Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8022,2,Mod(1,8022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8022, 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("8022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.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: | \(64.0559925015\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 53 x^{13} - x^{12} + 1068 x^{11} + 45 x^{10} - 10139 x^{9} - 615 x^{8} + 45390 x^{7} + 2130 x^{6} - 84842 x^{5} + 7822 x^{4} + 62828 x^{3} - 16144 x^{2} + \cdots + 4704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.600780\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8022.1 |
$q$-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 | ||||||||
\(5\) | 0.600780 | 0.268677 | 0.134339 | − | 0.990935i | \(-0.457109\pi\) | ||||
0.134339 | + | 0.990935i | \(0.457109\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.600780 | −0.189983 | ||||||||
\(11\) | 3.98407 | 1.20124 | 0.600620 | − | 0.799534i | \(-0.294920\pi\) | ||||
0.600620 | + | 0.799534i | \(0.294920\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.21056 | −0.613100 | −0.306550 | − | 0.951855i | \(-0.599175\pi\) | ||||
−0.306550 | + | 0.951855i | \(0.599175\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.600780 | 0.155121 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.291399 | 0.0706746 | 0.0353373 | − | 0.999375i | \(-0.488749\pi\) | ||||
0.0353373 | + | 0.999375i | \(0.488749\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.811418 | 0.186152 | 0.0930761 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930761 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(20\) | 0.600780 | 0.134339 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −3.98407 | −0.849406 | ||||||||
\(23\) | 1.18963 | 0.248055 | 0.124028 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124028 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.63906 | −0.927813 | ||||||||
\(26\) | 2.21056 | 0.433527 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −9.44157 | −1.75326 | −0.876628 | − | 0.481169i | \(-0.840212\pi\) | ||||
−0.876628 | + | 0.481169i | \(0.840212\pi\) | |||||||
\(30\) | −0.600780 | −0.109687 | ||||||||
\(31\) | 7.61531 | 1.36775 | 0.683875 | − | 0.729599i | \(-0.260293\pi\) | ||||
0.683875 | + | 0.729599i | \(0.260293\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.98407 | 0.693537 | ||||||||
\(34\) | −0.291399 | −0.0499745 | ||||||||
\(35\) | 0.600780 | 0.101550 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.07939 | −0.835046 | −0.417523 | − | 0.908666i | \(-0.637102\pi\) | ||||
−0.417523 | + | 0.908666i | \(0.637102\pi\) | |||||||
\(38\) | −0.811418 | −0.131629 | ||||||||
\(39\) | −2.21056 | −0.353974 | ||||||||
\(40\) | −0.600780 | −0.0949917 | ||||||||
\(41\) | 2.80141 | 0.437507 | 0.218754 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218754 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −4.76406 | −0.726513 | −0.363256 | − | 0.931689i | \(-0.618335\pi\) | ||||
−0.363256 | + | 0.931689i | \(0.618335\pi\) | |||||||
\(44\) | 3.98407 | 0.600620 | ||||||||
\(45\) | 0.600780 | 0.0895591 | ||||||||
\(46\) | −1.18963 | −0.175402 | ||||||||
\(47\) | 5.87638 | 0.857159 | 0.428579 | − | 0.903504i | \(-0.359014\pi\) | ||||
0.428579 | + | 0.903504i | \(0.359014\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.63906 | 0.656063 | ||||||||
\(51\) | 0.291399 | 0.0408040 | ||||||||
\(52\) | −2.21056 | −0.306550 | ||||||||
\(53\) | 11.5189 | 1.58224 | 0.791120 | − | 0.611661i | \(-0.209498\pi\) | ||||
0.791120 | + | 0.611661i | \(0.209498\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.39355 | 0.322746 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0.811418 | 0.107475 | ||||||||
\(58\) | 9.44157 | 1.23974 | ||||||||
\(59\) | −5.71021 | −0.743406 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(60\) | 0.600780 | 0.0775604 | ||||||||
\(61\) | 2.62535 | 0.336141 | 0.168071 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168071 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(62\) | −7.61531 | −0.967145 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.32806 | −0.164726 | ||||||||
\(66\) | −3.98407 | −0.490405 | ||||||||
\(67\) | 14.9062 | 1.82108 | 0.910540 | − | 0.413421i | \(-0.135666\pi\) | ||||
0.910540 | + | 0.413421i | \(0.135666\pi\) | |||||||
\(68\) | 0.291399 | 0.0353373 | ||||||||
\(69\) | 1.18963 | 0.143215 | ||||||||
\(70\) | −0.600780 | −0.0718070 | ||||||||
\(71\) | 11.6398 | 1.38139 | 0.690693 | − | 0.723148i | \(-0.257306\pi\) | ||||
0.690693 | + | 0.723148i | \(0.257306\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 16.8053 | 1.96691 | 0.983455 | − | 0.181154i | \(-0.0579832\pi\) | ||||
0.983455 | + | 0.181154i | \(0.0579832\pi\) | |||||||
\(74\) | 5.07939 | 0.590467 | ||||||||
\(75\) | −4.63906 | −0.535673 | ||||||||
\(76\) | 0.811418 | 0.0930761 | ||||||||
\(77\) | 3.98407 | 0.454026 | ||||||||
\(78\) | 2.21056 | 0.250297 | ||||||||
\(79\) | 1.60018 | 0.180035 | 0.0900173 | − | 0.995940i | \(-0.471308\pi\) | ||||
0.0900173 | + | 0.995940i | \(0.471308\pi\) | |||||||
\(80\) | 0.600780 | 0.0671693 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.80141 | −0.309364 | ||||||||
\(83\) | −5.30607 | −0.582417 | −0.291209 | − | 0.956660i | \(-0.594057\pi\) | ||||
−0.291209 | + | 0.956660i | \(0.594057\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0.175067 | 0.0189887 | ||||||||
\(86\) | 4.76406 | 0.513722 | ||||||||
\(87\) | −9.44157 | −1.01224 | ||||||||
\(88\) | −3.98407 | −0.424703 | ||||||||
\(89\) | −6.96178 | −0.737947 | −0.368974 | − | 0.929440i | \(-0.620291\pi\) | ||||
−0.368974 | + | 0.929440i | \(0.620291\pi\) | |||||||
\(90\) | −0.600780 | −0.0633278 | ||||||||
\(91\) | −2.21056 | −0.231730 | ||||||||
\(92\) | 1.18963 | 0.124028 | ||||||||
\(93\) | 7.61531 | 0.789671 | ||||||||
\(94\) | −5.87638 | −0.606103 | ||||||||
\(95\) | 0.487484 | 0.0500148 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.49961 | 0.456866 | 0.228433 | − | 0.973560i | \(-0.426640\pi\) | ||||
0.228433 | + | 0.973560i | \(0.426640\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.98407 | 0.400414 | ||||||||
\(100\) | −4.63906 | −0.463906 | ||||||||
\(101\) | 5.35438 | 0.532780 | 0.266390 | − | 0.963865i | \(-0.414169\pi\) | ||||
0.266390 | + | 0.963865i | \(0.414169\pi\) | |||||||
\(102\) | −0.291399 | −0.0288528 | ||||||||
\(103\) | −9.04862 | −0.891587 | −0.445794 | − | 0.895136i | \(-0.647079\pi\) | ||||
−0.445794 | + | 0.895136i | \(0.647079\pi\) | |||||||
\(104\) | 2.21056 | 0.216764 | ||||||||
\(105\) | 0.600780 | 0.0586302 | ||||||||
\(106\) | −11.5189 | −1.11881 | ||||||||
\(107\) | 15.9118 | 1.53825 | 0.769126 | − | 0.639097i | \(-0.220692\pi\) | ||||
0.769126 | + | 0.639097i | \(0.220692\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 1.54381 | 0.147870 | 0.0739349 | − | 0.997263i | \(-0.476444\pi\) | ||||
0.0739349 | + | 0.997263i | \(0.476444\pi\) | |||||||
\(110\) | −2.39355 | −0.228216 | ||||||||
\(111\) | −5.07939 | −0.482114 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −17.9097 | −1.68480 | −0.842401 | − | 0.538851i | \(-0.818859\pi\) | ||||
