Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.28279\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28279 | 1.61417 | 0.807087 | − | 0.590433i | \(-0.201043\pi\) | ||||
0.807087 | + | 0.590433i | \(0.201043\pi\) | |||||||
\(3\) | −0.445964 | −0.257478 | −0.128739 | − | 0.991679i | \(-0.541093\pi\) | ||||
−0.128739 | + | 0.991679i | \(0.541093\pi\) | |||||||
\(4\) | 3.21111 | 1.60556 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.01804 | −0.415614 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.76472 | 0.977475 | ||||||||
\(9\) | −2.80112 | −0.933705 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.882192 | 0.265991 | 0.132995 | − | 0.991117i | \(-0.457540\pi\) | ||||
0.132995 | + | 0.991117i | \(0.457540\pi\) | |||||||
\(12\) | −1.43204 | −0.413395 | ||||||||
\(13\) | 0.264745 | 0.0734271 | 0.0367136 | − | 0.999326i | \(-0.488311\pi\) | ||||
0.0367136 | + | 0.999326i | \(0.488311\pi\) | |||||||
\(14\) | −2.28279 | −0.610100 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.110972 | −0.0277430 | ||||||||
\(17\) | −6.80853 | −1.65131 | −0.825656 | − | 0.564174i | \(-0.809195\pi\) | ||||
−0.825656 | + | 0.564174i | \(0.809195\pi\) | |||||||
\(18\) | −6.39435 | −1.50716 | ||||||||
\(19\) | 2.33311 | 0.535252 | 0.267626 | − | 0.963523i | \(-0.413761\pi\) | ||||
0.267626 | + | 0.963523i | \(0.413761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.445964 | 0.0973174 | ||||||||
\(22\) | 2.01386 | 0.429356 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.23296 | −0.251678 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.604357 | 0.118524 | ||||||||
\(27\) | 2.58709 | 0.497886 | ||||||||
\(28\) | −3.21111 | −0.606844 | ||||||||
\(29\) | 4.70357 | 0.873430 | 0.436715 | − | 0.899600i | \(-0.356142\pi\) | ||||
0.436715 | + | 0.899600i | \(0.356142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.57993 | −1.00218 | −0.501092 | − | 0.865394i | \(-0.667068\pi\) | ||||
−0.501092 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(32\) | −5.78276 | −1.02226 | ||||||||
\(33\) | −0.393426 | −0.0684867 | ||||||||
\(34\) | −15.5424 | −2.66550 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.99470 | −1.49912 | ||||||||
\(37\) | 4.70000 | 0.772675 | 0.386337 | − | 0.922358i | \(-0.373740\pi\) | ||||
0.386337 | + | 0.922358i | \(0.373740\pi\) | |||||||
\(38\) | 5.32599 | 0.863989 | ||||||||
\(39\) | −0.118067 | −0.0189058 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.47644 | −0.855276 | −0.427638 | − | 0.903950i | \(-0.640654\pi\) | ||||
−0.427638 | + | 0.903950i | \(0.640654\pi\) | |||||||
\(42\) | 1.01804 | 0.157087 | ||||||||
\(43\) | −6.78709 | −1.03502 | −0.517511 | − | 0.855677i | \(-0.673141\pi\) | ||||
−0.517511 | + | 0.855677i | \(0.673141\pi\) | |||||||
\(44\) | 2.83282 | 0.427064 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.28279 | −0.336579 | ||||||||
\(47\) | −7.04416 | −1.02750 | −0.513748 | − | 0.857941i | \(-0.671743\pi\) | ||||
−0.513748 | + | 0.857941i | \(0.671743\pi\) | |||||||
\(48\) | 0.0494895 | 0.00714319 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.03636 | 0.425176 | ||||||||
\(52\) | 0.850127 | 0.117891 | ||||||||
\(53\) | −9.38516 | −1.28915 | −0.644576 | − | 0.764540i | \(-0.722966\pi\) | ||||
−0.644576 | + | 0.764540i | \(0.722966\pi\) | |||||||
\(54\) | 5.90578 | 0.803674 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.76472 | −0.369451 | ||||||||
\(57\) | −1.04048 | −0.137815 | ||||||||
\(58\) | 10.7372 | 1.40987 | ||||||||
\(59\) | 7.44091 | 0.968724 | 0.484362 | − | 0.874868i | \(-0.339052\pi\) | ||||
0.484362 | + | 0.874868i | \(0.339052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.6378 | −1.87418 | −0.937089 | − | 0.349090i | \(-0.886491\pi\) | ||||
−0.937089 | + | 0.349090i | \(0.886491\pi\) | |||||||
\(62\) | −12.7378 | −1.61770 | ||||||||
\(63\) | 2.80112 | 0.352907 | ||||||||
\(64\) | −12.9789 | −1.62236 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.898108 | −0.110549 | ||||||||
\(67\) | −4.23716 | −0.517651 | −0.258826 | − | 0.965924i | \(-0.583335\pi\) | ||||
−0.258826 | + | 0.965924i | \(0.583335\pi\) | |||||||
\(68\) | −21.8630 | −2.65128 | ||||||||
\(69\) | 0.445964 | 0.0536878 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.35459 | −1.11019 | −0.555093 | − | 0.831788i | \(-0.687317\pi\) | ||||
−0.555093 | + | 0.831788i | \(0.687317\pi\) | |||||||
\(72\) | −7.74429 | −0.912673 | ||||||||
\(73\) | −6.72564 | −0.787176 | −0.393588 | − | 0.919287i | \(-0.628766\pi\) | ||||
−0.393588 | + | 0.919287i | \(0.628766\pi\) | |||||||
\(74\) | 10.7291 | 1.24723 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.49188 | 0.859377 | ||||||||
\(77\) | −0.882192 | −0.100535 | ||||||||
\(78\) | −0.269522 | −0.0305173 | ||||||||
\(79\) | 14.6130 | 1.64409 | 0.822047 | − | 0.569420i | \(-0.192832\pi\) | ||||
0.822047 | + | 0.569420i | \(0.192832\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.24960 | 0.805511 | ||||||||
\(82\) | −12.5015 | −1.38056 | ||||||||
\(83\) | 0.193588 | 0.0212491 | 0.0106245 | − | 0.999944i | \(-0.496618\pi\) | ||||
0.0106245 | + | 0.999944i | \(0.496618\pi\) | |||||||
\(84\) | 1.43204 | 0.156249 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.4935 | −1.67071 | ||||||||
\(87\) | −2.09762 | −0.224889 | ||||||||
\(88\) | 2.43901 | 0.259999 | ||||||||
\(89\) | 16.7797 | 1.77865 | 0.889323 | − | 0.457279i | \(-0.151176\pi\) | ||||
0.889323 | + | 0.457279i | \(0.151176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.264745 | −0.0277528 | ||||||||
\(92\) | −3.21111 | −0.334782 | ||||||||
\(93\) | 2.48845 | 0.258040 | ||||||||
\(94\) | −16.0803 | −1.65856 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.57890 | 0.263208 | ||||||||
\(97\) | −10.0525 | −1.02068 | −0.510339 | − | 0.859973i | \(-0.670480\pi\) | ||||
−0.510339 | + | 0.859973i | \(0.670480\pi\) | |||||||
\(98\) | 2.28279 | 0.230596 | ||||||||
\(99\) | −2.47112 | −0.248357 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.79904 | −0.278515 | −0.139257 | − | 0.990256i | \(-0.544472\pi\) | ||||
−0.139257 | + | 0.990256i | \(0.544472\pi\) | |||||||
\(102\) | 6.93137 | 0.686308 | ||||||||
\(103\) | −3.72914 | −0.367443 | −0.183721 | − | 0.982978i | \(-0.558814\pi\) | ||||
−0.183721 | + | 0.982978i | \(0.558814\pi\) | |||||||
\(104\) | 0.731945 | 0.0717732 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.4243 | −2.08091 | ||||||||
\(107\) | −5.46111 | −0.527945 | −0.263972 | − | 0.964530i | \(-0.585033\pi\) | ||||
−0.263972 | + | 0.964530i | \(0.585033\pi\) | |||||||
\(108\) | 8.30745 | 0.799384 | ||||||||
\(109\) | 11.0426 | 1.05769 | 0.528845 | − | 0.848718i | \(-0.322625\pi\) | ||||
0.528845 | + | 0.848718i | \(0.322625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.09603 | −0.198946 | ||||||||
\(112\) | 0.110972 | 0.0104859 | ||||||||
\(113\) | −8.82162 | −0.829868 | −0.414934 | − | 0.909851i | \(-0.636195\pi\) | ||||
