Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.151613669376.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.3 | ||
Root | \(1.85439 - 1.88713i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.451 |
Dual form | 1050.3.p.c.901.3 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −3.97571 | − | 5.76140i | −0.567958 | − | 0.823057i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64728 | + | 2.85317i | −0.149753 | + | 0.259379i | −0.931136 | − | 0.364672i | \(-0.881181\pi\) |
0.781383 | + | 0.624051i | \(0.214514\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.250000 | − | 0.144338i | ||||
\(13\) | 7.72850i | 0.594500i | 0.954800 | + | 0.297250i | \(0.0960695\pi\) | ||||
−0.954800 | + | 0.297250i | \(0.903931\pi\) | |||||||
\(14\) | 4.24500 | − | 8.94315i | 0.303214 | − | 0.638797i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −10.9280 | − | 6.30929i | −0.642824 | − | 0.371135i | 0.142877 | − | 0.989740i | \(-0.454365\pi\) |
−0.785702 | + | 0.618606i | \(0.787698\pi\) | |||||||
\(18\) | −2.12132 | + | 3.67423i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.54304 | − | 0.890872i | 0.0812124 | − | 0.0468880i | −0.458844 | − | 0.888517i | \(-0.651736\pi\) |
0.540056 | + | 0.841629i | \(0.318403\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.974040 | + | 12.0852i | 0.0463829 | + | 0.575484i | ||||
\(22\) | −4.65921 | −0.211782 | ||||||||
\(23\) | 3.37819 | + | 5.85120i | 0.146878 | + | 0.254400i | 0.930072 | − | 0.367377i | \(-0.119744\pi\) |
−0.783194 | + | 0.621777i | \(0.786411\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.46544 | + | 5.46488i | −0.364055 | + | 0.210188i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 13.9547 | − | 1.12472i | 0.498384 | − | 0.0401687i | ||||
\(29\) | 39.2933 | 1.35494 | 0.677471 | − | 0.735550i | \(-0.263076\pi\) | ||||
0.677471 | + | 0.735550i | \(0.263076\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.46751 | + | 5.46607i | 0.305404 | + | 0.176325i | 0.644868 | − | 0.764294i | \(-0.276912\pi\) |
−0.339464 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 4.94184 | − | 2.85317i | 0.149753 | − | 0.0864598i | ||||
\(34\) | − | 17.8454i | − | 0.524864i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −17.1983 | − | 29.7883i | −0.464818 | − | 0.805089i | 0.534375 | − | 0.845248i | \(-0.320547\pi\) |
−0.999193 | + | 0.0401585i | \(0.987214\pi\) | |||||||
\(38\) | 2.18218 | + | 1.25988i | 0.0574258 | + | 0.0331548i | ||||
\(39\) | 6.69308 | − | 11.5928i | 0.171617 | − | 0.297250i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.8536i | 0.459844i | 0.973209 | + | 0.229922i | \(0.0738472\pi\) | ||||
−0.973209 | + | 0.229922i | \(0.926153\pi\) | |||||||
\(42\) | −14.1125 | + | 9.73845i | −0.336012 | + | 0.231868i | ||||
\(43\) | 77.4197 | 1.80046 | 0.900229 | − | 0.435416i | \(-0.143399\pi\) | ||||
0.900229 | + | 0.435416i | \(0.143399\pi\) | |||||||
\(44\) | −3.29456 | − | 5.70635i | −0.0748764 | − | 0.129690i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.77748 | + | 8.27485i | −0.103858 | + | 0.179888i | ||||
\(47\) | 11.1602 | − | 6.44335i | 0.237451 | − | 0.137093i | −0.376553 | − | 0.926395i | \(-0.622891\pi\) |
