Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(107,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.s (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.107 |
Dual form | 342.2.s.a.179.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.22474 | + | 0.707107i | −0.547723 | + | 0.316228i | −0.748203 | − | 0.663470i | \(-0.769083\pi\) |
0.200480 | + | 0.979698i | \(0.435750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44949 | 0.547856 | 0.273928 | − | 0.961750i | \(-0.411677\pi\) | ||||
0.273928 | + | 0.961750i | \(0.411677\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.22474 | + | 0.707107i | 0.387298 | + | 0.223607i | ||||
\(11\) | − | 0.635674i | − | 0.191663i | −0.995398 | − | 0.0958315i | \(-0.969449\pi\) | ||
0.995398 | − | 0.0958315i | \(-0.0305510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.17423 | + | 2.98735i | 1.43507 | + | 0.828541i | 0.997502 | − | 0.0706424i | \(-0.0225049\pi\) |
0.437573 | + | 0.899183i | \(0.355838\pi\) | |||||||
\(14\) | −0.724745 | − | 1.25529i | −0.193696 | − | 0.335492i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.77526 | − | 1.02494i | 0.430563 | − | 0.248585i | −0.269024 | − | 0.963134i | \(-0.586701\pi\) |
0.699586 | + | 0.714548i | \(0.253368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | − | 1.41421i | − | 0.316228i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.550510 | + | 0.317837i | −0.117369 | + | 0.0677631i | ||||
\(23\) | 4.89898 | + | 2.82843i | 1.02151 | + | 0.589768i | 0.914540 | − | 0.404495i | \(-0.132553\pi\) |
0.106967 | + | 0.994263i | \(0.465886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | − | 5.97469i | − | 1.17173i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.724745 | + | 1.25529i | −0.136964 | + | 0.237228i | ||||
\(29\) | 1.22474 | − | 2.12132i | 0.227429 | − | 0.393919i | −0.729616 | − | 0.683857i | \(-0.760301\pi\) |
0.957046 | + | 0.289938i | \(0.0936346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.953512i | − | 0.171256i | −0.996327 | − | 0.0856279i | \(-0.972710\pi\) | ||
0.996327 | − | 0.0856279i | \(-0.0272896\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.77526 | − | 1.02494i | −0.304454 | − | 0.175776i | ||||
\(35\) | −1.77526 | + | 1.02494i | −0.300073 | + | 0.173247i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.51059i | − | 0.412738i | −0.978474 | − | 0.206369i | \(-0.933835\pi\) | ||
0.978474 | − | 0.206369i | \(-0.0661648\pi\) | |||||||
\(38\) | −3.50000 | − | 2.59808i | −0.567775 | − | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.22474 | + | 0.707107i | −0.193649 | + | 0.111803i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.94949 | − | 3.37662i | −0.297294 | − | 0.514929i | 0.678222 | − | 0.734857i | \(-0.262751\pi\) |
−0.975516 | + | 0.219928i | \(0.929418\pi\) | |||||||
\(44\) | 0.550510 | + | 0.317837i | 0.0829925 | + | 0.0479158i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.65685i | − | 0.834058i | ||||||
\(47\) | −1.77526 | − | 1.02494i | −0.258948 | − | 0.149503i | 0.364907 | − | 0.931044i | \(-0.381101\pi\) |
−0.623854 | + | 0.781541i | \(0.714434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.17423 | + | 2.98735i | −0.717537 | + | 0.414270i | ||||
\(53\) | −2.44949 | + | 4.24264i | −0.336463 | + | 0.582772i | −0.983765 | − | 0.179463i | \(-0.942564\pi\) |
0.647302 | + | 0.762234i | \(0.275897\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.449490 | + | 0.778539i | 0.0606092 | + | 0.104978i | ||||
\(56\) | 1.44949 | 0.193696 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.44949 | −0.321634 | ||||||||
\(59\) | 7.22474 | + | 12.5136i | 0.940582 | + | 1.62914i | 0.764365 | + | 0.644784i | \(0.223053\pi\) |
0.176217 | + | 0.984351i | \(0.443614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72474 | − | 2.98735i | 0.220831 | − | 0.382490i | −0.734230 | − | 0.678901i | \(-0.762456\pi\) |
0.955061 | + | 0.296411i | \(0.0957898\pi\) | |||||||
\(62\) | −0.825765 | + | 0.476756i | −0.104872 | + | 0.0605481i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.44949 | −1.04803 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.84847 | − | 5.10867i | −1.08101 | − | 0.624123i | −0.149843 | − | 0.988710i | \(-0.547877\pi\) |
−0.931169 | + | 0.364587i | \(0.881210\pi\) | |||||||
\(68\) | 2.04989i | 0.248585i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.77526 | + | 1.02494i | 0.212184 | + | 0.122504i | ||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.05051 | + | 1.81954i | 0.122953 | + | 0.212961i | 0.920931 | − | 0.389726i | \(-0.127430\pi\) |
−0.797978 | + | 0.602687i | \(0.794097\pi\) | |||||||
\(74\) | −2.17423 | + | 1.25529i | −0.252750 | + | 0.145925i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.500000 | + | 4.33013i | −0.0573539 | + | 0.496700i | ||||
\(77\) | − | 0.921404i | − | 0.105004i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.825765 | − | 0.476756i | 0.0929059 | − | 0.0536392i | −0.452827 | − | 0.891598i | \(-0.649585\pi\) |
0.545733 | + | 0.837959i | \(0.316251\pi\) | |||||||
\(80\) | 1.22474 | + | 0.707107i | 0.136931 | + | 0.0790569i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.8065i | − | 1.29593i | −0.761669 | − | 0.647967i | \(-0.775620\pi\) | ||
0.761669 | − | 0.647967i | \(-0.224380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.44949 | + | 2.51059i | −0.157219 | + | 0.272312i | ||||
\(86\) | −1.94949 | + | 3.37662i | −0.210219 | + | 0.364110i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.635674i | − | 0.0677631i | ||||||
\(89\) | −6.12372 | + | 10.6066i | −0.649113 | + | 1.12430i | 0.334221 | + | 0.942495i | \(0.391527\pi\) |
−0.983335 | + | 0.181803i | \(0.941807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50000 | + | 4.33013i | 0.786214 | + | 0.453921i | ||||
\(92\) | −4.89898 | + | 2.82843i | −0.510754 | + | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.04989i | 0.211430i | ||||||||
\(95\) | −3.67423 | + | 4.94975i | −0.376969 | + | 0.507833i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3485 | + | 9.43879i | −1.65994 | + | 0.958364i | −0.687193 | + | 0.726474i | \(0.741158\pi\) |
−0.972742 | + | 0.231890i | \(0.925509\pi\) | |||||||
\(98\) | 2.44949 | + | 4.24264i | 0.247436 | + | 0.428571i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.50000 | − | 2.59808i | −0.150000 | − | 0.259808i | ||||
\(101\) | −11.4495 | − | 6.61037i | −1.13927 | − | 0.657756i | −0.193018 | − | 0.981195i | \(-0.561828\pi\) |
−0.946249 | + | 0.323439i | \(0.895161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.4600i | − | 1.42478i | −0.701782 | − | 0.712392i | \(-0.747612\pi\) | ||
0.701782 | − | 0.712392i | \(-0.252388\pi\) | |||||||
\(104\) | 5.17423 | + | 2.98735i | 0.507375 | + | 0.292933i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.89898 | 0.475831 | ||||||||
\(107\) | 15.7980 | 1.52725 | 0.763623 | − | 0.645662i | \(-0.223419\pi\) | ||||
0.763623 | + | 0.645662i | \(0.223419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.6969 | + | 8.48528i | −1.40771 | + | 0.812743i | −0.995167 | − | 0.0981950i | \(-0.968693\pi\) |
−0.412544 | + | 0.910938i | \(0.635360\pi\) | |||||||
\(110\) | 0.449490 | − | 0.778539i | 0.0428572 | − | 0.0742308i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.724745 | − | 1.25529i | −0.0684820 | − | 0.118614i | ||||
\(113\) | −17.1464 | −1.61300 | −0.806500 | − | 0.591234i | \(-0.798641\pi\) | ||||
−0.806500 | + | 0.591234i | \(0.798641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | −0.746004 | ||||||||
\(116\) | 1.22474 | + | 2.12132i | 0.113715 | + | 0.196960i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.22474 | − | 12.5136i | 0.665092 | − | 1.15197i | ||||
\(119\) | 2.57321 | − | 1.48565i | 0.235886 | − | 0.136189i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5959 | 0.963265 | ||||||||
\(122\) | −3.44949 | −0.312302 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.825765 | + | 0.476756i | 0.0741559 | + | 0.0428139i | ||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847 | + | 4.24264i | 0.652071 | + | 0.376473i | 0.789249 | − | 0.614073i | \(-0.210470\pi\) |
