Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 136x^{6} + 5308x^{4} + 58833x^{2} + 116964 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.1 | ||
Root | \(-8.73081i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.n.599.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | − 7.73081i | − 1.48779i | −0.668294 | − | 0.743897i | \(-0.732975\pi\) | ||||
0.668294 | − | 0.743897i | \(-0.267025\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −15.4616 | −1.05203 | ||||||||
\(7\) | 23.5622i | 1.27224i | 0.771589 | + | 0.636121i | \(0.219462\pi\) | ||||
−0.771589 | + | 0.636121i | \(0.780538\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −32.7654 | −1.21353 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.1352 | −0.880830 | −0.440415 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440415 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(12\) | 30.9232i | 0.743897i | ||||||||
\(13\) | − 40.0811i | − 0.855115i | −0.903988 | − | 0.427557i | \(-0.859374\pi\) | ||||
0.903988 | − | 0.427557i | \(-0.140626\pi\) | |||||||
\(14\) | 47.1245 | 0.899611 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 126.165i | 1.79997i | 0.435916 | + | 0.899987i | \(0.356424\pi\) | ||||
−0.435916 | + | 0.899987i | \(0.643576\pi\) | |||||||
\(18\) | 65.5308i | 0.858097i | ||||||||
\(19\) | −0.232742 | −0.00281024 | −0.00140512 | − | 0.999999i | \(-0.500447\pi\) | ||||
−0.00140512 | + | 0.999999i | \(0.500447\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 182.155 | 1.89283 | ||||||||
\(22\) | 64.2704i | 0.622841i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | 61.8465 | 0.526015 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −80.1621 | −0.604657 | ||||||||
\(27\) | 44.5711i | 0.317693i | ||||||||
\(28\) | − 94.2490i | − 0.636121i | ||||||||
\(29\) | 137.226 | 0.878695 | 0.439347 | − | 0.898317i | \(-0.355210\pi\) | ||||
0.439347 | + | 0.898317i | \(0.355210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 112.866 | 0.653914 | 0.326957 | − | 0.945039i | \(-0.393977\pi\) | ||||
0.326957 | + | 0.945039i | \(0.393977\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 248.431i | 1.31049i | ||||||||
\(34\) | 252.331 | 1.27277 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 131.062 | 0.606766 | ||||||||
\(37\) | 45.7057i | 0.203080i | 0.994831 | + | 0.101540i | \(0.0323771\pi\) | ||||
−0.994831 | + | 0.101540i | \(0.967623\pi\) | |||||||
\(38\) | 0.465483i | 0.00198714i | ||||||||
\(39\) | −309.859 | −1.27223 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −135.385 | −0.515696 | −0.257848 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257848 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(42\) | − 364.310i | − 1.33844i | ||||||||
\(43\) | − 543.528i | − 1.92761i | −0.266608 | − | 0.963805i | \(-0.585903\pi\) | ||||
0.266608 | − | 0.963805i | \(-0.414097\pi\) | |||||||
\(44\) | 128.541 | 0.440415 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 26.4344i | 0.0820394i | 0.999158 | + | 0.0410197i | \(0.0130606\pi\) | ||||
−0.999158 | + | 0.0410197i | \(0.986939\pi\) | |||||||
\(48\) | − 123.693i | − 0.371949i | ||||||||
\(49\) | −212.180 | −0.618599 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 975.359 | 2.67799 | ||||||||
\(52\) | 160.324i | 0.427557i | ||||||||
\(53\) | − 43.6958i | − 0.113247i | −0.998396 | − | 0.0566235i | \(-0.981967\pi\) | ||||
0.998396 | − | 0.0566235i | \(-0.0180335\pi\) | |||||||
\(54\) | 89.1422 | 0.224643 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −188.498 | −0.449805 | ||||||||
\(57\) | 1.79928i | 0.00418106i | ||||||||
\(58\) | − 274.451i | − 0.621331i | ||||||||
\(59\) | −202.248 | −0.446278 | −0.223139 | − | 0.974787i | \(-0.571630\pi\) | ||||
−0.223139 | + | 0.974787i | \(0.571630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 150.279 | 0.315430 | 0.157715 | − | 0.987485i | \(-0.449587\pi\) | ||||
0.157715 | + | 0.987485i | \(0.449587\pi\) | |||||||
\(62\) | − 225.732i | − 0.462387i | ||||||||
\(63\) | − 772.026i | − 1.54391i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 496.862 | 0.926659 | ||||||||
\(67\) | − 420.722i | − 0.767155i | −0.923509 | − | 0.383577i | \(-0.874692\pi\) | ||||
0.923509 | − | 0.383577i | \(-0.125308\pi\) | |||||||
\(68\) | − 504.661i | − 0.899987i | ||||||||
\(69\) | 177.809 | 0.310227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 667.381 | 1.11554 | 0.557771 | − | 0.829995i | \(-0.311657\pi\) | ||||
0.557771 | + | 0.829995i | \(0.311657\pi\) | |||||||
\(72\) | − 262.123i | − 0.429049i | ||||||||
\(73\) | − 602.960i | − 0.966728i | −0.875420 | − | 0.483364i | \(-0.839415\pi\) | ||||
0.875420 | − | 0.483364i | \(-0.160585\pi\) | |||||||
\(74\) | 91.4115 | 0.143600 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.930966 | 0.00140512 | ||||||||
\(77\) | − 757.178i | − 1.12063i | ||||||||
\(78\) | 619.718i | 0.899606i | ||||||||
\(79\) | 1378.88 | 1.96374 | 0.981872 | − | 0.189545i | \(-0.0607013\pi\) | ||||
0.981872 | + | 0.189545i | \(0.0607013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −540.095 | −0.740871 | ||||||||
\(82\) | 270.769i | 0.364652i | ||||||||
\(83\) | 485.178i | 0.641629i | 0.947142 | + | 0.320815i | \(0.103957\pi\) | ||||
−0.947142 | + | 0.320815i | \(0.896043\pi\) | |||||||
\(84\) | −728.621 | −0.946417 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1087.06 | −1.36303 | ||||||||
\(87\) | − 1060.86i | − 1.30732i | ||||||||
\(88\) | − 257.082i | − 0.311420i | ||||||||
\(89\) | 1127.71 | 1.34311 | 0.671556 | − | 0.740954i | \(-0.265626\pi\) | ||||
0.671556 | + | 0.740954i | \(0.265626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 944.400 | 1.08791 | ||||||||
\(92\) | − 92.0000i | − 0.104257i | ||||||||
\(93\) | − 872.545i | − 0.972890i | ||||||||
\(94\) | 52.8688 | 0.0580106 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −247.386 | −0.263007 | ||||||||
\(97\) | − 1486.24i | − 1.55572i | −0.628441 | − | 0.777858i | \(-0.716306\pi\) | ||||
0.628441 | − | 0.777858i | \(-0.283694\pi\) | |||||||
\(98\) | 424.359i | 0.437416i | ||||||||
\(99\) | 1052.92 | 1.06892 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1888.86 | 1.86087 | 0.930437 | − | 0.366451i | \(-0.119427\pi\) | ||||
0.930437 | + | 0.366451i | \(0.119427\pi\) | |||||||
\(102\) | − 1950.72i | − 1.89363i | ||||||||
\(103\) | 1497.17i | 1.43224i | 0.697979 | + | 0.716118i | \(0.254083\pi\) | ||||
−0.697979 | + | 0.716118i | \(0.745917\pi\) | |||||||
\(104\) | 320.649 | 0.302329 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −87.3917 | −0.0800777 | ||||||||
\(107\) | − 585.150i | − 0.528678i | −0.964430 | − | 0.264339i | \(-0.914846\pi\) | ||||
0.964430 | − | 0.264339i | \(-0.0851538\pi\) | |||||||
\(108\) | − 178.284i | − 0.158846i | ||||||||
\(109\) | 139.166 | 0.122290 | 0.0611452 | − | 0.998129i | \(-0.480525\pi\) | ||||
0.0611452 | + | 0.998129i | \(0.480525\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 353.342 | 0.302142 | ||||||||
\(112\) | 376.996i | 0.318060i | ||||||||
\(113\) | 1293.18i | 1.07656i | 0.842765 | + | 0.538282i | \(0.180927\pi\) | ||||
