Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 27 x^{17} + 161 x^{16} + 253 x^{15} - 2103 x^{14} - 683 x^{13} + 14442 x^{12} - 4144 x^{11} - 56325 x^{10} + 37245 x^{9} + 124233 x^{8} - 117486 x^{7} + \cdots - 4088 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.14522\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.14522 | −1.23854 | −0.619271 | − | 0.785177i | \(-0.712572\pi\) | ||||
−0.619271 | + | 0.785177i | \(0.712572\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.02869 | 1.35447 | 0.677236 | − | 0.735766i | \(-0.263178\pi\) | ||||
0.677236 | + | 0.735766i | \(0.263178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.82352 | −1.44515 | −0.722577 | − | 0.691290i | \(-0.757043\pi\) | ||||
−0.722577 | + | 0.691290i | \(0.757043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60196 | 0.533987 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.48254 | −0.447002 | −0.223501 | − | 0.974704i | \(-0.571749\pi\) | ||||
−0.223501 | + | 0.974704i | \(0.571749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.10378 | 0.860834 | 0.430417 | − | 0.902630i | \(-0.358366\pi\) | ||||
0.430417 | + | 0.902630i | \(0.358366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.49720 | −1.67757 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.84113 | −0.689076 | −0.344538 | − | 0.938772i | \(-0.611964\pi\) | ||||
−0.344538 | + | 0.938772i | \(0.611964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.20228 | 1.78989 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.29632 | 0.270301 | 0.135151 | − | 0.990825i | \(-0.456848\pi\) | ||||
0.135151 | + | 0.990825i | \(0.456848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.17297 | 0.834594 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.99910 | 0.577177 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.11758 | 0.578920 | 0.289460 | − | 0.957190i | \(-0.406524\pi\) | ||||
0.289460 | + | 0.957190i | \(0.406524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.16500 | −0.388846 | −0.194423 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194423 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.18036 | 0.553630 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.5803 | −1.95742 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.28871 | 1.36266 | 0.681328 | − | 0.731978i | \(-0.261403\pi\) | ||||
0.681328 | + | 0.731978i | \(0.261403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.65829 | −1.06618 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.09976 | 0.171753 | 0.0858766 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858766 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.67575 | −1.17054 | −0.585270 | − | 0.810838i | \(-0.699012\pi\) | ||||
−0.585270 | + | 0.810838i | \(0.699012\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.85184 | 0.723270 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.57658 | −0.959292 | −0.479646 | − | 0.877462i | \(-0.659235\pi\) | ||||
−0.479646 | + | 0.877462i | \(0.659235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.61931 | 1.08847 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.09485 | 0.853450 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.49015 | −0.605451 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.14522 | −0.284141 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.84950 | 1.15211 | 0.576054 | − | 0.817412i | \(-0.304592\pi\) | ||||
0.576054 | + | 0.817412i | \(0.304592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3974 | −1.97143 | −0.985717 | − | 0.168413i | \(-0.946136\pi\) | ||||
−0.985717 | + | 0.168413i | \(0.946136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.12513 | −0.771693 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.40040 | 1.16598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.82077 | 0.711120 | 0.355560 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355560 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.78089 | −0.334779 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.44343 | 0.646016 | 0.323008 | − | 0.946396i | \(-0.395306\pi\) | ||||
0.323008 | + | 0.946396i | \(0.395306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1933 | 1.19303 | 0.596515 | − | 0.802602i | \(-0.296552\pi\) | ||||
0.596515 | + | 0.802602i | \(0.296552\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.95193 | −1.03368 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.66851 | 0.645987 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.6867 | −1.98991 | −0.994953 | − | 0.100344i | \(-0.968006\pi\) | ||||
−0.994953 | + | 0.100344i | \(0.968006\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2396 | −1.24884 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.42418 | 0.705145 | 0.352573 | − | 0.935784i | \(-0.385307\pi\) | ||||
0.352573 | + | 0.935784i | \(0.385307\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.60492 | −0.933334 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.68788 | −0.717016 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1449 | −1.71136 | −0.855680 | − | 0.517505i | \(-0.826861\pi\) | ||||
−0.855680 | + | 0.517505i | \(0.826861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.8674 | −1.24404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.64440 | 0.481602 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.02869 | 0.310737 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.90916 | −0.396915 | −0.198457 | − | 0.980110i | \(-0.563593\pi\) | ||||
−0.198457 | + | 0.980110i | \(0.563593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.37496 | −0.238693 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5950 | 1.45226 | 0.726130 | − | 0.687558i | \(-0.241317\pi\) | ||||
0.726130 | + | 0.687558i | \(0.241317\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.6436 | −1.44287 | −0.721436 | − | 0.692481i | \(-0.756518\pi\) | ||||
−0.721436 | + | 0.692481i | \(0.756518\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24.8422 | 2.42435 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.24789 | −0.700680 | −0.350340 | − | 0.936623i | \(-0.613934\pi\) | ||||
−0.350340 | + | 0.936623i | \(0.613934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.892124 | −0.0854500 | −0.0427250 | − | 0.999087i | \(-0.513604\pi\) | ||||