−0.842401 | + | 0.538851i | \(0.818859\pi\) | |||||||
\(114\) | −0.811418 | −0.0759963 | ||||||||
\(115\) | 0.714708 | 0.0666468 | ||||||||
\(116\) | −9.44157 | −0.876628 | ||||||||
\(117\) | −2.21056 | −0.204367 | ||||||||
\(118\) | 5.71021 | 0.525667 | ||||||||
\(119\) | 0.291399 | 0.0267125 | ||||||||
\(120\) | −0.600780 | −0.0548435 | ||||||||
\(121\) | 4.87278 | 0.442980 | ||||||||
\(122\) | −2.62535 | −0.237688 | ||||||||
\(123\) | 2.80141 | 0.252595 | ||||||||
\(124\) | 7.61531 | 0.683875 | ||||||||
\(125\) | −5.79096 | −0.517959 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 19.1969 | 1.70345 | 0.851723 | − | 0.523992i | \(-0.175558\pi\) | ||||
0.851723 | + | 0.523992i | \(0.175558\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.76406 | −0.419452 | ||||||||
\(130\) | 1.32806 | 0.116479 | ||||||||
\(131\) | 16.1818 | 1.41381 | 0.706906 | − | 0.707307i | \(-0.250090\pi\) | ||||
0.706906 | + | 0.707307i | \(0.250090\pi\) | |||||||
\(132\) | 3.98407 | 0.346768 | ||||||||
\(133\) | 0.811418 | 0.0703589 | ||||||||
\(134\) | −14.9062 | −1.28770 | ||||||||
\(135\) | 0.600780 | 0.0517069 | ||||||||
\(136\) | −0.291399 | −0.0249873 | ||||||||
\(137\) | −6.36691 | −0.543962 | −0.271981 | − | 0.962303i | \(-0.587679\pi\) | ||||
−0.271981 | + | 0.962303i | \(0.587679\pi\) | |||||||
\(138\) | −1.18963 | −0.101268 | ||||||||
\(139\) | −12.0899 | −1.02545 | −0.512725 | − | 0.858553i | \(-0.671364\pi\) | ||||
−0.512725 | + | 0.858553i | \(0.671364\pi\) | |||||||
\(140\) | 0.600780 | 0.0507752 | ||||||||
\(141\) | 5.87638 | 0.494881 | ||||||||
\(142\) | −11.6398 | −0.976788 | ||||||||
\(143\) | −8.80703 | −0.736481 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.67231 | −0.471060 | ||||||||
\(146\) | −16.8053 | −1.39082 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −5.07939 | −0.417523 | ||||||||
\(149\) | 4.06155 | 0.332735 | 0.166368 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166368 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(150\) | 4.63906 | 0.378778 | ||||||||
\(151\) | 18.5807 | 1.51208 | 0.756040 | − | 0.654526i | \(-0.227132\pi\) | ||||
0.756040 | + | 0.654526i | \(0.227132\pi\) | |||||||
\(152\) | −0.811418 | −0.0658147 | ||||||||
\(153\) | 0.291399 | 0.0235582 | ||||||||
\(154\) | −3.98407 | −0.321045 | ||||||||
\(155\) | 4.57513 | 0.367483 | ||||||||
\(156\) | −2.21056 | −0.176987 | ||||||||
\(157\) | 4.70929 | 0.375842 | 0.187921 | − | 0.982184i | \(-0.439825\pi\) | ||||
0.187921 | + | 0.982184i | \(0.439825\pi\) | |||||||
\(158\) | −1.60018 | −0.127304 | ||||||||
\(159\) | 11.5189 | 0.913506 | ||||||||
\(160\) | −0.600780 | −0.0474959 | ||||||||
\(161\) | 1.18963 | 0.0937562 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 22.9695 | 1.79911 | 0.899553 | − | 0.436811i | \(-0.143892\pi\) | ||||
0.899553 | + | 0.436811i | \(0.143892\pi\) | |||||||
\(164\) | 2.80141 | 0.218754 | ||||||||
\(165\) | 2.39355 | 0.186337 | ||||||||
\(166\) | 5.30607 | 0.411831 | ||||||||
\(167\) | 2.85628 | 0.221025 | 0.110513 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110513 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −8.11341 | −0.624108 | ||||||||
\(170\) | −0.175067 | −0.0134270 | ||||||||
\(171\) | 0.811418 | 0.0620507 | ||||||||
\(172\) | −4.76406 | −0.363256 | ||||||||
\(173\) | −23.1834 | −1.76260 | −0.881302 | − | 0.472553i | \(-0.843332\pi\) | ||||
−0.881302 | + | 0.472553i | \(0.843332\pi\) | |||||||
\(174\) | 9.44157 | 0.715763 | ||||||||
\(175\) | −4.63906 | −0.350680 | ||||||||
\(176\) | 3.98407 | 0.300310 | ||||||||
\(177\) | −5.71021 | −0.429205 | ||||||||
\(178\) | 6.96178 | 0.521807 | ||||||||
\(179\) | 19.7984 | 1.47980 | 0.739900 | − | 0.672717i | \(-0.234873\pi\) | ||||
0.739900 | + | 0.672717i | \(0.234873\pi\) | |||||||
\(180\) | 0.600780 | 0.0447795 | ||||||||
\(181\) | −7.54151 | −0.560556 | −0.280278 | − | 0.959919i | \(-0.590427\pi\) | ||||
−0.280278 | + | 0.959919i | \(0.590427\pi\) | |||||||
\(182\) | 2.21056 | 0.163858 | ||||||||
\(183\) | 2.62535 | 0.194071 | ||||||||
\(184\) | −1.18963 | −0.0877009 | ||||||||
\(185\) | −3.05160 | −0.224358 | ||||||||
\(186\) | −7.61531 | −0.558382 | ||||||||
\(187\) | 1.16095 | 0.0848972 | ||||||||
\(188\) | 5.87638 | 0.428579 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −0.487484 | −0.0353658 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −9.25956 | −0.666518 | −0.333259 | − | 0.942835i | \(-0.608148\pi\) | ||||
−0.333259 | + | 0.942835i | \(0.608148\pi\) | |||||||
\(194\) | −4.49961 | −0.323053 | ||||||||
\(195\) | −1.32806 | −0.0951046 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −10.0613 | −0.716841 | −0.358420 | − | 0.933560i | \(-0.616685\pi\) | ||||
−0.358420 | + | 0.933560i | \(0.616685\pi\) | |||||||
\(198\) | −3.98407 | −0.283135 | ||||||||
\(199\) | 5.35710 | 0.379755 | 0.189877 | − | 0.981808i | \(-0.439191\pi\) | ||||
0.189877 | + | 0.981808i | \(0.439191\pi\) | |||||||
\(200\) | 4.63906 | 0.328031 | ||||||||
\(201\) | 14.9062 | 1.05140 | ||||||||
\(202\) | −5.35438 | −0.376733 | ||||||||
\(203\) | −9.44157 | −0.662668 | ||||||||
\(204\) | 0.291399 | 0.0204020 | ||||||||
\(205\) | 1.68303 | 0.117548 | ||||||||
\(206\) | 9.04862 | 0.630448 | ||||||||
\(207\) | 1.18963 | 0.0826852 | ||||||||
\(208\) | −2.21056 | −0.153275 | ||||||||
\(209\) | 3.23274 | 0.223614 | ||||||||
\(210\) | −0.600780 | −0.0414578 | ||||||||
\(211\) | 10.4729 | 0.720983 | 0.360491 | − | 0.932763i | \(-0.382609\pi\) | ||||
0.360491 | + | 0.932763i | \(0.382609\pi\) | |||||||
\(212\) | 11.5189 | 0.791120 | ||||||||
\(213\) | 11.6398 | 0.797544 | ||||||||
\(214\) | −15.9118 | −1.08771 | ||||||||
\(215\) | −2.86215 | −0.195197 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 7.61531 | 0.516961 | ||||||||
\(218\) | −1.54381 | −0.104560 | ||||||||
\(219\) | 16.8053 | 1.13560 | ||||||||
\(220\) | 2.39355 | 0.161373 | ||||||||
\(221\) | −0.644156 | −0.0433306 | ||||||||
\(222\) | 5.07939 | 0.340906 | ||||||||
\(223\) | −14.5234 | −0.972562 | −0.486281 | − | 0.873802i | \(-0.661647\pi\) | ||||
−0.486281 | + | 0.873802i | \(0.661647\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.63906 | −0.309271 | ||||||||
\(226\) | 17.9097 | 1.19134 | ||||||||
\(227\) | −6.06557 | −0.402586 | −0.201293 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201293 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(228\) | 0.811418 | 0.0537375 | ||||||||
\(229\) | −9.54355 | −0.630655 | −0.315328 | − | 0.948983i | \(-0.602114\pi\) | ||||
−0.315328 | + | 0.948983i | \(0.602114\pi\) | |||||||
\(230\) | −0.714708 | −0.0471264 | ||||||||
\(231\) | 3.98407 | 0.262132 | ||||||||
\(232\) | 9.44157 | 0.619869 | ||||||||
\(233\) | −6.93594 | −0.454388 | −0.227194 | − | 0.973849i | \(-0.572955\pi\) | ||||
−0.227194 | + | 0.973849i | \(0.572955\pi\) | |||||||
\(234\) | 2.21056 | 0.144509 | ||||||||
\(235\) | 3.53042 | 0.230299 | ||||||||
\(236\) | −5.71021 | −0.371703 | ||||||||
\(237\) | 1.60018 | 0.103943 | ||||||||
\(238\) | −0.291399 | −0.0188886 | ||||||||
\(239\) | −0.650366 | −0.0420687 | −0.0210343 | − | 0.999779i | \(-0.506696\pi\) | ||||
