Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(0\) |
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: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(2.72853\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 2.72853 | 1.57532 | 0.787658 | − | 0.616112i | \(-0.211293\pi\) | ||||
0.787658 | + | 0.616112i | \(0.211293\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.72853 | −1.11392 | ||||||||
\(7\) | 0.894798 | 0.338202 | 0.169101 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169101 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.44487 | 1.48162 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −5.03131 | −1.51700 | −0.758499 | − | 0.651674i | \(-0.774067\pi\) | ||||
−0.758499 | + | 0.651674i | \(0.774067\pi\) | |||||||
\(12\) | 2.72853 | 0.787658 | ||||||||
\(13\) | −5.35803 | −1.48605 | −0.743026 | − | 0.669263i | \(-0.766610\pi\) | ||||
−0.743026 | + | 0.669263i | \(0.766610\pi\) | |||||||
\(14\) | −0.894798 | −0.239145 | ||||||||
\(15\) | 2.72853 | 0.704503 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.62630 | 1.36458 | 0.682289 | − | 0.731083i | \(-0.260985\pi\) | ||||
0.682289 | + | 0.731083i | \(0.260985\pi\) | |||||||
\(18\) | −4.44487 | −1.04767 | ||||||||
\(19\) | −0.243411 | −0.0558423 | −0.0279211 | − | 0.999610i | \(-0.508889\pi\) | ||||
−0.0279211 | + | 0.999610i | \(0.508889\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.44148 | 0.532775 | ||||||||
\(22\) | 5.03131 | 1.07268 | ||||||||
\(23\) | 4.21762 | 0.879434 | 0.439717 | − | 0.898136i | \(-0.355079\pi\) | ||||
0.439717 | + | 0.898136i | \(0.355079\pi\) | |||||||
\(24\) | −2.72853 | −0.556958 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.35803 | 1.05080 | ||||||||
\(27\) | 3.94236 | 0.758707 | ||||||||
\(28\) | 0.894798 | 0.169101 | ||||||||
\(29\) | 7.69759 | 1.42941 | 0.714703 | − | 0.699428i | \(-0.246562\pi\) | ||||
0.714703 | + | 0.699428i | \(0.246562\pi\) | |||||||
\(30\) | −2.72853 | −0.498159 | ||||||||
\(31\) | 1.55876 | 0.279962 | 0.139981 | − | 0.990154i | \(-0.455296\pi\) | ||||
0.139981 | + | 0.990154i | \(0.455296\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −13.7281 | −2.38975 | ||||||||
\(34\) | −5.62630 | −0.964902 | ||||||||
\(35\) | 0.894798 | 0.151248 | ||||||||
\(36\) | 4.44487 | 0.740811 | ||||||||
\(37\) | 10.0042 | 1.64468 | 0.822342 | − | 0.568994i | \(-0.192667\pi\) | ||||
0.822342 | + | 0.568994i | \(0.192667\pi\) | |||||||
\(38\) | 0.243411 | 0.0394864 | ||||||||
\(39\) | −14.6195 | −2.34100 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.18356 | 0.497188 | 0.248594 | − | 0.968608i | \(-0.420032\pi\) | ||||
0.248594 | + | 0.968608i | \(0.420032\pi\) | |||||||
\(42\) | −2.44148 | −0.376729 | ||||||||
\(43\) | −3.19538 | −0.487290 | −0.243645 | − | 0.969864i | \(-0.578343\pi\) | ||||
−0.243645 | + | 0.969864i | \(0.578343\pi\) | |||||||
\(44\) | −5.03131 | −0.758499 | ||||||||
\(45\) | 4.44487 | 0.662602 | ||||||||
\(46\) | −4.21762 | −0.621854 | ||||||||
\(47\) | 4.78751 | 0.698329 | 0.349165 | − | 0.937061i | \(-0.386465\pi\) | ||||
0.349165 | + | 0.937061i | \(0.386465\pi\) | |||||||
\(48\) | 2.72853 | 0.393829 | ||||||||
\(49\) | −6.19934 | −0.885620 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 15.3515 | 2.14964 | ||||||||
\(52\) | −5.35803 | −0.743026 | ||||||||
\(53\) | −5.76361 | −0.791693 | −0.395847 | − | 0.918317i | \(-0.629549\pi\) | ||||
−0.395847 | + | 0.918317i | \(0.629549\pi\) | |||||||
\(54\) | −3.94236 | −0.536487 | ||||||||
\(55\) | −5.03131 | −0.678422 | ||||||||
\(56\) | −0.894798 | −0.119572 | ||||||||
\(57\) | −0.664153 | −0.0879692 | ||||||||
\(58\) | −7.69759 | −1.01074 | ||||||||
\(59\) | 7.35635 | 0.957715 | 0.478857 | − | 0.877893i | \(-0.341051\pi\) | ||||
0.478857 | + | 0.877893i | \(0.341051\pi\) | |||||||
\(60\) | 2.72853 | 0.352251 | ||||||||
\(61\) | 2.11101 | 0.270287 | 0.135143 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135143 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(62\) | −1.55876 | −0.197963 | ||||||||
\(63\) | 3.97726 | 0.501087 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.35803 | −0.664582 | ||||||||
\(66\) | 13.7281 | 1.68981 | ||||||||
\(67\) | 14.7072 | 1.79677 | 0.898386 | − | 0.439207i | \(-0.144740\pi\) | ||||
0.898386 | + | 0.439207i | \(0.144740\pi\) | |||||||
\(68\) | 5.62630 | 0.682289 | ||||||||
\(69\) | 11.5079 | 1.38539 | ||||||||
\(70\) | −0.894798 | −0.106949 | ||||||||
\(71\) | −2.41472 | −0.286574 | −0.143287 | − | 0.989681i | \(-0.545767\pi\) | ||||
−0.143287 | + | 0.989681i | \(0.545767\pi\) | |||||||
\(72\) | −4.44487 | −0.523833 | ||||||||
\(73\) | 10.4349 | 1.22131 | 0.610654 | − | 0.791898i | \(-0.290907\pi\) | ||||
0.610654 | + | 0.791898i | \(0.290907\pi\) | |||||||
\(74\) | −10.0042 | −1.16297 | ||||||||
\(75\) | 2.72853 | 0.315063 | ||||||||
\(76\) | −0.243411 | −0.0279211 | ||||||||
\(77\) | −4.50201 | −0.513052 | ||||||||
\(78\) | 14.6195 | 1.65534 | ||||||||
\(79\) | 8.03826 | 0.904375 | 0.452187 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452187 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.57776 | −0.286418 | ||||||||
\(82\) | −3.18356 | −0.351565 | ||||||||
\(83\) | 17.4940 | 1.92022 | 0.960110 | − | 0.279623i | \(-0.0902095\pi\) | ||||
0.960110 | + | 0.279623i | \(0.0902095\pi\) | |||||||
\(84\) | 2.44148 | 0.266387 | ||||||||
\(85\) | 5.62630 | 0.610257 | ||||||||
\(86\) | 3.19538 | 0.344566 | ||||||||
\(87\) | 21.0031 | 2.25177 | ||||||||
\(88\) | 5.03131 | 0.536340 | ||||||||
\(89\) | 12.8682 | 1.36402 | 0.682011 | − | 0.731342i | \(-0.261106\pi\) | ||||
0.682011 | + | 0.731342i | \(0.261106\pi\) | |||||||
\(90\) | −4.44487 | −0.468530 | ||||||||
\(91\) | −4.79436 | −0.502585 | ||||||||
\(92\) | 4.21762 | 0.439717 | ||||||||
\(93\) | 4.25313 | 0.441029 | ||||||||
\(94\) | −4.78751 | −0.493793 | ||||||||
\(95\) | −0.243411 | −0.0249734 | ||||||||
\(96\) | −2.72853 | −0.278479 | ||||||||
\(97\) | −1.78912 | −0.181657 | −0.0908287 | − | 0.995867i | \(-0.528952\pi\) | ||||
−0.0908287 | + | 0.995867i | \(0.528952\pi\) | |||||||
\(98\) | 6.19934 | 0.626228 | ||||||||
\(99\) | −22.3635 | −2.24762 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.23617 | −0.123003 | −0.0615016 | − | 0.998107i | \(-0.519589\pi\) | ||||
−0.0615016 | + | 0.998107i | \(0.519589\pi\) | |||||||
\(102\) | −15.3515 | −1.52003 | ||||||||
\(103\) | 8.59261 | 0.846655 | 0.423327 | − | 0.905977i | \(-0.360862\pi\) | ||||
0.423327 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(104\) | 5.35803 | 0.525398 | ||||||||
\(105\) | 2.44148 | 0.238264 | ||||||||
\(106\) | 5.76361 | 0.559812 | ||||||||
\(107\) | −12.3939 | −1.19816 | −0.599080 | − | 0.800689i | \(-0.704467\pi\) | ||||
−0.599080 | + | 0.800689i | \(0.704467\pi\) | |||||||
\(108\) | 3.94236 | 0.379354 | ||||||||
\(109\) | −5.77545 | −0.553188 | −0.276594 | − | 0.960987i | \(-0.589206\pi\) | ||||
−0.276594 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(110\) | 5.03131 | 0.479717 | ||||||||
\(111\) | 27.2968 | 2.59090 | ||||||||
\(112\) | 0.894798 | 0.0845505 | ||||||||
\(113\) | −15.1123 | −1.42164 | −0.710821 | − | 0.703373i | \(-0.751676\pi\) | ||||
