Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.760310\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.760310 | −0.340021 | −0.170010 | − | 0.985442i | \(-0.554380\pi\) | ||||
−0.170010 | + | 0.985442i | \(0.554380\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.62737 | −0.615089 | −0.307545 | − | 0.951534i | \(-0.599507\pi\) | ||||
−0.307545 | + | 0.951534i | \(0.599507\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.760310 | −0.240431 | ||||||||
\(11\) | 3.63001 | 1.09449 | 0.547245 | − | 0.836972i | \(-0.315677\pi\) | ||||
0.547245 | + | 0.836972i | \(0.315677\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.76098 | 1.87516 | 0.937580 | − | 0.347770i | \(-0.113061\pi\) | ||||
0.937580 | + | 0.347770i | \(0.113061\pi\) | |||||||
\(14\) | −1.62737 | −0.434934 | ||||||||
\(15\) | 0.760310 | 0.196311 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.10642 | 0.483247 | 0.241623 | − | 0.970370i | \(-0.422320\pi\) | ||||
0.241623 | + | 0.970370i | \(0.422320\pi\) | |||||||
\(20\) | −0.760310 | −0.170010 | ||||||||
\(21\) | 1.62737 | 0.355122 | ||||||||
\(22\) | 3.63001 | 0.773922 | ||||||||
\(23\) | 7.89371 | 1.64595 | 0.822976 | − | 0.568076i | \(-0.192312\pi\) | ||||
0.822976 | + | 0.568076i | \(0.192312\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.42193 | −0.884386 | ||||||||
\(26\) | 6.76098 | 1.32594 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.62737 | −0.307545 | ||||||||
\(29\) | −2.99423 | −0.556014 | −0.278007 | − | 0.960579i | \(-0.589674\pi\) | ||||
−0.278007 | + | 0.960579i | \(0.589674\pi\) | |||||||
\(30\) | 0.760310 | 0.138813 | ||||||||
\(31\) | −5.23504 | −0.940241 | −0.470121 | − | 0.882602i | \(-0.655790\pi\) | ||||
−0.470121 | + | 0.882602i | \(0.655790\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.63001 | −0.631904 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 1.23731 | 0.209143 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.67235 | 0.932528 | 0.466264 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466264 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(38\) | 2.10642 | 0.341707 | ||||||||
\(39\) | −6.76098 | −1.08262 | ||||||||
\(40\) | −0.760310 | −0.120216 | ||||||||
\(41\) | 4.04695 | 0.632028 | 0.316014 | − | 0.948755i | \(-0.397655\pi\) | ||||
0.316014 | + | 0.948755i | \(0.397655\pi\) | |||||||
\(42\) | 1.62737 | 0.251109 | ||||||||
\(43\) | −6.63746 | −1.01220 | −0.506102 | − | 0.862474i | \(-0.668914\pi\) | ||||
−0.506102 | + | 0.862474i | \(0.668914\pi\) | |||||||
\(44\) | 3.63001 | 0.547245 | ||||||||
\(45\) | −0.760310 | −0.113340 | ||||||||
\(46\) | 7.89371 | 1.16386 | ||||||||
\(47\) | −1.45271 | −0.211900 | −0.105950 | − | 0.994371i | \(-0.533788\pi\) | ||||
−0.105950 | + | 0.994371i | \(0.533788\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.35166 | −0.621665 | ||||||||
\(50\) | −4.42193 | −0.625355 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 6.76098 | 0.937580 | ||||||||
\(53\) | 1.88202 | 0.258515 | 0.129258 | − | 0.991611i | \(-0.458741\pi\) | ||||
0.129258 | + | 0.991611i | \(0.458741\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.75993 | −0.372150 | ||||||||
\(56\) | −1.62737 | −0.217467 | ||||||||
\(57\) | −2.10642 | −0.279003 | ||||||||
\(58\) | −2.99423 | −0.393161 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.760310 | 0.0981556 | ||||||||
\(61\) | 13.6670 | 1.74988 | 0.874941 | − | 0.484230i | \(-0.160900\pi\) | ||||
0.874941 | + | 0.484230i | \(0.160900\pi\) | |||||||
\(62\) | −5.23504 | −0.664851 | ||||||||
\(63\) | −1.62737 | −0.205030 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.14044 | −0.637593 | ||||||||
\(66\) | −3.63001 | −0.446824 | ||||||||
\(67\) | −12.0633 | −1.47377 | −0.736885 | − | 0.676018i | \(-0.763704\pi\) | ||||
−0.736885 | + | 0.676018i | \(0.763704\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −7.89371 | −0.950291 | ||||||||
\(70\) | 1.23731 | 0.147887 | ||||||||
\(71\) | 6.36534 | 0.755426 | 0.377713 | − | 0.925923i | \(-0.376711\pi\) | ||||
0.377713 | + | 0.925923i | \(0.376711\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.2842 | −1.55480 | −0.777402 | − | 0.629004i | \(-0.783463\pi\) | ||||
−0.777402 | + | 0.629004i | \(0.783463\pi\) | |||||||
\(74\) | 5.67235 | 0.659397 | ||||||||
\(75\) | 4.42193 | 0.510600 | ||||||||
\(76\) | 2.10642 | 0.241623 | ||||||||
\(77\) | −5.90739 | −0.673209 | ||||||||
\(78\) | −6.76098 | −0.765531 | ||||||||
\(79\) | 11.8018 | 1.32780 | 0.663901 | − | 0.747821i | \(-0.268900\pi\) | ||||
0.663901 | + | 0.747821i | \(0.268900\pi\) | |||||||
\(80\) | −0.760310 | −0.0850052 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.04695 | 0.446911 | ||||||||
\(83\) | 1.53380 | 0.168357 | 0.0841785 | − | 0.996451i | \(-0.473173\pi\) | ||||
0.0841785 | + | 0.996451i | \(0.473173\pi\) | |||||||
\(84\) | 1.62737 | 0.177561 | ||||||||
\(85\) | 0.760310 | 0.0824672 | ||||||||
\(86\) | −6.63746 | −0.715736 | ||||||||
\(87\) | 2.99423 | 0.321015 | ||||||||
\(88\) | 3.63001 | 0.386961 | ||||||||
\(89\) | 3.89084 | 0.412429 | 0.206214 | − | 0.978507i | \(-0.433886\pi\) | ||||
0.206214 | + | 0.978507i | \(0.433886\pi\) | |||||||
\(90\) | −0.760310 | −0.0801437 | ||||||||
\(91\) | −11.0026 | −1.15339 | ||||||||
\(92\) | 7.89371 | 0.822976 | ||||||||
\(93\) | 5.23504 | 0.542848 | ||||||||
\(94\) | −1.45271 | −0.149836 | ||||||||
\(95\) | −1.60153 | −0.164314 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 15.9005 | 1.61445 | 0.807224 | − | 0.590245i | \(-0.200969\pi\) | ||||
0.807224 | + | 0.590245i | \(0.200969\pi\) | |||||||
\(98\) | −4.35166 | −0.439584 | ||||||||
\(99\) | 3.63001 | 0.364830 | ||||||||
\(100\) | −4.42193 | −0.442193 | ||||||||
\(101\) | −9.09100 | −0.904588 | −0.452294 | − | 0.891869i | \(-0.649394\pi\) | ||||
−0.452294 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 13.9108 | 1.37068 | 0.685338 | − | 0.728225i | \(-0.259654\pi\) | ||||
0.685338 | + | 0.728225i | \(0.259654\pi\) | |||||||
\(104\) | 6.76098 | 0.662969 | ||||||||
\(105\) | −1.23731 | −0.120749 | ||||||||
\(106\) | 1.88202 | 0.182798 | ||||||||
\(107\) | −6.47874 | −0.626323 | −0.313162 | − | 0.949700i | \(-0.601388\pi\) | ||||
−0.313162 | + | 0.949700i | \(0.601388\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 9.60480 | 0.919973 | 0.459987 | − | 0.887926i | \(-0.347854\pi\) | ||||
0.459987 | + | 0.887926i | \(0.347854\pi\) | |||||||
\(110\) | −2.75993 | −0.263149 | ||||||||
\(111\) | −5.67235 | −0.538396 | ||||||||
\(112\) | −1.62737 | −0.153772 | ||||||||
\(113\) | −13.0169 | −1.22453 | −0.612264 | − | 0.790653i | \(-0.709741\pi\) | ||||
−0.612264 | + | 0.790653i | \(0.709741\pi\) | |||||||
\(114\) | −2.10642 | −0.197285 | ||||||||
\(115\) | −6.00166 | −0.559658 | ||||||||
\(116\) | −2.99423 | −0.278007 | ||||||||
\(117\) | 6.76098 | 0.625053 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 1.62737 | 0.149181 | ||||||||
\(120\) | 0.760310 | 0.0694065 | ||||||||
\(121\) | 2.17700 | 0.197909 | ||||||||
\(122\) | 13.6670 | 1.23735 | ||||||||
