Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{11} - 4 x^{10} - 212 x^{9} + 487 x^{8} + 16315 x^{7} - 9025 x^{6} - 516068 x^{5} - 504693 x^{4} + \cdots - 11394027 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(9.21174\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −7.21174 | −1.38790 | −0.693950 | − | 0.720023i | \(-0.744131\pi\) | ||||
−0.693950 | + | 0.720023i | \(0.744131\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 16.2698 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240632\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240632\pi\) | |||||||
\(6\) | −14.4235 | −0.981393 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 25.0092 | 0.926266 | ||||||||
\(10\) | 32.5396 | 1.02899 | ||||||||
\(11\) | 47.1866 | 1.29339 | 0.646695 | − | 0.762749i | \(-0.276151\pi\) | ||||
0.646695 | + | 0.762749i | \(0.276151\pi\) | |||||||
\(12\) | −28.8470 | −0.693950 | ||||||||
\(13\) | 15.5988 | 0.332794 | 0.166397 | − | 0.986059i | \(-0.446787\pi\) | ||||
0.166397 | + | 0.986059i | \(0.446787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −117.334 | −2.01969 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 124.933 | 1.78240 | 0.891198 | − | 0.453614i | \(-0.149865\pi\) | ||||
0.891198 | + | 0.453614i | \(0.149865\pi\) | |||||||
\(18\) | 50.0183 | 0.654969 | ||||||||
\(19\) | 27.0949 | 0.327158 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(20\) | 65.0792 | 0.727607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 94.3732 | 0.914565 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −57.6939 | −0.490697 | ||||||||
\(25\) | 139.706 | 1.11765 | ||||||||
\(26\) | 31.1976 | 0.235321 | ||||||||
\(27\) | 14.3573 | 0.102336 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −75.7411 | −0.484992 | −0.242496 | − | 0.970152i | \(-0.577966\pi\) | ||||
−0.242496 | + | 0.970152i | \(0.577966\pi\) | |||||||
\(30\) | −234.667 | −1.42814 | ||||||||
\(31\) | 101.299 | 0.586899 | 0.293450 | − | 0.955975i | \(-0.405197\pi\) | ||||
0.293450 | + | 0.955975i | \(0.405197\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −340.297 | −1.79510 | ||||||||
\(34\) | 249.866 | 1.26034 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 100.037 | 0.463133 | ||||||||
\(37\) | 158.715 | 0.705207 | 0.352603 | − | 0.935773i | \(-0.385296\pi\) | ||||
0.352603 | + | 0.935773i | \(0.385296\pi\) | |||||||
\(38\) | 54.1898 | 0.231335 | ||||||||
\(39\) | −112.494 | −0.461885 | ||||||||
\(40\) | 130.158 | 0.514496 | ||||||||
\(41\) | −344.393 | −1.31183 | −0.655916 | − | 0.754834i | \(-0.727717\pi\) | ||||
−0.655916 | + | 0.754834i | \(0.727717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 236.838 | 0.839940 | 0.419970 | − | 0.907538i | \(-0.362041\pi\) | ||||
0.419970 | + | 0.907538i | \(0.362041\pi\) | |||||||
\(44\) | 188.746 | 0.646695 | ||||||||
\(45\) | 406.894 | 1.34792 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 522.231 | 1.62075 | 0.810375 | − | 0.585912i | \(-0.199264\pi\) | ||||
0.810375 | + | 0.585912i | \(0.199264\pi\) | |||||||
\(48\) | −115.388 | −0.346975 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 279.413 | 0.790298 | ||||||||
\(51\) | −900.985 | −2.47379 | ||||||||
\(52\) | 62.3951 | 0.166397 | ||||||||
\(53\) | −323.061 | −0.837280 | −0.418640 | − | 0.908152i | \(-0.637493\pi\) | ||||
−0.418640 | + | 0.908152i | \(0.637493\pi\) | |||||||
\(54\) | 28.7147 | 0.0723625 | ||||||||
\(55\) | 767.716 | 1.88216 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −195.401 | −0.454062 | ||||||||
\(58\) | −151.482 | −0.342941 | ||||||||
\(59\) | 752.228 | 1.65986 | 0.829930 | − | 0.557867i | \(-0.188380\pi\) | ||||
0.829930 | + | 0.557867i | \(0.188380\pi\) | |||||||
\(60\) | −469.334 | −1.00985 | ||||||||
\(61\) | −751.789 | −1.57798 | −0.788990 | − | 0.614406i | \(-0.789396\pi\) | ||||
−0.788990 | + | 0.614406i | \(0.789396\pi\) | |||||||
\(62\) | 202.598 | 0.415000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 253.789 | 0.484287 | ||||||||
\(66\) | −680.595 | −1.26932 | ||||||||
\(67\) | −870.373 | −1.58706 | −0.793530 | − | 0.608532i | \(-0.791759\pi\) | ||||
−0.793530 | + | 0.608532i | \(0.791759\pi\) | |||||||
\(68\) | 499.733 | 0.891198 | ||||||||
\(69\) | −165.870 | −0.289397 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −386.315 | −0.645734 | −0.322867 | − | 0.946444i | \(-0.604647\pi\) | ||||
−0.322867 | + | 0.946444i | \(0.604647\pi\) | |||||||
\(72\) | 200.073 | 0.327484 | ||||||||
\(73\) | 972.125 | 1.55861 | 0.779306 | − | 0.626644i | \(-0.215572\pi\) | ||||
0.779306 | + | 0.626644i | \(0.215572\pi\) | |||||||
\(74\) | 317.431 | 0.498656 | ||||||||
\(75\) | −1007.53 | −1.55119 | ||||||||
\(76\) | 108.380 | 0.163579 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −224.989 | −0.326602 | ||||||||
\(79\) | −1011.48 | −1.44052 | −0.720259 | − | 0.693705i | \(-0.755977\pi\) | ||||
−0.720259 | + | 0.693705i | \(0.755977\pi\) | |||||||
\(80\) | 260.317 | 0.363804 | ||||||||
\(81\) | −778.789 | −1.06830 | ||||||||
\(82\) | −688.785 | −0.927605 | ||||||||
\(83\) | 70.9632 | 0.0938460 | 0.0469230 | − | 0.998899i | \(-0.485058\pi\) | ||||
0.0469230 | + | 0.998899i | \(0.485058\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2032.64 | 2.59377 | ||||||||
\(86\) | 473.676 | 0.593927 | ||||||||
\(87\) | 546.225 | 0.673121 | ||||||||
\(88\) | 377.493 | 0.457282 | ||||||||
\(89\) | −208.804 | −0.248688 | −0.124344 | − | 0.992239i | \(-0.539683\pi\) | ||||
−0.124344 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(90\) | 813.788 | 0.953120 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −730.544 | −0.814557 | ||||||||
\(94\) | 1044.46 | 1.14604 | ||||||||
\(95\) | 440.828 | 0.476085 | ||||||||
\(96\) | −230.776 | −0.245348 | ||||||||
\(97\) | −290.349 | −0.303922 | −0.151961 | − | 0.988386i | \(-0.548559\pi\) | ||||
−0.151961 | + | 0.988386i | \(0.548559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1180.10 | 1.19802 | ||||||||
\(100\) | 558.825 | 0.558825 | ||||||||
\(101\) | 1242.66 | 1.22425 | 0.612124 | − | 0.790762i | \(-0.290315\pi\) | ||||
0.612124 | + | 0.790762i | \(0.290315\pi\) | |||||||
\(102\) | −1801.97 | −1.74923 | ||||||||
\(103\) | −764.386 | −0.731235 | −0.365617 | − | 0.930765i | \(-0.619142\pi\) | ||||
−0.365617 | + | 0.930765i | \(0.619142\pi\) | |||||||
\(104\) | 124.790 | 0.117660 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −646.122 | −0.592047 | ||||||||
\(107\) | 717.558 | 0.648308 | 0.324154 | − | 0.946004i | \(-0.394920\pi\) | ||||
0.324154 | + | 0.946004i | \(0.394920\pi\) | |||||||
\(108\) | 57.4294 | 0.0511680 | ||||||||
\(109\) | −526.649 | −0.462787 | −0.231394 | − | 0.972860i | \(-0.574328\pi\) | ||||
−0.231394 | + | 0.972860i | \(0.574328\pi\) | |||||||
\(110\) | 1535.43 | 1.33089 | ||||||||
\(111\) | −1144.61 | −0.978756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −561.697 | −0.467610 | −0.233805 | − | 0.972283i | \(-0.575118\pi\) | ||||
−0.233805 | + | 0.972283i | \(0.575118\pi\) | |||||||
