Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (of order \(6\), degree \(2\), 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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 11x^{10} + 88x^{8} - 331x^{6} + 913x^{4} - 528x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.6 | ||
Root | \(0.669321 + 0.386433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.4.k.a.215.6 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 4.16156 | + | 7.20804i | 0.372221 | + | 0.644706i | 0.989907 | − | 0.141719i | \(-0.0452629\pi\) |
−0.617686 | + | 0.786425i | \(0.711930\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.6528 | − | 8.10467i | −0.899164 | − | 0.437611i | ||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.4161 | + | 8.32312i | 0.455876 | + | 0.263200i | ||||
\(11\) | 20.0413 | + | 11.5708i | 0.549334 | + | 0.317158i | 0.748853 | − | 0.662736i | \(-0.230605\pi\) |
−0.199519 | + | 0.979894i | \(0.563938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 39.4467i | − | 0.841580i | −0.907158 | − | 0.420790i | \(-0.861753\pi\) | ||
0.907158 | − | 0.420790i | \(-0.138247\pi\) | |||||||
\(14\) | −36.9481 | + | 2.61505i | −0.705342 | + | 0.0499216i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 50.8277 | − | 88.0362i | 0.725149 | − | 1.25599i | −0.233764 | − | 0.972293i | \(-0.575104\pi\) |
0.958913 | − | 0.283701i | \(-0.0915623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.7060 | − | 16.5734i | 0.346611 | − | 0.200116i | −0.316580 | − | 0.948566i | \(-0.602535\pi\) |
0.663192 | + | 0.748450i | \(0.269201\pi\) | |||||||
\(20\) | 33.2925 | 0.372221 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 46.2834 | 0.448529 | ||||||||
\(23\) | 25.0303 | − | 14.4512i | 0.226920 | − | 0.131013i | −0.382230 | − | 0.924067i | \(-0.624844\pi\) |
0.609151 | + | 0.793055i | \(0.291511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 27.8628 | − | 48.2598i | 0.222902 | − | 0.386078i | ||||
\(26\) | −39.4467 | − | 68.3236i | −0.297543 | − | 0.515360i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −61.3809 | + | 41.4775i | −0.414282 | + | 0.279947i | ||||
\(29\) | − | 177.789i | − | 1.13843i | −0.822187 | − | 0.569217i | \(-0.807246\pi\) | ||
0.822187 | − | 0.569217i | \(-0.192754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 135.306 | + | 78.1189i | 0.783924 | + | 0.452599i | 0.837819 | − | 0.545948i | \(-0.183830\pi\) |
−0.0538948 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 203.311i | − | 1.02552i | ||||||
\(35\) | −10.8827 | − | 153.762i | −0.0525575 | − | 0.742585i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.16181 | − | 15.8687i | −0.0407079 | − | 0.0705082i | 0.844954 | − | 0.534840i | \(-0.179628\pi\) |
−0.885662 | + | 0.464331i | \(0.846295\pi\) | |||||||
\(38\) | 33.1469 | − | 57.4120i | 0.141503 | − | 0.245091i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 57.6643 | − | 33.2925i | 0.227938 | − | 0.131600i | ||||
\(41\) | −123.758 | −0.471410 | −0.235705 | − | 0.971825i | \(-0.575740\pi\) | ||||
−0.235705 | + | 0.971825i | \(0.575740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 242.188 | 0.858914 | 0.429457 | − | 0.903087i | \(-0.358705\pi\) | ||||
0.429457 | + | 0.903087i | \(0.358705\pi\) | |||||||
\(44\) | 80.1652 | − | 46.2834i | 0.274667 | − | 0.158579i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 28.9025 | − | 50.0605i | 0.0926399 | − | 0.160457i | ||||
\(47\) | −31.7746 | − | 55.0352i | −0.0986128 | − | 0.170802i | 0.812498 | − | 0.582964i | \(-0.198107\pi\) |
−0.911111 | + | 0.412162i | \(0.864774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 211.629 | + | 269.930i | 0.616993 | + | 0.786969i | ||||
\(50\) | − | 111.451i | − | 0.315232i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −136.647 | − | 78.8933i | −0.364415 | − | 0.210395i | ||||
\(53\) | 54.9048 | + | 31.6993i | 0.142297 | + | 0.0821554i | 0.569458 | − | 0.822020i | \(-0.307153\pi\) |
−0.427161 | + | 0.904176i | \(0.640486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 192.611i | 0.472212i | ||||||||
\(56\) | −64.8374 | + | 133.222i | −0.154719 | + | 0.317903i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −177.789 | − | 307.939i | −0.402497 | − | 0.697145i | ||||
\(59\) | 215.903 | − | 373.955i | 0.476409 | − | 0.825165i | −0.523225 | − | 0.852194i | \(-0.675271\pi\) |
0.999635 | + | 0.0270293i | \(0.00860475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −749.448 | + | 432.694i | −1.57307 | + | 0.908210i | −0.577276 | + | 0.816549i | \(0.695884\pi\) |
−0.995790 | + | 0.0916609i | \(0.970782\pi\) | |||||||
\(62\) | 312.476 | 0.640072 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 284.333 | − | 164.160i | 0.542572 | − | 0.313254i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 93.3127 | − | 161.622i | 0.170149 | − | 0.294706i | −0.768323 | − | 0.640062i | \(-0.778909\pi\) |
0.938472 | + | 0.345356i | \(0.112242\pi\) | |||||||
\(68\) | −203.311 | − | 352.145i | −0.362574 | − | 0.627997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −172.611 | − | 255.440i | −0.294728 | − | 0.436157i | ||||
\(71\) | − | 1168.93i | − | 1.95389i | −0.213495 | − | 0.976944i | \(-0.568485\pi\) | ||
0.213495 | − | 0.976944i | \(-0.431515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −667.923 | − | 385.625i | −1.07088 | − | 0.618274i | −0.142460 | − | 0.989801i | \(-0.545501\pi\) |
−0.928422 | + | 0.371526i | \(0.878835\pi\) | |||||||
\(74\) | −31.7375 | − | 18.3236i | −0.0498568 | − | 0.0287848i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 132.587i | − | 0.200116i | ||||||
\(77\) | −239.965 | − | 355.114i | −0.355150 | − | 0.525572i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 323.607 | + | 560.504i | 0.460869 | + | 0.798248i | 0.999004 | − | 0.0446099i | \(-0.0142045\pi\) |
−0.538136 | + | 0.842858i | \(0.680871\pi\) | |||||||
\(80\) | 66.5850 | − | 115.329i | 0.0930554 | − | 0.161177i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −214.356 | + | 123.758i | −0.288679 | + | 0.166669i | ||||
\(83\) | −231.713 | −0.306431 | −0.153216 | − | 0.988193i | \(-0.548963\pi\) | ||||
−0.153216 | + | 0.988193i | \(0.548963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 846.090 | 1.07966 | ||||||||
\(86\) | 419.482 | − | 242.188i | 0.525976 | − | 0.303672i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 92.5667 | − | 160.330i | 0.112132 | − | 0.194219i | ||||
\(89\) | −129.606 | − | 224.485i | −0.154362 | − | 0.267364i | 0.778464 | − | 0.627689i | \(-0.215999\pi\) |
−0.932827 | + | 0.360325i | \(0.882666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −319.702 | + | 656.896i | −0.368285 | + | 0.756718i | ||||
\(92\) | − | 115.610i | − | 0.131013i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −110.070 | − | 63.5492i | −0.120776 | − | 0.0697298i | ||||
\(95\) | 238.924 | + | 137.943i | 0.258032 | + | 0.148975i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1357.81i | 1.42128i | 0.703555 | + | 0.710641i | \(0.251595\pi\) | ||||
−0.703555 | + | 0.710641i | \(0.748405\pi\) | |||||||
\(98\) | 636.482 | + | 255.904i | 0.656065 | + | 0.263778i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −111.451 | − | 193.039i | −0.111451 | − | 0.193039i | ||||
\(101\) | −622.990 | + | 1079.05i | −0.613761 | + | 1.06306i | 0.376840 | + | 0.926278i | \(0.377011\pi\) |
−0.990601 | + | 0.136786i | \(0.956323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 280.587 | − | 161.997i | 0.268418 | − | 0.154971i | −0.359750 | − | 0.933049i | \(-0.617138\pi\) |
0.628169 | + | 0.778077i | \(0.283805\pi\) | |||||||
\(104\) | −315.573 | −0.297543 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 126.797 | 0.116185 | ||||||||
\(107\) | 1497.33 | − | 864.484i | 1.35283 | − | 0.781055i | 0.364182 | − | 0.931328i | \(-0.381349\pi\) |
0.988644 | + | 0.150273i | \(0.0480154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −823.869 | + | 1426.98i | −0.723966 | + | 1.25395i | 0.235432 | + | 0.971891i | \(0.424349\pi\) |
−0.959398 | + | 0.282055i | \(0.908984\pi\) | |||||||
\(110\) | 192.611 | + | 333.612i | 0.166952 | + | 0.289170i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 20.9204 | + | 295.585i | 0.0176499 | + | 0.249376i | ||||
\(113\) | 1054.26i | 0.877669i | 0.898568 | + | 0.438834i | \(0.144608\pi\) | ||||
−0.898568 | + | 0.438834i | \(0.855392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 208.330 | + | 120.279i | 0.168929 | + | 0.0975314i | ||||
