Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,4,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (of order \(2\), degree \(1\), 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: | \(1.71105539017\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 38x^{4} + 301x^{2} + 560 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.6 | ||
Root | \(5.28644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.4.b.a.28.1 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.28644i | 1.86904i | 0.355914 | + | 0.934519i | \(0.384170\pi\) | ||||
−0.355914 | + | 0.934519i | \(0.615830\pi\) | |||||||
\(3\) | 1.10381i | 0.212427i | 0.994343 | + | 0.106214i | \(0.0338728\pi\) | ||||
−0.994343 | + | 0.106214i | \(0.966127\pi\) | |||||||
\(4\) | −19.9464 | −2.49330 | ||||||||
\(5\) | 15.1112 | 1.35159 | 0.675794 | − | 0.737090i | \(-0.263801\pi\) | ||||
0.675794 | + | 0.737090i | \(0.263801\pi\) | |||||||
\(6\) | −5.83520 | −0.397035 | ||||||||
\(7\) | −16.1112 | −0.869924 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(8\) | − | 63.1540i | − | 2.79104i | ||||||
\(9\) | 25.7816 | 0.954875 | ||||||||
\(10\) | 79.8845i | 2.52617i | ||||||||
\(11\) | 43.9832i | 1.20559i | 0.797898 | + | 0.602793i | \(0.205946\pi\) | ||||
−0.797898 | + | 0.602793i | \(0.794054\pi\) | |||||||
\(12\) | − | 22.0170i | − | 0.529646i | ||||||
\(13\) | 28.0112 | 0.597608 | 0.298804 | − | 0.954314i | \(-0.403412\pi\) | ||||
0.298804 | + | 0.954314i | \(0.403412\pi\) | |||||||
\(14\) | − | 85.1709i | − | 1.62592i | ||||||
\(15\) | 16.6798i | 0.287114i | ||||||||
\(16\) | 174.288 | 2.72325 | ||||||||
\(17\) | − | 68.9056i | − | 0.983062i | −0.870860 | − | 0.491531i | \(-0.836437\pi\) | ||
0.870860 | − | 0.491531i | \(-0.163563\pi\) | |||||||
\(18\) | 136.293i | 1.78470i | ||||||||
\(19\) | − | 96.2090i | − | 1.16168i | −0.814019 | − | 0.580838i | \(-0.802725\pi\) | ||
0.814019 | − | 0.580838i | \(-0.197275\pi\) | |||||||
\(20\) | −301.415 | −3.36992 | ||||||||
\(21\) | − | 17.7837i | − | 0.184796i | ||||||
\(22\) | −232.515 | −2.25329 | ||||||||
\(23\) | 29.2153 | 0.264861 | 0.132431 | − | 0.991192i | \(-0.457722\pi\) | ||||
0.132431 | + | 0.991192i | \(0.457722\pi\) | |||||||
\(24\) | 69.7097 | 0.592893 | ||||||||
\(25\) | 103.349 | 0.826791 | ||||||||
\(26\) | 148.079i | 1.11695i | ||||||||
\(27\) | 58.2606i | 0.415269i | ||||||||
\(28\) | 321.361 | 2.16898 | ||||||||
\(29\) | −131.360 | − | 84.4602i | −0.841136 | − | 0.540823i | ||||
\(30\) | −88.1769 | −0.536628 | ||||||||
\(31\) | − | 204.543i | − | 1.18506i | −0.805547 | − | 0.592532i | \(-0.798128\pi\) | ||
0.805547 | − | 0.592532i | \(-0.201872\pi\) | |||||||
\(32\) | 416.132i | 2.29882i | ||||||||
\(33\) | −48.5489 | −0.256100 | ||||||||
\(34\) | 364.265 | 1.83738 | ||||||||
\(35\) | −243.460 | −1.17578 | ||||||||
\(36\) | −514.251 | −2.38079 | ||||||||
\(37\) | 395.536i | 1.75745i | 0.477326 | + | 0.878726i | \(0.341606\pi\) | ||||
−0.477326 | + | 0.878726i | \(0.658394\pi\) | |||||||
\(38\) | 508.603 | 2.17122 | ||||||||
\(39\) | 30.9189i | 0.126948i | ||||||||
\(40\) | − | 954.333i | − | 3.77233i | ||||||
\(41\) | − | 255.250i | − | 0.972278i | −0.873881 | − | 0.486139i | \(-0.838405\pi\) | ||
0.873881 | − | 0.486139i | \(-0.161595\pi\) | |||||||
\(42\) | 94.0121 | 0.345390 | ||||||||
\(43\) | 268.729i | 0.953042i | 0.879163 | + | 0.476521i | \(0.158102\pi\) | ||||
−0.879163 | + | 0.476521i | \(0.841898\pi\) | |||||||
\(44\) | − | 877.308i | − | 3.00589i | ||||||
\(45\) | 389.592 | 1.29060 | ||||||||
\(46\) | 154.445i | 0.495036i | ||||||||
\(47\) | 65.3058i | 0.202677i | 0.994852 | + | 0.101339i | \(0.0323126\pi\) | ||||
−0.994852 | + | 0.101339i | \(0.967687\pi\) | |||||||
\(48\) | 192.380i | 0.578494i | ||||||||
\(49\) | −83.4287 | −0.243232 | ||||||||
\(50\) | 546.347i | 1.54530i | ||||||||
\(51\) | 76.0584 | 0.208829 | ||||||||
\(52\) | −558.723 | −1.49002 | ||||||||
\(53\) | −124.644 | −0.323040 | −0.161520 | − | 0.986869i | \(-0.551640\pi\) | ||||
−0.161520 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(54\) | −307.991 | −0.776154 | ||||||||
\(55\) | 664.640i | 1.62946i | ||||||||
\(56\) | 1017.49i | 2.42799i | ||||||||
\(57\) | 106.196 | 0.246772 | ||||||||
\(58\) | 446.494 | − | 694.427i | 1.01082 | − | 1.57212i | ||||
\(59\) | −84.3946 | −0.186224 | −0.0931122 | − | 0.995656i | \(-0.529682\pi\) | ||||
−0.0931122 | + | 0.995656i | \(0.529682\pi\) | |||||||
\(60\) | − | 332.703i | − | 0.715863i | ||||||
\(61\) | − | 110.352i | − | 0.231626i | −0.993271 | − | 0.115813i | \(-0.963053\pi\) | ||
0.993271 | − | 0.115813i | \(-0.0369473\pi\) | |||||||
\(62\) | 1081.30 | 2.21493 | ||||||||
\(63\) | −415.373 | −0.830668 | ||||||||
\(64\) | −805.548 | −1.57334 | ||||||||
\(65\) | 423.283 | 0.807720 | ||||||||
\(66\) | − | 256.651i | − | 0.478660i | ||||||
\(67\) | −737.197 | −1.34422 | −0.672112 | − | 0.740450i | \(-0.734613\pi\) | ||||
−0.672112 | + | 0.740450i | \(0.734613\pi\) | |||||||
\(68\) | 1374.42i | 2.45107i | ||||||||
\(69\) | 32.2480i | 0.0562638i | ||||||||
\(70\) | − | 1287.04i | − | 2.19758i | ||||||
\(71\) | −20.2796 | −0.0338978 | −0.0169489 | − | 0.999856i | \(-0.505395\pi\) | ||||
−0.0169489 | + | 0.999856i | \(0.505395\pi\) | |||||||
\(72\) | − | 1628.21i | − | 2.66509i | ||||||
\(73\) | − | 139.307i | − | 0.223351i | −0.993745 | − | 0.111676i | \(-0.964378\pi\) | ||
0.993745 | − | 0.111676i | \(-0.0356218\pi\) | |||||||
\(74\) | −2090.98 | −3.28474 | ||||||||
\(75\) | 114.077i | 0.175633i | ||||||||
\(76\) | 1919.02i | 2.89641i | ||||||||
\(77\) | − | 708.624i | − | 1.04877i | ||||||
\(78\) | −163.451 | −0.237271 | ||||||||
\(79\) | 77.1390i | 0.109858i | 0.998490 | + | 0.0549292i | \(0.0174933\pi\) | ||||
−0.998490 | + | 0.0549292i | \(0.982507\pi\) | |||||||
\(80\) | 2633.71 | 3.68072 | ||||||||
\(81\) | 631.795 | 0.866660 | ||||||||
\(82\) | 1349.36 | 1.81722 | ||||||||
\(83\) | −178.222 | −0.235691 | −0.117846 | − | 0.993032i | \(-0.537599\pi\) | ||||
−0.117846 | + | 0.993032i | \(0.537599\pi\) | |||||||
\(84\) | 354.720i | 0.460752i | ||||||||
\(85\) | − | 1041.25i | − | 1.32870i | ||||||
\(86\) | −1420.62 | −1.78127 | ||||||||
\(87\) | 93.2277 | − | 144.996i | 0.114886 | − | 0.178680i | ||||
\(88\) | 2777.72 | 3.36484 | ||||||||
\(89\) | − | 421.125i | − | 0.501564i | −0.968044 | − | 0.250782i | \(-0.919312\pi\) | ||
0.968044 | − | 0.250782i | \(-0.0806877\pi\) | |||||||
\(90\) | 2059.55i | 2.41218i | ||||||||
\(91\) | −451.294 | −0.519874 | ||||||||
\(92\) | −582.740 | −0.660379 | ||||||||
\(93\) | 225.776 | 0.251740 | ||||||||
\(94\) | −345.235 | −0.378812 | ||||||||
\(95\) | − | 1453.83i | − | 1.57011i | ||||||
\(96\) | −459.328 | −0.488333 | ||||||||
\(97\) | 1171.11i | 1.22585i | 0.790139 | + | 0.612927i | \(0.210008\pi\) | ||||
−0.790139 | + | 0.612927i | \(0.789992\pi\) | |||||||
\(98\) | − | 441.040i | − | 0.454610i | ||||||
\(99\) | 1133.96i | 1.15118i | ||||||||
\(100\) | −2061.44 | −2.06144 | ||||||||
\(101\) | 393.150i | 0.387326i | 0.981068 | + | 0.193663i | \(0.0620368\pi\) | ||||
−0.981068 | + | 0.193663i | \(0.937963\pi\) | |||||||
\(102\) | 402.078i | 0.390310i | ||||||||
\(103\) | −139.694 | −0.133635 | −0.0668176 | − | 0.997765i | \(-0.521285\pi\) | ||||
−0.0668176 | + | 0.997765i | \(0.521285\pi\) | |||||||
\(104\) | − | 1769.02i | − | 1.66795i | ||||||
\(105\) | − | 268.733i | − | 0.249768i | ||||||
\(106\) | − | 658.921i | − | 0.603774i | ||||||
\(107\) | 990.473 | 0.894885 | 0.447442 | − | 0.894313i | \(-0.352335\pi\) | ||||
0.447442 | + | 0.894313i | \(0.352335\pi\) | |||||||
\(108\) | − | 1162.09i | − | 1.03539i | ||||||