\(114\) | −390.802 | −0.321070 | ||||||||
\(115\) | 374.205 | 0.303433 | ||||||||
\(116\) | −302.965 | −0.242496 | ||||||||
\(117\) | 390.113 | 0.308256 | ||||||||
\(118\) | 1504.46 | 1.17370 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −938.668 | −0.714069 | ||||||||
\(121\) | 895.573 | 0.672857 | ||||||||
\(122\) | −1503.58 | −1.11580 | ||||||||
\(123\) | 2483.67 | 1.82069 | ||||||||
\(124\) | 405.197 | 0.293450 | ||||||||
\(125\) | 239.269 | 0.171207 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2396.56 | −1.67449 | −0.837246 | − | 0.546827i | \(-0.815836\pi\) | ||||
−0.837246 | + | 0.546827i | \(0.815836\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1708.01 | −1.16575 | ||||||||
\(130\) | 507.578 | 0.342443 | ||||||||
\(131\) | 858.844 | 0.572806 | 0.286403 | − | 0.958109i | \(-0.407540\pi\) | ||||
0.286403 | + | 0.958109i | \(0.407540\pi\) | |||||||
\(132\) | −1361.19 | −0.897548 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1740.75 | −1.12222 | ||||||||
\(135\) | 233.591 | 0.148921 | ||||||||
\(136\) | 999.465 | 0.630172 | ||||||||
\(137\) | 151.005 | 0.0941697 | 0.0470849 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470849 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(138\) | −331.740 | −0.204635 | ||||||||
\(139\) | −1987.82 | −1.21298 | −0.606492 | − | 0.795090i | \(-0.707424\pi\) | ||||
−0.606492 | + | 0.795090i | \(0.707424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3766.19 | −2.24944 | ||||||||
\(142\) | −772.630 | −0.456603 | ||||||||
\(143\) | 736.053 | 0.430432 | ||||||||
\(144\) | 400.147 | 0.231566 | ||||||||
\(145\) | −1232.29 | −0.705768 | ||||||||
\(146\) | 1944.25 | 1.10210 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 634.862 | 0.352603 | ||||||||
\(149\) | 1160.23 | 0.637915 | 0.318958 | − | 0.947769i | \(-0.396667\pi\) | ||||
0.318958 | + | 0.947769i | \(0.396667\pi\) | |||||||
\(150\) | −2015.05 | −1.09685 | ||||||||
\(151\) | 1500.02 | 0.808411 | 0.404205 | − | 0.914668i | \(-0.367548\pi\) | ||||
0.404205 | + | 0.914668i | \(0.367548\pi\) | |||||||
\(152\) | 216.759 | 0.115668 | ||||||||
\(153\) | 3124.47 | 1.65097 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1648.12 | 0.854065 | ||||||||
\(156\) | −449.977 | −0.230942 | ||||||||
\(157\) | −2825.24 | −1.43617 | −0.718085 | − | 0.695955i | \(-0.754981\pi\) | ||||
−0.718085 | + | 0.695955i | \(0.754981\pi\) | |||||||
\(158\) | −2022.97 | −1.01860 | ||||||||
\(159\) | 2329.83 | 1.16206 | ||||||||
\(160\) | 520.634 | 0.257248 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1557.58 | −0.755401 | ||||||||
\(163\) | 3629.02 | 1.74385 | 0.871923 | − | 0.489642i | \(-0.162873\pi\) | ||||
0.871923 | + | 0.489642i | \(0.162873\pi\) | |||||||
\(164\) | −1377.57 | −0.655916 | ||||||||
\(165\) | −5536.57 | −2.61225 | ||||||||
\(166\) | 141.926 | 0.0663592 | ||||||||
\(167\) | 854.192 | 0.395805 | 0.197902 | − | 0.980222i | \(-0.436587\pi\) | ||||
0.197902 | + | 0.980222i | \(0.436587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1953.68 | −0.889248 | ||||||||
\(170\) | 4065.27 | 1.83407 | ||||||||
\(171\) | 677.621 | 0.303035 | ||||||||
\(172\) | 947.351 | 0.419970 | ||||||||
\(173\) | −2567.49 | −1.12834 | −0.564170 | − | 0.825659i | \(-0.690804\pi\) | ||||
−0.564170 | + | 0.825659i | \(0.690804\pi\) | |||||||
\(174\) | 1092.45 | 0.475968 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 754.985 | 0.323347 | ||||||||
\(177\) | −5424.87 | −2.30372 | ||||||||
\(178\) | −417.609 | −0.175849 | ||||||||
\(179\) | −3427.63 | −1.43125 | −0.715623 | − | 0.698487i | \(-0.753857\pi\) | ||||
−0.715623 | + | 0.698487i | \(0.753857\pi\) | |||||||
\(180\) | 1627.58 | 0.673958 | ||||||||
\(181\) | 1081.50 | 0.444130 | 0.222065 | − | 0.975032i | \(-0.428720\pi\) | ||||
0.222065 | + | 0.975032i | \(0.428720\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5421.71 | 2.19008 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 2582.27 | 1.02623 | ||||||||
\(186\) | −1461.09 | −0.575979 | ||||||||
\(187\) | 5895.17 | 2.30533 | ||||||||
\(188\) | 2088.92 | 0.810375 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 881.657 | 0.336643 | ||||||||
\(191\) | −1975.98 | −0.748568 | −0.374284 | − | 0.927314i | \(-0.622112\pi\) | ||||
−0.374284 | + | 0.927314i | \(0.622112\pi\) | |||||||
\(192\) | −461.551 | −0.173487 | ||||||||
\(193\) | 1594.03 | 0.594514 | 0.297257 | − | 0.954798i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954798i | \(0.403928\pi\) | |||||||
\(194\) | −580.698 | −0.214906 | ||||||||
\(195\) | −1830.26 | −0.672142 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2249.35 | −0.813501 | −0.406751 | − | 0.913539i | \(-0.633338\pi\) | ||||
−0.406751 | + | 0.913539i | \(0.633338\pi\) | |||||||
\(198\) | 2360.19 | 0.847130 | ||||||||
\(199\) | 4968.79 | 1.76999 | 0.884995 | − | 0.465600i | \(-0.154161\pi\) | ||||
0.884995 | + | 0.465600i | \(0.154161\pi\) | |||||||
\(200\) | 1117.65 | 0.395149 | ||||||||
\(201\) | 6276.90 | 2.20268 | ||||||||
\(202\) | 2485.31 | 0.865674 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3603.94 | −1.23689 | ||||||||
\(205\) | −5603.20 | −1.90900 | ||||||||
\(206\) | −1528.77 | −0.517061 | ||||||||
\(207\) | 575.211 | 0.193140 | ||||||||
\(208\) | 249.580 | 0.0831985 | ||||||||
\(209\) | 1278.52 | 0.423142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2530.95 | 0.825771 | 0.412885 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412885 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(212\) | −1292.24 | −0.418640 | ||||||||
\(213\) | 2786.00 | 0.896214 | ||||||||
\(214\) | 1435.12 | 0.458423 | ||||||||
\(215\) | 3853.30 | 1.22229 | ||||||||
\(216\) | 114.859 | 0.0361812 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1053.30 | −0.327240 | ||||||||
\(219\) | −7010.71 | −2.16320 | ||||||||
\(220\) | 3070.86 | 0.941080 | ||||||||
\(221\) | 1948.80 | 0.593171 | ||||||||
\(222\) | −2289.23 | −0.692085 | ||||||||
\(223\) | 5807.13 | 1.74383 | 0.871915 | − | 0.489658i | \(-0.162878\pi\) | ||||
0.871915 | + | 0.489658i | \(0.162878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3493.94 | 1.03524 | ||||||||
\(226\) | −1123.39 | −0.330651 | ||||||||
\(227\) | 4762.82 | 1.39260 | 0.696299 | − | 0.717752i | \(-0.254829\pi\) | ||||
0.696299 | + | 0.717752i | \(0.254829\pi\) | |||||||
\(228\) | −781.605 | −0.227031 | ||||||||
\(229\) | 384.176 | 0.110861 | 0.0554303 | − | 0.998463i | \(-0.482347\pi\) | ||||
0.0554303 | + | 0.998463i | \(0.482347\pi\) | |||||||
\(230\) | 748.411 | 0.214560 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −605.929 | −0.171471 | ||||||||
\(233\) | 1398.62 | 0.393249 | 0.196624 | − | 0.980479i | \(-0.437002\pi\) | ||||
0.196624 | + | 0.980479i | \(0.437002\pi\) | |||||||
\(234\) | 780.225 | 0.217970 | ||||||||
\(235\) | 8496.59 | 2.35854 | ||||||||
\(236\) | 3008.91 | 0.829930 | ||||||||
