Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,4,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, 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("1911.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.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: | \(112.752650021\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-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 | \(-0.329178\pi\) | ||||
0.511264 | + | 0.859424i | \(0.329178\pi\) | |||||||
\(6\) | −12.6271 | −0.859169 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.2966 | −0.590356 | ||||||||
\(16\) | −47.3262 | −0.739472 | ||||||||
\(17\) | 20.3276 | 0.290010 | 0.145005 | − | 0.989431i | \(-0.453680\pi\) | ||||
0.145005 | + | 0.989431i | \(0.453680\pi\) | |||||||
\(18\) | 37.8814 | 0.496041 | ||||||||
\(19\) | −154.712 | −1.86807 | −0.934035 | − | 0.357181i | \(-0.883738\pi\) | ||||
−0.934035 | + | 0.357181i | \(0.883738\pi\) | |||||||
\(20\) | 111.076 | 1.24187 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −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 | \(-0.780640\pi\) | ||||
−0.771794 | + | 0.635873i | \(0.780640\pi\) | |||||||
\(32\) | −256.984 | −1.41965 | ||||||||
\(33\) | −77.6355 | −0.409534 | ||||||||
\(34\) | 85.5599 | 0.431571 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.767566\pi\) | ||||
−0.745032 | + | 0.667029i | \(0.767566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(48\) | 141.979 | 0.426934 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 464.136 | 1.07853 | ||||||||
\(58\) | −86.0843 | −0.194887 | ||||||||
\(59\) | 873.710 | 1.92792 | 0.963960 | − | 0.266045i | \(-0.0857171\pi\) | ||||
0.963960 | + | 0.266045i | \(0.0857171\pi\) | |||||||
\(60\) | −333.229 | −0.716995 | ||||||||
\(61\) | 187.068 | 0.392649 | 0.196325 | − | 0.980539i | \(-0.437099\pi\) | ||||
0.196325 | + | 0.980539i | \(0.437099\pi\) | |||||||
\(62\) | −1121.39 | −2.29705 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(-0.739596\pi\) | ||||
−0.683621 | + | 0.729838i | \(0.739596\pi\) | |||||||
\(74\) | 488.181 | 0.766890 | ||||||||
\(75\) | −17.0856 | −0.0263050 | ||||||||
\(76\) | −1503.20 | −2.26880 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(-0.407036\pi\) | ||||
0.287921 | + | 0.957654i | \(0.407036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 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 | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(90\) | 433.068 | 0.507216 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −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 | \(-0.721572\pi\) | ||||
−0.641223 | + | 0.767355i | \(0.721572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 232.907 | 0.236444 | ||||||||
\(100\) | 55.3351 | 0.0553351 | ||||||||
\(101\) | −645.416 | −0.635855 | −0.317927 | − | 0.948115i | \(-0.602987\pi\) | ||||
−0.317927 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(102\) | −256.680 | −0.249167 | ||||||||
\(103\) | 511.137 | 0.488969 | 0.244484 | − | 0.969653i | \(-0.421381\pi\) | ||||
0.244484 | + | 0.969653i | \(0.421381\pi\) | |||||||
\(104\) | −93.9010 | −0.0885360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −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 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | \(-0.732541\pi\) | ||||
−0.667278 | + | 0.744809i | \(0.732541\pi\) | |||||||
\(132\) | −754.314 | −0.497384 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −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 | \(-0.162739\pi\) | ||||
0.872128 | + | 0.489277i | \(0.162739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3045.82 | −1.57836 | ||||||||
\(156\) | 378.928 | 0.194478 | ||||||||
\(157\) | −3173.51 | −1.61321 | −0.806605 | − | 0.591091i | \(-0.798697\pi\) | ||||
−0.806605 | + | 0.591091i | \(0.798697\pi\) | |||||||
\(158\) | −1394.12 | −0.701966 | ||||||||
\(159\) | −239.953 | −0.119682 | ||||||||
\(160\) | −2937.89 | −1.45163 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | \(-0.288110\pi\) | ||||
0.617587 | + | 0.786502i | \(0.288110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 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 | \(-0.488440\pi\) | ||||
