Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,4,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (of order \(3\), 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: | \(6.72621774065\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.6967728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(1.56632 - 2.71294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.7 |
Dual form | 114.4.e.e.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 6.49420 | + | 11.2483i | 0.580859 | + | 1.00608i | 0.995378 | + | 0.0960362i | \(0.0306165\pi\) |
−0.414519 | + | 0.910041i | \(0.636050\pi\) | |||||||
\(6\) | −3.00000 | + | 5.19615i | −0.204124 | + | 0.353553i | ||||
\(7\) | −25.6033 | −1.38245 | −0.691223 | − | 0.722642i | \(-0.742928\pi\) | ||||
−0.691223 | + | 0.722642i | \(0.742928\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −12.9884 | + | 22.4966i | −0.410729 | + | 0.711404i | ||||
\(11\) | 26.7726 | 0.733841 | 0.366920 | − | 0.930252i | \(-0.380412\pi\) | ||||
0.366920 | + | 0.930252i | \(0.380412\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 4.29582 | − | 7.44059i | 0.0916498 | − | 0.158742i | −0.816556 | − | 0.577267i | \(-0.804119\pi\) |
0.908205 | + | 0.418525i | \(0.137453\pi\) | |||||||
\(14\) | −25.6033 | − | 44.3461i | −0.488768 | − | 0.846572i | ||||
\(15\) | −19.4826 | + | 33.7448i | −0.335359 | + | 0.580859i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.08468 | − | 7.07488i | −0.0582753 | − | 0.100936i | 0.835416 | − | 0.549618i | \(-0.185227\pi\) |
−0.893691 | + | 0.448682i | \(0.851893\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 11.5302 | + | 82.0125i | 0.139221 | + | 0.990261i | ||||
\(20\) | −51.9536 | −0.580859 | ||||||||
\(21\) | −38.4049 | − | 66.5192i | −0.399078 | − | 0.691223i | ||||
\(22\) | 26.7726 | + | 46.3715i | 0.259452 | + | 0.449384i | ||||
\(23\) | −78.4501 | + | 135.880i | −0.711217 | + | 1.23186i | 0.253184 | + | 0.967418i | \(0.418522\pi\) |
−0.964401 | + | 0.264445i | \(0.914811\pi\) | |||||||
\(24\) | −12.0000 | − | 20.7846i | −0.102062 | − | 0.176777i | ||||
\(25\) | −21.8492 | + | 37.8439i | −0.174794 | + | 0.302752i | ||||
\(26\) | 17.1833 | 0.129612 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 51.2065 | − | 88.6923i | 0.345611 | − | 0.598617i | ||||
\(29\) | 103.679 | − | 179.577i | 0.663884 | − | 1.14988i | −0.315702 | − | 0.948858i | \(-0.602240\pi\) |
0.979587 | − | 0.201023i | \(-0.0644266\pi\) | |||||||
\(30\) | −77.9304 | −0.474269 | ||||||||
\(31\) | 94.5197 | 0.547621 | 0.273810 | − | 0.961784i | \(-0.411716\pi\) | ||||
0.273810 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 40.1589 | + | 69.5573i | 0.211842 | + | 0.366920i | ||||
\(34\) | 8.16936 | − | 14.1498i | 0.0412069 | − | 0.0713724i | ||||
\(35\) | −166.273 | − | 287.993i | −0.803006 | − | 1.39085i | ||||
\(36\) | −18.0000 | − | 31.1769i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 197.387 | 0.877035 | 0.438517 | − | 0.898723i | \(-0.355504\pi\) | ||||
0.438517 | + | 0.898723i | \(0.355504\pi\) | |||||||
\(38\) | −130.520 | + | 101.983i | −0.557187 | + | 0.435366i | ||||
\(39\) | 25.7749 | 0.105828 | ||||||||
\(40\) | −51.9536 | − | 89.9862i | −0.205365 | − | 0.355702i | ||||
\(41\) | 188.369 | + | 326.265i | 0.717519 | + | 1.24278i | 0.961980 | + | 0.273120i | \(0.0880557\pi\) |
−0.244461 | + | 0.969659i | \(0.578611\pi\) | |||||||
\(42\) | 76.8098 | − | 133.038i | 0.282191 | − | 0.488768i | ||||
\(43\) | 254.122 | + | 440.152i | 0.901238 | + | 1.56099i | 0.825890 | + | 0.563832i | \(0.190673\pi\) |
0.0753479 | + | 0.997157i | \(0.475993\pi\) | |||||||
\(44\) | −53.5452 | + | 92.7431i | −0.183460 | + | 0.317762i | ||||
\(45\) | −116.896 | −0.387239 | ||||||||
\(46\) | −313.800 | −1.00581 | ||||||||
\(47\) | 183.244 | − | 317.387i | 0.568699 | − | 0.985015i | −0.427996 | − | 0.903780i | \(-0.640780\pi\) |
0.996695 | − | 0.0812344i | \(-0.0258862\pi\) | |||||||
\(48\) | 24.0000 | − | 41.5692i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 312.527 | 0.911156 | ||||||||
\(50\) | −87.3968 | −0.247196 | ||||||||
\(51\) | 12.2540 | − | 21.2246i | 0.0336453 | − | 0.0582753i | ||||
\(52\) | 17.1833 | + | 29.7623i | 0.0458249 | + | 0.0793711i | ||||
\(53\) | 101.665 | − | 176.088i | 0.263485 | − | 0.456370i | −0.703680 | − | 0.710517i | \(-0.748461\pi\) |
0.967166 | + | 0.254147i | \(0.0817946\pi\) | |||||||
\(54\) | −27.0000 | − | 46.7654i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 173.867 | + | 301.146i | 0.426258 | + | 0.738300i | ||||
\(56\) | 204.826 | 0.488768 | ||||||||
\(57\) | −195.780 | + | 152.975i | −0.454941 | + | 0.355474i | ||||
\(58\) | 414.715 | 0.938874 | ||||||||
\(59\) | −296.102 | − | 512.864i | −0.653376 | − | 1.13168i | −0.982298 | − | 0.187324i | \(-0.940019\pi\) |
0.328922 | − | 0.944357i | \(-0.393315\pi\) | |||||||
\(60\) | −77.9304 | − | 134.979i | −0.167679 | − | 0.290429i | ||||
\(61\) | 254.530 | − | 440.859i | 0.534250 | − | 0.925348i | −0.464949 | − | 0.885337i | \(-0.653927\pi\) |
0.999199 | − | 0.0400106i | \(-0.0127392\pi\) | |||||||
\(62\) | 94.5197 | + | 163.713i | 0.193613 | + | 0.335348i | ||||
\(63\) | 115.215 | − | 199.558i | 0.230408 | − | 0.399078i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 111.592 | 0.212942 | ||||||||
\(66\) | −80.3178 | + | 139.115i | −0.149795 | + | 0.259452i | ||||
\(67\) | 125.360 | − | 217.129i | 0.228584 | − | 0.395919i | −0.728805 | − | 0.684721i | \(-0.759924\pi\) |
0.957389 | + | 0.288803i | \(0.0932572\pi\) | |||||||
\(68\) | 32.6774 | 0.0582753 | ||||||||
\(69\) | −470.701 | −0.821242 | ||||||||
\(70\) | 332.545 | − | 575.985i | 0.567811 | − | 0.983477i | ||||
\(71\) | 57.7180 | + | 99.9706i | 0.0964771 | + | 0.167103i | 0.910224 | − | 0.414116i | \(-0.135909\pi\) |
−0.813747 | + | 0.581219i | \(0.802576\pi\) | |||||||
\(72\) | 36.0000 | − | 62.3538i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 416.335 | + | 721.114i | 0.667512 | + | 1.15616i | 0.978598 | + | 0.205782i | \(0.0659739\pi\) |
−0.311086 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(74\) | 197.387 | + | 341.885i | 0.310079 | + | 0.537072i | ||||
\(75\) | −131.095 | −0.201834 | ||||||||
\(76\) | −307.160 | − | 124.083i | −0.463601 | − | 0.187281i | ||||
\(77\) | −685.466 | −1.01449 | ||||||||
\(78\) | 25.7749 | + | 44.6435i | 0.0374159 | + | 0.0648062i | ||||
\(79\) | −184.715 | − | 319.935i | −0.263064 | − | 0.455640i | 0.703991 | − | 0.710209i | \(-0.251400\pi\) |
−0.967054 | + | 0.254569i | \(0.918066\pi\) | |||||||
\(80\) | 103.907 | − | 179.972i | 0.145215 | − | 0.251519i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −376.738 | + | 652.529i | −0.507363 | + | 0.878778i | ||||
\(83\) | −1288.29 | −1.70371 | −0.851854 | − | 0.523780i | \(-0.824521\pi\) | ||||
−0.851854 | + | 0.523780i | \(0.824521\pi\) | |||||||
\(84\) | 307.239 | 0.399078 | ||||||||
\(85\) | 53.0535 | − | 91.8913i | 0.0676995 | − | 0.117259i | ||||
\(86\) | −508.244 | + | 880.304i | −0.637271 | + | 1.10379i | ||||
\(87\) | 622.072 | 0.766588 | ||||||||
\(88\) | −214.181 | −0.259452 | ||||||||
\(89\) | −30.5372 | + | 52.8919i | −0.0363700 | + | 0.0629947i | −0.883637 | − | 0.468172i | \(-0.844913\pi\) |
0.847267 | + | 0.531167i | \(0.178246\pi\) | |||||||
\(90\) | −116.896 | − | 202.469i | −0.136910 | − | 0.237135i | ||||
\(91\) | −109.987 | + | 190.503i | −0.126701 | + | 0.219452i | ||||
\(92\) | −313.800 | − | 543.518i | −0.355608 | − | 0.615932i | ||||
\(93\) | 141.780 | + | 245.569i | 0.158084 | + | 0.273810i | ||||
\(94\) | 732.975 | 0.804261 | ||||||||
\(95\) | −847.621 | + | 662.300i | −0.915411 | + | 0.715269i | ||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −123.755 | − | 214.350i | −0.129541 | − | 0.224371i | 0.793958 | − | 0.607973i | \(-0.208017\pi\) |
−0.923499 | + | 0.383602i | \(0.874684\pi\) | |||||||
\(98\) | 312.527 | + | 541.312i | 0.322142 | + | 0.557967i | ||||
\(99\) | −120.477 | + | 208.672i | −0.122307 | + | 0.211842i | ||||
\(100\) | −87.3968 | − | 151.376i | −0.0873968 | − | 0.151376i | ||||
\(101\) | 423.006 | − | 732.668i | 0.416739 | − | 0.721813i | −0.578870 | − | 0.815420i | \(-0.696506\pi\) |
0.995609 | + | 0.0936064i | \(0.0298395\pi\) | |||||||
\(102\) | 49.0162 | 0.0475816 | ||||||||
\(103\) | −1422.55 | −1.36085 | −0.680427 | − | 0.732816i | \(-0.738206\pi\) | ||||
−0.680427 | + | 0.732816i | \(0.738206\pi\) | |||||||
\(104\) | −34.3666 | + | 59.5247i | −0.0324031 | + | 0.0561238i | ||||
\(105\) | 498.818 | − | 863.978i | 0.463616 | − | 0.803006i | ||||
\(106\) | 406.659 | 0.372624 | ||||||||
\(107\) | 286.239 | 0.258615 | 0.129307 | − | 0.991605i | \(-0.458725\pi\) | ||||
0.129307 | + | 0.991605i | \(0.458725\pi\) | |||||||
\(108\) | 54.0000 | − | 93.5307i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 16.1427 | + | 27.9600i | 0.0141852 | + | 0.0245695i | 0.873031 | − | 0.487665i | \(-0.162151\pi\) |
−0.858846 | + | 0.512234i | \(0.828818\pi\) | |||||||
\(110\) | −347.733 | + | 602.292i | −0.301410 | + | 0.522057i | ||||
\(111\) | 296.081 | + | 512.827i | 0.253178 | + | 0.438517i | ||||
\(112\) | 204.826 | + | 354.769i | 0.172806 | + | 0.299308i | ||||
\(113\) | −297.098 | −0.247333 | −0.123666 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123666 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(114\) | −460.740 | − | 186.125i | −0.378529 | − | 0.152914i | ||||
\(115\) | −2037.88 | −1.65247 | ||||||||
\(116\) | 414.715 | + | 718.307i | 0.331942 | + | 0.574941i | ||||
\(117\) | 38.6624 | + | 66.9653i | 0.0305499 | + | 0.0529140i | ||||
