Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.72920\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.72920 | −1.66775 | −0.833874 | − | 0.551955i | \(-0.813882\pi\) | ||||
−0.833874 | + | 0.551955i | \(0.813882\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.41012 | −1.28890 | −0.644452 | − | 0.764645i | \(-0.722914\pi\) | ||||
−0.644452 | + | 0.764645i | \(0.722914\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.72920 | 1.17928 | ||||||||
\(11\) | 5.39669 | 1.62716 | 0.813581 | − | 0.581451i | \(-0.197515\pi\) | ||||
0.813581 | + | 0.581451i | \(0.197515\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.44904 | −0.401891 | −0.200946 | − | 0.979602i | \(-0.564401\pi\) | ||||
−0.200946 | + | 0.979602i | \(0.564401\pi\) | |||||||
\(14\) | 3.41012 | 0.911392 | ||||||||
\(15\) | 3.72920 | 0.962875 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.42732 | −1.47453 | −0.737264 | − | 0.675605i | \(-0.763882\pi\) | ||||
−0.737264 | + | 0.675605i | \(0.763882\pi\) | |||||||
\(20\) | −3.72920 | −0.833874 | ||||||||
\(21\) | 3.41012 | 0.744149 | ||||||||
\(22\) | −5.39669 | −1.15058 | ||||||||
\(23\) | −6.84877 | −1.42807 | −0.714033 | − | 0.700112i | \(-0.753133\pi\) | ||||
−0.714033 | + | 0.700112i | \(0.753133\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 8.90692 | 1.78138 | ||||||||
\(26\) | 1.44904 | 0.284180 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.41012 | −0.644452 | ||||||||
\(29\) | −5.00277 | −0.928990 | −0.464495 | − | 0.885576i | \(-0.653764\pi\) | ||||
−0.464495 | + | 0.885576i | \(0.653764\pi\) | |||||||
\(30\) | −3.72920 | −0.680855 | ||||||||
\(31\) | 8.63951 | 1.55170 | 0.775851 | − | 0.630916i | \(-0.217321\pi\) | ||||
0.775851 | + | 0.630916i | \(0.217321\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.39669 | −0.939443 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 12.7170 | 2.14957 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.89487 | 1.13351 | 0.566755 | − | 0.823887i | \(-0.308199\pi\) | ||||
0.566755 | + | 0.823887i | \(0.308199\pi\) | |||||||
\(38\) | 6.42732 | 1.04265 | ||||||||
\(39\) | 1.44904 | 0.232032 | ||||||||
\(40\) | 3.72920 | 0.589638 | ||||||||
\(41\) | 9.01653 | 1.40815 | 0.704073 | − | 0.710128i | \(-0.251363\pi\) | ||||
0.704073 | + | 0.710128i | \(0.251363\pi\) | |||||||
\(42\) | −3.41012 | −0.526193 | ||||||||
\(43\) | −6.75841 | −1.03065 | −0.515324 | − | 0.856996i | \(-0.672328\pi\) | ||||
−0.515324 | + | 0.856996i | \(0.672328\pi\) | |||||||
\(44\) | 5.39669 | 0.813581 | ||||||||
\(45\) | −3.72920 | −0.555916 | ||||||||
\(46\) | 6.84877 | 1.00980 | ||||||||
\(47\) | 2.50567 | 0.365489 | 0.182744 | − | 0.983160i | \(-0.441502\pi\) | ||||
0.182744 | + | 0.983160i | \(0.441502\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.62890 | 0.661272 | ||||||||
\(50\) | −8.90692 | −1.25963 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −1.44904 | −0.200946 | ||||||||
\(53\) | 8.69169 | 1.19389 | 0.596947 | − | 0.802280i | \(-0.296380\pi\) | ||||
0.596947 | + | 0.802280i | \(0.296380\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −20.1253 | −2.71370 | ||||||||
\(56\) | 3.41012 | 0.455696 | ||||||||
\(57\) | 6.42732 | 0.851319 | ||||||||
\(58\) | 5.00277 | 0.656895 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 3.72920 | 0.481437 | ||||||||
\(61\) | 7.26008 | 0.929558 | 0.464779 | − | 0.885427i | \(-0.346134\pi\) | ||||
0.464779 | + | 0.885427i | \(0.346134\pi\) | |||||||
\(62\) | −8.63951 | −1.09722 | ||||||||
\(63\) | −3.41012 | −0.429634 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.40376 | 0.670253 | ||||||||
\(66\) | 5.39669 | 0.664286 | ||||||||
\(67\) | −5.37634 | −0.656825 | −0.328412 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328412 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 6.84877 | 0.824495 | ||||||||
\(70\) | −12.7170 | −1.51997 | ||||||||
\(71\) | 0.0579369 | 0.00687584 | 0.00343792 | − | 0.999994i | \(-0.498906\pi\) | ||||
0.00343792 | + | 0.999994i | \(0.498906\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.4086 | −1.45231 | −0.726157 | − | 0.687529i | \(-0.758696\pi\) | ||||
−0.726157 | + | 0.687529i | \(0.758696\pi\) | |||||||
\(74\) | −6.89487 | −0.801512 | ||||||||
\(75\) | −8.90692 | −1.02848 | ||||||||
\(76\) | −6.42732 | −0.737264 | ||||||||
\(77\) | −18.4033 | −2.09726 | ||||||||
\(78\) | −1.44904 | −0.164071 | ||||||||
\(79\) | −13.3662 | −1.50381 | −0.751905 | − | 0.659271i | \(-0.770865\pi\) | ||||
−0.751905 | + | 0.659271i | \(0.770865\pi\) | |||||||
\(80\) | −3.72920 | −0.416937 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.01653 | −0.995709 | ||||||||
\(83\) | 14.1536 | 1.55356 | 0.776782 | − | 0.629770i | \(-0.216851\pi\) | ||||
0.776782 | + | 0.629770i | \(0.216851\pi\) | |||||||
\(84\) | 3.41012 | 0.372074 | ||||||||
\(85\) | 3.72920 | 0.404488 | ||||||||
\(86\) | 6.75841 | 0.728778 | ||||||||
\(87\) | 5.00277 | 0.536353 | ||||||||
\(88\) | −5.39669 | −0.575289 | ||||||||
\(89\) | 5.41906 | 0.574419 | 0.287210 | − | 0.957868i | \(-0.407272\pi\) | ||||
0.287210 | + | 0.957868i | \(0.407272\pi\) | |||||||
\(90\) | 3.72920 | 0.393092 | ||||||||
\(91\) | 4.94140 | 0.517999 | ||||||||
\(92\) | −6.84877 | −0.714033 | ||||||||
\(93\) | −8.63951 | −0.895876 | ||||||||
\(94\) | −2.50567 | −0.258440 | ||||||||
\(95\) | 23.9687 | 2.45914 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 16.4862 | 1.67392 | 0.836960 | − | 0.547265i | \(-0.184331\pi\) | ||||
0.836960 | + | 0.547265i | \(0.184331\pi\) | |||||||
\(98\) | −4.62890 | −0.467590 | ||||||||
\(99\) | 5.39669 | 0.542388 | ||||||||
\(100\) | 8.90692 | 0.890692 | ||||||||
\(101\) | 9.67501 | 0.962699 | 0.481350 | − | 0.876529i | \(-0.340147\pi\) | ||||
0.481350 | + | 0.876529i | \(0.340147\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 13.3684 | 1.31722 | 0.658612 | − | 0.752483i | \(-0.271144\pi\) | ||||
0.658612 | + | 0.752483i | \(0.271144\pi\) | |||||||
\(104\) | 1.44904 | 0.142090 | ||||||||
\(105\) | −12.7170 | −1.24105 | ||||||||
\(106\) | −8.69169 | −0.844211 | ||||||||
\(107\) | 9.76675 | 0.944187 | 0.472094 | − | 0.881548i | \(-0.343498\pi\) | ||||
0.472094 | + | 0.881548i | \(0.343498\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.15105 | −0.876511 | −0.438256 | − | 0.898850i | \(-0.644404\pi\) | ||||
−0.438256 | + | 0.898850i | \(0.644404\pi\) | |||||||
\(110\) | 20.1253 | 1.91887 | ||||||||
\(111\) | −6.89487 | −0.654432 | ||||||||
\(112\) | −3.41012 | −0.322226 | ||||||||
\(113\) | −2.01354 | −0.189418 | −0.0947090 | − | 0.995505i | \(-0.530192\pi\) | ||||
−0.0947090 | + | 0.995505i | \(0.530192\pi\) | |||||||
\(114\) | −6.42732 | −0.601973 | ||||||||
\(115\) | 25.5404 | 2.38166 | ||||||||
\(116\) | −5.00277 | −0.464495 | ||||||||
\(117\) | −1.44904 | −0.133964 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 3.41012 | 0.312605 | ||||||||
\(120\) | −3.72920 | −0.340428 | ||||||||
\(121\) | 18.1242 | 1.64766 | ||||||||
\(122\) | −7.26008 | −0.657297 | ||||||||
\(123\) | −9.01653 | −0.812993 | ||||||||
