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 | 11.2 | ||
Character | \(\chi\) | \(=\) | 43.11 |
Dual form | 43.4.e.a.4.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{7}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32023 | − | 2.90947i | −0.820324 | − | 1.02865i | −0.998998 | − | 0.0447453i | \(-0.985752\pi\) |
0.178675 | − | 0.983908i | \(-0.442819\pi\) | |||||||
\(3\) | 3.61377 | − | 4.53152i | 0.695470 | − | 0.872091i | −0.301206 | − | 0.953559i | \(-0.597389\pi\) |
0.996676 | + | 0.0814675i | \(0.0259607\pi\) | |||||||
\(4\) | −1.30141 | + | 5.70184i | −0.162676 | + | 0.712730i | ||||
\(5\) | 13.3469 | − | 6.42753i | 1.19378 | − | 0.574896i | 0.271886 | − | 0.962330i | \(-0.412353\pi\) |
0.921897 | + | 0.387434i | \(0.126639\pi\) | |||||||
\(6\) | −21.5691 | −1.46759 | ||||||||
\(7\) | −12.2090 | −0.659222 | −0.329611 | − | 0.944117i | \(-0.606918\pi\) | ||||
−0.329611 | + | 0.944117i | \(0.606918\pi\) | |||||||
\(8\) | −7.21369 | + | 3.47393i | −0.318803 | + | 0.153527i | ||||
\(9\) | −1.46730 | − | 6.42866i | −0.0543444 | − | 0.238099i | ||||
\(10\) | −49.6685 | − | 23.9191i | −1.57066 | − | 0.756389i | ||||
\(11\) | −0.456732 | − | 2.00108i | −0.0125191 | − | 0.0548497i | 0.968283 | − | 0.249858i | \(-0.0803839\pi\) |
−0.980802 | + | 0.195008i | \(0.937527\pi\) | |||||||
\(12\) | 21.1350 | + | 26.5025i | 0.508430 | + | 0.637551i | ||||
\(13\) | −8.58668 | + | 4.13513i | −0.183194 | + | 0.0882214i | −0.523232 | − | 0.852190i | \(-0.675274\pi\) |
0.340039 | + | 0.940411i | \(0.389560\pi\) | |||||||
\(14\) | 28.3276 | + | 35.5216i | 0.540776 | + | 0.678111i | ||||
\(15\) | 19.1061 | − | 83.7093i | 0.328878 | − | 1.44091i | ||||
\(16\) | 68.9990 | + | 33.2282i | 1.07811 | + | 0.519190i | ||||
\(17\) | 66.7975 | + | 32.1680i | 0.952987 | + | 0.458934i | 0.844732 | − | 0.535189i | \(-0.179760\pi\) |
0.108254 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(18\) | −15.2995 | + | 19.1850i | −0.200341 | + | 0.251219i | ||||
\(19\) | 22.9418 | − | 100.515i | 0.277011 | − | 1.21367i | −0.624540 | − | 0.780993i | \(-0.714713\pi\) |
0.901551 | − | 0.432673i | \(-0.142429\pi\) | |||||||
\(20\) | 19.2790 | + | 84.4667i | 0.215546 | + | 0.944367i | ||||
\(21\) | −44.1203 | + | 55.3252i | −0.458469 | + | 0.574902i | ||||
\(22\) | −4.76235 | + | 5.97180i | −0.0461516 | + | 0.0578723i | ||||
\(23\) | 32.7067 | + | 143.298i | 0.296514 | + | 1.29911i | 0.875279 | + | 0.483619i | \(0.160678\pi\) |
−0.578764 | + | 0.815495i | \(0.696465\pi\) | |||||||
\(24\) | −10.3264 | + | 45.2429i | −0.0878279 | + | 0.384799i | ||||
\(25\) | 58.8904 | − | 73.8462i | 0.471123 | − | 0.590770i | ||||
\(26\) | 31.9541 | + | 15.3883i | 0.241027 | + | 0.116073i | ||||
\(27\) | 106.561 | + | 51.3171i | 0.759544 | + | 0.365777i | ||||
\(28\) | 15.8888 | − | 69.6136i | 0.107240 | − | 0.469847i | ||||
\(29\) | −63.7295 | − | 79.9142i | −0.408078 | − | 0.511714i | 0.534742 | − | 0.845015i | \(-0.320409\pi\) |
−0.942820 | + | 0.333302i | \(0.891837\pi\) | |||||||
\(30\) | −287.880 | + | 138.636i | −1.75198 | + | 0.843711i | ||||
\(31\) | −192.150 | − | 240.949i | −1.11326 | − | 1.39599i | −0.908860 | − | 0.417102i | \(-0.863046\pi\) |
−0.204404 | − | 0.978887i | \(-0.565526\pi\) | |||||||
\(32\) | −49.1638 | − | 215.401i | −0.271594 | − | 1.18993i | ||||
\(33\) | −10.7184 | − | 5.16173i | −0.0565406 | − | 0.0272285i | ||||
\(34\) | −61.3935 | − | 268.982i | −0.309673 | − | 1.35677i | ||||
\(35\) | −162.952 | + | 78.4735i | −0.786968 | + | 0.378984i | ||||
\(36\) | 38.5648 | 0.178541 | ||||||||
\(37\) | 434.968 | 1.93266 | 0.966329 | − | 0.257312i | \(-0.0828367\pi\) | ||||
0.966329 | + | 0.257312i | \(0.0828367\pi\) | |||||||
\(38\) | −345.675 | + | 166.468i | −1.47568 | + | 0.710650i | ||||
\(39\) | −12.2918 | + | 53.8541i | −0.0504685 | + | 0.221117i | ||||
\(40\) | −73.9516 | + | 92.7324i | −0.292319 | + | 0.366557i | ||||
\(41\) | 114.686 | + | 143.812i | 0.436853 | + | 0.547797i | 0.950711 | − | 0.310079i | \(-0.100355\pi\) |
−0.513857 | + | 0.857876i | \(0.671784\pi\) | |||||||
\(42\) | 263.336 | 0.967468 | ||||||||
\(43\) | −177.188 | + | 219.343i | −0.628393 | + | 0.777896i | ||||
\(44\) | 12.0042 | 0.0411296 | ||||||||
\(45\) | −60.9043 | − | 76.3716i | −0.201757 | − | 0.252996i | ||||
\(46\) | 341.033 | − | 427.642i | 1.09310 | − | 1.37070i | ||||
\(47\) | −77.5868 | + | 339.930i | −0.240791 | + | 1.05498i | 0.699507 | + | 0.714626i | \(0.253403\pi\) |
−0.940299 | + | 0.340351i | \(0.889454\pi\) | |||||||
\(48\) | 399.921 | − | 192.592i | 1.20257 | − | 0.579129i | ||||
\(49\) | −193.941 | −0.565426 | ||||||||
\(50\) | −351.492 | −0.994171 | ||||||||
\(51\) | 387.160 | − | 186.447i | 1.06301 | − | 0.511917i | ||||
\(52\) | −12.4031 | − | 54.3414i | −0.0330768 | − | 0.144919i | ||||
\(53\) | 180.020 | + | 86.6931i | 0.466560 | + | 0.224683i | 0.652367 | − | 0.757903i | \(-0.273776\pi\) |
−0.185808 | + | 0.982586i | \(0.559490\pi\) | |||||||
\(54\) | −97.9402 | − | 429.104i | −0.246814 | − | 1.08136i | ||||
\(55\) | −18.9579 | − | 23.7725i | −0.0464779 | − | 0.0582815i | ||||
\(56\) | 88.0717 | − | 42.4131i | 0.210162 | − | 0.101209i | ||||
\(57\) | −372.578 | − | 467.198i | −0.865774 | − | 1.08565i | ||||
\(58\) | −84.6414 | + | 370.838i | −0.191620 | + | 0.839542i | ||||
\(59\) | 141.395 | + | 68.0921i | 0.312001 | + | 0.150252i | 0.583331 | − | 0.812235i | \(-0.301749\pi\) |
−0.271330 | + | 0.962486i | \(0.587463\pi\) | |||||||
\(60\) | 452.432 | + | 217.880i | 0.973480 | + | 0.468803i | ||||
\(61\) | −162.877 | + | 204.241i | −0.341872 | + | 0.428694i | −0.922811 | − | 0.385253i | \(-0.874114\pi\) |
0.580939 | + | 0.813947i | \(0.302686\pi\) | |||||||
\(62\) | −255.201 | + | 1118.11i | −0.522752 | + | 2.29033i | ||||
\(63\) | 17.9142 | + | 78.4873i | 0.0358251 | + | 0.156960i | ||||
\(64\) | −130.641 | + | 163.818i | −0.255158 | + | 0.319958i | ||||
\(65\) | −88.0269 | + | 110.382i | −0.167975 | + | 0.210634i | ||||
\(66\) | 9.85130 | + | 43.1614i | 0.0183729 | + | 0.0804969i | ||||
\(67\) | 9.64329 | − | 42.2500i | 0.0175838 | − | 0.0770397i | −0.965375 | − | 0.260867i | \(-0.915992\pi\) |
0.982959 | + | 0.183827i | \(0.0588487\pi\) | |||||||
\(68\) | −270.348 | + | 339.005i | −0.482124 | + | 0.604565i | ||||
\(69\) | 767.551 | + | 369.633i | 1.33916 | + | 0.644907i | ||||
\(70\) | 606.401 | + | 292.027i | 1.03541 | + | 0.498628i | ||||
\(71\) | 145.706 | − | 638.382i | 0.243552 | − | 1.06707i | −0.694205 | − | 0.719777i | \(-0.744244\pi\) |
0.937757 | − | 0.347293i | \(-0.112899\pi\) | |||||||
\(72\) | 32.9174 | + | 41.2771i | 0.0538798 | + | 0.0675632i | ||||
\(73\) | −782.604 | + | 376.882i | −1.25475 | + | 0.604257i | −0.938782 | − | 0.344512i | \(-0.888044\pi\) |
−0.315971 | + | 0.948769i | \(0.602330\pi\) | |||||||
\(74\) | −1009.22 | − | 1265.53i | −1.58540 | − | 1.98803i | ||||
\(75\) | −121.819 | − | 533.726i | −0.187553 | − | 0.821725i | ||||
\(76\) | 543.262 | + | 261.621i | 0.819953 | + | 0.394868i | ||||
\(77\) | 5.57623 | + | 24.4311i | 0.00825286 | + | 0.0361581i | ||||
\(78\) | 185.207 | − | 89.1909i | 0.268853 | − | 0.129473i | ||||
\(79\) | −1354.05 | −1.92838 | −0.964190 | − | 0.265213i | \(-0.914558\pi\) | ||||
−0.964190 | + | 0.265213i | \(0.914558\pi\) | |||||||
\(80\) | 1134.50 | 1.58551 | ||||||||
\(81\) | 778.038 | − | 374.683i | 1.06727 | − | 0.513969i | ||||
\(82\) | 152.319 | − | 667.353i | 0.205132 | − | 0.898742i | ||||
\(83\) | 103.976 | − | 130.382i | 0.137504 | − | 0.172425i | −0.708312 | − | 0.705900i | \(-0.750543\pi\) |
0.845816 | + | 0.533475i | \(0.179114\pi\) | |||||||
\(84\) | −258.037 | − | 323.568i | −0.335168 | − | 0.420287i | ||||
\(85\) | 1098.30 | 1.40150 | ||||||||
\(86\) | 1049.29 | + | 6.59766i | 1.31567 | + | 0.00827261i | ||||
\(87\) | −592.436 | −0.730067 | ||||||||
\(88\) | 10.2463 | + | 12.8485i | 0.0124121 | + | 0.0155642i | ||||
\(89\) | −741.413 | + | 929.702i | −0.883029 | + | 1.10728i | 0.110519 | + | 0.993874i | \(0.464749\pi\) |
−0.993548 | + | 0.113410i | \(0.963823\pi\) | |||||||
\(90\) | −80.8892 | + | 354.399i | −0.0947385 | + | 0.415077i | ||||
\(91\) | 104.834 | − | 50.4856i | 0.120765 | − | 0.0581575i | ||||
\(92\) | −859.625 | −0.974153 | ||||||||
\(93\) | −1786.25 | −1.99167 | ||||||||
\(94\) | 1169.04 | − | 562.978i | 1.28273 | − | 0.617731i | ||||
\(95\) | −339.859 | − | 1489.02i | −0.367040 | − | 1.60811i | ||||
\(96\) | −1153.76 | − | 555.621i | −1.22662 | − | 0.590707i | ||||
\(97\) | 88.5766 | + | 388.079i | 0.0927174 | + | 0.406221i | 0.999894 | − | 0.0145276i | \(-0.00462444\pi\) |
−0.907177 | + | 0.420749i | \(0.861767\pi\) | |||||||
\(98\) | 449.987 | + | 564.266i | 0.463833 | + | 0.581628i | ||||
\(99\) | −12.1941 | + | 5.87235i | −0.0123793 | + | 0.00596155i | ||||
\(100\) | 344.419 | + | 431.888i | 0.344419 | + | 0.431888i | ||||
\(101\) | −131.921 | + | 577.982i | −0.129966 | + | 0.569420i | 0.867446 | + | 0.497531i | \(0.165760\pi\) |
−0.997413 | + | 0.0718889i | \(0.977097\pi\) | |||||||
\(102\) | −1440.76 | − | 693.834i | −1.39859 | − | 0.673527i | ||||
\(103\) | −580.377 | − | 279.495i | −0.555206 | − | 0.267373i | 0.135172 | − | 0.990822i | \(-0.456841\pi\) |
−0.690378 | + | 0.723449i | \(0.742556\pi\) | |||||||
\(104\) | 47.5765 | − | 59.6590i | 0.0448583 | − | 0.0562505i | ||||
\(105\) | −233.266 | + | 1022.00i | −0.216804 | + | 0.949880i | ||||
\(106\) | −165.456 | − | 724.911i | −0.151609 | − | 0.664241i | ||||
\(107\) | 134.091 | − | 168.144i | 0.121150 | − | 0.151917i | −0.717558 | − | 0.696499i | \(-0.754740\pi\) |
0.838708 | + | 0.544582i | \(0.183312\pi\) | |||||||
\(108\) | −431.282 | + | 540.810i | −0.384260 | + | 0.481847i | ||||
\(109\) | 333.055 | + | 1459.21i | 0.292669 | + | 1.28227i | 0.880796 | + | 0.473497i | \(0.157008\pi\) |
−0.588127 | + | 0.808769i | \(0.700134\pi\) | |||||||
\(110\) | −25.1787 | + | 110.315i | −0.0218245 | + | 0.0956194i | ||||
\(111\) | 1571.87 | − | 1971.07i | 1.34410 | − | 1.68545i | ||||
\(112\) | −842.407 | − | 405.682i | −0.710714 | − | 0.342262i | ||||
\(113\) | 393.620 | + | 189.558i | 0.327688 | + | 0.157806i | 0.590493 | − | 0.807043i | \(-0.298933\pi\) |
