Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6825,2,Mod(1,6825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6825.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: | \(54.4978993795\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.17428.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 6x^{2} + 4x + 6 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.787711\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37951 | 1.68257 | 0.841285 | − | 0.540593i | \(-0.181800\pi\) | ||||
0.841285 | + | 0.540593i | \(0.181800\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.66208 | 1.83104 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.37951 | −0.971432 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.95493 | 1.39828 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.57542 | 0.475007 | 0.237504 | − | 0.971387i | \(-0.423671\pi\) | ||||
0.237504 | + | 0.971387i | \(0.423671\pi\) | |||||||
\(12\) | −3.66208 | −1.05715 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.37951 | −0.635951 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.08666 | 0.521664 | ||||||||
\(17\) | −4.75902 | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(18\) | 2.37951 | 0.560856 | ||||||||
\(19\) | −2.23750 | −0.513317 | −0.256659 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256659 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 3.74873 | 0.799233 | ||||||||
\(23\) | −5.84568 | −1.21891 | −0.609454 | − | 0.792821i | \(-0.708611\pi\) | ||||
−0.609454 | + | 0.792821i | \(0.708611\pi\) | |||||||
\(24\) | −3.95493 | −0.807297 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.37951 | −0.466661 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.66208 | −0.692068 | ||||||||
\(29\) | 4.23750 | 0.786884 | 0.393442 | − | 0.919349i | \(-0.371284\pi\) | ||||
0.393442 | + | 0.919349i | \(0.371284\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.28055 | 1.30763 | 0.653813 | − | 0.756656i | \(-0.273168\pi\) | ||||
0.653813 | + | 0.756656i | \(0.273168\pi\) | |||||||
\(32\) | −2.94464 | −0.520544 | ||||||||
\(33\) | −1.57542 | −0.274246 | ||||||||
\(34\) | −11.3242 | −1.94208 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.66208 | 0.610346 | ||||||||
\(37\) | −10.4750 | −1.72208 | −0.861039 | − | 0.508538i | \(-0.830186\pi\) | ||||
−0.861039 | + | 0.508538i | \(0.830186\pi\) | |||||||
\(38\) | −5.32415 | −0.863692 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.25127 | −0.351589 | −0.175794 | − | 0.984427i | \(-0.556249\pi\) | ||||
−0.175794 | + | 0.984427i | \(0.556249\pi\) | |||||||
\(42\) | 2.37951 | 0.367167 | ||||||||
\(43\) | −0.913344 | −0.139284 | −0.0696418 | − | 0.997572i | \(-0.522186\pi\) | ||||
−0.0696418 | + | 0.997572i | \(0.522186\pi\) | |||||||
\(44\) | 5.76931 | 0.869757 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.9099 | −2.05090 | ||||||||
\(47\) | 2.09695 | 0.305871 | 0.152936 | − | 0.988236i | \(-0.451127\pi\) | ||||
0.152936 | + | 0.988236i | \(0.451127\pi\) | |||||||
\(48\) | −2.08666 | −0.301183 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.75902 | 0.666397 | ||||||||
\(52\) | −3.66208 | −0.507839 | ||||||||
\(53\) | −1.08666 | −0.149264 | −0.0746319 | − | 0.997211i | \(-0.523778\pi\) | ||||
−0.0746319 | + | 0.997211i | \(0.523778\pi\) | |||||||
\(54\) | −2.37951 | −0.323811 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.95493 | −0.528500 | ||||||||
\(57\) | 2.23750 | 0.296364 | ||||||||
\(58\) | 10.0832 | 1.32399 | ||||||||
\(59\) | −12.3344 | −1.60581 | −0.802904 | − | 0.596108i | \(-0.796713\pi\) | ||||
−0.802904 | + | 0.596108i | \(0.796713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.51805 | −0.962587 | −0.481294 | − | 0.876559i | \(-0.659833\pi\) | ||||
−0.481294 | + | 0.876559i | \(0.659833\pi\) | |||||||
\(62\) | 17.3242 | 2.20017 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −11.1801 | −1.39752 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.74873 | −0.461437 | ||||||||
\(67\) | 15.6914 | 1.91700 | 0.958502 | − | 0.285084i | \(-0.0920217\pi\) | ||||
0.958502 | + | 0.285084i | \(0.0920217\pi\) | |||||||
\(68\) | −17.4279 | −2.11345 | ||||||||
\(69\) | 5.84568 | 0.703737 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0504 | 1.19277 | 0.596383 | − | 0.802700i | \(-0.296604\pi\) | ||||
0.596383 | + | 0.802700i | \(0.296604\pi\) | |||||||
\(72\) | 3.95493 | 0.466093 | ||||||||
\(73\) | −15.0797 | −1.76495 | −0.882473 | − | 0.470363i | \(-0.844123\pi\) | ||||
−0.882473 | + | 0.470363i | \(0.844123\pi\) | |||||||
\(74\) | −24.9254 | −2.89752 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.19389 | −0.939904 | ||||||||
\(77\) | −1.57542 | −0.179536 | ||||||||
\(78\) | 2.37951 | 0.269427 | ||||||||
\(79\) | −11.7555 | −1.32260 | −0.661301 | − | 0.750121i | \(-0.729995\pi\) | ||||
−0.661301 | + | 0.750121i | \(0.729995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.35692 | −0.591572 | ||||||||
\(83\) | −7.42110 | −0.814572 | −0.407286 | − | 0.913301i | \(-0.633525\pi\) | ||||
−0.407286 | + | 0.913301i | \(0.633525\pi\) | |||||||
\(84\) | 3.66208 | 0.399565 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.17331 | −0.234354 | ||||||||
\(87\) | −4.23750 | −0.454308 | ||||||||
\(88\) | 6.23069 | 0.664193 | ||||||||
\(89\) | −11.1371 | −1.18053 | −0.590264 | − | 0.807210i | \(-0.700976\pi\) | ||||
−0.590264 | + | 0.807210i | \(0.700976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −21.4073 | −2.23187 | ||||||||
\(93\) | −7.28055 | −0.754958 | ||||||||
\(94\) | 4.98971 | 0.514649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.94464 | 0.300536 | ||||||||
\(97\) | 14.6047 | 1.48288 | 0.741442 | − | 0.671017i | \(-0.234142\pi\) | ||||
0.741442 | + | 0.671017i | \(0.234142\pi\) | |||||||
\(98\) | 2.37951 | 0.240367 | ||||||||
\(99\) | 1.57542 | 0.158336 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4349 | −1.13781 | −0.568906 | − | 0.822403i | \(-0.692633\pi\) | ||||
−0.568906 | + | 0.822403i | \(0.692633\pi\) | |||||||
\(102\) | 11.3242 | 1.12126 | ||||||||
\(103\) | −11.1508 | −1.09873 | −0.549363 | − | 0.835584i | \(-0.685129\pi\) | ||||
−0.549363 | + | 0.835584i | \(0.685129\pi\) | |||||||
\(104\) | −3.95493 | −0.387813 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.58571 | −0.251147 | ||||||||
\(107\) | −2.28403 | −0.220805 | −0.110403 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110403 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(108\) | −3.66208 | −0.352384 | ||||||||
\(109\) | 14.6689 | 1.40502 | 0.702512 | − | 0.711671i | \(-0.252062\pi\) | ||||
0.702512 | + | 0.711671i | \(0.252062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4750 | 0.994243 | ||||||||
\(112\) | −2.08666 | −0.197170 | ||||||||
\(113\) | 4.23750 | 0.398630 | 0.199315 | − | 0.979935i | \(-0.436128\pi\) | ||||
0.199315 | + | 0.979935i | \(0.436128\pi\) | |||||||