0.0363099 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(174\) | 258.253 | 0.112518 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −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 | \(-0.649670\pi\) | ||||
−0.453066 | + | 0.891477i | \(0.649670\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −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 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −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 | \(-0.765140\pi\) | ||||
−0.739927 | + | 0.672687i | \(0.765140\pi\) | |||||||
\(200\) | 41.1373 | 0.0145442 | ||||||||
\(201\) | 1827.61 | 0.641342 | ||||||||
\(202\) | −2716.59 | −0.946230 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −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 | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.2568 | 0.0151872 | ||||||||
\(226\) | 177.602 | 0.0522739 | ||||||||
\(227\) | −4138.67 | −1.21010 | −0.605051 | − | 0.796187i | \(-0.706847\pi\) | ||||
−0.605051 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(228\) | 4509.59 | 1.30989 | ||||||||
\(229\) | 835.354 | 0.241056 | 0.120528 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120528 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(230\) | −8681.50 | −2.48887 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −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 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(-0.643754\pi\) | ||||
−0.436420 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(242\) | −2783.46 | −0.739370 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1817.57 | 0.476877 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | \(-0.204792\pi\) | ||||
0.800078 | + | 0.599897i | \(0.204792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | \(-0.235529\pi\) | ||||
0.738511 | + | 0.674242i | \(0.235529\pi\) | |||||||
\(258\) | −1911.84 | −0.461342 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 777.700 | 0.178256 | ||||||||
\(268\) | −5919.08 | −1.34913 | ||||||||
\(269\) | 1935.79 | 0.438763 | 0.219381 | − | 0.975639i | \(-0.429596\pi\) | ||||
0.219381 | + | 0.975639i | \(0.429596\pi\) | |||||||
\(270\) | −1299.20 | −0.292841 | ||||||||
\(271\) | 4612.69 | 1.03395 | 0.516976 | − | 0.856000i | \(-0.327058\pi\) | ||||
0.516976 | + | 0.856000i | \(0.327058\pi\) | |||||||
\(272\) | −962.028 | −0.214454 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.618580\pi\) | ||||
−0.363973 | + | 0.931410i | \(0.618580\pi\) | |||||||
\(284\) | 2409.96 | 0.503539 | ||||||||
\(285\) | 5306.09 | 1.10283 | ||||||||
\(286\) | −1416.01 | −0.292764 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −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 | \(-0.586003\pi\) | ||||
−0.266911 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 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 | \(-0.513967\pi\) | ||||
−0.0438658 | + | 0.999037i | \(0.513967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1533.41 | −0.282306 | ||||||||
\(310\) | −12820.0 | −2.34880 | ||||||||
\(311\) | 1518.52 | 0.276872 | 0.138436 | − | 0.990371i | \(-0.455793\pi\) | ||||
0.138436 | + | 0.990371i | \(0.455793\pi\) | |||||||
\(312\) | 281.703 | 0.0511163 | ||||||||
\(313\) | −4049.86 | −0.731348 | −0.365674 | − | 0.930743i | \(-0.619161\pi\) | ||||
−0.365674 | + | 0.930743i | \(0.619161\pi\) | |||||||
\(314\) | −13357.5 | −2.40066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −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 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −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 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −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 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | \(-0.379748\pi\) | ||||
0.368861 | + | 0.929485i | \(0.379748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | −6650.35 | −1.00700 | ||||||||
\(353\) | 2859.64 | 0.431170 | 0.215585 | − | 0.976485i | \(-0.430834\pi\) | ||||
0.215585 | + | 0.976485i | \(0.430834\pi\) | |||||||
\(354\) | −11032.5 | −1.65641 | ||||||||
\(355\) | 2835.62 | 0.423941 | ||||||||
\(356\) | −2518.74 | −0.374980 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9748.98 | −1.39804 | ||||||||
\(366\) | −2362.14 | −0.337352 | ||||||||
