Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(1,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("39.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 16x - 8 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.20905 | 1.48812 | 0.744062 | − | 0.668111i | \(-0.232897\pi\) | ||||
0.744062 | + | 0.668111i | \(0.232897\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 9.71610 | 1.21451 | ||||||||
\(5\) | −11.4322 | −1.02253 | −0.511264 | − | 0.859424i | \(-0.670822\pi\) | ||||
−0.511264 | + | 0.859424i | \(0.670822\pi\) | |||||||
\(6\) | 12.6271 | 0.859169 | ||||||||
\(7\) | −11.2543 | −0.607675 | −0.303838 | − | 0.952724i | \(-0.598268\pi\) | ||||
−0.303838 | + | 0.952724i | \(0.598268\pi\) | |||||||
\(8\) | 7.22315 | 0.319221 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −48.1187 | −1.52165 | ||||||||
\(11\) | 25.8785 | 0.709333 | 0.354666 | − | 0.934993i | \(-0.384594\pi\) | ||||
0.354666 | + | 0.934993i | \(0.384594\pi\) | |||||||
\(12\) | 29.1483 | 0.701199 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | −47.3699 | −0.904296 | ||||||||
\(15\) | −34.2966 | −0.590356 | ||||||||
\(16\) | −47.3262 | −0.739472 | ||||||||
\(17\) | −20.3276 | −0.290010 | −0.145005 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145005 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(18\) | 37.8814 | 0.496041 | ||||||||
\(19\) | 154.712 | 1.86807 | 0.934035 | − | 0.357181i | \(-0.116262\pi\) | ||||
0.934035 | + | 0.357181i | \(0.116262\pi\) | |||||||
\(20\) | −111.076 | −1.24187 | ||||||||
\(21\) | −33.7629 | −0.350841 | ||||||||
\(22\) | 108.924 | 1.05558 | ||||||||
\(23\) | −180.418 | −1.63565 | −0.817823 | − | 0.575471i | \(-0.804819\pi\) | ||||
−0.817823 | + | 0.575471i | \(0.804819\pi\) | |||||||
\(24\) | 21.6695 | 0.184302 | ||||||||
\(25\) | 5.69520 | 0.0455616 | ||||||||
\(26\) | 54.7176 | 0.412731 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −109.348 | −0.738029 | ||||||||
\(29\) | −20.4522 | −0.130961 | −0.0654806 | − | 0.997854i | \(-0.520858\pi\) | ||||
−0.0654806 | + | 0.997854i | \(0.520858\pi\) | |||||||
\(30\) | −144.356 | −0.878523 | ||||||||
\(31\) | 266.424 | 1.54359 | 0.771794 | − | 0.635873i | \(-0.219360\pi\) | ||||
0.771794 | + | 0.635873i | \(0.219360\pi\) | |||||||
\(32\) | −256.984 | −1.41965 | ||||||||
\(33\) | 77.6355 | 0.409534 | ||||||||
\(34\) | −85.5599 | −0.431571 | ||||||||
\(35\) | 128.661 | 0.621364 | ||||||||
\(36\) | 87.4449 | 0.404837 | ||||||||
\(37\) | 115.984 | 0.515340 | 0.257670 | − | 0.966233i | \(-0.417045\pi\) | ||||
0.257670 | + | 0.966233i | \(0.417045\pi\) | |||||||
\(38\) | 651.190 | 2.77992 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | −82.5765 | −0.326412 | ||||||||
\(41\) | 391.184 | 1.49006 | 0.745032 | − | 0.667029i | \(-0.232434\pi\) | ||||
0.745032 | + | 0.667029i | \(0.232434\pi\) | |||||||
\(42\) | −142.110 | −0.522095 | ||||||||
\(43\) | 151.407 | 0.536963 | 0.268482 | − | 0.963285i | \(-0.413478\pi\) | ||||
0.268482 | + | 0.963285i | \(0.413478\pi\) | |||||||
\(44\) | 251.438 | 0.861494 | ||||||||
\(45\) | −102.890 | −0.340842 | ||||||||
\(46\) | −759.390 | −2.43404 | ||||||||
\(47\) | −467.365 | −1.45047 | −0.725236 | − | 0.688500i | \(-0.758269\pi\) | ||||
−0.725236 | + | 0.688500i | \(0.758269\pi\) | |||||||
\(48\) | −141.979 | −0.426934 | ||||||||
\(49\) | −216.341 | −0.630731 | ||||||||
\(50\) | 23.9714 | 0.0678012 | ||||||||
\(51\) | −60.9828 | −0.167437 | ||||||||
\(52\) | 126.309 | 0.336845 | ||||||||
\(53\) | 79.9842 | 0.207296 | 0.103648 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103648 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(54\) | 113.644 | 0.286390 | ||||||||
\(55\) | −295.848 | −0.725312 | ||||||||
\(56\) | −81.2915 | −0.193983 | ||||||||
\(57\) | 464.136 | 1.07853 | ||||||||
\(58\) | −86.0843 | −0.194887 | ||||||||
\(59\) | −873.710 | −1.92792 | −0.963960 | − | 0.266045i | \(-0.914283\pi\) | ||||
−0.963960 | + | 0.266045i | \(0.914283\pi\) | |||||||
\(60\) | −333.229 | −0.716995 | ||||||||
\(61\) | −187.068 | −0.392649 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(62\) | 1121.39 | 2.29705 | ||||||||
\(63\) | −101.289 | −0.202558 | ||||||||
\(64\) | −703.047 | −1.37314 | ||||||||
\(65\) | −148.619 | −0.283598 | ||||||||
\(66\) | 326.772 | 0.609437 | ||||||||
\(67\) | −609.204 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(68\) | −197.505 | −0.352221 | ||||||||
\(69\) | −541.255 | −0.944340 | ||||||||
\(70\) | 541.542 | 0.924667 | ||||||||
\(71\) | 248.038 | 0.414601 | 0.207301 | − | 0.978277i | \(-0.433532\pi\) | ||||
0.207301 | + | 0.978277i | \(0.433532\pi\) | |||||||
\(72\) | 65.0084 | 0.106407 | ||||||||
\(73\) | 852.765 | 1.36724 | 0.683621 | − | 0.729838i | \(-0.260404\pi\) | ||||
0.683621 | + | 0.729838i | \(0.260404\pi\) | |||||||
\(74\) | 488.181 | 0.766890 | ||||||||
\(75\) | 17.0856 | 0.0263050 | ||||||||
\(76\) | 1503.20 | 2.26880 | ||||||||
\(77\) | −291.244 | −0.431044 | ||||||||
\(78\) | 164.153 | 0.238291 | ||||||||
\(79\) | −331.221 | −0.471712 | −0.235856 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235856 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(80\) | 541.043 | 0.756130 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1646.51 | 2.21740 | ||||||||
\(83\) | −435.432 | −0.575842 | −0.287921 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287921 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(84\) | −328.044 | −0.426101 | ||||||||
\(85\) | 232.389 | 0.296543 | ||||||||
\(86\) | 637.281 | 0.799067 | ||||||||
\(87\) | −61.3566 | −0.0756105 | ||||||||
\(88\) | 186.924 | 0.226434 | ||||||||
\(89\) | 259.233 | 0.308749 | 0.154375 | − | 0.988012i | \(-0.450664\pi\) | ||||
0.154375 | + | 0.988012i | \(0.450664\pi\) | |||||||
\(90\) | −433.068 | −0.507216 | ||||||||
\(91\) | −146.306 | −0.168539 | ||||||||
\(92\) | −1752.96 | −1.98651 | ||||||||
\(93\) | 799.273 | 0.891191 | ||||||||
\(94\) | −1967.16 | −2.15848 | ||||||||
\(95\) | −1768.70 | −1.91015 | ||||||||
\(96\) | −770.951 | −0.819634 | ||||||||
\(97\) | 1225.17 | 1.28245 | 0.641223 | − | 0.767355i | \(-0.278428\pi\) | ||||
0.641223 | + | 0.767355i | \(0.278428\pi\) | |||||||
\(98\) | −910.589 | −0.938606 | ||||||||
\(99\) | 232.907 | 0.236444 | ||||||||
\(100\) | 55.3351 | 0.0553351 | ||||||||
\(101\) | 645.416 | 0.635855 | 0.317927 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317927 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(102\) | −256.680 | −0.249167 | ||||||||
\(103\) | −511.137 | −0.488969 | −0.244484 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244484 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(104\) | 93.9010 | 0.0885360 | ||||||||
\(105\) | 385.984 | 0.358745 | ||||||||
\(106\) | 336.657 | 0.308482 | ||||||||
\(107\) | 608.195 | 0.549499 | 0.274750 | − | 0.961516i | \(-0.411405\pi\) | ||||
0.274750 | + | 0.961516i | \(0.411405\pi\) | |||||||
\(108\) | 262.335 | 0.233733 | ||||||||
\(109\) | −1300.04 | −1.14239 | −0.571197 | − | 0.820813i | \(-0.693521\pi\) | ||||
−0.571197 | + | 0.820813i | \(0.693521\pi\) | |||||||
\(110\) | −1245.24 | −1.07935 | ||||||||
\(111\) | 347.951 | 0.297532 | ||||||||
\(112\) | 532.623 | 0.449359 | ||||||||
