Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + 1860 x^{8} - 5877 x^{7} - 2496 x^{6} + 6612 x^{5} + 1842 x^{4} - 3011 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.319955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.319955 | −0.226243 | −0.113121 | − | 0.993581i | \(-0.536085\pi\) | ||||
−0.113121 | + | 0.993581i | \(0.536085\pi\) | |||||||
\(3\) | 2.34279 | 1.35261 | 0.676305 | − | 0.736622i | \(-0.263580\pi\) | ||||
0.676305 | + | 0.736622i | \(0.263580\pi\) | |||||||
\(4\) | −1.89763 | −0.948814 | ||||||||
\(5\) | 1.26502 | 0.565736 | 0.282868 | − | 0.959159i | \(-0.408714\pi\) | ||||
0.282868 | + | 0.959159i | \(0.408714\pi\) | |||||||
\(6\) | −0.749588 | −0.306018 | ||||||||
\(7\) | 1.17463 | 0.443968 | 0.221984 | − | 0.975050i | \(-0.428747\pi\) | ||||
0.221984 | + | 0.975050i | \(0.428747\pi\) | |||||||
\(8\) | 1.24707 | 0.440905 | ||||||||
\(9\) | 2.48866 | 0.829553 | ||||||||
\(10\) | −0.404751 | −0.127994 | ||||||||
\(11\) | 1.82172 | 0.549269 | 0.274635 | − | 0.961549i | \(-0.411443\pi\) | ||||
0.274635 | + | 0.961549i | \(0.411443\pi\) | |||||||
\(12\) | −4.44574 | −1.28338 | ||||||||
\(13\) | −2.29601 | −0.636800 | −0.318400 | − | 0.947956i | \(-0.603145\pi\) | ||||
−0.318400 | + | 0.947956i | \(0.603145\pi\) | |||||||
\(14\) | −0.375829 | −0.100445 | ||||||||
\(15\) | 2.96368 | 0.765220 | ||||||||
\(16\) | 3.39625 | 0.849063 | ||||||||
\(17\) | 1.44346 | 0.350090 | 0.175045 | − | 0.984560i | \(-0.443993\pi\) | ||||
0.175045 | + | 0.984560i | \(0.443993\pi\) | |||||||
\(18\) | −0.796260 | −0.187680 | ||||||||
\(19\) | 6.82924 | 1.56673 | 0.783367 | − | 0.621559i | \(-0.213500\pi\) | ||||
0.783367 | + | 0.621559i | \(0.213500\pi\) | |||||||
\(20\) | −2.40055 | −0.536778 | ||||||||
\(21\) | 2.75191 | 0.600515 | ||||||||
\(22\) | −0.582869 | −0.124268 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.92162 | 0.596372 | ||||||||
\(25\) | −3.39971 | −0.679943 | ||||||||
\(26\) | 0.734622 | 0.144071 | ||||||||
\(27\) | −1.19797 | −0.230549 | ||||||||
\(28\) | −2.22901 | −0.421243 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.948247 | −0.173125 | ||||||||
\(31\) | −0.0171270 | −0.00307610 | −0.00153805 | − | 0.999999i | \(-0.500490\pi\) | ||||
−0.00153805 | + | 0.999999i | \(0.500490\pi\) | |||||||
\(32\) | −3.58078 | −0.632999 | ||||||||
\(33\) | 4.26790 | 0.742947 | ||||||||
\(34\) | −0.461842 | −0.0792053 | ||||||||
\(35\) | 1.48593 | 0.251169 | ||||||||
\(36\) | −4.72255 | −0.787092 | ||||||||
\(37\) | 11.3129 | 1.85982 | 0.929911 | − | 0.367785i | \(-0.119884\pi\) | ||||
0.929911 | + | 0.367785i | \(0.119884\pi\) | |||||||
\(38\) | −2.18505 | −0.354462 | ||||||||
\(39\) | −5.37908 | −0.861341 | ||||||||
\(40\) | 1.57757 | 0.249436 | ||||||||
\(41\) | −1.72398 | −0.269240 | −0.134620 | − | 0.990897i | \(-0.542981\pi\) | ||||
−0.134620 | + | 0.990897i | \(0.542981\pi\) | |||||||
\(42\) | −0.880488 | −0.135862 | ||||||||
\(43\) | 6.23644 | 0.951049 | 0.475524 | − | 0.879703i | \(-0.342258\pi\) | ||||
0.475524 | + | 0.879703i | \(0.342258\pi\) | |||||||
\(44\) | −3.45695 | −0.521154 | ||||||||
\(45\) | 3.14821 | 0.469308 | ||||||||
\(46\) | −0.319955 | −0.0471749 | ||||||||
\(47\) | 8.65063 | 1.26182 | 0.630912 | − | 0.775854i | \(-0.282681\pi\) | ||||
0.630912 | + | 0.775854i | \(0.282681\pi\) | |||||||
\(48\) | 7.95670 | 1.14845 | ||||||||
\(49\) | −5.62025 | −0.802892 | ||||||||
\(50\) | 1.08776 | 0.153832 | ||||||||
\(51\) | 3.38172 | 0.473535 | ||||||||
\(52\) | 4.35698 | 0.604205 | ||||||||
\(53\) | −10.1287 | −1.39129 | −0.695643 | − | 0.718388i | \(-0.744880\pi\) | ||||
−0.695643 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(54\) | 0.383296 | 0.0521599 | ||||||||
\(55\) | 2.30452 | 0.310741 | ||||||||
\(56\) | 1.46484 | 0.195748 | ||||||||
\(57\) | 15.9995 | 2.11918 | ||||||||
\(58\) | 0.319955 | 0.0420122 | ||||||||
\(59\) | −9.22383 | −1.20084 | −0.600420 | − | 0.799684i | \(-0.705000\pi\) | ||||
−0.600420 | + | 0.799684i | \(0.705000\pi\) | |||||||
\(60\) | −5.62397 | −0.726052 | ||||||||
\(61\) | −6.92452 | −0.886594 | −0.443297 | − | 0.896375i | \(-0.646191\pi\) | ||||
−0.443297 | + | 0.896375i | \(0.646191\pi\) | |||||||
\(62\) | 0.00547988 | 0.000695946 0 | ||||||||
\(63\) | 2.92325 | 0.368295 | ||||||||
\(64\) | −5.64681 | −0.705851 | ||||||||
\(65\) | −2.90451 | −0.360261 | ||||||||
\(66\) | −1.36554 | −0.168086 | ||||||||
\(67\) | 1.95263 | 0.238551 | 0.119276 | − | 0.992861i | \(-0.461943\pi\) | ||||
0.119276 | + | 0.992861i | \(0.461943\pi\) | |||||||
\(68\) | −2.73915 | −0.332171 | ||||||||
\(69\) | 2.34279 | 0.282039 | ||||||||
\(70\) | −0.475433 | −0.0568251 | ||||||||
\(71\) | 14.6951 | 1.74399 | 0.871997 | − | 0.489512i | \(-0.162825\pi\) | ||||
0.871997 | + | 0.489512i | \(0.162825\pi\) | |||||||
\(72\) | 3.10352 | 0.365754 | ||||||||
\(73\) | −8.10458 | −0.948569 | −0.474285 | − | 0.880372i | \(-0.657293\pi\) | ||||
−0.474285 | + | 0.880372i | \(0.657293\pi\) | |||||||
\(74\) | −3.61961 | −0.420771 | ||||||||
\(75\) | −7.96481 | −0.919697 | ||||||||
\(76\) | −12.9594 | −1.48654 | ||||||||
\(77\) | 2.13984 | 0.243858 | ||||||||
\(78\) | 1.72106 | 0.194872 | ||||||||
\(79\) | −11.4108 | −1.28382 | −0.641909 | − | 0.766780i | \(-0.721858\pi\) | ||||
−0.641909 | + | 0.766780i | \(0.721858\pi\) | |||||||
\(80\) | 4.29634 | 0.480345 | ||||||||
\(81\) | −10.2726 | −1.14139 | ||||||||
\(82\) | 0.551596 | 0.0609136 | ||||||||
\(83\) | −5.50317 | −0.604052 | −0.302026 | − | 0.953300i | \(-0.597663\pi\) | ||||
−0.302026 | + | 0.953300i | \(0.597663\pi\) | |||||||
\(84\) | −5.22210 | −0.569778 | ||||||||
\(85\) | 1.82601 | 0.198059 | ||||||||
\(86\) | −1.99538 | −0.215168 | ||||||||
\(87\) | −2.34279 | −0.251173 | ||||||||
\(88\) | 2.27181 | 0.242175 | ||||||||
\(89\) | 10.2159 | 1.08288 | 0.541440 | − | 0.840739i | \(-0.317879\pi\) | ||||
0.541440 | + | 0.840739i | \(0.317879\pi\) | |||||||
\(90\) | −1.00729 | −0.106177 | ||||||||
\(91\) | −2.69697 | −0.282719 | ||||||||
\(92\) | −1.89763 | −0.197841 | ||||||||
\(93\) | −0.0401250 | −0.00416077 | ||||||||
\(94\) | −2.76782 | −0.285478 | ||||||||
\(95\) | 8.63915 | 0.886358 | ||||||||
\(96\) | −8.38902 | −0.856201 | ||||||||
\(97\) | 5.50080 | 0.558522 | 0.279261 | − | 0.960215i | \(-0.409911\pi\) | ||||
0.279261 | + | 0.960215i | \(0.409911\pi\) | |||||||
\(98\) | 1.79823 | 0.181648 | ||||||||
\(99\) | 4.53364 | 0.455648 | ||||||||
\(100\) | 6.45139 | 0.645139 | ||||||||
\(101\) | 11.6974 | 1.16393 | 0.581967 | − | 0.813212i | \(-0.302283\pi\) | ||||
0.581967 | + | 0.813212i | \(0.302283\pi\) | |||||||
\(102\) | −1.08200 | −0.107134 | ||||||||
\(103\) | −1.00443 | −0.0989694 | −0.0494847 | − | 0.998775i | \(-0.515758\pi\) | ||||
−0.0494847 | + | 0.998775i | \(0.515758\pi\) | |||||||
\(104\) | −2.86328 | −0.280768 | ||||||||
\(105\) | 3.48123 | 0.339733 | ||||||||
\(106\) | 3.24074 | 0.314768 | ||||||||
\(107\) | −18.3779 | −1.77666 | −0.888331 | − | 0.459203i | \(-0.848135\pi\) | ||||
−0.888331 | + | 0.459203i | \(0.848135\pi\) | |||||||
\(108\) | 2.27329 | 0.218748 | ||||||||
\(109\) | 4.25095 | 0.407167 | 0.203584 | − | 0.979058i | \(-0.434741\pi\) | ||||
0.203584 | + | 0.979058i | \(0.434741\pi\) | |||||||
\(110\) | −0.737343 | −0.0703029 | ||||||||