−0.842765 | + | 0.538282i | \(0.819073\pi\) | |||||||
\(114\) | 3.59856 | 0.00295646 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −548.902 | −0.439347 | ||||||||
\(117\) | 1313.27i | 1.03771i | ||||||||
\(118\) | 404.495i | 0.315566i | ||||||||
\(119\) | −2972.74 | −2.29000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −298.328 | −0.224138 | ||||||||
\(122\) | − 300.557i | − 0.223043i | ||||||||
\(123\) | 1046.63i | 0.767250i | ||||||||
\(124\) | −451.464 | −0.326957 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1544.05 | −1.09171 | ||||||||
\(127\) | − 1298.43i | − 0.907221i | −0.891200 | − | 0.453610i | \(-0.850136\pi\) | ||||
0.891200 | − | 0.453610i | \(-0.149864\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −4201.91 | −2.86789 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −525.247 | −0.350313 | −0.175157 | − | 0.984541i | \(-0.556043\pi\) | ||||
−0.175157 | + | 0.984541i | \(0.556043\pi\) | |||||||
\(132\) | − 993.725i | − 0.655247i | ||||||||
\(133\) | − 5.48392i | − 0.00357531i | ||||||||
\(134\) | −841.444 | −0.542460 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1009.32 | −0.636387 | ||||||||
\(137\) | − 2428.12i | − 1.51422i | −0.653288 | − | 0.757109i | \(-0.726611\pi\) | ||||
0.653288 | − | 0.757109i | \(-0.273389\pi\) | |||||||
\(138\) | − 355.617i | − 0.219363i | ||||||||
\(139\) | −2456.46 | −1.49895 | −0.749476 | − | 0.662031i | \(-0.769695\pi\) | ||||
−0.749476 | + | 0.662031i | \(0.769695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 204.359 | 0.122058 | ||||||||
\(142\) | − 1334.76i | − 0.788808i | ||||||||
\(143\) | 1288.01i | 0.753211i | ||||||||
\(144\) | −524.246 | −0.303383 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1205.92 | −0.683580 | ||||||||
\(147\) | 1640.32i | 0.920349i | ||||||||
\(148\) | − 182.823i | − 0.101540i | ||||||||
\(149\) | 2405.39 | 1.32253 | 0.661266 | − | 0.750151i | \(-0.270019\pi\) | ||||
0.661266 | + | 0.750151i | \(0.270019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −649.276 | −0.349916 | −0.174958 | − | 0.984576i | \(-0.555979\pi\) | ||||
−0.174958 | + | 0.984576i | \(0.555979\pi\) | |||||||
\(152\) | − 1.86193i | 0 0.000993570i | ||||||||
\(153\) | − 4133.85i | − 2.18433i | ||||||||
\(154\) | −1514.36 | −0.792404 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1239.44 | 0.636117 | ||||||||
\(157\) | 3665.04i | 1.86307i | 0.363650 | + | 0.931536i | \(0.381530\pi\) | ||||
−0.363650 | + | 0.931536i | \(0.618470\pi\) | |||||||
\(158\) | − 2757.75i | − 1.38858i | ||||||||
\(159\) | −337.804 | −0.168488 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −541.932 | −0.265281 | ||||||||
\(162\) | 1080.19i | 0.523875i | ||||||||
\(163\) | 1055.27i | 0.507088i | 0.967324 | + | 0.253544i | \(0.0815963\pi\) | ||||
−0.967324 | + | 0.253544i | \(0.918404\pi\) | |||||||
\(164\) | 541.539 | 0.257848 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 970.356 | 0.453700 | ||||||||
\(167\) | − 731.805i | − 0.339095i | −0.985522 | − | 0.169547i | \(-0.945769\pi\) | ||||
0.985522 | − | 0.169547i | \(-0.0542306\pi\) | |||||||
\(168\) | 1457.24i | 0.669218i | ||||||||
\(169\) | 590.507 | 0.268779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.62587 | 0.00341032 | ||||||||
\(172\) | 2174.11i | 0.963805i | ||||||||
\(173\) | 521.773i | 0.229304i | 0.993406 | + | 0.114652i | \(0.0365754\pi\) | ||||
−0.993406 | + | 0.114652i | \(0.963425\pi\) | |||||||
\(174\) | −2121.73 | −0.924413 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −514.163 | −0.220208 | ||||||||
\(177\) | 1563.54i | 0.663970i | ||||||||
\(178\) | − 2255.42i | − 0.949723i | ||||||||
\(179\) | 1183.07 | 0.494005 | 0.247002 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247002 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1723.92 | 0.707946 | 0.353973 | − | 0.935256i | \(-0.384830\pi\) | ||||
0.353973 | + | 0.935256i | \(0.384830\pi\) | |||||||
\(182\) | − 1888.80i | − 0.769270i | ||||||||
\(183\) | − 1161.78i | − 0.469295i | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1745.09 | −0.687937 | ||||||||
\(187\) | − 4054.35i | − 1.58547i | ||||||||
\(188\) | − 105.738i | − 0.0410197i | ||||||||
\(189\) | −1050.20 | −0.404182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2798.12 | −1.06002 | −0.530012 | − | 0.847990i | \(-0.677813\pi\) | ||||
−0.530012 | + | 0.847990i | \(0.677813\pi\) | |||||||
\(192\) | 494.772i | 0.185974i | ||||||||
\(193\) | 497.686i | 0.185618i | 0.995684 | + | 0.0928089i | \(0.0295846\pi\) | ||||
−0.995684 | + | 0.0928089i | \(0.970415\pi\) | |||||||
\(194\) | −2972.47 | −1.10006 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 848.718 | 0.309300 | ||||||||
\(197\) | 296.489i | 0.107228i | 0.998562 | + | 0.0536141i | \(0.0170741\pi\) | ||||
−0.998562 | + | 0.0536141i | \(0.982926\pi\) | |||||||
\(198\) | − 2105.85i | − 0.755838i | ||||||||
\(199\) | −2347.43 | −0.836207 | −0.418103 | − | 0.908399i | \(-0.637305\pi\) | ||||
−0.418103 | + | 0.908399i | \(0.637305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3252.52 | −1.14137 | ||||||||
\(202\) | − 3777.71i | − 1.31584i | ||||||||
\(203\) | 3233.34i | 1.11791i | ||||||||
\(204\) | −3901.44 | −1.33900 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2994.34 | 1.01274 | ||||||||
\(207\) | − 753.604i | − 0.253039i | ||||||||
\(208\) | − 641.297i | − 0.213779i | ||||||||
\(209\) | 7.47920 | 0.00247535 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2838.61 | 0.926153 | 0.463076 | − | 0.886318i | \(-0.346746\pi\) | ||||
0.463076 | + | 0.886318i | \(0.346746\pi\) | |||||||
\(212\) | 174.783i | 0.0566235i | ||||||||
\(213\) | − 5159.39i | − 1.65970i | ||||||||
\(214\) | −1170.30 | −0.373832 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −356.569 | −0.112321 | ||||||||
\(217\) | 2659.38i | 0.831937i | ||||||||
\(218\) | − 278.331i | − 0.0864723i | ||||||||
\(219\) | −4661.37 | −1.43829 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5056.84 | 1.53918 | ||||||||
\(222\) | − 706.685i | − 0.213647i | ||||||||
\(223\) | 2124.68i | 0.638024i | 0.947751 | + | 0.319012i | \(0.103351\pi\) | ||||
−0.947751 | + | 0.319012i | \(0.896649\pi\) | |||||||
\(224\) | 753.992 | 0.224903 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2586.35 | 0.761246 | ||||||||
\(227\) | 1551.97i | 0.453780i | 0.973920 | + | 0.226890i | \(0.0728557\pi\) | ||||
−0.973920 | + | 0.226890i | \(0.927144\pi\) | |||||||
\(228\) | − 7.19712i | − 0.00209053i | ||||||||
\(229\) | 158.531 | 0.0457469 | 0.0228735 | − | 0.999738i | \(-0.492719\pi\) | ||||
0.0228735 | + | 0.999738i | \(0.492719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5853.60 | −1.66727 | ||||||||
\(232\) | 1097.80i | 0.310666i | ||||||||
\(233\) | 728.999i | 0.204971i | 0.994734 | + | 0.102486i | \(0.0326796\pi\) | ||||
−0.994734 | + | 0.102486i | \(0.967320\pi\) | |||||||
\(234\) | 2626.54 | 0.733772 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 808.991 | 0.223139 | ||||||||
\(237\) | − 10659.8i | − 2.92165i | ||||||||
