Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.928350\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.928350 | −0.656443 | −0.328221 | − | 0.944601i | \(-0.606449\pi\) | ||||
−0.328221 | + | 0.944601i | \(0.606449\pi\) | |||||||
\(3\) | 2.79733 | 1.61504 | 0.807521 | − | 0.589839i | \(-0.200809\pi\) | ||||
0.807521 | + | 0.589839i | \(0.200809\pi\) | |||||||
\(4\) | −1.13817 | −0.569083 | ||||||||
\(5\) | −3.35114 | −1.49867 | −0.749337 | − | 0.662189i | \(-0.769628\pi\) | ||||
−0.749337 | + | 0.662189i | \(0.769628\pi\) | |||||||
\(6\) | −2.59691 | −1.06018 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.91332 | 1.03001 | ||||||||
\(9\) | 4.82508 | 1.60836 | ||||||||
\(10\) | 3.11103 | 0.983793 | ||||||||
\(11\) | −0.213023 | −0.0642290 | −0.0321145 | − | 0.999484i | \(-0.510224\pi\) | ||||
−0.0321145 | + | 0.999484i | \(0.510224\pi\) | |||||||
\(12\) | −3.18383 | −0.919093 | ||||||||
\(13\) | 5.00897 | 1.38924 | 0.694619 | − | 0.719378i | \(-0.255573\pi\) | ||||
0.694619 | + | 0.719378i | \(0.255573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.37425 | −2.42042 | ||||||||
\(16\) | −0.428245 | −0.107061 | ||||||||
\(17\) | −2.11080 | −0.511944 | −0.255972 | − | 0.966684i | \(-0.582395\pi\) | ||||
−0.255972 | + | 0.966684i | \(0.582395\pi\) | |||||||
\(18\) | −4.47936 | −1.05580 | ||||||||
\(19\) | −1.21832 | −0.279502 | −0.139751 | − | 0.990187i | \(-0.544630\pi\) | ||||
−0.139751 | + | 0.990187i | \(0.544630\pi\) | |||||||
\(20\) | 3.81415 | 0.852870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.197760 | 0.0421626 | ||||||||
\(23\) | −7.54545 | −1.57333 | −0.786667 | − | 0.617378i | \(-0.788195\pi\) | ||||
−0.786667 | + | 0.617378i | \(0.788195\pi\) | |||||||
\(24\) | 8.14952 | 1.66351 | ||||||||
\(25\) | 6.23011 | 1.24602 | ||||||||
\(26\) | −4.65008 | −0.911955 | ||||||||
\(27\) | 5.10536 | 0.982527 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.66679 | 0.309516 | 0.154758 | − | 0.987952i | \(-0.450540\pi\) | ||||
0.154758 | + | 0.987952i | \(0.450540\pi\) | |||||||
\(30\) | 8.70258 | 1.58887 | ||||||||
\(31\) | 8.48574 | 1.52408 | 0.762042 | − | 0.647527i | \(-0.224197\pi\) | ||||
0.762042 | + | 0.647527i | \(0.224197\pi\) | |||||||
\(32\) | −5.42907 | −0.959733 | ||||||||
\(33\) | −0.595898 | −0.103732 | ||||||||
\(34\) | 1.95956 | 0.336062 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.49174 | −0.915291 | ||||||||
\(37\) | 7.74783 | 1.27374 | 0.636868 | − | 0.770973i | \(-0.280230\pi\) | ||||
0.636868 | + | 0.770973i | \(0.280230\pi\) | |||||||
\(38\) | 1.13103 | 0.183477 | ||||||||
\(39\) | 14.0118 | 2.24368 | ||||||||
\(40\) | −9.76292 | −1.54365 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.54077 | 0.539962 | 0.269981 | − | 0.962866i | \(-0.412983\pi\) | ||||
0.269981 | + | 0.962866i | \(0.412983\pi\) | |||||||
\(44\) | 0.242456 | 0.0365516 | ||||||||
\(45\) | −16.1695 | −2.41041 | ||||||||
\(46\) | 7.00481 | 1.03280 | ||||||||
\(47\) | −7.99292 | −1.16589 | −0.582944 | − | 0.812513i | \(-0.698099\pi\) | ||||
−0.582944 | + | 0.812513i | \(0.698099\pi\) | |||||||
\(48\) | −1.19794 | −0.172908 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.78372 | −0.817942 | ||||||||
\(51\) | −5.90461 | −0.826811 | ||||||||
\(52\) | −5.70104 | −0.790592 | ||||||||
\(53\) | 6.41670 | 0.881401 | 0.440701 | − | 0.897654i | \(-0.354730\pi\) | ||||
0.440701 | + | 0.897654i | \(0.354730\pi\) | |||||||
\(54\) | −4.73956 | −0.644972 | ||||||||
\(55\) | 0.713870 | 0.0962583 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.40805 | −0.451407 | ||||||||
\(58\) | −1.54737 | −0.203179 | ||||||||
\(59\) | 8.78829 | 1.14414 | 0.572069 | − | 0.820205i | \(-0.306141\pi\) | ||||
0.572069 | + | 0.820205i | \(0.306141\pi\) | |||||||
\(60\) | 10.6695 | 1.37742 | ||||||||
\(61\) | 10.2563 | 1.31318 | 0.656591 | − | 0.754247i | \(-0.271998\pi\) | ||||
0.656591 | + | 0.754247i | \(0.271998\pi\) | |||||||
\(62\) | −7.87774 | −1.00047 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.89657 | 0.737071 | ||||||||
\(65\) | −16.7857 | −2.08201 | ||||||||
\(66\) | 0.553202 | 0.0680944 | ||||||||
\(67\) | 0.727259 | 0.0888488 | 0.0444244 | − | 0.999013i | \(-0.485855\pi\) | ||||
0.0444244 | + | 0.999013i | \(0.485855\pi\) | |||||||
\(68\) | 2.40244 | 0.291339 | ||||||||
\(69\) | −21.1071 | −2.54100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.91355 | 0.464453 | 0.232226 | − | 0.972662i | \(-0.425399\pi\) | ||||
0.232226 | + | 0.972662i | \(0.425399\pi\) | |||||||
\(72\) | 14.0570 | 1.65663 | ||||||||
\(73\) | −12.0206 | −1.40691 | −0.703453 | − | 0.710742i | \(-0.748360\pi\) | ||||
−0.703453 | + | 0.710742i | \(0.748360\pi\) | |||||||
\(74\) | −7.19270 | −0.836134 | ||||||||
\(75\) | 17.4277 | 2.01238 | ||||||||
\(76\) | 1.38665 | 0.159060 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0078 | −1.47285 | ||||||||
\(79\) | 6.07849 | 0.683884 | 0.341942 | − | 0.939721i | \(-0.388915\pi\) | ||||
0.341942 | + | 0.939721i | \(0.388915\pi\) | |||||||
\(80\) | 1.43511 | 0.160450 | ||||||||
\(81\) | −0.193845 | −0.0215383 | ||||||||
\(82\) | −0.928350 | −0.102519 | ||||||||
\(83\) | 13.6638 | 1.49979 | 0.749897 | − | 0.661554i | \(-0.230103\pi\) | ||||
0.749897 | + | 0.661554i | \(0.230103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.07357 | 0.767237 | ||||||||
\(86\) | −3.28707 | −0.354454 | ||||||||
\(87\) | 4.66258 | 0.499881 | ||||||||
\(88\) | −0.620605 | −0.0661567 | ||||||||
\(89\) | 14.2081 | 1.50605 | 0.753027 | − | 0.657990i | \(-0.228593\pi\) | ||||
0.753027 | + | 0.657990i | \(0.228593\pi\) | |||||||
\(90\) | 15.0110 | 1.58229 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.58797 | 0.895358 | ||||||||
\(93\) | 23.7375 | 2.46146 | ||||||||
\(94\) | 7.42023 | 0.765338 | ||||||||
\(95\) | 4.08276 | 0.418882 | ||||||||
\(96\) | −15.1869 | −1.55001 | ||||||||
\(97\) | −13.0513 | −1.32516 | −0.662579 | − | 0.748992i | \(-0.730538\pi\) | ||||
−0.662579 | + | 0.748992i | \(0.730538\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.02786 | −0.103303 | ||||||||
\(100\) | −7.09090 | −0.709090 | ||||||||
\(101\) | 15.4114 | 1.53349 | 0.766747 | − | 0.641950i | \(-0.221874\pi\) | ||||
0.766747 | + | 0.641950i | \(0.221874\pi\) | |||||||
\(102\) | 5.48154 | 0.542754 | ||||||||
\(103\) | 8.92932 | 0.879832 | 0.439916 | − | 0.898039i | \(-0.355008\pi\) | ||||
0.439916 | + | 0.898039i | \(0.355008\pi\) | |||||||
\(104\) | 14.5927 | 1.43093 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.95694 | −0.578589 | ||||||||
\(107\) | 8.66116 | 0.837306 | 0.418653 | − | 0.908146i | \(-0.362502\pi\) | ||||
0.418653 | + | 0.908146i | \(0.362502\pi\) | |||||||
\(108\) | −5.81075 | −0.559139 | ||||||||
\(109\) | 9.67524 | 0.926720 | 0.463360 | − | 0.886170i | \(-0.346644\pi\) | ||||
0.463360 | + | 0.886170i | \(0.346644\pi\) | |||||||
\(110\) | −0.662722 | −0.0631880 | ||||||||
