Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.09783\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09783 | −0.776282 | −0.388141 | − | 0.921600i | \(-0.626883\pi\) | ||||
−0.388141 | + | 0.921600i | \(0.626883\pi\) | |||||||
\(3\) | −1.80555 | −1.04243 | −0.521216 | − | 0.853425i | \(-0.674522\pi\) | ||||
−0.521216 | + | 0.853425i | \(0.674522\pi\) | |||||||
\(4\) | −0.794772 | −0.397386 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.98218 | 0.809222 | ||||||||
\(7\) | 0.928281 | 0.350857 | 0.175429 | − | 0.984492i | \(-0.443869\pi\) | ||||
0.175429 | + | 0.984492i | \(0.443869\pi\) | |||||||
\(8\) | 3.06818 | 1.08477 | ||||||||
\(9\) | 0.259998 | 0.0866658 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.401264 | −0.120986 | −0.0604929 | − | 0.998169i | \(-0.519267\pi\) | ||||
−0.0604929 | + | 0.998169i | \(0.519267\pi\) | |||||||
\(12\) | 1.43500 | 0.414248 | ||||||||
\(13\) | 6.69327 | 1.85638 | 0.928189 | − | 0.372108i | \(-0.121365\pi\) | ||||
0.928189 | + | 0.372108i | \(0.121365\pi\) | |||||||
\(14\) | −1.01909 | −0.272364 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.77880 | −0.444699 | ||||||||
\(17\) | 1.90485 | 0.461994 | 0.230997 | − | 0.972954i | \(-0.425801\pi\) | ||||
0.230997 | + | 0.972954i | \(0.425801\pi\) | |||||||
\(18\) | −0.285433 | −0.0672772 | ||||||||
\(19\) | −0.291750 | −0.0669321 | −0.0334660 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334660 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.67605 | −0.365745 | ||||||||
\(22\) | 0.440520 | 0.0939191 | ||||||||
\(23\) | −2.38576 | −0.497465 | −0.248733 | − | 0.968572i | \(-0.580014\pi\) | ||||
−0.248733 | + | 0.968572i | \(0.580014\pi\) | |||||||
\(24\) | −5.53974 | −1.13080 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.34806 | −1.44107 | ||||||||
\(27\) | 4.94720 | 0.952089 | ||||||||
\(28\) | −0.737771 | −0.139426 | ||||||||
\(29\) | −2.80478 | −0.520835 | −0.260417 | − | 0.965496i | \(-0.583860\pi\) | ||||
−0.260417 | + | 0.965496i | \(0.583860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.86854 | −0.694811 | −0.347406 | − | 0.937715i | \(-0.612937\pi\) | ||||
−0.347406 | + | 0.937715i | \(0.612937\pi\) | |||||||
\(32\) | −4.18355 | −0.739554 | ||||||||
\(33\) | 0.724502 | 0.126120 | ||||||||
\(34\) | −2.09120 | −0.358638 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.206639 | −0.0344398 | ||||||||
\(37\) | −7.87504 | −1.29465 | −0.647325 | − | 0.762214i | \(-0.724112\pi\) | ||||
−0.647325 | + | 0.762214i | \(0.724112\pi\) | |||||||
\(38\) | 0.320292 | 0.0519582 | ||||||||
\(39\) | −12.0850 | −1.93515 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.82266 | −0.284652 | −0.142326 | − | 0.989820i | \(-0.545458\pi\) | ||||
−0.142326 | + | 0.989820i | \(0.545458\pi\) | |||||||
\(42\) | 1.84002 | 0.283921 | ||||||||
\(43\) | −5.42284 | −0.826975 | −0.413488 | − | 0.910510i | \(-0.635690\pi\) | ||||
−0.413488 | + | 0.910510i | \(0.635690\pi\) | |||||||
\(44\) | 0.318914 | 0.0480780 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.61916 | 0.386174 | ||||||||
\(47\) | −2.33696 | −0.340880 | −0.170440 | − | 0.985368i | \(-0.554519\pi\) | ||||
−0.170440 | + | 0.985368i | \(0.554519\pi\) | |||||||
\(48\) | 3.21170 | 0.463569 | ||||||||
\(49\) | −6.13829 | −0.876899 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.43930 | −0.481598 | ||||||||
\(52\) | −5.31962 | −0.737698 | ||||||||
\(53\) | 6.48568 | 0.890877 | 0.445439 | − | 0.895312i | \(-0.353048\pi\) | ||||
0.445439 | + | 0.895312i | \(0.353048\pi\) | |||||||
\(54\) | −5.43118 | −0.739090 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.84813 | 0.380598 | ||||||||
\(57\) | 0.526768 | 0.0697722 | ||||||||
\(58\) | 3.07917 | 0.404315 | ||||||||
\(59\) | −4.02672 | −0.524234 | −0.262117 | − | 0.965036i | \(-0.584421\pi\) | ||||
−0.262117 | + | 0.965036i | \(0.584421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.23608 | 1.18256 | 0.591279 | − | 0.806467i | \(-0.298623\pi\) | ||||
0.591279 | + | 0.806467i | \(0.298623\pi\) | |||||||
\(62\) | 4.24700 | 0.539370 | ||||||||
\(63\) | 0.241351 | 0.0304073 | ||||||||
\(64\) | 8.15041 | 1.01880 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.795379 | −0.0979044 | ||||||||
\(67\) | −4.99709 | −0.610492 | −0.305246 | − | 0.952274i | \(-0.598739\pi\) | ||||
−0.305246 | + | 0.952274i | \(0.598739\pi\) | |||||||
\(68\) | −1.51392 | −0.183590 | ||||||||
\(69\) | 4.30760 | 0.518574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.92064 | 1.05868 | 0.529342 | − | 0.848408i | \(-0.322439\pi\) | ||||
0.529342 | + | 0.848408i | \(0.322439\pi\) | |||||||
\(72\) | 0.797720 | 0.0940121 | ||||||||
\(73\) | 11.9653 | 1.40043 | 0.700217 | − | 0.713930i | \(-0.253086\pi\) | ||||
0.700217 | + | 0.713930i | \(0.253086\pi\) | |||||||
\(74\) | 8.64545 | 1.00501 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.231875 | 0.0265979 | ||||||||
\(77\) | −0.372486 | −0.0424487 | ||||||||
\(78\) | 13.2673 | 1.50222 | ||||||||
\(79\) | 0.645240 | 0.0725952 | 0.0362976 | − | 0.999341i | \(-0.488444\pi\) | ||||
0.0362976 | + | 0.999341i | \(0.488444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.71239 | −1.07915 | ||||||||
\(82\) | 2.00097 | 0.220970 | ||||||||
\(83\) | 8.84272 | 0.970614 | 0.485307 | − | 0.874344i | \(-0.338708\pi\) | ||||
0.485307 | + | 0.874344i | \(0.338708\pi\) | |||||||
\(84\) | 1.33208 | 0.145342 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.95335 | 0.641966 | ||||||||
\(87\) | 5.06416 | 0.542935 | ||||||||
\(88\) | −1.23115 | −0.131241 | ||||||||
\(89\) | −10.4841 | −1.11131 | −0.555657 | − | 0.831411i | \(-0.687533\pi\) | ||||
−0.555657 | + | 0.831411i | \(0.687533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.21323 | 0.651324 | ||||||||
\(92\) | 1.89613 | 0.197686 | ||||||||
\(93\) | 6.98484 | 0.724294 | ||||||||
\(94\) | 2.56558 | 0.264619 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.55359 | 0.770935 | ||||||||
\(97\) | 9.30216 | 0.944492 | 0.472246 | − | 0.881467i | \(-0.343443\pi\) | ||||
0.472246 | + | 0.881467i | \(0.343443\pi\) | |||||||
\(98\) | 6.73880 | 0.680721 | ||||||||
\(99\) | −0.104328 | −0.0104853 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.73764 | −0.968932 | −0.484466 | − | 0.874810i | \(-0.660986\pi\) | ||||
−0.484466 | + | 0.874810i | \(0.660986\pi\) | |||||||
\(102\) | 3.77576 | 0.373856 | ||||||||
\(103\) | −1.69308 | −0.166824 | −0.0834120 | − | 0.996515i | \(-0.526582\pi\) | ||||
−0.0834120 | + | 0.996515i | \(0.526582\pi\) | |||||||
\(104\) | 20.5362 | 2.01374 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.12017 | −0.691572 | ||||||||
\(107\) | −14.9785 | −1.44803 | −0.724014 | − | 0.689785i | \(-0.757705\pi\) | ||||
−0.724014 | + | 0.689785i | \(0.757705\pi\) | |||||||
\(108\) | −3.93189 | −0.378347 | ||||||||
\(109\) | 0.343011 | 0.0328545 | 0.0164272 | − | 0.999865i | \(-0.494771\pi\) | ||||
