Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [445,2,Mod(1,445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(445, 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("445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 445 = 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 445.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: | \(3.55334288995\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.35567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.162147 | 0.114655 | 0.0573277 | − | 0.998355i | \(-0.481742\pi\) | ||||
0.0573277 | + | 0.998355i | \(0.481742\pi\) | |||||||
\(3\) | 1.19353 | 0.689083 | 0.344542 | − | 0.938771i | \(-0.388034\pi\) | ||||
0.344542 | + | 0.938771i | \(0.388034\pi\) | |||||||
\(4\) | −1.97371 | −0.986854 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.193527 | 0.0790071 | ||||||||
\(7\) | −0.475281 | −0.179639 | −0.0898196 | − | 0.995958i | \(-0.528629\pi\) | ||||
−0.0898196 | + | 0.995958i | \(0.528629\pi\) | |||||||
\(8\) | −0.644326 | −0.227804 | ||||||||
\(9\) | −1.57549 | −0.525164 | ||||||||
\(10\) | −0.162147 | −0.0512754 | ||||||||
\(11\) | −5.19353 | −1.56591 | −0.782954 | − | 0.622080i | \(-0.786288\pi\) | ||||
−0.782954 | + | 0.622080i | \(0.786288\pi\) | |||||||
\(12\) | −2.35567 | −0.680025 | ||||||||
\(13\) | −1.30490 | −0.361914 | −0.180957 | − | 0.983491i | \(-0.557920\pi\) | ||||
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(14\) | −0.0770654 | −0.0205966 | ||||||||
\(15\) | −1.19353 | −0.308167 | ||||||||
\(16\) | 3.84294 | 0.960735 | ||||||||
\(17\) | −7.40330 | −1.79556 | −0.897782 | − | 0.440439i | \(-0.854823\pi\) | ||||
−0.897782 | + | 0.440439i | \(0.854823\pi\) | |||||||
\(18\) | −0.255462 | −0.0602129 | ||||||||
\(19\) | 6.83604 | 1.56830 | 0.784148 | − | 0.620574i | \(-0.213100\pi\) | ||||
0.784148 | + | 0.620574i | \(0.213100\pi\) | |||||||
\(20\) | 1.97371 | 0.441335 | ||||||||
\(21\) | −0.567260 | −0.123786 | ||||||||
\(22\) | −0.842116 | −0.179540 | ||||||||
\(23\) | 2.69195 | 0.561311 | 0.280656 | − | 0.959809i | \(-0.409448\pi\) | ||||
0.280656 | + | 0.959809i | \(0.409448\pi\) | |||||||
\(24\) | −0.769020 | −0.156976 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.211586 | −0.0414954 | ||||||||
\(27\) | −5.46097 | −1.05097 | ||||||||
\(28\) | 0.938065 | 0.177278 | ||||||||
\(29\) | −0.00689789 | −0.00128091 | −0.000640453 | − | 1.00000i | \(-0.500204\pi\) | ||||
−0.000640453 | 1.00000i | \(0.500204\pi\) | ||||||||
\(30\) | −0.193527 | −0.0353331 | ||||||||
\(31\) | −8.54230 | −1.53424 | −0.767121 | − | 0.641502i | \(-0.778312\pi\) | ||||
−0.767121 | + | 0.641502i | \(0.778312\pi\) | |||||||
\(32\) | 1.91177 | 0.337957 | ||||||||
\(33\) | −6.19862 | −1.07904 | ||||||||
\(34\) | −1.20042 | −0.205871 | ||||||||
\(35\) | 0.475281 | 0.0803371 | ||||||||
\(36\) | 3.10956 | 0.518261 | ||||||||
\(37\) | −4.56119 | −0.749855 | −0.374927 | − | 0.927054i | \(-0.622332\pi\) | ||||
−0.374927 | + | 0.927054i | \(0.622332\pi\) | |||||||
\(38\) | 1.10845 | 0.179814 | ||||||||
\(39\) | −1.55743 | −0.249389 | ||||||||
\(40\) | 0.644326 | 0.101877 | ||||||||
\(41\) | 3.41020 | 0.532584 | 0.266292 | − | 0.963892i | \(-0.414201\pi\) | ||||
0.266292 | + | 0.963892i | \(0.414201\pi\) | |||||||
\(42\) | −0.0919797 | −0.0141928 | ||||||||
\(43\) | 9.87858 | 1.50647 | 0.753235 | − | 0.657752i | \(-0.228492\pi\) | ||||
0.753235 | + | 0.657752i | \(0.228492\pi\) | |||||||
\(44\) | 10.2505 | 1.54532 | ||||||||
\(45\) | 1.57549 | 0.234861 | ||||||||
\(46\) | 0.436493 | 0.0643574 | ||||||||
\(47\) | −4.62493 | −0.674616 | −0.337308 | − | 0.941394i | \(-0.609516\pi\) | ||||
−0.337308 | + | 0.941394i | \(0.609516\pi\) | |||||||
\(48\) | 4.58665 | 0.662026 | ||||||||
\(49\) | −6.77411 | −0.967730 | ||||||||
\(50\) | 0.162147 | 0.0229311 | ||||||||
\(51\) | −8.83604 | −1.23729 | ||||||||
\(52\) | 2.57549 | 0.357157 | ||||||||
\(53\) | 2.86526 | 0.393574 | 0.196787 | − | 0.980446i | \(-0.436949\pi\) | ||||
0.196787 | + | 0.980446i | \(0.436949\pi\) | |||||||
\(54\) | −0.885482 | −0.120499 | ||||||||
\(55\) | 5.19353 | 0.700295 | ||||||||
\(56\) | 0.306236 | 0.0409224 | ||||||||
\(57\) | 8.15900 | 1.08069 | ||||||||
\(58\) | −0.00111847 | −0.000146863 0 | ||||||||
\(59\) | −1.13767 | −0.148111 | −0.0740557 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740557 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(60\) | 2.35567 | 0.304116 | ||||||||
\(61\) | 7.30684 | 0.935546 | 0.467773 | − | 0.883849i | \(-0.345057\pi\) | ||||
0.467773 | + | 0.883849i | \(0.345057\pi\) | |||||||
\(62\) | −1.38511 | −0.175909 | ||||||||
\(63\) | 0.748801 | 0.0943401 | ||||||||
\(64\) | −7.37589 | −0.921987 | ||||||||
\(65\) | 1.30490 | 0.161853 | ||||||||
\(66\) | −1.00509 | −0.123718 | ||||||||
\(67\) | −1.79531 | −0.219332 | −0.109666 | − | 0.993968i | \(-0.534978\pi\) | ||||
−0.109666 | + | 0.993968i | \(0.534978\pi\) | |||||||
\(68\) | 14.6120 | 1.77196 | ||||||||
\(69\) | 3.21292 | 0.386790 | ||||||||
\(70\) | 0.0770654 | 0.00921108 | ||||||||
\(71\) | 2.91492 | 0.345937 | 0.172969 | − | 0.984927i | \(-0.444664\pi\) | ||||
0.172969 | + | 0.984927i | \(0.444664\pi\) | |||||||
\(72\) | 1.01513 | 0.119634 | ||||||||
\(73\) | −2.26369 | −0.264945 | −0.132473 | − | 0.991187i | \(-0.542292\pi\) | ||||
−0.132473 | + | 0.991187i | \(0.542292\pi\) | |||||||
\(74\) | −0.739584 | −0.0859749 | ||||||||
\(75\) | 1.19353 | 0.137817 | ||||||||
\(76\) | −13.4924 | −1.54768 | ||||||||
\(77\) | 2.46838 | 0.281298 | ||||||||
\(78\) | −0.252534 | −0.0285938 | ||||||||
\(79\) | −10.5104 | −1.18251 | −0.591257 | − | 0.806483i | \(-0.701368\pi\) | ||||
−0.591257 | + | 0.806483i | \(0.701368\pi\) | |||||||
\(80\) | −3.84294 | −0.429654 | ||||||||
\(81\) | −1.79134 | −0.199038 | ||||||||
\(82\) | 0.552955 | 0.0610636 | ||||||||
\(83\) | 6.35650 | 0.697716 | 0.348858 | − | 0.937176i | \(-0.386569\pi\) | ||||
0.348858 | + | 0.937176i | \(0.386569\pi\) | |||||||
\(84\) | 1.11961 | 0.122159 | ||||||||
\(85\) | 7.40330 | 0.803001 | ||||||||
\(86\) | 1.60178 | 0.172725 | ||||||||
\(87\) | −0.00823281 | −0.000882650 0 | ||||||||
\(88\) | 3.34632 | 0.356719 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0.255462 | 0.0269280 | ||||||||
\(91\) | 0.620194 | 0.0650140 | ||||||||
\(92\) | −5.31313 | −0.553932 | ||||||||
\(93\) | −10.1955 | −1.05722 | ||||||||
\(94\) | −0.749920 | −0.0773483 | ||||||||
\(95\) | −6.83604 | −0.701363 | ||||||||
\(96\) | 2.28175 | 0.232880 | ||||||||
\(97\) | 18.3113 | 1.85923 | 0.929617 | − | 0.368528i | \(-0.120138\pi\) | ||||
0.929617 | + | 0.368528i | \(0.120138\pi\) | |||||||
\(98\) | −1.09840 | −0.110955 | ||||||||
\(99\) | 8.18237 | 0.822359 | ||||||||
\(100\) | −1.97371 | −0.197371 | ||||||||
\(101\) | −14.3545 | −1.42832 | −0.714162 | − | 0.699981i | \(-0.753192\pi\) | ||||
−0.714162 | + | 0.699981i | \(0.753192\pi\) | |||||||
\(102\) | −1.43274 | −0.141862 | ||||||||
\(103\) | 5.43964 | 0.535983 | 0.267992 | − | 0.963421i | \(-0.413640\pi\) | ||||
0.267992 | + | 0.963421i | \(0.413640\pi\) | |||||||
\(104\) | 0.840781 | 0.0824454 | ||||||||
\(105\) | 0.567260 | 0.0553589 | ||||||||
\(106\) | 0.464594 | 0.0451254 | ||||||||
\(107\) | −7.27486 | −0.703287 | −0.351643 | − | 0.936134i | \(-0.614377\pi\) | ||||
−0.351643 | + | 0.936134i | \(0.614377\pi\) | |||||||
