Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.42 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.78319 | 0.984008 | 0.492004 | − | 0.870593i | \(-0.336265\pi\) | ||||
0.492004 | + | 0.870593i | \(0.336265\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.253830 | −0.0317288 | ||||||||
\(5\) | −19.2360 | −1.72052 | −0.860260 | − | 0.509855i | \(-0.829699\pi\) | ||||
−0.860260 | + | 0.509855i | \(0.829699\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.5534 | 1.48775 | 0.743873 | − | 0.668321i | \(-0.232987\pi\) | ||||
0.743873 | + | 0.668321i | \(0.232987\pi\) | |||||||
\(8\) | −22.9720 | −1.01523 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −53.5375 | −1.69301 | ||||||||
\(11\) | −32.2259 | −0.883317 | −0.441658 | − | 0.897183i | \(-0.645610\pi\) | ||||
−0.441658 | + | 0.897183i | \(0.645610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.3407 | 0.220615 | 0.110307 | − | 0.993898i | \(-0.464816\pi\) | ||||
0.110307 | + | 0.993898i | \(0.464816\pi\) | |||||||
\(14\) | 76.6866 | 1.46395 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −61.9049 | −0.967264 | ||||||||
\(17\) | −38.8792 | −0.554682 | −0.277341 | − | 0.960771i | \(-0.589453\pi\) | ||||
−0.277341 | + | 0.960771i | \(0.589453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 137.845 | 1.66442 | 0.832208 | − | 0.554463i | \(-0.187076\pi\) | ||||
0.832208 | + | 0.554463i | \(0.187076\pi\) | |||||||
\(20\) | 4.88268 | 0.0545901 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −89.6910 | −0.869191 | ||||||||
\(23\) | 158.387 | 1.43592 | 0.717958 | − | 0.696087i | \(-0.245077\pi\) | ||||
0.717958 | + | 0.696087i | \(0.245077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 245.024 | 1.96019 | ||||||||
\(26\) | 28.7802 | 0.217087 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.99390 | −0.0472044 | ||||||||
\(29\) | 30.8395 | 0.197474 | 0.0987372 | − | 0.995114i | \(-0.468520\pi\) | ||||
0.0987372 | + | 0.995114i | \(0.468520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.0179 | 0.202884 | 0.101442 | − | 0.994841i | \(-0.467654\pi\) | ||||
0.101442 | + | 0.994841i | \(0.467654\pi\) | |||||||
\(32\) | 11.4827 | 0.0634334 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −108.208 | −0.545812 | ||||||||
\(35\) | −530.018 | −2.55970 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 105.071 | 0.466855 | 0.233427 | − | 0.972374i | \(-0.425006\pi\) | ||||
0.233427 | + | 0.972374i | \(0.425006\pi\) | |||||||
\(38\) | 383.651 | 1.63780 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 441.890 | 1.74672 | ||||||||
\(41\) | −295.652 | −1.12617 | −0.563086 | − | 0.826398i | \(-0.690386\pi\) | ||||
−0.563086 | + | 0.826398i | \(0.690386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −311.117 | −1.10337 | −0.551686 | − | 0.834052i | \(-0.686015\pi\) | ||||
−0.551686 | + | 0.834052i | \(0.686015\pi\) | |||||||
\(44\) | 8.17992 | 0.0280266 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 440.823 | 1.41295 | ||||||||
\(47\) | 122.518 | 0.380236 | 0.190118 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190118 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 416.192 | 1.21339 | ||||||||
\(50\) | 681.949 | 1.92884 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.62478 | −0.00699984 | ||||||||
\(53\) | −700.716 | −1.81605 | −0.908025 | − | 0.418915i | \(-0.862410\pi\) | ||||
−0.908025 | + | 0.418915i | \(0.862410\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 619.898 | 1.51977 | ||||||||
\(56\) | −632.958 | −1.51040 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 85.8324 | 0.194316 | ||||||||
\(59\) | 548.102 | 1.20944 | 0.604718 | − | 0.796439i | \(-0.293286\pi\) | ||||
0.604718 | + | 0.796439i | \(0.293286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 206.571 | 0.433586 | 0.216793 | − | 0.976218i | \(-0.430440\pi\) | ||||
0.216793 | + | 0.976218i | \(0.430440\pi\) | |||||||
\(62\) | 97.4616 | 0.199639 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 527.198 | 1.02968 | ||||||||
\(65\) | −198.914 | −0.379573 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 352.913 | 0.643511 | 0.321755 | − | 0.946823i | \(-0.395727\pi\) | ||||
0.321755 | + | 0.946823i | \(0.395727\pi\) | |||||||
\(68\) | 9.86873 | 0.0175994 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1475.14 | −2.51876 | ||||||||
\(71\) | −759.373 | −1.26931 | −0.634655 | − | 0.772796i | \(-0.718858\pi\) | ||||
−0.634655 | + | 0.772796i | \(0.718858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −587.570 | −0.942054 | −0.471027 | − | 0.882119i | \(-0.656116\pi\) | ||||
−0.471027 | + | 0.882119i | \(0.656116\pi\) | |||||||
\(74\) | 292.434 | 0.459389 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34.9894 | −0.0528099 | ||||||||
\(77\) | −887.935 | −1.31415 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −149.398 | −0.212767 | −0.106384 | − | 0.994325i | \(-0.533927\pi\) | ||||
−0.106384 | + | 0.994325i | \(0.533927\pi\) | |||||||
\(80\) | 1190.80 | 1.66420 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −822.857 | −1.10816 | ||||||||
\(83\) | −1024.10 | −1.35434 | −0.677168 | − | 0.735829i | \(-0.736793\pi\) | ||||
−0.677168 | + | 0.735829i | \(0.736793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 747.881 | 0.954343 | ||||||||
\(86\) | −865.900 | −1.08573 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 740.295 | 0.896769 | ||||||||
\(89\) | −1045.70 | −1.24544 | −0.622718 | − | 0.782447i | \(-0.713971\pi\) | ||||
−0.622718 | + | 0.782447i | \(0.713971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 284.922 | 0.328219 | ||||||||
\(92\) | −40.2035 | −0.0455599 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 340.991 | 0.374155 | ||||||||
\(95\) | −2651.60 | −2.86366 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1808.66 | −1.89321 | −0.946607 | − | 0.322390i | \(-0.895514\pi\) | ||||
−0.946607 | + | 0.322390i | \(0.895514\pi\) | |||||||
\(98\) | 1158.34 | 1.19398 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −62.1945 | −0.0621945 | ||||||||
\(101\) | −940.319 | −0.926388 | −0.463194 | − | 0.886257i | \(-0.653297\pi\) | ||||
−0.463194 | + | 0.886257i | \(0.653297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −105.854 | −0.101263 | −0.0506314 | − | 0.998717i | \(-0.516123\pi\) | ||||
−0.0506314 | + | 0.998717i | \(0.516123\pi\) | |||||||
\(104\) | −237.547 | −0.223975 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1950.23 | −1.78701 | ||||||||
\(107\) | 1946.90 | 1.75901 | 0.879506 | − | 0.475887i | \(-0.157873\pi\) | ||||
0.879506 | + | 0.475887i | \(0.157873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1837.70 | 1.61486 | 0.807431 | − | 0.589961i | \(-0.200857\pi\) | ||||
