Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.41421 | −1.93396 | −0.966979 | − | 0.254856i | \(-0.917972\pi\) | ||||
−0.966979 | + | 0.254856i | \(0.917972\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.24264 | −0.786456 | −0.393228 | − | 0.919441i | \(-0.628642\pi\) | ||||
−0.393228 | + | 0.919441i | \(0.628642\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.65685 | 1.06836 | 0.534178 | − | 0.845372i | \(-0.320621\pi\) | ||||
0.534178 | + | 0.845372i | \(0.320621\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.41421 | −1.36751 | ||||||||
\(23\) | −2.17157 | −0.452804 | −0.226402 | − | 0.974034i | \(-0.572696\pi\) | ||||
−0.226402 | + | 0.974034i | \(0.572696\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.48528 | 1.38998 | 0.694991 | − | 0.719019i | \(-0.255408\pi\) | ||||
0.694991 | + | 0.719019i | \(0.255408\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −1.41421 | −0.254000 | −0.127000 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127000 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.41421 | 1.11657 | ||||||||
\(34\) | −3.24264 | −0.556108 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.41421 | −1.38329 | −0.691644 | − | 0.722238i | \(-0.743113\pi\) | ||||
−0.691644 | + | 0.722238i | \(0.743113\pi\) | |||||||
\(38\) | 4.65685 | 0.755442 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 5.17157 | 0.807664 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.65685 | −1.32016 | −0.660079 | − | 0.751196i | \(-0.729477\pi\) | ||||
−0.660079 | + | 0.751196i | \(0.729477\pi\) | |||||||
\(44\) | −6.41421 | −0.966979 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −2.17157 | −0.320181 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | 3.24264 | 0.454061 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −5.65685 | −0.777029 | −0.388514 | − | 0.921443i | \(-0.627012\pi\) | ||||
−0.388514 | + | 0.921443i | \(0.627012\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −6.41421 | −0.864892 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.65685 | −0.616815 | ||||||||
\(58\) | 7.48528 | 0.982866 | ||||||||
\(59\) | 11.0711 | 1.44133 | 0.720665 | − | 0.693283i | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693283i | \(0.243837\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −10.4142 | −1.33340 | −0.666702 | − | 0.745325i | \(-0.732294\pi\) | ||||
−0.666702 | + | 0.745325i | \(0.732294\pi\) | |||||||
\(62\) | −1.41421 | −0.179605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 6.41421 | 0.789535 | ||||||||
\(67\) | −15.5563 | −1.90051 | −0.950255 | − | 0.311472i | \(-0.899178\pi\) | ||||
−0.950255 | + | 0.311472i | \(0.899178\pi\) | |||||||
\(68\) | −3.24264 | −0.393228 | ||||||||
\(69\) | 2.17157 | 0.261427 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.75736 | −0.683273 | −0.341636 | − | 0.939832i | \(-0.610981\pi\) | ||||
−0.341636 | + | 0.939832i | \(0.610981\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.0000 | −1.28745 | −0.643726 | − | 0.765256i | \(-0.722612\pi\) | ||||
−0.643726 | + | 0.765256i | \(0.722612\pi\) | |||||||
\(74\) | −8.41421 | −0.978132 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 4.65685 | 0.534178 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 2.24264 | 0.252317 | 0.126158 | − | 0.992010i | \(-0.459735\pi\) | ||||
0.126158 | + | 0.992010i | \(0.459735\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.17157 | 0.571105 | ||||||||
\(83\) | 3.65685 | 0.401392 | 0.200696 | − | 0.979654i | \(-0.435680\pi\) | ||||
0.200696 | + | 0.979654i | \(0.435680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.24264 | −0.351714 | ||||||||
\(86\) | −8.65685 | −0.933493 | ||||||||
\(87\) | −7.48528 | −0.802506 | ||||||||
\(88\) | −6.41421 | −0.683757 | ||||||||
\(89\) | 14.2426 | 1.50972 | 0.754858 | − | 0.655888i | \(-0.227706\pi\) | ||||
0.754858 | + | 0.655888i | \(0.227706\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.17157 | −0.226402 | ||||||||
\(93\) | 1.41421 | 0.146647 | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 4.65685 | 0.477783 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.31371 | −0.742595 | −0.371297 | − | 0.928514i | \(-0.621087\pi\) | ||||
−0.371297 | + | 0.928514i | \(0.621087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.41421 | −0.644653 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 12.5858 | 1.25233 | 0.626166 | − | 0.779690i | \(-0.284623\pi\) | ||||
0.626166 | + | 0.779690i | \(0.284623\pi\) | |||||||
\(102\) | 3.24264 | 0.321069 | ||||||||
\(103\) | −1.58579 | −0.156252 | −0.0781261 | − | 0.996943i | \(-0.524894\pi\) | ||||
−0.0781261 | + | 0.996943i | \(0.524894\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.65685 | −0.549442 | ||||||||
\(107\) | −17.5563 | −1.69724 | −0.848618 | − | 0.529006i | \(-0.822565\pi\) | ||||
−0.848618 | + | 0.529006i | \(0.822565\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.899495 | 0.0861560 | 0.0430780 | − | 0.999072i | \(-0.486284\pi\) | ||||
0.0430780 | + | 0.999072i | \(0.486284\pi\) | |||||||
\(110\) | −6.41421 | −0.611571 | ||||||||
\(111\) | 8.41421 | 0.798642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.58579 | 0.431394 | 0.215697 | − | 0.976460i | \(-0.430798\pi\) | ||||
0.215697 | + | 0.976460i | \(0.430798\pi\) | |||||||
\(114\) | −4.65685 | −0.436154 | ||||||||
\(115\) | −2.17157 | −0.202500 | ||||||||
\(116\) | 7.48528 | 0.694991 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 11.0711 | 1.01917 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 30.1421 | 2.74019 | ||||||||
\(122\) | −10.4142 | −0.942859 | ||||||||
\(123\) | −5.17157 | −0.466305 | ||||||||
\(124\) | −1.41421 | −0.127000 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.72792 | 0.597007 | 0.298503 | − | 0.954409i | \(-0.403513\pi\) | ||||
0.298503 | + | 0.954409i | \(0.403513\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.65685 | 0.762194 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | 5.72792 | 0.500451 | 0.250225 | − | 0.968188i | \(-0.419495\pi\) | ||||
0.250225 | + | 0.968188i | \(0.419495\pi\) | |||||||
\(132\) | 6.41421 | 0.558286 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.5563 | −1.34386 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −3.24264 | −0.278054 | ||||||||
\(137\) | −6.41421 | −0.548003 | −0.274002 | − | 0.961729i | \(-0.588347\pi\) | ||||