\(108\) | 10.7784 | 1.03715 | ||||||||
\(109\) | 3.92293 | 0.375749 | 0.187874 | − | 0.982193i | \(-0.439840\pi\) | ||||
0.187874 | + | 0.982193i | \(0.439840\pi\) | |||||||
\(110\) | 0.842116 | 0.0802926 | ||||||||
\(111\) | −5.44390 | −0.516712 | ||||||||
\(112\) | −1.82648 | −0.172586 | ||||||||
\(113\) | −15.2119 | −1.43102 | −0.715509 | − | 0.698603i | \(-0.753805\pi\) | ||||
−0.715509 | + | 0.698603i | \(0.753805\pi\) | |||||||
\(114\) | 1.32296 | 0.123907 | ||||||||
\(115\) | −2.69195 | −0.251026 | ||||||||
\(116\) | 0.0136144 | 0.00126407 | ||||||||
\(117\) | 2.05586 | 0.190064 | ||||||||
\(118\) | −0.184469 | −0.0169818 | ||||||||
\(119\) | 3.51865 | 0.322554 | ||||||||
\(120\) | 0.769020 | 0.0702016 | ||||||||
\(121\) | 15.9727 | 1.45207 | ||||||||
\(122\) | 1.18478 | 0.107265 | ||||||||
\(123\) | 4.07017 | 0.366995 | ||||||||
\(124\) | 16.8600 | 1.51407 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.121416 | 0.0108166 | ||||||||
\(127\) | 14.3082 | 1.26965 | 0.634823 | − | 0.772658i | \(-0.281073\pi\) | ||||
0.634823 | + | 0.772658i | \(0.281073\pi\) | |||||||
\(128\) | −5.01953 | −0.443668 | ||||||||
\(129\) | 11.7904 | 1.03808 | ||||||||
\(130\) | 0.211586 | 0.0185573 | ||||||||
\(131\) | −5.16529 | −0.451294 | −0.225647 | − | 0.974209i | \(-0.572450\pi\) | ||||
−0.225647 | + | 0.974209i | \(0.572450\pi\) | |||||||
\(132\) | 12.2343 | 1.06486 | ||||||||
\(133\) | −3.24904 | −0.281727 | ||||||||
\(134\) | −0.291105 | −0.0251476 | ||||||||
\(135\) | 5.46097 | 0.470006 | ||||||||
\(136\) | 4.77014 | 0.409036 | ||||||||
\(137\) | −10.1033 | −0.863181 | −0.431590 | − | 0.902070i | \(-0.642047\pi\) | ||||
−0.431590 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(138\) | 0.520966 | 0.0443476 | ||||||||
\(139\) | −21.0062 | −1.78172 | −0.890862 | − | 0.454275i | \(-0.849898\pi\) | ||||
−0.890862 | + | 0.454275i | \(0.849898\pi\) | |||||||
\(140\) | −0.938065 | −0.0792810 | ||||||||
\(141\) | −5.51998 | −0.464866 | ||||||||
\(142\) | 0.472646 | 0.0396636 | ||||||||
\(143\) | 6.77704 | 0.566724 | ||||||||
\(144\) | −6.05453 | −0.504544 | ||||||||
\(145\) | 0.00689789 | 0.000572838 0 | ||||||||
\(146\) | −0.367052 | −0.0303774 | ||||||||
\(147\) | −8.08508 | −0.666846 | ||||||||
\(148\) | 9.00245 | 0.739997 | ||||||||
\(149\) | −4.55954 | −0.373532 | −0.186766 | − | 0.982404i | \(-0.559801\pi\) | ||||
−0.186766 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(150\) | 0.193527 | 0.0158014 | ||||||||
\(151\) | 3.64071 | 0.296276 | 0.148138 | − | 0.988967i | \(-0.452672\pi\) | ||||
0.148138 | + | 0.988967i | \(0.452672\pi\) | |||||||
\(152\) | −4.40464 | −0.357263 | ||||||||
\(153\) | 11.6639 | 0.942967 | ||||||||
\(154\) | 0.400241 | 0.0322524 | ||||||||
\(155\) | 8.54230 | 0.686134 | ||||||||
\(156\) | 3.07392 | 0.246111 | ||||||||
\(157\) | 17.3667 | 1.38601 | 0.693006 | − | 0.720932i | \(-0.256286\pi\) | ||||
0.693006 | + | 0.720932i | \(0.256286\pi\) | |||||||
\(158\) | −1.70423 | −0.135582 | ||||||||
\(159\) | 3.41977 | 0.271205 | ||||||||
\(160\) | −1.91177 | −0.151139 | ||||||||
\(161\) | −1.27943 | −0.100834 | ||||||||
\(162\) | −0.290461 | −0.0228208 | ||||||||
\(163\) | −9.06918 | −0.710353 | −0.355177 | − | 0.934799i | \(-0.615579\pi\) | ||||
−0.355177 | + | 0.934799i | \(0.615579\pi\) | |||||||
\(164\) | −6.73074 | −0.525583 | ||||||||
\(165\) | 6.19862 | 0.482562 | ||||||||
\(166\) | 1.03069 | 0.0799970 | ||||||||
\(167\) | 4.29059 | 0.332016 | 0.166008 | − | 0.986124i | \(-0.446912\pi\) | ||||
0.166008 | + | 0.986124i | \(0.446912\pi\) | |||||||
\(168\) | 0.365500 | 0.0281990 | ||||||||
\(169\) | −11.2972 | −0.869018 | ||||||||
\(170\) | 1.20042 | 0.0920684 | ||||||||
\(171\) | −10.7701 | −0.823613 | ||||||||
\(172\) | −19.4974 | −1.48667 | ||||||||
\(173\) | 21.1969 | 1.61157 | 0.805787 | − | 0.592206i | \(-0.201743\pi\) | ||||
0.805787 | + | 0.592206i | \(0.201743\pi\) | |||||||
\(174\) | −0.00133493 | −0.000101201 0 | ||||||||
\(175\) | −0.475281 | −0.0359278 | ||||||||
\(176\) | −19.9584 | −1.50442 | ||||||||
\(177\) | −1.35783 | −0.102061 | ||||||||
\(178\) | −0.162147 | −0.0121534 | ||||||||
\(179\) | 0.468991 | 0.0350541 | 0.0175270 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175270 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(180\) | −3.10956 | −0.231773 | ||||||||
\(181\) | −22.2732 | −1.65555 | −0.827776 | − | 0.561058i | \(-0.810394\pi\) | ||||
−0.827776 | + | 0.561058i | \(0.810394\pi\) | |||||||
\(182\) | 0.100563 | 0.00745420 | ||||||||
\(183\) | 8.72092 | 0.644669 | ||||||||
\(184\) | −1.73450 | −0.127869 | ||||||||
\(185\) | 4.56119 | 0.335345 | ||||||||
\(186\) | −1.65317 | −0.121216 | ||||||||
\(187\) | 38.4493 | 2.81169 | ||||||||
\(188\) | 9.12827 | 0.665747 | ||||||||
\(189\) | 2.59550 | 0.188795 | ||||||||
\(190\) | −1.10845 | −0.0804151 | ||||||||
\(191\) | −21.3072 | −1.54173 | −0.770867 | − | 0.636996i | \(-0.780177\pi\) | ||||
−0.770867 | + | 0.636996i | \(0.780177\pi\) | |||||||
\(192\) | −8.80333 | −0.635325 | ||||||||
\(193\) | −1.33822 | −0.0963275 | −0.0481637 | − | 0.998839i | \(-0.515337\pi\) | ||||
−0.0481637 | + | 0.998839i | \(0.515337\pi\) | |||||||
\(194\) | 2.96913 | 0.213171 | ||||||||
\(195\) | 1.55743 | 0.111530 | ||||||||
\(196\) | 13.3701 | 0.955008 | ||||||||
\(197\) | −9.65959 | −0.688217 | −0.344109 | − | 0.938930i | \(-0.611819\pi\) | ||||
−0.344109 | + | 0.938930i | \(0.611819\pi\) | |||||||
\(198\) | 1.32675 | 0.0942879 | ||||||||
\(199\) | 9.85738 | 0.698771 | 0.349386 | − | 0.936979i | \(-0.386390\pi\) | ||||
0.349386 | + | 0.936979i | \(0.386390\pi\) | |||||||
\(200\) | −0.644326 | −0.0455607 | ||||||||
\(201\) | −2.14275 | −0.151138 | ||||||||
\(202\) | −2.32754 | −0.163765 | ||||||||
\(203\) | 0.00327843 | 0.000230101 0 | ||||||||
\(204\) | 17.4398 | 1.22103 | ||||||||
\(205\) | −3.41020 | −0.238179 | ||||||||
\(206\) | 0.882022 | 0.0614534 | ||||||||
\(207\) | −4.24116 | −0.294781 | ||||||||
\(208\) | −5.01466 | −0.347704 | ||||||||
\(209\) | −35.5032 | −2.45581 | ||||||||
\(210\) | 0.0919797 | 0.00634720 | ||||||||
\(211\) | −12.2510 | −0.843396 | −0.421698 | − | 0.906736i | \(-0.638566\pi\) | ||||
−0.421698 | + | 0.906736i | \(0.638566\pi\) | |||||||
\(212\) | −5.65519 | −0.388400 | ||||||||
\(213\) | 3.47903 | 0.238379 | ||||||||
\(214\) | −1.17960 | −0.0806356 | ||||||||
\(215\) | −9.87858 | −0.673714 | ||||||||
\(216\) | 3.51865 | 0.239414 | ||||||||
\(217\) | 4.05999 | 0.275610 | ||||||||
\(218\) | 0.636093 | 0.0430816 | ||||||||
\(219\) | −2.70178 | −0.182569 | ||||||||
\(220\) | −10.2505 | −0.691089 | ||||||||
\(221\) | 9.66057 | 0.649841 | ||||||||
\(222\) | −0.882713 | −0.0592438 | ||||||||
\(223\) | −22.4242 | −1.50163 | −0.750817 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750817 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(224\) | −0.908629 | −0.0607103 | ||||||||
\(225\) | −1.57549 | −0.105033 | ||||||||
\(226\) | −2.46657 | −0.164074 | ||||||||
\(227\) | −23.1665 | −1.53762 | −0.768809 | − | 0.639479i | \(-0.779150\pi\) | ||||
−0.768809 | + | 0.639479i | \(0.779150\pi\) | |||||||
\(228\) | −16.1035 | −1.06648 | ||||||||
\(229\) | 4.15788 | 0.274761 | 0.137380 | − | 0.990518i | \(-0.456132\pi\) | ||||
0.137380 | + | 0.990518i | \(0.456132\pi\) | |||||||
\(230\) | −0.436493 | −0.0287815 | ||||||||
\(231\) | 2.94608 | 0.193838 | ||||||||