−0.0427250 | + | 0.999087i | \(0.513604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.7811 | −1.68771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −21.0126 | −1.97670 | −0.988348 | − | 0.152209i | \(-0.951361\pi\) | ||||
−0.988348 | + | 0.152209i | \(0.951361\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.92615 | 0.366115 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.97214 | 0.459674 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.8631 | 0.995822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.80209 | −0.800190 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.35922 | −0.212724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.50482 | −0.224038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4111 | 1.45625 | 0.728123 | − | 0.685446i | \(-0.240393\pi\) | ||||
0.728123 | + | 0.685446i | \(0.240393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.4661 | 1.44976 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.25479 | 0.808595 | 0.404297 | − | 0.914628i | \(-0.367516\pi\) | ||||
0.404297 | + | 0.914628i | \(0.367516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.82352 | −0.331541 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.08335 | 0.781770 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0887 | −0.947372 | −0.473686 | − | 0.880694i | \(-0.657077\pi\) | ||||
−0.473686 | + | 0.880694i | \(0.657077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.25379 | 0.445621 | 0.222810 | − | 0.974862i | \(-0.428477\pi\) | ||||
0.222810 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.1082 | 1.18812 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.60147 | −0.384794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.44218 | 0.784131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.3451 | −1.34812 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8907 | 1.05605 | 0.528023 | − | 0.849230i | \(-0.322934\pi\) | ||||
0.528023 | + | 0.849230i | \(0.322934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.24419 | 0.182629 | 0.0913147 | − | 0.995822i | \(-0.470893\pi\) | ||||
0.0913147 | + | 0.995822i | \(0.470893\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.55138 | −0.367957 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.55712 | −0.526681 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.21299 | 0.495850 | 0.247925 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247925 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.14522 | 0.170127 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.95650 | −0.390627 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.06803 | 0.0836547 | 0.0418273 | − | 0.999125i | \(-0.486682\pi\) | ||||
0.0418273 | + | 0.999125i | \(0.486682\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.63234 | 0.749877 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.0303 | −1.54999 | −0.774994 | − | 0.631969i | \(-0.782247\pi\) | ||||
−0.774994 | + | 0.631969i | \(0.782247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.36653 | −0.258964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60196 | 0.122505 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.68062 | −0.583946 | −0.291973 | − | 0.956426i | \(-0.594312\pi\) | ||||
−0.291973 | + | 0.956426i | \(0.594312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.9554 | −1.20612 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.9841 | −1.42693 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.46057 | −0.482885 | −0.241443 | − | 0.970415i | \(-0.577621\pi\) | ||||
−0.241443 | + | 0.970415i | \(0.577621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.7458 | 1.83934 | 0.919670 | − | 0.392693i | \(-0.128457\pi\) | ||||
0.919670 | + | 0.392693i | \(0.128457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.0307 | 2.44170 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.1040 | 1.84568 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.21209 | 0.308018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.4671 | −0.834110 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52081 | 0.182399 | 0.0911997 | − | 0.995833i | \(-0.470930\pi\) | ||||
0.0911997 | + | 0.995833i | \(0.470930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.691989 | −0.0498104 | −0.0249052 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249052 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.1659 | −1.44411 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.955142 | 0.0680511 | 0.0340255 | − | 0.999421i | \(-0.489167\pi\) | ||||
0.0340255 | + | 0.999421i | \(0.489167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.83106 | −0.413353 | −0.206677 | − | 0.978409i | \(-0.566265\pi\) | ||||
−0.206677 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4868 | −0.880752 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.9201 | −0.836629 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.33082 | 0.232635 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.07665 | 0.144337 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.48254 | −0.102549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6821 | 0.873069 | 0.436535 | − | 0.899687i | \(-0.356206\pi\) | ||||
0.436535 | + | 0.899687i | \(0.356206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6773 | −0.800118 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.2475 | −1.58546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.27793 | 0.561942 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.8668 | −1.47762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.81826 | −0.593180 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.9122 | −1.53431 | −0.767156 | − | 0.641460i | \(-0.778329\pi\) | ||||
−0.767156 | + | 0.641460i | \(0.778329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.68493 | 0.445662 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.1536 | −1.66950 | −0.834750 | − | 0.550629i | \(-0.814388\pi\) | ||||
−0.834750 | + | 0.550629i | \(0.814388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1603 | 1.06790 | 0.533952 | − | 0.845515i | \(-0.320706\pi\) | ||||
0.533952 | + | 0.845515i | \(0.320706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.1602 | −0.800082 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.8752 | −0.777968 | −0.388984 | − | 0.921244i | \(-0.627174\pi\) | ||||
