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 | 1.2 | ||
Root | \(1.80194\) 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 | ||||||||
\(7\) | −1.35690 | −0.512858 | −0.256429 | − | 0.966563i | \(-0.582546\pi\) | ||||
−0.256429 | + | 0.966563i | \(0.582546\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.19806 | −0.964252 | −0.482126 | − | 0.876102i | \(-0.660135\pi\) | ||||
−0.482126 | + | 0.876102i | \(0.660135\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35690 | −0.362646 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.04892 | −0.496935 | −0.248468 | − | 0.968640i | \(-0.579927\pi\) | ||||
−0.248468 | + | 0.968640i | \(0.579927\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.34481 | 1.22618 | 0.613092 | − | 0.790011i | \(-0.289925\pi\) | ||||
0.613092 | + | 0.790011i | \(0.289925\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.35690 | 0.296099 | ||||||||
\(22\) | −3.19806 | −0.681829 | ||||||||
\(23\) | −8.32304 | −1.73547 | −0.867737 | − | 0.497023i | \(-0.834426\pi\) | ||||
−0.867737 | + | 0.497023i | \(0.834426\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.35690 | −0.256429 | ||||||||
\(29\) | 8.07069 | 1.49869 | 0.749345 | − | 0.662180i | \(-0.230369\pi\) | ||||
0.749345 | + | 0.662180i | \(0.230369\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 0.185981 | 0.0334031 | 0.0167016 | − | 0.999861i | \(-0.494683\pi\) | ||||
0.0167016 | + | 0.999861i | \(0.494683\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.19806 | 0.556711 | ||||||||
\(34\) | −2.04892 | −0.351386 | ||||||||
\(35\) | −1.35690 | −0.229357 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.46681 | 0.405541 | 0.202771 | − | 0.979226i | \(-0.435005\pi\) | ||||
0.202771 | + | 0.979226i | \(0.435005\pi\) | |||||||
\(38\) | 5.34481 | 0.867043 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −12.2349 | −1.91077 | −0.955385 | − | 0.295363i | \(-0.904559\pi\) | ||||
−0.955385 | + | 0.295363i | \(0.904559\pi\) | |||||||
\(42\) | 1.35690 | 0.209374 | ||||||||
\(43\) | −2.91185 | −0.444054 | −0.222027 | − | 0.975041i | \(-0.571267\pi\) | ||||
−0.222027 | + | 0.975041i | \(0.571267\pi\) | |||||||
\(44\) | −3.19806 | −0.482126 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −8.32304 | −1.22717 | ||||||||
\(47\) | −13.0978 | −1.91052 | −0.955258 | − | 0.295775i | \(-0.904422\pi\) | ||||
−0.955258 | + | 0.295775i | \(0.904422\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.15883 | −0.736976 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.04892 | 0.286906 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.74094 | 0.788579 | 0.394289 | − | 0.918986i | \(-0.370991\pi\) | ||||
0.394289 | + | 0.918986i | \(0.370991\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.19806 | −0.431227 | ||||||||
\(56\) | −1.35690 | −0.181323 | ||||||||
\(57\) | −5.34481 | −0.707938 | ||||||||
\(58\) | 8.07069 | 1.05973 | ||||||||
\(59\) | 1.62565 | 0.211641 | 0.105821 | − | 0.994385i | \(-0.466253\pi\) | ||||
0.105821 | + | 0.994385i | \(0.466253\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.28382 | 0.676523 | 0.338262 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338262 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(62\) | 0.185981 | 0.0236196 | ||||||||
\(63\) | −1.35690 | −0.170953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.19806 | 0.393654 | ||||||||
\(67\) | −1.55496 | −0.189968 | −0.0949842 | − | 0.995479i | \(-0.530280\pi\) | ||||
−0.0949842 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(68\) | −2.04892 | −0.248468 | ||||||||
\(69\) | 8.32304 | 1.00198 | ||||||||
\(70\) | −1.35690 | −0.162180 | ||||||||
\(71\) | 2.32304 | 0.275695 | 0.137847 | − | 0.990453i | \(-0.455982\pi\) | ||||
0.137847 | + | 0.990453i | \(0.455982\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.11529 | 0.598700 | 0.299350 | − | 0.954143i | \(-0.403230\pi\) | ||||
0.299350 | + | 0.954143i | \(0.403230\pi\) | |||||||
\(74\) | 2.46681 | 0.286761 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 5.34481 | 0.613092 | ||||||||
\(77\) | 4.33944 | 0.494525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.42327 | −0.160131 | −0.0800653 | − | 0.996790i | \(-0.525513\pi\) | ||||
−0.0800653 | + | 0.996790i | \(0.525513\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.2349 | −1.35112 | ||||||||
\(83\) | −11.1196 | −1.22054 | −0.610268 | − | 0.792195i | \(-0.708938\pi\) | ||||
−0.610268 | + | 0.792195i | \(0.708938\pi\) | |||||||
\(84\) | 1.35690 | 0.148049 | ||||||||
\(85\) | −2.04892 | −0.222236 | ||||||||
\(86\) | −2.91185 | −0.313993 | ||||||||
\(87\) | −8.07069 | −0.865269 | ||||||||
\(88\) | −3.19806 | −0.340915 | ||||||||
\(89\) | −3.37867 | −0.358138 | −0.179069 | − | 0.983837i | \(-0.557309\pi\) | ||||
−0.179069 | + | 0.983837i | \(0.557309\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.32304 | −0.867737 | ||||||||
\(93\) | −0.185981 | −0.0192853 | ||||||||
\(94\) | −13.0978 | −1.35094 | ||||||||
\(95\) | 5.34481 | 0.548366 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.74094 | 0.481369 | 0.240685 | − | 0.970603i | \(-0.422628\pi\) | ||||
0.240685 | + | 0.970603i | \(0.422628\pi\) | |||||||
\(98\) | −5.15883 | −0.521121 | ||||||||
\(99\) | −3.19806 | −0.321417 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.5918 | −1.25293 | −0.626465 | − | 0.779449i | \(-0.715499\pi\) | ||||
−0.626465 | + | 0.779449i | \(0.715499\pi\) | |||||||
\(102\) | 2.04892 | 0.202873 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35690 | 0.132419 | ||||||||
\(106\) | 5.74094 | 0.557609 | ||||||||
\(107\) | −5.08815 | −0.491890 | −0.245945 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245945 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.43296 | −0.616166 | −0.308083 | − | 0.951360i | \(-0.599687\pi\) | ||||
−0.308083 | + | 0.951360i | \(0.599687\pi\) | |||||||
\(110\) | −3.19806 | −0.304923 | ||||||||
\(111\) | −2.46681 | −0.234139 | ||||||||
\(112\) | −1.35690 | −0.128215 | ||||||||
\(113\) | −18.6571 | −1.75511 | −0.877556 | − | 0.479473i | \(-0.840828\pi\) | ||||
−0.877556 | + | 0.479473i | \(0.840828\pi\) | |||||||
\(114\) | −5.34481 | −0.500588 | ||||||||
\(115\) | −8.32304 | −0.776128 | ||||||||
\(116\) | 8.07069 | 0.749345 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.62565 | 0.149653 | ||||||||
\(119\) | 2.78017 | 0.254858 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −0.772398 | −0.0702180 | ||||||||
\(122\) | 5.28382 | 0.478374 | ||||||||
\(123\) | 12.2349 | 1.10318 | ||||||||
\(124\) | 0.185981 | 0.0167016 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.35690 | −0.120882 | ||||||||
\(127\) | −16.3763 | −1.45316 | −0.726580 | − | 0.687082i | \(-0.758891\pi\) | ||||