\(232\) | 0.00444449 | 0.000291795 0 | ||||||||
\(233\) | −11.7721 | −0.771215 | −0.385607 | − | 0.922663i | \(-0.626008\pi\) | ||||
−0.385607 | + | 0.922663i | \(0.626008\pi\) | |||||||
\(234\) | 0.333352 | 0.0217919 | ||||||||
\(235\) | 4.62493 | 0.301697 | ||||||||
\(236\) | 2.24542 | 0.146164 | ||||||||
\(237\) | −12.5445 | −0.814850 | ||||||||
\(238\) | 0.570539 | 0.0369825 | ||||||||
\(239\) | −20.3834 | −1.31849 | −0.659246 | − | 0.751927i | \(-0.729125\pi\) | ||||
−0.659246 | + | 0.751927i | \(0.729125\pi\) | |||||||
\(240\) | −4.58665 | −0.296067 | ||||||||
\(241\) | −11.3468 | −0.730908 | −0.365454 | − | 0.930829i | \(-0.619086\pi\) | ||||
−0.365454 | + | 0.930829i | \(0.619086\pi\) | |||||||
\(242\) | 2.58993 | 0.166487 | ||||||||
\(243\) | 14.2449 | 0.913811 | ||||||||
\(244\) | −14.4216 | −0.923247 | ||||||||
\(245\) | 6.77411 | 0.432782 | ||||||||
\(246\) | 0.659966 | 0.0420779 | ||||||||
\(247\) | −8.92036 | −0.567589 | ||||||||
\(248\) | 5.50403 | 0.349506 | ||||||||
\(249\) | 7.58665 | 0.480785 | ||||||||
\(250\) | −0.162147 | −0.0102551 | ||||||||
\(251\) | −16.0015 | −1.01000 | −0.505002 | − | 0.863118i | \(-0.668508\pi\) | ||||
−0.505002 | + | 0.863118i | \(0.668508\pi\) | |||||||
\(252\) | −1.47792 | −0.0930999 | ||||||||
\(253\) | −13.9807 | −0.878962 | ||||||||
\(254\) | 2.32003 | 0.145572 | ||||||||
\(255\) | 8.83604 | 0.553334 | ||||||||
\(256\) | 13.9379 | 0.871118 | ||||||||
\(257\) | 9.71532 | 0.606025 | 0.303012 | − | 0.952987i | \(-0.402008\pi\) | ||||
0.303012 | + | 0.952987i | \(0.402008\pi\) | |||||||
\(258\) | 1.91177 | 0.119022 | ||||||||
\(259\) | 2.16784 | 0.134703 | ||||||||
\(260\) | −2.57549 | −0.159725 | ||||||||
\(261\) | 0.0108676 | 0.000672686 0 | ||||||||
\(262\) | −0.837538 | −0.0517432 | ||||||||
\(263\) | 23.1738 | 1.42896 | 0.714479 | − | 0.699657i | \(-0.246664\pi\) | ||||
0.714479 | + | 0.699657i | \(0.246664\pi\) | |||||||
\(264\) | 3.99393 | 0.245809 | ||||||||
\(265\) | −2.86526 | −0.176012 | ||||||||
\(266\) | −0.526823 | −0.0323016 | ||||||||
\(267\) | −1.19353 | −0.0730427 | ||||||||
\(268\) | 3.54342 | 0.216449 | ||||||||
\(269\) | −4.92771 | −0.300448 | −0.150224 | − | 0.988652i | \(-0.547999\pi\) | ||||
−0.150224 | + | 0.988652i | \(0.547999\pi\) | |||||||
\(270\) | 0.885482 | 0.0538887 | ||||||||
\(271\) | 16.5952 | 1.00809 | 0.504044 | − | 0.863678i | \(-0.331845\pi\) | ||||
0.504044 | + | 0.863678i | \(0.331845\pi\) | |||||||
\(272\) | −28.4505 | −1.72506 | ||||||||
\(273\) | 0.740218 | 0.0448000 | ||||||||
\(274\) | −1.63822 | −0.0989684 | ||||||||
\(275\) | −5.19353 | −0.313181 | ||||||||
\(276\) | −6.34137 | −0.381706 | ||||||||
\(277\) | −12.9860 | −0.780256 | −0.390128 | − | 0.920761i | \(-0.627569\pi\) | ||||
−0.390128 | + | 0.920761i | \(0.627569\pi\) | |||||||
\(278\) | −3.40610 | −0.204284 | ||||||||
\(279\) | 13.4583 | 0.805730 | ||||||||
\(280\) | −0.306236 | −0.0183011 | ||||||||
\(281\) | 29.4497 | 1.75682 | 0.878412 | − | 0.477904i | \(-0.158603\pi\) | ||||
0.878412 | + | 0.477904i | \(0.158603\pi\) | |||||||
\(282\) | −0.895050 | −0.0532994 | ||||||||
\(283\) | −14.8999 | −0.885708 | −0.442854 | − | 0.896594i | \(-0.646034\pi\) | ||||
−0.442854 | + | 0.896594i | \(0.646034\pi\) | |||||||
\(284\) | −5.75320 | −0.341390 | ||||||||
\(285\) | −8.15900 | −0.483298 | ||||||||
\(286\) | 1.09888 | 0.0649780 | ||||||||
\(287\) | −1.62080 | −0.0956729 | ||||||||
\(288\) | −3.01199 | −0.177483 | ||||||||
\(289\) | 37.8089 | 2.22405 | ||||||||
\(290\) | 0.00111847 | 6.56790e−5 0 | ||||||||
\(291\) | 21.8551 | 1.28117 | ||||||||
\(292\) | 4.46787 | 0.261462 | ||||||||
\(293\) | −2.70575 | −0.158072 | −0.0790358 | − | 0.996872i | \(-0.525184\pi\) | ||||
−0.0790358 | + | 0.996872i | \(0.525184\pi\) | |||||||
\(294\) | −1.31097 | −0.0764575 | ||||||||
\(295\) | 1.13767 | 0.0662374 | ||||||||
\(296\) | 2.93889 | 0.170820 | ||||||||
\(297\) | 28.3617 | 1.64571 | ||||||||
\(298\) | −0.739316 | −0.0428274 | ||||||||
\(299\) | −3.51273 | −0.203147 | ||||||||
\(300\) | −2.35567 | −0.136005 | ||||||||
\(301\) | −4.69510 | −0.270621 | ||||||||
\(302\) | 0.590330 | 0.0339697 | ||||||||
\(303\) | −17.1325 | −0.984234 | ||||||||
\(304\) | 26.2705 | 1.50672 | ||||||||
\(305\) | −7.30684 | −0.418389 | ||||||||
\(306\) | 1.89126 | 0.108116 | ||||||||
\(307\) | −15.4273 | −0.880481 | −0.440241 | − | 0.897880i | \(-0.645107\pi\) | ||||
−0.440241 | + | 0.897880i | \(0.645107\pi\) | |||||||
\(308\) | −4.87187 | −0.277600 | ||||||||
\(309\) | 6.49235 | 0.369337 | ||||||||
\(310\) | 1.38511 | 0.0786690 | ||||||||
\(311\) | −9.28894 | −0.526728 | −0.263364 | − | 0.964697i | \(-0.584832\pi\) | ||||
−0.263364 | + | 0.964697i | \(0.584832\pi\) | |||||||
\(312\) | 1.00349 | 0.0568117 | ||||||||
\(313\) | −5.56675 | −0.314651 | −0.157326 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157326 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(314\) | 2.81596 | 0.158914 | ||||||||
\(315\) | −0.748801 | −0.0421902 | ||||||||
\(316\) | 20.7445 | 1.16697 | ||||||||
\(317\) | 30.9404 | 1.73778 | 0.868892 | − | 0.495002i | \(-0.164833\pi\) | ||||
0.868892 | + | 0.495002i | \(0.164833\pi\) | |||||||
\(318\) | 0.554506 | 0.0310952 | ||||||||
\(319\) | 0.0358244 | 0.00200578 | ||||||||
\(320\) | 7.37589 | 0.412325 | ||||||||
\(321\) | −8.68274 | −0.484623 | ||||||||
\(322\) | −0.207457 | −0.0115611 | ||||||||
\(323\) | −50.6093 | −2.81598 | ||||||||
\(324\) | 3.53559 | 0.196421 | ||||||||
\(325\) | −1.30490 | −0.0723829 | ||||||||
\(326\) | −1.47054 | −0.0814458 | ||||||||
\(327\) | 4.68213 | 0.258922 | ||||||||
\(328\) | −2.19728 | −0.121325 | ||||||||
\(329\) | 2.19814 | 0.121187 | ||||||||
\(330\) | 1.00509 | 0.0553283 | ||||||||
\(331\) | 0.0734460 | 0.00403696 | 0.00201848 | − | 0.999998i | \(-0.499357\pi\) | ||||
0.00201848 | + | 0.999998i | \(0.499357\pi\) | |||||||
\(332\) | −12.5459 | −0.688544 | ||||||||
\(333\) | 7.18612 | 0.393797 | ||||||||
\(334\) | 0.695708 | 0.0380674 | ||||||||
\(335\) | 1.79531 | 0.0980884 | ||||||||
\(336\) | −2.17995 | −0.118926 | ||||||||
\(337\) | 16.9619 | 0.923971 | 0.461986 | − | 0.886887i | \(-0.347137\pi\) | ||||
0.461986 | + | 0.886887i | \(0.347137\pi\) | |||||||
\(338\) | −1.83182 | −0.0996376 | ||||||||
\(339\) | −18.1559 | −0.986091 | ||||||||
\(340\) | −14.6120 | −0.792445 | ||||||||
\(341\) | 44.3647 | 2.40248 | ||||||||
\(342\) | −1.74635 | −0.0944317 | ||||||||
\(343\) | 6.54657 | 0.353481 | ||||||||
\(344\) | −6.36503 | −0.343179 | ||||||||
\(345\) | −3.21292 | −0.172978 | ||||||||
\(346\) | 3.43702 | 0.184776 | ||||||||
\(347\) | −21.2221 | −1.13926 | −0.569630 | − | 0.821901i | \(-0.692913\pi\) | ||||
−0.569630 | + | 0.821901i | \(0.692913\pi\) | |||||||
\(348\) | 0.0162492 | 0.000871047 0 | ||||||||
\(349\) | 7.48298 | 0.400555 | 0.200277 | − | 0.979739i | \(-0.435816\pi\) | ||||
0.200277 | + | 0.979739i | \(0.435816\pi\) | |||||||
\(350\) | −0.0770654 | −0.00411932 | ||||||||
\(351\) | 7.12603 | 0.380359 | ||||||||
\(352\) | −9.92885 | −0.529209 | ||||||||
\(353\) | 2.09475 | 0.111492 | 0.0557461 | − | 0.998445i | \(-0.482246\pi\) | ||||
0.0557461 | + | 0.998445i | \(0.482246\pi\) | |||||||
\(354\) | −0.220169 | −0.0117019 | ||||||||
\(355\) | −2.91492 | −0.154708 | ||||||||
\(356\) | 1.97371 | 0.104606 | ||||||||
\(357\) | 4.19960 | 0.222266 | ||||||||
\(358\) | 0.0760456 | 0.00401914 | ||||||||