\(111\) | 26.5036 | 2.51561 | ||||||||
\(112\) | 3.98934 | 0.376957 | ||||||||
\(113\) | −14.6737 | −1.38038 | −0.690191 | − | 0.723627i | \(-0.742474\pi\) | ||||
−0.690191 | + | 0.723627i | \(0.742474\pi\) | |||||||
\(114\) | −5.11911 | −0.479449 | ||||||||
\(115\) | 1.26502 | 0.117964 | ||||||||
\(116\) | 1.89763 | 0.176190 | ||||||||
\(117\) | −5.71399 | −0.528259 | ||||||||
\(118\) | 2.95122 | 0.271681 | ||||||||
\(119\) | 1.69553 | 0.155429 | ||||||||
\(120\) | 3.69591 | 0.337389 | ||||||||
\(121\) | −7.68134 | −0.698304 | ||||||||
\(122\) | 2.21554 | 0.200585 | ||||||||
\(123\) | −4.03891 | −0.364177 | ||||||||
\(124\) | 0.0325007 | 0.00291865 | ||||||||
\(125\) | −10.6258 | −0.950404 | ||||||||
\(126\) | −0.935310 | −0.0833240 | ||||||||
\(127\) | 7.03113 | 0.623912 | 0.311956 | − | 0.950097i | \(-0.399016\pi\) | ||||
0.311956 | + | 0.950097i | \(0.399016\pi\) | |||||||
\(128\) | 8.96830 | 0.792693 | ||||||||
\(129\) | 14.6107 | 1.28640 | ||||||||
\(130\) | 0.929315 | 0.0815063 | ||||||||
\(131\) | 6.42121 | 0.561023 | 0.280512 | − | 0.959851i | \(-0.409496\pi\) | ||||
0.280512 | + | 0.959851i | \(0.409496\pi\) | |||||||
\(132\) | −8.09889 | −0.704918 | ||||||||
\(133\) | 8.02182 | 0.695580 | ||||||||
\(134\) | −0.624753 | −0.0539704 | ||||||||
\(135\) | −1.51546 | −0.130430 | ||||||||
\(136\) | 1.80009 | 0.154356 | ||||||||
\(137\) | −9.61591 | −0.821542 | −0.410771 | − | 0.911738i | \(-0.634740\pi\) | ||||
−0.410771 | + | 0.911738i | \(0.634740\pi\) | |||||||
\(138\) | −0.749588 | −0.0638092 | ||||||||
\(139\) | −13.1215 | −1.11295 | −0.556476 | − | 0.830864i | \(-0.687847\pi\) | ||||
−0.556476 | + | 0.830864i | \(0.687847\pi\) | |||||||
\(140\) | −2.81975 | −0.238312 | ||||||||
\(141\) | 20.2666 | 1.70676 | ||||||||
\(142\) | −4.70179 | −0.394566 | ||||||||
\(143\) | −4.18269 | −0.349774 | ||||||||
\(144\) | 8.45211 | 0.704342 | ||||||||
\(145\) | −1.26502 | −0.105055 | ||||||||
\(146\) | 2.59310 | 0.214607 | ||||||||
\(147\) | −13.1670 | −1.08600 | ||||||||
\(148\) | −21.4676 | −1.76463 | ||||||||
\(149\) | 8.06760 | 0.660923 | 0.330462 | − | 0.943819i | \(-0.392796\pi\) | ||||
0.330462 | + | 0.943819i | \(0.392796\pi\) | |||||||
\(150\) | 2.54838 | 0.208075 | ||||||||
\(151\) | −19.8483 | −1.61523 | −0.807617 | − | 0.589708i | \(-0.799243\pi\) | ||||
−0.807617 | + | 0.589708i | \(0.799243\pi\) | |||||||
\(152\) | 8.51652 | 0.690781 | ||||||||
\(153\) | 3.59228 | 0.290418 | ||||||||
\(154\) | −0.684655 | −0.0551711 | ||||||||
\(155\) | −0.0216661 | −0.00174026 | ||||||||
\(156\) | 10.2075 | 0.817253 | ||||||||
\(157\) | −24.9057 | −1.98769 | −0.993844 | − | 0.110786i | \(-0.964663\pi\) | ||||
−0.993844 | + | 0.110786i | \(0.964663\pi\) | |||||||
\(158\) | 3.65096 | 0.290455 | ||||||||
\(159\) | −23.7294 | −1.88187 | ||||||||
\(160\) | −4.52978 | −0.358110 | ||||||||
\(161\) | 1.17463 | 0.0925737 | ||||||||
\(162\) | 3.28676 | 0.258232 | ||||||||
\(163\) | −13.6889 | −1.07220 | −0.536099 | − | 0.844155i | \(-0.680103\pi\) | ||||
−0.536099 | + | 0.844155i | \(0.680103\pi\) | |||||||
\(164\) | 3.27147 | 0.255459 | ||||||||
\(165\) | 5.39900 | 0.420312 | ||||||||
\(166\) | 1.76077 | 0.136662 | ||||||||
\(167\) | 7.67936 | 0.594246 | 0.297123 | − | 0.954839i | \(-0.403973\pi\) | ||||
0.297123 | + | 0.954839i | \(0.403973\pi\) | |||||||
\(168\) | 3.43181 | 0.264770 | ||||||||
\(169\) | −7.72832 | −0.594486 | ||||||||
\(170\) | −0.584242 | −0.0448093 | ||||||||
\(171\) | 16.9956 | 1.29969 | ||||||||
\(172\) | −11.8345 | −0.902369 | ||||||||
\(173\) | −12.1140 | −0.921012 | −0.460506 | − | 0.887657i | \(-0.652332\pi\) | ||||
−0.460506 | + | 0.887657i | \(0.652332\pi\) | |||||||
\(174\) | 0.749588 | 0.0568261 | ||||||||
\(175\) | −3.99340 | −0.301873 | ||||||||
\(176\) | 6.18702 | 0.466364 | ||||||||
\(177\) | −21.6095 | −1.62427 | ||||||||
\(178\) | −3.26862 | −0.244994 | ||||||||
\(179\) | −2.89201 | −0.216159 | −0.108079 | − | 0.994142i | \(-0.534470\pi\) | ||||
−0.108079 | + | 0.994142i | \(0.534470\pi\) | |||||||
\(180\) | −5.97414 | −0.445286 | ||||||||
\(181\) | 6.58438 | 0.489413 | 0.244707 | − | 0.969597i | \(-0.421308\pi\) | ||||
0.244707 | + | 0.969597i | \(0.421308\pi\) | |||||||
\(182\) | 0.862909 | 0.0639630 | ||||||||
\(183\) | −16.2227 | −1.19922 | ||||||||
\(184\) | 1.24707 | 0.0919350 | ||||||||
\(185\) | 14.3110 | 1.05217 | ||||||||
\(186\) | 0.0128382 | 0.000941343 0 | ||||||||
\(187\) | 2.62958 | 0.192294 | ||||||||
\(188\) | −16.4157 | −1.19724 | ||||||||
\(189\) | −1.40716 | −0.102356 | ||||||||
\(190\) | −2.76414 | −0.200532 | ||||||||
\(191\) | 3.98219 | 0.288141 | 0.144070 | − | 0.989567i | \(-0.453981\pi\) | ||||
0.144070 | + | 0.989567i | \(0.453981\pi\) | |||||||
\(192\) | −13.2293 | −0.954741 | ||||||||
\(193\) | 18.0090 | 1.29632 | 0.648160 | − | 0.761504i | \(-0.275539\pi\) | ||||
0.648160 | + | 0.761504i | \(0.275539\pi\) | |||||||
\(194\) | −1.76001 | −0.126361 | ||||||||
\(195\) | −6.80466 | −0.487292 | ||||||||
\(196\) | 10.6651 | 0.761796 | ||||||||
\(197\) | −0.368271 | −0.0262382 | −0.0131191 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131191 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(198\) | −1.45056 | −0.103087 | ||||||||
\(199\) | 13.2645 | 0.940296 | 0.470148 | − | 0.882588i | \(-0.344201\pi\) | ||||
0.470148 | + | 0.882588i | \(0.344201\pi\) | |||||||
\(200\) | −4.23967 | −0.299790 | ||||||||
\(201\) | 4.57459 | 0.322667 | ||||||||
\(202\) | −3.74264 | −0.263332 | ||||||||
\(203\) | −1.17463 | −0.0824428 | ||||||||
\(204\) | −6.41725 | −0.449297 | ||||||||
\(205\) | −2.18087 | −0.152319 | ||||||||
\(206\) | 0.321373 | 0.0223911 | ||||||||
\(207\) | 2.48866 | 0.172974 | ||||||||
\(208\) | −7.79784 | −0.540683 | ||||||||
\(209\) | 12.4410 | 0.860559 | ||||||||
\(210\) | −1.11384 | −0.0768621 | ||||||||
\(211\) | −1.81668 | −0.125066 | −0.0625328 | − | 0.998043i | \(-0.519918\pi\) | ||||
−0.0625328 | + | 0.998043i | \(0.519918\pi\) | |||||||
\(212\) | 19.2205 | 1.32007 | ||||||||
\(213\) | 34.4276 | 2.35894 | ||||||||
\(214\) | 5.88012 | 0.401957 | ||||||||
\(215\) | 7.88925 | 0.538043 | ||||||||
\(216\) | −1.49394 | −0.101650 | ||||||||
\(217\) | −0.0201179 | −0.00136569 | ||||||||
\(218\) | −1.36011 | −0.0921186 | ||||||||
\(219\) | −18.9873 | −1.28304 | ||||||||
\(220\) | −4.37312 | −0.294836 | ||||||||
\(221\) | −3.31420 | −0.222937 | ||||||||
\(222\) | −8.47998 | −0.569139 | ||||||||
\(223\) | −26.9316 | −1.80348 | −0.901738 | − | 0.432282i | \(-0.857708\pi\) | ||||
−0.901738 | + | 0.432282i | \(0.857708\pi\) | |||||||
\(224\) | −4.20609 | −0.281031 | ||||||||
\(225\) | −8.46073 | −0.564048 | ||||||||
\(226\) | 4.69492 | 0.312301 | ||||||||
\(227\) | 27.2783 | 1.81053 | 0.905263 | − | 0.424851i | \(-0.139674\pi\) | ||||
0.905263 | + | 0.424851i | \(0.139674\pi\) | |||||||
\(228\) | −30.3610 | −2.01071 | ||||||||
\(229\) | −9.32732 | −0.616367 | −0.308183 | − | 0.951327i | \(-0.599721\pi\) | ||||
−0.308183 | + | 0.951327i | \(0.599721\pi\) | |||||||
\(230\) | −0.404751 | −0.0266885 | ||||||||
\(231\) | 5.01320 | 0.329845 | ||||||||
\(232\) | −1.24707 | −0.0818740 | ||||||||
\(233\) | 5.70467 | 0.373725 | 0.186863 | − | 0.982386i | \(-0.440168\pi\) | ||||
0.186863 | + | 0.982386i | \(0.440168\pi\) | |||||||