\(113\) | 42.1953 | 0.0351274 | 0.0175637 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175637 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(114\) | 1953.57 | 1.60499 | ||||||||
\(115\) | 2062.58 | 1.67249 | ||||||||
\(116\) | −198.716 | −0.159054 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | −3677.49 | −2.86899 | ||||||||
\(119\) | 228.773 | 0.176232 | ||||||||
\(120\) | −247.729 | −0.188454 | ||||||||
\(121\) | −661.303 | −0.496847 | ||||||||
\(122\) | −787.378 | −0.584311 | ||||||||
\(123\) | 1173.55 | 0.860289 | ||||||||
\(124\) | 2588.61 | 1.87471 | ||||||||
\(125\) | 1363.92 | 0.975939 | ||||||||
\(126\) | −426.329 | −0.301432 | ||||||||
\(127\) | −311.018 | −0.217310 | −0.108655 | − | 0.994080i | \(-0.534654\pi\) | ||||
−0.108655 | + | 0.994080i | \(0.534654\pi\) | |||||||
\(128\) | −903.291 | −0.623753 | ||||||||
\(129\) | 454.222 | 0.310016 | ||||||||
\(130\) | −625.543 | −0.422029 | ||||||||
\(131\) | 2000.98 | 1.33456 | 0.667278 | − | 0.744809i | \(-0.267459\pi\) | ||||
0.667278 | + | 0.744809i | \(0.267459\pi\) | |||||||
\(132\) | 754.314 | 0.497384 | ||||||||
\(133\) | −1741.17 | −1.13518 | ||||||||
\(134\) | −2564.17 | −1.65306 | ||||||||
\(135\) | −308.669 | −0.196785 | ||||||||
\(136\) | −146.829 | −0.0925773 | ||||||||
\(137\) | 1038.53 | 0.647644 | 0.323822 | − | 0.946118i | \(-0.395032\pi\) | ||||
0.323822 | + | 0.946118i | \(0.395032\pi\) | |||||||
\(138\) | −2278.17 | −1.40529 | ||||||||
\(139\) | −2858.46 | −1.74426 | −0.872128 | − | 0.489277i | \(-0.837261\pi\) | ||||
−0.872128 | + | 0.489277i | \(0.837261\pi\) | |||||||
\(140\) | 1250.09 | 0.754655 | ||||||||
\(141\) | −1402.09 | −0.837430 | ||||||||
\(142\) | 1044.00 | 0.616978 | ||||||||
\(143\) | 336.421 | 0.196734 | ||||||||
\(144\) | −425.936 | −0.246491 | ||||||||
\(145\) | 233.814 | 0.133911 | ||||||||
\(146\) | 3589.33 | 2.03462 | ||||||||
\(147\) | −649.022 | −0.364153 | ||||||||
\(148\) | 1126.91 | 0.625887 | ||||||||
\(149\) | 743.479 | 0.408780 | 0.204390 | − | 0.978890i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978890i | \(0.434479\pi\) | |||||||
\(150\) | 71.9141 | 0.0391451 | ||||||||
\(151\) | 2277.24 | 1.22728 | 0.613640 | − | 0.789586i | \(-0.289705\pi\) | ||||
0.613640 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(152\) | 1117.51 | 0.596328 | ||||||||
\(153\) | −182.948 | −0.0966700 | ||||||||
\(154\) | −1225.86 | −0.641447 | ||||||||
\(155\) | −3045.82 | −1.57836 | ||||||||
\(156\) | 378.928 | 0.194478 | ||||||||
\(157\) | 3173.51 | 1.61321 | 0.806605 | − | 0.591091i | \(-0.201303\pi\) | ||||
0.806605 | + | 0.591091i | \(0.201303\pi\) | |||||||
\(158\) | −1394.12 | −0.701966 | ||||||||
\(159\) | 239.953 | 0.119682 | ||||||||
\(160\) | 2937.89 | 1.45163 | ||||||||
\(161\) | 2030.48 | 0.993941 | ||||||||
\(162\) | 340.933 | 0.165347 | ||||||||
\(163\) | −2314.65 | −1.11225 | −0.556126 | − | 0.831098i | \(-0.687713\pi\) | ||||
−0.556126 | + | 0.831098i | \(0.687713\pi\) | |||||||
\(164\) | 3800.78 | 1.80970 | ||||||||
\(165\) | −887.545 | −0.418759 | ||||||||
\(166\) | −1832.76 | −0.856925 | ||||||||
\(167\) | −2665.65 | −1.23517 | −0.617587 | − | 0.786502i | \(-0.711890\pi\) | ||||
−0.617587 | + | 0.786502i | \(0.711890\pi\) | |||||||
\(168\) | −243.874 | −0.111996 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 978.138 | 0.441293 | ||||||||
\(171\) | 1392.41 | 0.622690 | ||||||||
\(172\) | 1471.09 | 0.652148 | ||||||||
\(173\) | −165.243 | −0.0726198 | −0.0363099 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363099 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(174\) | −258.253 | −0.112518 | ||||||||
\(175\) | −64.0954 | −0.0276866 | ||||||||
\(176\) | −1224.73 | −0.524532 | ||||||||
\(177\) | −2621.13 | −1.11309 | ||||||||
\(178\) | 1091.13 | 0.459457 | ||||||||
\(179\) | 712.339 | 0.297446 | 0.148723 | − | 0.988879i | \(-0.452484\pi\) | ||||
0.148723 | + | 0.988879i | \(0.452484\pi\) | |||||||
\(180\) | −999.688 | −0.413957 | ||||||||
\(181\) | 2206.53 | 0.906133 | 0.453066 | − | 0.891477i | \(-0.350330\pi\) | ||||
0.453066 | + | 0.891477i | \(0.350330\pi\) | |||||||
\(182\) | −615.809 | −0.250806 | ||||||||
\(183\) | −561.204 | −0.226696 | ||||||||
\(184\) | −1303.19 | −0.522132 | ||||||||
\(185\) | −1325.95 | −0.526949 | ||||||||
\(186\) | 3364.18 | 1.32620 | ||||||||
\(187\) | −526.048 | −0.205714 | ||||||||
\(188\) | −4540.96 | −1.76162 | ||||||||
\(189\) | −303.866 | −0.116947 | ||||||||
\(190\) | −7444.54 | −2.84254 | ||||||||
\(191\) | 1470.64 | 0.557129 | 0.278565 | − | 0.960417i | \(-0.410141\pi\) | ||||
0.278565 | + | 0.960417i | \(0.410141\pi\) | |||||||
\(192\) | −2109.14 | −0.792782 | ||||||||
\(193\) | 369.560 | 0.137832 | 0.0689158 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689158 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(194\) | 5156.80 | 1.90844 | ||||||||
\(195\) | −445.856 | −0.163735 | ||||||||
\(196\) | −2101.99 | −0.766031 | ||||||||
\(197\) | −4273.41 | −1.54552 | −0.772761 | − | 0.634697i | \(-0.781125\pi\) | ||||
−0.772761 | + | 0.634697i | \(0.781125\pi\) | |||||||
\(198\) | 980.315 | 0.351858 | ||||||||
\(199\) | 4154.31 | 1.47985 | 0.739927 | − | 0.672687i | \(-0.234860\pi\) | ||||
0.739927 | + | 0.672687i | \(0.234860\pi\) | |||||||
\(200\) | 41.1373 | 0.0145442 | ||||||||
\(201\) | −1827.61 | −0.641342 | ||||||||
\(202\) | 2716.59 | 0.946230 | ||||||||
\(203\) | 230.175 | 0.0795819 | ||||||||
\(204\) | −592.515 | −0.203355 | ||||||||
\(205\) | −4472.09 | −1.52363 | ||||||||
\(206\) | −2151.40 | −0.727646 | ||||||||
\(207\) | −1623.77 | −0.545215 | ||||||||
\(208\) | −615.241 | −0.205093 | ||||||||
\(209\) | 4003.71 | 1.32508 | ||||||||
\(210\) | 1624.63 | 0.533857 | ||||||||
\(211\) | 1231.59 | 0.401830 | 0.200915 | − | 0.979609i | \(-0.435608\pi\) | ||||
0.200915 | + | 0.979609i | \(0.435608\pi\) | |||||||
\(212\) | 777.134 | 0.251763 | ||||||||
\(213\) | 744.114 | 0.239370 | ||||||||
\(214\) | 2559.92 | 0.817723 | ||||||||
\(215\) | −1730.92 | −0.549059 | ||||||||
\(216\) | 195.025 | 0.0614341 | ||||||||
\(217\) | −2998.42 | −0.938000 | ||||||||
\(218\) | −5471.92 | −1.70002 | ||||||||
\(219\) | 2558.30 | 0.789377 | ||||||||
\(220\) | −2874.49 | −0.880901 | ||||||||
\(221\) | −264.259 | −0.0804343 | ||||||||
\(222\) | 1464.54 | 0.442764 | ||||||||
\(223\) | −2187.24 | −0.656809 | −0.328404 | − | 0.944537i | \(-0.606511\pi\) | ||||
−0.328404 | + | 0.944537i | \(0.606511\pi\) | |||||||
\(224\) | 2892.17 | 0.862684 | ||||||||
\(225\) | 51.2568 | 0.0151872 | ||||||||
\(226\) | 177.602 | 0.0522739 | ||||||||
\(227\) | 4138.67 | 1.21010 | 0.605051 | − | 0.796187i | \(-0.293153\pi\) | ||||
0.605051 | + | 0.796187i | \(0.293153\pi\) | |||||||
\(228\) | 4509.59 | 1.30989 | ||||||||
\(229\) | −835.354 | −0.241056 | −0.120528 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120528 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(230\) | 8681.50 | 2.48887 | ||||||||
\(231\) | −873.733 | −0.248863 | ||||||||
\(232\) | −147.729 | −0.0418056 | ||||||||
\(233\) | 3685.51 | 1.03625 | 0.518124 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518124 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(234\) | 492.459 | 0.137577 | ||||||||
\(235\) | 5343.01 | 1.48315 | ||||||||
\(236\) | −8489.05 | −2.34148 | ||||||||
\(237\) | −993.662 | −0.272343 | ||||||||
