Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,4,Mod(37,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.f (of order \(5\), degree \(4\), 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: | \(11.6823781811\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 181.2 | ||
Root | \(2.22300 + 6.84169i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.181 |
Dual form | 198.4.f.d.163.2 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034 | + | 1.90211i | 0.218508 | + | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.23607 | + | 2.35114i | −0.404508 | + | 0.293893i | ||||
\(5\) | −1.67119 | + | 5.14341i | −0.149476 | + | 0.460041i | −0.997559 | − | 0.0698226i | \(-0.977757\pi\) |
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.9196 | − | 13.0193i | 0.967566 | − | 0.702978i | 0.0126708 | − | 0.999920i | \(-0.495967\pi\) |
0.954896 | + | 0.296942i | \(0.0959667\pi\) | |||||||
\(8\) | −6.47214 | − | 4.70228i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.8162 | −0.342038 | ||||||||
\(11\) | 11.0504 | + | 34.7691i | 0.302892 | + | 0.953025i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.7408 | + | 73.0668i | 0.506502 | + | 1.55885i | 0.798231 | + | 0.602351i | \(0.205769\pi\) |
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(14\) | 35.8392 | + | 26.0387i | 0.684173 | + | 0.497081i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.94427 | − | 15.2169i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −18.3211 | + | 56.3866i | −0.261384 | + | 0.804456i | 0.731121 | + | 0.682248i | \(0.238997\pi\) |
−0.992505 | + | 0.122208i | \(0.961003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −77.0690 | − | 55.9939i | −0.930571 | − | 0.676099i | 0.0155616 | − | 0.999879i | \(-0.495046\pi\) |
−0.946133 | + | 0.323780i | \(0.895046\pi\) | |||||||
\(20\) | −6.68478 | − | 20.5736i | −0.0747381 | − | 0.230020i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −59.3052 | + | 42.5075i | −0.574724 | + | 0.411938i | ||||
\(23\) | −142.484 | −1.29174 | −0.645868 | − | 0.763449i | \(-0.723505\pi\) | ||||
−0.645868 | + | 0.763449i | \(0.723505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 77.4654 | + | 56.2819i | 0.619723 | + | 0.450255i | ||||
\(26\) | −124.309 | + | 90.3155i | −0.937651 | + | 0.681243i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −27.3787 | + | 84.2629i | −0.184789 | + | 0.568721i | ||||
\(29\) | −16.5188 | + | 12.0016i | −0.105774 | + | 0.0768496i | −0.639415 | − | 0.768862i | \(-0.720823\pi\) |
0.533641 | + | 0.845711i | \(0.320823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 65.9146 | + | 202.864i | 0.381891 | + | 1.17534i | 0.938711 | + | 0.344706i | \(0.112021\pi\) |
−0.556820 | + | 0.830633i | \(0.687979\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −118.577 | −0.598110 | ||||||||
\(35\) | 37.0167 | + | 113.926i | 0.178770 | + | 0.550198i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 117.775 | − | 85.5683i | 0.523298 | − | 0.380199i | −0.294547 | − | 0.955637i | \(-0.595169\pi\) |
0.817845 | + | 0.575439i | \(0.195169\pi\) | |||||||
\(38\) | 58.8755 | − | 181.200i | 0.251339 | − | 0.773541i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 35.0020 | − | 25.4304i | 0.138357 | − | 0.100523i | ||||
\(41\) | 67.0130 | + | 48.6878i | 0.255260 | + | 0.185457i | 0.708055 | − | 0.706157i | \(-0.249573\pi\) |
−0.452795 | + | 0.891615i | \(0.649573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −151.373 | −0.536841 | −0.268420 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268420 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(44\) | −117.507 | − | 86.5342i | −0.402609 | − | 0.296489i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −88.0599 | − | 271.020i | −0.282255 | − | 0.868691i | ||||
\(47\) | 73.1063 | + | 53.1148i | 0.226886 | + | 0.164842i | 0.695421 | − | 0.718603i | \(-0.255218\pi\) |
−0.468535 | + | 0.883445i | \(0.655218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45.6154 | − | 140.390i | 0.132989 | − | 0.409300i | ||||
\(50\) | −59.1783 | + | 182.132i | −0.167381 | + | 0.515147i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −248.617 | − | 180.631i | −0.663019 | − | 0.481712i | ||||
\(53\) | 72.5723 | + | 223.355i | 0.188086 | + | 0.578870i | 0.999988 | − | 0.00492438i | \(-0.00156749\pi\) |
−0.811902 | + | 0.583794i | \(0.801567\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −197.299 | − | 1.26939i | −0.483705 | − | 0.00311208i | ||||
\(56\) | −177.199 | −0.422842 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −33.0375 | − | 24.0032i | −0.0747937 | − | 0.0543408i | ||||
\(59\) | 244.726 | − | 177.804i | 0.540009 | − | 0.392340i | −0.284079 | − | 0.958801i | \(-0.591688\pi\) |
0.824089 | + | 0.566461i | \(0.191688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46.1299 | + | 141.973i | −0.0968250 | + | 0.297997i | −0.987725 | − | 0.156203i | \(-0.950075\pi\) |
0.890900 | + | 0.454200i | \(0.150075\pi\) | |||||||
\(62\) | −345.133 | + | 250.754i | −0.706967 | + | 0.513642i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19.7771 | + | 60.8676i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −415.488 | −0.792845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 826.236 | 1.50658 | 0.753290 | − | 0.657689i | \(-0.228466\pi\) | ||||
0.753290 | + | 0.657689i | \(0.228466\pi\) | |||||||
\(68\) | −73.2844 | − | 225.546i | −0.130692 | − | 0.402228i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −193.822 | + | 140.820i | −0.330945 | + | 0.240445i | ||||
\(71\) | 277.796 | − | 854.967i | 0.464342 | − | 1.42910i | −0.395467 | − | 0.918480i | \(-0.629417\pi\) |
0.859808 | − | 0.510617i | \(-0.170583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 111.639 | − | 81.1105i | 0.178991 | − | 0.130045i | −0.494682 | − | 0.869074i | \(-0.664716\pi\) |
0.673673 | + | 0.739029i | \(0.264716\pi\) | |||||||
\(74\) | 235.549 | + | 171.137i | 0.370028 | + | 0.268841i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 381.050 | 0.575124 | ||||||||
\(77\) | 650.688 | + | 479.179i | 0.963024 | + | 0.709189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94.0829 | − | 289.557i | −0.133989 | − | 0.412377i | 0.861442 | − | 0.507856i | \(-0.169562\pi\) |
−0.995431 | + | 0.0954791i | \(0.969562\pi\) | |||||||
\(80\) | 70.0039 | + | 50.8608i | 0.0978335 | + | 0.0710802i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −51.1933 | + | 157.557i | −0.0689434 | + | 0.212186i | ||||
\(83\) | 236.180 | − | 726.886i | 0.312338 | − | 0.961279i | −0.664498 | − | 0.747290i | \(-0.731354\pi\) |
0.976836 | − | 0.213989i | \(-0.0686455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −259.401 | − | 188.466i | −0.331012 | − | 0.240494i | ||||
\(86\) | −93.5536 | − | 287.928i | −0.117304 | − | 0.361024i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 91.9746 | − | 276.992i | 0.111415 | − | 0.335539i | ||||
\(89\) | 313.100 | 0.372905 | 0.186452 | − | 0.982464i | \(-0.440301\pi\) | ||||
0.186452 | + | 0.982464i | \(0.440301\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1376.71 | + | 1000.24i | 1.58591 | + | 1.15223i | ||||
\(92\) | 461.088 | − | 335.000i | 0.522519 | − | 0.379632i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −55.8482 | + | 171.883i | −0.0612798 | + | 0.188600i | ||||
\(95\) | 416.797 | − | 302.821i | 0.450131 | − | 0.327040i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −180.004 | − | 553.996i | −0.188419 | − | 0.579894i | 0.811571 | − | 0.584253i | \(-0.198612\pi\) |
−0.999990 | + | 0.00435900i | \(0.998612\pi\) | |||||||
\(98\) | 295.229 | 0.304313 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −383.010 | −0.383010 | ||||||||
\(101\) | 43.7427 | + | 134.626i | 0.0430947 | + | 0.132632i | 0.970289 | − | 0.241949i | \(-0.0777867\pi\) |
−0.927194 | + | 0.374581i | \(0.877787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −680.691 | + | 494.551i | −0.651169 | + | 0.473102i | −0.863669 | − | 0.504059i | \(-0.831839\pi\) |
0.212500 | + | 0.977161i | \(0.431839\pi\) | |||||||
\(104\) | 189.927 | − | 584.534i | 0.179075 | − | 0.551137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −379.993 | + | 276.081i | −0.348191 | + | 0.252975i | ||||
\(107\) | −52.1265 | − | 37.8721i | −0.0470959 | − | 0.0342172i | 0.563988 | − | 0.825783i | \(-0.309266\pi\) |
−0.611084 | + | 0.791566i | \(0.709266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1559.04 | 1.36999 | 0.684995 | − | 0.728547i | \(-0.259804\pi\) | ||||
0.684995 | + | 0.728547i | \(0.259804\pi\) | |||||||
\(110\) | −119.523 | − | 376.069i | −0.103601 | − | 0.325971i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −109.515 | − | 337.052i | −0.0923944 | − | 0.284361i | ||||
\(113\) | −1811.50 | − | 1316.13i | −1.50807 | − | 1.09568i | −0.967024 | − | 0.254684i | \(-0.918029\pi\) |
