Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(59,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.59");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.p (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(44\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.14 | ||
Character | \(\chi\) | \(=\) | 105.59 |
Dual form | 105.4.p.a.89.14 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29175 | − | 2.23737i | −0.456701 | − | 0.791030i | 0.542083 | − | 0.840325i | \(-0.317636\pi\) |
−0.998784 | + | 0.0492950i | \(0.984303\pi\) | |||||||
\(3\) | −3.94402 | − | 3.38300i | −0.759027 | − | 0.651059i | ||||
\(4\) | 0.662782 | − | 1.14797i | 0.0828477 | − | 0.143496i | ||||
\(5\) | 1.23589 | + | 11.1118i | 0.110542 | + | 0.993871i | ||||
\(6\) | −2.47436 | + | 13.1942i | −0.168359 | + | 0.897753i | ||||
\(7\) | −1.81286 | + | 18.4313i | −0.0978853 | + | 0.995198i | ||||
\(8\) | −24.0925 | −1.06475 | ||||||||
\(9\) | 4.11059 | + | 26.6853i | 0.152244 | + | 0.988343i | ||||
\(10\) | 23.2648 | − | 17.1188i | 0.735698 | − | 0.541344i | ||||
\(11\) | −10.5104 | − | 6.06820i | −0.288092 | − | 0.166330i | 0.348989 | − | 0.937127i | \(-0.386525\pi\) |
−0.637081 | + | 0.770797i | \(0.719858\pi\) | |||||||
\(12\) | −6.49762 | + | 2.28543i | −0.156308 | + | 0.0549789i | ||||
\(13\) | 32.6517 | 0.696613 | 0.348306 | − | 0.937381i | \(-0.386757\pi\) | ||||
0.348306 | + | 0.937381i | \(0.386757\pi\) | |||||||
\(14\) | 43.5795 | − | 19.7526i | 0.831936 | − | 0.377078i | ||||
\(15\) | 32.7169 | − | 48.0063i | 0.563165 | − | 0.826344i | ||||
\(16\) | 25.8192 | + | 44.7201i | 0.403425 | + | 0.698752i | ||||
\(17\) | 66.2469 | + | 38.2477i | 0.945131 | + | 0.545672i | 0.891565 | − | 0.452892i | \(-0.149608\pi\) |
0.0535662 | + | 0.998564i | \(0.482941\pi\) | |||||||
\(18\) | 54.3950 | − | 43.6675i | 0.712279 | − | 0.571807i | ||||
\(19\) | −41.3069 | + | 23.8486i | −0.498761 | + | 0.287960i | −0.728202 | − | 0.685363i | \(-0.759644\pi\) |
0.229441 | + | 0.973323i | \(0.426310\pi\) | |||||||
\(20\) | 13.5752 | + | 5.94594i | 0.151775 | + | 0.0664776i | ||||
\(21\) | 69.5032 | − | 66.5606i | 0.722230 | − | 0.691653i | ||||
\(22\) | 31.3543i | 0.303853i | ||||||||
\(23\) | 34.5475 | + | 59.8381i | 0.313203 | + | 0.542483i | 0.979054 | − | 0.203602i | \(-0.0652648\pi\) |
−0.665851 | + | 0.746085i | \(0.731931\pi\) | |||||||
\(24\) | 95.0214 | + | 81.5051i | 0.808174 | + | 0.693215i | ||||
\(25\) | −121.945 | + | 27.4661i | −0.975561 | + | 0.219729i | ||||
\(26\) | −42.1778 | − | 73.0540i | −0.318144 | − | 0.551041i | ||||
\(27\) | 74.0641 | − | 119.153i | 0.527913 | − | 0.849299i | ||||
\(28\) | 19.9571 | + | 14.2971i | 0.134698 | + | 0.0964961i | ||||
\(29\) | 135.453i | 0.867343i | 0.901071 | + | 0.433671i | \(0.142782\pi\) | ||||
−0.901071 | + | 0.433671i | \(0.857218\pi\) | |||||||
\(30\) | −149.670 | − | 11.1880i | −0.910861 | − | 0.0680877i | ||||
\(31\) | −142.890 | − | 82.4973i | −0.827862 | − | 0.477966i | 0.0252582 | − | 0.999681i | \(-0.491959\pi\) |
−0.853120 | + | 0.521715i | \(0.825293\pi\) | |||||||
\(32\) | −29.6664 | + | 51.3838i | −0.163885 | + | 0.283858i | ||||
\(33\) | 20.9246 | + | 59.4899i | 0.110379 | + | 0.313814i | ||||
\(34\) | − | 197.625i | − | 0.996836i | ||||||
\(35\) | −207.046 | + | 2.63497i | −0.999919 | + | 0.0127255i | ||||
\(36\) | 33.3583 | + | 12.9677i | 0.154437 | + | 0.0600355i | ||||
\(37\) | −71.4057 | + | 41.2261i | −0.317271 | + | 0.183176i | −0.650175 | − | 0.759784i | \(-0.725305\pi\) |
0.332905 | + | 0.942960i | \(0.391971\pi\) | |||||||
\(38\) | 106.716 | + | 61.6126i | 0.455570 | + | 0.263023i | ||||
\(39\) | −128.779 | − | 110.461i | −0.528748 | − | 0.453536i | ||||
\(40\) | −29.7758 | − | 267.712i | −0.117699 | − | 1.05822i | ||||
\(41\) | 411.728 | 1.56832 | 0.784160 | − | 0.620559i | \(-0.213094\pi\) | ||||
0.784160 | + | 0.620559i | \(0.213094\pi\) | |||||||
\(42\) | −238.701 | − | 69.5249i | −0.876962 | − | 0.255427i | ||||
\(43\) | 432.567i | 1.53409i | 0.641594 | + | 0.767045i | \(0.278274\pi\) | ||||
−0.641594 | + | 0.767045i | \(0.721726\pi\) | |||||||
\(44\) | −13.9322 | + | 8.04378i | −0.0477356 | + | 0.0275601i | ||||
\(45\) | −291.442 | + | 78.6562i | −0.965457 | + | 0.260564i | ||||
\(46\) | 89.2533 | − | 154.591i | 0.286080 | − | 0.495505i | ||||
\(47\) | −179.518 | + | 103.645i | −0.557136 | + | 0.321662i | −0.751995 | − | 0.659169i | \(-0.770908\pi\) |
0.194859 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(48\) | 49.4570 | − | 263.724i | 0.148719 | − | 0.793025i | ||||
\(49\) | −336.427 | − | 66.8268i | −0.980837 | − | 0.194830i | ||||
\(50\) | 218.974 | + | 237.357i | 0.619352 | + | 0.671348i | ||||
\(51\) | −131.887 | − | 374.963i | −0.362116 | − | 1.02952i | ||||
\(52\) | 21.6410 | − | 37.4833i | 0.0577128 | − | 0.0999614i | ||||
\(53\) | −163.603 | + | 283.368i | −0.424010 | + | 0.734407i | −0.996327 | − | 0.0856251i | \(-0.972711\pi\) |
0.572317 | + | 0.820032i | \(0.306045\pi\) | |||||||
\(54\) | −362.262 | − | 11.7929i | −0.912919 | − | 0.0297187i | ||||
\(55\) | 54.4390 | − | 124.290i | 0.133465 | − | 0.304713i | ||||
\(56\) | 43.6764 | − | 444.057i | 0.104223 | − | 1.05964i | ||||
\(57\) | 243.595 | + | 45.6823i | 0.566052 | + | 0.106154i | ||||
\(58\) | 303.058 | − | 174.971i | 0.686094 | − | 0.396117i | ||||
\(59\) | −314.760 | + | 545.181i | −0.694547 | + | 1.20299i | 0.275786 | + | 0.961219i | \(0.411062\pi\) |
−0.970333 | + | 0.241772i | \(0.922271\pi\) | |||||||
\(60\) | −33.4257 | − | 69.3758i | −0.0719206 | − | 0.149273i | ||||
\(61\) | −145.338 | + | 83.9109i | −0.305059 | + | 0.176126i | −0.644713 | − | 0.764424i | \(-0.723023\pi\) |
0.339654 | + | 0.940550i | \(0.389690\pi\) | |||||||
\(62\) | 426.262i | 0.873151i | ||||||||
\(63\) | −499.296 | + | 27.3868i | −0.998499 | + | 0.0547685i | ||||
\(64\) | 566.393 | 1.10624 | ||||||||
\(65\) | 40.3541 | + | 362.820i | 0.0770048 | + | 0.692343i | ||||
\(66\) | 106.072 | − | 123.662i | 0.197826 | − | 0.230632i | ||||
\(67\) | −71.8202 | − | 41.4654i | −0.130959 | − | 0.0756090i | 0.433089 | − | 0.901351i | \(-0.357423\pi\) |
−0.564048 | + | 0.825742i | \(0.690757\pi\) | |||||||
\(68\) | 87.8145 | − | 50.6997i | 0.156604 | − | 0.0904153i | ||||
\(69\) | 66.1762 | − | 352.877i | 0.115459 | − | 0.615672i | ||||
\(70\) | 273.346 | + | 459.835i | 0.466731 | + | 0.785154i | ||||
\(71\) | − | 890.967i | − | 1.48927i | −0.667471 | − | 0.744636i | \(-0.732623\pi\) | ||
0.667471 | − | 0.744636i | \(-0.267377\pi\) | |||||||
\(72\) | −99.0344 | − | 642.915i | −0.162102 | − | 1.05234i | ||||
\(73\) | 169.743 | − | 294.003i | 0.272149 | − | 0.471375i | −0.697263 | − | 0.716815i | \(-0.745599\pi\) |
0.969412 | + | 0.245440i | \(0.0789324\pi\) | |||||||
\(74\) | 184.476 | + | 106.507i | 0.289796 | + | 0.167314i | ||||
\(75\) | 573.872 | + | 304.214i | 0.883533 | + | 0.468368i | ||||
\(76\) | 63.2256i | 0.0954273i | ||||||||
\(77\) | 130.899 | − | 182.720i | 0.193731 | − | 0.270427i | ||||
\(78\) | −80.7921 | + | 430.814i | −0.117281 | + | 0.625386i | ||||
\(79\) | 338.416 | + | 586.154i | 0.481960 | + | 0.834779i | 0.999786 | − | 0.0207073i | \(-0.00659180\pi\) |
−0.517826 | + | 0.855486i | \(0.673258\pi\) | |||||||
\(80\) | −465.012 | + | 342.168i | −0.649875 | + | 0.478194i | ||||
\(81\) | −695.206 | + | 219.384i | −0.953644 | + | 0.300938i | ||||
\(82\) | −531.848 | − | 921.188i | −0.716254 | − | 1.24059i | ||||
\(83\) | − | 683.794i | − | 0.904291i | −0.891944 | − | 0.452146i | \(-0.850659\pi\) | ||
0.891944 | − | 0.452146i | \(-0.149341\pi\) | |||||||
\(84\) | −30.3442 | − | 123.903i | −0.0394146 | − | 0.160939i | ||||
\(85\) | −343.127 | + | 783.394i | −0.437851 | + | 0.999659i | ||||
\(86\) | 967.813 | − | 558.767i | 1.21351 | − | 0.700621i | ||||
\(87\) | 458.237 | − | 534.228i | 0.564692 | − | 0.658337i | ||||
\(88\) | 253.223 | + | 146.198i | 0.306746 | + | 0.177100i | ||||
\(89\) | 487.836 | + | 844.956i | 0.581017 | + | 1.00635i | 0.995359 | + | 0.0962293i | \(0.0306782\pi\) |
−0.414343 | + | 0.910121i | \(0.635988\pi\) | |||||||
\(90\) | 552.452 | + | 550.459i | 0.647039 | + | 0.644705i | ||||
\(91\) | −59.1931 | + | 601.815i | −0.0681881 | + | 0.693267i | ||||
\(92\) | 91.5899 | 0.103792 | ||||||||
\(93\) | 284.471 | + | 808.767i | 0.317185 | + | 0.901776i | ||||
\(94\) | 463.783 | + | 267.765i | 0.508889 | + | 0.293807i | ||||
\(95\) | −316.052 | − | 429.521i | −0.341329 | − | 0.463873i | ||||
\(96\) | 290.836 | − | 102.297i | 0.309202 | − | 0.108757i | ||||
\(97\) | 1695.33 | 1.77459 | 0.887293 | − | 0.461206i | \(-0.152583\pi\) | ||||
0.887293 | + | 0.461206i | \(0.152583\pi\) | |||||||
\(98\) | 285.062 | + | 839.035i | 0.293833 | + | 0.864851i | ||||
\(99\) | 118.727 | − | 305.417i | 0.120531 | − | 0.310057i | ||||
\(100\) | −49.2927 | + | 158.194i | −0.0492927 | + | 0.158194i | ||||
\(101\) | 372.123 | − | 644.536i | 0.366610 | − | 0.634987i | −0.622423 | − | 0.782681i | \(-0.713852\pi\) |
0.989033 | + | 0.147694i | \(0.0471850\pi\) | |||||||
\(102\) | −668.566 | + | 779.438i | −0.648999 | + | 0.756626i | ||||
\(103\) | −929.457 | − | 1609.87i | −0.889147 | − | 1.54005i | −0.840886 | − | 0.541213i | \(-0.817965\pi\) |
−0.0482614 | − | 0.998835i | \(-0.515368\pi\) | |||||||
\(104\) | −786.663 | −0.741718 | ||||||||
\(105\) | 825.508 | + | 690.045i | 0.767251 | + | 0.641347i | ||||
\(106\) | 845.332 | 0.774584 | ||||||||
\(107\) | −612.991 | − | 1061.73i | −0.553833 | − | 0.959266i | −0.997993 | − | 0.0633193i | \(-0.979831\pi\) |
0.444161 | − | 0.895947i | \(-0.353502\pi\) | |||||||
\(108\) | −87.6963 | − | 163.996i | −0.0781350 | − | 0.146116i | ||||
\(109\) | −634.918 | + | 1099.71i | −0.557928 | + | 0.966360i | 0.439741 | + | 0.898124i | \(0.355070\pi\) |
−0.997669 | + | 0.0682351i | \(0.978263\pi\) | |||||||
\(110\) | −348.403 | + | 38.7506i | −0.301991 | + | 0.0335884i | ||||
\(111\) | 421.093 | + | 78.9691i | 0.360076 | + | 0.0675262i | ||||
\(112\) | −871.058 | + | 394.810i | −0.734886 | + | 0.333090i | ||||
\(113\) | −337.812 | −0.281227 | −0.140613 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140613 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(114\) | −212.455 | − | 604.023i | −0.174546 | − | 0.496245i | ||||