\(123\) | −4.04695 | −0.364901 | ||||||||
\(124\) | −5.23504 | −0.470121 | ||||||||
\(125\) | 7.16358 | 0.640730 | ||||||||
\(126\) | −1.62737 | −0.144978 | ||||||||
\(127\) | 17.5649 | 1.55863 | 0.779316 | − | 0.626631i | \(-0.215567\pi\) | ||||
0.779316 | + | 0.626631i | \(0.215567\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.63746 | 0.584396 | ||||||||
\(130\) | −5.14044 | −0.450847 | ||||||||
\(131\) | −13.0849 | −1.14323 | −0.571616 | − | 0.820521i | \(-0.693683\pi\) | ||||
−0.571616 | + | 0.820521i | \(0.693683\pi\) | |||||||
\(132\) | −3.63001 | −0.315952 | ||||||||
\(133\) | −3.42794 | −0.297240 | ||||||||
\(134\) | −12.0633 | −1.04211 | ||||||||
\(135\) | 0.760310 | 0.0654370 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 3.13775 | 0.268076 | 0.134038 | − | 0.990976i | \(-0.457206\pi\) | ||||
0.134038 | + | 0.990976i | \(0.457206\pi\) | |||||||
\(138\) | −7.89371 | −0.671957 | ||||||||
\(139\) | 4.21469 | 0.357485 | 0.178742 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178742 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(140\) | 1.23731 | 0.104572 | ||||||||
\(141\) | 1.45271 | 0.122340 | ||||||||
\(142\) | 6.36534 | 0.534167 | ||||||||
\(143\) | 24.5425 | 2.05234 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.27654 | 0.189056 | ||||||||
\(146\) | −13.2842 | −1.09941 | ||||||||
\(147\) | 4.35166 | 0.358918 | ||||||||
\(148\) | 5.67235 | 0.466264 | ||||||||
\(149\) | 14.7073 | 1.20487 | 0.602433 | − | 0.798169i | \(-0.294198\pi\) | ||||
0.602433 | + | 0.798169i | \(0.294198\pi\) | |||||||
\(150\) | 4.42193 | 0.361049 | ||||||||
\(151\) | −18.8361 | −1.53286 | −0.766431 | − | 0.642327i | \(-0.777969\pi\) | ||||
−0.766431 | + | 0.642327i | \(0.777969\pi\) | |||||||
\(152\) | 2.10642 | 0.170854 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −5.90739 | −0.476031 | ||||||||
\(155\) | 3.98025 | 0.319702 | ||||||||
\(156\) | −6.76098 | −0.541312 | ||||||||
\(157\) | 4.66776 | 0.372528 | 0.186264 | − | 0.982500i | \(-0.440362\pi\) | ||||
0.186264 | + | 0.982500i | \(0.440362\pi\) | |||||||
\(158\) | 11.8018 | 0.938897 | ||||||||
\(159\) | −1.88202 | −0.149254 | ||||||||
\(160\) | −0.760310 | −0.0601078 | ||||||||
\(161\) | −12.8460 | −1.01241 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 4.81393 | 0.377056 | 0.188528 | − | 0.982068i | \(-0.439628\pi\) | ||||
0.188528 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(164\) | 4.04695 | 0.316014 | ||||||||
\(165\) | 2.75993 | 0.214861 | ||||||||
\(166\) | 1.53380 | 0.119046 | ||||||||
\(167\) | 15.7377 | 1.21782 | 0.608908 | − | 0.793241i | \(-0.291608\pi\) | ||||
0.608908 | + | 0.793241i | \(0.291608\pi\) | |||||||
\(168\) | 1.62737 | 0.125555 | ||||||||
\(169\) | 32.7109 | 2.51622 | ||||||||
\(170\) | 0.760310 | 0.0583131 | ||||||||
\(171\) | 2.10642 | 0.161082 | ||||||||
\(172\) | −6.63746 | −0.506102 | ||||||||
\(173\) | −9.91658 | −0.753943 | −0.376972 | − | 0.926225i | \(-0.623035\pi\) | ||||
−0.376972 | + | 0.926225i | \(0.623035\pi\) | |||||||
\(174\) | 2.99423 | 0.226992 | ||||||||
\(175\) | 7.19613 | 0.543976 | ||||||||
\(176\) | 3.63001 | 0.273623 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 3.89084 | 0.291631 | ||||||||
\(179\) | −5.63912 | −0.421488 | −0.210744 | − | 0.977541i | \(-0.567589\pi\) | ||||
−0.210744 | + | 0.977541i | \(0.567589\pi\) | |||||||
\(180\) | −0.760310 | −0.0566701 | ||||||||
\(181\) | 21.3035 | 1.58348 | 0.791739 | − | 0.610859i | \(-0.209176\pi\) | ||||
0.791739 | + | 0.610859i | \(0.209176\pi\) | |||||||
\(182\) | −11.0026 | −0.815570 | ||||||||
\(183\) | −13.6670 | −1.01029 | ||||||||
\(184\) | 7.89371 | 0.581932 | ||||||||
\(185\) | −4.31274 | −0.317079 | ||||||||
\(186\) | 5.23504 | 0.383852 | ||||||||
\(187\) | −3.63001 | −0.265453 | ||||||||
\(188\) | −1.45271 | −0.105950 | ||||||||
\(189\) | 1.62737 | 0.118374 | ||||||||
\(190\) | −1.60153 | −0.116188 | ||||||||
\(191\) | 12.7185 | 0.920281 | 0.460140 | − | 0.887846i | \(-0.347799\pi\) | ||||
0.460140 | + | 0.887846i | \(0.347799\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.43280 | 0.319080 | 0.159540 | − | 0.987191i | \(-0.448999\pi\) | ||||
0.159540 | + | 0.987191i | \(0.448999\pi\) | |||||||
\(194\) | 15.9005 | 1.14159 | ||||||||
\(195\) | 5.14044 | 0.368115 | ||||||||
\(196\) | −4.35166 | −0.310833 | ||||||||
\(197\) | 19.1487 | 1.36429 | 0.682145 | − | 0.731217i | \(-0.261047\pi\) | ||||
0.682145 | + | 0.731217i | \(0.261047\pi\) | |||||||
\(198\) | 3.63001 | 0.257974 | ||||||||
\(199\) | 4.71773 | 0.334431 | 0.167216 | − | 0.985920i | \(-0.446522\pi\) | ||||
0.167216 | + | 0.985920i | \(0.446522\pi\) | |||||||
\(200\) | −4.42193 | −0.312678 | ||||||||
\(201\) | 12.0633 | 0.850882 | ||||||||
\(202\) | −9.09100 | −0.639640 | ||||||||
\(203\) | 4.87272 | 0.341998 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −3.07694 | −0.214903 | ||||||||
\(206\) | 13.9108 | 0.969215 | ||||||||
\(207\) | 7.89371 | 0.548651 | ||||||||
\(208\) | 6.76098 | 0.468790 | ||||||||
\(209\) | 7.64635 | 0.528909 | ||||||||
\(210\) | −1.23731 | −0.0853824 | ||||||||
\(211\) | 2.79613 | 0.192493 | 0.0962467 | − | 0.995358i | \(-0.469316\pi\) | ||||
0.0962467 | + | 0.995358i | \(0.469316\pi\) | |||||||
\(212\) | 1.88202 | 0.129258 | ||||||||
\(213\) | −6.36534 | −0.436146 | ||||||||
\(214\) | −6.47874 | −0.442877 | ||||||||
\(215\) | 5.04653 | 0.344170 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.51937 | 0.578332 | ||||||||
\(218\) | 9.60480 | 0.650519 | ||||||||
\(219\) | 13.2842 | 0.897666 | ||||||||
\(220\) | −2.75993 | −0.186075 | ||||||||
\(221\) | −6.76098 | −0.454793 | ||||||||
\(222\) | −5.67235 | −0.380703 | ||||||||
\(223\) | 16.1158 | 1.07919 | 0.539597 | − | 0.841923i | \(-0.318577\pi\) | ||||
0.539597 | + | 0.841923i | \(0.318577\pi\) | |||||||
\(224\) | −1.62737 | −0.108733 | ||||||||
\(225\) | −4.42193 | −0.294795 | ||||||||
\(226\) | −13.0169 | −0.865872 | ||||||||
\(227\) | 9.91198 | 0.657881 | 0.328941 | − | 0.944351i | \(-0.393308\pi\) | ||||
0.328941 | + | 0.944351i | \(0.393308\pi\) | |||||||
\(228\) | −2.10642 | −0.139501 | ||||||||
\(229\) | −21.8492 | −1.44383 | −0.721916 | − | 0.691980i | \(-0.756739\pi\) | ||||
−0.721916 | + | 0.691980i | \(0.756739\pi\) | |||||||
\(230\) | −6.00166 | −0.395738 | ||||||||
\(231\) | 5.90739 | 0.388678 | ||||||||
\(232\) | −2.99423 | −0.196581 | ||||||||
\(233\) | −13.5472 | −0.887505 | −0.443752 | − | 0.896149i | \(-0.646353\pi\) | ||||
−0.443752 | + | 0.896149i | \(0.646353\pi\) | |||||||
\(234\) | 6.76098 | 0.441979 | ||||||||
\(235\) | 1.10451 | 0.0720503 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | −11.8018 | −0.766606 | ||||||||
\(238\) | 1.62737 | 0.105487 | ||||||||
\(239\) | 1.71808 | 0.111133 | 0.0555666 | − | 0.998455i | \(-0.482303\pi\) | ||||
0.0555666 | + | 0.998455i | \(0.482303\pi\) | |||||||
\(240\) | 0.760310 | 0.0490778 | ||||||||
\(241\) | 11.4382 | 0.736800 | 0.368400 | − | 0.929667i | \(-0.379906\pi\) | ||||
0.368400 | + | 0.929667i | \(0.379906\pi\) | |||||||