\(238\) | 962.917 | 0.262255 | ||||||||
\(239\) | 3026.21 | 0.819034 | 0.409517 | − | 0.912303i | \(-0.365697\pi\) | ||||
0.409517 | + | 0.912303i | \(0.365697\pi\) | |||||||
\(240\) | 1623.13 | 0.436552 | ||||||||
\(241\) | 3265.58 | 0.872839 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(242\) | −2783.46 | −0.739370 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1817.57 | −0.476877 | ||||||||
\(245\) | 2473.25 | 0.644940 | ||||||||
\(246\) | 4939.53 | 1.28022 | ||||||||
\(247\) | 2011.25 | 0.518110 | ||||||||
\(248\) | 1924.42 | 0.492746 | ||||||||
\(249\) | −1306.30 | −0.332463 | ||||||||
\(250\) | 5740.79 | 1.45232 | ||||||||
\(251\) | −6363.16 | −1.60016 | −0.800078 | − | 0.599897i | \(-0.795208\pi\) | ||||
−0.800078 | + | 0.599897i | \(0.795208\pi\) | |||||||
\(252\) | −984.131 | −0.246010 | ||||||||
\(253\) | −4668.96 | −1.16022 | ||||||||
\(254\) | −1309.09 | −0.323385 | ||||||||
\(255\) | 697.168 | 0.171209 | ||||||||
\(256\) | 1822.38 | 0.444917 | ||||||||
\(257\) | −6085.36 | −1.47702 | −0.738511 | − | 0.674242i | \(-0.764471\pi\) | ||||
−0.738511 | + | 0.674242i | \(0.764471\pi\) | |||||||
\(258\) | 1911.84 | 0.461342 | ||||||||
\(259\) | −1305.31 | −0.313159 | ||||||||
\(260\) | −1443.99 | −0.344433 | ||||||||
\(261\) | −184.070 | −0.0436538 | ||||||||
\(262\) | 8422.24 | 1.98598 | ||||||||
\(263\) | 123.227 | 0.0288916 | 0.0144458 | − | 0.999896i | \(-0.495402\pi\) | ||||
0.0144458 | + | 0.999896i | \(0.495402\pi\) | |||||||
\(264\) | 560.773 | 0.130732 | ||||||||
\(265\) | −914.395 | −0.211965 | ||||||||
\(266\) | −7328.69 | −1.68929 | ||||||||
\(267\) | 777.700 | 0.178256 | ||||||||
\(268\) | −5919.08 | −1.34913 | ||||||||
\(269\) | −1935.79 | −0.438763 | −0.219381 | − | 0.975639i | \(-0.570404\pi\) | ||||
−0.219381 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(270\) | −1299.20 | −0.292841 | ||||||||
\(271\) | −4612.69 | −1.03395 | −0.516976 | − | 0.856000i | \(-0.672942\pi\) | ||||
−0.516976 | + | 0.856000i | \(0.672942\pi\) | |||||||
\(272\) | 962.028 | 0.214454 | ||||||||
\(273\) | −438.918 | −0.0973059 | ||||||||
\(274\) | 4371.20 | 0.963774 | ||||||||
\(275\) | 147.383 | 0.0323183 | ||||||||
\(276\) | −5258.89 | −1.14691 | ||||||||
\(277\) | −5834.30 | −1.26552 | −0.632761 | − | 0.774347i | \(-0.718078\pi\) | ||||
−0.632761 | + | 0.774347i | \(0.718078\pi\) | |||||||
\(278\) | −12031.4 | −2.59567 | ||||||||
\(279\) | 2397.82 | 0.514529 | ||||||||
\(280\) | 929.341 | 0.198353 | ||||||||
\(281\) | 4691.91 | 0.996071 | 0.498036 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498036 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(282\) | −5901.49 | −1.24620 | ||||||||
\(283\) | 3465.60 | 0.727945 | 0.363973 | − | 0.931410i | \(-0.381420\pi\) | ||||
0.363973 | + | 0.931410i | \(0.381420\pi\) | |||||||
\(284\) | 2409.96 | 0.503539 | ||||||||
\(285\) | −5306.09 | −1.10283 | ||||||||
\(286\) | 1416.01 | 0.292764 | ||||||||
\(287\) | −4402.50 | −0.905475 | ||||||||
\(288\) | −2312.85 | −0.473216 | ||||||||
\(289\) | −4499.79 | −0.915894 | ||||||||
\(290\) | 984.133 | 0.199277 | ||||||||
\(291\) | 3675.51 | 0.740420 | ||||||||
\(292\) | 8285.55 | 1.66053 | ||||||||
\(293\) | 2677.31 | 0.533822 | 0.266911 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266911 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(294\) | −2731.77 | −0.541904 | ||||||||
\(295\) | 9988.43 | 1.97135 | ||||||||
\(296\) | 837.767 | 0.164507 | ||||||||
\(297\) | 698.720 | 0.136511 | ||||||||
\(298\) | 3129.34 | 0.608315 | ||||||||
\(299\) | −2345.44 | −0.453646 | ||||||||
\(300\) | 166.005 | 0.0319477 | ||||||||
\(301\) | −1703.98 | −0.326299 | ||||||||
\(302\) | 9585.02 | 1.82634 | ||||||||
\(303\) | 1936.25 | 0.367111 | ||||||||
\(304\) | −7321.93 | −1.38139 | ||||||||
\(305\) | 2138.60 | 0.401494 | ||||||||
\(306\) | −770.039 | −0.143857 | ||||||||
\(307\) | 471.915 | 0.0877316 | 0.0438658 | − | 0.999037i | \(-0.486033\pi\) | ||||
0.0438658 | + | 0.999037i | \(0.486033\pi\) | |||||||
\(308\) | −2829.76 | −0.523508 | ||||||||
\(309\) | −1533.41 | −0.282306 | ||||||||
\(310\) | −12820.0 | −2.34880 | ||||||||
\(311\) | −1518.52 | −0.276872 | −0.138436 | − | 0.990371i | \(-0.544207\pi\) | ||||
−0.138436 | + | 0.990371i | \(0.544207\pi\) | |||||||
\(312\) | 281.703 | 0.0511163 | ||||||||
\(313\) | 4049.86 | 0.731348 | 0.365674 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(314\) | 13357.5 | 2.40066 | ||||||||
\(315\) | 1157.95 | 0.207121 | ||||||||
\(316\) | −3218.17 | −0.572900 | ||||||||
\(317\) | 3253.96 | 0.576532 | 0.288266 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288266 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(318\) | 1009.97 | 0.178102 | ||||||||
\(319\) | −529.272 | −0.0928951 | ||||||||
\(320\) | 8037.37 | 1.40407 | ||||||||
\(321\) | 1824.59 | 0.317254 | ||||||||
\(322\) | 8546.40 | 1.47911 | ||||||||
\(323\) | −3144.92 | −0.541759 | ||||||||
\(324\) | 787.004 | 0.134946 | ||||||||
\(325\) | 74.0375 | 0.0126365 | ||||||||
\(326\) | −9742.46 | −1.65517 | ||||||||
\(327\) | −3900.11 | −0.659561 | ||||||||
\(328\) | 2825.58 | 0.475660 | ||||||||
\(329\) | 5259.86 | 0.881415 | ||||||||
\(330\) | −3735.72 | −0.623165 | ||||||||
\(331\) | −3422.45 | −0.568322 | −0.284161 | − | 0.958777i | \(-0.591715\pi\) | ||||
−0.284161 | + | 0.958777i | \(0.591715\pi\) | |||||||
\(332\) | −4230.71 | −0.699368 | ||||||||
\(333\) | 1043.85 | 0.171780 | ||||||||
\(334\) | −11219.8 | −1.83809 | ||||||||
\(335\) | 6964.54 | 1.13586 | ||||||||
\(336\) | 1597.87 | 0.259437 | ||||||||
\(337\) | −9301.67 | −1.50354 | −0.751772 | − | 0.659423i | \(-0.770801\pi\) | ||||
−0.751772 | + | 0.659423i | \(0.770801\pi\) | |||||||
\(338\) | 711.329 | 0.114471 | ||||||||
\(339\) | 126.586 | 0.0202808 | ||||||||
\(340\) | 2257.92 | 0.360155 | ||||||||
\(341\) | 6894.66 | 1.09492 | ||||||||
\(342\) | 5860.71 | 0.926640 | ||||||||
\(343\) | 6294.99 | 0.990955 | ||||||||
\(344\) | 1093.64 | 0.171410 | ||||||||
\(345\) | 6187.74 | 0.965613 | ||||||||
\(346\) | −695.518 | −0.108067 | ||||||||
\(347\) | 216.898 | 0.0335554 | 0.0167777 | − | 0.999859i | \(-0.494659\pi\) | ||||
0.0167777 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(348\) | −596.147 | −0.0918299 | ||||||||
\(349\) | −4809.84 | −0.737721 | −0.368861 | − | 0.929485i | \(-0.620252\pi\) | ||||
−0.368861 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(350\) | −269.781 | −0.0412011 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | −6650.35 | −1.00700 | ||||||||
\(353\) | −2859.64 | −0.431170 | −0.215585 | − | 0.976485i | \(-0.569166\pi\) | ||||
−0.215585 | + | 0.976485i | \(0.569166\pi\) | |||||||
\(354\) | −11032.5 | −1.65641 | ||||||||
\(355\) | −2835.62 | −0.423941 | ||||||||
\(356\) | 2518.74 | 0.374980 | ||||||||
\(357\) | 686.319 | 0.101747 | ||||||||
\(358\) | 2998.27 | 0.442636 | ||||||||
\(359\) | 3686.04 | 0.541899 | 0.270949 | − | 0.962594i | \(-0.412662\pi\) | ||||
0.270949 | + | 0.962594i | \(0.412662\pi\) | |||||||
\(360\) | −743.188 | −0.108804 | ||||||||
\(361\) | 17076.8 | 2.48969 | ||||||||
\(362\) | 9287.39 | 1.34844 | ||||||||
\(363\) | −1983.91 | −0.286855 | ||||||||
\(364\) | −1421.52 | −0.204692 | ||||||||
\(365\) | −9748.98 | −1.39804 | ||||||||