\(367\) | 3470.59 | 0.493633 | 0.246816 | − | 0.969062i | \(-0.420616\pi\) | ||||
0.246816 | + | 0.969062i | \(0.420616\pi\) | |||||||
\(368\) | 8538.52 | 1.20951 | ||||||||
\(369\) | −3520.65 | −0.496688 | ||||||||
\(370\) | 5580.98 | 0.784166 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 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 | \(-0.427469\pi\) | ||||
0.225897 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(384\) | 2709.87 | 0.360124 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 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 | \(-0.667336\pi\) | ||||
−0.501819 | + | 0.864973i | \(0.667336\pi\) | |||||||
\(398\) | −17485.7 | −2.20221 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −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 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3001.48 | 0.365548 | ||||||||
\(408\) | −440.488 | −0.0534495 | ||||||||
\(409\) | 4783.73 | 0.578338 | 0.289169 | − | 0.957278i | \(-0.406621\pi\) | ||||
0.289169 | + | 0.957278i | \(0.406621\pi\) | |||||||
\(410\) | −18823.2 | −2.26735 | ||||||||
\(411\) | −3115.58 | −0.373917 | ||||||||
\(412\) | 4966.25 | 0.593859 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −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 | \(-0.304084\pi\) | ||||
0.577358 | + | 0.816491i | \(0.304084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | \(-0.629161\pi\) | ||||
−0.394727 | + | 0.918798i | \(0.629161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 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 | \(-0.393843\pi\) | ||||
0.327353 | + | 0.944902i | \(0.393843\pi\) | |||||||
\(440\) | 2136.96 | 0.231535 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(-0.554965\pi\) | ||||
−0.171822 | + | 0.985128i | \(0.554965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 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 | \(-0.370982\pi\) | ||||
0.394315 | + | 0.918975i | \(0.370982\pi\) | |||||||
\(468\) | −1136.78 | −0.112282 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 719.858 | 0.0690986 | ||||||||
\(478\) | 12737.5 | 1.21882 | ||||||||
\(479\) | −8431.98 | −0.804315 | −0.402158 | − | 0.915570i | \(-0.631740\pi\) | ||||
−0.402158 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(480\) | 8813.66 | 0.838097 | ||||||||
\(481\) | −1507.79 | −0.142930 | ||||||||
\(482\) | −13745.0 | −1.29889 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −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 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −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 | \(-0.659834\pi\) | ||||
−0.481298 | + | 0.876557i | \(0.659834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −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 | \(-0.200524\pi\) | ||||
0.808049 | + | 0.589115i | \(0.200524\pi\) | |||||||
\(510\) | −2934.41 | −0.254780 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −495.730 | −0.0419271 | ||||||||
\(520\) | −1073.49 | −0.0905305 | ||||||||
\(521\) | −17297.5 | −1.45454 | −0.727271 | − | 0.686350i | \(-0.759212\pi\) | ||||
−0.727271 | + | 0.686350i | \(0.759212\pi\) | |||||||
\(522\) | −774.759 | −0.0649622 | ||||||||
\(523\) | 5016.11 | 0.419386 | 0.209693 | − | 0.977767i | \(-0.432753\pi\) | ||||
0.209693 | + | 0.977767i | \(0.432753\pi\) | |||||||
\(524\) | −19441.8 | −1.62084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1578.14 | −0.118769 | ||||||||
\(562\) | 19748.5 | 1.48228 | ||||||||
\(563\) | 1880.07 | 0.140738 | 0.0703690 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703690 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(564\) | −13622.9 | −1.01707 | ||||||||
\(565\) | 482.385 | 0.0359187 | ||||||||
\(566\) | −14586.9 | −1.08327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1027.52 | −0.0745225 | ||||||||
\(576\) | −6327.42 | −0.457713 | ||||||||
\(577\) | −20508.1 | −1.47966 | −0.739831 | − | 0.672793i | \(-0.765094\pi\) | ||||
−0.739831 | + | 0.672793i | \(0.765094\pi\) | |||||||
\(578\) | −18939.8 | −1.36296 | ||||||||
\(579\) | −1108.68 | −0.0795771 | ||||||||
\(580\) | −2271.76 | −0.162637 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | \(-0.432708\pi\) | ||||