\(242\) | 2.17700 | 0.139943 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.6670 | 0.874941 | ||||||||
\(245\) | 3.30861 | 0.211379 | ||||||||
\(246\) | −4.04695 | −0.258024 | ||||||||
\(247\) | 14.2415 | 0.906165 | ||||||||
\(248\) | −5.23504 | −0.332425 | ||||||||
\(249\) | −1.53380 | −0.0972009 | ||||||||
\(250\) | 7.16358 | 0.453065 | ||||||||
\(251\) | −28.4694 | −1.79697 | −0.898487 | − | 0.439001i | \(-0.855333\pi\) | ||||
−0.898487 | + | 0.439001i | \(0.855333\pi\) | |||||||
\(252\) | −1.62737 | −0.102515 | ||||||||
\(253\) | 28.6543 | 1.80148 | ||||||||
\(254\) | 17.5649 | 1.10212 | ||||||||
\(255\) | −0.760310 | −0.0476124 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.31711 | 0.456429 | 0.228214 | − | 0.973611i | \(-0.426711\pi\) | ||||
0.228214 | + | 0.973611i | \(0.426711\pi\) | |||||||
\(258\) | 6.63746 | 0.413230 | ||||||||
\(259\) | −9.23103 | −0.573588 | ||||||||
\(260\) | −5.14044 | −0.318797 | ||||||||
\(261\) | −2.99423 | −0.185338 | ||||||||
\(262\) | −13.0849 | −0.808387 | ||||||||
\(263\) | 16.1806 | 0.997739 | 0.498870 | − | 0.866677i | \(-0.333749\pi\) | ||||
0.498870 | + | 0.866677i | \(0.333749\pi\) | |||||||
\(264\) | −3.63001 | −0.223412 | ||||||||
\(265\) | −1.43092 | −0.0879006 | ||||||||
\(266\) | −3.42794 | −0.210180 | ||||||||
\(267\) | −3.89084 | −0.238116 | ||||||||
\(268\) | −12.0633 | −0.736885 | ||||||||
\(269\) | 21.2237 | 1.29403 | 0.647016 | − | 0.762476i | \(-0.276017\pi\) | ||||
0.647016 | + | 0.762476i | \(0.276017\pi\) | |||||||
\(270\) | 0.760310 | 0.0462710 | ||||||||
\(271\) | −30.6748 | −1.86336 | −0.931681 | − | 0.363277i | \(-0.881658\pi\) | ||||
−0.931681 | + | 0.363277i | \(0.881658\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 11.0026 | 0.665910 | ||||||||
\(274\) | 3.13775 | 0.189558 | ||||||||
\(275\) | −16.0517 | −0.967952 | ||||||||
\(276\) | −7.89371 | −0.475145 | ||||||||
\(277\) | −23.1354 | −1.39007 | −0.695036 | − | 0.718975i | \(-0.744611\pi\) | ||||
−0.695036 | + | 0.718975i | \(0.744611\pi\) | |||||||
\(278\) | 4.21469 | 0.252780 | ||||||||
\(279\) | −5.23504 | −0.313414 | ||||||||
\(280\) | 1.23731 | 0.0739433 | ||||||||
\(281\) | 16.1851 | 0.965525 | 0.482763 | − | 0.875751i | \(-0.339633\pi\) | ||||
0.482763 | + | 0.875751i | \(0.339633\pi\) | |||||||
\(282\) | 1.45271 | 0.0865077 | ||||||||
\(283\) | −13.1301 | −0.780502 | −0.390251 | − | 0.920708i | \(-0.627612\pi\) | ||||
−0.390251 | + | 0.920708i | \(0.627612\pi\) | |||||||
\(284\) | 6.36534 | 0.377713 | ||||||||
\(285\) | 1.60153 | 0.0948667 | ||||||||
\(286\) | 24.5425 | 1.45123 | ||||||||
\(287\) | −6.58590 | −0.388754 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.27654 | 0.133683 | ||||||||
\(291\) | −15.9005 | −0.932102 | ||||||||
\(292\) | −13.2842 | −0.777402 | ||||||||
\(293\) | −17.6975 | −1.03390 | −0.516951 | − | 0.856015i | \(-0.672933\pi\) | ||||
−0.516951 | + | 0.856015i | \(0.672933\pi\) | |||||||
\(294\) | 4.35166 | 0.253794 | ||||||||
\(295\) | 0.760310 | 0.0442669 | ||||||||
\(296\) | 5.67235 | 0.329699 | ||||||||
\(297\) | −3.63001 | −0.210635 | ||||||||
\(298\) | 14.7073 | 0.851970 | ||||||||
\(299\) | 53.3692 | 3.08642 | ||||||||
\(300\) | 4.42193 | 0.255300 | ||||||||
\(301\) | 10.8016 | 0.622595 | ||||||||
\(302\) | −18.8361 | −1.08390 | ||||||||
\(303\) | 9.09100 | 0.522264 | ||||||||
\(304\) | 2.10642 | 0.120812 | ||||||||
\(305\) | −10.3912 | −0.594996 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 9.82541 | 0.560766 | 0.280383 | − | 0.959888i | \(-0.409539\pi\) | ||||
0.280383 | + | 0.959888i | \(0.409539\pi\) | |||||||
\(308\) | −5.90739 | −0.336605 | ||||||||
\(309\) | −13.9108 | −0.791361 | ||||||||
\(310\) | 3.98025 | 0.226063 | ||||||||
\(311\) | −30.4661 | −1.72758 | −0.863788 | − | 0.503856i | \(-0.831914\pi\) | ||||
−0.863788 | + | 0.503856i | \(0.831914\pi\) | |||||||
\(312\) | −6.76098 | −0.382765 | ||||||||
\(313\) | 33.0976 | 1.87079 | 0.935395 | − | 0.353605i | \(-0.115044\pi\) | ||||
0.935395 | + | 0.353605i | \(0.115044\pi\) | |||||||
\(314\) | 4.66776 | 0.263417 | ||||||||
\(315\) | 1.23731 | 0.0697144 | ||||||||
\(316\) | 11.8018 | 0.663901 | ||||||||
\(317\) | 17.9222 | 1.00661 | 0.503305 | − | 0.864109i | \(-0.332117\pi\) | ||||
0.503305 | + | 0.864109i | \(0.332117\pi\) | |||||||
\(318\) | −1.88202 | −0.105538 | ||||||||
\(319\) | −10.8691 | −0.608552 | ||||||||
\(320\) | −0.760310 | −0.0425026 | ||||||||
\(321\) | 6.47874 | 0.361608 | ||||||||
\(322\) | −12.8460 | −0.715880 | ||||||||
\(323\) | −2.10642 | −0.117205 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −29.8966 | −1.65836 | ||||||||
\(326\) | 4.81393 | 0.266619 | ||||||||
\(327\) | −9.60480 | −0.531147 | ||||||||
\(328\) | 4.04695 | 0.223456 | ||||||||
\(329\) | 2.36410 | 0.130337 | ||||||||
\(330\) | 2.75993 | 0.151929 | ||||||||
\(331\) | −7.50037 | −0.412258 | −0.206129 | − | 0.978525i | \(-0.566087\pi\) | ||||
−0.206129 | + | 0.978525i | \(0.566087\pi\) | |||||||
\(332\) | 1.53380 | 0.0841785 | ||||||||
\(333\) | 5.67235 | 0.310843 | ||||||||
\(334\) | 15.7377 | 0.861126 | ||||||||
\(335\) | 9.17187 | 0.501113 | ||||||||
\(336\) | 1.62737 | 0.0887805 | ||||||||
\(337\) | 28.6815 | 1.56238 | 0.781191 | − | 0.624292i | \(-0.214613\pi\) | ||||
0.781191 | + | 0.624292i | \(0.214613\pi\) | |||||||
\(338\) | 32.7109 | 1.77924 | ||||||||
\(339\) | 13.0169 | 0.706982 | ||||||||
\(340\) | 0.760310 | 0.0412336 | ||||||||
\(341\) | −19.0033 | −1.02908 | ||||||||
\(342\) | 2.10642 | 0.113902 | ||||||||
\(343\) | 18.4734 | 0.997469 | ||||||||
\(344\) | −6.63746 | −0.357868 | ||||||||
\(345\) | 6.00166 | 0.323119 | ||||||||
\(346\) | −9.91658 | −0.533119 | ||||||||
\(347\) | 33.0336 | 1.77334 | 0.886669 | − | 0.462404i | \(-0.153013\pi\) | ||||
0.886669 | + | 0.462404i | \(0.153013\pi\) | |||||||
\(348\) | 2.99423 | 0.160507 | ||||||||
\(349\) | −20.6185 | −1.10368 | −0.551841 | − | 0.833949i | \(-0.686075\pi\) | ||||
−0.551841 | + | 0.833949i | \(0.686075\pi\) | |||||||
\(350\) | 7.19613 | 0.384649 | ||||||||
\(351\) | −6.76098 | −0.360875 | ||||||||
\(352\) | 3.63001 | 0.193480 | ||||||||
\(353\) | −25.9945 | −1.38355 | −0.691775 | − | 0.722113i | \(-0.743171\pi\) | ||||
−0.691775 | + | 0.722113i | \(0.743171\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −4.83963 | −0.256861 | ||||||||
\(356\) | 3.89084 | 0.206214 | ||||||||
\(357\) | −1.62737 | −0.0861297 | ||||||||
\(358\) | −5.63912 | −0.298037 | ||||||||
\(359\) | 16.3148 | 0.861060 | 0.430530 | − | 0.902576i | \(-0.358327\pi\) | ||||
0.430530 | + | 0.902576i | \(0.358327\pi\) | |||||||
\(360\) | −0.760310 | −0.0400718 | ||||||||
\(361\) | −14.5630 | −0.766473 | ||||||||
\(362\) | 21.3035 | 1.11969 | ||||||||
\(363\) | −2.17700 | −0.114263 | ||||||||
\(364\) | −11.0026 | −0.576695 | ||||||||
\(365\) | 10.1001 | 0.528666 | ||||||||
\(366\) | −13.6670 | −0.714386 | ||||||||
\(367\) | −24.8592 | −1.29764 | −0.648821 | − | 0.760941i | \(-0.724737\pi\) | ||||
−0.648821 | + | 0.760941i | \(0.724737\pi\) | |||||||
\(368\) | 7.89371 | 0.411488 | ||||||||
\(369\) | 4.04695 | 0.210676 | ||||||||