−0.0210343 | + | 0.999779i | \(0.506696\pi\) | |||||||
\(240\) | 0.600780 | 0.0387802 | ||||||||
\(241\) | 6.26146 | 0.403336 | 0.201668 | − | 0.979454i | \(-0.435364\pi\) | ||||
0.201668 | + | 0.979454i | \(0.435364\pi\) | |||||||
\(242\) | −4.87278 | −0.313234 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.62535 | 0.168071 | ||||||||
\(245\) | 0.600780 | 0.0383825 | ||||||||
\(246\) | −2.80141 | −0.178611 | ||||||||
\(247\) | −1.79369 | −0.114130 | ||||||||
\(248\) | −7.61531 | −0.483573 | ||||||||
\(249\) | −5.30607 | −0.336259 | ||||||||
\(250\) | 5.79096 | 0.366252 | ||||||||
\(251\) | −21.3290 | −1.34627 | −0.673137 | − | 0.739518i | \(-0.735054\pi\) | ||||
−0.673137 | + | 0.739518i | \(0.735054\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 4.73957 | 0.297974 | ||||||||
\(254\) | −19.1969 | −1.20452 | ||||||||
\(255\) | 0.175067 | 0.0109631 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.04463 | −0.0651622 | −0.0325811 | − | 0.999469i | \(-0.510373\pi\) | ||||
−0.0325811 | + | 0.999469i | \(0.510373\pi\) | |||||||
\(258\) | 4.76406 | 0.296598 | ||||||||
\(259\) | −5.07939 | −0.315618 | ||||||||
\(260\) | −1.32806 | −0.0823630 | ||||||||
\(261\) | −9.44157 | −0.584418 | ||||||||
\(262\) | −16.1818 | −0.999717 | ||||||||
\(263\) | 6.29202 | 0.387982 | 0.193991 | − | 0.981003i | \(-0.437857\pi\) | ||||
0.193991 | + | 0.981003i | \(0.437857\pi\) | |||||||
\(264\) | −3.98407 | −0.245202 | ||||||||
\(265\) | 6.92032 | 0.425112 | ||||||||
\(266\) | −0.811418 | −0.0497512 | ||||||||
\(267\) | −6.96178 | −0.426054 | ||||||||
\(268\) | 14.9062 | 0.910540 | ||||||||
\(269\) | −24.7427 | −1.50859 | −0.754296 | − | 0.656535i | \(-0.772021\pi\) | ||||
−0.754296 | + | 0.656535i | \(0.772021\pi\) | |||||||
\(270\) | −0.600780 | −0.0365623 | ||||||||
\(271\) | 21.0873 | 1.28096 | 0.640480 | − | 0.767975i | \(-0.278735\pi\) | ||||
0.640480 | + | 0.767975i | \(0.278735\pi\) | |||||||
\(272\) | 0.291399 | 0.0176687 | ||||||||
\(273\) | −2.21056 | −0.133789 | ||||||||
\(274\) | 6.36691 | 0.384639 | ||||||||
\(275\) | −18.4823 | −1.11453 | ||||||||
\(276\) | 1.18963 | 0.0716075 | ||||||||
\(277\) | 12.6960 | 0.762831 | 0.381415 | − | 0.924404i | \(-0.375437\pi\) | ||||
0.381415 | + | 0.924404i | \(0.375437\pi\) | |||||||
\(278\) | 12.0899 | 0.725103 | ||||||||
\(279\) | 7.61531 | 0.455917 | ||||||||
\(280\) | −0.600780 | −0.0359035 | ||||||||
\(281\) | 6.29496 | 0.375526 | 0.187763 | − | 0.982214i | \(-0.439876\pi\) | ||||
0.187763 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(282\) | −5.87638 | −0.349934 | ||||||||
\(283\) | 28.4254 | 1.68971 | 0.844856 | − | 0.534994i | \(-0.179686\pi\) | ||||
0.844856 | + | 0.534994i | \(0.179686\pi\) | |||||||
\(284\) | 11.6398 | 0.690693 | ||||||||
\(285\) | 0.487484 | 0.0288761 | ||||||||
\(286\) | 8.80703 | 0.520771 | ||||||||
\(287\) | 2.80141 | 0.165362 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9151 | −0.995005 | ||||||||
\(290\) | 5.67231 | 0.333089 | ||||||||
\(291\) | 4.49961 | 0.263772 | ||||||||
\(292\) | 16.8053 | 0.983455 | ||||||||
\(293\) | 28.6147 | 1.67169 | 0.835844 | − | 0.548967i | \(-0.184979\pi\) | ||||
0.835844 | + | 0.548967i | \(0.184979\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −3.43058 | −0.199736 | ||||||||
\(296\) | 5.07939 | 0.295233 | ||||||||
\(297\) | 3.98407 | 0.231179 | ||||||||
\(298\) | −4.06155 | −0.235279 | ||||||||
\(299\) | −2.62976 | −0.152083 | ||||||||
\(300\) | −4.63906 | −0.267836 | ||||||||
\(301\) | −4.76406 | −0.274596 | ||||||||
\(302\) | −18.5807 | −1.06920 | ||||||||
\(303\) | 5.35438 | 0.307601 | ||||||||
\(304\) | 0.811418 | 0.0465380 | ||||||||
\(305\) | 1.57726 | 0.0903134 | ||||||||
\(306\) | −0.291399 | −0.0166582 | ||||||||
\(307\) | 33.6273 | 1.91921 | 0.959606 | − | 0.281348i | \(-0.0907814\pi\) | ||||
0.959606 | + | 0.281348i | \(0.0907814\pi\) | |||||||
\(308\) | 3.98407 | 0.227013 | ||||||||
\(309\) | −9.04862 | −0.514758 | ||||||||
\(310\) | −4.57513 | −0.259850 | ||||||||
\(311\) | −7.23048 | −0.410003 | −0.205001 | − | 0.978762i | \(-0.565720\pi\) | ||||
−0.205001 | + | 0.978762i | \(0.565720\pi\) | |||||||
\(312\) | 2.21056 | 0.125149 | ||||||||
\(313\) | −23.1287 | −1.30731 | −0.653655 | − | 0.756793i | \(-0.726765\pi\) | ||||
−0.653655 | + | 0.756793i | \(0.726765\pi\) | |||||||
\(314\) | −4.70929 | −0.265761 | ||||||||
\(315\) | 0.600780 | 0.0338501 | ||||||||
\(316\) | 1.60018 | 0.0900173 | ||||||||
\(317\) | 7.17192 | 0.402815 | 0.201408 | − | 0.979508i | \(-0.435448\pi\) | ||||
0.201408 | + | 0.979508i | \(0.435448\pi\) | |||||||
\(318\) | −11.5189 | −0.645947 | ||||||||
\(319\) | −37.6158 | −2.10608 | ||||||||
\(320\) | 0.600780 | 0.0335846 | ||||||||
\(321\) | 15.9118 | 0.888111 | ||||||||
\(322\) | −1.18963 | −0.0662956 | ||||||||
\(323\) | 0.236446 | 0.0131562 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 10.2549 | 0.568842 | ||||||||
\(326\) | −22.9695 | −1.27216 | ||||||||
\(327\) | 1.54381 | 0.0853726 | ||||||||
\(328\) | −2.80141 | −0.154682 | ||||||||
\(329\) | 5.87638 | 0.323976 | ||||||||
\(330\) | −2.39355 | −0.131761 | ||||||||
\(331\) | 26.0184 | 1.43010 | 0.715051 | − | 0.699073i | \(-0.246404\pi\) | ||||
0.715051 | + | 0.699073i | \(0.246404\pi\) | |||||||
\(332\) | −5.30607 | −0.291209 | ||||||||
\(333\) | −5.07939 | −0.278349 | ||||||||
\(334\) | −2.85628 | −0.156289 | ||||||||
\(335\) | 8.95534 | 0.489283 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −16.0449 | −0.874020 | −0.437010 | − | 0.899457i | \(-0.643963\pi\) | ||||
−0.437010 | + | 0.899457i | \(0.643963\pi\) | |||||||
\(338\) | 8.11341 | 0.441311 | ||||||||
\(339\) | −17.9097 | −0.972721 | ||||||||
\(340\) | 0.175067 | 0.00949433 | ||||||||
\(341\) | 30.3399 | 1.64300 | ||||||||
\(342\) | −0.811418 | −0.0438765 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.76406 | 0.256861 | ||||||||
\(345\) | 0.714708 | 0.0384786 | ||||||||
\(346\) | 23.1834 | 1.24635 | ||||||||
\(347\) | −2.80431 | −0.150543 | −0.0752717 | − | 0.997163i | \(-0.523982\pi\) | ||||
−0.0752717 | + | 0.997163i | \(0.523982\pi\) | |||||||
\(348\) | −9.44157 | −0.506121 | ||||||||
\(349\) | −1.70382 | −0.0912032 | −0.0456016 | − | 0.998960i | \(-0.514520\pi\) | ||||
−0.0456016 | + | 0.998960i | \(0.514520\pi\) | |||||||
\(350\) | 4.63906 | 0.247968 | ||||||||
\(351\) | −2.21056 | −0.117991 | ||||||||
\(352\) | −3.98407 | −0.212351 | ||||||||
\(353\) | 16.7576 | 0.891918 | 0.445959 | − | 0.895053i | \(-0.352863\pi\) | ||||
0.445959 | + | 0.895053i | \(0.352863\pi\) | |||||||
\(354\) | 5.71021 | 0.303494 | ||||||||
\(355\) | 6.99294 | 0.371147 | ||||||||
\(356\) | −6.96178 | −0.368974 | ||||||||
\(357\) | 0.291399 | 0.0154225 | ||||||||
\(358\) | −19.7984 | −1.04638 | ||||||||
\(359\) | −13.1677 | −0.694965 | −0.347482 | − | 0.937686i | \(-0.612963\pi\) | ||||
−0.347482 | + | 0.937686i | \(0.612963\pi\) | |||||||
\(360\) | −0.600780 | −0.0316639 | ||||||||
\(361\) | −18.3416 | −0.965347 | ||||||||
\(362\) | 7.54151 | 0.396373 | ||||||||
\(363\) | 4.87278 | 0.255754 | ||||||||
\(364\) | −2.21056 | −0.115865 | ||||||||
