Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + 33191 x^{7} - 16428 x^{6} - 71361 x^{5} + 21747 x^{4} + 65434 x^{3} - 11840 x^{2} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.17201\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | −1.17201 | −0.524137 | −0.262069 | − | 0.965049i | \(-0.584405\pi\) | ||||
−0.262069 | + | 0.965049i | \(0.584405\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.40989 | −1.66678 | −0.833390 | − | 0.552685i | \(-0.813603\pi\) | ||||
−0.833390 | + | 0.552685i | \(0.813603\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.17201 | −0.370621 | ||||||||
\(11\) | 0.445599 | 0.134353 | 0.0671766 | − | 0.997741i | \(-0.478601\pi\) | ||||
0.0671766 | + | 0.997741i | \(0.478601\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.40989 | −1.17859 | ||||||||
\(15\) | 1.17201 | 0.302611 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.53411 | 1.58475 | 0.792377 | − | 0.610031i | \(-0.208843\pi\) | ||||
0.792377 | + | 0.610031i | \(0.208843\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.79076 | −0.869659 | −0.434830 | − | 0.900513i | \(-0.643191\pi\) | ||||
−0.434830 | + | 0.900513i | \(0.643191\pi\) | |||||||
\(20\) | −1.17201 | −0.262069 | ||||||||
\(21\) | 4.40989 | 0.962316 | ||||||||
\(22\) | 0.445599 | 0.0950021 | ||||||||
\(23\) | −1.35290 | −0.282100 | −0.141050 | − | 0.990002i | \(-0.545048\pi\) | ||||
−0.141050 | + | 0.990002i | \(0.545048\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.62640 | −0.725280 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.40989 | −0.833390 | ||||||||
\(29\) | −5.72200 | −1.06255 | −0.531275 | − | 0.847200i | \(-0.678287\pi\) | ||||
−0.531275 | + | 0.847200i | \(0.678287\pi\) | |||||||
\(30\) | 1.17201 | 0.213978 | ||||||||
\(31\) | −7.97242 | −1.43189 | −0.715945 | − | 0.698157i | \(-0.754004\pi\) | ||||
−0.715945 | + | 0.698157i | \(0.754004\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.445599 | −0.0775689 | ||||||||
\(34\) | 6.53411 | 1.12059 | ||||||||
\(35\) | 5.16841 | 0.873621 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.80648 | 1.11898 | 0.559489 | − | 0.828838i | \(-0.310997\pi\) | ||||
0.559489 | + | 0.828838i | \(0.310997\pi\) | |||||||
\(38\) | −3.79076 | −0.614942 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.17201 | −0.185310 | ||||||||
\(41\) | 0.483328 | 0.0754832 | 0.0377416 | − | 0.999288i | \(-0.487984\pi\) | ||||
0.0377416 | + | 0.999288i | \(0.487984\pi\) | |||||||
\(42\) | 4.40989 | 0.680460 | ||||||||
\(43\) | −7.08156 | −1.07993 | −0.539964 | − | 0.841688i | \(-0.681562\pi\) | ||||
−0.539964 | + | 0.841688i | \(0.681562\pi\) | |||||||
\(44\) | 0.445599 | 0.0671766 | ||||||||
\(45\) | −1.17201 | −0.174712 | ||||||||
\(46\) | −1.35290 | −0.199475 | ||||||||
\(47\) | 3.11266 | 0.454028 | 0.227014 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227014 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 12.4471 | 1.77816 | ||||||||
\(50\) | −3.62640 | −0.512851 | ||||||||
\(51\) | −6.53411 | −0.914959 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −2.35869 | −0.323991 | −0.161995 | − | 0.986792i | \(-0.551793\pi\) | ||||
−0.161995 | + | 0.986792i | \(0.551793\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.522245 | −0.0704195 | ||||||||
\(56\) | −4.40989 | −0.589296 | ||||||||
\(57\) | 3.79076 | 0.502098 | ||||||||
\(58\) | −5.72200 | −0.751336 | ||||||||
\(59\) | 10.8330 | 1.41034 | 0.705168 | − | 0.709040i | \(-0.250872\pi\) | ||||
0.705168 | + | 0.709040i | \(0.250872\pi\) | |||||||
\(60\) | 1.17201 | 0.151305 | ||||||||
\(61\) | −2.55140 | −0.326674 | −0.163337 | − | 0.986570i | \(-0.552226\pi\) | ||||
−0.163337 | + | 0.986570i | \(0.552226\pi\) | |||||||
\(62\) | −7.97242 | −1.01250 | ||||||||
\(63\) | −4.40989 | −0.555594 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.17201 | 0.145369 | ||||||||
\(66\) | −0.445599 | −0.0548495 | ||||||||
\(67\) | −2.47808 | −0.302745 | −0.151373 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151373 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(68\) | 6.53411 | 0.792377 | ||||||||
\(69\) | 1.35290 | 0.162870 | ||||||||
\(70\) | 5.16841 | 0.617744 | ||||||||
\(71\) | 2.87156 | 0.340791 | 0.170395 | − | 0.985376i | \(-0.445495\pi\) | ||||
0.170395 | + | 0.985376i | \(0.445495\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.7695 | 1.37751 | 0.688757 | − | 0.724993i | \(-0.258157\pi\) | ||||
0.688757 | + | 0.724993i | \(0.258157\pi\) | |||||||
\(74\) | 6.80648 | 0.791237 | ||||||||
\(75\) | 3.62640 | 0.418741 | ||||||||
\(76\) | −3.79076 | −0.434830 | ||||||||
\(77\) | −1.96504 | −0.223937 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −11.5317 | −1.29741 | −0.648706 | − | 0.761039i | \(-0.724690\pi\) | ||||
−0.648706 | + | 0.761039i | \(0.724690\pi\) | |||||||
\(80\) | −1.17201 | −0.131034 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.483328 | 0.0533747 | ||||||||
\(83\) | −0.188229 | −0.0206608 | −0.0103304 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103304 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(84\) | 4.40989 | 0.481158 | ||||||||
\(85\) | −7.65802 | −0.830629 | ||||||||
\(86\) | −7.08156 | −0.763624 | ||||||||
\(87\) | 5.72200 | 0.613463 | ||||||||
\(88\) | 0.445599 | 0.0475011 | ||||||||
\(89\) | 2.37544 | 0.251796 | 0.125898 | − | 0.992043i | \(-0.459819\pi\) | ||||
0.125898 | + | 0.992043i | \(0.459819\pi\) | |||||||
\(90\) | −1.17201 | −0.123540 | ||||||||
\(91\) | 4.40989 | 0.462282 | ||||||||
\(92\) | −1.35290 | −0.141050 | ||||||||
\(93\) | 7.97242 | 0.826702 | ||||||||
\(94\) | 3.11266 | 0.321046 | ||||||||
\(95\) | 4.44279 | 0.455821 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.14559 | −0.522455 | −0.261228 | − | 0.965277i | \(-0.584127\pi\) | ||||
−0.261228 | + | 0.965277i | \(0.584127\pi\) | |||||||
\(98\) | 12.4471 | 1.25735 | ||||||||
\(99\) | 0.445599 | 0.0447844 | ||||||||
\(100\) | −3.62640 | −0.362640 | ||||||||
\(101\) | −7.45461 | −0.741761 | −0.370881 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370881 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(102\) | −6.53411 | −0.646973 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −5.16841 | −0.504386 | ||||||||
\(106\) | −2.35869 | −0.229096 | ||||||||
\(107\) | 8.79608 | 0.850349 | 0.425175 | − | 0.905111i | \(-0.360213\pi\) | ||||
0.425175 | + | 0.905111i | \(0.360213\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.173361 | 0.0166049 | 0.00830246 | − | 0.999966i | \(-0.497357\pi\) | ||||
0.00830246 | + | 0.999966i | \(0.497357\pi\) | |||||||
\(110\) | −0.522245 | −0.0497941 | ||||||||
\(111\) | −6.80648 | −0.646042 | ||||||||
\(112\) | −4.40989 | −0.416695 | ||||||||
\(113\) | 19.8490 | 1.86724 | 0.933619 | − | 0.358266i | \(-0.116632\pi\) | ||||
0.933619 | + | 0.358266i | \(0.116632\pi\) | |||||||
\(114\) | 3.79076 | 0.355037 | ||||||||
\(115\) | 1.58561 | 0.147859 | ||||||||
\(116\) | −5.72200 | −0.531275 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 10.8330 | 0.997258 | ||||||||
\(119\) | −28.8147 | −2.64144 | ||||||||
\(120\) | 1.17201 | 0.106989 | ||||||||
