Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.27841\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27841 | 1.61108 | 0.805541 | − | 0.592540i | \(-0.201875\pi\) | ||||
0.805541 | + | 0.592540i | \(0.201875\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.19117 | 1.59558 | ||||||||
\(5\) | 3.19117 | 1.42713 | 0.713567 | − | 0.700587i | \(-0.247078\pi\) | ||||
0.713567 | + | 0.700587i | \(0.247078\pi\) | |||||||
\(6\) | 2.27841 | 0.930158 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.71397 | 0.959535 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.27080 | 2.29923 | ||||||||
\(11\) | −2.80122 | −0.844600 | −0.422300 | − | 0.906456i | \(-0.638777\pi\) | ||||
−0.422300 | + | 0.906456i | \(0.638777\pi\) | |||||||
\(12\) | 3.19117 | 0.921211 | ||||||||
\(13\) | 4.10392 | 1.13822 | 0.569112 | − | 0.822260i | \(-0.307287\pi\) | ||||
0.569112 | + | 0.822260i | \(0.307287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.19117 | 0.823956 | ||||||||
\(16\) | −0.198780 | −0.0496951 | ||||||||
\(17\) | 0.365659 | 0.0886852 | 0.0443426 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443426 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(18\) | 2.27841 | 0.537027 | ||||||||
\(19\) | 1.56444 | 0.358907 | 0.179453 | − | 0.983766i | \(-0.442567\pi\) | ||||
0.179453 | + | 0.983766i | \(0.442567\pi\) | |||||||
\(20\) | 10.1836 | 2.27711 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.38234 | −1.36072 | ||||||||
\(23\) | −0.452904 | −0.0944369 | −0.0472185 | − | 0.998885i | \(-0.515036\pi\) | ||||
−0.0472185 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(24\) | 2.71397 | 0.553988 | ||||||||
\(25\) | 5.18356 | 1.03671 | ||||||||
\(26\) | 9.35044 | 1.83377 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.07202 | 1.49894 | 0.749468 | − | 0.662040i | \(-0.230309\pi\) | ||||
0.749468 | + | 0.662040i | \(0.230309\pi\) | |||||||
\(30\) | 7.27080 | 1.32746 | ||||||||
\(31\) | 4.36566 | 0.784095 | 0.392048 | − | 0.919945i | \(-0.371767\pi\) | ||||
0.392048 | + | 0.919945i | \(0.371767\pi\) | |||||||
\(32\) | −5.88085 | −1.03960 | ||||||||
\(33\) | −2.80122 | −0.487630 | ||||||||
\(34\) | 0.833122 | 0.142879 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.19117 | 0.531861 | ||||||||
\(37\) | −2.16688 | −0.356233 | −0.178116 | − | 0.984009i | \(-0.557000\pi\) | ||||
−0.178116 | + | 0.984009i | \(0.557000\pi\) | |||||||
\(38\) | 3.56444 | 0.578228 | ||||||||
\(39\) | 4.10392 | 0.657154 | ||||||||
\(40\) | 8.66075 | 1.36938 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.06229 | −1.07699 | −0.538495 | − | 0.842629i | \(-0.681007\pi\) | ||||
−0.538495 | + | 0.842629i | \(0.681007\pi\) | |||||||
\(44\) | −8.93916 | −1.34763 | ||||||||
\(45\) | 3.19117 | 0.475711 | ||||||||
\(46\) | −1.03190 | −0.152146 | ||||||||
\(47\) | −11.8027 | −1.72160 | −0.860799 | − | 0.508946i | \(-0.830035\pi\) | ||||
−0.860799 | + | 0.508946i | \(0.830035\pi\) | |||||||
\(48\) | −0.198780 | −0.0286915 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.8103 | 1.67023 | ||||||||
\(51\) | 0.365659 | 0.0512025 | ||||||||
\(52\) | 13.0963 | 1.81613 | ||||||||
\(53\) | 5.23280 | 0.718781 | 0.359390 | − | 0.933187i | \(-0.382985\pi\) | ||||
0.359390 | + | 0.933187i | \(0.382985\pi\) | |||||||
\(54\) | 2.27841 | 0.310053 | ||||||||
\(55\) | −8.93916 | −1.20536 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56444 | 0.207215 | ||||||||
\(58\) | 18.3914 | 2.41491 | ||||||||
\(59\) | 0.833122 | 0.108463 | 0.0542316 | − | 0.998528i | \(-0.482729\pi\) | ||||
0.0542316 | + | 0.998528i | \(0.482729\pi\) | |||||||
\(60\) | 10.1836 | 1.31469 | ||||||||
\(61\) | 9.06229 | 1.16031 | 0.580154 | − | 0.814507i | \(-0.302992\pi\) | ||||
0.580154 | + | 0.814507i | \(0.302992\pi\) | |||||||
\(62\) | 9.94678 | 1.26324 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0015 | −1.62518 | ||||||||
\(65\) | 13.0963 | 1.62440 | ||||||||
\(66\) | −6.38234 | −0.785611 | ||||||||
\(67\) | 0.145556 | 0.0177825 | 0.00889127 | − | 0.999960i | \(-0.497170\pi\) | ||||
0.00889127 | + | 0.999960i | \(0.497170\pi\) | |||||||
\(68\) | 1.16688 | 0.141505 | ||||||||
\(69\) | −0.452904 | −0.0545232 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.88780 | −0.342719 | −0.171359 | − | 0.985209i | \(-0.554816\pi\) | ||||
−0.171359 | + | 0.985209i | \(0.554816\pi\) | |||||||
\(72\) | 2.71397 | 0.319845 | ||||||||
\(73\) | 12.7480 | 1.49204 | 0.746020 | − | 0.665924i | \(-0.231962\pi\) | ||||
0.746020 | + | 0.665924i | \(0.231962\pi\) | |||||||
\(74\) | −4.93705 | −0.573920 | ||||||||
\(75\) | 5.18356 | 0.598546 | ||||||||
\(76\) | 4.99239 | 0.572666 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.35044 | 1.05873 | ||||||||
\(79\) | −4.01371 | −0.451578 | −0.225789 | − | 0.974176i | \(-0.572496\pi\) | ||||
−0.225789 | + | 0.974176i | \(0.572496\pi\) | |||||||
\(80\) | −0.634341 | −0.0709215 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.27841 | 0.251609 | ||||||||
\(83\) | −8.93916 | −0.981201 | −0.490600 | − | 0.871385i | \(-0.663223\pi\) | ||||
−0.490600 | + | 0.871385i | \(0.663223\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.16688 | 0.126566 | ||||||||
\(86\) | −16.0908 | −1.73512 | ||||||||
\(87\) | 8.07202 | 0.865412 | ||||||||
\(88\) | −7.60244 | −0.810423 | ||||||||
\(89\) | −0.731317 | −0.0775195 | −0.0387597 | − | 0.999249i | \(-0.512341\pi\) | ||||
−0.0387597 | + | 0.999249i | \(0.512341\pi\) | |||||||
\(90\) | 7.27080 | 0.766410 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.44529 | −0.150682 | ||||||||
\(93\) | 4.36566 | 0.452698 | ||||||||
\(94\) | −26.8914 | −2.77363 | ||||||||
\(95\) | 4.99239 | 0.512208 | ||||||||
\(96\) | −5.88085 | −0.600212 | ||||||||
\(97\) | −14.7820 | −1.50089 | −0.750443 | − | 0.660935i | \(-0.770160\pi\) | ||||
−0.750443 | + | 0.660935i | \(0.770160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.80122 | −0.281533 | ||||||||
\(100\) | 16.5416 | 1.65416 | ||||||||
\(101\) | 9.96345 | 0.991401 | 0.495700 | − | 0.868494i | \(-0.334911\pi\) | ||||
0.495700 | + | 0.868494i | \(0.334911\pi\) | |||||||
\(102\) | 0.833122 | 0.0824913 | ||||||||
\(103\) | −14.8367 | −1.46190 | −0.730952 | − | 0.682429i | \(-0.760923\pi\) | ||||
−0.730952 | + | 0.682429i | \(0.760923\pi\) | |||||||
\(104\) | 11.1379 | 1.09217 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.9225 | 1.15801 | ||||||||
\(107\) | −3.02031 | −0.291984 | −0.145992 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145992 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(108\) | 3.19117 | 0.307070 | ||||||||
\(109\) | 2.42034 | 0.231826 | 0.115913 | − | 0.993259i | \(-0.463021\pi\) | ||||
0.115913 | + | 0.993259i | \(0.463021\pi\) | |||||||
\(110\) | −20.3671 | −1.94193 | ||||||||
\(111\) | −2.16688 | −0.205671 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.39756 | 0.601832 | 0.300916 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300916 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(114\) | 3.56444 | 0.333840 | ||||||||