0.0164272 | + | 0.999865i | \(0.494771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.2188 | 1.34958 | ||||||||
\(112\) | −1.65122 | −0.156026 | ||||||||
\(113\) | −5.70596 | −0.536772 | −0.268386 | − | 0.963311i | \(-0.586490\pi\) | ||||
−0.268386 | + | 0.963311i | \(0.586490\pi\) | |||||||
\(114\) | −0.578302 | −0.0541629 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.22916 | 0.206972 | ||||||||
\(117\) | 1.74023 | 0.160885 | ||||||||
\(118\) | 4.42065 | 0.406954 | ||||||||
\(119\) | 1.76824 | 0.162094 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8390 | −0.985362 | ||||||||
\(122\) | −10.1396 | −0.917999 | ||||||||
\(123\) | 3.29090 | 0.296731 | ||||||||
\(124\) | 3.07461 | 0.276108 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.264962 | −0.0236047 | ||||||||
\(127\) | −0.639748 | −0.0567684 | −0.0283842 | − | 0.999597i | \(-0.509036\pi\) | ||||
−0.0283842 | + | 0.999597i | \(0.509036\pi\) | |||||||
\(128\) | −0.580660 | −0.0513236 | ||||||||
\(129\) | 9.79119 | 0.862066 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.53486 | −0.221472 | −0.110736 | − | 0.993850i | \(-0.535321\pi\) | ||||
−0.110736 | + | 0.993850i | \(0.535321\pi\) | |||||||
\(132\) | −0.575813 | −0.0501181 | ||||||||
\(133\) | −0.270826 | −0.0234836 | ||||||||
\(134\) | 5.48595 | 0.473914 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.84443 | 0.501155 | ||||||||
\(137\) | 3.35377 | 0.286532 | 0.143266 | − | 0.989684i | \(-0.454240\pi\) | ||||
0.143266 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(138\) | −4.72901 | −0.402560 | ||||||||
\(139\) | −6.27168 | −0.531957 | −0.265978 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265978 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.21948 | 0.355345 | ||||||||
\(142\) | −9.79334 | −0.821838 | ||||||||
\(143\) | −2.68577 | −0.224595 | ||||||||
\(144\) | −0.462482 | −0.0385402 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.1359 | −1.08713 | ||||||||
\(147\) | 11.0830 | 0.914108 | ||||||||
\(148\) | 6.25886 | 0.514475 | ||||||||
\(149\) | 8.33806 | 0.683080 | 0.341540 | − | 0.939867i | \(-0.389051\pi\) | ||||
0.341540 | + | 0.939867i | \(0.389051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1838 | 1.64254 | 0.821269 | − | 0.570541i | \(-0.193267\pi\) | ||||
0.821269 | + | 0.570541i | \(0.193267\pi\) | |||||||
\(152\) | −0.895142 | −0.0726056 | ||||||||
\(153\) | 0.495256 | 0.0400391 | ||||||||
\(154\) | 0.408926 | 0.0329522 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.60482 | 0.769001 | ||||||||
\(157\) | −4.99089 | −0.398316 | −0.199158 | − | 0.979967i | \(-0.563821\pi\) | ||||
−0.199158 | + | 0.979967i | \(0.563821\pi\) | |||||||
\(158\) | −0.708363 | −0.0563544 | ||||||||
\(159\) | −11.7102 | −0.928680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.21466 | −0.174539 | ||||||||
\(162\) | 10.6625 | 0.837729 | ||||||||
\(163\) | 12.7050 | 0.995133 | 0.497567 | − | 0.867426i | \(-0.334227\pi\) | ||||
0.497567 | + | 0.867426i | \(0.334227\pi\) | |||||||
\(164\) | 1.44860 | 0.113117 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.70779 | −0.753471 | ||||||||
\(167\) | −15.1031 | −1.16871 | −0.584357 | − | 0.811497i | \(-0.698653\pi\) | ||||
−0.584357 | + | 0.811497i | \(0.698653\pi\) | |||||||
\(168\) | −5.14244 | −0.396748 | ||||||||
\(169\) | 31.7998 | 2.44614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0758543 | −0.00580072 | ||||||||
\(172\) | 4.30992 | 0.328628 | ||||||||
\(173\) | 1.07463 | 0.0817025 | 0.0408513 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408513 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(174\) | −5.55958 | −0.421471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.713767 | 0.0538022 | ||||||||
\(177\) | 7.27042 | 0.546479 | ||||||||
\(178\) | 11.5098 | 0.862694 | ||||||||
\(179\) | −12.6395 | −0.944719 | −0.472360 | − | 0.881406i | \(-0.656598\pi\) | ||||
−0.472360 | + | 0.881406i | \(0.656598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.01905 | −0.596051 | −0.298026 | − | 0.954558i | \(-0.596328\pi\) | ||||
−0.298026 | + | 0.954558i | \(0.596328\pi\) | |||||||
\(182\) | −6.82107 | −0.505611 | ||||||||
\(183\) | −16.6762 | −1.23274 | ||||||||
\(184\) | −7.31994 | −0.539633 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.66816 | −0.562257 | ||||||||
\(187\) | −0.764349 | −0.0558947 | ||||||||
\(188\) | 1.85735 | 0.135461 | ||||||||
\(189\) | 4.59239 | 0.334047 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.52209 | −0.182492 | −0.0912460 | − | 0.995828i | \(-0.529085\pi\) | ||||
−0.0912460 | + | 0.995828i | \(0.529085\pi\) | |||||||
\(192\) | −14.7159 | −1.06203 | ||||||||
\(193\) | 27.1349 | 1.95322 | 0.976608 | − | 0.215029i | \(-0.0689845\pi\) | ||||
0.976608 | + | 0.215029i | \(0.0689845\pi\) | |||||||
\(194\) | −10.2122 | −0.733192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.87854 | 0.348467 | ||||||||
\(197\) | 1.17329 | 0.0835934 | 0.0417967 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417967 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(198\) | 0.114534 | 0.00813958 | ||||||||
\(199\) | −26.8259 | −1.90164 | −0.950819 | − | 0.309747i | \(-0.899756\pi\) | ||||
−0.950819 | + | 0.309747i | \(0.899756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.02248 | 0.636397 | ||||||||
\(202\) | 10.6903 | 0.752164 | ||||||||
\(203\) | −2.60362 | −0.182739 | ||||||||
\(204\) | 2.73345 | 0.191380 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.85871 | 0.129503 | ||||||||
\(207\) | −0.620292 | −0.0431132 | ||||||||
\(208\) | −11.9060 | −0.825529 | ||||||||
\(209\) | 0.117069 | 0.00809783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.07752 | 0.211865 | 0.105933 | − | 0.994373i | \(-0.466217\pi\) | ||||
0.105933 | + | 0.994373i | \(0.466217\pi\) | |||||||
\(212\) | −5.15464 | −0.354022 | ||||||||
\(213\) | −16.1066 | −1.10361 | ||||||||
\(214\) | 16.4439 | 1.12408 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.1789 | 1.03279 | ||||||||
\(217\) | −3.59110 | −0.243780 | ||||||||
\(218\) | −0.376567 | −0.0255043 | ||||||||
\(219\) | −21.6039 | −1.45986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7497 | 0.857636 | ||||||||
\(222\) | −15.6098 | −1.04766 | ||||||||
\(223\) | 4.73624 | 0.317162 | 0.158581 | − | 0.987346i | \(-0.449308\pi\) | ||||
0.158581 | + | 0.987346i | \(0.449308\pi\) | |||||||
\(224\) | −3.88351 | −0.259478 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.26417 | 0.416687 | ||||||||
\(227\) | 4.73421 | 0.314221 | 0.157110 | − | 0.987581i | \(-0.449782\pi\) | ||||
0.157110 | + | 0.987581i | \(0.449782\pi\) | |||||||
\(228\) | −0.418661 | −0.0277265 | ||||||||
\(229\) | 8.01736 | 0.529802 | 0.264901 | − | 0.964276i | \(-0.414661\pi\) | ||||
0.264901 | + | 0.964276i | \(0.414661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.672541 | 0.0442500 | ||||||||
\(232\) | −8.60557 | −0.564984 | ||||||||