\(370\) | −4.31274 | −0.224209 | ||||||||
\(371\) | −3.06275 | −0.159010 | ||||||||
\(372\) | 5.23504 | 0.271424 | ||||||||
\(373\) | −0.960167 | −0.0497156 | −0.0248578 | − | 0.999691i | \(-0.507913\pi\) | ||||
−0.0248578 | + | 0.999691i | \(0.507913\pi\) | |||||||
\(374\) | −3.63001 | −0.187704 | ||||||||
\(375\) | −7.16358 | −0.369926 | ||||||||
\(376\) | −1.45271 | −0.0749179 | ||||||||
\(377\) | −20.2439 | −1.04261 | ||||||||
\(378\) | 1.62737 | 0.0837031 | ||||||||
\(379\) | 21.4045 | 1.09948 | 0.549738 | − | 0.835337i | \(-0.314728\pi\) | ||||
0.549738 | + | 0.835337i | \(0.314728\pi\) | |||||||
\(380\) | −1.60153 | −0.0821570 | ||||||||
\(381\) | −17.5649 | −0.899877 | ||||||||
\(382\) | 12.7185 | 0.650737 | ||||||||
\(383\) | 2.36171 | 0.120678 | 0.0603388 | − | 0.998178i | \(-0.480782\pi\) | ||||
0.0603388 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.49144 | 0.228905 | ||||||||
\(386\) | 4.43280 | 0.225624 | ||||||||
\(387\) | −6.63746 | −0.337401 | ||||||||
\(388\) | 15.9005 | 0.807224 | ||||||||
\(389\) | −8.71266 | −0.441750 | −0.220875 | − | 0.975302i | \(-0.570891\pi\) | ||||
−0.220875 | + | 0.975302i | \(0.570891\pi\) | |||||||
\(390\) | 5.14044 | 0.260296 | ||||||||
\(391\) | −7.89371 | −0.399202 | ||||||||
\(392\) | −4.35166 | −0.219792 | ||||||||
\(393\) | 13.0849 | 0.660045 | ||||||||
\(394\) | 19.1487 | 0.964699 | ||||||||
\(395\) | −8.97299 | −0.451480 | ||||||||
\(396\) | 3.63001 | 0.182415 | ||||||||
\(397\) | −16.4192 | −0.824057 | −0.412029 | − | 0.911171i | \(-0.635180\pi\) | ||||
−0.412029 | + | 0.911171i | \(0.635180\pi\) | |||||||
\(398\) | 4.71773 | 0.236479 | ||||||||
\(399\) | 3.42794 | 0.171612 | ||||||||
\(400\) | −4.42193 | −0.221096 | ||||||||
\(401\) | 23.1727 | 1.15719 | 0.578594 | − | 0.815615i | \(-0.303601\pi\) | ||||
0.578594 | + | 0.815615i | \(0.303601\pi\) | |||||||
\(402\) | 12.0633 | 0.601664 | ||||||||
\(403\) | −35.3940 | −1.76310 | ||||||||
\(404\) | −9.09100 | −0.452294 | ||||||||
\(405\) | −0.760310 | −0.0377801 | ||||||||
\(406\) | 4.87272 | 0.241829 | ||||||||
\(407\) | 20.5907 | 1.02064 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 29.5640 | 1.46184 | 0.730922 | − | 0.682461i | \(-0.239090\pi\) | ||||
0.730922 | + | 0.682461i | \(0.239090\pi\) | |||||||
\(410\) | −3.07694 | −0.151959 | ||||||||
\(411\) | −3.13775 | −0.154774 | ||||||||
\(412\) | 13.9108 | 0.685338 | ||||||||
\(413\) | 1.62737 | 0.0800778 | ||||||||
\(414\) | 7.89371 | 0.387955 | ||||||||
\(415\) | −1.16617 | −0.0572449 | ||||||||
\(416\) | 6.76098 | 0.331485 | ||||||||
\(417\) | −4.21469 | −0.206394 | ||||||||
\(418\) | 7.64635 | 0.373995 | ||||||||
\(419\) | −6.58374 | −0.321637 | −0.160818 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160818 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(420\) | −1.23731 | −0.0603744 | ||||||||
\(421\) | 28.0737 | 1.36823 | 0.684114 | − | 0.729375i | \(-0.260189\pi\) | ||||
0.684114 | + | 0.729375i | \(0.260189\pi\) | |||||||
\(422\) | 2.79613 | 0.136113 | ||||||||
\(423\) | −1.45271 | −0.0706332 | ||||||||
\(424\) | 1.88202 | 0.0913990 | ||||||||
\(425\) | 4.42193 | 0.214495 | ||||||||
\(426\) | −6.36534 | −0.308402 | ||||||||
\(427\) | −22.2413 | −1.07633 | ||||||||
\(428\) | −6.47874 | −0.313162 | ||||||||
\(429\) | −24.5425 | −1.18492 | ||||||||
\(430\) | 5.04653 | 0.243365 | ||||||||
\(431\) | −39.1100 | −1.88386 | −0.941931 | − | 0.335808i | \(-0.890991\pi\) | ||||
−0.941931 | + | 0.335808i | \(0.890991\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −23.0413 | −1.10729 | −0.553647 | − | 0.832751i | \(-0.686764\pi\) | ||||
−0.553647 | + | 0.832751i | \(0.686764\pi\) | |||||||
\(434\) | 8.51937 | 0.408943 | ||||||||
\(435\) | −2.27654 | −0.109152 | ||||||||
\(436\) | 9.60480 | 0.459987 | ||||||||
\(437\) | 16.6275 | 0.795401 | ||||||||
\(438\) | 13.2842 | 0.634746 | ||||||||
\(439\) | 0.621975 | 0.0296853 | 0.0148426 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148426 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(440\) | −2.75993 | −0.131575 | ||||||||
\(441\) | −4.35166 | −0.207222 | ||||||||
\(442\) | −6.76098 | −0.321587 | ||||||||
\(443\) | −28.7111 | −1.36410 | −0.682052 | − | 0.731303i | \(-0.738912\pi\) | ||||
−0.682052 | + | 0.731303i | \(0.738912\pi\) | |||||||
\(444\) | −5.67235 | −0.269198 | ||||||||
\(445\) | −2.95825 | −0.140234 | ||||||||
\(446\) | 16.1158 | 0.763106 | ||||||||
\(447\) | −14.7073 | −0.695630 | ||||||||
\(448\) | −1.62737 | −0.0768862 | ||||||||
\(449\) | −6.66798 | −0.314681 | −0.157341 | − | 0.987544i | \(-0.550292\pi\) | ||||
−0.157341 | + | 0.987544i | \(0.550292\pi\) | |||||||
\(450\) | −4.42193 | −0.208452 | ||||||||
\(451\) | 14.6905 | 0.691748 | ||||||||
\(452\) | −13.0169 | −0.612264 | ||||||||
\(453\) | 18.8361 | 0.884998 | ||||||||
\(454\) | 9.91198 | 0.465192 | ||||||||
\(455\) | 8.36542 | 0.392177 | ||||||||
\(456\) | −2.10642 | −0.0986423 | ||||||||
\(457\) | 23.6303 | 1.10538 | 0.552690 | − | 0.833387i | \(-0.313601\pi\) | ||||
0.552690 | + | 0.833387i | \(0.313601\pi\) | |||||||
\(458\) | −21.8492 | −1.02094 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −6.00166 | −0.279829 | ||||||||
\(461\) | 0.780720 | 0.0363618 | 0.0181809 | − | 0.999835i | \(-0.494213\pi\) | ||||
0.0181809 | + | 0.999835i | \(0.494213\pi\) | |||||||
\(462\) | 5.90739 | 0.274837 | ||||||||
\(463\) | 0.833871 | 0.0387533 | 0.0193766 | − | 0.999812i | \(-0.493832\pi\) | ||||
0.0193766 | + | 0.999812i | \(0.493832\pi\) | |||||||
\(464\) | −2.99423 | −0.139003 | ||||||||
\(465\) | −3.98025 | −0.184580 | ||||||||
\(466\) | −13.5472 | −0.627561 | ||||||||
\(467\) | −36.4231 | −1.68546 | −0.842730 | − | 0.538336i | \(-0.819053\pi\) | ||||
−0.842730 | + | 0.538336i | \(0.819053\pi\) | |||||||
\(468\) | 6.76098 | 0.312527 | ||||||||
\(469\) | 19.6315 | 0.906500 | ||||||||
\(470\) | 1.10451 | 0.0509473 | ||||||||
\(471\) | −4.66776 | −0.215079 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −24.0941 | −1.10785 | ||||||||
\(474\) | −11.8018 | −0.542073 | ||||||||
\(475\) | −9.31446 | −0.427377 | ||||||||
\(476\) | 1.62737 | 0.0745905 | ||||||||
\(477\) | 1.88202 | 0.0861718 | ||||||||
\(478\) | 1.71808 | 0.0785831 | ||||||||
\(479\) | 3.13148 | 0.143081 | 0.0715405 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715405 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(480\) | 0.760310 | 0.0347032 | ||||||||
\(481\) | 38.3507 | 1.74864 | ||||||||
\(482\) | 11.4382 | 0.520996 | ||||||||
\(483\) | 12.8460 | 0.584514 | ||||||||
\(484\) | 2.17700 | 0.0989545 | ||||||||
\(485\) | −12.0893 | −0.548946 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.19919 | −0.0543407 | −0.0271703 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271703 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(488\) | 13.6670 | 0.618676 | ||||||||
\(489\) | −4.81393 | −0.217694 | ||||||||
\(490\) | 3.30861 | 0.149468 | ||||||||
\(491\) | −13.9339 | −0.628830 | −0.314415 | − | 0.949286i | \(-0.601808\pi\) | ||||
−0.314415 | + | 0.949286i | \(0.601808\pi\) | |||||||