\(118\) | 592.204 | − | 1025.73i | 0.462007 | − | 0.800219i | ||||
\(119\) | 104.581 | + | 181.140i | 0.0805625 | + | 0.139538i | ||||
\(120\) | 155.861 | − | 269.959i | 0.118567 | − | 0.205365i | ||||
\(121\) | −614.227 | −0.461478 | ||||||||
\(122\) | 1018.12 | 0.755543 | ||||||||
\(123\) | −565.107 | + | 978.794i | −0.414260 | + | 0.717519i | ||||
\(124\) | −189.039 | + | 327.426i | −0.136905 | + | 0.237127i | ||||
\(125\) | 1055.98 | 0.755596 | ||||||||
\(126\) | 460.859 | 0.325846 | ||||||||
\(127\) | −1333.60 | + | 2309.86i | −0.931792 | + | 1.61391i | −0.151534 | + | 0.988452i | \(0.548421\pi\) |
−0.780258 | + | 0.625458i | \(0.784912\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −762.365 | + | 1320.46i | −0.520330 | + | 0.901238i | ||||
\(130\) | 111.592 | + | 193.283i | 0.0752865 | + | 0.130400i | ||||
\(131\) | −411.138 | − | 712.112i | −0.274208 | − | 0.474943i | 0.695727 | − | 0.718307i | \(-0.255082\pi\) |
−0.969935 | + | 0.243364i | \(0.921749\pi\) | |||||||
\(132\) | −321.271 | −0.211842 | ||||||||
\(133\) | −295.210 | − | 2099.79i | −0.192466 | − | 1.36898i | ||||
\(134\) | 501.438 | 0.323266 | ||||||||
\(135\) | −175.343 | − | 303.704i | −0.111786 | − | 0.193620i | ||||
\(136\) | 32.6774 | + | 56.5990i | 0.0206034 | + | 0.0356862i | ||||
\(137\) | 1222.61 | − | 2117.62i | 0.762443 | − | 1.32059i | −0.179144 | − | 0.983823i | \(-0.557333\pi\) |
0.941588 | − | 0.336768i | \(-0.109334\pi\) | |||||||
\(138\) | −470.701 | − | 815.277i | −0.290353 | − | 0.502906i | ||||
\(139\) | −752.171 | + | 1302.80i | −0.458980 | + | 0.794977i | −0.998907 | − | 0.0467345i | \(-0.985119\pi\) |
0.539927 | + | 0.841712i | \(0.318452\pi\) | |||||||
\(140\) | 1330.18 | 0.803006 | ||||||||
\(141\) | 1099.46 | 0.656677 | ||||||||
\(142\) | −115.436 | + | 199.941i | −0.0682196 | + | 0.118160i | ||||
\(143\) | 115.010 | − | 199.204i | 0.0672564 | − | 0.116491i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 2693.24 | 1.54249 | ||||||||
\(146\) | −832.671 | + | 1442.23i | −0.472002 | + | 0.817532i | ||||
\(147\) | 468.790 | + | 811.968i | 0.263028 | + | 0.455578i | ||||
\(148\) | −394.775 | + | 683.770i | −0.219259 | + | 0.379767i | ||||
\(149\) | 360.374 | + | 624.186i | 0.198141 | + | 0.343190i | 0.947926 | − | 0.318492i | \(-0.103176\pi\) |
−0.749785 | + | 0.661682i | \(0.769843\pi\) | |||||||
\(150\) | −131.095 | − | 227.064i | −0.0713592 | − | 0.123598i | ||||
\(151\) | 1801.25 | 0.970752 | 0.485376 | − | 0.874306i | \(-0.338683\pi\) | ||||
0.485376 | + | 0.874306i | \(0.338683\pi\) | |||||||
\(152\) | −92.2414 | − | 656.100i | −0.0492222 | − | 0.350110i | ||||
\(153\) | 73.5243 | 0.0388502 | ||||||||
\(154\) | −685.466 | − | 1187.26i | −0.358678 | − | 0.621249i | ||||
\(155\) | 613.830 | + | 1063.18i | 0.318090 | + | 0.550948i | ||||
\(156\) | −51.5499 | + | 89.2870i | −0.0264570 | + | 0.0458249i | ||||
\(157\) | −1914.55 | − | 3316.11i | −0.973236 | − | 1.68569i | −0.685637 | − | 0.727943i | \(-0.740476\pi\) |
−0.287599 | − | 0.957751i | \(-0.592857\pi\) | |||||||
\(158\) | 369.429 | − | 639.870i | 0.186014 | − | 0.322186i | ||||
\(159\) | 609.988 | 0.304247 | ||||||||
\(160\) | 415.629 | 0.205365 | ||||||||
\(161\) | 2008.58 | − | 3478.96i | 0.983218 | − | 1.70298i | ||||
\(162\) | 81.0000 | − | 140.296i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −956.496 | −0.459623 | −0.229812 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229812 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(164\) | −1506.95 | −0.717519 | ||||||||
\(165\) | −521.600 | + | 903.438i | −0.246100 | + | 0.426258i | ||||
\(166\) | −1288.29 | − | 2231.38i | −0.602351 | − | 1.04330i | ||||
\(167\) | 1389.88 | − | 2407.35i | 0.644027 | − | 1.11549i | −0.340499 | − | 0.940245i | \(-0.610596\pi\) |
0.984525 | − | 0.175242i | \(-0.0560708\pi\) | |||||||
\(168\) | 307.239 | + | 532.154i | 0.141095 | + | 0.244384i | ||||
\(169\) | 1061.59 | + | 1838.73i | 0.483201 | + | 0.836928i | ||||
\(170\) | 212.214 | 0.0957415 | ||||||||
\(171\) | −691.110 | − | 279.188i | −0.309067 | − | 0.124854i | ||||
\(172\) | −2032.97 | −0.901238 | ||||||||
\(173\) | 154.776 | + | 268.080i | 0.0680196 | + | 0.117813i | 0.898029 | − | 0.439935i | \(-0.144999\pi\) |
−0.830010 | + | 0.557749i | \(0.811665\pi\) | |||||||
\(174\) | 622.072 | + | 1077.46i | 0.271030 | + | 0.469437i | ||||
\(175\) | 559.411 | − | 968.928i | 0.241643 | − | 0.418538i | ||||
\(176\) | −214.181 | − | 370.972i | −0.0917301 | − | 0.158881i | ||||
\(177\) | 888.306 | − | 1538.59i | 0.377227 | − | 0.653376i | ||||
\(178\) | −122.149 | −0.0514350 | ||||||||
\(179\) | 4650.29 | 1.94178 | 0.970890 | − | 0.239524i | \(-0.0769913\pi\) | ||||
0.970890 | + | 0.239524i | \(0.0769913\pi\) | |||||||
\(180\) | 233.791 | − | 404.938i | 0.0968098 | − | 0.167679i | ||||
\(181\) | 134.864 | − | 233.591i | 0.0553833 | − | 0.0959266i | −0.837005 | − | 0.547196i | \(-0.815695\pi\) |
0.892388 | + | 0.451269i | \(0.149029\pi\) | |||||||
\(182\) | −439.948 | −0.179182 | ||||||||
\(183\) | 1527.18 | 0.616899 | ||||||||
\(184\) | 627.601 | − | 1087.04i | 0.251453 | − | 0.435529i | ||||
\(185\) | 1281.87 | + | 2220.27i | 0.509433 | + | 0.882364i | ||||
\(186\) | −283.559 | + | 491.139i | −0.111783 | + | 0.193613i | ||||
\(187\) | −109.358 | − | 189.413i | −0.0427648 | − | 0.0740708i | ||||
\(188\) | 732.975 | + | 1269.55i | 0.284349 | + | 0.492507i | ||||
\(189\) | 691.288 | 0.266052 | ||||||||
\(190\) | −1994.76 | − | 805.822i | −0.761658 | − | 0.307687i | ||||
\(191\) | −1949.96 | −0.738715 | −0.369357 | − | 0.929287i | \(-0.620422\pi\) | ||||
−0.369357 | + | 0.929287i | \(0.620422\pi\) | |||||||
\(192\) | 96.0000 | + | 166.277i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −1465.65 | − | 2538.58i | −0.546631 | − | 0.946793i | −0.998502 | − | 0.0547095i | \(-0.982577\pi\) |
0.451871 | − | 0.892083i | \(-0.350757\pi\) | |||||||
\(194\) | 247.510 | − | 428.701i | 0.0915990 | − | 0.158654i | ||||
\(195\) | 167.388 | + | 289.924i | 0.0614712 | + | 0.106471i | ||||
\(196\) | −625.053 | + | 1082.62i | −0.227789 | + | 0.394542i | ||||
\(197\) | −1236.48 | −0.447186 | −0.223593 | − | 0.974683i | \(-0.571779\pi\) | ||||
−0.223593 | + | 0.974683i | \(0.571779\pi\) | |||||||
\(198\) | −481.907 | −0.172968 | ||||||||
\(199\) | 2254.50 | − | 3904.91i | 0.803103 | − | 1.39102i | −0.114461 | − | 0.993428i | \(-0.536514\pi\) |
0.917564 | − | 0.397588i | \(-0.130153\pi\) | |||||||
\(200\) | 174.794 | − | 302.752i | 0.0617989 | − | 0.107039i | ||||
\(201\) | 752.157 | 0.263946 | ||||||||
\(202\) | 1692.02 | 0.589358 | ||||||||
\(203\) | −2654.51 | + | 4597.75i | −0.917784 | + | 1.58965i | ||||
\(204\) | 49.0162 | + | 84.8985i | 0.0168226 | + | 0.0291377i | ||||
\(205\) | −2446.61 | + | 4237.65i | −0.833554 | + | 1.44376i | ||||
\(206\) | −1422.55 | − | 2463.93i | −0.481135 | − | 0.833350i | ||||
\(207\) | −706.051 | − | 1222.92i | −0.237072 | − | 0.410621i | ||||
\(208\) | −137.466 | −0.0458249 | ||||||||
\(209\) | 308.693 | + | 2195.69i | 0.102166 | + | 0.726694i | ||||
\(210\) | 1995.27 | 0.655651 | ||||||||
\(211\) | 0.952349 | + | 1.64952i | 0.000310722 | + | 0.000538187i | 0.866181 | − | 0.499731i | \(-0.166568\pi\) |
−0.865870 | + | 0.500269i | \(0.833234\pi\) | |||||||
\(212\) | 406.659 | + | 704.354i | 0.131743 | + | 0.228185i | ||||
\(213\) | −173.154 | + | 299.912i | −0.0557011 | + | 0.0964771i | ||||
\(214\) | 286.239 | + | 495.781i | 0.0914342 | + | 0.158369i | ||||
\(215\) | −3300.63 | + | 5716.87i | −1.04698 | + | 1.81343i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −2420.01 | −0.757056 | ||||||||
\(218\) | −32.2854 | + | 55.9200i | −0.0100305 | + | 0.0173733i | ||||
\(219\) | −1249.01 | + | 2163.34i | −0.385388 | + | 0.667512i | ||||
\(220\) | −1390.93 | −0.426258 | ||||||||
\(221\) | −70.1883 | −0.0213637 | ||||||||
\(222\) | −592.162 | + | 1025.65i | −0.179024 | + | 0.310079i | ||||
\(223\) | 2330.11 | + | 4035.88i | 0.699713 | + | 1.21194i | 0.968566 | + | 0.248757i | \(0.0800220\pi\) |
−0.268853 | + | 0.963181i | \(0.586645\pi\) | |||||||
\(224\) | −409.652 | + | 709.538i | −0.122192 | + | 0.211643i | ||||
\(225\) | −196.643 | − | 340.595i | −0.0582646 | − | 0.100917i | ||||
\(226\) | −297.098 | − | 514.588i | −0.0874453 | − | 0.151460i | ||||
\(227\) | −4045.15 | −1.18276 | −0.591380 | − | 0.806393i | \(-0.701416\pi\) | ||||
−0.591380 | + | 0.806393i | \(0.701416\pi\) | |||||||
\(228\) | −138.362 | − | 984.150i | −0.0401897 | − | 0.285864i | ||||
\(229\) | 5062.73 | 1.46094 | 0.730468 | − | 0.682947i | \(-0.239302\pi\) | ||||
0.730468 | + | 0.682947i | \(0.239302\pi\) | |||||||
\(230\) | −2037.88 | − | 3529.72i | −0.584235 | − | 1.01192i | ||||
\(231\) | −1028.20 | − | 1780.89i | −0.292859 | − | 0.507247i | ||||
\(232\) | −829.429 | + | 1436.61i | −0.234719 | + | 0.406544i | ||||
\(233\) | −216.545 | − | 375.066i | −0.0608854 | − | 0.105457i | 0.833976 | − | 0.551801i | \(-0.186059\pi\) |
−0.894861 | + | 0.446344i | \(0.852726\pi\) | |||||||
\(234\) | −77.3248 | + | 133.931i | −0.0216021 | + | 0.0374159i | ||||
\(235\) | 4760.08 | 1.32133 | ||||||||
\(236\) | 2368.82 | 0.653376 | ||||||||
\(237\) | 554.144 | − | 959.806i | 0.151880 | − | 0.263064i | ||||
\(238\) | −209.162 | + | 362.280i | −0.0569663 | + | 0.0986685i | ||||
\(239\) | −4165.22 | −1.12730 | −0.563652 | − | 0.826012i | \(-0.690604\pi\) | ||||
−0.563652 | + | 0.826012i | \(0.690604\pi\) | |||||||
\(240\) | 623.443 | 0.167679 | ||||||||
\(241\) | −2084.71 | + | 3610.82i | −0.557212 | + | 0.965119i | 0.440516 | + | 0.897745i | \(0.354795\pi\) |