\(233\) | −5.44207 | −0.356522 | −0.178261 | − | 0.983983i | \(-0.557047\pi\) | ||||
−0.178261 | + | 0.983983i | \(0.557047\pi\) | |||||||
\(234\) | −1.91048 | −0.124892 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.20032 | 0.208323 | ||||||||
\(237\) | −1.16501 | −0.0756756 | ||||||||
\(238\) | −1.94122 | −0.125831 | ||||||||
\(239\) | 4.22052 | 0.273003 | 0.136501 | − | 0.990640i | \(-0.456414\pi\) | ||||
0.136501 | + | 0.990640i | \(0.456414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 11.8994 | 0.764919 | ||||||||
\(243\) | 2.69457 | 0.172857 | ||||||||
\(244\) | −7.34057 | −0.469932 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.61285 | −0.230347 | ||||||||
\(247\) | −1.95276 | −0.124251 | ||||||||
\(248\) | −11.8694 | −0.753707 | ||||||||
\(249\) | −15.9659 | −1.01180 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.40591 | −0.214979 | −0.107490 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107490 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(252\) | −0.191819 | −0.0120834 | ||||||||
\(253\) | 0.957321 | 0.0601862 | ||||||||
\(254\) | 0.702334 | 0.0440683 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6634 | −0.978960 | ||||||||
\(257\) | 13.2411 | 0.825955 | 0.412978 | − | 0.910741i | \(-0.364489\pi\) | ||||
0.412978 | + | 0.910741i | \(0.364489\pi\) | |||||||
\(258\) | −10.7490 | −0.669207 | ||||||||
\(259\) | −7.31025 | −0.454237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.729236 | −0.0451386 | ||||||||
\(262\) | 2.78285 | 0.171925 | ||||||||
\(263\) | −21.0871 | −1.30029 | −0.650144 | − | 0.759811i | \(-0.725291\pi\) | ||||
−0.650144 | + | 0.759811i | \(0.725291\pi\) | |||||||
\(264\) | 2.22290 | 0.136810 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.297321 | 0.0182299 | ||||||||
\(267\) | 18.9296 | 1.15847 | ||||||||
\(268\) | 3.97155 | 0.242601 | ||||||||
\(269\) | −13.9324 | −0.849475 | −0.424737 | − | 0.905317i | \(-0.639634\pi\) | ||||
−0.424737 | + | 0.905317i | \(0.639634\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6583 | 0.647444 | 0.323722 | − | 0.946152i | \(-0.395066\pi\) | ||||
0.323722 | + | 0.946152i | \(0.395066\pi\) | |||||||
\(272\) | −3.38834 | −0.205448 | ||||||||
\(273\) | −11.2183 | −0.678961 | ||||||||
\(274\) | −3.68187 | −0.222430 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.42356 | −0.206074 | ||||||||
\(277\) | −2.42918 | −0.145955 | −0.0729777 | − | 0.997334i | \(-0.523250\pi\) | ||||
−0.0729777 | + | 0.997334i | \(0.523250\pi\) | |||||||
\(278\) | 6.88523 | 0.412949 | ||||||||
\(279\) | −1.00581 | −0.0602164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.2305 | 1.50513 | 0.752564 | − | 0.658519i | \(-0.228817\pi\) | ||||
0.752564 | + | 0.658519i | \(0.228817\pi\) | |||||||
\(282\) | −4.63227 | −0.275848 | ||||||||
\(283\) | −20.0356 | −1.19099 | −0.595495 | − | 0.803359i | \(-0.703044\pi\) | ||||
−0.595495 | + | 0.803359i | \(0.703044\pi\) | |||||||
\(284\) | −7.08987 | −0.420706 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.94852 | 0.174349 | ||||||||
\(287\) | −1.69194 | −0.0998723 | ||||||||
\(288\) | −1.08771 | −0.0640941 | ||||||||
\(289\) | −13.3715 | −0.786561 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.7955 | −0.984569 | ||||||||
\(292\) | −9.50970 | −0.556513 | ||||||||
\(293\) | 22.8324 | 1.33388 | 0.666942 | − | 0.745110i | \(-0.267603\pi\) | ||||
0.666942 | + | 0.745110i | \(0.267603\pi\) | |||||||
\(294\) | −12.1672 | −0.709606 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −24.1621 | −1.40439 | ||||||||
\(297\) | −1.98514 | −0.115189 | ||||||||
\(298\) | −9.15376 | −0.530263 | ||||||||
\(299\) | −15.9685 | −0.923484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.03392 | −0.290150 | ||||||||
\(302\) | −22.1584 | −1.27507 | ||||||||
\(303\) | 17.5818 | 1.01005 | ||||||||
\(304\) | 0.518964 | 0.0297646 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.543707 | −0.0310817 | ||||||||
\(307\) | 2.39567 | 0.136728 | 0.0683639 | − | 0.997660i | \(-0.478222\pi\) | ||||
0.0683639 | + | 0.997660i | \(0.478222\pi\) | |||||||
\(308\) | 0.296041 | 0.0168685 | ||||||||
\(309\) | 3.05693 | 0.173903 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.15705 | 0.349134 | 0.174567 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174567 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(312\) | −37.0790 | −2.09918 | ||||||||
\(313\) | 1.65380 | 0.0934784 | 0.0467392 | − | 0.998907i | \(-0.485117\pi\) | ||||
0.0467392 | + | 0.998907i | \(0.485117\pi\) | |||||||
\(314\) | 5.47914 | 0.309206 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.512818 | −0.0288483 | ||||||||
\(317\) | 7.44426 | 0.418111 | 0.209056 | − | 0.977904i | \(-0.432961\pi\) | ||||
0.209056 | + | 0.977904i | \(0.432961\pi\) | |||||||
\(318\) | 12.8558 | 0.720918 | ||||||||
\(319\) | 1.12546 | 0.0630136 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.0444 | 1.50947 | ||||||||
\(322\) | 2.43131 | 0.135492 | ||||||||
\(323\) | −0.555740 | −0.0309222 | ||||||||
\(324\) | 7.71913 | 0.428841 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.9479 | −0.772504 | ||||||||
\(327\) | −0.619322 | −0.0342486 | ||||||||
\(328\) | −5.59226 | −0.308781 | ||||||||
\(329\) | −2.16935 | −0.119600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5075 | −1.56691 | −0.783456 | − | 0.621447i | \(-0.786545\pi\) | ||||
−0.783456 | + | 0.621447i | \(0.786545\pi\) | |||||||
\(332\) | −7.02794 | −0.385708 | ||||||||
\(333\) | −2.04749 | −0.112202 | ||||||||
\(334\) | 16.5806 | 0.907252 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.98136 | 0.162646 | ||||||||
\(337\) | −1.51329 | −0.0824341 | −0.0412170 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412170 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(338\) | −34.9108 | −1.89890 | ||||||||
\(339\) | 10.3024 | 0.559549 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.55231 | 0.0840623 | ||||||||
\(342\) | 0.0832751 | 0.00450300 | ||||||||
\(343\) | −12.1960 | −0.658524 | ||||||||
\(344\) | −16.6383 | −0.897075 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.17976 | −0.0634242 | ||||||||
\(347\) | 18.5796 | 0.997407 | 0.498704 | − | 0.866773i | \(-0.333810\pi\) | ||||
0.498704 | + | 0.866773i | \(0.333810\pi\) | |||||||
\(348\) | −4.02485 | −0.215755 | ||||||||
\(349\) | −14.6495 | −0.784170 | −0.392085 | − | 0.919929i | \(-0.628246\pi\) | ||||
−0.392085 | + | 0.919929i | \(0.628246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.1129 | 1.76744 | ||||||||
\(352\) | 1.67871 | 0.0894755 | ||||||||
\(353\) | −15.6676 | −0.833901 | −0.416951 | − | 0.908929i | \(-0.636901\pi\) | ||||
−0.416951 | + | 0.908929i | \(0.636901\pi\) | |||||||
\(354\) | −7.98168 | −0.424222 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.33248 | 0.441621 | ||||||||
\(357\) | −3.19263 | −0.168972 | ||||||||
\(358\) | 13.8760 | 0.733369 | ||||||||