\(234\) | 1.82822 | 0.119515 | ||||||||
\(235\) | 10.9433 | 0.713859 | ||||||||
\(236\) | 17.5034 | 1.13938 | ||||||||
\(237\) | −26.7332 | −1.73651 | ||||||||
\(238\) | −0.542494 | −0.0351646 | ||||||||
\(239\) | −5.65400 | −0.365727 | −0.182863 | − | 0.983138i | \(-0.558537\pi\) | ||||
−0.182863 | + | 0.983138i | \(0.558537\pi\) | |||||||
\(240\) | 10.0654 | 0.649720 | ||||||||
\(241\) | −7.16163 | −0.461321 | −0.230661 | − | 0.973034i | \(-0.574089\pi\) | ||||
−0.230661 | + | 0.973034i | \(0.574089\pi\) | |||||||
\(242\) | 2.45769 | 0.157986 | ||||||||
\(243\) | −20.4725 | −1.31331 | ||||||||
\(244\) | 13.1402 | 0.841213 | ||||||||
\(245\) | −7.10975 | −0.454225 | ||||||||
\(246\) | 1.29227 | 0.0823923 | ||||||||
\(247\) | −15.6800 | −0.997696 | ||||||||
\(248\) | −0.0213586 | −0.00135627 | ||||||||
\(249\) | −12.8928 | −0.817046 | ||||||||
\(250\) | 3.39980 | 0.215022 | ||||||||
\(251\) | 2.75657 | 0.173993 | 0.0869966 | − | 0.996209i | \(-0.472273\pi\) | ||||
0.0869966 | + | 0.996209i | \(0.472273\pi\) | |||||||
\(252\) | −5.54724 | −0.349444 | ||||||||
\(253\) | 1.82172 | 0.114531 | ||||||||
\(254\) | −2.24965 | −0.141155 | ||||||||
\(255\) | 4.27796 | 0.267896 | ||||||||
\(256\) | 8.42417 | 0.526510 | ||||||||
\(257\) | 5.17910 | 0.323064 | 0.161532 | − | 0.986868i | \(-0.448357\pi\) | ||||
0.161532 | + | 0.986868i | \(0.448357\pi\) | |||||||
\(258\) | −4.67476 | −0.291038 | ||||||||
\(259\) | 13.2884 | 0.825701 | ||||||||
\(260\) | 5.51169 | 0.341820 | ||||||||
\(261\) | −2.48866 | −0.154044 | ||||||||
\(262\) | −2.05450 | −0.126927 | ||||||||
\(263\) | 15.2747 | 0.941878 | 0.470939 | − | 0.882166i | \(-0.343915\pi\) | ||||
0.470939 | + | 0.882166i | \(0.343915\pi\) | |||||||
\(264\) | 5.32236 | 0.327569 | ||||||||
\(265\) | −12.8131 | −0.787100 | ||||||||
\(266\) | −2.56663 | −0.157370 | ||||||||
\(267\) | 23.9336 | 1.46471 | ||||||||
\(268\) | −3.70536 | −0.226341 | ||||||||
\(269\) | 9.13142 | 0.556753 | 0.278376 | − | 0.960472i | \(-0.410204\pi\) | ||||
0.278376 | + | 0.960472i | \(0.410204\pi\) | |||||||
\(270\) | 0.484878 | 0.0295087 | ||||||||
\(271\) | 15.3194 | 0.930589 | 0.465295 | − | 0.885156i | \(-0.345948\pi\) | ||||
0.465295 | + | 0.885156i | \(0.345948\pi\) | |||||||
\(272\) | 4.90235 | 0.297249 | ||||||||
\(273\) | −6.31842 | −0.382408 | ||||||||
\(274\) | 3.07666 | 0.185868 | ||||||||
\(275\) | −6.19332 | −0.373472 | ||||||||
\(276\) | −4.44574 | −0.267602 | ||||||||
\(277\) | −8.47793 | −0.509390 | −0.254695 | − | 0.967021i | \(-0.581975\pi\) | ||||
−0.254695 | + | 0.967021i | \(0.581975\pi\) | |||||||
\(278\) | 4.19829 | 0.251797 | ||||||||
\(279\) | −0.0426233 | −0.00255179 | ||||||||
\(280\) | 1.85306 | 0.110742 | ||||||||
\(281\) | −16.6184 | −0.991369 | −0.495685 | − | 0.868503i | \(-0.665083\pi\) | ||||
−0.495685 | + | 0.868503i | \(0.665083\pi\) | |||||||
\(282\) | −6.48441 | −0.386141 | ||||||||
\(283\) | −18.9824 | −1.12838 | −0.564192 | − | 0.825643i | \(-0.690812\pi\) | ||||
−0.564192 | + | 0.825643i | \(0.690812\pi\) | |||||||
\(284\) | −27.8859 | −1.65473 | ||||||||
\(285\) | 20.2397 | 1.19890 | ||||||||
\(286\) | 1.33828 | 0.0791339 | ||||||||
\(287\) | −2.02503 | −0.119534 | ||||||||
\(288\) | −8.91135 | −0.525106 | ||||||||
\(289\) | −14.9164 | −0.877437 | ||||||||
\(290\) | 0.404751 | 0.0237678 | ||||||||
\(291\) | 12.8872 | 0.755462 | ||||||||
\(292\) | 15.3795 | 0.900016 | ||||||||
\(293\) | 3.35531 | 0.196020 | 0.0980098 | − | 0.995185i | \(-0.468752\pi\) | ||||
0.0980098 | + | 0.995185i | \(0.468752\pi\) | |||||||
\(294\) | 4.21287 | 0.245699 | ||||||||
\(295\) | −11.6684 | −0.679359 | ||||||||
\(296\) | 14.1079 | 0.820004 | ||||||||
\(297\) | −2.18236 | −0.126633 | ||||||||
\(298\) | −2.58127 | −0.149529 | ||||||||
\(299\) | −2.29601 | −0.132782 | ||||||||
\(300\) | 15.1143 | 0.872622 | ||||||||
\(301\) | 7.32551 | 0.422235 | ||||||||
\(302\) | 6.35058 | 0.365435 | ||||||||
\(303\) | 27.4045 | 1.57435 | ||||||||
\(304\) | 23.1938 | 1.33026 | ||||||||
\(305\) | −8.75968 | −0.501578 | ||||||||
\(306\) | −1.14937 | −0.0657050 | ||||||||
\(307\) | 12.5939 | 0.718770 | 0.359385 | − | 0.933189i | \(-0.382986\pi\) | ||||
0.359385 | + | 0.933189i | \(0.382986\pi\) | |||||||
\(308\) | −4.06063 | −0.231376 | ||||||||
\(309\) | −2.35317 | −0.133867 | ||||||||
\(310\) | 0.00693219 | 0.000393722 0 | ||||||||
\(311\) | 14.8454 | 0.841806 | 0.420903 | − | 0.907106i | \(-0.361713\pi\) | ||||
0.420903 | + | 0.907106i | \(0.361713\pi\) | |||||||
\(312\) | −6.70807 | −0.379770 | ||||||||
\(313\) | 1.46525 | 0.0828209 | 0.0414105 | − | 0.999142i | \(-0.486815\pi\) | ||||
0.0414105 | + | 0.999142i | \(0.486815\pi\) | |||||||
\(314\) | 7.96870 | 0.449700 | ||||||||
\(315\) | 3.69798 | 0.208358 | ||||||||
\(316\) | 21.6535 | 1.21811 | ||||||||
\(317\) | 31.5934 | 1.77446 | 0.887230 | − | 0.461327i | \(-0.152627\pi\) | ||||
0.887230 | + | 0.461327i | \(0.152627\pi\) | |||||||
\(318\) | 7.59236 | 0.425758 | ||||||||
\(319\) | −1.82172 | −0.101997 | ||||||||
\(320\) | −7.14335 | −0.399326 | ||||||||
\(321\) | −43.0556 | −2.40313 | ||||||||
\(322\) | −0.375829 | −0.0209441 | ||||||||
\(323\) | 9.85772 | 0.548498 | ||||||||
\(324\) | 19.4935 | 1.08297 | ||||||||
\(325\) | 7.80579 | 0.432987 | ||||||||
\(326\) | 4.37984 | 0.242577 | ||||||||
\(327\) | 9.95908 | 0.550738 | ||||||||
\(328\) | −2.14992 | −0.118709 | ||||||||
\(329\) | 10.1613 | 0.560210 | ||||||||
\(330\) | −1.72744 | −0.0950924 | ||||||||
\(331\) | 14.8236 | 0.814781 | 0.407390 | − | 0.913254i | \(-0.366439\pi\) | ||||
0.407390 | + | 0.913254i | \(0.366439\pi\) | |||||||
\(332\) | 10.4430 | 0.573133 | ||||||||
\(333\) | 28.1538 | 1.54282 | ||||||||
\(334\) | −2.45705 | −0.134444 | ||||||||
\(335\) | 2.47012 | 0.134957 | ||||||||
\(336\) | 9.34617 | 0.509875 | ||||||||
\(337\) | 6.06225 | 0.330232 | 0.165116 | − | 0.986274i | \(-0.447200\pi\) | ||||
0.165116 | + | 0.986274i | \(0.447200\pi\) | |||||||
\(338\) | 2.47272 | 0.134498 | ||||||||
\(339\) | −34.3773 | −1.86712 | ||||||||
\(340\) | −3.46509 | −0.187921 | ||||||||
\(341\) | −0.0312006 | −0.00168961 | ||||||||
\(342\) | −5.43785 | −0.294045 | ||||||||
\(343\) | −14.8241 | −0.800427 | ||||||||
\(344\) | 7.77727 | 0.419322 | ||||||||
\(345\) | 2.96368 | 0.159559 | ||||||||
\(346\) | 3.87595 | 0.208372 | ||||||||
\(347\) | 16.8175 | 0.902811 | 0.451406 | − | 0.892319i | \(-0.350923\pi\) | ||||
0.451406 | + | 0.892319i | \(0.350923\pi\) | |||||||
\(348\) | 4.44574 | 0.238317 | ||||||||
\(349\) | −6.17253 | −0.330408 | −0.165204 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165204 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(350\) | 1.27771 | 0.0682965 | ||||||||
\(351\) | 2.75055 | 0.146813 | ||||||||
\(352\) | −6.52318 | −0.347687 | ||||||||
\(353\) | 24.5929 | 1.30895 | 0.654474 | − | 0.756085i | \(-0.272890\pi\) | ||||
0.654474 | + | 0.756085i | \(0.272890\pi\) | |||||||
\(354\) | 6.91407 | 0.367479 | ||||||||
\(355\) | 18.5897 | 0.986640 | ||||||||
\(356\) | −19.3859 | −1.02745 | ||||||||
\(357\) | 3.97227 | 0.210235 | ||||||||
\(358\) | 0.925313 | 0.0489043 | ||||||||
\(359\) | 8.25123 | 0.435483 | 0.217742 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217742 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(360\) | 3.92603 | 0.206920 | ||||||||
