ||||||||
\(479\) | −36.7198 | −1.67777 | −0.838884 | − | 0.544310i | \(-0.816792\pi\) | ||||
−0.838884 | + | 0.544310i | \(0.816792\pi\) | |||||||
\(480\) | −7.38404 | −0.337034 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.219833 | 0.0100131 | ||||||||
\(483\) | 7.69574 | 0.350168 | ||||||||
\(484\) | −5.44504 | −0.247502 | ||||||||
\(485\) | 52.8853 | 2.40140 | ||||||||
\(486\) | 11.7875 | 0.534690 | ||||||||
\(487\) | −28.6547 | −1.29847 | −0.649234 | − | 0.760588i | \(-0.724911\pi\) | ||||
−0.649234 | + | 0.760588i | \(0.724911\pi\) | |||||||
\(488\) | −0.439665 | −0.0199027 | ||||||||
\(489\) | −8.87741 | −0.401450 | ||||||||
\(490\) | −20.7875 | −0.939082 | ||||||||
\(491\) | 30.4295 | 1.37326 | 0.686632 | − | 0.727005i | \(-0.259088\pi\) | ||||
0.686632 | + | 0.727005i | \(0.259088\pi\) | |||||||
\(492\) | −14.7235 | −0.663786 | ||||||||
\(493\) | −22.5327 | −1.01482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.1763 | 0.457390 | ||||||||
\(496\) | −8.49396 | −0.381390 | ||||||||
\(497\) | 0.683661 | 0.0306664 | ||||||||
\(498\) | −1.86831 | −0.0837211 | ||||||||
\(499\) | 15.9715 | 0.714984 | 0.357492 | − | 0.933916i | \(-0.383632\pi\) | ||||
0.357492 | + | 0.933916i | \(0.383632\pi\) | |||||||
\(500\) | 10.7681 | 0.481563 | ||||||||
\(501\) | 28.6848 | 1.28154 | ||||||||
\(502\) | 16.2543 | 0.725464 | ||||||||
\(503\) | −41.9711 | −1.87140 | −0.935698 | − | 0.352801i | \(-0.885229\pi\) | ||||
−0.935698 | + | 0.352801i | \(0.885229\pi\) | |||||||
\(504\) | −1.32975 | −0.0592317 | ||||||||
\(505\) | 31.5991 | 1.40614 | ||||||||
\(506\) | 7.97584 | 0.354569 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.4276 | 0.507017 | ||||||||
\(509\) | 0.914247 | 0.0405233 | 0.0202616 | − | 0.999795i | \(-0.493550\pi\) | ||||
0.0202616 | + | 0.999795i | \(0.493550\pi\) | |||||||
\(510\) | −44.0146 | −1.94900 | ||||||||
\(511\) | 7.01805 | 0.310460 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.36658 | −0.148638 | ||||||||
\(514\) | −22.4373 | −0.989666 | ||||||||
\(515\) | 67.7948 | 2.98739 | ||||||||
\(516\) | 1.05669 | 0.0465181 | ||||||||
\(517\) | −16.4698 | −0.724341 | ||||||||
\(518\) | 5.42758 | 0.238474 | ||||||||
\(519\) | 22.5133 | 0.988226 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.31096 | −0.145056 | −0.0725279 | − | 0.997366i | \(-0.523107\pi\) | ||||
−0.0725279 | + | 0.997366i | \(0.523107\pi\) | |||||||
\(522\) | −4.52888 | −0.198224 | ||||||||
\(523\) | −0.850855 | −0.0372053 | −0.0186026 | − | 0.999827i | \(-0.505922\pi\) | ||||
−0.0186026 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(524\) | 2.29590 | 0.100297 | ||||||||
\(525\) | 18.1655 | 0.792809 | ||||||||
\(526\) | −10.4940 | −0.457558 | ||||||||
\(527\) | −50.6305 | −2.20550 | ||||||||
\(528\) | −4.82908 | −0.210159 | ||||||||
\(529\) | −11.5483 | −0.502098 | ||||||||
\(530\) | −12.1957 | −0.529746 | ||||||||
\(531\) | −12.1564 | −0.527545 | ||||||||
\(532\) | 1.01208 | 0.0438793 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.68473 | 0.332551 | ||||||||
\(535\) | 65.0568 | 2.81265 | ||||||||
\(536\) | −2.14675 | −0.0927256 | ||||||||
\(537\) | −9.53809 | −0.411599 | ||||||||
\(538\) | 26.4155 | 1.13885 | ||||||||
\(539\) | −13.5948 | −0.585569 | ||||||||
\(540\) | 13.3056 | 0.572581 | ||||||||
\(541\) | −40.8853 | −1.75780 | −0.878898 | − | 0.477010i | \(-0.841721\pi\) | ||||
−0.878898 | + | 0.477010i | \(0.841721\pi\) | |||||||
\(542\) | 22.0301 | 0.946275 | ||||||||
\(543\) | 2.18492 | 0.0937637 | ||||||||
\(544\) | 5.96077 | 0.255566 | ||||||||
\(545\) | −21.9758 | −0.941341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.39075 | −0.102221 | −0.0511105 | − | 0.998693i | \(-0.516276\pi\) | ||||
−0.0511105 | + | 0.998693i | \(0.516276\pi\) | |||||||
\(548\) | −9.08038 | −0.387894 | ||||||||
