Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.10522\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.91913 | 1.10801 | 0.554005 | − | 0.832513i | \(-0.313099\pi\) | ||||
0.554005 | + | 0.832513i | \(0.313099\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.91913 | −0.783482 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.683063 | 0.227688 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.91913 | 0.554005 | ||||||||
\(13\) | −0.869151 | −0.241059 | −0.120530 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.91913 | −0.495517 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.15520 | −1.00778 | −0.503892 | − | 0.863767i | \(-0.668099\pi\) | ||||
−0.503892 | + | 0.863767i | \(0.668099\pi\) | |||||||
\(18\) | −0.683063 | −0.160999 | ||||||||
\(19\) | 7.56151 | 1.73473 | 0.867365 | − | 0.497672i | \(-0.165812\pi\) | ||||
0.867365 | + | 0.497672i | \(0.165812\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.91913 | −0.418789 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | −1.91913 | −0.391741 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.869151 | 0.170454 | ||||||||
\(27\) | −4.44651 | −0.855730 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.19588 | −0.222069 | −0.111034 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111034 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(30\) | 1.91913 | 0.350384 | ||||||||
\(31\) | 7.70820 | 1.38443 | 0.692217 | − | 0.721689i | \(-0.256634\pi\) | ||||
0.692217 | + | 0.721689i | \(0.256634\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.15520 | 0.712611 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.683063 | 0.113844 | ||||||||
\(37\) | 6.81263 | 1.11999 | 0.559995 | − | 0.828496i | \(-0.310803\pi\) | ||||
0.559995 | + | 0.828496i | \(0.310803\pi\) | |||||||
\(38\) | −7.56151 | −1.22664 | ||||||||
\(39\) | −1.66801 | −0.267096 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.86261 | −1.54028 | −0.770141 | − | 0.637874i | \(-0.779814\pi\) | ||||
−0.770141 | + | 0.637874i | \(0.779814\pi\) | |||||||
\(42\) | 1.91913 | 0.296128 | ||||||||
\(43\) | −6.62654 | −1.01054 | −0.505269 | − | 0.862962i | \(-0.668607\pi\) | ||||
−0.505269 | + | 0.862962i | \(0.668607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.683063 | −0.101825 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 10.7529 | 1.56847 | 0.784233 | − | 0.620466i | \(-0.213057\pi\) | ||||
0.784233 | + | 0.620466i | \(0.213057\pi\) | |||||||
\(48\) | 1.91913 | 0.277003 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −7.97437 | −1.11664 | ||||||||
\(52\) | −0.869151 | −0.120530 | ||||||||
\(53\) | −1.57656 | −0.216558 | −0.108279 | − | 0.994121i | \(-0.534534\pi\) | ||||
−0.108279 | + | 0.994121i | \(0.534534\pi\) | |||||||
\(54\) | 4.44651 | 0.605093 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 14.5115 | 1.92210 | ||||||||
\(58\) | 1.19588 | 0.157026 | ||||||||
\(59\) | −7.43146 | −0.967493 | −0.483747 | − | 0.875208i | \(-0.660724\pi\) | ||||
−0.483747 | + | 0.875208i | \(0.660724\pi\) | |||||||
\(60\) | −1.91913 | −0.247759 | ||||||||
\(61\) | −7.73830 | −0.990788 | −0.495394 | − | 0.868668i | \(-0.664976\pi\) | ||||
−0.495394 | + | 0.868668i | \(0.664976\pi\) | |||||||
\(62\) | −7.70820 | −0.978943 | ||||||||
\(63\) | −0.683063 | −0.0860578 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.869151 | 0.107805 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.56151 | 0.435108 | 0.217554 | − | 0.976048i | \(-0.430192\pi\) | ||||
0.217554 | + | 0.976048i | \(0.430192\pi\) | |||||||
\(68\) | −4.15520 | −0.503892 | ||||||||
\(69\) | −3.83826 | −0.462072 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −2.23528 | −0.265278 | −0.132639 | − | 0.991164i | \(-0.542345\pi\) | ||||
−0.132639 | + | 0.991164i | \(0.542345\pi\) | |||||||
\(72\) | −0.683063 | −0.0804997 | ||||||||
\(73\) | 17.0389 | 1.99425 | 0.997127 | − | 0.0757515i | \(-0.0241356\pi\) | ||||
0.997127 | + | 0.0757515i | \(0.0241356\pi\) | |||||||
\(74\) | −6.81263 | −0.791952 | ||||||||
\(75\) | 1.91913 | 0.221602 | ||||||||
\(76\) | 7.56151 | 0.867365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.66801 | 0.188865 | ||||||||
\(79\) | −3.13085 | −0.352248 | −0.176124 | − | 0.984368i | \(-0.556356\pi\) | ||||
−0.176124 | + | 0.984368i | \(0.556356\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.5826 | −1.17585 | ||||||||
\(82\) | 9.86261 | 1.08914 | ||||||||
\(83\) | −8.22953 | −0.903308 | −0.451654 | − | 0.892193i | \(-0.649166\pi\) | ||||
−0.451654 | + | 0.892193i | \(0.649166\pi\) | |||||||
\(84\) | −1.91913 | −0.209394 | ||||||||
\(85\) | 4.15520 | 0.450695 | ||||||||
\(86\) | 6.62654 | 0.714559 | ||||||||
\(87\) | −2.29505 | −0.246055 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.89429 | −1.04879 | −0.524396 | − | 0.851474i | \(-0.675709\pi\) | ||||
−0.524396 | + | 0.851474i | \(0.675709\pi\) | |||||||
\(90\) | 0.683063 | 0.0720011 | ||||||||
\(91\) | 0.869151 | 0.0911118 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 14.7931 | 1.53397 | ||||||||
\(94\) | −10.7529 | −1.10907 | ||||||||
\(95\) | −7.56151 | −0.775795 | ||||||||
\(96\) | −1.91913 | −0.195870 | ||||||||
\(97\) | 14.7984 | 1.50255 | 0.751274 | − | 0.659991i | \(-0.229440\pi\) | ||||
0.751274 | + | 0.659991i | \(0.229440\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −17.6082 | −1.75209 | −0.876043 | − | 0.482233i | \(-0.839826\pi\) | ||||
−0.876043 | + | 0.482233i | \(0.839826\pi\) | |||||||
\(102\) | 7.97437 | 0.789580 | ||||||||
\(103\) | −4.85282 | −0.478163 | −0.239081 | − | 0.971000i | \(-0.576846\pi\) | ||||
−0.239081 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(104\) | 0.869151 | 0.0852272 | ||||||||
\(105\) | 1.91913 | 0.187288 | ||||||||
\(106\) | 1.57656 | 0.153129 | ||||||||
\(107\) | −5.97309 | −0.577440 | −0.288720 | − | 0.957414i | \(-0.593230\pi\) | ||||
−0.288720 | + | 0.957414i | \(0.593230\pi\) | |||||||
\(108\) | −4.44651 | −0.427865 | ||||||||
\(109\) | −19.3651 | −1.85484 | −0.927422 | − | 0.374016i | \(-0.877981\pi\) | ||||
−0.927422 | + | 0.374016i | \(0.877981\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.0743 | 1.24096 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 13.4932 | 1.26934 | 0.634668 | − | 0.772785i | \(-0.281137\pi\) | ||||
0.634668 | + | 0.772785i | \(0.281137\pi\) | |||||||
\(114\) | −14.5115 | −1.35913 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | −1.19588 | −0.111034 | ||||||||
\(117\) | −0.593685 | −0.0548862 | ||||||||
\(118\) | 7.43146 | 0.684121 | ||||||||
\(119\) | 4.15520 | 0.380906 | ||||||||
\(120\) | 1.91913 | 0.175192 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.73830 | 0.700593 | ||||||||
\(123\) | −18.9276 | −1.70665 | ||||||||
\(124\) | 7.70820 | 0.692217 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.683063 | 0.0608521 | ||||||||