\(116\) | −615.879 | − | 355.578i | −0.492956 | − | 0.284608i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 863.611i | − | 0.673744i | ||||||
\(119\) | −1559.93 | + | 1054.10i | −1.20166 | + | 0.812012i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −397.731 | − | 688.891i | −0.298821 | − | 0.517574i | ||||
\(122\) | −865.388 | + | 1498.90i | −0.642202 | + | 1.11233i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 541.224 | − | 312.476i | 0.391962 | − | 0.226300i | ||||
\(125\) | 1504.20 | 1.07632 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1867.27 | 1.30467 | 0.652337 | − | 0.757929i | \(-0.273789\pi\) | ||||
0.652337 | + | 0.757929i | \(0.273789\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 328.319 | − | 568.666i | 0.221504 | − | 0.383656i | ||||
\(131\) | 1095.33 | + | 1897.16i | 0.730528 | + | 1.26531i | 0.956658 | + | 0.291214i | \(0.0940592\pi\) |
−0.226130 | + | 0.974097i | \(0.572607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −612.357 | + | 43.3404i | −0.399233 | + | 0.0282563i | ||||
\(134\) | − | 373.251i | − | 0.240627i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −704.289 | − | 406.622i | −0.444061 | − | 0.256379i | ||||
\(137\) | −1555.53 | − | 898.084i | −0.970056 | − | 0.560062i | −0.0708029 | − | 0.997490i | \(-0.522556\pi\) |
−0.899253 | + | 0.437428i | \(0.855889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 269.664i | 0.164551i | 0.996610 | + | 0.0822757i | \(0.0262188\pi\) | ||||
−0.996610 | + | 0.0822757i | \(0.973781\pi\) | |||||||
\(140\) | −554.412 | − | 269.825i | −0.334688 | − | 0.162888i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1168.93 | − | 2024.64i | −0.690804 | − | 1.19651i | ||||
\(143\) | 456.431 | − | 790.562i | 0.266914 | − | 0.462308i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1281.51 | − | 739.880i | 0.733955 | − | 0.423749i | ||||
\(146\) | −1542.50 | −0.874372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −73.2945 | −0.0407079 | ||||||||
\(149\) | −2000.93 | + | 1155.24i | −1.10015 | + | 0.635172i | −0.936260 | − | 0.351307i | \(-0.885737\pi\) |
−0.163889 | + | 0.986479i | \(0.552404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −336.013 | + | 581.992i | −0.181088 | + | 0.313654i | −0.942251 | − | 0.334906i | \(-0.891295\pi\) |
0.761163 | + | 0.648561i | \(0.224629\pi\) | |||||||
\(152\) | −132.587 | − | 229.648i | −0.0707517 | − | 0.122546i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −770.746 | − | 375.112i | −0.403302 | − | 0.196281i | ||||
\(155\) | 1300.39i | 0.673868i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 946.238 | + | 546.311i | 0.481007 | + | 0.277709i | 0.720836 | − | 0.693106i | \(-0.243758\pi\) |
−0.239829 | + | 0.970815i | \(0.577091\pi\) | |||||||
\(158\) | 1121.01 | + | 647.214i | 0.564447 | + | 0.325884i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 266.340i | − | 0.131600i | ||||||
\(161\) | −533.945 | + | 37.7907i | −0.261371 | + | 0.0184989i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −93.0142 | − | 161.105i | −0.0446959 | − | 0.0774156i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.887508 | + | 0.460793i | \(0.847565\pi\) | |||||||
\(164\) | −247.517 | + | 428.712i | −0.117853 | + | 0.204127i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −401.339 | + | 231.713i | −0.187650 | + | 0.108340i | ||||
\(167\) | −1250.77 | −0.579568 | −0.289784 | − | 0.957092i | \(-0.593583\pi\) | ||||
−0.289784 | + | 0.957092i | \(0.593583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 640.961 | 0.291744 | ||||||||
\(170\) | 1465.47 | − | 846.090i | 0.661156 | − | 0.381719i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 484.376 | − | 838.964i | 0.214729 | − | 0.371921i | ||||
\(173\) | 1959.52 | + | 3393.99i | 0.861154 | + | 1.49156i | 0.870816 | + | 0.491609i | \(0.163591\pi\) |
−0.00966227 | + | 0.999953i | \(0.503076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −855.122 | + | 577.840i | −0.369378 | + | 0.249603i | ||||
\(176\) | − | 370.267i | − | 0.158579i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −448.970 | − | 259.213i | −0.189055 | − | 0.109151i | ||||
\(179\) | 1677.56 | + | 968.538i | 0.700483 | + | 0.404424i | 0.807527 | − | 0.589830i | \(-0.200805\pi\) |
−0.107044 | + | 0.994254i | \(0.534139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 822.430i | 0.337739i | 0.985638 | + | 0.168870i | \(0.0540117\pi\) | ||||
−0.985638 | + | 0.168870i | \(0.945988\pi\) | |||||||
\(182\) | 103.155 | + | 1457.48i | 0.0420130 | + | 0.593602i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −115.610 | − | 200.242i | −0.0463199 | − | 0.0802285i | ||||
\(185\) | 76.2549 | − | 132.077i | 0.0303047 | − | 0.0524893i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2037.31 | − | 1176.24i | 0.796698 | − | 0.459974i | ||||
\(188\) | −254.197 | −0.0986128 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 551.771 | 0.210682 | ||||||||
\(191\) | −1590.75 | + | 918.417i | −0.602630 | + | 0.347928i | −0.770075 | − | 0.637953i | \(-0.779781\pi\) |
0.167446 | + | 0.985881i | \(0.446448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1809.83 | − | 3134.73i | 0.674999 | − | 1.16913i | −0.301470 | − | 0.953476i | \(-0.597477\pi\) |
0.976469 | − | 0.215657i | \(-0.0691892\pi\) | |||||||
\(194\) | 1357.81 | + | 2351.79i | 0.502499 | + | 0.870354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1358.32 | − | 193.242i | 0.495016 | − | 0.0704236i | ||||
\(197\) | − | 670.900i | − | 0.242638i | −0.992614 | − | 0.121319i | \(-0.961288\pi\) | ||
0.992614 | − | 0.121319i | \(-0.0387123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 708.411 | + | 409.002i | 0.252352 | + | 0.145695i | 0.620841 | − | 0.783937i | \(-0.286791\pi\) |
−0.368489 | + | 0.929632i | \(0.620125\pi\) | |||||||
\(200\) | −386.078 | − | 222.902i | −0.136499 | − | 0.0788079i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2491.96i | 0.867988i | ||||||||
\(203\) | −1440.92 | + | 2960.68i | −0.498191 | + | 1.02364i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −515.029 | − | 892.056i | −0.175469 | − | 0.303921i | ||||
\(206\) | 323.994 | − | 561.175i | 0.109581 | − | 0.189800i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −546.589 | + | 315.573i | −0.182207 | + | 0.105197i | ||||
\(209\) | 767.074 | 0.253874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −705.692 | −0.230246 | −0.115123 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115123 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(212\) | 219.619 | − | 126.797i | 0.0711486 | − | 0.0410777i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1728.97 | − | 2994.66i | 0.552289 | − | 0.956593i | ||||
\(215\) | 1007.88 | + | 1745.70i | 0.319706 | + | 0.553748i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1620.09 | − | 2397.51i | −0.506815 | − | 0.750015i | ||||
\(218\) | 3295.47i | 1.02384i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 667.224 | + | 385.222i | 0.204474 | + | 0.118053i | ||||
\(221\) | −3472.73 | − | 2004.98i | −1.05702 | − | 0.610270i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6345.19i | 1.90541i | 0.303904 | + | 0.952703i | \(0.401710\pi\) | ||||
−0.303904 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(224\) | 331.820 | + | 491.047i | 0.0989761 | + | 0.146471i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1054.26 | + | 1826.03i | 0.310303 | + | 0.537460i | ||||
\(227\) | −875.012 | + | 1515.57i | −0.255844 | + | 0.443135i | −0.965124 | − | 0.261792i | \(-0.915687\pi\) |
0.709280 | + | 0.704926i | \(0.249020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3514.42 | + | 2029.05i | −1.01414 | + | 0.585517i | −0.912403 | − | 0.409294i | \(-0.865775\pi\) |
−0.101742 | + | 0.994811i | \(0.532442\pi\) | |||||||
\(230\) | 481.117 | 0.137930 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1422.31 | −0.402497 | ||||||||
\(233\) | 5089.91 | − | 2938.66i | 1.43112 | − | 0.826258i | 0.433915 | − | 0.900954i | \(-0.357132\pi\) |
0.997206 | + | 0.0746957i | \(0.0237985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 264.464 | − | 458.065i | 0.0734116 | − | 0.127153i | ||||
\(236\) | −863.611 | − | 1495.82i | −0.238205 | − | 0.412583i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1647.77 | + | 3385.69i | −0.448777 | + | 0.922107i | ||||
\(239\) | − | 5691.65i | − | 1.54043i | −0.637786 | − | 0.770214i | \(-0.720150\pi\) | ||