0.807431 | + | 0.589961i | \(0.200857\pi\) | |||||||
\(110\) | 1725.30 | 1.49546 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1705.69 | −1.43904 | ||||||||
\(113\) | 1446.76 | 1.20442 | 0.602212 | − | 0.798336i | \(-0.294286\pi\) | ||||
0.602212 | + | 0.798336i | \(0.294286\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3046.74 | −2.47052 | ||||||||
\(116\) | −7.82801 | −0.00626563 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1525.47 | 1.19010 | ||||||||
\(119\) | −1071.26 | −0.825227 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −292.489 | −0.219751 | ||||||||
\(122\) | 574.928 | 0.426652 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.88860 | −0.00643726 | ||||||||
\(125\) | −2308.78 | −1.65203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1939.30 | −1.35500 | −0.677499 | − | 0.735524i | \(-0.736936\pi\) | ||||
−0.677499 | + | 0.735524i | \(0.736936\pi\) | |||||||
\(128\) | 1375.43 | 0.949783 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −553.616 | −0.373502 | ||||||||
\(131\) | 501.024 | 0.334158 | 0.167079 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167079 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3798.12 | 2.47623 | ||||||||
\(134\) | 982.226 | 0.633220 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 893.134 | 0.563130 | ||||||||
\(137\) | 2450.94 | 1.52845 | 0.764227 | − | 0.644947i | \(-0.223121\pi\) | ||||
0.764227 | + | 0.644947i | \(0.223121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 257.133 | 0.156905 | 0.0784523 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784523 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(140\) | 134.535 | 0.0812161 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2113.48 | −1.24901 | ||||||||
\(143\) | −333.239 | −0.194873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −593.230 | −0.339759 | ||||||||
\(146\) | −1635.32 | −0.926988 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26.6703 | −0.0148127 | ||||||||
\(149\) | −2187.75 | −1.20287 | −0.601434 | − | 0.798923i | \(-0.705404\pi\) | ||||
−0.601434 | + | 0.798923i | \(0.705404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1250.56 | −0.673970 | −0.336985 | − | 0.941510i | \(-0.609407\pi\) | ||||
−0.336985 | + | 0.941510i | \(0.609407\pi\) | |||||||
\(152\) | −3166.59 | −1.68976 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2471.30 | −1.29313 | ||||||||
\(155\) | −673.604 | −0.349066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1312.84 | −0.667363 | −0.333682 | − | 0.942686i | \(-0.608291\pi\) | ||||
−0.333682 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(158\) | −415.804 | −0.209365 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −220.881 | −0.109138 | ||||||||
\(161\) | 4364.12 | 2.13628 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1766.12 | −0.848670 | −0.424335 | − | 0.905505i | \(-0.639492\pi\) | ||||
−0.424335 | + | 0.905505i | \(0.639492\pi\) | |||||||
\(164\) | 75.0454 | 0.0357321 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2850.28 | −1.33268 | ||||||||
\(167\) | −780.417 | −0.361620 | −0.180810 | − | 0.983518i | \(-0.557872\pi\) | ||||
−0.180810 | + | 0.983518i | \(0.557872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2090.07 | −0.951329 | ||||||||
\(170\) | 2081.50 | 0.939081 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 78.9711 | 0.0350086 | ||||||||
\(173\) | 3049.96 | 1.34037 | 0.670185 | − | 0.742194i | \(-0.266215\pi\) | ||||
0.670185 | + | 0.742194i | \(0.266215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6751.26 | 2.91627 | ||||||||
\(176\) | 1994.94 | 0.854401 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2910.38 | −1.22552 | ||||||||
\(179\) | 1950.16 | 0.814312 | 0.407156 | − | 0.913359i | \(-0.366520\pi\) | ||||
0.407156 | + | 0.913359i | \(0.366520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2597.95 | −1.06687 | −0.533436 | − | 0.845840i | \(-0.679099\pi\) | ||||
−0.533436 | + | 0.845840i | \(0.679099\pi\) | |||||||
\(182\) | 792.993 | 0.322970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3638.48 | −1.45778 | ||||||||
\(185\) | −2021.15 | −0.803234 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1252.92 | 0.489960 | ||||||||
\(188\) | −31.0988 | −0.0120644 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7379.91 | −2.81787 | ||||||||
\(191\) | −1447.23 | −0.548260 | −0.274130 | − | 0.961693i | \(-0.588390\pi\) | ||||
−0.274130 | + | 0.961693i | \(0.588390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1220.05 | −0.455033 | −0.227516 | − | 0.973774i | \(-0.573061\pi\) | ||||
−0.227516 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(194\) | −5033.86 | −1.86294 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −105.642 | −0.0384994 | ||||||||
\(197\) | −2862.29 | −1.03518 | −0.517588 | − | 0.855630i | \(-0.673170\pi\) | ||||
−0.517588 | + | 0.855630i | \(0.673170\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −267.746 | −0.0953771 | −0.0476886 | − | 0.998862i | \(-0.515185\pi\) | ||||
−0.0476886 | + | 0.998862i | \(0.515185\pi\) | |||||||
\(200\) | −5628.70 | −1.99004 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2617.09 | −0.911573 | ||||||||
\(203\) | 849.736 | 0.293792 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5687.16 | 1.93760 | ||||||||
\(206\) | −294.611 | −0.0996434 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −640.140 | −0.213393 | ||||||||
\(209\) | −4442.20 | −1.47021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2491.09 | −0.812766 | −0.406383 | − | 0.913703i | \(-0.633210\pi\) | ||||
−0.406383 | + | 0.913703i | \(0.633210\pi\) | |||||||
\(212\) | 177.863 | 0.0576211 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5418.61 | 1.73088 | ||||||||
\(215\) | 5984.66 | 1.89837 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 964.863 | 0.301840 | ||||||||
\(218\) | 5114.69 | 1.58904 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −157.349 | −0.0482203 | ||||||||
\(221\) | −402.038 | −0.122371 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5470.72 | 1.64281 | 0.821405 | − | 0.570346i | \(-0.193191\pi\) | ||||
0.821405 | + | 0.570346i | \(0.193191\pi\) | |||||||
\(224\) | 316.387 | 0.0943728 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4026.62 | 1.18516 | ||||||||
\(227\) | −4177.85 | −1.22156 | −0.610779 | − | 0.791801i | \(-0.709144\pi\) | ||||
−0.610779 | + | 0.791801i | \(0.709144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3049.05 | 0.879857 | 0.439928 | − | 0.898033i | \(-0.355004\pi\) | ||||
0.439928 | + | 0.898033i | \(0.355004\pi\) | |||||||
\(230\) | −8479.67 | −2.43101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −708.446 | −0.200482 | ||||||||
