Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.36538000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.52231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | −2.52231 | −1.45626 | −0.728130 | − | 0.685440i | \(-0.759610\pi\) | ||||
−0.728130 | + | 0.685440i | \(0.759610\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.42123 | 0.635593 | 0.317797 | − | 0.948159i | \(-0.397057\pi\) | ||||
0.317797 | + | 0.948159i | \(0.397057\pi\) | |||||||
\(6\) | 2.52231 | 1.02973 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.36207 | 1.12069 | ||||||||
\(10\) | −1.42123 | −0.449432 | ||||||||
\(11\) | 1.22272 | 0.368663 | 0.184331 | − | 0.982864i | \(-0.440988\pi\) | ||||
0.184331 | + | 0.982864i | \(0.440988\pi\) | |||||||
\(12\) | −2.52231 | −0.728130 | ||||||||
\(13\) | −2.87837 | −0.798316 | −0.399158 | − | 0.916882i | \(-0.630697\pi\) | ||||
−0.399158 | + | 0.916882i | \(0.630697\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.58479 | −0.925588 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.92300 | 0.951467 | 0.475733 | − | 0.879590i | \(-0.342183\pi\) | ||||
0.475733 | + | 0.879590i | \(0.342183\pi\) | |||||||
\(18\) | −3.36207 | −0.792448 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.42123 | 0.317797 | ||||||||
\(21\) | −2.52231 | −0.550414 | ||||||||
\(22\) | −1.22272 | −0.260684 | ||||||||
\(23\) | −3.82191 | −0.796924 | −0.398462 | − | 0.917185i | \(-0.630456\pi\) | ||||
−0.398462 | + | 0.917185i | \(0.630456\pi\) | |||||||
\(24\) | 2.52231 | 0.514865 | ||||||||
\(25\) | −2.98011 | −0.596021 | ||||||||
\(26\) | 2.87837 | 0.564494 | ||||||||
\(27\) | −0.913260 | −0.175757 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 1.85516 | 0.344494 | 0.172247 | − | 0.985054i | \(-0.444897\pi\) | ||||
0.172247 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(30\) | 3.58479 | 0.654490 | ||||||||
\(31\) | 4.99711 | 0.897508 | 0.448754 | − | 0.893655i | \(-0.351868\pi\) | ||||
0.448754 | + | 0.893655i | \(0.351868\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.08408 | −0.536869 | ||||||||
\(34\) | −3.92300 | −0.672789 | ||||||||
\(35\) | 1.42123 | 0.240232 | ||||||||
\(36\) | 3.36207 | 0.560345 | ||||||||
\(37\) | 0.841807 | 0.138392 | 0.0691961 | − | 0.997603i | \(-0.477957\pi\) | ||||
0.0691961 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.26015 | 1.16255 | ||||||||
\(40\) | −1.42123 | −0.224716 | ||||||||
\(41\) | −7.37747 | −1.15217 | −0.576084 | − | 0.817391i | \(-0.695420\pi\) | ||||
−0.576084 | + | 0.817391i | \(0.695420\pi\) | |||||||
\(42\) | 2.52231 | 0.389202 | ||||||||
\(43\) | −4.80751 | −0.733138 | −0.366569 | − | 0.930391i | \(-0.619468\pi\) | ||||
−0.366569 | + | 0.930391i | \(0.619468\pi\) | |||||||
\(44\) | 1.22272 | 0.184331 | ||||||||
\(45\) | 4.77828 | 0.712303 | ||||||||
\(46\) | 3.82191 | 0.563510 | ||||||||
\(47\) | 6.55168 | 0.955661 | 0.477830 | − | 0.878452i | \(-0.341423\pi\) | ||||
0.477830 | + | 0.878452i | \(0.341423\pi\) | |||||||
\(48\) | −2.52231 | −0.364065 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.98011 | 0.421451 | ||||||||
\(51\) | −9.89504 | −1.38558 | ||||||||
\(52\) | −2.87837 | −0.399158 | ||||||||
\(53\) | −3.68427 | −0.506073 | −0.253036 | − | 0.967457i | \(-0.581429\pi\) | ||||
−0.253036 | + | 0.967457i | \(0.581429\pi\) | |||||||
\(54\) | 0.913260 | 0.124279 | ||||||||
\(55\) | 1.73776 | 0.234320 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.85516 | −0.243594 | ||||||||
\(59\) | −11.3276 | −1.47473 | −0.737367 | − | 0.675492i | \(-0.763931\pi\) | ||||
−0.737367 | + | 0.675492i | \(0.763931\pi\) | |||||||
\(60\) | −3.58479 | −0.462794 | ||||||||
\(61\) | −13.9313 | −1.78372 | −0.891859 | − | 0.452314i | \(-0.850599\pi\) | ||||
−0.891859 | + | 0.452314i | \(0.850599\pi\) | |||||||
\(62\) | −4.99711 | −0.634634 | ||||||||
\(63\) | 3.36207 | 0.423581 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.09082 | −0.507404 | ||||||||
\(66\) | 3.08408 | 0.379624 | ||||||||
\(67\) | 9.35356 | 1.14272 | 0.571360 | − | 0.820700i | \(-0.306416\pi\) | ||||
0.571360 | + | 0.820700i | \(0.306416\pi\) | |||||||
\(68\) | 3.92300 | 0.475733 | ||||||||
\(69\) | 9.64007 | 1.16053 | ||||||||
\(70\) | −1.42123 | −0.169869 | ||||||||
\(71\) | −9.04463 | −1.07340 | −0.536700 | − | 0.843773i | \(-0.680329\pi\) | ||||
−0.536700 | + | 0.843773i | \(0.680329\pi\) | |||||||
\(72\) | −3.36207 | −0.396224 | ||||||||
\(73\) | −4.26204 | −0.498834 | −0.249417 | − | 0.968396i | \(-0.580239\pi\) | ||||
−0.249417 | + | 0.968396i | \(0.580239\pi\) | |||||||
\(74\) | −0.841807 | −0.0978581 | ||||||||
\(75\) | 7.51677 | 0.867961 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.22272 | 0.139342 | ||||||||
\(78\) | −7.26015 | −0.822050 | ||||||||
\(79\) | 1.87884 | 0.211386 | 0.105693 | − | 0.994399i | \(-0.466294\pi\) | ||||
0.105693 | + | 0.994399i | \(0.466294\pi\) | |||||||
\(80\) | 1.42123 | 0.158898 | ||||||||
\(81\) | −7.78269 | −0.864743 | ||||||||
\(82\) | 7.37747 | 0.814706 | ||||||||
\(83\) | −3.84190 | −0.421703 | −0.210851 | − | 0.977518i | \(-0.567624\pi\) | ||||
−0.210851 | + | 0.977518i | \(0.567624\pi\) | |||||||
\(84\) | −2.52231 | −0.275207 | ||||||||
\(85\) | 5.57548 | 0.604746 | ||||||||
\(86\) | 4.80751 | 0.518407 | ||||||||
\(87\) | −4.67929 | −0.501673 | ||||||||
\(88\) | −1.22272 | −0.130342 | ||||||||
\(89\) | −18.4510 | −1.95580 | −0.977901 | − | 0.209068i | \(-0.932957\pi\) | ||||
−0.977901 | + | 0.209068i | \(0.932957\pi\) | |||||||
\(90\) | −4.77828 | −0.503675 | ||||||||
\(91\) | −2.87837 | −0.301735 | ||||||||
\(92\) | −3.82191 | −0.398462 | ||||||||
\(93\) | −12.6043 | −1.30700 | ||||||||
\(94\) | −6.55168 | −0.675754 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.52231 | 0.257433 | ||||||||
\(97\) | 17.7866 | 1.80596 | 0.902978 | − | 0.429686i | \(-0.141376\pi\) | ||||
0.902978 | + | 0.429686i | \(0.141376\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.11086 | 0.413157 | ||||||||
\(100\) | −2.98011 | −0.298011 | ||||||||
\(101\) | 9.40739 | 0.936070 | 0.468035 | − | 0.883710i | \(-0.344962\pi\) | ||||
0.468035 | + | 0.883710i | \(0.344962\pi\) | |||||||
\(102\) | 9.89504 | 0.979755 | ||||||||
\(103\) | 2.62267 | 0.258420 | 0.129210 | − | 0.991617i | \(-0.458756\pi\) | ||||
0.129210 | + | 0.991617i | \(0.458756\pi\) | |||||||
\(104\) | 2.87837 | 0.282247 | ||||||||
\(105\) | −3.58479 | −0.349840 | ||||||||
\(106\) | 3.68427 | 0.357848 | ||||||||
\(107\) | 19.3222 | 1.86795 | 0.933973 | − | 0.357345i | \(-0.116318\pi\) | ||||
0.933973 | + | 0.357345i | \(0.116318\pi\) | |||||||
\(108\) | −0.913260 | −0.0878785 | ||||||||
\(109\) | 10.4840 | 1.00419 | 0.502093 | − | 0.864814i | \(-0.332563\pi\) | ||||
0.502093 | + | 0.864814i | \(0.332563\pi\) | |||||||
\(110\) | −1.73776 | −0.165689 | ||||||||
\(111\) | −2.12330 | −0.201535 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 17.9428 | 1.68792 | 0.843958 | − | 0.536409i | \(-0.180219\pi\) | ||||
0.843958 | + | 0.536409i | \(0.180219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.43182 | −0.506519 | ||||||||
