Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} - 640 x^{4} + 274 x^{3} + 256 x^{2} - 74 x - 35 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.31287\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31287 | 0.928340 | 0.464170 | − | 0.885746i | \(-0.346353\pi\) | ||||
0.464170 | + | 0.885746i | \(0.346353\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.276371 | −0.138186 | ||||||||
\(5\) | −3.61438 | −1.61640 | −0.808200 | − | 0.588909i | \(-0.799558\pi\) | ||||
−0.808200 | + | 0.588909i | \(0.799558\pi\) | |||||||
\(6\) | 1.31287 | 0.535977 | ||||||||
\(7\) | −0.837447 | −0.316525 | −0.158263 | − | 0.987397i | \(-0.550589\pi\) | ||||
−0.158263 | + | 0.987397i | \(0.550589\pi\) | |||||||
\(8\) | −2.98858 | −1.05662 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.74521 | −1.50057 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.276371 | −0.0797815 | ||||||||
\(13\) | 1.11084 | 0.308093 | 0.154046 | − | 0.988064i | \(-0.450769\pi\) | ||||
0.154046 | + | 0.988064i | \(0.450769\pi\) | |||||||
\(14\) | −1.09946 | −0.293843 | ||||||||
\(15\) | −3.61438 | −0.933229 | ||||||||
\(16\) | −3.37088 | −0.842719 | ||||||||
\(17\) | 4.37994 | 1.06229 | 0.531146 | − | 0.847280i | \(-0.321762\pi\) | ||||
0.531146 | + | 0.847280i | \(0.321762\pi\) | |||||||
\(18\) | 1.31287 | 0.309447 | ||||||||
\(19\) | 3.54367 | 0.812973 | 0.406486 | − | 0.913657i | \(-0.366754\pi\) | ||||
0.406486 | + | 0.913657i | \(0.366754\pi\) | |||||||
\(20\) | 0.998910 | 0.223363 | ||||||||
\(21\) | −0.837447 | −0.182746 | ||||||||
\(22\) | 1.31287 | 0.279905 | ||||||||
\(23\) | 4.06422 | 0.847449 | 0.423724 | − | 0.905791i | \(-0.360722\pi\) | ||||
0.423724 | + | 0.905791i | \(0.360722\pi\) | |||||||
\(24\) | −2.98858 | −0.610041 | ||||||||
\(25\) | 8.06373 | 1.61275 | ||||||||
\(26\) | 1.45840 | 0.286015 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.231446 | 0.0437392 | ||||||||
\(29\) | −1.67338 | −0.310740 | −0.155370 | − | 0.987856i | \(-0.549657\pi\) | ||||
−0.155370 | + | 0.987856i | \(0.549657\pi\) | |||||||
\(30\) | −4.74521 | −0.866353 | ||||||||
\(31\) | −2.81104 | −0.504879 | −0.252439 | − | 0.967613i | \(-0.581233\pi\) | ||||
−0.252439 | + | 0.967613i | \(0.581233\pi\) | |||||||
\(32\) | 1.55164 | 0.274293 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 5.75030 | 0.986168 | ||||||||
\(35\) | 3.02685 | 0.511631 | ||||||||
\(36\) | −0.276371 | −0.0460619 | ||||||||
\(37\) | 1.86448 | 0.306519 | 0.153259 | − | 0.988186i | \(-0.451023\pi\) | ||||
0.153259 | + | 0.988186i | \(0.451023\pi\) | |||||||
\(38\) | 4.65237 | 0.754715 | ||||||||
\(39\) | 1.11084 | 0.177878 | ||||||||
\(40\) | 10.8019 | 1.70792 | ||||||||
\(41\) | 8.79562 | 1.37365 | 0.686823 | − | 0.726825i | \(-0.259005\pi\) | ||||
0.686823 | + | 0.726825i | \(0.259005\pi\) | |||||||
\(42\) | −1.09946 | −0.169650 | ||||||||
\(43\) | −0.247282 | −0.0377102 | −0.0188551 | − | 0.999822i | \(-0.506002\pi\) | ||||
−0.0188551 | + | 0.999822i | \(0.506002\pi\) | |||||||
\(44\) | −0.276371 | −0.0416645 | ||||||||
\(45\) | −3.61438 | −0.538800 | ||||||||
\(46\) | 5.33580 | 0.786720 | ||||||||
\(47\) | 7.35580 | 1.07295 | 0.536477 | − | 0.843915i | \(-0.319755\pi\) | ||||
0.536477 | + | 0.843915i | \(0.319755\pi\) | |||||||
\(48\) | −3.37088 | −0.486544 | ||||||||
\(49\) | −6.29868 | −0.899812 | ||||||||
\(50\) | 10.5866 | 1.49718 | ||||||||
\(51\) | 4.37994 | 0.613315 | ||||||||
\(52\) | −0.307006 | −0.0425740 | ||||||||
\(53\) | 2.90217 | 0.398644 | 0.199322 | − | 0.979934i | \(-0.436126\pi\) | ||||
0.199322 | + | 0.979934i | \(0.436126\pi\) | |||||||
\(54\) | 1.31287 | 0.178659 | ||||||||
\(55\) | −3.61438 | −0.487363 | ||||||||
\(56\) | 2.50278 | 0.334448 | ||||||||
\(57\) | 3.54367 | 0.469370 | ||||||||
\(58\) | −2.19694 | −0.288472 | ||||||||
\(59\) | −0.446773 | −0.0581649 | −0.0290825 | − | 0.999577i | \(-0.509259\pi\) | ||||
−0.0290825 | + | 0.999577i | \(0.509259\pi\) | |||||||
\(60\) | 0.998910 | 0.128959 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −3.69054 | −0.468699 | ||||||||
\(63\) | −0.837447 | −0.105508 | ||||||||
\(64\) | 8.77885 | 1.09736 | ||||||||
\(65\) | −4.01501 | −0.498001 | ||||||||
\(66\) | 1.31287 | 0.161603 | ||||||||
\(67\) | 13.5843 | 1.65959 | 0.829795 | − | 0.558069i | \(-0.188457\pi\) | ||||
0.829795 | + | 0.558069i | \(0.188457\pi\) | |||||||
\(68\) | −1.21049 | −0.146794 | ||||||||
\(69\) | 4.06422 | 0.489275 | ||||||||
\(70\) | 3.97386 | 0.474967 | ||||||||
\(71\) | 2.92885 | 0.347591 | 0.173795 | − | 0.984782i | \(-0.444397\pi\) | ||||
0.173795 | + | 0.984782i | \(0.444397\pi\) | |||||||
\(72\) | −2.98858 | −0.352208 | ||||||||
\(73\) | −3.22502 | −0.377460 | −0.188730 | − | 0.982029i | \(-0.560437\pi\) | ||||
−0.188730 | + | 0.982029i | \(0.560437\pi\) | |||||||
\(74\) | 2.44782 | 0.284554 | ||||||||
\(75\) | 8.06373 | 0.931120 | ||||||||
\(76\) | −0.979367 | −0.112341 | ||||||||
\(77\) | −0.837447 | −0.0954359 | ||||||||
\(78\) | 1.45840 | 0.165131 | ||||||||
\(79\) | −1.75929 | −0.197936 | −0.0989679 | − | 0.995091i | \(-0.531554\pi\) | ||||
−0.0989679 | + | 0.995091i | \(0.531554\pi\) | |||||||
\(80\) | 12.1836 | 1.36217 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5475 | 1.27521 | ||||||||
\(83\) | 0.319558 | 0.0350761 | 0.0175380 | − | 0.999846i | \(-0.494417\pi\) | ||||
0.0175380 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(84\) | 0.231446 | 0.0252529 | ||||||||
\(85\) | −15.8308 | −1.71709 | ||||||||
\(86\) | −0.324650 | −0.0350079 | ||||||||
\(87\) | −1.67338 | −0.179406 | ||||||||
\(88\) | −2.98858 | −0.318584 | ||||||||
\(89\) | 15.7237 | 1.66671 | 0.833356 | − | 0.552737i | \(-0.186417\pi\) | ||||
0.833356 | + | 0.552737i | \(0.186417\pi\) | |||||||
\(90\) | −4.74521 | −0.500189 | ||||||||
\(91\) | −0.930274 | −0.0975192 | ||||||||
\(92\) | −1.12323 | −0.117105 | ||||||||
\(93\) | −2.81104 | −0.291492 | ||||||||
\(94\) | 9.65721 | 0.996065 | ||||||||
\(95\) | −12.8081 | −1.31409 | ||||||||
\(96\) | 1.55164 | 0.158363 | ||||||||
\(97\) | −7.75619 | −0.787521 | −0.393761 | − | 0.919213i | \(-0.628826\pi\) | ||||
−0.393761 | + | 0.919213i | \(0.628826\pi\) | |||||||
\(98\) | −8.26935 | −0.835331 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.22858 | −0.222858 | ||||||||
\(101\) | 0.542833 | 0.0540139 | 0.0270069 | − | 0.999635i | \(-0.491402\pi\) | ||||
0.0270069 | + | 0.999635i | \(0.491402\pi\) | |||||||
\(102\) | 5.75030 | 0.569364 | ||||||||
\(103\) | −18.9963 | −1.87176 | −0.935878 | − | 0.352323i | \(-0.885392\pi\) | ||||
−0.935878 | + | 0.352323i | \(0.885392\pi\) | |||||||
\(104\) | −3.31985 | −0.325538 | ||||||||
\(105\) | 3.02685 | 0.295390 | ||||||||
\(106\) | 3.81017 | 0.370077 | ||||||||
\(107\) | 1.11430 | 0.107724 | 0.0538619 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538619 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(108\) | −0.276371 | −0.0265938 | ||||||||
\(109\) | −7.68359 | −0.735954 | −0.367977 | − | 0.929835i | \(-0.619950\pi\) | ||||
−0.367977 | + | 0.929835i | \(0.619950\pi\) | |||||||
\(110\) | −4.74521 | −0.452438 | ||||||||
\(111\) | 1.86448 | 0.176969 | ||||||||
\(112\) | 2.82293 | 0.266742 | ||||||||