\(121\) | −10.8014 | −0.981949 | ||||||||
\(122\) | −2.55140 | −0.230993 | ||||||||
\(123\) | −0.483328 | −0.0435802 | ||||||||
\(124\) | −7.97242 | −0.715945 | ||||||||
\(125\) | 10.1102 | 0.904283 | ||||||||
\(126\) | −4.40989 | −0.392864 | ||||||||
\(127\) | −0.472255 | −0.0419059 | −0.0209529 | − | 0.999780i | \(-0.506670\pi\) | ||||
−0.0209529 | + | 0.999780i | \(0.506670\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.08156 | 0.623496 | ||||||||
\(130\) | 1.17201 | 0.102792 | ||||||||
\(131\) | 8.07447 | 0.705469 | 0.352735 | − | 0.935723i | \(-0.385252\pi\) | ||||
0.352735 | + | 0.935723i | \(0.385252\pi\) | |||||||
\(132\) | −0.445599 | −0.0387844 | ||||||||
\(133\) | 16.7168 | 1.44953 | ||||||||
\(134\) | −2.47808 | −0.214073 | ||||||||
\(135\) | 1.17201 | 0.100870 | ||||||||
\(136\) | 6.53411 | 0.560295 | ||||||||
\(137\) | 10.2707 | 0.877485 | 0.438742 | − | 0.898613i | \(-0.355424\pi\) | ||||
0.438742 | + | 0.898613i | \(0.355424\pi\) | |||||||
\(138\) | 1.35290 | 0.115167 | ||||||||
\(139\) | 2.46420 | 0.209010 | 0.104505 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104505 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(140\) | 5.16841 | 0.436811 | ||||||||
\(141\) | −3.11266 | −0.262133 | ||||||||
\(142\) | 2.87156 | 0.240976 | ||||||||
\(143\) | −0.445599 | −0.0372629 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.70622 | 0.556922 | ||||||||
\(146\) | 11.7695 | 0.974049 | ||||||||
\(147\) | −12.4471 | −1.02662 | ||||||||
\(148\) | 6.80648 | 0.559489 | ||||||||
\(149\) | 13.2726 | 1.08733 | 0.543665 | − | 0.839302i | \(-0.317036\pi\) | ||||
0.543665 | + | 0.839302i | \(0.317036\pi\) | |||||||
\(150\) | 3.62640 | 0.296094 | ||||||||
\(151\) | −10.0014 | −0.813899 | −0.406950 | − | 0.913451i | \(-0.633408\pi\) | ||||
−0.406950 | + | 0.913451i | \(0.633408\pi\) | |||||||
\(152\) | −3.79076 | −0.307471 | ||||||||
\(153\) | 6.53411 | 0.528252 | ||||||||
\(154\) | −1.96504 | −0.158348 | ||||||||
\(155\) | 9.34373 | 0.750506 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −17.1361 | −1.36761 | −0.683805 | − | 0.729665i | \(-0.739676\pi\) | ||||
−0.683805 | + | 0.729665i | \(0.739676\pi\) | |||||||
\(158\) | −11.5317 | −0.917409 | ||||||||
\(159\) | 2.35869 | 0.187056 | ||||||||
\(160\) | −1.17201 | −0.0926552 | ||||||||
\(161\) | 5.96615 | 0.470199 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 4.56114 | 0.357256 | 0.178628 | − | 0.983917i | \(-0.442834\pi\) | ||||
0.178628 | + | 0.983917i | \(0.442834\pi\) | |||||||
\(164\) | 0.483328 | 0.0377416 | ||||||||
\(165\) | 0.522245 | 0.0406567 | ||||||||
\(166\) | −0.188229 | −0.0146094 | ||||||||
\(167\) | −14.7439 | −1.14092 | −0.570458 | − | 0.821327i | \(-0.693234\pi\) | ||||
−0.570458 | + | 0.821327i | \(0.693234\pi\) | |||||||
\(168\) | 4.40989 | 0.340230 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.65802 | −0.587343 | ||||||||
\(171\) | −3.79076 | −0.289886 | ||||||||
\(172\) | −7.08156 | −0.539964 | ||||||||
\(173\) | −2.88664 | −0.219467 | −0.109733 | − | 0.993961i | \(-0.535000\pi\) | ||||
−0.109733 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(174\) | 5.72200 | 0.433784 | ||||||||
\(175\) | 15.9920 | 1.20888 | ||||||||
\(176\) | 0.445599 | 0.0335883 | ||||||||
\(177\) | −10.8330 | −0.814258 | ||||||||
\(178\) | 2.37544 | 0.178047 | ||||||||
\(179\) | 16.6474 | 1.24429 | 0.622144 | − | 0.782903i | \(-0.286262\pi\) | ||||
0.622144 | + | 0.782903i | \(0.286262\pi\) | |||||||
\(180\) | −1.17201 | −0.0873562 | ||||||||
\(181\) | 7.52363 | 0.559227 | 0.279614 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279614 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(182\) | 4.40989 | 0.326883 | ||||||||
\(183\) | 2.55140 | 0.188605 | ||||||||
\(184\) | −1.35290 | −0.0997374 | ||||||||
\(185\) | −7.97723 | −0.586498 | ||||||||
\(186\) | 7.97242 | 0.584566 | ||||||||
\(187\) | 2.91160 | 0.212917 | ||||||||
\(188\) | 3.11266 | 0.227014 | ||||||||
\(189\) | 4.40989 | 0.320772 | ||||||||
\(190\) | 4.44279 | 0.322314 | ||||||||
\(191\) | 6.41617 | 0.464258 | 0.232129 | − | 0.972685i | \(-0.425431\pi\) | ||||
0.232129 | + | 0.972685i | \(0.425431\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 18.5408 | 1.33460 | 0.667300 | − | 0.744789i | \(-0.267450\pi\) | ||||
0.667300 | + | 0.744789i | \(0.267450\pi\) | |||||||
\(194\) | −5.14559 | −0.369432 | ||||||||
\(195\) | −1.17201 | −0.0839291 | ||||||||
\(196\) | 12.4471 | 0.889079 | ||||||||
\(197\) | 3.43025 | 0.244396 | 0.122198 | − | 0.992506i | \(-0.461006\pi\) | ||||
0.122198 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(198\) | 0.445599 | 0.0316674 | ||||||||
\(199\) | −20.4116 | −1.44694 | −0.723470 | − | 0.690356i | \(-0.757454\pi\) | ||||
−0.723470 | + | 0.690356i | \(0.757454\pi\) | |||||||
\(200\) | −3.62640 | −0.256425 | ||||||||
\(201\) | 2.47808 | 0.174790 | ||||||||
\(202\) | −7.45461 | −0.524504 | ||||||||
\(203\) | 25.2334 | 1.77104 | ||||||||
\(204\) | −6.53411 | −0.457479 | ||||||||
\(205\) | −0.566464 | −0.0395635 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −1.35290 | −0.0940333 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −1.68916 | −0.116842 | ||||||||
\(210\) | −5.16841 | −0.356654 | ||||||||
\(211\) | 10.3909 | 0.715339 | 0.357669 | − | 0.933848i | \(-0.383571\pi\) | ||||
0.357669 | + | 0.933848i | \(0.383571\pi\) | |||||||
\(212\) | −2.35869 | −0.161995 | ||||||||
\(213\) | −2.87156 | −0.196756 | ||||||||
\(214\) | 8.79608 | 0.601288 | ||||||||
\(215\) | 8.29963 | 0.566030 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 35.1575 | 2.38665 | ||||||||
\(218\) | 0.173361 | 0.0117415 | ||||||||
\(219\) | −11.7695 | −0.795308 | ||||||||
\(220\) | −0.522245 | −0.0352098 | ||||||||
\(221\) | −6.53411 | −0.439532 | ||||||||
\(222\) | −6.80648 | −0.456821 | ||||||||
\(223\) | −3.71253 | −0.248609 | −0.124305 | − | 0.992244i | \(-0.539670\pi\) | ||||
−0.124305 | + | 0.992244i | \(0.539670\pi\) | |||||||
\(224\) | −4.40989 | −0.294648 | ||||||||
\(225\) | −3.62640 | −0.241760 | ||||||||
\(226\) | 19.8490 | 1.32034 | ||||||||
\(227\) | −11.8872 | −0.788980 | −0.394490 | − | 0.918900i | \(-0.629079\pi\) | ||||
−0.394490 | + | 0.918900i | \(0.629079\pi\) | |||||||
\(228\) | 3.79076 | 0.251049 | ||||||||
\(229\) | 14.5836 | 0.963713 | 0.481857 | − | 0.876250i | \(-0.339963\pi\) | ||||
0.481857 | + | 0.876250i | \(0.339963\pi\) | |||||||
\(230\) | 1.58561 | 0.104552 | ||||||||
\(231\) | 1.96504 | 0.129290 | ||||||||
\(232\) | −5.72200 | −0.375668 | ||||||||
\(233\) | 4.17408 | 0.273453 | 0.136726 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136726 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −3.64805 | −0.237973 | ||||||||
\(236\) | 10.8330 | 0.705168 | ||||||||
\(237\) | 11.5317 | 0.749061 | ||||||||
\(238\) | −28.8147 | −1.86778 | ||||||||
\(239\) | −0.656747 | −0.0424814 | −0.0212407 | − | 0.999774i | \(-0.506762\pi\) | ||||
−0.0212407 | + | 0.999774i | \(0.506762\pi\) | |||||||
\(240\) | 1.17201 | 0.0756527 | ||||||||
\(241\) | 17.0766 | 1.10000 | 0.550000 | − | 0.835164i | \(-0.314628\pi\) | ||||