\(111\) | 21.6733 | 2.05714 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.53869 | 0.238820 | 0.119410 | − | 0.992845i | \(-0.461900\pi\) | ||||
0.119410 | + | 0.992845i | \(0.461900\pi\) | |||||||
\(114\) | 3.16386 | 0.296323 | ||||||||
\(115\) | 25.2858 | 2.35791 | ||||||||
\(116\) | −1.89709 | −0.176140 | ||||||||
\(117\) | 24.1687 | 2.23440 | ||||||||
\(118\) | −8.15861 | −0.751061 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −27.3102 | −2.49306 | ||||||||
\(121\) | −10.9546 | −0.995875 | ||||||||
\(122\) | −9.52142 | −0.862029 | ||||||||
\(123\) | 2.79733 | 0.252227 | ||||||||
\(124\) | −9.65819 | −0.867331 | ||||||||
\(125\) | −4.12227 | −0.368707 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.96966 | −0.618457 | −0.309228 | − | 0.950988i | \(-0.600071\pi\) | ||||
−0.309228 | + | 0.950988i | \(0.600071\pi\) | |||||||
\(128\) | 5.38406 | 0.475889 | ||||||||
\(129\) | 9.90471 | 0.872061 | ||||||||
\(130\) | 15.5830 | 1.36672 | ||||||||
\(131\) | 11.5194 | 1.00646 | 0.503229 | − | 0.864153i | \(-0.332145\pi\) | ||||
0.503229 | + | 0.864153i | \(0.332145\pi\) | |||||||
\(132\) | 0.678231 | 0.0590324 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.675151 | −0.0583241 | ||||||||
\(135\) | −17.1087 | −1.47249 | ||||||||
\(136\) | −6.14942 | −0.527309 | ||||||||
\(137\) | −22.4713 | −1.91986 | −0.959928 | − | 0.280248i | \(-0.909583\pi\) | ||||
−0.959928 | + | 0.280248i | \(0.909583\pi\) | |||||||
\(138\) | 19.5948 | 1.66802 | ||||||||
\(139\) | 19.7137 | 1.67209 | 0.836046 | − | 0.548659i | \(-0.184862\pi\) | ||||
0.836046 | + | 0.548659i | \(0.184862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.3589 | −1.88296 | ||||||||
\(142\) | −3.63314 | −0.304887 | ||||||||
\(143\) | −1.06703 | −0.0892294 | ||||||||
\(144\) | −2.06632 | −0.172193 | ||||||||
\(145\) | −5.58565 | −0.463863 | ||||||||
\(146\) | 11.1593 | 0.923553 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.81832 | −0.724861 | ||||||||
\(149\) | 11.3470 | 0.929583 | 0.464791 | − | 0.885420i | \(-0.346129\pi\) | ||||
0.464791 | + | 0.885420i | \(0.346129\pi\) | |||||||
\(150\) | −16.1790 | −1.32101 | ||||||||
\(151\) | −1.96596 | −0.159987 | −0.0799937 | − | 0.996795i | \(-0.525490\pi\) | ||||
−0.0799937 | + | 0.996795i | \(0.525490\pi\) | |||||||
\(152\) | −3.54935 | −0.287891 | ||||||||
\(153\) | −10.1848 | −0.823390 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.4369 | −2.28411 | ||||||||
\(156\) | −15.9477 | −1.27684 | ||||||||
\(157\) | 19.9793 | 1.59452 | 0.797261 | − | 0.603635i | \(-0.206282\pi\) | ||||
0.797261 | + | 0.603635i | \(0.206282\pi\) | |||||||
\(158\) | −5.64297 | −0.448930 | ||||||||
\(159\) | 17.9496 | 1.42350 | ||||||||
\(160\) | 18.1936 | 1.43833 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.179956 | 0.0141386 | ||||||||
\(163\) | 7.55741 | 0.591942 | 0.295971 | − | 0.955197i | \(-0.404357\pi\) | ||||
0.295971 | + | 0.955197i | \(0.404357\pi\) | |||||||
\(164\) | −1.13817 | −0.0888759 | ||||||||
\(165\) | 1.99693 | 0.155461 | ||||||||
\(166\) | −12.6848 | −0.984529 | ||||||||
\(167\) | −11.6052 | −0.898036 | −0.449018 | − | 0.893523i | \(-0.648226\pi\) | ||||
−0.449018 | + | 0.893523i | \(0.648226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0898 | 0.929983 | ||||||||
\(170\) | −6.56675 | −0.503647 | ||||||||
\(171\) | −5.87849 | −0.449540 | ||||||||
\(172\) | −4.02998 | −0.307283 | ||||||||
\(173\) | −13.3467 | −1.01473 | −0.507364 | − | 0.861732i | \(-0.669380\pi\) | ||||
−0.507364 | + | 0.861732i | \(0.669380\pi\) | |||||||
\(174\) | −4.32850 | −0.328143 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0912262 | 0.00687644 | ||||||||
\(177\) | 24.5838 | 1.84783 | ||||||||
\(178\) | −13.1901 | −0.988638 | ||||||||
\(179\) | −22.6130 | −1.69017 | −0.845087 | − | 0.534629i | \(-0.820451\pi\) | ||||
−0.845087 | + | 0.534629i | \(0.820451\pi\) | |||||||
\(180\) | 18.4036 | 1.37172 | ||||||||
\(181\) | −24.9397 | −1.85376 | −0.926878 | − | 0.375363i | \(-0.877518\pi\) | ||||
−0.926878 | + | 0.375363i | \(0.877518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.6903 | 2.12084 | ||||||||
\(184\) | −21.9823 | −1.62055 | ||||||||
\(185\) | −25.9640 | −1.90891 | ||||||||
\(186\) | −22.0367 | −1.61581 | ||||||||
\(187\) | 0.449650 | 0.0328816 | ||||||||
\(188\) | 9.09727 | 0.663487 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.79023 | −0.274972 | ||||||||
\(191\) | 3.96178 | 0.286665 | 0.143332 | − | 0.989675i | \(-0.454218\pi\) | ||||
0.143332 | + | 0.989675i | \(0.454218\pi\) | |||||||
\(192\) | 16.4947 | 1.19040 | ||||||||
\(193\) | 1.92686 | 0.138699 | 0.0693493 | − | 0.997592i | \(-0.477908\pi\) | ||||
0.0693493 | + | 0.997592i | \(0.477908\pi\) | |||||||
\(194\) | 12.1162 | 0.869890 | ||||||||
\(195\) | −46.9553 | −3.36254 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7779 | −1.83660 | −0.918300 | − | 0.395886i | \(-0.870437\pi\) | ||||
−0.918300 | + | 0.395886i | \(0.870437\pi\) | |||||||
\(198\) | 0.954209 | 0.0678127 | ||||||||
\(199\) | −2.22255 | −0.157553 | −0.0787763 | − | 0.996892i | \(-0.525101\pi\) | ||||
−0.0787763 | + | 0.996892i | \(0.525101\pi\) | |||||||
\(200\) | 18.1503 | 1.28342 | ||||||||
\(201\) | 2.03439 | 0.143495 | ||||||||
\(202\) | −14.3072 | −1.00665 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.72043 | 0.470524 | ||||||||
\(205\) | −3.35114 | −0.234053 | ||||||||
\(206\) | −8.28954 | −0.577559 | ||||||||
\(207\) | −36.4074 | −2.53049 | ||||||||
\(208\) | −2.14507 | −0.148734 | ||||||||
\(209\) | 0.259531 | 0.0179521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4514 | −1.20141 | −0.600703 | − | 0.799473i | \(-0.705112\pi\) | ||||
−0.600703 | + | 0.799473i | \(0.705112\pi\) | |||||||
\(212\) | −7.30327 | −0.501591 | ||||||||
\(213\) | 10.9475 | 0.750110 | ||||||||
\(214\) | −8.04059 | −0.549643 | ||||||||
\(215\) | −11.8656 | −0.809226 | ||||||||
\(216\) | 14.8735 | 1.01202 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.98201 | −0.608338 | ||||||||
\(219\) | −33.6257 | −2.27221 | ||||||||
\(220\) | −0.812503 | −0.0547790 | ||||||||
\(221\) | −10.5729 | −0.711212 | ||||||||
\(222\) | −20.1204 | −1.35039 | ||||||||
\(223\) | 25.4204 | 1.70228 | 0.851139 | − | 0.524940i | \(-0.175912\pi\) | ||||
0.851139 | + | 0.524940i | \(0.175912\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 30.0608 | 2.00405 | ||||||||
\(226\) | −2.35679 | −0.156772 | ||||||||
\(227\) | 16.6990 | 1.10835 | 0.554175 | − | 0.832400i | \(-0.313034\pi\) | ||||
0.554175 | + | 0.832400i | \(0.313034\pi\) | |||||||
\(228\) | 3.87893 | 0.256888 | ||||||||
\(229\) | 11.6228 | 0.768059 | 0.384030 | − | 0.923321i | \(-0.374536\pi\) | ||||
0.384030 | + | 0.923321i | \(0.374536\pi\) | |||||||
\(230\) | −23.4741 | −1.54784 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.85590 | 0.318805 | ||||||||
\(233\) | −16.9966 | −1.11348 | −0.556741 | − | 0.830686i | \(-0.687948\pi\) | ||||
−0.556741 | + | 0.830686i | \(0.687948\pi\) | |||||||
\(234\) | −22.4370 | −1.46675 | ||||||||