\(127\) | −2.68257 | −0.238040 | −0.119020 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119020 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.7172 | −1.11969 | ||||||||
\(130\) | −0.869151 | −0.0762296 | ||||||||
\(131\) | 1.19986 | 0.104832 | 0.0524159 | − | 0.998625i | \(-0.483308\pi\) | ||||
0.0524159 | + | 0.998625i | \(0.483308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.56151 | −0.655666 | ||||||||
\(134\) | −3.56151 | −0.307668 | ||||||||
\(135\) | 4.44651 | 0.382694 | ||||||||
\(136\) | 4.15520 | 0.356305 | ||||||||
\(137\) | −4.65822 | −0.397979 | −0.198989 | − | 0.980002i | \(-0.563766\pi\) | ||||
−0.198989 | + | 0.980002i | \(0.563766\pi\) | |||||||
\(138\) | 3.83826 | 0.326735 | ||||||||
\(139\) | −12.6208 | −1.07048 | −0.535241 | − | 0.844699i | \(-0.679779\pi\) | ||||
−0.535241 | + | 0.844699i | \(0.679779\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 20.6361 | 1.73788 | ||||||||
\(142\) | 2.23528 | 0.187580 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.683063 | 0.0569219 | ||||||||
\(145\) | 1.19588 | 0.0993123 | ||||||||
\(146\) | −17.0389 | −1.41015 | ||||||||
\(147\) | 1.91913 | 0.158287 | ||||||||
\(148\) | 6.81263 | 0.559995 | ||||||||
\(149\) | 16.1238 | 1.32091 | 0.660457 | − | 0.750864i | \(-0.270362\pi\) | ||||
0.660457 | + | 0.750864i | \(0.270362\pi\) | |||||||
\(150\) | −1.91913 | −0.156696 | ||||||||
\(151\) | 9.81017 | 0.798341 | 0.399170 | − | 0.916877i | \(-0.369298\pi\) | ||||
0.399170 | + | 0.916877i | \(0.369298\pi\) | |||||||
\(152\) | −7.56151 | −0.613320 | ||||||||
\(153\) | −2.83826 | −0.229460 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.70820 | −0.619138 | ||||||||
\(156\) | −1.66801 | −0.133548 | ||||||||
\(157\) | −2.74234 | −0.218863 | −0.109431 | − | 0.993994i | \(-0.534903\pi\) | ||||
−0.109431 | + | 0.993994i | \(0.534903\pi\) | |||||||
\(158\) | 3.13085 | 0.249077 | ||||||||
\(159\) | −3.02563 | −0.239948 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 10.5826 | 0.831449 | ||||||||
\(163\) | −9.38020 | −0.734714 | −0.367357 | − | 0.930080i | \(-0.619737\pi\) | ||||
−0.367357 | + | 0.930080i | \(0.619737\pi\) | |||||||
\(164\) | −9.86261 | −0.770141 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.22953 | 0.638735 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 1.91913 | 0.148064 | ||||||||
\(169\) | −12.2446 | −0.941891 | ||||||||
\(170\) | −4.15520 | −0.318689 | ||||||||
\(171\) | 5.16499 | 0.394977 | ||||||||
\(172\) | −6.62654 | −0.505269 | ||||||||
\(173\) | 9.14787 | 0.695499 | 0.347750 | − | 0.937587i | \(-0.386946\pi\) | ||||
0.347750 | + | 0.937587i | \(0.386946\pi\) | |||||||
\(174\) | 2.29505 | 0.173987 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.2619 | −1.07199 | ||||||||
\(178\) | 9.89429 | 0.741609 | ||||||||
\(179\) | 3.71474 | 0.277653 | 0.138826 | − | 0.990317i | \(-0.455667\pi\) | ||||
0.138826 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(180\) | −0.683063 | −0.0509125 | ||||||||
\(181\) | −21.4439 | −1.59392 | −0.796958 | − | 0.604035i | \(-0.793559\pi\) | ||||
−0.796958 | + | 0.604035i | \(0.793559\pi\) | |||||||
\(182\) | −0.869151 | −0.0644257 | ||||||||
\(183\) | −14.8508 | −1.09780 | ||||||||
\(184\) | 2.00000 | 0.147442 | ||||||||
\(185\) | −6.81263 | −0.500875 | ||||||||
\(186\) | −14.7931 | −1.08468 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.7529 | 0.784233 | ||||||||
\(189\) | 4.44651 | 0.323436 | ||||||||
\(190\) | 7.56151 | 0.548570 | ||||||||
\(191\) | −21.8922 | −1.58407 | −0.792033 | − | 0.610479i | \(-0.790977\pi\) | ||||
−0.792033 | + | 0.610479i | \(0.790977\pi\) | |||||||
\(192\) | 1.91913 | 0.138501 | ||||||||
\(193\) | 4.07880 | 0.293598 | 0.146799 | − | 0.989166i | \(-0.453103\pi\) | ||||
0.146799 | + | 0.989166i | \(0.453103\pi\) | |||||||
\(194\) | −14.7984 | −1.06246 | ||||||||
\(195\) | 1.66801 | 0.119449 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 14.2275 | 1.01366 | 0.506832 | − | 0.862045i | \(-0.330816\pi\) | ||||
0.506832 | + | 0.862045i | \(0.330816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.75085 | −0.620331 | −0.310166 | − | 0.950682i | \(-0.600385\pi\) | ||||
−0.310166 | + | 0.950682i | \(0.600385\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 6.83501 | 0.482105 | ||||||||
\(202\) | 17.6082 | 1.23891 | ||||||||
\(203\) | 1.19588 | 0.0839342 | ||||||||
\(204\) | −7.97437 | −0.558318 | ||||||||
\(205\) | 9.86261 | 0.688835 | ||||||||
\(206\) | 4.85282 | 0.338112 | ||||||||
\(207\) | −1.36613 | −0.0949523 | ||||||||
\(208\) | −0.869151 | −0.0602648 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.91913 | −0.132433 | ||||||||
\(211\) | −19.7695 | −1.36099 | −0.680494 | − | 0.732754i | \(-0.738235\pi\) | ||||
−0.680494 | + | 0.732754i | \(0.738235\pi\) | |||||||
\(212\) | −1.57656 | −0.108279 | ||||||||
\(213\) | −4.28979 | −0.293931 | ||||||||
\(214\) | 5.97309 | 0.408312 | ||||||||
\(215\) | 6.62654 | 0.451926 | ||||||||
\(216\) | 4.44651 | 0.302546 | ||||||||
\(217\) | −7.70820 | −0.523267 | ||||||||
\(218\) | 19.3651 | 1.31157 | ||||||||
\(219\) | 32.6999 | 2.20965 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.61149 | 0.242935 | ||||||||
\(222\) | −13.0743 | −0.877492 | ||||||||
\(223\) | 10.9231 | 0.731465 | 0.365733 | − | 0.930720i | \(-0.380818\pi\) | ||||
0.365733 | + | 0.930720i | \(0.380818\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0.683063 | 0.0455375 | ||||||||
\(226\) | −13.4932 | −0.897557 | ||||||||
\(227\) | −19.5668 | −1.29869 | −0.649346 | − | 0.760493i | \(-0.724957\pi\) | ||||
−0.649346 | + | 0.760493i | \(0.724957\pi\) | |||||||
\(228\) | 14.5115 | 0.961050 | ||||||||
\(229\) | −14.8613 | −0.982064 | −0.491032 | − | 0.871141i | \(-0.663380\pi\) | ||||
−0.491032 | + | 0.871141i | \(0.663380\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.19588 | 0.0785132 | ||||||||
\(233\) | 4.57784 | 0.299905 | 0.149952 | − | 0.988693i | \(-0.452088\pi\) | ||||
0.149952 | + | 0.988693i | \(0.452088\pi\) | |||||||
\(234\) | 0.593685 | 0.0388104 | ||||||||
\(235\) | −10.7529 | −0.701439 | ||||||||
\(236\) | −7.43146 | −0.483747 | ||||||||
\(237\) | −6.00851 | −0.390295 | ||||||||
\(238\) | −4.15520 | −0.269342 | ||||||||
\(239\) | −16.9479 | −1.09627 | −0.548136 | − | 0.836389i | \(-0.684662\pi\) | ||||
−0.548136 | + | 0.836389i | \(0.684662\pi\) | |||||||
\(240\) | −1.91913 | −0.123879 | ||||||||
\(241\) | 27.4289 | 1.76685 | 0.883425 | − | 0.468572i | \(-0.155231\pi\) | ||||
0.883425 | + | 0.468572i | \(0.155231\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.96990 | −0.447119 | ||||||||
\(244\) | −7.73830 | −0.495394 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 18.9276 | 1.20678 | ||||||||
\(247\) | −6.57210 | −0.418172 | ||||||||
\(248\) | −7.70820 | −0.489471 | ||||||||