−0.274002 | + | 0.961729i | \(0.588347\pi\) | |||||||
\(138\) | 2.17157 | 0.184857 | ||||||||
\(139\) | −19.7990 | −1.67933 | −0.839664 | − | 0.543106i | \(-0.817248\pi\) | ||||
−0.839664 | + | 0.543106i | \(0.817248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −5.75736 | −0.483147 | ||||||||
\(143\) | −6.41421 | −0.536383 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.48528 | 0.621619 | ||||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.41421 | −0.691644 | ||||||||
\(149\) | 8.48528 | 0.695141 | 0.347571 | − | 0.937654i | \(-0.387007\pi\) | ||||
0.347571 | + | 0.937654i | \(0.387007\pi\) | |||||||
\(150\) | 4.00000 | 0.326599 | ||||||||
\(151\) | −6.41421 | −0.521981 | −0.260991 | − | 0.965341i | \(-0.584049\pi\) | ||||
−0.260991 | + | 0.965341i | \(0.584049\pi\) | |||||||
\(152\) | 4.65685 | 0.377721 | ||||||||
\(153\) | −3.24264 | −0.262152 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.41421 | −0.113592 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −8.41421 | −0.671527 | −0.335764 | − | 0.941946i | \(-0.608994\pi\) | ||||
−0.335764 | + | 0.941946i | \(0.608994\pi\) | |||||||
\(158\) | 2.24264 | 0.178415 | ||||||||
\(159\) | 5.65685 | 0.448618 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −0.343146 | −0.0268772 | −0.0134386 | − | 0.999910i | \(-0.504278\pi\) | ||||
−0.0134386 | + | 0.999910i | \(0.504278\pi\) | |||||||
\(164\) | 5.17157 | 0.403832 | ||||||||
\(165\) | 6.41421 | 0.499346 | ||||||||
\(166\) | 3.65685 | 0.283827 | ||||||||
\(167\) | −23.1421 | −1.79079 | −0.895396 | − | 0.445270i | \(-0.853108\pi\) | ||||
−0.895396 | + | 0.445270i | \(0.853108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.24264 | −0.248699 | ||||||||
\(171\) | 4.65685 | 0.356119 | ||||||||
\(172\) | −8.65685 | −0.660079 | ||||||||
\(173\) | 17.8995 | 1.36087 | 0.680437 | − | 0.732807i | \(-0.261790\pi\) | ||||
0.680437 | + | 0.732807i | \(0.261790\pi\) | |||||||
\(174\) | −7.48528 | −0.567458 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.41421 | −0.483490 | ||||||||
\(177\) | −11.0711 | −0.832152 | ||||||||
\(178\) | 14.2426 | 1.06753 | ||||||||
\(179\) | −6.10051 | −0.455973 | −0.227987 | − | 0.973664i | \(-0.573214\pi\) | ||||
−0.227987 | + | 0.973664i | \(0.573214\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −22.8284 | −1.69682 | −0.848412 | − | 0.529337i | \(-0.822441\pi\) | ||||
−0.848412 | + | 0.529337i | \(0.822441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4142 | 0.769841 | ||||||||
\(184\) | −2.17157 | −0.160090 | ||||||||
\(185\) | −8.41421 | −0.618625 | ||||||||
\(186\) | 1.41421 | 0.103695 | ||||||||
\(187\) | 20.7990 | 1.52097 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.65685 | 0.337844 | ||||||||
\(191\) | −21.9706 | −1.58973 | −0.794867 | − | 0.606784i | \(-0.792459\pi\) | ||||
−0.794867 | + | 0.606784i | \(0.792459\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.75736 | 0.414424 | 0.207212 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207212 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(194\) | −7.31371 | −0.525094 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.58579 | 0.326724 | 0.163362 | − | 0.986566i | \(-0.447766\pi\) | ||||
0.163362 | + | 0.986566i | \(0.447766\pi\) | |||||||
\(198\) | −6.41421 | −0.455838 | ||||||||
\(199\) | 16.5563 | 1.17365 | 0.586824 | − | 0.809714i | \(-0.300378\pi\) | ||||
0.586824 | + | 0.809714i | \(0.300378\pi\) | |||||||
\(200\) | −4.00000 | −0.282843 | ||||||||
\(201\) | 15.5563 | 1.09726 | ||||||||
\(202\) | 12.5858 | 0.885533 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.24264 | 0.227030 | ||||||||
\(205\) | 5.17157 | 0.361198 | ||||||||
\(206\) | −1.58579 | −0.110487 | ||||||||
\(207\) | −2.17157 | −0.150935 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −29.8701 | −2.06616 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6569 | 0.871334 | 0.435667 | − | 0.900108i | \(-0.356513\pi\) | ||||
0.435667 | + | 0.900108i | \(0.356513\pi\) | |||||||
\(212\) | −5.65685 | −0.388514 | ||||||||
\(213\) | 5.75736 | 0.394488 | ||||||||
\(214\) | −17.5563 | −1.20013 | ||||||||
\(215\) | −8.65685 | −0.590393 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.899495 | 0.0609215 | ||||||||
\(219\) | 11.0000 | 0.743311 | ||||||||
\(220\) | −6.41421 | −0.432446 | ||||||||
\(221\) | −3.24264 | −0.218124 | ||||||||
\(222\) | 8.41421 | 0.564725 | ||||||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 4.58579 | 0.305042 | ||||||||
\(227\) | −5.07107 | −0.336579 | −0.168289 | − | 0.985738i | \(-0.553824\pi\) | ||||
−0.168289 | + | 0.985738i | \(0.553824\pi\) | |||||||
\(228\) | −4.65685 | −0.308408 | ||||||||
\(229\) | 3.89949 | 0.257686 | 0.128843 | − | 0.991665i | \(-0.458874\pi\) | ||||
0.128843 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(230\) | −2.17157 | −0.143189 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.48528 | 0.491433 | ||||||||
\(233\) | −6.14214 | −0.402385 | −0.201192 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201192 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 11.0711 | 0.720665 | ||||||||
\(237\) | −2.24264 | −0.145675 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3848 | −1.31858 | −0.659291 | − | 0.751888i | \(-0.729143\pi\) | ||||
−0.659291 | + | 0.751888i | \(0.729143\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −14.9706 | −0.964339 | −0.482169 | − | 0.876078i | \(-0.660151\pi\) | ||||
−0.482169 | + | 0.876078i | \(0.660151\pi\) | |||||||
\(242\) | 30.1421 | 1.93761 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.4142 | −0.666702 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.17157 | −0.329727 | ||||||||
\(247\) | 4.65685 | 0.296309 | ||||||||
\(248\) | −1.41421 | −0.0898027 | ||||||||
\(249\) | −3.65685 | −0.231744 | ||||||||
\(250\) | −9.00000 | −0.569210 | ||||||||
\(251\) | −6.55635 | −0.413833 | −0.206917 | − | 0.978359i | \(-0.566343\pi\) | ||||
−0.206917 | + | 0.978359i | \(0.566343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.9289 | 0.875704 | ||||||||
\(254\) | 6.72792 | 0.422147 | ||||||||
\(255\) | 3.24264 | 0.203062 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.82843 | 0.176432 | 0.0882162 | − | 0.996101i | \(-0.471883\pi\) | ||||
0.0882162 | + | 0.996101i | \(0.471883\pi\) | |||||||
\(258\) | 8.65685 | 0.538952 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 7.48528 | 0.463327 | ||||||||