\(235\) | 26.7854 | 1.74728 | ||||||||
\(236\) | −10.0025 | −0.651110 | ||||||||
\(237\) | 17.0036 | 1.10450 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.1928 | 1.11211 | 0.556056 | − | 0.831145i | \(-0.312314\pi\) | ||||
0.556056 | + | 0.831145i | \(0.312314\pi\) | |||||||
\(240\) | 4.01447 | 0.259133 | ||||||||
\(241\) | 15.5596 | 1.00228 | 0.501140 | − | 0.865366i | \(-0.332914\pi\) | ||||
0.501140 | + | 0.865366i | \(0.332914\pi\) | |||||||
\(242\) | 10.1697 | 0.653735 | ||||||||
\(243\) | −15.8583 | −1.01731 | ||||||||
\(244\) | −11.6734 | −0.747310 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.59691 | −0.165573 | ||||||||
\(247\) | −6.10253 | −0.388295 | ||||||||
\(248\) | 24.7217 | 1.56983 | ||||||||
\(249\) | 38.2222 | 2.42223 | ||||||||
\(250\) | 3.82691 | 0.242035 | ||||||||
\(251\) | −0.255136 | −0.0161040 | −0.00805201 | − | 0.999968i | \(-0.502563\pi\) | ||||
−0.00805201 | + | 0.999968i | \(0.502563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60736 | 0.101054 | ||||||||
\(254\) | 6.47028 | 0.405981 | ||||||||
\(255\) | 19.7871 | 1.23912 | ||||||||
\(256\) | −16.7914 | −1.04946 | ||||||||
\(257\) | −1.60836 | −0.100327 | −0.0501634 | − | 0.998741i | \(-0.515974\pi\) | ||||
−0.0501634 | + | 0.998741i | \(0.515974\pi\) | |||||||
\(258\) | −9.19504 | −0.572458 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 19.1050 | 1.18484 | ||||||||
\(261\) | 8.04241 | 0.497813 | ||||||||
\(262\) | −10.6941 | −0.660682 | ||||||||
\(263\) | −14.1955 | −0.875332 | −0.437666 | − | 0.899138i | \(-0.644195\pi\) | ||||
−0.437666 | + | 0.899138i | \(0.644195\pi\) | |||||||
\(264\) | −1.73604 | −0.106846 | ||||||||
\(265\) | −21.5032 | −1.32093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.7448 | 2.43234 | ||||||||
\(268\) | −0.827741 | −0.0505624 | ||||||||
\(269\) | −13.8844 | −0.846546 | −0.423273 | − | 0.906002i | \(-0.639119\pi\) | ||||
−0.423273 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(270\) | 15.8829 | 0.966603 | ||||||||
\(271\) | −15.9163 | −0.966844 | −0.483422 | − | 0.875388i | \(-0.660606\pi\) | ||||
−0.483422 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(272\) | 0.903939 | 0.0548093 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.8613 | 1.26027 | ||||||||
\(275\) | −1.32716 | −0.0800307 | ||||||||
\(276\) | 24.0234 | 1.44604 | ||||||||
\(277\) | 0.891025 | 0.0535365 | 0.0267683 | − | 0.999642i | \(-0.491478\pi\) | ||||
0.0267683 | + | 0.999642i | \(0.491478\pi\) | |||||||
\(278\) | −18.3012 | −1.09763 | ||||||||
\(279\) | 40.9444 | 2.45128 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1116 | 0.782174 | 0.391087 | − | 0.920354i | \(-0.372099\pi\) | ||||
0.391087 | + | 0.920354i | \(0.372099\pi\) | |||||||
\(282\) | 20.7569 | 1.23605 | ||||||||
\(283\) | −16.6776 | −0.991378 | −0.495689 | − | 0.868500i | \(-0.665084\pi\) | ||||
−0.495689 | + | 0.868500i | \(0.665084\pi\) | |||||||
\(284\) | −4.45427 | −0.264312 | ||||||||
\(285\) | 11.4208 | 0.676512 | ||||||||
\(286\) | 0.990576 | 0.0585740 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −26.1957 | −1.54360 | ||||||||
\(289\) | −12.5445 | −0.737914 | ||||||||
\(290\) | 5.18544 | 0.304499 | ||||||||
\(291\) | −36.5088 | −2.14019 | ||||||||
\(292\) | 13.6815 | 0.800647 | ||||||||
\(293\) | 1.62730 | 0.0950678 | 0.0475339 | − | 0.998870i | \(-0.484864\pi\) | ||||
0.0475339 | + | 0.998870i | \(0.484864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.4508 | −1.71469 | ||||||||
\(296\) | 22.5719 | 1.31196 | ||||||||
\(297\) | −1.08756 | −0.0631067 | ||||||||
\(298\) | −10.5340 | −0.610218 | ||||||||
\(299\) | −37.7949 | −2.18574 | ||||||||
\(300\) | −19.8356 | −1.14521 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.82510 | 0.105023 | ||||||||
\(303\) | 43.1109 | 2.47666 | ||||||||
\(304\) | 0.521740 | 0.0299238 | ||||||||
\(305\) | −34.3702 | −1.96803 | ||||||||
\(306\) | 9.45503 | 0.540508 | ||||||||
\(307\) | −8.30009 | −0.473711 | −0.236856 | − | 0.971545i | \(-0.576117\pi\) | ||||
−0.236856 | + | 0.971545i | \(0.576117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.9783 | 1.42097 | ||||||||
\(310\) | 26.3994 | 1.49938 | ||||||||
\(311\) | −0.157416 | −0.00892624 | −0.00446312 | − | 0.999990i | \(-0.501421\pi\) | ||||
−0.00446312 | + | 0.999990i | \(0.501421\pi\) | |||||||
\(312\) | 40.8207 | 2.31102 | ||||||||
\(313\) | 13.3874 | 0.756702 | 0.378351 | − | 0.925662i | \(-0.376491\pi\) | ||||
0.378351 | + | 0.925662i | \(0.376491\pi\) | |||||||
\(314\) | −18.5478 | −1.04671 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.91833 | −0.389187 | ||||||||
\(317\) | 32.4429 | 1.82218 | 0.911088 | − | 0.412211i | \(-0.135243\pi\) | ||||
0.911088 | + | 0.412211i | \(0.135243\pi\) | |||||||
\(318\) | −16.6636 | −0.934446 | ||||||||
\(319\) | −0.355066 | −0.0198799 | ||||||||
\(320\) | −19.7602 | −1.10463 | ||||||||
\(321\) | 24.2282 | 1.35228 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.57163 | 0.143089 | ||||||||
\(324\) | 0.220627 | 0.0122571 | ||||||||
\(325\) | 31.2064 | 1.73102 | ||||||||
\(326\) | −7.01592 | −0.388576 | ||||||||
\(327\) | 27.0649 | 1.49669 | ||||||||
\(328\) | 2.91332 | 0.160861 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.85385 | −0.102051 | ||||||||
\(331\) | −20.0148 | −1.10011 | −0.550057 | − | 0.835127i | \(-0.685394\pi\) | ||||
−0.550057 | + | 0.835127i | \(0.685394\pi\) | |||||||
\(332\) | −15.5517 | −0.853508 | ||||||||
\(333\) | 37.3839 | 2.04862 | ||||||||
\(334\) | 10.7737 | 0.589509 | ||||||||
\(335\) | −2.43714 | −0.133155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.20111 | −0.174376 | −0.0871878 | − | 0.996192i | \(-0.527788\pi\) | ||||
−0.0871878 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(338\) | −11.2235 | −0.610481 | ||||||||
\(339\) | 7.10157 | 0.385704 | ||||||||
\(340\) | −8.05090 | −0.436621 | ||||||||
\(341\) | −1.80766 | −0.0978904 | ||||||||
\(342\) | 5.45730 | 0.295097 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.3154 | 0.556168 | ||||||||
\(345\) | 70.7329 | 3.80813 | ||||||||
\(346\) | 12.3904 | 0.666110 | ||||||||
\(347\) | 6.12096 | 0.328590 | 0.164295 | − | 0.986411i | \(-0.447465\pi\) | ||||
0.164295 | + | 0.986411i | \(0.447465\pi\) | |||||||
\(348\) | −5.30679 | −0.284474 | ||||||||
\(349\) | 36.3598 | 1.94629 | 0.973147 | − | 0.230183i | \(-0.0739326\pi\) | ||||
0.973147 | + | 0.230183i | \(0.0739326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.5726 | 1.36496 | ||||||||
\(352\) | 1.15652 | 0.0616427 | ||||||||
\(353\) | −16.2502 | −0.864913 | −0.432456 | − | 0.901655i | \(-0.642353\pi\) | ||||
−0.432456 | + | 0.901655i | \(0.642353\pi\) | |||||||
\(354\) | −22.8224 | −1.21299 | ||||||||
\(355\) | −13.1148 | −0.696063 | ||||||||
\(356\) | −16.1712 | −0.857070 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.9928 | 1.10950 | ||||||||
\(359\) | −18.2251 | −0.961883 | −0.480942 | − | 0.876753i | \(-0.659705\pi\) | ||||
−0.480942 | + | 0.876753i | \(0.659705\pi\) | |||||||