\(115\) | −622.213 | + | 457.840i | −0.504536 | + | 0.371250i | ||||
\(116\) | 155.496 | + | 89.7756i | 0.124461 | + | 0.0718574i | ||||
\(117\) | 134.218 | + | 871.320i | 0.106055 | + | 0.688492i | ||||
\(118\) | 1626.36 | 1.26880 | ||||||||
\(119\) | −825.051 | + | 1151.68i | −0.635566 | + | 0.887179i | ||||
\(120\) | −788.234 | + | 1156.59i | −0.599630 | + | 0.879850i | ||||
\(121\) | −591.854 | − | 1025.12i | −0.444669 | − | 0.770189i | ||||
\(122\) | 375.479 | + | 216.783i | 0.278642 | + | 0.160874i | ||||
\(123\) | −1623.86 | − | 1392.88i | −1.19040 | − | 1.02107i | ||||
\(124\) | −189.409 | + | 109.355i | −0.137173 | + | 0.0791968i | ||||
\(125\) | −455.909 | − | 1321.09i | −0.326222 | − | 0.945293i | ||||
\(126\) | 706.239 | + | 1081.73i | 0.499339 | + | 0.764830i | ||||
\(127\) | 2065.91i | 1.44347i | 0.692171 | + | 0.721733i | \(0.256654\pi\) | ||||
−0.692171 | + | 0.721733i | \(0.743346\pi\) | |||||||
\(128\) | −494.305 | − | 856.161i | −0.341334 | − | 0.591208i | ||||
\(129\) | 1463.38 | − | 1706.05i | 0.998783 | − | 1.16442i | ||||
\(130\) | 759.636 | − | 558.959i | 0.512496 | − | 0.377107i | ||||
\(131\) | −189.871 | − | 328.867i | −0.126635 | − | 0.219337i | 0.795736 | − | 0.605643i | \(-0.207084\pi\) |
−0.922371 | + | 0.386306i | \(0.873751\pi\) | |||||||
\(132\) | 82.1612 | + | 15.4080i | 0.0541759 | + | 0.0101598i | ||||
\(133\) | −364.677 | − | 804.576i | −0.237756 | − | 0.524553i | ||||
\(134\) | 214.251i | 0.138123i | ||||||||
\(135\) | 1415.55 | + | 675.726i | 0.902450 | + | 0.430794i | ||||
\(136\) | −1596.06 | − | 921.483i | −1.00633 | − | 0.581004i | ||||
\(137\) | 343.405 | − | 594.794i | 0.214154 | − | 0.370925i | −0.738857 | − | 0.673862i | \(-0.764634\pi\) |
0.953010 | + | 0.302938i | \(0.0979674\pi\) | |||||||
\(138\) | −875.000 | + | 307.767i | −0.539746 | + | 0.189847i | ||||
\(139\) | − | 3103.20i | − | 1.89359i | −0.321831 | − | 0.946797i | \(-0.604298\pi\) | ||
0.321831 | − | 0.946797i | \(-0.395702\pi\) | |||||||
\(140\) | −134.201 | + | 239.429i | −0.0810149 | + | 0.144539i | ||||
\(141\) | 1058.65 | + | 198.533i | 0.632302 | + | 0.118578i | ||||
\(142\) | −1993.42 | + | 1150.90i | −1.17806 | + | 0.680152i | ||||
\(143\) | −343.184 | − | 198.137i | −0.200689 | − | 0.115868i | ||||
\(144\) | −1087.24 | + | 872.818i | −0.629188 | + | 0.505103i | ||||
\(145\) | −1505.13 | + | 167.405i | −0.862027 | + | 0.0958776i | ||||
\(146\) | −877.057 | −0.497163 | ||||||||
\(147\) | 1100.80 | + | 1401.70i | 0.617636 | + | 0.786464i | ||||
\(148\) | 109.296i | 0.0607030i | ||||||||
\(149\) | −960.174 | + | 554.357i | −0.527923 | + | 0.304796i | −0.740170 | − | 0.672420i | \(-0.765255\pi\) |
0.212247 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(150\) | −60.6575 | − | 1676.93i | −0.0330178 | − | 0.912806i | ||||
\(151\) | 1083.36 | − | 1876.43i | 0.583856 | − | 1.01127i | −0.411161 | − | 0.911563i | \(-0.634877\pi\) |
0.995017 | − | 0.0997055i | \(-0.0317901\pi\) | |||||||
\(152\) | 995.189 | − | 574.573i | 0.531056 | − | 0.306605i | ||||
\(153\) | −748.335 | + | 1925.04i | −0.395420 | + | 1.01719i | ||||
\(154\) | −577.901 | − | 56.8410i | −0.302394 | − | 0.0297427i | ||||
\(155\) | 740.099 | − | 1689.72i | 0.383524 | − | 0.875624i | ||||
\(156\) | −212.158 | + | 74.6233i | −0.108886 | + | 0.0382990i | ||||
\(157\) | −178.427 | + | 309.044i | −0.0907006 | + | 0.157098i | −0.907806 | − | 0.419390i | \(-0.862244\pi\) |
0.817106 | + | 0.576488i | \(0.195577\pi\) | |||||||
\(158\) | 874.296 | − | 1514.33i | 0.440223 | − | 0.762489i | ||||
\(159\) | 1603.89 | − | 564.141i | 0.799978 | − | 0.281379i | ||||
\(160\) | −607.632 | − | 266.143i | −0.300234 | − | 0.131503i | ||||
\(161\) | −1165.52 | + | 528.278i | −0.570535 | + | 0.258597i | ||||
\(162\) | 1388.87 | + | 1272.05i | 0.673582 | + | 0.616922i | ||||
\(163\) | 582.024 | − | 336.032i | 0.279679 | − | 0.161473i | −0.353599 | − | 0.935397i | \(-0.615042\pi\) |
0.633278 | + | 0.773924i | \(0.281709\pi\) | |||||||
\(164\) | 272.886 | − | 472.652i | 0.129932 | − | 0.225048i | ||||
\(165\) | −635.181 | + | 306.034i | −0.299689 | + | 0.144392i | ||||
\(166\) | −1529.90 | + | 883.289i | −0.715322 | + | 0.412991i | ||||
\(167\) | 537.655i | 0.249132i | 0.992211 | + | 0.124566i | \(0.0397538\pi\) | ||||
−0.992211 | + | 0.124566i | \(0.960246\pi\) | |||||||
\(168\) | −1674.51 | + | 1603.61i | −0.768994 | + | 0.736437i | ||||
\(169\) | −1130.86 | −0.514731 | ||||||||
\(170\) | 2195.98 | − | 244.244i | 0.990727 | − | 0.110192i | ||||
\(171\) | −806.201 | − | 1004.25i | −0.360537 | − | 0.449107i | ||||
\(172\) | 496.575 | + | 286.698i | 0.220136 | + | 0.127096i | ||||
\(173\) | −155.173 | + | 89.5891i | −0.0681941 | + | 0.0393719i | −0.533709 | − | 0.845668i | \(-0.679202\pi\) |
0.465515 | + | 0.885040i | \(0.345869\pi\) | |||||||
\(174\) | −1787.19 | − | 335.158i | −0.778660 | − | 0.146025i | ||||
\(175\) | −285.166 | − | 2297.40i | −0.123180 | − | 0.992384i | ||||
\(176\) | − | 626.704i | − | 0.268407i | ||||||
\(177\) | 3085.77 | − | 1085.37i | 1.31040 | − | 0.460911i | ||||
\(178\) | 1260.32 | − | 2182.94i | 0.530702 | − | 0.919203i | ||||
\(179\) | 4070.64 | + | 2350.19i | 1.69974 | + | 0.981348i | 0.945993 | + | 0.324188i | \(0.105091\pi\) |
0.753751 | + | 0.657160i | \(0.228242\pi\) | |||||||
\(180\) | −102.867 | + | 386.699i | −0.0425959 | + | 0.160127i | ||||
\(181\) | 4172.20i | 1.71335i | 0.515853 | + | 0.856677i | \(0.327475\pi\) | ||||
−0.515853 | + | 0.856677i | \(0.672525\pi\) | |||||||
\(182\) | 1422.94 | − | 644.955i | 0.579537 | − | 0.262677i | ||||
\(183\) | 857.086 | + | 160.732i | 0.346217 | + | 0.0649272i | ||||
\(184\) | −832.337 | − | 1441.65i | −0.333482 | − | 0.577608i | ||||
\(185\) | −546.347 | − | 742.496i | −0.217125 | − | 0.295078i | ||||
\(186\) | 1442.05 | − | 1681.19i | 0.568473 | − | 0.662745i | ||||
\(187\) | −464.189 | − | 803.999i | −0.181523 | − | 0.314408i | ||||
\(188\) | 274.775i | 0.106596i | ||||||||
\(189\) | 2061.88 | + | 1581.11i | 0.793545 | + | 0.608511i | ||||
\(190\) | −552.739 | + | 1261.96i | −0.211052 | + | 0.481853i | ||||
\(191\) | −3404.76 | + | 1965.74i | −1.28984 | + | 0.744689i | −0.978626 | − | 0.205650i | \(-0.934069\pi\) |
−0.311214 | + | 0.950340i | \(0.600736\pi\) | |||||||
\(192\) | −2233.87 | − | 1916.11i | −0.839663 | − | 0.720225i | ||||
\(193\) | 1644.08 | + | 949.207i | 0.613177 | + | 0.354018i | 0.774208 | − | 0.632932i | \(-0.218149\pi\) |
−0.161031 | + | 0.986949i | \(0.551482\pi\) | |||||||
\(194\) | −2189.94 | − | 3793.09i | −0.810456 | − | 1.40375i | ||||
\(195\) | 1068.26 | − | 1567.49i | 0.392308 | − | 0.575642i | ||||
\(196\) | −299.693 | + | 341.917i | −0.109218 | + | 0.124605i | ||||
\(197\) | −4662.35 | −1.68619 | −0.843093 | − | 0.537768i | \(-0.819268\pi\) | ||||
−0.843093 | + | 0.537768i | \(0.819268\pi\) | |||||||
\(198\) | −836.698 | + | 128.885i | −0.300311 | + | 0.0462597i | ||||
\(199\) | 3406.25 | + | 1966.60i | 1.21338 | + | 0.700545i | 0.963494 | − | 0.267730i | \(-0.0862735\pi\) |
0.249886 | + | 0.968275i | \(0.419607\pi\) | |||||||
\(200\) | 2937.97 | − | 661.727i | 1.03873 | − | 0.233956i | ||||
\(201\) | 142.983 | + | 406.508i | 0.0501752 | + | 0.142651i | ||||
\(202\) | −1922.75 | −0.669725 | ||||||||
\(203\) | −2496.57 | − | 245.557i | −0.863178 | − | 0.0849001i | ||||
\(204\) | −517.859 | − | 97.1159i | −0.177732 | − | 0.0333308i | ||||
\(205\) | 508.852 | + | 4575.05i | 0.173365 | + | 1.55871i | ||||
\(206\) | −2401.25 | + | 4159.08i | −0.812149 | + | 1.40668i | ||||
\(207\) | −1454.78 | + | 1167.88i | −0.488476 | + | 0.392141i | ||||
\(208\) | 843.041 | + | 1460.19i | 0.281031 | + | 0.486760i | ||||
\(209\) | 578.872 | 0.191586 | ||||||||
\(210\) | 477.539 | − | 2738.33i | 0.156921 | − | 0.899822i | ||||
\(211\) | 5232.39 | 1.70717 | 0.853584 | − | 0.520955i | \(-0.174424\pi\) | ||||
0.853584 | + | 0.520955i | \(0.174424\pi\) | |||||||
\(212\) | 216.866 | + | 375.622i | 0.0702566 | + | 0.121688i | ||||
\(213\) | −3014.14 | + | 3513.99i | −0.969604 | + | 1.13040i | ||||
\(214\) | −1583.66 | + | 2742.98i | −0.505872 | + | 0.876197i | ||||
\(215\) | −4806.61 | + | 534.607i | −1.52469 | + | 0.169581i | ||||
\(216\) | −1784.39 | + | 2870.70i | −0.562095 | + | 0.904290i | ||||
\(217\) | 1779.57 | − | 2484.09i | 0.556706 | − | 0.777100i | ||||
\(218\) | 3280.61 | 1.01923 | ||||||||
\(219\) | −1664.08 | + | 585.313i | −0.513462 | + | 0.180602i | ||||
\(220\) | −106.600 | − | 144.871i | −0.0326680 | − | 0.0443965i | ||||
\(221\) | 2163.08 | + | 1248.85i | 0.658390 | + | 0.380122i | ||||
\(222\) | −367.263 | − | 1044.15i | −0.111032 | − | 0.315670i | ||||
\(223\) | 4944.44 | 1.48477 | 0.742387 | − | 0.669971i | \(-0.233694\pi\) | ||||
0.742387 | + | 0.669971i | \(0.233694\pi\) | |||||||
\(224\) | −893.289 | − | 639.943i | −0.266453 | − | 0.190884i | ||||
\(225\) | −1234.21 | − | 3141.24i | −0.365690 | − | 0.930737i | ||||
\(226\) | 436.367 | + | 755.810i | 0.128437 | + | 0.222459i | ||||
\(227\) | 184.006 | + | 106.236i | 0.0538014 | + | 0.0310623i | 0.526659 | − | 0.850076i | \(-0.323444\pi\) |
−0.472858 | + | 0.881139i | \(0.656778\pi\) | |||||||
\(228\) | 213.892 | − | 249.363i | 0.0621288 | − | 0.0724319i | ||||
\(229\) | 1918.63 | − | 1107.72i | 0.553653 | − | 0.319652i | −0.196941 | − | 0.980415i | \(-0.563101\pi\) |
0.750594 | + | 0.660763i | \(0.229767\pi\) | |||||||
\(230\) | 1828.10 | + | 800.708i | 0.524092 | + | 0.229553i | ||||
\(231\) | −1134.41 | + | 277.821i | −0.323112 | + | 0.0791311i | ||||
\(232\) | − | 3263.40i | − | 0.923503i | ||||||
\(233\) | 840.672 | + | 1456.09i | 0.236370 | + | 0.409405i | 0.959670 | − | 0.281129i | \(-0.0907088\pi\) |
−0.723300 | + | 0.690534i | \(0.757376\pi\) | |||||||
\(234\) | 1776.09 | − | 1425.82i | 0.496182 | − | 0.398328i | ||||
\(235\) | −1373.55 | − | 1866.68i | −0.381278 | − | 0.518164i | ||||
\(236\) | 417.235 | + | 722.672i | 0.115083 | + | 0.199330i | ||||
\(237\) | 648.241 | − | 3456.67i | 0.177670 | − | 0.947404i | ||||
\(238\) | 3642.49 | + | 358.267i | 0.992049 | + | 0.0975756i | ||||
\(239\) | − | 2284.19i | − | 0.618208i | −0.951028 | − | 0.309104i | \(-0.899971\pi\) | ||
0.951028 | − | 0.309104i | \(-0.100029\pi\) | |||||||