0.637786 | − | 0.770214i | \(-0.279850\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3589.60 | − | 2072.46i | −0.959447 | − | 0.553937i | −0.0634443 | − | 0.997985i | \(-0.520209\pi\) |
−0.896003 | + | 0.444048i | \(0.853542\pi\) | |||||||
\(242\) | −1377.78 | − | 795.462i | −0.365980 | − | 0.211299i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3461.55i | 0.908210i | ||||||||
\(245\) | −1064.96 | + | 2648.76i | −0.277706 | + | 0.690706i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −653.767 | − | 1132.36i | −0.168414 | − | 0.291701i | ||||
\(248\) | 624.951 | − | 1082.45i | 0.160018 | − | 0.277159i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2605.35 | − | 1504.20i | 0.659108 | − | 0.380536i | ||||
\(251\) | −5103.36 | −1.28335 | −0.641676 | − | 0.766976i | \(-0.721761\pi\) | ||||
−0.641676 | + | 0.766976i | \(0.721761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 668.852 | 0.166207 | ||||||||
\(254\) | 3234.21 | − | 1867.27i | 0.798947 | − | 0.461272i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2269.28 | + | 3930.51i | 0.550793 | + | 0.954001i | 0.998218 | + | 0.0596795i | \(0.0190079\pi\) |
−0.447425 | + | 0.894322i | \(0.647659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.9586 | + | 338.511i | 0.00574794 | + | 0.0812127i | ||||
\(260\) | − | 1313.28i | − | 0.313254i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3794.32 | + | 2190.65i | 0.894710 | + | 0.516561i | ||||
\(263\) | −2581.50 | − | 1490.43i | −0.605254 | − | 0.349444i | 0.165852 | − | 0.986151i | \(-0.446963\pi\) |
−0.771106 | + | 0.636707i | \(0.780296\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 527.674i | 0.122320i | ||||||||
\(266\) | −1017.29 | + | 687.424i | −0.234489 | + | 0.158454i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −373.251 | − | 646.489i | −0.0850743 | − | 0.147353i | ||||
\(269\) | 2710.50 | − | 4694.73i | 0.614358 | − | 1.06410i | −0.376139 | − | 0.926563i | \(-0.622749\pi\) |
0.990497 | − | 0.137536i | \(-0.0439182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4424.12 | − | 2554.27i | 0.991683 | − | 0.572548i | 0.0859058 | − | 0.996303i | \(-0.472622\pi\) |
0.905777 | + | 0.423755i | \(0.139288\pi\) | |||||||
\(272\) | −1626.49 | −0.362574 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3592.34 | −0.792048 | ||||||||
\(275\) | 1116.81 | − | 644.792i | 0.244896 | − | 0.141391i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2134.85 | + | 3697.67i | −0.463071 | + | 0.802062i | −0.999112 | − | 0.0421295i | \(-0.986586\pi\) |
0.536041 | + | 0.844192i | \(0.319919\pi\) | |||||||
\(278\) | 269.664 | + | 467.072i | 0.0581777 | + | 0.100767i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1230.09 | + | 87.0616i | −0.262544 | + | 0.0185819i | ||||
\(281\) | − | 480.737i | − | 0.102058i | −0.998697 | − | 0.0510291i | \(-0.983750\pi\) | ||
0.998697 | − | 0.0510291i | \(-0.0162501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2695.76 | − | 1556.40i | −0.566241 | − | 0.326920i | 0.189405 | − | 0.981899i | \(-0.439344\pi\) |
−0.755647 | + | 0.654979i | \(0.772677\pi\) | |||||||
\(284\) | −4049.28 | − | 2337.85i | −0.846059 | − | 0.488472i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1825.72i | − | 0.377473i | ||||||
\(287\) | 2060.92 | + | 1003.02i | 0.423875 | + | 0.206294i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2710.41 | − | 4694.57i | −0.551681 | − | 0.955540i | ||||
\(290\) | 1479.76 | − | 2563.02i | 0.299636 | − | 0.518985i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2671.69 | + | 1542.50i | −0.535441 | + | 0.309137i | ||||
\(293\) | −179.301 | −0.0357504 | −0.0178752 | − | 0.999840i | \(-0.505690\pi\) | ||||
−0.0178752 | + | 0.999840i | \(0.505690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3593.97 | 0.709319 | ||||||||
\(296\) | −126.950 | + | 73.2945i | −0.0249284 | + | 0.0143924i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2310.47 | + | 4001.85i | −0.449134 | + | 0.777923i | ||||
\(299\) | −570.053 | − | 987.360i | −0.110258 | − | 0.190972i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4033.10 | − | 1962.85i | −0.772305 | − | 0.375871i | ||||
\(302\) | 1344.05i | 0.256098i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −459.296 | − | 265.175i | −0.0866528 | − | 0.0500290i | ||||
\(305\) | −6237.75 | − | 3601.37i | −1.17106 | − | 0.676110i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3188.08i | − | 0.592681i | −0.955082 | − | 0.296341i | \(-0.904234\pi\) | ||
0.955082 | − | 0.296341i | \(-0.0957664\pi\) | |||||||
\(308\) | −1710.08 | + | 121.033i | −0.316367 | + | 0.0223913i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1300.39 | + | 2252.34i | 0.238248 | + | 0.412658i | ||||
\(311\) | 1864.80 | − | 3229.93i | 0.340010 | − | 0.588914i | −0.644424 | − | 0.764668i | \(-0.722903\pi\) |
0.984434 | + | 0.175754i | \(0.0562362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3895.16 | + | 2248.87i | −0.703410 | + | 0.406114i | −0.808616 | − | 0.588337i | \(-0.799783\pi\) |
0.105206 | + | 0.994450i | \(0.466450\pi\) | |||||||
\(314\) | 2185.24 | 0.392740 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2588.86 | 0.460869 | ||||||||
\(317\) | 8301.79 | − | 4793.04i | 1.47090 | − | 0.849224i | 0.471433 | − | 0.881902i | \(-0.343737\pi\) |
0.999466 | + | 0.0326778i | \(0.0104035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2057.17 | − | 3563.12i | 0.361064 | − | 0.625381i | ||||
\(320\) | −266.340 | − | 461.314i | −0.0465277 | − | 0.0805883i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −887.030 | + | 599.401i | −0.153516 | + | 0.103737i | ||||
\(323\) | − | 3369.56i | − | 0.580456i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1903.69 | − | 1099.09i | −0.324916 | − | 0.187590i | ||||
\(326\) | −322.211 | − | 186.028i | −0.0547411 | − | 0.0316048i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 990.068i | 0.166669i | ||||||||
\(329\) | 83.0923 | + | 1174.01i | 0.0139241 | + | 0.196733i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5457.29 | + | 9452.31i | 0.906224 | + | 1.56963i | 0.819266 | + | 0.573413i | \(0.194381\pi\) |
0.0869572 | + | 0.996212i | \(0.472286\pi\) | |||||||
\(332\) | −463.426 | + | 802.677i | −0.0766078 | + | 0.132689i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2166.41 | + | 1250.77i | −0.354911 | + | 0.204908i | ||||
\(335\) | 1553.31 | 0.253332 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2637.13 | −0.426271 | −0.213136 | − | 0.977023i | \(-0.568368\pi\) | ||||
−0.213136 | + | 0.977023i | \(0.568368\pi\) | |||||||
\(338\) | 1110.18 | − | 640.961i | 0.178656 | − | 0.103147i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1692.18 | − | 2930.94i | 0.269916 | − | 0.467508i | ||||
\(341\) | 1807.80 | + | 3131.21i | 0.287091 | + | 0.497256i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1336.50 | − | 6210.26i | −0.210392 | − | 0.977617i | ||||
\(344\) | − | 1937.50i | − | 0.303672i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6787.98 | + | 3919.04i | 1.05469 | + | 0.608928i | ||||
\(347\) | −1782.87 | − | 1029.34i | −0.275819 | − | 0.159244i | 0.355710 | − | 0.934596i | \(-0.384239\pi\) |
−0.631529 | + | 0.775352i | \(0.717572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 320.118i | − | 0.0490989i | −0.999699 | − | 0.0245494i | \(-0.992185\pi\) | ||
0.999699 | − | 0.0245494i | \(-0.00781512\pi\) | |||||||
\(350\) | −903.276 | + | 1855.97i | −0.137949 | + | 0.283445i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −370.267 | − | 641.321i | −0.0560662 | − | 0.0971095i | ||||
\(353\) | 4150.23 | − | 7188.42i | 0.625764 | − | 1.08386i | −0.362629 | − | 0.931934i | \(-0.618121\pi\) |
0.988393 | − | 0.151921i | \(-0.0485460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8425.67 | − | 4864.56i | 1.25968 | − | 0.727279i | ||||
\(356\) | −1036.85 | −0.154362 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3874.15 | 0.571942 | ||||||||
\(359\) | 9676.82 | − | 5586.92i | 1.42263 | − | 0.821354i | 0.426105 | − | 0.904674i | \(-0.359886\pi\) |
0.996523 | + | 0.0833196i | \(0.0265522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2880.14 | + | 4988.55i | −0.419907 | + | 0.727300i | ||||
\(362\) | 822.430 | + | 1424.49i | 0.119409 | + | 0.206822i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1636.15 | + | 2421.27i | 0.235598 | + | 0.348652i | ||||
\(365\) | − | 6419.21i | − | 0.920540i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1963.55 | − | 1133.66i | −0.279282 | − | 0.161244i | 0.353816 | − | 0.935315i | \(-0.384884\pi\) |