−0.726580 | + | 0.687082i | \(0.758891\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.91185 | 0.256374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00969 | 0.262958 | 0.131479 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131479 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(132\) | 3.19806 | 0.278356 | ||||||||
\(133\) | −7.25236 | −0.628859 | ||||||||
\(134\) | −1.55496 | −0.134328 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −2.04892 | −0.175693 | ||||||||
\(137\) | −20.2892 | −1.73342 | −0.866711 | − | 0.498810i | \(-0.833771\pi\) | ||||
−0.866711 | + | 0.498810i | \(0.833771\pi\) | |||||||
\(138\) | 8.32304 | 0.708505 | ||||||||
\(139\) | −0.153457 | −0.0130160 | −0.00650802 | − | 0.999979i | \(-0.502072\pi\) | ||||
−0.00650802 | + | 0.999979i | \(0.502072\pi\) | |||||||
\(140\) | −1.35690 | −0.114679 | ||||||||
\(141\) | 13.0978 | 1.10304 | ||||||||
\(142\) | 2.32304 | 0.194946 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.07069 | 0.670234 | ||||||||
\(146\) | 5.11529 | 0.423345 | ||||||||
\(147\) | 5.15883 | 0.425493 | ||||||||
\(148\) | 2.46681 | 0.202771 | ||||||||
\(149\) | 10.7724 | 0.882509 | 0.441255 | − | 0.897382i | \(-0.354534\pi\) | ||||
0.441255 | + | 0.897382i | \(0.354534\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −17.3817 | −1.41450 | −0.707249 | − | 0.706964i | \(-0.750064\pi\) | ||||
−0.707249 | + | 0.706964i | \(0.750064\pi\) | |||||||
\(152\) | 5.34481 | 0.433522 | ||||||||
\(153\) | −2.04892 | −0.165645 | ||||||||
\(154\) | 4.33944 | 0.349682 | ||||||||
\(155\) | 0.185981 | 0.0149383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5429 | 1.24046 | 0.620228 | − | 0.784421i | \(-0.287040\pi\) | ||||
0.620228 | + | 0.784421i | \(0.287040\pi\) | |||||||
\(158\) | −1.42327 | −0.113229 | ||||||||
\(159\) | −5.74094 | −0.455286 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.2935 | 0.890053 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.00239 | 0.156840 | 0.0784198 | − | 0.996920i | \(-0.475013\pi\) | ||||
0.0784198 | + | 0.996920i | \(0.475013\pi\) | |||||||
\(164\) | −12.2349 | −0.955385 | ||||||||
\(165\) | 3.19806 | 0.248969 | ||||||||
\(166\) | −11.1196 | −0.863049 | ||||||||
\(167\) | 8.24027 | 0.637652 | 0.318826 | − | 0.947813i | \(-0.396712\pi\) | ||||
0.318826 | + | 0.947813i | \(0.396712\pi\) | |||||||
\(168\) | 1.35690 | 0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.04892 | −0.157145 | ||||||||
\(171\) | 5.34481 | 0.408728 | ||||||||
\(172\) | −2.91185 | −0.222027 | ||||||||
\(173\) | 12.7463 | 0.969084 | 0.484542 | − | 0.874768i | \(-0.338986\pi\) | ||||
0.484542 | + | 0.874768i | \(0.338986\pi\) | |||||||
\(174\) | −8.07069 | −0.611837 | ||||||||
\(175\) | −1.35690 | −0.102572 | ||||||||
\(176\) | −3.19806 | −0.241063 | ||||||||
\(177\) | −1.62565 | −0.122191 | ||||||||
\(178\) | −3.37867 | −0.253242 | ||||||||
\(179\) | 16.0422 | 1.19905 | 0.599526 | − | 0.800356i | \(-0.295356\pi\) | ||||
0.599526 | + | 0.800356i | \(0.295356\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 3.85086 | 0.286232 | 0.143116 | − | 0.989706i | \(-0.454288\pi\) | ||||
0.143116 | + | 0.989706i | \(0.454288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.28382 | −0.390591 | ||||||||
\(184\) | −8.32304 | −0.613583 | ||||||||
\(185\) | 2.46681 | 0.181364 | ||||||||
\(186\) | −0.185981 | −0.0136368 | ||||||||
\(187\) | 6.55257 | 0.479171 | ||||||||
\(188\) | −13.0978 | −0.955258 | ||||||||
\(189\) | 1.35690 | 0.0986997 | ||||||||
\(190\) | 5.34481 | 0.387754 | ||||||||
\(191\) | 11.8280 | 0.855845 | 0.427923 | − | 0.903815i | \(-0.359246\pi\) | ||||
0.427923 | + | 0.903815i | \(0.359246\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.872625 | −0.0628129 | −0.0314065 | − | 0.999507i | \(-0.509999\pi\) | ||||
−0.0314065 | + | 0.999507i | \(0.509999\pi\) | |||||||
\(194\) | 4.74094 | 0.340380 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.15883 | −0.368488 | ||||||||
\(197\) | −10.6213 | −0.756739 | −0.378369 | − | 0.925655i | \(-0.623515\pi\) | ||||
−0.378369 | + | 0.925655i | \(0.623515\pi\) | |||||||
\(198\) | −3.19806 | −0.227276 | ||||||||
\(199\) | 12.3424 | 0.874931 | 0.437466 | − | 0.899235i | \(-0.355876\pi\) | ||||
0.437466 | + | 0.899235i | \(0.355876\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 1.55496 | 0.109678 | ||||||||
\(202\) | −12.5918 | −0.885956 | ||||||||
\(203\) | −10.9511 | −0.768615 | ||||||||
\(204\) | 2.04892 | 0.143453 | ||||||||
\(205\) | −12.2349 | −0.854522 | ||||||||
\(206\) | −9.00000 | −0.627060 | ||||||||
\(207\) | −8.32304 | −0.578492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.0930 | −1.18235 | ||||||||
\(210\) | 1.35690 | 0.0936347 | ||||||||
\(211\) | 6.75733 | 0.465194 | 0.232597 | − | 0.972573i | \(-0.425278\pi\) | ||||
0.232597 | + | 0.972573i | \(0.425278\pi\) | |||||||
\(212\) | 5.74094 | 0.394289 | ||||||||
\(213\) | −2.32304 | −0.159172 | ||||||||
\(214\) | −5.08815 | −0.347819 | ||||||||
\(215\) | −2.91185 | −0.198587 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.252356 | −0.0171311 | ||||||||
\(218\) | −6.43296 | −0.435695 | ||||||||
\(219\) | −5.11529 | −0.345659 | ||||||||
\(220\) | −3.19806 | −0.215613 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.46681 | −0.165562 | ||||||||
\(223\) | −21.5972 | −1.44625 | −0.723127 | − | 0.690715i | \(-0.757296\pi\) | ||||
−0.723127 | + | 0.690715i | \(0.757296\pi\) | |||||||
\(224\) | −1.35690 | −0.0906614 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −18.6571 | −1.24105 | ||||||||
\(227\) | −10.2862 | −0.682720 | −0.341360 | − | 0.939933i | \(-0.610887\pi\) | ||||
−0.341360 | + | 0.939933i | \(0.610887\pi\) | |||||||
\(228\) | −5.34481 | −0.353969 | ||||||||
\(229\) | −4.25906 | −0.281447 | −0.140723 | − | 0.990049i | \(-0.544943\pi\) | ||||
−0.140723 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(230\) | −8.32304 | −0.548805 | ||||||||
\(231\) | −4.33944 | −0.285514 | ||||||||
\(232\) | 8.07069 | 0.529867 | ||||||||
\(233\) | 19.5133 | 1.27836 | 0.639181 | − | 0.769057i | \(-0.279274\pi\) | ||||
0.639181 | + | 0.769057i | \(0.279274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0978 | −0.854409 | ||||||||
\(236\) | 1.62565 | 0.105821 | ||||||||
\(237\) | 1.42327 | 0.0924514 | ||||||||
\(238\) | 2.78017 | 0.180211 | ||||||||
\(239\) | 7.16315 | 0.463345 | 0.231673 | − | 0.972794i | \(-0.425580\pi\) | ||||
0.231673 | + | 0.972794i | \(0.425580\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −17.9584 | −1.15680 | −0.578400 | − | 0.815753i | \(-0.696323\pi\) | ||||
−0.578400 | + | 0.815753i | \(0.696323\pi\) | |||||||
\(242\) | −0.772398 | −0.0496516 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.28382 | 0.338262 | ||||||||
\(245\) | −5.15883 | −0.329586 | ||||||||
\(246\) | 12.2349 | 0.780069 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.185981 | 0.0118098 | ||||||||
\(249\) | 11.1196 | 0.704676 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.68425 | −0.421906 | −0.210953 | − | 0.977496i | \(-0.567657\pi\) | ||||