\(240\) | 2991.57 | + | 223.623i | 0.804605 | + | 0.0601449i | ||||
\(241\) | 646.834 | + | 373.450i | 0.172889 | + | 0.0998175i | 0.583947 | − | 0.811792i | \(-0.301507\pi\) |
−0.411058 | + | 0.911609i | \(0.634841\pi\) | |||||||
\(242\) | −1529.05 | + | 2648.39i | −0.406162 | + | 0.703492i | ||||
\(243\) | 3484.08 | + | 1486.63i | 0.919770 | + | 0.392458i | ||||
\(244\) | 222.458i | 0.0583666i | ||||||||
\(245\) | 326.780 | − | 3820.91i | 0.0852130 | − | 0.996363i | ||||
\(246\) | −1018.76 | + | 5432.43i | −0.264040 | + | 1.40796i | ||||
\(247\) | −1348.74 | + | 778.697i | −0.347443 | + | 0.200596i | ||||
\(248\) | 3442.57 | + | 1987.57i | 0.881465 | + | 0.508914i | ||||
\(249\) | −2313.28 | + | 2696.90i | −0.588747 | + | 0.686382i | ||||
\(250\) | −2366.84 | + | 2726.55i | −0.598769 | + | 0.689768i | ||||
\(251\) | 3521.92 | 0.885664 | 0.442832 | − | 0.896605i | \(-0.353974\pi\) | ||||
0.442832 | + | 0.896605i | \(0.353974\pi\) | |||||||
\(252\) | −299.485 | + | 591.330i | −0.0748643 | + | 0.147819i | ||||
\(253\) | − | 838.565i | − | 0.208380i | ||||||
\(254\) | 4622.22 | − | 2668.64i | 1.14183 | − | 0.659233i | ||||
\(255\) | 4003.52 | − | 1928.92i | 0.983178 | − | 0.473701i | ||||
\(256\) | 988.539 | − | 1712.20i | 0.241343 | − | 0.418018i | ||||
\(257\) | 6839.53 | − | 3948.80i | 1.66007 | − | 0.958442i | 0.687392 | − | 0.726287i | \(-0.258755\pi\) |
0.972679 | − | 0.232156i | \(-0.0745779\pi\) | |||||||
\(258\) | −5707.38 | − | 1070.33i | −1.37723 | − | 0.258277i | ||||
\(259\) | −630.402 | − | 1390.84i | −0.151241 | − | 0.333677i | ||||
\(260\) | 443.253 | + | 194.145i | 0.105728 | + | 0.0463092i | ||||
\(261\) | −3614.59 | + | 556.790i | −0.857232 | + | 0.132048i | ||||
\(262\) | −490.531 | + | 849.625i | −0.115668 | + | 0.200343i | ||||
\(263\) | 258.845 | − | 448.333i | 0.0606884 | − | 0.105115i | −0.834085 | − | 0.551636i | \(-0.814004\pi\) |
0.894773 | + | 0.446521i | \(0.147337\pi\) | |||||||
\(264\) | −504.127 | − | 1433.26i | −0.117526 | − | 0.334133i | ||||
\(265\) | −3350.93 | − | 1467.71i | −0.776777 | − | 0.340229i | ||||
\(266\) | −1329.06 | + | 1855.23i | −0.306354 | + | 0.427636i | ||||
\(267\) | 934.455 | − | 4982.87i | 0.214186 | − | 1.14212i | ||||
\(268\) | −95.2022 | + | 54.9650i | −0.0216993 | + | 0.0125281i | ||||
\(269\) | −1191.97 | + | 2064.55i | −0.270169 | + | 0.467946i | −0.968905 | − | 0.247433i | \(-0.920413\pi\) |
0.698736 | + | 0.715380i | \(0.253746\pi\) | |||||||
\(270\) | −316.677 | − | 4039.97i | −0.0713791 | − | 0.910609i | ||||
\(271\) | 1345.79 | − | 776.994i | 0.301665 | − | 0.174166i | −0.341526 | − | 0.939872i | \(-0.610944\pi\) |
0.643190 | + | 0.765706i | \(0.277610\pi\) | |||||||
\(272\) | 3950.09i | 0.880550i | ||||||||
\(273\) | 2269.40 | − | 2173.32i | 0.503115 | − | 0.481814i | ||||
\(274\) | −1774.37 | −0.391217 | ||||||||
\(275\) | 1448.37 | + | 451.307i | 0.317599 | + | 0.0989631i | ||||
\(276\) | −361.232 | − | 309.849i | −0.0787813 | − | 0.0675750i | ||||
\(277\) | −777.348 | − | 448.802i | −0.168615 | − | 0.0973498i | 0.413318 | − | 0.910587i | \(-0.364370\pi\) |
−0.581933 | + | 0.813237i | \(0.697703\pi\) | |||||||
\(278\) | −6943.00 | + | 4008.54i | −1.49789 | + | 0.864807i | ||||
\(279\) | 1614.10 | − | 4152.16i | 0.346358 | − | 0.890979i | ||||
\(280\) | 4988.26 | − | 63.4831i | 1.06466 | − | 0.0135494i | ||||
\(281\) | 224.924i | 0.0477504i | 0.999715 | + | 0.0238752i | \(0.00760044\pi\) | ||||
−0.999715 | + | 0.0238752i | \(0.992400\pi\) | |||||||
\(282\) | −923.319 | − | 2625.05i | −0.194975 | − | 0.554325i | ||||
\(283\) | −65.4356 | + | 113.338i | −0.0137447 | + | 0.0238065i | −0.872816 | − | 0.488050i | \(-0.837709\pi\) |
0.859071 | + | 0.511856i | \(0.171042\pi\) | |||||||
\(284\) | −1022.80 | − | 590.516i | −0.213705 | − | 0.123383i | ||||
\(285\) | −206.555 | + | 2763.24i | −0.0429308 | + | 0.574318i | ||||
\(286\) | 1023.77i | 0.211668i | ||||||||
\(287\) | −746.406 | + | 7588.69i | −0.153515 | + | 1.56079i | ||||
\(288\) | −1493.14 | − | 580.439i | −0.305499 | − | 0.118759i | ||||
\(289\) | 469.268 | + | 812.796i | 0.0955156 | + | 0.165438i | ||||
\(290\) | 2318.79 | + | 3151.28i | 0.469531 | + | 0.638102i | ||||
\(291\) | −6686.42 | − | 5735.31i | −1.34696 | − | 1.15536i | ||||
\(292\) | −225.004 | − | 389.719i | −0.0450938 | − | 0.0781048i | ||||
\(293\) | − | 2981.70i | − | 0.594514i | −0.954798 | − | 0.297257i | \(-0.903928\pi\) | ||
0.954798 | − | 0.297257i | \(-0.0960718\pi\) | |||||||
\(294\) | 1714.17 | − | 4273.54i | 0.340042 | − | 0.847748i | ||||
\(295\) | −6446.96 | − | 2823.77i | −1.27240 | − | 0.557310i | ||||
\(296\) | 1720.34 | − | 993.240i | 0.337814 | − | 0.195037i | ||||
\(297\) | −1501.49 | + | 802.917i | −0.293351 | + | 0.156869i | ||||
\(298\) | 2480.60 | + | 1432.18i | 0.482206 | + | 0.278402i | ||||
\(299\) | 1128.04 | + | 1953.82i | 0.218181 | + | 0.377900i | ||||
\(300\) | 729.581 | − | 457.161i | 0.140408 | − | 0.0879807i | ||||
\(301\) | −7972.78 | − | 784.184i | −1.52672 | − | 0.150165i | ||||
\(302\) | −5597.68 | −1.06659 | ||||||||
\(303\) | −3648.13 | + | 1283.17i | −0.691681 | + | 0.243288i | ||||
\(304\) | −2133.02 | − | 1231.50i | −0.402425 | − | 0.232340i | ||||
\(305\) | −1112.02 | − | 1511.26i | −0.208768 | − | 0.283720i | ||||
\(306\) | 5273.68 | − | 812.355i | 0.985216 | − | 0.151762i | ||||
\(307\) | −5035.77 | −0.936178 | −0.468089 | − | 0.883681i | \(-0.655057\pi\) | ||||
−0.468089 | + | 0.883681i | \(0.655057\pi\) | |||||||
\(308\) | −123.000 | − | 271.372i | −0.0227552 | − | 0.0502041i | ||||
\(309\) | −1780.39 | + | 9493.70i | −0.327776 | + | 1.74783i | ||||
\(310\) | −4736.55 | + | 526.815i | −0.867800 | + | 0.0965197i | ||||
\(311\) | −3086.91 | + | 5346.69i | −0.562839 | + | 0.974865i | 0.434408 | + | 0.900716i | \(0.356957\pi\) |
−0.997247 | + | 0.0741493i | \(0.976376\pi\) | |||||||
\(312\) | 3102.61 | + | 2661.28i | 0.562984 | + | 0.482902i | ||||
\(313\) | 1726.42 | + | 2990.24i | 0.311766 | + | 0.539995i | 0.978745 | − | 0.205082i | \(-0.0657461\pi\) |
−0.666979 | + | 0.745077i | \(0.732413\pi\) | |||||||
\(314\) | 921.928 | 0.165692 | ||||||||
\(315\) | −921.395 | − | 5514.25i | −0.164809 | − | 0.986326i | ||||
\(316\) | 897.185 | 0.159717 | ||||||||
\(317\) | −3198.38 | − | 5539.76i | −0.566685 | − | 0.981527i | −0.996891 | − | 0.0787964i | \(-0.974892\pi\) |
0.430206 | − | 0.902731i | \(-0.358441\pi\) | |||||||
\(318\) | −3334.01 | − | 2859.76i | −0.587930 | − | 0.504300i | ||||
\(319\) | 821.954 | − | 1423.67i | 0.144265 | − | 0.249875i | ||||
\(320\) | 700.002 | + | 6293.66i | 0.122285 | + | 1.09946i | ||||
\(321\) | −1174.19 | + | 6261.24i | −0.204165 | + | 1.08869i | ||||
\(322\) | 2687.52 | + | 1925.31i | 0.465123 | + | 0.333209i | ||||
\(323\) | −3648.61 | −0.628527 | ||||||||
\(324\) | −208.923 | + | 943.481i | −0.0358236 | + | 0.161777i | ||||
\(325\) | −3981.72 | + | 896.815i | −0.679588 | + | 0.153066i | ||||
\(326\) | −1503.65 | − | 868.135i | −0.255459 | − | 0.147489i | ||||
\(327\) | 6224.46 | − | 2189.35i | 1.05264 | − | 0.370249i | ||||
\(328\) | −9919.57 | −1.66987 | ||||||||
\(329\) | −1584.87 | − | 3496.64i | −0.265582 | − | 0.585946i | ||||
\(330\) | 1505.20 | + | 1025.82i | 0.251087 | + | 0.171119i | ||||
\(331\) | −4608.49 | − | 7982.14i | −0.765273 | − | 1.32549i | −0.940102 | − | 0.340893i | \(-0.889271\pi\) |
0.174829 | − | 0.984599i | \(-0.444063\pi\) | |||||||
\(332\) | −784.977 | − | 453.206i | −0.129763 | − | 0.0749185i | ||||
\(333\) | −1393.65 | − | 1736.02i | −0.229344 | − | 0.285685i | ||||
\(334\) | 1202.93 | − | 694.514i | 0.197071 | − | 0.113779i | ||||
\(335\) | 371.994 | − | 849.300i | 0.0606693 | − | 0.138514i | ||||
\(336\) | 4771.11 | + | 1389.65i | 0.774659 | + | 0.225630i | ||||
\(337\) | 3384.09i | 0.547013i | 0.961870 | + | 0.273506i | \(0.0881835\pi\) | ||||
−0.961870 | + | 0.273506i | \(0.911817\pi\) | |||||||
\(338\) | 1460.79 | + | 2530.16i | 0.235078 | + | 0.407168i | ||||
\(339\) | 1332.34 | + | 1142.82i | 0.213459 | + | 0.183095i | ||||
\(340\) | 671.896 | + | 913.119i | 0.107173 | + | 0.145650i | ||||
\(341\) | 1001.22 | + | 1734.16i | 0.159000 | + | 0.275397i | ||||
\(342\) | −1205.48 | + | 3101.01i | −0.190600 | + | 0.490303i | ||||
\(343\) | 1841.60 | − | 6079.65i | 0.289904 | − | 0.957056i | ||||
\(344\) | − | 10421.6i | − | 1.63342i | ||||||
\(345\) | 4002.89 | + | 299.220i | 0.624662 | + | 0.0466941i | ||||
\(346\) | 400.888 | + | 231.453i | 0.0622887 | + | 0.0359624i | ||||
\(347\) | −725.161 | + | 1256.02i | −0.112186 | + | 0.194313i | −0.916652 | − | 0.399687i | \(-0.869119\pi\) |
0.804465 | + | 0.594000i | \(0.202452\pi\) | |||||||
\(348\) | −309.568 | − | 880.120i | −0.0476856 | − | 0.135573i | ||||
\(349\) | 483.673i | 0.0741846i | 0.999312 | + | 0.0370923i | \(0.0118096\pi\) | ||||
−0.999312 | + | 0.0370923i | \(0.988190\pi\) | |||||||
\(350\) | −4771.78 | + | 3605.68i | −0.728749 | + | 0.550663i | ||||
\(351\) | 2418.32 | − | 3890.56i | 0.367750 | − | 0.591632i | ||||
\(352\) | 623.614 | − | 360.044i | 0.0944282 | − | 0.0545181i | ||||
\(353\) | 8171.75 | + | 4717.96i | 1.23212 | + | 0.711365i | 0.967471 | − | 0.252980i | \(-0.0814108\pi\) |
0.264648 | + | 0.964345i | \(0.414744\pi\) | |||||||
\(354\) | −6414.40 | − | 5501.99i | −0.963056 | − | 0.826066i | ||||
\(355\) | 9900.26 | − | 1101.14i | 1.48014 | − | 0.164627i | ||||
\(356\) | 1293.31 | 0.192544 | ||||||||
\(357\) | 7150.16 | − | 1751.10i | 1.06002 | − | 0.259602i | ||||
\(358\) | − | 12143.4i | − | 1.79273i | ||||||
\(359\) | 1959.14 | − | 1131.11i | 0.288020 | − | 0.166289i | −0.349028 | − | 0.937112i | \(-0.613488\pi\) |
0.637049 | + | 0.770824i | \(0.280155\pi\) | |||||||
\(360\) | 7021.56 | − | 1895.03i | 1.02797 | − | 0.277435i | ||||
\(361\) | −2291.99 | + | 3969.84i | −0.334158 | + | 0.578779i | ||||
\(362\) | 9334.76 | − | 5389.43i | 1.35531 | − | 0.782491i | ||||
\(363\) | −1133.70 | + | 6045.34i | −0.163923 | + | 0.874099i | ||||
\(364\) | 651.634 | + | 466.824i | 0.0938322 | + | 0.0672204i | ||||
\(365\) | 3476.69 | + | 1522.79i | 0.498570 | + | 0.218374i | ||||
\(366\) | −747.520 | − | 2125.25i | −0.106758 | − | 0.303520i | ||||
\(367\) | −5083.85 | + | 8805.49i | −0.723092 | + | 1.25243i | 0.236662 | + | 0.971592i | \(0.423946\pi\) |