−0.388984 | + | 0.921244i | \(0.627174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.9184 | −1.29933 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.9418 | 2.46458 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.1080 | −1.36536 | −0.682680 | − | 0.730718i | \(-0.739186\pi\) | ||||
−0.682680 | + | 0.730718i | \(0.739186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2722 | 0.726108 | 0.363054 | − | 0.931768i | \(-0.381734\pi\) | ||||
0.363054 | + | 0.931768i | \(0.381734\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1141 | 0.969570 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.0765 | 1.47431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.10378 | 0.197489 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.7813 | −0.873352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.44066 | −0.595889 | −0.297945 | − | 0.954583i | \(-0.596301\pi\) | ||||
−0.297945 | + | 0.954583i | \(0.596301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.92184 | −0.120825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.4594 | 1.15597 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.8732 | −1.48917 | −0.744585 | − | 0.667527i | \(-0.767353\pi\) | ||||
−0.744585 | + | 0.667527i | \(0.767353\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.6921 | −1.96925 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.99424 | 0.309135 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.4779 | −1.32438 | −0.662191 | − | 0.749335i | \(-0.730373\pi\) | ||||
−0.662191 | + | 0.749335i | \(0.730373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.02869 | −0.186051 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.6344 | 2.11959 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.6765 | −1.87038 | −0.935189 | − | 0.354149i | \(-0.884771\pi\) | ||||
−0.935189 | + | 0.354149i | \(0.884771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.36429 | 0.386603 | 0.193301 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193301 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.4581 | 1.54079 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.18658 | −0.373065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.7836 | −1.60927 | −0.804636 | − | 0.593768i | \(-0.797640\pi\) | ||||
−0.804636 | + | 0.593768i | \(0.797640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.46825 | −0.207638 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.64873 | −0.575595 | −0.287797 | − | 0.957691i | \(-0.592923\pi\) | ||||
−0.287797 | + | 0.957691i | \(0.592923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.70423 | −0.220194 | −0.110097 | − | 0.993921i | \(-0.535116\pi\) | ||||
−0.110097 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.49720 | −0.384861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.20494 | −0.248210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.92796 | −0.525174 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.38599 | 0.491595 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.4580 | −1.25359 | −0.626796 | − | 0.779183i | \(-0.715634\pi\) | ||||
−0.626796 | + | 0.779183i | \(0.715634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8024 | 1.56050 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.44628 | −0.257999 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.02349 | 0.232685 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.3484 | 1.69161 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.3095 | −1.79868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −46.6339 | −2.67025 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8194 | −1.47359 | −0.736796 | − | 0.676115i | \(-0.763662\pi\) | ||||
−0.736796 | + | 0.676115i | \(0.763662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.4136 | 1.78706 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0750 | −0.628007 | −0.314003 | − | 0.949422i | \(-0.601670\pi\) | ||||
−0.314003 | + | 0.949422i | \(0.601670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.66099 | −0.206931 | −0.103466 | − | 0.994633i | \(-0.532993\pi\) | ||||
−0.103466 | + | 0.994633i | \(0.532993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.5511 | −1.04524 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.71390 | −0.208593 | −0.104297 | − | 0.994546i | \(-0.533259\pi\) | ||||
−0.104297 | + | 0.994546i | \(0.533259\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.62192 | −0.258778 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.5483 | 0.867821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.84113 | −0.158085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.9520 | 0.718447 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.91380 | 0.105833 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.1457 | 1.38633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.05962 | 0.388032 | 0.194016 | − | 0.980998i | \(-0.437849\pi\) | ||||
0.194016 | + | 0.980998i | \(0.437849\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.2782 | 0.727640 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.6293 | 0.963192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.177661 | −0.00967780 | −0.00483890 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483890 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 45.0765 | 2.44822 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.20969 | 0.173815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.36794 | −0.127857 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.42245 | −0.453449 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9072 | 0.746576 | 0.373288 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373288 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.40474 | 0.503424 | 0.251712 | − | 0.967802i | \(-0.419006\pi\) | ||||
0.251712 | + | 0.967802i | \(0.419006\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.30856 | 0.496854 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.5530 | −1.51972 | −0.759862 | − | 0.650084i | \(-0.774734\pi\) | ||||
−0.759862 | + | 0.650084i | \(0.774734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.4865 | 0.875010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.3038 | −1.23337 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.5193 | 1.61075 | 0.805373 | − | 0.592768i | \(-0.201965\pi\) | ||||