\(114\) | 5.32415 | 0.498653 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.5180 | 1.44081 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −29.3500 | −2.70188 | ||||||||
\(119\) | 4.75902 | 0.436259 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.51805 | −0.774368 | ||||||||
\(122\) | −17.8893 | −1.61962 | ||||||||
\(123\) | 2.25127 | 0.202990 | ||||||||
\(124\) | 26.6619 | 2.39431 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.37951 | −0.211984 | ||||||||
\(127\) | −4.84916 | −0.430293 | −0.215147 | − | 0.976582i | \(-0.569023\pi\) | ||||
−0.215147 | + | 0.976582i | \(0.569023\pi\) | |||||||
\(128\) | −20.7140 | −1.83087 | ||||||||
\(129\) | 0.913344 | 0.0804154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.36721 | −0.556305 | −0.278153 | − | 0.960537i | \(-0.589722\pi\) | ||||
−0.278153 | + | 0.960537i | \(0.589722\pi\) | |||||||
\(132\) | −5.76931 | −0.502154 | ||||||||
\(133\) | 2.23750 | 0.194016 | ||||||||
\(134\) | 37.3378 | 3.22549 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −18.8216 | −1.61394 | ||||||||
\(137\) | 18.0258 | 1.54005 | 0.770024 | − | 0.638015i | \(-0.220244\pi\) | ||||
0.770024 | + | 0.638015i | \(0.220244\pi\) | |||||||
\(138\) | 13.9099 | 1.18409 | ||||||||
\(139\) | 2.67585 | 0.226962 | 0.113481 | − | 0.993540i | \(-0.463800\pi\) | ||||
0.113481 | + | 0.993540i | \(0.463800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09695 | −0.176595 | ||||||||
\(142\) | 23.9151 | 2.00691 | ||||||||
\(143\) | −1.57542 | −0.131743 | ||||||||
\(144\) | 2.08666 | 0.173888 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −35.8823 | −2.96964 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −38.3603 | −3.15319 | ||||||||
\(149\) | −7.46471 | −0.611533 | −0.305766 | − | 0.952107i | \(-0.598913\pi\) | ||||
−0.305766 | + | 0.952107i | \(0.598913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0155 | 1.05919 | 0.529594 | − | 0.848251i | \(-0.322344\pi\) | ||||
0.529594 | + | 0.848251i | \(0.322344\pi\) | |||||||
\(152\) | −8.84916 | −0.717761 | ||||||||
\(153\) | −4.75902 | −0.384744 | ||||||||
\(154\) | −3.74873 | −0.302082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.66208 | 0.293201 | ||||||||
\(157\) | 17.1233 | 1.36659 | 0.683294 | − | 0.730143i | \(-0.260547\pi\) | ||||
0.683294 | + | 0.730143i | \(0.260547\pi\) | |||||||
\(158\) | −27.9725 | −2.22537 | ||||||||
\(159\) | 1.08666 | 0.0861774 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.84568 | 0.460704 | ||||||||
\(162\) | 2.37951 | 0.186952 | ||||||||
\(163\) | 0.849158 | 0.0665112 | 0.0332556 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332556 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(164\) | −8.24431 | −0.643773 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.6586 | −1.37057 | ||||||||
\(167\) | −18.3781 | −1.42214 | −0.711068 | − | 0.703123i | \(-0.751788\pi\) | ||||
−0.711068 | + | 0.703123i | \(0.751788\pi\) | |||||||
\(168\) | 3.95493 | 0.305130 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23750 | −0.171106 | ||||||||
\(172\) | −3.34474 | −0.255034 | ||||||||
\(173\) | 12.2565 | 0.931844 | 0.465922 | − | 0.884826i | \(-0.345723\pi\) | ||||
0.465922 | + | 0.884826i | \(0.345723\pi\) | |||||||
\(174\) | −10.0832 | −0.764404 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.28736 | 0.247794 | ||||||||
\(177\) | 12.3344 | 0.927114 | ||||||||
\(178\) | −26.5008 | −1.98632 | ||||||||
\(179\) | 18.5146 | 1.38384 | 0.691922 | − | 0.721972i | \(-0.256764\pi\) | ||||
0.691922 | + | 0.721972i | \(0.256764\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.1664 | −1.35029 | −0.675147 | − | 0.737683i | \(-0.735920\pi\) | ||||
−0.675147 | + | 0.737683i | \(0.735920\pi\) | |||||||
\(182\) | 2.37951 | 0.176381 | ||||||||
\(183\) | 7.51805 | 0.555750 | ||||||||
\(184\) | −23.1193 | −1.70438 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −17.3242 | −1.27027 | ||||||||
\(187\) | −7.49747 | −0.548269 | ||||||||
\(188\) | 7.67918 | 0.560062 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.5151 | 1.70149 | 0.850747 | − | 0.525575i | \(-0.176150\pi\) | ||||
0.850747 | + | 0.525575i | \(0.176150\pi\) | |||||||
\(192\) | 11.1801 | 0.806856 | ||||||||
\(193\) | −14.7344 | −1.06061 | −0.530303 | − | 0.847808i | \(-0.677922\pi\) | ||||
−0.530303 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(194\) | 34.7521 | 2.49505 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.66208 | 0.261577 | ||||||||
\(197\) | −14.5008 | −1.03314 | −0.516570 | − | 0.856245i | \(-0.672791\pi\) | ||||
−0.516570 | + | 0.856245i | \(0.672791\pi\) | |||||||
\(198\) | 3.74873 | 0.266411 | ||||||||
\(199\) | −13.5180 | −0.958269 | −0.479135 | − | 0.877741i | \(-0.659049\pi\) | ||||
−0.479135 | + | 0.877741i | \(0.659049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.6914 | −1.10678 | ||||||||
\(202\) | −27.2094 | −1.91445 | ||||||||
\(203\) | −4.23750 | −0.297414 | ||||||||
\(204\) | 17.4279 | 1.22020 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −26.5336 | −1.84868 | ||||||||
\(207\) | −5.84568 | −0.406303 | ||||||||
\(208\) | −2.08666 | −0.144684 | ||||||||
\(209\) | −3.52500 | −0.243830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.06419 | 0.279790 | 0.139895 | − | 0.990166i | \(-0.455323\pi\) | ||||
0.139895 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(212\) | −3.97942 | −0.273308 | ||||||||
\(213\) | −10.0504 | −0.688643 | ||||||||
\(214\) | −5.43487 | −0.371520 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.95493 | −0.269099 | ||||||||
\(217\) | −7.28055 | −0.494236 | ||||||||
\(218\) | 34.9048 | 2.36405 | ||||||||
\(219\) | 15.0797 | 1.01899 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.75902 | 0.320127 | ||||||||
\(222\) | 24.9254 | 1.67288 | ||||||||
\(223\) | 0.0641862 | 0.00429822 | 0.00214911 | − | 0.999998i | \(-0.499316\pi\) | ||||
0.00214911 | + | 0.999998i | \(0.499316\pi\) | |||||||
\(224\) | 2.94464 | 0.196747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0832 | 0.670723 | ||||||||
\(227\) | 1.68614 | 0.111913 | 0.0559564 | − | 0.998433i | \(-0.482179\pi\) | ||||
0.0559564 | + | 0.998433i | \(0.482179\pi\) | |||||||
\(228\) | 8.19389 | 0.542654 | ||||||||
\(229\) | 0.648310 | 0.0428415 | 0.0214208 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214208 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.57542 | 0.103655 | ||||||||
\(232\) | 16.7590 | 1.10028 | ||||||||
\(233\) | −3.10724 | −0.203562 | −0.101781 | − | 0.994807i | \(-0.532454\pi\) | ||||
−0.101781 | + | 0.994807i | \(0.532454\pi\) | |||||||
\(234\) | −2.37951 | −0.155554 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −45.1697 | −2.94030 | ||||||||
\(237\) | 11.7555 | 0.763605 | ||||||||
\(238\) | 11.3242 | 0.734036 | ||||||||
\(239\) | −15.0659 | −0.974534 | −0.487267 | − | 0.873253i | \(-0.662006\pi\) | ||||