0.550000 | + | 0.835164i | \(0.314628\pi\) | |||||||
\(242\) | −10.8014 | −0.694343 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.55140 | −0.163337 | ||||||||
\(245\) | −14.5881 | −0.931998 | ||||||||
\(246\) | −0.483328 | −0.0308159 | ||||||||
\(247\) | 3.79076 | 0.241200 | ||||||||
\(248\) | −7.97242 | −0.506249 | ||||||||
\(249\) | 0.188229 | 0.0119285 | ||||||||
\(250\) | 10.1102 | 0.639425 | ||||||||
\(251\) | 24.2454 | 1.53036 | 0.765178 | − | 0.643819i | \(-0.222651\pi\) | ||||
0.765178 | + | 0.643819i | \(0.222651\pi\) | |||||||
\(252\) | −4.40989 | −0.277797 | ||||||||
\(253\) | −0.602853 | −0.0379010 | ||||||||
\(254\) | −0.472255 | −0.0296319 | ||||||||
\(255\) | 7.65802 | 0.479564 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.8223 | −0.799832 | −0.399916 | − | 0.916552i | \(-0.630961\pi\) | ||||
−0.399916 | + | 0.916552i | \(0.630961\pi\) | |||||||
\(258\) | 7.08156 | 0.440878 | ||||||||
\(259\) | −30.0158 | −1.86509 | ||||||||
\(260\) | 1.17201 | 0.0726847 | ||||||||
\(261\) | −5.72200 | −0.354183 | ||||||||
\(262\) | 8.07447 | 0.498842 | ||||||||
\(263\) | 29.4695 | 1.81717 | 0.908584 | − | 0.417703i | \(-0.137165\pi\) | ||||
0.908584 | + | 0.417703i | \(0.137165\pi\) | |||||||
\(264\) | −0.445599 | −0.0274247 | ||||||||
\(265\) | 2.76440 | 0.169816 | ||||||||
\(266\) | 16.7168 | 1.02497 | ||||||||
\(267\) | −2.37544 | −0.145374 | ||||||||
\(268\) | −2.47808 | −0.151373 | ||||||||
\(269\) | 22.9635 | 1.40011 | 0.700054 | − | 0.714090i | \(-0.253159\pi\) | ||||
0.700054 | + | 0.714090i | \(0.253159\pi\) | |||||||
\(270\) | 1.17201 | 0.0713260 | ||||||||
\(271\) | 3.57490 | 0.217159 | 0.108580 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108580 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(272\) | 6.53411 | 0.396189 | ||||||||
\(273\) | −4.40989 | −0.266898 | ||||||||
\(274\) | 10.2707 | 0.620475 | ||||||||
\(275\) | −1.61592 | −0.0974438 | ||||||||
\(276\) | 1.35290 | 0.0814352 | ||||||||
\(277\) | 11.0480 | 0.663807 | 0.331904 | − | 0.943313i | \(-0.392309\pi\) | ||||
0.331904 | + | 0.943313i | \(0.392309\pi\) | |||||||
\(278\) | 2.46420 | 0.147793 | ||||||||
\(279\) | −7.97242 | −0.477296 | ||||||||
\(280\) | 5.16841 | 0.308872 | ||||||||
\(281\) | 18.7003 | 1.11557 | 0.557783 | − | 0.829987i | \(-0.311652\pi\) | ||||
0.557783 | + | 0.829987i | \(0.311652\pi\) | |||||||
\(282\) | −3.11266 | −0.185356 | ||||||||
\(283\) | 29.5791 | 1.75829 | 0.879147 | − | 0.476550i | \(-0.158113\pi\) | ||||
0.879147 | + | 0.476550i | \(0.158113\pi\) | |||||||
\(284\) | 2.87156 | 0.170395 | ||||||||
\(285\) | −4.44279 | −0.263168 | ||||||||
\(286\) | −0.445599 | −0.0263488 | ||||||||
\(287\) | −2.13142 | −0.125814 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 25.6946 | 1.51145 | ||||||||
\(290\) | 6.70622 | 0.393803 | ||||||||
\(291\) | 5.14559 | 0.301640 | ||||||||
\(292\) | 11.7695 | 0.688757 | ||||||||
\(293\) | 3.43588 | 0.200726 | 0.100363 | − | 0.994951i | \(-0.468000\pi\) | ||||
0.100363 | + | 0.994951i | \(0.468000\pi\) | |||||||
\(294\) | −12.4471 | −0.725930 | ||||||||
\(295\) | −12.6963 | −0.739209 | ||||||||
\(296\) | 6.80648 | 0.395619 | ||||||||
\(297\) | −0.445599 | −0.0258563 | ||||||||
\(298\) | 13.2726 | 0.768859 | ||||||||
\(299\) | 1.35290 | 0.0782404 | ||||||||
\(300\) | 3.62640 | 0.209370 | ||||||||
\(301\) | 31.2289 | 1.80000 | ||||||||
\(302\) | −10.0014 | −0.575514 | ||||||||
\(303\) | 7.45461 | 0.428256 | ||||||||
\(304\) | −3.79076 | −0.217415 | ||||||||
\(305\) | 2.99026 | 0.171222 | ||||||||
\(306\) | 6.53411 | 0.373530 | ||||||||
\(307\) | 19.4875 | 1.11221 | 0.556106 | − | 0.831111i | \(-0.312295\pi\) | ||||
0.556106 | + | 0.831111i | \(0.312295\pi\) | |||||||
\(308\) | −1.96504 | −0.111969 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 9.34373 | 0.530688 | ||||||||
\(311\) | 33.4413 | 1.89628 | 0.948140 | − | 0.317853i | \(-0.102962\pi\) | ||||
0.948140 | + | 0.317853i | \(0.102962\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 13.3906 | 0.756881 | 0.378440 | − | 0.925626i | \(-0.376460\pi\) | ||||
0.378440 | + | 0.925626i | \(0.376460\pi\) | |||||||
\(314\) | −17.1361 | −0.967046 | ||||||||
\(315\) | 5.16841 | 0.291207 | ||||||||
\(316\) | −11.5317 | −0.648706 | ||||||||
\(317\) | 17.0064 | 0.955177 | 0.477589 | − | 0.878584i | \(-0.341511\pi\) | ||||
0.477589 | + | 0.878584i | \(0.341511\pi\) | |||||||
\(318\) | 2.35869 | 0.132269 | ||||||||
\(319\) | −2.54972 | −0.142757 | ||||||||
\(320\) | −1.17201 | −0.0655171 | ||||||||
\(321\) | −8.79608 | −0.490949 | ||||||||
\(322\) | 5.96615 | 0.332481 | ||||||||
\(323\) | −24.7692 | −1.37820 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.62640 | 0.201157 | ||||||||
\(326\) | 4.56114 | 0.252618 | ||||||||
\(327\) | −0.173361 | −0.00958686 | ||||||||
\(328\) | 0.483328 | 0.0266873 | ||||||||
\(329\) | −13.7265 | −0.756765 | ||||||||
\(330\) | 0.522245 | 0.0287487 | ||||||||
\(331\) | −0.178182 | −0.00979379 | −0.00489689 | − | 0.999988i | \(-0.501559\pi\) | ||||
−0.00489689 | + | 0.999988i | \(0.501559\pi\) | |||||||
\(332\) | −0.188229 | −0.0103304 | ||||||||
\(333\) | 6.80648 | 0.372993 | ||||||||
\(334\) | −14.7439 | −0.806750 | ||||||||
\(335\) | 2.90432 | 0.158680 | ||||||||
\(336\) | 4.40989 | 0.240579 | ||||||||
\(337\) | 8.42074 | 0.458707 | 0.229353 | − | 0.973343i | \(-0.426339\pi\) | ||||
0.229353 | + | 0.973343i | \(0.426339\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −19.8490 | −1.07805 | ||||||||
\(340\) | −7.65802 | −0.415314 | ||||||||
\(341\) | −3.55251 | −0.192379 | ||||||||
\(342\) | −3.79076 | −0.204981 | ||||||||
\(343\) | −24.0211 | −1.29702 | ||||||||
\(344\) | −7.08156 | −0.381812 | ||||||||
\(345\) | −1.58561 | −0.0853664 | ||||||||
\(346\) | −2.88664 | −0.155186 | ||||||||
\(347\) | −32.1165 | −1.72410 | −0.862051 | − | 0.506822i | \(-0.830820\pi\) | ||||
−0.862051 | + | 0.506822i | \(0.830820\pi\) | |||||||
\(348\) | 5.72200 | 0.306732 | ||||||||
\(349\) | 11.1661 | 0.597707 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(350\) | 15.9920 | 0.854810 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0.445599 | 0.0237505 | ||||||||
\(353\) | −17.2853 | −0.920003 | −0.460001 | − | 0.887918i | \(-0.652151\pi\) | ||||
−0.460001 | + | 0.887918i | \(0.652151\pi\) | |||||||
\(354\) | −10.8330 | −0.575767 | ||||||||
\(355\) | −3.36548 | −0.178621 | ||||||||
\(356\) | 2.37544 | 0.125898 | ||||||||
\(357\) | 28.8147 | 1.52504 | ||||||||
\(358\) | 16.6474 | 0.879844 | ||||||||
\(359\) | −14.9764 | −0.790426 | −0.395213 | − | 0.918590i | \(-0.629329\pi\) | ||||
−0.395213 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(360\) | −1.17201 | −0.0617701 | ||||||||
\(361\) | −4.63016 | −0.243692 | ||||||||
\(362\) | 7.52363 | 0.395433 | ||||||||
\(363\) | 10.8014 | 0.566929 | ||||||||
\(364\) | 4.40989 | 0.231141 | ||||||||
\(365\) | −13.7939 | −0.722006 | ||||||||
\(366\) | 2.55140 | 0.133364 | ||||||||
\(367\) | −13.1108 | −0.684376 | −0.342188 | − | 0.939631i | \(-0.611168\pi\) | ||||
−0.342188 | + | 0.939631i | \(0.611168\pi\) | |||||||