\(262\) | 5.72792 | 0.353872 | ||||||||
\(263\) | 26.6274 | 1.64192 | 0.820958 | − | 0.570988i | \(-0.193440\pi\) | ||||
0.820958 | + | 0.570988i | \(0.193440\pi\) | |||||||
\(264\) | 6.41421 | 0.394768 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.2426 | −0.871635 | ||||||||
\(268\) | −15.5563 | −0.950255 | ||||||||
\(269\) | 13.2132 | 0.805623 | 0.402812 | − | 0.915283i | \(-0.368033\pi\) | ||||
0.402812 | + | 0.915283i | \(0.368033\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −28.3848 | −1.72425 | −0.862126 | − | 0.506694i | \(-0.830868\pi\) | ||||
−0.862126 | + | 0.506694i | \(0.830868\pi\) | |||||||
\(272\) | −3.24264 | −0.196614 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.41421 | −0.387497 | ||||||||
\(275\) | 25.6569 | 1.54717 | ||||||||
\(276\) | 2.17157 | 0.130713 | ||||||||
\(277\) | −4.58579 | −0.275533 | −0.137767 | − | 0.990465i | \(-0.543992\pi\) | ||||
−0.137767 | + | 0.990465i | \(0.543992\pi\) | |||||||
\(278\) | −19.7990 | −1.18746 | ||||||||
\(279\) | −1.41421 | −0.0846668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.9706 | 1.60893 | 0.804464 | − | 0.594001i | \(-0.202452\pi\) | ||||
0.804464 | + | 0.594001i | \(0.202452\pi\) | |||||||
\(282\) | 6.00000 | 0.357295 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | −5.75736 | −0.341636 | ||||||||
\(285\) | −4.65685 | −0.275848 | ||||||||
\(286\) | −6.41421 | −0.379280 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −6.48528 | −0.381487 | ||||||||
\(290\) | 7.48528 | 0.439551 | ||||||||
\(291\) | 7.31371 | 0.428737 | ||||||||
\(292\) | −11.0000 | −0.643726 | ||||||||
\(293\) | 19.7990 | 1.15667 | 0.578335 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578335 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.0711 | 0.644582 | ||||||||
\(296\) | −8.41421 | −0.489066 | ||||||||
\(297\) | 6.41421 | 0.372190 | ||||||||
\(298\) | 8.48528 | 0.491539 | ||||||||
\(299\) | −2.17157 | −0.125585 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.41421 | −0.369097 | ||||||||
\(303\) | −12.5858 | −0.723035 | ||||||||
\(304\) | 4.65685 | 0.267089 | ||||||||
\(305\) | −10.4142 | −0.596316 | ||||||||
\(306\) | −3.24264 | −0.185369 | ||||||||
\(307\) | −21.3137 | −1.21644 | −0.608219 | − | 0.793769i | \(-0.708116\pi\) | ||||
−0.608219 | + | 0.793769i | \(0.708116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.58579 | 0.0902122 | ||||||||
\(310\) | −1.41421 | −0.0803219 | ||||||||
\(311\) | −12.8284 | −0.727433 | −0.363717 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363717 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −15.8995 | −0.898693 | −0.449346 | − | 0.893358i | \(-0.648343\pi\) | ||||
−0.449346 | + | 0.893358i | \(0.648343\pi\) | |||||||
\(314\) | −8.41421 | −0.474842 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.24264 | 0.126158 | ||||||||
\(317\) | −15.4142 | −0.865748 | −0.432874 | − | 0.901454i | \(-0.642501\pi\) | ||||
−0.432874 | + | 0.901454i | \(0.642501\pi\) | |||||||
\(318\) | 5.65685 | 0.317221 | ||||||||
\(319\) | −48.0122 | −2.68817 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 17.5563 | 0.979900 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.1005 | −0.840215 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −0.343146 | −0.0190051 | ||||||||
\(327\) | −0.899495 | −0.0497422 | ||||||||
\(328\) | 5.17157 | 0.285552 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.41421 | 0.353091 | ||||||||
\(331\) | 3.75736 | 0.206523 | 0.103262 | − | 0.994654i | \(-0.467072\pi\) | ||||
0.103262 | + | 0.994654i | \(0.467072\pi\) | |||||||
\(332\) | 3.65685 | 0.200696 | ||||||||
\(333\) | −8.41421 | −0.461096 | ||||||||
\(334\) | −23.1421 | −1.26628 | ||||||||
\(335\) | −15.5563 | −0.849934 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.8284 | −1.51591 | −0.757956 | − | 0.652306i | \(-0.773802\pi\) | ||||
−0.757956 | + | 0.652306i | \(0.773802\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −4.58579 | −0.249066 | ||||||||
\(340\) | −3.24264 | −0.175857 | ||||||||
\(341\) | 9.07107 | 0.491226 | ||||||||
\(342\) | 4.65685 | 0.251814 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.65685 | −0.466746 | ||||||||
\(345\) | 2.17157 | 0.116914 | ||||||||
\(346\) | 17.8995 | 0.962283 | ||||||||
\(347\) | −13.4142 | −0.720113 | −0.360056 | − | 0.932931i | \(-0.617243\pi\) | ||||
−0.360056 | + | 0.932931i | \(0.617243\pi\) | |||||||
\(348\) | −7.48528 | −0.401253 | ||||||||
\(349\) | 23.8995 | 1.27931 | 0.639655 | − | 0.768662i | \(-0.279077\pi\) | ||||
0.639655 | + | 0.768662i | \(0.279077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −6.41421 | −0.341879 | ||||||||
\(353\) | 15.1716 | 0.807501 | 0.403751 | − | 0.914869i | \(-0.367706\pi\) | ||||
0.403751 | + | 0.914869i | \(0.367706\pi\) | |||||||
\(354\) | −11.0711 | −0.588421 | ||||||||
\(355\) | −5.75736 | −0.305569 | ||||||||
\(356\) | 14.2426 | 0.754858 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.10051 | −0.322422 | ||||||||
\(359\) | −6.14214 | −0.324170 | −0.162085 | − | 0.986777i | \(-0.551822\pi\) | ||||
−0.162085 | + | 0.986777i | \(0.551822\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 2.68629 | 0.141384 | ||||||||
\(362\) | −22.8284 | −1.19984 | ||||||||
\(363\) | −30.1421 | −1.58205 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | 10.4142 | 0.544360 | ||||||||
\(367\) | 6.34315 | 0.331110 | 0.165555 | − | 0.986201i | \(-0.447059\pi\) | ||||
0.165555 | + | 0.986201i | \(0.447059\pi\) | |||||||
\(368\) | −2.17157 | −0.113201 | ||||||||
\(369\) | 5.17157 | 0.269221 | ||||||||
\(370\) | −8.41421 | −0.437434 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.41421 | 0.0733236 | ||||||||
\(373\) | 30.8701 | 1.59839 | 0.799195 | − | 0.601071i | \(-0.205259\pi\) | ||||
0.799195 | + | 0.601071i | \(0.205259\pi\) | |||||||
\(374\) | 20.7990 | 1.07549 | ||||||||
\(375\) | 9.00000 | 0.464758 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | 7.48528 | 0.385512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8995 | 0.611236 | 0.305618 | − | 0.952154i | \(-0.401137\pi\) | ||||
0.305618 | + | 0.952154i | \(0.401137\pi\) | |||||||
\(380\) | 4.65685 | 0.238892 | ||||||||
\(381\) | −6.72792 | −0.344682 | ||||||||
\(382\) | −21.9706 | −1.12411 | ||||||||
\(383\) | 22.3137 | 1.14018 | 0.570089 | − | 0.821583i | \(-0.306909\pi\) | ||||
