Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} - 211 x^{3} - 64 x^{2} + 53 x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.05133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05133 | 0.743403 | 0.371702 | − | 0.928352i | \(-0.378774\pi\) | ||||
0.371702 | + | 0.928352i | \(0.378774\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.894704 | −0.447352 | ||||||||
\(5\) | −4.26226 | −1.90614 | −0.953071 | − | 0.302748i | \(-0.902096\pi\) | ||||
−0.953071 | + | 0.302748i | \(0.902096\pi\) | |||||||
\(6\) | −1.05133 | −0.429204 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.04329 | −1.07597 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.48105 | −1.41703 | ||||||||
\(11\) | −2.24822 | −0.677865 | −0.338932 | − | 0.940811i | \(-0.610066\pi\) | ||||
−0.338932 | + | 0.940811i | \(0.610066\pi\) | |||||||
\(12\) | 0.894704 | 0.258279 | ||||||||
\(13\) | 0.346093 | 0.0959888 | 0.0479944 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479944 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.26226 | 1.10051 | ||||||||
\(16\) | −1.41010 | −0.352525 | ||||||||
\(17\) | 4.66895 | 1.13239 | 0.566193 | − | 0.824273i | \(-0.308416\pi\) | ||||
0.566193 | + | 0.824273i | \(0.308416\pi\) | |||||||
\(18\) | 1.05133 | 0.247801 | ||||||||
\(19\) | −2.00040 | −0.458924 | −0.229462 | − | 0.973318i | \(-0.573697\pi\) | ||||
−0.229462 | + | 0.973318i | \(0.573697\pi\) | |||||||
\(20\) | 3.81346 | 0.852716 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36363 | −0.503927 | ||||||||
\(23\) | 2.47117 | 0.515275 | 0.257638 | − | 0.966242i | \(-0.417056\pi\) | ||||
0.257638 | + | 0.966242i | \(0.417056\pi\) | |||||||
\(24\) | 3.04329 | 0.621209 | ||||||||
\(25\) | 13.1669 | 2.63338 | ||||||||
\(26\) | 0.363858 | 0.0713584 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.18926 | 1.14932 | 0.574658 | − | 0.818394i | \(-0.305135\pi\) | ||||
0.574658 | + | 0.818394i | \(0.305135\pi\) | |||||||
\(30\) | 4.48105 | 0.818123 | ||||||||
\(31\) | −3.71258 | −0.666799 | −0.333400 | − | 0.942786i | \(-0.608196\pi\) | ||||
−0.333400 | + | 0.942786i | \(0.608196\pi\) | |||||||
\(32\) | 4.60410 | 0.813898 | ||||||||
\(33\) | 2.24822 | 0.391365 | ||||||||
\(34\) | 4.90861 | 0.841819 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.894704 | −0.149117 | ||||||||
\(37\) | −4.73147 | −0.777848 | −0.388924 | − | 0.921270i | \(-0.627153\pi\) | ||||
−0.388924 | + | 0.921270i | \(0.627153\pi\) | |||||||
\(38\) | −2.10309 | −0.341166 | ||||||||
\(39\) | −0.346093 | −0.0554192 | ||||||||
\(40\) | 12.9713 | 2.05094 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.374747 | −0.0571485 | −0.0285742 | − | 0.999592i | \(-0.509097\pi\) | ||||
−0.0285742 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(44\) | 2.01149 | 0.303244 | ||||||||
\(45\) | −4.26226 | −0.635380 | ||||||||
\(46\) | 2.59802 | 0.383057 | ||||||||
\(47\) | −3.92338 | −0.572284 | −0.286142 | − | 0.958187i | \(-0.592373\pi\) | ||||
−0.286142 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(48\) | 1.41010 | 0.203530 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.8427 | 1.95766 | ||||||||
\(51\) | −4.66895 | −0.653783 | ||||||||
\(52\) | −0.309650 | −0.0429408 | ||||||||
\(53\) | 10.4390 | 1.43391 | 0.716953 | − | 0.697121i | \(-0.245536\pi\) | ||||
0.716953 | + | 0.697121i | \(0.245536\pi\) | |||||||
\(54\) | −1.05133 | −0.143068 | ||||||||
\(55\) | 9.58251 | 1.29211 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00040 | 0.264960 | ||||||||
\(58\) | 6.50696 | 0.854405 | ||||||||
\(59\) | −7.37689 | −0.960389 | −0.480194 | − | 0.877162i | \(-0.659434\pi\) | ||||
−0.480194 | + | 0.877162i | \(0.659434\pi\) | |||||||
\(60\) | −3.81346 | −0.492316 | ||||||||
\(61\) | −11.7053 | −1.49871 | −0.749356 | − | 0.662168i | \(-0.769637\pi\) | ||||
−0.749356 | + | 0.662168i | \(0.769637\pi\) | |||||||
\(62\) | −3.90315 | −0.495701 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.66063 | 0.957579 | ||||||||
\(65\) | −1.47514 | −0.182968 | ||||||||
\(66\) | 2.36363 | 0.290942 | ||||||||
\(67\) | 14.2025 | 1.73511 | 0.867556 | − | 0.497339i | \(-0.165689\pi\) | ||||
0.867556 | + | 0.497339i | \(0.165689\pi\) | |||||||
\(68\) | −4.17732 | −0.506575 | ||||||||
\(69\) | −2.47117 | −0.297494 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60184 | 0.190104 | 0.0950519 | − | 0.995472i | \(-0.469698\pi\) | ||||
0.0950519 | + | 0.995472i | \(0.469698\pi\) | |||||||
\(72\) | −3.04329 | −0.358655 | ||||||||
\(73\) | 15.1789 | 1.77656 | 0.888279 | − | 0.459305i | \(-0.151901\pi\) | ||||
0.888279 | + | 0.459305i | \(0.151901\pi\) | |||||||
\(74\) | −4.97434 | −0.578255 | ||||||||
\(75\) | −13.1669 | −1.52038 | ||||||||
\(76\) | 1.78977 | 0.205301 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.363858 | −0.0411988 | ||||||||
\(79\) | 10.1626 | 1.14338 | 0.571692 | − | 0.820468i | \(-0.306287\pi\) | ||||
0.571692 | + | 0.820468i | \(0.306287\pi\) | |||||||
\(80\) | 6.01021 | 0.671962 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.05133 | 0.116100 | ||||||||
\(83\) | 12.3018 | 1.35030 | 0.675150 | − | 0.737681i | \(-0.264079\pi\) | ||||
0.675150 | + | 0.737681i | \(0.264079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.9003 | −2.15849 | ||||||||
\(86\) | −0.393984 | −0.0424843 | ||||||||
\(87\) | −6.18926 | −0.663558 | ||||||||
\(88\) | 6.84199 | 0.729359 | ||||||||
\(89\) | −7.79875 | −0.826666 | −0.413333 | − | 0.910580i | \(-0.635635\pi\) | ||||
−0.413333 | + | 0.910580i | \(0.635635\pi\) | |||||||
\(90\) | −4.48105 | −0.472344 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.21097 | −0.230509 | ||||||||
\(93\) | 3.71258 | 0.384977 | ||||||||
\(94\) | −4.12477 | −0.425438 | ||||||||
\(95\) | 8.52624 | 0.874774 | ||||||||
\(96\) | −4.60410 | −0.469904 | ||||||||
\(97\) | −12.3944 | −1.25847 | −0.629233 | − | 0.777217i | \(-0.716631\pi\) | ||||
−0.629233 | + | 0.777217i | \(0.716631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.24822 | −0.225955 | ||||||||
\(100\) | −11.7805 | −1.17805 | ||||||||
\(101\) | −9.64182 | −0.959397 | −0.479699 | − | 0.877433i | \(-0.659254\pi\) | ||||
−0.479699 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(102\) | −4.90861 | −0.486025 | ||||||||
\(103\) | 4.40291 | 0.433832 | 0.216916 | − | 0.976190i | \(-0.430400\pi\) | ||||
0.216916 | + | 0.976190i | \(0.430400\pi\) | |||||||
\(104\) | −1.05326 | −0.103281 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9748 | 1.06597 | ||||||||
\(107\) | 3.45652 | 0.334155 | 0.167077 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167077 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(108\) | 0.894704 | 0.0860929 | ||||||||
\(109\) | −18.0191 | −1.72592 | −0.862959 | − | 0.505274i | \(-0.831391\pi\) | ||||
−0.862959 | + | 0.505274i | \(0.831391\pi\) | |||||||
\(110\) | 10.0744 | 0.960555 | ||||||||
\(111\) | 4.73147 | 0.449091 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2569 | 1.52932 | 0.764659 | − | 0.644435i | \(-0.222907\pi\) | ||||