−0.487267 | + | 0.873253i | \(0.662006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.7280 | 1.65729 | 0.828643 | − | 0.559777i | \(-0.189113\pi\) | ||||
0.828643 | + | 0.559777i | \(0.189113\pi\) | |||||||
\(242\) | −20.2688 | −1.30293 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −27.5317 | −1.76253 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.35692 | 0.341544 | ||||||||
\(247\) | 2.23750 | 0.142369 | ||||||||
\(248\) | 28.7941 | 1.82843 | ||||||||
\(249\) | 7.42110 | 0.470293 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6258 | −0.733816 | −0.366908 | − | 0.930257i | \(-0.619584\pi\) | ||||
−0.366908 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(252\) | −3.66208 | −0.230689 | ||||||||
\(253\) | −9.20941 | −0.578991 | ||||||||
\(254\) | −11.5386 | −0.723998 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.9289 | −1.68305 | ||||||||
\(257\) | 12.5651 | 0.783791 | 0.391896 | − | 0.920010i | \(-0.371819\pi\) | ||||
0.391896 | + | 0.920010i | \(0.371819\pi\) | |||||||
\(258\) | 2.17331 | 0.135305 | ||||||||
\(259\) | 10.4750 | 0.650885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.23750 | 0.262295 | ||||||||
\(262\) | −15.1508 | −0.936022 | ||||||||
\(263\) | −9.37068 | −0.577821 | −0.288911 | − | 0.957356i | \(-0.593293\pi\) | ||||
−0.288911 | + | 0.957356i | \(0.593293\pi\) | |||||||
\(264\) | −6.23069 | −0.383472 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.32415 | 0.326445 | ||||||||
\(267\) | 11.1371 | 0.681578 | ||||||||
\(268\) | 57.4630 | 3.51011 | ||||||||
\(269\) | −10.3918 | −0.633600 | −0.316800 | − | 0.948492i | \(-0.602608\pi\) | ||||
−0.316800 | + | 0.948492i | \(0.602608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.13026 | −0.311641 | −0.155821 | − | 0.987785i | \(-0.549802\pi\) | ||||
−0.155821 | + | 0.987785i | \(0.549802\pi\) | |||||||
\(272\) | −9.93045 | −0.602122 | ||||||||
\(273\) | −1.00000 | −0.0605228 | ||||||||
\(274\) | 42.8926 | 2.59124 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.4073 | 1.28857 | ||||||||
\(277\) | −8.04361 | −0.483293 | −0.241647 | − | 0.970364i | \(-0.577688\pi\) | ||||
−0.241647 | + | 0.970364i | \(0.577688\pi\) | |||||||
\(278\) | 6.36721 | 0.381880 | ||||||||
\(279\) | 7.28055 | 0.435875 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.8525 | −1.66154 | −0.830770 | − | 0.556616i | \(-0.812100\pi\) | ||||
−0.830770 | + | 0.556616i | \(0.812100\pi\) | |||||||
\(282\) | −4.98971 | −0.297133 | ||||||||
\(283\) | −23.8197 | −1.41594 | −0.707968 | − | 0.706244i | \(-0.750388\pi\) | ||||
−0.707968 | + | 0.706244i | \(0.750388\pi\) | |||||||
\(284\) | 36.8054 | 2.18400 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.74873 | −0.221667 | ||||||||
\(287\) | 2.25127 | 0.132888 | ||||||||
\(288\) | −2.94464 | −0.173515 | ||||||||
\(289\) | 5.64831 | 0.332254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.6047 | −0.856143 | ||||||||
\(292\) | −55.2230 | −3.23168 | ||||||||
\(293\) | 16.4612 | 0.961675 | 0.480838 | − | 0.876810i | \(-0.340333\pi\) | ||||
0.480838 | + | 0.876810i | \(0.340333\pi\) | |||||||
\(294\) | −2.37951 | −0.138776 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −41.4279 | −2.40795 | ||||||||
\(297\) | −1.57542 | −0.0914152 | ||||||||
\(298\) | −17.7624 | −1.02895 | ||||||||
\(299\) | 5.84568 | 0.338064 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.913344 | 0.0526443 | ||||||||
\(302\) | 30.9706 | 1.78216 | ||||||||
\(303\) | 11.4349 | 0.656916 | ||||||||
\(304\) | −4.66889 | −0.267779 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.3242 | −0.647359 | ||||||||
\(307\) | −1.95639 | −0.111657 | −0.0558287 | − | 0.998440i | \(-0.517780\pi\) | ||||
−0.0558287 | + | 0.998440i | \(0.517780\pi\) | |||||||
\(308\) | −5.76931 | −0.328737 | ||||||||
\(309\) | 11.1508 | 0.634349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.67585 | −0.378552 | −0.189276 | − | 0.981924i | \(-0.560614\pi\) | ||||
−0.189276 | + | 0.981924i | \(0.560614\pi\) | |||||||
\(312\) | 3.95493 | 0.223904 | ||||||||
\(313\) | 6.78364 | 0.383434 | 0.191717 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191717 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(314\) | 40.7451 | 2.29938 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.0497 | −2.42174 | ||||||||
\(317\) | 30.6947 | 1.72399 | 0.861993 | − | 0.506920i | \(-0.169216\pi\) | ||||
0.861993 | + | 0.506920i | \(0.169216\pi\) | |||||||
\(318\) | 2.58571 | 0.145000 | ||||||||
\(319\) | 6.67585 | 0.373776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.28403 | 0.127482 | ||||||||
\(322\) | 13.9099 | 0.775167 | ||||||||
\(323\) | 10.6483 | 0.592488 | ||||||||
\(324\) | 3.66208 | 0.203449 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.02058 | 0.111910 | ||||||||
\(327\) | −14.6689 | −0.811191 | ||||||||
\(328\) | −8.90361 | −0.491620 | ||||||||
\(329\) | −2.09695 | −0.115608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8267 | −0.759983 | −0.379992 | − | 0.924990i | \(-0.624073\pi\) | ||||
−0.379992 | + | 0.924990i | \(0.624073\pi\) | |||||||
\(332\) | −27.1766 | −1.49151 | ||||||||
\(333\) | −10.4750 | −0.574026 | ||||||||
\(334\) | −43.7308 | −2.39284 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.08666 | 0.113836 | ||||||||
\(337\) | −23.8633 | −1.29992 | −0.649959 | − | 0.759969i | \(-0.725214\pi\) | ||||
−0.649959 | + | 0.759969i | \(0.725214\pi\) | |||||||
\(338\) | 2.37951 | 0.129428 | ||||||||
\(339\) | −4.23750 | −0.230149 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4699 | 0.621132 | ||||||||
\(342\) | −5.32415 | −0.287897 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.61221 | −0.194758 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.1645 | 1.56789 | ||||||||
\(347\) | 13.6012 | 0.730152 | 0.365076 | − | 0.930978i | \(-0.381043\pi\) | ||||
0.365076 | + | 0.930978i | \(0.381043\pi\) | |||||||
\(348\) | −15.5180 | −0.831855 | ||||||||
\(349\) | −16.4039 | −0.878078 | −0.439039 | − | 0.898468i | \(-0.644681\pi\) | ||||
−0.439039 | + | 0.898468i | \(0.644681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.63905 | −0.247262 | ||||||||
\(353\) | 4.73322 | 0.251924 | 0.125962 | − | 0.992035i | \(-0.459798\pi\) | ||||
0.125962 | + | 0.992035i | \(0.459798\pi\) | |||||||
\(354\) | 29.3500 | 1.55993 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −40.7848 | −2.16159 | ||||||||
\(357\) | −4.75902 | −0.251874 | ||||||||
\(358\) | 44.0556 | 2.32841 | ||||||||
\(359\) | −17.5479 | −0.926142 | −0.463071 | − | 0.886321i | \(-0.653253\pi\) | ||||
−0.463071 | + | 0.886321i | \(0.653253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9936 | −0.736505 | ||||||||
\(362\) | −43.2271 | −2.27196 | ||||||||
\(363\) | 8.51805 | 0.447082 | ||||||||
\(364\) | 3.66208 | 0.191945 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 17.8893 | 0.935088 | ||||||||