−0.997728 | + | 0.0673743i | \(0.978538\pi\) | |||||||
\(242\) | −614.227 | − | 1063.87i | −0.163157 | − | 0.282596i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 1018.12 | + | 1763.44i | 0.267125 | + | 0.462674i | ||||
\(245\) | 2029.61 | + | 3515.39i | 0.529253 | + | 0.916693i | ||||
\(246\) | −2260.43 | −0.585852 | ||||||||
\(247\) | 659.753 | + | 266.520i | 0.169956 | + | 0.0686570i | ||||
\(248\) | −756.158 | −0.193613 | ||||||||
\(249\) | −1932.43 | − | 3347.06i | −0.491818 | − | 0.851854i | ||||
\(250\) | 1055.98 | + | 1829.01i | 0.267143 | + | 0.462706i | ||||
\(251\) | 3566.12 | − | 6176.71i | 0.896780 | − | 1.55327i | 0.0651931 | − | 0.997873i | \(-0.479234\pi\) |
0.831587 | − | 0.555395i | \(-0.187433\pi\) | |||||||
\(252\) | 460.859 | + | 798.230i | 0.115204 | + | 0.199539i | ||||
\(253\) | −2100.31 | + | 3637.85i | −0.521920 | + | 0.903991i | ||||
\(254\) | −5334.38 | −1.31775 | ||||||||
\(255\) | 318.321 | 0.0781726 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 538.758 | − | 933.157i | 0.130766 | − | 0.226493i | −0.793206 | − | 0.608953i | \(-0.791590\pi\) |
0.923972 | + | 0.382460i | \(0.124923\pi\) | |||||||
\(258\) | −3049.46 | −0.735857 | ||||||||
\(259\) | −5053.76 | −1.21245 | ||||||||
\(260\) | −223.183 | + | 386.565i | −0.0532356 | + | 0.0922067i | ||||
\(261\) | 933.108 | + | 1616.19i | 0.221295 | + | 0.383294i | ||||
\(262\) | 822.276 | − | 1424.22i | 0.193895 | − | 0.335835i | ||||
\(263\) | −1244.58 | − | 2155.68i | −0.291803 | − | 0.505417i | 0.682433 | − | 0.730948i | \(-0.260922\pi\) |
−0.974236 | + | 0.225530i | \(0.927588\pi\) | |||||||
\(264\) | −321.271 | − | 556.458i | −0.0748973 | − | 0.129726i | ||||
\(265\) | 2640.92 | 0.612191 | ||||||||
\(266\) | 3341.73 | − | 2611.11i | 0.770280 | − | 0.601869i | ||||
\(267\) | −183.223 | −0.0419965 | ||||||||
\(268\) | 501.438 | + | 868.517i | 0.114292 | + | 0.197959i | ||||
\(269\) | 3090.64 | + | 5353.14i | 0.700519 | + | 1.21333i | 0.968284 | + | 0.249850i | \(0.0803814\pi\) |
−0.267765 | + | 0.963484i | \(0.586285\pi\) | |||||||
\(270\) | 350.687 | − | 607.407i | 0.0790449 | − | 0.136910i | ||||
\(271\) | −3016.36 | − | 5224.48i | −0.676128 | − | 1.17109i | −0.976138 | − | 0.217152i | \(-0.930323\pi\) |
0.300010 | − | 0.953936i | \(-0.403010\pi\) | |||||||
\(272\) | −65.3549 | + | 113.198i | −0.0145688 | + | 0.0252340i | ||||
\(273\) | −659.923 | −0.146302 | ||||||||
\(274\) | 4890.45 | 1.07826 | ||||||||
\(275\) | −584.961 | + | 1013.18i | −0.128271 | + | 0.222171i | ||||
\(276\) | 941.401 | − | 1630.55i | 0.205311 | − | 0.355608i | ||||
\(277\) | 912.717 | 0.197978 | 0.0989889 | − | 0.995089i | \(-0.468439\pi\) | ||||
0.0989889 | + | 0.995089i | \(0.468439\pi\) | |||||||
\(278\) | −3008.68 | −0.649096 | ||||||||
\(279\) | −425.339 | + | 736.708i | −0.0912701 | + | 0.158084i | ||||
\(280\) | 1330.18 | + | 2303.94i | 0.283905 | + | 0.491739i | ||||
\(281\) | 167.443 | − | 290.020i | 0.0355474 | − | 0.0615699i | −0.847704 | − | 0.530469i | \(-0.822016\pi\) |
0.883252 | + | 0.468899i | \(0.155349\pi\) | |||||||
\(282\) | 1099.46 | + | 1904.32i | 0.232170 | + | 0.402131i | ||||
\(283\) | 1388.47 | + | 2404.90i | 0.291646 | + | 0.505146i | 0.974199 | − | 0.225690i | \(-0.0724637\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(284\) | −461.744 | −0.0964771 | ||||||||
\(285\) | −2992.14 | − | 1208.73i | −0.621891 | − | 0.251225i | ||||
\(286\) | 460.042 | 0.0951149 | ||||||||
\(287\) | −4822.86 | − | 8353.43i | −0.991931 | − | 1.71808i | ||||
\(288\) | 144.000 | + | 249.415i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 2423.13 | − | 4196.99i | 0.493208 | − | 0.854261i | ||||
\(290\) | 2693.24 | + | 4664.83i | 0.545353 | + | 0.944580i | ||||
\(291\) | 371.266 | − | 643.051i | 0.0747903 | − | 0.129541i | ||||
\(292\) | −3330.68 | −0.667512 | ||||||||
\(293\) | −3067.85 | −0.611692 | −0.305846 | − | 0.952081i | \(-0.598939\pi\) | ||||
−0.305846 | + | 0.952081i | \(0.598939\pi\) | |||||||
\(294\) | −937.580 | + | 1623.94i | −0.185989 | + | 0.322142i | ||||
\(295\) | 3845.89 | − | 6661.28i | 0.759039 | − | 1.31469i | ||||
\(296\) | −1579.10 | −0.310079 | ||||||||
\(297\) | −722.861 | −0.141228 | ||||||||
\(298\) | −720.747 | + | 1248.37i | −0.140107 | + | 0.242672i | ||||
\(299\) | 674.016 | + | 1167.43i | 0.130366 | + | 0.225800i | ||||
\(300\) | 262.191 | − | 454.127i | 0.0504586 | − | 0.0873968i | ||||
\(301\) | −6506.35 | − | 11269.3i | −1.24591 | − | 2.15798i | ||||
\(302\) | 1801.25 | + | 3119.85i | 0.343213 | + | 0.594462i | ||||
\(303\) | 2538.04 | 0.481209 | ||||||||
\(304\) | 1044.16 | − | 815.867i | 0.196995 | − | 0.153925i | ||||
\(305\) | 6611.88 | 1.24129 | ||||||||
\(306\) | 73.5243 | + | 127.348i | 0.0137356 | + | 0.0237908i | ||||
\(307\) | 3743.90 | + | 6484.63i | 0.696013 | + | 1.20553i | 0.969838 | + | 0.243750i | \(0.0783776\pi\) |
−0.273825 | + | 0.961779i | \(0.588289\pi\) | |||||||
\(308\) | 1370.93 | − | 2374.52i | 0.253624 | − | 0.439289i | ||||
\(309\) | −2133.82 | − | 3695.89i | −0.392845 | − | 0.680427i | ||||
\(310\) | −1227.66 | + | 2126.37i | −0.224924 | + | 0.389579i | ||||
\(311\) | −6681.88 | −1.21831 | −0.609156 | − | 0.793051i | \(-0.708492\pi\) | ||||
−0.609156 | + | 0.793051i | \(0.708492\pi\) | |||||||
\(312\) | −206.200 | −0.0374159 | ||||||||
\(313\) | −4081.01 | + | 7068.52i | −0.736972 | + | 1.27647i | 0.216880 | + | 0.976198i | \(0.430412\pi\) |
−0.953853 | + | 0.300275i | \(0.902921\pi\) | |||||||
\(314\) | 3829.11 | − | 6632.21i | 0.688182 | − | 1.19197i | ||||
\(315\) | 2992.91 | 0.535337 | ||||||||
\(316\) | 1477.72 | 0.263064 | ||||||||
\(317\) | 1419.77 | − | 2459.11i | 0.251553 | − | 0.435702i | −0.712401 | − | 0.701773i | \(-0.752392\pi\) |
0.963954 | + | 0.266071i | \(0.0857255\pi\) | |||||||
\(318\) | 609.988 | + | 1056.53i | 0.107567 | + | 0.186312i | ||||
\(319\) | 2775.75 | − | 4807.74i | 0.487185 | − | 0.843830i | ||||
\(320\) | 415.629 | + | 719.890i | 0.0726073 | + | 0.125760i | ||||
\(321\) | 429.359 | + | 743.672i | 0.0746557 | + | 0.129307i | ||||
\(322\) | 8034.31 | 1.39048 | ||||||||
\(323\) | 533.131 | − | 416.570i | 0.0918397 | − | 0.0717602i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 187.721 | + | 325.142i | 0.0320396 | + | 0.0554942i | ||||
\(326\) | −956.496 | − | 1656.70i | −0.162501 | − | 0.281461i | ||||
\(327\) | −48.4281 | + | 83.8799i | −0.00818985 | + | 0.0141852i | ||||
\(328\) | −1506.95 | − | 2610.12i | −0.253681 | − | 0.439389i | ||||
\(329\) | −4691.63 | + | 8126.15i | −0.786195 | + | 1.36173i | ||||
\(330\) | −2086.40 | −0.348038 | ||||||||
\(331\) | 11056.2 | 1.83597 | 0.917984 | − | 0.396617i | \(-0.129816\pi\) | ||||
0.917984 | + | 0.396617i | \(0.129816\pi\) | |||||||
\(332\) | 2576.57 | − | 4462.75i | 0.425927 | − | 0.737727i | ||||
\(333\) | −888.243 | + | 1538.48i | −0.146172 | + | 0.253178i | ||||
\(334\) | 5559.54 | 0.910791 | ||||||||
\(335\) | 3256.44 | 0.531099 | ||||||||
\(336\) | −614.478 | + | 1064.31i | −0.0997694 | + | 0.172806i | ||||
\(337\) | 2525.16 | + | 4373.71i | 0.408174 | + | 0.706977i | 0.994685 | − | 0.102964i | \(-0.0328325\pi\) |
−0.586512 | + | 0.809941i | \(0.699499\pi\) | |||||||
\(338\) | −2123.18 | + | 3677.46i | −0.341674 | + | 0.591797i | ||||
\(339\) | −445.646 | − | 771.882i | −0.0713988 | − | 0.123666i | ||||
\(340\) | 212.214 | + | 367.565i | 0.0338497 | + | 0.0586295i | ||||
\(341\) | 2530.54 | 0.401866 | ||||||||
\(342\) | −207.543 | − | 1476.23i | −0.0328148 | − | 0.233407i | ||||
\(343\) | 780.217 | 0.122822 | ||||||||
\(344\) | −2032.97 | − | 3521.22i | −0.318636 | − | 0.551893i | ||||
\(345\) | −3056.82 | − | 5294.57i | −0.477026 | − | 0.826233i | ||||
\(346\) | −309.552 | + | 536.160i | −0.0480972 | + | 0.0833067i | ||||
\(347\) | 3007.43 | + | 5209.01i | 0.465265 | + | 0.805863i | 0.999213 | − | 0.0396541i | \(-0.0126256\pi\) |
−0.533948 | + | 0.845517i | \(0.679292\pi\) | |||||||
\(348\) | −1244.14 | + | 2154.92i | −0.191647 | + | 0.331942i | ||||
\(349\) | −2514.51 | −0.385669 | −0.192834 | − | 0.981231i | \(-0.561768\pi\) | ||||
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(350\) | 2237.64 | 0.341735 | ||||||||
\(351\) | −115.987 | + | 200.896i | −0.0176380 | + | 0.0305499i | ||||
\(352\) | 428.362 | − | 741.945i | 0.0648630 | − | 0.112346i | ||||
\(353\) | 4578.03 | 0.690266 | 0.345133 | − | 0.938554i | \(-0.387834\pi\) | ||||
0.345133 | + | 0.938554i | \(0.387834\pi\) | |||||||
\(354\) | 3553.23 | 0.533480 | ||||||||
\(355\) | −749.665 | + | 1298.46i | −0.112079 | + | 0.194127i | ||||
\(356\) | −122.149 | − | 211.568i | −0.0181850 | − | 0.0314974i | ||||
\(357\) | −313.743 | + | 543.419i | −0.0465128 | + | 0.0805625i | ||||
\(358\) | 4650.29 | + | 8054.53i | 0.686523 | + | 1.18909i | ||||
\(359\) | −3986.22 | − | 6904.33i | −0.586029 | − | 1.01503i | −0.994746 | − | 0.102371i | \(-0.967357\pi\) |
0.408717 | − | 0.912661i | \(-0.365976\pi\) | |||||||
\(360\) | 935.164 | 0.136910 | ||||||||
\(361\) | −6593.11 | + | 1891.24i | −0.961235 | + | 0.275731i | ||||
\(362\) | 539.456 | 0.0783238 | ||||||||
\(363\) | −921.341 | − | 1595.81i | −0.133217 | − | 0.230739i | ||||
\(364\) | −439.948 | − | 762.013i | −0.0633504 | − | 0.109726i | ||||
\(365\) | −5407.53 | + | 9366.11i | −0.775460 | + | 1.34314i | ||||
\(366\) | 1527.18 | + | 2645.15i | 0.218107 | + | 0.377772i | ||||
\(367\) | −2732.75 | + | 4733.26i | −0.388688 | + | 0.673227i | −0.992273 | − | 0.124071i | \(-0.960405\pi\) |
0.603585 | + | 0.797298i | \(0.293738\pi\) | |||||||
\(368\) | 2510.40 | 0.355608 | ||||||||