\(360\) | −47.1069 | −2.48275 | ||||||||
\(361\) | −17.5157 | −0.921879 | ||||||||
\(362\) | 23.1528 | 1.21688 | ||||||||
\(363\) | −30.6437 | −1.60838 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.2827 | 2.10849 | ||||||||
\(366\) | −26.6346 | −1.39221 | ||||||||
\(367\) | 19.8542 | 1.03638 | 0.518189 | − | 0.855266i | \(-0.326606\pi\) | ||||
0.518189 | + | 0.855266i | \(0.326606\pi\) | |||||||
\(368\) | 3.23130 | 0.168443 | ||||||||
\(369\) | 4.82508 | 0.251184 | ||||||||
\(370\) | 24.1037 | 1.25309 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −27.0172 | −1.40078 | ||||||||
\(373\) | −18.9596 | −0.981691 | −0.490845 | − | 0.871247i | \(-0.663312\pi\) | ||||
−0.490845 | + | 0.871247i | \(0.663312\pi\) | |||||||
\(374\) | −0.417432 | −0.0215849 | ||||||||
\(375\) | −11.5314 | −0.595477 | ||||||||
\(376\) | −23.2859 | −1.20088 | ||||||||
\(377\) | 8.34892 | 0.429991 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4927 | 1.36084 | 0.680420 | − | 0.732822i | \(-0.261797\pi\) | ||||
0.680420 | + | 0.732822i | \(0.261797\pi\) | |||||||
\(380\) | −4.64686 | −0.238379 | ||||||||
\(381\) | −19.4965 | −0.998834 | ||||||||
\(382\) | −3.67792 | −0.188179 | ||||||||
\(383\) | 4.78200 | 0.244349 | 0.122174 | − | 0.992509i | \(-0.461013\pi\) | ||||
0.122174 | + | 0.992509i | \(0.461013\pi\) | |||||||
\(384\) | 15.0610 | 0.768580 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.78880 | −0.0910477 | ||||||||
\(387\) | 17.0845 | 0.868453 | ||||||||
\(388\) | 14.8545 | 0.754125 | ||||||||
\(389\) | −18.4864 | −0.937297 | −0.468649 | − | 0.883385i | \(-0.655259\pi\) | ||||
−0.468649 | + | 0.883385i | \(0.655259\pi\) | |||||||
\(390\) | 43.5910 | 2.20731 | ||||||||
\(391\) | 15.9269 | 0.805459 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.2237 | 1.62547 | ||||||||
\(394\) | 23.9309 | 1.20562 | ||||||||
\(395\) | −20.3698 | −1.02492 | ||||||||
\(396\) | 1.16987 | 0.0587882 | ||||||||
\(397\) | 7.32932 | 0.367848 | 0.183924 | − | 0.982940i | \(-0.441120\pi\) | ||||
0.183924 | + | 0.982940i | \(0.441120\pi\) | |||||||
\(398\) | 2.06331 | 0.103424 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.66801 | −0.133401 | ||||||||
\(401\) | −20.7464 | −1.03603 | −0.518013 | − | 0.855373i | \(-0.673328\pi\) | ||||
−0.518013 | + | 0.855373i | \(0.673328\pi\) | |||||||
\(402\) | −1.88862 | −0.0941959 | ||||||||
\(403\) | 42.5048 | 2.11732 | ||||||||
\(404\) | −17.5408 | −0.872685 | ||||||||
\(405\) | 0.649599 | 0.0322789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.65047 | −0.0818107 | ||||||||
\(408\) | −17.2020 | −0.851626 | ||||||||
\(409\) | −22.2182 | −1.09862 | −0.549309 | − | 0.835619i | \(-0.685109\pi\) | ||||
−0.549309 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(410\) | 3.11103 | 0.153643 | ||||||||
\(411\) | −62.8598 | −3.10065 | ||||||||
\(412\) | −10.1631 | −0.500698 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 33.7988 | 1.66112 | ||||||||
\(415\) | −45.7892 | −2.24770 | ||||||||
\(416\) | −27.1941 | −1.33330 | ||||||||
\(417\) | 55.1457 | 2.70050 | ||||||||
\(418\) | −0.240935 | −0.0117845 | ||||||||
\(419\) | −12.9754 | −0.633891 | −0.316946 | − | 0.948444i | \(-0.602657\pi\) | ||||
−0.316946 | + | 0.948444i | \(0.602657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.74986 | 0.231494 | 0.115747 | − | 0.993279i | \(-0.463074\pi\) | ||||
0.115747 | + | 0.993279i | \(0.463074\pi\) | |||||||
\(422\) | 16.2010 | 0.788654 | ||||||||
\(423\) | −38.5665 | −1.87517 | ||||||||
\(424\) | 18.6939 | 0.907855 | ||||||||
\(425\) | −13.1505 | −0.637893 | ||||||||
\(426\) | −10.1631 | −0.492404 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.85784 | −0.476497 | ||||||||
\(429\) | −2.98483 | −0.144109 | ||||||||
\(430\) | 11.0154 | 0.531211 | ||||||||
\(431\) | −15.3617 | −0.739946 | −0.369973 | − | 0.929043i | \(-0.620633\pi\) | ||||
−0.369973 | + | 0.929043i | \(0.620633\pi\) | |||||||
\(432\) | −2.18634 | −0.105191 | ||||||||
\(433\) | −7.36716 | −0.354043 | −0.177021 | − | 0.984207i | \(-0.556646\pi\) | ||||
−0.177021 | + | 0.984207i | \(0.556646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.6249 | −0.749158 | ||||||||
\(436\) | −11.0120 | −0.527381 | ||||||||
\(437\) | 9.19277 | 0.439750 | ||||||||
\(438\) | 31.2164 | 1.49158 | ||||||||
\(439\) | 24.7483 | 1.18117 | 0.590585 | − | 0.806975i | \(-0.298897\pi\) | ||||
0.590585 | + | 0.806975i | \(0.298897\pi\) | |||||||
\(440\) | 2.07973 | 0.0991473 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.81538 | 0.466870 | ||||||||
\(443\) | −20.5194 | −0.974908 | −0.487454 | − | 0.873149i | \(-0.662074\pi\) | ||||
−0.487454 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(444\) | −24.6678 | −1.17068 | ||||||||
\(445\) | −47.6132 | −2.25708 | ||||||||
\(446\) | −23.5991 | −1.11745 | ||||||||
\(447\) | 31.7414 | 1.50131 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.31955 | 0.298238 | 0.149119 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149119 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(450\) | −27.9069 | −1.31555 | ||||||||
\(451\) | −0.213023 | −0.0100309 | ||||||||
\(452\) | −2.88945 | −0.135908 | ||||||||
\(453\) | −5.49944 | −0.258386 | ||||||||
\(454\) | −15.5025 | −0.727568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.92873 | −0.464955 | ||||||||
\(457\) | −13.8770 | −0.649141 | −0.324570 | − | 0.945862i | \(-0.605220\pi\) | ||||
−0.324570 | + | 0.945862i | \(0.605220\pi\) | |||||||
\(458\) | −10.7901 | −0.504187 | ||||||||
\(459\) | −10.7764 | −0.502998 | ||||||||
\(460\) | −28.7795 | −1.34185 | ||||||||
\(461\) | 3.52429 | 0.164142 | 0.0820712 | − | 0.996626i | \(-0.473847\pi\) | ||||
0.0820712 | + | 0.996626i | \(0.473847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.56453 | −0.258606 | −0.129303 | − | 0.991605i | \(-0.541274\pi\) | ||||
−0.129303 | + | 0.991605i | \(0.541274\pi\) | |||||||
\(464\) | −0.713796 | −0.0331371 | ||||||||
\(465\) | −79.5475 | −3.68893 | ||||||||
\(466\) | 15.7788 | 0.730937 | ||||||||
\(467\) | −16.0538 | −0.742882 | −0.371441 | − | 0.928457i | \(-0.621136\pi\) | ||||
−0.371441 | + | 0.928457i | \(0.621136\pi\) | |||||||
\(468\) | −27.5080 | −1.27156 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.8662 | −1.14699 | ||||||||
\(471\) | 55.8888 | 2.57522 | ||||||||
\(472\) | 25.6031 | 1.17848 | ||||||||
\(473\) | −0.754266 | −0.0346812 | ||||||||
\(474\) | −15.7853 | −0.725041 | ||||||||
\(475\) | −7.59027 | −0.348266 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.9611 | 1.41761 | ||||||||
\(478\) | −15.9610 | −0.730038 | ||||||||
\(479\) | 39.1087 | 1.78692 | 0.893462 | − | 0.449139i | \(-0.148269\pi\) | ||||
0.893462 | + | 0.449139i | \(0.148269\pi\) | |||||||
\(480\) | 50.8935 | 2.32296 | ||||||||
\(481\) | 38.8086 | 1.76952 | ||||||||
\(482\) | −14.4447 | −0.657940 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.4682 | 0.566735 | ||||||||
\(485\) | 43.7367 | 1.98598 | ||||||||