\(367\) | 11.1888 | 0.584052 | 0.292026 | − | 0.956410i | \(-0.405671\pi\) | ||||
0.292026 | + | 0.956410i | \(0.405671\pi\) | |||||||
\(368\) | −12.1979 | −0.635861 | ||||||||
\(369\) | −2.25127 | −0.117196 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.08666 | 0.0564164 | ||||||||
\(372\) | −26.6619 | −1.38236 | ||||||||
\(373\) | 5.43195 | 0.281256 | 0.140628 | − | 0.990063i | \(-0.455088\pi\) | ||||
0.140628 | + | 0.990063i | \(0.455088\pi\) | |||||||
\(374\) | −17.8403 | −0.922501 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.29328 | 0.427693 | ||||||||
\(377\) | −4.23750 | −0.218242 | ||||||||
\(378\) | 2.37951 | 0.122389 | ||||||||
\(379\) | 10.8422 | 0.556927 | 0.278463 | − | 0.960447i | \(-0.410175\pi\) | ||||
0.278463 | + | 0.960447i | \(0.410175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.84916 | 0.248430 | ||||||||
\(382\) | 55.9545 | 2.86288 | ||||||||
\(383\) | −10.5353 | −0.538328 | −0.269164 | − | 0.963094i | \(-0.586747\pi\) | ||||
−0.269164 | + | 0.963094i | \(0.586747\pi\) | |||||||
\(384\) | 20.7140 | 1.05705 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −35.0607 | −1.78454 | ||||||||
\(387\) | −0.913344 | −0.0464279 | ||||||||
\(388\) | 53.4836 | 2.71522 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.8197 | 1.40690 | ||||||||
\(392\) | 3.95493 | 0.199754 | ||||||||
\(393\) | 6.36721 | 0.321183 | ||||||||
\(394\) | −34.5048 | −1.73833 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.76931 | 0.289919 | ||||||||
\(397\) | 35.4400 | 1.77868 | 0.889340 | − | 0.457246i | \(-0.151164\pi\) | ||||
0.889340 | + | 0.457246i | \(0.151164\pi\) | |||||||
\(398\) | −32.1664 | −1.61235 | ||||||||
\(399\) | −2.23750 | −0.112015 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7241 | 1.18473 | 0.592363 | − | 0.805671i | \(-0.298195\pi\) | ||||
0.592363 | + | 0.805671i | \(0.298195\pi\) | |||||||
\(402\) | −37.3378 | −1.86224 | ||||||||
\(403\) | −7.28055 | −0.362670 | ||||||||
\(404\) | −41.8754 | −2.08338 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0832 | −0.500420 | ||||||||
\(407\) | −16.5025 | −0.818000 | ||||||||
\(408\) | 18.8216 | 0.931809 | ||||||||
\(409\) | −3.95639 | −0.195631 | −0.0978156 | − | 0.995205i | \(-0.531186\pi\) | ||||
−0.0978156 | + | 0.995205i | \(0.531186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0258 | −0.889147 | ||||||||
\(412\) | −40.8352 | −2.01181 | ||||||||
\(413\) | 12.3344 | 0.606938 | ||||||||
\(414\) | −13.9099 | −0.683633 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.94464 | 0.144373 | ||||||||
\(417\) | −2.67585 | −0.131037 | ||||||||
\(418\) | −8.38779 | −0.410260 | ||||||||
\(419\) | −18.0586 | −0.882219 | −0.441109 | − | 0.897453i | \(-0.645415\pi\) | ||||
−0.441109 | + | 0.897453i | \(0.645415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.4956 | 1.19384 | 0.596921 | − | 0.802300i | \(-0.296391\pi\) | ||||
0.596921 | + | 0.802300i | \(0.296391\pi\) | |||||||
\(422\) | 9.67078 | 0.470766 | ||||||||
\(423\) | 2.09695 | 0.101957 | ||||||||
\(424\) | −4.29765 | −0.208712 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −23.9151 | −1.15869 | ||||||||
\(427\) | 7.51805 | 0.363824 | ||||||||
\(428\) | −8.36428 | −0.404303 | ||||||||
\(429\) | 1.57542 | 0.0760621 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.7779 | −1.96420 | −0.982101 | − | 0.188357i | \(-0.939684\pi\) | ||||
−0.982101 | + | 0.188357i | \(0.939684\pi\) | |||||||
\(432\) | −2.08666 | −0.100394 | ||||||||
\(433\) | 18.0791 | 0.868828 | 0.434414 | − | 0.900713i | \(-0.356955\pi\) | ||||
0.434414 | + | 0.900713i | \(0.356955\pi\) | |||||||
\(434\) | −17.3242 | −0.831586 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 53.7186 | 2.57265 | ||||||||
\(437\) | 13.0797 | 0.625687 | ||||||||
\(438\) | 35.8823 | 1.71452 | ||||||||
\(439\) | 20.7561 | 0.990635 | 0.495317 | − | 0.868712i | \(-0.335052\pi\) | ||||
0.495317 | + | 0.868712i | \(0.335052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 11.3242 | 0.538635 | ||||||||
\(443\) | 8.24042 | 0.391514 | 0.195757 | − | 0.980652i | \(-0.437284\pi\) | ||||
0.195757 | + | 0.980652i | \(0.437284\pi\) | |||||||
\(444\) | 38.3603 | 1.82050 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.152732 | 0.00723206 | ||||||||
\(447\) | 7.46471 | 0.353069 | ||||||||
\(448\) | 11.1801 | 0.528211 | ||||||||
\(449\) | 36.1061 | 1.70395 | 0.851975 | − | 0.523582i | \(-0.175405\pi\) | ||||
0.851975 | + | 0.523582i | \(0.175405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.54669 | −0.167007 | ||||||||
\(452\) | 15.5180 | 0.729908 | ||||||||
\(453\) | −13.0155 | −0.611522 | ||||||||
\(454\) | 4.01218 | 0.188301 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.84916 | 0.414400 | ||||||||
\(457\) | 6.54052 | 0.305953 | 0.152976 | − | 0.988230i | \(-0.451114\pi\) | ||||
0.152976 | + | 0.988230i | \(0.451114\pi\) | |||||||
\(458\) | 1.54266 | 0.0720838 | ||||||||
\(459\) | 4.75902 | 0.222132 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.6987 | −0.684588 | −0.342294 | − | 0.939593i | \(-0.611204\pi\) | ||||
−0.342294 | + | 0.939593i | \(0.611204\pi\) | |||||||
\(462\) | 3.74873 | 0.174407 | ||||||||
\(463\) | −21.7775 | −1.01208 | −0.506042 | − | 0.862509i | \(-0.668892\pi\) | ||||
−0.506042 | + | 0.862509i | \(0.668892\pi\) | |||||||
\(464\) | 8.84220 | 0.410489 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.39371 | −0.342507 | ||||||||
\(467\) | −35.0086 | −1.62000 | −0.810001 | − | 0.586428i | \(-0.800534\pi\) | ||||
−0.810001 | + | 0.586428i | \(0.800534\pi\) | |||||||
\(468\) | −3.66208 | −0.169280 | ||||||||
\(469\) | −15.6914 | −0.724560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.1233 | −0.789000 | ||||||||
\(472\) | −48.7819 | −2.24537 | ||||||||
\(473\) | −1.43890 | −0.0661607 | ||||||||
\(474\) | 27.9725 | 1.28482 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.4279 | 0.798807 | ||||||||
\(477\) | −1.08666 | −0.0497546 | ||||||||
\(478\) | −35.8496 | −1.63972 | ||||||||
\(479\) | 31.7814 | 1.45213 | 0.726064 | − | 0.687628i | \(-0.241348\pi\) | ||||
0.726064 | + | 0.687628i | \(0.241348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.4750 | 0.477619 | ||||||||
\(482\) | 61.2201 | 2.78850 | ||||||||
\(483\) | −5.84568 | −0.265988 | ||||||||
\(484\) | −31.1938 | −1.41790 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.37951 | −0.107937 | ||||||||
\(487\) | 28.5817 | 1.29516 | 0.647580 | − | 0.761998i | \(-0.275781\pi\) | ||||
0.647580 | + | 0.761998i | \(0.275781\pi\) | |||||||
\(488\) | −29.7334 | −1.34597 | ||||||||
\(489\) | −0.849158 | −0.0384002 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7160 | 0.980028 | 0.490014 | − | 0.871715i | \(-0.336992\pi\) | ||||
0.490014 | + | 0.871715i | \(0.336992\pi\) | |||||||
\(492\) | 8.24431 | 0.371682 | ||||||||
