Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 16x^{7} + 76x^{6} + 30x^{5} - 366x^{4} + 300x^{3} + 101x^{2} - 106x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.217879\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.926601 | 0.414388 | 0.207194 | − | 0.978300i | \(-0.433567\pi\) | ||||
0.207194 | + | 0.978300i | \(0.433567\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.782121 | −0.295614 | −0.147807 | − | 0.989016i | \(-0.547221\pi\) | ||||
−0.147807 | + | 0.989016i | \(0.547221\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.926601 | 0.293017 | ||||||||
\(11\) | −4.19823 | −1.26581 | −0.632907 | − | 0.774228i | \(-0.718139\pi\) | ||||
−0.632907 | + | 0.774228i | \(0.718139\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.67596 | 0.464828 | 0.232414 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232414 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(14\) | −0.782121 | −0.209031 | ||||||||
\(15\) | −0.926601 | −0.239247 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.331752 | 0.0804618 | 0.0402309 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402309 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.926601 | 0.207194 | ||||||||
\(21\) | 0.782121 | 0.170673 | ||||||||
\(22\) | −4.19823 | −0.895066 | ||||||||
\(23\) | 0.149937 | 0.0312639 | 0.0156320 | − | 0.999878i | \(-0.495024\pi\) | ||||
0.0156320 | + | 0.999878i | \(0.495024\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.14141 | −0.828282 | ||||||||
\(26\) | 1.67596 | 0.328683 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.782121 | −0.147807 | ||||||||
\(29\) | 3.09255 | 0.574273 | 0.287136 | − | 0.957890i | \(-0.407297\pi\) | ||||
0.287136 | + | 0.957890i | \(0.407297\pi\) | |||||||
\(30\) | −0.926601 | −0.169173 | ||||||||
\(31\) | 4.21227 | 0.756545 | 0.378273 | − | 0.925694i | \(-0.376518\pi\) | ||||
0.378273 | + | 0.925694i | \(0.376518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.19823 | 0.730818 | ||||||||
\(34\) | 0.331752 | 0.0568951 | ||||||||
\(35\) | −0.724714 | −0.122499 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.0253 | −1.64815 | −0.824075 | − | 0.566481i | \(-0.808304\pi\) | ||||
−0.824075 | + | 0.566481i | \(0.808304\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.67596 | −0.268369 | ||||||||
\(40\) | 0.926601 | 0.146508 | ||||||||
\(41\) | −5.83159 | −0.910742 | −0.455371 | − | 0.890302i | \(-0.650493\pi\) | ||||
−0.455371 | + | 0.890302i | \(0.650493\pi\) | |||||||
\(42\) | 0.782121 | 0.120684 | ||||||||
\(43\) | 6.59799 | 1.00618 | 0.503092 | − | 0.864233i | \(-0.332196\pi\) | ||||
0.503092 | + | 0.864233i | \(0.332196\pi\) | |||||||
\(44\) | −4.19823 | −0.632907 | ||||||||
\(45\) | 0.926601 | 0.138129 | ||||||||
\(46\) | 0.149937 | 0.0221069 | ||||||||
\(47\) | −0.211837 | −0.0308996 | −0.0154498 | − | 0.999881i | \(-0.504918\pi\) | ||||
−0.0154498 | + | 0.999881i | \(0.504918\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.38829 | −0.912612 | ||||||||
\(50\) | −4.14141 | −0.585684 | ||||||||
\(51\) | −0.331752 | −0.0464546 | ||||||||
\(52\) | 1.67596 | 0.232414 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.89008 | −0.524539 | ||||||||
\(56\) | −0.782121 | −0.104515 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 3.09255 | 0.406072 | ||||||||
\(59\) | −9.04676 | −1.17779 | −0.588894 | − | 0.808211i | \(-0.700436\pi\) | ||||
−0.588894 | + | 0.808211i | \(0.700436\pi\) | |||||||
\(60\) | −0.926601 | −0.119624 | ||||||||
\(61\) | −0.848763 | −0.108673 | −0.0543365 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543365 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(62\) | 4.21227 | 0.534958 | ||||||||
\(63\) | −0.782121 | −0.0985380 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.55295 | 0.192620 | ||||||||
\(66\) | 4.19823 | 0.516767 | ||||||||
\(67\) | 1.44469 | 0.176497 | 0.0882484 | − | 0.996099i | \(-0.471873\pi\) | ||||
0.0882484 | + | 0.996099i | \(0.471873\pi\) | |||||||
\(68\) | 0.331752 | 0.0402309 | ||||||||
\(69\) | −0.149937 | −0.0180502 | ||||||||
\(70\) | −0.724714 | −0.0866199 | ||||||||
\(71\) | −8.46784 | −1.00495 | −0.502474 | − | 0.864593i | \(-0.667577\pi\) | ||||
−0.502474 | + | 0.864593i | \(0.667577\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.41498 | −0.984899 | −0.492450 | − | 0.870341i | \(-0.663898\pi\) | ||||
−0.492450 | + | 0.870341i | \(0.663898\pi\) | |||||||
\(74\) | −10.0253 | −1.16542 | ||||||||
\(75\) | 4.14141 | 0.478209 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 3.28353 | 0.374192 | ||||||||
\(78\) | −1.67596 | −0.189765 | ||||||||
\(79\) | 16.4095 | 1.84621 | 0.923104 | − | 0.384551i | \(-0.125644\pi\) | ||||
0.923104 | + | 0.384551i | \(0.125644\pi\) | |||||||
\(80\) | 0.926601 | 0.103597 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.83159 | −0.643992 | ||||||||
\(83\) | 11.2084 | 1.23029 | 0.615143 | − | 0.788415i | \(-0.289098\pi\) | ||||
0.615143 | + | 0.788415i | \(0.289098\pi\) | |||||||
\(84\) | 0.782121 | 0.0853364 | ||||||||
\(85\) | 0.307402 | 0.0333424 | ||||||||
\(86\) | 6.59799 | 0.711480 | ||||||||
\(87\) | −3.09255 | −0.331557 | ||||||||
\(88\) | −4.19823 | −0.447533 | ||||||||
\(89\) | 13.8033 | 1.46315 | 0.731573 | − | 0.681763i | \(-0.238786\pi\) | ||||
0.731573 | + | 0.681763i | \(0.238786\pi\) | |||||||
\(90\) | 0.926601 | 0.0976723 | ||||||||
\(91\) | −1.31081 | −0.137410 | ||||||||
\(92\) | 0.149937 | 0.0156320 | ||||||||
\(93\) | −4.21227 | −0.436792 | ||||||||
\(94\) | −0.211837 | −0.0218493 | ||||||||
\(95\) | −0.926601 | −0.0950672 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −13.9685 | −1.41828 | −0.709142 | − | 0.705066i | \(-0.750917\pi\) | ||||
−0.709142 | + | 0.705066i | \(0.750917\pi\) | |||||||
\(98\) | −6.38829 | −0.645314 | ||||||||
\(99\) | −4.19823 | −0.421938 | ||||||||
\(100\) | −4.14141 | −0.414141 | ||||||||
\(101\) | −18.3409 | −1.82499 | −0.912496 | − | 0.409085i | \(-0.865848\pi\) | ||||
−0.912496 | + | 0.409085i | \(0.865848\pi\) | |||||||
\(102\) | −0.331752 | −0.0328484 | ||||||||
\(103\) | 3.24954 | 0.320187 | 0.160093 | − | 0.987102i | \(-0.448820\pi\) | ||||
0.160093 | + | 0.987102i | \(0.448820\pi\) | |||||||
\(104\) | 1.67596 | 0.164342 | ||||||||
\(105\) | 0.724714 | 0.0707248 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −9.19467 | −0.888883 | −0.444441 | − | 0.895808i | \(-0.646598\pi\) | ||||
−0.444441 | + | 0.895808i | \(0.646598\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −14.6653 | −1.40468 | −0.702341 | − | 0.711841i | \(-0.747862\pi\) | ||||
−0.702341 | + | 0.711841i | \(0.747862\pi\) | |||||||
\(110\) | −3.89008 | −0.370905 | ||||||||
\(111\) | 10.0253 | 0.951560 | ||||||||
\(112\) | −0.782121 | −0.0739035 | ||||||||
\(113\) | −19.8904 | −1.87113 | −0.935566 | − | 0.353153i | \(-0.885110\pi\) | ||||
−0.935566 | + | 0.353153i | \(0.885110\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0.138931 | 0.0129554 | ||||||||
\(116\) | 3.09255 | 0.287136 | ||||||||
\(117\) | 1.67596 | 0.154943 | ||||||||
\(118\) | −9.04676 | −0.832821 | ||||||||
\(119\) | −0.259470 | −0.0237856 | ||||||||