\(368\) | −1.35290 | −0.0705250 | ||||||||
\(369\) | 0.483328 | 0.0251611 | ||||||||
\(370\) | −7.97723 | −0.414717 | ||||||||
\(371\) | 10.4015 | 0.540021 | ||||||||
\(372\) | 7.97242 | 0.413351 | ||||||||
\(373\) | 3.21477 | 0.166454 | 0.0832271 | − | 0.996531i | \(-0.473477\pi\) | ||||
0.0832271 | + | 0.996531i | \(0.473477\pi\) | |||||||
\(374\) | 2.91160 | 0.150555 | ||||||||
\(375\) | −10.1102 | −0.522088 | ||||||||
\(376\) | 3.11266 | 0.160523 | ||||||||
\(377\) | 5.72200 | 0.294698 | ||||||||
\(378\) | 4.40989 | 0.226820 | ||||||||
\(379\) | 24.4364 | 1.25521 | 0.627607 | − | 0.778530i | \(-0.284035\pi\) | ||||
0.627607 | + | 0.778530i | \(0.284035\pi\) | |||||||
\(380\) | 4.44279 | 0.227910 | ||||||||
\(381\) | 0.472255 | 0.0241944 | ||||||||
\(382\) | 6.41617 | 0.328280 | ||||||||
\(383\) | 18.0568 | 0.922659 | 0.461330 | − | 0.887229i | \(-0.347373\pi\) | ||||
0.461330 | + | 0.887229i | \(0.347373\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.30304 | 0.117374 | ||||||||
\(386\) | 18.5408 | 0.943704 | ||||||||
\(387\) | −7.08156 | −0.359976 | ||||||||
\(388\) | −5.14559 | −0.261228 | ||||||||
\(389\) | −1.98143 | −0.100462 | −0.0502312 | − | 0.998738i | \(-0.515996\pi\) | ||||
−0.0502312 | + | 0.998738i | \(0.515996\pi\) | |||||||
\(390\) | −1.17201 | −0.0593468 | ||||||||
\(391\) | −8.84002 | −0.447059 | ||||||||
\(392\) | 12.4471 | 0.628674 | ||||||||
\(393\) | −8.07447 | −0.407303 | ||||||||
\(394\) | 3.43025 | 0.172814 | ||||||||
\(395\) | 13.5152 | 0.680022 | ||||||||
\(396\) | 0.445599 | 0.0223922 | ||||||||
\(397\) | −22.7468 | −1.14163 | −0.570813 | − | 0.821080i | \(-0.693372\pi\) | ||||
−0.570813 | + | 0.821080i | \(0.693372\pi\) | |||||||
\(398\) | −20.4116 | −1.02314 | ||||||||
\(399\) | −16.7168 | −0.836887 | ||||||||
\(400\) | −3.62640 | −0.181320 | ||||||||
\(401\) | −22.0727 | −1.10226 | −0.551130 | − | 0.834419i | \(-0.685803\pi\) | ||||
−0.551130 | + | 0.834419i | \(0.685803\pi\) | |||||||
\(402\) | 2.47808 | 0.123595 | ||||||||
\(403\) | 7.97242 | 0.397135 | ||||||||
\(404\) | −7.45461 | −0.370881 | ||||||||
\(405\) | −1.17201 | −0.0582374 | ||||||||
\(406\) | 25.2334 | 1.25231 | ||||||||
\(407\) | 3.03296 | 0.150338 | ||||||||
\(408\) | −6.53411 | −0.323487 | ||||||||
\(409\) | 8.78100 | 0.434192 | 0.217096 | − | 0.976150i | \(-0.430341\pi\) | ||||
0.217096 | + | 0.976150i | \(0.430341\pi\) | |||||||
\(410\) | −0.566464 | −0.0279756 | ||||||||
\(411\) | −10.2707 | −0.506616 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −47.7723 | −2.35072 | ||||||||
\(414\) | −1.35290 | −0.0664916 | ||||||||
\(415\) | 0.220605 | 0.0108291 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −2.46420 | −0.120672 | ||||||||
\(418\) | −1.68916 | −0.0826195 | ||||||||
\(419\) | 12.0635 | 0.589343 | 0.294671 | − | 0.955599i | \(-0.404790\pi\) | ||||
0.294671 | + | 0.955599i | \(0.404790\pi\) | |||||||
\(420\) | −5.16841 | −0.252193 | ||||||||
\(421\) | 1.57768 | 0.0768914 | 0.0384457 | − | 0.999261i | \(-0.487759\pi\) | ||||
0.0384457 | + | 0.999261i | \(0.487759\pi\) | |||||||
\(422\) | 10.3909 | 0.505821 | ||||||||
\(423\) | 3.11266 | 0.151343 | ||||||||
\(424\) | −2.35869 | −0.114548 | ||||||||
\(425\) | −23.6953 | −1.14939 | ||||||||
\(426\) | −2.87156 | −0.139127 | ||||||||
\(427\) | 11.2514 | 0.544493 | ||||||||
\(428\) | 8.79608 | 0.425175 | ||||||||
\(429\) | 0.445599 | 0.0215137 | ||||||||
\(430\) | 8.29963 | 0.400243 | ||||||||
\(431\) | 25.2451 | 1.21601 | 0.608007 | − | 0.793931i | \(-0.291969\pi\) | ||||
0.608007 | + | 0.793931i | \(0.291969\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −17.2197 | −0.827524 | −0.413762 | − | 0.910385i | \(-0.635785\pi\) | ||||
−0.413762 | + | 0.910385i | \(0.635785\pi\) | |||||||
\(434\) | 35.1575 | 1.68761 | ||||||||
\(435\) | −6.70622 | −0.321539 | ||||||||
\(436\) | 0.173361 | 0.00830246 | ||||||||
\(437\) | 5.12853 | 0.245331 | ||||||||
\(438\) | −11.7695 | −0.562367 | ||||||||
\(439\) | −25.7156 | −1.22734 | −0.613670 | − | 0.789562i | \(-0.710308\pi\) | ||||
−0.613670 | + | 0.789562i | \(0.710308\pi\) | |||||||
\(440\) | −0.522245 | −0.0248971 | ||||||||
\(441\) | 12.4471 | 0.592719 | ||||||||
\(442\) | −6.53411 | −0.310796 | ||||||||
\(443\) | −21.4498 | −1.01911 | −0.509556 | − | 0.860438i | \(-0.670190\pi\) | ||||
−0.509556 | + | 0.860438i | \(0.670190\pi\) | |||||||
\(444\) | −6.80648 | −0.323021 | ||||||||
\(445\) | −2.78403 | −0.131976 | ||||||||
\(446\) | −3.71253 | −0.175793 | ||||||||
\(447\) | −13.2726 | −0.627771 | ||||||||
\(448\) | −4.40989 | −0.208348 | ||||||||
\(449\) | −9.64925 | −0.455376 | −0.227688 | − | 0.973734i | \(-0.573117\pi\) | ||||
−0.227688 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(450\) | −3.62640 | −0.170950 | ||||||||
\(451\) | 0.215371 | 0.0101414 | ||||||||
\(452\) | 19.8490 | 0.933619 | ||||||||
\(453\) | 10.0014 | 0.469905 | ||||||||
\(454\) | −11.8872 | −0.557893 | ||||||||
\(455\) | −5.16841 | −0.242299 | ||||||||
\(456\) | 3.79076 | 0.177518 | ||||||||
\(457\) | −21.4975 | −1.00561 | −0.502805 | − | 0.864400i | \(-0.667699\pi\) | ||||
−0.502805 | + | 0.864400i | \(0.667699\pi\) | |||||||
\(458\) | 14.5836 | 0.681448 | ||||||||
\(459\) | −6.53411 | −0.304986 | ||||||||
\(460\) | 1.58561 | 0.0739295 | ||||||||
\(461\) | 2.06933 | 0.0963783 | 0.0481891 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481891 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(462\) | 1.96504 | 0.0914221 | ||||||||
\(463\) | −1.41092 | −0.0655709 | −0.0327855 | − | 0.999462i | \(-0.510438\pi\) | ||||
−0.0327855 | + | 0.999462i | \(0.510438\pi\) | |||||||
\(464\) | −5.72200 | −0.265637 | ||||||||
\(465\) | −9.34373 | −0.433305 | ||||||||
\(466\) | 4.17408 | 0.193360 | ||||||||
\(467\) | −28.7723 | −1.33142 | −0.665711 | − | 0.746210i | \(-0.731872\pi\) | ||||
−0.665711 | + | 0.746210i | \(0.731872\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 10.9280 | 0.504610 | ||||||||
\(470\) | −3.64805 | −0.168272 | ||||||||
\(471\) | 17.1361 | 0.789590 | ||||||||
\(472\) | 10.8330 | 0.498629 | ||||||||
\(473\) | −3.15554 | −0.145092 | ||||||||
\(474\) | 11.5317 | 0.529666 | ||||||||
\(475\) | 13.7468 | 0.630747 | ||||||||
\(476\) | −28.8147 | −1.32072 | ||||||||
\(477\) | −2.35869 | −0.107997 | ||||||||
\(478\) | −0.656747 | −0.0300389 | ||||||||
\(479\) | 6.49308 | 0.296676 | 0.148338 | − | 0.988937i | \(-0.452608\pi\) | ||||
0.148338 | + | 0.988937i | \(0.452608\pi\) | |||||||
\(480\) | 1.17201 | 0.0534945 | ||||||||
\(481\) | −6.80648 | −0.310349 | ||||||||
\(482\) | 17.0766 | 0.777818 | ||||||||
\(483\) | −5.96615 | −0.271469 | ||||||||
\(484\) | −10.8014 | −0.490975 | ||||||||
\(485\) | 6.03066 | 0.273838 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 31.9604 | 1.44826 | 0.724132 | − | 0.689661i | \(-0.242241\pi\) | ||||
0.724132 | + | 0.689661i | \(0.242241\pi\) | |||||||
\(488\) | −2.55140 | −0.115497 | ||||||||
\(489\) | −4.56114 | −0.206262 | ||||||||
\(490\) | −14.5881 | −0.659022 | ||||||||
\(491\) | 14.3666 | 0.648357 | 0.324179 | − | 0.945996i | \(-0.394912\pi\) | ||||
0.324179 | + | 0.945996i | \(0.394912\pi\) | |||||||
