Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + 1317797 x^{12} - 1160501 x^{11} - 9914845 x^{10} + 7570653 x^{9} + \cdots + 150528 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-1.78835\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.78835 | 0.632277 | 0.316139 | − | 0.948713i | \(-0.397614\pi\) | ||||
0.316139 | + | 0.948713i | \(0.397614\pi\) | |||||||
\(3\) | −7.45188 | −1.43411 | −0.717057 | − | 0.697014i | \(-0.754511\pi\) | ||||
−0.717057 | + | 0.697014i | \(0.754511\pi\) | |||||||
\(4\) | −4.80180 | −0.600225 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −13.3266 | −0.906758 | ||||||||
\(7\) | −20.9424 | −1.13078 | −0.565392 | − | 0.824823i | \(-0.691275\pi\) | ||||
−0.565392 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(8\) | −22.8941 | −1.01179 | ||||||||
\(9\) | 28.5305 | 1.05669 | ||||||||
\(10\) | −8.94175 | −0.282763 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 35.7825 | 0.860792 | ||||||||
\(13\) | 37.7596 | 0.805586 | 0.402793 | − | 0.915291i | \(-0.368039\pi\) | ||||
0.402793 | + | 0.915291i | \(0.368039\pi\) | |||||||
\(14\) | −37.4524 | −0.714969 | ||||||||
\(15\) | 37.2594 | 0.641356 | ||||||||
\(16\) | −2.52827 | −0.0395042 | ||||||||
\(17\) | 119.316 | 1.70225 | 0.851126 | − | 0.524962i | \(-0.175921\pi\) | ||||
0.851126 | + | 0.524962i | \(0.175921\pi\) | |||||||
\(18\) | 51.0225 | 0.668118 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 24.0090 | 0.268429 | ||||||||
\(21\) | 156.060 | 1.62167 | ||||||||
\(22\) | −19.6719 | −0.190639 | ||||||||
\(23\) | −24.1294 | −0.218754 | −0.109377 | − | 0.994000i | \(-0.534886\pi\) | ||||
−0.109377 | + | 0.994000i | \(0.534886\pi\) | |||||||
\(24\) | 170.604 | 1.45102 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 67.5274 | 0.509354 | ||||||||
\(27\) | −11.4052 | −0.0812935 | ||||||||
\(28\) | 100.561 | 0.678725 | ||||||||
\(29\) | 1.45246 | 0.00930051 | 0.00465026 | − | 0.999989i | \(-0.498520\pi\) | ||||
0.00465026 | + | 0.999989i | \(0.498520\pi\) | |||||||
\(30\) | 66.6329 | 0.405515 | ||||||||
\(31\) | −7.62072 | −0.0441523 | −0.0220762 | − | 0.999756i | \(-0.507028\pi\) | ||||
−0.0220762 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(32\) | 178.631 | 0.986809 | ||||||||
\(33\) | 81.9707 | 0.432402 | ||||||||
\(34\) | 213.378 | 1.07629 | ||||||||
\(35\) | 104.712 | 0.505702 | ||||||||
\(36\) | −136.998 | −0.634249 | ||||||||
\(37\) | −402.545 | −1.78860 | −0.894298 | − | 0.447473i | \(-0.852324\pi\) | ||||
−0.894298 | + | 0.447473i | \(0.852324\pi\) | |||||||
\(38\) | 33.9787 | 0.145054 | ||||||||
\(39\) | −281.380 | −1.15530 | ||||||||
\(40\) | 114.471 | 0.452485 | ||||||||
\(41\) | 278.512 | 1.06088 | 0.530441 | − | 0.847722i | \(-0.322026\pi\) | ||||
0.530441 | + | 0.847722i | \(0.322026\pi\) | |||||||
\(42\) | 279.090 | 1.02535 | ||||||||
\(43\) | −228.717 | −0.811141 | −0.405571 | − | 0.914064i | \(-0.632927\pi\) | ||||
−0.405571 | + | 0.914064i | \(0.632927\pi\) | |||||||
\(44\) | 52.8198 | 0.180975 | ||||||||
\(45\) | −142.653 | −0.472564 | ||||||||
\(46\) | −43.1519 | −0.138313 | ||||||||
\(47\) | 409.518 | 1.27094 | 0.635472 | − | 0.772124i | \(-0.280806\pi\) | ||||
0.635472 | + | 0.772124i | \(0.280806\pi\) | |||||||
\(48\) | 18.8404 | 0.0566536 | ||||||||
\(49\) | 95.5842 | 0.278671 | ||||||||
\(50\) | 44.7088 | 0.126455 | ||||||||
\(51\) | −889.125 | −2.44122 | ||||||||
\(52\) | −181.314 | −0.483533 | ||||||||
\(53\) | 45.2974 | 0.117398 | 0.0586988 | − | 0.998276i | \(-0.481305\pi\) | ||||
0.0586988 | + | 0.998276i | \(0.481305\pi\) | |||||||
\(54\) | −20.3964 | −0.0514000 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 479.458 | 1.14411 | ||||||||
\(57\) | −141.586 | −0.329009 | ||||||||
\(58\) | 2.59751 | 0.00588050 | ||||||||
\(59\) | −203.531 | −0.449109 | −0.224555 | − | 0.974462i | \(-0.572093\pi\) | ||||
−0.224555 | + | 0.974462i | \(0.572093\pi\) | |||||||
\(60\) | −178.912 | −0.384958 | ||||||||
\(61\) | −196.662 | −0.412787 | −0.206394 | − | 0.978469i | \(-0.566173\pi\) | ||||
−0.206394 | + | 0.978469i | \(0.566173\pi\) | |||||||
\(62\) | −13.6285 | −0.0279165 | ||||||||
\(63\) | −597.497 | −1.19488 | ||||||||
\(64\) | 339.682 | 0.663441 | ||||||||
\(65\) | −188.798 | −0.360269 | ||||||||
\(66\) | 146.592 | 0.273398 | ||||||||
\(67\) | −81.1892 | −0.148042 | −0.0740212 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740212 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(68\) | −572.930 | −1.02173 | ||||||||
\(69\) | 179.810 | 0.313718 | ||||||||
\(70\) | 187.262 | 0.319744 | ||||||||
\(71\) | 257.755 | 0.430844 | 0.215422 | − | 0.976521i | \(-0.430887\pi\) | ||||
0.215422 | + | 0.976521i | \(0.430887\pi\) | |||||||
\(72\) | −653.181 | −1.06914 | ||||||||
\(73\) | 544.148 | 0.872435 | 0.436217 | − | 0.899841i | \(-0.356318\pi\) | ||||
0.436217 | + | 0.899841i | \(0.356318\pi\) | |||||||
\(74\) | −719.892 | −1.13089 | ||||||||
\(75\) | −186.297 | −0.286823 | ||||||||
\(76\) | −91.2342 | −0.137701 | ||||||||
\(77\) | 230.366 | 0.340944 | ||||||||
\(78\) | −503.206 | −0.730472 | ||||||||
\(79\) | 77.8441 | 0.110863 | 0.0554313 | − | 0.998463i | \(-0.482347\pi\) | ||||
0.0554313 | + | 0.998463i | \(0.482347\pi\) | |||||||
\(80\) | 12.6414 | 0.0176668 | ||||||||
\(81\) | −685.334 | −0.940101 | ||||||||
\(82\) | 498.076 | 0.670772 | ||||||||
\(83\) | −819.324 | −1.08352 | −0.541762 | − | 0.840532i | \(-0.682242\pi\) | ||||
−0.541762 | + | 0.840532i | \(0.682242\pi\) | |||||||
\(84\) | −749.371 | −0.973369 | ||||||||
\(85\) | −596.578 | −0.761270 | ||||||||
\(86\) | −409.027 | −0.512866 | ||||||||
\(87\) | −10.8236 | −0.0133380 | ||||||||
\(88\) | 251.835 | 0.305065 | ||||||||
\(89\) | 992.947 | 1.18261 | 0.591304 | − | 0.806448i | \(-0.298613\pi\) | ||||
0.591304 | + | 0.806448i | \(0.298613\pi\) | |||||||
\(90\) | −255.113 | −0.298792 | ||||||||
\(91\) | −790.776 | −0.910944 | ||||||||
\(92\) | 115.865 | 0.131301 | ||||||||
\(93\) | 56.7887 | 0.0633195 | ||||||||
\(94\) | 732.362 | 0.803589 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −1331.14 | −1.41520 | ||||||||
\(97\) | 1227.59 | 1.28498 | 0.642491 | − | 0.766294i | \(-0.277901\pi\) | ||||
0.642491 | + | 0.766294i | \(0.277901\pi\) | |||||||
\(98\) | 170.938 | 0.176197 | ||||||||
\(99\) | −313.836 | −0.318603 | ||||||||
\(100\) | −120.045 | −0.120045 | ||||||||
\(101\) | −602.090 | −0.593171 | −0.296585 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296585 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(102\) | −1590.07 | −1.54353 | ||||||||
\(103\) | −646.684 | −0.618638 | −0.309319 | − | 0.950958i | \(-0.600101\pi\) | ||||
−0.309319 | + | 0.950958i | \(0.600101\pi\) | |||||||
\(104\) | −864.472 | −0.815081 | ||||||||
\(105\) | −780.301 | −0.725234 | ||||||||
\(106\) | 81.0076 | 0.0742279 | ||||||||
\(107\) | −417.116 | −0.376861 | −0.188431 | − | 0.982087i | \(-0.560340\pi\) | ||||
−0.188431 | + | 0.982087i | \(0.560340\pi\) | |||||||
\(108\) | 54.7653 | 0.0487944 | ||||||||
\(109\) | 540.431 | 0.474898 | 0.237449 | − | 0.971400i | \(-0.423689\pi\) | ||||
0.237449 | + | 0.971400i | \(0.423689\pi\) | |||||||
\(110\) | 98.3593 | 0.0852563 | ||||||||
\(111\) | 2999.72 | 2.56505 | ||||||||