\(237\) | 7294.56 | 1.99929 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1755.23 | 0.475048 | 0.237524 | − | 0.971382i | \(-0.423664\pi\) | ||||
0.237524 | + | 0.971382i | \(0.423664\pi\) | |||||||
\(240\) | −1877.34 | −0.504923 | ||||||||
\(241\) | −2783.24 | −0.743917 | −0.371959 | − | 0.928249i | \(-0.621314\pi\) | ||||
−0.371959 | + | 0.928249i | \(0.621314\pi\) | |||||||
\(242\) | 1791.15 | 0.475782 | ||||||||
\(243\) | 5228.77 | 1.38035 | ||||||||
\(244\) | −3007.16 | −0.788990 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4967.34 | 1.28742 | ||||||||
\(247\) | 422.647 | 0.108876 | ||||||||
\(248\) | 810.394 | 0.207500 | ||||||||
\(249\) | −511.768 | −0.130249 | ||||||||
\(250\) | 478.537 | 0.121061 | ||||||||
\(251\) | −5021.71 | −1.26282 | −0.631410 | − | 0.775450i | \(-0.717523\pi\) | ||||
−0.631410 | + | 0.775450i | \(0.717523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1085.29 | 0.269690 | ||||||||
\(254\) | −4793.12 | −1.18404 | ||||||||
\(255\) | −14658.8 | −3.59989 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −974.857 | −0.236614 | −0.118307 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118307 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(258\) | −3416.02 | −0.824312 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1015.16 | 0.242143 | ||||||||
\(261\) | −1894.22 | −0.449232 | ||||||||
\(262\) | 1717.69 | 0.405035 | ||||||||
\(263\) | −491.619 | −0.115264 | −0.0576322 | − | 0.998338i | \(-0.518355\pi\) | ||||
−0.0576322 | + | 0.998338i | \(0.518355\pi\) | |||||||
\(264\) | −2722.38 | −0.634662 | ||||||||
\(265\) | −5256.14 | −1.21842 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1505.84 | 0.345154 | ||||||||
\(268\) | −3481.49 | −0.793530 | ||||||||
\(269\) | −358.977 | −0.0813651 | −0.0406825 | − | 0.999172i | \(-0.512953\pi\) | ||||
−0.0406825 | + | 0.999172i | \(0.512953\pi\) | |||||||
\(270\) | 467.182 | 0.105303 | ||||||||
\(271\) | 4638.86 | 1.03982 | 0.519909 | − | 0.854222i | \(-0.325966\pi\) | ||||
0.519909 | + | 0.854222i | \(0.325966\pi\) | |||||||
\(272\) | 1998.93 | 0.445599 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 302.011 | 0.0665881 | ||||||||
\(275\) | 6592.26 | 1.44556 | ||||||||
\(276\) | −663.480 | −0.144699 | ||||||||
\(277\) | 2524.96 | 0.547690 | 0.273845 | − | 0.961774i | \(-0.411704\pi\) | ||||
0.273845 | + | 0.961774i | \(0.411704\pi\) | |||||||
\(278\) | −3975.64 | −0.857709 | ||||||||
\(279\) | 2533.41 | 0.543625 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3278.39 | 0.695986 | 0.347993 | − | 0.937497i | \(-0.386863\pi\) | ||||
0.347993 | + | 0.937497i | \(0.386863\pi\) | |||||||
\(282\) | −7532.39 | −1.59059 | ||||||||
\(283\) | 6720.68 | 1.41167 | 0.705836 | − | 0.708375i | \(-0.250572\pi\) | ||||
0.705836 | + | 0.708375i | \(0.250572\pi\) | |||||||
\(284\) | −1545.26 | −0.322867 | ||||||||
\(285\) | −3179.14 | −0.660758 | ||||||||
\(286\) | 1472.11 | 0.304362 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 800.293 | 0.163742 | ||||||||
\(289\) | 10695.3 | 2.17694 | ||||||||
\(290\) | −2464.59 | −0.499053 | ||||||||
\(291\) | 2093.92 | 0.421814 | ||||||||
\(292\) | 3888.50 | 0.779306 | ||||||||
\(293\) | −1554.24 | −0.309896 | −0.154948 | − | 0.987923i | \(-0.549521\pi\) | ||||
−0.154948 | + | 0.987923i | \(0.549521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12238.6 | 2.41545 | ||||||||
\(296\) | 1269.72 | 0.249328 | ||||||||
\(297\) | 677.474 | 0.132360 | ||||||||
\(298\) | 2320.45 | 0.451074 | ||||||||
\(299\) | 358.772 | 0.0693924 | ||||||||
\(300\) | −4030.10 | −0.775593 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3000.04 | 0.571633 | ||||||||
\(303\) | −8961.72 | −1.69913 | ||||||||
\(304\) | 433.518 | 0.0817894 | ||||||||
\(305\) | −12231.5 | −2.29630 | ||||||||
\(306\) | 6248.95 | 1.16741 | ||||||||
\(307\) | 3942.91 | 0.733010 | 0.366505 | − | 0.930416i | \(-0.380554\pi\) | ||||
0.366505 | + | 0.930416i | \(0.380554\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5512.55 | 1.01488 | ||||||||
\(310\) | 3296.24 | 0.603915 | ||||||||
\(311\) | −7176.79 | −1.30855 | −0.654274 | − | 0.756258i | \(-0.727026\pi\) | ||||
−0.654274 | + | 0.756258i | \(0.727026\pi\) | |||||||
\(312\) | −899.954 | −0.163301 | ||||||||
\(313\) | −5888.35 | −1.06335 | −0.531676 | − | 0.846948i | \(-0.678438\pi\) | ||||
−0.531676 | + | 0.846948i | \(0.678438\pi\) | |||||||
\(314\) | −5650.48 | −1.01553 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4045.94 | −0.720259 | ||||||||
\(317\) | −8438.25 | −1.49508 | −0.747539 | − | 0.664218i | \(-0.768765\pi\) | ||||
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(318\) | 4659.67 | 0.821701 | ||||||||
\(319\) | −3573.97 | −0.627284 | ||||||||
\(320\) | 1041.27 | 0.181902 | ||||||||
\(321\) | −5174.84 | −0.899786 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3385.05 | 0.583125 | ||||||||
\(324\) | −3115.16 | −0.534149 | ||||||||
\(325\) | 2179.25 | 0.371947 | ||||||||
\(326\) | 7258.05 | 1.23309 | ||||||||
\(327\) | 3798.05 | 0.642302 | ||||||||
\(328\) | −2755.14 | −0.463803 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11073.1 | −1.84714 | ||||||||
\(331\) | 5617.36 | 0.932803 | 0.466402 | − | 0.884573i | \(-0.345550\pi\) | ||||
0.466402 | + | 0.884573i | \(0.345550\pi\) | |||||||
\(332\) | 283.853 | 0.0469230 | ||||||||
\(333\) | 3969.34 | 0.653209 | ||||||||
\(334\) | 1708.38 | 0.279876 | ||||||||
\(335\) | −14160.8 | −2.30951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1180.08 | 0.190750 | 0.0953752 | − | 0.995441i | \(-0.469595\pi\) | ||||
0.0953752 | + | 0.995441i | \(0.469595\pi\) | |||||||
\(338\) | −3907.36 | −0.628793 | ||||||||
\(339\) | 4050.81 | 0.648996 | ||||||||
\(340\) | 8130.55 | 1.29689 | ||||||||
\(341\) | 4779.96 | 0.759090 | ||||||||
\(342\) | 1355.24 | 0.214278 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1894.70 | 0.296964 | ||||||||
\(345\) | −2698.67 | −0.421135 | ||||||||
\(346\) | −5134.99 | −0.797857 | ||||||||
\(347\) | −583.578 | −0.0902827 | −0.0451413 | − | 0.998981i | \(-0.514374\pi\) | ||||
−0.0451413 | + | 0.998981i | \(0.514374\pi\) | |||||||
\(348\) | 2184.90 | 0.336560 | ||||||||
\(349\) | 10239.5 | 1.57051 | 0.785253 | − | 0.619175i | \(-0.212533\pi\) | ||||
0.785253 | + | 0.619175i | \(0.212533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 223.957 | 0.0340568 | ||||||||
\(352\) | 1509.97 | 0.228641 | ||||||||
\(353\) | −2364.68 | −0.356542 | −0.178271 | − | 0.983981i | \(-0.557050\pi\) | ||||
−0.178271 | + | 0.983981i | \(0.557050\pi\) | |||||||
\(354\) | −10849.7 | −1.62898 | ||||||||
\(355\) | −6285.26 | −0.939682 | ||||||||
\(356\) | −835.217 | −0.124344 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6855.26 | −1.01204 | ||||||||
\(359\) | −96.6164 | −0.0142040 | −0.00710198 | − | 0.999975i | \(-0.502261\pi\) | ||||
−0.00710198 | + | 0.999975i | \(0.502261\pi\) | |||||||
\(360\) | 3255.15 | 0.476560 | ||||||||
\(361\) | −6124.87 | −0.892968 | ||||||||
\(362\) | 2163.01 | 0.314047 | ||||||||
\(363\) | −6458.64 | −0.933859 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15816.3 | 2.26812 | ||||||||
\(366\) | 10843.4 | 1.54862 | ||||||||
\(367\) | 625.870 | 0.0890194 | 0.0445097 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445097 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −8612.98 | −1.21510 | ||||||||
\(370\) | 5164.53 | 0.725652 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2922.17 | −0.407279 | ||||||||
\(373\) | −1947.36 | −0.270323 | −0.135162 | − | 0.990824i | \(-0.543155\pi\) | ||||
−0.135162 | + | 0.990824i | \(0.543155\pi\) | |||||||
\(374\) | 11790.3 | 1.63012 | ||||||||
\(375\) | −1725.54 | −0.237618 | ||||||||
\(376\) | 4177.85 | 0.573021 | ||||||||
\(377\) | −1181.47 | −0.161403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6434.94 | 0.872139 | 0.436069 | − | 0.899913i | \(-0.356370\pi\) | ||||
0.436069 | + | 0.899913i | \(0.356370\pi\) | |||||||
\(380\) | 1763.31 | 0.238042 | ||||||||
\(381\) | 17283.4 | 2.32403 | ||||||||
\(382\) | −3951.95 | −0.529318 | ||||||||
\(383\) | 5381.85 | 0.718014 | 0.359007 | − | 0.933335i | \(-0.383115\pi\) | ||||
0.359007 | + | 0.933335i | \(0.383115\pi\) | |||||||
\(384\) | −923.103 | −0.122674 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3188.07 | 0.420385 | ||||||||
\(387\) | 5923.12 | 0.778008 | ||||||||
\(388\) | −1161.40 | −0.151961 | ||||||||
\(389\) | 1793.47 | 0.233760 | 0.116880 | − | 0.993146i | \(-0.462711\pi\) | ||||
0.116880 | + | 0.993146i | \(0.462711\pi\) | |||||||
\(390\) | −3660.52 | −0.475276 | ||||||||
\(391\) | 2873.46 | 0.371655 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6193.76 | −0.794997 | ||||||||
\(394\) | −4498.71 | −0.575232 | ||||||||
\(395\) | −16456.6 | −2.09626 | ||||||||
\(396\) | 4720.39 | 0.599011 | ||||||||
\(397\) | −4504.05 | −0.569399 | −0.284700 | − | 0.958617i | \(-0.591894\pi\) | ||||
−0.284700 | + | 0.958617i | \(0.591894\pi\) | |||||||
\(398\) | 9937.58 | 1.25157 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2235.30 | 0.279413 | ||||||||
\(401\) | 6831.76 | 0.850777 | 0.425389 | − | 0.905011i | \(-0.360137\pi\) | ||||
0.425389 | + | 0.905011i | \(0.360137\pi\) | |||||||
\(402\) | 12553.8 | 1.55753 | ||||||||
\(403\) | 1580.14 | 0.195317 | ||||||||
\(404\) | 4970.63 | 0.612124 | ||||||||
\(405\) | −12670.7 | −1.55460 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7489.24 | 0.912107 | ||||||||
\(408\) | −7207.88 | −0.874616 | ||||||||
\(409\) | 7577.51 | 0.916097 | 0.458048 | − | 0.888927i | \(-0.348549\pi\) | ||||
0.458048 | + | 0.888927i | \(0.348549\pi\) | |||||||
\(410\) | −11206.4 | −1.34986 | ||||||||
\(411\) | −1089.01 | −0.130698 | ||||||||
\(412\) | −3057.54 | −0.365617 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1150.42 | 0.136570 | ||||||||
\(415\) | 1154.56 | 0.136566 | ||||||||
\(416\) | 499.161 | 0.0588302 | ||||||||
\(417\) | 14335.6 | 1.68350 | ||||||||
\(418\) | 2557.03 | 0.299207 | ||||||||
\(419\) | −15291.7 | −1.78293 | −0.891463 | − | 0.453093i | \(-0.850321\pi\) | ||||
−0.891463 | + | 0.453093i | \(0.850321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4676.53 | −0.541378 | −0.270689 | − | 0.962667i | \(-0.587252\pi\) | ||||
−0.270689 | + | 0.962667i | \(0.587252\pi\) | |||||||
\(422\) | 5061.90 | 0.583908 | ||||||||
\(423\) | 13060.6 | 1.50124 | ||||||||
\(424\) | −2584.49 | −0.296023 | ||||||||
\(425\) | 17454.0 | 1.99210 | ||||||||
\(426\) | 5572.00 | 0.633719 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2870.23 | 0.324154 | ||||||||
\(429\) | −5308.22 | −0.597397 | ||||||||
\(430\) | 7706.61 | 0.864292 | ||||||||
\(431\) | 1791.88 | 0.200259 | 0.100130 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100130 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(432\) | 229.718 | 0.0255840 | ||||||||
\(433\) | −5834.03 | −0.647495 | −0.323748 | − | 0.946143i | \(-0.604943\pi\) | ||||
−0.323748 | + | 0.946143i | \(0.604943\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8886.97 | 0.979535 | ||||||||
\(436\) | −2106.59 | −0.231394 | ||||||||
\(437\) | 623.182 | 0.0682171 | ||||||||
\(438\) | −14021.4 | −1.52961 | ||||||||
\(439\) | 15116.1 | 1.64340 | 0.821700 | − | 0.569921i | \(-0.193026\pi\) | ||||
0.821700 | + | 0.569921i | \(0.193026\pi\) | |||||||
\(440\) | 6141.73 | 0.665444 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3897.61 | 0.419435 | ||||||||
\(443\) | 15050.6 | 1.61416 | 0.807082 | − | 0.590439i | \(-0.201045\pi\) | ||||
0.807082 | + | 0.590439i | \(0.201045\pi\) | |||||||
\(444\) | −4578.46 | −0.489378 | ||||||||
\(445\) | −3397.20 | −0.361894 | ||||||||
\(446\) | 11614.3 | 1.23307 | ||||||||
\(447\) | −8367.24 | −0.885362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4182.76 | 0.439636 | 0.219818 | − | 0.975541i | \(-0.429454\pi\) | ||||
0.219818 | + | 0.975541i | \(0.429454\pi\) | |||||||
\(450\) | 6987.88 | 0.732026 | ||||||||
\(451\) | −16250.7 | −1.69671 | ||||||||
\(452\) | −2246.79 | −0.233805 | ||||||||
\(453\) | −10817.8 | −1.12199 | ||||||||
\(454\) | 9525.64 | 0.984715 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1563.21 | −0.160535 | ||||||||
\(457\) | 63.6901 | 0.00651925 | 0.00325962 | − | 0.999995i | \(-0.498962\pi\) | ||||
0.00325962 | + | 0.999995i | \(0.498962\pi\) | |||||||
\(458\) | 768.353 | 0.0783903 | ||||||||
\(459\) | 1793.71 | 0.182403 | ||||||||
\(460\) | 1496.82 | 0.151717 | ||||||||
\(461\) | 13051.3 | 1.31856 | 0.659281 | − | 0.751896i | \(-0.270861\pi\) | ||||
0.659281 | + | 0.751896i | \(0.270861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5158.36 | 0.517774 | 0.258887 | − | 0.965908i | \(-0.416644\pi\) | ||||
0.258887 | + | 0.965908i | \(0.416644\pi\) | |||||||
\(464\) | −1211.86 | −0.121248 | ||||||||
\(465\) | −11885.8 | −1.18536 | ||||||||
\(466\) | 2797.25 | 0.278069 | ||||||||
\(467\) | −4486.79 | −0.444591 | −0.222296 | − | 0.974979i | \(-0.571355\pi\) | ||||
−0.222296 | + | 0.974979i | \(0.571355\pi\) | |||||||
\(468\) | 1560.45 | 0.154128 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 16993.2 | 1.66774 | ||||||||
\(471\) | 20374.9 | 1.99326 | ||||||||
\(472\) | 6017.83 | 0.586849 | ||||||||
\(473\) | 11175.6 | 1.08637 | ||||||||
\(474\) | 14589.1 | 1.41371 | ||||||||
\(475\) | 3785.33 | 0.365648 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8079.49 | −0.775544 | ||||||||
\(478\) | 3510.46 | 0.335910 | ||||||||
\(479\) | −7266.52 | −0.693144 | −0.346572 | − | 0.938023i | \(-0.612654\pi\) | ||||
−0.346572 | + | 0.938023i | \(0.612654\pi\) | |||||||
\(480\) | −3754.67 | −0.357035 | ||||||||
\(481\) | 2475.77 | 0.234689 | ||||||||
\(482\) | −5566.47 | −0.526029 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3582.29 | 0.336429 | ||||||||
\(485\) | −4723.92 | −0.442272 | ||||||||
\(486\) | 10457.5 | 0.976058 | ||||||||
\(487\) | 8606.70 | 0.800835 | 0.400418 | − | 0.916333i | \(-0.368865\pi\) | ||||
0.400418 | + | 0.916333i | \(0.368865\pi\) | |||||||
\(488\) | −6014.31 | −0.557900 | ||||||||
\(489\) | −26171.6 | −2.42028 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10692.5 | −0.982779 | −0.491389 | − | 0.870940i | \(-0.663511\pi\) | ||||
−0.491389 | + | 0.870940i | \(0.663511\pi\) | |||||||
\(492\) | 9934.68 | 0.910346 | ||||||||
\(493\) | −9462.58 | −0.864449 | ||||||||
\(494\) | 845.294 | 0.0769870 | ||||||||
\(495\) | 19199.9 | 1.74338 | ||||||||
\(496\) | 1620.79 | 0.146725 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1023.54 | −0.0920998 | ||||||||
\(499\) | −1940.11 | −0.174050 | −0.0870252 | − | 0.996206i | \(-0.527736\pi\) | ||||
−0.0870252 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(500\) | 957.074 | 0.0856033 | ||||||||
\(501\) | −6160.21 | −0.549337 | ||||||||
\(502\) | −10043.4 | −0.892948 | ||||||||
\(503\) | 15043.4 | 1.33350 | 0.666751 | − | 0.745280i | \(-0.267684\pi\) | ||||
0.666751 | + | 0.745280i | \(0.267684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20217.8 | 1.78154 | ||||||||
\(506\) | 2170.58 | 0.190700 | ||||||||
\(507\) | 14089.4 | 1.23419 | ||||||||
\(508\) | −9586.25 | −0.837246 | ||||||||
\(509\) | 2212.59 | 0.192675 | 0.0963374 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963374 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(510\) | −29317.7 | −2.54551 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 389.011 | 0.0334800 | ||||||||
\(514\) | −1949.71 | −0.167312 | ||||||||
\(515\) | −12436.4 | −1.06410 | ||||||||
\(516\) | −6832.05 | −0.582876 | ||||||||
\(517\) | 24642.3 | 2.09626 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18516.1 | 1.56602 | ||||||||
\(520\) | 2030.31 | 0.171221 | ||||||||
\(521\) | −237.881 | −0.0200034 | −0.0100017 | − | 0.999950i | \(-0.503184\pi\) | ||||
−0.0100017 | + | 0.999950i | \(0.503184\pi\) | |||||||
\(522\) | −3788.45 | −0.317655 | ||||||||
\(523\) | −16907.0 | −1.41356 | −0.706778 | − | 0.707435i | \(-0.749852\pi\) | ||||
−0.706778 | + | 0.707435i | \(0.749852\pi\) | |||||||
\(524\) | 3435.38 | 0.286403 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −983.238 | −0.0815042 | ||||||||
\(527\) | 12655.6 | 1.04609 | ||||||||
\(528\) | −5444.76 | −0.448774 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −10512.3 | −0.861555 | ||||||||
\(531\) | 18812.6 | 1.53747 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5372.11 | −0.436570 | ||||||||
\(534\) | 3011.68 | 0.244060 | ||||||||
\(535\) | 11674.5 | 0.943427 | ||||||||
\(536\) | −6962.98 | −0.561110 | ||||||||
\(537\) | 24719.2 | 1.98643 | ||||||||
\(538\) | −717.954 | −0.0575338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 934.364 | 0.0744604 | ||||||||
\(541\) | −1410.42 | −0.112086 | −0.0560431 | − | 0.998428i | \(-0.517848\pi\) | ||||
−0.0560431 | + | 0.998428i | \(0.517848\pi\) | |||||||
\(542\) | 9277.71 | 0.735262 | ||||||||
\(543\) | −7799.52 | −0.616408 | ||||||||
\(544\) | 3997.86 | 0.315086 | ||||||||
\(545\) | −8568.47 | −0.673455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23165.7 | −1.81078 | −0.905388 | − | 0.424585i | \(-0.860420\pi\) | ||||
−0.905388 | + | 0.424585i | \(0.860420\pi\) | |||||||
\(548\) | 604.021 | 0.0470849 | ||||||||
\(549\) | −18801.6 | −1.46163 | ||||||||
\(550\) | 13184.5 | 1.02216 | ||||||||
\(551\) | −2052.20 | −0.158669 | ||||||||
\(552\) | −1326.96 | −0.102317 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5049.92 | 0.387275 | ||||||||
\(555\) | −18622.6 | −1.42430 | ||||||||
\(556\) | −7951.29 | −0.606492 | ||||||||
\(557\) | −9563.65 | −0.727513 | −0.363757 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363757 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(558\) | 5066.82 | 0.384401 | ||||||||
\(559\) | 3694.38 | 0.279527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42514.4 | −3.19957 | ||||||||
\(562\) | 6556.77 | 0.492136 | ||||||||
\(563\) | −1124.59 | −0.0841841 | −0.0420920 | − | 0.999114i | \(-0.513402\pi\) | ||||
−0.0420920 | + | 0.999114i | \(0.513402\pi\) | |||||||
\(564\) | −15064.8 | −1.12472 | ||||||||
\(565\) | −9138.69 | −0.680474 | ||||||||
\(566\) | 13441.4 | 0.998203 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3090.52 | −0.228302 | ||||||||
\(569\) | −15300.7 | −1.12731 | −0.563653 | − | 0.826012i | \(-0.690604\pi\) | ||||
−0.563653 | + | 0.826012i | \(0.690604\pi\) | |||||||
\(570\) | −6358.28 | −0.467226 | ||||||||
\(571\) | 15344.6 | 1.12461 | 0.562303 | − | 0.826931i | \(-0.309915\pi\) | ||||
0.562303 | + | 0.826931i | \(0.309915\pi\) | |||||||
\(572\) | 2944.21 | 0.215216 | ||||||||
\(573\) | 14250.2 | 1.03894 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3213.24 | 0.233046 | ||||||||
\(576\) | 1600.59 | 0.115783 | ||||||||
\(577\) | −17787.8 | −1.28339 | −0.641693 | − | 0.766961i | \(-0.721768\pi\) | ||||
−0.641693 | + | 0.766961i | \(0.721768\pi\) | |||||||
\(578\) | 21390.6 | 1.53933 | ||||||||
\(579\) | −11495.8 | −0.825125 | ||||||||
\(580\) | −4929.17 | −0.352884 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4187.84 | 0.298267 | ||||||||
\(583\) | −15244.2 | −1.08293 | ||||||||
\(584\) | 7777.00 | 0.551052 | ||||||||
\(585\) | 6347.05 | 0.448578 | ||||||||
\(586\) | −3108.47 | −0.219129 | ||||||||
\(587\) | −28030.3 | −1.97093 | −0.985464 | − | 0.169884i | \(-0.945661\pi\) | ||||
−0.985464 | + | 0.169884i | \(0.945661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2744.69 | 0.192009 | ||||||||
\(590\) | 24477.2 | 1.70798 | ||||||||
\(591\) | 16221.7 | 1.12906 | ||||||||
\(592\) | 2539.45 | 0.176302 | ||||||||
\(593\) | −16069.1 | −1.11278 | −0.556389 | − | 0.830922i | \(-0.687813\pi\) | ||||
−0.556389 | + | 0.830922i | \(0.687813\pi\) | |||||||
\(594\) | 1354.95 | 0.0935929 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4640.90 | 0.318958 | ||||||||
\(597\) | −35833.6 | −2.45657 | ||||||||
\(598\) | 717.544 | 0.0490678 | ||||||||
\(599\) | −2013.96 | −0.137376 | −0.0686879 | − | 0.997638i | \(-0.521881\pi\) | ||||
−0.0686879 | + | 0.997638i | \(0.521881\pi\) | |||||||
\(600\) | −8060.20 | −0.548427 | ||||||||
\(601\) | −11300.5 | −0.766984 | −0.383492 | − | 0.923544i | \(-0.625279\pi\) | ||||
−0.383492 | + | 0.923544i | \(0.625279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21767.3 | −1.47004 | ||||||||
\(604\) | 6000.09 | 0.404205 | ||||||||
\(605\) | 14570.8 | 0.979152 | ||||||||
\(606\) | −17923.4 | −1.20147 | ||||||||
\(607\) | 4451.15 | 0.297639 | 0.148819 | − | 0.988864i | \(-0.452453\pi\) | ||||
0.148819 | + | 0.988864i | \(0.452453\pi\) | |||||||
\(608\) | 867.036 | 0.0578338 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24462.9 | −1.62373 | ||||||||
\(611\) | 8146.17 | 0.539376 | ||||||||
\(612\) | 12497.9 | 0.825486 | ||||||||
\(613\) | 17338.0 | 1.14237 | 0.571187 | − | 0.820820i | \(-0.306483\pi\) | ||||
0.571187 | + | 0.820820i | \(0.306483\pi\) | |||||||
\(614\) | 7885.83 | 0.518316 | ||||||||
\(615\) | 40408.8 | 2.64950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5994.66 | 0.391144 | 0.195572 | − | 0.980689i | \(-0.437344\pi\) | ||||
0.195572 | + | 0.980689i | \(0.437344\pi\) | |||||||
\(618\) | 11025.1 | 0.717629 | ||||||||
\(619\) | −17923.7 | −1.16383 | −0.581917 | − | 0.813248i | \(-0.697697\pi\) | ||||
−0.581917 | + | 0.813248i | \(0.697697\pi\) | |||||||
\(620\) | 6592.47 | 0.427032 | ||||||||
\(621\) | 330.219 | 0.0213385 | ||||||||
\(622\) | −14353.6 | −0.925283 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1799.91 | −0.115471 | ||||||||
\(625\) | −13570.4 | −0.868508 | ||||||||
\(626\) | −11776.7 | −0.751903 | ||||||||
\(627\) | −9220.32 | −0.587279 | ||||||||
\(628\) | −11301.0 | −0.718085 | ||||||||
\(629\) | 19828.8 | 1.25696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9861.28 | −0.622141 | −0.311071 | − | 0.950387i | \(-0.600688\pi\) | ||||
−0.311071 | + | 0.950387i | \(0.600688\pi\) | |||||||
\(632\) | −8091.88 | −0.509300 | ||||||||
\(633\) | −18252.5 | −1.14609 | ||||||||
\(634\) | −16876.5 | −1.05718 | ||||||||
\(635\) | −38991.6 | −2.43675 | ||||||||
\(636\) | 9319.33 | 0.581031 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7147.93 | −0.443557 | ||||||||
\(639\) | −9661.41 | −0.598121 | ||||||||
\(640\) | 2082.53 | 0.128624 | ||||||||
\(641\) | −12525.2 | −0.771788 | −0.385894 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385894 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(642\) | −10349.7 | −0.636245 | ||||||||
\(643\) | −25700.9 | −1.57628 | −0.788139 | − | 0.615498i | \(-0.788955\pi\) | ||||
−0.788139 | + | 0.615498i | \(0.788955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27789.0 | −1.69642 | ||||||||
\(646\) | 6770.10 | 0.412331 | ||||||||
\(647\) | −3951.92 | −0.240133 | −0.120066 | − | 0.992766i | \(-0.538311\pi\) | ||||
−0.120066 | + | 0.992766i | \(0.538311\pi\) | |||||||
\(648\) | −6230.31 | −0.377700 | ||||||||
\(649\) | 35495.1 | 2.14685 | ||||||||
\(650\) | 4358.50 | 0.263007 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14516.1 | 0.871923 | ||||||||
\(653\) | −18402.1 | −1.10280 | −0.551402 | − | 0.834240i | \(-0.685907\pi\) | ||||
−0.551402 | + | 0.834240i | \(0.685907\pi\) | |||||||
\(654\) | 7596.10 | 0.454176 | ||||||||
\(655\) | 13973.2 | 0.833556 | ||||||||
\(656\) | −5510.28 | −0.327958 | ||||||||
\(657\) | 24312.0 | 1.44369 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12627.9 | −0.746455 | −0.373228 | − | 0.927740i | \(-0.621749\pi\) | ||||
−0.373228 | + | 0.927740i | \(0.621749\pi\) | |||||||
\(660\) | −22146.3 | −1.30612 | ||||||||
\(661\) | −4711.79 | −0.277258 | −0.138629 | − | 0.990344i | \(-0.544270\pi\) | ||||
−0.138629 | + | 0.990344i | \(0.544270\pi\) | |||||||
\(662\) | 11234.7 | 0.659592 | ||||||||
\(663\) | −14054.3 | −0.823262 | ||||||||
\(664\) | 567.705 | 0.0331796 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7938.68 | 0.461888 | ||||||||
\(667\) | −1742.05 | −0.101128 | ||||||||
\(668\) | 3416.77 | 0.197902 | ||||||||
\(669\) | −41879.5 | −2.42026 | ||||||||
\(670\) | −28321.6 | −1.63307 | ||||||||
\(671\) | −35474.4 | −2.04094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28702.7 | 1.64399 | 0.821995 | − | 0.569494i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569494i | \(0.192861\pi\) | |||||||
\(674\) | 2360.15 | 0.134881 | ||||||||
\(675\) | 2005.81 | 0.114376 | ||||||||
\(676\) | −7814.71 | −0.444624 | ||||||||
\(677\) | −31186.5 | −1.77045 | −0.885226 | − | 0.465162i | \(-0.845996\pi\) | ||||
−0.885226 | + | 0.465162i | \(0.845996\pi\) | |||||||
\(678\) | 8101.62 | 0.458910 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16261.1 | 0.917036 | ||||||||
\(681\) | −34348.2 | −1.93279 | ||||||||
\(682\) | 9559.93 | 0.536757 | ||||||||
\(683\) | −9293.06 | −0.520628 | −0.260314 | − | 0.965524i | \(-0.583826\pi\) | ||||
−0.260314 | + | 0.965524i | \(0.583826\pi\) | |||||||
\(684\) | 2710.48 | 0.151517 | ||||||||
\(685\) | 2456.83 | 0.137037 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2770.58 | −0.153863 | ||||||||
\(688\) | 3789.41 | 0.209985 | ||||||||
\(689\) | −5039.36 | −0.278642 | ||||||||
\(690\) | −5397.34 | −0.297787 | ||||||||
\(691\) | −14601.0 | −0.803834 | −0.401917 | − | 0.915676i | \(-0.631656\pi\) | ||||
−0.401917 | + | 0.915676i | \(0.631656\pi\) | |||||||
\(692\) | −10270.0 | −0.564170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1167.16 | −0.0638395 | ||||||||
\(695\) | −32341.4 | −1.76515 | ||||||||
\(696\) | 4369.80 | 0.237984 | ||||||||
\(697\) | −43026.1 | −2.33820 | ||||||||
\(698\) | 20479.0 | 1.11052 | ||||||||
\(699\) | −10086.5 | −0.545789 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8708.03 | 0.469184 | 0.234592 | − | 0.972094i | \(-0.424625\pi\) | ||||
0.234592 | + | 0.972094i | \(0.424625\pi\) | |||||||
\(702\) | 447.914 | 0.0240818 | ||||||||
\(703\) | 4300.38 | 0.230714 | ||||||||
\(704\) | 3019.94 | 0.161674 | ||||||||
\(705\) | −61275.2 | −3.27341 | ||||||||
\(706\) | −4729.36 | −0.252113 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −21699.5 | −1.15186 | ||||||||
\(709\) | 33500.9 | 1.77455 | 0.887273 | − | 0.461245i | \(-0.152597\pi\) | ||||
0.887273 | + | 0.461245i | \(0.152597\pi\) | |||||||
\(710\) | −12570.5 | −0.664456 | ||||||||
\(711\) | −25296.4 | −1.33430 | ||||||||
\(712\) | −1670.43 | −0.0879244 | ||||||||
\(713\) | 2329.88 | 0.122377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11975.4 | 0.626372 | ||||||||
\(716\) | −13710.5 | −0.715623 | ||||||||
\(717\) | −12658.3 | −0.659319 | ||||||||
\(718\) | −193.233 | −0.0100437 | ||||||||
\(719\) | 32105.0 | 1.66525 | 0.832625 | − | 0.553837i | \(-0.186837\pi\) | ||||
0.832625 | + | 0.553837i | \(0.186837\pi\) | |||||||
\(720\) | 6510.31 | 0.336979 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12249.7 | −0.631424 | ||||||||
\(723\) | 20072.0 | 1.03248 | ||||||||
\(724\) | 4326.01 | 0.222065 | ||||||||
\(725\) | −10581.5 | −0.542052 | ||||||||
\(726\) | −12917.3 | −0.660338 | ||||||||
\(727\) | −15233.0 | −0.777113 | −0.388557 | − | 0.921425i | \(-0.627026\pi\) | ||||
−0.388557 | + | 0.921425i | \(0.627026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16681.2 | −0.847495 | ||||||||
\(730\) | 31632.6 | 1.60380 | ||||||||
\(731\) | 29588.9 | 1.49711 | ||||||||
\(732\) | 21686.8 | 1.09504 | ||||||||
\(733\) | 1809.92 | 0.0912019 | 0.0456009 | − | 0.998960i | \(-0.485480\pi\) | ||||
0.0456009 | + | 0.998960i | \(0.485480\pi\) | |||||||
\(734\) | 1251.74 | 0.0629462 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −41069.9 | −2.05269 | ||||||||
\(738\) | −17226.0 | −0.859209 | ||||||||
\(739\) | −8238.73 | −0.410104 | −0.205052 | − | 0.978751i | \(-0.565736\pi\) | ||||
−0.205052 | + | 0.978751i | \(0.565736\pi\) | |||||||
\(740\) | 10329.1 | 0.513114 | ||||||||
\(741\) | −3048.02 | −0.151109 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23854.1 | −1.17782 | −0.588910 | − | 0.808198i | \(-0.700443\pi\) | ||||
−0.588910 | + | 0.808198i | \(0.700443\pi\) | |||||||
\(744\) | −5844.35 | −0.287990 | ||||||||
\(745\) | 18876.6 | 0.928304 | ||||||||
\(746\) | −3894.72 | −0.191147 | ||||||||
\(747\) | 1774.73 | 0.0869263 | ||||||||
\(748\) | 23580.7 | 1.15267 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3451.08 | −0.168021 | ||||||||
\(751\) | −6437.83 | −0.312809 | −0.156405 | − | 0.987693i | \(-0.549990\pi\) | ||||
−0.156405 | + | 0.987693i | \(0.549990\pi\) | |||||||
\(752\) | 8355.70 | 0.405187 | ||||||||
\(753\) | 36215.3 | 1.75267 | ||||||||
\(754\) | −2362.94 | −0.114129 | ||||||||
\(755\) | 24405.0 | 1.17641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22816.8 | 1.09550 | 0.547749 | − | 0.836643i | \(-0.315485\pi\) | ||||
0.547749 | + | 0.836643i | \(0.315485\pi\) | |||||||
\(758\) | 12869.9 | 0.616695 | ||||||||
\(759\) | −7826.84 | −0.374303 | ||||||||
\(760\) | 3526.63 | 0.168321 | ||||||||
\(761\) | 29454.4 | 1.40305 | 0.701525 | − | 0.712645i | \(-0.252503\pi\) | ||||
0.701525 | + | 0.712645i | \(0.252503\pi\) | |||||||
\(762\) | 34566.8 | 1.64334 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7903.90 | −0.374284 | ||||||||
\(765\) | 50834.6 | 2.40252 | ||||||||
\(766\) | 10763.7 | 0.507713 | ||||||||
\(767\) | 11733.8 | 0.552392 | ||||||||
\(768\) | −1846.21 | −0.0867437 | ||||||||
\(769\) | 20044.0 | 0.939930 | 0.469965 | − | 0.882685i | \(-0.344267\pi\) | ||||
0.469965 | + | 0.882685i | \(0.344267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7030.41 | 0.328397 | ||||||||
\(772\) | 6376.14 | 0.297257 | ||||||||
\(773\) | −13982.7 | −0.650611 | −0.325305 | − | 0.945609i | \(-0.605467\pi\) | ||||
−0.325305 | + | 0.945609i | \(0.605467\pi\) | |||||||
\(774\) | 11846.2 | 0.550135 | ||||||||
\(775\) | 14152.1 | 0.655948 | ||||||||
\(776\) | −2322.79 | −0.107453 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3586.94 | 0.165293 | ||||||||
\(779\) | −9331.28 | −0.429176 | ||||||||
\(780\) | −7321.04 | −0.336071 | ||||||||
\(781\) | −18228.9 | −0.835186 | ||||||||
\(782\) | 5746.93 | 0.262800 | ||||||||
\(783\) | −1087.44 | −0.0496322 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −45966.1 | −2.08994 | ||||||||
\(786\) | −12387.5 | −0.562148 | ||||||||
\(787\) | −35277.3 | −1.59784 | −0.798919 | − | 0.601438i | \(-0.794595\pi\) | ||||
−0.798919 | + | 0.601438i | \(0.794595\pi\) | |||||||
\(788\) | −8997.41 | −0.406751 | ||||||||
\(789\) | 3545.43 | 0.159975 | ||||||||
\(790\) | −32913.3 | −1.48228 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9440.78 | 0.423565 | ||||||||
\(793\) | −11727.0 | −0.525142 | ||||||||
\(794\) | −9008.09 | −0.402626 | ||||||||
\(795\) | 37905.9 | 1.69105 | ||||||||
\(796\) | 19875.2 | 0.884995 | ||||||||
\(797\) | 3314.35 | 0.147303 | 0.0736513 | − | 0.997284i | \(-0.476535\pi\) | ||||
0.0736513 | + | 0.997284i | \(0.476535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65244.0 | 2.88882 | ||||||||
\(800\) | 4470.60 | 0.197575 | ||||||||
\(801\) | −5222.02 | −0.230351 | ||||||||
\(802\) | 13663.5 | 0.601590 | ||||||||
\(803\) | 45871.3 | 2.01589 | ||||||||
\(804\) | 25107.6 | 1.10134 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3160.29 | 0.138110 | ||||||||
\(807\) | 2588.85 | 0.112927 | ||||||||
\(808\) | 9941.25 | 0.432837 | ||||||||
\(809\) | −11588.9 | −0.503640 | −0.251820 | − | 0.967774i | \(-0.581029\pi\) | ||||
−0.251820 | + | 0.967774i | \(0.581029\pi\) | |||||||
\(810\) | −25341.5 | −1.09927 | ||||||||
\(811\) | −14907.0 | −0.645446 | −0.322723 | − | 0.946494i | \(-0.604598\pi\) | ||||
−0.322723 | + | 0.946494i | \(0.604598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33454.2 | −1.44316 | ||||||||
\(814\) | 14978.5 | 0.644957 | ||||||||
\(815\) | 59043.5 | 2.53767 | ||||||||
\(816\) | −14415.8 | −0.618447 | ||||||||
\(817\) | 6417.09 | 0.274793 | ||||||||
\(818\) | 15155.0 | 0.647778 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22412.8 | −0.954499 | ||||||||
\(821\) | −18754.7 | −0.797252 | −0.398626 | − | 0.917114i | \(-0.630513\pi\) | ||||
−0.398626 | + | 0.917114i | \(0.630513\pi\) | |||||||
\(822\) | −2178.02 | −0.0924176 | ||||||||
\(823\) | 19230.6 | 0.814505 | 0.407252 | − | 0.913316i | \(-0.366487\pi\) | ||||
0.407252 | + | 0.913316i | \(0.366487\pi\) | |||||||
\(824\) | −6115.09 | −0.258531 | ||||||||
\(825\) | −47541.7 | −2.00629 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3749.90 | −0.157675 | −0.0788373 | − | 0.996887i | \(-0.525121\pi\) | ||||
−0.0788373 | + | 0.996887i | \(0.525121\pi\) | |||||||
\(828\) | 2300.84 | 0.0965699 | ||||||||
\(829\) | −22579.0 | −0.945959 | −0.472979 | − | 0.881074i | \(-0.656821\pi\) | ||||
−0.472979 | + | 0.881074i | \(0.656821\pi\) | |||||||
\(830\) | 2309.11 | 0.0965668 | ||||||||
\(831\) | −18209.4 | −0.760139 | ||||||||
\(832\) | 998.322 | 0.0415993 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 28671.3 | 1.19041 | ||||||||
\(835\) | 13897.5 | 0.575981 | ||||||||
\(836\) | 5114.06 | 0.211571 | ||||||||
\(837\) | 1454.39 | 0.0600609 | ||||||||
\(838\) | −30583.3 | −1.26072 | ||||||||
\(839\) | 9740.05 | 0.400791 | 0.200396 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200396 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18652.3 | −0.764782 | ||||||||
\(842\) | −9353.07 | −0.382812 | ||||||||
\(843\) | −23642.9 | −0.965959 | ||||||||
\(844\) | 10123.8 | 0.412885 | ||||||||
\(845\) | −31785.9 | −1.29405 | ||||||||
\(846\) | 26121.1 | 1.06154 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5168.98 | −0.209320 | ||||||||
\(849\) | −48467.8 | −1.95926 | ||||||||
\(850\) | 34907.9 | 1.40862 | ||||||||
\(851\) | 3650.45 | 0.147046 | ||||||||
\(852\) | 11144.0 | 0.448107 | ||||||||
\(853\) | −34826.5 | −1.39793 | −0.698967 | − | 0.715154i | \(-0.746357\pi\) | ||||
−0.698967 | + | 0.715154i | \(0.746357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11024.8 | 0.440981 | ||||||||
\(856\) | 5740.46 | 0.229211 | ||||||||
\(857\) | −29060.4 | −1.15832 | −0.579162 | − | 0.815212i | \(-0.696620\pi\) | ||||
−0.579162 | + | 0.815212i | \(0.696620\pi\) | |||||||
\(858\) | −10616.4 | −0.422424 | ||||||||
\(859\) | 36275.1 | 1.44085 | 0.720426 | − | 0.693532i | \(-0.243946\pi\) | ||||
0.720426 | + | 0.693532i | \(0.243946\pi\) | |||||||
\(860\) | 15413.2 | 0.611147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3583.76 | 0.141605 | ||||||||
\(863\) | 25442.3 | 1.00355 | 0.501776 | − | 0.864997i | \(-0.332680\pi\) | ||||
0.501776 | + | 0.864997i | \(0.332680\pi\) | |||||||
\(864\) | 459.435 | 0.0180906 | ||||||||
\(865\) | −41772.6 | −1.64198 | ||||||||
\(866\) | −11668.1 | −0.457848 | ||||||||
\(867\) | −77131.7 | −3.02137 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47728.5 | −1.86315 | ||||||||
\(870\) | 17773.9 | 0.692636 | ||||||||
\(871\) | −13576.8 | −0.528164 | ||||||||
\(872\) | −4213.19 | −0.163620 | ||||||||
\(873\) | −7261.39 | −0.281513 | ||||||||
\(874\) | 1246.36 | 0.0482368 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28042.9 | −1.08160 | ||||||||
\(877\) | 37592.9 | 1.44746 | 0.723729 | − | 0.690084i | \(-0.242427\pi\) | ||||
0.723729 | + | 0.690084i | \(0.242427\pi\) | |||||||
\(878\) | 30232.2 | 1.16206 | ||||||||
\(879\) | 11208.7 | 0.430104 | ||||||||
\(880\) | 12283.5 | 0.470540 | ||||||||
\(881\) | 17562.2 | 0.671608 | 0.335804 | − | 0.941932i | \(-0.390992\pi\) | ||||
0.335804 | + | 0.941932i | \(0.390992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28211.0 | 1.07517 | 0.537586 | − | 0.843209i | \(-0.319337\pi\) | ||||
0.537586 | + | 0.843209i | \(0.319337\pi\) | |||||||
\(884\) | 7795.22 | 0.296586 | ||||||||
\(885\) | −88261.6 | −3.35241 | ||||||||
\(886\) | 30101.2 | 1.14139 | ||||||||
\(887\) | −39743.9 | −1.50448 | −0.752238 | − | 0.658892i | \(-0.771025\pi\) | ||||
−0.752238 | + | 0.658892i | \(0.771025\pi\) | |||||||
\(888\) | −9156.91 | −0.346043 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6794.41 | −0.255898 | ||||||||
\(891\) | −36748.4 | −1.38173 | ||||||||
\(892\) | 23228.5 | 0.871915 | ||||||||
\(893\) | 14149.8 | 0.530240 | ||||||||
\(894\) | −16734.5 | −0.626046 | ||||||||
\(895\) | −55766.8 | −2.08277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2587.37 | −0.0963096 | ||||||||
\(898\) | 8365.53 | 0.310870 | ||||||||
\(899\) | −7672.52 | −0.284642 | ||||||||
\(900\) | 13975.8 | 0.517621 | ||||||||
\(901\) | −40361.1 | −1.49237 | ||||||||
\(902\) | −32501.4 | −1.19976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4493.57 | −0.165325 | ||||||||
\(905\) | 17595.8 | 0.646304 | ||||||||
\(906\) | −21635.5 | −0.793369 | ||||||||
\(907\) | 10980.3 | 0.401978 | 0.200989 | − | 0.979594i | \(-0.435585\pi\) | ||||
0.200989 | + | 0.979594i | \(0.435585\pi\) | |||||||
\(908\) | 19051.3 | 0.696299 | ||||||||
\(909\) | 31077.8 | 1.13398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1972.75 | −0.0717453 | −0.0358727 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358727 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(912\) | −3126.42 | −0.113515 | ||||||||
\(913\) | 3348.51 | 0.121379 | ||||||||
\(914\) | 127.380 | 0.00460980 | ||||||||
\(915\) | 88210.1 | 3.18703 | ||||||||
\(916\) | 1536.71 | 0.0554303 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3587.42 | 0.128979 | ||||||||
\(919\) | −45431.0 | −1.63072 | −0.815359 | − | 0.578955i | \(-0.803461\pi\) | ||||
−0.815359 | + | 0.578955i | \(0.803461\pi\) | |||||||
\(920\) | 2993.64 | 0.107280 | ||||||||
\(921\) | −28435.3 | −1.01734 | ||||||||
\(922\) | 26102.5 | 0.932365 | ||||||||
\(923\) | −6026.04 | −0.214897 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22173.5 | 0.788175 | ||||||||
\(926\) | 10316.7 | 0.366122 | ||||||||
\(927\) | −19116.7 | −0.677318 | ||||||||
\(928\) | −2423.72 | −0.0857353 | ||||||||
\(929\) | −44731.4 | −1.57975 | −0.789875 | − | 0.613268i | \(-0.789855\pi\) | ||||
−0.789875 | + | 0.613268i | \(0.789855\pi\) | |||||||
\(930\) | −23771.6 | −0.838173 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5594.50 | 0.196624 | ||||||||
\(933\) | 51757.1 | 1.81613 | ||||||||
\(934\) | −8973.59 | −0.314373 | ||||||||
\(935\) | 95913.2 | 3.35476 | ||||||||
\(936\) | 3120.90 | 0.108985 | ||||||||
\(937\) | −30506.2 | −1.06360 | −0.531801 | − | 0.846869i | \(-0.678484\pi\) | ||||
−0.531801 | + | 0.846869i | \(0.678484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42465.2 | 1.47583 | ||||||||
\(940\) | 33986.4 | 1.17927 | ||||||||
\(941\) | 47720.6 | 1.65318 | 0.826592 | − | 0.562802i | \(-0.190277\pi\) | ||||
0.826592 | + | 0.562802i | \(0.190277\pi\) | |||||||
\(942\) | 40749.8 | 1.40945 | ||||||||
\(943\) | −7921.03 | −0.273536 | ||||||||
\(944\) | 12035.7 | 0.414965 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22351.1 | 0.768180 | ||||||||
\(947\) | −15551.0 | −0.533621 | −0.266810 | − | 0.963749i | \(-0.585970\pi\) | ||||
−0.266810 | + | 0.963749i | \(0.585970\pi\) | |||||||
\(948\) | 29178.2 | 0.999647 | ||||||||
\(949\) | 15164.0 | 0.518697 | ||||||||
\(950\) | 7570.65 | 0.258552 | ||||||||
\(951\) | 60854.5 | 2.07502 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48105.0 | −1.63512 | −0.817562 | − | 0.575840i | \(-0.804675\pi\) | ||||
−0.817562 | + | 0.575840i | \(0.804675\pi\) | |||||||
\(954\) | −16159.0 | −0.548392 | ||||||||
\(955\) | −32148.7 | −1.08933 | ||||||||
\(956\) | 7020.93 | 0.237524 | ||||||||
\(957\) | 25774.5 | 0.870607 | ||||||||
\(958\) | −14533.0 | −0.490127 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7509.35 | −0.252462 | ||||||||
\(961\) | −19529.5 | −0.655549 | ||||||||
\(962\) | 4951.53 | 0.165950 | ||||||||
\(963\) | 17945.5 | 0.600505 | ||||||||
\(964\) | −11132.9 | −0.371959 | ||||||||
\(965\) | 25934.6 | 0.865145 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12889.0 | 0.428627 | 0.214313 | − | 0.976765i | \(-0.431249\pi\) | ||||
0.214313 | + | 0.976765i | \(0.431249\pi\) | |||||||
\(968\) | 7164.59 | 0.237891 | ||||||||
\(969\) | −24412.1 | −0.809318 | ||||||||
\(970\) | −9447.84 | −0.312734 | ||||||||
\(971\) | −44069.6 | −1.45650 | −0.728250 | − | 0.685312i | \(-0.759666\pi\) | ||||
−0.728250 | + | 0.685312i | \(0.759666\pi\) | |||||||
\(972\) | 20915.1 | 0.690177 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 17213.4 | 0.566276 | ||||||||
\(975\) | −15716.2 | −0.516226 | ||||||||
\(976\) | −12028.6 | −0.394495 | ||||||||
\(977\) | 25964.2 | 0.850224 | 0.425112 | − | 0.905141i | \(-0.360235\pi\) | ||||
0.425112 | + | 0.905141i | \(0.360235\pi\) | |||||||
\(978\) | −52343.1 | −1.71140 | ||||||||
\(979\) | −9852.76 | −0.321650 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13171.0 | −0.428664 | ||||||||
\(982\) | −21384.9 | −0.694929 | ||||||||
\(983\) | 18666.0 | 0.605650 | 0.302825 | − | 0.953046i | \(-0.402070\pi\) | ||||
0.302825 | + | 0.953046i | \(0.402070\pi\) | |||||||
\(984\) | 19869.4 | 0.643712 | ||||||||
\(985\) | −36596.5 | −1.18382 | ||||||||
\(986\) | −18925.2 | −0.611258 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1690.59 | 0.0544380 | ||||||||
\(989\) | 5447.27 | 0.175140 | ||||||||
\(990\) | 38399.9 | 1.23276 | ||||||||
\(991\) | 49850.9 | 1.59795 | 0.798974 | − | 0.601365i | \(-0.205376\pi\) | ||||
0.798974 | + | 0.601365i | \(0.205376\pi\) | |||||||
\(992\) | 3241.58 | 0.103750 | ||||||||
\(993\) | −40510.9 | −1.29464 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 80841.2 | 2.57572 | ||||||||
\(996\) | −2047.07 | −0.0651244 | ||||||||
\(997\) | 37492.5 | 1.19097 | 0.595486 | − | 0.803366i | \(-0.296960\pi\) | ||||
0.595486 | + | 0.803366i | \(0.296960\pi\) | |||||||
\(998\) | −3880.21 | −0.123072 | ||||||||
\(999\) | 2278.73 | 0.0721680 |
(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 | 2254.4.a.y.1.2 | 11 | ||
7.2 | even | 3 | 322.4.e.a.277.10 | yes | 22 | ||
7.4 | even | 3 | 322.4.e.a.93.10 | ✓ | 22 | ||
7.6 | odd | 2 | 2254.4.a.v.1.10 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.e.a.93.10 | ✓ | 22 | 7.4 | even | 3 | ||
322.4.e.a.277.10 | yes | 22 | 7.2 | even | 3 | ||
2254.4.a.v.1.10 | 11 | 7.6 | odd | 2 | |||
2254.4.a.y.1.2 | 11 | 1.1 | even | 1 | trivial |