\(249\) | −15.7935 | −1.00087 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.21490 | 0.329162 | 0.164581 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164581 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(252\) | −0.683063 | −0.0430289 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.68257 | 0.168320 | ||||||||
\(255\) | 7.97437 | 0.499374 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.77372 | −0.110642 | −0.0553209 | − | 0.998469i | \(-0.517618\pi\) | ||||
−0.0553209 | + | 0.998469i | \(0.517618\pi\) | |||||||
\(258\) | 12.7172 | 0.791738 | ||||||||
\(259\) | −6.81263 | −0.423316 | ||||||||
\(260\) | 0.869151 | 0.0539024 | ||||||||
\(261\) | −0.816860 | −0.0505623 | ||||||||
\(262\) | −1.19986 | −0.0741273 | ||||||||
\(263\) | −14.0317 | −0.865231 | −0.432615 | − | 0.901579i | \(-0.642409\pi\) | ||||
−0.432615 | + | 0.901579i | \(0.642409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.57656 | 0.0968475 | ||||||||
\(266\) | 7.56151 | 0.463626 | ||||||||
\(267\) | −18.9884 | −1.16207 | ||||||||
\(268\) | 3.56151 | 0.217554 | ||||||||
\(269\) | −14.0382 | −0.855923 | −0.427962 | − | 0.903797i | \(-0.640768\pi\) | ||||
−0.427962 | + | 0.903797i | \(0.640768\pi\) | |||||||
\(270\) | −4.44651 | −0.270606 | ||||||||
\(271\) | 21.5635 | 1.30989 | 0.654944 | − | 0.755677i | \(-0.272692\pi\) | ||||
0.654944 | + | 0.755677i | \(0.272692\pi\) | |||||||
\(272\) | −4.15520 | −0.251946 | ||||||||
\(273\) | 1.66801 | 0.100953 | ||||||||
\(274\) | 4.65822 | 0.281414 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.83826 | −0.231036 | ||||||||
\(277\) | −10.4696 | −0.629056 | −0.314528 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314528 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(278\) | 12.6208 | 0.756945 | ||||||||
\(279\) | 5.26519 | 0.315218 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 27.5391 | 1.64285 | 0.821423 | − | 0.570319i | \(-0.193180\pi\) | ||||
0.821423 | + | 0.570319i | \(0.193180\pi\) | |||||||
\(282\) | −20.6361 | −1.22886 | ||||||||
\(283\) | −12.6529 | −0.752137 | −0.376068 | − | 0.926592i | \(-0.622724\pi\) | ||||
−0.376068 | + | 0.926592i | \(0.622724\pi\) | |||||||
\(284\) | −2.23528 | −0.132639 | ||||||||
\(285\) | −14.5115 | −0.859589 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.86261 | 0.582172 | ||||||||
\(288\) | −0.683063 | −0.0402499 | ||||||||
\(289\) | 0.265676 | 0.0156280 | ||||||||
\(290\) | −1.19588 | −0.0702244 | ||||||||
\(291\) | 28.4000 | 1.66484 | ||||||||
\(292\) | 17.0389 | 0.997127 | ||||||||
\(293\) | −26.4209 | −1.54352 | −0.771762 | − | 0.635911i | \(-0.780624\pi\) | ||||
−0.771762 | + | 0.635911i | \(0.780624\pi\) | |||||||
\(294\) | −1.91913 | −0.111926 | ||||||||
\(295\) | 7.43146 | 0.432676 | ||||||||
\(296\) | −6.81263 | −0.395976 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.1238 | −0.934028 | ||||||||
\(299\) | 1.73830 | 0.100529 | ||||||||
\(300\) | 1.91913 | 0.110801 | ||||||||
\(301\) | 6.62654 | 0.381948 | ||||||||
\(302\) | −9.81017 | −0.564512 | ||||||||
\(303\) | −33.7925 | −1.94133 | ||||||||
\(304\) | 7.56151 | 0.433683 | ||||||||
\(305\) | 7.73830 | 0.443094 | ||||||||
\(306\) | 2.83826 | 0.162253 | ||||||||
\(307\) | −24.8324 | −1.41726 | −0.708630 | − | 0.705580i | \(-0.750687\pi\) | ||||
−0.708630 | + | 0.705580i | \(0.750687\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.31320 | −0.529809 | ||||||||
\(310\) | 7.70820 | 0.437797 | ||||||||
\(311\) | 5.74086 | 0.325535 | 0.162767 | − | 0.986664i | \(-0.447958\pi\) | ||||
0.162767 | + | 0.986664i | \(0.447958\pi\) | |||||||
\(312\) | 1.66801 | 0.0944327 | ||||||||
\(313\) | −21.7694 | −1.23048 | −0.615239 | − | 0.788340i | \(-0.710941\pi\) | ||||
−0.615239 | + | 0.788340i | \(0.710941\pi\) | |||||||
\(314\) | 2.74234 | 0.154759 | ||||||||
\(315\) | 0.683063 | 0.0384862 | ||||||||
\(316\) | −3.13085 | −0.176124 | ||||||||
\(317\) | 6.86291 | 0.385460 | 0.192730 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192730 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(318\) | 3.02563 | 0.169669 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −11.4631 | −0.639810 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −31.4196 | −1.74823 | ||||||||
\(324\) | −10.5826 | −0.587923 | ||||||||
\(325\) | −0.869151 | −0.0482118 | ||||||||
\(326\) | 9.38020 | 0.519521 | ||||||||
\(327\) | −37.1642 | −2.05519 | ||||||||
\(328\) | 9.86261 | 0.544572 | ||||||||
\(329\) | −10.7529 | −0.592824 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.6399 | −1.13447 | −0.567235 | − | 0.823556i | \(-0.691987\pi\) | ||||
−0.567235 | + | 0.823556i | \(0.691987\pi\) | |||||||
\(332\) | −8.22953 | −0.451654 | ||||||||
\(333\) | 4.65345 | 0.255008 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −3.56151 | −0.194586 | ||||||||
\(336\) | −1.91913 | −0.104697 | ||||||||
\(337\) | 0.0255665 | 0.00139269 | 0.000696347 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000696347 | 1.00000i | \(0.499778\pi\) | ||||||||
\(338\) | 12.2446 | 0.666017 | ||||||||
\(339\) | 25.8953 | 1.40644 | ||||||||
\(340\) | 4.15520 | 0.225347 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.16499 | −0.279291 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.62654 | 0.357279 | ||||||||
\(345\) | 3.83826 | 0.206645 | ||||||||
\(346\) | −9.14787 | −0.491792 | ||||||||
\(347\) | 27.7393 | 1.48912 | 0.744562 | − | 0.667554i | \(-0.232659\pi\) | ||||
0.744562 | + | 0.667554i | \(0.232659\pi\) | |||||||
\(348\) | −2.29505 | −0.123027 | ||||||||
\(349\) | 7.76742 | 0.415780 | 0.207890 | − | 0.978152i | \(-0.433340\pi\) | ||||
0.207890 | + | 0.978152i | \(0.433340\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 3.86468 | 0.206282 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1303 | −1.23110 | −0.615550 | − | 0.788098i | \(-0.711066\pi\) | ||||
−0.615550 | + | 0.788098i | \(0.711066\pi\) | |||||||
\(354\) | 14.2619 | 0.758013 | ||||||||
\(355\) | 2.23528 | 0.118636 | ||||||||
\(356\) | −9.89429 | −0.524396 | ||||||||
\(357\) | 7.97437 | 0.422048 | ||||||||
\(358\) | −3.71474 | −0.196330 | ||||||||
\(359\) | −12.6100 | −0.665531 | −0.332766 | − | 0.943010i | \(-0.607982\pi\) | ||||
−0.332766 | + | 0.943010i | \(0.607982\pi\) | |||||||
\(360\) | 0.683063 | 0.0360006 | ||||||||
\(361\) | 38.1765 | 2.00929 | ||||||||
\(362\) | 21.4439 | 1.12707 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.869151 | 0.0455559 | ||||||||
\(365\) | −17.0389 | −0.891857 | ||||||||
\(366\) | 14.8508 | 0.776264 | ||||||||
\(367\) | 3.51354 | 0.183405 | 0.0917027 | − | 0.995786i | \(-0.470769\pi\) | ||||
0.0917027 | + | 0.995786i | \(0.470769\pi\) | |||||||
\(368\) | −2.00000 | −0.104257 | ||||||||
\(369\) | −6.73678 | −0.350703 | ||||||||
\(370\) | 6.81263 | 0.354172 | ||||||||
\(371\) | 1.57656 | 0.0818511 | ||||||||
\(372\) | 14.7931 | 0.766984 | ||||||||
\(373\) | −8.48915 | −0.439552 | −0.219776 | − | 0.975550i | \(-0.570533\pi\) | ||||
−0.219776 | + | 0.975550i | \(0.570533\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.91913 | −0.0991035 | ||||||||