−0.959754 | + | 0.280840i | \(0.909387\pi\) | |||||||
\(368\) | −1783.98 | + | 3089.94i | −0.252707 | + | 0.437702i | ||||
\(369\) | 1692.44 | + | 10987.1i | 0.238767 | + | 1.55004i | ||||
\(370\) | −955.497 | + | 2181.50i | −0.134254 | + | 0.306515i | ||||
\(371\) | −4926.26 | − | 3529.12i | −0.689376 | − | 0.493862i | ||||
\(372\) | 1116.98 | + | 209.472i | 0.155680 | + | 0.0291952i | ||||
\(373\) | 8969.88 | − | 5178.76i | 1.24516 | − | 0.718891i | 0.275016 | − | 0.961440i | \(-0.411317\pi\) |
0.970139 | + | 0.242549i | \(0.0779835\pi\) | |||||||
\(374\) | −1199.23 | + | 2077.13i | −0.165804 | + | 0.287181i | ||||
\(375\) | −2671.13 | + | 6752.74i | −0.367830 | + | 0.929893i | ||||
\(376\) | 4325.04 | − | 2497.06i | 0.593210 | − | 0.342490i | ||||
\(377\) | 4422.77i | 0.604202i | ||||||||
\(378\) | 874.090 | − | 6655.59i | 0.118937 | − | 0.905626i | ||||
\(379\) | −6236.84 | −0.845290 | −0.422645 | − | 0.906295i | \(-0.638898\pi\) | ||||
−0.422645 | + | 0.906295i | \(0.638898\pi\) | |||||||
\(380\) | −702.552 | + | 78.1402i | −0.0948425 | + | 0.0105487i | ||||
\(381\) | 6988.99 | − | 8148.01i | 0.939782 | − | 1.09563i | ||||
\(382\) | 8796.16 | + | 5078.47i | 1.17814 | + | 0.680201i | ||||
\(383\) | 3425.10 | − | 1977.48i | 0.456956 | − | 0.263824i | −0.253807 | − | 0.967255i | \(-0.581683\pi\) |
0.710764 | + | 0.703431i | \(0.248350\pi\) | |||||||
\(384\) | −946.847 | + | 5048.95i | −0.125830 | + | 0.670972i | ||||
\(385\) | 2192.13 | + | 1228.70i | 0.290185 | + | 0.162651i | ||||
\(386\) | − | 4904.54i | − | 0.646722i | ||||||
\(387\) | −11543.2 | + | 1778.10i | −1.51621 | + | 0.233556i | ||||
\(388\) | 1123.64 | − | 1946.19i | 0.147020 | − | 0.254647i | ||||
\(389\) | −217.269 | − | 125.440i | −0.0283187 | − | 0.0163498i | 0.485774 | − | 0.874085i | \(-0.338538\pi\) |
−0.514093 | + | 0.857735i | \(0.671871\pi\) | |||||||
\(390\) | −4886.98 | − | 365.306i | −0.634518 | − | 0.0474308i | ||||
\(391\) | 5285.45i | 0.683623i | ||||||||
\(392\) | 8105.38 | + | 1610.03i | 1.04435 | + | 0.207446i | ||||
\(393\) | −363.701 | + | 1939.39i | −0.0466826 | + | 0.248930i | ||||
\(394\) | 6022.57 | + | 10431.4i | 0.770083 | + | 1.33382i | ||||
\(395\) | −6095.00 | + | 4484.85i | −0.776386 | + | 0.571284i | ||||
\(396\) | −271.920 | − | 338.721i | −0.0345063 | − | 0.0429832i | ||||
\(397\) | 3611.42 | + | 6255.16i | 0.456554 | + | 0.790774i | 0.998776 | − | 0.0494607i | \(-0.0157503\pi\) |
−0.542222 | + | 0.840235i | \(0.682417\pi\) | |||||||
\(398\) | − | 10161.4i | − | 1.27976i | ||||||
\(399\) | −1283.59 | + | 4406.97i | −0.161052 | + | 0.552943i | ||||
\(400\) | −4376.81 | − | 4744.25i | −0.547101 | − | 0.593032i | ||||
\(401\) | 8738.34 | − | 5045.09i | 1.08821 | − | 0.628278i | 0.155110 | − | 0.987897i | \(-0.450427\pi\) |
0.933099 | + | 0.359619i | \(0.117093\pi\) | |||||||
\(402\) | 724.812 | − | 845.011i | 0.0899262 | − | 0.104839i | ||||
\(403\) | −4665.59 | − | 2693.68i | −0.576699 | − | 0.332957i | ||||
\(404\) | −493.273 | − | 854.373i | −0.0607456 | − | 0.105214i | ||||
\(405\) | −3296.96 | − | 7453.87i | −0.404511 | − | 0.914533i | ||||
\(406\) | 2675.54 | + | 5902.96i | 0.327056 | + | 0.721573i | ||||
\(407\) | 1000.67 | 0.121871 | ||||||||
\(408\) | 3177.49 | + | 9033.81i | 0.385562 | + | 1.09618i | ||||
\(409\) | 3700.63 | + | 2136.56i | 0.447395 | + | 0.258304i | 0.706729 | − | 0.707484i | \(-0.250170\pi\) |
−0.259334 | + | 0.965788i | \(0.583503\pi\) | |||||||
\(410\) | 9578.77 | − | 7048.29i | 1.15381 | − | 0.849001i | ||||
\(411\) | −3366.59 | + | 1184.14i | −0.404042 | + | 0.142115i | ||||
\(412\) | −2464.11 | −0.294655 | ||||||||
\(413\) | −9477.78 | − | 6789.78i | −1.12923 | − | 0.808967i | ||||
\(414\) | 4492.19 | + | 1746.29i | 0.533283 | + | 0.207308i | ||||
\(415\) | 7598.20 | − | 845.097i | 0.898749 | − | 0.0999619i | ||||
\(416\) | −968.660 | + | 1677.77i | −0.114165 | + | 0.197739i | ||||
\(417\) | −10498.1 | + | 12239.1i | −1.23284 | + | 1.43729i | ||||
\(418\) | −747.756 | − | 1295.15i | −0.0874974 | − | 0.151550i | ||||
\(419\) | 1318.97 | 0.153785 | 0.0768924 | − | 0.997039i | \(-0.475500\pi\) | ||||
0.0768924 | + | 0.997039i | \(0.475500\pi\) | |||||||
\(420\) | 1339.28 | − | 490.310i | 0.155596 | − | 0.0569636i | ||||
\(421\) | 4708.32 | 0.545058 | 0.272529 | − | 0.962148i | \(-0.412140\pi\) | ||||
0.272529 | + | 0.962148i | \(0.412140\pi\) | |||||||
\(422\) | −6758.92 | − | 11706.8i | −0.779666 | − | 1.35042i | ||||
\(423\) | −3503.71 | − | 4364.44i | −0.402733 | − | 0.501670i | ||||
\(424\) | 3941.60 | − | 6827.05i | 0.451465 | − | 0.781960i | ||||
\(425\) | −9129.00 | − | 2844.57i | −1.04193 | − | 0.324664i | ||||
\(426\) | 11755.6 | + | 2204.57i | 1.33700 | + | 0.250732i | ||||
\(427\) | −1283.11 | − | 2830.89i | −0.145419 | − | 0.320834i | ||||
\(428\) | −1625.12 | −0.183535 | ||||||||
\(429\) | 683.225 | + | 1942.45i | 0.0768914 | + | 0.218607i | ||||
\(430\) | 7405.03 | + | 10063.6i | 0.830471 | + | 1.12863i | ||||
\(431\) | 9603.33 | + | 5544.49i | 1.07326 | + | 0.619648i | 0.929071 | − | 0.369901i | \(-0.120608\pi\) |
0.144192 | + | 0.989550i | \(0.453942\pi\) | |||||||
\(432\) | 7240.83 | + | 235.714i | 0.806422 | + | 0.0262519i | ||||
\(433\) | −387.919 | −0.0430536 | −0.0215268 | − | 0.999768i | \(-0.506853\pi\) | ||||
−0.0215268 | + | 0.999768i | \(0.506853\pi\) | |||||||
\(434\) | −7856.58 | − | 772.755i | −0.868958 | − | 0.0854687i | ||||
\(435\) | 6502.58 | + | 4431.60i | 0.716724 | + | 0.488457i | ||||
\(436\) | 841.625 | + | 1457.74i | 0.0924461 | + | 0.160121i | ||||
\(437\) | −2854.11 | − | 1647.82i | −0.312427 | − | 0.180380i | ||||
\(438\) | 3459.13 | + | 2967.09i | 0.377360 | + | 0.323682i | ||||
\(439\) | −1331.58 | + | 768.791i | −0.144768 | + | 0.0835817i | −0.570634 | − | 0.821204i | \(-0.693303\pi\) |
0.425867 | + | 0.904786i | \(0.359969\pi\) | |||||||
\(440\) | −1311.57 | + | 2994.45i | −0.142106 | + | 0.324443i | ||||
\(441\) | 400.380 | − | 9252.34i | 0.0432329 | − | 0.999065i | ||||
\(442\) | − | 6452.81i | − | 0.694409i | ||||||
\(443\) | 545.648 | + | 945.089i | 0.0585203 | + | 0.101360i | 0.893801 | − | 0.448463i | \(-0.148028\pi\) |
−0.835281 | + | 0.549823i | \(0.814695\pi\) | |||||||
\(444\) | 369.747 | − | 431.064i | 0.0395212 | − | 0.0460752i | ||||
\(445\) | −8786.09 | + | 6465.02i | −0.935956 | + | 0.688700i | ||||
\(446\) | −6386.97 | − | 11062.6i | −0.678098 | − | 1.17450i | ||||
\(447\) | 5662.33 | + | 1061.88i | 0.599148 | + | 0.112360i | ||||
\(448\) | −1026.79 | + | 10439.4i | −0.108284 | + | 1.10092i | ||||
\(449\) | 7819.39i | 0.821871i | 0.911665 | + | 0.410935i | \(0.134798\pi\) | ||||
−0.911665 | + | 0.410935i | \(0.865202\pi\) | |||||||
\(450\) | −5433.83 | + | 6819.05i | −0.569229 | + | 0.714341i | ||||
\(451\) | −4327.44 | − | 2498.45i | −0.451821 | − | 0.260859i | ||||
\(452\) | −223.895 | + | 387.798i | −0.0232990 | + | 0.0403551i | ||||
\(453\) | −10620.7 | + | 3735.67i | −1.10156 | + | 0.387455i | ||||
\(454\) | − | 548.920i | − | 0.0567447i | ||||||
\(455\) | −6760.41 | + | 86.0364i | −0.696556 | + | 0.00886472i | ||||
\(456\) | −5868.82 | − | 1100.60i | −0.602704 | − | 0.113027i | ||||
\(457\) | 3727.79 | − | 2152.24i | 0.381573 | − | 0.220301i | −0.296930 | − | 0.954899i | \(-0.595963\pi\) |
0.678502 | + | 0.734598i | \(0.262629\pi\) | |||||||
\(458\) | −4956.77 | − | 2861.79i | −0.505709 | − | 0.291971i | ||||
\(459\) | 9463.85 | − | 5060.76i | 0.962385 | − | 0.514632i | ||||
\(460\) | 113.195 | + | 1017.73i | 0.0114734 | + | 0.103156i | ||||
\(461\) | −1794.36 | −0.181284 | −0.0906420 | − | 0.995884i | \(-0.528892\pi\) | ||||
−0.0906420 | + | 0.995884i | \(0.528892\pi\) | |||||||
\(462\) | 2086.96 | + | 2179.22i | 0.210161 | + | 0.219452i | ||||
\(463\) | 898.088i | 0.0901462i | 0.998984 | + | 0.0450731i | \(0.0143521\pi\) | ||||
−0.998984 | + | 0.0450731i | \(0.985648\pi\) | |||||||
\(464\) | −6057.47 | + | 3497.28i | −0.606058 | + | 0.349908i | ||||
\(465\) | −8635.30 | + | 4160.54i | −0.861188 | + | 0.414925i | ||||
\(466\) | 2171.87 | − | 3761.79i | 0.215901 | − | 0.373952i | ||||
\(467\) | −3696.55 | + | 2134.20i | −0.366287 | + | 0.211476i | −0.671835 | − | 0.740701i | \(-0.734494\pi\) |
0.305548 | + | 0.952177i | \(0.401160\pi\) | |||||||
\(468\) | 1089.21 | + | 423.417i | 0.107583 | + | 0.0418215i | ||||
\(469\) | 894.462 | − | 1248.57i | 0.0880649 | − | 0.122929i | ||||
\(470\) | −2402.17 | + | 5484.40i | −0.235753 | + | 0.538248i | ||||
\(471\) | 1749.22 | − | 615.258i | 0.171124 | − | 0.0601902i | ||||
\(472\) | 7583.37 | − | 13134.8i | 0.739519 | − | 1.28088i | ||||
\(473\) | 2624.90 | − | 4546.47i | 0.255165 | − | 0.441959i | ||||
\(474\) | −8571.21 | + | 3014.78i | −0.830567 | + | 0.292138i | ||||
\(475\) | 4382.15 | − | 4042.76i | 0.423299 | − | 0.390515i | ||||
\(476\) | 775.267 | + | 1710.45i | 0.0746519 | + | 0.164702i | ||||
\(477\) | −8234.25 | − | 3200.97i | −0.790399 | − | 0.307258i | ||||
\(478\) | −5110.57 | + | 2950.59i | −0.489021 | + | 0.282336i | ||||
\(479\) | −952.788 | + | 1650.28i | −0.0908852 | + | 0.157418i | −0.907884 | − | 0.419222i | \(-0.862303\pi\) |
0.816999 | + | 0.576640i | \(0.195636\pi\) | |||||||
\(480\) | 1496.15 | + | 3105.29i | 0.142270 | + | 0.295285i | ||||
\(481\) | −2331.52 | + | 1346.10i | −0.221015 | + | 0.127603i | ||||
\(482\) | − | 1929.61i | − | 0.182347i | ||||||
\(483\) | 6384.02 | + | 1859.43i | 0.601414 | + | 0.175170i | ||||
\(484\) | −1569.08 | −0.147359 | ||||||||
\(485\) | 2095.25 | + | 18838.2i | 0.196166 | + | 1.76371i | ||||
\(486\) | −1174.41 | − | 9715.54i | −0.109614 | − | 0.906802i | ||||
\(487\) | −13123.6 | − | 7576.94i | −1.22113 | − | 0.705018i | −0.255969 | − | 0.966685i | \(-0.582395\pi\) |
−0.965158 | + | 0.261667i | \(0.915728\pi\) | |||||||
\(488\) | 3501.56 | − | 2021.63i | 0.324812 | − | 0.187530i | ||||
\(489\) | −3432.31 | − | 643.673i | −0.317412 | − | 0.0595253i | ||||
\(490\) | −8970.90 | + | 4204.52i | −0.827070 | + | 0.387634i | ||||
\(491\) | − | 10242.6i | − | 0.941429i | −0.882286 | − | 0.470714i | \(-0.843996\pi\) | ||
0.882286 | − | 0.470714i | \(-0.156004\pi\) | |||||||
\(492\) | −2675.25 | + | 940.976i | −0.245141 | + | 0.0862245i | ||||