\(369\) | −3390.64 | −0.478346 | ||||||||
\(370\) | −2563.75 | + | 4440.54i | −0.360224 | + | 0.623926i | ||||
\(371\) | −2602.95 | + | 4508.44i | −0.364254 | + | 0.630907i | ||||
\(372\) | −1134.24 | −0.158084 | ||||||||
\(373\) | 9245.54 | 1.28342 | 0.641710 | − | 0.766947i | \(-0.278225\pi\) | ||||
0.641710 | + | 0.766947i | \(0.278225\pi\) | |||||||
\(374\) | 218.715 | − | 378.826i | 0.0302393 | − | 0.0523760i | ||||
\(375\) | 1583.97 | + | 2743.51i | 0.218122 | + | 0.377798i | ||||
\(376\) | −1465.95 | + | 2539.10i | −0.201065 | + | 0.348255i | ||||
\(377\) | −890.771 | − | 1542.86i | −0.121690 | − | 0.210773i | ||||
\(378\) | 691.288 | + | 1197.35i | 0.0940635 | + | 0.162923i | ||||
\(379\) | 6098.42 | 0.826530 | 0.413265 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413265 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(380\) | −599.034 | − | 4260.84i | −0.0808679 | − | 0.575202i | ||||
\(381\) | −8001.58 | −1.07594 | ||||||||
\(382\) | −1949.96 | − | 3377.44i | −0.261175 | − | 0.452368i | ||||
\(383\) | −2264.90 | − | 3922.93i | −0.302170 | − | 0.523374i | 0.674457 | − | 0.738314i | \(-0.264378\pi\) |
−0.976627 | + | 0.214940i | \(0.931044\pi\) | |||||||
\(384\) | −192.000 | + | 332.554i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −4451.55 | − | 7710.32i | −0.589278 | − | 1.02066i | ||||
\(386\) | 2931.30 | − | 5077.16i | 0.386526 | − | 0.669484i | ||||
\(387\) | −4574.19 | −0.600825 | ||||||||
\(388\) | 990.042 | 0.129541 | ||||||||
\(389\) | 2779.46 | − | 4814.17i | 0.362273 | − | 0.627475i | −0.626061 | − | 0.779774i | \(-0.715334\pi\) |
0.988335 | + | 0.152298i | \(0.0486674\pi\) | |||||||
\(390\) | −334.775 | + | 579.848i | −0.0434667 | + | 0.0752865i | ||||
\(391\) | 1281.77 | 0.165786 | ||||||||
\(392\) | −2500.21 | −0.322142 | ||||||||
\(393\) | 1233.41 | − | 2136.34i | 0.158314 | − | 0.274208i | ||||
\(394\) | −1236.48 | − | 2141.65i | −0.158104 | − | 0.273844i | ||||
\(395\) | 2399.15 | − | 4155.45i | 0.305606 | − | 0.529324i | ||||
\(396\) | −481.907 | − | 834.688i | −0.0611534 | − | 0.105921i | ||||
\(397\) | −4695.83 | − | 8133.41i | −0.593645 | − | 1.02822i | −0.993737 | − | 0.111748i | \(-0.964355\pi\) |
0.400092 | − | 0.916475i | \(-0.368978\pi\) | |||||||
\(398\) | 9018.01 | 1.13576 | ||||||||
\(399\) | 5012.59 | − | 3916.66i | 0.628931 | − | 0.491424i | ||||
\(400\) | 699.175 | 0.0873968 | ||||||||
\(401\) | −4766.06 | − | 8255.07i | −0.593531 | − | 1.02803i | −0.993752 | − | 0.111607i | \(-0.964400\pi\) |
0.400222 | − | 0.916418i | \(-0.368933\pi\) | |||||||
\(402\) | 752.157 | + | 1302.77i | 0.0933189 | + | 0.161633i | ||||
\(403\) | 406.040 | − | 703.282i | 0.0501893 | − | 0.0869304i | ||||
\(404\) | 1692.02 | + | 2930.67i | 0.208370 | + | 0.360907i | ||||
\(405\) | 526.030 | − | 911.111i | 0.0645399 | − | 0.111786i | ||||
\(406\) | −10618.0 | −1.29794 | ||||||||
\(407\) | 5284.58 | 0.643604 | ||||||||
\(408\) | −98.0323 | + | 169.797i | −0.0118954 | + | 0.0206034i | ||||
\(409\) | −3289.74 | + | 5698.00i | −0.397720 | + | 0.688871i | −0.993444 | − | 0.114318i | \(-0.963532\pi\) |
0.595725 | + | 0.803189i | \(0.296865\pi\) | |||||||
\(410\) | −9786.44 | −1.17882 | ||||||||
\(411\) | 7335.67 | 0.880394 | ||||||||
\(412\) | 2845.10 | − | 4927.86i | 0.340214 | − | 0.589267i | ||||
\(413\) | 7581.18 | + | 13131.0i | 0.903258 | + | 1.56449i | ||||
\(414\) | 1412.10 | − | 2445.83i | 0.167635 | − | 0.290353i | ||||
\(415\) | −8366.38 | − | 14491.0i | −0.989613 | − | 1.71406i | ||||
\(416\) | −137.466 | − | 238.099i | −0.0162015 | − | 0.0280619i | ||||
\(417\) | −4513.02 | −0.529985 | ||||||||
\(418\) | −3494.35 | + | 2730.36i | −0.408886 | + | 0.319489i | ||||
\(419\) | 4136.42 | 0.482285 | 0.241143 | − | 0.970490i | \(-0.422478\pi\) | ||||
0.241143 | + | 0.970490i | \(0.422478\pi\) | |||||||
\(420\) | 1995.27 | + | 3455.91i | 0.231808 | + | 0.401503i | ||||
\(421\) | −3896.23 | − | 6748.47i | −0.451047 | − | 0.781235i | 0.547405 | − | 0.836868i | \(-0.315616\pi\) |
−0.998451 | + | 0.0556325i | \(0.982282\pi\) | |||||||
\(422\) | −1.90470 | + | 3.29903i | −0.000219714 | + | 0.000380555i | ||||
\(423\) | 1649.19 | + | 2856.49i | 0.189566 | + | 0.328338i | ||||
\(424\) | −813.317 | + | 1408.71i | −0.0931561 | + | 0.161351i | ||||
\(425\) | 356.988 | 0.0407446 | ||||||||
\(426\) | −692.617 | −0.0787732 | ||||||||
\(427\) | −6516.80 | + | 11287.4i | −0.738571 | + | 1.27924i | ||||
\(428\) | −572.479 | + | 991.562i | −0.0646537 | + | 0.111984i | ||||
\(429\) | 690.063 | 0.0776610 | ||||||||
\(430\) | −13202.5 | −1.48066 | ||||||||
\(431\) | 3675.30 | − | 6365.80i | 0.410749 | − | 0.711438i | −0.584223 | − | 0.811593i | \(-0.698601\pi\) |
0.994972 | + | 0.100155i | \(0.0319340\pi\) | |||||||
\(432\) | 216.000 | + | 374.123i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −5346.31 | + | 9260.08i | −0.593365 | + | 1.02774i | 0.400410 | + | 0.916336i | \(0.368868\pi\) |
−0.993775 | + | 0.111403i | \(0.964466\pi\) | |||||||
\(434\) | −2420.01 | − | 4191.58i | −0.267660 | − | 0.463600i | ||||
\(435\) | 4039.86 | + | 6997.24i | 0.445279 | + | 0.771246i | ||||
\(436\) | −129.142 | −0.0141852 | ||||||||
\(437\) | −12048.4 | − | 4867.18i | −1.31888 | − | 0.532789i | ||||
\(438\) | −4996.02 | −0.545021 | ||||||||
\(439\) | 4809.83 | + | 8330.87i | 0.522917 | + | 0.905719i | 0.999644 | + | 0.0266676i | \(0.00848958\pi\) |
−0.476727 | + | 0.879051i | \(0.658177\pi\) | |||||||
\(440\) | −1390.93 | − | 2409.17i | −0.150705 | − | 0.261029i | ||||
\(441\) | −1406.37 | + | 2435.90i | −0.151859 | + | 0.263028i | ||||
\(442\) | −70.1883 | − | 121.570i | −0.00755321 | − | 0.0130825i | ||||
\(443\) | −6302.23 | + | 10915.8i | −0.675909 | + | 1.17071i | 0.300293 | + | 0.953847i | \(0.402916\pi\) |
−0.976202 | + | 0.216862i | \(0.930418\pi\) | |||||||
\(444\) | −2368.65 | −0.253178 | ||||||||
\(445\) | −793.258 | −0.0845034 | ||||||||
\(446\) | −4660.23 | + | 8071.75i | −0.494772 | + | 0.856970i | ||||
\(447\) | −1081.12 | + | 1872.56i | −0.114397 | + | 0.198141i | ||||
\(448\) | −1638.61 | −0.172806 | ||||||||
\(449\) | 14957.9 | 1.57218 | 0.786088 | − | 0.618114i | \(-0.212103\pi\) | ||||
0.786088 | + | 0.618114i | \(0.212103\pi\) | |||||||
\(450\) | 393.286 | − | 681.191i | 0.0411993 | − | 0.0713592i | ||||
\(451\) | 5043.13 | + | 8734.96i | 0.526545 | + | 0.912002i | ||||
\(452\) | 594.195 | − | 1029.18i | 0.0618332 | − | 0.107098i | ||||
\(453\) | 2701.87 | + | 4679.78i | 0.280232 | + | 0.485376i | ||||
\(454\) | −4045.15 | − | 7006.41i | −0.418168 | − | 0.724289i | ||||
\(455\) | −2857.11 | −0.294381 | ||||||||
\(456\) | 1566.24 | − | 1223.80i | 0.160846 | − | 0.125679i | ||||
\(457\) | −2003.50 | −0.205076 | −0.102538 | − | 0.994729i | \(-0.532696\pi\) | ||||
−0.102538 | + | 0.994729i | \(0.532696\pi\) | |||||||
\(458\) | 5062.73 | + | 8768.90i | 0.516519 | + | 0.894637i | ||||
\(459\) | 110.286 | + | 191.022i | 0.0112151 | + | 0.0194251i | ||||
\(460\) | 4075.76 | − | 7059.43i | 0.413116 | − | 0.715538i | ||||
\(461\) | 567.329 | + | 982.642i | 0.0573170 | + | 0.0992759i | 0.893260 | − | 0.449540i | \(-0.148412\pi\) |
−0.835943 | + | 0.548816i | \(0.815079\pi\) | |||||||
\(462\) | 2056.40 | − | 3561.79i | 0.207083 | − | 0.358678i | ||||
\(463\) | −2934.33 | −0.294536 | −0.147268 | − | 0.989097i | \(-0.547048\pi\) | ||||
−0.147268 | + | 0.989097i | \(0.547048\pi\) | |||||||
\(464\) | −3317.72 | −0.331942 | ||||||||
\(465\) | −1841.49 | + | 3189.55i | −0.183649 | + | 0.318090i | ||||
\(466\) | 433.089 | − | 750.132i | 0.0430525 | − | 0.0745691i | ||||
\(467\) | −930.578 | −0.0922098 | −0.0461049 | − | 0.998937i | \(-0.514681\pi\) | ||||
−0.0461049 | + | 0.998937i | \(0.514681\pi\) | |||||||
\(468\) | −309.299 | −0.0305499 | ||||||||
\(469\) | −3209.61 | + | 5559.21i | −0.316005 | + | 0.547336i | ||||
\(470\) | 4760.08 | + | 8244.70i | 0.467162 | + | 0.809149i | ||||
\(471\) | 5743.66 | − | 9948.32i | 0.561898 | − | 0.973236i | ||||
\(472\) | 2368.82 | + | 4102.91i | 0.231003 | + | 0.400110i | ||||
\(473\) | 6803.51 | + | 11784.0i | 0.661365 | + | 1.14552i | ||||
\(474\) | 2216.58 | 0.214791 | ||||||||
\(475\) | −3355.60 | − | 1355.56i | −0.324138 | − | 0.130942i | ||||
\(476\) | −836.649 | −0.0805625 | ||||||||
\(477\) | 914.982 | + | 1584.80i | 0.0878284 | + | 0.152123i | ||||
\(478\) | −4165.22 | − | 7214.38i | −0.398562 | − | 0.690330i | ||||
\(479\) | −7799.60 | + | 13509.3i | −0.743994 | + | 1.28863i | 0.206670 | + | 0.978411i | \(0.433737\pi\) |
−0.950663 | + | 0.310224i | \(0.899596\pi\) | |||||||
\(480\) | 623.443 | + | 1079.83i | 0.0592836 | + | 0.102682i | ||||
\(481\) | 847.942 | − | 1468.68i | 0.0803801 | − | 0.139222i | ||||
\(482\) | −8338.84 | −0.788016 | ||||||||
\(483\) | 12051.5 | 1.13532 | ||||||||
\(484\) | 1228.45 | − | 2127.74i | 0.115369 | − | 0.199826i | ||||
\(485\) | 1607.38 | − | 2784.07i | 0.150490 | − | 0.260656i | ||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 13580.1 | 1.26360 | 0.631799 | − | 0.775132i | \(-0.282317\pi\) | ||||
0.631799 | + | 0.775132i | \(0.282317\pi\) | |||||||
\(488\) | −2036.24 | + | 3526.87i | −0.188886 | + | 0.327160i | ||||
\(489\) | −1434.74 | − | 2485.05i | −0.132682 | − | 0.229812i | ||||
\(490\) | −4059.22 | + | 7030.77i | −0.374238 | + | 0.648200i | ||||
\(491\) | −398.489 | − | 690.202i | −0.0366264 | − | 0.0634387i | 0.847131 | − | 0.531384i | \(-0.178328\pi\) |
−0.883758 | + | 0.467945i | \(0.844994\pi\) | |||||||
\(492\) | −2260.43 | − | 3915.17i | −0.207130 | − | 0.358760i | ||||
\(493\) | −1693.98 | −0.154752 | ||||||||