−0.137178 | + | 0.990546i | \(0.543803\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.22474 | + | 7.31747i | 0.370535 | + | 0.641785i | ||||
\(131\) | 12.7980 | − | 7.38891i | 1.11816 | − | 0.645572i | 0.177232 | − | 0.984169i | \(-0.443286\pi\) |
0.940931 | + | 0.338598i | \(0.109953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.79796 | − | 2.51059i | 0.502747 | − | 0.217696i | ||||
\(134\) | 10.2173i | 0.882643i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.77526 | − | 1.02494i | 0.152227 | − | 0.0878882i | ||||
\(137\) | −5.44949 | − | 3.14626i | −0.465581 | − | 0.268804i | 0.248807 | − | 0.968553i | \(-0.419962\pi\) |
−0.714388 | + | 0.699750i | \(0.753295\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | − | 6.06218i | 0.296866 | − | 0.514187i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.975417 | + | 0.220366i | \(0.0707252\pi\) | |||||||
\(140\) | − | 2.04989i | − | 0.173247i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | − | 5.19615i | 0.251754 | − | 0.436051i | ||||
\(143\) | 1.89898 | − | 3.28913i | 0.158801 | − | 0.275051i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.46410i | 0.287678i | ||||||||
\(146\) | 1.05051 | − | 1.81954i | 0.0869408 | − | 0.150586i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.17423 | + | 1.25529i | 0.178721 | + | 0.103185i | ||||
\(149\) | 17.4495 | − | 10.0745i | 1.42952 | − | 0.825333i | 0.432435 | − | 0.901665i | \(-0.357654\pi\) |
0.997082 | + | 0.0763323i | \(0.0243210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.55708i | − | 0.126713i | −0.997991 | − | 0.0633566i | \(-0.979819\pi\) | ||
0.997991 | − | 0.0633566i | \(-0.0201806\pi\) | |||||||
\(152\) | 4.00000 | − | 1.73205i | 0.324443 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.797959 | + | 0.460702i | −0.0643014 | + | 0.0371244i | ||||
\(155\) | 0.674235 | + | 1.16781i | 0.0541558 | + | 0.0938006i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.17423 | − | 10.6941i | −0.492758 | − | 0.853481i | 0.507208 | − | 0.861824i | \(-0.330678\pi\) |
−0.999965 | + | 0.00834275i | \(0.997344\pi\) | |||||||
\(158\) | −0.825765 | − | 0.476756i | −0.0656944 | − | 0.0379287i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.41421i | − | 0.111803i | ||||||
\(161\) | 7.10102 | + | 4.09978i | 0.559639 | + | 0.323108i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.69694 | 0.602871 | 0.301435 | − | 0.953487i | \(-0.402534\pi\) | ||||
0.301435 | + | 0.953487i | \(0.402534\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.2247 | + | 5.90326i | −0.793594 | + | 0.458182i | ||||
\(167\) | 4.22474 | − | 7.31747i | 0.326921 | − | 0.566243i | −0.654979 | − | 0.755647i | \(-0.727322\pi\) |
0.981899 | + | 0.189404i | \(0.0606557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3485 | + | 19.6561i | 0.872959 | + | 1.51201i | ||||
\(170\) | 2.89898 | 0.222342 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.89898 | 0.297294 | ||||||||
\(173\) | −6.12372 | − | 10.6066i | −0.465578 | − | 0.806405i | 0.533649 | − | 0.845706i | \(-0.320820\pi\) |
−0.999227 | + | 0.0393009i | \(0.987487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.17423 | + | 3.76588i | −0.164357 | + | 0.284674i | ||||
\(176\) | −0.550510 | + | 0.317837i | −0.0414963 | + | 0.0239579i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.2474 | 0.917985 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.65153 | − | 2.68556i | −0.345746 | − | 0.199616i | 0.317064 | − | 0.948404i | \(-0.397303\pi\) |
−0.662810 | + | 0.748788i | \(0.730636\pi\) | |||||||
\(182\) | − | 8.66025i | − | 0.641941i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.89898 | + | 2.82843i | 0.361158 | + | 0.208514i | ||||
\(185\) | 1.77526 | + | 3.07483i | 0.130519 | + | 0.226066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.651531 | − | 1.12848i | −0.0476446 | − | 0.0825230i | ||||
\(188\) | 1.77526 | − | 1.02494i | 0.129474 | − | 0.0747517i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.12372 | + | 0.707107i | 0.444262 | + | 0.0512989i | ||||
\(191\) | − | 15.2706i | − | 1.10494i | −0.833532 | − | 0.552472i | \(-0.813685\pi\) | ||
0.833532 | − | 0.552472i | \(-0.186315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8485 | − | 8.57277i | 1.06882 | − | 0.617081i | 0.140958 | − | 0.990016i | \(-0.454982\pi\) |
0.927858 | + | 0.372934i | \(0.121648\pi\) | |||||||
\(194\) | 16.3485 | + | 9.43879i | 1.17375 | + | 0.677666i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.44949 | − | 4.24264i | 0.174964 | − | 0.303046i | ||||
\(197\) | − | 20.2918i | − | 1.44573i | −0.690989 | − | 0.722865i | \(-0.742825\pi\) | ||
0.690989 | − | 0.722865i | \(-0.257175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.62372 | + | 14.9367i | −0.611320 | + | 1.05884i | 0.379699 | + | 0.925110i | \(0.376028\pi\) |
−0.991018 | + | 0.133726i | \(0.957306\pi\) | |||||||
\(200\) | −1.50000 | + | 2.59808i | −0.106066 | + | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.2207i | 0.930207i | ||||||||
\(203\) | 1.77526 | − | 3.07483i | 0.124598 | − | 0.215811i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.5227 | + | 7.22999i | −0.872498 | + | 0.503737i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.97469i | − | 0.414270i | ||||||
\(209\) | −1.10102 | − | 2.54270i | −0.0761592 | − | 0.175882i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.15153 | − | 1.81954i | 0.216960 | − | 0.125262i | −0.387582 | − | 0.921835i | \(-0.626689\pi\) |
0.604542 | + | 0.796573i | \(0.293356\pi\) | |||||||
\(212\) | −2.44949 | − | 4.24264i | −0.168232 | − | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.89898 | − | 13.6814i | −0.539963 | − | 0.935244i | ||||
\(215\) | 4.77526 | + | 2.75699i | 0.325670 | + | 0.188025i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.38211i | − | 0.0938234i | ||||||
\(218\) | 14.6969 | + | 8.48528i | 0.995402 | + | 0.574696i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.898979 | −0.0606092 | ||||||||
\(221\) | 12.2474 | 0.823853 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.17423 | + | 1.25529i | −0.145598 | + | 0.0840608i | −0.571029 | − | 0.820930i | \(-0.693456\pi\) |
0.425432 | + | 0.904991i | \(0.360122\pi\) | |||||||
\(224\) | −0.724745 | + | 1.25529i | −0.0484241 | + | 0.0838729i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.57321 | + | 14.8492i | 0.570282 | + | 0.987757i | ||||
\(227\) | −23.1464 | −1.53628 | −0.768141 | − | 0.640280i | \(-0.778818\pi\) | ||||
−0.768141 | + | 0.640280i | \(0.778818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2474 | −1.27191 | −0.635954 | − | 0.771727i | \(-0.719393\pi\) | ||||
−0.635954 | + | 0.771727i | \(0.719393\pi\) | |||||||
\(230\) | 4.00000 | + | 6.92820i | 0.263752 | + | 0.456832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.22474 | − | 2.12132i | 0.0804084 | − | 0.139272i | ||||
\(233\) | −15.2474 | + | 8.80312i | −0.998894 | + | 0.576711i | −0.907921 | − | 0.419142i | \(-0.862331\pi\) |
−0.0909728 | + | 0.995853i | \(0.528998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.89898 | 0.189109 | ||||||||
\(236\) | −14.4495 | −0.940582 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.57321 | − | 1.48565i | −0.166797 | − | 0.0963001i | ||||
\(239\) | 22.4846i | 1.45440i | 0.686423 | + | 0.727202i | \(0.259180\pi\) | ||||
−0.686423 | + | 0.727202i | \(0.740820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1515 | + | 7.01569i | 0.782749 | + | 0.451920i | 0.837404 | − | 0.546585i | \(-0.184072\pi\) |
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | −5.29796 | − | 9.17633i | −0.340566 | − | 0.589877i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.72474 | + | 2.98735i | 0.110415 | + | 0.191245i | ||||
\(245\) | 6.00000 | − | 3.46410i | 0.383326 | − | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.8712 | + | 2.98735i | 1.64614 | + | 0.190080i | ||||
