Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.271062\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53088 | −1.08249 | −0.541246 | − | 0.840864i | \(-0.682047\pi\) | ||||
−0.541246 | + | 0.840864i | \(0.682047\pi\) | |||||||
\(3\) | 2.88726 | 1.66696 | 0.833479 | − | 0.552551i | \(-0.186345\pi\) | ||||
0.833479 | + | 0.552551i | \(0.186345\pi\) | |||||||
\(4\) | 0.343581 | 0.171790 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −4.42003 | −1.80447 | ||||||||
\(7\) | −3.86493 | −1.46081 | −0.730404 | − | 0.683015i | \(-0.760668\pi\) | ||||
−0.730404 | + | 0.683015i | \(0.760668\pi\) | |||||||
\(8\) | 2.53577 | 0.896531 | ||||||||
\(9\) | 5.33625 | 1.77875 | ||||||||
\(10\) | 1.53088 | 0.484105 | ||||||||
\(11\) | 4.75078 | 1.43241 | 0.716207 | − | 0.697888i | \(-0.245877\pi\) | ||||
0.716207 | + | 0.697888i | \(0.245877\pi\) | |||||||
\(12\) | 0.992006 | 0.286368 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 5.91673 | 1.58131 | ||||||||
\(15\) | −2.88726 | −0.745487 | ||||||||
\(16\) | −4.56911 | −1.14228 | ||||||||
\(17\) | −0.640094 | −0.155246 | −0.0776228 | − | 0.996983i | \(-0.524733\pi\) | ||||
−0.0776228 | + | 0.996983i | \(0.524733\pi\) | |||||||
\(18\) | −8.16914 | −1.92548 | ||||||||
\(19\) | 4.70598 | 1.07963 | 0.539813 | − | 0.841785i | \(-0.318495\pi\) | ||||
0.539813 | + | 0.841785i | \(0.318495\pi\) | |||||||
\(20\) | −0.343581 | −0.0768270 | ||||||||
\(21\) | −11.1591 | −2.43511 | ||||||||
\(22\) | −7.27285 | −1.55058 | ||||||||
\(23\) | −0.308077 | −0.0642385 | −0.0321192 | − | 0.999484i | \(-0.510226\pi\) | ||||
−0.0321192 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(24\) | 7.32143 | 1.49448 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.74536 | 1.29815 | ||||||||
\(28\) | −1.32792 | −0.250953 | ||||||||
\(29\) | 2.48779 | 0.461972 | 0.230986 | − | 0.972957i | \(-0.425805\pi\) | ||||
0.230986 | + | 0.972957i | \(0.425805\pi\) | |||||||
\(30\) | 4.42003 | 0.806984 | ||||||||
\(31\) | −0.635724 | −0.114179 | −0.0570897 | − | 0.998369i | \(-0.518182\pi\) | ||||
−0.0570897 | + | 0.998369i | \(0.518182\pi\) | |||||||
\(32\) | 1.92320 | 0.339977 | ||||||||
\(33\) | 13.7167 | 2.38777 | ||||||||
\(34\) | 0.979904 | 0.168052 | ||||||||
\(35\) | 3.86493 | 0.653293 | ||||||||
\(36\) | 1.83343 | 0.305572 | ||||||||
\(37\) | 5.15099 | 0.846817 | 0.423409 | − | 0.905939i | \(-0.360834\pi\) | ||||
0.423409 | + | 0.905939i | \(0.360834\pi\) | |||||||
\(38\) | −7.20428 | −1.16869 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.53577 | −0.400941 | ||||||||
\(41\) | 10.4049 | 1.62498 | 0.812488 | − | 0.582977i | \(-0.198112\pi\) | ||||
0.812488 | + | 0.582977i | \(0.198112\pi\) | |||||||
\(42\) | 17.0831 | 2.63598 | ||||||||
\(43\) | 8.56187 | 1.30567 | 0.652836 | − | 0.757499i | \(-0.273579\pi\) | ||||
0.652836 | + | 0.757499i | \(0.273579\pi\) | |||||||
\(44\) | 1.63228 | 0.246075 | ||||||||
\(45\) | −5.33625 | −0.795482 | ||||||||
\(46\) | 0.471628 | 0.0695377 | ||||||||
\(47\) | 2.89673 | 0.422532 | 0.211266 | − | 0.977429i | \(-0.432241\pi\) | ||||
0.211266 | + | 0.977429i | \(0.432241\pi\) | |||||||
\(48\) | −13.1922 | −1.90413 | ||||||||
\(49\) | 7.93772 | 1.13396 | ||||||||
\(50\) | −1.53088 | −0.216499 | ||||||||
\(51\) | −1.84812 | −0.258788 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.28060 | 0.175903 | 0.0879517 | − | 0.996125i | \(-0.471968\pi\) | ||||
0.0879517 | + | 0.996125i | \(0.471968\pi\) | |||||||
\(54\) | −10.3263 | −1.40523 | ||||||||
\(55\) | −4.75078 | −0.640595 | ||||||||
\(56\) | −9.80059 | −1.30966 | ||||||||
\(57\) | 13.5874 | 1.79969 | ||||||||
\(58\) | −3.80850 | −0.500081 | ||||||||
\(59\) | −4.06969 | −0.529828 | −0.264914 | − | 0.964272i | \(-0.585344\pi\) | ||||
−0.264914 | + | 0.964272i | \(0.585344\pi\) | |||||||
\(60\) | −0.992006 | −0.128067 | ||||||||
\(61\) | 0.335109 | 0.0429063 | 0.0214531 | − | 0.999770i | \(-0.493171\pi\) | ||||
0.0214531 | + | 0.999770i | \(0.493171\pi\) | |||||||
\(62\) | 0.973215 | 0.123598 | ||||||||
\(63\) | −20.6243 | −2.59841 | ||||||||
\(64\) | 6.19404 | 0.774255 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.9986 | −2.58475 | ||||||||
\(67\) | 0.721556 | 0.0881521 | 0.0440761 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440761 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(68\) | −0.219924 | −0.0266697 | ||||||||
\(69\) | −0.889497 | −0.107083 | ||||||||
\(70\) | −5.91673 | −0.707185 | ||||||||
\(71\) | −10.3222 | −1.22502 | −0.612510 | − | 0.790463i | \(-0.709840\pi\) | ||||
−0.612510 | + | 0.790463i | \(0.709840\pi\) | |||||||
\(72\) | 13.5315 | 1.59470 | ||||||||
\(73\) | −13.1133 | −1.53480 | −0.767400 | − | 0.641168i | \(-0.778450\pi\) | ||||
−0.767400 | + | 0.641168i | \(0.778450\pi\) | |||||||
\(74\) | −7.88552 | −0.916673 | ||||||||
\(75\) | 2.88726 | 0.333392 | ||||||||
\(76\) | 1.61689 | 0.185470 | ||||||||
\(77\) | −18.3614 | −2.09248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7026 | 1.20414 | 0.602069 | − | 0.798444i | \(-0.294343\pi\) | ||||
0.602069 | + | 0.798444i | \(0.294343\pi\) | |||||||
\(80\) | 4.56911 | 0.510842 | ||||||||
\(81\) | 3.46683 | 0.385204 | ||||||||
\(82\) | −15.9287 | −1.75903 | ||||||||
\(83\) | 8.94652 | 0.982008 | 0.491004 | − | 0.871157i | \(-0.336630\pi\) | ||||
0.491004 | + | 0.871157i | \(0.336630\pi\) | |||||||
\(84\) | −3.83404 | −0.418328 | ||||||||
\(85\) | 0.640094 | 0.0694279 | ||||||||
\(86\) | −13.1072 | −1.41338 | ||||||||
\(87\) | 7.18290 | 0.770088 | ||||||||
\(88\) | 12.0469 | 1.28420 | ||||||||
\(89\) | 0.0141672 | 0.00150172 | 0.000750858 | − | 1.00000i | \(-0.499761\pi\) | ||||
0.000750858 | 1.00000i | \(0.499761\pi\) | ||||||||
\(90\) | 8.16914 | 0.861103 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.105849 | −0.0110356 | ||||||||
\(93\) | −1.83550 | −0.190332 | ||||||||
\(94\) | −4.43454 | −0.457388 | ||||||||
\(95\) | −4.70598 | −0.482824 | ||||||||
\(96\) | 5.55278 | 0.566728 | ||||||||
\(97\) | 10.1257 | 1.02811 | 0.514054 | − | 0.857758i | \(-0.328143\pi\) | ||||
0.514054 | + | 0.857758i | \(0.328143\pi\) | |||||||
\(98\) | −12.1517 | −1.22750 | ||||||||
\(99\) | 25.3514 | 2.54791 | ||||||||
\(100\) | 0.343581 | 0.0343581 | ||||||||
\(101\) | 12.4363 | 1.23746 | 0.618730 | − | 0.785603i | \(-0.287647\pi\) | ||||
0.618730 | + | 0.785603i | \(0.287647\pi\) | |||||||
\(102\) | 2.82924 | 0.280136 | ||||||||
\(103\) | 10.2372 | 1.00871 | 0.504353 | − | 0.863498i | \(-0.331731\pi\) | ||||
0.504353 | + | 0.863498i | \(0.331731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1591 | 1.08901 | ||||||||
\(106\) | −1.96043 | −0.190414 | ||||||||
\(107\) | −15.3401 | −1.48298 | −0.741490 | − | 0.670964i | \(-0.765881\pi\) | ||||
−0.741490 | + | 0.670964i | \(0.765881\pi\) | |||||||
\(108\) | 2.31758 | 0.223009 | ||||||||
\(109\) | −0.515675 | −0.0493927 | −0.0246963 | − | 0.999695i | \(-0.507862\pi\) | ||||
−0.0246963 | + | 0.999695i | \(0.507862\pi\) | |||||||
\(110\) | 7.27285 | 0.693439 | ||||||||
\(111\) | 14.8722 | 1.41161 | ||||||||
\(112\) | 17.6593 | 1.66865 | ||||||||
\(113\) | −17.0097 | −1.60013 | −0.800067 | − | 0.599911i | \(-0.795203\pi\) | ||||
−0.800067 | + | 0.599911i | \(0.795203\pi\) | |||||||
\(114\) | −20.8006 | −1.94815 | ||||||||