\(120\) | −0.926601 | −0.0845867 | ||||||||
\(121\) | 6.62515 | 0.602286 | ||||||||
\(122\) | −0.848763 | −0.0768434 | ||||||||
\(123\) | 5.83159 | 0.525817 | ||||||||
\(124\) | 4.21227 | 0.378273 | ||||||||
\(125\) | −8.47044 | −0.757619 | ||||||||
\(126\) | −0.782121 | −0.0696769 | ||||||||
\(127\) | 3.58632 | 0.318235 | 0.159117 | − | 0.987260i | \(-0.449135\pi\) | ||||
0.159117 | + | 0.987260i | \(0.449135\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.59799 | −0.580921 | ||||||||
\(130\) | 1.55295 | 0.136203 | ||||||||
\(131\) | −14.6250 | −1.27780 | −0.638898 | − | 0.769292i | \(-0.720609\pi\) | ||||
−0.638898 | + | 0.769292i | \(0.720609\pi\) | |||||||
\(132\) | 4.19823 | 0.365409 | ||||||||
\(133\) | 0.782121 | 0.0678185 | ||||||||
\(134\) | 1.44469 | 0.124802 | ||||||||
\(135\) | −0.926601 | −0.0797491 | ||||||||
\(136\) | 0.331752 | 0.0284475 | ||||||||
\(137\) | −3.01463 | −0.257558 | −0.128779 | − | 0.991673i | \(-0.541106\pi\) | ||||
−0.128779 | + | 0.991673i | \(0.541106\pi\) | |||||||
\(138\) | −0.149937 | −0.0127634 | ||||||||
\(139\) | 6.69751 | 0.568075 | 0.284038 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284038 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(140\) | −0.724714 | −0.0612495 | ||||||||
\(141\) | 0.211837 | 0.0178399 | ||||||||
\(142\) | −8.46784 | −0.710605 | ||||||||
\(143\) | −7.03608 | −0.588387 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.86556 | 0.237972 | ||||||||
\(146\) | −8.41498 | −0.696429 | ||||||||
\(147\) | 6.38829 | 0.526897 | ||||||||
\(148\) | −10.0253 | −0.824075 | ||||||||
\(149\) | 8.53603 | 0.699299 | 0.349649 | − | 0.936881i | \(-0.386301\pi\) | ||||
0.349649 | + | 0.936881i | \(0.386301\pi\) | |||||||
\(150\) | 4.14141 | 0.338145 | ||||||||
\(151\) | −14.2099 | −1.15639 | −0.578195 | − | 0.815899i | \(-0.696243\pi\) | ||||
−0.578195 | + | 0.815899i | \(0.696243\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0.331752 | 0.0268206 | ||||||||
\(154\) | 3.28353 | 0.264594 | ||||||||
\(155\) | 3.90309 | 0.313504 | ||||||||
\(156\) | −1.67596 | −0.134184 | ||||||||
\(157\) | −3.89737 | −0.311044 | −0.155522 | − | 0.987832i | \(-0.549706\pi\) | ||||
−0.155522 | + | 0.987832i | \(0.549706\pi\) | |||||||
\(158\) | 16.4095 | 1.30547 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 0.926601 | 0.0732542 | ||||||||
\(161\) | −0.117268 | −0.00924205 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 13.0131 | 1.01927 | 0.509634 | − | 0.860391i | \(-0.329781\pi\) | ||||
0.509634 | + | 0.860391i | \(0.329781\pi\) | |||||||
\(164\) | −5.83159 | −0.455371 | ||||||||
\(165\) | 3.89008 | 0.302843 | ||||||||
\(166\) | 11.2084 | 0.869944 | ||||||||
\(167\) | 7.49380 | 0.579888 | 0.289944 | − | 0.957044i | \(-0.406363\pi\) | ||||
0.289944 | + | 0.957044i | \(0.406363\pi\) | |||||||
\(168\) | 0.782121 | 0.0603419 | ||||||||
\(169\) | −10.1911 | −0.783934 | ||||||||
\(170\) | 0.307402 | 0.0235767 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 6.59799 | 0.503092 | ||||||||
\(173\) | −2.08193 | −0.158286 | −0.0791432 | − | 0.996863i | \(-0.525218\pi\) | ||||
−0.0791432 | + | 0.996863i | \(0.525218\pi\) | |||||||
\(174\) | −3.09255 | −0.234446 | ||||||||
\(175\) | 3.23908 | 0.244852 | ||||||||
\(176\) | −4.19823 | −0.316454 | ||||||||
\(177\) | 9.04676 | 0.679996 | ||||||||
\(178\) | 13.8033 | 1.03460 | ||||||||
\(179\) | 5.99501 | 0.448088 | 0.224044 | − | 0.974579i | \(-0.428074\pi\) | ||||
0.224044 | + | 0.974579i | \(0.428074\pi\) | |||||||
\(180\) | 0.926601 | 0.0690647 | ||||||||
\(181\) | −10.6345 | −0.790458 | −0.395229 | − | 0.918583i | \(-0.629335\pi\) | ||||
−0.395229 | + | 0.918583i | \(0.629335\pi\) | |||||||
\(182\) | −1.31081 | −0.0971634 | ||||||||
\(183\) | 0.848763 | 0.0627423 | ||||||||
\(184\) | 0.149937 | 0.0110535 | ||||||||
\(185\) | −9.28945 | −0.682974 | ||||||||
\(186\) | −4.21227 | −0.308858 | ||||||||
\(187\) | −1.39277 | −0.101850 | ||||||||
\(188\) | −0.211837 | −0.0154498 | ||||||||
\(189\) | 0.782121 | 0.0568909 | ||||||||
\(190\) | −0.926601 | −0.0672227 | ||||||||
\(191\) | −14.0937 | −1.01978 | −0.509891 | − | 0.860239i | \(-0.670314\pi\) | ||||
−0.509891 | + | 0.860239i | \(0.670314\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.26766 | −0.307193 | −0.153597 | − | 0.988134i | \(-0.549086\pi\) | ||||
−0.153597 | + | 0.988134i | \(0.549086\pi\) | |||||||
\(194\) | −13.9685 | −1.00288 | ||||||||
\(195\) | −1.55295 | −0.111209 | ||||||||
\(196\) | −6.38829 | −0.456306 | ||||||||
\(197\) | −7.60094 | −0.541544 | −0.270772 | − | 0.962643i | \(-0.587279\pi\) | ||||
−0.270772 | + | 0.962643i | \(0.587279\pi\) | |||||||
\(198\) | −4.19823 | −0.298355 | ||||||||
\(199\) | 15.5322 | 1.10105 | 0.550524 | − | 0.834819i | \(-0.314428\pi\) | ||||
0.550524 | + | 0.834819i | \(0.314428\pi\) | |||||||
\(200\) | −4.14141 | −0.292842 | ||||||||
\(201\) | −1.44469 | −0.101900 | ||||||||
\(202\) | −18.3409 | −1.29046 | ||||||||
\(203\) | −2.41875 | −0.169763 | ||||||||
\(204\) | −0.331752 | −0.0232273 | ||||||||
\(205\) | −5.40356 | −0.377401 | ||||||||
\(206\) | 3.24954 | 0.226406 | ||||||||
\(207\) | 0.149937 | 0.0104213 | ||||||||
\(208\) | 1.67596 | 0.116207 | ||||||||
\(209\) | 4.19823 | 0.290398 | ||||||||
\(210\) | 0.724714 | 0.0500100 | ||||||||
\(211\) | 17.5152 | 1.20579 | 0.602897 | − | 0.797819i | \(-0.294013\pi\) | ||||
0.602897 | + | 0.797819i | \(0.294013\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | 8.46784 | 0.580207 | ||||||||
\(214\) | −9.19467 | −0.628535 | ||||||||
\(215\) | 6.11371 | 0.416951 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.29450 | −0.223645 | ||||||||
\(218\) | −14.6653 | −0.993260 | ||||||||
\(219\) | 8.41498 | 0.568632 | ||||||||
\(220\) | −3.89008 | −0.262269 | ||||||||
\(221\) | 0.556005 | 0.0374009 | ||||||||
\(222\) | 10.0253 | 0.672854 | ||||||||
\(223\) | 6.25847 | 0.419098 | 0.209549 | − | 0.977798i | \(-0.432800\pi\) | ||||
0.209549 | + | 0.977798i | \(0.432800\pi\) | |||||||
\(224\) | −0.782121 | −0.0522577 | ||||||||
\(225\) | −4.14141 | −0.276094 | ||||||||
\(226\) | −19.8904 | −1.32309 | ||||||||
\(227\) | −0.619197 | −0.0410975 | −0.0205488 | − | 0.999789i | \(-0.506541\pi\) | ||||
−0.0205488 | + | 0.999789i | \(0.506541\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 25.8321 | 1.70703 | 0.853517 | − | 0.521065i | \(-0.174465\pi\) | ||||
0.853517 | + | 0.521065i | \(0.174465\pi\) | |||||||
\(230\) | 0.138931 | 0.00916086 | ||||||||
\(231\) | −3.28353 | −0.216040 | ||||||||
\(232\) | 3.09255 | 0.203036 | ||||||||
\(233\) | −8.13029 | −0.532633 | −0.266317 | − | 0.963886i | \(-0.585807\pi\) | ||||
−0.266317 | + | 0.963886i | \(0.585807\pi\) | |||||||
\(234\) | 1.67596 | 0.109561 | ||||||||
\(235\) | −0.196288 | −0.0128044 | ||||||||
\(236\) | −9.04676 | −0.588894 | ||||||||
\(237\) | −16.4095 | −1.06591 | ||||||||
\(238\) | −0.259470 | −0.0168190 | ||||||||
\(239\) | −7.75661 | −0.501733 | −0.250867 | − | 0.968022i | \(-0.580716\pi\) | ||||
−0.250867 | + | 0.968022i | \(0.580716\pi\) | |||||||
\(240\) | −0.926601 | −0.0598118 | ||||||||