0.764659 | + | 0.644435i | \(0.222907\pi\) | |||||||
\(114\) | 2.10309 | 0.196972 | ||||||||
\(115\) | −10.5328 | −0.982187 | ||||||||
\(116\) | −5.53755 | −0.514149 | ||||||||
\(117\) | 0.346093 | 0.0319963 | ||||||||
\(118\) | −7.75555 | −0.713956 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.9713 | −1.18411 | ||||||||
\(121\) | −5.94550 | −0.540500 | ||||||||
\(122\) | −12.3062 | −1.11415 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 3.32166 | 0.298294 | ||||||||
\(125\) | −34.8094 | −3.11344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.48589 | −0.220587 | −0.110294 | − | 0.993899i | \(-0.535179\pi\) | ||||
−0.110294 | + | 0.993899i | \(0.535179\pi\) | |||||||
\(128\) | −1.15435 | −0.102031 | ||||||||
\(129\) | 0.374747 | 0.0329947 | ||||||||
\(130\) | −1.55086 | −0.136019 | ||||||||
\(131\) | 6.81857 | 0.595742 | 0.297871 | − | 0.954606i | \(-0.403724\pi\) | ||||
0.297871 | + | 0.954606i | \(0.403724\pi\) | |||||||
\(132\) | −2.01149 | −0.175078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.9315 | 1.28989 | ||||||||
\(135\) | 4.26226 | 0.366837 | ||||||||
\(136\) | −14.2090 | −1.21841 | ||||||||
\(137\) | −3.50002 | −0.299027 | −0.149513 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149513 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(138\) | −2.59802 | −0.221158 | ||||||||
\(139\) | −20.1733 | −1.71108 | −0.855540 | − | 0.517737i | \(-0.826775\pi\) | ||||
−0.855540 | + | 0.517737i | \(0.826775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.92338 | 0.330409 | ||||||||
\(142\) | 1.68407 | 0.141324 | ||||||||
\(143\) | −0.778093 | −0.0650674 | ||||||||
\(144\) | −1.41010 | −0.117508 | ||||||||
\(145\) | −26.3802 | −2.19076 | ||||||||
\(146\) | 15.9581 | 1.32070 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.23326 | 0.347972 | ||||||||
\(149\) | −13.0123 | −1.06601 | −0.533005 | − | 0.846112i | \(-0.678937\pi\) | ||||
−0.533005 | + | 0.846112i | \(0.678937\pi\) | |||||||
\(150\) | −13.8427 | −1.13026 | ||||||||
\(151\) | −10.8585 | −0.883652 | −0.441826 | − | 0.897101i | \(-0.645669\pi\) | ||||
−0.441826 | + | 0.897101i | \(0.645669\pi\) | |||||||
\(152\) | 6.08781 | 0.493787 | ||||||||
\(153\) | 4.66895 | 0.377462 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.8240 | 1.27101 | ||||||||
\(156\) | 0.309650 | 0.0247919 | ||||||||
\(157\) | −2.08189 | −0.166153 | −0.0830765 | − | 0.996543i | \(-0.526475\pi\) | ||||
−0.0830765 | + | 0.996543i | \(0.526475\pi\) | |||||||
\(158\) | 10.6843 | 0.849995 | ||||||||
\(159\) | −10.4390 | −0.827866 | ||||||||
\(160\) | −19.6239 | −1.55140 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.05133 | 0.0826003 | ||||||||
\(163\) | −13.1660 | −1.03124 | −0.515619 | − | 0.856818i | \(-0.672438\pi\) | ||||
−0.515619 | + | 0.856818i | \(0.672438\pi\) | |||||||
\(164\) | −0.894704 | −0.0698646 | ||||||||
\(165\) | −9.58251 | −0.745998 | ||||||||
\(166\) | 12.9333 | 1.00382 | ||||||||
\(167\) | 13.6237 | 1.05423 | 0.527117 | − | 0.849792i | \(-0.323273\pi\) | ||||
0.527117 | + | 0.849792i | \(0.323273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8802 | −0.990786 | ||||||||
\(170\) | −20.9218 | −1.60463 | ||||||||
\(171\) | −2.00040 | −0.152975 | ||||||||
\(172\) | 0.335288 | 0.0255655 | ||||||||
\(173\) | −11.4936 | −0.873841 | −0.436921 | − | 0.899500i | \(-0.643931\pi\) | ||||
−0.436921 | + | 0.899500i | \(0.643931\pi\) | |||||||
\(174\) | −6.50696 | −0.493291 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.17021 | 0.238964 | ||||||||
\(177\) | 7.37689 | 0.554481 | ||||||||
\(178\) | −8.19906 | −0.614546 | ||||||||
\(179\) | −22.3270 | −1.66880 | −0.834400 | − | 0.551159i | \(-0.814186\pi\) | ||||
−0.834400 | + | 0.551159i | \(0.814186\pi\) | |||||||
\(180\) | 3.81346 | 0.284239 | ||||||||
\(181\) | 0.572312 | 0.0425396 | 0.0212698 | − | 0.999774i | \(-0.493229\pi\) | ||||
0.0212698 | + | 0.999774i | \(0.493229\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7053 | 0.865282 | ||||||||
\(184\) | −7.52050 | −0.554419 | ||||||||
\(185\) | 20.1668 | 1.48269 | ||||||||
\(186\) | 3.90315 | 0.286193 | ||||||||
\(187\) | −10.4968 | −0.767604 | ||||||||
\(188\) | 3.51027 | 0.256012 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.96390 | 0.650310 | ||||||||
\(191\) | −0.378591 | −0.0273939 | −0.0136969 | − | 0.999906i | \(-0.504360\pi\) | ||||
−0.0136969 | + | 0.999906i | \(0.504360\pi\) | |||||||
\(192\) | −7.66063 | −0.552858 | ||||||||
\(193\) | 9.61273 | 0.691939 | 0.345970 | − | 0.938246i | \(-0.387550\pi\) | ||||
0.345970 | + | 0.938246i | \(0.387550\pi\) | |||||||
\(194\) | −13.0307 | −0.935547 | ||||||||
\(195\) | 1.47514 | 0.105637 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3730 | −0.739042 | −0.369521 | − | 0.929222i | \(-0.620478\pi\) | ||||
−0.369521 | + | 0.929222i | \(0.620478\pi\) | |||||||
\(198\) | −2.36363 | −0.167976 | ||||||||
\(199\) | 17.1983 | 1.21915 | 0.609576 | − | 0.792727i | \(-0.291340\pi\) | ||||
0.609576 | + | 0.792727i | \(0.291340\pi\) | |||||||
\(200\) | −40.0706 | −2.83342 | ||||||||
\(201\) | −14.2025 | −1.00177 | ||||||||
\(202\) | −10.1367 | −0.713219 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.17732 | 0.292471 | ||||||||
\(205\) | −4.26226 | −0.297689 | ||||||||
\(206\) | 4.62892 | 0.322512 | ||||||||
\(207\) | 2.47117 | 0.171758 | ||||||||
\(208\) | −0.488024 | −0.0338384 | ||||||||
\(209\) | 4.49735 | 0.311088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.94273 | −0.202586 | −0.101293 | − | 0.994857i | \(-0.532298\pi\) | ||||
−0.101293 | + | 0.994857i | \(0.532298\pi\) | |||||||
\(212\) | −9.33981 | −0.641461 | ||||||||
\(213\) | −1.60184 | −0.109757 | ||||||||
\(214\) | 3.63395 | 0.248412 | ||||||||
\(215\) | 1.59727 | 0.108933 | ||||||||
\(216\) | 3.04329 | 0.207070 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.9440 | −1.28305 | ||||||||
\(219\) | −15.1789 | −1.02570 | ||||||||
\(220\) | −8.57351 | −0.578026 | ||||||||
\(221\) | 1.61589 | 0.108696 | ||||||||
\(222\) | 4.97434 | 0.333856 | ||||||||
\(223\) | 1.34407 | 0.0900058 | 0.0450029 | − | 0.998987i | \(-0.485670\pi\) | ||||
0.0450029 | + | 0.998987i | \(0.485670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1669 | 0.877792 | ||||||||
\(226\) | 17.0914 | 1.13690 | ||||||||
\(227\) | 26.4743 | 1.75716 | 0.878579 | − | 0.477597i | \(-0.158492\pi\) | ||||
0.878579 | + | 0.477597i | \(0.158492\pi\) | |||||||
\(228\) | −1.78977 | −0.118530 | ||||||||
\(229\) | −14.7753 | −0.976378 | −0.488189 | − | 0.872738i | \(-0.662342\pi\) | ||||
−0.488189 | + | 0.872738i | \(0.662342\pi\) | |||||||
\(230\) | −11.0734 | −0.730161 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.8357 | −1.23663 | ||||||||
\(233\) | −11.9956 | −0.785860 | −0.392930 | − | 0.919568i | \(-0.628539\pi\) | ||||
−0.392930 | + | 0.919568i | \(0.628539\pi\) | |||||||
\(234\) | 0.363858 | 0.0237861 | ||||||||
\(235\) | 16.7225 | 1.09086 | ||||||||
