Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 121x^{5} + 402x^{4} + 4234x^{3} - 14542x^{2} - 40996x + 141664 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-4.00212\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.923414 | 0.177711 | 0.0888556 | − | 0.996045i | \(-0.471679\pi\) | ||||
0.0888556 | + | 0.996045i | \(0.471679\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.670967 | 0.0600131 | 0.0300066 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300066 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28.6780 | −1.54847 | −0.774233 | − | 0.632901i | \(-0.781864\pi\) | ||||
−0.774233 | + | 0.632901i | \(0.781864\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.1473 | −0.968419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24.1312 | −0.661439 | −0.330719 | − | 0.943729i | \(-0.607291\pi\) | ||||
−0.330719 | + | 0.943729i | \(0.607291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.5373 | 0.374152 | 0.187076 | − | 0.982345i | \(-0.440099\pi\) | ||||
0.187076 | + | 0.982345i | \(0.440099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.619580 | 0.0106650 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.1485 | −0.872393 | −0.436197 | − | 0.899851i | \(-0.643675\pi\) | ||||
−0.436197 | + | 0.899851i | \(0.643675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.4817 | −0.275180 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 160.534 | 1.45538 | 0.727689 | − | 0.685907i | \(-0.240594\pi\) | ||||
0.727689 | + | 0.685907i | \(0.240594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.550 | −0.996398 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −49.0770 | −0.349810 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −287.921 | −1.84364 | −0.921819 | − | 0.387620i | \(-0.873297\pi\) | ||||
−0.921819 | + | 0.387620i | \(0.873297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −47.5884 | −0.275714 | −0.137857 | − | 0.990452i | \(-0.544021\pi\) | ||||
−0.137857 | + | 0.990452i | \(0.544021\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −22.2831 | −0.117545 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.2420 | −0.0929283 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 237.442 | 1.05501 | 0.527504 | − | 0.849552i | \(-0.323128\pi\) | ||||
0.527504 | + | 0.849552i | \(0.323128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.1942 | 0.0664909 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 197.712 | 0.753109 | 0.376554 | − | 0.926395i | \(-0.377109\pi\) | ||||
0.376554 | + | 0.926395i | \(0.377109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −352.718 | −1.25091 | −0.625454 | − | 0.780261i | \(-0.715086\pi\) | ||||
−0.625454 | + | 0.780261i | \(0.715086\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.5440 | −0.0581178 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 357.106 | 1.10828 | 0.554141 | − | 0.832423i | \(-0.313047\pi\) | ||||
0.554141 | + | 0.832423i | \(0.313047\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 479.427 | 1.39775 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −56.4654 | −0.155034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −381.501 | −0.988739 | −0.494369 | − | 0.869252i | \(-0.664601\pi\) | ||||
−0.494369 | + | 0.869252i | \(0.664601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.1912 | −0.0396950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.5449 | 0.0407697 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 691.149 | 1.52508 | 0.762542 | − | 0.646938i | \(-0.223951\pi\) | ||||
0.762542 | + | 0.646938i | \(0.223951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 827.651 | 1.73721 | 0.868606 | − | 0.495504i | \(-0.165017\pi\) | ||||
0.868606 | + | 0.495504i | \(0.165017\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 749.852 | 1.49956 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.7669 | 0.0224540 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −166.560 | −0.303710 | −0.151855 | − | 0.988403i | \(-0.548525\pi\) | ||||
−0.151855 | + | 0.988403i | \(0.548525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 148.240 | 0.258637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 296.418 | 0.495470 | 0.247735 | − | 0.968828i | \(-0.420314\pi\) | ||||
0.247735 | + | 0.968828i | \(0.420314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −916.657 | −1.46968 | −0.734840 | − | 0.678241i | \(-0.762743\pi\) | ||||
−0.734840 | + | 0.678241i | \(0.762743\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −115.011 | −0.177071 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 692.034 | 1.02422 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1229.64 | 1.75120 | 0.875601 | − | 0.483036i | \(-0.160466\pi\) | ||||
0.875601 | + | 0.483036i | \(0.160466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 660.659 | 0.906254 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −547.516 | −0.724069 | −0.362035 | − | 0.932165i | \(-0.617918\pi\) | ||||
−0.362035 | + | 0.932165i | \(0.617918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −41.0286 | −0.0523550 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −265.870 | −0.327635 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −257.418 | −0.306587 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −502.934 | −0.579361 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −43.9438 | −0.0489974 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7484 | 0.0137679 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 206.366 | 0.216013 | 0.108007 | − | 0.994150i | \(-0.465553\pi\) | ||||
0.108007 | + | 0.994150i | \(0.465553\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 630.965 | 0.640550 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −560.665 | −0.552359 | −0.276179 | − | 0.961106i | \(-0.589068\pi\) | ||||
−0.276179 | + | 0.961106i | \(0.589068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1325.06 | 1.26759 | 0.633796 | − | 0.773500i | \(-0.281496\pi\) | ||||
0.633796 | + | 0.773500i | \(0.281496\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.7683 | −0.0165144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1278.56 | −1.15517 | −0.577583 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −313.965 | −0.275893 | −0.137947 | − | 0.990440i | \(-0.544050\pi\) | ||||
−0.137947 | + | 0.990440i | \(0.544050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 219.258 | 0.187487 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2248.70 | 1.87203 | 0.936016 | − | 0.351958i | \(-0.114484\pi\) | ||||