\(241\) | −5.37695 | −0.346359 | −0.173180 | − | 0.984890i | \(-0.555404\pi\) | ||||
−0.173180 | + | 0.984890i | \(0.555404\pi\) | |||||||
\(242\) | 6.62515 | 0.425881 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.848763 | −0.0543365 | ||||||||
\(245\) | −5.91939 | −0.378176 | ||||||||
\(246\) | 5.83159 | 0.371809 | ||||||||
\(247\) | −1.67596 | −0.106639 | ||||||||
\(248\) | 4.21227 | 0.267479 | ||||||||
\(249\) | −11.2084 | −0.710306 | ||||||||
\(250\) | −8.47044 | −0.535718 | ||||||||
\(251\) | −12.5236 | −0.790484 | −0.395242 | − | 0.918577i | \(-0.629339\pi\) | ||||
−0.395242 | + | 0.918577i | \(0.629339\pi\) | |||||||
\(252\) | −0.782121 | −0.0492690 | ||||||||
\(253\) | −0.629468 | −0.0395743 | ||||||||
\(254\) | 3.58632 | 0.225026 | ||||||||
\(255\) | −0.307402 | −0.0192503 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.06979 | −0.191489 | −0.0957443 | − | 0.995406i | \(-0.530523\pi\) | ||||
−0.0957443 | + | 0.995406i | \(0.530523\pi\) | |||||||
\(258\) | −6.59799 | −0.410773 | ||||||||
\(259\) | 7.84100 | 0.487216 | ||||||||
\(260\) | 1.55295 | 0.0963098 | ||||||||
\(261\) | 3.09255 | 0.191424 | ||||||||
\(262\) | −14.6250 | −0.903538 | ||||||||
\(263\) | 16.9553 | 1.04551 | 0.522755 | − | 0.852483i | \(-0.324904\pi\) | ||||
0.522755 | + | 0.852483i | \(0.324904\pi\) | |||||||
\(264\) | 4.19823 | 0.258383 | ||||||||
\(265\) | 0.926601 | 0.0569206 | ||||||||
\(266\) | 0.782121 | 0.0479549 | ||||||||
\(267\) | −13.8033 | −0.844748 | ||||||||
\(268\) | 1.44469 | 0.0882484 | ||||||||
\(269\) | 5.93047 | 0.361587 | 0.180794 | − | 0.983521i | \(-0.442133\pi\) | ||||
0.180794 | + | 0.983521i | \(0.442133\pi\) | |||||||
\(270\) | −0.926601 | −0.0563911 | ||||||||
\(271\) | −2.26289 | −0.137461 | −0.0687303 | − | 0.997635i | \(-0.521895\pi\) | ||||
−0.0687303 | + | 0.997635i | \(0.521895\pi\) | |||||||
\(272\) | 0.331752 | 0.0201154 | ||||||||
\(273\) | 1.31081 | 0.0793336 | ||||||||
\(274\) | −3.01463 | −0.182121 | ||||||||
\(275\) | 17.3866 | 1.04845 | ||||||||
\(276\) | −0.149937 | −0.00902512 | ||||||||
\(277\) | 11.2497 | 0.675930 | 0.337965 | − | 0.941159i | \(-0.390261\pi\) | ||||
0.337965 | + | 0.941159i | \(0.390261\pi\) | |||||||
\(278\) | 6.69751 | 0.401690 | ||||||||
\(279\) | 4.21227 | 0.252182 | ||||||||
\(280\) | −0.724714 | −0.0433099 | ||||||||
\(281\) | −21.8386 | −1.30278 | −0.651392 | − | 0.758741i | \(-0.725815\pi\) | ||||
−0.651392 | + | 0.758741i | \(0.725815\pi\) | |||||||
\(282\) | 0.211837 | 0.0126147 | ||||||||
\(283\) | −9.22107 | −0.548136 | −0.274068 | − | 0.961710i | \(-0.588369\pi\) | ||||
−0.274068 | + | 0.961710i | \(0.588369\pi\) | |||||||
\(284\) | −8.46784 | −0.502474 | ||||||||
\(285\) | 0.926601 | 0.0548871 | ||||||||
\(286\) | −7.03608 | −0.416052 | ||||||||
\(287\) | 4.56101 | 0.269228 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8899 | −0.993526 | ||||||||
\(290\) | 2.86556 | 0.168272 | ||||||||
\(291\) | 13.9685 | 0.818846 | ||||||||
\(292\) | −8.41498 | −0.492450 | ||||||||
\(293\) | 20.5377 | 1.19983 | 0.599913 | − | 0.800065i | \(-0.295202\pi\) | ||||
0.599913 | + | 0.800065i | \(0.295202\pi\) | |||||||
\(294\) | 6.38829 | 0.372572 | ||||||||
\(295\) | −8.38273 | −0.488061 | ||||||||
\(296\) | −10.0253 | −0.582709 | ||||||||
\(297\) | 4.19823 | 0.243606 | ||||||||
\(298\) | 8.53603 | 0.494479 | ||||||||
\(299\) | 0.251288 | 0.0145324 | ||||||||
\(300\) | 4.14141 | 0.239104 | ||||||||
\(301\) | −5.16043 | −0.297442 | ||||||||
\(302\) | −14.2099 | −0.817691 | ||||||||
\(303\) | 18.3409 | 1.05366 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.786464 | −0.0450328 | ||||||||
\(306\) | 0.331752 | 0.0189650 | ||||||||
\(307\) | −27.6440 | −1.57773 | −0.788863 | − | 0.614569i | \(-0.789330\pi\) | ||||
−0.788863 | + | 0.614569i | \(0.789330\pi\) | |||||||
\(308\) | 3.28353 | 0.187096 | ||||||||
\(309\) | −3.24954 | −0.184860 | ||||||||
\(310\) | 3.90309 | 0.221681 | ||||||||
\(311\) | 14.0486 | 0.796622 | 0.398311 | − | 0.917250i | \(-0.369596\pi\) | ||||
0.398311 | + | 0.917250i | \(0.369596\pi\) | |||||||
\(312\) | −1.67596 | −0.0948827 | ||||||||
\(313\) | −18.3113 | −1.03502 | −0.517508 | − | 0.855678i | \(-0.673140\pi\) | ||||
−0.517508 | + | 0.855678i | \(0.673140\pi\) | |||||||
\(314\) | −3.89737 | −0.219941 | ||||||||
\(315\) | −0.724714 | −0.0408330 | ||||||||
\(316\) | 16.4095 | 0.923104 | ||||||||
\(317\) | 11.3498 | 0.637466 | 0.318733 | − | 0.947844i | \(-0.396743\pi\) | ||||
0.318733 | + | 0.947844i | \(0.396743\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −12.9833 | −0.726923 | ||||||||
\(320\) | 0.926601 | 0.0517986 | ||||||||
\(321\) | 9.19467 | 0.513197 | ||||||||
\(322\) | −0.117268 | −0.00653512 | ||||||||
\(323\) | −0.331752 | −0.0184592 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.94085 | −0.385009 | ||||||||
\(326\) | 13.0131 | 0.720731 | ||||||||
\(327\) | 14.6653 | 0.810994 | ||||||||
\(328\) | −5.83159 | −0.321996 | ||||||||
\(329\) | 0.165682 | 0.00913434 | ||||||||
\(330\) | 3.89008 | 0.214142 | ||||||||
\(331\) | −1.52973 | −0.0840817 | −0.0420408 | − | 0.999116i | \(-0.513386\pi\) | ||||
−0.0420408 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(332\) | 11.2084 | 0.615143 | ||||||||
\(333\) | −10.0253 | −0.549383 | ||||||||
\(334\) | 7.49380 | 0.410043 | ||||||||
\(335\) | 1.33865 | 0.0731382 | ||||||||
\(336\) | 0.782121 | 0.0426682 | ||||||||
\(337\) | −30.0246 | −1.63555 | −0.817773 | − | 0.575540i | \(-0.804792\pi\) | ||||
−0.817773 | + | 0.575540i | \(0.804792\pi\) | |||||||
\(338\) | −10.1911 | −0.554325 | ||||||||
\(339\) | 19.8904 | 1.08030 | ||||||||
\(340\) | 0.307402 | 0.0166712 | ||||||||
\(341\) | −17.6841 | −0.957646 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 10.4713 | 0.565395 | ||||||||
\(344\) | 6.59799 | 0.355740 | ||||||||
\(345\) | −0.138931 | −0.00747981 | ||||||||
\(346\) | −2.08193 | −0.111925 | ||||||||
\(347\) | −19.7549 | −1.06050 | −0.530248 | − | 0.847842i | \(-0.677901\pi\) | ||||
−0.530248 | + | 0.847842i | \(0.677901\pi\) | |||||||
\(348\) | −3.09255 | −0.165778 | ||||||||
\(349\) | −26.5106 | −1.41908 | −0.709541 | − | 0.704664i | \(-0.751098\pi\) | ||||
−0.709541 | + | 0.704664i | \(0.751098\pi\) | |||||||
\(350\) | 3.23908 | 0.173136 | ||||||||
\(351\) | −1.67596 | −0.0894563 | ||||||||
\(352\) | −4.19823 | −0.223767 | ||||||||
\(353\) | 13.0469 | 0.694415 | 0.347207 | − | 0.937788i | \(-0.387130\pi\) | ||||
0.347207 | + | 0.937788i | \(0.387130\pi\) | |||||||
\(354\) | 9.04676 | 0.480830 | ||||||||
\(355\) | −7.84630 | −0.416438 | ||||||||
\(356\) | 13.8033 | 0.731573 | ||||||||
\(357\) | 0.259470 | 0.0137326 | ||||||||
\(358\) | 5.99501 | 0.316846 | ||||||||
\(359\) | 1.34879 | 0.0711863 | 0.0355932 | − | 0.999366i | \(-0.488668\pi\) | ||||
0.0355932 | + | 0.999366i | \(0.488668\pi\) | |||||||
\(360\) | 0.926601 | 0.0488361 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −10.6345 | −0.558938 | ||||||||
\(363\) | −6.62515 | −0.347730 | ||||||||
\(364\) | −1.31081 | −0.0687049 | ||||||||
\(365\) | −7.79733 | −0.408131 | ||||||||
\(366\) | 0.848763 | 0.0443655 | ||||||||
\(367\) | 7.04736 | 0.367869 | 0.183935 | − | 0.982938i | \(-0.441117\pi\) | ||||