\(365\) | 10.0963 | 0.528464 | ||||||||
\(366\) | −2.62535 | −0.137229 | ||||||||
\(367\) | 9.51113 | 0.496477 | 0.248239 | − | 0.968699i | \(-0.420148\pi\) | ||||
0.248239 | + | 0.968699i | \(0.420148\pi\) | |||||||
\(368\) | 1.18963 | 0.0620139 | ||||||||
\(369\) | 2.80141 | 0.145836 | ||||||||
\(370\) | 3.05160 | 0.158645 | ||||||||
\(371\) | 11.5189 | 0.598030 | ||||||||
\(372\) | 7.61531 | 0.394835 | ||||||||
\(373\) | 27.8130 | 1.44010 | 0.720052 | − | 0.693920i | \(-0.244118\pi\) | ||||
0.720052 | + | 0.693920i | \(0.244118\pi\) | |||||||
\(374\) | −1.16095 | −0.0600314 | ||||||||
\(375\) | −5.79096 | −0.299044 | ||||||||
\(376\) | −5.87638 | −0.303051 | ||||||||
\(377\) | 20.8712 | 1.07492 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −0.528092 | −0.0271263 | −0.0135631 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135631 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(380\) | 0.487484 | 0.0250074 | ||||||||
\(381\) | 19.1969 | 0.983485 | ||||||||
\(382\) | −1.00000 | −0.0511645 | ||||||||
\(383\) | 1.79471 | 0.0917055 | 0.0458528 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458528 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.39355 | 0.121987 | ||||||||
\(386\) | 9.25956 | 0.471299 | ||||||||
\(387\) | −4.76406 | −0.242171 | ||||||||
\(388\) | 4.49961 | 0.228433 | ||||||||
\(389\) | −23.0637 | −1.16938 | −0.584688 | − | 0.811258i | \(-0.698783\pi\) | ||||
−0.584688 | + | 0.811258i | \(0.698783\pi\) | |||||||
\(390\) | 1.32806 | 0.0672491 | ||||||||
\(391\) | 0.346658 | 0.0175312 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 16.1818 | 0.816265 | ||||||||
\(394\) | 10.0613 | 0.506883 | ||||||||
\(395\) | 0.961358 | 0.0483712 | ||||||||
\(396\) | 3.98407 | 0.200207 | ||||||||
\(397\) | 24.2450 | 1.21682 | 0.608412 | − | 0.793622i | \(-0.291807\pi\) | ||||
0.608412 | + | 0.793622i | \(0.291807\pi\) | |||||||
\(398\) | −5.35710 | −0.268527 | ||||||||
\(399\) | 0.811418 | 0.0406217 | ||||||||
\(400\) | −4.63906 | −0.231953 | ||||||||
\(401\) | −10.6619 | −0.532428 | −0.266214 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266214 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(402\) | −14.9062 | −0.743453 | ||||||||
\(403\) | −16.8341 | −0.838568 | ||||||||
\(404\) | 5.35438 | 0.266390 | ||||||||
\(405\) | 0.600780 | 0.0298530 | ||||||||
\(406\) | 9.44157 | 0.468577 | ||||||||
\(407\) | −20.2366 | −1.00309 | ||||||||
\(408\) | −0.291399 | −0.0144264 | ||||||||
\(409\) | −10.7685 | −0.532469 | −0.266234 | − | 0.963908i | \(-0.585780\pi\) | ||||
−0.266234 | + | 0.963908i | \(0.585780\pi\) | |||||||
\(410\) | −1.68303 | −0.0831191 | ||||||||
\(411\) | −6.36691 | −0.314056 | ||||||||
\(412\) | −9.04862 | −0.445794 | ||||||||
\(413\) | −5.71021 | −0.280981 | ||||||||
\(414\) | −1.18963 | −0.0584672 | ||||||||
\(415\) | −3.18779 | −0.156482 | ||||||||
\(416\) | 2.21056 | 0.108382 | ||||||||
\(417\) | −12.0899 | −0.592044 | ||||||||
\(418\) | −3.23274 | −0.158119 | ||||||||
\(419\) | 6.01704 | 0.293952 | 0.146976 | − | 0.989140i | \(-0.453046\pi\) | ||||
0.146976 | + | 0.989140i | \(0.453046\pi\) | |||||||
\(420\) | 0.600780 | 0.0293151 | ||||||||
\(421\) | 27.8137 | 1.35556 | 0.677778 | − | 0.735267i | \(-0.262943\pi\) | ||||
0.677778 | + | 0.735267i | \(0.262943\pi\) | |||||||
\(422\) | −10.4729 | −0.509812 | ||||||||
\(423\) | 5.87638 | 0.285720 | ||||||||
\(424\) | −11.5189 | −0.559406 | ||||||||
\(425\) | −1.35182 | −0.0655728 | ||||||||
\(426\) | −11.6398 | −0.563949 | ||||||||
\(427\) | 2.62535 | 0.127049 | ||||||||
\(428\) | 15.9118 | 0.769126 | ||||||||
\(429\) | −8.80703 | −0.425207 | ||||||||
\(430\) | 2.86215 | 0.138025 | ||||||||
\(431\) | −28.1741 | −1.35710 | −0.678550 | − | 0.734554i | \(-0.737391\pi\) | ||||
−0.678550 | + | 0.734554i | \(0.737391\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.5526 | 0.939640 | 0.469820 | − | 0.882762i | \(-0.344319\pi\) | ||||
0.469820 | + | 0.882762i | \(0.344319\pi\) | |||||||
\(434\) | −7.61531 | −0.365547 | ||||||||
\(435\) | −5.67231 | −0.271966 | ||||||||
\(436\) | 1.54381 | 0.0739349 | ||||||||
\(437\) | 0.965289 | 0.0461761 | ||||||||
\(438\) | −16.8053 | −0.802987 | ||||||||
\(439\) | −7.01706 | −0.334906 | −0.167453 | − | 0.985880i | \(-0.553554\pi\) | ||||
−0.167453 | + | 0.985880i | \(0.553554\pi\) | |||||||
\(440\) | −2.39355 | −0.114108 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.644156 | 0.0306394 | ||||||||
\(443\) | −33.9891 | −1.61487 | −0.807436 | − | 0.589956i | \(-0.799145\pi\) | ||||
−0.807436 | + | 0.589956i | \(0.799145\pi\) | |||||||
\(444\) | −5.07939 | −0.241057 | ||||||||
\(445\) | −4.18250 | −0.198270 | ||||||||
\(446\) | 14.5234 | 0.687705 | ||||||||
\(447\) | 4.06155 | 0.192105 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −19.7565 | −0.932368 | −0.466184 | − | 0.884688i | \(-0.654372\pi\) | ||||
−0.466184 | + | 0.884688i | \(0.654372\pi\) | |||||||
\(450\) | 4.63906 | 0.218688 | ||||||||
\(451\) | 11.1610 | 0.525551 | ||||||||
\(452\) | −17.9097 | −0.842401 | ||||||||
\(453\) | 18.5807 | 0.872999 | ||||||||
\(454\) | 6.06557 | 0.284672 | ||||||||
\(455\) | −1.32806 | −0.0622606 | ||||||||
\(456\) | −0.811418 | −0.0379981 | ||||||||
\(457\) | 39.2825 | 1.83756 | 0.918779 | − | 0.394772i | \(-0.129177\pi\) | ||||
0.918779 | + | 0.394772i | \(0.129177\pi\) | |||||||
\(458\) | 9.54355 | 0.445941 | ||||||||
\(459\) | 0.291399 | 0.0136013 | ||||||||
\(460\) | 0.714708 | 0.0333234 | ||||||||
\(461\) | −5.75616 | −0.268091 | −0.134045 | − | 0.990975i | \(-0.542797\pi\) | ||||
−0.134045 | + | 0.990975i | \(0.542797\pi\) | |||||||
\(462\) | −3.98407 | −0.185355 | ||||||||
\(463\) | −36.4705 | −1.69493 | −0.847464 | − | 0.530853i | \(-0.821872\pi\) | ||||
−0.847464 | + | 0.530853i | \(0.821872\pi\) | |||||||
\(464\) | −9.44157 | −0.438314 | ||||||||
\(465\) | 4.57513 | 0.212167 | ||||||||
\(466\) | 6.93594 | 0.321301 | ||||||||
\(467\) | −36.6938 | −1.69799 | −0.848993 | − | 0.528405i | \(-0.822790\pi\) | ||||
−0.848993 | + | 0.528405i | \(0.822790\pi\) | |||||||
\(468\) | −2.21056 | −0.102183 | ||||||||
\(469\) | 14.9062 | 0.688304 | ||||||||
\(470\) | −3.53042 | −0.162846 | ||||||||
\(471\) | 4.70929 | 0.216993 | ||||||||
\(472\) | 5.71021 | 0.262834 | ||||||||
\(473\) | −18.9803 | −0.872717 | ||||||||
\(474\) | −1.60018 | −0.0734988 | ||||||||
\(475\) | −3.76422 | −0.172714 | ||||||||
\(476\) | 0.291399 | 0.0133562 | ||||||||
\(477\) | 11.5189 | 0.527413 | ||||||||
\(478\) | 0.650366 | 0.0297470 | ||||||||
\(479\) | 30.8394 | 1.40909 | 0.704545 | − | 0.709659i | \(-0.251151\pi\) | ||||
0.704545 | + | 0.709659i | \(0.251151\pi\) | |||||||
\(480\) | −0.600780 | −0.0274217 | ||||||||
\(481\) | 11.2283 | 0.511967 | ||||||||
\(482\) | −6.26146 | −0.285202 | ||||||||
\(483\) | 1.18963 | 0.0541301 | ||||||||
\(484\) | 4.87278 | 0.221490 | ||||||||
\(485\) | 2.70328 | 0.122750 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 10.3033 | 0.466886 | 0.233443 | − | 0.972371i | \(-0.425001\pi\) | ||||
0.233443 | + | 0.972371i | \(0.425001\pi\) | |||||||
\(488\) | −2.62535 | −0.118844 | ||||||||