\(359\) | −1.57842 | −0.0833059 | −0.0416529 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416529 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(360\) | −1.01513 | −0.0535021 | ||||||||
\(361\) | 27.7315 | 1.45955 | ||||||||
\(362\) | −3.61153 | −0.189818 | ||||||||
\(363\) | 19.0639 | 1.00059 | ||||||||
\(364\) | −1.22408 | −0.0641593 | ||||||||
\(365\) | 2.26369 | 0.118487 | ||||||||
\(366\) | 1.41407 | 0.0739147 | ||||||||
\(367\) | 34.6898 | 1.81079 | 0.905397 | − | 0.424567i | \(-0.139574\pi\) | ||||
0.905397 | + | 0.424567i | \(0.139574\pi\) | |||||||
\(368\) | 10.3450 | 0.539272 | ||||||||
\(369\) | −5.37275 | −0.279694 | ||||||||
\(370\) | 0.739584 | 0.0384491 | ||||||||
\(371\) | −1.36180 | −0.0707013 | ||||||||
\(372\) | 20.1229 | 1.04332 | ||||||||
\(373\) | 28.3861 | 1.46977 | 0.734887 | − | 0.678189i | \(-0.237235\pi\) | ||||
0.734887 | + | 0.678189i | \(0.237235\pi\) | |||||||
\(374\) | 6.23444 | 0.322375 | ||||||||
\(375\) | −1.19353 | −0.0616335 | ||||||||
\(376\) | 2.97996 | 0.153680 | ||||||||
\(377\) | 0.00900106 | 0.000463578 0 | ||||||||
\(378\) | 0.420852 | 0.0216463 | ||||||||
\(379\) | −15.3669 | −0.789344 | −0.394672 | − | 0.918822i | \(-0.629142\pi\) | ||||
−0.394672 | + | 0.918822i | \(0.629142\pi\) | |||||||
\(380\) | 13.4924 | 0.692143 | ||||||||
\(381\) | 17.0772 | 0.874891 | ||||||||
\(382\) | −3.45490 | −0.176768 | ||||||||
\(383\) | −23.8489 | −1.21862 | −0.609311 | − | 0.792932i | \(-0.708554\pi\) | ||||
−0.609311 | + | 0.792932i | \(0.708554\pi\) | |||||||
\(384\) | −5.99094 | −0.305724 | ||||||||
\(385\) | −2.46838 | −0.125800 | ||||||||
\(386\) | −0.216989 | −0.0110445 | ||||||||
\(387\) | −15.5636 | −0.791144 | ||||||||
\(388\) | −36.1412 | −1.83479 | ||||||||
\(389\) | 11.7669 | 0.596603 | 0.298302 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298302 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(390\) | 0.252534 | 0.0127875 | ||||||||
\(391\) | −19.9294 | −1.00787 | ||||||||
\(392\) | 4.36473 | 0.220452 | ||||||||
\(393\) | −6.16492 | −0.310979 | ||||||||
\(394\) | −1.56628 | −0.0789078 | ||||||||
\(395\) | 10.5104 | 0.528836 | ||||||||
\(396\) | −16.1496 | −0.811548 | ||||||||
\(397\) | −11.2778 | −0.566019 | −0.283009 | − | 0.959117i | \(-0.591333\pi\) | ||||
−0.283009 | + | 0.959117i | \(0.591333\pi\) | |||||||
\(398\) | 1.59835 | 0.0801179 | ||||||||
\(399\) | −3.87782 | −0.194134 | ||||||||
\(400\) | 3.84294 | 0.192147 | ||||||||
\(401\) | 12.9916 | 0.648770 | 0.324385 | − | 0.945925i | \(-0.394843\pi\) | ||||
0.324385 | + | 0.945925i | \(0.394843\pi\) | |||||||
\(402\) | −0.347441 | −0.0173288 | ||||||||
\(403\) | 11.1469 | 0.555264 | ||||||||
\(404\) | 28.3315 | 1.40955 | ||||||||
\(405\) | 1.79134 | 0.0890125 | ||||||||
\(406\) | 0.000531589 0 | 2.63823e−5 0 | ||||||||
\(407\) | 23.6887 | 1.17420 | ||||||||
\(408\) | 5.69329 | 0.281860 | ||||||||
\(409\) | −14.2198 | −0.703124 | −0.351562 | − | 0.936165i | \(-0.614349\pi\) | ||||
−0.351562 | + | 0.936165i | \(0.614349\pi\) | |||||||
\(410\) | −0.552955 | −0.0273085 | ||||||||
\(411\) | −12.0585 | −0.594804 | ||||||||
\(412\) | −10.7363 | −0.528937 | ||||||||
\(413\) | 0.540710 | 0.0266066 | ||||||||
\(414\) | −0.687692 | −0.0337982 | ||||||||
\(415\) | −6.35650 | −0.312028 | ||||||||
\(416\) | −2.49467 | −0.122311 | ||||||||
\(417\) | −25.0715 | −1.22776 | ||||||||
\(418\) | −5.75674 | −0.281571 | ||||||||
\(419\) | −32.8278 | −1.60374 | −0.801871 | − | 0.597497i | \(-0.796162\pi\) | ||||
−0.801871 | + | 0.597497i | \(0.796162\pi\) | |||||||
\(420\) | −1.11961 | −0.0546312 | ||||||||
\(421\) | 35.9329 | 1.75126 | 0.875630 | − | 0.482982i | \(-0.160447\pi\) | ||||
0.875630 | + | 0.482982i | \(0.160447\pi\) | |||||||
\(422\) | −1.98647 | −0.0966999 | ||||||||
\(423\) | 7.28655 | 0.354284 | ||||||||
\(424\) | −1.84616 | −0.0896576 | ||||||||
\(425\) | −7.40330 | −0.359113 | ||||||||
\(426\) | 0.564116 | 0.0273315 | ||||||||
\(427\) | −3.47280 | −0.168061 | ||||||||
\(428\) | 14.3584 | 0.694042 | ||||||||
\(429\) | 8.08858 | 0.390520 | ||||||||
\(430\) | −1.60178 | −0.0772449 | ||||||||
\(431\) | −24.7729 | −1.19327 | −0.596634 | − | 0.802513i | \(-0.703496\pi\) | ||||
−0.596634 | + | 0.802513i | \(0.703496\pi\) | |||||||
\(432\) | −20.9862 | −1.00970 | ||||||||
\(433\) | 28.1739 | 1.35395 | 0.676976 | − | 0.736005i | \(-0.263290\pi\) | ||||
0.676976 | + | 0.736005i | \(0.263290\pi\) | |||||||
\(434\) | 0.658316 | 0.0316002 | ||||||||
\(435\) | 0.00823281 | 0.000394733 0 | ||||||||
\(436\) | −7.74273 | −0.370809 | ||||||||
\(437\) | 18.4023 | 0.880302 | ||||||||
\(438\) | −0.438086 | −0.0209326 | ||||||||
\(439\) | −0.128231 | −0.00612014 | −0.00306007 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00306007 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(440\) | −3.34632 | −0.159530 | ||||||||
\(441\) | 10.6726 | 0.508217 | ||||||||
\(442\) | 1.56644 | 0.0745077 | ||||||||
\(443\) | 3.96327 | 0.188301 | 0.0941504 | − | 0.995558i | \(-0.469987\pi\) | ||||
0.0941504 | + | 0.995558i | \(0.469987\pi\) | |||||||
\(444\) | 10.7447 | 0.509920 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | −3.63602 | −0.172170 | ||||||||
\(447\) | −5.44193 | −0.257395 | ||||||||
\(448\) | 3.50562 | 0.165625 | ||||||||
\(449\) | −5.39593 | −0.254650 | −0.127325 | − | 0.991861i | \(-0.540639\pi\) | ||||
−0.127325 | + | 0.991861i | \(0.540639\pi\) | |||||||
\(450\) | −0.255462 | −0.0120426 | ||||||||
\(451\) | −17.7110 | −0.833977 | ||||||||
\(452\) | 30.0239 | 1.41221 | ||||||||
\(453\) | 4.34528 | 0.204159 | ||||||||
\(454\) | −3.75639 | −0.176296 | ||||||||
\(455\) | −0.620194 | −0.0290751 | ||||||||
\(456\) | −5.25706 | −0.246184 | ||||||||
\(457\) | 0.665823 | 0.0311459 | 0.0155729 | − | 0.999879i | \(-0.495043\pi\) | ||||
0.0155729 | + | 0.999879i | \(0.495043\pi\) | |||||||
\(458\) | 0.674189 | 0.0315028 | ||||||||
\(459\) | 40.4293 | 1.88708 | ||||||||
\(460\) | 5.31313 | 0.247726 | ||||||||
\(461\) | 42.6998 | 1.98873 | 0.994365 | − | 0.106010i | \(-0.0338076\pi\) | ||||
0.994365 | + | 0.106010i | \(0.0338076\pi\) | |||||||
\(462\) | 0.477699 | 0.0222246 | ||||||||
\(463\) | 7.05789 | 0.328008 | 0.164004 | − | 0.986460i | \(-0.447559\pi\) | ||||
0.164004 | + | 0.986460i | \(0.447559\pi\) | |||||||
\(464\) | −0.0265082 | −0.00123061 | ||||||||
\(465\) | 10.1955 | 0.472804 | ||||||||
\(466\) | −1.90881 | −0.0884239 | ||||||||
\(467\) | −30.6233 | −1.41708 | −0.708540 | − | 0.705671i | \(-0.750646\pi\) | ||||
−0.708540 | + | 0.705671i | \(0.750646\pi\) | |||||||
\(468\) | −4.05767 | −0.187566 | ||||||||
\(469\) | 0.853277 | 0.0394007 | ||||||||
\(470\) | 0.749920 | 0.0345912 | ||||||||
\(471\) | 20.7276 | 0.955077 | ||||||||
\(472\) | 0.733027 | 0.0337403 | ||||||||
\(473\) | −51.3047 | −2.35899 | ||||||||
\(474\) | −2.03405 | −0.0934270 | ||||||||
\(475\) | 6.83604 | 0.313659 | ||||||||
\(476\) | −6.94478 | −0.318314 | ||||||||
\(477\) | −4.51420 | −0.206691 | ||||||||
\(478\) | −3.30511 | −0.151172 | ||||||||
\(479\) | 24.7778 | 1.13213 | 0.566063 | − | 0.824362i | \(-0.308466\pi\) | ||||
0.566063 | + | 0.824362i | \(0.308466\pi\) | |||||||
\(480\) | −2.28175 | −0.104147 | ||||||||
\(481\) | 5.95190 | 0.271383 | ||||||||
\(482\) | −1.83984 | −0.0838026 | ||||||||
\(483\) | −1.52704 | −0.0694827 | ||||||||