−0.541046 | − | 0.840993i | \(-0.681971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 238.118 | − | 732.853i | 0.193084 | − | 0.594251i | ||||
\(116\) | 25.2384 | − | 77.6758i | 0.0202011 | − | 0.0621726i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 489.451 | + | 355.607i | 0.381844 | + | 0.277426i | ||||
\(119\) | 405.809 | + | 1248.95i | 0.312609 | + | 0.962111i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1086.78 | + | 768.422i | −0.816513 | + | 0.577327i | ||||
\(122\) | −298.559 | −0.221559 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −690.267 | − | 501.508i | −0.499901 | − | 0.363200i | ||||
\(125\) | −965.846 | + | 701.728i | −0.691103 | + | 0.502116i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 337.896 | − | 1039.94i | 0.236090 | − | 0.726611i | −0.760885 | − | 0.648887i | \(-0.775235\pi\) |
0.996975 | − | 0.0777237i | \(-0.0247652\pi\) | |||||||
\(128\) | −103.554 | + | 75.2365i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −256.786 | − | 790.305i | −0.173243 | − | 0.533187i | ||||
\(131\) | 2466.16 | 1.64481 | 0.822403 | − | 0.568906i | \(-0.192633\pi\) | ||||
0.822403 | + | 0.568906i | \(0.192633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2110.05 | −1.37567 | ||||||||
\(134\) | 510.642 | + | 1571.60i | 0.329200 | + | 1.01317i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 383.722 | − | 278.790i | 0.241940 | − | 0.175780i | ||||
\(137\) | 300.762 | − | 925.650i | 0.187561 | − | 0.577253i | −0.812422 | − | 0.583069i | \(-0.801852\pi\) |
0.999983 | + | 0.00581676i | \(0.00185154\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1021.82 | − | 742.396i | 0.623523 | − | 0.453016i | −0.230627 | − | 0.973042i | \(-0.574078\pi\) |
0.854150 | + | 0.520026i | \(0.174078\pi\) | |||||||
\(140\) | −387.644 | − | 281.640i | −0.234013 | − | 0.170021i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1797.93 | 1.06253 | ||||||||
\(143\) | −2278.12 | + | 1632.86i | −1.33221 | + | 0.954872i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −34.1230 | − | 105.020i | −0.0195432 | − | 0.0601477i | ||||
\(146\) | 223.278 | + | 162.221i | 0.126566 | + | 0.0919555i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −179.944 | + | 553.810i | −0.0999411 | + | 0.307587i | ||||
\(149\) | 151.214 | − | 465.390i | 0.0831407 | − | 0.255881i | −0.900841 | − | 0.434149i | \(-0.857049\pi\) |
0.983982 | + | 0.178268i | \(0.0570493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1381.62 | − | 1003.80i | −0.744600 | − | 0.540983i | 0.149549 | − | 0.988754i | \(-0.452218\pi\) |
−0.894148 | + | 0.447771i | \(0.852218\pi\) | |||||||
\(152\) | 235.502 | + | 724.801i | 0.125669 | + | 0.386770i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −509.305 | + | 1533.83i | −0.266500 | + | 0.802595i | ||||
\(155\) | −1153.57 | −0.597787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2072.48 | − | 1505.75i | −1.05352 | − | 0.765424i | −0.0806377 | − | 0.996743i | \(-0.525696\pi\) |
−0.972878 | + | 0.231320i | \(0.925696\pi\) | |||||||
\(158\) | 492.624 | − | 357.913i | 0.248045 | − | 0.180215i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −53.4782 | + | 164.589i | −0.0264239 | + | 0.0813244i | ||||
\(161\) | −2553.25 | + | 1855.05i | −1.24984 | + | 0.908063i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 561.202 | + | 1727.20i | 0.269673 | + | 0.829969i | 0.990580 | + | 0.136936i | \(0.0437256\pi\) |
−0.720907 | + | 0.693032i | \(0.756274\pi\) | |||||||
\(164\) | −331.330 | −0.157759 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1528.59 | 0.714707 | ||||||||
\(167\) | −117.094 | − | 360.379i | −0.0542576 | − | 0.166988i | 0.920256 | − | 0.391318i | \(-0.127981\pi\) |
−0.974513 | + | 0.224330i | \(0.927981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2997.71 | + | 2177.97i | −1.36446 | + | 0.991336i | ||||
\(170\) | 198.165 | − | 609.888i | 0.0894032 | − | 0.275155i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 489.853 | − | 355.899i | 0.217157 | − | 0.157773i | ||||
\(173\) | 41.0349 | + | 29.8136i | 0.0180337 | + | 0.0131022i | 0.596766 | − | 0.802416i | \(-0.296452\pi\) |
−0.578732 | + | 0.815518i | \(0.696452\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2120.90 | 0.916142 | ||||||||
\(176\) | 583.714 | + | 3.75552i | 0.249995 | + | 0.00160842i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 193.506 | + | 595.551i | 0.0814826 | + | 0.250778i | ||||
\(179\) | 16.8824 | + | 12.2658i | 0.00704944 | + | 0.00512172i | 0.591304 | − | 0.806448i | \(-0.298613\pi\) |
−0.584255 | + | 0.811570i | \(0.698613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −54.4344 | + | 167.532i | −0.0223540 | + | 0.0687985i | −0.961611 | − | 0.274416i | \(-0.911516\pi\) |
0.939257 | + | 0.343214i | \(0.111516\pi\) | |||||||
\(182\) | −1051.71 | + | 3236.83i | −0.428340 | + | 1.31830i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 922.175 | + | 669.999i | 0.369476 | + | 0.268440i | ||||
\(185\) | 243.288 | + | 748.765i | 0.0966861 | + | 0.297569i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2162.96 | − | 13.9161i | −0.845837 | − | 0.00544197i | ||||
\(188\) | −361.457 | −0.140223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 833.594 | + | 605.642i | 0.318291 | + | 0.231252i | ||||
\(191\) | −937.829 | + | 681.372i | −0.355282 | + | 0.258128i | −0.751082 | − | 0.660209i | \(-0.770468\pi\) |
0.395799 | + | 0.918337i | \(0.370468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −397.068 | + | 1222.05i | −0.148091 | + | 0.455777i | −0.997396 | − | 0.0721261i | \(-0.977022\pi\) |
0.849305 | + | 0.527903i | \(0.177022\pi\) | |||||||
\(194\) | 942.514 | − | 684.776i | 0.348807 | − | 0.253423i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 182.462 | + | 561.559i | 0.0664947 | + | 0.204650i | ||||
\(197\) | 2685.06 | 0.971078 | 0.485539 | − | 0.874215i | \(-0.338623\pi\) | ||||
0.485539 | + | 0.874215i | \(0.338623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1333.54 | −0.475036 | −0.237518 | − | 0.971383i | \(-0.576334\pi\) | ||||
−0.237518 | + | 0.971383i | \(0.576334\pi\) | |||||||
\(200\) | −236.713 | − | 728.528i | −0.0836907 | − | 0.257574i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −229.040 | + | 166.407i | −0.0797781 | + | 0.0579622i | ||||
\(203\) | −139.757 | + | 430.126i | −0.0483201 | + | 0.148714i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −362.413 | + | 263.308i | −0.123473 | + | 0.0897085i | ||||
\(206\) | −1361.38 | − | 989.102i | −0.460446 | − | 0.334534i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1229.23 | 0.409768 | ||||||||
\(209\) | 1095.22 | − | 3298.37i | 0.362477 | − | 1.09164i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −503.132 | − | 1548.48i | −0.164156 | − | 0.505221i | 0.834817 | − | 0.550528i | \(-0.185574\pi\) |
−0.998973 | + | 0.0453065i | \(0.985574\pi\) | |||||||
\(212\) | −759.987 | − | 552.163i | −0.246208 | − | 0.178881i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 39.8211 | − | 122.557i | 0.0127202 | − | 0.0391487i | ||||
\(215\) | 252.974 | − | 778.573i | 0.0802449 | − | 0.246968i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3822.32 | + | 2777.08i | 1.19574 | + | 0.868757i | ||||
\(218\) | 963.540 | + | 2965.47i | 0.299354 | + | 0.921317i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 641.457 | − | 459.770i | 0.196577 | − | 0.140899i | ||||
\(221\) | −4554.94 | −1.38642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2126.25 | + | 1544.81i | 0.638495 | + | 0.463894i | 0.859333 | − | 0.511416i | \(-0.170879\pi\) |
−0.220837 | + | 0.975311i | \(0.570879\pi\) | |||||||
\(224\) | 573.427 | − | 416.619i | 0.171043 | − | 0.124270i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1383.87 | − | 4259.10i | 0.407316 | − | 1.25359i | ||||
\(227\) | 1377.40 | − | 1000.74i | 0.402736 | − | 0.292605i | −0.367919 | − | 0.929858i | \(-0.619930\pi\) |
0.770654 | + | 0.637253i | \(0.219930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1667.44 | + | 5131.85i | 0.481168 | + | 1.48088i | 0.837455 | + | 0.546506i | \(0.184043\pi\) |
−0.356287 | + | 0.934377i | \(0.615957\pi\) | |||||||
\(230\) | 1541.13 | 0.441823 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 163.346 | 0.0462251 | ||||||||
\(233\) | 1870.85 | + | 5757.87i | 0.526022 | + | 1.61893i | 0.762286 | + | 0.647241i | \(0.224077\pi\) |
−0.236264 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −395.366 | + | 287.250i | −0.109748 | + | 0.0797368i | ||||
\(236\) | −373.907 | + | 1150.77i | −0.103133 | + | 0.317410i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2124.84 | + | 1543.79i | −0.578711 | + | 0.420458i | ||||
\(239\) | 2537.56 | + | 1843.65i | 0.686783 | + | 0.498977i | 0.875601 | − | 0.483035i | \(-0.160466\pi\) |
−0.188818 | + | 0.982012i | \(0.560466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6499.26 | −1.73715 | −0.868577 | − | 0.495555i | \(-0.834965\pi\) | ||||
−0.868577 | + | 0.495555i | \(0.834965\pi\) | |||||||
\(242\) | −2133.29 | − | 1592.27i | −0.566666 | − | 0.422953i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −184.520 | − | 567.893i | −0.0484125 | − | 0.148998i | ||||
\(245\) | 645.850 | + | 469.237i | 0.168416 | + | 0.122361i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2261.61 | − | 6960.53i | 0.582603 | − | 1.79307i | ||||
\(248\) | 527.317 | − | 1622.91i | 0.135019 | − | 0.415545i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1931.69 | − | 1403.46i | −0.488684 | − | 0.355050i | ||||
\(251\) | −1719.92 | − | 5293.38i | −0.432512 | − | 1.33114i | −0.895615 | − | 0.444831i | \(-0.853264\pi\) |
0.463102 | − | 0.886305i | \(-0.346736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1574.50 | − | 4954.04i | −0.391256 | − | 1.23106i | ||||
\(254\) | 2186.91 | 0.540232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −207.108 | − | 150.473i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −4883.48 | + | 3548.05i | −1.18530 | + | 0.861173i | −0.992760 | − | 0.120116i | \(-0.961673\pi\) |
−0.192543 | + | 0.981289i | \(0.561673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 996.430 | − | 3066.70i | 0.239055 | − | 0.735735i | ||||
\(260\) | 1344.55 | − | 976.870i | 0.320712 | − | 0.233011i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1524.17 | + | 4690.92i | 0.359403 | + | 1.10613i | ||||
\(263\) | 708.442 | 0.166100 | 0.0830502 | − | 0.996545i | \(-0.473534\pi\) | ||||
0.0830502 | + | 0.996545i | \(0.473534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1270.09 | −0.294418 | ||||||||
\(266\) | −1304.08 | − | 4013.55i | −0.300595 | − | 0.925137i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2673.76 | + | 1942.60i | −0.609424 | + | 0.442773i | ||||
\(269\) | 1486.28 | − | 4574.30i | 0.336878 | − | 1.03680i | −0.628912 | − | 0.777477i | \(-0.716499\pi\) |
0.965790 | − | 0.259327i | \(-0.0835006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4239.96 | − | 3080.51i | 0.950404 | − | 0.690509i | −0.000498618 | − | 1.00000i | \(-0.500159\pi\) |
0.950902 | + | 0.309491i | \(0.100159\pi\) | |||||||
\(272\) | 767.444 | + | 557.581i | 0.171078 | + | 0.124295i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1946.57 | 0.429185 | ||||||||
\(275\) | −1100.85 | + | 3315.34i | −0.241395 | + | 0.726990i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1650.07 | − | 5078.40i | −0.357918 | − | 1.10156i | −0.954298 | − | 0.298856i | \(-0.903395\pi\) |
0.596380 | − | 0.802702i | \(-0.296605\pi\) | |||||||
\(278\) | 2043.64 | + | 1484.79i | 0.440897 | + | 0.320331i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 296.133 | − | 911.405i | 0.0632048 | − | 0.194524i | ||||
\(281\) | 1013.57 | − | 3119.44i | 0.215175 | − | 0.662242i | −0.783966 | − | 0.620804i | \(-0.786806\pi\) |
0.999141 | − | 0.0414376i | \(-0.0131938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3960.54 | + | 2877.50i | 0.831906 | + | 0.604415i | 0.920098 | − | 0.391688i | \(-0.128109\pi\) |
−0.0881920 | + | 0.996103i | \(0.528109\pi\) | |||||||
\(284\) | 1111.18 | + | 3419.87i | 0.232171 | + | 0.714549i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4513.84 | − | 3324.08i | −0.933248 | − | 0.687262i | ||||
\(287\) | 1834.73 | 0.377354 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1130.92 | + | 821.661i | 0.230189 | + | 0.167242i | ||||
\(290\) | 178.670 | − | 129.811i | 0.0361789 | − | 0.0262855i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −170.569 | + | 524.958i | −0.0341843 | + | 0.105208i | ||||
\(293\) | 5425.10 | − | 3941.57i | 1.08170 | − | 0.785901i | 0.103721 | − | 0.994606i | \(-0.466925\pi\) |
0.977978 | + | 0.208706i | \(0.0669251\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 505.532 | + | 1555.87i | 0.0997736 | + | 0.307072i | ||||
\(296\) | −1164.62 | −0.228690 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 978.680 | 0.190246 | ||||||||
\(299\) | −3382.69 | − | 10410.8i | −0.654267 | − | 2.01363i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2712.54 | + | 1970.77i | −0.519429 | + | 0.377387i | ||||
\(302\) | 1055.46 | − | 3248.38i | 0.201109 | − | 0.618951i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1233.10 | + | 895.903i | −0.232643 | + | 0.169025i | ||||
\(305\) | −653.134 | − | 474.530i | −0.122618 | − | 0.0890869i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9507.29 | 1.76746 | 0.883730 | − | 0.467998i | \(-0.155025\pi\) | ||||
0.883730 | + | 0.467998i | \(0.155025\pi\) | |||||||
\(308\) | −3232.29 | − | 20.7960i | −0.597977 | − | 0.00384728i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −712.946 | − | 2194.22i | −0.130621 | − | 0.402011i | ||||
\(311\) | 4666.47 | + | 3390.39i | 0.850840 | + | 0.618171i | 0.925378 | − | 0.379047i | \(-0.123748\pi\) |
−0.0745375 | + | 0.997218i | \(0.523748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1847.23 | − | 5685.18i | 0.333583 | − | 1.02666i | −0.633833 | − | 0.773470i | \(-0.718519\pi\) |
0.967416 | − | 0.253192i | \(-0.0814806\pi\) | |||||||
\(314\) | 1583.23 | − | 4872.69i | 0.284545 | − | 0.875739i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 985.249 | + | 715.825i | 0.175394 | + | 0.127431i | ||||
\(317\) | −1616.76 | − | 4975.87i | −0.286455 | − | 0.881617i | −0.985959 | − | 0.166988i | \(-0.946596\pi\) |
0.699504 | − | 0.714628i | \(-0.253404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −599.822 | − | 441.720i | −0.105278 | − | 0.0775285i | ||||
\(320\) | −346.118 | −0.0604644 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5106.50 | − | 3710.09i | −0.883771 | − | 0.642097i | ||||
\(323\) | 4569.29 | − | 3319.79i | 0.787128 | − | 0.571882i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2273.24 | + | 6996.32i | −0.387990 | + | 1.19411i | ||||
\(326\) | −2938.49 | + | 2134.94i | −0.499227 | + | 0.362710i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −204.773 | − | 630.228i | −0.0344717 | − | 0.106093i | ||||
\(329\) | 2001.55 | 0.335408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3963.72 | −0.658205 | −0.329102 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329102 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(332\) | 944.719 | + | 2907.55i | 0.156169 | + | 0.480639i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 613.114 | − | 445.453i | 0.100443 | − | 0.0729764i | ||||
\(335\) | −1380.80 | + | 4249.67i | −0.225198 | + | 0.693088i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4131.33 | + | 3001.58i | −0.667797 | + | 0.485183i | −0.869287 | − | 0.494308i | \(-0.835422\pi\) |
0.201490 | + | 0.979491i | \(0.435422\pi\) | |||||||
\(338\) | −5995.43 | − | 4355.93i | −0.964817 | − | 0.700981i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1282.55 | 0.204576 | ||||||||
\(341\) | −6325.03 | + | 4533.51i | −1.00446 | + | 0.719952i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1337.35 | + | 4115.94i | 0.210525 | + | 0.647929i | ||||
\(344\) | 979.706 | + | 711.798i | 0.153553 | + | 0.111563i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.3479 | + | 96.4789i | −0.00487073 | + | 0.0149906i | ||||
\(347\) | −2331.77 | + | 7176.44i | −0.360737 | + | 1.11023i | 0.591871 | + | 0.806033i | \(0.298390\pi\) |
−0.952608 | + | 0.304201i | \(0.901610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2634.74 | + | 1914.25i | 0.404109 | + | 0.293603i | 0.771213 | − | 0.636578i | \(-0.219650\pi\) |
−0.367103 | + | 0.930180i | \(0.619650\pi\) | |||||||
\(350\) | 1310.79 | + | 4034.19i | 0.200184 | + | 0.616104i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 353.612 | + | 1112.61i | 0.0535442 | + | 0.168473i | ||||
\(353\) | 6506.83 | 0.981087 | 0.490543 | − | 0.871417i | \(-0.336798\pi\) | ||||
0.490543 | + | 0.871417i | \(0.336798\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3933.19 | + | 2857.63i | 0.588034 | + | 0.427232i | ||||
\(356\) | −1013.21 | + | 736.142i | −0.150843 | + | 0.109594i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.8970 | + | 39.6929i | −0.00190399 | + | 0.00585988i | ||||
\(359\) | 3289.63 | − | 2390.06i | 0.483622 | − | 0.351372i | −0.319105 | − | 0.947720i | \(-0.603382\pi\) |
0.802726 | + | 0.596348i | \(0.203382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 684.768 | + | 2107.50i | 0.0998349 | + | 0.307260i | ||||
\(362\) | −352.307 | −0.0511514 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6806.81 | −0.980148 | ||||||||
\(365\) | 230.614 | + | 709.756i | 0.0330709 | + | 0.101782i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1126.37 | − | 818.358i | 0.160208 | − | 0.116398i | −0.504793 | − | 0.863240i | \(-0.668431\pi\) |
0.665001 | + | 0.746843i | \(0.268431\pi\) | |||||||
\(368\) | −704.479 | + | 2168.16i | −0.0997922 | + | 0.307129i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1273.87 | + | 925.524i | −0.178988 | + | 0.130042i | ||||
\(371\) | 4208.39 | + | 3057.58i | 0.588919 | + | 0.427875i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9440.30 | 1.31046 | 0.655228 | − | 0.755431i | \(-0.272572\pi\) | ||||
0.655228 | + | 0.755431i | \(0.272572\pi\) | |||||||
\(374\) | −1310.32 | − | 4122.80i | −0.181163 | − | 0.570014i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −223.393 | − | 687.533i | −0.0306399 | − | 0.0943000i | ||||
\(377\) | −1269.09 | − | 922.044i | −0.173372 | − | 0.125962i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 398.740 | − | 1227.20i | 0.0540420 | − | 0.166324i | −0.920393 | − | 0.390995i | \(-0.872131\pi\) |
0.974435 | + | 0.224671i | \(0.0721308\pi\) | |||||||
\(380\) | −636.809 | + | 1959.90i | −0.0859674 | + | 0.264581i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1875.66 | − | 1362.74i | −0.251222 | − | 0.182524i | ||||
\(383\) | 1746.84 | + | 5376.22i | 0.233053 | + | 0.717264i | 0.997374 | + | 0.0724273i | \(0.0230745\pi\) |
−0.764321 | + | 0.644836i | \(0.776925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3552.04 | + | 2545.95i | −0.470205 | + | 0.337023i | ||||
\(386\) | −2569.88 | −0.338868 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1885.03 | + | 1369.55i | 0.246644 | + | 0.179197i | ||||
\(389\) | −10386.2 | + | 7545.99i | −1.35373 | + | 0.983539i | −0.354909 | + | 0.934901i | \(0.615488\pi\) |
−0.998816 | + | 0.0486380i | \(0.984512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2610.46 | − | 8034.18i | 0.337639 | − | 1.03915i | ||||
\(392\) | −955.381 | + | 694.125i | −0.123097 | + | 0.0894352i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1659.46 | + | 5107.28i | 0.212188 | + | 0.653049i | ||||
\(395\) | 1646.54 | 0.209738 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7691.26 | 0.972326 | 0.486163 | − | 0.873868i | \(-0.338396\pi\) | ||||
0.486163 | + | 0.873868i | \(0.338396\pi\) | |||||||
\(398\) | −824.173 | − | 2536.54i | −0.103799 | − | 0.319461i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1239.45 | − | 900.510i | 0.154931 | − | 0.112564i | ||||
\(401\) | −2406.06 | + | 7405.09i | −0.299633 | + | 0.922176i | 0.681993 | + | 0.731359i | \(0.261114\pi\) |
−0.981626 | + | 0.190817i | \(0.938886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13257.8 | + | 9632.33i | −1.63875 | + | 1.19062i | ||||
\(404\) | −458.080 | − | 332.814i | −0.0564117 | − | 0.0409855i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −904.523 | −0.110568 | ||||||||
\(407\) | 4276.59 | + | 3149.36i | 0.520842 | + | 0.383557i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2737.85 | − | 8426.25i | −0.330998 | − | 1.01871i | −0.968660 | − | 0.248391i | \(-0.920098\pi\) |
0.637662 | − | 0.770316i | \(-0.279902\pi\) | |||||||
\(410\) | −724.826 | − | 526.617i | −0.0873087 | − | 0.0634335i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1040.00 | − | 3200.80i | 0.124362 | − | 0.382748i | ||||
\(413\) | 2070.50 | − | 6372.33i | 0.246689 | − | 0.759230i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3343.97 | + | 2429.54i | 0.395540 | + | 0.287377i | ||||
\(416\) | 759.706 | + | 2338.14i | 0.0895377 | + | 0.275569i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6950.76 | + | 44.7200i | 0.813332 | + | 0.00523284i | ||||
\(419\) | −9469.08 | −1.10405 | −0.552023 | − | 0.833829i | \(-0.686144\pi\) | ||||
−0.552023 | + | 0.833829i | \(0.686144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4189.04 | − | 3043.52i | −0.484944 | − | 0.352333i | 0.318292 | − | 0.947993i | \(-0.396891\pi\) |
−0.803237 | + | 0.595660i | \(0.796891\pi\) | |||||||
\(422\) | 2634.43 | − | 1914.03i | 0.303891 | − | 0.220790i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 580.578 | − | 1786.84i | 0.0664985 | − | 0.204661i | ||||
\(425\) | −4592.79 | + | 3336.86i | −0.524196 | + | 0.380850i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1021.77 | + | 3144.68i | 0.115801 | + | 0.356398i | ||||
\(428\) | 257.728 | 0.0291069 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1637.28 | 0.183620 | ||||||||
\(431\) | −3233.42 | − | 9951.43i | −0.361365 | − | 1.11217i | −0.952226 | − | 0.305393i | \(-0.901212\pi\) |
0.590862 | − | 0.806773i | \(-0.298788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12813.4 | + | 9309.48i | −1.42211 | + | 1.03322i | −0.430688 | + | 0.902501i | \(0.641729\pi\) |
−0.991419 | + | 0.130721i | \(0.958271\pi\) | |||||||
\(434\) | −2919.99 | + | 8986.81i | −0.322959 | + | 0.993965i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5045.16 | + | 3665.52i | −0.554173 | + | 0.402630i | ||||
\(437\) | 10981.1 | + | 7978.23i | 1.20205 | + | 0.873342i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4824.70 | −0.524534 | −0.262267 | − | 0.964995i | \(-0.584470\pi\) | ||||
−0.262267 | + | 0.964995i | \(0.584470\pi\) | |||||||
\(440\) | 1270.98 | + | 935.971i | 0.137708 | + | 0.101411i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2815.11 | − | 8664.01i | −0.302944 | − | 0.932364i | ||||
\(443\) | 2899.02 | + | 2106.26i | 0.310918 | + | 0.225895i | 0.732290 | − | 0.680993i | \(-0.238451\pi\) |
−0.421372 | + | 0.906888i | \(0.638451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −523.251 | + | 1610.40i | −0.0557404 | + | 0.171551i | ||||
\(446\) | −1624.31 | + | 4999.12i | −0.172452 | + | 0.530752i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1146.85 | + | 833.238i | 0.120946 | + | 0.0878723i | ||||
\(449\) | 2409.09 | + | 7414.42i | 0.253212 | + | 0.779306i | 0.994177 | + | 0.107762i | \(0.0343684\pi\) |
−0.740965 | + | 0.671544i | \(0.765632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −952.312 | + | 2868.00i | −0.0994293 | + | 0.299443i | ||||
\(452\) | 8956.57 | 0.932039 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2754.79 | + | 2001.47i | 0.284777 | + | 0.206903i | ||||
\(455\) | −7445.37 | + | 5409.38i | −0.767130 | + | 0.557353i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1034.60 | − | 3184.16i | 0.105900 | − | 0.325927i | −0.884041 | − | 0.467410i | \(-0.845187\pi\) |
0.989941 | + | 0.141483i | \(0.0451871\pi\) | |||||||
\(458\) | −8730.83 | + | 6343.32i | −0.890753 | + | 0.647170i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 952.474 | + | 2931.41i | 0.0965420 | + | 0.297126i | ||||
\(461\) | −7171.96 | −0.724580 | −0.362290 | − | 0.932065i | \(-0.618005\pi\) | ||||
−0.362290 | + | 0.932065i | \(0.618005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4034.74 | 0.404990 | 0.202495 | − | 0.979283i | \(-0.435095\pi\) | ||||
0.202495 | + | 0.979283i | \(0.435095\pi\) | |||||||
\(464\) | 100.954 | + | 310.703i | 0.0101006 | + | 0.0310863i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9795.87 | + | 7117.12i | −0.973788 | + | 0.707498i | ||||
\(467\) | 3653.15 | − | 11243.2i | 0.361986 | − | 1.11408i | −0.589860 | − | 0.807505i | \(-0.700817\pi\) |
0.951847 | − | 0.306574i | \(-0.0991827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14805.8 | − | 10757.1i | 1.45772 | − | 1.05909i | ||||
\(470\) | −790.732 | − | 574.501i | −0.0776037 | − | 0.0563824i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2419.98 | −0.235993 | ||||||||
\(473\) | −1672.73 | − | 5263.10i | −0.162605 | − | 0.511622i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2818.74 | − | 8675.18i | −0.272279 | − | 0.837988i | ||||
\(476\) | −4249.69 | − | 3087.58i | −0.409210 | − | 0.297309i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1938.53 | + | 5966.17i | −0.185494 | + | 0.570891i | ||||
\(479\) | 2676.07 | − | 8236.09i | 0.255267 | − | 0.785630i | −0.738510 | − | 0.674242i | \(-0.764470\pi\) |
0.993777 | − | 0.111388i | \(-0.0355296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9048.27 | + | 6573.95i | 0.857725 | + | 0.623173i | ||||
\(482\) | −4016.76 | − | 12362.3i | −0.379582 | − | 1.16823i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1710.22 | − | 5041.84i | 0.160614 | − | 0.473501i | ||||
\(485\) | 3150.25 | 0.294939 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6009.10 | − | 4365.87i | −0.559134 | − | 0.406235i | 0.272008 | − | 0.962295i | \(-0.412312\pi\) |
−0.831142 | + | 0.556060i | \(0.812312\pi\) | |||||||
\(488\) | 966.157 | − | 701.954i | 0.0896227 | − | 0.0651147i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −493.385 | + | 1518.48i | −0.0454875 | + | 0.139996i | ||||
\(491\) | −4485.10 | + | 3258.62i | −0.412240 | + | 0.299510i | −0.774508 | − | 0.632564i | \(-0.782002\pi\) |
0.362268 | + | 0.932074i | \(0.382002\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −374.086 | − | 1151.32i | −0.0341744 | − | 0.105178i | ||||
\(494\) | 14637.5 | 1.33314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3412.87 | 0.308956 | ||||||||