0.570089 | + | 0.821583i | \(0.306909\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.75736 | 0.293042 | ||||||||
\(387\) | −8.65685 | −0.440053 | ||||||||
\(388\) | −7.31371 | −0.371297 | ||||||||
\(389\) | 29.6569 | 1.50366 | 0.751831 | − | 0.659356i | \(-0.229171\pi\) | ||||
0.751831 | + | 0.659356i | \(0.229171\pi\) | |||||||
\(390\) | −1.00000 | −0.0506370 | ||||||||
\(391\) | 7.04163 | 0.356111 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.72792 | −0.288935 | ||||||||
\(394\) | 4.58579 | 0.231029 | ||||||||
\(395\) | 2.24264 | 0.112839 | ||||||||
\(396\) | −6.41421 | −0.322326 | ||||||||
\(397\) | 11.6569 | 0.585041 | 0.292520 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292520 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(398\) | 16.5563 | 0.829895 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −23.7990 | −1.18846 | −0.594232 | − | 0.804293i | \(-0.702544\pi\) | ||||
−0.594232 | + | 0.804293i | \(0.702544\pi\) | |||||||
\(402\) | 15.5563 | 0.775880 | ||||||||
\(403\) | −1.41421 | −0.0704470 | ||||||||
\(404\) | 12.5858 | 0.626166 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.9706 | 2.67522 | ||||||||
\(408\) | 3.24264 | 0.160535 | ||||||||
\(409\) | 8.79899 | 0.435082 | 0.217541 | − | 0.976051i | \(-0.430196\pi\) | ||||
0.217541 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(410\) | 5.17157 | 0.255406 | ||||||||
\(411\) | 6.41421 | 0.316390 | ||||||||
\(412\) | −1.58579 | −0.0781261 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.17157 | −0.106727 | ||||||||
\(415\) | 3.65685 | 0.179508 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 19.7990 | 0.969561 | ||||||||
\(418\) | −29.8701 | −1.46099 | ||||||||
\(419\) | −22.0711 | −1.07824 | −0.539121 | − | 0.842228i | \(-0.681243\pi\) | ||||
−0.539121 | + | 0.842228i | \(0.681243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.4558 | −1.72801 | −0.864006 | − | 0.503481i | \(-0.832052\pi\) | ||||
−0.864006 | + | 0.503481i | \(0.832052\pi\) | |||||||
\(422\) | 12.6569 | 0.616126 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | −5.65685 | −0.274721 | ||||||||
\(425\) | 12.9706 | 0.629165 | ||||||||
\(426\) | 5.75736 | 0.278945 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.5563 | −0.848618 | ||||||||
\(429\) | 6.41421 | 0.309681 | ||||||||
\(430\) | −8.65685 | −0.417471 | ||||||||
\(431\) | 13.5147 | 0.650981 | 0.325491 | − | 0.945545i | \(-0.394471\pi\) | ||||
0.325491 | + | 0.945545i | \(0.394471\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.48528 | −0.358892 | ||||||||
\(436\) | 0.899495 | 0.0430780 | ||||||||
\(437\) | −10.1127 | −0.483756 | ||||||||
\(438\) | 11.0000 | 0.525600 | ||||||||
\(439\) | 2.07107 | 0.0988467 | 0.0494233 | − | 0.998778i | \(-0.484262\pi\) | ||||
0.0494233 | + | 0.998778i | \(0.484262\pi\) | |||||||
\(440\) | −6.41421 | −0.305786 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.24264 | −0.154237 | ||||||||
\(443\) | −9.79899 | −0.465564 | −0.232782 | − | 0.972529i | \(-0.574783\pi\) | ||||
−0.232782 | + | 0.972529i | \(0.574783\pi\) | |||||||
\(444\) | 8.41421 | 0.399321 | ||||||||
\(445\) | 14.2426 | 0.675166 | ||||||||
\(446\) | 14.0000 | 0.662919 | ||||||||
\(447\) | −8.48528 | −0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0416 | 0.993016 | 0.496508 | − | 0.868032i | \(-0.334615\pi\) | ||||
0.496508 | + | 0.868032i | \(0.334615\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | −33.1716 | −1.56199 | ||||||||
\(452\) | 4.58579 | 0.215697 | ||||||||
\(453\) | 6.41421 | 0.301366 | ||||||||
\(454\) | −5.07107 | −0.237997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.65685 | −0.218077 | ||||||||
\(457\) | 39.6985 | 1.85702 | 0.928508 | − | 0.371311i | \(-0.121092\pi\) | ||||
0.928508 | + | 0.371311i | \(0.121092\pi\) | |||||||
\(458\) | 3.89949 | 0.182211 | ||||||||
\(459\) | 3.24264 | 0.151354 | ||||||||
\(460\) | −2.17157 | −0.101250 | ||||||||
\(461\) | 33.4853 | 1.55957 | 0.779783 | − | 0.626050i | \(-0.215330\pi\) | ||||
0.779783 | + | 0.626050i | \(0.215330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0711 | 1.11868 | 0.559339 | − | 0.828939i | \(-0.311055\pi\) | ||||
0.559339 | + | 0.828939i | \(0.311055\pi\) | |||||||
\(464\) | 7.48528 | 0.347495 | ||||||||
\(465\) | 1.41421 | 0.0655826 | ||||||||
\(466\) | −6.14214 | −0.284529 | ||||||||
\(467\) | −10.4142 | −0.481912 | −0.240956 | − | 0.970536i | \(-0.577461\pi\) | ||||
−0.240956 | + | 0.970536i | \(0.577461\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 8.41421 | 0.387706 | ||||||||
\(472\) | 11.0711 | 0.509587 | ||||||||
\(473\) | 55.5269 | 2.55313 | ||||||||
\(474\) | −2.24264 | −0.103008 | ||||||||
\(475\) | −18.6274 | −0.854685 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.65685 | −0.259010 | ||||||||
\(478\) | −20.3848 | −0.932378 | ||||||||
\(479\) | 33.1421 | 1.51430 | 0.757151 | − | 0.653239i | \(-0.226590\pi\) | ||||
0.757151 | + | 0.653239i | \(0.226590\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −8.41421 | −0.383655 | ||||||||
\(482\) | −14.9706 | −0.681890 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.1421 | 1.37010 | ||||||||
\(485\) | −7.31371 | −0.332098 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 8.34315 | 0.378064 | 0.189032 | − | 0.981971i | \(-0.439465\pi\) | ||||
0.189032 | + | 0.981971i | \(0.439465\pi\) | |||||||
\(488\) | −10.4142 | −0.471429 | ||||||||
\(489\) | 0.343146 | 0.0155176 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.8284 | 1.12049 | 0.560246 | − | 0.828327i | \(-0.310707\pi\) | ||||
0.560246 | + | 0.828327i | \(0.310707\pi\) | |||||||
\(492\) | −5.17157 | −0.233153 | ||||||||
\(493\) | −24.2721 | −1.09316 | ||||||||
\(494\) | 4.65685 | 0.209522 | ||||||||
\(495\) | −6.41421 | −0.288297 | ||||||||
\(496\) | −1.41421 | −0.0635001 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.65685 | −0.163868 | ||||||||
\(499\) | 22.0416 | 0.986719 | 0.493359 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493359 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | 23.1421 | 1.03391 | ||||||||
\(502\) | −6.55635 | −0.292624 | ||||||||
\(503\) | −22.3848 | −0.998088 | −0.499044 | − | 0.866577i | \(-0.666315\pi\) | ||||
−0.499044 | + | 0.866577i | \(0.666315\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.5858 | 0.560060 | ||||||||
\(506\) | 13.9289 | 0.619217 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.72792 | 0.298503 | ||||||||