\(116\) | 1.85516 | 0.172247 | ||||||||
\(117\) | −9.67728 | −0.894665 | ||||||||
\(118\) | 11.3276 | 1.04279 | ||||||||
\(119\) | 3.92300 | 0.359621 | ||||||||
\(120\) | 3.58479 | 0.327245 | ||||||||
\(121\) | −9.50496 | −0.864088 | ||||||||
\(122\) | 13.9313 | 1.26128 | ||||||||
\(123\) | 18.6083 | 1.67785 | ||||||||
\(124\) | 4.99711 | 0.448754 | ||||||||
\(125\) | −11.3416 | −1.01442 | ||||||||
\(126\) | −3.36207 | −0.299517 | ||||||||
\(127\) | −11.3031 | −1.00298 | −0.501492 | − | 0.865162i | \(-0.667215\pi\) | ||||
−0.501492 | + | 0.865162i | \(0.667215\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.1260 | 1.06764 | ||||||||
\(130\) | 4.09082 | 0.358789 | ||||||||
\(131\) | −2.59653 | −0.226860 | −0.113430 | − | 0.993546i | \(-0.536184\pi\) | ||||
−0.113430 | + | 0.993546i | \(0.536184\pi\) | |||||||
\(132\) | −3.08408 | −0.268434 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.35356 | −0.808025 | ||||||||
\(135\) | −1.29795 | −0.111710 | ||||||||
\(136\) | −3.92300 | −0.336394 | ||||||||
\(137\) | −16.9885 | −1.45142 | −0.725712 | − | 0.687999i | \(-0.758490\pi\) | ||||
−0.725712 | + | 0.687999i | \(0.758490\pi\) | |||||||
\(138\) | −9.64007 | −0.820617 | ||||||||
\(139\) | 20.1303 | 1.70743 | 0.853716 | − | 0.520739i | \(-0.174344\pi\) | ||||
0.853716 | + | 0.520739i | \(0.174344\pi\) | |||||||
\(140\) | 1.42123 | 0.120116 | ||||||||
\(141\) | −16.5254 | −1.39169 | ||||||||
\(142\) | 9.04463 | 0.759008 | ||||||||
\(143\) | −3.51943 | −0.294309 | ||||||||
\(144\) | 3.36207 | 0.280173 | ||||||||
\(145\) | 2.63661 | 0.218958 | ||||||||
\(146\) | 4.26204 | 0.352729 | ||||||||
\(147\) | −2.52231 | −0.208037 | ||||||||
\(148\) | 0.841807 | 0.0691961 | ||||||||
\(149\) | 3.63751 | 0.297996 | 0.148998 | − | 0.988837i | \(-0.452395\pi\) | ||||
0.148998 | + | 0.988837i | \(0.452395\pi\) | |||||||
\(150\) | −7.51677 | −0.613741 | ||||||||
\(151\) | −18.5627 | −1.51061 | −0.755306 | − | 0.655372i | \(-0.772512\pi\) | ||||
−0.755306 | + | 0.655372i | \(0.772512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.1894 | 1.06630 | ||||||||
\(154\) | −1.22272 | −0.0985293 | ||||||||
\(155\) | 7.10205 | 0.570450 | ||||||||
\(156\) | 7.26015 | 0.581277 | ||||||||
\(157\) | 7.84878 | 0.626401 | 0.313200 | − | 0.949687i | \(-0.398599\pi\) | ||||
0.313200 | + | 0.949687i | \(0.398599\pi\) | |||||||
\(158\) | −1.87884 | −0.149472 | ||||||||
\(159\) | 9.29288 | 0.736973 | ||||||||
\(160\) | −1.42123 | −0.112358 | ||||||||
\(161\) | −3.82191 | −0.301209 | ||||||||
\(162\) | 7.78269 | 0.611466 | ||||||||
\(163\) | 18.1480 | 1.42146 | 0.710730 | − | 0.703465i | \(-0.248365\pi\) | ||||
0.710730 | + | 0.703465i | \(0.248365\pi\) | |||||||
\(164\) | −7.37747 | −0.576084 | ||||||||
\(165\) | −4.38318 | −0.341230 | ||||||||
\(166\) | 3.84190 | 0.298189 | ||||||||
\(167\) | 19.2481 | 1.48946 | 0.744732 | − | 0.667364i | \(-0.232578\pi\) | ||||
0.744732 | + | 0.667364i | \(0.232578\pi\) | |||||||
\(168\) | 2.52231 | 0.194601 | ||||||||
\(169\) | −4.71500 | −0.362692 | ||||||||
\(170\) | −5.57548 | −0.427620 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.80751 | −0.366569 | ||||||||
\(173\) | 2.63060 | 0.200000 | 0.100000 | − | 0.994987i | \(-0.468116\pi\) | ||||
0.100000 | + | 0.994987i | \(0.468116\pi\) | |||||||
\(174\) | 4.67929 | 0.354736 | ||||||||
\(175\) | −2.98011 | −0.225275 | ||||||||
\(176\) | 1.22272 | 0.0921657 | ||||||||
\(177\) | 28.5719 | 2.14760 | ||||||||
\(178\) | 18.4510 | 1.38296 | ||||||||
\(179\) | −12.4273 | −0.928861 | −0.464430 | − | 0.885610i | \(-0.653741\pi\) | ||||
−0.464430 | + | 0.885610i | \(0.653741\pi\) | |||||||
\(180\) | 4.77828 | 0.356152 | ||||||||
\(181\) | −21.4062 | −1.59111 | −0.795554 | − | 0.605882i | \(-0.792820\pi\) | ||||
−0.795554 | + | 0.605882i | \(0.792820\pi\) | |||||||
\(182\) | 2.87837 | 0.213359 | ||||||||
\(183\) | 35.1391 | 2.59755 | ||||||||
\(184\) | 3.82191 | 0.281755 | ||||||||
\(185\) | 1.19640 | 0.0879611 | ||||||||
\(186\) | 12.6043 | 0.924192 | ||||||||
\(187\) | 4.79672 | 0.350771 | ||||||||
\(188\) | 6.55168 | 0.477830 | ||||||||
\(189\) | −0.913260 | −0.0664299 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.62706 | −0.696589 | −0.348295 | − | 0.937385i | \(-0.613239\pi\) | ||||
−0.348295 | + | 0.937385i | \(0.613239\pi\) | |||||||
\(192\) | −2.52231 | −0.182032 | ||||||||
\(193\) | −18.0674 | −1.30052 | −0.650258 | − | 0.759713i | \(-0.725339\pi\) | ||||
−0.650258 | + | 0.759713i | \(0.725339\pi\) | |||||||
\(194\) | −17.7866 | −1.27700 | ||||||||
\(195\) | 10.3183 | 0.738912 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.8396 | 0.914781 | 0.457390 | − | 0.889266i | \(-0.348784\pi\) | ||||
0.457390 | + | 0.889266i | \(0.348784\pi\) | |||||||
\(198\) | −4.11086 | −0.292146 | ||||||||
\(199\) | −5.67539 | −0.402318 | −0.201159 | − | 0.979559i | \(-0.564471\pi\) | ||||
−0.201159 | + | 0.979559i | \(0.564471\pi\) | |||||||
\(200\) | 2.98011 | 0.210725 | ||||||||
\(201\) | −23.5926 | −1.66410 | ||||||||
\(202\) | −9.40739 | −0.661902 | ||||||||
\(203\) | 1.85516 | 0.130207 | ||||||||
\(204\) | −9.89504 | −0.692791 | ||||||||
\(205\) | −10.4851 | −0.732310 | ||||||||
\(206\) | −2.62267 | −0.182730 | ||||||||
\(207\) | −12.8495 | −0.893105 | ||||||||
\(208\) | −2.87837 | −0.199579 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.58479 | 0.247374 | ||||||||
\(211\) | −1.91154 | −0.131596 | −0.0657979 | − | 0.997833i | \(-0.520959\pi\) | ||||
−0.0657979 | + | 0.997833i | \(0.520959\pi\) | |||||||
\(212\) | −3.68427 | −0.253036 | ||||||||
\(213\) | 22.8134 | 1.56315 | ||||||||
\(214\) | −19.3222 | −1.32084 | ||||||||
\(215\) | −6.83257 | −0.465977 | ||||||||
\(216\) | 0.913260 | 0.0621394 | ||||||||
\(217\) | 4.99711 | 0.339226 | ||||||||
\(218\) | −10.4840 | −0.710067 | ||||||||
\(219\) | 10.7502 | 0.726432 | ||||||||
\(220\) | 1.73776 | 0.117160 | ||||||||
\(221\) | −11.2918 | −0.759571 | ||||||||
\(222\) | 2.12330 | 0.142507 | ||||||||
\(223\) | −2.67452 | −0.179099 | −0.0895494 | − | 0.995982i | \(-0.528543\pi\) | ||||
−0.0895494 | + | 0.995982i | \(0.528543\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −10.0193 | −0.667955 | ||||||||
\(226\) | −17.9428 | −1.19354 | ||||||||
\(227\) | 2.75727 | 0.183006 | 0.0915032 | − | 0.995805i | \(-0.470833\pi\) | ||||
0.0915032 | + | 0.995805i | \(0.470833\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4798 | −1.02293 | −0.511467 | − | 0.859303i | \(-0.670898\pi\) | ||||
−0.511467 | + | 0.859303i | \(0.670898\pi\) | |||||||
\(230\) | 5.43182 | 0.358163 | ||||||||
\(231\) | −3.08408 | −0.202917 | ||||||||
\(232\) | −1.85516 | −0.121797 | ||||||||
\(233\) | −1.91201 | −0.125260 | −0.0626298 | − | 0.998037i | \(-0.519949\pi\) | ||||
−0.0626298 | + | 0.998037i | \(0.519949\pi\) | |||||||
\(234\) | 9.67728 | 0.632624 | ||||||||
\(235\) | 9.31144 | 0.607412 | ||||||||
\(236\) | −11.3276 | −0.737367 | ||||||||
\(237\) | −4.73902 | −0.307832 | ||||||||
\(238\) | −3.92300 | −0.254290 | ||||||||