\(376\) | −10.7529 | −0.554536 | ||||||||
\(377\) | 1.03940 | 0.0535317 | ||||||||
\(378\) | −4.44651 | −0.228704 | ||||||||
\(379\) | −19.0706 | −0.979590 | −0.489795 | − | 0.871838i | \(-0.662928\pi\) | ||||
−0.489795 | + | 0.871838i | \(0.662928\pi\) | |||||||
\(380\) | −7.56151 | −0.387897 | ||||||||
\(381\) | −5.14821 | −0.263751 | ||||||||
\(382\) | 21.8922 | 1.12010 | ||||||||
\(383\) | 1.33479 | 0.0682044 | 0.0341022 | − | 0.999418i | \(-0.489143\pi\) | ||||
0.0341022 | + | 0.999418i | \(0.489143\pi\) | |||||||
\(384\) | −1.91913 | −0.0979352 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.07880 | −0.207605 | ||||||||
\(387\) | −4.52634 | −0.230087 | ||||||||
\(388\) | 14.7984 | 0.751274 | ||||||||
\(389\) | −1.18211 | −0.0599354 | −0.0299677 | − | 0.999551i | \(-0.509540\pi\) | ||||
−0.0299677 | + | 0.999551i | \(0.509540\pi\) | |||||||
\(390\) | −1.66801 | −0.0844632 | ||||||||
\(391\) | 8.31040 | 0.420275 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 2.30268 | 0.116155 | ||||||||
\(394\) | −14.2275 | −0.716769 | ||||||||
\(395\) | 3.13085 | 0.157530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.9540 | −0.800708 | −0.400354 | − | 0.916361i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916361i | \(0.631113\pi\) | |||||||
\(398\) | 8.75085 | 0.438641 | ||||||||
\(399\) | −14.5115 | −0.726485 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.8135 | −0.589937 | −0.294969 | − | 0.955507i | \(-0.595309\pi\) | ||||
−0.294969 | + | 0.955507i | \(0.595309\pi\) | |||||||
\(402\) | −6.83501 | −0.340899 | ||||||||
\(403\) | −6.69959 | −0.333730 | ||||||||
\(404\) | −17.6082 | −0.876043 | ||||||||
\(405\) | 10.5826 | 0.525854 | ||||||||
\(406\) | −1.19588 | −0.0593504 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.97437 | 0.394790 | ||||||||
\(409\) | −17.2060 | −0.850780 | −0.425390 | − | 0.905010i | \(-0.639863\pi\) | ||||
−0.425390 | + | 0.905010i | \(0.639863\pi\) | |||||||
\(410\) | −9.86261 | −0.487080 | ||||||||
\(411\) | −8.93974 | −0.440965 | ||||||||
\(412\) | −4.85282 | −0.239081 | ||||||||
\(413\) | 7.43146 | 0.365678 | ||||||||
\(414\) | 1.36613 | 0.0671414 | ||||||||
\(415\) | 8.22953 | 0.403972 | ||||||||
\(416\) | 0.869151 | 0.0426136 | ||||||||
\(417\) | −24.2210 | −1.18611 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.07910 | −0.345837 | −0.172918 | − | 0.984936i | \(-0.555320\pi\) | ||||
−0.172918 | + | 0.984936i | \(0.555320\pi\) | |||||||
\(420\) | 1.91913 | 0.0936440 | ||||||||
\(421\) | −15.8752 | −0.773710 | −0.386855 | − | 0.922141i | \(-0.626439\pi\) | ||||
−0.386855 | + | 0.922141i | \(0.626439\pi\) | |||||||
\(422\) | 19.7695 | 0.962364 | ||||||||
\(423\) | 7.34488 | 0.357120 | ||||||||
\(424\) | 1.57656 | 0.0765647 | ||||||||
\(425\) | −4.15520 | −0.201557 | ||||||||
\(426\) | 4.28979 | 0.207841 | ||||||||
\(427\) | 7.73830 | 0.374483 | ||||||||
\(428\) | −5.97309 | −0.288720 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62654 | −0.319560 | ||||||||
\(431\) | −17.4697 | −0.841485 | −0.420742 | − | 0.907180i | \(-0.638230\pi\) | ||||
−0.420742 | + | 0.907180i | \(0.638230\pi\) | |||||||
\(432\) | −4.44651 | −0.213933 | ||||||||
\(433\) | 18.1892 | 0.874115 | 0.437057 | − | 0.899434i | \(-0.356021\pi\) | ||||
0.437057 | + | 0.899434i | \(0.356021\pi\) | |||||||
\(434\) | 7.70820 | 0.370006 | ||||||||
\(435\) | 2.29505 | 0.110039 | ||||||||
\(436\) | −19.3651 | −0.927422 | ||||||||
\(437\) | −15.1230 | −0.723433 | ||||||||
\(438\) | −32.6999 | −1.56246 | ||||||||
\(439\) | −16.5826 | −0.791445 | −0.395722 | − | 0.918370i | \(-0.629506\pi\) | ||||
−0.395722 | + | 0.918370i | \(0.629506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.683063 | 0.0325268 | ||||||||
\(442\) | −3.61149 | −0.171781 | ||||||||
\(443\) | −37.1961 | −1.76724 | −0.883619 | − | 0.468206i | \(-0.844901\pi\) | ||||
−0.883619 | + | 0.468206i | \(0.844901\pi\) | |||||||
\(444\) | 13.0743 | 0.620480 | ||||||||
\(445\) | 9.89429 | 0.469034 | ||||||||
\(446\) | −10.9231 | −0.517224 | ||||||||
\(447\) | 30.9437 | 1.46359 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 10.5728 | 0.498962 | 0.249481 | − | 0.968380i | \(-0.419740\pi\) | ||||
0.249481 | + | 0.968380i | \(0.419740\pi\) | |||||||
\(450\) | −0.683063 | −0.0321999 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.4932 | 0.634668 | ||||||||
\(453\) | 18.8270 | 0.884570 | ||||||||
\(454\) | 19.5668 | 0.918314 | ||||||||
\(455\) | −0.869151 | −0.0407464 | ||||||||
\(456\) | −14.5115 | −0.679565 | ||||||||
\(457\) | −1.57179 | −0.0735254 | −0.0367627 | − | 0.999324i | \(-0.511705\pi\) | ||||
−0.0367627 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(458\) | 14.8613 | 0.694424 | ||||||||
\(459\) | 18.4761 | 0.862391 | ||||||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 15.9056 | 0.740796 | 0.370398 | − | 0.928873i | \(-0.379221\pi\) | ||||
0.370398 | + | 0.928873i | \(0.379221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1265 | 1.02831 | 0.514153 | − | 0.857698i | \(-0.328106\pi\) | ||||
0.514153 | + | 0.857698i | \(0.328106\pi\) | |||||||
\(464\) | −1.19588 | −0.0555172 | ||||||||
\(465\) | −14.7931 | −0.686011 | ||||||||
\(466\) | −4.57784 | −0.212065 | ||||||||
\(467\) | 3.31217 | 0.153269 | 0.0766344 | − | 0.997059i | \(-0.475583\pi\) | ||||
0.0766344 | + | 0.997059i | \(0.475583\pi\) | |||||||
\(468\) | −0.593685 | −0.0274431 | ||||||||
\(469\) | −3.56151 | −0.164455 | ||||||||
\(470\) | 10.7529 | 0.495992 | ||||||||
\(471\) | −5.26292 | −0.242502 | ||||||||
\(472\) | 7.43146 | 0.342061 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.00851 | 0.275980 | ||||||||
\(475\) | 7.56151 | 0.346946 | ||||||||
\(476\) | 4.15520 | 0.190453 | ||||||||
\(477\) | −1.07689 | −0.0493075 | ||||||||
\(478\) | 16.9479 | 0.775181 | ||||||||
\(479\) | −26.3656 | −1.20467 | −0.602337 | − | 0.798242i | \(-0.705764\pi\) | ||||
−0.602337 | + | 0.798242i | \(0.705764\pi\) | |||||||
\(480\) | 1.91913 | 0.0875959 | ||||||||
\(481\) | −5.92120 | −0.269984 | ||||||||
\(482\) | −27.4289 | −1.24935 | ||||||||
\(483\) | 3.83826 | 0.174647 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.7984 | −0.671960 | ||||||||
\(486\) | 6.96990 | 0.316161 | ||||||||
\(487\) | 12.4706 | 0.565095 | 0.282547 | − | 0.959253i | \(-0.408821\pi\) | ||||
0.282547 | + | 0.959253i | \(0.408821\pi\) | |||||||
\(488\) | 7.73830 | 0.350296 | ||||||||
\(489\) | −18.0018 | −0.814071 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 36.6954 | 1.65604 | 0.828021 | − | 0.560698i | \(-0.189467\pi\) | ||||
0.828021 | + | 0.560698i | \(0.189467\pi\) | |||||||
\(492\) | −18.9276 | −0.853324 | ||||||||
\(493\) | 4.96911 | 0.223797 | ||||||||
\(494\) | 6.57210 | 0.295693 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.70820 | 0.346109 | ||||||||
\(497\) | 2.23528 | 0.100266 | ||||||||