\(248\) | − | 0.953512i | − | 0.0605481i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.79796 | + | 5.65685i | −0.619677 | + | 0.357771i | ||||
\(251\) | 1.22474 | + | 0.707107i | 0.0773052 | + | 0.0446322i | 0.538154 | − | 0.842846i | \(-0.319122\pi\) |
−0.460849 | + | 0.887478i | \(0.652455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.79796 | − | 3.11416i | 0.113037 | − | 0.195785i | ||||
\(254\) | − | 8.48528i | − | 0.532414i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.00000 | + | 10.3923i | −0.374270 | + | 0.648254i | −0.990217 | − | 0.139533i | \(-0.955440\pi\) |
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.63907i | − | 0.226121i | ||||||
\(260\) | 4.22474 | − | 7.31747i | 0.262008 | − | 0.453810i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.7980 | − | 7.38891i | −0.790661 | − | 0.456488i | ||||
\(263\) | 0.797959 | − | 0.460702i | 0.0492043 | − | 0.0284081i | −0.475196 | − | 0.879880i | \(-0.657623\pi\) |
0.524400 | + | 0.851472i | \(0.324290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.92820i | − | 0.425596i | ||||||
\(266\) | −5.07321 | − | 3.76588i | −0.311059 | − | 0.230901i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.84847 | − | 5.10867i | 0.540506 | − | 0.312061i | ||||
\(269\) | 10.2247 | + | 17.7098i | 0.623414 | + | 1.07978i | 0.988845 | + | 0.148946i | \(0.0475881\pi\) |
−0.365432 | + | 0.930838i | \(0.619079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6969 | − | 27.1879i | −0.953521 | − | 1.65155i | −0.737717 | − | 0.675110i | \(-0.764096\pi\) |
−0.215804 | − | 0.976437i | \(-0.569237\pi\) | |||||||
\(272\) | −1.77526 | − | 1.02494i | −0.107641 | − | 0.0621464i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.29253i | 0.380146i | ||||||||
\(275\) | 1.65153 | + | 0.953512i | 0.0995911 | + | 0.0574989i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.10102 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.77526 | + | 1.02494i | −0.106092 | + | 0.0612521i | ||||
\(281\) | −11.5732 | + | 20.0454i | −0.690400 | + | 1.19581i | 0.281307 | + | 0.959618i | \(0.409232\pi\) |
−0.971707 | + | 0.236190i | \(0.924101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.44949 | + | 12.9029i | 0.442826 | + | 0.766997i | 0.997898 | − | 0.0648050i | \(-0.0206425\pi\) |
−0.555072 | + | 0.831802i | \(0.687309\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.79796 | −0.224578 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.39898 | + | 11.0834i | −0.376411 | + | 0.651962i | ||||
\(290\) | 3.00000 | − | 1.73205i | 0.176166 | − | 0.101710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.10102 | −0.122953 | ||||||||
\(293\) | −10.6515 | −0.622269 | −0.311135 | − | 0.950366i | \(-0.600709\pi\) | ||||
−0.311135 | + | 0.950366i | \(0.600709\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.6969 | − | 10.2173i | −1.03036 | − | 0.594876i | ||||
\(296\) | − | 2.51059i | − | 0.145925i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.4495 | − | 10.0745i | −1.01082 | − | 0.583598i | ||||
\(299\) | 16.8990 | + | 29.2699i | 0.977293 | + | 1.69272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.82577 | − | 4.89437i | −0.162874 | − | 0.282107i | ||||
\(302\) | −1.34847 | + | 0.778539i | −0.0775957 | + | 0.0447999i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 2.59808i | −0.200739 | − | 0.149010i | ||||
\(305\) | 4.87832i | 0.279332i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.3485 | + | 7.70674i | −0.761837 | + | 0.439847i | −0.829955 | − | 0.557830i | \(-0.811634\pi\) |
0.0681177 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(308\) | 0.797959 | + | 0.460702i | 0.0454679 | + | 0.0262509i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.674235 | − | 1.16781i | 0.0382940 | − | 0.0663271i | ||||
\(311\) | 5.16404i | 0.292826i | 0.989224 | + | 0.146413i | \(0.0467729\pi\) | ||||
−0.989224 | + | 0.146413i | \(0.953227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3485 | + | 19.6561i | −0.641453 | + | 1.11103i | 0.343655 | + | 0.939096i | \(0.388335\pi\) |
−0.985108 | + | 0.171934i | \(0.944998\pi\) | |||||||
\(314\) | −6.17423 | + | 10.6941i | −0.348432 | + | 0.603502i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.953512i | 0.0536392i | ||||||||
\(317\) | 3.67423 | − | 6.36396i | 0.206366 | − | 0.357436i | −0.744201 | − | 0.667955i | \(-0.767170\pi\) |
0.950567 | + | 0.310520i | \(0.100503\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.34847 | − | 0.778539i | −0.0754998 | − | 0.0435898i | ||||
\(320\) | −1.22474 | + | 0.707107i | −0.0684653 | + | 0.0395285i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 8.19955i | − | 0.456943i | ||||||
\(323\) | 5.32577 | − | 7.17461i | 0.296334 | − | 0.399206i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5227 | + | 8.96204i | −0.861045 | + | 0.497124i | ||||
\(326\) | −3.84847 | − | 6.66574i | −0.213147 | − | 0.369181i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.57321 | − | 1.48565i | −0.141866 | − | 0.0819063i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.7026i | − | 1.02799i | −0.857794 | − | 0.513994i | \(-0.828165\pi\) | ||
0.857794 | − | 0.513994i | \(-0.171835\pi\) | |||||||
\(332\) | 10.2247 | + | 5.90326i | 0.561156 | + | 0.323983i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.44949 | −0.462336 | ||||||||
\(335\) | 14.4495 | 0.789460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.80306 | − | 1.04100i | 0.0982190 | − | 0.0567068i | −0.450086 | − | 0.892985i | \(-0.648607\pi\) |
0.548305 | + | 0.836278i | \(0.315273\pi\) | |||||||
\(338\) | 11.3485 | − | 19.6561i | 0.617275 | − | 1.06915i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.44949 | − | 2.51059i | −0.0786096 | − | 0.136156i | ||||
\(341\) | −0.606123 | −0.0328234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2474 | −0.931275 | ||||||||
\(344\) | −1.94949 | − | 3.37662i | −0.105109 | − | 0.182055i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.12372 | + | 10.6066i | −0.329213 | + | 0.570214i | ||||
\(347\) | −28.2247 | + | 16.2956i | −1.51518 | + | 0.874792i | −0.515342 | + | 0.856984i | \(0.672335\pi\) |
−0.999841 | + | 0.0178073i | \(0.994331\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2474 | 1.24441 | 0.622204 | − | 0.782855i | \(-0.286238\pi\) | ||||
0.622204 | + | 0.782855i | \(0.286238\pi\) | |||||||
\(350\) | 4.34847 | 0.232435 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.550510 | + | 0.317837i | 0.0293423 | + | 0.0169408i | ||||
\(353\) | − | 3.32124i | − | 0.176772i | −0.996086 | − | 0.0883858i | \(-0.971829\pi\) | ||
0.996086 | − | 0.0883858i | \(-0.0281708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.34847 | − | 4.24264i | −0.390016 | − | 0.225176i | ||||
\(356\) | −6.12372 | − | 10.6066i | −0.324557 | − | 0.562149i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | 9.79796 | − | 5.65685i | 0.517116 | − | 0.298557i | −0.218638 | − | 0.975806i | \(-0.570161\pi\) |
0.735754 | + | 0.677249i | \(0.236828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 5.37113i | 0.282300i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.50000 | + | 4.33013i | −0.393107 | + | 0.226960i | ||||
\(365\) | −2.57321 | − | 1.48565i | −0.134688 | − | 0.0777623i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.17423 | − | 12.4261i | 0.374492 | − | 0.648639i | −0.615759 | − | 0.787935i | \(-0.711150\pi\) |
0.990251 | + | 0.139295i | \(0.0444838\pi\) | |||||||
\(368\) | − | 5.65685i | − | 0.294884i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.77526 | − | 3.07483i | 0.0922911 | − | 0.159853i | ||||
\(371\) | −3.55051 | + | 6.14966i | −0.184333 | + | 0.319275i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.2993i | − | 0.636835i | −0.947951 | − | 0.318418i | \(-0.896849\pi\) | ||
0.947951 | − | 0.318418i | \(-0.103151\pi\) | |||||||
\(374\) | −0.651531 | + | 1.12848i | −0.0336899 | + | 0.0583525i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.77526 | − | 1.02494i | −0.0915518 | − | 0.0528575i | ||||
\(377\) | 12.6742 | − | 7.31747i | 0.652756 | − | 0.376869i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0526i | 0.978664i | 0.872098 | + | 0.489332i | \(0.162759\pi\) | ||||