\(239\) | 3.61595 | 0.233896 | 0.116948 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116948 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(240\) | −3.58479 | −0.231397 | ||||||||
\(241\) | −0.285715 | −0.0184045 | −0.00920226 | − | 0.999958i | \(-0.502929\pi\) | ||||
−0.00920226 | + | 0.999958i | \(0.502929\pi\) | |||||||
\(242\) | 9.50496 | 0.611002 | ||||||||
\(243\) | 22.3702 | 1.43505 | ||||||||
\(244\) | −13.9313 | −0.891859 | ||||||||
\(245\) | 1.42123 | 0.0907990 | ||||||||
\(246\) | −18.6083 | −1.18642 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.99711 | −0.317317 | ||||||||
\(249\) | 9.69047 | 0.614109 | ||||||||
\(250\) | 11.3416 | 0.717303 | ||||||||
\(251\) | 17.4569 | 1.10187 | 0.550935 | − | 0.834548i | \(-0.314271\pi\) | ||||
0.550935 | + | 0.834548i | \(0.314271\pi\) | |||||||
\(252\) | 3.36207 | 0.211791 | ||||||||
\(253\) | −4.67312 | −0.293796 | ||||||||
\(254\) | 11.3031 | 0.709217 | ||||||||
\(255\) | −14.0631 | −0.880667 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.07436 | −0.378908 | −0.189454 | − | 0.981890i | \(-0.560672\pi\) | ||||
−0.189454 | + | 0.981890i | \(0.560672\pi\) | |||||||
\(258\) | −12.1260 | −0.754934 | ||||||||
\(259\) | 0.841807 | 0.0523073 | ||||||||
\(260\) | −4.09082 | −0.253702 | ||||||||
\(261\) | 6.23717 | 0.386071 | ||||||||
\(262\) | 2.59653 | 0.160414 | ||||||||
\(263\) | −17.9415 | −1.10632 | −0.553161 | − | 0.833074i | \(-0.686579\pi\) | ||||
−0.553161 | + | 0.833074i | \(0.686579\pi\) | |||||||
\(264\) | 3.08408 | 0.189812 | ||||||||
\(265\) | −5.23619 | −0.321657 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 46.5392 | 2.84816 | ||||||||
\(268\) | 9.35356 | 0.571360 | ||||||||
\(269\) | 1.68138 | 0.102516 | 0.0512578 | − | 0.998685i | \(-0.483677\pi\) | ||||
0.0512578 | + | 0.998685i | \(0.483677\pi\) | |||||||
\(270\) | 1.29795 | 0.0789908 | ||||||||
\(271\) | 7.95578 | 0.483279 | 0.241640 | − | 0.970366i | \(-0.422315\pi\) | ||||
0.241640 | + | 0.970366i | \(0.422315\pi\) | |||||||
\(272\) | 3.92300 | 0.237867 | ||||||||
\(273\) | 7.26015 | 0.439404 | ||||||||
\(274\) | 16.9885 | 1.02631 | ||||||||
\(275\) | −3.64383 | −0.219731 | ||||||||
\(276\) | 9.64007 | 0.580264 | ||||||||
\(277\) | −30.0011 | −1.80259 | −0.901295 | − | 0.433205i | \(-0.857382\pi\) | ||||
−0.901295 | + | 0.433205i | \(0.857382\pi\) | |||||||
\(278\) | −20.1303 | −1.20734 | ||||||||
\(279\) | 16.8007 | 1.00583 | ||||||||
\(280\) | −1.42123 | −0.0849347 | ||||||||
\(281\) | 10.4565 | 0.623780 | 0.311890 | − | 0.950118i | \(-0.399038\pi\) | ||||
0.311890 | + | 0.950118i | \(0.399038\pi\) | |||||||
\(282\) | 16.5254 | 0.984073 | ||||||||
\(283\) | −8.05939 | −0.479081 | −0.239541 | − | 0.970886i | \(-0.576997\pi\) | ||||
−0.239541 | + | 0.970886i | \(0.576997\pi\) | |||||||
\(284\) | −9.04463 | −0.536700 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.51943 | 0.208108 | ||||||||
\(287\) | −7.37747 | −0.435478 | ||||||||
\(288\) | −3.36207 | −0.198112 | ||||||||
\(289\) | −1.61009 | −0.0947110 | ||||||||
\(290\) | −2.63661 | −0.154827 | ||||||||
\(291\) | −44.8634 | −2.62994 | ||||||||
\(292\) | −4.26204 | −0.249417 | ||||||||
\(293\) | 8.05923 | 0.470825 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(294\) | 2.52231 | 0.147104 | ||||||||
\(295\) | −16.0992 | −0.937331 | ||||||||
\(296\) | −0.841807 | −0.0489290 | ||||||||
\(297\) | −1.11666 | −0.0647951 | ||||||||
\(298\) | −3.63751 | −0.210715 | ||||||||
\(299\) | 11.0009 | 0.636197 | ||||||||
\(300\) | 7.51677 | 0.433981 | ||||||||
\(301\) | −4.80751 | −0.277100 | ||||||||
\(302\) | 18.5627 | 1.06816 | ||||||||
\(303\) | −23.7284 | −1.36316 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.7995 | −1.13372 | ||||||||
\(306\) | −13.1894 | −0.753988 | ||||||||
\(307\) | 14.3712 | 0.820207 | 0.410103 | − | 0.912039i | \(-0.365493\pi\) | ||||
0.410103 | + | 0.912039i | \(0.365493\pi\) | |||||||
\(308\) | 1.22272 | 0.0696708 | ||||||||
\(309\) | −6.61521 | −0.376326 | ||||||||
\(310\) | −7.10205 | −0.403369 | ||||||||
\(311\) | 28.8765 | 1.63744 | 0.818719 | − | 0.574195i | \(-0.194685\pi\) | ||||
0.818719 | + | 0.574195i | \(0.194685\pi\) | |||||||
\(312\) | −7.26015 | −0.411025 | ||||||||
\(313\) | −4.12543 | −0.233183 | −0.116592 | − | 0.993180i | \(-0.537197\pi\) | ||||
−0.116592 | + | 0.993180i | \(0.537197\pi\) | |||||||
\(314\) | −7.84878 | −0.442932 | ||||||||
\(315\) | 4.77828 | 0.269225 | ||||||||
\(316\) | 1.87884 | 0.105693 | ||||||||
\(317\) | −6.54790 | −0.367767 | −0.183883 | − | 0.982948i | \(-0.558867\pi\) | ||||
−0.183883 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(318\) | −9.29288 | −0.521119 | ||||||||
\(319\) | 2.26833 | 0.127002 | ||||||||
\(320\) | 1.42123 | 0.0794492 | ||||||||
\(321\) | −48.7366 | −2.72021 | ||||||||
\(322\) | 3.82191 | 0.212987 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.78269 | −0.432372 | ||||||||
\(325\) | 8.57784 | 0.475813 | ||||||||
\(326\) | −18.1480 | −1.00512 | ||||||||
\(327\) | −26.4440 | −1.46236 | ||||||||
\(328\) | 7.37747 | 0.407353 | ||||||||
\(329\) | 6.55168 | 0.361206 | ||||||||
\(330\) | 4.38318 | 0.241286 | ||||||||
\(331\) | −18.3461 | −1.00839 | −0.504195 | − | 0.863590i | \(-0.668211\pi\) | ||||
−0.504195 | + | 0.863590i | \(0.668211\pi\) | |||||||
\(332\) | −3.84190 | −0.210851 | ||||||||
\(333\) | 2.83022 | 0.155095 | ||||||||
\(334\) | −19.2481 | −1.05321 | ||||||||
\(335\) | 13.2936 | 0.726305 | ||||||||
\(336\) | −2.52231 | −0.137604 | ||||||||
\(337\) | −28.3353 | −1.54352 | −0.771762 | − | 0.635911i | \(-0.780624\pi\) | ||||
−0.771762 | + | 0.635911i | \(0.780624\pi\) | |||||||
\(338\) | 4.71500 | 0.256462 | ||||||||
\(339\) | −45.2574 | −2.45804 | ||||||||
\(340\) | 5.57548 | 0.302373 | ||||||||
\(341\) | 6.11006 | 0.330878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.80751 | 0.259203 | ||||||||
\(345\) | 13.7008 | 0.737624 | ||||||||
\(346\) | −2.63060 | −0.141422 | ||||||||
\(347\) | −15.9023 | −0.853682 | −0.426841 | − | 0.904327i | \(-0.640374\pi\) | ||||
−0.426841 | + | 0.904327i | \(0.640374\pi\) | |||||||
\(348\) | −4.67929 | −0.250836 | ||||||||
\(349\) | −3.46506 | −0.185480 | −0.0927402 | − | 0.995690i | \(-0.529563\pi\) | ||||
−0.0927402 | + | 0.995690i | \(0.529563\pi\) | |||||||
\(350\) | 2.98011 | 0.159293 | ||||||||
\(351\) | 2.62870 | 0.140310 | ||||||||
\(352\) | −1.22272 | −0.0651710 | ||||||||
\(353\) | −8.76647 | −0.466592 | −0.233296 | − | 0.972406i | \(-0.574951\pi\) | ||||
−0.233296 | + | 0.972406i | \(0.574951\pi\) | |||||||
\(354\) | −28.5719 | −1.51858 | ||||||||
\(355\) | −12.8545 | −0.682246 | ||||||||
\(356\) | −18.4510 | −0.977901 | ||||||||
\(357\) | −9.89504 | −0.523701 | ||||||||
\(358\) | 12.4273 | 0.656804 | ||||||||
\(359\) | 11.2383 | 0.593136 | 0.296568 | − | 0.955012i | \(-0.404158\pi\) | ||||
0.296568 | + | 0.955012i | \(0.404158\pi\) | |||||||
\(360\) | −4.77828 | −0.251837 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 21.4062 | 1.12508 | ||||||||
\(363\) | 23.9745 | 1.25834 | ||||||||
\(364\) | −2.87837 | −0.150867 | ||||||||