−0.210953 | + | 0.977496i | \(0.567657\pi\) | |||||||
\(252\) | −1.35690 | −0.0854764 | ||||||||
\(253\) | 26.6176 | 1.67343 | ||||||||
\(254\) | −16.3763 | −1.02754 | ||||||||
\(255\) | 2.04892 | 0.128308 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.91484 | 0.618471 | 0.309235 | − | 0.950986i | \(-0.399927\pi\) | ||||
0.309235 | + | 0.950986i | \(0.399927\pi\) | |||||||
\(258\) | 2.91185 | 0.181284 | ||||||||
\(259\) | −3.34721 | −0.207985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.07069 | 0.499563 | ||||||||
\(262\) | 3.00969 | 0.185939 | ||||||||
\(263\) | 13.8509 | 0.854080 | 0.427040 | − | 0.904233i | \(-0.359556\pi\) | ||||
0.427040 | + | 0.904233i | \(0.359556\pi\) | |||||||
\(264\) | 3.19806 | 0.196827 | ||||||||
\(265\) | 5.74094 | 0.352663 | ||||||||
\(266\) | −7.25236 | −0.444671 | ||||||||
\(267\) | 3.37867 | 0.206771 | ||||||||
\(268\) | −1.55496 | −0.0949842 | ||||||||
\(269\) | −17.8756 | −1.08990 | −0.544948 | − | 0.838470i | \(-0.683450\pi\) | ||||
−0.544948 | + | 0.838470i | \(0.683450\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −31.2083 | −1.89577 | −0.947886 | − | 0.318610i | \(-0.896784\pi\) | ||||
−0.947886 | + | 0.318610i | \(0.896784\pi\) | |||||||
\(272\) | −2.04892 | −0.124234 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2892 | −1.22571 | ||||||||
\(275\) | −3.19806 | −0.192850 | ||||||||
\(276\) | 8.32304 | 0.500988 | ||||||||
\(277\) | 22.9245 | 1.37740 | 0.688701 | − | 0.725046i | \(-0.258181\pi\) | ||||
0.688701 | + | 0.725046i | \(0.258181\pi\) | |||||||
\(278\) | −0.153457 | −0.00920373 | ||||||||
\(279\) | 0.185981 | 0.0111344 | ||||||||
\(280\) | −1.35690 | −0.0810900 | ||||||||
\(281\) | −28.0683 | −1.67441 | −0.837207 | − | 0.546886i | \(-0.815813\pi\) | ||||
−0.837207 | + | 0.546886i | \(0.815813\pi\) | |||||||
\(282\) | 13.0978 | 0.779965 | ||||||||
\(283\) | −24.8364 | −1.47637 | −0.738185 | − | 0.674599i | \(-0.764317\pi\) | ||||
−0.738185 | + | 0.674599i | \(0.764317\pi\) | |||||||
\(284\) | 2.32304 | 0.137847 | ||||||||
\(285\) | −5.34481 | −0.316599 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.6015 | 0.979955 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −12.8019 | −0.753055 | ||||||||
\(290\) | 8.07069 | 0.473927 | ||||||||
\(291\) | −4.74094 | −0.277919 | ||||||||
\(292\) | 5.11529 | 0.299350 | ||||||||
\(293\) | 28.4349 | 1.66118 | 0.830592 | − | 0.556882i | \(-0.188002\pi\) | ||||
0.830592 | + | 0.556882i | \(0.188002\pi\) | |||||||
\(294\) | 5.15883 | 0.300869 | ||||||||
\(295\) | 1.62565 | 0.0946488 | ||||||||
\(296\) | 2.46681 | 0.143381 | ||||||||
\(297\) | 3.19806 | 0.185570 | ||||||||
\(298\) | 10.7724 | 0.624028 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 3.95108 | 0.227737 | ||||||||
\(302\) | −17.3817 | −1.00020 | ||||||||
\(303\) | 12.5918 | 0.723380 | ||||||||
\(304\) | 5.34481 | 0.306546 | ||||||||
\(305\) | 5.28382 | 0.302550 | ||||||||
\(306\) | −2.04892 | −0.117129 | ||||||||
\(307\) | 10.1347 | 0.578416 | 0.289208 | − | 0.957266i | \(-0.406608\pi\) | ||||
0.289208 | + | 0.957266i | \(0.406608\pi\) | |||||||
\(308\) | 4.33944 | 0.247262 | ||||||||
\(309\) | 9.00000 | 0.511992 | ||||||||
\(310\) | 0.185981 | 0.0105630 | ||||||||
\(311\) | 20.0218 | 1.13533 | 0.567665 | − | 0.823259i | \(-0.307847\pi\) | ||||
0.567665 | + | 0.823259i | \(0.307847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.63640 | 0.488158 | 0.244079 | − | 0.969755i | \(-0.421514\pi\) | ||||
0.244079 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(314\) | 15.5429 | 0.877135 | ||||||||
\(315\) | −1.35690 | −0.0764524 | ||||||||
\(316\) | −1.42327 | −0.0800653 | ||||||||
\(317\) | −17.6256 | −0.989955 | −0.494977 | − | 0.868906i | \(-0.664824\pi\) | ||||
−0.494977 | + | 0.868906i | \(0.664824\pi\) | |||||||
\(318\) | −5.74094 | −0.321936 | ||||||||
\(319\) | −25.8106 | −1.44511 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 5.08815 | 0.283993 | ||||||||
\(322\) | 11.2935 | 0.629362 | ||||||||
\(323\) | −10.9511 | −0.609335 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00239 | 0.110902 | ||||||||
\(327\) | 6.43296 | 0.355744 | ||||||||
\(328\) | −12.2349 | −0.675559 | ||||||||
\(329\) | 17.7724 | 0.979824 | ||||||||
\(330\) | 3.19806 | 0.176048 | ||||||||
\(331\) | 31.5163 | 1.73229 | 0.866147 | − | 0.499790i | \(-0.166589\pi\) | ||||
0.866147 | + | 0.499790i | \(0.166589\pi\) | |||||||
\(332\) | −11.1196 | −0.610268 | ||||||||
\(333\) | 2.46681 | 0.135180 | ||||||||
\(334\) | 8.24027 | 0.450888 | ||||||||
\(335\) | −1.55496 | −0.0849564 | ||||||||
\(336\) | 1.35690 | 0.0740247 | ||||||||
\(337\) | −11.8116 | −0.643420 | −0.321710 | − | 0.946838i | \(-0.604258\pi\) | ||||
−0.321710 | + | 0.946838i | \(0.604258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6571 | 1.01331 | ||||||||
\(340\) | −2.04892 | −0.111118 | ||||||||
\(341\) | −0.594778 | −0.0322090 | ||||||||
\(342\) | 5.34481 | 0.289014 | ||||||||
\(343\) | 16.4983 | 0.890823 | ||||||||
\(344\) | −2.91185 | −0.156997 | ||||||||
\(345\) | 8.32304 | 0.448098 | ||||||||
\(346\) | 12.7463 | 0.685246 | ||||||||
\(347\) | −17.4101 | −0.934624 | −0.467312 | − | 0.884092i | \(-0.654778\pi\) | ||||
−0.467312 | + | 0.884092i | \(0.654778\pi\) | |||||||
\(348\) | −8.07069 | −0.432634 | ||||||||
\(349\) | −18.6799 | −0.999914 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(350\) | −1.35690 | −0.0725291 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.19806 | −0.170457 | ||||||||
\(353\) | −25.3991 | −1.35186 | −0.675929 | − | 0.736967i | \(-0.736257\pi\) | ||||
−0.675929 | + | 0.736967i | \(0.736257\pi\) | |||||||
\(354\) | −1.62565 | −0.0864021 | ||||||||
\(355\) | 2.32304 | 0.123294 | ||||||||
\(356\) | −3.37867 | −0.179069 | ||||||||
\(357\) | −2.78017 | −0.147142 | ||||||||
\(358\) | 16.0422 | 0.847857 | ||||||||
\(359\) | −34.0103 | −1.79499 | −0.897497 | − | 0.441021i | \(-0.854617\pi\) | ||||
−0.897497 | + | 0.441021i | \(0.854617\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 9.56704 | 0.503528 | ||||||||
\(362\) | 3.85086 | 0.202396 | ||||||||
\(363\) | 0.772398 | 0.0405404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.11529 | 0.267747 | ||||||||
\(366\) | −5.28382 | −0.276189 | ||||||||
\(367\) | −25.6437 | −1.33859 | −0.669295 | − | 0.742997i | \(-0.733404\pi\) | ||||
−0.669295 | + | 0.742997i | \(0.733404\pi\) | |||||||
\(368\) | −8.32304 | −0.433869 | ||||||||
\(369\) | −12.2349 | −0.636923 | ||||||||
\(370\) | 2.46681 | 0.128243 | ||||||||
\(371\) | −7.78986 | −0.404429 | ||||||||
\(372\) | −0.185981 | −0.00964265 | ||||||||
\(373\) | −16.3612 | −0.847151 | −0.423576 | − | 0.905861i | \(-0.639225\pi\) | ||||
−0.423576 | + | 0.905861i | \(0.639225\pi\) | |||||||
