Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,4,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(118.534837202\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.67229 | −1.65191 | −0.825953 | − | 0.563739i | \(-0.809362\pi\) | ||||
−0.825953 | + | 0.563739i | \(0.809362\pi\) | |||||||
\(3\) | −4.57802 | −0.881040 | −0.440520 | − | 0.897743i | \(-0.645206\pi\) | ||||
−0.440520 | + | 0.897743i | \(0.645206\pi\) | |||||||
\(4\) | 13.8303 | 1.72879 | ||||||||
\(5\) | 8.79022 | 0.786221 | 0.393110 | − | 0.919491i | \(-0.371399\pi\) | ||||
0.393110 | + | 0.919491i | \(0.371399\pi\) | |||||||
\(6\) | 21.3898 | 1.45539 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −27.2411 | −1.20390 | ||||||||
\(9\) | −6.04177 | −0.223769 | ||||||||
\(10\) | −41.0705 | −1.29876 | ||||||||
\(11\) | −42.1310 | −1.15482 | −0.577408 | − | 0.816456i | \(-0.695936\pi\) | ||||
−0.577408 | + | 0.816456i | \(0.695936\pi\) | |||||||
\(12\) | −63.3155 | −1.52313 | ||||||||
\(13\) | −83.3095 | −1.77738 | −0.888688 | − | 0.458512i | \(-0.848383\pi\) | ||||
−0.888688 | + | 0.458512i | \(0.848383\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −40.2418 | −0.692692 | ||||||||
\(16\) | 16.6356 | 0.259931 | ||||||||
\(17\) | −119.501 | −1.70489 | −0.852447 | − | 0.522814i | \(-0.824882\pi\) | ||||
−0.852447 | + | 0.522814i | \(0.824882\pi\) | |||||||
\(18\) | 28.2289 | 0.369645 | ||||||||
\(19\) | 85.2375 | 1.02920 | 0.514601 | − | 0.857430i | \(-0.327940\pi\) | ||||
0.514601 | + | 0.857430i | \(0.327940\pi\) | |||||||
\(20\) | 121.572 | 1.35921 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 196.848 | 1.90765 | ||||||||
\(23\) | 34.2798 | 0.310775 | 0.155388 | − | 0.987854i | \(-0.450337\pi\) | ||||
0.155388 | + | 0.987854i | \(0.450337\pi\) | |||||||
\(24\) | 124.710 | 1.06068 | ||||||||
\(25\) | −47.7321 | −0.381857 | ||||||||
\(26\) | 389.247 | 2.93606 | ||||||||
\(27\) | 151.266 | 1.07819 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 127.196 | 0.814476 | 0.407238 | − | 0.913322i | \(-0.366492\pi\) | ||||
0.407238 | + | 0.913322i | \(0.366492\pi\) | |||||||
\(30\) | 188.021 | 1.14426 | ||||||||
\(31\) | 140.862 | 0.816114 | 0.408057 | − | 0.912956i | \(-0.366206\pi\) | ||||
0.408057 | + | 0.912956i | \(0.366206\pi\) | |||||||
\(32\) | 140.202 | 0.774515 | ||||||||
\(33\) | 192.876 | 1.01744 | ||||||||
\(34\) | 558.343 | 2.81632 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −83.5597 | −0.386850 | ||||||||
\(37\) | −59.2646 | −0.263326 | −0.131663 | − | 0.991295i | \(-0.542032\pi\) | ||||
−0.131663 | + | 0.991295i | \(0.542032\pi\) | |||||||
\(38\) | −398.255 | −1.70014 | ||||||||
\(39\) | 381.392 | 1.56594 | ||||||||
\(40\) | −239.455 | −0.946528 | ||||||||
\(41\) | 41.0000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.8833 | 0.283304 | 0.141652 | − | 0.989916i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989916i | \(0.454759\pi\) | |||||||
\(44\) | −582.686 | −1.99644 | ||||||||
\(45\) | −53.1084 | −0.175932 | ||||||||
\(46\) | −160.165 | −0.513371 | ||||||||
\(47\) | 555.709 | 1.72465 | 0.862324 | − | 0.506357i | \(-0.169008\pi\) | ||||
0.862324 | + | 0.506357i | \(0.169008\pi\) | |||||||
\(48\) | −76.1579 | −0.229009 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 223.018 | 0.630791 | ||||||||
\(51\) | 547.076 | 1.50208 | ||||||||
\(52\) | −1152.20 | −3.07272 | ||||||||
\(53\) | 355.007 | 0.920076 | 0.460038 | − | 0.887899i | \(-0.347836\pi\) | ||||
0.460038 | + | 0.887899i | \(0.347836\pi\) | |||||||
\(54\) | −706.758 | −1.78107 | ||||||||
\(55\) | −370.340 | −0.907940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −390.219 | −0.906767 | ||||||||
\(58\) | −594.300 | −1.34544 | ||||||||
\(59\) | −686.660 | −1.51518 | −0.757589 | − | 0.652732i | \(-0.773623\pi\) | ||||
−0.757589 | + | 0.652732i | \(0.773623\pi\) | |||||||
\(60\) | −556.557 | −1.19752 | ||||||||
\(61\) | −236.667 | −0.496756 | −0.248378 | − | 0.968663i | \(-0.579898\pi\) | ||||
−0.248378 | + | 0.968663i | \(0.579898\pi\) | |||||||
\(62\) | −658.148 | −1.34814 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −788.151 | −1.53936 | ||||||||
\(65\) | −732.309 | −1.39741 | ||||||||
\(66\) | −901.175 | −1.68071 | ||||||||
\(67\) | 772.754 | 1.40906 | 0.704529 | − | 0.709675i | \(-0.251158\pi\) | ||||
0.704529 | + | 0.709675i | \(0.251158\pi\) | |||||||
\(68\) | −1652.74 | −2.94741 | ||||||||
\(69\) | −156.933 | −0.273805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 153.968 | 0.257361 | 0.128681 | − | 0.991686i | \(-0.458926\pi\) | ||||
0.128681 | + | 0.991686i | \(0.458926\pi\) | |||||||
\(72\) | 164.584 | 0.269395 | ||||||||
\(73\) | 1150.97 | 1.84535 | 0.922674 | − | 0.385580i | \(-0.125999\pi\) | ||||
0.922674 | + | 0.385580i | \(0.125999\pi\) | |||||||
\(74\) | 276.902 | 0.434989 | ||||||||
\(75\) | 218.518 | 0.336431 | ||||||||
\(76\) | 1178.86 | 1.77928 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1781.98 | −2.58678 | ||||||||
\(79\) | 691.539 | 0.984864 | 0.492432 | − | 0.870351i | \(-0.336108\pi\) | ||||
0.492432 | + | 0.870351i | \(0.336108\pi\) | |||||||
\(80\) | 146.230 | 0.204363 | ||||||||
\(81\) | −529.369 | −0.726158 | ||||||||
\(82\) | −191.564 | −0.257984 | ||||||||
\(83\) | 926.864 | 1.22574 | 0.612871 | − | 0.790183i | \(-0.290015\pi\) | ||||
0.612871 | + | 0.790183i | \(0.290015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1050.44 | −1.34042 | ||||||||
\(86\) | −373.238 | −0.467992 | ||||||||
\(87\) | −582.308 | −0.717585 | ||||||||
\(88\) | 1147.69 | 1.39028 | ||||||||
\(89\) | −751.374 | −0.894893 | −0.447447 | − | 0.894311i | \(-0.647667\pi\) | ||||
−0.447447 | + | 0.894311i | \(0.647667\pi\) | |||||||
\(90\) | 248.138 | 0.290623 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 474.101 | 0.537266 | ||||||||
\(93\) | −644.868 | −0.719029 | ||||||||
\(94\) | −2596.43 | −2.84896 | ||||||||
\(95\) | 749.256 | 0.809180 | ||||||||
\(96\) | −641.848 | −0.682379 | ||||||||
\(97\) | 432.897 | 0.453135 | 0.226567 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 254.545 | 0.258412 | ||||||||
\(100\) | −660.151 | −0.660151 | ||||||||
\(101\) | −1204.22 | −1.18638 | −0.593189 | − | 0.805063i | \(-0.702131\pi\) | ||||
−0.593189 | + | 0.805063i | \(0.702131\pi\) | |||||||
\(102\) | −2556.10 | −2.48129 | ||||||||
\(103\) | −298.418 | −0.285475 | −0.142738 | − | 0.989761i | \(-0.545591\pi\) | ||||
−0.142738 | + | 0.989761i | \(0.545591\pi\) | |||||||
\(104\) | 2269.44 | 2.13978 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1658.70 | −1.51988 | ||||||||
\(107\) | −171.445 | −0.154899 | −0.0774496 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774496 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(108\) | 2092.06 | 1.86397 | ||||||||
\(109\) | −648.154 | −0.569559 | −0.284780 | − | 0.958593i | \(-0.591920\pi\) | ||||
−0.284780 | + | 0.958593i | \(0.591920\pi\) | |||||||
\(110\) | 1730.34 | 1.49983 | ||||||||