\(486\) | 14.7221 | 0.667807 | ||||||||
\(487\) | −21.1878 | −0.960112 | −0.480056 | − | 0.877238i | \(-0.659384\pi\) | ||||
−0.480056 | + | 0.877238i | \(0.659384\pi\) | |||||||
\(488\) | 29.8798 | 1.35260 | ||||||||
\(489\) | 21.1406 | 0.956011 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.80565 | 0.397394 | 0.198697 | − | 0.980061i | \(-0.436329\pi\) | ||||
0.198697 | + | 0.980061i | \(0.436329\pi\) | |||||||
\(492\) | −3.18383 | −0.143538 | ||||||||
\(493\) | −3.51826 | −0.158455 | ||||||||
\(494\) | 5.66529 | 0.254893 | ||||||||
\(495\) | 3.44448 | 0.154818 | ||||||||
\(496\) | −3.63398 | −0.163170 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −35.4835 | −1.59006 | ||||||||
\(499\) | −22.7575 | −1.01876 | −0.509382 | − | 0.860541i | \(-0.670126\pi\) | ||||
−0.509382 | + | 0.860541i | \(0.670126\pi\) | |||||||
\(500\) | 4.69183 | 0.209825 | ||||||||
\(501\) | −32.4636 | −1.45037 | ||||||||
\(502\) | 0.236855 | 0.0105714 | ||||||||
\(503\) | −15.5778 | −0.694578 | −0.347289 | − | 0.937758i | \(-0.612898\pi\) | ||||
−0.347289 | + | 0.937758i | \(0.612898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.6458 | −2.29821 | ||||||||
\(506\) | −1.49219 | −0.0663359 | ||||||||
\(507\) | 33.8192 | 1.50196 | ||||||||
\(508\) | 7.93263 | 0.351953 | ||||||||
\(509\) | 8.00848 | 0.354970 | 0.177485 | − | 0.984124i | \(-0.443204\pi\) | ||||
0.177485 | + | 0.984124i | \(0.443204\pi\) | |||||||
\(510\) | −18.3694 | −0.813410 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.82020 | 0.213025 | ||||||||
\(513\) | −6.21996 | −0.274618 | ||||||||
\(514\) | 1.49312 | 0.0658588 | ||||||||
\(515\) | −29.9234 | −1.31858 | ||||||||
\(516\) | −11.2732 | −0.496275 | ||||||||
\(517\) | 1.70268 | 0.0748838 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.3350 | −1.63883 | ||||||||
\(520\) | −48.9022 | −2.14450 | ||||||||
\(521\) | −5.96444 | −0.261307 | −0.130654 | − | 0.991428i | \(-0.541708\pi\) | ||||
−0.130654 | + | 0.991428i | \(0.541708\pi\) | |||||||
\(522\) | −7.46617 | −0.326785 | ||||||||
\(523\) | 9.61460 | 0.420417 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(524\) | −13.1110 | −0.572758 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.1784 | 0.574605 | ||||||||
\(527\) | −17.9117 | −0.780246 | ||||||||
\(528\) | 0.255190 | 0.0111057 | ||||||||
\(529\) | 33.9337 | 1.47538 | ||||||||
\(530\) | 19.9625 | 0.867116 | ||||||||
\(531\) | 42.4042 | 1.84019 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.00897 | 0.216963 | ||||||||
\(534\) | −36.8970 | −1.59669 | ||||||||
\(535\) | −29.0247 | −1.25485 | ||||||||
\(536\) | 2.11874 | 0.0915154 | ||||||||
\(537\) | −63.2561 | −2.72970 | ||||||||
\(538\) | 12.8896 | 0.555709 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.4726 | 0.837967 | ||||||||
\(541\) | −13.6461 | −0.586691 | −0.293346 | − | 0.956006i | \(-0.594769\pi\) | ||||
−0.293346 | + | 0.956006i | \(0.594769\pi\) | |||||||
\(542\) | 14.7759 | 0.634677 | ||||||||
\(543\) | −69.7648 | −2.99389 | ||||||||
\(544\) | 11.4597 | 0.491330 | ||||||||
\(545\) | −32.4230 | −1.38885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.87328 | −0.122852 | −0.0614262 | − | 0.998112i | \(-0.519565\pi\) | ||||
−0.0614262 | + | 0.998112i | \(0.519565\pi\) | |||||||
\(548\) | 25.5761 | 1.09256 | ||||||||
\(549\) | 49.4874 | 2.11207 | ||||||||
\(550\) | 1.23207 | 0.0525356 | ||||||||
\(551\) | −2.03069 | −0.0865102 | ||||||||
\(552\) | −61.4918 | −2.61726 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.827183 | −0.0351436 | ||||||||
\(555\) | −72.6301 | −3.08297 | ||||||||
\(556\) | −22.4374 | −0.951559 | ||||||||
\(557\) | 16.3276 | 0.691823 | 0.345911 | − | 0.938267i | \(-0.387570\pi\) | ||||
0.345911 | + | 0.938267i | \(0.387570\pi\) | |||||||
\(558\) | −38.0107 | −1.60912 | ||||||||
\(559\) | 17.7356 | 0.750136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.25782 | 0.0531052 | ||||||||
\(562\) | −12.1722 | −0.513452 | ||||||||
\(563\) | −27.3560 | −1.15292 | −0.576459 | − | 0.817126i | \(-0.695566\pi\) | ||||
−0.576459 | + | 0.817126i | \(0.695566\pi\) | |||||||
\(564\) | 25.4481 | 1.07156 | ||||||||
\(565\) | −8.50750 | −0.357913 | ||||||||
\(566\) | 15.4826 | 0.650782 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.4014 | 0.478392 | ||||||||
\(569\) | −5.83582 | −0.244650 | −0.122325 | − | 0.992490i | \(-0.539035\pi\) | ||||
−0.122325 | + | 0.992490i | \(0.539035\pi\) | |||||||
\(570\) | −10.6025 | −0.444091 | ||||||||
\(571\) | 10.5953 | 0.443401 | 0.221700 | − | 0.975115i | \(-0.428839\pi\) | ||||
0.221700 | + | 0.975115i | \(0.428839\pi\) | |||||||
\(572\) | 1.21446 | 0.0507789 | ||||||||
\(573\) | 11.0824 | 0.462975 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −47.0090 | −1.96041 | ||||||||
\(576\) | 28.4514 | 1.18548 | ||||||||
\(577\) | 7.00274 | 0.291528 | 0.145764 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145764 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(578\) | 11.6457 | 0.484398 | ||||||||
\(579\) | 5.39008 | 0.224004 | ||||||||
\(580\) | 6.35740 | 0.263977 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 33.8930 | 1.40491 | ||||||||
\(583\) | −1.36691 | −0.0566115 | ||||||||
\(584\) | −35.0199 | −1.44913 | ||||||||
\(585\) | −80.9925 | −3.34863 | ||||||||
\(586\) | −1.51070 | −0.0624065 | ||||||||
\(587\) | −29.8962 | −1.23395 | −0.616974 | − | 0.786983i | \(-0.711642\pi\) | ||||
−0.616974 | + | 0.786983i | \(0.711642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3384 | −0.425985 | ||||||||
\(590\) | 27.3406 | 1.12560 | ||||||||
\(591\) | −72.1094 | −2.96618 | ||||||||
\(592\) | −3.31797 | −0.136368 | ||||||||
\(593\) | 18.6873 | 0.767395 | 0.383698 | − | 0.923459i | \(-0.374650\pi\) | ||||
0.383698 | + | 0.923459i | \(0.374650\pi\) | |||||||
\(594\) | 1.00964 | 0.0414259 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9148 | −0.529010 | ||||||||
\(597\) | −6.21723 | −0.254454 | ||||||||
\(598\) | 35.0869 | 1.43481 | ||||||||
\(599\) | −18.9893 | −0.775882 | −0.387941 | − | 0.921684i | \(-0.626814\pi\) | ||||
−0.387941 | + | 0.921684i | \(0.626814\pi\) | |||||||
\(600\) | 50.7724 | 2.07278 | ||||||||
\(601\) | 21.2130 | 0.865298 | 0.432649 | − | 0.901563i | \(-0.357579\pi\) | ||||
0.432649 | + | 0.901563i | \(0.357579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.50908 | 0.142901 | ||||||||
\(604\) | 2.23759 | 0.0910462 | ||||||||
\(605\) | 36.7104 | 1.49249 | ||||||||
\(606\) | −40.0220 | −1.62578 | ||||||||
\(607\) | 35.2077 | 1.42904 | 0.714518 | − | 0.699617i | \(-0.246646\pi\) | ||||
0.714518 | + | 0.699617i | \(0.246646\pi\) | |||||||
\(608\) | 6.61435 | 0.268247 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31.9076 | 1.29190 | ||||||||
\(611\) | −40.0363 | −1.61970 | ||||||||
\(612\) | 11.5920 | 0.468577 | ||||||||
\(613\) | 17.2390 | 0.696278 | 0.348139 | − | 0.937443i | \(-0.386814\pi\) | ||||
0.348139 | + | 0.937443i | \(0.386814\pi\) | |||||||