\(497\) | −6153.12 | − | 18937.4i | −0.555342 | − | 1.70917i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16513.7 | + | 11997.9i | −1.48147 | + | 1.07635i | −0.504391 | + | 0.863476i | \(0.668283\pi\) |
−0.977079 | + | 0.212875i | \(0.931717\pi\) | |||||||
\(500\) | 1475.68 | − | 4541.68i | 0.131989 | − | 0.406220i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9005.63 | − | 6542.98i | 0.800680 | − | 0.581728i | ||||
\(503\) | −147.841 | − | 107.413i | −0.0131052 | − | 0.00952148i | 0.581213 | − | 0.813751i | \(-0.302578\pi\) |
−0.594319 | + | 0.804230i | \(0.702578\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −765.540 | −0.0674576 | ||||||||
\(506\) | 8450.04 | − | 6056.64i | 0.742392 | − | 0.532115i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1351.58 | + | 4159.75i | 0.118045 | + | 0.363305i | ||||
\(509\) | 3847.11 | + | 2795.09i | 0.335010 | + | 0.243399i | 0.742554 | − | 0.669787i | \(-0.233614\pi\) |
−0.407543 | + | 0.913186i | \(0.633614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 944.519 | − | 2906.93i | 0.0817673 | − | 0.251654i | ||||
\(512\) | 158.217 | − | 486.941i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9766.95 | − | 7096.11i | −0.838136 | − | 0.608941i | ||||
\(515\) | −1406.11 | − | 4327.56i | −0.120312 | − | 0.370282i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1038.90 | + | 3128.78i | −0.0883770 | + | 0.266158i | ||||
\(518\) | 6449.03 | 0.547016 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2689.09 | + | 1953.74i | 0.226778 | + | 0.164764i | ||||
\(521\) | −9490.70 | + | 6895.40i | −0.798071 | + | 0.579833i | −0.910348 | − | 0.413844i | \(-0.864186\pi\) |
0.112277 | + | 0.993677i | \(0.464186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −106.252 | + | 327.011i | −0.00888353 | + | 0.0273407i | −0.955400 | − | 0.295315i | \(-0.904575\pi\) |
0.946517 | + | 0.322655i | \(0.104575\pi\) | |||||||
\(524\) | −7980.67 | + | 5798.29i | −0.665338 | + | 0.483396i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 437.841 | + | 1347.54i | 0.0362943 | + | 0.111702i | ||||
\(527\) | −12646.4 | −1.04533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8134.66 | 0.668584 | ||||||||
\(530\) | −784.956 | − | 2415.85i | −0.0643327 | − | 0.197996i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6828.26 | − | 4961.02i | 0.556471 | − | 0.404300i | ||||
\(533\) | −1966.51 | + | 6052.31i | −0.159811 | + | 0.491847i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 281.906 | − | 204.816i | 0.0227810 | − | 0.0165514i | ||||
\(536\) | −5347.51 | − | 3885.20i | −0.430928 | − | 0.313088i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9619.41 | 0.770859 | ||||||||
\(539\) | 5385.29 | + | 34.6480i | 0.430354 | + | 0.00276882i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5328.62 | − | 16399.8i | −0.423466 | − | 1.30329i | −0.904455 | − | 0.426568i | \(-0.859722\pi\) |
0.480989 | − | 0.876726i | \(-0.340278\pi\) | |||||||
\(542\) | 8479.93 | + | 6161.03i | 0.672037 | + | 0.488263i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −586.275 | + | 1804.37i | −0.0462065 | + | 0.142209i | ||||
\(545\) | −2605.46 | + | 8018.78i | −0.204781 | + | 0.630251i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6183.49 | + | 4492.57i | 0.483340 | + | 0.351167i | 0.802617 | − | 0.596494i | \(-0.203440\pi\) |
−0.319277 | + | 0.947661i | \(0.603440\pi\) | |||||||
\(548\) | 1203.05 | + | 3702.60i | 0.0937804 | + | 0.288626i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6986.50 | − | 44.9500i | −0.541646 | − | 0.00348486i | ||||
\(551\) | 1945.10 | 0.150388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5455.77 | − | 3963.85i | −0.419535 | − | 0.304810i | ||||
\(554\) | 8639.89 | − | 6277.25i | 0.662588 | − | 0.481399i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1561.20 | + | 4804.89i | −0.119082 | + | 0.366498i | ||||
\(557\) | 21120.3 | − | 15344.8i | 1.60664 | − | 1.16729i | 0.733684 | − | 0.679491i | \(-0.237799\pi\) |
0.872955 | − | 0.487800i | \(-0.162201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3593.72 | − | 11060.3i | −0.271911 | − | 0.836855i | ||||
\(560\) | 1916.62 | 0.144628 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6559.94 | 0.492374 | ||||||||
\(563\) | 5585.14 | + | 17189.3i | 0.418092 | + | 1.28675i | 0.909456 | + | 0.415800i | \(0.136498\pi\) |
−0.491364 | + | 0.870954i | \(0.663502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9796.79 | − | 7117.79i | 0.729476 | − | 0.529996i | ||||
\(566\) | −3025.58 | + | 9311.78i | −0.224690 | + | 0.691525i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5818.23 | + | 4227.19i | −0.429802 | + | 0.312269i | ||||
\(569\) | 6314.50 | + | 4587.76i | 0.465233 | + | 0.338012i | 0.795581 | − | 0.605848i | \(-0.207166\pi\) |
−0.330347 | + | 0.943859i | \(0.607166\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13039.6 | −0.955672 | −0.477836 | − | 0.878449i | \(-0.658579\pi\) | ||||
−0.477836 | + | 0.878449i | \(0.658579\pi\) | |||||||
\(572\) | 3533.06 | − | 10640.2i | 0.258260 | − | 0.777780i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1133.92 | + | 3489.86i | 0.0824548 | + | 0.253770i | ||||
\(575\) | −11037.6 | − | 8019.26i | −0.800519 | − | 0.581611i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2957.12 | + | 9101.06i | −0.213356 | + | 0.656642i | 0.785910 | + | 0.618340i | \(0.212195\pi\) |
−0.999266 | + | 0.0383013i | \(0.987805\pi\) | |||||||
\(578\) | −863.946 | + | 2658.95i | −0.0621720 | + | 0.191346i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 357.340 | + | 259.623i | 0.0255823 | + | 0.0185866i | ||||
\(581\) | −5231.34 | − | 16100.4i | −0.373550 | − | 1.14967i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6963.88 | + | 4991.42i | −0.494708 | + | 0.354586i | ||||
\(584\) | −1103.95 | −0.0782220 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10850.2 | + | 7883.14i | 0.764877 | + | 0.555716i | ||||
\(587\) | 7869.31 | − | 5717.39i | 0.553324 | − | 0.402013i | −0.275686 | − | 0.961248i | \(-0.588905\pi\) |
0.829009 | + | 0.559235i | \(0.188905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6279.19 | − | 19325.4i | 0.439269 | − | 1.35193i | ||||
\(590\) | −2647.00 | + | 1923.16i | −0.184704 | + | 0.134195i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −719.775 | − | 2215.24i | −0.0499706 | − | 0.153794i | ||||
\(593\) | −6926.77 | −0.479677 | −0.239838 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239838 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7102.06 | −0.489338 | ||||||||
\(596\) | 604.858 | + | 1861.56i | 0.0415704 | + | 0.127940i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17712.0 | − | 12868.5i | 1.21120 | − | 0.879987i | ||||
\(599\) | 6793.63 | − | 20908.7i | 0.463406 | − | 1.42622i | −0.397570 | − | 0.917572i | \(-0.630146\pi\) |
0.860976 | − | 0.508646i | \(-0.169854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5957.01 | − | 4328.02i | 0.404312 | − | 0.293750i | −0.366983 | − | 0.930228i | \(-0.619609\pi\) |
0.771295 | + | 0.636478i | \(0.219609\pi\) | |||||||
\(602\) | −5425.08 | − | 3941.55i | −0.367292 | − | 0.266853i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6831.10 | 0.460188 | ||||||||
\(605\) | −2136.09 | − | 6873.93i | −0.143544 | − | 0.461926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3142.21 | + | 9670.72i | 0.210113 | + | 0.646660i | 0.999465 | + | 0.0327190i | \(0.0104167\pi\) |
−0.789352 | + | 0.613941i | \(0.789583\pi\) | |||||||
\(608\) | −2466.21 | − | 1791.81i | −0.164503 | − | 0.119519i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 498.950 | − | 1535.61i | 0.0331179 | − | 0.101926i | ||||
\(611\) | −2145.32 | + | 6602.63i | −0.142047 | + | 0.437175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20293.8 | − | 14744.3i | −1.33713 | − | 0.971479i | −0.999544 | − | 0.0301824i | \(-0.990391\pi\) |
−0.337581 | − | 0.941296i | \(-0.609609\pi\) | |||||||
\(614\) | 5875.83 | + | 18083.9i | 0.386204 | + | 1.18861i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1958.11 | − | 6161.03i | −0.128075 | − | 0.402979i | ||||
\(617\) | 26335.5 | 1.71836 | 0.859178 | − | 0.511677i | \(-0.170976\pi\) | ||||
0.859178 | + | 0.511677i | \(0.170976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19936.7 | + | 14484.9i | 1.29455 | + | 0.940544i | 0.999887 | − | 0.0150577i | \(-0.00479321\pi\) |
0.294661 | + | 0.955602i | \(0.404793\pi\) | |||||||
\(620\) | 3733.03 | − | 2712.21i | 0.241810 | − | 0.175685i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3564.87 | + | 10971.5i | −0.229804 | + | 0.707264i | ||||
\(623\) | 5610.62 | − | 4076.35i | 0.360810 | − | 0.262144i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1703.48 | + | 5242.78i | 0.109023 | + | 0.335538i | ||||
\(626\) | 11955.5 | 0.763319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10246.9 | 0.651108 | ||||||||
\(629\) | 2667.14 | + | 8208.62i | 0.169071 | + | 0.520348i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6031.48 | + | 4382.13i | −0.380522 | + | 0.276465i | −0.761561 | − | 0.648094i | \(-0.775567\pi\) |
0.381039 | + | 0.924559i | \(0.375567\pi\) | |||||||
\(632\) | −752.663 | + | 2316.46i | −0.0473724 | + | 0.145797i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8465.45 | − | 6150.51i | 0.530293 | − | 0.385281i | ||||
\(635\) | 4784.13 | + | 3475.88i | 0.298980 | + | 0.217222i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11340.8 | 0.705397 | ||||||||
\(638\) | 469.491 | − | 1413.93i | 0.0291338 | − | 0.0877397i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −213.913 | − | 658.356i | −0.0132120 | − | 0.0406622i | ||||
\(641\) | −2247.99 | − | 1633.26i | −0.138518 | − | 0.100639i | 0.516368 | − | 0.856367i | \(-0.327284\pi\) |
−0.654887 | + | 0.755727i | \(0.727284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2335.46 | − | 7187.81i | 0.143237 | − | 0.440839i | −0.853543 | − | 0.521023i | \(-0.825551\pi\) |
0.996780 | + | 0.0801836i | \(0.0255507\pi\) | |||||||
\(644\) | 3901.02 | − | 12006.1i | 0.238698 | − | 0.734638i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9138.59 | + | 6639.57i | 0.556584 | + | 0.404382i | ||||
\(647\) | 8476.55 | + | 26088.1i | 0.515066 | + | 1.58521i | 0.783162 | + | 0.621817i | \(0.213605\pi\) |
−0.268096 | + | 0.963392i | \(0.586395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8886.37 | + | 6544.09i | 0.537474 | + | 0.395806i | ||||
\(650\) | −14712.7 | −0.887817 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5876.98 | − | 4269.88i | −0.353007 | − | 0.256474i | ||||
\(653\) | 230.350 | − | 167.359i | 0.0138044 | − | 0.0100295i | −0.580862 | − | 0.814002i | \(-0.697284\pi\) |
0.594666 | + | 0.803973i | \(0.297284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4121.44 | + | 12684.5i | −0.245859 | + | 0.756677i | ||||
\(656\) | 1072.21 | − | 779.004i | 0.0638150 | − | 0.0463643i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1237.03 | + | 3807.18i | 0.0732893 | + | 0.225561i | ||||
\(659\) | −20747.0 | −1.22639 | −0.613193 | − | 0.789933i | \(-0.710115\pi\) | ||||
−0.613193 | + | 0.789933i | \(0.710115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18908.8 | −1.11266 | −0.556328 | − | 0.830963i | \(-0.687790\pi\) | ||||
−0.556328 | + | 0.830963i | \(0.687790\pi\) | |||||||
\(662\) | −2449.71 | − | 7539.44i | −0.143823 | − | 0.442642i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4946.61 | + | 3593.92i | −0.289105 | + | 0.210047i | ||||
\(665\) | 3526.30 | − | 10852.8i | 0.205630 | − | 0.632865i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2353.66 | − | 1710.03i | 0.136633 | − | 0.0992694i | ||||
\(668\) | 1226.23 | + | 890.906i | 0.0710242 | + | 0.0516021i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8936.74 | −0.515308 | ||||||||
\(671\) | −5446.03 | − | 35.0388i | −0.313326 | − | 0.00201589i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9229.07 | + | 28404.2i | 0.528610 | + | 1.62689i | 0.757065 | + | 0.653340i | \(0.226633\pi\) |
−0.228455 | + | 0.973554i | \(0.573367\pi\) | |||||||
\(674\) | −8262.65 | − | 6003.17i | −0.472204 | − | 0.343076i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4580.10 | − | 14096.1i | 0.260588 | − | 0.802008i | ||||
\(677\) | 5340.04 | − | 16435.0i | 0.303153 | − | 0.933009i | −0.677207 | − | 0.735793i | \(-0.736810\pi\) |
0.980360 | − | 0.197216i | \(-0.0631901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10438.3 | − | 7583.84i | −0.589961 | − | 0.428632i | ||||
\(680\) | 792.659 | + | 2439.55i | 0.0447016 | + | 0.137577i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12532.3 | − | 9229.05i | −0.703648 | − | 0.518180i | ||||
\(683\) | −25104.0 | −1.40641 | −0.703204 | − | 0.710988i | \(-0.748248\pi\) | ||||
−0.703204 | + | 0.710988i | \(0.748248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4258.37 | + | 3093.88i | 0.237524 | + | 0.172571i | ||||
\(686\) | −7002.45 | + | 5087.58i | −0.389730 | + | 0.283156i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −748.429 | + | 2303.43i | −0.0414732 | + | 0.127641i | ||||
\(689\) | −14596.9 | + | 10605.2i | −0.807106 | + | 0.586397i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8085.06 | − | 24883.3i | −0.445109 | − | 1.36990i | −0.882364 | − | 0.470567i | \(-0.844050\pi\) |
0.437256 | − | 0.899337i | \(-0.355950\pi\) | |||||||
\(692\) | −202.888 | −0.0111454 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15091.5 | −0.825455 | ||||||||
\(695\) | 2110.79 | + | 6496.33i | 0.115204 | + | 0.354561i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3973.09 | + | 2886.62i | −0.215913 | + | 0.156870i | ||||
\(698\) | −2012.76 | + | 6194.64i | −0.109146 | + | 0.335917i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6863.37 | + | 4986.53i | −0.370587 | + | 0.269248i | ||||
\(701\) | −1229.26 | − | 893.108i | −0.0662317 | − | 0.0481201i | 0.554177 | − | 0.832399i | \(-0.313033\pi\) |
−0.620408 | + | 0.784279i | \(0.713033\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13868.1 | −0.744018 | ||||||||
\(704\) | −1897.77 | + | 1360.24i | −0.101598 | + | 0.0728210i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4021.44 | + | 12376.7i | 0.214375 | + | 0.659779i | ||||
\(707\) | 2536.59 | + | 1842.94i | 0.134934 | + | 0.0980354i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6716.14 | + | 20670.2i | −0.355755 | + | 1.09490i | 0.599816 | + | 0.800138i | \(0.295240\pi\) |
−0.955571 | + | 0.294762i | \(0.904760\pi\) | |||||||
\(710\) | −3004.69 | + | 9247.49i | −0.158823 | + | 0.488806i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2026.42 | − | 1472.28i | −0.106662 | − | 0.0774946i | ||||
\(713\) | −9391.77 | − | 28904.9i | −0.493302 | − | 1.51823i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4591.29 | − | 14446.1i | −0.240146 | − | 0.755601i | ||||
\(716\) | −83.4712 | −0.00435679 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6579.26 | + | 4780.11i | 0.341972 | + | 0.248457i | ||||
\(719\) | −11384.4 | + | 8271.22i | −0.590494 | + | 0.429019i | −0.842492 | − | 0.538709i | \(-0.818912\pi\) |
0.251998 | + | 0.967728i | \(0.418912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5758.97 | + | 17724.3i | −0.297469 | + | 0.915516i | ||||
\(722\) | −3585.49 | + | 2605.01i | −0.184817 | + | 0.134278i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −217.737 | − | 670.127i | −0.0111770 | − | 0.0343993i | ||||
\(725\) | −1955.10 | −0.100153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10409.2 | 0.531027 | 0.265513 | − | 0.964107i | \(-0.414459\pi\) | ||||
0.265513 | + | 0.964107i | \(0.414459\pi\) | |||||||
\(728\) | −4206.84 | − | 12947.3i | −0.214170 | − | 0.659148i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1207.51 | + | 877.307i | −0.0612218 | + | 0.0444803i | ||||
\(731\) | 2773.32 | − | 8535.39i | 0.140321 | − | 0.431865i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15690.8 | − | 11400.0i | 0.790658 | − | 0.574447i | −0.117501 | − | 0.993073i | \(-0.537488\pi\) |
0.908159 | + | 0.418626i | \(0.137488\pi\) | |||||||
\(734\) | 2252.75 | + | 1636.72i | 0.113284 | + | 0.0823056i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4559.48 | −0.228349 | ||||||||
\(737\) | 9130.21 | + | 28727.5i | 0.456331 | + | 1.43581i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2061.83 | − | 6345.68i | −0.102633 | − | 0.315872i | 0.886535 | − | 0.462662i | \(-0.153106\pi\) |
−0.989168 | + | 0.146790i | \(0.953106\pi\) | |||||||
\(740\) | −2547.75 | − | 1851.05i | −0.126564 | − | 0.0919539i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3214.93 | + | 9894.52i | −0.159062 | + | 0.489541i | ||||
\(743\) | −2028.75 | + | 6243.86i | −0.100172 | + | 0.308297i | −0.988567 | − | 0.150782i | \(-0.951821\pi\) |
0.888395 | + | 0.459080i | \(0.151821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2140.98 | + | 1555.52i | 0.105288 | + | 0.0764962i | ||||
\(746\) | 5834.43 | + | 17956.5i | 0.286345 | + | 0.881280i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7032.22 | − | 5040.40i | 0.343748 | − | 0.246384i | ||||
\(749\) | −1427.16 | −0.0696223 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15321.7 | − | 11131.9i | −0.744470 | − | 0.540889i | 0.149638 | − | 0.988741i | \(-0.452189\pi\) |
−0.894108 | + | 0.447852i | \(0.852189\pi\) | |||||||
\(752\) | 1169.70 | − | 849.837i | 0.0567215 | − | 0.0412106i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 969.495 | − | 2983.80i | 0.0468262 | − | 0.144116i | ||||
\(755\) | 7471.93 | − | 5428.68i | 0.360174 | − | 0.261682i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3386.32 | − | 10422.0i | −0.162586 | − | 0.500389i | 0.836264 | − | 0.548327i | \(-0.184735\pi\) |
−0.998850 | + | 0.0479377i | \(0.984735\pi\) | |||||||
\(758\) | 2580.70 | 0.123661 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4121.52 | −0.196715 | ||||||||
\(761\) | 10952.2 | + | 33707.5i | 0.521706 | + | 1.60565i | 0.770739 | + | 0.637151i | \(0.219887\pi\) |
−0.249033 | + | 0.968495i | \(0.580113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27937.4 | − | 20297.7i | 1.32556 | − | 0.963074i | ||||
\(764\) | 1432.87 | − | 4409.93i | 0.0678529 | − | 0.208830i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9146.57 | + | 6645.37i | −0.431435 | + | 0.313456i | ||||
\(767\) | 18801.5 | + | 13660.1i | 0.885115 | + | 0.643074i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4444.21 | 0.208404 | 0.104202 | − | 0.994556i | \(-0.466771\pi\) | ||||
0.104202 | + | 0.994556i | \(0.466771\pi\) | |||||||
\(770\) | −7037.98 | − | 5182.90i | −0.329391 | − | 0.242570i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1588.27 | − | 4888.19i | −0.0740455 | − | 0.227888i | ||||
\(773\) | 8219.75 | + | 5972.00i | 0.382463 | + | 0.277876i | 0.762360 | − | 0.647153i | \(-0.224041\pi\) |
−0.379897 | + | 0.925029i | \(0.624041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6311.48 | + | 19424.8i | −0.292536 | + | 0.900333i | ||||
\(776\) | −1440.03 | + | 4431.97i | −0.0666162 | + | 0.205024i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20772.3 | − | 15092.0i | −0.957228 | − | 0.695467i | ||||
\(779\) | −2438.40 | − | 7504.64i | −0.112150 | − | 0.345162i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32796.2 | + | 211.005i | 1.50261 | + | 0.00966754i | ||||
\(782\) | 16895.3 | 0.772600 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1910.76 | − | 1388.25i | −0.0870427 | − | 0.0632403i | ||||
\(785\) | 11208.2 | − | 8143.22i | 0.509601 | − | 0.370247i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5645.76 | + | 17375.9i | −0.255718 | + | 0.787018i | 0.737970 | + | 0.674834i | \(0.235785\pi\) |
−0.993687 | + | 0.112184i | \(0.964215\pi\) | |||||||
\(788\) | −8689.03 | + | 6312.95i | −0.392809 | + | 0.285393i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1017.62 | + | 3131.91i | 0.0458295 | + | 0.141049i | ||||
\(791\) | −49596.6 | −2.22939 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11468.7 | −0.513575 | ||||||||
\(794\) | 4753.46 | + | 14629.7i | 0.212461 | + | 0.653888i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4315.42 | − | 3135.34i | 0.192156 | − | 0.139609i | ||||
\(797\) | −5557.35 | + | 17103.8i | −0.246991 | + | 0.760159i | 0.748312 | + | 0.663347i | \(0.230865\pi\) |
−0.995303 | + | 0.0968123i | \(0.969135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4334.35 | + | 3149.09i | −0.191913 | + | 0.139433i | ||||
\(800\) | 2478.89 | + | 1801.02i | 0.109553 | + | 0.0795946i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15572.3 | −0.685634 | ||||||||
\(803\) | 4053.79 | + | 2985.29i | 0.178151 | + | 0.131194i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5274.28 | − | 16232.6i | −0.230924 | − | 0.710711i | ||||
\(806\) | −26515.5 | − | 19264.7i | −1.15877 | − | 0.841897i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 349.942 | − | 1077.01i | 0.0152363 | − | 0.0468924i | ||||
\(809\) | −1589.66 | + | 4892.47i | −0.0690846 | + | 0.212621i | −0.979638 | − | 0.200770i | \(-0.935656\pi\) |
0.910554 | + | 0.413391i | \(0.135656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6679.24 | + | 4852.75i | 0.289198 | + | 0.210115i | 0.722919 | − | 0.690932i | \(-0.242800\pi\) |
−0.433721 | + | 0.901047i | \(0.642800\pi\) | |||||||
\(812\) | −559.026 | − | 1720.51i | −0.0241601 | − | 0.0743570i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3347.36 | + | 10081.0i | −0.144134 | + | 0.434076i | ||||
\(815\) | −9821.58 | −0.422129 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11666.2 | + | 8475.96i | 0.499568 | + | 0.362958i | ||||
\(818\) | 14335.6 | − | 10415.4i | 0.612753 | − | 0.445191i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 553.717 | − | 1704.17i | 0.0235813 | − | 0.0725757i | ||||
\(821\) | 200.029 | − | 145.330i | 0.00850314 | − | 0.00617789i | −0.583526 | − | 0.812095i | \(-0.698327\pi\) |
0.592029 | + | 0.805917i | \(0.298327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3644.80 | + | 11217.5i | 0.154374 | + | 0.475114i | 0.998097 | − | 0.0616649i | \(-0.0196410\pi\) |
−0.843723 | + | 0.536779i | \(0.819641\pi\) | |||||||
\(824\) | 6731.04 | 0.284571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13400.5 | 0.564484 | ||||||||
\(827\) | 856.491 | + | 2636.01i | 0.0360134 | + | 0.110838i | 0.967447 | − | 0.253073i | \(-0.0814413\pi\) |
−0.931434 | + | 0.363911i | \(0.881441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22084.6 | − | 16045.4i | 0.925246 | − | 0.672231i | −0.0195780 | − | 0.999808i | \(-0.506232\pi\) |
0.944824 | + | 0.327578i | \(0.106232\pi\) | |||||||
\(830\) | −2554.57 | + | 7862.15i | −0.106832 | + | 0.328794i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3977.87 | + | 2890.10i | −0.165755 | + | 0.120428i | ||||
\(833\) | 7080.37 | + | 5144.19i | 0.294502 | + | 0.213968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2049.26 | 0.0849314 | ||||||||
\(836\) | 4210.74 | + | 13248.8i | 0.174200 | + | 0.548108i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5852.21 | − | 18011.3i | −0.241243 | − | 0.742469i | ||||
\(839\) | 7082.73 | + | 5145.91i | 0.291446 | + | 0.211748i | 0.723894 | − | 0.689911i | \(-0.242350\pi\) |
−0.432449 | + | 0.901659i | \(0.642350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7407.78 | + | 22798.8i | −0.303735 | + | 0.934799i | ||||
\(842\) | 3200.15 | − | 9849.03i | 0.130979 | − | 0.403112i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5268.86 | + | 3828.05i | 0.214884 | + | 0.156122i | ||||
\(845\) | −6192.41 | − | 19058.3i | −0.252101 | − | 0.775887i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9470.28 | + | 27918.9i | −0.384182 | + | 1.13259i | ||||
\(848\) | 3757.58 | 0.152165 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9185.58 | − | 6673.72i | −0.370662 | − | 0.269302i | ||||
\(851\) | −16781.0 | + | 12192.1i | −0.675964 | + | 0.491117i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12726.6 | − | 39168.6i | 0.510846 | − | 1.57222i | −0.279869 | − | 0.960038i | \(-0.590291\pi\) |
0.790715 | − | 0.612184i | \(-0.209709\pi\) | |||||||
\(854\) | −5350.05 | + | 3887.04i | −0.214373 | + | 0.155751i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 159.285 | + | 490.227i | 0.00636008 | + | 0.0195743i | ||||
\(857\) | 18020.0 | 0.718265 | 0.359132 | − | 0.933287i | \(-0.383073\pi\) | ||||
0.359132 | + | 0.933287i | \(0.383073\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6159.11 | 0.244640 | 0.122320 | − | 0.992491i | \(-0.460967\pi\) | ||||
0.122320 | + | 0.992491i | \(0.460967\pi\) | |||||||
\(860\) | 1011.89 | + | 3114.29i | 0.0401225 | + | 0.123484i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16930.4 | − | 12300.6i | 0.668969 | − | 0.486035i | ||||
\(863\) | −8940.66 | + | 27516.5i | −0.352658 | + | 1.08537i | 0.604697 | + | 0.796455i | \(0.293294\pi\) |
−0.957355 | + | 0.288914i | \(0.906706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −221.921 | + | 161.235i | −0.00872317 | + | 0.00633775i | ||||
\(866\) | −25626.8 | − | 18619.0i | −1.00558 | − | 0.730598i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18898.6 | −0.739009 | ||||||||
\(869\) | 9027.99 | − | 6470.89i | 0.352421 | − | 0.252601i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19615.5 | + | 60370.4i | 0.763085 | + | 2.34853i | ||||
\(872\) | −10090.3 | − | 7331.05i | −0.391859 | − | 0.284703i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8388.81 | + | 25818.1i | −0.324663 | + | 0.999211i | ||||
\(875\) | −8171.52 | + | 25149.4i | −0.315712 | + | 0.971661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36529.2 | + | 26540.1i | 1.40651 | + | 1.02189i | 0.993819 | + | 0.111013i | \(0.0354094\pi\) |
0.412686 | + | 0.910873i | \(0.364591\pi\) | |||||||
\(878\) | −2981.83 | − | 9177.13i | −0.114615 | − | 0.352748i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −994.816 | + | 2996.00i | −0.0381082 | + | 0.114767i | ||||
\(881\) | −22263.5 | −0.851391 | −0.425696 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425696 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30917.0 | − | 22462.5i | −1.17830 | − | 0.856086i | −0.186322 | − | 0.982489i | \(-0.559657\pi\) |
−0.991979 | + | 0.126402i | \(0.959657\pi\) | |||||||
\(884\) | 14740.1 | − | 10709.3i | 0.560818 | − | 0.407458i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2214.65 | + | 6816.00i | −0.0839760 | + | 0.258452i | ||||
\(887\) | 38962.7 | − | 28308.1i | 1.47490 | − | 1.07158i | 0.495750 | − | 0.868465i | \(-0.334893\pi\) |
0.979155 | − | 0.203116i | \(-0.0651068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7484.34 | − | 23034.4i | −0.282359 | − | 0.869010i | ||||
\(890\) | −3386.55 | −0.127548 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10512.8 | −0.394612 | ||||||||
\(893\) | −2660.12 | − | 8187.01i | −0.0996838 | − | 0.306795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −91.3017 | + | 66.3346i | −0.00340992 | + | 0.00247745i | ||||
\(896\) | −876.118 | + | 2696.41i | −0.0326663 | + | 0.100537i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12614.2 | + | 9164.73i | −0.468753 | + | 0.340569i | ||||
\(899\) | −3523.52 | − | 2559.99i | −0.130718 | − | 0.0949725i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13923.8 | −0.514838 | ||||||||
\(902\) | −6043.81 | − | 38.8849i | −0.223101 | − | 0.00143539i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5535.46 | + | 17036.4i | 0.203658 | + | 0.626795i | ||||
\(905\) | −770.714 | − | 559.956i | −0.0283087 | − | 0.0205675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2629.70 | − | 8093.38i | 0.0962709 | − | 0.296291i | −0.891312 | − | 0.453391i | \(-0.850214\pi\) |
0.987583 | + | 0.157099i | \(0.0502143\pi\) | |||||||
\(908\) | −2104.47 | + | 6476.90i | −0.0769157 | + | 0.236722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14890.7 | − | 10818.8i | −0.542443 | − | 0.394108i | ||||
\(911\) | −3486.78 | − | 10731.2i | −0.126808 | − | 0.390275i | 0.867418 | − | 0.497580i | \(-0.165778\pi\) |
−0.994226 | + | 0.107305i | \(0.965778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27883.0 | + | 179.395i | 1.01073 | + | 0.00650285i | ||||
\(914\) | 6696.04 | 0.242325 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17461.7 | − | 12686.6i | −0.629857 | − | 0.457618i | ||||
\(917\) | 44192.6 | − | 32107.8i | 1.59146 | − | 1.15626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8206.54 | − | 25257.1i | 0.294569 | − | 0.906590i | −0.688797 | − | 0.724954i | \(-0.741861\pi\) |
0.983366 | − | 0.181635i | \(-0.0581391\pi\) | |||||||
\(920\) | −4987.22 | + | 3623.42i | −0.178721 | + | 0.129849i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4432.51 | − | 13641.9i | −0.158327 | − | 0.487279i | ||||
\(923\) | 69064.7 | 2.46294 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13939.4 | 0.495486 | ||||||||
\(926\) | 2493.61 | + | 7674.54i | 0.0884936 | + | 0.272355i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −528.600 | + | 384.050i | −0.0186984 | + | 0.0135852i | ||||
\(929\) | 14806.0 | − | 45568.1i | 0.522893 | − | 1.60930i | −0.245551 | − | 0.969384i | \(-0.578969\pi\) |
0.768444 | − | 0.639916i | \(-0.221031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11376.5 | + | 8265.52i | −0.400483 | + | 0.290968i | ||||
\(932\) | −19591.7 | − | 14234.2i | −0.688572 | − | 0.500277i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23643.7 | 0.828314 | ||||||||
\(935\) | 3686.31 | − | 11101.8i | 0.128936 | − | 0.388306i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1767.25 | + | 5439.04i | 0.0616153 | + | 0.189633i | 0.977126 | − | 0.212661i | \(-0.0682131\pi\) |
−0.915511 | + | 0.402294i | \(0.868213\pi\) | |||||||
\(938\) | 29611.6 | + | 21514.1i | 1.03076 | + | 0.748892i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 604.066 | − | 1859.12i | 0.0209601 | − | 0.0645084i | ||||
\(941\) | 3431.82 | − | 10562.1i | 0.118889 | − | 0.365902i | −0.873850 | − | 0.486196i | \(-0.838384\pi\) |
0.992738 | + | 0.120295i | \(0.0383840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9548.27 | − | 6937.22i | −0.329729 | − | 0.239562i | ||||
\(944\) | −1495.63 | − | 4603.08i | −0.0515663 | − | 0.158705i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8977.20 | − | 6434.48i | 0.308535 | − | 0.221145i | ||||
\(947\) | −39759.1 | −1.36430 | −0.682152 | − | 0.731210i | \(-0.738956\pi\) | ||||
−0.682152 | + | 0.731210i | \(0.738956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8576.88 | + | 6231.47i | 0.293380 | + | 0.213153i | ||||
\(950\) | 14759.1 | − | 10723.1i | 0.504051 | − | 0.366214i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3246.47 | − | 9991.62i | 0.110524 | − | 0.340158i | ||||
\(953\) | −12889.2 | + | 9364.58i | −0.438115 | + | 0.318309i | −0.784885 | − | 0.619641i | \(-0.787278\pi\) |
0.346771 | + | 0.937950i | \(0.387278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1937.28 | − | 5962.34i | −0.0656429 | − | 0.202028i | ||||
\(956\) | −12546.4 | −0.424456 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17319.9 | 0.584113 | ||||||||
\(959\) | −6661.82 | − | 20503.0i | −0.224319 | − | 0.690381i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12707.8 | + | 9232.73i | −0.426564 | + | 0.309917i | ||||
\(962\) | −6912.26 | + | 21273.8i | −0.231664 | + | 0.712987i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21032.0 | − | 15280.7i | 0.702693 | − | 0.510537i | ||||
\(965\) | −5621.92 | − | 4084.56i | −0.187540 | − | 0.136256i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14952.9 | 0.497264 | 0.248632 | − | 0.968598i | \(-0.420019\pi\) | ||||
0.248632 | + | 0.968598i | \(0.420019\pi\) | |||||||
\(968\) | 10647.1 | + | 137.009i | 0.353524 | + | 0.00454922i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1946.96 | + | 5992.13i | 0.0644465 | + | 0.198346i | ||||
\(971\) | 22601.7 | + | 16421.1i | 0.746987 | + | 0.542718i | 0.894892 | − | 0.446284i | \(-0.147253\pi\) |
−0.147904 | + | 0.989002i | \(0.547253\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8645.09 | − | 26606.9i | 0.284840 | − | 0.876646i | ||||
\(974\) | 4590.54 | − | 14128.2i | 0.151017 | − | 0.464782i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1932.31 | + | 1403.91i | 0.0633728 | + | 0.0460430i | ||||
\(977\) | −10308.6 | − | 31726.5i | −0.337564 | − | 1.03892i | −0.965445 | − | 0.260607i | \(-0.916077\pi\) |
0.627881 | − | 0.778310i | \(-0.283923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3459.87 | + | 10886.2i | 0.112950 | + | 0.355387i | ||||
\(980\) | −3193.26 | −0.104087 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8970.20 | − | 6517.23i | −0.291498 | − | 0.211785i | ||||
\(983\) | 9991.42 | − | 7259.19i | 0.324188 | − | 0.235536i | −0.413772 | − | 0.910380i | \(-0.635789\pi\) |
0.737960 | + | 0.674844i | \(0.235789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4487.25 | + | 13810.4i | −0.145153 | + | 0.446735i | ||||
\(986\) | 1958.74 | − | 1423.11i | 0.0632647 | − | 0.0459645i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9046.45 | + | 27842.1i | 0.291301 | + | 0.896534i | ||||
\(989\) | 21568.2 | 0.693457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30154.0 | −0.966571 | −0.483286 | − | 0.875463i | \(-0.660557\pi\) | ||||
−0.483286 | + | 0.875463i | \(0.660557\pi\) | |||||||
\(992\) | 2109.27 | + | 6491.66i | 0.0675094 | + | 0.207773i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32218.2 | − | 23407.9i | 1.02807 | − | 0.746934i | ||||
\(995\) | 2228.60 | − | 6858.94i | 0.0710065 | − | 0.218536i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1693.35 | + | 1230.29i | −0.0537902 | + | 0.0390809i | −0.614355 | − | 0.789029i | \(-0.710584\pi\) |
0.560565 | + | 0.828110i | \(0.310584\pi\) | |||||||
\(998\) | −33027.3 | − | 23995.8i | −1.04756 | − | 0.761095i | ||||
\(999\) | 0 | 0 |
(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 | 198.4.f.d.181.2 | 8 | ||
3.2 | odd | 2 | 22.4.c.b.5.1 | ✓ | 8 | ||
11.3 | even | 5 | 2178.4.a.by.1.3 | 4 | |||
11.8 | odd | 10 | 2178.4.a.bt.1.3 | 4 | |||
11.9 | even | 5 | inner | 198.4.f.d.163.2 | 8 | ||
12.11 | even | 2 | 176.4.m.b.49.2 | 8 | |||
33.2 | even | 10 | 242.4.c.q.9.1 | 8 | |||
33.5 | odd | 10 | 242.4.c.r.81.2 | 8 | |||
33.8 | even | 10 | 242.4.a.o.1.3 | 4 | |||
33.14 | odd | 10 | 242.4.a.n.1.3 | 4 | |||
33.17 | even | 10 | 242.4.c.n.81.2 | 8 | |||
33.20 | odd | 10 | 22.4.c.b.9.1 | yes | 8 | ||
33.26 | odd | 10 | 242.4.c.r.3.2 | 8 | |||
33.29 | even | 10 | 242.4.c.n.3.2 | 8 | |||
33.32 | even | 2 | 242.4.c.q.27.1 | 8 | |||
132.47 | even | 10 | 1936.4.a.bn.1.2 | 4 | |||
132.107 | odd | 10 | 1936.4.a.bm.1.2 | 4 | |||
132.119 | even | 10 | 176.4.m.b.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.5.1 | ✓ | 8 | 3.2 | odd | 2 | ||
22.4.c.b.9.1 | yes | 8 | 33.20 | odd | 10 | ||
176.4.m.b.49.2 | 8 | 12.11 | even | 2 | |||
176.4.m.b.97.2 | 8 | 132.119 | even | 10 | |||
198.4.f.d.163.2 | 8 | 11.9 | even | 5 | inner | ||
198.4.f.d.181.2 | 8 | 1.1 | even | 1 | trivial | ||
242.4.a.n.1.3 | 4 | 33.14 | odd | 10 | |||
242.4.a.o.1.3 | 4 | 33.8 | even | 10 | |||
242.4.c.n.3.2 | 8 | 33.29 | even | 10 | |||
242.4.c.n.81.2 | 8 | 33.17 | even | 10 | |||
242.4.c.q.9.1 | 8 | 33.2 | even | 10 | |||
242.4.c.q.27.1 | 8 | 33.32 | even | 2 | |||
242.4.c.r.3.2 | 8 | 33.26 | odd | 10 | |||
242.4.c.r.81.2 | 8 | 33.5 | odd | 10 | |||
1936.4.a.bm.1.2 | 4 | 132.107 | odd | 10 | |||
1936.4.a.bn.1.2 | 4 | 132.47 | even | 10 | |||
2178.4.a.bt.1.3 | 4 | 11.8 | odd | 10 | |||
2178.4.a.by.1.3 | 4 | 11.3 | even | 5 |