−0.262805 | + | 0.964849i | \(0.584648\pi\) | |||||||
\(114\) | −494.834 | + | 2168.01i | −0.406539 | + | 1.78116i | ||||
\(115\) | 1357.58 | + | 1702.36i | 1.10083 | + | 1.38040i | ||||
\(116\) | 538.596 | − | 259.374i | 0.431098 | − | 0.207606i | ||||
\(117\) | 39.1826 | + | 49.1334i | 0.0309609 | + | 0.0388238i | ||||
\(118\) | −129.956 | − | 569.373i | −0.101385 | − | 0.444195i | ||||
\(119\) | −815.528 | − | 392.738i | −0.628230 | − | 0.302540i | ||||
\(120\) | 152.975 | + | 670.226i | 0.116372 | + | 0.509858i | ||||
\(121\) | 1195.39 | − | 575.671i | 0.898117 | − | 0.432510i | ||||
\(122\) | 972.143 | 0.721424 | ||||||||
\(123\) | 1066.14 | 0.781547 | ||||||||
\(124\) | 1623.92 | − | 782.037i | 1.17606 | − | 0.566363i | ||||
\(125\) | −100.696 | + | 441.178i | −0.0720522 | + | 0.315681i | ||||
\(126\) | 186.791 | − | 234.229i | 0.132069 | − | 0.165609i | ||||
\(127\) | −970.572 | − | 1217.06i | −0.678144 | − | 0.850366i | 0.317037 | − | 0.948413i | \(-0.397312\pi\) |
−0.995182 | + | 0.0980468i | \(0.968741\pi\) | |||||||
\(128\) | −987.780 | −0.682096 | ||||||||
\(129\) | 353.642 | + | 1595.59i | 0.241368 | + | 1.08902i | ||||
\(130\) | 525.396 | 0.354464 | ||||||||
\(131\) | −173.437 | − | 217.483i | −0.115674 | − | 0.145051i | 0.720623 | − | 0.693327i | \(-0.243856\pi\) |
−0.836297 | + | 0.548276i | \(0.815284\pi\) | |||||||
\(132\) | 43.3804 | − | 54.3973i | 0.0286044 | − | 0.0358688i | ||||
\(133\) | −280.096 | + | 1227.18i | −0.182612 | + | 0.800075i | ||||
\(134\) | −145.300 | + | 69.9727i | −0.0936716 | + | 0.0451099i | ||||
\(135\) | 1752.10 | 1.11701 | ||||||||
\(136\) | −593.606 | −0.374274 | ||||||||
\(137\) | 1595.33 | − | 768.268i | 0.994875 | − | 0.479106i | 0.135679 | − | 0.990753i | \(-0.456679\pi\) |
0.859196 | + | 0.511647i | \(0.170964\pi\) | |||||||
\(138\) | −705.455 | − | 3090.80i | −0.435161 | − | 1.90657i | ||||
\(139\) | 921.701 | + | 443.868i | 0.562429 | + | 0.270851i | 0.693422 | − | 0.720532i | \(-0.256102\pi\) |
−0.130993 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(140\) | −235.376 | − | 1031.25i | −0.142092 | − | 0.622547i | ||||
\(141\) | 1260.02 | + | 1580.01i | 0.752573 | + | 0.943696i | ||||
\(142\) | −2195.43 | + | 1057.26i | −1.29744 | + | 0.624813i | ||||
\(143\) | 12.1965 | + | 15.2939i | 0.00713233 | + | 0.00894366i | ||||
\(144\) | 112.370 | − | 492.327i | 0.0650292 | − | 0.284911i | ||||
\(145\) | −1364.24 | − | 656.984i | −0.781339 | − | 0.376273i | ||||
\(146\) | 2912.35 | + | 1402.51i | 1.65087 | + | 0.795019i | ||||
\(147\) | −700.858 | + | 878.848i | −0.393237 | + | 0.493103i | ||||
\(148\) | −566.071 | + | 2480.12i | −0.314397 | + | 1.37746i | ||||
\(149\) | −495.013 | − | 2168.79i | −0.272168 | − | 1.19245i | −0.907448 | − | 0.420164i | \(-0.861973\pi\) |
0.635280 | − | 0.772282i | \(-0.280885\pi\) | |||||||
\(150\) | −1270.21 | + | 1592.80i | −0.691416 | + | 0.867008i | ||||
\(151\) | −469.748 | + | 589.045i | −0.253162 | + | 0.317456i | −0.892131 | − | 0.451778i | \(-0.850790\pi\) |
0.638968 | + | 0.769233i | \(0.279362\pi\) | |||||||
\(152\) | 183.686 | + | 804.780i | 0.0980189 | + | 0.429449i | ||||
\(153\) | 108.785 | − | 476.619i | 0.0574820 | − | 0.251845i | ||||
\(154\) | 58.1433 | − | 72.9094i | 0.0304242 | − | 0.0381507i | ||||
\(155\) | −4113.31 | − | 1980.87i | −2.13154 | − | 1.02650i | ||||
\(156\) | −291.071 | − | 140.172i | −0.149387 | − | 0.0719408i | ||||
\(157\) | −66.2721 | + | 290.357i | −0.0336885 | + | 0.147599i | −0.988975 | − | 0.148083i | \(-0.952690\pi\) |
0.955286 | + | 0.295682i | \(0.0955468\pi\) | |||||||
\(158\) | 3141.69 | + | 3939.56i | 1.58190 | + | 1.98363i | ||||
\(159\) | 1043.40 | − | 502.476i | 0.520422 | − | 0.250622i | ||||
\(160\) | −2040.68 | − | 2558.93i | −1.00831 | − | 1.26438i | ||||
\(161\) | −399.315 | − | 1749.52i | −0.195469 | − | 0.856404i | ||||
\(162\) | −2895.35 | − | 1394.33i | −1.40420 | − | 0.676227i | ||||
\(163\) | −666.080 | − | 2918.29i | −0.320070 | − | 1.40232i | −0.837427 | − | 0.546549i | \(-0.815941\pi\) |
0.517357 | − | 0.855770i | \(-0.326916\pi\) | |||||||
\(164\) | −969.247 | + | 466.765i | −0.461497 | + | 0.222245i | ||||
\(165\) | −176.235 | −0.0831508 | ||||||||
\(166\) | −620.589 | −0.290163 | ||||||||
\(167\) | 270.467 | − | 130.250i | 0.125325 | − | 0.0603536i | −0.370170 | − | 0.928964i | \(-0.620701\pi\) |
0.495496 | + | 0.868610i | \(0.334986\pi\) | |||||||
\(168\) | 126.075 | − | 552.369i | 0.0578981 | − | 0.253668i | ||||
\(169\) | −1313.18 | + | 1646.67i | −0.597713 | + | 0.749508i | ||||
\(170\) | −2548.30 | − | 3195.47i | −1.14968 | − | 1.44166i | ||||
\(171\) | −679.837 | −0.304026 | ||||||||
\(172\) | −1020.07 | − | 1295.75i | −0.452205 | − | 0.574420i | ||||
\(173\) | −1441.64 | −0.633559 | −0.316780 | − | 0.948499i | \(-0.602602\pi\) | ||||
−0.316780 | + | 0.948499i | \(0.602602\pi\) | |||||||
\(174\) | 1374.59 | + | 1723.68i | 0.598891 | + | 0.750986i | ||||
\(175\) | −718.991 | + | 901.586i | −0.310575 | + | 0.389448i | ||||
\(176\) | 34.9780 | − | 153.249i | 0.0149805 | − | 0.0656338i | ||||
\(177\) | 819.529 | − | 394.664i | 0.348020 | − | 0.167598i | ||||
\(178\) | 4425.19 | 1.86338 | ||||||||
\(179\) | 4500.30 | 1.87915 | 0.939576 | − | 0.342340i | \(-0.111219\pi\) | ||||
0.939576 | + | 0.342340i | \(0.111219\pi\) | |||||||
\(180\) | 514.720 | − | 247.876i | 0.213139 | − | 0.102642i | ||||
\(181\) | −707.636 | − | 3100.36i | −0.290598 | − | 1.27319i | −0.883696 | − | 0.468062i | \(-0.844952\pi\) |
0.593098 | − | 0.805130i | \(-0.297905\pi\) | |||||||
\(182\) | −390.126 | − | 187.875i | −0.158891 | − | 0.0765176i | ||||
\(183\) | 336.923 | + | 1476.16i | 0.136099 | + | 0.596288i | ||||
\(184\) | −733.742 | − | 920.083i | −0.293979 | − | 0.368638i | ||||
\(185\) | 5805.47 | − | 2795.77i | 2.30717 | − | 1.11108i | ||||
\(186\) | 4144.50 | + | 5197.04i | 1.63382 | + | 2.04874i | ||||
\(187\) | 33.8620 | − | 148.359i | 0.0132419 | − | 0.0580165i | ||||
\(188\) | −1837.25 | − | 884.775i | −0.712742 | − | 0.343239i | ||||
\(189\) | −1301.00 | − | 626.529i | −0.500708 | − | 0.241128i | ||||
\(190\) | −3543.71 | + | 4443.67i | −1.35309 | + | 1.69672i | ||||
\(191\) | −813.190 | + | 3562.82i | −0.308065 | + | 1.34972i | 0.549565 | + | 0.835451i | \(0.314794\pi\) |
−0.857629 | + | 0.514268i | \(0.828064\pi\) | |||||||
\(192\) | 270.241 | + | 1184.00i | 0.101578 | + | 0.445042i | ||||
\(193\) | 1408.47 | − | 1766.16i | 0.525304 | − | 0.658710i | −0.446422 | − | 0.894823i | \(-0.647302\pi\) |
0.971726 | + | 0.236112i | \(0.0758733\pi\) | |||||||
\(194\) | 923.588 | − | 1158.14i | 0.341803 | − | 0.428607i | ||||
\(195\) | 182.091 | + | 797.791i | 0.0668707 | + | 0.292980i | ||||
\(196\) | 252.397 | − | 1105.82i | 0.0919813 | − | 0.402996i | ||||
\(197\) | 218.286 | − | 273.721i | 0.0789452 | − | 0.0989942i | −0.740790 | − | 0.671736i | \(-0.765549\pi\) |
0.819736 | + | 0.572742i | \(0.194120\pi\) | |||||||
\(198\) | 45.3784 | + | 21.8531i | 0.0162874 | + | 0.00784360i | ||||
\(199\) | −3228.65 | − | 1554.83i | −1.15011 | − | 0.553866i | −0.241046 | − | 0.970514i | \(-0.577490\pi\) |
−0.909068 | + | 0.416648i | \(0.863205\pi\) | |||||||
\(200\) | −168.280 | + | 737.284i | −0.0594961 | + | 0.260669i | ||||
\(201\) | −156.608 | − | 196.380i | −0.0549567 | − | 0.0689135i | ||||
\(202\) | 1987.71 | − | 957.230i | 0.692350 | − | 0.333418i | ||||
\(203\) | 778.071 | + | 975.670i | 0.269014 | + | 0.337333i | ||||
\(204\) | 559.235 | + | 2450.17i | 0.191933 | + | 0.840913i | ||||
\(205\) | 2455.06 | + | 1182.30i | 0.836434 | + | 0.402806i | ||||
\(206\) | 533.424 | + | 2337.08i | 0.180415 | + | 0.790448i | ||||
\(207\) | 873.221 | − | 420.521i | 0.293203 | − | 0.141199i | ||||
\(208\) | −729.875 | −0.243307 | ||||||||
\(209\) | −211.616 | −0.0700371 | ||||||||
\(210\) | 3514.72 | − | 1692.60i | 1.15495 | − | 0.556193i | ||||
\(211\) | −145.390 | + | 636.996i | −0.0474364 | + | 0.207832i | −0.993092 | − | 0.117337i | \(-0.962564\pi\) |
0.945656 | + | 0.325169i | \(0.105421\pi\) | |||||||
\(212\) | −728.590 | + | 913.623i | −0.236037 | + | 0.295981i | ||||
\(213\) | −2366.29 | − | 2967.24i | −0.761200 | − | 0.954515i | ||||
\(214\) | −800.332 | −0.255652 | ||||||||
\(215\) | −955.076 | + | 4066.43i | −0.302956 | + | 1.28990i | ||||
\(216\) | −946.971 | −0.298302 | ||||||||
\(217\) | 2345.95 | + | 2941.73i | 0.733888 | + | 0.920267i | ||||
\(218\) | 3472.77 | − | 4354.71i | 1.07892 | − | 1.35293i | ||||
\(219\) | −1120.30 | + | 4908.35i | −0.345675 | + | 1.51450i | ||||
\(220\) | 160.219 | − | 77.1574i | 0.0490998 | − | 0.0236452i | ||||
\(221\) | −706.588 | −0.215069 | ||||||||
\(222\) | −9381.86 | −2.83635 | ||||||||
\(223\) | −273.947 | + | 131.926i | −0.0822639 | + | 0.0396162i | −0.474563 | − | 0.880221i | \(-0.657394\pi\) |
0.392299 | + | 0.919838i | \(0.371680\pi\) | |||||||
\(224\) | 600.239 | + | 2629.82i | 0.179041 | + | 0.784430i | ||||
\(225\) | −561.142 | − | 270.232i | −0.166264 | − | 0.0800687i | ||||
\(226\) | −361.776 | − | 1585.04i | −0.106482 | − | 0.466529i | ||||
\(227\) | −817.299 | − | 1024.86i | −0.238969 | − | 0.299658i | 0.647856 | − | 0.761763i | \(-0.275666\pi\) |
−0.886825 | + | 0.462105i | \(0.847094\pi\) | |||||||
\(228\) | 3148.76 | − | 1516.36i | 0.914614 | − | 0.440455i | ||||
\(229\) | −2986.87 | − | 3745.41i | −0.861912 | − | 1.08080i | −0.995957 | − | 0.0898278i | \(-0.971368\pi\) |
0.134046 | − | 0.990975i | \(-0.457203\pi\) | |||||||
\(230\) | 1803.05 | − | 7899.70i | 0.516913 | − | 2.26474i | ||||
\(231\) | 130.861 | + | 63.0193i | 0.0372728 | + | 0.0179496i | ||||
\(232\) | 737.341 | + | 355.085i | 0.208659 | + | 0.100485i | ||||
\(233\) | 233.278 | − | 292.521i | 0.0655903 | − | 0.0822476i | −0.747954 | − | 0.663751i | \(-0.768964\pi\) |
0.813544 | + | 0.581503i | \(0.197535\pi\) | |||||||
\(234\) | 52.0398 | − | 228.001i | 0.0145382 | − | 0.0636962i | ||||
\(235\) | 1149.37 | + | 5035.70i | 0.319048 | + | 1.39784i | ||||
\(236\) | −572.263 | + | 717.595i | −0.157844 | + | 0.197930i | ||||
\(237\) | −4893.20 | + | 6135.88i | −1.34113 | + | 1.68172i | ||||
\(238\) | 749.551 | + | 3284.00i | 0.204144 | + | 0.894411i | ||||
