Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} - 3723 x^{12} - 14776 x^{11} + 14837 x^{10} + 21886 x^{9} - 28084 x^{8} - 14682 x^{7} + \cdots - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-0.590088\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | 0.590088 | 0.340688 | 0.170344 | − | 0.985385i | \(-0.445512\pi\) | ||||
0.170344 | + | 0.985385i | \(0.445512\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.936829 | 0.418963 | 0.209481 | − | 0.977813i | \(-0.432822\pi\) | ||||
0.209481 | + | 0.977813i | \(0.432822\pi\) | |||||||
\(6\) | 0.590088 | 0.240903 | ||||||||
\(7\) | 1.40799 | 0.532171 | 0.266085 | − | 0.963949i | \(-0.414270\pi\) | ||||
0.266085 | + | 0.963949i | \(0.414270\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.65180 | −0.883932 | ||||||||
\(10\) | 0.936829 | 0.296251 | ||||||||
\(11\) | −3.44267 | −1.03800 | −0.519001 | − | 0.854773i | \(-0.673696\pi\) | ||||
−0.519001 | + | 0.854773i | \(0.673696\pi\) | |||||||
\(12\) | 0.590088 | 0.170344 | ||||||||
\(13\) | 2.00043 | 0.554820 | 0.277410 | − | 0.960752i | \(-0.410524\pi\) | ||||
0.277410 | + | 0.960752i | \(0.410524\pi\) | |||||||
\(14\) | 1.40799 | 0.376301 | ||||||||
\(15\) | 0.552812 | 0.142735 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.141401 | 0.0342947 | 0.0171473 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171473 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(18\) | −2.65180 | −0.625034 | ||||||||
\(19\) | −6.42748 | −1.47456 | −0.737282 | − | 0.675585i | \(-0.763891\pi\) | ||||
−0.737282 | + | 0.675585i | \(0.763891\pi\) | |||||||
\(20\) | 0.936829 | 0.209481 | ||||||||
\(21\) | 0.830839 | 0.181304 | ||||||||
\(22\) | −3.44267 | −0.733979 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.590088 | 0.120451 | ||||||||
\(25\) | −4.12235 | −0.824470 | ||||||||
\(26\) | 2.00043 | 0.392317 | ||||||||
\(27\) | −3.33506 | −0.641832 | ||||||||
\(28\) | 1.40799 | 0.266085 | ||||||||
\(29\) | −8.45079 | −1.56927 | −0.784636 | − | 0.619956i | \(-0.787150\pi\) | ||||
−0.784636 | + | 0.619956i | \(0.787150\pi\) | |||||||
\(30\) | 0.552812 | 0.100929 | ||||||||
\(31\) | −6.58167 | −1.18210 | −0.591051 | − | 0.806634i | \(-0.701287\pi\) | ||||
−0.591051 | + | 0.806634i | \(0.701287\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.03148 | −0.353635 | ||||||||
\(34\) | 0.141401 | 0.0242500 | ||||||||
\(35\) | 1.31905 | 0.222960 | ||||||||
\(36\) | −2.65180 | −0.441966 | ||||||||
\(37\) | −2.90009 | −0.476772 | −0.238386 | − | 0.971170i | \(-0.576618\pi\) | ||||
−0.238386 | + | 0.971170i | \(0.576618\pi\) | |||||||
\(38\) | −6.42748 | −1.04267 | ||||||||
\(39\) | 1.18043 | 0.189020 | ||||||||
\(40\) | 0.936829 | 0.148126 | ||||||||
\(41\) | 3.03496 | 0.473981 | 0.236990 | − | 0.971512i | \(-0.423839\pi\) | ||||
0.236990 | + | 0.971512i | \(0.423839\pi\) | |||||||
\(42\) | 0.830839 | 0.128201 | ||||||||
\(43\) | −0.862799 | −0.131576 | −0.0657878 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657878 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(44\) | −3.44267 | −0.519001 | ||||||||
\(45\) | −2.48428 | −0.370335 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −4.76503 | −0.695052 | −0.347526 | − | 0.937670i | \(-0.612978\pi\) | ||||
−0.347526 | + | 0.937670i | \(0.612978\pi\) | |||||||
\(48\) | 0.590088 | 0.0851719 | ||||||||
\(49\) | −5.01756 | −0.716795 | ||||||||
\(50\) | −4.12235 | −0.582988 | ||||||||
\(51\) | 0.0834389 | 0.0116838 | ||||||||
\(52\) | 2.00043 | 0.277410 | ||||||||
\(53\) | −5.92958 | −0.814490 | −0.407245 | − | 0.913319i | \(-0.633510\pi\) | ||||
−0.407245 | + | 0.913319i | \(0.633510\pi\) | |||||||
\(54\) | −3.33506 | −0.453844 | ||||||||
\(55\) | −3.22519 | −0.434885 | ||||||||
\(56\) | 1.40799 | 0.188151 | ||||||||
\(57\) | −3.79278 | −0.502366 | ||||||||
\(58\) | −8.45079 | −1.10964 | ||||||||
\(59\) | −3.96755 | −0.516531 | −0.258266 | − | 0.966074i | \(-0.583151\pi\) | ||||
−0.258266 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(60\) | 0.552812 | 0.0713677 | ||||||||
\(61\) | 1.48572 | 0.190226 | 0.0951132 | − | 0.995466i | \(-0.469679\pi\) | ||||
0.0951132 | + | 0.995466i | \(0.469679\pi\) | |||||||
\(62\) | −6.58167 | −0.835873 | ||||||||
\(63\) | −3.73370 | −0.470403 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.87406 | 0.232449 | ||||||||
\(66\) | −2.03148 | −0.250058 | ||||||||
\(67\) | 5.37393 | 0.656530 | 0.328265 | − | 0.944586i | \(-0.393536\pi\) | ||||
0.328265 | + | 0.944586i | \(0.393536\pi\) | |||||||
\(68\) | 0.141401 | 0.0171473 | ||||||||
\(69\) | 0.590088 | 0.0710383 | ||||||||
\(70\) | 1.31905 | 0.157656 | ||||||||
\(71\) | 14.5679 | 1.72889 | 0.864443 | − | 0.502731i | \(-0.167671\pi\) | ||||
0.864443 | + | 0.502731i | \(0.167671\pi\) | |||||||
\(72\) | −2.65180 | −0.312517 | ||||||||
\(73\) | 10.7599 | 1.25935 | 0.629677 | − | 0.776857i | \(-0.283187\pi\) | ||||
0.629677 | + | 0.776857i | \(0.283187\pi\) | |||||||
\(74\) | −2.90009 | −0.337129 | ||||||||
\(75\) | −2.43255 | −0.280887 | ||||||||
\(76\) | −6.42748 | −0.737282 | ||||||||
\(77\) | −4.84724 | −0.552395 | ||||||||
\(78\) | 1.18043 | 0.133658 | ||||||||
\(79\) | −6.15727 | −0.692747 | −0.346374 | − | 0.938097i | \(-0.612587\pi\) | ||||
−0.346374 | + | 0.938097i | \(0.612587\pi\) | |||||||
\(80\) | 0.936829 | 0.104741 | ||||||||
\(81\) | 5.98741 | 0.665268 | ||||||||
\(82\) | 3.03496 | 0.335155 | ||||||||
\(83\) | 10.3262 | 1.13345 | 0.566724 | − | 0.823908i | \(-0.308211\pi\) | ||||
0.566724 | + | 0.823908i | \(0.308211\pi\) | |||||||
\(84\) | 0.830839 | 0.0906520 | ||||||||
\(85\) | 0.132468 | 0.0143682 | ||||||||
\(86\) | −0.862799 | −0.0930380 | ||||||||
\(87\) | −4.98671 | −0.534632 | ||||||||
\(88\) | −3.44267 | −0.366989 | ||||||||
\(89\) | −2.22548 | −0.235901 | −0.117950 | − | 0.993019i | \(-0.537632\pi\) | ||||
−0.117950 | + | 0.993019i | \(0.537632\pi\) | |||||||
\(90\) | −2.48428 | −0.261866 | ||||||||
\(91\) | 2.81659 | 0.295259 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.88377 | −0.402728 | ||||||||
\(94\) | −4.76503 | −0.491476 | ||||||||
\(95\) | −6.02145 | −0.617788 | ||||||||
\(96\) | 0.590088 | 0.0602256 | ||||||||
\(97\) | −2.07398 | −0.210581 | −0.105291 | − | 0.994441i | \(-0.533577\pi\) | ||||
−0.105291 | + | 0.994441i | \(0.533577\pi\) | |||||||
\(98\) | −5.01756 | −0.506850 | ||||||||
\(99\) | 9.12925 | 0.917524 | ||||||||
\(100\) | −4.12235 | −0.412235 | ||||||||
\(101\) | −3.99612 | −0.397629 | −0.198815 | − | 0.980037i | \(-0.563709\pi\) | ||||
−0.198815 | + | 0.980037i | \(0.563709\pi\) | |||||||
\(102\) | 0.0834389 | 0.00826168 | ||||||||
\(103\) | −9.91039 | −0.976499 | −0.488250 | − | 0.872704i | \(-0.662364\pi\) | ||||
−0.488250 | + | 0.872704i | \(0.662364\pi\) | |||||||
\(104\) | 2.00043 | 0.196158 | ||||||||
\(105\) | 0.778354 | 0.0759596 | ||||||||
\(106\) | −5.92958 | −0.575931 | ||||||||
\(107\) | −1.48043 | −0.143118 | −0.0715592 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715592 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(108\) | −3.33506 | −0.320916 | ||||||||
\(109\) | 12.9418 | 1.23960 | 0.619798 | − | 0.784761i | \(-0.287215\pi\) | ||||
0.619798 | + | 0.784761i | \(0.287215\pi\) | |||||||