\(366\) | −2362.14 | −0.337352 | ||||||||
\(367\) | −3470.59 | −0.493633 | −0.246816 | − | 0.969062i | \(-0.579384\pi\) | ||||
−0.246816 | + | 0.969062i | \(0.579384\pi\) | |||||||
\(368\) | 8538.52 | 1.20951 | ||||||||
\(369\) | 3520.65 | 0.496688 | ||||||||
\(370\) | −5580.98 | −0.784166 | ||||||||
\(371\) | −900.166 | −0.125968 | ||||||||
\(372\) | 7765.82 | 1.08236 | ||||||||
\(373\) | −11963.4 | −1.66070 | −0.830352 | − | 0.557240i | \(-0.811860\pi\) | ||||
−0.830352 | + | 0.557240i | \(0.811860\pi\) | |||||||
\(374\) | −2214.16 | −0.306127 | ||||||||
\(375\) | 4091.75 | 0.563459 | ||||||||
\(376\) | −3375.85 | −0.463021 | ||||||||
\(377\) | −265.879 | −0.0363221 | ||||||||
\(378\) | −1278.99 | −0.174032 | ||||||||
\(379\) | 345.604 | 0.0468403 | 0.0234202 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234202 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(380\) | −17184.8 | −2.31990 | ||||||||
\(381\) | −933.055 | −0.125464 | ||||||||
\(382\) | 6189.99 | 0.829078 | ||||||||
\(383\) | −3386.40 | −0.451793 | −0.225897 | − | 0.974151i | \(-0.572531\pi\) | ||||
−0.225897 | + | 0.974151i | \(0.572531\pi\) | |||||||
\(384\) | −2709.87 | −0.360124 | ||||||||
\(385\) | 3329.56 | 0.440754 | ||||||||
\(386\) | 1555.49 | 0.205110 | ||||||||
\(387\) | 1362.67 | 0.178988 | ||||||||
\(388\) | 11903.9 | 1.55755 | ||||||||
\(389\) | −1629.88 | −0.212438 | −0.106219 | − | 0.994343i | \(-0.533874\pi\) | ||||
−0.106219 | + | 0.994343i | \(0.533874\pi\) | |||||||
\(390\) | −1876.63 | −0.243659 | ||||||||
\(391\) | 3667.47 | 0.474353 | ||||||||
\(392\) | −1562.66 | −0.201343 | ||||||||
\(393\) | 6002.95 | 0.770506 | ||||||||
\(394\) | −17987.0 | −2.29993 | ||||||||
\(395\) | 3786.58 | 0.482338 | ||||||||
\(396\) | 2262.94 | 0.287165 | ||||||||
\(397\) | 7938.94 | 1.00364 | 0.501819 | − | 0.864973i | \(-0.332664\pi\) | ||||
0.501819 | + | 0.864973i | \(0.332664\pi\) | |||||||
\(398\) | 17485.7 | 2.20221 | ||||||||
\(399\) | −5223.52 | −0.655396 | ||||||||
\(400\) | −269.532 | −0.0336915 | ||||||||
\(401\) | 214.402 | 0.0267001 | 0.0133500 | − | 0.999911i | \(-0.495750\pi\) | ||||
0.0133500 | + | 0.999911i | \(0.495750\pi\) | |||||||
\(402\) | −7692.51 | −0.954396 | ||||||||
\(403\) | 3463.52 | 0.428114 | ||||||||
\(404\) | 6270.93 | 0.772253 | ||||||||
\(405\) | −926.008 | −0.113614 | ||||||||
\(406\) | 968.819 | 0.118428 | ||||||||
\(407\) | 3001.48 | 0.365548 | ||||||||
\(408\) | −440.488 | −0.0534495 | ||||||||
\(409\) | −4783.73 | −0.578338 | −0.289169 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289169 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(410\) | −18823.2 | −2.26735 | ||||||||
\(411\) | 3115.58 | 0.373917 | ||||||||
\(412\) | −4966.25 | −0.593859 | ||||||||
\(413\) | 9832.99 | 1.17155 | ||||||||
\(414\) | −6834.51 | −0.811347 | ||||||||
\(415\) | 4977.95 | 0.588815 | ||||||||
\(416\) | −3340.79 | −0.393739 | ||||||||
\(417\) | −8575.39 | −1.00705 | ||||||||
\(418\) | 16851.8 | 1.97189 | ||||||||
\(419\) | −9903.67 | −1.15472 | −0.577358 | − | 0.816491i | \(-0.695916\pi\) | ||||
−0.577358 | + | 0.816491i | \(0.695916\pi\) | |||||||
\(420\) | 3750.26 | 0.435700 | ||||||||
\(421\) | −12120.6 | −1.40314 | −0.701572 | − | 0.712598i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712598i | \(0.747518\pi\) | |||||||
\(422\) | 5183.82 | 0.597973 | ||||||||
\(423\) | −4206.28 | −0.483491 | ||||||||
\(424\) | 577.738 | 0.0661732 | ||||||||
\(425\) | −115.770 | −0.0132133 | ||||||||
\(426\) | 3132.01 | 0.356213 | ||||||||
\(427\) | 2105.32 | 0.238603 | ||||||||
\(428\) | 5909.28 | 0.667374 | ||||||||
\(429\) | 1009.26 | 0.113584 | ||||||||
\(430\) | −7285.53 | −0.817068 | ||||||||
\(431\) | −13672.6 | −1.52805 | −0.764023 | − | 0.645189i | \(-0.776779\pi\) | ||||
−0.764023 | + | 0.645189i | \(0.776779\pi\) | |||||||
\(432\) | −1277.81 | −0.142311 | ||||||||
\(433\) | 7113.10 | 0.789455 | 0.394727 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394727 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(434\) | −12620.5 | −1.39586 | ||||||||
\(435\) | 701.441 | 0.0773138 | ||||||||
\(436\) | −12631.3 | −1.38745 | ||||||||
\(437\) | −27912.9 | −3.05550 | ||||||||
\(438\) | 10768.0 | 1.17469 | ||||||||
\(439\) | −6022.04 | −0.654707 | −0.327353 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327353 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(440\) | −2136.96 | −0.231535 | ||||||||
\(441\) | −1947.07 | −0.210244 | ||||||||
\(442\) | −1112.28 | −0.119696 | ||||||||
\(443\) | −12994.4 | −1.39364 | −0.696821 | − | 0.717245i | \(-0.745403\pi\) | ||||
−0.696821 | + | 0.717245i | \(0.745403\pi\) | |||||||
\(444\) | 3380.72 | 0.361356 | ||||||||
\(445\) | −2963.61 | −0.315704 | ||||||||
\(446\) | −9206.20 | −0.977413 | ||||||||
\(447\) | 2230.44 | 0.236009 | ||||||||
\(448\) | 7912.30 | 0.834422 | ||||||||
\(449\) | 10984.3 | 1.15452 | 0.577260 | − | 0.816560i | \(-0.304122\pi\) | ||||
0.577260 | + | 0.816560i | \(0.304122\pi\) | |||||||
\(450\) | 215.742 | 0.0226004 | ||||||||
\(451\) | 10123.2 | 1.05695 | ||||||||
\(452\) | 409.973 | 0.0426627 | ||||||||
\(453\) | 6831.72 | 0.708570 | ||||||||
\(454\) | 17419.9 | 1.80078 | ||||||||
\(455\) | 1672.60 | 0.172335 | ||||||||
\(456\) | 3352.52 | 0.344290 | ||||||||
\(457\) | 9834.10 | 1.00661 | 0.503304 | − | 0.864109i | \(-0.332118\pi\) | ||||
0.503304 | + | 0.864109i | \(0.332118\pi\) | |||||||
\(458\) | −3516.05 | −0.358721 | ||||||||
\(459\) | −548.845 | −0.0558124 | ||||||||
\(460\) | 20040.2 | 2.03126 | ||||||||
\(461\) | 3401.42 | 0.343644 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(462\) | −3677.59 | −0.370339 | ||||||||
\(463\) | 1739.42 | 0.174596 | 0.0872979 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872979 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(464\) | 967.925 | 0.0968422 | ||||||||
\(465\) | −9137.45 | −0.911267 | ||||||||
\(466\) | 15512.5 | 1.54207 | ||||||||
\(467\) | −7958.82 | −0.788630 | −0.394315 | − | 0.918975i | \(-0.629018\pi\) | ||||
−0.394315 | + | 0.918975i | \(0.629018\pi\) | |||||||
\(468\) | 1136.78 | 0.112282 | ||||||||
\(469\) | 6856.16 | 0.675028 | ||||||||
\(470\) | 22489.0 | 2.20711 | ||||||||
\(471\) | 9520.54 | 0.931387 | ||||||||
\(472\) | −6310.94 | −0.615433 | ||||||||
\(473\) | 3918.20 | 0.380886 | ||||||||
\(474\) | −4182.37 | −0.405280 | ||||||||
\(475\) | 881.114 | 0.0851122 | ||||||||
\(476\) | 2222.78 | 0.214036 | ||||||||
\(477\) | 719.858 | 0.0690986 | ||||||||
\(478\) | 12737.5 | 1.21882 | ||||||||
\(479\) | 8431.98 | 0.804315 | 0.402158 | − | 0.915570i | \(-0.368260\pi\) | ||||
0.402158 | + | 0.915570i | \(0.368260\pi\) | |||||||
\(480\) | 8813.66 | 0.838097 | ||||||||
\(481\) | 1507.79 | 0.142930 | ||||||||
\(482\) | 13745.0 | 1.29889 | ||||||||
\(483\) | 6091.45 | 0.573852 | ||||||||
\(484\) | −6425.29 | −0.603427 | ||||||||
\(485\) | −14006.4 | −1.31133 | ||||||||
\(486\) | 1022.80 | 0.0954632 | ||||||||
\(487\) | −11684.7 | −1.08723 | −0.543617 | − | 0.839334i | \(-0.682945\pi\) | ||||
−0.543617 | + | 0.839334i | \(0.682945\pi\) | |||||||
\(488\) | −1351.22 | −0.125342 | ||||||||
\(489\) | −6943.94 | −0.642159 | ||||||||
\(490\) | 10410.0 | 0.959750 | ||||||||
\(491\) | −3954.70 | −0.363489 | −0.181745 | − | 0.983346i | \(-0.558174\pi\) | ||||