\(115\) | 0.308077 | 0.0287283 | ||||||||
\(116\) | 0.854759 | 0.0793624 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.23019 | 0.573535 | ||||||||
\(119\) | 2.47392 | 0.226784 | ||||||||
\(120\) | −7.32143 | −0.668352 | ||||||||
\(121\) | 11.5699 | 1.05181 | ||||||||
\(122\) | −0.513010 | −0.0464457 | ||||||||
\(123\) | 30.0417 | 2.70877 | ||||||||
\(124\) | −0.218423 | −0.0196149 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 31.5732 | 2.81276 | ||||||||
\(127\) | −21.7877 | −1.93335 | −0.966675 | − | 0.256007i | \(-0.917593\pi\) | ||||
−0.966675 | + | 0.256007i | \(0.917593\pi\) | |||||||
\(128\) | −13.3287 | −1.17810 | ||||||||
\(129\) | 24.7203 | 2.17650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8833 | −0.950874 | −0.475437 | − | 0.879750i | \(-0.657710\pi\) | ||||
−0.475437 | + | 0.879750i | \(0.657710\pi\) | |||||||
\(132\) | 4.71280 | 0.410197 | ||||||||
\(133\) | −18.1883 | −1.57713 | ||||||||
\(134\) | −1.10461 | −0.0954240 | ||||||||
\(135\) | −6.74536 | −0.580548 | ||||||||
\(136\) | −1.62313 | −0.139182 | ||||||||
\(137\) | −1.25583 | −0.107293 | −0.0536466 | − | 0.998560i | \(-0.517084\pi\) | ||||
−0.0536466 | + | 0.998560i | \(0.517084\pi\) | |||||||
\(138\) | 1.36171 | 0.115916 | ||||||||
\(139\) | 18.2380 | 1.54693 | 0.773463 | − | 0.633842i | \(-0.218523\pi\) | ||||
0.773463 | + | 0.633842i | \(0.218523\pi\) | |||||||
\(140\) | 1.32792 | 0.112230 | ||||||||
\(141\) | 8.36361 | 0.704343 | ||||||||
\(142\) | 15.8020 | 1.32608 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −24.3819 | −2.03183 | ||||||||
\(145\) | −2.48779 | −0.206600 | ||||||||
\(146\) | 20.0749 | 1.66141 | ||||||||
\(147\) | 22.9182 | 1.89026 | ||||||||
\(148\) | 1.76978 | 0.145475 | ||||||||
\(149\) | −21.0429 | −1.72390 | −0.861952 | − | 0.506991i | \(-0.830758\pi\) | ||||
−0.861952 | + | 0.506991i | \(0.830758\pi\) | |||||||
\(150\) | −4.42003 | −0.360894 | ||||||||
\(151\) | 16.2381 | 1.32144 | 0.660720 | − | 0.750632i | \(-0.270251\pi\) | ||||
0.660720 | + | 0.750632i | \(0.270251\pi\) | |||||||
\(152\) | 11.9333 | 0.967918 | ||||||||
\(153\) | −3.41570 | −0.276143 | ||||||||
\(154\) | 28.1091 | 2.26510 | ||||||||
\(155\) | 0.635724 | 0.0510626 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.30362 | −0.183849 | −0.0919246 | − | 0.995766i | \(-0.529302\pi\) | ||||
−0.0919246 | + | 0.995766i | \(0.529302\pi\) | |||||||
\(158\) | −16.3844 | −1.30347 | ||||||||
\(159\) | 3.69741 | 0.293224 | ||||||||
\(160\) | −1.92320 | −0.152042 | ||||||||
\(161\) | 1.19070 | 0.0938401 | ||||||||
\(162\) | −5.30729 | −0.416980 | ||||||||
\(163\) | −15.3183 | −1.19983 | −0.599913 | − | 0.800065i | \(-0.704798\pi\) | ||||
−0.599913 | + | 0.800065i | \(0.704798\pi\) | |||||||
\(164\) | 3.57493 | 0.279156 | ||||||||
\(165\) | −13.7167 | −1.06785 | ||||||||
\(166\) | −13.6960 | −1.06302 | ||||||||
\(167\) | −11.9904 | −0.927845 | −0.463922 | − | 0.885876i | \(-0.653558\pi\) | ||||
−0.463922 | + | 0.885876i | \(0.653558\pi\) | |||||||
\(168\) | −28.2968 | −2.18315 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.979904 | −0.0751552 | ||||||||
\(171\) | 25.1123 | 1.92039 | ||||||||
\(172\) | 2.94169 | 0.224302 | ||||||||
\(173\) | −9.18608 | −0.698404 | −0.349202 | − | 0.937047i | \(-0.613547\pi\) | ||||
−0.349202 | + | 0.937047i | \(0.613547\pi\) | |||||||
\(174\) | −10.9961 | −0.833615 | ||||||||
\(175\) | −3.86493 | −0.292162 | ||||||||
\(176\) | −21.7068 | −1.63622 | ||||||||
\(177\) | −11.7502 | −0.883202 | ||||||||
\(178\) | −0.0216882 | −0.00162560 | ||||||||
\(179\) | −2.63815 | −0.197185 | −0.0985923 | − | 0.995128i | \(-0.531434\pi\) | ||||
−0.0985923 | + | 0.995128i | \(0.531434\pi\) | |||||||
\(180\) | −1.83343 | −0.136656 | ||||||||
\(181\) | 9.36566 | 0.696144 | 0.348072 | − | 0.937468i | \(-0.386837\pi\) | ||||
0.348072 | + | 0.937468i | \(0.386837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.967545 | 0.0715230 | ||||||||
\(184\) | −0.781213 | −0.0575918 | ||||||||
\(185\) | −5.15099 | −0.378708 | ||||||||
\(186\) | 2.80992 | 0.206033 | ||||||||
\(187\) | −3.04094 | −0.222376 | ||||||||
\(188\) | 0.995262 | 0.0725870 | ||||||||
\(189\) | −26.0704 | −1.89634 | ||||||||
\(190\) | 7.20428 | 0.522653 | ||||||||
\(191\) | −6.30396 | −0.456138 | −0.228069 | − | 0.973645i | \(-0.573241\pi\) | ||||
−0.228069 | + | 0.973645i | \(0.573241\pi\) | |||||||
\(192\) | 17.8838 | 1.29065 | ||||||||
\(193\) | 8.22585 | 0.592110 | 0.296055 | − | 0.955171i | \(-0.404329\pi\) | ||||
0.296055 | + | 0.955171i | \(0.404329\pi\) | |||||||
\(194\) | −15.5012 | −1.11292 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.72725 | 0.194803 | ||||||||
\(197\) | −0.462516 | −0.0329529 | −0.0164764 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164764 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(198\) | −38.8098 | −2.75809 | ||||||||
\(199\) | −19.3271 | −1.37007 | −0.685033 | − | 0.728512i | \(-0.740212\pi\) | ||||
−0.685033 | + | 0.728512i | \(0.740212\pi\) | |||||||
\(200\) | 2.53577 | 0.179306 | ||||||||
\(201\) | 2.08332 | 0.146946 | ||||||||
\(202\) | −19.0385 | −1.33954 | ||||||||
\(203\) | −9.61516 | −0.674852 | ||||||||
\(204\) | −0.634977 | −0.0444573 | ||||||||
\(205\) | −10.4049 | −0.726712 | ||||||||
\(206\) | −15.6719 | −1.09192 | ||||||||
\(207\) | −1.64398 | −0.114264 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.3571 | 1.54647 | ||||||||
\(210\) | −17.0831 | −1.17885 | ||||||||
\(211\) | 18.8081 | 1.29480 | 0.647401 | − | 0.762149i | \(-0.275856\pi\) | ||||
0.647401 | + | 0.762149i | \(0.275856\pi\) | |||||||
\(212\) | 0.439988 | 0.0302185 | ||||||||
\(213\) | −29.8029 | −2.04206 | ||||||||
\(214\) | 23.4837 | 1.60532 | ||||||||
\(215\) | −8.56187 | −0.583914 | ||||||||
\(216\) | 17.1047 | 1.16383 | ||||||||
\(217\) | 2.45703 | 0.166794 | ||||||||
\(218\) | 0.789434 | 0.0534672 | ||||||||
\(219\) | −37.8616 | −2.55845 | ||||||||
\(220\) | −1.63228 | −0.110048 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −22.7675 | −1.52806 | ||||||||
\(223\) | 3.50267 | 0.234556 | 0.117278 | − | 0.993099i | \(-0.462583\pi\) | ||||
0.117278 | + | 0.993099i | \(0.462583\pi\) | |||||||
\(224\) | −7.43305 | −0.496642 | ||||||||
\(225\) | 5.33625 | 0.355750 | ||||||||
\(226\) | 26.0397 | 1.73213 | ||||||||
\(227\) | −24.5730 | −1.63097 | −0.815483 | − | 0.578781i | \(-0.803529\pi\) | ||||
−0.815483 | + | 0.578781i | \(0.803529\pi\) | |||||||
\(228\) | 4.66837 | 0.309170 | ||||||||
\(229\) | −17.8359 | −1.17863 | −0.589314 | − | 0.807904i | \(-0.700602\pi\) | ||||
−0.589314 | + | 0.807904i | \(0.700602\pi\) | |||||||
\(230\) | −0.471628 | −0.0310982 | ||||||||
\(231\) | −53.0142 | −3.48808 | ||||||||
\(232\) | 6.30848 | 0.414172 | ||||||||
\(233\) | 3.03322 | 0.198713 | 0.0993565 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993565 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.89673 | −0.188962 | ||||||||
\(236\) | −1.39827 | −0.0910194 | ||||||||
\(237\) | 30.9012 | 2.00725 | ||||||||
\(238\) | −3.78727 | −0.245492 | ||||||||
\(239\) | 6.93867 | 0.448825 | 0.224413 | − | 0.974494i | \(-0.427954\pi\) | ||||
0.224413 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(240\) | 13.1922 | 0.851553 | ||||||||