\(110\) | −3.22519 | −0.307510 | ||||||||
\(111\) | −1.71131 | −0.162430 | ||||||||
\(112\) | 1.40799 | 0.133043 | ||||||||
\(113\) | −13.0599 | −1.22857 | −0.614286 | − | 0.789083i | \(-0.710556\pi\) | ||||
−0.614286 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(114\) | −3.79278 | −0.355226 | ||||||||
\(115\) | 0.936829 | 0.0873598 | ||||||||
\(116\) | −8.45079 | −0.784636 | ||||||||
\(117\) | −5.30474 | −0.490423 | ||||||||
\(118\) | −3.96755 | −0.365243 | ||||||||
\(119\) | 0.199091 | 0.0182506 | ||||||||
\(120\) | 0.552812 | 0.0504646 | ||||||||
\(121\) | 0.851951 | 0.0774501 | ||||||||
\(122\) | 1.48572 | 0.134510 | ||||||||
\(123\) | 1.79089 | 0.161479 | ||||||||
\(124\) | −6.58167 | −0.591051 | ||||||||
\(125\) | −8.54609 | −0.764385 | ||||||||
\(126\) | −3.73370 | −0.332625 | ||||||||
\(127\) | 15.9305 | 1.41360 | 0.706800 | − | 0.707413i | \(-0.250138\pi\) | ||||
0.706800 | + | 0.707413i | \(0.250138\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.509128 | −0.0448262 | ||||||||
\(130\) | 1.87406 | 0.164366 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −2.03148 | −0.176817 | ||||||||
\(133\) | −9.04983 | −0.784720 | ||||||||
\(134\) | 5.37393 | 0.464237 | ||||||||
\(135\) | −3.12438 | −0.268904 | ||||||||
\(136\) | 0.141401 | 0.0121250 | ||||||||
\(137\) | 2.71237 | 0.231734 | 0.115867 | − | 0.993265i | \(-0.463035\pi\) | ||||
0.115867 | + | 0.993265i | \(0.463035\pi\) | |||||||
\(138\) | 0.590088 | 0.0502317 | ||||||||
\(139\) | −6.50910 | −0.552095 | −0.276047 | − | 0.961144i | \(-0.589025\pi\) | ||||
−0.276047 | + | 0.961144i | \(0.589025\pi\) | |||||||
\(140\) | 1.31905 | 0.111480 | ||||||||
\(141\) | −2.81179 | −0.236796 | ||||||||
\(142\) | 14.5679 | 1.22251 | ||||||||
\(143\) | −6.88682 | −0.575905 | ||||||||
\(144\) | −2.65180 | −0.220983 | ||||||||
\(145\) | −7.91695 | −0.657467 | ||||||||
\(146\) | 10.7599 | 0.890498 | ||||||||
\(147\) | −2.96080 | −0.244203 | ||||||||
\(148\) | −2.90009 | −0.238386 | ||||||||
\(149\) | −6.06260 | −0.496668 | −0.248334 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248334 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(150\) | −2.43255 | −0.198617 | ||||||||
\(151\) | 10.8693 | 0.884531 | 0.442266 | − | 0.896884i | \(-0.354175\pi\) | ||||
0.442266 | + | 0.896884i | \(0.354175\pi\) | |||||||
\(152\) | −6.42748 | −0.521337 | ||||||||
\(153\) | −0.374966 | −0.0303142 | ||||||||
\(154\) | −4.84724 | −0.390602 | ||||||||
\(155\) | −6.16590 | −0.495257 | ||||||||
\(156\) | 1.18043 | 0.0945102 | ||||||||
\(157\) | 22.1495 | 1.76772 | 0.883862 | − | 0.467747i | \(-0.154934\pi\) | ||||
0.883862 | + | 0.467747i | \(0.154934\pi\) | |||||||
\(158\) | −6.15727 | −0.489846 | ||||||||
\(159\) | −3.49897 | −0.277487 | ||||||||
\(160\) | 0.936829 | 0.0740629 | ||||||||
\(161\) | 1.40799 | 0.110965 | ||||||||
\(162\) | 5.98741 | 0.470415 | ||||||||
\(163\) | −0.433839 | −0.0339809 | −0.0169904 | − | 0.999856i | \(-0.505408\pi\) | ||||
−0.0169904 | + | 0.999856i | \(0.505408\pi\) | |||||||
\(164\) | 3.03496 | 0.236990 | ||||||||
\(165\) | −1.90315 | −0.148160 | ||||||||
\(166\) | 10.3262 | 0.801468 | ||||||||
\(167\) | 23.0084 | 1.78044 | 0.890220 | − | 0.455531i | \(-0.150551\pi\) | ||||
0.890220 | + | 0.455531i | \(0.150551\pi\) | |||||||
\(168\) | 0.830839 | 0.0641006 | ||||||||
\(169\) | −8.99827 | −0.692175 | ||||||||
\(170\) | 0.132468 | 0.0101599 | ||||||||
\(171\) | 17.0444 | 1.30341 | ||||||||
\(172\) | −0.862799 | −0.0657878 | ||||||||
\(173\) | 3.71260 | 0.282264 | 0.141132 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141132 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(174\) | −4.98671 | −0.378042 | ||||||||
\(175\) | −5.80423 | −0.438759 | ||||||||
\(176\) | −3.44267 | −0.259501 | ||||||||
\(177\) | −2.34121 | −0.175976 | ||||||||
\(178\) | −2.22548 | −0.166807 | ||||||||
\(179\) | 2.42372 | 0.181157 | 0.0905787 | − | 0.995889i | \(-0.471128\pi\) | ||||
0.0905787 | + | 0.995889i | \(0.471128\pi\) | |||||||
\(180\) | −2.48428 | −0.185167 | ||||||||
\(181\) | −14.2979 | −1.06276 | −0.531378 | − | 0.847135i | \(-0.678326\pi\) | ||||
−0.531378 | + | 0.847135i | \(0.678326\pi\) | |||||||
\(182\) | 2.81659 | 0.208780 | ||||||||
\(183\) | 0.876704 | 0.0648078 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −2.71689 | −0.199750 | ||||||||
\(186\) | −3.88377 | −0.284771 | ||||||||
\(187\) | −0.486795 | −0.0355980 | ||||||||
\(188\) | −4.76503 | −0.347526 | ||||||||
\(189\) | −4.69573 | −0.341564 | ||||||||
\(190\) | −6.02145 | −0.436842 | ||||||||
\(191\) | −20.4296 | −1.47824 | −0.739118 | − | 0.673576i | \(-0.764757\pi\) | ||||
−0.739118 | + | 0.673576i | \(0.764757\pi\) | |||||||
\(192\) | 0.590088 | 0.0425860 | ||||||||
\(193\) | −10.8576 | −0.781548 | −0.390774 | − | 0.920487i | \(-0.627793\pi\) | ||||
−0.390774 | + | 0.920487i | \(0.627793\pi\) | |||||||
\(194\) | −2.07398 | −0.148903 | ||||||||
\(195\) | 1.10586 | 0.0791925 | ||||||||
\(196\) | −5.01756 | −0.358397 | ||||||||
\(197\) | 14.0192 | 0.998829 | 0.499415 | − | 0.866363i | \(-0.333548\pi\) | ||||
0.499415 | + | 0.866363i | \(0.333548\pi\) | |||||||
\(198\) | 9.12925 | 0.648787 | ||||||||
\(199\) | 7.76683 | 0.550576 | 0.275288 | − | 0.961362i | \(-0.411227\pi\) | ||||
0.275288 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(200\) | −4.12235 | −0.291494 | ||||||||
\(201\) | 3.17110 | 0.223672 | ||||||||
\(202\) | −3.99612 | −0.281166 | ||||||||
\(203\) | −11.8986 | −0.835121 | ||||||||
\(204\) | 0.0834389 | 0.00584189 | ||||||||
\(205\) | 2.84324 | 0.198580 | ||||||||
\(206\) | −9.91039 | −0.690489 | ||||||||
\(207\) | −2.65180 | −0.184313 | ||||||||
\(208\) | 2.00043 | 0.138705 | ||||||||
\(209\) | 22.1277 | 1.53060 | ||||||||
\(210\) | 0.778354 | 0.0537116 | ||||||||
\(211\) | −11.8639 | −0.816746 | −0.408373 | − | 0.912815i | \(-0.633904\pi\) | ||||
−0.408373 | + | 0.912815i | \(0.633904\pi\) | |||||||
\(212\) | −5.92958 | −0.407245 | ||||||||
\(213\) | 8.59632 | 0.589010 | ||||||||
\(214\) | −1.48043 | −0.101200 | ||||||||
\(215\) | −0.808296 | −0.0551253 | ||||||||
\(216\) | −3.33506 | −0.226922 | ||||||||
\(217\) | −9.26693 | −0.629080 | ||||||||
\(218\) | 12.9418 | 0.876527 | ||||||||
\(219\) | 6.34931 | 0.429046 | ||||||||
\(220\) | −3.22519 | −0.217442 | ||||||||
\(221\) | 0.282862 | 0.0190274 | ||||||||
\(222\) | −1.71131 | −0.114856 | ||||||||
\(223\) | −29.2901 | −1.96141 | −0.980706 | − | 0.195487i | \(-0.937371\pi\) | ||||
−0.980706 | + | 0.195487i | \(0.937371\pi\) | |||||||
\(224\) | 1.40799 | 0.0940753 | ||||||||
\(225\) | 10.9316 | 0.728775 | ||||||||
\(226\) | −13.0599 | −0.868732 | ||||||||
\(227\) | 14.0155 | 0.930244 | 0.465122 | − | 0.885247i | \(-0.346010\pi\) | ||||
0.465122 | + | 0.885247i | \(0.346010\pi\) | |||||||
\(228\) | −3.79278 | −0.251183 | ||||||||
\(229\) | 16.2255 | 1.07221 | 0.536105 | − | 0.844152i | \(-0.319895\pi\) | ||||
0.536105 | + | 0.844152i | \(0.319895\pi\) | |||||||
\(230\) | 0.936829 | 0.0617727 | ||||||||
\(231\) | −2.86030 | −0.188194 | ||||||||
\(232\) | −8.45079 | −0.554822 | ||||||||
\(233\) | −24.5063 | −1.60546 | −0.802729 | − | 0.596344i | \(-0.796620\pi\) | ||||
−0.802729 | + | 0.596344i | \(0.796620\pi\) | |||||||
\(234\) | −5.30474 | −0.346781 | ||||||||