\(124\) | 8.63951 | 0.775851 | ||||||||
\(125\) | −14.5697 | −1.30315 | ||||||||
\(126\) | 3.41012 | 0.303797 | ||||||||
\(127\) | 1.18863 | 0.105474 | 0.0527371 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527371 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.75841 | 0.595044 | ||||||||
\(130\) | −5.40376 | −0.473941 | ||||||||
\(131\) | 13.5888 | 1.18726 | 0.593628 | − | 0.804739i | \(-0.297695\pi\) | ||||
0.593628 | + | 0.804739i | \(0.297695\pi\) | |||||||
\(132\) | −5.39669 | −0.469721 | ||||||||
\(133\) | 21.9179 | 1.90052 | ||||||||
\(134\) | 5.37634 | 0.464445 | ||||||||
\(135\) | 3.72920 | 0.320958 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −7.08660 | −0.605449 | −0.302725 | − | 0.953078i | \(-0.597896\pi\) | ||||
−0.302725 | + | 0.953078i | \(0.597896\pi\) | |||||||
\(138\) | −6.84877 | −0.583006 | ||||||||
\(139\) | 19.8948 | 1.68746 | 0.843729 | − | 0.536770i | \(-0.180356\pi\) | ||||
0.843729 | + | 0.536770i | \(0.180356\pi\) | |||||||
\(140\) | 12.7170 | 1.07478 | ||||||||
\(141\) | −2.50567 | −0.211015 | ||||||||
\(142\) | −0.0579369 | −0.00486195 | ||||||||
\(143\) | −7.82001 | −0.653942 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 18.6563 | 1.54932 | ||||||||
\(146\) | 12.4086 | 1.02694 | ||||||||
\(147\) | −4.62890 | −0.381785 | ||||||||
\(148\) | 6.89487 | 0.566755 | ||||||||
\(149\) | −13.8088 | −1.13126 | −0.565630 | − | 0.824659i | \(-0.691367\pi\) | ||||
−0.565630 | + | 0.824659i | \(0.691367\pi\) | |||||||
\(150\) | 8.90692 | 0.727247 | ||||||||
\(151\) | −7.58245 | −0.617051 | −0.308526 | − | 0.951216i | \(-0.599836\pi\) | ||||
−0.308526 | + | 0.951216i | \(0.599836\pi\) | |||||||
\(152\) | 6.42732 | 0.521324 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 18.4033 | 1.48298 | ||||||||
\(155\) | −32.2185 | −2.58785 | ||||||||
\(156\) | 1.44904 | 0.116016 | ||||||||
\(157\) | −5.58450 | −0.445691 | −0.222846 | − | 0.974854i | \(-0.571535\pi\) | ||||
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(158\) | 13.3662 | 1.06335 | ||||||||
\(159\) | −8.69169 | −0.689296 | ||||||||
\(160\) | 3.72920 | 0.294819 | ||||||||
\(161\) | 23.3551 | 1.84064 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.5107 | −0.901586 | −0.450793 | − | 0.892628i | \(-0.648859\pi\) | ||||
−0.450793 | + | 0.892628i | \(0.648859\pi\) | |||||||
\(164\) | 9.01653 | 0.704073 | ||||||||
\(165\) | 20.1253 | 1.56675 | ||||||||
\(166\) | −14.1536 | −1.09854 | ||||||||
\(167\) | −12.5643 | −0.972253 | −0.486126 | − | 0.873889i | \(-0.661591\pi\) | ||||
−0.486126 | + | 0.873889i | \(0.661591\pi\) | |||||||
\(168\) | −3.41012 | −0.263096 | ||||||||
\(169\) | −10.9003 | −0.838483 | ||||||||
\(170\) | −3.72920 | −0.286016 | ||||||||
\(171\) | −6.42732 | −0.491509 | ||||||||
\(172\) | −6.75841 | −0.515324 | ||||||||
\(173\) | 12.4630 | 0.947546 | 0.473773 | − | 0.880647i | \(-0.342892\pi\) | ||||
0.473773 | + | 0.880647i | \(0.342892\pi\) | |||||||
\(174\) | −5.00277 | −0.379259 | ||||||||
\(175\) | −30.3736 | −2.29603 | ||||||||
\(176\) | 5.39669 | 0.406791 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −5.41906 | −0.406176 | ||||||||
\(179\) | 21.1067 | 1.57759 | 0.788796 | − | 0.614655i | \(-0.210705\pi\) | ||||
0.788796 | + | 0.614655i | \(0.210705\pi\) | |||||||
\(180\) | −3.72920 | −0.277958 | ||||||||
\(181\) | −8.94724 | −0.665043 | −0.332522 | − | 0.943096i | \(-0.607899\pi\) | ||||
−0.332522 | + | 0.943096i | \(0.607899\pi\) | |||||||
\(182\) | −4.94140 | −0.366281 | ||||||||
\(183\) | −7.26008 | −0.536680 | ||||||||
\(184\) | 6.84877 | 0.504898 | ||||||||
\(185\) | −25.7123 | −1.89041 | ||||||||
\(186\) | 8.63951 | 0.633480 | ||||||||
\(187\) | −5.39669 | −0.394645 | ||||||||
\(188\) | 2.50567 | 0.182744 | ||||||||
\(189\) | 3.41012 | 0.248050 | ||||||||
\(190\) | −23.9687 | −1.73888 | ||||||||
\(191\) | 18.0589 | 1.30670 | 0.653348 | − | 0.757058i | \(-0.273364\pi\) | ||||
0.653348 | + | 0.757058i | \(0.273364\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −14.5709 | −1.04884 | −0.524418 | − | 0.851461i | \(-0.675717\pi\) | ||||
−0.524418 | + | 0.851461i | \(0.675717\pi\) | |||||||
\(194\) | −16.4862 | −1.18364 | ||||||||
\(195\) | −5.40376 | −0.386971 | ||||||||
\(196\) | 4.62890 | 0.330636 | ||||||||
\(197\) | −4.41973 | −0.314893 | −0.157446 | − | 0.987528i | \(-0.550326\pi\) | ||||
−0.157446 | + | 0.987528i | \(0.550326\pi\) | |||||||
\(198\) | −5.39669 | −0.383526 | ||||||||
\(199\) | −17.6247 | −1.24938 | −0.624692 | − | 0.780871i | \(-0.714775\pi\) | ||||
−0.624692 | + | 0.780871i | \(0.714775\pi\) | |||||||
\(200\) | −8.90692 | −0.629814 | ||||||||
\(201\) | 5.37634 | 0.379218 | ||||||||
\(202\) | −9.67501 | −0.680731 | ||||||||
\(203\) | 17.0600 | 1.19738 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −33.6244 | −2.34843 | ||||||||
\(206\) | −13.3684 | −0.931418 | ||||||||
\(207\) | −6.84877 | −0.476022 | ||||||||
\(208\) | −1.44904 | −0.100473 | ||||||||
\(209\) | −34.6862 | −2.39930 | ||||||||
\(210\) | 12.7170 | 0.877557 | ||||||||
\(211\) | 5.09679 | 0.350878 | 0.175439 | − | 0.984490i | \(-0.443866\pi\) | ||||
0.175439 | + | 0.984490i | \(0.443866\pi\) | |||||||
\(212\) | 8.69169 | 0.596947 | ||||||||
\(213\) | −0.0579369 | −0.00396977 | ||||||||
\(214\) | −9.76675 | −0.667641 | ||||||||
\(215\) | 25.2034 | 1.71886 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −29.4618 | −1.99999 | ||||||||
\(218\) | 9.15105 | 0.619787 | ||||||||
\(219\) | 12.4086 | 0.838494 | ||||||||
\(220\) | −20.1253 | −1.35685 | ||||||||
\(221\) | 1.44904 | 0.0974729 | ||||||||
\(222\) | 6.89487 | 0.462753 | ||||||||
\(223\) | −17.1560 | −1.14885 | −0.574426 | − | 0.818556i | \(-0.694775\pi\) | ||||
−0.574426 | + | 0.818556i | \(0.694775\pi\) | |||||||
\(224\) | 3.41012 | 0.227848 | ||||||||
\(225\) | 8.90692 | 0.593795 | ||||||||
\(226\) | 2.01354 | 0.133939 | ||||||||
\(227\) | −13.4350 | −0.891709 | −0.445855 | − | 0.895105i | \(-0.647100\pi\) | ||||
−0.445855 | + | 0.895105i | \(0.647100\pi\) | |||||||
\(228\) | 6.42732 | 0.425659 | ||||||||
\(229\) | 24.9330 | 1.64762 | 0.823810 | − | 0.566866i | \(-0.191844\pi\) | ||||
0.823810 | + | 0.566866i | \(0.191844\pi\) | |||||||
\(230\) | −25.5404 | −1.68408 | ||||||||
\(231\) | 18.4033 | 1.21085 | ||||||||
\(232\) | 5.00277 | 0.328448 | ||||||||
\(233\) | 8.01856 | 0.525313 | 0.262657 | − | 0.964889i | \(-0.415401\pi\) | ||||
0.262657 | + | 0.964889i | \(0.415401\pi\) | |||||||
\(234\) | 1.44904 | 0.0947267 | ||||||||
\(235\) | −9.34412 | −0.609543 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 13.3662 | 0.868226 | ||||||||
\(238\) | −3.41012 | −0.221045 | ||||||||
\(239\) | −0.912919 | −0.0590518 | −0.0295259 | − | 0.999564i | \(-0.509400\pi\) | ||||
−0.0295259 | + | 0.999564i | \(0.509400\pi\) | |||||||
\(240\) | 3.72920 | 0.240719 | ||||||||
\(241\) | −6.89595 | −0.444207 | −0.222104 | − | 0.975023i | \(-0.571292\pi\) | ||||
−0.222104 | + | 0.975023i | \(0.571292\pi\) | |||||||