\(374\) | 6.55257 | 0.338825 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −13.0978 | −0.675469 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.35690 | 0.0697912 | ||||||||
\(379\) | −22.8823 | −1.17539 | −0.587693 | − | 0.809084i | \(-0.699964\pi\) | ||||
−0.587693 | + | 0.809084i | \(0.699964\pi\) | |||||||
\(380\) | 5.34481 | 0.274183 | ||||||||
\(381\) | 16.3763 | 0.838982 | ||||||||
\(382\) | 11.8280 | 0.605174 | ||||||||
\(383\) | −11.9191 | −0.609040 | −0.304520 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.33944 | 0.221158 | ||||||||
\(386\) | −0.872625 | −0.0444155 | ||||||||
\(387\) | −2.91185 | −0.148018 | ||||||||
\(388\) | 4.74094 | 0.240685 | ||||||||
\(389\) | 8.07606 | 0.409473 | 0.204736 | − | 0.978817i | \(-0.434366\pi\) | ||||
0.204736 | + | 0.978817i | \(0.434366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.0532 | 0.862419 | ||||||||
\(392\) | −5.15883 | −0.260560 | ||||||||
\(393\) | −3.00969 | −0.151819 | ||||||||
\(394\) | −10.6213 | −0.535095 | ||||||||
\(395\) | −1.42327 | −0.0716126 | ||||||||
\(396\) | −3.19806 | −0.160709 | ||||||||
\(397\) | 20.5230 | 1.03002 | 0.515011 | − | 0.857184i | \(-0.327788\pi\) | ||||
0.515011 | + | 0.857184i | \(0.327788\pi\) | |||||||
\(398\) | 12.3424 | 0.618670 | ||||||||
\(399\) | 7.25236 | 0.363072 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 18.3274 | 0.915224 | 0.457612 | − | 0.889152i | \(-0.348705\pi\) | ||||
0.457612 | + | 0.889152i | \(0.348705\pi\) | |||||||
\(402\) | 1.55496 | 0.0775543 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.5918 | −0.626465 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.9511 | −0.543493 | ||||||||
\(407\) | −7.88902 | −0.391044 | ||||||||
\(408\) | 2.04892 | 0.101437 | ||||||||
\(409\) | −9.00000 | −0.445021 | −0.222511 | − | 0.974930i | \(-0.571425\pi\) | ||||
−0.222511 | + | 0.974930i | \(0.571425\pi\) | |||||||
\(410\) | −12.2349 | −0.604239 | ||||||||
\(411\) | 20.2892 | 1.00079 | ||||||||
\(412\) | −9.00000 | −0.443398 | ||||||||
\(413\) | −2.20583 | −0.108542 | ||||||||
\(414\) | −8.32304 | −0.409055 | ||||||||
\(415\) | −11.1196 | −0.545840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.153457 | 0.00751481 | ||||||||
\(418\) | −17.0930 | −0.836048 | ||||||||
\(419\) | −14.4185 | −0.704389 | −0.352195 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352195 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(420\) | 1.35690 | 0.0662097 | ||||||||
\(421\) | 19.9801 | 0.973773 | 0.486886 | − | 0.873465i | \(-0.338133\pi\) | ||||
0.486886 | + | 0.873465i | \(0.338133\pi\) | |||||||
\(422\) | 6.75733 | 0.328942 | ||||||||
\(423\) | −13.0978 | −0.636839 | ||||||||
\(424\) | 5.74094 | 0.278805 | ||||||||
\(425\) | −2.04892 | −0.0993871 | ||||||||
\(426\) | −2.32304 | −0.112552 | ||||||||
\(427\) | −7.16959 | −0.346961 | ||||||||
\(428\) | −5.08815 | −0.245945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.91185 | −0.140422 | ||||||||
\(431\) | 21.1812 | 1.02026 | 0.510131 | − | 0.860097i | \(-0.329597\pi\) | ||||
0.510131 | + | 0.860097i | \(0.329597\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 31.0291 | 1.49116 | 0.745581 | − | 0.666415i | \(-0.232172\pi\) | ||||
0.745581 | + | 0.666415i | \(0.232172\pi\) | |||||||
\(434\) | −0.252356 | −0.0121135 | ||||||||
\(435\) | −8.07069 | −0.386960 | ||||||||
\(436\) | −6.43296 | −0.308083 | ||||||||
\(437\) | −44.4851 | −2.12801 | ||||||||
\(438\) | −5.11529 | −0.244418 | ||||||||
\(439\) | 7.33406 | 0.350036 | 0.175018 | − | 0.984565i | \(-0.444002\pi\) | ||||
0.175018 | + | 0.984565i | \(0.444002\pi\) | |||||||
\(440\) | −3.19806 | −0.152462 | ||||||||
\(441\) | −5.15883 | −0.245659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.1360 | −0.861667 | −0.430834 | − | 0.902431i | \(-0.641780\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641780\pi\) | |||||||
\(444\) | −2.46681 | −0.117070 | ||||||||
\(445\) | −3.37867 | −0.160164 | ||||||||
\(446\) | −21.5972 | −1.02266 | ||||||||
\(447\) | −10.7724 | −0.509517 | ||||||||
\(448\) | −1.35690 | −0.0641073 | ||||||||
\(449\) | −4.55496 | −0.214962 | −0.107481 | − | 0.994207i | \(-0.534278\pi\) | ||||
−0.107481 | + | 0.994207i | \(0.534278\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 39.1280 | 1.84246 | ||||||||
\(452\) | −18.6571 | −0.877556 | ||||||||
\(453\) | 17.3817 | 0.816661 | ||||||||
\(454\) | −10.2862 | −0.482756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.34481 | −0.250294 | ||||||||
\(457\) | 9.98121 | 0.466901 | 0.233451 | − | 0.972369i | \(-0.424998\pi\) | ||||
0.233451 | + | 0.972369i | \(0.424998\pi\) | |||||||
\(458\) | −4.25906 | −0.199013 | ||||||||
\(459\) | 2.04892 | 0.0956353 | ||||||||
\(460\) | −8.32304 | −0.388064 | ||||||||
\(461\) | −16.1672 | −0.752981 | −0.376491 | − | 0.926420i | \(-0.622869\pi\) | ||||
−0.376491 | + | 0.926420i | \(0.622869\pi\) | |||||||
\(462\) | −4.33944 | −0.201889 | ||||||||
\(463\) | 3.88902 | 0.180738 | 0.0903690 | − | 0.995908i | \(-0.471195\pi\) | ||||
0.0903690 | + | 0.995908i | \(0.471195\pi\) | |||||||
\(464\) | 8.07069 | 0.374672 | ||||||||
\(465\) | −0.185981 | −0.00862465 | ||||||||
\(466\) | 19.5133 | 0.903938 | ||||||||
\(467\) | −0.872625 | −0.0403803 | −0.0201901 | − | 0.999796i | \(-0.506427\pi\) | ||||
−0.0201901 | + | 0.999796i | \(0.506427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.10992 | 0.0974269 | ||||||||
\(470\) | −13.0978 | −0.604158 | ||||||||
\(471\) | −15.5429 | −0.716178 | ||||||||
\(472\) | 1.62565 | 0.0748264 | ||||||||
\(473\) | 9.31229 | 0.428180 | ||||||||
\(474\) | 1.42327 | 0.0653730 | ||||||||
\(475\) | 5.34481 | 0.245237 | ||||||||
\(476\) | 2.78017 | 0.127429 | ||||||||
\(477\) | 5.74094 | 0.262860 | ||||||||
\(478\) | 7.16315 | 0.327635 | ||||||||
\(479\) | −31.6305 | −1.44524 | −0.722618 | − | 0.691247i | \(-0.757062\pi\) | ||||
−0.722618 | + | 0.691247i | \(0.757062\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.9584 | −0.817982 | ||||||||
\(483\) | −11.2935 | −0.513872 | ||||||||
\(484\) | −0.772398 | −0.0351090 | ||||||||
\(485\) | 4.74094 | 0.215275 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 21.7748 | 0.986710 | 0.493355 | − | 0.869828i | \(-0.335770\pi\) | ||||
0.493355 | + | 0.869828i | \(0.335770\pi\) | |||||||
\(488\) | 5.28382 | 0.239187 | ||||||||
\(489\) | −2.00239 | −0.0905513 | ||||||||
\(490\) | −5.15883 | −0.233052 | ||||||||
\(491\) | 42.9590 | 1.93871 | 0.969356 | − | 0.245662i | \(-0.0790053\pi\) | ||||
0.969356 | + | 0.245662i | \(0.0790053\pi\) | |||||||
\(492\) | 12.2349 | 0.551592 | ||||||||
\(493\) | −16.5362 | −0.744752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.19806 | −0.143742 | ||||||||
\(496\) | 0.185981 | 0.00835078 | ||||||||
\(497\) | −3.15213 | −0.141392 | ||||||||
\(498\) | 11.1196 | 0.498281 | ||||||||
\(499\) | −36.0978 | −1.61596 | −0.807981 | − | 0.589209i | \(-0.799439\pi\) | ||||