\(235\) | −4.46402 | −0.291201 | ||||||||
\(236\) | −3.96755 | −0.258266 | ||||||||
\(237\) | −3.63334 | −0.236010 | ||||||||
\(238\) | 0.199091 | 0.0129051 | ||||||||
\(239\) | −11.1756 | −0.722892 | −0.361446 | − | 0.932393i | \(-0.617717\pi\) | ||||
−0.361446 | + | 0.932393i | \(0.617717\pi\) | |||||||
\(240\) | 0.552812 | 0.0356839 | ||||||||
\(241\) | 12.1844 | 0.784868 | 0.392434 | − | 0.919780i | \(-0.371633\pi\) | ||||
0.392434 | + | 0.919780i | \(0.371633\pi\) | |||||||
\(242\) | 0.851951 | 0.0547655 | ||||||||
\(243\) | 13.5383 | 0.868481 | ||||||||
\(244\) | 1.48572 | 0.0951132 | ||||||||
\(245\) | −4.70060 | −0.300310 | ||||||||
\(246\) | 1.79089 | 0.114183 | ||||||||
\(247\) | −12.8577 | −0.818118 | ||||||||
\(248\) | −6.58167 | −0.417936 | ||||||||
\(249\) | 6.09337 | 0.386152 | ||||||||
\(250\) | −8.54609 | −0.540502 | ||||||||
\(251\) | −16.4845 | −1.04049 | −0.520247 | − | 0.854016i | \(-0.674160\pi\) | ||||
−0.520247 | + | 0.854016i | \(0.674160\pi\) | |||||||
\(252\) | −3.73370 | −0.235201 | ||||||||
\(253\) | −3.44267 | −0.216439 | ||||||||
\(254\) | 15.9305 | 0.999566 | ||||||||
\(255\) | 0.0781680 | 0.00489507 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.5385 | −1.03164 | −0.515821 | − | 0.856696i | \(-0.672513\pi\) | ||||
−0.515821 | + | 0.856696i | \(0.672513\pi\) | |||||||
\(258\) | −0.509128 | −0.0316969 | ||||||||
\(259\) | −4.08330 | −0.253724 | ||||||||
\(260\) | 1.87406 | 0.116224 | ||||||||
\(261\) | 22.4098 | 1.38713 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 27.6647 | 1.70588 | 0.852940 | − | 0.522009i | \(-0.174817\pi\) | ||||
0.852940 | + | 0.522009i | \(0.174817\pi\) | |||||||
\(264\) | −2.03148 | −0.125029 | ||||||||
\(265\) | −5.55500 | −0.341241 | ||||||||
\(266\) | −9.04983 | −0.554881 | ||||||||
\(267\) | −1.31323 | −0.0803685 | ||||||||
\(268\) | 5.37393 | 0.328265 | ||||||||
\(269\) | −22.9212 | −1.39753 | −0.698766 | − | 0.715350i | \(-0.746267\pi\) | ||||
−0.698766 | + | 0.715350i | \(0.746267\pi\) | |||||||
\(270\) | −3.12438 | −0.190144 | ||||||||
\(271\) | −4.22389 | −0.256583 | −0.128291 | − | 0.991737i | \(-0.540949\pi\) | ||||
−0.128291 | + | 0.991737i | \(0.540949\pi\) | |||||||
\(272\) | 0.141401 | 0.00857367 | ||||||||
\(273\) | 1.66204 | 0.100591 | ||||||||
\(274\) | 2.71237 | 0.163860 | ||||||||
\(275\) | 14.1919 | 0.855802 | ||||||||
\(276\) | 0.590088 | 0.0355191 | ||||||||
\(277\) | 10.7621 | 0.646632 | 0.323316 | − | 0.946291i | \(-0.395202\pi\) | ||||
0.323316 | + | 0.946291i | \(0.395202\pi\) | |||||||
\(278\) | −6.50910 | −0.390390 | ||||||||
\(279\) | 17.4532 | 1.04490 | ||||||||
\(280\) | 1.31905 | 0.0788282 | ||||||||
\(281\) | −5.81258 | −0.346749 | −0.173375 | − | 0.984856i | \(-0.555467\pi\) | ||||
−0.173375 | + | 0.984856i | \(0.555467\pi\) | |||||||
\(282\) | −2.81179 | −0.167440 | ||||||||
\(283\) | 14.4146 | 0.856858 | 0.428429 | − | 0.903575i | \(-0.359067\pi\) | ||||
0.428429 | + | 0.903575i | \(0.359067\pi\) | |||||||
\(284\) | 14.5679 | 0.864443 | ||||||||
\(285\) | −3.55319 | −0.210473 | ||||||||
\(286\) | −6.88682 | −0.407226 | ||||||||
\(287\) | 4.27319 | 0.252239 | ||||||||
\(288\) | −2.65180 | −0.156259 | ||||||||
\(289\) | −16.9800 | −0.998824 | ||||||||
\(290\) | −7.91695 | −0.464899 | ||||||||
\(291\) | −1.22383 | −0.0717424 | ||||||||
\(292\) | 10.7599 | 0.629677 | ||||||||
\(293\) | −3.66943 | −0.214370 | −0.107185 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107185 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(294\) | −2.96080 | −0.172678 | ||||||||
\(295\) | −3.71692 | −0.216407 | ||||||||
\(296\) | −2.90009 | −0.168564 | ||||||||
\(297\) | 11.4815 | 0.666224 | ||||||||
\(298\) | −6.06260 | −0.351197 | ||||||||
\(299\) | 2.00043 | 0.115688 | ||||||||
\(300\) | −2.43255 | −0.140443 | ||||||||
\(301\) | −1.21481 | −0.0700207 | ||||||||
\(302\) | 10.8693 | 0.625458 | ||||||||
\(303\) | −2.35807 | −0.135467 | ||||||||
\(304\) | −6.42748 | −0.368641 | ||||||||
\(305\) | 1.39186 | 0.0796978 | ||||||||
\(306\) | −0.374966 | −0.0214354 | ||||||||
\(307\) | 5.54957 | 0.316731 | 0.158365 | − | 0.987381i | \(-0.449378\pi\) | ||||
0.158365 | + | 0.987381i | \(0.449378\pi\) | |||||||
\(308\) | −4.84724 | −0.276197 | ||||||||
\(309\) | −5.84800 | −0.332681 | ||||||||
\(310\) | −6.16590 | −0.350200 | ||||||||
\(311\) | 24.3526 | 1.38091 | 0.690456 | − | 0.723375i | \(-0.257410\pi\) | ||||
0.690456 | + | 0.723375i | \(0.257410\pi\) | |||||||
\(312\) | 1.18043 | 0.0668288 | ||||||||
\(313\) | −2.81619 | −0.159181 | −0.0795903 | − | 0.996828i | \(-0.525361\pi\) | ||||
−0.0795903 | + | 0.996828i | \(0.525361\pi\) | |||||||
\(314\) | 22.1495 | 1.24997 | ||||||||
\(315\) | −3.49784 | −0.197081 | ||||||||
\(316\) | −6.15727 | −0.346374 | ||||||||
\(317\) | 5.22230 | 0.293313 | 0.146657 | − | 0.989187i | \(-0.453149\pi\) | ||||
0.146657 | + | 0.989187i | \(0.453149\pi\) | |||||||
\(318\) | −3.49897 | −0.196213 | ||||||||
\(319\) | 29.0933 | 1.62891 | ||||||||
\(320\) | 0.936829 | 0.0523704 | ||||||||
\(321\) | −0.873583 | −0.0487587 | ||||||||
\(322\) | 1.40799 | 0.0784643 | ||||||||
\(323\) | −0.908849 | −0.0505697 | ||||||||
\(324\) | 5.98741 | 0.332634 | ||||||||
\(325\) | −8.24648 | −0.457432 | ||||||||
\(326\) | −0.433839 | −0.0240281 | ||||||||
\(327\) | 7.63678 | 0.422315 | ||||||||
\(328\) | 3.03496 | 0.167577 | ||||||||
\(329\) | −6.70912 | −0.369886 | ||||||||
\(330\) | −1.90315 | −0.104765 | ||||||||
\(331\) | 27.1414 | 1.49183 | 0.745913 | − | 0.666044i | \(-0.232014\pi\) | ||||
0.745913 | + | 0.666044i | \(0.232014\pi\) | |||||||
\(332\) | 10.3262 | 0.566724 | ||||||||
\(333\) | 7.69045 | 0.421434 | ||||||||
\(334\) | 23.0084 | 1.25896 | ||||||||
\(335\) | 5.03446 | 0.275062 | ||||||||
\(336\) | 0.830839 | 0.0453260 | ||||||||
\(337\) | −32.4158 | −1.76580 | −0.882900 | − | 0.469562i | \(-0.844412\pi\) | ||||
−0.882900 | + | 0.469562i | \(0.844412\pi\) | |||||||
\(338\) | −8.99827 | −0.489441 | ||||||||
\(339\) | −7.70650 | −0.418560 | ||||||||
\(340\) | 0.132468 | 0.00718410 | ||||||||
\(341\) | 22.6585 | 1.22703 | ||||||||
\(342\) | 17.0444 | 0.921653 | ||||||||
\(343\) | −16.9206 | −0.913627 | ||||||||
\(344\) | −0.862799 | −0.0465190 | ||||||||
\(345\) | 0.552812 | 0.0297624 | ||||||||
\(346\) | 3.71260 | 0.199590 | ||||||||
\(347\) | −18.9938 | −1.01964 | −0.509820 | − | 0.860281i | \(-0.670288\pi\) | ||||
−0.509820 | + | 0.860281i | \(0.670288\pi\) | |||||||
\(348\) | −4.98671 | −0.267316 | ||||||||
\(349\) | 14.2188 | 0.761113 | 0.380556 | − | 0.924758i | \(-0.375733\pi\) | ||||
0.380556 | + | 0.924758i | \(0.375733\pi\) | |||||||
\(350\) | −5.80423 | −0.310249 | ||||||||
\(351\) | −6.67156 | −0.356101 | ||||||||
\(352\) | −3.44267 | −0.183495 | ||||||||
\(353\) | −2.04492 | −0.108840 | −0.0544201 | − | 0.998518i | \(-0.517331\pi\) | ||||
−0.0544201 | + | 0.998518i | \(0.517331\pi\) | |||||||
\(354\) | −2.34121 | −0.124434 | ||||||||
\(355\) | 13.6476 | 0.724339 | ||||||||
\(356\) | −2.22548 | −0.117950 | ||||||||
\(357\) | 0.117481 | 0.00621776 | ||||||||
\(358\) | 2.42372 | 0.128098 | ||||||||
\(359\) | 27.8198 | 1.46828 | 0.734138 | − | 0.679001i | \(-0.237587\pi\) | ||||
0.734138 | + | 0.679001i | \(0.237587\pi\) | |||||||