\(241\) | 6.59429 | 0.424776 | 0.212388 | − | 0.977185i | \(-0.431876\pi\) | ||||
0.212388 | + | 0.977185i | \(0.431876\pi\) | |||||||
\(242\) | −17.7121 | −1.13858 | ||||||||
\(243\) | −10.2264 | −0.656027 | ||||||||
\(244\) | 0.115137 | 0.00737089 | ||||||||
\(245\) | −7.93772 | −0.507122 | ||||||||
\(246\) | −45.9901 | −2.93222 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.61205 | −0.102365 | ||||||||
\(249\) | 25.8309 | 1.63697 | ||||||||
\(250\) | 1.53088 | 0.0968211 | ||||||||
\(251\) | −16.8636 | −1.06442 | −0.532211 | − | 0.846612i | \(-0.678639\pi\) | ||||
−0.532211 | + | 0.846612i | \(0.678639\pi\) | |||||||
\(252\) | −7.08610 | −0.446383 | ||||||||
\(253\) | −1.46361 | −0.0920161 | ||||||||
\(254\) | 33.3543 | 2.09284 | ||||||||
\(255\) | 1.84812 | 0.115733 | ||||||||
\(256\) | 8.01652 | 0.501033 | ||||||||
\(257\) | −10.6593 | −0.664906 | −0.332453 | − | 0.943120i | \(-0.607876\pi\) | ||||
−0.332453 | + | 0.943120i | \(0.607876\pi\) | |||||||
\(258\) | −37.8437 | −2.35605 | ||||||||
\(259\) | −19.9082 | −1.23704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.2755 | 0.821733 | ||||||||
\(262\) | 16.6609 | 1.02931 | ||||||||
\(263\) | 14.2995 | 0.881745 | 0.440873 | − | 0.897570i | \(-0.354669\pi\) | ||||
0.440873 | + | 0.897570i | \(0.354669\pi\) | |||||||
\(264\) | 34.7825 | 2.14071 | ||||||||
\(265\) | −1.28060 | −0.0786664 | ||||||||
\(266\) | 27.8441 | 1.70723 | ||||||||
\(267\) | 0.0409042 | 0.00250330 | ||||||||
\(268\) | 0.247913 | 0.0151437 | ||||||||
\(269\) | 10.7756 | 0.657001 | 0.328500 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328500 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(270\) | 10.3263 | 0.628439 | ||||||||
\(271\) | 19.4273 | 1.18012 | 0.590062 | − | 0.807358i | \(-0.299103\pi\) | ||||
0.590062 | + | 0.807358i | \(0.299103\pi\) | |||||||
\(272\) | 2.92466 | 0.177334 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.92253 | 0.116144 | ||||||||
\(275\) | 4.75078 | 0.286483 | ||||||||
\(276\) | −0.305614 | −0.0183958 | ||||||||
\(277\) | −1.04322 | −0.0626810 | −0.0313405 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313405 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(278\) | −27.9201 | −1.67454 | ||||||||
\(279\) | −3.39239 | −0.203097 | ||||||||
\(280\) | 9.80059 | 0.585697 | ||||||||
\(281\) | 9.04835 | 0.539780 | 0.269890 | − | 0.962891i | \(-0.413013\pi\) | ||||
0.269890 | + | 0.962891i | \(0.413013\pi\) | |||||||
\(282\) | −12.8037 | −0.762447 | ||||||||
\(283\) | −2.37857 | −0.141392 | −0.0706958 | − | 0.997498i | \(-0.522522\pi\) | ||||
−0.0706958 | + | 0.997498i | \(0.522522\pi\) | |||||||
\(284\) | −3.54651 | −0.210447 | ||||||||
\(285\) | −13.5874 | −0.804847 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.2144 | −2.37378 | ||||||||
\(288\) | 10.2627 | 0.604735 | ||||||||
\(289\) | −16.5903 | −0.975899 | ||||||||
\(290\) | 3.80850 | 0.223643 | ||||||||
\(291\) | 29.2355 | 1.71381 | ||||||||
\(292\) | −4.50549 | −0.263664 | ||||||||
\(293\) | 14.1290 | 0.825423 | 0.412712 | − | 0.910862i | \(-0.364582\pi\) | ||||
0.412712 | + | 0.910862i | \(0.364582\pi\) | |||||||
\(294\) | −35.0850 | −2.04620 | ||||||||
\(295\) | 4.06969 | 0.236946 | ||||||||
\(296\) | 13.0617 | 0.759198 | ||||||||
\(297\) | 32.0457 | 1.85948 | ||||||||
\(298\) | 32.2141 | 1.86611 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.992006 | 0.0572735 | ||||||||
\(301\) | −33.0910 | −1.90734 | ||||||||
\(302\) | −24.8586 | −1.43045 | ||||||||
\(303\) | 35.9069 | 2.06280 | ||||||||
\(304\) | −21.5022 | −1.23323 | ||||||||
\(305\) | −0.335109 | −0.0191883 | ||||||||
\(306\) | 5.22902 | 0.298923 | ||||||||
\(307\) | −24.3391 | −1.38910 | −0.694552 | − | 0.719442i | \(-0.744397\pi\) | ||||
−0.694552 | + | 0.719442i | \(0.744397\pi\) | |||||||
\(308\) | −6.30864 | −0.359468 | ||||||||
\(309\) | 29.5576 | 1.68147 | ||||||||
\(310\) | −0.973215 | −0.0552749 | ||||||||
\(311\) | 6.14513 | 0.348458 | 0.174229 | − | 0.984705i | \(-0.444257\pi\) | ||||
0.174229 | + | 0.984705i | \(0.444257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.39881 | 0.0790652 | 0.0395326 | − | 0.999218i | \(-0.487413\pi\) | ||||
0.0395326 | + | 0.999218i | \(0.487413\pi\) | |||||||
\(314\) | 3.52656 | 0.199015 | ||||||||
\(315\) | 20.6243 | 1.16205 | ||||||||
\(316\) | 3.67721 | 0.206859 | ||||||||
\(317\) | 8.92070 | 0.501036 | 0.250518 | − | 0.968112i | \(-0.419399\pi\) | ||||
0.250518 | + | 0.968112i | \(0.419399\pi\) | |||||||
\(318\) | −5.66027 | −0.317412 | ||||||||
\(319\) | 11.8190 | 0.661735 | ||||||||
\(320\) | −6.19404 | −0.346258 | ||||||||
\(321\) | −44.2907 | −2.47207 | ||||||||
\(322\) | −1.82281 | −0.101581 | ||||||||
\(323\) | −3.01227 | −0.167607 | ||||||||
\(324\) | 1.19114 | 0.0661743 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.4505 | 1.29880 | ||||||||
\(327\) | −1.48889 | −0.0823356 | ||||||||
\(328\) | 26.3845 | 1.45684 | ||||||||
\(329\) | −11.1957 | −0.617238 | ||||||||
\(330\) | 20.9986 | 1.15593 | ||||||||
\(331\) | −19.7654 | −1.08640 | −0.543202 | − | 0.839602i | \(-0.682788\pi\) | ||||
−0.543202 | + | 0.839602i | \(0.682788\pi\) | |||||||
\(332\) | 3.07385 | 0.168700 | ||||||||
\(333\) | 27.4870 | 1.50628 | ||||||||
\(334\) | 18.3558 | 1.00439 | ||||||||
\(335\) | −0.721556 | −0.0394228 | ||||||||
\(336\) | 50.9870 | 2.78157 | ||||||||
\(337\) | 20.2361 | 1.10233 | 0.551166 | − | 0.834396i | \(-0.314183\pi\) | ||||
0.551166 | + | 0.834396i | \(0.314183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −49.1112 | −2.66736 | ||||||||
\(340\) | 0.219924 | 0.0119271 | ||||||||
\(341\) | −3.02019 | −0.163552 | ||||||||
\(342\) | −38.4438 | −2.07880 | ||||||||
\(343\) | −3.62422 | −0.195689 | ||||||||
\(344\) | 21.7109 | 1.17058 | ||||||||
\(345\) | 0.889497 | 0.0478889 | ||||||||
\(346\) | 14.0627 | 0.756018 | ||||||||
\(347\) | 29.2678 | 1.57118 | 0.785589 | − | 0.618749i | \(-0.212360\pi\) | ||||
0.785589 | + | 0.618749i | \(0.212360\pi\) | |||||||
\(348\) | 2.46791 | 0.132294 | ||||||||
\(349\) | 0.195008 | 0.0104386 | 0.00521928 | − | 0.999986i | \(-0.498339\pi\) | ||||
0.00521928 | + | 0.999986i | \(0.498339\pi\) | |||||||
\(350\) | 5.91673 | 0.316263 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.13671 | 0.486988 | ||||||||
\(353\) | −12.2379 | −0.651358 | −0.325679 | − | 0.945480i | \(-0.605593\pi\) | ||||
−0.325679 | + | 0.945480i | \(0.605593\pi\) | |||||||
\(354\) | 17.9881 | 0.956059 | ||||||||
\(355\) | 10.3222 | 0.547846 | ||||||||
\(356\) | 0.00486757 | 0.000257981 0 | ||||||||
\(357\) | 7.14285 | 0.378040 | ||||||||
\(358\) | 4.03868 | 0.213451 | ||||||||
\(359\) | 2.43702 | 0.128621 | 0.0643104 | − | 0.997930i | \(-0.479515\pi\) | ||||
0.0643104 | + | 0.997930i | \(0.479515\pi\) | |||||||
\(360\) | −13.5315 | −0.713174 | ||||||||
\(361\) | 3.14628 | 0.165593 | ||||||||
\(362\) | −14.3377 | −0.753571 | ||||||||
\(363\) | 33.4053 | 1.75332 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.1133 | 0.686384 | ||||||||
\(366\) | −1.48119 | −0.0774231 | ||||||||
\(367\) | −28.8213 | −1.50446 | −0.752229 | − | 0.658901i | \(-0.771022\pi\) | ||||
−0.752229 | + | 0.658901i | \(0.771022\pi\) | |||||||
\(368\) | 1.40764 | 0.0733783 | ||||||||