\(113\) | 13.4812 | 1.26821 | 0.634103 | − | 0.773249i | \(-0.281370\pi\) | ||||
0.634103 | + | 0.773249i | \(0.281370\pi\) | |||||||
\(114\) | 4.65237 | 0.435735 | ||||||||
\(115\) | −14.6896 | −1.36982 | ||||||||
\(116\) | 0.462475 | 0.0429398 | ||||||||
\(117\) | 1.11084 | 0.102698 | ||||||||
\(118\) | −0.586555 | −0.0539968 | ||||||||
\(119\) | −3.66797 | −0.336242 | ||||||||
\(120\) | 10.8019 | 0.986070 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.31287 | 0.118862 | ||||||||
\(123\) | 8.79562 | 0.793074 | ||||||||
\(124\) | 0.776892 | 0.0697670 | ||||||||
\(125\) | −11.0735 | −0.990443 | ||||||||
\(126\) | −1.09946 | −0.0979476 | ||||||||
\(127\) | 2.50614 | 0.222384 | 0.111192 | − | 0.993799i | \(-0.464533\pi\) | ||||
0.111192 | + | 0.993799i | \(0.464533\pi\) | |||||||
\(128\) | 8.42222 | 0.744426 | ||||||||
\(129\) | −0.247282 | −0.0217720 | ||||||||
\(130\) | −5.27119 | −0.462314 | ||||||||
\(131\) | 7.59263 | 0.663371 | 0.331686 | − | 0.943390i | \(-0.392383\pi\) | ||||
0.331686 | + | 0.943390i | \(0.392383\pi\) | |||||||
\(132\) | −0.276371 | −0.0240550 | ||||||||
\(133\) | −2.96763 | −0.257326 | ||||||||
\(134\) | 17.8345 | 1.54066 | ||||||||
\(135\) | −3.61438 | −0.311076 | ||||||||
\(136\) | −13.0898 | −1.12244 | ||||||||
\(137\) | −10.8126 | −0.923782 | −0.461891 | − | 0.886937i | \(-0.652829\pi\) | ||||
−0.461891 | + | 0.886937i | \(0.652829\pi\) | |||||||
\(138\) | 5.33580 | 0.454213 | ||||||||
\(139\) | 9.10264 | 0.772076 | 0.386038 | − | 0.922483i | \(-0.373843\pi\) | ||||
0.386038 | + | 0.922483i | \(0.373843\pi\) | |||||||
\(140\) | −0.836534 | −0.0707001 | ||||||||
\(141\) | 7.35580 | 0.619470 | ||||||||
\(142\) | 3.84520 | 0.322682 | ||||||||
\(143\) | 1.11084 | 0.0928935 | ||||||||
\(144\) | −3.37088 | −0.280906 | ||||||||
\(145\) | 6.04825 | 0.502279 | ||||||||
\(146\) | −4.23404 | −0.350411 | ||||||||
\(147\) | −6.29868 | −0.519507 | ||||||||
\(148\) | −0.515289 | −0.0423565 | ||||||||
\(149\) | 6.88180 | 0.563779 | 0.281890 | − | 0.959447i | \(-0.409039\pi\) | ||||
0.281890 | + | 0.959447i | \(0.409039\pi\) | |||||||
\(150\) | 10.5866 | 0.864395 | ||||||||
\(151\) | 5.97340 | 0.486108 | 0.243054 | − | 0.970013i | \(-0.421851\pi\) | ||||
0.243054 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(152\) | −10.5905 | −0.859005 | ||||||||
\(153\) | 4.37994 | 0.354097 | ||||||||
\(154\) | −1.09946 | −0.0885970 | ||||||||
\(155\) | 10.1602 | 0.816085 | ||||||||
\(156\) | −0.307006 | −0.0245801 | ||||||||
\(157\) | −13.7456 | −1.09702 | −0.548511 | − | 0.836144i | \(-0.684805\pi\) | ||||
−0.548511 | + | 0.836144i | \(0.684805\pi\) | |||||||
\(158\) | −2.30972 | −0.183752 | ||||||||
\(159\) | 2.90217 | 0.230157 | ||||||||
\(160\) | −5.60820 | −0.443367 | ||||||||
\(161\) | −3.40357 | −0.268239 | ||||||||
\(162\) | 1.31287 | 0.103149 | ||||||||
\(163\) | 13.1473 | 1.02978 | 0.514888 | − | 0.857257i | \(-0.327833\pi\) | ||||
0.514888 | + | 0.857257i | \(0.327833\pi\) | |||||||
\(164\) | −2.43086 | −0.189818 | ||||||||
\(165\) | −3.61438 | −0.281379 | ||||||||
\(166\) | 0.419539 | 0.0325625 | ||||||||
\(167\) | −23.2428 | −1.79858 | −0.899292 | − | 0.437349i | \(-0.855918\pi\) | ||||
−0.899292 | + | 0.437349i | \(0.855918\pi\) | |||||||
\(168\) | 2.50278 | 0.193093 | ||||||||
\(169\) | −11.7660 | −0.905079 | ||||||||
\(170\) | −20.7838 | −1.59404 | ||||||||
\(171\) | 3.54367 | 0.270991 | ||||||||
\(172\) | 0.0683417 | 0.00521101 | ||||||||
\(173\) | 5.59970 | 0.425737 | 0.212869 | − | 0.977081i | \(-0.431719\pi\) | ||||
0.212869 | + | 0.977081i | \(0.431719\pi\) | |||||||
\(174\) | −2.19694 | −0.166549 | ||||||||
\(175\) | −6.75295 | −0.510475 | ||||||||
\(176\) | −3.37088 | −0.254089 | ||||||||
\(177\) | −0.446773 | −0.0335815 | ||||||||
\(178\) | 20.6432 | 1.54727 | ||||||||
\(179\) | 6.95344 | 0.519724 | 0.259862 | − | 0.965646i | \(-0.416323\pi\) | ||||
0.259862 | + | 0.965646i | \(0.416323\pi\) | |||||||
\(180\) | 0.998910 | 0.0744544 | ||||||||
\(181\) | 12.9447 | 0.962174 | 0.481087 | − | 0.876673i | \(-0.340242\pi\) | ||||
0.481087 | + | 0.876673i | \(0.340242\pi\) | |||||||
\(182\) | −1.22133 | −0.0905309 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −12.1463 | −0.895434 | ||||||||
\(185\) | −6.73894 | −0.495457 | ||||||||
\(186\) | −3.69054 | −0.270603 | ||||||||
\(187\) | 4.37994 | 0.320293 | ||||||||
\(188\) | −2.03293 | −0.148267 | ||||||||
\(189\) | −0.837447 | −0.0609153 | ||||||||
\(190\) | −16.8154 | −1.21992 | ||||||||
\(191\) | −18.5614 | −1.34306 | −0.671529 | − | 0.740978i | \(-0.734362\pi\) | ||||
−0.671529 | + | 0.740978i | \(0.734362\pi\) | |||||||
\(192\) | 8.77885 | 0.633559 | ||||||||
\(193\) | −10.6201 | −0.764450 | −0.382225 | − | 0.924069i | \(-0.624842\pi\) | ||||
−0.382225 | + | 0.924069i | \(0.624842\pi\) | |||||||
\(194\) | −10.1829 | −0.731087 | ||||||||
\(195\) | −4.01501 | −0.287521 | ||||||||
\(196\) | 1.74077 | 0.124341 | ||||||||
\(197\) | 8.69998 | 0.619848 | 0.309924 | − | 0.950761i | \(-0.399696\pi\) | ||||
0.309924 | + | 0.950761i | \(0.399696\pi\) | |||||||
\(198\) | 1.31287 | 0.0933016 | ||||||||
\(199\) | 13.2999 | 0.942803 | 0.471402 | − | 0.881919i | \(-0.343748\pi\) | ||||
0.471402 | + | 0.881919i | \(0.343748\pi\) | |||||||
\(200\) | −24.0991 | −1.70406 | ||||||||
\(201\) | 13.5843 | 0.958164 | ||||||||
\(202\) | 0.712669 | 0.0501432 | ||||||||
\(203\) | 1.40137 | 0.0983570 | ||||||||
\(204\) | −1.21049 | −0.0847513 | ||||||||
\(205\) | −31.7907 | −2.22036 | ||||||||
\(206\) | −24.9396 | −1.73763 | ||||||||
\(207\) | 4.06422 | 0.282483 | ||||||||
\(208\) | −3.74452 | −0.259636 | ||||||||
\(209\) | 3.54367 | 0.245120 | ||||||||
\(210\) | 3.97386 | 0.274223 | ||||||||
\(211\) | −4.35272 | −0.299654 | −0.149827 | − | 0.988712i | \(-0.547872\pi\) | ||||
−0.149827 | + | 0.988712i | \(0.547872\pi\) | |||||||
\(212\) | −0.802076 | −0.0550868 | ||||||||
\(213\) | 2.92885 | 0.200682 | ||||||||
\(214\) | 1.46294 | 0.100004 | ||||||||
\(215\) | 0.893772 | 0.0609548 | ||||||||
\(216\) | −2.98858 | −0.203347 | ||||||||
\(217\) | 2.35410 | 0.159807 | ||||||||
\(218\) | −10.0876 | −0.683216 | ||||||||
\(219\) | −3.22502 | −0.217927 | ||||||||
\(220\) | 0.998910 | 0.0673465 | ||||||||
\(221\) | 4.86544 | 0.327285 | ||||||||
\(222\) | 2.44782 | 0.164287 | ||||||||
\(223\) | 9.37001 | 0.627462 | 0.313731 | − | 0.949512i | \(-0.398421\pi\) | ||||
0.313731 | + | 0.949512i | \(0.398421\pi\) | |||||||
\(224\) | −1.29941 | −0.0868207 | ||||||||
\(225\) | 8.06373 | 0.537582 | ||||||||
\(226\) | 17.6991 | 1.17733 | ||||||||
\(227\) | −20.2223 | −1.34220 | −0.671100 | − | 0.741367i | \(-0.734178\pi\) | ||||
−0.671100 | + | 0.741367i | \(0.734178\pi\) | |||||||
\(228\) | −0.979367 | −0.0648602 | ||||||||
\(229\) | −12.0588 | −0.796866 | −0.398433 | − | 0.917197i | \(-0.630446\pi\) | ||||
−0.398433 | + | 0.917197i | \(0.630446\pi\) | |||||||
\(230\) | −19.2856 | −1.27165 | ||||||||
\(231\) | −0.837447 | −0.0551000 | ||||||||
\(232\) | 5.00104 | 0.328335 | ||||||||
\(233\) | −22.8322 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768935\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(234\) | 1.45840 | 0.0953383 | ||||||||
\(235\) | −26.5866 | −1.73432 | ||||||||
