Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(4,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.e (of order \(7\), degree \(6\), 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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 4.3 | ||
Character | \(\chi\) | \(=\) | 43.4 |
Dual form | 43.4.e.a.11.3 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{7}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29664 | + | 2.87990i | −0.811987 | + | 1.01820i | 0.187369 | + | 0.982290i | \(0.440004\pi\) |
−0.999355 | + | 0.0359092i | \(0.988567\pi\) | |||||||
\(3\) | −5.14704 | − | 6.45419i | −0.990549 | − | 1.24211i | −0.970197 | − | 0.242316i | \(-0.922093\pi\) |
−0.0203511 | − | 0.999793i | \(-0.506478\pi\) | |||||||
\(4\) | −1.23909 | − | 5.42880i | −0.154886 | − | 0.678600i | ||||
\(5\) | 11.0752 | + | 5.33352i | 0.990593 | + | 0.477044i | 0.857736 | − | 0.514091i | \(-0.171871\pi\) |
0.132857 | + | 0.991135i | \(0.457585\pi\) | |||||||
\(6\) | 30.4083 | 2.06903 | ||||||||
\(7\) | 28.5576 | 1.54196 | 0.770981 | − | 0.636858i | \(-0.219766\pi\) | ||||
0.770981 | + | 0.636858i | \(0.219766\pi\) | |||||||
\(8\) | −8.06984 | − | 3.88623i | −0.356640 | − | 0.171749i | ||||
\(9\) | −9.15641 | + | 40.1169i | −0.339126 | + | 1.48581i | ||||
\(10\) | −40.7957 | + | 19.6462i | −1.29007 | + | 0.621267i | ||||
\(11\) | 12.4283 | − | 54.4519i | 0.340661 | − | 1.49253i | −0.457022 | − | 0.889456i | \(-0.651084\pi\) |
0.797683 | − | 0.603078i | \(-0.206059\pi\) | |||||||
\(12\) | −28.6608 | + | 35.9395i | −0.689472 | + | 0.864571i | ||||
\(13\) | 63.9214 | + | 30.7829i | 1.36374 | + | 0.656742i | 0.965467 | − | 0.260526i | \(-0.0838959\pi\) |
0.398271 | + | 0.917268i | \(0.369610\pi\) | |||||||
\(14\) | −65.5865 | + | 82.2429i | −1.25205 | + | 1.57002i | ||||
\(15\) | −22.5808 | − | 98.9330i | −0.388689 | − | 1.70296i | ||||
\(16\) | 69.8612 | − | 33.6434i | 1.09158 | − | 0.525678i | ||||
\(17\) | −18.8533 | + | 9.07927i | −0.268976 | + | 0.129532i | −0.563511 | − | 0.826109i | \(-0.690550\pi\) |
0.294534 | + | 0.955641i | \(0.404835\pi\) | |||||||
\(18\) | −94.5036 | − | 118.504i | −1.23748 | − | 1.55176i | ||||
\(19\) | −5.65942 | − | 24.7955i | −0.0683347 | − | 0.299394i | 0.929199 | − | 0.369579i | \(-0.120498\pi\) |
−0.997534 | + | 0.0701852i | \(0.977641\pi\) | |||||||
\(20\) | 15.2315 | − | 66.7335i | 0.170293 | − | 0.746103i | ||||
\(21\) | −146.987 | − | 184.316i | −1.52739 | − | 1.91529i | ||||
\(22\) | 128.273 | + | 160.849i | 1.24308 | + | 1.55878i | ||||
\(23\) | −23.0933 | + | 101.178i | −0.209360 | + | 0.917267i | 0.755634 | + | 0.654995i | \(0.227329\pi\) |
−0.964994 | + | 0.262273i | \(0.915528\pi\) | |||||||
\(24\) | 16.4533 | + | 72.0868i | 0.139939 | + | 0.613111i | ||||
\(25\) | 16.2767 | + | 20.4103i | 0.130213 | + | 0.163282i | ||||
\(26\) | −235.456 | + | 113.390i | −1.77603 | + | 0.855291i | ||||
\(27\) | 105.233 | − | 50.6773i | 0.750074 | − | 0.361217i | ||||
\(28\) | −35.3853 | − | 155.033i | −0.238828 | − | 1.04638i | ||||
\(29\) | 58.6604 | − | 73.5578i | 0.375620 | − | 0.471012i | −0.557708 | − | 0.830037i | \(-0.688319\pi\) |
0.933328 | + | 0.359025i | \(0.116891\pi\) | |||||||
\(30\) | 336.777 | + | 162.183i | 2.04956 | + | 0.987017i | ||||
\(31\) | 10.0380 | − | 12.5872i | 0.0581573 | − | 0.0729270i | −0.751902 | − | 0.659275i | \(-0.770863\pi\) |
0.810059 | + | 0.586348i | \(0.199435\pi\) | |||||||
\(32\) | −47.6121 | + | 208.602i | −0.263022 | + | 1.15237i | ||||
\(33\) | −415.412 | + | 200.052i | −2.19133 | + | 1.05529i | ||||
\(34\) | 17.1519 | − | 75.1475i | 0.0865157 | − | 0.379050i | ||||
\(35\) | 316.280 | + | 152.312i | 1.52746 | + | 0.735585i | ||||
\(36\) | 229.132 | 1.06080 | ||||||||
\(37\) | −23.8504 | −0.105972 | −0.0529862 | − | 0.998595i | \(-0.516874\pi\) | ||||
−0.0529862 | + | 0.998595i | \(0.516874\pi\) | |||||||
\(38\) | 84.4063 | + | 40.6480i | 0.360329 | + | 0.173526i | ||||
\(39\) | −130.327 | − | 571.001i | −0.535104 | − | 2.34445i | ||||
\(40\) | −68.6475 | − | 86.0813i | −0.271353 | − | 0.340266i | ||||
\(41\) | −47.1291 | + | 59.0980i | −0.179520 | + | 0.225111i | −0.863447 | − | 0.504439i | \(-0.831699\pi\) |
0.683927 | + | 0.729550i | \(0.260271\pi\) | |||||||
\(42\) | 868.388 | 3.19036 | ||||||||
\(43\) | 279.591 | − | 36.5531i | 0.991562 | − | 0.129635i | ||||
\(44\) | −311.008 | −1.06560 | ||||||||
\(45\) | −315.373 | + | 395.465i | −1.04473 | + | 1.31005i | ||||
\(46\) | −238.347 | − | 298.877i | −0.763963 | − | 0.957979i | ||||
\(47\) | 1.23751 | + | 5.42187i | 0.00384061 | + | 0.0168268i | 0.976812 | − | 0.214099i | \(-0.0686816\pi\) |
−0.972971 | + | 0.230926i | \(0.925824\pi\) | |||||||
\(48\) | −576.719 | − | 277.733i | −1.73421 | − | 0.835153i | ||||
\(49\) | 472.534 | 1.37765 | ||||||||
\(50\) | −96.1613 | −0.271985 | ||||||||
\(51\) | 155.638 | + | 74.9514i | 0.427327 | + | 0.205790i | ||||
\(52\) | 87.9100 | − | 385.159i | 0.234441 | − | 1.02715i | ||||
\(53\) | −560.592 | + | 269.967i | −1.45289 | + | 0.699676i | −0.983095 | − | 0.183098i | \(-0.941387\pi\) |
−0.469797 | + | 0.882774i | \(0.655673\pi\) | |||||||
\(54\) | −95.7361 | + | 419.447i | −0.241260 | + | 1.05703i | ||||
\(55\) | 428.066 | − | 536.777i | 1.04946 | − | 1.31598i | ||||
\(56\) | −230.455 | − | 110.981i | −0.549925 | − | 0.264830i | ||||
\(57\) | −130.906 | + | 164.151i | −0.304191 | + | 0.381443i | ||||
\(58\) | 77.1172 | + | 337.872i | 0.174586 | + | 0.764911i | ||||
\(59\) | −170.772 | + | 82.2393i | −0.376823 | + | 0.181469i | −0.612702 | − | 0.790314i | \(-0.709917\pi\) |
0.235879 | + | 0.971782i | \(0.424203\pi\) | |||||||
\(60\) | −509.108 | + | 245.173i | −1.09543 | + | 0.527529i | ||||
\(61\) | −231.514 | − | 290.310i | −0.485941 | − | 0.609350i | 0.477053 | − | 0.878875i | \(-0.341705\pi\) |
−0.962994 | + | 0.269524i | \(0.913134\pi\) | |||||||
\(62\) | 13.1963 | + | 57.8169i | 0.0270312 | + | 0.118431i | ||||
\(63\) | −261.485 | + | 1145.64i | −0.522920 | + | 2.29106i | ||||
\(64\) | −104.642 | − | 131.217i | −0.204378 | − | 0.256282i | ||||
\(65\) | 543.759 | + | 681.852i | 1.03761 | + | 1.30113i | ||||
\(66\) | 377.924 | − | 1655.79i | 0.704836 | − | 3.08809i | ||||
\(67\) | 138.151 | + | 605.277i | 0.251907 | + | 1.10368i | 0.929669 | + | 0.368396i | \(0.120093\pi\) |
−0.677762 | + | 0.735282i | \(0.737050\pi\) | |||||||
\(68\) | 72.6504 | + | 91.1008i | 0.129561 | + | 0.162465i | ||||
\(69\) | 771.886 | − | 371.721i | 1.34673 | − | 0.648549i | ||||
\(70\) | −1165.03 | + | 561.047i | −1.98925 | + | 0.957971i | ||||
\(71\) | −143.403 | − | 628.291i | −0.239702 | − | 1.05020i | −0.941284 | − | 0.337615i | \(-0.890380\pi\) |
0.701582 | − | 0.712589i | \(-0.252477\pi\) | |||||||
\(72\) | 229.794 | − | 288.153i | 0.376132 | − | 0.471655i | ||||
\(73\) | −440.479 | − | 212.124i | −0.706222 | − | 0.340099i | 0.0460610 | − | 0.998939i | \(-0.485333\pi\) |
−0.752283 | + | 0.658840i | \(0.771047\pi\) | |||||||
\(74\) | 54.7758 | − | 68.6867i | 0.0860481 | − | 0.107901i | ||||
\(75\) | 47.9551 | − | 210.105i | 0.0738317 | − | 0.323478i | ||||
\(76\) | −127.597 | + | 61.4477i | −0.192585 | + | 0.0927438i | ||||
\(77\) | 354.922 | − | 1555.01i | 0.525287 | − | 2.30143i | ||||
\(78\) | 1943.74 | + | 936.057i | 2.82161 | + | 1.35882i | ||||
\(79\) | −1110.49 | −1.58151 | −0.790755 | − | 0.612132i | \(-0.790312\pi\) | ||||
−0.790755 | + | 0.612132i | \(0.790312\pi\) | |||||||
\(80\) | 953.162 | 1.33208 | ||||||||
\(81\) | 132.269 | + | 63.6975i | 0.181439 | + | 0.0873765i | ||||
\(82\) | −61.9577 | − | 271.454i | −0.0834400 | − | 0.365575i | ||||
\(83\) | −219.403 | − | 275.123i | −0.290152 | − | 0.363840i | 0.615296 | − | 0.788296i | \(-0.289037\pi\) |
−0.905448 | + | 0.424457i | \(0.860465\pi\) | |||||||
\(84\) | −818.483 | + | 1026.35i | −1.06314 | + | 1.33314i | ||||
\(85\) | −257.228 | −0.328239 | ||||||||
\(86\) | −536.851 | + | 889.143i | −0.673141 | + | 1.11487i | ||||
\(87\) | −776.684 | −0.957118 | ||||||||
\(88\) | −311.907 | + | 391.119i | −0.377834 | + | 0.473789i | ||||
\(89\) | −267.881 | − | 335.912i | −0.319049 | − | 0.400075i | 0.596283 | − | 0.802774i | \(-0.296643\pi\) |
−0.915332 | + | 0.402699i | \(0.868072\pi\) | |||||||
\(90\) | −414.601 | − | 1816.49i | −0.485586 | − | 2.12749i | ||||
\(91\) | 1825.44 | + | 879.084i | 2.10283 | + | 1.01267i | ||||
\(92\) | 577.891 | 0.654884 | ||||||||
\(93\) | −132.906 | −0.148191 | ||||||||
\(94\) | −18.4566 | − | 8.88821i | −0.0202516 | − | 0.00975265i | ||||
\(95\) | 69.5684 | − | 304.799i | 0.0751323 | − | 0.329176i | ||||
\(96\) | 1591.42 | − | 766.386i | 1.69191 | − | 0.814781i | ||||
\(97\) | −263.327 | + | 1153.71i | −0.275637 | + | 1.20765i | 0.627611 | + | 0.778527i | \(0.284033\pi\) |
−0.903248 | + | 0.429119i | \(0.858824\pi\) | |||||||
\(98\) | −1085.24 | + | 1360.85i | −1.11863 | + | 1.40272i | ||||
\(99\) | 2070.64 | + | 997.168i | 2.10209 | + | 1.01231i | ||||
\(100\) | 90.6351 | − | 113.653i | 0.0906351 | − | 0.113653i | ||||
\(101\) | 442.947 | + | 1940.68i | 0.436385 | + | 1.91193i | 0.409555 | + | 0.912286i | \(0.365684\pi\) |
0.0268300 | + | 0.999640i | \(0.491459\pi\) | |||||||
\(102\) | −573.298 | + | 276.086i | −0.556519 | + | 0.268005i | ||||
\(103\) | 372.002 | − | 179.147i | 0.355868 | − | 0.171377i | −0.247404 | − | 0.968912i | \(-0.579578\pi\) |
0.603272 | + | 0.797535i | \(0.293863\pi\) | |||||||
\(104\) | −396.206 | − | 496.826i | −0.373569 | − | 0.468441i | ||||
\(105\) | −644.853 | − | 2825.28i | −0.599345 | − | 2.62590i | ||||
\(106\) | 510.003 | − | 2234.47i | 0.467320 | − | 2.04746i | ||||
\(107\) | 29.8400 | + | 37.4182i | 0.0269602 | + | 0.0338070i | 0.795129 | − | 0.606441i | \(-0.207403\pi\) |
−0.768169 | + | 0.640248i | \(0.778832\pi\) | |||||||
\(108\) | −405.509 | − | 508.492i | −0.361298 | − | 0.453053i | ||||
\(109\) | −152.405 | + | 667.732i | −0.133925 | + | 0.586762i | 0.862775 | + | 0.505588i | \(0.168724\pi\) |
−0.996700 | + | 0.0811747i | \(0.974133\pi\) | |||||||
\(110\) | 562.751 | + | 2465.57i | 0.487784 | + | 2.13712i | ||||
\(111\) | 122.759 | + | 153.935i | 0.104971 | + | 0.131629i | ||||
\(112\) | 1995.07 | − | 960.773i | 1.68318 | − | 0.810576i | ||||