\(360\) | −2.48428 | −0.130933 | ||||||||
\(361\) | 22.3125 | 1.17434 | ||||||||
\(362\) | −14.2979 | −0.751482 | ||||||||
\(363\) | 0.502726 | 0.0263863 | ||||||||
\(364\) | 2.81659 | 0.147629 | ||||||||
\(365\) | 10.0802 | 0.527622 | ||||||||
\(366\) | 0.876704 | 0.0458260 | ||||||||
\(367\) | −13.4702 | −0.703139 | −0.351570 | − | 0.936162i | \(-0.614352\pi\) | ||||
−0.351570 | + | 0.936162i | \(0.614352\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −8.04808 | −0.418967 | ||||||||
\(370\) | −2.71689 | −0.141244 | ||||||||
\(371\) | −8.34879 | −0.433448 | ||||||||
\(372\) | −3.88377 | −0.201364 | ||||||||
\(373\) | 23.3405 | 1.20852 | 0.604262 | − | 0.796786i | \(-0.293468\pi\) | ||||
0.604262 | + | 0.796786i | \(0.293468\pi\) | |||||||
\(374\) | −0.486795 | −0.0251716 | ||||||||
\(375\) | −5.04295 | −0.260417 | ||||||||
\(376\) | −4.76503 | −0.245738 | ||||||||
\(377\) | −16.9052 | −0.870664 | ||||||||
\(378\) | −4.69573 | −0.241522 | ||||||||
\(379\) | −7.47226 | −0.383824 | −0.191912 | − | 0.981412i | \(-0.561469\pi\) | ||||
−0.191912 | + | 0.981412i | \(0.561469\pi\) | |||||||
\(380\) | −6.02145 | −0.308894 | ||||||||
\(381\) | 9.40038 | 0.481596 | ||||||||
\(382\) | −20.4296 | −1.04527 | ||||||||
\(383\) | 4.45858 | 0.227823 | 0.113911 | − | 0.993491i | \(-0.463662\pi\) | ||||
0.113911 | + | 0.993491i | \(0.463662\pi\) | |||||||
\(384\) | 0.590088 | 0.0301128 | ||||||||
\(385\) | −4.54104 | −0.231433 | ||||||||
\(386\) | −10.8576 | −0.552638 | ||||||||
\(387\) | 2.28797 | 0.116304 | ||||||||
\(388\) | −2.07398 | −0.105291 | ||||||||
\(389\) | −19.1214 | −0.969491 | −0.484746 | − | 0.874655i | \(-0.661088\pi\) | ||||
−0.484746 | + | 0.874655i | \(0.661088\pi\) | |||||||
\(390\) | 1.10586 | 0.0559976 | ||||||||
\(391\) | 0.141401 | 0.00715094 | ||||||||
\(392\) | −5.01756 | −0.253425 | ||||||||
\(393\) | −0.590088 | −0.0297660 | ||||||||
\(394\) | 14.0192 | 0.706279 | ||||||||
\(395\) | −5.76832 | −0.290235 | ||||||||
\(396\) | 9.12925 | 0.458762 | ||||||||
\(397\) | −26.9060 | −1.35037 | −0.675187 | − | 0.737647i | \(-0.735937\pi\) | ||||
−0.675187 | + | 0.737647i | \(0.735937\pi\) | |||||||
\(398\) | 7.76683 | 0.389316 | ||||||||
\(399\) | −5.34020 | −0.267344 | ||||||||
\(400\) | −4.12235 | −0.206118 | ||||||||
\(401\) | 24.0408 | 1.20054 | 0.600270 | − | 0.799798i | \(-0.295060\pi\) | ||||
0.600270 | + | 0.799798i | \(0.295060\pi\) | |||||||
\(402\) | 3.17110 | 0.158160 | ||||||||
\(403\) | −13.1662 | −0.655854 | ||||||||
\(404\) | −3.99612 | −0.198815 | ||||||||
\(405\) | 5.60918 | 0.278722 | ||||||||
\(406\) | −11.8986 | −0.590519 | ||||||||
\(407\) | 9.98405 | 0.494891 | ||||||||
\(408\) | 0.0834389 | 0.00413084 | ||||||||
\(409\) | −6.20525 | −0.306830 | −0.153415 | − | 0.988162i | \(-0.549027\pi\) | ||||
−0.153415 | + | 0.988162i | \(0.549027\pi\) | |||||||
\(410\) | 2.84324 | 0.140417 | ||||||||
\(411\) | 1.60054 | 0.0789488 | ||||||||
\(412\) | −9.91039 | −0.488250 | ||||||||
\(413\) | −5.58628 | −0.274883 | ||||||||
\(414\) | −2.65180 | −0.130329 | ||||||||
\(415\) | 9.67389 | 0.474872 | ||||||||
\(416\) | 2.00043 | 0.0980792 | ||||||||
\(417\) | −3.84095 | −0.188092 | ||||||||
\(418\) | 22.1277 | 1.08230 | ||||||||
\(419\) | −31.9967 | −1.56314 | −0.781571 | − | 0.623817i | \(-0.785581\pi\) | ||||
−0.781571 | + | 0.623817i | \(0.785581\pi\) | |||||||
\(420\) | 0.778354 | 0.0379798 | ||||||||
\(421\) | 3.43322 | 0.167325 | 0.0836625 | − | 0.996494i | \(-0.473338\pi\) | ||||
0.0836625 | + | 0.996494i | \(0.473338\pi\) | |||||||
\(422\) | −11.8639 | −0.577526 | ||||||||
\(423\) | 12.6359 | 0.614378 | ||||||||
\(424\) | −5.92958 | −0.287966 | ||||||||
\(425\) | −0.582903 | −0.0282749 | ||||||||
\(426\) | 8.59632 | 0.416493 | ||||||||
\(427\) | 2.09188 | 0.101233 | ||||||||
\(428\) | −1.48043 | −0.0715592 | ||||||||
\(429\) | −4.06383 | −0.196204 | ||||||||
\(430\) | −0.808296 | −0.0389795 | ||||||||
\(431\) | 25.7714 | 1.24136 | 0.620682 | − | 0.784062i | \(-0.286856\pi\) | ||||
0.620682 | + | 0.784062i | \(0.286856\pi\) | |||||||
\(432\) | −3.33506 | −0.160458 | ||||||||
\(433\) | −27.2835 | −1.31116 | −0.655581 | − | 0.755125i | \(-0.727576\pi\) | ||||
−0.655581 | + | 0.755125i | \(0.727576\pi\) | |||||||
\(434\) | −9.26693 | −0.444827 | ||||||||
\(435\) | −4.67170 | −0.223991 | ||||||||
\(436\) | 12.9418 | 0.619798 | ||||||||
\(437\) | −6.42748 | −0.307468 | ||||||||
\(438\) | 6.34931 | 0.303382 | ||||||||
\(439\) | −0.346172 | −0.0165219 | −0.00826094 | − | 0.999966i | \(-0.502630\pi\) | ||||
−0.00826094 | + | 0.999966i | \(0.502630\pi\) | |||||||
\(440\) | −3.22519 | −0.153755 | ||||||||
\(441\) | 13.3055 | 0.633598 | ||||||||
\(442\) | 0.282862 | 0.0134544 | ||||||||
\(443\) | 25.3185 | 1.20292 | 0.601459 | − | 0.798904i | \(-0.294586\pi\) | ||||
0.601459 | + | 0.798904i | \(0.294586\pi\) | |||||||
\(444\) | −1.71131 | −0.0812152 | ||||||||
\(445\) | −2.08490 | −0.0988336 | ||||||||
\(446\) | −29.2901 | −1.38693 | ||||||||
\(447\) | −3.57747 | −0.169209 | ||||||||
\(448\) | 1.40799 | 0.0665213 | ||||||||
\(449\) | 23.8631 | 1.12617 | 0.563084 | − | 0.826400i | \(-0.309615\pi\) | ||||
0.563084 | + | 0.826400i | \(0.309615\pi\) | |||||||
\(450\) | 10.9316 | 0.515322 | ||||||||
\(451\) | −10.4483 | −0.491993 | ||||||||
\(452\) | −13.0599 | −0.614286 | ||||||||
\(453\) | 6.41385 | 0.301349 | ||||||||
\(454\) | 14.0155 | 0.657782 | ||||||||
\(455\) | 2.63866 | 0.123702 | ||||||||
\(456\) | −3.79278 | −0.177613 | ||||||||
\(457\) | 15.1988 | 0.710968 | 0.355484 | − | 0.934682i | \(-0.384316\pi\) | ||||
0.355484 | + | 0.934682i | \(0.384316\pi\) | |||||||
\(458\) | 16.2255 | 0.758166 | ||||||||
\(459\) | −0.471579 | −0.0220114 | ||||||||
\(460\) | 0.936829 | 0.0436799 | ||||||||
\(461\) | 21.3324 | 0.993550 | 0.496775 | − | 0.867879i | \(-0.334517\pi\) | ||||
0.496775 | + | 0.867879i | \(0.334517\pi\) | |||||||
\(462\) | −2.86030 | −0.133073 | ||||||||
\(463\) | −41.1982 | −1.91464 | −0.957320 | − | 0.289029i | \(-0.906668\pi\) | ||||
−0.957320 | + | 0.289029i | \(0.906668\pi\) | |||||||
\(464\) | −8.45079 | −0.392318 | ||||||||
\(465\) | −3.63843 | −0.168728 | ||||||||
\(466\) | −24.5063 | −1.13523 | ||||||||
\(467\) | 6.68526 | 0.309357 | 0.154679 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154679 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(468\) | −5.30474 | −0.245212 | ||||||||
\(469\) | 7.56645 | 0.349386 | ||||||||
\(470\) | −4.46402 | −0.205910 | ||||||||
\(471\) | 13.0702 | 0.602242 | ||||||||
\(472\) | −3.96755 | −0.182621 | ||||||||
\(473\) | 2.97033 | 0.136576 | ||||||||
\(474\) | −3.63334 | −0.166885 | ||||||||
\(475\) | 26.4963 | 1.21573 | ||||||||
\(476\) | 0.199091 | 0.00912531 | ||||||||
\(477\) | 15.7240 | 0.719954 | ||||||||
\(478\) | −11.1756 | −0.511162 | ||||||||
\(479\) | 25.4479 | 1.16274 | 0.581371 | − | 0.813639i | \(-0.302516\pi\) | ||||
0.581371 | + | 0.813639i | \(0.302516\pi\) | |||||||
\(480\) | 0.552812 | 0.0252323 | ||||||||
\(481\) | −5.80144 | −0.264523 | ||||||||
\(482\) | 12.1844 | 0.554986 | ||||||||
\(483\) | 0.830839 | 0.0378045 | ||||||||
\(484\) | 0.851951 | 0.0387251 | ||||||||
\(485\) | −1.94297 | −0.0882257 | ||||||||
\(486\) | 13.5383 | 0.614109 | ||||||||