\(239\) | 911.572 | − | 3993.86i | 0.246714 | − | 1.08093i | −0.688052 | − | 0.725662i | \(-0.741534\pi\) |
0.934766 | − | 0.355264i | \(-0.115609\pi\) | |||||||
\(240\) | 4099.81 | − | 5141.00i | 1.10267 | − | 1.38271i | ||||
\(241\) | 5636.17 | + | 2714.24i | 1.50646 | + | 0.725475i | 0.991301 | − | 0.131618i | \(-0.0420171\pi\) |
0.515163 | + | 0.857092i | \(0.327731\pi\) | |||||||
\(242\) | −4448.48 | − | 2142.28i | −1.18165 | − | 0.569053i | ||||
\(243\) | 403.165 | − | 1766.38i | 0.106432 | − | 0.466311i | ||||
\(244\) | −952.580 | − | 1194.50i | −0.249929 | − | 0.313401i | ||||
\(245\) | −2588.51 | + | 1246.56i | −0.674996 | + | 0.325061i | ||||
\(246\) | −2473.68 | − | 3101.90i | −0.641122 | − | 0.803941i | ||||
\(247\) | 218.647 | + | 957.955i | 0.0563246 | + | 0.246774i | ||||
\(248\) | 2223.15 | + | 1070.61i | 0.569234 | + | 0.274129i | ||||
\(249\) | −215.082 | − | 942.338i | −0.0547401 | − | 0.239832i | ||||
\(250\) | 1517.23 | − | 730.661i | 0.383833 | − | 0.184844i | ||||
\(251\) | −404.137 | −0.101629 | −0.0508146 | − | 0.998708i | \(-0.516182\pi\) | ||||
−0.0508146 | + | 0.998708i | \(0.516182\pi\) | |||||||
\(252\) | −470.836 | −0.117698 | ||||||||
\(253\) | 271.811 | − | 130.897i | 0.0675439 | − | 0.0325274i | ||||
\(254\) | −1289.05 | + | 5647.70i | −0.318434 | + | 1.39515i | ||||
\(255\) | 3969.00 | − | 4976.97i | 0.974700 | − | 1.22223i | ||||
\(256\) | 3337.00 | + | 4184.47i | 0.814698 | + | 1.02160i | ||||
\(257\) | −2899.07 | −0.703655 | −0.351827 | − | 0.936065i | \(-0.614440\pi\) | ||||
−0.351827 | + | 0.936065i | \(0.614440\pi\) | |||||||
\(258\) | 3821.78 | − | 4731.03i | 0.922224 | − | 1.14163i | ||||
\(259\) | −5310.51 | −1.27405 | ||||||||
\(260\) | −514.823 | − | 645.568i | −0.122800 | − | 0.153986i | ||||
\(261\) | −420.231 | + | 526.953i | −0.0996615 | + | 0.124972i | ||||
\(262\) | −230.348 | + | 1009.22i | −0.0543166 | + | 0.237977i | ||||
\(263\) | −5275.61 | + | 2540.60i | −1.23691 | + | 0.595666i | −0.933973 | − | 0.357344i | \(-0.883682\pi\) |
−0.302940 | + | 0.953010i | \(0.597968\pi\) | |||||||
\(264\) | 95.2509 | 0.0222056 | ||||||||
\(265\) | 2959.93 | 0.686140 | ||||||||
\(266\) | 4220.33 | − | 2032.40i | 0.972801 | − | 0.468476i | ||||
\(267\) | 1533.67 | + | 6719.45i | 0.351532 | + | 1.54016i | ||||
\(268\) | 228.353 | + | 109.969i | 0.0520481 | + | 0.0250650i | ||||
\(269\) | −1474.19 | − | 6458.85i | −0.334137 | − | 1.46395i | −0.811038 | − | 0.584994i | \(-0.801097\pi\) |
0.476900 | − | 0.878957i | \(-0.341760\pi\) | |||||||
\(270\) | −4065.27 | − | 5097.69i | −0.916314 | − | 1.14902i | ||||
\(271\) | 3502.81 | − | 1686.86i | 0.785168 | − | 0.378117i | 0.00205593 | − | 0.999998i | \(-0.499346\pi\) |
0.783112 | + | 0.621881i | \(0.213631\pi\) | |||||||
\(272\) | 3540.08 | + | 4439.12i | 0.789150 | + | 0.989563i | ||||
\(273\) | 150.071 | − | 657.503i | 0.0332699 | − | 0.145765i | ||||
\(274\) | −5936.77 | − | 2859.00i | −1.30895 | − | 0.630359i | ||||
\(275\) | −174.669 | − | 84.1161i | −0.0383016 | − | 0.0184451i | ||||
\(276\) | −3106.48 | + | 3895.41i | −0.677494 | + | 0.849551i | ||||
\(277\) | −282.408 | + | 1237.31i | −0.0612571 | + | 0.268385i | −0.996277 | − | 0.0862104i | \(-0.972524\pi\) |
0.935020 | + | 0.354595i | \(0.115381\pi\) | |||||||
\(278\) | −847.134 | − | 3711.53i | −0.182761 | − | 0.800730i | ||||
\(279\) | −1267.04 | + | 1588.81i | −0.271883 | + | 0.340931i | ||||
\(280\) | 902.872 | − | 1132.17i | 0.192703 | − | 0.241642i | ||||
\(281\) | 287.652 | + | 1260.29i | 0.0610672 | + | 0.267553i | 0.996240 | − | 0.0866396i | \(-0.0276129\pi\) |
−0.935173 | + | 0.354193i | \(0.884756\pi\) | |||||||
\(282\) | 1673.48 | − | 7331.98i | 0.353383 | − | 1.54827i | ||||
\(283\) | −182.029 | + | 228.258i | −0.0382351 | + | 0.0479453i | −0.800581 | − | 0.599224i | \(-0.795476\pi\) |
0.762346 | + | 0.647169i | \(0.224047\pi\) | |||||||
\(284\) | 3450.33 | + | 1661.59i | 0.720913 | + | 0.347173i | ||||
\(285\) | −7975.69 | − | 3840.89i | −1.65768 | − | 0.798297i | ||||
\(286\) | 16.1986 | − | 70.9708i | 0.00334911 | − | 0.0146734i | ||||
\(287\) | −1400.20 | − | 1755.80i | −0.287983 | − | 0.361120i | ||||
\(288\) | −1312.60 | + | 632.115i | −0.268562 | + | 0.129332i | ||||
\(289\) | 363.922 | + | 456.344i | 0.0740733 | + | 0.0928850i | ||||
\(290\) | 1253.87 | + | 5493.57i | 0.253896 | + | 1.11239i | ||||
\(291\) | 2078.68 | + | 1001.04i | 0.418744 | + | 0.201657i | ||||
\(292\) | −1130.44 | − | 4952.76i | −0.226554 | − | 0.992598i | ||||
\(293\) | −4198.35 | + | 2021.82i | −0.837100 | + | 0.403126i | −0.802773 | − | 0.596285i | \(-0.796643\pi\) |
−0.0343267 | + | 0.999411i | \(0.510929\pi\) | |||||||
\(294\) | 4183.13 | 0.829814 | ||||||||
\(295\) | 2324.85 | 0.458840 | ||||||||
\(296\) | −3137.72 | + | 1511.05i | −0.616137 | + | 0.296716i | ||||
\(297\) | 54.0195 | − | 236.675i | 0.0105540 | − | 0.0462400i | ||||
\(298\) | −5161.50 | + | 6472.31i | −1.00335 | + | 1.25816i | ||||
\(299\) | −873.396 | − | 1095.20i | −0.168929 | − | 0.211830i | ||||
\(300\) | 3201.76 | 0.616178 | ||||||||
\(301\) | 2163.28 | − | 2677.95i | 0.414251 | − | 0.512806i | ||||
\(302\) | 2803.73 | 0.534227 | ||||||||
\(303\) | 2142.41 | + | 2686.49i | 0.406198 | + | 0.509357i | ||||
\(304\) | 4922.88 | − | 6173.10i | 0.928772 | − | 1.16464i | ||||
\(305\) | −861.134 | + | 3772.88i | −0.161667 | + | 0.708309i | ||||
\(306\) | −1639.11 | + | 789.356i | −0.306215 | + | 0.147466i | ||||
\(307\) | 4104.01 | 0.762959 | 0.381479 | − | 0.924377i | \(-0.375415\pi\) | ||||
0.381479 | + | 0.924377i | \(0.375415\pi\) | |||||||
\(308\) | −146.559 | −0.0271135 | ||||||||
\(309\) | −3363.88 | + | 1619.96i | −0.619303 | + | 0.298241i | ||||
\(310\) | 3780.54 | + | 16563.6i | 0.692646 | + | 3.03468i | ||||
\(311\) | −4819.98 | − | 2321.18i | −0.878829 | − | 0.423222i | −0.0606321 | − | 0.998160i | \(-0.519312\pi\) |
−0.818197 | + | 0.574939i | \(0.805026\pi\) | |||||||
\(312\) | −98.4158 | − | 431.188i | −0.0178580 | − | 0.0782410i | ||||
\(313\) | −1255.26 | − | 1574.04i | −0.226681 | − | 0.284250i | 0.655464 | − | 0.755226i | \(-0.272473\pi\) |
−0.882146 | + | 0.470977i | \(0.843902\pi\) | |||||||
\(314\) | 998.551 | − | 480.877i | 0.179463 | − | 0.0864250i | ||||
\(315\) | 743.578 | + | 932.418i | 0.133003 | + | 0.166780i | ||||
\(316\) | 1762.17 | − | 7720.55i | 0.313701 | − | 1.37441i | ||||
\(317\) | 3844.43 | + | 1851.38i | 0.681150 | + | 0.328025i | 0.742265 | − | 0.670106i | \(-0.233751\pi\) |
−0.0611153 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(318\) | −3882.87 | − | 1869.89i | −0.684718 | − | 0.329743i | ||||
\(319\) | −130.807 | + | 164.027i | −0.0229586 | + | 0.0287892i | ||||
\(320\) | −690.703 | + | 3026.17i | −0.120661 | + | 0.528650i | ||||
\(321\) | −277.377 | − | 1215.27i | −0.0482296 | − | 0.211308i | ||||
\(322\) | −4163.66 | + | 5221.07i | −0.720596 | + | 0.903599i | ||||
\(323\) | 4765.81 | − | 5976.14i | 0.820981 | − | 1.02948i | ||||
\(324\) | 1123.84 | + | 4923.86i | 0.192702 | + | 0.844284i | ||||
\(325\) | −200.309 | + | 877.613i | −0.0341882 | + | 0.149788i | ||||
\(326\) | −6945.22 | + | 8709.03i | −1.17994 | + | 1.47960i | ||||
\(327\) | 7816.02 | + | 3764.00i | 1.32180 | + | 0.636543i | ||||
\(328\) | −1326.90 | − | 639.003i | −0.223372 | − | 0.107570i | ||||
\(329\) | 947.254 | − | 4150.19i | 0.158735 | − | 0.695464i | ||||
\(330\) | 408.905 | + | 512.751i | 0.0682106 | + | 0.0855333i | ||||
\(331\) | −734.705 | + | 353.815i | −0.122003 | + | 0.0587536i | −0.493890 | − | 0.869525i | \(-0.664425\pi\) |
0.371887 | + | 0.928278i | \(0.378711\pi\) | |||||||
\(332\) | 608.100 | + | 762.534i | 0.100524 | + | 0.126053i | ||||
\(333\) | −638.229 | − | 2796.26i | −0.105029 | − | 0.460163i | ||||
\(334\) | −1006.50 | − | 484.706i | −0.164890 | − | 0.0794070i | ||||
\(335\) | −142.855 | − | 625.889i | −0.0232985 | − | 0.102078i | ||||
\(336\) | −4882.62 | + | 2351.34i | −0.792763 | + | 0.381775i | ||||
\(337\) | 8384.84 | 1.35534 | 0.677672 | − | 0.735364i | \(-0.262989\pi\) | ||||
0.677672 | + | 0.735364i | \(0.262989\pi\) | |||||||
\(338\) | 7837.80 | 1.26130 | ||||||||
\(339\) | 2281.44 | − | 1098.68i | 0.365518 | − | 0.176024i | ||||
\(340\) | −1429.34 | + | 6262.33i | −0.227990 | + | 0.998890i | ||||
\(341\) | −394.395 | + | 494.556i | −0.0626325 | + | 0.0785387i | ||||
\(342\) | 1577.38 | + | 1977.97i | 0.249400 | + | 0.312737i | ||||
\(343\) | 6555.50 | 1.03196 | ||||||||
\(344\) | 516.196 | − | 2197.81i | 0.0809053 | − | 0.344471i | ||||
\(345\) | 12620.2 | 1.96942 | ||||||||
\(346\) | 3344.93 | + | 4194.40i | 0.519724 | + | 0.651713i | ||||
\(347\) | 4755.65 | − | 5963.40i | 0.735726 | − | 0.922571i | −0.263387 | − | 0.964690i | \(-0.584840\pi\) |
0.999113 | + | 0.0421193i | \(0.0134110\pi\) | |||||||
\(348\) | 771.001 | − | 3377.98i | 0.118764 | − | 0.520341i | ||||
\(349\) | 1375.10 | − | 662.215i | 0.210910 | − | 0.101569i | −0.325446 | − | 0.945560i | \(-0.605515\pi\) |
0.536356 | + | 0.843992i | \(0.319800\pi\) | |||||||
\(350\) | 4291.36 | 0.655379 | ||||||||
\(351\) | −1127.21 | −0.171413 | ||||||||
\(352\) | −408.578 | + | 196.761i | −0.0618673 | + | 0.0297937i | ||||
\(353\) | −2501.08 | − | 10957.9i | −0.377107 | − | 1.65222i | −0.706270 | − | 0.707942i | \(-0.749624\pi\) |
0.329163 | − | 0.944273i | \(-0.393234\pi\) | |||||||
\(354\) | −3049.76 | − | 1468.69i | −0.457889 | − | 0.220508i | ||||
\(355\) | −2158.49 | − | 9456.95i | −0.322706 | − | 1.41387i | ||||
\(356\) | −4336.13 | − | 5437.34i | −0.645547 | − | 0.809490i | ||||
\(357\) | −4726.83 | + | 2276.32i | −0.700757 | + | 0.337467i | ||||
\(358\) | −10441.7 | − | 13093.5i | −1.54151 | − | 1.93300i | ||||
\(359\) | −873.046 | + | 3825.06i | −0.128350 | + | 0.562338i | 0.869328 | + | 0.494235i | \(0.164552\pi\) |
−0.997678 | + | 0.0681028i | \(0.978305\pi\) | |||||||
\(360\) | 704.654 | + | 339.343i | 0.103163 | + | 0.0496805i | ||||
\(361\) | −3397.13 | − | 1635.97i | −0.495280 | − | 0.238514i | ||||
\(362\) | −7378.53 | + | 9252.38i | −1.07129 | + | 1.34335i | ||||
\(363\) | 1711.21 | − | 7497.29i | 0.247425 | − | 1.08404i | ||||
\(364\) | 151.429 | + | 663.452i | 0.0218050 | + | 0.0955339i | ||||