\(493\) | −5180.75 | + | 8973.33i | −0.473285 | + | 0.819753i | ||||
\(494\) | 3484.47 | + | 2011.76i | 0.317356 | + | 0.183225i | ||||
\(495\) | 3540.48 | + | 941.815i | 0.321480 | + | 0.0855180i | ||||
\(496\) | − | 8520.05i | − | 0.771294i | ||||||
\(497\) | 16421.7 | + | 1615.20i | 1.48212 | + | 0.145778i | ||||
\(498\) | 9022.13 | + | 1691.95i | 0.811830 | + | 0.152245i | ||||
\(499\) | −1567.02 | − | 2714.16i | −0.140580 | − | 0.243492i | 0.787135 | − | 0.616781i | \(-0.211563\pi\) |
−0.927715 | + | 0.373289i | \(0.878230\pi\) | |||||||
\(500\) | −1818.74 | − | 352.222i | −0.162673 | − | 0.0315037i | ||||
\(501\) | 1818.89 | − | 2120.52i | 0.162199 | − | 0.189098i | ||||
\(502\) | −4549.43 | − | 7879.84i | −0.404484 | − | 0.700587i | ||||
\(503\) | 4924.57i | 0.436533i | 0.975889 | + | 0.218266i | \(0.0700402\pi\) | ||||
−0.975889 | + | 0.218266i | \(0.929960\pi\) | |||||||
\(504\) | 12029.3 | − | 659.818i | 1.06315 | − | 0.0583148i | ||||
\(505\) | 7621.87 | + | 3338.38i | 0.671621 | + | 0.294171i | ||||
\(506\) | −1876.18 | + | 1083.21i | −0.164835 | + | 0.0951675i | ||||
\(507\) | 4460.15 | + | 3825.72i | 0.390695 | + | 0.335120i | ||||
\(508\) | 2371.61 | + | 1369.25i | 0.207132 | + | 0.119588i | ||||
\(509\) | −3522.13 | − | 6100.51i | −0.306711 | − | 0.531238i | 0.670930 | − | 0.741521i | \(-0.265895\pi\) |
−0.977641 | + | 0.210282i | \(0.932562\pi\) | |||||||
\(510\) | −9487.25 | − | 6465.69i | −0.823730 | − | 0.561383i | ||||
\(511\) | 5111.14 | + | 3661.56i | 0.442472 | + | 0.316983i | ||||
\(512\) | −13016.6 | −1.12355 | ||||||||
\(513\) | −217.724 | + | 6688.18i | −0.0187383 | + | 0.575615i | ||||
\(514\) | −17669.9 | − | 10201.7i | −1.51631 | − | 0.875444i | ||||
\(515\) | 16739.8 | − | 12317.6i | 1.43232 | − | 1.05394i | ||||
\(516\) | −988.602 | − | 2810.65i | −0.0843426 | − | 0.239791i | ||||
\(517\) | 2515.75 | 0.214009 | ||||||||
\(518\) | −2297.50 | + | 3207.05i | −0.194877 | + | 0.272027i | ||||
\(519\) | 915.085 | + | 171.609i | 0.0773946 | + | 0.0145141i | ||||
\(520\) | −972.232 | − | 8741.26i | −0.0819908 | − | 0.737172i | ||||
\(521\) | 7268.50 | − | 12589.4i | 0.611207 | − | 1.05864i | −0.379830 | − | 0.925056i | \(-0.624018\pi\) |
0.991037 | − | 0.133586i | \(-0.0426491\pi\) | |||||||
\(522\) | 5914.88 | + | 7367.95i | 0.495953 | + | 0.617790i | ||||
\(523\) | 5313.05 | + | 9202.48i | 0.444213 | + | 0.769400i | 0.997997 | − | 0.0632605i | \(-0.0201499\pi\) |
−0.553784 | + | 0.832661i | \(0.686817\pi\) | |||||||
\(524\) | −503.373 | −0.0419655 | ||||||||
\(525\) | −6647.42 | + | 10025.7i | −0.552604 | + | 0.833444i | ||||
\(526\) | −1337.45 | −0.110866 | ||||||||
\(527\) | −6310.66 | − | 10930.4i | −0.521625 | − | 0.903482i | ||||
\(528\) | −2120.14 | + | 2471.73i | −0.174749 | + | 0.203728i | ||||
\(529\) | 3696.44 | − | 6402.41i | 0.303808 | − | 0.526211i | ||||
\(530\) | 1044.74 | + | 9393.18i | 0.0856239 | + | 0.769837i | ||||
\(531\) | −15842.1 | − | 6158.45i | −1.29471 | − | 0.503303i | ||||
\(532\) | −1165.33 | − | 114.619i | −0.0949690 | − | 0.00934093i | ||||
\(533\) | 13443.6 | 1.09251 | ||||||||
\(534\) | −12355.6 | + | 4345.89i | −1.00127 | + | 0.352181i | ||||
\(535\) | 11040.2 | − | 8123.64i | 0.892166 | − | 0.656478i | ||||
\(536\) | 1730.33 | + | 999.006i | 0.139438 | + | 0.0805047i | ||||
\(537\) | −8104.01 | − | 23040.2i | −0.651236 | − | 1.85150i | ||||
\(538\) | 6158.87 | 0.493546 | ||||||||
\(539\) | 3130.47 | + | 2743.89i | 0.250165 | + | 0.219272i | ||||
\(540\) | 1713.91 | − | 1177.15i | 0.136583 | − | 0.0938081i | ||||
\(541\) | −5100.34 | − | 8834.05i | −0.405325 | − | 0.702043i | 0.589034 | − | 0.808108i | \(-0.299508\pi\) |
−0.994359 | + | 0.106065i | \(0.966175\pi\) | |||||||
\(542\) | −3476.85 | − | 2007.36i | −0.275541 | − | 0.159084i | ||||
\(543\) | 14114.6 | − | 16455.2i | 1.11550 | − | 1.30048i | ||||
\(544\) | −3930.62 | + | 2269.34i | −0.309786 | + | 0.178855i | ||||
\(545\) | −13004.5 | − | 5695.97i | −1.02211 | − | 0.447686i | ||||
\(546\) | −7794.01 | − | 2270.11i | −0.610902 | − | 0.177934i | ||||
\(547\) | 9177.07i | 0.717336i | 0.933465 | + | 0.358668i | \(0.116769\pi\) | ||||
−0.933465 | + | 0.358668i | \(0.883231\pi\) | |||||||
\(548\) | −455.205 | − | 788.438i | −0.0354843 | − | 0.0614606i | ||||
\(549\) | −2836.61 | − | 3533.46i | −0.220516 | − | 0.274689i | ||||
\(550\) | −861.180 | − | 3823.50i | −0.0667651 | − | 0.296427i | ||||
\(551\) | −3230.36 | − | 5595.14i | −0.249760 | − | 0.432597i | ||||
\(552\) | −1594.35 | + | 8501.70i | −0.122935 | + | 0.655537i | ||||
\(553\) | −11417.1 | + | 5174.84i | −0.877947 | + | 0.397933i | ||||
\(554\) | 2318.95i | 0.177839i | ||||||||
\(555\) | −357.063 | + | 4776.71i | −0.0273090 | + | 0.365333i | ||||
\(556\) | −3562.38 | − | 2056.74i | −0.271724 | − | 0.156880i | ||||
\(557\) | −4456.31 | + | 7718.55i | −0.338994 | + | 0.587155i | −0.984244 | − | 0.176817i | \(-0.943420\pi\) |
0.645250 | + | 0.763972i | \(0.276753\pi\) | |||||||
\(558\) | −11374.9 | + | 1752.19i | −0.862973 | + | 0.132932i | ||||
\(559\) | 14124.1i | 1.06867i | ||||||||
\(560\) | −5463.60 | − | 9191.10i | −0.412284 | − | 0.693562i | ||||
\(561\) | −889.160 | + | 4741.34i | −0.0669169 | + | 0.356826i | ||||
\(562\) | 503.239 | − | 290.545i | 0.0377720 | − | 0.0218077i | ||||
\(563\) | 10512.1 | + | 6069.18i | 0.786915 | + | 0.454326i | 0.838875 | − | 0.544324i | \(-0.183214\pi\) |
−0.0519603 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(564\) | 929.565 | − | 1083.72i | 0.0694003 | − | 0.0809092i | ||||
\(565\) | −417.499 | − | 3753.70i | −0.0310873 | − | 0.279503i | ||||
\(566\) | 338.105 | 0.0251089 | ||||||||
\(567\) | −2783.23 | − | 13211.3i | −0.206145 | − | 0.978521i | ||||
\(568\) | 21465.6i | 1.58570i | ||||||||
\(569\) | 3112.21 | − | 1796.84i | 0.229298 | − | 0.132385i | −0.380950 | − | 0.924596i | \(-0.624403\pi\) |
0.610248 | + | 0.792210i | \(0.291070\pi\) | |||||||
\(570\) | 6449.22 | − | 3107.27i | 0.473909 | − | 0.228332i | ||||
\(571\) | −7584.54 | + | 13136.8i | −0.555873 | + | 0.962800i | 0.441962 | + | 0.897034i | \(0.354282\pi\) |
−0.997835 | + | 0.0657660i | \(0.979051\pi\) | |||||||
\(572\) | −454.912 | + | 262.644i | −0.0332532 | + | 0.0191987i | ||||
\(573\) | 20078.5 | + | 3765.39i | 1.46386 | + | 0.274523i | ||||
\(574\) | 17942.9 | − | 8132.68i | 1.30474 | − | 0.591379i | ||||
\(575\) | −5856.42 | − | 6348.08i | −0.424747 | − | 0.460405i | ||||
\(576\) | 2328.21 | + | 15114.3i | 0.168418 | + | 1.09334i | ||||
\(577\) | 2363.16 | − | 4093.11i | 0.170502 | − | 0.295318i | −0.768094 | − | 0.640338i | \(-0.778794\pi\) |
0.938595 | + | 0.345020i | \(0.112128\pi\) | |||||||
\(578\) | 1212.35 | − | 2099.85i | 0.0872442 | − | 0.151111i | ||||
\(579\) | −3273.09 | − | 9305.60i | −0.234931 | − | 0.667923i | ||||
\(580\) | −805.394 | + | 1838.80i | −0.0576589 | + | 0.131641i | ||||
\(581\) | 12603.2 | + | 1239.62i | 0.899949 | + | 0.0885168i | ||||
\(582\) | −4194.86 | + | 22368.6i | −0.298767 | + | 1.59314i | ||||
\(583\) | 3439.07 | − | 1985.55i | 0.244308 | − | 0.141051i | ||||
\(584\) | −4089.53 | + | 7083.27i | −0.289770 | + | 0.501897i | ||||
\(585\) | −9516.07 | + | 2568.26i | −0.672549 | + | 0.181512i | ||||
\(586\) | −6671.16 | + | 3851.60i | −0.470278 | + | 0.271515i | ||||
\(587\) | 5681.24i | 0.399471i | 0.979850 | + | 0.199736i | \(0.0640083\pi\) | ||||
−0.979850 | + | 0.199736i | \(0.935992\pi\) | |||||||
\(588\) | 2338.70 | − | 334.666i | 0.164025 | − | 0.0234717i | ||||
\(589\) | 7869.77 | 0.550541 | ||||||||
\(590\) | 2010.01 | + | 18071.8i | 0.140256 | + | 1.26103i | ||||
\(591\) | 18388.4 | + | 15772.7i | 1.27986 | + | 1.09781i | ||||
\(592\) | −3687.27 | − | 2128.85i | −0.255990 | − | 0.147796i | ||||
\(593\) | −2724.14 | + | 1572.78i | −0.188646 | + | 0.108915i | −0.591349 | − | 0.806416i | \(-0.701404\pi\) |
0.402703 | + | 0.915331i | \(0.368071\pi\) | |||||||
\(594\) | 3735.97 | + | 2322.23i | 0.258062 | + | 0.160408i | ||||
\(595\) | −13816.9 | − | 7744.47i | −0.951999 | − | 0.533600i | ||||
\(596\) | 1469.67i | 0.101007i | ||||||||
\(597\) | −6781.30 | − | 19279.7i | −0.464892 | − | 1.32171i | ||||
\(598\) | 2914.28 | − | 5047.67i | 0.199287 | − | 0.345175i | ||||
\(599\) | 4106.12 | + | 2370.67i | 0.280086 | + | 0.161708i | 0.633462 | − | 0.773773i | \(-0.281633\pi\) |
−0.353376 | + | 0.935481i | \(0.614966\pi\) | |||||||
\(600\) | −13826.0 | − | 7329.28i | −0.940742 | − | 0.498695i | ||||
\(601\) | − | 14984.2i | − | 1.01700i | −0.861061 | − | 0.508501i | \(-0.830200\pi\) | ||
0.861061 | − | 0.508501i | \(-0.169800\pi\) | |||||||
\(602\) | 8544.30 | + | 18851.0i | 0.578471 | + | 1.27626i | ||||
\(603\) | 811.292 | − | 2086.99i | 0.0547900 | − | 0.140943i | ||||
\(604\) | −1436.06 | − | 2487.32i | −0.0967423 | − | 0.167563i | ||||
\(605\) | 10659.5 | − | 7843.52i | 0.716314 | − | 0.527081i | ||||
\(606\) | 7583.38 | + | 6504.68i | 0.508339 | + | 0.436031i | ||||
\(607\) | 6373.16 | + | 11038.6i | 0.426159 | + | 0.738130i | 0.996528 | − | 0.0832593i | \(-0.0265330\pi\) |
−0.570369 | + | 0.821389i | \(0.693200\pi\) | |||||||
\(608\) | − | 2830.01i | − | 0.188770i | ||||||
\(609\) | 9015.81 | + | 9414.40i | 0.599900 | + | 0.626421i | ||||
\(610\) | −1944.80 | + | 4440.18i | −0.129087 | + | 0.294718i | ||||
\(611\) | −5861.57 | + | 3384.18i | −0.388108 | + | 0.224074i | ||||
\(612\) | 1713.90 | + | 2134.95i | 0.113203 | + | 0.141013i | ||||
\(613\) | −21008.0 | − | 12129.0i | −1.38419 | − | 0.799160i | −0.391534 | − | 0.920164i | \(-0.628055\pi\) |
−0.992652 | + | 0.121003i | \(0.961389\pi\) | |||||||
\(614\) | 6504.94 | + | 11266.9i | 0.427554 | + | 0.740545i | ||||
\(615\) | 13470.5 | − | 19765.5i | 0.883223 | − | 1.29597i | ||||
\(616\) | −3153.69 | + | 4402.19i | −0.206275 | + | 0.287937i | ||||
\(617\) | 14325.6 | 0.934731 | 0.467365 | − | 0.884064i | \(-0.345203\pi\) | ||||
0.467365 | + | 0.884064i | \(0.345203\pi\) | |||||||
\(618\) | 23540.7 | − | 8280.07i | 1.53228 | − | 0.538954i | ||||
\(619\) | −5631.07 | − | 3251.10i | −0.365641 | − | 0.211103i | 0.305911 | − | 0.952060i | \(-0.401039\pi\) |
−0.671552 | + | 0.740957i | \(0.734372\pi\) | |||||||
\(620\) | −1449.23 | − | 1969.53i | −0.0938748 | − | 0.127578i | ||||
\(621\) | 9688.64 | + | 315.399i | 0.626073 | + | 0.0203809i | ||||