\(498\) | 15.7935 | 0.707725 | ||||||||
\(499\) | 22.0831 | 0.988577 | 0.494289 | − | 0.869298i | \(-0.335429\pi\) | ||||
0.494289 | + | 0.869298i | \(0.335429\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −23.0296 | −1.02889 | ||||||||
\(502\) | −5.21490 | −0.232753 | ||||||||
\(503\) | 21.6517 | 0.965401 | 0.482700 | − | 0.875786i | \(-0.339656\pi\) | ||||
0.482700 | + | 0.875786i | \(0.339656\pi\) | |||||||
\(504\) | 0.683063 | 0.0304260 | ||||||||
\(505\) | 17.6082 | 0.783557 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.4989 | −1.04362 | ||||||||
\(508\) | −2.68257 | −0.119020 | ||||||||
\(509\) | 10.8021 | 0.478795 | 0.239398 | − | 0.970922i | \(-0.423050\pi\) | ||||
0.239398 | + | 0.970922i | \(0.423050\pi\) | |||||||
\(510\) | −7.97437 | −0.353111 | ||||||||
\(511\) | −17.0389 | −0.753757 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −33.6223 | −1.48446 | ||||||||
\(514\) | 1.77372 | 0.0782355 | ||||||||
\(515\) | 4.85282 | 0.213841 | ||||||||
\(516\) | −12.7172 | −0.559844 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.81263 | 0.299330 | ||||||||
\(519\) | 17.5560 | 0.770621 | ||||||||
\(520\) | −0.869151 | −0.0381148 | ||||||||
\(521\) | 25.9337 | 1.13618 | 0.568088 | − | 0.822968i | \(-0.307683\pi\) | ||||
0.568088 | + | 0.822968i | \(0.307683\pi\) | |||||||
\(522\) | 0.816860 | 0.0357530 | ||||||||
\(523\) | 23.7789 | 1.03978 | 0.519889 | − | 0.854234i | \(-0.325973\pi\) | ||||
0.519889 | + | 0.854234i | \(0.325973\pi\) | |||||||
\(524\) | 1.19986 | 0.0524159 | ||||||||
\(525\) | −1.91913 | −0.0837577 | ||||||||
\(526\) | 14.0317 | 0.611810 | ||||||||
\(527\) | −32.0291 | −1.39521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −1.57656 | −0.0684815 | ||||||||
\(531\) | −5.07615 | −0.220286 | ||||||||
\(532\) | −7.56151 | −0.327833 | ||||||||
\(533\) | 8.57210 | 0.371299 | ||||||||
\(534\) | 18.9884 | 0.821710 | ||||||||
\(535\) | 5.97309 | 0.258239 | ||||||||
\(536\) | −3.56151 | −0.153834 | ||||||||
\(537\) | 7.12908 | 0.307642 | ||||||||
\(538\) | 14.0382 | 0.605229 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.44651 | 0.191347 | ||||||||
\(541\) | −33.1087 | −1.42345 | −0.711727 | − | 0.702456i | \(-0.752087\pi\) | ||||
−0.711727 | + | 0.702456i | \(0.752087\pi\) | |||||||
\(542\) | −21.5635 | −0.926231 | ||||||||
\(543\) | −41.1537 | −1.76608 | ||||||||
\(544\) | 4.15520 | 0.178153 | ||||||||
\(545\) | 19.3651 | 0.829512 | ||||||||
\(546\) | −1.66801 | −0.0713844 | ||||||||
\(547\) | 26.2035 | 1.12038 | 0.560190 | − | 0.828364i | \(-0.310728\pi\) | ||||
0.560190 | + | 0.828364i | \(0.310728\pi\) | |||||||
\(548\) | −4.65822 | −0.198989 | ||||||||
\(549\) | −5.28575 | −0.225590 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.04265 | −0.385230 | ||||||||
\(552\) | 3.83826 | 0.163367 | ||||||||
\(553\) | 3.13085 | 0.133137 | ||||||||
\(554\) | 10.4696 | 0.444810 | ||||||||
\(555\) | −13.0743 | −0.554974 | ||||||||
\(556\) | −12.6208 | −0.535241 | ||||||||
\(557\) | −1.03615 | −0.0439030 | −0.0219515 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219515 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(558\) | −5.26519 | −0.222893 | ||||||||
\(559\) | 5.75946 | 0.243599 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.5391 | −1.16167 | ||||||||
\(563\) | 16.5668 | 0.698206 | 0.349103 | − | 0.937084i | \(-0.386486\pi\) | ||||
0.349103 | + | 0.937084i | \(0.386486\pi\) | |||||||
\(564\) | 20.6361 | 0.868939 | ||||||||
\(565\) | −13.4932 | −0.567665 | ||||||||
\(566\) | 12.6529 | 0.531841 | ||||||||
\(567\) | 10.5826 | 0.444428 | ||||||||
\(568\) | 2.23528 | 0.0937901 | ||||||||
\(569\) | −28.6394 | −1.20063 | −0.600314 | − | 0.799765i | \(-0.704958\pi\) | ||||
−0.600314 | + | 0.799765i | \(0.704958\pi\) | |||||||
\(570\) | 14.5115 | 0.607821 | ||||||||
\(571\) | 16.0059 | 0.669828 | 0.334914 | − | 0.942249i | \(-0.391293\pi\) | ||||
0.334914 | + | 0.942249i | \(0.391293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.0140 | −1.75516 | ||||||||
\(574\) | −9.86261 | −0.411657 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0.683063 | 0.0284609 | ||||||||
\(577\) | 35.1456 | 1.46313 | 0.731565 | − | 0.681771i | \(-0.238790\pi\) | ||||
0.731565 | + | 0.681771i | \(0.238790\pi\) | |||||||
\(578\) | −0.265676 | −0.0110507 | ||||||||
\(579\) | 7.82774 | 0.325310 | ||||||||
\(580\) | 1.19588 | 0.0496561 | ||||||||
\(581\) | 8.22953 | 0.341418 | ||||||||
\(582\) | −28.4000 | −1.17722 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −17.0389 | −0.705075 | ||||||||
\(585\) | 0.593685 | 0.0245458 | ||||||||
\(586\) | 26.4209 | 1.09144 | ||||||||
\(587\) | 30.2584 | 1.24890 | 0.624449 | − | 0.781066i | \(-0.285324\pi\) | ||||
0.624449 | + | 0.781066i | \(0.285324\pi\) | |||||||
\(588\) | 1.91913 | 0.0791436 | ||||||||
\(589\) | 58.2857 | 2.40162 | ||||||||
\(590\) | −7.43146 | −0.305948 | ||||||||
\(591\) | 27.3043 | 1.12315 | ||||||||
\(592\) | 6.81263 | 0.279997 | ||||||||
\(593\) | 16.7760 | 0.688907 | 0.344454 | − | 0.938803i | \(-0.388064\pi\) | ||||
0.344454 | + | 0.938803i | \(0.388064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.15520 | −0.170347 | ||||||||
\(596\) | 16.1238 | 0.660457 | ||||||||
\(597\) | −16.7940 | −0.687334 | ||||||||
\(598\) | −1.73830 | −0.0710844 | ||||||||
\(599\) | −22.6333 | −0.924772 | −0.462386 | − | 0.886679i | \(-0.653007\pi\) | ||||
−0.462386 | + | 0.886679i | \(0.653007\pi\) | |||||||
\(600\) | −1.91913 | −0.0783482 | ||||||||
\(601\) | −31.7235 | −1.29403 | −0.647014 | − | 0.762478i | \(-0.723983\pi\) | ||||
−0.647014 | + | 0.762478i | \(0.723983\pi\) | |||||||
\(602\) | −6.62654 | −0.270078 | ||||||||
\(603\) | 2.43274 | 0.0990687 | ||||||||
\(604\) | 9.81017 | 0.399170 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 33.7925 | 1.37273 | ||||||||
\(607\) | 15.2933 | 0.620735 | 0.310367 | − | 0.950617i | \(-0.399548\pi\) | ||||
0.310367 | + | 0.950617i | \(0.399548\pi\) | |||||||
\(608\) | −7.56151 | −0.306660 | ||||||||
\(609\) | 2.29505 | 0.0930000 | ||||||||
\(610\) | −7.73830 | −0.313315 | ||||||||
\(611\) | −9.34586 | −0.378093 | ||||||||
\(612\) | −2.83826 | −0.114730 | ||||||||
\(613\) | 9.73988 | 0.393390 | 0.196695 | − | 0.980465i | \(-0.436979\pi\) | ||||
0.196695 | + | 0.980465i | \(0.436979\pi\) | |||||||
\(614\) | 24.8324 | 1.00215 | ||||||||
\(615\) | 18.9276 | 0.763236 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.2611 | 1.21827 | 0.609133 | − | 0.793068i | \(-0.291518\pi\) | ||||
0.609133 | + | 0.793068i | \(0.291518\pi\) | |||||||
\(618\) | 9.31320 | 0.374632 | ||||||||
\(619\) | −27.0250 | −1.08623 | −0.543114 | − | 0.839659i | \(-0.682755\pi\) | ||||
−0.543114 | + | 0.839659i | \(0.682755\pi\) | |||||||
\(620\) | −7.70820 | −0.309569 | ||||||||
\(621\) | 8.89301 | 0.356864 | ||||||||
\(622\) | −5.74086 | −0.230188 | ||||||||
\(623\) | 9.89429 | 0.396406 | ||||||||