\(111\) | 271.314 | 0.232000 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1570.36 | 1.30732 | 0.653658 | − | 0.756790i | \(-0.273233\pi\) | ||||
0.653658 | + | 0.756790i | \(0.273233\pi\) | |||||||
\(114\) | 1823.22 | 1.49789 | ||||||||
\(115\) | 301.327 | 0.244338 | ||||||||
\(116\) | 1759.17 | 1.40806 | ||||||||
\(117\) | 503.336 | 0.397722 | ||||||||
\(118\) | 3208.28 | 2.50293 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1096.23 | 0.833929 | ||||||||
\(121\) | 444.019 | 0.333598 | ||||||||
\(122\) | 1105.78 | 0.820594 | ||||||||
\(123\) | −187.699 | −0.137595 | ||||||||
\(124\) | 1948.17 | 1.41089 | ||||||||
\(125\) | −1518.35 | −1.08644 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1093.83 | −0.764268 | −0.382134 | − | 0.924107i | \(-0.624811\pi\) | ||||
−0.382134 | + | 0.924107i | \(0.624811\pi\) | |||||||
\(128\) | 2560.85 | 1.76836 | ||||||||
\(129\) | −365.707 | −0.249602 | ||||||||
\(130\) | 3421.56 | 2.30839 | ||||||||
\(131\) | 2661.91 | 1.77536 | 0.887679 | − | 0.460462i | \(-0.152316\pi\) | ||||
0.887679 | + | 0.460462i | \(0.152316\pi\) | |||||||
\(132\) | 2667.54 | 1.75894 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3610.53 | −2.32763 | ||||||||
\(135\) | 1329.66 | 0.847695 | ||||||||
\(136\) | 3255.33 | 2.05252 | ||||||||
\(137\) | −533.178 | −0.332500 | −0.166250 | − | 0.986084i | \(-0.553166\pi\) | ||||
−0.166250 | + | 0.986084i | \(0.553166\pi\) | |||||||
\(138\) | 733.239 | 0.452300 | ||||||||
\(139\) | 280.727 | 0.171302 | 0.0856510 | − | 0.996325i | \(-0.472703\pi\) | ||||
0.0856510 | + | 0.996325i | \(0.472703\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2544.04 | −1.51948 | ||||||||
\(142\) | −719.385 | −0.425137 | ||||||||
\(143\) | 3509.91 | 2.05254 | ||||||||
\(144\) | −100.508 | −0.0581645 | ||||||||
\(145\) | 1118.08 | 0.640358 | ||||||||
\(146\) | −5377.66 | −3.04834 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −819.650 | −0.455235 | ||||||||
\(149\) | 1705.51 | 0.937721 | 0.468860 | − | 0.883272i | \(-0.344665\pi\) | ||||
0.468860 | + | 0.883272i | \(0.344665\pi\) | |||||||
\(150\) | −1020.98 | −0.555752 | ||||||||
\(151\) | −3421.70 | −1.84407 | −0.922034 | − | 0.387109i | \(-0.873474\pi\) | ||||
−0.922034 | + | 0.387109i | \(0.873474\pi\) | |||||||
\(152\) | −2321.96 | −1.23905 | ||||||||
\(153\) | 721.996 | 0.381503 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1238.21 | 0.641646 | ||||||||
\(156\) | 5274.78 | 2.70718 | ||||||||
\(157\) | 1919.08 | 0.975536 | 0.487768 | − | 0.872973i | \(-0.337811\pi\) | ||||
0.487768 | + | 0.872973i | \(0.337811\pi\) | |||||||
\(158\) | −3231.08 | −1.62690 | ||||||||
\(159\) | −1625.23 | −0.810623 | ||||||||
\(160\) | 1232.41 | 0.608940 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2473.37 | 1.19955 | ||||||||
\(163\) | −2508.79 | −1.20555 | −0.602773 | − | 0.797913i | \(-0.705937\pi\) | ||||
−0.602773 | + | 0.797913i | \(0.705937\pi\) | |||||||
\(164\) | 567.044 | 0.269992 | ||||||||
\(165\) | 1695.42 | 0.799931 | ||||||||
\(166\) | −4330.58 | −2.02481 | ||||||||
\(167\) | 773.040 | 0.358202 | 0.179101 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179101 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4743.47 | 2.15907 | ||||||||
\(170\) | 4907.95 | 2.21425 | ||||||||
\(171\) | −514.985 | −0.230303 | ||||||||
\(172\) | 1104.81 | 0.489774 | ||||||||
\(173\) | −4313.11 | −1.89549 | −0.947745 | − | 0.319029i | \(-0.896643\pi\) | ||||
−0.947745 | + | 0.319029i | \(0.896643\pi\) | |||||||
\(174\) | 2720.71 | 1.18538 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −700.873 | −0.300172 | ||||||||
\(177\) | 3143.54 | 1.33493 | ||||||||
\(178\) | 3510.64 | 1.47828 | ||||||||
\(179\) | −1298.92 | −0.542378 | −0.271189 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271189 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(180\) | −734.508 | −0.304150 | ||||||||
\(181\) | −378.170 | −0.155299 | −0.0776496 | − | 0.996981i | \(-0.524742\pi\) | ||||
−0.0776496 | + | 0.996981i | \(0.524742\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1083.47 | 0.437662 | ||||||||
\(184\) | −933.817 | −0.374141 | ||||||||
\(185\) | −520.949 | −0.207032 | ||||||||
\(186\) | 3013.01 | 1.18777 | ||||||||
\(187\) | 5034.68 | 1.96884 | ||||||||
\(188\) | 7685.64 | 2.98156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3500.75 | −1.33669 | ||||||||
\(191\) | −3361.69 | −1.27353 | −0.636763 | − | 0.771060i | \(-0.719727\pi\) | ||||
−0.636763 | + | 0.771060i | \(0.719727\pi\) | |||||||
\(192\) | 3608.17 | 1.35623 | ||||||||
\(193\) | −1961.54 | −0.731580 | −0.365790 | − | 0.930697i | \(-0.619201\pi\) | ||||
−0.365790 | + | 0.930697i | \(0.619201\pi\) | |||||||
\(194\) | −2022.62 | −0.748536 | ||||||||
\(195\) | 3352.52 | 1.23117 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2074.99 | 0.750443 | 0.375221 | − | 0.926935i | \(-0.377567\pi\) | ||||
0.375221 | + | 0.926935i | \(0.377567\pi\) | |||||||
\(198\) | −1189.31 | −0.426872 | ||||||||
\(199\) | −4333.80 | −1.54379 | −0.771896 | − | 0.635748i | \(-0.780692\pi\) | ||||
−0.771896 | + | 0.635748i | \(0.780692\pi\) | |||||||
\(200\) | 1300.27 | 0.459716 | ||||||||
\(201\) | −3537.68 | −1.24144 | ||||||||
\(202\) | 5626.46 | 1.95978 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7566.25 | 2.59678 | ||||||||
\(205\) | 360.399 | 0.122787 | ||||||||
\(206\) | 1394.30 | 0.471578 | ||||||||
\(207\) | −207.110 | −0.0695418 | ||||||||
\(208\) | −1385.90 | −0.461995 | ||||||||
\(209\) | −3591.14 | −1.18854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −383.533 | −0.125135 | −0.0625675 | − | 0.998041i | \(-0.519929\pi\) | ||||
−0.0625675 | + | 0.998041i | \(0.519929\pi\) | |||||||
\(212\) | 4909.87 | 1.59062 | ||||||||
\(213\) | −704.869 | −0.226746 | ||||||||
\(214\) | 801.041 | 0.255879 | ||||||||
\(215\) | 702.191 | 0.222740 | ||||||||
\(216\) | −4120.64 | −1.29803 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3028.37 | 0.940858 | ||||||||
\(219\) | −5269.14 | −1.62583 | ||||||||
\(220\) | −5121.93 | −1.56964 | ||||||||
\(221\) | 9955.55 | 3.03024 | ||||||||
\(222\) | −1267.66 | −0.383243 | ||||||||
\(223\) | −2641.01 | −0.793073 | −0.396537 | − | 0.918019i | \(-0.629788\pi\) | ||||
−0.396537 | + | 0.918019i | \(0.629788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 288.386 | 0.0854477 | ||||||||
\(226\) | −7337.17 | −2.15956 | ||||||||
\(227\) | 4559.88 | 1.33326 | 0.666629 | − | 0.745390i | \(-0.267736\pi\) | ||||
0.666629 | + | 0.745390i | \(0.267736\pi\) | |||||||
\(228\) | −5396.86 | −1.56761 | ||||||||
\(229\) | −453.898 | −0.130980 | −0.0654901 | − | 0.997853i | \(-0.520861\pi\) | ||||
−0.0654901 | + | 0.997853i | \(0.520861\pi\) | |||||||
\(230\) | −1407.89 | −0.403623 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3464.97 | −0.980544 | ||||||||
\(233\) | −1372.10 | −0.385791 | −0.192896 | − | 0.981219i | \(-0.561788\pi\) | ||||
−0.192896 | + | 0.981219i | \(0.561788\pi\) | |||||||
\(234\) | −2351.74 | −0.656999 | ||||||||
\(235\) | 4884.80 | 1.35595 | ||||||||