−0.181745 | + | 0.983346i | \(0.558174\pi\) | |||||||
\(492\) | 11402.3 | 1.04483 | ||||||||
\(493\) | 415.744 | 0.0379801 | ||||||||
\(494\) | 8465.47 | 0.771011 | ||||||||
\(495\) | −2662.63 | −0.241771 | ||||||||
\(496\) | −12608.8 | −1.14144 | ||||||||
\(497\) | −2791.49 | −0.251943 | ||||||||
\(498\) | −5498.27 | −0.494746 | ||||||||
\(499\) | −5690.37 | −0.510493 | −0.255246 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(500\) | 13251.9 | 1.18529 | ||||||||
\(501\) | −7996.95 | −0.713128 | ||||||||
\(502\) | −26782.8 | −2.38123 | ||||||||
\(503\) | 10859.1 | 0.962595 | 0.481298 | − | 0.876557i | \(-0.340166\pi\) | ||||
0.481298 | + | 0.876557i | \(0.340166\pi\) | |||||||
\(504\) | −731.623 | −0.0646609 | ||||||||
\(505\) | −7378.53 | −0.650178 | ||||||||
\(506\) | −19651.9 | −1.72655 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | −3021.88 | −0.263926 | ||||||||
\(509\) | −18558.6 | −1.61610 | −0.808049 | − | 0.589115i | \(-0.799476\pi\) | ||||
−0.808049 | + | 0.589115i | \(0.799476\pi\) | |||||||
\(510\) | 2934.41 | 0.254780 | ||||||||
\(511\) | −9597.27 | −0.830838 | ||||||||
\(512\) | 14896.8 | 1.28584 | ||||||||
\(513\) | 4177.22 | 0.359510 | ||||||||
\(514\) | −25613.6 | −2.19799 | ||||||||
\(515\) | 5843.42 | 0.499984 | ||||||||
\(516\) | 4413.27 | 0.376518 | ||||||||
\(517\) | −12094.7 | −1.02887 | ||||||||
\(518\) | −5494.13 | −0.466020 | ||||||||
\(519\) | −495.730 | −0.0419271 | ||||||||
\(520\) | −1073.49 | −0.0905305 | ||||||||
\(521\) | 17297.5 | 1.45454 | 0.727271 | − | 0.686350i | \(-0.240788\pi\) | ||||
0.727271 | + | 0.686350i | \(0.240788\pi\) | |||||||
\(522\) | −774.759 | −0.0649622 | ||||||||
\(523\) | −5016.11 | −0.419386 | −0.209693 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209693 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(524\) | 19441.8 | 1.62084 | ||||||||
\(525\) | −192.286 | −0.0159849 | ||||||||
\(526\) | 518.667 | 0.0429942 | ||||||||
\(527\) | −5415.77 | −0.447656 | ||||||||
\(528\) | −3674.19 | −0.302839 | ||||||||
\(529\) | 20383.8 | 1.67533 | ||||||||
\(530\) | −3848.73 | −0.315431 | ||||||||
\(531\) | −7863.39 | −0.642640 | ||||||||
\(532\) | −16917.4 | −1.37869 | ||||||||
\(533\) | 5085.39 | 0.413269 | ||||||||
\(534\) | 3273.38 | 0.265268 | ||||||||
\(535\) | −6953.01 | −0.561878 | ||||||||
\(536\) | −4400.37 | −0.354603 | ||||||||
\(537\) | 2137.02 | 0.171730 | ||||||||
\(538\) | −8147.83 | −0.652933 | ||||||||
\(539\) | −5598.57 | −0.447398 | ||||||||
\(540\) | −2999.06 | −0.238998 | ||||||||
\(541\) | 17642.3 | 1.40204 | 0.701018 | − | 0.713144i | \(-0.252729\pi\) | ||||
0.701018 | + | 0.713144i | \(0.252729\pi\) | |||||||
\(542\) | −19415.0 | −1.53865 | ||||||||
\(543\) | 6619.59 | 0.523156 | ||||||||
\(544\) | 5223.86 | 0.411712 | ||||||||
\(545\) | 14862.3 | 1.16813 | ||||||||
\(546\) | −1847.43 | −0.144803 | ||||||||
\(547\) | −18414.9 | −1.43943 | −0.719713 | − | 0.694271i | \(-0.755727\pi\) | ||||
−0.719713 | + | 0.694271i | \(0.755727\pi\) | |||||||
\(548\) | 10090.4 | 0.786571 | ||||||||
\(549\) | −1683.61 | −0.130883 | ||||||||
\(550\) | 620.343 | 0.0480937 | ||||||||
\(551\) | −3164.20 | −0.244645 | ||||||||
\(552\) | −3909.57 | −0.301453 | ||||||||
\(553\) | 3727.66 | 0.286648 | ||||||||
\(554\) | −24556.9 | −1.88325 | ||||||||
\(555\) | −3977.84 | −0.304234 | ||||||||
\(556\) | −27773.1 | −2.11842 | ||||||||
\(557\) | 8179.15 | 0.622193 | 0.311096 | − | 0.950378i | \(-0.399304\pi\) | ||||
0.311096 | + | 0.950378i | \(0.399304\pi\) | |||||||
\(558\) | 10092.5 | 0.765683 | ||||||||
\(559\) | 1968.30 | 0.148927 | ||||||||
\(560\) | −6089.05 | −0.459481 | ||||||||
\(561\) | −1578.14 | −0.118769 | ||||||||
\(562\) | 19748.5 | 1.48228 | ||||||||
\(563\) | −1880.07 | −0.140738 | −0.0703690 | − | 0.997521i | \(-0.522418\pi\) | ||||
−0.0703690 | + | 0.997521i | \(0.522418\pi\) | |||||||
\(564\) | −13622.9 | −1.01707 | ||||||||
\(565\) | −482.385 | −0.0359187 | ||||||||
\(566\) | 14586.9 | 1.08327 | ||||||||
\(567\) | −911.598 | −0.0675194 | ||||||||
\(568\) | 1791.62 | 0.132350 | ||||||||
\(569\) | 10118.3 | 0.745485 | 0.372743 | − | 0.927935i | \(-0.378417\pi\) | ||||
0.372743 | + | 0.927935i | \(0.378417\pi\) | |||||||
\(570\) | −22333.6 | −1.64114 | ||||||||
\(571\) | 23428.9 | 1.71711 | 0.858555 | − | 0.512721i | \(-0.171362\pi\) | ||||
0.858555 | + | 0.512721i | \(0.171362\pi\) | |||||||
\(572\) | 3268.70 | 0.238935 | ||||||||
\(573\) | 4411.92 | 0.321659 | ||||||||
\(574\) | −18530.3 | −1.34746 | ||||||||
\(575\) | −1027.52 | −0.0745225 | ||||||||
\(576\) | −6327.42 | −0.457713 | ||||||||
\(577\) | 20508.1 | 1.47966 | 0.739831 | − | 0.672793i | \(-0.234906\pi\) | ||||
0.739831 | + | 0.672793i | \(0.234906\pi\) | |||||||
\(578\) | −18939.8 | −1.36296 | ||||||||
\(579\) | 1108.68 | 0.0795771 | ||||||||
\(580\) | 2271.76 | 0.162637 | ||||||||
\(581\) | 4900.49 | 0.349925 | ||||||||
\(582\) | 15470.4 | 1.10184 | ||||||||
\(583\) | 2069.87 | 0.147042 | ||||||||
\(584\) | 6159.65 | 0.436452 | ||||||||
\(585\) | −1337.57 | −0.0945327 | ||||||||
\(586\) | 11268.9 | 0.794394 | ||||||||
\(587\) | −5968.43 | −0.419665 | −0.209833 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209833 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(588\) | −6305.97 | −0.442268 | ||||||||
\(589\) | 41219.0 | 2.88353 | ||||||||
\(590\) | 42041.8 | 2.93361 | ||||||||
\(591\) | −12820.2 | −0.892308 | ||||||||
\(592\) | −5489.06 | −0.381080 | ||||||||
\(593\) | −14659.5 | −1.01517 | −0.507584 | − | 0.861602i | \(-0.669461\pi\) | ||||
−0.507584 | + | 0.861602i | \(0.669461\pi\) | |||||||
\(594\) | 2940.95 | 0.203146 | ||||||||
\(595\) | −2615.38 | −0.180202 | ||||||||
\(596\) | 7223.72 | 0.496468 | ||||||||
\(597\) | 12462.9 | 0.854394 | ||||||||
\(598\) | −9872.07 | −0.675082 | ||||||||
\(599\) | 23635.9 | 1.61225 | 0.806125 | − | 0.591746i | \(-0.201561\pi\) | ||||
0.806125 | + | 0.591746i | \(0.201561\pi\) | |||||||
\(600\) | 123.412 | 0.00839711 | ||||||||
\(601\) | −11527.0 | −0.782356 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(602\) | −7172.15 | −0.485573 | ||||||||
\(603\) | −5482.83 | −0.370279 | ||||||||
\(604\) | 22125.9 | 1.49055 | ||||||||
\(605\) | 7560.15 | 0.508039 | ||||||||
\(606\) | 8149.77 | 0.546306 | ||||||||
\(607\) | −5098.56 | −0.340930 | −0.170465 | − | 0.985364i | \(-0.554527\pi\) | ||||
−0.170465 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(608\) | −39758.4 | −2.65200 | ||||||||
\(609\) | 690.525 | 0.0459466 | ||||||||
\(610\) | 9001.47 | 0.597473 | ||||||||
\(611\) | −6075.74 | −0.402288 | ||||||||
\(612\) | −1777.55 | −0.117407 | ||||||||
\(613\) | 1516.39 | 0.0999128 | 0.0499564 | − | 0.998751i | \(-0.484092\pi\) | ||||
0.0499564 | + | 0.998751i | \(0.484092\pi\) | |||||||
\(614\) | 1986.31 | 0.130556 | ||||||||
\(615\) | −13416.3 | −0.879668 | ||||||||
\(616\) | −2103.70 | −0.137598 | ||||||||
\(617\) | 18539.3 | 1.20966 | 0.604832 | − | 0.796353i | \(-0.293240\pi\) | ||||
0.604832 | + | 0.796353i | \(0.293240\pi\) | |||||||
\(618\) | −6454.20 | −0.420107 | ||||||||
\(619\) | 25684.9 | 1.66779 | 0.833897 | − | 0.551920i | \(-0.186105\pi\) | ||||
0.833897 | + | 0.551920i | \(0.186105\pi\) | |||||||
\(620\) | −29593.5 | −1.91694 | ||||||||
\(621\) | −4871.30 | −0.314780 | ||||||||