\(112\) | 52.9481 | 0.0446707 | ||||||||
\(113\) | −367.393 | −0.305853 | −0.152927 | − | 0.988238i | \(-0.548870\pi\) | ||||
−0.152927 | + | 0.988238i | \(0.548870\pi\) | |||||||
\(114\) | −253.205 | −0.208025 | ||||||||
\(115\) | 120.647 | 0.0978296 | ||||||||
\(116\) | −6.97442 | −0.00558240 | ||||||||
\(117\) | 1077.30 | 0.851251 | ||||||||
\(118\) | −363.984 | −0.283962 | ||||||||
\(119\) | −2498.75 | −1.92488 | ||||||||
\(120\) | −853.021 | −0.648915 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −351.701 | −0.260996 | ||||||||
\(123\) | −2075.43 | −1.52143 | ||||||||
\(124\) | 36.5932 | 0.0265013 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −1068.53 | −0.755497 | ||||||||
\(127\) | 1067.02 | 0.745535 | 0.372768 | − | 0.927925i | \(-0.378409\pi\) | ||||
0.372768 | + | 0.927925i | \(0.378409\pi\) | |||||||
\(128\) | −821.581 | −0.567330 | ||||||||
\(129\) | 1704.37 | 1.16327 | ||||||||
\(130\) | −337.637 | −0.227790 | ||||||||
\(131\) | 2114.17 | 1.41005 | 0.705023 | − | 0.709185i | \(-0.250937\pi\) | ||||
0.705023 | + | 0.709185i | \(0.250937\pi\) | |||||||
\(132\) | −393.607 | −0.259539 | ||||||||
\(133\) | −397.906 | −0.259420 | ||||||||
\(134\) | −145.195 | −0.0936039 | ||||||||
\(135\) | 57.0258 | 0.0363556 | ||||||||
\(136\) | −2731.62 | −1.72231 | ||||||||
\(137\) | 736.727 | 0.459437 | 0.229718 | − | 0.973257i | \(-0.426220\pi\) | ||||
0.229718 | + | 0.973257i | \(0.426220\pi\) | |||||||
\(138\) | 321.562 | 0.198357 | ||||||||
\(139\) | −1707.49 | −1.04193 | −0.520963 | − | 0.853579i | \(-0.674427\pi\) | ||||
−0.520963 | + | 0.853579i | \(0.674427\pi\) | |||||||
\(140\) | −502.806 | −0.303535 | ||||||||
\(141\) | −3051.68 | −1.82268 | ||||||||
\(142\) | 460.957 | 0.272413 | ||||||||
\(143\) | −415.355 | −0.242893 | ||||||||
\(144\) | −72.1329 | −0.0417436 | ||||||||
\(145\) | −7.26230 | −0.00415932 | ||||||||
\(146\) | 973.128 | 0.551621 | ||||||||
\(147\) | −712.282 | −0.399646 | ||||||||
\(148\) | 1932.94 | 1.07356 | ||||||||
\(149\) | −393.039 | −0.216101 | −0.108050 | − | 0.994145i | \(-0.534461\pi\) | ||||
−0.108050 | + | 0.994145i | \(0.534461\pi\) | |||||||
\(150\) | −333.164 | −0.181352 | ||||||||
\(151\) | −2977.78 | −1.60483 | −0.802413 | − | 0.596769i | \(-0.796451\pi\) | ||||
−0.802413 | + | 0.596769i | \(0.796451\pi\) | |||||||
\(152\) | −434.988 | −0.232120 | ||||||||
\(153\) | 3404.13 | 1.79874 | ||||||||
\(154\) | 411.976 | 0.215571 | ||||||||
\(155\) | 38.1036 | 0.0197455 | ||||||||
\(156\) | 1351.13 | 0.693442 | ||||||||
\(157\) | 2358.06 | 1.19868 | 0.599342 | − | 0.800493i | \(-0.295429\pi\) | ||||
0.599342 | + | 0.800493i | \(0.295429\pi\) | |||||||
\(158\) | 139.213 | 0.0700959 | ||||||||
\(159\) | −337.551 | −0.168362 | ||||||||
\(160\) | −893.157 | −0.441314 | ||||||||
\(161\) | 505.328 | 0.247363 | ||||||||
\(162\) | −1225.62 | −0.594405 | ||||||||
\(163\) | 1274.77 | 0.612565 | 0.306282 | − | 0.951941i | \(-0.400915\pi\) | ||||
0.306282 | + | 0.951941i | \(0.400915\pi\) | |||||||
\(164\) | −1337.36 | −0.636769 | ||||||||
\(165\) | −409.853 | −0.193376 | ||||||||
\(166\) | −1465.24 | −0.685087 | ||||||||
\(167\) | 2396.90 | 1.11065 | 0.555323 | − | 0.831635i | \(-0.312595\pi\) | ||||
0.555323 | + | 0.831635i | \(0.312595\pi\) | |||||||
\(168\) | −3572.86 | −1.64079 | ||||||||
\(169\) | −771.214 | −0.351031 | ||||||||
\(170\) | −1066.89 | −0.481334 | ||||||||
\(171\) | 542.080 | 0.242420 | ||||||||
\(172\) | 1098.26 | 0.486868 | ||||||||
\(173\) | 3707.72 | 1.62944 | 0.814719 | − | 0.579856i | \(-0.196891\pi\) | ||||
0.814719 | + | 0.579856i | \(0.196891\pi\) | |||||||
\(174\) | −19.3563 | −0.00843332 | ||||||||
\(175\) | −523.560 | −0.226157 | ||||||||
\(176\) | 27.8110 | 0.0119110 | ||||||||
\(177\) | 1516.69 | 0.644074 | ||||||||
\(178\) | 1775.74 | 0.747737 | ||||||||
\(179\) | −3584.65 | −1.49681 | −0.748406 | − | 0.663241i | \(-0.769180\pi\) | ||||
−0.748406 | + | 0.663241i | \(0.769180\pi\) | |||||||
\(180\) | 684.989 | 0.283645 | ||||||||
\(181\) | −4671.14 | −1.91825 | −0.959124 | − | 0.282986i | \(-0.908675\pi\) | ||||
−0.959124 | + | 0.282986i | \(0.908675\pi\) | |||||||
\(182\) | −1414.19 | −0.575969 | ||||||||
\(183\) | 1465.50 | 0.591984 | ||||||||
\(184\) | 552.422 | 0.221332 | ||||||||
\(185\) | 2012.73 | 0.799884 | ||||||||
\(186\) | 101.558 | 0.0400355 | ||||||||
\(187\) | −1312.47 | −0.513248 | ||||||||
\(188\) | −1966.42 | −0.762852 | ||||||||
\(189\) | 238.851 | 0.0919253 | ||||||||
\(190\) | −169.893 | −0.0648703 | ||||||||
\(191\) | −4407.46 | −1.66970 | −0.834850 | − | 0.550477i | \(-0.814446\pi\) | ||||
−0.834850 | + | 0.550477i | \(0.814446\pi\) | |||||||
\(192\) | −2531.27 | −0.951451 | ||||||||
\(193\) | −609.803 | −0.227433 | −0.113717 | − | 0.993513i | \(-0.536276\pi\) | ||||
−0.113717 | + | 0.993513i | \(0.536276\pi\) | |||||||
\(194\) | 2195.37 | 0.812465 | ||||||||
\(195\) | 1406.90 | 0.516667 | ||||||||
\(196\) | −458.976 | −0.167265 | ||||||||
\(197\) | 869.384 | 0.314422 | 0.157211 | − | 0.987565i | \(-0.449750\pi\) | ||||
0.157211 | + | 0.987565i | \(0.449750\pi\) | |||||||
\(198\) | −561.248 | −0.201445 | ||||||||
\(199\) | −1594.47 | −0.567986 | −0.283993 | − | 0.958826i | \(-0.591659\pi\) | ||||
−0.283993 | + | 0.958826i | \(0.591659\pi\) | |||||||
\(200\) | −572.353 | −0.202357 | ||||||||
\(201\) | 605.012 | 0.212310 | ||||||||
\(202\) | −1076.75 | −0.375048 | ||||||||
\(203\) | −30.4180 | −0.0105169 | ||||||||
\(204\) | 4269.40 | 1.46528 | ||||||||
\(205\) | −1392.56 | −0.474441 | ||||||||
\(206\) | −1156.50 | −0.391151 | ||||||||
\(207\) | −688.425 | −0.231154 | ||||||||
\(208\) | −95.4665 | −0.0318241 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −1395.45 | −0.458549 | ||||||||
\(211\) | −3299.68 | −1.07658 | −0.538292 | − | 0.842758i | \(-0.680930\pi\) | ||||
−0.538292 | + | 0.842758i | \(0.680930\pi\) | |||||||
\(212\) | −217.509 | −0.0704650 | ||||||||
\(213\) | −1920.76 | −0.617879 | ||||||||
\(214\) | −745.950 | −0.238281 | ||||||||
\(215\) | 1143.59 | 0.362753 | ||||||||
\(216\) | 261.111 | 0.0822516 | ||||||||
\(217\) | 159.596 | 0.0499267 | ||||||||
\(218\) | 966.480 | 0.300267 | ||||||||
\(219\) | −4054.93 | −1.25117 | ||||||||
\(220\) | −264.099 | −0.0809344 | ||||||||
\(221\) | 4505.30 | 1.37131 | ||||||||
\(222\) | 5364.55 | 1.62182 | ||||||||
\(223\) | −2928.53 | −0.879413 | −0.439707 | − | 0.898141i | \(-0.644918\pi\) | ||||
−0.439707 | + | 0.898141i | \(0.644918\pi\) | |||||||
\(224\) | −3740.97 | −1.11587 | ||||||||
\(225\) | 713.263 | 0.211337 | ||||||||
\(226\) | −657.027 | −0.193384 | ||||||||
\(227\) | −4913.12 | −1.43654 | −0.718272 | − | 0.695762i | \(-0.755067\pi\) | ||||
−0.718272 | + | 0.695762i | \(0.755067\pi\) | |||||||
\(228\) | 679.867 | 0.197479 | ||||||||
\(229\) | 5249.74 | 1.51490 | 0.757451 | − | 0.652892i | \(-0.226444\pi\) | ||||
0.757451 | + | 0.652892i | \(0.226444\pi\) | |||||||
\(230\) | 215.759 | 0.0618554 | ||||||||
\(231\) | −1716.66 | −0.488953 | ||||||||
\(232\) | −33.2528 | −0.00941013 | ||||||||
\(233\) | −6568.13 | −1.84675 | −0.923374 | − | 0.383901i | \(-0.874580\pi\) | ||||
−0.923374 | + | 0.383901i | \(0.874580\pi\) | |||||||
\(234\) | 1926.59 | 0.538227 | ||||||||