\(492\) | −0.483328 | −0.0217901 | ||||||||
\(493\) | −37.3882 | −1.68388 | ||||||||
\(494\) | 3.79076 | 0.170554 | ||||||||
\(495\) | −0.522245 | −0.0234732 | ||||||||
\(496\) | −7.97242 | −0.357972 | ||||||||
\(497\) | −12.6632 | −0.568024 | ||||||||
\(498\) | 0.188229 | 0.00843472 | ||||||||
\(499\) | 6.86384 | 0.307268 | 0.153634 | − | 0.988128i | \(-0.450902\pi\) | ||||
0.153634 | + | 0.988128i | \(0.450902\pi\) | |||||||
\(500\) | 10.1102 | 0.452142 | ||||||||
\(501\) | 14.7439 | 0.658709 | ||||||||
\(502\) | 24.2454 | 1.08212 | ||||||||
\(503\) | −9.95300 | −0.443782 | −0.221891 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221891 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(504\) | −4.40989 | −0.196432 | ||||||||
\(505\) | 8.73685 | 0.388785 | ||||||||
\(506\) | −0.602853 | −0.0268001 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −0.472255 | −0.0209529 | ||||||||
\(509\) | −9.36790 | −0.415225 | −0.207612 | − | 0.978211i | \(-0.566569\pi\) | ||||
−0.207612 | + | 0.978211i | \(0.566569\pi\) | |||||||
\(510\) | 7.65802 | 0.339103 | ||||||||
\(511\) | −51.9021 | −2.29601 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.79076 | 0.167366 | ||||||||
\(514\) | −12.8223 | −0.565567 | ||||||||
\(515\) | 1.17201 | 0.0516448 | ||||||||
\(516\) | 7.08156 | 0.311748 | ||||||||
\(517\) | 1.38700 | 0.0610001 | ||||||||
\(518\) | −30.0158 | −1.31882 | ||||||||
\(519\) | 2.88664 | 0.126709 | ||||||||
\(520\) | 1.17201 | 0.0513959 | ||||||||
\(521\) | −13.4274 | −0.588266 | −0.294133 | − | 0.955765i | \(-0.595031\pi\) | ||||
−0.294133 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(522\) | −5.72200 | −0.250445 | ||||||||
\(523\) | −33.8560 | −1.48042 | −0.740210 | − | 0.672376i | \(-0.765274\pi\) | ||||
−0.740210 | + | 0.672376i | \(0.765274\pi\) | |||||||
\(524\) | 8.07447 | 0.352735 | ||||||||
\(525\) | −15.9920 | −0.697949 | ||||||||
\(526\) | 29.4695 | 1.28493 | ||||||||
\(527\) | −52.0927 | −2.26919 | ||||||||
\(528\) | −0.445599 | −0.0193922 | ||||||||
\(529\) | −21.1697 | −0.920420 | ||||||||
\(530\) | 2.76440 | 0.120078 | ||||||||
\(531\) | 10.8330 | 0.470112 | ||||||||
\(532\) | 16.7168 | 0.724766 | ||||||||
\(533\) | −0.483328 | −0.0209353 | ||||||||
\(534\) | −2.37544 | −0.102795 | ||||||||
\(535\) | −10.3091 | −0.445700 | ||||||||
\(536\) | −2.47808 | −0.107037 | ||||||||
\(537\) | −16.6474 | −0.718390 | ||||||||
\(538\) | 22.9635 | 0.990026 | ||||||||
\(539\) | 5.54642 | 0.238901 | ||||||||
\(540\) | 1.17201 | 0.0504351 | ||||||||
\(541\) | 36.7350 | 1.57936 | 0.789680 | − | 0.613518i | \(-0.210246\pi\) | ||||
0.789680 | + | 0.613518i | \(0.210246\pi\) | |||||||
\(542\) | 3.57490 | 0.153555 | ||||||||
\(543\) | −7.52363 | −0.322870 | ||||||||
\(544\) | 6.53411 | 0.280148 | ||||||||
\(545\) | −0.203180 | −0.00870326 | ||||||||
\(546\) | −4.40989 | −0.188726 | ||||||||
\(547\) | −27.3146 | −1.16789 | −0.583944 | − | 0.811794i | \(-0.698491\pi\) | ||||
−0.583944 | + | 0.811794i | \(0.698491\pi\) | |||||||
\(548\) | 10.2707 | 0.438742 | ||||||||
\(549\) | −2.55140 | −0.108891 | ||||||||
\(550\) | −1.61592 | −0.0689032 | ||||||||
\(551\) | 21.6907 | 0.924056 | ||||||||
\(552\) | 1.35290 | 0.0575834 | ||||||||
\(553\) | 50.8533 | 2.16250 | ||||||||
\(554\) | 11.0480 | 0.469383 | ||||||||
\(555\) | 7.97723 | 0.338615 | ||||||||
\(556\) | 2.46420 | 0.104505 | ||||||||
\(557\) | −1.15626 | −0.0489925 | −0.0244962 | − | 0.999700i | \(-0.507798\pi\) | ||||
−0.0244962 | + | 0.999700i | \(0.507798\pi\) | |||||||
\(558\) | −7.97242 | −0.337500 | ||||||||
\(559\) | 7.08156 | 0.299518 | ||||||||
\(560\) | 5.16841 | 0.218405 | ||||||||
\(561\) | −2.91160 | −0.122928 | ||||||||
\(562\) | 18.7003 | 0.788825 | ||||||||
\(563\) | −13.1468 | −0.554073 | −0.277036 | − | 0.960859i | \(-0.589352\pi\) | ||||
−0.277036 | + | 0.960859i | \(0.589352\pi\) | |||||||
\(564\) | −3.11266 | −0.131067 | ||||||||
\(565\) | −23.2632 | −0.978689 | ||||||||
\(566\) | 29.5791 | 1.24330 | ||||||||
\(567\) | −4.40989 | −0.185198 | ||||||||
\(568\) | 2.87156 | 0.120488 | ||||||||
\(569\) | 25.2632 | 1.05909 | 0.529544 | − | 0.848283i | \(-0.322363\pi\) | ||||
0.529544 | + | 0.848283i | \(0.322363\pi\) | |||||||
\(570\) | −4.44279 | −0.186088 | ||||||||
\(571\) | 37.0533 | 1.55063 | 0.775317 | − | 0.631572i | \(-0.217590\pi\) | ||||
0.775317 | + | 0.631572i | \(0.217590\pi\) | |||||||
\(572\) | −0.445599 | −0.0186314 | ||||||||
\(573\) | −6.41617 | −0.268039 | ||||||||
\(574\) | −2.13142 | −0.0889639 | ||||||||
\(575\) | 4.90617 | 0.204601 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.6715 | 0.735674 | 0.367837 | − | 0.929890i | \(-0.380098\pi\) | ||||
0.367837 | + | 0.929890i | \(0.380098\pi\) | |||||||
\(578\) | 25.6946 | 1.06875 | ||||||||
\(579\) | −18.5408 | −0.770531 | ||||||||
\(580\) | 6.70622 | 0.278461 | ||||||||
\(581\) | 0.830067 | 0.0344370 | ||||||||
\(582\) | 5.14559 | 0.213291 | ||||||||
\(583\) | −1.05103 | −0.0435292 | ||||||||
\(584\) | 11.7695 | 0.487024 | ||||||||
\(585\) | 1.17201 | 0.0484565 | ||||||||
\(586\) | 3.43588 | 0.141935 | ||||||||
\(587\) | −32.9697 | −1.36080 | −0.680402 | − | 0.732839i | \(-0.738195\pi\) | ||||
−0.680402 | + | 0.732839i | \(0.738195\pi\) | |||||||
\(588\) | −12.4471 | −0.513310 | ||||||||
\(589\) | 30.2215 | 1.24526 | ||||||||
\(590\) | −12.6963 | −0.522700 | ||||||||
\(591\) | −3.43025 | −0.141102 | ||||||||
\(592\) | 6.80648 | 0.279745 | ||||||||
\(593\) | −6.45229 | −0.264964 | −0.132482 | − | 0.991185i | \(-0.542295\pi\) | ||||
−0.132482 | + | 0.991185i | \(0.542295\pi\) | |||||||
\(594\) | −0.445599 | −0.0182832 | ||||||||
\(595\) | 33.7710 | 1.38448 | ||||||||
\(596\) | 13.2726 | 0.543665 | ||||||||
\(597\) | 20.4116 | 0.835391 | ||||||||
\(598\) | 1.35290 | 0.0553243 | ||||||||
\(599\) | −41.9936 | −1.71581 | −0.857905 | − | 0.513808i | \(-0.828234\pi\) | ||||
−0.857905 | + | 0.513808i | \(0.828234\pi\) | |||||||
\(600\) | 3.62640 | 0.148047 | ||||||||
\(601\) | 4.32233 | 0.176311 | 0.0881557 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881557 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(602\) | 31.2289 | 1.27279 | ||||||||
\(603\) | −2.47808 | −0.100915 | ||||||||
\(604\) | −10.0014 | −0.406950 | ||||||||
\(605\) | 12.6594 | 0.514676 | ||||||||
\(606\) | 7.45461 | 0.302823 | ||||||||
\(607\) | 13.5384 | 0.549505 | 0.274753 | − | 0.961515i | \(-0.411404\pi\) | ||||
0.274753 | + | 0.961515i | \(0.411404\pi\) | |||||||
\(608\) | −3.79076 | −0.153736 | ||||||||
\(609\) | −25.2334 | −1.02251 | ||||||||
\(610\) | 2.99026 | 0.121072 | ||||||||
\(611\) | −3.11266 | −0.125925 | ||||||||
\(612\) | 6.53411 | 0.264126 | ||||||||
\(613\) | 2.56880 | 0.103753 | 0.0518763 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518763 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(614\) | 19.4875 | 0.786452 | ||||||||
\(615\) | 0.566464 | 0.0228420 | ||||||||
\(616\) | −1.96504 | −0.0791738 | ||||||||
\(617\) | −7.44553 | −0.299746 | −0.149873 | − | 0.988705i | \(-0.547886\pi\) | ||||