−0.710821 | + | 0.703373i | \(0.751676\pi\) | |||||||
\(114\) | 0.664153 | 0.0622036 | ||||||||
\(115\) | 4.21762 | 0.393295 | ||||||||
\(116\) | 7.69759 | 0.714703 | ||||||||
\(117\) | −23.8157 | −2.20177 | ||||||||
\(118\) | −7.35635 | −0.677207 | ||||||||
\(119\) | 5.03440 | 0.461502 | ||||||||
\(120\) | −2.72853 | −0.249079 | ||||||||
\(121\) | 14.3141 | 1.30128 | ||||||||
\(122\) | −2.11101 | −0.191122 | ||||||||
\(123\) | 8.68642 | 0.783228 | ||||||||
\(124\) | 1.55876 | 0.139981 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.97726 | −0.354322 | ||||||||
\(127\) | −10.4837 | −0.930280 | −0.465140 | − | 0.885237i | \(-0.653996\pi\) | ||||
−0.465140 | + | 0.885237i | \(0.653996\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.71868 | −0.767637 | ||||||||
\(130\) | 5.35803 | 0.469931 | ||||||||
\(131\) | 2.62399 | 0.229259 | 0.114629 | − | 0.993408i | \(-0.463432\pi\) | ||||
0.114629 | + | 0.993408i | \(0.463432\pi\) | |||||||
\(132\) | −13.7281 | −1.19488 | ||||||||
\(133\) | −0.217803 | −0.0188860 | ||||||||
\(134\) | −14.7072 | −1.27051 | ||||||||
\(135\) | 3.94236 | 0.339304 | ||||||||
\(136\) | −5.62630 | −0.482451 | ||||||||
\(137\) | −4.80349 | −0.410390 | −0.205195 | − | 0.978721i | \(-0.565783\pi\) | ||||
−0.205195 | + | 0.978721i | \(0.565783\pi\) | |||||||
\(138\) | −11.5079 | −0.979616 | ||||||||
\(139\) | 2.95063 | 0.250269 | 0.125135 | − | 0.992140i | \(-0.460064\pi\) | ||||
0.125135 | + | 0.992140i | \(0.460064\pi\) | |||||||
\(140\) | 0.894798 | 0.0756242 | ||||||||
\(141\) | 13.0628 | 1.10009 | ||||||||
\(142\) | 2.41472 | 0.202638 | ||||||||
\(143\) | 26.9579 | 2.25434 | ||||||||
\(144\) | 4.44487 | 0.370406 | ||||||||
\(145\) | 7.69759 | 0.639250 | ||||||||
\(146\) | −10.4349 | −0.863595 | ||||||||
\(147\) | −16.9151 | −1.39513 | ||||||||
\(148\) | 10.0042 | 0.822342 | ||||||||
\(149\) | −19.6552 | −1.61022 | −0.805108 | − | 0.593129i | \(-0.797892\pi\) | ||||
−0.805108 | + | 0.593129i | \(0.797892\pi\) | |||||||
\(150\) | −2.72853 | −0.222783 | ||||||||
\(151\) | 0.0952463 | 0.00775103 | 0.00387552 | − | 0.999992i | \(-0.498766\pi\) | ||||
0.00387552 | + | 0.999992i | \(0.498766\pi\) | |||||||
\(152\) | 0.243411 | 0.0197432 | ||||||||
\(153\) | 25.0081 | 2.02179 | ||||||||
\(154\) | 4.50201 | 0.362782 | ||||||||
\(155\) | 1.55876 | 0.125203 | ||||||||
\(156\) | −14.6195 | −1.17050 | ||||||||
\(157\) | 15.2271 | 1.21526 | 0.607628 | − | 0.794222i | \(-0.292121\pi\) | ||||
0.607628 | + | 0.794222i | \(0.292121\pi\) | |||||||
\(158\) | −8.03826 | −0.639490 | ||||||||
\(159\) | −15.7262 | −1.24717 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.77391 | 0.297426 | ||||||||
\(162\) | 2.57776 | 0.202528 | ||||||||
\(163\) | 5.79346 | 0.453779 | 0.226889 | − | 0.973921i | \(-0.427144\pi\) | ||||
0.226889 | + | 0.973921i | \(0.427144\pi\) | |||||||
\(164\) | 3.18356 | 0.248594 | ||||||||
\(165\) | −13.7281 | −1.06873 | ||||||||
\(166\) | −17.4940 | −1.35780 | ||||||||
\(167\) | −6.61990 | −0.512263 | −0.256132 | − | 0.966642i | \(-0.582448\pi\) | ||||
−0.256132 | + | 0.966642i | \(0.582448\pi\) | |||||||
\(168\) | −2.44148 | −0.188364 | ||||||||
\(169\) | 15.7085 | 1.20835 | ||||||||
\(170\) | −5.62630 | −0.431517 | ||||||||
\(171\) | −1.08193 | −0.0827371 | ||||||||
\(172\) | −3.19538 | −0.243645 | ||||||||
\(173\) | 16.5171 | 1.25578 | 0.627888 | − | 0.778304i | \(-0.283920\pi\) | ||||
0.627888 | + | 0.778304i | \(0.283920\pi\) | |||||||
\(174\) | −21.0031 | −1.59224 | ||||||||
\(175\) | 0.894798 | 0.0676404 | ||||||||
\(176\) | −5.03131 | −0.379250 | ||||||||
\(177\) | 20.0720 | 1.50870 | ||||||||
\(178\) | −12.8682 | −0.964509 | ||||||||
\(179\) | −24.8250 | −1.85551 | −0.927753 | − | 0.373195i | \(-0.878262\pi\) | ||||
−0.927753 | + | 0.373195i | \(0.878262\pi\) | |||||||
\(180\) | 4.44487 | 0.331301 | ||||||||
\(181\) | −3.80676 | −0.282954 | −0.141477 | − | 0.989942i | \(-0.545185\pi\) | ||||
−0.141477 | + | 0.989942i | \(0.545185\pi\) | |||||||
\(182\) | 4.79436 | 0.355381 | ||||||||
\(183\) | 5.75994 | 0.425787 | ||||||||
\(184\) | −4.21762 | −0.310927 | ||||||||
\(185\) | 10.0042 | 0.735525 | ||||||||
\(186\) | −4.25313 | −0.311854 | ||||||||
\(187\) | −28.3077 | −2.07006 | ||||||||
\(188\) | 4.78751 | 0.349165 | ||||||||
\(189\) | 3.52761 | 0.256596 | ||||||||
\(190\) | 0.243411 | 0.0176589 | ||||||||
\(191\) | −25.9989 | −1.88121 | −0.940606 | − | 0.339499i | \(-0.889742\pi\) | ||||
−0.940606 | + | 0.339499i | \(0.889742\pi\) | |||||||
\(192\) | 2.72853 | 0.196915 | ||||||||
\(193\) | −22.5354 | −1.62213 | −0.811067 | − | 0.584953i | \(-0.801113\pi\) | ||||
−0.811067 | + | 0.584953i | \(0.801113\pi\) | |||||||
\(194\) | 1.78912 | 0.128451 | ||||||||
\(195\) | −14.6195 | −1.04693 | ||||||||
\(196\) | −6.19934 | −0.442810 | ||||||||
\(197\) | −10.0738 | −0.717731 | −0.358865 | − | 0.933389i | \(-0.616836\pi\) | ||||
−0.358865 | + | 0.933389i | \(0.616836\pi\) | |||||||
\(198\) | 22.3635 | 1.58931 | ||||||||
\(199\) | 20.8793 | 1.48009 | 0.740047 | − | 0.672555i | \(-0.234803\pi\) | ||||
0.740047 | + | 0.672555i | \(0.234803\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 40.1290 | 2.83048 | ||||||||
\(202\) | 1.23617 | 0.0869764 | ||||||||
\(203\) | 6.88778 | 0.483428 | ||||||||
\(204\) | 15.3515 | 1.07482 | ||||||||
\(205\) | 3.18356 | 0.222349 | ||||||||
\(206\) | −8.59261 | −0.598675 | ||||||||
\(207\) | 18.7467 | 1.30299 | ||||||||
\(208\) | −5.35803 | −0.371513 | ||||||||
\(209\) | 1.22468 | 0.0847126 | ||||||||
\(210\) | −2.44148 | −0.168478 | ||||||||
\(211\) | 4.03377 | 0.277696 | 0.138848 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138848 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(212\) | −5.76361 | −0.395847 | ||||||||
\(213\) | −6.58862 | −0.451445 | ||||||||
\(214\) | 12.3939 | 0.847227 | ||||||||
\(215\) | −3.19538 | −0.217923 | ||||||||
\(216\) | −3.94236 | −0.268244 | ||||||||
\(217\) | 1.39478 | 0.0946836 | ||||||||
\(218\) | 5.77545 | 0.391163 | ||||||||
\(219\) | 28.4718 | 1.92395 | ||||||||
\(220\) | −5.03131 | −0.339211 | ||||||||
\(221\) | −30.1459 | −2.02783 | ||||||||
\(222\) | −27.2968 | −1.83204 | ||||||||
\(223\) | 16.9664 | 1.13616 | 0.568078 | − | 0.822974i | \(-0.307687\pi\) | ||||
0.568078 | + | 0.822974i | \(0.307687\pi\) | |||||||
\(224\) | −0.894798 | −0.0597862 | ||||||||
\(225\) | 4.44487 | 0.296324 | ||||||||
\(226\) | 15.1123 | 1.00525 | ||||||||
\(227\) | −20.1180 | −1.33528 | −0.667638 | − | 0.744486i | \(-0.732695\pi\) | ||||
−0.667638 | + | 0.744486i | \(0.732695\pi\) | |||||||
\(228\) | −0.664153 | −0.0439846 | ||||||||
\(229\) | −20.4312 | −1.35013 | −0.675066 | − | 0.737758i | \(-0.735885\pi\) | ||||
−0.675066 | + | 0.737758i | \(0.735885\pi\) | |||||||
\(230\) | −4.21762 | −0.278101 | ||||||||
\(231\) | −12.2839 | −0.808219 | ||||||||
\(232\) | −7.69759 | −0.505371 | ||||||||
\(233\) | −22.8310 | −1.49571 | −0.747853 | − | 0.663864i | \(-0.768915\pi\) | ||||
−0.747853 | + | 0.663864i | \(0.768915\pi\) | |||||||
\(234\) | 23.8157 | 1.55688 | ||||||||
\(235\) | 4.78751 | 0.312302 | ||||||||
\(236\) | 7.35635 | 0.478857 | ||||||||