−0.414934 | + | 0.909851i | \(0.636195\pi\) | |||||||
\(114\) | −2.37520 | −0.222458 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.1037 | 1.40234 | ||||||||
\(117\) | −0.741582 | −0.0685593 | ||||||||
\(118\) | 16.9860 | 1.56369 | ||||||||
\(119\) | 6.80853 | 0.624137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2217 | −0.929249 | ||||||||
\(122\) | −33.4150 | −3.02525 | ||||||||
\(123\) | 2.44230 | 0.220215 | ||||||||
\(124\) | −17.9178 | −1.60907 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.39435 | 0.569654 | ||||||||
\(127\) | 9.06252 | 0.804168 | 0.402084 | − | 0.915603i | \(-0.368286\pi\) | ||||
0.402084 | + | 0.915603i | \(0.368286\pi\) | |||||||
\(128\) | −18.0624 | −1.59651 | ||||||||
\(129\) | 3.02680 | 0.266495 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.80502 | 0.507187 | 0.253594 | − | 0.967311i | \(-0.418387\pi\) | ||||
0.253594 | + | 0.967311i | \(0.418387\pi\) | |||||||
\(132\) | −1.26334 | −0.109959 | ||||||||
\(133\) | −2.33311 | −0.202306 | ||||||||
\(134\) | −9.67253 | −0.835579 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −18.8237 | −1.61412 | ||||||||
\(137\) | 8.15908 | 0.697077 | 0.348538 | − | 0.937294i | \(-0.386678\pi\) | ||||
0.348538 | + | 0.937294i | \(0.386678\pi\) | |||||||
\(138\) | 1.01804 | 0.0866614 | ||||||||
\(139\) | −12.6407 | −1.07217 | −0.536085 | − | 0.844164i | \(-0.680097\pi\) | ||||
−0.536085 | + | 0.844164i | \(0.680097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.14144 | 0.264557 | ||||||||
\(142\) | −21.3545 | −1.79203 | ||||||||
\(143\) | 0.233556 | 0.0195309 | ||||||||
\(144\) | 0.310845 | 0.0259037 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.3532 | −1.27064 | ||||||||
\(147\) | −0.445964 | −0.0367825 | ||||||||
\(148\) | 15.0922 | 1.24057 | ||||||||
\(149\) | 15.3424 | 1.25690 | 0.628451 | − | 0.777849i | \(-0.283689\pi\) | ||||
0.628451 | + | 0.777849i | \(0.283689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0386 | 1.22383 | 0.611914 | − | 0.790925i | \(-0.290400\pi\) | ||||
0.611914 | + | 0.790925i | \(0.290400\pi\) | |||||||
\(152\) | 6.45038 | 0.523195 | ||||||||
\(153\) | 19.0715 | 1.54184 | ||||||||
\(154\) | −2.01386 | −0.162281 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.379126 | −0.0303544 | ||||||||
\(157\) | 4.39042 | 0.350394 | 0.175197 | − | 0.984533i | \(-0.443944\pi\) | ||||
0.175197 | + | 0.984533i | \(0.443944\pi\) | |||||||
\(158\) | 33.3584 | 2.65385 | ||||||||
\(159\) | 4.18545 | 0.331928 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 16.5493 | 1.30023 | ||||||||
\(163\) | 14.8954 | 1.16670 | 0.583350 | − | 0.812221i | \(-0.301742\pi\) | ||||
0.583350 | + | 0.812221i | \(0.301742\pi\) | |||||||
\(164\) | −17.5855 | −1.37320 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.441921 | 0.0342997 | ||||||||
\(167\) | 14.6029 | 1.13001 | 0.565003 | − | 0.825089i | \(-0.308875\pi\) | ||||
0.565003 | + | 0.825089i | \(0.308875\pi\) | |||||||
\(168\) | 1.23296 | 0.0951253 | ||||||||
\(169\) | −12.9299 | −0.994608 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.53531 | −0.499767 | ||||||||
\(172\) | −21.7941 | −1.66179 | ||||||||
\(173\) | −8.40444 | −0.638978 | −0.319489 | − | 0.947590i | \(-0.603511\pi\) | ||||
−0.319489 | + | 0.947590i | \(0.603511\pi\) | |||||||
\(174\) | −4.78843 | −0.363010 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.0978985 | −0.00737937 | ||||||||
\(177\) | −3.31838 | −0.249425 | ||||||||
\(178\) | 38.3045 | 2.87105 | ||||||||
\(179\) | −20.5071 | −1.53277 | −0.766386 | − | 0.642380i | \(-0.777947\pi\) | ||||
−0.766386 | + | 0.642380i | \(0.777947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.525089 | −0.0390296 | −0.0195148 | − | 0.999810i | \(-0.506212\pi\) | ||||
−0.0195148 | + | 0.999810i | \(0.506212\pi\) | |||||||
\(182\) | −0.604357 | −0.0447979 | ||||||||
\(183\) | 6.52794 | 0.482559 | ||||||||
\(184\) | −2.76472 | −0.203818 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.68060 | 0.416522 | ||||||||
\(187\) | −6.00643 | −0.439234 | ||||||||
\(188\) | −22.6196 | −1.64970 | ||||||||
\(189\) | −2.58709 | −0.188183 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1744 | 1.24270 | 0.621350 | − | 0.783533i | \(-0.286585\pi\) | ||||
0.621350 | + | 0.783533i | \(0.286585\pi\) | |||||||
\(192\) | 5.78811 | 0.417721 | ||||||||
\(193\) | 8.54149 | 0.614830 | 0.307415 | − | 0.951576i | \(-0.400536\pi\) | ||||
0.307415 | + | 0.951576i | \(0.400536\pi\) | |||||||
\(194\) | −22.9478 | −1.64755 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.21111 | 0.229365 | ||||||||
\(197\) | 13.8400 | 0.986059 | 0.493029 | − | 0.870013i | \(-0.335889\pi\) | ||||
0.493029 | + | 0.870013i | \(0.335889\pi\) | |||||||
\(198\) | −5.64104 | −0.400892 | ||||||||
\(199\) | 9.76488 | 0.692214 | 0.346107 | − | 0.938195i | \(-0.387503\pi\) | ||||
0.346107 | + | 0.938195i | \(0.387503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.88962 | 0.133284 | ||||||||
\(202\) | −6.38961 | −0.449571 | ||||||||
\(203\) | −4.70357 | −0.330126 | ||||||||
\(204\) | 9.75011 | 0.682644 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.51282 | −0.593117 | ||||||||
\(207\) | 2.80112 | 0.194691 | ||||||||
\(208\) | −0.0293793 | −0.00203709 | ||||||||
\(209\) | 2.05825 | 0.142372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.36816 | 0.438403 | 0.219201 | − | 0.975680i | \(-0.429655\pi\) | ||||
0.219201 | + | 0.975680i | \(0.429655\pi\) | |||||||
\(212\) | −30.1368 | −2.06981 | ||||||||
\(213\) | 4.17182 | 0.285848 | ||||||||
\(214\) | −12.4665 | −0.852195 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.15257 | 0.486671 | ||||||||
\(217\) | 5.57993 | 0.378790 | ||||||||
\(218\) | 25.2079 | 1.70730 | ||||||||
\(219\) | 2.99939 | 0.202680 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.80253 | −0.121251 | ||||||||
\(222\) | −4.78479 | −0.321134 | ||||||||
\(223\) | −11.9209 | −0.798282 | −0.399141 | − | 0.916890i | \(-0.630692\pi\) | ||||
−0.399141 | + | 0.916890i | \(0.630692\pi\) | |||||||
\(224\) | 5.78276 | 0.386377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.1379 | −1.33955 | ||||||||
\(227\) | −13.4339 | −0.891640 | −0.445820 | − | 0.895123i | \(-0.647088\pi\) | ||||
−0.445820 | + | 0.895123i | \(0.647088\pi\) | |||||||
\(228\) | −3.34111 | −0.221270 | ||||||||
\(229\) | −25.5676 | −1.68956 | −0.844779 | − | 0.535116i | \(-0.820268\pi\) | ||||
−0.844779 | + | 0.535116i | \(0.820268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.393426 | 0.0258855 | ||||||||
\(232\) | 13.0040 | 0.853756 | ||||||||
\(233\) | 23.0395 | 1.50937 | 0.754684 | − | 0.656089i | \(-0.227790\pi\) | ||||
0.754684 | + | 0.656089i | \(0.227790\pi\) | |||||||
\(234\) | −1.69287 | −0.110667 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 23.8936 | 1.55534 | ||||||||
\(237\) | −6.51689 | −0.423317 | ||||||||