0.614005 | + | 0.789302i | \(0.289558\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −17.3875 | + | 45.8113i | −0.354847 | + | 0.934924i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9280 | + | 18.9279i | 0.214275 | + | 0.371135i | ||||
\(52\) | −13.3862 | − | 7.72850i | −0.257426 | − | 0.148625i | ||||
\(53\) | 25.8440 | − | 44.7631i | 0.487622 | − | 0.844586i | −0.512276 | − | 0.858821i | \(-0.671198\pi\) |
0.999899 | + | 0.0142341i | \(0.00453101\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.2450 | + | 16.2957i | 0.200804 | + | 0.290995i | ||||
\(57\) | −3.08607 | −0.0541416 | ||||||||
\(58\) | 27.7846 | + | 48.1243i | 0.479044 | + | 0.829729i | ||||
\(59\) | 97.7973 | + | 56.4633i | 1.65758 | + | 0.957005i | 0.973827 | + | 0.227292i | \(0.0729872\pi\) |
0.683754 | + | 0.729713i | \(0.260346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22.7184 | + | 13.1165i | −0.372432 | + | 0.215024i | −0.674521 | − | 0.738256i | \(-0.735650\pi\) |
0.302088 | + | 0.953280i | \(0.402316\pi\) | |||||||
\(62\) | 15.4604i | 0.249361i | ||||||||
\(63\) | 9.00500 | − | 18.9713i | 0.142937 | − | 0.301132i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.98882 | + | 4.03500i | 0.105891 | + | 0.0611363i | ||||
\(67\) | 9.95656 | − | 17.2453i | 0.148605 | − | 0.257392i | −0.782107 | − | 0.623144i | \(-0.785855\pi\) |
0.930712 | + | 0.365752i | \(0.119188\pi\) | |||||||
\(68\) | 21.8560 | − | 12.6186i | 0.321412 | − | 0.185567i | ||||
\(69\) | − | 11.7024i | − | 0.169600i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 87.4319 | 1.23144 | 0.615718 | − | 0.787967i | \(-0.288866\pi\) | ||||
0.615718 | + | 0.787967i | \(0.288866\pi\) | |||||||
\(72\) | −4.24264 | − | 7.34847i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 52.7540 | + | 30.4575i | 0.722657 | + | 0.417226i | 0.815730 | − | 0.578433i | \(-0.196336\pi\) |
−0.0930727 | + | 0.995659i | \(0.529669\pi\) | |||||||
\(74\) | 24.3220 | − | 42.1270i | 0.328676 | − | 0.569284i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.56349i | 0.0468880i | ||||||||
\(77\) | 22.9874 | − | 1.85274i | 0.298537 | − | 0.0240615i | ||||
\(78\) | 18.9309 | 0.242704 | ||||||||
\(79\) | 17.7888 | + | 30.8112i | 0.225175 | + | 0.390015i | 0.956372 | − | 0.292152i | \(-0.0943712\pi\) |
−0.731197 | + | 0.682167i | \(0.761038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −23.0909 | + | 13.3315i | −0.281596 | + | 0.162580i | ||||
\(83\) | 46.6773i | 0.562377i | 0.959653 | + | 0.281188i | \(0.0907286\pi\) | ||||
−0.959653 | + | 0.281188i | \(0.909271\pi\) | |||||||
\(84\) | −21.9062 | − | 10.3981i | −0.260788 | − | 0.123787i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 54.7440 | + | 94.8194i | 0.636558 | + | 1.10255i | ||||
\(87\) | −58.9399 | − | 34.0290i | −0.677471 | − | 0.391138i | ||||
\(88\) | 4.65921 | − | 8.06999i | 0.0529456 | − | 0.0917044i | ||||
\(89\) | −47.4706 | + | 27.4072i | −0.533378 | + | 0.307946i | −0.742391 | − | 0.669967i | \(-0.766308\pi\) |
0.209013 | + | 0.977913i | \(0.432975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 44.5270 | − | 30.7263i | 0.489308 | − | 0.337651i | ||||
\(92\) | −13.5128 | −0.146878 | ||||||||
\(93\) | −9.46751 | − | 16.3982i | −0.101801 | − | 0.176325i | ||||
