Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + 2170 x^{12} - 42069 x^{11} + 19553 x^{10} + 84697 x^{9} - 82713 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.63154\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.63154 | −0.941968 | −0.470984 | − | 0.882142i | \(-0.656101\pi\) | ||||
−0.470984 | + | 0.882142i | \(0.656101\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.13171 | 0.506116 | 0.253058 | − | 0.967451i | \(-0.418564\pi\) | ||||
0.253058 | + | 0.967451i | \(0.418564\pi\) | |||||||
\(6\) | 1.63154 | 0.666072 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.338090 | −0.112697 | ||||||||
\(10\) | −1.13171 | −0.357878 | ||||||||
\(11\) | 4.25957 | 1.28431 | 0.642154 | − | 0.766576i | \(-0.278041\pi\) | ||||
0.642154 | + | 0.766576i | \(0.278041\pi\) | |||||||
\(12\) | −1.63154 | −0.470984 | ||||||||
\(13\) | 4.57626 | 1.26923 | 0.634614 | − | 0.772830i | \(-0.281159\pi\) | ||||
0.634614 | + | 0.772830i | \(0.281159\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.84643 | −0.476745 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.46210 | −1.08222 | −0.541109 | − | 0.840953i | \(-0.681995\pi\) | ||||
−0.541109 | + | 0.840953i | \(0.681995\pi\) | |||||||
\(18\) | 0.338090 | 0.0796887 | ||||||||
\(19\) | 4.98269 | 1.14311 | 0.571553 | − | 0.820565i | \(-0.306341\pi\) | ||||
0.571553 | + | 0.820565i | \(0.306341\pi\) | |||||||
\(20\) | 1.13171 | 0.253058 | ||||||||
\(21\) | −1.63154 | −0.356030 | ||||||||
\(22\) | −4.25957 | −0.908142 | ||||||||
\(23\) | −2.19484 | −0.457657 | −0.228828 | − | 0.973467i | \(-0.573489\pi\) | ||||
−0.228828 | + | 0.973467i | \(0.573489\pi\) | |||||||
\(24\) | 1.63154 | 0.333036 | ||||||||
\(25\) | −3.71923 | −0.743846 | ||||||||
\(26\) | −4.57626 | −0.897479 | ||||||||
\(27\) | 5.44621 | 1.04812 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −8.18975 | −1.52080 | −0.760399 | − | 0.649456i | \(-0.774997\pi\) | ||||
−0.760399 | + | 0.649456i | \(0.774997\pi\) | |||||||
\(30\) | 1.84643 | 0.337110 | ||||||||
\(31\) | −0.537753 | −0.0965833 | −0.0482917 | − | 0.998833i | \(-0.515378\pi\) | ||||
−0.0482917 | + | 0.998833i | \(0.515378\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.94963 | −1.20978 | ||||||||
\(34\) | 4.46210 | 0.765243 | ||||||||
\(35\) | 1.13171 | 0.191294 | ||||||||
\(36\) | −0.338090 | −0.0563484 | ||||||||
\(37\) | −0.285823 | −0.0469889 | −0.0234945 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234945 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(38\) | −4.98269 | −0.808299 | ||||||||
\(39\) | −7.46634 | −1.19557 | ||||||||
\(40\) | −1.13171 | −0.178939 | ||||||||
\(41\) | −6.78124 | −1.05905 | −0.529526 | − | 0.848294i | \(-0.677630\pi\) | ||||
−0.529526 | + | 0.848294i | \(0.677630\pi\) | |||||||
\(42\) | 1.63154 | 0.251751 | ||||||||
\(43\) | 0.00276006 | 0.000420905 0 | 0.000210453 | − | 1.00000i | \(-0.499933\pi\) | ||||
0.000210453 | 1.00000i | \(0.499933\pi\) | ||||||||
\(44\) | 4.25957 | 0.642154 | ||||||||
\(45\) | −0.382620 | −0.0570377 | ||||||||
\(46\) | 2.19484 | 0.323612 | ||||||||
\(47\) | −7.84608 | −1.14447 | −0.572234 | − | 0.820090i | \(-0.693923\pi\) | ||||
−0.572234 | + | 0.820090i | \(0.693923\pi\) | |||||||
\(48\) | −1.63154 | −0.235492 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.71923 | 0.525979 | ||||||||
\(51\) | 7.28007 | 1.01941 | ||||||||
\(52\) | 4.57626 | 0.634614 | ||||||||
\(53\) | −0.524949 | −0.0721073 | −0.0360537 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360537 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(54\) | −5.44621 | −0.741136 | ||||||||
\(55\) | 4.82059 | 0.650009 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −8.12943 | −1.07677 | ||||||||
\(58\) | 8.18975 | 1.07537 | ||||||||
\(59\) | −11.0613 | −1.44006 | −0.720028 | − | 0.693945i | \(-0.755871\pi\) | ||||
−0.720028 | + | 0.693945i | \(0.755871\pi\) | |||||||
\(60\) | −1.84643 | −0.238373 | ||||||||
\(61\) | −11.2944 | −1.44610 | −0.723048 | − | 0.690798i | \(-0.757260\pi\) | ||||
−0.723048 | + | 0.690798i | \(0.757260\pi\) | |||||||
\(62\) | 0.537753 | 0.0682947 | ||||||||
\(63\) | −0.338090 | −0.0425954 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.17900 | 0.642376 | ||||||||
\(66\) | 6.94963 | 0.855441 | ||||||||
\(67\) | −5.88748 | −0.719270 | −0.359635 | − | 0.933093i | \(-0.617099\pi\) | ||||
−0.359635 | + | 0.933093i | \(0.617099\pi\) | |||||||
\(68\) | −4.46210 | −0.541109 | ||||||||
\(69\) | 3.58097 | 0.431098 | ||||||||
\(70\) | −1.13171 | −0.135265 | ||||||||
\(71\) | 7.34167 | 0.871296 | 0.435648 | − | 0.900117i | \(-0.356519\pi\) | ||||
0.435648 | + | 0.900117i | \(0.356519\pi\) | |||||||
\(72\) | 0.338090 | 0.0398443 | ||||||||
\(73\) | 2.76410 | 0.323513 | 0.161756 | − | 0.986831i | \(-0.448284\pi\) | ||||
0.161756 | + | 0.986831i | \(0.448284\pi\) | |||||||
\(74\) | 0.285823 | 0.0332262 | ||||||||
\(75\) | 6.06806 | 0.700679 | ||||||||
\(76\) | 4.98269 | 0.571553 | ||||||||
\(77\) | 4.25957 | 0.485423 | ||||||||
\(78\) | 7.46634 | 0.845396 | ||||||||
\(79\) | 7.07373 | 0.795857 | 0.397928 | − | 0.917417i | \(-0.369729\pi\) | ||||
0.397928 | + | 0.917417i | \(0.369729\pi\) | |||||||
\(80\) | 1.13171 | 0.126529 | ||||||||
\(81\) | −7.87142 | −0.874603 | ||||||||
\(82\) | 6.78124 | 0.748862 | ||||||||
\(83\) | −10.8428 | −1.19015 | −0.595074 | − | 0.803671i | \(-0.702877\pi\) | ||||
−0.595074 | + | 0.803671i | \(0.702877\pi\) | |||||||
\(84\) | −1.63154 | −0.178015 | ||||||||
\(85\) | −5.04980 | −0.547728 | ||||||||
\(86\) | −0.00276006 | −0.000297625 0 | ||||||||
\(87\) | 13.3619 | 1.43254 | ||||||||
\(88\) | −4.25957 | −0.454071 | ||||||||
\(89\) | −7.78810 | −0.825537 | −0.412768 | − | 0.910836i | \(-0.635438\pi\) | ||||
−0.412768 | + | 0.910836i | \(0.635438\pi\) | |||||||
\(90\) | 0.382620 | 0.0403317 | ||||||||
\(91\) | 4.57626 | 0.479723 | ||||||||
\(92\) | −2.19484 | −0.228828 | ||||||||
\(93\) | 0.877364 | 0.0909784 | ||||||||
\(94\) | 7.84608 | 0.809261 | ||||||||
\(95\) | 5.63896 | 0.578545 | ||||||||
\(96\) | 1.63154 | 0.166518 | ||||||||
\(97\) | 15.5210 | 1.57592 | 0.787959 | − | 0.615728i | \(-0.211138\pi\) | ||||
0.787959 | + | 0.615728i | \(0.211138\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −1.44012 | −0.144737 | ||||||||
\(100\) | −3.71923 | −0.371923 | ||||||||
\(101\) | −11.4781 | −1.14211 | −0.571055 | − | 0.820912i | \(-0.693466\pi\) | ||||
−0.571055 | + | 0.820912i | \(0.693466\pi\) | |||||||
\(102\) | −7.28007 | −0.720834 | ||||||||
\(103\) | −0.837340 | −0.0825056 | −0.0412528 | − | 0.999149i | \(-0.513135\pi\) | ||||
−0.0412528 | + | 0.999149i | \(0.513135\pi\) | |||||||
\(104\) | −4.57626 | −0.448740 | ||||||||
\(105\) | −1.84643 | −0.180193 | ||||||||
\(106\) | 0.524949 | 0.0509876 | ||||||||
\(107\) | −4.85453 | −0.469305 | −0.234652 | − | 0.972079i | \(-0.575395\pi\) | ||||
−0.234652 | + | 0.972079i | \(0.575395\pi\) | |||||||
\(108\) | 5.44621 | 0.524062 | ||||||||
\(109\) | −0.840181 | −0.0804747 | −0.0402373 | − | 0.999190i | \(-0.512811\pi\) | ||||
−0.0402373 | + | 0.999190i | \(0.512811\pi\) | |||||||
\(110\) | −4.82059 | −0.459626 | ||||||||
\(111\) | 0.466330 | 0.0442621 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 6.08513 | 0.572441 | 0.286220 | − | 0.958164i | \(-0.407601\pi\) | ||||