\(493\) | −20.1664 | −0.908247 | ||||||||
\(494\) | 5.32415 | 0.239545 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.1920 | 0.682141 | ||||||||
\(497\) | −10.0504 | −0.450823 | ||||||||
\(498\) | 17.6586 | 0.791301 | ||||||||
\(499\) | −42.6895 | −1.91104 | −0.955522 | − | 0.294921i | \(-0.904707\pi\) | ||||
−0.955522 | + | 0.294921i | \(0.904707\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3781 | 0.821071 | ||||||||
\(502\) | −27.6638 | −1.23470 | ||||||||
\(503\) | −21.8922 | −0.976125 | −0.488063 | − | 0.872809i | \(-0.662296\pi\) | ||||
−0.488063 | + | 0.872809i | \(0.662296\pi\) | |||||||
\(504\) | −3.95493 | −0.176167 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −21.9139 | −0.974192 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −17.7580 | −0.787883 | ||||||||
\(509\) | −5.36546 | −0.237820 | −0.118910 | − | 0.992905i | \(-0.537940\pi\) | ||||
−0.118910 | + | 0.992905i | \(0.537940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0797 | 0.667087 | ||||||||
\(512\) | −22.6496 | −1.00098 | ||||||||
\(513\) | 2.23750 | 0.0987880 | ||||||||
\(514\) | 29.8989 | 1.31878 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.34474 | 0.147244 | ||||||||
\(517\) | 3.30357 | 0.145291 | ||||||||
\(518\) | 24.9254 | 1.09516 | ||||||||
\(519\) | −12.2565 | −0.538000 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5221 | −0.504791 | −0.252396 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252396 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(522\) | 10.0832 | 0.441329 | ||||||||
\(523\) | 3.62584 | 0.158547 | 0.0792734 | − | 0.996853i | \(-0.474740\pi\) | ||||
0.0792734 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(524\) | −23.3172 | −1.01862 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.2977 | −0.972224 | ||||||||
\(527\) | −34.6483 | −1.50930 | ||||||||
\(528\) | −3.28736 | −0.143064 | ||||||||
\(529\) | 11.1720 | 0.485738 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.3344 | −0.535269 | ||||||||
\(532\) | 8.19389 | 0.355250 | ||||||||
\(533\) | 2.25127 | 0.0975132 | ||||||||
\(534\) | 26.5008 | 1.14680 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 62.0583 | 2.68051 | ||||||||
\(537\) | −18.5146 | −0.798963 | ||||||||
\(538\) | −24.7275 | −1.06608 | ||||||||
\(539\) | 1.57542 | 0.0678582 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.2300 | 1.60064 | 0.800321 | − | 0.599572i | \(-0.204662\pi\) | ||||
0.800321 | + | 0.599572i | \(0.204662\pi\) | |||||||
\(542\) | −12.2075 | −0.524358 | ||||||||
\(543\) | 18.1664 | 0.779593 | ||||||||
\(544\) | 14.0136 | 0.600829 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.37951 | −0.101834 | ||||||||
\(547\) | 4.34529 | 0.185791 | 0.0928956 | − | 0.995676i | \(-0.470388\pi\) | ||||
0.0928956 | + | 0.995676i | \(0.470388\pi\) | |||||||
\(548\) | 66.0119 | 2.81989 | ||||||||
\(549\) | −7.51805 | −0.320862 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.48140 | −0.403921 | ||||||||
\(552\) | 23.1193 | 0.984022 | ||||||||
\(553\) | 11.7555 | 0.499897 | ||||||||
\(554\) | −19.1399 | −0.813175 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.79915 | 0.415577 | ||||||||
\(557\) | −28.0052 | −1.18662 | −0.593310 | − | 0.804974i | \(-0.702179\pi\) | ||||
−0.593310 | + | 0.804974i | \(0.702179\pi\) | |||||||
\(558\) | 17.3242 | 0.733390 | ||||||||
\(559\) | 0.913344 | 0.0386303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.49747 | 0.316543 | ||||||||
\(562\) | −66.2753 | −2.79566 | ||||||||
\(563\) | 22.2525 | 0.937829 | 0.468915 | − | 0.883243i | \(-0.344645\pi\) | ||||
0.468915 | + | 0.883243i | \(0.344645\pi\) | |||||||
\(564\) | −7.67918 | −0.323352 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −56.6793 | −2.38241 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 39.7487 | 1.66782 | ||||||||
\(569\) | 3.10724 | 0.130262 | 0.0651311 | − | 0.997877i | \(-0.479253\pi\) | ||||
0.0651311 | + | 0.997877i | \(0.479253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5772 | 0.693733 | 0.346866 | − | 0.937915i | \(-0.387246\pi\) | ||||
0.346866 | + | 0.937915i | \(0.387246\pi\) | |||||||
\(572\) | −5.76931 | −0.241227 | ||||||||
\(573\) | −23.5151 | −0.982358 | ||||||||
\(574\) | 5.35692 | 0.223593 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.1801 | −0.465839 | ||||||||
\(577\) | 7.45253 | 0.310253 | 0.155126 | − | 0.987895i | \(-0.450422\pi\) | ||||
0.155126 | + | 0.987895i | \(0.450422\pi\) | |||||||
\(578\) | 13.4402 | 0.559039 | ||||||||
\(579\) | 14.7344 | 0.612341 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.42110 | 0.307879 | ||||||||
\(582\) | −34.7521 | −1.44052 | ||||||||
\(583\) | −1.71194 | −0.0709014 | ||||||||
\(584\) | −59.6392 | −2.46789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.1697 | 1.61809 | ||||||||
\(587\) | −11.9892 | −0.494845 | −0.247423 | − | 0.968908i | \(-0.579584\pi\) | ||||
−0.247423 | + | 0.968908i | \(0.579584\pi\) | |||||||
\(588\) | −3.66208 | −0.151022 | ||||||||
\(589\) | −16.2902 | −0.671227 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5008 | 0.596483 | ||||||||
\(592\) | −21.8577 | −0.898347 | ||||||||
\(593\) | 33.4767 | 1.37473 | 0.687363 | − | 0.726314i | \(-0.258768\pi\) | ||||
0.687363 | + | 0.726314i | \(0.258768\pi\) | |||||||
\(594\) | −3.74873 | −0.153812 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.3363 | −1.11974 | ||||||||
\(597\) | 13.5180 | 0.553257 | ||||||||
\(598\) | 13.9099 | 0.568817 | ||||||||
\(599\) | −13.5863 | −0.555120 | −0.277560 | − | 0.960708i | \(-0.589526\pi\) | ||||
−0.277560 | + | 0.960708i | \(0.589526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.78364 | −0.276710 | −0.138355 | − | 0.990383i | \(-0.544182\pi\) | ||||
−0.138355 | + | 0.990383i | \(0.544182\pi\) | |||||||
\(602\) | 2.17331 | 0.0885776 | ||||||||
\(603\) | 15.6914 | 0.639002 | ||||||||
\(604\) | 47.6638 | 1.93941 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.2094 | 1.10531 | ||||||||
\(607\) | 17.4905 | 0.709918 | 0.354959 | − | 0.934882i | \(-0.384495\pi\) | ||||
0.354959 | + | 0.934882i | \(0.384495\pi\) | |||||||
\(608\) | 6.58863 | 0.267204 | ||||||||
\(609\) | 4.23750 | 0.171712 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.09695 | −0.0848334 | ||||||||
\(612\) | −17.4279 | −0.704482 | ||||||||
\(613\) | 38.2455 | 1.54472 | 0.772361 | − | 0.635184i | \(-0.219076\pi\) | ||||
0.772361 | + | 0.635184i | \(0.219076\pi\) | |||||||
\(614\) | −4.65526 | −0.187871 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.23069 | −0.251041 | ||||||||
\(617\) | 34.1542 | 1.37500 | 0.687498 | − | 0.726187i | \(-0.258709\pi\) | ||||
0.687498 | + | 0.726187i | \(0.258709\pi\) | |||||||
\(618\) | 26.5336 | 1.06734 | ||||||||
\(619\) | −8.56805 | −0.344379 | −0.172190 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172190 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.84568 | 0.234579 | ||||||||
