Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 3 x^{10} + 41 x^{9} - 11 x^{8} - 123 x^{7} + 44 x^{6} + 159 x^{5} - 39 x^{4} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.127418\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.872582 | 0.617008 | 0.308504 | − | 0.951223i | \(-0.400172\pi\) | ||||
0.308504 | + | 0.951223i | \(0.400172\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.23860 | −0.619301 | ||||||||
\(5\) | −3.32654 | −1.48767 | −0.743836 | − | 0.668362i | \(-0.766996\pi\) | ||||
−0.743836 | + | 0.668362i | \(0.766996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.82594 | −0.999122 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.90267 | −0.917906 | ||||||||
\(11\) | 6.60457 | 1.99135 | 0.995677 | − | 0.0928853i | \(-0.0296090\pi\) | ||||
0.995677 | + | 0.0928853i | \(0.0296090\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.02878 | −0.840032 | −0.420016 | − | 0.907517i | \(-0.637976\pi\) | ||||
−0.420016 | + | 0.907517i | \(0.637976\pi\) | |||||||
\(14\) | 0.872582 | 0.233207 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0113364 | 0.00283409 | ||||||||
\(17\) | −1.04478 | −0.253398 | −0.126699 | − | 0.991941i | \(-0.540438\pi\) | ||||
−0.126699 | + | 0.991941i | \(0.540438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10095 | −0.481992 | −0.240996 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240996 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(20\) | 4.12025 | 0.921316 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.76303 | 1.22868 | ||||||||
\(23\) | 7.22640 | 1.50681 | 0.753404 | − | 0.657558i | \(-0.228411\pi\) | ||||
0.753404 | + | 0.657558i | \(0.228411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.06584 | 1.21317 | ||||||||
\(26\) | −2.64286 | −0.518307 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.23860 | −0.234074 | ||||||||
\(29\) | −4.91361 | −0.912434 | −0.456217 | − | 0.889868i | \(-0.650796\pi\) | ||||
−0.456217 | + | 0.889868i | \(0.650796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.63150 | −1.37066 | −0.685329 | − | 0.728234i | \(-0.740342\pi\) | ||||
−0.685329 | + | 0.728234i | \(0.740342\pi\) | |||||||
\(32\) | 5.66178 | 1.00087 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.911660 | −0.156348 | ||||||||
\(35\) | −3.32654 | −0.562287 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.71082 | −0.445657 | −0.222828 | − | 0.974858i | \(-0.571529\pi\) | ||||
−0.222828 | + | 0.974858i | \(0.571529\pi\) | |||||||
\(38\) | −1.83325 | −0.297393 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.40060 | 1.48637 | ||||||||
\(41\) | −10.1822 | −1.59020 | −0.795100 | − | 0.606478i | \(-0.792582\pi\) | ||||
−0.795100 | + | 0.606478i | \(0.792582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.25676 | 0.954147 | 0.477074 | − | 0.878863i | \(-0.341697\pi\) | ||||
0.477074 | + | 0.878863i | \(0.341697\pi\) | |||||||
\(44\) | −8.18043 | −1.23325 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.30562 | 0.929713 | ||||||||
\(47\) | 4.84267 | 0.706376 | 0.353188 | − | 0.935552i | \(-0.385098\pi\) | ||||
0.353188 | + | 0.935552i | \(0.385098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.29294 | 0.748535 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.75145 | 0.520233 | ||||||||
\(53\) | −1.31492 | −0.180618 | −0.0903091 | − | 0.995914i | \(-0.528785\pi\) | ||||
−0.0903091 | + | 0.995914i | \(0.528785\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.9703 | −2.96248 | ||||||||
\(56\) | −2.82594 | −0.377633 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.28753 | −0.562980 | ||||||||
\(59\) | 3.93161 | 0.511852 | 0.255926 | − | 0.966696i | \(-0.417620\pi\) | ||||
0.255926 | + | 0.966696i | \(0.417620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7378 | −1.75895 | −0.879476 | − | 0.475944i | \(-0.842106\pi\) | ||||
−0.879476 | + | 0.475944i | \(0.842106\pi\) | |||||||
\(62\) | −6.65911 | −0.845707 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.91769 | 0.614711 | ||||||||
\(65\) | 10.0753 | 1.24969 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5096 | −1.65046 | −0.825229 | − | 0.564799i | \(-0.808954\pi\) | ||||
−0.825229 | + | 0.564799i | \(0.808954\pi\) | |||||||
\(68\) | 1.29407 | 0.156929 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.90267 | −0.346936 | ||||||||
\(71\) | 1.27486 | 0.151298 | 0.0756488 | − | 0.997135i | \(-0.475897\pi\) | ||||
0.0756488 | + | 0.997135i | \(0.475897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.47063 | −0.523248 | −0.261624 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261624 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(74\) | −2.36542 | −0.274974 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.60224 | 0.298498 | ||||||||
\(77\) | 6.60457 | 0.752661 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5488 | 1.18683 | 0.593416 | − | 0.804896i | \(-0.297779\pi\) | ||||
0.593416 | + | 0.804896i | \(0.297779\pi\) | |||||||
\(80\) | −0.0377108 | −0.00421620 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.88484 | −0.981167 | ||||||||
\(83\) | −0.980597 | −0.107635 | −0.0538173 | − | 0.998551i | \(-0.517139\pi\) | ||||
−0.0538173 | + | 0.998551i | \(0.517139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.47551 | 0.376972 | ||||||||
\(86\) | 5.45954 | 0.588717 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.6642 | −1.98961 | ||||||||
\(89\) | 10.5320 | 1.11639 | 0.558197 | − | 0.829709i | \(-0.311493\pi\) | ||||
0.558197 | + | 0.829709i | \(0.311493\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.02878 | −0.317502 | ||||||||
\(92\) | −8.95062 | −0.933167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.22563 | 0.435840 | ||||||||
\(95\) | 6.98889 | 0.717045 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3696 | −1.35747 | −0.678736 | − | 0.734382i | \(-0.737472\pi\) | ||||
−0.678736 | + | 0.734382i | \(0.737472\pi\) | |||||||
\(98\) | 0.872582 | 0.0881440 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.51316 | −0.751316 | ||||||||
\(101\) | 1.68723 | 0.167886 | 0.0839430 | − | 0.996471i | \(-0.473249\pi\) | ||||
0.0839430 | + | 0.996471i | \(0.473249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8124 | 1.16391 | 0.581957 | − | 0.813220i | \(-0.302287\pi\) | ||||
0.581957 | + | 0.813220i | \(0.302287\pi\) | |||||||
\(104\) | 8.55916 | 0.839295 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.14738 | −0.111443 | ||||||||
\(107\) | −2.72810 | −0.263736 | −0.131868 | − | 0.991267i | \(-0.542097\pi\) | ||||
−0.131868 | + | 0.991267i | \(0.542097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.86124 | 0.369840 | 0.184920 | − | 0.982754i | \(-0.440797\pi\) | ||||