\(238\) | 15.5424 | 1.00747 | ||||||||
\(239\) | −14.3124 | −0.925791 | −0.462896 | − | 0.886413i | \(-0.653190\pi\) | ||||
−0.462896 | + | 0.886413i | \(0.653190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.8646 | −1.53725 | −0.768626 | − | 0.639698i | \(-0.779059\pi\) | ||||
−0.768626 | + | 0.639698i | \(0.779059\pi\) | |||||||
\(242\) | −23.3340 | −1.49997 | ||||||||
\(243\) | −10.9943 | −0.705287 | ||||||||
\(244\) | −47.0037 | −3.00910 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.57524 | 0.355465 | ||||||||
\(247\) | 0.617679 | 0.0393020 | ||||||||
\(248\) | −15.4269 | −0.979610 | ||||||||
\(249\) | −0.0863335 | −0.00547116 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1289 | 1.33364 | 0.666821 | − | 0.745218i | \(-0.267655\pi\) | ||||
0.666821 | + | 0.745218i | \(0.267655\pi\) | |||||||
\(252\) | 8.99470 | 0.566613 | ||||||||
\(253\) | −0.882192 | −0.0554629 | ||||||||
\(254\) | 20.6878 | 1.29807 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.2750 | −0.954687 | ||||||||
\(257\) | 7.09291 | 0.442443 | 0.221222 | − | 0.975224i | \(-0.428996\pi\) | ||||
0.221222 | + | 0.975224i | \(0.428996\pi\) | |||||||
\(258\) | 6.90954 | 0.430169 | ||||||||
\(259\) | −4.70000 | −0.292044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1752 | −0.815527 | ||||||||
\(262\) | 13.2516 | 0.818688 | ||||||||
\(263\) | 7.64291 | 0.471282 | 0.235641 | − | 0.971840i | \(-0.424281\pi\) | ||||
0.235641 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(264\) | −1.08771 | −0.0669440 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.32599 | −0.326557 | ||||||||
\(267\) | −7.48316 | −0.457962 | ||||||||
\(268\) | −13.6060 | −0.831119 | ||||||||
\(269\) | −15.4396 | −0.941367 | −0.470684 | − | 0.882302i | \(-0.655993\pi\) | ||||
−0.470684 | + | 0.882302i | \(0.655993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8328 | −1.26550 | −0.632752 | − | 0.774355i | \(-0.718075\pi\) | ||||
−0.632752 | + | 0.774355i | \(0.718075\pi\) | |||||||
\(272\) | 0.755555 | 0.0458123 | ||||||||
\(273\) | 0.118067 | 0.00714574 | ||||||||
\(274\) | 18.6254 | 1.12520 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.43204 | 0.0861988 | ||||||||
\(277\) | −16.3374 | −0.981618 | −0.490809 | − | 0.871267i | \(-0.663299\pi\) | ||||
−0.490809 | + | 0.871267i | \(0.663299\pi\) | |||||||
\(278\) | −28.8560 | −1.73067 | ||||||||
\(279\) | 15.6300 | 0.935745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.89511 | 0.351673 | 0.175836 | − | 0.984419i | \(-0.443737\pi\) | ||||
0.175836 | + | 0.984419i | \(0.443737\pi\) | |||||||
\(282\) | 7.17125 | 0.427042 | ||||||||
\(283\) | 6.07866 | 0.361339 | 0.180669 | − | 0.983544i | \(-0.442174\pi\) | ||||
0.180669 | + | 0.983544i | \(0.442174\pi\) | |||||||
\(284\) | −30.0387 | −1.78247 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.533159 | 0.0315263 | ||||||||
\(287\) | 5.47644 | 0.323264 | ||||||||
\(288\) | 16.1982 | 0.954487 | ||||||||
\(289\) | 29.3561 | 1.72683 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.48307 | 0.262802 | ||||||||
\(292\) | −21.5968 | −1.26386 | ||||||||
\(293\) | −0.260282 | −0.0152058 | −0.00760292 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760292 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(294\) | −1.01804 | −0.0593734 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.9942 | 0.755270 | ||||||||
\(297\) | 2.28231 | 0.132433 | ||||||||
\(298\) | 35.0235 | 2.02886 | ||||||||
\(299\) | −0.264745 | −0.0153106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.78709 | 0.391202 | ||||||||
\(302\) | 34.3300 | 1.97547 | ||||||||
\(303\) | 1.24827 | 0.0717113 | ||||||||
\(304\) | −0.258909 | −0.0148495 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 43.5361 | 2.48880 | ||||||||
\(307\) | −18.1195 | −1.03413 | −0.517067 | − | 0.855945i | \(-0.672976\pi\) | ||||
−0.517067 | + | 0.855945i | \(0.672976\pi\) | |||||||
\(308\) | −2.83282 | −0.161415 | ||||||||
\(309\) | 1.66306 | 0.0946083 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.44175 | 0.308574 | 0.154287 | − | 0.988026i | \(-0.450692\pi\) | ||||
0.154287 | + | 0.988026i | \(0.450692\pi\) | |||||||
\(312\) | −0.326422 | −0.0184800 | ||||||||
\(313\) | 4.93195 | 0.278770 | 0.139385 | − | 0.990238i | \(-0.455487\pi\) | ||||
0.139385 | + | 0.990238i | \(0.455487\pi\) | |||||||
\(314\) | 10.0224 | 0.565597 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 46.9241 | 2.63969 | ||||||||
\(317\) | 16.0753 | 0.902880 | 0.451440 | − | 0.892302i | \(-0.350911\pi\) | ||||
0.451440 | + | 0.892302i | \(0.350911\pi\) | |||||||
\(318\) | 9.55449 | 0.535789 | ||||||||
\(319\) | 4.14945 | 0.232325 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.43546 | 0.135934 | ||||||||
\(322\) | 2.28279 | 0.127215 | ||||||||
\(323\) | −15.8850 | −0.883867 | ||||||||
\(324\) | 23.2793 | 1.29329 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.0031 | 1.88326 | ||||||||
\(327\) | −4.92461 | −0.272331 | ||||||||
\(328\) | −15.1408 | −0.836011 | ||||||||
\(329\) | 7.04416 | 0.388357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9626 | 1.04228 | 0.521138 | − | 0.853472i | \(-0.325508\pi\) | ||||
0.521138 | + | 0.853472i | \(0.325508\pi\) | |||||||
\(332\) | 0.621634 | 0.0341166 | ||||||||
\(333\) | −13.1652 | −0.721451 | ||||||||
\(334\) | 33.3353 | 1.82403 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0494895 | −0.00269987 | ||||||||
\(337\) | 14.0390 | 0.764754 | 0.382377 | − | 0.924006i | \(-0.375106\pi\) | ||||
0.382377 | + | 0.924006i | \(0.375106\pi\) | |||||||
\(338\) | −29.5162 | −1.60547 | ||||||||
\(339\) | 3.93413 | 0.213673 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.92257 | −0.266572 | ||||||||
\(342\) | −14.9187 | −0.806711 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −18.7644 | −1.01171 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.1855 | −1.03142 | ||||||||
\(347\) | 5.86904 | 0.315067 | 0.157533 | − | 0.987514i | \(-0.449646\pi\) | ||||
0.157533 | + | 0.987514i | \(0.449646\pi\) | |||||||
\(348\) | −6.73571 | −0.361072 | ||||||||
\(349\) | −27.9408 | −1.49564 | −0.747818 | − | 0.663904i | \(-0.768898\pi\) | ||||
−0.747818 | + | 0.663904i | \(0.768898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.684920 | 0.0365583 | ||||||||
\(352\) | −5.10150 | −0.271911 | ||||||||
\(353\) | −6.94530 | −0.369661 | −0.184830 | − | 0.982770i | \(-0.559174\pi\) | ||||
−0.184830 | + | 0.982770i | \(0.559174\pi\) | |||||||
\(354\) | −7.57515 | −0.402615 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 53.8816 | 2.85572 | ||||||||
\(357\) | −3.03636 | −0.160701 | ||||||||
\(358\) | −46.8133 | −2.47416 | ||||||||
\(359\) | −19.8558 | −1.04795 | −0.523974 | − | 0.851734i | \(-0.675551\pi\) | ||||
−0.523974 | + | 0.851734i | \(0.675551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5566 | −0.713506 | ||||||||
\(362\) | −1.19867 | −0.0630005 | ||||||||