\(487\) | −34.7009 | −1.57245 | −0.786224 | − | 0.617941i | \(-0.787967\pi\) | ||||
−0.786224 | + | 0.617941i | \(0.787967\pi\) | |||||||
\(488\) | 1.48572 | 0.0672552 | ||||||||
\(489\) | −0.256003 | −0.0115769 | ||||||||
\(490\) | −4.70060 | −0.212351 | ||||||||
\(491\) | −21.7959 | −0.983634 | −0.491817 | − | 0.870699i | \(-0.663667\pi\) | ||||
−0.491817 | + | 0.870699i | \(0.663667\pi\) | |||||||
\(492\) | 1.79089 | 0.0807397 | ||||||||
\(493\) | −1.19495 | −0.0538177 | ||||||||
\(494\) | −12.8577 | −0.578497 | ||||||||
\(495\) | 8.55255 | 0.384408 | ||||||||
\(496\) | −6.58167 | −0.295526 | ||||||||
\(497\) | 20.5114 | 0.920062 | ||||||||
\(498\) | 6.09337 | 0.273050 | ||||||||
\(499\) | −29.3583 | −1.31426 | −0.657128 | − | 0.753779i | \(-0.728229\pi\) | ||||
−0.657128 | + | 0.753779i | \(0.728229\pi\) | |||||||
\(500\) | −8.54609 | −0.382193 | ||||||||
\(501\) | 13.5770 | 0.606574 | ||||||||
\(502\) | −16.4845 | −0.735740 | ||||||||
\(503\) | −28.0748 | −1.25179 | −0.625896 | − | 0.779906i | \(-0.715267\pi\) | ||||
−0.625896 | + | 0.779906i | \(0.715267\pi\) | |||||||
\(504\) | −3.73370 | −0.166312 | ||||||||
\(505\) | −3.74369 | −0.166592 | ||||||||
\(506\) | −3.44267 | −0.153045 | ||||||||
\(507\) | −5.30978 | −0.235815 | ||||||||
\(508\) | 15.9305 | 0.706800 | ||||||||
\(509\) | −29.7702 | −1.31954 | −0.659771 | − | 0.751466i | \(-0.729347\pi\) | ||||
−0.659771 | + | 0.751466i | \(0.729347\pi\) | |||||||
\(510\) | 0.0781680 | 0.00346134 | ||||||||
\(511\) | 15.1499 | 0.670191 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 21.4360 | 0.946423 | ||||||||
\(514\) | −16.5385 | −0.729481 | ||||||||
\(515\) | −9.28434 | −0.409117 | ||||||||
\(516\) | −0.509128 | −0.0224131 | ||||||||
\(517\) | 16.4044 | 0.721466 | ||||||||
\(518\) | −4.08330 | −0.179410 | ||||||||
\(519\) | 2.19076 | 0.0961637 | ||||||||
\(520\) | 1.87406 | 0.0821831 | ||||||||
\(521\) | −5.61415 | −0.245961 | −0.122980 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122980 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(522\) | 22.4098 | 0.980849 | ||||||||
\(523\) | −23.2859 | −1.01822 | −0.509110 | − | 0.860701i | \(-0.670025\pi\) | ||||
−0.509110 | + | 0.860701i | \(0.670025\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −3.42501 | −0.149480 | ||||||||
\(526\) | 27.6647 | 1.20624 | ||||||||
\(527\) | −0.930652 | −0.0405398 | ||||||||
\(528\) | −2.03148 | −0.0884087 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −5.55500 | −0.241294 | ||||||||
\(531\) | 10.5211 | 0.456578 | ||||||||
\(532\) | −9.04983 | −0.392360 | ||||||||
\(533\) | 6.07122 | 0.262974 | ||||||||
\(534\) | −1.31323 | −0.0568291 | ||||||||
\(535\) | −1.38691 | −0.0599613 | ||||||||
\(536\) | 5.37393 | 0.232119 | ||||||||
\(537\) | 1.43021 | 0.0617181 | ||||||||
\(538\) | −22.9212 | −0.988205 | ||||||||
\(539\) | 17.2738 | 0.744035 | ||||||||
\(540\) | −3.12438 | −0.134452 | ||||||||
\(541\) | 23.1219 | 0.994087 | 0.497043 | − | 0.867726i | \(-0.334419\pi\) | ||||
0.497043 | + | 0.867726i | \(0.334419\pi\) | |||||||
\(542\) | −4.22389 | −0.181432 | ||||||||
\(543\) | −8.43703 | −0.362068 | ||||||||
\(544\) | 0.141401 | 0.00606250 | ||||||||
\(545\) | 12.1242 | 0.519345 | ||||||||
\(546\) | 1.66204 | 0.0711286 | ||||||||
\(547\) | 2.84341 | 0.121575 | 0.0607876 | − | 0.998151i | \(-0.480639\pi\) | ||||
0.0607876 | + | 0.998151i | \(0.480639\pi\) | |||||||
\(548\) | 2.71237 | 0.115867 | ||||||||
\(549\) | −3.93982 | −0.168147 | ||||||||
\(550\) | 14.1919 | 0.605144 | ||||||||
\(551\) | 54.3173 | 2.31399 | ||||||||
\(552\) | 0.590088 | 0.0251158 | ||||||||
\(553\) | −8.66939 | −0.368660 | ||||||||
\(554\) | 10.7621 | 0.457238 | ||||||||
\(555\) | −1.60321 | −0.0680523 | ||||||||
\(556\) | −6.50910 | −0.276047 | ||||||||
\(557\) | 37.7432 | 1.59923 | 0.799616 | − | 0.600512i | \(-0.205037\pi\) | ||||
0.799616 | + | 0.600512i | \(0.205037\pi\) | |||||||
\(558\) | 17.4532 | 0.738855 | ||||||||
\(559\) | −1.72597 | −0.0730008 | ||||||||
\(560\) | 1.31905 | 0.0557399 | ||||||||
\(561\) | −0.287252 | −0.0121278 | ||||||||
\(562\) | −5.81258 | −0.245189 | ||||||||
\(563\) | −37.6061 | −1.58491 | −0.792454 | − | 0.609932i | \(-0.791197\pi\) | ||||
−0.792454 | + | 0.609932i | \(0.791197\pi\) | |||||||
\(564\) | −2.81179 | −0.118398 | ||||||||
\(565\) | −12.2349 | −0.514726 | ||||||||
\(566\) | 14.4146 | 0.605890 | ||||||||
\(567\) | 8.43022 | 0.354036 | ||||||||
\(568\) | 14.5679 | 0.611254 | ||||||||
\(569\) | −1.58471 | −0.0664344 | −0.0332172 | − | 0.999448i | \(-0.510575\pi\) | ||||
−0.0332172 | + | 0.999448i | \(0.510575\pi\) | |||||||
\(570\) | −3.55319 | −0.148827 | ||||||||
\(571\) | −17.4302 | −0.729433 | −0.364716 | − | 0.931119i | \(-0.618834\pi\) | ||||
−0.364716 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(572\) | −6.88682 | −0.287952 | ||||||||
\(573\) | −12.0553 | −0.503617 | ||||||||
\(574\) | 4.27319 | 0.178360 | ||||||||
\(575\) | −4.12235 | −0.171914 | ||||||||
\(576\) | −2.65180 | −0.110491 | ||||||||
\(577\) | −34.6626 | −1.44302 | −0.721512 | − | 0.692402i | \(-0.756553\pi\) | ||||
−0.721512 | + | 0.692402i | \(0.756553\pi\) | |||||||
\(578\) | −16.9800 | −0.706275 | ||||||||
\(579\) | −6.40695 | −0.266264 | ||||||||
\(580\) | −7.91695 | −0.328733 | ||||||||
\(581\) | 14.5392 | 0.603187 | ||||||||
\(582\) | −1.22383 | −0.0507295 | ||||||||
\(583\) | 20.4136 | 0.845443 | ||||||||
\(584\) | 10.7599 | 0.445249 | ||||||||
\(585\) | −4.96963 | −0.205469 | ||||||||
\(586\) | −3.66943 | −0.151583 | ||||||||
\(587\) | 29.2368 | 1.20673 | 0.603366 | − | 0.797465i | \(-0.293826\pi\) | ||||
0.603366 | + | 0.797465i | \(0.293826\pi\) | |||||||
\(588\) | −2.96080 | −0.122102 | ||||||||
\(589\) | 42.3035 | 1.74309 | ||||||||
\(590\) | −3.71692 | −0.153023 | ||||||||
\(591\) | 8.27259 | 0.340289 | ||||||||
\(592\) | −2.90009 | −0.119193 | ||||||||
\(593\) | −22.5904 | −0.927676 | −0.463838 | − | 0.885920i | \(-0.653528\pi\) | ||||
−0.463838 | + | 0.885920i | \(0.653528\pi\) | |||||||
\(594\) | 11.4815 | 0.471091 | ||||||||
\(595\) | 0.186514 | 0.00764633 | ||||||||
\(596\) | −6.06260 | −0.248334 | ||||||||
\(597\) | 4.58312 | 0.187574 | ||||||||
\(598\) | 2.00043 | 0.0818037 | ||||||||
\(599\) | 25.3413 | 1.03542 | 0.517710 | − | 0.855556i | \(-0.326785\pi\) | ||||
0.517710 | + | 0.855556i | \(0.326785\pi\) | |||||||
\(600\) | −2.43255 | −0.0993085 | ||||||||
\(601\) | −28.1890 | −1.14985 | −0.574926 | − | 0.818205i | \(-0.694969\pi\) | ||||
−0.574926 | + | 0.818205i | \(0.694969\pi\) | |||||||
\(602\) | −1.21481 | −0.0495121 | ||||||||
\(603\) | −14.2506 | −0.580328 | ||||||||
\(604\) | 10.8693 | 0.442266 | ||||||||
\(605\) | 0.798133 | 0.0324487 | ||||||||
\(606\) | −2.35807 | −0.0957899 | ||||||||
\(607\) | −30.5821 | −1.24129 | −0.620645 | − | 0.784092i | \(-0.713129\pi\) | ||||
−0.620645 | + | 0.784092i | \(0.713129\pi\) | |||||||
\(608\) | −6.42748 | −0.260669 | ||||||||
\(609\) | −7.02125 | −0.284515 | ||||||||
\(610\) | 1.39186 | 0.0563549 | ||||||||
\(611\) | −9.53213 | −0.385629 | ||||||||
\(612\) | −0.374966 | −0.0151571 | ||||||||
\(613\) | −29.1459 | −1.17719 | −0.588596 | − | 0.808428i | \(-0.700319\pi\) | ||||
−0.588596 | + | 0.808428i | \(0.700319\pi\) | |||||||