\(237\) | 21.9326 | 1.42468 | ||||||||
\(238\) | −5.03440 | −0.326332 | ||||||||
\(239\) | −1.62500 | −0.105113 | −0.0525563 | − | 0.998618i | \(-0.516737\pi\) | ||||
−0.0525563 | + | 0.998618i | \(0.516737\pi\) | |||||||
\(240\) | 2.72853 | 0.176126 | ||||||||
\(241\) | 0.464813 | 0.0299412 | 0.0149706 | − | 0.999888i | \(-0.495235\pi\) | ||||
0.0149706 | + | 0.999888i | \(0.495235\pi\) | |||||||
\(242\) | −14.3141 | −0.920147 | ||||||||
\(243\) | −18.8606 | −1.20991 | ||||||||
\(244\) | 2.11101 | 0.135143 | ||||||||
\(245\) | −6.19934 | −0.396061 | ||||||||
\(246\) | −8.68642 | −0.553826 | ||||||||
\(247\) | 1.30420 | 0.0829844 | ||||||||
\(248\) | −1.55876 | −0.0989815 | ||||||||
\(249\) | 47.7330 | 3.02495 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 19.7893 | 1.24909 | 0.624546 | − | 0.780988i | \(-0.285284\pi\) | ||||
0.624546 | + | 0.780988i | \(0.285284\pi\) | |||||||
\(252\) | 3.97726 | 0.250544 | ||||||||
\(253\) | −21.2202 | −1.33410 | ||||||||
\(254\) | 10.4837 | 0.657807 | ||||||||
\(255\) | 15.3515 | 0.961349 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.0631 | −1.62577 | −0.812887 | − | 0.582422i | \(-0.802105\pi\) | ||||
−0.812887 | + | 0.582422i | \(0.802105\pi\) | |||||||
\(258\) | 8.71868 | 0.542801 | ||||||||
\(259\) | 8.95175 | 0.556235 | ||||||||
\(260\) | −5.35803 | −0.332291 | ||||||||
\(261\) | 34.2147 | 2.11784 | ||||||||
\(262\) | −2.62399 | −0.162110 | ||||||||
\(263\) | 4.82161 | 0.297313 | 0.148657 | − | 0.988889i | \(-0.452505\pi\) | ||||
0.148657 | + | 0.988889i | \(0.452505\pi\) | |||||||
\(264\) | 13.7281 | 0.844905 | ||||||||
\(265\) | −5.76361 | −0.354056 | ||||||||
\(266\) | 0.217803 | 0.0133544 | ||||||||
\(267\) | 35.1111 | 2.14877 | ||||||||
\(268\) | 14.7072 | 0.898386 | ||||||||
\(269\) | 14.3547 | 0.875223 | 0.437611 | − | 0.899164i | \(-0.355825\pi\) | ||||
0.437611 | + | 0.899164i | \(0.355825\pi\) | |||||||
\(270\) | −3.94236 | −0.239924 | ||||||||
\(271\) | −24.0039 | −1.45813 | −0.729066 | − | 0.684444i | \(-0.760045\pi\) | ||||
−0.729066 | + | 0.684444i | \(0.760045\pi\) | |||||||
\(272\) | 5.62630 | 0.341144 | ||||||||
\(273\) | −13.0815 | −0.791731 | ||||||||
\(274\) | 4.80349 | 0.290190 | ||||||||
\(275\) | −5.03131 | −0.303400 | ||||||||
\(276\) | 11.5079 | 0.692693 | ||||||||
\(277\) | −18.3925 | −1.10510 | −0.552549 | − | 0.833481i | \(-0.686345\pi\) | ||||
−0.552549 | + | 0.833481i | \(0.686345\pi\) | |||||||
\(278\) | −2.95063 | −0.176967 | ||||||||
\(279\) | 6.92849 | 0.414798 | ||||||||
\(280\) | −0.894798 | −0.0534744 | ||||||||
\(281\) | −12.0348 | −0.717937 | −0.358969 | − | 0.933350i | \(-0.616872\pi\) | ||||
−0.358969 | + | 0.933350i | \(0.616872\pi\) | |||||||
\(282\) | −13.0628 | −0.777881 | ||||||||
\(283\) | 29.3428 | 1.74425 | 0.872124 | − | 0.489284i | \(-0.162742\pi\) | ||||
0.872124 | + | 0.489284i | \(0.162742\pi\) | |||||||
\(284\) | −2.41472 | −0.143287 | ||||||||
\(285\) | −0.664153 | −0.0393410 | ||||||||
\(286\) | −26.9579 | −1.59406 | ||||||||
\(287\) | 2.84864 | 0.168150 | ||||||||
\(288\) | −4.44487 | −0.261916 | ||||||||
\(289\) | 14.6552 | 0.862071 | ||||||||
\(290\) | −7.69759 | −0.452018 | ||||||||
\(291\) | −4.88166 | −0.286168 | ||||||||
\(292\) | 10.4349 | 0.610654 | ||||||||
\(293\) | 3.78143 | 0.220913 | 0.110457 | − | 0.993881i | \(-0.464769\pi\) | ||||
0.110457 | + | 0.993881i | \(0.464769\pi\) | |||||||
\(294\) | 16.9151 | 0.986507 | ||||||||
\(295\) | 7.35635 | 0.428303 | ||||||||
\(296\) | −10.0042 | −0.581483 | ||||||||
\(297\) | −19.8352 | −1.15096 | ||||||||
\(298\) | 19.6552 | 1.13859 | ||||||||
\(299\) | −22.5981 | −1.30688 | ||||||||
\(300\) | 2.72853 | 0.157532 | ||||||||
\(301\) | −2.85922 | −0.164803 | ||||||||
\(302\) | −0.0952463 | −0.00548081 | ||||||||
\(303\) | −3.37292 | −0.193769 | ||||||||
\(304\) | −0.243411 | −0.0139606 | ||||||||
\(305\) | 2.11101 | 0.120876 | ||||||||
\(306\) | −25.0081 | −1.42962 | ||||||||
\(307\) | 15.5960 | 0.890113 | 0.445056 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445056 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(308\) | −4.50201 | −0.256526 | ||||||||
\(309\) | 23.4452 | 1.33375 | ||||||||
\(310\) | −1.55876 | −0.0885317 | ||||||||
\(311\) | −19.6206 | −1.11258 | −0.556292 | − | 0.830987i | \(-0.687776\pi\) | ||||
−0.556292 | + | 0.830987i | \(0.687776\pi\) | |||||||
\(312\) | 14.6195 | 0.827669 | ||||||||
\(313\) | −22.3404 | −1.26276 | −0.631378 | − | 0.775475i | \(-0.717510\pi\) | ||||
−0.631378 | + | 0.775475i | \(0.717510\pi\) | |||||||
\(314\) | −15.2271 | −0.859316 | ||||||||
\(315\) | 3.97726 | 0.224093 | ||||||||
\(316\) | 8.03826 | 0.452187 | ||||||||
\(317\) | −21.4639 | −1.20553 | −0.602765 | − | 0.797919i | \(-0.705934\pi\) | ||||
−0.602765 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(318\) | 15.7262 | 0.881880 | ||||||||
\(319\) | −38.7290 | −2.16841 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −33.8170 | −1.88748 | ||||||||
\(322\) | −3.77391 | −0.210312 | ||||||||
\(323\) | −1.36950 | −0.0762011 | ||||||||
\(324\) | −2.57776 | −0.143209 | ||||||||
\(325\) | −5.35803 | −0.297210 | ||||||||
\(326\) | −5.79346 | −0.320870 | ||||||||
\(327\) | −15.7585 | −0.871447 | ||||||||
\(328\) | −3.18356 | −0.175783 | ||||||||
\(329\) | 4.28385 | 0.236176 | ||||||||
\(330\) | 13.7281 | 0.755706 | ||||||||
\(331\) | 34.7309 | 1.90898 | 0.954492 | − | 0.298238i | \(-0.0963988\pi\) | ||||
0.954492 | + | 0.298238i | \(0.0963988\pi\) | |||||||
\(332\) | 17.4940 | 0.960110 | ||||||||
\(333\) | 44.4674 | 2.43680 | ||||||||
\(334\) | 6.61990 | 0.362225 | ||||||||
\(335\) | 14.7072 | 0.803541 | ||||||||
\(336\) | 2.44148 | 0.133194 | ||||||||
\(337\) | 3.67354 | 0.200111 | 0.100055 | − | 0.994982i | \(-0.468098\pi\) | ||||
0.100055 | + | 0.994982i | \(0.468098\pi\) | |||||||
\(338\) | −15.7085 | −0.854431 | ||||||||
\(339\) | −41.2342 | −2.23954 | ||||||||
\(340\) | 5.62630 | 0.305129 | ||||||||
\(341\) | −7.84262 | −0.424702 | ||||||||
\(342\) | 1.08193 | 0.0585040 | ||||||||
\(343\) | −11.8107 | −0.637720 | ||||||||
\(344\) | 3.19538 | 0.172283 | ||||||||
\(345\) | 11.5079 | 0.619564 | ||||||||
\(346\) | −16.5171 | −0.887967 | ||||||||
\(347\) | 2.85432 | 0.153228 | 0.0766141 | − | 0.997061i | \(-0.475589\pi\) | ||||
0.0766141 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(348\) | 21.0031 | 1.12588 | ||||||||
\(349\) | 29.4690 | 1.57744 | 0.788720 | − | 0.614753i | \(-0.210744\pi\) | ||||
0.788720 | + | 0.614753i | \(0.210744\pi\) | |||||||
\(350\) | −0.894798 | −0.0478290 | ||||||||
\(351\) | −21.1233 | −1.12748 | ||||||||
\(352\) | 5.03131 | 0.268170 | ||||||||
\(353\) | 10.0491 | 0.534861 | 0.267430 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267430 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(354\) | −20.0720 | −1.06681 | ||||||||
\(355\) | −2.41472 | −0.128160 | ||||||||
\(356\) | 12.8682 | 0.682011 | ||||||||
\(357\) | 13.7365 | 0.727012 | ||||||||
\(358\) | 24.8250 | 1.31204 | ||||||||
\(359\) | −20.8179 | −1.09872 | −0.549362 | − | 0.835584i | \(-0.685129\pi\) | ||||
−0.549362 | + | 0.835584i | \(0.685129\pi\) | |||||||
\(360\) | −4.44487 | −0.234265 | ||||||||