\(242\) | −18.1242 | −1.16507 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.26008 | 0.464779 | ||||||||
\(245\) | −17.2621 | −1.10283 | ||||||||
\(246\) | 9.01653 | 0.574873 | ||||||||
\(247\) | 9.31343 | 0.592600 | ||||||||
\(248\) | −8.63951 | −0.548610 | ||||||||
\(249\) | −14.1536 | −0.896950 | ||||||||
\(250\) | 14.5697 | 0.921468 | ||||||||
\(251\) | 22.9184 | 1.44660 | 0.723298 | − | 0.690536i | \(-0.242625\pi\) | ||||
0.723298 | + | 0.690536i | \(0.242625\pi\) | |||||||
\(252\) | −3.41012 | −0.214817 | ||||||||
\(253\) | −36.9607 | −2.32370 | ||||||||
\(254\) | −1.18863 | −0.0745816 | ||||||||
\(255\) | −3.72920 | −0.233531 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.80093 | 0.299473 | 0.149737 | − | 0.988726i | \(-0.452157\pi\) | ||||
0.149737 | + | 0.988726i | \(0.452157\pi\) | |||||||
\(258\) | −6.75841 | −0.420760 | ||||||||
\(259\) | −23.5123 | −1.46098 | ||||||||
\(260\) | 5.40376 | 0.335127 | ||||||||
\(261\) | −5.00277 | −0.309663 | ||||||||
\(262\) | −13.5888 | −0.839517 | ||||||||
\(263\) | 14.1103 | 0.870081 | 0.435041 | − | 0.900411i | \(-0.356734\pi\) | ||||
0.435041 | + | 0.900411i | \(0.356734\pi\) | |||||||
\(264\) | 5.39669 | 0.332143 | ||||||||
\(265\) | −32.4130 | −1.99112 | ||||||||
\(266\) | −21.9179 | −1.34387 | ||||||||
\(267\) | −5.41906 | −0.331641 | ||||||||
\(268\) | −5.37634 | −0.328412 | ||||||||
\(269\) | −23.2981 | −1.42051 | −0.710254 | − | 0.703945i | \(-0.751420\pi\) | ||||
−0.710254 | + | 0.703945i | \(0.751420\pi\) | |||||||
\(270\) | −3.72920 | −0.226952 | ||||||||
\(271\) | −0.524590 | −0.0318666 | −0.0159333 | − | 0.999873i | \(-0.505072\pi\) | ||||
−0.0159333 | + | 0.999873i | \(0.505072\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −4.94140 | −0.299067 | ||||||||
\(274\) | 7.08660 | 0.428117 | ||||||||
\(275\) | 48.0679 | 2.89860 | ||||||||
\(276\) | 6.84877 | 0.412247 | ||||||||
\(277\) | −23.6475 | −1.42084 | −0.710420 | − | 0.703778i | \(-0.751495\pi\) | ||||
−0.710420 | + | 0.703778i | \(0.751495\pi\) | |||||||
\(278\) | −19.8948 | −1.19321 | ||||||||
\(279\) | 8.63951 | 0.517234 | ||||||||
\(280\) | −12.7170 | −0.759986 | ||||||||
\(281\) | 10.7845 | 0.643352 | 0.321676 | − | 0.946850i | \(-0.395754\pi\) | ||||
0.321676 | + | 0.946850i | \(0.395754\pi\) | |||||||
\(282\) | 2.50567 | 0.149210 | ||||||||
\(283\) | −13.2487 | −0.787553 | −0.393776 | − | 0.919206i | \(-0.628832\pi\) | ||||
−0.393776 | + | 0.919206i | \(0.628832\pi\) | |||||||
\(284\) | 0.0579369 | 0.00343792 | ||||||||
\(285\) | −23.9687 | −1.41979 | ||||||||
\(286\) | 7.82001 | 0.462407 | ||||||||
\(287\) | −30.7474 | −1.81496 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −18.6563 | −1.09554 | ||||||||
\(291\) | −16.4862 | −0.966438 | ||||||||
\(292\) | −12.4086 | −0.726157 | ||||||||
\(293\) | 7.93575 | 0.463612 | 0.231806 | − | 0.972762i | \(-0.425537\pi\) | ||||
0.231806 | + | 0.972762i | \(0.425537\pi\) | |||||||
\(294\) | 4.62890 | 0.269963 | ||||||||
\(295\) | 3.72920 | 0.217122 | ||||||||
\(296\) | −6.89487 | −0.400756 | ||||||||
\(297\) | −5.39669 | −0.313148 | ||||||||
\(298\) | 13.8088 | 0.799922 | ||||||||
\(299\) | 9.92413 | 0.573927 | ||||||||
\(300\) | −8.90692 | −0.514241 | ||||||||
\(301\) | 23.0470 | 1.32840 | ||||||||
\(302\) | 7.58245 | 0.436321 | ||||||||
\(303\) | −9.67501 | −0.555815 | ||||||||
\(304\) | −6.42732 | −0.368632 | ||||||||
\(305\) | −27.0743 | −1.55027 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −16.7504 | −0.955996 | −0.477998 | − | 0.878361i | \(-0.658637\pi\) | ||||
−0.477998 | + | 0.878361i | \(0.658637\pi\) | |||||||
\(308\) | −18.4033 | −1.04863 | ||||||||
\(309\) | −13.3684 | −0.760499 | ||||||||
\(310\) | 32.2185 | 1.82989 | ||||||||
\(311\) | −25.3463 | −1.43726 | −0.718629 | − | 0.695394i | \(-0.755230\pi\) | ||||
−0.718629 | + | 0.695394i | \(0.755230\pi\) | |||||||
\(312\) | −1.44904 | −0.0820357 | ||||||||
\(313\) | −3.98350 | −0.225161 | −0.112580 | − | 0.993643i | \(-0.535912\pi\) | ||||
−0.112580 | + | 0.993643i | \(0.535912\pi\) | |||||||
\(314\) | 5.58450 | 0.315151 | ||||||||
\(315\) | 12.7170 | 0.716522 | ||||||||
\(316\) | −13.3662 | −0.751905 | ||||||||
\(317\) | −13.3269 | −0.748511 | −0.374255 | − | 0.927326i | \(-0.622102\pi\) | ||||
−0.374255 | + | 0.927326i | \(0.622102\pi\) | |||||||
\(318\) | 8.69169 | 0.487406 | ||||||||
\(319\) | −26.9984 | −1.51162 | ||||||||
\(320\) | −3.72920 | −0.208469 | ||||||||
\(321\) | −9.76675 | −0.545127 | ||||||||
\(322\) | −23.3551 | −1.30153 | ||||||||
\(323\) | 6.42732 | 0.357625 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −12.9065 | −0.715923 | ||||||||
\(326\) | 11.5107 | 0.637518 | ||||||||
\(327\) | 9.15105 | 0.506054 | ||||||||
\(328\) | −9.01653 | −0.497855 | ||||||||
\(329\) | −8.54461 | −0.471080 | ||||||||
\(330\) | −20.1253 | −1.10786 | ||||||||
\(331\) | 1.85247 | 0.101821 | 0.0509106 | − | 0.998703i | \(-0.483788\pi\) | ||||
0.0509106 | + | 0.998703i | \(0.483788\pi\) | |||||||
\(332\) | 14.1536 | 0.776782 | ||||||||
\(333\) | 6.89487 | 0.377836 | ||||||||
\(334\) | 12.5643 | 0.687486 | ||||||||
\(335\) | 20.0494 | 1.09542 | ||||||||
\(336\) | 3.41012 | 0.186037 | ||||||||
\(337\) | 24.5279 | 1.33612 | 0.668060 | − | 0.744108i | \(-0.267125\pi\) | ||||
0.668060 | + | 0.744108i | \(0.267125\pi\) | |||||||
\(338\) | 10.9003 | 0.592897 | ||||||||
\(339\) | 2.01354 | 0.109361 | ||||||||
\(340\) | 3.72920 | 0.202244 | ||||||||
\(341\) | 46.6248 | 2.52487 | ||||||||
\(342\) | 6.42732 | 0.347549 | ||||||||
\(343\) | 8.08572 | 0.436588 | ||||||||
\(344\) | 6.75841 | 0.364389 | ||||||||
\(345\) | −25.5404 | −1.37505 | ||||||||
\(346\) | −12.4630 | −0.670016 | ||||||||
\(347\) | −23.8090 | −1.27813 | −0.639066 | − | 0.769152i | \(-0.720679\pi\) | ||||
−0.639066 | + | 0.769152i | \(0.720679\pi\) | |||||||
\(348\) | 5.00277 | 0.268176 | ||||||||
\(349\) | −27.5691 | −1.47574 | −0.737871 | − | 0.674942i | \(-0.764169\pi\) | ||||
−0.737871 | + | 0.674942i | \(0.764169\pi\) | |||||||
\(350\) | 30.3736 | 1.62354 | ||||||||
\(351\) | 1.44904 | 0.0773440 | ||||||||
\(352\) | −5.39669 | −0.287644 | ||||||||
\(353\) | −15.1210 | −0.804812 | −0.402406 | − | 0.915461i | \(-0.631826\pi\) | ||||
−0.402406 | + | 0.915461i | \(0.631826\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | −0.216058 | −0.0114672 | ||||||||
\(356\) | 5.41906 | 0.287210 | ||||||||
\(357\) | −3.41012 | −0.180483 | ||||||||
\(358\) | −21.1067 | −1.11553 | ||||||||
\(359\) | −12.2143 | −0.644647 | −0.322324 | − | 0.946630i | \(-0.604464\pi\) | ||||
−0.322324 | + | 0.946630i | \(0.604464\pi\) | |||||||
\(360\) | 3.72920 | 0.196546 | ||||||||
\(361\) | 22.3104 | 1.17423 | ||||||||
\(362\) | 8.94724 | 0.470257 | ||||||||
\(363\) | −18.1242 | −0.951276 | ||||||||
\(364\) | 4.94140 | 0.258999 | ||||||||
\(365\) | 46.2741 | 2.42210 | ||||||||
\(366\) | 7.26008 | 0.379490 | ||||||||
\(367\) | −35.7303 | −1.86511 | −0.932553 | − | 0.361033i | \(-0.882424\pi\) | ||||
−0.932553 | + | 0.361033i | \(0.882424\pi\) | |||||||
\(368\) | −6.84877 | −0.357017 | ||||||||
\(369\) | 9.01653 | 0.469382 | ||||||||