0.286220 | + | 0.958164i | \(0.407601\pi\) | |||||||
\(114\) | 8.12943 | 0.761391 | ||||||||
\(115\) | −2.48393 | −0.231627 | ||||||||
\(116\) | −8.18975 | −0.760399 | ||||||||
\(117\) | −1.54719 | −0.143038 | ||||||||
\(118\) | 11.0613 | 1.01827 | ||||||||
\(119\) | −4.46210 | −0.409040 | ||||||||
\(120\) | 1.84643 | 0.168555 | ||||||||
\(121\) | 7.14390 | 0.649445 | ||||||||
\(122\) | 11.2944 | 1.02254 | ||||||||
\(123\) | 11.0638 | 0.997592 | ||||||||
\(124\) | −0.537753 | −0.0482917 | ||||||||
\(125\) | −9.86764 | −0.882589 | ||||||||
\(126\) | 0.338090 | 0.0301195 | ||||||||
\(127\) | −7.54825 | −0.669799 | −0.334899 | − | 0.942254i | \(-0.608702\pi\) | ||||
−0.334899 | + | 0.942254i | \(0.608702\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.00450314 | −0.000396479 0 | ||||||||
\(130\) | −5.17900 | −0.454229 | ||||||||
\(131\) | 2.63117 | 0.229887 | 0.114943 | − | 0.993372i | \(-0.463331\pi\) | ||||
0.114943 | + | 0.993372i | \(0.463331\pi\) | |||||||
\(132\) | −6.94963 | −0.604888 | ||||||||
\(133\) | 4.98269 | 0.432054 | ||||||||
\(134\) | 5.88748 | 0.508601 | ||||||||
\(135\) | 6.16354 | 0.530473 | ||||||||
\(136\) | 4.46210 | 0.382622 | ||||||||
\(137\) | 0.401572 | 0.0343086 | 0.0171543 | − | 0.999853i | \(-0.494539\pi\) | ||||
0.0171543 | + | 0.999853i | \(0.494539\pi\) | |||||||
\(138\) | −3.58097 | −0.304832 | ||||||||
\(139\) | −6.88303 | −0.583811 | −0.291906 | − | 0.956447i | \(-0.594289\pi\) | ||||
−0.291906 | + | 0.956447i | \(0.594289\pi\) | |||||||
\(140\) | 1.13171 | 0.0956470 | ||||||||
\(141\) | 12.8012 | 1.07805 | ||||||||
\(142\) | −7.34167 | −0.616099 | ||||||||
\(143\) | 19.4929 | 1.63008 | ||||||||
\(144\) | −0.338090 | −0.0281742 | ||||||||
\(145\) | −9.26843 | −0.769701 | ||||||||
\(146\) | −2.76410 | −0.228758 | ||||||||
\(147\) | −1.63154 | −0.134567 | ||||||||
\(148\) | −0.285823 | −0.0234945 | ||||||||
\(149\) | 16.0699 | 1.31650 | 0.658248 | − | 0.752801i | \(-0.271298\pi\) | ||||
0.658248 | + | 0.752801i | \(0.271298\pi\) | |||||||
\(150\) | −6.06806 | −0.495455 | ||||||||
\(151\) | −20.5194 | −1.66984 | −0.834921 | − | 0.550370i | \(-0.814487\pi\) | ||||
−0.834921 | + | 0.550370i | \(0.814487\pi\) | |||||||
\(152\) | −4.98269 | −0.404149 | ||||||||
\(153\) | 1.50859 | 0.121962 | ||||||||
\(154\) | −4.25957 | −0.343246 | ||||||||
\(155\) | −0.608581 | −0.0488824 | ||||||||
\(156\) | −7.46634 | −0.597785 | ||||||||
\(157\) | 9.01726 | 0.719655 | 0.359828 | − | 0.933019i | \(-0.382835\pi\) | ||||
0.359828 | + | 0.933019i | \(0.382835\pi\) | |||||||
\(158\) | −7.07373 | −0.562756 | ||||||||
\(159\) | 0.856473 | 0.0679228 | ||||||||
\(160\) | −1.13171 | −0.0894695 | ||||||||
\(161\) | −2.19484 | −0.172978 | ||||||||
\(162\) | 7.87142 | 0.618437 | ||||||||
\(163\) | −4.76823 | −0.373476 | −0.186738 | − | 0.982410i | \(-0.559792\pi\) | ||||
−0.186738 | + | 0.982410i | \(0.559792\pi\) | |||||||
\(164\) | −6.78124 | −0.529526 | ||||||||
\(165\) | −7.86497 | −0.612287 | ||||||||
\(166\) | 10.8428 | 0.841562 | ||||||||
\(167\) | −2.66178 | −0.205975 | −0.102988 | − | 0.994683i | \(-0.532840\pi\) | ||||
−0.102988 | + | 0.994683i | \(0.532840\pi\) | |||||||
\(168\) | 1.63154 | 0.125876 | ||||||||
\(169\) | 7.94219 | 0.610937 | ||||||||
\(170\) | 5.04980 | 0.387302 | ||||||||
\(171\) | −1.68460 | −0.128824 | ||||||||
\(172\) | 0.00276006 | 0.000210453 0 | ||||||||
\(173\) | 20.8332 | 1.58392 | 0.791961 | − | 0.610572i | \(-0.209060\pi\) | ||||
0.791961 | + | 0.610572i | \(0.209060\pi\) | |||||||
\(174\) | −13.3619 | −1.01296 | ||||||||
\(175\) | −3.71923 | −0.281148 | ||||||||
\(176\) | 4.25957 | 0.321077 | ||||||||
\(177\) | 18.0469 | 1.35649 | ||||||||
\(178\) | 7.78810 | 0.583743 | ||||||||
\(179\) | 9.64774 | 0.721106 | 0.360553 | − | 0.932739i | \(-0.382588\pi\) | ||||
0.360553 | + | 0.932739i | \(0.382588\pi\) | |||||||
\(180\) | −0.382620 | −0.0285188 | ||||||||
\(181\) | −14.4368 | −1.07308 | −0.536540 | − | 0.843875i | \(-0.680269\pi\) | ||||
−0.536540 | + | 0.843875i | \(0.680269\pi\) | |||||||
\(182\) | −4.57626 | −0.339215 | ||||||||
\(183\) | 18.4272 | 1.36218 | ||||||||
\(184\) | 2.19484 | 0.161806 | ||||||||
\(185\) | −0.323468 | −0.0237819 | ||||||||
\(186\) | −0.877364 | −0.0643314 | ||||||||
\(187\) | −19.0066 | −1.38990 | ||||||||
\(188\) | −7.84608 | −0.572234 | ||||||||
\(189\) | 5.44621 | 0.396154 | ||||||||
\(190\) | −5.63896 | −0.409093 | ||||||||
\(191\) | 14.8679 | 1.07581 | 0.537903 | − | 0.843007i | \(-0.319217\pi\) | ||||
0.537903 | + | 0.843007i | \(0.319217\pi\) | |||||||
\(192\) | −1.63154 | −0.117746 | ||||||||
\(193\) | −3.49277 | −0.251415 | −0.125707 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125707 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(194\) | −15.5210 | −1.11434 | ||||||||
\(195\) | −8.44973 | −0.605098 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −10.3062 | −0.734289 | −0.367144 | − | 0.930164i | \(-0.619664\pi\) | ||||
−0.367144 | + | 0.930164i | \(0.619664\pi\) | |||||||
\(198\) | 1.44012 | 0.102345 | ||||||||
\(199\) | −8.74513 | −0.619926 | −0.309963 | − | 0.950749i | \(-0.600317\pi\) | ||||
−0.309963 | + | 0.950749i | \(0.600317\pi\) | |||||||
\(200\) | 3.71923 | 0.262989 | ||||||||
\(201\) | 9.60564 | 0.677529 | ||||||||
\(202\) | 11.4781 | 0.807594 | ||||||||
\(203\) | −8.18975 | −0.574808 | ||||||||
\(204\) | 7.28007 | 0.509707 | ||||||||
\(205\) | −7.67440 | −0.536003 | ||||||||
\(206\) | 0.837340 | 0.0583402 | ||||||||
\(207\) | 0.742055 | 0.0515764 | ||||||||
\(208\) | 4.57626 | 0.317307 | ||||||||
\(209\) | 21.2241 | 1.46810 | ||||||||
\(210\) | 1.84643 | 0.127415 | ||||||||
\(211\) | 7.63204 | 0.525411 | 0.262706 | − | 0.964876i | \(-0.415385\pi\) | ||||
0.262706 | + | 0.964876i | \(0.415385\pi\) | |||||||
\(212\) | −0.524949 | −0.0360537 | ||||||||
\(213\) | −11.9782 | −0.820733 | ||||||||
\(214\) | 4.85453 | 0.331849 | ||||||||
\(215\) | 0.00312359 | 0.000213027 0 | ||||||||
\(216\) | −5.44621 | −0.370568 | ||||||||
\(217\) | −0.537753 | −0.0365051 | ||||||||
\(218\) | 0.840181 | 0.0569042 | ||||||||
\(219\) | −4.50972 | −0.304739 | ||||||||
\(220\) | 4.82059 | 0.325004 | ||||||||
\(221\) | −20.4197 | −1.37358 | ||||||||
\(222\) | −0.466330 | −0.0312980 | ||||||||
\(223\) | 0.0143017 | 0.000957713 0 | 0.000478857 | − | 1.00000i | \(-0.499848\pi\) | ||||
0.000478857 | 1.00000i | \(0.499848\pi\) | ||||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.25744 | 0.0838291 | ||||||||
\(226\) | −6.08513 | −0.404777 | ||||||||
\(227\) | −11.4591 | −0.760570 | −0.380285 | − | 0.924869i | \(-0.624174\pi\) | ||||
−0.380285 | + | 0.924869i | \(0.624174\pi\) | |||||||
\(228\) | −8.12943 | −0.538385 | ||||||||
\(229\) | −19.4007 | −1.28203 | −0.641016 | − | 0.767528i | \(-0.721487\pi\) | ||||
−0.641016 | + | 0.767528i | \(0.721487\pi\) | |||||||
\(230\) | 2.48393 | 0.163785 | ||||||||
\(231\) | −6.94963 | −0.457252 | ||||||||
\(232\) | 8.18975 | 0.537684 | ||||||||
\(233\) | 2.29636 | 0.150440 | 0.0752199 | − | 0.997167i | \(-0.476034\pi\) | ||||
0.0752199 | + | 0.997167i | \(0.476034\pi\) | |||||||
\(234\) | 1.54719 | 0.101143 | ||||||||