\(492\) | −4.04695 | −0.182451 | ||||||||
\(493\) | 2.99423 | 0.134853 | ||||||||
\(494\) | 14.2415 | 0.640755 | ||||||||
\(495\) | −2.75993 | −0.124050 | ||||||||
\(496\) | −5.23504 | −0.235060 | ||||||||
\(497\) | −10.3588 | −0.464655 | ||||||||
\(498\) | −1.53380 | −0.0687314 | ||||||||
\(499\) | −11.3864 | −0.509727 | −0.254863 | − | 0.966977i | \(-0.582031\pi\) | ||||
−0.254863 | + | 0.966977i | \(0.582031\pi\) | |||||||
\(500\) | 7.16358 | 0.320365 | ||||||||
\(501\) | −15.7377 | −0.703107 | ||||||||
\(502\) | −28.4694 | −1.27065 | ||||||||
\(503\) | −11.0211 | −0.491406 | −0.245703 | − | 0.969345i | \(-0.579019\pi\) | ||||
−0.245703 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(504\) | −1.62737 | −0.0724890 | ||||||||
\(505\) | 6.91197 | 0.307579 | ||||||||
\(506\) | 28.6543 | 1.27384 | ||||||||
\(507\) | −32.7109 | −1.45274 | ||||||||
\(508\) | 17.5649 | 0.779316 | ||||||||
\(509\) | −10.0579 | −0.445807 | −0.222903 | − | 0.974841i | \(-0.571553\pi\) | ||||
−0.222903 | + | 0.974841i | \(0.571553\pi\) | |||||||
\(510\) | −0.760310 | −0.0336671 | ||||||||
\(511\) | 21.6184 | 0.956343 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.10642 | −0.0930009 | ||||||||
\(514\) | 7.31711 | 0.322744 | ||||||||
\(515\) | −10.5766 | −0.466059 | ||||||||
\(516\) | 6.63746 | 0.292198 | ||||||||
\(517\) | −5.27336 | −0.231922 | ||||||||
\(518\) | −9.23103 | −0.405588 | ||||||||
\(519\) | 9.91658 | 0.435289 | ||||||||
\(520\) | −5.14044 | −0.225423 | ||||||||
\(521\) | −27.1618 | −1.18998 | −0.594990 | − | 0.803733i | \(-0.702844\pi\) | ||||
−0.594990 | + | 0.803733i | \(0.702844\pi\) | |||||||
\(522\) | −2.99423 | −0.131054 | ||||||||
\(523\) | −19.2310 | −0.840912 | −0.420456 | − | 0.907313i | \(-0.638130\pi\) | ||||
−0.420456 | + | 0.907313i | \(0.638130\pi\) | |||||||
\(524\) | −13.0849 | −0.571616 | ||||||||
\(525\) | −7.19613 | −0.314065 | ||||||||
\(526\) | 16.1806 | 0.705508 | ||||||||
\(527\) | 5.23504 | 0.228042 | ||||||||
\(528\) | −3.63001 | −0.157976 | ||||||||
\(529\) | 39.3106 | 1.70916 | ||||||||
\(530\) | −1.43092 | −0.0621551 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | −3.42794 | −0.148620 | ||||||||
\(533\) | 27.3614 | 1.18515 | ||||||||
\(534\) | −3.89084 | −0.168373 | ||||||||
\(535\) | 4.92585 | 0.212963 | ||||||||
\(536\) | −12.0633 | −0.521056 | ||||||||
\(537\) | 5.63912 | 0.243346 | ||||||||
\(538\) | 21.2237 | 0.915019 | ||||||||
\(539\) | −15.7966 | −0.680406 | ||||||||
\(540\) | 0.760310 | 0.0327185 | ||||||||
\(541\) | 38.0684 | 1.63669 | 0.818343 | − | 0.574730i | \(-0.194893\pi\) | ||||
0.818343 | + | 0.574730i | \(0.194893\pi\) | |||||||
\(542\) | −30.6748 | −1.31760 | ||||||||
\(543\) | −21.3035 | −0.914222 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −7.30262 | −0.312810 | ||||||||
\(546\) | 11.0026 | 0.470870 | ||||||||
\(547\) | 20.9084 | 0.893977 | 0.446988 | − | 0.894540i | \(-0.352497\pi\) | ||||
0.446988 | + | 0.894540i | \(0.352497\pi\) | |||||||
\(548\) | 3.13775 | 0.134038 | ||||||||
\(549\) | 13.6670 | 0.583294 | ||||||||
\(550\) | −16.0517 | −0.684445 | ||||||||
\(551\) | −6.30711 | −0.268692 | ||||||||
\(552\) | −7.89371 | −0.335978 | ||||||||
\(553\) | −19.2059 | −0.816717 | ||||||||
\(554\) | −23.1354 | −0.982929 | ||||||||
\(555\) | 4.31274 | 0.183066 | ||||||||
\(556\) | 4.21469 | 0.178742 | ||||||||
\(557\) | −17.2351 | −0.730275 | −0.365138 | − | 0.930954i | \(-0.618978\pi\) | ||||
−0.365138 | + | 0.930954i | \(0.618978\pi\) | |||||||
\(558\) | −5.23504 | −0.221617 | ||||||||
\(559\) | −44.8758 | −1.89804 | ||||||||
\(560\) | 1.23731 | 0.0522858 | ||||||||
\(561\) | 3.63001 | 0.153259 | ||||||||
\(562\) | 16.1851 | 0.682729 | ||||||||
\(563\) | −23.9392 | −1.00892 | −0.504458 | − | 0.863436i | \(-0.668308\pi\) | ||||
−0.504458 | + | 0.863436i | \(0.668308\pi\) | |||||||
\(564\) | 1.45271 | 0.0611702 | ||||||||
\(565\) | 9.89689 | 0.416365 | ||||||||
\(566\) | −13.1301 | −0.551898 | ||||||||
\(567\) | −1.62737 | −0.0683433 | ||||||||
\(568\) | 6.36534 | 0.267084 | ||||||||
\(569\) | 19.0343 | 0.797958 | 0.398979 | − | 0.916960i | \(-0.369365\pi\) | ||||
0.398979 | + | 0.916960i | \(0.369365\pi\) | |||||||
\(570\) | 1.60153 | 0.0670809 | ||||||||
\(571\) | −6.61480 | −0.276821 | −0.138410 | − | 0.990375i | \(-0.544199\pi\) | ||||
−0.138410 | + | 0.990375i | \(0.544199\pi\) | |||||||
\(572\) | 24.5425 | 1.02617 | ||||||||
\(573\) | −12.7185 | −0.531324 | ||||||||
\(574\) | −6.58590 | −0.274890 | ||||||||
\(575\) | −34.9054 | −1.45566 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 21.8713 | 0.910516 | 0.455258 | − | 0.890360i | \(-0.349547\pi\) | ||||
0.455258 | + | 0.890360i | \(0.349547\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −4.43280 | −0.184221 | ||||||||
\(580\) | 2.27654 | 0.0945281 | ||||||||
\(581\) | −2.49607 | −0.103555 | ||||||||
\(582\) | −15.9005 | −0.659096 | ||||||||
\(583\) | 6.83176 | 0.282943 | ||||||||
\(584\) | −13.2842 | −0.549706 | ||||||||
\(585\) | −5.14044 | −0.212531 | ||||||||
\(586\) | −17.6975 | −0.731079 | ||||||||
\(587\) | 20.9831 | 0.866066 | 0.433033 | − | 0.901378i | \(-0.357443\pi\) | ||||
0.433033 | + | 0.901378i | \(0.357443\pi\) | |||||||
\(588\) | 4.35166 | 0.179459 | ||||||||
\(589\) | −11.0272 | −0.454368 | ||||||||
\(590\) | 0.760310 | 0.0313015 | ||||||||
\(591\) | −19.1487 | −0.787673 | ||||||||
\(592\) | 5.67235 | 0.233132 | ||||||||
\(593\) | −40.4463 | −1.66093 | −0.830465 | − | 0.557071i | \(-0.811925\pi\) | ||||
−0.830465 | + | 0.557071i | \(0.811925\pi\) | |||||||
\(594\) | −3.63001 | −0.148941 | ||||||||
\(595\) | −1.23731 | −0.0507247 | ||||||||
\(596\) | 14.7073 | 0.602433 | ||||||||
\(597\) | −4.71773 | −0.193084 | ||||||||
\(598\) | 53.3692 | 2.18243 | ||||||||
\(599\) | −17.0129 | −0.695128 | −0.347564 | − | 0.937656i | \(-0.612991\pi\) | ||||
−0.347564 | + | 0.937656i | \(0.612991\pi\) | |||||||
\(600\) | 4.42193 | 0.180524 | ||||||||
\(601\) | 45.2452 | 1.84559 | 0.922795 | − | 0.385291i | \(-0.125899\pi\) | ||||
0.922795 | + | 0.385291i | \(0.125899\pi\) | |||||||
\(602\) | 10.8016 | 0.440241 | ||||||||
\(603\) | −12.0633 | −0.491257 | ||||||||
\(604\) | −18.8361 | −0.766431 | ||||||||
\(605\) | −1.65519 | −0.0672932 | ||||||||
\(606\) | 9.09100 | 0.369297 | ||||||||
\(607\) | −40.3211 | −1.63658 | −0.818292 | − | 0.574802i | \(-0.805079\pi\) | ||||
−0.818292 | + | 0.574802i | \(0.805079\pi\) | |||||||
\(608\) | 2.10642 | 0.0854268 | ||||||||
\(609\) | −4.87272 | −0.197453 | ||||||||
\(610\) | −10.3912 | −0.420726 | ||||||||
\(611\) | −9.82176 | −0.397346 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −13.0033 | −0.525198 | −0.262599 | − | 0.964905i | \(-0.584580\pi\) | ||||
−0.262599 | + | 0.964905i | \(0.584580\pi\) | |||||||
\(614\) | 9.82541 | 0.396521 | ||||||||
\(615\) | 3.07694 | 0.124074 | ||||||||
\(616\) | −5.90739 | −0.238015 | ||||||||
\(617\) | −37.4725 | −1.50859 | −0.754293 | − | 0.656538i | \(-0.772020\pi\) | ||||
−0.754293 | + | 0.656538i | \(0.772020\pi\) | |||||||
\(618\) | −13.9108 | −0.559576 | ||||||||