\(236\) | 0.123475 | 0.00803756 | ||||||||
\(237\) | −1.75929 | −0.114278 | ||||||||
\(238\) | −4.81557 | −0.312147 | ||||||||
\(239\) | 12.9994 | 0.840864 | 0.420432 | − | 0.907324i | \(-0.361879\pi\) | ||||
0.420432 | + | 0.907324i | \(0.361879\pi\) | |||||||
\(240\) | 12.1836 | 0.786450 | ||||||||
\(241\) | 25.7692 | 1.65994 | 0.829971 | − | 0.557807i | \(-0.188357\pi\) | ||||
0.829971 | + | 0.557807i | \(0.188357\pi\) | |||||||
\(242\) | 1.31287 | 0.0843945 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.276371 | −0.0176929 | ||||||||
\(245\) | 22.7658 | 1.45446 | ||||||||
\(246\) | 11.5475 | 0.736242 | ||||||||
\(247\) | 3.93646 | 0.250471 | ||||||||
\(248\) | 8.40103 | 0.533466 | ||||||||
\(249\) | 0.319558 | 0.0202512 | ||||||||
\(250\) | −14.5381 | −0.919467 | ||||||||
\(251\) | −2.41536 | −0.152456 | −0.0762281 | − | 0.997090i | \(-0.524288\pi\) | ||||
−0.0762281 | + | 0.997090i | \(0.524288\pi\) | |||||||
\(252\) | 0.231446 | 0.0145797 | ||||||||
\(253\) | 4.06422 | 0.255515 | ||||||||
\(254\) | 3.29024 | 0.206448 | ||||||||
\(255\) | −15.8308 | −0.991361 | ||||||||
\(256\) | −6.50042 | −0.406276 | ||||||||
\(257\) | 20.1663 | 1.25794 | 0.628969 | − | 0.777431i | \(-0.283477\pi\) | ||||
0.628969 | + | 0.777431i | \(0.283477\pi\) | |||||||
\(258\) | −0.324650 | −0.0202118 | ||||||||
\(259\) | −1.56140 | −0.0970209 | ||||||||
\(260\) | 1.10963 | 0.0688166 | ||||||||
\(261\) | −1.67338 | −0.103580 | ||||||||
\(262\) | 9.96814 | 0.615834 | ||||||||
\(263\) | −15.8182 | −0.975392 | −0.487696 | − | 0.873013i | \(-0.662163\pi\) | ||||
−0.487696 | + | 0.873013i | \(0.662163\pi\) | |||||||
\(264\) | −2.98858 | −0.183934 | ||||||||
\(265\) | −10.4895 | −0.644367 | ||||||||
\(266\) | −3.89612 | −0.238886 | ||||||||
\(267\) | 15.7237 | 0.962277 | ||||||||
\(268\) | −3.75432 | −0.229331 | ||||||||
\(269\) | 18.4287 | 1.12362 | 0.561808 | − | 0.827267i | \(-0.310106\pi\) | ||||
0.561808 | + | 0.827267i | \(0.310106\pi\) | |||||||
\(270\) | −4.74521 | −0.288784 | ||||||||
\(271\) | −11.2933 | −0.686017 | −0.343009 | − | 0.939332i | \(-0.611446\pi\) | ||||
−0.343009 | + | 0.939332i | \(0.611446\pi\) | |||||||
\(272\) | −14.7642 | −0.895214 | ||||||||
\(273\) | −0.930274 | −0.0563027 | ||||||||
\(274\) | −14.1955 | −0.857584 | ||||||||
\(275\) | 8.06373 | 0.486261 | ||||||||
\(276\) | −1.12323 | −0.0676107 | ||||||||
\(277\) | 25.1075 | 1.50856 | 0.754282 | − | 0.656550i | \(-0.227985\pi\) | ||||
0.754282 | + | 0.656550i | \(0.227985\pi\) | |||||||
\(278\) | 11.9506 | 0.716749 | ||||||||
\(279\) | −2.81104 | −0.168293 | ||||||||
\(280\) | −9.04599 | −0.540601 | ||||||||
\(281\) | 9.59612 | 0.572457 | 0.286228 | − | 0.958161i | \(-0.407598\pi\) | ||||
0.286228 | + | 0.958161i | \(0.407598\pi\) | |||||||
\(282\) | 9.65721 | 0.575079 | ||||||||
\(283\) | −28.2833 | −1.68126 | −0.840632 | − | 0.541606i | \(-0.817816\pi\) | ||||
−0.840632 | + | 0.541606i | \(0.817816\pi\) | |||||||
\(284\) | −0.809450 | −0.0480320 | ||||||||
\(285\) | −12.8081 | −0.758689 | ||||||||
\(286\) | 1.45840 | 0.0862367 | ||||||||
\(287\) | −7.36587 | −0.434793 | ||||||||
\(288\) | 1.55164 | 0.0914311 | ||||||||
\(289\) | 2.18390 | 0.128465 | ||||||||
\(290\) | 7.94056 | 0.466286 | ||||||||
\(291\) | −7.75619 | −0.454676 | ||||||||
\(292\) | 0.891303 | 0.0521596 | ||||||||
\(293\) | 9.34876 | 0.546160 | 0.273080 | − | 0.961991i | \(-0.411958\pi\) | ||||
0.273080 | + | 0.961991i | \(0.411958\pi\) | |||||||
\(294\) | −8.26935 | −0.482279 | ||||||||
\(295\) | 1.61481 | 0.0940177 | ||||||||
\(296\) | −5.57215 | −0.323875 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 9.03491 | 0.523379 | ||||||||
\(299\) | 4.51472 | 0.261093 | ||||||||
\(300\) | −2.22858 | −0.128667 | ||||||||
\(301\) | 0.207086 | 0.0119362 | ||||||||
\(302\) | 7.84230 | 0.451274 | ||||||||
\(303\) | 0.542833 | 0.0311849 | ||||||||
\(304\) | −11.9453 | −0.685108 | ||||||||
\(305\) | −3.61438 | −0.206959 | ||||||||
\(306\) | 5.75030 | 0.328723 | ||||||||
\(307\) | 16.0672 | 0.917005 | 0.458503 | − | 0.888693i | \(-0.348386\pi\) | ||||
0.458503 | + | 0.888693i | \(0.348386\pi\) | |||||||
\(308\) | 0.231446 | 0.0131879 | ||||||||
\(309\) | −18.9963 | −1.08066 | ||||||||
\(310\) | 13.3390 | 0.757604 | ||||||||
\(311\) | −5.53945 | −0.314113 | −0.157057 | − | 0.987590i | \(-0.550201\pi\) | ||||
−0.157057 | + | 0.987590i | \(0.550201\pi\) | |||||||
\(312\) | −3.31985 | −0.187949 | ||||||||
\(313\) | 6.72316 | 0.380016 | 0.190008 | − | 0.981783i | \(-0.439149\pi\) | ||||
0.190008 | + | 0.981783i | \(0.439149\pi\) | |||||||
\(314\) | −18.0462 | −1.01841 | ||||||||
\(315\) | 3.02685 | 0.170544 | ||||||||
\(316\) | 0.486218 | 0.0273519 | ||||||||
\(317\) | 25.5153 | 1.43308 | 0.716541 | − | 0.697545i | \(-0.245724\pi\) | ||||
0.716541 | + | 0.697545i | \(0.245724\pi\) | |||||||
\(318\) | 3.81017 | 0.213664 | ||||||||
\(319\) | −1.67338 | −0.0936916 | ||||||||
\(320\) | −31.7301 | −1.77377 | ||||||||
\(321\) | 1.11430 | 0.0621944 | ||||||||
\(322\) | −4.46845 | −0.249017 | ||||||||
\(323\) | 15.5211 | 0.863615 | ||||||||
\(324\) | −0.276371 | −0.0153540 | ||||||||
\(325\) | 8.95755 | 0.496876 | ||||||||
\(326\) | 17.2607 | 0.955982 | ||||||||
\(327\) | −7.68359 | −0.424903 | ||||||||
\(328\) | −26.2864 | −1.45142 | ||||||||
\(329\) | −6.16009 | −0.339617 | ||||||||
\(330\) | −4.74521 | −0.261215 | ||||||||
\(331\) | −3.18003 | −0.174790 | −0.0873950 | − | 0.996174i | \(-0.527854\pi\) | ||||
−0.0873950 | + | 0.996174i | \(0.527854\pi\) | |||||||
\(332\) | −0.0883167 | −0.00484701 | ||||||||
\(333\) | 1.86448 | 0.102173 | ||||||||
\(334\) | −30.5148 | −1.66970 | ||||||||
\(335\) | −49.0989 | −2.68256 | ||||||||
\(336\) | 2.82293 | 0.154003 | ||||||||
\(337\) | −3.13033 | −0.170520 | −0.0852599 | − | 0.996359i | \(-0.527172\pi\) | ||||
−0.0852599 | + | 0.996359i | \(0.527172\pi\) | |||||||
\(338\) | −15.4473 | −0.840220 | ||||||||
\(339\) | 13.4812 | 0.732199 | ||||||||
\(340\) | 4.37517 | 0.237277 | ||||||||
\(341\) | −2.81104 | −0.152227 | ||||||||
\(342\) | 4.65237 | 0.251572 | ||||||||
\(343\) | 11.1369 | 0.601338 | ||||||||
\(344\) | 0.739023 | 0.0398455 | ||||||||
\(345\) | −14.6896 | −0.790863 | ||||||||
\(346\) | 7.35168 | 0.395229 | ||||||||
\(347\) | 21.9508 | 1.17838 | 0.589190 | − | 0.807994i | \(-0.299447\pi\) | ||||
0.589190 | + | 0.807994i | \(0.299447\pi\) | |||||||
\(348\) | 0.462475 | 0.0247913 | ||||||||
\(349\) | 7.14342 | 0.382378 | 0.191189 | − | 0.981553i | \(-0.438766\pi\) | ||||
0.191189 | + | 0.981553i | \(0.438766\pi\) | |||||||
\(350\) | −8.86575 | −0.473894 | ||||||||
\(351\) | 1.11084 | 0.0592925 | ||||||||
\(352\) | 1.55164 | 0.0827025 | ||||||||
\(353\) | −7.76027 | −0.413037 | −0.206519 | − | 0.978443i | \(-0.566213\pi\) | ||||
−0.206519 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(354\) | −0.586555 | −0.0311751 | ||||||||
\(355\) | −10.5860 | −0.561845 | ||||||||
\(356\) | −4.34559 | −0.230316 | ||||||||
\(357\) | −3.66797 | −0.194130 | ||||||||
\(358\) | 9.12896 | 0.482480 | ||||||||
\(359\) | −5.97613 | −0.315408 | −0.157704 | − | 0.987486i | \(-0.550409\pi\) | ||||
−0.157704 | + | 0.987486i | \(0.550409\pi\) | |||||||
\(360\) | 10.8019 | 0.569308 | ||||||||