\(370\) | 25.7123 | 1.33672 | ||||||||
\(371\) | −29.6397 | −1.53882 | ||||||||
\(372\) | −8.63951 | −0.447938 | ||||||||
\(373\) | −5.24218 | −0.271430 | −0.135715 | − | 0.990748i | \(-0.543333\pi\) | ||||
−0.135715 | + | 0.990748i | \(0.543333\pi\) | |||||||
\(374\) | 5.39669 | 0.279056 | ||||||||
\(375\) | 14.5697 | 0.752375 | ||||||||
\(376\) | −2.50567 | −0.129220 | ||||||||
\(377\) | 7.24920 | 0.373353 | ||||||||
\(378\) | −3.41012 | −0.175398 | ||||||||
\(379\) | −7.59961 | −0.390366 | −0.195183 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195183 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(380\) | 23.9687 | 1.22957 | ||||||||
\(381\) | −1.18863 | −0.0608956 | ||||||||
\(382\) | −18.0589 | −0.923973 | ||||||||
\(383\) | 20.2254 | 1.03347 | 0.516735 | − | 0.856146i | \(-0.327147\pi\) | ||||
0.516735 | + | 0.856146i | \(0.327147\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 68.6297 | 3.49769 | ||||||||
\(386\) | 14.5709 | 0.741639 | ||||||||
\(387\) | −6.75841 | −0.343549 | ||||||||
\(388\) | 16.4862 | 0.836960 | ||||||||
\(389\) | 21.3128 | 1.08060 | 0.540300 | − | 0.841472i | \(-0.318311\pi\) | ||||
0.540300 | + | 0.841472i | \(0.318311\pi\) | |||||||
\(390\) | 5.40376 | 0.273630 | ||||||||
\(391\) | 6.84877 | 0.346357 | ||||||||
\(392\) | −4.62890 | −0.233795 | ||||||||
\(393\) | −13.5888 | −0.685463 | ||||||||
\(394\) | 4.41973 | 0.222663 | ||||||||
\(395\) | 49.8451 | 2.50798 | ||||||||
\(396\) | 5.39669 | 0.271194 | ||||||||
\(397\) | −16.0240 | −0.804220 | −0.402110 | − | 0.915591i | \(-0.631723\pi\) | ||||
−0.402110 | + | 0.915591i | \(0.631723\pi\) | |||||||
\(398\) | 17.6247 | 0.883448 | ||||||||
\(399\) | −21.9179 | −1.09727 | ||||||||
\(400\) | 8.90692 | 0.445346 | ||||||||
\(401\) | 21.6412 | 1.08071 | 0.540355 | − | 0.841437i | \(-0.318290\pi\) | ||||
0.540355 | + | 0.841437i | \(0.318290\pi\) | |||||||
\(402\) | −5.37634 | −0.268148 | ||||||||
\(403\) | −12.5190 | −0.623615 | ||||||||
\(404\) | 9.67501 | 0.481350 | ||||||||
\(405\) | −3.72920 | −0.185305 | ||||||||
\(406\) | −17.0600 | −0.846674 | ||||||||
\(407\) | 37.2095 | 1.84440 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 35.6246 | 1.76153 | 0.880763 | − | 0.473558i | \(-0.157031\pi\) | ||||
0.880763 | + | 0.473558i | \(0.157031\pi\) | |||||||
\(410\) | 33.6244 | 1.66059 | ||||||||
\(411\) | 7.08660 | 0.349556 | ||||||||
\(412\) | 13.3684 | 0.658612 | ||||||||
\(413\) | 3.41012 | 0.167801 | ||||||||
\(414\) | 6.84877 | 0.336599 | ||||||||
\(415\) | −52.7817 | −2.59095 | ||||||||
\(416\) | 1.44904 | 0.0710450 | ||||||||
\(417\) | −19.8948 | −0.974254 | ||||||||
\(418\) | 34.6862 | 1.69656 | ||||||||
\(419\) | −22.2459 | −1.08678 | −0.543392 | − | 0.839479i | \(-0.682860\pi\) | ||||
−0.543392 | + | 0.839479i | \(0.682860\pi\) | |||||||
\(420\) | −12.7170 | −0.620526 | ||||||||
\(421\) | −16.5179 | −0.805031 | −0.402515 | − | 0.915413i | \(-0.631864\pi\) | ||||
−0.402515 | + | 0.915413i | \(0.631864\pi\) | |||||||
\(422\) | −5.09679 | −0.248108 | ||||||||
\(423\) | 2.50567 | 0.121830 | ||||||||
\(424\) | −8.69169 | −0.422106 | ||||||||
\(425\) | −8.90692 | −0.432049 | ||||||||
\(426\) | 0.0579369 | 0.00280705 | ||||||||
\(427\) | −24.7577 | −1.19811 | ||||||||
\(428\) | 9.76675 | 0.472094 | ||||||||
\(429\) | 7.82001 | 0.377554 | ||||||||
\(430\) | −25.2034 | −1.21542 | ||||||||
\(431\) | −31.4356 | −1.51420 | −0.757100 | − | 0.653300i | \(-0.773384\pi\) | ||||
−0.757100 | + | 0.653300i | \(0.773384\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.6591 | −0.944758 | −0.472379 | − | 0.881395i | \(-0.656605\pi\) | ||||
−0.472379 | + | 0.881395i | \(0.656605\pi\) | |||||||
\(434\) | 29.4618 | 1.41421 | ||||||||
\(435\) | −18.6563 | −0.894501 | ||||||||
\(436\) | −9.15105 | −0.438256 | ||||||||
\(437\) | 44.0192 | 2.10572 | ||||||||
\(438\) | −12.4086 | −0.592905 | ||||||||
\(439\) | −23.4092 | −1.11726 | −0.558631 | − | 0.829416i | \(-0.688673\pi\) | ||||
−0.558631 | + | 0.829416i | \(0.688673\pi\) | |||||||
\(440\) | 20.1253 | 0.959437 | ||||||||
\(441\) | 4.62890 | 0.220424 | ||||||||
\(442\) | −1.44904 | −0.0689238 | ||||||||
\(443\) | −14.1011 | −0.669963 | −0.334982 | − | 0.942225i | \(-0.608730\pi\) | ||||
−0.334982 | + | 0.942225i | \(0.608730\pi\) | |||||||
\(444\) | −6.89487 | −0.327216 | ||||||||
\(445\) | −20.2087 | −0.957986 | ||||||||
\(446\) | 17.1560 | 0.812361 | ||||||||
\(447\) | 13.8088 | 0.653133 | ||||||||
\(448\) | −3.41012 | −0.161113 | ||||||||
\(449\) | −10.3411 | −0.488027 | −0.244013 | − | 0.969772i | \(-0.578464\pi\) | ||||
−0.244013 | + | 0.969772i | \(0.578464\pi\) | |||||||
\(450\) | −8.90692 | −0.419876 | ||||||||
\(451\) | 48.6594 | 2.29128 | ||||||||
\(452\) | −2.01354 | −0.0947090 | ||||||||
\(453\) | 7.58245 | 0.356255 | ||||||||
\(454\) | 13.4350 | 0.630533 | ||||||||
\(455\) | −18.4274 | −0.863892 | ||||||||
\(456\) | −6.42732 | −0.300987 | ||||||||
\(457\) | 25.8808 | 1.21065 | 0.605327 | − | 0.795977i | \(-0.293042\pi\) | ||||
0.605327 | + | 0.795977i | \(0.293042\pi\) | |||||||
\(458\) | −24.9330 | −1.16504 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 25.5404 | 1.19083 | ||||||||
\(461\) | −0.642862 | −0.0299411 | −0.0149705 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149705 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(462\) | −18.4033 | −0.856201 | ||||||||
\(463\) | −8.42833 | −0.391698 | −0.195849 | − | 0.980634i | \(-0.562746\pi\) | ||||
−0.195849 | + | 0.980634i | \(0.562746\pi\) | |||||||
\(464\) | −5.00277 | −0.232248 | ||||||||
\(465\) | 32.2185 | 1.49409 | ||||||||
\(466\) | −8.01856 | −0.371453 | ||||||||
\(467\) | 0.311005 | 0.0143916 | 0.00719580 | − | 0.999974i | \(-0.497709\pi\) | ||||
0.00719580 | + | 0.999974i | \(0.497709\pi\) | |||||||
\(468\) | −1.44904 | −0.0669819 | ||||||||
\(469\) | 18.3340 | 0.846583 | ||||||||
\(470\) | 9.34412 | 0.431012 | ||||||||
\(471\) | 5.58450 | 0.257320 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −36.4730 | −1.67703 | ||||||||
\(474\) | −13.3662 | −0.613928 | ||||||||
\(475\) | −57.2476 | −2.62670 | ||||||||
\(476\) | 3.41012 | 0.156302 | ||||||||
\(477\) | 8.69169 | 0.397965 | ||||||||
\(478\) | 0.912919 | 0.0417559 | ||||||||
\(479\) | −14.3397 | −0.655198 | −0.327599 | − | 0.944817i | \(-0.606239\pi\) | ||||
−0.327599 | + | 0.944817i | \(0.606239\pi\) | |||||||
\(480\) | −3.72920 | −0.170214 | ||||||||
\(481\) | −9.99094 | −0.455547 | ||||||||
\(482\) | 6.89595 | 0.314102 | ||||||||
\(483\) | −23.3551 | −1.06269 | ||||||||
\(484\) | 18.1242 | 0.823829 | ||||||||
\(485\) | −61.4803 | −2.79168 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.1595 | −0.686944 | −0.343472 | − | 0.939163i | \(-0.611603\pi\) | ||||
−0.343472 | + | 0.939163i | \(0.611603\pi\) | |||||||
\(488\) | −7.26008 | −0.328648 | ||||||||
\(489\) | 11.5107 | 0.520531 | ||||||||
\(490\) | 17.2621 | 0.779822 | ||||||||
\(491\) | −24.2062 | −1.09241 | −0.546206 | − | 0.837651i | \(-0.683928\pi\) | ||||
−0.546206 | + | 0.837651i | \(0.683928\pi\) | |||||||