\(115\) | −1.44529 | −0.134774 | ||||||||
\(116\) | 25.7592 | 2.39168 | ||||||||
\(117\) | 4.10392 | 0.379408 | ||||||||
\(118\) | 1.89820 | 0.174743 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.66075 | 0.790615 | ||||||||
\(121\) | −3.15317 | −0.286652 | ||||||||
\(122\) | 20.6476 | 1.86935 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 13.9316 | 1.25109 | ||||||||
\(125\) | 0.585761 | 0.0523921 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.60541 | −0.408664 | −0.204332 | − | 0.978902i | \(-0.565502\pi\) | ||||
−0.204332 | + | 0.978902i | \(0.565502\pi\) | |||||||
\(128\) | −17.8610 | −1.57870 | ||||||||
\(129\) | −7.06229 | −0.621800 | ||||||||
\(130\) | 29.8388 | 2.61704 | ||||||||
\(131\) | 15.0257 | 1.31281 | 0.656403 | − | 0.754411i | \(-0.272077\pi\) | ||||
0.656403 | + | 0.754411i | \(0.272077\pi\) | |||||||
\(132\) | −8.93916 | −0.778054 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.331638 | 0.0286491 | ||||||||
\(135\) | 3.19117 | 0.274652 | ||||||||
\(136\) | 0.992388 | 0.0850966 | ||||||||
\(137\) | 9.51519 | 0.812938 | 0.406469 | − | 0.913665i | \(-0.366760\pi\) | ||||
0.406469 | + | 0.913665i | \(0.366760\pi\) | |||||||
\(138\) | −1.03190 | −0.0878413 | ||||||||
\(139\) | −6.64553 | −0.563666 | −0.281833 | − | 0.959463i | \(-0.590942\pi\) | ||||
−0.281833 | + | 0.959463i | \(0.590942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8027 | −0.993965 | ||||||||
\(142\) | −6.57960 | −0.552148 | ||||||||
\(143\) | −11.4960 | −0.961343 | ||||||||
\(144\) | −0.198780 | −0.0165650 | ||||||||
\(145\) | 25.7592 | 2.13918 | ||||||||
\(146\) | 29.0452 | 2.40380 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.91487 | −0.568399 | ||||||||
\(149\) | −9.53399 | −0.781055 | −0.390528 | − | 0.920591i | \(-0.627707\pi\) | ||||
−0.390528 | + | 0.920591i | \(0.627707\pi\) | |||||||
\(150\) | 11.8103 | 0.964306 | ||||||||
\(151\) | 6.93916 | 0.564701 | 0.282351 | − | 0.959311i | \(-0.408886\pi\) | ||||
0.282351 | + | 0.959311i | \(0.408886\pi\) | |||||||
\(152\) | 4.24585 | 0.344384 | ||||||||
\(153\) | 0.365659 | 0.0295617 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.9316 | 1.11901 | ||||||||
\(156\) | 13.0963 | 1.04854 | ||||||||
\(157\) | 12.6629 | 1.01061 | 0.505304 | − | 0.862942i | \(-0.331381\pi\) | ||||
0.505304 | + | 0.862942i | \(0.331381\pi\) | |||||||
\(158\) | −9.14489 | −0.727529 | ||||||||
\(159\) | 5.23280 | 0.414988 | ||||||||
\(160\) | −18.7668 | −1.48365 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.27841 | 0.179009 | ||||||||
\(163\) | −12.2245 | −0.957499 | −0.478749 | − | 0.877952i | \(-0.658910\pi\) | ||||
−0.478749 | + | 0.877952i | \(0.658910\pi\) | |||||||
\(164\) | 3.19117 | 0.249188 | ||||||||
\(165\) | −8.93916 | −0.695913 | ||||||||
\(166\) | −20.3671 | −1.58079 | ||||||||
\(167\) | 15.6948 | 1.21450 | 0.607249 | − | 0.794512i | \(-0.292273\pi\) | ||||
0.607249 | + | 0.794512i | \(0.292273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.84219 | 0.295553 | ||||||||
\(170\) | 2.65863 | 0.203908 | ||||||||
\(171\) | 1.56444 | 0.119636 | ||||||||
\(172\) | −22.5370 | −1.71843 | ||||||||
\(173\) | 16.4188 | 1.24830 | 0.624150 | − | 0.781304i | \(-0.285445\pi\) | ||||
0.624150 | + | 0.781304i | \(0.285445\pi\) | |||||||
\(174\) | 18.3914 | 1.39425 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.556827 | 0.0419724 | ||||||||
\(177\) | 0.833122 | 0.0626213 | ||||||||
\(178\) | −1.66624 | −0.124890 | ||||||||
\(179\) | −18.7175 | −1.39902 | −0.699508 | − | 0.714625i | \(-0.746597\pi\) | ||||
−0.699508 | + | 0.714625i | \(0.746597\pi\) | |||||||
\(180\) | 10.1836 | 0.759038 | ||||||||
\(181\) | −25.1212 | −1.86724 | −0.933622 | − | 0.358259i | \(-0.883371\pi\) | ||||
−0.933622 | + | 0.358259i | \(0.883371\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.06229 | 0.669904 | ||||||||
\(184\) | −1.22917 | −0.0906155 | ||||||||
\(185\) | −6.91487 | −0.508392 | ||||||||
\(186\) | 9.94678 | 0.729333 | ||||||||
\(187\) | −1.02429 | −0.0749035 | ||||||||
\(188\) | −37.6643 | −2.74695 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.3747 | 0.825209 | ||||||||
\(191\) | −13.5006 | −0.976872 | −0.488436 | − | 0.872600i | \(-0.662432\pi\) | ||||
−0.488436 | + | 0.872600i | \(0.662432\pi\) | |||||||
\(192\) | −13.0015 | −0.938299 | ||||||||
\(193\) | −18.3139 | −1.31826 | −0.659131 | − | 0.752028i | \(-0.729076\pi\) | ||||
−0.659131 | + | 0.752028i | \(0.729076\pi\) | |||||||
\(194\) | −33.6795 | −2.41805 | ||||||||
\(195\) | 13.0963 | 0.937846 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6054 | 1.04059 | 0.520296 | − | 0.853986i | \(-0.325822\pi\) | ||||
0.520296 | + | 0.853986i | \(0.325822\pi\) | |||||||
\(198\) | −6.38234 | −0.453573 | ||||||||
\(199\) | 19.7917 | 1.40300 | 0.701500 | − | 0.712670i | \(-0.252514\pi\) | ||||
0.701500 | + | 0.712670i | \(0.252514\pi\) | |||||||
\(200\) | 14.0680 | 0.994761 | ||||||||
\(201\) | 0.145556 | 0.0102668 | ||||||||
\(202\) | 22.7009 | 1.59723 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.16688 | 0.0816978 | ||||||||
\(205\) | 3.19117 | 0.222881 | ||||||||
\(206\) | −33.8041 | −2.35525 | ||||||||
\(207\) | −0.452904 | −0.0314790 | ||||||||
\(208\) | −0.815779 | −0.0565641 | ||||||||
\(209\) | −4.38234 | −0.303133 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5431 | −1.62077 | −0.810386 | − | 0.585897i | \(-0.800742\pi\) | ||||
−0.810386 | + | 0.585897i | \(0.800742\pi\) | |||||||
\(212\) | 16.6988 | 1.14687 | ||||||||
\(213\) | −2.88780 | −0.197869 | ||||||||
\(214\) | −6.88152 | −0.470411 | ||||||||
\(215\) | −22.5370 | −1.53701 | ||||||||
\(216\) | 2.71397 | 0.184663 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.51453 | 0.373491 | ||||||||
\(219\) | 12.7480 | 0.861430 | ||||||||
\(220\) | −28.5264 | −1.92325 | ||||||||
\(221\) | 1.50064 | 0.100944 | ||||||||
\(222\) | −4.93705 | −0.331353 | ||||||||
\(223\) | −14.9945 | −1.00411 | −0.502053 | − | 0.864837i | \(-0.667422\pi\) | ||||
−0.502053 | + | 0.864837i | \(0.667422\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.18356 | 0.345570 | ||||||||
\(226\) | 14.5763 | 0.969600 | ||||||||
\(227\) | 6.47321 | 0.429642 | 0.214821 | − | 0.976653i | \(-0.431083\pi\) | ||||
0.214821 | + | 0.976653i | \(0.431083\pi\) | |||||||
\(228\) | 4.99239 | 0.330629 | ||||||||
\(229\) | −24.8914 | −1.64487 | −0.822434 | − | 0.568860i | \(-0.807385\pi\) | ||||
−0.822434 | + | 0.568860i | \(0.807385\pi\) | |||||||
\(230\) | −3.29297 | −0.217132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.9073 | 1.43828 | ||||||||
\(233\) | 7.89820 | 0.517428 | 0.258714 | − | 0.965954i | \(-0.416701\pi\) | ||||
0.258714 | + | 0.965954i | \(0.416701\pi\) | |||||||
\(234\) | 9.35044 | 0.611257 | ||||||||
\(235\) | −37.6643 | −2.45695 | ||||||||
\(236\) | 2.65863 | 0.173062 | ||||||||