\(238\) | 5945.47i | 1.61928i | ||||||||
\(239\) | 6201.60 | 1.67844 | 0.839222 | − | 0.543789i | \(-0.183011\pi\) | ||||
0.839222 | + | 0.543789i | \(0.183011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7223.04 | −1.93061 | −0.965305 | − | 0.261126i | \(-0.915906\pi\) | ||||
−0.965305 | + | 0.261126i | \(0.915906\pi\) | |||||||
\(242\) | 596.656i | 0.158490i | ||||||||
\(243\) | 5378.79i | 1.41996i | ||||||||
\(244\) | −601.115 | −0.157715 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2093.27 | 0.542527 | ||||||||
\(247\) | 9.32853i | 0.00240308i | ||||||||
\(248\) | 902.928i | 0.231193i | ||||||||
\(249\) | 3750.82 | 0.954612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5042.78 | 1.26812 | 0.634059 | − | 0.773285i | \(-0.281388\pi\) | ||||
0.634059 | + | 0.773285i | \(0.281388\pi\) | |||||||
\(252\) | 3088.10i | 0.771954i | ||||||||
\(253\) | − 739.110i | − 0.183666i | ||||||||
\(254\) | −2596.86 | −0.641502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2981.15i | 0.723577i | 0.932260 | + | 0.361788i | \(0.117834\pi\) | ||||
−0.932260 | + | 0.361788i | \(0.882166\pi\) | |||||||
\(258\) | 8403.82i | 2.02790i | ||||||||
\(259\) | −1076.93 | −0.258367 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4496.25 | −1.06632 | ||||||||
\(262\) | 1050.49i | 0.247709i | ||||||||
\(263\) | − 7242.86i | − 1.69815i | −0.528271 | − | 0.849076i | \(-0.677159\pi\) | ||||
0.528271 | − | 0.849076i | \(-0.322841\pi\) | |||||||
\(264\) | −1987.45 | −0.463330 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.9678 | −0.00252812 | ||||||||
\(267\) | − 8718.10i | − 1.99827i | ||||||||
\(268\) | 1682.89i | 0.383577i | ||||||||
\(269\) | 2567.58 | 0.581962 | 0.290981 | − | 0.956729i | \(-0.406018\pi\) | ||||
0.290981 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8066.27 | 1.80808 | 0.904042 | − | 0.427443i | \(-0.140586\pi\) | ||||
0.904042 | + | 0.427443i | \(0.140586\pi\) | |||||||
\(272\) | 2018.64i | 0.449994i | ||||||||
\(273\) | − 7300.98i | − 1.61859i | ||||||||
\(274\) | −4856.23 | −1.07071 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −711.234 | −0.155113 | ||||||||
\(277\) | 8991.54i | 1.95036i | 0.221418 | + | 0.975179i | \(0.428932\pi\) | ||||
−0.221418 | + | 0.975179i | \(0.571068\pi\) | |||||||
\(278\) | 4912.92i | 1.05992i | ||||||||
\(279\) | −3698.10 | −0.793546 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 968.130 | 0.205529 | 0.102765 | − | 0.994706i | \(-0.467231\pi\) | ||||
0.102765 | + | 0.994706i | \(0.467231\pi\) | |||||||
\(282\) | − 408.718i | − 0.0863079i | ||||||||
\(283\) | 2252.65i | 0.473167i | 0.971611 | + | 0.236583i | \(0.0760277\pi\) | ||||
−0.971611 | + | 0.236583i | \(0.923972\pi\) | |||||||
\(284\) | −2669.52 | −0.557771 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2576.03 | 0.532600 | ||||||||
\(287\) | − 3189.97i | − 0.656090i | ||||||||
\(288\) | 1048.49i | 0.214524i | ||||||||
\(289\) | −11004.7 | −2.23991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11489.8 | −2.31458 | ||||||||
\(292\) | 2411.84i | 0.483364i | ||||||||
\(293\) | − 2734.35i | − 0.545196i | −0.962128 | − | 0.272598i | \(-0.912117\pi\) | ||||
0.962128 | − | 0.272598i | \(-0.0878829\pi\) | |||||||
\(294\) | 3280.64 | 0.650785 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −365.646 | −0.0717998 | ||||||||
\(297\) | − 1432.30i | − 0.279834i | ||||||||
\(298\) | − 4810.78i | − 0.935172i | ||||||||
\(299\) | 921.865 | 0.178304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12806.7 | 2.45239 | ||||||||
\(302\) | 1298.55i | 0.247428i | ||||||||
\(303\) | − 14602.4i | − 2.76860i | ||||||||
\(304\) | −3.72387 | −0.000702560 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8267.71 | −1.54455 | ||||||||
\(307\) | − 7977.09i | − 1.48299i | −0.670961 | − | 0.741493i | \(-0.734118\pi\) | ||||
0.670961 | − | 0.741493i | \(-0.265882\pi\) | |||||||
\(308\) | 3028.71i | 0.560314i | ||||||||
\(309\) | 11574.3 | 2.13087 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7729.43 | 1.40931 | 0.704655 | − | 0.709550i | \(-0.251102\pi\) | ||||
0.704655 | + | 0.709550i | \(0.251102\pi\) | |||||||
\(312\) | − 2478.87i | − 0.449803i | ||||||||
\(313\) | − 5506.25i | − 0.994350i | −0.867650 | − | 0.497175i | \(-0.834371\pi\) | ||||
0.867650 | − | 0.497175i | \(-0.165629\pi\) | |||||||
\(314\) | 7330.08 | 1.31739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5515.51 | −0.981872 | ||||||||
\(317\) | 5231.37i | 0.926887i | 0.886126 | + | 0.463443i | \(0.153386\pi\) | ||||
−0.886126 | + | 0.463443i | \(0.846614\pi\) | |||||||
\(318\) | 675.608i | 0.119139i | ||||||||
\(319\) | −4409.77 | −0.773981 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4523.68 | −0.786565 | ||||||||
\(322\) | 1083.86i | 0.187582i | ||||||||
\(323\) | − 29.3639i | − 0.00505836i | ||||||||
\(324\) | 2160.38 | 0.370435 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2110.55 | 0.358566 | ||||||||
\(327\) | − 1075.86i | − 0.181943i | ||||||||
\(328\) | − 1083.08i | − 0.182326i | ||||||||
\(329\) | −622.854 | −0.104374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3551.61 | −0.589771 | −0.294885 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294885 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(332\) | − 1940.71i | − 0.320815i | ||||||||
\(333\) | − 1497.57i | − 0.246445i | ||||||||
\(334\) | −1463.61 | −0.239776 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2914.48 | 0.473209 | ||||||||
\(337\) | − 7002.99i | − 1.13198i | −0.824412 | − | 0.565990i | \(-0.808494\pi\) | ||||
0.824412 | − | 0.565990i | \(-0.191506\pi\) | |||||||
\(338\) | − 1181.01i | − 0.190055i | ||||||||
\(339\) | 9997.29 | 1.60171 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3626.97 | −0.575987 | ||||||||
\(342\) | − 15.2517i | − 0.00241146i | ||||||||
\(343\) | 3082.42i | 0.485234i | ||||||||
\(344\) | 4348.22 | 0.681513 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1043.55 | 0.162143 | ||||||||
\(347\) | − 10268.2i | − 1.58854i | −0.607562 | − | 0.794272i | \(-0.707852\pi\) | ||||
0.607562 | − | 0.794272i | \(-0.292148\pi\) | |||||||
\(348\) | 4243.46i | 0.653659i | ||||||||
\(349\) | −4515.58 | −0.692588 | −0.346294 | − | 0.938126i | \(-0.612560\pi\) | ||||
−0.346294 | + | 0.938126i | \(0.612560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1786.46 | 0.271664 | ||||||||
\(352\) | 1028.33i | 0.155710i | ||||||||
\(353\) | − 7838.63i | − 1.18189i | −0.806711 | − | 0.590947i | \(-0.798754\pi\) | ||||
0.806711 | − | 0.590947i | \(-0.201246\pi\) | |||||||
\(354\) | 3127.08 | 0.469498 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4510.84 | −0.671556 | ||||||||
\(357\) | 22981.7i | 3.40705i | ||||||||
\(358\) | − 2366.14i | − 0.349314i | ||||||||
\(359\) | 12464.8 | 1.83250 | 0.916250 | − | 0.400606i | \(-0.131201\pi\) | ||||
0.916250 | + | 0.400606i | \(0.131201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6858.95 | −0.999992 | ||||||||
\(362\) | − 3447.85i | − 0.500594i | ||||||||
\(363\) | 2306.32i | 0.333472i | ||||||||