\(359\) | −13.6489 | −0.720362 | −0.360181 | − | 0.932882i | \(-0.617285\pi\) | ||||
−0.360181 | + | 0.932882i | \(0.617285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9149 | −0.995520 | ||||||||
\(362\) | 8.80355 | 0.462704 | ||||||||
\(363\) | 19.5703 | 1.02717 | ||||||||
\(364\) | −4.93810 | −0.258827 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 18.3076 | 0.956952 | ||||||||
\(367\) | 3.98812 | 0.208178 | 0.104089 | − | 0.994568i | \(-0.466807\pi\) | ||||
0.104089 | + | 0.994568i | \(0.466807\pi\) | |||||||
\(368\) | 4.24378 | 0.221222 | ||||||||
\(369\) | −0.473888 | −0.0246696 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.02054 | 0.312571 | ||||||||
\(372\) | −5.55135 | −0.287824 | ||||||||
\(373\) | 19.1389 | 0.990977 | 0.495488 | − | 0.868615i | \(-0.334989\pi\) | ||||
0.495488 | + | 0.868615i | \(0.334989\pi\) | |||||||
\(374\) | 0.839124 | 0.0433901 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.17021 | −0.369775 | ||||||||
\(377\) | −18.7731 | −0.966866 | ||||||||
\(378\) | −5.04166 | −0.259315 | ||||||||
\(379\) | −15.3139 | −0.786624 | −0.393312 | − | 0.919405i | \(-0.628671\pi\) | ||||
−0.393312 | + | 0.919405i | \(0.628671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15509 | 0.0591773 | ||||||||
\(382\) | 2.76882 | 0.141665 | ||||||||
\(383\) | −33.7339 | −1.72372 | −0.861860 | − | 0.507146i | \(-0.830701\pi\) | ||||
−0.861860 | + | 0.507146i | \(0.830701\pi\) | |||||||
\(384\) | 1.04841 | 0.0535014 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −29.7895 | −1.51625 | ||||||||
\(387\) | −1.40992 | −0.0716705 | ||||||||
\(388\) | −7.39310 | −0.375328 | ||||||||
\(389\) | 13.4176 | 0.680297 | 0.340148 | − | 0.940372i | \(-0.389523\pi\) | ||||
0.340148 | + | 0.940372i | \(0.389523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.54452 | −0.229826 | ||||||||
\(392\) | −18.8334 | −0.951230 | ||||||||
\(393\) | 4.57681 | 0.230870 | ||||||||
\(394\) | −1.28807 | −0.0648921 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0829167 | 0.00416672 | ||||||||
\(397\) | −31.1766 | −1.56471 | −0.782354 | − | 0.622834i | \(-0.785981\pi\) | ||||
−0.782354 | + | 0.622834i | \(0.785981\pi\) | |||||||
\(398\) | 29.4503 | 1.47621 | ||||||||
\(399\) | 0.488989 | 0.0244801 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.98879 | −0.299066 | −0.149533 | − | 0.988757i | \(-0.547777\pi\) | ||||
−0.149533 | + | 0.988757i | \(0.547777\pi\) | |||||||
\(402\) | −9.90514 | −0.494024 | ||||||||
\(403\) | −25.8932 | −1.28983 | ||||||||
\(404\) | 7.73920 | 0.385040 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.85833 | 0.141857 | ||||||||
\(407\) | 3.15998 | 0.156634 | ||||||||
\(408\) | −10.5524 | −0.522421 | ||||||||
\(409\) | 16.5919 | 0.820418 | 0.410209 | − | 0.911991i | \(-0.365456\pi\) | ||||
0.410209 | + | 0.911991i | \(0.365456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.05539 | −0.298690 | ||||||||
\(412\) | 1.34561 | 0.0662935 | ||||||||
\(413\) | −3.73792 | −0.183931 | ||||||||
\(414\) | 0.680974 | 0.0334681 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −28.0016 | −1.37289 | ||||||||
\(417\) | 11.3238 | 0.554529 | ||||||||
\(418\) | −0.128522 | −0.00628620 | ||||||||
\(419\) | −21.8938 | −1.06958 | −0.534791 | − | 0.844985i | \(-0.679610\pi\) | ||||
−0.534791 | + | 0.844985i | \(0.679610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8937 | 0.823350 | 0.411675 | − | 0.911331i | \(-0.364944\pi\) | ||||
0.411675 | + | 0.911331i | \(0.364944\pi\) | |||||||
\(422\) | −3.37859 | −0.164467 | ||||||||
\(423\) | −0.607603 | −0.0295427 | ||||||||
\(424\) | 19.8993 | 0.966393 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.6823 | 0.856711 | ||||||||
\(427\) | 8.57367 | 0.414909 | ||||||||
\(428\) | 11.9045 | 0.575426 | ||||||||
\(429\) | 4.84928 | 0.234126 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4132 | 0.886935 | 0.443467 | − | 0.896291i | \(-0.353748\pi\) | ||||
0.443467 | + | 0.896291i | \(0.353748\pi\) | |||||||
\(432\) | −8.80006 | −0.423393 | ||||||||
\(433\) | −33.0770 | −1.58958 | −0.794790 | − | 0.606885i | \(-0.792419\pi\) | ||||
−0.794790 | + | 0.606885i | \(0.792419\pi\) | |||||||
\(434\) | 3.94241 | 0.189242 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.272615 | −0.0130559 | ||||||||
\(437\) | 0.696046 | 0.0332964 | ||||||||
\(438\) | 23.7174 | 1.13326 | ||||||||
\(439\) | −8.31851 | −0.397021 | −0.198510 | − | 0.980099i | \(-0.563610\pi\) | ||||
−0.198510 | + | 0.980099i | \(0.563610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.59594 | −0.0759972 | ||||||||
\(442\) | −13.9970 | −0.665768 | ||||||||
\(443\) | 4.36551 | 0.207412 | 0.103706 | − | 0.994608i | \(-0.466930\pi\) | ||||
0.103706 | + | 0.994608i | \(0.466930\pi\) | |||||||
\(444\) | −11.3007 | −0.536306 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.19958 | −0.246207 | ||||||||
\(447\) | −15.0548 | −0.712065 | ||||||||
\(448\) | 7.56587 | 0.357454 | ||||||||
\(449\) | −8.00996 | −0.378013 | −0.189007 | − | 0.981976i | \(-0.560527\pi\) | ||||
−0.189007 | + | 0.981976i | \(0.560527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.731370 | 0.0344389 | ||||||||
\(452\) | 4.53494 | 0.213306 | ||||||||
\(453\) | −36.4429 | −1.71223 | ||||||||
\(454\) | −5.19735 | −0.243924 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.61622 | 0.0756865 | ||||||||
\(457\) | −27.6916 | −1.29536 | −0.647680 | − | 0.761912i | \(-0.724261\pi\) | ||||
−0.647680 | + | 0.761912i | \(0.724261\pi\) | |||||||
\(458\) | −8.80169 | −0.411276 | ||||||||
\(459\) | 9.42368 | 0.439860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.49433 | −0.116173 | −0.0580864 | − | 0.998312i | \(-0.518500\pi\) | ||||
−0.0580864 | + | 0.998312i | \(0.518500\pi\) | |||||||
\(462\) | −0.738335 | −0.0343505 | ||||||||
\(463\) | 32.6945 | 1.51944 | 0.759721 | − | 0.650249i | \(-0.225335\pi\) | ||||
0.759721 | + | 0.650249i | \(0.225335\pi\) | |||||||
\(464\) | 4.98913 | 0.231614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.97446 | 0.276762 | ||||||||
\(467\) | −36.7488 | −1.70053 | −0.850266 | − | 0.526353i | \(-0.823559\pi\) | ||||
−0.850266 | + | 0.526353i | \(0.823559\pi\) | |||||||
\(468\) | −1.38309 | −0.0639333 | ||||||||
\(469\) | −4.63871 | −0.214196 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.01128 | 0.415218 | ||||||||
\(472\) | −12.3547 | −0.568671 | ||||||||
\(473\) | 2.17599 | 0.100052 | ||||||||
\(474\) | 1.27898 | 0.0587456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.40534 | −0.0644138 | ||||||||
\(477\) | 1.68626 | 0.0772086 | ||||||||
\(478\) | −4.63341 | −0.211927 | ||||||||
\(479\) | 4.00850 | 0.183153 | 0.0915764 | − | 0.995798i | \(-0.470809\pi\) | ||||
0.0915764 | + | 0.995798i | \(0.470809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.7098 | −2.40336 | ||||||||
\(482\) | 1.09783 | 0.0500047 | ||||||||
\(483\) | 3.99866 | 0.181945 | ||||||||