\(365\) | −6.05734 | −0.317056 | ||||||||
\(366\) | −35.1391 | −1.83675 | ||||||||
\(367\) | 5.92259 | 0.309156 | 0.154578 | − | 0.987981i | \(-0.450598\pi\) | ||||
0.154578 | + | 0.987981i | \(0.450598\pi\) | |||||||
\(368\) | −3.82191 | −0.199231 | ||||||||
\(369\) | −24.8036 | −1.29122 | ||||||||
\(370\) | −1.19640 | −0.0621979 | ||||||||
\(371\) | −3.68427 | −0.191278 | ||||||||
\(372\) | −12.6043 | −0.653502 | ||||||||
\(373\) | −22.7567 | −1.17829 | −0.589147 | − | 0.808026i | \(-0.700536\pi\) | ||||
−0.589147 | + | 0.808026i | \(0.700536\pi\) | |||||||
\(374\) | −4.79672 | −0.248032 | ||||||||
\(375\) | 28.6070 | 1.47726 | ||||||||
\(376\) | −6.55168 | −0.337877 | ||||||||
\(377\) | −5.33983 | −0.275015 | ||||||||
\(378\) | 0.913260 | 0.0469730 | ||||||||
\(379\) | −7.09293 | −0.364340 | −0.182170 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182170 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.5099 | 1.46060 | ||||||||
\(382\) | 9.62706 | 0.492563 | ||||||||
\(383\) | −20.1267 | −1.02842 | −0.514212 | − | 0.857663i | \(-0.671916\pi\) | ||||
−0.514212 | + | 0.857663i | \(0.671916\pi\) | |||||||
\(384\) | 2.52231 | 0.128716 | ||||||||
\(385\) | 1.73776 | 0.0885645 | ||||||||
\(386\) | 18.0674 | 0.919604 | ||||||||
\(387\) | −16.1632 | −0.821621 | ||||||||
\(388\) | 17.7866 | 0.902978 | ||||||||
\(389\) | −30.2580 | −1.53414 | −0.767070 | − | 0.641564i | \(-0.778286\pi\) | ||||
−0.767070 | + | 0.641564i | \(0.778286\pi\) | |||||||
\(390\) | −10.3183 | −0.522490 | ||||||||
\(391\) | −14.9934 | −0.758247 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 6.54927 | 0.330367 | ||||||||
\(394\) | −12.8396 | −0.646848 | ||||||||
\(395\) | 2.67026 | 0.134355 | ||||||||
\(396\) | 4.11086 | 0.206579 | ||||||||
\(397\) | 2.90935 | 0.146016 | 0.0730081 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730081 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(398\) | 5.67539 | 0.284482 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.98011 | −0.149005 | ||||||||
\(401\) | 28.7840 | 1.43741 | 0.718703 | − | 0.695317i | \(-0.244736\pi\) | ||||
0.718703 | + | 0.695317i | \(0.244736\pi\) | |||||||
\(402\) | 23.5926 | 1.17669 | ||||||||
\(403\) | −14.3835 | −0.716495 | ||||||||
\(404\) | 9.40739 | 0.468035 | ||||||||
\(405\) | −11.0610 | −0.549625 | ||||||||
\(406\) | −1.85516 | −0.0920699 | ||||||||
\(407\) | 1.02929 | 0.0510201 | ||||||||
\(408\) | 9.89504 | 0.489877 | ||||||||
\(409\) | −25.6553 | −1.26857 | −0.634285 | − | 0.773099i | \(-0.718706\pi\) | ||||
−0.634285 | + | 0.773099i | \(0.718706\pi\) | |||||||
\(410\) | 10.4851 | 0.517821 | ||||||||
\(411\) | 42.8503 | 2.11365 | ||||||||
\(412\) | 2.62267 | 0.129210 | ||||||||
\(413\) | −11.3276 | −0.557397 | ||||||||
\(414\) | 12.8495 | 0.631521 | ||||||||
\(415\) | −5.46022 | −0.268032 | ||||||||
\(416\) | 2.87837 | 0.141124 | ||||||||
\(417\) | −50.7750 | −2.48646 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.06546 | 0.0520512 | 0.0260256 | − | 0.999661i | \(-0.491715\pi\) | ||||
0.0260256 | + | 0.999661i | \(0.491715\pi\) | |||||||
\(420\) | −3.58479 | −0.174920 | ||||||||
\(421\) | −5.48941 | −0.267538 | −0.133769 | − | 0.991013i | \(-0.542708\pi\) | ||||
−0.133769 | + | 0.991013i | \(0.542708\pi\) | |||||||
\(422\) | 1.91154 | 0.0930523 | ||||||||
\(423\) | 22.0272 | 1.07100 | ||||||||
\(424\) | 3.68427 | 0.178924 | ||||||||
\(425\) | −11.6909 | −0.567094 | ||||||||
\(426\) | −22.8134 | −1.10531 | ||||||||
\(427\) | −13.9313 | −0.674182 | ||||||||
\(428\) | 19.3222 | 0.933973 | ||||||||
\(429\) | 8.87711 | 0.428591 | ||||||||
\(430\) | 6.83257 | 0.329496 | ||||||||
\(431\) | −22.2378 | −1.07116 | −0.535578 | − | 0.844486i | \(-0.679906\pi\) | ||||
−0.535578 | + | 0.844486i | \(0.679906\pi\) | |||||||
\(432\) | −0.913260 | −0.0439392 | ||||||||
\(433\) | −12.8888 | −0.619396 | −0.309698 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309698 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(434\) | −4.99711 | −0.239869 | ||||||||
\(435\) | −6.65035 | −0.318860 | ||||||||
\(436\) | 10.4840 | 0.502093 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −10.7502 | −0.513665 | ||||||||
\(439\) | 17.0046 | 0.811587 | 0.405793 | − | 0.913965i | \(-0.366995\pi\) | ||||
0.405793 | + | 0.913965i | \(0.366995\pi\) | |||||||
\(440\) | −1.73776 | −0.0828445 | ||||||||
\(441\) | 3.36207 | 0.160099 | ||||||||
\(442\) | 11.2918 | 0.537098 | ||||||||
\(443\) | 2.51156 | 0.119328 | 0.0596638 | − | 0.998219i | \(-0.480997\pi\) | ||||
0.0596638 | + | 0.998219i | \(0.480997\pi\) | |||||||
\(444\) | −2.12330 | −0.100767 | ||||||||
\(445\) | −26.2231 | −1.24309 | ||||||||
\(446\) | 2.67452 | 0.126642 | ||||||||
\(447\) | −9.17495 | −0.433960 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −11.7883 | −0.556326 | −0.278163 | − | 0.960534i | \(-0.589726\pi\) | ||||
−0.278163 | + | 0.960534i | \(0.589726\pi\) | |||||||
\(450\) | 10.0193 | 0.472316 | ||||||||
\(451\) | −9.02056 | −0.424762 | ||||||||
\(452\) | 17.9428 | 0.843958 | ||||||||
\(453\) | 46.8210 | 2.19984 | ||||||||
\(454\) | −2.75727 | −0.129405 | ||||||||
\(455\) | −4.09082 | −0.191781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.4286 | −1.28306 | −0.641528 | − | 0.767100i | \(-0.721699\pi\) | ||||
−0.641528 | + | 0.767100i | \(0.721699\pi\) | |||||||
\(458\) | 15.4798 | 0.723323 | ||||||||
\(459\) | −3.58272 | −0.167227 | ||||||||
\(460\) | −5.43182 | −0.253260 | ||||||||
\(461\) | 21.1906 | 0.986944 | 0.493472 | − | 0.869762i | \(-0.335728\pi\) | ||||
0.493472 | + | 0.869762i | \(0.335728\pi\) | |||||||
\(462\) | 3.08408 | 0.143484 | ||||||||
\(463\) | −21.9687 | −1.02097 | −0.510487 | − | 0.859886i | \(-0.670535\pi\) | ||||
−0.510487 | + | 0.859886i | \(0.670535\pi\) | |||||||
\(464\) | 1.85516 | 0.0861235 | ||||||||
\(465\) | −17.9136 | −0.830723 | ||||||||
\(466\) | 1.91201 | 0.0885719 | ||||||||
\(467\) | −5.91139 | −0.273547 | −0.136773 | − | 0.990602i | \(-0.543673\pi\) | ||||
−0.136773 | + | 0.990602i | \(0.543673\pi\) | |||||||
\(468\) | −9.67728 | −0.447332 | ||||||||
\(469\) | 9.35356 | 0.431907 | ||||||||
\(470\) | −9.31144 | −0.429505 | ||||||||
\(471\) | −19.7971 | −0.912202 | ||||||||
\(472\) | 11.3276 | 0.521397 | ||||||||
\(473\) | −5.87822 | −0.270281 | ||||||||
\(474\) | 4.73902 | 0.217670 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.92300 | 0.179810 | ||||||||
\(477\) | −12.3868 | −0.567151 | ||||||||
\(478\) | −3.61595 | −0.165390 | ||||||||
\(479\) | 25.5707 | 1.16836 | 0.584178 | − | 0.811626i | \(-0.301417\pi\) | ||||
0.584178 | + | 0.811626i | \(0.301417\pi\) | |||||||
\(480\) | 3.58479 | 0.163622 | ||||||||
\(481\) | −2.42303 | −0.110481 | ||||||||
\(482\) | 0.285715 | 0.0130140 | ||||||||
\(483\) | 9.64007 | 0.438638 | ||||||||
\(484\) | −9.50496 | −0.432044 | ||||||||
\(485\) | 25.2789 | 1.14785 | ||||||||
\(486\) | −22.3702 | −1.01473 | ||||||||
\(487\) | −33.0894 | −1.49942 | −0.749711 | − | 0.661765i | \(-0.769808\pi\) | ||||
−0.749711 | + | 0.661765i | \(0.769808\pi\) | |||||||