\(614\) | 7.70539 | 0.310964 | ||||||||
\(615\) | −9.37425 | −0.378006 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6614 | 0.872055 | 0.436027 | − | 0.899933i | \(-0.356385\pi\) | ||||
0.436027 | + | 0.899933i | \(0.356385\pi\) | |||||||
\(618\) | −23.1886 | −0.932783 | ||||||||
\(619\) | 19.8892 | 0.799416 | 0.399708 | − | 0.916643i | \(-0.369112\pi\) | ||||
0.399708 | + | 0.916643i | \(0.369112\pi\) | |||||||
\(620\) | 32.3659 | 1.29985 | ||||||||
\(621\) | −38.5222 | −1.54584 | ||||||||
\(622\) | 0.146137 | 0.00585956 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00047 | −0.240211 | ||||||||
\(625\) | −17.3363 | −0.693451 | ||||||||
\(626\) | −12.4282 | −0.496732 | ||||||||
\(627\) | 0.725995 | 0.0289934 | ||||||||
\(628\) | −22.7398 | −0.907415 | ||||||||
\(629\) | −16.3541 | −0.652081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.5292 | −1.13573 | −0.567865 | − | 0.823122i | \(-0.692230\pi\) | ||||
−0.567865 | + | 0.823122i | \(0.692230\pi\) | |||||||
\(632\) | 17.7086 | 0.704409 | ||||||||
\(633\) | −48.8175 | −1.94032 | ||||||||
\(634\) | −30.1184 | −1.19615 | ||||||||
\(635\) | 23.3563 | 0.926865 | ||||||||
\(636\) | −20.4297 | −0.810090 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.329626 | 0.0130500 | ||||||||
\(639\) | 18.8832 | 0.747007 | ||||||||
\(640\) | −18.0427 | −0.713202 | ||||||||
\(641\) | 8.47489 | 0.334738 | 0.167369 | − | 0.985894i | \(-0.446473\pi\) | ||||
0.167369 | + | 0.985894i | \(0.446473\pi\) | |||||||
\(642\) | −22.4922 | −0.887697 | ||||||||
\(643\) | 19.9388 | 0.786309 | 0.393155 | − | 0.919472i | \(-0.371384\pi\) | ||||
0.393155 | + | 0.919472i | \(0.371384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.1920 | −1.30693 | ||||||||
\(646\) | −2.38737 | −0.0939299 | ||||||||
\(647\) | 18.2089 | 0.715867 | 0.357933 | − | 0.933747i | \(-0.383482\pi\) | ||||
0.357933 | + | 0.933747i | \(0.383482\pi\) | |||||||
\(648\) | −0.564731 | −0.0221847 | ||||||||
\(649\) | −1.87211 | −0.0734868 | ||||||||
\(650\) | −28.9705 | −1.13632 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.60158 | −0.336864 | ||||||||
\(653\) | 34.2135 | 1.33888 | 0.669439 | − | 0.742867i | \(-0.266534\pi\) | ||||
0.669439 | + | 0.742867i | \(0.266534\pi\) | |||||||
\(654\) | −25.1257 | −0.982492 | ||||||||
\(655\) | −38.6032 | −1.50835 | ||||||||
\(656\) | −0.428245 | −0.0167202 | ||||||||
\(657\) | −58.0004 | −2.26281 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.42703 | 0.133498 | 0.0667491 | − | 0.997770i | \(-0.478737\pi\) | ||||
0.0667491 | + | 0.997770i | \(0.478737\pi\) | |||||||
\(660\) | −2.27284 | −0.0884703 | ||||||||
\(661\) | −37.8346 | −1.47160 | −0.735798 | − | 0.677201i | \(-0.763193\pi\) | ||||
−0.735798 | + | 0.677201i | \(0.763193\pi\) | |||||||
\(662\) | 18.5808 | 0.722162 | ||||||||
\(663\) | −29.5760 | −1.14864 | ||||||||
\(664\) | 39.8069 | 1.54481 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −34.7053 | −1.34480 | ||||||||
\(667\) | −12.5767 | −0.486972 | ||||||||
\(668\) | 13.2086 | 0.511057 | ||||||||
\(669\) | 71.1095 | 2.74925 | ||||||||
\(670\) | 2.26252 | 0.0874088 | ||||||||
\(671\) | −2.18483 | −0.0843444 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.1061 | 0.929222 | 0.464611 | − | 0.885515i | \(-0.346194\pi\) | ||||
0.464611 | + | 0.885515i | \(0.346194\pi\) | |||||||
\(674\) | 2.97175 | 0.114468 | ||||||||
\(675\) | 31.8069 | 1.22425 | ||||||||
\(676\) | −13.7602 | −0.529238 | ||||||||
\(677\) | −0.831150 | −0.0319437 | −0.0159719 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159719 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(678\) | −6.59274 | −0.253193 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.6076 | 0.790264 | ||||||||
\(681\) | 46.7126 | 1.79003 | ||||||||
\(682\) | 1.67814 | 0.0642594 | ||||||||
\(683\) | 1.39137 | 0.0532393 | 0.0266197 | − | 0.999646i | \(-0.491526\pi\) | ||||
0.0266197 | + | 0.999646i | \(0.491526\pi\) | |||||||
\(684\) | 6.69070 | 0.255825 | ||||||||
\(685\) | 75.3045 | 2.87724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.5130 | 1.24045 | ||||||||
\(688\) | −1.51632 | −0.0578090 | ||||||||
\(689\) | 32.1410 | 1.22448 | ||||||||
\(690\) | −65.6649 | −2.49982 | ||||||||
\(691\) | −16.4243 | −0.624809 | −0.312404 | − | 0.949949i | \(-0.601134\pi\) | ||||
−0.312404 | + | 0.949949i | \(0.601134\pi\) | |||||||
\(692\) | 15.1907 | 0.577464 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.68239 | −0.215701 | ||||||||
\(695\) | −66.0632 | −2.50592 | ||||||||
\(696\) | 13.5836 | 0.514884 | ||||||||
\(697\) | −2.11080 | −0.0799522 | ||||||||
\(698\) | −33.7546 | −1.27763 | ||||||||
\(699\) | −47.5451 | −1.79832 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7745 | 0.595796 | 0.297898 | − | 0.954598i | \(-0.403714\pi\) | ||||
0.297898 | + | 0.954598i | \(0.403714\pi\) | |||||||
\(702\) | −23.7403 | −0.896020 | ||||||||
\(703\) | −9.43934 | −0.356011 | ||||||||
\(704\) | −1.25611 | −0.0473413 | ||||||||
\(705\) | 74.9276 | 2.82194 | ||||||||
\(706\) | 15.0859 | 0.567766 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −27.9804 | −1.05157 | ||||||||
\(709\) | 11.7867 | 0.442657 | 0.221329 | − | 0.975199i | \(-0.428961\pi\) | ||||
0.221329 | + | 0.975199i | \(0.428961\pi\) | |||||||
\(710\) | 12.1752 | 0.456925 | ||||||||
\(711\) | 29.3292 | 1.09993 | ||||||||
\(712\) | 41.3926 | 1.55125 | ||||||||
\(713\) | −64.0287 | −2.39789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.57576 | 0.133726 | ||||||||
\(716\) | 25.7373 | 0.961850 | ||||||||
\(717\) | 48.0941 | 1.79611 | ||||||||
\(718\) | 16.9193 | 0.631421 | ||||||||
\(719\) | 42.9303 | 1.60103 | 0.800516 | − | 0.599311i | \(-0.204559\pi\) | ||||
0.800516 | + | 0.599311i | \(0.204559\pi\) | |||||||
\(720\) | 6.92451 | 0.258061 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.2607 | 0.605160 | ||||||||
\(723\) | 43.5253 | 1.61873 | ||||||||
\(724\) | 28.3856 | 1.05494 | ||||||||
\(725\) | 10.3843 | 0.385663 | ||||||||
\(726\) | 28.4481 | 1.05581 | ||||||||
\(727\) | −26.9295 | −0.998761 | −0.499381 | − | 0.866383i | \(-0.666439\pi\) | ||||
−0.499381 | + | 0.866383i | \(0.666439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7795 | −1.62146 | ||||||||
\(730\) | −37.3964 | −1.38410 | ||||||||
\(731\) | −7.47384 | −0.276430 | ||||||||
\(732\) | −32.6543 | −1.20694 | ||||||||
\(733\) | 8.48657 | 0.313459 | 0.156729 | − | 0.987642i | \(-0.449905\pi\) | ||||
0.156729 | + | 0.987642i | \(0.449905\pi\) | |||||||
\(734\) | −18.4316 | −0.680323 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.9648 | 1.50998 | ||||||||
\(737\) | −0.154923 | −0.00570667 | ||||||||
\(738\) | −4.47936 | −0.164888 | ||||||||
\(739\) | 28.1651 | 1.03607 | 0.518035 | − | 0.855360i | \(-0.326664\pi\) | ||||
0.518035 | + | 0.855360i | \(0.326664\pi\) | |||||||
\(740\) | 29.5514 | 1.08633 | ||||||||