−0.633098 | + | 0.774071i | \(0.718217\pi\) | |||||||
\(368\) | −400.484 | − | 231.220i | −0.0567301 | − | 0.0327531i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 305.020i | − | 0.0428573i | ||||||
\(371\) | −657.404 | − | 972.866i | −0.0919965 | − | 0.136142i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4268.99 | − | 7394.10i | −0.592600 | − | 1.02641i | −0.993881 | − | 0.110458i | \(-0.964768\pi\) |
0.401281 | − | 0.915955i | \(-0.368565\pi\) | |||||||
\(374\) | 2352.48 | − | 4074.61i | 0.325251 | − | 0.563350i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −440.282 | + | 254.197i | −0.0603878 | + | 0.0348649i | ||||
\(377\) | −7013.18 | −0.958083 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10475.3 | 1.41973 | 0.709866 | − | 0.704336i | \(-0.248755\pi\) | ||||
0.709866 | + | 0.704336i | \(0.248755\pi\) | |||||||
\(380\) | 955.695 | − | 551.771i | 0.129016 | − | 0.0744875i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1836.83 | + | 3181.49i | −0.246023 | + | 0.426124i | ||||
\(383\) | 5289.05 | + | 9160.91i | 0.705634 | + | 1.22219i | 0.966462 | + | 0.256809i | \(0.0826711\pi\) |
−0.260828 | + | 0.965385i | \(0.583996\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1561.05 | − | 3207.51i | 0.206645 | − | 0.424596i | ||||
\(386\) | − | 7239.34i | − | 0.954592i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4703.58 | + | 2715.61i | 0.615433 | + | 0.355321i | ||||
\(389\) | −9695.01 | − | 5597.42i | −1.26364 | − | 0.729564i | −0.289864 | − | 0.957068i | \(-0.593610\pi\) |
−0.973777 | + | 0.227504i | \(0.926944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2938.09i | − | 0.380014i | ||||||
\(392\) | 2159.44 | − | 1693.03i | 0.278235 | − | 0.218140i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −670.900 | − | 1162.03i | −0.0857854 | − | 0.148585i | ||||
\(395\) | −2693.42 | + | 4665.14i | −0.343091 | + | 0.594250i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −966.902 | + | 558.241i | −0.122235 | + | 0.0705726i | −0.559871 | − | 0.828580i | \(-0.689149\pi\) |
0.437636 | + | 0.899152i | \(0.355816\pi\) | |||||||
\(398\) | 1636.01 | 0.206044 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −891.610 | −0.111451 | ||||||||
\(401\) | 6854.16 | − | 3957.25i | 0.853568 | − | 0.492807i | −0.00828539 | − | 0.999966i | \(-0.502637\pi\) |
0.861853 | + | 0.507158i | \(0.169304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3081.53 | − | 5337.37i | 0.380898 | − | 0.659735i | ||||
\(404\) | 2491.96 | + | 4316.20i | 0.306880 | + | 0.531532i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 464.928 | + | 6568.96i | 0.0568324 | + | 0.802985i | ||||
\(407\) | − | 424.040i | − | 0.0516434i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9250.83 | − | 5340.97i | −1.11840 | − | 0.645706i | −0.177405 | − | 0.984138i | \(-0.556770\pi\) |
−0.940991 | + | 0.338431i | \(0.890104\pi\) | |||||||
\(410\) | −1784.11 | − | 1030.06i | −0.214905 | − | 0.124075i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1295.98i | − | 0.154971i | ||||||
\(413\) | −6626.16 | + | 4477.55i | −0.789472 | + | 0.533477i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −964.288 | − | 1670.19i | −0.114060 | − | 0.197558i | ||||
\(416\) | −631.147 | + | 1093.18i | −0.0743858 | + | 0.128840i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1328.61 | − | 767.074i | 0.155465 | − | 0.0897580i | ||||
\(419\) | 522.112 | 0.0608755 | 0.0304377 | − | 0.999537i | \(-0.490310\pi\) | ||||
0.0304377 | + | 0.999537i | \(0.490310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6758.66 | −0.782415 | −0.391208 | − | 0.920302i | \(-0.627943\pi\) | ||||
−0.391208 | + | 0.920302i | \(0.627943\pi\) | |||||||
\(422\) | −1222.30 | + | 705.692i | −0.140996 | + | 0.0814042i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 253.594 | − | 439.238i | 0.0290463 | − | 0.0503097i | ||||
\(425\) | −2832.40 | − | 4905.87i | −0.323275 | − | 0.559928i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15987.2 | − | 1131.52i | 1.81189 | − | 0.128239i | ||||
\(428\) | − | 6915.87i | − | 0.781055i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3491.40 | + | 2015.76i | 0.391559 | + | 0.226067i | ||||
\(431\) | −9598.90 | − | 5541.93i | −1.07277 | − | 0.619362i | −0.143831 | − | 0.989602i | \(-0.545942\pi\) |
−0.928936 | + | 0.370240i | \(0.879276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10214.3i | − | 1.13364i | −0.823842 | − | 0.566820i | \(-0.808173\pi\) | ||
0.823842 | − | 0.566820i | \(-0.191827\pi\) | |||||||
\(434\) | −5203.58 | − | 2532.51i | −0.575530 | − | 0.280102i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3295.47 | + | 5707.93i | 0.361983 | + | 0.626973i | ||||
\(437\) | 479.013 | − | 829.674i | 0.0524354 | − | 0.0908209i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5474.52 | + | 3160.71i | −0.595181 | + | 0.343628i | −0.767143 | − | 0.641476i | \(-0.778323\pi\) |
0.171963 | + | 0.985103i | \(0.444989\pi\) | |||||||
\(440\) | 1540.89 | 0.166952 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8019.93 | −0.863053 | ||||||||
\(443\) | 3186.24 | − | 1839.58i | 0.341722 | − | 0.197294i | −0.319311 | − | 0.947650i | \(-0.603451\pi\) |
0.661033 | + | 0.750356i | \(0.270118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1078.73 | − | 1868.42i | 0.114914 | − | 0.199037i | ||||
\(446\) | 6345.19 | + | 10990.2i | 0.673663 | + | 1.16682i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1065.78 | + | 518.699i | 0.112396 | + | 0.0547014i | ||||
\(449\) | 16168.6i | 1.69943i | 0.527242 | + | 0.849715i | \(0.323226\pi\) | ||||
−0.527242 | + | 0.849715i | \(0.676774\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2480.28 | − | 1431.99i | −0.258962 | − | 0.149512i | ||||
\(452\) | 3652.07 | + | 2108.52i | 0.380042 | + | 0.219417i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3500.05i | 0.361818i | ||||||||
\(455\) | −6065.39 | + | 429.286i | −0.624945 | + | 0.0442313i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 246.502 | + | 426.953i | 0.0252316 | + | 0.0437025i | 0.878366 | − | 0.477990i | \(-0.158634\pi\) |
−0.853134 | + | 0.521692i | \(0.825301\pi\) | |||||||
\(458\) | −4058.10 | + | 7028.83i | −0.414023 | + | 0.717109i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 833.320 | − | 481.117i | 0.0844646 | − | 0.0487657i | ||||
\(461\) | 9098.09 | 0.919176 | 0.459588 | − | 0.888132i | \(-0.347997\pi\) | ||||
0.459588 | + | 0.888132i | \(0.347997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9203.93 | 0.923851 | 0.461925 | − | 0.886919i | \(-0.347159\pi\) | ||||
0.461925 | + | 0.886919i | \(0.347159\pi\) | |||||||
\(464\) | −2463.52 | + | 1422.31i | −0.246478 | + | 0.142304i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5877.32 | − | 10179.8i | 0.584253 | − | 1.01196i | ||||
\(467\) | 7942.44 | + | 13756.7i | 0.787008 | + | 1.36314i | 0.927792 | + | 0.373097i | \(0.121704\pi\) |
−0.140785 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2863.81 | + | 1935.19i | −0.281958 | + | 0.190530i | ||||
\(470\) | − | 1057.86i | − | 0.103820i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2991.64 | − | 1727.22i | −0.291740 | − | 0.168436i | ||||
\(473\) | 4853.76 | + | 2802.32i | 0.471831 | + | 0.272412i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1847.13i | − | 0.178425i | ||||||
\(476\) | 531.669 | + | 7511.95i | 0.0511953 | + | 0.723339i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5691.65 | − | 9858.22i | −0.544623 | − | 0.943315i | ||||
\(479\) | 1082.19 | − | 1874.41i | 0.103229 | − | 0.178797i | −0.809785 | − | 0.586727i | \(-0.800416\pi\) |
0.913013 | + | 0.407930i | \(0.133749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −625.968 | + | 361.403i | −0.0593382 | + | 0.0342590i | ||||
\(482\) | −8289.84 | −0.783385 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3181.85 | −0.298821 | ||||||||
\(485\) | −9787.12 | + | 5650.60i | −0.916310 | + | 0.529032i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9822.99 | + | 17013.9i | −0.914009 | + | 1.58311i | −0.105662 | + | 0.994402i | \(0.533696\pi\) |
−0.808346 | + | 0.588707i | \(0.799637\pi\) | |||||||
\(488\) | 3461.55 | + | 5995.59i | 0.321101 | + | 0.556163i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 804.190 | + | 5652.75i | 0.0741421 | + | 0.521153i | ||||
\(491\) | − | 11831.2i | − | 1.08744i | −0.839266 | − | 0.543721i | \(-0.817015\pi\) | ||