\(622\) | −6391.51 | −0.412020 | ||||||||
\(623\) | −2917.49 | −0.187619 | ||||||||
\(624\) | −1845.72 | −0.118410 | ||||||||
\(625\) | −16304.5 | −1.04349 | ||||||||
\(626\) | 17046.1 | 1.08834 | ||||||||
\(627\) | 12011.1 | 0.765038 | ||||||||
\(628\) | 30834.2 | 1.95926 | ||||||||
\(629\) | −2357.67 | −0.149454 | ||||||||
\(630\) | 4873.88 | 0.308222 | ||||||||
\(631\) | −22410.9 | −1.41389 | −0.706945 | − | 0.707269i | \(-0.749927\pi\) | ||||
−0.706945 | + | 0.707269i | \(0.749927\pi\) | |||||||
\(632\) | −2392.46 | −0.150580 | ||||||||
\(633\) | 3694.77 | 0.231997 | ||||||||
\(634\) | 13696.1 | 0.857950 | ||||||||
\(635\) | 3555.62 | 0.222206 | ||||||||
\(636\) | 2331.40 | 0.145356 | ||||||||
\(637\) | −2812.43 | −0.174933 | ||||||||
\(638\) | −2227.73 | −0.138239 | ||||||||
\(639\) | 2232.34 | 0.138200 | ||||||||
\(640\) | 10326.6 | 0.637804 | ||||||||
\(641\) | 6827.81 | 0.420721 | 0.210361 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210361 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(642\) | 7679.77 | 0.472113 | ||||||||
\(643\) | −23264.3 | −1.42684 | −0.713418 | − | 0.700738i | \(-0.752854\pi\) | ||||
−0.713418 | + | 0.700738i | \(0.752854\pi\) | |||||||
\(644\) | 19728.4 | 1.20715 | ||||||||
\(645\) | −5192.76 | −0.316999 | ||||||||
\(646\) | −13237.1 | −0.806204 | ||||||||
\(647\) | 14745.9 | 0.896014 | 0.448007 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448007 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(648\) | 585.075 | 0.0354690 | ||||||||
\(649\) | −22610.3 | −1.36754 | ||||||||
\(650\) | 311.628 | 0.0188047 | ||||||||
\(651\) | −8995.26 | −0.541554 | ||||||||
\(652\) | −22489.3 | −1.35084 | ||||||||
\(653\) | 10909.0 | 0.653755 | 0.326878 | − | 0.945067i | \(-0.394003\pi\) | ||||
0.326878 | + | 0.945067i | \(0.394003\pi\) | |||||||
\(654\) | −16415.8 | −0.981509 | ||||||||
\(655\) | −22875.7 | −1.36462 | ||||||||
\(656\) | −18513.2 | −1.10186 | ||||||||
\(657\) | 7674.89 | 0.455747 | ||||||||
\(658\) | 22139.0 | 1.31166 | ||||||||
\(659\) | −4182.99 | −0.247263 | −0.123631 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123631 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(660\) | −8623.47 | −0.508588 | ||||||||
\(661\) | 2224.23 | 0.130881 | 0.0654406 | − | 0.997856i | \(-0.479155\pi\) | ||||
0.0654406 | + | 0.997856i | \(0.479155\pi\) | |||||||
\(662\) | −14405.2 | −0.845734 | ||||||||
\(663\) | −792.776 | −0.0464387 | ||||||||
\(664\) | −3145.19 | −0.183821 | ||||||||
\(665\) | 19905.4 | 1.16075 | ||||||||
\(666\) | 4393.63 | 0.255630 | ||||||||
\(667\) | 3689.95 | 0.214206 | ||||||||
\(668\) | −25899.7 | −1.50013 | ||||||||
\(669\) | −6561.72 | −0.379209 | ||||||||
\(670\) | 29314.1 | 1.69030 | ||||||||
\(671\) | −4841.04 | −0.278519 | ||||||||
\(672\) | 8676.51 | 0.498071 | ||||||||
\(673\) | −24152.5 | −1.38337 | −0.691687 | − | 0.722197i | \(-0.743132\pi\) | ||||
−0.691687 | + | 0.722197i | \(0.743132\pi\) | |||||||
\(674\) | −39151.2 | −2.23746 | ||||||||
\(675\) | 153.770 | 0.00876833 | ||||||||
\(676\) | 1642.02 | 0.0934240 | ||||||||
\(677\) | −15310.7 | −0.869187 | −0.434593 | − | 0.900627i | \(-0.643108\pi\) | ||||
−0.434593 | + | 0.900627i | \(0.643108\pi\) | |||||||
\(678\) | 532.806 | 0.0301804 | ||||||||
\(679\) | −13788.4 | −0.779310 | ||||||||
\(680\) | 1678.58 | 0.0946628 | ||||||||
\(681\) | 12416.0 | 0.698652 | ||||||||
\(682\) | 29020.0 | 1.62937 | ||||||||
\(683\) | 11399.6 | 0.638646 | 0.319323 | − | 0.947646i | \(-0.396545\pi\) | ||||
0.319323 | + | 0.947646i | \(0.396545\pi\) | |||||||
\(684\) | 13528.8 | 0.756265 | ||||||||
\(685\) | −11872.6 | −0.662233 | ||||||||
\(686\) | 26495.9 | 1.47466 | ||||||||
\(687\) | −2506.06 | −0.139174 | ||||||||
\(688\) | −7165.54 | −0.397069 | ||||||||
\(689\) | 1039.79 | 0.0574935 | ||||||||
\(690\) | 26044.5 | 1.43695 | ||||||||
\(691\) | −3323.23 | −0.182955 | −0.0914773 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914773 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(692\) | −1605.52 | −0.0881976 | ||||||||
\(693\) | −2621.20 | −0.143681 | ||||||||
\(694\) | 912.936 | 0.0499345 | ||||||||
\(695\) | 32678.5 | 1.78355 | ||||||||
\(696\) | −443.188 | −0.0241365 | ||||||||
\(697\) | −7951.82 | −0.432133 | ||||||||
\(698\) | −20244.8 | −1.09782 | ||||||||
\(699\) | 11056.5 | 0.598279 | ||||||||
\(700\) | −622.758 | −0.0336257 | ||||||||
\(701\) | −12670.4 | −0.682673 | −0.341336 | − | 0.939941i | \(-0.610880\pi\) | ||||
−0.341336 | + | 0.939941i | \(0.610880\pi\) | |||||||
\(702\) | 1477.38 | 0.0794302 | ||||||||
\(703\) | 17944.0 | 0.962692 | ||||||||
\(704\) | −18193.8 | −0.974012 | ||||||||
\(705\) | 16029.0 | 0.856295 | ||||||||
\(706\) | −12036.4 | −0.641635 | ||||||||
\(707\) | −7263.71 | −0.386393 | ||||||||
\(708\) | −25467.2 | −1.35186 | ||||||||
\(709\) | 13075.2 | 0.692594 | 0.346297 | − | 0.938125i | \(-0.387439\pi\) | ||||
0.346297 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(710\) | −11935.3 | −0.630877 | ||||||||
\(711\) | −2980.99 | −0.157237 | ||||||||
\(712\) | 1872.48 | 0.0985592 | ||||||||
\(713\) | −48067.8 | −2.52476 | ||||||||
\(714\) | 2888.75 | 0.151413 | ||||||||
\(715\) | −3846.03 | −0.201165 | ||||||||
\(716\) | 6921.16 | 0.361251 | ||||||||
\(717\) | 9078.62 | 0.472869 | ||||||||
\(718\) | 15514.7 | 0.806412 | ||||||||
\(719\) | −2988.41 | −0.155005 | −0.0775026 | − | 0.996992i | \(-0.524695\pi\) | ||||
−0.0775026 | + | 0.996992i | \(0.524695\pi\) | |||||||
\(720\) | 4869.38 | 0.252043 | ||||||||
\(721\) | 5752.48 | 0.297134 | ||||||||
\(722\) | 71877.0 | 3.70496 | ||||||||
\(723\) | 9796.73 | 0.503934 | ||||||||
\(724\) | 21438.9 | 1.10051 | ||||||||
\(725\) | −116.479 | −0.00596680 | ||||||||
\(726\) | −8350.37 | −0.426875 | ||||||||
\(727\) | −5507.46 | −0.280963 | −0.140482 | − | 0.990083i | \(-0.544865\pi\) | ||||
−0.140482 | + | 0.990083i | \(0.544865\pi\) | |||||||
\(728\) | −1056.79 | −0.0538011 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −41033.9 | −2.08046 | ||||||||
\(731\) | −3077.75 | −0.155725 | ||||||||
\(732\) | −5452.71 | −0.275325 | ||||||||
\(733\) | −36585.2 | −1.84353 | −0.921764 | − | 0.387751i | \(-0.873252\pi\) | ||||
−0.921764 | + | 0.387751i | \(0.873252\pi\) | |||||||
\(734\) | −14607.9 | −0.734587 | ||||||||
\(735\) | 7419.75 | 0.372356 | ||||||||
\(736\) | 46364.6 | 2.32204 | ||||||||
\(737\) | −15765.3 | −0.787953 | ||||||||
\(738\) | 14818.6 | 0.739133 | ||||||||
\(739\) | 6425.89 | 0.319865 | 0.159933 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159933 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(740\) | −12883.0 | −0.639986 | ||||||||
\(741\) | 6033.76 | 0.299131 | ||||||||
\(742\) | −3788.84 | −0.187457 | ||||||||
\(743\) | 20411.0 | 1.00782 | 0.503908 | − | 0.863757i | \(-0.331895\pi\) | ||||
0.503908 | + | 0.863757i | \(0.331895\pi\) | |||||||
\(744\) | 5773.27 | 0.284487 | ||||||||
\(745\) | −8499.60 | −0.417988 | ||||||||
\(746\) | −50354.6 | −2.47133 | ||||||||
\(747\) | −3918.89 | −0.191947 | ||||||||
\(748\) | −5111.13 | −0.249842 | ||||||||
\(749\) | −6844.81 | −0.333917 | ||||||||
\(750\) | 17222.4 | 0.838496 | ||||||||
\(751\) | −24259.5 | −1.17875 | −0.589375 | − | 0.807860i | \(-0.700626\pi\) | ||||