\(235\) | −2047.59 | −0.568383 | ||||||||
\(236\) | 977.314 | 0.269567 | ||||||||
\(237\) | −580.085 | −0.158990 | ||||||||
\(238\) | −4468.65 | −1.21706 | ||||||||
\(239\) | 6260.32 | 1.69434 | 0.847168 | − | 0.531324i | \(-0.178305\pi\) | ||||
0.847168 | + | 0.531324i | \(0.178305\pi\) | |||||||
\(240\) | −94.2019 | −0.0253363 | ||||||||
\(241\) | 2113.07 | 0.564792 | 0.282396 | − | 0.959298i | \(-0.408871\pi\) | ||||
0.282396 | + | 0.959298i | \(0.408871\pi\) | |||||||
\(242\) | 216.390 | 0.0574798 | ||||||||
\(243\) | 5414.96 | 1.42951 | ||||||||
\(244\) | 944.333 | 0.247765 | ||||||||
\(245\) | −477.921 | −0.124626 | ||||||||
\(246\) | −3711.60 | −0.961964 | ||||||||
\(247\) | 717.432 | 0.184814 | ||||||||
\(248\) | 174.470 | 0.0446727 | ||||||||
\(249\) | 6105.50 | 1.55390 | ||||||||
\(250\) | −223.544 | −0.0565526 | ||||||||
\(251\) | −969.609 | −0.243829 | −0.121915 | − | 0.992541i | \(-0.538903\pi\) | ||||
−0.121915 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(252\) | 2869.06 | 0.717199 | ||||||||
\(253\) | 265.424 | 0.0659567 | ||||||||
\(254\) | 1908.21 | 0.471385 | ||||||||
\(255\) | 4445.63 | 1.09175 | ||||||||
\(256\) | −4186.73 | −1.02215 | ||||||||
\(257\) | −951.570 | −0.230962 | −0.115481 | − | 0.993310i | \(-0.536841\pi\) | ||||
−0.115481 | + | 0.993310i | \(0.536841\pi\) | |||||||
\(258\) | 3048.02 | 0.735509 | ||||||||
\(259\) | 8430.26 | 2.02251 | ||||||||
\(260\) | 906.570 | 0.216243 | ||||||||
\(261\) | 41.4394 | 0.00982772 | ||||||||
\(262\) | 3780.88 | 0.891540 | ||||||||
\(263\) | 6299.17 | 1.47689 | 0.738447 | − | 0.674311i | \(-0.235559\pi\) | ||||
0.738447 | + | 0.674311i | \(0.235559\pi\) | |||||||
\(264\) | −1876.65 | −0.437498 | ||||||||
\(265\) | −226.487 | −0.0525018 | ||||||||
\(266\) | −711.595 | −0.164025 | ||||||||
\(267\) | −7399.32 | −1.69600 | ||||||||
\(268\) | 389.855 | 0.0888588 | ||||||||
\(269\) | 5074.67 | 1.15022 | 0.575108 | − | 0.818077i | \(-0.304960\pi\) | ||||
0.575108 | + | 0.818077i | \(0.304960\pi\) | |||||||
\(270\) | 101.982 | 0.0229868 | ||||||||
\(271\) | −8433.87 | −1.89048 | −0.945242 | − | 0.326370i | \(-0.894175\pi\) | ||||
−0.945242 | + | 0.326370i | \(0.894175\pi\) | |||||||
\(272\) | −301.662 | −0.0672461 | ||||||||
\(273\) | 5892.77 | 1.30640 | ||||||||
\(274\) | 1317.53 | 0.290491 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −863.410 | −0.188301 | ||||||||
\(277\) | −3816.53 | −0.827845 | −0.413922 | − | 0.910312i | \(-0.635841\pi\) | ||||
−0.413922 | + | 0.910312i | \(0.635841\pi\) | |||||||
\(278\) | −3053.60 | −0.658787 | ||||||||
\(279\) | −217.423 | −0.0466551 | ||||||||
\(280\) | −2397.29 | −0.511662 | ||||||||
\(281\) | −4097.68 | −0.869918 | −0.434959 | − | 0.900450i | \(-0.643237\pi\) | ||||
−0.434959 | + | 0.900450i | \(0.643237\pi\) | |||||||
\(282\) | −5457.47 | −1.15244 | ||||||||
\(283\) | 5871.93 | 1.23339 | 0.616696 | − | 0.787201i | \(-0.288471\pi\) | ||||
0.616696 | + | 0.787201i | \(0.288471\pi\) | |||||||
\(284\) | −1237.69 | −0.258603 | ||||||||
\(285\) | 707.929 | 0.147137 | ||||||||
\(286\) | −742.801 | −0.153576 | ||||||||
\(287\) | −5832.70 | −1.19963 | ||||||||
\(288\) | 5096.45 | 1.04275 | ||||||||
\(289\) | 9323.20 | 1.89766 | ||||||||
\(290\) | −12.9875 | −0.00262984 | ||||||||
\(291\) | −9147.87 | −1.84281 | ||||||||
\(292\) | −2612.89 | −0.523657 | ||||||||
\(293\) | −3042.30 | −0.606598 | −0.303299 | − | 0.952895i | \(-0.598088\pi\) | ||||
−0.303299 | + | 0.952895i | \(0.598088\pi\) | |||||||
\(294\) | −1273.81 | −0.252687 | ||||||||
\(295\) | 1017.65 | 0.200848 | ||||||||
\(296\) | 9215.91 | 1.80968 | ||||||||
\(297\) | 125.457 | 0.0245109 | ||||||||
\(298\) | −702.892 | −0.136636 | ||||||||
\(299\) | −911.117 | −0.176225 | ||||||||
\(300\) | 894.561 | 0.172158 | ||||||||
\(301\) | 4789.89 | 0.917225 | ||||||||
\(302\) | −5325.32 | −1.01470 | ||||||||
\(303\) | 4486.71 | 0.850675 | ||||||||
\(304\) | −48.0372 | −0.00906289 | ||||||||
\(305\) | 983.311 | 0.184604 | ||||||||
\(306\) | 6087.78 | 1.13731 | ||||||||
\(307\) | 6735.16 | 1.25210 | 0.626052 | − | 0.779781i | \(-0.284670\pi\) | ||||
0.626052 | + | 0.779781i | \(0.284670\pi\) | |||||||
\(308\) | −1106.17 | −0.204643 | ||||||||
\(309\) | 4819.01 | 0.887197 | ||||||||
\(310\) | 68.1426 | 0.0124846 | ||||||||
\(311\) | 5200.28 | 0.948169 | 0.474085 | − | 0.880479i | \(-0.342779\pi\) | ||||
0.474085 | + | 0.880479i | \(0.342779\pi\) | |||||||
\(312\) | 6441.94 | 1.16892 | ||||||||
\(313\) | 5226.57 | 0.943845 | 0.471922 | − | 0.881640i | \(-0.343560\pi\) | ||||
0.471922 | + | 0.881640i | \(0.343560\pi\) | |||||||
\(314\) | 4217.03 | 0.757901 | ||||||||
\(315\) | 2987.49 | 0.534368 | ||||||||
\(316\) | −373.792 | −0.0665425 | ||||||||
\(317\) | 6376.16 | 1.12972 | 0.564860 | − | 0.825187i | \(-0.308930\pi\) | ||||
0.564860 | + | 0.825187i | \(0.308930\pi\) | |||||||
\(318\) | −603.659 | −0.106451 | ||||||||
\(319\) | −15.9771 | −0.00280421 | ||||||||
\(320\) | −1698.41 | −0.296700 | ||||||||
\(321\) | 3108.30 | 0.540462 | ||||||||
\(322\) | 903.703 | 0.156402 | ||||||||
\(323\) | 2267.00 | 0.390523 | ||||||||
\(324\) | 3290.84 | 0.564273 | ||||||||
\(325\) | 943.990 | 0.161117 | ||||||||
\(326\) | 2279.74 | 0.387311 | ||||||||
\(327\) | −4027.23 | −0.681059 | ||||||||
\(328\) | −6376.27 | −1.07339 | ||||||||
\(329\) | −8576.29 | −1.43716 | ||||||||
\(330\) | −732.961 | −0.122267 | ||||||||
\(331\) | −4935.60 | −0.819593 | −0.409796 | − | 0.912177i | \(-0.634400\pi\) | ||||
−0.409796 | + | 0.912177i | \(0.634400\pi\) | |||||||
\(332\) | 3934.23 | 0.650358 | ||||||||
\(333\) | −11484.8 | −1.88998 | ||||||||
\(334\) | 4286.50 | 0.702236 | ||||||||
\(335\) | 405.946 | 0.0662066 | ||||||||
\(336\) | −394.563 | −0.0640630 | ||||||||
\(337\) | −5097.13 | −0.823911 | −0.411956 | − | 0.911204i | \(-0.635154\pi\) | ||||
−0.411956 | + | 0.911204i | \(0.635154\pi\) | |||||||
\(338\) | −1379.20 | −0.221949 | ||||||||
\(339\) | 2737.77 | 0.438628 | ||||||||
\(340\) | 2864.65 | 0.456933 | ||||||||
\(341\) | 83.8279 | 0.0133124 | ||||||||
\(342\) | 969.428 | 0.153277 | ||||||||
\(343\) | 5181.48 | 0.815667 | ||||||||
\(344\) | 5236.28 | 0.820702 | ||||||||
\(345\) | −899.048 | −0.140299 | ||||||||
\(346\) | 6630.70 | 1.03026 | ||||||||
\(347\) | 954.649 | 0.147690 | 0.0738448 | − | 0.997270i | \(-0.476473\pi\) | ||||
0.0738448 | + | 0.997270i | \(0.476473\pi\) | |||||||
\(348\) | 51.9726 | 0.00800581 | ||||||||
\(349\) | 3972.22 | 0.609249 | 0.304625 | − | 0.952472i | \(-0.401469\pi\) | ||||
0.304625 | + | 0.952472i | \(0.401469\pi\) | |||||||
\(350\) | −936.309 | −0.142994 | ||||||||
\(351\) | −430.654 | −0.0654889 | ||||||||
\(352\) | −1964.95 | −0.297534 | ||||||||
\(353\) | 1495.63 | 0.225508 | 0.112754 | − | 0.993623i | \(-0.464033\pi\) | ||||
0.112754 | + | 0.993623i | \(0.464033\pi\) | |||||||
\(354\) | 2712.37 | 0.407233 | ||||||||
\(355\) | −1288.78 | −0.192679 | ||||||||
\(356\) | −4767.94 | −0.709832 | ||||||||
\(357\) | 18620.4 | 2.76050 | ||||||||
\(358\) | −6410.61 | −0.946400 | ||||||||
\(359\) | 319.114 | 0.0469142 | 0.0234571 | − | 0.999725i | \(-0.492533\pi\) | ||||
0.0234571 | + | 0.999725i | \(0.492533\pi\) | |||||||