\(624\) | −1.66801 | −0.0667740 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.7694 | 0.870080 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.74234 | −0.109431 | ||||||||
\(629\) | −28.3078 | −1.12871 | ||||||||
\(630\) | −0.683063 | −0.0272139 | ||||||||
\(631\) | 10.8554 | 0.432146 | 0.216073 | − | 0.976377i | \(-0.430675\pi\) | ||||
0.216073 | + | 0.976377i | \(0.430675\pi\) | |||||||
\(632\) | 3.13085 | 0.124538 | ||||||||
\(633\) | −37.9402 | −1.50799 | ||||||||
\(634\) | −6.86291 | −0.272561 | ||||||||
\(635\) | 2.68257 | 0.106455 | ||||||||
\(636\) | −3.02563 | −0.119974 | ||||||||
\(637\) | −0.869151 | −0.0344370 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.52683 | −0.0604006 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −16.0629 | −0.634445 | −0.317223 | − | 0.948351i | \(-0.602750\pi\) | ||||
−0.317223 | + | 0.948351i | \(0.602750\pi\) | |||||||
\(642\) | 11.4631 | 0.452414 | ||||||||
\(643\) | 44.2034 | 1.74321 | 0.871605 | − | 0.490208i | \(-0.163079\pi\) | ||||
0.871605 | + | 0.490208i | \(0.163079\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 12.7172 | 0.500739 | ||||||||
\(646\) | 31.4196 | 1.23619 | ||||||||
\(647\) | −44.6177 | −1.75410 | −0.877051 | − | 0.480397i | \(-0.840492\pi\) | ||||
−0.877051 | + | 0.480397i | \(0.840492\pi\) | |||||||
\(648\) | 10.5826 | 0.415724 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.869151 | 0.0340909 | ||||||||
\(651\) | −14.7931 | −0.579785 | ||||||||
\(652\) | −9.38020 | −0.367357 | ||||||||
\(653\) | 6.77997 | 0.265321 | 0.132660 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132660 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(654\) | 37.1642 | 1.45324 | ||||||||
\(655\) | −1.19986 | −0.0468822 | ||||||||
\(656\) | −9.86261 | −0.385070 | ||||||||
\(657\) | 11.6386 | 0.454067 | ||||||||
\(658\) | 10.7529 | 0.419190 | ||||||||
\(659\) | −2.83294 | −0.110356 | −0.0551778 | − | 0.998477i | \(-0.517573\pi\) | ||||
−0.0551778 | + | 0.998477i | \(0.517573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.4484 | 1.41768 | 0.708839 | − | 0.705370i | \(-0.249219\pi\) | ||||
0.708839 | + | 0.705370i | \(0.249219\pi\) | |||||||
\(662\) | 20.6399 | 0.802192 | ||||||||
\(663\) | 6.93093 | 0.269175 | ||||||||
\(664\) | 8.22953 | 0.319368 | ||||||||
\(665\) | 7.56151 | 0.293223 | ||||||||
\(666\) | −4.65345 | −0.180318 | ||||||||
\(667\) | 2.39176 | 0.0926092 | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 20.9629 | 0.810472 | ||||||||
\(670\) | 3.56151 | 0.137593 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.91913 | 0.0740321 | ||||||||
\(673\) | −5.13572 | −0.197968 | −0.0989838 | − | 0.995089i | \(-0.531559\pi\) | ||||
−0.0989838 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(674\) | −0.0255665 | −0.000984783 0 | ||||||||
\(675\) | −4.44651 | −0.171146 | ||||||||
\(676\) | −12.2446 | −0.470945 | ||||||||
\(677\) | 28.3506 | 1.08960 | 0.544801 | − | 0.838565i | \(-0.316605\pi\) | ||||
0.544801 | + | 0.838565i | \(0.316605\pi\) | |||||||
\(678\) | −25.8953 | −0.994502 | ||||||||
\(679\) | −14.7984 | −0.567909 | ||||||||
\(680\) | −4.15520 | −0.159345 | ||||||||
\(681\) | −37.5512 | −1.43896 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0913 | 0.960094 | 0.480047 | − | 0.877243i | \(-0.340620\pi\) | ||||
0.480047 | + | 0.877243i | \(0.340620\pi\) | |||||||
\(684\) | 5.16499 | 0.197488 | ||||||||
\(685\) | 4.65822 | 0.177982 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −28.5208 | −1.08814 | ||||||||
\(688\) | −6.62654 | −0.252635 | ||||||||
\(689\) | 1.37027 | 0.0522032 | ||||||||
\(690\) | −3.83826 | −0.146120 | ||||||||
\(691\) | −49.3947 | −1.87906 | −0.939531 | − | 0.342465i | \(-0.888738\pi\) | ||||
−0.939531 | + | 0.342465i | \(0.888738\pi\) | |||||||
\(692\) | 9.14787 | 0.347750 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.7393 | −1.05297 | ||||||||
\(695\) | 12.6208 | 0.478734 | ||||||||
\(696\) | 2.29505 | 0.0869935 | ||||||||
\(697\) | 40.9811 | 1.55227 | ||||||||
\(698\) | −7.76742 | −0.294001 | ||||||||
\(699\) | 8.78548 | 0.332297 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 51.4479 | 1.94316 | 0.971580 | − | 0.236712i | \(-0.0760698\pi\) | ||||
0.971580 | + | 0.236712i | \(0.0760698\pi\) | |||||||
\(702\) | −3.86468 | −0.145863 | ||||||||
\(703\) | 51.5138 | 1.94288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.6361 | −0.777202 | ||||||||
\(706\) | 23.1303 | 0.870519 | ||||||||
\(707\) | 17.6082 | 0.662226 | ||||||||
\(708\) | −14.2619 | −0.535996 | ||||||||
\(709\) | −39.4201 | −1.48045 | −0.740226 | − | 0.672358i | \(-0.765282\pi\) | ||||
−0.740226 | + | 0.672358i | \(0.765282\pi\) | |||||||
\(710\) | −2.23528 | −0.0838884 | ||||||||
\(711\) | −2.13857 | −0.0802025 | ||||||||
\(712\) | 9.89429 | 0.370804 | ||||||||
\(713\) | −15.4164 | −0.577349 | ||||||||
\(714\) | −7.97437 | −0.298433 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.71474 | 0.138826 | ||||||||
\(717\) | −32.5253 | −1.21468 | ||||||||
\(718\) | 12.6100 | 0.470602 | ||||||||
\(719\) | 24.7392 | 0.922618 | 0.461309 | − | 0.887240i | \(-0.347380\pi\) | ||||
0.461309 | + | 0.887240i | \(0.347380\pi\) | |||||||
\(720\) | −0.683063 | −0.0254562 | ||||||||
\(721\) | 4.85282 | 0.180728 | ||||||||
\(722\) | −38.1765 | −1.42078 | ||||||||
\(723\) | 52.6396 | 1.95769 | ||||||||
\(724\) | −21.4439 | −0.796958 | ||||||||
\(725\) | −1.19588 | −0.0444138 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.2679 | −1.90142 | −0.950710 | − | 0.310081i | \(-0.899644\pi\) | ||||
−0.950710 | + | 0.310081i | \(0.899644\pi\) | |||||||
\(728\) | −0.869151 | −0.0322129 | ||||||||
\(729\) | 18.3717 | 0.680433 | ||||||||
\(730\) | 17.0389 | 0.630638 | ||||||||
\(731\) | 27.5346 | 1.01840 | ||||||||
\(732\) | −14.8508 | −0.548902 | ||||||||
\(733\) | −0.281620 | −0.0104019 | −0.00520094 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520094 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(734\) | −3.51354 | −0.129687 | ||||||||
\(735\) | −1.91913 | −0.0707882 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.73678 | 0.247984 | ||||||||
\(739\) | 1.44847 | 0.0532830 | 0.0266415 | − | 0.999645i | \(-0.491519\pi\) | ||||
0.0266415 | + | 0.999645i | \(0.491519\pi\) | |||||||
\(740\) | −6.81263 | −0.250437 | ||||||||
\(741\) | −12.6127 | −0.463340 | ||||||||
\(742\) | −1.57656 | −0.0578774 | ||||||||
\(743\) | −10.9338 | −0.401121 | −0.200560 | − | 0.979681i | \(-0.564276\pi\) | ||||
−0.200560 | + | 0.979681i | \(0.564276\pi\) | |||||||
\(744\) | −14.7931 | −0.542340 | ||||||||
\(745\) | −16.1238 | −0.590731 | ||||||||
\(746\) | 8.48915 | 0.310810 | ||||||||
\(747\) | −5.62128 | −0.205672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.97309 | 0.218252 | ||||||||
\(750\) | 1.91913 | 0.0700767 | ||||||||
\(751\) | −39.4330 | −1.43893 | −0.719465 | − | 0.694528i | \(-0.755613\pi\) | ||||