−0.589375 | + | 0.807860i | \(0.700626\pi\) | |||||||
\(752\) | 22118.6 | 1.07258 | ||||||||
\(753\) | −19089.5 | −0.923850 | ||||||||
\(754\) | −1119.10 | −0.0540518 | ||||||||
\(755\) | −26033.9 | −1.25493 | ||||||||
\(756\) | −2952.39 | −0.142034 | ||||||||
\(757\) | 9295.39 | 0.446297 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(758\) | 1454.66 | 0.0697042 | ||||||||
\(759\) | −14006.9 | −0.669851 | ||||||||
\(760\) | −12775.6 | −0.609761 | ||||||||
\(761\) | −21974.7 | −1.04676 | −0.523378 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(762\) | −3927.27 | −0.186706 | ||||||||
\(763\) | 14631.0 | 0.694204 | ||||||||
\(764\) | 14288.9 | 0.676641 | ||||||||
\(765\) | 2091.50 | 0.0988476 | ||||||||
\(766\) | −14253.5 | −0.672324 | ||||||||
\(767\) | −11358.2 | −0.534709 | ||||||||
\(768\) | 5467.13 | 0.256873 | ||||||||
\(769\) | 22987.4 | 1.07795 | 0.538977 | − | 0.842320i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842320i | \(0.318811\pi\) | |||||||
\(770\) | 14014.3 | 0.655897 | ||||||||
\(771\) | −18256.1 | −0.852759 | ||||||||
\(772\) | 3590.68 | 0.167398 | ||||||||
\(773\) | 31970.9 | 1.48760 | 0.743799 | − | 0.668404i | \(-0.233022\pi\) | ||||
0.743799 | + | 0.668404i | \(0.233022\pi\) | |||||||
\(774\) | 5735.53 | 0.266356 | ||||||||
\(775\) | 1517.34 | 0.0703283 | ||||||||
\(776\) | 8849.59 | 0.409384 | ||||||||
\(777\) | −3915.94 | −0.180803 | ||||||||
\(778\) | −6860.25 | −0.316133 | ||||||||
\(779\) | 60520.8 | 2.78354 | ||||||||
\(780\) | −4331.98 | −0.198859 | ||||||||
\(781\) | 6418.85 | 0.294090 | ||||||||
\(782\) | 15436.6 | 0.705896 | ||||||||
\(783\) | −552.209 | −0.0252035 | ||||||||
\(784\) | 10238.6 | 0.466408 | ||||||||
\(785\) | −36280.2 | −1.64955 | ||||||||
\(786\) | 25266.7 | 1.14661 | ||||||||
\(787\) | 6087.26 | 0.275715 | 0.137857 | − | 0.990452i | \(-0.455978\pi\) | ||||
0.137857 | + | 0.990452i | \(0.455978\pi\) | |||||||
\(788\) | −41520.9 | −1.87706 | ||||||||
\(789\) | 369.680 | 0.0166805 | ||||||||
\(790\) | 15937.9 | 0.717779 | ||||||||
\(791\) | −474.878 | −0.0213460 | ||||||||
\(792\) | 1682.32 | 0.0754780 | ||||||||
\(793\) | −2431.88 | −0.108901 | ||||||||
\(794\) | 33415.4 | 1.49354 | ||||||||
\(795\) | −2743.19 | −0.122378 | ||||||||
\(796\) | 40363.6 | 1.79730 | ||||||||
\(797\) | 23080.0 | 1.02577 | 0.512883 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512883 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(798\) | −21986.1 | −0.975311 | ||||||||
\(799\) | 9500.41 | 0.420651 | ||||||||
\(800\) | −1463.57 | −0.0646813 | ||||||||
\(801\) | 2333.10 | 0.102916 | ||||||||
\(802\) | 902.429 | 0.0397330 | ||||||||
\(803\) | 22068.3 | 0.969829 | ||||||||
\(804\) | −17757.3 | −0.778918 | ||||||||
\(805\) | −23212.9 | −1.01633 | ||||||||
\(806\) | 14578.1 | 0.637087 | ||||||||
\(807\) | −5807.37 | −0.253320 | ||||||||
\(808\) | 4661.94 | 0.202978 | ||||||||
\(809\) | −32377.8 | −1.40710 | −0.703550 | − | 0.710646i | \(-0.748403\pi\) | ||||
−0.703550 | + | 0.710646i | \(0.748403\pi\) | |||||||
\(810\) | −3897.61 | −0.169072 | ||||||||
\(811\) | 26352.8 | 1.14103 | 0.570513 | − | 0.821288i | \(-0.306744\pi\) | ||||
0.570513 | + | 0.821288i | \(0.306744\pi\) | |||||||
\(812\) | 2236.40 | 0.0966532 | ||||||||
\(813\) | −13838.1 | −0.596952 | ||||||||
\(814\) | 12633.4 | 0.543980 | ||||||||
\(815\) | 26461.5 | 1.13731 | ||||||||
\(816\) | 2886.08 | 0.123815 | ||||||||
\(817\) | 23424.5 | 1.00308 | ||||||||
\(818\) | −20135.0 | −0.860638 | ||||||||
\(819\) | −1316.75 | −0.0561796 | ||||||||
\(820\) | −43451.3 | −1.85047 | ||||||||
\(821\) | 35355.3 | 1.50294 | 0.751468 | − | 0.659770i | \(-0.229346\pi\) | ||||
0.751468 | + | 0.659770i | \(0.229346\pi\) | |||||||
\(822\) | 13113.6 | 0.556435 | ||||||||
\(823\) | −12663.3 | −0.536347 | −0.268173 | − | 0.963371i | \(-0.586420\pi\) | ||||
−0.268173 | + | 0.963371i | \(0.586420\pi\) | |||||||
\(824\) | −3692.02 | −0.156089 | ||||||||
\(825\) | 442.149 | 0.0186590 | ||||||||
\(826\) | 41387.6 | 1.74341 | ||||||||
\(827\) | −16295.2 | −0.685176 | −0.342588 | − | 0.939486i | \(-0.611303\pi\) | ||||
−0.342588 | + | 0.939486i | \(0.611303\pi\) | |||||||
\(828\) | −15776.7 | −0.662170 | ||||||||
\(829\) | 13638.9 | 0.571411 | 0.285705 | − | 0.958318i | \(-0.407772\pi\) | ||||
0.285705 | + | 0.958318i | \(0.407772\pi\) | |||||||
\(830\) | 20952.4 | 0.876229 | ||||||||
\(831\) | −17502.9 | −0.730649 | ||||||||
\(832\) | −9139.61 | −0.380840 | ||||||||
\(833\) | 4397.69 | 0.182918 | ||||||||
\(834\) | −36094.2 | −1.49861 | ||||||||
\(835\) | 30474.2 | 1.26300 | ||||||||
\(836\) | 38900.5 | 1.60933 | ||||||||
\(837\) | 7193.46 | 0.297064 | ||||||||
\(838\) | −41685.0 | −1.71836 | ||||||||
\(839\) | −1890.31 | −0.0777838 | −0.0388919 | − | 0.999243i | \(-0.512383\pi\) | ||||
−0.0388919 | + | 0.999243i | \(0.512383\pi\) | |||||||
\(840\) | 2788.02 | 0.114519 | ||||||||
\(841\) | −23970.7 | −0.982849 | ||||||||
\(842\) | −51016.4 | −2.08805 | ||||||||
\(843\) | 14075.7 | 0.575082 | ||||||||
\(844\) | 11966.3 | 0.488028 | ||||||||
\(845\) | −1932.04 | −0.0786559 | ||||||||
\(846\) | −17704.5 | −0.719494 | ||||||||
\(847\) | 7442.50 | 0.301921 | ||||||||
\(848\) | −3785.35 | −0.153289 | ||||||||
\(849\) | 10396.8 | 0.420279 | ||||||||
\(850\) | −487.280 | −0.0196630 | ||||||||
\(851\) | −20925.6 | −0.842914 | ||||||||
\(852\) | 7229.89 | 0.290718 | ||||||||
\(853\) | 1620.21 | 0.0650351 | 0.0325175 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325175 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(854\) | 8861.39 | 0.355071 | ||||||||
\(855\) | −15918.3 | −0.636718 | ||||||||
\(856\) | 4393.08 | 0.175412 | ||||||||
\(857\) | −14508.4 | −0.578292 | −0.289146 | − | 0.957285i | \(-0.593371\pi\) | ||||
−0.289146 | + | 0.957285i | \(0.593371\pi\) | |||||||
\(858\) | 4248.03 | 0.169027 | ||||||||
\(859\) | 29639.8 | 1.17730 | 0.588648 | − | 0.808389i | \(-0.299660\pi\) | ||||
0.588648 | + | 0.808389i | \(0.299660\pi\) | |||||||
\(860\) | −16817.8 | −0.666839 | ||||||||
\(861\) | −13207.5 | −0.522776 | ||||||||
\(862\) | −57548.8 | −2.27392 | ||||||||
\(863\) | 21528.8 | 0.849186 | 0.424593 | − | 0.905384i | \(-0.360417\pi\) | ||||
0.424593 | + | 0.905384i | \(0.360417\pi\) | |||||||
\(864\) | −6938.56 | −0.273211 | ||||||||
\(865\) | 1889.10 | 0.0742557 | ||||||||
\(866\) | 29939.4 | 1.17481 | ||||||||
\(867\) | −13499.4 | −0.528792 | ||||||||
\(868\) | −29132.9 | −1.13921 | ||||||||
\(869\) | −8571.50 | −0.334601 | ||||||||
\(870\) | 2952.40 | 0.115053 | ||||||||
\(871\) | −7919.65 | −0.308091 | ||||||||
\(872\) | −9390.36 | −0.364676 | ||||||||
\(873\) | 11026.5 | 0.427482 | ||||||||
\(874\) | −117487. | −4.54696 | ||||||||
\(875\) | −15349.9 | −0.593054 | ||||||||
\(876\) | 24856.7 | 0.958708 | ||||||||
\(877\) | 14865.3 | 0.572366 | 0.286183 | − | 0.958175i | \(-0.407613\pi\) | ||||
0.286183 | + | 0.958175i | \(0.407613\pi\) | |||||||
\(878\) | −25347.1 | −0.974285 | ||||||||
\(879\) | 8031.92 | 0.308202 | ||||||||
\(880\) | 14001.4 | 0.536348 | ||||||||
\(881\) | −21336.0 | −0.815921 | −0.407961 | − | 0.913000i | \(-0.633760\pi\) | ||||
−0.407961 | + | 0.913000i | \(0.633760\pi\) | |||||||
\(882\) | −8195.30 | −0.312869 | ||||||||
\(883\) | 37538.2 | 1.43065 | 0.715323 | − | 0.698794i | \(-0.246280\pi\) | ||||