\(492\) | −9.01653 | −0.406497 | ||||||||
\(493\) | 5.00277 | 0.225313 | ||||||||
\(494\) | −9.31343 | −0.419031 | ||||||||
\(495\) | −20.1253 | −0.904566 | ||||||||
\(496\) | 8.63951 | 0.387926 | ||||||||
\(497\) | −0.197572 | −0.00886229 | ||||||||
\(498\) | 14.1536 | 0.634240 | ||||||||
\(499\) | 9.06767 | 0.405924 | 0.202962 | − | 0.979187i | \(-0.434943\pi\) | ||||
0.202962 | + | 0.979187i | \(0.434943\pi\) | |||||||
\(500\) | −14.5697 | −0.651576 | ||||||||
\(501\) | 12.5643 | 0.561330 | ||||||||
\(502\) | −22.9184 | −1.02290 | ||||||||
\(503\) | −14.1050 | −0.628911 | −0.314455 | − | 0.949272i | \(-0.601822\pi\) | ||||
−0.314455 | + | 0.949272i | \(0.601822\pi\) | |||||||
\(504\) | 3.41012 | 0.151899 | ||||||||
\(505\) | −36.0800 | −1.60554 | ||||||||
\(506\) | 36.9607 | 1.64310 | ||||||||
\(507\) | 10.9003 | 0.484099 | ||||||||
\(508\) | 1.18863 | 0.0527371 | ||||||||
\(509\) | 25.9226 | 1.14900 | 0.574499 | − | 0.818505i | \(-0.305197\pi\) | ||||
0.574499 | + | 0.818505i | \(0.305197\pi\) | |||||||
\(510\) | 3.72920 | 0.165132 | ||||||||
\(511\) | 42.3147 | 1.87189 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.42732 | 0.283773 | ||||||||
\(514\) | −4.80093 | −0.211760 | ||||||||
\(515\) | −49.8533 | −2.19680 | ||||||||
\(516\) | 6.75841 | 0.297522 | ||||||||
\(517\) | 13.5223 | 0.594710 | ||||||||
\(518\) | 23.5123 | 1.03307 | ||||||||
\(519\) | −12.4630 | −0.547066 | ||||||||
\(520\) | −5.40376 | −0.236970 | ||||||||
\(521\) | −6.64697 | −0.291209 | −0.145605 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145605 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(522\) | 5.00277 | 0.218965 | ||||||||
\(523\) | 6.13178 | 0.268124 | 0.134062 | − | 0.990973i | \(-0.457198\pi\) | ||||
0.134062 | + | 0.990973i | \(0.457198\pi\) | |||||||
\(524\) | 13.5888 | 0.593628 | ||||||||
\(525\) | 30.3736 | 1.32561 | ||||||||
\(526\) | −14.1103 | −0.615240 | ||||||||
\(527\) | −8.63951 | −0.376343 | ||||||||
\(528\) | −5.39669 | −0.234861 | ||||||||
\(529\) | 23.9056 | 1.03937 | ||||||||
\(530\) | 32.4130 | 1.40793 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 21.9179 | 0.950262 | ||||||||
\(533\) | −13.0653 | −0.565921 | ||||||||
\(534\) | 5.41906 | 0.234506 | ||||||||
\(535\) | −36.4221 | −1.57467 | ||||||||
\(536\) | 5.37634 | 0.232223 | ||||||||
\(537\) | −21.1067 | −0.910823 | ||||||||
\(538\) | 23.2981 | 1.00445 | ||||||||
\(539\) | 24.9807 | 1.07600 | ||||||||
\(540\) | 3.72920 | 0.160479 | ||||||||
\(541\) | 8.39640 | 0.360989 | 0.180495 | − | 0.983576i | \(-0.442230\pi\) | ||||
0.180495 | + | 0.983576i | \(0.442230\pi\) | |||||||
\(542\) | 0.524590 | 0.0225331 | ||||||||
\(543\) | 8.94724 | 0.383963 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 34.1261 | 1.46180 | ||||||||
\(546\) | 4.94140 | 0.211472 | ||||||||
\(547\) | 2.56790 | 0.109795 | 0.0548977 | − | 0.998492i | \(-0.482517\pi\) | ||||
0.0548977 | + | 0.998492i | \(0.482517\pi\) | |||||||
\(548\) | −7.08660 | −0.302725 | ||||||||
\(549\) | 7.26008 | 0.309853 | ||||||||
\(550\) | −48.0679 | −2.04962 | ||||||||
\(551\) | 32.1544 | 1.36982 | ||||||||
\(552\) | −6.84877 | −0.291503 | ||||||||
\(553\) | 45.5802 | 1.93827 | ||||||||
\(554\) | 23.6475 | 1.00469 | ||||||||
\(555\) | 25.7123 | 1.09143 | ||||||||
\(556\) | 19.8948 | 0.843729 | ||||||||
\(557\) | −13.5198 | −0.572851 | −0.286425 | − | 0.958103i | \(-0.592467\pi\) | ||||
−0.286425 | + | 0.958103i | \(0.592467\pi\) | |||||||
\(558\) | −8.63951 | −0.365740 | ||||||||
\(559\) | 9.79320 | 0.414208 | ||||||||
\(560\) | 12.7170 | 0.537392 | ||||||||
\(561\) | 5.39669 | 0.227848 | ||||||||
\(562\) | −10.7845 | −0.454918 | ||||||||
\(563\) | −8.20834 | −0.345940 | −0.172970 | − | 0.984927i | \(-0.555336\pi\) | ||||
−0.172970 | + | 0.984927i | \(0.555336\pi\) | |||||||
\(564\) | −2.50567 | −0.105508 | ||||||||
\(565\) | 7.50889 | 0.315902 | ||||||||
\(566\) | 13.2487 | 0.556884 | ||||||||
\(567\) | −3.41012 | −0.143211 | ||||||||
\(568\) | −0.0579369 | −0.00243098 | ||||||||
\(569\) | −37.8164 | −1.58535 | −0.792673 | − | 0.609647i | \(-0.791311\pi\) | ||||
−0.792673 | + | 0.609647i | \(0.791311\pi\) | |||||||
\(570\) | 23.9687 | 1.00394 | ||||||||
\(571\) | −0.164607 | −0.00688859 | −0.00344429 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344429 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(572\) | −7.82001 | −0.326971 | ||||||||
\(573\) | −18.0589 | −0.754421 | ||||||||
\(574\) | 30.7474 | 1.28337 | ||||||||
\(575\) | −61.0014 | −2.54394 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.77447 | −0.282025 | −0.141012 | − | 0.990008i | \(-0.545036\pi\) | ||||
−0.141012 | + | 0.990008i | \(0.545036\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 14.5709 | 0.605546 | ||||||||
\(580\) | 18.6563 | 0.774661 | ||||||||
\(581\) | −48.2656 | −2.00239 | ||||||||
\(582\) | 16.4862 | 0.683375 | ||||||||
\(583\) | 46.9063 | 1.94266 | ||||||||
\(584\) | 12.4086 | 0.513471 | ||||||||
\(585\) | 5.40376 | 0.223418 | ||||||||
\(586\) | −7.93575 | −0.327823 | ||||||||
\(587\) | 21.9837 | 0.907363 | 0.453682 | − | 0.891164i | \(-0.350110\pi\) | ||||
0.453682 | + | 0.891164i | \(0.350110\pi\) | |||||||
\(588\) | −4.62890 | −0.190893 | ||||||||
\(589\) | −55.5289 | −2.28803 | ||||||||
\(590\) | −3.72920 | −0.153529 | ||||||||
\(591\) | 4.41973 | 0.181804 | ||||||||
\(592\) | 6.89487 | 0.283377 | ||||||||
\(593\) | 22.4242 | 0.920853 | 0.460427 | − | 0.887698i | \(-0.347696\pi\) | ||||
0.460427 | + | 0.887698i | \(0.347696\pi\) | |||||||
\(594\) | 5.39669 | 0.221429 | ||||||||
\(595\) | −12.7170 | −0.521346 | ||||||||
\(596\) | −13.8088 | −0.565630 | ||||||||
\(597\) | 17.6247 | 0.721332 | ||||||||
\(598\) | −9.92413 | −0.405828 | ||||||||
\(599\) | 34.7479 | 1.41976 | 0.709881 | − | 0.704322i | \(-0.248749\pi\) | ||||
0.709881 | + | 0.704322i | \(0.248749\pi\) | |||||||
\(600\) | 8.90692 | 0.363624 | ||||||||
\(601\) | −48.0849 | −1.96142 | −0.980712 | − | 0.195460i | \(-0.937380\pi\) | ||||
−0.980712 | + | 0.195460i | \(0.937380\pi\) | |||||||
\(602\) | −23.0470 | −0.939324 | ||||||||
\(603\) | −5.37634 | −0.218942 | ||||||||
\(604\) | −7.58245 | −0.308526 | ||||||||
\(605\) | −67.5889 | −2.74788 | ||||||||
\(606\) | 9.67501 | 0.393020 | ||||||||
\(607\) | 4.10121 | 0.166463 | 0.0832315 | − | 0.996530i | \(-0.473476\pi\) | ||||
0.0832315 | + | 0.996530i | \(0.473476\pi\) | |||||||
\(608\) | 6.42732 | 0.260662 | ||||||||
\(609\) | −17.0600 | −0.691307 | ||||||||
\(610\) | 27.0743 | 1.09621 | ||||||||
\(611\) | −3.63081 | −0.146887 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −5.61823 | −0.226918 | −0.113459 | − | 0.993543i | \(-0.536193\pi\) | ||||
−0.113459 | + | 0.993543i | \(0.536193\pi\) | |||||||
\(614\) | 16.7504 | 0.675992 | ||||||||
\(615\) | 33.6244 | 1.35587 | ||||||||
\(616\) | 18.4033 | 0.741492 | ||||||||
\(617\) | 9.18586 | 0.369809 | 0.184904 | − | 0.982757i | \(-0.440802\pi\) | ||||
0.184904 | + | 0.982757i | \(0.440802\pi\) | |||||||
\(618\) | 13.3684 | 0.537754 | ||||||||