\(361\) | −6.44243 | −0.339075 | ||||||||
\(362\) | 16.9947 | 0.893224 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0.257101 | 0.0134757 | ||||||||
\(365\) | 11.6565 | 0.610126 | ||||||||
\(366\) | 1.31287 | 0.0686248 | ||||||||
\(367\) | 25.5116 | 1.33170 | 0.665848 | − | 0.746088i | \(-0.268070\pi\) | ||||
0.665848 | + | 0.746088i | \(0.268070\pi\) | |||||||
\(368\) | −13.7000 | −0.714161 | ||||||||
\(369\) | 8.79562 | 0.457882 | ||||||||
\(370\) | −8.84735 | −0.459952 | ||||||||
\(371\) | −2.43041 | −0.126181 | ||||||||
\(372\) | 0.776892 | 0.0402800 | ||||||||
\(373\) | 3.08998 | 0.159993 | 0.0799967 | − | 0.996795i | \(-0.474509\pi\) | ||||
0.0799967 | + | 0.996795i | \(0.474509\pi\) | |||||||
\(374\) | 5.75030 | 0.297341 | ||||||||
\(375\) | −11.0735 | −0.571832 | ||||||||
\(376\) | −21.9834 | −1.13371 | ||||||||
\(377\) | −1.85887 | −0.0957367 | ||||||||
\(378\) | −1.09946 | −0.0565501 | ||||||||
\(379\) | 23.8740 | 1.22633 | 0.613163 | − | 0.789956i | \(-0.289897\pi\) | ||||
0.613163 | + | 0.789956i | \(0.289897\pi\) | |||||||
\(380\) | 3.53980 | 0.181588 | ||||||||
\(381\) | 2.50614 | 0.128394 | ||||||||
\(382\) | −24.3688 | −1.24681 | ||||||||
\(383\) | 4.74359 | 0.242386 | 0.121193 | − | 0.992629i | \(-0.461328\pi\) | ||||
0.121193 | + | 0.992629i | \(0.461328\pi\) | |||||||
\(384\) | 8.42222 | 0.429795 | ||||||||
\(385\) | 3.02685 | 0.154263 | ||||||||
\(386\) | −13.9428 | −0.709669 | ||||||||
\(387\) | −0.247282 | −0.0125701 | ||||||||
\(388\) | 2.14359 | 0.108824 | ||||||||
\(389\) | 10.1189 | 0.513048 | 0.256524 | − | 0.966538i | \(-0.417423\pi\) | ||||
0.256524 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(390\) | −5.27119 | −0.266917 | ||||||||
\(391\) | 17.8011 | 0.900238 | ||||||||
\(392\) | 18.8241 | 0.950762 | ||||||||
\(393\) | 7.59263 | 0.382997 | ||||||||
\(394\) | 11.4220 | 0.575430 | ||||||||
\(395\) | 6.35875 | 0.319943 | ||||||||
\(396\) | −0.276371 | −0.0138882 | ||||||||
\(397\) | −15.0570 | −0.755688 | −0.377844 | − | 0.925869i | \(-0.623334\pi\) | ||||
−0.377844 | + | 0.925869i | \(0.623334\pi\) | |||||||
\(398\) | 17.4610 | 0.875242 | ||||||||
\(399\) | −2.96763 | −0.148567 | ||||||||
\(400\) | −27.1818 | −1.35909 | ||||||||
\(401\) | 10.5678 | 0.527730 | 0.263865 | − | 0.964560i | \(-0.415003\pi\) | ||||
0.263865 | + | 0.964560i | \(0.415003\pi\) | |||||||
\(402\) | 17.8345 | 0.889502 | ||||||||
\(403\) | −3.12263 | −0.155550 | ||||||||
\(404\) | −0.150023 | −0.00746394 | ||||||||
\(405\) | −3.61438 | −0.179600 | ||||||||
\(406\) | 1.83982 | 0.0913087 | ||||||||
\(407\) | 1.86448 | 0.0924189 | ||||||||
\(408\) | −13.0898 | −0.648042 | ||||||||
\(409\) | 5.26303 | 0.260240 | 0.130120 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130120 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(410\) | −41.7371 | −2.06125 | ||||||||
\(411\) | −10.8126 | −0.533346 | ||||||||
\(412\) | 5.25002 | 0.258650 | ||||||||
\(413\) | 0.374149 | 0.0184107 | ||||||||
\(414\) | 5.33580 | 0.262240 | ||||||||
\(415\) | −1.15500 | −0.0566970 | ||||||||
\(416\) | 1.72363 | 0.0845078 | ||||||||
\(417\) | 9.10264 | 0.445758 | ||||||||
\(418\) | 4.65237 | 0.227555 | ||||||||
\(419\) | 19.6551 | 0.960216 | 0.480108 | − | 0.877209i | \(-0.340598\pi\) | ||||
0.480108 | + | 0.877209i | \(0.340598\pi\) | |||||||
\(420\) | −0.836534 | −0.0408187 | ||||||||
\(421\) | −3.75600 | −0.183056 | −0.0915280 | − | 0.995803i | \(-0.529175\pi\) | ||||
−0.0915280 | + | 0.995803i | \(0.529175\pi\) | |||||||
\(422\) | −5.71456 | −0.278180 | ||||||||
\(423\) | 7.35580 | 0.357651 | ||||||||
\(424\) | −8.67337 | −0.421216 | ||||||||
\(425\) | 35.3187 | 1.71321 | ||||||||
\(426\) | 3.84520 | 0.186301 | ||||||||
\(427\) | −0.837447 | −0.0405269 | ||||||||
\(428\) | −0.307962 | −0.0148859 | ||||||||
\(429\) | 1.11084 | 0.0536321 | ||||||||
\(430\) | 1.17341 | 0.0565867 | ||||||||
\(431\) | 6.44918 | 0.310646 | 0.155323 | − | 0.987864i | \(-0.450358\pi\) | ||||
0.155323 | + | 0.987864i | \(0.450358\pi\) | |||||||
\(432\) | −3.37088 | −0.162181 | ||||||||
\(433\) | 36.7936 | 1.76819 | 0.884094 | − | 0.467310i | \(-0.154777\pi\) | ||||
0.884094 | + | 0.467310i | \(0.154777\pi\) | |||||||
\(434\) | 3.09063 | 0.148355 | ||||||||
\(435\) | 6.04825 | 0.289991 | ||||||||
\(436\) | 2.12352 | 0.101698 | ||||||||
\(437\) | 14.4022 | 0.688953 | ||||||||
\(438\) | −4.23404 | −0.202310 | ||||||||
\(439\) | −9.74500 | −0.465104 | −0.232552 | − | 0.972584i | \(-0.574708\pi\) | ||||
−0.232552 | + | 0.972584i | \(0.574708\pi\) | |||||||
\(440\) | 10.8019 | 0.514959 | ||||||||
\(441\) | −6.29868 | −0.299937 | ||||||||
\(442\) | 6.38769 | 0.303831 | ||||||||
\(443\) | 6.37596 | 0.302931 | 0.151466 | − | 0.988463i | \(-0.451601\pi\) | ||||
0.151466 | + | 0.988463i | \(0.451601\pi\) | |||||||
\(444\) | −0.515289 | −0.0244545 | ||||||||
\(445\) | −56.8315 | −2.69407 | ||||||||
\(446\) | 12.3016 | 0.582498 | ||||||||
\(447\) | 6.88180 | 0.325498 | ||||||||
\(448\) | −7.35182 | −0.347341 | ||||||||
\(449\) | 17.4495 | 0.823495 | 0.411747 | − | 0.911298i | \(-0.364919\pi\) | ||||
0.411747 | + | 0.911298i | \(0.364919\pi\) | |||||||
\(450\) | 10.5866 | 0.499059 | ||||||||
\(451\) | 8.79562 | 0.414170 | ||||||||
\(452\) | −3.72582 | −0.175248 | ||||||||
\(453\) | 5.97340 | 0.280655 | ||||||||
\(454\) | −26.5492 | −1.24602 | ||||||||
\(455\) | 3.36236 | 0.157630 | ||||||||
\(456\) | −10.5905 | −0.495947 | ||||||||
\(457\) | −41.4643 | −1.93962 | −0.969808 | − | 0.243869i | \(-0.921583\pi\) | ||||
−0.969808 | + | 0.243869i | \(0.921583\pi\) | |||||||
\(458\) | −15.8316 | −0.739763 | ||||||||
\(459\) | 4.37994 | 0.204438 | ||||||||
\(460\) | 4.05979 | 0.189289 | ||||||||
\(461\) | −23.3164 | −1.08595 | −0.542976 | − | 0.839748i | \(-0.682702\pi\) | ||||
−0.542976 | + | 0.839748i | \(0.682702\pi\) | |||||||
\(462\) | −1.09946 | −0.0511515 | ||||||||
\(463\) | −38.3434 | −1.78197 | −0.890984 | − | 0.454036i | \(-0.849984\pi\) | ||||
−0.890984 | + | 0.454036i | \(0.849984\pi\) | |||||||
\(464\) | 5.64077 | 0.261866 | ||||||||
\(465\) | 10.1602 | 0.471167 | ||||||||
\(466\) | −29.9758 | −1.38860 | ||||||||
\(467\) | 26.9505 | 1.24712 | 0.623561 | − | 0.781775i | \(-0.285685\pi\) | ||||
0.623561 | + | 0.781775i | \(0.285685\pi\) | |||||||
\(468\) | −0.307006 | −0.0141913 | ||||||||
\(469\) | −11.3762 | −0.525302 | ||||||||
\(470\) | −34.9048 | −1.61004 | ||||||||
\(471\) | −13.7456 | −0.633366 | ||||||||
\(472\) | 1.33522 | 0.0614584 | ||||||||
\(473\) | −0.247282 | −0.0113701 | ||||||||
\(474\) | −2.30972 | −0.106089 | ||||||||
\(475\) | 28.5752 | 1.31112 | ||||||||
\(476\) | 1.01372 | 0.0464638 | ||||||||
\(477\) | 2.90217 | 0.132881 | ||||||||
\(478\) | 17.0666 | 0.780607 | ||||||||
\(479\) | 32.4812 | 1.48411 | 0.742053 | − | 0.670342i | \(-0.233852\pi\) | ||||
0.742053 | + | 0.670342i | \(0.233852\pi\) | |||||||
\(480\) | −5.60820 | −0.255978 | ||||||||
\(481\) | 2.07115 | 0.0944363 | ||||||||
\(482\) | 33.8317 | 1.54099 | ||||||||
\(483\) | −3.40357 | −0.154868 | ||||||||
\(484\) | −0.276371 | −0.0125623 | ||||||||
\(485\) | 28.0338 | 1.27295 | ||||||||
\(486\) | 1.31287 | 0.0595530 | ||||||||
\(487\) | −21.1728 | −0.959432 | −0.479716 | − | 0.877424i | \(-0.659260\pi\) | ||||