\(237\) | −4.01371 | −0.260719 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7951 | −1.15107 | −0.575533 | − | 0.817778i | \(-0.695206\pi\) | ||||
−0.575533 | + | 0.817778i | \(0.695206\pi\) | |||||||
\(240\) | −0.634341 | −0.0409466 | ||||||||
\(241\) | 19.1531 | 1.23376 | 0.616880 | − | 0.787057i | \(-0.288396\pi\) | ||||
0.616880 | + | 0.787057i | \(0.288396\pi\) | |||||||
\(242\) | −7.18422 | −0.461819 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 28.9193 | 1.85137 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.27841 | 0.145266 | ||||||||
\(247\) | 6.42034 | 0.408516 | ||||||||
\(248\) | 11.8483 | 0.752367 | ||||||||
\(249\) | −8.93916 | −0.566497 | ||||||||
\(250\) | 1.33461 | 0.0844079 | ||||||||
\(251\) | −2.92394 | −0.184558 | −0.0922788 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922788 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26868 | 0.0797614 | ||||||||
\(254\) | −10.4930 | −0.658391 | ||||||||
\(255\) | 1.16688 | 0.0730728 | ||||||||
\(256\) | −14.6918 | −0.918238 | ||||||||
\(257\) | −15.8663 | −0.989712 | −0.494856 | − | 0.868975i | \(-0.664779\pi\) | ||||
−0.494856 | + | 0.868975i | \(0.664779\pi\) | |||||||
\(258\) | −16.0908 | −1.00177 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 41.7925 | 2.59186 | ||||||||
\(261\) | 8.07202 | 0.499646 | ||||||||
\(262\) | 34.2349 | 2.11504 | ||||||||
\(263\) | 14.4717 | 0.892363 | 0.446182 | − | 0.894942i | \(-0.352784\pi\) | ||||
0.446182 | + | 0.894942i | \(0.352784\pi\) | |||||||
\(264\) | −7.60244 | −0.467898 | ||||||||
\(265\) | 16.6988 | 1.02580 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.731317 | −0.0447559 | ||||||||
\(268\) | 0.464495 | 0.0283735 | ||||||||
\(269\) | 3.38553 | 0.206419 | 0.103210 | − | 0.994660i | \(-0.467089\pi\) | ||||
0.103210 | + | 0.994660i | \(0.467089\pi\) | |||||||
\(270\) | 7.27080 | 0.442487 | ||||||||
\(271\) | 1.63646 | 0.0994079 | 0.0497039 | − | 0.998764i | \(-0.484172\pi\) | ||||
0.0497039 | + | 0.998764i | \(0.484172\pi\) | |||||||
\(272\) | −0.0726857 | −0.00440722 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.6795 | 1.30971 | ||||||||
\(275\) | −14.5203 | −0.875606 | ||||||||
\(276\) | −1.44529 | −0.0869964 | ||||||||
\(277\) | −28.5793 | −1.71716 | −0.858581 | − | 0.512679i | \(-0.828653\pi\) | ||||
−0.858581 | + | 0.512679i | \(0.828653\pi\) | |||||||
\(278\) | −15.1413 | −0.908112 | ||||||||
\(279\) | 4.36566 | 0.261365 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4814 | 1.04285 | 0.521427 | − | 0.853296i | \(-0.325400\pi\) | ||||
0.521427 | + | 0.853296i | \(0.325400\pi\) | |||||||
\(282\) | −26.8914 | −1.60136 | ||||||||
\(283\) | 30.8160 | 1.83182 | 0.915912 | − | 0.401380i | \(-0.131469\pi\) | ||||
0.915912 | + | 0.401380i | \(0.131469\pi\) | |||||||
\(284\) | −9.21546 | −0.546837 | ||||||||
\(285\) | 4.99239 | 0.295724 | ||||||||
\(286\) | −26.1926 | −1.54880 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.88085 | −0.346533 | ||||||||
\(289\) | −16.8663 | −0.992135 | ||||||||
\(290\) | 58.6901 | 3.44640 | ||||||||
\(291\) | −14.7820 | −0.866537 | ||||||||
\(292\) | 40.6810 | 2.38068 | ||||||||
\(293\) | −30.7661 | −1.79738 | −0.898688 | − | 0.438588i | \(-0.855479\pi\) | ||||
−0.898688 | + | 0.438588i | \(0.855479\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.65863 | 0.154792 | ||||||||
\(296\) | −5.88085 | −0.341818 | ||||||||
\(297\) | −2.80122 | −0.162543 | ||||||||
\(298\) | −21.7224 | −1.25834 | ||||||||
\(299\) | −1.85868 | −0.107490 | ||||||||
\(300\) | 16.5416 | 0.955030 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.8103 | 0.909780 | ||||||||
\(303\) | 9.96345 | 0.572386 | ||||||||
\(304\) | −0.310980 | −0.0178359 | ||||||||
\(305\) | 28.9193 | 1.65591 | ||||||||
\(306\) | 0.833122 | 0.0476264 | ||||||||
\(307\) | 30.1966 | 1.72341 | 0.861706 | − | 0.507409i | \(-0.169397\pi\) | ||||
0.861706 | + | 0.507409i | \(0.169397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.8367 | −0.844030 | ||||||||
\(310\) | 31.7418 | 1.80282 | ||||||||
\(311\) | −7.18321 | −0.407322 | −0.203661 | − | 0.979041i | \(-0.565284\pi\) | ||||
−0.203661 | + | 0.979041i | \(0.565284\pi\) | |||||||
\(312\) | 11.1379 | 0.630562 | ||||||||
\(313\) | −26.1415 | −1.47761 | −0.738803 | − | 0.673921i | \(-0.764609\pi\) | ||||
−0.738803 | + | 0.673921i | \(0.764609\pi\) | |||||||
\(314\) | 28.8513 | 1.62817 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.8084 | −0.720530 | ||||||||
\(317\) | −29.7226 | −1.66939 | −0.834695 | − | 0.550713i | \(-0.814356\pi\) | ||||
−0.834695 | + | 0.550713i | \(0.814356\pi\) | |||||||
\(318\) | 11.9225 | 0.668580 | ||||||||
\(319\) | −22.6115 | −1.26600 | ||||||||
\(320\) | −41.4898 | −2.31935 | ||||||||
\(321\) | −3.02031 | −0.168577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.572051 | 0.0318297 | ||||||||
\(324\) | 3.19117 | 0.177287 | ||||||||
\(325\) | 21.2729 | 1.18001 | ||||||||
\(326\) | −27.8525 | −1.54261 | ||||||||
\(327\) | 2.42034 | 0.133845 | ||||||||
\(328\) | 2.71397 | 0.149854 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.3671 | −1.12117 | ||||||||
\(331\) | 8.41882 | 0.462740 | 0.231370 | − | 0.972866i | \(-0.425679\pi\) | ||||
0.231370 | + | 0.972866i | \(0.425679\pi\) | |||||||
\(332\) | −28.5264 | −1.56559 | ||||||||
\(333\) | −2.16688 | −0.118744 | ||||||||
\(334\) | 35.7592 | 1.95666 | ||||||||
\(335\) | 0.464495 | 0.0253781 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6708 | 1.18049 | 0.590243 | − | 0.807226i | \(-0.299032\pi\) | ||||
0.590243 | + | 0.807226i | \(0.299032\pi\) | |||||||
\(338\) | 8.75409 | 0.476160 | ||||||||
\(339\) | 6.39756 | 0.347468 | ||||||||
\(340\) | 3.72371 | 0.201946 | ||||||||
\(341\) | −12.2292 | −0.662247 | ||||||||
\(342\) | 3.56444 | 0.192743 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −19.1669 | −1.03341 | ||||||||
\(345\) | −1.44529 | −0.0778119 | ||||||||
\(346\) | 37.4089 | 2.01111 | ||||||||
\(347\) | −16.4865 | −0.885043 | −0.442521 | − | 0.896758i | \(-0.645916\pi\) | ||||
−0.442521 | + | 0.896758i | \(0.645916\pi\) | |||||||
\(348\) | 25.7592 | 1.38084 | ||||||||
\(349\) | 3.67699 | 0.196825 | 0.0984123 | − | 0.995146i | \(-0.468624\pi\) | ||||
0.0984123 | + | 0.995146i | \(0.468624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.10392 | 0.219051 | ||||||||
\(352\) | 16.4736 | 0.878044 | ||||||||
\(353\) | −25.1817 | −1.34029 | −0.670143 | − | 0.742232i | \(-0.733767\pi\) | ||||
−0.670143 | + | 0.742232i | \(0.733767\pi\) | |||||||
\(354\) | 1.89820 | 0.100888 | ||||||||
\(355\) | −9.21546 | −0.489106 | ||||||||
\(356\) | −2.33376 | −0.123689 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.6463 | −2.25393 | ||||||||
\(359\) | −7.27807 | −0.384122 | −0.192061 | − | 0.981383i | \(-0.561517\pi\) | ||||
−0.192061 | + | 0.981383i | \(0.561517\pi\) | |||||||
\(360\) | 8.66075 | 0.456462 | ||||||||
\(361\) | −16.5525 | −0.871186 | ||||||||
\(362\) | −57.2365 | −3.00828 | ||||||||