\(614\) | 5.54957 | 0.223963 | ||||||||
\(615\) | 1.67776 | 0.0676538 | ||||||||
\(616\) | −4.84724 | −0.195301 | ||||||||
\(617\) | −4.72723 | −0.190311 | −0.0951555 | − | 0.995462i | \(-0.530335\pi\) | ||||
−0.0951555 | + | 0.995462i | \(0.530335\pi\) | |||||||
\(618\) | −5.84800 | −0.235241 | ||||||||
\(619\) | −7.98997 | −0.321144 | −0.160572 | − | 0.987024i | \(-0.551334\pi\) | ||||
−0.160572 | + | 0.987024i | \(0.551334\pi\) | |||||||
\(620\) | −6.16590 | −0.247629 | ||||||||
\(621\) | −3.33506 | −0.133831 | ||||||||
\(622\) | 24.3526 | 0.976452 | ||||||||
\(623\) | −3.13346 | −0.125539 | ||||||||
\(624\) | 1.18043 | 0.0472551 | ||||||||
\(625\) | 12.6055 | 0.504221 | ||||||||
\(626\) | −2.81619 | −0.112558 | ||||||||
\(627\) | 13.0573 | 0.521457 | ||||||||
\(628\) | 22.1495 | 0.883862 | ||||||||
\(629\) | −0.410075 | −0.0163508 | ||||||||
\(630\) | −3.49784 | −0.139357 | ||||||||
\(631\) | −30.6118 | −1.21864 | −0.609318 | − | 0.792926i | \(-0.708557\pi\) | ||||
−0.609318 | + | 0.792926i | \(0.708557\pi\) | |||||||
\(632\) | −6.15727 | −0.244923 | ||||||||
\(633\) | −7.00076 | −0.278255 | ||||||||
\(634\) | 5.22230 | 0.207404 | ||||||||
\(635\) | 14.9241 | 0.592246 | ||||||||
\(636\) | −3.49897 | −0.138743 | ||||||||
\(637\) | −10.0373 | −0.397692 | ||||||||
\(638\) | 29.0933 | 1.15181 | ||||||||
\(639\) | −38.6310 | −1.52822 | ||||||||
\(640\) | 0.936829 | 0.0370314 | ||||||||
\(641\) | −34.3486 | −1.35669 | −0.678343 | − | 0.734745i | \(-0.737302\pi\) | ||||
−0.678343 | + | 0.734745i | \(0.737302\pi\) | |||||||
\(642\) | −0.873583 | −0.0344776 | ||||||||
\(643\) | −30.5130 | −1.20331 | −0.601657 | − | 0.798754i | \(-0.705493\pi\) | ||||
−0.601657 | + | 0.798754i | \(0.705493\pi\) | |||||||
\(644\) | 1.40799 | 0.0554826 | ||||||||
\(645\) | −0.476966 | −0.0187805 | ||||||||
\(646\) | −0.908849 | −0.0357582 | ||||||||
\(647\) | −28.0890 | −1.10429 | −0.552147 | − | 0.833747i | \(-0.686191\pi\) | ||||
−0.552147 | + | 0.833747i | \(0.686191\pi\) | |||||||
\(648\) | 5.98741 | 0.235208 | ||||||||
\(649\) | 13.6590 | 0.536161 | ||||||||
\(650\) | −8.24648 | −0.323454 | ||||||||
\(651\) | −5.46831 | −0.214320 | ||||||||
\(652\) | −0.433839 | −0.0169904 | ||||||||
\(653\) | 6.21190 | 0.243090 | 0.121545 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121545 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(654\) | 7.63678 | 0.298622 | ||||||||
\(655\) | −0.936829 | −0.0366050 | ||||||||
\(656\) | 3.03496 | 0.118495 | ||||||||
\(657\) | −28.5331 | −1.11318 | ||||||||
\(658\) | −6.70912 | −0.261549 | ||||||||
\(659\) | 32.4953 | 1.26584 | 0.632919 | − | 0.774218i | \(-0.281857\pi\) | ||||
0.632919 | + | 0.774218i | \(0.281857\pi\) | |||||||
\(660\) | −1.90315 | −0.0740799 | ||||||||
\(661\) | −31.0967 | −1.20952 | −0.604761 | − | 0.796407i | \(-0.706731\pi\) | ||||
−0.604761 | + | 0.796407i | \(0.706731\pi\) | |||||||
\(662\) | 27.1414 | 1.05488 | ||||||||
\(663\) | 0.166914 | 0.00648239 | ||||||||
\(664\) | 10.3262 | 0.400734 | ||||||||
\(665\) | −8.47815 | −0.328769 | ||||||||
\(666\) | 7.69045 | 0.297999 | ||||||||
\(667\) | −8.45079 | −0.327216 | ||||||||
\(668\) | 23.0084 | 0.890220 | ||||||||
\(669\) | −17.2838 | −0.668229 | ||||||||
\(670\) | 5.03446 | 0.194498 | ||||||||
\(671\) | −5.11483 | −0.197456 | ||||||||
\(672\) | 0.830839 | 0.0320503 | ||||||||
\(673\) | −46.4303 | −1.78976 | −0.894879 | − | 0.446309i | \(-0.852738\pi\) | ||||
−0.894879 | + | 0.446309i | \(0.852738\pi\) | |||||||
\(674\) | −32.4158 | −1.24861 | ||||||||
\(675\) | 13.7483 | 0.529172 | ||||||||
\(676\) | −8.99827 | −0.346087 | ||||||||
\(677\) | −34.2065 | −1.31466 | −0.657331 | − | 0.753602i | \(-0.728315\pi\) | ||||
−0.657331 | + | 0.753602i | \(0.728315\pi\) | |||||||
\(678\) | −7.70650 | −0.295966 | ||||||||
\(679\) | −2.92015 | −0.112065 | ||||||||
\(680\) | 0.132468 | 0.00507993 | ||||||||
\(681\) | 8.27041 | 0.316923 | ||||||||
\(682\) | 22.6585 | 0.867638 | ||||||||
\(683\) | 30.5656 | 1.16956 | 0.584779 | − | 0.811193i | \(-0.301181\pi\) | ||||
0.584779 | + | 0.811193i | \(0.301181\pi\) | |||||||
\(684\) | 17.0444 | 0.651707 | ||||||||
\(685\) | 2.54103 | 0.0970878 | ||||||||
\(686\) | −16.9206 | −0.646032 | ||||||||
\(687\) | 9.57446 | 0.365288 | ||||||||
\(688\) | −0.862799 | −0.0328939 | ||||||||
\(689\) | −11.8617 | −0.451895 | ||||||||
\(690\) | 0.552812 | 0.0210452 | ||||||||
\(691\) | 25.5364 | 0.971449 | 0.485725 | − | 0.874112i | \(-0.338556\pi\) | ||||
0.485725 | + | 0.874112i | \(0.338556\pi\) | |||||||
\(692\) | 3.71260 | 0.141132 | ||||||||
\(693\) | 12.8539 | 0.488279 | ||||||||
\(694\) | −18.9938 | −0.720994 | ||||||||
\(695\) | −6.09792 | −0.231307 | ||||||||
\(696\) | −4.98671 | −0.189021 | ||||||||
\(697\) | 0.429145 | 0.0162550 | ||||||||
\(698\) | 14.2188 | 0.538188 | ||||||||
\(699\) | −14.4609 | −0.546960 | ||||||||
\(700\) | −5.80423 | −0.219379 | ||||||||
\(701\) | 43.9053 | 1.65828 | 0.829140 | − | 0.559041i | \(-0.188831\pi\) | ||||
0.829140 | + | 0.559041i | \(0.188831\pi\) | |||||||
\(702\) | −6.67156 | −0.251802 | ||||||||
\(703\) | 18.6403 | 0.703032 | ||||||||
\(704\) | −3.44267 | −0.129750 | ||||||||
\(705\) | −2.63417 | −0.0992085 | ||||||||
\(706\) | −2.04492 | −0.0769616 | ||||||||
\(707\) | −5.62651 | −0.211607 | ||||||||
\(708\) | −2.34121 | −0.0879879 | ||||||||
\(709\) | 43.4728 | 1.63265 | 0.816327 | − | 0.577590i | \(-0.196007\pi\) | ||||
0.816327 | + | 0.577590i | \(0.196007\pi\) | |||||||
\(710\) | 13.6476 | 0.512185 | ||||||||
\(711\) | 16.3278 | 0.612342 | ||||||||
\(712\) | −2.22548 | −0.0834035 | ||||||||
\(713\) | −6.58167 | −0.246485 | ||||||||
\(714\) | 0.117481 | 0.00439662 | ||||||||
\(715\) | −6.45178 | −0.241283 | ||||||||
\(716\) | 2.42372 | 0.0905787 | ||||||||
\(717\) | −6.59461 | −0.246280 | ||||||||
\(718\) | 27.8198 | 1.03823 | ||||||||
\(719\) | −13.5046 | −0.503638 | −0.251819 | − | 0.967774i | \(-0.581029\pi\) | ||||
−0.251819 | + | 0.967774i | \(0.581029\pi\) | |||||||
\(720\) | −2.48428 | −0.0925837 | ||||||||
\(721\) | −13.9537 | −0.519664 | ||||||||
\(722\) | 22.3125 | 0.830385 | ||||||||
\(723\) | 7.18989 | 0.267395 | ||||||||
\(724\) | −14.2979 | −0.531378 | ||||||||
\(725\) | 34.8371 | 1.29382 | ||||||||
\(726\) | 0.502726 | 0.0186579 | ||||||||
\(727\) | −23.0798 | −0.855983 | −0.427991 | − | 0.903783i | \(-0.640779\pi\) | ||||
−0.427991 | + | 0.903783i | \(0.640779\pi\) | |||||||
\(728\) | 2.81659 | 0.104390 | ||||||||
\(729\) | −9.97345 | −0.369387 | ||||||||
\(730\) | 10.0802 | 0.373085 | ||||||||
\(731\) | −0.122000 | −0.00451235 | ||||||||
\(732\) | 0.876704 | 0.0324039 | ||||||||
\(733\) | 24.7561 | 0.914389 | 0.457195 | − | 0.889367i | \(-0.348854\pi\) | ||||
0.457195 | + | 0.889367i | \(0.348854\pi\) | |||||||
\(734\) | −13.4702 | −0.497194 | ||||||||
\(735\) | −2.77377 | −0.102312 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −18.5007 | −0.681480 | ||||||||
\(738\) | −8.04808 | −0.296254 | ||||||||
\(739\) | −27.0300 | −0.994315 | −0.497157 | − | 0.867660i | \(-0.665623\pi\) | ||||
−0.497157 | + | 0.867660i | \(0.665623\pi\) | |||||||
\(740\) | −2.71689 | −0.0998749 | ||||||||
\(741\) | −7.58720 | −0.278723 | ||||||||
\(742\) | −8.34879 | −0.306494 | ||||||||