\(360\) | 3265.90 | 0.478134 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −8353.63 | −1.21286 | ||||||||
\(363\) | −901.677 | −0.130374 | ||||||||
\(364\) | 3797.15 | 0.546772 | ||||||||
\(365\) | −2720.74 | −0.390165 | ||||||||
\(366\) | 2620.83 | 0.374298 | ||||||||
\(367\) | −4571.59 | −0.650231 | −0.325116 | − | 0.945674i | \(-0.605403\pi\) | ||||
−0.325116 | + | 0.945674i | \(0.605403\pi\) | |||||||
\(368\) | 61.0057 | 0.00864169 | ||||||||
\(369\) | 7946.07 | 1.12102 | ||||||||
\(370\) | 3599.46 | 0.505749 | ||||||||
\(371\) | −948.636 | −0.132751 | ||||||||
\(372\) | −272.688 | −0.0380060 | ||||||||
\(373\) | −3209.95 | −0.445590 | −0.222795 | − | 0.974865i | \(-0.571518\pi\) | ||||
−0.222795 | + | 0.974865i | \(0.571518\pi\) | |||||||
\(374\) | −2347.16 | −0.324515 | ||||||||
\(375\) | 931.485 | 0.128271 | ||||||||
\(376\) | −9375.55 | −1.28592 | ||||||||
\(377\) | 54.8442 | 0.00749237 | ||||||||
\(378\) | 427.150 | 0.0581223 | ||||||||
\(379\) | −12645.1 | −1.71381 | −0.856905 | − | 0.515475i | \(-0.827616\pi\) | ||||
−0.856905 | + | 0.515475i | \(0.827616\pi\) | |||||||
\(380\) | 456.171 | 0.0615818 | ||||||||
\(381\) | −7951.33 | −1.06918 | ||||||||
\(382\) | −7882.09 | −1.05571 | ||||||||
\(383\) | 4590.06 | 0.612379 | 0.306189 | − | 0.951971i | \(-0.400946\pi\) | ||||
0.306189 | + | 0.951971i | \(0.400946\pi\) | |||||||
\(384\) | 6122.33 | 0.813616 | ||||||||
\(385\) | −1151.83 | −0.152475 | ||||||||
\(386\) | −1090.54 | −0.143801 | ||||||||
\(387\) | −6525.42 | −0.857121 | ||||||||
\(388\) | −5894.66 | −0.771278 | ||||||||
\(389\) | 8744.77 | 1.13979 | 0.569894 | − | 0.821718i | \(-0.306984\pi\) | ||||
0.569894 | + | 0.821718i | \(0.306984\pi\) | |||||||
\(390\) | 2516.03 | 0.326677 | ||||||||
\(391\) | −2879.01 | −0.372373 | ||||||||
\(392\) | −2188.32 | −0.281956 | ||||||||
\(393\) | −15754.5 | −2.02217 | ||||||||
\(394\) | 1554.76 | 0.198802 | ||||||||
\(395\) | −389.221 | −0.0495793 | ||||||||
\(396\) | 1506.98 | 0.191233 | ||||||||
\(397\) | −6465.26 | −0.817335 | −0.408668 | − | 0.912683i | \(-0.634007\pi\) | ||||
−0.408668 | + | 0.912683i | \(0.634007\pi\) | |||||||
\(398\) | −2851.48 | −0.359125 | ||||||||
\(399\) | 2965.14 | 0.372037 | ||||||||
\(400\) | −63.2068 | −0.00790085 | ||||||||
\(401\) | −123.393 | −0.0153664 | −0.00768320 | − | 0.999970i | \(-0.502446\pi\) | ||||
−0.00768320 | + | 0.999970i | \(0.502446\pi\) | |||||||
\(402\) | 1081.97 | 0.134239 | ||||||||
\(403\) | −287.755 | −0.0355685 | ||||||||
\(404\) | 2891.12 | 0.356036 | ||||||||
\(405\) | 3426.67 | 0.420426 | ||||||||
\(406\) | −54.3980 | −0.00664958 | ||||||||
\(407\) | 4428.00 | 0.539282 | ||||||||
\(408\) | 20355.7 | 2.47000 | ||||||||
\(409\) | −13319.8 | −1.61033 | −0.805163 | − | 0.593054i | \(-0.797922\pi\) | ||||
−0.805163 | + | 0.593054i | \(0.797922\pi\) | |||||||
\(410\) | −2490.38 | −0.299978 | ||||||||
\(411\) | −5490.00 | −0.658885 | ||||||||
\(412\) | 3105.25 | 0.371322 | ||||||||
\(413\) | 4262.42 | 0.507845 | ||||||||
\(414\) | −1231.14 | −0.146153 | ||||||||
\(415\) | 4096.62 | 0.484566 | ||||||||
\(416\) | 6745.05 | 0.794960 | ||||||||
\(417\) | 12724.0 | 1.49424 | ||||||||
\(418\) | −373.765 | −0.0437355 | ||||||||
\(419\) | 3291.83 | 0.383810 | 0.191905 | − | 0.981413i | \(-0.438533\pi\) | ||||
0.191905 | + | 0.981413i | \(0.438533\pi\) | |||||||
\(420\) | 3746.85 | 0.435304 | ||||||||
\(421\) | −5041.47 | −0.583626 | −0.291813 | − | 0.956475i | \(-0.594258\pi\) | ||||
−0.291813 | + | 0.956475i | \(0.594258\pi\) | |||||||
\(422\) | −5900.98 | −0.680700 | ||||||||
\(423\) | 11683.8 | 1.34299 | ||||||||
\(424\) | −1037.04 | −0.118781 | ||||||||
\(425\) | 2982.89 | 0.340450 | ||||||||
\(426\) | −3434.99 | −0.390671 | ||||||||
\(427\) | 4118.58 | 0.466773 | ||||||||
\(428\) | 2002.91 | 0.226202 | ||||||||
\(429\) | 3095.18 | 0.348337 | ||||||||
\(430\) | 2045.13 | 0.229361 | ||||||||
\(431\) | −1674.46 | −0.187137 | −0.0935684 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935684 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(432\) | 28.8353 | 0.00321144 | ||||||||
\(433\) | −2752.16 | −0.305451 | −0.152726 | − | 0.988269i | \(-0.548805\pi\) | ||||
−0.152726 | + | 0.988269i | \(0.548805\pi\) | |||||||
\(434\) | 285.414 | 0.0315675 | ||||||||
\(435\) | 54.1178 | 0.00596494 | ||||||||
\(436\) | −2595.04 | −0.285046 | ||||||||
\(437\) | −458.459 | −0.0501855 | ||||||||
\(438\) | −7251.63 | −0.791088 | ||||||||
\(439\) | 3465.38 | 0.376751 | 0.188375 | − | 0.982097i | \(-0.439678\pi\) | ||||
0.188375 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(440\) | −1259.18 | −0.136429 | ||||||||
\(441\) | 2727.07 | 0.294468 | ||||||||
\(442\) | 8057.06 | 0.867049 | ||||||||
\(443\) | −1779.53 | −0.190853 | −0.0954267 | − | 0.995436i | \(-0.530422\pi\) | ||||
−0.0954267 | + | 0.995436i | \(0.530422\pi\) | |||||||
\(444\) | −14404.1 | −1.53961 | ||||||||
\(445\) | −4964.74 | −0.528879 | ||||||||
\(446\) | −5237.25 | −0.556033 | ||||||||
\(447\) | 2928.88 | 0.309913 | ||||||||
\(448\) | −7113.75 | −0.750208 | ||||||||
\(449\) | 1657.89 | 0.174255 | 0.0871275 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871275 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(450\) | 1275.56 | 0.133624 | ||||||||
\(451\) | −3063.63 | −0.319868 | ||||||||
\(452\) | 1764.15 | 0.183581 | ||||||||
\(453\) | 22190.1 | 2.30150 | ||||||||
\(454\) | −8786.39 | −0.908294 | ||||||||
\(455\) | 3953.88 | 0.407386 | ||||||||
\(456\) | 3241.48 | 0.332886 | ||||||||
\(457\) | −2508.32 | −0.256749 | −0.128374 | − | 0.991726i | \(-0.540976\pi\) | ||||
−0.128374 | + | 0.991726i | \(0.540976\pi\) | |||||||
\(458\) | 9388.38 | 0.957839 | ||||||||
\(459\) | −1360.81 | −0.138382 | ||||||||
\(460\) | −579.323 | −0.0587198 | ||||||||
\(461\) | −7503.96 | −0.758122 | −0.379061 | − | 0.925372i | \(-0.623753\pi\) | ||||
−0.379061 | + | 0.925372i | \(0.623753\pi\) | |||||||
\(462\) | −3069.99 | −0.309154 | ||||||||
\(463\) | −12437.1 | −1.24839 | −0.624193 | − | 0.781271i | \(-0.714572\pi\) | ||||
−0.624193 | + | 0.781271i | \(0.714572\pi\) | |||||||
\(464\) | −3.67221 | −0.000367410 0 | ||||||||
\(465\) | −283.943 | −0.0283173 | ||||||||
\(466\) | −11746.1 | −1.16766 | ||||||||
\(467\) | −8190.30 | −0.811567 | −0.405784 | − | 0.913969i | \(-0.633001\pi\) | ||||
−0.405784 | + | 0.913969i | \(0.633001\pi\) | |||||||
\(468\) | −5172.98 | −0.510943 | ||||||||
\(469\) | 1700.30 | 0.167404 | ||||||||
\(470\) | −3661.81 | −0.359376 | ||||||||
\(471\) | −17572.0 | −1.71905 | ||||||||
\(472\) | 4659.65 | 0.454402 | ||||||||
\(473\) | 2515.89 | 0.244568 | ||||||||
\(474\) | −1037.40 | −0.100526 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 11998.5 | 1.15536 | ||||||||
\(477\) | 1292.36 | 0.124052 | ||||||||
\(478\) | 11195.6 | 1.07129 | ||||||||
\(479\) | −12906.5 | −1.23113 | −0.615567 | − | 0.788085i | \(-0.711073\pi\) | ||||
−0.615567 | + | 0.788085i | \(0.711073\pi\) | |||||||
\(480\) | 6655.70 | 0.632895 | ||||||||
\(481\) | −15199.9 | −1.44087 | ||||||||
\(482\) | 3778.91 | 0.357105 | ||||||||
\(483\) | −3765.64 | −0.354747 | ||||||||
\(484\) | −581.018 | −0.0545659 | ||||||||
\(485\) | −6137.96 | −0.574661 | ||||||||