\(365\) | −8022.92 | + | 10060.4i | −1.15052 | + | 1.44270i | ||||
\(366\) | 3513.10 | − | 4405.29i | 0.501729 | − | 0.629148i | ||||
\(367\) | −434.716 | − | 1904.61i | −0.0618310 | − | 0.270899i | 0.934557 | − | 0.355813i | \(-0.115796\pi\) |
−0.996388 | + | 0.0849132i | \(0.972939\pi\) | |||||||
\(368\) | −2504.79 | + | 10974.2i | −0.354812 | + | 1.55453i | ||||
\(369\) | 756.240 | − | 948.295i | 0.106689 | − | 0.133784i | ||||
\(370\) | −21604.2 | − | 10404.0i | −3.03554 | − | 1.46184i | ||||
\(371\) | −2197.86 | − | 1058.43i | −0.307566 | − | 0.148116i | ||||
\(372\) | 2324.64 | − | 10184.9i | 0.323997 | − | 1.41952i | ||||
\(373\) | −1801.29 | − | 2258.75i | −0.250047 | − | 0.313548i | 0.640929 | − | 0.767600i | \(-0.278549\pi\) |
−0.890975 | + | 0.454052i | \(0.849978\pi\) | |||||||
\(374\) | −510.214 | + | 245.706i | −0.0705415 | + | 0.0339710i | ||||
\(375\) | 1635.32 | + | 2050.62i | 0.225193 | + | 0.282383i | ||||
\(376\) | −621.206 | − | 2721.68i | −0.0852027 | − | 0.373298i | ||||
\(377\) | 877.680 | + | 422.668i | 0.119901 | + | 0.0577415i | ||||
\(378\) | 1195.75 | + | 5238.91i | 0.162705 | + | 0.712859i | ||||
\(379\) | −1984.04 | + | 955.464i | −0.268901 | + | 0.129496i | −0.563476 | − | 0.826133i | \(-0.690536\pi\) |
0.294575 | + | 0.955628i | \(0.404822\pi\) | |||||||
\(380\) | 8932.44 | 1.20585 | ||||||||
\(381\) | −9022.55 | −1.21323 | ||||||||
\(382\) | 12252.7 | − | 5900.59i | 1.64111 | − | 0.790315i | ||||
\(383\) | −3017.27 | + | 13219.5i | −0.402547 | + | 1.76367i | 0.214477 | + | 0.976729i | \(0.431195\pi\) |
−0.617024 | + | 0.786945i | \(0.711662\pi\) | |||||||
\(384\) | −3569.61 | + | 4476.15i | −0.474377 | + | 0.594850i | ||||
\(385\) | 231.457 | + | 290.237i | 0.0306393 | + | 0.0384204i | ||||
\(386\) | −8406.56 | −1.10850 | ||||||||
\(387\) | 1670.07 | + | 817.239i | 0.219366 | + | 0.107345i | ||||
\(388\) | −2328.04 | −0.304609 | ||||||||
\(389\) | 4156.14 | + | 5211.63i | 0.541709 | + | 0.679281i | 0.975059 | − | 0.221944i | \(-0.0712403\pi\) |
−0.433351 | + | 0.901225i | \(0.642669\pi\) | |||||||
\(390\) | 1898.66 | − | 2380.84i | 0.246519 | − | 0.309125i | ||||
\(391\) | −2424.87 | + | 10624.0i | −0.313634 | + | 1.37412i | ||||
\(392\) | 1399.03 | − | 673.738i | 0.180260 | − | 0.0868084i | ||||
\(393\) | −1612.29 | −0.206945 | ||||||||
\(394\) | −1302.86 | −0.166591 | ||||||||
\(395\) | −18072.3 | + | 8703.16i | −2.30207 | + | 1.10862i | ||||
\(396\) | −17.6138 | − | 77.1710i | −0.00223516 | − | 0.00979290i | ||||
\(397\) | −2666.65 | − | 1284.19i | −0.337117 | − | 0.162347i | 0.257664 | − | 0.966234i | \(-0.417047\pi\) |
−0.594781 | + | 0.803887i | \(0.702761\pi\) | |||||||
\(398\) | 2967.44 | + | 13001.2i | 0.373730 | + | 1.63742i | ||||
\(399\) | 4548.79 | + | 5704.00i | 0.570738 | + | 0.715682i | ||||
\(400\) | 6517.15 | − | 3138.50i | 0.814644 | − | 0.392312i | ||||
\(401\) | 322.281 | + | 404.127i | 0.0401345 | + | 0.0503271i | 0.801494 | − | 0.598003i | \(-0.204039\pi\) |
−0.761359 | + | 0.648330i | \(0.775468\pi\) | |||||||
\(402\) | −207.997 | + | 911.294i | −0.0258058 | + | 0.113063i | ||||
\(403\) | 2646.28 | + | 1274.38i | 0.327099 | + | 0.157523i | ||||
\(404\) | −3123.88 | − | 1504.38i | −0.384700 | − | 0.185262i | ||||
\(405\) | 7976.11 | − | 10001.7i | 0.978607 | − | 1.22713i | ||||
\(406\) | 1033.38 | − | 4527.55i | 0.126320 | − | 0.553445i | ||||
\(407\) | −198.664 | − | 870.404i | −0.0241951 | − | 0.106006i | ||||
\(408\) | −2145.15 | + | 2689.94i | −0.260296 | + | 0.326401i | ||||
\(409\) | 6808.45 | − | 8537.53i | 0.823120 | − | 1.03216i | −0.175740 | − | 0.984437i | \(-0.556232\pi\) |
0.998861 | − | 0.0477236i | \(-0.0151967\pi\) | |||||||
\(410\) | −2256.44 | − | 9886.13i | −0.271800 | − | 1.19083i | ||||
\(411\) | 2283.71 | − | 10005.6i | 0.274081 | − | 1.20083i | ||||
\(412\) | 2348.94 | − | 2945.48i | 0.280884 | − | 0.352217i | ||||
\(413\) | −1726.28 | − | 831.334i | −0.205678 | − | 0.0990491i | ||||
\(414\) | −3249.56 | − | 1564.91i | −0.385767 | − | 0.185775i | ||||
\(415\) | 549.724 | − | 2408.50i | 0.0650238 | − | 0.284888i | ||||
\(416\) | 1312.86 | + | 1646.28i | 0.154732 | + | 0.194028i | ||||
\(417\) | 5342.21 | − | 2572.67i | 0.627360 | − | 0.302120i | ||||
\(418\) | 490.996 | + | 615.690i | 0.0574531 | + | 0.0720439i | ||||
\(419\) | 2147.13 | + | 9407.21i | 0.250345 | + | 1.09683i | 0.931227 | + | 0.364439i | \(0.118739\pi\) |
−0.680883 | + | 0.732392i | \(0.738404\pi\) | |||||||
\(420\) | −5523.73 | − | 2660.09i | −0.641739 | − | 0.309045i | ||||
\(421\) | −3284.05 | − | 14388.3i | −0.380177 | − | 1.66566i | −0.696917 | − | 0.717152i | \(-0.745445\pi\) |
0.316739 | − | 0.948513i | \(-0.397412\pi\) | |||||||
\(422\) | 2190.66 | − | 1054.97i | 0.252701 | − | 0.121694i | ||||
\(423\) | 2299.14 | 0.264274 | ||||||||
\(424\) | −1599.77 | −0.183236 | ||||||||
\(425\) | 6309.21 | − | 3038.36i | 0.720098 | − | 0.346781i | ||||
\(426\) | −3142.76 | + | 13769.3i | −0.357434 | + | 1.56602i | ||||
\(427\) | 1988.55 | − | 2493.57i | 0.225370 | − | 0.282605i | ||||
\(428\) | 784.226 | + | 983.388i | 0.0885677 | + | 0.111060i | ||||
\(429\) | 113.380 | 0.0127600 | ||||||||
\(430\) | 14047.2 | − | 6656.28i | 1.57538 | − | 0.746498i | ||||
\(431\) | 11145.4 | 1.24560 | 0.622799 | − | 0.782382i | \(-0.285995\pi\) | ||||
0.622799 | + | 0.782382i | \(0.285995\pi\) | |||||||
\(432\) | 5647.44 | + | 7081.66i | 0.628964 | + | 0.788696i | ||||
\(433\) | −9173.53 | + | 11503.2i | −1.01813 | + | 1.27670i | −0.0576566 | + | 0.998336i | \(0.518363\pi\) |
−0.960476 | + | 0.278362i | \(0.910209\pi\) | |||||||
\(434\) | 3115.75 | − | 13651.0i | 0.344610 | − | 1.50983i | ||||
\(435\) | −7907.19 | + | 3807.90i | −0.871542 | + | 0.419712i | ||||
\(436\) | −8753.62 | −0.961519 | ||||||||
\(437\) | 15153.9 | 1.65883 | ||||||||
\(438\) | 16880.1 | − | 8129.01i | 1.84146 | − | 0.886802i | ||||
\(439\) | 1563.00 | + | 6847.96i | 0.169927 | + | 0.744500i | 0.986027 | + | 0.166588i | \(0.0532751\pi\) |
−0.816099 | + | 0.577912i | \(0.803868\pi\) | |||||||
\(440\) | 219.340 | + | 105.629i | 0.0237651 | + | 0.0114447i | ||||
\(441\) | 284.570 | + | 1246.78i | 0.0307278 | + | 0.134627i | ||||
\(442\) | 1639.44 | + | 2055.80i | 0.176426 | + | 0.221231i | ||||
\(443\) | −5421.87 | + | 2611.04i | −0.581492 | + | 0.280032i | −0.701417 | − | 0.712751i | \(-0.747449\pi\) |
0.119925 | + | 0.992783i | \(0.461735\pi\) | |||||||
\(444\) | 9193.06 | + | 11527.7i | 0.982620 | + | 1.23217i | ||||
\(445\) | −3919.87 | + | 17174.1i | −0.417573 | + | 1.82951i | ||||
\(446\) | 1019.45 | + | 490.943i | 0.108234 | + | 0.0521229i | ||||
\(447\) | −11616.8 | − | 5594.35i | −1.22921 | − | 0.591954i | ||||
\(448\) | 1594.99 | − | 2000.05i | 0.168206 | − | 0.210923i | ||||
\(449\) | 2528.78 | − | 11079.3i | 0.265792 | − | 1.16451i | −0.649065 | − | 0.760733i | \(-0.724840\pi\) |
0.914857 | − | 0.403778i | \(-0.132303\pi\) | |||||||
\(450\) | 515.745 | + | 2259.63i | 0.0540276 | + | 0.236711i | ||||
\(451\) | 235.398 | − | 295.180i | 0.0245775 | − | 0.0308192i | ||||
\(452\) | −1593.09 | + | 1997.67i | −0.165780 | + | 0.207882i | ||||
\(453\) | 971.710 | + | 4257.34i | 0.100784 | + | 0.441562i | ||||
\(454\) | −1085.48 | + | 4755.81i | −0.112212 | + | 0.491633i | ||||
\(455\) | 1074.72 | − | 1347.65i | 0.110733 | − | 0.138855i | ||||
\(456\) | 4310.67 | + | 2075.91i | 0.442688 | + | 0.213187i | ||||
\(457\) | 8198.95 | + | 3948.41i | 0.839236 | + | 0.404155i | 0.803571 | − | 0.595209i | \(-0.202931\pi\) |
0.0356652 | + | 0.999364i | \(0.488645\pi\) | |||||||
\(458\) | −3966.97 | + | 17380.4i | −0.404725 | + | 1.77322i | ||||
\(459\) | 5467.25 | + | 6855.71i | 0.555968 | + | 0.697162i | ||||
\(460\) | −11473.3 | + | 5525.26i | −1.16293 | + | 0.560036i | ||||
\(461\) | −3367.87 | − | 4223.17i | −0.340254 | − | 0.426665i | 0.582036 | − | 0.813163i | \(-0.302256\pi\) |
−0.922290 | + | 0.386498i | \(0.873685\pi\) | |||||||
\(462\) | −120.274 | − | 526.955i | −0.0121118 | − | 0.0530653i | ||||
\(463\) | 10327.5 | + | 4973.46i | 1.03663 | + | 0.499214i | 0.873211 | − | 0.487343i | \(-0.162034\pi\) |
0.163418 | + | 0.986557i | \(0.447748\pi\) | |||||||
\(464\) | −1741.87 | − | 7631.62i | −0.174276 | − | 0.763554i | ||||
\(465\) | −23840.9 | + | 11481.2i | −2.37762 | + | 1.14500i | ||||
\(466\) | −1392.34 | −0.138410 | ||||||||
\(467\) | −5843.46 | −0.579022 | −0.289511 | − | 0.957175i | \(-0.593493\pi\) | ||||
−0.289511 | + | 0.957175i | \(0.593493\pi\) | |||||||
\(468\) | −331.143 | + | 159.470i | −0.0327075 | + | 0.0157511i | ||||
\(469\) | −117.735 | + | 515.829i | −0.0115916 | + | 0.0507863i | ||||
\(470\) | 11984.4 | − | 15028.0i | 1.17617 | − | 1.47487i | ||||
\(471\) | 1076.27 | + | 1349.60i | 0.105290 | + | 0.132030i | ||||
\(472\) | −1256.53 | −0.122534 | ||||||||
\(473\) | 519.850 | + | 254.385i | 0.0505343 | + | 0.0247286i | ||||
\(474\) | 29205.5 | 2.83007 | ||||||||
\(475\) | −6071.57 | − | 7613.51i | −0.586490 | − | 0.735436i | ||||
\(476\) | 3300.66 | − | 4138.90i | 0.317827 | − | 0.398542i | ||||
\(477\) | 293.177 | − | 1284.49i | 0.0281418 | − | 0.123297i | ||||
\(478\) | −13735.1 | + | 6614.46i | −1.31428 | + | 0.632926i | ||||
\(479\) | −7333.33 | −0.699516 | −0.349758 | − | 0.936840i | \(-0.613736\pi\) | ||||
−0.349758 | + | 0.936840i | \(0.613736\pi\) | |||||||
\(480\) | −18970.4 | −1.80391 | ||||||||
\(481\) | −3734.93 | + | 1798.65i | −0.354050 | + | 0.170502i | ||||
\(482\) | −5180.20 | − | 22695.9i | −0.489526 | − | 2.14475i | ||||
\(483\) | −9371.00 | − | 4512.83i | −0.882806 | − | 0.425137i | ||||
\(484\) | 1726.69 | + | 7565.13i | 0.162161 | + | 0.710474i | ||||
\(485\) | 3676.61 | + | 4610.33i | 0.344219 | + | 0.431637i | ||||
\(486\) | −6074.67 | + | 2925.41i | −0.566981 | + | 0.273044i | ||||
\(487\) | −6171.60 | − | 7738.94i | −0.574254 | − | 0.720092i | 0.406867 | − | 0.913488i | \(-0.366621\pi\) |
−0.981121 | + | 0.193395i | \(0.938050\pi\) | |||||||
\(488\) | 465.423 | − | 2039.15i | 0.0431736 | − | 0.189156i | ||||
\(489\) | −15631.3 | − | 7527.66i | −1.44555 | − | 0.696140i | ||||
\(490\) | 9632.78 | + | 4638.90i | 0.888091 | + | 0.427682i | ||||