\(363\) | 4.55853 | 0.239261 | ||||||||
\(364\) | −0.850127 | −0.0445588 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.9019 | 0.778934 | ||||||||
\(367\) | −23.9055 | −1.24786 | −0.623928 | − | 0.781481i | \(-0.714464\pi\) | ||||
−0.623928 | + | 0.781481i | \(0.714464\pi\) | |||||||
\(368\) | 0.110972 | 0.00578481 | ||||||||
\(369\) | 15.3401 | 0.798576 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.38516 | 0.487253 | ||||||||
\(372\) | 7.99070 | 0.414298 | ||||||||
\(373\) | 3.02683 | 0.156723 | 0.0783617 | − | 0.996925i | \(-0.475031\pi\) | ||||
0.0783617 | + | 0.996925i | \(0.475031\pi\) | |||||||
\(374\) | −13.7114 | −0.709000 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.4751 | −1.00435 | ||||||||
\(377\) | 1.24525 | 0.0641335 | ||||||||
\(378\) | −5.90578 | −0.303760 | ||||||||
\(379\) | 7.30508 | 0.375237 | 0.187618 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187618 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.04156 | −0.207055 | ||||||||
\(382\) | 39.2056 | 2.00593 | ||||||||
\(383\) | 16.9449 | 0.865844 | 0.432922 | − | 0.901431i | \(-0.357482\pi\) | ||||
0.432922 | + | 0.901431i | \(0.357482\pi\) | |||||||
\(384\) | 8.05521 | 0.411066 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.4984 | 0.992442 | ||||||||
\(387\) | 19.0114 | 0.966405 | ||||||||
\(388\) | −32.2798 | −1.63876 | ||||||||
\(389\) | −7.80496 | −0.395727 | −0.197864 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197864 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.80853 | 0.344322 | ||||||||
\(392\) | 2.76472 | 0.139639 | ||||||||
\(393\) | −2.58883 | −0.130589 | ||||||||
\(394\) | 31.5938 | 1.59167 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.93506 | −0.398752 | ||||||||
\(397\) | 16.1944 | 0.812773 | 0.406386 | − | 0.913701i | \(-0.366789\pi\) | ||||
0.406386 | + | 0.913701i | \(0.366789\pi\) | |||||||
\(398\) | 22.2911 | 1.11735 | ||||||||
\(399\) | 1.04048 | 0.0520893 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.8572 | −1.04156 | −0.520779 | − | 0.853691i | \(-0.674358\pi\) | ||||
−0.520779 | + | 0.853691i | \(0.674358\pi\) | |||||||
\(402\) | 4.31360 | 0.215143 | ||||||||
\(403\) | −1.47726 | −0.0735875 | ||||||||
\(404\) | −8.98803 | −0.447171 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.7372 | −0.532880 | ||||||||
\(407\) | 4.14630 | 0.205525 | ||||||||
\(408\) | 8.39468 | 0.415599 | ||||||||
\(409\) | 11.4886 | 0.568075 | 0.284038 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284038 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.63866 | −0.179482 | ||||||||
\(412\) | −11.9747 | −0.589950 | ||||||||
\(413\) | −7.44091 | −0.366143 | ||||||||
\(414\) | 6.39435 | 0.314265 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.53096 | −0.0750614 | ||||||||
\(417\) | 5.63730 | 0.276060 | ||||||||
\(418\) | 4.69854 | 0.229813 | ||||||||
\(419\) | 13.4385 | 0.656513 | 0.328257 | − | 0.944589i | \(-0.393539\pi\) | ||||
0.328257 | + | 0.944589i | \(0.393539\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0763 | 0.686039 | 0.343019 | − | 0.939328i | \(-0.388550\pi\) | ||||
0.343019 | + | 0.939328i | \(0.388550\pi\) | |||||||
\(422\) | 14.5372 | 0.707658 | ||||||||
\(423\) | 19.7315 | 0.959379 | ||||||||
\(424\) | −25.9473 | −1.26011 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.52336 | 0.461409 | ||||||||
\(427\) | 14.6378 | 0.708373 | ||||||||
\(428\) | −17.5362 | −0.847646 | ||||||||
\(429\) | −0.104158 | −0.00502878 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.6543 | −0.994884 | −0.497442 | − | 0.867497i | \(-0.665727\pi\) | ||||
−0.497442 | + | 0.867497i | \(0.665727\pi\) | |||||||
\(432\) | −0.287094 | −0.0138128 | ||||||||
\(433\) | 37.2302 | 1.78917 | 0.894584 | − | 0.446900i | \(-0.147472\pi\) | ||||
0.894584 | + | 0.446900i | \(0.147472\pi\) | |||||||
\(434\) | 12.7378 | 0.611433 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35.4591 | 1.69818 | ||||||||
\(437\) | −2.33311 | −0.111608 | ||||||||
\(438\) | 6.84697 | 0.327161 | ||||||||
\(439\) | 10.6210 | 0.506914 | 0.253457 | − | 0.967347i | \(-0.418432\pi\) | ||||
0.253457 | + | 0.967347i | \(0.418432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80112 | −0.133386 | ||||||||
\(442\) | −4.11478 | −0.195720 | ||||||||
\(443\) | 3.29850 | 0.156717 | 0.0783583 | − | 0.996925i | \(-0.475032\pi\) | ||||
0.0783583 | + | 0.996925i | \(0.475032\pi\) | |||||||
\(444\) | −6.73060 | −0.319420 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −27.2129 | −1.28857 | ||||||||
\(447\) | −6.84218 | −0.323624 | ||||||||
\(448\) | 12.9789 | 0.613193 | ||||||||
\(449\) | 27.8179 | 1.31281 | 0.656405 | − | 0.754409i | \(-0.272076\pi\) | ||||
0.656405 | + | 0.754409i | \(0.272076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.83127 | −0.227496 | ||||||||
\(452\) | −28.3272 | −1.33240 | ||||||||
\(453\) | −6.70670 | −0.315108 | ||||||||
\(454\) | −30.6667 | −1.43926 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.87664 | −0.134711 | ||||||||
\(457\) | 31.9503 | 1.49457 | 0.747285 | − | 0.664503i | \(-0.231357\pi\) | ||||
0.747285 | + | 0.664503i | \(0.231357\pi\) | |||||||
\(458\) | −58.3655 | −2.72724 | ||||||||
\(459\) | −17.6143 | −0.822165 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.2902 | −1.27103 | −0.635515 | − | 0.772089i | \(-0.719212\pi\) | ||||
−0.635515 | + | 0.772089i | \(0.719212\pi\) | |||||||
\(462\) | 0.898108 | 0.0417838 | ||||||||
\(463\) | 22.3258 | 1.03757 | 0.518784 | − | 0.854905i | \(-0.326385\pi\) | ||||
0.518784 | + | 0.854905i | \(0.326385\pi\) | |||||||
\(464\) | −0.521963 | −0.0242315 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 52.5943 | 2.43638 | ||||||||
\(467\) | −1.52823 | −0.0707180 | −0.0353590 | − | 0.999375i | \(-0.511257\pi\) | ||||
−0.0353590 | + | 0.999375i | \(0.511257\pi\) | |||||||
\(468\) | −2.38130 | −0.110076 | ||||||||
\(469\) | 4.23716 | 0.195654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.95797 | −0.0902186 | ||||||||
\(472\) | 20.5720 | 0.946903 | ||||||||
\(473\) | −5.98752 | −0.275306 | ||||||||
\(474\) | −14.8767 | −0.683308 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.8630 | 1.00209 | ||||||||
\(477\) | 26.2889 | 1.20369 | ||||||||
\(478\) | −32.6721 | −1.49439 | ||||||||
\(479\) | 43.2948 | 1.97819 | 0.989094 | − | 0.147284i | \(-0.0470533\pi\) | ||||
0.989094 | + | 0.147284i | \(0.0470533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24430 | 0.0567353 | ||||||||
\(482\) | −54.4777 | −2.48139 | ||||||||
\(483\) | −0.445964 | −0.0202921 | ||||||||
\(484\) | −32.8232 | −1.49196 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −25.0977 | −1.13846 | ||||||||
\(487\) | −7.11107 | −0.322233 | −0.161117 | − | 0.986935i | \(-0.551510\pi\) | ||||
−0.161117 | + | 0.986935i | \(0.551510\pi\) | |||||||
\(488\) | −40.4694 | −1.83196 | ||||||||