\(361\) | −18.9408 | −0.996882 | ||||||||
\(362\) | 3.80676 | 0.200079 | ||||||||
\(363\) | 39.0565 | 2.04993 | ||||||||
\(364\) | −4.79436 | −0.251293 | ||||||||
\(365\) | 10.4349 | 0.546185 | ||||||||
\(366\) | −5.75994 | −0.301077 | ||||||||
\(367\) | −31.4818 | −1.64334 | −0.821668 | − | 0.569966i | \(-0.806956\pi\) | ||||
−0.821668 | + | 0.569966i | \(0.806956\pi\) | |||||||
\(368\) | 4.21762 | 0.219858 | ||||||||
\(369\) | 14.1505 | 0.736645 | ||||||||
\(370\) | −10.0042 | −0.520095 | ||||||||
\(371\) | −5.15727 | −0.267752 | ||||||||
\(372\) | 4.25313 | 0.220514 | ||||||||
\(373\) | −18.8122 | −0.974058 | −0.487029 | − | 0.873386i | \(-0.661919\pi\) | ||||
−0.487029 | + | 0.873386i | \(0.661919\pi\) | |||||||
\(374\) | 28.3077 | 1.46375 | ||||||||
\(375\) | 2.72853 | 0.140901 | ||||||||
\(376\) | −4.78751 | −0.246897 | ||||||||
\(377\) | −41.2439 | −2.12417 | ||||||||
\(378\) | −3.52761 | −0.181441 | ||||||||
\(379\) | 3.02315 | 0.155289 | 0.0776444 | − | 0.996981i | \(-0.475260\pi\) | ||||
0.0776444 | + | 0.996981i | \(0.475260\pi\) | |||||||
\(380\) | −0.243411 | −0.0124867 | ||||||||
\(381\) | −28.6051 | −1.46548 | ||||||||
\(382\) | 25.9989 | 1.33022 | ||||||||
\(383\) | −7.86592 | −0.401930 | −0.200965 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200965 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(384\) | −2.72853 | −0.139240 | ||||||||
\(385\) | −4.50201 | −0.229444 | ||||||||
\(386\) | 22.5354 | 1.14702 | ||||||||
\(387\) | −14.2030 | −0.721980 | ||||||||
\(388\) | −1.78912 | −0.0908287 | ||||||||
\(389\) | −26.1360 | −1.32515 | −0.662575 | − | 0.748996i | \(-0.730536\pi\) | ||||
−0.662575 | + | 0.748996i | \(0.730536\pi\) | |||||||
\(390\) | 14.6195 | 0.740289 | ||||||||
\(391\) | 23.7296 | 1.20006 | ||||||||
\(392\) | 6.19934 | 0.313114 | ||||||||
\(393\) | 7.15962 | 0.361155 | ||||||||
\(394\) | 10.0738 | 0.507512 | ||||||||
\(395\) | 8.03826 | 0.404449 | ||||||||
\(396\) | −22.3635 | −1.12381 | ||||||||
\(397\) | 23.8038 | 1.19468 | 0.597340 | − | 0.801988i | \(-0.296224\pi\) | ||||
0.597340 | + | 0.801988i | \(0.296224\pi\) | |||||||
\(398\) | −20.8793 | −1.04658 | ||||||||
\(399\) | −0.594283 | −0.0297514 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −40.1290 | −2.00146 | ||||||||
\(403\) | −8.35190 | −0.416038 | ||||||||
\(404\) | −1.23617 | −0.0615016 | ||||||||
\(405\) | −2.57776 | −0.128090 | ||||||||
\(406\) | −6.88778 | −0.341835 | ||||||||
\(407\) | −50.3344 | −2.49498 | ||||||||
\(408\) | −15.3515 | −0.760013 | ||||||||
\(409\) | −16.5119 | −0.816462 | −0.408231 | − | 0.912879i | \(-0.633854\pi\) | ||||
−0.408231 | + | 0.912879i | \(0.633854\pi\) | |||||||
\(410\) | −3.18356 | −0.157225 | ||||||||
\(411\) | −13.1065 | −0.646494 | ||||||||
\(412\) | 8.59261 | 0.423327 | ||||||||
\(413\) | 6.58244 | 0.323901 | ||||||||
\(414\) | −18.7467 | −0.921352 | ||||||||
\(415\) | 17.4940 | 0.858748 | ||||||||
\(416\) | 5.35803 | 0.262699 | ||||||||
\(417\) | 8.05088 | 0.394253 | ||||||||
\(418\) | −1.22468 | −0.0599009 | ||||||||
\(419\) | 24.3281 | 1.18850 | 0.594252 | − | 0.804279i | \(-0.297448\pi\) | ||||
0.594252 | + | 0.804279i | \(0.297448\pi\) | |||||||
\(420\) | 2.44148 | 0.119132 | ||||||||
\(421\) | 23.2449 | 1.13289 | 0.566443 | − | 0.824101i | \(-0.308319\pi\) | ||||
0.566443 | + | 0.824101i | \(0.308319\pi\) | |||||||
\(422\) | −4.03377 | −0.196361 | ||||||||
\(423\) | 21.2798 | 1.03466 | ||||||||
\(424\) | 5.76361 | 0.279906 | ||||||||
\(425\) | 5.62630 | 0.272915 | ||||||||
\(426\) | 6.58862 | 0.319220 | ||||||||
\(427\) | 1.88892 | 0.0914115 | ||||||||
\(428\) | −12.3939 | −0.599080 | ||||||||
\(429\) | 73.5555 | 3.55129 | ||||||||
\(430\) | 3.19538 | 0.154095 | ||||||||
\(431\) | −10.0840 | −0.485728 | −0.242864 | − | 0.970060i | \(-0.578087\pi\) | ||||
−0.242864 | + | 0.970060i | \(0.578087\pi\) | |||||||
\(432\) | 3.94236 | 0.189677 | ||||||||
\(433\) | 8.81685 | 0.423711 | 0.211855 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211855 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(434\) | −1.39478 | −0.0669514 | ||||||||
\(435\) | 21.0031 | 1.00702 | ||||||||
\(436\) | −5.77545 | −0.276594 | ||||||||
\(437\) | −1.02661 | −0.0491096 | ||||||||
\(438\) | −28.4718 | −1.36044 | ||||||||
\(439\) | −25.9384 | −1.23797 | −0.618985 | − | 0.785403i | \(-0.712456\pi\) | ||||
−0.618985 | + | 0.785403i | \(0.712456\pi\) | |||||||
\(440\) | 5.03131 | 0.239858 | ||||||||
\(441\) | −27.5552 | −1.31215 | ||||||||
\(442\) | 30.1459 | 1.43389 | ||||||||
\(443\) | 18.3380 | 0.871266 | 0.435633 | − | 0.900124i | \(-0.356524\pi\) | ||||
0.435633 | + | 0.900124i | \(0.356524\pi\) | |||||||
\(444\) | 27.2968 | 1.29545 | ||||||||
\(445\) | 12.8682 | 0.610009 | ||||||||
\(446\) | −16.9664 | −0.803384 | ||||||||
\(447\) | −53.6297 | −2.53660 | ||||||||
\(448\) | 0.894798 | 0.0422752 | ||||||||
\(449\) | 20.7522 | 0.979358 | 0.489679 | − | 0.871903i | \(-0.337114\pi\) | ||||
0.489679 | + | 0.871903i | \(0.337114\pi\) | |||||||
\(450\) | −4.44487 | −0.209533 | ||||||||
\(451\) | −16.0175 | −0.754233 | ||||||||
\(452\) | −15.1123 | −0.710821 | ||||||||
\(453\) | 0.259882 | 0.0122103 | ||||||||
\(454\) | 20.1180 | 0.944183 | ||||||||
\(455\) | −4.79436 | −0.224763 | ||||||||
\(456\) | 0.664153 | 0.0311018 | ||||||||
\(457\) | −19.5612 | −0.915034 | −0.457517 | − | 0.889201i | \(-0.651261\pi\) | ||||
−0.457517 | + | 0.889201i | \(0.651261\pi\) | |||||||
\(458\) | 20.4312 | 0.954687 | ||||||||
\(459\) | 22.1809 | 1.03531 | ||||||||
\(460\) | 4.21762 | 0.196647 | ||||||||
\(461\) | 3.79984 | 0.176976 | 0.0884880 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884880 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(462\) | 12.2839 | 0.571497 | ||||||||
\(463\) | 2.45295 | 0.113998 | 0.0569990 | − | 0.998374i | \(-0.481847\pi\) | ||||
0.0569990 | + | 0.998374i | \(0.481847\pi\) | |||||||
\(464\) | 7.69759 | 0.357352 | ||||||||
\(465\) | 4.25313 | 0.197234 | ||||||||
\(466\) | 22.8310 | 1.05762 | ||||||||
\(467\) | 15.9542 | 0.738271 | 0.369135 | − | 0.929376i | \(-0.379654\pi\) | ||||
0.369135 | + | 0.929376i | \(0.379654\pi\) | |||||||
\(468\) | −23.8157 | −1.10088 | ||||||||
\(469\) | 13.1600 | 0.607672 | ||||||||
\(470\) | −4.78751 | −0.220831 | ||||||||
\(471\) | 41.5476 | 1.91441 | ||||||||
\(472\) | −7.35635 | −0.338603 | ||||||||
\(473\) | 16.0769 | 0.739219 | ||||||||
\(474\) | −21.9326 | −1.00740 | ||||||||
\(475\) | −0.243411 | −0.0111685 | ||||||||
\(476\) | 5.03440 | 0.230751 | ||||||||
\(477\) | −25.6185 | −1.17299 | ||||||||
\(478\) | 1.62500 | 0.0743258 | ||||||||
\(479\) | −19.3798 | −0.885485 | −0.442743 | − | 0.896649i | \(-0.645994\pi\) | ||||
−0.442743 | + | 0.896649i | \(0.645994\pi\) | |||||||
\(480\) | −2.72853 | −0.124540 | ||||||||
\(481\) | −53.6029 | −2.44408 | ||||||||
\(482\) | −0.464813 | −0.0211716 | ||||||||
\(483\) | 10.2972 | 0.468540 | ||||||||
\(484\) | 14.3141 | 0.650642 | ||||||||
\(485\) | −1.78912 | −0.0812397 | ||||||||
\(486\) | 18.8606 | 0.855533 | ||||||||
\(487\) | 37.3488 | 1.69244 | 0.846219 | − | 0.532836i | \(-0.178874\pi\) | ||||
0.846219 | + | 0.532836i | \(0.178874\pi\) | |||||||