\(363\) | −3.15317 | −0.165498 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.6810 | 2.12934 | ||||||||
\(366\) | 20.6476 | 1.07927 | ||||||||
\(367\) | 6.77592 | 0.353700 | 0.176850 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176850 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(368\) | 0.0900283 | 0.00469305 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −15.7549 | −0.819061 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.9316 | 0.722317 | ||||||||
\(373\) | 28.4956 | 1.47545 | 0.737723 | − | 0.675104i | \(-0.235901\pi\) | ||||
0.737723 | + | 0.675104i | \(0.235901\pi\) | |||||||
\(374\) | −2.33376 | −0.120676 | ||||||||
\(375\) | 0.585761 | 0.0302486 | ||||||||
\(376\) | −32.0322 | −1.65193 | ||||||||
\(377\) | 33.1270 | 1.70613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8301 | 1.06997 | 0.534985 | − | 0.844862i | \(-0.320317\pi\) | ||||
0.534985 | + | 0.844862i | \(0.320317\pi\) | |||||||
\(380\) | 15.9316 | 0.817271 | ||||||||
\(381\) | −4.60541 | −0.235942 | ||||||||
\(382\) | −30.7600 | −1.57382 | ||||||||
\(383\) | −1.92567 | −0.0983974 | −0.0491987 | − | 0.998789i | \(-0.515667\pi\) | ||||
−0.0491987 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(384\) | −17.8610 | −0.911465 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.7266 | −2.12383 | ||||||||
\(387\) | −7.06229 | −0.358996 | ||||||||
\(388\) | −47.1719 | −2.39479 | ||||||||
\(389\) | −22.8513 | −1.15860 | −0.579302 | − | 0.815113i | \(-0.696675\pi\) | ||||
−0.579302 | + | 0.815113i | \(0.696675\pi\) | |||||||
\(390\) | 29.8388 | 1.51095 | ||||||||
\(391\) | −0.165608 | −0.00837516 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.0257 | 0.757949 | ||||||||
\(394\) | 33.2772 | 1.67648 | ||||||||
\(395\) | −12.8084 | −0.644462 | ||||||||
\(396\) | −8.93916 | −0.449210 | ||||||||
\(397\) | 11.3189 | 0.568078 | 0.284039 | − | 0.958813i | \(-0.408325\pi\) | ||||
0.284039 | + | 0.958813i | \(0.408325\pi\) | |||||||
\(398\) | 45.0938 | 2.26035 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.03039 | −0.0515194 | ||||||||
\(401\) | −3.89355 | −0.194435 | −0.0972174 | − | 0.995263i | \(-0.530994\pi\) | ||||
−0.0972174 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(402\) | 0.331638 | 0.0165406 | ||||||||
\(403\) | 17.9163 | 0.892476 | ||||||||
\(404\) | 31.7951 | 1.58186 | ||||||||
\(405\) | 3.19117 | 0.158570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.06990 | 0.300874 | ||||||||
\(408\) | 0.992388 | 0.0491305 | ||||||||
\(409\) | −1.72225 | −0.0851598 | −0.0425799 | − | 0.999093i | \(-0.513558\pi\) | ||||
−0.0425799 | + | 0.999093i | \(0.513558\pi\) | |||||||
\(410\) | 7.27080 | 0.359079 | ||||||||
\(411\) | 9.51519 | 0.469350 | ||||||||
\(412\) | −47.3464 | −2.33259 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.03190 | −0.0507152 | ||||||||
\(415\) | −28.5264 | −1.40030 | ||||||||
\(416\) | −24.1346 | −1.18329 | ||||||||
\(417\) | −6.64553 | −0.325433 | ||||||||
\(418\) | −9.98478 | −0.488371 | ||||||||
\(419\) | 9.49640 | 0.463929 | 0.231965 | − | 0.972724i | \(-0.425485\pi\) | ||||
0.231965 | + | 0.972724i | \(0.425485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1183 | 1.12672 | 0.563358 | − | 0.826213i | \(-0.309509\pi\) | ||||
0.563358 | + | 0.826213i | \(0.309509\pi\) | |||||||
\(422\) | −53.6408 | −2.61119 | ||||||||
\(423\) | −11.8027 | −0.573866 | ||||||||
\(424\) | 14.2017 | 0.689695 | ||||||||
\(425\) | 1.89541 | 0.0919410 | ||||||||
\(426\) | −6.57960 | −0.318783 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.63832 | −0.465886 | ||||||||
\(429\) | −11.4960 | −0.555032 | ||||||||
\(430\) | −51.3485 | −2.47625 | ||||||||
\(431\) | 21.0105 | 1.01204 | 0.506021 | − | 0.862521i | \(-0.331116\pi\) | ||||
0.506021 | + | 0.862521i | \(0.331116\pi\) | |||||||
\(432\) | −0.198780 | −0.00956382 | ||||||||
\(433\) | 18.5550 | 0.891695 | 0.445847 | − | 0.895109i | \(-0.352902\pi\) | ||||
0.445847 | + | 0.895109i | \(0.352902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.7592 | 1.23506 | ||||||||
\(436\) | 7.72371 | 0.369898 | ||||||||
\(437\) | −0.708540 | −0.0338941 | ||||||||
\(438\) | 29.0452 | 1.38783 | ||||||||
\(439\) | −20.7042 | −0.988157 | −0.494078 | − | 0.869417i | \(-0.664494\pi\) | ||||
−0.494078 | + | 0.869417i | \(0.664494\pi\) | |||||||
\(440\) | −24.2607 | −1.15658 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.41907 | 0.162628 | ||||||||
\(443\) | 19.7904 | 0.940271 | 0.470136 | − | 0.882594i | \(-0.344205\pi\) | ||||
0.470136 | + | 0.882594i | \(0.344205\pi\) | |||||||
\(444\) | −6.91487 | −0.328165 | ||||||||
\(445\) | −2.33376 | −0.110631 | ||||||||
\(446\) | −34.1637 | −1.61770 | ||||||||
\(447\) | −9.53399 | −0.450942 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.86648 | 0.135277 | 0.0676387 | − | 0.997710i | \(-0.478453\pi\) | ||||
0.0676387 | + | 0.997710i | \(0.478453\pi\) | |||||||
\(450\) | 11.8103 | 0.556742 | ||||||||
\(451\) | −2.80122 | −0.131904 | ||||||||
\(452\) | 20.4157 | 0.960273 | ||||||||
\(453\) | 6.93916 | 0.326030 | ||||||||
\(454\) | 14.7487 | 0.692189 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.24585 | 0.198830 | ||||||||
\(457\) | −2.53737 | −0.118693 | −0.0593465 | − | 0.998237i | \(-0.518902\pi\) | ||||
−0.0593465 | + | 0.998237i | \(0.518902\pi\) | |||||||
\(458\) | −56.7128 | −2.65002 | ||||||||
\(459\) | 0.365659 | 0.0170675 | ||||||||
\(460\) | −4.61217 | −0.215044 | ||||||||
\(461\) | −39.8223 | −1.85471 | −0.927354 | − | 0.374186i | \(-0.877922\pi\) | ||||
−0.927354 | + | 0.374186i | \(0.877922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8841 | 1.38883 | 0.694415 | − | 0.719574i | \(-0.255663\pi\) | ||||
0.694415 | + | 0.719574i | \(0.255663\pi\) | |||||||
\(464\) | −1.60456 | −0.0744898 | ||||||||
\(465\) | 13.9316 | 0.646060 | ||||||||
\(466\) | 17.9954 | 0.833619 | ||||||||
\(467\) | −4.18931 | −0.193858 | −0.0969290 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969290 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(468\) | 13.0963 | 0.605377 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −85.8149 | −3.95835 | ||||||||
\(471\) | 12.6629 | 0.583474 | ||||||||
\(472\) | 2.26107 | 0.104074 | ||||||||
\(473\) | 19.7830 | 0.909625 | ||||||||
\(474\) | −9.14489 | −0.420039 | ||||||||
\(475\) | 8.10936 | 0.372083 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.23280 | 0.239594 | ||||||||
\(478\) | −40.5445 | −1.85446 | ||||||||
\(479\) | −16.2393 | −0.741995 | −0.370997 | − | 0.928634i | \(-0.620984\pi\) | ||||
−0.370997 | + | 0.928634i | \(0.620984\pi\) | |||||||
\(480\) | −18.7668 | −0.856583 | ||||||||
\(481\) | −8.89270 | −0.405472 | ||||||||
\(482\) | 43.6387 | 1.98769 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0623 | −0.457377 | ||||||||
\(485\) | −47.1719 | −2.14197 | ||||||||
\(486\) | 2.27841 | 0.103351 | ||||||||
\(487\) | 38.6296 | 1.75048 | 0.875238 | − | 0.483692i | \(-0.160705\pi\) | ||||
0.875238 | + | 0.483692i | \(0.160705\pi\) | |||||||