\(549\) | −0.526746 | −0.0224810 | ||||||||
\(550\) | 18.8267 | 0.802773 | ||||||||
\(551\) | 3.44696 | 0.146845 | ||||||||
\(552\) | −6.93362 | −0.295115 | ||||||||
\(553\) | 17.1836 | 0.730720 | ||||||||
\(554\) | 2.17629 | 0.0924618 | ||||||||
\(555\) | 36.1086 | 1.53272 | ||||||||
\(556\) | 18.9051 | 0.801757 | ||||||||
\(557\) | 27.1508 | 1.15042 | 0.575208 | − | 0.818007i | \(-0.304921\pi\) | ||||
0.575208 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(558\) | −10.1763 | −0.430797 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.00000 | −0.169031 | ||||||||
\(561\) | −28.7851 | −1.21531 | ||||||||
\(562\) | −25.0030 | −1.05469 | ||||||||
\(563\) | −6.52409 | −0.274958 | −0.137479 | − | 0.990505i | \(-0.543900\pi\) | ||||
−0.137479 | + | 0.990505i | \(0.543900\pi\) | |||||||
\(564\) | 14.3177 | 0.602883 | ||||||||
\(565\) | −43.9711 | −1.84988 | ||||||||
\(566\) | −16.3153 | −0.685782 | ||||||||
\(567\) | 12.3854 | 0.520137 | ||||||||
\(568\) | −0.615957 | −0.0258450 | ||||||||
\(569\) | 7.30021 | 0.306041 | 0.153020 | − | 0.988223i | \(-0.451100\pi\) | ||||
0.153020 | + | 0.988223i | \(0.451100\pi\) | |||||||
\(570\) | 6.73317 | 0.282021 | ||||||||
\(571\) | −43.6722 | −1.82762 | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.82371 | −0.0761865 | ||||||||
\(574\) | −7.97584 | −0.332905 | ||||||||
\(575\) | 27.0315 | 1.12729 | ||||||||
\(576\) | 1.19806 | 0.0499193 | ||||||||
\(577\) | 16.8528 | 0.701590 | 0.350795 | − | 0.936452i | \(-0.385911\pi\) | ||||
0.350795 | + | 0.936452i | \(0.385911\pi\) | |||||||
\(578\) | 18.5308 | 0.770779 | ||||||||
\(579\) | 33.2282 | 1.38092 | ||||||||
\(580\) | −13.6233 | −0.565675 | ||||||||
\(581\) | −1.01208 | −0.0419882 | ||||||||
\(582\) | −30.0670 | −1.24632 | ||||||||
\(583\) | −7.97584 | −0.330325 | ||||||||
\(584\) | −6.32304 | −0.261649 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.87800 | 0.0775796 | ||||||||
\(587\) | −22.1825 | −0.915571 | −0.457785 | − | 0.889063i | \(-0.651357\pi\) | ||||
−0.457785 | + | 0.889063i | \(0.651357\pi\) | |||||||
\(588\) | 11.8183 | 0.487380 | ||||||||
\(589\) | 7.74525 | 0.319137 | ||||||||
\(590\) | −36.5676 | −1.50547 | ||||||||
\(591\) | −23.5034 | −0.966800 | ||||||||
\(592\) | −4.89008 | −0.200981 | ||||||||
\(593\) | 3.98493 | 0.163642 | 0.0818208 | − | 0.996647i | \(-0.473926\pi\) | ||||
0.0818208 | + | 0.996647i | \(0.473926\pi\) | |||||||
\(594\) | 8.70171 | 0.357035 | ||||||||
\(595\) | −23.8431 | −0.977471 | ||||||||
\(596\) | −18.6896 | −0.765557 | ||||||||
\(597\) | 7.78495 | 0.318617 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.2379 | 1.35806 | 0.679032 | − | 0.734109i | \(-0.262400\pi\) | ||||
0.679032 | + | 0.734109i | \(0.262400\pi\) | |||||||
\(600\) | −16.3666 | −0.668163 | ||||||||
\(601\) | 9.79715 | 0.399634 | 0.199817 | − | 0.979833i | \(-0.435965\pi\) | ||||
0.199817 | + | 0.979833i | \(0.435965\pi\) | |||||||
\(602\) | 0.572417 | 0.0233300 | ||||||||
\(603\) | −2.57194 | −0.104738 | ||||||||
\(604\) | 0.317667 | 0.0129257 | ||||||||
\(605\) | −19.6233 | −0.797799 | ||||||||
\(606\) | −17.9651 | −0.729782 | ||||||||
\(607\) | −24.2258 | −0.983295 | −0.491647 | − | 0.870794i | \(-0.663605\pi\) | ||||
−0.491647 | + | 0.870794i | \(0.663605\pi\) | |||||||
\(608\) | −0.911854 | −0.0369806 | ||||||||
\(609\) | −8.59658 | −0.348351 | ||||||||
\(610\) | −1.58450 | −0.0641545 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.14138 | 0.288673 | ||||||||
\(613\) | −15.0556 | −0.608091 | −0.304045 | − | 0.952658i | \(-0.598337\pi\) | ||||
−0.304045 | + | 0.952658i | \(0.598337\pi\) | |||||||
\(614\) | 23.9801 | 0.967760 | ||||||||
\(615\) | −53.0616 | −2.13965 | ||||||||
\(616\) | −2.61596 | −0.105400 | ||||||||
\(617\) | −2.01879 | −0.0812733 | −0.0406366 | − | 0.999174i | \(-0.512939\pi\) | ||||