\(488\) | −2.11101 | −0.0955608 | ||||||||
\(489\) | 15.8076 | 0.714845 | ||||||||
\(490\) | 6.19934 | 0.280057 | ||||||||
\(491\) | 4.55930 | 0.205759 | 0.102879 | − | 0.994694i | \(-0.467194\pi\) | ||||
0.102879 | + | 0.994694i | \(0.467194\pi\) | |||||||
\(492\) | 8.68642 | 0.391614 | ||||||||
\(493\) | 43.3089 | 1.95054 | ||||||||
\(494\) | −1.30420 | −0.0586789 | ||||||||
\(495\) | −22.3635 | −1.00517 | ||||||||
\(496\) | 1.55876 | 0.0699905 | ||||||||
\(497\) | −2.16068 | −0.0969199 | ||||||||
\(498\) | −47.7330 | −2.13897 | ||||||||
\(499\) | 22.5876 | 1.01116 | 0.505579 | − | 0.862780i | \(-0.331279\pi\) | ||||
0.505579 | + | 0.862780i | \(0.331279\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −18.0626 | −0.806976 | ||||||||
\(502\) | −19.7893 | −0.883241 | ||||||||
\(503\) | −32.2685 | −1.43878 | −0.719390 | − | 0.694606i | \(-0.755579\pi\) | ||||
−0.719390 | + | 0.694606i | \(0.755579\pi\) | |||||||
\(504\) | −3.97726 | −0.177161 | ||||||||
\(505\) | −1.23617 | −0.0550087 | ||||||||
\(506\) | 21.2202 | 0.943351 | ||||||||
\(507\) | 42.8611 | 1.90353 | ||||||||
\(508\) | −10.4837 | −0.465140 | ||||||||
\(509\) | 35.8416 | 1.58865 | 0.794326 | − | 0.607492i | \(-0.207824\pi\) | ||||
0.794326 | + | 0.607492i | \(0.207824\pi\) | |||||||
\(510\) | −15.3515 | −0.679776 | ||||||||
\(511\) | 9.33709 | 0.413049 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.959612 | −0.0423679 | ||||||||
\(514\) | 26.0631 | 1.14960 | ||||||||
\(515\) | 8.59261 | 0.378635 | ||||||||
\(516\) | −8.71868 | −0.383818 | ||||||||
\(517\) | −24.0874 | −1.05936 | ||||||||
\(518\) | −8.95175 | −0.393317 | ||||||||
\(519\) | 45.0675 | 1.97824 | ||||||||
\(520\) | 5.35803 | 0.234965 | ||||||||
\(521\) | 37.3168 | 1.63488 | 0.817440 | − | 0.576014i | \(-0.195393\pi\) | ||||
0.817440 | + | 0.576014i | \(0.195393\pi\) | |||||||
\(522\) | −34.2147 | −1.49754 | ||||||||
\(523\) | −19.1717 | −0.838321 | −0.419161 | − | 0.907912i | \(-0.637676\pi\) | ||||
−0.419161 | + | 0.907912i | \(0.637676\pi\) | |||||||
\(524\) | 2.62399 | 0.114629 | ||||||||
\(525\) | 2.44148 | 0.106555 | ||||||||
\(526\) | −4.82161 | −0.210232 | ||||||||
\(527\) | 8.77006 | 0.382030 | ||||||||
\(528\) | −13.7281 | −0.597438 | ||||||||
\(529\) | −5.21171 | −0.226596 | ||||||||
\(530\) | 5.76361 | 0.250355 | ||||||||
\(531\) | 32.6980 | 1.41897 | ||||||||
\(532\) | −0.217803 | −0.00944298 | ||||||||
\(533\) | −17.0576 | −0.738847 | ||||||||
\(534\) | −35.1111 | −1.51941 | ||||||||
\(535\) | −12.3939 | −0.535834 | ||||||||
\(536\) | −14.7072 | −0.635255 | ||||||||
\(537\) | −67.7357 | −2.92301 | ||||||||
\(538\) | −14.3547 | −0.618876 | ||||||||
\(539\) | 31.1908 | 1.34348 | ||||||||
\(540\) | 3.94236 | 0.169652 | ||||||||
\(541\) | −25.4853 | −1.09570 | −0.547849 | − | 0.836577i | \(-0.684553\pi\) | ||||
−0.547849 | + | 0.836577i | \(0.684553\pi\) | |||||||
\(542\) | 24.0039 | 1.03105 | ||||||||
\(543\) | −10.3868 | −0.445742 | ||||||||
\(544\) | −5.62630 | −0.241225 | ||||||||
\(545\) | −5.77545 | −0.247393 | ||||||||
\(546\) | 13.0815 | 0.559838 | ||||||||
\(547\) | 8.37489 | 0.358084 | 0.179042 | − | 0.983841i | \(-0.442700\pi\) | ||||
0.179042 | + | 0.983841i | \(0.442700\pi\) | |||||||
\(548\) | −4.80349 | −0.205195 | ||||||||
\(549\) | 9.38314 | 0.400463 | ||||||||
\(550\) | 5.03131 | 0.214536 | ||||||||
\(551\) | −1.87368 | −0.0798213 | ||||||||
\(552\) | −11.5079 | −0.489808 | ||||||||
\(553\) | 7.19262 | 0.305861 | ||||||||
\(554\) | 18.3925 | 0.781422 | ||||||||
\(555\) | 27.2968 | 1.15868 | ||||||||
\(556\) | 2.95063 | 0.125135 | ||||||||
\(557\) | −10.0136 | −0.424291 | −0.212145 | − | 0.977238i | \(-0.568045\pi\) | ||||
−0.212145 | + | 0.977238i | \(0.568045\pi\) | |||||||
\(558\) | −6.92849 | −0.293306 | ||||||||
\(559\) | 17.1209 | 0.724139 | ||||||||
\(560\) | 0.894798 | 0.0378121 | ||||||||
\(561\) | −77.2383 | −3.26100 | ||||||||
\(562\) | 12.0348 | 0.507658 | ||||||||
\(563\) | −29.9016 | −1.26020 | −0.630101 | − | 0.776513i | \(-0.716987\pi\) | ||||
−0.630101 | + | 0.776513i | \(0.716987\pi\) | |||||||
\(564\) | 13.0628 | 0.550045 | ||||||||
\(565\) | −15.1123 | −0.635777 | ||||||||
\(566\) | −29.3428 | −1.23337 | ||||||||
\(567\) | −2.30658 | −0.0968671 | ||||||||
\(568\) | 2.41472 | 0.101319 | ||||||||
\(569\) | 31.2502 | 1.31008 | 0.655039 | − | 0.755595i | \(-0.272652\pi\) | ||||
0.655039 | + | 0.755595i | \(0.272652\pi\) | |||||||
\(570\) | 0.664153 | 0.0278183 | ||||||||
\(571\) | −36.6838 | −1.53517 | −0.767585 | − | 0.640948i | \(-0.778542\pi\) | ||||
−0.767585 | + | 0.640948i | \(0.778542\pi\) | |||||||
\(572\) | 26.9579 | 1.12717 | ||||||||
\(573\) | −70.9387 | −2.96351 | ||||||||
\(574\) | −2.84864 | −0.118900 | ||||||||
\(575\) | 4.21762 | 0.175887 | ||||||||
\(576\) | 4.44487 | 0.185203 | ||||||||
\(577\) | 28.8918 | 1.20278 | 0.601391 | − | 0.798955i | \(-0.294613\pi\) | ||||
0.601391 | + | 0.798955i | \(0.294613\pi\) | |||||||
\(578\) | −14.6552 | −0.609576 | ||||||||
\(579\) | −61.4885 | −2.55537 | ||||||||
\(580\) | 7.69759 | 0.319625 | ||||||||
\(581\) | 15.6536 | 0.649422 | ||||||||
\(582\) | 4.88166 | 0.202351 | ||||||||
\(583\) | 28.9985 | 1.20100 | ||||||||
\(584\) | −10.4349 | −0.431798 | ||||||||
\(585\) | −23.8157 | −0.984660 | ||||||||
\(586\) | −3.78143 | −0.156209 | ||||||||
\(587\) | −16.4456 | −0.678784 | −0.339392 | − | 0.940645i | \(-0.610221\pi\) | ||||
−0.339392 | + | 0.940645i | \(0.610221\pi\) | |||||||
\(588\) | −16.9151 | −0.697566 | ||||||||
\(589\) | −0.379419 | −0.0156337 | ||||||||
\(590\) | −7.35635 | −0.302856 | ||||||||
\(591\) | −27.4867 | −1.13065 | ||||||||
\(592\) | 10.0042 | 0.411171 | ||||||||
\(593\) | 21.2403 | 0.872234 | 0.436117 | − | 0.899890i | \(-0.356353\pi\) | ||||
0.436117 | + | 0.899890i | \(0.356353\pi\) | |||||||
\(594\) | 19.8352 | 0.813850 | ||||||||
\(595\) | 5.03440 | 0.206390 | ||||||||
\(596\) | −19.6552 | −0.805108 | ||||||||
\(597\) | 56.9698 | 2.33162 | ||||||||
\(598\) | 22.5981 | 0.924106 | ||||||||
\(599\) | −0.763881 | −0.0312113 | −0.0156057 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156057 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(600\) | −2.72853 | −0.111392 | ||||||||
\(601\) | 16.2508 | 0.662884 | 0.331442 | − | 0.943476i | \(-0.392465\pi\) | ||||
0.331442 | + | 0.943476i | \(0.392465\pi\) | |||||||
\(602\) | 2.85922 | 0.116533 | ||||||||
\(603\) | 65.3716 | 2.66214 | ||||||||
\(604\) | 0.0952463 | 0.00387552 | ||||||||
\(605\) | 14.3141 | 0.581952 | ||||||||
\(606\) | 3.37292 | 0.137015 | ||||||||
\(607\) | −15.1357 | −0.614340 | −0.307170 | − | 0.951655i | \(-0.599382\pi\) | ||||
−0.307170 | + | 0.951655i | \(0.599382\pi\) | |||||||
\(608\) | 0.243411 | 0.00987161 | ||||||||
\(609\) | 18.7935 | 0.761552 | ||||||||
\(610\) | −2.11101 | −0.0854722 | ||||||||
\(611\) | −25.6516 | −1.03775 | ||||||||
\(612\) | 25.0081 | 1.01089 | ||||||||
\(613\) | −3.72696 | −0.150530 | −0.0752652 | − | 0.997164i | \(-0.523980\pi\) | ||||
−0.0752652 | + | 0.997164i | \(0.523980\pi\) | |||||||
\(614\) | −15.5960 | −0.629405 | ||||||||
\(615\) | 8.68642 | 0.350270 | ||||||||
\(616\) | 4.50201 | 0.181391 | ||||||||