\(236\) | 6.60013 | 0.429632 | ||||||||
\(237\) | −10.1626 | −0.660133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.3398 | 0.992248 | 0.496124 | − | 0.868252i | \(-0.334756\pi\) | ||||
0.496124 | + | 0.868252i | \(0.334756\pi\) | |||||||
\(240\) | −6.01021 | −0.387957 | ||||||||
\(241\) | 17.6355 | 1.13600 | 0.568000 | − | 0.823029i | \(-0.307717\pi\) | ||||
0.568000 | + | 0.823029i | \(0.307717\pi\) | |||||||
\(242\) | −6.25068 | −0.401809 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.4728 | 0.670451 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.05133 | −0.0670304 | ||||||||
\(247\) | −0.692325 | −0.0440516 | ||||||||
\(248\) | 11.2985 | 0.717453 | ||||||||
\(249\) | −12.3018 | −0.779596 | ||||||||
\(250\) | −36.5962 | −2.31454 | ||||||||
\(251\) | 21.4380 | 1.35315 | 0.676576 | − | 0.736373i | \(-0.263463\pi\) | ||||
0.676576 | + | 0.736373i | \(0.263463\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.55575 | −0.349287 | ||||||||
\(254\) | −2.61350 | −0.163985 | ||||||||
\(255\) | 19.9003 | 1.24620 | ||||||||
\(256\) | −16.5349 | −1.03343 | ||||||||
\(257\) | 8.64434 | 0.539219 | 0.269610 | − | 0.962970i | \(-0.413105\pi\) | ||||
0.269610 | + | 0.962970i | \(0.413105\pi\) | |||||||
\(258\) | 0.393984 | 0.0245283 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.31981 | 0.0818512 | ||||||||
\(261\) | 6.18926 | 0.383105 | ||||||||
\(262\) | 7.16858 | 0.442876 | ||||||||
\(263\) | −15.6653 | −0.965964 | −0.482982 | − | 0.875630i | \(-0.660446\pi\) | ||||
−0.482982 | + | 0.875630i | \(0.660446\pi\) | |||||||
\(264\) | −6.84199 | −0.421096 | ||||||||
\(265\) | −44.4937 | −2.73323 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.79875 | 0.477276 | ||||||||
\(268\) | −12.7070 | −0.776206 | ||||||||
\(269\) | 13.1787 | 0.803519 | 0.401760 | − | 0.915745i | \(-0.368399\pi\) | ||||
0.401760 | + | 0.915745i | \(0.368399\pi\) | |||||||
\(270\) | 4.48105 | 0.272708 | ||||||||
\(271\) | −7.35125 | −0.446556 | −0.223278 | − | 0.974755i | \(-0.571676\pi\) | ||||
−0.223278 | + | 0.974755i | \(0.571676\pi\) | |||||||
\(272\) | −6.58367 | −0.399194 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.67968 | −0.222297 | ||||||||
\(275\) | −29.6021 | −1.78507 | ||||||||
\(276\) | 2.21097 | 0.133085 | ||||||||
\(277\) | −1.18852 | −0.0714115 | −0.0357057 | − | 0.999362i | \(-0.511368\pi\) | ||||
−0.0357057 | + | 0.999362i | \(0.511368\pi\) | |||||||
\(278\) | −21.2088 | −1.27202 | ||||||||
\(279\) | −3.71258 | −0.222266 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.99493 | 0.417283 | 0.208641 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208641 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(282\) | 4.12477 | 0.245627 | ||||||||
\(283\) | −11.1116 | −0.660518 | −0.330259 | − | 0.943890i | \(-0.607136\pi\) | ||||
−0.330259 | + | 0.943890i | \(0.607136\pi\) | |||||||
\(284\) | −1.43318 | −0.0850433 | ||||||||
\(285\) | −8.52624 | −0.505051 | ||||||||
\(286\) | −0.818033 | −0.0483713 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.60410 | 0.271299 | ||||||||
\(289\) | 4.79907 | 0.282298 | ||||||||
\(290\) | −27.7344 | −1.62862 | ||||||||
\(291\) | 12.3944 | 0.726575 | ||||||||
\(292\) | −13.5806 | −0.794746 | ||||||||
\(293\) | 11.5761 | 0.676283 | 0.338141 | − | 0.941095i | \(-0.390202\pi\) | ||||
0.338141 | + | 0.941095i | \(0.390202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.4422 | 1.83064 | ||||||||
\(296\) | 14.3992 | 0.836938 | ||||||||
\(297\) | 2.24822 | 0.130455 | ||||||||
\(298\) | −13.6802 | −0.792475 | ||||||||
\(299\) | 0.855254 | 0.0494606 | ||||||||
\(300\) | 11.7805 | 0.680145 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.4159 | −0.656909 | ||||||||
\(303\) | 9.64182 | 0.553908 | ||||||||
\(304\) | 2.82077 | 0.161782 | ||||||||
\(305\) | 49.8911 | 2.85676 | ||||||||
\(306\) | 4.90861 | 0.280606 | ||||||||
\(307\) | 15.4598 | 0.882336 | 0.441168 | − | 0.897424i | \(-0.354564\pi\) | ||||
0.441168 | + | 0.897424i | \(0.354564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.40291 | −0.250473 | ||||||||
\(310\) | 16.6363 | 0.944876 | ||||||||
\(311\) | 16.4265 | 0.931462 | 0.465731 | − | 0.884926i | \(-0.345791\pi\) | ||||
0.465731 | + | 0.884926i | \(0.345791\pi\) | |||||||
\(312\) | 1.05326 | 0.0596291 | ||||||||
\(313\) | −29.9007 | −1.69009 | −0.845043 | − | 0.534699i | \(-0.820425\pi\) | ||||
−0.845043 | + | 0.534699i | \(0.820425\pi\) | |||||||
\(314\) | −2.18876 | −0.123519 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.09253 | −0.511495 | ||||||||
\(317\) | 4.91153 | 0.275859 | 0.137929 | − | 0.990442i | \(-0.455955\pi\) | ||||
0.137929 | + | 0.990442i | \(0.455955\pi\) | |||||||
\(318\) | −10.9748 | −0.615438 | ||||||||
\(319\) | −13.9148 | −0.779081 | ||||||||
\(320\) | −32.6516 | −1.82528 | ||||||||
\(321\) | −3.45652 | −0.192924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.33978 | −0.519679 | ||||||||
\(324\) | −0.894704 | −0.0497058 | ||||||||
\(325\) | 4.55696 | 0.252774 | ||||||||
\(326\) | −13.8418 | −0.766626 | ||||||||
\(327\) | 18.0191 | 0.996459 | ||||||||
\(328\) | −3.04329 | −0.168038 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.0744 | −0.554577 | ||||||||
\(331\) | 5.41473 | 0.297621 | 0.148810 | − | 0.988866i | \(-0.452456\pi\) | ||||
0.148810 | + | 0.988866i | \(0.452456\pi\) | |||||||
\(332\) | −11.0065 | −0.604059 | ||||||||
\(333\) | −4.73147 | −0.259283 | ||||||||
\(334\) | 14.3230 | 0.783722 | ||||||||
\(335\) | −60.5348 | −3.30737 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.3160 | 1.81484 | 0.907420 | − | 0.420225i | \(-0.138049\pi\) | ||||
0.907420 | + | 0.420225i | \(0.138049\pi\) | |||||||
\(338\) | −13.5414 | −0.736554 | ||||||||
\(339\) | −16.2569 | −0.882953 | ||||||||
\(340\) | 17.8048 | 0.965603 | ||||||||
\(341\) | 8.34671 | 0.452000 | ||||||||
\(342\) | −2.10309 | −0.113722 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.14047 | 0.0614898 | ||||||||
\(345\) | 10.5328 | 0.567066 | ||||||||
\(346\) | −12.0836 | −0.649616 | ||||||||
\(347\) | 32.8297 | 1.76239 | 0.881195 | − | 0.472753i | \(-0.156740\pi\) | ||||
0.881195 | + | 0.472753i | \(0.156740\pi\) | |||||||
\(348\) | 5.53755 | 0.296844 | ||||||||
\(349\) | 8.42964 | 0.451228 | 0.225614 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.346093 | −0.0184731 | ||||||||
\(352\) | −10.3510 | −0.551713 | ||||||||
\(353\) | −19.6337 | −1.04500 | −0.522499 | − | 0.852640i | \(-0.675000\pi\) | ||||
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(354\) | 7.75555 | 0.412203 | ||||||||
\(355\) | −6.82748 | −0.362365 | ||||||||
\(356\) | 6.97757 | 0.369810 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.4731 | −1.24059 | ||||||||
\(359\) | 8.78107 | 0.463447 | 0.231724 | − | 0.972782i | \(-0.425564\pi\) | ||||
0.231724 | + | 0.972782i | \(0.425564\pi\) | |||||||
\(360\) | 12.9713 | 0.683648 | ||||||||
\(361\) | −14.9984 | −0.789389 | ||||||||
\(362\) | 0.601689 | 0.0316241 | ||||||||