0.184920 | + | 0.982754i | \(0.440797\pi\) | |||||||
\(110\) | −19.1709 | −1.82788 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0113364 | 0.00107119 | ||||||||
\(113\) | 16.6002 | 1.56162 | 0.780810 | − | 0.624769i | \(-0.214807\pi\) | ||||
0.780810 | + | 0.624769i | \(0.214807\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.0389 | −2.24164 | ||||||||
\(116\) | 6.08600 | 0.565071 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.43065 | 0.315817 | ||||||||
\(119\) | −1.04478 | −0.0957753 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.6204 | 2.96549 | ||||||||
\(122\) | −11.9874 | −1.08529 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.45239 | 0.848849 | ||||||||
\(125\) | −3.54556 | −0.317125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −7.03247 | −0.621589 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.79156 | 0.771071 | ||||||||
\(131\) | −5.65694 | −0.494249 | −0.247125 | − | 0.968984i | \(-0.579486\pi\) | ||||
−0.247125 | + | 0.968984i | \(0.579486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.10095 | −0.182176 | ||||||||
\(134\) | −11.7882 | −1.01835 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.95250 | 0.253175 | ||||||||
\(137\) | −5.93739 | −0.507265 | −0.253633 | − | 0.967301i | \(-0.581625\pi\) | ||||
−0.253633 | + | 0.967301i | \(0.581625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.99353 | 0.169089 | 0.0845443 | − | 0.996420i | \(-0.473057\pi\) | ||||
0.0845443 | + | 0.996420i | \(0.473057\pi\) | |||||||
\(140\) | 4.12025 | 0.348225 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.11242 | 0.0933518 | ||||||||
\(143\) | −20.0038 | −1.67280 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3453 | 1.35740 | ||||||||
\(146\) | −3.90099 | −0.322848 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.35763 | 0.275996 | ||||||||
\(149\) | 11.7258 | 0.960612 | 0.480306 | − | 0.877101i | \(-0.340526\pi\) | ||||
0.480306 | + | 0.877101i | \(0.340526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.22469 | −0.0996640 | −0.0498320 | − | 0.998758i | \(-0.515869\pi\) | ||||
−0.0498320 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(152\) | 5.93717 | 0.481568 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.76303 | 0.464398 | ||||||||
\(155\) | 25.3865 | 2.03909 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6789 | 1.41093 | 0.705467 | − | 0.708743i | \(-0.250737\pi\) | ||||
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(158\) | 9.20468 | 0.732285 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −18.8341 | −1.48897 | ||||||||
\(161\) | 7.22640 | 0.569520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5753 | 1.06330 | 0.531650 | − | 0.846964i | \(-0.321572\pi\) | ||||
0.531650 | + | 0.846964i | \(0.321572\pi\) | |||||||
\(164\) | 12.6117 | 0.984812 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.855651 | −0.0664114 | ||||||||
\(167\) | 23.2440 | 1.79867 | 0.899336 | − | 0.437258i | \(-0.144050\pi\) | ||||
0.899336 | + | 0.437258i | \(0.144050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.82649 | −0.294345 | ||||||||
\(170\) | 3.03267 | 0.232595 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.74964 | −0.590904 | ||||||||
\(173\) | −20.6386 | −1.56913 | −0.784563 | − | 0.620049i | \(-0.787113\pi\) | ||||
−0.784563 | + | 0.620049i | \(0.787113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.06584 | 0.458535 | ||||||||
\(176\) | 0.0748718 | 0.00564367 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.19006 | 0.688824 | ||||||||
\(179\) | −10.1214 | −0.756511 | −0.378255 | − | 0.925701i | \(-0.623476\pi\) | ||||
−0.378255 | + | 0.925701i | \(0.623476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.9647 | 1.70696 | 0.853478 | − | 0.521130i | \(-0.174489\pi\) | ||||
0.853478 | + | 0.521130i | \(0.174489\pi\) | |||||||
\(182\) | −2.64286 | −0.195902 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.4214 | −1.50548 | ||||||||
\(185\) | 9.01765 | 0.662991 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.90036 | −0.504604 | ||||||||
\(188\) | −5.99814 | −0.437459 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.09838 | 0.442423 | ||||||||
\(191\) | 4.17969 | 0.302432 | 0.151216 | − | 0.988501i | \(-0.451681\pi\) | ||||
0.151216 | + | 0.988501i | \(0.451681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.41287 | −0.461608 | −0.230804 | − | 0.973000i | \(-0.574136\pi\) | ||||
−0.230804 | + | 0.973000i | \(0.574136\pi\) | |||||||
\(194\) | −11.6660 | −0.837572 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.23860 | −0.0884715 | ||||||||
\(197\) | 18.1337 | 1.29197 | 0.645986 | − | 0.763349i | \(-0.276446\pi\) | ||||
0.645986 | + | 0.763349i | \(0.276446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.80553 | −0.411543 | −0.205771 | − | 0.978600i | \(-0.565970\pi\) | ||||
−0.205771 | + | 0.978600i | \(0.565970\pi\) | |||||||
\(200\) | −17.1417 | −1.21210 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.47225 | 0.103587 | ||||||||
\(203\) | −4.91361 | −0.344868 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.8716 | 2.36570 | ||||||||
\(206\) | 10.3073 | 0.718144 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.0343353 | −0.00238073 | ||||||||
\(209\) | −13.8759 | −0.959816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9319 | 0.959111 | 0.479556 | − | 0.877511i | \(-0.340798\pi\) | ||||
0.479556 | + | 0.877511i | \(0.340798\pi\) | |||||||
\(212\) | 1.62866 | 0.111857 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.38049 | −0.162727 | ||||||||
\(215\) | −20.8133 | −1.41946 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.63150 | −0.518060 | ||||||||
\(218\) | 3.36925 | 0.228194 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 27.2125 | 1.83467 | ||||||||
\(221\) | 3.16442 | 0.212862 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.93412 | 0.598273 | 0.299136 | − | 0.954210i | \(-0.403301\pi\) | ||||
0.299136 | + | 0.954210i | \(0.403301\pi\) | |||||||
\(224\) | 5.66178 | 0.378294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.4851 | 0.963532 | ||||||||
\(227\) | 26.1285 | 1.73421 | 0.867104 | − | 0.498126i | \(-0.165978\pi\) | ||||
0.867104 | + | 0.498126i | \(0.165978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.03288 | −0.200419 | −0.100209 | − | 0.994966i | \(-0.531951\pi\) | ||||
−0.100209 | + | 0.994966i | \(0.531951\pi\) | |||||||
\(230\) | −20.9759 | −1.38311 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.8856 | 0.911633 | ||||||||
\(233\) | −9.42978 | −0.617766 | −0.308883 | − | 0.951100i | \(-0.599955\pi\) | ||||