0.183935 | + | 0.982938i | \(0.441117\pi\) | |||||||
\(368\) | 0.149937 | 0.00781598 | ||||||||
\(369\) | −5.83159 | −0.303581 | ||||||||
\(370\) | −9.28945 | −0.482936 | ||||||||
\(371\) | −0.782121 | −0.0406057 | ||||||||
\(372\) | −4.21227 | −0.218396 | ||||||||
\(373\) | −4.63270 | −0.239872 | −0.119936 | − | 0.992782i | \(-0.538269\pi\) | ||||
−0.119936 | + | 0.992782i | \(0.538269\pi\) | |||||||
\(374\) | −1.39277 | −0.0720186 | ||||||||
\(375\) | 8.47044 | 0.437412 | ||||||||
\(376\) | −0.211837 | −0.0109246 | ||||||||
\(377\) | 5.18300 | 0.266938 | ||||||||
\(378\) | 0.782121 | 0.0402280 | ||||||||
\(379\) | −1.15152 | −0.0591498 | −0.0295749 | − | 0.999563i | \(-0.509415\pi\) | ||||
−0.0295749 | + | 0.999563i | \(0.509415\pi\) | |||||||
\(380\) | −0.926601 | −0.0475336 | ||||||||
\(381\) | −3.58632 | −0.183733 | ||||||||
\(382\) | −14.0937 | −0.721095 | ||||||||
\(383\) | −21.9422 | −1.12119 | −0.560596 | − | 0.828089i | \(-0.689428\pi\) | ||||
−0.560596 | + | 0.828089i | \(0.689428\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.04252 | 0.155061 | ||||||||
\(386\) | −4.26766 | −0.217218 | ||||||||
\(387\) | 6.59799 | 0.335395 | ||||||||
\(388\) | −13.9685 | −0.709142 | ||||||||
\(389\) | −36.2915 | −1.84005 | −0.920026 | − | 0.391858i | \(-0.871832\pi\) | ||||
−0.920026 | + | 0.391858i | \(0.871832\pi\) | |||||||
\(390\) | −1.55295 | −0.0786366 | ||||||||
\(391\) | 0.0497418 | 0.00251555 | ||||||||
\(392\) | −6.38829 | −0.322657 | ||||||||
\(393\) | 14.6250 | 0.737735 | ||||||||
\(394\) | −7.60094 | −0.382930 | ||||||||
\(395\) | 15.2050 | 0.765047 | ||||||||
\(396\) | −4.19823 | −0.210969 | ||||||||
\(397\) | 0.247673 | 0.0124304 | 0.00621518 | − | 0.999981i | \(-0.498022\pi\) | ||||
0.00621518 | + | 0.999981i | \(0.498022\pi\) | |||||||
\(398\) | 15.5322 | 0.778559 | ||||||||
\(399\) | −0.782121 | −0.0391550 | ||||||||
\(400\) | −4.14141 | −0.207071 | ||||||||
\(401\) | 7.65273 | 0.382159 | 0.191080 | − | 0.981575i | \(-0.438801\pi\) | ||||
0.191080 | + | 0.981575i | \(0.438801\pi\) | |||||||
\(402\) | −1.44469 | −0.0720545 | ||||||||
\(403\) | 7.05960 | 0.351664 | ||||||||
\(404\) | −18.3409 | −0.912496 | ||||||||
\(405\) | 0.926601 | 0.0460432 | ||||||||
\(406\) | −2.41875 | −0.120041 | ||||||||
\(407\) | 42.0885 | 2.08625 | ||||||||
\(408\) | −0.331752 | −0.0164242 | ||||||||
\(409\) | 2.60227 | 0.128674 | 0.0643369 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643369 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(410\) | −5.40356 | −0.266863 | ||||||||
\(411\) | 3.01463 | 0.148701 | ||||||||
\(412\) | 3.24954 | 0.160093 | ||||||||
\(413\) | 7.07566 | 0.348170 | ||||||||
\(414\) | 0.149937 | 0.00736898 | ||||||||
\(415\) | 10.3858 | 0.509816 | ||||||||
\(416\) | 1.67596 | 0.0821708 | ||||||||
\(417\) | −6.69751 | −0.327978 | ||||||||
\(418\) | 4.19823 | 0.205342 | ||||||||
\(419\) | 19.4884 | 0.952070 | 0.476035 | − | 0.879426i | \(-0.342073\pi\) | ||||
0.476035 | + | 0.879426i | \(0.342073\pi\) | |||||||
\(420\) | 0.724714 | 0.0353624 | ||||||||
\(421\) | 13.4744 | 0.656703 | 0.328352 | − | 0.944556i | \(-0.393507\pi\) | ||||
0.328352 | + | 0.944556i | \(0.393507\pi\) | |||||||
\(422\) | 17.5152 | 0.852626 | ||||||||
\(423\) | −0.211837 | −0.0102999 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −1.37392 | −0.0666450 | ||||||||
\(426\) | 8.46784 | 0.410268 | ||||||||
\(427\) | 0.663835 | 0.0321252 | ||||||||
\(428\) | −9.19467 | −0.444441 | ||||||||
\(429\) | 7.03608 | 0.339705 | ||||||||
\(430\) | 6.11371 | 0.294829 | ||||||||
\(431\) | −5.56985 | −0.268290 | −0.134145 | − | 0.990962i | \(-0.542829\pi\) | ||||
−0.134145 | + | 0.990962i | \(0.542829\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 39.4783 | 1.89721 | 0.948603 | − | 0.316467i | \(-0.102497\pi\) | ||||
0.948603 | + | 0.316467i | \(0.102497\pi\) | |||||||
\(434\) | −3.29450 | −0.158141 | ||||||||
\(435\) | −2.86556 | −0.137393 | ||||||||
\(436\) | −14.6653 | −0.702341 | ||||||||
\(437\) | −0.149937 | −0.00717244 | ||||||||
\(438\) | 8.41498 | 0.402083 | ||||||||
\(439\) | 25.2570 | 1.20545 | 0.602725 | − | 0.797949i | \(-0.294082\pi\) | ||||
0.602725 | + | 0.797949i | \(0.294082\pi\) | |||||||
\(440\) | −3.89008 | −0.185452 | ||||||||
\(441\) | −6.38829 | −0.304204 | ||||||||
\(442\) | 0.556005 | 0.0264464 | ||||||||
\(443\) | −8.17156 | −0.388243 | −0.194121 | − | 0.980978i | \(-0.562186\pi\) | ||||
−0.194121 | + | 0.980978i | \(0.562186\pi\) | |||||||
\(444\) | 10.0253 | 0.475780 | ||||||||
\(445\) | 12.7901 | 0.606311 | ||||||||
\(446\) | 6.25847 | 0.296347 | ||||||||
\(447\) | −8.53603 | −0.403740 | ||||||||
\(448\) | −0.782121 | −0.0369517 | ||||||||
\(449\) | −27.2199 | −1.28459 | −0.642294 | − | 0.766458i | \(-0.722017\pi\) | ||||
−0.642294 | + | 0.766458i | \(0.722017\pi\) | |||||||
\(450\) | −4.14141 | −0.195228 | ||||||||
\(451\) | 24.4824 | 1.15283 | ||||||||
\(452\) | −19.8904 | −0.935566 | ||||||||
\(453\) | 14.2099 | 0.667642 | ||||||||
\(454\) | −0.619197 | −0.0290603 | ||||||||
\(455\) | −1.21459 | −0.0569410 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 21.0437 | 0.984385 | 0.492192 | − | 0.870486i | \(-0.336196\pi\) | ||||
0.492192 | + | 0.870486i | \(0.336196\pi\) | |||||||
\(458\) | 25.8321 | 1.20706 | ||||||||
\(459\) | −0.331752 | −0.0154849 | ||||||||
\(460\) | 0.138931 | 0.00647770 | ||||||||
\(461\) | 21.6102 | 1.00649 | 0.503244 | − | 0.864144i | \(-0.332140\pi\) | ||||
0.503244 | + | 0.864144i | \(0.332140\pi\) | |||||||
\(462\) | −3.28353 | −0.152763 | ||||||||
\(463\) | −5.20944 | −0.242103 | −0.121052 | − | 0.992646i | \(-0.538627\pi\) | ||||
−0.121052 | + | 0.992646i | \(0.538627\pi\) | |||||||
\(464\) | 3.09255 | 0.143568 | ||||||||
\(465\) | −3.90309 | −0.181001 | ||||||||
\(466\) | −8.13029 | −0.376629 | ||||||||
\(467\) | 3.52818 | 0.163265 | 0.0816324 | − | 0.996663i | \(-0.473987\pi\) | ||||
0.0816324 | + | 0.996663i | \(0.473987\pi\) | |||||||
\(468\) | 1.67596 | 0.0774714 | ||||||||
\(469\) | −1.12992 | −0.0521749 | ||||||||
\(470\) | −0.196288 | −0.00905409 | ||||||||
\(471\) | 3.89737 | 0.179581 | ||||||||
\(472\) | −9.04676 | −0.416411 | ||||||||
\(473\) | −27.6999 | −1.27364 | ||||||||
\(474\) | −16.4095 | −0.753711 | ||||||||
\(475\) | 4.14141 | 0.190021 | ||||||||
\(476\) | −0.259470 | −0.0118928 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | −7.75661 | −0.354779 | ||||||||
\(479\) | 7.53696 | 0.344372 | 0.172186 | − | 0.985064i | \(-0.444917\pi\) | ||||
0.172186 | + | 0.985064i | \(0.444917\pi\) | |||||||
\(480\) | −0.926601 | −0.0422933 | ||||||||
\(481\) | −16.8020 | −0.766107 | ||||||||
\(482\) | −5.37695 | −0.244913 | ||||||||
\(483\) | 0.117268 | 0.00533590 | ||||||||
\(484\) | 6.62515 | 0.301143 | ||||||||
\(485\) | −12.9432 | −0.587720 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −10.5849 | −0.479648 | −0.239824 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239824 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(488\) | −0.848763 | −0.0384217 | ||||||||
\(489\) | −13.0131 | −0.588475 | ||||||||