\(113\) | 453.467 | − | 218.378i | 0.377510 | − | 0.181799i | −0.235500 | − | 0.971874i | \(-0.575673\pi\) |
0.613010 | + | 0.790075i | \(0.289958\pi\) | |||||||
\(114\) | −172.094 | − | 753.991i | −0.141386 | − | 0.619454i | ||||
\(115\) | −795.399 | + | 997.398i | −0.644968 | + | 0.808764i | ||||
\(116\) | −472.016 | − | 227.311i | −0.377807 | − | 0.181942i | ||||
\(117\) | −1820.20 | + | 2282.46i | −1.43827 | + | 1.80354i | ||||
\(118\) | 155.361 | − | 680.680i | 0.121204 | − | 0.531031i | ||||
\(119\) | −538.404 | + | 259.282i | −0.414752 | + | 0.199734i | ||||
\(120\) | −202.253 | + | 886.128i | −0.153859 | + | 0.674100i | ||||
\(121\) | −1611.36 | − | 775.989i | −1.21064 | − | 0.583012i | ||||
\(122\) | 1367.77 | 1.01502 | ||||||||
\(123\) | 624.005 | 0.457436 | ||||||||
\(124\) | −80.7716 | − | 38.8975i | −0.0584960 | − | 0.0281702i | ||||
\(125\) | −270.509 | − | 1185.18i | −0.193561 | − | 0.848045i | ||||
\(126\) | −2698.79 | − | 3384.18i | −1.90815 | − | 2.39275i | ||||
\(127\) | −1182.37 | + | 1482.65i | −0.826132 | + | 1.03594i | 0.172570 | + | 0.984997i | \(0.444793\pi\) |
−0.998702 | + | 0.0509396i | \(0.983778\pi\) | |||||||
\(128\) | −1093.52 | −0.755111 | ||||||||
\(129\) | −1674.98 | − | 1616.39i | −1.14321 | − | 1.10322i | ||||
\(130\) | −3212.49 | −2.16734 | ||||||||
\(131\) | −36.0170 | + | 45.1639i | −0.0240215 | + | 0.0301220i | −0.793697 | − | 0.608313i | \(-0.791847\pi\) |
0.769676 | + | 0.638435i | \(0.220418\pi\) | |||||||
\(132\) | 1600.77 | + | 2007.30i | 1.05552 | + | 1.32359i | ||||
\(133\) | −161.619 | − | 708.100i | −0.105370 | − | 0.461654i | ||||
\(134\) | −2060.42 | − | 992.247i | −1.32831 | − | 0.639680i | ||||
\(135\) | 1435.76 | 0.915335 | ||||||||
\(136\) | 187.427 | 0.118175 | ||||||||
\(137\) | 1874.39 | + | 902.657i | 1.16890 | + | 0.562914i | 0.914659 | − | 0.404226i | \(-0.132459\pi\) |
0.254244 | + | 0.967140i | \(0.418174\pi\) | |||||||
\(138\) | −702.229 | + | 3076.67i | −0.433172 | + | 1.89785i | ||||
\(139\) | 1744.65 | − | 840.181i | 1.06460 | − | 0.512685i | 0.182239 | − | 0.983254i | \(-0.441666\pi\) |
0.882363 | + | 0.470569i | \(0.155951\pi\) | |||||||
\(140\) | 434.974 | − | 1905.75i | 0.262586 | − | 1.15046i | ||||
\(141\) | 28.6243 | − | 35.8937i | 0.0170964 | − | 0.0214383i | ||||
\(142\) | 2138.76 | + | 1029.97i | 1.26395 | + | 0.608687i | ||||
\(143\) | 2470.62 | − | 3098.06i | 1.44478 | − | 1.81170i | ||||
\(144\) | 709.989 | + | 3110.67i | 0.410873 | + | 1.80015i | ||||
\(145\) | 1042.00 | − | 501.799i | 0.596780 | − | 0.287394i | ||||
\(146\) | 1622.52 | − | 781.364i | 0.919731 | − | 0.442919i | ||||
\(147\) | −2432.15 | − | 3049.82i | −1.36463 | − | 1.71119i | ||||
\(148\) | 29.5527 | + | 129.479i | 0.0164136 | + | 0.0719128i | ||||
\(149\) | −108.724 | + | 476.352i | −0.0597787 | + | 0.261908i | −0.995982 | − | 0.0895506i | \(-0.971457\pi\) |
0.936204 | + | 0.351458i | \(0.114314\pi\) | |||||||
\(150\) | 494.946 | + | 620.643i | 0.269415 | + | 0.337835i | ||||
\(151\) | −2054.21 | − | 2575.90i | −1.10708 | − | 1.38823i | −0.913348 | − | 0.407181i | \(-0.866512\pi\) |
−0.193733 | − | 0.981054i | \(-0.562059\pi\) | |||||||
\(152\) | −50.6905 | + | 222.090i | −0.0270496 | + | 0.118512i | ||||
\(153\) | −191.603 | − | 839.469i | −0.101243 | − | 0.443576i | ||||
\(154\) | 3663.15 | + | 4593.45i | 1.91679 | + | 2.40358i | ||||
\(155\) | 178.307 | − | 85.8680i | 0.0923997 | − | 0.0444973i | ||||
\(156\) | −2938.36 | + | 1415.04i | −1.50806 | + | 0.726243i | ||||
\(157\) | 124.864 | + | 547.063i | 0.0634726 | + | 0.278092i | 0.996698 | − | 0.0812003i | \(-0.0258753\pi\) |
−0.933225 | + | 0.359292i | \(0.883018\pi\) | |||||||
\(158\) | 2550.39 | − | 3198.09i | 1.28417 | − | 1.61029i | ||||
\(159\) | 4627.81 | + | 2228.64i | 2.30823 | + | 1.11159i | ||||
\(160\) | −1639.89 | + | 2056.36i | −0.810282 | + | 1.01606i | ||||
\(161\) | −659.488 | + | 2889.41i | −0.322826 | + | 1.41439i | ||||
\(162\) | −487.218 | + | 234.632i | −0.236293 | + | 0.113793i | ||||
\(163\) | −144.061 | + | 631.171i | −0.0692251 | + | 0.303295i | −0.997674 | − | 0.0681650i | \(-0.978286\pi\) |
0.928449 | + | 0.371460i | \(0.121143\pi\) | |||||||
\(164\) | 379.228 | + | 182.627i | 0.180566 | + | 0.0869558i | ||||
\(165\) | −5667.73 | −2.67414 | ||||||||
\(166\) | 1296.22 | 0.606061 | ||||||||
\(167\) | −2346.26 | − | 1129.90i | −1.08718 | − | 0.523558i | −0.197574 | − | 0.980288i | \(-0.563306\pi\) |
−0.889605 | + | 0.456730i | \(0.849021\pi\) | |||||||
\(168\) | 469.867 | + | 2058.62i | 0.215780 | + | 0.945394i | ||||
\(169\) | 1768.55 | + | 2217.69i | 0.804982 | + | 1.00942i | ||||
\(170\) | 590.761 | − | 740.791i | 0.266525 | − | 0.334212i | ||||
\(171\) | 1046.54 | 0.468017 | ||||||||
\(172\) | −544.876 | − | 1472.55i | −0.241549 | − | 0.652795i | ||||
\(173\) | 1969.05 | 0.865344 | 0.432672 | − | 0.901552i | \(-0.357571\pi\) | ||||
0.432672 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(174\) | 1783.77 | − | 2236.77i | 0.777167 | − | 0.974536i | ||||
\(175\) | 464.821 | + | 582.868i | 0.200784 | + | 0.251775i | ||||
\(176\) | −963.691 | − | 4222.21i | −0.412733 | − | 1.80830i | ||||
\(177\) | 1409.76 | + | 678.903i | 0.598666 | + | 0.288302i | ||||
\(178\) | 1582.62 | 0.666419 | ||||||||
\(179\) | −1327.24 | −0.554203 | −0.277102 | − | 0.960841i | \(-0.589374\pi\) | ||||
−0.277102 | + | 0.960841i | \(0.589374\pi\) | |||||||
\(180\) | 2537.67 | + | 1222.08i | 1.05082 | + | 0.506047i | ||||
\(181\) | 557.329 | − | 2441.82i | 0.228873 | − | 1.00276i | −0.721688 | − | 0.692218i | \(-0.756634\pi\) |
0.950561 | − | 0.310538i | \(-0.100509\pi\) | |||||||
\(182\) | −6724.06 | + | 3238.14i | −2.73857 | + | 1.31883i | ||||
\(183\) | −682.100 | + | 2988.47i | −0.275531 | + | 1.20718i | ||||
\(184\) | 579.561 | − | 726.747i | 0.232206 | − | 0.291177i | ||||
\(185\) | −264.147 | − | 127.206i | −0.104975 | − | 0.0505535i | ||||
\(186\) | 305.239 | − | 382.757i | 0.120329 | − | 0.150888i | ||||
\(187\) | 260.069 | + | 1139.44i | 0.101701 | + | 0.445583i | ||||
\(188\) | 27.9009 | − | 13.4363i | 0.0108238 | − | 0.00521248i | ||||
\(189\) | 3005.18 | − | 1447.22i | 1.15659 | − | 0.556983i | ||||
\(190\) | 718.018 | + | 900.366i | 0.274160 | + | 0.343786i | ||||
\(191\) | −358.408 | − | 1570.29i | −0.135778 | − | 0.594881i | −0.996336 | − | 0.0855284i | \(-0.972742\pi\) |
0.860558 | − | 0.509352i | \(-0.170115\pi\) | |||||||
\(192\) | −308.301 | + | 1350.75i | −0.115884 | + | 0.507720i | ||||
\(193\) | −2211.26 | − | 2772.83i | −0.824716 | − | 1.03416i | −0.998778 | − | 0.0494261i | \(-0.984261\pi\) |
0.174062 | − | 0.984735i | \(-0.444311\pi\) | |||||||
\(194\) | −2717.81 | − | 3408.02i | −1.00581 | − | 1.26125i | ||||
\(195\) | 1602.05 | − | 7019.04i | 0.588334 | − | 2.57766i | ||||
\(196\) | −585.511 | − | 2565.29i | −0.213378 | − | 0.934872i | ||||
\(197\) | 1784.90 | + | 2238.20i | 0.645529 | + | 0.809468i | 0.991682 | − | 0.128710i | \(-0.0410837\pi\) |
−0.346153 | + | 0.938178i | \(0.612512\pi\) | |||||||
\(198\) | −7627.27 | + | 3673.10i | −2.73761 | + | 1.31836i | ||||
\(199\) | −1600.45 | + | 770.737i | −0.570116 | + | 0.274553i | −0.696653 | − | 0.717409i | \(-0.745328\pi\) |
0.126537 | + | 0.991962i | \(0.459614\pi\) | |||||||
\(200\) | −52.0310 | − | 227.962i | −0.0183957 | − | 0.0805969i | ||||
\(201\) | 3195.51 | − | 4007.04i | 1.12136 | − | 1.40614i | ||||
\(202\) | −6606.25 | − | 3181.40i | −2.30106 | − | 1.10813i | ||||
\(203\) | 1675.20 | − | 2100.63i | 0.579191 | − | 0.726283i | ||||
\(204\) | 214.046 | − | 937.799i | 0.0734620 | − | 0.321858i | ||||
\(205\) | −837.163 | + | 403.156i | −0.285219 | + | 0.137354i | ||||
\(206\) | −338.431 | + | 1482.76i | −0.114464 | + | 0.501501i | ||||
\(207\) | −3847.51 | − | 1852.86i | −1.29188 | − | 0.622139i | ||||
\(208\) | 5501.27 | 1.83387 | ||||||||
\(209\) | −1420.50 | −0.470134 | ||||||||
\(210\) | 9617.54 | + | 4631.56i | 3.16035 | + | 1.52194i | ||||
\(211\) | 1140.88 | + | 4998.51i | 0.372233 | + | 1.63086i | 0.720494 | + | 0.693462i | \(0.243915\pi\) |
−0.348260 | + | 0.937398i | \(0.613228\pi\) | |||||||
\(212\) | 2160.22 | + | 2708.83i | 0.699832 | + | 0.877562i | ||||
\(213\) | −3317.01 | + | 4159.39i | −1.06703 | + | 1.33801i | ||||
\(214\) | −176.292 | −0.0563136 | ||||||||
\(215\) | 3291.47 | + | 1086.37i | 1.04408 | + | 0.344604i | ||||
\(216\) | −1046.15 | −0.329545 | ||||||||
\(217\) | 286.661 | − | 359.461i | 0.0896764 | − | 0.112451i | ||||
\(218\) | −1572.98 | − | 1972.46i | −0.488696 | − | 0.612805i | ||||
\(219\) | 898.080 | + | 3934.74i | 0.277108 | + | 1.21409i | ||||
\(220\) | −3444.47 | − | 1658.77i | −1.05557 | − | 0.508337i | ||||
\(221\) | −1484.62 | −0.451883 | ||||||||
\(222\) | −725.250 | −0.219260 | ||||||||
\(223\) | 502.500 | + | 241.991i | 0.150896 | + | 0.0726679i | 0.507808 | − | 0.861470i | \(-0.330456\pi\) |
−0.356912 | + | 0.934138i | \(0.616170\pi\) | |||||||
\(224\) | −1359.68 | + | 5957.16i | −0.405570 | + | 1.77692i | ||||
\(225\) | −967.832 | + | 466.084i | −0.286765 | + | 0.138099i | ||||
\(226\) | −412.545 | + | 1807.48i | −0.121425 | + | 0.531999i | ||||
\(227\) | 1869.49 | − | 2344.27i | 0.546619 | − | 0.685439i | −0.429402 | − | 0.903113i | \(-0.641276\pi\) |
0.976021 | + | 0.217674i | \(0.0698471\pi\) | |||||||
\(228\) | 1053.34 | + | 507.264i | 0.305962 | + | 0.147344i | ||||
\(229\) | 590.042 | − | 739.889i | 0.170267 | − | 0.213508i | −0.689376 | − | 0.724404i | \(-0.742115\pi\) |
0.859642 | + | 0.510896i | \(0.170686\pi\) | |||||||
\(230\) | −1045.66 | − | 4581.34i | −0.299778 | − | 1.31341i | ||||
\(231\) | −11863.1 | + | 5712.99i | −3.37895 | + | 1.62722i | ||||
\(232\) | −759.243 | + | 365.632i | −0.214857 | + | 0.103469i | ||||
\(233\) | −619.126 | − | 776.359i | −0.174078 | − | 0.218287i | 0.687137 | − | 0.726528i | \(-0.258867\pi\) |
−0.861215 | + | 0.508241i | \(0.830296\pi\) | |||||||
\(234\) | −2392.91 | − | 10484.0i | −0.668501 | − | 2.92890i | ||||
\(235\) | −15.2121 | + | 66.6484i | −0.00422266 | + | 0.0185007i | ||||
\(236\) | 658.062 | + | 825.183i | 0.181509 | + | 0.227605i | ||||
\(237\) | 5715.71 | + | 7167.28i | 1.56656 | + | 1.96441i | ||||