\(741\) | −17.0708 | −0.627112 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.52995 | −0.0561286 | −0.0280643 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280643 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(744\) | 69.1548 | 2.53534 | ||||||||
\(745\) | −38.0253 | −1.39314 | ||||||||
\(746\) | 17.6011 | 0.644424 | ||||||||
\(747\) | 65.9288 | 2.41221 | ||||||||
\(748\) | −0.511776 | −0.0187124 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.7051 | 0.390896 | ||||||||
\(751\) | 30.5076 | 1.11324 | 0.556619 | − | 0.830768i | \(-0.312098\pi\) | ||||
0.556619 | + | 0.830768i | \(0.312098\pi\) | |||||||
\(752\) | 3.42293 | 0.124821 | ||||||||
\(753\) | −0.713700 | −0.0260087 | ||||||||
\(754\) | −7.75072 | −0.282264 | ||||||||
\(755\) | 6.58819 | 0.239769 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.9072 | −1.63218 | −0.816091 | − | 0.577924i | \(-0.803863\pi\) | ||||
−0.816091 | + | 0.577924i | \(0.803863\pi\) | |||||||
\(758\) | −24.5945 | −0.893314 | ||||||||
\(759\) | 4.49631 | 0.163206 | ||||||||
\(760\) | 11.8944 | 0.431454 | ||||||||
\(761\) | 20.2331 | 0.733448 | 0.366724 | − | 0.930330i | \(-0.380479\pi\) | ||||
0.366724 | + | 0.930330i | \(0.380479\pi\) | |||||||
\(762\) | 18.0995 | 0.655677 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.50917 | −0.163136 | ||||||||
\(765\) | 34.1305 | 1.23399 | ||||||||
\(766\) | −4.43937 | −0.160401 | ||||||||
\(767\) | 44.0203 | 1.58948 | ||||||||
\(768\) | −46.9713 | −1.69493 | ||||||||
\(769\) | 4.75064 | 0.171312 | 0.0856562 | − | 0.996325i | \(-0.472701\pi\) | ||||
0.0856562 | + | 0.996325i | \(0.472701\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.49913 | −0.162032 | ||||||||
\(772\) | −2.19309 | −0.0789310 | ||||||||
\(773\) | −16.4925 | −0.593195 | −0.296598 | − | 0.955003i | \(-0.595852\pi\) | ||||
−0.296598 | + | 0.955003i | \(0.595852\pi\) | |||||||
\(774\) | −15.8604 | −0.570089 | ||||||||
\(775\) | 52.8671 | 1.89904 | ||||||||
\(776\) | −38.0226 | −1.36493 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1618 | 0.615282 | ||||||||
\(779\) | −1.21832 | −0.0436509 | ||||||||
\(780\) | 53.4430 | 1.91357 | ||||||||
\(781\) | −0.833677 | −0.0298313 | ||||||||
\(782\) | −14.7857 | −0.528737 | ||||||||
\(783\) | 8.50958 | 0.304107 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −66.9533 | −2.38967 | ||||||||
\(786\) | −29.9149 | −1.06703 | ||||||||
\(787\) | −3.76198 | −0.134100 | −0.0670500 | − | 0.997750i | \(-0.521359\pi\) | ||||
−0.0670500 | + | 0.997750i | \(0.521359\pi\) | |||||||
\(788\) | 29.3395 | 1.04518 | ||||||||
\(789\) | −39.7096 | −1.41370 | ||||||||
\(790\) | 18.9103 | 0.672800 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.99447 | −0.106404 | ||||||||
\(793\) | 51.3734 | 1.82432 | ||||||||
\(794\) | −6.80417 | −0.241471 | ||||||||
\(795\) | −60.1517 | −2.13336 | ||||||||
\(796\) | 2.52964 | 0.0896606 | ||||||||
\(797\) | 6.88710 | 0.243954 | 0.121977 | − | 0.992533i | \(-0.461077\pi\) | ||||
0.121977 | + | 0.992533i | \(0.461077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8714 | 0.596869 | ||||||||
\(800\) | −33.8237 | −1.19585 | ||||||||
\(801\) | 68.5551 | 2.42228 | ||||||||
\(802\) | 19.2599 | 0.680092 | ||||||||
\(803\) | 2.56067 | 0.0903642 | ||||||||
\(804\) | −2.31547 | −0.0816603 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −39.4594 | −1.38990 | ||||||||
\(807\) | −38.8393 | −1.36721 | ||||||||
\(808\) | 44.8983 | 1.57952 | ||||||||
\(809\) | −20.0924 | −0.706412 | −0.353206 | − | 0.935546i | \(-0.614909\pi\) | ||||
−0.353206 | + | 0.935546i | \(0.614909\pi\) | |||||||
\(810\) | −0.603056 | −0.0211892 | ||||||||
\(811\) | −41.9779 | −1.47404 | −0.737021 | − | 0.675870i | \(-0.763768\pi\) | ||||
−0.737021 | + | 0.675870i | \(0.763768\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.5231 | −1.56149 | ||||||||
\(814\) | 1.53221 | 0.0537040 | ||||||||
\(815\) | −25.3259 | −0.887127 | ||||||||
\(816\) | 2.52862 | 0.0885194 | ||||||||
\(817\) | −4.31379 | −0.150920 | ||||||||
\(818\) | 20.6262 | 0.721180 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.81415 | 0.133196 | ||||||||
\(821\) | 8.31526 | 0.290205 | 0.145102 | − | 0.989417i | \(-0.453649\pi\) | ||||
0.145102 | + | 0.989417i | \(0.453649\pi\) | |||||||
\(822\) | 58.3559 | 2.03540 | ||||||||
\(823\) | 27.4626 | 0.957287 | 0.478644 | − | 0.878009i | \(-0.341129\pi\) | ||||
0.478644 | + | 0.878009i | \(0.341129\pi\) | |||||||
\(824\) | 26.0139 | 0.906239 | ||||||||
\(825\) | −3.71251 | −0.129253 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.14395 | −0.178873 | −0.0894363 | − | 0.995993i | \(-0.528507\pi\) | ||||
−0.0894363 | + | 0.995993i | \(0.528507\pi\) | |||||||
\(828\) | 41.4376 | 1.44006 | ||||||||
\(829\) | −40.2338 | −1.39738 | −0.698689 | − | 0.715425i | \(-0.746233\pi\) | ||||
−0.698689 | + | 0.715425i | \(0.746233\pi\) | |||||||
\(830\) | 42.5084 | 1.47549 | ||||||||
\(831\) | 2.49250 | 0.0864637 | ||||||||
\(832\) | 29.5357 | 1.02397 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −51.1946 | −1.77272 | ||||||||
\(835\) | 38.8905 | 1.34586 | ||||||||
\(836\) | −0.295389 | −0.0102163 | ||||||||
\(837\) | 43.3228 | 1.49745 | ||||||||
\(838\) | 12.0457 | 0.416113 | ||||||||
\(839\) | −53.2709 | −1.83912 | −0.919558 | − | 0.392955i | \(-0.871453\pi\) | ||||
−0.919558 | + | 0.392955i | \(0.871453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2218 | −0.904200 | ||||||||
\(842\) | −4.40953 | −0.151962 | ||||||||
\(843\) | 36.6776 | 1.26324 | ||||||||
\(844\) | 19.8626 | 0.683700 | ||||||||
\(845\) | −40.5145 | −1.39374 | ||||||||
\(846\) | 35.8032 | 1.23094 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.74792 | −0.0943639 | ||||||||
\(849\) | −46.6527 | −1.60112 | ||||||||
\(850\) | 12.2083 | 0.418740 | ||||||||
\(851\) | −58.4608 | −2.00401 | ||||||||
\(852\) | −12.4601 | −0.426875 | ||||||||
\(853\) | 15.3414 | 0.525280 | 0.262640 | − | 0.964894i | \(-0.415407\pi\) | ||||
0.262640 | + | 0.964894i | \(0.415407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.6996 | 0.673713 | ||||||||
\(856\) | 25.2327 | 0.862436 | ||||||||
\(857\) | −49.7610 | −1.69980 | −0.849901 | − | 0.526942i | \(-0.823339\pi\) | ||||
−0.849901 | + | 0.526942i | \(0.823339\pi\) | |||||||
\(858\) | 2.77097 | 0.0945994 | ||||||||
\(859\) | −49.3028 | −1.68219 | −0.841095 | − | 0.540888i | \(-0.818088\pi\) | ||||
−0.841095 | + | 0.540888i | \(0.818088\pi\) | |||||||
\(860\) | 13.5050 | 0.460517 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.2610 | 0.485732 | ||||||||
\(863\) | 38.3282 | 1.30471 | 0.652353 | − | 0.757915i | \(-0.273782\pi\) | ||||
0.652353 | + | 0.757915i | \(0.273782\pi\) | |||||||
\(864\) | −27.7174 | −0.942964 | ||||||||
\(865\) | 44.7264 | 1.52074 | ||||||||
\(866\) | 6.83930 | 0.232409 | ||||||||
\(867\) | −35.0912 | −1.19176 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.29486 | −0.0439251 | ||||||||
\(870\) | 14.5054 | 0.491779 | ||||||||
\(871\) | 3.64282 | 0.123432 | ||||||||
\(872\) | 28.1870 | 0.954534 | ||||||||
\(873\) | −62.9735 | −2.13133 | ||||||||