−0.149873 | + | 0.988705i | \(0.547886\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 17.2836 | 0.694688 | 0.347344 | − | 0.937738i | \(-0.387084\pi\) | ||||
0.347344 | + | 0.937738i | \(0.387084\pi\) | |||||||
\(620\) | 9.34373 | 0.375253 | ||||||||
\(621\) | 1.35290 | 0.0542901 | ||||||||
\(622\) | 33.4413 | 1.34087 | ||||||||
\(623\) | −10.4754 | −0.419688 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 6.28280 | 0.251312 | ||||||||
\(626\) | 13.3906 | 0.535196 | ||||||||
\(627\) | 1.68916 | 0.0674585 | ||||||||
\(628\) | −17.1361 | −0.683805 | ||||||||
\(629\) | 44.4743 | 1.77331 | ||||||||
\(630\) | 5.16841 | 0.205915 | ||||||||
\(631\) | −11.1178 | −0.442593 | −0.221297 | − | 0.975207i | \(-0.571029\pi\) | ||||
−0.221297 | + | 0.975207i | \(0.571029\pi\) | |||||||
\(632\) | −11.5317 | −0.458705 | ||||||||
\(633\) | −10.3909 | −0.413001 | ||||||||
\(634\) | 17.0064 | 0.675412 | ||||||||
\(635\) | 0.553486 | 0.0219644 | ||||||||
\(636\) | 2.35869 | 0.0935281 | ||||||||
\(637\) | −12.4471 | −0.493172 | ||||||||
\(638\) | −2.54972 | −0.100944 | ||||||||
\(639\) | 2.87156 | 0.113597 | ||||||||
\(640\) | −1.17201 | −0.0463276 | ||||||||
\(641\) | 3.74495 | 0.147917 | 0.0739584 | − | 0.997261i | \(-0.476437\pi\) | ||||
0.0739584 | + | 0.997261i | \(0.476437\pi\) | |||||||
\(642\) | −8.79608 | −0.347154 | ||||||||
\(643\) | 29.7447 | 1.17302 | 0.586508 | − | 0.809944i | \(-0.300502\pi\) | ||||
0.586508 | + | 0.809944i | \(0.300502\pi\) | |||||||
\(644\) | 5.96615 | 0.235099 | ||||||||
\(645\) | −8.29963 | −0.326797 | ||||||||
\(646\) | −24.7692 | −0.974532 | ||||||||
\(647\) | 8.05132 | 0.316530 | 0.158265 | − | 0.987397i | \(-0.449410\pi\) | ||||
0.158265 | + | 0.987397i | \(0.449410\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.82718 | 0.189483 | ||||||||
\(650\) | 3.62640 | 0.142239 | ||||||||
\(651\) | −35.1575 | −1.37793 | ||||||||
\(652\) | 4.56114 | 0.178628 | ||||||||
\(653\) | 3.25098 | 0.127221 | 0.0636103 | − | 0.997975i | \(-0.479739\pi\) | ||||
0.0636103 | + | 0.997975i | \(0.479739\pi\) | |||||||
\(654\) | −0.173361 | −0.00677893 | ||||||||
\(655\) | −9.46332 | −0.369763 | ||||||||
\(656\) | 0.483328 | 0.0188708 | ||||||||
\(657\) | 11.7695 | 0.459171 | ||||||||
\(658\) | −13.7265 | −0.535113 | ||||||||
\(659\) | −1.71860 | −0.0669471 | −0.0334735 | − | 0.999440i | \(-0.510657\pi\) | ||||
−0.0334735 | + | 0.999440i | \(0.510657\pi\) | |||||||
\(660\) | 0.522245 | 0.0203284 | ||||||||
\(661\) | −26.0578 | −1.01353 | −0.506765 | − | 0.862084i | \(-0.669159\pi\) | ||||
−0.506765 | + | 0.862084i | \(0.669159\pi\) | |||||||
\(662\) | −0.178182 | −0.00692525 | ||||||||
\(663\) | 6.53411 | 0.253764 | ||||||||
\(664\) | −0.188229 | −0.00730469 | ||||||||
\(665\) | −19.5922 | −0.759753 | ||||||||
\(666\) | 6.80648 | 0.263746 | ||||||||
\(667\) | 7.74132 | 0.299745 | ||||||||
\(668\) | −14.7439 | −0.570458 | ||||||||
\(669\) | 3.71253 | 0.143535 | ||||||||
\(670\) | 2.90432 | 0.112204 | ||||||||
\(671\) | −1.13690 | −0.0438897 | ||||||||
\(672\) | 4.40989 | 0.170115 | ||||||||
\(673\) | 22.1388 | 0.853390 | 0.426695 | − | 0.904396i | \(-0.359678\pi\) | ||||
0.426695 | + | 0.904396i | \(0.359678\pi\) | |||||||
\(674\) | 8.42074 | 0.324355 | ||||||||
\(675\) | 3.62640 | 0.139580 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 17.4143 | 0.669287 | 0.334643 | − | 0.942345i | \(-0.391384\pi\) | ||||
0.334643 | + | 0.942345i | \(0.391384\pi\) | |||||||
\(678\) | −19.8490 | −0.762297 | ||||||||
\(679\) | 22.6915 | 0.870818 | ||||||||
\(680\) | −7.65802 | −0.293672 | ||||||||
\(681\) | 11.8872 | 0.455518 | ||||||||
\(682\) | −3.55251 | −0.136033 | ||||||||
\(683\) | −29.1800 | −1.11654 | −0.558270 | − | 0.829659i | \(-0.688535\pi\) | ||||
−0.558270 | + | 0.829659i | \(0.688535\pi\) | |||||||
\(684\) | −3.79076 | −0.144943 | ||||||||
\(685\) | −12.0373 | −0.459922 | ||||||||
\(686\) | −24.0211 | −0.917130 | ||||||||
\(687\) | −14.5836 | −0.556400 | ||||||||
\(688\) | −7.08156 | −0.269982 | ||||||||
\(689\) | 2.35869 | 0.0898589 | ||||||||
\(690\) | −1.58561 | −0.0603632 | ||||||||
\(691\) | −20.3641 | −0.774687 | −0.387344 | − | 0.921935i | \(-0.626607\pi\) | ||||
−0.387344 | + | 0.921935i | \(0.626607\pi\) | |||||||
\(692\) | −2.88664 | −0.109733 | ||||||||
\(693\) | −1.96504 | −0.0746458 | ||||||||
\(694\) | −32.1165 | −1.21912 | ||||||||
\(695\) | −2.88805 | −0.109550 | ||||||||
\(696\) | 5.72200 | 0.216892 | ||||||||
\(697\) | 3.15812 | 0.119622 | ||||||||
\(698\) | 11.1661 | 0.422643 | ||||||||
\(699\) | −4.17408 | −0.157878 | ||||||||
\(700\) | 15.9920 | 0.604442 | ||||||||
\(701\) | −32.9142 | −1.24315 | −0.621577 | − | 0.783353i | \(-0.713508\pi\) | ||||
−0.621577 | + | 0.783353i | \(0.713508\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −25.8017 | −0.973130 | ||||||||
\(704\) | 0.445599 | 0.0167942 | ||||||||
\(705\) | 3.64805 | 0.137394 | ||||||||
\(706\) | −17.2853 | −0.650540 | ||||||||
\(707\) | 32.8740 | 1.23635 | ||||||||
\(708\) | −10.8330 | −0.407129 | ||||||||
\(709\) | 13.8759 | 0.521121 | 0.260561 | − | 0.965458i | \(-0.416093\pi\) | ||||
0.260561 | + | 0.965458i | \(0.416093\pi\) | |||||||
\(710\) | −3.36548 | −0.126304 | ||||||||
\(711\) | −11.5317 | −0.432471 | ||||||||
\(712\) | 2.37544 | 0.0890233 | ||||||||
\(713\) | 10.7859 | 0.403936 | ||||||||
\(714\) | 28.8147 | 1.07836 | ||||||||
\(715\) | 0.522245 | 0.0195309 | ||||||||
\(716\) | 16.6474 | 0.622144 | ||||||||
\(717\) | 0.656747 | 0.0245267 | ||||||||
\(718\) | −14.9764 | −0.558915 | ||||||||
\(719\) | −11.5182 | −0.429557 | −0.214778 | − | 0.976663i | \(-0.568903\pi\) | ||||
−0.214778 | + | 0.976663i | \(0.568903\pi\) | |||||||
\(720\) | −1.17201 | −0.0436781 | ||||||||
\(721\) | 4.40989 | 0.164233 | ||||||||
\(722\) | −4.63016 | −0.172317 | ||||||||
\(723\) | −17.0766 | −0.635086 | ||||||||
\(724\) | 7.52363 | 0.279614 | ||||||||
\(725\) | 20.7503 | 0.770646 | ||||||||
\(726\) | 10.8014 | 0.400879 | ||||||||
\(727\) | 27.2771 | 1.01165 | 0.505827 | − | 0.862635i | \(-0.331188\pi\) | ||||
0.505827 | + | 0.862635i | \(0.331188\pi\) | |||||||
\(728\) | 4.40989 | 0.163441 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.7939 | −0.510535 | ||||||||
\(731\) | −46.2717 | −1.71142 | ||||||||
\(732\) | 2.55140 | 0.0943025 | ||||||||
\(733\) | −23.4699 | −0.866881 | −0.433441 | − | 0.901182i | \(-0.642701\pi\) | ||||
−0.433441 | + | 0.901182i | \(0.642701\pi\) | |||||||
\(734\) | −13.1108 | −0.483927 | ||||||||
\(735\) | 14.5881 | 0.538089 | ||||||||
\(736\) | −1.35290 | −0.0498687 | ||||||||
\(737\) | −1.10423 | −0.0406748 | ||||||||
\(738\) | 0.483328 | 0.0177916 | ||||||||
\(739\) | −6.93906 | −0.255257 | −0.127629 | − | 0.991822i | \(-0.540737\pi\) | ||||
−0.127629 | + | 0.991822i | \(0.540737\pi\) | |||||||
\(740\) | −7.97723 | −0.293249 | ||||||||
\(741\) | −3.79076 | −0.139257 | ||||||||
\(742\) | 10.4015 | 0.381853 | ||||||||
\(743\) | −13.7515 | −0.504492 | −0.252246 | − | 0.967663i | \(-0.581169\pi\) | ||||
−0.252246 | + | 0.967663i | \(0.581169\pi\) | |||||||
\(744\) | 7.97242 | 0.292283 | ||||||||
\(745\) | −15.5555 | −0.569910 | ||||||||
\(746\) | 3.21477 | 0.117701 | ||||||||