\(236\) | −9496.74 | −2.61943 | ||||||||
\(237\) | −3165.88 | −0.867704 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5552.54 | 1.50278 | 0.751389 | − | 0.659859i | \(-0.229384\pi\) | ||||
0.751389 | + | 0.659859i | \(0.229384\pi\) | |||||||
\(240\) | −669.445 | −0.180052 | ||||||||
\(241\) | −1840.90 | −0.492046 | −0.246023 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246023 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(242\) | −2074.59 | −0.551073 | ||||||||
\(243\) | −1660.71 | −0.438415 | ||||||||
\(244\) | −3273.19 | −0.858788 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 876.984 | 0.227294 | ||||||||
\(247\) | −7101.09 | −1.82928 | ||||||||
\(248\) | −3837.23 | −0.982517 | ||||||||
\(249\) | −4243.20 | −1.07993 | ||||||||
\(250\) | 7094.19 | 1.79470 | ||||||||
\(251\) | 5253.89 | 1.32121 | 0.660603 | − | 0.750735i | \(-0.270301\pi\) | ||||
0.660603 | + | 0.750735i | \(0.270301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1444.24 | −0.358888 | ||||||||
\(254\) | 5110.71 | 1.26250 | ||||||||
\(255\) | 4808.92 | 1.18097 | ||||||||
\(256\) | −5659.86 | −1.38180 | ||||||||
\(257\) | −3017.69 | −0.732444 | −0.366222 | − | 0.930528i | \(-0.619349\pi\) | ||||
−0.366222 | + | 0.930528i | \(0.619349\pi\) | |||||||
\(258\) | 1708.69 | 0.412320 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10128.1 | −2.41583 | ||||||||
\(261\) | −768.491 | −0.182254 | ||||||||
\(262\) | −12437.2 | −2.93273 | ||||||||
\(263\) | 5033.85 | 1.18023 | 0.590115 | − | 0.807319i | \(-0.299082\pi\) | ||||
0.590115 | + | 0.807319i | \(0.299082\pi\) | |||||||
\(264\) | −5254.16 | −1.22489 | ||||||||
\(265\) | 3120.59 | 0.723383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3439.80 | 0.788437 | ||||||||
\(268\) | 10687.4 | 2.43597 | ||||||||
\(269\) | 4352.24 | 0.986471 | 0.493235 | − | 0.869896i | \(-0.335814\pi\) | ||||
0.493235 | + | 0.869896i | \(0.335814\pi\) | |||||||
\(270\) | −6212.56 | −1.40031 | ||||||||
\(271\) | 3291.73 | 0.737854 | 0.368927 | − | 0.929458i | \(-0.379725\pi\) | ||||
0.368927 | + | 0.929458i | \(0.379725\pi\) | |||||||
\(272\) | −1987.96 | −0.443154 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2491.16 | 0.549258 | ||||||||
\(275\) | 2011.00 | 0.440974 | ||||||||
\(276\) | −2170.44 | −0.473352 | ||||||||
\(277\) | −7901.49 | −1.71392 | −0.856958 | − | 0.515387i | \(-0.827648\pi\) | ||||
−0.856958 | + | 0.515387i | \(0.827648\pi\) | |||||||
\(278\) | −1311.64 | −0.282975 | ||||||||
\(279\) | −851.055 | −0.182621 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5269.92 | −1.11878 | −0.559390 | − | 0.828905i | \(-0.688964\pi\) | ||||
−0.559390 | + | 0.828905i | \(0.688964\pi\) | |||||||
\(282\) | 11886.5 | 2.51004 | ||||||||
\(283\) | 2980.39 | 0.626029 | 0.313014 | − | 0.949748i | \(-0.398661\pi\) | ||||
0.313014 | + | 0.949748i | \(0.398661\pi\) | |||||||
\(284\) | 2129.43 | 0.444925 | ||||||||
\(285\) | −3430.11 | −0.712919 | ||||||||
\(286\) | −16399.3 | −3.39061 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −847.069 | −0.173313 | ||||||||
\(289\) | 9367.43 | 1.90666 | ||||||||
\(290\) | −5224.02 | −1.05781 | ||||||||
\(291\) | −1981.81 | −0.399230 | ||||||||
\(292\) | 15918.3 | 3.19022 | ||||||||
\(293\) | −1480.79 | −0.295252 | −0.147626 | − | 0.989043i | \(-0.547163\pi\) | ||||
−0.147626 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6035.89 | −1.19126 | ||||||||
\(296\) | 1614.43 | 0.317017 | ||||||||
\(297\) | −6372.97 | −1.24511 | ||||||||
\(298\) | −7968.62 | −1.54903 | ||||||||
\(299\) | −2855.83 | −0.552364 | ||||||||
\(300\) | 3022.18 | 0.581619 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15987.2 | 3.04623 | ||||||||
\(303\) | 5512.93 | 1.04525 | ||||||||
\(304\) | 1417.97 | 0.267521 | ||||||||
\(305\) | −2080.35 | −0.390560 | ||||||||
\(306\) | −3373.38 | −0.630206 | ||||||||
\(307\) | 5858.84 | 1.08919 | 0.544596 | − | 0.838699i | \(-0.316683\pi\) | ||||
0.544596 | + | 0.838699i | \(0.316683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1366.16 | 0.251515 | ||||||||
\(310\) | −5785.27 | −1.05994 | ||||||||
\(311\) | −5308.21 | −0.967848 | −0.483924 | − | 0.875110i | \(-0.660789\pi\) | ||||
−0.483924 | + | 0.875110i | \(0.660789\pi\) | |||||||
\(312\) | −10389.5 | −1.88523 | ||||||||
\(313\) | −2974.07 | −0.537074 | −0.268537 | − | 0.963269i | \(-0.586540\pi\) | ||||
−0.268537 | + | 0.963269i | \(0.586540\pi\) | |||||||
\(314\) | −8966.50 | −1.61149 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9564.22 | 1.70263 | ||||||||
\(317\) | −887.400 | −0.157228 | −0.0786141 | − | 0.996905i | \(-0.525049\pi\) | ||||
−0.0786141 | + | 0.996905i | \(0.525049\pi\) | |||||||
\(318\) | 7593.55 | 1.33907 | ||||||||
\(319\) | −5358.91 | −0.940569 | ||||||||
\(320\) | −6928.02 | −1.21027 | ||||||||
\(321\) | 784.878 | 0.136472 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10185.9 | −1.75468 | ||||||||
\(324\) | −7321.36 | −1.25538 | ||||||||
\(325\) | 3976.54 | 0.678703 | ||||||||
\(326\) | 11721.8 | 1.99145 | ||||||||
\(327\) | 2967.26 | 0.501804 | ||||||||
\(328\) | −1116.88 | −0.188017 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7921.52 | −1.32141 | ||||||||
\(331\) | −3674.23 | −0.610133 | −0.305066 | − | 0.952331i | \(-0.598679\pi\) | ||||
−0.305066 | + | 0.952331i | \(0.598679\pi\) | |||||||
\(332\) | 12818.8 | 2.11905 | ||||||||
\(333\) | 358.063 | 0.0589241 | ||||||||
\(334\) | −3611.87 | −0.591715 | ||||||||
\(335\) | 6792.67 | 1.10783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3812.84 | −0.616316 | −0.308158 | − | 0.951335i | \(-0.599713\pi\) | ||||
−0.308158 | + | 0.951335i | \(0.599713\pi\) | |||||||
\(338\) | −22162.9 | −3.56658 | ||||||||
\(339\) | −7189.12 | −1.15180 | ||||||||
\(340\) | −14527.9 | −2.31731 | ||||||||
\(341\) | −5934.65 | −0.942461 | ||||||||
\(342\) | 2406.16 | 0.380440 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2176.11 | −0.341069 | ||||||||
\(345\) | −1379.48 | −0.215271 | ||||||||
\(346\) | 20152.1 | 3.13117 | ||||||||
\(347\) | −12635.9 | −1.95484 | −0.977418 | − | 0.211316i | \(-0.932225\pi\) | ||||
−0.977418 | + | 0.211316i | \(0.932225\pi\) | |||||||
\(348\) | −8053.51 | −1.24056 | ||||||||
\(349\) | 6725.07 | 1.03147 | 0.515737 | − | 0.856747i | \(-0.327518\pi\) | ||||
0.515737 | + | 0.856747i | \(0.327518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12601.9 | −1.91635 | ||||||||
\(352\) | −5906.86 | −0.894422 | ||||||||
\(353\) | −2076.20 | −0.313046 | −0.156523 | − | 0.987674i | \(-0.550028\pi\) | ||||
−0.156523 | + | 0.987674i | \(0.550028\pi\) | |||||||
\(354\) | −14687.5 | −2.20518 | ||||||||
\(355\) | 1353.41 | 0.202343 | ||||||||
\(356\) | −10391.8 | −1.54708 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6068.93 | 0.895958 | ||||||||
\(359\) | −1959.02 | −0.288004 | −0.144002 | − | 0.989577i | \(-0.545997\pi\) | ||||
−0.144002 | + | 0.989577i | \(0.545997\pi\) | |||||||
\(360\) | 1446.73 | 0.211804 | ||||||||
\(361\) | 406.432 | 0.0592553 | ||||||||