\(363\) | 5.94550 | 0.312058 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −64.6965 | −3.38637 | ||||||||
\(366\) | 12.3062 | 0.643253 | ||||||||
\(367\) | −15.7089 | −0.819999 | −0.410000 | − | 0.912086i | \(-0.634471\pi\) | ||||
−0.410000 | + | 0.912086i | \(0.634471\pi\) | |||||||
\(368\) | −3.48460 | −0.181647 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 21.2019 | 1.10224 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.32166 | −0.172220 | ||||||||
\(373\) | −13.7795 | −0.713473 | −0.356737 | − | 0.934205i | \(-0.616111\pi\) | ||||
−0.356737 | + | 0.934205i | \(0.616111\pi\) | |||||||
\(374\) | −11.0356 | −0.570639 | ||||||||
\(375\) | 34.8094 | 1.79755 | ||||||||
\(376\) | 11.9400 | 0.615759 | ||||||||
\(377\) | 2.14206 | 0.110321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6908 | −1.31965 | −0.659824 | − | 0.751420i | \(-0.729369\pi\) | ||||
−0.659824 | + | 0.751420i | \(0.729369\pi\) | |||||||
\(380\) | −7.62846 | −0.391332 | ||||||||
\(381\) | 2.48589 | 0.127356 | ||||||||
\(382\) | −0.398024 | −0.0203647 | ||||||||
\(383\) | 24.8594 | 1.27026 | 0.635128 | − | 0.772407i | \(-0.280947\pi\) | ||||
0.635128 | + | 0.772407i | \(0.280947\pi\) | |||||||
\(384\) | 1.15435 | 0.0589075 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1062 | 0.514390 | ||||||||
\(387\) | −0.374747 | −0.0190495 | ||||||||
\(388\) | 11.0894 | 0.562977 | ||||||||
\(389\) | 9.84230 | 0.499025 | 0.249512 | − | 0.968372i | \(-0.419730\pi\) | ||||
0.249512 | + | 0.968372i | \(0.419730\pi\) | |||||||
\(390\) | 1.55086 | 0.0785307 | ||||||||
\(391\) | 11.5378 | 0.583490 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.81857 | −0.343952 | ||||||||
\(394\) | −10.9054 | −0.549406 | ||||||||
\(395\) | −43.3157 | −2.17945 | ||||||||
\(396\) | 2.01149 | 0.101081 | ||||||||
\(397\) | −15.4375 | −0.774788 | −0.387394 | − | 0.921914i | \(-0.626625\pi\) | ||||
−0.387394 | + | 0.921914i | \(0.626625\pi\) | |||||||
\(398\) | 18.0811 | 0.906322 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.5666 | −0.928329 | ||||||||
\(401\) | 29.8758 | 1.49192 | 0.745962 | − | 0.665988i | \(-0.231990\pi\) | ||||
0.745962 | + | 0.665988i | \(0.231990\pi\) | |||||||
\(402\) | −14.9315 | −0.744717 | ||||||||
\(403\) | −1.28490 | −0.0640053 | ||||||||
\(404\) | 8.62658 | 0.429188 | ||||||||
\(405\) | −4.26226 | −0.211793 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6374 | 0.527276 | ||||||||
\(408\) | 14.2090 | 0.703449 | ||||||||
\(409\) | 9.99523 | 0.494233 | 0.247116 | − | 0.968986i | \(-0.420517\pi\) | ||||
0.247116 | + | 0.968986i | \(0.420517\pi\) | |||||||
\(410\) | −4.48105 | −0.221303 | ||||||||
\(411\) | 3.50002 | 0.172643 | ||||||||
\(412\) | −3.93930 | −0.194076 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.59802 | 0.127686 | ||||||||
\(415\) | −52.4335 | −2.57386 | ||||||||
\(416\) | 1.59345 | 0.0781251 | ||||||||
\(417\) | 20.1733 | 0.987893 | ||||||||
\(418\) | 4.72820 | 0.231264 | ||||||||
\(419\) | 30.0143 | 1.46629 | 0.733147 | − | 0.680070i | \(-0.238050\pi\) | ||||
0.733147 | + | 0.680070i | \(0.238050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.76729 | −0.134870 | −0.0674348 | − | 0.997724i | \(-0.521481\pi\) | ||||
−0.0674348 | + | 0.997724i | \(0.521481\pi\) | |||||||
\(422\) | −3.09379 | −0.150603 | ||||||||
\(423\) | −3.92338 | −0.190761 | ||||||||
\(424\) | −31.7689 | −1.54283 | ||||||||
\(425\) | 61.4754 | 2.98200 | ||||||||
\(426\) | −1.68407 | −0.0815933 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.09256 | −0.149485 | ||||||||
\(429\) | 0.778093 | 0.0375667 | ||||||||
\(430\) | 1.67926 | 0.0809812 | ||||||||
\(431\) | −16.9439 | −0.816160 | −0.408080 | − | 0.912946i | \(-0.633802\pi\) | ||||
−0.408080 | + | 0.912946i | \(0.633802\pi\) | |||||||
\(432\) | 1.41010 | 0.0678434 | ||||||||
\(433\) | −0.950181 | −0.0456628 | −0.0228314 | − | 0.999739i | \(-0.507268\pi\) | ||||
−0.0228314 | + | 0.999739i | \(0.507268\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.3802 | 1.26484 | ||||||||
\(436\) | 16.1218 | 0.772092 | ||||||||
\(437\) | −4.94334 | −0.236472 | ||||||||
\(438\) | −15.9581 | −0.762505 | ||||||||
\(439\) | −16.3634 | −0.780984 | −0.390492 | − | 0.920606i | \(-0.627695\pi\) | ||||
−0.390492 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(440\) | −29.1624 | −1.39026 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.69883 | 0.0808052 | ||||||||
\(443\) | −13.1007 | −0.622435 | −0.311217 | − | 0.950339i | \(-0.600737\pi\) | ||||
−0.311217 | + | 0.950339i | \(0.600737\pi\) | |||||||
\(444\) | −4.23326 | −0.200902 | ||||||||
\(445\) | 33.2403 | 1.57574 | ||||||||
\(446\) | 1.41307 | 0.0669106 | ||||||||
\(447\) | 13.0123 | 0.615461 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.2850 | −0.485378 | −0.242689 | − | 0.970104i | \(-0.578030\pi\) | ||||
−0.242689 | + | 0.970104i | \(0.578030\pi\) | |||||||
\(450\) | 13.8427 | 0.652553 | ||||||||
\(451\) | −2.24822 | −0.105865 | ||||||||
\(452\) | −14.5451 | −0.684144 | ||||||||
\(453\) | 10.8585 | 0.510177 | ||||||||
\(454\) | 27.8332 | 1.30628 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.08781 | −0.285088 | ||||||||
\(457\) | −7.57107 | −0.354160 | −0.177080 | − | 0.984197i | \(-0.556665\pi\) | ||||
−0.177080 | + | 0.984197i | \(0.556665\pi\) | |||||||
\(458\) | −15.5337 | −0.725843 | ||||||||
\(459\) | −4.66895 | −0.217928 | ||||||||
\(460\) | 9.42372 | 0.439383 | ||||||||
\(461\) | −37.7253 | −1.75704 | −0.878520 | − | 0.477705i | \(-0.841469\pi\) | ||||
−0.878520 | + | 0.477705i | \(0.841469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.46827 | −0.0682365 | −0.0341182 | − | 0.999418i | \(-0.510862\pi\) | ||||
−0.0341182 | + | 0.999418i | \(0.510862\pi\) | |||||||
\(464\) | −8.72746 | −0.405162 | ||||||||
\(465\) | −15.8240 | −0.733820 | ||||||||
\(466\) | −12.6114 | −0.584211 | ||||||||
\(467\) | 18.3223 | 0.847853 | 0.423927 | − | 0.905697i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905697i | \(0.360651\pi\) | |||||||
\(468\) | −0.309650 | −0.0143136 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.5809 | 0.810945 | ||||||||
\(471\) | 2.08189 | 0.0959285 | ||||||||
\(472\) | 22.4500 | 1.03335 | ||||||||
\(473\) | 0.842516 | 0.0387389 | ||||||||
\(474\) | −10.6843 | −0.490745 | ||||||||
\(475\) | −26.3391 | −1.20852 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4390 | 0.477969 | ||||||||
\(478\) | 16.1272 | 0.737640 | ||||||||
\(479\) | −6.47641 | −0.295915 | −0.147957 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147957 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(480\) | 19.6239 | 0.895704 | ||||||||
\(481\) | −1.63753 | −0.0746647 | ||||||||
\(482\) | 18.5407 | 0.844505 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.31946 | 0.241794 | ||||||||
\(485\) | 52.8284 | 2.39881 | ||||||||
\(486\) | −1.05133 | −0.0476893 | ||||||||
\(487\) | −0.574842 | −0.0260486 | −0.0130243 | − | 0.999915i | \(-0.504146\pi\) | ||||