\(622\) | 15950.0 | 1.02820 | ||||||||
\(623\) | −16458.0 | + | 7459.67i | −1.05839 | + | 0.479719i | ||||
\(624\) | 1614.86 | − | 8611.03i | 0.103599 | − | 0.552431i | ||||
\(625\) | 14116.2 | − | 6698.71i | 0.903439 | − | 0.428717i | ||||
\(626\) | 4460.19 | − | 7725.27i | 0.284768 | − | 0.493233i | ||||
\(627\) | −2283.08 | − | 1958.32i | −0.145419 | − | 0.124734i | ||||
\(628\) | 236.516 | + | 409.658i | 0.0150287 | + | 0.0260304i | ||||
\(629\) | −6307.20 | −0.399817 | ||||||||
\(630\) | −11147.2 | + | 9184.51i | −0.704945 | + | 0.580825i | ||||
\(631\) | 10656.1 | 0.672285 | 0.336142 | − | 0.941811i | \(-0.390878\pi\) | ||||
0.336142 | + | 0.941811i | \(0.390878\pi\) | |||||||
\(632\) | −8153.31 | − | 14121.9i | −0.513166 | − | 0.888830i | ||||
\(633\) | −20636.6 | − | 17701.2i | −1.29579 | − | 1.11147i | ||||
\(634\) | −8263.00 | + | 14311.9i | −0.517612 | + | 0.896530i | ||||
\(635\) | −22956.1 | + | 2553.25i | −1.43462 | + | 0.159563i | ||||
\(636\) | 415.409 | − | 2215.12i | 0.0258994 | − | 0.138106i | ||||
\(637\) | −10984.9 | − | 2182.01i | −0.683263 | − | 0.135721i | ||||
\(638\) | −4247.03 | −0.263545 | ||||||||
\(639\) | 23775.7 | − | 3662.39i | 1.47191 | − | 0.226732i | ||||
\(640\) | 8902.60 | − | 6550.75i | 0.549853 | − | 0.404596i | ||||
\(641\) | 868.420 | + | 501.383i | 0.0535110 | + | 0.0308946i | 0.526517 | − | 0.850165i | \(-0.323498\pi\) |
−0.473006 | + | 0.881059i | \(0.656831\pi\) | |||||||
\(642\) | 15525.5 | − | 5460.84i | 0.954427 | − | 0.335704i | ||||
\(643\) | 1055.62 | 0.0647429 | 0.0323715 | − | 0.999476i | \(-0.489694\pi\) | ||||
0.0323715 | + | 0.999476i | \(0.489694\pi\) | |||||||
\(644\) | −166.040 | + | 1688.12i | −0.0101598 | + | 0.103294i | ||||
\(645\) | 20765.9 | + | 14152.3i | 1.26769 | + | 0.863946i | ||||
\(646\) | 4713.08 | + | 8163.29i | 0.287049 | + | 0.497183i | ||||
\(647\) | −2003.89 | − | 1156.95i | −0.121764 | − | 0.0703004i | 0.437881 | − | 0.899033i | \(-0.355729\pi\) |
−0.559645 | + | 0.828733i | \(0.689062\pi\) | |||||||
\(648\) | 16749.3 | − | 5285.52i | 1.01539 | − | 0.320424i | ||||
\(649\) | 6616.53 | − | 3820.06i | 0.400187 | − | 0.231048i | ||||
\(650\) | 7149.88 | + | 7750.13i | 0.431448 | + | 0.467669i | ||||
\(651\) | −15422.3 | + | 3776.99i | −0.928494 | + | 0.227391i | ||||
\(652\) | − | 890.862i | − | 0.0535105i | ||||||
\(653\) | −816.618 | − | 1414.42i | −0.0489383 | − | 0.0847637i | 0.840519 | − | 0.541783i | \(-0.182250\pi\) |
−0.889457 | + | 0.457019i | \(0.848917\pi\) | |||||||
\(654\) | −12938.8 | − | 11098.3i | −0.773620 | − | 0.663576i | ||||
\(655\) | 3419.65 | − | 2516.26i | 0.203995 | − | 0.150104i | ||||
\(656\) | 10630.5 | + | 18412.5i | 0.632699 | + | 1.09587i | ||||
\(657\) | 8543.28 | + | 3321.10i | 0.507314 | + | 0.197212i | ||||
\(658\) | −5776.04 | + | 8062.71i | −0.342209 | + | 0.477686i | ||||
\(659\) | 1872.37i | 0.110679i | 0.998468 | + | 0.0553394i | \(0.0176241\pi\) | ||||
−0.998468 | + | 0.0553394i | \(0.982376\pi\) | |||||||
\(660\) | −69.6681 | + | 932.003i | −0.00410883 | + | 0.0549669i | ||||
\(661\) | 14858.1 | + | 8578.34i | 0.874303 | + | 0.504779i | 0.868776 | − | 0.495206i | \(-0.164907\pi\) |
0.00552696 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(662\) | −11906.0 | + | 20621.8i | −0.699003 | + | 1.21071i | ||||
\(663\) | −4306.34 | − | 12243.2i | −0.252254 | − | 0.717174i | ||||
\(664\) | 16474.3i | 0.962844i | ||||||||
\(665\) | 8489.60 | − | 5046.60i | 0.495056 | − | 0.294284i | ||||
\(666\) | −2083.87 | + | 5360.60i | −0.121244 | + | 0.311890i | ||||
\(667\) | −8105.23 | + | 4679.56i | −0.470519 | + | 0.271654i | ||||
\(668\) | 617.213 | + | 356.348i | 0.0357495 | + | 0.0206400i | ||||
\(669\) | −19501.0 | − | 16727.1i | −1.12698 | − | 0.966676i | ||||
\(670\) | −2380.72 | + | 264.792i | −0.137276 | + | 0.0152684i | ||||
\(671\) | 2036.75 | 0.117180 | ||||||||
\(672\) | 1358.22 | + | 5545.95i | 0.0779681 | + | 0.318362i | ||||
\(673\) | 3231.50i | 0.185090i | 0.995709 | + | 0.0925448i | \(0.0295001\pi\) | ||||
−0.995709 | + | 0.0925448i | \(0.970500\pi\) | |||||||
\(674\) | 7571.47 | − | 4371.39i | 0.432703 | − | 0.249821i | ||||
\(675\) | −5759.08 | + | 16564.4i | −0.328396 | + | 0.944540i | ||||
\(676\) | −749.516 | + | 1298.20i | −0.0426443 | + | 0.0738621i | ||||
\(677\) | 14559.6 | − | 8406.00i | 0.826546 | − | 0.477206i | −0.0261229 | − | 0.999659i | \(-0.508316\pi\) |
0.852668 | + | 0.522452i | \(0.174983\pi\) | |||||||
\(678\) | 835.867 | − | 4457.16i | 0.0473470 | − | 0.252472i | ||||
\(679\) | −3073.40 | + | 31247.2i | −0.173706 | + | 1.76606i | ||||
\(680\) | 8266.80 | − | 18873.9i | 0.466202 | − | 1.06439i | ||||
\(681\) | −366.327 | − | 1041.49i | −0.0206134 | − | 0.0586050i | ||||
\(682\) | 2586.65 | − | 4480.20i | 0.145231 | − | 0.251548i | ||||
\(683\) | −14648.5 | + | 25371.9i | −0.820656 | + | 1.42142i | 0.0845383 | + | 0.996420i | \(0.473058\pi\) |
−0.905194 | + | 0.424998i | \(0.860275\pi\) | |||||||
\(684\) | −1687.19 | + | 259.894i | −0.0943149 | + | 0.0145282i | ||||
\(685\) | 7033.66 | + | 3080.75i | 0.392325 | + | 0.171838i | ||||
\(686\) | −15981.3 | + | 3733.02i | −0.889459 | + | 0.207766i | ||||
\(687\) | −11314.5 | − | 2121.85i | −0.628350 | − | 0.117837i | ||||
\(688\) | −19344.5 | + | 11168.5i | −1.07195 | + | 0.618890i | ||||
\(689\) | −5341.91 | + | 9252.46i | −0.295371 | + | 0.511597i | ||||
\(690\) | −4501.26 | − | 9342.47i | −0.248348 | − | 0.515452i | ||||
\(691\) | −23145.1 | + | 13362.8i | −1.27421 | + | 0.735668i | −0.975778 | − | 0.218762i | \(-0.929798\pi\) |
−0.298436 | + | 0.954430i | \(0.596465\pi\) | |||||||
\(692\) | 237.512i | 0.0130475i | ||||||||
\(693\) | 5414.01 | + | 2741.98i | 0.296769 | + | 0.150302i | ||||
\(694\) | 3746.90 | 0.204943 | ||||||||
\(695\) | 34482.2 | − | 3835.22i | 1.88199 | − | 0.209321i | ||||
\(696\) | −11040.1 | + | 12870.9i | −0.601255 | + | 0.700964i | ||||
\(697\) | 27275.7 | + | 15747.6i | 1.48227 | + | 0.855788i | ||||
\(698\) | 1082.16 | − | 624.783i | 0.0586823 | − | 0.0338802i | ||||
\(699\) | 1610.32 | − | 8586.83i | 0.0871357 | − | 0.464641i | ||||
\(700\) | −2826.36 | − | 1195.31i | −0.152609 | − | 0.0645408i | ||||
\(701\) | 16227.9i | 0.874351i | 0.899376 | + | 0.437176i | \(0.144021\pi\) | ||||
−0.899376 | + | 0.437176i | \(0.855979\pi\) | |||||||
\(702\) | −11828.5 | − | 385.059i | −0.635951 | − | 0.0207024i | ||||
\(703\) | 1966.37 | − | 3405.85i | 0.105495 | − | 0.182723i | ||||
\(704\) | −5953.03 | − | 3436.99i | −0.318698 | − | 0.184000i | ||||
\(705\) | −897.678 | + | 12008.9i | −0.0479553 | + | 0.641535i | ||||
\(706\) | − | 24377.6i | − | 1.29952i | ||||||
\(707\) | 11205.0 | + | 8027.17i | 0.596052 | + | 0.427005i | ||||
\(708\) | 799.218 | − | 4261.74i | 0.0424244 | − | 0.226223i | ||||
\(709\) | −11759.5 | − | 20368.1i | −0.622903 | − | 1.07890i | −0.988942 | − | 0.148300i | \(-0.952620\pi\) |
0.366040 | − | 0.930599i | \(-0.380713\pi\) | |||||||
\(710\) | −15252.3 | − | 20728.2i | −0.806209 | − | 1.09565i | ||||
\(711\) | −14250.6 | + | 11440.2i | −0.751672 | + | 0.603432i | ||||
\(712\) | −11753.2 | − | 20357.1i | −0.618637 | − | 1.07151i | ||||
\(713\) | − | 11400.3i | − | 0.598801i | ||||||
\(714\) | −13154.0 | − | 13735.6i | −0.689465 | − | 0.719945i | ||||
\(715\) | 1777.53 | − | 4058.27i | 0.0929731 | − | 0.212267i | ||||
\(716\) | 5395.90 | − | 3115.32i | 0.281640 | − | 0.162605i | ||||
\(717\) | −7727.41 | + | 9008.88i | −0.402490 | + | 0.469237i | ||||
\(718\) | −5061.42 | − | 2922.21i | −0.263078 | − | 0.151888i | ||||
\(719\) | −1621.03 | − | 2807.70i | −0.0840808 | − | 0.145632i | 0.820918 | − | 0.571046i | \(-0.193462\pi\) |
−0.904999 | + | 0.425413i | \(0.860129\pi\) | |||||||
\(720\) | −11042.3 | − | 11002.5i | −0.571559 | − | 0.569497i | ||||
\(721\) | 31356.9 | − | 14212.7i | 1.61969 | − | 0.734129i | ||||
\(722\) | 11842.7 | 0.610442 | ||||||||
\(723\) | −1287.74 | − | 3661.13i | −0.0662403 | − | 0.188325i | ||||
\(724\) | 4789.57 | + | 2765.26i | 0.245860 | + | 0.141948i | ||||
\(725\) | −3720.36 | − | 16517.8i | −0.190580 | − | 0.846146i | ||||
\(726\) | 14990.1 | − | 5272.53i | 0.766303 | − | 0.269535i | ||||
\(727\) | 20213.6 | 1.03120 | 0.515599 | − | 0.856830i | \(-0.327569\pi\) | ||||
0.515599 | + | 0.856830i | \(0.327569\pi\) | |||||||
\(728\) | 1426.11 | − | 14499.2i | 0.0726033 | − | 0.738156i | ||||
\(729\) | −8712.03 | − | 17650.0i | −0.442617 | − | 0.896711i | ||||
\(730\) | −1083.95 | − | 9745.70i | −0.0549572 | − | 0.494116i | ||||
\(731\) | −16544.7 | + | 28656.2i | −0.837110 | + | 1.44992i | ||||
\(732\) | 752.577 | − | 877.380i | 0.0380001 | − | 0.0443018i | ||||
\(733\) | −14370.5 | − | 24890.4i | −0.724128 | − | 1.25423i | −0.959332 | − | 0.282280i | \(-0.908909\pi\) |
0.235204 | − | 0.971946i | \(-0.424424\pi\) | |||||||
\(734\) | 26268.2 | 1.32095 | ||||||||
\(735\) | −14215.0 | + | 13964.2i | −0.713370 | + | 0.700787i | ||||
\(736\) | −4099.61 | −0.205317 | ||||||||
\(737\) | 503.241 | + | 871.638i | 0.0251521 | + | 0.0435647i | ||||
\(738\) | 22395.9 | − | 17979.1i | 1.11708 | − | 0.896776i | ||||
\(739\) | 9414.85 | − | 16307.0i | 0.468648 | − | 0.811722i | −0.530710 | − | 0.847554i | \(-0.678075\pi\) |
0.999358 | + | 0.0358313i | \(0.0114079\pi\) | |||||||
\(740\) | −1214.47 | + | 135.078i | −0.0603309 | + | 0.00671021i | ||||
\(741\) | 7953.81 | + | 1491.60i | 0.394319 | + | 0.0739480i | ||||
\(742\) | −1532.47 | + | 15580.6i | −0.0758204 | + | 0.770864i | ||||
\(743\) | 5459.90 | 0.269589 | 0.134794 | − | 0.990874i | \(-0.456963\pi\) | ||||
0.134794 | + | 0.990874i | \(0.456963\pi\) | |||||||
\(744\) | −6853.61 | − | 19485.2i | −0.337723 | − | 0.960166i | ||||
\(745\) | −7346.58 | − | 9984.15i | −0.361286 | − | 0.490995i | ||||
\(746\) | −23173.6 | − | 13379.3i | −1.13733 | − | 0.656637i | ||||
\(747\) | 18247.2 | − | 2810.80i | 0.893750 | − | 0.137673i | ||||
\(748\) | −1230.62 | −0.0601552 | ||||||||
\(749\) | 20680.4 | − | 9373.47i | 1.00887 | − | 0.457275i | ||||
\(750\) | 18558.8 | − | 2746.52i | 0.903562 | − | 0.133719i | ||||
\(751\) | 7568.95 | + | 13109.8i | 0.367769 | + | 0.636995i | 0.989216 | − | 0.146461i | \(-0.0467882\pi\) |
−0.621447 | + | 0.783456i | \(0.713455\pi\) | |||||||