\(619\) | 19.2887 | 0.775280 | 0.387640 | − | 0.921811i | \(-0.373290\pi\) | ||||
0.387640 | + | 0.921811i | \(0.373290\pi\) | |||||||
\(620\) | −32.2185 | −1.29392 | ||||||||
\(621\) | 6.84877 | 0.274832 | ||||||||
\(622\) | 25.3463 | 1.01629 | ||||||||
\(623\) | −18.4796 | −0.740371 | ||||||||
\(624\) | 1.44904 | 0.0580080 | ||||||||
\(625\) | 9.79864 | 0.391945 | ||||||||
\(626\) | 3.98350 | 0.159213 | ||||||||
\(627\) | 34.6862 | 1.38523 | ||||||||
\(628\) | −5.58450 | −0.222846 | ||||||||
\(629\) | −6.89487 | −0.274916 | ||||||||
\(630\) | −12.7170 | −0.506658 | ||||||||
\(631\) | −8.10629 | −0.322706 | −0.161353 | − | 0.986897i | \(-0.551586\pi\) | ||||
−0.161353 | + | 0.986897i | \(0.551586\pi\) | |||||||
\(632\) | 13.3662 | 0.531677 | ||||||||
\(633\) | −5.09679 | −0.202579 | ||||||||
\(634\) | 13.3269 | 0.529277 | ||||||||
\(635\) | −4.43265 | −0.175904 | ||||||||
\(636\) | −8.69169 | −0.344648 | ||||||||
\(637\) | −6.70746 | −0.265759 | ||||||||
\(638\) | 26.9984 | 1.06888 | ||||||||
\(639\) | 0.0579369 | 0.00229195 | ||||||||
\(640\) | 3.72920 | 0.147410 | ||||||||
\(641\) | 37.6291 | 1.48626 | 0.743130 | − | 0.669147i | \(-0.233340\pi\) | ||||
0.743130 | + | 0.669147i | \(0.233340\pi\) | |||||||
\(642\) | 9.76675 | 0.385463 | ||||||||
\(643\) | 11.5791 | 0.456634 | 0.228317 | − | 0.973587i | \(-0.426678\pi\) | ||||
0.228317 | + | 0.973587i | \(0.426678\pi\) | |||||||
\(644\) | 23.3551 | 0.920320 | ||||||||
\(645\) | −25.2034 | −0.992384 | ||||||||
\(646\) | −6.42732 | −0.252879 | ||||||||
\(647\) | 22.4611 | 0.883036 | 0.441518 | − | 0.897252i | \(-0.354440\pi\) | ||||
0.441518 | + | 0.897252i | \(0.354440\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.39669 | −0.211839 | ||||||||
\(650\) | 12.9065 | 0.506234 | ||||||||
\(651\) | 29.4618 | 1.15470 | ||||||||
\(652\) | −11.5107 | −0.450793 | ||||||||
\(653\) | −3.89084 | −0.152260 | −0.0761301 | − | 0.997098i | \(-0.524256\pi\) | ||||
−0.0761301 | + | 0.997098i | \(0.524256\pi\) | |||||||
\(654\) | −9.15105 | −0.357834 | ||||||||
\(655\) | −50.6752 | −1.98004 | ||||||||
\(656\) | 9.01653 | 0.352036 | ||||||||
\(657\) | −12.4086 | −0.484105 | ||||||||
\(658\) | 8.54461 | 0.333104 | ||||||||
\(659\) | −31.4823 | −1.22638 | −0.613188 | − | 0.789937i | \(-0.710113\pi\) | ||||
−0.613188 | + | 0.789937i | \(0.710113\pi\) | |||||||
\(660\) | 20.1253 | 0.783377 | ||||||||
\(661\) | 26.5615 | 1.03312 | 0.516562 | − | 0.856250i | \(-0.327212\pi\) | ||||
0.516562 | + | 0.856250i | \(0.327212\pi\) | |||||||
\(662\) | −1.85247 | −0.0719985 | ||||||||
\(663\) | −1.44904 | −0.0562760 | ||||||||
\(664\) | −14.1536 | −0.549268 | ||||||||
\(665\) | −81.7362 | −3.16959 | ||||||||
\(666\) | −6.89487 | −0.267171 | ||||||||
\(667\) | 34.2628 | 1.32666 | ||||||||
\(668\) | −12.5643 | −0.486126 | ||||||||
\(669\) | 17.1560 | 0.663290 | ||||||||
\(670\) | −20.0494 | −0.774578 | ||||||||
\(671\) | 39.1804 | 1.51254 | ||||||||
\(672\) | −3.41012 | −0.131548 | ||||||||
\(673\) | −20.2553 | −0.780784 | −0.390392 | − | 0.920649i | \(-0.627661\pi\) | ||||
−0.390392 | + | 0.920649i | \(0.627661\pi\) | |||||||
\(674\) | −24.5279 | −0.944779 | ||||||||
\(675\) | −8.90692 | −0.342828 | ||||||||
\(676\) | −10.9003 | −0.419242 | ||||||||
\(677\) | −4.89243 | −0.188031 | −0.0940156 | − | 0.995571i | \(-0.529970\pi\) | ||||
−0.0940156 | + | 0.995571i | \(0.529970\pi\) | |||||||
\(678\) | −2.01354 | −0.0773296 | ||||||||
\(679\) | −56.2199 | −2.15752 | ||||||||
\(680\) | −3.72920 | −0.143008 | ||||||||
\(681\) | 13.4350 | 0.514828 | ||||||||
\(682\) | −46.6248 | −1.78535 | ||||||||
\(683\) | 15.7553 | 0.602861 | 0.301431 | − | 0.953488i | \(-0.402536\pi\) | ||||
0.301431 | + | 0.953488i | \(0.402536\pi\) | |||||||
\(684\) | −6.42732 | −0.245755 | ||||||||
\(685\) | 26.4274 | 1.00974 | ||||||||
\(686\) | −8.08572 | −0.308714 | ||||||||
\(687\) | −24.9330 | −0.951254 | ||||||||
\(688\) | −6.75841 | −0.257662 | ||||||||
\(689\) | −12.5946 | −0.479816 | ||||||||
\(690\) | 25.5404 | 0.972307 | ||||||||
\(691\) | −5.65293 | −0.215048 | −0.107524 | − | 0.994203i | \(-0.534292\pi\) | ||||
−0.107524 | + | 0.994203i | \(0.534292\pi\) | |||||||
\(692\) | 12.4630 | 0.473773 | ||||||||
\(693\) | −18.4033 | −0.699085 | ||||||||
\(694\) | 23.8090 | 0.903775 | ||||||||
\(695\) | −74.1918 | −2.81425 | ||||||||
\(696\) | −5.00277 | −0.189629 | ||||||||
\(697\) | −9.01653 | −0.341526 | ||||||||
\(698\) | 27.5691 | 1.04351 | ||||||||
\(699\) | −8.01856 | −0.303290 | ||||||||
\(700\) | −30.3736 | −1.14802 | ||||||||
\(701\) | −50.2178 | −1.89670 | −0.948350 | − | 0.317227i | \(-0.897248\pi\) | ||||
−0.948350 | + | 0.317227i | \(0.897248\pi\) | |||||||
\(702\) | −1.44904 | −0.0546905 | ||||||||
\(703\) | −44.3155 | −1.67139 | ||||||||
\(704\) | 5.39669 | 0.203395 | ||||||||
\(705\) | 9.34412 | 0.351920 | ||||||||
\(706\) | 15.1210 | 0.569088 | ||||||||
\(707\) | −32.9929 | −1.24083 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 45.8204 | 1.72082 | 0.860410 | − | 0.509603i | \(-0.170208\pi\) | ||||
0.860410 | + | 0.509603i | \(0.170208\pi\) | |||||||
\(710\) | 0.216058 | 0.00810851 | ||||||||
\(711\) | −13.3662 | −0.501270 | ||||||||
\(712\) | −5.41906 | −0.203088 | ||||||||
\(713\) | −59.1700 | −2.21593 | ||||||||
\(714\) | 3.41012 | 0.127620 | ||||||||
\(715\) | 29.1624 | 1.09061 | ||||||||
\(716\) | 21.1067 | 0.788796 | ||||||||
\(717\) | 0.912919 | 0.0340936 | ||||||||
\(718\) | 12.2143 | 0.455834 | ||||||||
\(719\) | 27.2899 | 1.01774 | 0.508871 | − | 0.860843i | \(-0.330063\pi\) | ||||
0.508871 | + | 0.860843i | \(0.330063\pi\) | |||||||
\(720\) | −3.72920 | −0.138979 | ||||||||
\(721\) | −45.5877 | −1.69777 | ||||||||
\(722\) | −22.3104 | −0.830307 | ||||||||
\(723\) | 6.89595 | 0.256463 | ||||||||
\(724\) | −8.94724 | −0.332522 | ||||||||
\(725\) | −44.5592 | −1.65489 | ||||||||
\(726\) | 18.1242 | 0.672654 | ||||||||
\(727\) | 7.19232 | 0.266749 | 0.133374 | − | 0.991066i | \(-0.457419\pi\) | ||||
0.133374 | + | 0.991066i | \(0.457419\pi\) | |||||||
\(728\) | −4.94140 | −0.183140 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −46.2741 | −1.71268 | ||||||||
\(731\) | 6.75841 | 0.249969 | ||||||||
\(732\) | −7.26008 | −0.268340 | ||||||||
\(733\) | 24.5020 | 0.905001 | 0.452501 | − | 0.891764i | \(-0.350532\pi\) | ||||
0.452501 | + | 0.891764i | \(0.350532\pi\) | |||||||
\(734\) | 35.7303 | 1.31883 | ||||||||
\(735\) | 17.2621 | 0.636722 | ||||||||
\(736\) | 6.84877 | 0.252449 | ||||||||
\(737\) | −29.0144 | −1.06876 | ||||||||
\(738\) | −9.01653 | −0.331903 | ||||||||
\(739\) | 34.7569 | 1.27855 | 0.639277 | − | 0.768977i | \(-0.279234\pi\) | ||||
0.639277 | + | 0.768977i | \(0.279234\pi\) | |||||||
\(740\) | −25.7123 | −0.945204 | ||||||||
\(741\) | −9.31343 | −0.342138 | ||||||||
\(742\) | 29.6397 | 1.08811 | ||||||||
\(743\) | −38.2351 | −1.40271 | −0.701355 | − | 0.712812i | \(-0.747421\pi\) | ||||
−0.701355 | + | 0.712812i | \(0.747421\pi\) | |||||||
\(744\) | 8.63951 | 0.316740 | ||||||||
\(745\) | 51.4957 | 1.88666 | ||||||||