\(494\) | 198.126 | + | 1409.25i | 0.0180448 | + | 0.128350i | ||||
\(495\) | −3129.60 | −0.284172 | ||||||||
\(496\) | −756.158 | − | 1309.70i | −0.0684526 | − | 0.118563i | ||||
\(497\) | −1477.77 | − | 2559.57i | −0.133374 | − | 0.231011i | ||||
\(498\) | 3864.86 | − | 6694.13i | 0.347768 | − | 0.602351i | ||||
\(499\) | −4450.66 | − | 7708.78i | −0.399277 | − | 0.691567i | 0.594360 | − | 0.804199i | \(-0.297405\pi\) |
−0.993637 | + | 0.112632i | \(0.964072\pi\) | |||||||
\(500\) | −2111.95 | + | 3658.01i | −0.188899 | + | 0.327183i | ||||
\(501\) | 8339.30 | 0.743658 | ||||||||
\(502\) | 14264.5 | 1.26824 | ||||||||
\(503\) | 10112.6 | − | 17515.5i | 0.896416 | − | 1.55264i | 0.0643734 | − | 0.997926i | \(-0.479495\pi\) |
0.832042 | − | 0.554712i | \(-0.187172\pi\) | |||||||
\(504\) | −921.717 | + | 1596.46i | −0.0814614 | + | 0.141095i | ||||
\(505\) | 10988.3 | 0.968266 | ||||||||
\(506\) | −8401.26 | −0.738106 | ||||||||
\(507\) | −3184.78 | + | 5516.19i | −0.278976 | + | 0.483201i | ||||
\(508\) | −5334.38 | − | 9239.43i | −0.465896 | − | 0.806955i | ||||
\(509\) | −10533.2 | + | 18244.0i | −0.917240 | + | 1.58871i | −0.113651 | + | 0.993521i | \(0.536255\pi\) |
−0.803588 | + | 0.595185i | \(0.797079\pi\) | |||||||
\(510\) | 318.321 | + | 551.348i | 0.0276382 | + | 0.0478708i | ||||
\(511\) | −10659.5 | − | 18462.9i | −0.922799 | − | 1.59833i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −311.315 | − | 2214.34i | −0.0267931 | − | 0.190576i | ||||
\(514\) | 2155.03 | 0.184931 | ||||||||
\(515\) | −9238.32 | − | 16001.2i | −0.790464 | − | 1.36912i | ||||
\(516\) | −3049.46 | − | 5281.82i | −0.260165 | − | 0.450619i | ||||
\(517\) | 4905.91 | − | 8497.29i | 0.417334 | − | 0.722844i | ||||
\(518\) | −5053.76 | − | 8753.37i | −0.428667 | − | 0.742473i | ||||
\(519\) | −464.328 | + | 804.239i | −0.0392712 | + | 0.0680196i | ||||
\(520\) | −892.734 | −0.0752865 | ||||||||
\(521\) | −1660.93 | −0.139668 | −0.0698338 | − | 0.997559i | \(-0.522247\pi\) | ||||
−0.0698338 | + | 0.997559i | \(0.522247\pi\) | |||||||
\(522\) | −1866.22 | + | 3232.38i | −0.156479 | + | 0.271030i | ||||
\(523\) | −11157.9 | + | 19326.0i | −0.932889 | + | 1.61581i | −0.154532 | + | 0.987988i | \(0.549387\pi\) |
−0.778356 | + | 0.627823i | \(0.783946\pi\) | |||||||
\(524\) | 3289.10 | 0.274208 | ||||||||
\(525\) | 3356.47 | 0.279025 | ||||||||
\(526\) | 2489.16 | − | 4311.36i | 0.206336 | − | 0.357384i | ||||
\(527\) | −386.083 | − | 668.715i | −0.0319128 | − | 0.0552745i | ||||
\(528\) | 642.543 | − | 1112.92i | 0.0529604 | − | 0.0917301i | ||||
\(529\) | −6225.34 | − | 10782.6i | −0.511658 | − | 0.886217i | ||||
\(530\) | 2640.92 | + | 4574.21i | 0.216442 | + | 0.374889i | ||||
\(531\) | 5329.84 | 0.435584 | ||||||||
\(532\) | 7864.30 | + | 3176.94i | 0.640903 | + | 0.258905i | ||||
\(533\) | 3236.80 | 0.263042 | ||||||||
\(534\) | −183.223 | − | 317.352i | −0.0148480 | − | 0.0257175i | ||||
\(535\) | 1858.89 | + | 3219.70i | 0.150219 | + | 0.260186i | ||||
\(536\) | −1002.88 | + | 1737.03i | −0.0808166 | + | 0.139978i | ||||
\(537\) | 6975.43 | + | 12081.8i | 0.560544 | + | 0.970890i | ||||
\(538\) | −6181.28 | + | 10706.3i | −0.495342 | + | 0.857957i | ||||
\(539\) | 8367.16 | 0.668644 | ||||||||
\(540\) | 1402.75 | 0.111786 | ||||||||
\(541\) | 5689.92 | − | 9855.22i | 0.452178 | − | 0.783196i | −0.546343 | − | 0.837562i | \(-0.683980\pi\) |
0.998521 | + | 0.0543657i | \(0.0173137\pi\) | |||||||
\(542\) | 6032.71 | − | 10449.0i | 0.478095 | − | 0.828084i | ||||
\(543\) | 809.185 | 0.0639511 | ||||||||
\(544\) | −261.420 | −0.0206034 | ||||||||
\(545\) | −209.668 | + | 363.155i | −0.0164792 | + | 0.0285429i | ||||
\(546\) | −659.923 | − | 1143.02i | −0.0517254 | − | 0.0895911i | ||||
\(547\) | 8265.48 | − | 14316.2i | 0.646081 | − | 1.11905i | −0.337969 | − | 0.941157i | \(-0.609740\pi\) |
0.984051 | − | 0.177888i | \(-0.0569266\pi\) | |||||||
\(548\) | 4890.45 | + | 8470.50i | 0.381222 | + | 0.660295i | ||||
\(549\) | 2290.77 | + | 3967.73i | 0.178083 | + | 0.308449i | ||||
\(550\) | −2339.84 | −0.181402 | ||||||||
\(551\) | 15923.0 | + | 6432.40i | 1.23111 | + | 0.497331i | ||||
\(552\) | 3765.61 | 0.290353 | ||||||||
\(553\) | 4729.30 | + | 8191.38i | 0.363671 | + | 0.629897i | ||||
\(554\) | 912.717 | + | 1580.87i | 0.0699957 | + | 0.121236i | ||||
\(555\) | −3845.62 | + | 6660.81i | −0.294121 | + | 0.509433i | ||||
\(556\) | −3008.68 | − | 5211.19i | −0.229490 | − | 0.397489i | ||||
\(557\) | 3662.66 | − | 6343.91i | 0.278621 | − | 0.482586i | −0.692421 | − | 0.721493i | \(-0.743456\pi\) |
0.971042 | + | 0.238908i | \(0.0767894\pi\) | |||||||
\(558\) | −1701.35 | −0.129075 | ||||||||
\(559\) | 4366.65 | 0.330393 | ||||||||
\(560\) | −2660.36 | + | 4607.88i | −0.200751 | + | 0.347712i | ||||
\(561\) | 328.073 | − | 568.239i | 0.0246903 | − | 0.0427648i | ||||
\(562\) | 669.773 | 0.0502716 | ||||||||
\(563\) | 10864.0 | 0.813258 | 0.406629 | − | 0.913593i | \(-0.366704\pi\) | ||||
0.406629 | + | 0.913593i | \(0.366704\pi\) | |||||||
\(564\) | −2198.92 | + | 3808.65i | −0.164169 | + | 0.284349i | ||||
\(565\) | −1929.41 | − | 3341.84i | −0.143665 | − | 0.248836i | ||||
\(566\) | −2776.94 | + | 4809.80i | −0.206225 | + | 0.357192i | ||||
\(567\) | 1036.93 | + | 1796.02i | 0.0768025 | + | 0.133026i | ||||
\(568\) | −461.744 | − | 799.765i | −0.0341098 | − | 0.0590799i | ||||
\(569\) | −19930.0 | −1.46838 | −0.734192 | − | 0.678941i | \(-0.762439\pi\) | ||||
−0.734192 | + | 0.678941i | \(0.762439\pi\) | |||||||
\(570\) | −898.551 | − | 6391.27i | −0.0660284 | − | 0.469650i | ||||
\(571\) | 1218.32 | 0.0892906 | 0.0446453 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446453 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(572\) | 460.042 | + | 796.816i | 0.0336282 | + | 0.0582457i | ||||
\(573\) | −2924.95 | − | 5066.16i | −0.213249 | − | 0.369357i | ||||
\(574\) | 9645.72 | − | 16706.9i | 0.701401 | − | 1.21486i | ||||
\(575\) | −3428.15 | − | 5937.72i | −0.248632 | − | 0.430644i | ||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −9186.43 | −0.662801 | −0.331400 | − | 0.943490i | \(-0.607521\pi\) | ||||
−0.331400 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(578\) | 9692.52 | 0.697501 | ||||||||
\(579\) | 4396.95 | − | 7615.74i | 0.315598 | − | 0.546631i | ||||
\(580\) | −5386.48 | + | 9329.65i | −0.385623 | + | 0.667919i | ||||
\(581\) | 32984.3 | 2.35528 | ||||||||
\(582\) | 1485.06 | 0.105769 | ||||||||
\(583\) | 2721.83 | − | 4714.35i | 0.193356 | − | 0.334903i | ||||
\(584\) | −3330.68 | − | 5768.91i | −0.236001 | − | 0.408766i | ||||
\(585\) | −502.163 | + | 869.772i | −0.0354904 | + | 0.0614712i | ||||
\(586\) | −3067.85 | − | 5313.67i | −0.216266 | − | 0.374583i | ||||
\(587\) | −272.446 | − | 471.890i | −0.0191568 | − | 0.0331805i | 0.856288 | − | 0.516499i | \(-0.172765\pi\) |
−0.875445 | + | 0.483318i | \(0.839432\pi\) | |||||||
\(588\) | −3750.32 | −0.263028 | ||||||||
\(589\) | 1089.83 | + | 7751.80i | 0.0762404 | + | 0.542287i | ||||
\(590\) | 15383.6 | 1.07344 | ||||||||
\(591\) | −1854.72 | − | 3212.47i | −0.129091 | − | 0.223593i | ||||
\(592\) | −1579.10 | − | 2735.08i | −0.109629 | − | 0.189884i | ||||
\(593\) | −6061.77 | + | 10499.3i | −0.419776 | + | 0.727073i | −0.995917 | − | 0.0902776i | \(-0.971225\pi\) |
0.576141 | + | 0.817350i | \(0.304558\pi\) | |||||||
\(594\) | −722.861 | − | 1252.03i | −0.0499315 | − | 0.0864840i | ||||
\(595\) | −1358.34 | + | 2352.72i | −0.0935908 | + | 0.162104i | ||||
\(596\) | −2882.99 | −0.198141 | ||||||||
\(597\) | 13527.0 | 0.927344 | ||||||||
\(598\) | −1348.03 | + | 2334.86i | −0.0921825 | + | 0.159665i | ||||
\(599\) | 12652.6 | − | 21915.0i | 0.863058 | − | 1.49486i | −0.00590371 | − | 0.999983i | \(-0.501879\pi\) |
0.868962 | − | 0.494879i | \(-0.164787\pi\) | |||||||
\(600\) | 1048.76 | 0.0713592 | ||||||||
\(601\) | −15329.1 | −1.04041 | −0.520206 | − | 0.854041i | \(-0.674145\pi\) | ||||
−0.520206 | + | 0.854041i | \(0.674145\pi\) | |||||||
\(602\) | 13012.7 | − | 22538.6i | 0.880993 | − | 1.52592i | ||||
\(603\) | 1128.24 | + | 1954.16i | 0.0761946 | + | 0.131973i | ||||
\(604\) | −3602.50 | + | 6239.71i | −0.242688 | + | 0.420348i | ||||
\(605\) | −3988.91 | − | 6909.00i | −0.268053 | − | 0.464282i | ||||
\(606\) | 2538.04 | + | 4396.01i | 0.170133 | + | 0.294679i | ||||
\(607\) | −1137.90 | −0.0760891 | −0.0380446 | − | 0.999276i | \(-0.512113\pi\) | ||||
−0.0380446 | + | 0.999276i | \(0.512113\pi\) | |||||||
\(608\) | 2457.28 | + | 992.667i | 0.163908 | + | 0.0662137i | ||||
\(609\) | −15927.1 | −1.05977 | ||||||||
\(610\) | 6611.88 | + | 11452.1i | 0.438864 | + | 0.760135i | ||||
\(611\) | −1574.37 | − | 2726.88i | −0.104242 | − | 0.180553i | ||||
\(612\) | −147.049 | + | 254.696i | −0.00971256 | + | 0.0168226i | ||||
\(613\) | 6426.89 | + | 11131.7i | 0.423458 | + | 0.733451i | 0.996275 | − | 0.0862324i | \(-0.0274827\pi\) |
−0.572817 | + | 0.819683i | \(0.694149\pi\) | |||||||
\(614\) | −7487.81 | + | 12969.3i | −0.492155 | + | 0.852438i | ||||
\(615\) | −14679.7 | −0.962506 | ||||||||
\(616\) | 5483.73 | 0.358678 | ||||||||
\(617\) | 9015.61 | − | 15615.5i | 0.588257 | − | 1.01889i | −0.406203 | − | 0.913783i | \(-0.633148\pi\) |
0.994461 | − | 0.105109i | \(-0.0335192\pi\) | |||||||
\(618\) | 4267.65 | − | 7391.79i | 0.277783 | − | 0.481135i | ||||
\(619\) | −28147.3 | −1.82768 | −0.913841 | − | 0.406071i | \(-0.866898\pi\) | ||||
−0.913841 | + | 0.406071i | \(0.866898\pi\) | |||||||
\(620\) | −4910.64 | −0.318090 | ||||||||