\(238\) | 489.817 | − | 2146.03i | 0.133404 | − | 0.584481i | ||||
\(239\) | 538.491 | + | 2359.28i | 0.145741 | + | 0.638533i | 0.994040 | + | 0.109016i | \(0.0347699\pi\) |
−0.848299 | + | 0.529518i | \(0.822373\pi\) | |||||||
\(240\) | −4905.97 | − | 6151.89i | −1.31949 | − | 1.65459i | ||||
\(241\) | −52.2632 | + | 25.1687i | −0.0139692 | + | 0.00672720i | −0.440855 | − | 0.897578i | \(-0.645325\pi\) |
0.426886 | + | 0.904305i | \(0.359611\pi\) | |||||||
\(242\) | 5935.49 | − | 2858.38i | 1.57664 | − | 0.759271i | ||||
\(243\) | −971.417 | − | 4256.06i | −0.256446 | − | 1.12356i | ||||
\(244\) | −1289.17 | + | 1616.56i | −0.338239 | + | 0.424139i | ||||
\(245\) | 5233.39 | + | 2520.27i | 1.36469 | + | 0.657200i | ||||
\(246\) | −1433.12 | + | 1797.07i | −0.371432 | + | 0.465761i | ||||
\(247\) | 401.521 | − | 1759.18i | 0.103434 | − | 0.453173i | ||||
\(248\) | −129.922 | + | 62.5671i | −0.0332663 | + | 0.0160202i | ||||
\(249\) | −646.418 | + | 2832.14i | −0.164518 | + | 0.720802i | ||||
\(250\) | 4034.46 | + | 1942.90i | 1.02065 | + | 0.491518i | ||||
\(251\) | −1283.94 | −0.322876 | −0.161438 | − | 0.986883i | \(-0.551613\pi\) | ||||
−0.161438 | + | 0.986883i | \(0.551613\pi\) | |||||||
\(252\) | 6543.45 | 1.63571 | ||||||||
\(253\) | 5222.34 | + | 2514.95i | 1.29773 | + | 0.624954i | ||||
\(254\) | −1554.39 | − | 6810.24i | −0.383982 | − | 1.68233i | ||||
\(255\) | 1323.96 | + | 1660.20i | 0.325136 | + | 0.407708i | ||||
\(256\) | 3348.56 | − | 4198.96i | 0.817518 | − | 1.02514i | ||||
\(257\) | −2588.04 | −0.628162 | −0.314081 | − | 0.949396i | \(-0.601696\pi\) | ||||
−0.314081 | + | 0.949396i | \(0.601696\pi\) | |||||||
\(258\) | 8501.89 | − | 1111.52i | 2.05157 | − | 0.268217i | ||||
\(259\) | −681.108 | −0.163405 | ||||||||
\(260\) | 3027.87 | − | 3796.83i | 0.722233 | − | 0.905651i | ||||
\(261\) | 2413.79 | + | 3026.80i | 0.572452 | + | 0.717832i | ||||
\(262\) | −47.3493 | − | 207.451i | −0.0111651 | − | 0.0489174i | ||||
\(263\) | 3332.12 | + | 1604.66i | 0.781244 | + | 0.376227i | 0.781606 | − | 0.623773i | \(-0.214401\pi\) |
−0.000361656 | 1.00000i | \(0.500115\pi\) | ||||||||
\(264\) | 4129.75 | 0.962760 | ||||||||
\(265\) | −7648.53 | −1.77300 | ||||||||
\(266\) | 2410.44 | + | 1160.81i | 0.555615 | + | 0.267570i | ||||
\(267\) | −789.245 | + | 3457.91i | −0.180903 | + | 0.792587i | ||||
\(268\) | 3114.75 | − | 1499.98i | 0.709938 | − | 0.341888i | ||||
\(269\) | 511.763 | − | 2242.18i | 0.115995 | − | 0.508209i | −0.883233 | − | 0.468934i | \(-0.844638\pi\) |
0.999228 | − | 0.0392745i | \(-0.0125047\pi\) | |||||||
\(270\) | −3297.42 | + | 4134.84i | −0.743240 | + | 0.931993i | ||||
\(271\) | −6369.96 | − | 3067.61i | −1.42785 | − | 0.687616i | −0.449253 | − | 0.893404i | \(-0.648310\pi\) |
−0.978597 | + | 0.205788i | \(0.934024\pi\) | |||||||
\(272\) | −1011.66 | + | 1268.58i | −0.225517 | + | 0.282790i | ||||
\(273\) | −3721.83 | − | 16306.4i | −0.825111 | − | 3.61505i | ||||
\(274\) | −6904.36 | + | 3324.97i | −1.52229 | + | 0.733097i | ||||
\(275\) | 1313.67 | − | 632.630i | 0.288063 | − | 0.138724i | ||||
\(276\) | −2974.43 | − | 3729.82i | −0.648694 | − | 0.813437i | ||||
\(277\) | 157.749 | + | 691.143i | 0.0342174 | + | 0.149916i | 0.989151 | − | 0.146904i | \(-0.0469309\pi\) |
−0.954933 | + | 0.296820i | \(0.904074\pi\) | |||||||
\(278\) | −1587.21 | + | 6954.03i | −0.342427 | + | 1.50027i | ||||
\(279\) | 413.049 | + | 517.947i | 0.0886330 | + | 0.111142i | ||||
\(280\) | −1960.41 | − | 2458.27i | −0.418416 | − | 0.524678i | ||||
\(281\) | −1891.97 | + | 8289.27i | −0.401657 | + | 1.75977i | 0.219034 | + | 0.975717i | \(0.429709\pi\) |
−0.620691 | + | 0.784055i | \(0.713148\pi\) | |||||||
\(282\) | 37.6305 | + | 164.870i | 0.00794633 | + | 0.0348151i | ||||
\(283\) | −506.944 | − | 635.688i | −0.106483 | − | 0.133526i | 0.725734 | − | 0.687975i | \(-0.241500\pi\) |
−0.832217 | + | 0.554450i | \(0.812929\pi\) | |||||||
\(284\) | −3233.18 | + | 1557.02i | −0.675541 | + | 0.325324i | ||||
\(285\) | −2325.30 | + | 1119.81i | −0.483295 | + | 0.232743i | ||||
\(286\) | 3247.97 | + | 14230.3i | 0.671526 | + | 2.94215i | ||||
\(287\) | −1345.89 | + | 1687.69i | −0.276813 | + | 0.347113i | ||||
\(288\) | −7932.51 | − | 3820.09i | −1.62301 | − | 0.781601i | ||||
\(289\) | −2790.19 | + | 3498.79i | −0.567920 | + | 0.712149i | ||||
\(290\) | −947.964 | + | 4153.30i | −0.191953 | + | 0.841001i | ||||
\(291\) | 8801.63 | − | 4238.64i | 1.77306 | − | 0.853861i | ||||
\(292\) | −605.784 | + | 2654.11i | −0.121407 | + | 0.531918i | ||||
\(293\) | 4289.97 | + | 2065.94i | 0.855367 | + | 0.411923i | 0.809567 | − | 0.587028i | \(-0.199702\pi\) |
0.0457999 | + | 0.998951i | \(0.485416\pi\) | |||||||
\(294\) | 14369.0 | 2.85039 | ||||||||
\(295\) | −2329.95 | −0.459847 | ||||||||
\(296\) | 192.469 | + | 92.6880i | 0.0377940 | + | 0.0182006i | ||||
\(297\) | −1451.62 | − | 6359.94i | −0.283607 | − | 1.24256i | ||||
\(298\) | −1122.14 | − | 1407.12i | −0.218135 | − | 0.273532i | ||||
\(299\) | −4590.72 | + | 5756.58i | −0.887920 | + | 1.11342i | ||||
\(300\) | −1200.04 | −0.230948 | ||||||||
\(301\) | 7984.42 | − | 1043.87i | 1.52895 | − | 0.199892i | ||||
\(302\) | 12136.1 | 2.31243 | ||||||||
\(303\) | 10245.6 | − | 12847.6i | 1.94256 | − | 2.43589i | ||||
\(304\) | −1229.58 | − | 1541.84i | −0.231978 | − | 0.290891i | ||||
\(305\) | −1015.69 | − | 4450.02i | −0.190682 | − | 0.835433i | ||||
\(306\) | 2857.63 | + | 1376.16i | 0.533856 | + | 0.257092i | ||||
\(307\) | −8092.16 | −1.50438 | −0.752189 | − | 0.658948i | \(-0.771002\pi\) | ||||
−0.752189 | + | 0.658948i | \(0.771002\pi\) | |||||||
\(308\) | −8881.63 | −1.64311 | ||||||||
\(309\) | −3070.95 | − | 1478.89i | −0.565374 | − | 0.272270i | ||||
\(310\) | −162.216 | + | 710.714i | −0.0297201 | + | 0.130212i | ||||
\(311\) | −1886.61 | + | 908.546i | −0.343987 | + | 0.165656i | −0.597898 | − | 0.801572i | \(-0.703997\pi\) |
0.253911 | + | 0.967228i | \(0.418283\pi\) | |||||||
\(312\) | −1167.32 | + | 5114.37i | −0.211816 | + | 0.928026i | ||||
\(313\) | 3575.15 | − | 4483.10i | 0.645621 | − | 0.809584i | −0.346072 | − | 0.938208i | \(-0.612485\pi\) |
0.991693 | + | 0.128624i | \(0.0410561\pi\) | |||||||
\(314\) | −1862.26 | − | 896.815i | −0.334692 | − | 0.161179i | ||||
\(315\) | −9006.28 | + | 11293.5i | −1.61094 | + | 2.02006i | ||||
\(316\) | 1375.99 | + | 6028.60i | 0.244954 | + | 1.07321i | ||||
\(317\) | 8604.01 | − | 4143.47i | 1.52445 | − | 0.734134i | 0.530885 | − | 0.847444i | \(-0.321859\pi\) |
0.993560 | + | 0.113310i | \(0.0361452\pi\) | |||||||
\(318\) | −17046.7 | + | 8209.25i | −3.00607 | + | 1.44765i | ||||
\(319\) | −3276.32 | − | 4108.37i | −0.575042 | − | 0.721080i | ||||
\(320\) | −459.078 | − | 2011.35i | −0.0801977 | − | 0.351369i | ||||
\(321\) | 87.9161 | − | 385.186i | 0.0152866 | − | 0.0669750i | ||||
\(322\) | −6806.59 | − | 8535.20i | −1.17800 | − | 1.47717i | ||||
\(323\) | 331.824 | + | 416.094i | 0.0571616 | + | 0.0716784i | ||||
\(324\) | 181.908 | − | 796.989i | 0.0311913 | − | 0.136658i | ||||
\(325\) | 412.138 | + | 1805.70i | 0.0703425 | + | 0.308191i | ||||
\(326\) | −1486.85 | − | 1864.45i | −0.252605 | − | 0.316756i | ||||
\(327\) | 5094.10 | − | 2453.19i | 0.861482 | − | 0.414868i | ||||
\(328\) | 609.993 | − | 293.757i | 0.102687 | − | 0.0494513i | ||||
\(329\) | 35.3402 | + | 154.835i | 0.00592208 | + | 0.0259463i | ||||
\(330\) | 13016.8 | − | 16322.5i | 2.17136 | − | 2.72280i | ||||
\(331\) | 1107.26 | + | 533.230i | 0.183869 | + | 0.0885467i | 0.523554 | − | 0.851993i | \(-0.324606\pi\) |
−0.339684 | + | 0.940539i | \(0.610320\pi\) | |||||||
\(332\) | −1221.73 | + | 1532.00i | −0.201961 | + | 0.253251i | ||||
\(333\) | 218.384 | − | 956.802i | 0.0359380 | − | 0.157455i | ||||
\(334\) | 8642.52 | − | 4162.02i | 1.41586 | − | 0.681843i | ||||
\(335\) | −1698.22 | + | 7440.38i | −0.276966 | + | 1.21347i | ||||
\(336\) | −16469.7 | − | 7931.38i | −2.67409 | − | 1.28778i | ||||
\(337\) | −2889.26 | −0.467027 | −0.233514 | − | 0.972354i | \(-0.575022\pi\) | ||||
−0.233514 | + | 0.972354i | \(0.575022\pi\) | |||||||
\(338\) | −10448.4 | −1.68142 | ||||||||
\(339\) | −3743.47 | − | 1802.76i | −0.599756 | − | 0.288827i | ||||
\(340\) | 318.728 | + | 1396.44i | 0.0508396 | + | 0.222743i | ||||
\(341\) | −560.644 | − | 703.026i | −0.0890340 | − | 0.111645i | ||||
\(342\) | −2403.53 | + | 3013.93i | −0.380023 | + | 0.476534i | ||||
\(343\) | 3699.17 | 0.582321 | ||||||||
\(344\) | −2398.30 | − | 791.576i | −0.375895 | − | 0.124067i | ||||
\(345\) | 10531.3 | 1.64345 | ||||||||
\(346\) | −4522.22 | + | 5670.68i | −0.702647 | + | 0.881092i | ||||
\(347\) | −1207.21 | − | 1513.80i | −0.186763 | − | 0.234193i | 0.679632 | − | 0.733554i | \(-0.262140\pi\) |
−0.866394 | + | 0.499361i | \(0.833568\pi\) | |||||||
\(348\) | 962.379 | + | 4216.46i | 0.148244 | + | 0.649500i | ||||
\(349\) | −1641.30 | − | 790.411i | −0.251739 | − | 0.121231i | 0.303759 | − | 0.952749i | \(-0.401758\pi\) |
−0.555498 | + | 0.831518i | \(0.687472\pi\) | |||||||
\(350\) | −2746.13 | −0.419391 | ||||||||
\(351\) | 8286.60 | 1.26013 | ||||||||
\(352\) | 10767.0 | + | 5185.13i | 1.63036 | + | 0.785138i | ||||
\(353\) | 188.098 | − | 824.111i | 0.0283610 | − | 0.124258i | −0.958766 | − | 0.284198i | \(-0.908273\pi\) |
0.987127 | + | 0.159940i | \(0.0511300\pi\) | |||||||
\(354\) | −5192.88 | + | 2500.76i | −0.779657 | + | 0.375463i | ||||
\(355\) | 1762.79 | − | 7723.28i | 0.263547 | − | 1.15467i | ||||
\(356\) | −1491.67 | + | 1870.50i | −0.222074 | + | 0.278472i | ||||
\(357\) | 4444.64 | + | 2140.43i | 0.658923 | + | 0.317320i | ||||
\(358\) | 3048.19 | − | 3822.31i | 0.450006 | − | 0.564289i | ||||
\(359\) | 1869.16 | + | 8189.34i | 0.274793 | + | 1.20395i | 0.904281 | + | 0.426937i | \(0.140407\pi\) |
−0.629489 | + | 0.777010i | \(0.716736\pi\) | |||||||
\(360\) | 4081.88 | − | 1965.73i | 0.597594 | − | 0.287786i | ||||
\(361\) | 5596.96 | − | 2695.35i | 0.816002 | − | 0.392966i | ||||
\(362\) | 5752.21 | + | 7213.04i | 0.835164 | + | 1.04726i | ||||
\(363\) | 3285.35 | + | 14394.0i | 0.475030 | + | 2.08124i | ||||