\(874\) | −8.53411 | −0.288671 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 38.2716 | 1.29308 | ||||||||
\(877\) | 22.3320 | 0.754099 | 0.377050 | − | 0.926193i | \(-0.376939\pi\) | ||||
0.377050 | + | 0.926193i | \(0.376939\pi\) | |||||||
\(878\) | −22.9751 | −0.775370 | ||||||||
\(879\) | 4.55210 | 0.153538 | ||||||||
\(880\) | −0.305711 | −0.0103055 | ||||||||
\(881\) | 31.3529 | 1.05631 | 0.528154 | − | 0.849149i | \(-0.322884\pi\) | ||||
0.528154 | + | 0.849149i | \(0.322884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.6378 | 0.930086 | 0.465043 | − | 0.885288i | \(-0.346039\pi\) | ||||
0.465043 | + | 0.885288i | \(0.346039\pi\) | |||||||
\(884\) | 12.0337 | 0.404739 | ||||||||
\(885\) | −82.3836 | −2.76929 | ||||||||
\(886\) | 19.0492 | 0.639971 | ||||||||
\(887\) | 39.8708 | 1.33873 | 0.669365 | − | 0.742934i | \(-0.266566\pi\) | ||||
0.669365 | + | 0.742934i | \(0.266566\pi\) | |||||||
\(888\) | 63.1411 | 2.11888 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 44.2017 | 1.48165 | ||||||||
\(891\) | 0.0412934 | 0.00138338 | ||||||||
\(892\) | −28.9327 | −0.968738 | ||||||||
\(893\) | 9.73794 | 0.325868 | ||||||||
\(894\) | −29.4671 | −0.985527 | ||||||||
\(895\) | 75.7792 | 2.53302 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −105.725 | −3.53005 | ||||||||
\(898\) | −5.86676 | −0.195776 | ||||||||
\(899\) | 14.1440 | 0.471728 | ||||||||
\(900\) | −34.2142 | −1.14047 | ||||||||
\(901\) | −13.5444 | −0.451228 | ||||||||
\(902\) | 0.197760 | 0.00658470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.39601 | 0.245988 | ||||||||
\(905\) | 83.5764 | 2.77817 | ||||||||
\(906\) | 5.10541 | 0.169616 | ||||||||
\(907\) | 16.8303 | 0.558839 | 0.279420 | − | 0.960169i | \(-0.409858\pi\) | ||||
0.279420 | + | 0.960169i | \(0.409858\pi\) | |||||||
\(908\) | −19.0062 | −0.630743 | ||||||||
\(909\) | 74.3613 | 2.46641 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7627 | −0.455978 | −0.227989 | − | 0.973664i | \(-0.573215\pi\) | ||||
−0.227989 | + | 0.973664i | \(0.573215\pi\) | |||||||
\(912\) | 1.45948 | 0.0483282 | ||||||||
\(913\) | −2.91071 | −0.0963303 | ||||||||
\(914\) | 12.8828 | 0.426124 | ||||||||
\(915\) | −96.1449 | −3.17845 | ||||||||
\(916\) | −13.2287 | −0.437089 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.0043 | 0.330190 | ||||||||
\(919\) | −8.00806 | −0.264161 | −0.132081 | − | 0.991239i | \(-0.542166\pi\) | ||||
−0.132081 | + | 0.991239i | \(0.542166\pi\) | |||||||
\(920\) | 73.6656 | 2.42868 | ||||||||
\(921\) | −23.2181 | −0.765063 | ||||||||
\(922\) | −3.27177 | −0.107750 | ||||||||
\(923\) | 19.6028 | 0.645235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.2698 | 1.58710 | ||||||||
\(926\) | 5.16583 | 0.169760 | ||||||||
\(927\) | 43.0847 | 1.41509 | ||||||||
\(928\) | −9.04914 | −0.297053 | ||||||||
\(929\) | −4.61272 | −0.151339 | −0.0756693 | − | 0.997133i | \(-0.524109\pi\) | ||||
−0.0756693 | + | 0.997133i | \(0.524109\pi\) | |||||||
\(930\) | 73.8479 | 2.42157 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.3449 | 0.633664 | ||||||||
\(933\) | −0.440345 | −0.0144163 | ||||||||
\(934\) | 14.9036 | 0.487659 | ||||||||
\(935\) | −1.50684 | −0.0492788 | ||||||||
\(936\) | 70.4110 | 2.30146 | ||||||||
\(937\) | −17.4245 | −0.569235 | −0.284618 | − | 0.958641i | \(-0.591867\pi\) | ||||
−0.284618 | + | 0.958641i | \(0.591867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.4491 | 1.22211 | ||||||||
\(940\) | −30.4862 | −0.994350 | ||||||||
\(941\) | 15.7178 | 0.512385 | 0.256193 | − | 0.966626i | \(-0.417532\pi\) | ||||
0.256193 | + | 0.966626i | \(0.417532\pi\) | |||||||
\(942\) | −51.8843 | −1.69048 | ||||||||
\(943\) | −7.54545 | −0.245713 | ||||||||
\(944\) | −3.76354 | −0.122493 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.700223 | 0.0227662 | ||||||||
\(947\) | −35.7603 | −1.16205 | −0.581027 | − | 0.813884i | \(-0.697349\pi\) | ||||
−0.581027 | + | 0.813884i | \(0.697349\pi\) | |||||||
\(948\) | −19.3529 | −0.628553 | ||||||||
\(949\) | −60.2109 | −1.95453 | ||||||||
\(950\) | 7.04643 | 0.228616 | ||||||||
\(951\) | 90.7537 | 2.94289 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0014 | 1.29577 | 0.647886 | − | 0.761737i | \(-0.275653\pi\) | ||||
0.647886 | + | 0.761737i | \(0.275653\pi\) | |||||||
\(954\) | −28.7427 | −0.930580 | ||||||||
\(955\) | −13.2765 | −0.429617 | ||||||||
\(956\) | −19.5683 | −0.632884 | ||||||||
\(957\) | −0.993238 | −0.0321068 | ||||||||
\(958\) | −36.3066 | −1.17301 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −55.2759 | −1.78402 | ||||||||
\(961\) | 41.0079 | 1.32283 | ||||||||
\(962\) | −36.0280 | −1.16159 | ||||||||
\(963\) | 41.7908 | 1.34669 | ||||||||
\(964\) | −17.7094 | −0.570381 | ||||||||
\(965\) | −6.45718 | −0.207864 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3732 | 0.976735 | 0.488367 | − | 0.872638i | \(-0.337593\pi\) | ||||
0.488367 | + | 0.872638i | \(0.337593\pi\) | |||||||
\(968\) | −31.9143 | −1.02576 | ||||||||
\(969\) | 7.19371 | 0.231095 | ||||||||
\(970\) | −40.6029 | −1.30368 | ||||||||
\(971\) | 9.47278 | 0.303996 | 0.151998 | − | 0.988381i | \(-0.451429\pi\) | ||||
0.151998 | + | 0.988381i | \(0.451429\pi\) | |||||||
\(972\) | 18.0494 | 0.578935 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.6697 | 0.630258 | ||||||||
\(975\) | 87.2948 | 2.79567 | ||||||||
\(976\) | −4.39220 | −0.140591 | ||||||||
\(977\) | −44.0590 | −1.40957 | −0.704785 | − | 0.709421i | \(-0.748957\pi\) | ||||
−0.704785 | + | 0.709421i | \(0.748957\pi\) | |||||||
\(978\) | −19.6259 | −0.627566 | ||||||||
\(979\) | −3.02665 | −0.0967323 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.6838 | 1.49050 | ||||||||
\(982\) | −8.17473 | −0.260866 | ||||||||
\(983\) | −13.2195 | −0.421635 | −0.210818 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210818 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(984\) | 8.14952 | 0.259797 | ||||||||
\(985\) | 86.3852 | 2.75246 | ||||||||
\(986\) | 3.26618 | 0.104016 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.94570 | 0.220972 | ||||||||
\(989\) | −26.7167 | −0.849540 | ||||||||
\(990\) | −3.19768 | −0.101629 | ||||||||
\(991\) | −11.8824 | −0.377456 | −0.188728 | − | 0.982029i | \(-0.560436\pi\) | ||||
−0.188728 | + | 0.982029i | \(0.560436\pi\) | |||||||
\(992\) | −46.0697 | −1.46272 | ||||||||
\(993\) | −55.9881 | −1.77673 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.44808 | 0.236120 | ||||||||
\(996\) | −43.5032 | −1.37845 | ||||||||
\(997\) | −48.9936 | −1.55164 | −0.775821 | − | 0.630953i | \(-0.782664\pi\) | ||||
−0.775821 | + | 0.630953i | \(0.782664\pi\) | |||||||
\(998\) | 21.1269 | 0.668760 | ||||||||
\(999\) | 39.5554 | 1.25148 |
(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 | 2009.2.a.u.1.8 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.8 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.8 | yes | 20 | 1.1 | even | 1 | trivial |