\(109\) | 1331.33 | 1.16990 | 0.584948 | − | 0.811071i | \(-0.301115\pi\) | ||||
0.584948 | + | 0.811071i | \(0.301115\pi\) | |||||||
\(110\) | −3513.58 | −3.04551 | ||||||||
\(111\) | −436.595 | −0.373331 | ||||||||
\(112\) | −2807.99 | −2.36902 | ||||||||
\(113\) | − | 550.551i | − | 0.458332i | −0.973387 | − | 0.229166i | \(-0.926400\pi\) | ||
0.973387 | − | 0.229166i | \(-0.0735998\pi\) | |||||||
\(114\) | 561.399i | 0.461226i | ||||||||
\(115\) | 441.479 | 0.357983 | ||||||||
\(116\) | 2620.16 | + | 1684.68i | 2.09721 | + | 1.34844i | ||||
\(117\) | 722.174 | 0.570641 | ||||||||
\(118\) | − | 446.147i | − | 0.348060i | ||||||
\(119\) | 1110.15i | 0.855190i | ||||||||
\(120\) | 1053.40 | 0.801347 | ||||||||
\(121\) | −603.526 | −0.453438 | ||||||||
\(122\) | 583.371 | 0.432917 | ||||||||
\(123\) | 281.747 | 0.206539 | ||||||||
\(124\) | 4079.90i | 2.95472i | ||||||||
\(125\) | −327.175 | −0.234107 | ||||||||
\(126\) | − | 2195.84i | − | 1.55255i | ||||||
\(127\) | 769.969i | 0.537982i | 0.963143 | + | 0.268991i | \(0.0866902\pi\) | ||||
−0.963143 | + | 0.268991i | \(0.913310\pi\) | |||||||
\(128\) | − | 929.427i | − | 0.641801i | ||||||
\(129\) | −296.625 | −0.202452 | ||||||||
\(130\) | 2237.66i | 1.50966i | ||||||||
\(131\) | − | 2325.57i | − | 1.55104i | −0.631326 | − | 0.775518i | \(-0.717489\pi\) | ||
0.631326 | − | 0.775518i | \(-0.282511\pi\) | |||||||
\(132\) | 968.377 | 0.638534 | ||||||||
\(133\) | 1550.04i | 1.01057i | ||||||||
\(134\) | − | 3897.15i | − | 2.51241i | ||||||
\(135\) | 880.389i | 0.561273i | ||||||||
\(136\) | −4351.66 | −2.74376 | ||||||||
\(137\) | 1421.60i | 0.886535i | 0.896389 | + | 0.443267i | \(0.146181\pi\) | ||||
−0.896389 | + | 0.443267i | \(0.853819\pi\) | |||||||
\(138\) | −170.477 | −0.105159 | ||||||||
\(139\) | 2368.97 | 1.44556 | 0.722782 | − | 0.691077i | \(-0.242863\pi\) | ||||
0.722782 | + | 0.691077i | \(0.242863\pi\) | |||||||
\(140\) | 4856.16 | 2.93157 | ||||||||
\(141\) | −72.0850 | −0.0430542 | ||||||||
\(142\) | − | 107.207i | − | 0.0633562i | ||||||
\(143\) | 1232.02i | 0.720468i | ||||||||
\(144\) | 4493.43 | 2.60036 | ||||||||
\(145\) | −1985.01 | − | 1276.30i | −1.13687 | − | 0.730970i | ||||
\(146\) | 736.437 | 0.417452 | ||||||||
\(147\) | − | 92.0890i | − | 0.0516692i | ||||||
\(148\) | − | 7889.53i | − | 4.38186i | ||||||
\(149\) | −675.196 | −0.371236 | −0.185618 | − | 0.982622i | \(-0.559429\pi\) | ||||
−0.185618 | + | 0.982622i | \(0.559429\pi\) | |||||||
\(150\) | −603.061 | −0.328265 | ||||||||
\(151\) | −1634.01 | −0.880621 | −0.440310 | − | 0.897846i | \(-0.645132\pi\) | ||||
−0.440310 | + | 0.897846i | \(0.645132\pi\) | |||||||
\(152\) | −6075.98 | −3.24228 | ||||||||
\(153\) | − | 1776.50i | − | 0.938701i | ||||||
\(154\) | 3746.09 | 1.96019 | ||||||||
\(155\) | − | 3090.89i | − | 1.60172i | ||||||
\(156\) | − | 616.721i | − | 0.316521i | ||||||
\(157\) | 2359.77i | 1.19956i | 0.800166 | + | 0.599778i | \(0.204745\pi\) | ||||
−0.800166 | + | 0.599778i | \(0.795255\pi\) | |||||||
\(158\) | −407.791 | −0.205330 | ||||||||
\(159\) | − | 137.582i | − | 0.0686226i | ||||||
\(160\) | 6288.26i | 3.10706i | ||||||||
\(161\) | −470.694 | −0.230409 | ||||||||
\(162\) | 3339.95i | 1.61982i | ||||||||
\(163\) | 223.466i | 0.107382i | 0.998558 | + | 0.0536909i | \(0.0170986\pi\) | ||||
−0.998558 | + | 0.0536909i | \(0.982901\pi\) | |||||||
\(164\) | 5091.33i | 2.42418i | ||||||||
\(165\) | −733.634 | −0.346141 | ||||||||
\(166\) | − | 942.158i | − | 0.440516i | ||||||
\(167\) | −3387.40 | −1.56961 | −0.784806 | − | 0.619742i | \(-0.787237\pi\) | ||||
−0.784806 | + | 0.619742i | \(0.787237\pi\) | |||||||
\(168\) | −1123.11 | −0.515772 | ||||||||
\(169\) | −1412.37 | −0.642865 | ||||||||
\(170\) | 5504.49 | 2.48338 | ||||||||
\(171\) | − | 2480.42i | − | 1.10926i | ||||||
\(172\) | − | 5360.18i | − | 2.37622i | ||||||
\(173\) | 1619.76 | 0.711839 | 0.355920 | − | 0.934517i | \(-0.384168\pi\) | ||||
0.355920 | + | 0.934517i | \(0.384168\pi\) | |||||||
\(174\) | 766.512 | + | 492.842i | 0.333961 | + | 0.214726i | ||||
\(175\) | −1665.08 | −0.719245 | ||||||||
\(176\) | 7665.76i | 3.28312i | ||||||||
\(177\) | − | 93.1552i | − | 0.0395592i | ||||||
\(178\) | 2226.25 | 0.937442 | ||||||||
\(179\) | 3919.41 | 1.63659 | 0.818296 | − | 0.574797i | \(-0.194919\pi\) | ||||
0.818296 | + | 0.574797i | \(0.194919\pi\) | |||||||
\(180\) | −7770.96 | −3.21785 | ||||||||
\(181\) | −1658.73 | −0.681172 | −0.340586 | − | 0.940213i | \(-0.610625\pi\) | ||||
−0.340586 | + | 0.940213i | \(0.610625\pi\) | |||||||
\(182\) | − | 2385.74i | − | 0.971663i | ||||||
\(183\) | 121.807 | 0.0492037 | ||||||||
\(184\) | − | 1845.06i | − | 0.739238i | ||||||
\(185\) | 5977.03i | 2.37535i | ||||||||
\(186\) | 1193.55i | 0.470512i | ||||||||
\(187\) | 3030.69 | 1.18517 | ||||||||
\(188\) | − | 1302.62i | − | 0.505336i | ||||||
\(189\) | − | 938.650i | − | 0.361252i | ||||||
\(190\) | 7685.61 | 2.93459 | ||||||||
\(191\) | 1913.06i | 0.724734i | 0.932035 | + | 0.362367i | \(0.118031\pi\) | ||||
−0.932035 | + | 0.362367i | \(0.881969\pi\) | |||||||
\(192\) | − | 889.169i | − | 0.334220i | ||||||
\(193\) | − | 3220.07i | − | 1.20096i | −0.799639 | − | 0.600480i | \(-0.794976\pi\) | ||
0.799639 | − | 0.600480i | \(-0.205024\pi\) | |||||||
\(194\) | −6190.98 | −2.29117 | ||||||||
\(195\) | 467.222i | 0.171582i | ||||||||
\(196\) | 1664.10 | 0.606452 | ||||||||
\(197\) | −3615.40 | −1.30755 | −0.653773 | − | 0.756690i | \(-0.726815\pi\) | ||||
−0.653773 | + | 0.756690i | \(0.726815\pi\) | |||||||
\(198\) | −5994.60 | −2.15161 | ||||||||
\(199\) | −3888.43 | −1.38514 | −0.692571 | − | 0.721349i | \(-0.743522\pi\) | ||||
−0.692571 | + | 0.721349i | \(0.743522\pi\) | |||||||
\(200\) | − | 6526.89i | − | 2.30761i | ||||||
\(201\) | − | 813.723i | − | 0.285550i | ||||||
\(202\) | −2078.36 | −0.723927 | ||||||||
\(203\) | 2116.37 | + | 1360.76i | 0.731725 | + | 0.470475i | ||||
\(204\) | −1517.09 | −0.520675 | ||||||||
\(205\) | − | 3857.14i | − | 1.31412i | ||||||
\(206\) | − | 738.482i | − | 0.249769i | ||||||
\(207\) | 753.217 | 0.252909 | ||||||||
\(208\) | 4882.02 | 1.62744 | ||||||||
\(209\) | 4231.58 | 1.40050 | ||||||||
\(210\) | 1420.64 | 0.466825 | ||||||||
\(211\) | − | 2986.97i | − | 0.974556i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) | ||
0.873247 | − | 0.487278i | \(-0.162010\pi\) | |||||||
\(212\) | 2486.20 | 0.805437 | ||||||||
\(213\) | − | 22.3847i | − | 0.00720081i | ||||||
\(214\) | 5236.07i | 1.67257i | ||||||||
\(215\) | 4060.83i | 1.28812i | ||||||||
\(216\) | 3679.39 | 1.15903 | ||||||||
\(217\) | 3295.44i | 1.03092i | ||||||||
\(218\) | 7038.01i | 2.18658i | ||||||||
\(219\) | 153.768 | 0.0474459 | ||||||||
\(220\) | − | 13257.2i | − | 4.06273i | ||||||
\(221\) | − | 1930.13i | − | 0.587486i | ||||||
\(222\) | − | 2308.03i | − | 0.697770i | ||||||
\(223\) | 844.880 | 0.253710 | 0.126855 | − | 0.991921i | \(-0.459512\pi\) | ||||
0.126855 | + | 0.991921i | \(0.459512\pi\) | |||||||
\(224\) | − | 6704.39i | − | 1.99980i | ||||||
\(225\) | 2664.50 | 0.789482 | ||||||||
\(226\) | 2910.45 | 0.856639 | ||||||||
\(227\) | 6128.60 | 1.79194 | 0.895969 | − | 0.444117i | \(-0.146483\pi\) | ||||
0.895969 | + | 0.444117i | \(0.146483\pi\) | |||||||
\(228\) | −2118.23 | −0.615277 | ||||||||
\(229\) | 6219.40i | 1.79471i | 0.441306 | + | 0.897357i | \(0.354515\pi\) | ||||
−0.441306 | + | 0.897357i | \(0.645485\pi\) | |||||||
\(230\) | 2333.85i | 0.669085i | ||||||||
\(231\) | 782.183 | 0.222787 | ||||||||
\(232\) | −5334.00 | + | 8295.91i | −1.50946 | + | 2.34764i | ||||
\(233\) | −3816.41 | −1.07305 | −0.536526 | − | 0.843884i | \(-0.680264\pi\) | ||||