−0.0406366 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(618\) | −38.5435 | −1.55045 | ||||||||
\(619\) | −7.84309 | −0.315240 | −0.157620 | − | 0.987500i | \(-0.550382\pi\) | ||||
−0.157620 | + | 0.987500i | \(0.550382\pi\) | |||||||
\(620\) | −30.6112 | −1.22937 | ||||||||
\(621\) | 12.4940 | 0.501365 | ||||||||
\(622\) | −5.38404 | −0.215880 | ||||||||
\(623\) | 4.16288 | 0.166782 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.13275 | −0.0453101 | ||||||||
\(626\) | 18.9487 | 0.757342 | ||||||||
\(627\) | 4.40342 | 0.175856 | ||||||||
\(628\) | 18.8901 | 0.753796 | ||||||||
\(629\) | −29.1487 | −1.16223 | ||||||||
\(630\) | −4.79225 | −0.190928 | ||||||||
\(631\) | 24.5327 | 0.976632 | 0.488316 | − | 0.872667i | \(-0.337611\pi\) | ||||
0.488316 | + | 0.872667i | \(0.337611\pi\) | |||||||
\(632\) | −15.4819 | −0.615836 | ||||||||
\(633\) | 51.3183 | 2.03972 | ||||||||
\(634\) | 11.5013 | 0.456773 | ||||||||
\(635\) | 41.1836 | 1.63432 | ||||||||
\(636\) | 6.93362 | 0.274936 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.90946 | −0.352729 | ||||||||
\(639\) | −0.737955 | −0.0291930 | ||||||||
\(640\) | 3.60388 | 0.142456 | ||||||||
\(641\) | −41.6015 | −1.64316 | −0.821580 | − | 0.570093i | \(-0.806907\pi\) | ||||
−0.821580 | + | 0.570093i | \(0.806907\pi\) | |||||||
\(642\) | −36.9869 | −1.45975 | ||||||||
\(643\) | 45.4118 | 1.79087 | 0.895433 | − | 0.445196i | \(-0.146866\pi\) | ||||
0.895433 | + | 0.445196i | \(0.146866\pi\) | |||||||
\(644\) | −3.75600 | −0.148007 | ||||||||
\(645\) | 3.80817 | 0.149946 | ||||||||
\(646\) | −5.43535 | −0.213851 | ||||||||
\(647\) | 35.8345 | 1.40880 | 0.704399 | − | 0.709804i | \(-0.251217\pi\) | ||||
0.704399 | + | 0.709804i | \(0.251217\pi\) | |||||||
\(648\) | −11.1588 | −0.438360 | ||||||||
\(649\) | −23.9148 | −0.938740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.3163 | −0.757067 | ||||||||
\(652\) | 4.33273 | 0.169683 | ||||||||
\(653\) | 18.5590 | 0.726270 | 0.363135 | − | 0.931737i | \(-0.381706\pi\) | ||||
0.363135 | + | 0.931737i | \(0.381706\pi\) | |||||||
\(654\) | 12.4940 | 0.488552 | ||||||||
\(655\) | 8.27413 | 0.323297 | ||||||||
\(656\) | 7.18598 | 0.280565 | ||||||||
\(657\) | −7.57540 | −0.295545 | ||||||||
\(658\) | 7.75600 | 0.302361 | ||||||||
\(659\) | −3.97525 | −0.154854 | −0.0774268 | − | 0.996998i | \(-0.524670\pi\) | ||||
−0.0774268 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(660\) | −17.4034 | −0.677427 | ||||||||
\(661\) | 1.23191 | 0.0479159 | 0.0239580 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239580 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(662\) | 34.6112 | 1.34520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.911854 | 0.0353868 | ||||||||
\(665\) | 3.64742 | 0.141441 | ||||||||
\(666\) | −5.85862 | −0.227017 | ||||||||
\(667\) | −12.7922 | −0.495318 | ||||||||
\(668\) | −14.0000 | −0.541676 | ||||||||
\(669\) | 26.6112 | 1.02885 | ||||||||
\(670\) | −7.73663 | −0.298892 | ||||||||
\(671\) | −1.03624 | −0.0400038 | ||||||||
\(672\) | 2.27413 | 0.0877263 | ||||||||
\(673\) | −36.8256 | −1.41952 | −0.709762 | − | 0.704442i | \(-0.751197\pi\) | ||||
−0.709762 | + | 0.704442i | \(0.751197\pi\) | |||||||
\(674\) | 1.95407 | 0.0752678 | ||||||||
\(675\) | 29.4916 | 1.13513 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.9215 | −0.996246 | −0.498123 | − | 0.867106i | \(-0.665977\pi\) | ||||
−0.498123 | + | 0.867106i | \(0.665977\pi\) | |||||||
\(678\) | 24.9989 | 0.960078 | ||||||||
\(679\) | −16.2875 | −0.625058 | ||||||||
\(680\) | 21.4819 | 0.823792 | ||||||||
\(681\) | −28.2851 | −1.08389 | ||||||||
\(682\) | −20.0194 | −0.766582 | ||||||||
\(683\) | 37.5472 | 1.43670 | 0.718352 | − | 0.695680i | \(-0.244897\pi\) | ||||
0.718352 | + | 0.695680i | \(0.244897\pi\) | |||||||