\(484\) | 8.61452 | 0.391569 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.95818 | −0.134186 | ||||||||
\(487\) | 32.2540 | 1.46157 | 0.730785 | − | 0.682608i | \(-0.239154\pi\) | ||||
0.730785 | + | 0.682608i | \(0.239154\pi\) | |||||||
\(488\) | 28.3380 | 1.28280 | ||||||||
\(489\) | −22.9395 | −1.03736 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.2117 | −1.00240 | −0.501201 | − | 0.865331i | \(-0.667108\pi\) | ||||
−0.501201 | + | 0.865331i | \(0.667108\pi\) | |||||||
\(492\) | −2.61552 | −0.117917 | ||||||||
\(493\) | −5.34269 | −0.240622 | ||||||||
\(494\) | 2.14380 | 0.0964541 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.88135 | 0.308982 | ||||||||
\(497\) | 8.28086 | 0.371447 | ||||||||
\(498\) | 17.5279 | 0.785442 | ||||||||
\(499\) | 24.4248 | 1.09340 | 0.546701 | − | 0.837328i | \(-0.315883\pi\) | ||||
0.546701 | + | 0.837328i | \(0.315883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.2694 | 1.21831 | ||||||||
\(502\) | 3.73910 | 0.166884 | ||||||||
\(503\) | −38.7703 | −1.72868 | −0.864341 | − | 0.502907i | \(-0.832264\pi\) | ||||
−0.864341 | + | 0.502907i | \(0.832264\pi\) | |||||||
\(504\) | 0.740508 | 0.0329848 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.05097 | −0.0467215 | ||||||||
\(507\) | −57.4161 | −2.54994 | ||||||||
\(508\) | 0.508453 | 0.0225590 | ||||||||
\(509\) | −42.1763 | −1.86943 | −0.934715 | − | 0.355397i | \(-0.884346\pi\) | ||||
−0.934715 | + | 0.355397i | \(0.884346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1072 | 0.491353 | ||||||||
\(512\) | 18.3570 | 0.811273 | ||||||||
\(513\) | −1.44335 | −0.0637253 | ||||||||
\(514\) | −14.5364 | −0.641174 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.78176 | −0.342573 | ||||||||
\(517\) | 0.937738 | 0.0412417 | ||||||||
\(518\) | 8.02541 | 0.352616 | ||||||||
\(519\) | −1.94029 | −0.0851694 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.76641 | 0.165009 | 0.0825047 | − | 0.996591i | \(-0.473708\pi\) | ||||
0.0825047 | + | 0.996591i | \(0.473708\pi\) | |||||||
\(522\) | 0.800576 | 0.0350403 | ||||||||
\(523\) | 25.8240 | 1.12920 | 0.564602 | − | 0.825363i | \(-0.309030\pi\) | ||||
0.564602 | + | 0.825363i | \(0.309030\pi\) | |||||||
\(524\) | 2.01464 | 0.0880098 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.1501 | 1.00939 | ||||||||
\(527\) | −7.36900 | −0.320999 | ||||||||
\(528\) | −1.28874 | −0.0560852 | ||||||||
\(529\) | −17.3082 | −0.752528 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.04694 | −0.0454332 | ||||||||
\(532\) | 0.215245 | 0.00933205 | ||||||||
\(533\) | −12.1996 | −0.528422 | ||||||||
\(534\) | −20.7814 | −0.899300 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.3320 | −0.662241 | ||||||||
\(537\) | 22.8212 | 0.984806 | ||||||||
\(538\) | 15.2954 | 0.659432 | ||||||||
\(539\) | 2.46308 | 0.106092 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4742 | −1.22420 | −0.612100 | − | 0.790780i | \(-0.709675\pi\) | ||||
−0.612100 | + | 0.790780i | \(0.709675\pi\) | |||||||
\(542\) | −11.7010 | −0.502599 | ||||||||
\(543\) | 14.4788 | 0.621343 | ||||||||
\(544\) | −7.96904 | −0.341670 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.3158 | 0.527066 | ||||||||
\(547\) | −25.6501 | −1.09672 | −0.548360 | − | 0.836242i | \(-0.684748\pi\) | ||||
−0.548360 | + | 0.836242i | \(0.684748\pi\) | |||||||
\(548\) | −2.66548 | −0.113864 | ||||||||
\(549\) | 2.40136 | 0.102487 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.818295 | 0.0348605 | ||||||||
\(552\) | 13.2165 | 0.562531 | ||||||||
\(553\) | 0.598964 | 0.0254705 | ||||||||
\(554\) | 2.66683 | 0.113303 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.98455 | 0.211392 | ||||||||
\(557\) | 24.0410 | 1.01865 | 0.509325 | − | 0.860574i | \(-0.329895\pi\) | ||||
0.509325 | + | 0.860574i | \(0.329895\pi\) | |||||||
\(558\) | 1.10421 | 0.0467449 | ||||||||
\(559\) | −36.2965 | −1.53518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.38007 | 0.0582665 | ||||||||
\(562\) | −27.6988 | −1.16840 | ||||||||
\(563\) | −44.9292 | −1.89354 | −0.946771 | − | 0.321909i | \(-0.895675\pi\) | ||||
−0.946771 | + | 0.321909i | \(0.895675\pi\) | |||||||
\(564\) | −3.35352 | −0.141209 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.9956 | 0.924544 | ||||||||
\(567\) | −9.01583 | −0.378629 | ||||||||
\(568\) | 27.3701 | 1.14843 | ||||||||
\(569\) | −2.81272 | −0.117915 | −0.0589577 | − | 0.998260i | \(-0.518778\pi\) | ||||
−0.0589577 | + | 0.998260i | \(0.518778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4480 | −0.479085 | −0.239543 | − | 0.970886i | \(-0.576997\pi\) | ||||
−0.239543 | + | 0.970886i | \(0.576997\pi\) | |||||||
\(572\) | 2.13457 | 0.0892510 | ||||||||
\(573\) | 4.55375 | 0.190236 | ||||||||
\(574\) | 1.85746 | 0.0775291 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.11909 | 0.0882953 | ||||||||
\(577\) | 27.0956 | 1.12801 | 0.564003 | − | 0.825773i | \(-0.309261\pi\) | ||||
0.564003 | + | 0.825773i | \(0.309261\pi\) | |||||||
\(578\) | 14.6797 | 0.610594 | ||||||||
\(579\) | −48.9934 | −2.03610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.20853 | 0.340547 | ||||||||
\(582\) | 18.4386 | 0.764304 | ||||||||
\(583\) | −2.60247 | −0.107783 | ||||||||
\(584\) | 36.7118 | 1.51914 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.0661 | −1.03547 | ||||||||
\(587\) | 17.1328 | 0.707146 | 0.353573 | − | 0.935407i | \(-0.384967\pi\) | ||||
0.353573 | + | 0.935407i | \(0.384967\pi\) | |||||||
\(588\) | −8.80843 | −0.363254 | ||||||||
\(589\) | 1.12865 | 0.0465052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.11843 | −0.0871405 | ||||||||
\(592\) | 14.0081 | 0.575729 | ||||||||
\(593\) | 2.35285 | 0.0966198 | 0.0483099 | − | 0.998832i | \(-0.484616\pi\) | ||||
0.0483099 | + | 0.998832i | \(0.484616\pi\) | |||||||
\(594\) | 2.17934 | 0.0894194 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.62685 | −0.271446 | ||||||||
\(597\) | 48.4354 | 1.98233 | ||||||||
\(598\) | 17.5307 | 0.716884 | ||||||||
\(599\) | −15.3944 | −0.628999 | −0.314499 | − | 0.949258i | \(-0.601837\pi\) | ||||
−0.314499 | + | 0.949258i | \(0.601837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.6544 | −1.53596 | −0.767978 | − | 0.640477i | \(-0.778737\pi\) | ||||
−0.767978 | + | 0.640477i | \(0.778737\pi\) | |||||||
\(602\) | 5.52638 | 0.225238 | ||||||||
\(603\) | −1.29923 | −0.0529088 | ||||||||
\(604\) | −16.0415 | −0.652721 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.3018 | −0.784081 | ||||||||
\(607\) | 2.72064 | 0.110427 | 0.0552137 | − | 0.998475i | \(-0.482416\pi\) | ||||
0.0552137 | + | 0.998475i | \(0.482416\pi\) | |||||||
\(608\) | 1.22055 | 0.0494999 | ||||||||
\(609\) | 4.70096 | 0.190493 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.6419 | −0.632803 | ||||||||
\(612\) | −0.393616 | −0.0159110 | ||||||||
\(613\) | −23.7816 | −0.960528 | −0.480264 | − | 0.877124i | \(-0.659459\pi\) | ||||