−0.308883 | + | 0.951100i | \(0.599955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1093 | −1.05086 | ||||||||
\(236\) | −4.86969 | −0.316990 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.911660 | −0.0590941 | ||||||||
\(239\) | 21.0020 | 1.35851 | 0.679253 | − | 0.733904i | \(-0.262304\pi\) | ||||
0.679253 | + | 0.733904i | \(0.262304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7376 | 0.756088 | 0.378044 | − | 0.925788i | \(-0.376597\pi\) | ||||
0.378044 | + | 0.925788i | \(0.376597\pi\) | |||||||
\(242\) | 28.4639 | 1.82973 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.0157 | 1.08932 | ||||||||
\(245\) | −3.32654 | −0.212525 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.36332 | 0.404889 | ||||||||
\(248\) | 21.5662 | 1.36945 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.09379 | −0.195668 | ||||||||
\(251\) | −9.44194 | −0.595970 | −0.297985 | − | 0.954571i | \(-0.596315\pi\) | ||||
−0.297985 | + | 0.954571i | \(0.596315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 47.7273 | 3.00059 | ||||||||
\(254\) | 0.872582 | 0.0547506 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9718 | −0.998237 | ||||||||
\(257\) | 24.0481 | 1.50008 | 0.750040 | − | 0.661392i | \(-0.230034\pi\) | ||||
0.750040 | + | 0.661392i | \(0.230034\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.71082 | −0.168442 | ||||||||
\(260\) | −12.4793 | −0.773936 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.93614 | −0.304956 | ||||||||
\(263\) | −17.0481 | −1.05123 | −0.525617 | − | 0.850721i | \(-0.676165\pi\) | ||||
−0.525617 | + | 0.850721i | \(0.676165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.37413 | 0.268701 | ||||||||
\(266\) | −1.83325 | −0.112404 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.7330 | 1.02213 | ||||||||
\(269\) | 3.11135 | 0.189702 | 0.0948512 | − | 0.995491i | \(-0.469762\pi\) | ||||
0.0948512 | + | 0.995491i | \(0.469762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.492934 | 0.0299436 | 0.0149718 | − | 0.999888i | \(-0.495234\pi\) | ||||
0.0149718 | + | 0.999888i | \(0.495234\pi\) | |||||||
\(272\) | −0.0118441 | −0.000718151 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.18085 | −0.312987 | ||||||||
\(275\) | 40.0623 | 2.41585 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7724 | 1.66868 | 0.834340 | − | 0.551250i | \(-0.185849\pi\) | ||||
0.834340 | + | 0.551250i | \(0.185849\pi\) | |||||||
\(278\) | 1.73951 | 0.104329 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.40060 | 0.561794 | ||||||||
\(281\) | −17.6887 | −1.05522 | −0.527609 | − | 0.849487i | \(-0.676911\pi\) | ||||
−0.527609 | + | 0.849487i | \(0.676911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9144 | −1.00546 | −0.502728 | − | 0.864445i | \(-0.667670\pi\) | ||||
−0.502728 | + | 0.864445i | \(0.667670\pi\) | |||||||
\(284\) | −1.57904 | −0.0936987 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.4549 | −1.03213 | ||||||||
\(287\) | −10.1822 | −0.601039 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9084 | −0.935790 | ||||||||
\(290\) | 14.2626 | 0.837529 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.53733 | 0.324048 | ||||||||
\(293\) | 0.0950654 | 0.00555378 | 0.00277689 | − | 0.999996i | \(-0.499116\pi\) | ||||
0.00277689 | + | 0.999996i | \(0.499116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0786 | −0.761467 | ||||||||
\(296\) | 7.66064 | 0.445266 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.2317 | 0.592705 | ||||||||
\(299\) | −21.8872 | −1.26577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.25676 | 0.360634 | ||||||||
\(302\) | −1.06864 | −0.0614935 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0238171 | −0.00136601 | ||||||||
\(305\) | 45.6994 | 2.61674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8559 | −1.01909 | −0.509545 | − | 0.860444i | \(-0.670186\pi\) | ||||
−0.509545 | + | 0.860444i | \(0.670186\pi\) | |||||||
\(308\) | −8.18043 | −0.466123 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.1518 | 1.25814 | ||||||||
\(311\) | 2.22365 | 0.126092 | 0.0630458 | − | 0.998011i | \(-0.479919\pi\) | ||||
0.0630458 | + | 0.998011i | \(0.479919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2359 | 1.14380 | 0.571899 | − | 0.820324i | \(-0.306207\pi\) | ||||
0.571899 | + | 0.820324i | \(0.306207\pi\) | |||||||
\(314\) | 15.4263 | 0.870558 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0658 | −0.735006 | ||||||||
\(317\) | −9.48926 | −0.532970 | −0.266485 | − | 0.963839i | \(-0.585862\pi\) | ||||
−0.266485 | + | 0.963839i | \(0.585862\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4523 | −1.81698 | ||||||||
\(320\) | −16.3589 | −0.914489 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.30562 | 0.351398 | ||||||||
\(323\) | 2.19504 | 0.122135 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3721 | −1.01910 | ||||||||
\(326\) | 11.8456 | 0.656065 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.7745 | 1.58880 | ||||||||
\(329\) | 4.84267 | 0.266985 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.0368 | −1.87083 | −0.935417 | − | 0.353546i | \(-0.884976\pi\) | ||||
−0.935417 | + | 0.353546i | \(0.884976\pi\) | |||||||
\(332\) | 1.21457 | 0.0666581 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.2823 | 1.10980 | ||||||||
\(335\) | 44.9401 | 2.45534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.31149 | −0.0714412 | −0.0357206 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357206 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(338\) | −3.33893 | −0.181614 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.30478 | −0.233459 | ||||||||
\(341\) | −50.4028 | −2.72946 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −17.6813 | −0.953310 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0089 | −0.968164 | ||||||||
\(347\) | 5.30126 | 0.284586 | 0.142293 | − | 0.989825i | \(-0.454552\pi\) | ||||
0.142293 | + | 0.989825i | \(0.454552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.2250 | 1.77850 | 0.889248 | − | 0.457426i | \(-0.151229\pi\) | ||||
0.889248 | + | 0.457426i | \(0.151229\pi\) | |||||||
\(350\) | 5.29294 | 0.282920 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 37.3936 | 1.99309 | ||||||||
\(353\) | −2.85830 | −0.152132 | −0.0760660 | − | 0.997103i | \(-0.524236\pi\) | ||||
−0.0760660 | + | 0.997103i | \(0.524236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.24085 | −0.225081 | ||||||||
\(356\) | −13.0450 | −0.691383 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.83177 | −0.466773 | ||||||||
\(359\) | 32.3399 | 1.70684 | 0.853418 | − | 0.521227i | \(-0.174525\pi\) | ||||