\(364\) | 2510.49 | − | 10999.2i | 0.361499 | − | 1.58383i | ||||
\(365\) | −3747.02 | − | 4698.61i | −0.537336 | − | 0.673799i | ||||
\(366\) | −7039.97 | − | 8827.84i | −1.00542 | − | 1.26076i | ||||
\(367\) | 1536.58 | − | 6732.22i | 0.218553 | − | 0.957545i | −0.739995 | − | 0.672613i | \(-0.765172\pi\) |
0.958548 | − | 0.284932i | \(-0.0919709\pi\) | |||||||
\(368\) | 1790.66 | + | 7845.38i | 0.253653 | + | 1.11133i | ||||
\(369\) | −1939.29 | − | 2431.80i | −0.273592 | − | 0.343074i | ||||
\(370\) | 972.994 | − | 468.569i | 0.136712 | − | 0.0658371i | ||||
\(371\) | −16009.1 | + | 7709.60i | −2.24031 | + | 1.07887i | ||||
\(372\) | 164.683 | + | 721.522i | 0.0229527 | + | 0.100562i | ||||
\(373\) | −5244.74 | + | 6576.70i | −0.728050 | + | 0.912945i | −0.998763 | − | 0.0497145i | \(-0.984169\pi\) |
0.270714 | + | 0.962660i | \(0.412740\pi\) | |||||||
\(374\) | −3878.76 | − | 1867.91i | −0.536272 | − | 0.258255i | ||||
\(375\) | −6257.04 | + | 7846.09i | −0.861633 | + | 1.08045i | ||||
\(376\) | 11.0842 | − | 48.5628i | 0.00152027 | − | 0.00666074i | ||||
\(377\) | 6013.98 | − | 2896.18i | 0.821580 | − | 0.395652i | ||||
\(378\) | −2733.99 | + | 11978.4i | −0.372014 | + | 1.62990i | ||||
\(379\) | −5507.14 | − | 2652.10i | −0.746392 | − | 0.359443i | 0.0217156 | − | 0.999764i | \(-0.493087\pi\) |
−0.768108 | + | 0.640321i | \(0.778801\pi\) | |||||||
\(380\) | −1740.89 | −0.235016 | ||||||||
\(381\) | 15655.0 | 2.10507 | ||||||||
\(382\) | 5345.42 | + | 2574.22i | 0.715956 | + | 0.344786i | ||||
\(383\) | −2228.68 | − | 9764.48i | −0.297337 | − | 1.30272i | −0.874075 | − | 0.485790i | \(-0.838532\pi\) |
0.576738 | − | 0.816929i | \(-0.304325\pi\) | |||||||
\(384\) | 5628.38 | + | 7057.77i | 0.747974 | + | 0.937930i | ||||
\(385\) | 12224.5 | − | 15329.0i | 1.61823 | − | 2.02920i | ||||
\(386\) | 13064.0 | 1.72264 | ||||||||
\(387\) | −1093.65 | + | 11551.0i | −0.143652 | + | 1.51723i | ||||
\(388\) | 6589.55 | 0.862201 | ||||||||
\(389\) | 1235.20 | − | 1548.89i | 0.160995 | − | 0.201882i | −0.694790 | − | 0.719212i | \(-0.744503\pi\) |
0.855786 | + | 0.517331i | \(0.173074\pi\) | |||||||
\(390\) | 16534.8 | + | 20734.0i | 2.14685 | + | 2.69207i | ||||
\(391\) | −483.241 | − | 2117.22i | −0.0625027 | − | 0.273842i | ||||
\(392\) | −3813.27 | − | 1836.37i | −0.491325 | − | 0.236609i | ||||
\(393\) | 476.877 | 0.0612094 | ||||||||
\(394\) | −10545.1 | −1.34836 | ||||||||
\(395\) | −12298.8 | − | 5922.79i | −1.56663 | − | 0.754451i | ||||
\(396\) | 2847.72 | − | 12476.7i | 0.361372 | − | 1.58327i | ||||
\(397\) | −3407.25 | + | 1640.84i | −0.430743 | + | 0.207435i | −0.636676 | − | 0.771131i | \(-0.719691\pi\) |
0.205934 | + | 0.978566i | \(0.433977\pi\) | |||||||
\(398\) | 1456.02 | − | 6379.25i | 0.183376 | − | 0.803425i | ||||
\(399\) | −3738.35 | + | 4687.74i | −0.469051 | + | 0.588171i | ||||
\(400\) | 1823.78 | + | 878.285i | 0.227972 | + | 0.109786i | ||||
\(401\) | 8481.00 | − | 10634.8i | 1.05616 | − | 1.32438i | 0.112434 | − | 0.993659i | \(-0.464135\pi\) |
0.943727 | − | 0.330725i | \(-0.107293\pi\) | |||||||
\(402\) | 4200.93 | + | 18405.5i | 0.521202 | + | 2.28354i | ||||
\(403\) | 1029.11 | − | 495.595i | 0.127206 | − | 0.0612590i | ||||
\(404\) | 9986.69 | − | 4809.33i | 1.22984 | − | 0.592261i | ||||
\(405\) | 1125.17 | + | 1410.92i | 0.138050 | + | 0.173109i | ||||
\(406\) | 2202.28 | + | 9648.81i | 0.269205 | + | 1.17946i | ||||
\(407\) | −296.419 | + | 1298.70i | −0.0361007 | + | 0.158167i | ||||
\(408\) | −964.696 | − | 1209.69i | −0.117058 | − | 0.146786i | ||||
\(409\) | 5891.98 | + | 7388.31i | 0.712322 | + | 0.893223i | 0.997876 | − | 0.0651393i | \(-0.0207492\pi\) |
−0.285554 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(410\) | 761.615 | − | 3336.85i | 0.0917402 | − | 0.401940i | ||||
\(411\) | −3821.63 | − | 16743.7i | −0.458655 | − | 2.00950i | ||||
\(412\) | −1433.49 | − | 1797.54i | −0.171415 | − | 0.214948i | ||||
\(413\) | −4876.82 | + | 2348.55i | −0.581048 | + | 0.279818i | ||||
\(414\) | 14172.4 | − | 6825.07i | 1.68245 | − | 0.810227i | ||||
\(415\) | −962.554 | − | 4217.23i | −0.113855 | − | 0.498833i | ||||
\(416\) | −9464.81 | + | 11868.5i | −1.11551 | + | 1.39880i | ||||
\(417\) | −14402.5 | − | 6935.88i | −1.69135 | − | 0.814511i | ||||
\(418\) | 3262.38 | − | 4090.90i | 0.381743 | − | 0.478690i | ||||
\(419\) | −1171.74 | + | 5133.74i | −0.136619 | + | 0.598568i | 0.859545 | + | 0.511061i | \(0.170747\pi\) |
−0.996164 | + | 0.0875071i | \(0.972110\pi\) | |||||||
\(420\) | −14538.9 | + | 7001.55i | −1.68911 | + | 0.813430i | ||||
\(421\) | −157.758 | + | 691.182i | −0.0182628 | + | 0.0800146i | −0.983238 | − | 0.182326i | \(-0.941637\pi\) |
0.964975 | + | 0.262341i | \(0.0844945\pi\) | |||||||
\(422\) | −17015.4 | − | 8194.18i | −1.96279 | − | 0.945229i | ||||
\(423\) | −228.840 | −0.0263039 | ||||||||
\(424\) | 5573.04 | 0.638328 | ||||||||
\(425\) | −492.179 | − | 237.021i | −0.0561746 | − | 0.0270523i | ||||
\(426\) | −4360.66 | − | 19105.3i | −0.495950 | − | 2.17290i | ||||
\(427\) | −6611.48 | − | 8290.54i | −0.749302 | − | 0.939595i | ||||
\(428\) | 166.161 | − | 208.360i | 0.0187657 | − | 0.0235314i | ||||
\(429\) | −32711.8 | −3.68145 | ||||||||
\(430\) | −10688.0 | + | 6984.10i | −1.19865 | + | 0.783263i | ||||
\(431\) | 12530.7 | 1.40042 | 0.700210 | − | 0.713937i | \(-0.253090\pi\) | ||||
0.700210 | + | 0.713937i | \(0.253090\pi\) | |||||||
\(432\) | 5646.72 | − | 7080.76i | 0.628884 | − | 0.788595i | ||||
\(433\) | 8500.02 | + | 10658.7i | 0.943383 | + | 1.18296i | 0.982973 | + | 0.183749i | \(0.0588233\pi\) |
−0.0395901 | + | 0.999216i | \(0.512605\pi\) | |||||||
\(434\) | 376.855 | + | 1651.11i | 0.0416811 | + | 0.182617i | ||||
\(435\) | −8601.90 | − | 4142.46i | −0.948114 | − | 0.456588i | ||||
\(436\) | 3813.82 | 0.418920 | ||||||||
\(437\) | 2639.47 | 0.288931 | ||||||||
\(438\) | −13394.2 | − | 6450.33i | −1.46119 | − | 0.703673i | ||||
\(439\) | 3746.95 | − | 16416.5i | 0.407363 | − | 1.78477i | −0.188914 | − | 0.981994i | \(-0.560497\pi\) |
0.596276 | − | 0.802779i | \(-0.296646\pi\) | |||||||
\(440\) | −5540.46 | + | 2668.14i | −0.600298 | + | 0.289088i | ||||
\(441\) | −4326.71 | + | 18956.6i | −0.467197 | + | 2.04692i | ||||
\(442\) | 3409.63 | − | 4275.55i | 0.366923 | − | 0.460106i | ||||
\(443\) | 7183.62 | + | 3459.45i | 0.770438 | + | 0.371023i | 0.777444 | − | 0.628952i | \(-0.216516\pi\) |
−0.00700629 | + | 0.999975i | \(0.502230\pi\) | |||||||
\(444\) | 683.572 | − | 857.172i | 0.0730650 | − | 0.0916206i | ||||
\(445\) | −1175.23 | − | 5149.04i | −0.125194 | − | 0.548512i | ||||
\(446\) | −1850.98 | + | 891.383i | −0.196516 | + | 0.0946372i | ||||
\(447\) | 3634.07 | − | 1750.08i | 0.384531 | − | 0.185181i | ||||
\(448\) | −2988.31 | − | 3747.22i | −0.315144 | − | 0.395178i | ||||
\(449\) | 55.3690 | + | 242.588i | 0.00581966 | + | 0.0254976i | 0.977754 | − | 0.209753i | \(-0.0672660\pi\) |
−0.971935 | + | 0.235251i | \(0.924409\pi\) | |||||||
\(450\) | 880.493 | − | 3857.69i | 0.0922374 | − | 0.404118i | ||||
\(451\) | 2632.26 | + | 3300.76i | 0.274830 | + | 0.344626i | ||||
\(452\) | −1747.42 | − | 2191.19i | −0.181840 | − | 0.228020i | ||||
\(453\) | −6052.22 | + | 26516.5i | −0.627722 | + | 2.75023i | ||||
\(454\) | 2457.70 | + | 10767.9i | 0.254066 | + | 1.11313i | ||||
\(455\) | 15528.4 | + | 19472.0i | 1.59996 | + | 2.00629i | ||||
\(456\) | 1694.31 | − | 815.939i | 0.173999 | − | 0.0837935i | ||||
\(457\) | −16688.1 | + | 8036.54i | −1.70817 | + | 0.822612i | −0.715946 | + | 0.698155i | \(0.754005\pi\) |
−0.992225 | + | 0.124457i | \(0.960281\pi\) | |||||||
\(458\) | 775.691 | + | 3398.53i | 0.0791390 | + | 0.346731i | ||||
\(459\) | −1523.87 | + | 1910.87i | −0.154963 | + | 0.194318i | ||||
\(460\) | 6400.24 | + | 3082.19i | 0.648724 | + | 0.312409i | ||||
\(461\) | 1945.91 | − | 2440.09i | 0.196594 | − | 0.246521i | −0.673757 | − | 0.738953i | \(-0.735320\pi\) |
0.870351 | + | 0.492432i | \(0.163892\pi\) | |||||||
\(462\) | 10792.6 | − | 47285.4i | 1.08683 | − | 4.76172i | ||||
\(463\) | 2381.26 | − | 1146.76i | 0.239021 | − | 0.115106i | −0.310539 | − | 0.950561i | \(-0.600510\pi\) |
0.549560 | + | 0.835454i | \(0.314795\pi\) | |||||||
\(464\) | 1623.35 | − | 7112.38i | 0.162419 | − | 0.711603i | ||||
\(465\) | −1471.96 | − | 708.859i | −0.146797 | − | 0.0706937i | ||||
\(466\) | 3657.75 | 0.363609 | ||||||||
\(467\) | −14644.0 | −1.45106 | −0.725528 | − | 0.688192i | \(-0.758405\pi\) | ||||
−0.725528 | + | 0.688192i | \(0.758405\pi\) | |||||||
\(468\) | 14646.4 | + | 7053.35i | 1.44665 | + | 0.696669i | ||||
\(469\) | 3945.24 | + | 17285.2i | 0.388432 | + | 1.70183i | ||||
\(470\) | −157.004 | − | 196.877i | −0.0154086 | − | 0.0193218i | ||||
\(471\) | 2888.17 | − | 3621.65i | 0.282547 | − | 0.354303i | ||||
\(472\) | 1697.70 | 0.165557 | ||||||||
\(473\) | 1484.45 | − | 15678.5i | 0.144302 | − | 1.52410i | ||||
\(474\) | −33768.0 | −3.27219 | ||||||||
\(475\) | 413.967 | − | 519.099i | 0.0399876 | − | 0.0501429i | ||||
\(476\) | 2074.72 | + | 2601.61i | 0.199779 | + | 0.250514i | ||||
\(477\) | −5697.22 | − | 24961.1i | −0.546871 | − | 2.39600i | ||||
\(478\) | −8031.23 | − | 3867.64i | −0.768494 | − | 0.370087i | ||||
\(479\) | 16033.1 | 1.52938 | 0.764689 | − | 0.644399i | \(-0.222892\pi\) | ||||
0.764689 | + | 0.644399i | \(0.222892\pi\) | |||||||
\(480\) | 21712.8 | 2.06468 | ||||||||
\(481\) | −1524.55 | − | 734.184i | −0.144519 | − | 0.0695965i | ||||
\(482\) | 47.5469 | − | 208.316i | 0.00449315 | − | 0.0196858i | ||||
\(483\) | 22043.2 | − | 10615.4i | 2.07660 | − | 1.00004i | ||||
\(484\) | −2216.07 | + | 9709.25i | −0.208121 | + | 0.911838i | ||||
\(485\) | −9069.74 | + | 11373.1i | −0.849145 | + | 1.06479i | ||||
\(486\) | 14488.0 | + | 6977.07i | 1.35224 | + | 0.651206i | ||||
\(487\) | −9958.89 | + | 12488.1i | −0.926654 | + | 1.16199i | 0.0598428 | + | 0.998208i | \(0.480940\pi\) |
−0.986497 | + | 0.163780i | \(0.947631\pi\) | |||||||
\(488\) | 740.073 | + | 3242.47i | 0.0686507 | + | 0.300778i | ||||
\(489\) | 4815.18 | − | 2318.87i | 0.445296 | − | 0.214443i | ||||