\(362\) | 1766.92 | 0.256540 | ||||||||
\(363\) | −2032.73 | −0.293913 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10117.2 | 1.45085 | ||||||||
\(366\) | −5062.27 | −0.722976 | ||||||||
\(367\) | 1289.63 | 0.183429 | 0.0917143 | − | 0.995785i | \(-0.470765\pi\) | ||||
0.0917143 | + | 0.995785i | \(0.470765\pi\) | |||||||
\(368\) | 570.264 | 0.0807800 | ||||||||
\(369\) | −247.712 | −0.0349469 | ||||||||
\(370\) | 2434.03 | 0.341997 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8918.75 | −1.24305 | ||||||||
\(373\) | −2762.27 | −0.383445 | −0.191722 | − | 0.981449i | \(-0.561407\pi\) | ||||
−0.191722 | + | 0.981449i | \(0.561407\pi\) | |||||||
\(374\) | −23523.5 | −3.25233 | ||||||||
\(375\) | 6951.04 | 0.957201 | ||||||||
\(376\) | −15138.1 | −2.07630 | ||||||||
\(377\) | −10596.7 | −1.44763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5567.32 | −0.754549 | −0.377275 | − | 0.926101i | \(-0.623139\pi\) | ||||
−0.377275 | + | 0.926101i | \(0.623139\pi\) | |||||||
\(380\) | 10362.5 | 1.39890 | ||||||||
\(381\) | 5007.59 | 0.673350 | ||||||||
\(382\) | 15706.8 | 2.10374 | ||||||||
\(383\) | 6255.76 | 0.834606 | 0.417303 | − | 0.908767i | \(-0.362975\pi\) | ||||
0.417303 | + | 0.908767i | \(0.362975\pi\) | |||||||
\(384\) | −11723.6 | −1.55799 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9164.91 | 1.20850 | ||||||||
\(387\) | −482.636 | −0.0633948 | ||||||||
\(388\) | 5987.12 | 0.783376 | ||||||||
\(389\) | −5651.60 | −0.736626 | −0.368313 | − | 0.929702i | \(-0.620064\pi\) | ||||
−0.368313 | + | 0.929702i | \(0.620064\pi\) | |||||||
\(390\) | −15664.0 | −2.03378 | ||||||||
\(391\) | −4096.46 | −0.529838 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12186.3 | −1.56416 | ||||||||
\(394\) | −9694.99 | −1.23966 | ||||||||
\(395\) | 6078.78 | 0.774321 | ||||||||
\(396\) | 3520.45 | 0.446741 | ||||||||
\(397\) | 6939.97 | 0.877348 | 0.438674 | − | 0.898646i | \(-0.355448\pi\) | ||||
0.438674 | + | 0.898646i | \(0.355448\pi\) | |||||||
\(398\) | 20248.8 | 2.55020 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −794.051 | −0.0992563 | ||||||||
\(401\) | 6266.85 | 0.780428 | 0.390214 | − | 0.920724i | \(-0.372401\pi\) | ||||
0.390214 | + | 0.920724i | \(0.372401\pi\) | |||||||
\(402\) | 16529.1 | 2.05074 | ||||||||
\(403\) | −11735.1 | −1.45054 | ||||||||
\(404\) | −16654.7 | −2.05100 | ||||||||
\(405\) | −4653.27 | −0.570921 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2496.88 | 0.304092 | ||||||||
\(408\) | −14902.9 | −1.80835 | ||||||||
\(409\) | 7891.58 | 0.954067 | 0.477034 | − | 0.878885i | \(-0.341712\pi\) | ||||
0.477034 | + | 0.878885i | \(0.341712\pi\) | |||||||
\(410\) | −1683.89 | −0.202833 | ||||||||
\(411\) | 2440.90 | 0.292945 | ||||||||
\(412\) | −4127.22 | −0.493528 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 967.680 | 0.114877 | ||||||||
\(415\) | 8147.34 | 0.963704 | ||||||||
\(416\) | −11680.2 | −1.37661 | ||||||||
\(417\) | −1285.17 | −0.150924 | ||||||||
\(418\) | 16778.9 | 1.96335 | ||||||||
\(419\) | 3864.91 | 0.450628 | 0.225314 | − | 0.974286i | \(-0.427659\pi\) | ||||
0.225314 | + | 0.974286i | \(0.427659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10936.4 | −1.26605 | −0.633025 | − | 0.774131i | \(-0.718187\pi\) | ||||
−0.633025 | + | 0.774131i | \(0.718187\pi\) | |||||||
\(422\) | 1791.98 | 0.206711 | ||||||||
\(423\) | −3357.46 | −0.385923 | ||||||||
\(424\) | −9670.78 | −1.10768 | ||||||||
\(425\) | 5704.02 | 0.651025 | ||||||||
\(426\) | 3293.36 | 0.374562 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2371.14 | −0.267788 | ||||||||
\(429\) | −16068.4 | −1.80837 | ||||||||
\(430\) | −3280.85 | −0.367945 | ||||||||
\(431\) | 2796.73 | 0.312561 | 0.156281 | − | 0.987713i | \(-0.450050\pi\) | ||||
0.156281 | + | 0.987713i | \(0.450050\pi\) | |||||||
\(432\) | 2516.39 | 0.280255 | ||||||||
\(433\) | 7251.19 | 0.804780 | 0.402390 | − | 0.915468i | \(-0.368180\pi\) | ||||
0.402390 | + | 0.915468i | \(0.368180\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5118.61 | −0.564181 | ||||||||
\(436\) | −8964.20 | −0.984649 | ||||||||
\(437\) | 2921.92 | 0.319850 | ||||||||
\(438\) | 24619.0 | 2.68571 | ||||||||
\(439\) | −6759.54 | −0.734886 | −0.367443 | − | 0.930046i | \(-0.619767\pi\) | ||||
−0.367443 | + | 0.930046i | \(0.619767\pi\) | |||||||
\(440\) | 10088.5 | 1.09307 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −46515.3 | −5.00567 | ||||||||
\(443\) | −17031.6 | −1.82663 | −0.913313 | − | 0.407258i | \(-0.866485\pi\) | ||||
−0.913313 | + | 0.407258i | \(0.866485\pi\) | |||||||
\(444\) | 3752.37 | 0.401080 | ||||||||
\(445\) | −6604.74 | −0.703584 | ||||||||
\(446\) | 12339.6 | 1.31008 | ||||||||
\(447\) | −7807.83 | −0.826169 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13802.5 | −1.45074 | −0.725369 | − | 0.688360i | \(-0.758331\pi\) | ||||
−0.725369 | + | 0.688360i | \(0.758331\pi\) | |||||||
\(450\) | −1347.42 | −0.141152 | ||||||||
\(451\) | −1727.37 | −0.180352 | ||||||||
\(452\) | 21718.6 | 2.26008 | ||||||||
\(453\) | 15664.6 | 1.62470 | ||||||||
\(454\) | −21305.1 | −2.20242 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10630.0 | 1.09165 | ||||||||
\(457\) | 10648.4 | 1.08996 | 0.544981 | − | 0.838449i | \(-0.316537\pi\) | ||||
0.544981 | + | 0.838449i | \(0.316537\pi\) | |||||||
\(458\) | 2120.75 | 0.216367 | ||||||||
\(459\) | −18076.4 | −1.83820 | ||||||||
\(460\) | 4167.45 | 0.422409 | ||||||||
\(461\) | 115.842 | 0.0117034 | 0.00585172 | − | 0.999983i | \(-0.498137\pi\) | ||||
0.00585172 | + | 0.999983i | \(0.498137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2528.09 | 0.253759 | 0.126879 | − | 0.991918i | \(-0.459504\pi\) | ||||
0.126879 | + | 0.991918i | \(0.459504\pi\) | |||||||
\(464\) | 2115.99 | 0.211707 | ||||||||
\(465\) | −5668.53 | −0.565316 | ||||||||
\(466\) | 6410.87 | 0.637291 | ||||||||
\(467\) | 10124.2 | 1.00320 | 0.501599 | − | 0.865100i | \(-0.332745\pi\) | ||||
0.501599 | + | 0.865100i | \(0.332745\pi\) | |||||||
\(468\) | 6961.31 | 0.687579 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22823.2 | −2.23991 | ||||||||
\(471\) | −8785.58 | −0.859486 | ||||||||
\(472\) | 18705.3 | 1.82412 | ||||||||
\(473\) | −3365.56 | −0.327164 | ||||||||
\(474\) | 14791.9 | 1.43337 | ||||||||
\(475\) | −4068.56 | −0.393007 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2144.87 | −0.205884 | ||||||||
\(478\) | −25943.1 | −2.48245 | ||||||||
\(479\) | 9296.88 | 0.886817 | 0.443409 | − | 0.896320i | \(-0.353769\pi\) | ||||
0.443409 | + | 0.896320i | \(0.353769\pi\) | |||||||
\(480\) | −5641.98 | −0.536500 | ||||||||
\(481\) | 4937.31 | 0.468029 | ||||||||
\(482\) | 8601.24 | 0.812813 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6140.94 | 0.576722 | ||||||||
\(485\) | 3805.26 | 0.356264 | ||||||||
\(486\) | 7759.34 | 0.724220 | ||||||||
\(487\) | 8041.25 | 0.748221 | 0.374111 | − | 0.927384i | \(-0.377948\pi\) | ||||
0.374111 | + | 0.927384i | \(0.377948\pi\) | |||||||