0.853418 | + | 0.521227i | \(0.174525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5860 | −0.767684 | ||||||||
\(362\) | 20.0386 | 1.05321 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.75145 | 0.196629 | ||||||||
\(365\) | 14.8717 | 0.778421 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.7299 | 1.65629 | 0.828145 | − | 0.560514i | \(-0.189397\pi\) | ||||
0.828145 | + | 0.560514i | \(0.189397\pi\) | |||||||
\(368\) | 0.0819210 | 0.00427043 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.86864 | 0.409071 | ||||||||
\(371\) | −1.31492 | −0.0682673 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1393 | −0.835659 | −0.417830 | − | 0.908525i | \(-0.637209\pi\) | ||||
−0.417830 | + | 0.908525i | \(0.637209\pi\) | |||||||
\(374\) | −6.02112 | −0.311345 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.6851 | −0.705756 | ||||||||
\(377\) | 14.8822 | 0.766475 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.0448 | −1.85150 | −0.925748 | − | 0.378141i | \(-0.876563\pi\) | ||||
−0.925748 | + | 0.378141i | \(0.876563\pi\) | |||||||
\(380\) | −8.65645 | −0.444067 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.64712 | 0.186603 | ||||||||
\(383\) | −19.4364 | −0.993154 | −0.496577 | − | 0.867993i | \(-0.665410\pi\) | ||||
−0.496577 | + | 0.867993i | \(0.665410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.9703 | −1.11971 | ||||||||
\(386\) | −5.59575 | −0.284816 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.5596 | 0.840684 | ||||||||
\(389\) | 18.9145 | 0.959004 | 0.479502 | − | 0.877541i | \(-0.340817\pi\) | ||||
0.479502 | + | 0.877541i | \(0.340817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.55003 | −0.381821 | ||||||||
\(392\) | −2.82594 | −0.142732 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.8231 | 0.797158 | ||||||||
\(395\) | −35.0909 | −1.76562 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.51339 | 0.176332 | 0.0881660 | − | 0.996106i | \(-0.471899\pi\) | ||||
0.0881660 | + | 0.996106i | \(0.471899\pi\) | |||||||
\(398\) | −5.06579 | −0.253925 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0687646 | 0.00343823 | ||||||||
\(401\) | −20.7230 | −1.03486 | −0.517428 | − | 0.855727i | \(-0.673110\pi\) | ||||
−0.517428 | + | 0.855727i | \(0.673110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.1141 | 1.15140 | ||||||||
\(404\) | −2.08981 | −0.103972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.28753 | −0.212786 | ||||||||
\(407\) | −17.9038 | −0.887460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.51998 | 0.322392 | 0.161196 | − | 0.986922i | \(-0.448465\pi\) | ||||
0.161196 | + | 0.986922i | \(0.448465\pi\) | |||||||
\(410\) | 29.5557 | 1.45965 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.6309 | −0.720813 | ||||||||
\(413\) | 3.93161 | 0.193462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.26199 | 0.160125 | ||||||||
\(416\) | −17.1483 | −0.840764 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.1078 | −0.592214 | ||||||||
\(419\) | 24.7810 | 1.21063 | 0.605317 | − | 0.795985i | \(-0.293046\pi\) | ||||
0.605317 | + | 0.795985i | \(0.293046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6407 | 1.15218 | 0.576089 | − | 0.817387i | \(-0.304578\pi\) | ||||
0.576089 | + | 0.817387i | \(0.304578\pi\) | |||||||
\(422\) | 12.1567 | 0.591780 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.71589 | 0.180460 | ||||||||
\(425\) | −6.33750 | −0.307414 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7378 | −0.664821 | ||||||||
\(428\) | 3.37903 | 0.163332 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.1613 | −0.875818 | ||||||||
\(431\) | 8.06794 | 0.388619 | 0.194310 | − | 0.980940i | \(-0.437753\pi\) | ||||
0.194310 | + | 0.980940i | \(0.437753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0478 | 1.29983 | 0.649917 | − | 0.760005i | \(-0.274804\pi\) | ||||
0.649917 | + | 0.760005i | \(0.274804\pi\) | |||||||
\(434\) | −6.65911 | −0.319647 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.78253 | −0.229042 | ||||||||
\(437\) | −15.1823 | −0.726269 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.24982 | 0.393742 | 0.196871 | − | 0.980429i | \(-0.436922\pi\) | ||||
0.196871 | + | 0.980429i | \(0.436922\pi\) | |||||||
\(440\) | 62.0870 | 2.95988 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.76122 | 0.131338 | ||||||||
\(443\) | −10.5434 | −0.500933 | −0.250467 | − | 0.968125i | \(-0.580584\pi\) | ||||
−0.250467 | + | 0.968125i | \(0.580584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.0352 | −1.66083 | ||||||||
\(446\) | 7.79575 | 0.369139 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.91769 | 0.232339 | ||||||||
\(449\) | −10.4549 | −0.493399 | −0.246699 | − | 0.969092i | \(-0.579346\pi\) | ||||
−0.246699 | + | 0.969092i | \(0.579346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −67.2494 | −3.16665 | ||||||||
\(452\) | −20.5611 | −0.967112 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.7992 | 1.07002 | ||||||||
\(455\) | 10.0753 | 0.472340 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.67165 | −0.218531 | −0.109265 | − | 0.994013i | \(-0.534850\pi\) | ||||
−0.109265 | + | 0.994013i | \(0.534850\pi\) | |||||||
\(458\) | −2.64644 | −0.123660 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 29.7746 | 1.38825 | ||||||||
\(461\) | 4.74068 | 0.220795 | 0.110398 | − | 0.993887i | \(-0.464788\pi\) | ||||
0.110398 | + | 0.993887i | \(0.464788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.0262 | 1.67428 | 0.837139 | − | 0.546990i | \(-0.184226\pi\) | ||||
0.837139 | + | 0.546990i | \(0.184226\pi\) | |||||||
\(464\) | −0.0557024 | −0.00258592 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.22825 | −0.381167 | ||||||||
\(467\) | −11.2569 | −0.520907 | −0.260454 | − | 0.965486i | \(-0.583872\pi\) | ||||
−0.260454 | + | 0.965486i | \(0.583872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5096 | −0.623814 | ||||||||
\(470\) | −14.0567 | −0.648387 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.1105 | −0.511402 | ||||||||
\(473\) | 41.3232 | 1.90005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7440 | −0.584737 | ||||||||
\(476\) | 1.29407 | 0.0593137 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.3259 | 0.838209 | ||||||||
\(479\) | 26.4912 | 1.21041 | 0.605206 | − | 0.796069i | \(-0.293091\pi\) | ||||
0.605206 | + | 0.796069i | \(0.293091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.21049 | 0.374366 | ||||||||
\(482\) | 10.2420 | 0.466512 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40.4037 | −1.83653 | ||||||||