\(619\) | −18.3333 | −0.736877 | −0.368438 | − | 0.929652i | \(-0.620107\pi\) | ||||
−0.368438 | + | 0.929652i | \(0.620107\pi\) | |||||||
\(620\) | 3.98025 | 0.159851 | ||||||||
\(621\) | −7.89371 | −0.316764 | ||||||||
\(622\) | −30.4661 | −1.22158 | ||||||||
\(623\) | −6.33185 | −0.253680 | ||||||||
\(624\) | −6.76098 | −0.270656 | ||||||||
\(625\) | 16.6631 | 0.666524 | ||||||||
\(626\) | 33.0976 | 1.32285 | ||||||||
\(627\) | −7.64635 | −0.305366 | ||||||||
\(628\) | 4.66776 | 0.186264 | ||||||||
\(629\) | −5.67235 | −0.226171 | ||||||||
\(630\) | 1.23731 | 0.0492955 | ||||||||
\(631\) | −6.20837 | −0.247151 | −0.123576 | − | 0.992335i | \(-0.539436\pi\) | ||||
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(632\) | 11.8018 | 0.469449 | ||||||||
\(633\) | −2.79613 | −0.111136 | ||||||||
\(634\) | 17.9222 | 0.711781 | ||||||||
\(635\) | −13.3548 | −0.529967 | ||||||||
\(636\) | −1.88202 | −0.0746270 | ||||||||
\(637\) | −29.4215 | −1.16572 | ||||||||
\(638\) | −10.8691 | −0.430311 | ||||||||
\(639\) | 6.36534 | 0.251809 | ||||||||
\(640\) | −0.760310 | −0.0300539 | ||||||||
\(641\) | 27.8091 | 1.09840 | 0.549198 | − | 0.835693i | \(-0.314933\pi\) | ||||
0.549198 | + | 0.835693i | \(0.314933\pi\) | |||||||
\(642\) | 6.47874 | 0.255695 | ||||||||
\(643\) | 36.1665 | 1.42627 | 0.713133 | − | 0.701028i | \(-0.247275\pi\) | ||||
0.713133 | + | 0.701028i | \(0.247275\pi\) | |||||||
\(644\) | −12.8460 | −0.506204 | ||||||||
\(645\) | −5.04653 | −0.198707 | ||||||||
\(646\) | −2.10642 | −0.0828761 | ||||||||
\(647\) | −20.5653 | −0.808505 | −0.404253 | − | 0.914647i | \(-0.632468\pi\) | ||||
−0.404253 | + | 0.914647i | \(0.632468\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.63001 | −0.142490 | ||||||||
\(650\) | −29.8966 | −1.17264 | ||||||||
\(651\) | −8.51937 | −0.333900 | ||||||||
\(652\) | 4.81393 | 0.188528 | ||||||||
\(653\) | 49.6694 | 1.94371 | 0.971857 | − | 0.235570i | \(-0.0756958\pi\) | ||||
0.971857 | + | 0.235570i | \(0.0756958\pi\) | |||||||
\(654\) | −9.60480 | −0.375577 | ||||||||
\(655\) | 9.94857 | 0.388723 | ||||||||
\(656\) | 4.04695 | 0.158007 | ||||||||
\(657\) | −13.2842 | −0.518268 | ||||||||
\(658\) | 2.36410 | 0.0921624 | ||||||||
\(659\) | 31.4123 | 1.22365 | 0.611825 | − | 0.790994i | \(-0.290436\pi\) | ||||
0.611825 | + | 0.790994i | \(0.290436\pi\) | |||||||
\(660\) | 2.75993 | 0.107430 | ||||||||
\(661\) | 11.6492 | 0.453100 | 0.226550 | − | 0.974000i | \(-0.427255\pi\) | ||||
0.226550 | + | 0.974000i | \(0.427255\pi\) | |||||||
\(662\) | −7.50037 | −0.291510 | ||||||||
\(663\) | 6.76098 | 0.262575 | ||||||||
\(664\) | 1.53380 | 0.0595232 | ||||||||
\(665\) | 2.60629 | 0.101068 | ||||||||
\(666\) | 5.67235 | 0.219799 | ||||||||
\(667\) | −23.6355 | −0.915172 | ||||||||
\(668\) | 15.7377 | 0.608908 | ||||||||
\(669\) | −16.1158 | −0.623073 | ||||||||
\(670\) | 9.17187 | 0.354340 | ||||||||
\(671\) | 49.6114 | 1.91523 | ||||||||
\(672\) | 1.62737 | 0.0627773 | ||||||||
\(673\) | −17.8651 | −0.688649 | −0.344325 | − | 0.938851i | \(-0.611892\pi\) | ||||
−0.344325 | + | 0.938851i | \(0.611892\pi\) | |||||||
\(674\) | 28.6815 | 1.10477 | ||||||||
\(675\) | 4.42193 | 0.170200 | ||||||||
\(676\) | 32.7109 | 1.25811 | ||||||||
\(677\) | 13.4427 | 0.516646 | 0.258323 | − | 0.966059i | \(-0.416830\pi\) | ||||
0.258323 | + | 0.966059i | \(0.416830\pi\) | |||||||
\(678\) | 13.0169 | 0.499912 | ||||||||
\(679\) | −25.8760 | −0.993030 | ||||||||
\(680\) | 0.760310 | 0.0291565 | ||||||||
\(681\) | −9.91198 | −0.379828 | ||||||||
\(682\) | −19.0033 | −0.727673 | ||||||||
\(683\) | −16.8098 | −0.643209 | −0.321604 | − | 0.946874i | \(-0.604222\pi\) | ||||
−0.321604 | + | 0.946874i | \(0.604222\pi\) | |||||||
\(684\) | 2.10642 | 0.0805411 | ||||||||
\(685\) | −2.38566 | −0.0911513 | ||||||||
\(686\) | 18.4734 | 0.705317 | ||||||||
\(687\) | 21.8492 | 0.833597 | ||||||||
\(688\) | −6.63746 | −0.253051 | ||||||||
\(689\) | 12.7243 | 0.484758 | ||||||||
\(690\) | 6.00166 | 0.228479 | ||||||||
\(691\) | −17.0396 | −0.648218 | −0.324109 | − | 0.946020i | \(-0.605065\pi\) | ||||
−0.324109 | + | 0.946020i | \(0.605065\pi\) | |||||||
\(692\) | −9.91658 | −0.376972 | ||||||||
\(693\) | −5.90739 | −0.224403 | ||||||||
\(694\) | 33.0336 | 1.25394 | ||||||||
\(695\) | −3.20447 | −0.121552 | ||||||||
\(696\) | 2.99423 | 0.113496 | ||||||||
\(697\) | −4.04695 | −0.153289 | ||||||||
\(698\) | −20.6185 | −0.780422 | ||||||||
\(699\) | 13.5472 | 0.512401 | ||||||||
\(700\) | 7.19613 | 0.271988 | ||||||||
\(701\) | −20.7107 | −0.782234 | −0.391117 | − | 0.920341i | \(-0.627911\pi\) | ||||
−0.391117 | + | 0.920341i | \(0.627911\pi\) | |||||||
\(702\) | −6.76098 | −0.255177 | ||||||||
\(703\) | 11.9484 | 0.450641 | ||||||||
\(704\) | 3.63001 | 0.136811 | ||||||||
\(705\) | −1.10451 | −0.0415983 | ||||||||
\(706\) | −25.9945 | −0.978318 | ||||||||
\(707\) | 14.7944 | 0.556402 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −18.2145 | −0.684060 | −0.342030 | − | 0.939689i | \(-0.611114\pi\) | ||||
−0.342030 | + | 0.939689i | \(0.611114\pi\) | |||||||
\(710\) | −4.83963 | −0.181628 | ||||||||
\(711\) | 11.8018 | 0.442600 | ||||||||
\(712\) | 3.89084 | 0.145815 | ||||||||
\(713\) | −41.3239 | −1.54759 | ||||||||
\(714\) | −1.62737 | −0.0609029 | ||||||||
\(715\) | −18.6599 | −0.697840 | ||||||||
\(716\) | −5.63912 | −0.210744 | ||||||||
\(717\) | −1.71808 | −0.0641628 | ||||||||
\(718\) | 16.3148 | 0.608861 | ||||||||
\(719\) | −28.4924 | −1.06259 | −0.531294 | − | 0.847187i | \(-0.678294\pi\) | ||||
−0.531294 | + | 0.847187i | \(0.678294\pi\) | |||||||
\(720\) | −0.760310 | −0.0283351 | ||||||||
\(721\) | −22.6381 | −0.843089 | ||||||||
\(722\) | −14.5630 | −0.541978 | ||||||||
\(723\) | −11.4382 | −0.425392 | ||||||||
\(724\) | 21.3035 | 0.791739 | ||||||||
\(725\) | 13.2403 | 0.491731 | ||||||||
\(726\) | −2.17700 | −0.0807960 | ||||||||
\(727\) | 27.0996 | 1.00507 | 0.502535 | − | 0.864557i | \(-0.332401\pi\) | ||||
0.502535 | + | 0.864557i | \(0.332401\pi\) | |||||||
\(728\) | −11.0026 | −0.407785 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.1001 | 0.373823 | ||||||||
\(731\) | 6.63746 | 0.245495 | ||||||||
\(732\) | −13.6670 | −0.505147 | ||||||||
\(733\) | −1.72996 | −0.0638975 | −0.0319488 | − | 0.999490i | \(-0.510171\pi\) | ||||
−0.0319488 | + | 0.999490i | \(0.510171\pi\) | |||||||
\(734\) | −24.8592 | −0.917571 | ||||||||
\(735\) | −3.30861 | −0.122040 | ||||||||
\(736\) | 7.89371 | 0.290966 | ||||||||
\(737\) | −43.7900 | −1.61303 | ||||||||
\(738\) | 4.04695 | 0.148970 | ||||||||
\(739\) | 31.5143 | 1.15927 | 0.579635 | − | 0.814876i | \(-0.303195\pi\) | ||||
0.579635 | + | 0.814876i | \(0.303195\pi\) | |||||||
\(740\) | −4.31274 | −0.158540 | ||||||||
\(741\) | −14.2415 | −0.523174 | ||||||||
\(742\) | −3.06275 | −0.112437 | ||||||||
\(743\) | 12.0144 | 0.440766 | 0.220383 | − | 0.975413i | \(-0.429269\pi\) | ||||
0.220383 | + | 0.975413i | \(0.429269\pi\) | |||||||
\(744\) | 5.23504 | 0.191926 | ||||||||
\(745\) | −11.1821 | −0.409680 | ||||||||