\(488\) | 6447.06 | 0.598043 | ||||||||
\(489\) | 11485.3 | 1.06213 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5080.22 | −0.466940 | −0.233470 | − | 0.972364i | \(-0.575008\pi\) | ||||
−0.233470 | + | 0.972364i | \(0.575008\pi\) | |||||||
\(492\) | −2595.94 | −0.237874 | ||||||||
\(493\) | −15200.1 | −1.38859 | ||||||||
\(494\) | 33178.4 | 3.02180 | ||||||||
\(495\) | 2237.51 | 0.203169 | ||||||||
\(496\) | 2343.32 | 0.212133 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19825.5 | 1.78394 | ||||||||
\(499\) | 8831.95 | 0.792330 | 0.396165 | − | 0.918179i | \(-0.370341\pi\) | ||||
0.396165 | + | 0.918179i | \(0.370341\pi\) | |||||||
\(500\) | −20999.3 | −1.87824 | ||||||||
\(501\) | −3538.99 | −0.315590 | ||||||||
\(502\) | −24547.7 | −2.18251 | ||||||||
\(503\) | 4336.89 | 0.384438 | 0.192219 | − | 0.981352i | \(-0.438432\pi\) | ||||
0.192219 | + | 0.981352i | \(0.438432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10585.3 | −0.932755 | ||||||||
\(506\) | 6747.92 | 0.592849 | ||||||||
\(507\) | −21715.7 | −1.90222 | ||||||||
\(508\) | −15128.1 | −1.32126 | ||||||||
\(509\) | 3231.76 | 0.281425 | 0.140712 | − | 0.990051i | \(-0.455061\pi\) | ||||
0.140712 | + | 0.990051i | \(0.455061\pi\) | |||||||
\(510\) | −22468.7 | −1.95084 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5957.71 | 0.514250 | ||||||||
\(513\) | 12893.5 | 1.10967 | ||||||||
\(514\) | 14099.5 | 1.20993 | ||||||||
\(515\) | −2623.16 | −0.224447 | ||||||||
\(516\) | −5057.85 | −0.431511 | ||||||||
\(517\) | −23412.5 | −1.99165 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19745.5 | 1.67000 | ||||||||
\(520\) | 19948.9 | 1.68234 | ||||||||
\(521\) | 1796.22 | 0.151044 | 0.0755218 | − | 0.997144i | \(-0.475938\pi\) | ||||
0.0755218 | + | 0.997144i | \(0.475938\pi\) | |||||||
\(522\) | 3590.62 | 0.301067 | ||||||||
\(523\) | −10359.5 | −0.866133 | −0.433066 | − | 0.901362i | \(-0.642568\pi\) | ||||
−0.433066 | + | 0.901362i | \(0.642568\pi\) | |||||||
\(524\) | 36815.1 | 3.06923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23519.6 | −1.94963 | ||||||||
\(527\) | −16833.1 | −1.39139 | ||||||||
\(528\) | 3208.61 | 0.264464 | ||||||||
\(529\) | −10991.9 | −0.903419 | ||||||||
\(530\) | −14580.3 | −1.19496 | ||||||||
\(531\) | 4148.64 | 0.339050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3415.69 | −0.277580 | ||||||||
\(534\) | −16071.8 | −1.30242 | ||||||||
\(535\) | −1507.04 | −0.121785 | ||||||||
\(536\) | −21050.6 | −1.69636 | ||||||||
\(537\) | 5946.47 | 0.477857 | ||||||||
\(538\) | −20334.9 | −1.62956 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 18389.6 | 1.46549 | ||||||||
\(541\) | −8456.25 | −0.672020 | −0.336010 | − | 0.941858i | \(-0.609078\pi\) | ||||
−0.336010 | + | 0.941858i | \(0.609078\pi\) | |||||||
\(542\) | −15379.9 | −1.21887 | ||||||||
\(543\) | 1731.27 | 0.136825 | ||||||||
\(544\) | −16754.3 | −1.32047 | ||||||||
\(545\) | −5697.42 | −0.447799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4114.92 | 0.321648 | 0.160824 | − | 0.986983i | \(-0.448585\pi\) | ||||
0.160824 | + | 0.986983i | \(0.448585\pi\) | |||||||
\(548\) | −7374.03 | −0.574823 | ||||||||
\(549\) | 1429.89 | 0.111159 | ||||||||
\(550\) | −9395.98 | −0.728447 | ||||||||
\(551\) | 10841.9 | 0.838259 | ||||||||
\(552\) | 4275.03 | 0.329633 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 36918.1 | 2.83123 | ||||||||
\(555\) | 2384.91 | 0.182403 | ||||||||
\(556\) | 3882.55 | 0.296146 | ||||||||
\(557\) | 6472.32 | 0.492354 | 0.246177 | − | 0.969225i | \(-0.420826\pi\) | ||||
0.246177 | + | 0.969225i | \(0.420826\pi\) | |||||||
\(558\) | 3976.38 | 0.301673 | ||||||||
\(559\) | −6655.04 | −0.503539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23048.9 | −1.73462 | ||||||||
\(562\) | 24622.6 | 1.84812 | ||||||||
\(563\) | 22085.2 | 1.65325 | 0.826627 | − | 0.562750i | \(-0.190257\pi\) | ||||
0.826627 | + | 0.562750i | \(0.190257\pi\) | |||||||
\(564\) | −35185.0 | −2.62687 | ||||||||
\(565\) | 13803.8 | 1.02784 | ||||||||
\(566\) | −13925.3 | −1.03414 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4194.26 | −0.309837 | ||||||||
\(569\) | 20469.4 | 1.50812 | 0.754060 | − | 0.656806i | \(-0.228093\pi\) | ||||
0.754060 | + | 0.656806i | \(0.228093\pi\) | |||||||
\(570\) | 16026.5 | 1.17768 | ||||||||
\(571\) | −14696.7 | −1.07712 | −0.538561 | − | 0.842586i | \(-0.681032\pi\) | ||||
−0.538561 | + | 0.842586i | \(0.681032\pi\) | |||||||
\(572\) | 48543.3 | 3.54842 | ||||||||
\(573\) | 15389.9 | 1.12203 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1636.25 | −0.118672 | ||||||||
\(576\) | 4761.82 | 0.344460 | ||||||||
\(577\) | −726.893 | −0.0524453 | −0.0262227 | − | 0.999656i | \(-0.508348\pi\) | ||||
−0.0262227 | + | 0.999656i | \(0.508348\pi\) | |||||||
\(578\) | −43767.4 | −3.14963 | ||||||||
\(579\) | 8979.98 | 0.644551 | ||||||||
\(580\) | 15463.5 | 1.10705 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9259.60 | 0.659490 | ||||||||
\(583\) | −14956.8 | −1.06252 | ||||||||
\(584\) | −31353.6 | −2.22161 | ||||||||
\(585\) | 4424.44 | 0.312697 | ||||||||
\(586\) | 6918.70 | 0.487729 | ||||||||
\(587\) | 11919.0 | 0.838074 | 0.419037 | − | 0.907969i | \(-0.362368\pi\) | ||||
0.419037 | + | 0.907969i | \(0.362368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12006.7 | 0.839946 | ||||||||
\(590\) | 28201.5 | 1.96786 | ||||||||
\(591\) | −9499.36 | −0.661170 | ||||||||
\(592\) | −985.901 | −0.0684464 | ||||||||
\(593\) | 27506.9 | 1.90485 | 0.952424 | − | 0.304777i | \(-0.0985821\pi\) | ||||
0.952424 | + | 0.304777i | \(0.0985821\pi\) | |||||||
\(594\) | 29776.4 | 2.05680 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23587.7 | 1.62112 | ||||||||
\(597\) | 19840.2 | 1.36014 | ||||||||
\(598\) | 13343.3 | 0.912454 | ||||||||
\(599\) | 949.174 | 0.0647449 | 0.0323724 | − | 0.999476i | \(-0.489694\pi\) | ||||
0.0323724 | + | 0.999476i | \(0.489694\pi\) | |||||||
\(600\) | −5952.67 | −0.405028 | ||||||||
\(601\) | −19058.3 | −1.29351 | −0.646757 | − | 0.762696i | \(-0.723875\pi\) | ||||
−0.646757 | + | 0.762696i | \(0.723875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4668.80 | −0.315304 | ||||||||
\(604\) | −47323.3 | −3.18801 | ||||||||
\(605\) | 3903.02 | 0.262282 | ||||||||
\(606\) | −25758.0 | −1.72665 | ||||||||
\(607\) | 15048.0 | 1.00623 | 0.503113 | − | 0.864221i | \(-0.332188\pi\) | ||||
0.503113 | + | 0.864221i | \(0.332188\pi\) | |||||||
\(608\) | 11950.5 | 0.797132 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9720.03 | 0.645168 | ||||||||
\(611\) | −46295.8 | −3.06535 | ||||||||
\(612\) | 9985.44 | 0.659539 | ||||||||
\(613\) | 5161.19 | 0.340063 | 0.170031 | − | 0.985439i | \(-0.445613\pi\) | ||||
0.170031 | + | 0.985439i | \(0.445613\pi\) | |||||||
\(614\) | −27374.2 | −1.79924 | ||||||||
\(615\) | −1649.91 | −0.108180 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16078.6 | 1.04911 | 0.524553 | − | 0.851378i | \(-0.324232\pi\) | ||||