\(490\) | −19277.4 | + | 9283.49i | −1.77727 | + | 0.855888i | ||||
\(491\) | 8560.56 | + | 10734.6i | 0.786828 | + | 0.986651i | 0.999954 | + | 0.00962653i | \(0.00306427\pi\) |
−0.213125 | + | 0.977025i | \(0.568364\pi\) | |||||||
\(492\) | −773.197 | − | 3387.60i | −0.0708504 | − | 0.310416i | ||||
\(493\) | −438.091 | + | 1919.40i | −0.0400216 | + | 0.175346i | ||||
\(494\) | 4144.11 | + | 5196.55i | 0.377434 | + | 0.473287i | ||||
\(495\) | 17614.3 | + | 22087.6i | 1.59940 | + | 2.00558i | ||||
\(496\) | 277.789 | − | 1217.07i | 0.0251474 | − | 0.110178i | ||||
\(497\) | −4095.25 | − | 17942.5i | −0.369612 | − | 1.61937i | ||||
\(498\) | −6671.69 | − | 8366.04i | −0.600333 | − | 0.752794i | ||||
\(499\) | 13996.2 | − | 6740.23i | 1.25563 | − | 0.604678i | 0.316612 | − | 0.948555i | \(-0.397455\pi\) |
0.939015 | + | 0.343877i | \(0.111740\pi\) | |||||||
\(500\) | −6098.91 | + | 2937.08i | −0.545503 | + | 0.262701i | ||||
\(501\) | 4783.71 | + | 20958.8i | 0.426588 | + | 1.86900i | ||||
\(502\) | 2948.76 | − | 3697.63i | 0.262171 | − | 0.328752i | ||||
\(503\) | −7887.63 | − | 3798.48i | −0.699189 | − | 0.336712i | 0.0502946 | − | 0.998734i | \(-0.483984\pi\) |
−0.749484 | + | 0.662023i | \(0.769698\pi\) | |||||||
\(504\) | 6562.36 | − | 8228.94i | 0.579981 | − | 0.727274i | ||||
\(505\) | −5444.92 | + | 23855.8i | −0.479794 | + | 2.10211i | ||||
\(506\) | −19236.7 | + | 9263.89i | −1.69007 | + | 0.813894i | ||||
\(507\) | 5210.58 | − | 22829.1i | 0.456430 | − | 1.99975i | ||||
\(508\) | 9514.08 | + | 4581.74i | 0.830943 | + | 0.400161i | ||||
\(509\) | 14111.2 | 1.22882 | 0.614408 | − | 0.788989i | \(-0.289395\pi\) | ||||
0.614408 | + | 0.788989i | \(0.289395\pi\) | |||||||
\(510\) | −7821.88 | −0.679134 | ||||||||
\(511\) | −12579.0 | − | 6057.73i | −1.08897 | − | 0.524419i | ||||
\(512\) | 2455.49 | + | 10758.2i | 0.211950 | + | 0.928614i | ||||
\(513\) | −1852.13 | − | 2322.49i | −0.159402 | − | 0.199884i | ||||
\(514\) | 5943.81 | − | 7453.30i | 0.510059 | − | 0.639593i | ||||
\(515\) | 5075.46 | 0.434275 | ||||||||
\(516\) | −6699.60 | + | 11096.0i | −0.571576 | + | 0.946655i | ||||
\(517\) | 310.611 | 0.0264230 | ||||||||
\(518\) | 1564.26 | − | 1961.52i | 0.132683 | − | 0.166379i | ||||
\(519\) | −10134.8 | − | 12708.6i | −0.857165 | − | 1.07485i | ||||
\(520\) | −1738.21 | − | 7615.60i | −0.146588 | − | 0.642243i | ||||
\(521\) | 5288.56 | + | 2546.83i | 0.444714 | + | 0.214163i | 0.642819 | − | 0.766018i | \(-0.277765\pi\) |
−0.198106 | + | 0.980181i | \(0.563479\pi\) | |||||||
\(522\) | −14260.5 | −1.19572 | ||||||||
\(523\) | 16310.7 | 1.36370 | 0.681851 | − | 0.731491i | \(-0.261175\pi\) | ||||
0.681851 | + | 0.731491i | \(0.261175\pi\) | |||||||
\(524\) | 289.814 | + | 139.567i | 0.0241614 | + | 0.0116355i | ||||
\(525\) | 1369.48 | − | 6000.09i | 0.113846 | − | 0.498791i | ||||
\(526\) | −12274.0 | + | 5910.83i | −1.01743 | + | 0.489970i | ||||
\(527\) | −74.9663 | + | 328.449i | −0.00619656 | + | 0.0271489i | ||||
\(528\) | −22290.7 | + | 27951.7i | −1.83727 | + | 2.30387i | ||||
\(529\) | 1258.33 | + | 605.981i | 0.103422 | + | 0.0498053i | ||||
\(530\) | 17566.0 | − | 22027.0i | 1.43965 | − | 1.80527i | ||||
\(531\) | −1735.53 | − | 7603.84i | −0.141837 | − | 0.621429i | ||||
\(532\) | −3643.87 | + | 1754.79i | −0.296958 | + | 0.143008i | ||||
\(533\) | −4831.76 | + | 2326.86i | −0.392658 | + | 0.189094i | ||||
\(534\) | −8145.82 | − | 10214.5i | −0.660120 | − | 0.827765i | ||||
\(535\) | 130.912 | + | 573.564i | 0.0105791 | + | 0.0463502i | ||||
\(536\) | 1237.39 | − | 5421.37i | 0.0997150 | − | 0.436880i | ||||
\(537\) | 6831.35 | + | 8566.24i | 0.548965 | + | 0.688381i | ||||
\(538\) | 5281.92 | + | 6623.32i | 0.423271 | + | 0.530765i | ||||
\(539\) | 5872.79 | − | 25730.4i | 0.469311 | − | 2.05619i | ||||
\(540\) | −1779.03 | − | 7794.43i | −0.141773 | − | 0.621146i | ||||
\(541\) | −4010.10 | − | 5028.51i | −0.318683 | − | 0.399616i | 0.596527 | − | 0.802593i | \(-0.296547\pi\) |
−0.915210 | + | 0.402977i | \(0.867976\pi\) | |||||||
\(542\) | 23463.9 | − | 11299.6i | 1.85952 | − | 0.895500i | ||||
\(543\) | −18628.5 | + | 8971.03i | −1.47224 | + | 0.708994i | ||||
\(544\) | −996.311 | − | 4365.12i | −0.0785229 | − | 0.344031i | ||||
\(545\) | −5249.28 | + | 6582.38i | −0.412577 | + | 0.517355i | ||||
\(546\) | 55508.5 | + | 26731.5i | 4.35082 | + | 2.09524i | ||||
\(547\) | 4681.93 | − | 5870.96i | 0.365969 | − | 0.458911i | −0.564418 | − | 0.825489i | \(-0.690899\pi\) |
0.930387 | + | 0.366578i | \(0.119471\pi\) | |||||||
\(548\) | 2577.81 | − | 11294.1i | 0.200947 | − | 0.880404i | ||||
\(549\) | 13766.2 | − | 6629.43i | 1.07017 | − | 0.515369i | ||||
\(550\) | −1195.12 | + | 5236.17i | −0.0926547 | + | 0.405947i | ||||
\(551\) | −2155.89 | − | 1038.22i | −0.166686 | − | 0.0802717i | ||||
\(552\) | −7673.59 | −0.591684 | ||||||||
\(553\) | −31712.7 | −2.43863 | ||||||||
\(554\) | −2352.72 | − | 1133.01i | −0.180428 | − | 0.0868897i | ||||
\(555\) | 538.561 | + | 2359.59i | 0.0411903 | + | 0.180467i | ||||
\(556\) | −6722.95 | − | 8430.32i | −0.512800 | − | 0.643031i | ||||
\(557\) | −10482.5 | + | 13144.6i | −0.797411 | + | 0.999922i | 0.202377 | + | 0.979308i | \(0.435133\pi\) |
−0.999788 | + | 0.0206138i | \(0.993438\pi\) | |||||||
\(558\) | −2440.26 | −0.185134 | ||||||||
\(559\) | 18997.0 | + | 6270.09i | 1.43737 | + | 0.474412i | ||||
\(560\) | 27220.0 | 2.05402 | ||||||||
\(561\) | 6015.56 | − | 7543.27i | 0.452722 | − | 0.567696i | ||||
\(562\) | −19527.1 | − | 24486.2i | −1.46566 | − | 1.83788i | ||||
\(563\) | 2440.01 | + | 10690.4i | 0.182654 | + | 0.800260i | 0.980360 | + | 0.197214i | \(0.0631893\pi\) |
−0.797706 | + | 0.603046i | \(0.793954\pi\) | |||||||
\(564\) | −230.327 | − | 110.920i | −0.0171960 | − | 0.00828115i | ||||
\(565\) | 6186.95 | 0.460685 | ||||||||
\(566\) | 2994.99 | 0.222418 | ||||||||
\(567\) | 3777.28 | + | 1819.04i | 0.279773 | + | 0.134731i | ||||
\(568\) | −1284.44 | + | 5627.51i | −0.0948838 | + | 0.415713i | ||||
\(569\) | 11560.5 | − | 5567.25i | 0.851743 | − | 0.410178i | 0.0435189 | − | 0.999053i | \(-0.486143\pi\) |
0.808224 | + | 0.588875i | \(0.200429\pi\) | |||||||
\(570\) | 2115.46 | − | 9268.44i | 0.155451 | − | 0.681074i | ||||
\(571\) | 6202.14 | − | 7777.24i | 0.454556 | − | 0.569995i | −0.500758 | − | 0.865587i | \(-0.666945\pi\) |
0.955314 | + | 0.295592i | \(0.0955169\pi\) | |||||||
\(572\) | −19880.1 | − | 9573.73i | −1.45319 | − | 0.699821i | ||||
\(573\) | −8290.20 | + | 10395.6i | −0.604412 | + | 0.757909i | ||||
\(574\) | −1769.36 | − | 7752.07i | −0.128661 | − | 0.563702i | ||||
\(575\) | −2440.96 | + | 1175.50i | −0.177035 | + | 0.0852555i | ||||
\(576\) | 6222.14 | − | 2996.43i | 0.450097 | − | 0.216755i | ||||
\(577\) | −811.426 | − | 1017.50i | −0.0585443 | − | 0.0734123i | 0.751697 | − | 0.659508i | \(-0.229236\pi\) |
−0.810242 | + | 0.586096i | \(0.800664\pi\) | |||||||
\(578\) | −3668.09 | − | 16071.0i | −0.263966 | − | 1.15651i | ||||
\(579\) | −6514.93 | + | 28543.8i | −0.467619 | + | 2.04877i | ||||
\(580\) | −4015.29 | − | 5035.01i | −0.287458 | − | 0.360461i | ||||
\(581\) | −6265.62 | − | 7856.84i | −0.447404 | − | 0.561027i | ||||
\(582\) | −8007.34 | + | 35082.5i | −0.570301 | + | 2.49865i | ||||
\(583\) | 7733.01 | + | 33880.5i | 0.549346 | + | 2.40684i | ||||
\(584\) | 2730.24 | + | 3423.61i | 0.193455 | + | 0.242585i | ||||
\(585\) | −32332.6 | + | 15570.6i | −2.28511 | + | 1.10045i | ||||
\(586\) | −15802.2 | + | 7609.95i | −1.11397 | + | 0.536458i | ||||
\(587\) | −2030.63 | − | 8896.76i | −0.142782 | − | 0.625568i | −0.994782 | − | 0.102026i | \(-0.967467\pi\) |
0.852000 | − | 0.523542i | \(-0.175390\pi\) | |||||||
\(588\) | −13543.2 | + | 16982.6i | −0.949851 | + | 1.19108i | ||||
\(589\) | −368.917 | − | 177.661i | −0.0258081 | − | 0.0124285i | ||||
\(590\) | 5351.07 | − | 6710.02i | 0.373390 | − | 0.468216i | ||||
\(591\) | 5258.78 | − | 23040.2i | 0.366019 | − | 1.60363i | ||||
\(592\) | −1666.22 | + | 802.407i | −0.115677 | + | 0.0557073i | ||||
\(593\) | 4639.21 | − | 20325.7i | 0.321264 | − | 1.40755i | −0.514043 | − | 0.857764i | \(-0.671853\pi\) |
0.835307 | − | 0.549784i | \(-0.185290\pi\) | |||||||
\(594\) | 21649.9 | + | 10426.0i | 1.49546 | + | 0.720176i | ||||
\(595\) | −7345.80 | −0.506132 | ||||||||
\(596\) | 2720.73 | 0.186989 | ||||||||
\(597\) | 13212.1 | + | 6362.60i | 0.905752 | + | 0.436187i | ||||
\(598\) | −6035.13 | − | 26441.6i | −0.412700 | − | 1.80816i | ||||
\(599\) | −495.194 | − | 620.954i | −0.0337781 | − | 0.0423564i | 0.764656 | − | 0.644439i | \(-0.222909\pi\) |
−0.798434 | + | 0.602083i | \(0.794338\pi\) | |||||||
\(600\) | −1203.51 | + | 1509.15i | −0.0818883 | + | 0.102685i | ||||
\(601\) | 1489.20 | 0.101075 | 0.0505373 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505373 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(602\) | −15331.1 | + | 25391.7i | −1.03796 | + | 1.71909i | ||||
\(603\) | −25546.8 | −1.72528 | ||||||||
\(604\) | −11438.7 | + | 14343.6i | −0.770585 | + | 0.966282i | ||||
\(605\) | −13707.3 | − | 17188.4i | −0.921125 | − | 1.15505i | ||||
\(606\) | 13469.3 | + | 59012.7i | 0.902891 | + | 3.95582i | ||||
\(607\) | −18876.4 | − | 9090.38i | −1.26222 | − | 0.607854i | −0.321460 | − | 0.946923i | \(-0.604174\pi\) |
−0.940761 | + | 0.339069i | \(0.889888\pi\) | |||||||
\(608\) | 5441.86 | 0.362987 | ||||||||
\(609\) | −22180.2 | −1.47584 | ||||||||
\(610\) | 15148.3 | + | 7295.03i | 1.00547 | + | 0.484208i | ||||
\(611\) | −87.7978 | + | 384.667i | −0.00581329 | + | 0.0254697i | ||||
\(612\) | −4319.89 | + | 2080.35i | −0.285329 | + | 0.137407i | ||||
\(613\) | 3888.19 | − | 17035.3i | 0.256187 | − | 1.12243i | −0.669104 | − | 0.743168i | \(-0.733322\pi\) |
0.925291 | − | 0.379258i | \(-0.123821\pi\) | |||||||
\(614\) | 18584.8 | − | 23304.6i | 1.22153 | − | 1.53176i | ||||
\(615\) | 6910.96 | + | 3328.14i | 0.453133 | + | 0.218217i | ||||
\(616\) | −8907.30 | + | 11169.4i | −0.582606 | + | 0.730565i | ||||
\(617\) | 1112.71 | + | 4875.11i | 0.0726031 | + | 0.318095i | 0.998169 | − | 0.0604924i | \(-0.0192671\pi\) |