\(622\) | −15.8853 | −0.636941 | ||||||||
\(623\) | 11.1371 | 0.446197 | ||||||||
\(624\) | 2.08666 | 0.0835331 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.1417 | 0.645154 | ||||||||
\(627\) | 3.52500 | 0.140775 | ||||||||
\(628\) | 62.7069 | 2.50228 | ||||||||
\(629\) | 49.8508 | 1.98768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7119 | −0.705101 | −0.352551 | − | 0.935793i | \(-0.614686\pi\) | ||||
−0.352551 | + | 0.935793i | \(0.614686\pi\) | |||||||
\(632\) | −46.4924 | −1.84937 | ||||||||
\(633\) | −4.06419 | −0.161537 | ||||||||
\(634\) | 73.0384 | 2.90073 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.97942 | 0.157794 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 15.8853 | 0.628903 | ||||||||
\(639\) | 10.0504 | 0.397588 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6117 | 0.656121 | 0.328061 | − | 0.944657i | \(-0.393605\pi\) | ||||
0.328061 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(642\) | 5.43487 | 0.214497 | ||||||||
\(643\) | −12.9500 | −0.510698 | −0.255349 | − | 0.966849i | \(-0.582190\pi\) | ||||
−0.255349 | + | 0.966849i | \(0.582190\pi\) | |||||||
\(644\) | 21.4073 | 0.843567 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.3378 | 0.996902 | ||||||||
\(647\) | 23.6775 | 0.930857 | 0.465428 | − | 0.885086i | \(-0.345900\pi\) | ||||
0.465428 | + | 0.885086i | \(0.345900\pi\) | |||||||
\(648\) | 3.95493 | 0.155364 | ||||||||
\(649\) | −19.4319 | −0.762771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.28055 | 0.285347 | ||||||||
\(652\) | 3.10968 | 0.121785 | ||||||||
\(653\) | −22.2811 | −0.871927 | −0.435963 | − | 0.899964i | \(-0.643592\pi\) | ||||
−0.435963 | + | 0.899964i | \(0.643592\pi\) | |||||||
\(654\) | −34.9048 | −1.36489 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.69762 | −0.183411 | ||||||||
\(657\) | −15.0797 | −0.588315 | ||||||||
\(658\) | −4.98971 | −0.194519 | ||||||||
\(659\) | 15.5165 | 0.604435 | 0.302218 | − | 0.953239i | \(-0.402273\pi\) | ||||
0.302218 | + | 0.953239i | \(0.402273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1444 | 1.09469 | 0.547346 | − | 0.836906i | \(-0.315638\pi\) | ||||
0.547346 | + | 0.836906i | \(0.315638\pi\) | |||||||
\(662\) | −32.9008 | −1.27872 | ||||||||
\(663\) | −4.75902 | −0.184825 | ||||||||
\(664\) | −29.3500 | −1.13900 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.9254 | −0.965839 | ||||||||
\(667\) | −24.7711 | −0.959139 | ||||||||
\(668\) | −67.3018 | −2.60399 | ||||||||
\(669\) | −0.0641862 | −0.00248158 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.8441 | −0.457236 | ||||||||
\(672\) | −2.94464 | −0.113592 | ||||||||
\(673\) | −7.13477 | −0.275025 | −0.137513 | − | 0.990500i | \(-0.543911\pi\) | ||||
−0.137513 | + | 0.990500i | \(0.543911\pi\) | |||||||
\(674\) | −56.7831 | −2.18720 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.66208 | 0.140849 | ||||||||
\(677\) | 10.7660 | 0.413770 | 0.206885 | − | 0.978365i | \(-0.433667\pi\) | ||||
0.206885 | + | 0.978365i | \(0.433667\pi\) | |||||||
\(678\) | −10.0832 | −0.387242 | ||||||||
\(679\) | −14.6047 | −0.560477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.68614 | −0.0646129 | ||||||||
\(682\) | 27.2928 | 1.04510 | ||||||||
\(683\) | 12.2020 | 0.466898 | 0.233449 | − | 0.972369i | \(-0.424999\pi\) | ||||
0.233449 | + | 0.972369i | \(0.424999\pi\) | |||||||
\(684\) | −8.19389 | −0.313301 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.37951 | −0.0908502 | ||||||||
\(687\) | −0.648310 | −0.0247346 | ||||||||
\(688\) | −1.90583 | −0.0726593 | ||||||||
\(689\) | 1.08666 | 0.0413983 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0367 | 1.21873 | 0.609366 | − | 0.792889i | \(-0.291424\pi\) | ||||
0.609366 | + | 0.792889i | \(0.291424\pi\) | |||||||
\(692\) | 44.8842 | 1.70624 | ||||||||
\(693\) | −1.57542 | −0.0598453 | ||||||||
\(694\) | 32.3643 | 1.22853 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −16.7590 | −0.635249 | ||||||||
\(697\) | 10.7138 | 0.405815 | ||||||||
\(698\) | −39.0332 | −1.47743 | ||||||||
\(699\) | 3.10724 | 0.117526 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.9513 | −0.564704 | −0.282352 | − | 0.959311i | \(-0.591115\pi\) | ||||
−0.282352 | + | 0.959311i | \(0.591115\pi\) | |||||||
\(702\) | 2.37951 | 0.0898089 | ||||||||
\(703\) | 23.4378 | 0.883973 | ||||||||
\(704\) | −17.6134 | −0.663830 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.2627 | 0.423879 | ||||||||
\(707\) | 11.4349 | 0.430053 | ||||||||
\(708\) | 45.1697 | 1.69758 | ||||||||
\(709\) | −8.58279 | −0.322333 | −0.161167 | − | 0.986927i | \(-0.551526\pi\) | ||||
−0.161167 | + | 0.986927i | \(0.551526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.7555 | −0.440867 | ||||||||
\(712\) | −44.0464 | −1.65071 | ||||||||
\(713\) | −42.5598 | −1.59388 | ||||||||
\(714\) | −11.3242 | −0.423796 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 67.8018 | 2.53387 | ||||||||
\(717\) | 15.0659 | 0.562648 | ||||||||
\(718\) | −41.7554 | −1.55830 | ||||||||
\(719\) | 35.9644 | 1.34125 | 0.670623 | − | 0.741798i | \(-0.266027\pi\) | ||||
0.670623 | + | 0.741798i | \(0.266027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1508 | 0.415279 | ||||||||
\(722\) | −33.2979 | −1.23922 | ||||||||
\(723\) | −25.7280 | −0.956835 | ||||||||
\(724\) | −66.5266 | −2.47244 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.2688 | 0.752246 | ||||||||
\(727\) | 31.5111 | 1.16868 | 0.584341 | − | 0.811508i | \(-0.301353\pi\) | ||||
0.584341 | + | 0.811508i | \(0.301353\pi\) | |||||||
\(728\) | 3.95493 | 0.146580 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.34662 | 0.160766 | ||||||||
\(732\) | 27.5317 | 1.01760 | ||||||||
\(733\) | 26.6047 | 0.982667 | 0.491334 | − | 0.870971i | \(-0.336510\pi\) | ||||
0.491334 | + | 0.870971i | \(0.336510\pi\) | |||||||
\(734\) | 26.6240 | 0.982708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.2134 | 0.634496 | ||||||||
\(737\) | 24.7205 | 0.910591 | ||||||||
\(738\) | −5.35692 | −0.197191 | ||||||||
\(739\) | −50.3397 | −1.85177 | −0.925887 | − | 0.377800i | \(-0.876681\pi\) | ||||
−0.925887 | + | 0.377800i | \(0.876681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.23750 | −0.0821966 | ||||||||
\(742\) | 2.58571 | 0.0949245 | ||||||||
\(743\) | −23.4021 | −0.858540 | −0.429270 | − | 0.903176i | \(-0.641229\pi\) | ||||
−0.429270 | + | 0.903176i | \(0.641229\pi\) | |||||||
\(744\) | −28.7941 | −1.05564 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.9254 | 0.473232 | ||||||||
\(747\) | −7.42110 | −0.271524 | ||||||||
\(748\) | −27.4563 | −1.00390 | ||||||||
\(749\) | 2.28403 | 0.0834565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.0305 | 1.78915 | 0.894574 | − | 0.446920i | \(-0.147479\pi\) | ||||
0.894574 | + | 0.446920i | \(0.147479\pi\) | |||||||