−0.536526 | + | 0.843884i | \(0.680264\pi\) | |||||||
\(234\) | 3817.73i | 1.06655i | ||||||||
\(235\) | 986.851i | 0.273936i | ||||||||
\(236\) | 1683.37 | 0.464314 | ||||||||
\(237\) | −85.1465 | −0.0233370 | ||||||||
\(238\) | −5868.75 | −1.59838 | ||||||||
\(239\) | 584.691 | 0.158245 | 0.0791224 | − | 0.996865i | \(-0.474788\pi\) | ||||
0.0791224 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(240\) | 2907.10i | 0.781885i | ||||||||
\(241\) | −1296.46 | −0.346523 | −0.173262 | − | 0.984876i | \(-0.555431\pi\) | ||||
−0.173262 | + | 0.984876i | \(0.555431\pi\) | |||||||
\(242\) | − | 3190.50i | − | 0.847492i | ||||||
\(243\) | 2270.42i | 0.599371i | ||||||||
\(244\) | 2201.13i | 0.577513i | ||||||||
\(245\) | −1260.71 | −0.328750 | ||||||||
\(246\) | 1489.44i | 0.386028i | ||||||||
\(247\) | − | 2694.93i | − | 0.694227i | ||||||
\(248\) | −12917.7 | −3.30756 | ||||||||
\(249\) | − | 196.722i | − | 0.0500673i | ||||||
\(250\) | − | 1729.59i | − | 0.437555i | ||||||
\(251\) | − | 6848.45i | − | 1.72219i | −0.508441 | − | 0.861097i | \(-0.669778\pi\) | ||
0.508441 | − | 0.861097i | \(-0.330222\pi\) | |||||||
\(252\) | 8285.21 | 2.07111 | ||||||||
\(253\) | 1284.98i | 0.319313i | ||||||||
\(254\) | −4070.39 | −1.00551 | ||||||||
\(255\) | 1149.33 | 0.282251 | ||||||||
\(256\) | −1531.03 | −0.373786 | ||||||||
\(257\) | 4908.41 | 1.19136 | 0.595678 | − | 0.803224i | \(-0.296884\pi\) | ||||
0.595678 | + | 0.803224i | \(0.296884\pi\) | |||||||
\(258\) | − | 1568.09i | − | 0.378391i | ||||||
\(259\) | − | 6372.57i | − | 1.52885i | ||||||
\(260\) | −8442.98 | −2.01389 | ||||||||
\(261\) | −3386.67 | − | 2177.52i | −0.803180 | − | 0.516418i | ||||
\(262\) | 12294.0 | 2.89894 | ||||||||
\(263\) | − | 5483.04i | − | 1.28555i | −0.766057 | − | 0.642773i | \(-0.777784\pi\) | ||
0.766057 | − | 0.642773i | \(-0.222216\pi\) | |||||||
\(264\) | 3066.06i | 0.714784i | ||||||||
\(265\) | −1883.52 | −0.436617 | ||||||||
\(266\) | −8194.21 | −1.88879 | ||||||||
\(267\) | 464.840 | 0.106546 | ||||||||
\(268\) | 14704.4 | 3.35156 | ||||||||
\(269\) | 3321.99i | 0.752957i | 0.926425 | + | 0.376479i | \(0.122865\pi\) | ||||
−0.926425 | + | 0.376479i | \(0.877135\pi\) | |||||||
\(270\) | −4654.12 | −1.04904 | ||||||||
\(271\) | 3672.45i | 0.823192i | 0.911366 | + | 0.411596i | \(0.135029\pi\) | ||||
−0.911366 | + | 0.411596i | \(0.864971\pi\) | |||||||
\(272\) | − | 12009.4i | − | 2.67713i | ||||||
\(273\) | − | 498.141i | − | 0.110435i | ||||||
\(274\) | −7515.18 | −1.65697 | ||||||||
\(275\) | 4545.62i | 0.996768i | ||||||||
\(276\) | − | 643.232i | − | 0.140283i | ||||||
\(277\) | −3272.17 | −0.709767 | −0.354884 | − | 0.934910i | \(-0.615480\pi\) | ||||
−0.354884 | + | 0.934910i | \(0.615480\pi\) | |||||||
\(278\) | 12523.4i | 2.70181i | ||||||||
\(279\) | − | 5273.45i | − | 1.13159i | ||||||
\(280\) | 15375.5i | 3.28164i | ||||||||
\(281\) | 374.989 | 0.0796083 | 0.0398042 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398042 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(282\) | − | 381.073i | − | 0.0804700i | ||||||
\(283\) | 3491.52 | 0.733390 | 0.366695 | − | 0.930341i | \(-0.380489\pi\) | ||||
0.366695 | + | 0.930341i | \(0.380489\pi\) | |||||||
\(284\) | 404.504 | 0.0845173 | ||||||||
\(285\) | 1604.75 | 0.333534 | ||||||||
\(286\) | −6513.01 | −1.34658 | ||||||||
\(287\) | 4112.39i | 0.845808i | ||||||||
\(288\) | 10728.5i | 2.19509i | ||||||||
\(289\) | 165.020 | 0.0335884 | ||||||||
\(290\) | 6747.06 | − | 10493.6i | 1.36621 | − | 2.12485i | ||||
\(291\) | −1292.67 | −0.260405 | ||||||||
\(292\) | 2778.67i | 0.556882i | ||||||||
\(293\) | − | 4208.27i | − | 0.839078i | −0.907737 | − | 0.419539i | \(-0.862192\pi\) | ||
0.907737 | − | 0.419539i | \(-0.137808\pi\) | |||||||
\(294\) | 486.823 | 0.0965717 | ||||||||
\(295\) | −1275.31 | −0.251699 | ||||||||
\(296\) | 24979.7 | 4.90511 | ||||||||
\(297\) | −2562.49 | −0.500643 | ||||||||
\(298\) | − | 3569.38i | − | 0.693855i | ||||||
\(299\) | 818.355 | 0.158283 | ||||||||
\(300\) | − | 2275.43i | − | 0.437906i | ||||||
\(301\) | − | 4329.55i | − | 0.829074i | ||||||
\(302\) | − | 8638.08i | − | 1.64591i | ||||||
\(303\) | −433.962 | −0.0822787 | ||||||||
\(304\) | − | 16768.1i | − | 3.16354i | ||||||
\(305\) | − | 1667.56i | − | 0.313063i | ||||||
\(306\) | 9391.34 | 1.75447 | ||||||||
\(307\) | 4418.40i | 0.821406i | 0.911769 | + | 0.410703i | \(0.134717\pi\) | ||||
−0.911769 | + | 0.410703i | \(0.865283\pi\) | |||||||
\(308\) | 14134.5i | 2.61490i | ||||||||
\(309\) | − | 154.195i | − | 0.0283878i | ||||||
\(310\) | 16339.8 | 2.99367 | ||||||||
\(311\) | 4608.82i | 0.840329i | 0.907448 | + | 0.420165i | \(0.138028\pi\) | ||||
−0.907448 | + | 0.420165i | \(0.861972\pi\) | |||||||
\(312\) | 1952.65 | 0.354318 | ||||||||
\(313\) | −4361.87 | −0.787692 | −0.393846 | − | 0.919176i | \(-0.628856\pi\) | ||||
−0.393846 | + | 0.919176i | \(0.628856\pi\) | |||||||
\(314\) | −12474.8 | −2.24202 | ||||||||
\(315\) | −6276.79 | −1.12272 | ||||||||
\(316\) | − | 1538.65i | − | 0.273910i | ||||||
\(317\) | − | 1780.78i | − | 0.315516i | −0.987478 | − | 0.157758i | \(-0.949573\pi\) | ||
0.987478 | − | 0.157758i | \(-0.0504265\pi\) | |||||||
\(318\) | 727.321 | 0.128258 | ||||||||
\(319\) | 3714.83 | − | 5777.64i | 0.652009 | − | 1.01406i | ||||
\(320\) | −12172.8 | −2.12650 | ||||||||
\(321\) | 1093.29i | 0.190098i | ||||||||
\(322\) | − | 2488.29i | − | 0.430643i | ||||||
\(323\) | −6629.34 | −1.14200 | ||||||||
\(324\) | −12602.0 | −2.16085 | ||||||||
\(325\) | 2894.93 | 0.494097 | ||||||||
\(326\) | −1181.34 | −0.200701 | ||||||||
\(327\) | 1469.53i | 0.248518i | ||||||||
\(328\) | −16120.1 | −2.71367 | ||||||||
\(329\) | − | 1052.16i | − | 0.176314i | ||||||
\(330\) | − | 3878.31i | − | 0.646951i | ||||||
\(331\) | 2653.52i | 0.440636i | 0.975428 | + | 0.220318i | \(0.0707095\pi\) | ||||
−0.975428 | + | 0.220318i | \(0.929290\pi\) | |||||||
\(332\) | 3554.89 | 0.587650 | ||||||||
\(333\) | 10197.6i | 1.67815i | ||||||||
\(334\) | − | 17907.3i | − | 2.93366i | ||||||
\(335\) | −11140.0 | −1.81684 | ||||||||
\(336\) | − | 3099.48i | − | 0.503245i | ||||||
\(337\) | 7284.33i | 1.17746i | 0.808331 | + | 0.588728i | \(0.200371\pi\) | ||||
−0.808331 | + | 0.588728i | \(0.799629\pi\) | |||||||
\(338\) | − | 7466.42i | − | 1.20154i | ||||||
\(339\) | 607.701 | 0.0973622 | ||||||||
\(340\) | 20769.2i | 3.31284i | ||||||||
\(341\) | 8996.46 | 1.42870 | ||||||||
\(342\) | 13112.6 | 2.07324 | ||||||||
\(343\) | 6870.29 | 1.08152 | ||||||||
\(344\) | 16971.3 | 2.65998 | ||||||||
\(345\) | 487.307i | 0.0760455i | ||||||||
\(346\) | 8562.77i | 1.33045i | ||||||||
\(347\) | −5506.92 | −0.851951 | −0.425976 | − | 0.904735i | \(-0.640069\pi\) | ||||
−0.425976 | + | 0.904735i | \(0.640069\pi\) | |||||||
\(348\) | −1859.56 | + | 2892.15i | −0.286445 | + | 0.445504i | ||||
\(349\) | 1176.85 | 0.180502 | 0.0902511 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902511 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(350\) | − | 8802.32i | − | 1.34430i | ||||||
\(351\) | 1631.95i | 0.248168i | ||||||||
\(352\) | −18302.8 | −2.77143 | ||||||||
\(353\) | 8886.53 | 1.33989 | 0.669947 | − | 0.742409i | \(-0.266317\pi\) | ||||
0.669947 | + | 0.742409i | \(0.266317\pi\) | |||||||
\(354\) | 492.459 | 0.0739376 | ||||||||
\(355\) | −306.449 | −0.0458158 | ||||||||
\(356\) | 8399.94i | 1.25055i | ||||||||
\(357\) | −1225.39 | −0.181666 | ||||||||
\(358\) | 20719.7i | 3.05885i | ||||||||
\(359\) | 10030.8i | 1.47466i | 0.675532 | + | 0.737331i | \(0.263914\pi\) | ||||
−0.675532 | + | 0.737331i | \(0.736086\pi\) | |||||||