\(361\) | 27.6385 | 1.45466 | ||||||||
\(362\) | −2.10671 | −0.110726 | ||||||||
\(363\) | −17.9958 | −0.944532 | ||||||||
\(364\) | 5.11784 | 0.268248 | ||||||||
\(365\) | −10.2525 | −0.536640 | ||||||||
\(366\) | 5.19053 | 0.271314 | ||||||||
\(367\) | −3.55943 | −0.185801 | −0.0929004 | − | 0.995675i | \(-0.529614\pi\) | ||||
−0.0929004 | + | 0.995675i | \(0.529614\pi\) | |||||||
\(368\) | 3.39625 | 0.177042 | ||||||||
\(369\) | −4.29039 | −0.223349 | ||||||||
\(370\) | −4.57889 | −0.238045 | ||||||||
\(371\) | −11.8975 | −0.617686 | ||||||||
\(372\) | 0.0761423 | 0.00394780 | ||||||||
\(373\) | 25.2920 | 1.30957 | 0.654785 | − | 0.755815i | \(-0.272759\pi\) | ||||
0.654785 | + | 0.755815i | \(0.272759\pi\) | |||||||
\(374\) | −0.841347 | −0.0435050 | ||||||||
\(375\) | −24.8941 | −1.28553 | ||||||||
\(376\) | 10.7879 | 0.556344 | ||||||||
\(377\) | 2.29601 | 0.118251 | ||||||||
\(378\) | 0.450230 | 0.0231573 | ||||||||
\(379\) | 2.33559 | 0.119971 | 0.0599855 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599855 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(380\) | −16.3939 | −0.840989 | ||||||||
\(381\) | 16.4725 | 0.843909 | ||||||||
\(382\) | −1.27412 | −0.0651898 | ||||||||
\(383\) | 13.9569 | 0.713165 | 0.356582 | − | 0.934264i | \(-0.383942\pi\) | ||||
0.356582 | + | 0.934264i | \(0.383942\pi\) | |||||||
\(384\) | 21.0108 | 1.07220 | ||||||||
\(385\) | 2.70695 | 0.137959 | ||||||||
\(386\) | −5.76209 | −0.293283 | ||||||||
\(387\) | 15.5204 | 0.788945 | ||||||||
\(388\) | −10.4385 | −0.529934 | ||||||||
\(389\) | 7.42722 | 0.376575 | 0.188287 | − | 0.982114i | \(-0.439706\pi\) | ||||
0.188287 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(390\) | 2.17719 | 0.110246 | ||||||||
\(391\) | 1.44346 | 0.0729988 | ||||||||
\(392\) | −7.00883 | −0.353999 | ||||||||
\(393\) | 15.0435 | 0.758846 | ||||||||
\(394\) | 0.117830 | 0.00593620 | ||||||||
\(395\) | −14.4350 | −0.726303 | ||||||||
\(396\) | −8.60316 | −0.432325 | ||||||||
\(397\) | 15.4152 | 0.773667 | 0.386834 | − | 0.922150i | \(-0.373569\pi\) | ||||
0.386834 | + | 0.922150i | \(0.373569\pi\) | |||||||
\(398\) | −4.24405 | −0.212735 | ||||||||
\(399\) | 18.7934 | 0.940848 | ||||||||
\(400\) | −11.5463 | −0.577314 | ||||||||
\(401\) | 33.0274 | 1.64931 | 0.824655 | − | 0.565636i | \(-0.191369\pi\) | ||||
0.824655 | + | 0.565636i | \(0.191369\pi\) | |||||||
\(402\) | −1.46366 | −0.0730009 | ||||||||
\(403\) | 0.0393239 | 0.00195886 | ||||||||
\(404\) | −22.1973 | −1.10436 | ||||||||
\(405\) | −12.9950 | −0.645728 | ||||||||
\(406\) | 0.375829 | 0.0186521 | ||||||||
\(407\) | 20.6088 | 1.02154 | ||||||||
\(408\) | 4.21723 | 0.208784 | ||||||||
\(409\) | −4.65642 | −0.230245 | −0.115123 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115123 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(410\) | 0.697782 | 0.0344610 | ||||||||
\(411\) | −22.5280 | −1.11123 | ||||||||
\(412\) | 1.90604 | 0.0939036 | ||||||||
\(413\) | −10.8346 | −0.533135 | ||||||||
\(414\) | −0.796260 | −0.0391340 | ||||||||
\(415\) | −6.96165 | −0.341734 | ||||||||
\(416\) | 8.22153 | 0.403094 | ||||||||
\(417\) | −30.7409 | −1.50539 | ||||||||
\(418\) | −3.98055 | −0.194695 | ||||||||
\(419\) | −18.0795 | −0.883242 | −0.441621 | − | 0.897202i | \(-0.645596\pi\) | ||||
−0.441621 | + | 0.897202i | \(0.645596\pi\) | |||||||
\(420\) | −6.60608 | −0.322344 | ||||||||
\(421\) | 8.63962 | 0.421069 | 0.210535 | − | 0.977586i | \(-0.432480\pi\) | ||||
0.210535 | + | 0.977586i | \(0.432480\pi\) | |||||||
\(422\) | 0.581257 | 0.0282952 | ||||||||
\(423\) | 21.5285 | 1.04675 | ||||||||
\(424\) | −12.6312 | −0.613424 | ||||||||
\(425\) | −4.90735 | −0.238041 | ||||||||
\(426\) | −11.0153 | −0.533693 | ||||||||
\(427\) | −8.13374 | −0.393619 | ||||||||
\(428\) | 34.8745 | 1.68572 | ||||||||
\(429\) | −9.79917 | −0.473108 | ||||||||
\(430\) | −2.52421 | −0.121728 | ||||||||
\(431\) | 22.3508 | 1.07660 | 0.538299 | − | 0.842754i | \(-0.319067\pi\) | ||||
0.538299 | + | 0.842754i | \(0.319067\pi\) | |||||||
\(432\) | −4.06859 | −0.195750 | ||||||||
\(433\) | 13.1909 | 0.633914 | 0.316957 | − | 0.948440i | \(-0.397339\pi\) | ||||
0.316957 | + | 0.948440i | \(0.397339\pi\) | |||||||
\(434\) | 0.00643683 | 0.000308978 0 | ||||||||
\(435\) | −2.96368 | −0.142098 | ||||||||
\(436\) | −8.06672 | −0.386326 | ||||||||
\(437\) | 6.82924 | 0.326687 | ||||||||
\(438\) | 6.07509 | 0.290279 | ||||||||
\(439\) | −30.5025 | −1.45580 | −0.727902 | − | 0.685682i | \(-0.759504\pi\) | ||||
−0.727902 | + | 0.685682i | \(0.759504\pi\) | |||||||
\(440\) | 2.87389 | 0.137007 | ||||||||
\(441\) | −13.9869 | −0.666042 | ||||||||
\(442\) | 1.06040 | 0.0504379 | ||||||||
\(443\) | 18.1792 | 0.863719 | 0.431860 | − | 0.901941i | \(-0.357858\pi\) | ||||
0.431860 | + | 0.901941i | \(0.357858\pi\) | |||||||
\(444\) | −50.2940 | −2.38685 | ||||||||
\(445\) | 12.9233 | 0.612624 | ||||||||
\(446\) | 8.61693 | 0.408023 | ||||||||
\(447\) | 18.9007 | 0.893971 | ||||||||
\(448\) | −6.63291 | −0.313375 | ||||||||
\(449\) | 15.4772 | 0.730415 | 0.365207 | − | 0.930926i | \(-0.380998\pi\) | ||||
0.365207 | + | 0.930926i | \(0.380998\pi\) | |||||||
\(450\) | 2.70706 | 0.127612 | ||||||||
\(451\) | −3.14060 | −0.147885 | ||||||||
\(452\) | 27.8452 | 1.30973 | ||||||||
\(453\) | −46.5004 | −2.18478 | ||||||||
\(454\) | −8.72785 | −0.409618 | ||||||||
\(455\) | −3.41173 | −0.159944 | ||||||||
\(456\) | 19.9524 | 0.934357 | ||||||||
\(457\) | −13.8500 | −0.647876 | −0.323938 | − | 0.946078i | \(-0.605007\pi\) | ||||
−0.323938 | + | 0.946078i | \(0.605007\pi\) | |||||||
\(458\) | 2.98433 | 0.139448 | ||||||||
\(459\) | −1.72921 | −0.0807128 | ||||||||
\(460\) | −2.40055 | −0.111926 | ||||||||
\(461\) | 6.58340 | 0.306619 | 0.153310 | − | 0.988178i | \(-0.451007\pi\) | ||||
0.153310 | + | 0.988178i | \(0.451007\pi\) | |||||||
\(462\) | −1.60400 | −0.0746249 | ||||||||
\(463\) | 40.5550 | 1.88475 | 0.942374 | − | 0.334561i | \(-0.108588\pi\) | ||||
0.942374 | + | 0.334561i | \(0.108588\pi\) | |||||||
\(464\) | −3.39625 | −0.157667 | ||||||||
\(465\) | −0.0507591 | −0.00235390 | ||||||||
\(466\) | −1.82524 | −0.0845526 | ||||||||
\(467\) | 14.8827 | 0.688688 | 0.344344 | − | 0.938844i | \(-0.388101\pi\) | ||||
0.344344 | + | 0.938844i | \(0.388101\pi\) | |||||||
\(468\) | 10.8430 | 0.501220 | ||||||||
\(469\) | 2.29361 | 0.105909 | ||||||||
\(470\) | −3.50135 | −0.161505 | ||||||||
\(471\) | −58.3487 | −2.68857 | ||||||||
\(472\) | −11.5027 | −0.529457 | ||||||||
\(473\) | 11.3611 | 0.522382 | ||||||||
\(474\) | 8.55342 | 0.392872 | ||||||||
\(475\) | −23.2175 | −1.06529 | ||||||||
\(476\) | −3.21748 | −0.147473 | ||||||||
\(477\) | −25.2069 | −1.15414 | ||||||||
\(478\) | 1.80903 | 0.0827430 | ||||||||
\(479\) | −28.0463 | −1.28147 | −0.640733 | − | 0.767764i | \(-0.721369\pi\) | ||||
−0.640733 | + | 0.767764i | \(0.721369\pi\) | |||||||
\(480\) | −10.6123 | −0.484384 | ||||||||
\(481\) | −25.9745 | −1.18433 | ||||||||
\(482\) | 2.29140 | 0.104371 | ||||||||
\(483\) | 2.75191 | 0.125216 | ||||||||
\(484\) | 14.5763 | 0.662560 | ||||||||
\(485\) | 6.95865 | 0.315976 | ||||||||
\(486\) | 6.55030 | 0.297127 | ||||||||