\(743\) | 23.6428 | 0.867369 | 0.433685 | − | 0.901065i | \(-0.357213\pi\) | ||||
0.433685 | + | 0.901065i | \(0.357213\pi\) | |||||||
\(744\) | −3.88377 | −0.142386 | ||||||||
\(745\) | −5.67963 | −0.208085 | ||||||||
\(746\) | 23.3405 | 0.854555 | ||||||||
\(747\) | −27.3830 | −1.00189 | ||||||||
\(748\) | −0.486795 | −0.0177990 | ||||||||
\(749\) | −2.08443 | −0.0761634 | ||||||||
\(750\) | −5.04295 | −0.184142 | ||||||||
\(751\) | 43.9382 | 1.60333 | 0.801664 | − | 0.597775i | \(-0.203948\pi\) | ||||
0.801664 | + | 0.597775i | \(0.203948\pi\) | |||||||
\(752\) | −4.76503 | −0.173763 | ||||||||
\(753\) | −9.72732 | −0.354483 | ||||||||
\(754\) | −16.9052 | −0.615652 | ||||||||
\(755\) | 10.1827 | 0.370586 | ||||||||
\(756\) | −4.69573 | −0.170782 | ||||||||
\(757\) | −21.4475 | −0.779522 | −0.389761 | − | 0.920916i | \(-0.627442\pi\) | ||||
−0.389761 | + | 0.920916i | \(0.627442\pi\) | |||||||
\(758\) | −7.47226 | −0.271405 | ||||||||
\(759\) | −2.03148 | −0.0737380 | ||||||||
\(760\) | −6.02145 | −0.218421 | ||||||||
\(761\) | 22.5640 | 0.817945 | 0.408972 | − | 0.912547i | \(-0.365887\pi\) | ||||
0.408972 | + | 0.912547i | \(0.365887\pi\) | |||||||
\(762\) | 9.40038 | 0.340540 | ||||||||
\(763\) | 18.2219 | 0.659677 | ||||||||
\(764\) | −20.4296 | −0.739118 | ||||||||
\(765\) | −0.351279 | −0.0127005 | ||||||||
\(766\) | 4.45858 | 0.161095 | ||||||||
\(767\) | −7.93682 | −0.286582 | ||||||||
\(768\) | 0.590088 | 0.0212930 | ||||||||
\(769\) | 44.8392 | 1.61694 | 0.808471 | − | 0.588536i | \(-0.200296\pi\) | ||||
0.808471 | + | 0.588536i | \(0.200296\pi\) | |||||||
\(770\) | −4.54104 | −0.163648 | ||||||||
\(771\) | −9.75916 | −0.351468 | ||||||||
\(772\) | −10.8576 | −0.390774 | ||||||||
\(773\) | 44.4563 | 1.59898 | 0.799490 | − | 0.600679i | \(-0.205103\pi\) | ||||
0.799490 | + | 0.600679i | \(0.205103\pi\) | |||||||
\(774\) | 2.28797 | 0.0822393 | ||||||||
\(775\) | 27.1319 | 0.974608 | ||||||||
\(776\) | −2.07398 | −0.0744517 | ||||||||
\(777\) | −2.40951 | −0.0864407 | ||||||||
\(778\) | −19.1214 | −0.685534 | ||||||||
\(779\) | −19.5071 | −0.698915 | ||||||||
\(780\) | 1.10586 | 0.0395962 | ||||||||
\(781\) | −50.1523 | −1.79459 | ||||||||
\(782\) | 0.141401 | 0.00505648 | ||||||||
\(783\) | 28.1839 | 1.00721 | ||||||||
\(784\) | −5.01756 | −0.179199 | ||||||||
\(785\) | 20.7503 | 0.740611 | ||||||||
\(786\) | −0.590088 | −0.0210478 | ||||||||
\(787\) | 52.7211 | 1.87930 | 0.939652 | − | 0.342133i | \(-0.111149\pi\) | ||||
0.939652 | + | 0.342133i | \(0.111149\pi\) | |||||||
\(788\) | 14.0192 | 0.499415 | ||||||||
\(789\) | 16.3246 | 0.581172 | ||||||||
\(790\) | −5.76832 | −0.205227 | ||||||||
\(791\) | −18.3882 | −0.653810 | ||||||||
\(792\) | 9.12925 | 0.324394 | ||||||||
\(793\) | 2.97207 | 0.105541 | ||||||||
\(794\) | −26.9060 | −0.954858 | ||||||||
\(795\) | −3.27794 | −0.116257 | ||||||||
\(796\) | 7.76683 | 0.275288 | ||||||||
\(797\) | 11.2097 | 0.397068 | 0.198534 | − | 0.980094i | \(-0.436382\pi\) | ||||
0.198534 | + | 0.980094i | \(0.436382\pi\) | |||||||
\(798\) | −5.34020 | −0.189041 | ||||||||
\(799\) | −0.673779 | −0.0238366 | ||||||||
\(800\) | −4.12235 | −0.145747 | ||||||||
\(801\) | 5.90153 | 0.208520 | ||||||||
\(802\) | 24.0408 | 0.848910 | ||||||||
\(803\) | −37.0428 | −1.30721 | ||||||||
\(804\) | 3.17110 | 0.111836 | ||||||||
\(805\) | 1.31905 | 0.0464903 | ||||||||
\(806\) | −13.1662 | −0.463759 | ||||||||
\(807\) | −13.5256 | −0.476122 | ||||||||
\(808\) | −3.99612 | −0.140583 | ||||||||
\(809\) | 22.7509 | 0.799878 | 0.399939 | − | 0.916542i | \(-0.369031\pi\) | ||||
0.399939 | + | 0.916542i | \(0.369031\pi\) | |||||||
\(810\) | 5.60918 | 0.197087 | ||||||||
\(811\) | −34.2471 | −1.20258 | −0.601289 | − | 0.799031i | \(-0.705346\pi\) | ||||
−0.601289 | + | 0.799031i | \(0.705346\pi\) | |||||||
\(812\) | −11.8986 | −0.417560 | ||||||||
\(813\) | −2.49247 | −0.0874146 | ||||||||
\(814\) | 9.98405 | 0.349941 | ||||||||
\(815\) | −0.406433 | −0.0142367 | ||||||||
\(816\) | 0.0834389 | 0.00292094 | ||||||||
\(817\) | 5.54562 | 0.194017 | ||||||||
\(818\) | −6.20525 | −0.216961 | ||||||||
\(819\) | −7.46902 | −0.260989 | ||||||||
\(820\) | 2.84324 | 0.0992901 | ||||||||
\(821\) | 0.758459 | 0.0264704 | 0.0132352 | − | 0.999912i | \(-0.495787\pi\) | ||||
0.0132352 | + | 0.999912i | \(0.495787\pi\) | |||||||
\(822\) | 1.60054 | 0.0558252 | ||||||||
\(823\) | 42.7619 | 1.49059 | 0.745293 | − | 0.666737i | \(-0.232310\pi\) | ||||
0.745293 | + | 0.666737i | \(0.232310\pi\) | |||||||
\(824\) | −9.91039 | −0.345245 | ||||||||
\(825\) | 8.37446 | 0.291561 | ||||||||
\(826\) | −5.58628 | −0.194371 | ||||||||
\(827\) | −36.5280 | −1.27020 | −0.635102 | − | 0.772428i | \(-0.719042\pi\) | ||||
−0.635102 | + | 0.772428i | \(0.719042\pi\) | |||||||
\(828\) | −2.65180 | −0.0921563 | ||||||||
\(829\) | 27.7964 | 0.965408 | 0.482704 | − | 0.875783i | \(-0.339655\pi\) | ||||
0.482704 | + | 0.875783i | \(0.339655\pi\) | |||||||
\(830\) | 9.67389 | 0.335786 | ||||||||
\(831\) | 6.35059 | 0.220299 | ||||||||
\(832\) | 2.00043 | 0.0693525 | ||||||||
\(833\) | −0.709486 | −0.0245822 | ||||||||
\(834\) | −3.84095 | −0.133001 | ||||||||
\(835\) | 21.5549 | 0.745938 | ||||||||
\(836\) | 22.1277 | 0.765301 | ||||||||
\(837\) | 21.9502 | 0.758712 | ||||||||
\(838\) | −31.9967 | −1.10531 | ||||||||
\(839\) | −14.0685 | −0.485700 | −0.242850 | − | 0.970064i | \(-0.578082\pi\) | ||||
−0.242850 | + | 0.970064i | \(0.578082\pi\) | |||||||
\(840\) | 0.778354 | 0.0268558 | ||||||||
\(841\) | 42.4159 | 1.46262 | ||||||||
\(842\) | 3.43322 | 0.118317 | ||||||||
\(843\) | −3.42993 | −0.118133 | ||||||||
\(844\) | −11.8639 | −0.408373 | ||||||||
\(845\) | −8.42985 | −0.289996 | ||||||||
\(846\) | 12.6359 | 0.434431 | ||||||||
\(847\) | 1.19954 | 0.0412167 | ||||||||
\(848\) | −5.92958 | −0.203623 | ||||||||
\(849\) | 8.50588 | 0.291921 | ||||||||
\(850\) | −0.582903 | −0.0199934 | ||||||||
\(851\) | −2.90009 | −0.0994139 | ||||||||
\(852\) | 8.59632 | 0.294505 | ||||||||
\(853\) | −4.51815 | −0.154698 | −0.0773492 | − | 0.997004i | \(-0.524646\pi\) | ||||
−0.0773492 | + | 0.997004i | \(0.524646\pi\) | |||||||
\(854\) | 2.09188 | 0.0715825 | ||||||||
\(855\) | 15.9677 | 0.546082 | ||||||||
\(856\) | −1.48043 | −0.0506000 | ||||||||
\(857\) | −38.4586 | −1.31372 | −0.656861 | − | 0.754012i | \(-0.728116\pi\) | ||||
−0.656861 | + | 0.754012i | \(0.728116\pi\) | |||||||
\(858\) | −4.06383 | −0.138737 | ||||||||
\(859\) | 7.79124 | 0.265834 | 0.132917 | − | 0.991127i | \(-0.457566\pi\) | ||||
0.132917 | + | 0.991127i | \(0.457566\pi\) | |||||||
\(860\) | −0.808296 | −0.0275627 | ||||||||
\(861\) | 2.52156 | 0.0859345 | ||||||||
\(862\) | 25.7714 | 0.877777 | ||||||||
\(863\) | 45.7539 | 1.55748 | 0.778740 | − | 0.627347i | \(-0.215859\pi\) | ||||
0.778740 | + | 0.627347i | \(0.215859\pi\) | |||||||
\(864\) | −3.33506 | −0.113461 | ||||||||
\(865\) | 3.47807 | 0.118258 | ||||||||
\(866\) | −27.2835 | −0.927132 | ||||||||
\(867\) | −10.0197 | −0.340287 | ||||||||
\(868\) | −9.26693 | −0.314540 | ||||||||
\(869\) | 21.1974 | 0.719074 | ||||||||
\(870\) | −4.67170 | −0.158385 | ||||||||
\(871\) | 10.7502 | 0.364256 | ||||||||
\(872\) | 12.9418 | 0.438263 | ||||||||