\(235\) | −8.87949 | −0.579234 | ||||||||
\(236\) | −11.0613 | −0.720028 | ||||||||
\(237\) | −11.5410 | −0.749671 | ||||||||
\(238\) | 4.46210 | 0.289235 | ||||||||
\(239\) | 2.01797 | 0.130532 | 0.0652659 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652659 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(240\) | −1.84643 | −0.119186 | ||||||||
\(241\) | 18.9709 | 1.22202 | 0.611012 | − | 0.791621i | \(-0.290763\pi\) | ||||
0.611012 | + | 0.791621i | \(0.290763\pi\) | |||||||
\(242\) | −7.14390 | −0.459227 | ||||||||
\(243\) | −3.49613 | −0.224277 | ||||||||
\(244\) | −11.2944 | −0.723048 | ||||||||
\(245\) | 1.13171 | 0.0723023 | ||||||||
\(246\) | −11.0638 | −0.705404 | ||||||||
\(247\) | 22.8021 | 1.45086 | ||||||||
\(248\) | 0.537753 | 0.0341474 | ||||||||
\(249\) | 17.6904 | 1.12108 | ||||||||
\(250\) | 9.86764 | 0.624085 | ||||||||
\(251\) | −18.2486 | −1.15184 | −0.575920 | − | 0.817506i | \(-0.695356\pi\) | ||||
−0.575920 | + | 0.817506i | \(0.695356\pi\) | |||||||
\(252\) | −0.338090 | −0.0212977 | ||||||||
\(253\) | −9.34908 | −0.587772 | ||||||||
\(254\) | 7.54825 | 0.473619 | ||||||||
\(255\) | 8.23893 | 0.515942 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.5693 | 0.846428 | 0.423214 | − | 0.906030i | \(-0.360902\pi\) | ||||
0.423214 | + | 0.906030i | \(0.360902\pi\) | |||||||
\(258\) | 0.00450314 | 0.000280353 0 | ||||||||
\(259\) | −0.285823 | −0.0177602 | ||||||||
\(260\) | 5.17900 | 0.321188 | ||||||||
\(261\) | 2.76888 | 0.171389 | ||||||||
\(262\) | −2.63117 | −0.162554 | ||||||||
\(263\) | −6.14923 | −0.379178 | −0.189589 | − | 0.981864i | \(-0.560716\pi\) | ||||
−0.189589 | + | 0.981864i | \(0.560716\pi\) | |||||||
\(264\) | 6.94963 | 0.427720 | ||||||||
\(265\) | −0.594090 | −0.0364947 | ||||||||
\(266\) | −4.98269 | −0.305508 | ||||||||
\(267\) | 12.7066 | 0.777629 | ||||||||
\(268\) | −5.88748 | −0.359635 | ||||||||
\(269\) | −21.1560 | −1.28991 | −0.644953 | − | 0.764223i | \(-0.723123\pi\) | ||||
−0.644953 | + | 0.764223i | \(0.723123\pi\) | |||||||
\(270\) | −6.16354 | −0.375101 | ||||||||
\(271\) | 3.35479 | 0.203789 | 0.101895 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101895 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(272\) | −4.46210 | −0.270554 | ||||||||
\(273\) | −7.46634 | −0.451883 | ||||||||
\(274\) | −0.401572 | −0.0242598 | ||||||||
\(275\) | −15.8423 | −0.955327 | ||||||||
\(276\) | 3.58097 | 0.215549 | ||||||||
\(277\) | 13.2730 | 0.797498 | 0.398749 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398749 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(278\) | 6.88303 | 0.412817 | ||||||||
\(279\) | 0.181809 | 0.0108846 | ||||||||
\(280\) | −1.13171 | −0.0676326 | ||||||||
\(281\) | −3.31705 | −0.197879 | −0.0989394 | − | 0.995093i | \(-0.531545\pi\) | ||||
−0.0989394 | + | 0.995093i | \(0.531545\pi\) | |||||||
\(282\) | −12.8012 | −0.762298 | ||||||||
\(283\) | 32.6018 | 1.93798 | 0.968988 | − | 0.247106i | \(-0.0794796\pi\) | ||||
0.968988 | + | 0.247106i | \(0.0794796\pi\) | |||||||
\(284\) | 7.34167 | 0.435648 | ||||||||
\(285\) | −9.20016 | −0.544971 | ||||||||
\(286\) | −19.4929 | −1.15264 | ||||||||
\(287\) | −6.78124 | −0.400284 | ||||||||
\(288\) | 0.338090 | 0.0199222 | ||||||||
\(289\) | 2.91030 | 0.171194 | ||||||||
\(290\) | 9.26843 | 0.544261 | ||||||||
\(291\) | −25.3231 | −1.48446 | ||||||||
\(292\) | 2.76410 | 0.161756 | ||||||||
\(293\) | 20.4707 | 1.19591 | 0.597955 | − | 0.801529i | \(-0.295980\pi\) | ||||
0.597955 | + | 0.801529i | \(0.295980\pi\) | |||||||
\(294\) | 1.63154 | 0.0951531 | ||||||||
\(295\) | −12.5182 | −0.728836 | ||||||||
\(296\) | 0.285823 | 0.0166131 | ||||||||
\(297\) | 23.1985 | 1.34611 | ||||||||
\(298\) | −16.0699 | −0.930903 | ||||||||
\(299\) | −10.0442 | −0.580870 | ||||||||
\(300\) | 6.06806 | 0.350340 | ||||||||
\(301\) | 0.00276006 | 0.000159087 0 | ||||||||
\(302\) | 20.5194 | 1.18076 | ||||||||
\(303\) | 18.7269 | 1.07583 | ||||||||
\(304\) | 4.98269 | 0.285777 | ||||||||
\(305\) | −12.7820 | −0.731893 | ||||||||
\(306\) | −1.50859 | −0.0862404 | ||||||||
\(307\) | 32.9099 | 1.87826 | 0.939132 | − | 0.343556i | \(-0.111632\pi\) | ||||
0.939132 | + | 0.343556i | \(0.111632\pi\) | |||||||
\(308\) | 4.25957 | 0.242711 | ||||||||
\(309\) | 1.36615 | 0.0777176 | ||||||||
\(310\) | 0.608581 | 0.0345651 | ||||||||
\(311\) | 8.56387 | 0.485612 | 0.242806 | − | 0.970075i | \(-0.421932\pi\) | ||||
0.242806 | + | 0.970075i | \(0.421932\pi\) | |||||||
\(312\) | 7.46634 | 0.422698 | ||||||||
\(313\) | 19.8106 | 1.11976 | 0.559880 | − | 0.828574i | \(-0.310847\pi\) | ||||
0.559880 | + | 0.828574i | \(0.310847\pi\) | |||||||
\(314\) | −9.01726 | −0.508873 | ||||||||
\(315\) | −0.382620 | −0.0215582 | ||||||||
\(316\) | 7.07373 | 0.397928 | ||||||||
\(317\) | 3.65393 | 0.205225 | 0.102613 | − | 0.994721i | \(-0.467280\pi\) | ||||
0.102613 | + | 0.994721i | \(0.467280\pi\) | |||||||
\(318\) | −0.856473 | −0.0480286 | ||||||||
\(319\) | −34.8848 | −1.95317 | ||||||||
\(320\) | 1.13171 | 0.0632645 | ||||||||
\(321\) | 7.92034 | 0.442070 | ||||||||
\(322\) | 2.19484 | 0.122314 | ||||||||
\(323\) | −22.2332 | −1.23709 | ||||||||
\(324\) | −7.87142 | −0.437301 | ||||||||
\(325\) | −17.0202 | −0.944110 | ||||||||
\(326\) | 4.76823 | 0.264088 | ||||||||
\(327\) | 1.37078 | 0.0758046 | ||||||||
\(328\) | 6.78124 | 0.374431 | ||||||||
\(329\) | −7.84608 | −0.432568 | ||||||||
\(330\) | 7.86497 | 0.432952 | ||||||||
\(331\) | −20.1991 | −1.11024 | −0.555121 | − | 0.831769i | \(-0.687328\pi\) | ||||
−0.555121 | + | 0.831769i | \(0.687328\pi\) | |||||||
\(332\) | −10.8428 | −0.595074 | ||||||||
\(333\) | 0.0966339 | 0.00529550 | ||||||||
\(334\) | 2.66178 | 0.145646 | ||||||||
\(335\) | −6.66292 | −0.364034 | ||||||||
\(336\) | −1.63154 | −0.0890076 | ||||||||
\(337\) | −15.9701 | −0.869945 | −0.434973 | − | 0.900444i | \(-0.643242\pi\) | ||||
−0.434973 | + | 0.900444i | \(0.643242\pi\) | |||||||
\(338\) | −7.94219 | −0.431998 | ||||||||
\(339\) | −9.92811 | −0.539221 | ||||||||
\(340\) | −5.04980 | −0.273864 | ||||||||
\(341\) | −2.29059 | −0.124043 | ||||||||
\(342\) | 1.68460 | 0.0910927 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.00276006 | −0.000148812 0 | ||||||||
\(345\) | 4.05262 | 0.218186 | ||||||||
\(346\) | −20.8332 | −1.12000 | ||||||||
\(347\) | −28.5250 | −1.53130 | −0.765650 | − | 0.643257i | \(-0.777583\pi\) | ||||
−0.765650 | + | 0.643257i | \(0.777583\pi\) | |||||||
\(348\) | 13.3619 | 0.716272 | ||||||||
\(349\) | 29.0357 | 1.55424 | 0.777122 | − | 0.629350i | \(-0.216679\pi\) | ||||
0.777122 | + | 0.629350i | \(0.216679\pi\) | |||||||
\(350\) | 3.71923 | 0.198801 | ||||||||
\(351\) | 24.9233 | 1.33031 | ||||||||
\(352\) | −4.25957 | −0.227036 | ||||||||
\(353\) | −21.1847 | −1.12755 | −0.563773 | − | 0.825930i | \(-0.690651\pi\) | ||||
−0.563773 | + | 0.825930i | \(0.690651\pi\) | |||||||
\(354\) | −18.0469 | −0.959181 | ||||||||
\(355\) | 8.30864 | 0.440977 | ||||||||
\(356\) | −7.78810 | −0.412768 | ||||||||
\(357\) | 7.28007 | 0.385302 | ||||||||
\(358\) | −9.64774 | −0.509899 | ||||||||
\(359\) | −22.9523 | −1.21137 | −0.605687 | − | 0.795703i | \(-0.707102\pi\) | ||||