0.524553 | + | 0.851378i | \(0.324232\pi\) | |||||||
\(618\) | −6383.11 | −0.415479 | ||||||||
\(619\) | −4486.17 | −0.291300 | −0.145650 | − | 0.989336i | \(-0.546527\pi\) | ||||
−0.145650 | + | 0.989336i | \(0.546527\pi\) | |||||||
\(620\) | 17124.8 | 1.10927 | ||||||||
\(621\) | 5185.35 | 0.335074 | ||||||||
\(622\) | 24801.5 | 1.59879 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6344.68 | 0.407036 | ||||||||
\(625\) | −7380.14 | −0.472329 | ||||||||
\(626\) | 13895.7 | 0.887196 | ||||||||
\(627\) | 16440.3 | 1.04715 | ||||||||
\(628\) | 26541.5 | 1.68650 | ||||||||
\(629\) | 7082.17 | 0.448942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22643.1 | −1.42854 | −0.714268 | − | 0.699873i | \(-0.753240\pi\) | ||||
−0.714268 | + | 0.699873i | \(0.753240\pi\) | |||||||
\(632\) | −18838.3 | −1.18567 | ||||||||
\(633\) | 1755.82 | 0.110249 | ||||||||
\(634\) | 4146.19 | 0.259726 | ||||||||
\(635\) | −9615.03 | −0.600883 | ||||||||
\(636\) | −22477.5 | −1.40140 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25038.4 | 1.55373 | ||||||||
\(639\) | −930.240 | −0.0575895 | ||||||||
\(640\) | 22510.5 | 1.39032 | ||||||||
\(641\) | 2410.02 | 0.148503 | 0.0742514 | − | 0.997240i | \(-0.476343\pi\) | ||||
0.0742514 | + | 0.997240i | \(0.476343\pi\) | |||||||
\(642\) | −3667.18 | −0.225439 | ||||||||
\(643\) | −21231.9 | −1.30218 | −0.651092 | − | 0.758999i | \(-0.725689\pi\) | ||||
−0.651092 | + | 0.758999i | \(0.725689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3214.64 | −0.196243 | ||||||||
\(646\) | 47591.7 | 2.89856 | ||||||||
\(647\) | −16581.8 | −1.00757 | −0.503786 | − | 0.863828i | \(-0.668060\pi\) | ||||
−0.503786 | + | 0.863828i | \(0.668060\pi\) | |||||||
\(648\) | 14420.6 | 0.874219 | ||||||||
\(649\) | 28929.7 | 1.74975 | ||||||||
\(650\) | −18579.6 | −1.12115 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −34697.5 | −2.08414 | ||||||||
\(653\) | −253.184 | −0.0151729 | −0.00758643 | − | 0.999971i | \(-0.502415\pi\) | ||||
−0.00758643 | + | 0.999971i | \(0.502415\pi\) | |||||||
\(654\) | −13863.9 | −0.828933 | ||||||||
\(655\) | 23398.8 | 1.39582 | ||||||||
\(656\) | 682.058 | 0.0405944 | ||||||||
\(657\) | −6953.87 | −0.412932 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13070.4 | −0.772613 | −0.386307 | − | 0.922370i | \(-0.626249\pi\) | ||||
−0.386307 | + | 0.922370i | \(0.626249\pi\) | |||||||
\(660\) | 23448.3 | 1.38291 | ||||||||
\(661\) | 979.244 | 0.0576221 | 0.0288110 | − | 0.999585i | \(-0.490828\pi\) | ||||
0.0288110 | + | 0.999585i | \(0.490828\pi\) | |||||||
\(662\) | 17167.1 | 1.00788 | ||||||||
\(663\) | −45576.7 | −2.66976 | ||||||||
\(664\) | −25248.8 | −1.47567 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1672.98 | −0.0973371 | ||||||||
\(667\) | 4360.27 | 0.253119 | ||||||||
\(668\) | 10691.4 | 0.619256 | ||||||||
\(669\) | 12090.6 | 0.698729 | ||||||||
\(670\) | −31737.4 | −1.83003 | ||||||||
\(671\) | 9971.02 | 0.573661 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12752.1 | −0.730397 | −0.365198 | − | 0.930930i | \(-0.618999\pi\) | ||||
−0.365198 | + | 0.930930i | \(0.618999\pi\) | |||||||
\(674\) | 17814.7 | 1.01810 | ||||||||
\(675\) | −7220.23 | −0.411714 | ||||||||
\(676\) | 65603.8 | 3.73258 | ||||||||
\(677\) | −19852.6 | −1.12703 | −0.563515 | − | 0.826106i | \(-0.690551\pi\) | ||||
−0.563515 | + | 0.826106i | \(0.690551\pi\) | |||||||
\(678\) | 33589.7 | 1.90266 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 28615.0 | 1.61373 | ||||||||
\(681\) | −20875.2 | −1.17465 | ||||||||
\(682\) | 27728.4 | 1.55686 | ||||||||
\(683\) | −109.524 | −0.00613589 | −0.00306794 | − | 0.999995i | \(-0.500977\pi\) | ||||
−0.00306794 | + | 0.999995i | \(0.500977\pi\) | |||||||
\(684\) | −7122.42 | −0.398147 | ||||||||
\(685\) | −4686.75 | −0.261418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2077.95 | 0.115399 | ||||||||
\(688\) | 1328.90 | 0.0736395 | ||||||||
\(689\) | −29575.5 | −1.63532 | ||||||||
\(690\) | 6445.33 | 0.355608 | ||||||||
\(691\) | −11393.2 | −0.627234 | −0.313617 | − | 0.949550i | \(-0.601541\pi\) | ||||
−0.313617 | + | 0.949550i | \(0.601541\pi\) | |||||||
\(692\) | −59651.8 | −3.27691 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 59038.4 | 3.22920 | ||||||||
\(695\) | 2467.65 | 0.134681 | ||||||||
\(696\) | 15862.7 | 0.863899 | ||||||||
\(697\) | −4899.53 | −0.266260 | ||||||||
\(698\) | −31421.5 | −1.70390 | ||||||||
\(699\) | 6281.51 | 0.339898 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10516.7 | −0.566634 | −0.283317 | − | 0.959026i | \(-0.591435\pi\) | ||||
−0.283317 | + | 0.959026i | \(0.591435\pi\) | |||||||
\(702\) | 58879.7 | 3.16563 | ||||||||
\(703\) | −5051.57 | −0.271015 | ||||||||
\(704\) | 33205.6 | 1.77767 | ||||||||
\(705\) | −22362.7 | −1.19465 | ||||||||
\(706\) | 9700.63 | 0.517122 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 43476.2 | 2.30782 | ||||||||
\(709\) | −6906.15 | −0.365819 | −0.182910 | − | 0.983130i | \(-0.558552\pi\) | ||||
−0.182910 | + | 0.983130i | \(0.558552\pi\) | |||||||
\(710\) | −6323.55 | −0.334251 | ||||||||
\(711\) | −4178.12 | −0.220382 | ||||||||
\(712\) | 20468.2 | 1.07736 | ||||||||
\(713\) | 4828.71 | 0.253628 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30852.9 | 1.61375 | ||||||||
\(716\) | −17964.5 | −0.937660 | ||||||||
\(717\) | −25419.6 | −1.32401 | ||||||||
\(718\) | 9153.14 | 0.475755 | ||||||||
\(719\) | −6819.71 | −0.353731 | −0.176865 | − | 0.984235i | \(-0.556596\pi\) | ||||
−0.176865 | + | 0.984235i | \(0.556596\pi\) | |||||||
\(720\) | −883.489 | −0.0457301 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1898.97 | −0.0978842 | ||||||||
\(723\) | 8427.68 | 0.433512 | ||||||||
\(724\) | −5230.22 | −0.268480 | ||||||||
\(725\) | −6071.35 | −0.311013 | ||||||||
\(726\) | 9497.50 | 0.485517 | ||||||||
\(727\) | 8740.29 | 0.445886 | 0.222943 | − | 0.974831i | \(-0.428434\pi\) | ||||
0.222943 | + | 0.974831i | \(0.428434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21895.7 | 1.11242 | ||||||||
\(730\) | −47270.8 | −2.39667 | ||||||||
\(731\) | −9546.11 | −0.483004 | ||||||||
\(732\) | 14984.7 | 0.756626 | ||||||||
\(733\) | −9568.62 | −0.482162 | −0.241081 | − | 0.970505i | \(-0.577502\pi\) | ||||
−0.241081 | + | 0.970505i | \(0.577502\pi\) | |||||||
\(734\) | −6025.55 | −0.303007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4806.10 | 0.240700 | ||||||||
\(737\) | −32556.9 | −1.62720 | ||||||||
\(738\) | 1157.39 | 0.0577289 | ||||||||
\(739\) | −2498.07 | −0.124348 | −0.0621738 | − | 0.998065i | \(-0.519803\pi\) | ||||
−0.0621738 | + | 0.998065i | \(0.519803\pi\) | |||||||
\(740\) | −7204.90 | −0.357915 | ||||||||
\(741\) | 32508.9 | 1.61167 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12492.2 | 0.616817 | 0.308408 | − | 0.951254i | \(-0.400204\pi\) | ||||
0.308408 | + | 0.951254i | \(0.400204\pi\) | |||||||
\(744\) | 17566.9 | 0.865637 | ||||||||
\(745\) | 14991.8 | 0.737256 | ||||||||
\(746\) | 12906.1 | 0.633415 | ||||||||