\(485\) | 44.4743 | 2.01947 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.91164 | 0.131939 | 0.0659694 | − | 0.997822i | \(-0.478986\pi\) | ||||
0.0659694 | + | 0.997822i | \(0.478986\pi\) | |||||||
\(488\) | 38.8224 | 1.75741 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.90267 | −0.131129 | ||||||||
\(491\) | −6.54337 | −0.295298 | −0.147649 | − | 0.989040i | \(-0.547171\pi\) | ||||
−0.147649 | + | 0.989040i | \(0.547171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.13366 | 0.231209 | ||||||||
\(494\) | 5.55252 | 0.249820 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.0865134 | −0.00388457 | ||||||||
\(497\) | 1.27486 | 0.0571851 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.2433 | 1.93584 | 0.967918 | − | 0.251268i | \(-0.0808476\pi\) | ||||
0.967918 | + | 0.251268i | \(0.0808476\pi\) | |||||||
\(500\) | 4.39154 | 0.196395 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.23886 | −0.367719 | ||||||||
\(503\) | 18.1223 | 0.808034 | 0.404017 | − | 0.914752i | \(-0.367614\pi\) | ||||
0.404017 | + | 0.914752i | \(0.367614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.61264 | −0.249759 | ||||||||
\(506\) | 41.6459 | 1.85139 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.23860 | −0.0549541 | ||||||||
\(509\) | 34.2778 | 1.51934 | 0.759668 | − | 0.650311i | \(-0.225362\pi\) | ||||
0.759668 | + | 0.650311i | \(0.225362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.47063 | −0.197769 | ||||||||
\(512\) | 0.128256 | 0.00566816 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.9839 | 0.925562 | ||||||||
\(515\) | −39.2945 | −1.73152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.9838 | 1.40665 | ||||||||
\(518\) | −2.36542 | −0.103930 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −28.4724 | −1.24860 | ||||||||
\(521\) | 31.2538 | 1.36926 | 0.684628 | − | 0.728893i | \(-0.259965\pi\) | ||||
0.684628 | + | 0.728893i | \(0.259965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.3748 | 1.02211 | 0.511055 | − | 0.859548i | \(-0.329255\pi\) | ||||
0.511055 | + | 0.859548i | \(0.329255\pi\) | |||||||
\(524\) | 7.00670 | 0.306089 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8759 | −0.648620 | ||||||||
\(527\) | 7.97327 | 0.347321 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.2208 | 1.27047 | ||||||||
\(530\) | 3.81679 | 0.165791 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.60224 | 0.112822 | ||||||||
\(533\) | 30.8398 | 1.33582 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.07513 | 0.392352 | ||||||||
\(536\) | 38.1773 | 1.64901 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.71491 | 0.117048 | ||||||||
\(539\) | 6.60457 | 0.284479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.7725 | −1.70995 | −0.854977 | − | 0.518665i | \(-0.826429\pi\) | ||||
−0.854977 | + | 0.518665i | \(0.826429\pi\) | |||||||
\(542\) | 0.430125 | 0.0184754 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.91534 | −0.253618 | ||||||||
\(545\) | −12.8445 | −0.550200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.5481 | −1.81922 | −0.909612 | − | 0.415459i | \(-0.863621\pi\) | ||||
−0.909612 | + | 0.415459i | \(0.863621\pi\) | |||||||
\(548\) | 7.35405 | 0.314150 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 34.9576 | 1.49060 | ||||||||
\(551\) | 10.3233 | 0.439786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.5488 | 0.448580 | ||||||||
\(554\) | 24.2337 | 1.02959 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.46918 | −0.104717 | ||||||||
\(557\) | 13.0751 | 0.554009 | 0.277005 | − | 0.960869i | \(-0.410658\pi\) | ||||
0.277005 | + | 0.960869i | \(0.410658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.9504 | −0.801515 | ||||||||
\(560\) | −0.0377108 | −0.00159357 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4348 | −0.651078 | ||||||||
\(563\) | 15.3131 | 0.645371 | 0.322685 | − | 0.946506i | \(-0.395414\pi\) | ||||
0.322685 | + | 0.946506i | \(0.395414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −55.2213 | −2.32318 | ||||||||
\(566\) | −14.7592 | −0.620375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.60267 | −0.151165 | ||||||||
\(569\) | −20.5726 | −0.862448 | −0.431224 | − | 0.902245i | \(-0.641918\pi\) | ||||
−0.431224 | + | 0.902245i | \(0.641918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.30560 | 0.263881 | 0.131941 | − | 0.991258i | \(-0.457879\pi\) | ||||
0.131941 | + | 0.991258i | \(0.457879\pi\) | |||||||
\(572\) | 24.7767 | 1.03597 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.88484 | −0.370846 | ||||||||
\(575\) | 43.8342 | 1.82801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.2579 | 1.38454 | 0.692272 | − | 0.721637i | \(-0.256610\pi\) | ||||
0.692272 | + | 0.721637i | \(0.256610\pi\) | |||||||
\(578\) | −13.8814 | −0.577390 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.2453 | −0.840641 | ||||||||
\(581\) | −0.980597 | −0.0406820 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.68449 | −0.359675 | ||||||||
\(584\) | 12.6338 | 0.522789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0829523 | 0.00342673 | ||||||||
\(587\) | −17.1095 | −0.706184 | −0.353092 | − | 0.935589i | \(-0.614870\pi\) | ||||
−0.353092 | + | 0.935589i | \(0.614870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0334 | 0.660645 | ||||||||
\(590\) | −11.4122 | −0.469832 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0307309 | −0.00126303 | ||||||||
\(593\) | 6.45593 | 0.265113 | 0.132557 | − | 0.991175i | \(-0.457681\pi\) | ||||
0.132557 | + | 0.991175i | \(0.457681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.47551 | 0.142482 | ||||||||
\(596\) | −14.5235 | −0.594907 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.0983 | −0.780989 | ||||||||
\(599\) | 34.2077 | 1.39769 | 0.698844 | − | 0.715274i | \(-0.253698\pi\) | ||||
0.698844 | + | 0.715274i | \(0.253698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.6074 | −1.12613 | −0.563065 | − | 0.826413i | \(-0.690378\pi\) | ||||
−0.563065 | + | 0.826413i | \(0.690378\pi\) | |||||||
\(602\) | 5.45954 | 0.222514 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.51691 | 0.0617220 | ||||||||
\(605\) | −108.513 | −4.41168 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.78542 | −0.397178 | −0.198589 | − | 0.980083i | \(-0.563636\pi\) | ||||
−0.198589 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(608\) | −11.8951 | −0.482411 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.8765 | 1.61455 | ||||||||
\(611\) | −14.6674 | −0.593379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.7718 | 0.960135 | 0.480068 | − | 0.877232i | \(-0.340612\pi\) | ||||
0.480068 | + | 0.877232i | \(0.340612\pi\) | |||||||