\(369\) | 55.5233 | 2.89043 | ||||||||
\(370\) | 7.88552 | 0.409949 | ||||||||
\(371\) | −4.94942 | −0.256961 | ||||||||
\(372\) | −0.630643 | −0.0326973 | ||||||||
\(373\) | 3.72479 | 0.192862 | 0.0964311 | − | 0.995340i | \(-0.469257\pi\) | ||||
0.0964311 | + | 0.995340i | \(0.469257\pi\) | |||||||
\(374\) | 4.65531 | 0.240720 | ||||||||
\(375\) | −2.88726 | −0.149097 | ||||||||
\(376\) | 7.34546 | 0.378813 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 39.9105 | 2.05278 | ||||||||
\(379\) | −27.1916 | −1.39674 | −0.698370 | − | 0.715737i | \(-0.746091\pi\) | ||||
−0.698370 | + | 0.715737i | \(0.746091\pi\) | |||||||
\(380\) | −1.61689 | −0.0829445 | ||||||||
\(381\) | −62.9068 | −3.22281 | ||||||||
\(382\) | 9.65057 | 0.493766 | ||||||||
\(383\) | −33.2900 | −1.70104 | −0.850519 | − | 0.525945i | \(-0.823712\pi\) | ||||
−0.850519 | + | 0.525945i | \(0.823712\pi\) | |||||||
\(384\) | −38.4834 | −1.96385 | ||||||||
\(385\) | 18.3614 | 0.935786 | ||||||||
\(386\) | −12.5928 | −0.640955 | ||||||||
\(387\) | 45.6883 | 2.32247 | ||||||||
\(388\) | 3.47899 | 0.176619 | ||||||||
\(389\) | −23.5358 | −1.19331 | −0.596655 | − | 0.802498i | \(-0.703504\pi\) | ||||
−0.596655 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.197198 | 0.00997274 | ||||||||
\(392\) | 20.1282 | 1.01663 | ||||||||
\(393\) | −31.4227 | −1.58507 | ||||||||
\(394\) | 0.708054 | 0.0356713 | ||||||||
\(395\) | −10.7026 | −0.538507 | ||||||||
\(396\) | 8.71024 | 0.437706 | ||||||||
\(397\) | −22.4582 | −1.12714 | −0.563572 | − | 0.826067i | \(-0.690573\pi\) | ||||
−0.563572 | + | 0.826067i | \(0.690573\pi\) | |||||||
\(398\) | 29.5875 | 1.48309 | ||||||||
\(399\) | −52.5143 | −2.62901 | ||||||||
\(400\) | −4.56911 | −0.228456 | ||||||||
\(401\) | −0.0227333 | −0.00113525 | −0.000567624 | − | 1.00000i | \(-0.500181\pi\) | ||||
−0.000567624 | 1.00000i | \(0.500181\pi\) | ||||||||
\(402\) | −3.18930 | −0.159068 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.27288 | 0.212584 | ||||||||
\(405\) | −3.46683 | −0.172268 | ||||||||
\(406\) | 14.7196 | 0.730523 | ||||||||
\(407\) | 24.4712 | 1.21299 | ||||||||
\(408\) | −4.68640 | −0.232011 | ||||||||
\(409\) | −28.7890 | −1.42352 | −0.711761 | − | 0.702421i | \(-0.752102\pi\) | ||||
−0.711761 | + | 0.702421i | \(0.752102\pi\) | |||||||
\(410\) | 15.9287 | 0.786660 | ||||||||
\(411\) | −3.62592 | −0.178853 | ||||||||
\(412\) | 3.51732 | 0.173286 | ||||||||
\(413\) | 15.7291 | 0.773977 | ||||||||
\(414\) | 2.51672 | 0.123690 | ||||||||
\(415\) | −8.94652 | −0.439167 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 52.6578 | 2.57866 | ||||||||
\(418\) | −34.2259 | −1.67404 | ||||||||
\(419\) | 17.4064 | 0.850358 | 0.425179 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425179 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(420\) | 3.83404 | 0.187082 | ||||||||
\(421\) | −30.1642 | −1.47011 | −0.735056 | − | 0.678007i | \(-0.762844\pi\) | ||||
−0.735056 | + | 0.678007i | \(0.762844\pi\) | |||||||
\(422\) | −28.7929 | −1.40161 | ||||||||
\(423\) | 15.4577 | 0.751579 | ||||||||
\(424\) | 3.24730 | 0.157703 | ||||||||
\(425\) | −0.640094 | −0.0310491 | ||||||||
\(426\) | 45.6245 | 2.21051 | ||||||||
\(427\) | −1.29517 | −0.0626778 | ||||||||
\(428\) | −5.27055 | −0.254762 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.1072 | 0.632083 | ||||||||
\(431\) | 10.1531 | 0.489056 | 0.244528 | − | 0.969642i | \(-0.421367\pi\) | ||||
0.244528 | + | 0.969642i | \(0.421367\pi\) | |||||||
\(432\) | −30.8203 | −1.48284 | ||||||||
\(433\) | 22.2687 | 1.07017 | 0.535083 | − | 0.844799i | \(-0.320280\pi\) | ||||
0.535083 | + | 0.844799i | \(0.320280\pi\) | |||||||
\(434\) | −3.76141 | −0.180554 | ||||||||
\(435\) | −7.18290 | −0.344394 | ||||||||
\(436\) | −0.177176 | −0.00848519 | ||||||||
\(437\) | −1.44981 | −0.0693536 | ||||||||
\(438\) | 57.9614 | 2.76950 | ||||||||
\(439\) | 37.8809 | 1.80796 | 0.903980 | − | 0.427576i | \(-0.140632\pi\) | ||||
0.903980 | + | 0.427576i | \(0.140632\pi\) | |||||||
\(440\) | −12.0469 | −0.574313 | ||||||||
\(441\) | 42.3577 | 2.01703 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.918139 | −0.0436221 | −0.0218110 | − | 0.999762i | \(-0.506943\pi\) | ||||
−0.0218110 | + | 0.999762i | \(0.506943\pi\) | |||||||
\(444\) | 5.10981 | 0.242501 | ||||||||
\(445\) | −0.0141672 | −0.000671588 0 | ||||||||
\(446\) | −5.36216 | −0.253906 | ||||||||
\(447\) | −60.7563 | −2.87368 | ||||||||
\(448\) | −23.9396 | −1.13104 | ||||||||
\(449\) | 34.7819 | 1.64146 | 0.820730 | − | 0.571317i | \(-0.193567\pi\) | ||||
0.820730 | + | 0.571317i | \(0.193567\pi\) | |||||||
\(450\) | −8.16914 | −0.385097 | ||||||||
\(451\) | 49.4315 | 2.32764 | ||||||||
\(452\) | −5.84419 | −0.274888 | ||||||||
\(453\) | 46.8837 | 2.20279 | ||||||||
\(454\) | 37.6182 | 1.76551 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 34.4545 | 1.61348 | ||||||||
\(457\) | −13.7197 | −0.641781 | −0.320890 | − | 0.947116i | \(-0.603982\pi\) | ||||
−0.320890 | + | 0.947116i | \(0.603982\pi\) | |||||||
\(458\) | 27.3045 | 1.27586 | ||||||||
\(459\) | −4.31767 | −0.201531 | ||||||||
\(460\) | 0.105849 | 0.00493525 | ||||||||
\(461\) | 32.5057 | 1.51394 | 0.756971 | − | 0.653449i | \(-0.226679\pi\) | ||||
0.756971 | + | 0.653449i | \(0.226679\pi\) | |||||||
\(462\) | 81.1582 | 3.77582 | ||||||||
\(463\) | 34.0054 | 1.58037 | 0.790183 | − | 0.612871i | \(-0.209985\pi\) | ||||
0.790183 | + | 0.612871i | \(0.209985\pi\) | |||||||
\(464\) | −11.3670 | −0.527701 | ||||||||
\(465\) | 1.83550 | 0.0851192 | ||||||||
\(466\) | −4.64349 | −0.215105 | ||||||||
\(467\) | −0.0693333 | −0.00320836 | −0.00160418 | − | 0.999999i | \(-0.500511\pi\) | ||||
−0.00160418 | + | 0.999999i | \(0.500511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.78877 | −0.128773 | ||||||||
\(470\) | 4.43454 | 0.204550 | ||||||||
\(471\) | −6.65115 | −0.306469 | ||||||||
\(472\) | −10.3198 | −0.475007 | ||||||||
\(473\) | 40.6755 | 1.87026 | ||||||||
\(474\) | −47.3059 | −2.17283 | ||||||||
\(475\) | 4.70598 | 0.215925 | ||||||||
\(476\) | 0.849992 | 0.0389593 | ||||||||
\(477\) | 6.83358 | 0.312888 | ||||||||
\(478\) | −10.6222 | −0.485850 | ||||||||
\(479\) | 9.16068 | 0.418562 | 0.209281 | − | 0.977856i | \(-0.432888\pi\) | ||||
0.209281 | + | 0.977856i | \(0.432888\pi\) | |||||||
\(480\) | −5.55278 | −0.253449 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.0950 | −0.459816 | ||||||||
\(483\) | 3.43785 | 0.156428 | ||||||||
\(484\) | 3.97520 | 0.180691 | ||||||||
\(485\) | −10.1257 | −0.459784 | ||||||||
\(486\) | 15.6554 | 0.710144 | ||||||||
\(487\) | 27.2691 | 1.23568 | 0.617841 | − | 0.786303i | \(-0.288008\pi\) | ||||
0.617841 | + | 0.786303i | \(0.288008\pi\) | |||||||
\(488\) | 0.849759 | 0.0384668 | ||||||||
\(489\) | −44.2280 | −2.00006 | ||||||||
\(490\) | 12.1517 | 0.548956 | ||||||||
\(491\) | −17.9855 | −0.811676 | −0.405838 | − | 0.913945i | \(-0.633020\pi\) | ||||
−0.405838 | + | 0.913945i | \(0.633020\pi\) | |||||||
\(492\) | 10.3218 | 0.465341 | ||||||||
\(493\) | −1.59242 | −0.0717191 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.3514 | −1.13946 | ||||||||
\(496\) | 2.90470 | 0.130425 | ||||||||
\(497\) | 39.8946 | 1.78952 | ||||||||