\(484\) | −31.5255 | −1.43298 | ||||||||
\(485\) | −18.3113 | −0.831474 | ||||||||
\(486\) | 2.30977 | 0.104773 | ||||||||
\(487\) | 41.0479 | 1.86006 | 0.930029 | − | 0.367486i | \(-0.119782\pi\) | ||||
0.930029 | + | 0.367486i | \(0.119782\pi\) | |||||||
\(488\) | −4.70799 | −0.213121 | ||||||||
\(489\) | −10.8243 | −0.489492 | ||||||||
\(490\) | 1.09840 | 0.0496208 | ||||||||
\(491\) | 32.1154 | 1.44935 | 0.724674 | − | 0.689092i | \(-0.241990\pi\) | ||||
0.724674 | + | 0.689092i | \(0.241990\pi\) | |||||||
\(492\) | −8.03332 | −0.362170 | ||||||||
\(493\) | 0.0510671 | 0.00229995 | ||||||||
\(494\) | −1.44641 | −0.0650771 | ||||||||
\(495\) | −8.18237 | −0.367770 | ||||||||
\(496\) | −32.8276 | −1.47400 | ||||||||
\(497\) | −1.38540 | −0.0621439 | ||||||||
\(498\) | 1.23015 | 0.0551246 | ||||||||
\(499\) | −29.5346 | −1.32215 | −0.661074 | − | 0.750321i | \(-0.729899\pi\) | ||||
−0.661074 | + | 0.750321i | \(0.729899\pi\) | |||||||
\(500\) | 1.97371 | 0.0882669 | ||||||||
\(501\) | 5.12094 | 0.228787 | ||||||||
\(502\) | −2.59459 | −0.115802 | ||||||||
\(503\) | 17.9883 | 0.802058 | 0.401029 | − | 0.916065i | \(-0.368653\pi\) | ||||
0.401029 | + | 0.916065i | \(0.368653\pi\) | |||||||
\(504\) | −0.482472 | −0.0214910 | ||||||||
\(505\) | 14.3545 | 0.638766 | ||||||||
\(506\) | −2.26694 | −0.100778 | ||||||||
\(507\) | −13.4836 | −0.598826 | ||||||||
\(508\) | −28.2402 | −1.25295 | ||||||||
\(509\) | 28.2936 | 1.25409 | 0.627045 | − | 0.778983i | \(-0.284264\pi\) | ||||
0.627045 | + | 0.778983i | \(0.284264\pi\) | |||||||
\(510\) | 1.43274 | 0.0634428 | ||||||||
\(511\) | 1.07589 | 0.0475946 | ||||||||
\(512\) | 12.2990 | 0.543546 | ||||||||
\(513\) | −37.3315 | −1.64822 | ||||||||
\(514\) | 1.57531 | 0.0694840 | ||||||||
\(515\) | −5.43964 | −0.239699 | ||||||||
\(516\) | −23.2707 | −1.02444 | ||||||||
\(517\) | 24.0197 | 1.05639 | ||||||||
\(518\) | 0.351510 | 0.0154445 | ||||||||
\(519\) | 25.2991 | 1.11051 | ||||||||
\(520\) | −0.840781 | −0.0368707 | ||||||||
\(521\) | −13.2784 | −0.581739 | −0.290870 | − | 0.956763i | \(-0.593945\pi\) | ||||
−0.290870 | + | 0.956763i | \(0.593945\pi\) | |||||||
\(522\) | 0.00176215 | 7.71271e−5 0 | ||||||||
\(523\) | −23.7559 | −1.03877 | −0.519386 | − | 0.854540i | \(-0.673839\pi\) | ||||
−0.519386 | + | 0.854540i | \(0.673839\pi\) | |||||||
\(524\) | 10.1948 | 0.445361 | ||||||||
\(525\) | −0.567260 | −0.0247573 | ||||||||
\(526\) | 3.75757 | 0.163838 | ||||||||
\(527\) | 63.2413 | 2.75483 | ||||||||
\(528\) | −23.8209 | −1.03667 | ||||||||
\(529\) | −15.7534 | −0.684930 | ||||||||
\(530\) | −0.464594 | −0.0201807 | ||||||||
\(531\) | 1.79238 | 0.0777828 | ||||||||
\(532\) | 6.41265 | 0.278024 | ||||||||
\(533\) | −4.44997 | −0.192750 | ||||||||
\(534\) | −0.193527 | −0.00837474 | ||||||||
\(535\) | 7.27486 | 0.314519 | ||||||||
\(536\) | 1.15677 | 0.0499647 | ||||||||
\(537\) | 0.559754 | 0.0241552 | ||||||||
\(538\) | −0.799014 | −0.0344479 | ||||||||
\(539\) | 35.1815 | 1.51538 | ||||||||
\(540\) | −10.7784 | −0.463827 | ||||||||
\(541\) | −12.9184 | −0.555404 | −0.277702 | − | 0.960667i | \(-0.589573\pi\) | ||||
−0.277702 | + | 0.960667i | \(0.589573\pi\) | |||||||
\(542\) | 2.69087 | 0.115583 | ||||||||
\(543\) | −26.5836 | −1.14081 | ||||||||
\(544\) | −14.1534 | −0.606824 | ||||||||
\(545\) | −3.92293 | −0.168040 | ||||||||
\(546\) | 0.120024 | 0.00513657 | ||||||||
\(547\) | 39.0481 | 1.66958 | 0.834788 | − | 0.550571i | \(-0.185590\pi\) | ||||
0.834788 | + | 0.550571i | \(0.185590\pi\) | |||||||
\(548\) | 19.9409 | 0.851834 | ||||||||
\(549\) | −11.5119 | −0.491315 | ||||||||
\(550\) | −0.842116 | −0.0359079 | ||||||||
\(551\) | −0.0471543 | −0.00200884 | ||||||||
\(552\) | −2.07017 | −0.0881122 | ||||||||
\(553\) | 4.99540 | 0.212426 | ||||||||
\(554\) | −2.10565 | −0.0894605 | ||||||||
\(555\) | 5.44390 | 0.231081 | ||||||||
\(556\) | 41.4601 | 1.75830 | ||||||||
\(557\) | 5.51252 | 0.233573 | 0.116786 | − | 0.993157i | \(-0.462741\pi\) | ||||
0.116786 | + | 0.993157i | \(0.462741\pi\) | |||||||
\(558\) | 2.18223 | 0.0923813 | ||||||||
\(559\) | −12.8906 | −0.545213 | ||||||||
\(560\) | 1.82648 | 0.0771827 | ||||||||
\(561\) | 45.8902 | 1.93749 | ||||||||
\(562\) | 4.77519 | 0.201429 | ||||||||
\(563\) | −37.2064 | −1.56806 | −0.784031 | − | 0.620722i | \(-0.786840\pi\) | ||||
−0.784031 | + | 0.620722i | \(0.786840\pi\) | |||||||
\(564\) | 10.8948 | 0.458755 | ||||||||
\(565\) | 15.2119 | 0.639971 | ||||||||
\(566\) | −2.41598 | −0.101551 | ||||||||
\(567\) | 0.851390 | 0.0357550 | ||||||||
\(568\) | −1.87816 | −0.0788057 | ||||||||
\(569\) | −27.0351 | −1.13337 | −0.566685 | − | 0.823935i | \(-0.691774\pi\) | ||||
−0.566685 | + | 0.823935i | \(0.691774\pi\) | |||||||
\(570\) | −1.32296 | −0.0554127 | ||||||||
\(571\) | 32.8494 | 1.37471 | 0.687353 | − | 0.726324i | \(-0.258773\pi\) | ||||
0.687353 | + | 0.726324i | \(0.258773\pi\) | |||||||
\(572\) | −13.3759 | −0.559274 | ||||||||
\(573\) | −25.4307 | −1.06238 | ||||||||
\(574\) | −0.262809 | −0.0109694 | ||||||||
\(575\) | 2.69195 | 0.112262 | ||||||||
\(576\) | 11.6207 | 0.484195 | ||||||||
\(577\) | 35.2109 | 1.46585 | 0.732925 | − | 0.680309i | \(-0.238155\pi\) | ||||
0.732925 | + | 0.680309i | \(0.238155\pi\) | |||||||
\(578\) | 6.13061 | 0.255000 | ||||||||
\(579\) | −1.59721 | −0.0663776 | ||||||||
\(580\) | −0.0136144 | −0.000565308 0 | ||||||||
\(581\) | −3.02112 | −0.125337 | ||||||||
\(582\) | 3.54374 | 0.146893 | ||||||||
\(583\) | −14.8808 | −0.616301 | ||||||||
\(584\) | 1.45856 | 0.0603555 | ||||||||
\(585\) | −2.05586 | −0.0849994 | ||||||||
\(586\) | −0.438730 | −0.0181238 | ||||||||
\(587\) | 40.2094 | 1.65962 | 0.829811 | − | 0.558045i | \(-0.188448\pi\) | ||||
0.829811 | + | 0.558045i | \(0.188448\pi\) | |||||||
\(588\) | 15.9576 | 0.658080 | ||||||||
\(589\) | −58.3956 | −2.40615 | ||||||||
\(590\) | 0.184469 | 0.00759448 | ||||||||
\(591\) | −11.5290 | −0.474239 | ||||||||
\(592\) | −17.5284 | −0.720412 | ||||||||
\(593\) | 29.5937 | 1.21527 | 0.607633 | − | 0.794218i | \(-0.292119\pi\) | ||||
0.607633 | + | 0.794218i | \(0.292119\pi\) | |||||||
\(594\) | 4.59877 | 0.188690 | ||||||||
\(595\) | −3.51865 | −0.144250 | ||||||||
\(596\) | 8.99920 | 0.368621 | ||||||||
\(597\) | 11.7651 | 0.481511 | ||||||||
\(598\) | −0.569580 | −0.0232919 | ||||||||
\(599\) | −8.74518 | −0.357318 | −0.178659 | − | 0.983911i | \(-0.557176\pi\) | ||||
−0.178659 | + | 0.983911i | \(0.557176\pi\) | |||||||
\(600\) | −0.769020 | −0.0313951 | ||||||||
\(601\) | 3.42482 | 0.139701 | 0.0698507 | − | 0.997557i | \(-0.477748\pi\) | ||||
0.0698507 | + | 0.997557i | \(0.477748\pi\) | |||||||
\(602\) | −0.761297 | −0.0310282 | ||||||||
\(603\) | 2.82850 | 0.115185 | ||||||||
\(604\) | −7.18569 | −0.292382 | ||||||||
\(605\) | −15.9727 | −0.649384 | ||||||||
\(606\) | −2.77798 | −0.112848 | ||||||||
\(607\) | −20.5908 | −0.835756 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(608\) | 13.0690 | 0.530017 | ||||||||
\(609\) | 0.00391290 | 0.000158559 0 | ||||||||
\(610\) | −1.18478 | −0.0479705 | ||||||||
\(611\) | 6.03508 | 0.244153 | ||||||||
\(612\) | −23.0210 | −0.930571 | ||||||||
\(613\) | −26.4547 | −1.06850 | −0.534248 | − | 0.845328i | \(-0.679405\pi\) | ||||
−0.534248 | + | 0.845328i | \(0.679405\pi\) | |||||||
\(614\) | −2.50149 | −0.100952 | ||||||||