\(491\) | 1164.28 | − | 1459.96i | 0.107013 | − | 0.134190i | −0.725441 | − | 0.688285i | \(-0.758364\pi\) |
0.832454 | + | 0.554095i | \(0.186935\pi\) | |||||||
\(492\) | −1387.48 | + | 6078.94i | −0.127139 | + | 0.557032i | ||||
\(493\) | −1686.29 | − | 7388.12i | −0.154050 | − | 0.674937i | ||||
\(494\) | 2279.83 | − | 2858.82i | 0.207641 | − | 0.260373i | ||||
\(495\) | −125.008 | + | 156.755i | −0.0113509 | + | 0.0142336i | ||||
\(496\) | −5251.89 | − | 23010.0i | −0.475437 | − | 2.08302i | ||||
\(497\) | −1778.93 | + | 7793.98i | −0.160555 | + | 0.703436i | ||||
\(498\) | −2242.66 | + | 2812.21i | −0.201800 | + | 0.253049i | ||||
\(499\) | 7588.00 | + | 3654.19i | 0.680733 | + | 0.327824i | 0.742098 | − | 0.670292i | \(-0.233831\pi\) |
−0.0613648 | + | 0.998115i | \(0.519545\pi\) | |||||||
\(500\) | −2384.48 | − | 1148.31i | −0.213274 | − | 0.102708i | ||||
\(501\) | 387.174 | − | 1696.32i | 0.0345262 | − | 0.151269i | ||||
\(502\) | 937.690 | + | 1175.83i | 0.0833688 | + | 0.104541i | ||||
\(503\) | 12243.2 | − | 5896.01i | 1.08528 | − | 0.522644i | 0.196280 | − | 0.980548i | \(-0.437114\pi\) |
0.889002 | + | 0.457904i | \(0.151400\pi\) | |||||||
\(504\) | −401.887 | − | 503.950i | −0.0355188 | − | 0.0445391i | ||||
\(505\) | 1954.27 | + | 8562.20i | 0.172205 | + | 0.754481i | ||||
\(506\) | −1011.51 | − | 487.115i | −0.0888674 | − | 0.0427963i | ||||
\(507\) | 2716.41 | + | 11901.4i | 0.237949 | + | 1.04252i | ||||
\(508\) | 8202.59 | − | 3950.16i | 0.716399 | − | 0.345000i | ||||
\(509\) | −1287.12 | −0.112084 | −0.0560420 | − | 0.998428i | \(-0.517848\pi\) | ||||
−0.0560420 | + | 0.998428i | \(0.517848\pi\) | |||||||
\(510\) | −23689.3 | −2.05683 | ||||||||
\(511\) | 9554.79 | − | 4601.34i | 0.827160 | − | 0.398339i | ||||
\(512\) | 2673.58 | − | 11713.7i | 0.230774 | − | 1.01109i | ||||
\(513\) | 7602.83 | − | 9533.65i | 0.654334 | − | 0.820508i | ||||
\(514\) | 6726.51 | + | 8434.77i | 0.577225 | + | 0.723817i | ||||
\(515\) | −9542.70 | −0.816508 | ||||||||
\(516\) | −9558.01 | − | 60.0984i | −0.815442 | − | 0.00512729i | ||||
\(517\) | 715.662 | 0.0608796 | ||||||||
\(518\) | 12321.6 | + | 15450.8i | 1.04513 | + | 1.31056i | ||||
\(519\) | −5209.74 | + | 6532.81i | −0.440621 | + | 0.552521i | ||||
\(520\) | 251.539 | − | 1102.06i | 0.0212129 | − | 0.0929397i | ||||
\(521\) | 16530.4 | − | 7960.64i | 1.39004 | − | 0.669409i | 0.418926 | − | 0.908020i | \(-0.362407\pi\) |
0.971115 | + | 0.238612i | \(0.0766923\pi\) | |||||||
\(522\) | 2508.19 | 0.210307 | ||||||||
\(523\) | −10556.8 | −0.882635 | −0.441318 | − | 0.897351i | \(-0.645489\pi\) | ||||
−0.441318 | + | 0.897351i | \(0.645489\pi\) | |||||||
\(524\) | 1465.77 | − | 705.877i | 0.122199 | − | 0.0588481i | ||||
\(525\) | 1487.29 | + | 6516.24i | 0.123639 | + | 0.541699i | ||||
\(526\) | 19632.4 | + | 9454.47i | 1.62740 | + | 0.783716i | ||||
\(527\) | −5084.32 | − | 22275.8i | −0.420259 | − | 1.84127i | ||||
\(528\) | −568.047 | − | 712.308i | −0.0468202 | − | 0.0587107i | ||||
\(529\) | −8502.39 | + | 4094.53i | −0.698807 | + | 0.336528i | ||||
\(530\) | −6867.71 | − | 8611.84i | −0.562857 | − | 0.705801i | ||||
\(531\) | 230.273 | − | 1008.89i | 0.0188192 | − | 0.0824522i | ||||
\(532\) | −6632.67 | − | 3194.12i | −0.540531 | − | 0.260306i | ||||
\(533\) | −1579.46 | − | 760.626i | −0.128356 | − | 0.0618131i | ||||
\(534\) | 15991.6 | − | 20052.8i | 1.29593 | − | 1.62504i | ||||
\(535\) | 708.942 | − | 3106.08i | 0.0572902 | − | 0.251005i | ||||
\(536\) | 77.2099 | + | 338.279i | 0.00622194 | + | 0.0272601i | ||||
\(537\) | 16263.0 | − | 20393.2i | 1.30689 | − | 1.63879i | ||||
\(538\) | −15371.4 | + | 19275.1i | −1.23180 | + | 1.54463i | ||||
\(539\) | 88.5792 | + | 388.091i | 0.00707862 | + | 0.0310135i | ||||
\(540\) | −2280.20 | + | 9990.21i | −0.181711 | + | 0.796130i | ||||
\(541\) | −11627.6 | + | 14580.5i | −0.924046 | + | 1.15872i | 0.0629571 | + | 0.998016i | \(0.479947\pi\) |
−0.987003 | + | 0.160701i | \(0.948625\pi\) | |||||||
\(542\) | −13035.2 | − | 6277.42i | −1.03304 | − | 0.497487i | ||||
\(543\) | −16606.6 | − | 7997.30i | −1.31244 | − | 0.632039i | ||||
\(544\) | 3644.99 | − | 15969.7i | 0.287275 | − | 1.25863i | ||||
\(545\) | 13824.4 | + | 17335.2i | 1.08655 | + | 1.36249i | ||||
\(546\) | −2261.18 | + | 1088.93i | −0.177234 | + | 0.0853514i | ||||
\(547\) | 7852.82 | + | 9847.12i | 0.613825 | + | 0.769712i | 0.987461 | − | 0.157863i | \(-0.0504606\pi\) |
−0.373636 | + | 0.927575i | \(0.621889\pi\) | |||||||
\(548\) | 2304.37 | + | 10096.1i | 0.179631 | + | 0.787016i | ||||
\(549\) | 1551.98 | + | 747.396i | 0.120650 | + | 0.0581022i | ||||
\(550\) | 160.538 | + | 703.363i | 0.0124461 | + | 0.0545300i | ||||
\(551\) | −9494.62 | + | 4572.37i | −0.734091 | + | 0.353520i | ||||
\(552\) | −6820.95 | −0.525940 | ||||||||
\(553\) | 16531.5 | 1.27123 | ||||||||
\(554\) | 4255.16 | − | 2049.18i | 0.326326 | − | 0.157150i | ||||
\(555\) | 8310.55 | − | 36410.9i | 0.635609 | − | 2.78479i | ||||
\(556\) | −3730.37 | + | 4677.74i | −0.284538 | + | 0.356799i | ||||
\(557\) | −1633.17 | − | 2047.93i | −0.124236 | − | 0.155787i | 0.715823 | − | 0.698281i | \(-0.246052\pi\) |
−0.840060 | + | 0.542494i | \(0.817480\pi\) | |||||||
\(558\) | 7562.41 | 0.573732 | ||||||||
\(559\) | 614.445 | − | 2616.12i | 0.0464906 | − | 0.197943i | ||||
\(560\) | −13851.0 | −1.04520 | ||||||||
\(561\) | −549.922 | − | 689.581i | −0.0413864 | − | 0.0518968i | ||||
\(562\) | 2999.35 | − | 3761.06i | 0.225124 | − | 0.282297i | ||||
\(563\) | −681.347 | + | 2985.17i | −0.0510041 | + | 0.223464i | −0.994006 | − | 0.109323i | \(-0.965132\pi\) |
0.943002 | + | 0.332787i | \(0.107989\pi\) | |||||||
\(564\) | −10648.8 | + | 5128.18i | −0.795026 | + | 0.382864i | ||||
\(565\) | 6472.00 | 0.481910 | ||||||||
\(566\) | 1086.46 | 0.0806842 | ||||||||
\(567\) | −9499.04 | + | 4574.50i | −0.703566 | + | 0.338820i | ||||
\(568\) | 1166.61 | + | 5111.26i | 0.0861795 | + | 0.377577i | ||||
\(569\) | 6444.71 | + | 3103.61i | 0.474826 | + | 0.228664i | 0.655962 | − | 0.754794i | \(-0.272263\pi\) |
−0.181136 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(570\) | 7330.44 | + | 32116.8i | 0.538664 | + | 2.36004i | ||||
\(571\) | 273.964 | + | 343.540i | 0.0200788 | + | 0.0251781i | 0.791770 | − | 0.610820i | \(-0.209160\pi\) |
−0.771691 | + | 0.635998i | \(0.780589\pi\) | |||||||
\(572\) | −103.076 | + | 49.6389i | −0.00753468 | + | 0.00362851i | ||||
\(573\) | 13206.3 | + | 16560.2i | 0.962829 | + | 1.20735i | ||||
\(574\) | −1859.66 | + | 8147.69i | −0.135228 | + | 0.592470i | ||||
\(575\) | 12508.1 | + | 6023.58i | 0.907172 | + | 0.436871i | ||||
\(576\) | 1244.82 | + | 599.475i | 0.0900479 | + | 0.0433648i | ||||
\(577\) | −7932.54 | + | 9947.10i | −0.572333 | + | 0.717683i | −0.980784 | − | 0.195097i | \(-0.937498\pi\) |
0.408451 | + | 0.912780i | \(0.366069\pi\) | |||||||
\(578\) | 483.338 | − | 2117.64i | 0.0347824 | − | 0.152392i | ||||
\(579\) | −2913.53 | − | 12765.0i | −0.209123 | − | 0.916226i | ||||
\(580\) | 5521.45 | − | 6923.68i | 0.395286 | − | 0.495673i | ||||
\(581\) | −1269.44 | + | 1591.82i | −0.0906457 | + | 0.113666i | ||||
\(582\) | −1910.52 | − | 8370.51i | −0.136071 | − | 0.596167i | ||||
\(583\) | 91.2584 | − | 399.829i | 0.00648291 | − | 0.0284035i | ||||
\(584\) | 4336.20 | − | 5437.42i | 0.307249 | − | 0.385278i | ||||
\(585\) | 838.772 | + | 403.931i | 0.0592803 | + | 0.0285479i | ||||
\(586\) | 15623.5 | + | 7523.90i | 1.10137 | + | 0.530392i | ||||
\(587\) | −291.547 | + | 1277.35i | −0.0204999 | + | 0.0898158i | −0.984143 | − | 0.177377i | \(-0.943239\pi\) |
0.963643 | + | 0.267193i | \(0.0860960\pi\) | |||||||
\(588\) | −4098.95 | − | 5139.92i | −0.287479 | − | 0.360488i | ||||
\(589\) | −28627.1 | + | 13786.1i | −2.00265 | + | 0.964425i | ||||
\(590\) | −5394.17 | − | 6764.07i | −0.376397 | − | 0.471987i | ||||
\(591\) | −451.541 | − | 1978.33i | −0.0314280 | − | 0.137695i | ||||
\(592\) | 30012.4 | + | 14453.2i | 2.08362 | + | 1.00342i | ||||
\(593\) | −1896.68 | − | 8309.89i | −0.131344 | − | 0.575457i | −0.997175 | − | 0.0751194i | \(-0.976066\pi\) |
0.865830 | − | 0.500338i | \(-0.166791\pi\) | |||||||
\(594\) | −813.937 | + | 391.971i | −0.0562226 | + | 0.0270754i | ||||
\(595\) | −13409.1 | −0.923899 | ||||||||
\(596\) | 13010.3 | 0.894167 | ||||||||
\(597\) | −18713.3 | + | 9011.87i | −1.28289 | + | 0.617808i | ||||
\(598\) | −1159.99 | + | 5082.24i | −0.0793235 | + | 0.347539i | ||||
\(599\) | −13160.2 | + | 16502.4i | −0.897685 | + | 1.12566i | 0.0938200 | + | 0.995589i | \(0.470092\pi\) |
−0.991505 | + | 0.130072i | \(0.958479\pi\) | |||||||
\(600\) | 2732.89 | + | 3426.94i | 0.185950 | + | 0.233174i | ||||
\(601\) | −27867.5 | −1.89141 | −0.945705 | − | 0.325026i | \(-0.894627\pi\) | ||||
−0.945705 | + | 0.325026i | \(0.894627\pi\) | |||||||
\(602\) | −12810.7 | − | 80.5506i | −0.867320 | − | 0.00545349i | ||||
\(603\) | −285.761 | −0.0192986 | ||||||||
\(604\) | −2747.31 | − | 3445.01i | −0.185077 | − | 0.232079i | ||||
\(605\) | 12254.7 | − | 15366.9i | 0.823509 | − | 1.03265i | ||||
\(606\) | 2845.41 | − | 12466.6i | 0.190737 | − | 0.835675i | ||||
\(607\) | 19277.4 | − | 9283.50i | 1.28904 | − | 0.620767i | 0.341339 | − | 0.939940i | \(-0.389119\pi\) |
0.947696 | + | 0.319173i | \(0.103405\pi\) | |||||||
\(608\) | −22778.8 | −1.51942 | ||||||||
\(609\) | 7233.03 | 0.481276 | ||||||||
\(610\) | 12975.1 | − | 6248.48i | 0.861224 | − | 0.414744i | ||||
\(611\) | −739.441 | − | 3239.70i | −0.0489600 | − | 0.214508i | ||||
\(612\) | 2576.03 | + | 1240.55i | 0.170147 | + | 0.0819384i | ||||
\(613\) | −4891.76 | − | 21432.2i | −0.322311 | − | 1.41214i | −0.833430 | − | 0.552625i | \(-0.813626\pi\) |
0.511119 | − | 0.859510i | \(-0.329231\pi\) | |||||||
\(614\) | −9522.23 | − | 11940.5i | −0.625873 | − | 0.784820i | ||||
\(615\) | 14229.6 | − | 6852.62i | 0.932998 | − | 0.449308i | ||||
\(616\) | −125.097 | − | 156.867i | −0.00818230 | − | 0.0102603i | ||||
\(617\) | −2467.89 | + | 10812.5i | −0.161027 | + | 0.705504i | 0.828360 | + | 0.560196i | \(0.189274\pi\) |
−0.989387 | + | 0.145308i | \(0.953583\pi\) | |||||||