−0.480264 | + | 0.877124i | \(0.659459\pi\) | |||||||
\(614\) | −2.63003 | −0.106139 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.14286 | −0.0460469 | ||||||||
\(617\) | −15.5878 | −0.627541 | −0.313770 | − | 0.949499i | \(-0.601592\pi\) | ||||
−0.313770 | + | 0.949499i | \(0.601592\pi\) | |||||||
\(618\) | −3.35599 | −0.134998 | ||||||||
\(619\) | 2.18172 | 0.0876906 | 0.0438453 | − | 0.999038i | \(-0.486039\pi\) | ||||
0.0438453 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.8028 | −0.473631 | ||||||||
\(622\) | −6.75939 | −0.271027 | ||||||||
\(623\) | −9.73221 | −0.389913 | ||||||||
\(624\) | 21.4968 | 0.860559 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.81559 | −0.0725656 | ||||||||
\(627\) | −0.211373 | −0.00844144 | ||||||||
\(628\) | 3.96661 | 0.158285 | ||||||||
\(629\) | −15.0008 | −0.598120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6467 | −1.49869 | −0.749345 | − | 0.662180i | \(-0.769632\pi\) | ||||
−0.749345 | + | 0.662180i | \(0.769632\pi\) | |||||||
\(632\) | 1.97971 | 0.0787488 | ||||||||
\(633\) | −5.55661 | −0.220855 | ||||||||
\(634\) | −8.17253 | −0.324573 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.30694 | 0.369044 | ||||||||
\(637\) | −41.0853 | −1.62786 | ||||||||
\(638\) | −1.23556 | −0.0489163 | ||||||||
\(639\) | 2.31934 | 0.0917518 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.393382 | 0.0155376 | 0.00776882 | − | 0.999970i | \(-0.497527\pi\) | ||||
0.00776882 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(642\) | −29.6902 | −1.17178 | ||||||||
\(643\) | 39.1158 | 1.54258 | 0.771288 | − | 0.636486i | \(-0.219613\pi\) | ||||
0.771288 | + | 0.636486i | \(0.219613\pi\) | |||||||
\(644\) | 1.76014 | 0.0693594 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.610108 | 0.0240044 | ||||||||
\(647\) | 38.5541 | 1.51572 | 0.757859 | − | 0.652419i | \(-0.226246\pi\) | ||||
0.757859 | + | 0.652419i | \(0.226246\pi\) | |||||||
\(648\) | −29.7994 | −1.17063 | ||||||||
\(649\) | 1.61578 | 0.0634249 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.48389 | 0.254124 | ||||||||
\(652\) | −10.0976 | −0.395452 | ||||||||
\(653\) | −14.8795 | −0.582281 | −0.291141 | − | 0.956680i | \(-0.594035\pi\) | ||||
−0.291141 | + | 0.956680i | \(0.594035\pi\) | |||||||
\(654\) | 0.679909 | 0.0265866 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.24214 | 0.126584 | ||||||||
\(657\) | 3.11095 | 0.121370 | ||||||||
\(658\) | 2.38158 | 0.0928436 | ||||||||
\(659\) | 15.0109 | 0.584743 | 0.292371 | − | 0.956305i | \(-0.405556\pi\) | ||||
0.292371 | + | 0.956305i | \(0.405556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4143 | −0.794024 | −0.397012 | − | 0.917813i | \(-0.629953\pi\) | ||||
−0.397012 | + | 0.917813i | \(0.629953\pi\) | |||||||
\(662\) | 31.2963 | 1.21637 | ||||||||
\(663\) | −23.0201 | −0.894028 | ||||||||
\(664\) | 27.1311 | 1.05289 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.24780 | 0.0871003 | ||||||||
\(667\) | 6.69153 | 0.259097 | ||||||||
\(668\) | 12.0035 | 0.464430 | ||||||||
\(669\) | −8.55150 | −0.330620 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.70611 | −0.143073 | ||||||||
\(672\) | 7.01186 | 0.270488 | ||||||||
\(673\) | 35.8056 | 1.38020 | 0.690102 | − | 0.723712i | \(-0.257566\pi\) | ||||
0.690102 | + | 0.723712i | \(0.257566\pi\) | |||||||
\(674\) | 1.66133 | 0.0639921 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.2736 | −0.972062 | ||||||||
\(677\) | −34.1574 | −1.31278 | −0.656388 | − | 0.754424i | \(-0.727917\pi\) | ||||
−0.656388 | + | 0.754424i | \(0.727917\pi\) | |||||||
\(678\) | −11.3103 | −0.434368 | ||||||||
\(679\) | 8.63502 | 0.331382 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.54784 | −0.327554 | ||||||||
\(682\) | −1.70417 | −0.0652561 | ||||||||
\(683\) | 12.9413 | 0.495185 | 0.247593 | − | 0.968864i | \(-0.420361\pi\) | ||||
0.247593 | + | 0.968864i | \(0.420361\pi\) | |||||||
\(684\) | 0.0602869 | 0.00230513 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.3892 | 0.511200 | ||||||||
\(687\) | −14.4757 | −0.552283 | ||||||||
\(688\) | 9.64612 | 0.367755 | ||||||||
\(689\) | 43.4104 | 1.65381 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.406449 | 0.0154620 | 0.00773102 | − | 0.999970i | \(-0.497539\pi\) | ||||
0.00773102 | + | 0.999970i | \(0.497539\pi\) | |||||||
\(692\) | −0.854084 | −0.0324674 | ||||||||
\(693\) | −0.0968455 | −0.00367886 | ||||||||
\(694\) | −20.3973 | −0.774270 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.5378 | 0.588957 | ||||||||
\(697\) | −3.47190 | −0.131508 | ||||||||
\(698\) | 16.0826 | 0.608737 | ||||||||
\(699\) | 9.82591 | 0.371650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1730 | 0.422000 | 0.211000 | − | 0.977486i | \(-0.432328\pi\) | ||||
0.211000 | + | 0.977486i | \(0.432328\pi\) | |||||||
\(702\) | −36.3524 | −1.37203 | ||||||||
\(703\) | 2.29755 | 0.0866536 | ||||||||
\(704\) | −3.27047 | −0.123261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.2003 | 0.647343 | ||||||||
\(707\) | −9.03927 | −0.339957 | ||||||||
\(708\) | −5.77833 | −0.217163 | ||||||||
\(709\) | 4.23412 | 0.159016 | 0.0795078 | − | 0.996834i | \(-0.474665\pi\) | ||||
0.0795078 | + | 0.996834i | \(0.474665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.167761 | 0.00629152 | ||||||||
\(712\) | −32.1672 | −1.20552 | ||||||||
\(713\) | 9.22942 | 0.345644 | ||||||||
\(714\) | 3.50496 | 0.131170 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.0455 | 0.375418 | ||||||||
\(717\) | −7.62034 | −0.284587 | ||||||||
\(718\) | 14.9842 | 0.559204 | ||||||||
\(719\) | −2.66311 | −0.0993173 | −0.0496586 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496586 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.57165 | −0.0585314 | ||||||||
\(722\) | 20.7653 | 0.772805 | ||||||||
\(723\) | 1.80555 | 0.0671490 | ||||||||
\(724\) | 6.37331 | 0.236862 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.4848 | −0.797377 | ||||||||
\(727\) | 7.67222 | 0.284547 | 0.142273 | − | 0.989827i | \(-0.454559\pi\) | ||||
0.142273 | + | 0.989827i | \(0.454559\pi\) | |||||||
\(728\) | 19.0633 | 0.706534 | ||||||||
\(729\) | 24.2720 | 0.898963 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.3297 | −0.382058 | ||||||||
\(732\) | 13.2537 | 0.489872 | ||||||||
\(733\) | 44.4174 | 1.64059 | 0.820297 | − | 0.571938i | \(-0.193808\pi\) | ||||
0.820297 | + | 0.571938i | \(0.193808\pi\) | |||||||
\(734\) | −4.37827 | −0.161605 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.98094 | 0.367902 | ||||||||
\(737\) | 2.00516 | 0.0738609 | ||||||||
\(738\) | 0.520248 | 0.0191506 | ||||||||
\(739\) | −38.5453 | −1.41791 | −0.708955 | − | 0.705253i | \(-0.750833\pi\) | ||||
−0.708955 | + | 0.705253i | \(0.750833\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.52580 | 0.129524 | ||||||||
\(742\) | −6.60952 | −0.242643 | ||||||||