−0.807981 | + | 0.589209i | \(0.799439\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.24027 | −0.368148 | ||||||||
\(502\) | −6.68425 | −0.298333 | ||||||||
\(503\) | −21.4534 | −0.956560 | −0.478280 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478280 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(504\) | −1.35690 | −0.0604409 | ||||||||
\(505\) | −12.5918 | −0.560327 | ||||||||
\(506\) | 26.6176 | 1.18330 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.3763 | −0.726580 | ||||||||
\(509\) | 0.545860 | 0.0241948 | 0.0120974 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120974 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(510\) | 2.04892 | 0.0907276 | ||||||||
\(511\) | −6.94092 | −0.307048 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.34481 | −0.235979 | ||||||||
\(514\) | 9.91484 | 0.437325 | ||||||||
\(515\) | −9.00000 | −0.396587 | ||||||||
\(516\) | 2.91185 | 0.128187 | ||||||||
\(517\) | 41.8877 | 1.84222 | ||||||||
\(518\) | −3.34721 | −0.147068 | ||||||||
\(519\) | −12.7463 | −0.559501 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6136 | 1.29739 | 0.648697 | − | 0.761047i | \(-0.275314\pi\) | ||||
0.648697 | + | 0.761047i | \(0.275314\pi\) | |||||||
\(522\) | 8.07069 | 0.353244 | ||||||||
\(523\) | 44.4543 | 1.94385 | 0.971924 | − | 0.235293i | \(-0.0756050\pi\) | ||||
0.971924 | + | 0.235293i | \(0.0756050\pi\) | |||||||
\(524\) | 3.00969 | 0.131479 | ||||||||
\(525\) | 1.35690 | 0.0592198 | ||||||||
\(526\) | 13.8509 | 0.603926 | ||||||||
\(527\) | −0.381059 | −0.0165992 | ||||||||
\(528\) | 3.19806 | 0.139178 | ||||||||
\(529\) | 46.2731 | 2.01187 | ||||||||
\(530\) | 5.74094 | 0.249370 | ||||||||
\(531\) | 1.62565 | 0.0705470 | ||||||||
\(532\) | −7.25236 | −0.314430 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.37867 | 0.146209 | ||||||||
\(535\) | −5.08815 | −0.219980 | ||||||||
\(536\) | −1.55496 | −0.0671640 | ||||||||
\(537\) | −16.0422 | −0.692273 | ||||||||
\(538\) | −17.8756 | −0.770672 | ||||||||
\(539\) | 16.4983 | 0.710631 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 18.7651 | 0.806775 | 0.403387 | − | 0.915029i | \(-0.367833\pi\) | ||||
0.403387 | + | 0.915029i | \(0.367833\pi\) | |||||||
\(542\) | −31.2083 | −1.34051 | ||||||||
\(543\) | −3.85086 | −0.165256 | ||||||||
\(544\) | −2.04892 | −0.0878466 | ||||||||
\(545\) | −6.43296 | −0.275558 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0116 | 1.36872 | 0.684359 | − | 0.729145i | \(-0.260082\pi\) | ||||
0.684359 | + | 0.729145i | \(0.260082\pi\) | |||||||
\(548\) | −20.2892 | −0.866711 | ||||||||
\(549\) | 5.28382 | 0.225508 | ||||||||
\(550\) | −3.19806 | −0.136366 | ||||||||
\(551\) | 43.1363 | 1.83767 | ||||||||
\(552\) | 8.32304 | 0.354252 | ||||||||
\(553\) | 1.93123 | 0.0821243 | ||||||||
\(554\) | 22.9245 | 0.973970 | ||||||||
\(555\) | −2.46681 | −0.104710 | ||||||||
\(556\) | −0.153457 | −0.00650802 | ||||||||
\(557\) | −8.23490 | −0.348924 | −0.174462 | − | 0.984664i | \(-0.555819\pi\) | ||||
−0.174462 | + | 0.984664i | \(0.555819\pi\) | |||||||
\(558\) | 0.185981 | 0.00787319 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.35690 | −0.0573393 | ||||||||
\(561\) | −6.55257 | −0.276650 | ||||||||
\(562\) | −28.0683 | −1.18399 | ||||||||
\(563\) | −30.2295 | −1.27402 | −0.637011 | − | 0.770855i | \(-0.719830\pi\) | ||||
−0.637011 | + | 0.770855i | \(0.719830\pi\) | |||||||
\(564\) | 13.0978 | 0.551518 | ||||||||
\(565\) | −18.6571 | −0.784910 | ||||||||
\(566\) | −24.8364 | −1.04395 | ||||||||
\(567\) | −1.35690 | −0.0569843 | ||||||||
\(568\) | 2.32304 | 0.0974728 | ||||||||
\(569\) | 44.3110 | 1.85761 | 0.928806 | − | 0.370566i | \(-0.120836\pi\) | ||||
0.928806 | + | 0.370566i | \(0.120836\pi\) | |||||||
\(570\) | −5.34481 | −0.223870 | ||||||||
\(571\) | 34.4873 | 1.44325 | 0.721623 | − | 0.692286i | \(-0.243396\pi\) | ||||
0.721623 | + | 0.692286i | \(0.243396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8280 | −0.494123 | ||||||||
\(574\) | 16.6015 | 0.692932 | ||||||||
\(575\) | −8.32304 | −0.347095 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.1715 | −0.589968 | −0.294984 | − | 0.955502i | \(-0.595314\pi\) | ||||
−0.294984 | + | 0.955502i | \(0.595314\pi\) | |||||||
\(578\) | −12.8019 | −0.532490 | ||||||||
\(579\) | 0.872625 | 0.0362651 | ||||||||
\(580\) | 8.07069 | 0.335117 | ||||||||
\(581\) | 15.0881 | 0.625962 | ||||||||
\(582\) | −4.74094 | −0.196518 | ||||||||
\(583\) | −18.3599 | −0.760389 | ||||||||
\(584\) | 5.11529 | 0.211672 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.4349 | 1.17463 | ||||||||
\(587\) | −1.12737 | −0.0465317 | −0.0232659 | − | 0.999729i | \(-0.507406\pi\) | ||||
−0.0232659 | + | 0.999729i | \(0.507406\pi\) | |||||||
\(588\) | 5.15883 | 0.212747 | ||||||||
\(589\) | 0.994032 | 0.0409584 | ||||||||
\(590\) | 1.62565 | 0.0669268 | ||||||||
\(591\) | 10.6213 | 0.436903 | ||||||||
\(592\) | 2.46681 | 0.101385 | ||||||||
\(593\) | 18.3913 | 0.755242 | 0.377621 | − | 0.925960i | \(-0.376742\pi\) | ||||
0.377621 | + | 0.925960i | \(0.376742\pi\) | |||||||
\(594\) | 3.19806 | 0.131218 | ||||||||
\(595\) | 2.78017 | 0.113976 | ||||||||
\(596\) | 10.7724 | 0.441255 | ||||||||
\(597\) | −12.3424 | −0.505142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1226 | 0.536174 | 0.268087 | − | 0.963395i | \(-0.413608\pi\) | ||||
0.268087 | + | 0.963395i | \(0.413608\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 25.5754 | 1.04324 | 0.521621 | − | 0.853177i | \(-0.325327\pi\) | ||||
0.521621 | + | 0.853177i | \(0.325327\pi\) | |||||||
\(602\) | 3.95108 | 0.161034 | ||||||||
\(603\) | −1.55496 | −0.0633228 | ||||||||
\(604\) | −17.3817 | −0.707249 | ||||||||
\(605\) | −0.772398 | −0.0314024 | ||||||||
\(606\) | 12.5918 | 0.511507 | ||||||||
\(607\) | 44.4782 | 1.80531 | 0.902656 | − | 0.430362i | \(-0.141614\pi\) | ||||
0.902656 | + | 0.430362i | \(0.141614\pi\) | |||||||
\(608\) | 5.34481 | 0.216761 | ||||||||
\(609\) | 10.9511 | 0.443760 | ||||||||
\(610\) | 5.28382 | 0.213935 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.04892 | −0.0828226 | ||||||||
\(613\) | −21.7657 | −0.879108 | −0.439554 | − | 0.898216i | \(-0.644863\pi\) | ||||
−0.439554 | + | 0.898216i | \(0.644863\pi\) | |||||||
\(614\) | 10.1347 | 0.409002 | ||||||||
\(615\) | 12.2349 | 0.493359 | ||||||||
\(616\) | 4.33944 | 0.174841 | ||||||||
\(617\) | −17.3569 | −0.698762 | −0.349381 | − | 0.936981i | \(-0.613608\pi\) | ||||
−0.349381 | + | 0.936981i | \(0.613608\pi\) | |||||||
\(618\) | 9.00000 | 0.362033 | ||||||||
\(619\) | 36.8049 | 1.47931 | 0.739657 | − | 0.672984i | \(-0.234988\pi\) | ||||
0.739657 | + | 0.672984i | \(0.234988\pi\) | |||||||
\(620\) | 0.185981 | 0.00746916 | ||||||||
\(621\) | 8.32304 | 0.333992 | ||||||||
\(622\) | 20.0218 | 0.802800 | ||||||||
\(623\) | 4.58450 | 0.183674 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.63640 | 0.345180 | ||||||||
\(627\) | 17.0930 | 0.682631 | ||||||||
\(628\) | 15.5429 | 0.620228 | ||||||||
\(629\) | −5.05429 | −0.201528 | ||||||||
\(630\) | −1.35690 | −0.0540600 | ||||||||
\(631\) | 11.7554 | 0.467976 | 0.233988 | − | 0.972240i | \(-0.424822\pi\) | ||||
0.233988 | + | 0.972240i | \(0.424822\pi\) | |||||||
\(632\) | −1.42327 | −0.0566147 | ||||||||
\(633\) | −6.75733 | −0.268580 | ||||||||
\(634\) | −17.6256 | −0.700004 | ||||||||
\(635\) | −16.3763 | −0.649873 | ||||||||
\(636\) | −5.74094 | −0.227643 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.8106 | −1.02185 | ||||||||
\(639\) | 2.32304 | 0.0918982 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 33.0858 | 1.30681 | 0.653404 | − | 0.757009i | \(-0.273340\pi\) | ||||
0.653404 | + | 0.757009i | \(0.273340\pi\) | |||||||
\(642\) | 5.08815 | 0.200813 | ||||||||
\(643\) | −10.3461 | −0.408012 | −0.204006 | − | 0.978970i | \(-0.565396\pi\) | ||||
−0.204006 | + | 0.978970i | \(0.565396\pi\) | |||||||
\(644\) | 11.2935 | 0.445026 | ||||||||
\(645\) | 2.91185 | 0.114654 | ||||||||
\(646\) | −10.9511 | −0.430865 | ||||||||
\(647\) | −11.0030 | −0.432572 | −0.216286 | − | 0.976330i | \(-0.569394\pi\) | ||||
−0.216286 | + | 0.976330i | \(0.569394\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.19892 | −0.204075 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.252356 | 0.00989063 | ||||||||
\(652\) | 2.00239 | 0.0784198 | ||||||||
\(653\) | −30.8224 | −1.20617 | −0.603086 | − | 0.797676i | \(-0.706063\pi\) | ||||
−0.603086 | + | 0.797676i | \(0.706063\pi\) | |||||||
\(654\) | 6.43296 | 0.251549 | ||||||||
\(655\) | 3.00969 | 0.117598 | ||||||||
\(656\) | −12.2349 | −0.477693 | ||||||||
\(657\) | 5.11529 | 0.199567 | ||||||||
\(658\) | 17.7724 | 0.692840 | ||||||||
\(659\) | −33.2010 | −1.29333 | −0.646665 | − | 0.762774i | \(-0.723837\pi\) | ||||
−0.646665 | + | 0.762774i | \(0.723837\pi\) | |||||||
\(660\) | 3.19806 | 0.124484 | ||||||||
\(661\) | 37.4252 | 1.45567 | 0.727836 | − | 0.685752i | \(-0.240526\pi\) | ||||
0.727836 | + | 0.685752i | \(0.240526\pi\) | |||||||
\(662\) | 31.5163 | 1.22492 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.1196 | −0.431524 | ||||||||
\(665\) | −7.25236 | −0.281234 | ||||||||
\(666\) | 2.46681 | 0.0955870 | ||||||||
\(667\) | −67.1727 | −2.60094 | ||||||||
\(668\) | 8.24027 | 0.318826 | ||||||||
\(669\) | 21.5972 | 0.834995 | ||||||||
\(670\) | −1.55496 | −0.0600733 | ||||||||
\(671\) | −16.8980 | −0.652339 | ||||||||
\(672\) | 1.35690 | 0.0523434 | ||||||||
\(673\) | −34.9409 | −1.34687 | −0.673437 | − | 0.739245i | \(-0.735183\pi\) | ||||
−0.673437 | + | 0.739245i | \(0.735183\pi\) | |||||||
\(674\) | −11.8116 | −0.454967 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3913 | 1.12960 | 0.564800 | − | 0.825228i | \(-0.308953\pi\) | ||||
0.564800 | + | 0.825228i | \(0.308953\pi\) | |||||||
\(678\) | 18.6571 | 0.716522 | ||||||||
\(679\) | −6.43296 | −0.246874 | ||||||||
\(680\) | −2.04892 | −0.0785724 | ||||||||
\(681\) | 10.2862 | 0.394168 | ||||||||
\(682\) | −0.594778 | −0.0227752 | ||||||||
\(683\) | 28.9855 | 1.10910 | 0.554550 | − | 0.832150i | \(-0.312890\pi\) | ||||
0.554550 | + | 0.832150i | \(0.312890\pi\) | |||||||
\(684\) | 5.34481 | 0.204364 | ||||||||
\(685\) | −20.2892 | −0.775210 | ||||||||
\(686\) | 16.4983 | 0.629907 | ||||||||
\(687\) | 4.25906 | 0.162493 | ||||||||
\(688\) | −2.91185 | −0.111013 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8.32304 | 0.316853 | ||||||||
\(691\) | −1.37627 | −0.0523559 | −0.0261780 | − | 0.999657i | \(-0.508334\pi\) | ||||
−0.0261780 | + | 0.999657i | \(0.508334\pi\) | |||||||
\(692\) | 12.7463 | 0.484542 | ||||||||
\(693\) | 4.33944 | 0.164842 | ||||||||
\(694\) | −17.4101 | −0.660879 | ||||||||
\(695\) | −0.153457 | −0.00582095 | ||||||||
\(696\) | −8.07069 | −0.305919 | ||||||||
\(697\) | 25.0683 | 0.949529 | ||||||||
\(698\) | −18.6799 | −0.707046 | ||||||||
\(699\) | −19.5133 | −0.738062 | ||||||||
\(700\) | −1.35690 | −0.0512858 | ||||||||
\(701\) | 9.21014 | 0.347862 | 0.173931 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173931 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1847 | 0.497269 | ||||||||
\(704\) | −3.19806 | −0.120532 | ||||||||
\(705\) | 13.0978 | 0.493293 | ||||||||
\(706\) | −25.3991 | −0.955908 | ||||||||
\(707\) | 17.0858 | 0.642576 | ||||||||
\(708\) | −1.62565 | −0.0610955 | ||||||||
\(709\) | −46.1613 | −1.73363 | −0.866813 | − | 0.498634i | \(-0.833835\pi\) | ||||
−0.866813 | + | 0.498634i | \(0.833835\pi\) | |||||||
\(710\) | 2.32304 | 0.0871823 | ||||||||
\(711\) | −1.42327 | −0.0533769 | ||||||||
\(712\) | −3.37867 | −0.126621 | ||||||||
\(713\) | −1.54793 | −0.0579703 | ||||||||
\(714\) | −2.78017 | −0.104045 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0422 | 0.599526 | ||||||||
\(717\) | −7.16315 | −0.267513 | ||||||||
\(718\) | −34.0103 | −1.26925 | ||||||||
\(719\) | −46.3588 | −1.72889 | −0.864446 | − | 0.502726i | \(-0.832331\pi\) | ||||
−0.864446 | + | 0.502726i | \(0.832331\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 12.2121 | 0.454801 | ||||||||
\(722\) | 9.56704 | 0.356048 | ||||||||
\(723\) | 17.9584 | 0.667879 | ||||||||
\(724\) | 3.85086 | 0.143116 | ||||||||
\(725\) | 8.07069 | 0.299738 | ||||||||
\(726\) | 0.772398 | 0.0286664 | ||||||||
\(727\) | −1.67217 | −0.0620174 | −0.0310087 | − | 0.999519i | \(-0.509872\pi\) | ||||
−0.0310087 | + | 0.999519i | \(0.509872\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.11529 | 0.189325 | ||||||||
\(731\) | 5.96615 | 0.220666 | ||||||||
\(732\) | −5.28382 | −0.195295 | ||||||||
\(733\) | 33.6189 | 1.24174 | 0.620872 | − | 0.783912i | \(-0.286779\pi\) | ||||
0.620872 | + | 0.783912i | \(0.286779\pi\) | |||||||
\(734\) | −25.6437 | −0.946526 | ||||||||
\(735\) | 5.15883 | 0.190286 | ||||||||
\(736\) | −8.32304 | −0.306791 | ||||||||
\(737\) | 4.97285 | 0.183177 | ||||||||
\(738\) | −12.2349 | −0.450373 | ||||||||
\(739\) | 31.8437 | 1.17139 | 0.585694 | − | 0.810532i | \(-0.300822\pi\) | ||||
0.585694 | + | 0.810532i | \(0.300822\pi\) | |||||||
\(740\) | 2.46681 | 0.0906818 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.78986 | −0.285975 | ||||||||
\(743\) | −23.4010 | −0.858500 | −0.429250 | − | 0.903186i | \(-0.641222\pi\) | ||||
−0.429250 | + | 0.903186i | \(0.641222\pi\) | |||||||
\(744\) | −0.185981 | −0.00681838 | ||||||||
\(745\) | 10.7724 | 0.394670 | ||||||||
\(746\) | −16.3612 | −0.599026 | ||||||||
\(747\) | −11.1196 | −0.406845 | ||||||||
\(748\) | 6.55257 | 0.239586 | ||||||||
\(749\) | 6.90408 | 0.252270 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −39.0146 | −1.42366 | −0.711831 | − | 0.702350i | \(-0.752134\pi\) | ||||
−0.711831 | + | 0.702350i | \(0.752134\pi\) | |||||||
\(752\) | −13.0978 | −0.477629 | ||||||||