\(746\) | −0.960167 | −0.0351542 | ||||||||
\(747\) | 1.53380 | 0.0561190 | ||||||||
\(748\) | −3.63001 | −0.132726 | ||||||||
\(749\) | 10.5433 | 0.385245 | ||||||||
\(750\) | −7.16358 | −0.261577 | ||||||||
\(751\) | 24.4977 | 0.893932 | 0.446966 | − | 0.894551i | \(-0.352504\pi\) | ||||
0.446966 | + | 0.894551i | \(0.352504\pi\) | |||||||
\(752\) | −1.45271 | −0.0529749 | ||||||||
\(753\) | 28.4694 | 1.03748 | ||||||||
\(754\) | −20.2439 | −0.737240 | ||||||||
\(755\) | 14.3213 | 0.521205 | ||||||||
\(756\) | 1.62737 | 0.0591870 | ||||||||
\(757\) | 41.6452 | 1.51362 | 0.756811 | − | 0.653634i | \(-0.226756\pi\) | ||||
0.756811 | + | 0.653634i | \(0.226756\pi\) | |||||||
\(758\) | 21.4045 | 0.777447 | ||||||||
\(759\) | −28.6543 | −1.04008 | ||||||||
\(760\) | −1.60153 | −0.0580938 | ||||||||
\(761\) | 48.1386 | 1.74502 | 0.872512 | − | 0.488594i | \(-0.162490\pi\) | ||||
0.872512 | + | 0.488594i | \(0.162490\pi\) | |||||||
\(762\) | −17.5649 | −0.636309 | ||||||||
\(763\) | −15.6306 | −0.565866 | ||||||||
\(764\) | 12.7185 | 0.460140 | ||||||||
\(765\) | 0.760310 | 0.0274891 | ||||||||
\(766\) | 2.36171 | 0.0853320 | ||||||||
\(767\) | −6.76098 | −0.244125 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 9.40598 | 0.339188 | 0.169594 | − | 0.985514i | \(-0.445754\pi\) | ||||
0.169594 | + | 0.985514i | \(0.445754\pi\) | |||||||
\(770\) | 4.49144 | 0.161860 | ||||||||
\(771\) | −7.31711 | −0.263519 | ||||||||
\(772\) | 4.43280 | 0.159540 | ||||||||
\(773\) | 39.6916 | 1.42761 | 0.713803 | − | 0.700347i | \(-0.246971\pi\) | ||||
0.713803 | + | 0.700347i | \(0.246971\pi\) | |||||||
\(774\) | −6.63746 | −0.238579 | ||||||||
\(775\) | 23.1490 | 0.831536 | ||||||||
\(776\) | 15.9005 | 0.570793 | ||||||||
\(777\) | 9.23103 | 0.331161 | ||||||||
\(778\) | −8.71266 | −0.312364 | ||||||||
\(779\) | 8.52460 | 0.305425 | ||||||||
\(780\) | 5.14044 | 0.184057 | ||||||||
\(781\) | 23.1063 | 0.826807 | ||||||||
\(782\) | −7.89371 | −0.282278 | ||||||||
\(783\) | 2.99423 | 0.107005 | ||||||||
\(784\) | −4.35166 | −0.155416 | ||||||||
\(785\) | −3.54895 | −0.126667 | ||||||||
\(786\) | 13.0849 | 0.466723 | ||||||||
\(787\) | 11.9056 | 0.424391 | 0.212195 | − | 0.977227i | \(-0.431939\pi\) | ||||
0.212195 | + | 0.977227i | \(0.431939\pi\) | |||||||
\(788\) | 19.1487 | 0.682145 | ||||||||
\(789\) | −16.1806 | −0.576045 | ||||||||
\(790\) | −8.97299 | −0.319245 | ||||||||
\(791\) | 21.1834 | 0.753194 | ||||||||
\(792\) | 3.63001 | 0.128987 | ||||||||
\(793\) | 92.4024 | 3.28131 | ||||||||
\(794\) | −16.4192 | −0.582697 | ||||||||
\(795\) | 1.43092 | 0.0507495 | ||||||||
\(796\) | 4.71773 | 0.167216 | ||||||||
\(797\) | 10.0394 | 0.355615 | 0.177807 | − | 0.984065i | \(-0.443100\pi\) | ||||
0.177807 | + | 0.984065i | \(0.443100\pi\) | |||||||
\(798\) | 3.42794 | 0.121348 | ||||||||
\(799\) | 1.45271 | 0.0513932 | ||||||||
\(800\) | −4.42193 | −0.156339 | ||||||||
\(801\) | 3.89084 | 0.137476 | ||||||||
\(802\) | 23.1727 | 0.818256 | ||||||||
\(803\) | −48.2220 | −1.70172 | ||||||||
\(804\) | 12.0633 | 0.425441 | ||||||||
\(805\) | 9.76695 | 0.344240 | ||||||||
\(806\) | −35.3940 | −1.24670 | ||||||||
\(807\) | −21.2237 | −0.747110 | ||||||||
\(808\) | −9.09100 | −0.319820 | ||||||||
\(809\) | −22.7120 | −0.798511 | −0.399256 | − | 0.916840i | \(-0.630731\pi\) | ||||
−0.399256 | + | 0.916840i | \(0.630731\pi\) | |||||||
\(810\) | −0.760310 | −0.0267146 | ||||||||
\(811\) | 30.6184 | 1.07516 | 0.537579 | − | 0.843213i | \(-0.319339\pi\) | ||||
0.537579 | + | 0.843213i | \(0.319339\pi\) | |||||||
\(812\) | 4.87272 | 0.170999 | ||||||||
\(813\) | 30.6748 | 1.07581 | ||||||||
\(814\) | 20.5907 | 0.721704 | ||||||||
\(815\) | −3.66008 | −0.128207 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −13.9813 | −0.489144 | ||||||||
\(818\) | 29.5640 | 1.03368 | ||||||||
\(819\) | −11.0026 | −0.384464 | ||||||||
\(820\) | −3.07694 | −0.107451 | ||||||||
\(821\) | −53.7150 | −1.87467 | −0.937333 | − | 0.348436i | \(-0.886713\pi\) | ||||
−0.937333 | + | 0.348436i | \(0.886713\pi\) | |||||||
\(822\) | −3.13775 | −0.109441 | ||||||||
\(823\) | −32.2014 | −1.12247 | −0.561235 | − | 0.827657i | \(-0.689674\pi\) | ||||
−0.561235 | + | 0.827657i | \(0.689674\pi\) | |||||||
\(824\) | 13.9108 | 0.484607 | ||||||||
\(825\) | 16.0517 | 0.558847 | ||||||||
\(826\) | 1.62737 | 0.0566236 | ||||||||
\(827\) | −26.8042 | −0.932074 | −0.466037 | − | 0.884765i | \(-0.654319\pi\) | ||||
−0.466037 | + | 0.884765i | \(0.654319\pi\) | |||||||
\(828\) | 7.89371 | 0.274325 | ||||||||
\(829\) | 37.6158 | 1.30645 | 0.653225 | − | 0.757164i | \(-0.273416\pi\) | ||||
0.653225 | + | 0.757164i | \(0.273416\pi\) | |||||||
\(830\) | −1.16617 | −0.0404782 | ||||||||
\(831\) | 23.1354 | 0.802558 | ||||||||
\(832\) | 6.76098 | 0.234395 | ||||||||
\(833\) | 4.35166 | 0.150776 | ||||||||
\(834\) | −4.21469 | −0.145943 | ||||||||
\(835\) | −11.9655 | −0.414083 | ||||||||
\(836\) | 7.64635 | 0.264454 | ||||||||
\(837\) | 5.23504 | 0.180949 | ||||||||
\(838\) | −6.58374 | −0.227431 | ||||||||
\(839\) | −23.5356 | −0.812539 | −0.406270 | − | 0.913753i | \(-0.633171\pi\) | ||||
−0.406270 | + | 0.913753i | \(0.633171\pi\) | |||||||
\(840\) | −1.23731 | −0.0426912 | ||||||||
\(841\) | −20.0346 | −0.690849 | ||||||||
\(842\) | 28.0737 | 0.967484 | ||||||||
\(843\) | −16.1851 | −0.557446 | ||||||||
\(844\) | 2.79613 | 0.0962467 | ||||||||
\(845\) | −24.8704 | −0.855568 | ||||||||
\(846\) | −1.45271 | −0.0499452 | ||||||||
\(847\) | −3.54279 | −0.121732 | ||||||||
\(848\) | 1.88202 | 0.0646289 | ||||||||
\(849\) | 13.1301 | 0.450623 | ||||||||
\(850\) | 4.42193 | 0.151671 | ||||||||
\(851\) | 44.7759 | 1.53490 | ||||||||
\(852\) | −6.36534 | −0.218073 | ||||||||
\(853\) | −49.0153 | −1.67825 | −0.839125 | − | 0.543938i | \(-0.816933\pi\) | ||||
−0.839125 | + | 0.543938i | \(0.816933\pi\) | |||||||
\(854\) | −22.2413 | −0.761083 | ||||||||
\(855\) | −1.60153 | −0.0547713 | ||||||||
\(856\) | −6.47874 | −0.221439 | ||||||||
\(857\) | 27.2238 | 0.929948 | 0.464974 | − | 0.885324i | \(-0.346064\pi\) | ||||
0.464974 | + | 0.885324i | \(0.346064\pi\) | |||||||
\(858\) | −24.5425 | −0.837866 | ||||||||
\(859\) | −19.4563 | −0.663839 | −0.331920 | − | 0.943308i | \(-0.607696\pi\) | ||||
−0.331920 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(860\) | 5.04653 | 0.172085 | ||||||||
\(861\) | 6.58590 | 0.224447 | ||||||||
\(862\) | −39.1100 | −1.33209 | ||||||||
\(863\) | 33.7437 | 1.14865 | 0.574324 | − | 0.818628i | \(-0.305265\pi\) | ||||
0.574324 | + | 0.818628i | \(0.305265\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 7.53967 | 0.256357 | ||||||||
\(866\) | −23.0413 | −0.782975 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 8.51937 | 0.289166 | ||||||||
\(869\) | 42.8405 | 1.45327 | ||||||||
\(870\) | −2.27654 | −0.0771819 | ||||||||
\(871\) | −81.5600 | −2.76355 | ||||||||
\(872\) | 9.60480 | 0.325260 | ||||||||
\(873\) | 15.9005 | 0.538149 | ||||||||
\(874\) | 16.6275 | 0.562433 | ||||||||
\(875\) | −11.6578 | −0.394107 | ||||||||