−0.719465 | + | 0.694528i | \(0.755613\pi\) | |||||||
\(752\) | 10.7529 | 0.392116 | ||||||||
\(753\) | 10.0081 | 0.364715 | ||||||||
\(754\) | −1.03940 | −0.0378527 | ||||||||
\(755\) | −9.81017 | −0.357029 | ||||||||
\(756\) | 4.44651 | 0.161718 | ||||||||
\(757\) | −22.1713 | −0.805829 | −0.402914 | − | 0.915238i | \(-0.632003\pi\) | ||||
−0.402914 | + | 0.915238i | \(0.632003\pi\) | |||||||
\(758\) | 19.0706 | 0.692675 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.56151 | 0.274285 | ||||||||
\(761\) | −29.0999 | −1.05487 | −0.527435 | − | 0.849595i | \(-0.676846\pi\) | ||||
−0.527435 | + | 0.849595i | \(0.676846\pi\) | |||||||
\(762\) | 5.14821 | 0.186500 | ||||||||
\(763\) | 19.3651 | 0.701065 | ||||||||
\(764\) | −21.8922 | −0.792033 | ||||||||
\(765\) | 2.83826 | 0.102618 | ||||||||
\(766\) | −1.33479 | −0.0482278 | ||||||||
\(767\) | 6.45906 | 0.233223 | ||||||||
\(768\) | 1.91913 | 0.0692507 | ||||||||
\(769\) | 36.2631 | 1.30768 | 0.653840 | − | 0.756633i | \(-0.273157\pi\) | ||||
0.653840 | + | 0.756633i | \(0.273157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.40400 | −0.122592 | ||||||||
\(772\) | 4.07880 | 0.146799 | ||||||||
\(773\) | −4.25546 | −0.153058 | −0.0765291 | − | 0.997067i | \(-0.524384\pi\) | ||||
−0.0765291 | + | 0.997067i | \(0.524384\pi\) | |||||||
\(774\) | 4.52634 | 0.162696 | ||||||||
\(775\) | 7.70820 | 0.276887 | ||||||||
\(776\) | −14.7984 | −0.531231 | ||||||||
\(777\) | −13.0743 | −0.469039 | ||||||||
\(778\) | 1.18211 | 0.0423807 | ||||||||
\(779\) | −74.5763 | −2.67197 | ||||||||
\(780\) | 1.66801 | 0.0597245 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.31040 | −0.297179 | ||||||||
\(783\) | 5.31748 | 0.190031 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 2.74234 | 0.0978784 | ||||||||
\(786\) | −2.30268 | −0.0821339 | ||||||||
\(787\) | −8.32019 | −0.296583 | −0.148291 | − | 0.988944i | \(-0.547377\pi\) | ||||
−0.148291 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(788\) | 14.2275 | 0.506832 | ||||||||
\(789\) | −26.9286 | −0.958685 | ||||||||
\(790\) | −3.13085 | −0.111391 | ||||||||
\(791\) | −13.4932 | −0.479764 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.72575 | 0.238838 | ||||||||
\(794\) | 15.9540 | 0.566186 | ||||||||
\(795\) | 3.02563 | 0.107308 | ||||||||
\(796\) | −8.75085 | −0.310166 | ||||||||
\(797\) | 2.63097 | 0.0931938 | 0.0465969 | − | 0.998914i | \(-0.485162\pi\) | ||||
0.0465969 | + | 0.998914i | \(0.485162\pi\) | |||||||
\(798\) | 14.5115 | 0.513703 | ||||||||
\(799\) | −44.6803 | −1.58067 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −6.75842 | −0.238797 | ||||||||
\(802\) | 11.8135 | 0.417149 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.83501 | 0.241052 | ||||||||
\(805\) | −2.00000 | −0.0704907 | ||||||||
\(806\) | 6.69959 | 0.235983 | ||||||||
\(807\) | −26.9411 | −0.948372 | ||||||||
\(808\) | 17.6082 | 0.619456 | ||||||||
\(809\) | −9.79837 | −0.344492 | −0.172246 | − | 0.985054i | \(-0.555102\pi\) | ||||
−0.172246 | + | 0.985054i | \(0.555102\pi\) | |||||||
\(810\) | −10.5826 | −0.371835 | ||||||||
\(811\) | 27.5065 | 0.965883 | 0.482941 | − | 0.875653i | \(-0.339568\pi\) | ||||
0.482941 | + | 0.875653i | \(0.339568\pi\) | |||||||
\(812\) | 1.19588 | 0.0419671 | ||||||||
\(813\) | 41.3831 | 1.45137 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.38020 | 0.328574 | ||||||||
\(816\) | −7.97437 | −0.279159 | ||||||||
\(817\) | −50.1067 | −1.75301 | ||||||||
\(818\) | 17.2060 | 0.601593 | ||||||||
\(819\) | 0.593685 | 0.0207450 | ||||||||
\(820\) | 9.86261 | 0.344417 | ||||||||
\(821\) | 44.1139 | 1.53958 | 0.769792 | − | 0.638295i | \(-0.220360\pi\) | ||||
0.769792 | + | 0.638295i | \(0.220360\pi\) | |||||||
\(822\) | 8.93974 | 0.311809 | ||||||||
\(823\) | 26.5906 | 0.926889 | 0.463444 | − | 0.886126i | \(-0.346613\pi\) | ||||
0.463444 | + | 0.886126i | \(0.346613\pi\) | |||||||
\(824\) | 4.85282 | 0.169056 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.43146 | −0.258573 | ||||||||
\(827\) | −36.8252 | −1.28054 | −0.640270 | − | 0.768150i | \(-0.721177\pi\) | ||||
−0.640270 | + | 0.768150i | \(0.721177\pi\) | |||||||
\(828\) | −1.36613 | −0.0474761 | ||||||||
\(829\) | −44.3460 | −1.54020 | −0.770100 | − | 0.637923i | \(-0.779794\pi\) | ||||
−0.770100 | + | 0.637923i | \(0.779794\pi\) | |||||||
\(830\) | −8.22953 | −0.285651 | ||||||||
\(831\) | −20.0925 | −0.697000 | ||||||||
\(832\) | −0.869151 | −0.0301324 | ||||||||
\(833\) | −4.15520 | −0.143969 | ||||||||
\(834\) | 24.2210 | 0.838703 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.2746 | −1.18470 | ||||||||
\(838\) | 7.07910 | 0.244543 | ||||||||
\(839\) | 18.4856 | 0.638194 | 0.319097 | − | 0.947722i | \(-0.396620\pi\) | ||||
0.319097 | + | 0.947722i | \(0.396620\pi\) | |||||||
\(840\) | −1.91913 | −0.0662163 | ||||||||
\(841\) | −27.5699 | −0.950685 | ||||||||
\(842\) | 15.8752 | 0.547096 | ||||||||
\(843\) | 52.8512 | 1.82029 | ||||||||
\(844\) | −19.7695 | −0.680494 | ||||||||
\(845\) | 12.2446 | 0.421226 | ||||||||
\(846\) | −7.34488 | −0.252522 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.57656 | −0.0541394 | ||||||||
\(849\) | −24.2826 | −0.833376 | ||||||||
\(850\) | 4.15520 | 0.142522 | ||||||||
\(851\) | −13.6253 | −0.467068 | ||||||||
\(852\) | −4.28979 | −0.146966 | ||||||||
\(853\) | −20.2660 | −0.693894 | −0.346947 | − | 0.937885i | \(-0.612782\pi\) | ||||
−0.346947 | + | 0.937885i | \(0.612782\pi\) | |||||||
\(854\) | −7.73830 | −0.264799 | ||||||||
\(855\) | −5.16499 | −0.176639 | ||||||||
\(856\) | 5.97309 | 0.204156 | ||||||||
\(857\) | −34.4745 | −1.17763 | −0.588813 | − | 0.808269i | \(-0.700404\pi\) | ||||
−0.588813 | + | 0.808269i | \(0.700404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.96220 | 0.271667 | 0.135833 | − | 0.990732i | \(-0.456629\pi\) | ||||
0.135833 | + | 0.990732i | \(0.456629\pi\) | |||||||
\(860\) | 6.62654 | 0.225963 | ||||||||
\(861\) | 18.9276 | 0.645052 | ||||||||
\(862\) | 17.4697 | 0.595020 | ||||||||
\(863\) | −29.8949 | −1.01763 | −0.508817 | − | 0.860874i | \(-0.669917\pi\) | ||||
−0.508817 | + | 0.860874i | \(0.669917\pi\) | |||||||
\(864\) | 4.44651 | 0.151273 | ||||||||
\(865\) | −9.14787 | −0.311037 | ||||||||
\(866\) | −18.1892 | −0.618093 | ||||||||
\(867\) | 0.509868 | 0.0173160 | ||||||||
\(868\) | −7.70820 | −0.261633 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.29505 | −0.0778094 | ||||||||
\(871\) | −3.09549 | −0.104887 | ||||||||
\(872\) | 19.3651 | 0.655787 | ||||||||
\(873\) | 10.1082 | 0.342111 | ||||||||
\(874\) | 15.1230 | 0.511544 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 32.6999 | 1.10483 | ||||||||
\(877\) | 2.51288 | 0.0848539 | 0.0424270 | − | 0.999100i | \(-0.486491\pi\) | ||||
0.0424270 | + | 0.999100i | \(0.486491\pi\) | |||||||
\(878\) | 16.5826 | 0.559636 | ||||||||