\(684\) | −1.09246 | −0.0417712 | ||||||||
\(685\) | −32.7245 | −1.25034 | ||||||||
\(686\) | 14.1715 | 0.541071 | ||||||||
\(687\) | −23.6862 | −0.903684 | ||||||||
\(688\) | −0.515729 | −0.0196620 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −24.9879 | −0.951274 | ||||||||
\(691\) | 45.2549 | 1.72158 | 0.860788 | − | 0.508963i | \(-0.169971\pi\) | ||||
0.860788 | + | 0.508963i | \(0.169971\pi\) | |||||||
\(692\) | −10.9879 | −0.417698 | ||||||||
\(693\) | −3.13408 | −0.119054 | ||||||||
\(694\) | −6.41550 | −0.243529 | ||||||||
\(695\) | 68.1318 | 2.58439 | ||||||||
\(696\) | 7.74525 | 0.293583 | ||||||||
\(697\) | 42.8340 | 1.62245 | ||||||||
\(698\) | 1.08575 | 0.0410964 | ||||||||
\(699\) | −20.0277 | −0.757519 | ||||||||
\(700\) | −8.86592 | −0.335100 | ||||||||
\(701\) | 36.0823 | 1.36281 | 0.681405 | − | 0.731907i | \(-0.261369\pi\) | ||||
0.681405 | + | 0.731907i | \(0.261369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.45904 | 0.168176 | ||||||||
\(704\) | 2.35690 | 0.0888289 | ||||||||
\(705\) | 51.5991 | 1.94333 | ||||||||
\(706\) | 4.28919 | 0.161426 | ||||||||
\(707\) | −9.73184 | −0.366004 | ||||||||
\(708\) | 20.7899 | 0.781331 | ||||||||
\(709\) | −19.0664 | −0.716053 | −0.358026 | − | 0.933711i | \(-0.616550\pi\) | ||||
−0.358026 | + | 0.933711i | \(0.616550\pi\) | |||||||
\(710\) | −2.21983 | −0.0833088 | ||||||||
\(711\) | −18.5483 | −0.695614 | ||||||||
\(712\) | −3.75063 | −0.140561 | ||||||||
\(713\) | −28.7439 | −1.07647 | ||||||||
\(714\) | 13.5555 | 0.507304 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.65519 | 0.173972 | ||||||||
\(717\) | −1.93495 | −0.0722621 | ||||||||
\(718\) | −15.5060 | −0.578680 | ||||||||
\(719\) | −15.3056 | −0.570802 | −0.285401 | − | 0.958408i | \(-0.592127\pi\) | ||||
−0.285401 | + | 0.958408i | \(0.592127\pi\) | |||||||
\(720\) | 4.31767 | 0.160910 | ||||||||
\(721\) | −20.8793 | −0.777587 | ||||||||
\(722\) | −18.1685 | −0.676162 | ||||||||
\(723\) | −0.450419 | −0.0167513 | ||||||||
\(724\) | −1.06638 | −0.0396315 | ||||||||
\(725\) | −30.1957 | −1.12144 | ||||||||
\(726\) | 11.1564 | 0.414054 | ||||||||
\(727\) | 3.46250 | 0.128417 | 0.0642085 | − | 0.997937i | \(-0.479548\pi\) | ||||
0.0642085 | + | 0.997937i | \(0.479548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.32496 | 0.345369 | ||||||||
\(730\) | −22.7875 | −0.843402 | ||||||||
\(731\) | −3.07415 | −0.113701 | ||||||||
\(732\) | 0.900837 | 0.0332959 | ||||||||
\(733\) | −26.0930 | −0.963769 | −0.481884 | − | 0.876235i | \(-0.660047\pi\) | ||||
−0.481884 | + | 0.876235i | \(0.660047\pi\) | |||||||
\(734\) | 17.4276 | 0.643264 | ||||||||
\(735\) | 42.5918 | 1.57102 | ||||||||
\(736\) | 3.38404 | 0.124737 | ||||||||
\(737\) | −5.05967 | −0.186375 | ||||||||
\(738\) | 8.60925 | 0.316911 | ||||||||
\(739\) | −26.4993 | −0.974794 | −0.487397 | − | 0.873181i | \(-0.662054\pi\) | ||||
−0.487397 | + | 0.873181i | \(0.662054\pi\) | |||||||
\(740\) | −17.6233 | −0.647844 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.75600 | 0.137887 | ||||||||
\(743\) | −0.415502 | −0.0152433 | −0.00762164 | − | 0.999971i | \(-0.502426\pi\) | ||||
−0.00762164 | + | 0.999971i | \(0.502426\pi\) | |||||||
\(744\) | 17.4034 | 0.638040 | ||||||||
\(745\) | −67.3551 | −2.46770 | ||||||||
\(746\) | 8.19567 | 0.300065 | ||||||||
\(747\) | 1.09246 | 0.0399709 | ||||||||
\(748\) | 14.0489 | 0.513679 | ||||||||
\(749\) | −20.0361 | −0.732103 | ||||||||
\(750\) | −22.0629 | −0.805624 | ||||||||
\(751\) | 2.90946 | 0.106168 | 0.0530839 | − | 0.998590i | \(-0.483095\pi\) | ||||
0.0530839 | + | 0.998590i | \(0.483095\pi\) | |||||||
\(752\) | −6.98792 | −0.254823 | ||||||||
\(753\) | −33.3037 | −1.21365 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.14483 | 0.0416647 | ||||||||
\(756\) | −4.09783 | −0.149037 | ||||||||