\(488\) | 13.9313 | 0.630639 | ||||||||
\(489\) | −45.7749 | −2.07001 | ||||||||
\(490\) | −1.42123 | −0.0642046 | ||||||||
\(491\) | −38.7050 | −1.74673 | −0.873367 | − | 0.487062i | \(-0.838068\pi\) | ||||
−0.873367 | + | 0.487062i | \(0.838068\pi\) | |||||||
\(492\) | 18.6083 | 0.838927 | ||||||||
\(493\) | 7.27778 | 0.327775 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.84248 | 0.262600 | ||||||||
\(496\) | 4.99711 | 0.224377 | ||||||||
\(497\) | −9.04463 | −0.405707 | ||||||||
\(498\) | −9.69047 | −0.434240 | ||||||||
\(499\) | −34.0924 | −1.52618 | −0.763092 | − | 0.646290i | \(-0.776320\pi\) | ||||
−0.763092 | + | 0.646290i | \(0.776320\pi\) | |||||||
\(500\) | −11.3416 | −0.507210 | ||||||||
\(501\) | −48.5498 | −2.16904 | ||||||||
\(502\) | −17.4569 | −0.779140 | ||||||||
\(503\) | −38.6263 | −1.72226 | −0.861130 | − | 0.508385i | \(-0.830243\pi\) | ||||
−0.861130 | + | 0.508385i | \(0.830243\pi\) | |||||||
\(504\) | −3.36207 | −0.149759 | ||||||||
\(505\) | 13.3701 | 0.594960 | ||||||||
\(506\) | 4.67312 | 0.207745 | ||||||||
\(507\) | 11.8927 | 0.528174 | ||||||||
\(508\) | −11.3031 | −0.501492 | ||||||||
\(509\) | −6.60339 | −0.292690 | −0.146345 | − | 0.989234i | \(-0.546751\pi\) | ||||
−0.146345 | + | 0.989234i | \(0.546751\pi\) | |||||||
\(510\) | 14.0631 | 0.622725 | ||||||||
\(511\) | −4.26204 | −0.188542 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.07436 | 0.267929 | ||||||||
\(515\) | 3.72742 | 0.164250 | ||||||||
\(516\) | 12.1260 | 0.533819 | ||||||||
\(517\) | 8.01085 | 0.352317 | ||||||||
\(518\) | −0.841807 | −0.0369869 | ||||||||
\(519\) | −6.63519 | −0.291252 | ||||||||
\(520\) | 4.09082 | 0.179394 | ||||||||
\(521\) | −27.1001 | −1.18728 | −0.593639 | − | 0.804731i | \(-0.702309\pi\) | ||||
−0.593639 | + | 0.804731i | \(0.702309\pi\) | |||||||
\(522\) | −6.23717 | −0.272994 | ||||||||
\(523\) | 16.7594 | 0.732838 | 0.366419 | − | 0.930450i | \(-0.380584\pi\) | ||||
0.366419 | + | 0.930450i | \(0.380584\pi\) | |||||||
\(524\) | −2.59653 | −0.113430 | ||||||||
\(525\) | 7.51677 | 0.328059 | ||||||||
\(526\) | 17.9415 | 0.782288 | ||||||||
\(527\) | 19.6037 | 0.853949 | ||||||||
\(528\) | −3.08408 | −0.134217 | ||||||||
\(529\) | −8.39298 | −0.364912 | ||||||||
\(530\) | 5.23619 | 0.227446 | ||||||||
\(531\) | −38.0844 | −1.65272 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.2351 | 0.919794 | ||||||||
\(534\) | −46.5392 | −2.01395 | ||||||||
\(535\) | 27.4613 | 1.18725 | ||||||||
\(536\) | −9.35356 | −0.404012 | ||||||||
\(537\) | 31.3456 | 1.35266 | ||||||||
\(538\) | −1.68138 | −0.0724895 | ||||||||
\(539\) | 1.22272 | 0.0526661 | ||||||||
\(540\) | −1.29795 | −0.0558550 | ||||||||
\(541\) | −5.43274 | −0.233572 | −0.116786 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116786 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(542\) | −7.95578 | −0.341730 | ||||||||
\(543\) | 53.9931 | 2.31707 | ||||||||
\(544\) | −3.92300 | −0.168197 | ||||||||
\(545\) | 14.9002 | 0.638254 | ||||||||
\(546\) | −7.26015 | −0.310706 | ||||||||
\(547\) | −8.21665 | −0.351318 | −0.175659 | − | 0.984451i | \(-0.556206\pi\) | ||||
−0.175659 | + | 0.984451i | \(0.556206\pi\) | |||||||
\(548\) | −16.9885 | −0.725712 | ||||||||
\(549\) | −46.8380 | −1.99900 | ||||||||
\(550\) | 3.64383 | 0.155373 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −9.64007 | −0.410309 | ||||||||
\(553\) | 1.87884 | 0.0798963 | ||||||||
\(554\) | 30.0011 | 1.27462 | ||||||||
\(555\) | −3.01770 | −0.128094 | ||||||||
\(556\) | 20.1303 | 0.853716 | ||||||||
\(557\) | −7.40318 | −0.313683 | −0.156841 | − | 0.987624i | \(-0.550131\pi\) | ||||
−0.156841 | + | 0.987624i | \(0.550131\pi\) | |||||||
\(558\) | −16.8007 | −0.711229 | ||||||||
\(559\) | 13.8378 | 0.585275 | ||||||||
\(560\) | 1.42123 | 0.0600579 | ||||||||
\(561\) | −12.0988 | −0.510813 | ||||||||
\(562\) | −10.4565 | −0.441079 | ||||||||
\(563\) | −10.0619 | −0.424061 | −0.212030 | − | 0.977263i | \(-0.568008\pi\) | ||||
−0.212030 | + | 0.977263i | \(0.568008\pi\) | |||||||
\(564\) | −16.5254 | −0.695845 | ||||||||
\(565\) | 25.5008 | 1.07283 | ||||||||
\(566\) | 8.05939 | 0.338762 | ||||||||
\(567\) | −7.78269 | −0.326842 | ||||||||
\(568\) | 9.04463 | 0.379504 | ||||||||
\(569\) | −1.54777 | −0.0648857 | −0.0324429 | − | 0.999474i | \(-0.510329\pi\) | ||||
−0.0324429 | + | 0.999474i | \(0.510329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.8448 | −1.50006 | −0.750028 | − | 0.661406i | \(-0.769960\pi\) | ||||
−0.750028 | + | 0.661406i | \(0.769960\pi\) | |||||||
\(572\) | −3.51943 | −0.147155 | ||||||||
\(573\) | 24.2825 | 1.01441 | ||||||||
\(574\) | 7.37747 | 0.307930 | ||||||||
\(575\) | 11.3897 | 0.474984 | ||||||||
\(576\) | 3.36207 | 0.140086 | ||||||||
\(577\) | −9.67971 | −0.402972 | −0.201486 | − | 0.979491i | \(-0.564577\pi\) | ||||
−0.201486 | + | 0.979491i | \(0.564577\pi\) | |||||||
\(578\) | 1.61009 | 0.0669708 | ||||||||
\(579\) | 45.5715 | 1.89389 | ||||||||
\(580\) | 2.63661 | 0.109479 | ||||||||
\(581\) | −3.84190 | −0.159389 | ||||||||
\(582\) | 44.8634 | 1.85965 | ||||||||
\(583\) | −4.50481 | −0.186570 | ||||||||
\(584\) | 4.26204 | 0.176365 | ||||||||
\(585\) | −13.7536 | −0.568643 | ||||||||
\(586\) | −8.05923 | −0.332924 | ||||||||
\(587\) | 30.1678 | 1.24516 | 0.622578 | − | 0.782558i | \(-0.286085\pi\) | ||||
0.622578 | + | 0.782558i | \(0.286085\pi\) | |||||||
\(588\) | −2.52231 | −0.104019 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 16.0992 | 0.662793 | ||||||||
\(591\) | −32.3854 | −1.33216 | ||||||||
\(592\) | 0.841807 | 0.0345980 | ||||||||
\(593\) | −29.6496 | −1.21756 | −0.608782 | − | 0.793337i | \(-0.708342\pi\) | ||||
−0.608782 | + | 0.793337i | \(0.708342\pi\) | |||||||
\(594\) | 1.11666 | 0.0458170 | ||||||||
\(595\) | 5.57548 | 0.228572 | ||||||||
\(596\) | 3.63751 | 0.148998 | ||||||||
\(597\) | 14.3151 | 0.585879 | ||||||||
\(598\) | −11.0009 | −0.449859 | ||||||||
\(599\) | 31.6080 | 1.29147 | 0.645733 | − | 0.763563i | \(-0.276552\pi\) | ||||
0.645733 | + | 0.763563i | \(0.276552\pi\) | |||||||
\(600\) | −7.51677 | −0.306871 | ||||||||
\(601\) | 22.8515 | 0.932132 | 0.466066 | − | 0.884750i | \(-0.345671\pi\) | ||||
0.466066 | + | 0.884750i | \(0.345671\pi\) | |||||||
\(602\) | 4.80751 | 0.195939 | ||||||||
\(603\) | 31.4474 | 1.28064 | ||||||||
\(604\) | −18.5627 | −0.755306 | ||||||||
\(605\) | −13.5087 | −0.549208 | ||||||||
\(606\) | 23.7284 | 0.963900 | ||||||||
\(607\) | 2.70015 | 0.109596 | 0.0547978 | − | 0.998497i | \(-0.482549\pi\) | ||||
0.0547978 | + | 0.998497i | \(0.482549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.67929 | −0.189615 | ||||||||
\(610\) | 19.7995 | 0.801660 | ||||||||
\(611\) | −18.8582 | −0.762919 | ||||||||
\(612\) | 13.1894 | 0.533150 | ||||||||
\(613\) | −45.9337 | −1.85525 | −0.927623 | − | 0.373517i | \(-0.878152\pi\) | ||||
−0.927623 | + | 0.373517i | \(0.878152\pi\) | |||||||
\(614\) | −14.3712 | −0.579974 | ||||||||
\(615\) | 26.4467 | 1.06643 | ||||||||
\(616\) | −1.22272 | −0.0492647 | ||||||||