−0.479716 | + | 0.877424i | \(0.659260\pi\) | |||||||
\(488\) | −2.98858 | −0.135287 | ||||||||
\(489\) | 13.1473 | 0.594542 | ||||||||
\(490\) | 29.8886 | 1.35023 | ||||||||
\(491\) | −17.4594 | −0.787930 | −0.393965 | − | 0.919125i | \(-0.628897\pi\) | ||||
−0.393965 | + | 0.919125i | \(0.628897\pi\) | |||||||
\(492\) | −2.43086 | −0.109591 | ||||||||
\(493\) | −7.32933 | −0.330096 | ||||||||
\(494\) | 5.16807 | 0.232522 | ||||||||
\(495\) | −3.61438 | −0.162454 | ||||||||
\(496\) | 9.47568 | 0.425471 | ||||||||
\(497\) | −2.45276 | −0.110021 | ||||||||
\(498\) | 0.419539 | 0.0188000 | ||||||||
\(499\) | −28.8978 | −1.29364 | −0.646822 | − | 0.762641i | \(-0.723902\pi\) | ||||
−0.646822 | + | 0.762641i | \(0.723902\pi\) | |||||||
\(500\) | 3.06039 | 0.136865 | ||||||||
\(501\) | −23.2428 | −1.03841 | ||||||||
\(502\) | −3.17105 | −0.141531 | ||||||||
\(503\) | −14.6656 | −0.653905 | −0.326953 | − | 0.945041i | \(-0.606022\pi\) | ||||
−0.326953 | + | 0.945041i | \(0.606022\pi\) | |||||||
\(504\) | 2.50278 | 0.111483 | ||||||||
\(505\) | −1.96200 | −0.0873080 | ||||||||
\(506\) | 5.33580 | 0.237205 | ||||||||
\(507\) | −11.7660 | −0.522547 | ||||||||
\(508\) | −0.692626 | −0.0307303 | ||||||||
\(509\) | 11.3607 | 0.503556 | 0.251778 | − | 0.967785i | \(-0.418985\pi\) | ||||
0.251778 | + | 0.967785i | \(0.418985\pi\) | |||||||
\(510\) | −20.7838 | −0.920320 | ||||||||
\(511\) | 2.70078 | 0.119476 | ||||||||
\(512\) | −25.3786 | −1.12159 | ||||||||
\(513\) | 3.54367 | 0.156457 | ||||||||
\(514\) | 26.4757 | 1.16779 | ||||||||
\(515\) | 68.6597 | 3.02551 | ||||||||
\(516\) | 0.0683417 | 0.00300858 | ||||||||
\(517\) | 7.35580 | 0.323508 | ||||||||
\(518\) | −2.04992 | −0.0900684 | ||||||||
\(519\) | 5.59970 | 0.245799 | ||||||||
\(520\) | 11.9992 | 0.526199 | ||||||||
\(521\) | 4.14492 | 0.181592 | 0.0907961 | − | 0.995870i | \(-0.471059\pi\) | ||||
0.0907961 | + | 0.995870i | \(0.471059\pi\) | |||||||
\(522\) | −2.19694 | −0.0961573 | ||||||||
\(523\) | 5.81064 | 0.254082 | 0.127041 | − | 0.991897i | \(-0.459452\pi\) | ||||
0.127041 | + | 0.991897i | \(0.459452\pi\) | |||||||
\(524\) | −2.09838 | −0.0916683 | ||||||||
\(525\) | −6.75295 | −0.294723 | ||||||||
\(526\) | −20.7673 | −0.905495 | ||||||||
\(527\) | −12.3122 | −0.536329 | ||||||||
\(528\) | −3.37088 | −0.146699 | ||||||||
\(529\) | −6.48210 | −0.281830 | ||||||||
\(530\) | −13.7714 | −0.598192 | ||||||||
\(531\) | −0.446773 | −0.0193883 | ||||||||
\(532\) | 0.820168 | 0.0355588 | ||||||||
\(533\) | 9.77057 | 0.423210 | ||||||||
\(534\) | 20.6432 | 0.893319 | ||||||||
\(535\) | −4.02752 | −0.174125 | ||||||||
\(536\) | −40.5978 | −1.75356 | ||||||||
\(537\) | 6.95344 | 0.300063 | ||||||||
\(538\) | 24.1945 | 1.04310 | ||||||||
\(539\) | −6.29868 | −0.271303 | ||||||||
\(540\) | 0.998910 | 0.0429863 | ||||||||
\(541\) | 20.0635 | 0.862598 | 0.431299 | − | 0.902209i | \(-0.358055\pi\) | ||||
0.431299 | + | 0.902209i | \(0.358055\pi\) | |||||||
\(542\) | −14.8266 | −0.636857 | ||||||||
\(543\) | 12.9447 | 0.555511 | ||||||||
\(544\) | 6.79608 | 0.291380 | ||||||||
\(545\) | 27.7714 | 1.18960 | ||||||||
\(546\) | −1.22133 | −0.0522680 | ||||||||
\(547\) | 23.1230 | 0.988669 | 0.494334 | − | 0.869272i | \(-0.335412\pi\) | ||||
0.494334 | + | 0.869272i | \(0.335412\pi\) | |||||||
\(548\) | 2.98829 | 0.127653 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 10.5866 | 0.451416 | ||||||||
\(551\) | −5.92992 | −0.252623 | ||||||||
\(552\) | −12.1463 | −0.516979 | ||||||||
\(553\) | 1.47331 | 0.0626517 | ||||||||
\(554\) | 32.9629 | 1.40046 | ||||||||
\(555\) | −6.73894 | −0.286052 | ||||||||
\(556\) | −2.51571 | −0.106690 | ||||||||
\(557\) | 10.3408 | 0.438154 | 0.219077 | − | 0.975708i | \(-0.429695\pi\) | ||||
0.219077 | + | 0.975708i | \(0.429695\pi\) | |||||||
\(558\) | −3.69054 | −0.156233 | ||||||||
\(559\) | −0.274692 | −0.0116182 | ||||||||
\(560\) | −10.2031 | −0.431161 | ||||||||
\(561\) | 4.37994 | 0.184921 | ||||||||
\(562\) | 12.5985 | 0.531434 | ||||||||
\(563\) | 8.42500 | 0.355071 | 0.177536 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(564\) | −2.03293 | −0.0856019 | ||||||||
\(565\) | −48.7262 | −2.04993 | ||||||||
\(566\) | −37.1322 | −1.56078 | ||||||||
\(567\) | −0.837447 | −0.0351695 | ||||||||
\(568\) | −8.75311 | −0.367272 | ||||||||
\(569\) | 6.71812 | 0.281638 | 0.140819 | − | 0.990035i | \(-0.455026\pi\) | ||||
0.140819 | + | 0.990035i | \(0.455026\pi\) | |||||||
\(570\) | −16.8154 | −0.704321 | ||||||||
\(571\) | 6.05227 | 0.253279 | 0.126640 | − | 0.991949i | \(-0.459581\pi\) | ||||
0.126640 | + | 0.991949i | \(0.459581\pi\) | |||||||
\(572\) | −0.307006 | −0.0128365 | ||||||||
\(573\) | −18.5614 | −0.775415 | ||||||||
\(574\) | −9.67043 | −0.403636 | ||||||||
\(575\) | 32.7728 | 1.36672 | ||||||||
\(576\) | 8.77885 | 0.365785 | ||||||||
\(577\) | 39.9435 | 1.66287 | 0.831435 | − | 0.555622i | \(-0.187520\pi\) | ||||
0.831435 | + | 0.555622i | \(0.187520\pi\) | |||||||
\(578\) | 2.86718 | 0.119259 | ||||||||
\(579\) | −10.6201 | −0.441356 | ||||||||
\(580\) | −1.67156 | −0.0694078 | ||||||||
\(581\) | −0.267613 | −0.0111025 | ||||||||
\(582\) | −10.1829 | −0.422093 | ||||||||
\(583\) | 2.90217 | 0.120196 | ||||||||
\(584\) | 9.63824 | 0.398833 | ||||||||
\(585\) | −4.01501 | −0.166000 | ||||||||
\(586\) | 12.2737 | 0.507022 | ||||||||
\(587\) | 1.60472 | 0.0662339 | 0.0331169 | − | 0.999451i | \(-0.489457\pi\) | ||||
0.0331169 | + | 0.999451i | \(0.489457\pi\) | |||||||
\(588\) | 1.74077 | 0.0717883 | ||||||||
\(589\) | −9.96140 | −0.410452 | ||||||||
\(590\) | 2.12003 | 0.0872804 | ||||||||
\(591\) | 8.69998 | 0.357870 | ||||||||
\(592\) | −6.28493 | −0.258309 | ||||||||
\(593\) | −12.8886 | −0.529273 | −0.264636 | − | 0.964348i | \(-0.585252\pi\) | ||||
−0.264636 | + | 0.964348i | \(0.585252\pi\) | |||||||
\(594\) | 1.31287 | 0.0538677 | ||||||||
\(595\) | 13.2574 | 0.543502 | ||||||||
\(596\) | −1.90193 | −0.0779062 | ||||||||
\(597\) | 13.2999 | 0.544328 | ||||||||
\(598\) | 5.92724 | 0.242383 | ||||||||
\(599\) | −46.2862 | −1.89120 | −0.945601 | − | 0.325329i | \(-0.894525\pi\) | ||||
−0.945601 | + | 0.325329i | \(0.894525\pi\) | |||||||
\(600\) | −24.0991 | −0.983842 | ||||||||
\(601\) | −33.8954 | −1.38262 | −0.691311 | − | 0.722557i | \(-0.742967\pi\) | ||||
−0.691311 | + | 0.722557i | \(0.742967\pi\) | |||||||
\(602\) | 0.271877 | 0.0110809 | ||||||||
\(603\) | 13.5843 | 0.553196 | ||||||||
\(604\) | −1.65088 | −0.0671732 | ||||||||
\(605\) | −3.61438 | −0.146945 | ||||||||
\(606\) | 0.712669 | 0.0289502 | ||||||||
\(607\) | 20.3795 | 0.827179 | 0.413589 | − | 0.910464i | \(-0.364275\pi\) | ||||
0.413589 | + | 0.910464i | \(0.364275\pi\) | |||||||
\(608\) | 5.49848 | 0.222993 | ||||||||
\(609\) | 1.40137 | 0.0567864 | ||||||||
\(610\) | −4.74521 | −0.192128 | ||||||||
\(611\) | 8.17115 | 0.330569 | ||||||||
\(612\) | −1.21049 | −0.0489312 | ||||||||
\(613\) | −16.8249 | −0.679553 | −0.339776 | − | 0.940506i | \(-0.610351\pi\) | ||||
−0.339776 | + | 0.940506i | \(0.610351\pi\) | |||||||
\(614\) | 21.0942 | 0.851292 | ||||||||
\(615\) | −31.7907 | −1.28192 | ||||||||