\(94\) | 15.7829 | + | 9.11228i | 0.167903 | + | 0.0969391i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | + | 4.89898i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | − | 45.7447i | − | 0.471595i | −0.971802 | − | 0.235798i | \(-0.924230\pi\) | ||
0.971802 | − | 0.235798i | \(-0.0757703\pi\) | |||||||
\(98\) | −68.4020 | + | 11.0982i | −0.697979 | + | 0.113247i | ||||
\(99\) | −9.88368 | −0.0998352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 79.2589 | + | 45.7601i | 0.784741 | + | 0.453071i | 0.838108 | − | 0.545504i | \(-0.183662\pi\) |
−0.0533667 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(102\) | −15.4545 | + | 26.7681i | −0.151515 | + | 0.262432i | ||||
\(103\) | −43.7414 | + | 25.2541i | −0.424674 | + | 0.245186i | −0.697075 | − | 0.716998i | \(-0.745516\pi\) |
0.272401 | + | 0.962184i | \(0.412182\pi\) | |||||||
\(104\) | − | 21.8595i | − | 0.210188i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 73.0978 | 0.689602 | ||||||||
\(107\) | −46.9747 | − | 81.3626i | −0.439016 | − | 0.760398i | 0.558598 | − | 0.829439i | \(-0.311340\pi\) |
−0.997614 | + | 0.0690404i | \(0.978006\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −60.3052 | + | 104.452i | −0.553258 | + | 0.958272i | 0.444778 | + | 0.895641i | \(0.353282\pi\) |
−0.998037 | + | 0.0626310i | \(0.980051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 59.5766i | 0.536726i | ||||||||
\(112\) | −12.0067 | + | 25.2951i | −0.107202 | + | 0.225849i | ||||
\(113\) | −10.7318 | −0.0949713 | −0.0474856 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474856 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(114\) | −2.18218 | − | 3.77965i | −0.0191419 | − | 0.0331548i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.2933 | + | 68.0580i | −0.338735 | + | 0.586707i | ||||
\(117\) | −20.0792 | + | 11.5928i | −0.171617 | + | 0.0990834i | ||||
\(118\) | 159.702i | 1.35341i | ||||||||
\(119\) | 7.09622 | + | 88.0446i | 0.0596321 | + | 0.739870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 55.0729 | + | 95.3891i | 0.455148 | + | 0.788340i | ||||
\(122\) | −32.1286 | − | 18.5495i | −0.263349 | − | 0.152045i | ||||
\(123\) | 16.3277 | − | 28.2804i | 0.132746 | − | 0.229922i | ||||
\(124\) | −18.9350 | + | 10.9321i | −0.152702 | + | 0.0881624i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29.6025 | − | 2.38590i | 0.234940 | − | 0.0189357i | ||||
\(127\) | 117.281 | 0.923476 | 0.461738 | − | 0.887016i | \(-0.347226\pi\) | ||||
0.461738 | + | 0.887016i | \(0.347226\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −116.130 | − | 67.0475i | −0.900229 | − | 0.519748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 80.2758 | − | 46.3473i | 0.612792 | − | 0.353796i | −0.161265 | − | 0.986911i | \(-0.551557\pi\) |
0.774058 | + | 0.633115i | \(0.218224\pi\) | |||||||
\(132\) | 11.4127i | 0.0864598i | ||||||||
\(133\) | −11.2673 | − | 5.34820i | −0.0847168 | − | 0.0402120i | ||||
\(134\) | 28.1614 | 0.210160 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.9091 | + | 17.8454i | 0.227273 | + | 0.131216i | ||||
\(137\) | 13.7370 | − | 23.7932i | 0.100270 | − | 0.173673i | −0.811526 | − | 0.584317i | \(-0.801363\pi\) |
0.911796 | + | 0.410644i | \(0.134696\pi\) | |||||||