\(618\) | 12518.2 | + | 6028.45i | 0.814816 | + | 0.392394i | ||||
\(619\) | 12627.0 | + | 6080.86i | 0.819909 | + | 0.394847i | 0.796321 | − | 0.604874i | \(-0.206777\pi\) |
0.0235882 | + | 0.999722i | \(0.492491\pi\) | |||||||
\(620\) | 16647.7 | − | 20875.5i | 1.07837 | − | 1.35223i | ||||
\(621\) | −3868.35 | + | 16948.4i | −0.249971 | + | 1.09519i | ||||
\(622\) | 4430.03 | + | 19409.2i | 0.285576 | + | 1.25119i | ||||
\(623\) | 9051.88 | − | 11350.7i | 0.582112 | − | 0.729946i | ||||
\(624\) | −2637.60 | + | 3307.45i | −0.169212 | + | 0.212186i | ||||
\(625\) | 4118.92 | + | 18046.2i | 0.263611 | + | 1.15496i | ||||
\(626\) | −1667.15 | + | 7304.27i | −0.106442 | + | 0.466353i | ||||
\(627\) | −764.730 | + | 958.941i | −0.0487087 | + | 0.0610788i | ||||
\(628\) | −1569.32 | − | 755.746i | −0.0997178 | − | 0.0480215i | ||||
\(629\) | 29054.8 | + | 13992.0i | 1.84180 | + | 0.886962i | ||||
\(630\) | 987.573 | − | 4326.84i | 0.0624537 | − | 0.273628i | ||||
\(631\) | −12830.8 | − | 16089.3i | −0.809486 | − | 1.01506i | −0.999446 | − | 0.0332717i | \(-0.989407\pi\) |
0.189960 | − | 0.981792i | \(-0.439164\pi\) | |||||||
\(632\) | 9767.66 | − | 4703.86i | 0.614773 | − | 0.296059i | ||||
\(633\) | 2361.15 | + | 2960.79i | 0.148258 | + | 0.185910i | ||||
\(634\) | −3533.41 | − | 15480.9i | −0.221340 | − | 0.969754i | ||||
\(635\) | −20776.8 | − | 10005.6i | −1.29843 | − | 0.625291i | ||||
\(636\) | 1507.15 | + | 6603.24i | 0.0939658 | + | 0.411691i | ||||
\(637\) | 1665.31 | − | 801.972i | 0.103582 | − | 0.0498827i | ||||
\(638\) | 780.733 | 0.0484475 | ||||||||
\(639\) | −4317.74 | −0.267304 | ||||||||
\(640\) | −13183.8 | + | 6348.99i | −0.814275 | + | 0.392134i | ||||
\(641\) | 4803.59 | − | 21045.9i | 0.295991 | − | 1.29682i | −0.580048 | − | 0.814583i | \(-0.696966\pi\) |
0.876039 | − | 0.482240i | \(-0.160177\pi\) | |||||||
\(642\) | −2892.21 | + | 3626.72i | −0.177798 | + | 0.222952i | ||||
\(643\) | 4100.11 | + | 5141.37i | 0.251466 | + | 0.315328i | 0.891502 | − | 0.453017i | \(-0.149652\pi\) |
−0.640036 | + | 0.768345i | \(0.721081\pi\) | |||||||
\(644\) | 10495.1 | 0.642183 | ||||||||
\(645\) | 14975.7 | + | 19023.1i | 0.914213 | + | 1.16129i | ||||
\(646\) | −28445.2 | −1.73245 | ||||||||
\(647\) | 6429.19 | + | 8061.94i | 0.390661 | + | 0.489873i | 0.937804 | − | 0.347166i | \(-0.112856\pi\) |
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(648\) | −4310.90 | + | 5405.70i | −0.261340 | + | 0.327710i | ||||
\(649\) | 71.6779 | − | 314.041i | 0.00433529 | − | 0.0189942i | ||||
\(650\) | 3018.15 | − | 1453.47i | 0.182126 | − | 0.0877071i | ||||
\(651\) | 21808.3 | 1.31295 | ||||||||
\(652\) | 17506.5 | 1.05154 | ||||||||
\(653\) | −9277.82 | + | 4467.96i | −0.556002 | + | 0.267756i | −0.690714 | − | 0.723128i | \(-0.742703\pi\) |
0.134712 | + | 0.990885i | \(0.456989\pi\) | |||||||
\(654\) | −7183.69 | − | 31473.8i | −0.429518 | − | 1.88184i | ||||
\(655\) | −3712.73 | − | 1787.96i | −0.221478 | − | 0.106658i | ||||
\(656\) | 3134.63 | + | 13733.7i | 0.186565 | + | 0.817395i | ||||
\(657\) | 3571.16 | + | 4478.10i | 0.212061 | + | 0.265917i | ||||
\(658\) | −14272.7 | + | 6873.38i | −0.845605 | + | 0.407222i | ||||
\(659\) | 8097.02 | + | 10153.3i | 0.478627 | + | 0.600179i | 0.961260 | − | 0.275644i | \(-0.0888909\pi\) |
−0.482633 | + | 0.875823i | \(0.660320\pi\) | |||||||
\(660\) | 229.354 | − | 1004.86i | 0.0135266 | − | 0.0592641i | ||||
\(661\) | −6054.62 | − | 2915.75i | −0.356274 | − | 0.171573i | 0.247181 | − | 0.968969i | \(-0.420496\pi\) |
−0.603456 | + | 0.797397i | \(0.706210\pi\) | |||||||
\(662\) | 2734.10 | + | 1316.67i | 0.160519 | + | 0.0773019i | ||||
\(663\) | −2553.44 | + | 3201.92i | −0.149574 | + | 0.187560i | ||||
\(664\) | −297.113 | + | 1301.74i | −0.0173648 | + | 0.0760801i | ||||
\(665\) | 4149.32 | + | 18179.4i | 0.241961 | + | 1.06010i | ||||
\(666\) | −6654.81 | + | 8344.87i | −0.387190 | + | 0.485521i | ||||
\(667\) | 9367.13 | − | 11746.0i | 0.543773 | − | 0.681870i | ||||
\(668\) | 390.677 | + | 1711.67i | 0.0226284 | + | 0.0991413i | ||||
\(669\) | −392.156 | + | 1718.15i | −0.0226631 | + | 0.0992935i | ||||
\(670\) | −1489.55 | + | 1867.84i | −0.0858901 | + | 0.107703i | ||||
\(671\) | 483.092 | + | 232.645i | 0.0277937 | + | 0.0133847i | ||||
\(672\) | 14086.2 | + | 6783.56i | 0.808612 | + | 0.389407i | ||||
\(673\) | 1305.09 | − | 5717.97i | 0.0747511 | − | 0.327506i | −0.923702 | − | 0.383113i | \(-0.874852\pi\) |
0.998453 | + | 0.0556067i | \(0.0177093\pi\) | |||||||
\(674\) | −19454.7 | − | 24395.4i | −1.11182 | − | 1.39418i | ||||
\(675\) | 10065.0 | − | 4847.05i | 0.573929 | − | 0.276390i | ||||
\(676\) | −7680.07 | − | 9630.51i | −0.436964 | − | 0.547935i | ||||
\(677\) | −5015.19 | − | 21973.0i | −0.284711 | − | 1.24740i | −0.891677 | − | 0.452673i | \(-0.850471\pi\) |
0.606965 | − | 0.794728i | \(-0.292387\pi\) | |||||||
\(678\) | −8490.03 | − | 4088.58i | −0.480911 | − | 0.231595i | ||||
\(679\) | −1081.43 | − | 4738.05i | −0.0611214 | − | 0.267790i | ||||
\(680\) | −7922.79 | + | 3815.42i | −0.446802 | + | 0.215168i | ||||
\(681\) | −7597.70 | −0.427525 | ||||||||
\(682\) | 2353.98 | 0.132168 | ||||||||
\(683\) | −13642.7 | + | 6569.97i | −0.764309 | + | 0.368072i | −0.775074 | − | 0.631870i | \(-0.782287\pi\) |
0.0107655 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(684\) | 884.745 | − | 3876.32i | 0.0494577 | − | 0.216688i | ||||
\(685\) | 16354.6 | − | 20508.0i | 0.912228 | − | 1.14390i | ||||
\(686\) | −15210.2 | − | 19073.0i | −0.846544 | − | 1.06153i | ||||
\(687\) | −27766.3 | −1.54199 | ||||||||
\(688\) | −19514.2 | + | 9246.83i | −1.08135 | + | 0.512401i | ||||
\(689\) | −1904.26 | −0.105293 | ||||||||
\(690\) | −29281.8 | − | 36718.2i | −1.61557 | − | 2.02585i | ||||
\(691\) | −6214.59 | + | 7792.85i | −0.342133 | + | 0.429021i | −0.922895 | − | 0.385052i | \(-0.874183\pi\) |
0.580762 | + | 0.814074i | \(0.302755\pi\) | |||||||
\(692\) | 1876.16 | − | 8219.99i | 0.103065 | − | 0.451557i | ||||
\(693\) | 148.877 | − | 71.6954i | 0.00816070 | − | 0.00392999i | ||||
\(694\) | −28384.5 | −1.55254 | ||||||||
\(695\) | 15154.8 | 0.827129 | ||||||||
\(696\) | 4273.65 | − | 2058.08i | 0.232748 | − | 0.112085i | ||||
\(697\) | 3034.61 | + | 13295.5i | 0.164913 | + | 0.722530i | ||||
\(698\) | −5117.25 | − | 2464.34i | −0.277494 | − | 0.133634i | ||||
\(699\) | −482.554 | − | 2114.21i | −0.0261114 | − | 0.114401i | ||||
\(700\) | −4205.00 | − | 5272.90i | −0.227049 | − | 0.284710i | ||||
\(701\) | −13465.6 | + | 6484.71i | −0.725521 | + | 0.349392i | −0.759921 | − | 0.650016i | \(-0.774762\pi\) |
0.0344001 | + | 0.999408i | \(0.489048\pi\) | |||||||
\(702\) | 2615.38 | + | 3279.58i | 0.140614 | + | 0.176325i | ||||
\(703\) | 9978.96 | − | 43720.7i | 0.535368 | − | 2.34560i | ||||
\(704\) | 387.481 | + | 186.601i | 0.0207439 | + | 0.00998976i | ||||
\(705\) | 26972.9 | + | 12989.5i | 1.44094 | + | 0.693918i | ||||
\(706\) | −26078.7 | + | 32701.7i | −1.39021 | + | 1.74326i | ||||
\(707\) | 1610.62 | − | 7056.57i | 0.0856767 | − | 0.375374i | ||||
\(708\) | 1183.77 | + | 5186.44i | 0.0628374 | + | 0.275308i | ||||
\(709\) | −10258.6 | + | 12863.8i | −0.543397 | + | 0.681398i | −0.975392 | − | 0.220478i | \(-0.929238\pi\) |
0.431995 | + | 0.901876i | \(0.357810\pi\) | |||||||
\(710\) | −22506.6 | + | 28222.3i | −1.18966 | + | 1.49178i | ||||
\(711\) | 1986.79 | + | 8704.70i | 0.104797 | + | 0.459144i | ||||
\(712\) | 2118.60 | − | 9282.20i | 0.111514 | − | 0.488575i | ||||
\(713\) | 28242.8 | − | 35415.3i | 1.48345 | − | 1.86019i | ||||
\(714\) | 17590.2 | + | 8470.99i | 0.921984 | + | 0.444004i | ||||
\(715\) | 261.088 | + | 125.733i | 0.0136561 | + | 0.00657645i | ||||
\(716\) | −5856.73 | + | 25660.0i | −0.305693 | + | 1.33933i | ||||
\(717\) | −14804.0 | − | 18563.7i | −0.771084 | − | 0.966909i | ||||
\(718\) | 13154.6 | − | 6334.91i | 0.683739 | − | 0.329271i | ||||
\(719\) | 11083.5 | + | 13898.2i | 0.574887 | + | 0.720886i | 0.981231 | − | 0.192834i | \(-0.0617679\pi\) |
−0.406344 | + | 0.913720i | \(0.633197\pi\) | |||||||
\(720\) | −1664.65 | − | 7293.30i | −0.0861636 | − | 0.377507i | ||||
\(721\) | 7085.80 | + | 3412.34i | 0.366004 | + | 0.176258i | ||||
\(722\) | 3122.29 | + | 13679.7i | 0.160941 | + | 0.705130i | ||||
\(723\) | 32667.4 | − | 15731.8i | 1.68038 | − | 0.809228i | ||||
\(724\) | 18598.7 | 0.954716 | ||||||||
\(725\) | −9654.41 | −0.494560 | ||||||||
\(726\) | −25783.6 | + | 12416.7i | −1.31807 | + | 0.634748i | ||||
\(727\) | 174.081 | − | 762.700i | 0.00888077 | − | 0.0389092i | −0.970293 | − | 0.241931i | \(-0.922219\pi\) |
0.979174 | + | 0.203022i | \(0.0650763\pi\) | |||||||
\(728\) | −580.860 | + | 728.375i | −0.0295716 | + | 0.0370816i | ||||
\(729\) | 7989.86 | + | 10019.0i | 0.405927 | + | 0.509016i | ||||
\(730\) | 47885.5 | 2.42784 | ||||||||
\(731\) | −18891.5 | + | 8951.80i | −0.955854 | + | 0.452933i | ||||
\(732\) | −8855.29 | −0.447132 | ||||||||
\(733\) | −23988.9 | − | 30081.1i | −1.20880 | − | 1.51579i | −0.796386 | − | 0.604788i | \(-0.793258\pi\) |
−0.412412 | − | 0.910997i | \(-0.635314\pi\) | |||||||
\(734\) | −4532.78 | + | 5683.93i | −0.227940 | + | 0.285828i | ||||
\(735\) | −3705.46 | + | 16234.7i | −0.185956 | + | 0.814729i | ||||
\(736\) | 29258.4 | − | 14090.1i | 1.46533 | − | 0.705664i | ||||
\(737\) | −88.9499 | −0.00444574 | ||||||||
\(738\) | −4513.68 | −0.225137 | ||||||||
\(739\) | −11082.0 | + | 5336.79i | −0.551633 | + | 0.265652i | −0.688869 | − | 0.724886i | \(-0.741892\pi\) |
0.137236 | + | 0.990538i | \(0.456178\pi\) | |||||||
\(740\) | 8385.74 | + | 36740.3i | 0.416576 | + | 1.82514i | ||||
\(741\) | 5131.13 | + | 2471.02i | 0.254382 | + | 0.122504i | ||||
\(742\) | 2020.05 | + | 8850.41i | 0.0999438 | + | 0.437883i | ||||
\(743\) | 23867.7 | + | 29929.2i | 1.17850 | + | 1.47779i | 0.844781 | + | 0.535112i | \(0.179731\pi\) |
0.333714 | + | 0.942674i | \(0.391698\pi\) | |||||||
\(744\) | 12885.4 | − | 6205.30i | 0.634951 | − | 0.305776i | ||||
\(745\) | −20546.9 | − | 25764.9i | −1.01044 | − | 1.26705i | ||||
\(746\) | −2392.36 | + | 10481.6i | −0.117414 | + | 0.514422i | ||||