\(616\) | 2.50278 | 0.100840 | ||||||||
\(617\) | −1.36945 | −0.0551318 | −0.0275659 | − | 0.999620i | \(-0.508776\pi\) | ||||
−0.0275659 | + | 0.999620i | \(0.508776\pi\) | |||||||
\(618\) | −24.9396 | −1.00322 | ||||||||
\(619\) | −42.6806 | −1.71548 | −0.857740 | − | 0.514084i | \(-0.828132\pi\) | ||||
−0.857740 | + | 0.514084i | \(0.828132\pi\) | |||||||
\(620\) | −2.80798 | −0.112771 | ||||||||
\(621\) | 4.06422 | 0.163092 | ||||||||
\(622\) | −7.27258 | −0.291604 | ||||||||
\(623\) | −13.1678 | −0.527556 | ||||||||
\(624\) | −3.74452 | −0.149901 | ||||||||
\(625\) | −0.294885 | −0.0117954 | ||||||||
\(626\) | 8.82664 | 0.352784 | ||||||||
\(627\) | 3.54367 | 0.141520 | ||||||||
\(628\) | 3.79890 | 0.151593 | ||||||||
\(629\) | 8.16632 | 0.325612 | ||||||||
\(630\) | 3.97386 | 0.158322 | ||||||||
\(631\) | −31.4686 | −1.25275 | −0.626373 | − | 0.779524i | \(-0.715461\pi\) | ||||
−0.626373 | + | 0.779524i | \(0.715461\pi\) | |||||||
\(632\) | 5.25779 | 0.209143 | ||||||||
\(633\) | −4.35272 | −0.173005 | ||||||||
\(634\) | 33.4983 | 1.33039 | ||||||||
\(635\) | −9.05815 | −0.359462 | ||||||||
\(636\) | −0.802076 | −0.0318044 | ||||||||
\(637\) | −6.99686 | −0.277226 | ||||||||
\(638\) | −2.19694 | −0.0869776 | ||||||||
\(639\) | 2.92885 | 0.115864 | ||||||||
\(640\) | −30.4411 | −1.20329 | ||||||||
\(641\) | −15.2489 | −0.602294 | −0.301147 | − | 0.953578i | \(-0.597370\pi\) | ||||
−0.301147 | + | 0.953578i | \(0.597370\pi\) | |||||||
\(642\) | 1.46294 | 0.0577375 | ||||||||
\(643\) | −29.6334 | −1.16863 | −0.584313 | − | 0.811529i | \(-0.698636\pi\) | ||||
−0.584313 | + | 0.811529i | \(0.698636\pi\) | |||||||
\(644\) | 0.940649 | 0.0370668 | ||||||||
\(645\) | 0.893772 | 0.0351922 | ||||||||
\(646\) | 20.3771 | 0.801728 | ||||||||
\(647\) | 31.1055 | 1.22288 | 0.611442 | − | 0.791289i | \(-0.290590\pi\) | ||||
0.611442 | + | 0.791289i | \(0.290590\pi\) | |||||||
\(648\) | −2.98858 | −0.117403 | ||||||||
\(649\) | −0.446773 | −0.0175374 | ||||||||
\(650\) | 11.7601 | 0.461269 | ||||||||
\(651\) | 2.35410 | 0.0922645 | ||||||||
\(652\) | −3.63354 | −0.142300 | ||||||||
\(653\) | −24.3750 | −0.953867 | −0.476934 | − | 0.878939i | \(-0.658252\pi\) | ||||
−0.476934 | + | 0.878939i | \(0.658252\pi\) | |||||||
\(654\) | −10.0876 | −0.394455 | ||||||||
\(655\) | −27.4426 | −1.07227 | ||||||||
\(656\) | −29.6489 | −1.15760 | ||||||||
\(657\) | −3.22502 | −0.125820 | ||||||||
\(658\) | −8.08740 | −0.315280 | ||||||||
\(659\) | −20.4867 | −0.798049 | −0.399025 | − | 0.916940i | \(-0.630651\pi\) | ||||
−0.399025 | + | 0.916940i | \(0.630651\pi\) | |||||||
\(660\) | 0.998910 | 0.0388825 | ||||||||
\(661\) | −36.1634 | −1.40659 | −0.703297 | − | 0.710896i | \(-0.748290\pi\) | ||||
−0.703297 | + | 0.710896i | \(0.748290\pi\) | |||||||
\(662\) | −4.17496 | −0.162265 | ||||||||
\(663\) | 4.86544 | 0.188958 | ||||||||
\(664\) | −0.955026 | −0.0370622 | ||||||||
\(665\) | 10.7261 | 0.415942 | ||||||||
\(666\) | 2.44782 | 0.0948512 | ||||||||
\(667\) | −6.80101 | −0.263336 | ||||||||
\(668\) | 6.42365 | 0.248538 | ||||||||
\(669\) | 9.37001 | 0.362265 | ||||||||
\(670\) | −64.4605 | −2.49033 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −1.29941 | −0.0501260 | ||||||||
\(673\) | −19.7440 | −0.761076 | −0.380538 | − | 0.924765i | \(-0.624261\pi\) | ||||
−0.380538 | + | 0.924765i | \(0.624261\pi\) | |||||||
\(674\) | −4.10971 | −0.158300 | ||||||||
\(675\) | 8.06373 | 0.310373 | ||||||||
\(676\) | 3.25179 | 0.125069 | ||||||||
\(677\) | 16.9323 | 0.650761 | 0.325380 | − | 0.945583i | \(-0.394508\pi\) | ||||
0.325380 | + | 0.945583i | \(0.394508\pi\) | |||||||
\(678\) | 17.6991 | 0.679729 | ||||||||
\(679\) | 6.49539 | 0.249270 | ||||||||
\(680\) | 47.3115 | 1.81431 | ||||||||
\(681\) | −20.2223 | −0.774919 | ||||||||
\(682\) | −3.69054 | −0.141318 | ||||||||
\(683\) | 22.3016 | 0.853346 | 0.426673 | − | 0.904406i | \(-0.359685\pi\) | ||||
0.426673 | + | 0.904406i | \(0.359685\pi\) | |||||||
\(684\) | −0.979367 | −0.0374470 | ||||||||
\(685\) | 39.0808 | 1.49320 | ||||||||
\(686\) | 14.6214 | 0.558246 | ||||||||
\(687\) | −12.0588 | −0.460071 | ||||||||
\(688\) | 0.833558 | 0.0317791 | ||||||||
\(689\) | 3.22386 | 0.122819 | ||||||||
\(690\) | −19.2856 | −0.734190 | ||||||||
\(691\) | −13.5228 | −0.514431 | −0.257216 | − | 0.966354i | \(-0.582805\pi\) | ||||
−0.257216 | + | 0.966354i | \(0.582805\pi\) | |||||||
\(692\) | −1.54760 | −0.0588307 | ||||||||
\(693\) | −0.837447 | −0.0318120 | ||||||||
\(694\) | 28.8185 | 1.09394 | ||||||||
\(695\) | −32.9004 | −1.24798 | ||||||||
\(696\) | 5.00104 | 0.189564 | ||||||||
\(697\) | 38.5243 | 1.45921 | ||||||||
\(698\) | 9.37838 | 0.354977 | ||||||||
\(699\) | −22.8322 | −0.863595 | ||||||||
\(700\) | 1.86632 | 0.0705403 | ||||||||
\(701\) | 0.111492 | 0.00421098 | 0.00210549 | − | 0.999998i | \(-0.499330\pi\) | ||||
0.00210549 | + | 0.999998i | \(0.499330\pi\) | |||||||
\(702\) | 1.45840 | 0.0550436 | ||||||||
\(703\) | 6.60710 | 0.249191 | ||||||||
\(704\) | 8.77885 | 0.330865 | ||||||||
\(705\) | −26.5866 | −1.00131 | ||||||||
\(706\) | −10.1882 | −0.383439 | ||||||||
\(707\) | −0.454594 | −0.0170967 | ||||||||
\(708\) | 0.123475 | 0.00464048 | ||||||||
\(709\) | −16.1234 | −0.605526 | −0.302763 | − | 0.953066i | \(-0.597909\pi\) | ||||
−0.302763 | + | 0.953066i | \(0.597909\pi\) | |||||||
\(710\) | −13.8980 | −0.521583 | ||||||||
\(711\) | −1.75929 | −0.0659786 | ||||||||
\(712\) | −46.9916 | −1.76109 | ||||||||
\(713\) | −11.4247 | −0.427859 | ||||||||
\(714\) | −4.81557 | −0.180218 | ||||||||
\(715\) | −4.01501 | −0.150153 | ||||||||
\(716\) | −1.92173 | −0.0718184 | ||||||||
\(717\) | 12.9994 | 0.485473 | ||||||||
\(718\) | −7.84589 | −0.292806 | ||||||||
\(719\) | −1.62281 | −0.0605205 | −0.0302602 | − | 0.999542i | \(-0.509634\pi\) | ||||
−0.0302602 | + | 0.999542i | \(0.509634\pi\) | |||||||
\(720\) | 12.1836 | 0.454057 | ||||||||
\(721\) | 15.9084 | 0.592458 | ||||||||
\(722\) | −8.45808 | −0.314777 | ||||||||
\(723\) | 25.7692 | 0.958368 | ||||||||
\(724\) | −3.57755 | −0.132959 | ||||||||
\(725\) | −13.4937 | −0.501144 | ||||||||
\(726\) | 1.31287 | 0.0487252 | ||||||||
\(727\) | −21.1068 | −0.782807 | −0.391404 | − | 0.920219i | \(-0.628010\pi\) | ||||
−0.391404 | + | 0.920219i | \(0.628010\pi\) | |||||||
\(728\) | 2.78020 | 0.103041 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.3034 | 0.566405 | ||||||||
\(731\) | −1.08308 | −0.0400593 | ||||||||
\(732\) | −0.276371 | −0.0102150 | ||||||||
\(733\) | −32.6890 | −1.20739 | −0.603697 | − | 0.797213i | \(-0.706307\pi\) | ||||
−0.603697 | + | 0.797213i | \(0.706307\pi\) | |||||||
\(734\) | 33.4934 | 1.23627 | ||||||||
\(735\) | 22.7658 | 0.839730 | ||||||||
\(736\) | 6.30620 | 0.232450 | ||||||||
\(737\) | 13.5843 | 0.500385 | ||||||||
\(738\) | 11.5475 | 0.425070 | ||||||||
\(739\) | −46.9356 | −1.72655 | −0.863277 | − | 0.504730i | \(-0.831592\pi\) | ||||
−0.863277 | + | 0.504730i | \(0.831592\pi\) | |||||||
\(740\) | 1.86245 | 0.0684650 | ||||||||
\(741\) | 3.93646 | 0.144610 | ||||||||
\(742\) | −3.19082 | −0.117139 | ||||||||
\(743\) | −19.1077 | −0.700993 | −0.350497 | − | 0.936564i | \(-0.613987\pi\) | ||||