\(615\) | −4.07017 | −0.164125 | ||||||||
\(616\) | −1.59044 | −0.0640808 | ||||||||
\(617\) | −43.8302 | −1.76454 | −0.882268 | − | 0.470747i | \(-0.843985\pi\) | ||||
−0.882268 | + | 0.470747i | \(0.843985\pi\) | |||||||
\(618\) | 1.05272 | 0.0423465 | ||||||||
\(619\) | −0.0432321 | −0.00173765 | −0.000868823 | − | 1.00000i | \(-0.500277\pi\) | ||||
−0.000868823 | 1.00000i | \(0.500277\pi\) | ||||||||
\(620\) | −16.8600 | −0.677115 | ||||||||
\(621\) | −14.7007 | −0.589919 | ||||||||
\(622\) | −1.50618 | −0.0603922 | ||||||||
\(623\) | 0.475281 | 0.0190417 | ||||||||
\(624\) | −5.98513 | −0.239597 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.902633 | −0.0360765 | ||||||||
\(627\) | −42.3740 | −1.69225 | ||||||||
\(628\) | −34.2768 | −1.36779 | ||||||||
\(629\) | 33.7679 | 1.34641 | ||||||||
\(630\) | −0.121416 | −0.00483733 | ||||||||
\(631\) | −29.9042 | −1.19047 | −0.595233 | − | 0.803553i | \(-0.702940\pi\) | ||||
−0.595233 | + | 0.803553i | \(0.702940\pi\) | |||||||
\(632\) | 6.77213 | 0.269381 | ||||||||
\(633\) | −14.6219 | −0.581170 | ||||||||
\(634\) | 5.01689 | 0.199246 | ||||||||
\(635\) | −14.3082 | −0.567803 | ||||||||
\(636\) | −6.74963 | −0.267640 | ||||||||
\(637\) | 8.83954 | 0.350235 | ||||||||
\(638\) | 0.00580882 | 0.000229973 0 | ||||||||
\(639\) | −4.59243 | −0.181674 | ||||||||
\(640\) | 5.01953 | 0.198414 | ||||||||
\(641\) | −16.3131 | −0.644330 | −0.322165 | − | 0.946684i | \(-0.604411\pi\) | ||||
−0.322165 | + | 0.946684i | \(0.604411\pi\) | |||||||
\(642\) | −1.40788 | −0.0555647 | ||||||||
\(643\) | 17.2134 | 0.678832 | 0.339416 | − | 0.940636i | \(-0.389771\pi\) | ||||
0.339416 | + | 0.940636i | \(0.389771\pi\) | |||||||
\(644\) | 2.52523 | 0.0995080 | ||||||||
\(645\) | −11.7904 | −0.464245 | ||||||||
\(646\) | −8.20616 | −0.322867 | ||||||||
\(647\) | 28.3178 | 1.11329 | 0.556645 | − | 0.830751i | \(-0.312088\pi\) | ||||
0.556645 | + | 0.830751i | \(0.312088\pi\) | |||||||
\(648\) | 1.15421 | 0.0453416 | ||||||||
\(649\) | 5.90850 | 0.231929 | ||||||||
\(650\) | −0.211586 | −0.00829909 | ||||||||
\(651\) | 4.84571 | 0.189918 | ||||||||
\(652\) | 17.8999 | 0.701015 | ||||||||
\(653\) | 27.2771 | 1.06743 | 0.533717 | − | 0.845663i | \(-0.320795\pi\) | ||||
0.533717 | + | 0.845663i | \(0.320795\pi\) | |||||||
\(654\) | 0.759194 | 0.0296868 | ||||||||
\(655\) | 5.16529 | 0.201825 | ||||||||
\(656\) | 13.1052 | 0.511672 | ||||||||
\(657\) | 3.56644 | 0.139140 | ||||||||
\(658\) | 0.356422 | 0.0138948 | ||||||||
\(659\) | −36.6207 | −1.42654 | −0.713270 | − | 0.700889i | \(-0.752787\pi\) | ||||
−0.713270 | + | 0.700889i | \(0.752787\pi\) | |||||||
\(660\) | −12.2343 | −0.476218 | ||||||||
\(661\) | −39.6430 | −1.54193 | −0.770967 | − | 0.636875i | \(-0.780227\pi\) | ||||
−0.770967 | + | 0.636875i | \(0.780227\pi\) | |||||||
\(662\) | 0.0119091 | 0.000462859 0 | ||||||||
\(663\) | 11.5302 | 0.447794 | ||||||||
\(664\) | −4.09566 | −0.158942 | ||||||||
\(665\) | 3.24904 | 0.125992 | ||||||||
\(666\) | 1.16521 | 0.0451509 | ||||||||
\(667\) | −0.0185688 | −0.000718987 0 | ||||||||
\(668\) | −8.46838 | −0.327652 | ||||||||
\(669\) | −26.7638 | −1.03475 | ||||||||
\(670\) | 0.291105 | 0.0112464 | ||||||||
\(671\) | −37.9483 | −1.46498 | ||||||||
\(672\) | −1.08447 | −0.0418345 | ||||||||
\(673\) | 7.70607 | 0.297047 | 0.148524 | − | 0.988909i | \(-0.452548\pi\) | ||||
0.148524 | + | 0.988909i | \(0.452548\pi\) | |||||||
\(674\) | 2.75032 | 0.105938 | ||||||||
\(675\) | −5.46097 | −0.210193 | ||||||||
\(676\) | 22.2974 | 0.857594 | ||||||||
\(677\) | −16.9048 | −0.649706 | −0.324853 | − | 0.945765i | \(-0.605315\pi\) | ||||
−0.324853 | + | 0.945765i | \(0.605315\pi\) | |||||||
\(678\) | −2.94392 | −0.113061 | ||||||||
\(679\) | −8.70302 | −0.333991 | ||||||||
\(680\) | −4.77014 | −0.182926 | ||||||||
\(681\) | −27.6499 | −1.05955 | ||||||||
\(682\) | 7.19361 | 0.275458 | ||||||||
\(683\) | −7.11167 | −0.272120 | −0.136060 | − | 0.990701i | \(-0.543444\pi\) | ||||
−0.136060 | + | 0.990701i | \(0.543444\pi\) | |||||||
\(684\) | 21.2571 | 0.812786 | ||||||||
\(685\) | 10.1033 | 0.386026 | ||||||||
\(686\) | 1.06151 | 0.0405285 | ||||||||
\(687\) | 4.96255 | 0.189333 | ||||||||
\(688\) | 37.9628 | 1.44732 | ||||||||
\(689\) | −3.73888 | −0.142440 | ||||||||
\(690\) | −0.520966 | −0.0198328 | ||||||||
\(691\) | 18.0632 | 0.687156 | 0.343578 | − | 0.939124i | \(-0.388361\pi\) | ||||
0.343578 | + | 0.939124i | \(0.388361\pi\) | |||||||
\(692\) | −41.8366 | −1.59039 | ||||||||
\(693\) | −3.88892 | −0.147728 | ||||||||
\(694\) | −3.44110 | −0.130622 | ||||||||
\(695\) | 21.0062 | 0.796811 | ||||||||
\(696\) | 0.00530461 | 0.000201071 0 | ||||||||
\(697\) | −25.2468 | −0.956289 | ||||||||
\(698\) | 1.21334 | 0.0459258 | ||||||||
\(699\) | −14.0503 | −0.531431 | ||||||||
\(700\) | 0.938065 | 0.0354555 | ||||||||
\(701\) | 14.5894 | 0.551034 | 0.275517 | − | 0.961296i | \(-0.411151\pi\) | ||||
0.275517 | + | 0.961296i | \(0.411151\pi\) | |||||||
\(702\) | 1.15547 | 0.0436102 | ||||||||
\(703\) | −31.1805 | −1.17599 | ||||||||
\(704\) | 38.3069 | 1.44375 | ||||||||
\(705\) | 5.51998 | 0.207895 | ||||||||
\(706\) | 0.339658 | 0.0127832 | ||||||||
\(707\) | 6.82240 | 0.256583 | ||||||||
\(708\) | 2.67997 | 0.100719 | ||||||||
\(709\) | 19.9577 | 0.749527 | 0.374763 | − | 0.927120i | \(-0.377724\pi\) | ||||
0.374763 | + | 0.927120i | \(0.377724\pi\) | |||||||
\(710\) | −0.472646 | −0.0177381 | ||||||||
\(711\) | 16.5591 | 0.621014 | ||||||||
\(712\) | 0.644326 | 0.0241471 | ||||||||
\(713\) | −22.9955 | −0.861188 | ||||||||
\(714\) | 0.680953 | 0.0254840 | ||||||||
\(715\) | −6.77704 | −0.253447 | ||||||||
\(716\) | −0.925652 | −0.0345932 | ||||||||
\(717\) | −24.3281 | −0.908551 | ||||||||
\(718\) | −0.255937 | −0.00955147 | ||||||||
\(719\) | −1.62038 | −0.0604298 | −0.0302149 | − | 0.999543i | \(-0.509619\pi\) | ||||
−0.0302149 | + | 0.999543i | \(0.509619\pi\) | |||||||
\(720\) | 6.05453 | 0.225639 | ||||||||
\(721\) | −2.58535 | −0.0962836 | ||||||||
\(722\) | 4.49658 | 0.167345 | ||||||||
\(723\) | −13.5427 | −0.503657 | ||||||||
\(724\) | 43.9608 | 1.63379 | ||||||||
\(725\) | −0.00689789 | −0.000256181 0 | ||||||||
\(726\) | 3.09115 | 0.114724 | ||||||||
\(727\) | 5.61596 | 0.208284 | 0.104142 | − | 0.994562i | \(-0.466790\pi\) | ||||
0.104142 | + | 0.994562i | \(0.466790\pi\) | |||||||
\(728\) | −0.399607 | −0.0148104 | ||||||||
\(729\) | 22.3757 | 0.828730 | ||||||||
\(730\) | 0.367052 | 0.0135852 | ||||||||
\(731\) | −73.1342 | −2.70496 | ||||||||
\(732\) | −17.2125 | −0.636194 | ||||||||
\(733\) | 48.1350 | 1.77791 | 0.888953 | − | 0.457998i | \(-0.151433\pi\) | ||||
0.888953 | + | 0.457998i | \(0.151433\pi\) | |||||||
\(734\) | 5.62485 | 0.207617 | ||||||||
\(735\) | 8.08508 | 0.298223 | ||||||||
\(736\) | 5.14641 | 0.189699 | ||||||||
\(737\) | 9.32400 | 0.343454 | ||||||||
\(738\) | −0.871176 | −0.0320684 | ||||||||
\(739\) | −8.98910 | −0.330669 | −0.165335 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165335 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(740\) | −9.00245 | −0.330937 | ||||||||
\(741\) | −10.6467 | −0.391116 | ||||||||
\(742\) | −0.220813 | −0.00810629 | ||||||||
\(743\) | 2.20072 | 0.0807365 | 0.0403683 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403683 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(744\) | 6.56920 | 0.240839 | ||||||||