−0.605687 | + | 0.795703i | \(0.707102\pi\) | |||||||
\(360\) | 0.382620 | 0.0201659 | ||||||||
\(361\) | 5.82717 | 0.306693 | ||||||||
\(362\) | 14.4368 | 0.758782 | ||||||||
\(363\) | −11.6555 | −0.611757 | ||||||||
\(364\) | 4.57626 | 0.239861 | ||||||||
\(365\) | 3.12816 | 0.163735 | ||||||||
\(366\) | −18.4272 | −0.963204 | ||||||||
\(367\) | −17.8076 | −0.929547 | −0.464773 | − | 0.885430i | \(-0.653864\pi\) | ||||
−0.464773 | + | 0.885430i | \(0.653864\pi\) | |||||||
\(368\) | −2.19484 | −0.114414 | ||||||||
\(369\) | 2.29267 | 0.119352 | ||||||||
\(370\) | 0.323468 | 0.0168163 | ||||||||
\(371\) | −0.524949 | −0.0272540 | ||||||||
\(372\) | 0.877364 | 0.0454892 | ||||||||
\(373\) | −20.3958 | −1.05606 | −0.528028 | − | 0.849227i | \(-0.677069\pi\) | ||||
−0.528028 | + | 0.849227i | \(0.677069\pi\) | |||||||
\(374\) | 19.0066 | 0.982807 | ||||||||
\(375\) | 16.0994 | 0.831370 | ||||||||
\(376\) | 7.84608 | 0.404631 | ||||||||
\(377\) | −37.4785 | −1.93024 | ||||||||
\(378\) | −5.44621 | −0.280123 | ||||||||
\(379\) | −15.7131 | −0.807127 | −0.403563 | − | 0.914952i | \(-0.632229\pi\) | ||||
−0.403563 | + | 0.914952i | \(0.632229\pi\) | |||||||
\(380\) | 5.63896 | 0.289272 | ||||||||
\(381\) | 12.3152 | 0.630929 | ||||||||
\(382\) | −14.8679 | −0.760710 | ||||||||
\(383\) | −13.6780 | −0.698914 | −0.349457 | − | 0.936952i | \(-0.613634\pi\) | ||||
−0.349457 | + | 0.936952i | \(0.613634\pi\) | |||||||
\(384\) | 1.63154 | 0.0832590 | ||||||||
\(385\) | 4.82059 | 0.245680 | ||||||||
\(386\) | 3.49277 | 0.177777 | ||||||||
\(387\) | −0.000933149 0 | −4.74346e−5 0 | ||||||||
\(388\) | 15.5210 | 0.787959 | ||||||||
\(389\) | 3.11248 | 0.157809 | 0.0789044 | − | 0.996882i | \(-0.474858\pi\) | ||||
0.0789044 | + | 0.996882i | \(0.474858\pi\) | |||||||
\(390\) | 8.44973 | 0.427869 | ||||||||
\(391\) | 9.79360 | 0.495284 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −4.29285 | −0.216546 | ||||||||
\(394\) | 10.3062 | 0.519220 | ||||||||
\(395\) | 8.00541 | 0.402796 | ||||||||
\(396\) | −1.44012 | −0.0723687 | ||||||||
\(397\) | −12.8864 | −0.646748 | −0.323374 | − | 0.946271i | \(-0.604817\pi\) | ||||
−0.323374 | + | 0.946271i | \(0.604817\pi\) | |||||||
\(398\) | 8.74513 | 0.438354 | ||||||||
\(399\) | −8.12943 | −0.406981 | ||||||||
\(400\) | −3.71923 | −0.185962 | ||||||||
\(401\) | 9.90827 | 0.494796 | 0.247398 | − | 0.968914i | \(-0.420425\pi\) | ||||
0.247398 | + | 0.968914i | \(0.420425\pi\) | |||||||
\(402\) | −9.60564 | −0.479086 | ||||||||
\(403\) | −2.46090 | −0.122586 | ||||||||
\(404\) | −11.4781 | −0.571055 | ||||||||
\(405\) | −8.90817 | −0.442651 | ||||||||
\(406\) | 8.18975 | 0.406451 | ||||||||
\(407\) | −1.21748 | −0.0603483 | ||||||||
\(408\) | −7.28007 | −0.360417 | ||||||||
\(409\) | 15.4593 | 0.764414 | 0.382207 | − | 0.924077i | \(-0.375164\pi\) | ||||
0.382207 | + | 0.924077i | \(0.375164\pi\) | |||||||
\(410\) | 7.67440 | 0.379011 | ||||||||
\(411\) | −0.655179 | −0.0323176 | ||||||||
\(412\) | −0.837340 | −0.0412528 | ||||||||
\(413\) | −11.0613 | −0.544290 | ||||||||
\(414\) | −0.742055 | −0.0364700 | ||||||||
\(415\) | −12.2709 | −0.602353 | ||||||||
\(416\) | −4.57626 | −0.224370 | ||||||||
\(417\) | 11.2299 | 0.549931 | ||||||||
\(418\) | −21.2241 | −1.03810 | ||||||||
\(419\) | −3.59983 | −0.175863 | −0.0879315 | − | 0.996127i | \(-0.528026\pi\) | ||||
−0.0879315 | + | 0.996127i | \(0.528026\pi\) | |||||||
\(420\) | −1.84643 | −0.0900964 | ||||||||
\(421\) | −7.04424 | −0.343315 | −0.171658 | − | 0.985157i | \(-0.554912\pi\) | ||||
−0.171658 | + | 0.985157i | \(0.554912\pi\) | |||||||
\(422\) | −7.63204 | −0.371522 | ||||||||
\(423\) | 2.65268 | 0.128978 | ||||||||
\(424\) | 0.524949 | 0.0254938 | ||||||||
\(425\) | 16.5956 | 0.805003 | ||||||||
\(426\) | 11.9782 | 0.580346 | ||||||||
\(427\) | −11.2944 | −0.546573 | ||||||||
\(428\) | −4.85453 | −0.234652 | ||||||||
\(429\) | −31.8034 | −1.53548 | ||||||||
\(430\) | −0.00312359 | −0.000150633 0 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 5.44621 | 0.262031 | ||||||||
\(433\) | 26.0320 | 1.25102 | 0.625510 | − | 0.780216i | \(-0.284891\pi\) | ||||
0.625510 | + | 0.780216i | \(0.284891\pi\) | |||||||
\(434\) | 0.537753 | 0.0258130 | ||||||||
\(435\) | 15.1218 | 0.725033 | ||||||||
\(436\) | −0.840181 | −0.0402373 | ||||||||
\(437\) | −10.9362 | −0.523150 | ||||||||
\(438\) | 4.50972 | 0.215483 | ||||||||
\(439\) | −21.6498 | −1.03329 | −0.516645 | − | 0.856199i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856199i | \(0.672819\pi\) | |||||||
\(440\) | −4.82059 | −0.229813 | ||||||||
\(441\) | −0.338090 | −0.0160995 | ||||||||
\(442\) | 20.4197 | 0.971267 | ||||||||
\(443\) | −4.41468 | −0.209748 | −0.104874 | − | 0.994486i | \(-0.533444\pi\) | ||||
−0.104874 | + | 0.994486i | \(0.533444\pi\) | |||||||
\(444\) | 0.466330 | 0.0221310 | ||||||||
\(445\) | −8.81387 | −0.417818 | ||||||||
\(446\) | −0.0143017 | −0.000677206 0 | ||||||||
\(447\) | −26.2186 | −1.24010 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 0.922409 | 0.0435312 | 0.0217656 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217656 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(450\) | −1.25744 | −0.0592761 | ||||||||
\(451\) | −28.8851 | −1.36015 | ||||||||
\(452\) | 6.08513 | 0.286220 | ||||||||
\(453\) | 33.4781 | 1.57294 | ||||||||
\(454\) | 11.4591 | 0.537804 | ||||||||
\(455\) | 5.17900 | 0.242795 | ||||||||
\(456\) | 8.12943 | 0.380696 | ||||||||
\(457\) | 14.9046 | 0.697208 | 0.348604 | − | 0.937270i | \(-0.386656\pi\) | ||||
0.348604 | + | 0.937270i | \(0.386656\pi\) | |||||||
\(458\) | 19.4007 | 0.906533 | ||||||||
\(459\) | −24.3015 | −1.13430 | ||||||||
\(460\) | −2.48393 | −0.115814 | ||||||||
\(461\) | 22.1832 | 1.03317 | 0.516587 | − | 0.856235i | \(-0.327202\pi\) | ||||
0.516587 | + | 0.856235i | \(0.327202\pi\) | |||||||
\(462\) | 6.94963 | 0.323326 | ||||||||
\(463\) | −33.8708 | −1.57411 | −0.787054 | − | 0.616884i | \(-0.788395\pi\) | ||||
−0.787054 | + | 0.616884i | \(0.788395\pi\) | |||||||
\(464\) | −8.18975 | −0.380200 | ||||||||
\(465\) | 0.992921 | 0.0460456 | ||||||||
\(466\) | −2.29636 | −0.106377 | ||||||||
\(467\) | 29.2811 | 1.35497 | 0.677485 | − | 0.735537i | \(-0.263070\pi\) | ||||
0.677485 | + | 0.735537i | \(0.263070\pi\) | |||||||
\(468\) | −1.54719 | −0.0715189 | ||||||||
\(469\) | −5.88748 | −0.271859 | ||||||||
\(470\) | 8.87949 | 0.409580 | ||||||||
\(471\) | −14.7120 | −0.677892 | ||||||||
\(472\) | 11.0613 | 0.509137 | ||||||||
\(473\) | 0.0117567 | 0.000540571 0 | ||||||||
\(474\) | 11.5410 | 0.530098 | ||||||||
\(475\) | −18.5318 | −0.850296 | ||||||||
\(476\) | −4.46210 | −0.204520 | ||||||||
\(477\) | 0.177480 | 0.00812626 | ||||||||
\(478\) | −2.01797 | −0.0922999 | ||||||||
\(479\) | −30.9658 | −1.41486 | −0.707431 | − | 0.706782i | \(-0.750146\pi\) | ||||
−0.707431 | + | 0.706782i | \(0.750146\pi\) | |||||||
\(480\) | 1.84643 | 0.0842774 | ||||||||
\(481\) | −1.30800 | −0.0596396 | ||||||||
\(482\) | −18.9709 | −0.864102 | ||||||||
\(483\) | 3.58097 | 0.162940 | ||||||||
\(484\) | 7.14390 | 0.324723 | ||||||||
\(485\) | 17.5653 | 0.797598 | ||||||||
\(486\) | 3.49613 | 0.158588 | ||||||||