\(488\) | 24.5948 | 1.11336 | ||||||||
\(489\) | −12.2245 | −0.552812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.1119 | −1.94561 | −0.972807 | − | 0.231618i | \(-0.925598\pi\) | ||||
−0.972807 | + | 0.231618i | \(0.925598\pi\) | |||||||
\(492\) | 3.19117 | 0.143869 | ||||||||
\(493\) | 2.95160 | 0.132934 | ||||||||
\(494\) | 14.6282 | 0.658153 | ||||||||
\(495\) | −8.93916 | −0.401786 | ||||||||
\(496\) | −0.867807 | −0.0389657 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −20.3671 | −0.912672 | ||||||||
\(499\) | −23.4401 | −1.04933 | −0.524663 | − | 0.851310i | \(-0.675808\pi\) | ||||
−0.524663 | + | 0.851310i | \(0.675808\pi\) | |||||||
\(500\) | 1.86926 | 0.0835959 | ||||||||
\(501\) | 15.6948 | 0.701191 | ||||||||
\(502\) | −6.66195 | −0.297337 | ||||||||
\(503\) | 38.4461 | 1.71423 | 0.857113 | − | 0.515128i | \(-0.172256\pi\) | ||||
0.857113 | + | 0.515128i | \(0.172256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7951 | 1.41486 | ||||||||
\(506\) | 2.89058 | 0.128502 | ||||||||
\(507\) | 3.84219 | 0.170638 | ||||||||
\(508\) | −14.6966 | −0.652058 | ||||||||
\(509\) | −5.36136 | −0.237638 | −0.118819 | − | 0.992916i | \(-0.537911\pi\) | ||||
−0.118819 | + | 0.992916i | \(0.537911\pi\) | |||||||
\(510\) | 2.65863 | 0.117726 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.24797 | 0.0993470 | ||||||||
\(513\) | 1.56444 | 0.0690717 | ||||||||
\(514\) | −36.1500 | −1.59451 | ||||||||
\(515\) | −47.3464 | −2.08633 | ||||||||
\(516\) | −22.5370 | −0.992134 | ||||||||
\(517\) | 33.0619 | 1.45406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.4188 | 0.720706 | ||||||||
\(520\) | 35.5431 | 1.55867 | ||||||||
\(521\) | 17.0851 | 0.748510 | 0.374255 | − | 0.927326i | \(-0.377898\pi\) | ||||
0.374255 | + | 0.927326i | \(0.377898\pi\) | |||||||
\(522\) | 18.3914 | 0.804970 | ||||||||
\(523\) | 42.0270 | 1.83771 | 0.918857 | − | 0.394592i | \(-0.129114\pi\) | ||||
0.918857 | + | 0.394592i | \(0.129114\pi\) | |||||||
\(524\) | 47.9497 | 2.09469 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.9725 | 1.43767 | ||||||||
\(527\) | 1.59634 | 0.0695377 | ||||||||
\(528\) | 0.556827 | 0.0242328 | ||||||||
\(529\) | −22.7949 | −0.991082 | ||||||||
\(530\) | 38.0467 | 1.65264 | ||||||||
\(531\) | 0.833122 | 0.0361544 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.10392 | 0.177761 | ||||||||
\(534\) | −1.66624 | −0.0721054 | ||||||||
\(535\) | −9.63832 | −0.416701 | ||||||||
\(536\) | 0.395036 | 0.0170630 | ||||||||
\(537\) | −18.7175 | −0.807722 | ||||||||
\(538\) | 7.71363 | 0.332558 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.1836 | 0.438231 | ||||||||
\(541\) | −15.4916 | −0.666035 | −0.333017 | − | 0.942921i | \(-0.608067\pi\) | ||||
−0.333017 | + | 0.942921i | \(0.608067\pi\) | |||||||
\(542\) | 3.72853 | 0.160154 | ||||||||
\(543\) | −25.1212 | −1.07805 | ||||||||
\(544\) | −2.15038 | −0.0921970 | ||||||||
\(545\) | 7.72371 | 0.330847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2850 | 0.568026 | 0.284013 | − | 0.958820i | \(-0.408334\pi\) | ||||
0.284013 | + | 0.958820i | \(0.408334\pi\) | |||||||
\(548\) | 30.3646 | 1.29711 | ||||||||
\(549\) | 9.06229 | 0.386769 | ||||||||
\(550\) | −33.0832 | −1.41067 | ||||||||
\(551\) | 12.6282 | 0.537979 | ||||||||
\(552\) | −1.22917 | −0.0523169 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −65.1154 | −2.76649 | ||||||||
\(555\) | −6.91487 | −0.293520 | ||||||||
\(556\) | −21.2070 | −0.899377 | ||||||||
\(557\) | 24.5401 | 1.03980 | 0.519900 | − | 0.854227i | \(-0.325969\pi\) | ||||
0.519900 | + | 0.854227i | \(0.325969\pi\) | |||||||
\(558\) | 9.94678 | 0.421081 | ||||||||
\(559\) | −28.9831 | −1.22585 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.02429 | −0.0432456 | ||||||||
\(562\) | 39.8299 | 1.68012 | ||||||||
\(563\) | −5.33376 | −0.224791 | −0.112396 | − | 0.993664i | \(-0.535852\pi\) | ||||
−0.112396 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(564\) | −37.6643 | −1.58595 | ||||||||
\(565\) | 20.4157 | 0.858895 | ||||||||
\(566\) | 70.2117 | 2.95122 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.83742 | −0.328851 | ||||||||
\(569\) | 35.9729 | 1.50806 | 0.754031 | − | 0.656839i | \(-0.228107\pi\) | ||||
0.754031 | + | 0.656839i | \(0.228107\pi\) | |||||||
\(570\) | 11.3747 | 0.476435 | ||||||||
\(571\) | 0.235268 | 0.00984565 | 0.00492282 | − | 0.999988i | \(-0.498433\pi\) | ||||
0.00492282 | + | 0.999988i | \(0.498433\pi\) | |||||||
\(572\) | −36.6856 | −1.53390 | ||||||||
\(573\) | −13.5006 | −0.563997 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.34765 | −0.0979039 | ||||||||
\(576\) | −13.0015 | −0.541727 | ||||||||
\(577\) | −2.22639 | −0.0926857 | −0.0463428 | − | 0.998926i | \(-0.514757\pi\) | ||||
−0.0463428 | + | 0.998926i | \(0.514757\pi\) | |||||||
\(578\) | −38.4284 | −1.59841 | ||||||||
\(579\) | −18.3139 | −0.761099 | ||||||||
\(580\) | 82.2019 | 3.41325 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −33.6795 | −1.39606 | ||||||||
\(583\) | −14.6582 | −0.607082 | ||||||||
\(584\) | 34.5977 | 1.43166 | ||||||||
\(585\) | 13.0963 | 0.541466 | ||||||||
\(586\) | −70.0980 | −2.89572 | ||||||||
\(587\) | 4.42906 | 0.182807 | 0.0914034 | − | 0.995814i | \(-0.470865\pi\) | ||||
0.0914034 | + | 0.995814i | \(0.470865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.82981 | 0.281417 | ||||||||
\(590\) | 6.05746 | 0.249382 | ||||||||
\(591\) | 14.6054 | 0.600786 | ||||||||
\(592\) | 0.430733 | 0.0177030 | ||||||||
\(593\) | −5.51308 | −0.226395 | −0.113197 | − | 0.993573i | \(-0.536109\pi\) | ||||
−0.113197 | + | 0.993573i | \(0.536109\pi\) | |||||||
\(594\) | −6.38234 | −0.261870 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.4246 | −1.24624 | ||||||||
\(597\) | 19.7917 | 0.810022 | ||||||||
\(598\) | −4.23485 | −0.173176 | ||||||||
\(599\) | −22.8187 | −0.932346 | −0.466173 | − | 0.884693i | \(-0.654368\pi\) | ||||
−0.466173 | + | 0.884693i | \(0.654368\pi\) | |||||||
\(600\) | 14.0680 | 0.574325 | ||||||||
\(601\) | −5.71233 | −0.233011 | −0.116505 | − | 0.993190i | \(-0.537169\pi\) | ||||
−0.116505 | + | 0.993190i | \(0.537169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.145556 | 0.00592751 | ||||||||
\(604\) | 22.1440 | 0.901028 | ||||||||
\(605\) | −10.0623 | −0.409090 | ||||||||
\(606\) | 22.7009 | 0.922160 | ||||||||
\(607\) | −31.4136 | −1.27504 | −0.637520 | − | 0.770434i | \(-0.720040\pi\) | ||||
−0.637520 | + | 0.770434i | \(0.720040\pi\) | |||||||
\(608\) | −9.20024 | −0.373119 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 65.8901 | 2.66781 | ||||||||
\(611\) | −48.4373 | −1.95956 | ||||||||
\(612\) | 1.16688 | 0.0471683 | ||||||||
\(613\) | −32.3543 | −1.30678 | −0.653389 | − | 0.757022i | \(-0.726654\pi\) | ||||
−0.653389 | + | 0.757022i | \(0.726654\pi\) | |||||||
\(614\) | 68.8004 | 2.77656 | ||||||||