\(745\) | 4.55954 | 0.167049 | ||||||||
\(746\) | 4.60272 | 0.168518 | ||||||||
\(747\) | −10.0146 | −0.366416 | ||||||||
\(748\) | −75.8876 | −2.77473 | ||||||||
\(749\) | 3.45760 | 0.126338 | ||||||||
\(750\) | −0.193527 | −0.00706661 | ||||||||
\(751\) | −22.7671 | −0.830781 | −0.415391 | − | 0.909643i | \(-0.636355\pi\) | ||||
−0.415391 | + | 0.909643i | \(0.636355\pi\) | |||||||
\(752\) | −17.7733 | −0.648127 | ||||||||
\(753\) | −19.0982 | −0.695977 | ||||||||
\(754\) | 0.00145950 | 5.31517e−5 0 | ||||||||
\(755\) | −3.64071 | −0.132499 | ||||||||
\(756\) | −5.12275 | −0.186313 | ||||||||
\(757\) | −30.2022 | −1.09772 | −0.548859 | − | 0.835915i | \(-0.684937\pi\) | ||||
−0.548859 | + | 0.835915i | \(0.684937\pi\) | |||||||
\(758\) | −2.49170 | −0.0905026 | ||||||||
\(759\) | −16.6864 | −0.605678 | ||||||||
\(760\) | 4.40464 | 0.159773 | ||||||||
\(761\) | 17.4802 | 0.633656 | 0.316828 | − | 0.948483i | \(-0.397382\pi\) | ||||
0.316828 | + | 0.948483i | \(0.397382\pi\) | |||||||
\(762\) | 2.76902 | 0.100311 | ||||||||
\(763\) | −1.86449 | −0.0674992 | ||||||||
\(764\) | 42.0542 | 1.52147 | ||||||||
\(765\) | −11.6639 | −0.421708 | ||||||||
\(766\) | −3.86703 | −0.139722 | ||||||||
\(767\) | 1.48454 | 0.0536036 | ||||||||
\(768\) | 16.6352 | 0.600273 | ||||||||
\(769\) | −28.0588 | −1.01183 | −0.505913 | − | 0.862585i | \(-0.668844\pi\) | ||||
−0.505913 | + | 0.862585i | \(0.668844\pi\) | |||||||
\(770\) | −0.400241 | −0.0144237 | ||||||||
\(771\) | 11.5955 | 0.417602 | ||||||||
\(772\) | 2.64126 | 0.0950612 | ||||||||
\(773\) | −2.19223 | −0.0788489 | −0.0394245 | − | 0.999223i | \(-0.512552\pi\) | ||||
−0.0394245 | + | 0.999223i | \(0.512552\pi\) | |||||||
\(774\) | −2.52360 | −0.0907090 | ||||||||
\(775\) | −8.54230 | −0.306849 | ||||||||
\(776\) | −11.7985 | −0.423540 | ||||||||
\(777\) | 2.58738 | 0.0928218 | ||||||||
\(778\) | 1.90796 | 0.0684038 | ||||||||
\(779\) | 23.3123 | 0.835249 | ||||||||
\(780\) | −3.07392 | −0.110064 | ||||||||
\(781\) | −15.1387 | −0.541706 | ||||||||
\(782\) | −3.23149 | −0.115558 | ||||||||
\(783\) | 0.0376692 | 0.00134619 | ||||||||
\(784\) | −26.0325 | −0.929732 | ||||||||
\(785\) | −17.3667 | −0.619843 | ||||||||
\(786\) | −0.999624 | −0.0356554 | ||||||||
\(787\) | −36.7899 | −1.31142 | −0.655709 | − | 0.755013i | \(-0.727630\pi\) | ||||
−0.655709 | + | 0.755013i | \(0.727630\pi\) | |||||||
\(788\) | 19.0652 | 0.679170 | ||||||||
\(789\) | 27.6585 | 0.984670 | ||||||||
\(790\) | 1.70423 | 0.0606339 | ||||||||
\(791\) | 7.22994 | 0.257067 | ||||||||
\(792\) | −5.27211 | −0.187336 | ||||||||
\(793\) | −9.53471 | −0.338587 | ||||||||
\(794\) | −1.82867 | −0.0648971 | ||||||||
\(795\) | −3.41977 | −0.121287 | ||||||||
\(796\) | −19.4556 | −0.689585 | ||||||||
\(797\) | −42.4563 | −1.50388 | −0.751941 | − | 0.659231i | \(-0.770882\pi\) | ||||
−0.751941 | + | 0.659231i | \(0.770882\pi\) | |||||||
\(798\) | −0.628777 | −0.0222585 | ||||||||
\(799\) | 34.2398 | 1.21132 | ||||||||
\(800\) | 1.91177 | 0.0675914 | ||||||||
\(801\) | 1.57549 | 0.0556673 | ||||||||
\(802\) | 2.10655 | 0.0743850 | ||||||||
\(803\) | 11.7566 | 0.414880 | ||||||||
\(804\) | 4.22917 | 0.149151 | ||||||||
\(805\) | 1.27943 | 0.0450941 | ||||||||
\(806\) | 1.80743 | 0.0636641 | ||||||||
\(807\) | −5.88135 | −0.207033 | ||||||||
\(808\) | 9.24896 | 0.325377 | ||||||||
\(809\) | 28.4853 | 1.00149 | 0.500744 | − | 0.865595i | \(-0.333060\pi\) | ||||
0.500744 | + | 0.865595i | \(0.333060\pi\) | |||||||
\(810\) | 0.290461 | 0.0102058 | ||||||||
\(811\) | −17.7783 | −0.624282 | −0.312141 | − | 0.950036i | \(-0.601046\pi\) | ||||
−0.312141 | + | 0.950036i | \(0.601046\pi\) | |||||||
\(812\) | −0.00647067 | −0.000227076 0 | ||||||||
\(813\) | 19.8069 | 0.694657 | ||||||||
\(814\) | 3.84105 | 0.134629 | ||||||||
\(815\) | 9.06918 | 0.317680 | ||||||||
\(816\) | −33.9564 | −1.18871 | ||||||||
\(817\) | 67.5304 | 2.36259 | ||||||||
\(818\) | −2.30570 | −0.0806169 | ||||||||
\(819\) | −0.977111 | −0.0341430 | ||||||||
\(820\) | 6.73074 | 0.235048 | ||||||||
\(821\) | 31.1566 | 1.08737 | 0.543687 | − | 0.839288i | \(-0.317028\pi\) | ||||
0.543687 | + | 0.839288i | \(0.317028\pi\) | |||||||
\(822\) | −1.95526 | −0.0681974 | ||||||||
\(823\) | 20.4644 | 0.713346 | 0.356673 | − | 0.934229i | \(-0.383911\pi\) | ||||
0.356673 | + | 0.934229i | \(0.383911\pi\) | |||||||
\(824\) | −3.50490 | −0.122099 | ||||||||
\(825\) | −6.19862 | −0.215808 | ||||||||
\(826\) | 0.0876747 | 0.00305059 | ||||||||
\(827\) | −16.0701 | −0.558812 | −0.279406 | − | 0.960173i | \(-0.590138\pi\) | ||||
−0.279406 | + | 0.960173i | \(0.590138\pi\) | |||||||
\(828\) | 8.37080 | 0.290906 | ||||||||
\(829\) | −34.1508 | −1.18611 | −0.593053 | − | 0.805163i | \(-0.702078\pi\) | ||||
−0.593053 | + | 0.805163i | \(0.702078\pi\) | |||||||
\(830\) | −1.03069 | −0.0357757 | ||||||||
\(831\) | −15.4992 | −0.537661 | ||||||||
\(832\) | 9.62481 | 0.333680 | ||||||||
\(833\) | 50.1508 | 1.73762 | ||||||||
\(834\) | −4.06527 | −0.140769 | ||||||||
\(835\) | −4.29059 | −0.148482 | ||||||||
\(836\) | 70.0729 | 2.42352 | ||||||||
\(837\) | 46.6493 | 1.61244 | ||||||||
\(838\) | −5.32293 | −0.183878 | ||||||||
\(839\) | −2.87004 | −0.0990846 | −0.0495423 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495423 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(840\) | −0.365500 | −0.0126110 | ||||||||
\(841\) | −29.0000 | −0.999998 | ||||||||
\(842\) | 5.82641 | 0.200791 | ||||||||
\(843\) | 35.1491 | 1.21060 | ||||||||
\(844\) | 24.1800 | 0.832309 | ||||||||
\(845\) | 11.2972 | 0.388637 | ||||||||
\(846\) | 1.18149 | 0.0406206 | ||||||||
\(847\) | −7.59153 | −0.260848 | ||||||||
\(848\) | 11.0110 | 0.378121 | ||||||||
\(849\) | −17.7835 | −0.610327 | ||||||||
\(850\) | −1.20042 | −0.0411742 | ||||||||
\(851\) | −12.2785 | −0.420902 | ||||||||
\(852\) | −6.86660 | −0.235246 | ||||||||
\(853\) | 22.6448 | 0.775344 | 0.387672 | − | 0.921797i | \(-0.373279\pi\) | ||||
0.387672 | + | 0.921797i | \(0.373279\pi\) | |||||||
\(854\) | −0.563105 | −0.0192691 | ||||||||
\(855\) | 10.7701 | 0.368331 | ||||||||
\(856\) | 4.68738 | 0.160211 | ||||||||
\(857\) | 22.5002 | 0.768594 | 0.384297 | − | 0.923210i | \(-0.374444\pi\) | ||||
0.384297 | + | 0.923210i | \(0.374444\pi\) | |||||||
\(858\) | 1.31154 | 0.0447752 | ||||||||
\(859\) | −38.7537 | −1.32226 | −0.661129 | − | 0.750272i | \(-0.729923\pi\) | ||||
−0.661129 | + | 0.750272i | \(0.729923\pi\) | |||||||
\(860\) | 19.4974 | 0.664857 | ||||||||
\(861\) | −1.93447 | −0.0659266 | ||||||||
\(862\) | −4.01686 | −0.136815 | ||||||||
\(863\) | 29.5580 | 1.00617 | 0.503083 | − | 0.864238i | \(-0.332199\pi\) | ||||
0.503083 | + | 0.864238i | \(0.332199\pi\) | |||||||
\(864\) | −10.4401 | −0.355181 | ||||||||
\(865\) | −21.1969 | −0.720718 | ||||||||
\(866\) | 4.56832 | 0.155238 | ||||||||
\(867\) | 45.1259 | 1.53256 | ||||||||
\(868\) | −8.01324 | −0.271987 | ||||||||
\(869\) | 54.5861 | 1.85171 | ||||||||
\(870\) | 0.00133493 | 4.52583e−5 0 | ||||||||
\(871\) | 2.34270 | 0.0793795 | ||||||||
\(872\) | −2.52765 | −0.0855969 | ||||||||
\(873\) | −28.8494 | −0.976403 | ||||||||
\(874\) | 2.98388 | 0.100931 | ||||||||
\(875\) | 0.475281 | 0.0160674 | ||||||||
\(876\) | 5.33253 | 0.180169 | ||||||||