\(498\) | −39.5439 | −1.77200 | ||||||||
\(499\) | −12.9963 | −0.581792 | −0.290896 | − | 0.956755i | \(-0.593953\pi\) | ||||
−0.290896 | + | 0.956755i | \(0.593953\pi\) | |||||||
\(500\) | −0.343581 | −0.0153654 | ||||||||
\(501\) | −34.6194 | −1.54668 | ||||||||
\(502\) | 25.8161 | 1.15223 | ||||||||
\(503\) | −6.92255 | −0.308661 | −0.154331 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154331 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(504\) | −52.2984 | −2.32956 | ||||||||
\(505\) | −12.4363 | −0.553409 | ||||||||
\(506\) | 2.24060 | 0.0996068 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.48585 | −0.332131 | ||||||||
\(509\) | −1.39866 | −0.0619945 | −0.0309972 | − | 0.999519i | \(-0.509868\pi\) | ||||
−0.0309972 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(510\) | −2.82924 | −0.125281 | ||||||||
\(511\) | 50.6822 | 2.24205 | ||||||||
\(512\) | 14.3851 | 0.635739 | ||||||||
\(513\) | 31.7436 | 1.40151 | ||||||||
\(514\) | 16.3180 | 0.719756 | ||||||||
\(515\) | −10.2372 | −0.451107 | ||||||||
\(516\) | 8.49343 | 0.373902 | ||||||||
\(517\) | 13.7617 | 0.605241 | ||||||||
\(518\) | 30.4770 | 1.33908 | ||||||||
\(519\) | −26.5226 | −1.16421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.4736 | −0.853154 | −0.426577 | − | 0.904451i | \(-0.640281\pi\) | ||||
−0.426577 | + | 0.904451i | \(0.640281\pi\) | |||||||
\(522\) | −20.3231 | −0.889520 | ||||||||
\(523\) | −8.05342 | −0.352152 | −0.176076 | − | 0.984377i | \(-0.556340\pi\) | ||||
−0.176076 | + | 0.984377i | \(0.556340\pi\) | |||||||
\(524\) | −3.73928 | −0.163351 | ||||||||
\(525\) | −11.1591 | −0.487021 | ||||||||
\(526\) | −21.8908 | −0.954483 | ||||||||
\(527\) | 0.406923 | 0.0177259 | ||||||||
\(528\) | −62.6732 | −2.72750 | ||||||||
\(529\) | −22.9051 | −0.995873 | ||||||||
\(530\) | 1.96043 | 0.0851558 | ||||||||
\(531\) | −21.7169 | −0.942432 | ||||||||
\(532\) | −6.24916 | −0.270935 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0626193 | −0.00270980 | ||||||||
\(535\) | 15.3401 | 0.663209 | ||||||||
\(536\) | 1.82970 | 0.0790311 | ||||||||
\(537\) | −7.61702 | −0.328699 | ||||||||
\(538\) | −16.4961 | −0.711199 | ||||||||
\(539\) | 37.7103 | 1.62430 | ||||||||
\(540\) | −2.31758 | −0.0997327 | ||||||||
\(541\) | 7.04652 | 0.302954 | 0.151477 | − | 0.988461i | \(-0.451597\pi\) | ||||
0.151477 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(542\) | −29.7408 | −1.27748 | ||||||||
\(543\) | 27.0411 | 1.16044 | ||||||||
\(544\) | −1.23103 | −0.0527800 | ||||||||
\(545\) | 0.515675 | 0.0220891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.5338 | 1.69034 | 0.845172 | − | 0.534494i | \(-0.179498\pi\) | ||||
0.845172 | + | 0.534494i | \(0.179498\pi\) | |||||||
\(548\) | −0.431481 | −0.0184319 | ||||||||
\(549\) | 1.78822 | 0.0763196 | ||||||||
\(550\) | −7.27285 | −0.310115 | ||||||||
\(551\) | 11.7075 | 0.498757 | ||||||||
\(552\) | −2.25556 | −0.0960031 | ||||||||
\(553\) | −41.3649 | −1.75901 | ||||||||
\(554\) | 1.59704 | 0.0678518 | ||||||||
\(555\) | −14.8722 | −0.631291 | ||||||||
\(556\) | 6.26622 | 0.265747 | ||||||||
\(557\) | 8.81508 | 0.373507 | 0.186753 | − | 0.982407i | \(-0.440203\pi\) | ||||
0.186753 | + | 0.982407i | \(0.440203\pi\) | |||||||
\(558\) | 5.19332 | 0.219851 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −17.6593 | −0.746243 | ||||||||
\(561\) | −8.77999 | −0.370691 | ||||||||
\(562\) | −13.8519 | −0.584307 | ||||||||
\(563\) | 10.7679 | 0.453813 | 0.226907 | − | 0.973917i | \(-0.427139\pi\) | ||||
0.226907 | + | 0.973917i | \(0.427139\pi\) | |||||||
\(564\) | 2.87358 | 0.120999 | ||||||||
\(565\) | 17.0097 | 0.715602 | ||||||||
\(566\) | 3.64130 | 0.153055 | ||||||||
\(567\) | −13.3991 | −0.562709 | ||||||||
\(568\) | −26.1748 | −1.09827 | ||||||||
\(569\) | −22.5894 | −0.946995 | −0.473498 | − | 0.880795i | \(-0.657009\pi\) | ||||
−0.473498 | + | 0.880795i | \(0.657009\pi\) | |||||||
\(570\) | 20.8006 | 0.871241 | ||||||||
\(571\) | −5.95207 | −0.249087 | −0.124543 | − | 0.992214i | \(-0.539747\pi\) | ||||
−0.124543 | + | 0.992214i | \(0.539747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.2011 | −0.760364 | ||||||||
\(574\) | 61.5632 | 2.56960 | ||||||||
\(575\) | −0.308077 | −0.0128477 | ||||||||
\(576\) | 33.0530 | 1.37721 | ||||||||
\(577\) | 21.0425 | 0.876010 | 0.438005 | − | 0.898972i | \(-0.355685\pi\) | ||||
0.438005 | + | 0.898972i | \(0.355685\pi\) | |||||||
\(578\) | 25.3977 | 1.05640 | ||||||||
\(579\) | 23.7501 | 0.987022 | ||||||||
\(580\) | −0.854759 | −0.0354919 | ||||||||
\(581\) | −34.5777 | −1.43452 | ||||||||
\(582\) | −44.7559 | −1.85519 | ||||||||
\(583\) | 6.08383 | 0.251966 | ||||||||
\(584\) | −33.2524 | −1.37600 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.6297 | −0.893515 | ||||||||
\(587\) | −19.8969 | −0.821232 | −0.410616 | − | 0.911808i | \(-0.634686\pi\) | ||||
−0.410616 | + | 0.911808i | \(0.634686\pi\) | |||||||
\(588\) | 7.87427 | 0.324729 | ||||||||
\(589\) | −2.99171 | −0.123271 | ||||||||
\(590\) | −6.23019 | −0.256493 | ||||||||
\(591\) | −1.33540 | −0.0549311 | ||||||||
\(592\) | −23.5354 | −0.967301 | ||||||||
\(593\) | −35.4858 | −1.45723 | −0.728614 | − | 0.684925i | \(-0.759835\pi\) | ||||
−0.728614 | + | 0.684925i | \(0.759835\pi\) | |||||||
\(594\) | −49.0580 | −2.01287 | ||||||||
\(595\) | −2.47392 | −0.101421 | ||||||||
\(596\) | −7.22995 | −0.296150 | ||||||||
\(597\) | −55.8024 | −2.28384 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5055 | 0.510962 | 0.255481 | − | 0.966814i | \(-0.417766\pi\) | ||||
0.255481 | + | 0.966814i | \(0.417766\pi\) | |||||||
\(600\) | 7.32143 | 0.298896 | ||||||||
\(601\) | −10.9255 | −0.445661 | −0.222831 | − | 0.974857i | \(-0.571530\pi\) | ||||
−0.222831 | + | 0.974857i | \(0.571530\pi\) | |||||||
\(602\) | 50.6583 | 2.06468 | ||||||||
\(603\) | 3.85041 | 0.156801 | ||||||||
\(604\) | 5.57911 | 0.227011 | ||||||||
\(605\) | −11.5699 | −0.470383 | ||||||||
\(606\) | −54.9690 | −2.23296 | ||||||||
\(607\) | −2.90532 | −0.117923 | −0.0589616 | − | 0.998260i | \(-0.518779\pi\) | ||||
−0.0589616 | + | 0.998260i | \(0.518779\pi\) | |||||||
\(608\) | 9.05056 | 0.367049 | ||||||||
\(609\) | −27.7614 | −1.12495 | ||||||||
\(610\) | 0.513010 | 0.0207712 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.17357 | −0.0474388 | ||||||||
\(613\) | −19.2621 | −0.777990 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(614\) | 37.2601 | 1.50370 | ||||||||
\(615\) | −30.0417 | −1.21140 | ||||||||
\(616\) | −46.5604 | −1.87597 | ||||||||
\(617\) | −0.902301 | −0.0363253 | −0.0181626 | − | 0.999835i | \(-0.505782\pi\) | ||||
−0.0181626 | + | 0.999835i | \(0.505782\pi\) | |||||||
\(618\) | −45.2489 | −1.82018 | ||||||||
\(619\) | 23.8784 | 0.959752 | 0.479876 | − | 0.877336i | \(-0.340682\pi\) | ||||
0.479876 | + | 0.877336i | \(0.340682\pi\) | |||||||
\(620\) | 0.218423 | 0.00877207 | ||||||||
\(621\) | −2.07809 | −0.0833909 | ||||||||
\(622\) | −9.40743 | −0.377204 | ||||||||
\(623\) | −0.0547552 | −0.00219372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.14140 | −0.0855875 | ||||||||
\(627\) | 64.5506 | 2.57790 | ||||||||
\(628\) | −0.791481 | −0.0315835 | ||||||||
\(629\) | −3.29712 | −0.131465 | ||||||||