\(614\) | −15.5807 | −0.628787 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.6642 | −0.752000 | ||||||||
\(617\) | 24.5701 | 0.989155 | 0.494577 | − | 0.869134i | \(-0.335323\pi\) | ||||
0.494577 | + | 0.869134i | \(0.335323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0072 | 1.12571 | 0.562853 | − | 0.826557i | \(-0.309704\pi\) | ||||
0.562853 | + | 0.826557i | \(0.309704\pi\) | |||||||
\(620\) | −31.4437 | −1.26281 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.94031 | 0.0777995 | ||||||||
\(623\) | 10.5320 | 0.421957 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.5348 | −0.741391 | ||||||||
\(626\) | 17.6574 | 0.705733 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.8972 | −0.873792 | ||||||||
\(629\) | 2.83223 | 0.112928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.38443 | −0.214351 | −0.107175 | − | 0.994240i | \(-0.534181\pi\) | ||||
−0.107175 | + | 0.994240i | \(0.534181\pi\) | |||||||
\(632\) | −29.8103 | −1.18579 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.28015 | −0.328847 | ||||||||
\(635\) | −3.32654 | −0.132010 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.02878 | −0.120005 | ||||||||
\(638\) | −28.3173 | −1.12109 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.3938 | 0.924720 | ||||||||
\(641\) | 2.15591 | 0.0851532 | 0.0425766 | − | 0.999093i | \(-0.486443\pi\) | ||||
0.0425766 | + | 0.999093i | \(0.486443\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.08832 | −0.279536 | −0.139768 | − | 0.990184i | \(-0.544636\pi\) | ||||
−0.139768 | + | 0.990184i | \(0.544636\pi\) | |||||||
\(644\) | −8.95062 | −0.352704 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.91535 | 0.0753586 | ||||||||
\(647\) | −31.1591 | −1.22499 | −0.612495 | − | 0.790475i | \(-0.709834\pi\) | ||||
−0.612495 | + | 0.790475i | \(0.709834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.9666 | 1.01928 | ||||||||
\(650\) | −16.0312 | −0.628794 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.8144 | −0.658503 | ||||||||
\(653\) | 20.6765 | 0.809134 | 0.404567 | − | 0.914508i | \(-0.367422\pi\) | ||||
0.404567 | + | 0.914508i | \(0.367422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8180 | 0.735281 | ||||||||
\(656\) | −0.115430 | −0.00450677 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.22563 | 0.164732 | ||||||||
\(659\) | −22.2427 | −0.866451 | −0.433225 | − | 0.901286i | \(-0.642625\pi\) | ||||
−0.433225 | + | 0.901286i | \(0.642625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5285 | −0.837363 | −0.418681 | − | 0.908133i | \(-0.637508\pi\) | ||||
−0.418681 | + | 0.908133i | \(0.637508\pi\) | |||||||
\(662\) | −29.6999 | −1.15432 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.77111 | 0.107540 | ||||||||
\(665\) | 6.98889 | 0.271018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.5077 | −1.37486 | ||||||||
\(668\) | −28.7900 | −1.11392 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 39.2139 | 1.51496 | ||||||||
\(671\) | −90.7326 | −3.50269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.41685 | −0.324446 | −0.162223 | − | 0.986754i | \(-0.551866\pi\) | ||||
−0.162223 | + | 0.986754i | \(0.551866\pi\) | |||||||
\(674\) | −1.14438 | −0.0440798 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.73950 | 0.182288 | ||||||||
\(677\) | 18.8247 | 0.723493 | 0.361746 | − | 0.932277i | \(-0.382181\pi\) | ||||
0.361746 | + | 0.932277i | \(0.382181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3696 | −0.513076 | ||||||||
\(680\) | −9.82161 | −0.376641 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −43.9806 | −1.68410 | ||||||||
\(683\) | −21.2533 | −0.813234 | −0.406617 | − | 0.913599i | \(-0.633292\pi\) | ||||
−0.406617 | + | 0.913599i | \(0.633292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.7509 | 0.754644 | ||||||||
\(686\) | 0.872582 | 0.0333153 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0709289 | 0.00270414 | ||||||||
\(689\) | 3.98260 | 0.151725 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3622 | −0.432239 | −0.216119 | − | 0.976367i | \(-0.569340\pi\) | ||||
−0.216119 | + | 0.976367i | \(0.569340\pi\) | |||||||
\(692\) | 25.5630 | 0.971761 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.62578 | 0.175592 | ||||||||
\(695\) | −6.63154 | −0.251548 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6383 | 0.402953 | ||||||||
\(698\) | 28.9915 | 1.09735 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.51316 | −0.283971 | ||||||||
\(701\) | −21.8895 | −0.826757 | −0.413378 | − | 0.910559i | \(-0.635651\pi\) | ||||
−0.413378 | + | 0.910559i | \(0.635651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.69531 | 0.214803 | ||||||||
\(704\) | 32.4793 | 1.22411 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.49410 | −0.0938668 | ||||||||
\(707\) | 1.68723 | 0.0634549 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.2254 | 0.609356 | 0.304678 | − | 0.952455i | \(-0.401451\pi\) | ||||
0.304678 | + | 0.952455i | \(0.401451\pi\) | |||||||
\(710\) | −3.70049 | −0.138877 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −29.7629 | −1.11541 | ||||||||
\(713\) | −55.1482 | −2.06532 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 66.5434 | 2.48858 | ||||||||
\(716\) | 12.5364 | 0.468508 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.2192 | 1.05313 | ||||||||
\(719\) | 3.90181 | 0.145513 | 0.0727565 | − | 0.997350i | \(-0.476820\pi\) | ||||
0.0727565 | + | 0.997350i | \(0.476820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8124 | 0.439918 | ||||||||
\(722\) | −12.7275 | −0.473668 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.4442 | −1.05712 | ||||||||
\(725\) | −29.8052 | −1.10694 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.56486 | 0.354741 | 0.177370 | − | 0.984144i | \(-0.443241\pi\) | ||||
0.177370 | + | 0.984144i | \(0.443241\pi\) | |||||||
\(728\) | 8.55916 | 0.317224 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.9768 | 0.480292 | ||||||||
\(731\) | −6.53697 | −0.241779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.9924 | −1.29247 | −0.646236 | − | 0.763137i | \(-0.723658\pi\) | ||||
−0.646236 | + | 0.763137i | \(0.723658\pi\) | |||||||
\(734\) | 27.6870 | 1.02194 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.9143 | 1.50812 | ||||||||
\(737\) | −89.2250 | −3.28664 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.9015 | 0.437802 | 0.218901 | − | 0.975747i | \(-0.429753\pi\) | ||||
0.218901 | + | 0.975747i | \(0.429753\pi\) | |||||||
\(740\) | −11.1693 | −0.410591 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.14738 | −0.0421215 | ||||||||
\(743\) | 21.4671 | 0.787550 | 0.393775 | − | 0.919207i | \(-0.371169\pi\) | ||||