\(490\) | −5.91939 | −0.267411 | ||||||||
\(491\) | −15.6741 | −0.707364 | −0.353682 | − | 0.935366i | \(-0.615071\pi\) | ||||
−0.353682 | + | 0.935366i | \(0.615071\pi\) | |||||||
\(492\) | 5.83159 | 0.262909 | ||||||||
\(493\) | 1.02596 | 0.0462070 | ||||||||
\(494\) | −1.67596 | −0.0754051 | ||||||||
\(495\) | −3.89008 | −0.174846 | ||||||||
\(496\) | 4.21227 | 0.189136 | ||||||||
\(497\) | 6.62287 | 0.297076 | ||||||||
\(498\) | −11.2084 | −0.502262 | ||||||||
\(499\) | −24.7962 | −1.11003 | −0.555015 | − | 0.831840i | \(-0.687288\pi\) | ||||
−0.555015 | + | 0.831840i | \(0.687288\pi\) | |||||||
\(500\) | −8.47044 | −0.378809 | ||||||||
\(501\) | −7.49380 | −0.334798 | ||||||||
\(502\) | −12.5236 | −0.558957 | ||||||||
\(503\) | −16.5036 | −0.735857 | −0.367929 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367929 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(504\) | −0.782121 | −0.0348384 | ||||||||
\(505\) | −16.9947 | −0.756256 | ||||||||
\(506\) | −0.629468 | −0.0279833 | ||||||||
\(507\) | 10.1911 | 0.452605 | ||||||||
\(508\) | 3.58632 | 0.159117 | ||||||||
\(509\) | −10.1343 | −0.449193 | −0.224597 | − | 0.974452i | \(-0.572106\pi\) | ||||
−0.224597 | + | 0.974452i | \(0.572106\pi\) | |||||||
\(510\) | −0.307402 | −0.0136120 | ||||||||
\(511\) | 6.58154 | 0.291150 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −3.06979 | −0.135403 | ||||||||
\(515\) | 3.01103 | 0.132682 | ||||||||
\(516\) | −6.59799 | −0.290460 | ||||||||
\(517\) | 0.889340 | 0.0391131 | ||||||||
\(518\) | 7.84100 | 0.344514 | ||||||||
\(519\) | 2.08193 | 0.0913867 | ||||||||
\(520\) | 1.55295 | 0.0681013 | ||||||||
\(521\) | −43.7732 | −1.91774 | −0.958869 | − | 0.283849i | \(-0.908389\pi\) | ||||
−0.958869 | + | 0.283849i | \(0.908389\pi\) | |||||||
\(522\) | 3.09255 | 0.135357 | ||||||||
\(523\) | −1.72443 | −0.0754040 | −0.0377020 | − | 0.999289i | \(-0.512004\pi\) | ||||
−0.0377020 | + | 0.999289i | \(0.512004\pi\) | |||||||
\(524\) | −14.6250 | −0.638898 | ||||||||
\(525\) | −3.23908 | −0.141365 | ||||||||
\(526\) | 16.9553 | 0.739287 | ||||||||
\(527\) | 1.39743 | 0.0608730 | ||||||||
\(528\) | 4.19823 | 0.182705 | ||||||||
\(529\) | −22.9775 | −0.999023 | ||||||||
\(530\) | 0.926601 | 0.0402490 | ||||||||
\(531\) | −9.04676 | −0.392596 | ||||||||
\(532\) | 0.782121 | 0.0339092 | ||||||||
\(533\) | −9.77353 | −0.423339 | ||||||||
\(534\) | −13.8033 | −0.597327 | ||||||||
\(535\) | −8.51979 | −0.368343 | ||||||||
\(536\) | 1.44469 | 0.0624010 | ||||||||
\(537\) | −5.99501 | −0.258704 | ||||||||
\(538\) | 5.93047 | 0.255681 | ||||||||
\(539\) | 26.8195 | 1.15520 | ||||||||
\(540\) | −0.926601 | −0.0398745 | ||||||||
\(541\) | 6.52896 | 0.280702 | 0.140351 | − | 0.990102i | \(-0.455177\pi\) | ||||
0.140351 | + | 0.990102i | \(0.455177\pi\) | |||||||
\(542\) | −2.26289 | −0.0971993 | ||||||||
\(543\) | 10.6345 | 0.456371 | ||||||||
\(544\) | 0.331752 | 0.0142238 | ||||||||
\(545\) | −13.5889 | −0.582084 | ||||||||
\(546\) | 1.31081 | 0.0560973 | ||||||||
\(547\) | 13.6643 | 0.584242 | 0.292121 | − | 0.956381i | \(-0.405639\pi\) | ||||
0.292121 | + | 0.956381i | \(0.405639\pi\) | |||||||
\(548\) | −3.01463 | −0.128779 | ||||||||
\(549\) | −0.848763 | −0.0362243 | ||||||||
\(550\) | 17.3866 | 0.741367 | ||||||||
\(551\) | −3.09255 | −0.131747 | ||||||||
\(552\) | −0.149937 | −0.00638172 | ||||||||
\(553\) | −12.8342 | −0.545765 | ||||||||
\(554\) | 11.2497 | 0.477955 | ||||||||
\(555\) | 9.28945 | 0.394315 | ||||||||
\(556\) | 6.69751 | 0.284038 | ||||||||
\(557\) | 24.8490 | 1.05289 | 0.526443 | − | 0.850210i | \(-0.323525\pi\) | ||||
0.526443 | + | 0.850210i | \(0.323525\pi\) | |||||||
\(558\) | 4.21227 | 0.178319 | ||||||||
\(559\) | 11.0580 | 0.467703 | ||||||||
\(560\) | −0.724714 | −0.0306247 | ||||||||
\(561\) | 1.39277 | 0.0588029 | ||||||||
\(562\) | −21.8386 | −0.921208 | ||||||||
\(563\) | −28.5775 | −1.20440 | −0.602200 | − | 0.798346i | \(-0.705709\pi\) | ||||
−0.602200 | + | 0.798346i | \(0.705709\pi\) | |||||||
\(564\) | 0.211837 | 0.00891993 | ||||||||
\(565\) | −18.4305 | −0.775375 | ||||||||
\(566\) | −9.22107 | −0.387590 | ||||||||
\(567\) | −0.782121 | −0.0328460 | ||||||||
\(568\) | −8.46784 | −0.355302 | ||||||||
\(569\) | 12.4014 | 0.519894 | 0.259947 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259947 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(570\) | 0.926601 | 0.0388110 | ||||||||
\(571\) | −1.84998 | −0.0774194 | −0.0387097 | − | 0.999250i | \(-0.512325\pi\) | ||||
−0.0387097 | + | 0.999250i | \(0.512325\pi\) | |||||||
\(572\) | −7.03608 | −0.294193 | ||||||||
\(573\) | 14.0937 | 0.588771 | ||||||||
\(574\) | 4.56101 | 0.190373 | ||||||||
\(575\) | −0.620949 | −0.0258954 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.6027 | 1.02423 | 0.512113 | − | 0.858918i | \(-0.328863\pi\) | ||||
0.512113 | + | 0.858918i | \(0.328863\pi\) | |||||||
\(578\) | −16.8899 | −0.702529 | ||||||||
\(579\) | 4.26766 | 0.177358 | ||||||||
\(580\) | 2.86556 | 0.118986 | ||||||||
\(581\) | −8.76636 | −0.363690 | ||||||||
\(582\) | 13.9685 | 0.579012 | ||||||||
\(583\) | −4.19823 | −0.173873 | ||||||||
\(584\) | −8.41498 | −0.348215 | ||||||||
\(585\) | 1.55295 | 0.0642065 | ||||||||
\(586\) | 20.5377 | 0.848406 | ||||||||
\(587\) | −16.4405 | −0.678572 | −0.339286 | − | 0.940683i | \(-0.610186\pi\) | ||||
−0.339286 | + | 0.940683i | \(0.610186\pi\) | |||||||
\(588\) | 6.38829 | 0.263449 | ||||||||
\(589\) | −4.21227 | −0.173563 | ||||||||
\(590\) | −8.38273 | −0.345112 | ||||||||
\(591\) | 7.60094 | 0.312661 | ||||||||
\(592\) | −10.0253 | −0.412037 | ||||||||
\(593\) | 35.4418 | 1.45542 | 0.727710 | − | 0.685885i | \(-0.240585\pi\) | ||||
0.727710 | + | 0.685885i | \(0.240585\pi\) | |||||||
\(594\) | 4.19823 | 0.172256 | ||||||||
\(595\) | −0.240426 | −0.00985649 | ||||||||
\(596\) | 8.53603 | 0.349649 | ||||||||
\(597\) | −15.5322 | −0.635691 | ||||||||
\(598\) | 0.251288 | 0.0102759 | ||||||||
\(599\) | 39.6790 | 1.62124 | 0.810619 | − | 0.585574i | \(-0.199131\pi\) | ||||
0.810619 | + | 0.585574i | \(0.199131\pi\) | |||||||
\(600\) | 4.14141 | 0.169072 | ||||||||
\(601\) | 38.0169 | 1.55074 | 0.775370 | − | 0.631507i | \(-0.217563\pi\) | ||||
0.775370 | + | 0.631507i | \(0.217563\pi\) | |||||||
\(602\) | −5.16043 | −0.210323 | ||||||||
\(603\) | 1.44469 | 0.0588322 | ||||||||
\(604\) | −14.2099 | −0.578195 | ||||||||
\(605\) | 6.13887 | 0.249581 | ||||||||
\(606\) | 18.3409 | 0.745050 | ||||||||
\(607\) | −34.2258 | −1.38918 | −0.694590 | − | 0.719406i | \(-0.744414\pi\) | ||||
−0.694590 | + | 0.719406i | \(0.744414\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 2.41875 | 0.0980127 | ||||||||
\(610\) | −0.786464 | −0.0318430 | ||||||||
\(611\) | −0.355030 | −0.0143630 | ||||||||
\(612\) | 0.331752 | 0.0134103 | ||||||||
\(613\) | −10.5287 | −0.425248 | −0.212624 | − | 0.977134i | \(-0.568201\pi\) | ||||
−0.212624 | + | 0.977134i | \(0.568201\pi\) | |||||||
\(614\) | −27.6440 | −1.11562 | ||||||||
\(615\) | 5.40356 | 0.217892 | ||||||||
\(616\) | 3.28353 | 0.132297 | ||||||||
\(617\) | −4.29010 | −0.172713 | −0.0863564 | − | 0.996264i | \(-0.527522\pi\) | ||||