\(747\) | −5599.90 | −0.274283 | ||||||||
\(748\) | 69631.4 | 3.40371 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −32477.3 | −1.58121 | ||||||||
\(751\) | −22541.4 | −1.09527 | −0.547634 | − | 0.836718i | \(-0.684471\pi\) | ||||
−0.547634 | + | 0.836718i | \(0.684471\pi\) | |||||||
\(752\) | 9244.53 | 0.448289 | ||||||||
\(753\) | −24052.4 | −1.16404 | ||||||||
\(754\) | 49510.8 | 2.39135 | ||||||||
\(755\) | −30077.5 | −1.44984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10189.6 | −0.489228 | −0.244614 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244614 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(758\) | 26012.2 | 1.24644 | ||||||||
\(759\) | 6611.75 | 0.316194 | ||||||||
\(760\) | −20410.5 | −0.974168 | ||||||||
\(761\) | 33068.7 | 1.57522 | 0.787609 | − | 0.616176i | \(-0.211319\pi\) | ||||
0.787609 | + | 0.616176i | \(0.211319\pi\) | |||||||
\(762\) | −23396.9 | −1.11231 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −46493.3 | −2.20166 | ||||||||
\(765\) | 6346.50 | 0.299945 | ||||||||
\(766\) | −29228.7 | −1.37869 | ||||||||
\(767\) | 57205.3 | 2.69304 | ||||||||
\(768\) | 25910.9 | 1.21742 | ||||||||
\(769\) | 14017.9 | 0.657345 | 0.328673 | − | 0.944444i | \(-0.393399\pi\) | ||||
0.328673 | + | 0.944444i | \(0.393399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13815.0 | 0.645312 | ||||||||
\(772\) | −27128.8 | −1.26475 | ||||||||
\(773\) | 39494.0 | 1.83765 | 0.918823 | − | 0.394670i | \(-0.129141\pi\) | ||||
0.918823 | + | 0.394670i | \(0.129141\pi\) | |||||||
\(774\) | 2255.02 | 0.104722 | ||||||||
\(775\) | −6723.63 | −0.311639 | ||||||||
\(776\) | −11792.6 | −0.545527 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26405.9 | 1.21684 | ||||||||
\(779\) | 3494.74 | 0.160734 | ||||||||
\(780\) | 46366.5 | 2.12844 | ||||||||
\(781\) | −6486.83 | −0.297205 | ||||||||
\(782\) | 19139.9 | 0.875243 | ||||||||
\(783\) | 19240.5 | 0.878159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16869.1 | 0.766987 | ||||||||
\(786\) | 56937.8 | 2.58385 | ||||||||
\(787\) | −19488.5 | −0.882706 | −0.441353 | − | 0.897333i | \(-0.645501\pi\) | ||||
−0.441353 | + | 0.897333i | \(0.645501\pi\) | |||||||
\(788\) | 28697.9 | 1.29736 | ||||||||
\(789\) | −23045.1 | −1.03983 | ||||||||
\(790\) | −28401.9 | −1.27910 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6934.09 | −0.311101 | ||||||||
\(793\) | 19716.6 | 0.882923 | ||||||||
\(794\) | −32425.6 | −1.44930 | ||||||||
\(795\) | −14286.1 | −0.637329 | ||||||||
\(796\) | −59937.9 | −2.66890 | ||||||||
\(797\) | 15683.6 | 0.697040 | 0.348520 | − | 0.937301i | \(-0.386684\pi\) | ||||
0.348520 | + | 0.937301i | \(0.386684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66407.6 | −2.94034 | ||||||||
\(800\) | −6692.15 | −0.295754 | ||||||||
\(801\) | 4539.63 | 0.200249 | ||||||||
\(802\) | −29280.6 | −1.28919 | ||||||||
\(803\) | −48491.3 | −2.13104 | ||||||||
\(804\) | −48927.3 | −2.14619 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 54830.0 | 2.39616 | ||||||||
\(807\) | −19924.6 | −0.869120 | ||||||||
\(808\) | 32804.2 | 1.42828 | ||||||||
\(809\) | 27845.5 | 1.21013 | 0.605065 | − | 0.796176i | \(-0.293147\pi\) | ||||
0.605065 | + | 0.796176i | \(0.293147\pi\) | |||||||
\(810\) | 21741.5 | 0.943107 | ||||||||
\(811\) | 20777.0 | 0.899605 | 0.449802 | − | 0.893128i | \(-0.351494\pi\) | ||||
0.449802 | + | 0.893128i | \(0.351494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15069.6 | −0.650079 | ||||||||
\(814\) | −11666.1 | −0.502332 | ||||||||
\(815\) | −22052.8 | −0.947825 | ||||||||
\(816\) | 9100.93 | 0.390437 | ||||||||
\(817\) | 6809.05 | 0.291577 | ||||||||
\(818\) | −36871.8 | −1.57603 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4984.44 | 0.212273 | ||||||||
\(821\) | 33249.5 | 1.41342 | 0.706708 | − | 0.707506i | \(-0.250180\pi\) | ||||
0.706708 | + | 0.707506i | \(0.250180\pi\) | |||||||
\(822\) | −11404.6 | −0.483918 | ||||||||
\(823\) | −14421.7 | −0.610825 | −0.305413 | − | 0.952220i | \(-0.598794\pi\) | ||||
−0.305413 | + | 0.952220i | \(0.598794\pi\) | |||||||
\(824\) | 8129.22 | 0.343683 | ||||||||
\(825\) | −9206.39 | −0.388516 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25779.1 | 1.08395 | 0.541975 | − | 0.840395i | \(-0.317677\pi\) | ||||
0.541975 | + | 0.840395i | \(0.317677\pi\) | |||||||
\(828\) | −2864.41 | −0.120223 | ||||||||
\(829\) | 8440.89 | 0.353636 | 0.176818 | − | 0.984244i | \(-0.443420\pi\) | ||||
0.176818 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(830\) | −38066.8 | −1.59195 | ||||||||
\(831\) | 36173.2 | 1.51003 | ||||||||
\(832\) | 65660.4 | 2.73602 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6004.71 | 0.249312 | ||||||||
\(835\) | 6795.19 | 0.281626 | ||||||||
\(836\) | −49666.7 | −2.05473 | ||||||||
\(837\) | 21307.6 | 0.879926 | ||||||||
\(838\) | −18058.0 | −0.744396 | ||||||||
\(839\) | −23882.2 | −0.982723 | −0.491362 | − | 0.870956i | \(-0.663501\pi\) | ||||
−0.491362 | + | 0.870956i | \(0.663501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8210.05 | −0.336629 | ||||||||
\(842\) | 51098.0 | 2.09140 | ||||||||
\(843\) | 24125.8 | 0.985689 | ||||||||
\(844\) | −5304.39 | −0.216333 | ||||||||
\(845\) | 41696.2 | 1.69750 | ||||||||
\(846\) | 15687.1 | 0.637508 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5905.75 | 0.239156 | ||||||||
\(849\) | −13644.3 | −0.551556 | ||||||||
\(850\) | −26650.9 | −1.07543 | ||||||||
\(851\) | −2031.58 | −0.0818350 | ||||||||
\(852\) | −9748.58 | −0.391996 | ||||||||
\(853\) | −21167.4 | −0.849658 | −0.424829 | − | 0.905274i | \(-0.639666\pi\) | ||||
−0.424829 | + | 0.905274i | \(0.639666\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4526.83 | −0.181069 | ||||||||
\(856\) | 4670.34 | 0.186483 | ||||||||
\(857\) | −1745.05 | −0.0695563 | −0.0347781 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347781 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(858\) | 75076.4 | 2.98726 | ||||||||
\(859\) | −17565.4 | −0.697700 | −0.348850 | − | 0.937179i | \(-0.613428\pi\) | ||||
−0.348850 | + | 0.937179i | \(0.613428\pi\) | |||||||
\(860\) | 9711.55 | 0.385071 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13067.2 | −0.516321 | ||||||||
\(863\) | 5881.37 | 0.231986 | 0.115993 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115993 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(864\) | 21207.8 | 0.835074 | ||||||||
\(865\) | −37913.2 | −1.49027 | ||||||||
\(866\) | −33879.7 | −1.32942 | ||||||||
\(867\) | −42884.3 | −1.67985 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29135.2 | −1.13734 | ||||||||
\(870\) | 23915.7 | 0.931973 | ||||||||
\(871\) | −64377.7 | −2.50443 | ||||||||
\(872\) | 17656.4 | 0.685690 | ||||||||
\(873\) | −2615.46 | −0.101398 | ||||||||
\(874\) | −13652.1 | −0.528362 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −72874.0 | −2.81071 | ||||||||
\(877\) | −18859.4 | −0.726152 | −0.363076 | − | 0.931759i | \(-0.618274\pi\) | ||||