\(615\) | 3.19117 | 0.128680 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.8668 | 0.960842 | 0.480421 | − | 0.877038i | \(-0.340484\pi\) | ||||
0.480421 | + | 0.877038i | \(0.340484\pi\) | |||||||
\(618\) | −33.8041 | −1.35980 | ||||||||
\(619\) | 25.7006 | 1.03299 | 0.516496 | − | 0.856289i | \(-0.327236\pi\) | ||||
0.516496 | + | 0.856289i | \(0.327236\pi\) | |||||||
\(620\) | 44.4579 | 1.78547 | ||||||||
\(621\) | −0.452904 | −0.0181744 | ||||||||
\(622\) | −16.3663 | −0.656230 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.815779 | −0.0326573 | ||||||||
\(625\) | −24.0485 | −0.961941 | ||||||||
\(626\) | −59.5612 | −2.38054 | ||||||||
\(627\) | −4.38234 | −0.175014 | ||||||||
\(628\) | 40.4094 | 1.61251 | ||||||||
\(629\) | −0.792338 | −0.0315926 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.74765 | −0.149192 | −0.0745958 | − | 0.997214i | \(-0.523767\pi\) | ||||
−0.0745958 | + | 0.997214i | \(0.523767\pi\) | |||||||
\(632\) | −10.8931 | −0.433305 | ||||||||
\(633\) | −23.5431 | −0.935753 | ||||||||
\(634\) | −67.7205 | −2.68952 | ||||||||
\(635\) | −14.6966 | −0.583218 | ||||||||
\(636\) | 16.6988 | 0.662149 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −51.5184 | −2.03963 | ||||||||
\(639\) | −2.88780 | −0.114240 | ||||||||
\(640\) | −56.9974 | −2.25302 | ||||||||
\(641\) | 42.2215 | 1.66765 | 0.833824 | − | 0.552030i | \(-0.186146\pi\) | ||||
0.833824 | + | 0.552030i | \(0.186146\pi\) | |||||||
\(642\) | −6.88152 | −0.271592 | ||||||||
\(643\) | 0.685358 | 0.0270279 | 0.0135139 | − | 0.999909i | \(-0.495698\pi\) | ||||
0.0135139 | + | 0.999909i | \(0.495698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.5370 | −0.887392 | ||||||||
\(646\) | 1.30337 | 0.0512803 | ||||||||
\(647\) | 26.8433 | 1.05532 | 0.527659 | − | 0.849456i | \(-0.323070\pi\) | ||||
0.527659 | + | 0.849456i | \(0.323070\pi\) | |||||||
\(648\) | 2.71397 | 0.106615 | ||||||||
\(649\) | −2.33376 | −0.0916080 | ||||||||
\(650\) | 48.4685 | 1.90109 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −39.0105 | −1.52777 | ||||||||
\(653\) | 20.9486 | 0.819781 | 0.409891 | − | 0.912135i | \(-0.365567\pi\) | ||||
0.409891 | + | 0.912135i | \(0.365567\pi\) | |||||||
\(654\) | 5.51453 | 0.215635 | ||||||||
\(655\) | 47.9497 | 1.87355 | ||||||||
\(656\) | −0.198780 | −0.00776107 | ||||||||
\(657\) | 12.7480 | 0.497347 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9586 | −1.59552 | −0.797761 | − | 0.602974i | \(-0.793982\pi\) | ||||
−0.797761 | + | 0.602974i | \(0.793982\pi\) | |||||||
\(660\) | −28.5264 | −1.11039 | ||||||||
\(661\) | −24.5184 | −0.953656 | −0.476828 | − | 0.878997i | \(-0.658214\pi\) | ||||
−0.476828 | + | 0.878997i | \(0.658214\pi\) | |||||||
\(662\) | 19.1816 | 0.745513 | ||||||||
\(663\) | 1.50064 | 0.0582798 | ||||||||
\(664\) | −24.2607 | −0.941496 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.93705 | −0.191307 | ||||||||
\(667\) | −3.65585 | −0.141555 | ||||||||
\(668\) | 50.0847 | 1.93783 | ||||||||
\(669\) | −14.9945 | −0.579721 | ||||||||
\(670\) | 1.05831 | 0.0408861 | ||||||||
\(671\) | −25.3855 | −0.979995 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3565 | −0.707592 | −0.353796 | − | 0.935323i | \(-0.615109\pi\) | ||||
−0.353796 | + | 0.935323i | \(0.615109\pi\) | |||||||
\(674\) | 49.3751 | 1.90186 | ||||||||
\(675\) | 5.18356 | 0.199515 | ||||||||
\(676\) | 12.2611 | 0.471580 | ||||||||
\(677\) | 37.4309 | 1.43858 | 0.719292 | − | 0.694707i | \(-0.244466\pi\) | ||||
0.719292 | + | 0.694707i | \(0.244466\pi\) | |||||||
\(678\) | 14.5763 | 0.559799 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.16688 | 0.121444 | ||||||||
\(681\) | 6.47321 | 0.248054 | ||||||||
\(682\) | −27.8631 | −1.06693 | ||||||||
\(683\) | 35.2411 | 1.34846 | 0.674232 | − | 0.738519i | \(-0.264475\pi\) | ||||
0.674232 | + | 0.738519i | \(0.264475\pi\) | |||||||
\(684\) | 4.99239 | 0.190889 | ||||||||
\(685\) | 30.3646 | 1.16017 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.8914 | −0.949665 | ||||||||
\(688\) | 1.40384 | 0.0535211 | ||||||||
\(689\) | 21.4750 | 0.818133 | ||||||||
\(690\) | −3.29297 | −0.125361 | ||||||||
\(691\) | −19.9907 | −0.760483 | −0.380241 | − | 0.924887i | \(-0.624159\pi\) | ||||
−0.380241 | + | 0.924887i | \(0.624159\pi\) | |||||||
\(692\) | 52.3952 | 1.99177 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −37.5631 | −1.42588 | ||||||||
\(695\) | −21.2070 | −0.804427 | ||||||||
\(696\) | 21.9073 | 0.830393 | ||||||||
\(697\) | 0.365659 | 0.0138503 | ||||||||
\(698\) | 8.37769 | 0.317100 | ||||||||
\(699\) | 7.89820 | 0.298737 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.6705 | 1.04510 | 0.522550 | − | 0.852609i | \(-0.324981\pi\) | ||||
0.522550 | + | 0.852609i | \(0.324981\pi\) | |||||||
\(702\) | 9.35044 | 0.352909 | ||||||||
\(703\) | −3.38995 | −0.127854 | ||||||||
\(704\) | 36.4199 | 1.37263 | ||||||||
\(705\) | −37.6643 | −1.41852 | ||||||||
\(706\) | −57.3743 | −2.15931 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.65863 | 0.0999175 | ||||||||
\(709\) | 2.59151 | 0.0973263 | 0.0486631 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486631 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(710\) | −20.9966 | −0.787989 | ||||||||
\(711\) | −4.01371 | −0.150526 | ||||||||
\(712\) | −1.98478 | −0.0743826 | ||||||||
\(713\) | −1.97722 | −0.0740476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.6856 | −1.37197 | ||||||||
\(716\) | −59.7309 | −2.23225 | ||||||||
\(717\) | −17.7951 | −0.664569 | ||||||||
\(718\) | −16.5824 | −0.618851 | ||||||||
\(719\) | 46.5093 | 1.73450 | 0.867252 | − | 0.497869i | \(-0.165884\pi\) | ||||
0.867252 | + | 0.497869i | \(0.165884\pi\) | |||||||
\(720\) | −0.634341 | −0.0236405 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.7135 | −1.40355 | ||||||||
\(723\) | 19.1531 | 0.712312 | ||||||||
\(724\) | −80.1660 | −2.97935 | ||||||||
\(725\) | 41.8418 | 1.55396 | ||||||||
\(726\) | −7.18422 | −0.266631 | ||||||||
\(727\) | −48.2686 | −1.79018 | −0.895092 | − | 0.445881i | \(-0.852890\pi\) | ||||
−0.895092 | + | 0.445881i | \(0.852890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 92.6882 | 3.43054 | ||||||||
\(731\) | −2.58239 | −0.0955131 | ||||||||
\(732\) | 28.9193 | 1.06889 | ||||||||
\(733\) | −18.7387 | −0.692131 | −0.346066 | − | 0.938210i | \(-0.612483\pi\) | ||||
−0.346066 | + | 0.938210i | \(0.612483\pi\) | |||||||
\(734\) | 15.4383 | 0.569840 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.66346 | 0.0981764 | ||||||||
\(737\) | −0.407735 | −0.0150191 | ||||||||
\(738\) | 2.27841 | 0.0838696 | ||||||||
\(739\) | 1.91819 | 0.0705617 | 0.0352809 | − | 0.999377i | \(-0.488767\pi\) | ||||
0.0352809 | + | 0.999377i | \(0.488767\pi\) | |||||||
\(740\) | −22.0665 | −0.811182 | ||||||||
\(741\) | 6.42034 | 0.235857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7346 | −0.467188 | −0.233594 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233594 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(744\) | 11.8483 | 0.434379 | ||||||||