\(487\) | −18.2380 | −0.826440 | −0.413220 | − | 0.910631i | \(-0.635596\pi\) | ||||
−0.413220 | + | 0.910631i | \(0.635596\pi\) | |||||||
\(488\) | −8.63534 | −0.390903 | ||||||||
\(489\) | −32.0702 | −1.45027 | ||||||||
\(490\) | 2.27480 | 0.102765 | ||||||||
\(491\) | −5.07847 | −0.229188 | −0.114594 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114594 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(492\) | 7.66436 | 0.345536 | ||||||||
\(493\) | −1.44346 | −0.0650101 | ||||||||
\(494\) | 5.01691 | 0.225721 | ||||||||
\(495\) | 5.73516 | 0.257776 | ||||||||
\(496\) | −0.0581677 | −0.00261181 | ||||||||
\(497\) | 17.2613 | 0.774277 | ||||||||
\(498\) | 4.12511 | 0.184851 | ||||||||
\(499\) | −14.0668 | −0.629717 | −0.314859 | − | 0.949139i | \(-0.601957\pi\) | ||||
−0.314859 | + | 0.949139i | \(0.601957\pi\) | |||||||
\(500\) | 20.1639 | 0.901757 | ||||||||
\(501\) | 17.9911 | 0.803783 | ||||||||
\(502\) | −0.881980 | −0.0393647 | ||||||||
\(503\) | −23.3184 | −1.03972 | −0.519859 | − | 0.854252i | \(-0.674016\pi\) | ||||
−0.519859 | + | 0.854252i | \(0.674016\pi\) | |||||||
\(504\) | 3.64549 | 0.162383 | ||||||||
\(505\) | 14.7975 | 0.658479 | ||||||||
\(506\) | −0.582869 | −0.0259117 | ||||||||
\(507\) | −18.1058 | −0.804108 | ||||||||
\(508\) | −13.3425 | −0.591977 | ||||||||
\(509\) | 2.42877 | 0.107654 | 0.0538268 | − | 0.998550i | \(-0.482858\pi\) | ||||
0.0538268 | + | 0.998550i | \(0.482858\pi\) | |||||||
\(510\) | −1.36876 | −0.0606095 | ||||||||
\(511\) | −9.51987 | −0.421134 | ||||||||
\(512\) | −20.6319 | −0.911812 | ||||||||
\(513\) | −8.18119 | −0.361208 | ||||||||
\(514\) | −1.65708 | −0.0730908 | ||||||||
\(515\) | −1.27063 | −0.0559906 | ||||||||
\(516\) | −27.7256 | −1.22055 | ||||||||
\(517\) | 15.7590 | 0.693081 | ||||||||
\(518\) | −4.25170 | −0.186809 | ||||||||
\(519\) | −28.3806 | −1.24577 | ||||||||
\(520\) | −3.62212 | −0.158841 | ||||||||
\(521\) | 17.0976 | 0.749058 | 0.374529 | − | 0.927215i | \(-0.377805\pi\) | ||||
0.374529 | + | 0.927215i | \(0.377805\pi\) | |||||||
\(522\) | 0.796260 | 0.0348513 | ||||||||
\(523\) | −33.4942 | −1.46460 | −0.732298 | − | 0.680984i | \(-0.761552\pi\) | ||||
−0.732298 | + | 0.680984i | \(0.761552\pi\) | |||||||
\(524\) | −12.1851 | −0.532307 | ||||||||
\(525\) | −9.35570 | −0.408316 | ||||||||
\(526\) | −4.88722 | −0.213093 | ||||||||
\(527\) | −0.0247222 | −0.00107691 | ||||||||
\(528\) | 14.4949 | 0.630808 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 4.09961 | 0.178076 | ||||||||
\(531\) | −22.9550 | −0.996161 | ||||||||
\(532\) | −15.2224 | −0.659976 | ||||||||
\(533\) | 3.95828 | 0.171452 | ||||||||
\(534\) | −7.65769 | −0.331381 | ||||||||
\(535\) | −23.2485 | −1.00512 | ||||||||
\(536\) | 2.43506 | 0.105178 | ||||||||
\(537\) | −6.77536 | −0.292378 | ||||||||
\(538\) | −2.92165 | −0.125961 | ||||||||
\(539\) | −10.2385 | −0.441004 | ||||||||
\(540\) | 2.87577 | 0.123753 | ||||||||
\(541\) | 30.4452 | 1.30894 | 0.654471 | − | 0.756087i | \(-0.272891\pi\) | ||||
0.654471 | + | 0.756087i | \(0.272891\pi\) | |||||||
\(542\) | −4.90154 | −0.210539 | ||||||||
\(543\) | 15.4258 | 0.661985 | ||||||||
\(544\) | −5.16871 | −0.221607 | ||||||||
\(545\) | 5.37755 | 0.230349 | ||||||||
\(546\) | 2.02161 | 0.0865170 | ||||||||
\(547\) | −37.8141 | −1.61681 | −0.808406 | − | 0.588625i | \(-0.799669\pi\) | ||||
−0.808406 | + | 0.588625i | \(0.799669\pi\) | |||||||
\(548\) | 18.2474 | 0.779491 | ||||||||
\(549\) | −17.2328 | −0.735476 | ||||||||
\(550\) | 1.98159 | 0.0844952 | ||||||||
\(551\) | −6.82924 | −0.290935 | ||||||||
\(552\) | 2.92162 | 0.124352 | ||||||||
\(553\) | −13.4035 | −0.569975 | ||||||||
\(554\) | 2.71256 | 0.115246 | ||||||||
\(555\) | 33.5277 | 1.42317 | ||||||||
\(556\) | 24.8997 | 1.05598 | ||||||||
\(557\) | −17.3216 | −0.733939 | −0.366970 | − | 0.930233i | \(-0.619605\pi\) | ||||
−0.366970 | + | 0.930233i | \(0.619605\pi\) | |||||||
\(558\) | 0.0136376 | 0.000577324 0 | ||||||||
\(559\) | −14.3190 | −0.605628 | ||||||||
\(560\) | 5.04661 | 0.213258 | ||||||||
\(561\) | 6.16054 | 0.260098 | ||||||||
\(562\) | 5.31714 | 0.224290 | ||||||||
\(563\) | −45.6216 | −1.92272 | −0.961362 | − | 0.275289i | \(-0.911227\pi\) | ||||
−0.961362 | + | 0.275289i | \(0.911227\pi\) | |||||||
\(564\) | −38.4585 | −1.61939 | ||||||||
\(565\) | −18.5625 | −0.780932 | ||||||||
\(566\) | 6.07351 | 0.255289 | ||||||||
\(567\) | −12.0664 | −0.506743 | ||||||||
\(568\) | 18.3258 | 0.768935 | ||||||||
\(569\) | 1.42662 | 0.0598069 | 0.0299035 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299035 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(570\) | −6.47580 | −0.271242 | ||||||||
\(571\) | −25.9511 | −1.08602 | −0.543009 | − | 0.839727i | \(-0.682715\pi\) | ||||
−0.543009 | + | 0.839727i | \(0.682715\pi\) | |||||||
\(572\) | 7.93720 | 0.331871 | ||||||||
\(573\) | 9.32942 | 0.389742 | ||||||||
\(574\) | 0.647921 | 0.0270437 | ||||||||
\(575\) | −3.39971 | −0.141778 | ||||||||
\(576\) | −14.0530 | −0.585541 | ||||||||
\(577\) | 31.8837 | 1.32734 | 0.663669 | − | 0.748027i | \(-0.268998\pi\) | ||||
0.663669 | + | 0.748027i | \(0.268998\pi\) | |||||||
\(578\) | 4.77259 | 0.198514 | ||||||||
\(579\) | 42.1914 | 1.75341 | ||||||||
\(580\) | 2.40055 | 0.0996772 | ||||||||
\(581\) | −6.46419 | −0.268180 | ||||||||
\(582\) | −4.12334 | −0.170918 | ||||||||
\(583\) | −18.4517 | −0.764190 | ||||||||
\(584\) | −10.1070 | −0.418229 | ||||||||
\(585\) | −7.22834 | −0.298855 | ||||||||
\(586\) | −1.07355 | −0.0443480 | ||||||||
\(587\) | −23.2980 | −0.961611 | −0.480806 | − | 0.876827i | \(-0.659656\pi\) | ||||
−0.480806 | + | 0.876827i | \(0.659656\pi\) | |||||||
\(588\) | 24.9862 | 1.03041 | ||||||||
\(589\) | −0.116965 | −0.00481944 | ||||||||
\(590\) | 3.73336 | 0.153700 | ||||||||
\(591\) | −0.862781 | −0.0354901 | ||||||||
\(592\) | 38.4213 | 1.57911 | ||||||||
\(593\) | −9.93025 | −0.407787 | −0.203893 | − | 0.978993i | \(-0.565360\pi\) | ||||
−0.203893 | + | 0.978993i | \(0.565360\pi\) | |||||||
\(594\) | 0.698257 | 0.0286498 | ||||||||
\(595\) | 2.14488 | 0.0879317 | ||||||||
\(596\) | −15.3093 | −0.627093 | ||||||||
\(597\) | 31.0759 | 1.27185 | ||||||||
\(598\) | 0.734622 | 0.0300409 | ||||||||
\(599\) | 30.8661 | 1.26116 | 0.630578 | − | 0.776126i | \(-0.282818\pi\) | ||||
0.630578 | + | 0.776126i | \(0.282818\pi\) | |||||||
\(600\) | −9.93266 | −0.405499 | ||||||||
\(601\) | 12.4372 | 0.507322 | 0.253661 | − | 0.967293i | \(-0.418365\pi\) | ||||
0.253661 | + | 0.967293i | \(0.418365\pi\) | |||||||
\(602\) | −2.34384 | −0.0955276 | ||||||||
\(603\) | 4.85942 | 0.197891 | ||||||||
\(604\) | 37.6647 | 1.53256 | ||||||||
\(605\) | −9.71708 | −0.395055 | ||||||||
\(606\) | −8.76822 | −0.356185 | ||||||||
\(607\) | −26.6894 | −1.08329 | −0.541645 | − | 0.840607i | \(-0.682198\pi\) | ||||
−0.541645 | + | 0.840607i | \(0.682198\pi\) | |||||||
\(608\) | −24.4540 | −0.991742 | ||||||||
\(609\) | −2.75191 | −0.111513 | ||||||||
\(610\) | 2.80271 | 0.113478 | ||||||||
\(611\) | −19.8620 | −0.803529 | ||||||||
\(612\) | −6.81681 | −0.275553 | ||||||||
\(613\) | 3.68416 | 0.148802 | 0.0744010 | − | 0.997228i | \(-0.476296\pi\) | ||||
0.0744010 | + | 0.997228i | \(0.476296\pi\) | |||||||