\(757\) | 12.3720 | 0.449667 | 0.224833 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224833 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(758\) | −15.0476 | −0.546553 | ||||||||
\(759\) | −16.3418 | −0.593171 | ||||||||
\(760\) | −3.28621 | −0.119203 | ||||||||
\(761\) | 42.4306 | 1.53811 | 0.769053 | − | 0.639184i | \(-0.220728\pi\) | ||||
0.769053 | + | 0.639184i | \(0.220728\pi\) | |||||||
\(762\) | −23.4142 | −0.848206 | ||||||||
\(763\) | 6.76809 | 0.245021 | ||||||||
\(764\) | 0.890084 | 0.0322021 | ||||||||
\(765\) | 25.7366 | 0.930510 | ||||||||
\(766\) | −11.1207 | −0.401806 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.04892 | −0.0739339 | ||||||||
\(769\) | 13.3341 | 0.480839 | 0.240419 | − | 0.970669i | \(-0.422715\pi\) | ||||
0.240419 | + | 0.970669i | \(0.422715\pi\) | |||||||
\(770\) | −9.42758 | −0.339747 | ||||||||
\(771\) | 45.9721 | 1.65565 | ||||||||
\(772\) | −16.2174 | −0.583678 | ||||||||
\(773\) | −5.85384 | −0.210548 | −0.105274 | − | 0.994443i | \(-0.533572\pi\) | ||||
−0.105274 | + | 0.994443i | \(0.533572\pi\) | |||||||
\(774\) | −0.617876 | −0.0222091 | ||||||||
\(775\) | −67.8491 | −2.43721 | ||||||||
\(776\) | 14.6746 | 0.526786 | ||||||||
\(777\) | −11.1207 | −0.398952 | ||||||||
\(778\) | −8.04354 | −0.288375 | ||||||||
\(779\) | −6.55257 | −0.234770 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.45175 | −0.0519476 | ||||||||
\(782\) | 20.1715 | 0.721332 | ||||||||
\(783\) | −13.9565 | −0.498763 | ||||||||
\(784\) | −5.76809 | −0.206003 | ||||||||
\(785\) | 68.0775 | 2.42979 | ||||||||
\(786\) | −4.70410 | −0.167790 | ||||||||
\(787\) | −23.2965 | −0.830430 | −0.415215 | − | 0.909723i | \(-0.636294\pi\) | ||||
−0.415215 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(788\) | 11.4711 | 0.408642 | ||||||||
\(789\) | 21.5013 | 0.765465 | ||||||||
\(790\) | −55.7948 | −1.98509 | ||||||||
\(791\) | 13.5421 | 0.481503 | ||||||||
\(792\) | 2.82371 | 0.100336 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.9081 | −0.777491 | ||||||||
\(795\) | 24.9879 | 0.886230 | ||||||||
\(796\) | −3.79954 | −0.134671 | ||||||||
\(797\) | 35.8103 | 1.26847 | 0.634233 | − | 0.773142i | \(-0.281316\pi\) | ||||
0.634233 | + | 0.773142i | \(0.281316\pi\) | |||||||
\(798\) | −2.07367 | −0.0734072 | ||||||||
\(799\) | −41.6534 | −1.47359 | ||||||||
\(800\) | 7.98792 | 0.282416 | ||||||||
\(801\) | −4.49349 | −0.158769 | ||||||||
\(802\) | 17.4426 | 0.615921 | ||||||||
\(803\) | −14.9028 | −0.525907 | ||||||||
\(804\) | 4.39852 | 0.155124 | ||||||||
\(805\) | −13.5362 | −0.477087 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.1232 | −1.90523 | ||||||||
\(808\) | 8.76809 | 0.308460 | ||||||||
\(809\) | 28.3744 | 0.997589 | 0.498795 | − | 0.866720i | \(-0.333776\pi\) | ||||
0.498795 | + | 0.866720i | \(0.333776\pi\) | |||||||
\(810\) | −40.2150 | −1.41301 | ||||||||
\(811\) | 5.20344 | 0.182717 | 0.0913587 | − | 0.995818i | \(-0.470879\pi\) | ||||
0.0913587 | + | 0.995818i | \(0.470879\pi\) | |||||||
\(812\) | 4.19567 | 0.147239 | ||||||||
\(813\) | −45.1379 | −1.58306 | ||||||||
\(814\) | −11.5254 | −0.403966 | ||||||||
\(815\) | 15.6146 | 0.546957 | ||||||||
\(816\) | −12.2131 | −0.427545 | ||||||||
\(817\) | 0.470270 | 0.0164527 | ||||||||
\(818\) | −17.4330 | −0.609529 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.8974 | 0.904376 | ||||||||
\(821\) | −5.65338 | −0.197304 | −0.0986522 | − | 0.995122i | \(-0.531453\pi\) | ||||
−0.0986522 | + | 0.995122i | \(0.531453\pi\) | |||||||
\(822\) | 18.6049 | 0.648922 | ||||||||
\(823\) | 39.0616 | 1.36160 | 0.680801 | − | 0.732469i | \(-0.261632\pi\) | ||||
0.680801 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(824\) | 18.8116 | 0.655334 | ||||||||
\(825\) | −38.5743 | −1.34299 | ||||||||
\(826\) | 11.2620 | 0.391857 | ||||||||