\(747\) | −0.188229 | −0.00688692 | ||||||||
\(748\) | 2.91160 | 0.106458 | ||||||||
\(749\) | −38.7897 | −1.41735 | ||||||||
\(750\) | −10.1102 | −0.369172 | ||||||||
\(751\) | 3.48376 | 0.127124 | 0.0635622 | − | 0.997978i | \(-0.479754\pi\) | ||||
0.0635622 | + | 0.997978i | \(0.479754\pi\) | |||||||
\(752\) | 3.11266 | 0.113507 | ||||||||
\(753\) | −24.2454 | −0.883551 | ||||||||
\(754\) | 5.72200 | 0.208383 | ||||||||
\(755\) | 11.7217 | 0.426595 | ||||||||
\(756\) | 4.40989 | 0.160386 | ||||||||
\(757\) | −9.49162 | −0.344979 | −0.172489 | − | 0.985011i | \(-0.555181\pi\) | ||||
−0.172489 | + | 0.985011i | \(0.555181\pi\) | |||||||
\(758\) | 24.4364 | 0.887570 | ||||||||
\(759\) | 0.602853 | 0.0218822 | ||||||||
\(760\) | 4.44279 | 0.161157 | ||||||||
\(761\) | 2.52052 | 0.0913688 | 0.0456844 | − | 0.998956i | \(-0.485453\pi\) | ||||
0.0456844 | + | 0.998956i | \(0.485453\pi\) | |||||||
\(762\) | 0.472255 | 0.0171080 | ||||||||
\(763\) | −0.764500 | −0.0276768 | ||||||||
\(764\) | 6.41617 | 0.232129 | ||||||||
\(765\) | −7.65802 | −0.276876 | ||||||||
\(766\) | 18.0568 | 0.652419 | ||||||||
\(767\) | −10.8330 | −0.391157 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −24.5967 | −0.886981 | −0.443490 | − | 0.896279i | \(-0.646260\pi\) | ||||
−0.443490 | + | 0.896279i | \(0.646260\pi\) | |||||||
\(770\) | 2.30304 | 0.0829959 | ||||||||
\(771\) | 12.8223 | 0.461783 | ||||||||
\(772\) | 18.5408 | 0.667300 | ||||||||
\(773\) | 22.5085 | 0.809573 | 0.404787 | − | 0.914411i | \(-0.367346\pi\) | ||||
0.404787 | + | 0.914411i | \(0.367346\pi\) | |||||||
\(774\) | −7.08156 | −0.254541 | ||||||||
\(775\) | 28.9112 | 1.03852 | ||||||||
\(776\) | −5.14559 | −0.184716 | ||||||||
\(777\) | 30.0158 | 1.07681 | ||||||||
\(778\) | −1.98143 | −0.0710376 | ||||||||
\(779\) | −1.83218 | −0.0656447 | ||||||||
\(780\) | −1.17201 | −0.0419645 | ||||||||
\(781\) | 1.27956 | 0.0457864 | ||||||||
\(782\) | −8.84002 | −0.316119 | ||||||||
\(783\) | 5.72200 | 0.204488 | ||||||||
\(784\) | 12.4471 | 0.444539 | ||||||||
\(785\) | 20.0836 | 0.716815 | ||||||||
\(786\) | −8.07447 | −0.288007 | ||||||||
\(787\) | 12.1689 | 0.433774 | 0.216887 | − | 0.976197i | \(-0.430410\pi\) | ||||
0.216887 | + | 0.976197i | \(0.430410\pi\) | |||||||
\(788\) | 3.43025 | 0.122198 | ||||||||
\(789\) | −29.4695 | −1.04914 | ||||||||
\(790\) | 13.5152 | 0.480848 | ||||||||
\(791\) | −87.5319 | −3.11228 | ||||||||
\(792\) | 0.445599 | 0.0158337 | ||||||||
\(793\) | 2.55140 | 0.0906030 | ||||||||
\(794\) | −22.7468 | −0.807252 | ||||||||
\(795\) | −2.76440 | −0.0980430 | ||||||||
\(796\) | −20.4116 | −0.723470 | ||||||||
\(797\) | −22.6668 | −0.802899 | −0.401449 | − | 0.915881i | \(-0.631493\pi\) | ||||
−0.401449 | + | 0.915881i | \(0.631493\pi\) | |||||||
\(798\) | −16.7168 | −0.591769 | ||||||||
\(799\) | 20.3384 | 0.719523 | ||||||||
\(800\) | −3.62640 | −0.128213 | ||||||||
\(801\) | 2.37544 | 0.0839320 | ||||||||
\(802\) | −22.0727 | −0.779415 | ||||||||
\(803\) | 5.24447 | 0.185073 | ||||||||
\(804\) | 2.47808 | 0.0873950 | ||||||||
\(805\) | −6.99237 | −0.246448 | ||||||||
\(806\) | 7.97242 | 0.280817 | ||||||||
\(807\) | −22.9635 | −0.808353 | ||||||||
\(808\) | −7.45461 | −0.262252 | ||||||||
\(809\) | −25.6679 | −0.902434 | −0.451217 | − | 0.892414i | \(-0.649010\pi\) | ||||
−0.451217 | + | 0.892414i | \(0.649010\pi\) | |||||||
\(810\) | −1.17201 | −0.0411801 | ||||||||
\(811\) | 3.52014 | 0.123609 | 0.0618044 | − | 0.998088i | \(-0.480315\pi\) | ||||
0.0618044 | + | 0.998088i | \(0.480315\pi\) | |||||||
\(812\) | 25.2334 | 0.885518 | ||||||||
\(813\) | −3.57490 | −0.125377 | ||||||||
\(814\) | 3.03296 | 0.106305 | ||||||||
\(815\) | −5.34569 | −0.187251 | ||||||||
\(816\) | −6.53411 | −0.228740 | ||||||||
\(817\) | 26.8445 | 0.939169 | ||||||||
\(818\) | 8.78100 | 0.307020 | ||||||||
\(819\) | 4.40989 | 0.154094 | ||||||||
\(820\) | −0.566464 | −0.0197818 | ||||||||
\(821\) | 46.5064 | 1.62308 | 0.811542 | − | 0.584293i | \(-0.198628\pi\) | ||||
0.811542 | + | 0.584293i | \(0.198628\pi\) | |||||||
\(822\) | −10.2707 | −0.358232 | ||||||||
\(823\) | 18.0385 | 0.628784 | 0.314392 | − | 0.949293i | \(-0.398199\pi\) | ||||
0.314392 | + | 0.949293i | \(0.398199\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 1.61592 | 0.0562592 | ||||||||
\(826\) | −47.7723 | −1.66221 | ||||||||
\(827\) | −1.68552 | −0.0586113 | −0.0293057 | − | 0.999570i | \(-0.509330\pi\) | ||||
−0.0293057 | + | 0.999570i | \(0.509330\pi\) | |||||||
\(828\) | −1.35290 | −0.0470166 | ||||||||
\(829\) | 15.8168 | 0.549339 | 0.274669 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274669 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(830\) | 0.220605 | 0.00765731 | ||||||||
\(831\) | −11.0480 | −0.383249 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 81.3307 | 2.81794 | ||||||||
\(834\) | −2.46420 | −0.0853281 | ||||||||
\(835\) | 17.2799 | 0.597997 | ||||||||
\(836\) | −1.68916 | −0.0584208 | ||||||||
\(837\) | 7.97242 | 0.275567 | ||||||||
\(838\) | 12.0635 | 0.416728 | ||||||||
\(839\) | −43.8438 | −1.51365 | −0.756827 | − | 0.653615i | \(-0.773252\pi\) | ||||
−0.756827 | + | 0.653615i | \(0.773252\pi\) | |||||||
\(840\) | −5.16841 | −0.178327 | ||||||||
\(841\) | 3.74133 | 0.129012 | ||||||||
\(842\) | 1.57768 | 0.0543704 | ||||||||
\(843\) | −18.7003 | −0.644073 | ||||||||
\(844\) | 10.3909 | 0.357669 | ||||||||
\(845\) | −1.17201 | −0.0403182 | ||||||||
\(846\) | 3.11266 | 0.107015 | ||||||||
\(847\) | 47.6331 | 1.63669 | ||||||||
\(848\) | −2.35869 | −0.0809977 | ||||||||
\(849\) | −29.5791 | −1.01515 | ||||||||
\(850\) | −23.6953 | −0.812742 | ||||||||
\(851\) | −9.20851 | −0.315664 | ||||||||
\(852\) | −2.87156 | −0.0983779 | ||||||||
\(853\) | −6.88736 | −0.235819 | −0.117909 | − | 0.993024i | \(-0.537619\pi\) | ||||
−0.117909 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(854\) | 11.2514 | 0.385015 | ||||||||
\(855\) | 4.44279 | 0.151940 | ||||||||
\(856\) | 8.79608 | 0.300644 | ||||||||
\(857\) | 19.8738 | 0.678877 | 0.339439 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339439 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(858\) | 0.445599 | 0.0152125 | ||||||||
\(859\) | −22.5579 | −0.769665 | −0.384833 | − | 0.922986i | \(-0.625741\pi\) | ||||
−0.384833 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(860\) | 8.29963 | 0.283015 | ||||||||
\(861\) | 2.13142 | 0.0726387 | ||||||||
\(862\) | 25.2451 | 0.859852 | ||||||||
\(863\) | −16.4555 | −0.560152 | −0.280076 | − | 0.959978i | \(-0.590360\pi\) | ||||
−0.280076 | + | 0.959978i | \(0.590360\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 3.38315 | 0.115031 | ||||||||
\(866\) | −17.2197 | −0.585148 | ||||||||
\(867\) | −25.6946 | −0.872635 | ||||||||
\(868\) | 35.1575 | 1.19332 | ||||||||
\(869\) | −5.13850 | −0.174312 | ||||||||
\(870\) | −6.70622 | −0.227362 | ||||||||
\(871\) | 2.47808 | 0.0839664 | ||||||||
\(872\) | 0.173361 | 0.00587073 | ||||||||
\(873\) | −5.14559 | −0.174152 | ||||||||
\(874\) | 5.12853 | 0.173475 | ||||||||
\(875\) | −44.5848 | −1.50724 | ||||||||