\(487\) | −18.9577 | −0.859057 | −0.429529 | − | 0.903053i | \(-0.641320\pi\) | ||||
−0.429529 | + | 0.903053i | \(0.641320\pi\) | |||||||
\(488\) | 11.2944 | 0.511272 | ||||||||
\(489\) | 7.77953 | 0.351803 | ||||||||
\(490\) | −1.13171 | −0.0511255 | ||||||||
\(491\) | −3.89068 | −0.175584 | −0.0877919 | − | 0.996139i | \(-0.527981\pi\) | ||||
−0.0877919 | + | 0.996139i | \(0.527981\pi\) | |||||||
\(492\) | 11.0638 | 0.498796 | ||||||||
\(493\) | 36.5435 | 1.64583 | ||||||||
\(494\) | −22.8021 | −1.02591 | ||||||||
\(495\) | −1.62980 | −0.0732539 | ||||||||
\(496\) | −0.537753 | −0.0241458 | ||||||||
\(497\) | 7.34167 | 0.329319 | ||||||||
\(498\) | −17.6904 | −0.792724 | ||||||||
\(499\) | −26.0709 | −1.16709 | −0.583546 | − | 0.812080i | \(-0.698335\pi\) | ||||
−0.583546 | + | 0.812080i | \(0.698335\pi\) | |||||||
\(500\) | −9.86764 | −0.441294 | ||||||||
\(501\) | 4.34280 | 0.194022 | ||||||||
\(502\) | 18.2486 | 0.814475 | ||||||||
\(503\) | 34.7034 | 1.54735 | 0.773673 | − | 0.633585i | \(-0.218417\pi\) | ||||
0.773673 | + | 0.633585i | \(0.218417\pi\) | |||||||
\(504\) | 0.338090 | 0.0150597 | ||||||||
\(505\) | −12.9898 | −0.578040 | ||||||||
\(506\) | 9.34908 | 0.415617 | ||||||||
\(507\) | −12.9580 | −0.575483 | ||||||||
\(508\) | −7.54825 | −0.334899 | ||||||||
\(509\) | 25.4382 | 1.12753 | 0.563764 | − | 0.825936i | \(-0.309353\pi\) | ||||
0.563764 | + | 0.825936i | \(0.309353\pi\) | |||||||
\(510\) | −8.23893 | −0.364826 | ||||||||
\(511\) | 2.76410 | 0.122276 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 27.1368 | 1.19812 | ||||||||
\(514\) | −13.5693 | −0.598515 | ||||||||
\(515\) | −0.947626 | −0.0417574 | ||||||||
\(516\) | −0.00450314 | −0.000198239 0 | ||||||||
\(517\) | −33.4209 | −1.46985 | ||||||||
\(518\) | 0.285823 | 0.0125583 | ||||||||
\(519\) | −33.9902 | −1.49200 | ||||||||
\(520\) | −5.17900 | −0.227114 | ||||||||
\(521\) | −20.2813 | −0.888542 | −0.444271 | − | 0.895893i | \(-0.646537\pi\) | ||||
−0.444271 | + | 0.895893i | \(0.646537\pi\) | |||||||
\(522\) | −2.76888 | −0.121190 | ||||||||
\(523\) | 13.9852 | 0.611529 | 0.305764 | − | 0.952107i | \(-0.401088\pi\) | ||||
0.305764 | + | 0.952107i | \(0.401088\pi\) | |||||||
\(524\) | 2.63117 | 0.114943 | ||||||||
\(525\) | 6.06806 | 0.264832 | ||||||||
\(526\) | 6.14923 | 0.268119 | ||||||||
\(527\) | 2.39951 | 0.104524 | ||||||||
\(528\) | −6.94963 | −0.302444 | ||||||||
\(529\) | −18.1827 | −0.790550 | ||||||||
\(530\) | 0.594090 | 0.0258056 | ||||||||
\(531\) | 3.73971 | 0.162290 | ||||||||
\(532\) | 4.98269 | 0.216027 | ||||||||
\(533\) | −31.0327 | −1.34418 | ||||||||
\(534\) | −12.7066 | −0.549867 | ||||||||
\(535\) | −5.49392 | −0.237523 | ||||||||
\(536\) | 5.88748 | 0.254300 | ||||||||
\(537\) | −15.7406 | −0.679258 | ||||||||
\(538\) | 21.1560 | 0.912101 | ||||||||
\(539\) | 4.25957 | 0.183472 | ||||||||
\(540\) | 6.16354 | 0.265236 | ||||||||
\(541\) | −29.5588 | −1.27083 | −0.635417 | − | 0.772169i | \(-0.719172\pi\) | ||||
−0.635417 | + | 0.772169i | \(0.719172\pi\) | |||||||
\(542\) | −3.35479 | −0.144101 | ||||||||
\(543\) | 23.5542 | 1.01081 | ||||||||
\(544\) | 4.46210 | 0.191311 | ||||||||
\(545\) | −0.950841 | −0.0407295 | ||||||||
\(546\) | 7.46634 | 0.319530 | ||||||||
\(547\) | −23.1185 | −0.988476 | −0.494238 | − | 0.869327i | \(-0.664553\pi\) | ||||
−0.494238 | + | 0.869327i | \(0.664553\pi\) | |||||||
\(548\) | 0.401572 | 0.0171543 | ||||||||
\(549\) | 3.81852 | 0.162970 | ||||||||
\(550\) | 15.8423 | 0.675519 | ||||||||
\(551\) | −40.8070 | −1.73844 | ||||||||
\(552\) | −3.58097 | −0.152416 | ||||||||
\(553\) | 7.07373 | 0.300805 | ||||||||
\(554\) | −13.2730 | −0.563916 | ||||||||
\(555\) | 0.527750 | 0.0224018 | ||||||||
\(556\) | −6.88303 | −0.291906 | ||||||||
\(557\) | −37.9454 | −1.60780 | −0.803900 | − | 0.594765i | \(-0.797245\pi\) | ||||
−0.803900 | + | 0.594765i | \(0.797245\pi\) | |||||||
\(558\) | −0.181809 | −0.00769660 | ||||||||
\(559\) | 0.0126308 | 0.000534224 0 | ||||||||
\(560\) | 1.13171 | 0.0478235 | ||||||||
\(561\) | 31.0099 | 1.30924 | ||||||||
\(562\) | 3.31705 | 0.139921 | ||||||||
\(563\) | −1.50645 | −0.0634894 | −0.0317447 | − | 0.999496i | \(-0.510106\pi\) | ||||
−0.0317447 | + | 0.999496i | \(0.510106\pi\) | |||||||
\(564\) | 12.8012 | 0.539026 | ||||||||
\(565\) | 6.88660 | 0.289721 | ||||||||
\(566\) | −32.6018 | −1.37036 | ||||||||
\(567\) | −7.87142 | −0.330569 | ||||||||
\(568\) | −7.34167 | −0.308050 | ||||||||
\(569\) | −0.668840 | −0.0280392 | −0.0140196 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140196 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(570\) | 9.20016 | 0.385352 | ||||||||
\(571\) | −12.7813 | −0.534882 | −0.267441 | − | 0.963574i | \(-0.586178\pi\) | ||||
−0.267441 | + | 0.963574i | \(0.586178\pi\) | |||||||
\(572\) | 19.4929 | 0.815039 | ||||||||
\(573\) | −24.2576 | −1.01337 | ||||||||
\(574\) | 6.78124 | 0.283043 | ||||||||
\(575\) | 8.16313 | 0.340426 | ||||||||
\(576\) | −0.338090 | −0.0140871 | ||||||||
\(577\) | 21.5570 | 0.897428 | 0.448714 | − | 0.893675i | \(-0.351882\pi\) | ||||
0.448714 | + | 0.893675i | \(0.351882\pi\) | |||||||
\(578\) | −2.91030 | −0.121052 | ||||||||
\(579\) | 5.69857 | 0.236825 | ||||||||
\(580\) | −9.26843 | −0.384850 | ||||||||
\(581\) | −10.8428 | −0.449834 | ||||||||
\(582\) | 25.3231 | 1.04967 | ||||||||
\(583\) | −2.23606 | −0.0926079 | ||||||||
\(584\) | −2.76410 | −0.114379 | ||||||||
\(585\) | −1.75097 | −0.0723938 | ||||||||
\(586\) | −20.4707 | −0.845637 | ||||||||
\(587\) | 8.35060 | 0.344666 | 0.172333 | − | 0.985039i | \(-0.444869\pi\) | ||||
0.172333 | + | 0.985039i | \(0.444869\pi\) | |||||||
\(588\) | −1.63154 | −0.0672834 | ||||||||
\(589\) | −2.67946 | −0.110405 | ||||||||
\(590\) | 12.5182 | 0.515365 | ||||||||
\(591\) | 16.8150 | 0.691676 | ||||||||
\(592\) | −0.285823 | −0.0117472 | ||||||||
\(593\) | 25.9889 | 1.06724 | 0.533618 | − | 0.845726i | \(-0.320832\pi\) | ||||
0.533618 | + | 0.845726i | \(0.320832\pi\) | |||||||
\(594\) | −23.1985 | −0.951846 | ||||||||
\(595\) | −5.04980 | −0.207022 | ||||||||
\(596\) | 16.0699 | 0.658248 | ||||||||
\(597\) | 14.2680 | 0.583950 | ||||||||
\(598\) | 10.0442 | 0.410737 | ||||||||
\(599\) | −10.8328 | −0.442617 | −0.221308 | − | 0.975204i | \(-0.571033\pi\) | ||||
−0.221308 | + | 0.975204i | \(0.571033\pi\) | |||||||
\(600\) | −6.06806 | −0.247728 | ||||||||
\(601\) | 6.90108 | 0.281501 | 0.140751 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140751 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(602\) | −0.00276006 | −0.000112492 0 | ||||||||
\(603\) | 1.99050 | 0.0810595 | ||||||||
\(604\) | −20.5194 | −0.834921 | ||||||||
\(605\) | 8.08482 | 0.328695 | ||||||||
\(606\) | −18.7269 | −0.760727 | ||||||||
\(607\) | −37.9678 | −1.54106 | −0.770532 | − | 0.637401i | \(-0.780009\pi\) | ||||
−0.770532 | + | 0.637401i | \(0.780009\pi\) | |||||||
\(608\) | −4.98269 | −0.202075 | ||||||||
\(609\) | 13.3619 | 0.541451 | ||||||||
\(610\) | 12.7820 | 0.517526 | ||||||||
\(611\) | −35.9057 | −1.45259 | ||||||||
\(612\) | 1.50859 | 0.0609812 | ||||||||
\(613\) | −40.6488 | −1.64179 | −0.820895 | − | 0.571079i | \(-0.806525\pi\) | ||||
−0.820895 | + | 0.571079i | \(0.806525\pi\) | |||||||