−0.925566 | + | 0.378587i | \(0.876410\pi\) | |||||||
\(618\) | 11312.0 | − | 5447.55i | 0.736300 | − | 0.354584i | ||||
\(619\) | −7554.77 | + | 3638.18i | −0.490552 | + | 0.236237i | −0.662772 | − | 0.748821i | \(-0.730620\pi\) |
0.172220 | + | 0.985058i | \(0.444906\pi\) | |||||||
\(620\) | −687.098 | − | 861.593i | −0.0445073 | − | 0.0558104i | ||||
\(621\) | 2697.28 | + | 11817.6i | 0.174297 | + | 0.763643i | ||||
\(622\) | 1716.36 | − | 7519.87i | 0.110643 | − | 0.484758i | ||||
\(623\) | −7650.03 | − | 9592.84i | −0.491962 | − | 0.616900i | ||||
\(624\) | −28315.2 | − | 35506.2i | −1.81653 | − | 2.27786i | ||||
\(625\) | 4051.37 | − | 17750.2i | 0.259288 | − | 1.13601i | ||||
\(626\) | 4700.03 | + | 20592.2i | 0.300081 | + | 1.31474i | ||||
\(627\) | 7311.37 | + | 9168.17i | 0.465691 | + | 0.583958i | ||||
\(628\) | 2815.18 | − | 1355.72i | 0.178882 | − | 0.0861450i | ||||
\(629\) | 449.659 | − | 216.544i | 0.0285041 | − | 0.0137268i | ||||
\(630\) | −11840.0 | − | 51874.4i | −0.748756 | − | 3.28052i | ||||
\(631\) | 11766.7 | − | 14754.9i | 0.742352 | − | 0.930880i | −0.257017 | − | 0.966407i | \(-0.582740\pi\) |
0.999369 | + | 0.0355271i | \(0.0113110\pi\) | |||||||
\(632\) | 8961.44 | + | 4315.60i | 0.564030 | + | 0.271622i | ||||
\(633\) | 26389.1 | − | 33090.9i | 1.65699 | − | 2.07780i | ||||
\(634\) | −7827.56 | + | 34294.8i | −0.490334 | + | 2.14830i | ||||
\(635\) | −21002.7 | + | 10114.4i | −1.31255 | + | 0.632090i | ||||
\(636\) | 6364.55 | − | 27884.9i | 0.396809 | − | 1.73854i | ||||
\(637\) | 30205.0 | + | 14546.0i | 1.87875 | + | 0.904760i | ||||
\(638\) | 19356.2 | 1.20113 | ||||||||
\(639\) | 26518.1 | 1.64169 | ||||||||
\(640\) | −12110.9 | − | 5832.30i | −0.748008 | − | 0.360222i | ||||
\(641\) | 331.171 | + | 1450.96i | 0.0204064 | + | 0.0894061i | 0.984106 | − | 0.177584i | \(-0.0568281\pi\) |
−0.963699 | + | 0.266990i | \(0.913971\pi\) | |||||||
\(642\) | 907.384 | + | 1137.82i | 0.0557813 | + | 0.0699476i | ||||
\(643\) | 2621.18 | − | 3286.85i | 0.160761 | − | 0.201587i | −0.694927 | − | 0.719080i | \(-0.744563\pi\) |
0.855687 | + | 0.517493i | \(0.173135\pi\) | |||||||
\(644\) | 16503.2 | 1.00981 | ||||||||
\(645\) | −9929.69 | − | 26835.3i | −0.606172 | − | 1.63820i | ||||
\(646\) | −1960.39 | −0.119397 | ||||||||
\(647\) | −11961.8 | + | 14999.6i | −0.726842 | + | 0.911431i | −0.998703 | − | 0.0509055i | \(-0.983789\pi\) |
0.271862 | + | 0.962336i | \(0.412361\pi\) | |||||||
\(648\) | −819.848 | − | 1028.06i | −0.0497017 | − | 0.0623239i | ||||
\(649\) | 2355.69 | + | 10320.9i | 0.142479 | + | 0.624241i | ||||
\(650\) | −6146.76 | − | 2960.12i | −0.370917 | − | 0.178624i | ||||
\(651\) | −3795.48 | −0.228505 | ||||||||
\(652\) | 3605.00 | 0.216538 | ||||||||
\(653\) | −17035.0 | − | 8203.64i | −1.02088 | − | 0.491629i | −0.152905 | − | 0.988241i | \(-0.548863\pi\) |
−0.867972 | + | 0.496612i | \(0.834577\pi\) | |||||||
\(654\) | −4634.40 | + | 20304.6i | −0.277094 | + | 1.21403i | ||||
\(655\) | −639.777 | + | 308.100i | −0.0381651 | + | 0.0183794i | ||||
\(656\) | −1304.24 | + | 5714.24i | −0.0776249 | + | 0.340097i | ||||
\(657\) | 12542.9 | − | 15728.4i | 0.744820 | − | 0.933975i | ||||
\(658\) | −527.074 | − | 253.826i | −0.0312272 | − | 0.0150382i | ||||
\(659\) | 15425.7 | − | 19343.2i | 0.911833 | − | 1.14340i | −0.0773917 | − | 0.997001i | \(-0.524659\pi\) |
0.989225 | − | 0.146402i | \(-0.0467694\pi\) | |||||||
\(660\) | 7022.82 | + | 30769.0i | 0.414186 | + | 1.81467i | ||||
\(661\) | −10647.5 | + | 5127.55i | −0.626534 | + | 0.301723i | −0.720079 | − | 0.693892i | \(-0.755894\pi\) |
0.0935450 | + | 0.995615i | \(0.470180\pi\) | |||||||
\(662\) | −4078.64 | + | 1964.17i | −0.239458 | + | 0.115317i | ||||
\(663\) | 7641.38 | + | 9581.99i | 0.447612 | + | 0.561287i | ||||
\(664\) | 701.358 | + | 3072.85i | 0.0409909 | + | 0.179593i | ||||
\(665\) | 1986.70 | − | 8704.32i | 0.115851 | − | 0.507577i | ||||
\(666\) | 2253.95 | + | 2826.36i | 0.131139 | + | 0.164443i | ||||
\(667\) | 6087.80 | + | 7633.86i | 0.353404 | + | 0.443155i | ||||
\(668\) | −3226.77 | + | 14137.4i | −0.186897 | + | 0.818851i | ||||
\(669\) | −1024.53 | − | 4488.77i | −0.0592088 | − | 0.259411i | ||||
\(670\) | −17527.3 | − | 21978.6i | −1.01066 | − | 1.26732i | ||||
\(671\) | −18685.2 | + | 8998.34i | −1.07502 | + | 0.517701i | ||||
\(672\) | 45447.0 | − | 21886.1i | 2.60886 | − | 1.25636i | ||||
\(673\) | 2204.18 | + | 9657.13i | 0.126248 | + | 0.553128i | 0.998002 | + | 0.0631842i | \(0.0201256\pi\) |
−0.871754 | + | 0.489944i | \(0.837017\pi\) | |||||||
\(674\) | 6635.61 | − | 8320.79i | 0.379220 | − | 0.475526i | ||||
\(675\) | 2747.17 | + | 1322.97i | 0.156650 | + | 0.0754386i | ||||
\(676\) | 9847.99 | − | 12349.0i | 0.560309 | − | 0.702605i | ||||
\(677\) | 259.310 | − | 1136.11i | 0.0147210 | − | 0.0644969i | −0.967034 | − | 0.254648i | \(-0.918041\pi\) |
0.981755 | + | 0.190151i | \(0.0608977\pi\) | |||||||
\(678\) | 13789.2 | − | 6640.53i | 0.781078 | − | 0.376147i | ||||
\(679\) | −7519.98 | + | 32947.2i | −0.425023 | + | 1.86215i | ||||
\(680\) | 2075.79 | + | 999.647i | 0.117063 | + | 0.0563746i | ||||
\(681\) | −24752.7 | −1.39284 | ||||||||
\(682\) | 3312.25 | 0.185971 | ||||||||
\(683\) | −6207.40 | − | 2989.33i | −0.347759 | − | 0.167472i | 0.251847 | − | 0.967767i | \(-0.418962\pi\) |
−0.599607 | + | 0.800295i | \(0.704676\pi\) | |||||||
\(684\) | −1296.75 | − | 5681.45i | −0.0724892 | − | 0.317596i | ||||
\(685\) | 15944.8 | + | 19994.2i | 0.889372 | + | 1.11524i | ||||
\(686\) | −8495.67 | + | 10653.2i | −0.472837 | + | 0.592919i | ||||
\(687\) | −7812.35 | −0.433857 | ||||||||
\(688\) | 18302.8 | − | 11960.0i | 1.01422 | − | 0.662749i | ||||
\(689\) | −44144.2 | −2.44087 | ||||||||
\(690\) | −24186.8 | + | 30329.2i | −1.33446 | + | 1.67335i | ||||
\(691\) | −4243.79 | − | 5321.54i | −0.233634 | − | 0.292968i | 0.651169 | − | 0.758933i | \(-0.274279\pi\) |
−0.884803 | + | 0.465965i | \(0.845707\pi\) | |||||||
\(692\) | −2439.83 | − | 10689.6i | −0.134030 | − | 0.587222i | ||||
\(693\) | 59132.4 | + | 28476.7i | 3.24135 | + | 1.56095i | ||||
\(694\) | 7132.13 | 0.390104 | ||||||||
\(695\) | 23803.5 | 1.29916 | ||||||||
\(696\) | 6267.71 | + | 3018.37i | 0.341346 | + | 0.164384i | ||||
\(697\) | 351.972 | − | 1542.09i | 0.0191275 | − | 0.0838032i | ||||
\(698\) | 6045.80 | − | 2911.50i | 0.327846 | − | 0.157883i | ||||
\(699\) | −1824.10 | + | 7991.90i | −0.0987036 | + | 0.432449i | ||||
\(700\) | 2588.32 | − | 3245.65i | 0.139756 | − | 0.175248i | ||||
\(701\) | −29185.6 | − | 14055.0i | −1.57250 | − | 0.757278i | −0.574385 | − | 0.818585i | \(-0.694759\pi\) |
−0.998119 | + | 0.0613073i | \(0.980473\pi\) | |||||||
\(702\) | −19031.4 | + | 23864.6i | −1.02321 | + | 1.28306i | ||||
\(703\) | 134.979 | + | 591.383i | 0.00724159 | + | 0.0317275i | ||||
\(704\) | −8445.51 | + | 4067.14i | −0.452134 | + | 0.217736i | ||||
\(705\) | 508.458 | − | 244.861i | 0.0271626 | − | 0.0130808i | ||||
\(706\) | 1941.36 | + | 2434.39i | 0.103490 | + | 0.129773i | ||||
\(707\) | 12649.5 | + | 55421.0i | 0.672889 | + | 2.94812i | ||||
\(708\) | 1938.81 | − | 8494.50i | 0.102917 | − | 0.450908i | ||||
\(709\) | 3931.22 | + | 4929.60i | 0.208237 | + | 0.261121i | 0.874972 | − | 0.484174i | \(-0.160880\pi\) |
−0.666734 | + | 0.745295i | \(0.732308\pi\) | |||||||
\(710\) | 18193.8 | + | 22814.3i | 0.961690 | + | 1.20592i | ||||
\(711\) | 10168.1 | − | 44549.2i | 0.536332 | − | 2.34982i | ||||
\(712\) | 856.325 | + | 3751.81i | 0.0450732 | + | 0.197479i | ||||
\(713\) | 1041.75 | + | 1306.31i | 0.0547177 | + | 0.0686138i | ||||
\(714\) | −16372.0 | + | 7884.33i | −0.858132 | + | 0.413254i | ||||
\(715\) | 43886.1 | − | 21134.4i | 2.29545 | − | 1.10543i | ||||
\(716\) | 1644.56 | + | 7205.31i | 0.0858383 | + | 0.376082i | ||||
\(717\) | 12455.6 | − | 15618.9i | 0.648764 | − | 0.813524i | ||||
\(718\) | −27877.3 | − | 13425.0i | −1.44899 | − | 0.697794i | ||||
\(719\) | −5465.74 | + | 6853.82i | −0.283502 | + | 0.355500i | −0.903108 | − | 0.429413i | \(-0.858721\pi\) |
0.619607 | + | 0.784912i | \(0.287292\pi\) | |||||||
\(720\) | −8727.55 | + | 38237.9i | −0.451745 | + | 1.97922i | ||||
\(721\) | 10623.5 | − | 5115.99i | 0.548736 | − | 0.264257i | ||||
\(722\) | −5091.87 | + | 22308.9i | −0.262465 | + | 1.14993i | ||||
\(723\) | 431.444 | + | 207.773i | 0.0221931 | + | 0.0106876i | ||||
\(724\) | −13946.7 | −0.715919 | ||||||||
\(725\) | 2456.13 | 0.125819 | ||||||||
\(726\) | −48998.7 | − | 23596.5i | −2.50484 | − | 1.20627i | ||||
\(727\) | −508.007 | − | 2225.72i | −0.0259160 | − | 0.113545i | 0.960315 | − | 0.278916i | \(-0.0899751\pi\) |
−0.986231 | + | 0.165371i | \(0.947118\pi\) | |||||||
\(728\) | −11314.7 | − | 14188.1i | −0.576029 | − | 0.722318i | ||||
\(729\) | −19998.1 | + | 25076.8i | −1.01601 | + | 1.27403i | ||||
\(730\) | 22137.1 | 1.12237 | ||||||||
\(731\) | −4939.33 | + | 3227.63i | −0.249915 | + | 0.163308i | ||||
\(732\) | 17069.0 | 0.861869 | ||||||||
\(733\) | 7467.28 | − | 9363.67i | 0.376276 | − | 0.471835i | −0.557250 | − | 0.830345i | \(-0.688144\pi\) |
0.933526 | + | 0.358510i | \(0.116715\pi\) | |||||||
\(734\) | 15859.1 | + | 19886.7i | 0.797508 | + | 1.00004i | ||||
\(735\) | −10670.2 | − | 46749.2i | −0.535478 | − | 2.34608i | ||||
\(736\) | −20006.5 | − | 9634.62i | −1.00197 | − | 0.482523i | ||||
\(737\) | 34675.5 | 1.73309 | ||||||||
\(738\) | 11457.2 | 0.571471 | ||||||||
\(739\) | −16801.3 | − | 8091.09i | −0.836329 | − | 0.402755i | −0.0338437 | − | 0.999427i | \(-0.510775\pi\) |
−0.802485 | + | 0.596673i | \(0.796489\pi\) | |||||||
\(740\) | −363.277 | + | 1591.62i | −0.0180464 | + | 0.0790664i | ||||
\(741\) | −13420.7 | + | 6463.07i | −0.665347 | + | 0.320414i | ||||
\(742\) | 14564.4 | − | 63811.0i | 0.720589 | − | 3.15711i | ||||
\(743\) | 524.947 | − | 658.262i | 0.0259198 | − | 0.0325024i | −0.768703 | − | 0.639606i | \(-0.779097\pi\) |
0.794622 | + | 0.607104i | \(0.207669\pi\) | |||||||
\(744\) | 1072.53 | + | 516.505i | 0.0528508 | + | 0.0254516i | ||||
\(745\) | −3744.77 | + | 4695.79i | −0.184158 | + | 0.230927i | ||||