−0.0863564 | + | 0.996264i | \(0.527522\pi\) | |||||||
\(618\) | −3.24954 | −0.130716 | ||||||||
\(619\) | −27.7701 | −1.11617 | −0.558087 | − | 0.829782i | \(-0.688465\pi\) | ||||
−0.558087 | + | 0.829782i | \(0.688465\pi\) | |||||||
\(620\) | 3.90309 | 0.156752 | ||||||||
\(621\) | −0.149937 | −0.00601674 | ||||||||
\(622\) | 14.0486 | 0.563297 | ||||||||
\(623\) | −10.7958 | −0.432527 | ||||||||
\(624\) | −1.67596 | −0.0670922 | ||||||||
\(625\) | 12.8583 | 0.514334 | ||||||||
\(626\) | −18.3113 | −0.731867 | ||||||||
\(627\) | −4.19823 | −0.167661 | ||||||||
\(628\) | −3.89737 | −0.155522 | ||||||||
\(629\) | −3.32592 | −0.132613 | ||||||||
\(630\) | −0.724714 | −0.0288733 | ||||||||
\(631\) | 25.3230 | 1.00809 | 0.504046 | − | 0.863677i | \(-0.331844\pi\) | ||||
0.504046 | + | 0.863677i | \(0.331844\pi\) | |||||||
\(632\) | 16.4095 | 0.652733 | ||||||||
\(633\) | −17.5152 | −0.696166 | ||||||||
\(634\) | 11.3498 | 0.450757 | ||||||||
\(635\) | 3.32309 | 0.131873 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −10.7065 | −0.424208 | ||||||||
\(638\) | −12.9833 | −0.514012 | ||||||||
\(639\) | −8.46784 | −0.334982 | ||||||||
\(640\) | 0.926601 | 0.0366271 | ||||||||
\(641\) | 1.63996 | 0.0647747 | 0.0323874 | − | 0.999475i | \(-0.489689\pi\) | ||||
0.0323874 | + | 0.999475i | \(0.489689\pi\) | |||||||
\(642\) | 9.19467 | 0.362885 | ||||||||
\(643\) | −26.6621 | −1.05145 | −0.525724 | − | 0.850655i | \(-0.676206\pi\) | ||||
−0.525724 | + | 0.850655i | \(0.676206\pi\) | |||||||
\(644\) | −0.117268 | −0.00462103 | ||||||||
\(645\) | −6.11371 | −0.240727 | ||||||||
\(646\) | −0.331752 | −0.0130526 | ||||||||
\(647\) | 2.42564 | 0.0953617 | 0.0476808 | − | 0.998863i | \(-0.484817\pi\) | ||||
0.0476808 | + | 0.998863i | \(0.484817\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 37.9804 | 1.49086 | ||||||||
\(650\) | −6.94085 | −0.272243 | ||||||||
\(651\) | 3.29450 | 0.129122 | ||||||||
\(652\) | 13.0131 | 0.509634 | ||||||||
\(653\) | 29.1302 | 1.13995 | 0.569976 | − | 0.821661i | \(-0.306953\pi\) | ||||
0.569976 | + | 0.821661i | \(0.306953\pi\) | |||||||
\(654\) | 14.6653 | 0.573459 | ||||||||
\(655\) | −13.5516 | −0.529504 | ||||||||
\(656\) | −5.83159 | −0.227685 | ||||||||
\(657\) | −8.41498 | −0.328300 | ||||||||
\(658\) | 0.165682 | 0.00645895 | ||||||||
\(659\) | 16.5266 | 0.643786 | 0.321893 | − | 0.946776i | \(-0.395681\pi\) | ||||
0.321893 | + | 0.946776i | \(0.395681\pi\) | |||||||
\(660\) | 3.89008 | 0.151421 | ||||||||
\(661\) | 18.3133 | 0.712304 | 0.356152 | − | 0.934428i | \(-0.384088\pi\) | ||||
0.356152 | + | 0.934428i | \(0.384088\pi\) | |||||||
\(662\) | −1.52973 | −0.0594547 | ||||||||
\(663\) | −0.556005 | −0.0215934 | ||||||||
\(664\) | 11.2084 | 0.434972 | ||||||||
\(665\) | 0.724714 | 0.0281032 | ||||||||
\(666\) | −10.0253 | −0.388473 | ||||||||
\(667\) | 0.463687 | 0.0179540 | ||||||||
\(668\) | 7.49380 | 0.289944 | ||||||||
\(669\) | −6.25847 | −0.241967 | ||||||||
\(670\) | 1.33865 | 0.0517165 | ||||||||
\(671\) | 3.56330 | 0.137560 | ||||||||
\(672\) | 0.782121 | 0.0301710 | ||||||||
\(673\) | 43.7839 | 1.68775 | 0.843873 | − | 0.536543i | \(-0.180270\pi\) | ||||
0.843873 | + | 0.536543i | \(0.180270\pi\) | |||||||
\(674\) | −30.0246 | −1.15651 | ||||||||
\(675\) | 4.14141 | 0.159403 | ||||||||
\(676\) | −10.1911 | −0.391967 | ||||||||
\(677\) | −8.25364 | −0.317213 | −0.158607 | − | 0.987342i | \(-0.550700\pi\) | ||||
−0.158607 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(678\) | 19.8904 | 0.763886 | ||||||||
\(679\) | 10.9250 | 0.419264 | ||||||||
\(680\) | 0.307402 | 0.0117883 | ||||||||
\(681\) | 0.619197 | 0.0237277 | ||||||||
\(682\) | −17.6841 | −0.677158 | ||||||||
\(683\) | −50.0861 | −1.91649 | −0.958245 | − | 0.285948i | \(-0.907692\pi\) | ||||
−0.958245 | + | 0.285948i | \(0.907692\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −2.79336 | −0.106729 | ||||||||
\(686\) | 10.4713 | 0.399795 | ||||||||
\(687\) | −25.8321 | −0.985557 | ||||||||
\(688\) | 6.59799 | 0.251546 | ||||||||
\(689\) | 1.67596 | 0.0638491 | ||||||||
\(690\) | −0.138931 | −0.00528902 | ||||||||
\(691\) | 34.6500 | 1.31815 | 0.659074 | − | 0.752078i | \(-0.270948\pi\) | ||||
0.659074 | + | 0.752078i | \(0.270948\pi\) | |||||||
\(692\) | −2.08193 | −0.0791432 | ||||||||
\(693\) | 3.28353 | 0.124731 | ||||||||
\(694\) | −19.7549 | −0.749884 | ||||||||
\(695\) | 6.20591 | 0.235404 | ||||||||
\(696\) | −3.09255 | −0.117223 | ||||||||
\(697\) | −1.93464 | −0.0732799 | ||||||||
\(698\) | −26.5106 | −1.00344 | ||||||||
\(699\) | 8.13029 | 0.307516 | ||||||||
\(700\) | 3.23908 | 0.122426 | ||||||||
\(701\) | 28.7541 | 1.08603 | 0.543013 | − | 0.839724i | \(-0.317283\pi\) | ||||
0.543013 | + | 0.839724i | \(0.317283\pi\) | |||||||
\(702\) | −1.67596 | −0.0632551 | ||||||||
\(703\) | 10.0253 | 0.378111 | ||||||||
\(704\) | −4.19823 | −0.158227 | ||||||||
\(705\) | 0.196288 | 0.00739263 | ||||||||
\(706\) | 13.0469 | 0.491026 | ||||||||
\(707\) | 14.3448 | 0.539493 | ||||||||
\(708\) | 9.04676 | 0.339998 | ||||||||
\(709\) | 48.1115 | 1.80687 | 0.903433 | − | 0.428729i | \(-0.141038\pi\) | ||||
0.903433 | + | 0.428729i | \(0.141038\pi\) | |||||||
\(710\) | −7.84630 | −0.294466 | ||||||||
\(711\) | 16.4095 | 0.615403 | ||||||||
\(712\) | 13.8033 | 0.517300 | ||||||||
\(713\) | 0.631572 | 0.0236526 | ||||||||
\(714\) | 0.259470 | 0.00971044 | ||||||||
\(715\) | −6.51964 | −0.243821 | ||||||||
\(716\) | 5.99501 | 0.224044 | ||||||||
\(717\) | 7.75661 | 0.289676 | ||||||||
\(718\) | 1.34879 | 0.0503363 | ||||||||
\(719\) | −29.8717 | −1.11403 | −0.557013 | − | 0.830504i | \(-0.688052\pi\) | ||||
−0.557013 | + | 0.830504i | \(0.688052\pi\) | |||||||
\(720\) | 0.926601 | 0.0345324 | ||||||||
\(721\) | −2.54153 | −0.0946517 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 5.37695 | 0.199971 | ||||||||
\(724\) | −10.6345 | −0.395229 | ||||||||
\(725\) | −12.8075 | −0.475660 | ||||||||
\(726\) | −6.62515 | −0.245882 | ||||||||
\(727\) | 3.06414 | 0.113643 | 0.0568214 | − | 0.998384i | \(-0.481903\pi\) | ||||
0.0568214 | + | 0.998384i | \(0.481903\pi\) | |||||||
\(728\) | −1.31081 | −0.0485817 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.79733 | −0.288592 | ||||||||
\(731\) | 2.18890 | 0.0809594 | ||||||||
\(732\) | 0.848763 | 0.0313712 | ||||||||
\(733\) | −3.18666 | −0.117702 | −0.0588510 | − | 0.998267i | \(-0.518744\pi\) | ||||
−0.0588510 | + | 0.998267i | \(0.518744\pi\) | |||||||
\(734\) | 7.04736 | 0.260123 | ||||||||
\(735\) | 5.91939 | 0.218340 | ||||||||
\(736\) | 0.149937 | 0.00552673 | ||||||||
\(737\) | −6.06514 | −0.223412 | ||||||||
\(738\) | −5.83159 | −0.214664 | ||||||||
\(739\) | 35.9719 | 1.32325 | 0.661625 | − | 0.749835i | \(-0.269867\pi\) | ||||
0.661625 | + | 0.749835i | \(0.269867\pi\) | |||||||
\(740\) | −9.28945 | −0.341487 | ||||||||
\(741\) | 1.67596 | 0.0615680 | ||||||||
\(742\) | −0.782121 | −0.0287126 | ||||||||
\(743\) | −47.8091 | −1.75395 | −0.876973 | − | 0.480540i | \(-0.840441\pi\) | ||||
−0.876973 | + | 0.480540i | \(0.840441\pi\) | |||||||