\(614\) | −32.9099 | −1.32813 | ||||||||
\(615\) | 12.5211 | 0.504898 | ||||||||
\(616\) | −4.25957 | −0.171623 | ||||||||
\(617\) | −2.27059 | −0.0914103 | −0.0457052 | − | 0.998955i | \(-0.514553\pi\) | ||||
−0.0457052 | + | 0.998955i | \(0.514553\pi\) | |||||||
\(618\) | −1.36615 | −0.0549546 | ||||||||
\(619\) | −39.0898 | −1.57115 | −0.785575 | − | 0.618767i | \(-0.787633\pi\) | ||||
−0.785575 | + | 0.618767i | \(0.787633\pi\) | |||||||
\(620\) | −0.608581 | −0.0244412 | ||||||||
\(621\) | −11.9536 | −0.479681 | ||||||||
\(622\) | −8.56387 | −0.343380 | ||||||||
\(623\) | −7.78810 | −0.312024 | ||||||||
\(624\) | −7.46634 | −0.298893 | ||||||||
\(625\) | 7.42885 | 0.297154 | ||||||||
\(626\) | −19.8106 | −0.791790 | ||||||||
\(627\) | −34.6279 | −1.38290 | ||||||||
\(628\) | 9.01726 | 0.359828 | ||||||||
\(629\) | 1.27537 | 0.0508522 | ||||||||
\(630\) | 0.382620 | 0.0152440 | ||||||||
\(631\) | 23.0675 | 0.918304 | 0.459152 | − | 0.888358i | \(-0.348153\pi\) | ||||
0.459152 | + | 0.888358i | \(0.348153\pi\) | |||||||
\(632\) | −7.07373 | −0.281378 | ||||||||
\(633\) | −12.4520 | −0.494921 | ||||||||
\(634\) | −3.65393 | −0.145116 | ||||||||
\(635\) | −8.54243 | −0.338996 | ||||||||
\(636\) | 0.856473 | 0.0339614 | ||||||||
\(637\) | 4.57626 | 0.181318 | ||||||||
\(638\) | 34.8848 | 1.38110 | ||||||||
\(639\) | −2.48215 | −0.0981922 | ||||||||
\(640\) | −1.13171 | −0.0447348 | ||||||||
\(641\) | −42.4129 | −1.67521 | −0.837604 | − | 0.546278i | \(-0.816044\pi\) | ||||
−0.837604 | + | 0.546278i | \(0.816044\pi\) | |||||||
\(642\) | −7.92034 | −0.312591 | ||||||||
\(643\) | −5.50822 | −0.217223 | −0.108612 | − | 0.994084i | \(-0.534640\pi\) | ||||
−0.108612 | + | 0.994084i | \(0.534640\pi\) | |||||||
\(644\) | −2.19484 | −0.0864890 | ||||||||
\(645\) | −0.00509624 | −0.000200664 0 | ||||||||
\(646\) | 22.2332 | 0.874755 | ||||||||
\(647\) | 9.96669 | 0.391831 | 0.195916 | − | 0.980621i | \(-0.437232\pi\) | ||||
0.195916 | + | 0.980621i | \(0.437232\pi\) | |||||||
\(648\) | 7.87142 | 0.309219 | ||||||||
\(649\) | −47.1162 | −1.84947 | ||||||||
\(650\) | 17.0202 | 0.667587 | ||||||||
\(651\) | 0.877364 | 0.0343866 | ||||||||
\(652\) | −4.76823 | −0.186738 | ||||||||
\(653\) | −7.20354 | −0.281896 | −0.140948 | − | 0.990017i | \(-0.545015\pi\) | ||||
−0.140948 | + | 0.990017i | \(0.545015\pi\) | |||||||
\(654\) | −1.37078 | −0.0536019 | ||||||||
\(655\) | 2.97772 | 0.116349 | ||||||||
\(656\) | −6.78124 | −0.264763 | ||||||||
\(657\) | −0.934514 | −0.0364589 | ||||||||
\(658\) | 7.84608 | 0.305872 | ||||||||
\(659\) | −25.8502 | −1.00698 | −0.503491 | − | 0.864000i | \(-0.667951\pi\) | ||||
−0.503491 | + | 0.864000i | \(0.667951\pi\) | |||||||
\(660\) | −7.86497 | −0.306144 | ||||||||
\(661\) | −34.7135 | −1.35020 | −0.675099 | − | 0.737727i | \(-0.735899\pi\) | ||||
−0.675099 | + | 0.737727i | \(0.735899\pi\) | |||||||
\(662\) | 20.1991 | 0.785060 | ||||||||
\(663\) | 33.3155 | 1.29387 | ||||||||
\(664\) | 10.8428 | 0.420781 | ||||||||
\(665\) | 5.63896 | 0.218669 | ||||||||
\(666\) | −0.0966339 | −0.00374449 | ||||||||
\(667\) | 17.9752 | 0.696004 | ||||||||
\(668\) | −2.66178 | −0.102988 | ||||||||
\(669\) | −0.0233338 | −0.000902135 0 | ||||||||
\(670\) | 6.66292 | 0.257411 | ||||||||
\(671\) | −48.1091 | −1.85723 | ||||||||
\(672\) | 1.63154 | 0.0629379 | ||||||||
\(673\) | −22.2863 | −0.859073 | −0.429537 | − | 0.903049i | \(-0.641323\pi\) | ||||
−0.429537 | + | 0.903049i | \(0.641323\pi\) | |||||||
\(674\) | 15.9701 | 0.615144 | ||||||||
\(675\) | −20.2557 | −0.779644 | ||||||||
\(676\) | 7.94219 | 0.305469 | ||||||||
\(677\) | −20.4389 | −0.785531 | −0.392765 | − | 0.919639i | \(-0.628482\pi\) | ||||
−0.392765 | + | 0.919639i | \(0.628482\pi\) | |||||||
\(678\) | 9.92811 | 0.381287 | ||||||||
\(679\) | 15.5210 | 0.595641 | ||||||||
\(680\) | 5.04980 | 0.193651 | ||||||||
\(681\) | 18.6960 | 0.716432 | ||||||||
\(682\) | 2.29059 | 0.0877114 | ||||||||
\(683\) | −20.6173 | −0.788898 | −0.394449 | − | 0.918918i | \(-0.629065\pi\) | ||||
−0.394449 | + | 0.918918i | \(0.629065\pi\) | |||||||
\(684\) | −1.68460 | −0.0644122 | ||||||||
\(685\) | 0.454463 | 0.0173641 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 31.6529 | 1.20763 | ||||||||
\(688\) | 0.00276006 | 0.000105226 0 | ||||||||
\(689\) | −2.40231 | −0.0915206 | ||||||||
\(690\) | −4.05262 | −0.154280 | ||||||||
\(691\) | 42.0521 | 1.59974 | 0.799869 | − | 0.600175i | \(-0.204902\pi\) | ||||
0.799869 | + | 0.600175i | \(0.204902\pi\) | |||||||
\(692\) | 20.8332 | 0.791961 | ||||||||
\(693\) | −1.44012 | −0.0547056 | ||||||||
\(694\) | 28.5250 | 1.08279 | ||||||||
\(695\) | −7.78960 | −0.295476 | ||||||||
\(696\) | −13.3619 | −0.506481 | ||||||||
\(697\) | 30.2585 | 1.14612 | ||||||||
\(698\) | −29.0357 | −1.09902 | ||||||||
\(699\) | −3.74660 | −0.141709 | ||||||||
\(700\) | −3.71923 | −0.140574 | ||||||||
\(701\) | 9.58941 | 0.362187 | 0.181093 | − | 0.983466i | \(-0.442036\pi\) | ||||
0.181093 | + | 0.983466i | \(0.442036\pi\) | |||||||
\(702\) | −24.9233 | −0.940670 | ||||||||
\(703\) | −1.42416 | −0.0537134 | ||||||||
\(704\) | 4.25957 | 0.160538 | ||||||||
\(705\) | 14.4872 | 0.545620 | ||||||||
\(706\) | 21.1847 | 0.797296 | ||||||||
\(707\) | −11.4781 | −0.431677 | ||||||||
\(708\) | 18.0469 | 0.678243 | ||||||||
\(709\) | 3.96897 | 0.149058 | 0.0745289 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745289 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(710\) | −8.30864 | −0.311818 | ||||||||
\(711\) | −2.39156 | −0.0896905 | ||||||||
\(712\) | 7.78810 | 0.291871 | ||||||||
\(713\) | 1.18028 | 0.0442020 | ||||||||
\(714\) | −7.28007 | −0.272450 | ||||||||
\(715\) | 22.0603 | 0.825009 | ||||||||
\(716\) | 9.64774 | 0.360553 | ||||||||
\(717\) | −3.29239 | −0.122957 | ||||||||
\(718\) | 22.9523 | 0.856571 | ||||||||
\(719\) | 22.3423 | 0.833226 | 0.416613 | − | 0.909084i | \(-0.363217\pi\) | ||||
0.416613 | + | 0.909084i | \(0.363217\pi\) | |||||||
\(720\) | −0.382620 | −0.0142594 | ||||||||
\(721\) | −0.837340 | −0.0311842 | ||||||||
\(722\) | −5.82717 | −0.216865 | ||||||||
\(723\) | −30.9518 | −1.15111 | ||||||||
\(724\) | −14.4368 | −0.536540 | ||||||||
\(725\) | 30.4596 | 1.13124 | ||||||||
\(726\) | 11.6555 | 0.432577 | ||||||||
\(727\) | 18.9447 | 0.702619 | 0.351310 | − | 0.936259i | \(-0.385736\pi\) | ||||
0.351310 | + | 0.936259i | \(0.385736\pi\) | |||||||
\(728\) | −4.57626 | −0.169608 | ||||||||
\(729\) | 29.3183 | 1.08586 | ||||||||
\(730\) | −3.12816 | −0.115778 | ||||||||
\(731\) | −0.0123156 | −0.000455511 0 | ||||||||
\(732\) | 18.4272 | 0.681088 | ||||||||
\(733\) | 37.8644 | 1.39855 | 0.699277 | − | 0.714851i | \(-0.253505\pi\) | ||||
0.699277 | + | 0.714851i | \(0.253505\pi\) | |||||||
\(734\) | 17.8076 | 0.657289 | ||||||||
\(735\) | −1.84643 | −0.0681064 | ||||||||
\(736\) | 2.19484 | 0.0809030 | ||||||||
\(737\) | −25.0781 | −0.923764 | ||||||||
\(738\) | −2.29267 | −0.0843944 | ||||||||
\(739\) | 3.08276 | 0.113401 | 0.0567006 | − | 0.998391i | \(-0.481942\pi\) | ||||
0.0567006 | + | 0.998391i | \(0.481942\pi\) | |||||||
\(740\) | −0.323468 | −0.0118909 | ||||||||
\(741\) | −37.2024 | −1.36667 | ||||||||
\(742\) | 0.524949 | 0.0192715 | ||||||||