−0.0130243 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(488\) | 35.6227 | 1.61256 | ||||||||
\(489\) | 13.1660 | 0.595386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.62113 | −0.253678 | −0.126839 | − | 0.991923i | \(-0.540483\pi\) | ||||
−0.126839 | + | 0.991923i | \(0.540483\pi\) | |||||||
\(492\) | 0.894704 | 0.0403364 | ||||||||
\(493\) | 28.8973 | 1.30147 | ||||||||
\(494\) | −0.727862 | −0.0327481 | ||||||||
\(495\) | 9.58251 | 0.430702 | ||||||||
\(496\) | 5.23511 | 0.235063 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.9333 | −0.579554 | ||||||||
\(499\) | 11.4910 | 0.514409 | 0.257205 | − | 0.966357i | \(-0.417199\pi\) | ||||
0.257205 | + | 0.966357i | \(0.417199\pi\) | |||||||
\(500\) | 31.1441 | 1.39280 | ||||||||
\(501\) | −13.6237 | −0.608663 | ||||||||
\(502\) | 22.5384 | 1.00594 | ||||||||
\(503\) | −19.5016 | −0.869534 | −0.434767 | − | 0.900543i | \(-0.643169\pi\) | ||||
−0.434767 | + | 0.900543i | \(0.643169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.0960 | 1.82875 | ||||||||
\(506\) | −5.84093 | −0.259661 | ||||||||
\(507\) | 12.8802 | 0.572031 | ||||||||
\(508\) | 2.22414 | 0.0986802 | ||||||||
\(509\) | −9.19847 | −0.407715 | −0.203858 | − | 0.979001i | \(-0.565348\pi\) | ||||
−0.203858 | + | 0.979001i | \(0.565348\pi\) | |||||||
\(510\) | 20.9218 | 0.926432 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.0749 | −0.666223 | ||||||||
\(513\) | 2.00040 | 0.0883200 | ||||||||
\(514\) | 9.08806 | 0.400857 | ||||||||
\(515\) | −18.7664 | −0.826945 | ||||||||
\(516\) | −0.335288 | −0.0147602 | ||||||||
\(517\) | 8.82064 | 0.387931 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.4936 | 0.504513 | ||||||||
\(520\) | 4.48927 | 0.196868 | ||||||||
\(521\) | −10.7828 | −0.472403 | −0.236202 | − | 0.971704i | \(-0.575903\pi\) | ||||
−0.236202 | + | 0.971704i | \(0.575903\pi\) | |||||||
\(522\) | 6.50696 | 0.284802 | ||||||||
\(523\) | −2.56702 | −0.112248 | −0.0561240 | − | 0.998424i | \(-0.517874\pi\) | ||||
−0.0561240 | + | 0.998424i | \(0.517874\pi\) | |||||||
\(524\) | −6.10060 | −0.266506 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.4694 | −0.718100 | ||||||||
\(527\) | −17.3338 | −0.755074 | ||||||||
\(528\) | −3.17021 | −0.137966 | ||||||||
\(529\) | −16.8933 | −0.734491 | ||||||||
\(530\) | −46.7776 | −2.03189 | ||||||||
\(531\) | −7.37689 | −0.320130 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.346093 | 0.0149909 | ||||||||
\(534\) | 8.19906 | 0.354808 | ||||||||
\(535\) | −14.7326 | −0.636946 | ||||||||
\(536\) | −43.2224 | −1.86692 | ||||||||
\(537\) | 22.3270 | 0.963482 | ||||||||
\(538\) | 13.8552 | 0.597339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.81346 | −0.164105 | ||||||||
\(541\) | 24.0028 | 1.03196 | 0.515980 | − | 0.856601i | \(-0.327428\pi\) | ||||
0.515980 | + | 0.856601i | \(0.327428\pi\) | |||||||
\(542\) | −7.72859 | −0.331971 | ||||||||
\(543\) | −0.572312 | −0.0245603 | ||||||||
\(544\) | 21.4963 | 0.921647 | ||||||||
\(545\) | 76.8022 | 3.28984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3624 | 0.614090 | 0.307045 | − | 0.951695i | \(-0.400660\pi\) | ||||
0.307045 | + | 0.951695i | \(0.400660\pi\) | |||||||
\(548\) | 3.13148 | 0.133770 | ||||||||
\(549\) | −11.7053 | −0.499571 | ||||||||
\(550\) | −31.1216 | −1.32703 | ||||||||
\(551\) | −12.3810 | −0.527449 | ||||||||
\(552\) | 7.52050 | 0.320094 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.24953 | −0.0530875 | ||||||||
\(555\) | −20.1668 | −0.856031 | ||||||||
\(556\) | 18.0492 | 0.765455 | ||||||||
\(557\) | −25.2968 | −1.07186 | −0.535929 | − | 0.844263i | \(-0.680039\pi\) | ||||
−0.535929 | + | 0.844263i | \(0.680039\pi\) | |||||||
\(558\) | −3.90315 | −0.165234 | ||||||||
\(559\) | −0.129697 | −0.00548561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.4968 | 0.443177 | ||||||||
\(562\) | 7.35399 | 0.310209 | ||||||||
\(563\) | −42.5322 | −1.79252 | −0.896260 | − | 0.443530i | \(-0.853726\pi\) | ||||
−0.896260 | + | 0.443530i | \(0.853726\pi\) | |||||||
\(564\) | −3.51027 | −0.147809 | ||||||||
\(565\) | −69.2911 | −2.91510 | ||||||||
\(566\) | −11.6820 | −0.491031 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.87488 | −0.204545 | ||||||||
\(569\) | −39.2312 | −1.64466 | −0.822329 | − | 0.569013i | \(-0.807325\pi\) | ||||
−0.822329 | + | 0.569013i | \(0.807325\pi\) | |||||||
\(570\) | −8.96390 | −0.375457 | ||||||||
\(571\) | 12.0130 | 0.502728 | 0.251364 | − | 0.967893i | \(-0.419121\pi\) | ||||
0.251364 | + | 0.967893i | \(0.419121\pi\) | |||||||
\(572\) | 0.696162 | 0.0291080 | ||||||||
\(573\) | 0.378591 | 0.0158159 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.5376 | 1.35691 | ||||||||
\(576\) | 7.66063 | 0.319193 | ||||||||
\(577\) | −42.5206 | −1.77016 | −0.885078 | − | 0.465443i | \(-0.845895\pi\) | ||||
−0.885078 | + | 0.465443i | \(0.845895\pi\) | |||||||
\(578\) | 5.04541 | 0.209861 | ||||||||
\(579\) | −9.61273 | −0.399491 | ||||||||
\(580\) | 23.6025 | 0.980040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.0307 | 0.540138 | ||||||||
\(583\) | −23.4692 | −0.971994 | ||||||||
\(584\) | −46.1938 | −1.91151 | ||||||||
\(585\) | −1.47514 | −0.0609894 | ||||||||
\(586\) | 12.1703 | 0.502751 | ||||||||
\(587\) | −43.3776 | −1.79038 | −0.895192 | − | 0.445681i | \(-0.852962\pi\) | ||||
−0.895192 | + | 0.445681i | \(0.852962\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.42666 | 0.306010 | ||||||||
\(590\) | 33.0562 | 1.36090 | ||||||||
\(591\) | 10.3730 | 0.426686 | ||||||||
\(592\) | 6.67183 | 0.274211 | ||||||||
\(593\) | −42.2748 | −1.73602 | −0.868008 | − | 0.496550i | \(-0.834600\pi\) | ||||
−0.868008 | + | 0.496550i | \(0.834600\pi\) | |||||||
\(594\) | 2.36363 | 0.0969807 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.6422 | 0.476881 | ||||||||
\(597\) | −17.1983 | −0.703878 | ||||||||
\(598\) | 0.899155 | 0.0367692 | ||||||||
\(599\) | −28.0250 | −1.14507 | −0.572536 | − | 0.819879i | \(-0.694040\pi\) | ||||
−0.572536 | + | 0.819879i | \(0.694040\pi\) | |||||||
\(600\) | 40.0706 | 1.63588 | ||||||||
\(601\) | 1.15074 | 0.0469396 | 0.0234698 | − | 0.999725i | \(-0.492529\pi\) | ||||
0.0234698 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.2025 | 0.578371 | ||||||||
\(604\) | 9.71513 | 0.395303 | ||||||||
\(605\) | 25.3413 | 1.03027 | ||||||||
\(606\) | 10.1367 | 0.411777 | ||||||||
\(607\) | 42.1717 | 1.71170 | 0.855849 | − | 0.517226i | \(-0.173035\pi\) | ||||
0.855849 | + | 0.517226i | \(0.173035\pi\) | |||||||
\(608\) | −9.21006 | −0.373517 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 52.4521 | 2.12372 | ||||||||
\(611\) | −1.35785 | −0.0549329 | ||||||||
\(612\) | −4.17732 | −0.168858 | ||||||||
\(613\) | −29.9745 | −1.21066 | −0.605330 | − | 0.795975i | \(-0.706959\pi\) | ||||
−0.605330 | + | 0.795975i | \(0.706959\pi\) | |||||||
\(614\) | 16.2533 | 0.655932 | ||||||||
\(615\) | 4.26226 | 0.171871 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.9897 | 0.683979 | 0.341989 | − | 0.939704i | \(-0.388899\pi\) | ||||