\(509\) | −18.7990 | −0.833251 | −0.416625 | − | 0.909078i | \(-0.636787\pi\) | ||||
−0.416625 | + | 0.909078i | \(0.636787\pi\) | |||||||
\(510\) | 3.24264 | 0.143587 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.65685 | −0.205605 | ||||||||
\(514\) | 2.82843 | 0.124757 | ||||||||
\(515\) | −1.58579 | −0.0698781 | ||||||||
\(516\) | 8.65685 | 0.381097 | ||||||||
\(517\) | 38.4853 | 1.69258 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.8995 | −0.785701 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | 9.24264 | 0.404927 | 0.202464 | − | 0.979290i | \(-0.435105\pi\) | ||||
0.202464 | + | 0.979290i | \(0.435105\pi\) | |||||||
\(522\) | 7.48528 | 0.327622 | ||||||||
\(523\) | −13.7574 | −0.601567 | −0.300784 | − | 0.953692i | \(-0.597248\pi\) | ||||
−0.300784 | + | 0.953692i | \(0.597248\pi\) | |||||||
\(524\) | 5.72792 | 0.250225 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.6274 | 1.16101 | ||||||||
\(527\) | 4.58579 | 0.199760 | ||||||||
\(528\) | 6.41421 | 0.279143 | ||||||||
\(529\) | −18.2843 | −0.794968 | ||||||||
\(530\) | −5.65685 | −0.245718 | ||||||||
\(531\) | 11.0711 | 0.480443 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.17157 | 0.224006 | ||||||||
\(534\) | −14.2426 | −0.616339 | ||||||||
\(535\) | −17.5563 | −0.759027 | ||||||||
\(536\) | −15.5563 | −0.671932 | ||||||||
\(537\) | 6.10051 | 0.263256 | ||||||||
\(538\) | 13.2132 | 0.569662 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 11.3848 | 0.489470 | 0.244735 | − | 0.969590i | \(-0.421299\pi\) | ||||
0.244735 | + | 0.969590i | \(0.421299\pi\) | |||||||
\(542\) | −28.3848 | −1.21923 | ||||||||
\(543\) | 22.8284 | 0.979662 | ||||||||
\(544\) | −3.24264 | −0.139027 | ||||||||
\(545\) | 0.899495 | 0.0385301 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.5147 | 0.748875 | 0.374438 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374438 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(548\) | −6.41421 | −0.274002 | ||||||||
\(549\) | −10.4142 | −0.444468 | ||||||||
\(550\) | 25.6569 | 1.09401 | ||||||||
\(551\) | 34.8579 | 1.48499 | ||||||||
\(552\) | 2.17157 | 0.0924283 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.58579 | −0.194831 | ||||||||
\(555\) | 8.41421 | 0.357163 | ||||||||
\(556\) | −19.7990 | −0.839664 | ||||||||
\(557\) | −28.4853 | −1.20696 | −0.603480 | − | 0.797378i | \(-0.706220\pi\) | ||||
−0.603480 | + | 0.797378i | \(0.706220\pi\) | |||||||
\(558\) | −1.41421 | −0.0598684 | ||||||||
\(559\) | −8.65685 | −0.366146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.7990 | −0.878134 | ||||||||
\(562\) | 26.9706 | 1.13768 | ||||||||
\(563\) | 23.2426 | 0.979561 | 0.489780 | − | 0.871846i | \(-0.337077\pi\) | ||||
0.489780 | + | 0.871846i | \(0.337077\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 4.58579 | 0.192925 | ||||||||
\(566\) | 8.48528 | 0.356663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.75736 | −0.241573 | ||||||||
\(569\) | −9.79899 | −0.410795 | −0.205398 | − | 0.978679i | \(-0.565849\pi\) | ||||
−0.205398 | + | 0.978679i | \(0.565849\pi\) | |||||||
\(570\) | −4.65685 | −0.195054 | ||||||||
\(571\) | −44.6274 | −1.86760 | −0.933800 | − | 0.357796i | \(-0.883528\pi\) | ||||
−0.933800 | + | 0.357796i | \(0.883528\pi\) | |||||||
\(572\) | −6.41421 | −0.268192 | ||||||||
\(573\) | 21.9706 | 0.917833 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.68629 | 0.362243 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.14214 | −0.255700 | −0.127850 | − | 0.991793i | \(-0.540808\pi\) | ||||
−0.127850 | + | 0.991793i | \(0.540808\pi\) | |||||||
\(578\) | −6.48528 | −0.269752 | ||||||||
\(579\) | −5.75736 | −0.239268 | ||||||||
\(580\) | 7.48528 | 0.310809 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.31371 | 0.303163 | ||||||||
\(583\) | 36.2843 | 1.50274 | ||||||||
\(584\) | −11.0000 | −0.455183 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 19.7990 | 0.817889 | ||||||||
\(587\) | −8.82843 | −0.364388 | −0.182194 | − | 0.983263i | \(-0.558320\pi\) | ||||
−0.182194 | + | 0.983263i | \(0.558320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.58579 | −0.271363 | ||||||||
\(590\) | 11.0711 | 0.455789 | ||||||||
\(591\) | −4.58579 | −0.188634 | ||||||||
\(592\) | −8.41421 | −0.345822 | ||||||||
\(593\) | −15.8995 | −0.652914 | −0.326457 | − | 0.945212i | \(-0.605855\pi\) | ||||
−0.326457 | + | 0.945212i | \(0.605855\pi\) | |||||||
\(594\) | 6.41421 | 0.263178 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.48528 | 0.347571 | ||||||||
\(597\) | −16.5563 | −0.677606 | ||||||||
\(598\) | −2.17157 | −0.0888022 | ||||||||
\(599\) | −1.68629 | −0.0689000 | −0.0344500 | − | 0.999406i | \(-0.510968\pi\) | ||||
−0.0344500 | + | 0.999406i | \(0.510968\pi\) | |||||||
\(600\) | 4.00000 | 0.163299 | ||||||||
\(601\) | 9.45584 | 0.385712 | 0.192856 | − | 0.981227i | \(-0.438225\pi\) | ||||
0.192856 | + | 0.981227i | \(0.438225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.5563 | −0.633504 | ||||||||
\(604\) | −6.41421 | −0.260991 | ||||||||
\(605\) | 30.1421 | 1.22545 | ||||||||
\(606\) | −12.5858 | −0.511263 | ||||||||
\(607\) | 19.7279 | 0.800732 | 0.400366 | − | 0.916355i | \(-0.368883\pi\) | ||||
0.400366 | + | 0.916355i | \(0.368883\pi\) | |||||||
\(608\) | 4.65685 | 0.188860 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.4142 | −0.421659 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | −3.24264 | −0.131076 | ||||||||
\(613\) | 25.8701 | 1.04488 | 0.522441 | − | 0.852676i | \(-0.325022\pi\) | ||||
0.522441 | + | 0.852676i | \(0.325022\pi\) | |||||||
\(614\) | −21.3137 | −0.860151 | ||||||||
\(615\) | −5.17157 | −0.208538 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2426 | 0.613646 | 0.306823 | − | 0.951767i | \(-0.400734\pi\) | ||||
0.306823 | + | 0.951767i | \(0.400734\pi\) | |||||||
\(618\) | 1.58579 | 0.0637897 | ||||||||
\(619\) | 25.8284 | 1.03813 | 0.519066 | − | 0.854734i | \(-0.326280\pi\) | ||||
0.519066 | + | 0.854734i | \(0.326280\pi\) | |||||||
\(620\) | −1.41421 | −0.0567962 | ||||||||
\(621\) | 2.17157 | 0.0871422 | ||||||||
\(622\) | −12.8284 | −0.514373 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −15.8995 | −0.635472 | ||||||||
\(627\) | 29.8701 | 1.19290 | ||||||||
\(628\) | −8.41421 | −0.335764 | ||||||||