\(486\) | 9683.85 | 0.903845 | ||||||||
\(487\) | 12808.3 | 1.19179 | 0.595893 | − | 0.803064i | \(-0.296798\pi\) | ||||
0.595893 | + | 0.803064i | \(0.296798\pi\) | |||||||
\(488\) | 4502.41 | 0.417652 | ||||||||
\(489\) | −9499.47 | −0.878488 | ||||||||
\(490\) | −854.690 | −0.0787979 | ||||||||
\(491\) | −16694.4 | −1.53443 | −0.767217 | − | 0.641387i | \(-0.778359\pi\) | ||||
−0.767217 | + | 0.641387i | \(0.778359\pi\) | |||||||
\(492\) | 9965.83 | 0.913199 | ||||||||
\(493\) | 173.301 | 0.0158318 | ||||||||
\(494\) | 1283.02 | 0.116854 | ||||||||
\(495\) | 1569.18 | 0.142483 | ||||||||
\(496\) | 19.2672 | 0.00174420 | ||||||||
\(497\) | −5398.01 | −0.487191 | ||||||||
\(498\) | 10918.8 | 0.982494 | ||||||||
\(499\) | 16314.1 | 1.46357 | 0.731785 | − | 0.681536i | \(-0.238688\pi\) | ||||
0.731785 | + | 0.681536i | \(0.238688\pi\) | |||||||
\(500\) | 600.225 | 0.0536858 | ||||||||
\(501\) | −17861.4 | −1.59279 | ||||||||
\(502\) | −1734.00 | −0.154168 | ||||||||
\(503\) | −9513.14 | −0.843281 | −0.421640 | − | 0.906763i | \(-0.638545\pi\) | ||||
−0.421640 | + | 0.906763i | \(0.638545\pi\) | |||||||
\(504\) | 13679.2 | 1.20897 | ||||||||
\(505\) | 3010.45 | 0.265274 | ||||||||
\(506\) | 474.670 | 0.0417029 | ||||||||
\(507\) | 5746.99 | 0.503418 | ||||||||
\(508\) | −5123.63 | −0.447489 | ||||||||
\(509\) | −5737.09 | −0.499592 | −0.249796 | − | 0.968299i | \(-0.580364\pi\) | ||||
−0.249796 | + | 0.968299i | \(0.580364\pi\) | |||||||
\(510\) | 7950.34 | 0.690288 | ||||||||
\(511\) | −11395.8 | −0.986535 | ||||||||
\(512\) | −914.689 | −0.0789530 | ||||||||
\(513\) | −216.698 | −0.0186500 | ||||||||
\(514\) | −1701.74 | −0.146032 | ||||||||
\(515\) | 3233.42 | 0.276663 | ||||||||
\(516\) | −8184.07 | −0.698224 | ||||||||
\(517\) | −4504.70 | −0.383204 | ||||||||
\(518\) | 15076.3 | 1.27879 | ||||||||
\(519\) | −27629.5 | −2.33680 | ||||||||
\(520\) | 4322.36 | 0.364515 | ||||||||
\(521\) | −14832.1 | −1.24723 | −0.623614 | − | 0.781732i | \(-0.714336\pi\) | ||||
−0.623614 | + | 0.781732i | \(0.714336\pi\) | |||||||
\(522\) | 74.1082 | 0.00621384 | ||||||||
\(523\) | −11485.4 | −0.960269 | −0.480134 | − | 0.877195i | \(-0.659412\pi\) | ||||
−0.480134 | + | 0.877195i | \(0.659412\pi\) | |||||||
\(524\) | −10151.8 | −0.846345 | ||||||||
\(525\) | 3901.51 | 0.324335 | ||||||||
\(526\) | 11265.1 | 0.933807 | ||||||||
\(527\) | −909.270 | −0.0751583 | ||||||||
\(528\) | −207.244 | −0.0170817 | ||||||||
\(529\) | −11584.8 | −0.952147 | ||||||||
\(530\) | −405.038 | −0.0331957 | ||||||||
\(531\) | −5806.83 | −0.474567 | ||||||||
\(532\) | 1910.66 | 0.155710 | ||||||||
\(533\) | 10516.5 | 0.854633 | ||||||||
\(534\) | −13232.6 | −1.07234 | ||||||||
\(535\) | 2085.58 | 0.168537 | ||||||||
\(536\) | 1858.75 | 0.149787 | ||||||||
\(537\) | 26712.4 | 2.14660 | ||||||||
\(538\) | 9075.30 | 0.727256 | ||||||||
\(539\) | −1051.43 | −0.0840225 | ||||||||
\(540\) | −273.827 | −0.0218215 | ||||||||
\(541\) | −13934.3 | −1.10736 | −0.553679 | − | 0.832730i | \(-0.686777\pi\) | ||||
−0.553679 | + | 0.832730i | \(0.686777\pi\) | |||||||
\(542\) | −15082.7 | −1.19531 | ||||||||
\(543\) | 34808.8 | 2.75099 | ||||||||
\(544\) | 21313.5 | 1.67980 | ||||||||
\(545\) | −2702.16 | −0.212381 | ||||||||
\(546\) | 10538.3 | 0.826006 | ||||||||
\(547\) | 11970.4 | 0.935681 | 0.467841 | − | 0.883813i | \(-0.345032\pi\) | ||||
0.467841 | + | 0.883813i | \(0.345032\pi\) | |||||||
\(548\) | −3537.62 | −0.275766 | ||||||||
\(549\) | −5610.87 | −0.436186 | ||||||||
\(550\) | −491.796 | −0.0381278 | ||||||||
\(551\) | 27.5967 | 0.00213368 | ||||||||
\(552\) | −4116.58 | −0.317415 | ||||||||
\(553\) | −1630.24 | −0.125362 | ||||||||
\(554\) | −6825.29 | −0.523427 | ||||||||
\(555\) | −14998.6 | −1.14713 | ||||||||
\(556\) | 8199.05 | 0.625391 | ||||||||
\(557\) | −868.155 | −0.0660411 | −0.0330205 | − | 0.999455i | \(-0.510513\pi\) | ||||
−0.0330205 | + | 0.999455i | \(0.510513\pi\) | |||||||
\(558\) | −388.828 | −0.0294990 | ||||||||
\(559\) | −8636.27 | −0.653445 | ||||||||
\(560\) | −264.740 | −0.0199774 | ||||||||
\(561\) | 9780.38 | 0.736057 | ||||||||
\(562\) | −7328.09 | −0.550030 | ||||||||
\(563\) | −4001.26 | −0.299526 | −0.149763 | − | 0.988722i | \(-0.547851\pi\) | ||||
−0.149763 | + | 0.988722i | \(0.547851\pi\) | |||||||
\(564\) | 14653.6 | 1.09402 | ||||||||
\(565\) | 1836.96 | 0.136782 | ||||||||
\(566\) | 10501.1 | 0.779846 | ||||||||
\(567\) | 14352.5 | 1.06305 | ||||||||
\(568\) | −5901.07 | −0.435922 | ||||||||
\(569\) | 6500.31 | 0.478923 | 0.239461 | − | 0.970906i | \(-0.423029\pi\) | ||||
0.239461 | + | 0.970906i | \(0.423029\pi\) | |||||||
\(570\) | 1266.02 | 0.0930314 | ||||||||
\(571\) | −7316.14 | −0.536202 | −0.268101 | − | 0.963391i | \(-0.586396\pi\) | ||||
−0.268101 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(572\) | 1994.45 | 0.145791 | ||||||||
\(573\) | 32843.9 | 2.39454 | ||||||||
\(574\) | −10430.9 | −0.758498 | ||||||||
\(575\) | −603.235 | −0.0437507 | ||||||||
\(576\) | 9691.29 | 0.701048 | ||||||||
\(577\) | −4347.60 | −0.313679 | −0.156839 | − | 0.987624i | \(-0.550131\pi\) | ||||
−0.156839 | + | 0.987624i | \(0.550131\pi\) | |||||||
\(578\) | 16673.1 | 1.19985 | ||||||||
\(579\) | 4544.18 | 0.326165 | ||||||||
\(580\) | 34.8721 | 0.00249653 | ||||||||
\(581\) | 17158.6 | 1.22523 | ||||||||
\(582\) | −16359.6 | −1.16517 | ||||||||
\(583\) | −498.271 | −0.0353967 | ||||||||
\(584\) | −12457.8 | −0.882717 | ||||||||
\(585\) | −5386.50 | −0.380691 | ||||||||
\(586\) | −5440.70 | −0.383538 | ||||||||
\(587\) | 898.208 | 0.0631567 | 0.0315784 | − | 0.999501i | \(-0.489947\pi\) | ||||
0.0315784 | + | 0.999501i | \(0.489947\pi\) | |||||||
\(588\) | 3420.24 | 0.239878 | ||||||||
\(589\) | −144.794 | −0.0101292 | ||||||||
\(590\) | 1819.92 | 0.126991 | ||||||||
\(591\) | −6478.55 | −0.450917 | ||||||||
\(592\) | 1017.74 | 0.0706571 | ||||||||
\(593\) | −23375.2 | −1.61873 | −0.809364 | − | 0.587307i | \(-0.800188\pi\) | ||||
−0.809364 | + | 0.587307i | \(0.800188\pi\) | |||||||
\(594\) | 224.361 | 0.0154977 | ||||||||
\(595\) | 12493.8 | 0.860831 | ||||||||
\(596\) | 1887.30 | 0.129709 | ||||||||
\(597\) | 11881.8 | 0.814557 | ||||||||
\(598\) | −1629.40 | −0.111423 | ||||||||
\(599\) | 18358.9 | 1.25229 | 0.626147 | − | 0.779705i | \(-0.284631\pi\) | ||||
0.626147 | + | 0.779705i | \(0.284631\pi\) | |||||||
\(600\) | 4265.10 | 0.290204 | ||||||||
\(601\) | 12042.5 | 0.817342 | 0.408671 | − | 0.912682i | \(-0.365992\pi\) | ||||
0.408671 | + | 0.912682i | \(0.365992\pi\) | |||||||
\(602\) | 8566.01 | 0.579941 | ||||||||
\(603\) | −2316.37 | −0.156434 | ||||||||
\(604\) | 14298.7 | 0.963257 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | 8023.80 | 0.537862 | ||||||||
\(607\) | −22486.3 | −1.50361 | −0.751804 | − | 0.659387i | \(-0.770816\pi\) | ||||
−0.751804 | + | 0.659387i | \(0.770816\pi\) | |||||||
\(608\) | 3394.00 | 0.226389 | ||||||||
\(609\) | 226.671 | 0.0150824 | ||||||||
\(610\) | 1758.50 | 0.116721 | ||||||||
\(611\) | 15463.2 | 1.02385 | ||||||||
\(612\) | −16346.0 | −1.07965 | ||||||||
\(613\) | 2950.06 | 0.194375 | 0.0971874 | − | 0.995266i | \(-0.469015\pi\) | ||||