\(630\) | −31.5732 | −1.25791 | ||||||||
\(631\) | 45.4774 | 1.81043 | 0.905213 | − | 0.424958i | \(-0.139711\pi\) | ||||
0.905213 | + | 0.424958i | \(0.139711\pi\) | |||||||
\(632\) | 27.1394 | 1.07955 | ||||||||
\(633\) | 54.3038 | 2.15838 | ||||||||
\(634\) | −13.6565 | −0.542368 | ||||||||
\(635\) | 21.7877 | 0.864620 | ||||||||
\(636\) | 1.27036 | 0.0503730 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.0934 | −0.716323 | ||||||||
\(639\) | −55.0819 | −2.17901 | ||||||||
\(640\) | 13.3287 | 0.526864 | ||||||||
\(641\) | 38.7591 | 1.53089 | 0.765447 | − | 0.643499i | \(-0.222518\pi\) | ||||
0.765447 | + | 0.643499i | \(0.222518\pi\) | |||||||
\(642\) | 67.8036 | 2.67599 | ||||||||
\(643\) | 14.5186 | 0.572559 | 0.286279 | − | 0.958146i | \(-0.407581\pi\) | ||||
0.286279 | + | 0.958146i | \(0.407581\pi\) | |||||||
\(644\) | 0.409101 | 0.0161208 | ||||||||
\(645\) | −24.7203 | −0.973361 | ||||||||
\(646\) | 4.61141 | 0.181434 | ||||||||
\(647\) | −5.86833 | −0.230708 | −0.115354 | − | 0.993324i | \(-0.536800\pi\) | ||||
−0.115354 | + | 0.993324i | \(0.536800\pi\) | |||||||
\(648\) | 8.79110 | 0.345347 | ||||||||
\(649\) | −19.3342 | −0.758933 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.09408 | 0.278039 | ||||||||
\(652\) | −5.26309 | −0.206119 | ||||||||
\(653\) | −13.9308 | −0.545154 | −0.272577 | − | 0.962134i | \(-0.587876\pi\) | ||||
−0.272577 | + | 0.962134i | \(0.587876\pi\) | |||||||
\(654\) | 2.27930 | 0.0891276 | ||||||||
\(655\) | 10.8833 | 0.425244 | ||||||||
\(656\) | −47.5413 | −1.85618 | ||||||||
\(657\) | −69.9761 | −2.73003 | ||||||||
\(658\) | 17.1392 | 0.668156 | ||||||||
\(659\) | 32.4177 | 1.26281 | 0.631406 | − | 0.775452i | \(-0.282478\pi\) | ||||
0.631406 | + | 0.775452i | \(0.282478\pi\) | |||||||
\(660\) | −4.71280 | −0.183446 | ||||||||
\(661\) | −42.0999 | −1.63750 | −0.818748 | − | 0.574154i | \(-0.805331\pi\) | ||||
−0.818748 | + | 0.574154i | \(0.805331\pi\) | |||||||
\(662\) | 30.2584 | 1.17603 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.6863 | 0.880400 | ||||||||
\(665\) | 18.1883 | 0.705313 | ||||||||
\(666\) | −42.0791 | −1.63053 | ||||||||
\(667\) | −0.766432 | −0.0296764 | ||||||||
\(668\) | −4.11967 | −0.159395 | ||||||||
\(669\) | 10.1131 | 0.390996 | ||||||||
\(670\) | 1.10461 | 0.0426749 | ||||||||
\(671\) | 1.59203 | 0.0614595 | ||||||||
\(672\) | −21.4611 | −0.827881 | ||||||||
\(673\) | 9.29450 | 0.358277 | 0.179138 | − | 0.983824i | \(-0.442669\pi\) | ||||
0.179138 | + | 0.983824i | \(0.442669\pi\) | |||||||
\(674\) | −30.9790 | −1.19327 | ||||||||
\(675\) | 6.74536 | 0.259629 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.6554 | −1.75468 | −0.877340 | − | 0.479870i | \(-0.840684\pi\) | ||||
−0.877340 | + | 0.479870i | \(0.840684\pi\) | |||||||
\(678\) | 75.1832 | 2.88739 | ||||||||
\(679\) | −39.1351 | −1.50187 | ||||||||
\(680\) | 1.62313 | 0.0622443 | ||||||||
\(681\) | −70.9485 | −2.71875 | ||||||||
\(682\) | 4.62353 | 0.177044 | ||||||||
\(683\) | 12.5289 | 0.479403 | 0.239702 | − | 0.970847i | \(-0.422950\pi\) | ||||
0.239702 | + | 0.970847i | \(0.422950\pi\) | |||||||
\(684\) | 8.62811 | 0.329904 | ||||||||
\(685\) | 1.25583 | 0.0479830 | ||||||||
\(686\) | 5.54822 | 0.211832 | ||||||||
\(687\) | −51.4968 | −1.96472 | ||||||||
\(688\) | −39.1201 | −1.49144 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.36171 | −0.0518394 | ||||||||
\(691\) | 5.09243 | 0.193725 | 0.0968625 | − | 0.995298i | \(-0.469119\pi\) | ||||
0.0968625 | + | 0.995298i | \(0.469119\pi\) | |||||||
\(692\) | −3.15616 | −0.119979 | ||||||||
\(693\) | −97.9813 | −3.72200 | ||||||||
\(694\) | −44.8054 | −1.70079 | ||||||||
\(695\) | −18.2380 | −0.691806 | ||||||||
\(696\) | 18.2142 | 0.690408 | ||||||||
\(697\) | −6.66013 | −0.252270 | ||||||||
\(698\) | −0.298534 | −0.0112997 | ||||||||
\(699\) | 8.75769 | 0.331246 | ||||||||
\(700\) | −1.32792 | −0.0501906 | ||||||||
\(701\) | −33.0018 | −1.24646 | −0.623230 | − | 0.782039i | \(-0.714180\pi\) | ||||
−0.623230 | + | 0.782039i | \(0.714180\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.2405 | 0.914246 | ||||||||
\(704\) | 29.4265 | 1.10905 | ||||||||
\(705\) | −8.36361 | −0.314992 | ||||||||
\(706\) | 18.7347 | 0.705090 | ||||||||
\(707\) | −48.0656 | −1.80769 | ||||||||
\(708\) | −4.03716 | −0.151726 | ||||||||
\(709\) | 9.50378 | 0.356922 | 0.178461 | − | 0.983947i | \(-0.442888\pi\) | ||||
0.178461 | + | 0.983947i | \(0.442888\pi\) | |||||||
\(710\) | −15.8020 | −0.593039 | ||||||||
\(711\) | 57.1119 | 2.14186 | ||||||||
\(712\) | 0.0359247 | 0.00134633 | ||||||||
\(713\) | 0.195852 | 0.00733472 | ||||||||
\(714\) | −10.9348 | −0.409225 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.906418 | −0.0338744 | ||||||||
\(717\) | 20.0337 | 0.748174 | ||||||||
\(718\) | −3.73077 | −0.139231 | ||||||||
\(719\) | 32.8065 | 1.22348 | 0.611739 | − | 0.791060i | \(-0.290470\pi\) | ||||
0.611739 | + | 0.791060i | \(0.290470\pi\) | |||||||
\(720\) | 24.3819 | 0.908662 | ||||||||
\(721\) | −39.5663 | −1.47353 | ||||||||
\(722\) | −4.81656 | −0.179254 | ||||||||
\(723\) | 19.0394 | 0.708083 | ||||||||
\(724\) | 3.21786 | 0.119591 | ||||||||
\(725\) | 2.48779 | 0.0923944 | ||||||||
\(726\) | −51.1393 | −1.89796 | ||||||||
\(727\) | −23.3248 | −0.865070 | −0.432535 | − | 0.901617i | \(-0.642381\pi\) | ||||
−0.432535 | + | 0.901617i | \(0.642381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.9269 | −1.47877 | ||||||||
\(730\) | −20.0749 | −0.743005 | ||||||||
\(731\) | −5.48040 | −0.202700 | ||||||||
\(732\) | 0.332430 | 0.0122870 | ||||||||
\(733\) | 41.5378 | 1.53423 | 0.767117 | − | 0.641507i | \(-0.221690\pi\) | ||||
0.767117 | + | 0.641507i | \(0.221690\pi\) | |||||||
\(734\) | 44.1218 | 1.62857 | ||||||||
\(735\) | −22.9182 | −0.845352 | ||||||||
\(736\) | −0.592494 | −0.0218396 | ||||||||
\(737\) | 3.42795 | 0.126270 | ||||||||
\(738\) | −84.9993 | −3.12887 | ||||||||
\(739\) | −1.05857 | −0.0389401 | −0.0194701 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194701 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(740\) | −1.76978 | −0.0650584 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.57695 | 0.278158 | ||||||||
\(743\) | −19.0752 | −0.699800 | −0.349900 | − | 0.936787i | \(-0.613784\pi\) | ||||
−0.349900 | + | 0.936787i | \(0.613784\pi\) | |||||||
\(744\) | −4.65441 | −0.170639 | ||||||||
\(745\) | 21.0429 | 0.770953 | ||||||||
\(746\) | −5.70219 | −0.208772 | ||||||||
\(747\) | 47.7409 | 1.74675 | ||||||||
\(748\) | −1.04481 | −0.0382021 | ||||||||
\(749\) | 59.2884 | 2.16635 | ||||||||
\(750\) | 4.42003 | 0.161397 | ||||||||
\(751\) | 46.7588 | 1.70625 | 0.853127 | − | 0.521703i | \(-0.174703\pi\) | ||||
0.853127 | + | 0.521703i | \(0.174703\pi\) | |||||||
\(752\) | −13.2355 | −0.482649 | ||||||||
\(753\) | −48.6896 | −1.77435 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.2381 | −0.590966 | ||||||||
\(756\) | −8.95729 | −0.325773 | ||||||||
\(757\) | 15.0982 | 0.548752 | 0.274376 | − | 0.961623i | \(-0.411529\pi\) | ||||
0.274376 | + | 0.961623i | \(0.411529\pi\) | |||||||
\(758\) | 41.6270 | 1.51196 | ||||||||
\(759\) | −4.22581 | −0.153387 | ||||||||
\(760\) | −11.9333 | −0.432866 | ||||||||