\(621\) | 2118.15 | − | 3668.75i | 0.136874 | − | 0.237072i | ||||
\(622\) | −6681.88 | − | 11573.4i | −0.430738 | − | 0.746060i | ||||
\(623\) | 781.851 | − | 1354.21i | 0.0502796 | − | 0.0870868i | ||||
\(624\) | −206.200 | − | 357.148i | −0.0132285 | − | 0.0229125i | ||||
\(625\) | 9588.88 | + | 16608.4i | 0.613688 | + | 1.06294i | ||||
\(626\) | −16324.0 | −1.04224 | ||||||||
\(627\) | −5241.53 | + | 4095.54i | −0.333854 | + | 0.260862i | ||||
\(628\) | 15316.4 | 0.973236 | ||||||||
\(629\) | −806.264 | − | 1396.49i | −0.0511095 | − | 0.0885242i | ||||
\(630\) | 2992.91 | + | 5183.87i | 0.189270 | + | 0.327826i | ||||
\(631\) | −512.279 | + | 887.293i | −0.0323193 | + | 0.0559787i | −0.881733 | − | 0.471749i | \(-0.843623\pi\) |
0.849413 | + | 0.527728i | \(0.176956\pi\) | |||||||
\(632\) | 1477.72 | + | 2559.48i | 0.0930070 | + | 0.161093i | ||||
\(633\) | −2.85705 | + | 4.94855i | −0.000179396 | + | 0.000310722i | ||||
\(634\) | 5679.08 | 0.355749 | ||||||||
\(635\) | −34642.5 | −2.16496 | ||||||||
\(636\) | −1219.98 | + | 2113.06i | −0.0760616 | + | 0.131743i | ||||
\(637\) | 1342.56 | − | 2325.38i | 0.0835073 | − | 0.144639i | ||||
\(638\) | 11103.0 | 0.688984 | ||||||||
\(639\) | −1038.92 | −0.0643180 | ||||||||
\(640\) | −831.257 | + | 1439.78i | −0.0513411 | + | 0.0889255i | ||||
\(641\) | −8738.48 | − | 15135.5i | −0.538454 | − | 0.932630i | −0.998988 | − | 0.0449875i | \(-0.985675\pi\) |
0.460533 | − | 0.887642i | \(-0.347658\pi\) | |||||||
\(642\) | −858.718 | + | 1487.34i | −0.0527896 | + | 0.0914342i | ||||
\(643\) | 6716.23 | + | 11632.9i | 0.411917 | + | 0.713460i | 0.995099 | − | 0.0988805i | \(-0.0315262\pi\) |
−0.583183 | + | 0.812341i | \(0.698193\pi\) | |||||||
\(644\) | 8034.31 | + | 13915.8i | 0.491609 | + | 0.851492i | ||||
\(645\) | −19803.8 | −1.20895 | ||||||||
\(646\) | 1254.65 | + | 506.841i | 0.0764142 | + | 0.0308690i | ||||
\(647\) | −2658.09 | −0.161515 | −0.0807575 | − | 0.996734i | \(-0.525734\pi\) | ||||
−0.0807575 | + | 0.996734i | \(0.525734\pi\) | |||||||
\(648\) | 324.000 | + | 561.184i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −7927.43 | − | 13730.7i | −0.479474 | − | 0.830474i | ||||
\(650\) | −375.442 | + | 650.284i | −0.0226554 | + | 0.0392404i | ||||
\(651\) | −3630.02 | − | 6287.37i | −0.218543 | − | 0.378528i | ||||
\(652\) | 1912.99 | − | 3313.40i | 0.114906 | − | 0.199023i | ||||
\(653\) | −9989.77 | −0.598668 | −0.299334 | − | 0.954148i | \(-0.596764\pi\) | ||||
−0.299334 | + | 0.954148i | \(0.596764\pi\) | |||||||
\(654\) | −193.712 | −0.0115822 | ||||||||
\(655\) | 5340.02 | − | 9249.19i | 0.318553 | − | 0.551749i | ||||
\(656\) | 3013.90 | − | 5220.23i | 0.179380 | − | 0.310695i | ||||
\(657\) | −7494.03 | −0.445008 | ||||||||
\(658\) | −18766.5 | −1.11185 | ||||||||
\(659\) | −10032.3 | + | 17376.5i | −0.593025 | + | 1.02715i | 0.400797 | + | 0.916167i | \(0.368733\pi\) |
−0.993822 | + | 0.110983i | \(0.964600\pi\) | |||||||
\(660\) | −2086.40 | − | 3613.75i | −0.123050 | − | 0.213129i | ||||
\(661\) | −11859.5 | + | 20541.3i | −0.697855 | + | 1.20872i | 0.271354 | + | 0.962480i | \(0.412529\pi\) |
−0.969209 | + | 0.246241i | \(0.920805\pi\) | |||||||
\(662\) | 11056.2 | + | 19150.0i | 0.649113 | + | 1.12430i | ||||
\(663\) | −105.282 | − | 182.355i | −0.00616717 | − | 0.0106818i | ||||
\(664\) | 10306.3 | 0.602351 | ||||||||
\(665\) | 21701.8 | − | 16957.0i | 1.26551 | − | 0.988821i | ||||
\(666\) | −3552.97 | −0.206719 | ||||||||
\(667\) | 16267.2 | + | 28175.6i | 0.944331 | + | 1.63563i | ||||
\(668\) | 5559.54 | + | 9629.40i | 0.322013 | + | 0.557743i | ||||
\(669\) | −6990.34 | + | 12107.6i | −0.403979 | + | 0.699713i | ||||
\(670\) | 3256.44 | + | 5640.32i | 0.187772 | + | 0.325231i | ||||
\(671\) | 6814.44 | − | 11803.0i | 0.392054 | − | 0.679058i | ||||
\(672\) | −2457.91 | −0.141095 | ||||||||
\(673\) | −10144.0 | −0.581014 | −0.290507 | − | 0.956873i | \(-0.593824\pi\) | ||||
−0.290507 | + | 0.956873i | \(0.593824\pi\) | |||||||
\(674\) | −5050.33 | + | 8747.43i | −0.288622 | + | 0.499908i | ||||
\(675\) | 589.929 | − | 1021.79i | 0.0336391 | − | 0.0582646i | ||||
\(676\) | −8492.73 | −0.483201 | ||||||||
\(677\) | −16883.4 | −0.958469 | −0.479234 | − | 0.877687i | \(-0.659086\pi\) | ||||
−0.479234 | + | 0.877687i | \(0.659086\pi\) | |||||||
\(678\) | 891.293 | − | 1543.76i | 0.0504866 | − | 0.0874453i | ||||
\(679\) | 3168.54 | + | 5488.07i | 0.179083 | + | 0.310181i | ||||
\(680\) | −424.428 | + | 735.130i | −0.0239354 | + | 0.0414573i | ||||
\(681\) | −6067.73 | − | 10509.6i | −0.341433 | − | 0.591380i | ||||
\(682\) | 2530.54 | + | 4383.02i | 0.142081 | + | 0.246092i | ||||
\(683\) | −16610.2 | −0.930560 | −0.465280 | − | 0.885164i | \(-0.654046\pi\) | ||||
−0.465280 | + | 0.885164i | \(0.654046\pi\) | |||||||
\(684\) | 2349.35 | − | 1835.70i | 0.131330 | − | 0.102617i | ||||
\(685\) | 31759.5 | 1.77149 | ||||||||
\(686\) | 780.217 | + | 1351.38i | 0.0434240 | + | 0.0752125i | ||||
\(687\) | 7594.09 | + | 13153.3i | 0.421736 | + | 0.730468i | ||||
\(688\) | 4065.95 | − | 7042.43i | 0.225309 | − | 0.390247i | ||||
\(689\) | −873.467 | − | 1512.89i | −0.0482967 | − | 0.0836524i | ||||
\(690\) | 6113.65 | − | 10589.1i | 0.337308 | − | 0.584235i | ||||
\(691\) | 24812.1 | 1.36598 | 0.682992 | − | 0.730426i | \(-0.260678\pi\) | ||||
0.682992 | + | 0.730426i | \(0.260678\pi\) | |||||||
\(692\) | −1238.21 | −0.0680196 | ||||||||
\(693\) | 3084.60 | − | 5342.68i | 0.169082 | − | 0.292859i | ||||
\(694\) | −6014.85 | + | 10418.0i | −0.328992 | + | 0.569831i | ||||
\(695\) | −19539.0 | −1.06641 | ||||||||
\(696\) | −4976.58 | −0.271030 | ||||||||
\(697\) | 1538.85 | − | 2665.37i | 0.0836273 | − | 0.144847i | ||||
\(698\) | −2514.51 | − | 4355.25i | −0.136355 | − | 0.236173i | ||||
\(699\) | 649.634 | − | 1125.20i | 0.0351522 | − | 0.0608854i | ||||
\(700\) | 2237.64 | + | 3875.71i | 0.120821 | + | 0.209269i | ||||
\(701\) | −6533.58 | − | 11316.5i | −0.352025 | − | 0.609726i | 0.634579 | − | 0.772858i | \(-0.281174\pi\) |
−0.986604 | + | 0.163132i | \(0.947840\pi\) | |||||||
\(702\) | −463.949 | −0.0249439 | ||||||||
\(703\) | 2275.91 | + | 16188.2i | 0.122102 | + | 0.868494i | ||||
\(704\) | 1713.45 | 0.0917301 | ||||||||
\(705\) | 7140.12 | + | 12367.1i | 0.381436 | + | 0.660667i | ||||
\(706\) | 4578.03 | + | 7929.37i | 0.244046 | + | 0.422700i | ||||
\(707\) | −10830.3 | + | 18758.7i | −0.576119 | + | 0.997868i | ||||
\(708\) | 3553.23 | + | 6154.37i | 0.188614 | + | 0.326688i | ||||
\(709\) | −5222.61 | + | 9045.83i | −0.276642 | + | 0.479158i | −0.970548 | − | 0.240907i | \(-0.922555\pi\) |
0.693906 | + | 0.720066i | \(0.255888\pi\) | |||||||
\(710\) | −2998.66 | −0.158504 | ||||||||
\(711\) | 3324.86 | 0.175376 | ||||||||
\(712\) | 244.297 | − | 423.135i | 0.0128587 | − | 0.0222720i | ||||
\(713\) | −7415.08 | + | 12843.3i | −0.389477 | + | 0.674594i | ||||
\(714\) | −1254.97 | −0.0657790 | ||||||||
\(715\) | 2987.60 | 0.156266 | ||||||||
\(716\) | −9300.57 | + | 16109.1i | −0.485445 | + | 0.840816i | ||||
\(717\) | −6247.83 | − | 10821.6i | −0.325425 | − | 0.563652i | ||||
\(718\) | 7972.44 | − | 13808.7i | 0.414385 | − | 0.717736i | ||||
\(719\) | −324.001 | − | 561.185i | −0.0168055 | − | 0.0291080i | 0.857500 | − | 0.514483i | \(-0.172016\pi\) |
−0.874306 | + | 0.485375i | \(0.838683\pi\) | |||||||
\(720\) | 935.164 | + | 1619.75i | 0.0484049 | + | 0.0838397i | ||||
\(721\) | 36421.9 | 1.88131 | ||||||||
\(722\) | −9868.83 | − | 9528.36i | −0.508698 | − | 0.491148i | ||||
\(723\) | −12508.3 | −0.643413 | ||||||||
\(724\) | 539.456 | + | 934.366i | 0.0276916 | + | 0.0479633i | ||||
\(725\) | 4530.59 | + | 7847.22i | 0.232086 | + | 0.401984i | ||||
\(726\) | 1842.68 | − | 3191.62i | 0.0941988 | − | 0.163157i | ||||
\(727\) | −8436.61 | − | 14612.6i | −0.430394 | − | 0.745465i | 0.566513 | − | 0.824053i | \(-0.308292\pi\) |
−0.996907 | + | 0.0785881i | \(0.974959\pi\) | |||||||
\(728\) | 879.897 | − | 1524.03i | 0.0447955 | − | 0.0775881i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −21630.1 | −1.09667 | ||||||||
\(731\) | 2076.01 | − | 3595.76i | 0.105040 | − | 0.181934i | ||||
\(732\) | −3054.36 | + | 5290.31i | −0.154225 | + | 0.267125i | ||||
\(733\) | −23662.1 | −1.19233 | −0.596166 | − | 0.802861i | \(-0.703310\pi\) | ||||
−0.596166 | + | 0.802861i | \(0.703310\pi\) | |||||||
\(734\) | −10931.0 | −0.549688 | ||||||||
\(735\) | −6088.83 | + | 10546.2i | −0.305564 | + | 0.529253i | ||||
\(736\) | 2510.40 | + | 4348.15i | 0.125727 | + | 0.217765i | ||||
\(737\) | 3356.20 | − | 5813.12i | 0.167744 | − | 0.290541i | ||||
\(738\) | −3390.64 | − | 5872.76i | −0.169121 | − | 0.292926i | ||||
\(739\) | −8638.65 | − | 14962.6i | −0.430011 | − | 0.744800i | 0.566863 | − | 0.823812i | \(-0.308157\pi\) |
−0.996874 | + | 0.0790119i | \(0.974823\pi\) | |||||||
\(740\) | −10255.0 | −0.509433 | ||||||||
\(741\) | 297.190 | + | 2113.87i | 0.0147335 | + | 0.104797i | ||||
\(742\) | −10411.8 | −0.515133 | ||||||||
\(743\) | −12899.3 | − | 22342.2i | −0.636915 | − | 1.10317i | −0.986106 | − | 0.166118i | \(-0.946877\pi\) |
0.349190 | − | 0.937052i | \(-0.386457\pi\) | |||||||
\(744\) | −1134.24 | − | 1964.55i | −0.0558913 | − | 0.0968066i | ||||
\(745\) | −4680.68 | + | 8107.17i | −0.230184 | + | 0.398690i | ||||
\(746\) | 9245.54 | + | 16013.7i | 0.453758 | + | 0.785932i | ||||
\(747\) | 5797.28 | − | 10041.2i | 0.283951 | − | 0.491818i | ||||
\(748\) | 874.861 | 0.0427648 | ||||||||
\(749\) | −7328.66 | −0.357521 | ||||||||
\(750\) | −3167.93 | + | 5487.02i | −0.154235 | + | 0.267143i | ||||