\(743\) | −12.0168 | −0.440854 | −0.220427 | − | 0.975404i | \(-0.570745\pi\) | ||||
−0.220427 | + | 0.975404i | \(0.570745\pi\) | |||||||
\(744\) | −0.877364 | −0.0321657 | ||||||||
\(745\) | 18.1864 | 0.666300 | ||||||||
\(746\) | 20.3958 | 0.746745 | ||||||||
\(747\) | 3.66584 | 0.134126 | ||||||||
\(748\) | −19.0066 | −0.694950 | ||||||||
\(749\) | −4.85453 | −0.177381 | ||||||||
\(750\) | −16.0994 | −0.587868 | ||||||||
\(751\) | 29.2469 | 1.06724 | 0.533618 | − | 0.845726i | \(-0.320832\pi\) | ||||
0.533618 | + | 0.845726i | \(0.320832\pi\) | |||||||
\(752\) | −7.84608 | −0.286117 | ||||||||
\(753\) | 29.7732 | 1.08500 | ||||||||
\(754\) | 37.4785 | 1.36489 | ||||||||
\(755\) | −23.2220 | −0.845134 | ||||||||
\(756\) | 5.44621 | 0.198077 | ||||||||
\(757\) | −13.3418 | −0.484915 | −0.242458 | − | 0.970162i | \(-0.577954\pi\) | ||||
−0.242458 | + | 0.970162i | \(0.577954\pi\) | |||||||
\(758\) | 15.7131 | 0.570725 | ||||||||
\(759\) | 15.2534 | 0.553662 | ||||||||
\(760\) | −5.63896 | −0.204546 | ||||||||
\(761\) | 9.74403 | 0.353221 | 0.176610 | − | 0.984281i | \(-0.443487\pi\) | ||||
0.176610 | + | 0.984281i | \(0.443487\pi\) | |||||||
\(762\) | −12.3152 | −0.446134 | ||||||||
\(763\) | −0.840181 | −0.0304166 | ||||||||
\(764\) | 14.8679 | 0.537903 | ||||||||
\(765\) | 1.70729 | 0.0617271 | ||||||||
\(766\) | 13.6780 | 0.494207 | ||||||||
\(767\) | −50.6193 | −1.82776 | ||||||||
\(768\) | −1.63154 | −0.0588730 | ||||||||
\(769\) | 3.62512 | 0.130725 | 0.0653626 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653626 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(770\) | −4.82059 | −0.173722 | ||||||||
\(771\) | −22.1388 | −0.797308 | ||||||||
\(772\) | −3.49277 | −0.125707 | ||||||||
\(773\) | −14.9357 | −0.537200 | −0.268600 | − | 0.963252i | \(-0.586561\pi\) | ||||
−0.268600 | + | 0.963252i | \(0.586561\pi\) | |||||||
\(774\) | 0.000933149 0 | 3.35414e−5 0 | ||||||||
\(775\) | 2.00003 | 0.0718432 | ||||||||
\(776\) | −15.5210 | −0.557171 | ||||||||
\(777\) | 0.466330 | 0.0167295 | ||||||||
\(778\) | −3.11248 | −0.111588 | ||||||||
\(779\) | −33.7888 | −1.21061 | ||||||||
\(780\) | −8.44973 | −0.302549 | ||||||||
\(781\) | 31.2723 | 1.11901 | ||||||||
\(782\) | −9.79360 | −0.350219 | ||||||||
\(783\) | −44.6032 | −1.59399 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.2049 | 0.364229 | ||||||||
\(786\) | 4.29285 | 0.153121 | ||||||||
\(787\) | −6.11167 | −0.217858 | −0.108929 | − | 0.994050i | \(-0.534742\pi\) | ||||
−0.108929 | + | 0.994050i | \(0.534742\pi\) | |||||||
\(788\) | −10.3062 | −0.367144 | ||||||||
\(789\) | 10.0327 | 0.357173 | ||||||||
\(790\) | −8.00541 | −0.284820 | ||||||||
\(791\) | 6.08513 | 0.216362 | ||||||||
\(792\) | 1.44012 | 0.0511724 | ||||||||
\(793\) | −51.6860 | −1.83542 | ||||||||
\(794\) | 12.8864 | 0.457320 | ||||||||
\(795\) | 0.969280 | 0.0343768 | ||||||||
\(796\) | −8.74513 | −0.309963 | ||||||||
\(797\) | −31.0721 | −1.10063 | −0.550314 | − | 0.834958i | \(-0.685492\pi\) | ||||
−0.550314 | + | 0.834958i | \(0.685492\pi\) | |||||||
\(798\) | 8.12943 | 0.287779 | ||||||||
\(799\) | 35.0100 | 1.23856 | ||||||||
\(800\) | 3.71923 | 0.131495 | ||||||||
\(801\) | 2.63308 | 0.0930354 | ||||||||
\(802\) | −9.90827 | −0.349873 | ||||||||
\(803\) | 11.7738 | 0.415490 | ||||||||
\(804\) | 9.60564 | 0.338765 | ||||||||
\(805\) | −2.48393 | −0.0875469 | ||||||||
\(806\) | 2.46090 | 0.0866815 | ||||||||
\(807\) | 34.5168 | 1.21505 | ||||||||
\(808\) | 11.4781 | 0.403797 | ||||||||
\(809\) | −24.2082 | −0.851116 | −0.425558 | − | 0.904931i | \(-0.639922\pi\) | ||||
−0.425558 | + | 0.904931i | \(0.639922\pi\) | |||||||
\(810\) | 8.90817 | 0.313001 | ||||||||
\(811\) | −31.3099 | −1.09944 | −0.549720 | − | 0.835349i | \(-0.685266\pi\) | ||||
−0.549720 | + | 0.835349i | \(0.685266\pi\) | |||||||
\(812\) | −8.18975 | −0.287404 | ||||||||
\(813\) | −5.47347 | −0.191963 | ||||||||
\(814\) | 1.21748 | 0.0426727 | ||||||||
\(815\) | −5.39625 | −0.189022 | ||||||||
\(816\) | 7.28007 | 0.254853 | ||||||||
\(817\) | 0.0137525 | 0.000481139 0 | ||||||||
\(818\) | −15.4593 | −0.540522 | ||||||||
\(819\) | −1.54719 | −0.0540632 | ||||||||
\(820\) | −7.67440 | −0.268002 | ||||||||
\(821\) | 35.0922 | 1.22473 | 0.612363 | − | 0.790577i | \(-0.290219\pi\) | ||||
0.612363 | + | 0.790577i | \(0.290219\pi\) | |||||||
\(822\) | 0.655179 | 0.0228520 | ||||||||
\(823\) | 16.2807 | 0.567510 | 0.283755 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283755 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(824\) | 0.837340 | 0.0291701 | ||||||||
\(825\) | 25.8473 | 0.899888 | ||||||||
\(826\) | 11.0613 | 0.384871 | ||||||||
\(827\) | 17.9961 | 0.625787 | 0.312893 | − | 0.949788i | \(-0.398702\pi\) | ||||
0.312893 | + | 0.949788i | \(0.398702\pi\) | |||||||
\(828\) | 0.742055 | 0.0257882 | ||||||||
\(829\) | 28.5139 | 0.990328 | 0.495164 | − | 0.868800i | \(-0.335108\pi\) | ||||
0.495164 | + | 0.868800i | \(0.335108\pi\) | |||||||
\(830\) | 12.2709 | 0.425928 | ||||||||
\(831\) | −21.6554 | −0.751218 | ||||||||
\(832\) | 4.57626 | 0.158653 | ||||||||
\(833\) | −4.46210 | −0.154602 | ||||||||
\(834\) | −11.2299 | −0.388860 | ||||||||
\(835\) | −3.01237 | −0.104247 | ||||||||
\(836\) | 21.2241 | 0.734050 | ||||||||
\(837\) | −2.92872 | −0.101231 | ||||||||
\(838\) | 3.59983 | 0.124354 | ||||||||
\(839\) | 51.2089 | 1.76793 | 0.883964 | − | 0.467556i | \(-0.154865\pi\) | ||||
0.883964 | + | 0.467556i | \(0.154865\pi\) | |||||||
\(840\) | 1.84643 | 0.0637077 | ||||||||
\(841\) | 38.0721 | 1.31283 | ||||||||
\(842\) | 7.04424 | 0.242761 | ||||||||
\(843\) | 5.41189 | 0.186395 | ||||||||
\(844\) | 7.63204 | 0.262706 | ||||||||
\(845\) | 8.98825 | 0.309205 | ||||||||
\(846\) | −2.65268 | −0.0912011 | ||||||||
\(847\) | 7.14390 | 0.245467 | ||||||||
\(848\) | −0.524949 | −0.0180268 | ||||||||
\(849\) | −53.1910 | −1.82551 | ||||||||
\(850\) | −16.5956 | −0.569223 | ||||||||
\(851\) | 0.627336 | 0.0215048 | ||||||||
\(852\) | −11.9782 | −0.410366 | ||||||||
\(853\) | −23.5534 | −0.806453 | −0.403226 | − | 0.915100i | \(-0.632111\pi\) | ||||
−0.403226 | + | 0.915100i | \(0.632111\pi\) | |||||||
\(854\) | 11.2944 | 0.386486 | ||||||||
\(855\) | −1.90648 | −0.0652001 | ||||||||
\(856\) | 4.85453 | 0.165924 | ||||||||
\(857\) | −42.7907 | −1.46170 | −0.730851 | − | 0.682537i | \(-0.760877\pi\) | ||||
−0.730851 | + | 0.682537i | \(0.760877\pi\) | |||||||
\(858\) | 31.8034 | 1.08575 | ||||||||
\(859\) | −3.12743 | −0.106707 | −0.0533533 | − | 0.998576i | \(-0.516991\pi\) | ||||
−0.0533533 | + | 0.998576i | \(0.516991\pi\) | |||||||
\(860\) | 0.00312359 | 0.000106513 0 | ||||||||
\(861\) | 11.0638 | 0.377054 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 11.4305 | 0.389098 | 0.194549 | − | 0.980893i | \(-0.437676\pi\) | ||||
0.194549 | + | 0.980893i | \(0.437676\pi\) | |||||||
\(864\) | −5.44621 | −0.185284 | ||||||||
\(865\) | 23.5772 | 0.801648 | ||||||||
\(866\) | −26.0320 | −0.884605 | ||||||||
\(867\) | −4.74826 | −0.161259 | ||||||||
\(868\) | −0.537753 | −0.0182525 | ||||||||
\(869\) | 30.1310 | 1.02212 | ||||||||
\(870\) | −15.1218 | −0.512676 | ||||||||
\(871\) | −26.9427 | −0.912917 | ||||||||