0.209833 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 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 | \(-0.330539\pi\) | ||||
0.507584 | + | 0.861602i | \(0.330539\pi\) | |||||||
\(594\) | −2940.95 | −0.203146 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(-0.372068\pi\) | ||||
0.391178 | + | 0.920315i | \(0.372068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −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 | \(-0.445473\pi\) | ||||
0.170465 | + | 0.985364i | \(0.445473\pi\) | |||||||
\(608\) | 39758.4 | 2.65200 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 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 | \(-0.813895\pi\) | ||||
−0.833897 | + | 0.551920i | \(0.813895\pi\) | |||||||
\(620\) | −29593.5 | −1.91694 | ||||||||
\(621\) | 4871.30 | 0.314780 | ||||||||
\(622\) | 6391.51 | 0.412020 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −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 | \(-0.247146\pi\) | ||||
0.713418 | + | 0.700738i | \(0.247146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5192.76 | −0.316999 | ||||||||
\(646\) | −13237.1 | −0.806204 | ||||||||
\(647\) | −14745.9 | −0.896014 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(648\) | 585.075 | 0.0354690 | ||||||||
\(649\) | 22610.3 | 1.36754 | ||||||||
\(650\) | −311.628 | −0.0188047 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −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 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(-0.520845\pi\) | ||||
−0.0654406 | + | 0.997856i | \(0.520845\pi\) | |||||||
\(662\) | −14405.2 | −0.845734 | ||||||||
\(663\) | 792.776 | 0.0464387 | ||||||||
\(664\) | 3145.19 | 0.183821 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | \(-0.356892\pi\) | ||||
0.434593 | + | 0.900627i | \(0.356892\pi\) | |||||||
\(678\) | −532.806 | −0.0301804 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −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 | \(-0.470841\pi\) | ||||
0.0914773 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(692\) | 1605.52 | 0.0881976 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −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 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −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 | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(720\) | −4869.38 | −0.252043 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | \(-0.455135\pi\) | ||||
0.140482 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 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 | \(-0.126748\pi\) | ||||
0.921764 | + | 0.387751i | \(0.126748\pi\) | |||||||
\(734\) | 14607.9 | 0.734587 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 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 | \(-0.324672\pi\) | ||||
0.523378 | + | 0.852101i | \(0.324672\pi\) | |||||||
\(762\) | 3927.27 | 0.186706 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.681189\pi\) | ||||
−0.538977 | + | 0.842320i | \(0.681189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18256.1 | −0.852759 | ||||||||
\(772\) | 3590.68 | 0.167398 | ||||||||
\(773\) | −31970.9 | −1.48760 | −0.743799 | − | 0.668404i | \(-0.766978\pi\) | ||||
−0.743799 | + | 0.668404i | \(0.766978\pi\) | |||||||
\(774\) | 5735.53 | 0.266356 | ||||||||
\(775\) | −1517.34 | −0.0703283 | ||||||||
\(776\) | −8849.59 | −0.409384 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36280.2 | −1.64955 | ||||||||
\(786\) | 25266.7 | 1.14661 | ||||||||
\(787\) | −6087.26 | −0.275715 | −0.137857 | − | 0.990452i | \(-0.544022\pi\) | ||||
−0.137857 | + | 0.990452i | \(0.544022\pi\) | |||||||
\(788\) | −41520.9 | −1.87706 | ||||||||
\(789\) | −369.680 | −0.0166805 | ||||||||
\(790\) | −15937.9 | −0.717779 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.671423\pi\) | ||||
−0.512883 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(-0.693256\pi\) | ||||
−0.570513 | + | 0.821288i | \(0.693256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −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 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | \(-0.592228\pi\) | ||||
−0.285705 | + | 0.958318i | \(0.592228\pi\) | |||||||
\(830\) | 20952.4 | 0.876229 | ||||||||
\(831\) | 17502.9 | 0.730649 | ||||||||