\(629\) | 27.2843 | 1.08790 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.04163 | 0.280323 | 0.140161 | − | 0.990129i | \(-0.455238\pi\) | ||||
0.140161 | + | 0.990129i | \(0.455238\pi\) | |||||||
\(632\) | 2.24264 | 0.0892075 | ||||||||
\(633\) | −12.6569 | −0.503065 | ||||||||
\(634\) | −15.4142 | −0.612177 | ||||||||
\(635\) | 6.72792 | 0.266989 | ||||||||
\(636\) | 5.65685 | 0.224309 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −48.0122 | −1.90082 | ||||||||
\(639\) | −5.75736 | −0.227758 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 18.2426 | 0.720541 | 0.360270 | − | 0.932848i | \(-0.382684\pi\) | ||||
0.360270 | + | 0.932848i | \(0.382684\pi\) | |||||||
\(642\) | 17.5563 | 0.692894 | ||||||||
\(643\) | −34.1127 | −1.34527 | −0.672637 | − | 0.739973i | \(-0.734838\pi\) | ||||
−0.672637 | + | 0.739973i | \(0.734838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.65685 | 0.340863 | ||||||||
\(646\) | −15.1005 | −0.594121 | ||||||||
\(647\) | 16.6863 | 0.656006 | 0.328003 | − | 0.944677i | \(-0.393624\pi\) | ||||
0.328003 | + | 0.944677i | \(0.393624\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −71.0122 | −2.78747 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.343146 | −0.0134386 | ||||||||
\(653\) | 17.0000 | 0.665261 | 0.332631 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332631 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(654\) | −0.899495 | −0.0351730 | ||||||||
\(655\) | 5.72792 | 0.223808 | ||||||||
\(656\) | 5.17157 | 0.201916 | ||||||||
\(657\) | −11.0000 | −0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.7990 | −1.78408 | −0.892038 | − | 0.451961i | \(-0.850725\pi\) | ||||
−0.892038 | + | 0.451961i | \(0.850725\pi\) | |||||||
\(660\) | 6.41421 | 0.249673 | ||||||||
\(661\) | −0.343146 | −0.0133468 | −0.00667341 | − | 0.999978i | \(-0.502124\pi\) | ||||
−0.00667341 | + | 0.999978i | \(0.502124\pi\) | |||||||
\(662\) | 3.75736 | 0.146034 | ||||||||
\(663\) | 3.24264 | 0.125934 | ||||||||
\(664\) | 3.65685 | 0.141913 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.41421 | −0.326044 | ||||||||
\(667\) | −16.2548 | −0.629390 | ||||||||
\(668\) | −23.1421 | −0.895396 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | −15.5563 | −0.600994 | ||||||||
\(671\) | 66.7990 | 2.57875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.48528 | 0.288536 | 0.144268 | − | 0.989539i | \(-0.453917\pi\) | ||||
0.144268 | + | 0.989539i | \(0.453917\pi\) | |||||||
\(674\) | −27.8284 | −1.07191 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 9.51472 | 0.365680 | 0.182840 | − | 0.983143i | \(-0.441471\pi\) | ||||
0.182840 | + | 0.983143i | \(0.441471\pi\) | |||||||
\(678\) | −4.58579 | −0.176116 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.24264 | −0.124350 | ||||||||
\(681\) | 5.07107 | 0.194324 | ||||||||
\(682\) | 9.07107 | 0.347349 | ||||||||
\(683\) | −1.24264 | −0.0475483 | −0.0237742 | − | 0.999717i | \(-0.507568\pi\) | ||||
−0.0237742 | + | 0.999717i | \(0.507568\pi\) | |||||||
\(684\) | 4.65685 | 0.178059 | ||||||||
\(685\) | −6.41421 | −0.245075 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.89949 | −0.148775 | ||||||||
\(688\) | −8.65685 | −0.330039 | ||||||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 2.17157 | 0.0826704 | ||||||||
\(691\) | 24.1421 | 0.918410 | 0.459205 | − | 0.888330i | \(-0.348134\pi\) | ||||
0.459205 | + | 0.888330i | \(0.348134\pi\) | |||||||
\(692\) | 17.8995 | 0.680437 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.4142 | −0.509197 | ||||||||
\(695\) | −19.7990 | −0.751018 | ||||||||
\(696\) | −7.48528 | −0.283729 | ||||||||
\(697\) | −16.7696 | −0.635192 | ||||||||
\(698\) | 23.8995 | 0.904609 | ||||||||
\(699\) | 6.14214 | 0.232317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.5147 | 1.19029 | 0.595147 | − | 0.803617i | \(-0.297094\pi\) | ||||
0.595147 | + | 0.803617i | \(0.297094\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −39.1838 | −1.47784 | ||||||||
\(704\) | −6.41421 | −0.241745 | ||||||||
\(705\) | 6.00000 | 0.225973 | ||||||||
\(706\) | 15.1716 | 0.570990 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.0711 | −0.416076 | ||||||||
\(709\) | −48.1421 | −1.80802 | −0.904008 | − | 0.427516i | \(-0.859389\pi\) | ||||
−0.904008 | + | 0.427516i | \(0.859389\pi\) | |||||||
\(710\) | −5.75736 | −0.216070 | ||||||||
\(711\) | 2.24264 | 0.0841056 | ||||||||
\(712\) | 14.2426 | 0.533766 | ||||||||
\(713\) | 3.07107 | 0.115012 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.41421 | −0.239878 | ||||||||
\(716\) | −6.10051 | −0.227987 | ||||||||
\(717\) | 20.3848 | 0.761283 | ||||||||
\(718\) | −6.14214 | −0.229222 | ||||||||
\(719\) | 14.8701 | 0.554560 | 0.277280 | − | 0.960789i | \(-0.410567\pi\) | ||||
0.277280 | + | 0.960789i | \(0.410567\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.68629 | 0.0999734 | ||||||||
\(723\) | 14.9706 | 0.556761 | ||||||||
\(724\) | −22.8284 | −0.848412 | ||||||||
\(725\) | −29.9411 | −1.11199 | ||||||||
\(726\) | −30.1421 | −1.11868 | ||||||||
\(727\) | 41.8701 | 1.55287 | 0.776437 | − | 0.630195i | \(-0.217025\pi\) | ||||
0.776437 | + | 0.630195i | \(0.217025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | 28.0711 | 1.03825 | ||||||||
\(732\) | 10.4142 | 0.384920 | ||||||||
\(733\) | 8.44365 | 0.311873 | 0.155937 | − | 0.987767i | \(-0.450160\pi\) | ||||
0.155937 | + | 0.987767i | \(0.450160\pi\) | |||||||
\(734\) | 6.34315 | 0.234130 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.17157 | −0.0800452 | ||||||||
\(737\) | 99.7817 | 3.67551 | ||||||||
\(738\) | 5.17157 | 0.190368 | ||||||||
\(739\) | 8.34315 | 0.306908 | 0.153454 | − | 0.988156i | \(-0.450960\pi\) | ||||
0.153454 | + | 0.988156i | \(0.450960\pi\) | |||||||
\(740\) | −8.41421 | −0.309313 | ||||||||
\(741\) | −4.65685 | −0.171074 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2843 | 1.25777 | 0.628884 | − | 0.777499i | \(-0.283512\pi\) | ||||
0.628884 | + | 0.777499i | \(0.283512\pi\) | |||||||
\(744\) | 1.41421 | 0.0518476 | ||||||||
\(745\) | 8.48528 | 0.310877 | ||||||||
\(746\) | 30.8701 | 1.13023 | ||||||||
\(747\) | 3.65685 | 0.133797 | ||||||||
\(748\) | 20.7990 | 0.760486 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | −21.2132 | −0.774081 | −0.387040 | − | 0.922063i | \(-0.626503\pi\) | ||||
−0.387040 | + | 0.922063i | \(0.626503\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 6.55635 | 0.238927 | ||||||||