\(364\) | −3777.60 | −0.543956 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2323.55 | −0.331842 | ||||||||
\(367\) | 3936.14i | 0.559850i | 0.960022 | + | 0.279925i | \(0.0903096\pi\) | ||||
−0.960022 | + | 0.279925i | \(0.909690\pi\) | |||||||
\(368\) | 368.000i | 0.0521286i | ||||||||
\(369\) | 4435.93 | 0.625814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1029.57 | 0.144077 | ||||||||
\(372\) | 3490.18i | 0.486445i | ||||||||
\(373\) | − 1920.72i | − 0.266625i | −0.991074 | − | 0.133313i | \(-0.957439\pi\) | ||||
0.991074 | − | 0.133313i | \(-0.0425614\pi\) | |||||||
\(374\) | −8108.69 | −1.12110 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −211.475 | −0.0290053 | ||||||||
\(377\) | − 5500.15i | − 0.751385i | ||||||||
\(378\) | 2100.39i | 0.285800i | ||||||||
\(379\) | 13074.5 | 1.77201 | 0.886004 | − | 0.463678i | \(-0.153470\pi\) | ||||
0.886004 | + | 0.463678i | \(0.153470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10037.9 | −1.34976 | ||||||||
\(382\) | 5596.23i | 0.749550i | ||||||||
\(383\) | − 8838.22i | − 1.17914i | −0.807716 | − | 0.589571i | \(-0.799297\pi\) | ||||
0.807716 | − | 0.589571i | \(-0.200703\pi\) | |||||||
\(384\) | 989.543 | 0.131504 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 995.372 | 0.131252 | ||||||||
\(387\) | 17808.9i | 2.33922i | ||||||||
\(388\) | 5944.94i | 0.777858i | ||||||||
\(389\) | 12687.3 | 1.65365 | 0.826827 | − | 0.562456i | \(-0.190144\pi\) | ||||
0.826827 | + | 0.562456i | \(0.190144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2901.80 | −0.375321 | ||||||||
\(392\) | − 1697.44i | − 0.218708i | ||||||||
\(393\) | 4060.58i | 0.521194i | ||||||||
\(394\) | 592.977 | 0.0758218 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4211.69 | −0.534458 | ||||||||
\(397\) | 8060.49i | 1.01900i | 0.860470 | + | 0.509501i | \(0.170170\pi\) | ||||
−0.860470 | + | 0.509501i | \(0.829830\pi\) | |||||||
\(398\) | 4694.87i | 0.591287i | ||||||||
\(399\) | −42.3951 | −0.00531932 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12325.1 | 1.53488 | 0.767440 | − | 0.641121i | \(-0.221530\pi\) | ||||
0.767440 | + | 0.641121i | \(0.221530\pi\) | |||||||
\(402\) | 6505.04i | 0.807070i | ||||||||
\(403\) | − 4523.79i | − 0.559171i | ||||||||
\(404\) | −7555.43 | −0.930437 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6466.69 | 0.790483 | ||||||||
\(407\) | − 1468.76i | − 0.178879i | ||||||||
\(408\) | 7802.87i | 0.946813i | ||||||||
\(409\) | 10806.7 | 1.30650 | 0.653250 | − | 0.757143i | \(-0.273405\pi\) | ||||
0.653250 | + | 0.757143i | \(0.273405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18771.3 | −2.25285 | ||||||||
\(412\) | − 5988.67i | − 0.716118i | ||||||||
\(413\) | − 4765.41i | − 0.567774i | ||||||||
\(414\) | −1507.21 | −0.178926 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1282.59 | −0.151164 | ||||||||
\(417\) | 18990.4i | 2.23013i | ||||||||
\(418\) | − 14.9584i | − 0.00175033i | ||||||||
\(419\) | 1823.74 | 0.212639 | 0.106319 | − | 0.994332i | \(-0.466093\pi\) | ||||
0.106319 | + | 0.994332i | \(0.466093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5995.43 | 0.694060 | 0.347030 | − | 0.937854i | \(-0.387190\pi\) | ||||
0.347030 | + | 0.937854i | \(0.387190\pi\) | |||||||
\(422\) | − 5677.23i | − 0.654889i | ||||||||
\(423\) | − 866.133i | − 0.0995575i | ||||||||
\(424\) | 349.567 | 0.0400388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10318.8 | −1.17358 | ||||||||
\(427\) | 3540.91i | 0.401303i | ||||||||
\(428\) | 2340.60i | 0.264339i | ||||||||
\(429\) | 9957.39 | 1.12062 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3887.80 | 0.434499 | 0.217249 | − | 0.976116i | \(-0.430292\pi\) | ||||
0.217249 | + | 0.976116i | \(0.430292\pi\) | |||||||
\(432\) | 713.137i | 0.0794232i | ||||||||
\(433\) | 4422.93i | 0.490884i | 0.969411 | + | 0.245442i | \(0.0789330\pi\) | ||||
−0.969411 | + | 0.245442i | \(0.921067\pi\) | |||||||
\(434\) | 5318.75 | 0.588268 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −556.662 | −0.0611452 | ||||||||
\(437\) | − 5.35306i | 0 0.000585976i | ||||||||
\(438\) | 9322.74i | 1.01703i | ||||||||
\(439\) | 1748.08 | 0.190048 | 0.0950242 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950242 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6952.14 | 0.750690 | ||||||||
\(442\) | − 10113.7i | − 1.08837i | ||||||||
\(443\) | − 3371.31i | − 0.361571i | −0.983523 | − | 0.180785i | \(-0.942136\pi\) | ||||
0.983523 | − | 0.180785i | \(-0.0578639\pi\) | |||||||
\(444\) | −1413.37 | −0.151071 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4249.37 | 0.451151 | ||||||||
\(447\) | − 18595.6i | − 1.96766i | ||||||||
\(448\) | − 1507.98i | − 0.159030i | ||||||||
\(449\) | −13314.7 | −1.39947 | −0.699734 | − | 0.714404i | \(-0.746698\pi\) | ||||
−0.699734 | + | 0.714404i | \(0.746698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4350.61 | 0.454240 | ||||||||
\(452\) | − 5172.70i | − 0.538282i | ||||||||
\(453\) | 5019.43i | 0.520603i | ||||||||
\(454\) | 3103.94 | 0.320871 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.3942 | −0.00147823 | ||||||||
\(457\) | 3767.20i | 0.385607i | 0.981237 | + | 0.192803i | \(0.0617579\pi\) | ||||
−0.981237 | + | 0.192803i | \(0.938242\pi\) | |||||||
\(458\) | − 317.063i | − 0.0323480i | ||||||||
\(459\) | −5623.32 | −0.571839 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9674.06 | 0.977366 | 0.488683 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488683 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(462\) | 11707.2i | 1.17893i | ||||||||
\(463\) | − 2977.73i | − 0.298892i | −0.988770 | − | 0.149446i | \(-0.952251\pi\) | ||||
0.988770 | − | 0.149446i | \(-0.0477490\pi\) | |||||||
\(464\) | 2195.61 | 0.219674 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1458.00 | 0.144937 | ||||||||
\(467\) | − 10701.0i | − 1.06035i | −0.847888 | − | 0.530176i | \(-0.822126\pi\) | ||||
0.847888 | − | 0.530176i | \(-0.177874\pi\) | |||||||
\(468\) | − 5253.09i | − 0.518855i | ||||||||
\(469\) | 9913.16 | 0.976006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28333.7 | 2.77187 | ||||||||
\(472\) | − 1617.98i | − 0.157783i | ||||||||
\(473\) | 17466.4i | 1.69790i | ||||||||
\(474\) | −21319.7 | −2.06592 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11890.9 | 1.14500 | ||||||||
\(477\) | 1431.71i | 0.137429i | ||||||||
\(478\) | − 12403.2i | − 1.18684i | ||||||||
\(479\) | −2337.15 | −0.222937 | −0.111469 | − | 0.993768i | \(-0.535555\pi\) | ||||
−0.111469 | + | 0.993768i | \(0.535555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1831.94 | 0.173657 | ||||||||
\(482\) | 14446.1i | 1.36515i | ||||||||
\(483\) | 4189.57i | 0.394683i | ||||||||
\(484\) | 1193.31 | 0.112069 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10757.6 | 1.00406 | ||||||||
\(487\) | − 7183.85i | − 0.668442i | −0.942495 | − | 0.334221i | \(-0.891527\pi\) | ||||
0.942495 | − | 0.334221i | \(-0.108473\pi\) | |||||||
\(488\) | 1202.23i | 0.111521i | ||||||||
\(489\) | 8158.12 | 0.754443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12084.2 | −1.11070 | −0.555350 | − | 0.831617i | \(-0.687416\pi\) | ||||
−0.555350 | + | 0.831617i | \(0.687416\pi\) | |||||||
\(492\) | − 4186.53i | − 0.383625i | ||||||||
\(493\) | 17313.1i | 1.58163i | ||||||||
\(494\) | 18.6571 | 0.00169923 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1805.86 | 0.163478 | ||||||||
\(497\) | 15725.0i | 1.41924i | ||||||||
\(498\) | − 7501.64i | − 0.675013i | ||||||||
\(499\) | −7145.78 | −0.641060 | −0.320530 | − | 0.947238i | \(-0.603861\pi\) | ||||
−0.320530 | + | 0.947238i | \(0.603861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5657.45 | −0.504503 | ||||||||
\(502\) | − 10085.6i | − 0.896695i | ||||||||
\(503\) | − 20436.2i | − 1.81154i | −0.423771 | − | 0.905770i | \(-0.639294\pi\) | ||||
0.423771 | − | 0.905770i | \(-0.360706\pi\) | |||||||
\(504\) | 6176.21 | 0.545854 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1478.22 | −0.129871 | ||||||||
\(507\) | − 4565.10i | − 0.399888i | ||||||||
\(508\) | 5193.72i | 0.453610i | ||||||||
\(509\) | −19721.7 | −1.71738 | −0.858690 | − | 0.512495i | \(-0.828721\pi\) | ||||
−0.858690 | + | 0.512495i | \(0.828721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14207.1 | 1.22991 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | − 10.3735i | 0 0.000892794i | ||||||||
\(514\) | 5962.30 | 0.511646 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16807.6 | 1.43394 | ||||||||
\(517\) | − 849.475i | − 0.0722628i | ||||||||
\(518\) | 2153.86i | 0.182693i | ||||||||
\(519\) | 4033.73 | 0.341158 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3483.23 | 0.292904 | 0.146452 | − | 0.989218i | \(-0.453215\pi\) | ||||
0.146452 | + | 0.989218i | \(0.453215\pi\) | |||||||
\(522\) | 8992.50i | 0.754006i | ||||||||
\(523\) | − 15689.0i | − 1.31172i | −0.754881 | − | 0.655862i | \(-0.772305\pi\) | ||||
0.754881 | − | 0.655862i | \(-0.227695\pi\) | |||||||
\(524\) | 2100.99 | 0.175157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14485.7 | −1.20077 | ||||||||
\(527\) | 14239.8i | 1.17703i | ||||||||
\(528\) | 3974.90i | 0.327624i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6626.72 | 0.541573 | ||||||||
\(532\) | 21.9357i | 0.00178765i | ||||||||
\(533\) | 5426.36i | 0.440979i | ||||||||
\(534\) | −17436.2 | −1.41299 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3365.78 | 0.271230 | ||||||||
\(537\) | − 9146.09i | − 0.734977i | ||||||||
\(538\) | − 5135.15i | − 0.411510i | ||||||||
\(539\) | 6818.43 | 0.544881 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7620.73 | 0.605621 | 0.302810 | − | 0.953051i | \(-0.402075\pi\) | ||||
0.302810 | + | 0.953051i | \(0.402075\pi\) | |||||||
\(542\) | − 16132.5i | − 1.27851i | ||||||||
\(543\) | − 13327.3i | − 1.05328i | ||||||||
\(544\) | 4037.29 | 0.318194 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14602.0 | −1.14452 | ||||||||
\(547\) | 5925.62i | 0.463183i | 0.972813 | + | 0.231592i | \(0.0743933\pi\) | ||||
−0.972813 | + | 0.231592i | \(0.925607\pi\) | |||||||
\(548\) | 9712.47i | 0.757109i | ||||||||
\(549\) | −4923.94 | −0.382784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.9381 | −0.00246934 | ||||||||
\(552\) | 1422.47i | 0.109682i | ||||||||
\(553\) | 32489.4i | 2.49836i | ||||||||
\(554\) | 17983.1 | 1.37911 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9825.85 | 0.749476 | ||||||||
\(557\) | − 5456.16i | − 0.415054i | −0.978229 | − | 0.207527i | \(-0.933459\pi\) | ||||
0.978229 | − | 0.207527i | \(-0.0665414\pi\) | |||||||
\(558\) | 7396.20i | 0.561122i | ||||||||
\(559\) | −21785.2 | −1.64833 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31343.4 | −2.35886 | ||||||||
\(562\) | − 1936.26i | − 0.145331i | ||||||||
\(563\) | 9194.29i | 0.688265i | 0.938921 | + | 0.344132i | \(0.111827\pi\) | ||||
−0.938921 | + | 0.344132i | \(0.888173\pi\) | |||||||
\(564\) | −817.437 | −0.0610289 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4505.30 | 0.334580 | ||||||||
\(567\) | − 12725.8i | − 0.942567i | ||||||||
\(568\) | 5339.05i | 0.394404i | ||||||||
\(569\) | −338.831 | −0.0249640 | −0.0124820 | − | 0.999922i | \(-0.503973\pi\) | ||||
−0.0124820 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1725.34 | −0.126451 | −0.0632254 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632254 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(572\) | − 5152.06i | − 0.376605i | ||||||||
\(573\) | 21631.7i | 1.57710i | ||||||||
\(574\) | −6379.93 | −0.463926 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2096.98 | 0.151692 | ||||||||
\(577\) | 23300.0i | 1.68109i | 0.541738 | + | 0.840547i | \(0.317766\pi\) | ||||
−0.541738 | + | 0.840547i | \(0.682234\pi\) | |||||||
\(578\) | 22009.3i | 1.58385i | ||||||||
\(579\) | 3847.52 | 0.276161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11431.9 | −0.816307 | ||||||||
\(582\) | 22979.6i | 1.63666i | ||||||||
\(583\) | 1404.18i | 0.0997513i | ||||||||
\(584\) | 4823.68 | 0.341790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5468.70 | −0.385512 | ||||||||
\(587\) | 15653.3i | 1.10065i | 0.834950 | + | 0.550325i | \(0.185496\pi\) | ||||
−0.834950 | + | 0.550325i | \(0.814504\pi\) | |||||||
\(588\) | − 6561.28i | − 0.460174i | ||||||||
\(589\) | −26.2686 | −0.00183766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2292.10 | 0.159533 | ||||||||
\(592\) | 731.292i | 0.0507701i | ||||||||
\(593\) | 2658.08i | 0.184072i | 0.995756 | + | 0.0920358i | \(0.0293374\pi\) | ||||
−0.995756 | + | 0.0920358i | \(0.970663\pi\) | |||||||
\(594\) | −2864.60 | −0.197872 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9621.57 | −0.661266 | ||||||||
\(597\) | 18147.6i | 1.24410i | ||||||||
\(598\) | − 1843.73i | − 0.126080i | ||||||||
\(599\) | −19417.6 | −1.32451 | −0.662256 | − | 0.749278i | \(-0.730401\pi\) | ||||
−0.662256 | + | 0.749278i | \(0.730401\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18469.0 | −1.25352 | −0.626760 | − | 0.779213i | \(-0.715619\pi\) | ||||
−0.626760 | + | 0.779213i | \(0.715619\pi\) | |||||||
\(602\) | − 25613.5i | − 1.73410i | ||||||||
\(603\) | 13785.1i | 0.930968i | ||||||||
\(604\) | 2597.10 | 0.174958 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −29204.8 | −1.95770 | ||||||||
\(607\) | 3968.56i | 0.265369i | 0.991158 | + | 0.132684i | \(0.0423596\pi\) | ||||
−0.991158 | + | 0.132684i | \(0.957640\pi\) | |||||||
\(608\) | 7.44773i | 0 0.000496785i | ||||||||
\(609\) | 24996.4 | 1.66322 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1059.52 | 0.0701531 | ||||||||
\(612\) | 16535.4i | 1.09216i | ||||||||
\(613\) | 11478.7i | 0.756311i | 0.925742 | + | 0.378156i | \(0.123442\pi\) | ||||
−0.925742 | + | 0.378156i | \(0.876558\pi\) | |||||||
\(614\) | −15954.2 | −1.04863 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6057.42 | 0.396202 | ||||||||
\(617\) | − 15691.1i | − 1.02382i | −0.859039 | − | 0.511911i | \(-0.828938\pi\) | ||||
0.859039 | − | 0.511911i | \(-0.171062\pi\) | |||||||
\(618\) | − 23148.6i | − 1.50676i | ||||||||
\(619\) | 18249.4 | 1.18499 | 0.592494 | − | 0.805575i | \(-0.298144\pi\) | ||||
0.592494 | + | 0.805575i | \(0.298144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1025.14 | −0.0662436 | ||||||||
\(622\) | − 15458.9i | − 0.996533i | ||||||||
\(623\) | 26571.4i | 1.70876i | ||||||||
\(624\) | −4957.75 | −0.318059 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11012.5 | −0.703111 | ||||||||
\(627\) | − 57.8203i | − 0.00368281i | ||||||||
\(628\) | − 14660.2i | − 0.931536i | ||||||||
\(629\) | −5766.48 | −0.365540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23528.8 | −1.48442 | −0.742208 | − | 0.670169i | \(-0.766222\pi\) | ||||
−0.742208 | + | 0.670169i | \(0.766222\pi\) | |||||||
\(632\) | 11031.0i | 0.694288i | ||||||||
\(633\) | − 21944.8i | − 1.37793i | ||||||||
\(634\) | 10462.7 | 0.655408 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1351.22 | 0.0842441 | ||||||||
\(637\) | 8504.38i | 0.528973i | ||||||||
\(638\) | 8819.55i | 0.547287i | ||||||||
\(639\) | −21867.0 | −1.35375 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3748.79 | 0.230996 | 0.115498 | − | 0.993308i | \(-0.463154\pi\) | ||||
0.115498 | + | 0.993308i | \(0.463154\pi\) | |||||||
\(642\) | 9047.36i | 0.556185i | ||||||||
\(643\) | − 15924.3i | − 0.976660i | −0.872659 | − | 0.488330i | \(-0.837606\pi\) | ||||
0.872659 | − | 0.488330i | \(-0.162394\pi\) | |||||||
\(644\) | 2167.73 | 0.132640 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −58.7278 | −0.00357680 | ||||||||
\(647\) | − 2854.11i | − 0.173426i | −0.996233 | − | 0.0867129i | \(-0.972364\pi\) | ||||
0.996233 | − | 0.0867129i | \(-0.0276363\pi\) | |||||||
\(648\) | − 4320.76i | − 0.261937i | ||||||||
\(649\) | 6499.27 | 0.393095 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20559.1 | 1.23775 | ||||||||
\(652\) | − 4221.09i | − 0.253544i | ||||||||
\(653\) | − 7925.97i | − 0.474988i | −0.971389 | − | 0.237494i | \(-0.923674\pi\) | ||||
0.971389 | − | 0.237494i | \(-0.0763260\pi\) | |||||||
\(654\) | −2151.72 | −0.128653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2166.15 | −0.128924 | ||||||||
\(657\) | 19756.2i | 1.17316i | ||||||||
\(658\) | 1245.71i | 0.0738035i | ||||||||
\(659\) | 5799.43 | 0.342813 | 0.171406 | − | 0.985200i | \(-0.445169\pi\) | ||||
0.171406 | + | 0.985200i | \(0.445169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22324.8 | 1.31367 | 0.656833 | − | 0.754036i | \(-0.271896\pi\) | ||||
0.656833 | + | 0.754036i | \(0.271896\pi\) | |||||||
\(662\) | 7103.22i | 0.417031i | ||||||||
\(663\) | − 39093.4i | − 2.28999i | ||||||||
\(664\) | −3881.42 | −0.226850 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2995.13 | −0.174263 | ||||||||
\(667\) | 3156.19i | 0.183221i | ||||||||
\(668\) | 2927.22i | 0.169547i | ||||||||
\(669\) | 16425.5 | 0.949249 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4829.24 | −0.277840 | ||||||||
\(672\) | − 5828.97i | − 0.334609i | ||||||||
\(673\) | 23253.5i | 1.33188i | 0.746005 | + | 0.665940i | \(0.231969\pi\) | ||||
−0.746005 | + | 0.665940i | \(0.768031\pi\) | |||||||
\(674\) | −14006.0 | −0.800430 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2362.03 | −0.134389 | ||||||||
\(677\) | − 19003.7i | − 1.07884i | −0.842038 | − | 0.539419i | \(-0.818644\pi\) | ||||
0.842038 | − | 0.539419i | \(-0.181356\pi\) | |||||||
\(678\) | − 19994.6i | − 1.13258i | ||||||||
\(679\) | 35019.1 | 1.97925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11998.0 | 0.675131 | ||||||||
\(682\) | 7253.94i | 0.407284i | ||||||||
\(683\) | 11222.5i | 0.628722i | 0.949304 | + | 0.314361i | \(0.101790\pi\) | ||||
−0.949304 | + | 0.314361i | \(0.898210\pi\) | |||||||
\(684\) | −30.5035 | −0.00170516 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6164.85 | 0.343112 | ||||||||
\(687\) | − 1225.58i | − 0.0680620i | ||||||||
\(688\) | − 8696.45i | − 0.481902i | ||||||||
\(689\) | −1751.38 | −0.0968391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4297.68 | 0.236601 | 0.118301 | − | 0.992978i | \(-0.462255\pi\) | ||||
0.118301 | + | 0.992978i | \(0.462255\pi\) | |||||||
\(692\) | − 2087.09i | − 0.114652i | ||||||||
\(693\) | 24809.2i | 1.35992i | ||||||||
\(694\) | −20536.4 | −1.12327 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8486.92 | 0.462206 | ||||||||
\(697\) | − 17080.8i | − 0.928240i | ||||||||
\(698\) | 9031.15i | 0.489734i | ||||||||
\(699\) | 5635.75 | 0.304955 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25769.6 | 1.38845 | 0.694225 | − | 0.719758i | \(-0.255747\pi\) | ||||
0.694225 | + | 0.719758i | \(0.255747\pi\) | |||||||
\(702\) | − 3572.91i | − 0.192095i | ||||||||
\(703\) | − 10.6376i | 0 0.000570705i | ||||||||
\(704\) | 2056.65 | 0.110104 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15677.3 | −0.835725 | ||||||||
\(707\) | 44505.7i | 2.36748i | ||||||||
\(708\) | − 6254.15i | − 0.331985i | ||||||||
\(709\) | 4900.01 | 0.259554 | 0.129777 | − | 0.991543i | \(-0.458574\pi\) | ||||
0.129777 | + | 0.991543i | \(0.458574\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45179.4 | −2.38307 | ||||||||
\(712\) | 9021.67i | 0.474862i | ||||||||
\(713\) | 2595.92i | 0.136350i | ||||||||
\(714\) | 45963.3 | 2.40915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4732.28 | −0.247002 | ||||||||
\(717\) | − 47943.4i | − 2.49718i | ||||||||
\(718\) | − 24929.6i | − 1.29577i | ||||||||
\(719\) | −7631.85 | −0.395855 | −0.197928 | − | 0.980217i | \(-0.563421\pi\) | ||||
−0.197928 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35276.6 | −1.82215 | ||||||||
\(722\) | 13717.9i | 0.707101i | ||||||||
\(723\) | 55839.9i | 2.87235i | ||||||||
\(724\) | −6895.70 | −0.353973 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4612.64 | 0.235800 | ||||||||
\(727\) | − 36985.6i | − 1.88682i | −0.331628 | − | 0.943410i | \(-0.607598\pi\) | ||||
0.331628 | − | 0.943410i | \(-0.392402\pi\) | |||||||
\(728\) | 7555.20i | 0.384635i | ||||||||
\(729\) | 26999.8 | 1.37173 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68574.3 | 3.46965 | ||||||||
\(732\) | 4647.10i | 0.234647i | ||||||||
\(733\) | 22227.3i | 1.12003i | 0.828482 | + | 0.560015i | \(0.189205\pi\) | ||||
−0.828482 | + | 0.560015i | \(0.810795\pi\) | |||||||
\(734\) | 7872.29 | 0.395874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 13520.0i | 0.675733i | ||||||||
\(738\) | − 8871.86i | − 0.442517i | ||||||||
\(739\) | 17899.1 | 0.890974 | 0.445487 | − | 0.895288i | \(-0.353030\pi\) | ||||
0.445487 | + | 0.895288i | \(0.353030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 72.1171 | 0.00357529 | ||||||||
\(742\) | − 2059.14i | − 0.101878i | ||||||||
\(743\) | 29843.4i | 1.47355i | 0.676137 | + | 0.736776i | \(0.263653\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(744\) | 6980.36 | 0.343968 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3841.44 | −0.188532 | ||||||||
\(747\) | − 15897.0i | − 0.778638i | ||||||||
\(748\) | 16217.4i | 0.792736i | ||||||||
\(749\) | 13787.4 | 0.672606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9399.65 | −0.456722 | −0.228361 | − | 0.973577i | \(-0.573337\pi\) | ||||
−0.228361 | + | 0.973577i | \(0.573337\pi\) | |||||||
\(752\) | 422.950i | 0.0205098i | ||||||||
\(753\) | − 38984.8i | − 1.88670i | ||||||||
\(754\) | −11000.3 | −0.531309 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4200.78 | 0.202091 | ||||||||
\(757\) | 29871.6i | 1.43422i | 0.696961 | + | 0.717109i | \(0.254535\pi\) | ||||
−0.696961 | + | 0.717109i | \(0.745465\pi\) | |||||||
\(758\) | − 26149.0i | − 1.25300i | ||||||||
\(759\) | −5713.92 | −0.273257 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −273.955 | −0.0130497 | −0.00652487 | − | 0.999979i | \(-0.502077\pi\) | ||||
−0.00652487 | + | 0.999979i | \(0.502077\pi\) | |||||||
\(762\) | 20075.8i | 0.954423i | ||||||||
\(763\) | 3279.05i | 0.155583i | ||||||||
\(764\) | 11192.5 | 0.530012 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17676.4 | −0.833780 | ||||||||
\(767\) | 8106.31i | 0.381619i | ||||||||
\(768\) | − 1979.09i | − 0.0929872i | ||||||||
\(769\) | 13273.8 | 0.622450 | 0.311225 | − | 0.950336i | \(-0.399261\pi\) | ||||
0.311225 | + | 0.950336i | \(0.399261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23046.7 | 1.07653 | ||||||||
\(772\) | − 1990.74i | − 0.0928089i | ||||||||
\(773\) | − 34161.1i | − 1.58951i | −0.606933 | − | 0.794753i | \(-0.707600\pi\) | ||||
0.606933 | − | 0.794753i | \(-0.292400\pi\) | |||||||
\(774\) | 35617.8 | 1.65408 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11889.9 | 0.550028 | ||||||||
\(777\) | 8325.54i | 0.384398i | ||||||||
\(778\) | − 25374.6i | − 1.16931i | ||||||||
\(779\) | 31.5096 | 0.00144923 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21446.4 | −0.982603 | ||||||||
\(782\) | 5803.60i | 0.265392i | ||||||||
\(783\) | 6116.29i | 0.279155i | ||||||||
\(784\) | −3394.87 | −0.154650 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8121.17 | 0.368540 | ||||||||
\(787\) | − 38489.6i | − 1.74334i | −0.490095 | − | 0.871669i | \(-0.663038\pi\) | ||||
0.490095 | − | 0.871669i | \(-0.336962\pi\) | |||||||
\(788\) | − 1185.95i | − 0.0536141i | ||||||||
\(789\) | −55993.2 | −2.52650 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30470.1 | −1.36965 | ||||||||
\(792\) | 8423.38i | 0.377919i | ||||||||
\(793\) | − 6023.33i | − 0.269729i | ||||||||
\(794\) | 16121.0 | 0.720544 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9389.73 | 0.418103 | ||||||||
\(797\) | 17176.8i | 0.763405i | 0.924285 | + | 0.381702i | \(0.124662\pi\) | ||||
−0.924285 | + | 0.381702i | \(0.875338\pi\) | |||||||
\(798\) | 84.7902i | 0.00376133i | ||||||||
\(799\) | −3335.10 | −0.147669 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36949.8 | −1.62991 | ||||||||
\(802\) | − 24650.2i | − 1.08532i | ||||||||
\(803\) | 19376.2i | 0.851523i | ||||||||
\(804\) | 13010.1 | 0.570684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9047.58 | −0.395394 | ||||||||
\(807\) | − 19849.4i | − 0.865841i | ||||||||
\(808\) | 15110.9i | 0.657918i | ||||||||
\(809\) | −8226.61 | −0.357518 | −0.178759 | − | 0.983893i | \(-0.557208\pi\) | ||||
−0.178759 | + | 0.983893i | \(0.557208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27867.9 | 1.20662 | 0.603312 | − | 0.797505i | \(-0.293847\pi\) | ||||
0.603312 | + | 0.797505i | \(0.293847\pi\) | |||||||
\(812\) | − 12933.4i | − 0.558956i | ||||||||
\(813\) | − 62358.8i | − 2.69006i | ||||||||
\(814\) | −2937.53 | −0.126487 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15605.7 | 0.669498 | ||||||||
\(817\) | 126.502i | 0.00541705i | ||||||||
\(818\) | − 21613.5i | − 0.923835i | ||||||||
\(819\) | −30943.6 | −1.32022 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17637.5 | −0.749761 | −0.374880 | − | 0.927073i | \(-0.622316\pi\) | ||||
−0.374880 | + | 0.927073i | \(0.622316\pi\) | |||||||
\(822\) | 37542.6i | 1.59300i | ||||||||
\(823\) | − 28048.6i | − 1.18799i | −0.804470 | − | 0.593993i | \(-0.797551\pi\) | ||||
0.804470 | − | 0.593993i | \(-0.202449\pi\) | |||||||
\(824\) | −11977.3 | −0.506372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9530.82 | −0.401477 | ||||||||
\(827\) | − 32592.9i | − 1.37046i | −0.728329 | − | 0.685228i | \(-0.759703\pi\) | ||||
0.728329 | − | 0.685228i | \(-0.240297\pi\) | |||||||
\(828\) | 3014.42i | 0.126520i | ||||||||
\(829\) | −18815.9 | −0.788303 | −0.394152 | − | 0.919045i | \(-0.628962\pi\) | ||||
−0.394152 | + | 0.919045i | \(0.628962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69511.9 | 2.90173 | ||||||||
\(832\) | 2565.19i | 0.106889i | ||||||||
\(833\) | − 26769.7i | − 1.11346i | ||||||||
\(834\) | 37980.9 | 1.57694 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −29.9168 | −0.00123767 | ||||||||
\(837\) | 5030.56i | 0.207744i | ||||||||
\(838\) | − 3647.48i | − 0.150358i | ||||||||
\(839\) | −7612.72 | −0.313254 | −0.156627 | − | 0.987658i | \(-0.550062\pi\) | ||||
−0.156627 | + | 0.987658i | \(0.550062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5558.14 | −0.227896 | ||||||||
\(842\) | − 11990.9i | − 0.490775i | ||||||||
\(843\) | − 7484.43i | − 0.305786i | ||||||||
\(844\) | −11354.5 | −0.463076 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1732.27 | −0.0703978 | ||||||||
\(847\) | − 7029.28i | − 0.285158i | ||||||||
\(848\) | − 699.134i | − 0.0283117i | ||||||||
\(849\) | 17414.8 | 0.703975 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1051.23 | −0.0423452 | ||||||||
\(852\) | 20637.6i | 0.829849i | ||||||||
\(853\) | 31421.4i | 1.26125i | 0.776086 | + | 0.630627i | \(0.217202\pi\) | ||||
−0.776086 | + | 0.630627i | \(0.782798\pi\) | |||||||
\(854\) | 7081.81 | 0.283764 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4681.20 | 0.186916 | ||||||||
\(857\) | 20909.5i | 0.833435i | 0.909036 | + | 0.416718i | \(0.136820\pi\) | ||||
−0.909036 | + | 0.416718i | \(0.863180\pi\) | |||||||
\(858\) | − 19914.8i | − 0.792400i | ||||||||
\(859\) | −23304.5 | −0.925655 | −0.462828 | − | 0.886448i | \(-0.653165\pi\) | ||||
−0.462828 | + | 0.886448i | \(0.653165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24661.0 | −0.976127 | ||||||||
\(862\) | − 7775.61i | − 0.307237i | ||||||||
\(863\) | 19146.3i | 0.755211i | 0.925966 | + | 0.377606i | \(0.123253\pi\) | ||||
−0.925966 | + | 0.377606i | \(0.876747\pi\) | |||||||
\(864\) | 1426.27 | 0.0561607 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8845.87 | 0.347107 | ||||||||
\(867\) | 85075.0i | 3.33252i | ||||||||
\(868\) | − 10637.5i | − 0.415968i | ||||||||
\(869\) | −44310.5 | −1.72972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16863.0 | −0.656005 | ||||||||
\(872\) | 1113.32i | 0.0432362i | ||||||||
\(873\) | 48697.1i | 1.88791i | ||||||||
\(874\) | −10.7061 | −0.000414347 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18645.5 | 0.719146 | ||||||||
\(877\) | 31389.0i | 1.20859i | 0.796762 | + | 0.604293i | \(0.206544\pi\) | ||||
−0.796762 | + | 0.604293i | \(0.793456\pi\) | |||||||
\(878\) | − 3496.16i | − 0.134384i | ||||||||