0.936016 | + | 0.351958i | \(0.114484\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 107.713 | 0.0873418 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −458.553 | −0.362335 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1753.62 | 1.35087 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −748.686 | −0.562499 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 182.570 | 0.133836 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −167.440 | −0.119810 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1045.71 | 0.730644 | 0.365322 | − | 0.930881i | \(-0.380959\pi\) | ||||
0.365322 | + | 0.930881i | \(0.380959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −325.705 | −0.222300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1723.55 | 1.14952 | 0.574761 | − | 0.818321i | \(-0.305095\pi\) | ||||
0.574761 | + | 0.818321i | \(0.305095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −544.882 | −0.355243 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −32.9290 | −0.0209932 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −740.069 | −0.461521 | −0.230761 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230761 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −988.103 | −0.602948 | −0.301474 | − | 0.953474i | \(-0.597479\pi\) | ||||
−0.301474 | + | 0.953474i | \(0.597479\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 329.756 | 0.196954 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −423.196 | −0.247478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −193.185 | −0.110642 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 442.710 | 0.248395 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2070.89 | −1.13862 | −0.569308 | − | 0.822125i | \(-0.692789\pi\) | ||||
−0.569308 | + | 0.822125i | \(0.692789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2702.62 | −1.45653 | −0.728267 | − | 0.685294i | \(-0.759674\pi\) | ||||
−0.728267 | + | 0.685294i | \(0.759674\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1598.87 | 0.844842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.9303 | −0.0165465 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 190.958 | 0.0970706 | 0.0485353 | − | 0.998821i | \(-0.484545\pi\) | ||||
0.0485353 | + | 0.998821i | \(0.484545\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −352.283 | −0.175710 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4603.80 | −2.25360 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3222.79 | 1.54864 | 0.774320 | − | 0.632795i | \(-0.218092\pi\) | ||||
0.774320 | + | 0.632795i | \(0.218092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.9512 | −0.00705424 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3334.86 | 1.54526 | 0.772632 | − | 0.634854i | \(-0.218940\pi\) | ||||
0.772632 | + | 0.634854i | \(0.218940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1889.44 | −0.860011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −496.799 | −0.222170 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1037.10 | −0.455774 | −0.227887 | − | 0.973688i | \(-0.573182\pi\) | ||||
−0.227887 | + | 0.973688i | \(0.573182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3571.84 | 1.54289 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 638.217 | 0.271025 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1524.12 | −0.636412 | −0.318206 | − | 0.948022i | \(-0.603080\pi\) | ||||
−0.318206 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4005.50 | 1.64490 | 0.822448 | − | 0.568840i | \(-0.192608\pi\) | ||||
0.822448 | + | 0.568840i | \(0.192608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 764.265 | 0.308722 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 159.316 | 0.0633143 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1475.59 | 0.577035 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1407.43 | 0.541669 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3756.82 | 1.42322 | 0.711608 | − | 0.702577i | \(-0.247967\pi\) | ||||
0.711608 | + | 0.702577i | \(0.247967\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −774.721 | −0.288941 | −0.144471 | − | 0.989509i | \(-0.546148\pi\) | ||||
−0.144471 | + | 0.989509i | \(0.546148\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.8658 | 0.00399032 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −384.941 | −0.139218 | −0.0696089 | − | 0.997574i | \(-0.522175\pi\) | ||||
−0.0696089 | + | 0.997574i | \(0.522175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −620.031 | −0.220869 | −0.110434 | − | 0.993883i | \(-0.535224\pi\) | ||||
−0.110434 | + | 0.993883i | \(0.535224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −153.804 | −0.0539726 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8256.98 | 2.85481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 132.658 | 0.0451964 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4197.54 | −1.40942 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −458.492 | −0.151744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2811.84 | 0.917418 | 0.458709 | − | 0.888586i | \(-0.348312\pi\) | ||||
0.458709 | + | 0.888586i | \(0.348312\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 273.716 | 0.0880504 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −236.662 | −0.0750709 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1364.74 | 0.426934 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −846.454 | −0.261178 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1072.38 | −0.326407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5415.68 | 1.62628 | 0.813141 | − | 0.582066i | \(-0.197756\pi\) | ||||
0.813141 | + | 0.582066i | \(0.197756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3256.64 | 0.964931 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3930.45 | 1.14922 | 0.574611 | − | 0.818427i | \(-0.305153\pi\) | ||||
0.574611 | + | 0.818427i | \(0.305153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2136.62 | −0.616558 | −0.308279 | − | 0.951296i | \(-0.599753\pi\) | ||||
−0.308279 | + | 0.951296i | \(0.599753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 639.034 | 0.182014 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2841.83 | 0.799031 | 0.399516 | − | 0.916726i | \(-0.369178\pi\) | ||||
0.399516 | + | 0.916726i | \(0.369178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 239.606 | 0.0665114 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1135.46 | 0.311208 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4786.45 | −1.29544 | −0.647720 | − | 0.761879i | \(-0.724277\pi\) | ||||
−0.647720 | + | 0.761879i | \(0.724277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3583.38 | 0.957783 | 0.478891 | − | 0.877874i | \(-0.341039\pi\) | ||||
0.478891 | + | 0.877874i | \(0.341039\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1935.14 | 0.510861 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 321.680 | 0.0838832 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 333.209 | 0.0858362 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −505.584 | −0.128675 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2241.78 | 0.563744 | 0.281872 | − | 0.959452i | \(-0.409045\pi\) | ||||
0.281872 | + | 0.959452i | \(0.409045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3873.88 | −0.962643 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −37.8864 | −0.00930407 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3307.64 | −0.802819 | −0.401410 | − | 0.915899i | \(-0.631480\pi\) | ||||
−0.401410 | + | 0.915899i | \(0.631480\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6809.37 | −1.63364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7528.35 | 1.78541 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5733.35 | −1.34423 | −0.672117 | − | 0.740445i | \(-0.734615\pi\) | ||||
−0.672117 | + | 0.740445i | \(0.734615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −255.974 | −0.0593373 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −237.703 | −0.0544839 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4863.10 | −1.10226 | −0.551131 | − | 0.834419i | \(-0.685804\pi\) | ||||
−0.551131 | + | 0.834419i | \(0.685804\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6428.81 | −1.44104 | −0.720521 | − | 0.693433i | \(-0.756097\pi\) | ||||
−0.720521 | + | 0.693433i | \(0.756097\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −464.417 | −0.102959 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3005.53 | 0.659056 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6855.48 | −1.48702 | −0.743512 | − | 0.668722i | \(-0.766842\pi\) | ||||
−0.743512 | + | 0.668722i | \(0.766842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1244.31 | 0.267007 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1682.58 | 0.357203 | 0.178602 | − | 0.983921i | \(-0.442843\pi\) | ||||
0.178602 | + | 0.983921i | \(0.442843\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5894.74 | 1.23818 | 0.619091 | − | 0.785319i | \(-0.287501\pi\) | ||||
0.619091 | + | 0.785319i | \(0.287501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.7720 | 0.00244672 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5669.99 | −1.16616 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1173.86 | −0.238930 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 190.561 | 0.0383879 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6625.17 | 1.32098 | 0.660489 | − | 0.750836i | \(-0.270349\pi\) | ||||
0.660489 | + | 0.750836i | \(0.270349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 463.738 | 0.0915251 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1184.29 | 0.231378 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2815.34 | 0.544532 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10115.3 | 1.93699 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −517.726 | −0.0981603 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 555.327 | 0.104255 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4185.59 | 0.778125 | 0.389062 | − | 0.921211i | \(-0.372799\pi\) | ||||
0.389062 | + | 0.921211i | \(0.372799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1223.58 | 0.225265 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 507.256 | 0.0924882 | 0.0462441 | − | 0.998930i | \(-0.485275\pi\) | ||||
0.0462441 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10307.5 | 1.86139 | 0.930696 | − | 0.365793i | \(-0.119202\pi\) | ||||
0.930696 | + | 0.365793i | \(0.119202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 503.126 | 0.0899935 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.58898 | −0.00169896 | −0.000849481 | − | 1.00000i | \(-0.500270\pi\) | ||||
−0.000849481 | 1.00000i | \(0.500270\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6947.86 | 1.21945 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1180.64 | −0.205286 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1161.82 | −0.200141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2184.27 | −0.372804 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −289.919 | −0.0490293 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10241.1 | −1.71614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1770.81 | −0.294055 | −0.147028 | − | 0.989132i | \(-0.546971\pi\) | ||||
−0.147028 | + | 0.989132i | \(0.546971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6208.48 | −1.02169 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −111.756 | −0.0182266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1494.60 | 0.241590 | 0.120795 | − | 0.992677i | \(-0.461456\pi\) | ||||
0.120795 | + | 0.992677i | \(0.461456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2076.48 | 0.332681 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1148.36 | 0.182368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3912.46 | −0.615898 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 99.4638 | 0.0155216 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12738.1 | −1.97065 | −0.985326 | − | 0.170685i | \(-0.945402\pi\) | ||||
−0.985326 | + | 0.170685i | \(0.945402\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2634.06 | −0.404006 | −0.202003 | − | 0.979385i | \(-0.564745\pi\) | ||||
−0.202003 | + | 0.979385i | \(0.564745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −860.677 | −0.130882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8694.21 | −1.31090 | −0.655448 | − | 0.755241i | \(-0.727520\pi\) | ||||
−0.655448 | + | 0.755241i | \(0.727520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 198.887 | 0.0297347 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1619.31 | 0.240065 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4297.38 | −0.631774 | −0.315887 | − | 0.948797i | \(-0.602302\pi\) | ||||
−0.315887 | + | 0.948797i | \(0.602302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −691.347 | −0.0999623 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −615.047 | −0.0882000 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7786.34 | 1.10748 | 0.553738 | − | 0.832691i | \(-0.313201\pi\) | ||||
0.553738 | + | 0.832691i | \(0.313201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5169.64 | −0.729324 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10940.7 | 1.53103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3268.99 | −0.453785 | −0.226893 | − | 0.973920i | \(-0.572857\pi\) | ||||
−0.226893 | + | 0.973920i | \(0.572857\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −154.616 | −0.0212916 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5049.35 | −0.689800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2284.10 | −0.309569 | −0.154784 | − | 0.987948i | \(-0.549468\pi\) | ||||
−0.154784 | + | 0.987948i | \(0.549468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 965.624 | 0.129844 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9724.98 | 1.29745 | 0.648725 | − | 0.761023i | \(-0.275303\pi\) | ||||
0.648725 | + | 0.761023i | \(0.275303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 464.332 | 0.0614663 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9222.64 | 1.21140 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4135.23 | 0.538984 | 0.269492 | − | 0.963003i | \(-0.413144\pi\) | ||||
0.269492 | + | 0.963003i | \(0.413144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9816.43 | −1.26966 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1591.55 | 0.204283 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 825.045 | 0.105095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1908.00 | −0.241208 | −0.120604 | − | 0.992701i | \(-0.538483\pi\) | ||||
−0.120604 | + | 0.992701i | \(0.538483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −503.152 | −0.0631305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7253.91 | 0.903349 | 0.451675 | − | 0.892183i | \(-0.350827\pi\) | ||||
0.451675 | + | 0.892183i | \(0.350827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −834.572 | −0.103159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 443.280 | 0.0543871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5729.77 | −0.697823 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3288.67 | −0.397589 | −0.198795 | − | 0.980041i | \(-0.563703\pi\) | ||||
−0.198795 | + | 0.980041i | \(0.563703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −683.390 | −0.0820174 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19820.8 | −2.36154 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −367.365 | −0.0434536 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −912.429 | −0.107151 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2946.70 | 0.343570 | 0.171785 | − | 0.985134i | \(-0.445047\pi\) | ||||
0.171785 | + | 0.985134i | \(0.445047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3705.67 | 0.428987 | 0.214493 | − | 0.976725i | \(-0.431190\pi\) | ||||
0.214493 | + | 0.976725i | \(0.431190\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9337.35 | −1.07328 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7616.03 | 0.869251 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23735.4 | −2.69001 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −390.785 | −0.0439796 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7988.10 | 0.892746 | 0.446373 | − | 0.894847i | \(-0.352716\pi\) | ||||
0.446373 | + | 0.894847i | \(0.352716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8406.05 | 0.932954 | 0.466477 | − | 0.884533i | \(-0.345523\pi\) | ||||
0.466477 | + | 0.884533i | \(0.345523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −178.390 | −0.0196624 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3050.15 | 0.333887 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 984.085 | 0.106988 | 0.0534941 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534941 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12535.7 | −1.35360 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7540.20 | −0.808681 | −0.404341 | − | 0.914608i | \(-0.632499\pi\) | ||||
−0.404341 | + | 0.914608i | \(0.632499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −172.719 | −0.0183992 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1912.29 | −0.202345 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2931.72 | −0.308143 | −0.154072 | − | 0.988060i | \(-0.549239\pi\) | ||||
−0.154072 | + | 0.988060i | \(0.549239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4771.03 | −0.498135 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2495.64 | −0.258842 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −337.452 | −0.0347692 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6833.35 | 0.699455 | 0.349727 | − | 0.936852i | \(-0.386274\pi\) | ||||
0.349727 | + | 0.936852i | \(0.386274\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3000.98 | 0.305172 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4006.80 | −0.404805 | −0.202402 | − | 0.979302i | \(-0.564875\pi\) | ||||
−0.202402 | + | 0.979302i | \(0.564875\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1786.36 | −0.179307 | −0.0896536 | − | 0.995973i | \(-0.528576\pi\) | ||||
−0.0896536 | + | 0.995973i | \(0.528576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −29.4848 | −0.00294049 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10194.6 | −1.01017 | −0.505085 | − | 0.863070i | \(-0.668539\pi\) | ||||
−0.505085 | + | 0.863070i | \(0.668539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4776.61 | 0.470284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 176.333 | 0.0172505 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8511.51 | 0.827399 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2366.45 | −0.228589 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9975.21 | 0.957513 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 153.262 | 0.0146195 | 0.00730973 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00730973 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4164.10 | 0.394733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4251.21 | −0.400491 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 138.465 | 0.0129636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3387.94 | −0.315241 | −0.157620 | − | 0.987500i | \(-0.550382\pi\) | ||||
−0.157620 | + | 0.987500i | \(0.550382\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2975.97 | 0.275210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8555.18 | −0.786334 | −0.393167 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393167 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17605.9 | 1.60838 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 423.357 | 0.0384414 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8500.67 | −0.767218 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12148.2 | −1.08984 | −0.544919 | − | 0.838489i | \(-0.683440\pi\) | ||||
−0.544919 | + | 0.838489i | \(0.683440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3079.46 | 0.274611 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4758.81 | −0.421839 | −0.210919 | − | 0.977503i | \(-0.567646\pi\) | ||||
−0.210919 | + | 0.977503i | \(0.567646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −376.188 | −0.0331488 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1744.74 | −0.152833 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11419.1 | 0.994386 | 0.497193 | − | 0.867640i | \(-0.334364\pi\) | ||||
0.497193 | + | 0.867640i | \(0.334364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26287.9 | 2.27575 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −932.462 | −0.0802519 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 889.071 | 0.0760722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8617.38 | −0.733060 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −957.669 | −0.0809962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8619.66 | 0.724826 | 0.362413 | − | 0.932018i | \(-0.381953\pi\) | ||||
0.362413 | + | 0.932018i | \(0.381953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20411.3 | −1.70654 | −0.853271 | − | 0.521467i | \(-0.825385\pi\) | ||||
−0.853271 | + | 0.521467i | \(0.825385\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3298.29 | 0.274189 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2909.96 | 0.240531 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13604.2 | 1.11813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18071.7 | −1.47692 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3467.34 | 0.281777 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −857.869 | −0.0693250 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1407.39 | −0.113097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11569.1 | −0.924524 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4553.14 | 0.361838 | 0.180919 | − | 0.983498i | \(-0.442093\pi\) | ||||
0.180919 | + | 0.983498i | \(0.442093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3698.73 | 0.292316 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −210.660 | −0.0165572 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16216.8 | 1.26761 | 0.633804 | − | 0.773494i | \(-0.281493\pi\) | ||||
0.633804 | + | 0.773494i | \(0.281493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21640.9 | −1.68235 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5470.49 | −0.422960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35263.5 | −2.71168 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 147.115 | 0.0112517 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −175.385 | −0.0133417 | −0.00667084 | − | 0.999978i | \(-0.502123\pi\) | ||||
−0.00667084 | + | 0.999978i | \(0.502123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6185.73 | −0.468029 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1362.58 | 0.102545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6323.70 | 0.473378 | 0.236689 | − | 0.971585i | \(-0.423938\pi\) | ||||
0.236689 | + | 0.971585i | \(0.423938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1508.80 | 0.112346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18946.4 | −1.40330 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12606.5 | 0.928811 | 0.464406 | − | 0.885623i | \(-0.346268\pi\) | ||||
0.464406 | + | 0.885623i | \(0.346268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8389.93 | −0.614899 | −0.307450 | − | 0.951564i | \(-0.599476\pi\) | ||||
−0.307450 | + | 0.951564i | \(0.599476\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3469.10 | 0.252921 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19994.5 | −1.45014 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22630.3 | −1.63278 | −0.816389 | − | 0.577502i | \(-0.804027\pi\) | ||||
−0.816389 | + | 0.577502i | \(0.804027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −715.388 | −0.0513480 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15701.7 | 1.12120 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9206.06 | 0.653990 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −307.674 | −0.0217449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5085.58 | −0.357589 | −0.178794 | − | 0.983886i | \(-0.557220\pi\) | ||||
−0.178794 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −904.180 | −0.0632531 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −355.460 | −0.0247405 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11917.6 | 0.825293 | 0.412647 | − | 0.910891i | \(-0.364604\pi\) | ||||
0.412647 | + | 0.910891i | \(0.364604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1176.62 | 0.0810700 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −572.545 | −0.0392508 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3541.30 | 0.241559 | 0.120779 | − | 0.992679i | \(-0.461461\pi\) | ||||
0.120779 | + | 0.992679i | \(0.461461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8131.45 | 0.551895 | 0.275947 | − | 0.961173i | \(-0.411008\pi\) | ||||
0.275947 | + | 0.961173i | \(0.411008\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4355.10 | 0.294118 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −502.344 | −0.0337573 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18658.0 | 1.24762 | 0.623809 | − | 0.781577i | \(-0.285584\pi\) | ||||
0.623809 | + | 0.781577i | \(0.285584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7624.62 | 0.507332 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6262.67 | 0.414665 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23985.1 | −1.58034 | −0.790172 | − | 0.612885i | \(-0.790009\pi\) | ||||
−0.790172 | + | 0.612885i | \(0.790009\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 122.499 | 0.00803190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12011.0 | −0.783706 | −0.391853 | − | 0.920028i | \(-0.628166\pi\) | ||||
−0.391853 | + | 0.920028i | \(0.628166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21339.0 | −1.38560 | −0.692800 | − | 0.721129i | \(-0.743623\pi\) | ||||
−0.692800 | + | 0.721129i | \(0.743623\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7878.53 | −0.509106 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7382.22 | 0.474739 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15456.4 | 0.989208 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −423.378 | −0.0269667 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14519.3 | −0.920382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −595.619 | −0.0375772 | −0.0187886 | − | 0.999823i | \(-0.505981\pi\) | ||||
−0.0187886 | + | 0.999823i | \(0.505981\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2596.50 | 0.163035 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 701.637 | 0.0438482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8407.86 | 0.522969 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7750.53 | −0.479822 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7385.91 | 0.455111 | 0.227555 | − | 0.973765i | \(-0.426927\pi\) | ||||
0.227555 | + | 0.973765i | \(0.426927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29627.4 | −1.81710 | −0.908548 | − | 0.417781i | \(-0.862808\pi\) | ||||
−0.908548 | + | 0.417781i | \(0.862808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −218.537 | −0.0133409 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8698.54 | 0.528555 | 0.264277 | − | 0.964447i | \(-0.414867\pi\) | ||||
0.264277 | + | 0.964447i | \(0.414867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16678.3 | −1.00875 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1260.22 | 0.0758709 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3594.96 | 0.215439 | 0.107719 | − | 0.994181i | \(-0.465645\pi\) | ||||
0.107719 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1156.45 | 0.0689864 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23968.1 | 1.42327 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25031.1 | 1.47962 | 0.739811 | − | 0.672814i | \(-0.234915\pi\) | ||||
0.739811 | + | 0.672814i | \(0.234915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22574.8 | −1.32838 | −0.664191 | − | 0.747563i | \(-0.731224\pi\) | ||||
−0.664191 | + | 0.747563i | \(0.731224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −990.250 | −0.0580062 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −365.598 | −0.0213192 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46221.1 | −2.68319 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5000.92 | 0.289009 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19972.2 | −1.14906 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19302.8 | −1.10560 | −0.552799 | − | 0.833315i | \(-0.686440\pi\) | ||||
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6112.53 | 0.348550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23517.4 | −1.33508 | −0.667538 | − | 0.744576i | \(-0.732652\pi\) | ||||
−0.667538 | + | 0.744576i | \(0.732652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5918.16 | −0.334489 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3629.44 | 0.204230 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14773.7 | 0.827671 | 0.413835 | − | 0.910352i | \(-0.364189\pi\) | ||||
0.413835 | + | 0.910352i | \(0.364189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −496.562 | −0.0276973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1972.98 | −0.109569 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6690.49 | −0.369938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4165.18 | −0.229306 | −0.114653 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114653 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18094.8 | −0.991869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −662.985 | −0.0361848 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12089.8 | −0.657007 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2624.18 | 0.141997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19303.8 | −1.04008 | −0.520039 | − | 0.854143i | \(-0.674083\pi\) | ||||
−0.520039 | + | 0.854143i | \(0.674083\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4511.41 | 0.242035 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 221.256 | 0.0118198 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16078.7 | 0.855309 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7913.04 | 0.419155 | 0.209577 | − | 0.977792i | \(-0.432791\pi\) | ||||
0.209577 | + | 0.977792i | \(0.432791\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32151.7 | −1.69590 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7639.57 | −0.401268 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −283.950 | −0.0148519 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4419.88 | −0.230214 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35512.6 | 1.84200 | 0.921000 | − | 0.389563i | \(-0.127374\pi\) | ||||
0.921000 | + | 0.389563i | \(0.127374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38000.1 | −1.96282 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3308.94 | 0.170209 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35860.4 | 1.83700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2510.77 | −0.128087 | −0.0640435 | − | 0.997947i | \(-0.520400\pi\) | ||||
−0.0640435 | + | 0.997947i | \(0.520400\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16050.9 | −0.815468 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21568.2 | 1.09128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5261.38 | 0.265121 | 0.132560 | − | 0.991175i | \(-0.457680\pi\) | ||||
0.132560 | + | 0.991175i | \(0.457680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 297.044 | 0.0149070 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4019.29 | 0.200885 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10267.1 | −0.511071 | −0.255535 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 307.689 | 0.0152541 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19722.5 | 0.973819 | 0.486910 | − | 0.873452i | \(-0.338124\pi\) | ||||
0.486910 | + | 0.873452i | \(0.338124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1389.50 | −0.0683318 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14316.1 | 0.701202 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36666.4 | 1.78873 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27422.3 | −1.33243 | −0.666214 | − | 0.745760i | \(-0.732086\pi\) | ||||
−0.666214 | + | 0.745760i | \(0.732086\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2070.09 | 0.100184 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1813.37 | −0.0874111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6549.67 | 0.314467 | 0.157234 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157234 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3577.20 | −0.171072 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24815.5 | 1.18208 | 0.591038 | − | 0.806644i | \(-0.298718\pi\) | ||||
0.591038 | + | 0.806644i | \(0.298718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9003.87 | 0.427211 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1072.79 | 0.0507016 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12120.9 | 0.570613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1759.56 | 0.0825116 | 0.0412558 | − | 0.999149i | \(-0.486864\pi\) | ||||
0.0412558 | + | 0.999149i | \(0.486864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3054.32 | −0.142670 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20707.5 | 0.963517 | 0.481758 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481758 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5927.13 | 0.274721 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6287.87 | −0.290317 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3756.53 | 0.172775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7152.91 | −0.327723 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14130.3 | 0.644923 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 128.126 | 0.00582551 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16060.1 | 0.727422 | 0.363711 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363711 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5294.26 | −0.238885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −64488.1 | −2.89878 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14514.8 | 0.649980 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −236.370 | −0.0105449 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6369.68 | 0.283094 | 0.141547 | − | 0.989932i | \(-0.454792\pi\) | ||||
0.141547 | + | 0.989932i | \(0.454792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21836.5 | −0.966857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6730.78 | 0.296904 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22120.0 | 0.972103 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3089.00 | −0.135246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4490.66 | −0.195884 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18129.0 | 0.787863 | 0.393932 | − | 0.919140i | \(-0.371115\pi\) | ||||
0.393932 | + | 0.919140i | \(0.371115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29297.4 | −1.26852 | −0.634260 | − | 0.773120i | \(-0.718695\pi\) | ||||
−0.634260 | + | 0.773120i | \(0.718695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5936.45 | −0.256089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2162.38 | 0.0929386 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6701.65 | −0.286978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13150.4 | 0.561064 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42698.9 | 1.81510 | 0.907552 | − | 0.419939i | \(-0.137949\pi\) | ||||
0.907552 | + | 0.419939i | \(0.137949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27961.5 | −1.18430 | −0.592149 | − | 0.805829i | \(-0.701720\pi\) | ||||
−0.592149 | + | 0.805829i | \(0.701720\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2775.35 | 0.117122 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22115.7 | −0.929912 | −0.464956 | − | 0.885334i | \(-0.653930\pi\) | ||||
−0.464956 | + | 0.885334i | \(0.653930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7144.36 | 0.299317 | 0.149659 | − | 0.988738i | \(-0.452183\pi\) | ||||
0.149659 | + | 0.988738i | \(0.452183\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6330.45 | −0.264261 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29316.3 | −1.21939 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2237.58 | 0.0927361 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2335.50 | 0.0964475 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9019.32 | −0.371134 | −0.185567 | − | 0.982632i | \(-0.559412\pi\) | ||||
−0.185567 | + | 0.982632i | \(0.559412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58509.2 | 2.39900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1553.72 | 0.0634790 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1267.75 | −0.0516119 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21470.8 | 0.871011 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5443.28 | 0.220039 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38117.6 | 1.53544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37503.6 | 1.50539 | 0.752695 | − | 0.658369i | \(-0.228754\pi\) | ||||
0.752695 | + | 0.658369i | \(0.228754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −333.336 | −0.0133331 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19556.1 | 0.779490 | 0.389745 | − | 0.920923i | \(-0.372563\pi\) | ||||
0.389745 | + | 0.920923i | \(0.372563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38405.1 | 1.52545 | 0.762727 | − | 0.646720i | \(-0.223860\pi\) | ||||
0.762727 | + | 0.646720i | \(0.223860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5235.75 | −0.207240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22495.9 | 0.887334 | 0.443667 | − | 0.896192i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896192i | \(0.353677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −695.857 | −0.0273524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1083.96 | −0.0424604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29672.6 | −1.15831 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2921.01 | −0.113633 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5395.91 | −0.209191 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4801.83 | 0.185522 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44597.3 | −1.71716 | −0.858578 | − | 0.512683i | \(-0.828651\pi\) | ||||
−0.858578 | + | 0.512683i | \(0.828651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6117.78 | 0.234753 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36144.0 | 1.38220 | 0.691102 | − | 0.722758i | \(-0.257126\pi\) | ||||
0.691102 | + | 0.722758i | \(0.257126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14216.5 | 0.541815 | 0.270908 | − | 0.962605i | \(-0.412676\pi\) | ||||
0.270908 | + | 0.962605i | \(0.412676\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 428.223 | 0.0162650 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22404.0 | −0.848088 | −0.424044 | − | 0.905642i | \(-0.639390\pi\) | ||||
−0.424044 | + | 0.905642i | \(0.639390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29988.9 | −1.13138 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15942.5 | −0.599431 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6785.01 | 0.254257 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1022.63 | −0.0381930 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2599.72 | 0.0967694 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13701.7 | 0.508317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23328.2 | 0.862569 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9340.57 | 0.344224 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2687.56 | 0.0987153 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16211.5 | 0.593489 | 0.296745 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296745 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14659.9 | 0.534915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8529.11 | −0.310189 | −0.155094 | − | 0.987900i | \(-0.549568\pi\) | ||||
−0.155094 | + | 0.987900i | \(0.549568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13212.2 | 0.478927 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 512.796 | 0.0185274 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49428.0 | −1.78000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18155.1 | 0.651666 | 0.325833 | − | 0.945427i | \(-0.394355\pi\) | ||||
0.325833 | + | 0.945427i | \(0.394355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3865.03 | 0.138281 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5198.37 | 0.185381 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29573.4 | −1.05121 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34646.8 | −1.22756 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26472.1 | 0.934898 | 0.467449 | − | 0.884020i | \(-0.345173\pi\) | ||||
0.467449 | + | 0.884020i | \(0.345173\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9109.12 | 0.320665 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 468.407 | 0.0164362 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 990.069 | 0.0346296 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3891.08 | −0.135663 | −0.0678313 | − | 0.997697i | \(-0.521608\pi\) | ||||
−0.0678313 | + | 0.997697i | \(0.521608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9518.12 | 0.330790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5700.50 | 0.197483 | 0.0987413 | − | 0.995113i | \(-0.468518\pi\) | ||||
0.0987413 | + | 0.995113i | \(0.468518\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31739.6 | 1.09606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 944.338 | 0.0325072 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16631.9 | −0.570712 | −0.285356 | − | 0.958422i | \(-0.592112\pi\) | ||||
−0.285356 | + | 0.958422i | \(0.592112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16075.7 | −0.549883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.85460 | −0.000301924 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12213.3 | −0.415140 | −0.207570 | − | 0.978220i | \(-0.566556\pi\) | ||||
−0.207570 | + | 0.978220i | \(0.566556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2520.70 | 0.0854116 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6415.75 | 0.216710 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21223.7 | 0.714650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27526.3 | −0.923982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33430.8 | 1.11868 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −519.812 | −0.0173402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34551.6 | 1.14902 | 0.574512 | − | 0.818496i | \(-0.305192\pi\) | ||||
0.574512 | + | 0.818496i | \(0.305192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1072.84 | −0.0355672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55055.9 | 1.81959 | 0.909797 | − | 0.415053i | \(-0.136237\pi\) | ||||
0.909797 | + | 0.415053i | \(0.136237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28336.8 | 0.933645 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2016.98 | −0.0662514 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23388.2 | −0.765871 | −0.382935 | − | 0.923775i | \(-0.625087\pi\) | ||||
−0.382935 | + | 0.923775i | \(0.625087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6211.79 | 0.202788 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8209.33 | 0.267180 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9127.57 | −0.296159 | −0.148079 | − | 0.988975i | \(-0.547309\pi\) | ||||
−0.148079 | + | 0.988975i | \(0.547309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −258.282 | −0.00835489 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9456.75 | −0.304976 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56623.4 | −1.82054 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39058.6 | 1.25201 | 0.626003 | − | 0.779820i | \(-0.284690\pi\) | ||||
0.626003 | + | 0.779820i | \(0.284690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1635.19 | −0.0522569 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −416.020 | −0.0132550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9990.46 | 0.317353 | 0.158677 | − | 0.987331i | \(-0.449277\pi\) | ||||
0.158677 | + | 0.987331i | \(0.449277\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11653.0 | −0.369052 |
(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 | 1216.4.a.bf.1.4 | 7 | ||
4.3 | odd | 2 | 1216.4.a.bg.1.4 | 7 | |||
8.3 | odd | 2 | 608.4.a.j.1.4 | ✓ | 7 | ||
8.5 | even | 2 | 608.4.a.k.1.4 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.j.1.4 | ✓ | 7 | 8.3 | odd | 2 | ||
608.4.a.k.1.4 | yes | 7 | 8.5 | even | 2 | ||
1216.4.a.bf.1.4 | 7 | 1.1 | even | 1 | trivial | ||
1216.4.a.bg.1.4 | 7 | 4.3 | odd | 2 |