\(744\) | −4.21227 | −0.154429 | ||||||||
\(745\) | 7.90949 | 0.289781 | ||||||||
\(746\) | −4.63270 | −0.169615 | ||||||||
\(747\) | 11.2084 | 0.410096 | ||||||||
\(748\) | −1.39277 | −0.0509248 | ||||||||
\(749\) | 7.19135 | 0.262766 | ||||||||
\(750\) | 8.47044 | 0.309297 | ||||||||
\(751\) | 9.04037 | 0.329888 | 0.164944 | − | 0.986303i | \(-0.447256\pi\) | ||||
0.164944 | + | 0.986303i | \(0.447256\pi\) | |||||||
\(752\) | −0.211837 | −0.00772489 | ||||||||
\(753\) | 12.5236 | 0.456386 | ||||||||
\(754\) | 5.18300 | 0.188754 | ||||||||
\(755\) | −13.1669 | −0.479194 | ||||||||
\(756\) | 0.782121 | 0.0284455 | ||||||||
\(757\) | 36.9450 | 1.34279 | 0.671395 | − | 0.741100i | \(-0.265696\pi\) | ||||
0.671395 | + | 0.741100i | \(0.265696\pi\) | |||||||
\(758\) | −1.15152 | −0.0418252 | ||||||||
\(759\) | 0.629468 | 0.0228482 | ||||||||
\(760\) | −0.926601 | −0.0336113 | ||||||||
\(761\) | −19.4165 | −0.703849 | −0.351925 | − | 0.936028i | \(-0.614473\pi\) | ||||
−0.351925 | + | 0.936028i | \(0.614473\pi\) | |||||||
\(762\) | −3.58632 | −0.129919 | ||||||||
\(763\) | 11.4700 | 0.415244 | ||||||||
\(764\) | −14.0937 | −0.509891 | ||||||||
\(765\) | 0.307402 | 0.0111141 | ||||||||
\(766\) | −21.9422 | −0.792802 | ||||||||
\(767\) | −15.1620 | −0.547469 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 47.0334 | 1.69607 | 0.848033 | − | 0.529943i | \(-0.177787\pi\) | ||||
0.848033 | + | 0.529943i | \(0.177787\pi\) | |||||||
\(770\) | 3.04252 | 0.109645 | ||||||||
\(771\) | 3.06979 | 0.110556 | ||||||||
\(772\) | −4.26766 | −0.153597 | ||||||||
\(773\) | 5.93932 | 0.213622 | 0.106811 | − | 0.994279i | \(-0.465936\pi\) | ||||
0.106811 | + | 0.994279i | \(0.465936\pi\) | |||||||
\(774\) | 6.59799 | 0.237160 | ||||||||
\(775\) | −17.4447 | −0.626633 | ||||||||
\(776\) | −13.9685 | −0.501439 | ||||||||
\(777\) | −7.84100 | −0.281294 | ||||||||
\(778\) | −36.2915 | −1.30111 | ||||||||
\(779\) | 5.83159 | 0.208939 | ||||||||
\(780\) | −1.55295 | −0.0556045 | ||||||||
\(781\) | 35.5499 | 1.27208 | ||||||||
\(782\) | 0.0497418 | 0.00177876 | ||||||||
\(783\) | −3.09255 | −0.110519 | ||||||||
\(784\) | −6.38829 | −0.228153 | ||||||||
\(785\) | −3.61131 | −0.128893 | ||||||||
\(786\) | 14.6250 | 0.521658 | ||||||||
\(787\) | 15.4545 | 0.550894 | 0.275447 | − | 0.961316i | \(-0.411174\pi\) | ||||
0.275447 | + | 0.961316i | \(0.411174\pi\) | |||||||
\(788\) | −7.60094 | −0.270772 | ||||||||
\(789\) | −16.9553 | −0.603625 | ||||||||
\(790\) | 15.2050 | 0.540970 | ||||||||
\(791\) | 15.5567 | 0.553133 | ||||||||
\(792\) | −4.19823 | −0.149178 | ||||||||
\(793\) | −1.42249 | −0.0505143 | ||||||||
\(794\) | 0.247673 | 0.00878959 | ||||||||
\(795\) | −0.926601 | −0.0328631 | ||||||||
\(796\) | 15.5322 | 0.550524 | ||||||||
\(797\) | 3.49048 | 0.123639 | 0.0618195 | − | 0.998087i | \(-0.480310\pi\) | ||||
0.0618195 | + | 0.998087i | \(0.480310\pi\) | |||||||
\(798\) | −0.782121 | −0.0276868 | ||||||||
\(799\) | −0.0702773 | −0.00248623 | ||||||||
\(800\) | −4.14141 | −0.146421 | ||||||||
\(801\) | 13.8033 | 0.487716 | ||||||||
\(802\) | 7.65273 | 0.270227 | ||||||||
\(803\) | 35.3281 | 1.24670 | ||||||||
\(804\) | −1.44469 | −0.0509502 | ||||||||
\(805\) | −0.108661 | −0.00382980 | ||||||||
\(806\) | 7.05960 | 0.248664 | ||||||||
\(807\) | −5.93047 | −0.208762 | ||||||||
\(808\) | −18.3409 | −0.645232 | ||||||||
\(809\) | 31.3872 | 1.10351 | 0.551757 | − | 0.834005i | \(-0.313958\pi\) | ||||
0.551757 | + | 0.834005i | \(0.313958\pi\) | |||||||
\(810\) | 0.926601 | 0.0325574 | ||||||||
\(811\) | 55.4180 | 1.94599 | 0.972995 | − | 0.230825i | \(-0.0741424\pi\) | ||||
0.972995 | + | 0.230825i | \(0.0741424\pi\) | |||||||
\(812\) | −2.41875 | −0.0848815 | ||||||||
\(813\) | 2.26289 | 0.0793629 | ||||||||
\(814\) | 42.0885 | 1.47520 | ||||||||
\(815\) | 12.0580 | 0.422373 | ||||||||
\(816\) | −0.331752 | −0.0116137 | ||||||||
\(817\) | −6.59799 | −0.230835 | ||||||||
\(818\) | 2.60227 | 0.0909861 | ||||||||
\(819\) | −1.31081 | −0.0458033 | ||||||||
\(820\) | −5.40356 | −0.188700 | ||||||||
\(821\) | 22.9887 | 0.802311 | 0.401156 | − | 0.916010i | \(-0.368609\pi\) | ||||
0.401156 | + | 0.916010i | \(0.368609\pi\) | |||||||
\(822\) | 3.01463 | 0.105147 | ||||||||
\(823\) | −5.69726 | −0.198594 | −0.0992969 | − | 0.995058i | \(-0.531659\pi\) | ||||
−0.0992969 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(824\) | 3.24954 | 0.113203 | ||||||||
\(825\) | −17.3866 | −0.605324 | ||||||||
\(826\) | 7.07566 | 0.246194 | ||||||||
\(827\) | 17.8996 | 0.622429 | 0.311214 | − | 0.950340i | \(-0.399264\pi\) | ||||
0.311214 | + | 0.950340i | \(0.399264\pi\) | |||||||
\(828\) | 0.149937 | 0.00521065 | ||||||||
\(829\) | 12.9390 | 0.449389 | 0.224695 | − | 0.974429i | \(-0.427862\pi\) | ||||
0.224695 | + | 0.974429i | \(0.427862\pi\) | |||||||
\(830\) | 10.3858 | 0.360495 | ||||||||
\(831\) | −11.2497 | −0.390248 | ||||||||
\(832\) | 1.67596 | 0.0581036 | ||||||||
\(833\) | −2.11933 | −0.0734304 | ||||||||
\(834\) | −6.69751 | −0.231916 | ||||||||
\(835\) | 6.94376 | 0.240299 | ||||||||
\(836\) | 4.19823 | 0.145199 | ||||||||
\(837\) | −4.21227 | −0.145597 | ||||||||
\(838\) | 19.4884 | 0.673215 | ||||||||
\(839\) | 0.700273 | 0.0241761 | 0.0120880 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120880 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(840\) | 0.724714 | 0.0250050 | ||||||||
\(841\) | −19.4361 | −0.670211 | ||||||||
\(842\) | 13.4744 | 0.464359 | ||||||||
\(843\) | 21.8386 | 0.752163 | ||||||||
\(844\) | 17.5152 | 0.602897 | ||||||||
\(845\) | −9.44312 | −0.324853 | ||||||||
\(846\) | −0.211837 | −0.00728310 | ||||||||
\(847\) | −5.18167 | −0.178044 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | 9.22107 | 0.316466 | ||||||||
\(850\) | −1.37392 | −0.0471252 | ||||||||
\(851\) | −1.50316 | −0.0515276 | ||||||||
\(852\) | 8.46784 | 0.290103 | ||||||||
\(853\) | 45.8864 | 1.57112 | 0.785560 | − | 0.618785i | \(-0.212375\pi\) | ||||
0.785560 | + | 0.618785i | \(0.212375\pi\) | |||||||
\(854\) | 0.663835 | 0.0227160 | ||||||||
\(855\) | −0.926601 | −0.0316891 | ||||||||
\(856\) | −9.19467 | −0.314268 | ||||||||
\(857\) | −12.3197 | −0.420835 | −0.210417 | − | 0.977612i | \(-0.567482\pi\) | ||||
−0.210417 | + | 0.977612i | \(0.567482\pi\) | |||||||
\(858\) | 7.03608 | 0.240208 | ||||||||
\(859\) | −42.5135 | −1.45054 | −0.725271 | − | 0.688464i | \(-0.758285\pi\) | ||||
−0.725271 | + | 0.688464i | \(0.758285\pi\) | |||||||
\(860\) | 6.11371 | 0.208476 | ||||||||
\(861\) | −4.56101 | −0.155439 | ||||||||
\(862\) | −5.56985 | −0.189710 | ||||||||
\(863\) | 39.0220 | 1.32833 | 0.664163 | − | 0.747588i | \(-0.268788\pi\) | ||||
0.664163 | + | 0.747588i | \(0.268788\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.92912 | −0.0655920 | ||||||||
\(866\) | 39.4783 | 1.34153 | ||||||||
\(867\) | 16.8899 | 0.573612 | ||||||||
\(868\) | −3.29450 | −0.111823 | ||||||||
\(869\) | −68.8907 | −2.33696 | ||||||||
\(870\) | −2.86556 | −0.0971516 | ||||||||
\(871\) | 2.42124 | 0.0820407 | ||||||||
\(872\) | −14.6653 | −0.496630 | ||||||||
\(873\) | −13.9685 | −0.472761 | ||||||||