\(761\) | −20.5311 | −0.744253 | −0.372127 | − | 0.928182i | \(-0.621371\pi\) | ||||
−0.372127 | + | 0.928182i | \(0.621371\pi\) | |||||||
\(762\) | 96.3025 | 3.48867 | ||||||||
\(763\) | 1.99305 | 0.0721532 | ||||||||
\(764\) | −2.16592 | −0.0783602 | ||||||||
\(765\) | 3.41570 | 0.123495 | ||||||||
\(766\) | 50.9628 | 1.84136 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 23.1458 | 0.835201 | ||||||||
\(769\) | 33.9725 | 1.22508 | 0.612540 | − | 0.790440i | \(-0.290148\pi\) | ||||
0.612540 | + | 0.790440i | \(0.290148\pi\) | |||||||
\(770\) | −28.1091 | −1.01298 | ||||||||
\(771\) | −30.7760 | −1.10837 | ||||||||
\(772\) | 2.82625 | 0.101719 | ||||||||
\(773\) | 10.8481 | 0.390177 | 0.195089 | − | 0.980786i | \(-0.437501\pi\) | ||||
0.195089 | + | 0.980786i | \(0.437501\pi\) | |||||||
\(774\) | −69.9431 | −2.51405 | ||||||||
\(775\) | −0.635724 | −0.0228359 | ||||||||
\(776\) | 25.6764 | 0.921731 | ||||||||
\(777\) | −57.4802 | −2.06209 | ||||||||
\(778\) | 36.0303 | 1.29175 | ||||||||
\(779\) | 48.9654 | 1.75437 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.0385 | −1.75474 | ||||||||
\(782\) | −0.301886 | −0.0107954 | ||||||||
\(783\) | 16.7811 | 0.599707 | ||||||||
\(784\) | −36.2683 | −1.29530 | ||||||||
\(785\) | 2.30362 | 0.0822198 | ||||||||
\(786\) | 48.1043 | 1.71582 | ||||||||
\(787\) | 9.91801 | 0.353539 | 0.176769 | − | 0.984252i | \(-0.443435\pi\) | ||||
0.176769 | + | 0.984252i | \(0.443435\pi\) | |||||||
\(788\) | −0.158912 | −0.00566099 | ||||||||
\(789\) | 41.2863 | 1.46983 | ||||||||
\(790\) | 16.3844 | 0.582930 | ||||||||
\(791\) | 65.7412 | 2.33749 | ||||||||
\(792\) | 64.2853 | 2.28428 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 34.3807 | 1.22013 | ||||||||
\(795\) | −3.69741 | −0.131134 | ||||||||
\(796\) | −6.64044 | −0.235364 | ||||||||
\(797\) | −33.0159 | −1.16948 | −0.584742 | − | 0.811219i | \(-0.698804\pi\) | ||||
−0.584742 | + | 0.811219i | \(0.698804\pi\) | |||||||
\(798\) | 80.3929 | 2.84588 | ||||||||
\(799\) | −1.85418 | −0.0655962 | ||||||||
\(800\) | 1.92320 | 0.0679955 | ||||||||
\(801\) | 0.0755996 | 0.00267118 | ||||||||
\(802\) | 0.0348019 | 0.00122890 | ||||||||
\(803\) | −62.2986 | −2.19847 | ||||||||
\(804\) | 0.715788 | 0.0252439 | ||||||||
\(805\) | −1.19070 | −0.0419666 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.1120 | 1.09519 | ||||||||
\(808\) | 31.5357 | 1.10942 | ||||||||
\(809\) | −11.0248 | −0.387610 | −0.193805 | − | 0.981040i | \(-0.562083\pi\) | ||||
−0.193805 | + | 0.981040i | \(0.562083\pi\) | |||||||
\(810\) | 5.30729 | 0.186479 | ||||||||
\(811\) | −31.2682 | −1.09797 | −0.548987 | − | 0.835831i | \(-0.684986\pi\) | ||||
−0.548987 | + | 0.835831i | \(0.684986\pi\) | |||||||
\(812\) | −3.30359 | −0.115933 | ||||||||
\(813\) | 56.0916 | 1.96722 | ||||||||
\(814\) | −37.4624 | −1.31306 | ||||||||
\(815\) | 15.3183 | 0.536578 | ||||||||
\(816\) | 8.44425 | 0.295608 | ||||||||
\(817\) | 40.2920 | 1.40964 | ||||||||
\(818\) | 44.0723 | 1.54095 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.57493 | −0.124842 | ||||||||
\(821\) | −12.3719 | −0.431782 | −0.215891 | − | 0.976417i | \(-0.569266\pi\) | ||||
−0.215891 | + | 0.976417i | \(0.569266\pi\) | |||||||
\(822\) | 5.55083 | 0.193607 | ||||||||
\(823\) | −47.6643 | −1.66147 | −0.830737 | − | 0.556665i | \(-0.812081\pi\) | ||||
−0.830737 | + | 0.556665i | \(0.812081\pi\) | |||||||
\(824\) | 25.9593 | 0.904336 | ||||||||
\(825\) | 13.7167 | 0.477555 | ||||||||
\(826\) | −24.0793 | −0.837825 | ||||||||
\(827\) | −18.9966 | −0.660575 | −0.330287 | − | 0.943880i | \(-0.607146\pi\) | ||||
−0.330287 | + | 0.943880i | \(0.607146\pi\) | |||||||
\(828\) | −0.564839 | −0.0196295 | ||||||||
\(829\) | −44.5434 | −1.54706 | −0.773528 | − | 0.633762i | \(-0.781510\pi\) | ||||
−0.773528 | + | 0.633762i | \(0.781510\pi\) | |||||||
\(830\) | 13.6960 | 0.475395 | ||||||||
\(831\) | −3.01205 | −0.104487 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.08088 | −0.176042 | ||||||||
\(834\) | −80.6125 | −2.79138 | ||||||||
\(835\) | 11.9904 | 0.414945 | ||||||||
\(836\) | 7.68147 | 0.265669 | ||||||||
\(837\) | −4.28819 | −0.148222 | ||||||||
\(838\) | −26.6470 | −0.920506 | ||||||||
\(839\) | 23.6568 | 0.816724 | 0.408362 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408362 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(840\) | 28.2968 | 0.976333 | ||||||||
\(841\) | −22.8109 | −0.786582 | ||||||||
\(842\) | 46.1776 | 1.59138 | ||||||||
\(843\) | 26.1249 | 0.899790 | ||||||||
\(844\) | 6.46210 | 0.222435 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.6638 | −0.813579 | ||||||||
\(847\) | −44.7169 | −1.53649 | ||||||||
\(848\) | −5.85119 | −0.200931 | ||||||||
\(849\) | −6.86756 | −0.235694 | ||||||||
\(850\) | 0.979904 | 0.0336104 | ||||||||
\(851\) | −1.58690 | −0.0543983 | ||||||||
\(852\) | −10.2397 | −0.350806 | ||||||||
\(853\) | 1.85306 | 0.0634474 | 0.0317237 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317237 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(854\) | 1.98275 | 0.0678483 | ||||||||
\(855\) | −25.1123 | −0.858823 | ||||||||
\(856\) | −38.8989 | −1.32954 | ||||||||
\(857\) | 32.9142 | 1.12433 | 0.562163 | − | 0.827026i | \(-0.309969\pi\) | ||||
0.562163 | + | 0.827026i | \(0.309969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.9147 | 1.08892 | 0.544458 | − | 0.838788i | \(-0.316735\pi\) | ||||
0.544458 | + | 0.838788i | \(0.316735\pi\) | |||||||
\(860\) | −2.94169 | −0.100311 | ||||||||
\(861\) | −116.109 | −3.95699 | ||||||||
\(862\) | −15.5431 | −0.529400 | ||||||||
\(863\) | 11.5883 | 0.394469 | 0.197235 | − | 0.980356i | \(-0.436804\pi\) | ||||
0.197235 | + | 0.980356i | \(0.436804\pi\) | |||||||
\(864\) | 12.9727 | 0.441340 | ||||||||
\(865\) | 9.18608 | 0.312336 | ||||||||
\(866\) | −34.0906 | −1.15845 | ||||||||
\(867\) | −47.9004 | −1.62678 | ||||||||
\(868\) | 0.844189 | 0.0286537 | ||||||||
\(869\) | 50.8457 | 1.72482 | ||||||||
\(870\) | 10.9961 | 0.372804 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.30763 | −0.0442821 | ||||||||
\(873\) | 54.0333 | 1.82875 | ||||||||
\(874\) | 2.21947 | 0.0750748 | ||||||||
\(875\) | 3.86493 | 0.130659 | ||||||||
\(876\) | −13.0085 | −0.439517 | ||||||||
\(877\) | 48.0221 | 1.62159 | 0.810796 | − | 0.585328i | \(-0.199034\pi\) | ||||
0.810796 | + | 0.585328i | \(0.199034\pi\) | |||||||
\(878\) | −57.9910 | −1.95710 | ||||||||
\(879\) | 40.7940 | 1.37595 | ||||||||
\(880\) | 21.7068 | 0.731738 | ||||||||
\(881\) | −32.4131 | −1.09202 | −0.546012 | − | 0.837777i | \(-0.683855\pi\) | ||||
−0.546012 | + | 0.837777i | \(0.683855\pi\) | |||||||
\(882\) | −64.8443 | −2.18342 | ||||||||
\(883\) | 53.6030 | 1.80389 | 0.901943 | − | 0.431856i | \(-0.142141\pi\) | ||||
0.901943 | + | 0.431856i | \(0.142141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.7502 | 0.394980 | ||||||||
\(886\) | 1.40556 | 0.0472206 | ||||||||
\(887\) | −39.8878 | −1.33930 | −0.669650 | − | 0.742677i | \(-0.733556\pi\) | ||||
−0.669650 | + | 0.742677i | \(0.733556\pi\) | |||||||
\(888\) | 37.7126 | 1.26555 | ||||||||
\(889\) | 84.2082 | 2.82425 | ||||||||
\(890\) | 0.0216882 | 0.000726989 0 | ||||||||
\(891\) | 16.4702 | 0.551771 | ||||||||