0.341989 | + | 0.939704i | \(0.388899\pi\) | |||||||
\(618\) | −4.62892 | −0.186202 | ||||||||
\(619\) | −4.99009 | −0.200569 | −0.100284 | − | 0.994959i | \(-0.531975\pi\) | ||||
−0.100284 | + | 0.994959i | \(0.531975\pi\) | |||||||
\(620\) | −14.1578 | −0.568590 | ||||||||
\(621\) | −2.47117 | −0.0991648 | ||||||||
\(622\) | 17.2697 | 0.692452 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.488024 | 0.0195366 | ||||||||
\(625\) | 82.5322 | 3.30129 | ||||||||
\(626\) | −31.4355 | −1.25641 | ||||||||
\(627\) | −4.49735 | −0.179607 | ||||||||
\(628\) | 1.86268 | 0.0743289 | ||||||||
\(629\) | −22.0910 | −0.880825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.1594 | −1.55891 | −0.779456 | − | 0.626458i | \(-0.784504\pi\) | ||||
−0.779456 | + | 0.626458i | \(0.784504\pi\) | |||||||
\(632\) | −30.9278 | −1.23024 | ||||||||
\(633\) | 2.94273 | 0.116963 | ||||||||
\(634\) | 5.16364 | 0.205074 | ||||||||
\(635\) | 10.5955 | 0.420471 | ||||||||
\(636\) | 9.33981 | 0.370347 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.6291 | −0.579171 | ||||||||
\(639\) | 1.60184 | 0.0633680 | ||||||||
\(640\) | 4.92013 | 0.194485 | ||||||||
\(641\) | 35.5086 | 1.40251 | 0.701253 | − | 0.712912i | \(-0.252624\pi\) | ||||
0.701253 | + | 0.712912i | \(0.252624\pi\) | |||||||
\(642\) | −3.63395 | −0.143421 | ||||||||
\(643\) | −28.2461 | −1.11392 | −0.556959 | − | 0.830540i | \(-0.688032\pi\) | ||||
−0.556959 | + | 0.830540i | \(0.688032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.59727 | −0.0628925 | ||||||||
\(646\) | −9.81920 | −0.386331 | ||||||||
\(647\) | −21.9398 | −0.862544 | −0.431272 | − | 0.902222i | \(-0.641935\pi\) | ||||
−0.431272 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(648\) | −3.04329 | −0.119552 | ||||||||
\(649\) | 16.5849 | 0.651014 | ||||||||
\(650\) | 4.79087 | 0.187913 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.7796 | 0.461326 | ||||||||
\(653\) | 45.6206 | 1.78527 | 0.892636 | − | 0.450778i | \(-0.148853\pi\) | ||||
0.892636 | + | 0.450778i | \(0.148853\pi\) | |||||||
\(654\) | 18.9440 | 0.740771 | ||||||||
\(655\) | −29.0625 | −1.13557 | ||||||||
\(656\) | −1.41010 | −0.0550551 | ||||||||
\(657\) | 15.1789 | 0.592186 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.26037 | −0.360733 | −0.180366 | − | 0.983599i | \(-0.557728\pi\) | ||||
−0.180366 | + | 0.983599i | \(0.557728\pi\) | |||||||
\(660\) | 8.57351 | 0.333723 | ||||||||
\(661\) | 8.79472 | 0.342075 | 0.171038 | − | 0.985265i | \(-0.445288\pi\) | ||||
0.171038 | + | 0.985265i | \(0.445288\pi\) | |||||||
\(662\) | 5.69267 | 0.221252 | ||||||||
\(663\) | −1.61589 | −0.0627559 | ||||||||
\(664\) | −37.4380 | −1.45288 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.97434 | −0.192752 | ||||||||
\(667\) | 15.2947 | 0.592214 | ||||||||
\(668\) | −12.1892 | −0.471614 | ||||||||
\(669\) | −1.34407 | −0.0519649 | ||||||||
\(670\) | −63.6421 | −2.45871 | ||||||||
\(671\) | 26.3161 | 1.01592 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4719 | −0.789135 | −0.394568 | − | 0.918867i | \(-0.629106\pi\) | ||||
−0.394568 | + | 0.918867i | \(0.629106\pi\) | |||||||
\(674\) | 35.0262 | 1.34916 | ||||||||
\(675\) | −13.1669 | −0.506793 | ||||||||
\(676\) | 11.5240 | 0.443230 | ||||||||
\(677\) | 8.68940 | 0.333961 | 0.166980 | − | 0.985960i | \(-0.446598\pi\) | ||||
0.166980 | + | 0.985960i | \(0.446598\pi\) | |||||||
\(678\) | −17.0914 | −0.656390 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 60.5623 | 2.32246 | ||||||||
\(681\) | −26.4743 | −1.01450 | ||||||||
\(682\) | 8.77515 | 0.336018 | ||||||||
\(683\) | −4.49190 | −0.171878 | −0.0859389 | − | 0.996300i | \(-0.527389\pi\) | ||||
−0.0859389 | + | 0.996300i | \(0.527389\pi\) | |||||||
\(684\) | 1.78977 | 0.0684335 | ||||||||
\(685\) | 14.9180 | 0.569987 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.7753 | 0.563712 | ||||||||
\(688\) | 0.528431 | 0.0201462 | ||||||||
\(689\) | 3.61286 | 0.137639 | ||||||||
\(690\) | 11.0734 | 0.421559 | ||||||||
\(691\) | −2.49897 | −0.0950654 | −0.0475327 | − | 0.998870i | \(-0.515136\pi\) | ||||
−0.0475327 | + | 0.998870i | \(0.515136\pi\) | |||||||
\(692\) | 10.2834 | 0.390915 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.5149 | 1.31017 | ||||||||
\(695\) | 85.9840 | 3.26156 | ||||||||
\(696\) | 18.8357 | 0.713966 | ||||||||
\(697\) | 4.66895 | 0.176849 | ||||||||
\(698\) | 8.86234 | 0.335445 | ||||||||
\(699\) | 11.9956 | 0.453717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1085 | −0.683949 | −0.341975 | − | 0.939709i | \(-0.611096\pi\) | ||||
−0.341975 | + | 0.939709i | \(0.611096\pi\) | |||||||
\(702\) | −0.363858 | −0.0137329 | ||||||||
\(703\) | 9.46485 | 0.356973 | ||||||||
\(704\) | −17.2228 | −0.649109 | ||||||||
\(705\) | −16.7225 | −0.629805 | ||||||||
\(706\) | −20.6416 | −0.776855 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.60013 | −0.248048 | ||||||||
\(709\) | 9.04329 | 0.339628 | 0.169814 | − | 0.985476i | \(-0.445683\pi\) | ||||
0.169814 | + | 0.985476i | \(0.445683\pi\) | |||||||
\(710\) | −7.17794 | −0.269383 | ||||||||
\(711\) | 10.1626 | 0.381128 | ||||||||
\(712\) | 23.7339 | 0.889464 | ||||||||
\(713\) | −9.17443 | −0.343585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.31644 | 0.124028 | ||||||||
\(716\) | 19.9761 | 0.746541 | ||||||||
\(717\) | −15.3398 | −0.572875 | ||||||||
\(718\) | 9.23181 | 0.344528 | ||||||||
\(719\) | 27.2172 | 1.01503 | 0.507515 | − | 0.861643i | \(-0.330564\pi\) | ||||
0.507515 | + | 0.861643i | \(0.330564\pi\) | |||||||
\(720\) | 6.01021 | 0.223987 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.7683 | −0.586834 | ||||||||
\(723\) | −17.6355 | −0.655870 | ||||||||
\(724\) | −0.512050 | −0.0190302 | ||||||||
\(725\) | 81.4932 | 3.02658 | ||||||||
\(726\) | 6.25068 | 0.231985 | ||||||||
\(727\) | −23.1275 | −0.857753 | −0.428876 | − | 0.903363i | \(-0.641090\pi\) | ||||
−0.428876 | + | 0.903363i | \(0.641090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −68.0174 | −2.51744 | ||||||||
\(731\) | −1.74968 | −0.0647141 | ||||||||
\(732\) | −10.4728 | −0.387085 | ||||||||
\(733\) | 33.7507 | 1.24661 | 0.623305 | − | 0.781979i | \(-0.285790\pi\) | ||||
0.623305 | + | 0.781979i | \(0.285790\pi\) | |||||||
\(734\) | −16.5153 | −0.609590 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.3775 | 0.419381 | ||||||||
\(737\) | −31.9304 | −1.17617 | ||||||||
\(738\) | 1.05133 | 0.0387000 | ||||||||
\(739\) | 9.45395 | 0.347769 | 0.173885 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173885 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(740\) | −18.0433 | −0.663284 | ||||||||
\(741\) | 0.692325 | 0.0254332 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.9106 | −0.400269 | −0.200135 | − | 0.979768i | \(-0.564138\pi\) | ||||
−0.200135 | + | 0.979768i | \(0.564138\pi\) | |||||||
\(744\) | −11.2985 | −0.414222 | ||||||||
\(745\) | 55.4619 | 2.03197 | ||||||||