0.715323 | + | 0.698794i | \(0.246280\pi\) | |||||||
\(884\) | −2567.57 | −0.0976884 | ||||||||
\(885\) | 29965.3 | 1.13816 | ||||||||
\(886\) | −54694.1 | −2.07391 | ||||||||
\(887\) | 34575.0 | 1.30881 | 0.654406 | − | 0.756144i | \(-0.272919\pi\) | ||||
0.654406 | + | 0.756144i | \(0.272919\pi\) | |||||||
\(888\) | 2513.30 | 0.0949784 | ||||||||
\(889\) | 3500.29 | 0.132054 | ||||||||
\(890\) | −12474.0 | −0.469807 | ||||||||
\(891\) | 2096.16 | 0.0788148 | ||||||||
\(892\) | −21251.4 | −0.797703 | ||||||||
\(893\) | −72306.9 | −2.70958 | ||||||||
\(894\) | 9388.02 | 0.351211 | ||||||||
\(895\) | −8143.61 | −0.304146 | ||||||||
\(896\) | 10165.9 | 0.379039 | ||||||||
\(897\) | −7036.32 | −0.261913 | ||||||||
\(898\) | 46233.3 | 1.71807 | ||||||||
\(899\) | −5448.96 | −0.202150 | ||||||||
\(900\) | 498.016 | 0.0184450 | ||||||||
\(901\) | −1625.89 | −0.0601178 | ||||||||
\(902\) | 42609.2 | 1.57287 | ||||||||
\(903\) | −5111.95 | −0.188389 | ||||||||
\(904\) | 304.783 | 0.0112134 | ||||||||
\(905\) | −25225.5 | −0.926545 | ||||||||
\(906\) | 28755.0 | 1.05444 | ||||||||
\(907\) | −10424.8 | −0.381641 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(908\) | 40211.7 | 1.46968 | ||||||||
\(909\) | 5808.75 | 0.211952 | ||||||||
\(910\) | 7040.05 | 0.256456 | ||||||||
\(911\) | 10961.8 | 0.398661 | 0.199331 | − | 0.979932i | \(-0.436123\pi\) | ||||
0.199331 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(912\) | −21965.8 | −0.797543 | ||||||||
\(913\) | −11268.3 | −0.408464 | ||||||||
\(914\) | 41392.2 | 1.49796 | ||||||||
\(915\) | 6415.80 | 0.231803 | ||||||||
\(916\) | −8116.38 | −0.292765 | ||||||||
\(917\) | −22519.7 | −0.810976 | ||||||||
\(918\) | −2310.12 | −0.0830558 | ||||||||
\(919\) | −10779.2 | −0.386914 | −0.193457 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193457 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(920\) | 14898.3 | 0.533895 | ||||||||
\(921\) | 1415.74 | 0.0506519 | ||||||||
\(922\) | 14316.7 | 0.511384 | ||||||||
\(923\) | 3224.49 | 0.114990 | ||||||||
\(924\) | −8489.28 | −0.302248 | ||||||||
\(925\) | 660.549 | 0.0234797 | ||||||||
\(926\) | 7321.32 | 0.259820 | ||||||||
\(927\) | −4600.23 | −0.162990 | ||||||||
\(928\) | 5255.88 | 0.185919 | ||||||||
\(929\) | 5429.07 | 0.191735 | 0.0958675 | − | 0.995394i | \(-0.469437\pi\) | ||||
0.0958675 | + | 0.995394i | \(0.469437\pi\) | |||||||
\(930\) | −38460.0 | −1.35608 | ||||||||
\(931\) | −33470.5 | −1.17825 | ||||||||
\(932\) | 35808.8 | 1.25854 | ||||||||
\(933\) | −4555.55 | −0.159852 | ||||||||
\(934\) | −33499.1 | −1.17358 | ||||||||
\(935\) | 6013.88 | 0.210348 | ||||||||
\(936\) | 845.109 | 0.0295120 | ||||||||
\(937\) | −21300.1 | −0.742631 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(938\) | 28857.9 | 1.00453 | ||||||||
\(939\) | 12149.6 | 0.422244 | ||||||||
\(940\) | 51913.2 | 1.80130 | ||||||||
\(941\) | 26851.2 | 0.930207 | 0.465103 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465103 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(942\) | 40072.4 | 1.38602 | ||||||||
\(943\) | −70576.7 | −2.43722 | ||||||||
\(944\) | 41349.4 | 1.42564 | ||||||||
\(945\) | 3473.86 | 0.119582 | ||||||||
\(946\) | 16491.9 | 0.566805 | ||||||||
\(947\) | −8021.68 | −0.275258 | −0.137629 | − | 0.990484i | \(-0.543948\pi\) | ||||
−0.137629 | + | 0.990484i | \(0.543948\pi\) | |||||||
\(948\) | −9654.52 | −0.330764 | ||||||||
\(949\) | 11085.9 | 0.379204 | ||||||||
\(950\) | 3708.65 | 0.126658 | ||||||||
\(951\) | 9761.88 | 0.332861 | ||||||||
\(952\) | 1652.46 | 0.0562569 | ||||||||
\(953\) | 35715.0 | 1.21398 | 0.606990 | − | 0.794709i | \(-0.292377\pi\) | ||||
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(954\) | 3029.92 | 0.102827 | ||||||||
\(955\) | −16812.6 | −0.569680 | ||||||||
\(956\) | 29402.9 | 0.994726 | ||||||||
\(957\) | −1587.82 | −0.0536330 | ||||||||
\(958\) | 35490.6 | 1.19692 | ||||||||
\(959\) | −11687.9 | −0.393557 | ||||||||
\(960\) | 24112.1 | 0.810641 | ||||||||
\(961\) | 41190.9 | 1.38266 | ||||||||
\(962\) | 6346.35 | 0.212697 | ||||||||
\(963\) | 5473.76 | 0.183166 | ||||||||
\(964\) | 31728.7 | 1.06007 | ||||||||
\(965\) | −4224.88 | −0.140936 | ||||||||
\(966\) | 25639.2 | 0.853963 | ||||||||
\(967\) | 53338.8 | 1.77380 | 0.886898 | − | 0.461965i | \(-0.152855\pi\) | ||||
0.886898 | + | 0.461965i | \(0.152855\pi\) | |||||||
\(968\) | −4776.69 | −0.158604 | ||||||||
\(969\) | −9434.77 | −0.312785 | ||||||||
\(970\) | −58953.6 | −1.95143 | ||||||||
\(971\) | 23112.9 | 0.763882 | 0.381941 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381941 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(972\) | 2361.01 | 0.0779110 | ||||||||
\(973\) | 32170.0 | 1.05994 | ||||||||
\(974\) | −49181.3 | −1.61794 | ||||||||
\(975\) | 222.113 | 0.00729569 | ||||||||
\(976\) | 8853.22 | 0.290353 | ||||||||
\(977\) | −52874.6 | −1.73143 | −0.865715 | − | 0.500538i | \(-0.833136\pi\) | ||||
−0.865715 | + | 0.500538i | \(0.833136\pi\) | |||||||
\(978\) | −29227.4 | −0.955612 | ||||||||
\(979\) | 6708.57 | 0.219006 | ||||||||
\(980\) | 24030.4 | 0.783287 | ||||||||
\(981\) | −11700.3 | −0.380798 | ||||||||
\(982\) | −16645.5 | −0.540917 | ||||||||
\(983\) | 45173.1 | 1.46572 | 0.732858 | − | 0.680381i | \(-0.238186\pi\) | ||||
0.732858 | + | 0.680381i | \(0.238186\pi\) | |||||||
\(984\) | 8476.73 | 0.274622 | ||||||||
\(985\) | 48854.5 | 1.58034 | ||||||||
\(986\) | 1749.89 | 0.0565190 | ||||||||
\(987\) | 15779.6 | 0.508885 | ||||||||
\(988\) | 19541.6 | 0.629251 | ||||||||
\(989\) | −27316.7 | −0.878281 | ||||||||
\(990\) | −11207.2 | −0.359785 | ||||||||
\(991\) | 60485.6 | 1.93884 | 0.969418 | − | 0.245414i | \(-0.0789239\pi\) | ||||
0.969418 | + | 0.245414i | \(0.0789239\pi\) | |||||||
\(992\) | −68466.7 | −2.19135 | ||||||||
\(993\) | −10267.3 | −0.328121 | ||||||||
\(994\) | −11749.5 | −0.374922 | ||||||||
\(995\) | −47492.8 | −1.51319 | ||||||||
\(996\) | −12692.1 | −0.403780 | ||||||||
\(997\) | −18108.1 | −0.575214 | −0.287607 | − | 0.957749i | \(-0.592860\pi\) | ||||
−0.287607 | + | 0.957749i | \(0.592860\pi\) | |||||||
\(998\) | −23951.1 | −0.759677 | ||||||||
\(999\) | 3131.56 | 0.0991773 |
(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 | 39.4.a.c.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 117.4.a.f.1.1 | 3 | |||
4.3 | odd | 2 | 624.4.a.t.1.1 | 3 | |||
5.4 | even | 2 | 975.4.a.l.1.1 | 3 | |||
7.6 | odd | 2 | 1911.4.a.k.1.3 | 3 | |||
8.3 | odd | 2 | 2496.4.a.bp.1.3 | 3 | |||
8.5 | even | 2 | 2496.4.a.bl.1.3 | 3 | |||
12.11 | even | 2 | 1872.4.a.bk.1.3 | 3 | |||
13.5 | odd | 4 | 507.4.b.g.337.1 | 6 | |||
13.8 | odd | 4 | 507.4.b.g.337.6 | 6 | |||
13.12 | even | 2 | 507.4.a.h.1.1 | 3 | |||
39.38 | odd | 2 | 1521.4.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
117.4.a.f.1.1 | 3 | 3.2 | odd | 2 | |||
507.4.a.h.1.1 | 3 | 13.12 | even | 2 | |||
507.4.b.g.337.1 | 6 | 13.5 | odd | 4 | |||
507.4.b.g.337.6 | 6 | 13.8 | odd | 4 | |||
624.4.a.t.1.1 | 3 | 4.3 | odd | 2 | |||
975.4.a.l.1.1 | 3 | 5.4 | even | 2 | |||
1521.4.a.u.1.3 | 3 | 39.38 | odd | 2 | |||
1872.4.a.bk.1.3 | 3 | 12.11 | even | 2 | |||
1911.4.a.k.1.3 | 3 | 7.6 | odd | 2 | |||
2496.4.a.bl.1.3 | 3 | 8.5 | even | 2 | |||
2496.4.a.bp.1.3 | 3 | 8.3 | odd | 2 |