\(877\) | −0.306586 | −0.0103527 | −0.00517633 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517633 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(878\) | −0.0207923 | −0.000701707 0 | ||||||||
\(879\) | −3.22939 | −0.108925 | ||||||||
\(880\) | 19.9584 | 0.672798 | ||||||||
\(881\) | 4.86851 | 0.164024 | 0.0820121 | − | 0.996631i | \(-0.473865\pi\) | ||||
0.0820121 | + | 0.996631i | \(0.473865\pi\) | |||||||
\(882\) | 1.73053 | 0.0582698 | ||||||||
\(883\) | 54.1155 | 1.82113 | 0.910565 | − | 0.413366i | \(-0.135647\pi\) | ||||
0.910565 | + | 0.413366i | \(0.135647\pi\) | |||||||
\(884\) | −19.0672 | −0.641298 | ||||||||
\(885\) | 1.35783 | 0.0456431 | ||||||||
\(886\) | 0.642634 | 0.0215897 | ||||||||
\(887\) | −42.0954 | −1.41343 | −0.706713 | − | 0.707500i | \(-0.749823\pi\) | ||||
−0.706713 | + | 0.707500i | \(0.749823\pi\) | |||||||
\(888\) | 3.50765 | 0.117709 | ||||||||
\(889\) | −6.80040 | −0.228078 | ||||||||
\(890\) | 0.162147 | 0.00543519 | ||||||||
\(891\) | 9.30338 | 0.311675 | ||||||||
\(892\) | 44.2588 | 1.48189 | ||||||||
\(893\) | −31.6162 | −1.05800 | ||||||||
\(894\) | −0.882394 | −0.0295117 | ||||||||
\(895\) | −0.468991 | −0.0156767 | ||||||||
\(896\) | 2.38568 | 0.0797001 | ||||||||
\(897\) | −4.19254 | −0.139985 | ||||||||
\(898\) | −0.874935 | −0.0291970 | ||||||||
\(899\) | 0.0589238 | 0.00196522 | ||||||||
\(900\) | 3.10956 | 0.103652 | ||||||||
\(901\) | −21.2124 | −0.706688 | ||||||||
\(902\) | −2.87178 | −0.0956200 | ||||||||
\(903\) | −5.60373 | −0.186480 | ||||||||
\(904\) | 9.80144 | 0.325991 | ||||||||
\(905\) | 22.2732 | 0.740386 | ||||||||
\(906\) | 0.704575 | 0.0234079 | ||||||||
\(907\) | −3.59534 | −0.119381 | −0.0596907 | − | 0.998217i | \(-0.519011\pi\) | ||||
−0.0596907 | + | 0.998217i | \(0.519011\pi\) | |||||||
\(908\) | 45.7240 | 1.51740 | ||||||||
\(909\) | 22.6154 | 0.750105 | ||||||||
\(910\) | −0.100563 | −0.00333362 | ||||||||
\(911\) | 51.3001 | 1.69965 | 0.849823 | − | 0.527068i | \(-0.176709\pi\) | ||||
0.849823 | + | 0.527068i | \(0.176709\pi\) | |||||||
\(912\) | 31.3546 | 1.03825 | ||||||||
\(913\) | −33.0127 | −1.09256 | ||||||||
\(914\) | 0.107961 | 0.00357104 | ||||||||
\(915\) | −8.72092 | −0.288305 | ||||||||
\(916\) | −8.20645 | −0.271149 | ||||||||
\(917\) | 2.45496 | 0.0810700 | ||||||||
\(918\) | 6.55549 | 0.216363 | ||||||||
\(919\) | −24.6752 | −0.813959 | −0.406979 | − | 0.913437i | \(-0.633418\pi\) | ||||
−0.406979 | + | 0.913437i | \(0.633418\pi\) | |||||||
\(920\) | 1.73450 | 0.0571846 | ||||||||
\(921\) | −18.4129 | −0.606725 | ||||||||
\(922\) | 6.92366 | 0.228019 | ||||||||
\(923\) | −3.80368 | −0.125200 | ||||||||
\(924\) | −5.81471 | −0.191290 | ||||||||
\(925\) | −4.56119 | −0.149971 | ||||||||
\(926\) | 1.14442 | 0.0376079 | ||||||||
\(927\) | −8.57011 | −0.281479 | ||||||||
\(928\) | −0.0131872 | −0.000432891 0 | ||||||||
\(929\) | −6.23375 | −0.204523 | −0.102261 | − | 0.994758i | \(-0.532608\pi\) | ||||
−0.102261 | + | 0.994758i | \(0.532608\pi\) | |||||||
\(930\) | 1.65317 | 0.0542095 | ||||||||
\(931\) | −46.3081 | −1.51769 | ||||||||
\(932\) | 23.2347 | 0.761076 | ||||||||
\(933\) | −11.0866 | −0.362959 | ||||||||
\(934\) | −4.96549 | −0.162476 | ||||||||
\(935\) | −38.4493 | −1.25743 | ||||||||
\(936\) | −1.32464 | −0.0432974 | ||||||||
\(937\) | −10.7283 | −0.350479 | −0.175240 | − | 0.984526i | \(-0.556070\pi\) | ||||
−0.175240 | + | 0.984526i | \(0.556070\pi\) | |||||||
\(938\) | 0.138356 | 0.00451750 | ||||||||
\(939\) | −6.64407 | −0.216821 | ||||||||
\(940\) | −9.12827 | −0.297731 | ||||||||
\(941\) | 11.6152 | 0.378644 | 0.189322 | − | 0.981915i | \(-0.439371\pi\) | ||||
0.189322 | + | 0.981915i | \(0.439371\pi\) | |||||||
\(942\) | 3.36092 | 0.109505 | ||||||||
\(943\) | 9.18011 | 0.298945 | ||||||||
\(944\) | −4.37198 | −0.142296 | ||||||||
\(945\) | −2.59550 | −0.0844315 | ||||||||
\(946\) | −8.31891 | −0.270471 | ||||||||
\(947\) | 9.67739 | 0.314473 | 0.157236 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157236 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(948\) | 24.7591 | 0.804139 | ||||||||
\(949\) | 2.95390 | 0.0958875 | ||||||||
\(950\) | 1.10845 | 0.0359627 | ||||||||
\(951\) | 36.9282 | 1.19748 | ||||||||
\(952\) | −2.26715 | −0.0734789 | ||||||||
\(953\) | 18.4382 | 0.597273 | 0.298636 | − | 0.954367i | \(-0.403468\pi\) | ||||
0.298636 | + | 0.954367i | \(0.403468\pi\) | |||||||
\(954\) | −0.731965 | −0.0236983 | ||||||||
\(955\) | 21.3072 | 0.689485 | ||||||||
\(956\) | 40.2309 | 1.30116 | ||||||||
\(957\) | 0.0427573 | 0.00138215 | ||||||||
\(958\) | 4.01765 | 0.129804 | ||||||||
\(959\) | 4.80189 | 0.155061 | ||||||||
\(960\) | 8.80333 | 0.284126 | ||||||||
\(961\) | 41.9709 | 1.35390 | ||||||||
\(962\) | 0.965083 | 0.0311155 | ||||||||
\(963\) | 11.4615 | 0.369341 | ||||||||
\(964\) | 22.3952 | 0.721300 | ||||||||
\(965\) | 1.33822 | 0.0430790 | ||||||||
\(966\) | −0.247605 | −0.00796656 | ||||||||
\(967\) | −45.7382 | −1.47084 | −0.735420 | − | 0.677611i | \(-0.763015\pi\) | ||||
−0.735420 | + | 0.677611i | \(0.763015\pi\) | |||||||
\(968\) | −10.2916 | −0.330786 | ||||||||
\(969\) | −60.4036 | −1.94044 | ||||||||
\(970\) | −2.96913 | −0.0953330 | ||||||||
\(971\) | −18.8604 | −0.605259 | −0.302629 | − | 0.953108i | \(-0.597864\pi\) | ||||
−0.302629 | + | 0.953108i | \(0.597864\pi\) | |||||||
\(972\) | −28.1153 | −0.901799 | ||||||||
\(973\) | 9.98384 | 0.320067 | ||||||||
\(974\) | 6.65580 | 0.213266 | ||||||||
\(975\) | −1.55743 | −0.0498778 | ||||||||
\(976\) | 28.0798 | 0.898812 | ||||||||
\(977\) | −5.89342 | −0.188547 | −0.0942736 | − | 0.995546i | \(-0.530053\pi\) | ||||
−0.0942736 | + | 0.995546i | \(0.530053\pi\) | |||||||
\(978\) | −1.75513 | −0.0561229 | ||||||||
\(979\) | 5.19353 | 0.165986 | ||||||||
\(980\) | −13.3701 | −0.427093 | ||||||||
\(981\) | −6.18056 | −0.197330 | ||||||||
\(982\) | 5.20742 | 0.166175 | ||||||||
\(983\) | 2.88660 | 0.0920683 | 0.0460341 | − | 0.998940i | \(-0.485342\pi\) | ||||
0.0460341 | + | 0.998940i | \(0.485342\pi\) | |||||||
\(984\) | −2.62251 | −0.0836027 | ||||||||
\(985\) | 9.65959 | 0.307780 | ||||||||
\(986\) | 0.00828040 | 0.000263702 0 | ||||||||
\(987\) | 2.62354 | 0.0835082 | ||||||||
\(988\) | 17.6062 | 0.560127 | ||||||||
\(989\) | 26.5927 | 0.845599 | ||||||||
\(990\) | −1.32675 | −0.0421668 | ||||||||
\(991\) | 15.8725 | 0.504206 | 0.252103 | − | 0.967700i | \(-0.418878\pi\) | ||||
0.252103 | + | 0.967700i | \(0.418878\pi\) | |||||||
\(992\) | −16.3309 | −0.518508 | ||||||||
\(993\) | 0.0876598 | 0.00278180 | ||||||||
\(994\) | −0.224639 | −0.00712513 | ||||||||
\(995\) | −9.85738 | −0.312500 | ||||||||
\(996\) | −14.9738 | −0.474464 | ||||||||
\(997\) | −28.4316 | −0.900437 | −0.450218 | − | 0.892918i | \(-0.648654\pi\) | ||||
−0.450218 | + | 0.892918i | \(0.648654\pi\) | |||||||
\(998\) | −4.78895 | −0.151591 | ||||||||
\(999\) | 24.9085 | 0.788071 |
(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 | 445.2.a.d.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 4005.2.a.l.1.3 | 4 | |||
4.3 | odd | 2 | 7120.2.a.bc.1.1 | 4 | |||
5.4 | even | 2 | 2225.2.a.i.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
445.2.a.d.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2225.2.a.i.1.3 | 4 | 5.4 | even | 2 | |||
4005.2.a.l.1.3 | 4 | 3.2 | odd | 2 | |||
7120.2.a.bc.1.1 | 4 | 4.3 | odd | 2 |