\(827\) | −5.40283 | −0.187875 | −0.0939374 | − | 0.995578i | \(-0.529945\pi\) | ||||
−0.0939374 | + | 0.995578i | \(0.529945\pi\) | |||||||
\(828\) | 4.05429 | 0.140896 | ||||||||
\(829\) | −8.38537 | −0.291236 | −0.145618 | − | 0.989341i | \(-0.546517\pi\) | ||||
−0.145618 | + | 0.989341i | \(0.546517\pi\) | |||||||
\(830\) | 3.28621 | 0.114066 | ||||||||
\(831\) | −4.45904 | −0.154682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.3822 | −1.19127 | ||||||||
\(834\) | −38.7351 | −1.34129 | ||||||||
\(835\) | −50.4543 | −1.74604 | ||||||||
\(836\) | −2.14914 | −0.0743297 | ||||||||
\(837\) | −31.3599 | −1.08396 | ||||||||
\(838\) | 9.97584 | 0.344610 | ||||||||
\(839\) | −3.98062 | −0.137426 | −0.0687132 | − | 0.997636i | \(-0.521889\pi\) | ||||
−0.0687132 | + | 0.997636i | \(0.521889\pi\) | |||||||
\(840\) | 8.19567 | 0.282777 | ||||||||
\(841\) | −14.7103 | −0.507253 | ||||||||
\(842\) | 0.615957 | 0.0212273 | ||||||||
\(843\) | 51.2290 | 1.76442 | ||||||||
\(844\) | −25.0465 | −0.862137 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.37196 | −0.287834 | ||||||||
\(847\) | 6.04354 | 0.207659 | ||||||||
\(848\) | −3.38404 | −0.116209 | ||||||||
\(849\) | 33.4286 | 1.14727 | ||||||||
\(850\) | 47.6142 | 1.63315 | ||||||||
\(851\) | −16.5483 | −0.567267 | ||||||||
\(852\) | 1.26205 | 0.0432370 | ||||||||
\(853\) | 6.29350 | 0.215485 | 0.107743 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107743 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(854\) | 0.487991 | 0.0166987 | ||||||||
\(855\) | −3.93708 | −0.134645 | ||||||||
\(856\) | 18.0519 | 0.617001 | ||||||||
\(857\) | 4.37627 | 0.149491 | 0.0747453 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747453 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0261 | 0.512683 | 0.256342 | − | 0.966586i | \(-0.417483\pi\) | ||||
0.256342 | + | 0.966586i | \(0.417483\pi\) | |||||||
\(860\) | −1.85862 | −0.0633786 | ||||||||
\(861\) | 16.3418 | 0.556928 | ||||||||
\(862\) | −14.7922 | −0.503826 | ||||||||
\(863\) | 6.21121 | 0.211432 | 0.105716 | − | 0.994396i | \(-0.466287\pi\) | ||||
0.105716 | + | 0.994396i | \(0.466287\pi\) | |||||||
\(864\) | 3.69202 | 0.125605 | ||||||||
\(865\) | −39.5991 | −1.34641 | ||||||||
\(866\) | 16.5321 | 0.561784 | ||||||||
\(867\) | −37.9681 | −1.28946 | ||||||||
\(868\) | 9.42758 | 0.319993 | ||||||||
\(869\) | −36.4892 | −1.23781 | ||||||||
\(870\) | 27.9129 | 0.946337 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.09783 | −0.206499 | ||||||||
\(873\) | 17.5810 | 0.595028 | ||||||||
\(874\) | −3.08575 | −0.104377 | ||||||||
\(875\) | −11.9517 | −0.404040 | ||||||||
\(876\) | 12.9554 | 0.437722 | ||||||||
\(877\) | 38.2198 | 1.29059 | 0.645296 | − | 0.763933i | \(-0.276734\pi\) | ||||
0.645296 | + | 0.763933i | \(0.276734\pi\) | |||||||
\(878\) | 3.50125 | 0.118162 | ||||||||
\(879\) | −3.84787 | −0.129785 | ||||||||
\(880\) | 8.49396 | 0.286331 | ||||||||
\(881\) | 26.7832 | 0.902347 | 0.451174 | − | 0.892436i | \(-0.351006\pi\) | ||||
0.451174 | + | 0.892436i | \(0.351006\pi\) | |||||||
\(882\) | −6.91053 | −0.232690 | ||||||||
\(883\) | −34.4956 | −1.16087 | −0.580435 | − | 0.814307i | \(-0.697117\pi\) | ||||
−0.580435 | + | 0.814307i | \(0.697117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 74.9241 | 2.51854 | ||||||||
\(886\) | 17.4077 | 0.584824 | ||||||||
\(887\) | −23.9866 | −0.805391 | −0.402695 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402695 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(888\) | 10.0194 | 0.336228 | ||||||||
\(889\) | −12.6837 | −0.425396 | ||||||||
\(890\) | −13.5168 | −0.453084 | ||||||||
\(891\) | −26.3002 | −0.881090 | ||||||||
\(892\) | −12.9879 | −0.434868 | ||||||||
\(893\) | 6.37196 | 0.213230 | ||||||||
\(894\) | 38.2935 | 1.28073 | ||||||||