\(746\) | 5.24218 | 0.191930 | ||||||||
\(747\) | 14.1536 | 0.517855 | ||||||||
\(748\) | −5.39669 | −0.197322 | ||||||||
\(749\) | −33.3058 | −1.21697 | ||||||||
\(750\) | −14.5697 | −0.532010 | ||||||||
\(751\) | −52.1115 | −1.90157 | −0.950787 | − | 0.309844i | \(-0.899723\pi\) | ||||
−0.950787 | + | 0.309844i | \(0.899723\pi\) | |||||||
\(752\) | 2.50567 | 0.0913722 | ||||||||
\(753\) | −22.9184 | −0.835193 | ||||||||
\(754\) | −7.24920 | −0.264000 | ||||||||
\(755\) | 28.2765 | 1.02909 | ||||||||
\(756\) | 3.41012 | 0.124025 | ||||||||
\(757\) | 46.5082 | 1.69037 | 0.845185 | − | 0.534474i | \(-0.179490\pi\) | ||||
0.845185 | + | 0.534474i | \(0.179490\pi\) | |||||||
\(758\) | 7.59961 | 0.276030 | ||||||||
\(759\) | 36.9607 | 1.34159 | ||||||||
\(760\) | −23.9687 | −0.869438 | ||||||||
\(761\) | 44.8810 | 1.62693 | 0.813467 | − | 0.581611i | \(-0.197577\pi\) | ||||
0.813467 | + | 0.581611i | \(0.197577\pi\) | |||||||
\(762\) | 1.18863 | 0.0430597 | ||||||||
\(763\) | 31.2061 | 1.12974 | ||||||||
\(764\) | 18.0589 | 0.653348 | ||||||||
\(765\) | 3.72920 | 0.134829 | ||||||||
\(766\) | −20.2254 | −0.730773 | ||||||||
\(767\) | 1.44904 | 0.0523218 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −6.92105 | −0.249579 | −0.124790 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124790 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(770\) | −68.6297 | −2.47324 | ||||||||
\(771\) | −4.80093 | −0.172901 | ||||||||
\(772\) | −14.5709 | −0.524418 | ||||||||
\(773\) | −19.9056 | −0.715953 | −0.357977 | − | 0.933731i | \(-0.616533\pi\) | ||||
−0.357977 | + | 0.933731i | \(0.616533\pi\) | |||||||
\(774\) | 6.75841 | 0.242926 | ||||||||
\(775\) | 76.9514 | 2.76418 | ||||||||
\(776\) | −16.4862 | −0.591820 | ||||||||
\(777\) | 23.5123 | 0.843499 | ||||||||
\(778\) | −21.3128 | −0.764100 | ||||||||
\(779\) | −57.9521 | −2.07635 | ||||||||
\(780\) | −5.40376 | −0.193485 | ||||||||
\(781\) | 0.312667 | 0.0111881 | ||||||||
\(782\) | −6.84877 | −0.244911 | ||||||||
\(783\) | 5.00277 | 0.178784 | ||||||||
\(784\) | 4.62890 | 0.165318 | ||||||||
\(785\) | 20.8257 | 0.743301 | ||||||||
\(786\) | 13.5888 | 0.484695 | ||||||||
\(787\) | −31.3782 | −1.11851 | −0.559256 | − | 0.828995i | \(-0.688913\pi\) | ||||
−0.559256 | + | 0.828995i | \(0.688913\pi\) | |||||||
\(788\) | −4.41973 | −0.157446 | ||||||||
\(789\) | −14.1103 | −0.502342 | ||||||||
\(790\) | −49.8451 | −1.77341 | ||||||||
\(791\) | 6.86641 | 0.244141 | ||||||||
\(792\) | −5.39669 | −0.191763 | ||||||||
\(793\) | −10.5201 | −0.373581 | ||||||||
\(794\) | 16.0240 | 0.568669 | ||||||||
\(795\) | 32.4130 | 1.14957 | ||||||||
\(796\) | −17.6247 | −0.624692 | ||||||||
\(797\) | 22.6892 | 0.803694 | 0.401847 | − | 0.915707i | \(-0.368368\pi\) | ||||
0.401847 | + | 0.915707i | \(0.368368\pi\) | |||||||
\(798\) | 21.9179 | 0.775885 | ||||||||
\(799\) | −2.50567 | −0.0886441 | ||||||||
\(800\) | −8.90692 | −0.314907 | ||||||||
\(801\) | 5.41906 | 0.191473 | ||||||||
\(802\) | −21.6412 | −0.764178 | ||||||||
\(803\) | −66.9652 | −2.36315 | ||||||||
\(804\) | 5.37634 | 0.189609 | ||||||||
\(805\) | −87.0958 | −3.06972 | ||||||||
\(806\) | 12.5190 | 0.440963 | ||||||||
\(807\) | 23.2981 | 0.820131 | ||||||||
\(808\) | −9.67501 | −0.340366 | ||||||||
\(809\) | 5.75662 | 0.202392 | 0.101196 | − | 0.994867i | \(-0.467733\pi\) | ||||
0.101196 | + | 0.994867i | \(0.467733\pi\) | |||||||
\(810\) | 3.72920 | 0.131031 | ||||||||
\(811\) | 53.5935 | 1.88192 | 0.940961 | − | 0.338516i | \(-0.109925\pi\) | ||||
0.940961 | + | 0.338516i | \(0.109925\pi\) | |||||||
\(812\) | 17.0600 | 0.598689 | ||||||||
\(813\) | 0.524590 | 0.0183982 | ||||||||
\(814\) | −37.2095 | −1.30419 | ||||||||
\(815\) | 42.9256 | 1.50362 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 43.4384 | 1.51972 | ||||||||
\(818\) | −35.6246 | −1.24559 | ||||||||
\(819\) | 4.94140 | 0.172666 | ||||||||
\(820\) | −33.6244 | −1.17422 | ||||||||
\(821\) | 21.4024 | 0.746950 | 0.373475 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373475 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(822\) | −7.08660 | −0.247174 | ||||||||
\(823\) | −16.6260 | −0.579547 | −0.289773 | − | 0.957095i | \(-0.593580\pi\) | ||||
−0.289773 | + | 0.957095i | \(0.593580\pi\) | |||||||
\(824\) | −13.3684 | −0.465709 | ||||||||
\(825\) | −48.0679 | −1.67351 | ||||||||
\(826\) | −3.41012 | −0.118653 | ||||||||
\(827\) | 20.0328 | 0.696610 | 0.348305 | − | 0.937381i | \(-0.386757\pi\) | ||||
0.348305 | + | 0.937381i | \(0.386757\pi\) | |||||||
\(828\) | −6.84877 | −0.238011 | ||||||||
\(829\) | 20.9181 | 0.726515 | 0.363257 | − | 0.931689i | \(-0.381665\pi\) | ||||
0.363257 | + | 0.931689i | \(0.381665\pi\) | |||||||
\(830\) | 52.7817 | 1.83208 | ||||||||
\(831\) | 23.6475 | 0.820323 | ||||||||
\(832\) | −1.44904 | −0.0502364 | ||||||||
\(833\) | −4.62890 | −0.160382 | ||||||||
\(834\) | 19.8948 | 0.688902 | ||||||||
\(835\) | 46.8547 | 1.62147 | ||||||||
\(836\) | −34.6862 | −1.19965 | ||||||||
\(837\) | −8.63951 | −0.298625 | ||||||||
\(838\) | 22.2459 | 0.768473 | ||||||||
\(839\) | 4.78548 | 0.165213 | 0.0826065 | − | 0.996582i | \(-0.473676\pi\) | ||||
0.0826065 | + | 0.996582i | \(0.473676\pi\) | |||||||
\(840\) | 12.7170 | 0.438778 | ||||||||
\(841\) | −3.97234 | −0.136977 | ||||||||
\(842\) | 16.5179 | 0.569243 | ||||||||
\(843\) | −10.7845 | −0.371439 | ||||||||
\(844\) | 5.09679 | 0.175439 | ||||||||
\(845\) | 40.6493 | 1.39838 | ||||||||
\(846\) | −2.50567 | −0.0861465 | ||||||||
\(847\) | −61.8058 | −2.12367 | ||||||||
\(848\) | 8.69169 | 0.298474 | ||||||||
\(849\) | 13.2487 | 0.454694 | ||||||||
\(850\) | 8.90692 | 0.305505 | ||||||||
\(851\) | −47.2213 | −1.61873 | ||||||||
\(852\) | −0.0579369 | −0.00198488 | ||||||||
\(853\) | 53.2174 | 1.82213 | 0.911064 | − | 0.412264i | \(-0.135262\pi\) | ||||
0.911064 | + | 0.412264i | \(0.135262\pi\) | |||||||
\(854\) | 24.7577 | 0.847192 | ||||||||
\(855\) | 23.9687 | 0.819714 | ||||||||
\(856\) | −9.76675 | −0.333821 | ||||||||
\(857\) | 6.26206 | 0.213908 | 0.106954 | − | 0.994264i | \(-0.465890\pi\) | ||||
0.106954 | + | 0.994264i | \(0.465890\pi\) | |||||||
\(858\) | −7.82001 | −0.266971 | ||||||||
\(859\) | 8.18485 | 0.279264 | 0.139632 | − | 0.990203i | \(-0.455408\pi\) | ||||
0.139632 | + | 0.990203i | \(0.455408\pi\) | |||||||
\(860\) | 25.2034 | 0.859430 | ||||||||
\(861\) | 30.7474 | 1.04787 | ||||||||
\(862\) | 31.4356 | 1.07070 | ||||||||
\(863\) | 18.5631 | 0.631895 | 0.315948 | − | 0.948777i | \(-0.397678\pi\) | ||||
0.315948 | + | 0.948777i | \(0.397678\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −46.4771 | −1.58027 | ||||||||
\(866\) | 19.6591 | 0.668045 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −29.4618 | −0.999997 | ||||||||
\(869\) | −72.1330 | −2.44695 | ||||||||
\(870\) | 18.6563 | 0.632508 | ||||||||
\(871\) | 7.79053 | 0.263972 | ||||||||
\(872\) | 9.15105 | 0.309893 | ||||||||
\(873\) | 16.4862 | 0.557973 | ||||||||
\(874\) | −44.0192 | −1.48897 | ||||||||