\(745\) | −30.4246 | −1.11467 | ||||||||
\(746\) | 64.9247 | 2.37706 | ||||||||
\(747\) | −8.93916 | −0.327067 | ||||||||
\(748\) | −3.26868 | −0.119515 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.33461 | 0.0487329 | ||||||||
\(751\) | −33.0529 | −1.20612 | −0.603060 | − | 0.797696i | \(-0.706052\pi\) | ||||
−0.603060 | + | 0.797696i | \(0.706052\pi\) | |||||||
\(752\) | 2.34614 | 0.0855549 | ||||||||
\(753\) | −2.92394 | −0.106554 | ||||||||
\(754\) | 75.4769 | 2.74871 | ||||||||
\(755\) | 22.1440 | 0.805904 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.8255 | 1.15672 | 0.578359 | − | 0.815782i | \(-0.303693\pi\) | ||||
0.578359 | + | 0.815782i | \(0.303693\pi\) | |||||||
\(758\) | 47.4596 | 1.72381 | ||||||||
\(759\) | 1.26868 | 0.0460503 | ||||||||
\(760\) | 13.5492 | 0.491482 | ||||||||
\(761\) | 11.3657 | 0.412005 | 0.206002 | − | 0.978551i | \(-0.433955\pi\) | ||||
0.206002 | + | 0.978551i | \(0.433955\pi\) | |||||||
\(762\) | −10.4930 | −0.380122 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −43.0828 | −1.55868 | ||||||||
\(765\) | 1.16688 | 0.0421886 | ||||||||
\(766\) | −4.38748 | −0.158526 | ||||||||
\(767\) | 3.41907 | 0.123455 | ||||||||
\(768\) | −14.6918 | −0.530145 | ||||||||
\(769\) | 21.5566 | 0.777351 | 0.388676 | − | 0.921375i | \(-0.372933\pi\) | ||||
0.388676 | + | 0.921375i | \(0.372933\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8663 | −0.571411 | ||||||||
\(772\) | −58.4427 | −2.10340 | ||||||||
\(773\) | −21.2790 | −0.765353 | −0.382677 | − | 0.923882i | \(-0.624998\pi\) | ||||
−0.382677 | + | 0.923882i | \(0.624998\pi\) | |||||||
\(774\) | −16.0908 | −0.578373 | ||||||||
\(775\) | 22.6296 | 0.812881 | ||||||||
\(776\) | −40.1180 | −1.44015 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −52.0646 | −1.86661 | ||||||||
\(779\) | 1.56444 | 0.0560518 | ||||||||
\(780\) | 41.7925 | 1.49641 | ||||||||
\(781\) | 8.08936 | 0.289460 | ||||||||
\(782\) | −0.377324 | −0.0134931 | ||||||||
\(783\) | 8.07202 | 0.288471 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.4094 | 1.44227 | ||||||||
\(786\) | 34.2349 | 1.22112 | ||||||||
\(787\) | 3.79573 | 0.135303 | 0.0676515 | − | 0.997709i | \(-0.478449\pi\) | ||||
0.0676515 | + | 0.997709i | \(0.478449\pi\) | |||||||
\(788\) | 46.6083 | 1.66035 | ||||||||
\(789\) | 14.4717 | 0.515206 | ||||||||
\(790\) | −29.1829 | −1.03828 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.60244 | −0.270141 | ||||||||
\(793\) | 37.1909 | 1.32069 | ||||||||
\(794\) | 25.7891 | 0.915221 | ||||||||
\(795\) | 16.6988 | 0.592244 | ||||||||
\(796\) | 63.1588 | 2.23860 | ||||||||
\(797\) | −25.8936 | −0.917197 | −0.458598 | − | 0.888644i | \(-0.651648\pi\) | ||||
−0.458598 | + | 0.888644i | \(0.651648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.31575 | −0.152680 | ||||||||
\(800\) | −30.4837 | −1.07776 | ||||||||
\(801\) | −0.731317 | −0.0258398 | ||||||||
\(802\) | −8.87112 | −0.313250 | ||||||||
\(803\) | −35.7099 | −1.26018 | ||||||||
\(804\) | 0.464495 | 0.0163815 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.8208 | 1.43785 | ||||||||
\(807\) | 3.38553 | 0.119176 | ||||||||
\(808\) | 27.0406 | 0.951284 | ||||||||
\(809\) | 13.1402 | 0.461987 | 0.230993 | − | 0.972955i | \(-0.425802\pi\) | ||||
0.230993 | + | 0.972955i | \(0.425802\pi\) | |||||||
\(810\) | 7.27080 | 0.255470 | ||||||||
\(811\) | 4.66221 | 0.163712 | 0.0818561 | − | 0.996644i | \(-0.473915\pi\) | ||||
0.0818561 | + | 0.996644i | \(0.473915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.63646 | 0.0573932 | ||||||||
\(814\) | 13.8297 | 0.484732 | ||||||||
\(815\) | −39.0105 | −1.36648 | ||||||||
\(816\) | −0.0726857 | −0.00254451 | ||||||||
\(817\) | −11.0485 | −0.386539 | ||||||||
\(818\) | −3.92400 | −0.137199 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.1836 | 0.355625 | ||||||||
\(821\) | 34.3697 | 1.19951 | 0.599756 | − | 0.800183i | \(-0.295264\pi\) | ||||
0.599756 | + | 0.800183i | \(0.295264\pi\) | |||||||
\(822\) | 21.6795 | 0.756161 | ||||||||
\(823\) | 8.02673 | 0.279794 | 0.139897 | − | 0.990166i | \(-0.455323\pi\) | ||||
0.139897 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(824\) | −40.2664 | −1.40275 | ||||||||
\(825\) | −14.5203 | −0.505531 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.5305 | −1.47893 | −0.739464 | − | 0.673196i | \(-0.764921\pi\) | ||||
−0.739464 | + | 0.673196i | \(0.764921\pi\) | |||||||
\(828\) | −1.44529 | −0.0502274 | ||||||||
\(829\) | −43.9410 | −1.52613 | −0.763066 | − | 0.646320i | \(-0.776307\pi\) | ||||
−0.763066 | + | 0.646320i | \(0.776307\pi\) | |||||||
\(830\) | −64.9949 | −2.25601 | ||||||||
\(831\) | −28.5793 | −0.991403 | ||||||||
\(832\) | −53.3570 | −1.84982 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.1413 | −0.524299 | ||||||||
\(835\) | 50.0847 | 1.73325 | ||||||||
\(836\) | −13.9848 | −0.483674 | ||||||||
\(837\) | 4.36566 | 0.150899 | ||||||||
\(838\) | 21.6367 | 0.747428 | ||||||||
\(839\) | 16.2516 | 0.561068 | 0.280534 | − | 0.959844i | \(-0.409489\pi\) | ||||
0.280534 | + | 0.959844i | \(0.409489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.1575 | 1.24681 | ||||||||
\(842\) | 52.6730 | 1.81523 | ||||||||
\(843\) | 17.4814 | 0.602093 | ||||||||
\(844\) | −75.1299 | −2.58608 | ||||||||
\(845\) | 12.2611 | 0.421794 | ||||||||
\(846\) | −26.8914 | −0.924545 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.04018 | −0.0357198 | ||||||||
\(849\) | 30.8160 | 1.05760 | ||||||||
\(850\) | 4.31853 | 0.148124 | ||||||||
\(851\) | 0.981387 | 0.0336415 | ||||||||
\(852\) | −9.21546 | −0.315716 | ||||||||
\(853\) | −29.6899 | −1.01656 | −0.508282 | − | 0.861191i | \(-0.669719\pi\) | ||||
−0.508282 | + | 0.861191i | \(0.669719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.99239 | 0.170736 | ||||||||
\(856\) | −8.19705 | −0.280169 | ||||||||
\(857\) | −24.4882 | −0.836500 | −0.418250 | − | 0.908332i | \(-0.637356\pi\) | ||||
−0.418250 | + | 0.908332i | \(0.637356\pi\) | |||||||
\(858\) | −26.1926 | −0.894201 | ||||||||
\(859\) | 13.8849 | 0.473748 | 0.236874 | − | 0.971540i | \(-0.423877\pi\) | ||||
0.236874 | + | 0.971540i | \(0.423877\pi\) | |||||||
\(860\) | −71.9192 | −2.45243 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.8707 | 1.63048 | ||||||||
\(863\) | 8.72548 | 0.297019 | 0.148509 | − | 0.988911i | \(-0.452552\pi\) | ||||
0.148509 | + | 0.988911i | \(0.452552\pi\) | |||||||
\(864\) | −5.88085 | −0.200071 | ||||||||
\(865\) | 52.3952 | 1.78149 | ||||||||
\(866\) | 42.2759 | 1.43659 | ||||||||
\(867\) | −16.8663 | −0.572809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.2433 | 0.381402 | ||||||||
\(870\) | 58.6901 | 1.98978 | ||||||||
\(871\) | 0.597352 | 0.0202405 | ||||||||
\(872\) | 6.56874 | 0.222445 | ||||||||
\(873\) | −14.7820 | −0.500295 | ||||||||
\(874\) | −1.61435 | −0.0546061 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.6810 | 1.37448 | ||||||||