\(138\) | 14.3325 | − | 8.27485i | 0.103858 | − | 0.0599626i | ||||
\(139\) | 67.0127i | 0.482106i | 0.970512 | + | 0.241053i | \(0.0774928\pi\) | ||||
−0.970512 | + | 0.241053i | \(0.922507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.3204 | −0.158301 | ||||||||
\(142\) | 61.8237 | + | 107.082i | 0.435378 | + | 0.754097i | ||||
\(143\) | −22.0507 | − | 12.7310i | −0.154201 | − | 0.0890280i | ||||
\(144\) | 6.00000 | − | 10.3923i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 86.1469i | 0.590047i | ||||||||
\(147\) | 65.7550 | − | 53.6589i | 0.447313 | − | 0.365027i | ||||
\(148\) | 68.7931 | 0.464818 | ||||||||
\(149\) | −25.5567 | − | 44.2656i | −0.171522 | − | 0.297084i | 0.767430 | − | 0.641132i | \(-0.221535\pi\) |
−0.938952 | + | 0.344048i | \(0.888202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.6090 | − | 143.083i | 0.547079 | − | 0.947569i | −0.451394 | − | 0.892325i | \(-0.649073\pi\) |
0.998473 | − | 0.0552442i | \(-0.0175937\pi\) | |||||||
\(152\) | −4.36436 | + | 2.51977i | −0.0287129 | + | 0.0165774i | ||||
\(153\) | − | 37.8558i | − | 0.247423i | ||||||
\(154\) | 18.5237 | + | 26.8436i | 0.120284 | + | 0.174309i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.3862 | + | 23.1855i | 0.0858087 | + | 0.148625i | ||||
\(157\) | −165.248 | − | 95.4059i | −1.05253 | − | 0.607681i | −0.129176 | − | 0.991622i | \(-0.541233\pi\) |
−0.923358 | + | 0.383941i | \(0.874567\pi\) | |||||||
\(158\) | −25.1572 | + | 43.5736i | −0.159223 | + | 0.275782i | ||||
\(159\) | −77.5319 | + | 44.7631i | −0.487622 | + | 0.281529i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.2804 | − | 42.7258i | 0.125965 | − | 0.265377i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 124.101 | + | 214.949i | 0.761356 | + | 1.31871i | 0.942152 | + | 0.335186i | \(0.108799\pi\) |
−0.180796 | + | 0.983521i | \(0.557867\pi\) | |||||||
\(164\) | −32.6554 | − | 18.8536i | −0.199118 | − | 0.114961i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −57.1678 | + | 33.0058i | −0.344384 | + | 0.198830i | ||||
\(167\) | − | 29.2974i | − | 0.175433i | −0.996145 | − | 0.0877167i | \(-0.972043\pi\) | ||
0.996145 | − | 0.0877167i | \(-0.0279570\pi\) | |||||||
\(168\) | −2.75500 | − | 34.1820i | −0.0163988 | − | 0.203464i | ||||
\(169\) | 109.270 | 0.646570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62911 | + | 2.67262i | 0.0270708 | + | 0.0156293i | ||||
\(172\) | −77.4197 | + | 134.095i | −0.450115 | + | 0.779622i | ||||
\(173\) | 19.9982 | − | 11.5460i | 0.115597 | − | 0.0667397i | −0.441087 | − | 0.897464i | \(-0.645407\pi\) |
0.556683 | + | 0.830725i | \(0.312074\pi\) | |||||||
\(174\) | − | 96.2485i | − | 0.553152i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.1782 | 0.0748764 | ||||||||
\(177\) | −97.7973 | − | 169.390i | −0.552527 | − | 0.957005i | ||||
\(178\) | −67.1336 | − | 38.7596i | −0.377155 | − | 0.217751i | ||||
\(179\) | 104.717 | − | 181.376i | 0.585014 | − | 1.01327i | −0.409860 | − | 0.912148i | \(-0.634423\pi\) |
0.994874 | − | 0.101125i | \(-0.0322442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 243.667i | − | 1.34622i | −0.739540 | − | 0.673112i | \(-0.764957\pi\) | ||
0.739540 | − | 0.673112i | \(-0.235043\pi\) | |||||||
\(182\) | 69.1172 | + | 32.8075i | 0.379765 | + | 0.180261i | ||||
\(183\) | 45.4367 | 0.248288 | ||||||||
\(184\) | −9.55497 | − | 16.5497i | −0.0519292 | − | 0.0899440i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.3891 | − | 23.1906i | 0.0719843 | − | 0.124681i | ||||
\(187\) | 36.0030 | − | 20.7863i | 0.192529 | − | 0.111157i | ||||
\(188\) | 25.7734i | 0.137093i | ||||||||
\(189\) | −29.9371 | + | 20.6584i | −0.158397 | + | 0.109304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 118.423 | + | 205.114i | 0.620014 | + | 1.07390i | 0.989483 | + | 0.144653i | \(0.0462064\pi\) |
−0.369468 | + | 0.929243i | \(0.620460\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −66.4460 | + | 115.088i | −0.344280 | + | 0.596310i | −0.985223 | − | 0.171278i | \(-0.945210\pi\) |
0.640943 | + | 0.767589i | \(0.278544\pi\) | |||||||
\(194\) | 56.0256 | − | 32.3464i | 0.288792 | − | 0.166734i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −61.9600 | − | 75.9273i | −0.316122 | − | 0.387384i | ||||
\(197\) | 105.779 | 0.536950 | 0.268475 | − | 0.963287i | \(-0.413480\pi\) | ||||
0.268475 | + | 0.963287i | \(0.413480\pi\) | |||||||
\(198\) | −6.98882 | − | 12.1050i | −0.0352971 | − | 0.0611363i | ||||
\(199\) | 174.541 | + | 100.771i | 0.877091 | + | 0.506389i | 0.869698 | − | 0.493584i | \(-0.164313\pi\) |
0.00739279 | + | 0.999973i | \(0.497647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.8697 | + | 17.2453i | −0.148605 | + | 0.0857973i | ||||
\(202\) | 129.429i | 0.640739i | ||||||||
\(203\) | −156.219 | − | 226.384i | −0.769550 | − | 1.11519i | ||||
\(204\) | −43.7121 | −0.214275 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −61.8597 | − | 35.7147i | −0.300290 | − | 0.173372i | ||||
\(207\) | −10.1346 | + | 17.5536i | −0.0489593 | + | 0.0848000i | ||||
\(208\) | 26.7723 | − | 15.4570i | 0.128713 | − | 0.0743125i | ||||
\(209\) | 5.87006i | 0.0280864i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29.6045 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(212\) | 51.6880 | + | 89.5262i | 0.243811 | + | 0.422293i | ||||
\(213\) | −131.148 | − | 75.7183i | −0.615718 | − | 0.355485i | ||||
\(214\) | 66.4323 | − | 115.064i | 0.310431 | − | 0.537683i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −6.14783 | − | 76.2777i | −0.0283310 | − | 0.351510i | ||||
\(218\) | −170.569 | −0.782426 | ||||||||
\(219\) | −52.7540 | − | 91.3726i | −0.240886 | − | 0.417226i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 48.7614 | − | 84.4572i | 0.220640 | − | 0.382159i | ||||
\(222\) | −72.9661 | + | 42.1270i | −0.328676 | + | 0.189761i | ||||
\(223\) | 328.532i | 1.47324i | 0.676307 | + | 0.736620i | \(0.263579\pi\) | ||||
−0.676307 | + | 0.736620i | \(0.736421\pi\) | |||||||
\(224\) | −39.4700 | + | 3.18120i | −0.176205 | + | 0.0142018i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.58850 | − | 13.1437i | −0.0335774 | − | 0.0581578i | ||||
\(227\) | −315.628 | − | 182.228i | −1.39043 | − | 0.802766i | −0.397069 | − | 0.917789i | \(-0.629972\pi\) |
−0.993363 | + | 0.115023i | \(0.963306\pi\) | |||||||
\(228\) | 3.08607 | − | 5.34523i | 0.0135354 | − | 0.0234440i | ||||
\(229\) | −260.716 | + | 150.525i | −1.13850 | + | 0.657313i | −0.946059 | − | 0.323996i | \(-0.894974\pi\) |