\(489\) | −6.64282 | −0.300399 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2647 | −1.09505 | −0.547526 | − | 0.836789i | \(-0.684430\pi\) | ||||
−0.547526 | + | 0.836789i | \(0.684430\pi\) | |||||||
\(492\) | 7.84250 | 0.353567 | ||||||||
\(493\) | −32.0244 | −1.44231 | ||||||||
\(494\) | 1.41003 | 0.0634402 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.619215 | 0.0278036 | ||||||||
\(497\) | 9.35459 | 0.419611 | ||||||||
\(498\) | −0.197081 | −0.00883141 | ||||||||
\(499\) | −5.46235 | −0.244529 | −0.122264 | − | 0.992498i | \(-0.539016\pi\) | ||||
−0.122264 | + | 0.992498i | \(0.539016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.51237 | −0.290951 | ||||||||
\(502\) | 48.2327 | 2.15273 | ||||||||
\(503\) | −26.9673 | −1.20241 | −0.601206 | − | 0.799094i | \(-0.705313\pi\) | ||||
−0.601206 | + | 0.799094i | \(0.705313\pi\) | |||||||
\(504\) | 7.74429 | 0.344958 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.01386 | −0.0895268 | ||||||||
\(507\) | 5.76628 | 0.256089 | ||||||||
\(508\) | 29.1008 | 1.29114 | ||||||||
\(509\) | −37.3594 | −1.65593 | −0.827964 | − | 0.560782i | \(-0.810501\pi\) | ||||
−0.827964 | + | 0.560782i | \(0.810501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.72564 | 0.297525 | ||||||||
\(512\) | 1.25533 | 0.0554785 | ||||||||
\(513\) | 6.03596 | 0.266494 | ||||||||
\(514\) | 16.1916 | 0.714181 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.71941 | 0.427873 | ||||||||
\(517\) | −6.21430 | −0.273305 | ||||||||
\(518\) | −10.7291 | −0.471409 | ||||||||
\(519\) | 3.74808 | 0.164522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.810893 | 0.0355259 | 0.0177629 | − | 0.999842i | \(-0.494346\pi\) | ||||
0.0177629 | + | 0.999842i | \(0.494346\pi\) | |||||||
\(522\) | −30.0762 | −1.31640 | ||||||||
\(523\) | −6.06391 | −0.265156 | −0.132578 | − | 0.991173i | \(-0.542326\pi\) | ||||
−0.132578 | + | 0.991173i | \(0.542326\pi\) | |||||||
\(524\) | 18.6406 | 0.814318 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4471 | 0.760731 | ||||||||
\(527\) | 37.9911 | 1.65492 | ||||||||
\(528\) | 0.0436592 | 0.00190002 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.8429 | −0.904503 | ||||||||
\(532\) | −7.49188 | −0.324814 | ||||||||
\(533\) | −1.44986 | −0.0628005 | ||||||||
\(534\) | −17.0824 | −0.739230 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.7145 | −0.505991 | ||||||||
\(537\) | 9.14543 | 0.394654 | ||||||||
\(538\) | −35.2452 | −1.51953 | ||||||||
\(539\) | 0.882192 | 0.0379987 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.4476 | −1.65299 | −0.826495 | − | 0.562944i | \(-0.809669\pi\) | ||||
−0.826495 | + | 0.562944i | \(0.809669\pi\) | |||||||
\(542\) | −47.5569 | −2.04274 | ||||||||
\(543\) | 0.234171 | 0.0100492 | ||||||||
\(544\) | 39.3721 | 1.68806 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.269522 | 0.0115345 | ||||||||
\(547\) | −22.1779 | −0.948257 | −0.474128 | − | 0.880456i | \(-0.657237\pi\) | ||||
−0.474128 | + | 0.880456i | \(0.657237\pi\) | |||||||
\(548\) | 26.1997 | 1.11920 | ||||||||
\(549\) | 41.0022 | 1.74993 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9739 | 0.467505 | ||||||||
\(552\) | 1.23296 | 0.0524785 | ||||||||
\(553\) | −14.6130 | −0.621409 | ||||||||
\(554\) | −37.2947 | −1.58450 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.5907 | −1.72143 | ||||||||
\(557\) | 41.7266 | 1.76801 | 0.884007 | − | 0.467473i | \(-0.154836\pi\) | ||||
0.884007 | + | 0.467473i | \(0.154836\pi\) | |||||||
\(558\) | 35.6800 | 1.51046 | ||||||||
\(559\) | −1.79685 | −0.0759987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.67866 | 0.113093 | ||||||||
\(562\) | 13.4573 | 0.567661 | ||||||||
\(563\) | 34.9538 | 1.47313 | 0.736564 | − | 0.676368i | \(-0.236447\pi\) | ||||
0.736564 | + | 0.676368i | \(0.236447\pi\) | |||||||
\(564\) | 10.0875 | 0.424762 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.8763 | 0.583263 | ||||||||
\(567\) | −7.24960 | −0.304454 | ||||||||
\(568\) | −25.8628 | −1.08518 | ||||||||
\(569\) | −43.3891 | −1.81897 | −0.909483 | − | 0.415742i | \(-0.863522\pi\) | ||||
−0.909483 | + | 0.415742i | \(0.863522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.5626 | −1.65564 | −0.827822 | − | 0.560990i | \(-0.810421\pi\) | ||||
−0.827822 | + | 0.560990i | \(0.810421\pi\) | |||||||
\(572\) | 0.749976 | 0.0313581 | ||||||||
\(573\) | −7.65919 | −0.319967 | ||||||||
\(574\) | 12.5015 | 0.521805 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 36.3553 | 1.51480 | ||||||||
\(577\) | −39.3010 | −1.63612 | −0.818061 | − | 0.575132i | \(-0.804951\pi\) | ||||
−0.818061 | + | 0.575132i | \(0.804951\pi\) | |||||||
\(578\) | 67.0138 | 2.78741 | ||||||||
\(579\) | −3.80920 | −0.158305 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.193588 | −0.00803140 | ||||||||
\(582\) | 10.2339 | 0.424208 | ||||||||
\(583\) | −8.27952 | −0.342903 | ||||||||
\(584\) | −18.5945 | −0.769445 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.594169 | −0.0245449 | ||||||||
\(587\) | −17.0358 | −0.703143 | −0.351572 | − | 0.936161i | \(-0.614353\pi\) | ||||
−0.351572 | + | 0.936161i | \(0.614353\pi\) | |||||||
\(588\) | −1.43204 | −0.0590564 | ||||||||
\(589\) | −13.0186 | −0.536421 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.17215 | −0.253888 | ||||||||
\(592\) | −0.521567 | −0.0214363 | ||||||||
\(593\) | −23.9734 | −0.984470 | −0.492235 | − | 0.870462i | \(-0.663820\pi\) | ||||
−0.492235 | + | 0.870462i | \(0.663820\pi\) | |||||||
\(594\) | 5.21003 | 0.213770 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 49.2663 | 2.01803 | ||||||||
\(597\) | −4.35479 | −0.178230 | ||||||||
\(598\) | −0.604357 | −0.0247140 | ||||||||
\(599\) | 13.8754 | 0.566934 | 0.283467 | − | 0.958982i | \(-0.408515\pi\) | ||||
0.283467 | + | 0.958982i | \(0.408515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.76901 | 0.235323 | 0.117661 | − | 0.993054i | \(-0.462460\pi\) | ||||
0.117661 | + | 0.993054i | \(0.462460\pi\) | |||||||
\(602\) | 15.4935 | 0.631467 | ||||||||
\(603\) | 11.8688 | 0.483334 | ||||||||
\(604\) | 48.2908 | 1.96492 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.84954 | 0.115754 | ||||||||
\(607\) | 5.73749 | 0.232878 | 0.116439 | − | 0.993198i | \(-0.462852\pi\) | ||||
0.116439 | + | 0.993198i | \(0.462852\pi\) | |||||||
\(608\) | −13.4918 | −0.547165 | ||||||||
\(609\) | 2.09762 | 0.0850000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.86491 | −0.0754461 | ||||||||
\(612\) | 61.2407 | 2.47551 | ||||||||
\(613\) | 44.2651 | 1.78785 | 0.893926 | − | 0.448214i | \(-0.147940\pi\) | ||||
0.893926 | + | 0.448214i | \(0.147940\pi\) | |||||||
\(614\) | −41.3629 | −1.66927 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.43901 | −0.0982705 | ||||||||
\(617\) | 16.9073 | 0.680663 | 0.340332 | − | 0.940305i | \(-0.389461\pi\) | ||||
0.340332 | + | 0.940305i | \(0.389461\pi\) | |||||||