\(489\) | 22.9695 | 1.03871 | ||||||||
\(490\) | −0.600780 | −0.0271405 | ||||||||
\(491\) | −20.2337 | −0.913132 | −0.456566 | − | 0.889690i | \(-0.650921\pi\) | ||||
−0.456566 | + | 0.889690i | \(0.650921\pi\) | |||||||
\(492\) | 2.80141 | 0.126297 | ||||||||
\(493\) | −2.75126 | −0.123911 | ||||||||
\(494\) | 1.79369 | 0.0807020 | ||||||||
\(495\) | 2.39355 | 0.107582 | ||||||||
\(496\) | 7.61531 | 0.341938 | ||||||||
\(497\) | 11.6398 | 0.522115 | ||||||||
\(498\) | 5.30607 | 0.237771 | ||||||||
\(499\) | 41.8077 | 1.87157 | 0.935785 | − | 0.352572i | \(-0.114693\pi\) | ||||
0.935785 | + | 0.352572i | \(0.114693\pi\) | |||||||
\(500\) | −5.79096 | −0.258980 | ||||||||
\(501\) | 2.85628 | 0.127609 | ||||||||
\(502\) | 21.3290 | 0.951959 | ||||||||
\(503\) | 28.3288 | 1.26312 | 0.631560 | − | 0.775327i | \(-0.282415\pi\) | ||||
0.631560 | + | 0.775327i | \(0.282415\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 3.21680 | 0.143146 | ||||||||
\(506\) | −4.73957 | −0.210700 | ||||||||
\(507\) | −8.11341 | −0.360329 | ||||||||
\(508\) | 19.1969 | 0.851723 | ||||||||
\(509\) | 12.4573 | 0.552161 | 0.276080 | − | 0.961135i | \(-0.410964\pi\) | ||||
0.276080 | + | 0.961135i | \(0.410964\pi\) | |||||||
\(510\) | −0.175067 | −0.00775209 | ||||||||
\(511\) | 16.8053 | 0.743422 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.811418 | 0.0358250 | ||||||||
\(514\) | 1.04463 | 0.0460767 | ||||||||
\(515\) | −5.43624 | −0.239549 | ||||||||
\(516\) | −4.76406 | −0.209726 | ||||||||
\(517\) | 23.4119 | 1.02965 | ||||||||
\(518\) | 5.07939 | 0.223175 | ||||||||
\(519\) | −23.1834 | −1.01764 | ||||||||
\(520\) | 1.32806 | 0.0582394 | ||||||||
\(521\) | −37.1101 | −1.62582 | −0.812912 | − | 0.582386i | \(-0.802119\pi\) | ||||
−0.812912 | + | 0.582386i | \(0.802119\pi\) | |||||||
\(522\) | 9.44157 | 0.413246 | ||||||||
\(523\) | −15.6601 | −0.684770 | −0.342385 | − | 0.939560i | \(-0.611235\pi\) | ||||
−0.342385 | + | 0.939560i | \(0.611235\pi\) | |||||||
\(524\) | 16.1818 | 0.706906 | ||||||||
\(525\) | −4.63906 | −0.202465 | ||||||||
\(526\) | −6.29202 | −0.274345 | ||||||||
\(527\) | 2.21909 | 0.0966652 | ||||||||
\(528\) | 3.98407 | 0.173384 | ||||||||
\(529\) | −21.5848 | −0.938468 | ||||||||
\(530\) | −6.92032 | −0.300599 | ||||||||
\(531\) | −5.71021 | −0.247802 | ||||||||
\(532\) | 0.811418 | 0.0351794 | ||||||||
\(533\) | −6.19270 | −0.268236 | ||||||||
\(534\) | 6.96178 | 0.301266 | ||||||||
\(535\) | 9.55950 | 0.413293 | ||||||||
\(536\) | −14.9062 | −0.643849 | ||||||||
\(537\) | 19.7984 | 0.854363 | ||||||||
\(538\) | 24.7427 | 1.06674 | ||||||||
\(539\) | 3.98407 | 0.171606 | ||||||||
\(540\) | 0.600780 | 0.0258535 | ||||||||
\(541\) | −8.78722 | −0.377792 | −0.188896 | − | 0.981997i | \(-0.560491\pi\) | ||||
−0.188896 | + | 0.981997i | \(0.560491\pi\) | |||||||
\(542\) | −21.0873 | −0.905775 | ||||||||
\(543\) | −7.54151 | −0.323637 | ||||||||
\(544\) | −0.291399 | −0.0124936 | ||||||||
\(545\) | 0.927488 | 0.0397292 | ||||||||
\(546\) | 2.21056 | 0.0946034 | ||||||||
\(547\) | 13.6520 | 0.583718 | 0.291859 | − | 0.956461i | \(-0.405726\pi\) | ||||
0.291859 | + | 0.956461i | \(0.405726\pi\) | |||||||
\(548\) | −6.36691 | −0.271981 | ||||||||
\(549\) | 2.62535 | 0.112047 | ||||||||
\(550\) | 18.4823 | 0.788089 | ||||||||
\(551\) | −7.66106 | −0.326372 | ||||||||
\(552\) | −1.18963 | −0.0506341 | ||||||||
\(553\) | 1.60018 | 0.0680467 | ||||||||
\(554\) | −12.6960 | −0.539403 | ||||||||
\(555\) | −3.05160 | −0.129533 | ||||||||
\(556\) | −12.0899 | −0.512725 | ||||||||
\(557\) | 4.32923 | 0.183435 | 0.0917177 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917177 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(558\) | −7.61531 | −0.322382 | ||||||||
\(559\) | 10.5313 | 0.445425 | ||||||||
\(560\) | 0.600780 | 0.0253876 | ||||||||
\(561\) | 1.16095 | 0.0490154 | ||||||||
\(562\) | −6.29496 | −0.265537 | ||||||||
\(563\) | −7.33859 | −0.309285 | −0.154642 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(564\) | 5.87638 | 0.247440 | ||||||||
\(565\) | −10.7598 | −0.452668 | ||||||||
\(566\) | −28.4254 | −1.19481 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −11.6398 | −0.488394 | ||||||||
\(569\) | 0.843687 | 0.0353692 | 0.0176846 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176846 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(570\) | −0.487484 | −0.0204185 | ||||||||
\(571\) | 9.09512 | 0.380619 | 0.190309 | − | 0.981724i | \(-0.439051\pi\) | ||||
0.190309 | + | 0.981724i | \(0.439051\pi\) | |||||||
\(572\) | −8.80703 | −0.368240 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −2.80141 | −0.116929 | ||||||||
\(575\) | −5.51878 | −0.230149 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −28.7246 | −1.19582 | −0.597910 | − | 0.801563i | \(-0.704002\pi\) | ||||
−0.597910 | + | 0.801563i | \(0.704002\pi\) | |||||||
\(578\) | 16.9151 | 0.703575 | ||||||||
\(579\) | −9.25956 | −0.384814 | ||||||||
\(580\) | −5.67231 | −0.235530 | ||||||||
\(581\) | −5.30607 | −0.220133 | ||||||||
\(582\) | −4.49961 | −0.186515 | ||||||||
\(583\) | 45.8920 | 1.90065 | ||||||||
\(584\) | −16.8053 | −0.695408 | ||||||||
\(585\) | −1.32806 | −0.0549087 | ||||||||
\(586\) | −28.6147 | −1.18206 | ||||||||
\(587\) | 29.2293 | 1.20642 | 0.603212 | − | 0.797581i | \(-0.293887\pi\) | ||||
0.603212 | + | 0.797581i | \(0.293887\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 6.17920 | 0.254610 | ||||||||
\(590\) | 3.43058 | 0.141235 | ||||||||
\(591\) | −10.0613 | −0.413868 | ||||||||
\(592\) | −5.07939 | −0.208762 | ||||||||
\(593\) | 15.6551 | 0.642878 | 0.321439 | − | 0.946930i | \(-0.395834\pi\) | ||||
0.321439 | + | 0.946930i | \(0.395834\pi\) | |||||||
\(594\) | −3.98407 | −0.163468 | ||||||||
\(595\) | 0.175067 | 0.00717704 | ||||||||
\(596\) | 4.06155 | 0.166368 | ||||||||
\(597\) | 5.35710 | 0.219251 | ||||||||
\(598\) | 2.62976 | 0.107539 | ||||||||
\(599\) | −46.2954 | −1.89158 | −0.945789 | − | 0.324781i | \(-0.894709\pi\) | ||||
−0.945789 | + | 0.324781i | \(0.894709\pi\) | |||||||
\(600\) | 4.63906 | 0.189389 | ||||||||
\(601\) | −20.1477 | −0.821840 | −0.410920 | − | 0.911671i | \(-0.634792\pi\) | ||||
−0.410920 | + | 0.911671i | \(0.634792\pi\) | |||||||
\(602\) | 4.76406 | 0.194169 | ||||||||
\(603\) | 14.9062 | 0.607027 | ||||||||
\(604\) | 18.5807 | 0.756040 | ||||||||
\(605\) | 2.92747 | 0.119019 | ||||||||
\(606\) | −5.35438 | −0.217507 | ||||||||
\(607\) | −7.05084 | −0.286185 | −0.143092 | − | 0.989709i | \(-0.545705\pi\) | ||||
−0.143092 | + | 0.989709i | \(0.545705\pi\) | |||||||
\(608\) | −0.811418 | −0.0329074 | ||||||||
\(609\) | −9.44157 | −0.382592 | ||||||||
\(610\) | −1.57726 | −0.0638612 | ||||||||
\(611\) | −12.9901 | −0.525524 | ||||||||
\(612\) | 0.291399 | 0.0117791 | ||||||||
\(613\) | 23.4082 | 0.945447 | 0.472724 | − | 0.881211i | \(-0.343271\pi\) | ||||
0.472724 | + | 0.881211i | \(0.343271\pi\) | |||||||
\(614\) | −33.6273 | −1.35709 | ||||||||
\(615\) | 1.68303 | 0.0678665 | ||||||||
\(616\) | −3.98407 | −0.160523 | ||||||||
\(617\) | −27.3958 | −1.10291 | −0.551457 | − | 0.834203i | \(-0.685928\pi\) | ||||