\(832\) | 9139.61 | 0.380840 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | \(-0.487617\pi\) | ||||
0.0388919 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −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 | \(-0.510352\pi\) | ||||
−0.0325175 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15918.3 | −0.636718 | ||||||||
\(856\) | 4393.08 | 0.175412 | ||||||||
\(857\) | 14508.4 | 0.578292 | 0.289146 | − | 0.957285i | \(-0.406629\pi\) | ||||
0.289146 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(858\) | 4248.03 | 0.169027 | ||||||||
\(859\) | −29639.8 | −1.17730 | −0.588648 | − | 0.808389i | \(-0.700340\pi\) | ||||
−0.588648 | + | 0.808389i | \(0.700340\pi\) | |||||||
\(860\) | 16817.8 | 0.666839 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −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 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | \(-0.366240\pi\) | ||||
0.407961 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 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 | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756144i | \(0.727081\pi\) | |||||||
\(888\) | −2513.30 | −0.0949784 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −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 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −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 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 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 | \(-0.530563\pi\) | ||||
−0.0958675 | + | 0.995394i | \(0.530563\pi\) | |||||||
\(930\) | 38460.0 | 1.35608 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.378907\pi\) | ||||
0.371315 | + | 0.928507i | \(0.378907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12149.6 | 0.422244 | ||||||||
\(940\) | 51913.2 | 1.80130 | ||||||||
\(941\) | −26851.2 | −0.930207 | −0.465103 | − | 0.885256i | \(-0.653983\pi\) | ||||
−0.465103 | + | 0.885256i | \(0.653983\pi\) | |||||||
\(942\) | 40072.4 | 1.38602 | ||||||||
\(943\) | 70576.7 | 2.43722 | ||||||||
\(944\) | −41349.4 | −1.42564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 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 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 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 | \(-0.624744\pi\) | ||||
−0.381941 | + | 0.924187i | \(0.624744\pi\) | |||||||
\(972\) | −2361.01 | −0.0779110 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −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 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11700.3 | −0.380798 | ||||||||
\(982\) | −16645.5 | −0.540917 | ||||||||
\(983\) | −45173.1 | −1.46572 | −0.732858 | − | 0.680381i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680381i | \(0.761814\pi\) | |||||||
\(984\) | 8476.73 | 0.274622 | ||||||||
\(985\) | −48854.5 | −1.58034 | ||||||||
\(986\) | −1749.89 | −0.0565190 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47492.8 | −1.51319 | ||||||||
\(996\) | −12692.1 | −0.403780 | ||||||||
\(997\) | 18108.1 | 0.575214 | 0.287607 | − | 0.957749i | \(-0.407140\pi\) | ||||
0.287607 | + | 0.957749i | \(0.407140\pi\) | |||||||
\(998\) | −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 | 1911.4.a.k.1.3 | 3 | ||
7.6 | odd | 2 | 39.4.a.c.1.3 | ✓ | 3 | ||
21.20 | even | 2 | 117.4.a.f.1.1 | 3 | |||
28.27 | even | 2 | 624.4.a.t.1.1 | 3 | |||
35.34 | odd | 2 | 975.4.a.l.1.1 | 3 | |||
56.13 | odd | 2 | 2496.4.a.bl.1.3 | 3 | |||
56.27 | even | 2 | 2496.4.a.bp.1.3 | 3 | |||
84.83 | odd | 2 | 1872.4.a.bk.1.3 | 3 | |||
91.34 | even | 4 | 507.4.b.g.337.6 | 6 | |||
91.83 | even | 4 | 507.4.b.g.337.1 | 6 | |||
91.90 | odd | 2 | 507.4.a.h.1.1 | 3 | |||
273.272 | even | 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 | 7.6 | odd | 2 | ||
117.4.a.f.1.1 | 3 | 21.20 | even | 2 | |||
507.4.a.h.1.1 | 3 | 91.90 | odd | 2 | |||
507.4.b.g.337.1 | 6 | 91.83 | even | 4 | |||
507.4.b.g.337.6 | 6 | 91.34 | even | 4 | |||
624.4.a.t.1.1 | 3 | 28.27 | even | 2 | |||
975.4.a.l.1.1 | 3 | 35.34 | odd | 2 | |||
1521.4.a.u.1.3 | 3 | 273.272 | even | 2 | |||
1872.4.a.bk.1.3 | 3 | 84.83 | odd | 2 | |||
1911.4.a.k.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2496.4.a.bl.1.3 | 3 | 56.13 | odd | 2 | |||
2496.4.a.bp.1.3 | 3 | 56.27 | even | 2 |