\(618\) | 3.79642 | 0.152714 | ||||||||
\(619\) | −4.93954 | −0.198537 | −0.0992685 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992685 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58709 | −0.103816 | ||||||||
\(622\) | 12.4224 | 0.498091 | ||||||||
\(623\) | −16.7797 | −0.672265 | ||||||||
\(624\) | 0.0131021 | 0.000524504 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.2586 | 0.449984 | ||||||||
\(627\) | −0.917906 | −0.0366576 | ||||||||
\(628\) | 14.0982 | 0.562578 | ||||||||
\(629\) | −32.0001 | −1.27593 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.96371 | 0.0781742 | 0.0390871 | − | 0.999236i | \(-0.487555\pi\) | ||||
0.0390871 | + | 0.999236i | \(0.487555\pi\) | |||||||
\(632\) | 40.4009 | 1.60706 | ||||||||
\(633\) | −2.83997 | −0.112879 | ||||||||
\(634\) | 36.6965 | 1.45740 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.4400 | 0.532929 | ||||||||
\(637\) | 0.264745 | 0.0104896 | ||||||||
\(638\) | 9.47231 | 0.375012 | ||||||||
\(639\) | 26.2033 | 1.03659 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.55011 | 0.337709 | 0.168855 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168855 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(642\) | 5.55963 | 0.219421 | ||||||||
\(643\) | −17.1715 | −0.677176 | −0.338588 | − | 0.940935i | \(-0.609949\pi\) | ||||
−0.338588 | + | 0.940935i | \(0.609949\pi\) | |||||||
\(644\) | 3.21111 | 0.126536 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.2622 | −1.42672 | ||||||||
\(647\) | −15.7971 | −0.621050 | −0.310525 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310525 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(648\) | 20.0431 | 0.787367 | ||||||||
\(649\) | 6.56431 | 0.257672 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.48845 | −0.0975300 | ||||||||
\(652\) | 47.8309 | 1.87320 | ||||||||
\(653\) | 4.99317 | 0.195398 | 0.0976988 | − | 0.995216i | \(-0.468852\pi\) | ||||
0.0976988 | + | 0.995216i | \(0.468852\pi\) | |||||||
\(654\) | −11.2418 | −0.439590 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.607731 | 0.0237279 | ||||||||
\(657\) | 18.8393 | 0.734990 | ||||||||
\(658\) | 16.0803 | 0.626876 | ||||||||
\(659\) | −6.35794 | −0.247670 | −0.123835 | − | 0.992303i | \(-0.539519\pi\) | ||||
−0.123835 | + | 0.992303i | \(0.539519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.5733 | 1.57812 | 0.789059 | − | 0.614318i | \(-0.210569\pi\) | ||||
0.789059 | + | 0.614318i | \(0.210569\pi\) | |||||||
\(662\) | 43.2875 | 1.68242 | ||||||||
\(663\) | 0.803863 | 0.0312194 | ||||||||
\(664\) | 0.535217 | 0.0207704 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −30.0534 | −1.16455 | ||||||||
\(667\) | −4.70357 | −0.182123 | ||||||||
\(668\) | 46.8916 | 1.81429 | ||||||||
\(669\) | 5.31629 | 0.205540 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9134 | −0.498515 | ||||||||
\(672\) | −2.57890 | −0.0994834 | ||||||||
\(673\) | −13.2627 | −0.511239 | −0.255619 | − | 0.966777i | \(-0.582279\pi\) | ||||
−0.255619 | + | 0.966777i | \(0.582279\pi\) | |||||||
\(674\) | 32.0481 | 1.23445 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −41.5194 | −1.59690 | ||||||||
\(677\) | −23.2209 | −0.892450 | −0.446225 | − | 0.894921i | \(-0.647232\pi\) | ||||
−0.446225 | + | 0.894921i | \(0.647232\pi\) | |||||||
\(678\) | 8.98078 | 0.344905 | ||||||||
\(679\) | 10.0525 | 0.385780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.99104 | 0.229577 | ||||||||
\(682\) | −11.2372 | −0.430294 | ||||||||
\(683\) | −42.1710 | −1.61363 | −0.806814 | − | 0.590805i | \(-0.798810\pi\) | ||||
−0.806814 | + | 0.590805i | \(0.798810\pi\) | |||||||
\(684\) | −20.9856 | −0.802405 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.28279 | −0.0871572 | ||||||||
\(687\) | 11.4023 | 0.435023 | ||||||||
\(688\) | 0.753176 | 0.0287146 | ||||||||
\(689\) | −2.48468 | −0.0946587 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.6905 | 1.35773 | 0.678865 | − | 0.734263i | \(-0.262472\pi\) | ||||
0.678865 | + | 0.734263i | \(0.262472\pi\) | |||||||
\(692\) | −26.9876 | −1.02592 | ||||||||
\(693\) | 2.47112 | 0.0938702 | ||||||||
\(694\) | 13.3978 | 0.508573 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.79933 | −0.219823 | ||||||||
\(697\) | 37.2865 | 1.41233 | ||||||||
\(698\) | −63.7829 | −2.41422 | ||||||||
\(699\) | −10.2748 | −0.388628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.10394 | 0.0794646 | 0.0397323 | − | 0.999210i | \(-0.487349\pi\) | ||||
0.0397323 | + | 0.999210i | \(0.487349\pi\) | |||||||
\(702\) | 1.56353 | 0.0590115 | ||||||||
\(703\) | 10.9656 | 0.413575 | ||||||||
\(704\) | −11.4498 | −0.431532 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.8546 | −0.596697 | ||||||||
\(707\) | 2.79904 | 0.105269 | ||||||||
\(708\) | −10.6557 | −0.400466 | ||||||||
\(709\) | −0.895305 | −0.0336239 | −0.0168119 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168119 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.9328 | −1.53510 | ||||||||
\(712\) | 46.3912 | 1.73858 | ||||||||
\(713\) | 5.57993 | 0.208970 | ||||||||
\(714\) | −6.93137 | −0.259400 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −65.8506 | −2.46095 | ||||||||
\(717\) | 6.38281 | 0.238371 | ||||||||
\(718\) | −45.3265 | −1.69157 | ||||||||
\(719\) | −5.44754 | −0.203159 | −0.101579 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101579 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.72914 | 0.138880 | ||||||||
\(722\) | −30.9468 | −1.15172 | ||||||||
\(723\) | 10.6427 | 0.395808 | ||||||||
\(724\) | −1.68612 | −0.0626642 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.4062 | 0.386209 | ||||||||
\(727\) | −23.7030 | −0.879096 | −0.439548 | − | 0.898219i | \(-0.644861\pi\) | ||||
−0.439548 | + | 0.898219i | \(0.644861\pi\) | |||||||
\(728\) | −0.731945 | −0.0271277 | ||||||||
\(729\) | −16.8457 | −0.623915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.2101 | 1.70914 | ||||||||
\(732\) | 20.9620 | 0.774776 | ||||||||
\(733\) | 27.9487 | 1.03231 | 0.516155 | − | 0.856495i | \(-0.327363\pi\) | ||||
0.516155 | + | 0.856495i | \(0.327363\pi\) | |||||||
\(734\) | −54.5712 | −2.01426 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.78276 | 0.213155 | ||||||||
\(737\) | −3.73799 | −0.137691 | ||||||||
\(738\) | 35.0183 | 1.28904 | ||||||||
\(739\) | −45.9992 | −1.69211 | −0.846054 | − | 0.533098i | \(-0.821028\pi\) | ||||
−0.846054 | + | 0.533098i | \(0.821028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.275463 | −0.0101194 | ||||||||
\(742\) | 21.4243 | 0.786512 | ||||||||
\(743\) | −3.58745 | −0.131611 | −0.0658053 | − | 0.997832i | \(-0.520962\pi\) | ||||
−0.0658053 | + | 0.997832i | \(0.520962\pi\) | |||||||
\(744\) | 6.87986 | 0.252228 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.90961 | 0.252979 | ||||||||
\(747\) | −0.542263 | −0.0198404 | ||||||||