\(746\) | −14.4868 | −0.530398 | ||||||||
\(747\) | 12.3018 | 0.450100 | ||||||||
\(748\) | 9.39155 | 0.343389 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 36.5962 | 1.33630 | ||||||||
\(751\) | −41.5320 | −1.51552 | −0.757762 | − | 0.652531i | \(-0.773707\pi\) | ||||
−0.757762 | + | 0.652531i | \(0.773707\pi\) | |||||||
\(752\) | 5.53236 | 0.201744 | ||||||||
\(753\) | −21.4380 | −0.781242 | ||||||||
\(754\) | 2.25201 | 0.0820133 | ||||||||
\(755\) | 46.2817 | 1.68437 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.7227 | −0.644142 | −0.322071 | − | 0.946716i | \(-0.604379\pi\) | ||||
−0.322071 | + | 0.946716i | \(0.604379\pi\) | |||||||
\(758\) | −27.0095 | −0.981030 | ||||||||
\(759\) | 5.55575 | 0.201661 | ||||||||
\(760\) | −25.9478 | −0.941227 | ||||||||
\(761\) | 0.980289 | 0.0355354 | 0.0177677 | − | 0.999842i | \(-0.494344\pi\) | ||||
0.0177677 | + | 0.999842i | \(0.494344\pi\) | |||||||
\(762\) | 2.61350 | 0.0946770 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.338726 | 0.0122547 | ||||||||
\(765\) | −19.9003 | −0.719496 | ||||||||
\(766\) | 26.1355 | 0.944313 | ||||||||
\(767\) | −2.55309 | −0.0921866 | ||||||||
\(768\) | 16.5349 | 0.596650 | ||||||||
\(769\) | 9.98688 | 0.360136 | 0.180068 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180068 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.64434 | −0.311318 | ||||||||
\(772\) | −8.60054 | −0.309540 | ||||||||
\(773\) | 4.24629 | 0.152729 | 0.0763643 | − | 0.997080i | \(-0.475669\pi\) | ||||
0.0763643 | + | 0.997080i | \(0.475669\pi\) | |||||||
\(774\) | −0.393984 | −0.0141614 | ||||||||
\(775\) | −48.8831 | −1.75593 | ||||||||
\(776\) | 37.7199 | 1.35407 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.3475 | 0.370976 | ||||||||
\(779\) | −2.00040 | −0.0716719 | ||||||||
\(780\) | −1.31981 | −0.0472568 | ||||||||
\(781\) | −3.60130 | −0.128865 | ||||||||
\(782\) | 12.1300 | 0.433769 | ||||||||
\(783\) | −6.18926 | −0.221186 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.87357 | 0.316711 | ||||||||
\(786\) | −7.16858 | −0.255695 | ||||||||
\(787\) | 41.1788 | 1.46787 | 0.733933 | − | 0.679222i | \(-0.237683\pi\) | ||||
0.733933 | + | 0.679222i | \(0.237683\pi\) | |||||||
\(788\) | 9.28072 | 0.330612 | ||||||||
\(789\) | 15.6653 | 0.557699 | ||||||||
\(790\) | −45.5392 | −1.62021 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.84199 | 0.243120 | ||||||||
\(793\) | −4.05112 | −0.143860 | ||||||||
\(794\) | −16.2300 | −0.575980 | ||||||||
\(795\) | 44.4937 | 1.57803 | ||||||||
\(796\) | −15.3873 | −0.545390 | ||||||||
\(797\) | 15.2255 | 0.539316 | 0.269658 | − | 0.962956i | \(-0.413089\pi\) | ||||
0.269658 | + | 0.962956i | \(0.413089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3181 | −0.648047 | ||||||||
\(800\) | 60.6216 | 2.14330 | ||||||||
\(801\) | −7.79875 | −0.275555 | ||||||||
\(802\) | 31.4093 | 1.10910 | ||||||||
\(803\) | −34.1256 | −1.20427 | ||||||||
\(804\) | 12.7070 | 0.448143 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.35085 | −0.0475817 | ||||||||
\(807\) | −13.1787 | −0.463912 | ||||||||
\(808\) | 29.3429 | 1.03228 | ||||||||
\(809\) | −50.6646 | −1.78127 | −0.890637 | − | 0.454715i | \(-0.849741\pi\) | ||||
−0.890637 | + | 0.454715i | \(0.849741\pi\) | |||||||
\(810\) | −4.48105 | −0.157448 | ||||||||
\(811\) | −8.70882 | −0.305808 | −0.152904 | − | 0.988241i | \(-0.548863\pi\) | ||||
−0.152904 | + | 0.988241i | \(0.548863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.35125 | 0.257819 | ||||||||
\(814\) | 11.1834 | 0.391979 | ||||||||
\(815\) | 56.1168 | 1.96569 | ||||||||
\(816\) | 6.58367 | 0.230475 | ||||||||
\(817\) | 0.749646 | 0.0262268 | ||||||||
\(818\) | 10.5083 | 0.367414 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.81346 | 0.133172 | ||||||||
\(821\) | −2.59866 | −0.0906938 | −0.0453469 | − | 0.998971i | \(-0.514439\pi\) | ||||
−0.0453469 | + | 0.998971i | \(0.514439\pi\) | |||||||
\(822\) | 3.67968 | 0.128343 | ||||||||
\(823\) | −44.7617 | −1.56029 | −0.780147 | − | 0.625596i | \(-0.784856\pi\) | ||||
−0.780147 | + | 0.625596i | \(0.784856\pi\) | |||||||
\(824\) | −13.3993 | −0.466788 | ||||||||
\(825\) | 29.6021 | 1.03061 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.57720 | 0.333032 | 0.166516 | − | 0.986039i | \(-0.446748\pi\) | ||||
0.166516 | + | 0.986039i | \(0.446748\pi\) | |||||||
\(828\) | −2.21097 | −0.0768364 | ||||||||
\(829\) | 30.0318 | 1.04305 | 0.521523 | − | 0.853237i | \(-0.325364\pi\) | ||||
0.521523 | + | 0.853237i | \(0.325364\pi\) | |||||||
\(830\) | −55.1250 | −1.91342 | ||||||||
\(831\) | 1.18852 | 0.0412294 | ||||||||
\(832\) | 2.65129 | 0.0919168 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.2088 | 0.734402 | ||||||||
\(835\) | −58.0679 | −2.00952 | ||||||||
\(836\) | −4.02380 | −0.139166 | ||||||||
\(837\) | 3.71258 | 0.128326 | ||||||||
\(838\) | 31.5550 | 1.09005 | ||||||||
\(839\) | 0.824294 | 0.0284578 | 0.0142289 | − | 0.999899i | \(-0.495471\pi\) | ||||
0.0142289 | + | 0.999899i | \(0.495471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.30692 | 0.320928 | ||||||||
\(842\) | −2.90934 | −0.100262 | ||||||||
\(843\) | −6.99493 | −0.240918 | ||||||||
\(844\) | 2.63287 | 0.0906273 | ||||||||
\(845\) | 54.8989 | 1.88858 | ||||||||
\(846\) | −4.12477 | −0.141813 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.7200 | −0.505487 | ||||||||
\(849\) | 11.1116 | 0.381350 | ||||||||
\(850\) | 64.6310 | 2.21683 | ||||||||
\(851\) | −11.6923 | −0.400806 | ||||||||
\(852\) | 1.43318 | 0.0490998 | ||||||||
\(853\) | −27.1552 | −0.929777 | −0.464889 | − | 0.885369i | \(-0.653906\pi\) | ||||
−0.464889 | + | 0.885369i | \(0.653906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.52624 | 0.291591 | ||||||||
\(856\) | −10.5192 | −0.359539 | ||||||||
\(857\) | −14.1642 | −0.483840 | −0.241920 | − | 0.970296i | \(-0.577777\pi\) | ||||
−0.241920 | + | 0.970296i | \(0.577777\pi\) | |||||||
\(858\) | 0.818033 | 0.0279272 | ||||||||
\(859\) | 41.4434 | 1.41403 | 0.707015 | − | 0.707198i | \(-0.250041\pi\) | ||||
0.707015 | + | 0.707198i | \(0.250041\pi\) | |||||||
\(860\) | −1.42908 | −0.0487314 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.8137 | −0.606736 | ||||||||
\(863\) | 51.3552 | 1.74815 | 0.874076 | − | 0.485789i | \(-0.161468\pi\) | ||||
0.874076 | + | 0.485789i | \(0.161468\pi\) | |||||||
\(864\) | −4.60410 | −0.156635 | ||||||||
\(865\) | 48.9887 | 1.66567 | ||||||||
\(866\) | −0.998955 | −0.0339459 | ||||||||
\(867\) | −4.79907 | −0.162985 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.8478 | −0.775059 | ||||||||
\(870\) | 27.7344 | 0.940283 | ||||||||
\(871\) | 4.91538 | 0.166551 | ||||||||
\(872\) | 54.8374 | 1.85703 | ||||||||
\(873\) | −12.3944 | −0.419488 | ||||||||
\(874\) | −5.19709 | −0.175794 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5806 | 0.458847 | ||||||||
\(877\) | 27.3268 | 0.922761 | 0.461381 | − | 0.887202i | \(-0.347354\pi\) | ||||