−0.872098 | + | 0.489332i | \(0.837241\pi\) | |||||||
\(380\) | −2.44949 | − | 5.65685i | −0.125656 | − | 0.290191i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.2247 | + | 7.63531i | −0.676637 | + | 0.390656i | ||||
\(383\) | −5.44949 | − | 9.43879i | −0.278456 | − | 0.482300i | 0.692545 | − | 0.721374i | \(-0.256489\pi\) |
−0.971001 | + | 0.239075i | \(0.923156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.651531 | + | 1.12848i | 0.0332051 | + | 0.0575129i | ||||
\(386\) | −14.8485 | − | 8.57277i | −0.755767 | − | 0.436342i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 18.8776i | − | 0.958364i | ||||||
\(389\) | 22.8990 | + | 13.2207i | 1.16102 | + | 0.670318i | 0.951549 | − | 0.307496i | \(-0.0994912\pi\) |
0.209475 | + | 0.977814i | \(0.432824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5959 | 0.586431 | ||||||||
\(392\) | −4.89898 | −0.247436 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.5732 | + | 10.1459i | −0.885326 | + | 0.511143i | ||||
\(395\) | −0.674235 | + | 1.16781i | −0.0339244 | + | 0.0587588i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8258 | − | 18.7508i | −0.543330 | − | 0.941074i | −0.998710 | − | 0.0507775i | \(-0.983830\pi\) |
0.455380 | − | 0.890297i | \(-0.349503\pi\) | |||||||
\(398\) | 17.2474 | 0.864536 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 0.123724 | + | 0.214297i | 0.00617850 | + | 0.0107015i | 0.869098 | − | 0.494640i | \(-0.164700\pi\) |
−0.862920 | + | 0.505341i | \(0.831367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.84847 | − | 4.93369i | 0.141892 | − | 0.245765i | ||||
\(404\) | 11.4495 | − | 6.61037i | 0.569633 | − | 0.328878i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.55051 | −0.176209 | ||||||||
\(407\) | −1.59592 | −0.0791067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0454 | − | 14.4600i | −1.23842 | − | 0.715000i | −0.269645 | − | 0.962960i | \(-0.586906\pi\) |
−0.968770 | + | 0.247960i | \(0.920240\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.5227 | + | 7.22999i | 0.616949 | + | 0.356196i | ||||
\(413\) | 10.4722 | + | 18.1384i | 0.515303 | + | 0.892531i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.34847 | + | 14.4600i | 0.409810 | + | 0.709812i | ||||
\(416\) | −5.17423 | + | 2.98735i | −0.253688 | + | 0.146467i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.65153 | + | 2.22486i | −0.0807790 | + | 0.108821i | ||||
\(419\) | − | 3.74983i | − | 0.183191i | −0.995796 | − | 0.0915956i | \(-0.970803\pi\) | ||
0.995796 | − | 0.0915956i | \(-0.0291967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.34847 | − | 0.778539i | 0.0657204 | − | 0.0379437i | −0.466780 | − | 0.884374i | \(-0.654586\pi\) |
0.532500 | + | 0.846430i | \(0.321253\pi\) | |||||||
\(422\) | −3.15153 | − | 1.81954i | −0.153414 | − | 0.0885737i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.44949 | + | 4.24264i | −0.118958 | + | 0.206041i | ||||
\(425\) | 6.14966i | 0.298303i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50000 | − | 4.33013i | 0.120983 | − | 0.209550i | ||||
\(428\) | −7.89898 | + | 13.6814i | −0.381812 | + | 0.661317i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 5.51399i | − | 0.265908i | ||||||
\(431\) | −8.02270 | + | 13.8957i | −0.386440 | + | 0.669334i | −0.991968 | − | 0.126490i | \(-0.959629\pi\) |
0.605528 | + | 0.795824i | \(0.292962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.1969 | + | 14.5475i | 1.21089 | + | 0.699106i | 0.962953 | − | 0.269670i | \(-0.0869148\pi\) |
0.247935 | + | 0.968777i | \(0.420248\pi\) | |||||||
\(434\) | −1.19694 | + | 0.691053i | −0.0574549 | + | 0.0331716i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 16.9706i | − | 0.812743i | ||||||
\(437\) | 24.4949 | + | 2.82843i | 1.17175 | + | 0.135302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5227 | + | 7.22999i | −0.597676 | + | 0.345068i | −0.768127 | − | 0.640298i | \(-0.778811\pi\) |
0.170451 | + | 0.985366i | \(0.445478\pi\) | |||||||
\(440\) | 0.449490 | + | 0.778539i | 0.0214286 | + | 0.0371154i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.12372 | − | 10.6066i | −0.291276 | − | 0.504505i | ||||
\(443\) | −25.7753 | − | 14.8814i | −1.22462 | − | 0.707034i | −0.258720 | − | 0.965952i | \(-0.583301\pi\) |
−0.965899 | + | 0.258918i | \(0.916634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 17.3205i | − | 0.821071i | ||||||
\(446\) | 2.17423 | + | 1.25529i | 0.102953 | + | 0.0594399i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.44949 | 0.0684820 | ||||||||
\(449\) | −18.2474 | −0.861150 | −0.430575 | − | 0.902555i | \(-0.641689\pi\) | ||||
−0.430575 | + | 0.902555i | \(0.641689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.57321 | − | 14.8492i | 0.403250 | − | 0.698450i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.5732 | + | 20.0454i | 0.543158 | + | 0.940777i | ||||
\(455\) | −12.2474 | −0.574169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6969 | 0.921384 | 0.460692 | − | 0.887560i | \(-0.347601\pi\) | ||||
0.460692 | + | 0.887560i | \(0.347601\pi\) | |||||||
\(458\) | 9.62372 | + | 16.6688i | 0.449687 | + | 0.778881i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.00000 | − | 6.92820i | 0.186501 | − | 0.323029i | ||||
\(461\) | 9.12372 | − | 5.26758i | 0.424934 | − | 0.245336i | −0.272252 | − | 0.962226i | \(-0.587768\pi\) |
0.697186 | + | 0.716890i | \(0.254435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.1464 | 1.86576 | 0.932881 | − | 0.360184i | \(-0.117286\pi\) | ||||
0.932881 | + | 0.360184i | \(0.117286\pi\) | |||||||
\(464\) | −2.44949 | −0.113715 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.2474 | + | 8.80312i | 0.706324 | + | 0.407797i | ||||
\(467\) | − | 21.0703i | − | 0.975019i | −0.873118 | − | 0.487510i | \(-0.837905\pi\) | ||
0.873118 | − | 0.487510i | \(-0.162095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8258 | − | 7.40496i | −0.592239 | − | 0.341929i | ||||
\(470\) | −1.44949 | − | 2.51059i | −0.0668600 | − | 0.115805i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.22474 | + | 12.5136i | 0.332546 | + | 0.575986i | ||||
\(473\) | −2.14643 | + | 1.23924i | −0.0986929 | + | 0.0569804i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.50000 | + | 12.9904i | −0.0688247 | + | 0.596040i | ||||
\(476\) | 2.97129i | 0.136189i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.4722 | − | 11.2423i | 0.890637 | − | 0.514210i | ||||
\(479\) | −8.14643 | − | 4.70334i | −0.372220 | − | 0.214901i | 0.302208 | − | 0.953242i | \(-0.402276\pi\) |
−0.674428 | + | 0.738341i | \(0.735610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | − | 12.9904i | 0.341971 | − | 0.592310i | ||||
\(482\) | − | 14.0314i | − | 0.639112i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.29796 | + | 9.17633i | −0.240816 | + | 0.417106i | ||||
\(485\) | 13.3485 | − | 23.1202i | 0.606123 | − | 1.04984i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.6622i | 1.79727i | 0.438702 | + | 0.898633i | \(0.355439\pi\) | ||||
−0.438702 | + | 0.898633i | \(0.644561\pi\) | |||||||
\(488\) | 1.72474 | − | 2.98735i | 0.0780755 | − | 0.135231i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.00000 | − | 3.46410i | −0.271052 | − | 0.156492i | ||||
\(491\) | 26.1464 | − | 15.0956i | 1.17997 | − | 0.681257i | 0.223964 | − | 0.974597i | \(-0.428100\pi\) |
0.956008 | + | 0.293340i | \(0.0947669\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.02118i | − | 0.226143i | ||||||
\(494\) | −10.3485 | − | 23.8988i | −0.465600 | − | 1.07526i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.825765 | + | 0.476756i | −0.0370780 | + | 0.0214070i | ||||
\(497\) | 4.34847 | + | 7.53177i | 0.195056 | + | 0.337846i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.7474 | + | 37.6677i | 0.973550 | + | 1.68624i | 0.684641 | + | 0.728881i | \(0.259959\pi\) |
0.288909 | + | 0.957357i | \(0.406708\pi\) | |||||||
\(500\) | 9.79796 | + | 5.65685i | 0.438178 | + | 0.252982i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 1.41421i | − | 0.0631194i | ||||||
\(503\) | −35.5176 | − | 20.5061i | −1.58365 | − | 0.914322i | −0.994320 | − | 0.106430i | \(-0.966058\pi\) |
−0.589331 | − | 0.807891i | \(-0.700609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.6969 | 0.832003 | ||||||||
\(506\) | −3.59592 | −0.159858 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.34847 | + | 4.24264i | −0.326036 | + | 0.188237i | ||||
\(509\) | −6.67423 | + | 11.5601i | −0.295830 | + | 0.512393i | −0.975178 | − | 0.221424i | \(-0.928930\pi\) |
0.679347 | + | 0.733817i | \(0.262263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52270 | + | 2.63740i | 0.0673605 | + | 0.116672i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | 10.2247 | + | 17.7098i | 0.450556 | + | 0.780386i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.651531 | + | 1.12848i | −0.0286543 | + | 0.0496307i | ||||
\(518\) | −3.15153 | + | 1.81954i | −0.138470 | + | 0.0799459i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.44949 | −0.370535 | ||||||||
\(521\) | −8.20204 | −0.359338 | −0.179669 | − | 0.983727i | \(-0.557503\pi\) | ||||
−0.179669 | + | 0.983727i | \(0.557503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5000 | + | 7.79423i | 0.590314 | + | 0.340818i | 0.765222 | − | 0.643767i | \(-0.222629\pi\) |
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | 14.7778i | 0.645572i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.797959 | − | 0.460702i | −0.0347927 | − | 0.0200876i | ||||
\(527\) | −0.977296 | − | 1.69273i | −0.0425717 | − | 0.0737363i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50000 | + | 7.79423i | 0.195652 | + | 0.338880i | ||||
\(530\) | −6.00000 | + | 3.46410i | −0.260623 | + | 0.150471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.724745 | + | 6.27647i | −0.0314217 | + | 0.272120i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3485 | + | 11.1708i | −0.836507 | + | 0.482958i | ||||
\(536\) | −8.84847 | − | 5.10867i | −0.382196 | − | 0.220661i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.2247 | − | 17.7098i | 0.440820 | − | 0.763523i | ||||
\(539\) | 3.11416i | 0.134136i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1742 | + | 26.2825i | −0.652391 | + | 1.12997i | 0.330150 | + | 0.943929i | \(0.392901\pi\) |
−0.982541 | + | 0.186046i | \(0.940433\pi\) | |||||||
\(542\) | −15.6969 | + | 27.1879i | −0.674241 | + | 1.16782i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.04989i | 0.0878882i | ||||||||
\(545\) | 12.0000 | − | 20.7846i | 0.514024 | − | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80306 | − | 1.04100i | −0.0770933 | − | 0.0445099i | 0.460958 | − | 0.887422i | \(-0.347506\pi\) |
−0.538051 | + | 0.842912i | \(0.680839\pi\) | |||||||
\(548\) | 5.44949 | − | 3.14626i | 0.232791 | − | 0.134402i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 1.90702i | − | 0.0813158i | ||||||
\(551\) | 1.22474 | − | 10.6066i | 0.0521759 | − | 0.451856i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.19694 | − | 0.691053i | 0.0508990 | − | 0.0293866i | ||||
\(554\) | −4.55051 | − | 7.88171i | −0.193333 | − | 0.334862i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.50000 | + | 6.06218i | 0.148433 | + | 0.257094i | ||||
\(557\) | 22.5959 | + | 13.0458i | 0.957420 | + | 0.552767i | 0.895378 | − | 0.445307i | \(-0.146905\pi\) |
0.0620418 | + | 0.998074i | \(0.480239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.2952i | − | 0.985282i | ||||||
\(560\) | 1.77526 | + | 1.02494i | 0.0750182 | + | 0.0433118i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.1464 | 0.976373 | ||||||||
\(563\) | −25.5959 | −1.07874 | −0.539370 | − | 0.842069i | \(-0.681337\pi\) | ||||
−0.539370 | + | 0.842069i | \(0.681337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0000 | − | 12.1244i | 0.883477 | − | 0.510075i | ||||
\(566\) | 7.44949 | − | 12.9029i | 0.313125 | − | 0.542349i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | 31.1010 | 1.30382 | 0.651911 | − | 0.758295i | \(-0.273967\pi\) | ||||
0.651911 | + | 0.758295i | \(0.273967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.69694 | −0.154712 | −0.0773560 | − | 0.997004i | \(-0.524648\pi\) | ||||
−0.0773560 | + | 0.997004i | \(0.524648\pi\) | |||||||
\(572\) | 1.89898 | + | 3.28913i | 0.0794003 | + | 0.137525i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.6969 | + | 8.48528i | −0.612905 | + | 0.353861i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.79796 | 0.241372 | 0.120686 | − | 0.992691i | \(-0.461491\pi\) | ||||
0.120686 | + | 0.992691i | \(0.461491\pi\) | |||||||
\(578\) | 12.7980 | 0.532325 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.00000 | − | 1.73205i | −0.124568 | − | 0.0719195i | ||||
\(581\) | − | 17.1134i | − | 0.709985i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.69694 | + | 1.55708i | 0.111696 | + | 0.0644876i | ||||
\(584\) | 1.05051 | + | 1.81954i | 0.0434704 | + | 0.0752930i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.32577 | + | 9.22450i | 0.220005 | + | 0.381060i | ||||
\(587\) | 24.1237 | − | 13.9278i | 0.995693 | − | 0.574863i | 0.0887216 | − | 0.996056i | \(-0.471722\pi\) |
0.906971 | + | 0.421193i | \(0.138389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65153 | − | 3.81405i | −0.0680501 | − | 0.157155i | ||||
\(590\) | 20.4347i | 0.841282i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.17423 | + | 1.25529i | −0.0893605 | + | 0.0515923i | ||||
\(593\) | −13.4722 | − | 7.77817i | −0.553237 | − | 0.319411i | 0.197190 | − | 0.980365i | \(-0.436818\pi\) |
−0.750426 | + | 0.660954i | \(0.770152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.10102 | + | 3.63907i | −0.0861334 | + | 0.149188i | ||||
\(596\) | 20.1489i | 0.825333i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.8990 | − | 29.2699i | 0.691051 | − | 1.19693i | ||||
\(599\) | 18.7980 | − | 32.5590i | 0.768064 | − | 1.33033i | −0.170548 | − | 0.985349i | \(-0.554554\pi\) |
0.938611 | − | 0.344976i | \(-0.112113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.2173i | − | 0.416774i | −0.978046 | − | 0.208387i | \(-0.933179\pi\) | ||
0.978046 | − | 0.208387i | \(-0.0668213\pi\) | |||||||
\(602\) | −2.82577 | + | 4.89437i | −0.115170 | + | 0.199480i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.34847 | + | 0.778539i | 0.0548684 | + | 0.0316783i | ||||
\(605\) | −12.9773 | + | 7.49245i | −0.527602 | + | 0.304611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.16064i | − | 0.0876979i | −0.999038 | − | 0.0438489i | \(-0.986038\pi\) | ||
0.999038 | − | 0.0438489i | \(-0.0139620\pi\) | |||||||
\(608\) | −0.500000 | + | 4.33013i | −0.0202777 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.22474 | − | 2.43916i | 0.171055 | − | 0.0987586i | ||||
\(611\) | −6.12372 | − | 10.6066i | −0.247739 | − | 0.429097i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.44949 | − | 16.3670i | −0.381661 | − | 0.661057i | 0.609639 | − | 0.792680i | \(-0.291315\pi\) |
−0.991300 | + | 0.131623i | \(0.957981\pi\) | |||||||
\(614\) | 13.3485 | + | 7.70674i | 0.538700 | + | 0.311019i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.921404i | − | 0.0371244i | ||||||
\(617\) | −28.1010 | − | 16.2241i | −1.13130 | − | 0.653159i | −0.187042 | − | 0.982352i | \(-0.559890\pi\) |
−0.944263 | + | 0.329193i | \(0.893223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3939 | −1.46279 | −0.731397 | − | 0.681952i | \(-0.761131\pi\) | ||||
−0.731397 | + | 0.681952i | \(0.761131\pi\) | |||||||
\(620\) | −1.34847 | −0.0541558 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.47219 | − | 2.58202i | 0.179319 | − | 0.103530i | ||||
\(623\) | −8.87628 | + | 15.3742i | −0.355620 | + | 0.615953i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 22.6969 | 0.907152 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.3485 | 0.492758 | ||||||||
\(629\) | −2.57321 | − | 4.45694i | −0.102601 | − | 0.177710i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.27526 | + | 12.6011i | −0.289623 | + | 0.501642i | −0.973720 | − | 0.227749i | \(-0.926863\pi\) |
0.684096 | + | 0.729392i | \(0.260197\pi\) | |||||||
\(632\) | 0.825765 | − | 0.476756i | 0.0328472 | − | 0.0189643i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.34847 | −0.291845 | ||||||||
\(635\) | −12.0000 | −0.476205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.3485 | − | 14.6349i | −1.00434 | − | 0.579858i | ||||
\(638\) | 1.55708i | 0.0616453i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.22474 | + | 0.707107i | 0.0484123 | + | 0.0279508i | ||||
\(641\) | 23.0227 | + | 39.8765i | 0.909342 | + | 1.57503i | 0.814980 | + | 0.579489i | \(0.196748\pi\) |
0.0943619 | + | 0.995538i | \(0.469919\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.2980 | − | 36.8891i | −0.839910 | − | 1.45477i | −0.889970 | − | 0.456020i | \(-0.849275\pi\) |
0.0500601 | − | 0.998746i | \(-0.484059\pi\) | |||||||
\(644\) | −7.10102 | + | 4.09978i | −0.279819 | + | 0.161554i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.87628 | − | 1.02494i | −0.349232 | − | 0.0403259i | ||||
\(647\) | − | 2.97129i | − | 0.116814i | −0.998293 | − | 0.0584068i | \(-0.981398\pi\) | ||
0.998293 | − | 0.0584068i | \(-0.0186020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.95459 | − | 4.59259i | 0.312245 | − | 0.180275i | ||||
\(650\) | 15.5227 | + | 8.96204i | 0.608851 | + | 0.351520i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.84847 | + | 6.66574i | −0.150718 | + | 0.261051i | ||||
\(653\) | − | 38.3908i | − | 1.50235i | −0.660103 | − | 0.751175i | \(-0.729487\pi\) | ||
0.660103 | − | 0.751175i | \(-0.270513\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4495 | + | 18.0990i | −0.408295 | + | 0.707188i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.97129i | 0.115833i | ||||||||
\(659\) | 5.69694 | − | 9.86739i | 0.221921 | − | 0.384379i | −0.733470 | − | 0.679722i | \(-0.762101\pi\) |
0.955391 | + | 0.295343i | \(0.0954339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6969 | − | 13.6814i | −0.921704 | − | 0.532146i | −0.0375258 | − | 0.999296i | \(-0.511948\pi\) |
−0.884178 | + | 0.467150i | \(0.845281\pi\) | |||||||
\(662\) | −16.1969 | + | 9.35131i | −0.629512 | + | 0.363449i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.8065i | − | 0.458182i | ||||||
\(665\) | −5.32577 | + | 7.17461i | −0.206524 | + | 0.278219i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | − | 6.92820i | 0.464642 | − | 0.268261i | ||||
\(668\) | 4.22474 | + | 7.31747i | 0.163460 | + | 0.283122i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.22474 | − | 12.5136i | −0.279116 | − | 0.483444i | ||||
\(671\) | −1.89898 | − | 1.09638i | −0.0733093 | − | 0.0423251i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0526i | 0.734422i | 0.930138 | + | 0.367211i | \(0.119687\pi\) | ||||
−0.930138 | + | 0.367211i | \(0.880313\pi\) | |||||||
\(674\) | −1.80306 | − | 1.04100i | −0.0694513 | − | 0.0400977i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.6969 | −0.872959 | ||||||||
\(677\) | 37.3485 | 1.43542 | 0.717709 | − | 0.696343i | \(-0.245191\pi\) | ||||
0.717709 | + | 0.696343i | \(0.245191\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.6969 | + | 13.6814i | −0.909405 | + | 0.525045i | ||||
\(680\) | −1.44949 | + | 2.51059i | −0.0555854 | + | 0.0962767i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.303062 | + | 0.524918i | 0.0116048 | + | 0.0201001i | ||||
\(683\) | −28.0454 | −1.07313 | −0.536564 | − | 0.843860i | \(-0.680278\pi\) | ||||
−0.536564 | + | 0.843860i | \(0.680278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.89898 | 0.340013 | ||||||||
\(686\) | 8.62372 | + | 14.9367i | 0.329255 | + | 0.570287i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.94949 | + | 3.37662i | −0.0743236 | + | 0.128732i | ||||
\(689\) | −25.3485 | + | 14.6349i | −0.965700 | + | 0.557547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.696938 | −0.0265128 | −0.0132564 | − | 0.999912i | \(-0.504220\pi\) | ||||
−0.0132564 | + | 0.999912i | \(0.504220\pi\) | |||||||
\(692\) | 12.2474 | 0.465578 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.2247 | + | 16.2956i | 1.07140 | + | 0.618571i | ||||
\(695\) | 9.89949i | 0.375509i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −11.6237 | − | 20.1329i | −0.439964 | − | 0.762041i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.17423 | − | 3.76588i | −0.0821783 | − | 0.142337i | ||||
\(701\) | 13.4722 | − | 7.77817i | 0.508838 | − | 0.293778i | −0.223518 | − | 0.974700i | \(-0.571754\pi\) |
0.732356 | + | 0.680922i | \(0.238421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.34847 | − | 10.0424i | −0.164006 | − | 0.378755i | ||||
\(704\) | − | 0.635674i | − | 0.0239579i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.87628 | + | 1.66062i | −0.108250 | + | 0.0624982i | ||||
\(707\) | −16.5959 | − | 9.58166i | −0.624154 | − | 0.360355i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.17423 | + | 5.49794i | −0.119211 | + | 0.206479i | −0.919455 | − | 0.393195i | \(-0.871370\pi\) |
0.800244 | + | 0.599674i | \(0.204703\pi\) | |||||||
\(710\) | 8.48528i | 0.318447i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.12372 | + | 10.6066i | −0.229496 | + | 0.397499i | ||||
\(713\) | 2.69694 | − | 4.67123i | 0.101001 | − | 0.174939i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.37113i | 0.200869i | ||||||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.79796 | − | 5.65685i | −0.365657 | − | 0.211112i | ||||
\(719\) | 17.1464 | − | 9.89949i | 0.639454 | − | 0.369189i | −0.144950 | − | 0.989439i | \(-0.546302\pi\) |
0.784404 | + | 0.620250i | \(0.212969\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 20.9596i | − | 0.780576i | ||||||
\(722\) | −18.5000 | − | 4.33013i | −0.688499 | − | 0.161151i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.65153 | − | 2.68556i | 0.172873 | − | 0.0998081i | ||||
\(725\) | 3.67423 | + | 6.36396i | 0.136458 | + | 0.236352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.82577 | − | 8.35847i | −0.178978 | − | 0.309999i | 0.762553 | − | 0.646926i | \(-0.223946\pi\) |
−0.941531 | + | 0.336927i | \(0.890612\pi\) | |||||||
\(728\) | 7.50000 | + | 4.33013i | 0.277968 | + | 0.160485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.97129i | 0.109972i | ||||||||
\(731\) | −6.92168 | − | 3.99624i | −0.256008 | − | 0.147806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6969 | −1.13382 | −0.566909 | − | 0.823781i | \(-0.691861\pi\) | ||||
−0.566909 | + | 0.823781i | \(0.691861\pi\) | |||||||
\(734\) | −14.3485 | −0.529612 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.89898 | + | 2.82843i | −0.180579 | + | 0.104257i | ||||
\(737\) | −3.24745 | + | 5.62475i | −0.119621 | + | 0.207190i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.1969 | − | 40.1783i | −0.853313 | − | 1.47798i | −0.878201 | − | 0.478292i | \(-0.841256\pi\) |
0.0248879 | − | 0.999690i | \(-0.492077\pi\) | |||||||
\(740\) | −3.55051 | −0.130519 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.10102 | 0.260687 | ||||||||
\(743\) | −23.6969 | − | 41.0443i | −0.869356 | − | 1.50577i | −0.862656 | − | 0.505792i | \(-0.831200\pi\) |
−0.00670079 | − | 0.999978i | \(-0.502133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2474 | + | 24.6773i | −0.521986 | + | 0.904107i | ||||
\(746\) | −10.6515 | + | 6.14966i | −0.389980 | + | 0.225155i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.30306 | 0.0476446 | ||||||||
\(749\) | 22.8990 | 0.836711 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2196 | + | 13.9832i | 0.883787 | + | 0.510255i | 0.871905 | − | 0.489675i | \(-0.162884\pi\) |
0.0118820 | + | 0.999929i | \(0.496218\pi\) | |||||||
\(752\) | 2.04989i | 0.0747517i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.6742 | − | 7.31747i | −0.461568 | − | 0.266487i | ||||
\(755\) | 1.10102 | + | 1.90702i | 0.0400702 | + | 0.0694037i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1742 | − | 21.0864i | −0.442480 | − | 0.766398i | 0.555393 | − | 0.831588i | \(-0.312568\pi\) |
−0.997873 | + | 0.0651902i | \(0.979235\pi\) | |||||||
\(758\) | 16.5000 | − | 9.52628i | 0.599307 | − | 0.346010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.67423 | + | 4.94975i | −0.133278 | + | 0.179546i | ||||
\(761\) | 44.8262i | 1.62495i | 0.582996 | + | 0.812475i | \(0.301880\pi\) | ||||
−0.582996 | + | 0.812475i | \(0.698120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.3031 | + | 12.2993i | −0.771223 | + | 0.445266i | ||||
\(764\) | 13.2247 | + | 7.63531i | 0.478454 | + | 0.276236i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.44949 | + | 9.43879i | −0.196898 | + | 0.341037i | ||||
\(767\) | 86.3312i | 3.11724i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.29796 | − | 2.24813i | 0.0468056 | − | 0.0810697i | −0.841673 | − | 0.539987i | \(-0.818429\pi\) |
0.888479 | + | 0.458917i | \(0.151763\pi\) | |||||||
\(770\) | 0.651531 | − | 1.12848i | 0.0234795 | − | 0.0406678i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.1455i | 0.617081i | ||||||||
\(773\) | 4.47219 | − | 7.74607i | 0.160854 | − | 0.278607i | −0.774321 | − | 0.632792i | \(-0.781909\pi\) |
0.935175 | + | 0.354186i | \(0.115242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.47730 | + | 1.43027i | 0.0889871 | + | 0.0513767i | ||||
\(776\) | −16.3485 | + | 9.43879i | −0.586876 | + | 0.338833i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 26.4415i | − | 0.947972i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30306 | − | 1.90702i | 0.118193 | − | 0.0682387i | ||||
\(782\) | −5.79796 | − | 10.0424i | −0.207335 | − | 0.359114i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.44949 | + | 4.24264i | 0.0874818 | + | 0.151523i | ||||
\(785\) | 15.1237 | + | 8.73169i | 0.539789 | + | 0.311647i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0737i | 0.858136i | 0.903272 | + | 0.429068i | \(0.141158\pi\) | ||||
−0.903272 | + | 0.429068i | \(0.858842\pi\) | |||||||
\(788\) | 17.5732 | + | 10.1459i | 0.626020 | + | 0.361433i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.34847 | 0.0479764 | ||||||||
\(791\) | −24.8536 | −0.883691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8485 | − | 10.3048i | 0.633818 | − | 0.365935i | ||||
\(794\) | −10.8258 | + | 18.7508i | −0.384192 | + | 0.665440i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.62372 | − | 14.9367i | −0.305660 | − | 0.529418i | ||||
\(797\) | 38.0908 | 1.34925 | 0.674623 | − | 0.738162i | \(-0.264306\pi\) | ||||
0.674623 | + | 0.738162i | \(0.264306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.20204 | −0.148658 | ||||||||
\(800\) | −1.50000 | − | 2.59808i | −0.0530330 | − | 0.0918559i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.123724 | − | 0.214297i | 0.00436886 | − | 0.00756709i | ||||
\(803\) | 1.15663 | − | 0.667783i | 0.0408167 | − | 0.0235655i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.5959 | −0.408702 | ||||||||
\(806\) | −5.69694 | −0.200666 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.4495 | − | 6.61037i | −0.402792 | − | 0.232552i | ||||
\(809\) | 5.16404i | 0.181558i | 0.995871 | + | 0.0907791i | \(0.0289357\pi\) | ||||
−0.995871 | + | 0.0907791i | \(0.971064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6969 | + | 10.2173i | 0.621424 | + | 0.358779i | 0.777423 | − | 0.628978i | \(-0.216526\pi\) |
−0.155999 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(812\) | 1.77526 | + | 3.07483i | 0.0622992 | + | 0.107905i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.797959 | + | 1.38211i | 0.0279684 | + | 0.0484428i | ||||
\(815\) | −9.42679 | + | 5.44256i | −0.330206 | + | 0.190644i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6464 | − | 10.1298i | −0.477428 | − | 0.354398i | ||||
\(818\) | 28.9199i | 1.01116i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1691 | − | 19.7276i | −1.19251 | − | 0.688497i | −0.233636 | − | 0.972324i | \(-0.575062\pi\) |
−0.958875 | + | 0.283828i | \(0.908396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.3485 | + | 30.0484i | −0.604730 | + | 1.04742i | 0.387365 | + | 0.921927i | \(0.373385\pi\) |
−0.992094 | + | 0.125496i | \(0.959948\pi\) | |||||||
\(824\) | − | 14.4600i | − | 0.503737i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.4722 | − | 18.1384i | 0.364374 | − | 0.631115i | ||||
\(827\) | −23.8207 | + | 41.2586i | −0.828326 | + | 1.43470i | 0.0710253 | + | 0.997475i | \(0.477373\pi\) |
−0.899351 | + | 0.437228i | \(0.855960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.9959i | − | 0.381902i | −0.981600 | − | 0.190951i | \(-0.938843\pi\) | ||
0.981600 | − | 0.190951i | \(-0.0611572\pi\) | |||||||
\(830\) | 8.34847 | − | 14.4600i | 0.289780 | − | 0.501913i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.17423 | + | 2.98735i | 0.179384 | + | 0.103568i | ||||
\(833\) | −8.69694 | + | 5.02118i | −0.301331 | + | 0.173974i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9494i | 0.413525i | ||||||||
\(836\) | 2.75255 | + | 0.317837i | 0.0951990 | + | 0.0109926i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.24745 | + | 1.87492i | −0.112181 | + | 0.0647679i | ||||
\(839\) | −5.02270 | − | 8.69958i | −0.173403 | − | 0.300343i | 0.766204 | − | 0.642597i | \(-0.222143\pi\) |
−0.939607 | + | 0.342254i | \(0.888810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | + | 19.9186i | 0.396552 | + | 0.686848i | ||||
\(842\) | −1.34847 | − | 0.778539i | −0.0464713 | − | 0.0268302i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.63907i | 0.125262i | ||||||||
\(845\) | −27.7980 | − | 16.0492i | −0.956279 | − | 0.552108i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3587 | 0.527730 | ||||||||
\(848\) | 4.89898 | 0.168232 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.32577 | − | 3.07483i | 0.182672 | − | 0.105466i | ||||
\(851\) | 7.10102 | − | 12.2993i | 0.243420 | − | 0.421616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8258 | + | 25.6790i | 0.507625 | + | 0.879231i | 0.999961 | + | 0.00882655i | \(0.00280961\pi\) |
−0.492337 | + | 0.870405i | \(0.663857\pi\) | |||||||
\(854\) | −5.00000 | −0.171096 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7980 | 0.539963 | ||||||||
\(857\) | 3.42679 | + | 5.93537i | 0.117057 | + | 0.202748i | 0.918600 | − | 0.395188i | \(-0.129321\pi\) |
−0.801543 | + | 0.597937i | \(0.795987\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.94949 | + | 3.37662i | −0.0665157 | + | 0.115209i | −0.897365 | − | 0.441288i | \(-0.854522\pi\) |
0.830850 | + | 0.556497i | \(0.187855\pi\) | |||||||
\(860\) | −4.77526 | + | 2.75699i | −0.162835 | + | 0.0940127i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0454 | 0.546509 | ||||||||
\(863\) | 37.3485 | 1.27136 | 0.635678 | − | 0.771954i | \(-0.280720\pi\) | ||||
0.635678 | + | 0.771954i | \(0.280720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0000 | + | 8.66025i | 0.510015 | + | 0.294457i | ||||
\(866\) | − | 29.0949i | − | 0.988686i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.19694 | + | 0.691053i | 0.0406267 | + | 0.0234559i | ||||
\(869\) | −0.303062 | − | 0.524918i | −0.0102807 | − | 0.0178066i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.5227 | − | 52.8669i | −1.03422 | − | 1.79133i | ||||
\(872\) | −14.6969 | + | 8.48528i | −0.497701 | + | 0.287348i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.79796 | − | 22.6274i | −0.331421 | − | 0.765384i | ||||
\(875\) | − | 16.3991i | − | 0.554391i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5227 | − | 14.1582i | 0.828073 | − | 0.478088i | −0.0251195 | − | 0.999684i | \(-0.507997\pi\) |
0.853192 | + | 0.521596i | \(0.174663\pi\) | |||||||
\(878\) | 12.5227 | + | 7.22999i | 0.422621 | + | 0.244000i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.449490 | − | 0.778539i | 0.0151523 | − | 0.0262445i | ||||
\(881\) | 2.04989i | 0.0690625i | 0.999404 | + | 0.0345312i | \(0.0109938\pi\) | ||||
−0.999404 | + | 0.0345312i | \(0.989006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.94949 | − | 5.10867i | 0.0992582 | − | 0.171920i | −0.812120 | − | 0.583491i | \(-0.801686\pi\) |
0.911378 | + | 0.411571i | \(0.135020\pi\) | |||||||
\(884\) | −6.12372 | + | 10.6066i | −0.205963 | + | 0.356739i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.7627i | 0.999897i | ||||||||
\(887\) | −11.3258 | + | 19.6168i | −0.380282 | + | 0.658668i | −0.991102 | − | 0.133101i | \(-0.957506\pi\) |
0.610820 | + | 0.791769i | \(0.290840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6515 | + | 6.14966i | 0.357241 | + | 0.206253i | ||||
\(890\) | −15.0000 | + | 8.66025i | −0.502801 | + | 0.290292i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 2.51059i | − | 0.0840608i | ||||||
\(893\) | −8.87628 | − | 1.02494i | −0.297033 | − | 0.0342984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969 | − | 8.48528i | 0.491264 | − | 0.283632i | ||||
\(896\) | −0.724745 | − | 1.25529i | −0.0242120 | − | 0.0419365i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.12372 | + | 15.8028i | 0.304463 | + | 0.527345i | ||||
\(899\) | −2.02270 | − | 1.16781i | −0.0674610 | − | 0.0389486i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0424i | 0.334560i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.1464 | −0.570282 | ||||||||
\(905\) | 7.59592 | 0.252497 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.6969 | − | 20.6096i | 1.18530 | − | 0.684332i | 0.228063 | − | 0.973646i | \(-0.426761\pi\) |
0.957234 | + | 0.289315i | \(0.0934274\pi\) | |||||||
\(908\) | 11.5732 | − | 20.0454i | 0.384071 | − | 0.665230i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.12372 | + | 10.6066i | 0.202999 | + | 0.351605i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.50510 | −0.248383 | ||||||||
\(914\) | −9.84847 | − | 17.0580i | −0.325758 | − | 0.564230i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.62372 | − | 16.6688i | 0.317977 | − | 0.550752i | ||||
\(917\) | 18.5505 | − | 10.7101i | 0.612592 | − | 0.353680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.04541 | 0.298380 | 0.149190 | − | 0.988809i | \(-0.452333\pi\) | ||||
0.149190 | + | 0.988809i | \(0.452333\pi\) | |||||||
\(920\) | −8.00000 | −0.263752 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.12372 | − | 5.26758i | −0.300474 | − | 0.173479i | ||||
\(923\) | 35.8481i | 1.17996i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.52270 | + | 3.76588i | 0.214465 | + | 0.123822i | ||||
\(926\) | −20.0732 | − | 34.7678i | −0.659647 | − | 1.14254i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.22474 | + | 2.12132i | 0.0402042 | + | 0.0696358i | ||||
\(929\) | −35.5732 | + | 20.5382i | −1.16712 | + | 0.673837i | −0.953000 | − | 0.302971i | \(-0.902022\pi\) |
−0.214119 | + | 0.976807i | \(0.568688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.5959 | + | 8.48528i | −0.642230 | + | 0.278094i | ||||
\(932\) | − | 17.6062i | − | 0.576711i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.2474 | + | 10.5352i | −0.597075 | + | 0.344721i | ||||
\(935\) | 1.59592 | + | 0.921404i | 0.0521921 | + | 0.0301331i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.19694 | + | 14.1975i | −0.267782 | + | 0.463813i | −0.968289 | − | 0.249833i | \(-0.919624\pi\) |
0.700507 | + | 0.713646i | \(0.252957\pi\) | |||||||
\(938\) | 14.8099i | 0.483561i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.44949 | + | 2.51059i | −0.0472771 | + | 0.0818864i | ||||
\(941\) | 20.4495 | − | 35.4196i | 0.666634 | − | 1.15464i | −0.312205 | − | 0.950015i | \(-0.601068\pi\) |
0.978839 | − | 0.204630i | \(-0.0655990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 7.22474 | − | 12.5136i | 0.235145 | − | 0.407284i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.14643 | + | 1.23924i | 0.0697864 | + | 0.0402912i | ||||
\(947\) | 33.4949 | − | 19.3383i | 1.08844 | − | 0.628410i | 0.155278 | − | 0.987871i | \(-0.450373\pi\) |
0.933160 | + | 0.359461i | \(0.117039\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5529i | 0.407486i | ||||||||
\(950\) | 12.0000 | − | 5.19615i | 0.389331 | − | 0.168585i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.57321 | − | 1.48565i | 0.0833983 | − | 0.0481501i | ||||
\(953\) | −0.550510 | − | 0.953512i | −0.0178328 | − | 0.0308873i | 0.856971 | − | 0.515364i | \(-0.172343\pi\) |
−0.874804 | + | 0.484477i | \(0.839010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7980 | + | 18.7026i | 0.349414 | + | 0.605202i | ||||
\(956\) | −19.4722 | − | 11.2423i | −0.629776 | − | 0.363601i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.40669i | 0.303916i | ||||||||
\(959\) | −7.89898 | − | 4.56048i | −0.255071 | − | 0.147266i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0908 | 0.970671 | ||||||||
\(962\) | −15.0000 | −0.483619 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.1515 | + | 7.01569i | −0.391374 | + | 0.225960i | ||||
\(965\) | −12.1237 | + | 20.9989i | −0.390276 | + | 0.675979i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.17423 | − | 10.6941i | −0.198550 | − | 0.343899i | 0.749508 | − | 0.661995i | \(-0.230290\pi\) |
−0.948058 | + | 0.318096i | \(0.896957\pi\) | |||||||
\(968\) | 10.5959 | 0.340566 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.6969 | −0.857187 | ||||||||
\(971\) | 14.8207 | + | 25.6701i | 0.475618 | + | 0.823794i | 0.999610 | − | 0.0279290i | \(-0.00889124\pi\) |
−0.523992 | + | 0.851723i | \(0.675558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.07321 | − | 8.78706i | 0.162640 | − | 0.281700i | ||||
\(974\) | 34.3485 | − | 19.8311i | 1.10060 | − | 0.635429i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.44949 | −0.110415 | ||||||||
\(977\) | −0.247449 | −0.00791659 | −0.00395829 | − | 0.999992i | \(-0.501260\pi\) | ||||
−0.00395829 | + | 0.999992i | \(0.501260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.74235 | + | 3.89270i | 0.215486 | + | 0.124411i | ||||
\(980\) | 6.92820i | 0.221313i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.1464 | − | 15.0956i | −0.834366 | − | 0.481721i | ||||
\(983\) | −9.24745 | − | 16.0171i | −0.294948 | − | 0.510865i | 0.680025 | − | 0.733189i | \(-0.261969\pi\) |
−0.974973 | + | 0.222324i | \(0.928636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3485 | + | 24.8523i | 0.457180 | + | 0.791859i | ||||
\(986\) | −4.34847 | + | 2.51059i | −0.138483 | + | 0.0799535i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.5227 | + | 20.9114i | −0.493843 | + | 0.665281i | ||||
\(989\) | − | 22.0560i | − | 0.701339i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.8712 | − | 30.5252i | 1.67951 | − | 0.969664i | 0.717534 | − | 0.696523i | \(-0.245271\pi\) |
0.961974 | − | 0.273141i | \(-0.0880626\pi\) | |||||||
\(992\) | 0.825765 | + | 0.476756i | 0.0262181 | + | 0.0151370i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.34847 | − | 7.53177i | 0.137925 | − | 0.238893i | ||||
\(995\) | − | 24.3916i | − | 0.773265i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5227 | − | 35.5464i | 0.649961 | − | 1.12576i | −0.333171 | − | 0.942866i | \(-0.608119\pi\) |
0.983132 | − | 0.182898i | \(-0.0585479\pi\) | |||||||
\(998\) | 21.7474 | − | 37.6677i | 0.688403 | − | 1.19235i | ||||
\(999\) | 0 | 0 |
(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 | 342.2.s.a.107.1 | ✓ | 4 | |
3.2 | odd | 2 | 342.2.s.b.107.2 | yes | 4 | ||
4.3 | odd | 2 | 2736.2.dc.b.449.1 | 4 | |||
12.11 | even | 2 | 2736.2.dc.a.449.2 | 4 | |||
19.8 | odd | 6 | 342.2.s.b.179.2 | yes | 4 | ||
57.8 | even | 6 | inner | 342.2.s.a.179.1 | yes | 4 | |
76.27 | even | 6 | 2736.2.dc.a.1889.2 | 4 | |||
228.179 | odd | 6 | 2736.2.dc.b.1889.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.s.a.107.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
342.2.s.a.179.1 | yes | 4 | 57.8 | even | 6 | inner | |
342.2.s.b.107.2 | yes | 4 | 3.2 | odd | 2 | ||
342.2.s.b.179.2 | yes | 4 | 19.8 | odd | 6 | ||
2736.2.dc.a.449.2 | 4 | 12.11 | even | 2 | |||
2736.2.dc.a.1889.2 | 4 | 76.27 | even | 6 | |||
2736.2.dc.b.449.1 | 4 | 4.3 | odd | 2 | |||
2736.2.dc.b.1889.1 | 4 | 228.179 | odd | 6 |