\(895\) | 16.7767 | 0.560784 | ||||||||
\(896\) | −1.10992 | −0.0370797 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.1497 | 1.13959 | ||||||||
\(899\) | 32.1086 | 1.07088 | ||||||||
\(900\) | 9.57002 | 0.319001 | ||||||||
\(901\) | −20.1715 | −0.672010 | ||||||||
\(902\) | 16.9366 | 0.563927 | ||||||||
\(903\) | −1.17283 | −0.0390295 | ||||||||
\(904\) | −12.2010 | −0.405801 | ||||||||
\(905\) | −3.84309 | −0.127748 | ||||||||
\(906\) | −0.650874 | −0.0216238 | ||||||||
\(907\) | 23.9269 | 0.794480 | 0.397240 | − | 0.917715i | \(-0.369968\pi\) | ||||
0.397240 | + | 0.917715i | \(0.369968\pi\) | |||||||
\(908\) | 13.8049 | 0.458132 | ||||||||
\(909\) | 10.5047 | 0.348419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.8866 | −1.18898 | −0.594488 | − | 0.804104i | \(-0.702645\pi\) | ||||
−0.594488 | + | 0.804104i | \(0.702645\pi\) | |||||||
\(912\) | 1.86831 | 0.0618660 | ||||||||
\(913\) | 2.14914 | 0.0711263 | ||||||||
\(914\) | 9.40342 | 0.311037 | ||||||||
\(915\) | 3.24651 | 0.107326 | ||||||||
\(916\) | 11.5603 | 0.381964 | ||||||||
\(917\) | −2.54825 | −0.0841507 | ||||||||
\(918\) | 22.0073 | 0.726349 | ||||||||
\(919\) | 33.2465 | 1.09670 | 0.548351 | − | 0.836249i | \(-0.315256\pi\) | ||||
0.548351 | + | 0.836249i | \(0.315256\pi\) | |||||||
\(920\) | 12.1957 | 0.402079 | ||||||||
\(921\) | −49.1333 | −1.61900 | ||||||||
\(922\) | −0.733169 | −0.0241456 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.35988 | 0.176327 | ||||||||
\(925\) | −39.0616 | −1.28434 | ||||||||
\(926\) | 7.24267 | 0.238009 | ||||||||
\(927\) | 22.5375 | 0.740229 | ||||||||
\(928\) | −3.78017 | −0.124090 | ||||||||
\(929\) | 54.2583 | 1.78016 | 0.890079 | − | 0.455806i | \(-0.150649\pi\) | ||||
0.890079 | + | 0.455806i | \(0.150649\pi\) | |||||||
\(930\) | 62.7198 | 2.05666 | ||||||||
\(931\) | 5.25965 | 0.172378 | ||||||||
\(932\) | 9.77479 | 0.320184 | ||||||||
\(933\) | 11.0315 | 0.361154 | ||||||||
\(934\) | 30.2446 | 0.989633 | ||||||||
\(935\) | 50.6305 | 1.65580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5265 | 0.539897 | 0.269948 | − | 0.962875i | \(-0.412993\pi\) | ||||
0.269948 | + | 0.962875i | \(0.412993\pi\) | |||||||
\(938\) | 2.38271 | 0.0777984 | ||||||||
\(939\) | −38.8243 | −1.26698 | ||||||||
\(940\) | −25.1836 | −0.821398 | ||||||||
\(941\) | 41.7017 | 1.35944 | 0.679718 | − | 0.733473i | \(-0.262102\pi\) | ||||
0.679718 | + | 0.733473i | \(0.262102\pi\) | |||||||
\(942\) | −38.7042 | −1.26105 | ||||||||
\(943\) | 24.3177 | 0.791892 | ||||||||
\(944\) | −10.1468 | −0.330249 | ||||||||
\(945\) | −14.7681 | −0.480406 | ||||||||
\(946\) | −1.21552 | −0.0395200 | ||||||||
\(947\) | −3.00106 | −0.0975215 | −0.0487608 | − | 0.998810i | \(-0.515527\pi\) | ||||
−0.0487608 | + | 0.998810i | \(0.515527\pi\) | |||||||
\(948\) | 31.7211 | 1.03025 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.28382 | −0.236318 | ||||||||
\(951\) | −23.5651 | −0.764151 | ||||||||
\(952\) | −6.61596 | −0.214424 | ||||||||
\(953\) | 38.1450 | 1.23564 | 0.617818 | − | 0.786321i | \(-0.288017\pi\) | ||||
0.617818 | + | 0.786321i | \(0.288017\pi\) | |||||||
\(954\) | −4.05429 | −0.131263 | ||||||||
\(955\) | 3.20775 | 0.103800 | ||||||||
\(956\) | 0.944378 | 0.0305434 | ||||||||
\(957\) | 18.2547 | 0.590092 | ||||||||
\(958\) | −36.7198 | −1.18636 | ||||||||
\(959\) | 10.0785 | 0.325450 | ||||||||
\(960\) | −7.38404 | −0.238319 | ||||||||
\(961\) | 41.1473 | 1.32733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.6273 | 0.696930 | ||||||||
\(964\) | 0.219833 | 0.00708033 | ||||||||
\(965\) | −58.4456 | −1.88143 | ||||||||
\(966\) | 7.69574 | 0.247606 | ||||||||
\(967\) | 26.8793 | 0.864381 | 0.432190 | − | 0.901782i | \(-0.357741\pi\) | ||||
0.432190 | + | 0.901782i | \(0.357741\pi\) | |||||||
\(968\) | −5.44504 | −0.175010 | ||||||||