\(747\) | −990.743 | − | 477.117i | −0.0485266 | − | 0.0233692i | ||||
\(748\) | 801.851 | + | 386.151i | 0.0391960 | + | 0.0188758i | ||||
\(749\) | −1637.11 | + | 2052.87i | −0.0798647 | + | 0.100147i | ||||
\(750\) | 2171.92 | − | 9515.81i | 0.105743 | − | 0.463291i | ||||
\(751\) | −2795.89 | − | 12249.6i | −0.135850 | − | 0.595199i | −0.996321 | − | 0.0856991i | \(-0.972688\pi\) |
0.860471 | − | 0.509500i | \(-0.170170\pi\) | |||||||
\(752\) | −16648.7 | + | 20876.8i | −0.807333 | + | 1.01236i | ||||
\(753\) | −1460.46 | + | 1831.36i | −0.0706800 | + | 0.0886299i | ||||
\(754\) | −806.674 | − | 3534.27i | −0.0389620 | − | 0.170704i | ||||
\(755\) | −2483.57 | + | 10881.2i | −0.119717 | + | 0.524515i | ||||
\(756\) | 5265.50 | − | 6602.73i | 0.253313 | − | 0.317644i | ||||
\(757\) | 11589.4 | + | 5581.18i | 0.556441 | + | 0.267968i | 0.690899 | − | 0.722952i | \(-0.257215\pi\) |
−0.134458 | + | 0.990919i | \(0.542929\pi\) | |||||||
\(758\) | 7383.32 | + | 3555.62i | 0.353792 | + | 0.170377i | ||||
\(759\) | 389.098 | − | 1704.75i | 0.0186079 | − | 0.0815263i | ||||
\(760\) | 7624.38 | + | 9560.67i | 0.363902 | + | 0.456318i | ||||
\(761\) | 3241.17 | − | 1560.86i | 0.154392 | − | 0.0743512i | −0.355092 | − | 0.934831i | \(-0.615551\pi\) |
0.509484 | + | 0.860480i | \(0.329836\pi\) | |||||||
\(762\) | 20934.4 | + | 26250.8i | 0.995238 | + | 1.24799i | ||||
\(763\) | −4066.26 | − | 17815.4i | −0.192934 | − | 0.845298i | ||||
\(764\) | −19256.3 | − | 9273.36i | −0.911871 | − | 0.439134i | ||||
\(765\) | −1611.54 | − | 7060.60i | −0.0761637 | − | 0.333695i | ||||
\(766\) | 45462.6 | − | 21893.7i | 2.14443 | − | 1.03270i | ||||
\(767\) | −1495.68 | −0.0704119 | ||||||||
\(768\) | 31021.1 | 1.45752 | ||||||||
\(769\) | −17105.8 | + | 8237.74i | −0.802149 | + | 0.386295i | −0.789596 | − | 0.613627i | \(-0.789710\pi\) |
−0.0125526 | + | 0.999921i | \(0.503996\pi\) | |||||||
\(770\) | 307.406 | − | 1346.83i | 0.0143872 | − | 0.0630344i | ||||
\(771\) | −10476.6 | + | 13137.2i | −0.489371 | + | 0.613651i | ||||
\(772\) | 8237.38 | + | 10329.3i | 0.384028 | + | 0.481556i | ||||
\(773\) | 23805.7 | 1.10767 | 0.553836 | − | 0.832626i | \(-0.313164\pi\) | ||||
0.553836 | + | 0.832626i | \(0.313164\pi\) | |||||||
\(774\) | −1497.21 | − | 6755.20i | −0.0695297 | − | 0.313709i | ||||
\(775\) | −29108.9 | −1.34919 | ||||||||
\(776\) | −1987.12 | − | 2491.77i | −0.0919247 | − | 0.115270i | ||||
\(777\) | −19190.9 | + | 24064.7i | −0.886063 | + | 1.11109i | ||||
\(778\) | 5519.92 | − | 24184.3i | 0.254368 | − | 1.11446i | ||||
\(779\) | 17086.3 | − | 8228.35i | 0.785856 | − | 0.378448i | ||||
\(780\) | −4785.85 | −0.219694 | ||||||||
\(781\) | −1344.00 | −0.0615775 | ||||||||
\(782\) | 36536.6 | − | 17595.1i | 1.67077 | − | 0.804602i | ||||
\(783\) | −2690.11 | − | 11786.2i | −0.122780 | − | 0.537935i | ||||
\(784\) | −13381.8 | − | 6444.31i | −0.609592 | − | 0.293564i | ||||
\(785\) | 981.751 | + | 4301.33i | 0.0446372 | + | 0.195568i | ||||
\(786\) | 3740.88 | + | 4690.92i | 0.169762 | + | 0.212875i | ||||
\(787\) | −5334.70 | + | 2569.05i | −0.241628 | + | 0.116362i | −0.550779 | − | 0.834651i | \(-0.685669\pi\) |
0.309151 | + | 0.951013i | \(0.399955\pi\) | |||||||
\(788\) | 1276.64 | + | 1600.85i | 0.0577136 | + | 0.0723706i | ||||
\(789\) | −7552.05 | + | 33087.7i | −0.340760 | + | 1.49297i | ||||
\(790\) | 67253.4 | + | 32387.6i | 3.02882 | + | 1.45860i | ||||
\(791\) | −4805.70 | − | 2314.30i | −0.216019 | − | 0.104029i | ||||
\(792\) | 67.5641 | − | 84.7227i | 0.00303129 | − | 0.00380112i | ||||
\(793\) | 554.008 | − | 2427.27i | 0.0248088 | − | 0.108695i | ||||
\(794\) | 2450.92 | + | 10738.2i | 0.109546 | + | 0.479954i | ||||
\(795\) | 10696.5 | − | 13413.0i | 0.477190 | − | 0.598377i | ||||
\(796\) | 13067.2 | − | 16385.7i | 0.581853 | − | 0.729620i | ||||
\(797\) | 7007.66 | + | 30702.6i | 0.311448 | + | 1.36454i | 0.852136 | + | 0.523320i | \(0.175307\pi\) |
−0.540688 | + | 0.841223i | \(0.681836\pi\) | |||||||
\(798\) | 6041.41 | − | 26469.1i | 0.268000 | − | 1.17418i | ||||
\(799\) | −16117.5 | + | 20210.7i | −0.713636 | + | 0.894871i | ||||
\(800\) | −18801.8 | − | 9054.47i | −0.830930 | − | 0.400155i | ||||
\(801\) | 7064.61 | + | 3402.14i | 0.311630 | + | 0.150073i | ||||
\(802\) | 428.033 | − | 1875.33i | 0.0188458 | − | 0.0825690i | ||||
\(803\) | 1111.61 | + | 1393.92i | 0.0488517 | + | 0.0612581i | ||||
\(804\) | 1323.54 | − | 637.384i | 0.0580568 | − | 0.0279587i | ||||
\(805\) | −16574.7 | − | 20784.0i | −0.725690 | − | 0.909987i | ||||
\(806\) | −2432.20 | − | 10656.1i | −0.106291 | − | 0.465691i | ||||
\(807\) | −34595.8 | − | 16660.4i | −1.50908 | − | 0.726735i | ||||
\(808\) | −1056.23 | − | 4627.67i | −0.0459879 | − | 0.201486i | ||||
\(809\) | 8072.60 | − | 3887.56i | 0.350825 | − | 0.168948i | −0.250168 | − | 0.968202i | \(-0.580486\pi\) |
0.600994 | + | 0.799254i | \(0.294772\pi\) | |||||||
\(810\) | −47606.1 | −2.06507 | ||||||||
\(811\) | 15879.3 | 0.687543 | 0.343772 | − | 0.939053i | \(-0.388295\pi\) | ||||
0.343772 | + | 0.939053i | \(0.388295\pi\) | |||||||
\(812\) | −6575.70 | + | 3166.69i | −0.284189 | + | 0.136858i | ||||
\(813\) | 5014.28 | − | 21969.0i | 0.216308 | − | 0.947707i | ||||
\(814\) | −2071.47 | + | 2597.54i | −0.0891953 | + | 0.111847i | ||||
\(815\) | −27647.5 | − | 34668.9i | −1.18828 | − | 1.49006i | ||||
\(816\) | 32909.0 | 1.41182 | ||||||||
\(817\) | 17982.2 | + | 22842.1i | 0.770033 | + | 0.978145i | ||||
\(818\) | −40636.8 | −1.73696 | ||||||||
\(819\) | −478.379 | − | 599.868i | −0.0204101 | − | 0.0255935i | ||||
\(820\) | −9936.30 | + | 12459.7i | −0.423159 | + | 0.530625i | ||||
\(821\) | −254.398 | + | 1114.59i | −0.0108143 | + | 0.0473805i | −0.980047 | − | 0.198765i | \(-0.936307\pi\) |
0.969233 | + | 0.246145i | \(0.0791641\pi\) | |||||||
\(822\) | −34409.7 | + | 16570.8i | −1.46007 | + | 0.703132i | ||||
\(823\) | 6089.64 | 0.257924 | 0.128962 | − | 0.991650i | \(-0.458835\pi\) | ||||
0.128962 | + | 0.991650i | \(0.458835\pi\) | |||||||
\(824\) | 5157.61 | 0.218051 | ||||||||
\(825\) | −1012.39 | + | 487.540i | −0.0427234 | + | 0.0205745i | ||||
\(826\) | 1586.62 | + | 6951.46i | 0.0668350 | + | 0.292823i | ||||
\(827\) | 313.181 | + | 150.820i | 0.0131685 | + | 0.00634163i | 0.440456 | − | 0.897774i | \(-0.354817\pi\) |
−0.427288 | + | 0.904116i | \(0.640531\pi\) | |||||||
\(828\) | 1261.33 | + | 5526.24i | 0.0529398 | + | 0.231944i | ||||
\(829\) | −6495.05 | − | 8144.53i | −0.272114 | − | 0.341220i | 0.626932 | − | 0.779074i | \(-0.284310\pi\) |
−0.899046 | + | 0.437854i | \(0.855739\pi\) | |||||||
\(830\) | −8282.94 | + | 3988.85i | −0.346392 | + | 0.166813i | ||||
\(831\) | 4586.33 | + | 5751.08i | 0.191454 | + | 0.240075i | ||||
\(832\) | 444.361 | − | 1946.87i | 0.0185162 | − | 0.0811246i | ||||
\(833\) | −12954.8 | − | 6238.70i | −0.538844 | − | 0.259493i | ||||
\(834\) | −19880.2 | − | 9573.82i | −0.825415 | − | 0.397499i | ||||
\(835\) | 2772.71 | − | 3476.87i | 0.114914 | − | 0.144098i | ||||
\(836\) | 275.398 | − | 1206.60i | 0.0113934 | − | 0.0499176i | ||||
\(837\) | −8110.94 | − | 35536.3i | −0.334952 | − | 1.46752i | ||||
\(838\) | 22388.2 | − | 28073.9i | 0.922896 | − | 1.15727i | ||||
\(839\) | 16926.3 | − | 21224.9i | 0.696497 | − | 0.873380i | −0.300259 | − | 0.953858i | \(-0.597073\pi\) |
0.996756 | + | 0.0804776i | \(0.0256445\pi\) | |||||||
\(840\) | −1867.66 | − | 8182.77i | −0.0767149 | − | 0.336110i | ||||
\(841\) | 3102.23 | − | 13591.7i | 0.127198 | − | 0.557290i | ||||
\(842\) | −34242.7 | + | 42939.0i | −1.40152 | + | 1.75746i | ||||
\(843\) | 6750.52 | + | 3250.88i | 0.275801 | + | 0.132819i | ||||
\(844\) | −3442.84 | − | 1657.98i | −0.140412 | − | 0.0676187i | ||||
\(845\) | −6942.80 | + | 30418.4i | −0.282651 | + | 1.23837i | ||||
\(846\) | −5334.52 | − | 6689.27i | −0.216790 | − | 0.271846i | ||||
\(847\) | −14594.5 | + | 7028.35i | −0.592059 | + | 0.285120i | ||||
\(848\) | 9540.56 | + | 11963.5i | 0.386349 | + | 0.484467i | ||||
\(849\) | 376.542 | + | 1649.74i | 0.0152213 | + | 0.0666890i | ||||
\(850\) | −23478.8 | − | 11306.8i | −0.947432 | − | 0.456259i | ||||
\(851\) | 14226.4 | + | 62329.9i | 0.573060 | + | 2.51074i | ||||
\(852\) | 19998.2 | − | 9630.63i | 0.804140 | − | 0.387253i | ||||
\(853\) | −28796.5 | −1.15589 | −0.577945 | − | 0.816076i | \(-0.696145\pi\) | ||||
−0.577945 | + | 0.816076i | \(0.696145\pi\) | |||||||
\(854\) | −11868.9 | −0.475579 | ||||||||
\(855\) | −9073.72 | + | 4369.67i | −0.362941 | + | 0.174783i | ||||
\(856\) | −383.167 | + | 1678.76i | −0.0152995 | + | 0.0670315i | ||||
\(857\) | 114.500 | − | 143.579i | 0.00456388 | − | 0.00572293i | −0.779544 | − | 0.626347i | \(-0.784549\pi\) |
0.784108 | + | 0.620624i | \(0.213121\pi\) | |||||||
\(858\) | −263.068 | − | 329.876i | −0.0104673 | − | 0.0131256i | ||||
\(859\) | 29667.8 | 1.17841 | 0.589203 | − | 0.807985i | \(-0.299442\pi\) | ||||
0.589203 | + | 0.807985i | \(0.299442\pi\) | |||||||
\(860\) | −21943.2 | − | 10737.8i | −0.870066 | − | 0.425762i | ||||
\(861\) | −13016.4 | −0.515213 | ||||||||
\(862\) | −25859.7 | − | 32427.1i | −1.02179 | − | 1.28129i | ||||
\(863\) | −23212.9 | + | 29108.1i | −0.915617 | + | 1.14815i | 0.0729451 | + | 0.997336i | \(0.476760\pi\) |
−0.988562 | + | 0.150812i | \(0.951811\pi\) | |||||||
\(864\) | 5814.80 | − | 25476.3i | 0.228962 | − | 1.00315i | ||||
\(865\) | −19241.4 | + | 9266.17i | −0.756332 | + | 0.364230i | ||||
\(866\) | 54753.0 | 2.14848 | ||||||||
\(867\) | 3383.06 | 0.132520 | ||||||||
\(868\) | −19826.3 | + | 9547.86i | −0.775288 | + | 0.373359i | ||||
\(869\) | 618.436 | + | 2709.55i | 0.0241416 | + | 0.105771i | ||||
\(870\) | 29425.4 | + | 14170.5i | 1.14668 | + | 0.552214i | ||||
\(871\) | 91.9054 | + | 402.664i | 0.00357531 | + | 0.0156645i | ||||
\(872\) | −7471.75 | − | 9369.27i | −0.290167 | − | 0.363857i | ||||
\(873\) | 2364.86 | − | 1138.86i | 0.0916821 | − | 0.0441518i | ||||
\(874\) | −35160.4 | − | 44089.7i | −1.36078 | − | 1.70636i | ||||
\(875\) | 1229.39 | − | 5386.33i | 0.0474984 | − | 0.208104i | ||||
\(876\) | −26528.7 | − | 12775.5i | −1.02320 | − | 0.492746i | ||||