0.393775 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.0062 | −1.42908 | ||||||||
\(746\) | −14.0828 | −0.515609 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.54679 | 0.312502 | ||||||||
\(749\) | −2.72810 | −0.0996827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3470 | −0.633001 | −0.316500 | − | 0.948592i | \(-0.602508\pi\) | ||||
−0.316500 | + | 0.948592i | \(0.602508\pi\) | |||||||
\(752\) | 0.0548983 | 0.00200193 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.9860 | 0.472921 | ||||||||
\(755\) | 4.07398 | 0.148267 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2869 | −1.60963 | −0.804817 | − | 0.593523i | \(-0.797737\pi\) | ||||
−0.804817 | + | 0.593523i | \(0.797737\pi\) | |||||||
\(758\) | −31.4520 | −1.14239 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.7502 | −0.716416 | ||||||||
\(761\) | 6.94913 | 0.251906 | 0.125953 | − | 0.992036i | \(-0.459801\pi\) | ||||
0.125953 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.86124 | 0.139786 | ||||||||
\(764\) | −5.17697 | −0.187296 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.9599 | −0.612785 | ||||||||
\(767\) | −11.9080 | −0.429972 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.2806 | 0.659216 | 0.329608 | − | 0.944118i | \(-0.393083\pi\) | ||||
0.329608 | + | 0.944118i | \(0.393083\pi\) | |||||||
\(770\) | −19.1709 | −0.690872 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.94298 | 0.285874 | ||||||||
\(773\) | 16.5561 | 0.595480 | 0.297740 | − | 0.954647i | \(-0.403767\pi\) | ||||
0.297740 | + | 0.954647i | \(0.403767\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.2915 | −1.66284 | ||||||||
\(776\) | 37.7816 | 1.35628 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.5045 | 0.591714 | ||||||||
\(779\) | 21.3924 | 0.766463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.41988 | 0.301287 | ||||||||
\(782\) | −6.58802 | −0.235587 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0113364 | 0.000404870 0 | ||||||||
\(785\) | −58.8096 | −2.09901 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7462 | −0.561292 | −0.280646 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280646 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(788\) | −22.4604 | −0.800120 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.6197 | −1.08940 | ||||||||
\(791\) | 16.6002 | 0.590237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.6089 | 1.47758 | ||||||||
\(794\) | 3.06572 | 0.108798 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.19073 | 0.254869 | ||||||||
\(797\) | −18.3944 | −0.651563 | −0.325782 | − | 0.945445i | \(-0.605627\pi\) | ||||
−0.325782 | + | 0.945445i | \(0.605627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.05955 | −0.178994 | ||||||||
\(800\) | 34.3435 | 1.21422 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.0825 | −0.638515 | ||||||||
\(803\) | −29.5266 | −1.04197 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0389 | −0.847259 | ||||||||
\(806\) | 20.1690 | 0.710422 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.76802 | −0.167739 | ||||||||
\(809\) | −27.0690 | −0.951694 | −0.475847 | − | 0.879528i | \(-0.657858\pi\) | ||||
−0.475847 | + | 0.879528i | \(0.657858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.80138 | 0.0983697 | 0.0491848 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491848 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(812\) | 6.08600 | 0.213577 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.6226 | −0.547570 | ||||||||
\(815\) | −45.1588 | −1.58184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.1452 | −0.459891 | ||||||||
\(818\) | 5.68921 | 0.198919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −41.9534 | −1.46508 | ||||||||
\(821\) | 14.0701 | 0.491050 | 0.245525 | − | 0.969390i | \(-0.421040\pi\) | ||||
0.245525 | + | 0.969390i | \(0.421040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.7025 | −1.07022 | −0.535110 | − | 0.844782i | \(-0.679730\pi\) | ||||
−0.535110 | + | 0.844782i | \(0.679730\pi\) | |||||||
\(824\) | −33.3813 | −1.16289 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.43065 | 0.119368 | ||||||||
\(827\) | 0.701213 | 0.0243836 | 0.0121918 | − | 0.999926i | \(-0.496119\pi\) | ||||
0.0121918 | + | 0.999926i | \(0.496119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3394 | 1.22739 | 0.613693 | − | 0.789544i | \(-0.289683\pi\) | ||||
0.613693 | + | 0.789544i | \(0.289683\pi\) | |||||||
\(830\) | 2.84635 | 0.0987984 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.8946 | −0.516378 | ||||||||
\(833\) | −1.04478 | −0.0361996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −77.3219 | −2.67583 | ||||||||
\(836\) | 17.1867 | 0.594414 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.6235 | 0.746971 | ||||||||
\(839\) | 45.1445 | 1.55856 | 0.779281 | − | 0.626674i | \(-0.215584\pi\) | ||||
0.779281 | + | 0.626674i | \(0.215584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.85644 | −0.167463 | ||||||||
\(842\) | 20.6285 | 0.710904 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.2561 | −0.593978 | ||||||||
\(845\) | 12.7290 | 0.437890 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.6204 | 1.12085 | ||||||||
\(848\) | −0.0149064 | −0.000511888 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.52998 | −0.189677 | ||||||||
\(851\) | −19.5895 | −0.671519 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6456 | 0.364497 | 0.182248 | − | 0.983253i | \(-0.441662\pi\) | ||||
0.182248 | + | 0.983253i | \(0.441662\pi\) | |||||||
\(854\) | −11.9874 | −0.410200 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.70946 | 0.263504 | ||||||||
\(857\) | 40.4813 | 1.38281 | 0.691407 | − | 0.722466i | \(-0.256991\pi\) | ||||
0.691407 | + | 0.722466i | \(0.256991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.8061 | −1.39229 | −0.696143 | − | 0.717903i | \(-0.745102\pi\) | ||||
−0.696143 | + | 0.717903i | \(0.745102\pi\) | |||||||
\(860\) | 25.7794 | 0.879072 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.03994 | 0.239781 | ||||||||
\(863\) | −30.5500 | −1.03994 | −0.519968 | − | 0.854186i | \(-0.674056\pi\) | ||||
−0.519968 | + | 0.854186i | \(0.674056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.6551 | 2.33434 | ||||||||
\(866\) | 23.6014 | 0.802008 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.45239 | 0.320835 | ||||||||
\(869\) | 69.6703 | 2.36340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.9175 | 1.38644 | ||||||||
\(872\) | −10.9116 | −0.369515 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.2478 | −0.448114 | ||||||||