\(746\) | −6894.94 | − | 30208.7i | −0.338393 | − | 1.48260i | ||||
\(747\) | 13046.0 | − | 6282.64i | 0.638995 | − | 0.307724i | ||||
\(748\) | 5863.53 | − | 2823.73i | 0.286620 | − | 0.138029i | ||||
\(749\) | 852.157 | + | 1068.57i | 0.0415716 | + | 0.0521291i | ||||
\(750\) | −8225.74 | − | 36039.3i | −0.400482 | − | 1.75463i | ||||
\(751\) | −5518.18 | + | 24176.7i | −0.268124 | + | 1.17473i | 0.644069 | + | 0.764967i | \(0.277245\pi\) |
−0.912193 | + | 0.409761i | \(0.865612\pi\) | |||||||
\(752\) | 268.864 | + | 337.145i | 0.0130378 | + | 0.0163489i | ||||
\(753\) | 6608.51 | + | 8286.81i | 0.319824 | + | 0.401047i | ||||
\(754\) | −5471.26 | + | 23971.2i | −0.264259 | + | 1.15780i | ||||
\(755\) | −9012.11 | − | 39484.6i | −0.434416 | − | 1.90330i | ||||
\(756\) | −11580.3 | − | 14521.3i | −0.557107 | − | 0.698591i | ||||
\(757\) | 14585.2 | − | 7023.88i | 0.700276 | − | 0.337235i | −0.0496407 | − | 0.998767i | \(-0.515808\pi\) |
0.749917 | + | 0.661532i | \(0.230093\pi\) | |||||||
\(758\) | 20285.7 | − | 9769.08i | 0.972045 | − | 0.468112i | ||||
\(759\) | −10647.7 | − | 46650.5i | −0.509204 | − | 2.23097i | ||||
\(760\) | −1745.93 | + | 2189.32i | −0.0833308 | + | 0.104493i | ||||
\(761\) | −3601.55 | − | 1734.41i | −0.171558 | − | 0.0826182i | 0.346134 | − | 0.938185i | \(-0.387494\pi\) |
−0.517692 | + | 0.855567i | \(0.673209\pi\) | |||||||
\(762\) | −35954.1 | + | 45085.0i | −1.70929 | + | 2.14338i | ||||
\(763\) | −4352.33 | + | 19068.8i | −0.206507 | + | 0.904766i | ||||
\(764\) | −8080.69 | + | 3891.45i | −0.382656 | + | 0.184277i | ||||
\(765\) | 2355.29 | − | 10319.2i | 0.111314 | − | 0.487700i | ||||
\(766\) | 33239.2 | + | 16007.2i | 1.56786 | + | 0.755042i | ||||
\(767\) | −13447.5 | −0.633066 | ||||||||
\(768\) | −44336.0 | −2.08312 | ||||||||
\(769\) | −10286.1 | − | 4953.53i | −0.482349 | − | 0.232287i | 0.176876 | − | 0.984233i | \(-0.443401\pi\) |
−0.659224 | + | 0.751946i | \(0.729115\pi\) | |||||||
\(770\) | 16070.8 | + | 70410.7i | 0.752144 | + | 3.29536i | ||||
\(771\) | 13320.8 | + | 16703.7i | 0.622225 | + | 0.780245i | ||||
\(772\) | −12313.2 | + | 15440.3i | −0.574044 | + | 0.719829i | ||||
\(773\) | −25632.5 | −1.19267 | −0.596337 | − | 0.802734i | \(-0.703378\pi\) | ||||
−0.596337 | + | 0.802734i | \(0.703378\pi\) | |||||||
\(774\) | −30754.0 | − | 29678.1i | −1.42820 | − | 1.37824i | ||||
\(775\) | 420.294 | 0.0194805 | ||||||||
\(776\) | 6608.60 | − | 8286.92i | 0.305715 | − | 0.383354i | ||||
\(777\) | 3505.69 | + | 4396.00i | 0.161861 | + | 0.202967i | ||||
\(778\) | 1623.84 | + | 7114.51i | 0.0748297 | + | 0.327850i | ||||
\(779\) | 1732.09 | + | 834.130i | 0.0796644 | + | 0.0383643i | ||||
\(780\) | −40090.0 | −1.84032 | ||||||||
\(781\) | −35993.9 | −1.64912 | ||||||||
\(782\) | 7207.21 | + | 3470.81i | 0.329577 | + | 0.158716i | ||||
\(783\) | 2445.27 | − | 10713.4i | 0.111605 | − | 0.488974i | ||||
\(784\) | 33011.8 | − | 15897.6i | 1.50382 | − | 0.724200i | ||||
\(785\) | −1534.89 | + | 6724.78i | −0.0697866 | + | 0.305755i | ||||
\(786\) | −1095.22 | + | 1373.36i | −0.0497012 | + | 0.0623233i | ||||
\(787\) | 1567.86 | + | 755.041i | 0.0710142 | + | 0.0341986i | 0.469054 | − | 0.883170i | \(-0.344595\pi\) |
−0.398040 | + | 0.917368i | \(0.630309\pi\) | |||||||
\(788\) | 9939.08 | − | 12463.2i | 0.449321 | − | 0.563431i | ||||
\(789\) | −6793.75 | − | 29765.4i | −0.306545 | − | 1.34306i | ||||
\(790\) | 45303.1 | − | 21816.8i | 2.04027 | − | 0.982541i | ||||
\(791\) | 12949.9 | − | 6236.35i | 0.582106 | − | 0.280328i | ||||
\(792\) | −12834.5 | − | 16094.0i | −0.575827 | − | 0.722064i | ||||
\(793\) | −5862.13 | − | 25683.7i | −0.262510 | − | 1.15013i | ||||
\(794\) | 3099.77 | − | 13581.0i | 0.138547 | − | 0.607016i | ||||
\(795\) | 39367.3 | + | 49365.0i | 1.75624 | + | 2.20226i | ||||
\(796\) | 6167.28 | + | 7733.52i | 0.274615 | + | 0.344356i | ||||
\(797\) | 5065.13 | − | 22191.8i | 0.225114 | − | 0.986290i | −0.728450 | − | 0.685099i | \(-0.759759\pi\) |
0.953564 | − | 0.301191i | \(-0.0973840\pi\) | |||||||
\(798\) | −4914.57 | − | 21532.1i | −0.218012 | − | 0.955175i | ||||
\(799\) | −72.5577 | − | 90.9845i | −0.00321265 | − | 0.00402854i | ||||
\(800\) | −5032.59 | + | 2423.57i | −0.222411 | + | 0.107108i | ||||
\(801\) | 15928.6 | − | 7670.80i | 0.702633 | − | 0.338370i | ||||
\(802\) | 11149.4 | + | 48848.9i | 0.490898 | + | 2.15076i | ||||
\(803\) | −17024.9 | + | 21348.6i | −0.748191 | + | 0.938201i | ||||
\(804\) | −25712.9 | − | 12382.7i | −1.12789 | − | 0.543164i | ||||
\(805\) | −22714.6 | + | 28483.3i | −0.994517 | + | 1.24708i | ||||
\(806\) | −936.244 | + | 4101.96i | −0.0409154 | + | 0.179262i | ||||
\(807\) | −17105.5 | + | 8237.58i | −0.746149 | + | 0.359327i | ||||
\(808\) | 3967.40 | − | 17382.3i | 0.172739 | − | 0.756817i | ||||
\(809\) | −8861.48 | − | 4267.46i | −0.385109 | − | 0.185459i | 0.231304 | − | 0.972881i | \(-0.425701\pi\) |
−0.616413 | + | 0.787423i | \(0.711415\pi\) | |||||||
\(810\) | −6647.43 | −0.288354 | ||||||||
\(811\) | 28928.9 | 1.25257 | 0.626283 | − | 0.779595i | \(-0.284575\pi\) | ||||
0.626283 | + | 0.779595i | \(0.284575\pi\) | |||||||
\(812\) | −13479.6 | − | 6491.44i | −0.582564 | − | 0.280548i | ||||
\(813\) | 12987.5 | + | 56902.0i | 0.560261 | + | 2.45466i | ||||
\(814\) | −3059.35 | − | 3836.31i | −0.131733 | − | 0.165187i | ||||
\(815\) | −4961.85 | + | 6221.97i | −0.213259 | + | 0.267419i | ||||
\(816\) | 13394.7 | 0.574642 | ||||||||
\(817\) | −2488.67 | − | 6725.73i | −0.106570 | − | 0.288009i | ||||
\(818\) | −34809.4 | −1.48787 | ||||||||
\(819\) | −51980.6 | + | 65181.6i | −2.21776 | + | 2.78099i | ||||
\(820\) | 3225.97 | + | 4045.24i | 0.137385 | + | 0.172276i | ||||
\(821\) | 1754.82 | + | 7688.36i | 0.0745963 | + | 0.326828i | 0.998433 | − | 0.0559589i | \(-0.0178216\pi\) |
−0.923837 | + | 0.382787i | \(0.874964\pi\) | |||||||
\(822\) | 56997.0 | + | 27448.3i | 2.41849 | + | 1.16468i | ||||
\(823\) | 8877.58 | 0.376006 | 0.188003 | − | 0.982168i | \(-0.439799\pi\) | ||||
0.188003 | + | 0.982168i | \(0.439799\pi\) | |||||||
\(824\) | −3698.20 | −0.156351 | ||||||||
\(825\) | −10844.6 | − | 5222.50i | −0.457650 | − | 0.220393i | ||||
\(826\) | 4436.72 | − | 19438.6i | 0.186893 | − | 0.818830i | ||||
\(827\) | −13313.1 | + | 6411.23i | −0.559783 | + | 0.269577i | −0.692308 | − | 0.721602i | \(-0.743406\pi\) |
0.132525 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(828\) | −5291.41 | + | 23183.2i | −0.222088 | + | 0.973033i | ||||
\(829\) | 25409.4 | − | 31862.3i | 1.06454 | − | 1.33489i | 0.125112 | − | 0.992143i | \(-0.460071\pi\) |
0.939427 | − | 0.342748i | \(-0.111358\pi\) | |||||||
\(830\) | 14355.8 | + | 6913.41i | 0.600360 | + | 0.289118i | ||||
\(831\) | 3648.82 | − | 4575.48i | 0.152318 | − | 0.191001i | ||||
\(832\) | −2649.61 | − | 11608.7i | −0.110407 | − | 0.483726i | ||||
\(833\) | −8908.82 | + | 4290.26i | −0.370555 | + | 0.178450i | ||||
\(834\) | 53052.0 | − | 25548.5i | 2.20269 | − | 1.06076i | ||||
\(835\) | −19958.9 | − | 25027.6i | −0.827192 | − | 1.03727i | ||||
\(836\) | 1760.12 | + | 7711.61i | 0.0728172 | + | 0.319033i | ||||
\(837\) | 418.436 | − | 1833.29i | 0.0172799 | − | 0.0757081i | ||||
\(838\) | −12093.6 | − | 15164.9i | −0.498528 | − | 0.625134i | ||||
\(839\) | −20258.6 | − | 25403.5i | −0.833618 | − | 1.04532i | −0.998260 | − | 0.0589701i | \(-0.981218\pi\) |
0.164642 | − | 0.986353i | \(-0.447353\pi\) | |||||||
\(840\) | −5775.85 | + | 25305.6i | −0.237245 | + | 1.03944i | ||||
\(841\) | 3457.35 | + | 15147.6i | 0.141759 | + | 0.621085i | ||||
\(842\) | −1628.22 | − | 2041.73i | −0.0666416 | − | 0.0835659i | ||||
\(843\) | 63238.5 | − | 30454.1i | 2.58369 | − | 1.24424i | ||||
\(844\) | 25722.2 | − | 12387.2i | 1.04905 | − | 0.505194i | ||||
\(845\) | 7758.87 | + | 33993.8i | 0.315874 | + | 1.38393i | ||||
\(846\) | 525.563 | − | 659.035i | 0.0213584 | − | 0.0267826i | ||||
\(847\) | −46016.4 | − | 22160.3i | −1.86676 | − | 0.898983i | ||||
\(848\) | −30081.1 | + | 37720.4i | −1.21815 | + | 1.52751i | ||||
\(849\) | −1493.59 | + | 6543.82i | −0.0603766 | + | 0.264527i | ||||
\(850\) | 1812.96 | − | 873.075i | 0.0731576 | − | 0.0352308i | ||||
\(851\) | 550.784 | − | 2413.14i | 0.0221864 | − | 0.0972050i | ||||
\(852\) | 26690.6 | + | 12853.5i | 1.07324 | + | 0.516847i | ||||
\(853\) | 9047.76 | 0.363176 | 0.181588 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181588 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(854\) | 39060.2 | 1.56512 | ||||||||
\(855\) | 11590.6 | + | 5581.74i | 0.463614 | + | 0.223265i | ||||
\(856\) | −95.3883 | − | 417.923i | −0.00380877 | − | 0.0166873i | ||||
\(857\) | 3605.64 | + | 4521.32i | 0.143718 | + | 0.180216i | 0.848480 | − | 0.529227i | \(-0.177518\pi\) |
−0.704763 | + | 0.709443i | \(0.748946\pi\) | |||||||
\(858\) | 75127.5 | − | 94206.9i | 2.98929 | − | 3.74845i | ||||
\(859\) | 46957.7 | 1.86516 | 0.932582 | − | 0.360959i | \(-0.117550\pi\) | ||||
0.932582 | + | 0.360959i | \(0.117550\pi\) | |||||||
\(860\) | 1819.27 | − | 19214.8i | 0.0721354 | − | 0.761884i | ||||
\(861\) | 17820.1 | 0.705349 | ||||||||
\(862\) | −28778.5 | + | 36087.1i | −1.13712 | + | 1.42591i | ||||
\(863\) | 22348.2 | + | 28023.8i | 0.881509 | + | 1.10538i | 0.993742 | + | 0.111695i | \(0.0356281\pi\) |
−0.112234 | + | 0.993682i | \(0.535800\pi\) | |||||||
\(864\) | 5561.06 | + | 24364.6i | 0.218971 | + | 0.959375i | ||||
\(865\) | 21807.6 | + | 10502.0i | 0.857203 | + | 0.412807i | ||||
\(866\) | −50217.5 | −1.97051 | ||||||||
\(867\) | 36943.1 | 1.44712 | ||||||||
\(868\) | −2306.64 | − | 1110.82i | −0.0901986 | − | 0.0434374i | ||||
\(869\) | −13801.4 | + | 60468.0i | −0.538759 | + | 2.36046i | ||||
\(870\) | 31685.4 | − | 15258.9i | 1.23475 | − | 0.594626i | ||||
\(871\) | −9801.42 | + | 42942.8i | −0.381296 | + | 1.67057i | ||||
\(872\) | 3824.85 | − | 4796.21i | 0.148539 | − | 0.186261i | ||||
\(873\) | −43872.2 | − | 21127.7i | −1.70086 | − | 0.819089i | ||||
\(874\) | −6061.91 | + | 7601.40i | −0.234608 | + | 0.294189i | ||||
\(875\) | −7725.09 | − | 33845.8i | −0.298464 | − | 1.30765i | ||||
\(876\) | 20248.1 | − | 9750.99i | 0.780960 | − | 0.376091i | ||||