−0.551457 | + | 0.834203i | \(0.685928\pi\) | |||||||
\(618\) | 9.04862 | 0.363989 | ||||||||
\(619\) | −2.18096 | −0.0876600 | −0.0438300 | − | 0.999039i | \(-0.513956\pi\) | ||||
−0.0438300 | + | 0.999039i | \(0.513956\pi\) | |||||||
\(620\) | 4.57513 | 0.183742 | ||||||||
\(621\) | 1.18963 | 0.0477383 | ||||||||
\(622\) | 7.23048 | 0.289916 | ||||||||
\(623\) | −6.96178 | −0.278918 | ||||||||
\(624\) | −2.21056 | −0.0884934 | ||||||||
\(625\) | 19.7162 | 0.788649 | ||||||||
\(626\) | 23.1287 | 0.924408 | ||||||||
\(627\) | 3.23274 | 0.129103 | ||||||||
\(628\) | 4.70929 | 0.187921 | ||||||||
\(629\) | −1.48013 | −0.0590166 | ||||||||
\(630\) | −0.600780 | −0.0239357 | ||||||||
\(631\) | −32.8276 | −1.30685 | −0.653423 | − | 0.756993i | \(-0.726668\pi\) | ||||
−0.653423 | + | 0.756993i | \(0.726668\pi\) | |||||||
\(632\) | −1.60018 | −0.0636518 | ||||||||
\(633\) | 10.4729 | 0.416260 | ||||||||
\(634\) | −7.17192 | −0.284833 | ||||||||
\(635\) | 11.5331 | 0.457677 | ||||||||
\(636\) | 11.5189 | 0.456753 | ||||||||
\(637\) | −2.21056 | −0.0875857 | ||||||||
\(638\) | 37.6158 | 1.48922 | ||||||||
\(639\) | 11.6398 | 0.460462 | ||||||||
\(640\) | −0.600780 | −0.0237479 | ||||||||
\(641\) | −15.0772 | −0.595513 | −0.297756 | − | 0.954642i | \(-0.596238\pi\) | ||||
−0.297756 | + | 0.954642i | \(0.596238\pi\) | |||||||
\(642\) | −15.9118 | −0.627989 | ||||||||
\(643\) | −16.3606 | −0.645199 | −0.322599 | − | 0.946536i | \(-0.604557\pi\) | ||||
−0.322599 | + | 0.946536i | \(0.604557\pi\) | |||||||
\(644\) | 1.18963 | 0.0468781 | ||||||||
\(645\) | −2.86215 | −0.112697 | ||||||||
\(646\) | −0.236446 | −0.00930286 | ||||||||
\(647\) | 49.1364 | 1.93175 | 0.965875 | − | 0.259007i | \(-0.0833953\pi\) | ||||
0.965875 | + | 0.259007i | \(0.0833953\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −22.7498 | −0.893009 | ||||||||
\(650\) | −10.2549 | −0.402232 | ||||||||
\(651\) | 7.61531 | 0.298468 | ||||||||
\(652\) | 22.9695 | 0.899553 | ||||||||
\(653\) | −2.88589 | −0.112934 | −0.0564669 | − | 0.998404i | \(-0.517984\pi\) | ||||
−0.0564669 | + | 0.998404i | \(0.517984\pi\) | |||||||
\(654\) | −1.54381 | −0.0603676 | ||||||||
\(655\) | 9.72173 | 0.379859 | ||||||||
\(656\) | 2.80141 | 0.109377 | ||||||||
\(657\) | 16.8053 | 0.655636 | ||||||||
\(658\) | −5.87638 | −0.229085 | ||||||||
\(659\) | 13.5442 | 0.527607 | 0.263804 | − | 0.964576i | \(-0.415023\pi\) | ||||
0.263804 | + | 0.964576i | \(0.415023\pi\) | |||||||
\(660\) | 2.39355 | 0.0931687 | ||||||||
\(661\) | 45.4190 | 1.76660 | 0.883298 | − | 0.468813i | \(-0.155318\pi\) | ||||
0.883298 | + | 0.468813i | \(0.155318\pi\) | |||||||
\(662\) | −26.0184 | −1.01123 | ||||||||
\(663\) | −0.644156 | −0.0250169 | ||||||||
\(664\) | 5.30607 | 0.205916 | ||||||||
\(665\) | 0.487484 | 0.0189038 | ||||||||
\(666\) | 5.07939 | 0.196822 | ||||||||
\(667\) | −11.2320 | −0.434905 | ||||||||
\(668\) | 2.85628 | 0.110513 | ||||||||
\(669\) | −14.5234 | −0.561509 | ||||||||
\(670\) | −8.95534 | −0.345975 | ||||||||
\(671\) | 10.4595 | 0.403786 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 11.9755 | 0.461620 | 0.230810 | − | 0.972999i | \(-0.425862\pi\) | ||||
0.230810 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(674\) | 16.0449 | 0.618025 | ||||||||
\(675\) | −4.63906 | −0.178558 | ||||||||
\(676\) | −8.11341 | −0.312054 | ||||||||
\(677\) | −4.86100 | −0.186823 | −0.0934117 | − | 0.995628i | \(-0.529777\pi\) | ||||
−0.0934117 | + | 0.995628i | \(0.529777\pi\) | |||||||
\(678\) | 17.9097 | 0.687818 | ||||||||
\(679\) | 4.49961 | 0.172679 | ||||||||
\(680\) | −0.175067 | −0.00671350 | ||||||||
\(681\) | −6.06557 | −0.232433 | ||||||||
\(682\) | −30.3399 | −1.16177 | ||||||||
\(683\) | −1.30802 | −0.0500501 | −0.0250251 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250251 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(684\) | 0.811418 | 0.0310254 | ||||||||
\(685\) | −3.82511 | −0.146150 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −9.54355 | −0.364109 | ||||||||
\(688\) | −4.76406 | −0.181628 | ||||||||
\(689\) | −25.4632 | −0.970071 | ||||||||
\(690\) | −0.714708 | −0.0272085 | ||||||||
\(691\) | −31.3551 | −1.19280 | −0.596402 | − | 0.802686i | \(-0.703404\pi\) | ||||
−0.596402 | + | 0.802686i | \(0.703404\pi\) | |||||||
\(692\) | −23.1834 | −0.881302 | ||||||||
\(693\) | 3.98407 | 0.151342 | ||||||||
\(694\) | 2.80431 | 0.106450 | ||||||||
\(695\) | −7.26336 | −0.275515 | ||||||||
\(696\) | 9.44157 | 0.357882 | ||||||||
\(697\) | 0.816328 | 0.0309206 | ||||||||
\(698\) | 1.70382 | 0.0644904 | ||||||||
\(699\) | −6.93594 | −0.262341 | ||||||||
\(700\) | −4.63906 | −0.175340 | ||||||||
\(701\) | −29.6420 | −1.11956 | −0.559781 | − | 0.828641i | \(-0.689115\pi\) | ||||
−0.559781 | + | 0.828641i | \(0.689115\pi\) | |||||||
\(702\) | 2.21056 | 0.0834324 | ||||||||
\(703\) | −4.12151 | −0.155446 | ||||||||
\(704\) | 3.98407 | 0.150155 | ||||||||
\(705\) | 3.53042 | 0.132963 | ||||||||
\(706\) | −16.7576 | −0.630681 | ||||||||
\(707\) | 5.35438 | 0.201372 | ||||||||
\(708\) | −5.71021 | −0.214603 | ||||||||
\(709\) | 5.86898 | 0.220414 | 0.110207 | − | 0.993909i | \(-0.464849\pi\) | ||||
0.110207 | + | 0.993909i | \(0.464849\pi\) | |||||||
\(710\) | −6.99294 | −0.262441 | ||||||||
\(711\) | 1.60018 | 0.0600115 | ||||||||
\(712\) | 6.96178 | 0.260904 | ||||||||
\(713\) | 9.05942 | 0.339278 | ||||||||
\(714\) | −0.291399 | −0.0109053 | ||||||||
\(715\) | −5.29109 | −0.197876 | ||||||||
\(716\) | 19.7984 | 0.739900 | ||||||||
\(717\) | −0.650366 | −0.0242883 | ||||||||
\(718\) | 13.1677 | 0.491414 | ||||||||
\(719\) | 2.00973 | 0.0749501 | 0.0374751 | − | 0.999298i | \(-0.488069\pi\) | ||||
0.0374751 | + | 0.999298i | \(0.488069\pi\) | |||||||
\(720\) | 0.600780 | 0.0223898 | ||||||||
\(721\) | −9.04862 | −0.336988 | ||||||||
\(722\) | 18.3416 | 0.682604 | ||||||||
\(723\) | 6.26146 | 0.232866 | ||||||||
\(724\) | −7.54151 | −0.280278 | ||||||||
\(725\) | 43.8000 | 1.62669 | ||||||||
\(726\) | −4.87278 | −0.180846 | ||||||||
\(727\) | 11.5401 | 0.428000 | 0.214000 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.214000 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(728\) | 2.21056 | 0.0819290 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.0963 | −0.373680 | ||||||||
\(731\) | −1.38824 | −0.0513460 | ||||||||
\(732\) | 2.62535 | 0.0970356 | ||||||||
\(733\) | 26.4861 | 0.978285 | 0.489142 | − | 0.872204i | \(-0.337310\pi\) | ||||
0.489142 | + | 0.872204i | \(0.337310\pi\) | |||||||
\(734\) | −9.51113 | −0.351062 | ||||||||
\(735\) | 0.600780 | 0.0221601 | ||||||||
\(736\) | −1.18963 | −0.0438504 | ||||||||
\(737\) | 59.3872 | 2.18756 | ||||||||
\(738\) | −2.80141 | −0.103121 | ||||||||
\(739\) | 6.26547 | 0.230479 | 0.115240 | − | 0.993338i | \(-0.463236\pi\) | ||||
0.115240 | + | 0.993338i | \(0.463236\pi\) | |||||||
\(740\) | −3.05160 | −0.112179 | ||||||||
\(741\) | −1.79369 | −0.0658929 | ||||||||
\(742\) | −11.5189 | −0.422871 | ||||||||
\(743\) | 43.8083 | 1.60717 | 0.803585 | − | 0.595190i | \(-0.202923\pi\) | ||||