\(614\) | −4.02948 | −0.162617 | ||||||||
\(615\) | −5.10932 | −0.206028 | ||||||||
\(616\) | 2.66853 | 0.107518 | ||||||||
\(617\) | 17.9696 | 0.723428 | 0.361714 | − | 0.932289i | \(-0.382192\pi\) | ||||
0.361714 | + | 0.932289i | \(0.382192\pi\) | |||||||
\(618\) | 0.752909 | 0.0302864 | ||||||||
\(619\) | 23.1024 | 0.928564 | 0.464282 | − | 0.885687i | \(-0.346312\pi\) | ||||
0.464282 | + | 0.885687i | \(0.346312\pi\) | |||||||
\(620\) | 0.0411142 | 0.00165119 | ||||||||
\(621\) | −1.19797 | −0.0480727 | ||||||||
\(622\) | −4.74987 | −0.190452 | ||||||||
\(623\) | 11.9999 | 0.480764 | ||||||||
\(624\) | −18.2687 | −0.731333 | ||||||||
\(625\) | 3.55662 | 0.142265 | ||||||||
\(626\) | −0.468815 | −0.0187376 | ||||||||
\(627\) | 29.1465 | 1.16400 | ||||||||
\(628\) | 47.2617 | 1.88595 | ||||||||
\(629\) | 16.3296 | 0.651105 | ||||||||
\(630\) | −1.18319 | −0.0471394 | ||||||||
\(631\) | 42.7618 | 1.70232 | 0.851160 | − | 0.524906i | \(-0.175900\pi\) | ||||
0.851160 | + | 0.524906i | \(0.175900\pi\) | |||||||
\(632\) | −14.2301 | −0.566042 | ||||||||
\(633\) | −4.25610 | −0.169165 | ||||||||
\(634\) | −10.1085 | −0.401459 | ||||||||
\(635\) | 8.89455 | 0.352969 | ||||||||
\(636\) | 45.0296 | 1.78554 | ||||||||
\(637\) | 12.9042 | 0.511282 | ||||||||
\(638\) | 0.582869 | 0.0230760 | ||||||||
\(639\) | 36.5712 | 1.44673 | ||||||||
\(640\) | 11.3451 | 0.448455 | ||||||||
\(641\) | −37.1432 | −1.46707 | −0.733535 | − | 0.679652i | \(-0.762131\pi\) | ||||
−0.733535 | + | 0.679652i | \(0.762131\pi\) | |||||||
\(642\) | 13.7759 | 0.543691 | ||||||||
\(643\) | 7.50458 | 0.295952 | 0.147976 | − | 0.988991i | \(-0.452724\pi\) | ||||
0.147976 | + | 0.988991i | \(0.452724\pi\) | |||||||
\(644\) | −2.22901 | −0.0878353 | ||||||||
\(645\) | 18.4829 | 0.727762 | ||||||||
\(646\) | −3.15403 | −0.124094 | ||||||||
\(647\) | 40.6186 | 1.59688 | 0.798440 | − | 0.602074i | \(-0.205659\pi\) | ||||
0.798440 | + | 0.602074i | \(0.205659\pi\) | |||||||
\(648\) | −12.8106 | −0.503247 | ||||||||
\(649\) | −16.8032 | −0.659585 | ||||||||
\(650\) | −2.49751 | −0.0979602 | ||||||||
\(651\) | −0.0471320 | −0.00184725 | ||||||||
\(652\) | 25.9765 | 1.01732 | ||||||||
\(653\) | −16.0997 | −0.630031 | −0.315016 | − | 0.949087i | \(-0.602010\pi\) | ||||
−0.315016 | + | 0.949087i | \(0.602010\pi\) | |||||||
\(654\) | −3.18646 | −0.124600 | ||||||||
\(655\) | 8.12298 | 0.317391 | ||||||||
\(656\) | −5.85506 | −0.228602 | ||||||||
\(657\) | −20.1695 | −0.786888 | ||||||||
\(658\) | −3.25116 | −0.126743 | ||||||||
\(659\) | −28.4479 | −1.10817 | −0.554087 | − | 0.832459i | \(-0.686933\pi\) | ||||
−0.554087 | + | 0.832459i | \(0.686933\pi\) | |||||||
\(660\) | −10.2453 | −0.398798 | ||||||||
\(661\) | 1.18518 | 0.0460982 | 0.0230491 | − | 0.999734i | \(-0.492663\pi\) | ||||
0.0230491 | + | 0.999734i | \(0.492663\pi\) | |||||||
\(662\) | −4.74290 | −0.184338 | ||||||||
\(663\) | −7.76447 | −0.301547 | ||||||||
\(664\) | −6.86283 | −0.266329 | ||||||||
\(665\) | 10.1478 | 0.393515 | ||||||||
\(666\) | −9.00797 | −0.349052 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −14.5726 | −0.563829 | ||||||||
\(669\) | −63.0952 | −2.43940 | ||||||||
\(670\) | −0.790328 | −0.0305330 | ||||||||
\(671\) | −12.6145 | −0.486978 | ||||||||
\(672\) | −9.85399 | −0.380126 | ||||||||
\(673\) | 29.9312 | 1.15376 | 0.576882 | − | 0.816828i | \(-0.304269\pi\) | ||||
0.576882 | + | 0.816828i | \(0.304269\pi\) | |||||||
\(674\) | −1.93965 | −0.0747126 | ||||||||
\(675\) | 4.07274 | 0.156760 | ||||||||
\(676\) | 14.6655 | 0.564057 | ||||||||
\(677\) | −10.1849 | −0.391438 | −0.195719 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195719 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(678\) | 10.9992 | 0.422422 | ||||||||
\(679\) | 6.46140 | 0.247966 | ||||||||
\(680\) | 2.27716 | 0.0873250 | ||||||||
\(681\) | 63.9074 | 2.44894 | ||||||||
\(682\) | 0.00998281 | 0.000382262 0 | ||||||||
\(683\) | −35.9185 | −1.37438 | −0.687192 | − | 0.726476i | \(-0.741157\pi\) | ||||
−0.687192 | + | 0.726476i | \(0.741157\pi\) | |||||||
\(684\) | −32.2514 | −1.23316 | ||||||||
\(685\) | −12.1644 | −0.464776 | ||||||||
\(686\) | 4.74305 | 0.181091 | ||||||||
\(687\) | −21.8519 | −0.833704 | ||||||||
\(688\) | 21.1805 | 0.807500 | ||||||||
\(689\) | 23.2557 | 0.885970 | ||||||||
\(690\) | −0.948247 | −0.0360991 | ||||||||
\(691\) | −7.29905 | −0.277669 | −0.138835 | − | 0.990316i | \(-0.544336\pi\) | ||||
−0.138835 | + | 0.990316i | \(0.544336\pi\) | |||||||
\(692\) | 22.9879 | 0.873869 | ||||||||
\(693\) | 5.32534 | 0.202293 | ||||||||
\(694\) | −5.38085 | −0.204254 | ||||||||
\(695\) | −16.5990 | −0.629636 | ||||||||
\(696\) | −2.92162 | −0.110744 | ||||||||
\(697\) | −2.48849 | −0.0942583 | ||||||||
\(698\) | 1.97493 | 0.0747523 | ||||||||
\(699\) | 13.3648 | 0.505504 | ||||||||
\(700\) | 7.57800 | 0.286421 | ||||||||
\(701\) | 4.13360 | 0.156124 | 0.0780620 | − | 0.996949i | \(-0.475127\pi\) | ||||
0.0780620 | + | 0.996949i | \(0.475127\pi\) | |||||||
\(702\) | −0.880052 | −0.0332154 | ||||||||
\(703\) | 77.2582 | 2.91385 | ||||||||
\(704\) | −10.2869 | −0.387702 | ||||||||
\(705\) | 25.6377 | 0.965573 | ||||||||
\(706\) | −7.86863 | −0.296140 | ||||||||
\(707\) | 13.7401 | 0.516750 | ||||||||
\(708\) | 41.0068 | 1.54113 | ||||||||
\(709\) | 0.363807 | 0.0136631 | 0.00683153 | − | 0.999977i | \(-0.497825\pi\) | ||||
0.00683153 | + | 0.999977i | \(0.497825\pi\) | |||||||
\(710\) | −5.94788 | −0.223220 | ||||||||
\(711\) | −28.3977 | −1.06500 | ||||||||
\(712\) | 12.7399 | 0.477447 | ||||||||
\(713\) | −0.0171270 | −0.000641412 0 | ||||||||
\(714\) | −1.27095 | −0.0475640 | ||||||||
\(715\) | −5.29121 | −0.197880 | ||||||||
\(716\) | 5.48795 | 0.205094 | ||||||||
\(717\) | −13.2461 | −0.494686 | ||||||||
\(718\) | −2.64003 | −0.0985249 | ||||||||
\(719\) | −21.2848 | −0.793789 | −0.396894 | − | 0.917864i | \(-0.629912\pi\) | ||||
−0.396894 | + | 0.917864i | \(0.629912\pi\) | |||||||
\(720\) | 10.6921 | 0.398472 | ||||||||
\(721\) | −1.17983 | −0.0439393 | ||||||||
\(722\) | −8.84308 | −0.329105 | ||||||||
\(723\) | −16.7782 | −0.623988 | ||||||||
\(724\) | −12.4947 | −0.464362 | ||||||||
\(725\) | 3.39971 | 0.126262 | ||||||||
\(726\) | 5.75784 | 0.213693 | ||||||||
\(727\) | −16.7296 | −0.620466 | −0.310233 | − | 0.950661i | \(-0.600407\pi\) | ||||
−0.310233 | + | 0.950661i | \(0.600407\pi\) | |||||||
\(728\) | −3.36330 | −0.124652 | ||||||||
\(729\) | −17.1451 | −0.635005 | ||||||||
\(730\) | 3.28034 | 0.121411 | ||||||||
\(731\) | 9.00205 | 0.332953 | ||||||||
\(732\) | 30.7846 | 1.13783 | ||||||||
\(733\) | −4.74919 | −0.175415 | −0.0877077 | − | 0.996146i | \(-0.527954\pi\) | ||||
−0.0877077 | + | 0.996146i | \(0.527954\pi\) | |||||||
\(734\) | 1.13886 | 0.0420361 | ||||||||
\(735\) | −16.6566 | −0.614389 | ||||||||
\(736\) | −3.58078 | −0.131989 | ||||||||
\(737\) | 3.55714 | 0.131029 | ||||||||
\(738\) | 1.37273 | 0.0505310 | ||||||||
\(739\) | −13.9169 | −0.511943 | −0.255972 | − | 0.966684i | \(-0.582395\pi\) | ||||
−0.255972 | + | 0.966684i | \(0.582395\pi\) | |||||||
\(740\) | −27.1570 | −0.998312 | ||||||||
\(741\) | −36.7350 | −1.34949 | ||||||||
\(742\) | 3.80666 | 0.139747 | ||||||||