\(877\) | 13.8071 | 0.466233 | 0.233116 | − | 0.972449i | \(-0.425108\pi\) | ||||
0.233116 | + | 0.972449i | \(0.425108\pi\) | |||||||
\(878\) | −47.1727 | −1.59200 | ||||||||
\(879\) | −30.7661 | −1.03772 | ||||||||
\(880\) | 1.77693 | 0.0599003 | ||||||||
\(881\) | −4.03317 | −0.135881 | −0.0679405 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679405 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.1604 | −0.409229 | −0.204615 | − | 0.978843i | \(-0.565594\pi\) | ||||
−0.204615 | + | 0.978843i | \(0.565594\pi\) | |||||||
\(884\) | 4.78878 | 0.161064 | ||||||||
\(885\) | 2.65863 | 0.0893689 | ||||||||
\(886\) | 45.0908 | 1.51485 | ||||||||
\(887\) | −41.2121 | −1.38377 | −0.691883 | − | 0.722009i | \(-0.743219\pi\) | ||||
−0.691883 | + | 0.722009i | \(0.743219\pi\) | |||||||
\(888\) | −5.88085 | −0.197349 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.31726 | −0.178235 | ||||||||
\(891\) | −2.80122 | −0.0938444 | ||||||||
\(892\) | −47.8500 | −1.60214 | ||||||||
\(893\) | −18.4646 | −0.617893 | ||||||||
\(894\) | −21.7224 | −0.726505 | ||||||||
\(895\) | −59.7309 | −1.99658 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.85868 | −0.0620596 | ||||||||
\(898\) | 6.53102 | 0.217943 | ||||||||
\(899\) | 35.2397 | 1.17531 | ||||||||
\(900\) | 16.5416 | 0.551387 | ||||||||
\(901\) | 1.91342 | 0.0637452 | ||||||||
\(902\) | −6.38234 | −0.212509 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.3628 | 0.577479 | ||||||||
\(905\) | −80.1660 | −2.66481 | ||||||||
\(906\) | 15.8103 | 0.525262 | ||||||||
\(907\) | 27.4728 | 0.912220 | 0.456110 | − | 0.889923i | \(-0.349242\pi\) | ||||
0.456110 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(908\) | 20.6571 | 0.685531 | ||||||||
\(909\) | 9.96345 | 0.330467 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.4883 | 1.63962 | 0.819811 | − | 0.572635i | \(-0.194079\pi\) | ||||
0.819811 | + | 0.572635i | \(0.194079\pi\) | |||||||
\(912\) | −0.310980 | −0.0102976 | ||||||||
\(913\) | 25.0406 | 0.828722 | ||||||||
\(914\) | −5.78117 | −0.191224 | ||||||||
\(915\) | 28.9193 | 0.956042 | ||||||||
\(916\) | −79.4326 | −2.62453 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.833122 | 0.0274971 | ||||||||
\(919\) | 28.1560 | 0.928781 | 0.464391 | − | 0.885630i | \(-0.346273\pi\) | ||||
0.464391 | + | 0.885630i | \(0.346273\pi\) | |||||||
\(920\) | −3.92249 | −0.129321 | ||||||||
\(921\) | 30.1966 | 0.995012 | ||||||||
\(922\) | −90.7316 | −2.98809 | ||||||||
\(923\) | −11.8513 | −0.390091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.2321 | −0.369310 | ||||||||
\(926\) | 68.0883 | 2.23752 | ||||||||
\(927\) | −14.8367 | −0.487301 | ||||||||
\(928\) | −47.4704 | −1.55829 | ||||||||
\(929\) | 8.89204 | 0.291738 | 0.145869 | − | 0.989304i | \(-0.453402\pi\) | ||||
0.145869 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(930\) | 31.7418 | 1.04086 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.2045 | 0.825600 | ||||||||
\(933\) | −7.18321 | −0.235168 | ||||||||
\(934\) | −9.54498 | −0.312321 | ||||||||
\(935\) | −3.26868 | −0.106897 | ||||||||
\(936\) | 11.1379 | 0.364055 | ||||||||
\(937\) | 34.2560 | 1.11910 | 0.559548 | − | 0.828798i | \(-0.310975\pi\) | ||||
0.559548 | + | 0.828798i | \(0.310975\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.1415 | −0.853096 | ||||||||
\(940\) | −120.193 | −3.92027 | ||||||||
\(941\) | 8.67367 | 0.282754 | 0.141377 | − | 0.989956i | \(-0.454847\pi\) | ||||
0.141377 | + | 0.989956i | \(0.454847\pi\) | |||||||
\(942\) | 28.8513 | 0.940025 | ||||||||
\(943\) | −0.452904 | −0.0147486 | ||||||||
\(944\) | −0.165608 | −0.00539009 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.0739 | 1.46548 | ||||||||
\(947\) | 52.3599 | 1.70147 | 0.850735 | − | 0.525595i | \(-0.176157\pi\) | ||||
0.850735 | + | 0.525595i | \(0.176157\pi\) | |||||||
\(948\) | −12.8084 | −0.415998 | ||||||||
\(949\) | 52.3168 | 1.69828 | ||||||||
\(950\) | 18.4765 | 0.599456 | ||||||||
\(951\) | −29.7226 | −0.963823 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.6281 | −1.02454 | −0.512268 | − | 0.858826i | \(-0.671194\pi\) | ||||
−0.512268 | + | 0.858826i | \(0.671194\pi\) | |||||||
\(954\) | 11.9225 | 0.386005 | ||||||||
\(955\) | −43.0828 | −1.39413 | ||||||||
\(956\) | −56.7870 | −1.83662 | ||||||||
\(957\) | −22.6115 | −0.730926 | ||||||||
\(958\) | −36.9999 | −1.19541 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −41.4898 | −1.33908 | ||||||||
\(961\) | −11.9410 | −0.385194 | ||||||||
\(962\) | −20.2613 | −0.653249 | ||||||||
\(963\) | −3.02031 | −0.0973282 | ||||||||
\(964\) | 61.1208 | 1.96857 | ||||||||
\(965\) | −58.4427 | −1.88134 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.9468 | −1.54187 | −0.770933 | − | 0.636916i | \(-0.780210\pi\) | ||||
−0.770933 | + | 0.636916i | \(0.780210\pi\) | |||||||
\(968\) | −8.55762 | −0.275052 | ||||||||
\(969\) | 0.572051 | 0.0183769 | ||||||||
\(970\) | −107.477 | −3.45088 | ||||||||
\(971\) | 22.6526 | 0.726958 | 0.363479 | − | 0.931602i | \(-0.381589\pi\) | ||||
0.363479 | + | 0.931602i | \(0.381589\pi\) | |||||||
\(972\) | 3.19117 | 0.102357 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 88.0143 | 2.82016 | ||||||||
\(975\) | 21.2729 | 0.681279 | ||||||||
\(976\) | −1.80140 | −0.0576616 | ||||||||
\(977\) | −47.6870 | −1.52564 | −0.762822 | − | 0.646609i | \(-0.776187\pi\) | ||||
−0.762822 | + | 0.646609i | \(0.776187\pi\) | |||||||
\(978\) | −27.8525 | −0.890626 | ||||||||
\(979\) | 2.04858 | 0.0654729 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.42034 | 0.0772754 | ||||||||
\(982\) | −98.2268 | −3.13454 | ||||||||
\(983\) | 18.4217 | 0.587560 | 0.293780 | − | 0.955873i | \(-0.405087\pi\) | ||||
0.293780 | + | 0.955873i | \(0.405087\pi\) | |||||||
\(984\) | 2.71397 | 0.0865184 | ||||||||
\(985\) | 46.6083 | 1.48506 | ||||||||
\(986\) | 6.72498 | 0.214167 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.4884 | 0.651822 | ||||||||
\(989\) | 3.19854 | 0.101708 | ||||||||
\(990\) | −20.3671 | −0.647309 | ||||||||
\(991\) | −32.0800 | −1.01906 | −0.509528 | − | 0.860454i | \(-0.670180\pi\) | ||||
−0.509528 | + | 0.860454i | \(0.670180\pi\) | |||||||
\(992\) | −25.6738 | −0.815144 | ||||||||
\(993\) | 8.41882 | 0.267163 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.1588 | 2.00227 | ||||||||
\(996\) | −28.5264 | −0.903893 | ||||||||
\(997\) | −1.39045 | −0.0440360 | −0.0220180 | − | 0.999758i | \(-0.507009\pi\) | ||||
−0.0220180 | + | 0.999758i | \(0.507009\pi\) | |||||||
\(998\) | −53.4063 | −1.69055 | ||||||||
\(999\) | −2.16688 | −0.0685570 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6027.2.a.u.1.4 | 4 | ||
7.6 | odd | 2 | 861.2.a.i.1.4 | ✓ | 4 | ||
21.20 | even | 2 | 2583.2.a.o.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.i.1.4 | ✓ | 4 | 7.6 | odd | 2 | ||
2583.2.a.o.1.1 | 4 | 21.20 | even | 2 | |||
6027.2.a.u.1.4 | 4 | 1.1 | even | 1 | trivial |