Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,4,Mod(1,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.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: | \(14.2784622214\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.978025.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 99x^{2} + 100x + 2420 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 11 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-7.19378\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 242.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 7.57575 | 1.45795 | 0.728977 | − | 0.684539i | \(-0.239996\pi\) | ||||
0.728977 | + | 0.684539i | \(0.239996\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.40810 | 0.483715 | 0.241858 | − | 0.970312i | \(-0.422243\pi\) | ||||
0.241858 | + | 0.970312i | \(0.422243\pi\) | |||||||
\(6\) | −15.1515 | −1.03093 | ||||||||
\(7\) | −22.1498 | −1.19598 | −0.597989 | − | 0.801504i | \(-0.704033\pi\) | ||||
−0.597989 | + | 0.801504i | \(0.704033\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 30.3919 | 1.12563 | ||||||||
\(10\) | −10.8162 | −0.342038 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 30.3030 | 0.728977 | ||||||||
\(13\) | 76.8269 | 1.63907 | 0.819537 | − | 0.573027i | \(-0.194231\pi\) | ||||
0.819537 | + | 0.573027i | \(0.194231\pi\) | |||||||
\(14\) | 44.2996 | 0.845684 | ||||||||
\(15\) | 40.9704 | 0.705234 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 59.2883 | 0.845855 | 0.422927 | − | 0.906164i | \(-0.361003\pi\) | ||||
0.422927 | + | 0.906164i | \(0.361003\pi\) | |||||||
\(18\) | −60.7839 | −0.795939 | ||||||||
\(19\) | 95.2626 | 1.15025 | 0.575124 | − | 0.818066i | \(-0.304954\pi\) | ||||
0.575124 | + | 0.818066i | \(0.304954\pi\) | |||||||
\(20\) | 21.6324 | 0.241858 | ||||||||
\(21\) | −167.801 | −1.74368 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 142.484 | 1.29174 | 0.645868 | − | 0.763449i | \(-0.276495\pi\) | ||||
0.645868 | + | 0.763449i | \(0.276495\pi\) | |||||||
\(24\) | −60.6060 | −0.515464 | ||||||||
\(25\) | −95.7524 | −0.766020 | ||||||||
\(26\) | −153.654 | −1.15900 | ||||||||
\(27\) | 25.6965 | 0.183159 | ||||||||
\(28\) | −88.5993 | −0.597989 | ||||||||
\(29\) | −20.4183 | −0.130744 | −0.0653721 | − | 0.997861i | \(-0.520823\pi\) | ||||
−0.0653721 | + | 0.997861i | \(0.520823\pi\) | |||||||
\(30\) | −81.9408 | −0.498676 | ||||||||
\(31\) | 213.304 | 1.23582 | 0.617912 | − | 0.786247i | \(-0.287979\pi\) | ||||
0.617912 | + | 0.786247i | \(0.287979\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −118.577 | −0.598110 | ||||||||
\(35\) | −119.788 | −0.578513 | ||||||||
\(36\) | 121.568 | 0.562814 | ||||||||
\(37\) | −145.578 | −0.646832 | −0.323416 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323416 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(38\) | −190.525 | −0.813349 | ||||||||
\(39\) | 582.021 | 2.38969 | ||||||||
\(40\) | −43.2648 | −0.171019 | ||||||||
\(41\) | 82.8326 | 0.315519 | 0.157759 | − | 0.987478i | \(-0.449573\pi\) | ||||
0.157759 | + | 0.987478i | \(0.449573\pi\) | |||||||
\(42\) | 335.603 | 1.23297 | ||||||||
\(43\) | −151.373 | −0.536841 | −0.268420 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268420 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 164.363 | 0.544483 | ||||||||
\(46\) | −284.968 | −0.913396 | ||||||||
\(47\) | 90.3643 | 0.280447 | 0.140223 | − | 0.990120i | \(-0.455218\pi\) | ||||
0.140223 | + | 0.990120i | \(0.455218\pi\) | |||||||
\(48\) | 121.212 | 0.364488 | ||||||||
\(49\) | 147.615 | 0.430363 | ||||||||
\(50\) | 191.505 | 0.541658 | ||||||||
\(51\) | 449.153 | 1.23322 | ||||||||
\(52\) | 307.308 | 0.819537 | ||||||||
\(53\) | −234.849 | −0.608660 | −0.304330 | − | 0.952567i | \(-0.598433\pi\) | ||||
−0.304330 | + | 0.952567i | \(0.598433\pi\) | |||||||
\(54\) | −51.3931 | −0.129513 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 177.199 | 0.422842 | ||||||||
\(57\) | 721.685 | 1.67701 | ||||||||
\(58\) | 40.8366 | 0.0924502 | ||||||||
\(59\) | 302.497 | 0.667488 | 0.333744 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333744 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(60\) | 163.882 | 0.352617 | ||||||||
\(61\) | −149.279 | −0.313332 | −0.156666 | − | 0.987652i | \(-0.550075\pi\) | ||||
−0.156666 | + | 0.987652i | \(0.550075\pi\) | |||||||
\(62\) | −426.608 | −0.873860 | ||||||||
\(63\) | −673.176 | −1.34623 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 415.488 | 0.792845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 826.236 | 1.50658 | 0.753290 | − | 0.657689i | \(-0.228466\pi\) | ||||
0.753290 | + | 0.657689i | \(0.228466\pi\) | |||||||
\(68\) | 237.153 | 0.422927 | ||||||||
\(69\) | 1079.42 | 1.88329 | ||||||||
\(70\) | 239.577 | 0.409070 | ||||||||
\(71\) | −898.965 | −1.50264 | −0.751321 | − | 0.659937i | \(-0.770583\pi\) | ||||
−0.751321 | + | 0.659937i | \(0.770583\pi\) | |||||||
\(72\) | −243.136 | −0.397969 | ||||||||
\(73\) | −137.993 | −0.221245 | −0.110623 | − | 0.993862i | \(-0.535284\pi\) | ||||
−0.110623 | + | 0.993862i | \(0.535284\pi\) | |||||||
\(74\) | 291.155 | 0.457380 | ||||||||
\(75\) | −725.396 | −1.11682 | ||||||||
\(76\) | 381.050 | 0.575124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1164.04 | −1.68977 | ||||||||
\(79\) | −304.459 | −0.433598 | −0.216799 | − | 0.976216i | \(-0.569562\pi\) | ||||
−0.216799 | + | 0.976216i | \(0.569562\pi\) | |||||||
\(80\) | 86.5296 | 0.120929 | ||||||||
\(81\) | −625.912 | −0.858590 | ||||||||
\(82\) | −165.665 | −0.223106 | ||||||||
\(83\) | −764.294 | −1.01075 | −0.505374 | − | 0.862900i | \(-0.668646\pi\) | ||||
−0.505374 | + | 0.862900i | \(0.668646\pi\) | |||||||
\(84\) | −671.206 | −0.871840 | ||||||||
\(85\) | 320.637 | 0.409153 | ||||||||
\(86\) | 302.746 | 0.379604 | ||||||||
\(87\) | −154.684 | −0.190619 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −313.100 | −0.372905 | −0.186452 | − | 0.982464i | \(-0.559699\pi\) | ||||
−0.186452 | + | 0.982464i | \(0.559699\pi\) | |||||||
\(90\) | −328.725 | −0.385008 | ||||||||
\(91\) | −1701.70 | −1.96030 | ||||||||
\(92\) | 569.936 | 0.645868 | ||||||||
\(93\) | 1615.94 | 1.80177 | ||||||||
\(94\) | −180.729 | −0.198306 | ||||||||
\(95\) | 515.189 | 0.556393 | ||||||||
\(96\) | −242.424 | −0.257732 | ||||||||
\(97\) | −582.505 | −0.609737 | −0.304868 | − | 0.952394i | \(-0.598612\pi\) | ||||
−0.304868 | + | 0.952394i | \(0.598612\pi\) | |||||||
\(98\) | −295.229 | −0.304313 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −383.010 | −0.383010 | ||||||||
\(101\) | −141.554 | −0.139457 | −0.0697286 | − | 0.997566i | \(-0.522213\pi\) | ||||
−0.0697286 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(102\) | −898.307 | −0.872016 | ||||||||
\(103\) | 841.380 | 0.804890 | 0.402445 | − | 0.915444i | \(-0.368161\pi\) | ||||
0.402445 | + | 0.915444i | \(0.368161\pi\) | |||||||
\(104\) | −614.615 | −0.579500 | ||||||||
\(105\) | −907.487 | −0.843444 | ||||||||
\(106\) | 469.698 | 0.430387 | ||||||||
\(107\) | −64.4319 | −0.0582137 | −0.0291069 | − | 0.999576i | \(-0.509266\pi\) | ||||
−0.0291069 | + | 0.999576i | \(0.509266\pi\) | |||||||
\(108\) | 102.786 | 0.0915797 | ||||||||
\(109\) | 1559.04 | 1.36999 | 0.684995 | − | 0.728547i | \(-0.259804\pi\) | ||||
0.684995 | + | 0.728547i | \(0.259804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1102.86 | −0.943052 | ||||||||
\(112\) | −354.397 | −0.298994 | ||||||||
\(113\) | −2239.14 | −1.86408 | −0.932039 | − | 0.362359i | \(-0.881971\pi\) | ||||
−0.932039 | + | 0.362359i | \(0.881971\pi\) | |||||||
\(114\) | −1443.37 | −1.18582 | ||||||||
\(115\) | 770.567 | 0.624833 | ||||||||
\(116\) | −81.6732 | −0.0653721 | ||||||||
\(117\) | 2334.92 | 1.84499 | ||||||||
\(118\) | −604.995 | −0.471986 | ||||||||
\(119\) | −1313.23 | −1.01162 | ||||||||
\(120\) | −327.763 | −0.249338 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 298.559 | 0.221559 | ||||||||
\(123\) | 627.519 | 0.460012 | ||||||||
\(124\) | 853.217 | 0.617912 | ||||||||
\(125\) | −1193.85 | −0.854251 | ||||||||
\(126\) | 1346.35 | 0.951925 | ||||||||
\(127\) | 1093.46 | 0.764004 | 0.382002 | − | 0.924162i | \(-0.375235\pi\) | ||||
0.382002 | + | 0.924162i | \(0.375235\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1146.76 | −0.782688 | ||||||||
\(130\) | −830.976 | −0.560626 | ||||||||
\(131\) | −2466.16 | −1.64481 | −0.822403 | − | 0.568906i | \(-0.807367\pi\) | ||||
−0.822403 | + | 0.568906i | \(0.807367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2110.05 | −1.37567 | ||||||||
\(134\) | −1652.47 | −1.06531 | ||||||||
\(135\) | 138.970 | 0.0885970 | ||||||||
\(136\) | −474.307 | −0.299055 | ||||||||
\(137\) | −973.286 | −0.606959 | −0.303480 | − | 0.952838i | \(-0.598148\pi\) | ||||
−0.303480 | + | 0.952838i | \(0.598148\pi\) | |||||||
\(138\) | −2158.84 | −1.33169 | ||||||||
\(139\) | −1263.04 | −0.770717 | −0.385358 | − | 0.922767i | \(-0.625922\pi\) | ||||
−0.385358 | + | 0.922767i | \(0.625922\pi\) | |||||||
\(140\) | −479.154 | −0.289256 | ||||||||
\(141\) | 684.577 | 0.408878 | ||||||||
\(142\) | 1797.93 | 1.06253 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 486.271 | 0.281407 | ||||||||
\(145\) | −110.424 | −0.0632430 | ||||||||
\(146\) | 275.987 | 0.156444 | ||||||||
\(147\) | 1118.29 | 0.627449 | ||||||||
\(148\) | −582.310 | −0.323416 | ||||||||
\(149\) | −489.340 | −0.269049 | −0.134525 | − | 0.990910i | \(-0.542951\pi\) | ||||
−0.134525 | + | 0.990910i | \(0.542951\pi\) | |||||||
\(150\) | 1450.79 | 0.789712 | ||||||||
\(151\) | 1707.77 | 0.920376 | 0.460188 | − | 0.887822i | \(-0.347782\pi\) | ||||
0.460188 | + | 0.887822i | \(0.347782\pi\) | |||||||
\(152\) | −762.100 | −0.406674 | ||||||||
\(153\) | 1801.89 | 0.952118 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1153.57 | 0.597787 | ||||||||
\(156\) | 2328.09 | 1.19485 | ||||||||
\(157\) | 2561.73 | 1.30222 | 0.651108 | − | 0.758985i | \(-0.274304\pi\) | ||||
0.651108 | + | 0.758985i | \(0.274304\pi\) | |||||||
\(158\) | 608.917 | 0.306600 | ||||||||
\(159\) | −1779.16 | −0.887397 | ||||||||
\(160\) | −173.059 | −0.0855096 | ||||||||
\(161\) | −3155.99 | −1.54489 | ||||||||
\(162\) | 1251.82 | 0.607115 | ||||||||
\(163\) | 1816.09 | 0.872681 | 0.436340 | − | 0.899782i | \(-0.356274\pi\) | ||||
0.436340 | + | 0.899782i | \(0.356274\pi\) | |||||||
\(164\) | 331.330 | 0.157759 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1528.59 | 0.714707 | ||||||||
\(167\) | 378.925 | 0.175581 | 0.0877907 | − | 0.996139i | \(-0.472019\pi\) | ||||
0.0877907 | + | 0.996139i | \(0.472019\pi\) | |||||||
\(168\) | 1342.41 | 0.616484 | ||||||||
\(169\) | 3705.38 | 1.68656 | ||||||||
\(170\) | −641.275 | −0.289315 | ||||||||
\(171\) | 2895.21 | 1.29475 | ||||||||
\(172\) | −605.491 | −0.268420 | ||||||||
\(173\) | 50.7220 | 0.0222909 | 0.0111454 | − | 0.999938i | \(-0.496452\pi\) | ||||
0.0111454 | + | 0.999938i | \(0.496452\pi\) | |||||||
\(174\) | 309.368 | 0.134788 | ||||||||
\(175\) | 2120.90 | 0.916142 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2291.64 | 0.973167 | ||||||||
\(178\) | 626.199 | 0.263683 | ||||||||
\(179\) | 20.8678 | 0.00871359 | 0.00435679 | − | 0.999991i | \(-0.498613\pi\) | ||||
0.00435679 | + | 0.999991i | \(0.498613\pi\) | |||||||
\(180\) | 657.451 | 0.272242 | ||||||||
\(181\) | −176.153 | −0.0723391 | −0.0361695 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361695 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(182\) | 3403.41 | 1.38614 | ||||||||
\(183\) | −1130.90 | −0.456824 | ||||||||
\(184\) | −1139.87 | −0.456698 | ||||||||
\(185\) | −787.298 | −0.312883 | ||||||||
\(186\) | −3231.88 | −1.27405 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 361.457 | 0.140223 | ||||||||
\(189\) | −569.174 | −0.219055 | ||||||||
\(190\) | −1030.38 | −0.393429 | ||||||||
\(191\) | −1159.22 | −0.439153 | −0.219576 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219576 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(192\) | 484.848 | 0.182244 | ||||||||
\(193\) | −1284.94 | −0.479232 | −0.239616 | − | 0.970868i | \(-0.577022\pi\) | ||||
−0.239616 | + | 0.970868i | \(0.577022\pi\) | |||||||
\(194\) | 1165.01 | 0.431149 | ||||||||
\(195\) | 3147.63 | 1.15593 | ||||||||
\(196\) | 590.458 | 0.215181 | ||||||||
\(197\) | −2685.06 | −0.971078 | −0.485539 | − | 0.874215i | \(-0.661377\pi\) | ||||
−0.485539 | + | 0.874215i | \(0.661377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1333.54 | −0.475036 | −0.237518 | − | 0.971383i | \(-0.576334\pi\) | ||||
−0.237518 | + | 0.971383i | \(0.576334\pi\) | |||||||
\(200\) | 766.020 | 0.270829 | ||||||||
\(201\) | 6259.36 | 2.19652 | ||||||||
\(202\) | 283.109 | 0.0986112 | ||||||||
\(203\) | 452.262 | 0.156367 | ||||||||
\(204\) | 1796.61 | 0.616608 | ||||||||
\(205\) | 447.967 | 0.152621 | ||||||||
\(206\) | −1682.76 | −0.569143 | ||||||||
\(207\) | 4330.36 | 1.45401 | ||||||||
\(208\) | 1229.23 | 0.409768 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1814.97 | 0.596405 | ||||||||
\(211\) | −1628.17 | −0.531221 | −0.265611 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265611 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(212\) | −939.395 | −0.304330 | ||||||||
\(213\) | −6810.33 | −2.19078 | ||||||||
\(214\) | 128.864 | 0.0411633 | ||||||||
\(215\) | −818.640 | −0.259678 | ||||||||
\(216\) | −205.572 | −0.0647566 | ||||||||
\(217\) | −4724.65 | −1.47802 | ||||||||
\(218\) | −3118.08 | −0.968730 | ||||||||
\(219\) | −1045.40 | −0.322565 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4554.94 | 1.38642 | ||||||||
\(222\) | 2205.72 | 0.666838 | ||||||||
\(223\) | −2628.19 | −0.789224 | −0.394612 | − | 0.918848i | \(-0.629121\pi\) | ||||
−0.394612 | + | 0.918848i | \(0.629121\pi\) | |||||||
\(224\) | 708.794 | 0.211421 | ||||||||
\(225\) | −2910.10 | −0.862253 | ||||||||
\(226\) | 4478.28 | 1.31810 | ||||||||
\(227\) | 1702.56 | 0.497809 | 0.248904 | − | 0.968528i | \(-0.419930\pi\) | ||||
0.248904 | + | 0.968528i | \(0.419930\pi\) | |||||||
\(228\) | 2886.74 | 0.838505 | ||||||||
\(229\) | 5395.95 | 1.55709 | 0.778546 | − | 0.627587i | \(-0.215957\pi\) | ||||
0.778546 | + | 0.627587i | \(0.215957\pi\) | |||||||
\(230\) | −1541.13 | −0.441823 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 163.346 | 0.0462251 | ||||||||
\(233\) | −6054.18 | −1.70224 | −0.851122 | − | 0.524969i | \(-0.824077\pi\) | ||||
−0.851122 | + | 0.524969i | \(0.824077\pi\) | |||||||
\(234\) | −4669.84 | −1.30460 | ||||||||
\(235\) | 488.699 | 0.135656 | ||||||||
\(236\) | 1209.99 | 0.333744 | ||||||||
\(237\) | −2306.50 | −0.632166 | ||||||||
\(238\) | 2626.45 | 0.715326 | ||||||||
\(239\) | 3136.60 | 0.848911 | 0.424456 | − | 0.905449i | \(-0.360466\pi\) | ||||
0.424456 | + | 0.905449i | \(0.360466\pi\) | |||||||
\(240\) | 655.526 | 0.176309 | ||||||||
\(241\) | −6499.26 | −1.73715 | −0.868577 | − | 0.495555i | \(-0.834965\pi\) | ||||
−0.868577 | + | 0.495555i | \(0.834965\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5435.56 | −1.43494 | ||||||||
\(244\) | −597.118 | −0.156666 | ||||||||
\(245\) | 798.314 | 0.208173 | ||||||||
\(246\) | −1255.04 | −0.325277 | ||||||||
\(247\) | 7318.73 | 1.88534 | ||||||||
\(248\) | −1706.43 | −0.436930 | ||||||||
\(249\) | −5790.10 | −1.47362 | ||||||||
\(250\) | 2387.70 | 0.604046 | ||||||||
\(251\) | 5565.79 | 1.39964 | 0.699820 | − | 0.714320i | \(-0.253264\pi\) | ||||
0.699820 | + | 0.714320i | \(0.253264\pi\) | |||||||
\(252\) | −2692.70 | −0.673113 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2186.91 | −0.540232 | ||||||||
\(255\) | 2429.07 | 0.596526 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6036.31 | −1.46512 | −0.732558 | − | 0.680705i | \(-0.761673\pi\) | ||||
−0.732558 | + | 0.680705i | \(0.761673\pi\) | |||||||
\(258\) | 2293.53 | 0.553444 | ||||||||
\(259\) | 3224.52 | 0.773597 | ||||||||
\(260\) | 1661.95 | 0.396422 | ||||||||
\(261\) | −620.552 | −0.147169 | ||||||||
\(262\) | 4932.32 | 1.16305 | ||||||||
\(263\) | −708.442 | −0.166100 | −0.0830502 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830502 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1270.09 | −0.294418 | ||||||||
\(266\) | 4220.10 | 0.972747 | ||||||||
\(267\) | −2371.96 | −0.543677 | ||||||||
\(268\) | 3304.95 | 0.753290 | ||||||||
\(269\) | −4809.71 | −1.09016 | −0.545080 | − | 0.838384i | \(-0.683501\pi\) | ||||
−0.545080 | + | 0.838384i | \(0.683501\pi\) | |||||||
\(270\) | −277.939 | −0.0626475 | ||||||||
\(271\) | −5240.88 | −1.17476 | −0.587382 | − | 0.809310i | \(-0.699841\pi\) | ||||
−0.587382 | + | 0.809310i | \(0.699841\pi\) | |||||||
\(272\) | 948.613 | 0.211464 | ||||||||
\(273\) | −12891.7 | −2.85802 | ||||||||
\(274\) | 1946.57 | 0.429185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4317.69 | 0.941646 | ||||||||
\(277\) | −5339.75 | −1.15825 | −0.579123 | − | 0.815240i | \(-0.696605\pi\) | ||||
−0.579123 | + | 0.815240i | \(0.696605\pi\) | |||||||
\(278\) | 2526.08 | 0.544979 | ||||||||
\(279\) | 6482.73 | 1.39108 | ||||||||
\(280\) | 958.308 | 0.204535 | ||||||||
\(281\) | −3279.97 | −0.696322 | −0.348161 | − | 0.937435i | \(-0.613194\pi\) | ||||
−0.348161 | + | 0.937435i | \(0.613194\pi\) | |||||||
\(282\) | −1369.15 | −0.289120 | ||||||||
\(283\) | −4895.49 | −1.02829 | −0.514146 | − | 0.857703i | \(-0.671891\pi\) | ||||
−0.514146 | + | 0.857703i | \(0.671891\pi\) | |||||||
\(284\) | −3595.86 | −0.751321 | ||||||||
\(285\) | 3902.95 | 0.811195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1834.73 | −0.377354 | ||||||||
\(288\) | −972.542 | −0.198985 | ||||||||
\(289\) | −1397.89 | −0.284529 | ||||||||
\(290\) | 220.848 | 0.0447195 | ||||||||
\(291\) | −4412.91 | −0.888968 | ||||||||
\(292\) | −551.974 | −0.110623 | ||||||||
\(293\) | 6705.80 | 1.33705 | 0.668527 | − | 0.743688i | \(-0.266925\pi\) | ||||
0.668527 | + | 0.743688i | \(0.266925\pi\) | |||||||
\(294\) | −2236.58 | −0.443674 | ||||||||
\(295\) | 1635.94 | 0.322874 | ||||||||
\(296\) | 1164.62 | 0.228690 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 978.680 | 0.190246 | ||||||||
\(299\) | 10946.6 | 2.11725 | ||||||||
\(300\) | −2901.59 | −0.558410 | ||||||||
\(301\) | 3352.88 | 0.642049 | ||||||||
\(302\) | −3415.55 | −0.650804 | ||||||||
\(303\) | −1072.38 | −0.203322 | ||||||||
\(304\) | 1524.20 | 0.287562 | ||||||||
\(305\) | −807.318 | −0.151564 | ||||||||
\(306\) | −3603.78 | −0.673249 | ||||||||
\(307\) | 9507.29 | 1.76746 | 0.883730 | − | 0.467998i | \(-0.155025\pi\) | ||||
0.883730 | + | 0.467998i | \(0.155025\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6374.08 | 1.17349 | ||||||||
\(310\) | −2307.14 | −0.422699 | ||||||||
\(311\) | 5768.07 | 1.05170 | 0.525848 | − | 0.850579i | \(-0.323748\pi\) | ||||
0.525848 | + | 0.850579i | \(0.323748\pi\) | |||||||
\(312\) | −4656.17 | −0.844884 | ||||||||
\(313\) | 5977.75 | 1.07950 | 0.539748 | − | 0.841826i | \(-0.318519\pi\) | ||||
0.539748 | + | 0.841826i | \(0.318519\pi\) | |||||||
\(314\) | −5123.45 | −0.920806 | ||||||||
\(315\) | −3640.60 | −0.651190 | ||||||||
\(316\) | −1217.83 | −0.216799 | ||||||||
\(317\) | 5231.93 | 0.926987 | 0.463493 | − | 0.886100i | \(-0.346596\pi\) | ||||
0.463493 | + | 0.886100i | \(0.346596\pi\) | |||||||
\(318\) | 3558.31 | 0.627485 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 346.118 | 0.0604644 | ||||||||
\(321\) | −488.120 | −0.0848729 | ||||||||
\(322\) | 6311.99 | 1.09240 | ||||||||
\(323\) | 5647.96 | 0.972944 | ||||||||
\(324\) | −2503.65 | −0.429295 | ||||||||
\(325\) | −7356.37 | −1.25556 | ||||||||
\(326\) | −3632.17 | −0.617078 | ||||||||
\(327\) | 11810.9 | 1.99738 | ||||||||
\(328\) | −662.661 | −0.111553 | ||||||||
\(329\) | −2001.55 | −0.335408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3963.72 | −0.658205 | −0.329102 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329102 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(332\) | −3057.17 | −0.505374 | ||||||||
\(333\) | −4424.39 | −0.728093 | ||||||||
\(334\) | −757.850 | −0.124155 | ||||||||
\(335\) | 4468.37 | 0.728756 | ||||||||
\(336\) | −2684.82 | −0.435920 | ||||||||
\(337\) | 5106.60 | 0.825443 | 0.412721 | − | 0.910857i | \(-0.364578\pi\) | ||||
0.412721 | + | 0.910857i | \(0.364578\pi\) | |||||||
\(338\) | −7410.75 | −1.19258 | ||||||||
\(339\) | −16963.2 | −2.71774 | ||||||||
\(340\) | 1282.55 | 0.204576 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5790.43 | −0.915528 | ||||||||
\(343\) | 4327.75 | 0.681273 | ||||||||
\(344\) | 1210.98 | 0.189802 | ||||||||
\(345\) | 5837.62 | 0.910977 | ||||||||
\(346\) | −101.444 | −0.0157620 | ||||||||
\(347\) | 7545.75 | 1.16737 | 0.583685 | − | 0.811980i | \(-0.301610\pi\) | ||||
0.583685 | + | 0.811980i | \(0.301610\pi\) | |||||||
\(348\) | −618.736 | −0.0953095 | ||||||||
\(349\) | −3256.71 | −0.499507 | −0.249753 | − | 0.968309i | \(-0.580350\pi\) | ||||
−0.249753 | + | 0.968309i | \(0.580350\pi\) | |||||||
\(350\) | −4241.80 | −0.647811 | ||||||||
\(351\) | 1974.19 | 0.300212 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6506.83 | −0.981087 | −0.490543 | − | 0.871417i | \(-0.663202\pi\) | ||||
−0.490543 | + | 0.871417i | \(0.663202\pi\) | |||||||
\(354\) | −4583.29 | −0.688133 | ||||||||
\(355\) | −4861.69 | −0.726851 | ||||||||
\(356\) | −1252.40 | −0.186452 | ||||||||
\(357\) | −9948.67 | −1.47490 | ||||||||
\(358\) | −41.7356 | −0.00616144 | ||||||||
\(359\) | 4066.21 | 0.597789 | 0.298895 | − | 0.954286i | \(-0.403382\pi\) | ||||
0.298895 | + | 0.954286i | \(0.403382\pi\) | |||||||
\(360\) | −1314.90 | −0.192504 | ||||||||
\(361\) | 2215.95 | 0.323073 | ||||||||
\(362\) | 352.307 | 0.0511514 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6806.81 | −0.980148 | ||||||||
\(365\) | −746.282 | −0.107020 | ||||||||
\(366\) | 2261.81 | 0.323023 | ||||||||
\(367\) | −1392.27 | −0.198028 | −0.0990138 | − | 0.995086i | \(-0.531569\pi\) | ||||
−0.0990138 | + | 0.995086i | \(0.531569\pi\) | |||||||
\(368\) | 2279.74 | 0.322934 | ||||||||
\(369\) | 2517.44 | 0.355157 | ||||||||
\(370\) | 1574.60 | 0.221241 | ||||||||
\(371\) | 5201.86 | 0.727944 | ||||||||
\(372\) | 6463.75 | 0.900887 | ||||||||
\(373\) | 9440.30 | 1.31046 | 0.655228 | − | 0.755431i | \(-0.272572\pi\) | ||||
0.655228 | + | 0.755431i | \(0.272572\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9044.32 | −1.24546 | ||||||||
\(376\) | −722.915 | −0.0991529 | ||||||||
\(377\) | −1568.68 | −0.214299 | ||||||||
\(378\) | 1138.35 | 0.154895 | ||||||||
\(379\) | 1290.35 | 0.174884 | 0.0874418 | − | 0.996170i | \(-0.472131\pi\) | ||||
0.0874418 | + | 0.996170i | \(0.472131\pi\) | |||||||
\(380\) | 2060.76 | 0.278196 | ||||||||
\(381\) | 8283.74 | 1.11388 | ||||||||
\(382\) | 2318.44 | 0.310528 | ||||||||
\(383\) | −5652.89 | −0.754176 | −0.377088 | − | 0.926177i | \(-0.623075\pi\) | ||||
−0.377088 | + | 0.926177i | \(0.623075\pi\) | |||||||
\(384\) | −969.696 | −0.128866 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2569.88 | 0.338868 | ||||||||
\(387\) | −4600.52 | −0.604283 | ||||||||
\(388\) | −2330.02 | −0.304868 | ||||||||
\(389\) | −12838.0 | −1.67330 | −0.836648 | − | 0.547741i | \(-0.815488\pi\) | ||||
−0.836648 | + | 0.547741i | \(0.815488\pi\) | |||||||
\(390\) | −6295.26 | −0.817366 | ||||||||
\(391\) | 8447.63 | 1.09262 | ||||||||
\(392\) | −1180.92 | −0.152156 | ||||||||
\(393\) | −18683.0 | −2.39805 | ||||||||
\(394\) | 5370.12 | 0.686656 | ||||||||
\(395\) | −1646.54 | −0.209738 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7691.26 | 0.972326 | 0.486163 | − | 0.873868i | \(-0.338396\pi\) | ||||
0.486163 | + | 0.873868i | \(0.338396\pi\) | |||||||
\(398\) | 2667.08 | 0.335901 | ||||||||
\(399\) | −15985.2 | −2.00567 | ||||||||
\(400\) | −1532.04 | −0.191505 | ||||||||
\(401\) | 7786.17 | 0.969633 | 0.484817 | − | 0.874616i | \(-0.338886\pi\) | ||||
0.484817 | + | 0.874616i | \(0.338886\pi\) | |||||||
\(402\) | −12518.7 | −1.55318 | ||||||||
\(403\) | 16387.5 | 2.02561 | ||||||||
\(404\) | −566.217 | −0.0697286 | ||||||||
\(405\) | −3385.00 | −0.415313 | ||||||||
\(406\) | −904.523 | −0.110568 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3593.23 | −0.436008 | ||||||||
\(409\) | −8859.88 | −1.07113 | −0.535566 | − | 0.844493i | \(-0.679902\pi\) | ||||
−0.535566 | + | 0.844493i | \(0.679902\pi\) | |||||||
\(410\) | −895.934 | −0.107920 | ||||||||
\(411\) | −7373.37 | −0.884918 | ||||||||
\(412\) | 3365.52 | 0.402445 | ||||||||
\(413\) | −6700.26 | −0.798301 | ||||||||
\(414\) | −8660.73 | −1.02814 | ||||||||
\(415\) | −4133.38 | −0.488914 | ||||||||
\(416\) | −2458.46 | −0.289750 | ||||||||
\(417\) | −9568.47 | −1.12367 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9469.08 | 1.10405 | 0.552023 | − | 0.833829i | \(-0.313856\pi\) | ||||
0.552023 | + | 0.833829i | \(0.313856\pi\) | |||||||
\(420\) | −3629.95 | −0.421722 | ||||||||
\(421\) | 5177.94 | 0.599424 | 0.299712 | − | 0.954030i | \(-0.403109\pi\) | ||||
0.299712 | + | 0.954030i | \(0.403109\pi\) | |||||||
\(422\) | 3256.34 | 0.375630 | ||||||||
\(423\) | 2746.35 | 0.315678 | ||||||||
\(424\) | 1878.79 | 0.215194 | ||||||||
\(425\) | −5677.00 | −0.647941 | ||||||||
\(426\) | 13620.7 | 1.54912 | ||||||||
\(427\) | 3306.51 | 0.374739 | ||||||||
\(428\) | −257.728 | −0.0291069 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1637.28 | 0.183620 | ||||||||
\(431\) | 10463.6 | 1.16940 | 0.584700 | − | 0.811249i | \(-0.301212\pi\) | ||||
0.584700 | + | 0.811249i | \(0.301212\pi\) | |||||||
\(432\) | 411.145 | 0.0457898 | ||||||||
\(433\) | 15838.2 | 1.75782 | 0.878911 | − | 0.476986i | \(-0.158271\pi\) | ||||
0.878911 | + | 0.476986i | \(0.158271\pi\) | |||||||
\(434\) | 9449.30 | 1.04512 | ||||||||
\(435\) | −836.546 | −0.0922053 | ||||||||
\(436\) | 6236.16 | 0.684995 | ||||||||
\(437\) | 13573.4 | 1.48582 | ||||||||
\(438\) | 2090.81 | 0.228088 | ||||||||
\(439\) | −4824.70 | −0.524534 | −0.262267 | − | 0.964995i | \(-0.584470\pi\) | ||||
−0.262267 | + | 0.964995i | \(0.584470\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4486.29 | 0.484429 | ||||||||
\(442\) | −9109.88 | −0.980346 | ||||||||
\(443\) | 3583.38 | 0.384315 | 0.192158 | − | 0.981364i | \(-0.438451\pi\) | ||||
0.192158 | + | 0.981364i | \(0.438451\pi\) | |||||||
\(444\) | −4411.44 | −0.471526 | ||||||||
\(445\) | −1693.27 | −0.180380 | ||||||||
\(446\) | 5256.39 | 0.558066 | ||||||||
\(447\) | −3707.12 | −0.392261 | ||||||||
\(448\) | −1417.59 | −0.149497 | ||||||||
\(449\) | −7795.98 | −0.819410 | −0.409705 | − | 0.912218i | \(-0.634368\pi\) | ||||
−0.409705 | + | 0.912218i | \(0.634368\pi\) | |||||||
\(450\) | 5820.21 | 0.609705 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8956.57 | −0.932039 | ||||||||
\(453\) | 12937.7 | 1.34186 | ||||||||
\(454\) | −3405.11 | −0.352004 | ||||||||
\(455\) | −9202.98 | −0.948225 | ||||||||
\(456\) | −5773.48 | −0.592912 | ||||||||
\(457\) | 3348.02 | 0.342700 | 0.171350 | − | 0.985210i | \(-0.445187\pi\) | ||||
0.171350 | + | 0.985210i | \(0.445187\pi\) | |||||||
\(458\) | −10791.9 | −1.10103 | ||||||||
\(459\) | 1523.51 | 0.154926 | ||||||||
\(460\) | 3082.27 | 0.312416 | ||||||||
\(461\) | 7171.96 | 0.724580 | 0.362290 | − | 0.932065i | \(-0.381995\pi\) | ||||
0.362290 | + | 0.932065i | \(0.381995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4034.74 | 0.404990 | 0.202495 | − | 0.979283i | \(-0.435095\pi\) | ||||
0.202495 | + | 0.979283i | \(0.435095\pi\) | |||||||
\(464\) | −326.693 | −0.0326861 | ||||||||
\(465\) | 8739.16 | 0.871546 | ||||||||
\(466\) | 12108.4 | 1.20367 | ||||||||
\(467\) | −11821.8 | −1.17141 | −0.585706 | − | 0.810523i | \(-0.699183\pi\) | ||||
−0.585706 | + | 0.810523i | \(0.699183\pi\) | |||||||
\(468\) | 9339.68 | 0.922493 | ||||||||
\(469\) | −18301.0 | −1.80184 | ||||||||
\(470\) | −977.399 | −0.0959235 | ||||||||
\(471\) | 19407.0 | 1.89857 | ||||||||
\(472\) | −2419.98 | −0.235993 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4613.00 | 0.447009 | ||||||||
\(475\) | −9121.62 | −0.881113 | ||||||||
\(476\) | −5252.90 | −0.505812 | ||||||||
\(477\) | −7137.51 | −0.685124 | ||||||||
\(478\) | −6273.20 | −0.600271 | ||||||||
\(479\) | −8659.94 | −0.826060 | −0.413030 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413030 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(480\) | −1311.05 | −0.124669 | ||||||||
\(481\) | −11184.3 | −1.06021 | ||||||||
\(482\) | 12998.5 | 1.22835 | ||||||||
\(483\) | −23909.0 | −2.25238 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3150.25 | −0.294939 | ||||||||
\(486\) | 10871.1 | 1.01466 | ||||||||
\(487\) | 7427.66 | 0.691128 | 0.345564 | − | 0.938395i | \(-0.387688\pi\) | ||||
0.345564 | + | 0.938395i | \(0.387688\pi\) | |||||||
\(488\) | 1194.24 | 0.110780 | ||||||||
\(489\) | 13758.2 | 1.27233 | ||||||||
\(490\) | −1596.63 | −0.147201 | ||||||||
\(491\) | −5543.89 | −0.509556 | −0.254778 | − | 0.967000i | \(-0.582002\pi\) | ||||
−0.254778 | + | 0.967000i | \(0.582002\pi\) | |||||||
\(492\) | 2510.07 | 0.230006 | ||||||||
\(493\) | −1210.57 | −0.110591 | ||||||||
\(494\) | −14637.5 | −1.33314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3412.87 | 0.308956 | ||||||||
\(497\) | 19911.9 | 1.79713 | ||||||||
\(498\) | 11580.2 | 1.04201 | ||||||||
\(499\) | 20412.0 | 1.83120 | 0.915599 | − | 0.402093i | \(-0.131717\pi\) | ||||
0.915599 | + | 0.402093i | \(0.131717\pi\) | |||||||
\(500\) | −4775.41 | −0.427125 | ||||||||
\(501\) | 2870.64 | 0.255990 | ||||||||
\(502\) | −11131.6 | −0.989694 | ||||||||
\(503\) | −182.742 | −0.0161989 | −0.00809946 | − | 0.999967i | \(-0.502578\pi\) | ||||
−0.00809946 | + | 0.999967i | \(0.502578\pi\) | |||||||
\(504\) | 5385.41 | 0.475963 | ||||||||
\(505\) | −765.540 | −0.0674576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28071.0 | 2.45893 | ||||||||
\(508\) | 4373.82 | 0.382002 | ||||||||
\(509\) | 4755.29 | 0.414095 | 0.207048 | − | 0.978331i | \(-0.433614\pi\) | ||||
0.207048 | + | 0.978331i | \(0.433614\pi\) | |||||||
\(510\) | −4858.13 | −0.421807 | ||||||||
\(511\) | 3056.53 | 0.264604 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2447.92 | 0.210679 | ||||||||
\(514\) | 12072.6 | 1.03599 | ||||||||
\(515\) | 4550.27 | 0.389337 | ||||||||
\(516\) | −4587.05 | −0.391344 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6449.03 | −0.547016 | ||||||||
\(519\) | 384.257 | 0.0324990 | ||||||||
\(520\) | −3323.90 | −0.280313 | ||||||||
\(521\) | −11731.1 | −0.986470 | −0.493235 | − | 0.869896i | \(-0.664186\pi\) | ||||
−0.493235 | + | 0.869896i | \(0.664186\pi\) | |||||||
\(522\) | 1241.10 | 0.104064 | ||||||||
\(523\) | −343.839 | −0.0287477 | −0.0143738 | − | 0.999897i | \(-0.504575\pi\) | ||||
−0.0143738 | + | 0.999897i | \(0.504575\pi\) | |||||||
\(524\) | −9864.65 | −0.822403 | ||||||||
\(525\) | 16067.4 | 1.33569 | ||||||||
\(526\) | 1416.88 | 0.117451 | ||||||||
\(527\) | 12646.4 | 1.04533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8134.66 | 0.668584 | ||||||||
\(530\) | 2540.17 | 0.208185 | ||||||||
\(531\) | 9193.49 | 0.751343 | ||||||||
\(532\) | −8440.19 | −0.687836 | ||||||||
\(533\) | 6363.77 | 0.517159 | ||||||||
\(534\) | 4743.93 | 0.384438 | ||||||||
\(535\) | −348.454 | −0.0281589 | ||||||||
\(536\) | −6609.89 | −0.532656 | ||||||||
\(537\) | 158.089 | 0.0127040 | ||||||||
\(538\) | 9619.41 | 0.770859 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 555.878 | 0.0442985 | ||||||||
\(541\) | −17243.8 | −1.37037 | −0.685183 | − | 0.728371i | \(-0.740278\pi\) | ||||
−0.685183 | + | 0.728371i | \(0.740278\pi\) | |||||||
\(542\) | 10481.8 | 0.830683 | ||||||||
\(543\) | −1334.49 | −0.105467 | ||||||||
\(544\) | −1897.23 | −0.149527 | ||||||||
\(545\) | 8431.45 | 0.662685 | ||||||||
\(546\) | 25783.3 | 2.02092 | ||||||||
\(547\) | −7643.21 | −0.597441 | −0.298720 | − | 0.954341i | \(-0.596560\pi\) | ||||
−0.298720 | + | 0.954341i | \(0.596560\pi\) | |||||||
\(548\) | −3893.14 | −0.303480 | ||||||||
\(549\) | −4536.89 | −0.352696 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1945.10 | −0.150388 | ||||||||
\(552\) | −8635.38 | −0.665844 | ||||||||
\(553\) | 6743.70 | 0.518574 | ||||||||
\(554\) | 10679.5 | 0.819004 | ||||||||
\(555\) | −5964.37 | −0.456168 | ||||||||
\(556\) | −5052.16 | −0.385358 | ||||||||
\(557\) | 26106.2 | 1.98591 | 0.992957 | − | 0.118471i | \(-0.0377994\pi\) | ||||
0.992957 | + | 0.118471i | \(0.0377994\pi\) | |||||||
\(558\) | −12965.5 | −0.983641 | ||||||||
\(559\) | −11629.5 | −0.879921 | ||||||||
\(560\) | −1916.62 | −0.144628 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6559.94 | 0.492374 | ||||||||
\(563\) | −18073.9 | −1.35297 | −0.676487 | − | 0.736455i | \(-0.736498\pi\) | ||||
−0.676487 | + | 0.736455i | \(0.736498\pi\) | |||||||
\(564\) | 2738.31 | 0.204439 | ||||||||
\(565\) | −12109.5 | −0.901682 | ||||||||
\(566\) | 9790.98 | 0.727112 | ||||||||
\(567\) | 13863.8 | 1.02685 | ||||||||
\(568\) | 7191.72 | 0.531264 | ||||||||
\(569\) | 7805.16 | 0.575060 | 0.287530 | − | 0.957772i | \(-0.407166\pi\) | ||||
0.287530 | + | 0.957772i | \(0.407166\pi\) | |||||||
\(570\) | −7805.89 | −0.573601 | ||||||||
\(571\) | −13039.6 | −0.955672 | −0.477836 | − | 0.878449i | \(-0.658579\pi\) | ||||
−0.477836 | + | 0.878449i | \(0.658579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8781.96 | −0.640264 | ||||||||
\(574\) | 3669.45 | 0.266829 | ||||||||
\(575\) | −13643.2 | −0.989496 | ||||||||
\(576\) | 1945.08 | 0.140703 | ||||||||
\(577\) | −9569.43 | −0.690434 | −0.345217 | − | 0.938523i | \(-0.612195\pi\) | ||||
−0.345217 | + | 0.938523i | \(0.612195\pi\) | |||||||
\(578\) | 2795.79 | 0.201193 | ||||||||
\(579\) | −9734.36 | −0.698698 | ||||||||
\(580\) | −441.697 | −0.0316215 | ||||||||
\(581\) | 16929.0 | 1.20883 | ||||||||
\(582\) | 8825.83 | 0.628595 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1103.95 | 0.0782220 | ||||||||
\(585\) | 12627.5 | 0.892448 | ||||||||
\(586\) | −13411.6 | −0.945440 | ||||||||
\(587\) | 9727.00 | 0.683946 | 0.341973 | − | 0.939710i | \(-0.388905\pi\) | ||||
0.341973 | + | 0.939710i | \(0.388905\pi\) | |||||||
\(588\) | 4473.16 | 0.313725 | ||||||||
\(589\) | 20319.9 | 1.42151 | ||||||||
\(590\) | −3271.87 | −0.228307 | ||||||||
\(591\) | −20341.3 | −1.41579 | ||||||||
\(592\) | −2329.24 | −0.161708 | ||||||||
\(593\) | 6926.77 | 0.479677 | 0.239838 | − | 0.970813i | \(-0.422906\pi\) | ||||
0.239838 | + | 0.970813i | \(0.422906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7102.06 | −0.489338 | ||||||||
\(596\) | −1957.36 | −0.134525 | ||||||||
\(597\) | −10102.6 | −0.692580 | ||||||||
\(598\) | −21893.2 | −1.49712 | ||||||||
\(599\) | −21984.7 | −1.49961 | −0.749807 | − | 0.661656i | \(-0.769854\pi\) | ||||
−0.749807 | + | 0.661656i | \(0.769854\pi\) | |||||||
\(600\) | 5803.17 | 0.394856 | ||||||||
\(601\) | −7363.27 | −0.499757 | −0.249878 | − | 0.968277i | \(-0.580391\pi\) | ||||
−0.249878 | + | 0.968277i | \(0.580391\pi\) | |||||||
\(602\) | −6705.76 | −0.453998 | ||||||||
\(603\) | 25110.9 | 1.69585 | ||||||||
\(604\) | 6831.10 | 0.460188 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2144.76 | 0.143771 | ||||||||
\(607\) | 10168.4 | 0.679938 | 0.339969 | − | 0.940437i | \(-0.389583\pi\) | ||||
0.339969 | + | 0.940437i | \(0.389583\pi\) | |||||||
\(608\) | −3048.40 | −0.203337 | ||||||||
\(609\) | 3426.22 | 0.227976 | ||||||||
\(610\) | 1614.64 | 0.107172 | ||||||||
\(611\) | 6942.41 | 0.459673 | ||||||||
\(612\) | 7207.55 | 0.476059 | ||||||||
\(613\) | 25084.5 | 1.65278 | 0.826389 | − | 0.563099i | \(-0.190391\pi\) | ||||
0.826389 | + | 0.563099i | \(0.190391\pi\) | |||||||
\(614\) | −19014.6 | −1.24978 | ||||||||
\(615\) | 3393.68 | 0.222515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26335.5 | −1.71836 | −0.859178 | − | 0.511677i | \(-0.829024\pi\) | ||||
−0.859178 | + | 0.511677i | \(0.829024\pi\) | |||||||
\(618\) | −12748.2 | −0.829784 | ||||||||
\(619\) | −24643.2 | −1.60015 | −0.800075 | − | 0.599901i | \(-0.795207\pi\) | ||||
−0.800075 | + | 0.599901i | \(0.795207\pi\) | |||||||
\(620\) | 4614.28 | 0.298894 | ||||||||
\(621\) | 3661.34 | 0.236594 | ||||||||
\(622\) | −11536.1 | −0.743661 | ||||||||
\(623\) | 6935.10 | 0.445986 | ||||||||
\(624\) | 9312.34 | 0.597423 | ||||||||
\(625\) | 5512.59 | 0.352806 | ||||||||
\(626\) | −11955.5 | −0.763319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10246.9 | 0.651108 | ||||||||
\(629\) | −8631.05 | −0.547126 | ||||||||
\(630\) | 7281.21 | 0.460461 | ||||||||
\(631\) | 7455.32 | 0.470351 | 0.235176 | − | 0.971953i | \(-0.424433\pi\) | ||||
0.235176 | + | 0.971953i | \(0.424433\pi\) | |||||||
\(632\) | 2435.67 | 0.153300 | ||||||||
\(633\) | −12334.6 | −0.774496 | ||||||||
\(634\) | −10463.9 | −0.655478 | ||||||||
\(635\) | 5913.52 | 0.369560 | ||||||||
\(636\) | −7116.62 | −0.443699 | ||||||||
\(637\) | 11340.8 | 0.705397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27321.3 | −1.69141 | ||||||||
\(640\) | −692.237 | −0.0427548 | ||||||||
\(641\) | −2778.67 | −0.171218 | −0.0856090 | − | 0.996329i | \(-0.527284\pi\) | ||||
−0.0856090 | + | 0.996329i | \(0.527284\pi\) | |||||||
\(642\) | 976.240 | 0.0600142 | ||||||||
\(643\) | 7557.71 | 0.463526 | 0.231763 | − | 0.972772i | \(-0.425551\pi\) | ||||
0.231763 | + | 0.972772i | \(0.425551\pi\) | |||||||
\(644\) | −12624.0 | −0.772444 | ||||||||
\(645\) | −6201.81 | −0.378598 | ||||||||
\(646\) | −11295.9 | −0.687975 | ||||||||
\(647\) | −27430.7 | −1.66679 | −0.833394 | − | 0.552679i | \(-0.813605\pi\) | ||||
−0.833394 | + | 0.552679i | \(0.813605\pi\) | |||||||
\(648\) | 5007.30 | 0.303557 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 14712.7 | 0.887817 | ||||||||
\(651\) | −35792.7 | −2.15488 | ||||||||
\(652\) | 7264.35 | 0.436340 | ||||||||
\(653\) | 284.728 | 0.0170632 | 0.00853160 | − | 0.999964i | \(-0.497284\pi\) | ||||
0.00853160 | + | 0.999964i | \(0.497284\pi\) | |||||||
\(654\) | −23621.8 | −1.41236 | ||||||||
\(655\) | −13337.2 | −0.795617 | ||||||||
\(656\) | 1325.32 | 0.0788797 | ||||||||
\(657\) | −4193.89 | −0.249040 | ||||||||
\(658\) | 4003.11 | 0.237169 | ||||||||
\(659\) | 20747.0 | 1.22639 | 0.613193 | − | 0.789933i | \(-0.289885\pi\) | ||||
0.613193 | + | 0.789933i | \(0.289885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18908.8 | −1.11266 | −0.556328 | − | 0.830963i | \(-0.687790\pi\) | ||||
−0.556328 | + | 0.830963i | \(0.687790\pi\) | |||||||
\(662\) | 7927.44 | 0.465421 | ||||||||
\(663\) | 34507.1 | 2.02133 | ||||||||
\(664\) | 6114.35 | 0.357354 | ||||||||
\(665\) | −11411.4 | −0.665434 | ||||||||
\(666\) | 8848.77 | 0.514839 | ||||||||
\(667\) | −2909.28 | −0.168887 | ||||||||
\(668\) | 1515.70 | 0.0877907 | ||||||||
\(669\) | −19910.5 | −1.15065 | ||||||||
\(670\) | −8936.74 | −0.515308 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5369.65 | 0.308242 | ||||||||
\(673\) | 29865.9 | 1.71062 | 0.855309 | − | 0.518118i | \(-0.173367\pi\) | ||||
0.855309 | + | 0.518118i | \(0.173367\pi\) | |||||||
\(674\) | −10213.2 | −0.583676 | ||||||||
\(675\) | −2460.51 | −0.140304 | ||||||||
\(676\) | 14821.5 | 0.843281 | ||||||||
\(677\) | −17280.7 | −0.981024 | −0.490512 | − | 0.871435i | \(-0.663190\pi\) | ||||
−0.490512 | + | 0.871435i | \(0.663190\pi\) | |||||||
\(678\) | 33926.3 | 1.92173 | ||||||||
\(679\) | 12902.4 | 0.729232 | ||||||||
\(680\) | −2565.10 | −0.144657 | ||||||||
\(681\) | 12898.1 | 0.725782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25104.0 | 1.40641 | 0.703204 | − | 0.710988i | \(-0.251752\pi\) | ||||
0.703204 | + | 0.710988i | \(0.251752\pi\) | |||||||
\(684\) | 11580.9 | 0.647376 | ||||||||
\(685\) | −5263.63 | −0.293595 | ||||||||
\(686\) | −8655.51 | −0.481733 | ||||||||
\(687\) | 40878.3 | 2.27017 | ||||||||
\(688\) | −2421.97 | −0.134210 | ||||||||
\(689\) | −18042.7 | −0.997638 | ||||||||
\(690\) | −11675.2 | −0.644158 | ||||||||
\(691\) | −26163.8 | −1.44040 | −0.720201 | − | 0.693765i | \(-0.755950\pi\) | ||||
−0.720201 | + | 0.693765i | \(0.755950\pi\) | |||||||
\(692\) | 202.888 | 0.0111454 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15091.5 | −0.825455 | ||||||||
\(695\) | −6830.64 | −0.372807 | ||||||||
\(696\) | 1237.47 | 0.0673940 | ||||||||
\(697\) | 4911.00 | 0.266883 | ||||||||
\(698\) | 6513.42 | 0.353205 | ||||||||
\(699\) | −45865.0 | −2.48179 | ||||||||
\(700\) | 8483.60 | 0.458071 | ||||||||
\(701\) | −1519.45 | −0.0818669 | −0.0409334 | − | 0.999162i | \(-0.513033\pi\) | ||||
−0.0409334 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(702\) | −3948.37 | −0.212282 | ||||||||
\(703\) | −13868.1 | −0.744018 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3702.26 | 0.197781 | ||||||||
\(706\) | 13013.7 | 0.693733 | ||||||||
\(707\) | 3135.40 | 0.166788 | ||||||||
\(708\) | 9166.58 | 0.486583 | ||||||||
\(709\) | −21733.9 | −1.15125 | −0.575623 | − | 0.817715i | \(-0.695240\pi\) | ||||
−0.575623 | + | 0.817715i | \(0.695240\pi\) | |||||||
\(710\) | 9723.39 | 0.513961 | ||||||||
\(711\) | −9253.09 | −0.488070 | ||||||||
\(712\) | 2504.80 | 0.131842 | ||||||||
\(713\) | 30392.4 | 1.59636 | ||||||||
\(714\) | 19897.3 | 1.04291 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 83.4712 | 0.00435679 | ||||||||
\(717\) | 23762.1 | 1.23767 | ||||||||
\(718\) | −8132.42 | −0.422701 | ||||||||
\(719\) | −14071.8 | −0.729890 | −0.364945 | − | 0.931029i | \(-0.618912\pi\) | ||||
−0.364945 | + | 0.931029i | \(0.618912\pi\) | |||||||
\(720\) | 2629.80 | 0.136121 | ||||||||
\(721\) | −18636.4 | −0.962630 | ||||||||
\(722\) | −4431.91 | −0.228447 | ||||||||
\(723\) | −49236.7 | −2.53269 | ||||||||
\(724\) | −704.613 | −0.0361695 | ||||||||
\(725\) | 1955.10 | 0.100153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10409.2 | 0.531027 | 0.265513 | − | 0.964107i | \(-0.414459\pi\) | ||||
0.265513 | + | 0.964107i | \(0.414459\pi\) | |||||||
\(728\) | 13613.6 | 0.693069 | ||||||||
\(729\) | −24278.8 | −1.23349 | ||||||||
\(730\) | 1492.56 | 0.0756744 | ||||||||
\(731\) | −8974.65 | −0.454089 | ||||||||
\(732\) | −4523.61 | −0.228412 | ||||||||
\(733\) | −19394.9 | −0.977307 | −0.488653 | − | 0.872478i | \(-0.662512\pi\) | ||||
−0.488653 | + | 0.872478i | \(0.662512\pi\) | |||||||
\(734\) | 2784.55 | 0.140027 | ||||||||
\(735\) | 6047.83 | 0.303507 | ||||||||
\(736\) | −4559.48 | −0.228349 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5034.89 | −0.251134 | ||||||||
\(739\) | −6672.24 | −0.332128 | −0.166064 | − | 0.986115i | \(-0.553106\pi\) | ||||
−0.166064 | + | 0.986115i | \(0.553106\pi\) | |||||||
\(740\) | −3149.19 | −0.156441 | ||||||||
\(741\) | 55444.8 | 2.74874 | ||||||||
\(742\) | −10403.7 | −0.514734 | ||||||||
\(743\) | 6565.18 | 0.324163 | 0.162082 | − | 0.986777i | \(-0.448179\pi\) | ||||
0.162082 | + | 0.986777i | \(0.448179\pi\) | |||||||
\(744\) | −12927.5 | −0.637023 | ||||||||
\(745\) | −2646.40 | −0.130143 | ||||||||
\(746\) | −18880.6 | −0.926633 | ||||||||
\(747\) | −23228.4 | −1.13773 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1427.16 | 0.0696223 | ||||||||
\(750\) | 18088.6 | 0.880671 | ||||||||
\(751\) | 18938.7 | 0.920216 | 0.460108 | − | 0.887863i | \(-0.347811\pi\) | ||||
0.460108 | + | 0.887863i | \(0.347811\pi\) | |||||||
\(752\) | 1445.83 | 0.0701117 | ||||||||
\(753\) | 42165.0 | 2.04061 | ||||||||
\(754\) | 3137.35 | 0.151533 | ||||||||
\(755\) | 9235.82 | 0.445200 | ||||||||
\(756\) | −2276.70 | −0.109527 | ||||||||
\(757\) | −10958.4 | −0.526141 | −0.263070 | − | 0.964777i | \(-0.584735\pi\) | ||||
−0.263070 | + | 0.964777i | \(0.584735\pi\) | |||||||
\(758\) | −2580.70 | −0.123661 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4121.52 | −0.196715 | ||||||||
\(761\) | −35442.2 | −1.68828 | −0.844138 | − | 0.536126i | \(-0.819887\pi\) | ||||
−0.844138 | + | 0.536126i | \(0.819887\pi\) | |||||||
\(762\) | −16567.5 | −0.787633 | ||||||||
\(763\) | −34532.5 | −1.63848 | ||||||||
\(764\) | −4636.88 | −0.219576 | ||||||||
\(765\) | 9744.79 | 0.460554 | ||||||||
\(766\) | 11305.8 | 0.533283 | ||||||||
\(767\) | 23240.0 | 1.09406 | ||||||||
\(768\) | 1939.39 | 0.0911221 | ||||||||
\(769\) | 4444.21 | 0.208404 | 0.104202 | − | 0.994556i | \(-0.466771\pi\) | ||||
0.104202 | + | 0.994556i | \(0.466771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45729.5 | −2.13607 | ||||||||
\(772\) | −5139.75 | −0.239616 | ||||||||
\(773\) | 10160.2 | 0.472750 | 0.236375 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236375 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(774\) | 9201.03 | 0.427292 | ||||||||
\(775\) | −20424.4 | −0.946666 | ||||||||
\(776\) | 4660.04 | 0.215575 | ||||||||
\(777\) | 24428.1 | 1.12787 | ||||||||
\(778\) | 25676.0 | 1.18320 | ||||||||
\(779\) | 7890.84 | 0.362925 | ||||||||
\(780\) | 12590.5 | 0.577965 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16895.3 | −0.772600 | ||||||||
\(783\) | −524.680 | −0.0239470 | ||||||||
\(784\) | 2361.83 | 0.107591 | ||||||||
\(785\) | 13854.1 | 0.629902 | ||||||||
\(786\) | 37366.0 | 1.69568 | ||||||||
\(787\) | −18270.1 | −0.827520 | −0.413760 | − | 0.910386i | \(-0.635785\pi\) | ||||
−0.413760 | + | 0.910386i | \(0.635785\pi\) | |||||||
\(788\) | −10740.2 | −0.485539 | ||||||||
\(789\) | −5366.98 | −0.242167 | ||||||||
\(790\) | 3293.09 | 0.148307 | ||||||||
\(791\) | 49596.6 | 2.22939 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11468.7 | −0.513575 | ||||||||
\(794\) | −15382.5 | −0.687538 | ||||||||
\(795\) | −9621.85 | −0.429248 | ||||||||
\(796\) | −5334.16 | −0.237518 | ||||||||
\(797\) | 17984.0 | 0.799279 | 0.399639 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399639 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(798\) | 31970.4 | 1.41822 | ||||||||
\(799\) | 5357.55 | 0.237217 | ||||||||
\(800\) | 3064.08 | 0.135414 | ||||||||
\(801\) | −9515.71 | −0.419752 | ||||||||
\(802\) | −15572.3 | −0.685634 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 25037.4 | 1.09826 | ||||||||
\(805\) | −17067.9 | −0.747286 | ||||||||
\(806\) | −32775.0 | −1.43232 | ||||||||
\(807\) | −36437.1 | −1.58940 | ||||||||
\(808\) | 1132.43 | 0.0493056 | ||||||||
\(809\) | 5144.24 | 0.223562 | 0.111781 | − | 0.993733i | \(-0.464344\pi\) | ||||
0.111781 | + | 0.993733i | \(0.464344\pi\) | |||||||
\(810\) | 6769.99 | 0.293671 | ||||||||
\(811\) | −8255.99 | −0.357469 | −0.178734 | − | 0.983897i | \(-0.557200\pi\) | ||||
−0.178734 | + | 0.983897i | \(0.557200\pi\) | |||||||
\(812\) | 1809.05 | 0.0781836 | ||||||||
\(813\) | −39703.6 | −1.71275 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9821.58 | 0.422129 | ||||||||
\(816\) | 7186.46 | 0.308304 | ||||||||
\(817\) | −14420.2 | −0.617500 | ||||||||
\(818\) | 17719.8 | 0.757405 | ||||||||
\(819\) | −51718.1 | −2.20656 | ||||||||
\(820\) | 1791.87 | 0.0763106 | ||||||||
\(821\) | 247.250 | 0.0105105 | 0.00525523 | − | 0.999986i | \(-0.498327\pi\) | ||||
0.00525523 | + | 0.999986i | \(0.498327\pi\) | |||||||
\(822\) | 14746.7 | 0.625732 | ||||||||
\(823\) | 11794.8 | 0.499564 | 0.249782 | − | 0.968302i | \(-0.419641\pi\) | ||||
0.249782 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(824\) | −6731.04 | −0.284571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13400.5 | 0.564484 | ||||||||
\(827\) | −2771.66 | −0.116542 | −0.0582709 | − | 0.998301i | \(-0.518559\pi\) | ||||
−0.0582709 | + | 0.998301i | \(0.518559\pi\) | |||||||
\(828\) | 17321.5 | 0.727007 | ||||||||
\(829\) | −27298.0 | −1.14367 | −0.571834 | − | 0.820370i | \(-0.693768\pi\) | ||||
−0.571834 | + | 0.820370i | \(0.693768\pi\) | |||||||
\(830\) | 8266.75 | 0.345715 | ||||||||
\(831\) | −40452.6 | −1.68867 | ||||||||
\(832\) | 4916.92 | 0.204884 | ||||||||
\(833\) | 8751.82 | 0.364025 | ||||||||
\(834\) | 19136.9 | 0.794554 | ||||||||
\(835\) | 2049.26 | 0.0849314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5481.18 | 0.226353 | ||||||||
\(838\) | −18938.2 | −0.780678 | ||||||||
\(839\) | 8754.74 | 0.360247 | 0.180123 | − | 0.983644i | \(-0.442350\pi\) | ||||
0.180123 | + | 0.983644i | \(0.442350\pi\) | |||||||
\(840\) | 7259.90 | 0.298203 | ||||||||
\(841\) | −23972.1 | −0.982906 | ||||||||
\(842\) | −10355.9 | −0.423857 | ||||||||
\(843\) | −24848.2 | −1.01521 | ||||||||
\(844\) | −6512.67 | −0.265611 | ||||||||
\(845\) | 20039.1 | 0.815816 | ||||||||
\(846\) | −5492.70 | −0.223218 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3757.58 | −0.152165 | ||||||||
\(849\) | −37087.0 | −1.49920 | ||||||||
\(850\) | 11354.0 | 0.458164 | ||||||||
\(851\) | −20742.5 | −0.835537 | ||||||||
\(852\) | −27241.3 | −1.09539 | ||||||||
\(853\) | 41184.3 | 1.65313 | 0.826566 | − | 0.562839i | \(-0.190291\pi\) | ||||
0.826566 | + | 0.562839i | \(0.190291\pi\) | |||||||
\(854\) | −6613.03 | −0.264980 | ||||||||
\(855\) | 15657.6 | 0.626291 | ||||||||
\(856\) | 515.455 | 0.0205817 | ||||||||
\(857\) | −18020.0 | −0.718265 | −0.359132 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359132 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6159.11 | 0.244640 | 0.122320 | − | 0.992491i | \(-0.460967\pi\) | ||||
0.122320 | + | 0.992491i | \(0.460967\pi\) | |||||||
\(860\) | −3274.56 | −0.129839 | ||||||||
\(861\) | −13899.4 | −0.550164 | ||||||||
\(862\) | −20927.1 | −0.826891 | ||||||||
\(863\) | 28932.6 | 1.14122 | 0.570612 | − | 0.821220i | \(-0.306706\pi\) | ||||
0.570612 | + | 0.821220i | \(0.306706\pi\) | |||||||
\(864\) | −822.289 | −0.0323783 | ||||||||
\(865\) | 274.309 | 0.0107824 | ||||||||
\(866\) | −31676.5 | −1.24297 | ||||||||
\(867\) | −10590.1 | −0.414831 | ||||||||
\(868\) | −18898.6 | −0.739009 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1673.09 | 0.0651990 | ||||||||
\(871\) | 63477.2 | 2.46940 | ||||||||
\(872\) | −12472.3 | −0.484365 | ||||||||
\(873\) | −17703.5 | −0.686337 | ||||||||
\(874\) | −27146.8 | −1.05063 | ||||||||
\(875\) | 26443.6 | 1.02166 | ||||||||
\(876\) | −4181.61 | −0.161283 | ||||||||
\(877\) | −45152.6 | −1.73854 | −0.869268 | − | 0.494341i | \(-0.835409\pi\) | ||||
−0.869268 | + | 0.494341i | \(0.835409\pi\) | |||||||
\(878\) | 9649.40 | 0.370902 | ||||||||
\(879\) | 50801.4 | 1.94936 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22263.5 | 0.851391 | 0.425696 | − | 0.904866i | \(-0.360029\pi\) | ||||
0.425696 | + | 0.904866i | \(0.360029\pi\) | |||||||
\(882\) | −8972.58 | −0.342543 | ||||||||
\(883\) | 38215.5 | 1.45646 | 0.728230 | − | 0.685332i | \(-0.240343\pi\) | ||||
0.728230 | + | 0.685332i | \(0.240343\pi\) | |||||||
\(884\) | 18219.8 | 0.693209 | ||||||||
\(885\) | 12393.4 | 0.470736 | ||||||||
\(886\) | −7166.77 | −0.271752 | ||||||||
\(887\) | 48160.6 | 1.82308 | 0.911541 | − | 0.411208i | \(-0.134893\pi\) | ||||
0.911541 | + | 0.411208i | \(0.134893\pi\) | |||||||
\(888\) | 8822.87 | 0.333419 | ||||||||
\(889\) | −24219.8 | −0.913731 | ||||||||
\(890\) | 3386.55 | 0.127548 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10512.8 | −0.394612 | ||||||||
\(893\) | 8608.34 | 0.322583 | ||||||||
\(894\) | 7414.23 | 0.277370 | ||||||||
\(895\) | 112.855 | 0.00421490 | ||||||||
\(896\) | 2835.18 | 0.105711 | ||||||||
\(897\) | 82928.7 | 3.08685 | ||||||||
\(898\) | 15592.0 | 0.579411 | ||||||||
\(899\) | −4355.31 | −0.161577 | ||||||||
\(900\) | −11640.4 | −0.431126 | ||||||||
\(901\) | −13923.8 | −0.514838 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25400.6 | 0.936078 | ||||||||
\(904\) | 17913.1 | 0.659051 | ||||||||
\(905\) | −952.655 | −0.0349915 | ||||||||
\(906\) | −25875.3 | −0.948842 | ||||||||
\(907\) | 8509.88 | 0.311539 | 0.155770 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155770 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(908\) | 6810.22 | 0.248904 | ||||||||
\(909\) | −4302.11 | −0.156977 | ||||||||
\(910\) | 18406.0 | 0.670496 | ||||||||
\(911\) | 11283.5 | 0.410360 | 0.205180 | − | 0.978724i | \(-0.434222\pi\) | ||||
0.205180 | + | 0.978724i | \(0.434222\pi\) | |||||||
\(912\) | 11547.0 | 0.419252 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6696.04 | −0.242325 | ||||||||
\(915\) | −6116.04 | −0.220973 | ||||||||
\(916\) | 21583.8 | 0.778546 | ||||||||
\(917\) | 54625.0 | 1.96715 | ||||||||
\(918\) | −3047.01 | −0.109549 | ||||||||
\(919\) | 26556.9 | 0.953245 | 0.476622 | − | 0.879108i | \(-0.341861\pi\) | ||||
0.476622 | + | 0.879108i | \(0.341861\pi\) | |||||||
\(920\) | −6164.54 | −0.220912 | ||||||||
\(921\) | 72024.9 | 2.57687 | ||||||||
\(922\) | −14343.9 | −0.512355 | ||||||||
\(923\) | −69064.7 | −2.46294 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13939.4 | 0.495486 | ||||||||
\(926\) | −8069.49 | −0.286371 | ||||||||
\(927\) | 25571.2 | 0.906006 | ||||||||
\(928\) | 653.386 | 0.0231125 | ||||||||
\(929\) | −47913.1 | −1.69212 | −0.846059 | − | 0.533089i | \(-0.821031\pi\) | ||||
−0.846059 | + | 0.533089i | \(0.821031\pi\) | |||||||
\(930\) | −17478.3 | −0.616276 | ||||||||
\(931\) | 14062.1 | 0.495025 | ||||||||
\(932\) | −24216.7 | −0.851122 | ||||||||
\(933\) | 43697.5 | 1.53332 | ||||||||
\(934\) | 23643.7 | 0.828314 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18679.4 | −0.652301 | ||||||||
\(937\) | 5718.95 | 0.199391 | 0.0996957 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996957 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(938\) | 36602.0 | 1.27409 | ||||||||
\(939\) | 45285.9 | 1.57386 | ||||||||
\(940\) | 1954.80 | 0.0678281 | ||||||||
\(941\) | −11105.6 | −0.384732 | −0.192366 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192366 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(942\) | −38814.0 | −1.34249 | ||||||||
\(943\) | 11802.3 | 0.407567 | ||||||||
\(944\) | 4839.96 | 0.166872 | ||||||||
\(945\) | −3078.15 | −0.105960 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39759.1 | 1.36430 | 0.682152 | − | 0.731210i | \(-0.261044\pi\) | ||||
0.682152 | + | 0.731210i | \(0.261044\pi\) | |||||||
\(948\) | −9226.01 | −0.316083 | ||||||||
\(949\) | −10601.6 | −0.362637 | ||||||||
\(950\) | 18243.2 | 0.623041 | ||||||||
\(951\) | 39635.8 | 1.35150 | ||||||||
\(952\) | 10505.8 | 0.357663 | ||||||||
\(953\) | −15932.0 | −0.541539 | −0.270770 | − | 0.962644i | \(-0.587278\pi\) | ||||
−0.270770 | + | 0.962644i | \(0.587278\pi\) | |||||||
\(954\) | 14275.0 | 0.484456 | ||||||||
\(955\) | −6269.18 | −0.212425 | ||||||||
\(956\) | 12546.4 | 0.424456 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17319.9 | 0.584113 | ||||||||
\(959\) | 21558.1 | 0.725910 | ||||||||
\(960\) | 2622.11 | 0.0881543 | ||||||||
\(961\) | 15707.7 | 0.527262 | ||||||||
\(962\) | 22368.6 | 0.749679 | ||||||||
\(963\) | −1958.21 | −0.0655270 | ||||||||
\(964\) | −25997.0 | −0.868577 | ||||||||
\(965\) | −6949.07 | −0.231812 | ||||||||
\(966\) | 47818.0 | 1.59267 | ||||||||
\(967\) | 14952.9 | 0.497264 | 0.248632 | − | 0.968598i | \(-0.420019\pi\) | ||||
0.248632 | + | 0.968598i | \(0.420019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42787.5 | 1.41851 | ||||||||
\(970\) | 6300.50 | 0.208553 | ||||||||
\(971\) | 27937.3 | 0.923327 | 0.461663 | − | 0.887055i | \(-0.347253\pi\) | ||||
0.461663 | + | 0.887055i | \(0.347253\pi\) | |||||||
\(972\) | −21742.2 | −0.717472 | ||||||||
\(973\) | 27976.1 | 0.921760 | ||||||||
\(974\) | −14855.3 | −0.488701 | ||||||||
\(975\) | −55730.0 | −1.83055 | ||||||||
\(976\) | −2388.47 | −0.0783331 | ||||||||
\(977\) | 33359.2 | 1.09238 | 0.546191 | − | 0.837661i | \(-0.316077\pi\) | ||||
0.546191 | + | 0.837661i | \(0.316077\pi\) | |||||||
\(978\) | −27516.4 | −0.899671 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3193.26 | 0.104087 | ||||||||
\(981\) | 47382.3 | 1.54210 | ||||||||
\(982\) | 11087.8 | 0.360311 | ||||||||
\(983\) | 12350.1 | 0.400718 | 0.200359 | − | 0.979723i | \(-0.435789\pi\) | ||||
0.200359 | + | 0.979723i | \(0.435789\pi\) | |||||||
\(984\) | −5020.15 | −0.162639 | ||||||||
\(985\) | −14521.1 | −0.469725 | ||||||||
\(986\) | 2421.13 | 0.0781994 | ||||||||
\(987\) | −15163.3 | −0.489009 | ||||||||
\(988\) | 29274.9 | 0.942671 | ||||||||
\(989\) | −21568.2 | −0.693457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30154.0 | −0.966571 | −0.483286 | − | 0.875463i | \(-0.660557\pi\) | ||||
−0.483286 | + | 0.875463i | \(0.660557\pi\) | |||||||
\(992\) | −6825.73 | −0.218465 | ||||||||
\(993\) | −30028.1 | −0.959632 | ||||||||
\(994\) | −39823.8 | −1.27076 | ||||||||
\(995\) | −7211.91 | −0.229782 | ||||||||
\(996\) | −23160.4 | −0.736812 | ||||||||
\(997\) | 2093.09 | 0.0664884 | 0.0332442 | − | 0.999447i | \(-0.489416\pi\) | ||||
0.0332442 | + | 0.999447i | \(0.489416\pi\) | |||||||
\(998\) | −40824.0 | −1.29485 | ||||||||
\(999\) | −3740.84 | −0.118473 |
(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 | 242.4.a.n.1.3 | 4 | ||
3.2 | odd | 2 | 2178.4.a.by.1.3 | 4 | |||
4.3 | odd | 2 | 1936.4.a.bn.1.2 | 4 | |||
11.2 | odd | 10 | 242.4.c.n.81.2 | 8 | |||
11.3 | even | 5 | 22.4.c.b.9.1 | yes | 8 | ||
11.4 | even | 5 | 22.4.c.b.5.1 | ✓ | 8 | ||
11.5 | even | 5 | 242.4.c.r.3.2 | 8 | |||
11.6 | odd | 10 | 242.4.c.n.3.2 | 8 | |||
11.7 | odd | 10 | 242.4.c.q.27.1 | 8 | |||
11.8 | odd | 10 | 242.4.c.q.9.1 | 8 | |||
11.9 | even | 5 | 242.4.c.r.81.2 | 8 | |||
11.10 | odd | 2 | 242.4.a.o.1.3 | 4 | |||
33.14 | odd | 10 | 198.4.f.d.163.2 | 8 | |||
33.26 | odd | 10 | 198.4.f.d.181.2 | 8 | |||
33.32 | even | 2 | 2178.4.a.bt.1.3 | 4 | |||
44.3 | odd | 10 | 176.4.m.b.97.2 | 8 | |||
44.15 | odd | 10 | 176.4.m.b.49.2 | 8 | |||
44.43 | even | 2 | 1936.4.a.bm.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.5.1 | ✓ | 8 | 11.4 | even | 5 | ||
22.4.c.b.9.1 | yes | 8 | 11.3 | even | 5 | ||
176.4.m.b.49.2 | 8 | 44.15 | odd | 10 | |||
176.4.m.b.97.2 | 8 | 44.3 | odd | 10 | |||
198.4.f.d.163.2 | 8 | 33.14 | odd | 10 | |||
198.4.f.d.181.2 | 8 | 33.26 | odd | 10 | |||
242.4.a.n.1.3 | 4 | 1.1 | even | 1 | trivial | ||
242.4.a.o.1.3 | 4 | 11.10 | odd | 2 | |||
242.4.c.n.3.2 | 8 | 11.6 | odd | 10 | |||
242.4.c.n.81.2 | 8 | 11.2 | odd | 10 | |||
242.4.c.q.9.1 | 8 | 11.8 | odd | 10 | |||
242.4.c.q.27.1 | 8 | 11.7 | odd | 10 | |||
242.4.c.r.3.2 | 8 | 11.5 | even | 5 | |||
242.4.c.r.81.2 | 8 | 11.9 | even | 5 | |||
1936.4.a.bm.1.2 | 4 | 44.43 | even | 2 | |||
1936.4.a.bn.1.2 | 4 | 4.3 | odd | 2 | |||
2178.4.a.bt.1.3 | 4 | 33.32 | even | 2 | |||
2178.4.a.by.1.3 | 4 | 3.2 | odd | 2 |