\(892\) | 1.20345 | 0.0402946 | ||||||||
\(893\) | 13.6320 | 0.456177 | ||||||||
\(894\) | 93.0104 | 3.11073 | ||||||||
\(895\) | 2.63815 | 0.0881837 | ||||||||
\(896\) | 51.5146 | 1.72098 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −53.2468 | −1.77687 | ||||||||
\(899\) | −1.58155 | −0.0527477 | ||||||||
\(900\) | 1.83343 | 0.0611145 | ||||||||
\(901\) | −0.819702 | −0.0273082 | ||||||||
\(902\) | −75.6735 | −2.51965 | ||||||||
\(903\) | −95.5424 | −3.17945 | ||||||||
\(904\) | −43.1326 | −1.43457 | ||||||||
\(905\) | −9.36566 | −0.311325 | ||||||||
\(906\) | −71.7731 | −2.38450 | ||||||||
\(907\) | 33.5672 | 1.11458 | 0.557290 | − | 0.830318i | \(-0.311841\pi\) | ||||
0.557290 | + | 0.830318i | \(0.311841\pi\) | |||||||
\(908\) | −8.44281 | −0.280185 | ||||||||
\(909\) | 66.3634 | 2.20113 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.2448 | −0.836399 | −0.418199 | − | 0.908355i | \(-0.637339\pi\) | ||||
−0.418199 | + | 0.908355i | \(0.637339\pi\) | |||||||
\(912\) | −62.0823 | −2.05575 | ||||||||
\(913\) | 42.5029 | 1.40664 | ||||||||
\(914\) | 21.0032 | 0.694723 | ||||||||
\(915\) | −0.967545 | −0.0319861 | ||||||||
\(916\) | −6.12807 | −0.202477 | ||||||||
\(917\) | 42.0631 | 1.38904 | ||||||||
\(918\) | 6.60981 | 0.218156 | ||||||||
\(919\) | 30.1551 | 0.994726 | 0.497363 | − | 0.867543i | \(-0.334302\pi\) | ||||
0.497363 | + | 0.867543i | \(0.334302\pi\) | |||||||
\(920\) | 0.781213 | 0.0257558 | ||||||||
\(921\) | −70.2732 | −2.31558 | ||||||||
\(922\) | −49.7622 | −1.63883 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.2147 | −0.599219 | ||||||||
\(925\) | 5.15099 | 0.169363 | ||||||||
\(926\) | −52.0581 | −1.71074 | ||||||||
\(927\) | 54.6285 | 1.79424 | ||||||||
\(928\) | 4.78453 | 0.157060 | ||||||||
\(929\) | 34.6023 | 1.13526 | 0.567632 | − | 0.823283i | \(-0.307860\pi\) | ||||
0.567632 | + | 0.823283i | \(0.307860\pi\) | |||||||
\(930\) | −2.80992 | −0.0921410 | ||||||||
\(931\) | 37.3548 | 1.22425 | ||||||||
\(932\) | 1.04216 | 0.0341370 | ||||||||
\(933\) | 17.7426 | 0.580866 | ||||||||
\(934\) | 0.106141 | 0.00347303 | ||||||||
\(935\) | 3.04094 | 0.0994495 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.7809 | −0.515541 | −0.257771 | − | 0.966206i | \(-0.582988\pi\) | ||||
−0.257771 | + | 0.966206i | \(0.582988\pi\) | |||||||
\(938\) | 4.26926 | 0.139396 | ||||||||
\(939\) | 4.03871 | 0.131798 | ||||||||
\(940\) | −0.995262 | −0.0324619 | ||||||||
\(941\) | 22.5246 | 0.734280 | 0.367140 | − | 0.930166i | \(-0.380337\pi\) | ||||
0.367140 | + | 0.930166i | \(0.380337\pi\) | |||||||
\(942\) | 10.1821 | 0.331750 | ||||||||
\(943\) | −3.20552 | −0.104386 | ||||||||
\(944\) | 18.5949 | 0.605211 | ||||||||
\(945\) | 26.0704 | 0.848070 | ||||||||
\(946\) | −62.2692 | −2.02455 | ||||||||
\(947\) | 5.97656 | 0.194212 | 0.0971060 | − | 0.995274i | \(-0.469041\pi\) | ||||
0.0971060 | + | 0.995274i | \(0.469041\pi\) | |||||||
\(948\) | 10.6171 | 0.344826 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.20428 | −0.233738 | ||||||||
\(951\) | 25.7563 | 0.835207 | ||||||||
\(952\) | 6.27330 | 0.203319 | ||||||||
\(953\) | −0.933220 | −0.0302300 | −0.0151150 | − | 0.999886i | \(-0.504811\pi\) | ||||
−0.0151150 | + | 0.999886i | \(0.504811\pi\) | |||||||
\(954\) | −10.4614 | −0.338699 | ||||||||
\(955\) | 6.30396 | 0.203991 | ||||||||
\(956\) | 2.38400 | 0.0771039 | ||||||||
\(957\) | 34.1244 | 1.10308 | ||||||||
\(958\) | −14.0239 | −0.453091 | ||||||||
\(959\) | 4.85372 | 0.156735 | ||||||||
\(960\) | −17.8838 | −0.577197 | ||||||||
\(961\) | −30.5959 | −0.986963 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81.8585 | −2.63785 | ||||||||
\(964\) | 2.26567 | 0.0729724 | ||||||||
\(965\) | −8.22585 | −0.264800 | ||||||||
\(966\) | −5.26292 | −0.169332 | ||||||||
\(967\) | 39.4196 | 1.26765 | 0.633825 | − | 0.773477i | \(-0.281484\pi\) | ||||
0.633825 | + | 0.773477i | \(0.281484\pi\) | |||||||
\(968\) | 29.3386 | 0.942979 | ||||||||
\(969\) | −8.69720 | −0.279394 | ||||||||
\(970\) | 15.5012 | 0.497713 | ||||||||
\(971\) | −37.6269 | −1.20750 | −0.603752 | − | 0.797172i | \(-0.706328\pi\) | ||||
−0.603752 | + | 0.797172i | \(0.706328\pi\) | |||||||
\(972\) | −3.51361 | −0.112699 | ||||||||
\(973\) | −70.4886 | −2.25976 | ||||||||
\(974\) | −41.7456 | −1.33762 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.53115 | −0.0490109 | ||||||||
\(977\) | 62.0293 | 1.98449 | 0.992247 | − | 0.124282i | \(-0.0396627\pi\) | ||||
0.992247 | + | 0.124282i | \(0.0396627\pi\) | |||||||
\(978\) | 67.7076 | 2.16505 | ||||||||
\(979\) | 0.0673051 | 0.00215108 | ||||||||
\(980\) | −2.72725 | −0.0871187 | ||||||||
\(981\) | −2.75177 | −0.0878573 | ||||||||
\(982\) | 27.5336 | 0.878633 | ||||||||
\(983\) | 27.9591 | 0.891757 | 0.445879 | − | 0.895093i | \(-0.352891\pi\) | ||||
0.445879 | + | 0.895093i | \(0.352891\pi\) | |||||||
\(984\) | 76.1789 | 2.42849 | ||||||||
\(985\) | 0.462516 | 0.0147370 | ||||||||
\(986\) | 2.43780 | 0.0776354 | ||||||||
\(987\) | −32.3248 | −1.02891 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.63771 | −0.0838744 | ||||||||
\(990\) | 38.8098 | 1.23346 | ||||||||
\(991\) | 56.5077 | 1.79503 | 0.897513 | − | 0.440988i | \(-0.145372\pi\) | ||||
0.897513 | + | 0.440988i | \(0.145372\pi\) | |||||||
\(992\) | −1.22263 | −0.0388184 | ||||||||
\(993\) | −57.0678 | −1.81099 | ||||||||
\(994\) | −61.0738 | −1.93714 | ||||||||
\(995\) | 19.3271 | 0.612712 | ||||||||
\(996\) | 8.87500 | 0.281215 | ||||||||
\(997\) | −6.01115 | −0.190375 | −0.0951875 | − | 0.995459i | \(-0.530345\pi\) | ||||
−0.0951875 | + | 0.995459i | \(0.530345\pi\) | |||||||
\(998\) | 19.8957 | 0.629786 | ||||||||
\(999\) | 34.7453 | 1.09929 |
(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 | 845.2.a.n.1.4 | ✓ | 9 | |
3.2 | odd | 2 | 7605.2.a.cs.1.6 | 9 | |||
5.4 | even | 2 | 4225.2.a.bt.1.6 | 9 | |||
13.2 | odd | 12 | 845.2.m.j.316.6 | 36 | |||
13.3 | even | 3 | 845.2.e.p.191.6 | 18 | |||
13.4 | even | 6 | 845.2.e.o.146.4 | 18 | |||
13.5 | odd | 4 | 845.2.c.h.506.13 | 18 | |||
13.6 | odd | 12 | 845.2.m.j.361.13 | 36 | |||
13.7 | odd | 12 | 845.2.m.j.361.6 | 36 | |||
13.8 | odd | 4 | 845.2.c.h.506.6 | 18 | |||
13.9 | even | 3 | 845.2.e.p.146.6 | 18 | |||
13.10 | even | 6 | 845.2.e.o.191.4 | 18 | |||
13.11 | odd | 12 | 845.2.m.j.316.13 | 36 | |||
13.12 | even | 2 | 845.2.a.o.1.6 | yes | 9 | ||
39.38 | odd | 2 | 7605.2.a.cp.1.4 | 9 | |||
65.64 | even | 2 | 4225.2.a.bs.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.n.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial | |
845.2.a.o.1.6 | yes | 9 | 13.12 | even | 2 | ||
845.2.c.h.506.6 | 18 | 13.8 | odd | 4 | |||
845.2.c.h.506.13 | 18 | 13.5 | odd | 4 | |||
845.2.e.o.146.4 | 18 | 13.4 | even | 6 | |||
845.2.e.o.191.4 | 18 | 13.10 | even | 6 | |||
845.2.e.p.146.6 | 18 | 13.9 | even | 3 | |||
845.2.e.p.191.6 | 18 | 13.3 | even | 3 | |||
845.2.m.j.316.6 | 36 | 13.2 | odd | 12 | |||
845.2.m.j.316.13 | 36 | 13.11 | odd | 12 | |||
845.2.m.j.361.6 | 36 | 13.7 | odd | 12 | |||
845.2.m.j.361.13 | 36 | 13.6 | odd | 12 | |||
4225.2.a.bs.1.4 | 9 | 65.64 | even | 2 | |||
4225.2.a.bt.1.6 | 9 | 5.4 | even | 2 | |||
7605.2.a.cp.1.4 | 9 | 39.38 | odd | 2 | |||
7605.2.a.cs.1.6 | 9 | 3.2 | odd | 2 |