\(751\) | −7578.27 | + | 13125.9i | −0.368222 | + | 0.637780i | −0.989288 | − | 0.145979i | \(-0.953367\pi\) |
0.621065 | + | 0.783759i | \(0.286700\pi\) | |||||||
\(752\) | −5863.80 | −0.284349 | ||||||||
\(753\) | 21396.7 | 1.03551 | ||||||||
\(754\) | 1781.54 | − | 3085.72i | 0.0860476 | − | 0.149039i | ||||
\(755\) | 11697.7 | + | 20261.0i | 0.563870 | + | 0.976651i | ||||
\(756\) | −1382.58 | + | 2394.69i | −0.0665130 | + | 0.115204i | ||||
\(757\) | −3727.46 | − | 6456.14i | −0.178965 | − | 0.309977i | 0.762561 | − | 0.646916i | \(-0.223942\pi\) |
−0.941526 | + | 0.336939i | \(0.890608\pi\) | |||||||
\(758\) | 6098.42 | + | 10562.8i | 0.292222 | + | 0.506144i | ||||
\(759\) | −12601.9 | −0.602661 | ||||||||
\(760\) | 6780.97 | − | 5298.40i | 0.323647 | − | 0.252886i | ||||
\(761\) | 23295.2 | 1.10966 | 0.554830 | − | 0.831964i | \(-0.312783\pi\) | ||||
0.554830 | + | 0.831964i | \(0.312783\pi\) | |||||||
\(762\) | −8001.58 | − | 13859.1i | −0.380402 | − | 0.658876i | ||||
\(763\) | −413.306 | − | 715.867i | −0.0196103 | − | 0.0339661i | ||||
\(764\) | 3899.93 | − | 6754.88i | 0.184679 | − | 0.319873i | ||||
\(765\) | 477.481 | + | 827.021i | 0.0225665 | + | 0.0390863i | ||||
\(766\) | 4529.81 | − | 7845.86i | 0.213667 | − | 0.370082i | ||||
\(767\) | −5088.01 | −0.239527 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 18986.9 | − | 32886.3i | 0.890358 | − | 1.54215i | 0.0509122 | − | 0.998703i | \(-0.483787\pi\) |
0.839446 | − | 0.543443i | \(-0.182880\pi\) | |||||||
\(770\) | 8903.10 | − | 15420.6i | 0.416683 | − | 0.721716i | ||||
\(771\) | 3232.55 | 0.150995 | ||||||||
\(772\) | 11725.2 | 0.546631 | ||||||||
\(773\) | −4169.69 | + | 7222.11i | −0.194014 | + | 0.336043i | −0.946577 | − | 0.322478i | \(-0.895484\pi\) |
0.752563 | + | 0.658521i | \(0.228818\pi\) | |||||||
\(774\) | −4574.19 | − | 7922.73i | −0.212424 | − | 0.367929i | ||||
\(775\) | −2065.18 | + | 3577.00i | −0.0957206 | + | 0.165793i | ||||
\(776\) | 990.042 | + | 1714.80i | 0.0457995 | + | 0.0793271i | ||||
\(777\) | −7580.64 | − | 13130.1i | −0.350005 | − | 0.606226i | ||||
\(778\) | 11117.8 | 0.512332 | ||||||||
\(779\) | −24585.9 | + | 19210.5i | −1.13078 | + | 0.883553i | ||||
\(780\) | −1339.10 | −0.0614712 | ||||||||
\(781\) | 1545.26 | + | 2676.47i | 0.0707988 | + | 0.122627i | ||||
\(782\) | 1281.77 | + | 2220.10i | 0.0586140 | + | 0.101522i | ||||
\(783\) | −2799.32 | + | 4848.57i | −0.127765 | + | 0.221295i | ||||
\(784\) | −2500.21 | − | 4330.50i | −0.113895 | − | 0.197271i | ||||
\(785\) | 24867.0 | − | 43070.9i | 1.13063 | − | 1.95830i | ||||
\(786\) | 4933.66 | 0.223890 | ||||||||
\(787\) | −42901.7 | −1.94318 | −0.971588 | − | 0.236680i | \(-0.923941\pi\) | ||||
−0.971588 | + | 0.236680i | \(0.923941\pi\) | |||||||
\(788\) | 2472.96 | − | 4283.29i | 0.111796 | − | 0.193637i | ||||
\(789\) | 3733.74 | − | 6467.03i | 0.168472 | − | 0.291803i | ||||
\(790\) | 9596.59 | 0.432192 | ||||||||
\(791\) | 7606.67 | 0.341924 | ||||||||
\(792\) | 963.814 | − | 1669.38i | 0.0432420 | − | 0.0748973i | ||||
\(793\) | −2186.83 | − | 3787.71i | −0.0979278 | − | 0.169616i | ||||
\(794\) | 9391.66 | − | 16266.8i | 0.419770 | − | 0.727063i | ||||
\(795\) | 3961.38 | + | 6861.32i | 0.176724 | + | 0.306095i | ||||
\(796\) | 9018.01 | + | 15619.7i | 0.401552 | + | 0.695508i | ||||
\(797\) | 5540.21 | 0.246229 | 0.123114 | − | 0.992392i | \(-0.460712\pi\) | ||||
0.123114 | + | 0.992392i | \(0.460712\pi\) | |||||||
\(798\) | 11796.4 | + | 4765.41i | 0.523295 | + | 0.211395i | ||||
\(799\) | −2993.97 | −0.132564 | ||||||||
\(800\) | 699.175 | + | 1211.01i | 0.0308995 | + | 0.0535194i | ||||
\(801\) | −274.834 | − | 476.027i | −0.0121233 | − | 0.0209982i | ||||
\(802\) | 9532.13 | − | 16510.1i | 0.419690 | − | 0.726924i | ||||
\(803\) | 11146.4 | + | 19306.1i | 0.489847 | + | 0.848440i | ||||
\(804\) | −1504.31 | + | 2605.55i | −0.0659864 | + | 0.114292i | ||||
\(805\) | 52176.4 | 2.28444 | ||||||||
\(806\) | 1624.16 | 0.0709784 | ||||||||
\(807\) | −9271.92 | + | 16059.4i | −0.404445 | + | 0.700519i | ||||
\(808\) | −3384.05 | + | 5861.34i | −0.147340 | + | 0.255200i | ||||
\(809\) | 20817.8 | 0.904715 | 0.452357 | − | 0.891837i | \(-0.350583\pi\) | ||||
0.452357 | + | 0.891837i | \(0.350583\pi\) | |||||||
\(810\) | 2104.12 | 0.0912731 | ||||||||
\(811\) | 10334.0 | − | 17899.0i | 0.447441 | − | 0.774991i | −0.550777 | − | 0.834652i | \(-0.685669\pi\) |
0.998219 | + | 0.0596612i | \(0.0190020\pi\) | |||||||
\(812\) | −10618.0 | − | 18391.0i | −0.458892 | − | 0.794824i | ||||
\(813\) | 9049.07 | − | 15673.5i | 0.390363 | − | 0.676128i | ||||
\(814\) | 5284.58 | + | 9153.15i | 0.227548 | + | 0.394125i | ||||
\(815\) | −6211.68 | − | 10758.9i | −0.266976 | − | 0.462416i | ||||
\(816\) | −392.129 | −0.0168226 | ||||||||
\(817\) | −33167.9 | + | 25916.2i | −1.42032 | + | 1.10978i | ||||
\(818\) | −13159.0 | −0.562461 | ||||||||
\(819\) | −989.884 | − | 1714.53i | −0.0422336 | − | 0.0731508i | ||||
\(820\) | −9786.44 | − | 16950.6i | −0.416777 | − | 0.721879i | ||||
\(821\) | 3750.50 | − | 6496.07i | 0.159432 | − | 0.276144i | −0.775232 | − | 0.631676i | \(-0.782367\pi\) |
0.934664 | + | 0.355532i | \(0.115700\pi\) | |||||||
\(822\) | 7335.67 | + | 12705.7i | 0.311266 | + | 0.539129i | ||||
\(823\) | 181.148 | − | 313.757i | 0.00767244 | − | 0.0132891i | −0.862164 | − | 0.506630i | \(-0.830891\pi\) |
0.869836 | + | 0.493341i | \(0.164224\pi\) | |||||||
\(824\) | 11380.4 | 0.481135 | ||||||||
\(825\) | −3509.76 | −0.148114 | ||||||||
\(826\) | −15162.4 | + | 26262.0i | −0.638700 | + | 1.10626i | ||||
\(827\) | 4389.51 | − | 7602.85i | 0.184568 | − | 0.319682i | −0.758863 | − | 0.651251i | \(-0.774245\pi\) |
0.943431 | + | 0.331569i | \(0.107578\pi\) | |||||||
\(828\) | 5648.41 | 0.237072 | ||||||||
\(829\) | 11789.0 | 0.493909 | 0.246954 | − | 0.969027i | \(-0.420570\pi\) | ||||
0.246954 | + | 0.969027i | \(0.420570\pi\) | |||||||
\(830\) | 16732.8 | − | 28982.0i | 0.699762 | − | 1.21202i | ||||
\(831\) | 1369.08 | + | 2371.31i | 0.0571513 | + | 0.0989889i | ||||
\(832\) | 274.933 | − | 476.198i | 0.0114562 | − | 0.0198428i | ||||
\(833\) | −1276.57 | − | 2211.09i | −0.0530979 | − | 0.0919683i | ||||
\(834\) | −4513.02 | − | 7816.79i | −0.187378 | − | 0.324548i | ||||
\(835\) | 36104.7 | 1.49635 | ||||||||
\(836\) | −8223.48 | − | 3322.04i | −0.340209 | − | 0.137434i | ||||
\(837\) | −2552.03 | −0.105390 | ||||||||
\(838\) | 4136.42 | + | 7164.49i | 0.170514 | + | 0.295338i | ||||
\(839\) | 5380.60 | + | 9319.48i | 0.221405 | + | 0.383485i | 0.955235 | − | 0.295848i | \(-0.0956023\pi\) |
−0.733830 | + | 0.679334i | \(0.762269\pi\) | |||||||
\(840\) | −3990.54 | + | 6911.82i | −0.163913 | + | 0.283905i | ||||
\(841\) | −9304.03 | − | 16115.1i | −0.381485 | − | 0.660751i | ||||
\(842\) | 7792.46 | − | 13496.9i | 0.318938 | − | 0.552417i | ||||
\(843\) | 1004.66 | 0.0410466 | ||||||||
\(844\) | −7.61879 | −0.000310722 | ||||||||
\(845\) | −13788.4 | + | 23882.2i | −0.561343 | + | 0.972274i | ||||
\(846\) | −3298.39 | + | 5712.97i | −0.134044 | + | 0.232170i | ||||
\(847\) | 15726.2 | 0.637968 | ||||||||
\(848\) | −3253.27 | −0.131743 | ||||||||
\(849\) | −4165.41 | + | 7214.69i | −0.168382 | + | 0.291646i | ||||
\(850\) | 356.988 | + | 618.322i | 0.0144054 | + | 0.0249509i | ||||
\(851\) | −15485.1 | + | 26820.9i | −0.623762 | + | 1.08039i | ||||
\(852\) | −692.617 | − | 1199.65i | −0.0278505 | − | 0.0482385i | ||||
\(853\) | −2445.13 | − | 4235.09i | −0.0981472 | − | 0.169996i | 0.812771 | − | 0.582584i | \(-0.197958\pi\) |
−0.910918 | + | 0.412588i | \(0.864625\pi\) | |||||||
\(854\) | −26067.2 | −1.04450 | ||||||||
\(855\) | −1347.83 | − | 9586.90i | −0.0539119 | − | 0.383468i | ||||
\(856\) | −2289.91 | −0.0914342 | ||||||||
\(857\) | 15162.2 | + | 26261.7i | 0.604353 | + | 1.04677i | 0.992153 | + | 0.125026i | \(0.0399015\pi\) |
−0.387801 | + | 0.921743i | \(0.626765\pi\) | |||||||
\(858\) | 690.063 | + | 1195.22i | 0.0274573 | + | 0.0475574i | ||||
\(859\) | 7535.78 | − | 13052.4i | 0.299322 | − | 0.518441i | −0.676659 | − | 0.736296i | \(-0.736573\pi\) |
0.975981 | + | 0.217856i | \(0.0699062\pi\) | |||||||
\(860\) | −13202.5 | − | 22867.5i | −0.523492 | − | 0.906714i | ||||
\(861\) | 14468.6 | − | 25060.3i | 0.572692 | − | 0.991931i | ||||
\(862\) | 14701.2 | 0.580887 | ||||||||
\(863\) | 283.180 | 0.0111698 | 0.00558490 | − | 0.999984i | \(-0.498222\pi\) | ||||
0.00558490 | + | 0.999984i | \(0.498222\pi\) | |||||||
\(864\) | −432.000 | + | 748.246i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −2010.29 | + | 3481.93i | −0.0790196 | + | 0.136866i | ||||
\(866\) | −21385.2 | −0.839145 | ||||||||
\(867\) | 14538.8 | 0.569508 | ||||||||
\(868\) | 4840.02 | − | 8383.17i | 0.189264 | − | 0.327815i | ||||
\(869\) | −4945.30 | − | 8565.50i | −0.193047 | − | 0.334367i | ||||
\(870\) | −8079.72 | + | 13994.5i | −0.314860 | + | 0.545353i | ||||
\(871\) | −1077.05 | − | 1865.50i | −0.0418993 | − | 0.0725717i | ||||
\(872\) | −129.142 | − | 223.680i | −0.00501524 | − | 0.00868665i | ||||
\(873\) | 2227.59 | 0.0863604 | ||||||||
\(874\) | −3618.17 | − | 25735.6i | −0.140030 | − | 0.996017i | ||||
\(875\) | −27036.4 | −1.04457 | ||||||||
\(876\) | −4996.02 | − | 8653.37i | −0.192694 | − | 0.333756i | ||||
\(877\) | 1100.91 | + | 1906.84i | 0.0423891 | + | 0.0734200i | 0.886442 | − | 0.462841i | \(-0.153170\pi\) |
−0.844052 | + | 0.536261i | \(0.819836\pi\) | |||||||
\(878\) | −9619.66 | + | 16661.7i | −0.369758 | + | 0.640440i | ||||