0.0971874 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(614\) | 12044.8 | 0.791677 | ||||||||
\(615\) | 10377.2 | 0.680403 | ||||||||
\(616\) | −5274.03 | −0.344962 | ||||||||
\(617\) | 7637.57 | 0.498342 | 0.249171 | − | 0.968459i | \(-0.419842\pi\) | ||||
0.249171 | + | 0.968459i | \(0.419842\pi\) | |||||||
\(618\) | 8618.08 | 0.560955 | ||||||||
\(619\) | 790.824 | 0.0513504 | 0.0256752 | − | 0.999670i | \(-0.491826\pi\) | ||||
0.0256752 | + | 0.999670i | \(0.491826\pi\) | |||||||
\(620\) | −182.966 | −0.0118518 | ||||||||
\(621\) | 275.200 | 0.0177832 | ||||||||
\(622\) | 9299.92 | 0.599506 | ||||||||
\(623\) | −20794.7 | −1.33727 | ||||||||
\(624\) | 711.405 | 0.0456394 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 9346.94 | 0.596772 | ||||||||
\(627\) | 1557.44 | 0.0991998 | ||||||||
\(628\) | −11322.9 | −0.719481 | ||||||||
\(629\) | −48029.9 | −3.04464 | ||||||||
\(630\) | 5342.67 | 0.337869 | ||||||||
\(631\) | 11969.8 | 0.755164 | 0.377582 | − | 0.925976i | \(-0.376756\pi\) | ||||
0.377582 | + | 0.925976i | \(0.376756\pi\) | |||||||
\(632\) | −1782.17 | −0.112169 | ||||||||
\(633\) | 24588.8 | 1.54395 | ||||||||
\(634\) | 11402.8 | 0.714296 | ||||||||
\(635\) | −5335.11 | −0.333413 | ||||||||
\(636\) | 1620.85 | 0.101055 | ||||||||
\(637\) | 3609.22 | 0.224494 | ||||||||
\(638\) | −28.5726 | −0.00177304 | ||||||||
\(639\) | 7353.89 | 0.455266 | ||||||||
\(640\) | 4107.91 | 0.253718 | ||||||||
\(641\) | −23883.4 | −1.47167 | −0.735833 | − | 0.677163i | \(-0.763209\pi\) | ||||
−0.735833 | + | 0.677163i | \(0.763209\pi\) | |||||||
\(642\) | 5558.73 | 0.341722 | ||||||||
\(643\) | −10055.6 | −0.616725 | −0.308363 | − | 0.951269i | \(-0.599781\pi\) | ||||
−0.308363 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(644\) | −2426.49 | −0.148473 | ||||||||
\(645\) | −8521.87 | −0.520230 | ||||||||
\(646\) | 4054.18 | 0.246919 | ||||||||
\(647\) | 22455.5 | 1.36448 | 0.682239 | − | 0.731129i | \(-0.261006\pi\) | ||||
0.682239 | + | 0.731129i | \(0.261006\pi\) | |||||||
\(648\) | 15690.1 | 0.951182 | ||||||||
\(649\) | 2238.84 | 0.135411 | ||||||||
\(650\) | 1688.18 | 0.101871 | ||||||||
\(651\) | −1189.29 | −0.0716006 | ||||||||
\(652\) | −6121.22 | −0.367677 | ||||||||
\(653\) | −9295.71 | −0.557074 | −0.278537 | − | 0.960425i | \(-0.589849\pi\) | ||||
−0.278537 | + | 0.960425i | \(0.589849\pi\) | |||||||
\(654\) | −7202.09 | −0.430618 | ||||||||
\(655\) | −10570.9 | −0.630591 | ||||||||
\(656\) | −704.153 | −0.0419094 | ||||||||
\(657\) | 15524.8 | 0.921889 | ||||||||
\(658\) | −15337.4 | −0.908685 | ||||||||
\(659\) | −30903.1 | −1.82673 | −0.913365 | − | 0.407142i | \(-0.866525\pi\) | ||||
−0.913365 | + | 0.407142i | \(0.866525\pi\) | |||||||
\(660\) | 1968.03 | 0.116069 | ||||||||
\(661\) | 8031.50 | 0.472601 | 0.236300 | − | 0.971680i | \(-0.424065\pi\) | ||||
0.236300 | + | 0.971680i | \(0.424065\pi\) | |||||||
\(662\) | −8826.58 | −0.518210 | ||||||||
\(663\) | −33573.0 | −1.96662 | ||||||||
\(664\) | 18757.7 | 1.09629 | ||||||||
\(665\) | 1989.53 | 0.116016 | ||||||||
\(666\) | −20538.9 | −1.19499 | ||||||||
\(667\) | −35.0470 | −0.00203452 | ||||||||
\(668\) | −11509.4 | −0.666637 | ||||||||
\(669\) | 21823.1 | 1.26118 | ||||||||
\(670\) | 725.974 | 0.0418609 | ||||||||
\(671\) | 2163.28 | 0.124460 | ||||||||
\(672\) | 27877.3 | 1.60028 | ||||||||
\(673\) | 2762.96 | 0.158253 | 0.0791265 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791265 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(674\) | −9115.45 | −0.520941 | ||||||||
\(675\) | −285.129 | −0.0162587 | ||||||||
\(676\) | 3703.22 | 0.210697 | ||||||||
\(677\) | −12500.7 | −0.709662 | −0.354831 | − | 0.934930i | \(-0.615462\pi\) | ||||
−0.354831 | + | 0.934930i | \(0.615462\pi\) | |||||||
\(678\) | 4896.08 | 0.277335 | ||||||||
\(679\) | −25708.7 | −1.45304 | ||||||||
\(680\) | 13658.1 | 0.770242 | ||||||||
\(681\) | 36612.0 | 2.06017 | ||||||||
\(682\) | 149.914 | 0.00841714 | ||||||||
\(683\) | 24987.8 | 1.39990 | 0.699951 | − | 0.714191i | \(-0.253205\pi\) | ||||
0.699951 | + | 0.714191i | \(0.253205\pi\) | |||||||
\(684\) | −2602.96 | −0.145507 | ||||||||
\(685\) | −3683.63 | −0.205466 | ||||||||
\(686\) | 9266.30 | 0.515728 | ||||||||
\(687\) | −39120.4 | −2.17254 | ||||||||
\(688\) | 578.260 | 0.0320435 | ||||||||
\(689\) | 1710.41 | 0.0945740 | ||||||||
\(690\) | −1607.81 | −0.0887078 | ||||||||
\(691\) | −10223.2 | −0.562823 | −0.281411 | − | 0.959587i | \(-0.590803\pi\) | ||||
−0.281411 | + | 0.959587i | \(0.590803\pi\) | |||||||
\(692\) | −17803.7 | −0.978030 | ||||||||
\(693\) | 6572.47 | 0.360271 | ||||||||
\(694\) | 1707.25 | 0.0933807 | ||||||||
\(695\) | 8537.47 | 0.465964 | ||||||||
\(696\) | 247.796 | 0.0134952 | ||||||||
\(697\) | 33230.8 | 1.80589 | ||||||||
\(698\) | 7103.72 | 0.385215 | ||||||||
\(699\) | 48944.9 | 2.64845 | ||||||||
\(700\) | 2514.03 | 0.135745 | ||||||||
\(701\) | −6778.24 | −0.365208 | −0.182604 | − | 0.983187i | \(-0.558453\pi\) | ||||
−0.182604 | + | 0.983187i | \(0.558453\pi\) | |||||||
\(702\) | −770.160 | −0.0414072 | ||||||||
\(703\) | −7648.36 | −0.410332 | ||||||||
\(704\) | −3736.50 | −0.200035 | ||||||||
\(705\) | 15258.4 | 0.815127 | ||||||||
\(706\) | 2674.71 | 0.142584 | ||||||||
\(707\) | 12609.2 | 0.670748 | ||||||||
\(708\) | −7282.83 | −0.386590 | ||||||||
\(709\) | 35011.7 | 1.85457 | 0.927285 | − | 0.374355i | \(-0.122136\pi\) | ||||
0.927285 | + | 0.374355i | \(0.122136\pi\) | |||||||
\(710\) | −2304.78 | −0.121827 | ||||||||
\(711\) | 2220.93 | 0.117147 | ||||||||
\(712\) | −22732.6 | −1.19655 | ||||||||
\(713\) | 183.884 | 0.00965847 | ||||||||
\(714\) | 33299.8 | 1.74540 | ||||||||
\(715\) | 2076.78 | 0.108625 | ||||||||
\(716\) | 17212.8 | 0.898424 | ||||||||
\(717\) | −46651.2 | −2.42987 | ||||||||
\(718\) | 570.688 | 0.0296628 | ||||||||
\(719\) | −25327.1 | −1.31369 | −0.656844 | − | 0.754026i | \(-0.728109\pi\) | ||||
−0.656844 | + | 0.754026i | \(0.728109\pi\) | |||||||
\(720\) | 360.664 | 0.0186683 | ||||||||
\(721\) | 13543.1 | 0.699545 | ||||||||
\(722\) | 645.595 | 0.0332778 | ||||||||
\(723\) | −15746.4 | −0.809977 | ||||||||
\(724\) | 22429.9 | 1.15138 | ||||||||
\(725\) | 36.3115 | 0.00186010 | ||||||||
\(726\) | −1612.52 | −0.0824326 | ||||||||
\(727\) | −8027.09 | −0.409503 | −0.204751 | − | 0.978814i | \(-0.565639\pi\) | ||||
−0.204751 | + | 0.978814i | \(0.565639\pi\) | |||||||
\(728\) | 18104.1 | 0.921680 | ||||||||
\(729\) | −21847.6 | −1.10998 | ||||||||
\(730\) | −4865.64 | −0.246692 | ||||||||
\(731\) | −27289.5 | −1.38077 | ||||||||
\(732\) | −7037.06 | −0.355324 | ||||||||
\(733\) | 23016.3 | 1.15979 | 0.579895 | − | 0.814691i | \(-0.303094\pi\) | ||||
0.579895 | + | 0.814691i | \(0.303094\pi\) | |||||||
\(734\) | −8175.60 | −0.411127 | ||||||||
\(735\) | 3561.41 | 0.178727 | ||||||||
\(736\) | −4310.27 | −0.215868 | ||||||||
\(737\) | 893.081 | 0.0446365 | ||||||||
\(738\) | 14210.4 | 0.708795 | ||||||||
\(739\) | −36678.1 | −1.82575 | −0.912874 | − | 0.408242i | \(-0.866142\pi\) | ||||
−0.912874 | + | 0.408242i | \(0.866142\pi\) | |||||||
\(740\) | −9664.71 | −0.480111 | ||||||||
\(741\) | −5346.22 | −0.265045 | ||||||||
\(742\) | −1696.49 | −0.0839357 | ||||||||