0.839266 | − | 0.543721i | \(-0.182985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15651.9 | − | 9036.60i | −1.42987 | − | 0.825534i | ||||
\(494\) | −2264.71 | − | 1307.53i | −0.206264 | − | 0.119086i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2499.80i | − | 0.226300i | ||||||
\(497\) | −9473.77 | + | 19465.9i | −0.855043 | + | 1.75687i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3858.68 | + | 6683.42i | 0.346168 | + | 0.599581i | 0.985565 | − | 0.169295i | \(-0.0541492\pi\) |
−0.639397 | + | 0.768877i | \(0.720816\pi\) | |||||||
\(500\) | 3008.40 | − | 5210.71i | 0.269080 | − | 0.466060i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8839.28 | + | 5103.36i | −0.785890 | + | 0.453734i | ||||
\(503\) | −17416.4 | −1.54386 | −0.771928 | − | 0.635710i | \(-0.780707\pi\) | ||||
−0.771928 | + | 0.635710i | \(0.780707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10370.4 | −0.913819 | ||||||||
\(506\) | 1158.48 | − | 668.852i | 0.101780 | − | 0.0587630i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3734.55 | − | 6468.42i | 0.326169 | − | 0.564941i | ||||
\(509\) | 3499.63 | + | 6061.54i | 0.304751 | + | 0.527845i | 0.977206 | − | 0.212294i | \(-0.0680933\pi\) |
−0.672455 | + | 0.740138i | \(0.734760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7997.39 | + | 11835.0i | 0.692336 | + | 1.02456i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7861.01 | + | 4538.56i | 0.674581 | + | 0.389469i | ||||
\(515\) | 2335.36 | + | 1348.32i | 0.199822 | + | 0.115367i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1470.64i | − | 0.125103i | ||||||
\(518\) | 380.009 | + | 562.360i | 0.0322329 | + | 0.0477002i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1313.28 | − | 2274.66i | −0.110752 | − | 0.191828i | ||||
\(521\) | −7707.54 | + | 13349.9i | −0.648126 | + | 1.12259i | 0.335444 | + | 0.942060i | \(0.391114\pi\) |
−0.983570 | + | 0.180527i | \(0.942220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1871.65 | − | 1080.60i | 0.156485 | − | 0.0903465i | −0.419713 | − | 0.907657i | \(-0.637869\pi\) |
0.576198 | + | 0.817310i | \(0.304536\pi\) | |||||||
\(524\) | 8762.61 | 0.730528 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5961.71 | −0.494188 | ||||||||
\(527\) | 13754.6 | − | 7941.21i | 1.13692 | − | 0.656403i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5665.82 | + | 9813.50i | −0.465671 | + | 0.806567i | ||||
\(530\) | 527.674 | + | 913.959i | 0.0432466 | + | 0.0749054i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1074.58 | + | 2207.95i | −0.0875730 | + | 0.179937i | ||||
\(533\) | 4881.86i | 0.396729i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12462.5 | + | 7195.21i | 1.00710 | + | 0.581450i | ||||
\(536\) | −1292.98 | − | 746.502i | −0.104194 | − | 0.0601566i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10842.0i | − | 0.868833i | ||||||
\(539\) | 1117.99 | + | 7858.47i | 0.0893417 | + | 0.627993i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11313.2 | + | 19595.0i | 0.899060 | + | 1.55722i | 0.828698 | + | 0.559696i | \(0.189082\pi\) |
0.0703617 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(542\) | 5108.53 | − | 8848.23i | 0.404853 | − | 0.701226i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2817.16 | + | 1626.49i | −0.222031 | + | 0.128189i | ||||
\(545\) | −13714.3 | −1.07790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8918.09 | 0.697093 | 0.348547 | − | 0.937291i | \(-0.386675\pi\) | ||||
0.348547 | + | 0.937291i | \(0.386675\pi\) | |||||||
\(548\) | −6222.11 | + | 3592.34i | −0.485028 | + | 0.280031i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1289.58 | − | 2233.63i | 0.0999783 | − | 0.173168i | ||||
\(551\) | −2946.57 | − | 5103.61i | −0.227819 | − | 0.394594i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −846.250 | − | 11956.7i | −0.0650745 | − | 0.919438i | ||||
\(554\) | 8539.39i | 0.654881i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 934.145 | + | 539.329i | 0.0712528 | + | 0.0411378i | ||||
\(557\) | 11159.0 | + | 6442.63i | 0.848870 | + | 0.490095i | 0.860269 | − | 0.509840i | \(-0.170295\pi\) |
−0.0113997 | + | 0.999935i | \(0.503629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9553.51i | − | 0.722845i | ||||||
\(560\) | −2043.52 | + | 1380.89i | −0.154205 | + | 0.104202i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −480.737 | − | 832.660i | −0.0360830 | − | 0.0624976i | ||||
\(563\) | −8851.98 | + | 15332.1i | −0.662640 | + | 1.14773i | 0.317279 | + | 0.948332i | \(0.397231\pi\) |
−0.979919 | + | 0.199394i | \(0.936103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7599.15 | + | 4387.37i | −0.565839 | + | 0.326687i | ||||
\(566\) | −6225.59 | −0.462334 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9351.41 | −0.690804 | ||||||||
\(569\) | 19264.2 | − | 11122.2i | 1.41933 | − | 0.819449i | 0.423087 | − | 0.906089i | \(-0.360946\pi\) |
0.996240 | + | 0.0866403i | \(0.0276131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9048.83 | + | 15673.0i | −0.663191 | + | 1.14868i | 0.316582 | + | 0.948565i | \(0.397465\pi\) |
−0.979772 | + | 0.200115i | \(0.935869\pi\) | |||||||
\(572\) | −1825.72 | − | 3162.25i | −0.133457 | − | 0.231154i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4572.64 | − | 323.635i | 0.332506 | − | 0.0235336i | ||||
\(575\) | − | 1610.61i | − | 0.116812i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17496.4 | + | 10101.5i | 1.26236 | + | 0.728826i | 0.973531 | − | 0.228554i | \(-0.0733997\pi\) |
0.288832 | + | 0.957380i | \(0.406733\pi\) | |||||||
\(578\) | −9389.13 | − | 5420.82i | −0.675669 | − | 0.390098i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 5919.04i | − | 0.423749i | ||||||
\(581\) | 3858.66 | + | 1877.96i | 0.275532 | + | 0.134098i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 733.575 | + | 1270.59i | 0.0521125 | + | 0.0902615i | ||||
\(584\) | −3085.00 | + | 5343.38i | −0.218593 | + | 0.378614i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −310.558 | + | 179.301i | −0.0218926 | + | 0.0126397i | ||||
\(587\) | 19836.9 | 1.39482 | 0.697408 | − | 0.716675i | \(-0.254337\pi\) | ||||
0.697408 | + | 0.716675i | \(0.254337\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5178.79 | 0.362289 | ||||||||
\(590\) | 6224.94 | − | 3593.97i | 0.434367 | − | 0.250782i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −146.589 | + | 253.900i | −0.0101770 | + | 0.0176270i | ||||
\(593\) | 127.658 | + | 221.110i | 0.00884026 | + | 0.0153118i | 0.870412 | − | 0.492325i | \(-0.163853\pi\) |
−0.861571 | + | 0.507636i | \(0.830519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14089.7 | − | 6857.29i | −0.970795 | − | 0.472473i | ||||
\(596\) | 9241.88i | 0.635172i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1974.72 | − | 1140.11i | −0.135037 | − | 0.0779638i | ||||
\(599\) | −1582.54 | − | 913.681i | −0.107948 | − | 0.0623238i | 0.445054 | − | 0.895504i | \(-0.353184\pi\) |
−0.553002 | + | 0.833180i | \(0.686518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9233.47i | 0.626690i | 0.949639 | + | 0.313345i | \(0.101450\pi\) | ||||
−0.949639 | + | 0.313345i | \(0.898550\pi\) | |||||||
\(602\) | −8948.38 | + | 633.334i | −0.605829 | + | 0.0428784i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1344.05 | + | 2327.97i | 0.0905442 | + | 0.156827i | ||||
\(605\) | 3310.37 | − | 5733.72i | 0.222455 | − | 0.385304i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3718.73 | + | 2147.01i | −0.248663 | + | 0.143566i | −0.619152 | − | 0.785271i | \(-0.712524\pi\) |
0.370489 | + | 0.928837i | \(0.379190\pi\) | |||||||
\(608\) | −1060.70 | −0.0707517 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14405.5 | −0.956165 | ||||||||
\(611\) | −2170.96 | + | 1253.40i | −0.143744 | + | 0.0829905i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3825.38 | + | 6625.75i | −0.252048 | + | 0.436561i | −0.964090 | − | 0.265577i | \(-0.914438\pi\) |
0.712041 | + | 0.702138i | \(0.247771\pi\) | |||||||
\(614\) | −3188.08 | − | 5521.91i | −0.209545 | − | 0.362942i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2840.92 | + | 1919.72i | −0.185818 | + | 0.125564i | ||||
\(617\) | − | 1771.89i | − | 0.115614i | −0.998328 | − | 0.0578069i | \(-0.981589\pi\) | ||
0.998328 | − | 0.0578069i | \(-0.0184108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8545.25 | + | 4933.60i | 0.554867 | + | 0.320353i | 0.751083 | − | 0.660208i | \(-0.229532\pi\) |
−0.196216 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(620\) | 4504.67 | + | 2600.77i | 0.291793 | + | 0.168467i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 7459.20i | − | 0.480847i | ||||||
\(623\) | 338.928 | + | 4788.71i | 0.0217959 | + | 0.307955i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2776.98 | + | 4809.87i | 0.177727 | + | 0.307831i | ||||
\(626\) | −4497.74 | + | 7790.31i | −0.287166 | + | 0.497386i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3784.95 | − | 2185.24i | 0.240503 | − | 0.138855i | ||||
\(629\) | −1862.70 | −0.118077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8657.42 | −0.546191 | −0.273095 | − | 0.961987i | \(-0.588047\pi\) | ||||
−0.273095 | + | 0.961987i | \(0.588047\pi\) | |||||||
\(632\) | 4484.03 | − | 2588.86i | 0.282223 | − | 0.162942i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9586.08 | − | 16603.6i | 0.600492 | − | 1.04008i | ||||
\(635\) | 7770.77 | + | 13459.4i | 0.485628 | + | 0.841132i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10647.8 | − | 8348.04i | 0.662297 | − | 0.519249i | ||||
\(638\) | − | 8228.67i | − | 0.510621i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −922.629 | − | 532.680i | −0.0569845 | − | 0.0329000i | ||||
\(641\) | −2344.82 | − | 1353.78i | −0.144485 | − | 0.0834185i | 0.426015 | − | 0.904716i | \(-0.359917\pi\) |
−0.570500 | + | 0.821298i | \(0.693251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4164.00i | 0.255384i | 0.991814 | + | 0.127692i | \(0.0407569\pi\) | ||||
−0.991814 | + | 0.127692i | \(0.959243\pi\) | |||||||
\(644\) | −936.980 | + | 1925.22i | −0.0573326 | + | 0.117802i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3369.56 | − | 5836.24i | −0.205222 | − | 0.355455i | ||||
\(647\) | −8381.49 | + | 14517.2i | −0.509289 | + | 0.882115i | 0.490653 | + | 0.871355i | \(0.336758\pi\) |
−0.999942 | + | 0.0107600i | \(0.996575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8653.94 | − | 4996.35i | 0.523416 | − | 0.302194i | ||||
\(650\) | −4396.38 | −0.265293 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −744.114 | −0.0446959 | ||||||||
\(653\) | −10249.1 | + | 5917.34i | −0.614211 | + | 0.354615i | −0.774612 | − | 0.632437i | \(-0.782055\pi\) |
0.160401 | + | 0.987052i | \(0.448721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9116.54 | + | 15790.3i | −0.543836 | + | 0.941952i | ||||
\(656\) | 990.068 | + | 1714.85i | 0.0589263 | + | 0.102063i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1317.93 | + | 1950.35i | 0.0780825 | + | 0.115551i | ||||
\(659\) | 3368.19i | 0.199099i | 0.995033 | + | 0.0995493i | \(0.0317401\pi\) | ||||
−0.995033 | + | 0.0995493i | \(0.968260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23010.5 | − | 13285.1i | −1.35401 | − | 0.781740i | −0.365205 | − | 0.930927i | \(-0.619001\pi\) |
−0.988809 | + | 0.149187i | \(0.952334\pi\) | |||||||
\(662\) | 18904.6 | + | 10914.6i | 1.10989 | + | 0.640797i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1853.70i | 0.108340i | ||||||||
\(665\) | −2860.76 | − | 4233.53i | −0.166820 | − | 0.246871i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2569.27 | − | 4450.10i | −0.149149 | − | 0.258334i | ||||
\(668\) | −2501.55 | + | 4332.81i | −0.144892 | + | 0.250960i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2690.41 | − | 1553.31i | 0.155133 | − | 0.0895663i | ||||
\(671\) | −20026.5 | −1.15219 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9144.44 | −0.523763 | −0.261881 | − | 0.965100i | \(-0.584343\pi\) | ||||
−0.261881 | + | 0.965100i | \(0.584343\pi\) | |||||||
\(674\) | −4567.64 | + | 2637.13i | −0.261037 | + | 0.150710i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1281.92 | − | 2220.35i | 0.0729359 | − | 0.126329i | ||||
\(677\) | 833.748 | + | 1444.09i | 0.0473317 | + | 0.0819809i | 0.888721 | − | 0.458449i | \(-0.151595\pi\) |
−0.841389 | + | 0.540430i | \(0.818262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11004.6 | − | 22611.2i | 0.621969 | − | 1.27797i | ||||
\(680\) | − | 6768.72i | − | 0.381719i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6262.41 | + | 3615.61i | 0.351613 | + | 0.203004i | ||||
\(683\) | −7775.82 | − | 4489.37i | −0.435627 | − | 0.251509i | 0.266114 | − | 0.963942i | \(-0.414260\pi\) |
−0.701741 | + | 0.712432i | \(0.747594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14949.7i | − | 0.833869i | ||||||
\(686\) | −8525.15 | − | 9419.99i | −0.474478 | − | 0.524281i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1937.50 | − | 3355.85i | −0.107364 | − | 0.185960i | ||||
\(689\) | 1250.43 | − | 2165.81i | 0.0691403 | − | 0.119754i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23895.7 | − | 13796.2i | 1.31554 | − | 0.759527i | 0.332531 | − | 0.943092i | \(-0.392097\pi\) |
0.983007 | + | 0.183566i | \(0.0587640\pi\) | |||||||
\(692\) | 15676.2 | 0.861154 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4117.36 | −0.225206 | ||||||||
\(695\) | −1943.75 | + | 1122.23i | −0.106087 | + | 0.0612495i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6290.36 | + | 10895.2i | −0.341843 | + | 0.592089i | ||||
\(698\) | −320.118 | − | 554.460i | −0.0173591 | − | 0.0300668i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 291.451 | + | 4117.91i | 0.0157369 | + | 0.222346i | ||||
\(701\) | − | 26713.1i | − | 1.43929i | −0.694344 | − | 0.719644i | \(-0.744305\pi\) | ||
0.694344 | − | 0.719644i | \(-0.255695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −525.998 | − | 303.685i | −0.0282196 | − | 0.0162926i | ||||
\(704\) | −1282.64 | − | 740.534i | −0.0686668 | − | 0.0396448i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 16600.9i | − | 0.884964i | ||||||
\(707\) | 19119.8 | − | 12920.0i | 1.01708 | − | 0.687281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9177.34 | + | 15895.6i | 0.486124 | + | 0.841992i | 0.999873 | − | 0.0159488i | \(-0.00507688\pi\) |
−0.513748 | + | 0.857941i | \(0.671744\pi\) | |||||||
\(710\) | 9729.12 | − | 16851.3i | 0.514264 | − | 0.890731i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1795.88 | + | 1036.85i | −0.0945273 | + | 0.0545754i | ||||
\(713\) | 4515.66 | 0.237185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7597.87 | 0.397404 | ||||||||
\(716\) | 6710.23 | − | 3874.15i | 0.350242 | − | 0.202212i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11173.8 | − | 19353.6i | 0.580785 | − | 1.00595i | ||||
\(719\) | 7775.70 | + | 13467.9i | 0.403317 | + | 0.698565i | 0.994124 | − | 0.108248i | \(-0.0345240\pi\) |
−0.590807 | + | 0.806813i | \(0.701191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5985.49 | + | 423.631i | −0.309169 | + | 0.0218819i | ||||
\(722\) | 11520.6i | 0.593838i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2848.98 | + | 1644.86i | 0.146245 | + | 0.0844348i | ||||
\(725\) | −8580.06 | − | 4953.70i | −0.439525 | − | 0.253760i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27003.3i | 1.37757i | 0.724964 | + | 0.688787i | \(0.241856\pi\) | ||||
−0.724964 | + | 0.688787i | \(0.758144\pi\) | |||||||
\(728\) | 5255.17 | + | 2557.62i | 0.267540 | + | 0.130208i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6419.21 | − | 11118.4i | −0.325460 | − | 0.563713i | ||||
\(731\) | 12309.9 | − | 21321.3i | 0.622841 | − | 1.07879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13000.2 | + | 7505.67i | −0.655079 | + | 0.378210i | −0.790400 | − | 0.612592i | \(-0.790127\pi\) |
0.135320 | + | 0.990802i | \(0.456794\pi\) | |||||||
\(734\) | −4534.62 | −0.228033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −924.879 | −0.0463199 | ||||||||
\(737\) | 3740.21 | − | 2159.41i | 0.186937 | − | 0.107928i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7159.79 | − | 12401.1i | 0.356397 | − | 0.617298i | −0.630959 | − | 0.775816i | \(-0.717338\pi\) |
0.987356 | + | 0.158519i | \(0.0506718\pi\) | |||||||
\(740\) | −305.020 | − | 528.309i | −0.0151524 | − | 0.0262447i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2111.52 | − | 1027.65i | −0.104470 | − | 0.0508440i | ||||
\(743\) | − | 27470.1i | − | 1.35637i | −0.734892 | − | 0.678184i | \(-0.762767\pi\) | ||
0.734892 | − | 0.678184i | \(-0.237233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16654.0 | − | 9615.17i | −0.818998 | − | 0.472849i | ||||
\(746\) | −14788.2 | − | 8537.97i | −0.725783 | − | 0.419031i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9409.91i | − | 0.459974i | ||||||