\(752\) | −9270.01 | − | 5352.04i | −0.449525 | − | 0.259533i | ||||
\(753\) | −13890.5 | − | 11914.7i | −0.672243 | − | 0.576620i | ||||
\(754\) | 9895.37 | − | 5713.10i | 0.477942 | − | 0.275940i | ||||
\(755\) | 22189.4 | + | 9718.99i | 1.06961 | + | 0.468490i | ||||
\(756\) | 3181.65 | − | 1319.06i | 0.153063 | − | 0.0634572i | ||||
\(757\) | 17650.3i | 0.847441i | 0.905793 | + | 0.423720i | \(0.139276\pi\) | ||||
−0.905793 | + | 0.423720i | \(0.860724\pi\) | |||||||
\(758\) | 8056.42 | + | 13954.1i | 0.386045 | + | 0.668650i | ||||
\(759\) | −2836.87 | + | 3307.32i | −0.135668 | + | 0.158166i | ||||
\(760\) | 7614.49 | + | 10348.2i | 0.363430 | + | 0.493908i | ||||
\(761\) | 5364.99 | + | 9292.43i | 0.255559 | + | 0.442642i | 0.965047 | − | 0.262076i | \(-0.0844071\pi\) |
−0.709488 | + | 0.704718i | \(0.751074\pi\) | |||||||
\(762\) | −27258.1 | − | 5111.81i | −1.29588 | − | 0.243020i | ||||
\(763\) | −19118.1 | − | 13696.0i | −0.907106 | − | 0.649841i | ||||
\(764\) | 5211.42i | 0.246783i | ||||||||
\(765\) | −22315.5 | − | 5936.23i | −1.05467 | − | 0.280555i | ||||
\(766\) | −8848.71 | − | 5108.81i | −0.417385 | − | 0.240977i | ||||
\(767\) | −10277.5 | + | 17801.1i | −0.483830 | + | 0.838019i | ||||
\(768\) | −9691.19 | + | 3408.72i | −0.455340 | + | 0.160158i | ||||
\(769\) | − | 9715.37i | − | 0.455585i | −0.973710 | − | 0.227793i | \(-0.926849\pi\) | ||
0.973710 | − | 0.227793i | \(-0.0731508\pi\) | |||||||
\(770\) | −82.6177 | − | 6491.78i | −0.00386667 | − | 0.303828i | ||||
\(771\) | −40334.1 | − | 7563.99i | −1.88404 | − | 0.353321i | ||||
\(772\) | 2179.33 | − | 1258.23i | 0.101601 | − | 0.0586591i | ||||
\(773\) | 31321.2 | + | 18083.3i | 1.45737 | + | 0.841412i | 0.998881 | − | 0.0472884i | \(-0.0150580\pi\) |
0.458488 | + | 0.888701i | \(0.348391\pi\) | |||||||
\(774\) | 18889.1 | + | 23529.5i | 0.877203 | + | 1.09270i | ||||
\(775\) | 19690.6 | + | 6135.53i | 0.912653 | + | 0.284380i | ||||
\(776\) | −40844.8 | −1.88949 | ||||||||
\(777\) | −2218.89 | + | 7618.14i | −0.102448 | + | 0.351737i | ||||
\(778\) | 648.149i | 0.0298679i | ||||||||
\(779\) | −17007.2 | + | 9819.13i | −0.782217 | + | 0.451613i | ||||
\(780\) | −1091.41 | − | 2265.24i | −0.0501008 | − | 0.103985i | ||||
\(781\) | −5406.56 | + | 9364.44i | −0.247711 | + | 0.429047i | ||||
\(782\) | 11825.5 | − | 6827.46i | 0.540767 | − | 0.312212i | ||||
\(783\) | 16139.6 | + | 10032.2i | 0.736633 | + | 0.457881i | ||||
\(784\) | −5697.77 | − | 16770.5i | −0.259556 | − | 0.763961i | ||||
\(785\) | −3654.56 | − | 1600.70i | −0.166162 | − | 0.0727789i | ||||
\(786\) | 4808.95 | − | 1691.47i | 0.218231 | − | 0.0767592i | ||||
\(787\) | −6252.10 | + | 10829.0i | −0.283181 | + | 0.490484i | −0.972166 | − | 0.234291i | \(-0.924723\pi\) |
0.688985 | + | 0.724775i | \(0.258056\pi\) | |||||||
\(788\) | −3090.12 | + | 5352.25i | −0.139697 | + | 0.241962i | ||||
\(789\) | −2537.60 | + | 892.559i | −0.114501 | + | 0.0402737i | ||||
\(790\) | 17907.5 | + | 7843.48i | 0.806479 | + | 0.353239i | ||||
\(791\) | 612.406 | − | 6226.32i | 0.0275280 | − | 0.279876i | ||||
\(792\) | −2860.44 | + | 7358.28i | −0.128335 | + | 0.330133i | ||||
\(793\) | −4745.54 | + | 2739.84i | −0.212508 | + | 0.122692i | ||||
\(794\) | 9330.07 | − | 16160.2i | 0.417017 | − | 0.722295i | ||||
\(795\) | 8250.87 | + | 17124.9i | 0.368086 | + | 0.763971i | ||||
\(796\) | 4515.20 | − | 2606.85i | 0.201052 | − | 0.116077i | ||||
\(797\) | − | 4447.92i | − | 0.197683i | −0.995103 | − | 0.0988415i | \(-0.968486\pi\) | ||
0.995103 | − | 0.0988415i | \(-0.0315137\pi\) | |||||||
\(798\) | 11518.1 | − | 2820.82i | 0.510947 | − | 0.125133i | ||||
\(799\) | −15856.7 | −0.702088 | ||||||||
\(800\) | 2206.37 | − | 7080.82i | 0.0975085 | − | 0.312931i | ||||
\(801\) | −20542.6 | + | 16491.3i | −0.906163 | + | 0.727454i | ||||
\(802\) | −22575.5 | − | 13033.9i | −0.993974 | − | 0.573871i | ||||
\(803\) | −3568.13 | + | 2060.06i | −0.156808 | + | 0.0905331i | ||||
\(804\) | 561.426 | + | 105.286i | 0.0246268 | + | 0.00461836i | ||||
\(805\) | −7310.60 | − | 12298.2i | −0.320081 | − | 0.538453i | ||||
\(806\) | 13918.2i | 0.608248i | ||||||||
\(807\) | 11685.5 | − | 4110.19i | 0.509726 | − | 0.179288i | ||||
\(808\) | −8965.38 | + | 15528.5i | −0.390348 | + | 0.676102i | ||||
\(809\) | −22616.3 | − | 13057.5i | −0.982875 | − | 0.567463i | −0.0797384 | − | 0.996816i | \(-0.525409\pi\) |
−0.903137 | + | 0.429352i | \(0.858742\pi\) | |||||||
\(810\) | −12418.2 | + | 17005.0i | −0.538682 | + | 0.737649i | ||||
\(811\) | − | 33688.6i | − | 1.45865i | −0.684166 | − | 0.729327i | \(-0.739833\pi\) | ||
0.684166 | − | 0.729327i | \(-0.260167\pi\) | |||||||
\(812\) | −1936.58 | + | 2703.24i | −0.0836952 | + | 0.116829i | ||||
\(813\) | −7936.41 | − | 1488.34i | −0.342364 | − | 0.0642047i | ||||
\(814\) | −1292.61 | − | 2238.87i | −0.0556586 | − | 0.0964036i | ||||
\(815\) | 4453.24 | + | 6052.04i | 0.191399 | + | 0.260115i | ||||
\(816\) | 13363.2 | − | 15579.3i | 0.573290 | − | 0.668361i | ||||
\(817\) | −10316.1 | − | 17868.0i | −0.441756 | − | 0.765144i | ||||
\(818\) | − | 11039.6i | − | 0.471870i | ||||||
\(819\) | −16302.9 | + | 894.228i | −0.695567 | + | 0.0381524i | ||||
\(820\) | 5589.28 | + | 2448.11i | 0.238032 | + | 0.104258i | ||||
\(821\) | −15513.4 | + | 8956.66i | −0.659465 | + | 0.380742i | −0.792073 | − | 0.610426i | \(-0.790998\pi\) |
0.132608 | + | 0.991169i | \(0.457665\pi\) | |||||||
\(822\) | 6998.14 | + | 6002.69i | 0.296944 | + | 0.254705i | ||||
\(823\) | 18081.6 | + | 10439.4i | 0.765837 | + | 0.442156i | 0.831388 | − | 0.555693i | \(-0.187547\pi\) |
−0.0655503 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(824\) | 22393.0 | + | 38785.8i | 0.946719 | + | 1.63976i | ||||
\(825\) | −4185.61 | − | 6679.79i | −0.176635 | − | 0.281891i | ||||
\(826\) | −2948.37 | + | 29976.0i | −0.124197 | + | 1.26271i | ||||
\(827\) | −28982.3 | −1.21864 | −0.609319 | − | 0.792925i | \(-0.708557\pi\) | ||||
−0.609319 | + | 0.792925i | \(0.708557\pi\) | |||||||
\(828\) | 376.488 | + | 2444.10i | 0.0158018 | + | 0.102583i | ||||
\(829\) | 11443.1 | + | 6606.65i | 0.479414 | + | 0.276790i | 0.720172 | − | 0.693795i | \(-0.244063\pi\) |
−0.240758 | + | 0.970585i | \(0.577396\pi\) | |||||||
\(830\) | −11705.7 | − | 15908.3i | −0.489533 | − | 0.665285i | ||||
\(831\) | 1547.58 | + | 4399.85i | 0.0646027 | + | 0.183669i | ||||
\(832\) | 18493.7 | 0.770618 | ||||||||
\(833\) | −19731.3 | − | 17294.6i | −0.820706 | − | 0.719356i | ||||
\(834\) | 40944.2 | + | 7678.41i | 1.69998 | + | 0.318803i | ||||
\(835\) | −5974.33 | + | 664.485i | −0.247605 | + | 0.0275394i | ||||
\(836\) | 383.666 | − | 664.528i | 0.0158724 | − | 0.0274919i | ||||
\(837\) | −20412.8 | + | 10915.7i | −0.842975 | + | 0.450778i | ||||
\(838\) | −1703.77 | − | 2951.02i | −0.0702337 | − | 0.121648i | ||||
\(839\) | −2177.04 | −0.0895824 | −0.0447912 | − | 0.998996i | \(-0.514262\pi\) | ||||
−0.0447912 | + | 0.998996i | \(0.514262\pi\) | |||||||
\(840\) | −19888.6 | − | 16624.9i | −0.816930 | − | 0.682874i | ||||
\(841\) | 6041.55 | 0.247716 | ||||||||
\(842\) | −6081.95 | − | 10534.3i | −0.248929 | − | 0.431157i | ||||
\(843\) | 760.920 | − | 887.107i | 0.0310884 | − | 0.0362439i | ||||
\(844\) | 3467.93 | − | 6006.63i | 0.141435 | − | 0.244973i | ||||
\(845\) | −1397.63 | − | 12566.0i | −0.0568993 | − | 0.511576i | ||||
\(846\) | −5238.97 | + | 13476.8i | −0.212907 | + | 0.547687i | ||||
\(847\) | 19967.3 | − | 9050.25i | 0.810016 | − | 0.367143i | ||||
\(848\) | −16896.3 | −0.684225 | ||||||||
\(849\) | 641.502 | − | 225.638i | 0.0259320 | − | 0.00912117i | ||||
\(850\) | 5427.99 | + | 24099.4i | 0.219033 | + | 0.972475i | ||||
\(851\) | −4933.78 | − | 2848.52i | −0.198740 | − | 0.114743i | ||||
\(852\) | 2036.24 | + | 5789.16i | 0.0818785 | + | 0.232786i | ||||
\(853\) | −42546.6 | −1.70782 | −0.853909 | − | 0.520423i | \(-0.825774\pi\) | ||||
−0.853909 | + | 0.520423i | \(0.825774\pi\) | |||||||
\(854\) | −4676.29 | + | 6527.58i | −0.187376 | + | 0.261557i | ||||
\(855\) | 10162.7 | − | 10199.5i | 0.406500 | − | 0.407972i | ||||
\(856\) | 14768.5 | + | 25579.8i | 0.589693 | + | 1.02138i | ||||
\(857\) | −31839.1 | − | 18382.3i | −1.26908 | − | 0.732705i | −0.294268 | − | 0.955723i | \(-0.595076\pi\) |
−0.974814 | + | 0.223018i | \(0.928409\pi\) | |||||||
\(858\) | 3463.43 | − | 4037.78i | 0.137808 | − | 0.160661i | ||||
\(859\) | −9893.25 | + | 5711.87i | −0.392961 | + | 0.226876i | −0.683442 | − | 0.730005i | \(-0.739518\pi\) |
0.290481 | + | 0.956881i | \(0.406185\pi\) | |||||||
\(860\) | −2572.02 | + | 5872.18i | −0.101983 | + | 0.232837i | ||||
\(861\) | 28616.4 | − | 27404.9i | 1.13269 | − | 1.08473i | ||||
\(862\) | − | 28648.3i | − | 1.13198i | ||||||
\(863\) | −10052.6 | − | 17411.5i | −0.396516 | − | 0.686785i | 0.596778 | − | 0.802407i | \(-0.296447\pi\) |
−0.993293 | + | 0.115621i | \(0.963114\pi\) | |||||||
\(864\) | 3925.33 | + | 7340.54i | 0.154563 | + | 0.289040i | ||||
\(865\) | −1187.28 | − | 1613.53i | −0.0466689 | − | 0.0634239i | ||||
\(866\) | 501.093 | + | 867.919i | 0.0196626 | + | 0.0340567i | ||||
\(867\) | 898.889 | − | 4793.22i | 0.0352109 | − | 0.187758i | ||||
\(868\) | −1672.19 | − | 3689.31i | −0.0653893 | − | 0.144266i | ||||
\(869\) | − | 8214.31i | − | 0.320658i | ||||||
\(870\) | 1515.44 | − | 20273.2i | 0.0590554 | − | 0.790029i | ||||
\(871\) | −2345.05 | − | 1353.92i | −0.0912275 | − | 0.0526702i | ||||
\(872\) | 15296.8 | − | 26494.8i | 0.594053 | − | 1.02893i | ||||
\(873\) | 6968.81 | + | 45240.4i | 0.270170 | + | 1.75390i | ||||
\(874\) | 8514.26i | 0.329518i | ||||||||
\(875\) | 25175.9 | − | 6008.06i | 0.972686 | − | 0.232125i | ||||
\(876\) | −430.999 | + | 2298.25i | −0.0166234 | + | 0.0886424i | ||||
\(877\) | 16336.0 | − | 9431.61i | 0.628995 | − | 0.363150i | −0.151368 | − | 0.988477i | \(-0.548368\pi\) |
0.780363 | + | 0.625327i | \(0.215034\pi\) | |||||||
\(878\) | 3440.14 | + | 1986.17i | 0.132231 | + | 0.0763438i | ||||
\(879\) | −10087.1 | + | 11759.9i | −0.387064 | + | 0.451252i | ||||
\(880\) | 6963.82 | − | 774.540i | 0.266762 | − | 0.0296701i | ||||