0.803585 | + | 0.595190i | \(0.202923\pi\) | |||||||
\(744\) | −7.61531 | −0.279191 | ||||||||
\(745\) | 2.44010 | 0.0893984 | ||||||||
\(746\) | −27.8130 | −1.01831 | ||||||||
\(747\) | −5.30607 | −0.194139 | ||||||||
\(748\) | 1.16095 | 0.0424486 | ||||||||
\(749\) | 15.9118 | 0.581405 | ||||||||
\(750\) | 5.79096 | 0.211456 | ||||||||
\(751\) | −35.7985 | −1.30631 | −0.653153 | − | 0.757226i | \(-0.726554\pi\) | ||||
−0.653153 | + | 0.757226i | \(0.726554\pi\) | |||||||
\(752\) | 5.87638 | 0.214290 | ||||||||
\(753\) | −21.3290 | −0.777272 | ||||||||
\(754\) | −20.8712 | −0.760084 | ||||||||
\(755\) | 11.1629 | 0.406261 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 14.8736 | 0.540590 | 0.270295 | − | 0.962778i | \(-0.412879\pi\) | ||||
0.270295 | + | 0.962778i | \(0.412879\pi\) | |||||||
\(758\) | 0.528092 | 0.0191812 | ||||||||
\(759\) | 4.73957 | 0.172036 | ||||||||
\(760\) | −0.487484 | −0.0176829 | ||||||||
\(761\) | −14.0187 | −0.508178 | −0.254089 | − | 0.967181i | \(-0.581776\pi\) | ||||
−0.254089 | + | 0.967181i | \(0.581776\pi\) | |||||||
\(762\) | −19.1969 | −0.695429 | ||||||||
\(763\) | 1.54381 | 0.0558895 | ||||||||
\(764\) | 1.00000 | 0.0361787 | ||||||||
\(765\) | 0.175067 | 0.00632955 | ||||||||
\(766\) | −1.79471 | −0.0648456 | ||||||||
\(767\) | 12.6228 | 0.455782 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −13.4016 | −0.483273 | −0.241636 | − | 0.970367i | \(-0.577684\pi\) | ||||
−0.241636 | + | 0.970367i | \(0.577684\pi\) | |||||||
\(770\) | −2.39355 | −0.0862575 | ||||||||
\(771\) | −1.04463 | −0.0376214 | ||||||||
\(772\) | −9.25956 | −0.333259 | ||||||||
\(773\) | 25.5943 | 0.920564 | 0.460282 | − | 0.887773i | \(-0.347748\pi\) | ||||
0.460282 | + | 0.887773i | \(0.347748\pi\) | |||||||
\(774\) | 4.76406 | 0.171241 | ||||||||
\(775\) | −35.3279 | −1.26902 | ||||||||
\(776\) | −4.49961 | −0.161527 | ||||||||
\(777\) | −5.07939 | −0.182222 | ||||||||
\(778\) | 23.0637 | 0.826874 | ||||||||
\(779\) | 2.27312 | 0.0814429 | ||||||||
\(780\) | −1.32806 | −0.0475523 | ||||||||
\(781\) | 46.3736 | 1.65938 | ||||||||
\(782\) | −0.346658 | −0.0123965 | ||||||||
\(783\) | −9.44157 | −0.337414 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 2.82925 | 0.100980 | ||||||||
\(786\) | −16.1818 | −0.577187 | ||||||||
\(787\) | 33.1324 | 1.18104 | 0.590522 | − | 0.807022i | \(-0.298922\pi\) | ||||
0.590522 | + | 0.807022i | \(0.298922\pi\) | |||||||
\(788\) | −10.0613 | −0.358420 | ||||||||
\(789\) | 6.29202 | 0.224002 | ||||||||
\(790\) | −0.961358 | −0.0342036 | ||||||||
\(791\) | −17.9097 | −0.636796 | ||||||||
\(792\) | −3.98407 | −0.141568 | ||||||||
\(793\) | −5.80349 | −0.206088 | ||||||||
\(794\) | −24.2450 | −0.860424 | ||||||||
\(795\) | 6.92032 | 0.245438 | ||||||||
\(796\) | 5.35710 | 0.189877 | ||||||||
\(797\) | −22.9225 | −0.811955 | −0.405978 | − | 0.913883i | \(-0.633069\pi\) | ||||
−0.405978 | + | 0.913883i | \(0.633069\pi\) | |||||||
\(798\) | −0.811418 | −0.0287239 | ||||||||
\(799\) | 1.71237 | 0.0605794 | ||||||||
\(800\) | 4.63906 | 0.164016 | ||||||||
\(801\) | −6.96178 | −0.245982 | ||||||||
\(802\) | 10.6619 | 0.376484 | ||||||||
\(803\) | 66.9533 | 2.36273 | ||||||||
\(804\) | 14.9062 | 0.525701 | ||||||||
\(805\) | 0.714708 | 0.0251901 | ||||||||
\(806\) | 16.8341 | 0.592957 | ||||||||
\(807\) | −24.7427 | −0.870986 | ||||||||
\(808\) | −5.35438 | −0.188366 | ||||||||
\(809\) | 32.7460 | 1.15129 | 0.575644 | − | 0.817701i | \(-0.304752\pi\) | ||||
0.575644 | + | 0.817701i | \(0.304752\pi\) | |||||||
\(810\) | −0.600780 | −0.0211093 | ||||||||
\(811\) | −25.3283 | −0.889399 | −0.444699 | − | 0.895680i | \(-0.646689\pi\) | ||||
−0.444699 | + | 0.895680i | \(0.646689\pi\) | |||||||
\(812\) | −9.44157 | −0.331334 | ||||||||
\(813\) | 21.0873 | 0.739562 | ||||||||
\(814\) | 20.2366 | 0.709293 | ||||||||
\(815\) | 13.7996 | 0.483379 | ||||||||
\(816\) | 0.291399 | 0.0102010 | ||||||||
\(817\) | −3.86565 | −0.135242 | ||||||||
\(818\) | 10.7685 | 0.376512 | ||||||||
\(819\) | −2.21056 | −0.0772434 | ||||||||
\(820\) | 1.68303 | 0.0587741 | ||||||||
\(821\) | 6.88758 | 0.240378 | 0.120189 | − | 0.992751i | \(-0.461650\pi\) | ||||
0.120189 | + | 0.992751i | \(0.461650\pi\) | |||||||
\(822\) | 6.36691 | 0.222071 | ||||||||
\(823\) | −36.0166 | −1.25546 | −0.627730 | − | 0.778431i | \(-0.716016\pi\) | ||||
−0.627730 | + | 0.778431i | \(0.716016\pi\) | |||||||
\(824\) | 9.04862 | 0.315224 | ||||||||
\(825\) | −18.4823 | −0.643472 | ||||||||
\(826\) | 5.71021 | 0.198684 | ||||||||
\(827\) | 28.3474 | 0.985735 | 0.492868 | − | 0.870104i | \(-0.335949\pi\) | ||||
0.492868 | + | 0.870104i | \(0.335949\pi\) | |||||||
\(828\) | 1.18963 | 0.0413426 | ||||||||
\(829\) | −27.8916 | −0.968716 | −0.484358 | − | 0.874870i | \(-0.660947\pi\) | ||||
−0.484358 | + | 0.874870i | \(0.660947\pi\) | |||||||
\(830\) | 3.18779 | 0.110650 | ||||||||
\(831\) | 12.6960 | 0.440421 | ||||||||
\(832\) | −2.21056 | −0.0766375 | ||||||||
\(833\) | 0.291399 | 0.0100964 | ||||||||
\(834\) | 12.0899 | 0.418638 | ||||||||
\(835\) | 1.71600 | 0.0593845 | ||||||||
\(836\) | 3.23274 | 0.111807 | ||||||||
\(837\) | 7.61531 | 0.263224 | ||||||||
\(838\) | −6.01704 | −0.207855 | ||||||||
\(839\) | 29.4805 | 1.01778 | 0.508890 | − | 0.860831i | \(-0.330056\pi\) | ||||
0.508890 | + | 0.860831i | \(0.330056\pi\) | |||||||
\(840\) | −0.600780 | −0.0207289 | ||||||||
\(841\) | 60.1432 | 2.07390 | ||||||||
\(842\) | −27.8137 | −0.958523 | ||||||||
\(843\) | 6.29496 | 0.216810 | ||||||||
\(844\) | 10.4729 | 0.360491 | ||||||||
\(845\) | −4.87438 | −0.167684 | ||||||||
\(846\) | −5.87638 | −0.202034 | ||||||||
\(847\) | 4.87278 | 0.167431 | ||||||||
\(848\) | 11.5189 | 0.395560 | ||||||||
\(849\) | 28.4254 | 0.975556 | ||||||||
\(850\) | 1.35182 | 0.0463670 | ||||||||
\(851\) | −6.04260 | −0.207138 | ||||||||
\(852\) | 11.6398 | 0.398772 | ||||||||
\(853\) | −36.0783 | −1.23530 | −0.617649 | − | 0.786454i | \(-0.711915\pi\) | ||||
−0.617649 | + | 0.786454i | \(0.711915\pi\) | |||||||
\(854\) | −2.62535 | −0.0898375 | ||||||||
\(855\) | 0.487484 | 0.0166716 | ||||||||
\(856\) | −15.9118 | −0.543854 | ||||||||
\(857\) | −2.69038 | −0.0919017 | −0.0459509 | − | 0.998944i | \(-0.514632\pi\) | ||||
−0.0459509 | + | 0.998944i | \(0.514632\pi\) | |||||||
\(858\) | 8.80703 | 0.300667 | ||||||||
\(859\) | 25.2024 | 0.859894 | 0.429947 | − | 0.902854i | \(-0.358532\pi\) | ||||
0.429947 | + | 0.902854i | \(0.358532\pi\) | |||||||
\(860\) | −2.86215 | −0.0975987 | ||||||||
\(861\) | 2.80141 | 0.0954719 | ||||||||
\(862\) | 28.1741 | 0.959615 | ||||||||
\(863\) | 6.36768 | 0.216758 | 0.108379 | − | 0.994110i | \(-0.465434\pi\) | ||||
0.108379 | + | 0.994110i | \(0.465434\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −13.9282 | −0.473571 | ||||||||
\(866\) | −19.5526 | −0.664426 | ||||||||
\(867\) | −16.9151 | −0.574466 | ||||||||
\(868\) | 7.61531 | 0.258480 | ||||||||
\(869\) | 6.37523 | 0.216265 | ||||||||
\(870\) | 5.67231 | 0.192309 | ||||||||
\(871\) | −32.9511 | −1.11650 | ||||||||
\(872\) | −1.54381 | −0.0522798 | ||||||||
\(873\) | 4.49961 | 0.152289 | ||||||||