\(754\) | 7.48528 | 0.272598 | ||||||||
\(755\) | −6.41421 | −0.233437 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.7279 | −1.11683 | −0.558413 | − | 0.829563i | \(-0.688589\pi\) | ||||
−0.558413 | + | 0.829563i | \(0.688589\pi\) | |||||||
\(758\) | 11.8995 | 0.432209 | ||||||||
\(759\) | −13.9289 | −0.505588 | ||||||||
\(760\) | 4.65685 | 0.168922 | ||||||||
\(761\) | −44.0833 | −1.59802 | −0.799008 | − | 0.601320i | \(-0.794642\pi\) | ||||
−0.799008 | + | 0.601320i | \(0.794642\pi\) | |||||||
\(762\) | −6.72792 | −0.243727 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.9706 | −0.794867 | ||||||||
\(765\) | −3.24264 | −0.117238 | ||||||||
\(766\) | 22.3137 | 0.806227 | ||||||||
\(767\) | 11.0711 | 0.399753 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 28.9411 | 1.04364 | 0.521822 | − | 0.853054i | \(-0.325253\pi\) | ||||
0.521822 | + | 0.853054i | \(0.325253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.82843 | −0.101863 | ||||||||
\(772\) | 5.75736 | 0.207212 | ||||||||
\(773\) | −54.2548 | −1.95141 | −0.975705 | − | 0.219087i | \(-0.929692\pi\) | ||||
−0.975705 | + | 0.219087i | \(0.929692\pi\) | |||||||
\(774\) | −8.65685 | −0.311164 | ||||||||
\(775\) | 5.65685 | 0.203200 | ||||||||
\(776\) | −7.31371 | −0.262547 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.6569 | 1.06325 | ||||||||
\(779\) | 24.0833 | 0.862872 | ||||||||
\(780\) | −1.00000 | −0.0358057 | ||||||||
\(781\) | 36.9289 | 1.32142 | ||||||||
\(782\) | 7.04163 | 0.251808 | ||||||||
\(783\) | −7.48528 | −0.267502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.41421 | −0.300316 | ||||||||
\(786\) | −5.72792 | −0.204308 | ||||||||
\(787\) | 13.9706 | 0.497997 | 0.248998 | − | 0.968504i | \(-0.419899\pi\) | ||||
0.248998 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(788\) | 4.58579 | 0.163362 | ||||||||
\(789\) | −26.6274 | −0.947961 | ||||||||
\(790\) | 2.24264 | 0.0797896 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.41421 | −0.227919 | ||||||||
\(793\) | −10.4142 | −0.369820 | ||||||||
\(794\) | 11.6569 | 0.413686 | ||||||||
\(795\) | 5.65685 | 0.200628 | ||||||||
\(796\) | 16.5563 | 0.586824 | ||||||||
\(797\) | −6.24264 | −0.221126 | −0.110563 | − | 0.993869i | \(-0.535265\pi\) | ||||
−0.110563 | + | 0.993869i | \(0.535265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.4558 | 0.688298 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | 14.2426 | 0.503239 | ||||||||
\(802\) | −23.7990 | −0.840372 | ||||||||
\(803\) | 70.5563 | 2.48988 | ||||||||
\(804\) | 15.5563 | 0.548630 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.41421 | −0.0498135 | ||||||||
\(807\) | −13.2132 | −0.465127 | ||||||||
\(808\) | 12.5858 | 0.442766 | ||||||||
\(809\) | 35.8995 | 1.26216 | 0.631080 | − | 0.775718i | \(-0.282612\pi\) | ||||
0.631080 | + | 0.775718i | \(0.282612\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 15.8284 | 0.555811 | 0.277906 | − | 0.960608i | \(-0.410360\pi\) | ||||
0.277906 | + | 0.960608i | \(0.410360\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.3848 | 0.995498 | ||||||||
\(814\) | 53.9706 | 1.89167 | ||||||||
\(815\) | −0.343146 | −0.0120199 | ||||||||
\(816\) | 3.24264 | 0.113515 | ||||||||
\(817\) | −40.3137 | −1.41040 | ||||||||
\(818\) | 8.79899 | 0.307649 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.17157 | 0.180599 | ||||||||
\(821\) | −23.7990 | −0.830590 | −0.415295 | − | 0.909687i | \(-0.636322\pi\) | ||||
−0.415295 | + | 0.909687i | \(0.636322\pi\) | |||||||
\(822\) | 6.41421 | 0.223721 | ||||||||
\(823\) | 24.0416 | 0.838039 | 0.419019 | − | 0.907977i | \(-0.362374\pi\) | ||||
0.419019 | + | 0.907977i | \(0.362374\pi\) | |||||||
\(824\) | −1.58579 | −0.0552435 | ||||||||
\(825\) | −25.6569 | −0.893257 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.38478 | 0.117700 | 0.0588501 | − | 0.998267i | \(-0.481257\pi\) | ||||
0.0588501 | + | 0.998267i | \(0.481257\pi\) | |||||||
\(828\) | −2.17157 | −0.0754674 | ||||||||
\(829\) | 8.61522 | 0.299219 | 0.149610 | − | 0.988745i | \(-0.452198\pi\) | ||||
0.149610 | + | 0.988745i | \(0.452198\pi\) | |||||||
\(830\) | 3.65685 | 0.126931 | ||||||||
\(831\) | 4.58579 | 0.159079 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.7990 | 0.685583 | ||||||||
\(835\) | −23.1421 | −0.800867 | ||||||||
\(836\) | −29.8701 | −1.03308 | ||||||||
\(837\) | 1.41421 | 0.0488824 | ||||||||
\(838\) | −22.0711 | −0.762432 | ||||||||
\(839\) | 38.9706 | 1.34541 | 0.672707 | − | 0.739909i | \(-0.265132\pi\) | ||||
0.672707 | + | 0.739909i | \(0.265132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0294 | 0.932050 | ||||||||
\(842\) | −35.4558 | −1.22189 | ||||||||
\(843\) | −26.9706 | −0.928916 | ||||||||
\(844\) | 12.6569 | 0.435667 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.65685 | −0.194257 | ||||||||
\(849\) | −8.48528 | −0.291214 | ||||||||
\(850\) | 12.9706 | 0.444887 | ||||||||
\(851\) | 18.2721 | 0.626359 | ||||||||
\(852\) | 5.75736 | 0.197244 | ||||||||
\(853\) | 52.9706 | 1.81368 | 0.906839 | − | 0.421478i | \(-0.138488\pi\) | ||||
0.906839 | + | 0.421478i | \(0.138488\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.65685 | 0.159261 | ||||||||
\(856\) | −17.5563 | −0.600064 | ||||||||
\(857\) | −30.4853 | −1.04136 | −0.520679 | − | 0.853753i | \(-0.674321\pi\) | ||||
−0.520679 | + | 0.853753i | \(0.674321\pi\) | |||||||
\(858\) | 6.41421 | 0.218978 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | −8.65685 | −0.295196 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.5147 | 0.460313 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 17.8995 | 0.608601 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.48528 | 0.220252 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.3848 | −0.487970 | ||||||||
\(870\) | −7.48528 | −0.253775 | ||||||||
\(871\) | −15.5563 | −0.527107 | ||||||||
\(872\) | 0.899495 | 0.0304607 | ||||||||
\(873\) | −7.31371 | −0.247532 | ||||||||
\(874\) | −10.1127 | −0.342067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000 | 0.371656 | ||||||||
\(877\) | 8.48528 | 0.286528 | 0.143264 | − | 0.989685i | \(-0.454240\pi\) | ||||
0.143264 | + | 0.989685i | \(0.454240\pi\) | |||||||
\(878\) | 2.07107 | 0.0698952 | ||||||||
\(879\) | −19.7990 | −0.667803 | ||||||||
\(880\) | −6.41421 | −0.216223 | ||||||||
\(881\) | 53.7279 | 1.81014 | 0.905070 | − | 0.425263i | \(-0.139818\pi\) | ||||