\(879\) | −50.7051 | −1.71024 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.5748 | 1.06378 | 0.531890 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531890 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(882\) | −0.683063 | −0.0229999 | ||||||||
\(883\) | 21.6431 | 0.728349 | 0.364174 | − | 0.931331i | \(-0.381351\pi\) | ||||
0.364174 | + | 0.931331i | \(0.381351\pi\) | |||||||
\(884\) | 3.61149 | 0.121468 | ||||||||
\(885\) | 14.2619 | 0.479410 | ||||||||
\(886\) | 37.1961 | 1.24963 | ||||||||
\(887\) | −34.3585 | −1.15365 | −0.576823 | − | 0.816869i | \(-0.695708\pi\) | ||||
−0.576823 | + | 0.816869i | \(0.695708\pi\) | |||||||
\(888\) | −13.0743 | −0.438746 | ||||||||
\(889\) | 2.68257 | 0.0899706 | ||||||||
\(890\) | −9.89429 | −0.331657 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.9231 | 0.365733 | ||||||||
\(893\) | 81.3079 | 2.72087 | ||||||||
\(894\) | −30.9437 | −1.03491 | ||||||||
\(895\) | −3.71474 | −0.124170 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 3.33603 | 0.111387 | ||||||||
\(898\) | −10.5728 | −0.352820 | ||||||||
\(899\) | −9.21807 | −0.307440 | ||||||||
\(900\) | 0.683063 | 0.0227688 | ||||||||
\(901\) | 6.55093 | 0.218243 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7172 | 0.423202 | ||||||||
\(904\) | −13.4932 | −0.448778 | ||||||||
\(905\) | 21.4439 | 0.712821 | ||||||||
\(906\) | −18.8270 | −0.625485 | ||||||||
\(907\) | 15.8784 | 0.527234 | 0.263617 | − | 0.964627i | \(-0.415084\pi\) | ||||
0.263617 | + | 0.964627i | \(0.415084\pi\) | |||||||
\(908\) | −19.5668 | −0.649346 | ||||||||
\(909\) | −12.0275 | −0.398928 | ||||||||
\(910\) | 0.869151 | 0.0288121 | ||||||||
\(911\) | 19.4184 | 0.643361 | 0.321680 | − | 0.946848i | \(-0.395752\pi\) | ||||
0.321680 | + | 0.946848i | \(0.395752\pi\) | |||||||
\(912\) | 14.5115 | 0.480525 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.57179 | 0.0519903 | ||||||||
\(915\) | 14.8508 | 0.490953 | ||||||||
\(916\) | −14.8613 | −0.491032 | ||||||||
\(917\) | −1.19986 | −0.0396227 | ||||||||
\(918\) | −18.4761 | −0.609803 | ||||||||
\(919\) | −32.2285 | −1.06312 | −0.531560 | − | 0.847021i | \(-0.678394\pi\) | ||||
−0.531560 | + | 0.847021i | \(0.678394\pi\) | |||||||
\(920\) | −2.00000 | −0.0659380 | ||||||||
\(921\) | −47.6566 | −1.57034 | ||||||||
\(922\) | −15.9056 | −0.523822 | ||||||||
\(923\) | 1.94279 | 0.0639478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.81263 | 0.223998 | ||||||||
\(926\) | −22.1265 | −0.727122 | ||||||||
\(927\) | −3.31478 | −0.108872 | ||||||||
\(928\) | 1.19588 | 0.0392566 | ||||||||
\(929\) | 30.0808 | 0.986918 | 0.493459 | − | 0.869769i | \(-0.335732\pi\) | ||||
0.493459 | + | 0.869769i | \(0.335732\pi\) | |||||||
\(930\) | 14.7931 | 0.485083 | ||||||||
\(931\) | 7.56151 | 0.247819 | ||||||||
\(932\) | 4.57784 | 0.149952 | ||||||||
\(933\) | 11.0175 | 0.360696 | ||||||||
\(934\) | −3.31217 | −0.108377 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.593685 | 0.0194052 | ||||||||
\(937\) | 5.16706 | 0.168801 | 0.0844003 | − | 0.996432i | \(-0.473103\pi\) | ||||
0.0844003 | + | 0.996432i | \(0.473103\pi\) | |||||||
\(938\) | 3.56151 | 0.116288 | ||||||||
\(939\) | −41.7783 | −1.36338 | ||||||||
\(940\) | −10.7529 | −0.350720 | ||||||||
\(941\) | 20.8799 | 0.680666 | 0.340333 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340333 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(942\) | 5.26292 | 0.171475 | ||||||||
\(943\) | 19.7252 | 0.642342 | ||||||||
\(944\) | −7.43146 | −0.241873 | ||||||||
\(945\) | −4.44651 | −0.144645 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.5179 | 0.731733 | 0.365867 | − | 0.930667i | \(-0.380773\pi\) | ||||
0.365867 | + | 0.930667i | \(0.380773\pi\) | |||||||
\(948\) | −6.00851 | −0.195147 | ||||||||
\(949\) | −14.8094 | −0.480733 | ||||||||
\(950\) | −7.56151 | −0.245328 | ||||||||
\(951\) | 13.1708 | 0.427093 | ||||||||
\(952\) | −4.15520 | −0.134671 | ||||||||
\(953\) | 3.73512 | 0.120992 | 0.0604961 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604961 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(954\) | 1.07689 | 0.0348656 | ||||||||
\(955\) | 21.8922 | 0.708416 | ||||||||
\(956\) | −16.9479 | −0.548136 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.3656 | 0.851834 | ||||||||
\(959\) | 4.65822 | 0.150422 | ||||||||
\(960\) | −1.91913 | −0.0619397 | ||||||||
\(961\) | 28.4164 | 0.916658 | ||||||||
\(962\) | 5.92120 | 0.190907 | ||||||||
\(963\) | −4.07999 | −0.131476 | ||||||||
\(964\) | 27.4289 | 0.883425 | ||||||||
\(965\) | −4.07880 | −0.131301 | ||||||||
\(966\) | −3.83826 | −0.123494 | ||||||||
\(967\) | 17.0337 | 0.547767 | 0.273884 | − | 0.961763i | \(-0.411692\pi\) | ||||
0.273884 | + | 0.961763i | \(0.411692\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.2983 | −1.93706 | ||||||||
\(970\) | 14.7984 | 0.475147 | ||||||||
\(971\) | 31.4811 | 1.01028 | 0.505139 | − | 0.863038i | \(-0.331441\pi\) | ||||
0.505139 | + | 0.863038i | \(0.331441\pi\) | |||||||
\(972\) | −6.96990 | −0.223560 | ||||||||
\(973\) | 12.6208 | 0.404604 | ||||||||
\(974\) | −12.4706 | −0.399582 | ||||||||
\(975\) | −1.66801 | −0.0534192 | ||||||||
\(976\) | −7.73830 | −0.247697 | ||||||||
\(977\) | 26.7352 | 0.855335 | 0.427668 | − | 0.903936i | \(-0.359335\pi\) | ||||
0.427668 | + | 0.903936i | \(0.359335\pi\) | |||||||
\(978\) | 18.0018 | 0.575635 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −13.2276 | −0.422325 | ||||||||
\(982\) | −36.6954 | −1.17100 | ||||||||
\(983\) | 22.6689 | 0.723027 | 0.361513 | − | 0.932367i | \(-0.382260\pi\) | ||||
0.361513 | + | 0.932367i | \(0.382260\pi\) | |||||||
\(984\) | 18.9276 | 0.603391 | ||||||||
\(985\) | −14.2275 | −0.453324 | ||||||||
\(986\) | −4.96911 | −0.158249 | ||||||||
\(987\) | −20.6361 | −0.656856 | ||||||||
\(988\) | −6.57210 | −0.209086 | ||||||||
\(989\) | 13.2531 | 0.421424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.56237 | 0.176695 | 0.0883473 | − | 0.996090i | \(-0.471841\pi\) | ||||
0.0883473 | + | 0.996090i | \(0.471841\pi\) | |||||||
\(992\) | −7.70820 | −0.244736 | ||||||||
\(993\) | −39.6106 | −1.25701 | ||||||||
\(994\) | −2.23528 | −0.0708987 | ||||||||
\(995\) | 8.75085 | 0.277421 | ||||||||
\(996\) | −15.7935 | −0.500437 | ||||||||
\(997\) | 40.0101 | 1.26713 | 0.633566 | − | 0.773689i | \(-0.281590\pi\) | ||||
0.633566 | + | 0.773689i | \(0.281590\pi\) | |||||||
\(998\) | −22.0831 | −0.699030 | ||||||||
\(999\) | −30.2924 | −0.958409 |
(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 | 8470.2.a.cq.1.3 | 4 | ||
11.3 | even | 5 | 770.2.n.e.141.1 | yes | 8 | ||
11.4 | even | 5 | 770.2.n.e.71.1 | ✓ | 8 | ||
11.10 | odd | 2 | 8470.2.a.ct.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.71.1 | ✓ | 8 | 11.4 | even | 5 | ||
770.2.n.e.141.1 | yes | 8 | 11.3 | even | 5 | ||
8470.2.a.cq.1.3 | 4 | 1.1 | even | 1 | trivial | ||
8470.2.a.ct.1.3 | 4 | 11.10 | odd | 2 |