0.805373 | + | 0.592768i | \(0.201965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.8824 | 0.991068 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.8722 | 1.61593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.8374 | −1.71410 | −0.857049 | − | 0.515235i | \(-0.827705\pi\) | ||||
−0.857049 | + | 0.515235i | \(0.827705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.76177 | 0.0917139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.82352 | 0.198507 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.3555 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.37338 | 0.277480 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.67628 | 0.498354 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.543560 | 0.0279208 | 0.0139604 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139604 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.2053 | −1.80362 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5427 | 0.640902 | 0.320451 | − | 0.947265i | \(-0.396165\pi\) | ||||
0.320451 | + | 0.947265i | \(0.396165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.1682 | 0.874971 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.2962 | −0.625053 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.7321 | 0.848353 | 0.424177 | − | 0.905579i | \(-0.360564\pi\) | ||||
0.424177 | + | 0.905579i | \(0.360564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.68302 | −0.186258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.8535 | −1.00148 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −53.5675 | −2.69527 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.02006 | 0.402516 | 0.201258 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201258 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.20228 | 0.410628 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2845 | 1.21271 | 0.606354 | − | 0.795195i | \(-0.292631\pi\) | ||||
0.606354 | + | 0.795195i | \(0.292631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.71969 | −0.334732 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.0413 | −1.69153 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.2883 | −0.609110 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8905 | −0.835181 | −0.417591 | − | 0.908635i | \(-0.637125\pi\) | ||||
−0.417591 | + | 0.908635i | \(0.637125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.7877 | 1.17336 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.8363 | −1.66497 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.4569 | 0.955099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.2705 | −0.551920 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.0565 | 1.61492 | 0.807459 | − | 0.589924i | \(-0.200842\pi\) | ||||
0.807459 | + | 0.589924i | \(0.200842\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.3865 | −1.57842 | −0.789211 | − | 0.614122i | \(-0.789510\pi\) | ||||
−0.789211 | + | 0.614122i | \(0.789510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.5354 | −0.512249 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8560 | −0.575099 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 58.8722 | 2.84903 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.87116 | 0.476584 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.1246 | 1.16204 | 0.581021 | − | 0.813889i | \(-0.302653\pi\) | ||||
0.581021 | + | 0.813889i | \(0.302653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.6411 | −1.23223 | −0.616117 | − | 0.787655i | \(-0.711295\pi\) | ||||
−0.616117 | + | 0.787655i | \(0.711295\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.2555 | −0.971179 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.29632 | 0.0620114 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.2214 | −0.726476 | −0.363238 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363238 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2058 | 0.581230 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.2764 | −0.963360 | −0.481680 | − | 0.876347i | \(-0.659973\pi\) | ||||
−0.481680 | + | 0.876347i | \(0.659973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.8980 | −2.31799 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.6533 | −1.30796 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3425 | 0.629671 | 0.314835 | − | 0.949146i | \(-0.398051\pi\) | ||||
0.314835 | + | 0.949146i | \(0.398051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.63043 | −0.0767739 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.81427 | −0.226194 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.9426 | −1.68502 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.2859 | 0.761824 | 0.380912 | − | 0.924611i | \(-0.375610\pi\) | ||||
0.380912 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.52085 | −0.397719 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7784 | 1.57322 | 0.786608 | − | 0.617452i | \(-0.211835\pi\) | ||||
0.786608 | + | 0.617452i | \(0.211835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2626 | 0.709313 | 0.354656 | − | 0.934997i | \(-0.384598\pi\) | ||||
0.354656 | + | 0.934997i | \(0.384598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.0665 | 0.652316 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.91781 | 0.366393 | 0.183196 | − | 0.983076i | \(-0.441356\pi\) | ||||
0.183196 | + | 0.983076i | \(0.441356\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.2558 | −1.02768 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3282 | −0.614131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3796 | 0.523233 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.17297 | 0.191469 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60196 | −0.0733487 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.31547 | 0.334252 | 0.167126 | − | 0.985936i | \(-0.446551\pi\) | ||||
0.167126 | + | 0.985936i | \(0.446551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.7264 | 1.17302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.6328 | 0.483808 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8396 | −0.537610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1675 | 0.506048 | 0.253024 | − | 0.967460i | \(-0.418575\pi\) | ||||