\(881\) | 32703.4 | 1.25063 | 0.625316 | − | 0.780372i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780372i | \(0.284970\pi\) | |||||||
\(882\) | −21218.1 | + | 11055.9i | −0.810035 | + | 0.422076i | ||||
\(883\) | 12412.4i | 0.473058i | 0.971624 | + | 0.236529i | \(0.0760099\pi\) | ||||
−0.971624 | + | 0.236529i | \(0.923990\pi\) | |||||||
\(884\) | 2867.30 | − | 1655.43i | 0.109092 | − | 0.0629845i | ||||
\(885\) | 15874.1 | + | 32947.1i | 0.602940 | + | 1.25142i | ||||
\(886\) | 1409.68 | − | 2441.63i | 0.0534526 | − | 0.0925827i | ||||
\(887\) | 15934.5 | − | 9199.81i | 0.603190 | − | 0.348252i | −0.167106 | − | 0.985939i | \(-0.553442\pi\) |
0.770295 | + | 0.637687i | \(0.220109\pi\) | |||||||
\(888\) | −10145.2 | − | 1902.56i | −0.383390 | − | 0.0718985i | ||||
\(889\) | −38077.5 | − | 3745.22i | −1.43653 | − | 0.141294i | ||||
\(890\) | 25814.0 | + | 11306.6i | 0.972234 | + | 0.425839i | ||||
\(891\) | 8638.18 | + | 1912.83i | 0.324792 | + | 0.0719216i | ||||
\(892\) | 3277.09 | − | 5676.08i | 0.123010 | − | 0.213060i | ||||
\(893\) | 4943.56 | − | 8562.49i | 0.185252 | − | 0.320865i | ||||
\(894\) | −4938.49 | − | 14040.4i | −0.184751 | − | 0.525259i | ||||
\(895\) | −21084.0 | + | 48136.8i | −0.787441 | + | 1.79781i | ||||
\(896\) | 16676.3 | − | 7558.59i | 0.621781 | − | 0.281824i | ||||
\(897\) | 2160.77 | − | 11522.0i | 0.0804303 | − | 0.428885i | ||||
\(898\) | 17494.9 | − | 10100.7i | 0.650124 | − | 0.375349i | ||||
\(899\) | 11174.5 | − | 19354.8i | 0.414561 | − | 0.718040i | ||||
\(900\) | −4424.06 | − | 665.121i | −0.163854 | − | 0.0246341i | ||||
\(901\) | −21676.3 | + | 12514.8i | −0.801491 | + | 0.462741i | ||||
\(902\) | 12909.4i | 0.476538i | ||||||||
\(903\) | 28791.9 | + | 30064.8i | 1.06106 | + | 1.10797i | ||||
\(904\) | 8138.74 | 0.299436 | ||||||||
\(905\) | −46360.7 | + | 5156.40i | −1.70285 | + | 0.189397i | ||||
\(906\) | 22077.4 | + | 18937.0i | 0.809572 | + | 0.694414i | ||||
\(907\) | 25348.0 | + | 14634.7i | 0.927968 | + | 0.535763i | 0.886168 | − | 0.463363i | \(-0.153358\pi\) |
0.0417996 | + | 0.999126i | \(0.486691\pi\) | |||||||
\(908\) | 243.912 | − | 140.823i | 0.00891465 | − | 0.00514688i | ||||
\(909\) | 18729.2 | + | 7280.78i | 0.683399 | + | 0.265664i | ||||
\(910\) | 8925.24 | + | 15014.4i | 0.325130 | + | 0.546948i | ||||
\(911\) | 42129.2i | 1.53217i | 0.642742 | + | 0.766083i | \(0.277797\pi\) | ||||
−0.642742 | + | 0.766083i | \(0.722203\pi\) | |||||||
\(912\) | 4246.51 | + | 12073.1i | 0.154184 | + | 0.438355i | ||||
\(913\) | −4149.40 | + | 7186.97i | −0.150411 | + | 0.260519i | ||||
\(914\) | −9630.73 | − | 5560.30i | −0.348530 | − | 0.201224i | ||||
\(915\) | −726.761 | + | 9722.44i | −0.0262579 | + | 0.351272i | ||||
\(916\) | − | 2936.71i | − | 0.105930i | ||||||
\(917\) | 6405.66 | − | 2903.39i | 0.230680 | − | 0.104557i | ||||
\(918\) | −23547.7 | − | 14636.9i | −0.846612 | − | 0.526242i | ||||
\(919\) | 16255.3 | + | 28154.9i | 0.583473 | + | 1.01060i | 0.995064 | + | 0.0992359i | \(0.0316399\pi\) |
−0.411591 | + | 0.911369i | \(0.635027\pi\) | |||||||
\(920\) | 14990.7 | − | 11030.5i | 0.537205 | − | 0.395288i | ||||
\(921\) | 19861.2 | + | 17036.0i | 0.710584 | + | 0.609507i | ||||
\(922\) | 2317.86 | + | 4014.66i | 0.0827926 | + | 0.143401i | ||||
\(923\) | − | 29091.6i | − | 1.03745i | ||||||
\(924\) | −432.936 | + | 1486.41i | −0.0154140 | + | 0.0529212i | ||||
\(925\) | 7575.25 | − | 6988.55i | 0.269268 | − | 0.248413i | ||||
\(926\) | 2009.36 | − | 1160.10i | 0.0713083 | − | 0.0411699i | ||||
\(927\) | 39139.1 | − | 31420.3i | 1.38673 | − | 1.11324i | ||||
\(928\) | −6960.07 | − | 4018.40i | −0.246202 | − | 0.142145i | ||||
\(929\) | −27011.6 | − | 46785.4i | −0.953951 | − | 1.65229i | −0.736750 | − | 0.676166i | \(-0.763640\pi\) |
−0.217202 | − | 0.976127i | \(-0.569693\pi\) | |||||||
\(930\) | 20463.3 | + | 13946.0i | 0.721524 | + | 0.491728i | ||||
\(931\) | 15490.5 | − | 5262.89i | 0.545307 | − | 0.185268i | ||||
\(932\) | 2228.73 | 0.0783310 | ||||||||
\(933\) | 30262.7 | − | 10644.4i | 1.06190 | − | 0.373508i | ||||
\(934\) | 9550.01 | + | 5513.70i | 0.334567 | + | 0.193163i | ||||
\(935\) | 8360.20 | − | 6151.64i | 0.292415 | − | 0.215166i | ||||
\(936\) | −3233.65 | − | 20992.3i | −0.112922 | − | 0.733072i | ||||
\(937\) | −45989.7 | −1.60343 | −0.801716 | − | 0.597705i | \(-0.796080\pi\) | ||||
−0.801716 | + | 0.597705i | \(0.796080\pi\) | |||||||
\(938\) | −3948.93 | − | 388.408i | −0.137460 | − | 0.0135202i | ||||
\(939\) | 3306.97 | − | 17634.0i | 0.114930 | − | 0.612849i | ||||
\(940\) | −3053.25 | + | 339.593i | −0.105943 | + | 0.0117833i | ||||
\(941\) | 22403.8 | − | 38804.6i | 0.776137 | − | 1.34431i | −0.158017 | − | 0.987436i | \(-0.550510\pi\) |
0.934153 | − | 0.356872i | \(-0.116157\pi\) | |||||||
\(942\) | −3636.10 | − | 3118.89i | −0.125765 | − | 0.107876i | ||||
\(943\) | 14224.2 | + | 24637.0i | 0.491202 | + | 0.850786i | ||||
\(944\) | −32507.4 | −1.12079 | ||||||||
\(945\) | −15020.7 | + | 24865.4i | −0.517062 | + | 0.855948i | ||||
\(946\) | −13562.8 | −0.466137 | ||||||||
\(947\) | 14870.7 | + | 25756.8i | 0.510278 | + | 0.883827i | 0.999929 | + | 0.0119085i | \(0.00379070\pi\) |
−0.489651 | + | 0.871918i | \(0.662876\pi\) | |||||||
\(948\) | −3538.51 | − | 3035.18i | −0.121230 | − | 0.103985i | ||||
\(949\) | 5542.39 | − | 9599.70i | 0.189582 | − | 0.328366i | ||||
\(950\) | −14705.8 | − | 4582.29i | −0.502230 | − | 0.156494i | ||||
\(951\) | −6126.55 | + | 32669.1i | −0.208903 | + | 1.11395i | ||||
\(952\) | 19877.6 | − | 27746.9i | 0.676718 | − | 0.944624i | ||||
\(953\) | 49096.6 | 1.66883 | 0.834415 | − | 0.551136i | \(-0.185806\pi\) | ||||
0.834415 | + | 0.551136i | \(0.185806\pi\) | |||||||
\(954\) | 3474.81 | + | 22557.9i | 0.117926 | + | 0.765555i | ||||
\(955\) | −26050.8 | − | 35403.6i | −0.882707 | − | 1.19962i | ||||
\(956\) | −2622.18 | − | 1513.92i | −0.0887107 | − | 0.0512171i | ||||
\(957\) | −8058.07 | + | 2834.30i | −0.272184 | + | 0.0957365i | ||||
\(958\) | 4923.04 | 0.166030 | ||||||||
\(959\) | 10340.3 | + | 7407.68i | 0.348181 | + | 0.249433i | ||||
\(960\) | 18530.6 | − | 27190.4i | 0.622994 | − | 0.914132i | ||||
\(961\) | −1283.89 | − | 2223.76i | −0.0430965 | − | 0.0746453i | ||||
\(962\) | 6023.46 | + | 3477.65i | 0.201875 | + | 0.116553i | ||||
\(963\) | 25812.8 | − | 20722.2i | 0.863767 | − | 0.693419i | ||||
\(964\) | 857.419 | − | 495.031i | 0.0286469 | − | 0.0165393i | ||||
\(965\) | −8515.52 | + | 19441.8i | −0.284067 | + | 0.648553i | ||||
\(966\) | −4086.30 | − | 16685.3i | −0.136102 | − | 0.555737i | ||||
\(967\) | − | 3589.62i | − | 0.119374i | −0.998217 | − | 0.0596868i | \(-0.980990\pi\) | ||
0.998217 | − | 0.0596868i | \(-0.0190102\pi\) | |||||||
\(968\) | 14259.3 | + | 24697.8i | 0.473461 | + | 0.820058i | ||||
\(969\) | 14390.2 | + | 12343.3i | 0.477069 | + | 0.409208i | ||||
\(970\) | 39441.6 | − | 29022.1i | 1.30556 | − | 0.960662i | ||||
\(971\) | −13191.9 | − | 22849.1i | −0.435993 | − | 0.755162i | 0.561383 | − | 0.827556i | \(-0.310269\pi\) |
−0.997376 | + | 0.0723940i | \(0.976936\pi\) | |||||||
\(972\) | 4015.80 | − | 3014.32i | 0.132517 | − | 0.0994695i | ||||
\(973\) | 57196.0 | + | 5625.66i | 1.88450 | + | 0.185355i | ||||
\(974\) | 39149.9i | 1.28793i | ||||||||
\(975\) | 18737.9 | + | 9933.12i | 0.615480 | + | 0.326271i | ||||
\(976\) | −7505.01 | − | 4333.02i | −0.246137 | − | 0.142107i | ||||
\(977\) | 6508.74 | − | 11273.5i | 0.213135 | − | 0.369161i | −0.739559 | − | 0.673092i | \(-0.764966\pi\) |
0.952694 | + | 0.303931i | \(0.0982992\pi\) | |||||||
\(978\) | 2993.54 | + | 8510.81i | 0.0978761 | + | 0.278268i | ||||
\(979\) | − | 11841.1i | − | 0.386562i | ||||||
\(980\) | −4169.71 | − | 2907.56i | −0.135915 | − | 0.0947741i | ||||
\(981\) | −31956.0 | − | 12422.5i | −1.04004 | − | 0.404302i | ||||
\(982\) | −22916.5 | + | 13230.8i | −0.744698 | + | 0.429952i | ||||
\(983\) | −21833.3 | − | 12605.5i | −0.708418 | − | 0.409006i | 0.102057 | − | 0.994779i | \(-0.467458\pi\) |
−0.810475 | + | 0.585773i | \(0.800791\pi\) | |||||||
\(984\) | 39123.0 | + | 33557.9i | 1.26747 | + | 1.08718i | ||||
\(985\) | −5762.17 | − | 51807.2i | −0.186394 | − | 1.67585i | ||||
\(986\) | 26768.9 | 0.864599 | ||||||||
\(987\) | −5578.41 | + | 19152.4i | −0.179901 | + | 0.617659i | ||||
\(988\) | 2064.43i | 0.0664758i | ||||||||
\(989\) | −25884.0 | + | 14944.1i | −0.832217 | + | 0.480481i | ||||
\(990\) | −2466.21 | − | 9137.95i | −0.0791731 | − | 0.293357i | ||||
\(991\) | −8240.66 | + | 14273.2i | −0.264151 | + | 0.457522i | −0.967341 | − | 0.253480i | \(-0.918425\pi\) |
0.703190 | + | 0.711002i | \(0.251758\pi\) | |||||||
\(992\) | 8478.04 | − | 4894.80i | 0.271349 | − | 0.156663i | ||||
\(993\) | −8827.62 | + | 47072.2i | −0.282111 | + | 1.50432i | ||||
\(994\) | −17598.9 | − | 38827.8i | −0.561571 | − | 1.23898i | ||||
\(995\) | −17642.7 | + | 40280.1i | −0.562123 | + | 1.28338i | ||||
\(996\) | 1562.76 | + | 4443.03i | 0.0497170 | + | 0.141348i | ||||
\(997\) | −14621.2 | + | 25324.6i | −0.464451 | + | 0.804452i | −0.999177 | − | 0.0405732i | \(-0.987082\pi\) |
0.534726 | + | 0.845026i | \(0.320415\pi\) | |||||||
\(998\) | −4048.39 | + | 7012.01i | −0.128406 | + | 0.222406i | ||||
\(999\) | −376.370 | + | 11561.6i | −0.0119198 | + | 0.366159i |
(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 | 105.4.p.a.59.14 | yes | 88 | |
3.2 | odd | 2 | inner | 105.4.p.a.59.32 | yes | 88 | |
5.4 | even | 2 | inner | 105.4.p.a.59.31 | yes | 88 | |
7.5 | odd | 6 | inner | 105.4.p.a.89.13 | yes | 88 | |
15.14 | odd | 2 | inner | 105.4.p.a.59.13 | ✓ | 88 | |
21.5 | even | 6 | inner | 105.4.p.a.89.31 | yes | 88 | |
35.19 | odd | 6 | inner | 105.4.p.a.89.32 | yes | 88 | |
105.89 | even | 6 | inner | 105.4.p.a.89.14 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.p.a.59.13 | ✓ | 88 | 15.14 | odd | 2 | inner | |
105.4.p.a.59.14 | yes | 88 | 1.1 | even | 1 | trivial | |
105.4.p.a.59.31 | yes | 88 | 5.4 | even | 2 | inner | |
105.4.p.a.59.32 | yes | 88 | 3.2 | odd | 2 | inner | |
105.4.p.a.89.13 | yes | 88 | 7.5 | odd | 6 | inner | |
105.4.p.a.89.14 | yes | 88 | 105.89 | even | 6 | inner | |
105.4.p.a.89.31 | yes | 88 | 21.5 | even | 6 | inner | |
105.4.p.a.89.32 | yes | 88 | 35.19 | odd | 6 | inner |