\(617\) | 26.5890 | 1.07043 | 0.535217 | − | 0.844715i | \(-0.320230\pi\) | ||||
0.535217 | + | 0.844715i | \(0.320230\pi\) | |||||||
\(618\) | 6.61521 | 0.266103 | ||||||||
\(619\) | 30.5279 | 1.22702 | 0.613510 | − | 0.789687i | \(-0.289757\pi\) | ||||
0.613510 | + | 0.789687i | \(0.289757\pi\) | |||||||
\(620\) | 7.10205 | 0.285225 | ||||||||
\(621\) | 3.49040 | 0.140065 | ||||||||
\(622\) | −28.8765 | −1.15784 | ||||||||
\(623\) | −18.4510 | −0.739224 | ||||||||
\(624\) | 7.26015 | 0.290639 | ||||||||
\(625\) | −1.21844 | −0.0487375 | ||||||||
\(626\) | 4.12543 | 0.164886 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.84878 | 0.313200 | ||||||||
\(629\) | 3.30241 | 0.131676 | ||||||||
\(630\) | −4.77828 | −0.190371 | ||||||||
\(631\) | 6.96559 | 0.277296 | 0.138648 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138648 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(632\) | −1.87884 | −0.0747361 | ||||||||
\(633\) | 4.82150 | 0.191638 | ||||||||
\(634\) | 6.54790 | 0.260050 | ||||||||
\(635\) | −16.0642 | −0.637490 | ||||||||
\(636\) | 9.29288 | 0.368487 | ||||||||
\(637\) | −2.87837 | −0.114045 | ||||||||
\(638\) | −2.26833 | −0.0898042 | ||||||||
\(639\) | −30.4087 | −1.20295 | ||||||||
\(640\) | −1.42123 | −0.0561790 | ||||||||
\(641\) | 28.6345 | 1.13099 | 0.565497 | − | 0.824751i | \(-0.308684\pi\) | ||||
0.565497 | + | 0.824751i | \(0.308684\pi\) | |||||||
\(642\) | 48.7366 | 1.92348 | ||||||||
\(643\) | 35.5025 | 1.40008 | 0.700040 | − | 0.714104i | \(-0.253165\pi\) | ||||
0.700040 | + | 0.714104i | \(0.253165\pi\) | |||||||
\(644\) | −3.82191 | −0.150604 | ||||||||
\(645\) | 17.2339 | 0.678584 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.9592 | −1.21713 | −0.608567 | − | 0.793503i | \(-0.708255\pi\) | ||||
−0.608567 | + | 0.793503i | \(0.708255\pi\) | |||||||
\(648\) | 7.78269 | 0.305733 | ||||||||
\(649\) | −13.8505 | −0.543680 | ||||||||
\(650\) | −8.57784 | −0.336451 | ||||||||
\(651\) | −12.6043 | −0.494001 | ||||||||
\(652\) | 18.1480 | 0.710730 | ||||||||
\(653\) | 4.34571 | 0.170061 | 0.0850305 | − | 0.996378i | \(-0.472901\pi\) | ||||
0.0850305 | + | 0.996378i | \(0.472901\pi\) | |||||||
\(654\) | 26.4440 | 1.03404 | ||||||||
\(655\) | −3.69027 | −0.144191 | ||||||||
\(656\) | −7.37747 | −0.288042 | ||||||||
\(657\) | −14.3293 | −0.559039 | ||||||||
\(658\) | −6.55168 | −0.255411 | ||||||||
\(659\) | −2.04990 | −0.0798528 | −0.0399264 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399264 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(660\) | −4.38318 | −0.170615 | ||||||||
\(661\) | −45.2457 | −1.75986 | −0.879928 | − | 0.475108i | \(-0.842409\pi\) | ||||
−0.879928 | + | 0.475108i | \(0.842409\pi\) | |||||||
\(662\) | 18.3461 | 0.713040 | ||||||||
\(663\) | 28.4816 | 1.10613 | ||||||||
\(664\) | 3.84190 | 0.149095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.83022 | −0.109669 | ||||||||
\(667\) | −7.09025 | −0.274536 | ||||||||
\(668\) | 19.2481 | 0.744732 | ||||||||
\(669\) | 6.74597 | 0.260814 | ||||||||
\(670\) | −13.2936 | −0.513575 | ||||||||
\(671\) | −17.0340 | −0.657591 | ||||||||
\(672\) | 2.52231 | 0.0973004 | ||||||||
\(673\) | 22.8180 | 0.879569 | 0.439784 | − | 0.898103i | \(-0.355055\pi\) | ||||
0.439784 | + | 0.898103i | \(0.355055\pi\) | |||||||
\(674\) | 28.3353 | 1.09144 | ||||||||
\(675\) | 2.72161 | 0.104755 | ||||||||
\(676\) | −4.71500 | −0.181346 | ||||||||
\(677\) | 37.7097 | 1.44930 | 0.724652 | − | 0.689115i | \(-0.242001\pi\) | ||||
0.724652 | + | 0.689115i | \(0.242001\pi\) | |||||||
\(678\) | 45.2574 | 1.73810 | ||||||||
\(679\) | 17.7866 | 0.682587 | ||||||||
\(680\) | −5.57548 | −0.213810 | ||||||||
\(681\) | −6.95470 | −0.266505 | ||||||||
\(682\) | −6.11006 | −0.233966 | ||||||||
\(683\) | −6.67991 | −0.255600 | −0.127800 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127800 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.1445 | −0.922515 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 39.0449 | 1.48966 | ||||||||
\(688\) | −4.80751 | −0.183284 | ||||||||
\(689\) | 10.6047 | 0.404006 | ||||||||
\(690\) | −13.7008 | −0.521579 | ||||||||
\(691\) | −9.27273 | −0.352751 | −0.176376 | − | 0.984323i | \(-0.556437\pi\) | ||||
−0.176376 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(692\) | 2.63060 | 0.100000 | ||||||||
\(693\) | 4.11086 | 0.156159 | ||||||||
\(694\) | 15.9023 | 0.603645 | ||||||||
\(695\) | 28.6098 | 1.08523 | ||||||||
\(696\) | 4.67929 | 0.177368 | ||||||||
\(697\) | −28.9418 | −1.09625 | ||||||||
\(698\) | 3.46506 | 0.131155 | ||||||||
\(699\) | 4.82268 | 0.182411 | ||||||||
\(700\) | −2.98011 | −0.112637 | ||||||||
\(701\) | 7.55523 | 0.285357 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(702\) | −2.62870 | −0.0992138 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.22272 | 0.0460829 | ||||||||
\(705\) | −23.4864 | −0.884549 | ||||||||
\(706\) | 8.76647 | 0.329931 | ||||||||
\(707\) | 9.40739 | 0.353801 | ||||||||
\(708\) | 28.5719 | 1.07380 | ||||||||
\(709\) | 47.6195 | 1.78839 | 0.894193 | − | 0.447681i | \(-0.147750\pi\) | ||||
0.894193 | + | 0.447681i | \(0.147750\pi\) | |||||||
\(710\) | 12.8545 | 0.482421 | ||||||||
\(711\) | 6.31679 | 0.236898 | ||||||||
\(712\) | 18.4510 | 0.691481 | ||||||||
\(713\) | −19.0985 | −0.715246 | ||||||||
\(714\) | 9.89504 | 0.370312 | ||||||||
\(715\) | −5.00192 | −0.187061 | ||||||||
\(716\) | −12.4273 | −0.464430 | ||||||||
\(717\) | −9.12056 | −0.340614 | ||||||||
\(718\) | −11.2383 | −0.419410 | ||||||||
\(719\) | −45.0257 | −1.67918 | −0.839588 | − | 0.543224i | \(-0.817203\pi\) | ||||
−0.839588 | + | 0.543224i | \(0.817203\pi\) | |||||||
\(720\) | 4.77828 | 0.178076 | ||||||||
\(721\) | 2.62267 | 0.0976734 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.720663 | 0.0268018 | ||||||||
\(724\) | −21.4062 | −0.795554 | ||||||||
\(725\) | −5.52857 | −0.205326 | ||||||||
\(726\) | −23.9745 | −0.889778 | ||||||||
\(727\) | 20.7456 | 0.769413 | 0.384707 | − | 0.923039i | \(-0.374303\pi\) | ||||
0.384707 | + | 0.923039i | \(0.374303\pi\) | |||||||
\(728\) | 2.87837 | 0.106679 | ||||||||
\(729\) | −33.0765 | −1.22506 | ||||||||
\(730\) | 6.05734 | 0.224192 | ||||||||
\(731\) | −18.8598 | −0.697556 | ||||||||
\(732\) | 35.1391 | 1.29878 | ||||||||
\(733\) | −20.4921 | −0.756892 | −0.378446 | − | 0.925623i | \(-0.623542\pi\) | ||||
−0.378446 | + | 0.925623i | \(0.623542\pi\) | |||||||
\(734\) | −5.92259 | −0.218607 | ||||||||
\(735\) | −3.58479 | −0.132227 | ||||||||
\(736\) | 3.82191 | 0.140878 | ||||||||
\(737\) | 11.4368 | 0.421278 | ||||||||
\(738\) | 24.8036 | 0.913033 | ||||||||
\(739\) | −18.8930 | −0.694989 | −0.347495 | − | 0.937682i | \(-0.612968\pi\) | ||||
−0.347495 | + | 0.937682i | \(0.612968\pi\) | |||||||
\(740\) | 1.19640 | 0.0439806 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.68427 | 0.135254 | ||||||||
\(743\) | −38.6114 | −1.41651 | −0.708257 | − | 0.705955i | \(-0.750518\pi\) | ||||
−0.708257 | + | 0.705955i | \(0.750518\pi\) | |||||||