0.253024 | + | 0.967460i | \(0.418575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.29116 | −0.103610 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.7187 | −1.11554 | −0.557770 | − | 0.829995i | \(-0.688343\pi\) | ||||
−0.557770 | + | 0.829995i | \(0.688343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.85746 | −0.398920 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.19303 | −0.323303 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.8131 | −0.933593 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0080 | 0.716616 | 0.358308 | − | 0.933604i | \(-0.383354\pi\) | ||||
0.358308 | + | 0.933604i | \(0.383354\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.9693 | 1.91973 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1409 | 0.942627 | 0.471314 | − | 0.881966i | \(-0.343780\pi\) | ||||
0.471314 | + | 0.881966i | \(0.343780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.2038 | 1.96704 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.22195 | 0.320738 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.4724 | 1.12904 | 0.564522 | − | 0.825418i | \(-0.309061\pi\) | ||||
0.564522 | + | 0.825418i | \(0.309061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.9741 | −1.72411 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.99910 | 0.132414 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −44.3508 | −1.95433 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.75002 | 0.428805 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.4766 | 0.723242 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.752754 | 0.0329788 | 0.0164894 | − | 0.999864i | \(-0.494751\pi\) | ||||
0.0164894 | + | 0.999864i | \(0.494751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5050 | −0.721715 | −0.360857 | − | 0.932621i | \(-0.617516\pi\) | ||||
−0.360857 | + | 0.932621i | \(0.617516\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 34.2279 | 1.49383 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.15106 | 0.267944 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3196 | −0.926937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.1765 | 0.615210 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.41341 | 0.147851 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.9516 | −0.949051 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.8593 | 0.598074 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.2959 | −0.486549 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7793 | −0.764391 | −0.382195 | − | 0.924082i | \(-0.624832\pi\) | ||||
−0.382195 | + | 0.924082i | \(0.624832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −53.0851 | −2.27810 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.70197 | −0.115740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.17104 | −0.135584 | −0.0677920 | − | 0.997699i | \(-0.521595\pi\) | ||||
−0.0677920 | + | 0.997699i | \(0.521595\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.6660 | −1.05272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.11758 | 0.132813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 67.6253 | 2.87572 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −53.8535 | −2.28595 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.2902 | 0.563123 | 0.281561 | − | 0.959543i | \(-0.409148\pi\) | ||||
0.281561 | + | 0.959543i | \(0.409148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.8238 | −1.00764 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.03584 | −0.381493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.1988 | 1.10415 | 0.552073 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552073 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −63.6406 | −2.67738 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.9749 | 1.80477 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.5647 | −1.40711 | −0.703553 | − | 0.710642i | \(-0.748404\pi\) | ||||
−0.703553 | + | 0.710642i | \(0.748404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.546415 | 0.0228667 | 0.0114334 | − | 0.999935i | \(-0.496361\pi\) | ||||
0.0114334 | + | 0.999935i | \(0.496361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.40769 | −0.225909 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.40950 | 0.225592 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.5698 | −1.60568 | −0.802840 | − | 0.596195i | \(-0.796679\pi\) | ||||
−0.802840 | + | 0.596195i | \(0.796679\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.48447 | 0.0616923 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.5630 | −1.01904 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.48254 | 0.0614004 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0591 | 0.622616 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.4541 | −0.472760 | −0.236380 | − | 0.971661i | \(-0.575961\pi\) | ||||
−0.236380 | + | 0.971661i | \(0.575961\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.16500 | −0.0892073 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.04899 | −0.0842841 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.6229 | 0.887947 | 0.443973 | − | 0.896040i | \(-0.353568\pi\) | ||||
0.443973 | + | 0.896040i | \(0.353568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.9011 | 1.34881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.5089 | 0.511955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.14548 | −0.0468029 | −0.0234014 | − | 0.999726i | \(-0.507450\pi\) | ||||
−0.0234014 | + | 0.999726i | \(0.507450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.9585 | 1.71152 | 0.855762 | − | 0.517369i | \(-0.173089\pi\) | ||||
0.855762 | + | 0.517369i | \(0.173089\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.32464 | 0.379729 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.6588 | −1.08383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5281 | −0.914386 | −0.457193 | − | 0.889367i | \(-0.651145\pi\) | ||||
−0.457193 | + | 0.889367i | \(0.651145\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.5713 | 1.03620 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.4123 | −0.825792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.2153 | 1.09921 | 0.549607 | − | 0.835423i | \(-0.314777\pi\) | ||||