\(877\) | 9496.43 | − | 4573.24i | 0.365646 | − | 0.176086i | −0.242034 | − | 0.970268i | \(-0.577815\pi\) |
0.607680 | + | 0.794182i | \(0.292100\pi\) | |||||||
\(878\) | 38672.4 | + | 48493.6i | 1.48648 | + | 1.86399i | ||||
\(879\) | −8746.68 | − | 38321.7i | −0.335629 | − | 1.47049i | ||||
\(880\) | 11846.2 | − | 51901.5i | 0.453789 | − | 1.98818i | ||||
\(881\) | 6208.92 | + | 7785.74i | 0.237439 | + | 0.297739i | 0.886247 | − | 0.463213i | \(-0.153304\pi\) |
−0.648808 | + | 0.760952i | \(0.724732\pi\) | |||||||
\(882\) | −44656.1 | − | 55997.0i | −1.70482 | − | 2.13778i | ||||
\(883\) | 940.565 | − | 4120.88i | 0.0358466 | − | 0.157054i | −0.953837 | − | 0.300325i | \(-0.902905\pi\) |
0.989684 | + | 0.143271i | \(0.0457620\pi\) | |||||||
\(884\) | 1839.57 | + | 8059.68i | 0.0699903 | + | 0.306647i | ||||
\(885\) | 11992.3 | + | 15037.9i | 0.455501 | + | 0.571180i | ||||
\(886\) | −26461.1 | + | 12743.0i | −1.00336 | + | 0.483193i | ||||
\(887\) | −25919.5 | + | 12482.2i | −0.981163 | + | 0.472503i | −0.854505 | − | 0.519444i | \(-0.826139\pi\) |
−0.126658 | + | 0.991946i | \(0.540425\pi\) | |||||||
\(888\) | −392.419 | − | 1719.30i | −0.0148296 | − | 0.0649728i | ||||
\(889\) | −33765.7 | + | 42340.9i | −1.27387 | + | 1.59738i | ||||
\(890\) | 17527.8 | + | 8440.95i | 0.660150 | + | 0.317911i | ||||
\(891\) | 5112.33 | − | 6410.66i | 0.192222 | − | 0.241038i | ||||
\(892\) | 691.080 | − | 3027.82i | 0.0259407 | − | 0.113653i | ||||
\(893\) | 127.435 | − | 61.3693i | 0.00477540 | − | 0.00229971i | ||||
\(894\) | −3306.12 | + | 14485.1i | −0.123684 | + | 0.541894i | ||||
\(895\) | −14699.4 | − | 7078.85i | −0.548990 | − | 0.264380i | ||||
\(896\) | −31228.2 | −1.16435 | ||||||||
\(897\) | 60782.6 | 2.26251 | ||||||||
\(898\) | −825.791 | − | 397.680i | −0.0306871 | − | 0.0147781i | ||||
\(899\) | −337.058 | − | 1476.75i | −0.0125045 | − | 0.0547856i | ||||
\(900\) | 3729.50 | + | 4676.65i | 0.138130 | + | 0.173209i | ||||
\(901\) | 8117.92 | − | 10179.5i | 0.300163 | − | 0.376393i | ||||
\(902\) | −15551.2 | −0.574057 | ||||||||
\(903\) | −47833.5 | − | 46160.1i | −1.76279 | − | 1.70112i | ||||
\(904\) | −4508.08 | −0.165859 | ||||||||
\(905\) | 19196.0 | − | 24071.0i | 0.705079 | − | 0.884141i | ||||
\(906\) | −62465.1 | − | 78328.7i | −2.29058 | − | 2.87229i | ||||
\(907\) | 3870.31 | + | 16956.9i | 0.141688 | + | 0.620778i | 0.995043 | + | 0.0994466i | \(0.0317073\pi\) |
−0.853354 | + | 0.521331i | \(0.825436\pi\) | |||||||
\(908\) | −15043.0 | − | 7244.34i | −0.549802 | − | 0.264771i | ||||
\(909\) | −81909.7 | −2.98875 | ||||||||
\(910\) | −91740.7 | −3.34195 | ||||||||
\(911\) | 22111.8 | + | 10648.5i | 0.804169 | + | 0.387267i | 0.790364 | − | 0.612637i | \(-0.209891\pi\) |
0.0138048 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(912\) | −3622.65 | + | 15871.9i | −0.131533 | + | 0.576283i | ||||
\(913\) | −17707.8 | + | 8527.62i | −0.641886 | + | 0.309116i | ||||
\(914\) | 15182.1 | − | 66517.0i | 0.549430 | − | 2.40721i | ||||
\(915\) | −23493.4 | + | 29459.8i | −0.848819 | + | 1.06439i | ||||
\(916\) | −4747.82 | − | 2286.43i | −0.171258 | − | 0.0824736i | ||||
\(917\) | −1028.56 | + | 1289.77i | −0.0370403 | + | 0.0464471i | ||||
\(918\) | −2003.33 | − | 8777.18i | −0.0720260 | − | 0.315567i | ||||
\(919\) | −42499.5 | + | 20466.7i | −1.52550 | + | 0.734640i | −0.993683 | − | 0.112222i | \(-0.964203\pi\) |
−0.531813 | + | 0.846862i | \(0.678489\pi\) | |||||||
\(920\) | 10294.9 | − | 4957.74i | 0.368925 | − | 0.177665i | ||||
\(921\) | 41650.7 | + | 52228.3i | 1.49016 | + | 1.86860i | ||||
\(922\) | 2558.16 | + | 11208.0i | 0.0913759 | + | 0.400344i | ||||
\(923\) | 10174.1 | − | 44575.6i | 0.362822 | − | 1.58963i | ||||
\(924\) | 45714.1 | + | 57323.7i | 1.62758 | + | 2.04092i | ||||
\(925\) | −388.204 | − | 486.793i | −0.0137990 | − | 0.0173034i | ||||
\(926\) | −2166.37 | + | 9491.49i | −0.0768805 | + | 0.336836i | ||||
\(927\) | 3780.60 | + | 16563.9i | 0.133949 | + | 0.586871i | ||||
\(928\) | 12551.4 | + | 15738.9i | 0.443986 | + | 0.556741i | ||||
\(929\) | 38178.6 | − | 18385.9i | 1.34833 | − | 0.649323i | 0.386329 | − | 0.922361i | \(-0.373743\pi\) |
0.962003 | + | 0.273038i | \(0.0880286\pi\) | |||||||
\(930\) | 5422.01 | − | 2611.10i | 0.191177 | − | 0.0920661i | ||||
\(931\) | −2674.27 | − | 11716.7i | −0.0941413 | − | 0.412460i | ||||
\(932\) | −3447.54 | + | 4323.08i | −0.121167 | + | 0.151939i | ||||
\(933\) | 15574.4 | + | 7500.24i | 0.546498 | + | 0.263180i | ||||
\(934\) | 33632.1 | − | 42173.3i | 1.17824 | − | 1.47746i | ||||
\(935\) | −3196.90 | + | 14006.6i | −0.111818 | + | 0.489907i | ||||
\(936\) | 23558.9 | − | 11345.4i | 0.822701 | − | 0.396192i | ||||
\(937\) | 662.842 | − | 2904.10i | 0.0231100 | − | 0.101252i | −0.962058 | − | 0.272847i | \(-0.912035\pi\) |
0.985168 | + | 0.171595i | \(0.0548920\pi\) | |||||||
\(938\) | −58840.6 | − | 28336.1i | −2.04820 | − | 0.986362i | ||||
\(939\) | −47336.2 | −1.64511 | ||||||||
\(940\) | 380.670 | 0.0132086 | ||||||||
\(941\) | −16918.0 | − | 8147.27i | −0.586090 | − | 0.282246i | 0.117247 | − | 0.993103i | \(-0.462593\pi\) |
−0.703337 | + | 0.710857i | \(0.748307\pi\) | |||||||
\(942\) | 3796.90 | + | 16635.3i | 0.131326 | + | 0.575379i | ||||
\(943\) | −4891.07 | − | 6133.21i | −0.168903 | − | 0.211797i | ||||
\(944\) | −9163.51 | + | 11490.7i | −0.315939 | + | 0.396175i | ||||
\(945\) | 41001.7 | 1.41141 | ||||||||
\(946\) | 41743.4 | + | 40283.1i | 1.43467 | + | 1.38448i | ||||
\(947\) | 53490.4 | 1.83548 | 0.917742 | − | 0.397177i | \(-0.130010\pi\) | ||||
0.917742 | + | 0.397177i | \(0.130010\pi\) | |||||||
\(948\) | 31827.4 | − | 39910.3i | 1.09041 | − | 1.36733i | ||||
\(949\) | −21626.3 | − | 27118.5i | −0.739745 | − | 0.927611i | ||||
\(950\) | 544.217 | + | 2384.37i | 0.0185860 | + | 0.0814307i | ||||
\(951\) | −71027.9 | − | 34205.2i | −2.42191 | − | 1.16633i | ||||
\(952\) | 5352.46 | 0.182221 | ||||||||
\(953\) | −2203.86 | −0.0749108 | −0.0374554 | − | 0.999298i | \(-0.511925\pi\) | ||||
−0.0374554 | + | 0.999298i | \(0.511925\pi\) | |||||||
\(954\) | 84970.1 | + | 40919.4i | 2.88366 | + | 1.38870i | ||||
\(955\) | 4405.74 | − | 19302.8i | 0.149284 | − | 0.654057i | ||||
\(956\) | 12140.8 | − | 5846.72i | 0.410735 | − | 0.197800i | ||||
\(957\) | −9652.85 | + | 42291.9i | −0.326053 | + | 1.42853i | ||||
\(958\) | −36822.4 | + | 46173.8i | −1.24183 | + | 1.55721i | ||||
\(959\) | 53527.9 | + | 25777.7i | 1.80240 | + | 0.867992i | ||||
\(960\) | −10618.8 | + | 13315.5i | −0.356999 | + | 0.447662i | ||||
\(961\) | 6571.44 | + | 28791.4i | 0.220585 | + | 0.966445i | ||||
\(962\) | 5615.72 | − | 2704.39i | 0.188210 | − | 0.0906373i | ||||
\(963\) | −1774.33 | + | 854.470i | −0.0593737 | + | 0.0285929i | ||||
\(964\) | 201.394 | + | 252.540i | 0.00672871 | + | 0.00843753i | ||||
\(965\) | −9701.13 | − | 42503.4i | −0.323617 | − | 1.41786i | ||||
\(966\) | −20053.9 | + | 87862.0i | −0.667935 | + | 2.92641i | ||||
\(967\) | −8410.10 | − | 10545.9i | −0.279680 | − | 0.350708i | 0.622073 | − | 0.782959i | \(-0.286291\pi\) |
−0.901753 | + | 0.432251i | \(0.857719\pi\) | |||||||
\(968\) | 9987.72 | + | 12524.2i | 0.331630 | + | 0.415850i | ||||
\(969\) | 977.637 | − | 4283.31i | 0.0324110 | − | 0.142002i | ||||
\(970\) | −11923.4 | − | 52239.9i | −0.394678 | − | 1.72920i | ||||
\(971\) | 6875.81 | + | 8622.00i | 0.227245 | + | 0.284957i | 0.882362 | − | 0.470571i | \(-0.155952\pi\) |
−0.655117 | + | 0.755528i | \(0.727381\pi\) | |||||||
\(972\) | −21901.6 | + | 10547.3i | −0.722731 | + | 0.348049i | ||||
\(973\) | 49823.1 | − | 23993.5i | 1.64158 | − | 0.790542i | ||||
\(974\) | −13092.3 | − | 57361.3i | −0.430704 | − | 1.88704i | ||||
\(975\) | 9533.00 | − | 11954.0i | 0.313129 | − | 0.392651i | ||||
\(976\) | −25940.9 | − | 12492.5i | −0.850766 | − | 0.409707i | ||||
\(977\) | 2883.63 | − | 3615.96i | 0.0944275 | − | 0.118408i | −0.732373 | − | 0.680904i | \(-0.761587\pi\) |
0.826800 | + | 0.562495i | \(0.190159\pi\) | |||||||
\(978\) | −4380.64 | + | 19192.9i | −0.143229 | + | 0.627525i | ||||
\(979\) | −21620.4 | + | 10411.8i | −0.705812 | + | 0.339901i | ||||
\(980\) | 7197.39 | − | 31533.8i | 0.234604 | − | 1.02787i | ||||
\(981\) | −25391.8 | − | 12228.1i | −0.826400 | − | 0.397973i | ||||
\(982\) | −50575.2 | −1.64350 | ||||||||
\(983\) | −34064.0 | −1.10526 | −0.552631 | − | 0.833426i | \(-0.686376\pi\) | ||||
−0.552631 | + | 0.833426i | \(0.686376\pi\) | |||||||
\(984\) | −5035.62 | − | 2425.03i | −0.163140 | − | 0.0785640i | ||||
\(985\) | 7830.64 | + | 34308.3i | 0.253304 | + | 1.10980i | ||||
\(986\) | −4521.55 | − | 5669.85i | −0.146040 | − | 0.183128i | ||||
\(987\) | 817.439 | − | 1025.04i | 0.0263621 | − | 0.0330570i | ||||
\(988\) | −10047.7 | −0.323544 | ||||||||
\(989\) | −2758.29 | + | 29132.6i | −0.0886840 | + | 0.936667i | ||||
\(990\) | −104064. | −3.34077 | ||||||||
\(991\) | −10081.0 | + | 12641.2i | −0.323143 | + | 0.405208i | −0.916695 | − | 0.399587i | \(-0.869153\pi\) |
0.593553 | + | 0.804795i | \(0.297725\pi\) | |||||||
\(992\) | 2147.80 | + | 2693.25i | 0.0687426 | + | 0.0862004i | ||||
\(993\) | −2257.57 | − | 9891.04i | −0.0721467 | − | 0.316095i | ||||
\(994\) | 61077.8 | + | 29413.5i | 1.94897 | + | 0.938572i | ||||
\(995\) | −21836.0 | −0.695727 | ||||||||
\(996\) | 16176.1 | 0.514617 | ||||||||
\(997\) | −22876.7 | − | 11016.8i | −0.726693 | − | 0.349957i | 0.0336897 | − | 0.999432i | \(-0.489274\pi\) |
−0.760382 | + | 0.649476i | \(0.774988\pi\) | |||||||
\(998\) | −12733.2 | + | 55787.7i | −0.403869 | + | 1.76947i | ||||
\(999\) | −2509.84 | + | 1208.67i | −0.0794872 | + | 0.0382790i |
(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 | 43.4.e.a.4.3 | ✓ | 60 | |
43.11 | even | 7 | inner | 43.4.e.a.11.3 | yes | 60 | |
43.21 | even | 7 | 1849.4.a.h.1.7 | 30 | |||
43.22 | odd | 14 | 1849.4.a.g.1.24 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.3 | ✓ | 60 | 1.1 | even | 1 | trivial | |
43.4.e.a.11.3 | yes | 60 | 43.11 | even | 7 | inner | |
1849.4.a.g.1.24 | 30 | 43.22 | odd | 14 | |||
1849.4.a.h.1.7 | 30 | 43.21 | even | 7 |