\(752\) | 4.37561 | 0.159562 | ||||||||
\(753\) | 11.6258 | 0.423669 | ||||||||
\(754\) | −10.0832 | −0.367208 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.66208 | 0.133188 | ||||||||
\(757\) | 35.3883 | 1.28621 | 0.643106 | − | 0.765778i | \(-0.277646\pi\) | ||||
0.643106 | + | 0.765778i | \(0.277646\pi\) | |||||||
\(758\) | 25.7992 | 0.937067 | ||||||||
\(759\) | 9.20941 | 0.334280 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.7051 | 1.00431 | 0.502155 | − | 0.864778i | \(-0.332541\pi\) | ||||
0.502155 | + | 0.864778i | \(0.332541\pi\) | |||||||
\(762\) | 11.5386 | 0.418000 | ||||||||
\(763\) | −14.6689 | −0.531049 | ||||||||
\(764\) | 86.1142 | 3.11550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.0689 | −0.905775 | ||||||||
\(767\) | 12.3344 | 0.445371 | ||||||||
\(768\) | 26.9289 | 0.971712 | ||||||||
\(769\) | 21.1383 | 0.762265 | 0.381133 | − | 0.924520i | \(-0.375534\pi\) | ||||
0.381133 | + | 0.924520i | \(0.375534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5651 | −0.452522 | ||||||||
\(772\) | −53.9586 | −1.94201 | ||||||||
\(773\) | 41.4537 | 1.49099 | 0.745493 | − | 0.666513i | \(-0.232214\pi\) | ||||
0.745493 | + | 0.666513i | \(0.232214\pi\) | |||||||
\(774\) | −2.17331 | −0.0781181 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 57.7606 | 2.07349 | ||||||||
\(777\) | −10.4750 | −0.375788 | ||||||||
\(778\) | 14.2771 | 0.511858 | ||||||||
\(779\) | 5.03721 | 0.180477 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8336 | 0.566572 | ||||||||
\(782\) | 66.1974 | 2.36721 | ||||||||
\(783\) | −4.23750 | −0.151436 | ||||||||
\(784\) | 2.08666 | 0.0745234 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.1508 | 0.540413 | ||||||||
\(787\) | 28.7711 | 1.02558 | 0.512789 | − | 0.858515i | \(-0.328612\pi\) | ||||
0.512789 | + | 0.858515i | \(0.328612\pi\) | |||||||
\(788\) | −53.1031 | −1.89172 | ||||||||
\(789\) | 9.37068 | 0.333605 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.23750 | −0.150668 | ||||||||
\(792\) | 6.23069 | 0.221398 | ||||||||
\(793\) | 7.51805 | 0.266974 | ||||||||
\(794\) | 84.3298 | 2.99275 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −49.5041 | −1.75463 | ||||||||
\(797\) | −19.5357 | −0.691990 | −0.345995 | − | 0.938236i | \(-0.612459\pi\) | ||||
−0.345995 | + | 0.938236i | \(0.612459\pi\) | |||||||
\(798\) | −5.32415 | −0.188473 | ||||||||
\(799\) | −9.97942 | −0.353046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1371 | −0.393509 | ||||||||
\(802\) | 56.4518 | 1.99338 | ||||||||
\(803\) | −23.7569 | −0.838362 | ||||||||
\(804\) | −57.4630 | −2.02656 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.3242 | −0.610217 | ||||||||
\(807\) | 10.3918 | 0.365809 | ||||||||
\(808\) | −45.2241 | −1.59098 | ||||||||
\(809\) | −36.1824 | −1.27211 | −0.636053 | − | 0.771645i | \(-0.719434\pi\) | ||||
−0.636053 | + | 0.771645i | \(0.719434\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.794087 | 0.0278842 | 0.0139421 | − | 0.999903i | \(-0.495562\pi\) | ||||
0.0139421 | + | 0.999903i | \(0.495562\pi\) | |||||||
\(812\) | −15.5180 | −0.544577 | ||||||||
\(813\) | 5.13026 | 0.179926 | ||||||||
\(814\) | −39.2680 | −1.37634 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.93045 | 0.347635 | ||||||||
\(817\) | 2.04361 | 0.0714967 | ||||||||
\(818\) | −9.41429 | −0.329163 | ||||||||
\(819\) | 1.00000 | 0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8525 | −0.553256 | −0.276628 | − | 0.960977i | \(-0.589217\pi\) | ||||
−0.276628 | + | 0.960977i | \(0.589217\pi\) | |||||||
\(822\) | −42.8926 | −1.49605 | ||||||||
\(823\) | 20.0412 | 0.698591 | 0.349295 | − | 0.937013i | \(-0.386421\pi\) | ||||
0.349295 | + | 0.937013i | \(0.386421\pi\) | |||||||
\(824\) | −44.1008 | −1.53633 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.3500 | 1.02122 | ||||||||
\(827\) | −34.7848 | −1.20959 | −0.604794 | − | 0.796382i | \(-0.706744\pi\) | ||||
−0.604794 | + | 0.796382i | \(0.706744\pi\) | |||||||
\(828\) | −21.4073 | −0.743956 | ||||||||
\(829\) | −30.6793 | −1.06554 | −0.532769 | − | 0.846261i | \(-0.678848\pi\) | ||||
−0.532769 | + | 0.846261i | \(0.678848\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.04361 | 0.279030 | ||||||||
\(832\) | 11.1801 | 0.387601 | ||||||||
\(833\) | −4.75902 | −0.164890 | ||||||||
\(834\) | −6.36721 | −0.220478 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.9088 | −0.446461 | ||||||||
\(837\) | −7.28055 | −0.251653 | ||||||||
\(838\) | −42.9706 | −1.48439 | ||||||||
\(839\) | 39.8238 | 1.37487 | 0.687436 | − | 0.726245i | \(-0.258736\pi\) | ||||
0.687436 | + | 0.726245i | \(0.258736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0436 | −0.380814 | ||||||||
\(842\) | 58.2875 | 2.00872 | ||||||||
\(843\) | 27.8525 | 0.959291 | ||||||||
\(844\) | 14.8834 | 0.512307 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.98971 | 0.171550 | ||||||||
\(847\) | 8.51805 | 0.292684 | ||||||||
\(848\) | −2.26748 | −0.0778655 | ||||||||
\(849\) | 23.8197 | 0.817491 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.2335 | 2.09906 | ||||||||
\(852\) | −36.8054 | −1.26093 | ||||||||
\(853\) | −24.7505 | −0.847440 | −0.423720 | − | 0.905793i | \(-0.639276\pi\) | ||||
−0.423720 | + | 0.905793i | \(0.639276\pi\) | |||||||
\(854\) | 17.8893 | 0.612159 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.03317 | −0.308748 | ||||||||
\(857\) | −6.47097 | −0.221044 | −0.110522 | − | 0.993874i | \(-0.535252\pi\) | ||||
−0.110522 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(858\) | 3.74873 | 0.127980 | ||||||||
\(859\) | 31.0741 | 1.06023 | 0.530117 | − | 0.847925i | \(-0.322148\pi\) | ||||
0.530117 | + | 0.847925i | \(0.322148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.25127 | −0.0767230 | ||||||||
\(862\) | −97.0314 | −3.30490 | ||||||||
\(863\) | −28.6391 | −0.974885 | −0.487442 | − | 0.873155i | \(-0.662070\pi\) | ||||
−0.487442 | + | 0.873155i | \(0.662070\pi\) | |||||||
\(864\) | 2.94464 | 0.100179 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43.0195 | 1.46186 | ||||||||
\(867\) | −5.64831 | −0.191827 | ||||||||
\(868\) | −26.6619 | −0.904965 | ||||||||
\(869\) | −18.5199 | −0.628246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6914 | −0.531681 | ||||||||
\(872\) | 58.0145 | 1.96462 | ||||||||
\(873\) | 14.6047 | 0.494294 | ||||||||
\(874\) | 31.1233 | 1.05276 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 55.2230 | 1.86581 | ||||||||
\(877\) | −0.00110921 | −3.74555e−5 0 | −1.87278e−5 | − | 1.00000i | \(-0.500006\pi\) | ||||
−1.87278e−5 | 1.00000i | \(0.500006\pi\) | ||||||||
\(878\) | 49.3894 | 1.66681 | ||||||||
\(879\) | −16.4612 | −0.555223 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.9479 | 0.806824 | 0.403412 | − | 0.915019i | \(-0.367824\pi\) | ||||
0.403412 | + | 0.915019i | \(0.367824\pi\) | |||||||