\(875\) | −3.54556 | −0.119862 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1242 | 0.882152 | 0.441076 | − | 0.897470i | \(-0.354597\pi\) | ||||
0.441076 | + | 0.897470i | \(0.354597\pi\) | |||||||
\(878\) | 7.19864 | 0.242942 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.249064 | −0.00839594 | ||||||||
\(881\) | 34.3437 | 1.15707 | 0.578534 | − | 0.815658i | \(-0.303625\pi\) | ||||
0.578534 | + | 0.815658i | \(0.303625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.923623 | −0.0310824 | −0.0155412 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155412 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(884\) | −3.91946 | −0.131826 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.20000 | −0.309080 | ||||||||
\(887\) | 26.5716 | 0.892185 | 0.446093 | − | 0.894987i | \(-0.352815\pi\) | ||||
0.446093 | + | 0.894987i | \(0.352815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −30.5711 | −1.02474 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0658 | −0.370511 | ||||||||
\(893\) | −10.1742 | −0.340467 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.6693 | 1.12544 | ||||||||
\(896\) | −7.03247 | −0.234938 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.12278 | −0.304431 | ||||||||
\(899\) | 37.4982 | 1.25064 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.37381 | 0.0457682 | ||||||||
\(902\) | −58.6806 | −1.95385 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.9114 | −1.56025 | ||||||||
\(905\) | −76.3930 | −2.53939 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7472 | −0.522879 | −0.261439 | − | 0.965220i | \(-0.584197\pi\) | ||||
−0.261439 | + | 0.965220i | \(0.584197\pi\) | |||||||
\(908\) | −32.3628 | −1.07400 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.79156 | 0.291437 | ||||||||
\(911\) | −28.6067 | −0.947781 | −0.473891 | − | 0.880584i | \(-0.657151\pi\) | ||||
−0.473891 | + | 0.880584i | \(0.657151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.47642 | −0.214338 | ||||||||
\(914\) | −4.07640 | −0.134835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.75654 | 0.124119 | ||||||||
\(917\) | −5.65694 | −0.186809 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.3252 | −1.42917 | −0.714583 | − | 0.699550i | \(-0.753384\pi\) | ||||
−0.714583 | + | 0.699550i | \(0.753384\pi\) | |||||||
\(920\) | 67.9325 | 2.23967 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.13663 | 0.136233 | ||||||||
\(923\) | −3.86126 | −0.127095 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4434 | −0.540657 | ||||||||
\(926\) | 31.4358 | 1.03304 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.8198 | −0.913229 | ||||||||
\(929\) | 35.6112 | 1.16837 | 0.584183 | − | 0.811622i | \(-0.301415\pi\) | ||||
0.584183 | + | 0.811622i | \(0.301415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.10095 | −0.0688559 | ||||||||
\(932\) | 11.6797 | 0.382583 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.82256 | −0.321404 | ||||||||
\(935\) | 22.9543 | 0.750685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.25543 | −0.106350 | −0.0531752 | − | 0.998585i | \(-0.516934\pi\) | ||||
−0.0531752 | + | 0.998585i | \(0.516934\pi\) | |||||||
\(938\) | −11.7882 | −0.384899 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.9530 | 0.650796 | ||||||||
\(941\) | −10.9105 | −0.355671 | −0.177836 | − | 0.984060i | \(-0.556910\pi\) | ||||
−0.177836 | + | 0.984060i | \(0.556910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.5810 | −2.39613 | ||||||||
\(944\) | 0.0445701 | 0.00145063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.0579 | 1.17234 | ||||||||
\(947\) | 29.1120 | 0.946013 | 0.473006 | − | 0.881059i | \(-0.343169\pi\) | ||||
0.473006 | + | 0.881059i | \(0.343169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.5406 | 0.439545 | ||||||||
\(950\) | −11.1202 | −0.360788 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.95250 | 0.0956912 | ||||||||
\(953\) | 27.4183 | 0.888166 | 0.444083 | − | 0.895986i | \(-0.353529\pi\) | ||||
0.444083 | + | 0.895986i | \(0.353529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9039 | −0.449919 | ||||||||
\(956\) | −26.0131 | −0.841323 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.1157 | 0.746834 | ||||||||
\(959\) | −5.93739 | −0.191728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.2398 | 0.878703 | ||||||||
\(962\) | 7.16432 | 0.230987 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.5383 | −0.468246 | ||||||||
\(965\) | 21.3326 | 0.686722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.4120 | 1.87840 | 0.939202 | − | 0.343365i | \(-0.111567\pi\) | ||||
0.939202 | + | 0.343365i | \(0.111567\pi\) | |||||||
\(968\) | −92.1834 | −2.96289 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.8075 | 1.24603 | ||||||||
\(971\) | −42.6688 | −1.36931 | −0.684654 | − | 0.728868i | \(-0.740047\pi\) | ||||
−0.684654 | + | 0.728868i | \(0.740047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.99353 | 0.0639095 | ||||||||
\(974\) | 2.54064 | 0.0814073 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.155737 | −0.00498502 | ||||||||
\(977\) | 42.0709 | 1.34597 | 0.672984 | − | 0.739657i | \(-0.265012\pi\) | ||||
0.672984 | + | 0.739657i | \(0.265012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 69.5596 | 2.22313 | ||||||||
\(980\) | 4.12025 | 0.131617 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.70963 | −0.182202 | ||||||||
\(983\) | −41.0399 | −1.30897 | −0.654485 | − | 0.756075i | \(-0.727114\pi\) | ||||
−0.654485 | + | 0.756075i | \(0.727114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60.3224 | −1.92203 | ||||||||
\(986\) | 4.47954 | 0.142658 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.88162 | −0.250748 | ||||||||
\(989\) | 45.2139 | 1.43772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9222 | −0.886979 | −0.443490 | − | 0.896279i | \(-0.646260\pi\) | ||||
−0.443490 | + | 0.896279i | \(0.646260\pi\) | |||||||
\(992\) | −43.2079 | −1.37185 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.11242 | 0.0352837 | ||||||||
\(995\) | 19.3123 | 0.612241 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1660 | −1.01871 | −0.509354 | − | 0.860557i | \(-0.670116\pi\) | ||||
−0.509354 | + | 0.860557i | \(0.670116\pi\) | |||||||
\(998\) | 37.7333 | 1.19443 | ||||||||
\(999\) | 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 | 8001.2.a.n.1.7 | 12 | ||
3.2 | odd | 2 | 889.2.a.a.1.6 | ✓ | 12 | ||
21.20 | even | 2 | 6223.2.a.i.1.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.a.1.6 | ✓ | 12 | 3.2 | odd | 2 | ||
6223.2.a.i.1.6 | 12 | 21.20 | even | 2 | |||
8001.2.a.n.1.7 | 12 | 1.1 | even | 1 | trivial |