Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27492 | 0.804305 | 0.402152 | − | 0.915573i | \(-0.368262\pi\) | ||||
0.402152 | + | 0.915573i | \(0.368262\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.82475 | −0.353094 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −24.6254 | −1.08830 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.7492 | 1.11694 | 0.558470 | − | 0.829525i | \(-0.311389\pi\) | ||||
0.558470 | + | 0.829525i | \(0.311389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −53.2990 | −1.13711 | −0.568557 | − | 0.822644i | \(-0.692498\pi\) | ||||
−0.568557 | + | 0.822644i | \(0.692498\pi\) | |||||||
\(14\) | −15.9244 | −0.303999 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −33.4228 | −0.522231 | ||||||||
\(17\) | 4.54983 | 0.0649116 | 0.0324558 | − | 0.999473i | \(-0.489667\pi\) | ||||
0.0324558 | + | 0.999473i | \(0.489667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 122.598 | 1.48031 | 0.740156 | − | 0.672436i | \(-0.234752\pi\) | ||||
0.740156 | + | 0.672436i | \(0.234752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 92.7010 | 0.898360 | ||||||||
\(23\) | 131.347 | 1.19077 | 0.595387 | − | 0.803439i | \(-0.296999\pi\) | ||||
0.595387 | + | 0.803439i | \(0.296999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −121.251 | −0.914586 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 19.7733 | 0.133457 | ||||||||
\(29\) | 216.598 | 1.38694 | 0.693470 | − | 0.720486i | \(-0.256081\pi\) | ||||
0.693470 | + | 0.720486i | \(0.256081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −251.794 | −1.45882 | −0.729412 | − | 0.684075i | \(-0.760206\pi\) | ||||
−0.729412 | + | 0.684075i | \(0.760206\pi\) | |||||||
\(32\) | 120.969 | 0.668267 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.3505 | 0.0522087 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8970 | −0.0528610 | −0.0264305 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264305 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(38\) | 278.900 | 1.19062 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 111.752 | 0.425678 | 0.212839 | − | 0.977087i | \(-0.431729\pi\) | ||||
0.212839 | + | 0.977087i | \(0.431729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.196 | −1.30935 | −0.654673 | − | 0.755912i | \(-0.727194\pi\) | ||||
−0.654673 | + | 0.755912i | \(0.727194\pi\) | |||||||
\(44\) | −115.106 | −0.394385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 298.804 | 0.957744 | ||||||||
\(47\) | −262.694 | −0.815275 | −0.407637 | − | 0.913144i | \(-0.633647\pi\) | ||||
−0.407637 | + | 0.913144i | \(0.633647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 150.556 | 0.401508 | ||||||||
\(53\) | −567.100 | −1.46976 | −0.734879 | − | 0.678199i | \(-0.762761\pi\) | ||||
−0.734879 | + | 0.678199i | \(0.762761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 172.378 | 0.411339 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 492.743 | 1.11552 | ||||||||
\(59\) | −839.890 | −1.85330 | −0.926648 | − | 0.375931i | \(-0.877323\pi\) | ||||
−0.926648 | + | 0.375931i | \(0.877323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −485.794 | −1.01966 | −0.509832 | − | 0.860274i | \(-0.670293\pi\) | ||||
−0.509832 | + | 0.860274i | \(0.670293\pi\) | |||||||
\(62\) | −572.811 | −1.17334 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 542.577 | 1.05972 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 333.691 | 0.608460 | 0.304230 | − | 0.952599i | \(-0.401601\pi\) | ||||
0.304230 | + | 0.952599i | \(0.401601\pi\) | |||||||
\(68\) | −12.8522 | −0.0229199 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −590.248 | −0.986613 | −0.493306 | − | 0.869856i | \(-0.664212\pi\) | ||||
−0.493306 | + | 0.869856i | \(0.664212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −490.701 | −0.786743 | −0.393371 | − | 0.919380i | \(-0.628691\pi\) | ||||
−0.393371 | + | 0.919380i | \(0.628691\pi\) | |||||||
\(74\) | −27.0647 | −0.0425164 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −346.309 | −0.522689 | ||||||||
\(77\) | −285.244 | −0.422164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 121.691 | 0.173308 | 0.0866539 | − | 0.996238i | \(-0.472383\pi\) | ||||
0.0866539 | + | 0.996238i | \(0.472383\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 254.228 | 0.342375 | ||||||||
\(83\) | 609.608 | 0.806183 | 0.403091 | − | 0.915160i | \(-0.367936\pi\) | ||||
0.403091 | + | 0.915160i | \(0.367936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −839.890 | −1.05311 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1003.47 | −1.21557 | ||||||||
\(89\) | −719.038 | −0.856381 | −0.428190 | − | 0.903689i | \(-0.640849\pi\) | ||||
−0.428190 | + | 0.903689i | \(0.640849\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 373.093 | 0.429789 | ||||||||
\(92\) | −371.023 | −0.420455 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −597.608 | −0.655729 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 637.877 | 0.667697 | 0.333849 | − | 0.942627i | \(-0.391653\pi\) | ||||
0.333849 | + | 0.942627i | \(0.391653\pi\) | |||||||
\(98\) | 111.471 | 0.114901 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −671.148 | −0.661205 | −0.330603 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330603 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 912.412 | 0.872841 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(104\) | 1312.51 | 1.23752 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1290.10 | −1.18213 | ||||||||
\(107\) | −116.736 | −0.105470 | −0.0527350 | − | 0.998609i | \(-0.516794\pi\) | ||||
−0.0527350 | + | 0.998609i | \(0.516794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 837.176 | 0.735660 | 0.367830 | − | 0.929893i | \(-0.380101\pi\) | ||||
0.367830 | + | 0.929893i | \(0.380101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 233.959 | 0.197385 | ||||||||
\(113\) | −1086.58 | −0.904572 | −0.452286 | − | 0.891873i | \(-0.649391\pi\) | ||||
−0.452286 | + | 0.891873i | \(0.649391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −611.836 | −0.489720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1910.68 | −1.49061 | ||||||||