\(876\) | 13.2842 | 0.448833 | ||||||||
\(877\) | −11.1955 | −0.378047 | −0.189023 | − | 0.981973i | \(-0.560532\pi\) | ||||
−0.189023 | + | 0.981973i | \(0.560532\pi\) | |||||||
\(878\) | 0.621975 | 0.0209906 | ||||||||
\(879\) | 17.6975 | 0.596923 | ||||||||
\(880\) | −2.75993 | −0.0930374 | ||||||||
\(881\) | −1.41166 | −0.0475602 | −0.0237801 | − | 0.999717i | \(-0.507570\pi\) | ||||
−0.0237801 | + | 0.999717i | \(0.507570\pi\) | |||||||
\(882\) | −4.35166 | −0.146528 | ||||||||
\(883\) | 38.6523 | 1.30075 | 0.650377 | − | 0.759612i | \(-0.274611\pi\) | ||||
0.650377 | + | 0.759612i | \(0.274611\pi\) | |||||||
\(884\) | −6.76098 | −0.227396 | ||||||||
\(885\) | −0.760310 | −0.0255575 | ||||||||
\(886\) | −28.7111 | −0.964567 | ||||||||
\(887\) | −33.7339 | −1.13267 | −0.566336 | − | 0.824174i | \(-0.691640\pi\) | ||||
−0.566336 | + | 0.824174i | \(0.691640\pi\) | |||||||
\(888\) | −5.67235 | −0.190352 | ||||||||
\(889\) | −28.5846 | −0.958698 | ||||||||
\(890\) | −2.95825 | −0.0991606 | ||||||||
\(891\) | 3.63001 | 0.121610 | ||||||||
\(892\) | 16.1158 | 0.539597 | ||||||||
\(893\) | −3.06003 | −0.102400 | ||||||||
\(894\) | −14.7073 | −0.491885 | ||||||||
\(895\) | 4.28748 | 0.143315 | ||||||||
\(896\) | −1.62737 | −0.0543667 | ||||||||
\(897\) | −53.3692 | −1.78195 | ||||||||
\(898\) | −6.66798 | −0.222513 | ||||||||
\(899\) | 15.6749 | 0.522787 | ||||||||
\(900\) | −4.42193 | −0.147398 | ||||||||
\(901\) | −1.88202 | −0.0626992 | ||||||||
\(902\) | 14.6905 | 0.489140 | ||||||||
\(903\) | −10.8016 | −0.359456 | ||||||||
\(904\) | −13.0169 | −0.432936 | ||||||||
\(905\) | −16.1973 | −0.538416 | ||||||||
\(906\) | 18.8361 | 0.625788 | ||||||||
\(907\) | 37.9649 | 1.26061 | 0.630303 | − | 0.776349i | \(-0.282931\pi\) | ||||
0.630303 | + | 0.776349i | \(0.282931\pi\) | |||||||
\(908\) | 9.91198 | 0.328941 | ||||||||
\(909\) | −9.09100 | −0.301529 | ||||||||
\(910\) | 8.36542 | 0.277311 | ||||||||
\(911\) | −21.8495 | −0.723907 | −0.361953 | − | 0.932196i | \(-0.617890\pi\) | ||||
−0.361953 | + | 0.932196i | \(0.617890\pi\) | |||||||
\(912\) | −2.10642 | −0.0697507 | ||||||||
\(913\) | 5.56773 | 0.184265 | ||||||||
\(914\) | 23.6303 | 0.781621 | ||||||||
\(915\) | 10.3912 | 0.343521 | ||||||||
\(916\) | −21.8492 | −0.721916 | ||||||||
\(917\) | 21.2940 | 0.703190 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −3.53742 | −0.116689 | −0.0583443 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583443 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(920\) | −6.00166 | −0.197869 | ||||||||
\(921\) | −9.82541 | −0.323758 | ||||||||
\(922\) | 0.780720 | 0.0257116 | ||||||||
\(923\) | 43.0359 | 1.41655 | ||||||||
\(924\) | 5.90739 | 0.194339 | ||||||||
\(925\) | −25.0827 | −0.824715 | ||||||||
\(926\) | 0.833871 | 0.0274027 | ||||||||
\(927\) | 13.9108 | 0.456892 | ||||||||
\(928\) | −2.99423 | −0.0982903 | ||||||||
\(929\) | 18.5301 | 0.607952 | 0.303976 | − | 0.952680i | \(-0.401686\pi\) | ||||
0.303976 | + | 0.952680i | \(0.401686\pi\) | |||||||
\(930\) | −3.98025 | −0.130518 | ||||||||
\(931\) | −9.16643 | −0.300418 | ||||||||
\(932\) | −13.5472 | −0.443752 | ||||||||
\(933\) | 30.4661 | 0.997416 | ||||||||
\(934\) | −36.4231 | −1.19180 | ||||||||
\(935\) | 2.75993 | 0.0902595 | ||||||||
\(936\) | 6.76098 | 0.220990 | ||||||||
\(937\) | 5.89175 | 0.192475 | 0.0962376 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962376 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(938\) | 19.6315 | 0.640993 | ||||||||
\(939\) | −33.0976 | −1.08010 | ||||||||
\(940\) | 1.10451 | 0.0360252 | ||||||||
\(941\) | −32.1850 | −1.04920 | −0.524601 | − | 0.851348i | \(-0.675786\pi\) | ||||
−0.524601 | + | 0.851348i | \(0.675786\pi\) | |||||||
\(942\) | −4.66776 | −0.152084 | ||||||||
\(943\) | 31.9455 | 1.04029 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −1.23731 | −0.0402496 | ||||||||
\(946\) | −24.0941 | −0.783366 | ||||||||
\(947\) | 20.6768 | 0.671905 | 0.335953 | − | 0.941879i | \(-0.390942\pi\) | ||||
0.335953 | + | 0.941879i | \(0.390942\pi\) | |||||||
\(948\) | −11.8018 | −0.383303 | ||||||||
\(949\) | −89.8146 | −2.91551 | ||||||||
\(950\) | −9.31446 | −0.302201 | ||||||||
\(951\) | −17.9222 | −0.581167 | ||||||||
\(952\) | 1.62737 | 0.0527435 | ||||||||
\(953\) | −21.1557 | −0.685300 | −0.342650 | − | 0.939463i | \(-0.611324\pi\) | ||||
−0.342650 | + | 0.939463i | \(0.611324\pi\) | |||||||
\(954\) | 1.88202 | 0.0609327 | ||||||||
\(955\) | −9.67002 | −0.312915 | ||||||||
\(956\) | 1.71808 | 0.0555666 | ||||||||
\(957\) | 10.8691 | 0.351347 | ||||||||
\(958\) | 3.13148 | 0.101174 | ||||||||
\(959\) | −5.10628 | −0.164891 | ||||||||
\(960\) | 0.760310 | 0.0245389 | ||||||||
\(961\) | −3.59435 | −0.115947 | ||||||||
\(962\) | 38.3507 | 1.23647 | ||||||||
\(963\) | −6.47874 | −0.208774 | ||||||||
\(964\) | 11.4382 | 0.368400 | ||||||||
\(965\) | −3.37030 | −0.108494 | ||||||||
\(966\) | 12.8460 | 0.413314 | ||||||||
\(967\) | −45.2397 | −1.45481 | −0.727405 | − | 0.686208i | \(-0.759274\pi\) | ||||
−0.727405 | + | 0.686208i | \(0.759274\pi\) | |||||||
\(968\) | 2.17700 | 0.0699714 | ||||||||
\(969\) | 2.10642 | 0.0676681 | ||||||||
\(970\) | −12.0893 | −0.388163 | ||||||||
\(971\) | 21.7060 | 0.696579 | 0.348289 | − | 0.937387i | \(-0.386763\pi\) | ||||
0.348289 | + | 0.937387i | \(0.386763\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.85887 | −0.219885 | ||||||||
\(974\) | −1.19919 | −0.0384246 | ||||||||
\(975\) | 29.8966 | 0.957457 | ||||||||
\(976\) | 13.6670 | 0.437470 | ||||||||
\(977\) | −14.8045 | −0.473638 | −0.236819 | − | 0.971554i | \(-0.576105\pi\) | ||||
−0.236819 | + | 0.971554i | \(0.576105\pi\) | |||||||
\(978\) | −4.81393 | −0.153933 | ||||||||
\(979\) | 14.1238 | 0.451399 | ||||||||
\(980\) | 3.30861 | 0.105690 | ||||||||
\(981\) | 9.60480 | 0.306658 | ||||||||
\(982\) | −13.9339 | −0.444650 | ||||||||
\(983\) | −24.8315 | −0.792003 | −0.396001 | − | 0.918250i | \(-0.629602\pi\) | ||||
−0.396001 | + | 0.918250i | \(0.629602\pi\) | |||||||
\(984\) | −4.04695 | −0.129012 | ||||||||
\(985\) | −14.5590 | −0.463887 | ||||||||
\(986\) | 2.99423 | 0.0953556 | ||||||||
\(987\) | −2.36410 | −0.0752503 | ||||||||
\(988\) | 14.2415 | 0.453082 | ||||||||
\(989\) | −52.3942 | −1.66604 | ||||||||
\(990\) | −2.75993 | −0.0877165 | ||||||||
\(991\) | 10.0925 | 0.320599 | 0.160299 | − | 0.987068i | \(-0.448754\pi\) | ||||
0.160299 | + | 0.987068i | \(0.448754\pi\) | |||||||
\(992\) | −5.23504 | −0.166213 | ||||||||
\(993\) | 7.50037 | 0.238017 | ||||||||
\(994\) | −10.3588 | −0.328561 | ||||||||
\(995\) | −3.58694 | −0.113714 | ||||||||
\(996\) | −1.53380 | −0.0486005 | ||||||||
\(997\) | −5.58073 | −0.176744 | −0.0883718 | − | 0.996088i | \(-0.528166\pi\) | ||||
−0.0883718 | + | 0.996088i | \(0.528166\pi\) | |||||||
\(998\) | −11.3864 | −0.360431 | ||||||||
\(999\) | −5.67235 | −0.179465 |
(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 | 6018.2.a.z.1.5 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.z.1.5 | ✓ | 11 | 1.1 | even | 1 | trivial |