\(969\) | 11.1366 | 0.357759 | ||||||||
\(970\) | 52.8853 | 1.69804 | ||||||||
\(971\) | 3.13647 | 0.100654 | 0.0503271 | − | 0.998733i | \(-0.483974\pi\) | ||||
0.0503271 | + | 0.998733i | \(0.483974\pi\) | |||||||
\(972\) | 11.7875 | 0.378083 | ||||||||
\(973\) | −20.9831 | −0.672688 | ||||||||
\(974\) | −28.6547 | −0.918156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.439665 | −0.0140733 | ||||||||
\(977\) | −35.8864 | −1.14811 | −0.574053 | − | 0.818818i | \(-0.694630\pi\) | ||||
−0.574053 | + | 0.818818i | \(0.694630\pi\) | |||||||
\(978\) | −8.87741 | −0.283868 | ||||||||
\(979\) | −8.83984 | −0.282522 | ||||||||
\(980\) | −20.7875 | −0.664031 | ||||||||
\(981\) | −7.30559 | −0.233249 | ||||||||
\(982\) | 30.4295 | 0.971044 | ||||||||
\(983\) | 30.4370 | 0.970790 | 0.485395 | − | 0.874295i | \(-0.338676\pi\) | ||||
0.485395 | + | 0.874295i | \(0.338676\pi\) | |||||||
\(984\) | −14.7235 | −0.469367 | ||||||||
\(985\) | 41.3405 | 1.31722 | ||||||||
\(986\) | −22.5327 | −0.717588 | ||||||||
\(987\) | −15.8914 | −0.505829 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.74525 | −0.0554957 | ||||||||
\(990\) | 10.1763 | 0.323424 | ||||||||
\(991\) | 31.4470 | 0.998946 | 0.499473 | − | 0.866330i | \(-0.333527\pi\) | ||||
0.499473 | + | 0.866330i | \(0.333527\pi\) | |||||||
\(992\) | −8.49396 | −0.269683 | ||||||||
\(993\) | −70.9154 | −2.25043 | ||||||||
\(994\) | 0.683661 | 0.0216844 | ||||||||
\(995\) | −13.6931 | −0.434100 | ||||||||
\(996\) | −1.86831 | −0.0591998 | ||||||||
\(997\) | 19.1099 | 0.605217 | 0.302609 | − | 0.953115i | \(-0.402143\pi\) | ||||
0.302609 | + | 0.953115i | \(0.402143\pi\) | |||||||
\(998\) | 15.9715 | 0.505570 | ||||||||
\(999\) | −18.0543 | −0.571213 |
(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 | 338.2.a.h.1.1 | yes | 3 | |
3.2 | odd | 2 | 3042.2.a.z.1.1 | 3 | |||
4.3 | odd | 2 | 2704.2.a.w.1.3 | 3 | |||
5.4 | even | 2 | 8450.2.a.bn.1.3 | 3 | |||
13.2 | odd | 12 | 338.2.e.e.147.6 | 12 | |||
13.3 | even | 3 | 338.2.c.h.191.3 | 6 | |||
13.4 | even | 6 | 338.2.c.i.315.3 | 6 | |||
13.5 | odd | 4 | 338.2.b.d.337.1 | 6 | |||
13.6 | odd | 12 | 338.2.e.e.23.3 | 12 | |||
13.7 | odd | 12 | 338.2.e.e.23.6 | 12 | |||
13.8 | odd | 4 | 338.2.b.d.337.4 | 6 | |||
13.9 | even | 3 | 338.2.c.h.315.3 | 6 | |||
13.10 | even | 6 | 338.2.c.i.191.3 | 6 | |||
13.11 | odd | 12 | 338.2.e.e.147.3 | 12 | |||
13.12 | even | 2 | 338.2.a.g.1.1 | ✓ | 3 | ||
39.5 | even | 4 | 3042.2.b.n.1351.6 | 6 | |||
39.8 | even | 4 | 3042.2.b.n.1351.1 | 6 | |||
39.38 | odd | 2 | 3042.2.a.bi.1.3 | 3 | |||
52.31 | even | 4 | 2704.2.f.m.337.5 | 6 | |||
52.47 | even | 4 | 2704.2.f.m.337.6 | 6 | |||
52.51 | odd | 2 | 2704.2.a.v.1.3 | 3 | |||
65.64 | even | 2 | 8450.2.a.bx.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
338.2.a.g.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
338.2.a.h.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
338.2.b.d.337.1 | 6 | 13.5 | odd | 4 | |||
338.2.b.d.337.4 | 6 | 13.8 | odd | 4 | |||
338.2.c.h.191.3 | 6 | 13.3 | even | 3 | |||
338.2.c.h.315.3 | 6 | 13.9 | even | 3 | |||
338.2.c.i.191.3 | 6 | 13.10 | even | 6 | |||
338.2.c.i.315.3 | 6 | 13.4 | even | 6 | |||
338.2.e.e.23.3 | 12 | 13.6 | odd | 12 | |||
338.2.e.e.23.6 | 12 | 13.7 | odd | 12 | |||
338.2.e.e.147.3 | 12 | 13.11 | odd | 12 | |||
338.2.e.e.147.6 | 12 | 13.2 | odd | 12 | |||
2704.2.a.v.1.3 | 3 | 52.51 | odd | 2 | |||
2704.2.a.w.1.3 | 3 | 4.3 | odd | 2 | |||
2704.2.f.m.337.5 | 6 | 52.31 | even | 4 | |||
2704.2.f.m.337.6 | 6 | 52.47 | even | 4 | |||
3042.2.a.z.1.1 | 3 | 3.2 | odd | 2 | |||
3042.2.a.bi.1.3 | 3 | 39.38 | odd | 2 | |||
3042.2.b.n.1351.1 | 6 | 39.8 | even | 4 | |||
3042.2.b.n.1351.6 | 6 | 39.5 | even | 4 | |||
8450.2.a.bn.1.3 | 3 | 5.4 | even | 2 | |||
8450.2.a.bx.1.3 | 3 | 65.64 | even | 2 |