\(872\) | 0.840181 | 0.0284521 | ||||||||
\(873\) | −5.24750 | −0.177601 | ||||||||
\(874\) | 10.9362 | 0.369923 | ||||||||
\(875\) | −9.86764 | −0.333587 | ||||||||
\(876\) | −4.50972 | −0.152369 | ||||||||
\(877\) | 27.2350 | 0.919662 | 0.459831 | − | 0.888006i | \(-0.347910\pi\) | ||||
0.459831 | + | 0.888006i | \(0.347910\pi\) | |||||||
\(878\) | 21.6498 | 0.730647 | ||||||||
\(879\) | −33.3987 | −1.12651 | ||||||||
\(880\) | 4.82059 | 0.162502 | ||||||||
\(881\) | −1.56039 | −0.0525709 | −0.0262854 | − | 0.999654i | \(-0.508368\pi\) | ||||
−0.0262854 | + | 0.999654i | \(0.508368\pi\) | |||||||
\(882\) | 0.338090 | 0.0113841 | ||||||||
\(883\) | 21.6417 | 0.728303 | 0.364151 | − | 0.931340i | \(-0.381359\pi\) | ||||
0.364151 | + | 0.931340i | \(0.381359\pi\) | |||||||
\(884\) | −20.4197 | −0.686790 | ||||||||
\(885\) | 20.4238 | 0.686540 | ||||||||
\(886\) | 4.41468 | 0.148314 | ||||||||
\(887\) | −36.2668 | −1.21772 | −0.608860 | − | 0.793278i | \(-0.708373\pi\) | ||||
−0.608860 | + | 0.793278i | \(0.708373\pi\) | |||||||
\(888\) | −0.466330 | −0.0156490 | ||||||||
\(889\) | −7.54825 | −0.253160 | ||||||||
\(890\) | 8.81387 | 0.295442 | ||||||||
\(891\) | −33.5288 | −1.12326 | ||||||||
\(892\) | 0.0143017 | 0.000478857 0 | ||||||||
\(893\) | −39.0946 | −1.30825 | ||||||||
\(894\) | 26.2186 | 0.876881 | ||||||||
\(895\) | 10.9184 | 0.364963 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 16.3874 | 0.547161 | ||||||||
\(898\) | −0.922409 | −0.0307812 | ||||||||
\(899\) | 4.40407 | 0.146884 | ||||||||
\(900\) | 1.25744 | 0.0419146 | ||||||||
\(901\) | 2.34237 | 0.0780358 | ||||||||
\(902\) | 28.8851 | 0.961770 | ||||||||
\(903\) | −0.00450314 | −0.000149855 0 | ||||||||
\(904\) | −6.08513 | −0.202388 | ||||||||
\(905\) | −16.3383 | −0.543103 | ||||||||
\(906\) | −33.4781 | −1.11223 | ||||||||
\(907\) | 7.17032 | 0.238087 | 0.119043 | − | 0.992889i | \(-0.462017\pi\) | ||||
0.119043 | + | 0.992889i | \(0.462017\pi\) | |||||||
\(908\) | −11.4591 | −0.380285 | ||||||||
\(909\) | 3.88062 | 0.128712 | ||||||||
\(910\) | −5.17900 | −0.171682 | ||||||||
\(911\) | −25.8384 | −0.856065 | −0.428032 | − | 0.903763i | \(-0.640793\pi\) | ||||
−0.428032 | + | 0.903763i | \(0.640793\pi\) | |||||||
\(912\) | −8.12943 | −0.269192 | ||||||||
\(913\) | −46.1855 | −1.52852 | ||||||||
\(914\) | −14.9046 | −0.493000 | ||||||||
\(915\) | 20.8542 | 0.689419 | ||||||||
\(916\) | −19.4007 | −0.641016 | ||||||||
\(917\) | 2.63117 | 0.0868889 | ||||||||
\(918\) | 24.3015 | 0.802070 | ||||||||
\(919\) | 13.9390 | 0.459804 | 0.229902 | − | 0.973214i | \(-0.426159\pi\) | ||||
0.229902 | + | 0.973214i | \(0.426159\pi\) | |||||||
\(920\) | 2.48393 | 0.0818926 | ||||||||
\(921\) | −53.6936 | −1.76926 | ||||||||
\(922\) | −22.1832 | −0.730564 | ||||||||
\(923\) | 33.5974 | 1.10587 | ||||||||
\(924\) | −6.94963 | −0.228626 | ||||||||
\(925\) | 1.06304 | 0.0349526 | ||||||||
\(926\) | 33.8708 | 1.11306 | ||||||||
\(927\) | 0.283097 | 0.00929811 | ||||||||
\(928\) | 8.18975 | 0.268842 | ||||||||
\(929\) | −41.0531 | −1.34691 | −0.673455 | − | 0.739229i | \(-0.735190\pi\) | ||||
−0.673455 | + | 0.739229i | \(0.735190\pi\) | |||||||
\(930\) | −0.992921 | −0.0325592 | ||||||||
\(931\) | 4.98269 | 0.163301 | ||||||||
\(932\) | 2.29636 | 0.0752199 | ||||||||
\(933\) | −13.9723 | −0.457431 | ||||||||
\(934\) | −29.2811 | −0.958108 | ||||||||
\(935\) | −21.5100 | −0.703451 | ||||||||
\(936\) | 1.54719 | 0.0505715 | ||||||||
\(937\) | 21.5908 | 0.705341 | 0.352671 | − | 0.935748i | \(-0.385274\pi\) | ||||
0.352671 | + | 0.935748i | \(0.385274\pi\) | |||||||
\(938\) | 5.88748 | 0.192233 | ||||||||
\(939\) | −32.3217 | −1.05478 | ||||||||
\(940\) | −8.87949 | −0.289617 | ||||||||
\(941\) | −37.7679 | −1.23120 | −0.615600 | − | 0.788059i | \(-0.711086\pi\) | ||||
−0.615600 | + | 0.788059i | \(0.711086\pi\) | |||||||
\(942\) | 14.7120 | 0.479342 | ||||||||
\(943\) | 14.8838 | 0.484682 | ||||||||
\(944\) | −11.0613 | −0.360014 | ||||||||
\(945\) | 6.16354 | 0.200500 | ||||||||
\(946\) | −0.0117567 | −0.000382242 0 | ||||||||
\(947\) | 12.6737 | 0.411841 | 0.205921 | − | 0.978569i | \(-0.433981\pi\) | ||||
0.205921 | + | 0.978569i | \(0.433981\pi\) | |||||||
\(948\) | −11.5410 | −0.374836 | ||||||||
\(949\) | 12.6492 | 0.410611 | ||||||||
\(950\) | 18.5318 | 0.601250 | ||||||||
\(951\) | −5.96152 | −0.193316 | ||||||||
\(952\) | 4.46210 | 0.144617 | ||||||||
\(953\) | 26.8236 | 0.868901 | 0.434450 | − | 0.900696i | \(-0.356943\pi\) | ||||
0.434450 | + | 0.900696i | \(0.356943\pi\) | |||||||
\(954\) | −0.177480 | −0.00574614 | ||||||||
\(955\) | 16.8262 | 0.544483 | ||||||||
\(956\) | 2.01797 | 0.0652659 | ||||||||
\(957\) | 56.9158 | 1.83983 | ||||||||
\(958\) | 30.9658 | 1.00046 | ||||||||
\(959\) | 0.401572 | 0.0129674 | ||||||||
\(960\) | −1.84643 | −0.0595931 | ||||||||
\(961\) | −30.7108 | −0.990672 | ||||||||
\(962\) | 1.30800 | 0.0421716 | ||||||||
\(963\) | 1.64127 | 0.0528892 | ||||||||
\(964\) | 18.9709 | 0.611012 | ||||||||
\(965\) | −3.95280 | −0.127245 | ||||||||
\(966\) | −3.58097 | −0.115216 | ||||||||
\(967\) | 28.9365 | 0.930535 | 0.465267 | − | 0.885170i | \(-0.345958\pi\) | ||||
0.465267 | + | 0.885170i | \(0.345958\pi\) | |||||||
\(968\) | −7.14390 | −0.229614 | ||||||||
\(969\) | 36.2743 | 1.16530 | ||||||||
\(970\) | −17.5653 | −0.563987 | ||||||||
\(971\) | 24.0696 | 0.772430 | 0.386215 | − | 0.922409i | \(-0.373782\pi\) | ||||
0.386215 | + | 0.922409i | \(0.373782\pi\) | |||||||
\(972\) | −3.49613 | −0.112139 | ||||||||
\(973\) | −6.88303 | −0.220660 | ||||||||
\(974\) | 18.9577 | 0.607445 | ||||||||
\(975\) | 27.7690 | 0.889321 | ||||||||
\(976\) | −11.2944 | −0.361524 | ||||||||
\(977\) | 17.9735 | 0.575023 | 0.287511 | − | 0.957777i | \(-0.407172\pi\) | ||||
0.287511 | + | 0.957777i | \(0.407172\pi\) | |||||||
\(978\) | −7.77953 | −0.248762 | ||||||||
\(979\) | −33.1739 | −1.06024 | ||||||||
\(980\) | 1.13171 | 0.0361512 | ||||||||
\(981\) | 0.284057 | 0.00906924 | ||||||||
\(982\) | 3.89068 | 0.124157 | ||||||||
\(983\) | 56.2876 | 1.79530 | 0.897648 | − | 0.440714i | \(-0.145275\pi\) | ||||
0.897648 | + | 0.440714i | \(0.145275\pi\) | |||||||
\(984\) | −11.0638 | −0.352702 | ||||||||
\(985\) | −11.6637 | −0.371635 | ||||||||
\(986\) | −36.5435 | −1.16378 | ||||||||
\(987\) | 12.8012 | 0.407465 | ||||||||
\(988\) | 22.8021 | 0.725431 | ||||||||
\(989\) | −0.00605790 | −0.000192630 0 | ||||||||
\(990\) | 1.62980 | 0.0517983 | ||||||||
\(991\) | 50.9832 | 1.61953 | 0.809767 | − | 0.586751i | \(-0.199593\pi\) | ||||
0.809767 | + | 0.586751i | \(0.199593\pi\) | |||||||
\(992\) | 0.537753 | 0.0170737 | ||||||||
\(993\) | 32.9556 | 1.04581 | ||||||||
\(994\) | −7.34167 | −0.232864 | ||||||||
\(995\) | −9.89695 | −0.313754 | ||||||||
\(996\) | 17.6904 | 0.560541 | ||||||||
\(997\) | −24.8437 | −0.786807 | −0.393404 | − | 0.919366i | \(-0.628702\pi\) | ||||
−0.393404 | + | 0.919366i | \(0.628702\pi\) | |||||||
\(998\) | 26.0709 | 0.825259 | ||||||||
\(999\) | −1.55665 | −0.0492503 |
(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 | 6034.2.a.k.1.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.k.1.6 | ✓ | 20 | 1.1 | even | 1 | trivial |