\(879\) | −21138.7 | −0.811139 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44496.3 | 1.70161 | 0.850806 | − | 0.525480i | \(-0.176114\pi\) | ||||
0.850806 | + | 0.525480i | \(0.176114\pi\) | |||||||
\(882\) | − 13904.3i | − 0.530818i | ||||||||
\(883\) | − 8906.65i | − 0.339448i | −0.985492 | − | 0.169724i | \(-0.945712\pi\) | ||||
0.985492 | − | 0.169724i | \(-0.0542876\pi\) | |||||||
\(884\) | −20227.4 | −0.769592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6742.62 | −0.255669 | ||||||||
\(887\) | − 36584.7i | − 1.38489i | −0.721472 | − | 0.692444i | \(-0.756534\pi\) | ||||
0.721472 | − | 0.692444i | \(-0.243466\pi\) | |||||||
\(888\) | 2826.74i | 0.106823i | ||||||||
\(889\) | 30593.9 | 1.15420 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17356.1 | 0.652581 | ||||||||
\(892\) | − 8498.74i | − 0.319012i | ||||||||
\(893\) | − 6.15238i | 0 0.000230551i | ||||||||
\(894\) | −37191.2 | −1.39134 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3015.97 | −0.112451 | ||||||||
\(897\) | − 7126.76i | − 0.265279i | ||||||||
\(898\) | 26629.5i | 0.989573i | ||||||||
\(899\) | 15488.1 | 0.574591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5512.90 | 0.203842 | ||||||||
\(902\) | − 8701.23i | − 0.321197i | ||||||||
\(903\) | − 99006.4i | − 3.64865i | ||||||||
\(904\) | −10345.4 | −0.380623 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10038.9 | 0.368122 | ||||||||
\(907\) | − 21346.1i | − 0.781463i | −0.920505 | − | 0.390731i | \(-0.872222\pi\) | ||||
0.920505 | − | 0.390731i | \(-0.127778\pi\) | |||||||
\(908\) | − 6207.89i | − 0.226890i | ||||||||
\(909\) | −61889.1 | −2.25823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10208.0 | −0.371246 | −0.185623 | − | 0.982621i | \(-0.559430\pi\) | ||||
−0.185623 | + | 0.982621i | \(0.559430\pi\) | |||||||
\(912\) | 28.7885i | 0.00104527i | ||||||||
\(913\) | − 15591.3i | − 0.565166i | ||||||||
\(914\) | 7534.40 | 0.272665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −634.125 | −0.0228735 | ||||||||
\(917\) | − 12376.0i | − 0.445683i | ||||||||
\(918\) | 11246.6i | 0.404351i | ||||||||
\(919\) | −1758.00 | −0.0631025 | −0.0315513 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315513 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −61669.3 | −2.20638 | ||||||||
\(922\) | − 19348.1i | − 0.691102i | ||||||||
\(923\) | − 26749.3i | − 0.953917i | ||||||||
\(924\) | 23414.4 | 0.833633 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5955.46 | −0.211348 | ||||||||
\(927\) | − 49055.3i | − 1.73807i | ||||||||
\(928\) | − 4391.22i | − 0.155333i | ||||||||
\(929\) | 845.008 | 0.0298426 | 0.0149213 | − | 0.999889i | \(-0.495250\pi\) | ||||
0.0149213 | + | 0.999889i | \(0.495250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.3830 | 0.00173841 | ||||||||
\(932\) | − 2915.99i | − 0.102486i | ||||||||
\(933\) | − 59754.7i | − 2.09676i | ||||||||
\(934\) | −21402.0 | −0.749782 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10506.2 | −0.366886 | ||||||||
\(937\) | 3851.61i | 0.134287i | 0.997743 | + | 0.0671433i | \(0.0213885\pi\) | ||||
−0.997743 | + | 0.0671433i | \(0.978612\pi\) | |||||||
\(938\) | − 19826.3i | − 0.690141i | ||||||||
\(939\) | −42567.7 | −1.47939 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4379.36 | −0.151714 | −0.0758571 | − | 0.997119i | \(-0.524169\pi\) | ||||
−0.0758571 | + | 0.997119i | \(0.524169\pi\) | |||||||
\(942\) | − 56667.5i | − 1.96001i | ||||||||
\(943\) | − 3113.85i | − 0.107530i | ||||||||
\(944\) | −3235.96 | −0.111570 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34932.8 | 1.20059 | ||||||||
\(947\) | 29746.9i | 1.02074i | 0.859954 | + | 0.510371i | \(0.170492\pi\) | ||||
−0.859954 | + | 0.510371i | \(0.829508\pi\) | |||||||
\(948\) | 42639.3i | 1.46082i | ||||||||
\(949\) | −24167.3 | −0.826663 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40442.7 | 1.37902 | ||||||||
\(952\) | − 23781.9i | − 0.809638i | ||||||||
\(953\) | − 4306.61i | − 0.146385i | −0.997318 | − | 0.0731924i | \(-0.976681\pi\) | ||||
0.997318 | − | 0.0731924i | \(-0.0233187\pi\) | |||||||
\(954\) | 2863.42 | 0.0971769 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24806.4 | −0.839222 | ||||||||
\(957\) | 34091.1i | 1.15152i | ||||||||
\(958\) | 4674.29i | 0.157640i | ||||||||
\(959\) | 57211.9 | 1.92645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17052.3 | −0.572397 | ||||||||
\(962\) | − 3663.87i | − 0.122794i | ||||||||
\(963\) | 19172.7i | 0.641568i | ||||||||
\(964\) | 28892.2 | 0.965305 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8379.14 | 0.279083 | ||||||||
\(967\) | − 12233.4i | − 0.406824i | −0.979093 | − | 0.203412i | \(-0.934797\pi\) | ||||
0.979093 | − | 0.203412i | \(-0.0652031\pi\) | |||||||
\(968\) | − 2386.63i | − 0.0792449i | ||||||||
\(969\) | −227.007 | −0.00752581 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48207.7 | 1.59326 | 0.796631 | − | 0.604465i | \(-0.206613\pi\) | ||||
0.796631 | + | 0.604465i | \(0.206613\pi\) | |||||||
\(972\) | − 21515.2i | − 0.709978i | ||||||||
\(973\) | − 57879.8i | − 1.90703i | ||||||||
\(974\) | −14367.7 | −0.472660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2404.46 | 0.0788575 | ||||||||
\(977\) | 28662.9i | 0.938595i | 0.883040 | + | 0.469298i | \(0.155493\pi\) | ||||
−0.883040 | + | 0.469298i | \(0.844507\pi\) | |||||||
\(978\) | − 16316.2i | − 0.533472i | ||||||||
\(979\) | −36239.2 | −1.18305 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4559.81 | −0.148403 | ||||||||
\(982\) | 24168.4i | 0.785383i | ||||||||
\(983\) | 20944.1i | 0.679567i | 0.940504 | + | 0.339783i | \(0.110354\pi\) | ||||
−0.940504 | + | 0.339783i | \(0.889646\pi\) | |||||||
\(984\) | −8373.06 | −0.271264 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 34626.2 | 1.11838 | ||||||||
\(987\) | 4815.16i | 0.155287i | ||||||||
\(988\) | − 37.3141i | − 0.00120154i | ||||||||
\(989\) | 12501.1 | 0.401934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36440.2 | −1.16808 | −0.584038 | − | 0.811727i | \(-0.698528\pi\) | ||||
−0.584038 | + | 0.811727i | \(0.698528\pi\) | |||||||
\(992\) | − 3611.71i | − 0.115597i | ||||||||
\(993\) | 27456.8i | 0.877458i | ||||||||
\(994\) | 31450.0 | 1.00355 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15003.3 | −0.477306 | ||||||||
\(997\) | − 11945.0i | − 0.379439i | −0.981838 | − | 0.189720i | \(-0.939242\pi\) | ||||
0.981838 | − | 0.189720i | \(-0.0607579\pi\) | |||||||
\(998\) | 14291.6i | 0.453298i | ||||||||
\(999\) | −2037.15 | −0.0645172 |
(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 | 1150.4.b.n.599.1 | 8 | ||
5.2 | odd | 4 | 1150.4.a.p.1.1 | 4 | |||
5.3 | odd | 4 | 230.4.a.h.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1150.4.b.n.599.8 | 8 | ||
15.8 | even | 4 | 2070.4.a.bj.1.3 | 4 | |||
20.3 | even | 4 | 1840.4.a.m.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
1150.4.a.p.1.1 | 4 | 5.2 | odd | 4 | |||
1150.4.b.n.599.1 | 8 | 1.1 | even | 1 | trivial | ||
1150.4.b.n.599.8 | 8 | 5.4 | even | 2 | inner | ||
1840.4.a.m.1.1 | 4 | 20.3 | even | 4 | |||
2070.4.a.bj.1.3 | 4 | 15.8 | even | 4 |