\(874\) | −0.149937 | −0.00507168 | ||||||||
\(875\) | 6.62491 | 0.223963 | ||||||||
\(876\) | 8.41498 | 0.284316 | ||||||||
\(877\) | 40.2448 | 1.35897 | 0.679486 | − | 0.733689i | \(-0.262203\pi\) | ||||
0.679486 | + | 0.733689i | \(0.262203\pi\) | |||||||
\(878\) | 25.2570 | 0.852382 | ||||||||
\(879\) | −20.5377 | −0.692720 | ||||||||
\(880\) | −3.89008 | −0.131135 | ||||||||
\(881\) | −31.3607 | −1.05657 | −0.528284 | − | 0.849068i | \(-0.677164\pi\) | ||||
−0.528284 | + | 0.849068i | \(0.677164\pi\) | |||||||
\(882\) | −6.38829 | −0.215105 | ||||||||
\(883\) | 14.3976 | 0.484516 | 0.242258 | − | 0.970212i | \(-0.422112\pi\) | ||||
0.242258 | + | 0.970212i | \(0.422112\pi\) | |||||||
\(884\) | 0.556005 | 0.0187005 | ||||||||
\(885\) | 8.38273 | 0.281782 | ||||||||
\(886\) | −8.17156 | −0.274529 | ||||||||
\(887\) | −39.1132 | −1.31329 | −0.656646 | − | 0.754199i | \(-0.728026\pi\) | ||||
−0.656646 | + | 0.754199i | \(0.728026\pi\) | |||||||
\(888\) | 10.0253 | 0.336427 | ||||||||
\(889\) | −2.80494 | −0.0940746 | ||||||||
\(890\) | 12.7901 | 0.428727 | ||||||||
\(891\) | −4.19823 | −0.140646 | ||||||||
\(892\) | 6.25847 | 0.209549 | ||||||||
\(893\) | 0.211837 | 0.00708884 | ||||||||
\(894\) | −8.53603 | −0.285488 | ||||||||
\(895\) | 5.55498 | 0.185683 | ||||||||
\(896\) | −0.782121 | −0.0261288 | ||||||||
\(897\) | −0.251288 | −0.00839026 | ||||||||
\(898\) | −27.2199 | −0.908341 | ||||||||
\(899\) | 13.0267 | 0.434463 | ||||||||
\(900\) | −4.14141 | −0.138047 | ||||||||
\(901\) | 0.331752 | 0.0110523 | ||||||||
\(902\) | 24.4824 | 0.815174 | ||||||||
\(903\) | 5.16043 | 0.171728 | ||||||||
\(904\) | −19.8904 | −0.661545 | ||||||||
\(905\) | −9.85395 | −0.327556 | ||||||||
\(906\) | 14.2099 | 0.472094 | ||||||||
\(907\) | 11.1385 | 0.369849 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(908\) | −0.619197 | −0.0205488 | ||||||||
\(909\) | −18.3409 | −0.608331 | ||||||||
\(910\) | −1.21459 | −0.0402634 | ||||||||
\(911\) | 10.1461 | 0.336155 | 0.168077 | − | 0.985774i | \(-0.446244\pi\) | ||||
0.168077 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −47.0556 | −1.55731 | ||||||||
\(914\) | 21.0437 | 0.696065 | ||||||||
\(915\) | 0.786464 | 0.0259997 | ||||||||
\(916\) | 25.8321 | 0.853517 | ||||||||
\(917\) | 11.4385 | 0.377734 | ||||||||
\(918\) | −0.331752 | −0.0109495 | ||||||||
\(919\) | −11.3027 | −0.372842 | −0.186421 | − | 0.982470i | \(-0.559689\pi\) | ||||
−0.186421 | + | 0.982470i | \(0.559689\pi\) | |||||||
\(920\) | 0.138931 | 0.00458043 | ||||||||
\(921\) | 27.6440 | 0.910901 | ||||||||
\(922\) | 21.6102 | 0.711694 | ||||||||
\(923\) | −14.1918 | −0.467128 | ||||||||
\(924\) | −3.28353 | −0.108020 | ||||||||
\(925\) | 41.5189 | 1.36513 | ||||||||
\(926\) | −5.20944 | −0.171193 | ||||||||
\(927\) | 3.24954 | 0.106729 | ||||||||
\(928\) | 3.09255 | 0.101518 | ||||||||
\(929\) | −26.9442 | −0.884011 | −0.442005 | − | 0.897012i | \(-0.645733\pi\) | ||||
−0.442005 | + | 0.897012i | \(0.645733\pi\) | |||||||
\(930\) | −3.90309 | −0.127987 | ||||||||
\(931\) | 6.38829 | 0.209368 | ||||||||
\(932\) | −8.13029 | −0.266317 | ||||||||
\(933\) | −14.0486 | −0.459930 | ||||||||
\(934\) | 3.52818 | 0.115446 | ||||||||
\(935\) | −1.29054 | −0.0422053 | ||||||||
\(936\) | 1.67596 | 0.0547806 | ||||||||
\(937\) | −37.6440 | −1.22978 | −0.614889 | − | 0.788614i | \(-0.710799\pi\) | ||||
−0.614889 | + | 0.788614i | \(0.710799\pi\) | |||||||
\(938\) | −1.12992 | −0.0368932 | ||||||||
\(939\) | 18.3113 | 0.597567 | ||||||||
\(940\) | −0.196288 | −0.00640221 | ||||||||
\(941\) | 38.6897 | 1.26125 | 0.630625 | − | 0.776088i | \(-0.282799\pi\) | ||||
0.630625 | + | 0.776088i | \(0.282799\pi\) | |||||||
\(942\) | 3.89737 | 0.126983 | ||||||||
\(943\) | −0.874369 | −0.0284734 | ||||||||
\(944\) | −9.04676 | −0.294447 | ||||||||
\(945\) | 0.724714 | 0.0235749 | ||||||||
\(946\) | −27.6999 | −0.900602 | ||||||||
\(947\) | −36.5240 | −1.18687 | −0.593436 | − | 0.804881i | \(-0.702229\pi\) | ||||
−0.593436 | + | 0.804881i | \(0.702229\pi\) | |||||||
\(948\) | −16.4095 | −0.532954 | ||||||||
\(949\) | −14.1032 | −0.457809 | ||||||||
\(950\) | 4.14141 | 0.134365 | ||||||||
\(951\) | −11.3498 | −0.368041 | ||||||||
\(952\) | −0.259470 | −0.00840949 | ||||||||
\(953\) | −0.0467423 | −0.00151413 | −0.000757065 | − | 1.00000i | \(-0.500241\pi\) | ||||
−0.000757065 | 1.00000i | \(0.500241\pi\) | ||||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | −13.0592 | −0.422586 | ||||||||
\(956\) | −7.75661 | −0.250867 | ||||||||
\(957\) | 12.9833 | 0.419689 | ||||||||
\(958\) | 7.53696 | 0.243508 | ||||||||
\(959\) | 2.35781 | 0.0761376 | ||||||||
\(960\) | −0.926601 | −0.0299059 | ||||||||
\(961\) | −13.2568 | −0.427639 | ||||||||
\(962\) | −16.8020 | −0.541719 | ||||||||
\(963\) | −9.19467 | −0.296294 | ||||||||
\(964\) | −5.37695 | −0.173180 | ||||||||
\(965\) | −3.95442 | −0.127297 | ||||||||
\(966\) | 0.117268 | 0.00377305 | ||||||||
\(967\) | 29.6933 | 0.954872 | 0.477436 | − | 0.878667i | \(-0.341566\pi\) | ||||
0.477436 | + | 0.878667i | \(0.341566\pi\) | |||||||
\(968\) | 6.62515 | 0.212940 | ||||||||
\(969\) | 0.331752 | 0.0106574 | ||||||||
\(970\) | −12.9432 | −0.415581 | ||||||||
\(971\) | −20.8945 | −0.670538 | −0.335269 | − | 0.942123i | \(-0.608827\pi\) | ||||
−0.335269 | + | 0.942123i | \(0.608827\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −5.23826 | −0.167931 | ||||||||
\(974\) | −10.5849 | −0.339162 | ||||||||
\(975\) | 6.94085 | 0.222285 | ||||||||
\(976\) | −0.848763 | −0.0271682 | ||||||||
\(977\) | −1.90091 | −0.0608156 | −0.0304078 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304078 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(978\) | −13.0131 | −0.416114 | ||||||||
\(979\) | −57.9494 | −1.85207 | ||||||||
\(980\) | −5.91939 | −0.189088 | ||||||||
\(981\) | −14.6653 | −0.468227 | ||||||||
\(982\) | −15.6741 | −0.500182 | ||||||||
\(983\) | 27.6214 | 0.880986 | 0.440493 | − | 0.897756i | \(-0.354804\pi\) | ||||
0.440493 | + | 0.897756i | \(0.354804\pi\) | |||||||
\(984\) | 5.83159 | 0.185904 | ||||||||
\(985\) | −7.04303 | −0.224410 | ||||||||
\(986\) | 1.02596 | 0.0326733 | ||||||||
\(987\) | −0.165682 | −0.00527371 | ||||||||
\(988\) | −1.67596 | −0.0533195 | ||||||||
\(989\) | 0.989280 | 0.0314573 | ||||||||
\(990\) | −3.89008 | −0.123635 | ||||||||
\(991\) | −2.75269 | −0.0874419 | −0.0437210 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437210 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(992\) | 4.21227 | 0.133740 | ||||||||
\(993\) | 1.52973 | 0.0485446 | ||||||||
\(994\) | 6.62287 | 0.210065 | ||||||||
\(995\) | 14.3921 | 0.456262 | ||||||||
\(996\) | −11.2084 | −0.355153 | ||||||||
\(997\) | −22.2864 | −0.705818 | −0.352909 | − | 0.935658i | \(-0.614808\pi\) | ||||
−0.352909 | + | 0.935658i | \(0.614808\pi\) | |||||||
\(998\) | −24.7962 | −0.784910 | ||||||||
\(999\) | 10.0253 | 0.317187 |
(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 | 6042.2.a.bb.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bb.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |