Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,4,Mod(3,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.c (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.2784622214\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(-2.53202 + 7.79275i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 242.9 |
Dual form | 242.4.c.q.27.1 |
$q$-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 \(\left(\mathbb{Z}/242\mathbb{Z}\right)^\times\).
\(n\) | \(123\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||
\(3\) | −6.12891 | + | 4.45291i | −1.17951 | + | 0.856963i | −0.992116 | − | 0.125322i | \(-0.960004\pi\) |
−0.187393 | + | 0.982285i | \(0.560004\pi\) | |||||||
\(4\) | −3.23607 | − | 2.35114i | −0.404508 | − | 0.293893i | ||||
\(5\) | 1.67119 | + | 5.14341i | 0.149476 | + | 0.460041i | 0.997559 | − | 0.0698226i | \(-0.0222433\pi\) |
−0.848083 | + | 0.529863i | \(0.822243\pi\) | |||||||
\(6\) | 4.68207 | + | 14.4099i | 0.318574 | + | 0.980471i | ||||
\(7\) | −17.9196 | − | 13.0193i | −0.967566 | − | 0.702978i | −0.0126708 | − | 0.999920i | \(-0.504033\pi\) |
−0.954896 | + | 0.296942i | \(0.904033\pi\) | |||||||
\(8\) | −6.47214 | + | 4.70228i | −0.286031 | + | 0.207813i | ||||
\(9\) | 9.39163 | − | 28.9045i | 0.347838 | − | 1.07054i | ||||
\(10\) | 10.8162 | 0.342038 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 30.3030 | 0.728977 | ||||||||
\(13\) | −23.7408 | + | 73.0668i | −0.506502 | + | 1.55885i | 0.291730 | + | 0.956501i | \(0.405769\pi\) |
−0.798231 | + | 0.602351i | \(0.794231\pi\) | |||||||
\(14\) | −35.8392 | + | 26.0387i | −0.684173 | + | 0.497081i | ||||
\(15\) | −33.1458 | − | 24.0818i | −0.570546 | − | 0.414526i | ||||
\(16\) | 4.94427 | + | 15.2169i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −18.3211 | − | 56.3866i | −0.261384 | − | 0.804456i | −0.992505 | − | 0.122208i | \(-0.961003\pi\) |
0.731121 | − | 0.682248i | \(-0.238997\pi\) | |||||||
\(18\) | −49.1752 | − | 35.7279i | −0.643928 | − | 0.467841i | ||||
\(19\) | 77.0690 | − | 55.9939i | 0.930571 | − | 0.676099i | −0.0155616 | − | 0.999879i | \(-0.504954\pi\) |
0.946133 | + | 0.323780i | \(0.104954\pi\) | |||||||
\(20\) | 6.68478 | − | 20.5736i | 0.0747381 | − | 0.230020i | ||||
\(21\) | 167.801 | 1.74368 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 142.484 | 1.29174 | 0.645868 | − | 0.763449i | \(-0.276495\pi\) | ||||
0.645868 | + | 0.763449i | \(0.276495\pi\) | |||||||
\(24\) | 18.7283 | − | 57.6397i | 0.159287 | − | 0.490236i | ||||
\(25\) | 77.4654 | − | 56.2819i | 0.619723 | − | 0.450255i | ||||
\(26\) | 124.309 | + | 90.3155i | 0.937651 | + | 0.681243i | ||||
\(27\) | 7.94067 | + | 24.4389i | 0.0565994 | + | 0.174195i | ||||
\(28\) | 27.3787 | + | 84.2629i | 0.184789 | + | 0.568721i | ||||
\(29\) | −16.5188 | − | 12.0016i | −0.105774 | − | 0.0768496i | 0.533641 | − | 0.845711i | \(-0.320823\pi\) |
−0.639415 | + | 0.768862i | \(0.720823\pi\) | |||||||
\(30\) | −66.2915 | + | 48.1636i | −0.403437 | + | 0.293114i | ||||
\(31\) | 65.9146 | − | 202.864i | 0.381891 | − | 1.17534i | −0.556820 | − | 0.830633i | \(-0.687979\pi\) |
0.938711 | − | 0.344706i | \(-0.112021\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −118.577 | −0.598110 | ||||||||
\(35\) | 37.0167 | − | 113.926i | 0.178770 | − | 0.550198i | ||||
\(36\) | −98.3504 | + | 71.4558i | −0.455326 | + | 0.330814i | ||||
\(37\) | 117.775 | + | 85.5683i | 0.523298 | + | 0.380199i | 0.817845 | − | 0.575439i | \(-0.195169\pi\) |
−0.294547 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(38\) | −58.8755 | − | 181.200i | −0.251339 | − | 0.773541i | ||||
\(39\) | −179.855 | − | 553.535i | −0.738456 | − | 2.27273i | ||||
\(40\) | −35.0020 | − | 25.4304i | −0.138357 | − | 0.100523i | ||||
\(41\) | 67.0130 | − | 48.6878i | 0.255260 | − | 0.185457i | −0.452795 | − | 0.891615i | \(-0.649573\pi\) |
0.708055 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(42\) | 103.707 | − | 319.177i | 0.381008 | − | 1.17262i | ||||
\(43\) | 151.373 | 0.536841 | 0.268420 | − | 0.963302i | \(-0.413498\pi\) | ||||
0.268420 | + | 0.963302i | \(0.413498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 164.363 | 0.544483 | ||||||||
\(46\) | 88.0599 | − | 271.020i | 0.282255 | − | 0.868691i | ||||
\(47\) | −73.1063 | + | 53.1148i | −0.226886 | + | 0.164842i | −0.695421 | − | 0.718603i | \(-0.744782\pi\) |
0.468535 | + | 0.883445i | \(0.344782\pi\) | |||||||
\(48\) | −98.0625 | − | 71.2466i | −0.294877 | − | 0.214241i | ||||
\(49\) | 45.6154 | + | 140.390i | 0.132989 | + | 0.409300i | ||||
\(50\) | −59.1783 | − | 182.132i | −0.167381 | − | 0.515147i | ||||
\(51\) | 363.373 | + | 264.006i | 0.997693 | + | 0.724867i | ||||
\(52\) | 248.617 | − | 180.631i | 0.663019 | − | 0.481712i | ||||
\(53\) | −72.5723 | + | 223.355i | −0.188086 | + | 0.578870i | −0.999988 | − | 0.00492438i | \(-0.998433\pi\) |
0.811902 | + | 0.583794i | \(0.198433\pi\) | |||||||
\(54\) | 51.3931 | 0.129513 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 177.199 | 0.422842 | ||||||||
\(57\) | −223.013 | + | 686.363i | −0.518224 | + | 1.59493i | ||||
\(58\) | −33.0375 | + | 24.0032i | −0.0747937 | + | 0.0543408i | ||||
\(59\) | −244.726 | − | 177.804i | −0.540009 | − | 0.392340i | 0.284079 | − | 0.958801i | \(-0.408312\pi\) |
−0.824089 | + | 0.566461i | \(0.808312\pi\) | |||||||
\(60\) | 50.6422 | + | 155.861i | 0.108965 | + | 0.335359i | ||||
\(61\) | 46.1299 | + | 141.973i | 0.0968250 | + | 0.297997i | 0.987725 | − | 0.156203i | \(-0.0499253\pi\) |
−0.890900 | + | 0.454200i | \(0.849925\pi\) | |||||||
\(62\) | −345.133 | − | 250.754i | −0.706967 | − | 0.513642i | ||||
\(63\) | −544.611 | + | 395.683i | −1.08912 | + | 0.791292i | ||||
\(64\) | 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 | ||||
\(69\) | −873.271 | + | 634.468i | −1.52362 | + | 1.10697i | ||||
\(70\) | −193.822 | − | 140.820i | −0.330945 | − | 0.240445i | ||||
\(71\) | −277.796 | − | 854.967i | −0.464342 | − | 1.42910i | −0.859808 | − | 0.510617i | \(-0.829417\pi\) |
0.395467 | − | 0.918480i | \(-0.370583\pi\) | |||||||
\(72\) | 75.1330 | + | 231.236i | 0.122979 | + | 0.378491i | ||||
\(73\) | −111.639 | − | 81.1105i | −0.178991 | − | 0.130045i | 0.494682 | − | 0.869074i | \(-0.335284\pi\) |
−0.673673 | + | 0.739029i | \(0.735284\pi\) | |||||||
\(74\) | 235.549 | − | 171.137i | 0.370028 | − | 0.268841i | ||||
\(75\) | −224.160 | + | 689.893i | −0.345117 | + | 1.06216i | ||||
\(76\) | −381.050 | −0.575124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1164.04 | −1.68977 | ||||||||
\(79\) | 94.0829 | − | 289.557i | 0.133989 | − | 0.412377i | −0.861442 | − | 0.507856i | \(-0.830438\pi\) |
0.995431 | + | 0.0954791i | \(0.0304383\pi\) | |||||||
\(80\) | −70.0039 | + | 50.8608i | −0.0978335 | + | 0.0710802i | ||||
\(81\) | 506.374 | + | 367.902i | 0.694614 | + | 0.504667i | ||||
\(82\) | −51.1933 | − | 157.557i | −0.0689434 | − | 0.212186i | ||||
\(83\) | 236.180 | + | 726.886i | 0.312338 | + | 0.961279i | 0.976836 | + | 0.213989i | \(0.0686455\pi\) |
−0.664498 | + | 0.747290i | \(0.731354\pi\) | |||||||
\(84\) | −543.017 | − | 394.525i | −0.705333 | − | 0.512455i | ||||
\(85\) | 259.401 | − | 188.466i | 0.331012 | − | 0.240494i | ||||
\(86\) | 93.5536 | − | 287.928i | 0.117304 | − | 0.361024i | ||||
\(87\) | 154.684 | 0.190619 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −313.100 | −0.372905 | −0.186452 | − | 0.982464i | \(-0.559699\pi\) | ||||
−0.186452 | + | 0.982464i | \(0.559699\pi\) | |||||||
\(90\) | 101.582 | − | 312.636i | 0.118974 | − | 0.366164i | ||||
\(91\) | 1376.71 | − | 1000.24i | 1.58591 | − | 1.15223i | ||||
\(92\) | −461.088 | − | 335.000i | −0.522519 | − | 0.379632i | ||||
\(93\) | 499.352 | + | 1536.85i | 0.556779 | + | 1.71359i | ||||
\(94\) | 55.8482 | + | 171.883i | 0.0612798 | + | 0.188600i | ||||
\(95\) | 416.797 | + | 302.821i | 0.450131 | + | 0.327040i | ||||
\(96\) | −196.125 | + | 142.493i | −0.208510 | + | 0.151491i | ||||
\(97\) | −180.004 | + | 553.996i | −0.188419 | + | 0.579894i | −0.999990 | − | 0.00435900i | \(-0.998612\pi\) |
0.811571 | + | 0.584253i | \(0.198612\pi\) | |||||||
\(98\) | 295.229 | 0.304313 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −383.010 | −0.383010 | ||||||||
\(101\) | 43.7427 | − | 134.626i | 0.0430947 | − | 0.132632i | −0.927194 | − | 0.374581i | \(-0.877787\pi\) |
0.970289 | + | 0.241949i | \(0.0777867\pi\) | |||||||
\(102\) | 726.746 | − | 528.012i | 0.705476 | − | 0.512558i | ||||
\(103\) | −680.691 | − | 494.551i | −0.651169 | − | 0.473102i | 0.212500 | − | 0.977161i | \(-0.431839\pi\) |
−0.863669 | + | 0.504059i | \(0.831839\pi\) | |||||||
\(104\) | −189.927 | − | 584.534i | −0.179075 | − | 0.551137i | ||||
\(105\) | 280.429 | + | 863.071i | 0.260639 | + | 0.802163i | ||||
\(106\) | 379.993 | + | 276.081i | 0.348191 | + | 0.252975i | ||||
\(107\) | −52.1265 | + | 37.8721i | −0.0470959 | + | 0.0342172i | −0.611084 | − | 0.791566i | \(-0.709266\pi\) |
0.563988 | + | 0.825783i | \(0.309266\pi\) | |||||||
\(108\) | 31.7627 | − | 97.7555i | 0.0282997 | − | 0.0870974i | ||||
\(109\) | −1559.04 | −1.36999 | −0.684995 | − | 0.728547i | \(-0.740196\pi\) | ||||
−0.684995 | + | 0.728547i | \(0.740196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1102.86 | −0.943052 | ||||||||
\(112\) | 109.515 | − | 337.052i | 0.0923944 | − | 0.284361i | ||||
\(113\) | 1811.50 | − | 1316.13i | 1.50807 | − | 1.09568i | 0.541046 | − | 0.840993i | \(-0.318029\pi\) |
0.967024 | − | 0.254684i | \(-0.0819714\pi\) | |||||||
\(114\) | 1167.71 | + | 848.392i | 0.959352 | + | 0.697010i | ||||
\(115\) | 238.118 | + | 732.853i | 0.193084 | + | 0.594251i | ||||
\(116\) | 25.2384 | + | 77.6758i | 0.0202011 | + | 0.0621726i | ||||
\(117\) | 1888.99 | + | 1372.43i | 1.49263 | + | 1.08446i | ||||
\(118\) | −489.451 | + | 355.607i | −0.381844 | + | 0.277426i | ||||
\(119\) | −405.809 | + | 1248.95i | −0.312609 | + | 0.962111i | ||||
\(120\) | 327.763 | 0.249338 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 298.559 | 0.221559 | ||||||||
\(123\) | −193.914 | + | 596.806i | −0.142151 | + | 0.437497i | ||||
\(124\) | −690.267 | + | 501.508i | −0.499901 | + | 0.363200i | ||||
\(125\) | 965.846 | + | 701.728i | 0.691103 | + | 0.502116i | ||||
\(126\) | 416.046 | + | 1280.46i | 0.294161 | + | 0.905335i | ||||
\(127\) | −337.896 | − | 1039.94i | −0.236090 | − | 0.726611i | −0.996975 | − | 0.0777237i | \(-0.975235\pi\) |
0.760885 | − | 0.648887i | \(-0.224765\pi\) | |||||||
\(128\) | −103.554 | − | 75.2365i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | −927.750 | + | 674.050i | −0.633208 | + | 0.460053i | ||||
\(130\) | −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 | ||||
\(135\) | −112.429 | + | 81.6842i | −0.0716765 | + | 0.0520760i | ||||
\(136\) | 383.722 | + | 278.790i | 0.241940 | + | 0.175780i | ||||
\(137\) | −300.762 | − | 925.650i | −0.187561 | − | 0.577253i | 0.812422 | − | 0.583069i | \(-0.198148\pi\) |
−0.999983 | + | 0.00581676i | \(0.998148\pi\) | |||||||
\(138\) | 667.120 | + | 2053.18i | 0.411514 | + | 1.26651i | ||||
\(139\) | −1021.82 | − | 742.396i | −0.623523 | − | 0.453016i | 0.230627 | − | 0.973042i | \(-0.425922\pi\) |
−0.854150 | + | 0.520026i | \(0.825922\pi\) | |||||||
\(140\) | −387.644 | + | 281.640i | −0.234013 | + | 0.170021i | ||||
\(141\) | 211.546 | − | 651.072i | 0.126350 | − | 0.388866i | ||||
\(142\) | −1797.93 | −1.06253 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 486.271 | 0.281407 | ||||||||
\(145\) | 34.1230 | − | 105.020i | 0.0195432 | − | 0.0601477i | ||||
\(146\) | −223.278 | + | 162.221i | −0.126566 | + | 0.0919555i | ||||
\(147\) | −904.716 | − | 657.314i | −0.507617 | − | 0.368805i | ||||
\(148\) | −179.944 | − | 553.810i | −0.0999411 | − | 0.307587i | ||||
\(149\) | 151.214 | + | 465.390i | 0.0831407 | + | 0.255881i | 0.983982 | − | 0.178268i | \(-0.0570493\pi\) |
−0.900841 | + | 0.434149i | \(0.857049\pi\) | |||||||
\(150\) | 1173.72 | + | 852.755i | 0.638890 | + | 0.464181i | ||||
\(151\) | 1381.62 | − | 1003.80i | 0.744600 | − | 0.540983i | −0.149549 | − | 0.988754i | \(-0.547782\pi\) |
0.894148 | + | 0.447771i | \(0.147782\pi\) | |||||||
\(152\) | −235.502 | + | 724.801i | −0.125669 | + | 0.386770i | ||||
\(153\) | −1801.89 | −0.952118 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1153.57 | 0.597787 | ||||||||
\(156\) | −719.418 | + | 2214.14i | −0.369228 | + | 1.13637i | ||||
\(157\) | −2072.48 | + | 1505.75i | −1.05352 | + | 0.765424i | −0.972878 | − | 0.231320i | \(-0.925696\pi\) |
−0.0806377 | + | 0.996743i | \(0.525696\pi\) | |||||||
\(158\) | −492.624 | − | 357.913i | −0.248045 | − | 0.180215i | ||||
\(159\) | −549.789 | − | 1692.08i | −0.274221 | − | 0.843965i | ||||
\(160\) | 53.4782 | + | 164.589i | 0.0264239 | + | 0.0813244i | ||||
\(161\) | −2553.25 | − | 1855.05i | −1.24984 | − | 0.908063i | ||||
\(162\) | 1012.75 | − | 735.804i | 0.491166 | − | 0.356853i | ||||
\(163\) | 561.202 | − | 1727.20i | 0.269673 | − | 0.829969i | −0.720907 | − | 0.693032i | \(-0.756274\pi\) |
0.990580 | − | 0.136936i | \(-0.0437256\pi\) | |||||||
\(164\) | −331.330 | −0.157759 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1528.59 | 0.714707 | ||||||||
\(167\) | −117.094 | + | 360.379i | −0.0542576 | + | 0.166988i | −0.974513 | − | 0.224330i | \(-0.927981\pi\) |
0.920256 | + | 0.391318i | \(0.127981\pi\) | |||||||
\(168\) | −1086.03 | + | 789.050i | −0.498746 | + | 0.362360i | ||||
\(169\) | −2997.71 | − | 2177.97i | −1.36446 | − | 0.991336i | ||||
\(170\) | −198.165 | − | 609.888i | −0.0894032 | − | 0.275155i | ||||
\(171\) | −894.671 | − | 2753.51i | −0.400100 | − | 1.23138i | ||||
\(172\) | −489.853 | − | 355.899i | −0.217157 | − | 0.157773i | ||||
\(173\) | 41.0349 | − | 29.8136i | 0.0180337 | − | 0.0131022i | −0.578732 | − | 0.815518i | \(-0.696452\pi\) |
0.596766 | + | 0.802416i | \(0.296452\pi\) | |||||||
\(174\) | 95.5999 | − | 294.226i | 0.0416518 | − | 0.128191i | ||||
\(175\) | −2120.90 | −0.916142 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2291.64 | 0.973167 | ||||||||
\(178\) | −193.506 | + | 595.551i | −0.0814826 | + | 0.250778i | ||||
\(179\) | −16.8824 | + | 12.2658i | −0.00704944 | + | 0.00512172i | −0.591304 | − | 0.806448i | \(-0.701387\pi\) |
0.584255 | + | 0.811570i | \(0.301387\pi\) | |||||||
\(180\) | −531.889 | − | 386.440i | −0.220248 | − | 0.160020i | ||||
\(181\) | −54.4344 | − | 167.532i | −0.0223540 | − | 0.0687985i | 0.939257 | − | 0.343214i | \(-0.111516\pi\) |
−0.961611 | + | 0.274416i | \(0.911516\pi\) | |||||||
\(182\) | −1051.71 | − | 3236.83i | −0.428340 | − | 1.31830i | ||||
\(183\) | −914.920 | − | 664.728i | −0.369578 | − | 0.268514i | ||||
\(184\) | −922.175 | + | 669.999i | −0.369476 | + | 0.268440i | ||||
\(185\) | −243.288 | + | 748.765i | −0.0966861 | + | 0.297569i | ||||
\(186\) | 3231.88 | 1.27405 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 361.457 | 0.140223 | ||||||||
\(189\) | 175.884 | − | 541.316i | 0.0676916 | − | 0.208333i | ||||
\(190\) | 833.594 | − | 605.642i | 0.318291 | − | 0.231252i | ||||
\(191\) | 937.829 | + | 681.372i | 0.355282 | + | 0.258128i | 0.751082 | − | 0.660209i | \(-0.229532\pi\) |
−0.395799 | + | 0.918337i | \(0.629532\pi\) | |||||||
\(192\) | 149.826 | + | 461.118i | 0.0563165 | + | 0.173324i | ||||
\(193\) | 397.068 | + | 1222.05i | 0.148091 | + | 0.455777i | 0.997396 | − | 0.0721261i | \(-0.0229784\pi\) |
−0.849305 | + | 0.527903i | \(0.822978\pi\) | |||||||
\(194\) | 942.514 | + | 684.776i | 0.348807 | + | 0.253423i | ||||
\(195\) | 2546.49 | − | 1850.13i | 0.935168 | − | 0.679439i | ||||
\(196\) | 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 | ||||
\(201\) | −5063.93 | + | 3679.16i | −1.77702 | + | 1.29108i | ||||
\(202\) | −229.040 | − | 166.407i | −0.0797781 | − | 0.0579622i | ||||
\(203\) | 139.757 | + | 430.126i | 0.0483201 | + | 0.148714i | ||||
\(204\) | −555.184 | − | 1708.68i | −0.190542 | − | 0.586429i | ||||
\(205\) | 362.413 | + | 263.308i | 0.123473 | + | 0.0897085i | ||||
\(206\) | −1361.38 | + | 989.102i | −0.460446 | + | 0.334534i | ||||
\(207\) | 1338.16 | − | 4118.42i | 0.449315 | − | 1.38285i | ||||
\(208\) | −1229.23 | −0.409768 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1814.97 | 0.596405 | ||||||||
\(211\) | 503.132 | − | 1548.48i | 0.164156 | − | 0.505221i | −0.834817 | − | 0.550528i | \(-0.814426\pi\) |
0.998973 | + | 0.0453065i | \(0.0144264\pi\) | |||||||
\(212\) | 759.987 | − | 552.163i | 0.246208 | − | 0.178881i | ||||
\(213\) | 5509.68 | + | 4003.01i | 1.77238 | + | 1.28771i | ||||
\(214\) | 39.8211 | + | 122.557i | 0.0127202 | + | 0.0391487i | ||||
\(215\) | 252.974 | + | 778.573i | 0.0802449 | + | 0.246968i | ||||
\(216\) | −166.312 | − | 120.832i | −0.0523892 | − | 0.0380630i | ||||
\(217\) | −3822.32 | + | 2777.08i | −1.19574 | + | 0.868757i | ||||
\(218\) | −963.540 | + | 2965.47i | −0.299354 | + | 0.921317i | ||||
\(219\) | 1045.40 | 0.322565 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4554.94 | 1.38642 | ||||||||
\(222\) | −681.604 | + | 2097.76i | −0.206064 | + | 0.634201i | ||||
\(223\) | 2126.25 | − | 1544.81i | 0.638495 | − | 0.463894i | −0.220837 | − | 0.975311i | \(-0.570879\pi\) |
0.859333 | + | 0.511416i | \(0.170879\pi\) | |||||||
\(224\) | −573.427 | − | 416.619i | −0.171043 | − | 0.124270i | ||||
\(225\) | −899.271 | − | 2767.67i | −0.266451 | − | 0.820051i | ||||
\(226\) | −1383.87 | − | 4259.10i | −0.407316 | − | 1.25359i | ||||
\(227\) | 1377.40 | + | 1000.74i | 0.402736 | + | 0.292605i | 0.770654 | − | 0.637253i | \(-0.219930\pi\) |
−0.367919 | + | 0.929858i | \(0.619930\pi\) | |||||||
\(228\) | 2335.42 | − | 1696.78i | 0.678364 | − | 0.492861i | ||||
\(229\) | 1667.44 | − | 5131.85i | 0.481168 | − | 1.48088i | −0.356287 | − | 0.934377i | \(-0.615957\pi\) |
0.837455 | − | 0.546506i | \(-0.184043\pi\) | |||||||
\(230\) | 1541.13 | 0.441823 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 163.346 | 0.0462251 | ||||||||
\(233\) | 1870.85 | − | 5757.87i | 0.526022 | − | 1.61893i | −0.236264 | − | 0.971689i | \(-0.575923\pi\) |
0.762286 | − | 0.647241i | \(-0.224077\pi\) | |||||||
\(234\) | 3777.98 | − | 2744.86i | 1.05545 | − | 0.766826i | ||||
\(235\) | −395.366 | − | 287.250i | −0.109748 | − | 0.0797368i | ||||
\(236\) | 373.907 | + | 1150.77i | 0.103133 | + | 0.317410i | ||||
\(237\) | 712.748 | + | 2193.61i | 0.195350 | + | 0.601226i | ||||
\(238\) | 2124.84 | + | 1543.79i | 0.578711 | + | 0.420458i | ||||
\(239\) | 2537.56 | − | 1843.65i | 0.686783 | − | 0.498977i | −0.188818 | − | 0.982012i | \(-0.560466\pi\) |
0.875601 | + | 0.483035i | \(0.160466\pi\) | |||||||
\(240\) | 202.569 | − | 623.443i | 0.0544823 | − | 0.167679i | ||||
\(241\) | 6499.26 | 1.73715 | 0.868577 | − | 0.495555i | \(-0.165035\pi\) | ||||
0.868577 | + | 0.495555i | \(0.165035\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5435.56 | −1.43494 | ||||||||
\(244\) | 184.520 | − | 567.893i | 0.0484125 | − | 0.148998i | ||||
\(245\) | −645.850 | + | 469.237i | −0.168416 | + | 0.122361i | ||||
\(246\) | 1015.35 | + | 737.692i | 0.263155 | + | 0.191193i | ||||
\(247\) | 2261.61 | + | 6960.53i | 0.582603 | + | 1.79307i | ||||
\(248\) | 527.317 | + | 1622.91i | 0.135019 | + | 0.415545i | ||||
\(249\) | −4684.29 | − | 3403.33i | −1.19219 | − | 0.866174i | ||||
\(250\) | 1931.69 | − | 1403.46i | 0.488684 | − | 0.355050i | ||||
\(251\) | 1719.92 | − | 5293.38i | 0.432512 | − | 1.33114i | −0.463102 | − | 0.886305i | \(-0.653264\pi\) |
0.895615 | − | 0.444831i | \(-0.146736\pi\) | |||||||
\(252\) | 2692.70 | 0.673113 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2186.91 | −0.540232 | ||||||||
\(255\) | −750.623 | + | 2310.18i | −0.184337 | + | 0.567330i | ||||
\(256\) | −207.108 | + | 150.473i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 4883.48 | + | 3548.05i | 1.18530 | + | 0.861173i | 0.992760 | − | 0.120116i | \(-0.0383265\pi\) |
0.192543 | + | 0.981289i | \(0.438327\pi\) | |||||||
\(258\) | 708.738 | + | 2181.27i | 0.171024 | + | 0.526357i | ||||
\(259\) | −996.430 | − | 3066.70i | −0.239055 | − | 0.735735i | ||||
\(260\) | 1344.55 | + | 976.870i | 0.320712 | + | 0.233011i | ||||
\(261\) | −502.037 | + | 364.751i | −0.119063 | + | 0.0865040i | ||||
\(262\) | 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 | ||||
\(267\) | 1918.96 | − | 1394.21i | 0.439844 | − | 0.319566i | ||||
\(268\) | −2673.76 | − | 1942.60i | −0.609424 | − | 0.442773i | ||||
\(269\) | −1486.28 | − | 4574.30i | −0.336878 | − | 1.03680i | −0.965790 | − | 0.259327i | \(-0.916499\pi\) |
0.628912 | − | 0.777477i | \(-0.283501\pi\) | |||||||
\(270\) | 85.8879 | + | 264.336i | 0.0193591 | + | 0.0595813i | ||||
\(271\) | −4239.96 | − | 3080.51i | −0.950404 | − | 0.690509i | 0.000498618 | − | 1.00000i | \(-0.499841\pi\) |
−0.950902 | + | 0.309491i | \(0.899841\pi\) | |||||||
\(272\) | 767.444 | − | 557.581i | 0.171078 | − | 0.124295i | ||||
\(273\) | −3983.74 | + | 12260.7i | −0.883177 | + | 2.71814i | ||||
\(274\) | −1946.57 | −0.429185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4317.69 | 0.941646 | ||||||||
\(277\) | 1650.07 | − | 5078.40i | 0.357918 | − | 1.10156i | −0.596380 | − | 0.802702i | \(-0.703395\pi\) |
0.954298 | − | 0.298856i | \(-0.0966051\pi\) | |||||||
\(278\) | −2043.64 | + | 1484.79i | −0.440897 | + | 0.320331i | ||||
\(279\) | −5244.64 | − | 3810.45i | −1.12541 | − | 0.817655i | ||||
\(280\) | 296.133 | + | 911.405i | 0.0632048 | + | 0.194524i | ||||
\(281\) | 1013.57 | + | 3119.44i | 0.215175 | + | 0.662242i | 0.999141 | + | 0.0414376i | \(0.0131938\pi\) |
−0.783966 | + | 0.620804i | \(0.786806\pi\) | |||||||
\(282\) | −1107.67 | − | 804.769i | −0.233903 | − | 0.169941i | ||||
\(283\) | −3960.54 | + | 2877.50i | −0.831906 | + | 0.604415i | −0.920098 | − | 0.391688i | \(-0.871891\pi\) |
0.0881920 | + | 0.996103i | \(0.471891\pi\) | |||||||
\(284\) | −1111.18 | + | 3419.87i | −0.232171 | + | 0.714549i | ||||
\(285\) | −3902.95 | −0.811195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1834.73 | −0.377354 | ||||||||
\(288\) | 300.532 | − | 924.943i | 0.0614897 | − | 0.189246i | ||||
\(289\) | 1130.92 | − | 821.661i | 0.230189 | − | 0.167242i | ||||
\(290\) | −178.670 | − | 129.811i | −0.0361789 | − | 0.0262855i | ||||
\(291\) | −1363.67 | − | 4196.93i | −0.274706 | − | 0.845459i | ||||
\(292\) | 170.569 | + | 524.958i | 0.0341843 | + | 0.105208i | ||||
\(293\) | 5425.10 | + | 3941.57i | 1.08170 | + | 0.785901i | 0.977978 | − | 0.208706i | \(-0.0669251\pi\) |
0.103721 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(294\) | −1809.43 | + | 1314.63i | −0.358939 | + | 0.260785i | ||||
\(295\) | 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 | ||||
\(300\) | 2347.43 | − | 1705.51i | 0.451763 | − | 0.328225i | ||||
\(301\) | −2712.54 | − | 1970.77i | −0.519429 | − | 0.377387i | ||||
\(302\) | −1055.46 | − | 3248.38i | −0.201109 | − | 0.618951i | ||||
\(303\) | 331.384 | + | 1019.89i | 0.0628300 | + | 0.193371i | ||||
\(304\) | 1233.10 | + | 895.903i | 0.232643 | + | 0.169025i | ||||
\(305\) | −653.134 | + | 474.530i | −0.122618 | + | 0.0890869i | ||||
\(306\) | −1113.63 | + | 3427.39i | −0.208045 | + | 0.640298i | ||||
\(307\) | −9507.29 | −1.76746 | −0.883730 | − | 0.467998i | \(-0.844975\pi\) | ||||
−0.883730 | + | 0.467998i | \(0.844975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6374.08 | 1.17349 | ||||||||
\(310\) | 712.946 | − | 2194.22i | 0.130621 | − | 0.402011i | ||||
\(311\) | −4666.47 | + | 3390.39i | −0.850840 | + | 0.618171i | −0.925378 | − | 0.379047i | \(-0.876252\pi\) |
0.0745375 | + | 0.997218i | \(0.476252\pi\) | |||||||
\(312\) | 3766.92 | + | 2736.83i | 0.683525 | + | 0.496610i | ||||
\(313\) | 1847.23 | + | 5685.18i | 0.333583 | + | 1.02666i | 0.967416 | + | 0.253192i | \(0.0814806\pi\) |
−0.633833 | + | 0.773470i | \(0.718519\pi\) | |||||||
\(314\) | 1583.23 | + | 4872.69i | 0.284545 | + | 0.875739i | ||||
\(315\) | −2945.31 | − | 2139.89i | −0.526824 | − | 0.382760i | ||||
\(316\) | −985.249 | + | 715.825i | −0.175394 | + | 0.127431i | ||||
\(317\) | 1616.76 | − | 4975.87i | 0.286455 | − | 0.881617i | −0.699504 | − | 0.714628i | \(-0.746596\pi\) |
0.985959 | − | 0.166988i | \(-0.0534042\pi\) | |||||||
\(318\) | −3558.31 | −0.627485 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 346.118 | 0.0604644 | ||||||||
\(321\) | 150.837 | − | 464.230i | 0.0262272 | − | 0.0807189i | ||||
\(322\) | −5106.50 | + | 3710.09i | −0.883771 | + | 0.642097i | ||||
\(323\) | −4569.29 | − | 3319.79i | −0.787128 | − | 0.571882i | ||||
\(324\) | −773.670 | − | 2381.11i | −0.132659 | − | 0.408284i | ||||
\(325\) | 2273.24 | + | 6996.32i | 0.387990 | + | 1.19411i | ||||
\(326\) | −2938.49 | − | 2134.94i | −0.499227 | − | 0.362710i | ||||
\(327\) | 9555.22 | − | 6942.27i | 1.61592 | − | 1.17403i | ||||
\(328\) | −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 | ||||
\(333\) | 3579.40 | − | 2600.59i | 0.589039 | − | 0.427962i | ||||
\(334\) | 613.114 | + | 445.453i | 0.100443 | + | 0.0729764i | ||||
\(335\) | 1380.80 | + | 4249.67i | 0.225198 | + | 0.693088i | ||||
\(336\) | 829.656 | + | 2553.42i | 0.134707 | + | 0.414585i | ||||
\(337\) | 4131.33 | + | 3001.58i | 0.667797 | + | 0.485183i | 0.869287 | − | 0.494308i | \(-0.164578\pi\) |
−0.201490 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(338\) | −5995.43 | + | 4355.93i | −0.964817 | + | 0.700981i | ||||
\(339\) | −5241.91 | + | 16132.9i | −0.839827 | + | 2.58472i | ||||
\(340\) | −1282.55 | −0.204576 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5790.43 | −0.915528 | ||||||||
\(343\) | −1337.35 | + | 4115.94i | −0.210525 | + | 0.647929i | ||||
\(344\) | −979.706 | + | 711.798i | −0.153553 | + | 0.111563i | ||||
\(345\) | −4722.74 | − | 3431.27i | −0.736996 | − | 0.535459i | ||||
\(346\) | −31.3479 | − | 96.4789i | −0.00487073 | − | 0.0149906i | ||||
\(347\) | −2331.77 | − | 7176.44i | −0.360737 | − | 1.11023i | −0.952608 | − | 0.304201i | \(-0.901610\pi\) |
0.591871 | − | 0.806033i | \(-0.298390\pi\) | |||||||
\(348\) | −500.568 | − | 363.684i | −0.0771070 | − | 0.0560215i | ||||
\(349\) | −2634.74 | + | 1914.25i | −0.404109 | + | 0.293603i | −0.771213 | − | 0.636578i | \(-0.780350\pi\) |
0.367103 | + | 0.930180i | \(0.380350\pi\) | |||||||
\(350\) | −1310.79 | + | 4034.19i | −0.200184 | + | 0.616104i | ||||
\(351\) | −1974.19 | −0.300212 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6506.83 | −0.981087 | −0.490543 | − | 0.871417i | \(-0.663202\pi\) | ||||
−0.490543 | + | 0.871417i | \(0.663202\pi\) | |||||||
\(354\) | 1416.31 | − | 4358.97i | 0.212645 | − | 0.654453i | ||||
\(355\) | 3933.19 | − | 2857.63i | 0.588034 | − | 0.427232i | ||||
\(356\) | 1013.21 | + | 736.142i | 0.150843 | + | 0.109594i | ||||
\(357\) | −3074.31 | − | 9461.75i | −0.455769 | − | 1.40271i | ||||
\(358\) | 12.8970 | + | 39.6929i | 0.00190399 | + | 0.00585988i | ||||
\(359\) | 3289.63 | + | 2390.06i | 0.483622 | + | 0.351372i | 0.802726 | − | 0.596348i | \(-0.203382\pi\) |
−0.319105 | + | 0.947720i | \(0.603382\pi\) | |||||||
\(360\) | −1063.78 | + | 772.880i | −0.155739 | + | 0.113151i | ||||
\(361\) | 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 | ||||
\(366\) | −1829.84 | + | 1329.46i | −0.261331 | + | 0.189868i | ||||
\(367\) | 1126.37 | + | 818.358i | 0.160208 | + | 0.116398i | 0.665001 | − | 0.746843i | \(-0.268431\pi\) |
−0.504793 | + | 0.863240i | \(0.668431\pi\) | |||||||
\(368\) | 704.479 | + | 2168.16i | 0.0997922 | + | 0.307129i | ||||
\(369\) | −777.933 | − | 2394.23i | −0.109749 | − | 0.337774i | ||||
\(370\) | 1273.87 | + | 925.524i | 0.178988 | + | 0.130042i | ||||
\(371\) | 4208.39 | − | 3057.58i | 0.588919 | − | 0.427875i | ||||
\(372\) | 1997.41 | − | 6147.39i | 0.278389 | − | 0.856794i | ||||
\(373\) | −9440.30 | −1.31046 | −0.655228 | − | 0.755431i | \(-0.727428\pi\) | ||||
−0.655228 | + | 0.755431i | \(0.727428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9044.32 | −1.24546 | ||||||||
\(376\) | 223.393 | − | 687.533i | 0.0306399 | − | 0.0943000i | ||||
\(377\) | 1269.09 | − | 922.044i | 0.173372 | − | 0.125962i | ||||
\(378\) | −920.943 | − | 669.104i | −0.125313 | − | 0.0910450i | ||||
\(379\) | 398.740 | + | 1227.20i | 0.0540420 | + | 0.166324i | 0.974435 | − | 0.224671i | \(-0.0721308\pi\) |
−0.920393 | + | 0.390995i | \(0.872131\pi\) | |||||||
\(380\) | −636.809 | − | 1959.90i | −0.0859674 | − | 0.264581i | ||||
\(381\) | 6701.69 | + | 4869.06i | 0.901149 | + | 0.654723i | ||||
\(382\) | 1875.66 | − | 1362.74i | 0.251222 | − | 0.182524i | ||||
\(383\) | −1746.84 | + | 5376.22i | −0.233053 | + | 0.717264i | 0.764321 | + | 0.644836i | \(0.223075\pi\) |
−0.997374 | + | 0.0724273i | \(0.976925\pi\) | |||||||
\(384\) | 969.696 | 0.128866 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2569.88 | 0.338868 | ||||||||
\(387\) | 1421.64 | − | 4375.35i | 0.186734 | − | 0.574707i | ||||
\(388\) | 1885.03 | − | 1369.55i | 0.246644 | − | 0.179197i | ||||
\(389\) | 10386.2 | + | 7545.99i | 1.35373 | + | 0.983539i | 0.998816 | + | 0.0486380i | \(0.0154881\pi\) |
0.354909 | + | 0.934901i | \(0.384512\pi\) | |||||||
\(390\) | −1945.34 | − | 5987.15i | −0.252580 | − | 0.777362i | ||||
\(391\) | −2610.46 | − | 8034.18i | −0.337639 | − | 1.03915i | ||||
\(392\) | −955.381 | − | 694.125i | −0.123097 | − | 0.0894352i | ||||
\(393\) | −15114.9 | + | 10981.6i | −1.94006 | + | 1.40954i | ||||
\(394\) | 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 | ||||
\(399\) | 12932.3 | − | 9395.86i | 1.62262 | − | 1.17890i | ||||
\(400\) | 1239.45 | + | 900.510i | 0.154931 | + | 0.112564i | ||||
\(401\) | 2406.06 | + | 7405.09i | 0.299633 | + | 0.922176i | 0.981626 | + | 0.190817i | \(0.0611136\pi\) |
−0.681993 | + | 0.731359i | \(0.738886\pi\) | |||||||
\(402\) | 3868.50 | + | 11906.0i | 0.479958 | + | 1.47716i | ||||
\(403\) | 13257.8 | + | 9632.33i | 1.63875 | + | 1.19062i | ||||
\(404\) | −458.080 | + | 332.814i | −0.0564117 | + | 0.0409855i | ||||
\(405\) | −1046.02 | + | 3219.32i | −0.128339 | + | 0.394986i | ||||
\(406\) | 904.523 | 0.110568 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3593.23 | −0.436008 | ||||||||
\(409\) | 2737.85 | − | 8426.25i | 0.330998 | − | 1.01871i | −0.637662 | − | 0.770316i | \(-0.720098\pi\) |
0.968660 | − | 0.248391i | \(-0.0799017\pi\) | |||||||
\(410\) | 724.826 | − | 526.617i | 0.0873087 | − | 0.0634335i | ||||
\(411\) | 5965.18 | + | 4333.96i | 0.715914 | + | 0.520142i | ||||
\(412\) | 1040.00 | + | 3200.80i | 0.124362 | + | 0.382748i | ||||
\(413\) | 2070.50 | + | 6372.33i | 0.246689 | + | 0.759230i | ||||
\(414\) | −7006.68 | − | 5090.65i | −0.831786 | − | 0.604328i | ||||
\(415\) | −3343.97 | + | 2429.54i | −0.395540 | + | 0.287377i | ||||
\(416\) | −759.706 | + | 2338.14i | −0.0895377 | + | 0.275569i | ||||
\(417\) | 9568.47 | 1.12367 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9469.08 | 1.10405 | 0.552023 | − | 0.833829i | \(-0.313856\pi\) | ||||
0.552023 | + | 0.833829i | \(0.313856\pi\) | |||||||
\(420\) | 1121.72 | − | 3452.29i | 0.130319 | − | 0.401082i | ||||
\(421\) | −4189.04 | + | 3043.52i | −0.484944 | + | 0.352333i | −0.803237 | − | 0.595660i | \(-0.796891\pi\) |
0.318292 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(422\) | −2634.43 | − | 1914.03i | −0.303891 | − | 0.220790i | ||||
\(423\) | 848.668 | + | 2611.93i | 0.0975500 | + | 0.300228i | ||||
\(424\) | −580.578 | − | 1786.84i | −0.0664985 | − | 0.204661i | ||||
\(425\) | −4592.79 | − | 3336.86i | −0.524196 | − | 0.380850i | ||||
\(426\) | 11019.4 | − | 8006.03i | 1.25326 | − | 0.910548i | ||||
\(427\) | 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 | 0.590862 | + | 0.806773i | \(0.298788\pi\) |
−0.952226 | + | 0.305393i | \(0.901212\pi\) | |||||||
\(432\) | −332.623 | + | 241.665i | −0.0370448 | + | 0.0269146i | ||||
\(433\) | −12813.4 | − | 9309.48i | −1.42211 | − | 1.03322i | −0.991419 | − | 0.130721i | \(-0.958271\pi\) |
−0.430688 | − | 0.902501i | \(-0.641729\pi\) | |||||||
\(434\) | 2919.99 | + | 8986.81i | 0.322959 | + | 0.993965i | ||||
\(435\) | 258.507 | + | 795.603i | 0.0284930 | + | 0.0876925i | ||||
\(436\) | 5045.16 | + | 3665.52i | 0.554173 | + | 0.402630i | ||||
\(437\) | 10981.1 | − | 7978.23i | 1.20205 | − | 0.873342i | ||||
\(438\) | 646.095 | − | 1988.47i | 0.0704831 | − | 0.216925i | ||||
\(439\) | 4824.70 | 0.524534 | 0.262267 | − | 0.964995i | \(-0.415530\pi\) | ||||
0.262267 | + | 0.964995i | \(0.415530\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4486.29 | 0.484429 | ||||||||
\(442\) | 2815.11 | − | 8664.01i | 0.302944 | − | 0.932364i | ||||
\(443\) | −2899.02 | + | 2106.26i | −0.310918 | + | 0.225895i | −0.732290 | − | 0.680993i | \(-0.761549\pi\) |
0.421372 | + | 0.906888i | \(0.361549\pi\) | |||||||
\(444\) | 3568.93 | + | 2592.98i | 0.381472 | + | 0.277156i | ||||
\(445\) | −523.251 | − | 1610.40i | −0.0557404 | − | 0.171551i | ||||
\(446\) | −1624.31 | − | 4999.12i | −0.172452 | − | 0.530752i | ||||
\(447\) | −2999.12 | − | 2178.99i | −0.317346 | − | 0.230565i | ||||
\(448\) | −1146.85 | + | 833.238i | −0.120946 | + | 0.0878723i | ||||
\(449\) | −2409.09 | + | 7414.42i | −0.253212 | + | 0.779306i | 0.740965 | + | 0.671544i | \(0.234368\pi\) |
−0.994177 | + | 0.107762i | \(0.965632\pi\) | |||||||
\(450\) | −5820.21 | −0.609705 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8956.57 | −0.932039 | ||||||||
\(453\) | −3997.96 | + | 12304.5i | −0.414659 | + | 1.27619i | ||||
\(454\) | 2754.79 | − | 2001.47i | 0.284777 | − | 0.206903i | ||||
\(455\) | 7445.37 | + | 5409.38i | 0.767130 | + | 0.557353i | ||||
\(456\) | −1784.10 | − | 5490.91i | −0.183220 | − | 0.563893i | ||||
\(457\) | −1034.60 | − | 3184.16i | −0.105900 | − | 0.325927i | 0.884041 | − | 0.467410i | \(-0.154813\pi\) |
−0.989941 | + | 0.141483i | \(0.954813\pi\) | |||||||
\(458\) | −8730.83 | − | 6343.32i | −0.890753 | − | 0.647170i | ||||
\(459\) | 1232.54 | − | 895.494i | 0.125338 | − | 0.0910634i | ||||
\(460\) | 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 | ||||
\(465\) | −7070.13 | + | 5136.75i | −0.705095 | + | 0.512282i | ||||
\(466\) | −9795.87 | − | 7117.12i | −0.973788 | − | 0.707498i | ||||
\(467\) | −3653.15 | − | 11243.2i | −0.361986 | − | 1.11408i | −0.951847 | − | 0.306574i | \(-0.900817\pi\) |
0.589860 | − | 0.807505i | \(-0.299183\pi\) | |||||||
\(468\) | −2886.12 | − | 8882.56i | −0.285066 | − | 0.877343i | ||||
\(469\) | −14805.8 | − | 10757.1i | −1.45772 | − | 1.05909i | ||||
\(470\) | −790.732 | + | 574.501i | −0.0776037 | + | 0.0563824i | ||||
\(471\) | 5997.09 | − | 18457.1i | 0.586691 | − | 1.80565i | ||||
\(472\) | 2419.98 | 0.235993 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4613.00 | 0.447009 | ||||||||
\(475\) | 2818.74 | − | 8675.18i | 0.272279 | − | 0.837988i | ||||
\(476\) | 4249.69 | − | 3087.58i | 0.409210 | − | 0.297309i | ||||
\(477\) | 5774.37 | + | 4195.33i | 0.554277 | + | 0.402706i | ||||
\(478\) | −1938.53 | − | 5966.17i | −0.185494 | − | 0.570891i | ||||
\(479\) | 2676.07 | + | 8236.09i | 0.255267 | + | 0.785630i | 0.993777 | + | 0.111388i | \(0.0355296\pi\) |
−0.738510 | + | 0.674242i | \(0.764470\pi\) | |||||||
\(480\) | −1060.66 | − | 770.618i | −0.100859 | − | 0.0732786i | ||||
\(481\) | −9048.27 | + | 6573.95i | −0.857725 | + | 0.623173i | ||||
\(482\) | 4016.76 | − | 12362.3i | 0.379582 | − | 1.16823i | ||||
\(483\) | 23909.0 | 2.25238 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3150.25 | −0.294939 | ||||||||
\(486\) | −3359.36 | + | 10339.0i | −0.313547 | + | 0.964997i | ||||
\(487\) | −6009.10 | + | 4365.87i | −0.559134 | + | 0.406235i | −0.831142 | − | 0.556060i | \(-0.812312\pi\) |
0.272008 | + | 0.962295i | \(0.412312\pi\) | |||||||
\(488\) | −966.157 | − | 701.954i | −0.0896227 | − | 0.0651147i | ||||
\(489\) | 4251.52 | + | 13084.8i | 0.393171 | + | 1.21006i | ||||
\(490\) | 493.385 | + | 1518.48i | 0.0454875 | + | 0.139996i | ||||
\(491\) | −4485.10 | − | 3258.62i | −0.412240 | − | 0.299510i | 0.362268 | − | 0.932074i | \(-0.382002\pi\) |
−0.774508 | + | 0.632564i | \(0.782002\pi\) | |||||||
\(492\) | 2030.69 | − | 1475.38i | 0.186079 | − | 0.135194i | ||||
\(493\) | −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 | ||||
\(498\) | −9368.57 | + | 6806.67i | −0.843003 | + | 0.612478i | ||||
\(499\) | −16513.7 | − | 11997.9i | −1.48147 | − | 1.07635i | −0.977079 | − | 0.212875i | \(-0.931717\pi\) |
−0.504391 | − | 0.863476i | \(-0.668283\pi\) | |||||||
\(500\) | −1475.68 | − | 4541.68i | −0.131989 | − | 0.406220i | ||||
\(501\) | −887.077 | − | 2730.14i | −0.0791051 | − | 0.243460i | ||||
\(502\) | −9005.63 | − | 6542.98i | −0.800680 | − | 0.581728i | ||||
\(503\) | −147.841 | + | 107.413i | −0.0131052 | + | 0.00952148i | −0.594319 | − | 0.804230i | \(-0.702578\pi\) |
0.581213 | + | 0.813751i | \(0.302578\pi\) | |||||||
\(504\) | 1664.18 | − | 5121.83i | 0.147081 | − | 0.452667i | ||||
\(505\) | 765.540 | 0.0674576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28071.0 | 2.45893 | ||||||||
\(508\) | −1351.58 | + | 4159.75i | −0.118045 | + | 0.363305i | ||||
\(509\) | −3847.11 | + | 2795.09i | −0.335010 | + | 0.243399i | −0.742554 | − | 0.669787i | \(-0.766386\pi\) |
0.407543 | + | 0.913186i | \(0.366386\pi\) | |||||||
\(510\) | 3930.31 | + | 2855.54i | 0.341249 | + | 0.247932i | ||||
\(511\) | 944.519 | + | 2906.93i | 0.0817673 | + | 0.251654i | ||||
\(512\) | 158.217 | + | 486.941i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | 1980.41 | + | 1438.85i | 0.170443 | + | 0.123834i | ||||
\(514\) | 9766.95 | − | 7096.11i | 0.838136 | − | 0.608941i | ||||
\(515\) | 1406.11 | − | 4327.56i | 0.120312 | − | 0.370282i | ||||
\(516\) | 4587.05 | 0.391344 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6449.03 | −0.547016 | ||||||||
\(519\) | −118.742 | + | 365.450i | −0.0100428 | + | 0.0309084i | ||||
\(520\) | 2689.09 | − | 1953.74i | 0.226778 | − | 0.164764i | ||||
\(521\) | 9490.70 | + | 6895.40i | 0.798071 | + | 0.579833i | 0.910348 | − | 0.413844i | \(-0.135814\pi\) |
−0.112277 | + | 0.993677i | \(0.535814\pi\) | |||||||
\(522\) | 383.522 | + | 1180.36i | 0.0321577 | + | 0.0989712i | ||||
\(523\) | 106.252 | + | 327.011i | 0.00888353 | + | 0.0273407i | 0.955400 | − | 0.295315i | \(-0.0954245\pi\) |
−0.946517 | + | 0.322655i | \(0.895425\pi\) | |||||||
\(524\) | −7980.67 | − | 5798.29i | −0.665338 | − | 0.483396i | ||||
\(525\) | 12998.8 | − | 9444.18i | 1.08060 | − | 0.785101i | ||||
\(526\) | 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 | ||||
\(531\) | −7437.69 | + | 5403.80i | −0.607850 | + | 0.441629i | ||||
\(532\) | 6828.26 | + | 4961.02i | 0.556471 | + | 0.404300i | ||||
\(533\) | 1966.51 | + | 6052.31i | 0.159811 | + | 0.491847i | ||||
\(534\) | −1465.95 | − | 4511.74i | −0.118798 | − | 0.365622i | ||||
\(535\) | −281.906 | − | 204.816i | −0.0227810 | − | 0.0165514i | ||||
\(536\) | −5347.51 | + | 3885.20i | −0.430928 | + | 0.313088i | ||||
\(537\) | 48.8522 | − | 150.352i | 0.00392575 | − | 0.0120822i | ||||
\(538\) | −9619.41 | −0.770859 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 555.878 | 0.0442985 | ||||||||
\(541\) | 5328.62 | − | 16399.8i | 0.423466 | − | 1.30329i | −0.480989 | − | 0.876726i | \(-0.659722\pi\) |
0.904455 | − | 0.426568i | \(-0.140278\pi\) | |||||||
\(542\) | −8479.93 | + | 6161.03i | −0.672037 | + | 0.488263i | ||||
\(543\) | 1079.63 | + | 784.395i | 0.0853246 | + | 0.0619919i | ||||
\(544\) | −586.275 | − | 1804.37i | −0.0462065 | − | 0.142209i | ||||
\(545\) | −2605.46 | − | 8018.78i | −0.204781 | − | 0.630251i | ||||
\(546\) | 20859.2 | + | 15155.1i | 1.63496 | + | 1.18787i | ||||
\(547\) | −6183.49 | + | 4492.57i | −0.483340 | + | 0.351167i | −0.802617 | − | 0.596494i | \(-0.796560\pi\) |
0.319277 | + | 0.947661i | \(0.396560\pi\) | |||||||
\(548\) | −1203.05 | + | 3702.60i | −0.0937804 | + | 0.288626i | ||||
\(549\) | 4536.89 | 0.352696 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1945.10 | −0.150388 | ||||||||
\(552\) | 2668.48 | − | 8212.73i | 0.205757 | − | 0.633256i | ||||
\(553\) | −5455.77 | + | 3963.85i | −0.419535 | + | 0.304810i | ||||
\(554\) | −8639.89 | − | 6277.25i | −0.662588 | − | 0.481399i | ||||
\(555\) | −1843.09 | − | 5672.45i | −0.140964 | − | 0.433842i | ||||
\(556\) | 1561.20 | + | 4804.89i | 0.119082 | + | 0.366498i | ||||
\(557\) | 21120.3 | + | 15344.8i | 1.60664 | + | 1.16729i | 0.872955 | + | 0.487800i | \(0.162201\pi\) |
0.733684 | + | 0.679491i | \(0.237799\pi\) | |||||||
\(558\) | −10489.3 | + | 7620.90i | −0.795782 | + | 0.578170i | ||||
\(559\) | −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 | −0.491364 | − | 0.870954i | \(-0.663502\pi\) |
0.909456 | − | 0.415800i | \(-0.136498\pi\) | |||||||
\(564\) | −2215.34 | + | 1609.54i | −0.165395 | + | 0.120166i | ||||
\(565\) | 9796.79 | + | 7117.79i | 0.729476 | + | 0.529996i | ||||
\(566\) | 3025.58 | + | 9311.78i | 0.224690 | + | 0.691525i | ||||
\(567\) | −4284.16 | − | 13185.3i | −0.317316 | − | 0.976597i | ||||
\(568\) | 5818.23 | + | 4227.19i | 0.429802 | + | 0.312269i | ||||
\(569\) | 6314.50 | − | 4587.76i | 0.465233 | − | 0.338012i | −0.330347 | − | 0.943859i | \(-0.607166\pi\) |
0.795581 | + | 0.605848i | \(0.207166\pi\) | |||||||
\(570\) | −2412.15 | + | 7423.84i | −0.177253 | + | 0.545527i | ||||
\(571\) | 13039.6 | 0.955672 | 0.477836 | − | 0.878449i | \(-0.341421\pi\) | ||||
0.477836 | + | 0.878449i | \(0.341421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8781.96 | −0.640264 | ||||||||
\(574\) | −1133.92 | + | 3489.86i | −0.0824548 | + | 0.253770i | ||||
\(575\) | 11037.6 | − | 8019.26i | 0.800519 | − | 0.581611i | ||||
\(576\) | −1573.61 | − | 1143.29i | −0.113831 | − | 0.0827034i | ||||
\(577\) | −2957.12 | − | 9101.06i | −0.213356 | − | 0.656642i | −0.999266 | − | 0.0383013i | \(-0.987805\pi\) |
0.785910 | − | 0.618340i | \(-0.212195\pi\) | |||||||
\(578\) | −863.946 | − | 2658.95i | −0.0621720 | − | 0.191346i | ||||
\(579\) | −7875.26 | − | 5721.71i | −0.565259 | − | 0.410685i | ||||
\(580\) | −357.340 | + | 259.623i | −0.0255823 | + | 0.0185866i | ||||
\(581\) | 5231.34 | − | 16100.4i | 0.373550 | − | 1.14967i | ||||
\(582\) | −8825.83 | −0.628595 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1103.95 | 0.0782220 | ||||||||
\(585\) | −3902.11 | + | 12009.4i | −0.275782 | + | 0.848769i | ||||
\(586\) | 10850.2 | − | 7883.14i | 0.764877 | − | 0.555716i | ||||
\(587\) | −7869.31 | − | 5717.39i | −0.553324 | − | 0.402013i | 0.275686 | − | 0.961248i | \(-0.411095\pi\) |
−0.829009 | + | 0.559235i | \(0.811095\pi\) | |||||||
\(588\) | 1382.28 | + | 4254.23i | 0.0969462 | + | 0.298370i | ||||
\(589\) | −6279.19 | − | 19325.4i | −0.439269 | − | 1.35193i | ||||
\(590\) | −2647.00 | − | 1923.16i | −0.184704 | − | 0.134195i | ||||
\(591\) | −16456.5 | + | 11956.3i | −1.14540 | + | 0.832179i | ||||
\(592\) | −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 | ||||
\(597\) | 8173.14 | − | 5938.13i | 0.560309 | − | 0.407088i | ||||
\(598\) | 17712.0 | + | 12868.5i | 1.21120 | + | 0.879987i | ||||
\(599\) | −6793.63 | − | 20908.7i | −0.463406 | − | 1.42622i | −0.860976 | − | 0.508646i | \(-0.830146\pi\) |
0.397570 | − | 0.917572i | \(-0.369854\pi\) | |||||||
\(600\) | −1793.28 | − | 5519.14i | −0.122017 | − | 0.375530i | ||||
\(601\) | −5957.01 | − | 4328.02i | −0.404312 | − | 0.293750i | 0.366983 | − | 0.930228i | \(-0.380391\pi\) |
−0.771295 | + | 0.636478i | \(0.780391\pi\) | |||||||
\(602\) | −5425.08 | + | 3941.55i | −0.367292 | + | 0.266853i | ||||
\(603\) | 7759.71 | − | 23881.9i | 0.524046 | − | 1.61285i | ||||
\(604\) | −6831.10 | −0.460188 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2144.76 | 0.143771 | ||||||||
\(607\) | −3142.21 | + | 9670.72i | −0.210113 | + | 0.646660i | 0.789352 | + | 0.613941i | \(0.210417\pi\) |
−0.999465 | + | 0.0327190i | \(0.989583\pi\) | |||||||
\(608\) | 2466.21 | − | 1791.81i | 0.164503 | − | 0.119519i | ||||
\(609\) | −2771.87 | − | 2013.88i | −0.184437 | − | 0.134001i | ||||
\(610\) | 498.950 | + | 1535.61i | 0.0331179 | + | 0.101926i | ||||
\(611\) | −2145.32 | − | 6602.63i | −0.142047 | − | 0.437175i | ||||
\(612\) | 5831.03 | + | 4236.49i | 0.385140 | + | 0.279820i | ||||
\(613\) | 20293.8 | − | 14744.3i | 1.33713 | − | 0.971479i | 0.337581 | − | 0.941296i | \(-0.390391\pi\) |
0.999544 | − | 0.0301824i | \(-0.00960883\pi\) | |||||||
\(614\) | −5875.83 | + | 18083.9i | −0.386204 | + | 1.18861i | ||||
\(615\) | −3393.68 | −0.222515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26335.5 | −1.71836 | −0.859178 | − | 0.511677i | \(-0.829024\pi\) | ||||
−0.859178 | + | 0.511677i | \(0.829024\pi\) | |||||||
\(618\) | 3939.40 | − | 12124.2i | 0.256417 | − | 0.789171i | ||||
\(619\) | 19936.7 | − | 14484.9i | 1.29455 | − | 0.940544i | 0.294661 | − | 0.955602i | \(-0.404793\pi\) |
0.999887 | + | 0.0150577i | \(0.00479321\pi\) | |||||||
\(620\) | −3733.03 | − | 2712.21i | −0.241810 | − | 0.175685i | ||||
\(621\) | 1131.42 | + | 3482.15i | 0.0731115 | + | 0.225014i | ||||
\(622\) | 3564.87 | + | 10971.5i | 0.229804 | + | 0.707264i | ||||
\(623\) | 5610.62 | + | 4076.35i | 0.360810 | + | 0.262144i | ||||
\(624\) | 7533.84 | − | 5473.66i | 0.483326 | − | 0.351157i | ||||
\(625\) | 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 | ||||
\(630\) | −5890.62 | + | 4279.79i | −0.372521 | + | 0.270652i | ||||
\(631\) | −6031.48 | − | 4382.13i | −0.380522 | − | 0.276465i | 0.381039 | − | 0.924559i | \(-0.375567\pi\) |
−0.761561 | + | 0.648094i | \(0.775567\pi\) | |||||||
\(632\) | 752.663 | + | 2316.46i | 0.0473724 | + | 0.145797i | ||||
\(633\) | 3811.60 | + | 11730.9i | 0.239332 | + | 0.736589i | ||||
\(634\) | −8465.45 | − | 6150.51i | −0.530293 | − | 0.385281i | ||||
\(635\) | 4784.13 | − | 3475.88i | 0.298980 | − | 0.217222i | ||||
\(636\) | −2199.16 | + | 6768.31i | −0.137110 | + | 0.421983i | ||||
\(637\) | −11340.8 | −0.705397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27321.3 | −1.69141 | ||||||||
\(640\) | 213.913 | − | 658.356i | 0.0132120 | − | 0.0406622i | ||||
\(641\) | 2247.99 | − | 1633.26i | 0.138518 | − | 0.100639i | −0.516368 | − | 0.856367i | \(-0.672716\pi\) |
0.654887 | + | 0.755727i | \(0.272716\pi\) | |||||||
\(642\) | −789.795 | − | 573.820i | −0.0485525 | − | 0.0352755i | ||||
\(643\) | 2335.46 | + | 7187.81i | 0.143237 | + | 0.440839i | 0.996780 | − | 0.0801836i | \(-0.0255507\pi\) |
−0.853543 | + | 0.521023i | \(0.825551\pi\) | |||||||
\(644\) | 3901.02 | + | 12006.1i | 0.238698 | + | 0.734638i | ||||
\(645\) | −5017.37 | − | 3645.33i | −0.306292 | − | 0.222535i | ||||
\(646\) | −9138.59 | + | 6639.57i | −0.556584 | + | 0.404382i | ||||
\(647\) | −8476.55 | + | 26088.1i | −0.515066 | + | 1.58521i | 0.268096 | + | 0.963392i | \(0.413605\pi\) |
−0.783162 | + | 0.621817i | \(0.786395\pi\) | |||||||
\(648\) | −5007.30 | −0.303557 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 14712.7 | 0.887817 | ||||||||
\(651\) | 11060.6 | − | 34040.9i | 0.665895 | − | 2.04941i | ||||
\(652\) | −5876.98 | + | 4269.88i | −0.353007 | + | 0.256474i | ||||
\(653\) | −230.350 | − | 167.359i | −0.0138044 | − | 0.0100295i | 0.580862 | − | 0.814002i | \(-0.302716\pi\) |
−0.594666 | + | 0.803973i | \(0.702716\pi\) | |||||||
\(654\) | −7299.54 | − | 22465.7i | −0.436444 | − | 1.34324i | ||||
\(655\) | 4121.44 | + | 12684.5i | 0.245859 | + | 0.756677i | ||||
\(656\) | 1072.21 | + | 779.004i | 0.0638150 | + | 0.0463643i | ||||
\(657\) | −3392.93 | + | 2465.11i | −0.201477 | + | 0.146382i | ||||
\(658\) | 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 | ||||
\(663\) | −27916.8 | + | 20282.8i | −1.63529 | + | 1.18811i | ||||
\(664\) | −4946.61 | − | 3593.92i | −0.289105 | − | 0.210047i | ||||
\(665\) | −3526.30 | − | 10852.8i | −0.205630 | − | 0.632865i | ||||
\(666\) | −2734.42 | − | 8415.68i | −0.159094 | − | 0.489641i | ||||
\(667\) | −2353.66 | − | 1710.03i | −0.136633 | − | 0.0992694i | ||||
\(668\) | 1226.23 | − | 890.906i | 0.0710242 | − | 0.0516021i | ||||
\(669\) | −6152.69 | + | 18936.0i | −0.355571 | + | 1.09433i | ||||
\(670\) | 8936.74 | 0.515308 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5369.65 | 0.308242 | ||||||||
\(673\) | −9229.07 | + | 28404.2i | −0.528610 | + | 1.62689i | 0.228455 | + | 0.973554i | \(0.426633\pi\) |
−0.757065 | + | 0.653340i | \(0.773367\pi\) | |||||||
\(674\) | 8262.65 | − | 6003.17i | 0.472204 | − | 0.343076i | ||||
\(675\) | 1990.59 | + | 1446.25i | 0.113508 | + | 0.0824684i | ||||
\(676\) | 4580.10 | + | 14096.1i | 0.260588 | + | 0.802008i | ||||
\(677\) | 5340.04 | + | 16435.0i | 0.303153 | + | 0.933009i | 0.980360 | + | 0.197216i | \(0.0631901\pi\) |
−0.677207 | + | 0.735793i | \(0.736810\pi\) | |||||||
\(678\) | 27447.0 | + | 19941.4i | 1.55471 | + | 1.12956i | ||||
\(679\) | 10438.3 | − | 7583.84i | 0.589961 | − | 0.428632i | ||||
\(680\) | −792.659 | + | 2439.55i | −0.0447016 | + | 0.137577i | ||||
\(681\) | −12898.1 | −0.725782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25104.0 | 1.40641 | 0.703204 | − | 0.710988i | \(-0.251752\pi\) | ||||
0.703204 | + | 0.710988i | \(0.251752\pi\) | |||||||
\(684\) | −3578.68 | + | 11014.1i | −0.200050 | + | 0.615691i | ||||
\(685\) | 4258.37 | − | 3093.88i | 0.237524 | − | 0.172571i | ||||
\(686\) | 7002.45 | + | 5087.58i | 0.389730 | + | 0.283156i | ||||
\(687\) | 12632.1 | + | 38877.6i | 0.701521 | + | 2.15906i | ||||
\(688\) | 748.429 | + | 2303.43i | 0.0414732 | + | 0.127641i | ||||
\(689\) | −14596.9 | − | 10605.2i | −0.807106 | − | 0.586397i | ||||
\(690\) | −9445.47 | + | 6862.54i | −0.521135 | + | 0.378627i | ||||
\(691\) | −8085.06 | + | 24883.3i | −0.445109 | + | 1.36990i | 0.437256 | + | 0.899337i | \(0.355950\pi\) |
−0.882364 | + | 0.470567i | \(0.844050\pi\) | |||||||
\(692\) | −202.888 | −0.0111454 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15091.5 | −0.825455 | ||||||||
\(695\) | 2110.79 | − | 6496.33i | 0.115204 | − | 0.354561i | ||||
\(696\) | −1001.14 | + | 727.367i | −0.0545229 | + | 0.0396132i | ||||
\(697\) | −3973.09 | − | 2886.62i | −0.215913 | − | 0.156870i | ||||
\(698\) | 2012.76 | + | 6194.64i | 0.109146 | + | 0.335917i | ||||
\(699\) | 14173.1 | + | 43620.2i | 0.766916 | + | 2.36032i | ||||
\(700\) | 6863.37 | + | 4986.53i | 0.370587 | + | 0.269248i | ||||
\(701\) | −1229.26 | + | 893.108i | −0.0662317 | + | 0.0481201i | −0.620408 | − | 0.784279i | \(-0.713033\pi\) |
0.554177 | + | 0.832399i | \(0.313033\pi\) | |||||||
\(702\) | −1220.11 | + | 3755.13i | −0.0655987 | + | 0.201892i | ||||
\(703\) | 13868.1 | 0.744018 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3702.26 | 0.197781 | ||||||||
\(706\) | −4021.44 | + | 12376.7i | −0.214375 | + | 0.659779i | ||||
\(707\) | −2536.59 | + | 1842.94i | −0.134934 | + | 0.0980354i | ||||
\(708\) | −7415.92 | − | 5387.98i | −0.393654 | − | 0.286007i | ||||
\(709\) | −6716.14 | − | 20670.2i | −0.355755 | − | 1.09490i | −0.955571 | − | 0.294762i | \(-0.904760\pi\) |
0.599816 | − | 0.800138i | \(-0.295240\pi\) | |||||||
\(710\) | −3004.69 | − | 9247.49i | −0.158823 | − | 0.488806i | ||||
\(711\) | −7485.91 | − | 5438.83i | −0.394857 | − | 0.286881i | ||||
\(712\) | 2026.42 | − | 1472.28i | 0.106662 | − | 0.0774946i | ||||
\(713\) | 9391.77 | − | 28904.9i | 0.493302 | − | 1.51823i | ||||
\(714\) | −19897.3 | −1.04291 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 83.4712 | 0.00435679 | ||||||||
\(717\) | −7342.89 | + | 22599.1i | −0.382462 | + | 1.17710i | ||||
\(718\) | 6579.26 | − | 4780.11i | 0.341972 | − | 0.248457i | ||||
\(719\) | 11384.4 | + | 8271.22i | 0.590494 | + | 0.429019i | 0.842492 | − | 0.538709i | \(-0.181088\pi\) |
−0.251998 | + | 0.967728i | \(0.581088\pi\) | |||||||
\(720\) | 812.654 | + | 2501.09i | 0.0420636 | + | 0.129459i | ||||
\(721\) | 5758.97 | + | 17724.3i | 0.297469 | + | 0.915516i | ||||
\(722\) | −3585.49 | − | 2605.01i | −0.184817 | − | 0.134278i | ||||
\(723\) | −39833.4 | + | 28940.6i | −2.04899 | + | 1.48868i | ||||
\(724\) | −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 | ||||
\(729\) | 19642.0 | − | 14270.7i | 0.997915 | − | 0.725027i | ||||
\(730\) | −1207.51 | − | 877.307i | −0.0612218 | − | 0.0444803i | ||||
\(731\) | −2773.32 | − | 8535.39i | −0.140321 | − | 0.431865i | ||||
\(732\) | 1397.87 | + | 4302.21i | 0.0705832 | + | 0.217233i | ||||
\(733\) | −15690.8 | − | 11400.0i | −0.790658 | − | 0.574447i | 0.117501 | − | 0.993073i | \(-0.462512\pi\) |
−0.908159 | + | 0.418626i | \(0.862512\pi\) | |||||||
\(734\) | 2252.75 | − | 1636.72i | 0.113284 | − | 0.0823056i | ||||
\(735\) | 1868.88 | − | 5751.82i | 0.0937887 | − | 0.288652i | ||||
\(736\) | 4559.48 | 0.228349 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5034.89 | −0.251134 | ||||||||
\(739\) | 2061.83 | − | 6345.68i | 0.102633 | − | 0.315872i | −0.886535 | − | 0.462662i | \(-0.846894\pi\) |
0.989168 | + | 0.146790i | \(0.0468942\pi\) | |||||||
\(740\) | 2547.75 | − | 1851.05i | 0.126564 | − | 0.0919539i | ||||
\(741\) | −44855.8 | − | 32589.7i | −2.22378 | − | 1.61567i | ||||
\(742\) | −3214.93 | − | 9894.52i | −0.159062 | − | 0.489541i | ||||
\(743\) | −2028.75 | − | 6243.86i | −0.100172 | − | 0.308297i | 0.888395 | − | 0.459080i | \(-0.151821\pi\) |
−0.988567 | + | 0.150782i | \(0.951821\pi\) | |||||||
\(744\) | −10458.6 | − | 7598.60i | −0.515363 | − | 0.374433i | ||||
\(745\) | −2140.98 | + | 1555.52i | −0.105288 | + | 0.0764962i | ||||
\(746\) | −5834.43 | + | 17956.5i | −0.286345 | + | 0.881280i | ||||
\(747\) | 23228.4 | 1.13773 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1427.16 | 0.0696223 | ||||||||
\(750\) | −5589.70 | + | 17203.3i | −0.272142 | + | 0.837568i | ||||
\(751\) | −15321.7 | + | 11131.9i | −0.744470 | + | 0.540889i | −0.894108 | − | 0.447852i | \(-0.852189\pi\) |
0.149638 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(752\) | −1169.70 | − | 849.837i | −0.0567215 | − | 0.0412106i | ||||
\(753\) | 13029.7 | + | 40101.3i | 0.630583 | + | 1.94073i | ||||
\(754\) | −969.495 | − | 2983.80i | −0.0468262 | − | 0.144116i | ||||
\(755\) | 7471.93 | + | 5428.68i | 0.360174 | + | 0.261682i | ||||
\(756\) | −1841.89 | + | 1338.21i | −0.0886094 | + | 0.0643785i | ||||
\(757\) | −3386.32 | + | 10422.0i | −0.162586 | + | 0.500389i | −0.998850 | − | 0.0479377i | \(-0.984735\pi\) |
0.836264 | + | 0.548327i | \(0.184735\pi\) | |||||||
\(758\) | 2580.70 | 0.123661 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4121.52 | −0.196715 | ||||||||
\(761\) | 10952.2 | − | 33707.5i | 0.521706 | − | 1.60565i | −0.249033 | − | 0.968495i | \(-0.580113\pi\) |
0.770739 | − | 0.637151i | \(-0.219887\pi\) | |||||||
\(762\) | 13403.4 | − | 9738.12i | 0.637209 | − | 0.462959i | ||||
\(763\) | 27937.4 | + | 20297.7i | 1.32556 | + | 0.963074i | ||||
\(764\) | −1432.87 | − | 4409.93i | −0.0678529 | − | 0.208830i | ||||
\(765\) | −3011.31 | − | 9267.85i | −0.142319 | − | 0.438013i | ||||
\(766\) | 9146.57 | + | 6645.37i | 0.431435 | + | 0.313456i | ||||
\(767\) | 18801.5 | − | 13660.1i | 0.885115 | − | 0.643074i | ||||
\(768\) | 599.305 | − | 1844.47i | 0.0281583 | − | 0.0866622i | ||||
\(769\) | −4444.21 | −0.208404 | −0.104202 | − | 0.994556i | \(-0.533229\pi\) | ||||
−0.104202 | + | 0.994556i | \(0.533229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45729.5 | −2.13607 | ||||||||
\(772\) | 1588.27 | − | 4888.19i | 0.0740455 | − | 0.227888i | ||||
\(773\) | −8219.75 | + | 5972.00i | −0.382463 | + | 0.277876i | −0.762360 | − | 0.647153i | \(-0.775959\pi\) |
0.379897 | + | 0.925029i | \(0.375959\pi\) | |||||||
\(774\) | −7443.79 | − | 5408.23i | −0.345687 | − | 0.251156i | ||||
\(775\) | −6311.48 | − | 19424.8i | −0.292536 | − | 0.900333i | ||||
\(776\) | −1440.03 | − | 4431.97i | −0.0666162 | − | 0.205024i | ||||
\(777\) | 19762.8 | + | 14358.5i | 0.912465 | + | 0.662945i | ||||
\(778\) | 20772.3 | − | 15092.0i | 0.957228 | − | 0.695467i | ||||
\(779\) | 2438.40 | − | 7504.64i | 0.112150 | − | 0.345162i | ||||
\(780\) | −12590.5 | −0.577965 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16895.3 | −0.772600 | ||||||||
\(783\) | 162.135 | − | 499.000i | 0.00740004 | − | 0.0227750i | ||||
\(784\) | −1910.76 | + | 1388.25i | −0.0870427 | + | 0.0632403i | ||||
\(785\) | −11208.2 | − | 8143.22i | −0.509601 | − | 0.370247i | ||||
\(786\) | 11546.7 | + | 35537.2i | 0.523993 | + | 1.61268i | ||||
\(787\) | 5645.76 | + | 17375.9i | 0.255718 | + | 0.787018i | 0.993687 | + | 0.112184i | \(0.0357847\pi\) |
−0.737970 | + | 0.674834i | \(0.764215\pi\) | |||||||
\(788\) | −8689.03 | − | 6312.95i | −0.392809 | − | 0.285393i | ||||
\(789\) | −4341.98 | + | 3154.63i | −0.195917 | + | 0.142342i | ||||
\(790\) | 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 | ||||
\(795\) | 7784.24 | − | 5655.58i | 0.347269 | − | 0.252305i | ||||
\(796\) | 4315.42 | + | 3135.34i | 0.192156 | + | 0.139609i | ||||
\(797\) | 5557.35 | + | 17103.8i | 0.246991 | + | 0.760159i | 0.995303 | + | 0.0968123i | \(0.0308647\pi\) |
−0.748312 | + | 0.663347i | \(0.769135\pi\) | |||||||
\(798\) | −9879.39 | − | 30405.6i | −0.438254 | − | 1.34881i | ||||
\(799\) | 4334.35 | + | 3149.09i | 0.191913 | + | 0.139433i | ||||
\(800\) | 2478.89 | − | 1801.02i | 0.109553 | − | 0.0795946i | ||||
\(801\) | −2940.52 | + | 9049.98i | −0.129710 | + | 0.399208i | ||||
\(802\) | 15572.3 | 0.685634 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 25037.4 | 1.09826 | ||||||||
\(805\) | 5274.28 | − | 16232.6i | 0.230924 | − | 0.710711i | ||||
\(806\) | 26515.5 | − | 19264.7i | 1.15877 | − | 0.841897i | ||||
\(807\) | 29478.2 | + | 21417.2i | 1.28585 | + | 0.934227i | ||||
\(808\) | 349.942 | + | 1077.01i | 0.0152363 | + | 0.0468924i | ||||
\(809\) | −1589.66 | − | 4892.47i | −0.0690846 | − | 0.212621i | 0.910554 | − | 0.413391i | \(-0.135656\pi\) |
−0.979638 | + | 0.200770i | \(0.935656\pi\) | |||||||
\(810\) | 5477.04 | + | 3979.30i | 0.237585 | + | 0.172615i | ||||
\(811\) | −6679.24 | + | 4852.75i | −0.289198 | + | 0.210115i | −0.722919 | − | 0.690932i | \(-0.757200\pi\) |
0.433721 | + | 0.901047i | \(0.357200\pi\) | |||||||
\(812\) | 559.026 | − | 1720.51i | 0.0241601 | − | 0.0743570i | ||||
\(813\) | 39703.6 | 1.71275 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9821.58 | 0.422129 | ||||||||
\(816\) | −2220.74 | + | 6834.73i | −0.0952712 | + | 0.293215i | ||||
\(817\) | 11666.2 | − | 8475.96i | 0.499568 | − | 0.362958i | ||||
\(818\) | −14335.6 | − | 10415.4i | −0.612753 | − | 0.445191i | ||||
\(819\) | −15981.8 | − | 49186.8i | −0.681866 | − | 2.09857i | ||||
\(820\) | −553.717 | − | 1704.17i | −0.0235813 | − | 0.0725757i | ||||
\(821\) | 200.029 | + | 145.330i | 0.00850314 | + | 0.00617789i | 0.592029 | − | 0.805917i | \(-0.298327\pi\) |
−0.583526 | + | 0.812095i | \(0.698327\pi\) | |||||||
\(822\) | 11930.4 | − | 8667.92i | 0.506228 | − | 0.367796i | ||||
\(823\) | 3644.80 | − | 11217.5i | 0.154374 | − | 0.475114i | −0.843723 | − | 0.536779i | \(-0.819641\pi\) |
0.998097 | + | 0.0616649i | \(0.0196410\pi\) | |||||||
\(824\) | 6731.04 | 0.284571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13400.5 | 0.564484 | ||||||||
\(827\) | 856.491 | − | 2636.01i | 0.0360134 | − | 0.110838i | −0.931434 | − | 0.363911i | \(-0.881441\pi\) |
0.967447 | + | 0.253073i | \(0.0814413\pi\) | |||||||
\(828\) | −14013.4 | + | 10181.3i | −0.588161 | + | 0.427324i | ||||
\(829\) | 22084.6 | + | 16045.4i | 0.925246 | + | 0.672231i | 0.944824 | − | 0.327578i | \(-0.106232\pi\) |
−0.0195780 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(830\) | 2554.57 | + | 7862.15i | 0.106832 | + | 0.328794i | ||||
\(831\) | 12500.5 | + | 38472.7i | 0.521828 | + | 1.60602i | ||||
\(832\) | 3977.87 | + | 2890.10i | 0.165755 | + | 0.120428i | ||||
\(833\) | 7080.37 | − | 5144.19i | 0.294502 | − | 0.213968i | ||||
\(834\) | 5913.64 | − | 18200.3i | 0.245531 | − | 0.755666i | ||||
\(835\) | −2049.26 | −0.0849314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5481.18 | 0.226353 | ||||||||
\(838\) | 5852.21 | − | 18011.3i | 0.241243 | − | 0.742469i | ||||
\(839\) | −7082.73 | + | 5145.91i | −0.291446 | + | 0.211748i | −0.723894 | − | 0.689911i | \(-0.757650\pi\) |
0.432449 | + | 0.901659i | \(0.357650\pi\) | |||||||
\(840\) | −5873.38 | − | 4267.26i | −0.241251 | − | 0.175279i | ||||
\(841\) | −7407.78 | − | 22798.8i | −0.303735 | − | 0.934799i | ||||
\(842\) | 3200.15 | + | 9849.03i | 0.130979 | + | 0.403112i | ||||
\(843\) | −20102.6 | − | 14605.4i | −0.821318 | − | 0.596723i | ||||
\(844\) | −5268.86 | + | 3828.05i | −0.214884 | + | 0.156122i | ||||
\(845\) | 6192.41 | − | 19058.3i | 0.252101 | − | 0.775887i | ||||
\(846\) | 5492.70 | 0.223218 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3757.58 | −0.152165 | ||||||||
\(849\) | 11460.5 | − | 35271.8i | 0.463279 | − | 1.42583i | ||||
\(850\) | −9185.58 | + | 6673.72i | −0.370662 | + | 0.269302i | ||||
\(851\) | 16781.0 | + | 12192.1i | 0.675964 | + | 0.491117i | ||||
\(852\) | −8418.04 | − | 25908.0i | −0.338494 | − | 1.04178i | ||||
\(853\) | −12726.6 | − | 39168.6i | −0.510846 | − | 1.57222i | −0.790715 | − | 0.612184i | \(-0.790291\pi\) |
0.279869 | − | 0.960038i | \(-0.409709\pi\) | |||||||
\(854\) | −5350.05 | − | 3887.04i | −0.214373 | − | 0.155751i | ||||
\(855\) | 12667.3 | − | 9203.31i | 0.506680 | − | 0.368125i | ||||
\(856\) | 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 | ||||
\(861\) | 11244.9 | − | 8169.88i | 0.445092 | − | 0.323378i | ||||
\(862\) | 16930.4 | + | 12300.6i | 0.668969 | + | 0.486035i | ||||
\(863\) | 8940.66 | + | 27516.5i | 0.352658 | + | 1.08537i | 0.957355 | + | 0.288914i | \(0.0932941\pi\) |
−0.604697 | + | 0.796455i | \(0.706706\pi\) | |||||||
\(864\) | 254.101 | + | 782.044i | 0.0100054 | + | 0.0307936i | ||||
\(865\) | 221.921 | + | 161.235i | 0.00872317 | + | 0.00633775i | ||||
\(866\) | −25626.8 | + | 18619.0i | −1.00558 | + | 0.730598i | ||||
\(867\) | −3272.52 | + | 10071.8i | −0.128190 | + | 0.394527i | ||||
\(868\) | 18898.6 | 0.739009 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1673.09 | 0.0651990 | ||||||||
\(871\) | −19615.5 | + | 60370.4i | −0.763085 | + | 2.34853i | ||||
\(872\) | 10090.3 | − | 7331.05i | 0.391859 | − | 0.284703i | ||||
\(873\) | 14322.4 | + | 10405.8i | 0.555258 | + | 0.403419i | ||||
\(874\) | −8388.81 | − | 25818.1i | −0.324663 | − | 0.999211i | ||||
\(875\) | −8171.52 | − | 25149.4i | −0.315712 | − | 0.971661i | ||||
\(876\) | −3383.00 | − | 2457.89i | −0.130480 | − | 0.0947996i | ||||
\(877\) | −36529.2 | + | 26540.1i | −1.40651 | + | 1.02189i | −0.412686 | + | 0.910873i | \(0.635409\pi\) |
−0.993819 | + | 0.111013i | \(0.964591\pi\) | |||||||
\(878\) | 2981.83 | − | 9177.13i | 0.114615 | − | 0.352748i | ||||
\(879\) | −50801.4 | −1.94936 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22263.5 | 0.851391 | 0.425696 | − | 0.904866i | \(-0.360029\pi\) | ||||
0.425696 | + | 0.904866i | \(0.360029\pi\) | |||||||
\(882\) | 2772.68 | − | 8533.44i | 0.105852 | − | 0.325777i | ||||
\(883\) | −30917.0 | + | 22462.5i | −1.17830 | + | 0.856086i | −0.991979 | − | 0.126402i | \(-0.959657\pi\) |
−0.186322 | + | 0.982489i | \(0.559657\pi\) | |||||||
\(884\) | −14740.1 | − | 10709.3i | −0.560818 | − | 0.407458i | ||||
\(885\) | 3829.78 | + | 11786.9i | 0.145465 | + | 0.447696i | ||||
\(886\) | 2214.65 | + | 6816.00i | 0.0839760 | + | 0.258452i | ||||
\(887\) | 38962.7 | + | 28308.1i | 1.47490 | + | 1.07158i | 0.979155 | + | 0.203116i | \(0.0651068\pi\) |
0.495750 | + | 0.868465i | \(0.334893\pi\) | |||||||
\(888\) | 7137.85 | − | 5185.95i | 0.269742 | − | 0.195979i | ||||
\(889\) | −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 | ||||
\(894\) | −5998.24 | + | 4357.98i | −0.224397 | + | 0.163034i | ||||
\(895\) | −91.3017 | − | 66.3346i | −0.00340992 | − | 0.00247745i | ||||
\(896\) | 876.118 | + | 2696.41i | 0.0326663 | + | 0.100537i | ||||
\(897\) | −25626.4 | − | 78869.9i | −0.953890 | − | 2.93577i | ||||
\(898\) | 12614.2 | + | 9164.73i | 0.468753 | + | 0.340569i | ||||
\(899\) | −3523.52 | + | 2559.99i | −0.130718 | + | 0.0949725i | ||||
\(900\) | −3597.09 | + | 11070.7i | −0.133225 | + | 0.410026i | ||||
\(901\) | 13923.8 | 0.514838 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25400.6 | 0.936078 | ||||||||
\(904\) | −5535.46 | + | 17036.4i | −0.203658 | + | 0.626795i | ||||
\(905\) | 770.714 | − | 559.956i | 0.0283087 | − | 0.0205675i | ||||
\(906\) | 20933.6 | + | 15209.1i | 0.767629 | + | 0.557715i | ||||
\(907\) | 2629.70 | + | 8093.38i | 0.0962709 | + | 0.296291i | 0.987583 | − | 0.157099i | \(-0.0502143\pi\) |
−0.891312 | + | 0.453391i | \(0.850214\pi\) | |||||||
\(908\) | −2104.47 | − | 6476.90i | −0.0769157 | − | 0.236722i | ||||
\(909\) | −3480.48 | − | 2528.72i | −0.126997 | − | 0.0922688i | ||||
\(910\) | 14890.7 | − | 10818.8i | 0.542443 | − | 0.394108i | ||||
\(911\) | 3486.78 | − | 10731.2i | 0.126808 | − | 0.390275i | −0.867418 | − | 0.497580i | \(-0.834222\pi\) |
0.994226 | + | 0.107305i | \(0.0342221\pi\) | |||||||
\(912\) | −11547.0 | −0.419252 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6696.04 | −0.242325 | ||||||||
\(915\) | 1889.96 | − | 5816.70i | 0.0682843 | − | 0.210158i | ||||
\(916\) | −17461.7 | + | 12686.6i | −0.629857 | + | 0.457618i | ||||
\(917\) | −44192.6 | − | 32107.8i | −1.59146 | − | 1.15626i | ||||
\(918\) | −941.578 | − | 2897.88i | −0.0338526 | − | 0.104188i | ||||
\(919\) | −8206.54 | − | 25257.1i | −0.294569 | − | 0.906590i | −0.983366 | − | 0.181635i | \(-0.941861\pi\) |
0.688797 | − | 0.724954i | \(-0.258139\pi\) | |||||||
\(920\) | −4987.22 | − | 3623.42i | −0.178721 | − | 0.129849i | ||||
\(921\) | 58269.3 | − | 42335.2i | 2.08473 | − | 1.51465i | ||||
\(922\) | −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 | ||||
\(927\) | −20687.5 | + | 15030.4i | −0.732974 | + | 0.532537i | ||||
\(928\) | −528.600 | − | 384.050i | −0.0186984 | − | 0.0135852i | ||||
\(929\) | −14806.0 | − | 45568.1i | −0.522893 | − | 1.60930i | −0.768444 | − | 0.639916i | \(-0.778969\pi\) |
0.245551 | − | 0.969384i | \(-0.421031\pi\) | |||||||
\(930\) | 5401.10 | + | 16622.9i | 0.190440 | + | 0.586113i | ||||
\(931\) | 11376.5 | + | 8265.52i | 0.400483 | + | 0.290968i | ||||
\(932\) | −19591.7 | + | 14234.2i | −0.688572 | + | 0.500277i | ||||
\(933\) | 13503.3 | − | 41558.8i | 0.473823 | − | 1.45828i | ||||
\(934\) | −23643.7 | −0.828314 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18679.4 | −0.652301 | ||||||||
\(937\) | −1767.25 | + | 5439.04i | −0.0616153 | + | 0.189633i | −0.977126 | − | 0.212661i | \(-0.931787\pi\) |
0.915511 | + | 0.402294i | \(0.131787\pi\) | |||||||
\(938\) | −29611.6 | + | 21514.1i | −1.03076 | + | 0.748892i | ||||
\(939\) | −36637.1 | − | 26618.4i | −1.27328 | − | 0.925089i | ||||
\(940\) | 604.066 | + | 1859.12i | 0.0209601 | + | 0.0645084i | ||||
\(941\) | 3431.82 | + | 10562.1i | 0.118889 | + | 0.365902i | 0.992738 | − | 0.120295i | \(-0.0383840\pi\) |
−0.873850 | + | 0.486196i | \(0.838384\pi\) | |||||||
\(942\) | −31401.2 | − | 22814.3i | −1.08610 | − | 0.789097i | ||||
\(943\) | 9548.27 | − | 6937.22i | 0.329729 | − | 0.239562i | ||||
\(944\) | 1495.63 | − | 4603.08i | 0.0515663 | − | 0.158705i | ||||
\(945\) | 3078.15 | 0.105960 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39759.1 | 1.36430 | 0.682152 | − | 0.731210i | \(-0.261044\pi\) | ||||
0.682152 | + | 0.731210i | \(0.261044\pi\) | |||||||
\(948\) | 2850.99 | − | 8774.45i | 0.0976750 | − | 0.300613i | ||||
\(949\) | 8576.88 | − | 6231.47i | 0.293380 | − | 0.213153i | ||||
\(950\) | −14759.1 | − | 10723.1i | −0.504051 | − | 0.366214i | ||||
\(951\) | 12248.1 | + | 37695.9i | 0.417637 | + | 1.28536i | ||||
\(952\) | −3246.47 | − | 9991.62i | −0.110524 | − | 0.340158i | ||||
\(953\) | −12889.2 | − | 9364.58i | −0.438115 | − | 0.318309i | 0.346771 | − | 0.937950i | \(-0.387278\pi\) |
−0.784885 | + | 0.619641i | \(0.787278\pi\) | |||||||
\(954\) | 11548.7 | − | 8390.65i | 0.391933 | − | 0.284756i | ||||
\(955\) | −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 | ||||
\(960\) | −2121.33 | + | 1541.24i | −0.0713183 | + | 0.0518158i | ||||
\(961\) | −12707.8 | − | 9232.73i | −0.426564 | − | 0.309917i | ||||
\(962\) | 6912.26 | + | 21273.8i | 0.231664 | + | 0.712987i | ||||
\(963\) | 605.121 | + | 1862.37i | 0.0202490 | + | 0.0623199i | ||||
\(964\) | −21032.0 | − | 15280.7i | −0.702693 | − | 0.510537i | ||||
\(965\) | −5621.92 | + | 4084.56i | −0.187540 | + | 0.136256i | ||||
\(966\) | 14776.6 | − | 45477.6i | 0.492162 | − | 1.51472i | ||||
\(967\) | −14952.9 | −0.497264 | −0.248632 | − | 0.968598i | \(-0.579981\pi\) | ||||
−0.248632 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42787.5 | 1.41851 | ||||||||
\(970\) | −1946.96 | + | 5992.13i | −0.0644465 | + | 0.198346i | ||||
\(971\) | −22601.7 | + | 16421.1i | −0.746987 | + | 0.542718i | −0.894892 | − | 0.446284i | \(-0.852747\pi\) |
0.147904 | + | 0.989002i | \(0.452747\pi\) | |||||||
\(972\) | 17589.8 | + | 12779.8i | 0.580447 | + | 0.421719i | ||||
\(973\) | 8645.09 | + | 26606.9i | 0.284840 | + | 0.876646i | ||||
\(974\) | 4590.54 | + | 14128.2i | 0.151017 | + | 0.464782i | ||||
\(975\) | −45086.5 | − | 32757.3i | −1.48095 | − | 1.07597i | ||||
\(976\) | −1932.31 | + | 1403.91i | −0.0633728 | + | 0.0460430i | ||||
\(977\) | 10308.6 | − | 31726.5i | 0.337564 | − | 1.03892i | −0.627881 | − | 0.778310i | \(-0.716077\pi\) |
0.965445 | − | 0.260607i | \(-0.0839226\pi\) | |||||||
\(978\) | 27516.4 | 0.899671 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3193.26 | 0.104087 | ||||||||
\(981\) | −14641.9 | + | 45063.2i | −0.476535 | + | 1.46662i | ||||
\(982\) | −8970.20 | + | 6517.23i | −0.291498 | + | 0.211785i | ||||
\(983\) | −9991.42 | − | 7259.19i | −0.324188 | − | 0.235536i | 0.413772 | − | 0.910380i | \(-0.364211\pi\) |
−0.737960 | + | 0.674844i | \(0.764211\pi\) | |||||||
\(984\) | −1551.31 | − | 4774.45i | −0.0502581 | − | 0.154679i | ||||
\(985\) | 4487.25 | + | 13810.4i | 0.145153 | + | 0.446735i | ||||
\(986\) | 1958.74 | + | 1423.11i | 0.0632647 | + | 0.0459645i | ||||
\(987\) | −12267.3 | + | 8912.74i | −0.395617 | + | 0.287432i | ||||
\(988\) | 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 | ||||
\(993\) | 24293.3 | − | 17650.1i | 0.776358 | − | 0.564057i | ||||
\(994\) | 32218.2 | + | 23407.9i | 1.02807 | + | 0.746934i | ||||
\(995\) | −2228.60 | − | 6858.94i | −0.0710065 | − | 0.218536i | ||||
\(996\) | 7156.95 | + | 22026.8i | 0.227687 | + | 0.700750i | ||||
\(997\) | 1693.35 | + | 1230.29i | 0.0537902 | + | 0.0390809i | 0.614355 | − | 0.789029i | \(-0.289416\pi\) |
−0.560565 | + | 0.828110i | \(0.689416\pi\) | |||||||
\(998\) | −33027.3 | + | 23995.8i | −1.04756 | + | 0.761095i | ||||
\(999\) | −1155.98 | + | 3557.75i | −0.0366103 | + | 0.112675i |
(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 | 242.4.c.q.9.1 | 8 | ||
11.2 | odd | 10 | 242.4.c.r.3.2 | 8 | |||
11.3 | even | 5 | 242.4.c.n.81.2 | 8 | |||
11.4 | even | 5 | 242.4.a.o.1.3 | 4 | |||
11.5 | even | 5 | inner | 242.4.c.q.27.1 | 8 | ||
11.6 | odd | 10 | 22.4.c.b.5.1 | ✓ | 8 | ||
11.7 | odd | 10 | 242.4.a.n.1.3 | 4 | |||
11.8 | odd | 10 | 242.4.c.r.81.2 | 8 | |||
11.9 | even | 5 | 242.4.c.n.3.2 | 8 | |||
11.10 | odd | 2 | 22.4.c.b.9.1 | yes | 8 | ||
33.17 | even | 10 | 198.4.f.d.181.2 | 8 | |||
33.26 | odd | 10 | 2178.4.a.bt.1.3 | 4 | |||
33.29 | even | 10 | 2178.4.a.by.1.3 | 4 | |||
33.32 | even | 2 | 198.4.f.d.163.2 | 8 | |||
44.7 | even | 10 | 1936.4.a.bn.1.2 | 4 | |||
44.15 | odd | 10 | 1936.4.a.bm.1.2 | 4 | |||
44.39 | even | 10 | 176.4.m.b.49.2 | 8 | |||
44.43 | even | 2 | 176.4.m.b.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.5.1 | ✓ | 8 | 11.6 | odd | 10 | ||
22.4.c.b.9.1 | yes | 8 | 11.10 | odd | 2 | ||
176.4.m.b.49.2 | 8 | 44.39 | even | 10 | |||
176.4.m.b.97.2 | 8 | 44.43 | even | 2 | |||
198.4.f.d.163.2 | 8 | 33.32 | even | 2 | |||
198.4.f.d.181.2 | 8 | 33.17 | even | 10 | |||
242.4.a.n.1.3 | 4 | 11.7 | odd | 10 | |||
242.4.a.o.1.3 | 4 | 11.4 | even | 5 | |||
242.4.c.n.3.2 | 8 | 11.9 | even | 5 | |||
242.4.c.n.81.2 | 8 | 11.3 | even | 5 | |||
242.4.c.q.9.1 | 8 | 1.1 | even | 1 | trivial | ||
242.4.c.q.27.1 | 8 | 11.5 | even | 5 | inner | ||
242.4.c.r.3.2 | 8 | 11.2 | odd | 10 | |||
242.4.c.r.81.2 | 8 | 11.8 | odd | 10 | |||
1936.4.a.bm.1.2 | 4 | 44.15 | odd | 10 | |||
1936.4.a.bn.1.2 | 4 | 44.7 | even | 10 | |||
2178.4.a.bt.1.3 | 4 | 33.26 | odd | 10 | |||
2178.4.a.by.1.3 | 4 | 33.29 | even | 10 |