\(879\) | −4601.77 | − | 7970.51i | −0.176580 | − | 0.305846i | ||||
\(880\) | 2781.87 | − | 4818.33i | 0.106564 | − | 0.184575i | ||||
\(881\) | 21218.9 | 0.811443 | 0.405722 | − | 0.913997i | \(-0.367020\pi\) | ||||
0.405722 | + | 0.913997i | \(0.367020\pi\) | |||||||
\(882\) | −5625.48 | −0.214762 | ||||||||
\(883\) | 4365.12 | − | 7560.60i | 0.166362 | − | 0.288148i | −0.770776 | − | 0.637106i | \(-0.780131\pi\) |
0.937138 | + | 0.348958i | \(0.113465\pi\) | |||||||
\(884\) | 140.377 | − | 243.139i | 0.00534092 | − | 0.00925075i | ||||
\(885\) | 23075.3 | 0.876463 | ||||||||
\(886\) | −25208.9 | −0.955880 | ||||||||
\(887\) | 5773.98 | − | 10000.8i | 0.218570 | − | 0.378574i | −0.735801 | − | 0.677197i | \(-0.763194\pi\) |
0.954371 | + | 0.298624i | \(0.0965276\pi\) | |||||||
\(888\) | −2368.65 | − | 4102.62i | −0.0895120 | − | 0.155039i | ||||
\(889\) | 34144.4 | − | 59139.8i | 1.28815 | − | 2.23114i | ||||
\(890\) | −793.258 | − | 1373.96i | −0.0298765 | − | 0.0517476i | ||||
\(891\) | −1084.29 | − | 1878.05i | −0.0407689 | − | 0.0706139i | ||||
\(892\) | −18640.9 | −0.699713 | ||||||||
\(893\) | 28142.6 | + | 11368.7i | 1.05460 | + | 0.426025i | ||||
\(894\) | −4324.48 | −0.161781 | ||||||||
\(895\) | 30199.9 | + | 52307.7i | 1.12790 | + | 1.95358i | ||||
\(896\) | −1638.61 | − | 2838.15i | −0.0610960 | − | 0.105821i | ||||
\(897\) | −2022.05 | + | 3502.29i | −0.0752667 | + | 0.130366i | ||||
\(898\) | 14957.9 | + | 25907.9i | 0.555848 | + | 0.962758i | ||||
\(899\) | 9799.68 | − | 16973.5i | 0.363557 | − | 0.629699i | ||||
\(900\) | 1573.14 | 0.0582646 | ||||||||
\(901\) | −1661.07 | −0.0614188 | ||||||||
\(902\) | −10086.3 | + | 17469.9i | −0.372323 | + | 0.644883i | ||||
\(903\) | 19519.0 | − | 33808.0i | 0.719328 | − | 1.24591i | ||||
\(904\) | 2376.78 | 0.0874453 | ||||||||
\(905\) | 3503.34 | 0.128679 | ||||||||
\(906\) | −5403.75 | + | 9359.56i | −0.198154 | + | 0.343213i | ||||
\(907\) | 3641.48 | + | 6307.22i | 0.133311 | + | 0.230902i | 0.924951 | − | 0.380086i | \(-0.124106\pi\) |
−0.791640 | + | 0.610988i | \(0.790772\pi\) | |||||||
\(908\) | 8090.31 | − | 14012.8i | 0.295690 | − | 0.512150i | ||||
\(909\) | 3807.05 | + | 6594.01i | 0.138913 | + | 0.240604i | ||||
\(910\) | −2857.11 | − | 4948.66i | −0.104079 | − | 0.180271i | ||||
\(911\) | 32720.6 | 1.18999 | 0.594995 | − | 0.803729i | \(-0.297154\pi\) | ||||
0.594995 | + | 0.803729i | \(0.297154\pi\) | |||||||
\(912\) | 3685.92 | + | 1489.00i | 0.133830 | + | 0.0540633i | ||||
\(913\) | −34490.8 | −1.25025 | ||||||||
\(914\) | −2003.50 | − | 3470.16i | −0.0725053 | − | 0.125583i | ||||
\(915\) | 9917.81 | + | 17178.2i | 0.358331 | + | 0.620647i | ||||
\(916\) | −10125.5 | + | 17537.8i | −0.365234 | + | 0.632604i | ||||
\(917\) | 10526.5 | + | 18232.4i | 0.379078 | + | 0.656583i | ||||
\(918\) | −220.573 | + | 382.043i | −0.00793027 | + | 0.0137356i | ||||
\(919\) | 1970.84 | 0.0707421 | 0.0353710 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353710 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(920\) | 16303.1 | 0.584235 | ||||||||
\(921\) | −11231.7 | + | 19453.9i | −0.401843 | + | 0.696013i | ||||
\(922\) | −1134.66 | + | 1965.28i | −0.0405292 | + | 0.0701987i | ||||
\(923\) | 991.786 | 0.0353684 | ||||||||
\(924\) | 8225.59 | 0.292859 | ||||||||
\(925\) | −4312.76 | + | 7469.92i | −0.153300 | + | 0.265524i | ||||
\(926\) | −2934.33 | − | 5082.42i | −0.104134 | − | 0.180366i | ||||
\(927\) | 6401.47 | − | 11087.7i | 0.226809 | − | 0.392845i | ||||
\(928\) | −3317.72 | − | 5746.45i | −0.117359 | − | 0.203272i | ||||
\(929\) | −5378.74 | − | 9316.25i | −0.189958 | − | 0.329017i | 0.755278 | − | 0.655404i | \(-0.227502\pi\) |
−0.945236 | + | 0.326388i | \(0.894168\pi\) | |||||||
\(930\) | −7365.95 | −0.259720 | ||||||||
\(931\) | 3603.49 | + | 25631.1i | 0.126852 | + | 0.902283i | ||||
\(932\) | 1732.36 | 0.0608854 | ||||||||
\(933\) | −10022.8 | − | 17360.0i | −0.351696 | − | 0.609156i | ||||
\(934\) | −930.578 | − | 1611.81i | −0.0326011 | − | 0.0564668i | ||||
\(935\) | 1420.38 | − | 2460.17i | 0.0496806 | − | 0.0860494i | ||||
\(936\) | −309.299 | − | 535.722i | −0.0108010 | − | 0.0187079i | ||||
\(937\) | −16289.2 | + | 28213.7i | −0.567923 | + | 0.983671i | 0.428848 | + | 0.903377i | \(0.358920\pi\) |
−0.996771 | + | 0.0802948i | \(0.974414\pi\) | |||||||
\(938\) | −12838.5 | −0.446898 | ||||||||
\(939\) | −24486.1 | −0.850982 | ||||||||
\(940\) | −9520.16 | + | 16489.4i | −0.330334 | + | 0.572154i | ||||
\(941\) | −22922.7 | + | 39703.3i | −0.794112 | + | 1.37544i | 0.129290 | + | 0.991607i | \(0.458730\pi\) |
−0.923402 | + | 0.383835i | \(0.874603\pi\) | |||||||
\(942\) | 22974.7 | 0.794644 | ||||||||
\(943\) | −59110.3 | −2.04125 | ||||||||
\(944\) | −4737.63 | + | 8205.82i | −0.163344 | + | 0.282920i | ||||
\(945\) | 4489.36 | + | 7775.80i | 0.154539 | + | 0.267669i | ||||
\(946\) | −13607.0 | + | 23568.0i | −0.467655 | + | 0.810003i | ||||
\(947\) | 14122.0 | + | 24460.0i | 0.484586 | + | 0.839328i | 0.999843 | − | 0.0177080i | \(-0.00563693\pi\) |
−0.515257 | + | 0.857036i | \(0.672304\pi\) | |||||||
\(948\) | 2216.58 | + | 3839.22i | 0.0759399 | + | 0.131532i | ||||
\(949\) | 7154.01 | 0.244709 | ||||||||
\(950\) | −1007.70 | − | 7167.64i | −0.0344149 | − | 0.244788i | ||||
\(951\) | 8518.62 | 0.290468 | ||||||||
\(952\) | −836.649 | − | 1449.12i | −0.0284831 | − | 0.0493342i | ||||
\(953\) | 22346.7 | + | 38705.7i | 0.759582 | + | 1.31563i | 0.943064 | + | 0.332611i | \(0.107930\pi\) |
−0.183483 | + | 0.983023i | \(0.558737\pi\) | |||||||
\(954\) | −1829.96 | + | 3169.59i | −0.0621041 | + | 0.107567i | ||||
\(955\) | −12663.5 | − | 21933.7i | −0.429089 | − | 0.743204i | ||||
\(956\) | 8330.45 | − | 14428.8i | 0.281826 | − | 0.488137i | ||||
\(957\) | 16654.5 | 0.562553 | ||||||||
\(958\) | −31198.4 | −1.05217 | ||||||||
\(959\) | −31302.8 | + | 54218.1i | −1.05404 | + | 1.82564i | ||||
\(960\) | −1246.89 | + | 2159.67i | −0.0419199 | + | 0.0726073i | ||||
\(961\) | −20857.0 | −0.700112 | ||||||||
\(962\) | 3391.77 | 0.113675 | ||||||||
\(963\) | −1288.08 | + | 2231.01i | −0.0431025 | + | 0.0746557i | ||||
\(964\) | −8338.84 | − | 14443.3i | −0.278606 | − | 0.482560i | ||||
\(965\) | 19036.4 | − | 32972.1i | 0.635031 | − | 1.09991i | ||||
\(966\) | 12051.5 | + | 20873.8i | 0.401397 | + | 0.695240i | ||||
\(967\) | −22790.5 | − | 39474.3i | −0.757905 | − | 1.31273i | −0.943917 | − | 0.330182i | \(-0.892890\pi\) |
0.186013 | − | 0.982547i | \(-0.440443\pi\) | |||||||
\(968\) | 4913.82 | 0.163157 | ||||||||
\(969\) | 1881.98 | + | 760.261i | 0.0623919 | + | 0.0252045i | ||||
\(970\) | 6429.53 | 0.212824 | ||||||||
\(971\) | 2367.98 | + | 4101.46i | 0.0782616 | + | 0.135553i | 0.902500 | − | 0.430690i | \(-0.141730\pi\) |
−0.824238 | + | 0.566243i | \(0.808396\pi\) | |||||||
\(972\) | 486.000 | + | 841.777i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 19258.0 | − | 33355.9i | 0.634516 | − | 1.09901i | ||||
\(974\) | 13580.1 | + | 23521.4i | 0.446749 | + | 0.773792i | ||||
\(975\) | −563.162 | + | 975.426i | −0.0184981 | + | 0.0320396i | ||||
\(976\) | −8144.96 | −0.267125 | ||||||||
\(977\) | −57565.1 | −1.88503 | −0.942514 | − | 0.334167i | \(-0.891545\pi\) | ||||
−0.942514 | + | 0.334167i | \(0.891545\pi\) | |||||||
\(978\) | 2869.49 | − | 4970.10i | 0.0938202 | − | 0.162501i | ||||
\(979\) | −817.560 | + | 1416.06i | −0.0266898 | + | 0.0462281i | ||||
\(980\) | −16236.9 | −0.529253 | ||||||||
\(981\) | −290.569 | −0.00945682 | ||||||||
\(982\) | 796.977 | − | 1380.40i | 0.0258987 | − | 0.0448579i | ||||
\(983\) | −17314.2 | − | 29989.0i | −0.561786 | − | 0.973043i | −0.997341 | − | 0.0728802i | \(-0.976781\pi\) |
0.435554 | − | 0.900162i | \(-0.356552\pi\) | |||||||
\(984\) | 4520.85 | − | 7830.35i | 0.146463 | − | 0.253681i | ||||
\(985\) | −8029.95 | − | 13908.3i | −0.259752 | − | 0.449903i | ||||
\(986\) | −1693.98 | − | 2934.05i | −0.0547132 | − | 0.0947661i | ||||
\(987\) | −28149.8 | −0.907820 | ||||||||
\(988\) | −2242.76 | + | 1752.41i | −0.0722183 | + | 0.0564288i | ||||
\(989\) | −79743.5 | −2.56390 | ||||||||
\(990\) | −3129.60 | − | 5420.63i | −0.100470 | − | 0.174019i | ||||
\(991\) | −15787.8 | − | 27345.2i | −0.506069 | − | 0.876537i | −0.999975 | − | 0.00702215i | \(-0.997765\pi\) |
0.493906 | − | 0.869515i | \(-0.335569\pi\) | |||||||
\(992\) | 1512.32 | − | 2619.41i | 0.0484033 | − | 0.0838369i | ||||
\(993\) | 16584.3 | + | 28724.9i | 0.529998 | + | 0.917984i | ||||
\(994\) | 2955.54 | − | 5119.14i | 0.0943099 | − | 0.163350i | ||||
\(995\) | 58564.8 | 1.86596 | ||||||||
\(996\) | 15459.4 | 0.491818 | ||||||||
\(997\) | −19361.7 | + | 33535.4i | −0.615035 | + | 1.06527i | 0.375343 | + | 0.926886i | \(0.377525\pi\) |
−0.990378 | + | 0.138386i | \(0.955808\pi\) | |||||||
\(998\) | 8901.33 | − | 15417.6i | 0.282331 | − | 0.489012i | ||||
\(999\) | −5329.46 | −0.168785 |
(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 | 114.4.e.e.7.3 | ✓ | 6 | |
3.2 | odd | 2 | 342.4.g.g.235.1 | 6 | |||
19.7 | even | 3 | 2166.4.a.s.1.1 | 3 | |||
19.11 | even | 3 | inner | 114.4.e.e.49.3 | yes | 6 | |
19.12 | odd | 6 | 2166.4.a.w.1.1 | 3 | |||
57.11 | odd | 6 | 342.4.g.g.163.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.e.7.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
114.4.e.e.49.3 | yes | 6 | 19.11 | even | 3 | inner | |
342.4.g.g.163.1 | 6 | 57.11 | odd | 6 | |||
342.4.g.g.235.1 | 6 | 3.2 | odd | 2 | |||
2166.4.a.s.1.1 | 3 | 19.7 | even | 3 | |||
2166.4.a.w.1.1 | 3 | 19.12 | odd | 6 |