−0.350497 | + | 0.936564i | \(0.613987\pi\) | |||||||
\(744\) | 8.40103 | 0.307997 | ||||||||
\(745\) | −24.8734 | −0.911292 | ||||||||
\(746\) | 4.05675 | 0.148528 | ||||||||
\(747\) | 0.319558 | 0.0116920 | ||||||||
\(748\) | −1.21049 | −0.0442599 | ||||||||
\(749\) | −0.933171 | −0.0340973 | ||||||||
\(750\) | −14.5381 | −0.530855 | ||||||||
\(751\) | −30.0661 | −1.09713 | −0.548565 | − | 0.836108i | \(-0.684826\pi\) | ||||
−0.548565 | + | 0.836108i | \(0.684826\pi\) | |||||||
\(752\) | −24.7955 | −0.904199 | ||||||||
\(753\) | −2.41536 | −0.0880206 | ||||||||
\(754\) | −2.44046 | −0.0888762 | ||||||||
\(755\) | −21.5901 | −0.785745 | ||||||||
\(756\) | 0.231446 | 0.00841762 | ||||||||
\(757\) | 25.3394 | 0.920976 | 0.460488 | − | 0.887666i | \(-0.347674\pi\) | ||||
0.460488 | + | 0.887666i | \(0.347674\pi\) | |||||||
\(758\) | 31.3435 | 1.13845 | ||||||||
\(759\) | 4.06422 | 0.147522 | ||||||||
\(760\) | 38.2782 | 1.38850 | ||||||||
\(761\) | 1.16161 | 0.0421084 | 0.0210542 | − | 0.999778i | \(-0.493298\pi\) | ||||
0.0210542 | + | 0.999778i | \(0.493298\pi\) | |||||||
\(762\) | 3.29024 | 0.119193 | ||||||||
\(763\) | 6.43460 | 0.232948 | ||||||||
\(764\) | 5.12985 | 0.185591 | ||||||||
\(765\) | −15.8308 | −0.572363 | ||||||||
\(766\) | 6.22772 | 0.225016 | ||||||||
\(767\) | −0.496296 | −0.0179202 | ||||||||
\(768\) | −6.50042 | −0.234564 | ||||||||
\(769\) | 43.2961 | 1.56130 | 0.780648 | − | 0.624971i | \(-0.214889\pi\) | ||||
0.780648 | + | 0.624971i | \(0.214889\pi\) | |||||||
\(770\) | 3.97386 | 0.143208 | ||||||||
\(771\) | 20.1663 | 0.726270 | ||||||||
\(772\) | 2.93509 | 0.105636 | ||||||||
\(773\) | −45.6382 | −1.64149 | −0.820747 | − | 0.571292i | \(-0.806442\pi\) | ||||
−0.820747 | + | 0.571292i | \(0.806442\pi\) | |||||||
\(774\) | −0.324650 | −0.0116693 | ||||||||
\(775\) | −22.6675 | −0.814241 | ||||||||
\(776\) | 23.1800 | 0.832113 | ||||||||
\(777\) | −1.56140 | −0.0560151 | ||||||||
\(778\) | 13.2848 | 0.476283 | ||||||||
\(779\) | 31.1687 | 1.11674 | ||||||||
\(780\) | 1.10963 | 0.0397313 | ||||||||
\(781\) | 2.92885 | 0.104803 | ||||||||
\(782\) | 23.3705 | 0.835727 | ||||||||
\(783\) | −1.67338 | −0.0598019 | ||||||||
\(784\) | 21.2321 | 0.758289 | ||||||||
\(785\) | 49.6819 | 1.77322 | ||||||||
\(786\) | 9.96814 | 0.355552 | ||||||||
\(787\) | 20.1357 | 0.717760 | 0.358880 | − | 0.933384i | \(-0.383159\pi\) | ||||
0.358880 | + | 0.933384i | \(0.383159\pi\) | |||||||
\(788\) | −2.40443 | −0.0856541 | ||||||||
\(789\) | −15.8182 | −0.563143 | ||||||||
\(790\) | 8.34821 | 0.297016 | ||||||||
\(791\) | −11.2898 | −0.401419 | ||||||||
\(792\) | −2.98858 | −0.106195 | ||||||||
\(793\) | 1.11084 | 0.0394473 | ||||||||
\(794\) | −19.7679 | −0.701535 | ||||||||
\(795\) | −10.4895 | −0.372026 | ||||||||
\(796\) | −3.67570 | −0.130282 | ||||||||
\(797\) | −32.4143 | −1.14817 | −0.574087 | − | 0.818794i | \(-0.694643\pi\) | ||||
−0.574087 | + | 0.818794i | \(0.694643\pi\) | |||||||
\(798\) | −3.89612 | −0.137921 | ||||||||
\(799\) | 32.2180 | 1.13979 | ||||||||
\(800\) | 12.5120 | 0.442365 | ||||||||
\(801\) | 15.7237 | 0.555571 | ||||||||
\(802\) | 13.8741 | 0.489913 | ||||||||
\(803\) | −3.22502 | −0.113809 | ||||||||
\(804\) | −3.75432 | −0.132405 | ||||||||
\(805\) | 12.3018 | 0.433581 | ||||||||
\(806\) | −4.09961 | −0.144403 | ||||||||
\(807\) | 18.4287 | 0.648720 | ||||||||
\(808\) | −1.62230 | −0.0570723 | ||||||||
\(809\) | −15.1263 | −0.531811 | −0.265905 | − | 0.963999i | \(-0.585671\pi\) | ||||
−0.265905 | + | 0.963999i | \(0.585671\pi\) | |||||||
\(810\) | −4.74521 | −0.166730 | ||||||||
\(811\) | 40.8120 | 1.43310 | 0.716552 | − | 0.697534i | \(-0.245719\pi\) | ||||
0.716552 | + | 0.697534i | \(0.245719\pi\) | |||||||
\(812\) | −0.387299 | −0.0135915 | ||||||||
\(813\) | −11.2933 | −0.396072 | ||||||||
\(814\) | 2.44782 | 0.0857961 | ||||||||
\(815\) | −47.5194 | −1.66453 | ||||||||
\(816\) | −14.7642 | −0.516852 | ||||||||
\(817\) | −0.876286 | −0.0306574 | ||||||||
\(818\) | 6.90968 | 0.241591 | ||||||||
\(819\) | −0.930274 | −0.0325064 | ||||||||
\(820\) | 8.78604 | 0.306822 | ||||||||
\(821\) | −22.2786 | −0.777528 | −0.388764 | − | 0.921337i | \(-0.627098\pi\) | ||||
−0.388764 | + | 0.921337i | \(0.627098\pi\) | |||||||
\(822\) | −14.1955 | −0.495126 | ||||||||
\(823\) | −38.1070 | −1.32833 | −0.664163 | − | 0.747588i | \(-0.731212\pi\) | ||||
−0.664163 | + | 0.747588i | \(0.731212\pi\) | |||||||
\(824\) | 56.7718 | 1.97774 | ||||||||
\(825\) | 8.06373 | 0.280743 | ||||||||
\(826\) | 0.491209 | 0.0170913 | ||||||||
\(827\) | 20.0408 | 0.696887 | 0.348443 | − | 0.937330i | \(-0.386710\pi\) | ||||
0.348443 | + | 0.937330i | \(0.386710\pi\) | |||||||
\(828\) | −1.12323 | −0.0390351 | ||||||||
\(829\) | 10.5019 | 0.364746 | 0.182373 | − | 0.983229i | \(-0.441622\pi\) | ||||
0.182373 | + | 0.983229i | \(0.441622\pi\) | |||||||
\(830\) | −1.51637 | −0.0526340 | ||||||||
\(831\) | 25.1075 | 0.870970 | ||||||||
\(832\) | 9.75194 | 0.338088 | ||||||||
\(833\) | −27.5879 | −0.955863 | ||||||||
\(834\) | 11.9506 | 0.413815 | ||||||||
\(835\) | 84.0084 | 2.90723 | ||||||||
\(836\) | −0.979367 | −0.0338721 | ||||||||
\(837\) | −2.81104 | −0.0971639 | ||||||||
\(838\) | 25.8046 | 0.891406 | ||||||||
\(839\) | 23.5773 | 0.813979 | 0.406990 | − | 0.913433i | \(-0.366579\pi\) | ||||
0.406990 | + | 0.913433i | \(0.366579\pi\) | |||||||
\(840\) | −9.04599 | −0.312116 | ||||||||
\(841\) | −26.1998 | −0.903441 | ||||||||
\(842\) | −4.93114 | −0.169938 | ||||||||
\(843\) | 9.59612 | 0.330508 | ||||||||
\(844\) | 1.20297 | 0.0414078 | ||||||||
\(845\) | 42.5269 | 1.46297 | ||||||||
\(846\) | 9.65721 | 0.332022 | ||||||||
\(847\) | −0.837447 | −0.0287750 | ||||||||
\(848\) | −9.78285 | −0.335945 | ||||||||
\(849\) | −28.2833 | −0.970679 | ||||||||
\(850\) | 46.3689 | 1.59044 | ||||||||
\(851\) | 7.57766 | 0.259759 | ||||||||
\(852\) | −0.809450 | −0.0277313 | ||||||||
\(853\) | 43.7066 | 1.49649 | 0.748243 | − | 0.663425i | \(-0.230898\pi\) | ||||
0.748243 | + | 0.663425i | \(0.230898\pi\) | |||||||
\(854\) | −1.09946 | −0.0376227 | ||||||||
\(855\) | −12.8081 | −0.438029 | ||||||||
\(856\) | −3.33019 | −0.113823 | ||||||||
\(857\) | 50.7072 | 1.73213 | 0.866063 | − | 0.499935i | \(-0.166643\pi\) | ||||
0.866063 | + | 0.499935i | \(0.166643\pi\) | |||||||
\(858\) | 1.45840 | 0.0497888 | ||||||||
\(859\) | 28.6892 | 0.978861 | 0.489431 | − | 0.872042i | \(-0.337205\pi\) | ||||
0.489431 | + | 0.872042i | \(0.337205\pi\) | |||||||
\(860\) | −0.247013 | −0.00842307 | ||||||||
\(861\) | −7.36587 | −0.251028 | ||||||||
\(862\) | 8.46694 | 0.288385 | ||||||||
\(863\) | 30.4241 | 1.03565 | 0.517824 | − | 0.855487i | \(-0.326742\pi\) | ||||
0.517824 | + | 0.855487i | \(0.326742\pi\) | |||||||
\(864\) | 1.55164 | 0.0527878 | ||||||||
\(865\) | −20.2394 | −0.688161 | ||||||||
\(866\) | 48.3052 | 1.64148 | ||||||||
\(867\) | 2.18390 | 0.0741691 | ||||||||
\(868\) | −0.650606 | −0.0220830 | ||||||||
\(869\) | −1.75929 | −0.0596799 | ||||||||
\(870\) | 7.94056 | 0.269210 | ||||||||
\(871\) | 15.0901 | 0.511308 | ||||||||
\(872\) | 22.9630 | 0.777626 | ||||||||
\(873\) | −7.75619 | −0.262507 | ||||||||
\(874\) | 18.9083 | 0.639582 | ||||||||