\(743\) | 0.115038 | 0.00422033 | 0.00211016 | − | 0.999998i | \(-0.499328\pi\) | ||||
0.00211016 | + | 0.999998i | \(0.499328\pi\) | |||||||
\(744\) | −0.0500386 | −0.00183450 | ||||||||
\(745\) | 10.2057 | 0.373908 | ||||||||
\(746\) | −8.09231 | −0.296281 | ||||||||
\(747\) | −13.6955 | −0.501093 | ||||||||
\(748\) | −4.98996 | −0.182451 | ||||||||
\(749\) | −21.5873 | −0.788781 | ||||||||
\(750\) | 7.96500 | 0.290841 | ||||||||
\(751\) | −26.3015 | −0.959754 | −0.479877 | − | 0.877336i | \(-0.659319\pi\) | ||||
−0.479877 | + | 0.877336i | \(0.659319\pi\) | |||||||
\(752\) | 29.3797 | 1.07137 | ||||||||
\(753\) | 6.45806 | 0.235345 | ||||||||
\(754\) | −0.734622 | −0.0267534 | ||||||||
\(755\) | −25.1086 | −0.913795 | ||||||||
\(756\) | 2.67028 | 0.0971170 | ||||||||
\(757\) | −19.5102 | −0.709109 | −0.354554 | − | 0.935035i | \(-0.615367\pi\) | ||||
−0.354554 | + | 0.935035i | \(0.615367\pi\) | |||||||
\(758\) | −0.747284 | −0.0271426 | ||||||||
\(759\) | 4.26790 | 0.154915 | ||||||||
\(760\) | 10.7736 | 0.390800 | ||||||||
\(761\) | −25.8077 | −0.935529 | −0.467765 | − | 0.883853i | \(-0.654941\pi\) | ||||
−0.467765 | + | 0.883853i | \(0.654941\pi\) | |||||||
\(762\) | −5.27045 | −0.190928 | ||||||||
\(763\) | 4.99329 | 0.180769 | ||||||||
\(764\) | −7.55671 | −0.273392 | ||||||||
\(765\) | 4.54432 | 0.164300 | ||||||||
\(766\) | −4.46559 | −0.161348 | ||||||||
\(767\) | 21.1781 | 0.764695 | ||||||||
\(768\) | 19.7360 | 0.712163 | ||||||||
\(769\) | 6.83296 | 0.246403 | 0.123201 | − | 0.992382i | \(-0.460684\pi\) | ||||
0.123201 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(770\) | −0.866105 | −0.0312123 | ||||||||
\(771\) | 12.1335 | 0.436979 | ||||||||
\(772\) | −34.1745 | −1.22997 | ||||||||
\(773\) | 33.1309 | 1.19164 | 0.595819 | − | 0.803119i | \(-0.296828\pi\) | ||||
0.595819 | + | 0.803119i | \(0.296828\pi\) | |||||||
\(774\) | −4.96583 | −0.178493 | ||||||||
\(775\) | 0.0582270 | 0.00209157 | ||||||||
\(776\) | 6.85987 | 0.246255 | ||||||||
\(777\) | 31.1319 | 1.11685 | ||||||||
\(778\) | −2.37638 | −0.0851973 | ||||||||
\(779\) | −11.7734 | −0.421828 | ||||||||
\(780\) | 12.9127 | 0.462349 | ||||||||
\(781\) | 26.7704 | 0.957922 | ||||||||
\(782\) | −0.461842 | −0.0165155 | ||||||||
\(783\) | 1.19797 | 0.0428118 | ||||||||
\(784\) | −19.0878 | −0.681706 | ||||||||
\(785\) | −31.5063 | −1.12451 | ||||||||
\(786\) | −4.81326 | −0.171683 | ||||||||
\(787\) | −36.8898 | −1.31498 | −0.657490 | − | 0.753464i | \(-0.728382\pi\) | ||||
−0.657490 | + | 0.753464i | \(0.728382\pi\) | |||||||
\(788\) | 0.698841 | 0.0248952 | ||||||||
\(789\) | 35.7854 | 1.27399 | ||||||||
\(790\) | 4.61855 | 0.164321 | ||||||||
\(791\) | −17.2361 | −0.612846 | ||||||||
\(792\) | 5.65375 | 0.200897 | ||||||||
\(793\) | 15.8988 | 0.564583 | ||||||||
\(794\) | −4.93218 | −0.175037 | ||||||||
\(795\) | −30.0183 | −1.06464 | ||||||||
\(796\) | −25.1711 | −0.892166 | ||||||||
\(797\) | −9.88897 | −0.350285 | −0.175143 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175143 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(798\) | −6.01306 | −0.212860 | ||||||||
\(799\) | 12.4868 | 0.441752 | ||||||||
\(800\) | 12.1736 | 0.430403 | ||||||||
\(801\) | 25.4238 | 0.898306 | ||||||||
\(802\) | −10.5673 | −0.373144 | ||||||||
\(803\) | −14.7643 | −0.521020 | ||||||||
\(804\) | −8.68087 | −0.306151 | ||||||||
\(805\) | 1.48593 | 0.0523723 | ||||||||
\(806\) | −0.0125819 | −0.000443178 0 | ||||||||
\(807\) | 21.3930 | 0.753069 | ||||||||
\(808\) | 14.5874 | 0.513184 | ||||||||
\(809\) | −16.8507 | −0.592438 | −0.296219 | − | 0.955120i | \(-0.595726\pi\) | ||||
−0.296219 | + | 0.955120i | \(0.595726\pi\) | |||||||
\(810\) | 4.15783 | 0.146091 | ||||||||
\(811\) | −33.4678 | −1.17521 | −0.587607 | − | 0.809146i | \(-0.699930\pi\) | ||||
−0.587607 | + | 0.809146i | \(0.699930\pi\) | |||||||
\(812\) | 2.22901 | 0.0782229 | ||||||||
\(813\) | 35.8902 | 1.25872 | ||||||||
\(814\) | −6.59391 | −0.231116 | ||||||||
\(815\) | −17.3168 | −0.606581 | ||||||||
\(816\) | 11.4852 | 0.402061 | ||||||||
\(817\) | 42.5902 | 1.49004 | ||||||||
\(818\) | 1.48985 | 0.0520913 | ||||||||
\(819\) | −6.71182 | −0.234530 | ||||||||
\(820\) | 4.13849 | 0.144522 | ||||||||
\(821\) | 53.1757 | 1.85584 | 0.927922 | − | 0.372774i | \(-0.121593\pi\) | ||||
0.927922 | + | 0.372774i | \(0.121593\pi\) | |||||||
\(822\) | 7.20797 | 0.251407 | ||||||||
\(823\) | 5.95055 | 0.207423 | 0.103712 | − | 0.994607i | \(-0.466928\pi\) | ||||
0.103712 | + | 0.994607i | \(0.466928\pi\) | |||||||
\(824\) | −1.25259 | −0.0436361 | ||||||||
\(825\) | −14.5096 | −0.505161 | ||||||||
\(826\) | 3.46658 | 0.120618 | ||||||||
\(827\) | −20.3489 | −0.707602 | −0.353801 | − | 0.935321i | \(-0.615111\pi\) | ||||
−0.353801 | + | 0.935321i | \(0.615111\pi\) | |||||||
\(828\) | −4.72255 | −0.164120 | ||||||||
\(829\) | −38.1095 | −1.32360 | −0.661799 | − | 0.749682i | \(-0.730207\pi\) | ||||
−0.661799 | + | 0.749682i | \(0.730207\pi\) | |||||||
\(830\) | 2.22742 | 0.0773148 | ||||||||
\(831\) | −19.8620 | −0.689005 | ||||||||
\(832\) | 12.9652 | 0.449486 | ||||||||
\(833\) | −8.11259 | −0.281085 | ||||||||
\(834\) | 9.83572 | 0.340583 | ||||||||
\(835\) | 9.71457 | 0.336187 | ||||||||
\(836\) | −23.6083 | −0.816510 | ||||||||
\(837\) | 0.0205176 | 0.000709191 0 | ||||||||
\(838\) | 5.78464 | 0.199827 | ||||||||
\(839\) | −14.9607 | −0.516502 | −0.258251 | − | 0.966078i | \(-0.583146\pi\) | ||||
−0.258251 | + | 0.966078i | \(0.583146\pi\) | |||||||
\(840\) | 4.34133 | 0.149790 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −2.76429 | −0.0952638 | ||||||||
\(843\) | −38.9333 | −1.34094 | ||||||||
\(844\) | 3.44739 | 0.118664 | ||||||||
\(845\) | −9.77651 | −0.336322 | ||||||||
\(846\) | −6.88815 | −0.236819 | ||||||||
\(847\) | −9.02272 | −0.310024 | ||||||||
\(848\) | −34.3996 | −1.18129 | ||||||||
\(849\) | −44.4717 | −1.52626 | ||||||||
\(850\) | 1.57013 | 0.0538551 | ||||||||
\(851\) | 11.3129 | 0.387800 | ||||||||
\(852\) | −65.3308 | −2.23820 | ||||||||
\(853\) | −29.0903 | −0.996034 | −0.498017 | − | 0.867167i | \(-0.665938\pi\) | ||||
−0.498017 | + | 0.867167i | \(0.665938\pi\) | |||||||
\(854\) | 2.60243 | 0.0890535 | ||||||||
\(855\) | 21.4999 | 0.735281 | ||||||||
\(856\) | −22.9185 | −0.783339 | ||||||||
\(857\) | 33.7905 | 1.15426 | 0.577130 | − | 0.816652i | \(-0.304172\pi\) | ||||
0.577130 | + | 0.816652i | \(0.304172\pi\) | |||||||
\(858\) | 3.13530 | 0.107037 | ||||||||
\(859\) | 50.1146 | 1.70989 | 0.854944 | − | 0.518721i | \(-0.173592\pi\) | ||||
0.854944 | + | 0.518721i | \(0.173592\pi\) | |||||||
\(860\) | −14.9709 | −0.510502 | ||||||||
\(861\) | −4.74423 | −0.161683 | ||||||||
\(862\) | −7.15125 | −0.243572 | ||||||||
\(863\) | −13.8990 | −0.473128 | −0.236564 | − | 0.971616i | \(-0.576021\pi\) | ||||
−0.236564 | + | 0.971616i | \(0.576021\pi\) | |||||||
\(864\) | 4.28965 | 0.145937 | ||||||||
\(865\) | −15.3245 | −0.521049 | ||||||||
\(866\) | −4.22050 | −0.143418 | ||||||||
\(867\) | −34.9460 | −1.18683 | ||||||||
\(868\) | 0.0381763 | 0.00129579 | ||||||||
\(869\) | −20.7873 | −0.705162 | ||||||||
\(870\) | 0.948247 | 0.0321486 | ||||||||
\(871\) | −4.48326 | −0.151909 | ||||||||
\(872\) | 5.30122 | 0.179522 | ||||||||