\(875\) | 49.6843 | 1.67964 | ||||||||
\(876\) | 12.4086 | 0.419247 | ||||||||
\(877\) | −0.271813 | −0.00917847 | −0.00458923 | − | 0.999989i | \(-0.501461\pi\) | ||||
−0.00458923 | + | 0.999989i | \(0.501461\pi\) | |||||||
\(878\) | 23.4092 | 0.790024 | ||||||||
\(879\) | −7.93575 | −0.267666 | ||||||||
\(880\) | −20.1253 | −0.678424 | ||||||||
\(881\) | 24.5046 | 0.825582 | 0.412791 | − | 0.910826i | \(-0.364554\pi\) | ||||
0.412791 | + | 0.910826i | \(0.364554\pi\) | |||||||
\(882\) | −4.62890 | −0.155863 | ||||||||
\(883\) | 34.0358 | 1.14540 | 0.572698 | − | 0.819766i | \(-0.305897\pi\) | ||||
0.572698 | + | 0.819766i | \(0.305897\pi\) | |||||||
\(884\) | 1.44904 | 0.0487365 | ||||||||
\(885\) | −3.72920 | −0.125356 | ||||||||
\(886\) | 14.1011 | 0.473736 | ||||||||
\(887\) | 11.8849 | 0.399057 | 0.199528 | − | 0.979892i | \(-0.436059\pi\) | ||||
0.199528 | + | 0.979892i | \(0.436059\pi\) | |||||||
\(888\) | 6.89487 | 0.231377 | ||||||||
\(889\) | −4.05338 | −0.135946 | ||||||||
\(890\) | 20.2087 | 0.677399 | ||||||||
\(891\) | 5.39669 | 0.180796 | ||||||||
\(892\) | −17.1560 | −0.574426 | ||||||||
\(893\) | −16.1047 | −0.538923 | ||||||||
\(894\) | −13.8088 | −0.461835 | ||||||||
\(895\) | −78.7112 | −2.63103 | ||||||||
\(896\) | 3.41012 | 0.113924 | ||||||||
\(897\) | −9.92413 | −0.331357 | ||||||||
\(898\) | 10.3411 | 0.345087 | ||||||||
\(899\) | −43.2214 | −1.44152 | ||||||||
\(900\) | 8.90692 | 0.296897 | ||||||||
\(901\) | −8.69169 | −0.289562 | ||||||||
\(902\) | −48.6594 | −1.62018 | ||||||||
\(903\) | −23.0470 | −0.766955 | ||||||||
\(904\) | 2.01354 | 0.0669694 | ||||||||
\(905\) | 33.3660 | 1.10912 | ||||||||
\(906\) | −7.58245 | −0.251910 | ||||||||
\(907\) | −3.97541 | −0.132001 | −0.0660007 | − | 0.997820i | \(-0.521024\pi\) | ||||
−0.0660007 | + | 0.997820i | \(0.521024\pi\) | |||||||
\(908\) | −13.4350 | −0.445855 | ||||||||
\(909\) | 9.67501 | 0.320900 | ||||||||
\(910\) | 18.4274 | 0.610864 | ||||||||
\(911\) | −46.2699 | −1.53299 | −0.766496 | − | 0.642249i | \(-0.778001\pi\) | ||||
−0.766496 | + | 0.642249i | \(0.778001\pi\) | |||||||
\(912\) | 6.42732 | 0.212830 | ||||||||
\(913\) | 76.3828 | 2.52790 | ||||||||
\(914\) | −25.8808 | −0.856062 | ||||||||
\(915\) | 27.0743 | 0.895048 | ||||||||
\(916\) | 24.9330 | 0.823810 | ||||||||
\(917\) | −46.3393 | −1.53026 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −56.0361 | −1.84846 | −0.924231 | − | 0.381834i | \(-0.875293\pi\) | ||||
−0.924231 | + | 0.381834i | \(0.875293\pi\) | |||||||
\(920\) | −25.5404 | −0.842042 | ||||||||
\(921\) | 16.7504 | 0.551945 | ||||||||
\(922\) | 0.642862 | 0.0211715 | ||||||||
\(923\) | −0.0839528 | −0.00276334 | ||||||||
\(924\) | 18.4033 | 0.605426 | ||||||||
\(925\) | 61.4120 | 2.01922 | ||||||||
\(926\) | 8.42833 | 0.276972 | ||||||||
\(927\) | 13.3684 | 0.439074 | ||||||||
\(928\) | 5.00277 | 0.164224 | ||||||||
\(929\) | 53.2321 | 1.74649 | 0.873244 | − | 0.487284i | \(-0.162012\pi\) | ||||
0.873244 | + | 0.487284i | \(0.162012\pi\) | |||||||
\(930\) | −32.2185 | −1.05648 | ||||||||
\(931\) | −29.7514 | −0.975064 | ||||||||
\(932\) | 8.01856 | 0.262657 | ||||||||
\(933\) | 25.3463 | 0.829801 | ||||||||
\(934\) | −0.311005 | −0.0101764 | ||||||||
\(935\) | 20.1253 | 0.658168 | ||||||||
\(936\) | 1.44904 | 0.0473633 | ||||||||
\(937\) | 33.3503 | 1.08951 | 0.544753 | − | 0.838597i | \(-0.316623\pi\) | ||||
0.544753 | + | 0.838597i | \(0.316623\pi\) | |||||||
\(938\) | −18.3340 | −0.598625 | ||||||||
\(939\) | 3.98350 | 0.129996 | ||||||||
\(940\) | −9.34412 | −0.304772 | ||||||||
\(941\) | −48.6087 | −1.58460 | −0.792299 | − | 0.610133i | \(-0.791116\pi\) | ||||
−0.792299 | + | 0.610133i | \(0.791116\pi\) | |||||||
\(942\) | −5.58450 | −0.181953 | ||||||||
\(943\) | −61.7521 | −2.01093 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −12.7170 | −0.413684 | ||||||||
\(946\) | 36.4730 | 1.18584 | ||||||||
\(947\) | −46.3613 | −1.50654 | −0.753270 | − | 0.657711i | \(-0.771525\pi\) | ||||
−0.753270 | + | 0.657711i | \(0.771525\pi\) | |||||||
\(948\) | 13.3662 | 0.434113 | ||||||||
\(949\) | 17.9805 | 0.583672 | ||||||||
\(950\) | 57.2476 | 1.85736 | ||||||||
\(951\) | 13.3269 | 0.432153 | ||||||||
\(952\) | −3.41012 | −0.110523 | ||||||||
\(953\) | 13.6861 | 0.443335 | 0.221667 | − | 0.975122i | \(-0.428850\pi\) | ||||
0.221667 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(954\) | −8.69169 | −0.281404 | ||||||||
\(955\) | −67.3452 | −2.17924 | ||||||||
\(956\) | −0.912919 | −0.0295259 | ||||||||
\(957\) | 26.9984 | 0.872733 | ||||||||
\(958\) | 14.3397 | 0.463295 | ||||||||
\(959\) | 24.1662 | 0.780366 | ||||||||
\(960\) | 3.72920 | 0.120359 | ||||||||
\(961\) | 43.6412 | 1.40778 | ||||||||
\(962\) | 9.99094 | 0.322121 | ||||||||
\(963\) | 9.76675 | 0.314729 | ||||||||
\(964\) | −6.89595 | −0.222104 | ||||||||
\(965\) | 54.3378 | 1.74919 | ||||||||
\(966\) | 23.3551 | 0.751438 | ||||||||
\(967\) | −2.60879 | −0.0838930 | −0.0419465 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419465 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(968\) | −18.1242 | −0.582535 | ||||||||
\(969\) | −6.42732 | −0.206475 | ||||||||
\(970\) | 61.4803 | 1.97401 | ||||||||
\(971\) | −51.4859 | −1.65226 | −0.826131 | − | 0.563479i | \(-0.809463\pi\) | ||||
−0.826131 | + | 0.563479i | \(0.809463\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −67.8437 | −2.17497 | ||||||||
\(974\) | 15.1595 | 0.485742 | ||||||||
\(975\) | 12.9065 | 0.413338 | ||||||||
\(976\) | 7.26008 | 0.232389 | ||||||||
\(977\) | −35.3155 | −1.12984 | −0.564922 | − | 0.825144i | \(-0.691094\pi\) | ||||
−0.564922 | + | 0.825144i | \(0.691094\pi\) | |||||||
\(978\) | −11.5107 | −0.368071 | ||||||||
\(979\) | 29.2450 | 0.934673 | ||||||||
\(980\) | −17.2621 | −0.551417 | ||||||||
\(981\) | −9.15105 | −0.292170 | ||||||||
\(982\) | 24.2062 | 0.772451 | ||||||||
\(983\) | 6.75397 | 0.215418 | 0.107709 | − | 0.994182i | \(-0.465648\pi\) | ||||
0.107709 | + | 0.994182i | \(0.465648\pi\) | |||||||
\(984\) | 9.01653 | 0.287437 | ||||||||
\(985\) | 16.4821 | 0.525162 | ||||||||
\(986\) | −5.00277 | −0.159320 | ||||||||
\(987\) | 8.54461 | 0.271978 | ||||||||
\(988\) | 9.31343 | 0.296300 | ||||||||
\(989\) | 46.2867 | 1.47183 | ||||||||
\(990\) | 20.1253 | 0.639625 | ||||||||
\(991\) | −51.3017 | −1.62965 | −0.814827 | − | 0.579705i | \(-0.803168\pi\) | ||||
−0.814827 | + | 0.579705i | \(0.803168\pi\) | |||||||
\(992\) | −8.63951 | −0.274305 | ||||||||
\(993\) | −1.85247 | −0.0587865 | ||||||||
\(994\) | 0.197572 | 0.00626659 | ||||||||
\(995\) | 65.7261 | 2.08366 | ||||||||
\(996\) | −14.1536 | −0.448475 | ||||||||
\(997\) | −47.0178 | −1.48907 | −0.744534 | − | 0.667585i | \(-0.767328\pi\) | ||||
−0.744534 | + | 0.667585i | \(0.767328\pi\) | |||||||
\(998\) | −9.06767 | −0.287032 | ||||||||
\(999\) | −6.89487 | −0.218144 |
(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 | 6018.2.a.v.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.v.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |