Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(3.17270 + 3.17270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.k.199.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −1.16129 | + | 2.01141i | −0.438926 | + | 0.760243i | −0.997607 | − | 0.0691402i | \(-0.977974\pi\) |
0.558681 | + | 0.829383i | \(0.311308\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.62926 | − | 2.67270i | 1.39577 | − | 0.805850i | 0.401827 | − | 0.915716i | \(-0.368375\pi\) |
0.993946 | + | 0.109865i | \(0.0350420\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 0.161290 | − | 3.60194i | 0.0447338 | − | 0.998999i | ||||
\(14\) | −2.32258 | −0.620736 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.48387 | + | 2.01141i | 0.799254 | + | 0.461450i | 0.843210 | − | 0.537584i | \(-0.180663\pi\) |
−0.0439559 | + | 0.999033i | \(0.513996\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.32258i | 0.506828i | ||||||||
\(22\) | 4.62926 | + | 2.67270i | 0.986961 | + | 0.569822i | ||||
\(23\) | 4.27464 | − | 2.46797i | 0.891325 | − | 0.514607i | 0.0169494 | − | 0.999856i | \(-0.494605\pi\) |
0.874376 | + | 0.485250i | \(0.161271\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.20002 | − | 1.66129i | 0.627575 | − | 0.325806i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.16129 | − | 2.01141i | −0.219463 | − | 0.380121i | ||||
\(29\) | 2.14539 | + | 3.71592i | 0.398388 | + | 0.690029i | 0.993527 | − | 0.113594i | \(-0.0362363\pi\) |
−0.595139 | + | 0.803623i | \(0.702903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.47183i | − | 0.623560i | −0.950154 | − | 0.311780i | \(-0.899075\pi\) | ||
0.950154 | − | 0.311780i | \(-0.100925\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 2.67270 | − | 4.62926i | 0.465258 | − | 0.805850i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.57463 | + | 2.72733i | 0.258867 | + | 0.448371i | 0.965939 | − | 0.258771i | \(-0.0833175\pi\) |
−0.707072 | + | 0.707142i | \(0.749984\pi\) | |||||||
\(38\) | 4.02283i | 0.652589i | ||||||||
\(39\) | −1.66129 | − | 3.20002i | −0.266019 | − | 0.512413i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.29078 | − | 1.32258i | 0.357759 | − | 0.206552i | −0.310338 | − | 0.950626i | \(-0.600442\pi\) |
0.668097 | + | 0.744074i | \(0.267109\pi\) | |||||||
\(42\) | −2.01141 | + | 1.16129i | −0.310368 | + | 0.179191i | ||||
\(43\) | 10.6095 | + | 6.12539i | 1.61793 | + | 0.934113i | 0.987454 | + | 0.157906i | \(0.0504744\pi\) |
0.630478 | + | 0.776207i | \(0.282859\pi\) | |||||||
\(44\) | 5.34541i | 0.805850i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.27464 | + | 2.46797i | 0.630262 | + | 0.363882i | ||||
\(47\) | 1.81894 | 0.265320 | 0.132660 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132660 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 0.802812 | + | 1.39051i | 0.114687 | + | 0.198644i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 3.03873 | + | 1.94065i | 0.421396 | + | 0.269120i | ||||
\(53\) | − | 5.48693i | − | 0.753687i | −0.926277 | − | 0.376844i | \(-0.877009\pi\) | ||
0.926277 | − | 0.376844i | \(-0.122991\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.16129 | − | 2.01141i | 0.155184 | − | 0.268786i | ||||
\(57\) | 4.02283 | 0.532836 | ||||||||
\(58\) | −2.14539 | + | 3.71592i | −0.281703 | + | 0.487924i | ||||
\(59\) | −5.87744 | − | 3.39334i | −0.765177 | − | 0.441775i | 0.0659742 | − | 0.997821i | \(-0.478984\pi\) |
−0.831152 | + | 0.556046i | \(0.812318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.267949 | + | 0.464102i | −0.0343074 | + | 0.0594221i | −0.882669 | − | 0.469995i | \(-0.844256\pi\) |
0.848362 | + | 0.529417i | \(0.177589\pi\) | |||||||
\(62\) | 3.00670 | − | 1.73592i | 0.381851 | − | 0.220462i | ||||
\(63\) | 1.16129 | + | 2.01141i | 0.146309 | + | 0.253414i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.34541 | 0.657974 | ||||||||
\(67\) | −2.05463 | − | 3.55872i | −0.251013 | − | 0.434767i | 0.712792 | − | 0.701376i | \(-0.247430\pi\) |
−0.963805 | + | 0.266608i | \(0.914097\pi\) | |||||||
\(68\) | 3.46410 | − | 2.00000i | 0.420084 | − | 0.242536i | ||||
\(69\) | 2.46797 | − | 4.27464i | 0.297108 | − | 0.514607i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7454 | + | 7.93593i | 1.63128 | + | 0.941822i | 0.983698 | + | 0.179830i | \(0.0575547\pi\) |
0.647586 | + | 0.761992i | \(0.275779\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −13.5734 | −1.58864 | −0.794321 | − | 0.607498i | \(-0.792173\pi\) | ||||
−0.794321 | + | 0.607498i | \(0.792173\pi\) | |||||||
\(74\) | −1.57463 | + | 2.72733i | −0.183047 | + | 0.317046i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.48387 | + | 2.01141i | −0.399627 | + | 0.230725i | ||||
\(77\) | 12.4151i | 1.41484i | ||||||||
\(78\) | 1.94065 | − | 3.03873i | 0.219736 | − | 0.344068i | ||||
\(79\) | 7.96774 | 0.896441 | 0.448220 | − | 0.893923i | \(-0.352058\pi\) | ||||
0.448220 | + | 0.893923i | \(0.352058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.29078 | + | 1.32258i | 0.252974 | + | 0.146054i | ||||
\(83\) | −11.3360 | −1.24428 | −0.622142 | − | 0.782904i | \(-0.713737\pi\) | ||||
−0.622142 | + | 0.782904i | \(0.713737\pi\) | |||||||
\(84\) | −2.01141 | − | 1.16129i | −0.219463 | − | 0.126707i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.2508i | 1.32104i | ||||||||
\(87\) | 3.71592 | + | 2.14539i | 0.398388 | + | 0.230010i | ||||
\(88\) | −4.62926 | + | 2.67270i | −0.493480 | + | 0.284911i | ||||
\(89\) | 1.50670 | − | 0.869891i | 0.159709 | − | 0.0922083i | −0.418015 | − | 0.908440i | \(-0.637274\pi\) |
0.577725 | + | 0.816232i | \(0.303941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.05769 | + | 4.50732i | 0.739847 | + | 0.472495i | ||||
\(92\) | 4.93593i | 0.514607i | ||||||||
\(93\) | −1.73592 | − | 3.00670i | −0.180006 | − | 0.311780i | ||||
\(94\) | 0.909471 | + | 1.57525i | 0.0938048 | + | 0.162475i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −8.05463 | + | 13.9510i | −0.817824 | + | 1.41651i | 0.0894586 | + | 0.995991i | \(0.471486\pi\) |
−0.907282 | + | 0.420522i | \(0.861847\pi\) | |||||||
\(98\) | −0.802812 | + | 1.39051i | −0.0810962 | + | 0.140463i | ||||
\(99\) | − | 5.34541i | − | 0.537233i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.34541 | + | 10.9906i | 0.631391 | + | 1.09360i | 0.987267 | + | 0.159069i | \(0.0508492\pi\) |
−0.355876 | + | 0.934533i | \(0.615817\pi\) | |||||||
\(102\) | −2.00000 | − | 3.46410i | −0.198030 | − | 0.342997i | ||||
\(103\) | − | 4.79612i | − | 0.472575i | −0.971683 | − | 0.236288i | \(-0.924069\pi\) | ||
0.971683 | − | 0.236288i | \(-0.0759308\pi\) | |||||||
\(104\) | −0.161290 | + | 3.60194i | −0.0158158 | + | 0.353199i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.75182 | − | 2.74346i | 0.461537 | − | 0.266469i | ||||
\(107\) | −2.66025 | + | 1.53590i | −0.257176 | + | 0.148481i | −0.623046 | − | 0.782185i | \(-0.714105\pi\) |
0.365869 | + | 0.930666i | \(0.380772\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 6.69081i | − | 0.640864i | −0.947272 | − | 0.320432i | \(-0.896172\pi\) | ||
0.947272 | − | 0.320432i | \(-0.103828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.72733 | + | 1.57463i | 0.258867 | + | 0.149457i | ||||
\(112\) | 2.32258 | 0.219463 | ||||||||
\(113\) | 6.15720 | + | 3.55486i | 0.579220 | + | 0.334413i | 0.760823 | − | 0.648959i | \(-0.224795\pi\) |
−0.181603 | + | 0.983372i | \(0.558129\pi\) | |||||||
\(114\) | 2.01141 | + | 3.48387i | 0.188386 | + | 0.326294i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.29078 | −0.398388 | ||||||||
\(117\) | −3.03873 | − | 1.94065i | −0.280931 | − | 0.179413i | ||||
\(118\) | − | 6.78668i | − | 0.624765i | ||||||
\(119\) | 8.04565 | − | 4.64516i | 0.737544 | − | 0.425821i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.78668 | − | 15.2190i | 0.798789 | − | 1.38354i | ||||
\(122\) | −0.535898 | −0.0485180 | ||||||||
\(123\) | 1.32258 | − | 2.29078i | 0.119253 | − | 0.206552i | ||||
\(124\) | 3.00670 | + | 1.73592i | 0.270009 | + | 0.155890i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.16129 | + | 2.01141i | −0.103456 | + | 0.179191i | ||||
\(127\) | −1.84644 | + | 1.06604i | −0.163845 | + | 0.0945961i | −0.579680 | − | 0.814844i | \(-0.696823\pi\) |
0.415835 | + | 0.909440i | \(0.363489\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 12.2508 | 1.07862 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25851 | 0.109957 | 0.0549785 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549785 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(132\) | 2.67270 | + | 4.62926i | 0.232629 | + | 0.402925i | ||||
\(133\) | −8.09156 | + | 4.67167i | −0.701628 | + | 0.405085i | ||||
\(134\) | 2.05463 | − | 3.55872i | 0.177493 | − | 0.307427i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | 9.85744 | − | 17.0736i | 0.842178 | − | 1.45870i | −0.0458713 | − | 0.998947i | \(-0.514606\pi\) |
0.888049 | − | 0.459748i | \(-0.152060\pi\) | |||||||
\(138\) | 4.93593 | 0.420175 | ||||||||
\(139\) | 2.83871 | − | 4.91679i | 0.240776 | − | 0.417037i | −0.720159 | − | 0.693809i | \(-0.755931\pi\) |
0.960936 | + | 0.276772i | \(0.0892647\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.57525 | − | 0.909471i | 0.132660 | − | 0.0765913i | ||||
\(142\) | 15.8719i | 1.33194i | ||||||||
\(143\) | −8.88027 | − | 17.1054i | −0.742605 | − | 1.43043i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.78668 | − | 11.7549i | −0.561670 | − | 0.972841i | ||||
\(147\) | 1.39051 | + | 0.802812i | 0.114687 | + | 0.0662148i | ||||
\(148\) | −3.14925 | −0.258867 | ||||||||
\(149\) | 16.8680 | + | 9.73875i | 1.38188 | + | 0.797829i | 0.992382 | − | 0.123198i | \(-0.0393150\pi\) |
0.389499 | + | 0.921027i | \(0.372648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.5170i | − | 1.18138i | −0.806899 | − | 0.590690i | \(-0.798856\pi\) | ||
0.806899 | − | 0.590690i | \(-0.201144\pi\) | |||||||
\(152\) | −3.48387 | − | 2.01141i | −0.282579 | − | 0.163147i | ||||
\(153\) | −3.46410 | + | 2.00000i | −0.280056 | + | 0.161690i | ||||
\(154\) | −10.7518 | + | 6.20757i | −0.866406 | + | 0.500220i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.60194 | + | 0.161290i | 0.288386 | + | 0.0129135i | ||||
\(157\) | − | 24.3829i | − | 1.94596i | −0.230879 | − | 0.972982i | \(-0.574160\pi\) | ||
0.230879 | − | 0.972982i | \(-0.425840\pi\) | |||||||
\(158\) | 3.98387 | + | 6.90026i | 0.316940 | + | 0.548956i | ||||
\(159\) | −2.74346 | − | 4.75182i | −0.217571 | − | 0.376844i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4641i | 0.903498i | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −11.8134 | + | 20.4614i | −0.925295 | + | 1.60266i | −0.134208 | + | 0.990953i | \(0.542849\pi\) |
−0.791086 | + | 0.611704i | \(0.790484\pi\) | |||||||
\(164\) | 2.64516i | 0.206552i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.66799 | − | 9.81724i | −0.439921 | − | 0.761966i | ||||
\(167\) | −8.37357 | − | 14.5035i | −0.647967 | − | 1.12231i | −0.983608 | − | 0.180321i | \(-0.942286\pi\) |
0.335641 | − | 0.941990i | \(-0.391047\pi\) | |||||||
\(168\) | − | 2.32258i | − | 0.179191i | ||||||
\(169\) | −12.9480 | − | 1.16191i | −0.995998 | − | 0.0893780i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.48387 | − | 2.01141i | 0.266418 | − | 0.153817i | ||||
\(172\) | −10.6095 | + | 6.12539i | −0.808966 | + | 0.467057i | ||||
\(173\) | 13.9708 | + | 8.06604i | 1.06218 | + | 0.613250i | 0.926034 | − | 0.377439i | \(-0.123195\pi\) |
0.136146 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(174\) | 4.29078i | 0.325283i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.62926 | − | 2.67270i | −0.348943 | − | 0.201463i | ||||
\(177\) | −6.78668 | −0.510118 | ||||||||
\(178\) | 1.50670 | + | 0.869891i | 0.112932 | + | 0.0652011i | ||||
\(179\) | −3.66412 | − | 6.34644i | −0.273869 | − | 0.474355i | 0.695980 | − | 0.718061i | \(-0.254970\pi\) |
−0.969849 | + | 0.243706i | \(0.921637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5734 | −1.45488 | −0.727438 | − | 0.686173i | \(-0.759289\pi\) | ||||
−0.727438 | + | 0.686173i | \(0.759289\pi\) | |||||||
\(182\) | −0.374609 | + | 8.36580i | −0.0277678 | + | 0.620114i | ||||
\(183\) | 0.535898i | 0.0396147i | ||||||||
\(184\) | −4.27464 | + | 2.46797i | −0.315131 | + | 0.181941i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.73592 | − | 3.00670i | 0.127284 | − | 0.220462i | ||||
\(187\) | −21.3816 | −1.56358 | ||||||||
\(188\) | −0.909471 | + | 1.57525i | −0.0663300 | + | 0.114887i | ||||
\(189\) | 2.01141 | + | 1.16129i | 0.146309 | + | 0.0844714i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.51873 | − | 14.7549i | 0.616394 | − | 1.06763i | −0.373744 | − | 0.927532i | \(-0.621926\pi\) |
0.990138 | − | 0.140094i | \(-0.0447404\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 3.07746 | + | 5.33031i | 0.221520 | + | 0.383684i | 0.955270 | − | 0.295736i | \(-0.0955648\pi\) |
−0.733750 | + | 0.679420i | \(0.762231\pi\) | |||||||
\(194\) | −16.1093 | −1.15658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.60562 | −0.114687 | ||||||||
\(197\) | 6.89334 | + | 11.9396i | 0.491130 | + | 0.850662i | 0.999948 | − | 0.0102119i | \(-0.00325060\pi\) |
−0.508818 | + | 0.860874i | \(0.669917\pi\) | |||||||
\(198\) | 4.62926 | − | 2.67270i | 0.328987 | − | 0.189941i | ||||
\(199\) | −1.14152 | + | 1.97717i | −0.0809203 | + | 0.140158i | −0.903646 | − | 0.428281i | \(-0.859119\pi\) |
0.822725 | + | 0.568439i | \(0.192453\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.55872 | − | 2.05463i | −0.251013 | − | 0.144922i | ||||
\(202\) | −6.34541 | + | 10.9906i | −0.446461 | + | 0.773293i | ||||
\(203\) | −9.96567 | −0.699453 | ||||||||
\(204\) | 2.00000 | − | 3.46410i | 0.140028 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.15356 | − | 2.39806i | 0.289392 | − | 0.167081i | ||||
\(207\) | − | 4.93593i | − | 0.343071i | ||||||
\(208\) | −3.20002 | + | 1.66129i | −0.221881 | + | 0.115190i | ||||
\(209\) | 21.5036 | 1.48744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2387 | − | 19.4661i | −0.773707 | − | 1.34010i | −0.935518 | − | 0.353278i | \(-0.885067\pi\) |
0.161811 | − | 0.986822i | \(-0.448267\pi\) | |||||||
\(212\) | 4.75182 | + | 2.74346i | 0.326356 | + | 0.188422i | ||||
\(213\) | 15.8719 | 1.08752 | ||||||||
\(214\) | −2.66025 | − | 1.53590i | −0.181851 | − | 0.104992i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 6.98329 | + | 4.03180i | 0.474057 | + | 0.273697i | ||||
\(218\) | 5.79441 | − | 3.34541i | 0.392447 | − | 0.226579i | ||||
\(219\) | −11.7549 | + | 6.78668i | −0.794321 | + | 0.458601i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.76261 | + | 12.1549i | −0.522170 | + | 0.817628i | ||||
\(222\) | 3.14925i | 0.211364i | ||||||||
\(223\) | 0.689457 | + | 1.19417i | 0.0461694 | + | 0.0799678i | 0.888187 | − | 0.459483i | \(-0.151965\pi\) |
−0.842017 | + | 0.539451i | \(0.818632\pi\) | |||||||
\(224\) | 1.16129 | + | 2.01141i | 0.0775919 | + | 0.134393i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.10972i | 0.472931i | ||||||||
\(227\) | −9.66025 | + | 16.7321i | −0.641174 | + | 1.11055i | 0.343998 | + | 0.938971i | \(0.388219\pi\) |
−0.985171 | + | 0.171575i | \(0.945115\pi\) | |||||||
\(228\) | −2.01141 | + | 3.48387i | −0.133209 | + | 0.230725i | ||||
\(229\) | − | 15.7626i | − | 1.04162i | −0.853672 | − | 0.520811i | \(-0.825630\pi\) | ||
0.853672 | − | 0.520811i | \(-0.174370\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.20757 | + | 10.7518i | 0.408428 | + | 0.707418i | ||||
\(232\) | −2.14539 | − | 3.71592i | −0.140852 | − | 0.243962i | ||||
\(233\) | − | 16.5549i | − | 1.08455i | −0.840201 | − | 0.542275i | \(-0.817563\pi\) | ||
0.840201 | − | 0.542275i | \(-0.182437\pi\) | |||||||
\(234\) | 0.161290 | − | 3.60194i | 0.0105438 | − | 0.235466i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.87744 | − | 3.39334i | 0.382589 | − | 0.220888i | ||||
\(237\) | 6.90026 | − | 3.98387i | 0.448220 | − | 0.258780i | ||||
\(238\) | 8.04565 | + | 4.64516i | 0.521522 | + | 0.301101i | ||||
\(239\) | 26.2006i | 1.69477i | 0.530976 | + | 0.847387i | \(0.321825\pi\) | ||||
−0.530976 | + | 0.847387i | \(0.678175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5529 | − | 7.82479i | −0.873021 | − | 0.504039i | −0.00466988 | − | 0.999989i | \(-0.501486\pi\) |
−0.868351 | + | 0.495950i | \(0.834820\pi\) | |||||||
\(242\) | 17.5734 | 1.12966 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −0.267949 | − | 0.464102i | −0.0171537 | − | 0.0297111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.64516 | 0.168649 | ||||||||
\(247\) | 7.80691 | − | 12.2243i | 0.496742 | − | 0.777812i | ||||
\(248\) | 3.47183i | 0.220462i | ||||||||
\(249\) | −9.81724 | + | 5.66799i | −0.622142 | + | 0.359194i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1708 | + | 24.5446i | −0.894454 | + | 1.54924i | −0.0599750 | + | 0.998200i | \(0.519102\pi\) |
−0.834479 | + | 0.551040i | \(0.814231\pi\) | |||||||
\(252\) | −2.32258 | −0.146309 | ||||||||
\(253\) | 13.1923 | − | 22.8497i | 0.829392 | − | 1.43655i | ||||
\(254\) | −1.84644 | − | 1.06604i | −0.115856 | − | 0.0668895i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −10.8334 | + | 6.25465i | −0.675767 | + | 0.390154i | −0.798258 | − | 0.602315i | \(-0.794245\pi\) |
0.122491 | + | 0.992470i | \(0.460912\pi\) | |||||||
\(258\) | 6.12539 | + | 10.6095i | 0.381350 | + | 0.660518i | ||||
\(259\) | −7.31439 | −0.454494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.29078 | 0.265592 | ||||||||
\(262\) | 0.629257 | + | 1.08991i | 0.0388756 | + | 0.0673346i | ||||
\(263\) | −9.27159 | + | 5.35295i | −0.571711 | + | 0.330077i | −0.757832 | − | 0.652449i | \(-0.773741\pi\) |
0.186122 | + | 0.982527i | \(0.440408\pi\) | |||||||
\(264\) | −2.67270 | + | 4.62926i | −0.164493 | + | 0.284911i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.09156 | − | 4.67167i | −0.496126 | − | 0.286438i | ||||
\(267\) | 0.869891 | − | 1.50670i | 0.0532365 | − | 0.0922083i | ||||
\(268\) | 4.10926 | 0.251013 | ||||||||
\(269\) | 3.76261 | − | 6.51703i | 0.229410 | − | 0.397350i | −0.728223 | − | 0.685340i | \(-0.759654\pi\) |
0.957633 | + | 0.287990i | \(0.0929869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.52920 | − | 4.92434i | 0.518112 | − | 0.299132i | −0.218050 | − | 0.975938i | \(-0.569970\pi\) |
0.736162 | + | 0.676805i | \(0.236636\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 8.36580 | + | 0.374609i | 0.506321 | + | 0.0226723i | ||||
\(274\) | 19.7149 | 1.19102 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.46797 | + | 4.27464i | 0.148554 | + | 0.257303i | ||||
\(277\) | −0.825410 | − | 0.476550i | −0.0495941 | − | 0.0286331i | 0.474998 | − | 0.879987i | \(-0.342449\pi\) |
−0.524592 | + | 0.851354i | \(0.675782\pi\) | |||||||
\(278\) | 5.67742 | 0.340509 | ||||||||
\(279\) | −3.00670 | − | 1.73592i | −0.180006 | − | 0.103927i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.57336i | 0.332479i | 0.986085 | + | 0.166239i | \(0.0531625\pi\) | ||||
−0.986085 | + | 0.166239i | \(0.946838\pi\) | |||||||
\(282\) | 1.57525 | + | 0.909471i | 0.0938048 | + | 0.0541582i | ||||
\(283\) | −19.0642 | + | 11.0067i | −1.13325 | + | 0.654280i | −0.944749 | − | 0.327794i | \(-0.893695\pi\) |
−0.188497 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(284\) | −13.7454 | + | 7.93593i | −0.815642 | + | 0.470911i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.3736 | − | 16.2432i | 0.613402 | − | 0.960483i | ||||
\(287\) | 6.14359i | 0.362645i | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1093i | 0.944342i | ||||||||
\(292\) | 6.78668 | − | 11.7549i | 0.397160 | − | 0.687902i | ||||
\(293\) | −3.42151 | + | 5.92623i | −0.199887 | + | 0.346214i | −0.948491 | − | 0.316803i | \(-0.897391\pi\) |
0.748605 | + | 0.663016i | \(0.230724\pi\) | |||||||
\(294\) | 1.60562i | 0.0936419i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.57463 | − | 2.72733i | −0.0915233 | − | 0.158523i | ||||
\(297\) | −2.67270 | − | 4.62926i | −0.155086 | − | 0.268617i | ||||
\(298\) | 19.4775i | 1.12830i | ||||||||
\(299\) | −8.20002 | − | 15.7951i | −0.474219 | − | 0.913453i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6414 | + | 14.2267i | −1.42031 | + | 0.820014i | ||||
\(302\) | 12.5721 | − | 7.25851i | 0.723444 | − | 0.417681i | ||||
\(303\) | 10.9906 | + | 6.34541i | 0.631391 | + | 0.364534i | ||||
\(304\) | − | 4.02283i | − | 0.230725i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.46410 | − | 2.00000i | −0.198030 | − | 0.114332i | ||||
\(307\) | 4.75442 | 0.271349 | 0.135675 | − | 0.990753i | \(-0.456680\pi\) | ||||
0.135675 | + | 0.990753i | \(0.456680\pi\) | |||||||
\(308\) | −10.7518 | − | 6.20757i | −0.612642 | − | 0.353709i | ||||
\(309\) | −2.39806 | − | 4.15356i | −0.136421 | − | 0.236288i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.93639 | 0.109803 | 0.0549013 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549013 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(312\) | 1.66129 | + | 3.20002i | 0.0940520 | + | 0.181165i | ||||
\(313\) | 25.5545i | 1.44443i | 0.691671 | + | 0.722213i | \(0.256875\pi\) | ||||
−0.691671 | + | 0.722213i | \(0.743125\pi\) | |||||||
\(314\) | 21.1162 | − | 12.1914i | 1.19166 | − | 0.688002i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.98387 | + | 6.90026i | −0.224110 | + | 0.388170i | ||||
\(317\) | 12.6667 | 0.711435 | 0.355717 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355717 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(318\) | 2.74346 | − | 4.75182i | 0.153846 | − | 0.266469i | ||||
\(319\) | 19.8631 | + | 11.4680i | 1.11212 | + | 0.642083i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.53590 | + | 2.66025i | −0.0857255 | + | 0.148481i | ||||
\(322\) | −9.92820 | + | 5.73205i | −0.553277 | + | 0.319435i | ||||
\(323\) | −8.04565 | − | 13.9355i | −0.447672 | − | 0.775391i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.6267 | −1.30856 | ||||||||
\(327\) | −3.34541 | − | 5.79441i | −0.185001 | − | 0.320432i | ||||
\(328\) | −2.29078 | + | 1.32258i | −0.126487 | + | 0.0730272i | ||||
\(329\) | −2.11232 | + | 3.65864i | −0.116456 | + | 0.201708i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.5231 | − | 11.8490i | −1.12805 | − | 0.651282i | −0.184609 | − | 0.982812i | \(-0.559102\pi\) |
−0.943445 | + | 0.331530i | \(0.892435\pi\) | |||||||
\(332\) | 5.66799 | − | 9.81724i | 0.311071 | − | 0.538791i | ||||
\(333\) | 3.14925 | 0.172578 | ||||||||
\(334\) | 8.37357 | − | 14.5035i | 0.458182 | − | 0.793594i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.01141 | − | 1.16129i | 0.109732 | − | 0.0633536i | ||||
\(337\) | − | 19.5554i | − | 1.06525i | −0.846351 | − | 0.532625i | \(-0.821205\pi\) | ||
0.846351 | − | 0.532625i | \(-0.178795\pi\) | |||||||
\(338\) | −5.46774 | − | 11.7942i | −0.297406 | − | 0.641521i | ||||
\(339\) | 7.10972 | 0.386147 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.27918 | − | 16.0720i | −0.502496 | − | 0.870348i | ||||
\(342\) | 3.48387 | + | 2.01141i | 0.188386 | + | 0.108765i | ||||
\(343\) | −19.9872 | −1.07921 | ||||||||
\(344\) | −10.6095 | − | 6.12539i | −0.572025 | − | 0.330259i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.1321i | 0.867266i | ||||||||
\(347\) | −19.9510 | − | 11.5187i | −1.07103 | − | 0.618358i | −0.142565 | − | 0.989785i | \(-0.545535\pi\) |
−0.928462 | + | 0.371427i | \(0.878868\pi\) | |||||||
\(348\) | −3.71592 | + | 2.14539i | −0.199194 | + | 0.115005i | ||||
\(349\) | −13.2679 | + | 7.66025i | −0.710217 | + | 0.410044i | −0.811141 | − | 0.584850i | \(-0.801153\pi\) |
0.100924 | + | 0.994894i | \(0.467820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.60194 | − | 0.161290i | −0.192257 | − | 0.00860902i | ||||
\(352\) | − | 5.34541i | − | 0.284911i | ||||||
\(353\) | 14.2039 | + | 24.6018i | 0.755996 | + | 1.30942i | 0.944877 | + | 0.327424i | \(0.106181\pi\) |
−0.188881 | + | 0.982000i | \(0.560486\pi\) | |||||||
\(354\) | −3.39334 | − | 5.87744i | −0.180354 | − | 0.312382i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.73978i | 0.0922083i | ||||||||
\(357\) | 4.64516 | − | 8.04565i | 0.245848 | − | 0.425821i | ||||
\(358\) | 3.66412 | − | 6.34644i | 0.193655 | − | 0.335420i | ||||
\(359\) | 23.5734i | 1.24415i | 0.782956 | + | 0.622077i | \(0.213711\pi\) | ||||
−0.782956 | + | 0.622077i | \(0.786289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.40844 | − | 2.43948i | −0.0741282 | − | 0.128394i | ||||
\(362\) | −9.78668 | − | 16.9510i | −0.514377 | − | 0.890926i | ||||
\(363\) | − | 17.5734i | − | 0.922362i | ||||||
\(364\) | −7.43230 | + | 3.85848i | −0.389558 | + | 0.202239i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.464102 | + | 0.267949i | −0.0242590 | + | 0.0140059i | ||||
\(367\) | −23.8078 | + | 13.7454i | −1.24276 | + | 0.717506i | −0.969655 | − | 0.244479i | \(-0.921383\pi\) |
−0.273103 | + | 0.961985i | \(0.588050\pi\) | |||||||
\(368\) | −4.27464 | − | 2.46797i | −0.222831 | − | 0.128652i | ||||
\(369\) | − | 2.64516i | − | 0.137701i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0365 | + | 6.37191i | 0.572985 | + | 0.330813i | ||||
\(372\) | 3.47183 | 0.180006 | ||||||||
\(373\) | −22.8129 | − | 13.1710i | −1.18121 | − | 0.681971i | −0.224914 | − | 0.974379i | \(-0.572210\pi\) |
−0.956294 | + | 0.292408i | \(0.905544\pi\) | |||||||
\(374\) | −10.6908 | − | 18.5170i | −0.552809 | − | 0.957493i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.81894 | −0.0938048 | ||||||||
\(377\) | 13.7306 | − | 7.12822i | 0.707160 | − | 0.367122i | ||||
\(378\) | 2.32258i | 0.119461i | ||||||||
\(379\) | −0.388456 | + | 0.224275i | −0.0199537 | + | 0.0115202i | −0.509944 | − | 0.860208i | \(-0.670334\pi\) |
0.489990 | + | 0.871728i | \(0.337000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06604 | + | 1.84644i | −0.0546151 | + | 0.0945961i | ||||
\(382\) | 17.0375 | 0.871713 | ||||||||
\(383\) | −6.06133 | + | 10.4985i | −0.309719 | + | 0.536450i | −0.978301 | − | 0.207189i | \(-0.933568\pi\) |
0.668582 | + | 0.743639i | \(0.266902\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.07746 | + | 5.33031i | −0.156638 | + | 0.271306i | ||||
\(387\) | 10.6095 | − | 6.12539i | 0.539311 | − | 0.311371i | ||||
\(388\) | −8.05463 | − | 13.9510i | −0.408912 | − | 0.708256i | ||||
\(389\) | −18.6195 | −0.944045 | −0.472022 | − | 0.881587i | \(-0.656476\pi\) | ||||
−0.472022 | + | 0.881587i | \(0.656476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7437 | −0.998484 | ||||||||
\(392\) | −0.802812 | − | 1.39051i | −0.0405481 | − | 0.0702314i | ||||
\(393\) | 1.08991 | − | 0.629257i | 0.0549785 | − | 0.0317418i | ||||
\(394\) | −6.89334 | + | 11.9396i | −0.347281 | + | 0.601509i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.62926 | + | 2.67270i | 0.232629 | + | 0.134308i | ||||
\(397\) | 5.65208 | − | 9.78970i | 0.283670 | − | 0.491331i | −0.688616 | − | 0.725126i | \(-0.741781\pi\) |
0.972286 | + | 0.233796i | \(0.0751147\pi\) | |||||||
\(398\) | −2.28304 | −0.114439 | ||||||||
\(399\) | −4.67167 | + | 8.09156i | −0.233876 | + | 0.405085i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.30406 | + | 0.752899i | −0.0651216 | + | 0.0375980i | −0.532207 | − | 0.846614i | \(-0.678637\pi\) |
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(402\) | − | 4.10926i | − | 0.204951i | ||||||
\(403\) | −12.5053 | − | 0.559971i | −0.622935 | − | 0.0278942i | ||||
\(404\) | −12.6908 | −0.631391 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.98283 | − | 8.63052i | −0.247294 | − | 0.428326i | ||||
\(407\) | 14.5787 | + | 8.41702i | 0.722640 | + | 0.417216i | ||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | −9.64697 | − | 5.56968i | −0.477012 | − | 0.275403i | 0.242158 | − | 0.970237i | \(-0.422145\pi\) |
−0.719170 | + | 0.694834i | \(0.755478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 19.7149i | − | 0.972464i | ||||||
\(412\) | 4.15356 | + | 2.39806i | 0.204631 | + | 0.118144i | ||||
\(413\) | 13.6508 | − | 7.88130i | 0.671713 | − | 0.387814i | ||||
\(414\) | 4.27464 | − | 2.46797i | 0.210087 | − | 0.121294i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.03873 | − | 1.94065i | −0.148986 | − | 0.0951483i | ||||
\(417\) | − | 5.67742i | − | 0.278024i | ||||||
\(418\) | 10.7518 | + | 18.6227i | 0.525889 | + | 0.910866i | ||||
\(419\) | −7.75488 | − | 13.4318i | −0.378851 | − | 0.656188i | 0.612045 | − | 0.790823i | \(-0.290347\pi\) |
−0.990895 | + | 0.134635i | \(0.957014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.4452i | 1.92244i | 0.275778 | + | 0.961221i | \(0.411065\pi\) | ||||
−0.275778 | + | 0.961221i | \(0.588935\pi\) | |||||||
\(422\) | 11.2387 | − | 19.4661i | 0.547094 | − | 0.947594i | ||||
\(423\) | 0.909471 | − | 1.57525i | 0.0442200 | − | 0.0765913i | ||||
\(424\) | 5.48693i | 0.266469i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.93593 | + | 13.7454i | 0.384497 | + | 0.665969i | ||||
\(427\) | −0.622333 | − | 1.07791i | −0.0301168 | − | 0.0521639i | ||||
\(428\) | − | 3.07180i | − | 0.148481i | ||||||
\(429\) | −16.2432 | − | 10.3736i | −0.784231 | − | 0.500841i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.86621 | − | 1.07746i | 0.0898921 | − | 0.0518993i | −0.454380 | − | 0.890808i | \(-0.650139\pi\) |
0.544272 | + | 0.838909i | \(0.316806\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 1.15994 | + | 0.669689i | 0.0557429 | + | 0.0321832i | 0.527612 | − | 0.849485i | \(-0.323087\pi\) |
−0.471870 | + | 0.881668i | \(0.656421\pi\) | |||||||
\(434\) | 8.06361i | 0.387066i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.79441 | + | 3.34541i | 0.277502 | + | 0.160216i | ||||
\(437\) | 19.8564 | 0.949861 | ||||||||
\(438\) | −11.7549 | − | 6.78668i | −0.561670 | − | 0.324280i | ||||
\(439\) | 15.8490 | + | 27.4513i | 0.756434 | + | 1.31018i | 0.944658 | + | 0.328055i | \(0.106393\pi\) |
−0.188225 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60562 | 0.0764583 | ||||||||
\(442\) | −14.4078 | − | 0.645159i | −0.685308 | − | 0.0306871i | ||||
\(443\) | − | 28.0904i | − | 1.33461i | −0.744782 | − | 0.667307i | \(-0.767447\pi\) | ||
0.744782 | − | 0.667307i | \(-0.232553\pi\) | |||||||
\(444\) | −2.72733 | + | 1.57463i | −0.129434 | + | 0.0747285i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.689457 | + | 1.19417i | −0.0326467 | + | 0.0565458i | ||||
\(447\) | 19.4775 | 0.921254 | ||||||||
\(448\) | −1.16129 | + | 2.01141i | −0.0548658 | + | 0.0950303i | ||||
\(449\) | −25.0426 | − | 14.4583i | −1.18183 | − | 0.682332i | −0.225395 | − | 0.974267i | \(-0.572367\pi\) |
−0.956438 | + | 0.291936i | \(0.905701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.06973 | − | 12.2451i | 0.332900 | − | 0.576600i | ||||
\(452\) | −6.15720 | + | 3.55486i | −0.289610 | + | 0.167206i | ||||
\(453\) | −7.25851 | − | 12.5721i | −0.341035 | − | 0.590690i | ||||
\(454\) | −19.3205 | −0.906756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.02283 | −0.188386 | ||||||||
\(457\) | −4.84950 | − | 8.39958i | −0.226850 | − | 0.392916i | 0.730023 | − | 0.683423i | \(-0.239509\pi\) |
−0.956873 | + | 0.290507i | \(0.906176\pi\) | |||||||
\(458\) | 13.6508 | − | 7.88130i | 0.637861 | − | 0.368269i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3905 | + | 5.99896i | 0.483934 | + | 0.279400i | 0.722055 | − | 0.691836i | \(-0.243198\pi\) |
−0.238120 | + | 0.971236i | \(0.576531\pi\) | |||||||
\(462\) | −6.20757 | + | 10.7518i | −0.288802 | + | 0.500220i | ||||
\(463\) | 6.42664 | 0.298671 | 0.149336 | − | 0.988787i | \(-0.452287\pi\) | ||||
0.149336 | + | 0.988787i | \(0.452287\pi\) | |||||||
\(464\) | 2.14539 | − | 3.71592i | 0.0995971 | − | 0.172507i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.3370 | − | 8.27747i | 0.664149 | − | 0.383447i | ||||
\(467\) | − | 26.2642i | − | 1.21536i | −0.794182 | − | 0.607681i | \(-0.792100\pi\) | ||
0.794182 | − | 0.607681i | \(-0.207900\pi\) | |||||||
\(468\) | 3.20002 | − | 1.66129i | 0.147921 | − | 0.0767932i | ||||
\(469\) | 9.54409 | 0.440705 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1914 | − | 21.1162i | −0.561752 | − | 0.972982i | ||||
\(472\) | 5.87744 | + | 3.39334i | 0.270531 | + | 0.156191i | ||||
\(473\) | 65.4854 | 3.01102 | ||||||||
\(474\) | 6.90026 | + | 3.98387i | 0.316940 | + | 0.182985i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.29032i | 0.425821i | ||||||||
\(477\) | −4.75182 | − | 2.74346i | −0.217571 | − | 0.125615i | ||||
\(478\) | −22.6904 | + | 13.1003i | −1.03783 | + | 0.599193i | ||||
\(479\) | 22.2418 | − | 12.8413i | 1.01625 | − | 0.586735i | 0.103237 | − | 0.994657i | \(-0.467080\pi\) |
0.913017 | + | 0.407922i | \(0.133747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0777 | − | 5.23182i | 0.459502 | − | 0.238551i | ||||
\(482\) | − | 15.6496i | − | 0.712818i | ||||||
\(483\) | 5.73205 | + | 9.92820i | 0.260817 | + | 0.451749i | ||||
\(484\) | 8.78668 | + | 15.2190i | 0.399395 | + | 0.691772i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −4.68946 | + | 8.12238i | −0.212500 | + | 0.368060i | −0.952496 | − | 0.304551i | \(-0.901494\pi\) |
0.739997 | + | 0.672611i | \(0.234827\pi\) | |||||||
\(488\) | 0.267949 | − | 0.464102i | 0.0121295 | − | 0.0210089i | ||||
\(489\) | 23.6267i | 1.06844i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.86927 | − | 6.70177i | −0.174618 | − | 0.302447i | 0.765411 | − | 0.643541i | \(-0.222536\pi\) |
−0.940029 | + | 0.341095i | \(0.889202\pi\) | |||||||
\(492\) | 1.32258 | + | 2.29078i | 0.0596265 | + | 0.103276i | ||||
\(493\) | − | 17.1631i | − | 0.772987i | ||||||
\(494\) | 14.4900 | + | 0.648841i | 0.651935 | + | 0.0291927i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00670 | + | 1.73592i | −0.135005 | + | 0.0779450i | ||||
\(497\) | −31.9249 | + | 18.4318i | −1.43203 | + | 0.826781i | ||||
\(498\) | −9.81724 | − | 5.66799i | −0.439921 | − | 0.253989i | ||||
\(499\) | 3.18106i | 0.142404i | 0.997462 | + | 0.0712019i | \(0.0226834\pi\) | ||||
−0.997462 | + | 0.0712019i | \(0.977317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5035 | − | 8.37357i | −0.647967 | − | 0.374104i | ||||
\(502\) | −28.3416 | −1.26495 | ||||||||
\(503\) | 30.3765 | + | 17.5379i | 1.35442 | + | 0.781975i | 0.988865 | − | 0.148814i | \(-0.0475456\pi\) |
0.365556 | + | 0.930789i | \(0.380879\pi\) | |||||||
\(504\) | −1.16129 | − | 2.01141i | −0.0517280 | − | 0.0895955i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.3846 | 1.17294 | ||||||||
\(507\) | −11.7942 | + | 5.46774i | −0.523800 | + | 0.242831i | ||||
\(508\) | − | 2.13209i | − | 0.0945961i | ||||||
\(509\) | 16.2697 | − | 9.39334i | 0.721144 | − | 0.416353i | −0.0940298 | − | 0.995569i | \(-0.529975\pi\) |
0.815173 | + | 0.579217i | \(0.196642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7626 | − | 27.3016i | 0.697297 | − | 1.20775i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.01141 | − | 3.48387i | 0.0888061 | − | 0.153817i | ||||
\(514\) | −10.8334 | − | 6.25465i | −0.477839 | − | 0.275881i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.12539 | + | 10.6095i | −0.269655 | + | 0.467057i | ||||
\(517\) | 8.42035 | − | 4.86149i | 0.370327 | − | 0.213808i | ||||
\(518\) | −3.65720 | − | 6.33445i | −0.160688 | − | 0.278320i | ||||
\(519\) | 16.1321 | 0.708120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28512 | 0.231545 | 0.115773 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(522\) | 2.14539 | + | 3.71592i | 0.0939011 | + | 0.162641i | ||||
\(523\) | −17.9721 | + | 10.3762i | −0.785863 | + | 0.453718i | −0.838504 | − | 0.544895i | \(-0.816569\pi\) |
0.0526409 | + | 0.998614i | \(0.483236\pi\) | |||||||
\(524\) | −0.629257 | + | 1.08991i | −0.0274892 | + | 0.0476127i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.27159 | − | 5.35295i | −0.404260 | − | 0.233400i | ||||
\(527\) | −6.94367 | + | 12.0268i | −0.302471 | + | 0.523895i | ||||
\(528\) | −5.34541 | −0.232629 | ||||||||
\(529\) | 0.681725 | − | 1.18078i | 0.0296402 | − | 0.0513384i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.87744 | + | 3.39334i | −0.255059 | + | 0.147258i | ||||
\(532\) | − | 9.34333i | − | 0.405085i | ||||||
\(533\) | −4.39438 | − | 8.46456i | −0.190342 | − | 0.366641i | ||||
\(534\) | 1.73978 | 0.0752877 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.05463 | + | 3.55872i | 0.0887465 | + | 0.153713i | ||||
\(537\) | −6.34644 | − | 3.66412i | −0.273869 | − | 0.158118i | ||||
\(538\) | 7.52522 | 0.324435 | ||||||||
\(539\) | 7.43284 | + | 4.29135i | 0.320155 | + | 0.184842i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7365i | 1.23548i | 0.786384 | + | 0.617739i | \(0.211951\pi\) | ||||
−0.786384 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(542\) | 8.52920 | + | 4.92434i | 0.366361 | + | 0.211518i | ||||
\(543\) | −16.9510 | + | 9.78668i | −0.727438 | + | 0.419987i | ||||
\(544\) | −3.46410 | + | 2.00000i | −0.148522 | + | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.85848 | + | 7.43230i | 0.165128 | + | 0.318073i | ||||
\(547\) | − | 18.3768i | − | 0.785737i | −0.919595 | − | 0.392869i | \(-0.871483\pi\) | ||
0.919595 | − | 0.392869i | \(-0.128517\pi\) | |||||||
\(548\) | 9.85744 | + | 17.0736i | 0.421089 | + | 0.729348i | ||||
\(549\) | 0.267949 | + | 0.464102i | 0.0114358 | + | 0.0198074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.2610i | 0.735345i | ||||||||
\(552\) | −2.46797 | + | 4.27464i | −0.105044 | + | 0.181941i | ||||
\(553\) | −9.25285 | + | 16.0264i | −0.393471 | + | 0.681512i | ||||
\(554\) | − | 0.953101i | − | 0.0404934i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.83871 | + | 4.91679i | 0.120388 | + | 0.208518i | ||||
\(557\) | −13.2693 | − | 22.9831i | −0.562238 | − | 0.973826i | −0.997301 | − | 0.0734252i | \(-0.976607\pi\) |
0.435062 | − | 0.900400i | \(-0.356726\pi\) | |||||||
\(558\) | − | 3.47183i | − | 0.146974i | ||||||
\(559\) | 23.7745 | − | 37.2268i | 1.00555 | − | 1.57453i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.5170 | + | 10.6908i | −0.781790 | + | 0.451366i | ||||
\(562\) | −4.82667 | + | 2.78668i | −0.203601 | + | 0.117549i | ||||
\(563\) | −5.24908 | − | 3.03056i | −0.221222 | − | 0.127723i | 0.385294 | − | 0.922794i | \(-0.374100\pi\) |
−0.606516 | + | 0.795071i | \(0.707433\pi\) | |||||||
\(564\) | 1.81894i | 0.0765913i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.0642 | − | 11.0067i | −0.801326 | − | 0.462646i | ||||
\(567\) | 2.32258 | 0.0975392 | ||||||||
\(568\) | −13.7454 | − | 7.93593i | −0.576746 | − | 0.332984i | ||||
\(569\) | 7.24818 | + | 12.5542i | 0.303860 | + | 0.526300i | 0.977007 | − | 0.213208i | \(-0.0683913\pi\) |
−0.673147 | + | 0.739509i | \(0.735058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.90413 | −0.121534 | −0.0607670 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607670 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(572\) | 19.2538 | + | 0.862160i | 0.805044 | + | 0.0360487i | ||||
\(573\) | − | 17.0375i | − | 0.711750i | ||||||
\(574\) | −5.32051 | + | 3.07180i | −0.222074 | + | 0.128214i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 18.8180 | 0.783405 | 0.391702 | − | 0.920092i | \(-0.371886\pi\) | ||||
0.391702 | + | 0.920092i | \(0.371886\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | 5.33031 | + | 3.07746i | 0.221520 | + | 0.127895i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.1643 | − | 22.8013i | 0.546149 | − | 0.945958i | ||||
\(582\) | −13.9510 | + | 8.05463i | −0.578289 | + | 0.333875i | ||||
\(583\) | −14.6649 | − | 25.4004i | −0.607359 | − | 1.05198i | ||||
\(584\) | 13.5734 | 0.561670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.84302 | −0.282682 | ||||||||
\(587\) | 1.96820 | + | 3.40901i | 0.0812361 | + | 0.140705i | 0.903781 | − | 0.427995i | \(-0.140780\pi\) |
−0.822545 | + | 0.568700i | \(0.807447\pi\) | |||||||
\(588\) | −1.39051 | + | 0.802812i | −0.0573437 | + | 0.0331074i | ||||
\(589\) | 6.98329 | − | 12.0954i | 0.287741 | − | 0.498383i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9396 | + | 6.89334i | 0.491130 | + | 0.283554i | ||||
\(592\) | 1.57463 | − | 2.72733i | 0.0647168 | − | 0.112093i | ||||
\(593\) | 20.1227 | 0.826338 | 0.413169 | − | 0.910654i | \(-0.364422\pi\) | ||||
0.413169 | + | 0.910654i | \(0.364422\pi\) | |||||||
\(594\) | 2.67270 | − | 4.62926i | 0.109662 | − | 0.189941i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.8680 | + | 9.73875i | −0.690940 | + | 0.398915i | ||||
\(597\) | 2.28304i | 0.0934388i | ||||||||
\(598\) | 9.57893 | − | 14.9990i | 0.391712 | − | 0.613353i | ||||
\(599\) | −48.1172 | −1.96601 | −0.983007 | − | 0.183567i | \(-0.941236\pi\) | ||||
−0.983007 | + | 0.183567i | \(0.941236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.12109 | + | 3.67383i | 0.0865209 | + | 0.149859i | 0.906038 | − | 0.423196i | \(-0.139092\pi\) |
−0.819517 | + | 0.573054i | \(0.805758\pi\) | |||||||
\(602\) | −24.6414 | − | 14.2267i | −1.00431 | − | 0.579837i | ||||
\(603\) | −4.10926 | −0.167342 | ||||||||
\(604\) | 12.5721 | + | 7.25851i | 0.511552 | + | 0.295345i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.6908i | 0.515529i | ||||||||
\(607\) | 10.4516 | + | 6.03424i | 0.424218 | + | 0.244922i | 0.696880 | − | 0.717188i | \(-0.254571\pi\) |
−0.272663 | + | 0.962110i | \(0.587904\pi\) | |||||||
\(608\) | 3.48387 | − | 2.01141i | 0.141290 | − | 0.0815736i | ||||
\(609\) | −8.63052 | + | 4.98283i | −0.349726 | + | 0.201915i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.293377 | − | 6.55172i | 0.0118688 | − | 0.265054i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 20.8711 | + | 36.1497i | 0.842974 | + | 1.46007i | 0.887369 | + | 0.461060i | \(0.152531\pi\) |
−0.0443946 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(614\) | 2.37721 | + | 4.11745i | 0.0959364 | + | 0.166167i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 12.4151i | − | 0.500220i | ||||||
\(617\) | −16.7293 | + | 28.9760i | −0.673497 | + | 1.16653i | 0.303409 | + | 0.952860i | \(0.401875\pi\) |
−0.976906 | + | 0.213670i | \(0.931458\pi\) | |||||||
\(618\) | 2.39806 | − | 4.15356i | 0.0964640 | − | 0.167081i | ||||
\(619\) | 38.0978i | 1.53128i | 0.643270 | + | 0.765639i | \(0.277577\pi\) | ||||
−0.643270 | + | 0.765639i | \(0.722423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.46797 | − | 4.27464i | −0.0990361 | − | 0.171536i | ||||
\(622\) | 0.968196 | + | 1.67696i | 0.0388211 | + | 0.0672401i | ||||
\(623\) | 4.04078i | 0.161891i | ||||||||
\(624\) | −1.94065 | + | 3.03873i | −0.0776883 | + | 0.121646i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.1308 | + | 12.7772i | −0.884526 | + | 0.510681i | ||||
\(627\) | 18.6227 | − | 10.7518i | 0.743719 | − | 0.429386i | ||||
\(628\) | 21.1162 | + | 12.1914i | 0.842628 | + | 0.486491i | ||||
\(629\) | − | 12.5970i | − | 0.502276i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.4775 | − | 12.4000i | −0.855005 | − | 0.493638i | 0.00733109 | − | 0.999973i | \(-0.497666\pi\) |
−0.862337 | + | 0.506335i | \(0.831000\pi\) | |||||||
\(632\) | −7.96774 | −0.316940 | ||||||||
\(633\) | −19.4661 | − | 11.2387i | −0.773707 | − | 0.446700i | ||||
\(634\) | 6.33337 | + | 10.9697i | 0.251530 | + | 0.435663i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.48693 | 0.217571 | ||||||||
\(637\) | 5.13802 | − | 2.66741i | 0.203576 | − | 0.105686i | ||||
\(638\) | 22.9359i | 0.908042i | ||||||||
\(639\) | 13.7454 | − | 7.93593i | 0.543761 | − | 0.313941i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.04259 | − | 3.53788i | 0.0806776 | − | 0.139738i | −0.822864 | − | 0.568239i | \(-0.807625\pi\) |
0.903541 | + | 0.428501i | \(0.140958\pi\) | |||||||
\(642\) | −3.07180 | −0.121234 | ||||||||
\(643\) | 18.2908 | − | 31.6806i | 0.721318 | − | 1.24936i | −0.239154 | − | 0.970982i | \(-0.576870\pi\) |
0.960472 | − | 0.278377i | \(-0.0897966\pi\) | |||||||
\(644\) | −9.92820 | − | 5.73205i | −0.391226 | − | 0.225874i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.04565 | − | 13.9355i | 0.316552 | − | 0.548284i | ||||
\(647\) | 14.9251 | − | 8.61704i | 0.586768 | − | 0.338771i | −0.177050 | − | 0.984202i | \(-0.556656\pi\) |
0.763818 | + | 0.645431i | \(0.223322\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −36.2776 | −1.42402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.06361 | 0.316038 | ||||||||
\(652\) | −11.8134 | − | 20.4614i | −0.462647 | − | 0.801329i | ||||
\(653\) | −18.9897 | + | 10.9637i | −0.743123 | + | 0.429042i | −0.823204 | − | 0.567746i | \(-0.807816\pi\) |
0.0800806 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(654\) | 3.34541 | − | 5.79441i | 0.130816 | − | 0.226579i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.29078 | − | 1.32258i | −0.0894397 | − | 0.0516381i | ||||
\(657\) | −6.78668 | + | 11.7549i | −0.264774 | + | 0.458601i | ||||
\(658\) | −4.22464 | −0.164694 | ||||||||
\(659\) | −24.2379 | + | 41.9813i | −0.944176 | + | 1.63536i | −0.186783 | + | 0.982401i | \(0.559806\pi\) |
−0.757393 | + | 0.652960i | \(0.773527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.8267 | + | 14.9110i | −1.00454 | + | 0.579972i | −0.909589 | − | 0.415510i | \(-0.863603\pi\) |
−0.0949524 | + | 0.995482i | \(0.530270\pi\) | |||||||
\(662\) | − | 23.6981i | − | 0.921052i | ||||||
\(663\) | −0.645159 | + | 14.4078i | −0.0250559 | + | 0.559551i | ||||
\(664\) | 11.3360 | 0.439921 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.57463 | + | 2.72733i | 0.0610155 | + | 0.105682i | ||||
\(667\) | 18.3415 | + | 10.5895i | 0.710187 | + | 0.410027i | ||||
\(668\) | 16.7471 | 0.647967 | ||||||||
\(669\) | 1.19417 | + | 0.689457i | 0.0461694 | + | 0.0266559i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.86459i | 0.110586i | ||||||||
\(672\) | 2.01141 | + | 1.16129i | 0.0775919 | + | 0.0447977i | ||||
\(673\) | 26.5627 | − | 15.3360i | 1.02392 | − | 0.591158i | 0.108680 | − | 0.994077i | \(-0.465338\pi\) |
0.915236 | + | 0.402919i | \(0.132004\pi\) | |||||||
\(674\) | 16.9355 | − | 9.77770i | 0.652330 | − | 0.376623i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.48023 | − | 10.6323i | 0.287701 | − | 0.408935i | ||||
\(677\) | − | 21.0831i | − | 0.810290i | −0.914252 | − | 0.405145i | \(-0.867221\pi\) | ||
0.914252 | − | 0.405145i | \(-0.132779\pi\) | |||||||
\(678\) | 3.55486 | + | 6.15720i | 0.136524 | + | 0.236466i | ||||
\(679\) | −18.7075 | − | 32.4024i | −0.717929 | − | 1.24349i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.3205i | 0.740363i | ||||||||
\(682\) | 9.27918 | − | 16.0720i | 0.355318 | − | 0.615429i | ||||
\(683\) | 6.66799 | − | 11.5493i | 0.255143 | − | 0.441921i | −0.709791 | − | 0.704412i | \(-0.751211\pi\) |
0.964934 | + | 0.262491i | \(0.0845440\pi\) | |||||||
\(684\) | 4.02283i | 0.153817i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.99362 | − | 17.3095i | −0.381558 | − | 0.660878i | ||||
\(687\) | −7.88130 | − | 13.6508i | −0.300691 | − | 0.520811i | ||||
\(688\) | − | 12.2508i | − | 0.467057i | ||||||
\(689\) | −19.7636 | − | 0.884986i | −0.752933 | − | 0.0337153i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.2289 | + | 17.4527i | −1.14996 | + | 0.663932i | −0.948878 | − | 0.315642i | \(-0.897780\pi\) |
−0.201085 | + | 0.979574i | \(0.564447\pi\) | |||||||
\(692\) | −13.9708 | + | 8.06604i | −0.531090 | + | 0.306625i | ||||
\(693\) | 10.7518 | + | 6.20757i | 0.408428 | + | 0.235806i | ||||
\(694\) | − | 23.0375i | − | 0.874490i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.71592 | − | 2.14539i | −0.140852 | − | 0.0813207i | ||||
\(697\) | −10.5806 | −0.400770 | ||||||||
\(698\) | −13.2679 | − | 7.66025i | −0.502199 | − | 0.289945i | ||||
\(699\) | −8.27747 | − | 14.3370i | −0.313083 | − | 0.542275i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.6715 | 1.49837 | 0.749186 | − | 0.662360i | \(-0.230445\pi\) | ||||
0.749186 | + | 0.662360i | \(0.230445\pi\) | |||||||
\(702\) | −1.66129 | − | 3.20002i | −0.0627013 | − | 0.120777i | ||||
\(703\) | 12.6689i | 0.477817i | ||||||||
\(704\) | 4.62926 | − | 2.67270i | 0.174472 | − | 0.100731i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.2039 | + | 24.6018i | −0.534570 | + | 0.925903i | ||||
\(707\) | −29.4754 | −1.10854 | ||||||||
\(708\) | 3.39334 | − | 5.87744i | 0.127530 | − | 0.220888i | ||||
\(709\) | −2.45467 | − | 1.41720i | −0.0921869 | − | 0.0532242i | 0.453198 | − | 0.891410i | \(-0.350283\pi\) |
−0.545385 | + | 0.838186i | \(0.683616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.98387 | − | 6.90026i | 0.149407 | − | 0.258780i | ||||
\(712\) | −1.50670 | + | 0.869891i | −0.0564658 | + | 0.0326005i | ||||
\(713\) | −8.56837 | − | 14.8409i | −0.320888 | − | 0.555794i | ||||
\(714\) | 9.29032 | 0.347681 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.32824 | 0.273869 | ||||||||
\(717\) | 13.1003 | + | 22.6904i | 0.489239 | + | 0.847387i | ||||
\(718\) | −20.4151 | + | 11.7867i | −0.761886 | + | 0.439875i | ||||
\(719\) | 21.8564 | − | 37.8564i | 0.815106 | − | 1.41181i | −0.0941451 | − | 0.995558i | \(-0.530012\pi\) |
0.909251 | − | 0.416247i | \(-0.136655\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.64697 | + | 5.56968i | 0.359272 | + | 0.207426i | ||||
\(722\) | 1.40844 | − | 2.43948i | 0.0524165 | − | 0.0907881i | ||||
\(723\) | −15.6496 | −0.582014 | ||||||||
\(724\) | 9.78668 | − | 16.9510i | 0.363719 | − | 0.629980i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.2190 | − | 8.78668i | 0.564829 | − | 0.326104i | ||||
\(727\) | 16.2568i | 0.602932i | 0.953477 | + | 0.301466i | \(0.0974759\pi\) | ||||
−0.953477 | + | 0.301466i | \(0.902524\pi\) | |||||||
\(728\) | −7.05769 | − | 4.50732i | −0.261575 | − | 0.167052i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.5016 | − | 42.4380i | −0.906223 | − | 1.56962i | ||||
\(732\) | −0.464102 | − | 0.267949i | −0.0171537 | − | 0.00990369i | ||||
\(733\) | 4.96774 | 0.183488 | 0.0917438 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917438 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(734\) | −23.8078 | − | 13.7454i | −0.878762 | − | 0.507354i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 4.93593i | − | 0.181941i | ||||||
\(737\) | −19.0228 | − | 10.9828i | −0.700715 | − | 0.404558i | ||||
\(738\) | 2.29078 | − | 1.32258i | 0.0843246 | − | 0.0486848i | ||||
\(739\) | −43.0306 | + | 24.8437i | −1.58291 | + | 0.913892i | −0.588475 | + | 0.808515i | \(0.700271\pi\) |
−0.994432 | + | 0.105377i | \(0.966395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.648841 | − | 14.4900i | 0.0238358 | − | 0.532303i | ||||
\(742\) | 12.7438i | 0.467841i | ||||||||
\(743\) | 10.7710 | + | 18.6559i | 0.395150 | + | 0.684420i | 0.993120 | − | 0.117098i | \(-0.0373593\pi\) |
−0.597970 | + | 0.801518i | \(0.704026\pi\) | |||||||
\(744\) | 1.73592 | + | 3.00670i | 0.0636418 | + | 0.110231i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 26.3421i | − | 0.964452i | ||||||
\(747\) | −5.66799 | + | 9.81724i | −0.207381 | + | 0.359194i | ||||
\(748\) | 10.6908 | − | 18.5170i | 0.390895 | − | 0.677050i | ||||
\(749\) | − | 7.13449i | − | 0.260689i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.17436 | − | 5.49816i | −0.115834 | − | 0.200631i | 0.802279 | − | 0.596950i | \(-0.203621\pi\) |
−0.918113 | + | 0.396319i | \(0.870287\pi\) | |||||||
\(752\) | −0.909471 | − | 1.57525i | −0.0331650 | − | 0.0574435i | ||||
\(753\) | 28.3416i | 1.03283i | ||||||||
\(754\) | 13.0385 | + | 8.32690i | 0.474834 | + | 0.303248i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.01141 | + | 1.16129i | −0.0731544 | + | 0.0422357i | ||||
\(757\) | 41.6651 | − | 24.0554i | 1.51434 | − | 0.874307i | 0.514485 | − | 0.857499i | \(-0.327983\pi\) |
0.999859 | − | 0.0168078i | \(-0.00535036\pi\) | |||||||
\(758\) | −0.388456 | − | 0.224275i | −0.0141094 | − | 0.00814604i | ||||
\(759\) | − | 26.3846i | − | 0.957699i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.1734 | + | 16.8433i | 1.05754 | + | 0.610569i | 0.924750 | − | 0.380576i | \(-0.124274\pi\) |
0.132786 | + | 0.991145i | \(0.457608\pi\) | |||||||
\(762\) | −2.13209 | −0.0772374 | ||||||||
\(763\) | 13.4580 | + | 7.76997i | 0.487212 | + | 0.281292i | ||||
\(764\) | 8.51873 | + | 14.7549i | 0.308197 | + | 0.533813i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.1227 | −0.438009 | ||||||||
\(767\) | −13.1706 | + | 20.6229i | −0.475562 | + | 0.744649i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 5.18651 | − | 2.99443i | 0.187030 | − | 0.107982i | −0.403561 | − | 0.914953i | \(-0.632228\pi\) |
0.590592 | + | 0.806971i | \(0.298894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.25465 | + | 10.8334i | −0.225256 | + | 0.390154i | ||||
\(772\) | −6.15491 | −0.221520 | ||||||||
\(773\) | −6.74409 | + | 11.6811i | −0.242568 | + | 0.420140i | −0.961445 | − | 0.274997i | \(-0.911323\pi\) |
0.718877 | + | 0.695137i | \(0.244656\pi\) | |||||||
\(774\) | 10.6095 | + | 6.12539i | 0.381350 | + | 0.220173i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.05463 | − | 13.9510i | 0.289144 | − | 0.500813i | ||||
\(777\) | −6.33445 | + | 3.65720i | −0.227247 | + | 0.131201i | ||||
\(778\) | −9.30974 | − | 16.1249i | −0.333770 | − | 0.578107i | ||||
\(779\) | 10.6410 | 0.381254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 84.8416 | 3.03587 | ||||||||
\(782\) | −9.87187 | − | 17.0986i | −0.353017 | − | 0.611444i | ||||
\(783\) | 3.71592 | − | 2.14539i | 0.132796 | − | 0.0766699i | ||||
\(784\) | 0.802812 | − | 1.39051i | 0.0286718 | − | 0.0496611i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.08991 | + | 0.629257i | 0.0388756 | + | 0.0224449i | ||||
\(787\) | −27.3244 | + | 47.3272i | −0.974009 | + | 1.68703i | −0.290841 | + | 0.956772i | \(0.593935\pi\) |
−0.683168 | + | 0.730261i | \(0.739398\pi\) | |||||||
\(788\) | −13.7867 | −0.491130 | ||||||||
\(789\) | −5.35295 | + | 9.27159i | −0.190570 | + | 0.330077i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3006 | + | 8.25644i | −0.508470 | + | 0.293565i | ||||
\(792\) | 5.34541i | 0.189941i | ||||||||
\(793\) | 1.62845 | + | 1.03999i | 0.0578279 | + | 0.0369312i | ||||
\(794\) | 11.3042 | 0.401170 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.14152 | − | 1.97717i | −0.0404602 | − | 0.0700791i | ||||
\(797\) | 33.1899 | + | 19.1622i | 1.17565 | + | 0.678760i | 0.955003 | − | 0.296595i | \(-0.0958512\pi\) |
0.220643 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(798\) | −9.34333 | −0.330750 | ||||||||
\(799\) | −6.30100 | − | 3.63788i | −0.222913 | − | 0.128699i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.73978i | − | 0.0614722i | ||||||
\(802\) | −1.30406 | − | 0.752899i | −0.0460479 | − | 0.0265858i | ||||
\(803\) | −62.8346 | + | 36.2776i | −2.21738 | + | 1.28021i | ||||
\(804\) | 3.55872 | − | 2.05463i | 0.125507 | − | 0.0724612i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.76772 | − | 11.1099i | −0.203159 | − | 0.391331i | ||||
\(807\) | − | 7.52522i | − | 0.264900i | ||||||
\(808\) | −6.34541 | − | 10.9906i | −0.223231 | − | 0.386647i | ||||
\(809\) | 5.69081 | + | 9.85677i | 0.200078 | + | 0.346546i | 0.948553 | − | 0.316617i | \(-0.102547\pi\) |
−0.748475 | + | 0.663163i | \(0.769214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8899i | 0.382397i | 0.981551 | + | 0.191198i | \(0.0612374\pi\) | ||||
−0.981551 | + | 0.191198i | \(0.938763\pi\) | |||||||
\(812\) | 4.98283 | − | 8.63052i | 0.174863 | − | 0.302872i | ||||
\(813\) | 4.92434 | − | 8.52920i | 0.172704 | − | 0.299132i | ||||
\(814\) | 16.8340i | 0.590033i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 24.6414 | + | 42.6801i | 0.862093 | + | 1.49319i | ||||
\(818\) | − | 11.1394i | − | 0.389479i | ||||||
\(819\) | 7.43230 | − | 3.85848i | 0.259705 | − | 0.134826i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.46194 | + | 0.844051i | −0.0510220 | + | 0.0294576i | −0.525294 | − | 0.850921i | \(-0.676045\pi\) |
0.474272 | + | 0.880378i | \(0.342711\pi\) | |||||||
\(822\) | 17.0736 | − | 9.85744i | 0.595510 | − | 0.343818i | ||||
\(823\) | 5.87006 | + | 3.38908i | 0.204617 | + | 0.118136i | 0.598807 | − | 0.800893i | \(-0.295641\pi\) |
−0.394190 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(824\) | 4.79612i | 0.167081i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.6508 | + | 7.88130i | 0.474973 | + | 0.274226i | ||||
\(827\) | 30.2298 | 1.05119 | 0.525597 | − | 0.850733i | \(-0.323842\pi\) | ||||
0.525597 | + | 0.850733i | \(0.323842\pi\) | |||||||
\(828\) | 4.27464 | + | 2.46797i | 0.148554 | + | 0.0857678i | ||||
\(829\) | 5.22023 | + | 9.04170i | 0.181306 | + | 0.314031i | 0.942326 | − | 0.334698i | \(-0.108634\pi\) |
−0.761020 | + | 0.648729i | \(0.775301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.953101 | −0.0330627 | ||||||||
\(832\) | 0.161290 | − | 3.60194i | 0.00559172 | − | 0.124875i | ||||
\(833\) | − | 6.42249i | − | 0.222526i | ||||||
\(834\) | 4.91679 | − | 2.83871i | 0.170255 | − | 0.0982965i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.7518 | + | 18.6227i | −0.371859 | + | 0.644079i | ||||
\(837\) | −3.47183 | −0.120004 | ||||||||
\(838\) | 7.75488 | − | 13.4318i | 0.267888 | − | 0.463995i | ||||
\(839\) | −9.69647 | − | 5.59826i | −0.334759 | − | 0.193273i | 0.323193 | − | 0.946333i | \(-0.395244\pi\) |
−0.657952 | + | 0.753060i | \(0.728577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.29462 | − | 9.17056i | 0.182573 | − | 0.316226i | ||||
\(842\) | −34.1606 | + | 19.7226i | −1.17725 | + | 0.679686i | ||||
\(843\) | 2.78668 | + | 4.82667i | 0.0959784 | + | 0.166239i | ||||
\(844\) | 22.4775 | 0.773707 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.81894 | 0.0625365 | ||||||||
\(847\) | 20.4078 | + | 35.3473i | 0.701219 | + | 1.21455i | ||||
\(848\) | −4.75182 | + | 2.74346i | −0.163178 | + | 0.0942109i | ||||
\(849\) | −11.0067 | + | 19.0642i | −0.377749 | + | 0.654280i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.4619 | + | 7.77225i | 0.461469 | + | 0.266429i | ||||
\(852\) | −7.93593 | + | 13.7454i | −0.271881 | + | 0.470911i | ||||
\(853\) | 21.8185 | 0.747051 | 0.373525 | − | 0.927620i | \(-0.378149\pi\) | ||||
0.373525 | + | 0.927620i | \(0.378149\pi\) | |||||||
\(854\) | 0.622333 | − | 1.07791i | 0.0212958 | − | 0.0368854i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.66025 | − | 1.53590i | 0.0909256 | − | 0.0524959i | ||||
\(857\) | 9.42369i | 0.321907i | 0.986962 | + | 0.160954i | \(0.0514569\pi\) | ||||
−0.986962 | + | 0.160954i | \(0.948543\pi\) | |||||||
\(858\) | 0.862160 | − | 19.2538i | 0.0294336 | − | 0.657315i | ||||
\(859\) | −24.4775 | −0.835161 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.07180 | + | 5.32051i | 0.104687 | + | 0.181322i | ||||
\(862\) | 1.86621 | + | 1.07746i | 0.0635633 | + | 0.0366983i | ||||
\(863\) | −29.7873 | −1.01397 | −0.506986 | − | 0.861954i | \(-0.669240\pi\) | ||||
−0.506986 | + | 0.861954i | \(0.669240\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.33938i | 0.0455139i | ||||||||
\(867\) | −0.866025 | − | 0.500000i | −0.0294118 | − | 0.0169809i | ||||
\(868\) | −6.98329 | + | 4.03180i | −0.237028 | + | 0.136848i | ||||
\(869\) | 36.8847 | − | 21.2954i | 1.25123 | − | 0.722397i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.1497 | + | 6.82667i | −0.445561 | + | 0.231313i | ||||
\(872\) | 6.69081i | 0.226579i | ||||||||
\(873\) | 8.05463 | + | 13.9510i | 0.272608 | + | 0.472171i | ||||
\(874\) | 9.92820 | + | 17.1962i | 0.335826 | + | 0.581669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 13.5734i | − | 0.458601i | ||||||
\(877\) | 0.954895 | − | 1.65393i | 0.0322445 | − | 0.0558491i | −0.849453 | − | 0.527665i | \(-0.823068\pi\) |
0.881697 | + | 0.471815i | \(0.156401\pi\) | |||||||
\(878\) | −15.8490 | + | 27.4513i | −0.534879 | + | 0.926438i | ||||
\(879\) | 6.84302i | 0.230809i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.18412 | + | 5.51505i | 0.107276 | + | 0.185807i | 0.914666 | − | 0.404211i | \(-0.132454\pi\) |
−0.807390 | + | 0.590018i | \(0.799121\pi\) | |||||||
\(882\) | 0.802812 | + | 1.39051i | 0.0270321 | + | 0.0468209i | ||||
\(883\) | − | 34.9897i | − | 1.17750i | −0.808316 | − | 0.588749i | \(-0.799621\pi\) | ||
0.808316 | − | 0.588749i | \(-0.200379\pi\) | |||||||
\(884\) | −6.64516 | − | 12.8001i | −0.223501 | − | 0.430513i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.3270 | − | 14.0452i | 0.817281 | − | 0.471858i | ||||
\(887\) | −18.5331 | + | 10.7001i | −0.622279 | + | 0.359273i | −0.777756 | − | 0.628567i | \(-0.783642\pi\) |
0.155477 | + | 0.987840i | \(0.450309\pi\) | |||||||
\(888\) | −2.72733 | − | 1.57463i | −0.0915233 | − | 0.0528410i | ||||