\(617\) | −0.00373384 | −0.000150319 0 | −7.51593e−5 | − | 1.00000i | \(-0.500024\pi\) | ||||
−7.51593e−5 | 1.00000i | \(0.500024\pi\) | ||||||||
\(618\) | −23.4452 | −0.943103 | ||||||||
\(619\) | −1.15230 | −0.0463147 | −0.0231573 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231573 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(620\) | 1.55876 | 0.0626014 | ||||||||
\(621\) | 16.6274 | 0.667233 | ||||||||
\(622\) | 19.6206 | 0.786715 | ||||||||
\(623\) | 11.5144 | 0.461315 | ||||||||
\(624\) | −14.6195 | −0.585250 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.3404 | 0.892903 | ||||||||
\(627\) | 3.34156 | 0.133449 | ||||||||
\(628\) | 15.2271 | 0.607628 | ||||||||
\(629\) | 56.2867 | 2.24430 | ||||||||
\(630\) | −3.97726 | −0.158458 | ||||||||
\(631\) | 44.5712 | 1.77435 | 0.887176 | − | 0.461431i | \(-0.152664\pi\) | ||||
0.887176 | + | 0.461431i | \(0.152664\pi\) | |||||||
\(632\) | −8.03826 | −0.319745 | ||||||||
\(633\) | 11.0062 | 0.437459 | ||||||||
\(634\) | 21.4639 | 0.852438 | ||||||||
\(635\) | −10.4837 | −0.416034 | ||||||||
\(636\) | −15.7262 | −0.623584 | ||||||||
\(637\) | 33.2163 | 1.31608 | ||||||||
\(638\) | 38.7290 | 1.53329 | ||||||||
\(639\) | −10.7331 | −0.424594 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −7.59158 | −0.299849 | −0.149925 | − | 0.988697i | \(-0.547903\pi\) | ||||
−0.149925 | + | 0.988697i | \(0.547903\pi\) | |||||||
\(642\) | 33.8170 | 1.33465 | ||||||||
\(643\) | 35.9825 | 1.41901 | 0.709506 | − | 0.704699i | \(-0.248918\pi\) | ||||
0.709506 | + | 0.704699i | \(0.248918\pi\) | |||||||
\(644\) | 3.77391 | 0.148713 | ||||||||
\(645\) | −8.71868 | −0.343298 | ||||||||
\(646\) | 1.36950 | 0.0538823 | ||||||||
\(647\) | −22.9325 | −0.901570 | −0.450785 | − | 0.892633i | \(-0.648856\pi\) | ||||
−0.450785 | + | 0.892633i | \(0.648856\pi\) | |||||||
\(648\) | 2.57776 | 0.101264 | ||||||||
\(649\) | −37.0121 | −1.45285 | ||||||||
\(650\) | 5.35803 | 0.210159 | ||||||||
\(651\) | 3.80569 | 0.149157 | ||||||||
\(652\) | 5.79346 | 0.226889 | ||||||||
\(653\) | 3.88956 | 0.152210 | 0.0761051 | − | 0.997100i | \(-0.475752\pi\) | ||||
0.0761051 | + | 0.997100i | \(0.475752\pi\) | |||||||
\(654\) | 15.7585 | 0.616206 | ||||||||
\(655\) | 2.62399 | 0.102528 | ||||||||
\(656\) | 3.18356 | 0.124297 | ||||||||
\(657\) | 46.3815 | 1.80952 | ||||||||
\(658\) | −4.28385 | −0.167002 | ||||||||
\(659\) | 17.5907 | 0.685238 | 0.342619 | − | 0.939474i | \(-0.388686\pi\) | ||||
0.342619 | + | 0.939474i | \(0.388686\pi\) | |||||||
\(660\) | −13.7281 | −0.534365 | ||||||||
\(661\) | 29.5701 | 1.15015 | 0.575073 | − | 0.818102i | \(-0.304974\pi\) | ||||
0.575073 | + | 0.818102i | \(0.304974\pi\) | |||||||
\(662\) | −34.7309 | −1.34986 | ||||||||
\(663\) | −82.2539 | −3.19448 | ||||||||
\(664\) | −17.4940 | −0.678900 | ||||||||
\(665\) | −0.217803 | −0.00844605 | ||||||||
\(666\) | −44.4674 | −1.72308 | ||||||||
\(667\) | 32.4655 | 1.25707 | ||||||||
\(668\) | −6.61990 | −0.256132 | ||||||||
\(669\) | 46.2934 | 1.78981 | ||||||||
\(670\) | −14.7072 | −0.568189 | ||||||||
\(671\) | −10.6211 | −0.410024 | ||||||||
\(672\) | −2.44148 | −0.0941822 | ||||||||
\(673\) | −9.96166 | −0.383994 | −0.191997 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191997 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(674\) | −3.67354 | −0.141500 | ||||||||
\(675\) | 3.94236 | 0.151741 | ||||||||
\(676\) | 15.7085 | 0.604174 | ||||||||
\(677\) | 16.1733 | 0.621589 | 0.310794 | − | 0.950477i | \(-0.399405\pi\) | ||||
0.310794 | + | 0.950477i | \(0.399405\pi\) | |||||||
\(678\) | 41.2342 | 1.58359 | ||||||||
\(679\) | −1.60090 | −0.0614369 | ||||||||
\(680\) | −5.62630 | −0.215759 | ||||||||
\(681\) | −54.8924 | −2.10348 | ||||||||
\(682\) | 7.84262 | 0.300309 | ||||||||
\(683\) | 28.4972 | 1.09042 | 0.545208 | − | 0.838301i | \(-0.316451\pi\) | ||||
0.545208 | + | 0.838301i | \(0.316451\pi\) | |||||||
\(684\) | −1.08193 | −0.0413686 | ||||||||
\(685\) | −4.80349 | −0.183532 | ||||||||
\(686\) | 11.8107 | 0.450936 | ||||||||
\(687\) | −55.7471 | −2.12688 | ||||||||
\(688\) | −3.19538 | −0.121823 | ||||||||
\(689\) | 30.8816 | 1.17650 | ||||||||
\(690\) | −11.5079 | −0.438098 | ||||||||
\(691\) | 9.68828 | 0.368560 | 0.184280 | − | 0.982874i | \(-0.441005\pi\) | ||||
0.184280 | + | 0.982874i | \(0.441005\pi\) | |||||||
\(692\) | 16.5171 | 0.627888 | ||||||||
\(693\) | −20.0108 | −0.760149 | ||||||||
\(694\) | −2.85432 | −0.108349 | ||||||||
\(695\) | 2.95063 | 0.111924 | ||||||||
\(696\) | −21.0031 | −0.796120 | ||||||||
\(697\) | 17.9116 | 0.678451 | ||||||||
\(698\) | −29.4690 | −1.11542 | ||||||||
\(699\) | −62.2949 | −2.35621 | ||||||||
\(700\) | 0.894798 | 0.0338202 | ||||||||
\(701\) | 25.8560 | 0.976568 | 0.488284 | − | 0.872685i | \(-0.337623\pi\) | ||||
0.488284 | + | 0.872685i | \(0.337623\pi\) | |||||||
\(702\) | 21.1233 | 0.797247 | ||||||||
\(703\) | −2.43513 | −0.0918428 | ||||||||
\(704\) | −5.03131 | −0.189625 | ||||||||
\(705\) | 13.0628 | 0.491975 | ||||||||
\(706\) | −10.0491 | −0.378204 | ||||||||
\(707\) | −1.10612 | −0.0415999 | ||||||||
\(708\) | 20.0720 | 0.754352 | ||||||||
\(709\) | −1.29263 | −0.0485458 | −0.0242729 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242729 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(710\) | 2.41472 | 0.0906227 | ||||||||
\(711\) | 35.7290 | 1.33994 | ||||||||
\(712\) | −12.8682 | −0.482254 | ||||||||
\(713\) | 6.57426 | 0.246208 | ||||||||
\(714\) | −13.7365 | −0.514075 | ||||||||
\(715\) | 26.9579 | 1.00817 | ||||||||
\(716\) | −24.8250 | −0.927753 | ||||||||
\(717\) | −4.43386 | −0.165586 | ||||||||
\(718\) | 20.8179 | 0.776916 | ||||||||
\(719\) | 23.0518 | 0.859688 | 0.429844 | − | 0.902903i | \(-0.358568\pi\) | ||||
0.429844 | + | 0.902903i | \(0.358568\pi\) | |||||||
\(720\) | 4.44487 | 0.165650 | ||||||||
\(721\) | 7.68865 | 0.286340 | ||||||||
\(722\) | 18.9408 | 0.704902 | ||||||||
\(723\) | 1.26825 | 0.0471669 | ||||||||
\(724\) | −3.80676 | −0.141477 | ||||||||
\(725\) | 7.69759 | 0.285881 | ||||||||
\(726\) | −39.0565 | −1.44952 | ||||||||
\(727\) | −27.2377 | −1.01019 | −0.505094 | − | 0.863064i | \(-0.668542\pi\) | ||||
−0.505094 | + | 0.863064i | \(0.668542\pi\) | |||||||
\(728\) | 4.79436 | 0.177691 | ||||||||
\(729\) | −43.7283 | −1.61957 | ||||||||
\(730\) | −10.4349 | −0.386211 | ||||||||
\(731\) | −17.9781 | −0.664946 | ||||||||
\(732\) | 5.75994 | 0.212894 | ||||||||
\(733\) | 6.86877 | 0.253704 | 0.126852 | − | 0.991922i | \(-0.459513\pi\) | ||||
0.126852 | + | 0.991922i | \(0.459513\pi\) | |||||||
\(734\) | 31.4818 | 1.16201 | ||||||||
\(735\) | −16.9151 | −0.623922 | ||||||||
\(736\) | −4.21762 | −0.155463 | ||||||||
\(737\) | −73.9966 | −2.72570 | ||||||||
\(738\) | −14.1505 | −0.520886 | ||||||||
\(739\) | 25.7942 | 0.948854 | 0.474427 | − | 0.880295i | \(-0.342655\pi\) | ||||
0.474427 | + | 0.880295i | \(0.342655\pi\) | |||||||
\(740\) | 10.0042 | 0.367762 | ||||||||
\(741\) | 3.55855 | 0.130727 | ||||||||
\(742\) | 5.15727 | 0.189329 | ||||||||
\(743\) | −6.59485 | −0.241942 | −0.120971 | − | 0.992656i | \(-0.538601\pi\) | ||||