\(360\) | − | 24604.3i | − | 3.60211i | ||||||
\(361\) | −2397.17 | −0.349493 | ||||||||
\(362\) | − | 8768.75i | − | 1.27314i | ||||||
\(363\) | − | 666.175i | − | 0.0963227i | ||||||
\(364\) | 9001.70 | 1.29620 | ||||||||
\(365\) | − | 2105.10i | − | 0.301879i | ||||||
\(366\) | 643.928i | 0.0919635i | ||||||||
\(367\) | 3757.93i | 0.534502i | 0.963627 | + | 0.267251i | \(0.0861153\pi\) | ||||
−0.963627 | + | 0.267251i | \(0.913885\pi\) | |||||||
\(368\) | 5091.88 | 0.721284 | ||||||||
\(369\) | − | 6580.77i | − | 0.928404i | ||||||
\(370\) | −31597.2 | −4.43962 | ||||||||
\(371\) | 2008.16 | 0.281020 | ||||||||
\(372\) | −4503.41 | −0.627664 | ||||||||
\(373\) | 10917.6 | 1.51553 | 0.757765 | − | 0.652528i | \(-0.226292\pi\) | ||||
0.757765 | + | 0.652528i | \(0.226292\pi\) | |||||||
\(374\) | 16021.6i | 2.21512i | ||||||||
\(375\) | − | 361.137i | − | 0.0497308i | ||||||
\(376\) | 4124.32 | 0.565680 | ||||||||
\(377\) | −3679.55 | − | 2365.83i | −0.502670 | − | 0.323200i | ||||
\(378\) | 4962.11 | 0.675195 | ||||||||
\(379\) | − | 4846.58i | − | 0.656866i | −0.944527 | − | 0.328433i | \(-0.893480\pi\) | ||
0.944527 | − | 0.328433i | \(-0.106520\pi\) | |||||||
\(380\) | 28998.8i | 3.91475i | ||||||||
\(381\) | −849.896 | −0.114282 | ||||||||
\(382\) | −10113.3 | −1.35456 | ||||||||
\(383\) | −4309.20 | −0.574908 | −0.287454 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287454 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(384\) | 1025.91 | 0.136336 | ||||||||
\(385\) | − | 10708.2i | − | 1.41750i | ||||||
\(386\) | 17022.7 | 2.24464 | ||||||||
\(387\) | 6928.27i | 0.910036i | ||||||||
\(388\) | − | 23359.4i | − | 3.05642i | ||||||
\(389\) | 393.410i | 0.0512769i | 0.999671 | + | 0.0256384i | \(0.00816186\pi\) | ||||
−0.999671 | + | 0.0256384i | \(0.991838\pi\) | |||||||
\(390\) | −2469.94 | −0.320693 | ||||||||
\(391\) | − | 2013.10i | − | 0.260375i | ||||||
\(392\) | 5268.85i | 0.678870i | ||||||||
\(393\) | 2566.97 | 0.329483 | ||||||||
\(394\) | − | 19112.6i | − | 2.44385i | ||||||
\(395\) | 1165.66i | 0.148483i | ||||||||
\(396\) | − | 22618.4i | − | 2.87025i | ||||||
\(397\) | −11339.5 | −1.43353 | −0.716766 | − | 0.697314i | \(-0.754378\pi\) | ||||
−0.716766 | + | 0.697314i | \(0.754378\pi\) | |||||||
\(398\) | − | 20555.9i | − | 2.58888i | ||||||
\(399\) | −1710.95 | −0.214673 | ||||||||
\(400\) | 18012.5 | 2.25156 | ||||||||
\(401\) | 3865.08 | 0.481329 | 0.240664 | − | 0.970608i | \(-0.422635\pi\) | ||||
0.240664 | + | 0.970608i | \(0.422635\pi\) | |||||||
\(402\) | 4301.69 | 0.533704 | ||||||||
\(403\) | − | 5729.49i | − | 0.708204i | ||||||
\(404\) | − | 7841.94i | − | 0.965721i | ||||||
\(405\) | 9547.19 | 1.17137 | ||||||||
\(406\) | −7193.56 | + | 11188.1i | −0.879336 | + | 1.36762i | ||||
\(407\) | −17397.0 | −2.11876 | ||||||||
\(408\) | − | 4803.39i | − | 0.582851i | ||||||
\(409\) | 13673.2i | 1.65305i | 0.562899 | + | 0.826526i | \(0.309686\pi\) | ||||
−0.562899 | + | 0.826526i | \(0.690314\pi\) | |||||||
\(410\) | 20390.5 | 2.45614 | ||||||||
\(411\) | −1569.17 | −0.188324 | ||||||||
\(412\) | 2786.39 | 0.333193 | ||||||||
\(413\) | 1359.70 | 0.162001 | ||||||||
\(414\) | 3981.84i | 0.472697i | ||||||||
\(415\) | −2693.15 | −0.318558 | ||||||||
\(416\) | 11656.3i | 1.37380i | ||||||||
\(417\) | 2614.88i | 0.307077i | ||||||||
\(418\) | 22370.0i | 2.61759i | ||||||||
\(419\) | 16494.7 | 1.92319 | 0.961597 | − | 0.274465i | \(-0.0885007\pi\) | ||||
0.961597 | + | 0.274465i | \(0.0885007\pi\) | |||||||
\(420\) | 5360.25i | 0.622746i | ||||||||
\(421\) | − | 14117.6i | − | 1.63432i | −0.576412 | − | 0.817159i | \(-0.695548\pi\) | ||
0.576412 | − | 0.817159i | \(-0.304452\pi\) | |||||||
\(422\) | 15790.4 | 1.82148 | ||||||||
\(423\) | 1683.69i | 0.193531i | ||||||||
\(424\) | 7871.75i | 0.901618i | ||||||||
\(425\) | − | 7121.32i | − | 0.812787i | ||||||
\(426\) | 118.335 | 0.0134586 | ||||||||
\(427\) | 1777.91i | 0.201497i | ||||||||
\(428\) | −19756.4 | −2.23122 | ||||||||
\(429\) | −1359.91 | −0.153047 | ||||||||
\(430\) | −21467.3 | −2.40755 | ||||||||
\(431\) | −9592.11 | −1.07201 | −0.536004 | − | 0.844215i | \(-0.680067\pi\) | ||||
−0.536004 | + | 0.844215i | \(0.680067\pi\) | |||||||
\(432\) | 10154.1i | 1.13088i | ||||||||
\(433\) | 4582.98i | 0.508646i | 0.967119 | + | 0.254323i | \(0.0818527\pi\) | ||||
−0.967119 | + | 0.254323i | \(0.918147\pi\) | |||||||
\(434\) | −17421.1 | −1.92682 | ||||||||
\(435\) | 1408.78 | − | 2191.07i | 0.155278 | − | 0.241502i | ||||
\(436\) | −26555.3 | −2.91690 | ||||||||
\(437\) | − | 2810.77i | − | 0.307683i | ||||||
\(438\) | 812.883i | 0.0886782i | ||||||||
\(439\) | −3068.67 | −0.333621 | −0.166810 | − | 0.985989i | \(-0.553347\pi\) | ||||
−0.166810 | + | 0.985989i | \(0.553347\pi\) | |||||||
\(440\) | 41974.7 | 4.54787 | ||||||||
\(441\) | −2150.93 | −0.232256 | ||||||||
\(442\) | 10203.5 | 1.09803 | ||||||||
\(443\) | 1166.32i | 0.125087i | 0.998042 | + | 0.0625437i | \(0.0199213\pi\) | ||||
−0.998042 | + | 0.0625437i | \(0.980079\pi\) | |||||||
\(444\) | 8708.50 | 0.930827 | ||||||||
\(445\) | − | 6363.72i | − | 0.677908i | ||||||
\(446\) | 4466.41i | 0.474194i | ||||||||
\(447\) | − | 745.285i | − | 0.0788608i | ||||||
\(448\) | 12978.4 | 1.36868 | ||||||||
\(449\) | − | 17012.4i | − | 1.78811i | −0.447953 | − | 0.894057i | \(-0.647847\pi\) | ||
0.447953 | − | 0.894057i | \(-0.352153\pi\) | |||||||
\(450\) | 14085.7i | 1.47557i | ||||||||
\(451\) | 11226.7 | 1.17217 | ||||||||
\(452\) | 10981.5i | 1.14276i | ||||||||
\(453\) | − | 1803.63i | − | 0.187068i | ||||||
\(454\) | 32398.5i | 3.34920i | ||||||||
\(455\) | −6819.61 | −0.702655 | ||||||||
\(456\) | − | 6706.70i | − | 0.688750i | ||||||
\(457\) | 10704.5 | 1.09570 | 0.547851 | − | 0.836576i | \(-0.315446\pi\) | ||||
0.547851 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(458\) | −32878.4 | −3.35439 | ||||||||
\(459\) | 4014.48 | 0.408235 | ||||||||
\(460\) | −8805.92 | −0.892561 | ||||||||
\(461\) | − | 4080.29i | − | 0.412230i | −0.978528 | − | 0.206115i | \(-0.933918\pi\) | ||
0.978528 | − | 0.206115i | \(-0.0660822\pi\) | |||||||
\(462\) | 4134.96i | 0.416398i | ||||||||
\(463\) | 12486.5 | 1.25334 | 0.626671 | − | 0.779284i | \(-0.284417\pi\) | ||||
0.626671 | + | 0.779284i | \(0.284417\pi\) | |||||||
\(464\) | −22894.5 | − | 14720.4i | −2.29063 | − | 1.47280i | ||||
\(465\) | 3411.74 | 0.340249 | ||||||||
\(466\) | − | 20175.2i | − | 2.00558i | ||||||
\(467\) | − | 11387.4i | − | 1.12836i | −0.825652 | − | 0.564180i | \(-0.809192\pi\) | ||
0.825652 | − | 0.564180i | \(-0.190808\pi\) | |||||||
\(468\) | −14404.8 | −1.42278 | ||||||||
\(469\) | 11877.1 | 1.16937 | ||||||||
\(470\) | −5216.92 | −0.511997 | ||||||||
\(471\) | −2604.73 | −0.254819 | ||||||||
\(472\) | 5329.85i | 0.519759i | ||||||||
\(473\) | −11819.6 | −1.14897 | ||||||||
\(474\) | − | 450.122i | − | 0.0436177i | ||||||
\(475\) | − | 9943.09i | − | 0.960464i | ||||||
\(476\) | − | 22143.6i | − | 2.13225i | ||||||
\(477\) | −3213.52 | −0.308463 | ||||||||
\(478\) | 3090.93i | 0.295766i | ||||||||
\(479\) | 4606.66i | 0.439423i | 0.975565 | + | 0.219711i | \(0.0705116\pi\) | ||||
−0.975565 | + | 0.219711i | \(0.929488\pi\) | |||||||
\(480\) | −6941.01 | −0.660026 | ||||||||
\(481\) | 11079.4i | 1.05027i | ||||||||
\(482\) | − | 6853.64i | − | 0.647665i | ||||||
\(483\) | − | 519.555i | − | 0.0489452i | ||||||
\(484\) | 12038.2 | 1.13056 | ||||||||
\(485\) | 17696.8i | 1.65685i | ||||||||
\(486\) | −12002.4 | −1.12025 | ||||||||
\(487\) | 12954.0 | 1.20535 | 0.602673 | − | 0.797988i | \(-0.294102\pi\) | ||||
0.602673 | + | 0.797988i | \(0.294102\pi\) | |||||||
\(488\) | −6969.19 | −0.646476 | ||||||||
\(489\) | −246.663 | −0.0228109 | ||||||||
\(490\) | − | 6664.66i | − | 0.614446i | ||||||
\(491\) | 15855.1i | 1.45730i | 0.684889 | + | 0.728648i | \(0.259851\pi\) | ||||
−0.684889 | + | 0.728648i | \(0.740149\pi\) | |||||||
\(492\) | −5619.84 | −0.514963 | ||||||||
\(493\) | −5819.78 | + | 9051.44i | −0.531663 | + | 0.826889i | ||||
\(494\) | 14246.6 | 1.29754 | ||||||||
\(495\) | 17135.5i | 1.55593i | ||||||||
\(496\) | − | 35649.4i | − | 3.22723i | ||||||
\(497\) | 326.728 | 0.0294885 | ||||||||
\(498\) | 1039.96 | 0.0935777 | ||||||||
\(499\) | −5174.21 | −0.464188 | −0.232094 | − | 0.972693i | \(-0.574558\pi\) | ||||
−0.232094 | + | 0.972693i | \(0.574558\pi\) | |||||||
\(500\) | 6525.96 | 0.583700 | ||||||||
\(501\) | − | 3739.03i | − | 0.333429i | ||||||
\(502\) | 36203.9 | 3.21884 | ||||||||
\(503\) | − | 14427.3i | − | 1.27889i | −0.768835 | − | 0.639447i | \(-0.779163\pi\) | ||
0.768835 | − | 0.639447i | \(-0.220837\pi\) | |||||||
\(504\) | 26232.5i | 2.31843i | ||||||||
\(505\) | 5940.98i | 0.523505i | ||||||||
\(506\) | −6792.98 | −0.596808 | ||||||||
\(507\) | − | 1558.99i | − | 0.136562i | ||||||
\(508\) | − | 15358.1i | − | 1.34135i | ||||||
\(509\) | −7950.93 | −0.692375 | −0.346187 | − | 0.938165i | \(-0.612524\pi\) | ||||
−0.346187 | + | 0.938165i | \(0.612524\pi\) | |||||||
\(510\) | 6075.88i | 0.527539i | ||||||||
\(511\) | 2244.40i | 0.194299i | ||||||||
\(512\) | − | 15529.1i | − | 1.34042i | ||||||
\(513\) | 5605.20 | 0.482408 | ||||||||
\(514\) | 25948.0i | 2.22669i | ||||||||
\(515\) | −2110.94 | −0.180620 | ||||||||
\(516\) | 5916.60 | 0.504775 | ||||||||
\(517\) | −2872.36 | −0.244345 | ||||||||
\(518\) | 33688.2 | 2.85748 | ||||||||
\(519\) | 1787.90i | 0.151214i | ||||||||
\(520\) | − | 26732.0i | − | 2.25438i | ||||||
\(521\) | 1504.77 | 0.126536 | 0.0632680 | − | 0.997997i | \(-0.479848\pi\) | ||||
0.0632680 | + | 0.997997i | \(0.479848\pi\) | |||||||
\(522\) | 11511.3 | − | 17903.4i | 0.965205 | − | 1.50117i | ||||
\(523\) | 5742.09 | 0.480085 | 0.240042 | − | 0.970762i | \(-0.422839\pi\) | ||||
0.240042 | + | 0.970762i | \(0.422839\pi\) | |||||||
\(524\) | 46386.7i | 3.86720i | ||||||||
\(525\) | − | 1837.92i | − | 0.152787i | ||||||
\(526\) | 28985.7 | 2.40273 | ||||||||
\(527\) | −14094.1 | −1.16499 | ||||||||
\(528\) | −8461.51 | −0.697424 | ||||||||
\(529\) | −11313.5 | −0.929848 | ||||||||
\(530\) | − | 9957.10i | − | 0.816055i | ||||||
\(531\) | −2175.83 | −0.177821 | ||||||||
\(532\) | − | 30917.8i | − | 2.51966i | ||||||
\(533\) | − | 7149.87i | − | 0.581041i | ||||||
\(534\) | 2457.35i | 0.199138i | ||||||||
\(535\) | 14967.3 | 1.20952 | ||||||||
\(536\) | 46556.9i | 3.75178i | ||||||||
\(537\) | 4326.26i | 0.347657i | ||||||||
\(538\) | −17561.5 | −1.40731 | ||||||||
\(539\) | − | 3669.46i | − | 0.293237i | ||||||
\(540\) | − | 17560.6i | − | 1.39942i | ||||||
\(541\) | 24646.5i | 1.95866i | 0.202270 | + | 0.979330i | \(0.435168\pi\) | ||||
−0.202270 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(542\) | −19414.2 | −1.53858 | ||||||||
\(543\) | − | 1830.91i | − | 0.144700i | ||||||
\(544\) | 28673.8 | 2.25989 | ||||||||
\(545\) | 20118.1 | 1.58122 | ||||||||
\(546\) | 2633.39 | 0.206408 | ||||||||
\(547\) | −13689.9 | −1.07009 | −0.535045 | − | 0.844823i | \(-0.679705\pi\) | ||||
−0.535045 | + | 0.844823i | \(0.679705\pi\) | |||||||
\(548\) | − | 28355.8i | − | 2.21040i | ||||||
\(549\) | − | 2845.06i | − | 0.221173i | ||||||
\(550\) | −24030.1 | −1.86300 | ||||||||
\(551\) | −8125.83 | + | 12638.0i | −0.628262 | + | 0.977128i | ||||
\(552\) | 2036.59 | 0.157034 | ||||||||
\(553\) | − | 1242.80i | − | 0.0955685i | ||||||
\(554\) | − | 17298.1i | − | 1.32658i | ||||||
\(555\) | −6597.48 | −0.504590 | ||||||||
\(556\) | −47252.4 | −3.60423 | ||||||||
\(557\) | 6626.46 | 0.504079 | 0.252040 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252040 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(558\) | 27877.7 | 2.11498 | ||||||||
\(559\) | 7527.42i | 0.569546i | ||||||||
\(560\) | −42432.2 | −3.20194 | ||||||||
\(561\) | 3345.29i | 0.251762i | ||||||||
\(562\) | 1982.35i | 0.148791i | ||||||||
\(563\) | − | 9393.71i | − | 0.703193i | −0.936152 | − | 0.351597i | \(-0.885639\pi\) | ||
0.936152 | − | 0.351597i | \(-0.114361\pi\) | |||||||
\(564\) | 1437.84 | 0.107347 | ||||||||
\(565\) | − | 8319.49i | − | 0.619476i | ||||||
\(566\) | 18457.7i | 1.37073i | ||||||||
\(567\) | −10179.0 | −0.753928 | ||||||||
\(568\) | 1280.73i | 0.0946099i | ||||||||
\(569\) | − | 16343.1i | − | 1.20411i | −0.798454 | − | 0.602056i | \(-0.794348\pi\) | ||
0.798454 | − | 0.602056i | \(-0.205652\pi\) | |||||||
\(570\) | 8483.41i | 0.623388i | ||||||||
\(571\) | 6948.21 | 0.509236 | 0.254618 | − | 0.967042i | \(-0.418050\pi\) | ||||
0.254618 | + | 0.967042i | \(0.418050\pi\) | |||||||
\(572\) | − | 24574.4i | − | 1.79634i | ||||||
\(573\) | −2111.65 | −0.153953 | ||||||||
\(574\) | −21739.9 | −1.58085 | ||||||||
\(575\) | 3019.37 | 0.218985 | ||||||||
\(576\) | −20768.3 | −1.50234 | ||||||||
\(577\) | − | 4998.50i | − | 0.360642i | −0.983608 | − | 0.180321i | \(-0.942286\pi\) | ||
0.983608 | − | 0.180321i | \(-0.0577136\pi\) | |||||||
\(578\) | 872.367i | 0.0627780i | ||||||||
\(579\) | 3554.33 | 0.255117 | ||||||||
\(580\) | 39593.8 | + | 25457.5i | 2.83456 | + | 1.82253i | ||||
\(581\) | 2871.37 | 0.205034 | ||||||||
\(582\) | − | 6833.64i | − | 0.486707i | ||||||
\(583\) | − | 5482.24i | − | 0.389453i | ||||||
\(584\) | −8797.78 | −0.623382 | ||||||||
\(585\) | 10912.9 | 0.771271 | ||||||||
\(586\) | 22246.8 | 1.56827 | ||||||||
\(587\) | 3270.44 | 0.229958 | 0.114979 | − | 0.993368i | \(-0.463320\pi\) | ||||
0.114979 | + | 0.993368i | \(0.463320\pi\) | |||||||
\(588\) | 1836.85i | 0.128827i | ||||||||
\(589\) | −19678.9 | −1.37666 | ||||||||
\(590\) | − | 6741.82i | − | 0.470434i | ||||||
\(591\) | − | 3990.70i | − | 0.277759i | ||||||
\(592\) | 68937.3i | 4.78599i | ||||||||
\(593\) | −18552.1 | −1.28473 | −0.642363 | − | 0.766401i | \(-0.722046\pi\) | ||||
−0.642363 | + | 0.766401i | \(0.722046\pi\) | |||||||
\(594\) | − | 13546.5i | − | 0.935720i | ||||||
\(595\) | 16775.8i | 1.15586i | ||||||||
\(596\) | 13467.7 | 0.925605 | ||||||||
\(597\) | − | 4292.07i | − | 0.294242i | ||||||
\(598\) | 4326.18i | 0.295837i | ||||||||
\(599\) | − | 3093.91i | − | 0.211041i | −0.994417 | − | 0.105521i | \(-0.966349\pi\) | ||
0.994417 | − | 0.105521i | \(-0.0336509\pi\) | |||||||
\(600\) | 7204.42 | 0.490199 | ||||||||
\(601\) | − | 18480.1i | − | 1.25428i | −0.778908 | − | 0.627138i | \(-0.784226\pi\) | ||
0.778908 | − | 0.627138i | \(-0.215774\pi\) | |||||||
\(602\) | 22887.9 | 1.54957 | ||||||||
\(603\) | −19006.1 | −1.28357 | ||||||||
\(604\) | 32592.6 | 2.19565 | ||||||||
\(605\) | −9120.01 | −0.612861 | ||||||||
\(606\) | − | 2294.11i | − | 0.153782i | ||||||
\(607\) | − | 25620.3i | − | 1.71317i | −0.516005 | − | 0.856586i | \(-0.672581\pi\) | ||
0.516005 | − | 0.856586i | \(-0.327419\pi\) | |||||||
\(608\) | 40035.6 | 2.67049 | ||||||||
\(609\) | −1502.01 | + | 2336.06i | −0.0999418 | + | 0.155438i | ||||
\(610\) | 8815.44 | 0.585126 | ||||||||
\(611\) | 1829.29i | 0.121122i | ||||||||
\(612\) | 35434.8i | 2.34047i | ||||||||
\(613\) | −17878.4 | −1.17798 | −0.588990 | − | 0.808140i | \(-0.700474\pi\) | ||||
−0.588990 | + | 0.808140i | \(0.700474\pi\) | |||||||
\(614\) | −23357.6 | −1.53524 | ||||||||
\(615\) | 4257.54 | 0.279155 | ||||||||
\(616\) | −44752.4 | −2.92715 | ||||||||
\(617\) | 11940.2i | 0.779086i | 0.921008 | + | 0.389543i | \(0.127367\pi\) | ||||
−0.921008 | + | 0.389543i | \(0.872633\pi\) | |||||||
\(618\) | 815.140 | 0.0530578 | ||||||||
\(619\) | − | 1604.39i | − | 0.104177i | −0.998642 | − | 0.0520886i | \(-0.983412\pi\) | ||
0.998642 | − | 0.0520886i | \(-0.0165878\pi\) | |||||||
\(620\) | 61652.2i | 3.99357i | ||||||||
\(621\) | 1702.10i | 0.109989i | ||||||||
\(622\) | −24364.3 | −1.57061 | ||||||||
\(623\) | 6784.84i | 0.436322i | ||||||||
\(624\) | 5388.80i | 0.345713i | ||||||||
\(625\) | −17862.6 | −1.14321 | ||||||||
\(626\) | − | 23058.8i | − | 1.47223i | ||||||
\(627\) | 4670.85i | 0.297505i | ||||||||
\(628\) | − | 47069.0i | − | 2.99086i | ||||||
\(629\) | 27254.6 | 1.72769 | ||||||||
\(630\) | − | 33181.9i | − | 2.09841i | ||||||
\(631\) | 25956.1 | 1.63755 | 0.818775 | − | 0.574115i | \(-0.194654\pi\) | ||||
0.818775 | + | 0.574115i | \(0.194654\pi\) | |||||||
\(632\) | 4871.64 | 0.306619 | ||||||||
\(633\) | 3297.03 | 0.207022 | ||||||||
\(634\) | 9413.97 | 0.589711 | ||||||||
\(635\) | 11635.2i | 0.727130i | ||||||||
\(636\) | 2744.28i | 0.171097i | ||||||||
\(637\) | −2336.94 | −0.145358 | ||||||||
\(638\) | 30543.1 | + | 19638.2i | 1.89532 | + | 1.21863i | ||||
\(639\) | −522.840 | −0.0323681 | ||||||||
\(640\) | − | 14044.8i | − | 0.867451i | ||||||
\(641\) | 9646.69i | 0.594417i | 0.954813 | + | 0.297209i | \(0.0960557\pi\) | ||||
−0.954813 | + | 0.297209i | \(0.903944\pi\) | |||||||
\(642\) | −5779.61 | −0.355300 | ||||||||
\(643\) | 2551.86 | 0.156509 | 0.0782546 | − | 0.996933i | \(-0.475065\pi\) | ||||
0.0782546 | + | 0.996933i | \(0.475065\pi\) | |||||||
\(644\) | 9388.66 | 0.574480 | ||||||||
\(645\) | −4482.36 | −0.273632 | ||||||||
\(646\) | − | 35045.6i | − | 2.13444i | ||||||
\(647\) | 6430.59 | 0.390746 | 0.195373 | − | 0.980729i | \(-0.437408\pi\) | ||||
0.195373 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(648\) | − | 39900.4i | − | 2.41888i | ||||||
\(649\) | − | 3711.95i | − | 0.224510i | ||||||
\(650\) | 15303.8i | 0.923486i | ||||||||
\(651\) | −3637.52 | −0.218995 | ||||||||
\(652\) | − | 4457.35i | − | 0.267735i | ||||||
\(653\) | 21430.7i | 1.28430i | 0.766580 | + | 0.642149i | \(0.221957\pi\) | ||||
−0.766580 | + | 0.642149i | \(0.778043\pi\) | |||||||
\(654\) | −7768.60 | −0.464489 | ||||||||
\(655\) | − | 35142.1i | − | 2.09636i | ||||||
\(656\) | − | 44487.1i | − | 2.64776i | ||||||
\(657\) | − | 3591.56i | − | 0.213272i | ||||||
\(658\) | 5562.16 | 0.329537 | ||||||||
\(659\) | − | 23348.6i | − | 1.38017i | −0.723729 | − | 0.690084i | \(-0.757574\pi\) | ||
0.723729 | − | 0.690084i | \(-0.242426\pi\) | |||||||
\(660\) | 14633.4 | 0.863035 | ||||||||
\(661\) | 8442.89 | 0.496808 | 0.248404 | − | 0.968656i | \(-0.420094\pi\) | ||||
0.248404 | + | 0.968656i | \(0.420094\pi\) | |||||||
\(662\) | −14027.7 | −0.823565 | ||||||||
\(663\) | 2130.49 | 0.124798 | ||||||||
\(664\) | 11255.4i | 0.657823i | ||||||||
\(665\) | 23423.1i | 1.36588i | ||||||||
\(666\) | −53908.7 | −3.13652 | ||||||||
\(667\) | −3837.72 | − | 2467.53i | −0.222784 | − | 0.143243i | ||||
\(668\) | 67566.5 | 3.91351 | ||||||||
\(669\) | 932.584i | 0.0538950i | ||||||||
\(670\) | − | 58890.6i | − | 3.39574i | ||||||
\(671\) | 4853.65 | 0.279245 | ||||||||
\(672\) | 7400.34 | 0.424813 | ||||||||
\(673\) | −17804.0 | −1.01975 | −0.509875 | − | 0.860248i | \(-0.670308\pi\) | ||||
−0.509875 | + | 0.860248i | \(0.670308\pi\) | |||||||
\(674\) | −38508.2 | −2.20071 | ||||||||
\(675\) | 6021.17i | 0.343341i | ||||||||
\(676\) | 28171.8 | 1.60286 | ||||||||
\(677\) | 18135.2i | 1.02953i | 0.857330 | + | 0.514766i | \(0.172121\pi\) | ||||
−0.857330 | + | 0.514766i | \(0.827879\pi\) | |||||||
\(678\) | 3212.57i | 0.181974i | ||||||||
\(679\) | − | 18868.0i | − | 1.06640i | ||||||
\(680\) | −65758.9 | −3.70844 | ||||||||
\(681\) | 6764.79i | 0.380657i | ||||||||
\(682\) | 47559.2i | 2.67029i | ||||||||
\(683\) | 24553.7 | 1.37558 | 0.687789 | − | 0.725911i | \(-0.258581\pi\) | ||||
0.687789 | + | 0.725911i | \(0.258581\pi\) | |||||||
\(684\) | 49475.5i | 2.76571i | ||||||||
\(685\) | 21482.1i | 1.19823i | ||||||||
\(686\) | 36319.3i | 2.02140i | ||||||||
\(687\) | −6865.00 | −0.381246 | ||||||||
\(688\) | 46836.3i | 2.59537i | ||||||||
\(689\) | −3491.42 | −0.193052 | ||||||||
\(690\) | −2576.12 | −0.142132 | ||||||||
\(691\) | 9633.82 | 0.530373 | 0.265187 | − | 0.964197i | \(-0.414566\pi\) | ||||
0.265187 | + | 0.964197i | \(0.414566\pi\) | |||||||
\(692\) | −32308.4 | −1.77483 | ||||||||
\(693\) | − | 18269.5i | − | 1.00144i | ||||||
\(694\) | − | 29112.0i | − | 1.59233i | ||||||
\(695\) | 35798.0 | 1.95381 | ||||||||
\(696\) | −9157.07 | − | 5887.70i | −0.498704 | − | 0.320650i | ||||
\(697\) | −17588.2 | −0.955810 | ||||||||
\(698\) | 6221.34i | 0.337365i | ||||||||
\(699\) | − | 4212.57i | − | 0.227946i | ||||||
\(700\) | 33212.3 | 1.79330 | ||||||||
\(701\) | −3582.74 | −0.193036 | −0.0965180 | − | 0.995331i | \(-0.530771\pi\) | ||||
−0.0965180 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(702\) | −8627.20 | −0.463836 | ||||||||
\(703\) | 38054.1 | 2.04159 | ||||||||
\(704\) | − | 35430.6i | − | 1.89679i | ||||||
\(705\) | −1089.29 | −0.0581916 | ||||||||
\(706\) | 46978.1i | 2.50431i | ||||||||
\(707\) | − | 6334.13i | − | 0.336944i | ||||||
\(708\) | 1858.11i | 0.0986330i | ||||||||
\(709\) | 16096.5 | 0.852631 | 0.426315 | − | 0.904575i | \(-0.359811\pi\) | ||||
0.426315 | + | 0.904575i | \(0.359811\pi\) | |||||||
\(710\) | − | 1620.02i | − | 0.0856315i | ||||||
\(711\) | 1988.77i | 0.104901i | ||||||||
\(712\) | −26595.7 | −1.39988 | ||||||||
\(713\) | − | 5975.78i | − | 0.313878i | ||||||
\(714\) | − | 6477.96i | − | 0.339540i | ||||||
\(715\) | 18617.4i | 0.973776i | ||||||||
\(716\) | −78178.1 | −4.08052 | ||||||||
\(717\) | 645.385i | 0.0336156i | ||||||||
\(718\) | −53027.0 | −2.75620 | ||||||||
\(719\) | 11121.1 | 0.576837 | 0.288419 | − | 0.957504i | \(-0.406871\pi\) | ||||
0.288419 | + | 0.957504i | \(0.406871\pi\) | |||||||
\(720\) | 67901.2 | 3.51462 | ||||||||
\(721\) | 2250.63 | 0.116252 | ||||||||
\(722\) | − | 12672.5i | − | 0.653215i | ||||||
\(723\) | − | 1431.04i | − | 0.0736111i | ||||||
\(724\) | 33085.7 | 1.69837 | ||||||||
\(725\) | −13575.9 | − | 8728.87i | −0.695444 | − | 0.447148i | ||||
\(726\) | 3521.69 | 0.180031 | ||||||||
\(727\) | 16605.7i | 0.847139i | 0.905864 | + | 0.423569i | \(0.139223\pi\) | ||||
−0.905864 | + | 0.423569i | \(0.860777\pi\) | |||||||
\(728\) | 28501.0i | 1.45099i | ||||||||
\(729\) | 14552.4 | 0.739337 | ||||||||
\(730\) | 11128.5 | 0.564223 | ||||||||
\(731\) | 18516.9 | 0.936900 | ||||||||
\(732\) | −2429.62 | −0.122680 | ||||||||
\(733\) | 31570.9i | 1.59086i | 0.606047 | + | 0.795429i | \(0.292754\pi\) | ||||
−0.606047 | + | 0.795429i | \(0.707246\pi\) | |||||||
\(734\) | −19866.1 | −0.999005 | ||||||||
\(735\) | − | 1391.58i | − | 0.0698355i | ||||||
\(736\) | 12157.4i | 0.608870i | ||||||||
\(737\) | − | 32424.3i | − | 1.62058i | ||||||
\(738\) | 34788.8 | 1.73522 | ||||||||
\(739\) | 18181.6i | 0.905036i | 0.891755 | + | 0.452518i | \(0.149474\pi\) | ||||
−0.891755 | + | 0.452518i | \(0.850526\pi\) | |||||||
\(740\) | − | 119220.i | − | 5.92247i | ||||||
\(741\) | 2974.68 | 0.147473 | ||||||||
\(742\) | 10616.0i | 0.525238i | ||||||||
\(743\) | − | 5488.34i | − | 0.270993i | −0.990778 | − | 0.135496i | \(-0.956737\pi\) | ||
0.990778 | − | 0.135496i | \(-0.0432629\pi\) | |||||||
\(744\) | − | 14258.6i | − | 0.702616i | ||||||
\(745\) | −10203.0 | −0.501759 | ||||||||
\(746\) | 57715.2i | 2.83258i | ||||||||
\(747\) | −4594.84 | −0.225056 | ||||||||
\(748\) | −60451.4 | −2.95498 | ||||||||
\(749\) | −15957.7 | −0.778482 | ||||||||
\(750\) | 1909.13 | 0.0929487 | ||||||||
\(751\) | − | 3778.15i | − | 0.183577i | −0.995779 | − | 0.0917887i | \(-0.970742\pi\) | ||
0.995779 | − | 0.0917887i | \(-0.0292584\pi\) | |||||||
\(752\) | 11382.0i | 0.551942i | ||||||||
\(753\) | 7559.36 | 0.365841 | ||||||||
\(754\) | 12506.8 | − | 19451.7i | 0.604074 | − | 0.939509i | ||||
\(755\) | −24691.9 | −1.19024 | ||||||||
\(756\) | 18722.7i | 0.900712i | ||||||||
\(757\) | − | 34334.1i | − | 1.64847i | −0.566247 | − | 0.824236i | \(-0.691605\pi\) | ||
0.566247 | − | 0.824236i | \(-0.308395\pi\) | |||||||
\(758\) | 25621.1 | 1.22771 | ||||||||
\(759\) | −1418.37 | −0.0678309 | ||||||||
\(760\) | −91815.5 | −4.38223 | ||||||||
\(761\) | −16919.9 | −0.805974 | −0.402987 | − | 0.915206i | \(-0.632028\pi\) | ||||
−0.402987 | + | 0.915206i | \(0.632028\pi\) | |||||||
\(762\) | − | 4492.92i | − | 0.213598i | ||||||
\(763\) | −21449.4 | −1.01772 | ||||||||
\(764\) | − | 38158.7i | − | 1.80698i | ||||||
\(765\) | − | 26845.0i | − | 1.26874i | ||||||
\(766\) | − | 22780.3i | − | 1.07453i | ||||||
\(767\) | −2363.99 | −0.111289 | ||||||||
\(768\) | − | 1689.96i | − | 0.0794025i | ||||||
\(769\) | 15516.6i | 0.727623i | 0.931473 | + | 0.363811i | \(0.118525\pi\) | ||||
−0.931473 | + | 0.363811i | \(0.881475\pi\) | |||||||
\(770\) | 56608.0 | 2.64937 | ||||||||
\(771\) | 5417.93i | 0.253077i | ||||||||
\(772\) | 64228.8i | 2.99436i | ||||||||
\(773\) | 13036.6i | 0.606588i | 0.952897 | + | 0.303294i | \(0.0980865\pi\) | ||||
−0.952897 | + | 0.303294i | \(0.901914\pi\) | |||||||
\(774\) | −36625.9 | −1.70089 | ||||||||
\(775\) | − | 21139.3i | − | 0.979801i | ||||||
\(776\) | 73960.0 | 3.42141 | ||||||||
\(777\) | 7034.07 | 0.324770 | ||||||||
\(778\) | −2079.74 | −0.0958384 | ||||||||
\(779\) | −24557.4 | −1.12947 | ||||||||
\(780\) | − | 9319.41i | − | 0.427806i | ||||||
\(781\) | − | 891.961i | − | 0.0408667i | ||||||
\(782\) | 10642.1 | 0.486651 | ||||||||
\(783\) | 4920.71 | − | 7653.12i | 0.224587 | − | 0.349298i | ||||
\(784\) | −14540.6 | −0.662383 | ||||||||
\(785\) | 35659.1i | 1.62131i | ||||||||
\(786\) | 13570.1i | 0.615815i | ||||||||
\(787\) | −14835.9 | −0.671975 | −0.335987 | − | 0.941867i | \(-0.609070\pi\) | ||||
−0.335987 | + | 0.941867i | \(0.609070\pi\) | |||||||
\(788\) | 72114.3 | 3.26011 | ||||||||
\(789\) | 6052.21 | 0.273085 | ||||||||
\(790\) | −6162.21 | −0.277521 | ||||||||
\(791\) | 8870.05i | 0.398714i | ||||||||
\(792\) | 71614.0 | 3.21300 | ||||||||
\(793\) | − | 3091.10i | − | 0.138421i | ||||||
\(794\) | − | 59945.4i | − | 2.67932i | ||||||
\(795\) | − | 2079.04i | − | 0.0927495i | ||||||
\(796\) | 77560.2 | 3.45358 | ||||||||
\(797\) | − | 38449.3i | − | 1.70884i | −0.519583 | − | 0.854420i | \(-0.673913\pi\) | ||
0.519583 | − | 0.854420i | \(-0.326087\pi\) | |||||||
\(798\) | − | 9044.81i | − | 0.401232i | ||||||
\(799\) | 4499.94 | 0.199245 | ||||||||
\(800\) | 43006.7i | 1.90065i | ||||||||
\(801\) | − | 10857.3i | − | 0.478931i | ||||||
\(802\) | 20432.5i | 0.899621i | ||||||||
\(803\) | 6127.17 | 0.269269 | ||||||||
\(804\) | 16230.8i | 0.711963i | ||||||||
\(805\) | −7112.76 | −0.311418 | ||||||||
\(806\) | 30288.6 | 1.32366 | ||||||||
\(807\) | −3666.83 | −0.159949 | ||||||||
\(808\) | 24829.0 | 1.08104 | ||||||||
\(809\) | − | 2871.72i | − | 0.124802i | −0.998051 | − | 0.0624008i | \(-0.980124\pi\) | ||
0.998051 | − | 0.0624008i | \(-0.0198757\pi\) | |||||||
\(810\) | 50470.6i | 2.18933i | ||||||||
\(811\) | −29135.9 | −1.26153 | −0.630764 | − | 0.775975i | \(-0.717258\pi\) | ||||
−0.630764 | + | 0.775975i | \(0.717258\pi\) | |||||||
\(812\) | −42214.0 | − | 27142.2i | −1.82441 | − | 1.17304i | ||||
\(813\) | −4053.67 | −0.174869 | ||||||||
\(814\) | − | 91967.9i | − | 3.96004i | ||||||
\(815\) | 3376.85i | 0.145136i | ||||||||
\(816\) | 13256.1 | 0.568695 | ||||||||
\(817\) | 25854.2 | 1.10713 | ||||||||
\(818\) | −72282.7 | −3.08962 | ||||||||
\(819\) | −11635.1 | −0.496414 | ||||||||
\(820\) | 76936.2i | 3.27650i | ||||||||
\(821\) | 46283.9 | 1.96750 | 0.983752 | − | 0.179534i | \(-0.0574589\pi\) | ||||
0.983752 | + | 0.179534i | \(0.0574589\pi\) | |||||||
\(822\) | − | 8295.30i | − | 0.351985i | ||||||
\(823\) | − | 1912.88i | − | 0.0810193i | −0.999179 | − | 0.0405097i | \(-0.987102\pi\) | ||
0.999179 | − | 0.0405097i | \(-0.0128982\pi\) | |||||||
\(824\) | 8822.21i | 0.372981i | ||||||||
\(825\) | −5017.48 | −0.211741 | ||||||||
\(826\) | 7187.97i | 0.302786i | ||||||||
\(827\) | 15268.9i | 0.642020i | 0.947076 | + | 0.321010i | \(0.104022\pi\) | ||||
−0.947076 | + | 0.321010i | \(0.895978\pi\) | |||||||
\(828\) | −15024.0 | −0.630579 | ||||||||
\(829\) | − | 18328.2i | − | 0.767873i | −0.923360 | − | 0.383936i | \(-0.874568\pi\) | ||
0.923360 | − | 0.383936i | \(-0.125432\pi\) | |||||||
\(830\) | − | 14237.2i | − | 0.595396i | ||||||
\(831\) | − | 3611.84i | − | 0.150774i | ||||||
\(832\) | −22564.4 | −0.940239 | ||||||||
\(833\) | 5748.70i | 0.239113i | ||||||||
\(834\) | −13823.4 | −0.573939 | ||||||||
\(835\) | −51187.8 | −2.12147 | ||||||||
\(836\) | −84404.9 | −3.49187 | ||||||||
\(837\) | 11916.8 | 0.492120 | ||||||||
\(838\) | 87198.1i | 3.59452i | ||||||||
\(839\) | 19835.2i | 0.816193i | 0.912939 | + | 0.408096i | \(0.133807\pi\) | ||||
−0.912939 | + | 0.408096i | \(0.866193\pi\) | |||||||
\(840\) | −16971.5 | −0.697111 | ||||||||
\(841\) | 10121.9 | + | 22189.4i | 0.415021 | + | 0.909812i | ||||
\(842\) | 74631.6 | 3.05460 | ||||||||
\(843\) | 413.914i | 0.0169110i | ||||||||
\(844\) | 59579.3i | 2.42986i | ||||||||
\(845\) | −21342.7 | −0.868888 | ||||||||
\(846\) | −8900.72 | −0.361718 | ||||||||
\(847\) | 9723.53 | 0.394456 | ||||||||
\(848\) | −21723.9 | −0.879720 | ||||||||
\(849\) | 3853.96i | 0.155792i | ||||||||
\(850\) | 37646.4 | 1.51913 | ||||||||
\(851\) | 11555.7i | 0.465481i | ||||||||
\(852\) | 446.494i | 0.0179538i | ||||||||
\(853\) | − | 19348.3i | − | 0.776639i | −0.921525 | − | 0.388320i | \(-0.873056\pi\) | ||
0.921525 | − | 0.388320i | \(-0.126944\pi\) | |||||||
\(854\) | −9398.81 | −0.376605 | ||||||||
\(855\) | − | 37482.2i | − | 1.49926i | ||||||
\(856\) | − | 62552.3i | − | 2.49766i | ||||||
\(857\) | −5065.74 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(858\) | − | 7189.10i | − | 0.286051i | ||||||
\(859\) | 15166.2i | 0.602403i | 0.953561 | + | 0.301201i | \(0.0973876\pi\) | ||||
−0.953561 | + | 0.301201i | \(0.902612\pi\) | |||||||
\(860\) | − | 80998.9i | − | 3.21167i | ||||||
\(861\) | −4539.28 | −0.179673 | ||||||||
\(862\) | − | 50708.1i | − | 2.00362i | ||||||
\(863\) | 1090.76 | 0.0430241 | 0.0215120 | − | 0.999769i | \(-0.493152\pi\) | ||||
0.0215120 | + | 0.999769i | \(0.493152\pi\) | |||||||
\(864\) | −24244.1 | −0.954630 | ||||||||
\(865\) | 24476.6 | 0.962114 | ||||||||
\(866\) | −24227.6 | −0.950679 | ||||||||
\(867\) | 182.150i | 0.00713510i | ||||||||
\(868\) | − | 65732.1i | − | 2.57038i | ||||||
\(869\) | −3392.83 | −0.132444 | ||||||||
\(870\) | 11582.9 | + | 7447.45i | 0.451377 | + | 0.290221i | ||||
\(871\) | −20649.8 | −0.803319 | ||||||||
\(872\) | − | 84079.0i | − | 3.26522i | ||||||
\(873\) | 30193.0i | 1.17054i | ||||||||
\(874\) | 14859.0 | 0.575071 | ||||||||
\(875\) | 5271.18 | 0.203655 | ||||||||
\(876\) | −3067.12 | −0.118297 | ||||||||
\(877\) | −29404.1 | −1.13216 | −0.566081 | − | 0.824350i | \(-0.691541\pi\) | ||||
−0.566081 | + | 0.824350i | \(0.691541\pi\) | |||||||
\(878\) | − | 16222.3i | − | 0.623550i | ||||||
\(879\) | 4645.11 | 0.178243 | ||||||||
\(880\) | 115839.i | 4.43742i | ||||||||