\(748\) | −19.2873 | −0.705215 | ||||||||
\(749\) | 5.46111 | 0.199544 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.5746 | −1.04270 | −0.521351 | − | 0.853342i | \(-0.674572\pi\) | ||||
−0.521351 | + | 0.853342i | \(0.674572\pi\) | |||||||
\(752\) | 0.781703 | 0.0285058 | ||||||||
\(753\) | −9.42272 | −0.343383 | ||||||||
\(754\) | 2.84263 | 0.103523 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.30745 | −0.302139 | ||||||||
\(757\) | −9.49105 | −0.344958 | −0.172479 | − | 0.985013i | \(-0.555178\pi\) | ||||
−0.172479 | + | 0.985013i | \(0.555178\pi\) | |||||||
\(758\) | 16.6759 | 0.605698 | ||||||||
\(759\) | 0.393426 | 0.0142805 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.8526 | 0.538405 | 0.269202 | − | 0.963084i | \(-0.413240\pi\) | ||||
0.269202 | + | 0.963084i | \(0.413240\pi\) | |||||||
\(762\) | −9.22602 | −0.334223 | ||||||||
\(763\) | −11.0426 | −0.399769 | ||||||||
\(764\) | 55.1491 | 1.99523 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.6816 | 1.39762 | ||||||||
\(767\) | 1.96995 | 0.0711306 | ||||||||
\(768\) | 6.81210 | 0.245811 | ||||||||
\(769\) | −9.25706 | −0.333818 | −0.166909 | − | 0.985972i | \(-0.553379\pi\) | ||||
−0.166909 | + | 0.985972i | \(0.553379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.16318 | −0.113919 | ||||||||
\(772\) | 27.4277 | 0.987144 | ||||||||
\(773\) | 6.93020 | 0.249262 | 0.124631 | − | 0.992203i | \(-0.460225\pi\) | ||||
0.124631 | + | 0.992203i | \(0.460225\pi\) | |||||||
\(774\) | 43.3990 | 1.55995 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27.7924 | −0.997688 | ||||||||
\(777\) | 2.09603 | 0.0751947 | ||||||||
\(778\) | −17.8171 | −0.638773 | ||||||||
\(779\) | −12.7771 | −0.457788 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.25255 | −0.295299 | ||||||||
\(782\) | 15.5424 | 0.555796 | ||||||||
\(783\) | 12.1686 | 0.434869 | ||||||||
\(784\) | −0.110972 | −0.00396328 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.90975 | −0.210794 | ||||||||
\(787\) | −35.6582 | −1.27108 | −0.635539 | − | 0.772069i | \(-0.719222\pi\) | ||||
−0.635539 | + | 0.772069i | \(0.719222\pi\) | |||||||
\(788\) | 44.4418 | 1.58317 | ||||||||
\(789\) | −3.40847 | −0.121345 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.82162 | 0.313661 | ||||||||
\(792\) | −6.83195 | −0.242763 | ||||||||
\(793\) | −3.87529 | −0.137616 | ||||||||
\(794\) | 36.9683 | 1.31196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.3562 | 1.11139 | ||||||||
\(797\) | −12.0573 | −0.427092 | −0.213546 | − | 0.976933i | \(-0.568501\pi\) | ||||
−0.213546 | + | 0.976933i | \(0.568501\pi\) | |||||||
\(798\) | 2.37520 | 0.0840812 | ||||||||
\(799\) | 47.9604 | 1.69672 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.0019 | −1.66073 | ||||||||
\(802\) | −47.6125 | −1.68126 | ||||||||
\(803\) | −5.93330 | −0.209382 | ||||||||
\(804\) | 6.06779 | 0.213994 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.37227 | −0.118783 | ||||||||
\(807\) | 6.88550 | 0.242381 | ||||||||
\(808\) | −7.73854 | −0.272241 | ||||||||
\(809\) | −19.3977 | −0.681988 | −0.340994 | − | 0.940065i | \(-0.610764\pi\) | ||||
−0.340994 | + | 0.940065i | \(0.610764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.5308 | −1.24765 | −0.623827 | − | 0.781562i | \(-0.714423\pi\) | ||||
−0.623827 | + | 0.781562i | \(0.714423\pi\) | |||||||
\(812\) | −15.1037 | −0.530036 | ||||||||
\(813\) | 9.29069 | 0.325839 | ||||||||
\(814\) | 9.46512 | 0.331752 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.336951 | −0.0117956 | ||||||||
\(817\) | −15.8350 | −0.553997 | ||||||||
\(818\) | 26.2260 | 0.916972 | ||||||||
\(819\) | 0.741582 | 0.0259130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.0925 | 1.18984 | 0.594918 | − | 0.803786i | \(-0.297184\pi\) | ||||
0.594918 | + | 0.803786i | \(0.297184\pi\) | |||||||
\(822\) | −8.30628 | −0.289715 | ||||||||
\(823\) | −52.9679 | −1.84634 | −0.923172 | − | 0.384386i | \(-0.874413\pi\) | ||||
−0.923172 | + | 0.384386i | \(0.874413\pi\) | |||||||
\(824\) | −10.3100 | −0.359166 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.9860 | −0.591019 | ||||||||
\(827\) | −15.6761 | −0.545110 | −0.272555 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272555 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(828\) | 8.99470 | 0.312588 | ||||||||
\(829\) | 54.4072 | 1.88964 | 0.944820 | − | 0.327590i | \(-0.106237\pi\) | ||||
0.944820 | + | 0.327590i | \(0.106237\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.28589 | 0.252745 | ||||||||
\(832\) | −3.43609 | −0.119125 | ||||||||
\(833\) | −6.80853 | −0.235902 | ||||||||
\(834\) | 12.8688 | 0.445608 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.60927 | 0.228587 | ||||||||
\(837\) | −14.4358 | −0.498974 | ||||||||
\(838\) | 30.6772 | 1.05973 | ||||||||
\(839\) | −28.8881 | −0.997329 | −0.498664 | − | 0.866795i | \(-0.666176\pi\) | ||||
−0.498664 | + | 0.866795i | \(0.666176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.87646 | −0.237119 | ||||||||
\(842\) | 32.1333 | 1.10739 | ||||||||
\(843\) | −2.62901 | −0.0905478 | ||||||||
\(844\) | 20.4489 | 0.703880 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 45.0428 | 1.54860 | ||||||||
\(847\) | 10.2217 | 0.351223 | ||||||||
\(848\) | 1.04149 | 0.0357649 | ||||||||
\(849\) | −2.71086 | −0.0930366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.70000 | −0.161114 | ||||||||
\(852\) | 13.3962 | 0.458945 | ||||||||
\(853\) | −4.34440 | −0.148750 | −0.0743748 | − | 0.997230i | \(-0.523696\pi\) | ||||
−0.0743748 | + | 0.997230i | \(0.523696\pi\) | |||||||
\(854\) | 33.4150 | 1.14344 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.0984 | −0.516053 | ||||||||
\(857\) | −6.66146 | −0.227551 | −0.113776 | − | 0.993506i | \(-0.536295\pi\) | ||||
−0.113776 | + | 0.993506i | \(0.536295\pi\) | |||||||
\(858\) | −0.237770 | −0.00811733 | ||||||||
\(859\) | −5.08899 | −0.173634 | −0.0868171 | − | 0.996224i | \(-0.527670\pi\) | ||||
−0.0868171 | + | 0.996224i | \(0.527670\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.44230 | −0.0832333 | ||||||||
\(862\) | −47.1494 | −1.60592 | ||||||||
\(863\) | 22.8511 | 0.777861 | 0.388931 | − | 0.921267i | \(-0.372845\pi\) | ||||
0.388931 | + | 0.921267i | \(0.372845\pi\) | |||||||
\(864\) | −14.9605 | −0.508967 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 84.9885 | 2.88803 | ||||||||
\(867\) | −13.0918 | −0.444620 | ||||||||
\(868\) | 17.9178 | 0.608169 | ||||||||
\(869\) | 12.8915 | 0.437314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12177 | −0.0380096 | ||||||||
\(872\) | 30.5297 | 1.03387 | ||||||||
\(873\) | 28.1583 | 0.953013 | ||||||||
\(874\) | −5.32599 | −0.180154 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.63140 | 0.325415 | ||||||||
\(877\) | 23.9219 | 0.807786 | 0.403893 | − | 0.914806i | \(-0.367657\pi\) | ||||