\(749\) | −31941.0 | + | 2260.67i | −1.55821 | + | 0.110285i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18562.1 | + | 32150.5i | 0.901919 | + | 1.56217i | 0.825001 | + | 0.565131i | \(0.191174\pi\) |
0.0769175 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(752\) | −508.394 | + | 880.564i | −0.0246532 | + | 0.0427006i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12147.2 | + | 7013.18i | −0.586703 | + | 0.338733i | ||||
\(755\) | −5593.35 | −0.269620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30289.1 | 1.45426 | 0.727132 | − | 0.686498i | \(-0.240853\pi\) | ||||
0.727132 | + | 0.686498i | \(0.240853\pi\) | |||||||
\(758\) | 18143.7 | − | 10475.3i | 0.869405 | − | 0.501951i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1103.54 | − | 1911.39i | 0.0526706 | − | 0.0912282i | ||||
\(761\) | −18626.4 | − | 32261.9i | −0.887263 | − | 1.53678i | −0.843098 | − | 0.537760i | \(-0.819271\pi\) |
−0.0441643 | − | 0.999024i | \(-0.514063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25284.9 | − | 17086.0i | 1.19971 | − | 0.810688i | ||||
\(764\) | 7347.34i | 0.347928i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18321.8 | + | 10578.1i | 0.864222 | + | 0.498959i | ||||
\(767\) | −14751.3 | − | 8516.64i | −0.694442 | − | 0.400936i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24044.8i | 1.12754i | 0.825932 | + | 0.563770i | \(0.190650\pi\) | ||||
−0.825932 | + | 0.563770i | \(0.809350\pi\) | |||||||
\(770\) | −503.688 | − | 7116.61i | −0.0235736 | − | 0.333071i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7239.34 | − | 12538.9i | −0.337499 | − | 0.584566i | ||||
\(773\) | 14130.8 | − | 24475.2i | 0.657501 | − | 1.13882i | −0.323760 | − | 0.946139i | \(-0.604947\pi\) |
0.981261 | − | 0.192685i | \(-0.0617196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7540.00 | − | 4353.22i | 0.349477 | − | 0.201771i | ||||
\(776\) | 10862.5 | 0.502499 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22389.7 | −1.03176 | ||||||||
\(779\) | −3552.61 | + | 2051.10i | −0.163396 | + | 0.0943368i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13525.5 | − | 23426.8i | 0.619692 | − | 1.07334i | ||||
\(782\) | −2938.09 | − | 5088.92i | −0.134355 | − | 0.232710i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2047.23 | − | 5091.85i | 0.0932596 | − | 0.231954i | ||||
\(785\) | 9094.03i | 0.413477i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8810.30 | − | 5086.63i | −0.399051 | − | 0.230392i | 0.287023 | − | 0.957924i | \(-0.407334\pi\) |
−0.686074 | + | 0.727531i | \(0.740668\pi\) | |||||||
\(788\) | −2324.06 | − | 1341.80i | −0.105065 | − | 0.0606594i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10773.7i | 0.485203i | ||||||||
\(791\) | 8544.44 | − | 17556.4i | 0.384078 | − | 0.789168i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17068.3 | + | 29563.2i | 0.764331 | + | 1.32386i | ||||
\(794\) | −1116.48 | + | 1933.80i | −0.0499024 | + | 0.0864334i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2833.65 | − | 1636.01i | 0.126176 | − | 0.0728476i | ||||
\(797\) | 32606.8 | 1.44917 | 0.724587 | − | 0.689184i | \(-0.242031\pi\) | ||||
0.724587 | + | 0.689184i | \(0.242031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6460.12 | −0.286036 | ||||||||
\(800\) | −1544.31 | + | 891.610i | −0.0682497 | + | 0.0394040i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7914.51 | − | 13708.3i | 0.348468 | − | 0.603563i | ||||
\(803\) | −8924.02 | − | 15456.9i | −0.392182 | − | 0.679278i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2494.44 | − | 3691.43i | −0.109214 | − | 0.161622i | ||||
\(806\) | − | 12326.1i | − | 0.538671i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8632.40 | + | 4983.92i | 0.375850 | + | 0.216997i | ||||
\(809\) | 22305.4 | + | 12878.0i | 0.969365 | + | 0.559663i | 0.899042 | − | 0.437861i | \(-0.144264\pi\) |
0.0703222 | + | 0.997524i | \(0.477597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3614.74i | 0.156511i | 0.996933 | + | 0.0782556i | \(0.0249350\pi\) | ||||
−0.996933 | + | 0.0782556i | \(0.975065\pi\) | |||||||
\(812\) | 7374.24 | + | 10912.8i | 0.318701 | + | 0.471633i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −424.040 | − | 734.458i | −0.0182587 | − | 0.0316250i | ||||
\(815\) | 774.169 | − | 1340.90i | 0.0332736 | − | 0.0576315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6952.25 | − | 4013.89i | 0.297709 | − | 0.171883i | ||||
\(818\) | −21363.9 | −0.913167 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4120.23 | −0.175469 | ||||||||
\(821\) | −16618.7 | + | 9594.81i | −0.706451 | + | 0.407870i | −0.809746 | − | 0.586781i | \(-0.800395\pi\) |
0.103295 | + | 0.994651i | \(0.467062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12693.6 | + | 21985.9i | −0.537630 | + | 0.931203i | 0.461401 | + | 0.887192i | \(0.347347\pi\) |
−0.999031 | + | 0.0440111i | \(0.985986\pi\) | |||||||
\(824\) | −1295.98 | − | 2244.70i | −0.0547907 | − | 0.0949002i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6999.28 | + | 14381.5i | −0.294838 | + | 0.605807i | ||||
\(827\) | − | 2224.78i | − | 0.0935468i | −0.998906 | − | 0.0467734i | \(-0.985106\pi\) | ||
0.998906 | − | 0.0467734i | \(-0.0148939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3840.87 | + | 2217.53i | 0.160916 | + | 0.0929047i | 0.578295 | − | 0.815828i | \(-0.303718\pi\) |
−0.417380 | + | 0.908732i | \(0.637051\pi\) | |||||||
\(830\) | −3340.39 | − | 1928.58i | −0.139695 | − | 0.0806528i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2524.59i | 0.105197i | ||||||||
\(833\) | 34520.2 | − | 4911.03i | 1.43584 | − | 0.204270i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5205.18 | − | 9015.63i | −0.215728 | − | 0.373651i | ||||
\(836\) | 1534.15 | − | 2657.22i | 0.0634685 | − | 0.109931i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 904.324 | − | 522.112i | 0.0372785 | − | 0.0215227i | ||||
\(839\) | 33407.6 | 1.37468 | 0.687340 | − | 0.726336i | \(-0.258778\pi\) | ||||
0.687340 | + | 0.726336i | \(0.258778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7219.91 | −0.296031 | ||||||||
\(842\) | −11706.3 | + | 6758.66i | −0.479129 | + | 0.276626i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1411.38 | + | 2444.59i | −0.0575615 | + | 0.0996994i | ||||
\(845\) | 2667.40 | + | 4620.07i | 0.108593 | + | 0.188089i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1040.09 | + | 14695.4i | 0.0421934 | + | 0.596151i | ||||
\(848\) | − | 1014.38i | − | 0.0410777i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9811.74 | − | 5664.81i | −0.395929 | − | 0.228590i | ||||
\(851\) | −458.645 | − | 264.799i | −0.0184749 | − | 0.0106665i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36851.9i | − | 1.47923i | −0.673029 | − | 0.739616i | \(-0.735007\pi\) | ||
0.673029 | − | 0.739616i | \(-0.264993\pi\) | |||||||
\(854\) | 26559.2 | − | 17947.1i | 1.06421 | − | 0.719129i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6915.87 | − | 11978.6i | −0.276145 | − | 0.478296i | ||||
\(857\) | −645.110 | + | 1117.36i | −0.0257136 | + | 0.0445372i | −0.878596 | − | 0.477566i | \(-0.841519\pi\) |
0.852882 | + | 0.522103i | \(0.174852\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10713.8 | + | 6185.59i | −0.425551 | + | 0.245692i | −0.697450 | − | 0.716634i | \(-0.745682\pi\) |
0.271898 | + | 0.962326i | \(0.412349\pi\) | |||||||
\(860\) | 8063.04 | 0.319706 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22167.7 | −0.875911 | ||||||||
\(863\) | 4672.03 | − | 2697.40i | 0.184285 | − | 0.106397i | −0.405020 | − | 0.914308i | \(-0.632735\pi\) |
0.589304 | + | 0.807911i | \(0.299402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16309.3 | + | 28248.6i | −0.641080 | + | 1.11038i | ||||
\(866\) | −10214.3 | − | 17691.6i | −0.400802 | − | 0.694210i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11545.4 | + | 817.140i | −0.451470 | + | 0.0319534i | ||||
\(869\) | 14977.6i | 0.584674i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6375.46 | − | 3680.87i | −0.248019 | − | 0.143194i | ||||
\(872\) | 11415.9 | + | 6590.95i | 0.443337 | + | 0.255961i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1916.05i | − | 0.0741549i | ||||||
\(875\) | −25049.1 | − | 12191.1i | −0.967788 | − | 0.471009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11228.9 | − | 19449.0i | −0.432352 | − | 0.748856i | 0.564723 | − | 0.825280i | \(-0.308983\pi\) |