\(744\) | 12.6043 | 0.462096 | ||||||||
\(745\) | 5.16974 | 0.189405 | ||||||||
\(746\) | 22.7567 | 0.833180 | ||||||||
\(747\) | −12.9167 | −0.472599 | ||||||||
\(748\) | 4.79672 | 0.175385 | ||||||||
\(749\) | 19.3222 | 0.706017 | ||||||||
\(750\) | −28.6070 | −1.04458 | ||||||||
\(751\) | −4.43470 | −0.161825 | −0.0809123 | − | 0.996721i | \(-0.525783\pi\) | ||||
−0.0809123 | + | 0.996721i | \(0.525783\pi\) | |||||||
\(752\) | 6.55168 | 0.238915 | ||||||||
\(753\) | −44.0318 | −1.60461 | ||||||||
\(754\) | 5.33983 | 0.194465 | ||||||||
\(755\) | −26.3819 | −0.960135 | ||||||||
\(756\) | −0.913260 | −0.0332149 | ||||||||
\(757\) | 38.7770 | 1.40937 | 0.704687 | − | 0.709518i | \(-0.251087\pi\) | ||||
0.704687 | + | 0.709518i | \(0.251087\pi\) | |||||||
\(758\) | 7.09293 | 0.257627 | ||||||||
\(759\) | 11.7871 | 0.427844 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0453 | −0.835391 | −0.417695 | − | 0.908587i | \(-0.637162\pi\) | ||||
−0.417695 | + | 0.908587i | \(0.637162\pi\) | |||||||
\(762\) | −28.5099 | −1.03280 | ||||||||
\(763\) | 10.4840 | 0.379547 | ||||||||
\(764\) | −9.62706 | −0.348295 | ||||||||
\(765\) | 18.7452 | 0.677733 | ||||||||
\(766\) | 20.1267 | 0.727206 | ||||||||
\(767\) | 32.6051 | 1.17730 | ||||||||
\(768\) | −2.52231 | −0.0910162 | ||||||||
\(769\) | −53.1943 | −1.91824 | −0.959118 | − | 0.283007i | \(-0.908668\pi\) | ||||
−0.959118 | + | 0.283007i | \(0.908668\pi\) | |||||||
\(770\) | −1.73776 | −0.0626246 | ||||||||
\(771\) | 15.3215 | 0.551789 | ||||||||
\(772\) | −18.0674 | −0.650258 | ||||||||
\(773\) | 27.8717 | 1.00248 | 0.501238 | − | 0.865310i | \(-0.332878\pi\) | ||||
0.501238 | + | 0.865310i | \(0.332878\pi\) | |||||||
\(774\) | 16.1632 | 0.580974 | ||||||||
\(775\) | −14.8919 | −0.534934 | ||||||||
\(776\) | −17.7866 | −0.638502 | ||||||||
\(777\) | −2.12330 | −0.0761730 | ||||||||
\(778\) | 30.2580 | 1.08480 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 10.3183 | 0.369456 | ||||||||
\(781\) | −11.0590 | −0.395723 | ||||||||
\(782\) | 14.9934 | 0.536161 | ||||||||
\(783\) | −1.69424 | −0.0605472 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 11.1549 | 0.398136 | ||||||||
\(786\) | −6.54927 | −0.233605 | ||||||||
\(787\) | 24.7006 | 0.880483 | 0.440241 | − | 0.897879i | \(-0.354893\pi\) | ||||
0.440241 | + | 0.897879i | \(0.354893\pi\) | |||||||
\(788\) | 12.8396 | 0.457390 | ||||||||
\(789\) | 45.2542 | 1.61109 | ||||||||
\(790\) | −2.67026 | −0.0950036 | ||||||||
\(791\) | 17.9428 | 0.637972 | ||||||||
\(792\) | −4.11086 | −0.146073 | ||||||||
\(793\) | 40.0993 | 1.42397 | ||||||||
\(794\) | −2.90935 | −0.103249 | ||||||||
\(795\) | 13.2073 | 0.468415 | ||||||||
\(796\) | −5.67539 | −0.201159 | ||||||||
\(797\) | 53.0008 | 1.87738 | 0.938692 | − | 0.344758i | \(-0.112039\pi\) | ||||
0.938692 | + | 0.344758i | \(0.112039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.7022 | 0.909280 | ||||||||
\(800\) | 2.98011 | 0.105363 | ||||||||
\(801\) | −62.0336 | −2.19185 | ||||||||
\(802\) | −28.7840 | −1.01640 | ||||||||
\(803\) | −5.21127 | −0.183902 | ||||||||
\(804\) | −23.5926 | −0.832048 | ||||||||
\(805\) | −5.43182 | −0.191446 | ||||||||
\(806\) | 14.3835 | 0.506638 | ||||||||
\(807\) | −4.24097 | −0.149289 | ||||||||
\(808\) | −9.40739 | −0.330951 | ||||||||
\(809\) | 24.5013 | 0.861419 | 0.430710 | − | 0.902491i | \(-0.358263\pi\) | ||||
0.430710 | + | 0.902491i | \(0.358263\pi\) | |||||||
\(810\) | 11.0610 | 0.388643 | ||||||||
\(811\) | −32.5875 | −1.14430 | −0.572151 | − | 0.820148i | \(-0.693891\pi\) | ||||
−0.572151 | + | 0.820148i | \(0.693891\pi\) | |||||||
\(812\) | 1.85516 | 0.0651033 | ||||||||
\(813\) | −20.0670 | −0.703780 | ||||||||
\(814\) | −1.02929 | −0.0360766 | ||||||||
\(815\) | 25.7925 | 0.903471 | ||||||||
\(816\) | −9.89504 | −0.346396 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 25.6553 | 0.897015 | ||||||||
\(819\) | −9.67728 | −0.338152 | ||||||||
\(820\) | −10.4851 | −0.366155 | ||||||||
\(821\) | 32.4658 | 1.13307 | 0.566533 | − | 0.824039i | \(-0.308285\pi\) | ||||
0.566533 | + | 0.824039i | \(0.308285\pi\) | |||||||
\(822\) | −42.8503 | −1.49458 | ||||||||
\(823\) | −23.3268 | −0.813122 | −0.406561 | − | 0.913624i | \(-0.633272\pi\) | ||||
−0.406561 | + | 0.913624i | \(0.633272\pi\) | |||||||
\(824\) | −2.62267 | −0.0913651 | ||||||||
\(825\) | 9.19088 | 0.319985 | ||||||||
\(826\) | 11.3276 | 0.394139 | ||||||||
\(827\) | −37.5495 | −1.30572 | −0.652862 | − | 0.757477i | \(-0.726432\pi\) | ||||
−0.652862 | + | 0.757477i | \(0.726432\pi\) | |||||||
\(828\) | −12.8495 | −0.446553 | ||||||||
\(829\) | −50.5787 | −1.75667 | −0.878336 | − | 0.478044i | \(-0.841346\pi\) | ||||
−0.878336 | + | 0.478044i | \(0.841346\pi\) | |||||||
\(830\) | 5.46022 | 0.189527 | ||||||||
\(831\) | 75.6722 | 2.62504 | ||||||||
\(832\) | −2.87837 | −0.0997895 | ||||||||
\(833\) | 3.92300 | 0.135924 | ||||||||
\(834\) | 50.7750 | 1.75819 | ||||||||
\(835\) | 27.3560 | 0.946693 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.56366 | −0.157743 | ||||||||
\(838\) | −1.06546 | −0.0368058 | ||||||||
\(839\) | 18.9843 | 0.655412 | 0.327706 | − | 0.944780i | \(-0.393724\pi\) | ||||
0.327706 | + | 0.944780i | \(0.393724\pi\) | |||||||
\(840\) | 3.58479 | 0.123687 | ||||||||
\(841\) | −25.5584 | −0.881324 | ||||||||
\(842\) | 5.48941 | 0.189178 | ||||||||
\(843\) | −26.3745 | −0.908386 | ||||||||
\(844\) | −1.91154 | −0.0657979 | ||||||||
\(845\) | −6.70109 | −0.230525 | ||||||||
\(846\) | −22.0272 | −0.757312 | ||||||||
\(847\) | −9.50496 | −0.326594 | ||||||||
\(848\) | −3.68427 | −0.126518 | ||||||||
\(849\) | 20.3283 | 0.697666 | ||||||||
\(850\) | 11.6909 | 0.400996 | ||||||||
\(851\) | −3.21731 | −0.110288 | ||||||||
\(852\) | 22.8134 | 0.781574 | ||||||||
\(853\) | −34.5054 | −1.18144 | −0.590722 | − | 0.806875i | \(-0.701157\pi\) | ||||
−0.590722 | + | 0.806875i | \(0.701157\pi\) | |||||||
\(854\) | 13.9313 | 0.476718 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.3222 | −0.660418 | ||||||||
\(857\) | −18.5707 | −0.634363 | −0.317181 | − | 0.948365i | \(-0.602736\pi\) | ||||
−0.317181 | + | 0.948365i | \(0.602736\pi\) | |||||||
\(858\) | −8.87711 | −0.303059 | ||||||||
\(859\) | −19.8310 | −0.676624 | −0.338312 | − | 0.941034i | \(-0.609856\pi\) | ||||
−0.338312 | + | 0.941034i | \(0.609856\pi\) | |||||||
\(860\) | −6.83257 | −0.232989 | ||||||||
\(861\) | 18.6083 | 0.634169 | ||||||||
\(862\) | 22.2378 | 0.757422 | ||||||||
\(863\) | 48.3278 | 1.64510 | 0.822549 | − | 0.568694i | \(-0.192551\pi\) | ||||
0.822549 | + | 0.568694i | \(0.192551\pi\) | |||||||
\(864\) | 0.913260 | 0.0310697 | ||||||||
\(865\) | 3.73868 | 0.127119 | ||||||||
\(866\) | 12.8888 | 0.437979 | ||||||||
\(867\) | 4.06115 | 0.137924 | ||||||||
\(868\) | 4.99711 | 0.169613 | ||||||||
\(869\) | 2.29729 | 0.0779301 | ||||||||
\(870\) | 6.65035 | 0.225468 | ||||||||
\(871\) | −26.9230 | −0.912251 | ||||||||
\(872\) | −10.4840 | −0.355034 | ||||||||
\(873\) | 59.7999 | 2.02392 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3416 | −0.383415 | ||||||||