0.905070 | + | 0.425263i | \(0.139818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5980 | −1.50084 | −0.750421 | − | 0.660960i | \(-0.770149\pi\) | ||||
−0.750421 | + | 0.660960i | \(0.770149\pi\) | |||||||
\(884\) | −3.24264 | −0.109062 | ||||||||
\(885\) | −11.0711 | −0.372150 | ||||||||
\(886\) | −9.79899 | −0.329204 | ||||||||
\(887\) | 2.82843 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(888\) | 8.41421 | 0.282363 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.2426 | 0.477414 | ||||||||
\(891\) | −6.41421 | −0.214884 | ||||||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | −27.9411 | −0.935014 | ||||||||
\(894\) | −8.48528 | −0.283790 | ||||||||
\(895\) | −6.10051 | −0.203917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.17157 | 0.0725067 | ||||||||
\(898\) | 21.0416 | 0.702168 | ||||||||
\(899\) | −10.5858 | −0.353056 | ||||||||
\(900\) | −4.00000 | −0.133333 | ||||||||
\(901\) | 18.3431 | 0.611099 | ||||||||
\(902\) | −33.1716 | −1.10449 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.58579 | 0.152521 | ||||||||
\(905\) | −22.8284 | −0.758843 | ||||||||
\(906\) | 6.41421 | 0.213098 | ||||||||
\(907\) | −17.5147 | −0.581567 | −0.290783 | − | 0.956789i | \(-0.593916\pi\) | ||||
−0.290783 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(908\) | −5.07107 | −0.168289 | ||||||||
\(909\) | 12.5858 | 0.417444 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.8284 | −1.38584 | −0.692919 | − | 0.721016i | \(-0.743676\pi\) | ||||
−0.692919 | + | 0.721016i | \(0.743676\pi\) | |||||||
\(912\) | −4.65685 | −0.154204 | ||||||||
\(913\) | −23.4558 | −0.776275 | ||||||||
\(914\) | 39.6985 | 1.31311 | ||||||||
\(915\) | 10.4142 | 0.344283 | ||||||||
\(916\) | 3.89949 | 0.128843 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.24264 | 0.107023 | ||||||||
\(919\) | 50.4853 | 1.66536 | 0.832678 | − | 0.553758i | \(-0.186807\pi\) | ||||
0.832678 | + | 0.553758i | \(0.186807\pi\) | |||||||
\(920\) | −2.17157 | −0.0715946 | ||||||||
\(921\) | 21.3137 | 0.702311 | ||||||||
\(922\) | 33.4853 | 1.10278 | ||||||||
\(923\) | −5.75736 | −0.189506 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.6569 | 1.10663 | ||||||||
\(926\) | 24.0711 | 0.791024 | ||||||||
\(927\) | −1.58579 | −0.0520841 | ||||||||
\(928\) | 7.48528 | 0.245716 | ||||||||
\(929\) | −25.1716 | −0.825853 | −0.412926 | − | 0.910764i | \(-0.635493\pi\) | ||||
−0.412926 | + | 0.910764i | \(0.635493\pi\) | |||||||
\(930\) | 1.41421 | 0.0463739 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.14214 | −0.201192 | ||||||||
\(933\) | 12.8284 | 0.419984 | ||||||||
\(934\) | −10.4142 | −0.340763 | ||||||||
\(935\) | 20.7990 | 0.680200 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 17.2132 | 0.562331 | 0.281165 | − | 0.959659i | \(-0.409279\pi\) | ||||
0.281165 | + | 0.959659i | \(0.409279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.8995 | 0.518860 | ||||||||
\(940\) | −6.00000 | −0.195698 | ||||||||
\(941\) | −11.9411 | −0.389270 | −0.194635 | − | 0.980876i | \(-0.562352\pi\) | ||||
−0.194635 | + | 0.980876i | \(0.562352\pi\) | |||||||
\(942\) | 8.41421 | 0.274150 | ||||||||
\(943\) | −11.2304 | −0.365714 | ||||||||
\(944\) | 11.0711 | 0.360333 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55.5269 | 1.80534 | ||||||||
\(947\) | 7.72792 | 0.251124 | 0.125562 | − | 0.992086i | \(-0.459927\pi\) | ||||
0.125562 | + | 0.992086i | \(0.459927\pi\) | |||||||
\(948\) | −2.24264 | −0.0728376 | ||||||||
\(949\) | −11.0000 | −0.357075 | ||||||||
\(950\) | −18.6274 | −0.604353 | ||||||||
\(951\) | 15.4142 | 0.499840 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.9411 | −1.09946 | −0.549730 | − | 0.835342i | \(-0.685270\pi\) | ||||
−0.549730 | + | 0.835342i | \(0.685270\pi\) | |||||||
\(954\) | −5.65685 | −0.183147 | ||||||||
\(955\) | −21.9706 | −0.710951 | ||||||||
\(956\) | −20.3848 | −0.659291 | ||||||||
\(957\) | 48.0122 | 1.55201 | ||||||||
\(958\) | 33.1421 | 1.07077 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | −8.41421 | −0.271285 | ||||||||
\(963\) | −17.5563 | −0.565745 | ||||||||
\(964\) | −14.9706 | −0.482169 | ||||||||
\(965\) | 5.75736 | 0.185336 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.5858 | 1.27299 | 0.636497 | − | 0.771280i | \(-0.280383\pi\) | ||||
0.636497 | + | 0.771280i | \(0.280383\pi\) | |||||||
\(968\) | 30.1421 | 0.968805 | ||||||||
\(969\) | 15.1005 | 0.485098 | ||||||||
\(970\) | −7.31371 | −0.234829 | ||||||||
\(971\) | −11.7990 | −0.378648 | −0.189324 | − | 0.981915i | \(-0.560630\pi\) | ||||
−0.189324 | + | 0.981915i | \(0.560630\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.34315 | 0.267332 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | −10.4142 | −0.333351 | ||||||||
\(977\) | 0.272078 | 0.00870454 | 0.00435227 | − | 0.999991i | \(-0.498615\pi\) | ||||
0.00435227 | + | 0.999991i | \(0.498615\pi\) | |||||||
\(978\) | 0.343146 | 0.0109726 | ||||||||
\(979\) | −91.3553 | −2.91973 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.899495 | 0.0287187 | ||||||||
\(982\) | 24.8284 | 0.792307 | ||||||||
\(983\) | −11.6274 | −0.370857 | −0.185429 | − | 0.982658i | \(-0.559367\pi\) | ||||
−0.185429 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(984\) | −5.17157 | −0.164864 | ||||||||
\(985\) | 4.58579 | 0.146115 | ||||||||
\(986\) | −24.2721 | −0.772980 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.65685 | 0.148154 | ||||||||
\(989\) | 18.7990 | 0.597773 | ||||||||
\(990\) | −6.41421 | −0.203857 | ||||||||
\(991\) | −19.6569 | −0.624421 | −0.312210 | − | 0.950013i | \(-0.601069\pi\) | ||||
−0.312210 | + | 0.950013i | \(0.601069\pi\) | |||||||
\(992\) | −1.41421 | −0.0449013 | ||||||||
\(993\) | −3.75736 | −0.119236 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5563 | 0.524872 | ||||||||
\(996\) | −3.65685 | −0.115872 | ||||||||
\(997\) | −47.2548 | −1.49658 | −0.748288 | − | 0.663374i | \(-0.769124\pi\) | ||||
−0.748288 | + | 0.663374i | \(0.769124\pi\) | |||||||
\(998\) | 22.0416 | 0.697716 | ||||||||
\(999\) | 8.41421 | 0.266214 |
(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 | 3822.2.a.bq.1.1 | ✓ | 2 | |
7.6 | odd | 2 | 3822.2.a.br.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bq.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3822.2.a.br.1.1 | yes | 2 | 7.6 | odd | 2 |