\(889\) | − | 4.95194i | − | 0.166083i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.62926 | − | 2.67270i | −0.155086 | − | 0.0895389i | ||||
\(892\) | −1.37891 | −0.0461694 | ||||||||
\(893\) | 6.33696 | + | 3.65864i | 0.212058 | + | 0.122432i | ||||
\(894\) | 9.73875 | + | 16.8680i | 0.325712 | + | 0.564150i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.32258 | −0.0775919 | ||||||||
\(897\) | −14.9990 | − | 9.57893i | −0.500801 | − | 0.319831i | ||||
\(898\) | − | 28.9167i | − | 0.964963i | ||||||
\(899\) | 12.9011 | − | 7.44843i | 0.430274 | − | 0.248419i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9739 | + | 19.0073i | −0.365592 | + | 0.633224i | ||||
\(902\) | 14.1395 | 0.470792 | ||||||||
\(903\) | −14.2267 | + | 24.6414i | −0.473435 | + | 0.820014i | ||||
\(904\) | −6.15720 | − | 3.55486i | −0.204785 | − | 0.118233i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.25851 | − | 12.5721i | 0.241148 | − | 0.417681i | ||||
\(907\) | 28.1192 | − | 16.2347i | 0.933684 | − | 0.539063i | 0.0457093 | − | 0.998955i | \(-0.485445\pi\) |
0.887975 | + | 0.459892i | \(0.152112\pi\) | |||||||
\(908\) | −9.66025 | − | 16.7321i | −0.320587 | − | 0.555273i | ||||
\(909\) | 12.6908 | 0.420928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.4380 | 1.14098 | 0.570490 | − | 0.821304i | \(-0.306753\pi\) | ||||
0.570490 | + | 0.821304i | \(0.306753\pi\) | |||||||
\(912\) | −2.01141 | − | 3.48387i | −0.0666045 | − | 0.115362i | ||||
\(913\) | −52.4771 | + | 30.2977i | −1.73674 | + | 1.00271i | ||||
\(914\) | 4.84950 | − | 8.39958i | 0.160407 | − | 0.277833i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.6508 | + | 7.88130i | 0.451036 | + | 0.260406i | ||||
\(917\) | −1.46150 | + | 2.53139i | −0.0482630 | + | 0.0835939i | ||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | 18.2413 | − | 31.5949i | 0.601727 | − | 1.04222i | −0.390833 | − | 0.920462i | \(-0.627813\pi\) |
0.992560 | − | 0.121759i | \(-0.0388536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.11745 | − | 2.37721i | 0.135675 | − | 0.0783317i | ||||
\(922\) | 11.9979i | 0.395131i | ||||||||
\(923\) | 30.8018 | − | 48.2303i | 1.01385 | − | 1.58752i | ||||
\(924\) | −12.4151 | −0.408428 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.21332 | + | 5.56563i | 0.105596 | + | 0.182898i | ||||
\(927\) | −4.15356 | − | 2.39806i | −0.136421 | − | 0.0787626i | ||||
\(928\) | 4.29078 | 0.140852 | ||||||||
\(929\) | −43.2233 | − | 24.9550i | −1.41811 | − | 0.818747i | −0.421978 | − | 0.906606i | \(-0.638664\pi\) |
−0.996133 | + | 0.0878597i | \(0.971997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.45914i | 0.211690i | ||||||||
\(932\) | 14.3370 | + | 8.27747i | 0.469624 | + | 0.271138i | ||||
\(933\) | 1.67696 | − | 0.968196i | 0.0549013 | − | 0.0316973i | ||||
\(934\) | 22.7454 | − | 13.1321i | 0.744254 | − | 0.429695i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.03873 | + | 1.94065i | 0.0993239 | + | 0.0634322i | ||||
\(937\) | 15.8873i | 0.519017i | 0.965741 | + | 0.259508i | \(0.0835605\pi\) | ||||
−0.965741 | + | 0.259508i | \(0.916440\pi\) | |||||||
\(938\) | 4.77204 | + | 8.26542i | 0.155813 | + | 0.269876i | ||||
\(939\) | 12.7772 | + | 22.1308i | 0.416970 | + | 0.722213i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.99273i | − | 0.227956i | −0.993483 | − | 0.113978i | \(-0.963641\pi\) | ||
0.993483 | − | 0.113978i | \(-0.0363594\pi\) | |||||||
\(942\) | 12.1914 | − | 21.1162i | 0.397218 | − | 0.688002i | ||||
\(943\) | 6.52817 | − | 11.3071i | 0.212586 | − | 0.368210i | ||||
\(944\) | 6.78668i | 0.220888i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.7427 | + | 56.7120i | 1.06456 | + | 1.84387i | ||||
\(947\) | 26.1532 | + | 45.2987i | 0.849865 | + | 1.47201i | 0.881328 | + | 0.472505i | \(0.156650\pi\) |
−0.0314631 | + | 0.999505i | \(0.510017\pi\) | |||||||
\(948\) | 7.96774i | 0.258780i | ||||||||
\(949\) | −2.18925 | + | 48.8905i | −0.0710659 | + | 1.58705i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9697 | − | 6.33337i | 0.355717 | − | 0.205374i | ||||
\(952\) | −8.04565 | + | 4.64516i | −0.260761 | + | 0.150550i | ||||
\(953\) | 25.0132 | + | 14.4414i | 0.810256 | + | 0.467802i | 0.847045 | − | 0.531521i | \(-0.178379\pi\) |
−0.0367885 | + | 0.999323i | \(0.511713\pi\) | |||||||
\(954\) | − | 5.48693i | − | 0.177646i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.6904 | − | 13.1003i | −0.733859 | − | 0.423693i | ||||
\(957\) | 22.9359 | 0.741413 | ||||||||
\(958\) | 22.2418 | + | 12.8413i | 0.718600 | + | 0.414884i | ||||
\(959\) | 22.8947 | + | 39.6548i | 0.739308 | + | 1.28052i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.9464 | 0.611173 | ||||||||
\(962\) | 9.56973 | + | 6.11160i | 0.308540 | + | 0.197046i | ||||
\(963\) | 3.07180i | 0.0989873i | ||||||||
\(964\) | 13.5529 | − | 7.82479i | 0.436510 | − | 0.252019i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.73205 | + | 9.92820i | −0.184426 | + | 0.319435i | ||||
\(967\) | −10.8610 | −0.349265 | −0.174633 | − | 0.984634i | \(-0.555874\pi\) | ||||
−0.174633 | + | 0.984634i | \(0.555874\pi\) | |||||||
\(968\) | −8.78668 | + | 15.2190i | −0.282415 | + | 0.489156i | ||||
\(969\) | −13.9355 | − | 8.04565i | −0.447672 | − | 0.258464i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.4990 | − | 21.6488i | 0.401111 | − | 0.694744i | −0.592749 | − | 0.805387i | \(-0.701958\pi\) |
0.993860 | + | 0.110643i | \(0.0352909\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | 6.59313 | + | 11.4196i | 0.211366 | + | 0.366097i | ||||
\(974\) | −9.37891 | −0.300520 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | 21.3827 | + | 37.0359i | 0.684092 | + | 1.18488i | 0.973721 | + | 0.227743i | \(0.0731346\pi\) |
−0.289629 | + | 0.957139i | \(0.593532\pi\) | |||||||
\(978\) | −20.4614 | + | 11.8134i | −0.654282 | + | 0.377750i | ||||
\(979\) | 4.64992 | − | 8.05390i | 0.148612 | − | 0.257404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.79441 | − | 3.34541i | −0.185001 | − | 0.106811i | ||||
\(982\) | 3.86927 | − | 6.70177i | 0.123473 | − | 0.213862i | ||||
\(983\) | −10.1288 | −0.323058 | −0.161529 | − | 0.986868i | \(-0.551642\pi\) | ||||
−0.161529 | + | 0.986868i | \(0.551642\pi\) | |||||||
\(984\) | −1.32258 | + | 2.29078i | −0.0421623 | + | 0.0730272i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.8637 | − | 8.58155i | 0.473356 | − | 0.273292i | ||||
\(987\) | 4.22464i | 0.134472i | ||||||||
\(988\) | 6.68308 | + | 12.8731i | 0.212617 | + | 0.409548i | ||||
\(989\) | 60.4691 | 1.92280 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1241 | − | 17.5355i | −0.321604 | − | 0.557035i | 0.659215 | − | 0.751954i | \(-0.270889\pi\) |
−0.980819 | + | 0.194920i | \(0.937555\pi\) | |||||||
\(992\) | −3.00670 | − | 1.73592i | −0.0954627 | − | 0.0551154i | ||||
\(993\) | −23.6981 | −0.752036 | ||||||||
\(994\) | −31.9249 | − | 18.4318i | −1.01260 | − | 0.584622i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 11.3360i | − | 0.359194i | ||||||
\(997\) | −18.0100 | − | 10.3981i | −0.570381 | − | 0.329310i | 0.186920 | − | 0.982375i | \(-0.440149\pi\) |
−0.757302 | + | 0.653065i | \(0.773483\pi\) | |||||||
\(998\) | −2.75488 | + | 1.59053i | −0.0872041 | + | 0.0503473i | ||||
\(999\) | 2.72733 | − | 1.57463i | 0.0862890 | − | 0.0498190i |
(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 | 1950.2.y.k.49.3 | 8 | ||
5.2 | odd | 4 | 390.2.bb.c.361.1 | yes | 8 | ||
5.3 | odd | 4 | 1950.2.bc.g.751.4 | 8 | |||
5.4 | even | 2 | 1950.2.y.j.49.2 | 8 | |||
13.4 | even | 6 | 1950.2.y.j.199.2 | 8 | |||
15.2 | even | 4 | 1170.2.bs.f.361.3 | 8 | |||
65.2 | even | 12 | 5070.2.a.bz.1.2 | 4 | |||
65.4 | even | 6 | inner | 1950.2.y.k.199.3 | 8 | ||
65.17 | odd | 12 | 390.2.bb.c.121.1 | ✓ | 8 | ||
65.37 | even | 12 | 5070.2.a.ca.1.3 | 4 | |||
65.42 | odd | 12 | 5070.2.b.ba.1351.3 | 8 | |||
65.43 | odd | 12 | 1950.2.bc.g.901.4 | 8 | |||
65.62 | odd | 12 | 5070.2.b.ba.1351.6 | 8 | |||
195.17 | even | 12 | 1170.2.bs.f.901.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.1 | ✓ | 8 | 65.17 | odd | 12 | ||
390.2.bb.c.361.1 | yes | 8 | 5.2 | odd | 4 | ||
1170.2.bs.f.361.3 | 8 | 15.2 | even | 4 | |||
1170.2.bs.f.901.3 | 8 | 195.17 | even | 12 | |||
1950.2.y.j.49.2 | 8 | 5.4 | even | 2 | |||
1950.2.y.j.199.2 | 8 | 13.4 | even | 6 | |||
1950.2.y.k.49.3 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.y.k.199.3 | 8 | 65.4 | even | 6 | inner | ||
1950.2.bc.g.751.4 | 8 | 5.3 | odd | 4 | |||
1950.2.bc.g.901.4 | 8 | 65.43 | odd | 12 | |||
5070.2.a.bz.1.2 | 4 | 65.2 | even | 12 | |||
5070.2.a.ca.1.3 | 4 | 65.37 | even | 12 | |||
5070.2.b.ba.1351.3 | 8 | 65.42 | odd | 12 | |||
5070.2.b.ba.1351.6 | 8 | 65.62 | odd | 12 |