\(876\) | 10.7502 | 0.363216 | ||||||||
\(877\) | −46.2497 | −1.56174 | −0.780871 | − | 0.624692i | \(-0.785224\pi\) | ||||
−0.780871 | + | 0.624692i | \(0.785224\pi\) | |||||||
\(878\) | −17.0046 | −0.573878 | ||||||||
\(879\) | −20.3279 | −0.685644 | ||||||||
\(880\) | 1.73776 | 0.0585799 | ||||||||
\(881\) | −9.15551 | −0.308457 | −0.154228 | − | 0.988035i | \(-0.549289\pi\) | ||||
−0.154228 | + | 0.988035i | \(0.549289\pi\) | |||||||
\(882\) | −3.36207 | −0.113207 | ||||||||
\(883\) | 45.5264 | 1.53208 | 0.766042 | − | 0.642790i | \(-0.222223\pi\) | ||||
0.766042 | + | 0.642790i | \(0.222223\pi\) | |||||||
\(884\) | −11.2918 | −0.379785 | ||||||||
\(885\) | 40.6072 | 1.36500 | ||||||||
\(886\) | −2.51156 | −0.0843774 | ||||||||
\(887\) | −8.12938 | −0.272958 | −0.136479 | − | 0.990643i | \(-0.543579\pi\) | ||||
−0.136479 | + | 0.990643i | \(0.543579\pi\) | |||||||
\(888\) | 2.12330 | 0.0712533 | ||||||||
\(889\) | −11.3031 | −0.379092 | ||||||||
\(890\) | 26.2231 | 0.879001 | ||||||||
\(891\) | −9.51602 | −0.318799 | ||||||||
\(892\) | −2.67452 | −0.0895494 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 9.17495 | 0.306856 | ||||||||
\(895\) | −17.6621 | −0.590378 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −27.7477 | −0.926468 | ||||||||
\(898\) | 11.7883 | 0.393382 | ||||||||
\(899\) | 9.27044 | 0.309186 | ||||||||
\(900\) | −10.0193 | −0.333978 | ||||||||
\(901\) | −14.4534 | −0.481512 | ||||||||
\(902\) | 9.02056 | 0.300352 | ||||||||
\(903\) | 12.1260 | 0.403529 | ||||||||
\(904\) | −17.9428 | −0.596769 | ||||||||
\(905\) | −30.4231 | −1.01130 | ||||||||
\(906\) | −46.8210 | −1.55552 | ||||||||
\(907\) | −16.9768 | −0.563706 | −0.281853 | − | 0.959458i | \(-0.590949\pi\) | ||||
−0.281853 | + | 0.959458i | \(0.590949\pi\) | |||||||
\(908\) | 2.75727 | 0.0915032 | ||||||||
\(909\) | 31.6283 | 1.04905 | ||||||||
\(910\) | 4.09082 | 0.135609 | ||||||||
\(911\) | 40.6971 | 1.34836 | 0.674178 | − | 0.738569i | \(-0.264498\pi\) | ||||
0.674178 | + | 0.738569i | \(0.264498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.69755 | −0.155466 | ||||||||
\(914\) | 27.4286 | 0.907257 | ||||||||
\(915\) | 49.9407 | 1.65099 | ||||||||
\(916\) | −15.4798 | −0.511467 | ||||||||
\(917\) | −2.59653 | −0.0857451 | ||||||||
\(918\) | 3.58272 | 0.118247 | ||||||||
\(919\) | 37.2379 | 1.22837 | 0.614183 | − | 0.789164i | \(-0.289486\pi\) | ||||
0.614183 | + | 0.789164i | \(0.289486\pi\) | |||||||
\(920\) | 5.43182 | 0.179082 | ||||||||
\(921\) | −36.2487 | −1.19443 | ||||||||
\(922\) | −21.1906 | −0.697875 | ||||||||
\(923\) | 26.0338 | 0.856912 | ||||||||
\(924\) | −3.08408 | −0.101459 | ||||||||
\(925\) | −2.50867 | −0.0824847 | ||||||||
\(926\) | 21.9687 | 0.721937 | ||||||||
\(927\) | 8.81761 | 0.289608 | ||||||||
\(928\) | −1.85516 | −0.0608985 | ||||||||
\(929\) | 58.4574 | 1.91793 | 0.958963 | − | 0.283532i | \(-0.0915064\pi\) | ||||
0.958963 | + | 0.283532i | \(0.0915064\pi\) | |||||||
\(930\) | 17.9136 | 0.587410 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.91201 | −0.0626298 | ||||||||
\(933\) | −72.8357 | −2.38453 | ||||||||
\(934\) | 5.91139 | 0.193427 | ||||||||
\(935\) | 6.81723 | 0.222947 | ||||||||
\(936\) | 9.67728 | 0.316312 | ||||||||
\(937\) | 17.8662 | 0.583664 | 0.291832 | − | 0.956470i | \(-0.405735\pi\) | ||||
0.291832 | + | 0.956470i | \(0.405735\pi\) | |||||||
\(938\) | −9.35356 | −0.305405 | ||||||||
\(939\) | 10.4056 | 0.339575 | ||||||||
\(940\) | 9.31144 | 0.303706 | ||||||||
\(941\) | 21.3224 | 0.695089 | 0.347545 | − | 0.937663i | \(-0.387015\pi\) | ||||
0.347545 | + | 0.937663i | \(0.387015\pi\) | |||||||
\(942\) | 19.7971 | 0.645024 | ||||||||
\(943\) | 28.1961 | 0.918190 | ||||||||
\(944\) | −11.3276 | −0.368684 | ||||||||
\(945\) | −1.29795 | −0.0422224 | ||||||||
\(946\) | 5.87822 | 0.191117 | ||||||||
\(947\) | −35.0239 | −1.13812 | −0.569061 | − | 0.822295i | \(-0.692693\pi\) | ||||
−0.569061 | + | 0.822295i | \(0.692693\pi\) | |||||||
\(948\) | −4.73902 | −0.153916 | ||||||||
\(949\) | 12.2677 | 0.398227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.5159 | 0.535564 | ||||||||
\(952\) | −3.92300 | −0.127145 | ||||||||
\(953\) | −2.15394 | −0.0697729 | −0.0348865 | − | 0.999391i | \(-0.511107\pi\) | ||||
−0.0348865 | + | 0.999391i | \(0.511107\pi\) | |||||||
\(954\) | 12.3868 | 0.401036 | ||||||||
\(955\) | −13.6823 | −0.442748 | ||||||||
\(956\) | 3.61595 | 0.116948 | ||||||||
\(957\) | −5.72145 | −0.184948 | ||||||||
\(958\) | −25.5707 | −0.826152 | ||||||||
\(959\) | −16.9885 | −0.548587 | ||||||||
\(960\) | −3.58479 | −0.115699 | ||||||||
\(961\) | −6.02885 | −0.194479 | ||||||||
\(962\) | 2.42303 | 0.0781216 | ||||||||
\(963\) | 64.9625 | 2.09339 | ||||||||
\(964\) | −0.285715 | −0.00920226 | ||||||||
\(965\) | −25.6779 | −0.826599 | ||||||||
\(966\) | −9.64007 | −0.310164 | ||||||||
\(967\) | 50.8485 | 1.63518 | 0.817589 | − | 0.575802i | \(-0.195310\pi\) | ||||
0.817589 | + | 0.575802i | \(0.195310\pi\) | |||||||
\(968\) | 9.50496 | 0.305501 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.2789 | −0.811655 | ||||||||
\(971\) | 52.9962 | 1.70073 | 0.850364 | − | 0.526195i | \(-0.176382\pi\) | ||||
0.850364 | + | 0.526195i | \(0.176382\pi\) | |||||||
\(972\) | 22.3702 | 0.717523 | ||||||||
\(973\) | 20.1303 | 0.645348 | ||||||||
\(974\) | 33.0894 | 1.06025 | ||||||||
\(975\) | −21.6360 | −0.692907 | ||||||||
\(976\) | −13.9313 | −0.445929 | ||||||||
\(977\) | −15.8968 | −0.508583 | −0.254291 | − | 0.967128i | \(-0.581842\pi\) | ||||
−0.254291 | + | 0.967128i | \(0.581842\pi\) | |||||||
\(978\) | 45.7749 | 1.46372 | ||||||||
\(979\) | −22.5604 | −0.721032 | ||||||||
\(980\) | 1.42123 | 0.0453995 | ||||||||
\(981\) | 35.2480 | 1.12538 | ||||||||
\(982\) | 38.7050 | 1.23513 | ||||||||
\(983\) | −23.6553 | −0.754487 | −0.377244 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(984\) | −18.6083 | −0.593211 | ||||||||
\(985\) | 18.2480 | 0.581429 | ||||||||
\(986\) | −7.27778 | −0.231772 | ||||||||
\(987\) | −16.5254 | −0.526009 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.3739 | 0.584255 | ||||||||
\(990\) | −5.84248 | −0.185686 | ||||||||
\(991\) | −39.8094 | −1.26459 | −0.632293 | − | 0.774729i | \(-0.717886\pi\) | ||||
−0.632293 | + | 0.774729i | \(0.717886\pi\) | |||||||
\(992\) | −4.99711 | −0.158659 | ||||||||
\(993\) | 46.2745 | 1.46848 | ||||||||
\(994\) | 9.04463 | 0.286878 | ||||||||
\(995\) | −8.06603 | −0.255710 | ||||||||
\(996\) | 9.69047 | 0.307054 | ||||||||
\(997\) | 26.5487 | 0.840805 | 0.420403 | − | 0.907338i | \(-0.361889\pi\) | ||||
0.420403 | + | 0.907338i | \(0.361889\pi\) | |||||||
\(998\) | 34.0924 | 1.07918 | ||||||||
\(999\) | −0.768788 | −0.0243234 |
(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 | 5054.2.a.z.1.1 | ✓ | 6 | |
19.18 | odd | 2 | 5054.2.a.be.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.z.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
5054.2.a.be.1.6 | yes | 6 | 19.18 | odd | 2 |