\(743\) | −17081.1 | −0.843397 | −0.421698 | − | 0.906736i | \(-0.638566\pi\) | ||||
−0.421698 | + | 0.906736i | \(0.638566\pi\) | |||||||
\(744\) | −1300.13 | −0.0640658 | ||||||||
\(745\) | 1965.20 | 0.0966432 | ||||||||
\(746\) | −5740.52 | −0.281736 | ||||||||
\(747\) | −23375.7 | −1.14494 | ||||||||
\(748\) | 6302.23 | 0.308064 | ||||||||
\(749\) | 8735.41 | 0.426148 | ||||||||
\(750\) | 1665.82 | 0.0811029 | ||||||||
\(751\) | −13376.4 | −0.649948 | −0.324974 | − | 0.945723i | \(-0.605355\pi\) | ||||
−0.324974 | + | 0.945723i | \(0.605355\pi\) | |||||||
\(752\) | −1035.37 | −0.0502076 | ||||||||
\(753\) | 7225.41 | 0.349679 | ||||||||
\(754\) | 98.0807 | 0.00473725 | ||||||||
\(755\) | 14888.9 | 0.717700 | ||||||||
\(756\) | −1146.92 | −0.0551759 | ||||||||
\(757\) | 27388.9 | 1.31501 | 0.657507 | − | 0.753448i | \(-0.271611\pi\) | ||||
0.657507 | + | 0.753448i | \(0.271611\pi\) | |||||||
\(758\) | −22613.8 | −1.08360 | ||||||||
\(759\) | −1977.90 | −0.0945894 | ||||||||
\(760\) | 2174.94 | 0.103807 | ||||||||
\(761\) | −7526.75 | −0.358534 | −0.179267 | − | 0.983800i | \(-0.557373\pi\) | ||||
−0.179267 | + | 0.983800i | \(0.557373\pi\) | |||||||
\(762\) | −14219.8 | −0.676020 | ||||||||
\(763\) | −11317.9 | −0.537007 | ||||||||
\(764\) | 21163.8 | 1.00220 | ||||||||
\(765\) | −17020.7 | −0.804423 | ||||||||
\(766\) | 8208.64 | 0.387193 | ||||||||
\(767\) | −7685.23 | −0.361796 | ||||||||
\(768\) | 31199.0 | 1.46588 | ||||||||
\(769\) | −30913.3 | −1.44963 | −0.724814 | − | 0.688945i | \(-0.758074\pi\) | ||||
−0.724814 | + | 0.688945i | \(0.758074\pi\) | |||||||
\(770\) | −2059.88 | −0.0964064 | ||||||||
\(771\) | 7090.98 | 0.331226 | ||||||||
\(772\) | 2928.15 | 0.136511 | ||||||||
\(773\) | 13304.9 | 0.619072 | 0.309536 | − | 0.950888i | \(-0.399826\pi\) | ||||
0.309536 | + | 0.950888i | \(0.399826\pi\) | |||||||
\(774\) | −11669.7 | −0.541938 | ||||||||
\(775\) | −190.518 | −0.00883046 | ||||||||
\(776\) | −28104.6 | −1.30013 | ||||||||
\(777\) | −62821.3 | −2.90052 | ||||||||
\(778\) | 15638.7 | 0.720662 | ||||||||
\(779\) | 5291.72 | 0.243383 | ||||||||
\(780\) | −6755.65 | −0.310117 | ||||||||
\(781\) | −2835.31 | −0.129904 | ||||||||
\(782\) | −5148.69 | −0.235443 | ||||||||
\(783\) | −16.5655 | −0.000756071 0 | ||||||||
\(784\) | −241.663 | −0.0110087 | ||||||||
\(785\) | −11790.3 | −0.536068 | ||||||||
\(786\) | −28174.6 | −1.27857 | ||||||||
\(787\) | 36927.8 | 1.67260 | 0.836298 | − | 0.548275i | \(-0.184715\pi\) | ||||
0.836298 | + | 0.548275i | \(0.184715\pi\) | |||||||
\(788\) | −4174.61 | −0.188724 | ||||||||
\(789\) | −46940.6 | −2.11804 | ||||||||
\(790\) | −696.063 | −0.0313478 | ||||||||
\(791\) | 7694.08 | 0.345854 | ||||||||
\(792\) | 7184.99 | 0.322358 | ||||||||
\(793\) | −7425.88 | −0.332536 | ||||||||
\(794\) | −11562.2 | −0.516783 | ||||||||
\(795\) | 1687.75 | 0.0752937 | ||||||||
\(796\) | 7656.35 | 0.340920 | ||||||||
\(797\) | −20336.3 | −0.903825 | −0.451912 | − | 0.892062i | \(-0.649258\pi\) | ||||
−0.451912 | + | 0.892062i | \(0.649258\pi\) | |||||||
\(798\) | 5302.72 | 0.235231 | ||||||||
\(799\) | 48861.8 | 2.16346 | ||||||||
\(800\) | 4465.79 | 0.197362 | ||||||||
\(801\) | 28329.3 | 1.24965 | ||||||||
\(802\) | −220.669 | −0.00971583 | ||||||||
\(803\) | −5985.63 | −0.263049 | ||||||||
\(804\) | −2905.15 | −0.127434 | ||||||||
\(805\) | −2526.64 | −0.110624 | ||||||||
\(806\) | −514.607 | −0.0224892 | ||||||||
\(807\) | −37815.9 | −1.64954 | ||||||||
\(808\) | 13784.3 | 0.600162 | ||||||||
\(809\) | −13172.1 | −0.572444 | −0.286222 | − | 0.958163i | \(-0.592399\pi\) | ||||
−0.286222 | + | 0.958163i | \(0.592399\pi\) | |||||||
\(810\) | 6128.09 | 0.265826 | ||||||||
\(811\) | 5941.27 | 0.257246 | 0.128623 | − | 0.991694i | \(-0.458944\pi\) | ||||
0.128623 | + | 0.991694i | \(0.458944\pi\) | |||||||
\(812\) | 146.061 | 0.00631249 | ||||||||
\(813\) | 62848.2 | 2.71117 | ||||||||
\(814\) | 7918.81 | 0.340976 | ||||||||
\(815\) | −6373.87 | −0.273947 | ||||||||
\(816\) | 2247.95 | 0.0964387 | ||||||||
\(817\) | −4345.63 | −0.186089 | ||||||||
\(818\) | −23820.5 | −1.01817 | ||||||||
\(819\) | −22561.2 | −0.962581 | ||||||||
\(820\) | 6686.79 | 0.284772 | ||||||||
\(821\) | 45085.3 | 1.91655 | 0.958276 | − | 0.285844i | \(-0.0922739\pi\) | ||||
0.958276 | + | 0.285844i | \(0.0922739\pi\) | |||||||
\(822\) | −9818.04 | −0.416598 | ||||||||
\(823\) | 35942.4 | 1.52233 | 0.761163 | − | 0.648560i | \(-0.224629\pi\) | ||||
0.761163 | + | 0.648560i | \(0.224629\pi\) | |||||||
\(824\) | 14805.3 | 0.625929 | ||||||||
\(825\) | 2049.27 | 0.0864804 | ||||||||
\(826\) | 7622.70 | 0.321099 | ||||||||
\(827\) | 2665.67 | 0.112085 | 0.0560426 | − | 0.998428i | \(-0.482152\pi\) | ||||
0.0560426 | + | 0.998428i | \(0.482152\pi\) | |||||||
\(828\) | 3305.68 | 0.138744 | ||||||||
\(829\) | −30744.8 | −1.28807 | −0.644036 | − | 0.764995i | \(-0.722741\pi\) | ||||
−0.644036 | + | 0.764995i | \(0.722741\pi\) | |||||||
\(830\) | 7326.19 | 0.306380 | ||||||||
\(831\) | 28440.3 | 1.18722 | ||||||||
\(832\) | 12826.2 | 0.534459 | ||||||||
\(833\) | 11404.7 | 0.474368 | ||||||||
\(834\) | 22755.0 | 0.944776 | ||||||||
\(835\) | −11984.5 | −0.496696 | ||||||||
\(836\) | 1003.58 | 0.0415185 | ||||||||
\(837\) | 86.9155 | 0.00358929 | ||||||||
\(838\) | 5886.95 | 0.242675 | ||||||||
\(839\) | 23177.1 | 0.953711 | 0.476855 | − | 0.878982i | \(-0.341777\pi\) | ||||
0.476855 | + | 0.878982i | \(0.341777\pi\) | |||||||
\(840\) | 17864.3 | 0.733782 | ||||||||
\(841\) | −24386.9 | −0.999914 | ||||||||
\(842\) | −9015.92 | −0.369013 | ||||||||
\(843\) | 30535.4 | 1.24756 | ||||||||
\(844\) | 15844.4 | 0.646193 | ||||||||
\(845\) | 3856.07 | 0.156986 | ||||||||
\(846\) | 20894.6 | 0.849140 | ||||||||
\(847\) | −2534.03 | −0.102798 | ||||||||
\(848\) | −114.524 | −0.00463771 | ||||||||
\(849\) | −43756.9 | −1.76883 | ||||||||
\(850\) | 5334.45 | 0.215259 | ||||||||
\(851\) | 9713.18 | 0.391262 | ||||||||
\(852\) | 9223.11 | 0.370867 | ||||||||
\(853\) | 4953.65 | 0.198839 | 0.0994195 | − | 0.995046i | \(-0.468301\pi\) | ||||
0.0994195 | + | 0.995046i | \(0.468301\pi\) | |||||||
\(854\) | 7365.46 | 0.295130 | ||||||||
\(855\) | −2710.40 | −0.108414 | ||||||||
\(856\) | 9549.50 | 0.381303 | ||||||||
\(857\) | 34235.9 | 1.36462 | 0.682308 | − | 0.731065i | \(-0.260976\pi\) | ||||
0.682308 | + | 0.731065i | \(0.260976\pi\) | |||||||
\(858\) | 5535.26 | 0.220246 | ||||||||
\(859\) | −30624.0 | −1.21639 | −0.608195 | − | 0.793788i | \(-0.708106\pi\) | ||||
−0.608195 | + | 0.793788i | \(0.708106\pi\) | |||||||
\(860\) | −5491.28 | −0.217734 | ||||||||
\(861\) | 43464.6 | 1.72041 | ||||||||
\(862\) | −2994.52 | −0.118322 | ||||||||
\(863\) | −9692.26 | −0.382304 | −0.191152 | − | 0.981560i | \(-0.561222\pi\) | ||||
−0.191152 | + | 0.981560i | \(0.561222\pi\) | |||||||
\(864\) | −2037.32 | −0.0802211 | ||||||||
\(865\) | −18538.6 | −0.728707 | ||||||||
\(866\) | −4921.82 | −0.193130 | ||||||||
\(867\) | −69475.3 | −2.72146 | ||||||||
\(868\) | −766.349 | −0.0299673 | ||||||||
\(869\) | −856.285 | −0.0334263 | ||||||||
\(870\) | 96.7815 | 0.00377149 | ||||||||
\(871\) | −3065.67 | −0.119261 | ||||||||