\(743\) | −26.0745 | −0.956579 | −0.478289 | − | 0.878202i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878202i | \(0.658743\pi\) | |||||||
\(744\) | 21.4307 | 0.785689 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21.0113 | −0.769278 | ||||||||
\(747\) | 2.29908 | 0.0841191 | ||||||||
\(748\) | 0.607483 | 0.0222118 | ||||||||
\(749\) | −13.9043 | −0.508051 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.56686 | −0.166647 | −0.0833235 | − | 0.996523i | \(-0.526553\pi\) | ||||
−0.0833235 | + | 0.996523i | \(0.526553\pi\) | |||||||
\(752\) | 4.15697 | 0.151589 | ||||||||
\(753\) | 6.14953 | 0.224101 | ||||||||
\(754\) | 20.6097 | 0.750561 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.64990 | −0.132746 | ||||||||
\(757\) | 30.9168 | 1.12369 | 0.561844 | − | 0.827243i | \(-0.310092\pi\) | ||||
0.561844 | + | 0.827243i | \(0.310092\pi\) | |||||||
\(758\) | 16.8121 | 0.610642 | ||||||||
\(759\) | −1.72849 | −0.0627401 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8579 | 0.393598 | 0.196799 | − | 0.980444i | \(-0.436945\pi\) | ||||
0.196799 | + | 0.980444i | \(0.436945\pi\) | |||||||
\(762\) | −1.26810 | −0.0459383 | ||||||||
\(763\) | 0.318410 | 0.0115272 | ||||||||
\(764\) | 2.00449 | 0.0725197 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.0340 | 1.33809 | ||||||||
\(767\) | −26.9519 | −0.973177 | ||||||||
\(768\) | 28.2809 | 1.02050 | ||||||||
\(769\) | 48.3748 | 1.74444 | 0.872220 | − | 0.489113i | \(-0.162680\pi\) | ||||
0.872220 | + | 0.489113i | \(0.162680\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9074 | −0.861003 | ||||||||
\(772\) | −21.5661 | −0.776180 | ||||||||
\(773\) | −46.1527 | −1.66000 | −0.829999 | − | 0.557765i | \(-0.811659\pi\) | ||||
−0.829999 | + | 0.557765i | \(0.811659\pi\) | |||||||
\(774\) | 1.54786 | 0.0556365 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.5407 | 1.02455 | ||||||||
\(777\) | 13.1990 | 0.473511 | ||||||||
\(778\) | −14.7302 | −0.528102 | ||||||||
\(779\) | 0.531762 | 0.0190524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.57954 | −0.128086 | ||||||||
\(782\) | 4.98910 | 0.178410 | ||||||||
\(783\) | −13.8758 | −0.495881 | ||||||||
\(784\) | 10.9188 | 0.389956 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.02456 | −0.179220 | ||||||||
\(787\) | 1.78318 | 0.0635635 | 0.0317818 | − | 0.999495i | \(-0.489882\pi\) | ||||
0.0317818 | + | 0.999495i | \(0.489882\pi\) | |||||||
\(788\) | −0.932497 | −0.0332188 | ||||||||
\(789\) | 38.0738 | 1.35546 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.29674 | −0.188330 | ||||||||
\(792\) | −0.320097 | −0.0113741 | ||||||||
\(793\) | 61.8195 | 2.19528 | ||||||||
\(794\) | 34.2266 | 1.21466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.3205 | 0.755684 | ||||||||
\(797\) | 23.4124 | 0.829310 | 0.414655 | − | 0.909979i | \(-0.363902\pi\) | ||||
0.414655 | + | 0.909979i | \(0.363902\pi\) | |||||||
\(798\) | −0.536826 | −0.0190034 | ||||||||
\(799\) | −4.45155 | −0.157485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.72585 | −0.0963130 | ||||||||
\(802\) | 6.57467 | 0.232160 | ||||||||
\(803\) | −4.80126 | −0.169433 | ||||||||
\(804\) | −7.17081 | −0.252895 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.4263 | 1.00127 | ||||||||
\(807\) | 25.1556 | 0.885520 | ||||||||
\(808\) | −29.8768 | −1.05106 | ||||||||
\(809\) | −2.49926 | −0.0878692 | −0.0439346 | − | 0.999034i | \(-0.513989\pi\) | ||||
−0.0439346 | + | 0.999034i | \(0.513989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.8265 | −0.871778 | −0.435889 | − | 0.900001i | \(-0.643566\pi\) | ||||
−0.435889 | + | 0.900001i | \(0.643566\pi\) | |||||||
\(812\) | 2.06929 | 0.0726177 | ||||||||
\(813\) | −19.2440 | −0.674916 | ||||||||
\(814\) | −3.46911 | −0.121592 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.11780 | 0.214166 | ||||||||
\(817\) | 1.58211 | 0.0553512 | ||||||||
\(818\) | −18.2151 | −0.636876 | ||||||||
\(819\) | 1.61543 | 0.0564475 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4914 | 1.62256 | 0.811280 | − | 0.584657i | \(-0.198771\pi\) | ||||
0.811280 | + | 0.584657i | \(0.198771\pi\) | |||||||
\(822\) | 6.64778 | 0.231868 | ||||||||
\(823\) | 18.3671 | 0.640237 | 0.320118 | − | 0.947378i | \(-0.396277\pi\) | ||||
0.320118 | + | 0.947378i | \(0.396277\pi\) | |||||||
\(824\) | −5.19467 | −0.180965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.10360 | 0.142783 | ||||||||
\(827\) | 17.3399 | 0.602968 | 0.301484 | − | 0.953471i | \(-0.402518\pi\) | ||||
0.301484 | + | 0.953471i | \(0.402518\pi\) | |||||||
\(828\) | 0.492990 | 0.0171326 | ||||||||
\(829\) | 23.9714 | 0.832560 | 0.416280 | − | 0.909236i | \(-0.363334\pi\) | ||||
0.416280 | + | 0.909236i | \(0.363334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.38600 | 0.152149 | ||||||||
\(832\) | 54.5529 | 1.89128 | ||||||||
\(833\) | −11.6925 | −0.405122 | ||||||||
\(834\) | −12.4316 | −0.430471 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0930431 | −0.00321796 | ||||||||
\(837\) | −19.1385 | −0.661522 | ||||||||
\(838\) | 24.0356 | 0.830297 | ||||||||
\(839\) | −40.4460 | −1.39635 | −0.698175 | − | 0.715927i | \(-0.746004\pi\) | ||||
−0.698175 | + | 0.715927i | \(0.746004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1332 | −0.728731 | ||||||||
\(842\) | −18.5464 | −0.639152 | ||||||||
\(843\) | −45.5549 | −1.56899 | ||||||||
\(844\) | −2.44593 | −0.0841923 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.667044 | 0.0229334 | ||||||||
\(847\) | −10.0616 | −0.345722 | ||||||||
\(848\) | −11.5367 | −0.396172 | ||||||||
\(849\) | 36.1751 | 1.24153 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7880 | 0.644043 | ||||||||
\(852\) | 12.8011 | 0.438558 | ||||||||
\(853\) | 0.00791683 | 0.000271067 0 | 0.000135534 | − | 1.00000i | \(-0.499957\pi\) | ||||
0.000135534 | 1.00000i | \(0.499957\pi\) | ||||||||
\(854\) | −9.41243 | −0.322087 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.9568 | −1.57077 | ||||||||
\(857\) | −46.1409 | −1.57614 | −0.788072 | − | 0.615583i | \(-0.788921\pi\) | ||||
−0.788072 | + | 0.615583i | \(0.788921\pi\) | |||||||
\(858\) | −5.32368 | −0.181748 | ||||||||
\(859\) | 14.7880 | 0.504560 | 0.252280 | − | 0.967654i | \(-0.418820\pi\) | ||||
0.252280 | + | 0.967654i | \(0.418820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.05488 | 0.104110 | ||||||||
\(862\) | −20.2146 | −0.688512 | ||||||||
\(863\) | −44.4021 | −1.51147 | −0.755733 | − | 0.654880i | \(-0.772719\pi\) | ||||
−0.755733 | + | 0.654880i | \(0.772719\pi\) | |||||||
\(864\) | −20.6969 | −0.704122 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.3129 | 1.23396 | ||||||||
\(867\) | 24.1429 | 0.819937 | ||||||||
\(868\) | 2.85410 | 0.0968745 | ||||||||
\(869\) | −0.258912 | −0.00878298 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4469 | −1.13330 | ||||||||
\(872\) | 1.05242 | 0.0356394 | ||||||||
\(873\) | 2.41854 | 0.0818552 | ||||||||