0.549607 | + | 0.835423i | \(0.314777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.14534 | −0.288128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4037 | 0.781165 | 0.390582 | − | 0.920568i | \(-0.372274\pi\) | ||||
0.390582 | + | 0.920568i | \(0.372274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.1627 | −1.49369 | −0.746847 | − | 0.664996i | \(-0.768433\pi\) | ||||
−0.746847 | + | 0.664996i | \(0.768433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.88779 | 0.156012 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 61.7305 | 2.47318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.4512 | −1.13805 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.18036 | 0.127012 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.5493 | −0.938974 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.1586 | 1.59869 | 0.799345 | − | 0.600873i | \(-0.205180\pi\) | ||||
0.799345 | + | 0.600873i | \(0.205180\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.2058 | −1.08133 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.7040 | 1.97244 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.6487 | 0.936995 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.72015 | 0.344964 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.4433 | −1.04445 | −0.522223 | − | 0.852809i | \(-0.674897\pi\) | ||||
−0.522223 | + | 0.852809i | \(0.674897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9877 | 0.433311 | 0.216655 | − | 0.976248i | \(-0.430485\pi\) | ||||
0.216655 | + | 0.976248i | \(0.430485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.8709 | 1.96366 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.20933 | 0.165486 | 0.0827429 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827429 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.1197 | −0.514994 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.7580 | −0.695989 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.1871 | −0.868250 | −0.434125 | − | 0.900853i | \(-0.642942\pi\) | ||||
−0.434125 | + | 0.900853i | \(0.642942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0299 | 1.09522 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.3292 | 0.637062 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8360 | 1.00643 | 0.503214 | − | 0.864162i | \(-0.332151\pi\) | ||||
0.503214 | + | 0.864162i | \(0.332151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7374 | −0.573217 | −0.286608 | − | 0.958048i | \(-0.592528\pi\) | ||||
−0.286608 | + | 0.958048i | \(0.592528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.9171 | 0.734679 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.5803 | −0.449063 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.04138 | 0.156483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 49.1516 | 1.90031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.8272 | 0.881234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.0620 | 1.96830 | 0.984148 | − | 0.177349i | \(-0.0567520\pi\) | ||||
0.984148 | + | 0.177349i | \(0.0567520\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.5152 | 0.481709 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0726 | 1.04049 | 0.520243 | − | 0.854018i | \(-0.325841\pi\) | ||||
0.520243 | + | 0.854018i | \(0.325841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.9467 | 0.573603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 53.9599 | 2.06775 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4011 | 1.20153 | 0.600765 | − | 0.799426i | \(-0.294863\pi\) | ||||
0.600765 | + | 0.799426i | \(0.294863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.5843 | −1.28319 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.6674 | −1.32264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.10378 | −0.118245 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59280 | 0.0986349 | 0.0493174 | − | 0.998783i | \(-0.484295\pi\) | ||||
0.0493174 | + | 0.998783i | \(0.484295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.08072 | 0.344948 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.9121 | 0.603581 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.12456 | −0.118351 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.4748 | 0.963546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4060 | 0.997343 | 0.498671 | − | 0.866791i | \(-0.333821\pi\) | ||||
0.498671 | + | 0.866791i | \(0.333821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.28871 | 0.312615 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 42.7294 | 1.60928 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55.8044 | −2.09874 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2019 | −0.458253 | −0.229126 | − | 0.973397i | \(-0.573587\pi\) | ||||
−0.229126 | + | 0.973397i | \(0.573587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.3333 | −1.06258 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.80653 | −0.105105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.9364 | −0.521193 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.2812 | 1.69106 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.1197 | −0.787633 | −0.393816 | − | 0.919189i | \(-0.628845\pi\) | ||||
−0.393816 | + | 0.919189i | \(0.628845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.9899 | 2.08517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.1814 | −0.899316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.0096 | 0.483163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.890804 | 0.0330381 | 0.0165191 | − | 0.999864i | \(-0.494742\pi\) | ||||
0.0165191 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.29578 | 0.0479917 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8078 | 0.806591 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.01027 | 0.111187 | 0.0555934 | − | 0.998453i | \(-0.482295\pi\) | ||||
0.0555934 | + | 0.998453i | \(0.482295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −49.5042 | −1.82599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.62950 | −0.317872 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.9331 | −0.622892 | −0.311446 | − | 0.950264i | \(-0.600813\pi\) | ||||
−0.311446 | + | 0.950264i | \(0.600813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.65829 | −0.244598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.3879 | 0.931392 | 0.465696 | − | 0.884945i | \(-0.345804\pi\) | ||||