\(876\) | −11.7695 | −0.397654 | ||||||||
\(877\) | −12.4616 | −0.420800 | −0.210400 | − | 0.977615i | \(-0.567477\pi\) | ||||
−0.210400 | + | 0.977615i | \(0.567477\pi\) | |||||||
\(878\) | −25.7156 | −0.867861 | ||||||||
\(879\) | −3.43588 | −0.115889 | ||||||||
\(880\) | −0.522245 | −0.0176049 | ||||||||
\(881\) | −31.3557 | −1.05640 | −0.528199 | − | 0.849120i | \(-0.677133\pi\) | ||||
−0.528199 | + | 0.849120i | \(0.677133\pi\) | |||||||
\(882\) | 12.4471 | 0.419116 | ||||||||
\(883\) | −0.473730 | −0.0159423 | −0.00797114 | − | 0.999968i | \(-0.502537\pi\) | ||||
−0.00797114 | + | 0.999968i | \(0.502537\pi\) | |||||||
\(884\) | −6.53411 | −0.219766 | ||||||||
\(885\) | 12.6963 | 0.426783 | ||||||||
\(886\) | −21.4498 | −0.720621 | ||||||||
\(887\) | −32.5755 | −1.09378 | −0.546889 | − | 0.837205i | \(-0.684188\pi\) | ||||
−0.546889 | + | 0.837205i | \(0.684188\pi\) | |||||||
\(888\) | −6.80648 | −0.228410 | ||||||||
\(889\) | 2.08259 | 0.0698479 | ||||||||
\(890\) | −2.78403 | −0.0933208 | ||||||||
\(891\) | 0.445599 | 0.0149281 | ||||||||
\(892\) | −3.71253 | −0.124305 | ||||||||
\(893\) | −11.7993 | −0.394850 | ||||||||
\(894\) | −13.2726 | −0.443901 | ||||||||
\(895\) | −19.5109 | −0.652177 | ||||||||
\(896\) | −4.40989 | −0.147324 | ||||||||
\(897\) | −1.35290 | −0.0451721 | ||||||||
\(898\) | −9.64925 | −0.322000 | ||||||||
\(899\) | 45.6182 | 1.52145 | ||||||||
\(900\) | −3.62640 | −0.120880 | ||||||||
\(901\) | −15.4119 | −0.513446 | ||||||||
\(902\) | 0.215371 | 0.00717106 | ||||||||
\(903\) | −31.2289 | −1.03923 | ||||||||
\(904\) | 19.8490 | 0.660169 | ||||||||
\(905\) | −8.81774 | −0.293112 | ||||||||
\(906\) | 10.0014 | 0.332273 | ||||||||
\(907\) | −48.6651 | −1.61590 | −0.807949 | − | 0.589252i | \(-0.799422\pi\) | ||||
−0.807949 | + | 0.589252i | \(0.799422\pi\) | |||||||
\(908\) | −11.8872 | −0.394490 | ||||||||
\(909\) | −7.45461 | −0.247254 | ||||||||
\(910\) | −5.16841 | −0.171331 | ||||||||
\(911\) | 49.7482 | 1.64823 | 0.824116 | − | 0.566422i | \(-0.191673\pi\) | ||||
0.824116 | + | 0.566422i | \(0.191673\pi\) | |||||||
\(912\) | 3.79076 | 0.125525 | ||||||||
\(913\) | −0.0838745 | −0.00277584 | ||||||||
\(914\) | −21.4975 | −0.711074 | ||||||||
\(915\) | −2.99026 | −0.0988549 | ||||||||
\(916\) | 14.5836 | 0.481857 | ||||||||
\(917\) | −35.6075 | −1.17586 | ||||||||
\(918\) | −6.53411 | −0.215658 | ||||||||
\(919\) | 44.6682 | 1.47347 | 0.736734 | − | 0.676183i | \(-0.236367\pi\) | ||||
0.736734 | + | 0.676183i | \(0.236367\pi\) | |||||||
\(920\) | 1.58561 | 0.0522760 | ||||||||
\(921\) | −19.4875 | −0.642136 | ||||||||
\(922\) | 2.06933 | 0.0681497 | ||||||||
\(923\) | −2.87156 | −0.0945184 | ||||||||
\(924\) | 1.96504 | 0.0646452 | ||||||||
\(925\) | −24.6830 | −0.811573 | ||||||||
\(926\) | −1.41092 | −0.0463656 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −5.72200 | −0.187834 | ||||||||
\(929\) | −23.8368 | −0.782061 | −0.391030 | − | 0.920378i | \(-0.627881\pi\) | ||||
−0.391030 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(930\) | −9.34373 | −0.306393 | ||||||||
\(931\) | −47.1840 | −1.54639 | ||||||||
\(932\) | 4.17408 | 0.136726 | ||||||||
\(933\) | −33.4413 | −1.09482 | ||||||||
\(934\) | −28.7723 | −0.941458 | ||||||||
\(935\) | −3.41241 | −0.111598 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −11.4196 | −0.373063 | −0.186532 | − | 0.982449i | \(-0.559725\pi\) | ||||
−0.186532 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(938\) | 10.9280 | 0.356813 | ||||||||
\(939\) | −13.3906 | −0.436985 | ||||||||
\(940\) | −3.64805 | −0.118986 | ||||||||
\(941\) | 21.3611 | 0.696352 | 0.348176 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348176 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(942\) | 17.1361 | 0.558324 | ||||||||
\(943\) | −0.653896 | −0.0212938 | ||||||||
\(944\) | 10.8330 | 0.352584 | ||||||||
\(945\) | −5.16841 | −0.168129 | ||||||||
\(946\) | −3.15554 | −0.102595 | ||||||||
\(947\) | 19.3464 | 0.628672 | 0.314336 | − | 0.949312i | \(-0.398218\pi\) | ||||
0.314336 | + | 0.949312i | \(0.398218\pi\) | |||||||
\(948\) | 11.5317 | 0.374531 | ||||||||
\(949\) | −11.7695 | −0.382053 | ||||||||
\(950\) | 13.7468 | 0.446005 | ||||||||
\(951\) | −17.0064 | −0.551472 | ||||||||
\(952\) | −28.8147 | −0.933889 | ||||||||
\(953\) | −4.95543 | −0.160522 | −0.0802611 | − | 0.996774i | \(-0.525575\pi\) | ||||
−0.0802611 | + | 0.996774i | \(0.525575\pi\) | |||||||
\(954\) | −2.35869 | −0.0763653 | ||||||||
\(955\) | −7.51979 | −0.243335 | ||||||||
\(956\) | −0.656747 | −0.0212407 | ||||||||
\(957\) | 2.54972 | 0.0824208 | ||||||||
\(958\) | 6.49308 | 0.209782 | ||||||||
\(959\) | −45.2926 | −1.46257 | ||||||||
\(960\) | 1.17201 | 0.0378263 | ||||||||
\(961\) | 32.5595 | 1.05031 | ||||||||
\(962\) | −6.80648 | −0.219450 | ||||||||
\(963\) | 8.79608 | 0.283450 | ||||||||
\(964\) | 17.0766 | 0.550000 | ||||||||
\(965\) | −21.7300 | −0.699513 | ||||||||
\(966\) | −5.96615 | −0.191958 | ||||||||
\(967\) | 56.4647 | 1.81578 | 0.907891 | − | 0.419206i | \(-0.137692\pi\) | ||||
0.907891 | + | 0.419206i | \(0.137692\pi\) | |||||||
\(968\) | −10.8014 | −0.347171 | ||||||||
\(969\) | 24.7692 | 0.795702 | ||||||||
\(970\) | 6.03066 | 0.193633 | ||||||||
\(971\) | 23.9443 | 0.768408 | 0.384204 | − | 0.923248i | \(-0.374476\pi\) | ||||
0.384204 | + | 0.923248i | \(0.374476\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −10.8668 | −0.348375 | ||||||||
\(974\) | 31.9604 | 1.02408 | ||||||||
\(975\) | −3.62640 | −0.116138 | ||||||||
\(976\) | −2.55140 | −0.0816684 | ||||||||
\(977\) | 15.0721 | 0.482198 | 0.241099 | − | 0.970500i | \(-0.422492\pi\) | ||||
0.241099 | + | 0.970500i | \(0.422492\pi\) | |||||||
\(978\) | −4.56114 | −0.145849 | ||||||||
\(979\) | 1.05849 | 0.0338296 | ||||||||
\(980\) | −14.5881 | −0.465999 | ||||||||
\(981\) | 0.173361 | 0.00553498 | ||||||||
\(982\) | 14.3666 | 0.458458 | ||||||||
\(983\) | 8.53695 | 0.272286 | 0.136143 | − | 0.990689i | \(-0.456529\pi\) | ||||
0.136143 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(984\) | −0.483328 | −0.0154079 | ||||||||
\(985\) | −4.02028 | −0.128097 | ||||||||
\(986\) | −37.3882 | −1.19068 | ||||||||
\(987\) | 13.7265 | 0.436918 | ||||||||
\(988\) | 3.79076 | 0.120600 | ||||||||
\(989\) | 9.58066 | 0.304647 | ||||||||
\(990\) | −0.522245 | −0.0165980 | ||||||||
\(991\) | −40.2817 | −1.27959 | −0.639796 | − | 0.768545i | \(-0.720981\pi\) | ||||
−0.639796 | + | 0.768545i | \(0.720981\pi\) | |||||||
\(992\) | −7.97242 | −0.253125 | ||||||||
\(993\) | 0.178182 | 0.00565444 | ||||||||
\(994\) | −12.6632 | −0.401653 | ||||||||
\(995\) | 23.9225 | 0.758395 | ||||||||
\(996\) | 0.188229 | 0.00596425 | ||||||||
\(997\) | 27.8162 | 0.880949 | 0.440474 | − | 0.897765i | \(-0.354810\pi\) | ||||
0.440474 | + | 0.897765i | \(0.354810\pi\) | |||||||
\(998\) | 6.86384 | 0.217271 | ||||||||
\(999\) | −6.80648 | −0.215347 |
(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 | 8034.2.a.bc.1.6 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.6 | ✓ | 15 | 1.1 | even | 1 | trivial |