\(753\) | 6.68425 | 0.243588 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3817 | −0.632583 | ||||||||
\(756\) | 1.35690 | 0.0493498 | ||||||||
\(757\) | 43.0224 | 1.56367 | 0.781837 | − | 0.623483i | \(-0.214283\pi\) | ||||
0.781837 | + | 0.623483i | \(0.214283\pi\) | |||||||
\(758\) | −22.8823 | −0.831123 | ||||||||
\(759\) | −26.6176 | −0.966158 | ||||||||
\(760\) | 5.34481 | 0.193877 | ||||||||
\(761\) | −14.9903 | −0.543398 | −0.271699 | − | 0.962382i | \(-0.587586\pi\) | ||||
−0.271699 | + | 0.962382i | \(0.587586\pi\) | |||||||
\(762\) | 16.3763 | 0.593250 | ||||||||
\(763\) | 8.72886 | 0.316006 | ||||||||
\(764\) | 11.8280 | 0.427923 | ||||||||
\(765\) | −2.04892 | −0.0740788 | ||||||||
\(766\) | −11.9191 | −0.430656 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 19.9138 | 0.718109 | 0.359055 | − | 0.933317i | \(-0.383099\pi\) | ||||
0.359055 | + | 0.933317i | \(0.383099\pi\) | |||||||
\(770\) | 4.33944 | 0.156382 | ||||||||
\(771\) | −9.91484 | −0.357074 | ||||||||
\(772\) | −0.872625 | −0.0314065 | ||||||||
\(773\) | −25.5566 | −0.919208 | −0.459604 | − | 0.888124i | \(-0.652009\pi\) | ||||
−0.459604 | + | 0.888124i | \(0.652009\pi\) | |||||||
\(774\) | −2.91185 | −0.104664 | ||||||||
\(775\) | 0.185981 | 0.00668062 | ||||||||
\(776\) | 4.74094 | 0.170190 | ||||||||
\(777\) | 3.34721 | 0.120080 | ||||||||
\(778\) | 8.07606 | 0.289541 | ||||||||
\(779\) | −65.3933 | −2.34296 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.42924 | −0.265839 | ||||||||
\(782\) | 17.0532 | 0.609822 | ||||||||
\(783\) | −8.07069 | −0.288423 | ||||||||
\(784\) | −5.15883 | −0.184244 | ||||||||
\(785\) | 15.5429 | 0.554749 | ||||||||
\(786\) | −3.00969 | −0.107352 | ||||||||
\(787\) | −28.6297 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(788\) | −10.6213 | −0.378369 | ||||||||
\(789\) | −13.8509 | −0.493103 | ||||||||
\(790\) | −1.42327 | −0.0506377 | ||||||||
\(791\) | 25.3157 | 0.900124 | ||||||||
\(792\) | −3.19806 | −0.113638 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.5230 | 0.728335 | ||||||||
\(795\) | −5.74094 | −0.203610 | ||||||||
\(796\) | 12.3424 | 0.437466 | ||||||||
\(797\) | 1.00431 | 0.0355746 | 0.0177873 | − | 0.999842i | \(-0.494338\pi\) | ||||
0.0177873 | + | 0.999842i | \(0.494338\pi\) | |||||||
\(798\) | 7.25236 | 0.256731 | ||||||||
\(799\) | 26.8364 | 0.949403 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −3.37867 | −0.119379 | ||||||||
\(802\) | 18.3274 | 0.647161 | ||||||||
\(803\) | −16.3590 | −0.577297 | ||||||||
\(804\) | 1.55496 | 0.0548391 | ||||||||
\(805\) | 11.2935 | 0.398044 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.8756 | 0.629251 | ||||||||
\(808\) | −12.5918 | −0.442978 | ||||||||
\(809\) | 49.8743 | 1.75349 | 0.876743 | − | 0.480959i | \(-0.159711\pi\) | ||||
0.876743 | + | 0.480959i | \(0.159711\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 7.95646 | 0.279389 | 0.139695 | − | 0.990195i | \(-0.455388\pi\) | ||||
0.139695 | + | 0.990195i | \(0.455388\pi\) | |||||||
\(812\) | −10.9511 | −0.384308 | ||||||||
\(813\) | 31.2083 | 1.09452 | ||||||||
\(814\) | −7.88902 | −0.276510 | ||||||||
\(815\) | 2.00239 | 0.0701408 | ||||||||
\(816\) | 2.04892 | 0.0717265 | ||||||||
\(817\) | −15.5633 | −0.544492 | ||||||||
\(818\) | −9.00000 | −0.314678 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.2349 | −0.427261 | ||||||||
\(821\) | 52.9071 | 1.84647 | 0.923235 | − | 0.384236i | \(-0.125535\pi\) | ||||
0.923235 | + | 0.384236i | \(0.125535\pi\) | |||||||
\(822\) | 20.2892 | 0.707667 | ||||||||
\(823\) | 21.8006 | 0.759921 | 0.379961 | − | 0.925003i | \(-0.375937\pi\) | ||||
0.379961 | + | 0.925003i | \(0.375937\pi\) | |||||||
\(824\) | −9.00000 | −0.313530 | ||||||||
\(825\) | 3.19806 | 0.111342 | ||||||||
\(826\) | −2.20583 | −0.0767507 | ||||||||
\(827\) | −27.3139 | −0.949799 | −0.474899 | − | 0.880040i | \(-0.657516\pi\) | ||||
−0.474899 | + | 0.880040i | \(0.657516\pi\) | |||||||
\(828\) | −8.32304 | −0.289246 | ||||||||
\(829\) | 40.8471 | 1.41868 | 0.709340 | − | 0.704867i | \(-0.248993\pi\) | ||||
0.709340 | + | 0.704867i | \(0.248993\pi\) | |||||||
\(830\) | −11.1196 | −0.385967 | ||||||||
\(831\) | −22.9245 | −0.795243 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5700 | 0.366230 | ||||||||
\(834\) | 0.153457 | 0.00531377 | ||||||||
\(835\) | 8.24027 | 0.285166 | ||||||||
\(836\) | −17.0930 | −0.591175 | ||||||||
\(837\) | −0.185981 | −0.00642843 | ||||||||
\(838\) | −14.4185 | −0.498078 | ||||||||
\(839\) | 43.0823 | 1.48737 | 0.743683 | − | 0.668532i | \(-0.233077\pi\) | ||||
0.743683 | + | 0.668532i | \(0.233077\pi\) | |||||||
\(840\) | 1.35690 | 0.0468174 | ||||||||
\(841\) | 36.1360 | 1.24607 | ||||||||
\(842\) | 19.9801 | 0.688561 | ||||||||
\(843\) | 28.0683 | 0.966723 | ||||||||
\(844\) | 6.75733 | 0.232597 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.0978 | −0.450313 | ||||||||
\(847\) | 1.04806 | 0.0360119 | ||||||||
\(848\) | 5.74094 | 0.197145 | ||||||||
\(849\) | 24.8364 | 0.852382 | ||||||||
\(850\) | −2.04892 | −0.0702773 | ||||||||
\(851\) | −20.5314 | −0.703807 | ||||||||
\(852\) | −2.32304 | −0.0795862 | ||||||||
\(853\) | −24.6813 | −0.845071 | −0.422535 | − | 0.906346i | \(-0.638860\pi\) | ||||
−0.422535 | + | 0.906346i | \(0.638860\pi\) | |||||||
\(854\) | −7.16959 | −0.245338 | ||||||||
\(855\) | 5.34481 | 0.182789 | ||||||||
\(856\) | −5.08815 | −0.173909 | ||||||||
\(857\) | 43.1075 | 1.47252 | 0.736262 | − | 0.676696i | \(-0.236589\pi\) | ||||
0.736262 | + | 0.676696i | \(0.236589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.1323 | −1.43753 | −0.718767 | − | 0.695251i | \(-0.755293\pi\) | ||||
−0.718767 | + | 0.695251i | \(0.755293\pi\) | |||||||
\(860\) | −2.91185 | −0.0992934 | ||||||||
\(861\) | −16.6015 | −0.565777 | ||||||||
\(862\) | 21.1812 | 0.721434 | ||||||||
\(863\) | 47.9342 | 1.63170 | 0.815850 | − | 0.578264i | \(-0.196270\pi\) | ||||
0.815850 | + | 0.578264i | \(0.196270\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 12.7463 | 0.433388 | ||||||||
\(866\) | 31.0291 | 1.05441 | ||||||||
\(867\) | 12.8019 | 0.434777 | ||||||||
\(868\) | −0.252356 | −0.00856553 | ||||||||
\(869\) | 4.55171 | 0.154406 | ||||||||
\(870\) | −8.07069 | −0.273622 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.43296 | −0.217848 | ||||||||
\(873\) | 4.74094 | 0.160456 | ||||||||
\(874\) | −44.4851 | −1.50473 | ||||||||
\(875\) | −1.35690 | −0.0458715 | ||||||||
\(876\) | −5.11529 | −0.172830 | ||||||||
\(877\) | −38.6674 | −1.30570 | −0.652852 | − | 0.757485i | \(-0.726428\pi\) | ||||
−0.652852 | + | 0.757485i | \(0.726428\pi\) | |||||||
\(878\) | 7.33406 | 0.247513 | ||||||||
\(879\) | −28.4349 | −0.959085 | ||||||||
\(880\) | −3.19806 | −0.107807 | ||||||||
\(881\) | 25.4980 | 0.859050 | 0.429525 | − | 0.903055i | \(-0.358681\pi\) | ||||