0.465696 | + | 0.884945i | \(0.345804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.0419 | 1.43038 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.2913 | 0.376538 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.7124 | 1.01259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.37394 | 0.232588 | 0.116294 | − | 0.993215i | \(-0.462898\pi\) | ||||
0.116294 | + | 0.993215i | \(0.462898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.2523 | 0.738034 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.79695 | 0.247366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.4743 | 0.744153 | 0.372076 | − | 0.928202i | \(-0.378646\pi\) | ||||
0.372076 | + | 0.928202i | \(0.378646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.12277 | 0.149647 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.9087 | −0.721691 | −0.360846 | − | 0.932626i | \(-0.617512\pi\) | ||||
−0.360846 | + | 0.932626i | \(0.617512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.41106 | 0.123489 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7847 | −0.498388 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.4669 | 0.991773 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.8936 | 1.18617 | 0.593087 | − | 0.805138i | \(-0.297909\pi\) | ||||
0.593087 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.2133 | 1.84440 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.8542 | −1.07378 | −0.536890 | − | 0.843652i | \(-0.680401\pi\) | ||||
−0.536890 | + | 0.843652i | \(0.680401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.03449 | −0.324528 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 67.9864 | 2.43900 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.09976 | 0.0394029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.07008 | −0.288770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.34993 | 0.334139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.8172 | 0.671615 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5326 | 1.23096 | 0.615478 | − | 0.788154i | \(-0.288963\pi\) | ||||
0.615478 | + | 0.788154i | \(0.288963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 46.0747 | 1.64030 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 80.3420 | 2.85663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.7901 | −1.69708 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.49720 | 0.230432 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.89808 | 0.138077 | 0.0690385 | − | 0.997614i | \(-0.478007\pi\) | ||||
0.0690385 | + | 0.997614i | \(0.478007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.6849 | 0.661026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.8635 | −0.913843 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1119 | −0.533286 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0117 | −0.529093 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.8077 | 2.31654 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.2632 | 1.02884 | 0.514419 | − | 0.857539i | \(-0.328008\pi\) | ||||
0.514419 | + | 0.857539i | \(0.328008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.8879 | −0.698357 | −0.349179 | − | 0.937056i | \(-0.613539\pi\) | ||||
−0.349179 | + | 0.937056i | \(0.613539\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.6528 | −0.478824 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.23474 | 0.113308 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.67575 | −0.268540 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.0111 | −0.664300 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.5798 | −1.34645 | −0.673223 | − | 0.739440i | \(-0.735091\pi\) | ||||
−0.673223 | + | 0.739440i | \(0.735091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.46305 | −0.225288 | −0.112644 | − | 0.993635i | \(-0.535932\pi\) | ||||
−0.112644 | + | 0.993635i | \(0.535932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.2716 | 0.462057 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.6368 | −0.578518 | −0.289259 | − | 0.957251i | \(-0.593409\pi\) | ||||
−0.289259 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.49402 | 0.0866208 | 0.0433104 | − | 0.999062i | \(-0.486210\pi\) | ||||
0.0433104 | + | 0.999062i | \(0.486210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 57.4567 | 1.99315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.6475 | −0.750041 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −60.6655 | −2.09942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.49306 | −0.224433 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.9880 | 1.20792 | 0.603959 | − | 0.797015i | \(-0.293589\pi\) | ||||
0.603959 | + | 0.797015i | \(0.293589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2807 | −0.664852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.6986 | 0.712899 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.1962 | −0.350760 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.6550 | 1.15640 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.94638 | 0.272719 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.7448 | 0.368328 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6756 | 0.981834 | 0.490917 | − | 0.871206i | \(-0.336662\pi\) | ||||
0.490917 | + | 0.871206i | \(0.336662\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.85184 | 0.165930 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.9259 | −1.80792 | −0.903958 | − | 0.427622i | \(-0.859351\pi\) | ||||
−0.903958 | + | 0.427622i | \(0.859351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.3655 | −0.831340 | −0.415670 | − | 0.909515i | \(-0.636453\pi\) | ||||
−0.415670 | + | 0.909515i | \(0.636453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.02052 | 0.307418 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.39312 | 0.0814627 | 0.0407313 | − | 0.999170i | \(-0.487031\pi\) | ||||
0.0407313 | + | 0.999170i | \(0.487031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.2622 | −0.790939 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.1524 | 0.650450 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.2211 | 0.889491 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0664 | 0.612157 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.26231 | −0.211947 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.57721 | 0.323769 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0858 | 0.813319 | 0.406659 | − | 0.913580i | \(-0.366694\pi\) | ||||