−0.120971 | + | 0.992656i | \(0.538601\pi\) | |||||||
\(744\) | −4.25313 | −0.155927 | ||||||||
\(745\) | −19.6552 | −0.720110 | ||||||||
\(746\) | 18.8122 | 0.688763 | ||||||||
\(747\) | 77.7586 | 2.84504 | ||||||||
\(748\) | −28.3077 | −1.03503 | ||||||||
\(749\) | −11.0900 | −0.405220 | ||||||||
\(750\) | −2.72853 | −0.0996318 | ||||||||
\(751\) | −21.0220 | −0.767103 | −0.383552 | − | 0.923519i | \(-0.625299\pi\) | ||||
−0.383552 | + | 0.923519i | \(0.625299\pi\) | |||||||
\(752\) | 4.78751 | 0.174582 | ||||||||
\(753\) | 53.9958 | 1.96772 | ||||||||
\(754\) | 41.2439 | 1.50202 | ||||||||
\(755\) | 0.0952463 | 0.00346637 | ||||||||
\(756\) | 3.52761 | 0.128298 | ||||||||
\(757\) | −9.18875 | −0.333971 | −0.166985 | − | 0.985959i | \(-0.553403\pi\) | ||||
−0.166985 | + | 0.985959i | \(0.553403\pi\) | |||||||
\(758\) | −3.02315 | −0.109806 | ||||||||
\(759\) | −57.8998 | −2.10163 | ||||||||
\(760\) | 0.243411 | 0.00882944 | ||||||||
\(761\) | 29.3852 | 1.06521 | 0.532606 | − | 0.846363i | \(-0.321213\pi\) | ||||
0.532606 | + | 0.846363i | \(0.321213\pi\) | |||||||
\(762\) | 28.6051 | 1.03625 | ||||||||
\(763\) | −5.16786 | −0.187089 | ||||||||
\(764\) | −25.9989 | −0.940606 | ||||||||
\(765\) | 25.0081 | 0.904171 | ||||||||
\(766\) | 7.86592 | 0.284207 | ||||||||
\(767\) | −39.4156 | −1.42321 | ||||||||
\(768\) | 2.72853 | 0.0984573 | ||||||||
\(769\) | 32.8609 | 1.18499 | 0.592497 | − | 0.805572i | \(-0.298142\pi\) | ||||
0.592497 | + | 0.805572i | \(0.298142\pi\) | |||||||
\(770\) | 4.50201 | 0.162241 | ||||||||
\(771\) | −71.1140 | −2.56111 | ||||||||
\(772\) | −22.5354 | −0.811067 | ||||||||
\(773\) | −29.4283 | −1.05846 | −0.529231 | − | 0.848478i | \(-0.677519\pi\) | ||||
−0.529231 | + | 0.848478i | \(0.677519\pi\) | |||||||
\(774\) | 14.2030 | 0.510517 | ||||||||
\(775\) | 1.55876 | 0.0559924 | ||||||||
\(776\) | 1.78912 | 0.0642256 | ||||||||
\(777\) | 24.4251 | 0.876246 | ||||||||
\(778\) | 26.1360 | 0.937022 | ||||||||
\(779\) | −0.774912 | −0.0277641 | ||||||||
\(780\) | −14.6195 | −0.523464 | ||||||||
\(781\) | 12.1492 | 0.434732 | ||||||||
\(782\) | −23.7296 | −0.848567 | ||||||||
\(783\) | 30.3466 | 1.08450 | ||||||||
\(784\) | −6.19934 | −0.221405 | ||||||||
\(785\) | 15.2271 | 0.543479 | ||||||||
\(786\) | −7.15962 | −0.255375 | ||||||||
\(787\) | 3.57112 | 0.127297 | 0.0636484 | − | 0.997972i | \(-0.479726\pi\) | ||||
0.0636484 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(788\) | −10.0738 | −0.358865 | ||||||||
\(789\) | 13.1559 | 0.468363 | ||||||||
\(790\) | −8.03826 | −0.285988 | ||||||||
\(791\) | −13.5224 | −0.480802 | ||||||||
\(792\) | 22.3635 | 0.794653 | ||||||||
\(793\) | −11.3108 | −0.401660 | ||||||||
\(794\) | −23.8038 | −0.844766 | ||||||||
\(795\) | −15.7262 | −0.557750 | ||||||||
\(796\) | 20.8793 | 0.740047 | ||||||||
\(797\) | 17.8650 | 0.632810 | 0.316405 | − | 0.948624i | \(-0.397524\pi\) | ||||
0.316405 | + | 0.948624i | \(0.397524\pi\) | |||||||
\(798\) | 0.594283 | 0.0210374 | ||||||||
\(799\) | 26.9359 | 0.952924 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 57.1972 | 2.02096 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −52.5010 | −1.85272 | ||||||||
\(804\) | 40.1290 | 1.41524 | ||||||||
\(805\) | 3.77391 | 0.133013 | ||||||||
\(806\) | 8.35190 | 0.294183 | ||||||||
\(807\) | 39.1673 | 1.37875 | ||||||||
\(808\) | 1.23617 | 0.0434882 | ||||||||
\(809\) | 11.4972 | 0.404222 | 0.202111 | − | 0.979363i | \(-0.435220\pi\) | ||||
0.202111 | + | 0.979363i | \(0.435220\pi\) | |||||||
\(810\) | 2.57776 | 0.0905733 | ||||||||
\(811\) | 47.1499 | 1.65566 | 0.827829 | − | 0.560981i | \(-0.189576\pi\) | ||||
0.827829 | + | 0.560981i | \(0.189576\pi\) | |||||||
\(812\) | 6.88778 | 0.241714 | ||||||||
\(813\) | −65.4952 | −2.29702 | ||||||||
\(814\) | 50.3344 | 1.76422 | ||||||||
\(815\) | 5.79346 | 0.202936 | ||||||||
\(816\) | 15.3515 | 0.537410 | ||||||||
\(817\) | 0.777789 | 0.0272114 | ||||||||
\(818\) | 16.5119 | 0.577326 | ||||||||
\(819\) | −21.3103 | −0.744641 | ||||||||
\(820\) | 3.18356 | 0.111175 | ||||||||
\(821\) | 43.4740 | 1.51725 | 0.758627 | − | 0.651525i | \(-0.225871\pi\) | ||||
0.758627 | + | 0.651525i | \(0.225871\pi\) | |||||||
\(822\) | 13.1065 | 0.457140 | ||||||||
\(823\) | −34.8654 | −1.21533 | −0.607666 | − | 0.794193i | \(-0.707894\pi\) | ||||
−0.607666 | + | 0.794193i | \(0.707894\pi\) | |||||||
\(824\) | −8.59261 | −0.299338 | ||||||||
\(825\) | −13.7281 | −0.477950 | ||||||||
\(826\) | −6.58244 | −0.229033 | ||||||||
\(827\) | −46.6846 | −1.62338 | −0.811692 | − | 0.584086i | \(-0.801453\pi\) | ||||
−0.811692 | + | 0.584086i | \(0.801453\pi\) | |||||||
\(828\) | 18.7467 | 0.651494 | ||||||||
\(829\) | −5.34913 | −0.185783 | −0.0928915 | − | 0.995676i | \(-0.529611\pi\) | ||||
−0.0928915 | + | 0.995676i | \(0.529611\pi\) | |||||||
\(830\) | −17.4940 | −0.607227 | ||||||||
\(831\) | −50.1844 | −1.74088 | ||||||||
\(832\) | −5.35803 | −0.185756 | ||||||||
\(833\) | −34.8793 | −1.20850 | ||||||||
\(834\) | −8.05088 | −0.278779 | ||||||||
\(835\) | −6.61990 | −0.229091 | ||||||||
\(836\) | 1.22468 | 0.0423563 | ||||||||
\(837\) | 6.14520 | 0.212409 | ||||||||
\(838\) | −24.3281 | −0.840399 | ||||||||
\(839\) | −37.2921 | −1.28747 | −0.643733 | − | 0.765250i | \(-0.722615\pi\) | ||||
−0.643733 | + | 0.765250i | \(0.722615\pi\) | |||||||
\(840\) | −2.44148 | −0.0842391 | ||||||||
\(841\) | 30.2529 | 1.04320 | ||||||||
\(842\) | −23.2449 | −0.801072 | ||||||||
\(843\) | −32.8374 | −1.13098 | ||||||||
\(844\) | 4.03377 | 0.138848 | ||||||||
\(845\) | 15.7085 | 0.540390 | ||||||||
\(846\) | −21.2798 | −0.731615 | ||||||||
\(847\) | 12.8082 | 0.440097 | ||||||||
\(848\) | −5.76361 | −0.197923 | ||||||||
\(849\) | 80.0627 | 2.74774 | ||||||||
\(850\) | −5.62630 | −0.192980 | ||||||||
\(851\) | 42.1940 | 1.44639 | ||||||||
\(852\) | −6.58862 | −0.225722 | ||||||||
\(853\) | 4.77536 | 0.163505 | 0.0817526 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817526 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(854\) | −1.88892 | −0.0646377 | ||||||||
\(855\) | −1.08193 | −0.0370012 | ||||||||
\(856\) | 12.3939 | 0.423614 | ||||||||
\(857\) | −48.4486 | −1.65497 | −0.827486 | − | 0.561486i | \(-0.810230\pi\) | ||||
−0.827486 | + | 0.561486i | \(0.810230\pi\) | |||||||
\(858\) | −73.5555 | −2.51114 | ||||||||
\(859\) | 51.4333 | 1.75488 | 0.877441 | − | 0.479684i | \(-0.159249\pi\) | ||||
0.877441 | + | 0.479684i | \(0.159249\pi\) | |||||||
\(860\) | −3.19538 | −0.108961 | ||||||||
\(861\) | 7.77259 | 0.264889 | ||||||||
\(862\) | 10.0840 | 0.343462 | ||||||||
\(863\) | −2.60248 | −0.0885896 | −0.0442948 | − | 0.999019i | \(-0.514104\pi\) | ||||
−0.0442948 | + | 0.999019i | \(0.514104\pi\) | |||||||
\(864\) | −3.94236 | −0.134122 | ||||||||
\(865\) | 16.5171 | 0.561600 | ||||||||
\(866\) | −8.81685 | −0.299609 | ||||||||
\(867\) | 39.9871 | 1.35803 | ||||||||
\(868\) | 1.39478 | 0.0473418 | ||||||||
\(869\) | −40.4430 | −1.37194 | ||||||||
\(870\) | −21.0031 | −0.712071 | ||||||||
\(871\) | −78.8017 | −2.67010 | ||||||||
\(872\) | 5.77545 | 0.195582 | ||||||||
\(873\) | −7.95239 | −0.269148 | ||||||||