\(881\) | − | 17945.9i | − | 0.686279i | −0.939284 | − | 0.343140i | \(-0.888510\pi\) | ||
0.939284 | − | 0.343140i | \(-0.111490\pi\) | |||||||
\(882\) | − | 11370.7i | − | 0.434096i | ||||||
\(883\) | −2077.31 | −0.0791699 | −0.0395849 | − | 0.999216i | \(-0.512604\pi\) | ||||
−0.0395849 | + | 0.999216i | \(0.512604\pi\) | |||||||
\(884\) | 38499.1i | 1.46478i | ||||||||
\(885\) | − | 1407.69i | − | 0.0534677i | ||||||
\(886\) | −6165.70 | −0.233793 | ||||||||
\(887\) | 19087.8i | 0.722553i | 0.932459 | + | 0.361277i | \(0.117659\pi\) | ||||
−0.932459 | + | 0.361277i | \(0.882341\pi\) | |||||||
\(888\) | 27572.7i | 1.04198i | ||||||||
\(889\) | − | 12405.1i | − | 0.468004i | ||||||
\(890\) | 33641.4 | 1.26704 | ||||||||
\(891\) | 27788.4i | 1.04483i | ||||||||
\(892\) | −16852.3 | −0.632576 | ||||||||
\(893\) | 6283.01 | 0.235446 | ||||||||
\(894\) | 3939.90 | 0.147394 | ||||||||
\(895\) | 59227.0 | 2.21200 | ||||||||
\(896\) | 14974.2i | 0.558318i | ||||||||
\(897\) | 903.305i | 0.0336237i | ||||||||
\(898\) | 89934.8 | 3.34205 | ||||||||
\(899\) | −17275.7 | + | 26868.8i | −0.640910 | + | 0.996801i | ||||
\(900\) | −53147.2 | −1.96842 | ||||||||
\(901\) | 8588.65i | 0.317569i | ||||||||
\(902\) | 59349.4i | 2.19082i | ||||||||
\(903\) | 4778.99 | 0.176118 | ||||||||
\(904\) | −34769.5 | −1.27922 | ||||||||
\(905\) | −25065.4 | −0.920665 | ||||||||
\(906\) | 9534.76 | 0.349637 | ||||||||
\(907\) | − | 24351.0i | − | 0.891468i | −0.895166 | − | 0.445734i | \(-0.852943\pi\) | ||
0.895166 | − | 0.445734i | \(-0.147057\pi\) | |||||||
\(908\) | −122244. | −4.46784 | ||||||||
\(909\) | 10136.1i | 0.369848i | ||||||||
\(910\) | − | 36051.4i | − | 1.31329i | ||||||
\(911\) | 5244.81i | 0.190745i | 0.995442 | + | 0.0953723i | \(0.0304042\pi\) | ||||
−0.995442 | + | 0.0953723i | \(0.969596\pi\) | |||||||
\(912\) | 18508.7 | 0.672023 | ||||||||
\(913\) | − | 7838.77i | − | 0.284146i | ||||||
\(914\) | 56588.7i | 2.04791i | ||||||||
\(915\) | 1840.66 | 0.0665031 | ||||||||
\(916\) | − | 124055.i | − | 4.47476i | ||||||
\(917\) | 37467.7i | 1.34928i | ||||||||
\(918\) | 21222.3i | 0.763007i | ||||||||
\(919\) | −44920.3 | −1.61239 | −0.806195 | − | 0.591651i | \(-0.798477\pi\) | ||||
−0.806195 | + | 0.591651i | \(0.798477\pi\) | |||||||
\(920\) | − | 27881.1i | − | 0.999145i | ||||||
\(921\) | −4877.06 | −0.174489 | ||||||||
\(922\) | 21570.2 | 0.770474 | ||||||||
\(923\) | −568.055 | −0.0202576 | ||||||||
\(924\) | −15601.7 | −0.555476 | ||||||||
\(925\) | 40878.2i | 1.45305i | ||||||||
\(926\) | 66009.1i | 2.34254i | ||||||||
\(927\) | −3601.53 | −0.127605 | ||||||||
\(928\) | 35146.6 | − | 54663.1i | 1.24326 | − | 1.93362i | ||||
\(929\) | 23724.7 | 0.837870 | 0.418935 | − | 0.908016i | \(-0.362404\pi\) | ||||
0.418935 | + | 0.908016i | \(0.362404\pi\) | |||||||
\(930\) | 18036.0i | 0.635938i | ||||||||
\(931\) | 8026.59i | 0.282557i | ||||||||
\(932\) | 76123.7 | 2.67544 | ||||||||
\(933\) | −5087.24 | −0.178509 | ||||||||
\(934\) | 60198.6 | 2.10895 | ||||||||
\(935\) | 45797.4 | 1.60186 | ||||||||
\(936\) | − | 45608.1i | − | 1.59268i | ||||||
\(937\) | 11968.6 | 0.417288 | 0.208644 | − | 0.977992i | \(-0.433095\pi\) | ||||
0.208644 | + | 0.977992i | \(0.433095\pi\) | |||||||
\(938\) | 62787.8i | 2.18560i | ||||||||
\(939\) | − | 4814.66i | − | 0.167327i | ||||||
\(940\) | − | 19684.1i | − | 0.683006i | ||||||
\(941\) | 24728.4 | 0.856665 | 0.428333 | − | 0.903621i | \(-0.359101\pi\) | ||||
0.428333 | + | 0.903621i | \(0.359101\pi\) | |||||||
\(942\) | − | 13769.7i | − | 0.476266i | ||||||
\(943\) | − | 7457.21i | − | 0.257519i | ||||||
\(944\) | −14709.0 | −0.507136 | ||||||||
\(945\) | − | 14184.1i | − | 0.488265i | ||||||
\(946\) | − | 62483.5i | − | 2.14748i | ||||||
\(947\) | 22561.4i | 0.774177i | 0.922043 | + | 0.387089i | \(0.126519\pi\) | ||||
−0.922043 | + | 0.387089i | \(0.873481\pi\) | |||||||
\(948\) | 1698.37 | 0.0581861 | ||||||||
\(949\) | − | 3902.15i | − | 0.133477i | ||||||
\(950\) | 52563.5 | 1.79514 | ||||||||
\(951\) | 1965.63 | 0.0670242 | ||||||||
\(952\) | 70110.6 | 2.38687 | ||||||||
\(953\) | −2244.63 | −0.0762968 | −0.0381484 | − | 0.999272i | \(-0.512146\pi\) | ||||
−0.0381484 | + | 0.999272i | \(0.512146\pi\) | |||||||
\(954\) | − | 16988.1i | − | 0.576529i | ||||||
\(955\) | 28908.7i | 0.979542i | ||||||||
\(956\) | −11662.5 | −0.394552 | ||||||||
\(957\) | 6377.39 | + | 4100.46i | 0.215415 | + | 0.138505i | ||||
\(958\) | −24352.8 | −0.821298 | ||||||||
\(959\) | − | 22903.7i | − | 0.771218i | ||||||
\(960\) | − | 13436.4i | − | 0.451728i | ||||||
\(961\) | −12046.8 | −0.404377 | ||||||||
\(962\) | −58570.7 | −1.96299 | ||||||||
\(963\) | 25536.0 | 0.854503 | ||||||||
\(964\) | 25859.7 | 0.863987 | ||||||||
\(965\) | − | 48659.1i | − | 1.62320i | ||||||
\(966\) | 2746.59 | 0.0914805 | ||||||||
\(967\) | − | 12600.9i | − | 0.419047i | −0.977804 | − | 0.209524i | \(-0.932809\pi\) | ||
0.977804 | − | 0.209524i | \(-0.0671913\pi\) | |||||||
\(968\) | 38115.0i | 1.26556i | ||||||||
\(969\) | − | 7317.50i | − | 0.242592i | ||||||
\(970\) | −93553.3 | −3.09672 | ||||||||
\(971\) | − | 51444.9i | − | 1.70025i | −0.526577 | − | 0.850127i | \(-0.676525\pi\) | ||
0.526577 | − | 0.850127i | \(-0.323475\pi\) | |||||||
\(972\) | − | 45286.7i | − | 1.49441i | ||||||
\(973\) | −38167.0 | −1.25753 | ||||||||
\(974\) | 68480.7i | 2.25284i | ||||||||
\(975\) | 3195.43i | 0.104960i | ||||||||
\(976\) | − | 19233.1i | − | 0.630775i | ||||||
\(977\) | 52349.5 | 1.71424 | 0.857118 | − | 0.515120i | \(-0.172253\pi\) | ||||
0.857118 | + | 0.515120i | \(0.172253\pi\) | |||||||
\(978\) | − | 1303.97i | − | 0.0426344i | ||||||
\(979\) | 18522.5 | 0.604678 | ||||||||
\(980\) | 25146.6 | 0.819673 | ||||||||
\(981\) | 34323.9 | 1.11710 | ||||||||
\(982\) | −83817.1 | −2.72374 | ||||||||
\(983\) | − | 43551.4i | − | 1.41310i | −0.707665 | − | 0.706548i | \(-0.750251\pi\) | ||
0.707665 | − | 0.706548i | \(-0.249749\pi\) | |||||||
\(984\) | − | 17793.4i | − | 0.576457i | ||||||
\(985\) | −54633.1 | −1.76727 | ||||||||
\(986\) | −47849.9 | − | 30765.9i | −1.54549 | − | 0.993698i | ||||
\(987\) | 1161.38 | 0.0374539 | ||||||||
\(988\) | 53754.2i | 1.73092i | ||||||||
\(989\) | 7851.00i | 0.252424i | ||||||||
\(990\) | −90585.7 | −2.90808 | ||||||||
\(991\) | −13980.1 | −0.448126 | −0.224063 | − | 0.974575i | \(-0.571932\pi\) | ||||
−0.224063 | + | 0.974575i | \(0.571932\pi\) | |||||||
\(992\) | 85116.8 | 2.72425 | ||||||||
\(993\) | −2928.97 | −0.0936032 | ||||||||
\(994\) | 1727.23i | 0.0551151i | ||||||||
\(995\) | −58758.9 | −1.87214 | ||||||||
\(996\) | 3923.90i | 0.124833i | ||||||||
\(997\) | 25485.2i | 0.809553i | 0.914416 | + | 0.404776i | \(0.132651\pi\) | ||||
−0.914416 | + | 0.404776i | \(0.867349\pi\) | |||||||
\(998\) | − | 27353.2i | − | 0.867584i | ||||||
\(999\) | −23044.2 | −0.729815 |
(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 | 29.4.b.a.28.6 | yes | 6 | |
3.2 | odd | 2 | 261.4.c.c.28.1 | 6 | |||
4.3 | odd | 2 | 464.4.e.a.289.3 | 6 | |||
29.12 | odd | 4 | 841.4.a.c.1.1 | 6 | |||
29.17 | odd | 4 | 841.4.a.c.1.6 | 6 | |||
29.28 | even | 2 | inner | 29.4.b.a.28.1 | ✓ | 6 | |
87.86 | odd | 2 | 261.4.c.c.28.6 | 6 | |||
116.115 | odd | 2 | 464.4.e.a.289.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.b.a.28.1 | ✓ | 6 | 29.28 | even | 2 | inner | |
29.4.b.a.28.6 | yes | 6 | 1.1 | even | 1 | trivial | |
261.4.c.c.28.1 | 6 | 3.2 | odd | 2 | |||
261.4.c.c.28.6 | 6 | 87.86 | odd | 2 | |||
464.4.e.a.289.3 | 6 | 4.3 | odd | 2 | |||
464.4.e.a.289.4 | 6 | 116.115 | odd | 2 | |||
841.4.a.c.1.1 | 6 | 29.12 | odd | 4 | |||
841.4.a.c.1.6 | 6 | 29.17 | odd | 4 |