\(882\) | 2.37951 | 0.0801223 | ||||||||
\(883\) | −51.9965 | −1.74982 | −0.874911 | − | 0.484283i | \(-0.839081\pi\) | ||||
−0.874911 | + | 0.484283i | \(0.839081\pi\) | |||||||
\(884\) | 17.4279 | 0.586164 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.6082 | 0.658750 | ||||||||
\(887\) | −10.8697 | −0.364970 | −0.182485 | − | 0.983209i | \(-0.558414\pi\) | ||||
−0.182485 | + | 0.983209i | \(0.558414\pi\) | |||||||
\(888\) | 41.4279 | 1.39023 | ||||||||
\(889\) | 4.84916 | 0.162636 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.57542 | 0.0527786 | ||||||||
\(892\) | 0.235055 | 0.00787021 | ||||||||
\(893\) | −4.69192 | −0.157009 | ||||||||
\(894\) | 17.7624 | 0.594062 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.7140 | 0.692005 | ||||||||
\(897\) | −5.84568 | −0.195182 | ||||||||
\(898\) | 85.9148 | 2.86701 | ||||||||
\(899\) | 30.8513 | 1.02895 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.17142 | 0.172285 | ||||||||
\(902\) | −8.43940 | −0.281001 | ||||||||
\(903\) | −0.913344 | −0.0303942 | ||||||||
\(904\) | 16.7590 | 0.557397 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −30.9706 | −1.02893 | ||||||||
\(907\) | 25.4892 | 0.846354 | 0.423177 | − | 0.906047i | \(-0.360915\pi\) | ||||
0.423177 | + | 0.906047i | \(0.360915\pi\) | |||||||
\(908\) | 6.17476 | 0.204917 | ||||||||
\(909\) | −11.4349 | −0.379271 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2059 | 1.39834 | 0.699172 | − | 0.714953i | \(-0.253552\pi\) | ||||
0.699172 | + | 0.714953i | \(0.253552\pi\) | |||||||
\(912\) | 4.66889 | 0.154602 | ||||||||
\(913\) | −11.6914 | −0.386928 | ||||||||
\(914\) | 15.5632 | 0.514786 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.37416 | 0.0784445 | ||||||||
\(917\) | 6.36721 | 0.210264 | ||||||||
\(918\) | 11.3242 | 0.373753 | ||||||||
\(919\) | −29.4033 | −0.969925 | −0.484963 | − | 0.874535i | \(-0.661167\pi\) | ||||
−0.484963 | + | 0.874535i | \(0.661167\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95639 | 0.0644654 | ||||||||
\(922\) | −34.9758 | −1.15187 | ||||||||
\(923\) | −10.0504 | −0.330814 | ||||||||
\(924\) | 5.76931 | 0.189797 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −51.8197 | −1.70290 | ||||||||
\(927\) | −11.1508 | −0.366242 | ||||||||
\(928\) | −12.4779 | −0.409608 | ||||||||
\(929\) | −13.3759 | −0.438849 | −0.219425 | − | 0.975629i | \(-0.570418\pi\) | ||||
−0.219425 | + | 0.975629i | \(0.570418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.23750 | −0.0733311 | ||||||||
\(932\) | −11.3789 | −0.372730 | ||||||||
\(933\) | 6.67585 | 0.218557 | ||||||||
\(934\) | −83.3033 | −2.72577 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.95493 | −0.129271 | ||||||||
\(937\) | 24.9981 | 0.816653 | 0.408326 | − | 0.912836i | \(-0.366113\pi\) | ||||
0.408326 | + | 0.912836i | \(0.366113\pi\) | |||||||
\(938\) | −37.3378 | −1.21912 | ||||||||
\(939\) | −6.78364 | −0.221376 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5369 | 0.343493 | 0.171746 | − | 0.985141i | \(-0.445059\pi\) | ||||
0.171746 | + | 0.985141i | \(0.445059\pi\) | |||||||
\(942\) | −40.7451 | −1.32755 | ||||||||
\(943\) | 13.1602 | 0.428555 | ||||||||
\(944\) | −25.7377 | −0.837692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.42388 | −0.111320 | ||||||||
\(947\) | 52.7779 | 1.71505 | 0.857525 | − | 0.514442i | \(-0.172001\pi\) | ||||
0.857525 | + | 0.514442i | \(0.172001\pi\) | |||||||
\(948\) | 43.0497 | 1.39819 | ||||||||
\(949\) | 15.0797 | 0.489508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.6947 | −0.995344 | ||||||||
\(952\) | 18.8216 | 0.610012 | ||||||||
\(953\) | −21.8486 | −0.707746 | −0.353873 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353873 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(954\) | −2.58571 | −0.0837155 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −55.1726 | −1.78441 | ||||||||
\(957\) | −6.67585 | −0.215799 | ||||||||
\(958\) | 75.6241 | 2.44330 | ||||||||
\(959\) | −18.0258 | −0.582084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0064 | 0.709884 | ||||||||
\(962\) | 24.9254 | 0.803627 | ||||||||
\(963\) | −2.28403 | −0.0736017 | ||||||||
\(964\) | 94.2180 | 3.03456 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.9099 | −0.447543 | ||||||||
\(967\) | −1.94143 | −0.0624323 | −0.0312162 | − | 0.999513i | \(-0.509938\pi\) | ||||
−0.0312162 | + | 0.999513i | \(0.509938\pi\) | |||||||
\(968\) | −33.6883 | −1.08278 | ||||||||
\(969\) | −10.6483 | −0.342073 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.9077 | −0.478412 | −0.239206 | − | 0.970969i | \(-0.576887\pi\) | ||||
−0.239206 | + | 0.970969i | \(0.576887\pi\) | |||||||
\(972\) | −3.66208 | −0.117461 | ||||||||
\(973\) | −2.67585 | −0.0857837 | ||||||||
\(974\) | 68.0105 | 2.17920 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.6876 | −0.502147 | ||||||||
\(977\) | 16.5353 | 0.529011 | 0.264505 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264505 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(978\) | −2.02058 | −0.0646110 | ||||||||
\(979\) | −17.5456 | −0.560759 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.6689 | 0.468342 | ||||||||
\(982\) | 51.6734 | 1.64897 | ||||||||
\(983\) | 30.0694 | 0.959065 | 0.479533 | − | 0.877524i | \(-0.340806\pi\) | ||||
0.479533 | + | 0.877524i | \(0.340806\pi\) | |||||||
\(984\) | 8.90361 | 0.283837 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −47.9861 | −1.52819 | ||||||||
\(987\) | 2.09695 | 0.0667465 | ||||||||
\(988\) | 8.19389 | 0.260682 | ||||||||
\(989\) | 5.33912 | 0.169774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5902 | 1.38469 | 0.692345 | − | 0.721567i | \(-0.256578\pi\) | ||||
0.692345 | + | 0.721567i | \(0.256578\pi\) | |||||||
\(992\) | −21.4386 | −0.680677 | ||||||||
\(993\) | 13.8267 | 0.438777 | ||||||||
\(994\) | −23.9151 | −0.758541 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.1766 | 0.861125 | ||||||||
\(997\) | −57.8577 | −1.83237 | −0.916186 | − | 0.400753i | \(-0.868749\pi\) | ||||
−0.916186 | + | 0.400753i | \(0.868749\pi\) | |||||||
\(998\) | −101.580 | −3.21546 | ||||||||
\(999\) | 10.4750 | 0.331414 |
(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 | 6825.2.a.bg.1.4 | 4 | ||
5.4 | even | 2 | 273.2.a.e.1.1 | ✓ | 4 | ||
15.14 | odd | 2 | 819.2.a.k.1.4 | 4 | |||
20.19 | odd | 2 | 4368.2.a.br.1.2 | 4 | |||
35.34 | odd | 2 | 1911.2.a.s.1.1 | 4 | |||
65.64 | even | 2 | 3549.2.a.w.1.4 | 4 | |||
105.104 | even | 2 | 5733.2.a.bf.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.a.e.1.1 | ✓ | 4 | 5.4 | even | 2 | ||
819.2.a.k.1.4 | 4 | 15.14 | odd | 2 | |||
1911.2.a.s.1.1 | 4 | 35.34 | odd | 2 | |||
3549.2.a.w.1.4 | 4 | 65.64 | even | 2 | |||
4368.2.a.br.1.2 | 4 | 20.19 | odd | 2 | |||
5733.2.a.bf.1.4 | 4 | 105.104 | even | 2 | |||
6825.2.a.bg.1.4 | 4 | 1.1 | even | 1 | trivial |