0.403893 | + | 0.914806i | \(0.367657\pi\) | |||||||
\(878\) | 24.2456 | 0.818248 | ||||||||
\(879\) | 0.116077 | 0.00391516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.4566 | 1.22825 | 0.614127 | − | 0.789207i | \(-0.289508\pi\) | ||||
0.614127 | + | 0.789207i | \(0.289508\pi\) | |||||||
\(882\) | −6.39435 | −0.215309 | ||||||||
\(883\) | −56.8606 | −1.91351 | −0.956755 | − | 0.290893i | \(-0.906047\pi\) | ||||
−0.956755 | + | 0.290893i | \(0.906047\pi\) | |||||||
\(884\) | −5.78812 | −0.194676 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.52977 | 0.252968 | ||||||||
\(887\) | 49.9258 | 1.67635 | 0.838173 | − | 0.545405i | \(-0.183624\pi\) | ||||
0.838173 | + | 0.545405i | \(0.183624\pi\) | |||||||
\(888\) | −5.79493 | −0.194465 | ||||||||
\(889\) | −9.06252 | −0.303947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.39554 | 0.214259 | ||||||||
\(892\) | −38.2794 | −1.28169 | ||||||||
\(893\) | −16.4348 | −0.549969 | ||||||||
\(894\) | −15.6192 | −0.522386 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.0624 | 0.603424 | ||||||||
\(897\) | 0.118067 | 0.00394214 | ||||||||
\(898\) | 63.5024 | 2.11910 | ||||||||
\(899\) | −26.2456 | −0.875339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.8992 | 2.12879 | ||||||||
\(902\) | −11.0288 | −0.367218 | ||||||||
\(903\) | −3.02680 | −0.100726 | ||||||||
\(904\) | −24.3893 | −0.811176 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.3100 | −0.508639 | ||||||||
\(907\) | −29.8857 | −0.992337 | −0.496169 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496169 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(908\) | −43.1378 | −1.43158 | ||||||||
\(909\) | 7.84043 | 0.260051 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.04089 | −0.0676177 | −0.0338089 | − | 0.999428i | \(-0.510764\pi\) | ||||
−0.0338089 | + | 0.999428i | \(0.510764\pi\) | |||||||
\(912\) | 0.115464 | 0.00382340 | ||||||||
\(913\) | 0.170782 | 0.00565206 | ||||||||
\(914\) | 72.9356 | 2.41250 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −82.1006 | −2.71268 | ||||||||
\(917\) | −5.80502 | −0.191699 | ||||||||
\(918\) | −40.2097 | −1.32712 | ||||||||
\(919\) | 14.8402 | 0.489534 | 0.244767 | − | 0.969582i | \(-0.421289\pi\) | ||||
0.244767 | + | 0.969582i | \(0.421289\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.08065 | 0.266266 | ||||||||
\(922\) | −62.2976 | −2.05166 | ||||||||
\(923\) | −2.47658 | −0.0815178 | ||||||||
\(924\) | 1.26334 | 0.0415607 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 50.9651 | 1.67482 | ||||||||
\(927\) | 10.4457 | 0.343083 | ||||||||
\(928\) | −27.1996 | −0.892870 | ||||||||
\(929\) | 31.6908 | 1.03974 | 0.519871 | − | 0.854245i | \(-0.325980\pi\) | ||||
0.519871 | + | 0.854245i | \(0.325980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.33311 | 0.0764645 | ||||||||
\(932\) | 73.9825 | 2.42338 | ||||||||
\(933\) | −2.42683 | −0.0794508 | ||||||||
\(934\) | −3.48862 | −0.114151 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.05026 | −0.0670150 | ||||||||
\(937\) | 7.19925 | 0.235189 | 0.117595 | − | 0.993062i | \(-0.462482\pi\) | ||||
0.117595 | + | 0.993062i | \(0.462482\pi\) | |||||||
\(938\) | 9.67253 | 0.315819 | ||||||||
\(939\) | −2.19947 | −0.0717771 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1066 | 1.30744 | 0.653719 | − | 0.756737i | \(-0.273208\pi\) | ||||
0.653719 | + | 0.756737i | \(0.273208\pi\) | |||||||
\(942\) | −4.46963 | −0.145629 | ||||||||
\(943\) | 5.47644 | 0.178337 | ||||||||
\(944\) | −0.825731 | −0.0268753 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.6682 | −0.444392 | ||||||||
\(947\) | −14.3124 | −0.465092 | −0.232546 | − | 0.972585i | \(-0.574706\pi\) | ||||
−0.232546 | + | 0.972585i | \(0.574706\pi\) | |||||||
\(948\) | −20.9265 | −0.679660 | ||||||||
\(949\) | −1.78058 | −0.0578001 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.16902 | −0.232471 | ||||||||
\(952\) | 18.8237 | 0.610078 | ||||||||
\(953\) | −54.0632 | −1.75128 | −0.875639 | − | 0.482965i | \(-0.839560\pi\) | ||||
−0.875639 | + | 0.482965i | \(0.839560\pi\) | |||||||
\(954\) | 60.0120 | 1.94296 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −45.9587 | −1.48641 | ||||||||
\(957\) | −1.85051 | −0.0598184 | ||||||||
\(958\) | 98.8327 | 3.19314 | ||||||||
\(959\) | −8.15908 | −0.263470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.135607 | 0.00437440 | ||||||||
\(962\) | 2.84048 | 0.0915806 | ||||||||
\(963\) | 15.2972 | 0.492945 | ||||||||
\(964\) | −76.6319 | −2.46815 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.01804 | −0.0327549 | ||||||||
\(967\) | −37.5902 | −1.20882 | −0.604410 | − | 0.796673i | \(-0.706591\pi\) | ||||
−0.604410 | + | 0.796673i | \(0.706591\pi\) | |||||||
\(968\) | −28.2602 | −0.908317 | ||||||||
\(969\) | 7.08416 | 0.227576 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.4833 | −0.657340 | −0.328670 | − | 0.944445i | \(-0.606600\pi\) | ||||
−0.328670 | + | 0.944445i | \(0.606600\pi\) | |||||||
\(972\) | −35.3041 | −1.13238 | ||||||||
\(973\) | 12.6407 | 0.405242 | ||||||||
\(974\) | −16.2331 | −0.520141 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.62438 | 0.0519953 | ||||||||
\(977\) | 26.8695 | 0.859633 | 0.429816 | − | 0.902916i | \(-0.358578\pi\) | ||||
0.429816 | + | 0.902916i | \(0.358578\pi\) | |||||||
\(978\) | −15.1642 | −0.484896 | ||||||||
\(979\) | 14.8029 | 0.473104 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.9316 | −0.987571 | ||||||||
\(982\) | −55.3912 | −1.76760 | ||||||||
\(983\) | 7.27097 | 0.231908 | 0.115954 | − | 0.993255i | \(-0.463008\pi\) | ||||
0.115954 | + | 0.993255i | \(0.463008\pi\) | |||||||
\(984\) | 6.75226 | 0.215254 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −73.1048 | −2.32813 | ||||||||
\(987\) | −3.14144 | −0.0999933 | ||||||||
\(988\) | 1.98344 | 0.0631016 | ||||||||
\(989\) | 6.78709 | 0.215817 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2644 | 0.357826 | 0.178913 | − | 0.983865i | \(-0.442742\pi\) | ||||
0.178913 | + | 0.983865i | \(0.442742\pi\) | |||||||
\(992\) | 32.2674 | 1.02449 | ||||||||
\(993\) | −8.45662 | −0.268363 | ||||||||
\(994\) | 21.3545 | 0.677325 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.277227 | −0.00878427 | ||||||||
\(997\) | −2.08601 | −0.0660647 | −0.0330323 | − | 0.999454i | \(-0.510516\pi\) | ||||
−0.0330323 | + | 0.999454i | \(0.510516\pi\) | |||||||
\(998\) | −12.4694 | −0.394712 | ||||||||
\(999\) | 12.1593 | 0.384704 |
(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 | 4025.2.a.t.1.8 | 8 | ||
5.4 | even | 2 | 805.2.a.m.1.1 | ✓ | 8 | ||
15.14 | odd | 2 | 7245.2.a.bp.1.8 | 8 | |||
35.34 | odd | 2 | 5635.2.a.bb.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.m.1.1 | ✓ | 8 | 5.4 | even | 2 | ||
4025.2.a.t.1.8 | 8 | 1.1 | even | 1 | trivial | ||
5635.2.a.bb.1.1 | 8 | 35.34 | odd | 2 | |||
7245.2.a.bp.1.8 | 8 | 15.14 | odd | 2 |