0.406659 | + | 0.913580i | \(0.366694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.0322 | 1.55263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.6130 | 0.526015 | 0.263007 | − | 0.964794i | \(-0.415286\pi\) | ||||
0.263007 | + | 0.964794i | \(0.415286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.1886 | −0.342875 | −0.171438 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171438 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.4970 | −1.93274 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.54690 | 0.253400 | 0.126700 | − | 0.991941i | \(-0.459561\pi\) | ||||
0.126700 | + | 0.991941i | \(0.459561\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −62.7480 | −2.10450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.6631 | 0.558236 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.57658 | −0.220077 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.5671 | −0.654055 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.63127 | −0.288190 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.74956 | −0.225110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.84113 | 0.0946519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −62.9586 | −2.09513 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 74.9473 | 2.49133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.08325 | −0.0691733 | −0.0345867 | − | 0.999402i | \(-0.511011\pi\) | ||||
−0.0345867 | + | 0.999402i | \(0.511011\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.3806 | 0.775487 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1346 | −1.13093 | −0.565464 | − | 0.824773i | \(-0.691303\pi\) | ||||
−0.565464 | + | 0.824773i | \(0.691303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.52408 | −0.315201 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 100.040 | 3.30722 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.3859 | −1.16854 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.2084 | 0.930509 | 0.465255 | − | 0.885177i | \(-0.345963\pi\) | ||||
0.465255 | + | 0.885177i | \(0.345963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55.3883 | 1.82511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8952 | 0.556113 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5886 | 1.13726 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.4584 | −0.770474 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.6040 | 1.26656 | 0.633278 | − | 0.773925i | \(-0.281709\pi\) | ||||
0.633278 | + | 0.773925i | \(0.281709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.61931 | 0.249713 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.7583 | 0.777813 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7571 | 0.417202 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.7681 | −1.36450 | −0.682252 | − | 0.731117i | \(-0.738999\pi\) | ||||
−0.682252 | + | 0.731117i | \(0.738999\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.85361 | 0.256293 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4863 | −0.472241 | −0.236121 | − | 0.971724i | \(-0.575876\pi\) | ||||
−0.236121 | + | 0.971724i | \(0.575876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.42564 | 0.0464251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.7304 | −1.12978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.78786 | −0.285567 | −0.142784 | − | 0.989754i | \(-0.545605\pi\) | ||||
−0.142784 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.6376 | 1.02700 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.96712 | 0.258352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.10693 | −0.0682503 | −0.0341251 | − | 0.999418i | \(-0.510864\pi\) | ||||
−0.0341251 | + | 0.999418i | \(0.510864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.63475 | 0.247055 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.91503 | 0.320508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.3979 | 1.36910 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3128 | −0.848799 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.6108 | −0.374154 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.09582 | −0.0674668 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.5717 | 0.790173 | 0.395086 | − | 0.918644i | \(-0.370715\pi\) | ||||
0.395086 | + | 0.918644i | \(0.370715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.09485 | 0.195795 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6548 | −0.630754 | −0.315377 | − | 0.948966i | \(-0.602131\pi\) | ||||
−0.315377 | + | 0.948966i | \(0.602131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0880 | −0.643991 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.7848 | −0.889827 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.6754 | 0.885414 | 0.442707 | − | 0.896666i | \(-0.354018\pi\) | ||||
0.442707 | + | 0.896666i | \(0.354018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9355 | 0.764981 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.42915 | −0.0456292 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.66299 | 0.308202 | 0.154101 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154101 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.89283 | 0.0921733 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −53.9430 | −1.71702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.95022 | −0.316398 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.5629 | −0.430841 | −0.215421 | − | 0.976521i | \(-0.569112\pi\) | ||||
−0.215421 | + | 0.976521i | \(0.569112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.1444 | −0.480594 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.6605 | −0.559875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.0813 | −1.30106 | −0.650530 | − | 0.759481i | \(-0.725453\pi\) | ||||
−0.650530 | + | 0.759481i | \(0.725453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.8587 | 0.786494 |
(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 | 4028.2.a.c.1.4 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.c.1.4 | ✓ | 19 | 1.1 | even | 1 | trivial |