\(873\) | 5.49978 | 0.186139 | ||||||||
\(874\) | −6.42748 | −0.217413 | ||||||||
\(875\) | −12.0328 | −0.406783 | ||||||||
\(876\) | 6.34931 | 0.214523 | ||||||||
\(877\) | 17.3672 | 0.586449 | 0.293225 | − | 0.956044i | \(-0.405272\pi\) | ||||
0.293225 | + | 0.956044i | \(0.405272\pi\) | |||||||
\(878\) | −0.346172 | −0.0116827 | ||||||||
\(879\) | −2.16529 | −0.0730334 | ||||||||
\(880\) | −3.22519 | −0.108721 | ||||||||
\(881\) | 12.9803 | 0.437319 | 0.218659 | − | 0.975801i | \(-0.429832\pi\) | ||||
0.218659 | + | 0.975801i | \(0.429832\pi\) | |||||||
\(882\) | 13.3055 | 0.448021 | ||||||||
\(883\) | −21.2687 | −0.715748 | −0.357874 | − | 0.933770i | \(-0.616498\pi\) | ||||
−0.357874 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(884\) | 0.282862 | 0.00951369 | ||||||||
\(885\) | −2.19331 | −0.0737273 | ||||||||
\(886\) | 25.3185 | 0.850591 | ||||||||
\(887\) | 2.61349 | 0.0877524 | 0.0438762 | − | 0.999037i | \(-0.486029\pi\) | ||||
0.0438762 | + | 0.999037i | \(0.486029\pi\) | |||||||
\(888\) | −1.71131 | −0.0574278 | ||||||||
\(889\) | 22.4299 | 0.752276 | ||||||||
\(890\) | −2.08490 | −0.0698859 | ||||||||
\(891\) | −20.6126 | −0.690550 | ||||||||
\(892\) | −29.2901 | −0.980706 | ||||||||
\(893\) | 30.6272 | 1.02490 | ||||||||
\(894\) | −3.57747 | −0.119649 | ||||||||
\(895\) | 2.27061 | 0.0758983 | ||||||||
\(896\) | 1.40799 | 0.0470377 | ||||||||
\(897\) | 1.18043 | 0.0394135 | ||||||||
\(898\) | 23.8631 | 0.796321 | ||||||||
\(899\) | 55.6203 | 1.85504 | ||||||||
\(900\) | 10.9316 | 0.364388 | ||||||||
\(901\) | −0.838446 | −0.0279327 | ||||||||
\(902\) | −10.4483 | −0.347892 | ||||||||
\(903\) | −0.716847 | −0.0238552 | ||||||||
\(904\) | −13.0599 | −0.434366 | ||||||||
\(905\) | −13.3947 | −0.445255 | ||||||||
\(906\) | 6.41385 | 0.213086 | ||||||||
\(907\) | 35.6302 | 1.18308 | 0.591540 | − | 0.806275i | \(-0.298520\pi\) | ||||
0.591540 | + | 0.806275i | \(0.298520\pi\) | |||||||
\(908\) | 14.0155 | 0.465122 | ||||||||
\(909\) | 10.5969 | 0.351477 | ||||||||
\(910\) | 2.63866 | 0.0874709 | ||||||||
\(911\) | 3.27725 | 0.108580 | 0.0542900 | − | 0.998525i | \(-0.482710\pi\) | ||||
0.0542900 | + | 0.998525i | \(0.482710\pi\) | |||||||
\(912\) | −3.79278 | −0.125592 | ||||||||
\(913\) | −35.5497 | −1.17652 | ||||||||
\(914\) | 15.1988 | 0.502730 | ||||||||
\(915\) | 0.821322 | 0.0271521 | ||||||||
\(916\) | 16.2255 | 0.536105 | ||||||||
\(917\) | −1.40799 | −0.0464960 | ||||||||
\(918\) | −0.471579 | −0.0155644 | ||||||||
\(919\) | 18.4871 | 0.609832 | 0.304916 | − | 0.952379i | \(-0.401372\pi\) | ||||
0.304916 | + | 0.952379i | \(0.401372\pi\) | |||||||
\(920\) | 0.936829 | 0.0308864 | ||||||||
\(921\) | 3.27474 | 0.107906 | ||||||||
\(922\) | 21.3324 | 0.702546 | ||||||||
\(923\) | 29.1420 | 0.959221 | ||||||||
\(924\) | −2.86030 | −0.0940970 | ||||||||
\(925\) | 11.9552 | 0.393084 | ||||||||
\(926\) | −41.1982 | −1.35386 | ||||||||
\(927\) | 26.2803 | 0.863159 | ||||||||
\(928\) | −8.45079 | −0.277411 | ||||||||
\(929\) | 53.7010 | 1.76187 | 0.880937 | − | 0.473234i | \(-0.156913\pi\) | ||||
0.880937 | + | 0.473234i | \(0.156913\pi\) | |||||||
\(930\) | −3.63843 | −0.119309 | ||||||||
\(931\) | 32.2503 | 1.05696 | ||||||||
\(932\) | −24.5063 | −0.802729 | ||||||||
\(933\) | 14.3702 | 0.470459 | ||||||||
\(934\) | 6.68526 | 0.218749 | ||||||||
\(935\) | −0.456044 | −0.0149142 | ||||||||
\(936\) | −5.30474 | −0.173391 | ||||||||
\(937\) | 0.0532100 | 0.00173829 | 0.000869147 | − | 1.00000i | \(-0.499723\pi\) | ||||
0.000869147 | 1.00000i | \(0.499723\pi\) | ||||||||
\(938\) | 7.56645 | 0.247053 | ||||||||
\(939\) | −1.66180 | −0.0542309 | ||||||||
\(940\) | −4.46402 | −0.145600 | ||||||||
\(941\) | −51.3211 | −1.67302 | −0.836510 | − | 0.547952i | \(-0.815408\pi\) | ||||
−0.836510 | + | 0.547952i | \(0.815408\pi\) | |||||||
\(942\) | 13.0702 | 0.425849 | ||||||||
\(943\) | 3.03496 | 0.0988318 | ||||||||
\(944\) | −3.96755 | −0.129133 | ||||||||
\(945\) | −4.39910 | −0.143103 | ||||||||
\(946\) | 2.97033 | 0.0965738 | ||||||||
\(947\) | −4.21479 | −0.136962 | −0.0684812 | − | 0.997652i | \(-0.521815\pi\) | ||||
−0.0684812 | + | 0.997652i | \(0.521815\pi\) | |||||||
\(948\) | −3.63334 | −0.118005 | ||||||||
\(949\) | 21.5245 | 0.698715 | ||||||||
\(950\) | 26.4963 | 0.859654 | ||||||||
\(951\) | 3.08162 | 0.0999282 | ||||||||
\(952\) | 0.199091 | 0.00645257 | ||||||||
\(953\) | −39.7049 | −1.28617 | −0.643083 | − | 0.765796i | \(-0.722345\pi\) | ||||
−0.643083 | + | 0.765796i | \(0.722345\pi\) | |||||||
\(954\) | 15.7240 | 0.509084 | ||||||||
\(955\) | −19.1391 | −0.619326 | ||||||||
\(956\) | −11.1756 | −0.361446 | ||||||||
\(957\) | 17.1676 | 0.554949 | ||||||||
\(958\) | 25.4479 | 0.822183 | ||||||||
\(959\) | 3.81899 | 0.123322 | ||||||||
\(960\) | 0.552812 | 0.0178419 | ||||||||
\(961\) | 12.3184 | 0.397366 | ||||||||
\(962\) | −5.80144 | −0.187046 | ||||||||
\(963\) | 3.92579 | 0.126507 | ||||||||
\(964\) | 12.1844 | 0.392434 | ||||||||
\(965\) | −10.1717 | −0.327439 | ||||||||
\(966\) | 0.830839 | 0.0267318 | ||||||||
\(967\) | −24.0568 | −0.773614 | −0.386807 | − | 0.922161i | \(-0.626422\pi\) | ||||
−0.386807 | + | 0.922161i | \(0.626422\pi\) | |||||||
\(968\) | 0.851951 | 0.0273827 | ||||||||
\(969\) | −0.536301 | −0.0172285 | ||||||||
\(970\) | −1.94297 | −0.0623850 | ||||||||
\(971\) | 24.9454 | 0.800535 | 0.400267 | − | 0.916398i | \(-0.368917\pi\) | ||||
0.400267 | + | 0.916398i | \(0.368917\pi\) | |||||||
\(972\) | 13.5383 | 0.434240 | ||||||||
\(973\) | −9.16476 | −0.293809 | ||||||||
\(974\) | −34.7009 | −1.11189 | ||||||||
\(975\) | −4.86615 | −0.155842 | ||||||||
\(976\) | 1.48572 | 0.0475566 | ||||||||
\(977\) | −9.20105 | −0.294368 | −0.147184 | − | 0.989109i | \(-0.547021\pi\) | ||||
−0.147184 | + | 0.989109i | \(0.547021\pi\) | |||||||
\(978\) | −0.256003 | −0.00818608 | ||||||||
\(979\) | 7.66159 | 0.244866 | ||||||||
\(980\) | −4.70060 | −0.150155 | ||||||||
\(981\) | −34.3189 | −1.09572 | ||||||||
\(982\) | −21.7959 | −0.695534 | ||||||||
\(983\) | −8.26546 | −0.263627 | −0.131814 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131814 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(984\) | 1.79089 | 0.0570916 | ||||||||
\(985\) | 13.1336 | 0.418472 | ||||||||
\(986\) | −1.19495 | −0.0380549 | ||||||||
\(987\) | −3.95898 | −0.126016 | ||||||||
\(988\) | −12.8577 | −0.409059 | ||||||||
\(989\) | −0.862799 | −0.0274354 | ||||||||
\(990\) | 8.55255 | 0.271818 | ||||||||
\(991\) | 14.8110 | 0.470487 | 0.235243 | − | 0.971937i | \(-0.424411\pi\) | ||||
0.235243 | + | 0.971937i | \(0.424411\pi\) | |||||||
\(992\) | −6.58167 | −0.208968 | ||||||||
\(993\) | 16.0158 | 0.508246 | ||||||||
\(994\) | 20.5114 | 0.650582 | ||||||||
\(995\) | 7.27619 | 0.230671 | ||||||||
\(996\) | 6.09337 | 0.193076 | ||||||||
\(997\) | −19.4318 | −0.615412 | −0.307706 | − | 0.951481i | \(-0.599561\pi\) | ||||
−0.307706 | + | 0.951481i | \(0.599561\pi\) | |||||||
\(998\) | −29.3583 | −0.929320 | ||||||||
\(999\) | 9.67198 | 0.306008 |
(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 | 6026.2.a.f.1.14 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.f.1.14 | ✓ | 20 | 1.1 | even | 1 | trivial |