\(119\) | −31.8488 | −0.0245343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 329.495 | 0.247554 | ||||||||
\(122\) | −1105.14 | −0.820121 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 711.256 | 0.515102 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 537.113 | 0.375284 | 0.187642 | − | 0.982237i | \(-0.439916\pi\) | ||||
0.187642 | + | 0.982237i | \(0.439916\pi\) | |||||||
\(128\) | 266.564 | 0.184071 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1497.39 | −0.998683 | −0.499341 | − | 0.866405i | \(-0.666425\pi\) | ||||
−0.499341 | + | 0.866405i | \(0.666425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −858.186 | −0.559505 | ||||||||
\(134\) | 759.120 | 0.489388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −112.042 | −0.0706433 | ||||||||
\(137\) | −1380.09 | −0.860650 | −0.430325 | − | 0.902674i | \(-0.641601\pi\) | ||||
−0.430325 | + | 0.902674i | \(0.641601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −141.980 | −0.0866374 | −0.0433187 | − | 0.999061i | \(-0.513793\pi\) | ||||
−0.0433187 | + | 0.999061i | \(0.513793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1342.76 | −0.793537 | ||||||||
\(143\) | −2171.89 | −1.27009 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1116.30 | −0.632781 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 33.6061 | 0.0186649 | ||||||||
\(149\) | 1943.87 | 1.06878 | 0.534390 | − | 0.845238i | \(-0.320542\pi\) | ||||
0.534390 | + | 0.845238i | \(0.320542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2654.76 | −1.43074 | −0.715370 | − | 0.698746i | \(-0.753742\pi\) | ||||
−0.715370 | + | 0.698746i | \(0.753742\pi\) | |||||||
\(152\) | −3019.03 | −1.61102 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −648.907 | −0.339548 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1665.22 | −0.846489 | −0.423244 | − | 0.906016i | \(-0.639109\pi\) | ||||
−0.423244 | + | 0.906016i | \(0.639109\pi\) | |||||||
\(158\) | 276.837 | 0.139392 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −919.430 | −0.450070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33.0732 | 0.0158926 | 0.00794629 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794629 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(164\) | −315.673 | −0.150304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1386.81 | 0.648417 | ||||||||
\(167\) | 1654.48 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 643.784 | 0.293029 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1042.89 | 0.462322 | ||||||||
\(173\) | 64.1909 | 0.0282101 | 0.0141050 | − | 0.999901i | \(-0.495510\pi\) | ||||
0.0141050 | + | 0.999901i | \(0.495510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1361.95 | −0.583300 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1635.75 | −0.688791 | ||||||||
\(179\) | −3914.68 | −1.63462 | −0.817309 | − | 0.576200i | \(-0.804535\pi\) | ||||
−0.817309 | + | 0.576200i | \(0.804535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2058.04 | −0.845156 | −0.422578 | − | 0.906327i | \(-0.638875\pi\) | ||||
−0.422578 | + | 0.906327i | \(0.638875\pi\) | |||||||
\(182\) | 848.756 | 0.345681 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3234.48 | −1.29592 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 185.402 | 0.0725023 | ||||||||
\(188\) | 742.046 | 0.287869 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −428.048 | −0.162160 | −0.0810798 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810798 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1604.93 | −0.598576 | −0.299288 | − | 0.954163i | \(-0.596749\pi\) | ||||
−0.299288 | + | 0.954163i | \(0.596749\pi\) | |||||||
\(194\) | 1451.12 | 0.537032 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −138.413 | −0.0504420 | ||||||||
\(197\) | 3738.83 | 1.35218 | 0.676092 | − | 0.736817i | \(-0.263672\pi\) | ||||
0.676092 | + | 0.736817i | \(0.263672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −349.030 | −0.124332 | −0.0621660 | − | 0.998066i | \(-0.519801\pi\) | ||||
−0.0621660 | + | 0.998066i | \(0.519801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1526.81 | −0.531810 | ||||||||
\(203\) | −1516.19 | −0.524214 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2075.66 | 0.702030 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1781.40 | 0.593836 | ||||||||
\(209\) | 4995.77 | 1.65342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2588.58 | 0.844574 | 0.422287 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422287 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(212\) | 1601.92 | 0.518962 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −265.565 | −0.0848300 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1762.56 | 0.551384 | ||||||||
\(218\) | 1904.51 | 0.591695 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −242.502 | −0.0738119 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3236.21 | 0.971804 | 0.485902 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485902 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(224\) | −846.785 | −0.252581 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2471.88 | −0.727552 | ||||||||
\(227\) | −5631.62 | −1.64662 | −0.823312 | − | 0.567589i | \(-0.807876\pi\) | ||||
−0.823312 | + | 0.567589i | \(0.807876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3770.25 | 1.08797 | 0.543985 | − | 0.839095i | \(-0.316915\pi\) | ||||
0.543985 | + | 0.839095i | \(0.316915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5333.82 | −1.50941 | ||||||||
\(233\) | −6560.90 | −1.84472 | −0.922358 | − | 0.386336i | \(-0.873741\pi\) | ||||
−0.922358 | + | 0.386336i | \(0.873741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2372.48 | 0.654387 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −72.4535 | −0.0197330 | ||||||||
\(239\) | 771.444 | 0.208789 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1252.10 | 0.334668 | 0.167334 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167334 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(242\) | 749.574 | 0.199109 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1372.25 | 0.360037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6534.35 | −1.68328 | ||||||||
\(248\) | 6200.53 | 1.58764 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5166.27 | −1.29917 | −0.649586 | − | 0.760288i | \(-0.725058\pi\) | ||||
−0.649586 | + | 0.760288i | \(0.725058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5352.29 | 1.33002 | ||||||||
\(254\) | 1221.89 | 0.301843 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3734.21 | −0.911672 | ||||||||
\(257\) | 2767.45 | 0.671707 | 0.335854 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335854 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 83.2791 | 0.0199796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3406.44 | −0.803245 | ||||||||
\(263\) | −4101.78 | −0.961699 | −0.480849 | − | 0.876803i | \(-0.659672\pi\) | ||||
−0.480849 | + | 0.876803i | \(0.659672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1952.30 | −0.450013 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −942.594 | −0.214844 | ||||||||
\(269\) | 6950.84 | 1.57546 | 0.787732 | − | 0.616018i | \(-0.211255\pi\) | ||||
0.787732 | + | 0.616018i | \(0.211255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7140.29 | −1.60052 | −0.800262 | − | 0.599651i | \(-0.795306\pi\) | ||||
−0.800262 | + | 0.599651i | \(0.795306\pi\) | |||||||
\(272\) | −152.068 | −0.0338988 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3139.59 | −0.692225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1320.51 | −0.286433 | −0.143217 | − | 0.989691i | \(-0.545745\pi\) | ||||
−0.143217 | + | 0.989691i | \(0.545745\pi\) | |||||||
\(278\) | −322.993 | −0.0696829 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 204.309 | 0.0433738 | 0.0216869 | − | 0.999765i | \(-0.493096\pi\) | ||||
0.0216869 | + | 0.999765i | \(0.493096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −975.794 | −0.204964 | −0.102482 | − | 0.994735i | \(-0.532678\pi\) | ||||
−0.102482 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(284\) | 1667.30 | 0.348367 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4940.87 | −1.02154 | ||||||||
\(287\) | −782.267 | −0.160891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4892.30 | −0.995786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1386.11 | 0.277794 | ||||||||
\(293\) | 607.919 | 0.121212 | 0.0606058 | − | 0.998162i | \(-0.480697\pi\) | ||||
0.0606058 | + | 0.998162i | \(0.480697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 292.969 | 0.0575286 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4422.14 | 0.859624 | ||||||||
\(299\) | −7000.67 | −1.35405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2584.37 | 0.494886 | ||||||||
\(302\) | −6039.37 | −1.15075 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4097.56 | −0.773064 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8037.08 | −1.49414 | −0.747069 | − | 0.664747i | \(-0.768539\pi\) | ||||
−0.747069 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(308\) | 805.744 | 0.149063 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5311.60 | −0.968468 | −0.484234 | − | 0.874939i | \(-0.660902\pi\) | ||||
−0.484234 | + | 0.874939i | \(0.660902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1531.61 | 0.276587 | 0.138293 | − | 0.990391i | \(-0.455838\pi\) | ||||
0.138293 | + | 0.990391i | \(0.455838\pi\) | |||||||
\(314\) | −3788.23 | −0.680835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −343.747 | −0.0611939 | ||||||||
\(317\) | 4219.19 | 0.747549 | 0.373775 | − | 0.927520i | \(-0.378063\pi\) | ||||
0.373775 | + | 0.927520i | \(0.378063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8826.19 | 1.54913 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2091.63 | −0.361993 | ||||||||
\(323\) | 557.801 | 0.0960893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 75.2387 | 0.0127825 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2751.95 | −0.463265 | ||||||||
\(329\) | 1838.86 | 0.308145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8298.19 | 1.37797 | 0.688987 | − | 0.724773i | \(-0.258056\pi\) | ||||
0.688987 | + | 0.724773i | \(0.258056\pi\) | |||||||
\(332\) | −1721.99 | −0.284658 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3763.79 | 0.616604 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4348.44 | 0.702892 | 0.351446 | − | 0.936208i | \(-0.385690\pi\) | ||||
0.351446 | + | 0.936208i | \(0.385690\pi\) | |||||||
\(338\) | 1464.56 | 0.235684 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10260.4 | −1.62942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 9091.60 | 1.42496 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 146.029 | 0.0226895 | ||||||||
\(347\) | −8345.54 | −1.29110 | −0.645550 | − | 0.763718i | \(-0.723372\pi\) | ||||
−0.645550 | + | 0.763718i | \(0.723372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9982.54 | −1.53110 | −0.765549 | − | 0.643378i | \(-0.777532\pi\) | ||||
−0.765549 | + | 0.643378i | \(0.777532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4929.40 | 0.746414 | ||||||||
\(353\) | 8801.59 | 1.32709 | 0.663543 | − | 0.748138i | \(-0.269052\pi\) | ||||
0.663543 | + | 0.748138i | \(0.269052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2031.10 | 0.302383 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8905.56 | −1.31473 | ||||||||
\(359\) | 524.039 | 0.0770409 | 0.0385205 | − | 0.999258i | \(-0.487736\pi\) | ||||
0.0385205 | + | 0.999258i | \(0.487736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8171.27 | 1.19132 | ||||||||
\(362\) | −4681.88 | −0.679763 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1053.90 | −0.151756 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6362.72 | 0.904991 | 0.452495 | − | 0.891767i | \(-0.350534\pi\) | ||||
0.452495 | + | 0.891767i | \(0.350534\pi\) | |||||||
\(368\) | −4389.99 | −0.621858 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3969.70 | 0.555516 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11265.8 | 1.56387 | 0.781935 | − | 0.623361i | \(-0.214233\pi\) | ||||
0.781935 | + | 0.623361i | \(0.214233\pi\) | |||||||
\(374\) | 421.774 | 0.0583140 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6468.96 | 0.887263 | ||||||||
\(377\) | −11544.5 | −1.57711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1151.71 | −0.156094 | −0.0780470 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780470 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −973.774 | −0.130426 | ||||||||
\(383\) | −151.554 | −0.0202195 | −0.0101097 | − | 0.999949i | \(-0.503218\pi\) | ||||
−0.0101097 | + | 0.999949i | \(0.503218\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3651.08 | −0.481437 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1801.84 | −0.235760 | ||||||||
\(389\) | −4794.18 | −0.624870 | −0.312435 | − | 0.949939i | \(-0.601145\pi\) | ||||
−0.312435 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 597.608 | 0.0772950 | ||||||||
\(392\) | −1206.65 | −0.155471 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8505.52 | 1.08757 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4623.94 | 0.584556 | 0.292278 | − | 0.956333i | \(-0.405587\pi\) | ||||
0.292278 | + | 0.956333i | \(0.405587\pi\) | |||||||
\(398\) | −794.014 | −0.100001 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3610.63 | 0.449642 | 0.224821 | − | 0.974400i | \(-0.427820\pi\) | ||||
0.224821 | + | 0.974400i | \(0.427820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13420.4 | 1.65885 | ||||||||
\(404\) | 1895.83 | 0.233467 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3449.20 | −0.421628 | ||||||||
\(407\) | −484.794 | −0.0590426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8959.57 | 1.08318 | 0.541592 | − | 0.840641i | \(-0.317822\pi\) | ||||
0.541592 | + | 0.840641i | \(0.317822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2577.34 | −0.308195 | ||||||||
\(413\) | 5879.23 | 0.700480 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6447.54 | −0.759896 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11365.0 | 1.32985 | ||||||||
\(419\) | 7078.28 | 0.825290 | 0.412645 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412645 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11551.5 | 1.33725 | 0.668626 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668626 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(422\) | 5888.80 | 0.679295 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13965.1 | 1.59954 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3400.56 | 0.385397 | ||||||||
\(428\) | 329.750 | 0.0372408 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4064.38 | 0.454232 | 0.227116 | − | 0.973868i | \(-0.427070\pi\) | ||||
0.227116 | + | 0.973868i | \(0.427070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17456.3 | −1.93740 | −0.968701 | − | 0.248229i | \(-0.920151\pi\) | ||||
−0.968701 | + | 0.248229i | \(0.920151\pi\) | |||||||
\(434\) | 4009.67 | 0.443480 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2364.81 | −0.259757 | ||||||||
\(437\) | 16102.9 | 1.76271 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4595.39 | 0.499604 | 0.249802 | − | 0.968297i | \(-0.419635\pi\) | ||||
0.249802 | + | 0.968297i | \(0.419635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −551.671 | −0.0593672 | ||||||||
\(443\) | −306.214 | −0.0328412 | −0.0164206 | − | 0.999865i | \(-0.505227\pi\) | ||||
−0.0164206 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7362.10 | 0.781627 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3798.04 | −0.400537 | ||||||||
\(449\) | −9229.22 | −0.970053 | −0.485026 | − | 0.874500i | \(-0.661190\pi\) | ||||
−0.485026 | + | 0.874500i | \(0.661190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4553.82 | 0.475457 | ||||||||
\(452\) | 3069.31 | 0.319399 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12811.5 | −1.32439 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10992.2 | 1.12515 | 0.562577 | − | 0.826745i | \(-0.309810\pi\) | ||||
0.562577 | + | 0.826745i | \(0.309810\pi\) | |||||||
\(458\) | 8577.01 | 0.875059 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7387.88 | −0.746394 | −0.373197 | − | 0.927752i | \(-0.621739\pi\) | ||||
−0.373197 | + | 0.927752i | \(0.621739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10163.8 | −1.02020 | −0.510101 | − | 0.860114i | \(-0.670392\pi\) | ||||
−0.510101 | + | 0.860114i | \(0.670392\pi\) | |||||||
\(464\) | −7239.30 | −0.724302 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14925.5 | −1.48371 | ||||||||
\(467\) | −15814.6 | −1.56705 | −0.783524 | − | 0.621362i | \(-0.786580\pi\) | ||||
−0.783524 | + | 0.621362i | \(0.786580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2335.84 | −0.229976 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20682.6 | 2.01694 | ||||||||
\(473\) | −15044.4 | −1.46246 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 89.9651 | 0.00866290 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1754.97 | 0.167930 | ||||||||
\(479\) | 1444.85 | 0.137823 | 0.0689113 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689113 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 634.099 | 0.0601090 | ||||||||
\(482\) | 2848.43 | 0.269175 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −930.742 | −0.0874100 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 489.402 | 0.0455378 | 0.0227689 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227689 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(488\) | 11962.9 | 1.10970 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3941.30 | 0.362257 | 0.181129 | − | 0.983459i | \(-0.442025\pi\) | ||||
0.181129 | + | 0.983459i | \(0.442025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 985.485 | 0.0900284 | ||||||||
\(494\) | −14865.1 | −1.35387 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8415.65 | 0.761843 | ||||||||
\(497\) | 4131.73 | 0.372905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0894 | 0.000994850 0 | 0.000497425 | − | 1.00000i | \(-0.499842\pi\) | ||||
0.000497425 | 1.00000i | \(0.499842\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11752.8 | −1.04493 | ||||||||
\(503\) | 7088.41 | 0.628343 | 0.314172 | − | 0.949366i | \(-0.398273\pi\) | ||||
0.314172 | + | 0.949366i | \(0.398273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12176.0 | 1.06974 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1517.21 | −0.132511 | ||||||||
\(509\) | −17588.4 | −1.53162 | −0.765810 | − | 0.643067i | \(-0.777662\pi\) | ||||
−0.765810 | + | 0.643067i | \(0.777662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3434.91 | 0.297361 | ||||||||
\(512\) | −10627.5 | −0.917333 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6295.72 | 0.540257 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10704.6 | −0.910613 | ||||||||
\(518\) | 189.453 | 0.0160697 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11646.6 | 0.979360 | 0.489680 | − | 0.871902i | \(-0.337114\pi\) | ||||
0.489680 | + | 0.871902i | \(0.337114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8965.82 | −0.749614 | −0.374807 | − | 0.927103i | \(-0.622291\pi\) | ||||
−0.374807 | + | 0.927103i | \(0.622291\pi\) | |||||||
\(524\) | 4229.75 | 0.352629 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9331.22 | −0.773499 | ||||||||
\(527\) | −1145.62 | −0.0946946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5085.08 | 0.417941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2424.16 | 0.197558 | ||||||||
\(533\) | −5956.30 | −0.484045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8217.28 | −0.662187 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15812.6 | 1.26715 | ||||||||
\(539\) | 1996.71 | 0.159563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −195.272 | −0.0155183 | −0.00775914 | − | 0.999970i | \(-0.502470\pi\) | ||||
−0.00775914 | + | 0.999970i | \(0.502470\pi\) | |||||||
\(542\) | −16243.6 | −1.28731 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 550.390 | 0.0433783 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1399.26 | 0.109375 | 0.0546874 | − | 0.998504i | \(-0.482584\pi\) | ||||
0.0546874 | + | 0.998504i | \(0.482584\pi\) | |||||||
\(548\) | 3898.41 | 0.303890 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26554.5 | 2.05310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −851.837 | −0.0655042 | ||||||||
\(554\) | −3004.06 | −0.230380 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 401.059 | 0.0305911 | ||||||||
\(557\) | 43.0467 | 0.00327459 | 0.00163730 | − | 0.999999i | \(-0.499479\pi\) | ||||
0.00163730 | + | 0.999999i | \(0.499479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19677.8 | 1.48888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 464.786 | 0.0348858 | ||||||||
\(563\) | −19232.9 | −1.43973 | −0.719865 | − | 0.694114i | \(-0.755797\pi\) | ||||
−0.719865 | + | 0.694114i | \(0.755797\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2219.85 | −0.164854 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14535.1 | 1.07373 | ||||||||
\(569\) | −5163.98 | −0.380466 | −0.190233 | − | 0.981739i | \(-0.560924\pi\) | ||||
−0.190233 | + | 0.981739i | \(0.560924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10231.9 | −0.749899 | −0.374950 | − | 0.927045i | \(-0.622340\pi\) | ||||
−0.374950 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(572\) | 6135.05 | 0.448460 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1779.59 | −0.129406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16563.7 | −1.19507 | −0.597537 | − | 0.801842i | \(-0.703854\pi\) | ||||
−0.597537 | + | 0.801842i | \(0.703854\pi\) | |||||||
\(578\) | −11129.6 | −0.800916 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4267.26 | −0.304708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23108.8 | −1.64163 | ||||||||
\(584\) | 12083.7 | 0.856212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1382.96 | 0.0974910 | ||||||||
\(587\) | 16020.6 | 1.12648 | 0.563239 | − | 0.826294i | \(-0.309555\pi\) | ||||
0.563239 | + | 0.826294i | \(0.309555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30869.4 | −2.15951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 397.631 | 0.0276057 | ||||||||
\(593\) | −6771.14 | −0.468900 | −0.234450 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234450 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5490.95 | −0.377379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15926.0 | −1.08906 | ||||||||
\(599\) | −11070.2 | −0.755120 | −0.377560 | − | 0.925985i | \(-0.623237\pi\) | ||||
−0.377560 | + | 0.925985i | \(0.623237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24187.7 | −1.64166 | −0.820830 | − | 0.571173i | \(-0.806489\pi\) | ||||
−0.820830 | + | 0.571173i | \(0.806489\pi\) | |||||||
\(602\) | 5879.23 | 0.398039 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7499.05 | 0.505185 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10074.1 | 0.673631 | 0.336816 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(608\) | 14830.6 | 0.989243 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14001.3 | 0.927060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11114.6 | 0.732323 | 0.366161 | − | 0.930551i | \(-0.380672\pi\) | ||||
0.366161 | + | 0.930551i | \(0.380672\pi\) | |||||||
\(614\) | −18283.7 | −1.20174 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7024.26 | 0.459441 | ||||||||
\(617\) | 20496.4 | 1.33737 | 0.668683 | − | 0.743548i | \(-0.266858\pi\) | ||||
0.668683 | + | 0.743548i | \(0.266858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16714.4 | −1.08532 | −0.542658 | − | 0.839954i | \(-0.682582\pi\) | ||||
−0.542658 | + | 0.839954i | \(0.682582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12083.5 | −0.778943 | ||||||||
\(623\) | 5033.27 | 0.323682 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3484.28 | 0.222460 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4703.82 | 0.298890 | ||||||||
\(629\) | −54.1295 | −0.00343129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9168.53 | 0.578437 | 0.289218 | − | 0.957263i | \(-0.406605\pi\) | ||||
0.289218 | + | 0.957263i | \(0.406605\pi\) | |||||||
\(632\) | −2996.69 | −0.188611 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9598.30 | 0.601257 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2611.65 | −0.162445 | ||||||||
\(638\) | 20078.9 | 1.24597 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4273.37 | 0.263319 | 0.131660 | − | 0.991295i | \(-0.457969\pi\) | ||||
0.131660 | + | 0.991295i | \(0.457969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2955.75 | −0.181281 | −0.0906404 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(644\) | 2597.16 | 0.158917 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1268.95 | 0.0772851 | ||||||||
\(647\) | 22701.2 | 1.37941 | 0.689704 | − | 0.724091i | \(-0.257741\pi\) | ||||
0.689704 | + | 0.724091i | \(0.257741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34224.8 | −2.07002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −93.4235 | −0.00561158 | ||||||||
\(653\) | 1537.81 | 0.0921582 | 0.0460791 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460791 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3735.08 | −0.222302 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4183.26 | 0.247842 | ||||||||
\(659\) | −12338.1 | −0.729323 | −0.364661 | − | 0.931140i | \(-0.618815\pi\) | ||||
−0.364661 | + | 0.931140i | \(0.618815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1845.10 | 0.108572 | 0.0542859 | − | 0.998525i | \(-0.482712\pi\) | ||||
0.0542859 | + | 0.998525i | \(0.482712\pi\) | |||||||
\(662\) | 18877.7 | 1.10831 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15011.8 | −0.877369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28449.5 | 1.65153 | ||||||||
\(668\) | −4673.48 | −0.270692 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19795.7 | −1.13890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23955.4 | −1.37208 | −0.686041 | − | 0.727563i | \(-0.740653\pi\) | ||||
−0.686041 | + | 0.727563i | \(0.740653\pi\) | |||||||
\(674\) | 9892.34 | 0.565339 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1818.53 | −0.103467 | ||||||||
\(677\) | −3678.26 | −0.208814 | −0.104407 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104407 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4465.14 | −0.252366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −23341.6 | −1.31055 | ||||||||
\(683\) | 4390.87 | 0.245991 | 0.122996 | − | 0.992407i | \(-0.460750\pi\) | ||||
0.122996 | + | 0.992407i | \(0.460750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −780.297 | −0.0434284 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12339.6 | 0.683781 | ||||||||
\(689\) | 30225.8 | 1.67128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10371.7 | 0.570994 | 0.285497 | − | 0.958380i | \(-0.407841\pi\) | ||||
0.285497 | + | 0.958380i | \(0.407841\pi\) | |||||||
\(692\) | −181.323 | −0.00996081 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18985.4 | −1.03844 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 508.455 | 0.0276314 | ||||||||
\(698\) | −22709.4 | −1.23147 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −109.675 | −0.00590922 | −0.00295461 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295461 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1458.55 | −0.0782508 | ||||||||
\(704\) | 22109.6 | 1.18364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20022.9 | 1.06738 | ||||||||
\(707\) | 4698.03 | 0.249912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26918.8 | 1.42589 | 0.712944 | − | 0.701221i | \(-0.247361\pi\) | ||||
0.712944 | + | 0.701221i | \(0.247361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17706.6 | 0.931999 | ||||||||
\(713\) | −33072.4 | −1.73713 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11058.0 | 0.577174 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1192.14 | 0.0619644 | ||||||||
\(719\) | −15170.8 | −0.786889 | −0.393445 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6386.88 | −0.329903 | ||||||||
\(722\) | 18589.0 | 0.958185 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5813.46 | 0.298419 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33286.9 | 1.69813 | 0.849066 | − | 0.528288i | \(-0.177166\pi\) | ||||
0.849066 | + | 0.528288i | \(0.177166\pi\) | |||||||
\(728\) | −9187.57 | −0.467739 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1679.78 | −0.0849917 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20544.0 | −1.03521 | −0.517607 | − | 0.855619i | \(-0.673177\pi\) | ||||
−0.517607 | + | 0.855619i | \(0.673177\pi\) | |||||||
\(734\) | 14474.7 | 0.727888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15889.0 | 0.795755 | ||||||||
\(737\) | 13597.6 | 0.679614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34357.2 | 1.71022 | 0.855109 | − | 0.518449i | \(-0.173490\pi\) | ||||
0.855109 | + | 0.518449i | \(0.173490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9030.73 | 0.446804 | ||||||||
\(743\) | 8166.99 | 0.403254 | 0.201627 | − | 0.979462i | \(-0.435377\pi\) | ||||
0.201627 | + | 0.979462i | \(0.435377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25628.9 | 1.25783 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −523.715 | −0.0256001 | ||||||||
\(749\) | 817.151 | 0.0398639 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17080.1 | 0.829909 | 0.414954 | − | 0.909842i | \(-0.363798\pi\) | ||||
0.414954 | + | 0.909842i | \(0.363798\pi\) | |||||||
\(752\) | 8779.97 | 0.425761 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26262.7 | −1.26848 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16324.0 | 0.783758 | 0.391879 | − | 0.920017i | \(-0.371825\pi\) | ||||
0.391879 | + | 0.920017i | \(0.371825\pi\) | |||||||
\(758\) | −2620.06 | −0.125547 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32366.2 | 1.54175 | 0.770875 | − | 0.636986i | \(-0.219819\pi\) | ||||
0.770875 | + | 0.636986i | \(0.219819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5860.23 | −0.278053 | ||||||||
\(764\) | 1209.13 | 0.0572576 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −344.774 | −0.0162626 | ||||||||
\(767\) | 44765.3 | 2.10741 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7948.44 | −0.372728 | −0.186364 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186364 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4533.52 | 0.211354 | ||||||||
\(773\) | 17819.3 | 0.829127 | 0.414564 | − | 0.910020i | \(-0.363934\pi\) | ||||
0.414564 | + | 0.910020i | \(0.363934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15708.0 | −0.726655 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10906.4 | −0.502586 | ||||||||
\(779\) | 13700.6 | 0.630136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24052.1 | −1.10199 | ||||||||
\(782\) | 1359.51 | 0.0621687 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1637.72 | −0.0746044 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2912.38 | −0.131912 | −0.0659562 | − | 0.997823i | \(-0.521010\pi\) | ||||
−0.0659562 | + | 0.997823i | \(0.521010\pi\) | |||||||
\(788\) | −10561.3 | −0.477448 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7606.05 | 0.341896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25892.3 | 1.15948 | ||||||||
\(794\) | 10519.1 | 0.470162 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 985.923 | 0.0439009 | ||||||||
\(797\) | −33789.1 | −1.50172 | −0.750861 | − | 0.660460i | \(-0.770361\pi\) | ||||
−0.750861 | + | 0.660460i | \(0.770361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1195.22 | −0.0529208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8213.90 | 0.361649 | ||||||||
\(803\) | −19995.7 | −0.878744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30530.2 | 1.33422 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16527.3 | 0.719589 | ||||||||
\(809\) | −1252.13 | −0.0544159 | −0.0272079 | − | 0.999630i | \(-0.508662\pi\) | ||||
−0.0272079 | + | 0.999630i | \(0.508662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31913.1 | −1.38178 | −0.690889 | − | 0.722961i | \(-0.742781\pi\) | ||||
−0.690889 | + | 0.722961i | \(0.742781\pi\) | |||||||
\(812\) | 4282.85 | 0.185097 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1102.87 | −0.0474882 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45262.7 | −1.93824 | ||||||||
\(818\) | 20382.3 | 0.871210 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30742.4 | −1.30684 | −0.653421 | − | 0.756995i | \(-0.726667\pi\) | ||||
−0.653421 | + | 0.756995i | \(0.726667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13822.6 | 0.585449 | 0.292724 | − | 0.956197i | \(-0.405438\pi\) | ||||
0.292724 | + | 0.956197i | \(0.405438\pi\) | |||||||
\(824\) | −22468.5 | −0.949913 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13374.8 | 0.563399 | ||||||||
\(827\) | −42107.1 | −1.77051 | −0.885253 | − | 0.465110i | \(-0.846015\pi\) | ||||
−0.885253 | + | 0.465110i | \(0.846015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38763.8 | −1.62403 | −0.812015 | − | 0.583636i | \(-0.801629\pi\) | ||||
−0.812015 | + | 0.583636i | \(0.801629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28918.8 | −1.20502 | ||||||||
\(833\) | 222.942 | 0.00927308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14111.8 | −0.583812 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16102.5 | 0.663784 | ||||||||
\(839\) | −16896.3 | −0.695262 | −0.347631 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347631 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22525.7 | 0.923601 | ||||||||
\(842\) | 26278.6 | 1.07556 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7312.09 | −0.298214 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2306.47 | −0.0935668 | ||||||||
\(848\) | 18954.0 | 0.767552 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1562.64 | −0.0629455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46429.3 | −1.86367 | −0.931833 | − | 0.362887i | \(-0.881791\pi\) | ||||
−0.931833 | + | 0.362887i | \(0.881791\pi\) | |||||||
\(854\) | 7735.99 | 0.309977 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2874.67 | 0.114783 | ||||||||
\(857\) | 21206.4 | 0.845272 | 0.422636 | − | 0.906300i | \(-0.361105\pi\) | ||||
0.422636 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13876.2 | 0.551163 | 0.275581 | − | 0.961278i | \(-0.411130\pi\) | ||||
0.275581 | + | 0.961278i | \(0.411130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9246.12 | 0.365341 | ||||||||
\(863\) | 14337.1 | 0.565515 | 0.282757 | − | 0.959191i | \(-0.408751\pi\) | ||||
0.282757 | + | 0.959191i | \(0.408751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39711.6 | −1.55826 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4978.79 | −0.194690 | ||||||||
\(869\) | 4958.81 | 0.193574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17785.4 | −0.691889 | ||||||||
\(872\) | −20615.8 | −0.800619 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36632.8 | 1.41776 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24369.3 | 0.938304 | 0.469152 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469152 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(878\) | 10454.1 | 0.401834 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26127.0 | 0.999140 | 0.499570 | − | 0.866273i | \(-0.333491\pi\) | ||||
0.499570 | + | 0.866273i | \(0.333491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15713.1 | 0.598855 | 0.299428 | − | 0.954119i | \(-0.403204\pi\) | ||||
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(884\) | 685.007 | 0.0260625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −696.611 | −0.0264143 | ||||||||
\(887\) | 13139.5 | 0.497385 | 0.248692 | − | 0.968583i | \(-0.419999\pi\) | ||||
0.248692 | + | 0.968583i | \(0.419999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3759.79 | −0.141844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9141.48 | −0.343138 | ||||||||
\(893\) | −32205.8 | −1.20686 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1865.95 | −0.0695725 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20995.7 | −0.780218 | ||||||||
\(899\) | −54538.1 | −2.02330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2580.21 | −0.0954043 | ||||||||
\(902\) | 10359.6 | 0.382412 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26757.4 | 0.984446 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3799.71 | 0.139104 | 0.0695519 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695519 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(908\) | 15907.9 | 0.581413 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51528.4 | 1.87400 | 0.936998 | − | 0.349334i | \(-0.113592\pi\) | ||||
0.936998 | + | 0.349334i | \(0.113592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24841.0 | 0.900458 | ||||||||
\(914\) | 25006.4 | 0.904966 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10650.0 | −0.384156 | ||||||||
\(917\) | 10481.7 | 0.377467 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16984.7 | −0.609657 | −0.304828 | − | 0.952407i | \(-0.598599\pi\) | ||||
−0.304828 | + | 0.952407i | \(0.598599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16806.8 | −0.600329 | ||||||||
\(923\) | 31459.6 | 1.12189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23121.9 | −0.820553 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26201.7 | 0.926846 | ||||||||
\(929\) | 5451.85 | 0.192540 | 0.0962699 | − | 0.995355i | \(-0.469309\pi\) | ||||
0.0962699 | + | 0.995355i | \(0.469309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6007.30 | 0.211473 | ||||||||
\(932\) | 18532.9 | 0.651358 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35976.8 | −1.26038 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42429.4 | −1.47930 | −0.739652 | − | 0.672989i | \(-0.765010\pi\) | ||||
−0.739652 | + | 0.672989i | \(0.765010\pi\) | |||||||
\(938\) | −5313.84 | −0.184971 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32977.9 | 1.14245 | 0.571226 | − | 0.820793i | \(-0.306468\pi\) | ||||
0.571226 | + | 0.820793i | \(0.306468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14678.4 | 0.506886 | ||||||||
\(944\) | 28071.5 | 0.967848 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34224.8 | −1.17626 | ||||||||
\(947\) | −23753.4 | −0.815082 | −0.407541 | − | 0.913187i | \(-0.633614\pi\) | ||||
−0.407541 | + | 0.913187i | \(0.633614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26153.9 | 0.894616 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 784.291 | 0.0267006 | ||||||||
\(953\) | −28074.3 | −0.954267 | −0.477134 | − | 0.878831i | \(-0.658324\pi\) | ||||
−0.477134 | + | 0.878831i | \(0.658324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2179.14 | −0.0737221 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3286.92 | 0.110851 | ||||||||
\(959\) | 9660.63 | 0.325295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33609.2 | 1.12817 | ||||||||
\(962\) | 1442.52 | 0.0483460 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3536.88 | −0.118169 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11150.3 | 0.370806 | 0.185403 | − | 0.982663i | \(-0.440641\pi\) | ||||
0.185403 | + | 0.982663i | \(0.440641\pi\) | |||||||
\(968\) | −8113.95 | −0.269414 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6059.04 | −0.200251 | −0.100126 | − | 0.994975i | \(-0.531924\pi\) | ||||
−0.100126 | + | 0.994975i | \(0.531924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 993.861 | 0.0327459 | ||||||||
\(974\) | 1113.35 | 0.0366263 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16236.6 | 0.532500 | ||||||||
\(977\) | 5700.49 | 0.186668 | 0.0933341 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933341 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29300.2 | −0.956526 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8966.12 | 0.291365 | ||||||||
\(983\) | 197.480 | 0.00640757 | 0.00320378 | − | 0.999995i | \(-0.498980\pi\) | ||||
0.00320378 | + | 0.999995i | \(0.498980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2241.90 | 0.0724103 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18457.9 | 0.594357 | ||||||||
\(989\) | −48492.9 | −1.55913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20620.8 | 0.660990 | 0.330495 | − | 0.943808i | \(-0.392784\pi\) | ||||
0.330495 | + | 0.943808i | \(0.392784\pi\) | |||||||
\(992\) | −30459.3 | −0.974884 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9399.35 | 0.299929 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19326.8 | −0.613928 | −0.306964 | − | 0.951721i | \(-0.599313\pi\) | ||||
−0.306964 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(998\) | 25.2275 | 0.000800162 0 | ||||||||
\(999\) | 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 | 1575.4.a.p.1.2 | 2 | ||
3.2 | odd | 2 | 525.4.a.n.1.1 | 2 | |||
5.4 | even | 2 | 63.4.a.e.1.1 | 2 | |||
15.2 | even | 4 | 525.4.d.g.274.2 | 4 | |||
15.8 | even | 4 | 525.4.d.g.274.3 | 4 | |||
15.14 | odd | 2 | 21.4.a.c.1.2 | ✓ | 2 | ||
20.19 | odd | 2 | 1008.4.a.ba.1.2 | 2 | |||
35.4 | even | 6 | 441.4.e.q.226.2 | 4 | |||
35.9 | even | 6 | 441.4.e.q.361.2 | 4 | |||
35.19 | odd | 6 | 441.4.e.p.361.2 | 4 | |||
35.24 | odd | 6 | 441.4.e.p.226.2 | 4 | |||
35.34 | odd | 2 | 441.4.a.r.1.1 | 2 | |||
60.59 | even | 2 | 336.4.a.m.1.1 | 2 | |||
105.44 | odd | 6 | 147.4.e.l.67.1 | 4 | |||
105.59 | even | 6 | 147.4.e.m.79.1 | 4 | |||
105.74 | odd | 6 | 147.4.e.l.79.1 | 4 | |||
105.89 | even | 6 | 147.4.e.m.67.1 | 4 | |||
105.104 | even | 2 | 147.4.a.i.1.2 | 2 | |||
120.29 | odd | 2 | 1344.4.a.bg.1.2 | 2 | |||
120.59 | even | 2 | 1344.4.a.bo.1.2 | 2 | |||
420.419 | odd | 2 | 2352.4.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
63.4.a.e.1.1 | 2 | 5.4 | even | 2 | |||
147.4.a.i.1.2 | 2 | 105.104 | even | 2 | |||
147.4.e.l.67.1 | 4 | 105.44 | odd | 6 | |||
147.4.e.l.79.1 | 4 | 105.74 | odd | 6 | |||
147.4.e.m.67.1 | 4 | 105.89 | even | 6 | |||
147.4.e.m.79.1 | 4 | 105.59 | even | 6 | |||
336.4.a.m.1.1 | 2 | 60.59 | even | 2 | |||
441.4.a.r.1.1 | 2 | 35.34 | odd | 2 | |||
441.4.e.p.226.2 | 4 | 35.24 | odd | 6 | |||
441.4.e.p.361.2 | 4 | 35.19 | odd | 6 | |||
441.4.e.q.226.2 | 4 | 35.4 | even | 6 | |||
441.4.e.q.361.2 | 4 | 35.9 | even | 6 | |||
525.4.a.n.1.1 | 2 | 3.2 | odd | 2 | |||
525.4.d.g.274.2 | 4 | 15.2 | even | 4 | |||
525.4.d.g.274.3 | 4 | 15.8 | even | 4 | |||
1008.4.a.ba.1.2 | 2 | 20.19 | odd | 2 | |||
1344.4.a.bg.1.2 | 2 | 120.29 | odd | 2 | |||
1344.4.a.bo.1.2 | 2 | 120.59 | even | 2 | |||
1575.4.a.p.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.bz.1.2 | 2 | 420.419 | odd | 2 |