\(874\) | −0.764139 | −0.0258474 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.1702 | 0.580127 | ||||||||
\(877\) | 25.0137 | 0.844654 | 0.422327 | − | 0.906444i | \(-0.361213\pi\) | ||||
0.422327 | + | 0.906444i | \(0.361213\pi\) | |||||||
\(878\) | 9.13230 | 0.308200 | ||||||||
\(879\) | −41.2250 | −1.39048 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6234 | 0.896966 | 0.448483 | − | 0.893791i | \(-0.351964\pi\) | ||||
0.448483 | + | 0.893791i | \(0.351964\pi\) | |||||||
\(882\) | 1.75207 | 0.0589953 | ||||||||
\(883\) | 27.5946 | 0.928632 | 0.464316 | − | 0.885670i | \(-0.346300\pi\) | ||||
0.464316 | + | 0.885670i | \(0.346300\pi\) | |||||||
\(884\) | −10.1331 | −0.340812 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.79258 | −0.161010 | ||||||||
\(887\) | 24.3390 | 0.817222 | 0.408611 | − | 0.912709i | \(-0.366013\pi\) | ||||
0.408611 | + | 0.912709i | \(0.366013\pi\) | |||||||
\(888\) | 43.6257 | 1.46398 | ||||||||
\(889\) | −0.593866 | −0.0199176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.89724 | 0.130562 | ||||||||
\(892\) | −3.76423 | −0.126036 | ||||||||
\(893\) | 0.681807 | 0.0228158 | ||||||||
\(894\) | 16.5275 | 0.552764 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.539016 | −0.0180072 | ||||||||
\(897\) | 28.8319 | 0.962670 | ||||||||
\(898\) | 8.79356 | 0.293445 | ||||||||
\(899\) | 10.8504 | 0.361882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.3543 | 0.411580 | ||||||||
\(902\) | −0.802919 | −0.0267343 | ||||||||
\(903\) | 9.08897 | 0.302462 | ||||||||
\(904\) | −17.5069 | −0.582272 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 40.0080 | 1.32918 | ||||||||
\(907\) | 14.8454 | 0.492934 | 0.246467 | − | 0.969151i | \(-0.420730\pi\) | ||||
0.246467 | + | 0.969151i | \(0.420730\pi\) | |||||||
\(908\) | −3.76262 | −0.124867 | ||||||||
\(909\) | −2.53176 | −0.0839733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.0619 | −0.962863 | −0.481432 | − | 0.876484i | \(-0.659883\pi\) | ||||
−0.481432 | + | 0.876484i | \(0.659883\pi\) | |||||||
\(912\) | −0.937013 | −0.0310276 | ||||||||
\(913\) | −3.54827 | −0.117431 | ||||||||
\(914\) | 30.4007 | 1.00557 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.37197 | −0.210536 | ||||||||
\(917\) | −2.35306 | −0.0777050 | ||||||||
\(918\) | −10.3456 | −0.341455 | ||||||||
\(919\) | 21.9333 | 0.723513 | 0.361756 | − | 0.932273i | \(-0.382177\pi\) | ||||
0.361756 | + | 0.932273i | \(0.382177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.32549 | −0.142530 | ||||||||
\(922\) | 2.73835 | 0.0901829 | ||||||||
\(923\) | 59.7082 | 1.96532 | ||||||||
\(924\) | −0.534516 | −0.0175843 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −35.8930 | −1.17952 | ||||||||
\(927\) | −0.440196 | −0.0144579 | ||||||||
\(928\) | 11.7339 | 0.385185 | ||||||||
\(929\) | 42.5016 | 1.39443 | 0.697217 | − | 0.716860i | \(-0.254421\pi\) | ||||
0.697217 | + | 0.716860i | \(0.254421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.79085 | 0.0586927 | ||||||||
\(932\) | 4.32520 | 0.141677 | ||||||||
\(933\) | −11.1168 | −0.363949 | ||||||||
\(934\) | 40.3439 | 1.32009 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.33935 | 0.174522 | ||||||||
\(937\) | 39.0038 | 1.27420 | 0.637099 | − | 0.770782i | \(-0.280134\pi\) | ||||
0.637099 | + | 0.770782i | \(0.280134\pi\) | |||||||
\(938\) | 5.09251 | 0.166276 | ||||||||
\(939\) | −2.98601 | −0.0974449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.4491 | −0.536226 | −0.268113 | − | 0.963387i | \(-0.586400\pi\) | ||||
−0.268113 | + | 0.963387i | \(0.586400\pi\) | |||||||
\(942\) | −9.89284 | −0.322326 | ||||||||
\(943\) | 4.34844 | 0.141605 | ||||||||
\(944\) | 7.16271 | 0.233126 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.38887 | −0.0776688 | ||||||||
\(947\) | −13.2820 | −0.431606 | −0.215803 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215803 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(948\) | 0.925917 | 0.0300724 | ||||||||
\(949\) | 80.0871 | 2.59974 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.4410 | −0.435853 | ||||||||
\(952\) | 5.42527 | 0.175834 | ||||||||
\(953\) | −35.6158 | −1.15371 | −0.576855 | − | 0.816847i | \(-0.695720\pi\) | ||||
−0.576855 | + | 0.816847i | \(0.695720\pi\) | |||||||
\(954\) | −1.85123 | −0.0599357 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.35435 | −0.108487 | ||||||||
\(957\) | −2.03207 | −0.0656874 | ||||||||
\(958\) | −4.40064 | −0.142178 | ||||||||
\(959\) | 3.11324 | 0.100532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0344 | −0.517237 | ||||||||
\(962\) | 57.8663 | 1.86569 | ||||||||
\(963\) | −3.89438 | −0.125495 | ||||||||
\(964\) | 0.794772 | 0.0255979 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.38985 | −0.141241 | ||||||||
\(967\) | −58.4495 | −1.87961 | −0.939805 | − | 0.341711i | \(-0.888994\pi\) | ||||
−0.939805 | + | 0.341711i | \(0.888994\pi\) | |||||||
\(968\) | −33.2560 | −1.06889 | ||||||||
\(969\) | 1.00342 | 0.0322343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.6770 | −1.40166 | −0.700831 | − | 0.713328i | \(-0.747187\pi\) | ||||
−0.700831 | + | 0.713328i | \(0.747187\pi\) | |||||||
\(972\) | −2.14157 | −0.0686909 | ||||||||
\(973\) | −5.82188 | −0.186641 | ||||||||
\(974\) | −35.4094 | −1.13459 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.4291 | −0.525882 | ||||||||
\(977\) | 6.96622 | 0.222869 | 0.111435 | − | 0.993772i | \(-0.464455\pi\) | ||||
0.111435 | + | 0.993772i | \(0.464455\pi\) | |||||||
\(978\) | 25.1836 | 0.805284 | ||||||||
\(979\) | 4.20691 | 0.134453 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0891819 | 0.00284736 | ||||||||
\(982\) | 24.3847 | 0.778147 | ||||||||
\(983\) | −7.12795 | −0.227346 | −0.113673 | − | 0.993518i | \(-0.536262\pi\) | ||||
−0.113673 | + | 0.993518i | \(0.536262\pi\) | |||||||
\(984\) | 10.0971 | 0.321883 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.86536 | 0.186791 | ||||||||
\(987\) | 3.91687 | 0.124675 | ||||||||
\(988\) | 1.55200 | 0.0493757 | ||||||||
\(989\) | 12.9376 | 0.411391 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1981 | −0.419252 | −0.209626 | − | 0.977782i | \(-0.567225\pi\) | ||||
−0.209626 | + | 0.977782i | \(0.567225\pi\) | |||||||
\(992\) | 16.1842 | 0.513850 | ||||||||
\(993\) | 51.4716 | 1.63340 | ||||||||
\(994\) | −9.09097 | −0.288348 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.6893 | 0.402075 | ||||||||
\(997\) | −5.19129 | −0.164410 | −0.0822049 | − | 0.996615i | \(-0.526196\pi\) | ||||
−0.0822049 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(998\) | −26.8142 | −0.848789 | ||||||||
\(999\) | −38.9594 | −1.23262 |
(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 | 6025.2.a.i.1.5 | 15 | ||
5.4 | even | 2 | 1205.2.a.c.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.11 | ✓ | 15 | 5.4 | even | 2 | ||
6025.2.a.i.1.5 | 15 | 1.1 | even | 1 | trivial |