\(233\) | −265.914 | −0.0747666 | −0.0373833 | − | 0.999301i | \(-0.511902\pi\) | ||||
−0.0373833 | + | 0.999301i | \(0.511902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2356.76 | −0.654203 | ||||||||
\(236\) | −139.125 | −0.0383740 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2981.52 | −0.812029 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6888.63 | −1.84123 | −0.920614 | − | 0.390475i | \(-0.872311\pi\) | ||||
−0.920614 | + | 0.390475i | \(0.872311\pi\) | |||||||
\(242\) | −814.054 | −0.216237 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −52.4340 | −0.0137571 | ||||||||
\(245\) | −8005.88 | −2.08766 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1425.42 | 0.367195 | ||||||||
\(248\) | −804.431 | −0.205973 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6425.79 | −1.62561 | ||||||||
\(251\) | 1646.85 | 0.414136 | 0.207068 | − | 0.978327i | \(-0.433608\pi\) | ||||
0.207068 | + | 0.978327i | \(0.433608\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5104.18 | −1.26837 | ||||||||
\(254\) | −5397.44 | −1.33333 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −389.487 | −0.0950895 | ||||||||
\(257\) | 5771.91 | 1.40094 | 0.700471 | − | 0.713681i | \(-0.252973\pi\) | ||||
0.700471 | + | 0.713681i | \(0.252973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2895.08 | 0.694562 | ||||||||
\(260\) | 50.4904 | 0.0120434 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1394.45 | 0.328814 | ||||||||
\(263\) | −1656.33 | −0.388341 | −0.194171 | − | 0.980968i | \(-0.562202\pi\) | ||||
−0.194171 | + | 0.980968i | \(0.562202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13479.0 | 3.12455 | ||||||||
\(266\) | 10570.9 | 2.43663 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −89.5801 | −0.0204178 | ||||||||
\(269\) | −2471.45 | −0.560174 | −0.280087 | − | 0.959975i | \(-0.590363\pi\) | ||||
−0.280087 | + | 0.959975i | \(0.590363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 44.2396 | 0.00991648 | 0.00495824 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495824 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(272\) | 2406.82 | 0.536525 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6821.45 | 1.50401 | ||||||||
\(275\) | −7896.13 | −1.73147 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2924.86 | −0.634433 | −0.317217 | − | 0.948353i | \(-0.602748\pi\) | ||||
−0.317217 | + | 0.948353i | \(0.602748\pi\) | |||||||
\(278\) | 715.651 | 0.154395 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12175.6 | 2.59868 | ||||||||
\(281\) | −7081.71 | −1.50341 | −0.751707 | − | 0.659497i | \(-0.770769\pi\) | ||||
−0.751707 | + | 0.659497i | \(0.770769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 473.768 | 0.0995143 | 0.0497572 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497572 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(284\) | 192.752 | 0.0402737 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −927.468 | −0.191756 | ||||||||
\(287\) | −8146.23 | −1.67546 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3401.40 | −0.692327 | ||||||||
\(290\) | −1651.07 | −0.334325 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 149.143 | 0.0298902 | ||||||||
\(293\) | −9805.59 | −1.95512 | −0.977558 | − | 0.210668i | \(-0.932436\pi\) | ||||
−0.977558 | + | 0.210668i | \(0.932436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10543.3 | −2.08086 | ||||||||
\(296\) | −2413.70 | −0.473965 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6088.92 | −1.18363 | ||||||||
\(299\) | 1637.84 | 0.316784 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8572.36 | −1.64154 | ||||||||
\(302\) | −3480.56 | −0.663191 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8533.31 | −1.60993 | ||||||||
\(305\) | −3973.60 | −0.745993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1384.15 | −0.257321 | −0.128660 | − | 0.991689i | \(-0.541068\pi\) | ||||
−0.128660 | + | 0.991689i | \(0.541068\pi\) | |||||||
\(308\) | 225.385 | 0.0416964 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1874.77 | −0.343483 | ||||||||
\(311\) | 1774.27 | 0.323504 | 0.161752 | − | 0.986831i | \(-0.448285\pi\) | ||||
0.161752 | + | 0.986831i | \(0.448285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3700.09 | 0.668184 | 0.334092 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(314\) | −3653.89 | −0.656690 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 37.9218 | 0.00675085 | ||||||||
\(317\) | 3471.60 | 0.615093 | 0.307547 | − | 0.951533i | \(-0.400492\pi\) | ||||
0.307547 | + | 0.951533i | \(0.400492\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −993.833 | −0.174433 | ||||||||
\(320\) | −10141.2 | −1.77159 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12146.2 | 2.10211 | ||||||||
\(323\) | −5359.33 | −0.923222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2533.72 | 0.432448 | ||||||||
\(326\) | −4915.45 | −0.835097 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6791.72 | 1.14332 | ||||||||
\(329\) | 3375.79 | 0.565694 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11769.1 | −1.95434 | −0.977172 | − | 0.212451i | \(-0.931855\pi\) | ||||
−0.977172 | + | 0.212451i | \(0.931855\pi\) | |||||||
\(332\) | 259.948 | 0.0429714 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2172.05 | −0.355837 | ||||||||
\(335\) | −6788.64 | −1.10717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10992.7 | −1.77689 | −0.888444 | − | 0.458985i | \(-0.848213\pi\) | ||||
−0.888444 | + | 0.458985i | \(0.848213\pi\) | |||||||
\(338\) | −5817.07 | −0.936115 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −189.835 | −0.0302801 | ||||||||
\(341\) | −1128.48 | −0.179211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2016.70 | 0.317468 | ||||||||
\(344\) | 7146.99 | 1.12017 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8488.63 | 1.31893 | ||||||||
\(347\) | −6679.54 | −1.03336 | −0.516681 | − | 0.856178i | \(-0.672833\pi\) | ||||
−0.516681 | + | 0.856178i | \(0.672833\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7868.92 | 1.20692 | 0.603458 | − | 0.797395i | \(-0.293789\pi\) | ||||
0.603458 | + | 0.797395i | \(0.293789\pi\) | |||||||
\(350\) | 18790.1 | 2.86963 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −370.040 | −0.0560318 | ||||||||
\(353\) | 8705.88 | 1.31266 | 0.656328 | − | 0.754476i | \(-0.272109\pi\) | ||||
0.656328 | + | 0.754476i | \(0.272109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14607.3 | 2.18387 | ||||||||
\(356\) | 265.430 | 0.0395162 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5427.68 | 0.801290 | ||||||||
\(359\) | 1128.36 | 0.165885 | 0.0829425 | − | 0.996554i | \(-0.473568\pi\) | ||||
0.0829425 | + | 0.996554i | \(0.473568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12142.4 | 1.77028 | ||||||||
\(362\) | −7230.59 | −1.04981 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −72.3218 | −0.0104140 | ||||||||
\(365\) | 11302.5 | 1.62082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2218.05 | −0.315480 | −0.157740 | − | 0.987481i | \(-0.550421\pi\) | ||||
−0.157740 | + | 0.987481i | \(0.550421\pi\) | |||||||
\(368\) | −9804.96 | −1.38891 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5625.26 | −0.790388 | ||||||||
\(371\) | −19307.1 | −2.70182 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8888.30 | −1.23383 | −0.616915 | − | 0.787030i | \(-0.711618\pi\) | ||||
−0.616915 | + | 0.787030i | \(0.711618\pi\) | |||||||
\(374\) | 3487.12 | 0.482125 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2814.48 | −0.386026 | ||||||||
\(377\) | 318.902 | 0.0435658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10662.5 | 1.44511 | 0.722556 | − | 0.691312i | \(-0.242967\pi\) | ||||
0.722556 | + | 0.691312i | \(0.242967\pi\) | |||||||
\(380\) | 673.056 | 0.0908606 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4027.91 | −0.539492 | ||||||||
\(383\) | −3150.75 | −0.420354 | −0.210177 | − | 0.977663i | \(-0.567404\pi\) | ||||
−0.210177 | + | 0.977663i | \(0.567404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17080.3 | 2.26102 | ||||||||
\(386\) | −3395.65 | −0.447756 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 459.093 | 0.0600694 | ||||||||
\(389\) | 11728.0 | 1.52862 | 0.764311 | − | 0.644848i | \(-0.223079\pi\) | ||||
0.764311 | + | 0.644848i | \(0.223079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6157.98 | −0.796477 | ||||||||
\(392\) | −9560.77 | −1.23187 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7966.31 | −1.01862 | ||||||||
\(395\) | 2873.83 | 0.366070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6710.89 | 0.848388 | 0.424194 | − | 0.905571i | \(-0.360558\pi\) | ||||
0.424194 | + | 0.905571i | \(0.360558\pi\) | |||||||
\(398\) | −745.190 | −0.0938518 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15168.2 | −1.89602 | ||||||||
\(401\) | −6300.52 | −0.784621 | −0.392311 | − | 0.919833i | \(-0.628324\pi\) | ||||
−0.392311 | + | 0.919833i | \(0.628324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 362.109 | 0.0447592 | ||||||||
\(404\) | 238.681 | 0.0293932 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2364.98 | 0.289093 | ||||||||
\(407\) | −3386.02 | −0.412381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1919.04 | −0.232006 | −0.116003 | − | 0.993249i | \(-0.537008\pi\) | ||||
−0.116003 | + | 0.993249i | \(0.537008\pi\) | |||||||
\(410\) | 15828.5 | 1.90662 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.8689 | 0.00321295 | ||||||||
\(413\) | 15102.1 | 1.79934 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19699.6 | 2.33016 | ||||||||
\(416\) | 118.739 | 0.0139943 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12363.5 | −1.44669 | ||||||||
\(419\) | 11720.7 | 1.36658 | 0.683288 | − | 0.730149i | \(-0.260550\pi\) | ||||
0.683288 | + | 0.730149i | \(0.260550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11285.6 | 1.30647 | 0.653236 | − | 0.757154i | \(-0.273411\pi\) | ||||
0.653236 | + | 0.757154i | \(0.273411\pi\) | |||||||
\(422\) | −6933.18 | −0.799768 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16096.8 | 1.84371 | ||||||||
\(425\) | −9526.35 | −1.08728 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5691.75 | 0.645065 | ||||||||
\(428\) | −494.183 | −0.0558114 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16656.5 | 1.86801 | ||||||||
\(431\) | −12144.7 | −1.35728 | −0.678641 | − | 0.734471i | \(-0.737431\pi\) | ||||
−0.678641 | + | 0.734471i | \(0.737431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11643.9 | −1.29231 | −0.646154 | − | 0.763207i | \(-0.723624\pi\) | ||||
−0.646154 | + | 0.763207i | \(0.723624\pi\) | |||||||
\(434\) | 2685.40 | 0.297012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −466.465 | −0.0512377 | ||||||||
\(437\) | 21833.0 | 2.38996 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4286.79 | −0.466054 | −0.233027 | − | 0.972470i | \(-0.574863\pi\) | ||||
−0.233027 | + | 0.972470i | \(0.574863\pi\) | |||||||
\(440\) | −14240.3 | −1.54291 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1118.95 | −0.120414 | ||||||||
\(443\) | 861.239 | 0.0923673 | 0.0461836 | − | 0.998933i | \(-0.485294\pi\) | ||||
0.0461836 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20115.0 | 2.14280 | ||||||||
\(446\) | 15226.1 | 1.61654 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14526.1 | 1.53191 | ||||||||
\(449\) | 4202.34 | 0.441694 | 0.220847 | − | 0.975308i | \(-0.429118\pi\) | ||||
0.220847 | + | 0.975308i | \(0.429118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9527.66 | 0.994767 | ||||||||
\(452\) | −367.232 | −0.0382149 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11627.8 | −1.20202 | ||||||||
\(455\) | −5480.76 | −0.564708 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16451.8 | 1.68399 | 0.841993 | − | 0.539488i | \(-0.181382\pi\) | ||||
0.841993 | + | 0.539488i | \(0.181382\pi\) | |||||||
\(458\) | 8486.11 | 0.865786 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 773.355 | 0.0783867 | ||||||||
\(461\) | −3581.86 | −0.361874 | −0.180937 | − | 0.983495i | \(-0.557913\pi\) | ||||
−0.180937 | + | 0.983495i | \(0.557913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5277.24 | −0.529706 | −0.264853 | − | 0.964289i | \(-0.585323\pi\) | ||||
−0.264853 | + | 0.964289i | \(0.585323\pi\) | |||||||
\(464\) | −1909.12 | −0.191010 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −740.091 | −0.0735709 | ||||||||
\(467\) | 14263.7 | 1.41337 | 0.706687 | − | 0.707526i | \(-0.250189\pi\) | ||||
0.706687 | + | 0.707526i | \(0.250189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9723.98 | 0.957381 | ||||||||
\(470\) | −6559.31 | −0.643741 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12591.0 | −1.22786 | ||||||||
\(473\) | 10026.0 | 0.974626 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33775.4 | 3.26258 | ||||||||
\(476\) | 271.918 | 0.0261834 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 665.183 | 0.0636502 | ||||||||
\(479\) | −13713.0 | −1.30807 | −0.654034 | − | 0.756465i | \(-0.726925\pi\) | ||||
−0.654034 | + | 0.756465i | \(0.726925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1086.51 | 0.102995 | ||||||||
\(482\) | −19172.4 | −1.81178 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 74.2426 | 0.00697245 | ||||||||
\(485\) | 34791.4 | 3.25731 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11160.8 | −1.03848 | −0.519242 | − | 0.854627i | \(-0.673786\pi\) | ||||
−0.519242 | + | 0.854627i | \(0.673786\pi\) | |||||||
\(488\) | −4745.35 | −0.440189 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22281.9 | −2.05427 | ||||||||
\(491\) | −6933.48 | −0.637279 | −0.318639 | − | 0.947876i | \(-0.603226\pi\) | ||||
−0.318639 | + | 0.947876i | \(0.603226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1199.02 | −0.109536 | ||||||||
\(494\) | 3967.21 | 0.361323 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2167.78 | −0.196242 | ||||||||
\(497\) | −20923.3 | −1.88841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 134.621 | 0.0120771 | 0.00603855 | − | 0.999982i | \(-0.498078\pi\) | ||||
0.00603855 | + | 0.999982i | \(0.498078\pi\) | |||||||
\(500\) | 586.039 | 0.0524170 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4583.50 | 0.407513 | ||||||||
\(503\) | 4654.45 | 0.412588 | 0.206294 | − | 0.978490i | \(-0.433860\pi\) | ||||
0.206294 | + | 0.978490i | \(0.433860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18088.0 | 1.59387 | ||||||||
\(506\) | −14205.9 | −1.24808 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 492.252 | 0.0429925 | ||||||||
\(509\) | 645.594 | 0.0562190 | 0.0281095 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281095 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16189.6 | −1.40154 | ||||||||
\(512\) | −12087.5 | −1.04335 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16064.3 | 1.37854 | ||||||||
\(515\) | 2036.20 | 0.174225 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3948.25 | −0.335869 | ||||||||
\(518\) | 8057.57 | 0.683454 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4569.45 | 0.385353 | ||||||||
\(521\) | 7410.59 | 0.623155 | 0.311578 | − | 0.950221i | \(-0.399143\pi\) | ||||
0.311578 | + | 0.950221i | \(0.399143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17542.7 | 1.46671 | 0.733356 | − | 0.679845i | \(-0.237953\pi\) | ||||
0.733356 | + | 0.679845i | \(0.237953\pi\) | |||||||
\(524\) | −127.175 | −0.0106024 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4609.89 | −0.382131 | ||||||||
\(527\) | −1361.47 | −0.112536 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12919.6 | 1.06185 | ||||||||
\(530\) | 37514.6 | 3.07458 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −964.077 | −0.0785678 | ||||||||
\(533\) | −3057.25 | −0.248450 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −37450.7 | −3.02642 | ||||||||
\(536\) | −8107.13 | −0.653311 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6878.52 | −0.551216 | ||||||||
\(539\) | −13412.2 | −1.07181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9430.61 | 0.749452 | 0.374726 | − | 0.927136i | \(-0.377737\pi\) | ||||
0.374726 | + | 0.927136i | \(0.377737\pi\) | |||||||
\(542\) | 123.127 | 0.00975789 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −446.437 | −0.0351854 | ||||||||
\(545\) | −35350.1 | −2.77841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2020.15 | 0.157908 | 0.0789539 | − | 0.996878i | \(-0.474842\pi\) | ||||
0.0789539 | + | 0.996878i | \(0.474842\pi\) | |||||||
\(548\) | −622.124 | −0.0484960 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21976.5 | −1.70378 | ||||||||
\(551\) | 4251.09 | 0.328680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4116.44 | −0.316544 | ||||||||
\(554\) | −8140.46 | −0.624287 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −65.2681 | −0.00497839 | ||||||||
\(557\) | 389.740 | 0.0296478 | 0.0148239 | − | 0.999890i | \(-0.495281\pi\) | ||||
0.0148239 | + | 0.999890i | \(0.495281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3217.17 | −0.243420 | ||||||||
\(560\) | 32810.7 | 2.47591 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19709.8 | −1.47937 | ||||||||
\(563\) | 1680.19 | 0.125775 | 0.0628877 | − | 0.998021i | \(-0.479969\pi\) | ||||
0.0628877 | + | 0.998021i | \(0.479969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27829.9 | −2.07224 | ||||||||
\(566\) | 1318.59 | 0.0979229 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17444.3 | 1.28864 | ||||||||
\(569\) | 17076.6 | 1.25815 | 0.629075 | − | 0.777345i | \(-0.283434\pi\) | ||||
0.629075 | + | 0.777345i | \(0.283434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16649.1 | −1.22022 | −0.610109 | − | 0.792317i | \(-0.708875\pi\) | ||||
−0.610109 | + | 0.792317i | \(0.708875\pi\) | |||||||
\(572\) | 84.5861 | 0.00618308 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22672.5 | −1.64866 | ||||||||
\(575\) | 38808.7 | 2.81467 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18039.8 | 1.30157 | 0.650784 | − | 0.759263i | \(-0.274440\pi\) | ||||
0.650784 | + | 0.759263i | \(0.274440\pi\) | |||||||
\(578\) | −9466.77 | −0.681256 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 150.580 | 0.0107801 | ||||||||
\(581\) | −28217.6 | −2.01491 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22581.2 | 1.60415 | ||||||||
\(584\) | 13497.7 | 0.956400 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27290.9 | −1.92385 | ||||||||
\(587\) | −9120.89 | −0.641328 | −0.320664 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320664 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4827.05 | 0.337683 | ||||||||
\(590\) | −29344.0 | −2.04758 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6504.44 | −0.451572 | ||||||||
\(593\) | 3798.44 | 0.263041 | 0.131520 | − | 0.991313i | \(-0.458014\pi\) | ||||
0.131520 | + | 0.991313i | \(0.458014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20606.7 | 1.41982 | ||||||||
\(596\) | 555.317 | 0.0381655 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4558.41 | 0.311718 | ||||||||
\(599\) | −3224.19 | −0.219928 | −0.109964 | − | 0.993936i | \(-0.535074\pi\) | ||||
−0.109964 | + | 0.993936i | \(0.535074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6429.69 | 0.436393 | 0.218197 | − | 0.975905i | \(-0.429983\pi\) | ||||
0.218197 | + | 0.975905i | \(0.429983\pi\) | |||||||
\(602\) | −23858.5 | −1.61528 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 317.431 | 0.0213842 | ||||||||
\(605\) | 5626.32 | 0.378087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3889.56 | −0.260086 | −0.130043 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130043 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(608\) | 1582.83 | 0.105580 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11059.3 | −0.734063 | ||||||||
\(611\) | 1266.92 | 0.0838857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18334.8 | 1.20805 | 0.604025 | − | 0.796966i | \(-0.293563\pi\) | ||||
0.604025 | + | 0.796966i | \(0.293563\pi\) | |||||||
\(614\) | −3852.35 | −0.253205 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20397.7 | 1.33416 | ||||||||
\(617\) | −4169.61 | −0.272062 | −0.136031 | − | 0.990705i | \(-0.543435\pi\) | ||||
−0.136031 | + | 0.990705i | \(0.543435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5923.21 | −0.384610 | −0.192305 | − | 0.981335i | \(-0.561596\pi\) | ||||
−0.192305 | + | 0.981335i | \(0.561596\pi\) | |||||||
\(620\) | 170.981 | 0.0110754 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4938.15 | 0.318331 | ||||||||
\(623\) | −28812.6 | −1.85289 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13783.8 | 0.882161 | ||||||||
\(626\) | 10298.1 | 0.657498 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 333.239 | 0.0211746 | ||||||||
\(629\) | −4085.10 | −0.258956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28967.5 | −1.82754 | −0.913771 | − | 0.406229i | \(-0.866843\pi\) | ||||
−0.913771 | + | 0.406229i | \(0.866843\pi\) | |||||||
\(632\) | 3431.98 | 0.216007 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9662.14 | 0.605256 | ||||||||
\(635\) | 37304.3 | 2.33130 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4303.72 | 0.267692 | ||||||||
\(638\) | −2766.03 | −0.171643 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26457.8 | −1.63412 | ||||||||
\(641\) | 22652.4 | 1.39581 | 0.697907 | − | 0.716188i | \(-0.254115\pi\) | ||||
0.697907 | + | 0.716188i | \(0.254115\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11734.9 | −0.719719 | −0.359859 | − | 0.933007i | \(-0.617175\pi\) | ||||
−0.359859 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(644\) | −1107.75 | −0.0677815 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14916.0 | −0.908458 | ||||||||
\(647\) | −10592.2 | −0.643621 | −0.321810 | − | 0.946804i | \(-0.604291\pi\) | ||||
−0.321810 | + | 0.946804i | \(0.604291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17663.1 | −1.06832 | ||||||||
\(650\) | 7051.83 | 0.425532 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 448.295 | 0.0269273 | ||||||||
\(653\) | −19626.6 | −1.17618 | −0.588091 | − | 0.808795i | \(-0.700120\pi\) | ||||
−0.588091 | + | 0.808795i | \(0.700120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9637.71 | −0.574926 | ||||||||
\(656\) | 18302.3 | 1.08931 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9395.48 | 0.556647 | ||||||||
\(659\) | −5563.31 | −0.328856 | −0.164428 | − | 0.986389i | \(-0.552578\pi\) | ||||
−0.164428 | + | 0.986389i | \(0.552578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1537.13 | −0.0904497 | −0.0452249 | − | 0.998977i | \(-0.514400\pi\) | ||||
−0.0452249 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(662\) | −32755.7 | −1.92309 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23525.7 | 1.37496 | ||||||||
\(665\) | −73060.6 | −4.26040 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4884.59 | 0.283557 | ||||||||
\(668\) | 198.094 | 0.0114738 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18894.1 | −1.08947 | ||||||||
\(671\) | −6656.95 | −0.382993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14786.3 | 0.846911 | 0.423456 | − | 0.905917i | \(-0.360817\pi\) | ||||
0.423456 | + | 0.905917i | \(0.360817\pi\) | |||||||
\(674\) | −30594.8 | −1.74847 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 530.523 | 0.0301845 | ||||||||
\(677\) | 1268.81 | 0.0720298 | 0.0360149 | − | 0.999351i | \(-0.488534\pi\) | ||||
0.0360149 | + | 0.999351i | \(0.488534\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49834.9 | −2.81662 | ||||||||
\(680\) | −17180.3 | −0.968876 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3140.79 | −0.176345 | ||||||||
\(683\) | −13430.8 | −0.752435 | −0.376218 | − | 0.926531i | \(-0.622776\pi\) | ||||
−0.376218 | + | 0.926531i | \(0.622776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47146.4 | −2.62974 | ||||||||
\(686\) | 5612.87 | 0.312391 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19259.7 | 1.06725 | ||||||||
\(689\) | −7245.89 | −0.400648 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.2231 | −0.00160882 | −0.000804412 | − | 1.00000i | \(-0.500256\pi\) | ||||
−0.000804412 | 1.00000i | \(0.500256\pi\) | ||||||||
\(692\) | −774.172 | −0.0425283 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18590.5 | −1.01684 | ||||||||
\(695\) | −4946.21 | −0.269957 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11494.7 | 0.624668 | ||||||||
\(698\) | 21900.7 | 1.18761 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1713.67 | −0.0925297 | ||||||||
\(701\) | 13868.8 | 0.747241 | 0.373620 | − | 0.927582i | \(-0.378116\pi\) | ||||
0.373620 | + | 0.927582i | \(0.378116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14483.6 | 0.777041 | ||||||||
\(704\) | −16989.4 | −0.909537 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24230.2 | 1.29166 | ||||||||
\(707\) | −25909.0 | −1.37823 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12022.0 | −0.636808 | −0.318404 | − | 0.947955i | \(-0.603147\pi\) | ||||
−0.318404 | + | 0.947955i | \(0.603147\pi\) | |||||||
\(710\) | 40655.0 | 2.14895 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24021.8 | 1.26440 | ||||||||
\(713\) | 5546.39 | 0.291324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6410.18 | 0.335283 | ||||||||
\(716\) | −495.010 | −0.0258371 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3140.45 | 0.163232 | ||||||||
\(719\) | −25462.8 | −1.32073 | −0.660363 | − | 0.750947i | \(-0.729597\pi\) | ||||
−0.660363 | + | 0.750947i | \(0.729597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2916.63 | −0.150653 | ||||||||
\(722\) | 33794.5 | 1.74197 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 659.438 | 0.0338506 | ||||||||
\(725\) | 7556.43 | 0.387088 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16110.0 | −0.821850 | −0.410925 | − | 0.911669i | \(-0.634794\pi\) | ||||
−0.410925 | + | 0.911669i | \(0.634794\pi\) | |||||||
\(728\) | −6545.23 | −0.333217 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 31457.1 | 1.59490 | ||||||||
\(731\) | 12096.0 | 0.612021 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11795.4 | −0.594372 | −0.297186 | − | 0.954820i | \(-0.596048\pi\) | ||||
−0.297186 | + | 0.954820i | \(0.596048\pi\) | |||||||
\(734\) | −6173.25 | −0.310435 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1818.71 | 0.0910849 | ||||||||
\(737\) | −11373.0 | −0.568424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 859.661 | 0.0427918 | 0.0213959 | − | 0.999771i | \(-0.493189\pi\) | ||||
0.0213959 | + | 0.999771i | \(0.493189\pi\) | |||||||
\(740\) | 513.030 | 0.0254856 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −53735.5 | −2.65861 | ||||||||
\(743\) | −27738.6 | −1.36962 | −0.684812 | − | 0.728720i | \(-0.740116\pi\) | ||||
−0.684812 | + | 0.728720i | \(0.740116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42083.5 | 2.06956 | ||||||||
\(746\) | −24737.9 | −1.21410 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −318.029 | −0.0155458 | ||||||||
\(749\) | 53643.9 | 2.61696 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2287.94 | −0.111169 | −0.0555847 | − | 0.998454i | \(-0.517702\pi\) | ||||
−0.0555847 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(752\) | −7584.46 | −0.367788 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 887.567 | 0.0428691 | ||||||||
\(755\) | 24055.8 | 1.15958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23515.8 | 1.12906 | 0.564530 | − | 0.825413i | \(-0.309058\pi\) | ||||
0.564530 | + | 0.825413i | \(0.309058\pi\) | |||||||
\(758\) | 29675.9 | 1.42200 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 60912.5 | 2.90727 | ||||||||
\(761\) | 5118.88 | 0.243836 | 0.121918 | − | 0.992540i | \(-0.461096\pi\) | ||||
0.121918 | + | 0.992540i | \(0.461096\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50635.1 | 2.40251 | ||||||||
\(764\) | 367.350 | 0.0173956 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8769.14 | −0.413632 | ||||||||
\(767\) | 5667.76 | 0.266820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32713.5 | −1.53404 | −0.767021 | − | 0.641622i | \(-0.778262\pi\) | ||||
−0.767021 | + | 0.641622i | \(0.778262\pi\) | |||||||
\(770\) | 47537.9 | 2.22487 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 309.687 | 0.0144376 | ||||||||
\(773\) | 1838.02 | 0.0855225 | 0.0427612 | − | 0.999085i | \(-0.486385\pi\) | ||||
0.0427612 | + | 0.999085i | \(0.486385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8580.22 | 0.397691 | ||||||||
\(776\) | 41548.6 | 1.92205 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32641.3 | 1.50418 | ||||||||
\(779\) | −40754.3 | −1.87442 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24471.5 | 1.12120 | ||||||||
\(782\) | −17138.9 | −0.783739 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25764.4 | −1.17367 | ||||||||
\(785\) | 25253.8 | 1.14821 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31329.4 | 1.41902 | 0.709512 | − | 0.704693i | \(-0.248915\pi\) | ||||
0.709512 | + | 0.704693i | \(0.248915\pi\) | |||||||
\(788\) | 726.536 | 0.0328449 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7998.41 | 0.360216 | ||||||||
\(791\) | 39863.3 | 1.79188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2136.09 | 0.0956554 | ||||||||
\(794\) | 18677.7 | 0.834820 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 67.9622 | 0.00302620 | ||||||||
\(797\) | −7083.13 | −0.314802 | −0.157401 | − | 0.987535i | \(-0.550312\pi\) | ||||
−0.157401 | + | 0.987535i | \(0.550312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4763.40 | −0.210910 | ||||||||
\(800\) | 2813.53 | 0.124342 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17535.6 | −0.772073 | ||||||||
\(803\) | 18935.0 | 0.832132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −83948.2 | −3.67551 | ||||||||
\(806\) | 1007.82 | 0.0440434 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21601.0 | 0.940496 | ||||||||
\(809\) | 40383.7 | 1.75502 | 0.877512 | − | 0.479555i | \(-0.159202\pi\) | ||||
0.877512 | + | 0.479555i | \(0.159202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16572.3 | −0.717549 | −0.358774 | − | 0.933424i | \(-0.616805\pi\) | ||||
−0.358774 | + | 0.933424i | \(0.616805\pi\) | |||||||
\(812\) | −215.689 | −0.00932166 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9423.96 | −0.405786 | ||||||||
\(815\) | 33973.1 | 1.46015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42886.1 | −1.83647 | ||||||||
\(818\) | −5341.06 | −0.228296 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1443.57 | −0.0614778 | ||||||||
\(821\) | −2812.98 | −0.119578 | −0.0597890 | − | 0.998211i | \(-0.519043\pi\) | ||||
−0.0597890 | + | 0.998211i | \(0.519043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14450.1 | 0.612029 | 0.306015 | − | 0.952027i | \(-0.401004\pi\) | ||||
0.306015 | + | 0.952027i | \(0.401004\pi\) | |||||||
\(824\) | 2431.67 | 0.102805 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42032.1 | 1.77056 | ||||||||
\(827\) | 25351.1 | 1.06595 | 0.532977 | − | 0.846130i | \(-0.321073\pi\) | ||||
0.532977 | + | 0.846130i | \(0.321073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23430.1 | 0.981617 | 0.490808 | − | 0.871268i | \(-0.336702\pi\) | ||||
0.490808 | + | 0.871268i | \(0.336702\pi\) | |||||||
\(830\) | 54827.9 | 2.29290 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5451.59 | 0.227163 | ||||||||
\(833\) | −16181.2 | −0.673045 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15012.1 | 0.622174 | ||||||||
\(836\) | 1127.56 | 0.0466479 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32621.1 | 1.34472 | ||||||||
\(839\) | −36286.4 | −1.49314 | −0.746572 | − | 0.665305i | \(-0.768301\pi\) | ||||
−0.746572 | + | 0.665305i | \(0.768301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23437.9 | −0.961004 | ||||||||
\(842\) | 31409.9 | 1.28558 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 632.314 | 0.0257881 | ||||||||
\(845\) | 40204.6 | 1.63678 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8059.08 | −0.326934 | ||||||||
\(848\) | 43377.7 | 1.75660 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26513.7 | −1.06990 | ||||||||
\(851\) | 16642.0 | 0.670364 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32090.8 | −1.28812 | −0.644060 | − | 0.764975i | \(-0.722751\pi\) | ||||
−0.644060 | + | 0.764975i | \(0.722751\pi\) | |||||||
\(854\) | 15841.2 | 0.634749 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44724.3 | −1.78580 | ||||||||
\(857\) | 13271.5 | 0.528992 | 0.264496 | − | 0.964387i | \(-0.414794\pi\) | ||||
0.264496 | + | 0.964387i | \(0.414794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31122.1 | −1.23617 | −0.618086 | − | 0.786110i | \(-0.712092\pi\) | ||||
−0.618086 | + | 0.786110i | \(0.712092\pi\) | |||||||
\(860\) | −1519.09 | −0.0602331 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33801.0 | −1.33558 | ||||||||
\(863\) | 29880.8 | 1.17863 | 0.589313 | − | 0.807905i | \(-0.299399\pi\) | ||||
0.589313 | + | 0.807905i | \(0.299399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58669.0 | −2.30614 | ||||||||
\(866\) | −32407.2 | −1.27164 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −244.912 | −0.00957700 | ||||||||
\(869\) | 4814.50 | 0.187941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3649.37 | 0.141968 | ||||||||
\(872\) | −42215.7 | −1.63946 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 60765.4 | 2.35174 | ||||||||
\(875\) | −63614.9 | −2.45780 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14277.6 | 0.549737 | 0.274869 | − | 0.961482i | \(-0.411366\pi\) | ||||
0.274869 | + | 0.961482i | \(0.411366\pi\) | |||||||
\(878\) | −11931.0 | −0.458600 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −38374.8 | −1.47001 | ||||||||
\(881\) | −29068.3 | −1.11162 | −0.555809 | − | 0.831310i | \(-0.687591\pi\) | ||||
−0.555809 | + | 0.831310i | \(0.687591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19579.3 | 0.746203 | 0.373102 | − | 0.927790i | \(-0.378294\pi\) | ||||
0.373102 | + | 0.927790i | \(0.378294\pi\) | |||||||
\(884\) | 102.050 | 0.00388269 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2397.00 | 0.0908901 | ||||||||
\(887\) | 1135.24 | 0.0429738 | 0.0214869 | − | 0.999769i | \(-0.493160\pi\) | ||||
0.0214869 | + | 0.999769i | \(0.493160\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53434.3 | −2.01589 | ||||||||
\(890\) | 55984.1 | 2.10853 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1388.64 | −0.0521244 | ||||||||
\(893\) | 16888.5 | 0.632870 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37513.3 | −1.40104 | ||||||||
\(896\) | 37897.9 | 1.41304 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11695.9 | 0.434631 | ||||||||
\(899\) | 1079.94 | 0.0400644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27243.3 | 1.00733 | ||||||||
\(902\) | 26517.3 | 0.978859 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33235.0 | −1.22277 | ||||||||
\(905\) | 49974.1 | 1.83558 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42319.8 | −1.54929 | −0.774645 | − | 0.632396i | \(-0.782072\pi\) | ||||
−0.774645 | + | 0.632396i | \(0.782072\pi\) | |||||||
\(908\) | 1060.47 | 0.0387586 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15254.0 | −0.555677 | ||||||||
\(911\) | 20188.8 | 0.734233 | 0.367116 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367116 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33002.7 | 1.19631 | ||||||||
\(914\) | 45788.5 | 1.65706 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −773.942 | −0.0279168 | ||||||||
\(917\) | 13804.9 | 0.497142 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29559.7 | 1.06103 | 0.530514 | − | 0.847676i | \(-0.321999\pi\) | ||||
0.530514 | + | 0.847676i | \(0.321999\pi\) | |||||||
\(920\) | 69989.8 | 2.50815 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9969.01 | −0.356087 | ||||||||
\(923\) | −7852.44 | −0.280029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25745.0 | 0.915125 | ||||||||
\(926\) | −14687.6 | −0.521235 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 354.120 | 0.0125265 | ||||||||
\(929\) | −35279.7 | −1.24595 | −0.622975 | − | 0.782242i | \(-0.714076\pi\) | ||||
−0.622975 | + | 0.782242i | \(0.714076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57370.2 | 2.01958 | ||||||||
\(932\) | 67.4971 | 0.00237225 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39698.7 | 1.39077 | ||||||||
\(935\) | −24101.2 | −0.842987 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33500.7 | −1.16801 | −0.584003 | − | 0.811751i | \(-0.698514\pi\) | ||||
−0.584003 | + | 0.811751i | \(0.698514\pi\) | |||||||
\(938\) | 27063.7 | 0.942070 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 598.216 | 0.0207571 | ||||||||
\(941\) | −51286.9 | −1.77673 | −0.888366 | − | 0.459137i | \(-0.848159\pi\) | ||||
−0.888366 | + | 0.459137i | \(0.848159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46827.5 | −1.61709 | ||||||||
\(944\) | −33930.2 | −1.16985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27904.4 | 0.959040 | ||||||||
\(947\) | 23115.3 | 0.793186 | 0.396593 | − | 0.917995i | \(-0.370192\pi\) | ||||
0.396593 | + | 0.917995i | \(0.370192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6075.89 | −0.207831 | ||||||||
\(950\) | 94003.6 | 3.21040 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24608.9 | 0.837794 | ||||||||
\(953\) | −54712.6 | −1.85972 | −0.929861 | − | 0.367911i | \(-0.880073\pi\) | ||||
−0.929861 | + | 0.367911i | \(0.880073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27838.9 | 0.943293 | ||||||||
\(956\) | −60.6655 | −0.00205237 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38166.1 | −1.28715 | ||||||||
\(959\) | 67531.9 | 2.27395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28564.7 | −0.958838 | ||||||||
\(962\) | 3023.97 | 0.101348 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1748.54 | 0.0584199 | ||||||||
\(965\) | 23469.0 | 0.782894 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53949.5 | −1.79411 | −0.897053 | − | 0.441923i | \(-0.854296\pi\) | ||||
−0.897053 | + | 0.441923i | \(0.854296\pi\) | |||||||
\(968\) | 6719.07 | 0.223098 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 96831.3 | 3.20522 | ||||||||
\(971\) | −54124.5 | −1.78881 | −0.894407 | − | 0.447253i | \(-0.852402\pi\) | ||||
−0.894407 | + | 0.447253i | \(0.852402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7084.90 | 0.233434 | ||||||||
\(974\) | −31062.6 | −1.02188 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12787.8 | −0.419392 | ||||||||
\(977\) | −58614.1 | −1.91938 | −0.959688 | − | 0.281067i | \(-0.909312\pi\) | ||||
−0.959688 | + | 0.281067i | \(0.909312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33698.6 | 1.10011 | ||||||||
\(980\) | 2032.14 | 0.0662390 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19297.2 | −0.627087 | ||||||||
\(983\) | −18587.9 | −0.603116 | −0.301558 | − | 0.953448i | \(-0.597507\pi\) | ||||
−0.301558 | + | 0.953448i | \(0.597507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55059.1 | 1.78104 | ||||||||
\(986\) | −3337.10 | −0.107784 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −361.814 | −0.0116507 | ||||||||
\(989\) | −49277.1 | −1.58435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13247.9 | 0.424657 | 0.212328 | − | 0.977198i | \(-0.431895\pi\) | ||||
0.212328 | + | 0.977198i | \(0.431895\pi\) | |||||||
\(992\) | 402.099 | 0.0128696 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −58233.7 | −1.85821 | ||||||||
\(995\) | 5150.37 | 0.164098 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33371.1 | 1.06005 | 0.530026 | − | 0.847981i | \(-0.322182\pi\) | ||||
0.530026 | + | 0.847981i | \(0.322182\pi\) | |||||||
\(998\) | 374.677 | 0.0118840 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.g.1.42 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.18 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.42 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.18 | yes | 59 | 3.2 | odd | 2 |