\(872\) | −12372.7 | −0.480496 | ||||||||
\(873\) | 35023.8 | 1.35782 | ||||||||
\(874\) | −819.885 | −0.0317312 | ||||||||
\(875\) | 2617.80 | 0.101140 | ||||||||
\(876\) | 19471.0 | 0.750985 | ||||||||
\(877\) | −11304.4 | −0.435258 | −0.217629 | − | 0.976032i | \(-0.569832\pi\) | ||||
−0.217629 | + | 0.976032i | \(0.569832\pi\) | |||||||
\(878\) | 6197.31 | 0.238211 | ||||||||
\(879\) | 22670.9 | 0.869931 | ||||||||
\(880\) | −139.055 | −0.00532675 | ||||||||
\(881\) | 48137.7 | 1.84086 | 0.920431 | − | 0.390904i | \(-0.127838\pi\) | ||||
0.920431 | + | 0.390904i | \(0.127838\pi\) | |||||||
\(882\) | 4876.95 | 0.186185 | ||||||||
\(883\) | −17405.5 | −0.663355 | −0.331677 | − | 0.943393i | \(-0.607615\pi\) | ||||
−0.331677 | + | 0.943393i | \(0.607615\pi\) | |||||||
\(884\) | −21633.6 | −0.823095 | ||||||||
\(885\) | −7583.43 | −0.288039 | ||||||||
\(886\) | −3182.42 | −0.120672 | ||||||||
\(887\) | −9812.61 | −0.371449 | −0.185725 | − | 0.982602i | \(-0.559463\pi\) | ||||
−0.185725 | + | 0.982602i | \(0.559463\pi\) | |||||||
\(888\) | −68675.9 | −2.59528 | ||||||||
\(889\) | −22346.0 | −0.843039 | ||||||||
\(890\) | −8878.69 | −0.334398 | ||||||||
\(891\) | 7538.67 | 0.283451 | ||||||||
\(892\) | 14062.2 | 0.527846 | ||||||||
\(893\) | 7780.84 | 0.291574 | ||||||||
\(894\) | 5237.86 | 0.195951 | ||||||||
\(895\) | 17923.2 | 0.669395 | ||||||||
\(896\) | 17205.9 | 0.641527 | ||||||||
\(897\) | 6789.53 | 0.252727 | ||||||||
\(898\) | 2964.88 | 0.110177 | ||||||||
\(899\) | −11.0688 | −0.000410639 0 | ||||||||
\(900\) | −3424.95 | −0.126850 | ||||||||
\(901\) | 5404.68 | 0.199840 | ||||||||
\(902\) | −5478.84 | −0.202245 | ||||||||
\(903\) | −35693.7 | −1.31541 | ||||||||
\(904\) | 8411.13 | 0.309458 | ||||||||
\(905\) | 23355.7 | 0.857867 | ||||||||
\(906\) | 39683.7 | 1.45519 | ||||||||
\(907\) | −15424.5 | −0.564677 | −0.282339 | − | 0.959315i | \(-0.591110\pi\) | ||||
−0.282339 | + | 0.959315i | \(0.591110\pi\) | |||||||
\(908\) | 23591.9 | 0.862250 | ||||||||
\(909\) | −17177.9 | −0.626795 | ||||||||
\(910\) | 7070.93 | 0.257581 | ||||||||
\(911\) | −10631.5 | −0.386650 | −0.193325 | − | 0.981135i | \(-0.561927\pi\) | ||||
−0.193325 | + | 0.981135i | \(0.561927\pi\) | |||||||
\(912\) | 357.967 | 0.0129972 | ||||||||
\(913\) | 9012.56 | 0.326695 | ||||||||
\(914\) | −4485.75 | −0.162336 | ||||||||
\(915\) | −7327.51 | −0.264743 | ||||||||
\(916\) | −25208.2 | −0.909283 | ||||||||
\(917\) | −44275.8 | −1.59446 | ||||||||
\(918\) | −2433.61 | −0.0874958 | ||||||||
\(919\) | −26902.6 | −0.965654 | −0.482827 | − | 0.875716i | \(-0.660390\pi\) | ||||
−0.482827 | + | 0.875716i | \(0.660390\pi\) | |||||||
\(920\) | −2762.11 | −0.0989826 | ||||||||
\(921\) | −50189.6 | −1.79566 | ||||||||
\(922\) | −13419.7 | −0.479343 | ||||||||
\(923\) | 9732.73 | 0.347082 | ||||||||
\(924\) | 8243.08 | 0.293482 | ||||||||
\(925\) | −10063.6 | −0.357719 | ||||||||
\(926\) | −22241.9 | −0.789326 | ||||||||
\(927\) | −18450.2 | −0.653705 | ||||||||
\(928\) | 259.455 | 0.00917783 | ||||||||
\(929\) | −40771.9 | −1.43992 | −0.719959 | − | 0.694017i | \(-0.755839\pi\) | ||||
−0.719959 | + | 0.694017i | \(0.755839\pi\) | |||||||
\(930\) | −507.790 | −0.0179044 | ||||||||
\(931\) | 1816.10 | 0.0639315 | ||||||||
\(932\) | 31538.8 | 1.10846 | ||||||||
\(933\) | −38751.8 | −1.35978 | ||||||||
\(934\) | −14647.1 | −0.513135 | ||||||||
\(935\) | 6562.35 | 0.229531 | ||||||||
\(936\) | −24663.8 | −0.861285 | ||||||||
\(937\) | 39610.1 | 1.38101 | 0.690504 | − | 0.723329i | \(-0.257389\pi\) | ||||
0.690504 | + | 0.723329i | \(0.257389\pi\) | |||||||
\(938\) | 3040.73 | 0.105846 | ||||||||
\(939\) | −38947.8 | −1.35358 | ||||||||
\(940\) | 9832.12 | 0.341158 | ||||||||
\(941\) | 1106.42 | 0.0383298 | 0.0191649 | − | 0.999816i | \(-0.493899\pi\) | ||||
0.0191649 | + | 0.999816i | \(0.493899\pi\) | |||||||
\(942\) | −31424.8 | −1.08692 | ||||||||
\(943\) | −6720.32 | −0.232072 | ||||||||
\(944\) | 514.581 | 0.0177417 | ||||||||
\(945\) | −1194.26 | −0.0411103 | ||||||||
\(946\) | 4499.30 | 0.154635 | ||||||||
\(947\) | −38680.7 | −1.32730 | −0.663650 | − | 0.748043i | \(-0.730994\pi\) | ||||
−0.663650 | + | 0.748043i | \(0.730994\pi\) | |||||||
\(948\) | 2785.45 | 0.0954297 | ||||||||
\(949\) | 20546.8 | 0.702822 | ||||||||
\(950\) | 849.466 | 0.0290109 | ||||||||
\(951\) | −47514.4 | −1.62015 | ||||||||
\(952\) | 57206.7 | 1.94756 | ||||||||
\(953\) | −25521.3 | −0.867489 | −0.433745 | − | 0.901036i | \(-0.642808\pi\) | ||||
−0.433745 | + | 0.901036i | \(0.642808\pi\) | |||||||
\(954\) | 2311.19 | 0.0784355 | ||||||||
\(955\) | 22037.3 | 0.746713 | ||||||||
\(956\) | −30060.8 | −1.01698 | ||||||||
\(957\) | 119.059 | 0.00402156 | ||||||||
\(958\) | −23081.3 | −0.778418 | ||||||||
\(959\) | −15428.8 | −0.519523 | ||||||||
\(960\) | 12656.3 | 0.425502 | ||||||||
\(961\) | −29732.9 | −0.998051 | ||||||||
\(962\) | −27182.8 | −0.911028 | ||||||||
\(963\) | −11900.5 | −0.398224 | ||||||||
\(964\) | −10146.6 | −0.339003 | ||||||||
\(965\) | 3049.02 | 0.101711 | ||||||||
\(966\) | −6734.29 | −0.224298 | ||||||||
\(967\) | 16055.5 | 0.533931 | 0.266965 | − | 0.963706i | \(-0.413979\pi\) | ||||
0.266965 | + | 0.963706i | \(0.413979\pi\) | |||||||
\(968\) | −2770.19 | −0.0919806 | ||||||||
\(969\) | −16893.4 | −0.560055 | ||||||||
\(970\) | −10976.8 | −0.363345 | ||||||||
\(971\) | −35027.9 | −1.15767 | −0.578836 | − | 0.815444i | \(-0.696493\pi\) | ||||
−0.578836 | + | 0.815444i | \(0.696493\pi\) | |||||||
\(972\) | −26001.6 | −0.858026 | ||||||||
\(973\) | 35759.0 | 1.17819 | ||||||||
\(974\) | 22905.7 | 0.753539 | ||||||||
\(975\) | −7034.50 | −0.231061 | ||||||||
\(976\) | 497.215 | 0.0163068 | ||||||||
\(977\) | 29736.9 | 0.973765 | 0.486882 | − | 0.873467i | \(-0.338134\pi\) | ||||
0.486882 | + | 0.873467i | \(0.338134\pi\) | |||||||
\(978\) | −16988.4 | −0.555448 | ||||||||
\(979\) | −10922.4 | −0.356570 | ||||||||
\(980\) | 2294.88 | 0.0748034 | ||||||||
\(981\) | 15418.8 | 0.501818 | ||||||||
\(982\) | −29855.4 | −0.970188 | ||||||||
\(983\) | 8193.33 | 0.265846 | 0.132923 | − | 0.991126i | \(-0.457564\pi\) | ||||
0.132923 | + | 0.991126i | \(0.457564\pi\) | |||||||
\(984\) | 47515.2 | 1.53936 | ||||||||
\(985\) | −4346.92 | −0.140614 | ||||||||
\(986\) | 309.923 | 0.0100101 | ||||||||
\(987\) | 63909.5 | 2.06105 | ||||||||
\(988\) | −3444.97 | −0.110930 | ||||||||
\(989\) | 5518.82 | 0.177440 | ||||||||
\(990\) | 2806.24 | 0.0900891 | ||||||||
\(991\) | 54024.4 | 1.73173 | 0.865864 | − | 0.500280i | \(-0.166770\pi\) | ||||
0.865864 | + | 0.500280i | \(0.166770\pi\) | |||||||
\(992\) | −1361.30 | −0.0435699 | ||||||||
\(993\) | 36779.5 | 1.17539 | ||||||||
\(994\) | −9653.54 | −0.308040 | ||||||||
\(995\) | 7972.37 | 0.254011 | ||||||||
\(996\) | −29317.4 | −0.932688 | ||||||||
\(997\) | −59848.2 | −1.90111 | −0.950557 | − | 0.310550i | \(-0.899487\pi\) | ||||
−0.950557 | + | 0.310550i | \(0.899487\pi\) | |||||||
\(998\) | 29175.4 | 0.925382 | ||||||||
\(999\) | 4591.09 | 0.145401 |
(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 | 1045.4.a.c.1.15 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.c.1.15 | ✓ | 20 | 1.1 | even | 1 | trivial |