\(874\) | 1.02661 | 0.0347257 | ||||||||
\(875\) | 0.894798 | 0.0302497 | ||||||||
\(876\) | 28.4718 | 0.961973 | ||||||||
\(877\) | −39.3222 | −1.32782 | −0.663908 | − | 0.747814i | \(-0.731103\pi\) | ||||
−0.663908 | + | 0.747814i | \(0.731103\pi\) | |||||||
\(878\) | 25.9384 | 0.875377 | ||||||||
\(879\) | 10.3177 | 0.348008 | ||||||||
\(880\) | −5.03131 | −0.169606 | ||||||||
\(881\) | 29.4359 | 0.991722 | 0.495861 | − | 0.868402i | \(-0.334853\pi\) | ||||
0.495861 | + | 0.868402i | \(0.334853\pi\) | |||||||
\(882\) | 27.5552 | 0.927833 | ||||||||
\(883\) | 43.6761 | 1.46982 | 0.734909 | − | 0.678166i | \(-0.237225\pi\) | ||||
0.734909 | + | 0.678166i | \(0.237225\pi\) | |||||||
\(884\) | −30.1459 | −1.01392 | ||||||||
\(885\) | 20.0720 | 0.674713 | ||||||||
\(886\) | −18.3380 | −0.616078 | ||||||||
\(887\) | 14.1872 | 0.476359 | 0.238180 | − | 0.971221i | \(-0.423449\pi\) | ||||
0.238180 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(888\) | −27.2968 | −0.916020 | ||||||||
\(889\) | −9.38081 | −0.314622 | ||||||||
\(890\) | −12.8682 | −0.431342 | ||||||||
\(891\) | 12.9695 | 0.434496 | ||||||||
\(892\) | 16.9664 | 0.568078 | ||||||||
\(893\) | −1.16533 | −0.0389963 | ||||||||
\(894\) | 53.6297 | 1.79365 | ||||||||
\(895\) | −24.8250 | −0.829808 | ||||||||
\(896\) | −0.894798 | −0.0298931 | ||||||||
\(897\) | −61.6596 | −2.05876 | ||||||||
\(898\) | −20.7522 | −0.692511 | ||||||||
\(899\) | 11.9987 | 0.400179 | ||||||||
\(900\) | 4.44487 | 0.148162 | ||||||||
\(901\) | −32.4278 | −1.08033 | ||||||||
\(902\) | 16.0175 | 0.533324 | ||||||||
\(903\) | −7.80145 | −0.259616 | ||||||||
\(904\) | 15.1123 | 0.502626 | ||||||||
\(905\) | −3.80676 | −0.126541 | ||||||||
\(906\) | −0.259882 | −0.00863401 | ||||||||
\(907\) | −12.5778 | −0.417639 | −0.208820 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208820 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(908\) | −20.1180 | −0.667638 | ||||||||
\(909\) | −5.49460 | −0.182244 | ||||||||
\(910\) | 4.79436 | 0.158931 | ||||||||
\(911\) | −21.2296 | −0.703368 | −0.351684 | − | 0.936119i | \(-0.614391\pi\) | ||||
−0.351684 | + | 0.936119i | \(0.614391\pi\) | |||||||
\(912\) | −0.664153 | −0.0219923 | ||||||||
\(913\) | −88.0180 | −2.91297 | ||||||||
\(914\) | 19.5612 | 0.647027 | ||||||||
\(915\) | 5.75994 | 0.190418 | ||||||||
\(916\) | −20.4312 | −0.675066 | ||||||||
\(917\) | 2.34794 | 0.0775357 | ||||||||
\(918\) | −22.1809 | −0.732078 | ||||||||
\(919\) | −27.0226 | −0.891394 | −0.445697 | − | 0.895184i | \(-0.647044\pi\) | ||||
−0.445697 | + | 0.895184i | \(0.647044\pi\) | |||||||
\(920\) | −4.21762 | −0.139051 | ||||||||
\(921\) | 42.5542 | 1.40221 | ||||||||
\(922\) | −3.79984 | −0.125141 | ||||||||
\(923\) | 12.9381 | 0.425864 | ||||||||
\(924\) | −12.2839 | −0.404109 | ||||||||
\(925\) | 10.0042 | 0.328937 | ||||||||
\(926\) | −2.45295 | −0.0806088 | ||||||||
\(927\) | 38.1930 | 1.25442 | ||||||||
\(928\) | −7.69759 | −0.252686 | ||||||||
\(929\) | −52.2035 | −1.71274 | −0.856370 | − | 0.516363i | \(-0.827286\pi\) | ||||
−0.856370 | + | 0.516363i | \(0.827286\pi\) | |||||||
\(930\) | −4.25313 | −0.139465 | ||||||||
\(931\) | 1.50899 | 0.0494550 | ||||||||
\(932\) | −22.8310 | −0.747853 | ||||||||
\(933\) | −53.5354 | −1.75267 | ||||||||
\(934\) | −15.9542 | −0.522036 | ||||||||
\(935\) | −28.3077 | −0.925760 | ||||||||
\(936\) | 23.8157 | 0.778442 | ||||||||
\(937\) | −32.6730 | −1.06738 | −0.533690 | − | 0.845680i | \(-0.679195\pi\) | ||||
−0.533690 | + | 0.845680i | \(0.679195\pi\) | |||||||
\(938\) | −13.1600 | −0.429689 | ||||||||
\(939\) | −60.9565 | −1.98924 | ||||||||
\(940\) | 4.78751 | 0.156151 | ||||||||
\(941\) | 24.2253 | 0.789723 | 0.394862 | − | 0.918741i | \(-0.370793\pi\) | ||||
0.394862 | + | 0.918741i | \(0.370793\pi\) | |||||||
\(942\) | −41.5476 | −1.35369 | ||||||||
\(943\) | 13.4270 | 0.437244 | ||||||||
\(944\) | 7.35635 | 0.239429 | ||||||||
\(945\) | 3.52761 | 0.114753 | ||||||||
\(946\) | −16.0769 | −0.522707 | ||||||||
\(947\) | 1.20884 | 0.0392820 | 0.0196410 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196410 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(948\) | 21.9326 | 0.712338 | ||||||||
\(949\) | −55.9103 | −1.81493 | ||||||||
\(950\) | 0.243411 | 0.00789729 | ||||||||
\(951\) | −58.5647 | −1.89909 | ||||||||
\(952\) | −5.03440 | −0.163166 | ||||||||
\(953\) | −32.3480 | −1.04785 | −0.523927 | − | 0.851763i | \(-0.675533\pi\) | ||||
−0.523927 | + | 0.851763i | \(0.675533\pi\) | |||||||
\(954\) | 25.6185 | 0.829429 | ||||||||
\(955\) | −25.9989 | −0.841304 | ||||||||
\(956\) | −1.62500 | −0.0525563 | ||||||||
\(957\) | −105.673 | −3.41593 | ||||||||
\(958\) | 19.3798 | 0.626133 | ||||||||
\(959\) | −4.29815 | −0.138795 | ||||||||
\(960\) | 2.72853 | 0.0880629 | ||||||||
\(961\) | −28.5703 | −0.921621 | ||||||||
\(962\) | 53.6029 | 1.72823 | ||||||||
\(963\) | −55.0891 | −1.77522 | ||||||||
\(964\) | 0.464813 | 0.0149706 | ||||||||
\(965\) | −22.5354 | −0.725440 | ||||||||
\(966\) | −10.2972 | −0.331308 | ||||||||
\(967\) | −35.7776 | −1.15053 | −0.575265 | − | 0.817967i | \(-0.695101\pi\) | ||||
−0.575265 | + | 0.817967i | \(0.695101\pi\) | |||||||
\(968\) | −14.3141 | −0.460073 | ||||||||
\(969\) | −3.73672 | −0.120041 | ||||||||
\(970\) | 1.78912 | 0.0574451 | ||||||||
\(971\) | −4.46037 | −0.143140 | −0.0715700 | − | 0.997436i | \(-0.522801\pi\) | ||||
−0.0715700 | + | 0.997436i | \(0.522801\pi\) | |||||||
\(972\) | −18.8606 | −0.604953 | ||||||||
\(973\) | 2.64022 | 0.0846415 | ||||||||
\(974\) | −37.3488 | −1.19673 | ||||||||
\(975\) | −14.6195 | −0.468200 | ||||||||
\(976\) | 2.11101 | 0.0675717 | ||||||||
\(977\) | −40.5221 | −1.29642 | −0.648208 | − | 0.761463i | \(-0.724481\pi\) | ||||
−0.648208 | + | 0.761463i | \(0.724481\pi\) | |||||||
\(978\) | −15.8076 | −0.505472 | ||||||||
\(979\) | −64.7437 | −2.06922 | ||||||||
\(980\) | −6.19934 | −0.198031 | ||||||||
\(981\) | −25.6711 | −0.819616 | ||||||||
\(982\) | −4.55930 | −0.145493 | ||||||||
\(983\) | −20.0733 | −0.640238 | −0.320119 | − | 0.947377i | \(-0.603723\pi\) | ||||
−0.320119 | + | 0.947377i | \(0.603723\pi\) | |||||||
\(984\) | −8.68642 | −0.276913 | ||||||||
\(985\) | −10.0738 | −0.320979 | ||||||||
\(986\) | −43.3089 | −1.37924 | ||||||||
\(987\) | 11.6886 | 0.372052 | ||||||||
\(988\) | 1.30420 | 0.0414922 | ||||||||
\(989\) | −13.4769 | −0.428540 | ||||||||
\(990\) | 22.3635 | 0.710759 | ||||||||
\(991\) | 54.2591 | 1.72360 | 0.861799 | − | 0.507251i | \(-0.169338\pi\) | ||||
0.861799 | + | 0.507251i | \(0.169338\pi\) | |||||||
\(992\) | −1.55876 | −0.0494907 | ||||||||
\(993\) | 94.7643 | 3.00725 | ||||||||
\(994\) | 2.16068 | 0.0685327 | ||||||||
\(995\) | 20.8793 | 0.661918 | ||||||||
\(996\) | 47.7330 | 1.51248 | ||||||||
\(997\) | −3.22505 | −0.102138 | −0.0510692 | − | 0.998695i | \(-0.516263\pi\) | ||||
−0.0510692 | + | 0.998695i | \(0.516263\pi\) | |||||||
\(998\) | −22.5876 | −0.714997 | ||||||||
\(999\) | 39.4402 | 1.24783 |
(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 | 4010.2.a.m.1.18 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.18 | ✓ | 20 | 1.1 | even | 1 | trivial |