\(877\) | 8933.98 | + | 4302.38i | 0.343990 | + | 0.165657i | 0.597899 | − | 0.801571i | \(-0.296002\pi\) |
−0.253910 | + | 0.967228i | \(0.581717\pi\) | |||||||
\(878\) | 16297.4 | − | 20436.3i | 0.626437 | − | 0.785527i | ||||
\(879\) | −6009.95 | + | 26331.3i | −0.230615 | + | 1.01039i | ||||
\(880\) | −518.162 | − | 2270.22i | −0.0198491 | − | 0.0869647i | ||||
\(881\) | 19815.5 | − | 24847.9i | 0.757778 | − | 0.950223i | −0.242021 | − | 0.970271i | \(-0.577810\pi\) |
0.999799 | + | 0.0200476i | \(0.00638177\pi\) | |||||||
\(882\) | 2967.21 | − | 3720.76i | 0.113278 | − | 0.142046i | ||||
\(883\) | 6767.83 | + | 29651.8i | 0.257934 | + | 1.13008i | 0.923456 | + | 0.383704i | \(0.125352\pi\) |
−0.665522 | + | 0.746378i | \(0.731791\pi\) | |||||||
\(884\) | 919.559 | − | 4028.85i | 0.0349865 | − | 0.153286i | ||||
\(885\) | 8401.45 | − | 10535.1i | 0.319109 | − | 0.400150i | ||||
\(886\) | 20176.7 | + | 9716.59i | 0.765068 | + | 0.368437i | ||||
\(887\) | −29512.3 | − | 14212.4i | −1.11717 | − | 0.537999i | −0.218151 | − | 0.975915i | \(-0.570002\pi\) |
−0.899016 | + | 0.437916i | \(0.855717\pi\) | |||||||
\(888\) | −4491.66 | + | 19679.2i | −0.169741 | + | 0.743685i | ||||
\(889\) | 11849.7 | + | 14859.0i | 0.447048 | + | 0.560580i | ||||
\(890\) | 59062.5 | − | 28443.0i | 2.22447 | − | 1.07125i | ||||
\(891\) | −1105.12 | − | 1385.78i | −0.0415523 | − | 0.0521049i | ||||
\(892\) | −395.704 | − | 1733.69i | −0.0148533 | − | 0.0650766i | ||||
\(893\) | 32388.0 | + | 15597.2i | 1.21369 | + | 0.584481i | ||||
\(894\) | 10677.0 | + | 46778.9i | 0.399431 | + | 1.75002i | ||||
\(895\) | 60065.1 | − | 28925.8i | 2.24330 | − | 1.08032i | ||||
\(896\) | 12059.8 | 0.449653 | ||||||||
\(897\) | −8119.19 | −0.302221 | ||||||||
\(898\) | −38102.3 | + | 18349.1i | −1.41591 | + | 0.681868i | ||||
\(899\) | −7009.60 | + | 30711.0i | −0.260048 | + | 1.13934i | ||||
\(900\) | 2271.09 | − | 2847.86i | 0.0841146 | − | 0.105476i | ||||
\(901\) | 9236.15 | + | 11581.8i | 0.341510 | + | 0.428240i | ||||
\(902\) | −1404.99 | −0.0518638 | ||||||||
\(903\) | −4317.60 | − | 19480.5i | −0.159115 | − | 0.717906i | ||||
\(904\) | −3497.97 | −0.128695 | ||||||||
\(905\) | −29372.4 | − | 36831.8i | −1.07886 | − | 1.35285i | ||||
\(906\) | 10132.0 | − | 12705.2i | 0.371539 | − | 0.465895i | ||||
\(907\) | −2467.67 | + | 10811.6i | −0.0903394 | + | 0.395803i | −0.999800 | − | 0.0199869i | \(-0.993638\pi\) |
0.909461 | + | 0.415789i | \(0.136495\pi\) | |||||||
\(908\) | 6907.23 | − | 3326.35i | 0.252450 | − | 0.121573i | ||||
\(909\) | 3909.22 | 0.142641 | ||||||||
\(910\) | −6414.55 | −0.233670 | ||||||||
\(911\) | −24549.0 | + | 11822.2i | −0.892804 | + | 0.429952i | −0.823285 | − | 0.567629i | \(-0.807861\pi\) |
−0.0695197 | + | 0.997581i | \(0.522147\pi\) | |||||||
\(912\) | −10183.4 | − | 44616.3i | −0.369743 | − | 1.61995i | ||||
\(913\) | −308.393 | − | 148.514i | −0.0111789 | − | 0.00538346i | ||||
\(914\) | −7535.65 | − | 33015.8i | −0.272710 | − | 1.19482i | ||||
\(915\) | 13984.9 | + | 17536.5i | 0.505276 | + | 0.633596i | ||||
\(916\) | 25242.9 | − | 12156.3i | 0.910533 | − | 0.438490i | ||||
\(917\) | 2117.49 | + | 2655.25i | 0.0762548 | + | 0.0956205i | ||||
\(918\) | 7261.25 | − | 31813.6i | 0.261064 | − | 1.14380i | ||||
\(919\) | 2792.06 | + | 1344.58i | 0.100219 | + | 0.0482630i | 0.483322 | − | 0.875443i | \(-0.339430\pi\) |
−0.383103 | + | 0.923706i | \(0.625144\pi\) | |||||||
\(920\) | −15707.0 | − | 7564.11i | −0.562876 | − | 0.271067i | ||||
\(921\) | 14830.9 | − | 18597.4i | 0.530615 | − | 0.665370i | ||||
\(922\) | −4472.98 | + | 19597.4i | −0.159772 | + | 0.700007i | ||||
\(923\) | 1388.66 | + | 6084.10i | 0.0495213 | + | 0.216967i | ||||
\(924\) | −529.630 | + | 664.135i | −0.0188566 | + | 0.0236455i | ||||
\(925\) | 25615.4 | − | 32120.7i | 0.910519 | − | 1.14176i | ||||
\(926\) | −9491.98 | − | 41587.1i | −0.336853 | − | 1.47585i | ||||
\(927\) | −945.191 | + | 4141.15i | −0.0334888 | + | 0.146724i | ||||
\(928\) | −14080.4 | + | 17656.3i | −0.498073 | + | 0.624564i | ||||
\(929\) | −14137.3 | − | 6808.18i | −0.499279 | − | 0.240440i | 0.167256 | − | 0.985913i | \(-0.446509\pi\) |
−0.666536 | + | 0.745473i | \(0.732224\pi\) | |||||||
\(930\) | 88720.4 | + | 42725.5i | 3.12823 | + | 1.50648i | ||||
\(931\) | −4449.36 | + | 19493.9i | −0.156629 | + | 0.686238i | ||||
\(932\) | 1364.32 | + | 1710.80i | 0.0479504 | + | 0.0601279i | ||||
\(933\) | −27936.7 | + | 13453.6i | −0.980287 | + | 0.472081i | ||||
\(934\) | 13558.2 | + | 17001.4i | 0.474985 | + | 0.595613i | ||||
\(935\) | −501.629 | − | 2197.78i | −0.0175455 | − | 0.0768718i | ||||
\(936\) | −453.337 | − | 218.315i | −0.0158310 | − | 0.00762379i | ||||
\(937\) | 6733.72 | + | 29502.4i | 0.234772 | + | 1.02860i | 0.945624 | + | 0.325261i | \(0.105452\pi\) |
−0.710853 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(938\) | 1773.96 | − | 854.294i | 0.0617504 | − | 0.0297374i | ||||
\(939\) | −11669.0 | −0.405542 | ||||||||
\(940\) | −30208.6 | −1.04819 | ||||||||
\(941\) | 46762.7 | − | 22519.7i | 1.62000 | − | 0.780150i | 0.620009 | − | 0.784595i | \(-0.287129\pi\) |
0.999990 | + | 0.00444443i | \(0.00141471\pi\) | |||||||
\(942\) | 1429.43 | − | 6262.73i | 0.0494408 | − | 0.216615i | ||||
\(943\) | −16856.9 | + | 21137.9i | −0.582117 | + | 0.729952i | ||||
\(944\) | 7493.52 | + | 9396.58i | 0.258362 | + | 0.323975i | ||||
\(945\) | −21391.4 | −0.736361 | ||||||||
\(946\) | −466.042 | − | 2102.72i | −0.0160173 | − | 0.0722678i | ||||
\(947\) | −18308.0 | −0.628225 | −0.314112 | − | 0.949386i | \(-0.601707\pi\) | ||||
−0.314112 | + | 0.949386i | \(0.601707\pi\) | |||||||
\(948\) | −28617.8 | − | 35885.6i | −0.980445 | − | 1.22944i | ||||
\(949\) | 5161.52 | − | 6472.34i | 0.176554 | − | 0.221392i | ||||
\(950\) | −8063.87 | + | 35330.1i | −0.275396 | + | 1.20659i | ||||
\(951\) | 22282.4 | − | 10730.6i | 0.759787 | − | 0.365894i | ||||
\(952\) | 7247.31 | 0.246730 | ||||||||
\(953\) | −1809.03 | −0.0614904 | −0.0307452 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307452 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(954\) | −4417.43 | + | 2127.32i | −0.149916 | + | 0.0721956i | ||||
\(955\) | 12046.5 | + | 52779.4i | 0.408185 | + | 1.78838i | ||||
\(956\) | 21586.0 | + | 10395.3i | 0.730274 | + | 0.351681i | ||||
\(957\) | 270.585 | + | 1185.51i | 0.00913977 | + | 0.0400440i | ||||
\(958\) | 17015.0 | + | 21336.1i | 0.573830 | + | 0.719560i | ||||
\(959\) | −19477.3 | + | 9379.76i | −0.655843 | + | 0.315838i | ||||
\(960\) | 11217.1 | + | 14065.8i | 0.377115 | + | 0.472887i | ||||
\(961\) | −14505.5 | + | 63552.5i | −0.486907 | + | 2.13328i | ||||
\(962\) | 13899.0 | + | 6693.41i | 0.465823 | + | 0.224329i | ||||
\(963\) | −1277.69 | − | 615.305i | −0.0427551 | − | 0.0205898i | ||||
\(964\) | −22811.1 | + | 28604.2i | −0.762133 | + | 0.955684i | ||||
\(965\) | 7446.61 | − | 32625.7i | 0.248409 | − | 1.08835i | ||||
\(966\) | 8612.87 | + | 37735.4i | 0.286868 | + | 1.25685i | ||||
\(967\) | −5966.89 | + | 7482.25i | −0.198431 | + | 0.248824i | −0.871084 | − | 0.491133i | \(-0.836583\pi\) |
0.672654 | + | 0.739957i | \(0.265154\pi\) | |||||||
\(968\) | −6623.36 | + | 8305.43i | −0.219920 | + | 0.275771i | ||||
\(969\) | −9858.46 | − | 43192.7i | −0.326831 | − | 1.43194i | ||||
\(970\) | 4883.04 | − | 21394.0i | 0.161634 | − | 0.708165i | ||||
\(971\) | 15393.4 | − | 19302.7i | 0.508751 | − | 0.637953i | −0.459427 | − | 0.888215i | \(-0.651945\pi\) |
0.968178 | + | 0.250262i | \(0.0805167\pi\) | |||||||
\(972\) | 9546.95 | + | 4597.57i | 0.315040 | + | 0.151715i | ||||
\(973\) | −11253.0 | − | 5419.16i | −0.370766 | − | 0.178551i | ||||
\(974\) | −8196.72 | + | 35912.2i | −0.269651 | + | 1.18142i | ||||
\(975\) | 3253.05 | + | 4079.19i | 0.106852 | + | 0.133989i | ||||
\(976\) | −18024.9 | + | 8680.32i | −0.591150 | + | 0.284683i | ||||
\(977\) | −35949.8 | − | 45079.6i | −1.17721 | − | 1.47618i | −0.846455 | − | 0.532461i | \(-0.821267\pi\) |
−0.330757 | − | 0.943716i | \(-0.607304\pi\) | |||||||
\(978\) | 14366.7 | + | 62944.8i | 0.469732 | + | 2.05803i | ||||
\(979\) | 2199.03 | + | 1059.00i | 0.0717889 | + | 0.0345717i | ||||
\(980\) | −3738.99 | − | 16381.6i | −0.121875 | − | 0.533970i | ||||
\(981\) | 8892.07 | − | 4282.20i | 0.289401 | − | 0.139368i | ||||
\(982\) | −6949.11 | −0.225820 | ||||||||
\(983\) | 22540.1 | 0.731351 | 0.365676 | − | 0.930742i | \(-0.380838\pi\) | ||||
0.365676 | + | 0.930742i | \(0.380838\pi\) | |||||||
\(984\) | −7690.78 | + | 3703.68i | −0.249160 | + | 0.119989i | ||||
\(985\) | 1154.08 | − | 5056.37i | 0.0373321 | − | 0.163563i | ||||
\(986\) | −17582.9 | + | 22048.3i | −0.567906 | + | 0.712131i | ||||
\(987\) | −15383.5 | − | 19290.3i | −0.496112 | − | 0.622105i | ||||
\(988\) | −5746.65 | −0.185046 | ||||||||
\(989\) | −37226.6 | − | 18216.6i | −1.19690 | − | 0.585697i | ||||
\(990\) | 746.123 | 0.0239529 | ||||||||
\(991\) | 12302.7 | + | 15427.1i | 0.394356 | + | 0.494507i | 0.938883 | − | 0.344236i | \(-0.111862\pi\) |
−0.544527 | + | 0.838744i | \(0.683291\pi\) | |||||||
\(992\) | −42453.7 | + | 53235.2i | −1.35878 | + | 1.70385i | ||||
\(993\) | −1051.73 | + | 4607.93i | −0.0336109 | + | 0.147259i | ||||
\(994\) | 26803.9 | − | 12908.1i | 0.855299 | − | 0.411890i | ||||
\(995\) | −53086.1 | −1.69140 | ||||||||
\(996\) | 5652.97 | 0.179841 | ||||||||
\(997\) | 31081.7 | − | 14968.2i | 0.987330 | − | 0.475473i | 0.130710 | − | 0.991421i | \(-0.458274\pi\) |
0.856620 | + | 0.515948i | \(0.172560\pi\) | |||||||
\(998\) | −6974.12 | − | 30555.6i | −0.221204 | − | 0.969160i | ||||
\(999\) | 46350.7 | + | 22321.3i | 1.46794 | + | 0.706922i |
(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.11.2 | yes | 60 | |
43.2 | odd | 14 | 1849.4.a.g.1.25 | 30 | |||
43.4 | even | 7 | inner | 43.4.e.a.4.2 | ✓ | 60 | |
43.41 | even | 7 | 1849.4.a.h.1.6 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.2 | ✓ | 60 | 43.4 | even | 7 | inner | |
43.4.e.a.11.2 | yes | 60 | 1.1 | even | 1 | trivial | |
1849.4.a.g.1.25 | 30 | 43.2 | odd | 14 | |||
1849.4.a.h.1.6 | 30 | 43.41 | even | 7 |