0.461381 | + | 0.887202i | \(0.347354\pi\) | |||||||
\(878\) | −17.2034 | −0.580586 | ||||||||
\(879\) | −11.5761 | −0.390452 | ||||||||
\(880\) | −13.5123 | −0.455499 | ||||||||
\(881\) | −32.1796 | −1.08416 | −0.542079 | − | 0.840328i | \(-0.682363\pi\) | ||||
−0.542079 | + | 0.840328i | \(0.682363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.3505 | 1.18964 | 0.594820 | − | 0.803859i | \(-0.297223\pi\) | ||||
0.594820 | + | 0.803859i | \(0.297223\pi\) | |||||||
\(884\) | −1.44574 | −0.0486255 | ||||||||
\(885\) | −31.4422 | −1.05692 | ||||||||
\(886\) | −13.7732 | −0.462720 | ||||||||
\(887\) | 26.1857 | 0.879231 | 0.439616 | − | 0.898186i | \(-0.355115\pi\) | ||||
0.439616 | + | 0.898186i | \(0.355115\pi\) | |||||||
\(888\) | −14.3992 | −0.483207 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 34.9466 | 1.17141 | ||||||||
\(891\) | −2.24822 | −0.0753183 | ||||||||
\(892\) | −1.20255 | −0.0402643 | ||||||||
\(893\) | 7.84835 | 0.262635 | ||||||||
\(894\) | 13.6802 | 0.457536 | ||||||||
\(895\) | 95.1636 | 3.18097 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.855254 | −0.0285561 | ||||||||
\(898\) | −10.8129 | −0.360832 | ||||||||
\(899\) | −22.9781 | −0.766363 | ||||||||
\(900\) | −11.7805 | −0.392682 | ||||||||
\(901\) | 48.7391 | 1.62374 | ||||||||
\(902\) | −2.36363 | −0.0787001 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.4744 | −1.64549 | ||||||||
\(905\) | −2.43934 | −0.0810865 | ||||||||
\(906\) | 11.4159 | 0.379267 | ||||||||
\(907\) | 17.6397 | 0.585718 | 0.292859 | − | 0.956156i | \(-0.405393\pi\) | ||||
0.292859 | + | 0.956156i | \(0.405393\pi\) | |||||||
\(908\) | −23.6866 | −0.786068 | ||||||||
\(909\) | −9.64182 | −0.319799 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.8015 | 1.88192 | 0.940958 | − | 0.338523i | \(-0.109927\pi\) | ||||
0.940958 | + | 0.338523i | \(0.109927\pi\) | |||||||
\(912\) | −2.82077 | −0.0934049 | ||||||||
\(913\) | −27.6572 | −0.915320 | ||||||||
\(914\) | −7.95969 | −0.263283 | ||||||||
\(915\) | −49.8911 | −1.64935 | ||||||||
\(916\) | 13.2195 | 0.436785 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.90861 | −0.162008 | ||||||||
\(919\) | −56.8023 | −1.87373 | −0.936867 | − | 0.349686i | \(-0.886288\pi\) | ||||
−0.936867 | + | 0.349686i | \(0.886288\pi\) | |||||||
\(920\) | 32.0543 | 1.05680 | ||||||||
\(921\) | −15.4598 | −0.509417 | ||||||||
\(922\) | −39.6617 | −1.30619 | ||||||||
\(923\) | 0.554386 | 0.0182478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −62.2986 | −2.04837 | ||||||||
\(926\) | −1.54364 | −0.0507272 | ||||||||
\(927\) | 4.40291 | 0.144611 | ||||||||
\(928\) | 28.4960 | 0.935426 | ||||||||
\(929\) | 16.4404 | 0.539391 | 0.269696 | − | 0.962946i | \(-0.413077\pi\) | ||||
0.269696 | + | 0.962946i | \(0.413077\pi\) | |||||||
\(930\) | −16.6363 | −0.545524 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.7325 | 0.351556 | ||||||||
\(933\) | −16.4265 | −0.537780 | ||||||||
\(934\) | 19.2628 | 0.630297 | ||||||||
\(935\) | 44.7402 | 1.46316 | ||||||||
\(936\) | −1.05326 | −0.0344269 | ||||||||
\(937\) | 46.5074 | 1.51933 | 0.759665 | − | 0.650314i | \(-0.225363\pi\) | ||||
0.759665 | + | 0.650314i | \(0.225363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.9007 | 0.975771 | ||||||||
\(940\) | −14.9617 | −0.487996 | ||||||||
\(941\) | −17.9670 | −0.585709 | −0.292854 | − | 0.956157i | \(-0.594605\pi\) | ||||
−0.292854 | + | 0.956157i | \(0.594605\pi\) | |||||||
\(942\) | 2.18876 | 0.0713136 | ||||||||
\(943\) | 2.47117 | 0.0804725 | ||||||||
\(944\) | 10.4021 | 0.338561 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.885763 | 0.0287986 | ||||||||
\(947\) | −26.6907 | −0.867332 | −0.433666 | − | 0.901074i | \(-0.642780\pi\) | ||||
−0.433666 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(948\) | 9.09253 | 0.295312 | ||||||||
\(949\) | 5.25331 | 0.170530 | ||||||||
\(950\) | −27.6911 | −0.898417 | ||||||||
\(951\) | −4.91153 | −0.159267 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.3116 | 1.43539 | 0.717697 | − | 0.696355i | \(-0.245196\pi\) | ||||
0.717697 | + | 0.696355i | \(0.245196\pi\) | |||||||
\(954\) | 10.9748 | 0.355323 | ||||||||
\(955\) | 1.61365 | 0.0522166 | ||||||||
\(956\) | −13.7246 | −0.443884 | ||||||||
\(957\) | 13.9148 | 0.449803 | ||||||||
\(958\) | −6.80885 | −0.219984 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 32.6516 | 1.05383 | ||||||||
\(961\) | −17.2167 | −0.555379 | ||||||||
\(962\) | −1.72158 | −0.0555060 | ||||||||
\(963\) | 3.45652 | 0.111385 | ||||||||
\(964\) | −15.7785 | −0.508191 | ||||||||
\(965\) | −40.9720 | −1.31893 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.6508 | −1.46803 | −0.734016 | − | 0.679132i | \(-0.762356\pi\) | ||||
−0.734016 | + | 0.679132i | \(0.762356\pi\) | |||||||
\(968\) | 18.0939 | 0.581559 | ||||||||
\(969\) | 9.33978 | 0.300037 | ||||||||
\(970\) | 55.5401 | 1.78329 | ||||||||
\(971\) | 44.2849 | 1.42117 | 0.710584 | − | 0.703612i | \(-0.248431\pi\) | ||||
0.710584 | + | 0.703612i | \(0.248431\pi\) | |||||||
\(972\) | 0.894704 | 0.0286976 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.604349 | −0.0193646 | ||||||||
\(975\) | −4.55696 | −0.145939 | ||||||||
\(976\) | 16.5056 | 0.528333 | ||||||||
\(977\) | 2.79496 | 0.0894186 | 0.0447093 | − | 0.999000i | \(-0.485764\pi\) | ||||
0.0447093 | + | 0.999000i | \(0.485764\pi\) | |||||||
\(978\) | 13.8418 | 0.442612 | ||||||||
\(979\) | 17.5333 | 0.560367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0191 | −0.575306 | ||||||||
\(982\) | −5.90967 | −0.188585 | ||||||||
\(983\) | 59.3041 | 1.89151 | 0.945753 | − | 0.324887i | \(-0.105326\pi\) | ||||
0.945753 | + | 0.324887i | \(0.105326\pi\) | |||||||
\(984\) | 3.04329 | 0.0970166 | ||||||||
\(985\) | 44.2122 | 1.40872 | ||||||||
\(986\) | 30.3806 | 0.967517 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.619425 | 0.0197065 | ||||||||
\(989\) | −0.926066 | −0.0294472 | ||||||||
\(990\) | 10.0744 | 0.320185 | ||||||||
\(991\) | 3.98616 | 0.126625 | 0.0633123 | − | 0.997994i | \(-0.479834\pi\) | ||||
0.0633123 | + | 0.997994i | \(0.479834\pi\) | |||||||
\(992\) | −17.0931 | −0.542707 | ||||||||
\(993\) | −5.41473 | −0.171831 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.3035 | −2.32388 | ||||||||
\(996\) | 11.0065 | 0.348753 | ||||||||
\(997\) | −14.6032 | −0.462488 | −0.231244 | − | 0.972896i | \(-0.574280\pi\) | ||||
−0.231244 | + | 0.972896i | \(0.574280\pi\) | |||||||
\(998\) | 12.0809 | 0.382413 | ||||||||
\(999\) | 4.73147 | 0.149697 |
(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 | 6027.2.a.bf.1.9 | 12 | ||
7.3 | odd | 6 | 861.2.i.e.247.4 | ✓ | 24 | ||
7.5 | odd | 6 | 861.2.i.e.739.4 | yes | 24 | ||
7.6 | odd | 2 | 6027.2.a.bg.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.e.247.4 | ✓ | 24 | 7.3 | odd | 6 | ||
861.2.i.e.739.4 | yes | 24 | 7.5 | odd | 6 | ||
6027.2.a.bf.1.9 | 12 | 1.1 | even | 1 | trivial | ||
6027.2.a.bg.1.9 | 12 | 7.6 | odd | 2 |