\(875\) | 9.27346 | 0.313500 | ||||||||
\(876\) | 0.891303 | 0.0301143 | ||||||||
\(877\) | −35.6625 | −1.20424 | −0.602118 | − | 0.798407i | \(-0.705676\pi\) | ||||
−0.602118 | + | 0.798407i | \(0.705676\pi\) | |||||||
\(878\) | −12.7939 | −0.431774 | ||||||||
\(879\) | 9.34876 | 0.315326 | ||||||||
\(880\) | 12.1836 | 0.410710 | ||||||||
\(881\) | −21.9830 | −0.740627 | −0.370314 | − | 0.928907i | \(-0.620750\pi\) | ||||
−0.370314 | + | 0.928907i | \(0.620750\pi\) | |||||||
\(882\) | −8.26935 | −0.278444 | ||||||||
\(883\) | −24.6476 | −0.829458 | −0.414729 | − | 0.909945i | \(-0.636124\pi\) | ||||
−0.414729 | + | 0.909945i | \(0.636124\pi\) | |||||||
\(884\) | −1.34467 | −0.0452260 | ||||||||
\(885\) | 1.61481 | 0.0542812 | ||||||||
\(886\) | 8.37081 | 0.281223 | ||||||||
\(887\) | −21.9777 | −0.737938 | −0.368969 | − | 0.929442i | \(-0.620289\pi\) | ||||
−0.368969 | + | 0.929442i | \(0.620289\pi\) | |||||||
\(888\) | −5.57215 | −0.186989 | ||||||||
\(889\) | −2.09876 | −0.0703902 | ||||||||
\(890\) | −74.6124 | −2.50101 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −2.58960 | −0.0867063 | ||||||||
\(893\) | 26.0665 | 0.872282 | ||||||||
\(894\) | 9.03491 | 0.302173 | ||||||||
\(895\) | −25.1323 | −0.840082 | ||||||||
\(896\) | −7.05316 | −0.235630 | ||||||||
\(897\) | 4.51472 | 0.150742 | ||||||||
\(898\) | 22.9090 | 0.764483 | ||||||||
\(899\) | 4.70396 | 0.156886 | ||||||||
\(900\) | −2.22858 | −0.0742861 | ||||||||
\(901\) | 12.7113 | 0.423476 | ||||||||
\(902\) | 11.5475 | 0.384490 | ||||||||
\(903\) | 0.207086 | 0.00689139 | ||||||||
\(904\) | −40.2897 | −1.34002 | ||||||||
\(905\) | −46.7871 | −1.55526 | ||||||||
\(906\) | 7.84230 | 0.260543 | ||||||||
\(907\) | 19.5697 | 0.649801 | 0.324900 | − | 0.945748i | \(-0.394669\pi\) | ||||
0.324900 | + | 0.945748i | \(0.394669\pi\) | |||||||
\(908\) | 5.58885 | 0.185473 | ||||||||
\(909\) | 0.542833 | 0.0180046 | ||||||||
\(910\) | 4.41434 | 0.146334 | ||||||||
\(911\) | 29.9244 | 0.991440 | 0.495720 | − | 0.868482i | \(-0.334904\pi\) | ||||
0.495720 | + | 0.868482i | \(0.334904\pi\) | |||||||
\(912\) | −11.9453 | −0.395547 | ||||||||
\(913\) | 0.319558 | 0.0105758 | ||||||||
\(914\) | −54.4372 | −1.80062 | ||||||||
\(915\) | −3.61438 | −0.119488 | ||||||||
\(916\) | 3.33270 | 0.110115 | ||||||||
\(917\) | −6.35842 | −0.209974 | ||||||||
\(918\) | 5.75030 | 0.189788 | ||||||||
\(919\) | 13.0486 | 0.430433 | 0.215217 | − | 0.976566i | \(-0.430954\pi\) | ||||
0.215217 | + | 0.976566i | \(0.430954\pi\) | |||||||
\(920\) | 43.9012 | 1.44738 | ||||||||
\(921\) | 16.0672 | 0.529433 | ||||||||
\(922\) | −30.6114 | −1.00813 | ||||||||
\(923\) | 3.25350 | 0.107090 | ||||||||
\(924\) | 0.231446 | 0.00761402 | ||||||||
\(925\) | 15.0347 | 0.494337 | ||||||||
\(926\) | −50.3399 | −1.65427 | ||||||||
\(927\) | −18.9963 | −0.623919 | ||||||||
\(928\) | −2.59649 | −0.0852338 | ||||||||
\(929\) | −48.1672 | −1.58032 | −0.790158 | − | 0.612904i | \(-0.790001\pi\) | ||||
−0.790158 | + | 0.612904i | \(0.790001\pi\) | |||||||
\(930\) | 13.3390 | 0.437403 | ||||||||
\(931\) | −22.3204 | −0.731522 | ||||||||
\(932\) | 6.31018 | 0.206697 | ||||||||
\(933\) | −5.53945 | −0.181353 | ||||||||
\(934\) | 35.3826 | 1.15775 | ||||||||
\(935\) | −15.8308 | −0.517722 | ||||||||
\(936\) | −3.31985 | −0.108513 | ||||||||
\(937\) | −44.7933 | −1.46333 | −0.731667 | − | 0.681663i | \(-0.761257\pi\) | ||||
−0.731667 | + | 0.681663i | \(0.761257\pi\) | |||||||
\(938\) | −14.9354 | −0.487659 | ||||||||
\(939\) | 6.72316 | 0.219402 | ||||||||
\(940\) | 7.34778 | 0.239658 | ||||||||
\(941\) | 24.4400 | 0.796722 | 0.398361 | − | 0.917229i | \(-0.369579\pi\) | ||||
0.398361 | + | 0.917229i | \(0.369579\pi\) | |||||||
\(942\) | −18.0462 | −0.587978 | ||||||||
\(943\) | 35.7474 | 1.16409 | ||||||||
\(944\) | 1.50602 | 0.0490167 | ||||||||
\(945\) | 3.02685 | 0.0984635 | ||||||||
\(946\) | −0.324650 | −0.0105553 | ||||||||
\(947\) | −11.3436 | −0.368617 | −0.184309 | − | 0.982868i | \(-0.559005\pi\) | ||||
−0.184309 | + | 0.982868i | \(0.559005\pi\) | |||||||
\(948\) | 0.486218 | 0.0157916 | ||||||||
\(949\) | −3.58250 | −0.116293 | ||||||||
\(950\) | 37.5155 | 1.21716 | ||||||||
\(951\) | 25.5153 | 0.827391 | ||||||||
\(952\) | 10.9620 | 0.355281 | ||||||||
\(953\) | −13.2016 | −0.427641 | −0.213821 | − | 0.976873i | \(-0.568591\pi\) | ||||
−0.213821 | + | 0.976873i | \(0.568591\pi\) | |||||||
\(954\) | 3.81017 | 0.123359 | ||||||||
\(955\) | 67.0881 | 2.17092 | ||||||||
\(956\) | −3.59267 | −0.116195 | ||||||||
\(957\) | −1.67338 | −0.0540928 | ||||||||
\(958\) | 42.6436 | 1.37775 | ||||||||
\(959\) | 9.05497 | 0.292400 | ||||||||
\(960\) | −31.7301 | −1.02408 | ||||||||
\(961\) | −23.0980 | −0.745098 | ||||||||
\(962\) | 2.71915 | 0.0876689 | ||||||||
\(963\) | 1.11430 | 0.0359079 | ||||||||
\(964\) | −7.12187 | −0.229380 | ||||||||
\(965\) | 38.3850 | 1.23566 | ||||||||
\(966\) | −4.46845 | −0.143770 | ||||||||
\(967\) | 16.6355 | 0.534961 | 0.267480 | − | 0.963563i | \(-0.413809\pi\) | ||||
0.267480 | + | 0.963563i | \(0.413809\pi\) | |||||||
\(968\) | −2.98858 | −0.0960566 | ||||||||
\(969\) | 15.5211 | 0.498608 | ||||||||
\(970\) | 36.8047 | 1.18173 | ||||||||
\(971\) | −10.0363 | −0.322080 | −0.161040 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161040 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(972\) | −0.276371 | −0.00886461 | ||||||||
\(973\) | −7.62298 | −0.244382 | ||||||||
\(974\) | −27.7972 | −0.890679 | ||||||||
\(975\) | 8.95755 | 0.286871 | ||||||||
\(976\) | −3.37088 | −0.107899 | ||||||||
\(977\) | 11.7119 | 0.374695 | 0.187348 | − | 0.982294i | \(-0.440011\pi\) | ||||
0.187348 | + | 0.982294i | \(0.440011\pi\) | |||||||
\(978\) | 17.2607 | 0.551937 | ||||||||
\(979\) | 15.7237 | 0.502533 | ||||||||
\(980\) | −6.29182 | −0.200985 | ||||||||
\(981\) | −7.68359 | −0.245318 | ||||||||
\(982\) | −22.9219 | −0.731466 | ||||||||
\(983\) | 13.8777 | 0.442631 | 0.221316 | − | 0.975202i | \(-0.428965\pi\) | ||||
0.221316 | + | 0.975202i | \(0.428965\pi\) | |||||||
\(984\) | −26.2864 | −0.837980 | ||||||||
\(985\) | −31.4450 | −1.00192 | ||||||||
\(986\) | −9.62246 | −0.306442 | ||||||||
\(987\) | −6.16009 | −0.196078 | ||||||||
\(988\) | −1.08793 | −0.0346115 | ||||||||
\(989\) | −1.00501 | −0.0319575 | ||||||||
\(990\) | −4.74521 | −0.150813 | ||||||||
\(991\) | 13.9982 | 0.444666 | 0.222333 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222333 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(992\) | −4.36172 | −0.138485 | ||||||||
\(993\) | −3.18003 | −0.100915 | ||||||||
\(994\) | −3.22015 | −0.102137 | ||||||||
\(995\) | −48.0708 | −1.52395 | ||||||||
\(996\) | −0.0883167 | −0.00279842 | ||||||||
\(997\) | −42.5735 | −1.34832 | −0.674158 | − | 0.738587i | \(-0.735493\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(998\) | −37.9391 | −1.20094 | ||||||||
\(999\) | 1.86448 | 0.0589896 |
(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 | 2013.2.a.g.1.9 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.h.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.g.1.9 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.h.1.5 | 13 | 3.2 | odd | 2 |