−0.997075 | + | 0.0764243i | \(0.975650\pi\) | |||||||
\(878\) | −6321.43 | + | 10949.0i | −0.242982 | + | 0.420856i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2668.90 | − | 1540.89i | 0.102237 | − | 0.0590265i | ||||
\(881\) | 16245.3 | 0.621247 | 0.310623 | − | 0.950533i | \(-0.399462\pi\) | ||||
0.310623 | + | 0.950533i | \(0.399462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15876.5 | −0.605081 | −0.302540 | − | 0.953137i | \(-0.597835\pi\) | ||||
−0.302540 | + | 0.953137i | \(0.597835\pi\) | |||||||
\(884\) | −13890.9 | + | 8019.93i | −0.528510 | + | 0.305135i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3679.16 | − | 6372.49i | 0.139508 | − | 0.241634i | ||||
\(887\) | 10331.9 | + | 17895.3i | 0.391105 | + | 0.677413i | 0.992596 | − | 0.121466i | \(-0.0387596\pi\) |
−0.601491 | + | 0.798880i | \(0.705426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31095.2 | − | 15133.6i | −1.17312 | − | 0.570940i | ||||
\(890\) | − | 4314.92i | − | 0.162513i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21980.4 | + | 12690.4i | 0.825065 | + | 0.476351i | ||||
\(893\) | −1824.24 | − | 1053.23i | −0.0683606 | − | 0.0394680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16122.5i | 0.602141i | ||||||||
\(896\) | 2364.68 | − | 167.363i | 0.0881678 | − | 0.00624020i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16168.6 | + | 28004.9i | 0.600839 | + | 1.04068i | ||||
\(899\) | 13888.7 | − | 24055.9i | 0.515254 | − | 0.892446i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5581.37 | − | 3222.41i | 0.206373 | − | 0.119150i | ||||
\(902\) | −5727.96 | −0.211441 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8434.09 | 0.310303 | ||||||||
\(905\) | −5928.11 | + | 3422.60i | −0.217743 | + | 0.125714i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12054.3 | − | 20878.7i | 0.441298 | − | 0.764351i | −0.556488 | − | 0.830856i | \(-0.687851\pi\) |
0.997786 | + | 0.0665047i | \(0.0211847\pi\) | |||||||
\(908\) | 3500.05 | + | 6062.26i | 0.127922 | + | 0.221567i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10076.3 | + | 6808.93i | −0.367061 | + | 0.248037i | ||||
\(911\) | 47902.4i | 1.74213i | 0.491171 | + | 0.871063i | \(0.336569\pi\) | ||||
−0.491171 | + | 0.871063i | \(0.663431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4643.82 | − | 2681.11i | −0.168333 | − | 0.0971872i | ||||
\(914\) | 853.907 | + | 493.003i | 0.0309023 | + | 0.0178415i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16232.4i | 0.585517i | ||||||||
\(917\) | −2864.34 | − | 40470.2i | −0.103150 | − | 1.45741i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19752.6 | − | 34212.6i | −0.709009 | − | 1.22804i | −0.965225 | − | 0.261420i | \(-0.915809\pi\) |
0.256216 | − | 0.966619i | \(-0.417524\pi\) | |||||||
\(920\) | 962.235 | − | 1666.64i | 0.0344825 | − | 0.0597255i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15758.3 | − | 9098.09i | 0.562878 | − | 0.324978i | ||||
\(923\) | −46110.3 | −1.64435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1021.10 | −0.0362956 | ||||||||
\(926\) | 15941.7 | − | 9203.93i | 0.565741 | − | 0.326631i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2844.62 | + | 4927.03i | −0.100624 | + | 0.174286i | ||||
\(929\) | −23541.7 | − | 40775.4i | −0.831407 | − | 1.44004i | −0.896923 | − | 0.442188i | \(-0.854203\pi\) |
0.0655155 | − | 0.997852i | \(-0.479131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10548.7 | + | 4241.21i | 0.371342 | + | 0.149302i | ||||
\(932\) | − | 23509.3i | − | 0.826258i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27513.4 | + | 15884.9i | 0.963883 | + | 0.556498i | ||||
\(935\) | 16956.7 | + | 9789.98i | 0.593096 | + | 0.342424i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25357.7i | 0.884099i | 0.896991 | + | 0.442050i | \(0.145748\pi\) | ||||
−0.896991 | + | 0.442050i | \(0.854252\pi\) | |||||||
\(938\) | −3025.08 | + | 6215.65i | −0.105301 | + | 0.216363i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1057.86 | − | 1832.26i | −0.0367058 | − | 0.0635763i | ||||
\(941\) | −8535.03 | + | 14783.1i | −0.295679 | + | 0.512131i | −0.975143 | − | 0.221578i | \(-0.928879\pi\) |
0.679464 | + | 0.733709i | \(0.262213\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3097.71 | + | 1788.46i | −0.106973 | + | 0.0617607i | ||||
\(944\) | −6908.89 | −0.238205 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11209.3 | 0.385248 | ||||||||
\(947\) | −33746.1 | + | 19483.3i | −1.15797 | + | 0.668556i | −0.950817 | − | 0.309752i | \(-0.899754\pi\) |
−0.207156 | + | 0.978308i | \(0.566421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15211.6 | + | 26347.3i | −0.520327 | + | 0.901233i | ||||
\(950\) | −1847.13 | − | 3199.32i | −0.0630829 | − | 0.109263i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8432.82 | + | 12479.4i | 0.287090 | + | 0.424853i | ||||
\(953\) | − | 22611.7i | − | 0.768589i | −0.923211 | − | 0.384295i | \(-0.874445\pi\) | ||
0.923211 | − | 0.384295i | \(-0.125555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13240.0 | − | 7644.10i | −0.448623 | − | 0.259013i | ||||
\(956\) | −19716.4 | − | 11383.3i | −0.667025 | − | 0.385107i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 4328.76i | − | 0.145987i | ||||||
\(959\) | 18625.1 | + | 27562.6i | 0.627151 | + | 0.928095i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2690.37 | − | 4659.86i | −0.0903083 | − | 0.156419i | ||||
\(962\) | −722.806 | + | 1251.94i | −0.0242247 | + | 0.0419585i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14358.4 | + | 8289.84i | −0.479724 | + | 0.276969i | ||||
\(965\) | 30127.0 | 1.00500 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8946.41 | 0.297515 | 0.148758 | − | 0.988874i | \(-0.452473\pi\) | ||||
0.148758 | + | 0.988874i | \(0.452473\pi\) | |||||||
\(968\) | −5511.12 | + | 3181.85i | −0.182990 | + | 0.105649i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11301.2 | + | 19574.2i | −0.374082 | + | 0.647929i | ||||
\(971\) | −29157.3 | − | 50501.9i | −0.963648 | − | 1.66909i | −0.713205 | − | 0.700955i | \(-0.752757\pi\) |
−0.250443 | − | 0.968131i | \(-0.580576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2185.54 | − | 4490.66i | 0.0720095 | − | 0.147959i | ||||
\(974\) | 39292.0i | 1.29260i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11991.2 | + | 6923.11i | 0.393267 | + | 0.227053i | ||||
\(977\) | 2795.29 | + | 1613.86i | 0.0915346 | + | 0.0528475i | 0.545069 | − | 0.838391i | \(-0.316504\pi\) |
−0.453534 | + | 0.891239i | \(0.649837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5998.62i | − | 0.195829i | ||||||
\(980\) | 7045.64 | + | 8986.65i | 0.229658 | + | 0.292927i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11831.2 | − | 20492.2i | −0.384469 | − | 0.665920i | ||||
\(983\) | 4506.86 | − | 7806.10i | 0.146232 | − | 0.253282i | −0.783600 | − | 0.621266i | \(-0.786619\pi\) |
0.929832 | + | 0.367984i | \(0.119952\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4835.87 | − | 2791.99i | 0.156430 | − | 0.0903149i | ||||
\(986\) | −36146.4 | −1.16748 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5230.13 | −0.168414 | ||||||||
\(989\) | 6062.03 | − | 3499.91i | 0.194905 | − | 0.112529i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14685.7 | + | 25436.4i | −0.470744 | + | 0.815353i | −0.999440 | − | 0.0334585i | \(-0.989348\pi\) |
0.528696 | + | 0.848811i | \(0.322681\pi\) | |||||||
\(992\) | −2499.80 | − | 4329.79i | −0.0800090 | − | 0.138580i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3056.81 | + | 43189.6i | 0.0975412 | + | 1.37816i | ||||
\(995\) | 6808.34i | 0.216924i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16427.1 | − | 9484.18i | −0.521816 | − | 0.301271i | 0.215861 | − | 0.976424i | \(-0.430744\pi\) |
−0.737677 | + | 0.675153i | \(0.764077\pi\) | |||||||
\(998\) | 13366.8 | + | 7717.35i | 0.423968 | + | 0.244778i | ||||
\(999\) | 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 | 378.4.k.a.269.6 | yes | 12 | |
3.2 | odd | 2 | inner | 378.4.k.a.269.1 | yes | 12 | |
7.5 | odd | 6 | inner | 378.4.k.a.215.1 | ✓ | 12 | |
21.5 | even | 6 | inner | 378.4.k.a.215.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.k.a.215.1 | ✓ | 12 | 7.5 | odd | 6 | inner | |
378.4.k.a.215.6 | yes | 12 | 21.5 | even | 6 | inner | |
378.4.k.a.269.1 | yes | 12 | 3.2 | odd | 2 | inner | |
378.4.k.a.269.6 | yes | 12 | 1.1 | even | 1 | trivial |