−0.363076 | + | 0.931759i | \(0.618274\pi\) | |||||||
\(878\) | 31582.6 | 1.21396 | ||||||||
\(879\) | 6779.10 | 0.260129 | ||||||||
\(880\) | −6160.82 | −0.236002 | ||||||||
\(881\) | 33493.6 | 1.28085 | 0.640424 | − | 0.768021i | \(-0.278759\pi\) | ||||
0.640424 | + | 0.768021i | \(0.278759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22692.0 | −0.864833 | −0.432416 | − | 0.901674i | \(-0.642339\pi\) | ||||
−0.432416 | + | 0.901674i | \(0.642339\pi\) | |||||||
\(884\) | 137689. | 5.23865 | ||||||||
\(885\) | 27632.4 | 1.04955 | ||||||||
\(886\) | 79576.6 | 3.01741 | ||||||||
\(887\) | −21455.6 | −0.812187 | −0.406093 | − | 0.913832i | \(-0.633109\pi\) | ||||
−0.406093 | + | 0.913832i | \(0.633109\pi\) | |||||||
\(888\) | −7390.90 | −0.279304 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 30859.3 | 1.16225 | ||||||||
\(891\) | 22302.8 | 0.838579 | ||||||||
\(892\) | −36526.1 | −1.37106 | ||||||||
\(893\) | 47367.2 | 1.77501 | ||||||||
\(894\) | 36480.5 | 1.36475 | ||||||||
\(895\) | −11417.8 | −0.426429 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13074.0 | 0.486655 | ||||||||
\(898\) | 64489.5 | 2.39648 | ||||||||
\(899\) | 17917.1 | 0.664705 | ||||||||
\(900\) | 3988.48 | 0.147721 | ||||||||
\(901\) | −42423.6 | −1.56863 | ||||||||
\(902\) | 8070.78 | 0.297924 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −42778.2 | −1.57387 | ||||||||
\(905\) | −3324.20 | −0.122100 | ||||||||
\(906\) | −73189.7 | −2.68385 | ||||||||
\(907\) | 37640.8 | 1.37800 | 0.688998 | − | 0.724763i | \(-0.258051\pi\) | ||||
0.688998 | + | 0.724763i | \(0.258051\pi\) | |||||||
\(908\) | 63064.6 | 2.30493 | ||||||||
\(909\) | 7275.60 | 0.265475 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31246.2 | 1.13637 | 0.568185 | − | 0.822901i | \(-0.307646\pi\) | ||||
0.568185 | + | 0.822901i | \(0.307646\pi\) | |||||||
\(912\) | −6491.51 | −0.235697 | ||||||||
\(913\) | −39049.7 | −1.41551 | ||||||||
\(914\) | −49752.6 | −1.80051 | ||||||||
\(915\) | 9523.90 | 0.344099 | ||||||||
\(916\) | −6277.57 | −0.226437 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 84458.1 | 3.03653 | ||||||||
\(919\) | −37653.3 | −1.35154 | −0.675772 | − | 0.737111i | \(-0.736190\pi\) | ||||
−0.675772 | + | 0.737111i | \(0.736190\pi\) | |||||||
\(920\) | −8208.46 | −0.294157 | ||||||||
\(921\) | −26821.9 | −0.959621 | ||||||||
\(922\) | −541.247 | −0.0193330 | ||||||||
\(923\) | −12827.0 | −0.457428 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2828.83 | 0.100553 | ||||||||
\(926\) | −11812.0 | −0.419185 | ||||||||
\(927\) | 1802.97 | 0.0638806 | ||||||||
\(928\) | 17833.2 | 0.630824 | ||||||||
\(929\) | 16083.8 | 0.568020 | 0.284010 | − | 0.958821i | \(-0.408335\pi\) | ||||
0.284010 | + | 0.958821i | \(0.408335\pi\) | |||||||
\(930\) | 26485.0 | 0.933848 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18976.6 | −0.666953 | ||||||||
\(933\) | 24301.1 | 0.852713 | ||||||||
\(934\) | −47303.4 | −1.65719 | ||||||||
\(935\) | 44256.0 | 1.54794 | ||||||||
\(936\) | −13711.4 | −0.478816 | ||||||||
\(937\) | −21508.6 | −0.749898 | −0.374949 | − | 0.927045i | \(-0.622340\pi\) | ||||
−0.374949 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13615.3 | 0.473184 | ||||||||
\(940\) | 67558.4 | 2.34416 | ||||||||
\(941\) | 16725.0 | 0.579406 | 0.289703 | − | 0.957117i | \(-0.406443\pi\) | ||||
0.289703 | + | 0.957117i | \(0.406443\pi\) | |||||||
\(942\) | 41048.8 | 1.41979 | ||||||||
\(943\) | 1405.47 | 0.0485349 | ||||||||
\(944\) | −11423.0 | −0.393841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15724.9 | 0.540444 | ||||||||
\(947\) | −45072.4 | −1.54663 | −0.773313 | − | 0.634025i | \(-0.781402\pi\) | ||||
−0.773313 | + | 0.634025i | \(0.781402\pi\) | |||||||
\(948\) | −43785.2 | −1.50008 | ||||||||
\(949\) | −95886.5 | −3.27988 | ||||||||
\(950\) | 19009.5 | 0.649211 | ||||||||
\(951\) | 4062.53 | 0.138524 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2861.43 | 0.0972623 | 0.0486311 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486311 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(954\) | 10021.5 | 0.340102 | ||||||||
\(955\) | −29550.0 | −1.00127 | ||||||||
\(956\) | 76793.5 | 2.59799 | ||||||||
\(957\) | 24533.2 | 0.828679 | ||||||||
\(958\) | −43437.8 | −1.46494 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 31716.6 | 1.06630 | ||||||||
\(961\) | −9948.92 | −0.333957 | ||||||||
\(962\) | −23068.6 | −0.773139 | ||||||||
\(963\) | 1035.83 | 0.0346616 | ||||||||
\(964\) | −25460.3 | −0.850645 | ||||||||
\(965\) | −17242.4 | −0.575184 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1341.05 | −0.0445971 | −0.0222985 | − | 0.999751i | \(-0.507098\pi\) | ||||
−0.0222985 | + | 0.999751i | \(0.507098\pi\) | |||||||
\(968\) | −12095.6 | −0.401618 | ||||||||
\(969\) | 46631.4 | 1.54594 | ||||||||
\(970\) | −17779.3 | −0.588514 | ||||||||
\(971\) | −13674.4 | −0.451939 | −0.225969 | − | 0.974134i | \(-0.572555\pi\) | ||||
−0.225969 | + | 0.974134i | \(0.572555\pi\) | |||||||
\(972\) | −22968.2 | −0.757928 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −37571.1 | −1.23599 | ||||||||
\(975\) | −18204.7 | −0.597965 | ||||||||
\(976\) | −3937.09 | −0.129122 | ||||||||
\(977\) | −8477.45 | −0.277603 | −0.138801 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138801 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(978\) | −53662.7 | −1.75454 | ||||||||
\(979\) | 31656.1 | 1.03344 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3916.00 | 0.127450 | ||||||||
\(982\) | 23736.3 | 0.771340 | ||||||||
\(983\) | −16136.5 | −0.523577 | −0.261788 | − | 0.965125i | \(-0.584312\pi\) | ||||
−0.261788 | + | 0.965125i | \(0.584312\pi\) | |||||||
\(984\) | 5113.11 | 0.165650 | ||||||||
\(985\) | 18239.7 | 0.590014 | ||||||||
\(986\) | 71019.2 | 2.29383 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −98210.5 | −3.16244 | ||||||||
\(989\) | 2738.38 | 0.0880439 | ||||||||
\(990\) | −10454.3 | −0.335616 | ||||||||
\(991\) | −33090.4 | −1.06070 | −0.530348 | − | 0.847780i | \(-0.677939\pi\) | ||||
−0.530348 | + | 0.847780i | \(0.677939\pi\) | |||||||
\(992\) | 19749.2 | 0.632093 | ||||||||
\(993\) | 16820.7 | 0.537551 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38095.0 | −1.21376 | ||||||||
\(996\) | −58684.9 | −1.86697 | ||||||||
\(997\) | 39943.4 | 1.26883 | 0.634413 | − | 0.772994i | \(-0.281242\pi\) | ||||
0.634413 | + | 0.772994i | \(0.281242\pi\) | |||||||
\(998\) | −41265.5 | −1.30885 | ||||||||
\(999\) | −8964.71 | −0.283915 |
(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 | 2009.4.a.j.1.4 | 36 | ||
7.2 | even | 3 | 287.4.e.a.165.33 | ✓ | 72 | ||
7.4 | even | 3 | 287.4.e.a.247.33 | yes | 72 | ||
7.6 | odd | 2 | 2009.4.a.k.1.4 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.4.e.a.165.33 | ✓ | 72 | 7.2 | even | 3 | ||
287.4.e.a.247.33 | yes | 72 | 7.4 | even | 3 | ||
2009.4.a.j.1.4 | 36 | 1.1 | even | 1 | trivial | ||
2009.4.a.k.1.4 | 36 | 7.6 | odd | 2 |