0.429525 | + | 0.903055i | \(0.358681\pi\) | |||||||
\(882\) | −5.15883 | −0.173707 | ||||||||
\(883\) | −31.8377 | −1.07142 | −0.535712 | − | 0.844401i | \(-0.679957\pi\) | ||||
−0.535712 | + | 0.844401i | \(0.679957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.62565 | −0.0546455 | ||||||||
\(886\) | −18.1360 | −0.609291 | ||||||||
\(887\) | −7.83446 | −0.263055 | −0.131528 | − | 0.991312i | \(-0.541988\pi\) | ||||
−0.131528 | + | 0.991312i | \(0.541988\pi\) | |||||||
\(888\) | −2.46681 | −0.0827808 | ||||||||
\(889\) | 22.2209 | 0.745265 | ||||||||
\(890\) | −3.37867 | −0.113253 | ||||||||
\(891\) | −3.19806 | −0.107139 | ||||||||
\(892\) | −21.5972 | −0.723127 | ||||||||
\(893\) | −70.0055 | −2.34264 | ||||||||
\(894\) | −10.7724 | −0.360283 | ||||||||
\(895\) | 16.0422 | 0.536232 | ||||||||
\(896\) | −1.35690 | −0.0453307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.55496 | −0.152001 | ||||||||
\(899\) | 1.50099 | 0.0500609 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −11.7627 | −0.391873 | ||||||||
\(902\) | 39.1280 | 1.30282 | ||||||||
\(903\) | −3.95108 | −0.131484 | ||||||||
\(904\) | −18.6571 | −0.620526 | ||||||||
\(905\) | 3.85086 | 0.128007 | ||||||||
\(906\) | 17.3817 | 0.577467 | ||||||||
\(907\) | 33.1089 | 1.09936 | 0.549681 | − | 0.835375i | \(-0.314749\pi\) | ||||
0.549681 | + | 0.835375i | \(0.314749\pi\) | |||||||
\(908\) | −10.2862 | −0.341360 | ||||||||
\(909\) | −12.5918 | −0.417643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.0556 | −0.465684 | −0.232842 | − | 0.972515i | \(-0.574802\pi\) | ||||
−0.232842 | + | 0.972515i | \(0.574802\pi\) | |||||||
\(912\) | −5.34481 | −0.176984 | ||||||||
\(913\) | 35.5612 | 1.17690 | ||||||||
\(914\) | 9.98121 | 0.330149 | ||||||||
\(915\) | −5.28382 | −0.174678 | ||||||||
\(916\) | −4.25906 | −0.140723 | ||||||||
\(917\) | −4.08383 | −0.134860 | ||||||||
\(918\) | 2.04892 | 0.0676243 | ||||||||
\(919\) | −27.1830 | −0.896684 | −0.448342 | − | 0.893862i | \(-0.647985\pi\) | ||||
−0.448342 | + | 0.893862i | \(0.647985\pi\) | |||||||
\(920\) | −8.32304 | −0.274403 | ||||||||
\(921\) | −10.1347 | −0.333949 | ||||||||
\(922\) | −16.1672 | −0.532438 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.33944 | −0.142757 | ||||||||
\(925\) | 2.46681 | 0.0811083 | ||||||||
\(926\) | 3.88902 | 0.127801 | ||||||||
\(927\) | −9.00000 | −0.295599 | ||||||||
\(928\) | 8.07069 | 0.264933 | ||||||||
\(929\) | −50.3521 | −1.65200 | −0.826000 | − | 0.563671i | \(-0.809389\pi\) | ||||
−0.826000 | + | 0.563671i | \(0.809389\pi\) | |||||||
\(930\) | −0.185981 | −0.00609855 | ||||||||
\(931\) | −27.5730 | −0.903669 | ||||||||
\(932\) | 19.5133 | 0.639181 | ||||||||
\(933\) | −20.0218 | −0.655483 | ||||||||
\(934\) | −0.872625 | −0.0285532 | ||||||||
\(935\) | 6.55257 | 0.214292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6394 | 0.870271 | 0.435135 | − | 0.900365i | \(-0.356701\pi\) | ||||
0.435135 | + | 0.900365i | \(0.356701\pi\) | |||||||
\(938\) | 2.10992 | 0.0688912 | ||||||||
\(939\) | −8.63640 | −0.281838 | ||||||||
\(940\) | −13.0978 | −0.427204 | ||||||||
\(941\) | −25.7198 | −0.838440 | −0.419220 | − | 0.907885i | \(-0.637696\pi\) | ||||
−0.419220 | + | 0.907885i | \(0.637696\pi\) | |||||||
\(942\) | −15.5429 | −0.506414 | ||||||||
\(943\) | 101.832 | 3.31609 | ||||||||
\(944\) | 1.62565 | 0.0529103 | ||||||||
\(945\) | 1.35690 | 0.0441398 | ||||||||
\(946\) | 9.31229 | 0.302769 | ||||||||
\(947\) | 14.4862 | 0.470738 | 0.235369 | − | 0.971906i | \(-0.424370\pi\) | ||||
0.235369 | + | 0.971906i | \(0.424370\pi\) | |||||||
\(948\) | 1.42327 | 0.0462257 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.34481 | 0.173409 | ||||||||
\(951\) | 17.6256 | 0.571551 | ||||||||
\(952\) | 2.78017 | 0.0901057 | ||||||||
\(953\) | −29.3690 | −0.951354 | −0.475677 | − | 0.879620i | \(-0.657797\pi\) | ||||
−0.475677 | + | 0.879620i | \(0.657797\pi\) | |||||||
\(954\) | 5.74094 | 0.185870 | ||||||||
\(955\) | 11.8280 | 0.382746 | ||||||||
\(956\) | 7.16315 | 0.231673 | ||||||||
\(957\) | 25.8106 | 0.834337 | ||||||||
\(958\) | −31.6305 | −1.02194 | ||||||||
\(959\) | 27.5303 | 0.889000 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −30.9654 | −0.998884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.08815 | −0.163963 | ||||||||
\(964\) | −17.9584 | −0.578400 | ||||||||
\(965\) | −0.872625 | −0.0280908 | ||||||||
\(966\) | −11.2935 | −0.363363 | ||||||||
\(967\) | −21.9360 | −0.705415 | −0.352707 | − | 0.935734i | \(-0.614739\pi\) | ||||
−0.352707 | + | 0.935734i | \(0.614739\pi\) | |||||||
\(968\) | −0.772398 | −0.0248258 | ||||||||
\(969\) | 10.9511 | 0.351799 | ||||||||
\(970\) | 4.74094 | 0.152222 | ||||||||
\(971\) | 34.9754 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310337\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310337\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.208225 | 0.00667538 | ||||||||
\(974\) | 21.7748 | 0.697709 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.28382 | 0.169131 | ||||||||
\(977\) | −7.72289 | −0.247077 | −0.123539 | − | 0.992340i | \(-0.539424\pi\) | ||||
−0.123539 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(978\) | −2.00239 | −0.0640295 | ||||||||
\(979\) | 10.8052 | 0.345335 | ||||||||
\(980\) | −5.15883 | −0.164793 | ||||||||
\(981\) | −6.43296 | −0.205389 | ||||||||
\(982\) | 42.9590 | 1.37088 | ||||||||
\(983\) | 29.0489 | 0.926517 | 0.463258 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463258 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(984\) | 12.2349 | 0.390034 | ||||||||
\(985\) | −10.6213 | −0.338424 | ||||||||
\(986\) | −16.5362 | −0.526619 | ||||||||
\(987\) | −17.7724 | −0.565702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.2355 | 0.770644 | ||||||||
\(990\) | −3.19806 | −0.101641 | ||||||||
\(991\) | 37.7192 | 1.19819 | 0.599094 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599094 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(992\) | 0.185981 | 0.00590489 | ||||||||
\(993\) | −31.5163 | −1.00014 | ||||||||
\(994\) | −3.15213 | −0.0999795 | ||||||||
\(995\) | 12.3424 | 0.391281 | ||||||||
\(996\) | 11.1196 | 0.352338 | ||||||||
\(997\) | −7.18060 | −0.227412 | −0.113706 | − | 0.993514i | \(-0.536272\pi\) | ||||
−0.113706 | + | 0.993514i | \(0.536272\pi\) | |||||||
\(998\) | −36.0978 | −1.14266 | ||||||||
\(999\) | −2.46681 | −0.0780465 |
(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.1.2 | yes | 3 | |
13.5 | odd | 4 | 5070.2.b.s.1351.2 | 6 | |||
13.8 | odd | 4 | 5070.2.b.s.1351.5 | 6 | |||
13.12 | even | 2 | 5070.2.a.bk.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bk.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
5070.2.a.bt.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
5070.2.b.s.1351.2 | 6 | 13.5 | odd | 4 | |||
5070.2.b.s.1351.5 | 6 | 13.8 | odd | 4 |