\(873\) | 13.6896 | 0.463323 | ||||||||
\(874\) | −2.18505 | −0.0739105 | ||||||||
\(875\) | −12.4814 | −0.421949 | ||||||||
\(876\) | 36.0309 | 1.21737 | ||||||||
\(877\) | 57.5237 | 1.94244 | 0.971218 | − | 0.238190i | \(-0.0765543\pi\) | ||||
0.971218 | + | 0.238190i | \(0.0765543\pi\) | |||||||
\(878\) | 9.75943 | 0.329365 | ||||||||
\(879\) | 7.86079 | 0.265138 | ||||||||
\(880\) | 7.82672 | 0.263839 | ||||||||
\(881\) | −58.4376 | −1.96881 | −0.984406 | − | 0.175912i | \(-0.943712\pi\) | ||||
−0.984406 | + | 0.175912i | \(0.943712\pi\) | |||||||
\(882\) | 4.47518 | 0.150687 | ||||||||
\(883\) | −1.51349 | −0.0509330 | −0.0254665 | − | 0.999676i | \(-0.508107\pi\) | ||||
−0.0254665 | + | 0.999676i | \(0.508107\pi\) | |||||||
\(884\) | 6.28912 | 0.211526 | ||||||||
\(885\) | −27.3365 | −0.918907 | ||||||||
\(886\) | −5.81653 | −0.195410 | ||||||||
\(887\) | −29.0687 | −0.976032 | −0.488016 | − | 0.872835i | \(-0.662279\pi\) | ||||
−0.488016 | + | 0.872835i | \(0.662279\pi\) | |||||||
\(888\) | 33.0518 | 1.10915 | ||||||||
\(889\) | 8.25897 | 0.276997 | ||||||||
\(890\) | −4.13489 | −0.138602 | ||||||||
\(891\) | −18.7137 | −0.626933 | ||||||||
\(892\) | 51.1063 | 1.71116 | ||||||||
\(893\) | 59.0772 | 1.97694 | ||||||||
\(894\) | −6.04737 | −0.202254 | ||||||||
\(895\) | −3.65846 | −0.122289 | ||||||||
\(896\) | 10.5344 | 0.351930 | ||||||||
\(897\) | −5.37908 | −0.179602 | ||||||||
\(898\) | −4.95202 | −0.165251 | ||||||||
\(899\) | 0.0171270 | 0.000571218 0 | ||||||||
\(900\) | 16.0553 | 0.535177 | ||||||||
\(901\) | −14.6204 | −0.487075 | ||||||||
\(902\) | 1.00485 | 0.0334579 | ||||||||
\(903\) | 17.1621 | 0.571120 | ||||||||
\(904\) | −18.2990 | −0.608617 | ||||||||
\(905\) | 8.32941 | 0.276879 | ||||||||
\(906\) | 14.8781 | 0.494290 | ||||||||
\(907\) | 12.3587 | 0.410362 | 0.205181 | − | 0.978724i | \(-0.434222\pi\) | ||||
0.205181 | + | 0.978724i | \(0.434222\pi\) | |||||||
\(908\) | −51.7641 | −1.71785 | ||||||||
\(909\) | 29.1108 | 0.965545 | ||||||||
\(910\) | 1.09160 | 0.0361862 | ||||||||
\(911\) | −38.6517 | −1.28059 | −0.640294 | − | 0.768130i | \(-0.721188\pi\) | ||||
−0.640294 | + | 0.768130i | \(0.721188\pi\) | |||||||
\(912\) | 54.3382 | 1.79932 | ||||||||
\(913\) | −10.0252 | −0.331787 | ||||||||
\(914\) | 4.43138 | 0.146577 | ||||||||
\(915\) | −20.5221 | −0.678439 | ||||||||
\(916\) | 17.6998 | 0.584818 | ||||||||
\(917\) | 7.54254 | 0.249077 | ||||||||
\(918\) | 0.553271 | 0.0182607 | ||||||||
\(919\) | 33.6053 | 1.10854 | 0.554269 | − | 0.832338i | \(-0.312998\pi\) | ||||
0.554269 | + | 0.832338i | \(0.312998\pi\) | |||||||
\(920\) | 1.57757 | 0.0520110 | ||||||||
\(921\) | 29.5048 | 0.972216 | ||||||||
\(922\) | −2.10639 | −0.0693704 | ||||||||
\(923\) | −33.7403 | −1.11057 | ||||||||
\(924\) | −9.51320 | −0.312961 | ||||||||
\(925\) | −38.4605 | −1.26457 | ||||||||
\(926\) | −12.9758 | −0.426410 | ||||||||
\(927\) | −2.49968 | −0.0821004 | ||||||||
\(928\) | 3.58078 | 0.117545 | ||||||||
\(929\) | 26.8238 | 0.880061 | 0.440031 | − | 0.897983i | \(-0.354968\pi\) | ||||
0.440031 | + | 0.897983i | \(0.354968\pi\) | |||||||
\(930\) | 0.0162406 | 0.000532552 0 | ||||||||
\(931\) | −38.3820 | −1.25792 | ||||||||
\(932\) | −10.8253 | −0.354596 | ||||||||
\(933\) | 34.7797 | 1.13864 | ||||||||
\(934\) | −4.76179 | −0.155811 | ||||||||
\(935\) | 3.32648 | 0.108787 | ||||||||
\(936\) | −7.12574 | −0.232912 | ||||||||
\(937\) | 2.02573 | 0.0661778 | 0.0330889 | − | 0.999452i | \(-0.489466\pi\) | ||||
0.0330889 | + | 0.999452i | \(0.489466\pi\) | |||||||
\(938\) | −0.733853 | −0.0239612 | ||||||||
\(939\) | 3.43278 | 0.112024 | ||||||||
\(940\) | −20.7662 | −0.677320 | ||||||||
\(941\) | −45.9973 | −1.49947 | −0.749734 | − | 0.661739i | \(-0.769819\pi\) | ||||
−0.749734 | + | 0.661739i | \(0.769819\pi\) | |||||||
\(942\) | 18.6690 | 0.608268 | ||||||||
\(943\) | −1.72398 | −0.0561404 | ||||||||
\(944\) | −31.3265 | −1.01959 | ||||||||
\(945\) | −1.78010 | −0.0579066 | ||||||||
\(946\) | −3.63503 | −0.118185 | ||||||||
\(947\) | 28.2766 | 0.918866 | 0.459433 | − | 0.888212i | \(-0.348053\pi\) | ||||
0.459433 | + | 0.888212i | \(0.348053\pi\) | |||||||
\(948\) | 50.7296 | 1.64762 | ||||||||
\(949\) | 18.6082 | 0.604049 | ||||||||
\(950\) | 7.42855 | 0.241014 | ||||||||
\(951\) | 74.0166 | 2.40015 | ||||||||
\(952\) | 2.11444 | 0.0685293 | ||||||||
\(953\) | 22.0521 | 0.714338 | 0.357169 | − | 0.934040i | \(-0.383742\pi\) | ||||
0.357169 | + | 0.934040i | \(0.383742\pi\) | |||||||
\(954\) | 8.06508 | 0.261117 | ||||||||
\(955\) | 5.03756 | 0.163012 | ||||||||
\(956\) | 10.7292 | 0.347007 | ||||||||
\(957\) | −4.26790 | −0.137962 | ||||||||
\(958\) | 8.97355 | 0.289922 | ||||||||
\(959\) | −11.2951 | −0.364739 | ||||||||
\(960\) | −16.7354 | −0.540132 | ||||||||
\(961\) | −30.9997 | −0.999991 | ||||||||
\(962\) | 8.31067 | 0.267947 | ||||||||
\(963\) | −45.7364 | −1.47384 | ||||||||
\(964\) | 13.5901 | 0.437708 | ||||||||
\(965\) | 22.7819 | 0.733375 | ||||||||
\(966\) | −0.880488 | −0.0283292 | ||||||||
\(967\) | −50.2308 | −1.61531 | −0.807656 | − | 0.589654i | \(-0.799264\pi\) | ||||
−0.807656 | + | 0.589654i | \(0.799264\pi\) | |||||||
\(968\) | −9.57915 | −0.307885 | ||||||||
\(969\) | 23.0946 | 0.741904 | ||||||||
\(970\) | −2.22646 | −0.0714872 | ||||||||
\(971\) | 18.4011 | 0.590520 | 0.295260 | − | 0.955417i | \(-0.404594\pi\) | ||||
0.295260 | + | 0.955417i | \(0.404594\pi\) | |||||||
\(972\) | 38.8493 | 1.24609 | ||||||||
\(973\) | −15.4129 | −0.494115 | ||||||||
\(974\) | 5.83533 | 0.186976 | ||||||||
\(975\) | 18.2873 | 0.585663 | ||||||||
\(976\) | −23.5174 | −0.752774 | ||||||||
\(977\) | 20.0251 | 0.640660 | 0.320330 | − | 0.947306i | \(-0.396206\pi\) | ||||
0.320330 | + | 0.947306i | \(0.396206\pi\) | |||||||
\(978\) | 10.2610 | 0.328112 | ||||||||
\(979\) | 18.6104 | 0.594793 | ||||||||
\(980\) | 13.4917 | 0.430975 | ||||||||
\(981\) | 10.5792 | 0.337767 | ||||||||
\(982\) | 1.62489 | 0.0518522 | ||||||||
\(983\) | 58.8340 | 1.87651 | 0.938256 | − | 0.345942i | \(-0.112441\pi\) | ||||
0.938256 | + | 0.345942i | \(0.112441\pi\) | |||||||
\(984\) | −5.03680 | −0.160567 | ||||||||
\(985\) | −0.465872 | −0.0148439 | ||||||||
\(986\) | 0.461842 | 0.0147081 | ||||||||
\(987\) | 23.8057 | 0.757745 | ||||||||
\(988\) | 29.7549 | 0.946628 | ||||||||
\(989\) | 6.23644 | 0.198307 | ||||||||
\(990\) | −1.83500 | −0.0583200 | ||||||||
\(991\) | −1.41402 | −0.0449178 | −0.0224589 | − | 0.999748i | \(-0.507149\pi\) | ||||
−0.0224589 | + | 0.999748i | \(0.507149\pi\) | |||||||
\(992\) | 0.0613282 | 0.00194717 | ||||||||
\(993\) | 34.7286 | 1.10208 | ||||||||
\(994\) | −5.52286 | −0.175175 | ||||||||
\(995\) | 16.7799 | 0.531959 | ||||||||
\(996\) | 24.4657 | 0.775225 | ||||||||
\(997\) | 51.9389 | 1.64492 | 0.822460 | − | 0.568823i | \(-0.192601\pi\) | ||||
0.822460 | + | 0.568823i | \(0.192601\pi\) | |||||||
\(998\) | 4.50075 | 0.142469 | ||||||||
\(999\) | −13.5524 | −0.428779 |
(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 | 667.2.a.d.1.7 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.q.1.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.d.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.q.1.10 | 16 | 3.2 | odd | 2 |