\(874\) | −0.965289 | −0.0326514 | ||||||||
\(875\) | −5.79096 | −0.195770 | ||||||||
\(876\) | 16.8053 | 0.567798 | ||||||||
\(877\) | −40.1524 | −1.35585 | −0.677924 | − | 0.735132i | \(-0.737120\pi\) | ||||
−0.677924 | + | 0.735132i | \(0.737120\pi\) | |||||||
\(878\) | 7.01706 | 0.236814 | ||||||||
\(879\) | 28.6147 | 0.965150 | ||||||||
\(880\) | 2.39355 | 0.0806865 | ||||||||
\(881\) | 18.2610 | 0.615229 | 0.307614 | − | 0.951511i | \(-0.400469\pi\) | ||||
0.307614 | + | 0.951511i | \(0.400469\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −50.7678 | −1.70847 | −0.854236 | − | 0.519886i | \(-0.825975\pi\) | ||||
−0.854236 | + | 0.519886i | \(0.825975\pi\) | |||||||
\(884\) | −0.644156 | −0.0216653 | ||||||||
\(885\) | −3.43058 | −0.115318 | ||||||||
\(886\) | 33.9891 | 1.14189 | ||||||||
\(887\) | 1.55143 | 0.0520919 | 0.0260459 | − | 0.999661i | \(-0.491708\pi\) | ||||
0.0260459 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(888\) | 5.07939 | 0.170453 | ||||||||
\(889\) | 19.1969 | 0.643842 | ||||||||
\(890\) | 4.18250 | 0.140198 | ||||||||
\(891\) | 3.98407 | 0.133471 | ||||||||
\(892\) | −14.5234 | −0.486281 | ||||||||
\(893\) | 4.76821 | 0.159562 | ||||||||
\(894\) | −4.06155 | −0.135839 | ||||||||
\(895\) | 11.8945 | 0.397588 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −2.62976 | −0.0878051 | ||||||||
\(898\) | 19.7565 | 0.659284 | ||||||||
\(899\) | −71.9005 | −2.39802 | ||||||||
\(900\) | −4.63906 | −0.154635 | ||||||||
\(901\) | 3.35659 | 0.111824 | ||||||||
\(902\) | −11.1610 | −0.371621 | ||||||||
\(903\) | −4.76406 | −0.158538 | ||||||||
\(904\) | 17.9097 | 0.595668 | ||||||||
\(905\) | −4.53079 | −0.150609 | ||||||||
\(906\) | −18.5807 | −0.617304 | ||||||||
\(907\) | −5.33208 | −0.177049 | −0.0885243 | − | 0.996074i | \(-0.528215\pi\) | ||||
−0.0885243 | + | 0.996074i | \(0.528215\pi\) | |||||||
\(908\) | −6.06557 | −0.201293 | ||||||||
\(909\) | 5.35438 | 0.177593 | ||||||||
\(910\) | 1.32806 | 0.0440249 | ||||||||
\(911\) | 44.8143 | 1.48477 | 0.742383 | − | 0.669976i | \(-0.233696\pi\) | ||||
0.742383 | + | 0.669976i | \(0.233696\pi\) | |||||||
\(912\) | 0.811418 | 0.0268687 | ||||||||
\(913\) | −21.1397 | −0.699623 | ||||||||
\(914\) | −39.2825 | −1.29935 | ||||||||
\(915\) | 1.57726 | 0.0521425 | ||||||||
\(916\) | −9.54355 | −0.315328 | ||||||||
\(917\) | 16.1818 | 0.534371 | ||||||||
\(918\) | −0.291399 | −0.00961760 | ||||||||
\(919\) | 45.7974 | 1.51072 | 0.755358 | − | 0.655313i | \(-0.227463\pi\) | ||||
0.755358 | + | 0.655313i | \(0.227463\pi\) | |||||||
\(920\) | −0.714708 | −0.0235632 | ||||||||
\(921\) | 33.6273 | 1.10806 | ||||||||
\(922\) | 5.75616 | 0.189569 | ||||||||
\(923\) | −25.7305 | −0.846928 | ||||||||
\(924\) | 3.98407 | 0.131066 | ||||||||
\(925\) | 23.5636 | 0.774766 | ||||||||
\(926\) | 36.4705 | 1.19850 | ||||||||
\(927\) | −9.04862 | −0.297196 | ||||||||
\(928\) | 9.44157 | 0.309935 | ||||||||
\(929\) | −1.60488 | −0.0526543 | −0.0263272 | − | 0.999653i | \(-0.508381\pi\) | ||||
−0.0263272 | + | 0.999653i | \(0.508381\pi\) | |||||||
\(930\) | −4.57513 | −0.150024 | ||||||||
\(931\) | 0.811418 | 0.0265932 | ||||||||
\(932\) | −6.93594 | −0.227194 | ||||||||
\(933\) | −7.23048 | −0.236715 | ||||||||
\(934\) | 36.6938 | 1.20066 | ||||||||
\(935\) | 0.697477 | 0.0228100 | ||||||||
\(936\) | 2.21056 | 0.0722545 | ||||||||
\(937\) | −31.0306 | −1.01373 | −0.506863 | − | 0.862027i | \(-0.669195\pi\) | ||||
−0.506863 | + | 0.862027i | \(0.669195\pi\) | |||||||
\(938\) | −14.9062 | −0.486704 | ||||||||
\(939\) | −23.1287 | −0.754776 | ||||||||
\(940\) | 3.53042 | 0.115150 | ||||||||
\(941\) | 33.8741 | 1.10427 | 0.552133 | − | 0.833756i | \(-0.313814\pi\) | ||||
0.552133 | + | 0.833756i | \(0.313814\pi\) | |||||||
\(942\) | −4.70929 | −0.153437 | ||||||||
\(943\) | 3.33265 | 0.108526 | ||||||||
\(944\) | −5.71021 | −0.185851 | ||||||||
\(945\) | 0.600780 | 0.0195434 | ||||||||
\(946\) | 18.9803 | 0.617104 | ||||||||
\(947\) | −20.5142 | −0.666621 | −0.333310 | − | 0.942817i | \(-0.608166\pi\) | ||||
−0.333310 | + | 0.942817i | \(0.608166\pi\) | |||||||
\(948\) | 1.60018 | 0.0519715 | ||||||||
\(949\) | −37.1492 | −1.20591 | ||||||||
\(950\) | 3.76422 | 0.122127 | ||||||||
\(951\) | 7.17192 | 0.232566 | ||||||||
\(952\) | −0.291399 | −0.00944429 | ||||||||
\(953\) | 4.80130 | 0.155529 | 0.0777647 | − | 0.996972i | \(-0.475222\pi\) | ||||
0.0777647 | + | 0.996972i | \(0.475222\pi\) | |||||||
\(954\) | −11.5189 | −0.372937 | ||||||||
\(955\) | 0.600780 | 0.0194408 | ||||||||
\(956\) | −0.650366 | −0.0210343 | ||||||||
\(957\) | −37.6158 | −1.21595 | ||||||||
\(958\) | −30.8394 | −0.996377 | ||||||||
\(959\) | −6.36691 | −0.205598 | ||||||||
\(960\) | 0.600780 | 0.0193901 | ||||||||
\(961\) | 26.9930 | 0.870741 | ||||||||
\(962\) | −11.2283 | −0.362015 | ||||||||
\(963\) | 15.9118 | 0.512751 | ||||||||
\(964\) | 6.26146 | 0.201668 | ||||||||
\(965\) | −5.56296 | −0.179078 | ||||||||
\(966\) | −1.18963 | −0.0382758 | ||||||||
\(967\) | 31.4244 | 1.01054 | 0.505271 | − | 0.862961i | \(-0.331393\pi\) | ||||
0.505271 | + | 0.862961i | \(0.331393\pi\) | |||||||
\(968\) | −4.87278 | −0.156617 | ||||||||
\(969\) | 0.236446 | 0.00759575 | ||||||||
\(970\) | −2.70328 | −0.0867970 | ||||||||
\(971\) | −37.4560 | −1.20202 | −0.601010 | − | 0.799242i | \(-0.705235\pi\) | ||||
−0.601010 | + | 0.799242i | \(0.705235\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −12.0899 | −0.387584 | ||||||||
\(974\) | −10.3033 | −0.330138 | ||||||||
\(975\) | 10.2549 | 0.328421 | ||||||||
\(976\) | 2.62535 | 0.0840353 | ||||||||
\(977\) | −59.1854 | −1.89351 | −0.946755 | − | 0.321956i | \(-0.895660\pi\) | ||||
−0.946755 | + | 0.321956i | \(0.895660\pi\) | |||||||
\(978\) | −22.9695 | −0.734482 | ||||||||
\(979\) | −27.7362 | −0.886452 | ||||||||
\(980\) | 0.600780 | 0.0191912 | ||||||||
\(981\) | 1.54381 | 0.0492899 | ||||||||
\(982\) | 20.2337 | 0.645682 | ||||||||
\(983\) | −40.8301 | −1.30228 | −0.651138 | − | 0.758959i | \(-0.725708\pi\) | ||||
−0.651138 | + | 0.758959i | \(0.725708\pi\) | |||||||
\(984\) | −2.80141 | −0.0893057 | ||||||||
\(985\) | −6.04466 | −0.192599 | ||||||||
\(986\) | 2.75126 | 0.0876181 | ||||||||
\(987\) | 5.87638 | 0.187047 | ||||||||
\(988\) | −1.79369 | −0.0570649 | ||||||||
\(989\) | −5.66748 | −0.180215 | ||||||||
\(990\) | −2.39355 | −0.0760720 | ||||||||
\(991\) | −40.0915 | −1.27355 | −0.636774 | − | 0.771051i | \(-0.719731\pi\) | ||||
−0.636774 | + | 0.771051i | \(0.719731\pi\) | |||||||
\(992\) | −7.61531 | −0.241786 | ||||||||
\(993\) | 26.0184 | 0.825669 | ||||||||
\(994\) | −11.6398 | −0.369191 | ||||||||
\(995\) | 3.21844 | 0.102031 | ||||||||
\(996\) | −5.30607 | −0.168129 | ||||||||
\(997\) | −50.9674 | −1.61415 | −0.807077 | − | 0.590446i | \(-0.798952\pi\) | ||||
−0.807077 | + | 0.590446i | \(0.798952\pi\) | |||||||
\(998\) | −41.8077 | −1.32340 | ||||||||
\(999\) | −5.07939 | −0.160705 |
(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 | 8022.2.a.z.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8022.2.a.z.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |