Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,4,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, 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("2450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.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: | \(144.554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{22}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 22 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 98) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.69042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-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 | ||||||||
\(3\) | −9.38083 | −1.80534 | −0.902671 | − | 0.430331i | \(-0.858397\pi\) | ||||
−0.902671 | + | 0.430331i | \(0.858397\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 18.7617 | 1.27657 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 61.0000 | 2.25926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.0000 | 0.548202 | 0.274101 | − | 0.961701i | \(-0.411620\pi\) | ||||
0.274101 | + | 0.961701i | \(0.411620\pi\) | |||||||
\(12\) | −37.5233 | −0.902671 | ||||||||
\(13\) | 65.6658 | 1.40096 | 0.700478 | − | 0.713674i | \(-0.252970\pi\) | ||||
0.700478 | + | 0.713674i | \(0.252970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 56.2850 | 0.803007 | 0.401503 | − | 0.915858i | \(-0.368488\pi\) | ||||
0.401503 | + | 0.915858i | \(0.368488\pi\) | |||||||
\(18\) | −122.000 | −1.59754 | ||||||||
\(19\) | −9.38083 | −0.113269 | −0.0566345 | − | 0.998395i | \(-0.518037\pi\) | ||||
−0.0566345 | + | 0.998395i | \(0.518037\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −40.0000 | −0.387638 | ||||||||
\(23\) | −48.0000 | −0.435161 | −0.217580 | − | 0.976042i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976042i | \(0.569816\pi\) | |||||||
\(24\) | 75.0467 | 0.638285 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −131.332 | −0.990625 | ||||||||
\(27\) | −318.948 | −2.27339 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −166.000 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 206.378 | 1.19570 | 0.597849 | − | 0.801609i | \(-0.296022\pi\) | ||||
0.597849 | + | 0.801609i | \(0.296022\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −187.617 | −0.989693 | ||||||||
\(34\) | −112.570 | −0.567812 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 244.000 | 1.12963 | ||||||||
\(37\) | 78.0000 | 0.346571 | 0.173285 | − | 0.984872i | \(-0.444562\pi\) | ||||
0.173285 | + | 0.984872i | \(0.444562\pi\) | |||||||
\(38\) | 18.7617 | 0.0800933 | ||||||||
\(39\) | −616.000 | −2.52920 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −393.995 | −1.50077 | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||||
−0.750386 | + | 0.661000i | \(0.770132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −436.000 | −1.54626 | −0.773132 | − | 0.634245i | \(-0.781311\pi\) | ||||
−0.773132 | + | 0.634245i | \(0.781311\pi\) | |||||||
\(44\) | 80.0000 | 0.274101 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 96.0000 | 0.307705 | ||||||||
\(47\) | 206.378 | 0.640497 | 0.320249 | − | 0.947334i | \(-0.396234\pi\) | ||||
0.320249 | + | 0.947334i | \(0.396234\pi\) | |||||||
\(48\) | −150.093 | −0.451335 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −528.000 | −1.44970 | ||||||||
\(52\) | 262.663 | 0.700478 | ||||||||
\(53\) | −62.0000 | −0.160686 | −0.0803430 | − | 0.996767i | \(-0.525602\pi\) | ||||
−0.0803430 | + | 0.996767i | \(0.525602\pi\) | |||||||
\(54\) | 637.897 | 1.60753 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 88.0000 | 0.204489 | ||||||||
\(58\) | 332.000 | 0.751616 | ||||||||
\(59\) | 666.039 | 1.46968 | 0.734838 | − | 0.678243i | \(-0.237258\pi\) | ||||
0.734838 | + | 0.678243i | \(0.237258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −272.044 | −0.571011 | −0.285506 | − | 0.958377i | \(-0.592162\pi\) | ||||
−0.285506 | + | 0.958377i | \(0.592162\pi\) | |||||||
\(62\) | −412.757 | −0.845486 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 375.233 | 0.699819 | ||||||||
\(67\) | −580.000 | −1.05759 | −0.528793 | − | 0.848751i | \(-0.677355\pi\) | ||||
−0.528793 | + | 0.848751i | \(0.677355\pi\) | |||||||
\(68\) | 225.140 | 0.401503 | ||||||||
\(69\) | 450.280 | 0.785613 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −544.000 | −0.909309 | −0.454654 | − | 0.890668i | \(-0.650237\pi\) | ||||
−0.454654 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(72\) | −488.000 | −0.798769 | ||||||||
\(73\) | −600.373 | −0.962580 | −0.481290 | − | 0.876561i | \(-0.659832\pi\) | ||||
−0.481290 | + | 0.876561i | \(0.659832\pi\) | |||||||
\(74\) | −156.000 | −0.245063 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.5233 | −0.0566345 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1232.00 | 1.78842 | ||||||||
\(79\) | −680.000 | −0.968430 | −0.484215 | − | 0.874949i | \(-0.660895\pi\) | ||||
−0.484215 | + | 0.874949i | \(0.660895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1345.00 | 1.84499 | ||||||||
\(82\) | 787.990 | 1.06121 | ||||||||
\(83\) | 196.997 | 0.260521 | 0.130261 | − | 0.991480i | \(-0.458419\pi\) | ||||
0.130261 | + | 0.991480i | \(0.458419\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 872.000 | 1.09337 | ||||||||
\(87\) | 1557.22 | 1.91898 | ||||||||
\(88\) | −160.000 | −0.193819 | ||||||||
\(89\) | 1500.93 | 1.78762 | 0.893812 | − | 0.448441i | \(-0.148021\pi\) | ||||
0.893812 | + | 0.448441i | \(0.148021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −192.000 | −0.217580 | ||||||||
\(93\) | −1936.00 | −2.15864 | ||||||||
\(94\) | −412.757 | −0.452900 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 300.187 | 0.319142 | ||||||||
\(97\) | −656.658 | −0.687356 | −0.343678 | − | 0.939088i | \(-0.611673\pi\) | ||||
−0.343678 | + | 0.939088i | \(0.611673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1220.00 | 1.23853 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −121.951 | −0.120144 | −0.0600721 | − | 0.998194i | \(-0.519133\pi\) | ||||
−0.0600721 | + | 0.998194i | \(0.519133\pi\) | |||||||
\(102\) | 1056.00 | 1.02509 | ||||||||
\(103\) | −1369.60 | −1.31020 | −0.655101 | − | 0.755541i | \(-0.727374\pi\) | ||||
−0.655101 | + | 0.755541i | \(0.727374\pi\) | |||||||
\(104\) | −525.327 | −0.495313 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 124.000 | 0.113622 | ||||||||
\(107\) | 260.000 | 0.234908 | 0.117454 | − | 0.993078i | \(-0.462527\pi\) | ||||
0.117454 | + | 0.993078i | \(0.462527\pi\) | |||||||
\(108\) | −1275.79 | −1.13670 | ||||||||
\(109\) | 1882.00 | 1.65379 | 0.826894 | − | 0.562358i | \(-0.190106\pi\) | ||||
0.826894 | + | 0.562358i | \(0.190106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −731.705 | −0.625679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1286.00 | 1.07059 | 0.535295 | − | 0.844665i | \(-0.320200\pi\) | ||||
0.535295 | + | 0.844665i | \(0.320200\pi\) | |||||||
\(114\) | −176.000 | −0.144596 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −664.000 | −0.531473 | ||||||||
\(117\) | 4005.62 | 3.16512 | ||||||||
\(118\) | −1332.08 | −1.03922 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 544.088 | 0.403766 | ||||||||
\(123\) | 3696.00 | 2.70941 | ||||||||
\(124\) | 825.513 | 0.597849 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2312.00 | −1.61541 | −0.807704 | − | 0.589588i | \(-0.799290\pi\) | ||||
−0.807704 | + | 0.589588i | \(0.799290\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 4090.04 | 2.79154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 253.282 | 0.168927 | 0.0844633 | − | 0.996427i | \(-0.473082\pi\) | ||||
0.0844633 | + | 0.996427i | \(0.473082\pi\) | |||||||
\(132\) | −750.467 | −0.494846 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1160.00 | 0.747826 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −450.280 | −0.283906 | ||||||||
\(137\) | 1114.00 | 0.694711 | 0.347356 | − | 0.937733i | \(-0.387080\pi\) | ||||
0.347356 | + | 0.937733i | \(0.387080\pi\) | |||||||
\(138\) | −900.560 | −0.555513 | ||||||||
\(139\) | −1378.98 | −0.841466 | −0.420733 | − | 0.907185i | \(-0.638227\pi\) | ||||
−0.420733 | + | 0.907185i | \(0.638227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1936.00 | −1.15632 | ||||||||
\(142\) | 1088.00 | 0.642978 | ||||||||
\(143\) | 1313.32 | 0.768007 | ||||||||
\(144\) | 976.000 | 0.564815 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1200.75 | 0.680647 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 312.000 | 0.173285 | ||||||||
\(149\) | −946.000 | −0.520130 | −0.260065 | − | 0.965591i | \(-0.583744\pi\) | ||||
−0.260065 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 832.000 | 0.448392 | 0.224196 | − | 0.974544i | \(-0.428024\pi\) | ||||
0.224196 | + | 0.974544i | \(0.428024\pi\) | |||||||
\(152\) | 75.0467 | 0.0400466 | ||||||||
\(153\) | 3433.38 | 1.81420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2464.00 | −1.26460 | ||||||||
\(157\) | 2879.92 | 1.46396 | 0.731982 | − | 0.681324i | \(-0.238596\pi\) | ||||
0.731982 | + | 0.681324i | \(0.238596\pi\) | |||||||
\(158\) | 1360.00 | 0.684783 | ||||||||
\(159\) | 581.612 | 0.290093 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2690.00 | −1.30461 | ||||||||
\(163\) | −636.000 | −0.305616 | −0.152808 | − | 0.988256i | \(-0.548832\pi\) | ||||
−0.152808 | + | 0.988256i | \(0.548832\pi\) | |||||||
\(164\) | −1575.98 | −0.750386 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −393.995 | −0.184216 | ||||||||
\(167\) | −656.658 | −0.304274 | −0.152137 | − | 0.988359i | \(-0.548615\pi\) | ||||
−0.152137 | + | 0.988359i | \(0.548615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2115.00 | 0.962676 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −572.231 | −0.255904 | ||||||||
\(172\) | −1744.00 | −0.773132 | ||||||||
\(173\) | 666.039 | 0.292705 | 0.146353 | − | 0.989232i | \(-0.453247\pi\) | ||||
0.146353 | + | 0.989232i | \(0.453247\pi\) | |||||||
\(174\) | −3114.44 | −1.35692 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 320.000 | 0.137051 | ||||||||
\(177\) | −6248.00 | −2.65327 | ||||||||
\(178\) | −3001.87 | −1.26404 | ||||||||
\(179\) | −3228.00 | −1.34789 | −0.673944 | − | 0.738782i | \(-0.735401\pi\) | ||||
−0.673944 | + | 0.738782i | \(0.735401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2823.63 | 1.15955 | 0.579776 | − | 0.814776i | \(-0.303140\pi\) | ||||
0.579776 | + | 0.814776i | \(0.303140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2552.00 | 1.03087 | ||||||||
\(184\) | 384.000 | 0.153852 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3872.00 | 1.52639 | ||||||||
\(187\) | 1125.70 | 0.440210 | ||||||||
\(188\) | 825.513 | 0.320249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2136.00 | −0.809191 | −0.404596 | − | 0.914496i | \(-0.632588\pi\) | ||||
−0.404596 | + | 0.914496i | \(0.632588\pi\) | |||||||
\(192\) | −600.373 | −0.225668 | ||||||||
\(193\) | −1658.00 | −0.618370 | −0.309185 | − | 0.951002i | \(-0.600056\pi\) | ||||
−0.309185 | + | 0.951002i | \(0.600056\pi\) | |||||||
\(194\) | 1313.32 | 0.486034 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 978.000 | 0.353704 | 0.176852 | − | 0.984237i | \(-0.443409\pi\) | ||||
0.176852 | + | 0.984237i | \(0.443409\pi\) | |||||||
\(198\) | −2440.00 | −0.875774 | ||||||||
\(199\) | 4934.32 | 1.75771 | 0.878855 | − | 0.477088i | \(-0.158308\pi\) | ||||
0.878855 | + | 0.477088i | \(0.158308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5440.88 | 1.90930 | ||||||||
\(202\) | 243.902 | 0.0849547 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2112.00 | −0.724851 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2739.20 | 0.926453 | ||||||||
\(207\) | −2928.00 | −0.983140 | ||||||||
\(208\) | 1050.65 | 0.350239 | ||||||||
\(209\) | −187.617 | −0.0620943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1556.00 | 0.507675 | 0.253838 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253838 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(212\) | −248.000 | −0.0803430 | ||||||||
\(213\) | 5103.17 | 1.64161 | ||||||||
\(214\) | −520.000 | −0.166105 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2551.59 | 0.803766 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3764.00 | −1.16940 | ||||||||
\(219\) | 5632.00 | 1.73779 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3696.00 | 1.12498 | ||||||||
\(222\) | 1463.41 | 0.442422 | ||||||||
\(223\) | 2889.30 | 0.867630 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2572.00 | −0.757022 | ||||||||
\(227\) | −1979.36 | −0.578742 | −0.289371 | − | 0.957217i | \(-0.593446\pi\) | ||||
−0.289371 | + | 0.957217i | \(0.593446\pi\) | |||||||
\(228\) | 352.000 | 0.102245 | ||||||||
\(229\) | −2767.35 | −0.798565 | −0.399282 | − | 0.916828i | \(-0.630741\pi\) | ||||
−0.399282 | + | 0.916828i | \(0.630741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1328.00 | 0.375808 | ||||||||
\(233\) | 6490.00 | 1.82478 | 0.912391 | − | 0.409321i | \(-0.134234\pi\) | ||||
0.912391 | + | 0.409321i | \(0.134234\pi\) | |||||||
\(234\) | −8011.23 | −2.23808 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2664.16 | 0.734838 | ||||||||
\(237\) | 6378.97 | 1.74835 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4296.00 | −1.16270 | −0.581350 | − | 0.813654i | \(-0.697475\pi\) | ||||
−0.581350 | + | 0.813654i | \(0.697475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4521.56 | −1.20854 | −0.604272 | − | 0.796778i | \(-0.706536\pi\) | ||||
−0.604272 | + | 0.796778i | \(0.706536\pi\) | |||||||
\(242\) | 1862.00 | 0.494603 | ||||||||
\(243\) | −4005.62 | −1.05745 | ||||||||
\(244\) | −1088.18 | −0.285506 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7392.00 | −1.91584 | ||||||||
\(247\) | −616.000 | −0.158685 | ||||||||
\(248\) | −1651.03 | −0.422743 | ||||||||
\(249\) | −1848.00 | −0.470330 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5581.59 | −1.40361 | −0.701807 | − | 0.712367i | \(-0.747623\pi\) | ||||
−0.701807 | + | 0.712367i | \(0.747623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −960.000 | −0.238556 | ||||||||
\(254\) | 4624.00 | 1.14227 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1500.93 | −0.364302 | −0.182151 | − | 0.983271i | \(-0.558306\pi\) | ||||
−0.182151 | + | 0.983271i | \(0.558306\pi\) | |||||||
\(258\) | −8180.09 | −1.97391 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10126.0 | −2.40147 | ||||||||
\(262\) | −506.565 | −0.119449 | ||||||||
\(263\) | 400.000 | 0.0937835 | 0.0468917 | − | 0.998900i | \(-0.485068\pi\) | ||||
0.0468917 | + | 0.998900i | \(0.485068\pi\) | |||||||
\(264\) | 1500.93 | 0.349909 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14080.0 | −3.22727 | ||||||||
\(268\) | −2320.00 | −0.528793 | ||||||||
\(269\) | 272.044 | 0.0616610 | 0.0308305 | − | 0.999525i | \(-0.490185\pi\) | ||||
0.0308305 | + | 0.999525i | \(0.490185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6904.29 | −1.54762 | −0.773812 | − | 0.633416i | \(-0.781652\pi\) | ||||
−0.773812 | + | 0.633416i | \(0.781652\pi\) | |||||||
\(272\) | 900.560 | 0.200752 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2228.00 | −0.491235 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1801.12 | 0.392807 | ||||||||
\(277\) | 6770.00 | 1.46848 | 0.734242 | − | 0.678888i | \(-0.237538\pi\) | ||||
0.734242 | + | 0.678888i | \(0.237538\pi\) | |||||||
\(278\) | 2757.96 | 0.595006 | ||||||||
\(279\) | 12589.1 | 2.70139 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1878.00 | 0.398691 | 0.199345 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199345 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(282\) | 3872.00 | 0.817639 | ||||||||
\(283\) | 384.614 | 0.0807878 | 0.0403939 | − | 0.999184i | \(-0.487139\pi\) | ||||
0.0403939 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(284\) | −2176.00 | −0.454654 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2626.63 | −0.543063 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1952.00 | −0.399384 | ||||||||
\(289\) | −1745.00 | −0.355180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6160.00 | 1.24091 | ||||||||
\(292\) | −2401.49 | −0.481290 | ||||||||
\(293\) | −3742.95 | −0.746299 | −0.373149 | − | 0.927771i | \(-0.621722\pi\) | ||||
−0.373149 | + | 0.927771i | \(0.621722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −624.000 | −0.122531 | ||||||||
\(297\) | −6378.97 | −1.24628 | ||||||||
\(298\) | 1892.00 | 0.367787 | ||||||||
\(299\) | −3151.96 | −0.609641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1664.00 | −0.317061 | ||||||||
\(303\) | 1144.00 | 0.216901 | ||||||||
\(304\) | −150.093 | −0.0283172 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6866.77 | −1.28283 | ||||||||
\(307\) | 722.324 | 0.134284 | 0.0671420 | − | 0.997743i | \(-0.478612\pi\) | ||||
0.0671420 | + | 0.997743i | \(0.478612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12848.0 | 2.36536 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7279.53 | −1.32728 | −0.663640 | − | 0.748052i | \(-0.730989\pi\) | ||||
−0.663640 | + | 0.748052i | \(0.730989\pi\) | |||||||
\(312\) | 4928.00 | 0.894209 | ||||||||
\(313\) | 1519.69 | 0.274435 | 0.137218 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137218 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(314\) | −5759.83 | −1.03518 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2720.00 | −0.484215 | ||||||||
\(317\) | −2358.00 | −0.417787 | −0.208893 | − | 0.977938i | \(-0.566986\pi\) | ||||
−0.208893 | + | 0.977938i | \(0.566986\pi\) | |||||||
\(318\) | −1163.22 | −0.205127 | ||||||||
\(319\) | −3320.00 | −0.582709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2439.02 | −0.424089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −528.000 | −0.0909557 | ||||||||
\(324\) | 5380.00 | 0.922497 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1272.00 | 0.216103 | ||||||||
\(327\) | −17654.7 | −2.98565 | ||||||||
\(328\) | 3151.96 | 0.530603 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2372.00 | 0.393888 | 0.196944 | − | 0.980415i | \(-0.436898\pi\) | ||||
0.196944 | + | 0.980415i | \(0.436898\pi\) | |||||||
\(332\) | 787.990 | 0.130261 | ||||||||
\(333\) | 4758.00 | 0.782993 | ||||||||
\(334\) | 1313.32 | 0.215154 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 250.000 | 0.0404106 | 0.0202053 | − | 0.999796i | \(-0.493568\pi\) | ||||
0.0202053 | + | 0.999796i | \(0.493568\pi\) | |||||||
\(338\) | −4230.00 | −0.680715 | ||||||||
\(339\) | −12063.7 | −1.93278 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4127.57 | 0.655485 | ||||||||
\(342\) | 1144.46 | 0.180951 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3488.00 | 0.546687 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1332.08 | −0.206974 | ||||||||
\(347\) | −9540.00 | −1.47589 | −0.737945 | − | 0.674861i | \(-0.764204\pi\) | ||||
−0.737945 | + | 0.674861i | \(0.764204\pi\) | |||||||
\(348\) | 6228.87 | 0.959490 | ||||||||
\(349\) | 5712.93 | 0.876235 | 0.438117 | − | 0.898918i | \(-0.355645\pi\) | ||||
0.438117 | + | 0.898918i | \(0.355645\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20944.0 | −3.18492 | ||||||||
\(352\) | −640.000 | −0.0969094 | ||||||||
\(353\) | 4390.23 | 0.661950 | 0.330975 | − | 0.943640i | \(-0.392622\pi\) | ||||
0.330975 | + | 0.943640i | \(0.392622\pi\) | |||||||
\(354\) | 12496.0 | 1.87614 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6003.73 | 0.893812 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6456.00 | 0.953101 | ||||||||
\(359\) | 1840.00 | 0.270506 | 0.135253 | − | 0.990811i | \(-0.456815\pi\) | ||||
0.135253 | + | 0.990811i | \(0.456815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6771.00 | −0.987170 | ||||||||
\(362\) | −5647.26 | −0.819927 | ||||||||
\(363\) | 8733.55 | 1.26279 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5104.00 | −0.728935 | ||||||||
\(367\) | −2964.34 | −0.421628 | −0.210814 | − | 0.977526i | \(-0.567611\pi\) | ||||
−0.210814 | + | 0.977526i | \(0.567611\pi\) | |||||||
\(368\) | −768.000 | −0.108790 | ||||||||
\(369\) | −24033.7 | −3.39063 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7744.00 | −1.07932 | ||||||||
\(373\) | −3982.00 | −0.552762 | −0.276381 | − | 0.961048i | \(-0.589135\pi\) | ||||
−0.276381 | + | 0.961048i | \(0.589135\pi\) | |||||||
\(374\) | −2251.40 | −0.311276 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1651.03 | −0.226450 | ||||||||
\(377\) | −10900.5 | −1.48914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2676.00 | 0.362683 | 0.181342 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181342 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21688.5 | 2.91636 | ||||||||
\(382\) | 4272.00 | 0.572185 | ||||||||
\(383\) | 7035.62 | 0.938652 | 0.469326 | − | 0.883025i | \(-0.344497\pi\) | ||||
0.469326 | + | 0.883025i | \(0.344497\pi\) | |||||||
\(384\) | 1200.75 | 0.159571 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3316.00 | 0.437254 | ||||||||
\(387\) | −26596.0 | −3.49341 | ||||||||
\(388\) | −2626.63 | −0.343678 | ||||||||
\(389\) | 8658.00 | 1.12848 | 0.564239 | − | 0.825611i | \(-0.309170\pi\) | ||||
0.564239 | + | 0.825611i | \(0.309170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2701.68 | −0.349437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2376.00 | −0.304970 | ||||||||
\(394\) | −1956.00 | −0.250106 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4880.00 | 0.619266 | ||||||||
\(397\) | −9052.50 | −1.14441 | −0.572207 | − | 0.820109i | \(-0.693912\pi\) | ||||
−0.572207 | + | 0.820109i | \(0.693912\pi\) | |||||||
\(398\) | −9868.63 | −1.24289 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5706.00 | −0.710584 | −0.355292 | − | 0.934755i | \(-0.615619\pi\) | ||||
−0.355292 | + | 0.934755i | \(0.615619\pi\) | |||||||
\(402\) | −10881.8 | −1.35008 | ||||||||
\(403\) | 13552.0 | 1.67512 | ||||||||
\(404\) | −487.803 | −0.0600721 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1560.00 | 0.189991 | ||||||||
\(408\) | 4224.00 | 0.512547 | ||||||||
\(409\) | −2420.25 | −0.292601 | −0.146301 | − | 0.989240i | \(-0.546737\pi\) | ||||
−0.146301 | + | 0.989240i | \(0.546737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10450.2 | −1.25419 | ||||||||
\(412\) | −5478.41 | −0.655101 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5856.00 | 0.695185 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2101.31 | −0.247656 | ||||||||
\(417\) | 12936.0 | 1.51913 | ||||||||
\(418\) | 375.233 | 0.0439073 | ||||||||
\(419\) | 1510.31 | 0.176095 | 0.0880473 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880473 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16770.0 | −1.94138 | −0.970689 | − | 0.240341i | \(-0.922741\pi\) | ||||
−0.970689 | + | 0.240341i | \(0.922741\pi\) | |||||||
\(422\) | −3112.00 | −0.358981 | ||||||||
\(423\) | 12589.1 | 1.44705 | ||||||||
\(424\) | 496.000 | 0.0568111 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10206.3 | −1.16080 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1040.00 | 0.117454 | ||||||||
\(429\) | −12320.0 | −1.38652 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1336.00 | 0.149311 | 0.0746553 | − | 0.997209i | \(-0.476214\pi\) | ||||
0.0746553 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(432\) | −5103.17 | −0.568348 | ||||||||
\(433\) | −11163.2 | −1.23896 | −0.619479 | − | 0.785013i | \(-0.712656\pi\) | ||||
−0.619479 | + | 0.785013i | \(0.712656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7528.00 | 0.826894 | ||||||||
\(437\) | 450.280 | 0.0492902 | ||||||||
\(438\) | −11264.0 | −1.22880 | ||||||||
\(439\) | 3602.24 | 0.391630 | 0.195815 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195815 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7392.00 | −0.795479 | ||||||||
\(443\) | −6348.00 | −0.680818 | −0.340409 | − | 0.940277i | \(-0.610566\pi\) | ||||
−0.340409 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(444\) | −2926.82 | −0.312839 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5778.59 | −0.613507 | ||||||||
\(447\) | 8874.27 | 0.939012 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7170.00 | 0.753615 | 0.376808 | − | 0.926292i | \(-0.377022\pi\) | ||||
0.376808 | + | 0.926292i | \(0.377022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7879.90 | −0.822727 | ||||||||
\(452\) | 5144.00 | 0.535295 | ||||||||
\(453\) | −7804.85 | −0.809501 | ||||||||
\(454\) | 3958.71 | 0.409232 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −704.000 | −0.0722979 | ||||||||
\(457\) | −6866.00 | −0.702796 | −0.351398 | − | 0.936226i | \(-0.614294\pi\) | ||||
−0.351398 | + | 0.936226i | \(0.614294\pi\) | |||||||
\(458\) | 5534.69 | 0.564671 | ||||||||
\(459\) | −17952.0 | −1.82555 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1378.98 | −0.139318 | −0.0696590 | − | 0.997571i | \(-0.522191\pi\) | ||||
−0.0696590 | + | 0.997571i | \(0.522191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2648.00 | −0.265795 | −0.132897 | − | 0.991130i | \(-0.542428\pi\) | ||||
−0.132897 | + | 0.991130i | \(0.542428\pi\) | |||||||
\(464\) | −2656.00 | −0.265736 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12980.0 | −1.29032 | ||||||||
\(467\) | −12335.8 | −1.22234 | −0.611170 | − | 0.791500i | \(-0.709301\pi\) | ||||
−0.611170 | + | 0.791500i | \(0.709301\pi\) | |||||||
\(468\) | 16022.5 | 1.58256 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27016.0 | −2.64295 | ||||||||
\(472\) | −5328.31 | −0.519609 | ||||||||
\(473\) | −8720.00 | −0.847666 | ||||||||
\(474\) | −12757.9 | −1.23627 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3782.00 | −0.363031 | ||||||||
\(478\) | 8592.00 | 0.822153 | ||||||||
\(479\) | 13339.5 | 1.27244 | 0.636221 | − | 0.771507i | \(-0.280497\pi\) | ||||
0.636221 | + | 0.771507i | \(0.280497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5121.93 | 0.485530 | ||||||||
\(482\) | 9043.12 | 0.854570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3724.00 | −0.349737 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8011.23 | 0.747730 | ||||||||
\(487\) | −13936.0 | −1.29672 | −0.648358 | − | 0.761336i | \(-0.724544\pi\) | ||||
−0.648358 | + | 0.761336i | \(0.724544\pi\) | |||||||
\(488\) | 2176.35 | 0.201883 | ||||||||
\(489\) | 5966.21 | 0.551741 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12276.0 | −1.12833 | −0.564163 | − | 0.825663i | \(-0.690801\pi\) | ||||
−0.564163 | + | 0.825663i | \(0.690801\pi\) | |||||||
\(492\) | 14784.0 | 1.35470 | ||||||||
\(493\) | −9343.31 | −0.853553 | ||||||||
\(494\) | 1232.00 | 0.112207 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3302.05 | 0.298924 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3696.00 | 0.332574 | ||||||||
\(499\) | −2220.00 | −0.199160 | −0.0995800 | − | 0.995030i | \(-0.531750\pi\) | ||||
−0.0995800 | + | 0.995030i | \(0.531750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6160.00 | 0.549318 | ||||||||
\(502\) | 11163.2 | 0.992505 | ||||||||
\(503\) | −11294.5 | −1.00119 | −0.500594 | − | 0.865682i | \(-0.666885\pi\) | ||||
−0.500594 | + | 0.865682i | \(0.666885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1920.00 | 0.168685 | ||||||||
\(507\) | −19840.5 | −1.73796 | ||||||||
\(508\) | −9248.00 | −0.807704 | ||||||||
\(509\) | 15881.7 | 1.38300 | 0.691499 | − | 0.722377i | \(-0.256951\pi\) | ||||
0.691499 | + | 0.722377i | \(0.256951\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2992.00 | 0.257505 | ||||||||
\(514\) | 3001.87 | 0.257600 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16360.2 | 1.39577 | ||||||||
\(517\) | 4127.57 | 0.351122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6248.00 | −0.528433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11613.5 | −0.976575 | −0.488287 | − | 0.872683i | \(-0.662378\pi\) | ||||
−0.488287 | + | 0.872683i | \(0.662378\pi\) | |||||||
\(522\) | 20252.0 | 1.69810 | ||||||||
\(523\) | 12617.2 | 1.05490 | 0.527450 | − | 0.849586i | \(-0.323148\pi\) | ||||
0.527450 | + | 0.849586i | \(0.323148\pi\) | |||||||
\(524\) | 1013.13 | 0.0844633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −800.000 | −0.0663149 | ||||||||
\(527\) | 11616.0 | 0.960154 | ||||||||
\(528\) | −3001.87 | −0.247423 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40628.4 | 3.32038 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25872.0 | −2.10252 | ||||||||
\(534\) | 28160.0 | 2.28203 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4640.00 | 0.373913 | ||||||||
\(537\) | 30281.3 | 2.43340 | ||||||||
\(538\) | −544.088 | −0.0436009 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1798.00 | 0.142887 | 0.0714437 | − | 0.997445i | \(-0.477239\pi\) | ||||
0.0714437 | + | 0.997445i | \(0.477239\pi\) | |||||||
\(542\) | 13808.6 | 1.09433 | ||||||||
\(543\) | −26488.0 | −2.09339 | ||||||||
\(544\) | −1801.12 | −0.141953 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1276.00 | −0.0997401 | −0.0498700 | − | 0.998756i | \(-0.515881\pi\) | ||||
−0.0498700 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(548\) | 4456.00 | 0.347356 | ||||||||
\(549\) | −16594.7 | −1.29006 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1557.22 | 0.120399 | ||||||||
\(552\) | −3602.24 | −0.277756 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13540.0 | −1.03837 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5515.93 | −0.420733 | ||||||||
\(557\) | −2694.00 | −0.204934 | −0.102467 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102467 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(558\) | −25178.2 | −1.91017 | ||||||||
\(559\) | −28630.3 | −2.16625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10560.0 | −0.794730 | ||||||||
\(562\) | −3756.00 | −0.281917 | ||||||||
\(563\) | −15769.2 | −1.18045 | −0.590223 | − | 0.807240i | \(-0.700960\pi\) | ||||
−0.590223 | + | 0.807240i | \(0.700960\pi\) | |||||||
\(564\) | −7744.00 | −0.578158 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −769.228 | −0.0571256 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4352.00 | 0.321489 | ||||||||
\(569\) | 12606.0 | 0.928772 | 0.464386 | − | 0.885633i | \(-0.346275\pi\) | ||||
0.464386 | + | 0.885633i | \(0.346275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6852.00 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 5253.27 | 0.384004 | ||||||||
\(573\) | 20037.5 | 1.46087 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3904.00 | 0.282407 | ||||||||
\(577\) | 14371.4 | 1.03690 | 0.518449 | − | 0.855108i | \(-0.326509\pi\) | ||||
0.518449 | + | 0.855108i | \(0.326509\pi\) | |||||||
\(578\) | 3490.00 | 0.251150 | ||||||||
\(579\) | 15553.4 | 1.11637 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12320.0 | −0.877458 | ||||||||
\(583\) | −1240.00 | −0.0880884 | ||||||||
\(584\) | 4802.99 | 0.340324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7485.90 | 0.527713 | ||||||||
\(587\) | 18977.4 | 1.33438 | 0.667191 | − | 0.744887i | \(-0.267497\pi\) | ||||
0.667191 | + | 0.744887i | \(0.267497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1936.00 | −0.135435 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9174.45 | −0.638556 | ||||||||
\(592\) | 1248.00 | 0.0866427 | ||||||||
\(593\) | 8217.61 | 0.569067 | 0.284534 | − | 0.958666i | \(-0.408161\pi\) | ||||
0.284534 | + | 0.958666i | \(0.408161\pi\) | |||||||
\(594\) | 12757.9 | 0.881253 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3784.00 | −0.260065 | ||||||||
\(597\) | −46288.0 | −3.17327 | ||||||||
\(598\) | 6303.92 | 0.431081 | ||||||||
\(599\) | −19104.0 | −1.30312 | −0.651559 | − | 0.758598i | \(-0.725885\pi\) | ||||
−0.651559 | + | 0.758598i | \(0.725885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21538.4 | −1.46185 | −0.730923 | − | 0.682460i | \(-0.760910\pi\) | ||||
−0.730923 | + | 0.682460i | \(0.760910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35380.0 | −2.38936 | ||||||||
\(604\) | 3328.00 | 0.224196 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2288.00 | −0.153372 | ||||||||
\(607\) | 13733.5 | 0.918331 | 0.459166 | − | 0.888351i | \(-0.348148\pi\) | ||||
0.459166 | + | 0.888351i | \(0.348148\pi\) | |||||||
\(608\) | 300.187 | 0.0200233 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13552.0 | 0.897308 | ||||||||
\(612\) | 13733.5 | 0.907100 | ||||||||
\(613\) | −28034.0 | −1.84712 | −0.923558 | − | 0.383458i | \(-0.874733\pi\) | ||||
−0.923558 | + | 0.383458i | \(0.874733\pi\) | |||||||
\(614\) | −1444.65 | −0.0949532 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8258.00 | 0.538824 | 0.269412 | − | 0.963025i | \(-0.413171\pi\) | ||||
0.269412 | + | 0.963025i | \(0.413171\pi\) | |||||||
\(618\) | −25696.0 | −1.67256 | ||||||||
\(619\) | 5131.31 | 0.333191 | 0.166595 | − | 0.986025i | \(-0.446723\pi\) | ||||
0.166595 | + | 0.986025i | \(0.446723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15309.5 | 0.989291 | ||||||||
\(622\) | 14559.1 | 0.938529 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9856.00 | −0.632301 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3039.39 | −0.194055 | ||||||||
\(627\) | 1760.00 | 0.112101 | ||||||||
\(628\) | 11519.7 | 0.731982 | ||||||||
\(629\) | 4390.23 | 0.278299 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 912.000 | 0.0575375 | 0.0287687 | − | 0.999586i | \(-0.490841\pi\) | ||||
0.0287687 | + | 0.999586i | \(0.490841\pi\) | |||||||
\(632\) | 5440.00 | 0.342392 | ||||||||
\(633\) | −14596.6 | −0.916527 | ||||||||
\(634\) | 4716.00 | 0.295420 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2326.45 | 0.145047 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6640.00 | 0.412038 | ||||||||
\(639\) | −33184.0 | −2.05436 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −890.000 | −0.0548407 | −0.0274203 | − | 0.999624i | \(-0.508729\pi\) | ||||
−0.0274203 | + | 0.999624i | \(0.508729\pi\) | |||||||
\(642\) | 4878.03 | 0.299876 | ||||||||
\(643\) | −29352.6 | −1.80024 | −0.900120 | − | 0.435642i | \(-0.856521\pi\) | ||||
−0.900120 | + | 0.435642i | \(0.856521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1056.00 | 0.0643154 | ||||||||
\(647\) | 11876.1 | 0.721637 | 0.360818 | − | 0.932636i | \(-0.382497\pi\) | ||||
0.360818 | + | 0.932636i | \(0.382497\pi\) | |||||||
\(648\) | −10760.0 | −0.652304 | ||||||||
\(649\) | 13320.8 | 0.805680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2544.00 | −0.152808 | ||||||||
\(653\) | 21526.0 | 1.29001 | 0.645006 | − | 0.764178i | \(-0.276855\pi\) | ||||
0.645006 | + | 0.764178i | \(0.276855\pi\) | |||||||
\(654\) | 35309.4 | 2.11118 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6303.92 | −0.375193 | ||||||||
\(657\) | −36622.8 | −2.17472 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23452.0 | 1.38628 | 0.693141 | − | 0.720802i | \(-0.256226\pi\) | ||||
0.693141 | + | 0.720802i | \(0.256226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26669.7 | 1.56934 | 0.784668 | − | 0.619916i | \(-0.212833\pi\) | ||||
0.784668 | + | 0.619916i | \(0.212833\pi\) | |||||||
\(662\) | −4744.00 | −0.278521 | ||||||||
\(663\) | −34671.6 | −2.03097 | ||||||||
\(664\) | −1575.98 | −0.0921082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9516.00 | −0.553660 | ||||||||
\(667\) | 7968.00 | 0.462552 | ||||||||
\(668\) | −2626.63 | −0.152137 | ||||||||
\(669\) | −27104.0 | −1.56637 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5440.88 | −0.313030 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13858.0 | 0.793739 | 0.396870 | − | 0.917875i | \(-0.370096\pi\) | ||||
0.396870 | + | 0.917875i | \(0.370096\pi\) | |||||||
\(674\) | −500.000 | −0.0285746 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8460.00 | 0.481338 | ||||||||
\(677\) | 32448.3 | 1.84208 | 0.921041 | − | 0.389466i | \(-0.127340\pi\) | ||||
0.921041 | + | 0.389466i | \(0.127340\pi\) | |||||||
\(678\) | 24127.5 | 1.36668 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18568.0 | 1.04483 | ||||||||
\(682\) | −8255.13 | −0.463498 | ||||||||
\(683\) | 27812.0 | 1.55812 | 0.779060 | − | 0.626949i | \(-0.215696\pi\) | ||||
0.779060 | + | 0.626949i | \(0.215696\pi\) | |||||||
\(684\) | −2288.92 | −0.127952 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25960.0 | 1.44168 | ||||||||
\(688\) | −6976.00 | −0.386566 | ||||||||
\(689\) | −4071.28 | −0.225114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1303.94 | 0.0717859 | 0.0358929 | − | 0.999356i | \(-0.488572\pi\) | ||||
0.0358929 | + | 0.999356i | \(0.488572\pi\) | |||||||
\(692\) | 2664.16 | 0.146353 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19080.0 | 1.04361 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12457.7 | −0.678462 | ||||||||
\(697\) | −22176.0 | −1.20513 | ||||||||
\(698\) | −11425.9 | −0.619592 | ||||||||
\(699\) | −60881.6 | −3.29435 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22906.0 | 1.23416 | 0.617081 | − | 0.786900i | \(-0.288315\pi\) | ||||
0.617081 | + | 0.786900i | \(0.288315\pi\) | |||||||
\(702\) | 41888.0 | 2.25208 | ||||||||
\(703\) | −731.705 | −0.0392557 | ||||||||
\(704\) | 1280.00 | 0.0685253 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8780.46 | −0.468069 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24992.0 | −1.32663 | ||||||||
\(709\) | −15086.0 | −0.799107 | −0.399553 | − | 0.916710i | \(-0.630835\pi\) | ||||
−0.399553 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41480.0 | −2.18793 | ||||||||
\(712\) | −12007.5 | −0.632021 | ||||||||
\(713\) | −9906.16 | −0.520321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12912.0 | −0.673944 | ||||||||
\(717\) | 40300.1 | 2.09907 | ||||||||
\(718\) | −3680.00 | −0.191276 | ||||||||
\(719\) | 20544.0 | 1.06559 | 0.532797 | − | 0.846243i | \(-0.321141\pi\) | ||||
0.532797 | + | 0.846243i | \(0.321141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13542.0 | 0.698035 | ||||||||
\(723\) | 42416.0 | 2.18184 | ||||||||
\(724\) | 11294.5 | 0.579776 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −17467.1 | −0.892927 | ||||||||
\(727\) | −7223.24 | −0.368494 | −0.184247 | − | 0.982880i | \(-0.558985\pi\) | ||||
−0.184247 | + | 0.982880i | \(0.558985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1261.00 | 0.0640654 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24540.3 | −1.24166 | ||||||||
\(732\) | 10208.0 | 0.515435 | ||||||||
\(733\) | 29427.7 | 1.48286 | 0.741430 | − | 0.671031i | \(-0.234148\pi\) | ||||
0.741430 | + | 0.671031i | \(0.234148\pi\) | |||||||
\(734\) | 5928.69 | 0.298136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1536.00 | 0.0769262 | ||||||||
\(737\) | −11600.0 | −0.579771 | ||||||||
\(738\) | 48067.4 | 2.39754 | ||||||||
\(739\) | 32668.0 | 1.62613 | 0.813066 | − | 0.582171i | \(-0.197797\pi\) | ||||
0.813066 | + | 0.582171i | \(0.197797\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5778.59 | 0.286480 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37056.0 | 1.82968 | 0.914840 | − | 0.403816i | \(-0.132316\pi\) | ||||
0.914840 | + | 0.403816i | \(0.132316\pi\) | |||||||
\(744\) | 15488.0 | 0.763196 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7964.00 | 0.390862 | ||||||||
\(747\) | 12016.8 | 0.588586 | ||||||||
\(748\) | 4502.80 | 0.220105 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19608.0 | −0.952738 | −0.476369 | − | 0.879246i | \(-0.658047\pi\) | ||||
−0.476369 | + | 0.879246i | \(0.658047\pi\) | |||||||
\(752\) | 3302.05 | 0.160124 | ||||||||
\(753\) | 52360.0 | 2.53400 | ||||||||
\(754\) | 21801.1 | 1.05298 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19378.0 | −0.930390 | −0.465195 | − | 0.885208i | \(-0.654016\pi\) | ||||
−0.465195 | + | 0.885208i | \(0.654016\pi\) | |||||||
\(758\) | −5352.00 | −0.256456 | ||||||||
\(759\) | 9005.60 | 0.430675 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13977.4 | 0.665810 | 0.332905 | − | 0.942960i | \(-0.391971\pi\) | ||||
0.332905 | + | 0.942960i | \(0.391971\pi\) | |||||||
\(762\) | −43377.0 | −2.06218 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8544.00 | −0.404596 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14071.2 | −0.663727 | ||||||||
\(767\) | 43736.0 | 2.05895 | ||||||||
\(768\) | −2401.49 | −0.112834 | ||||||||
\(769\) | −8536.56 | −0.400307 | −0.200154 | − | 0.979765i | \(-0.564144\pi\) | ||||
−0.200154 | + | 0.979765i | \(0.564144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14080.0 | 0.657690 | ||||||||
\(772\) | −6632.00 | −0.309185 | ||||||||
\(773\) | −29296.3 | −1.36315 | −0.681576 | − | 0.731748i | \(-0.738705\pi\) | ||||
−0.681576 | + | 0.731748i | \(0.738705\pi\) | |||||||
\(774\) | 53192.0 | 2.47022 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5253.27 | 0.243017 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17316.0 | −0.797955 | ||||||||
\(779\) | 3696.00 | 0.169991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10880.0 | −0.498485 | ||||||||
\(782\) | 5403.36 | 0.247089 | ||||||||
\(783\) | 52945.4 | 2.41649 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4752.00 | 0.215647 | ||||||||
\(787\) | 13780.4 | 0.624167 | 0.312084 | − | 0.950055i | \(-0.398973\pi\) | ||||
0.312084 | + | 0.950055i | \(0.398973\pi\) | |||||||
\(788\) | 3912.00 | 0.176852 | ||||||||
\(789\) | −3752.33 | −0.169311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9760.00 | −0.437887 | ||||||||
\(793\) | −17864.0 | −0.799961 | ||||||||
\(794\) | 18105.0 | 0.809222 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19737.3 | 0.878855 | ||||||||
\(797\) | −34868.6 | −1.54970 | −0.774848 | − | 0.632148i | \(-0.782174\pi\) | ||||
−0.774848 | + | 0.632148i | \(0.782174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11616.0 | 0.514324 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 91556.9 | 4.03871 | ||||||||
\(802\) | 11412.0 | 0.502459 | ||||||||
\(803\) | −12007.5 | −0.527689 | ||||||||
\(804\) | 21763.5 | 0.954652 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27104.0 | −1.18449 | ||||||||
\(807\) | −2552.00 | −0.111319 | ||||||||
\(808\) | 975.606 | 0.0424774 | ||||||||
\(809\) | 14034.0 | 0.609900 | 0.304950 | − | 0.952368i | \(-0.401360\pi\) | ||||
0.304950 | + | 0.952368i | \(0.401360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6632.25 | 0.287164 | 0.143582 | − | 0.989638i | \(-0.454138\pi\) | ||||
0.143582 | + | 0.989638i | \(0.454138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64768.0 | 2.79399 | ||||||||
\(814\) | −3120.00 | −0.134344 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8448.00 | −0.362425 | ||||||||
\(817\) | 4090.04 | 0.175144 | ||||||||
\(818\) | 4840.51 | 0.206900 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28622.0 | 1.21670 | 0.608352 | − | 0.793667i | \(-0.291831\pi\) | ||||
0.608352 | + | 0.793667i | \(0.291831\pi\) | |||||||
\(822\) | 20900.5 | 0.886847 | ||||||||
\(823\) | −24688.0 | −1.04565 | −0.522825 | − | 0.852440i | \(-0.675122\pi\) | ||||
−0.522825 | + | 0.852440i | \(0.675122\pi\) | |||||||
\(824\) | 10956.8 | 0.463226 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30756.0 | 1.29322 | 0.646609 | − | 0.762822i | \(-0.276187\pi\) | ||||
0.646609 | + | 0.762822i | \(0.276187\pi\) | |||||||
\(828\) | −11712.0 | −0.491570 | ||||||||
\(829\) | −23236.3 | −0.973499 | −0.486750 | − | 0.873542i | \(-0.661818\pi\) | ||||
−0.486750 | + | 0.873542i | \(0.661818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −63508.2 | −2.65111 | ||||||||
\(832\) | 4202.61 | 0.175119 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −25872.0 | −1.07419 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −750.467 | −0.0310472 | ||||||||
\(837\) | −65824.0 | −2.71829 | ||||||||
\(838\) | −3020.63 | −0.124518 | ||||||||
\(839\) | 24033.7 | 0.988957 | 0.494479 | − | 0.869190i | \(-0.335359\pi\) | ||||
0.494479 | + | 0.869190i | \(0.335359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | 33540.0 | 1.37276 | ||||||||
\(843\) | −17617.2 | −0.719773 | ||||||||
\(844\) | 6224.00 | 0.253838 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25178.2 | −1.02322 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −992.000 | −0.0401715 | ||||||||
\(849\) | −3608.00 | −0.145850 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3744.00 | −0.150814 | ||||||||
\(852\) | 20412.7 | 0.820807 | ||||||||
\(853\) | −23574.0 | −0.946260 | −0.473130 | − | 0.880993i | \(-0.656876\pi\) | ||||
−0.473130 | + | 0.880993i | \(0.656876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2080.00 | −0.0830525 | ||||||||
\(857\) | 24484.0 | 0.975912 | 0.487956 | − | 0.872868i | \(-0.337743\pi\) | ||||
0.487956 | + | 0.872868i | \(0.337743\pi\) | |||||||
\(858\) | 24640.0 | 0.980415 | ||||||||
\(859\) | 32954.9 | 1.30897 | 0.654485 | − | 0.756075i | \(-0.272885\pi\) | ||||
0.654485 | + | 0.756075i | \(0.272885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2672.00 | −0.105579 | ||||||||
\(863\) | −40872.0 | −1.61217 | −0.806083 | − | 0.591803i | \(-0.798416\pi\) | ||||
−0.806083 | + | 0.591803i | \(0.798416\pi\) | |||||||
\(864\) | 10206.3 | 0.401883 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22326.4 | 0.876075 | ||||||||
\(867\) | 16369.6 | 0.641222 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13600.0 | −0.530896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38086.2 | −1.48163 | ||||||||
\(872\) | −15056.0 | −0.584702 | ||||||||
\(873\) | −40056.2 | −1.55292 | ||||||||
\(874\) | −900.560 | −0.0348534 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22528.0 | 0.868893 | ||||||||
\(877\) | 12006.0 | 0.462273 | 0.231137 | − | 0.972921i | \(-0.425756\pi\) | ||||
0.231137 | + | 0.972921i | \(0.425756\pi\) | |||||||
\(878\) | −7204.48 | −0.276924 | ||||||||
\(879\) | 35112.0 | 1.34732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35722.2 | −1.36607 | −0.683037 | − | 0.730383i | \(-0.739341\pi\) | ||||
−0.683037 | + | 0.730383i | \(0.739341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19588.0 | −0.746533 | −0.373267 | − | 0.927724i | \(-0.621762\pi\) | ||||
−0.373267 | + | 0.927724i | \(0.621762\pi\) | |||||||
\(884\) | 14784.0 | 0.562488 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12696.0 | 0.481411 | ||||||||
\(887\) | −40243.8 | −1.52340 | −0.761699 | − | 0.647931i | \(-0.775634\pi\) | ||||
−0.761699 | + | 0.647931i | \(0.775634\pi\) | |||||||
\(888\) | 5853.64 | 0.221211 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26900.0 | 1.01143 | ||||||||
\(892\) | 11557.2 | 0.433815 | ||||||||
\(893\) | −1936.00 | −0.0725485 | ||||||||
\(894\) | −17748.5 | −0.663982 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29568.0 | 1.10061 | ||||||||
\(898\) | −14340.0 | −0.532886 | ||||||||
\(899\) | −34258.8 | −1.27096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3489.67 | −0.129032 | ||||||||
\(902\) | 15759.8 | 0.581756 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10288.0 | −0.378511 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15609.7 | 0.572404 | ||||||||
\(907\) | −15868.0 | −0.580913 | −0.290457 | − | 0.956888i | \(-0.593807\pi\) | ||||
−0.290457 | + | 0.956888i | \(0.593807\pi\) | |||||||
\(908\) | −7917.42 | −0.289371 | ||||||||
\(909\) | −7439.00 | −0.271437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39832.0 | 1.44862 | 0.724310 | − | 0.689474i | \(-0.242158\pi\) | ||||
0.724310 | + | 0.689474i | \(0.242158\pi\) | |||||||
\(912\) | 1408.00 | 0.0511223 | ||||||||
\(913\) | 3939.95 | 0.142818 | ||||||||
\(914\) | 13732.0 | 0.496952 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11069.4 | −0.399282 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 35904.0 | 1.29086 | ||||||||
\(919\) | −30528.0 | −1.09578 | −0.547892 | − | 0.836549i | \(-0.684570\pi\) | ||||
−0.547892 | + | 0.836549i | \(0.684570\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6776.00 | −0.242429 | ||||||||
\(922\) | 2757.96 | 0.0985127 | ||||||||
\(923\) | −35722.2 | −1.27390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5296.00 | 0.187945 | ||||||||
\(927\) | −83545.7 | −2.96009 | ||||||||
\(928\) | 5312.00 | 0.187904 | ||||||||
\(929\) | 16604.1 | 0.586396 | 0.293198 | − | 0.956052i | \(-0.405280\pi\) | ||||
0.293198 | + | 0.956052i | \(0.405280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25960.0 | 0.912391 | ||||||||
\(933\) | 68288.0 | 2.39619 | ||||||||
\(934\) | 24671.6 | 0.864324 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −32044.9 | −1.11904 | ||||||||
\(937\) | 29943.6 | 1.04399 | 0.521993 | − | 0.852950i | \(-0.325189\pi\) | ||||
0.521993 | + | 0.852950i | \(0.325189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14256.0 | −0.495449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5375.22 | −0.186214 | −0.0931068 | − | 0.995656i | \(-0.529680\pi\) | ||||
−0.0931068 | + | 0.995656i | \(0.529680\pi\) | |||||||
\(942\) | 54032.0 | 1.86885 | ||||||||
\(943\) | 18911.8 | 0.653077 | ||||||||
\(944\) | 10656.6 | 0.367419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17440.0 | 0.599390 | ||||||||
\(947\) | −45212.0 | −1.55142 | −0.775709 | − | 0.631091i | \(-0.782607\pi\) | ||||
−0.775709 | + | 0.631091i | \(0.782607\pi\) | |||||||
\(948\) | 25515.9 | 0.874174 | ||||||||
\(949\) | −39424.0 | −1.34853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22120.0 | 0.754248 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34218.0 | −1.16310 | −0.581548 | − | 0.813512i | \(-0.697553\pi\) | ||||
−0.581548 | + | 0.813512i | \(0.697553\pi\) | |||||||
\(954\) | 7564.00 | 0.256702 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17184.0 | −0.581350 | ||||||||
\(957\) | 31144.4 | 1.05199 | ||||||||
\(958\) | −26679.1 | −0.899752 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12801.0 | 0.429694 | ||||||||
\(962\) | −10243.9 | −0.343322 | ||||||||
\(963\) | 15860.0 | 0.530718 | ||||||||
\(964\) | −18086.2 | −0.604272 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14464.0 | −0.481004 | −0.240502 | − | 0.970649i | \(-0.577312\pi\) | ||||
−0.240502 | + | 0.970649i | \(0.577312\pi\) | |||||||
\(968\) | 7448.00 | 0.247301 | ||||||||
\(969\) | 4953.08 | 0.164206 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37832.9 | −1.25038 | −0.625188 | − | 0.780474i | \(-0.714978\pi\) | ||||
−0.625188 | + | 0.780474i | \(0.714978\pi\) | |||||||
\(972\) | −16022.5 | −0.528725 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 27872.0 | 0.916916 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4352.71 | −0.142753 | ||||||||
\(977\) | −42062.0 | −1.37736 | −0.688681 | − | 0.725065i | \(-0.741810\pi\) | ||||
−0.688681 | + | 0.725065i | \(0.741810\pi\) | |||||||
\(978\) | −11932.4 | −0.390140 | ||||||||
\(979\) | 30018.7 | 0.979980 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 114802. | 3.73634 | ||||||||
\(982\) | 24552.0 | 0.797847 | ||||||||
\(983\) | −43020.5 | −1.39587 | −0.697935 | − | 0.716161i | \(-0.745898\pi\) | ||||
−0.697935 | + | 0.716161i | \(0.745898\pi\) | |||||||
\(984\) | −29568.0 | −0.957920 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18686.6 | 0.603553 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2464.00 | −0.0793424 | ||||||||
\(989\) | 20928.0 | 0.672873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21272.0 | 0.681864 | 0.340932 | − | 0.940088i | \(-0.389257\pi\) | ||||
0.340932 | + | 0.940088i | \(0.389257\pi\) | |||||||
\(992\) | −6604.11 | −0.211372 | ||||||||
\(993\) | −22251.3 | −0.711102 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7392.00 | −0.235165 | ||||||||
\(997\) | 121.951 | 0.00387384 | 0.00193692 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193692 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(998\) | 4440.00 | 0.140827 | ||||||||
\(999\) | −24878.0 | −0.787892 |
(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 | 2450.4.a.bs.1.1 | 2 | ||
5.4 | even | 2 | 98.4.a.h.1.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 2450.4.a.bs.1.2 | 2 | ||
15.14 | odd | 2 | 882.4.a.w.1.2 | 2 | |||
20.19 | odd | 2 | 784.4.a.z.1.1 | 2 | |||
35.4 | even | 6 | 98.4.c.g.79.1 | 4 | |||
35.9 | even | 6 | 98.4.c.g.67.1 | 4 | |||
35.19 | odd | 6 | 98.4.c.g.67.2 | 4 | |||
35.24 | odd | 6 | 98.4.c.g.79.2 | 4 | |||
35.34 | odd | 2 | 98.4.a.h.1.1 | ✓ | 2 | ||
105.44 | odd | 6 | 882.4.g.bi.361.1 | 4 | |||
105.59 | even | 6 | 882.4.g.bi.667.2 | 4 | |||
105.74 | odd | 6 | 882.4.g.bi.667.1 | 4 | |||
105.89 | even | 6 | 882.4.g.bi.361.2 | 4 | |||
105.104 | even | 2 | 882.4.a.w.1.1 | 2 | |||
140.139 | even | 2 | 784.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.4.a.h.1.1 | ✓ | 2 | 35.34 | odd | 2 | ||
98.4.a.h.1.2 | yes | 2 | 5.4 | even | 2 | ||
98.4.c.g.67.1 | 4 | 35.9 | even | 6 | |||
98.4.c.g.67.2 | 4 | 35.19 | odd | 6 | |||
98.4.c.g.79.1 | 4 | 35.4 | even | 6 | |||
98.4.c.g.79.2 | 4 | 35.24 | odd | 6 | |||
784.4.a.z.1.1 | 2 | 20.19 | odd | 2 | |||
784.4.a.z.1.2 | 2 | 140.139 | even | 2 | |||
882.4.a.w.1.1 | 2 | 105.104 | even | 2 | |||
882.4.a.w.1.2 | 2 | 15.14 | odd | 2 | |||
882.4.g.bi.361.1 | 4 | 105.44 | odd | 6 | |||
882.4.g.bi.361.2 | 4 | 105.89 | even | 6 | |||
882.4.g.bi.667.1 | 4 | 105.74 | odd | 6 | |||
882.4.g.bi.667.2 | 4 | 105.59 | even | 6 | |||
2450.4.a.bs.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2450.4.a.bs.1.2 | 2 | 7.6 | odd | 2 | inner |