−0.192441 | + | 0.981309i | \(0.561640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −36.0856 | − | 17.1285i | −0.156215 | − | 0.0741496i | ||||
\(232\) | −111.138 | −0.479044 | ||||||||
\(233\) | −141.013 | − | 244.241i | −0.605204 | − | 1.04824i | −0.992019 | − | 0.126087i | \(-0.959758\pi\) |
0.386815 | − | 0.922157i | \(-0.373575\pi\) | |||||||
\(234\) | −28.3963 | − | 16.3946i | −0.121352 | − | 0.0700625i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −195.595 | + | 112.927i | −0.828790 | + | 0.478502i | ||||
\(237\) | − | 61.6224i | − | 0.260010i | ||||||
\(238\) | −102.814 | + | 70.9480i | −0.431993 | + | 0.298101i | ||||
\(239\) | 83.0347 | 0.347425 | 0.173713 | − | 0.984796i | \(-0.444424\pi\) | ||||
0.173713 | + | 0.984796i | \(0.444424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −287.369 | − | 165.912i | −1.19240 | − | 0.688433i | −0.233551 | − | 0.972345i | \(-0.575035\pi\) |
−0.958851 | + | 0.283911i | \(0.908368\pi\) | |||||||
\(242\) | −77.8849 | + | 134.901i | −0.321838 | + | 0.557440i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 52.4658i | − | 0.215024i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 46.1817 | 0.187731 | ||||||||
\(247\) | 6.88511 | + | 11.9254i | 0.0278749 | + | 0.0482808i | ||||
\(248\) | −26.7782 | − | 15.4604i | −0.107977 | − | 0.0623403i | ||||
\(249\) | 40.4237 | − | 70.0159i | 0.162344 | − | 0.281188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 419.075i | − | 1.66962i | −0.550537 | − | 0.834811i | \(-0.685577\pi\) | ||
0.550537 | − | 0.834811i | \(-0.314423\pi\) | |||||||
\(252\) | 23.8542 | + | 34.5684i | 0.0946597 | + | 0.137176i | ||||
\(253\) | −22.2593 | −0.0879815 | ||||||||
\(254\) | 82.9305 | + | 143.640i | 0.326498 | + | 0.565511i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 289.215 | − | 166.979i | 1.12535 | − | 0.649722i | 0.182590 | − | 0.983189i | \(-0.441552\pi\) |
0.942762 | + | 0.333467i | \(0.108219\pi\) | |||||||
\(258\) | − | 189.639i | − | 0.735034i | ||||||
\(259\) | −103.247 | + | 217.516i | −0.398637 | + | 0.839829i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 58.9399 | + | 102.087i | 0.225824 | + | 0.391138i | ||||
\(262\) | 113.527 | + | 65.5449i | 0.433310 | + | 0.250171i | ||||
\(263\) | 102.188 | − | 176.995i | 0.388549 | − | 0.672986i | −0.603706 | − | 0.797207i | \(-0.706310\pi\) |
0.992255 | + | 0.124221i | \(0.0396432\pi\) | |||||||
\(264\) | −13.9776 | + | 8.06999i | −0.0529456 | + | 0.0305681i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.41702 | − | 17.5814i | −0.00532715 | − | 0.0660953i | ||||
\(267\) | 94.9412 | 0.355585 | ||||||||
\(268\) | 19.9131 | + | 34.4905i | 0.0743027 | + | 0.128696i | ||||
\(269\) | −120.768 | − | 69.7257i | −0.448953 | − | 0.259203i | 0.258435 | − | 0.966029i | \(-0.416793\pi\) |
−0.707388 | + | 0.706825i | \(0.750127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −323.213 | + | 186.607i | −1.19267 | + | 0.688586i | −0.958910 | − | 0.283709i | \(-0.908435\pi\) |
−0.233756 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(272\) | 50.4743i | 0.185567i | ||||||||
\(273\) | −93.4002 | + | 7.52787i | −0.342125 | + | 0.0275746i | ||||
\(274\) | 38.8542 | 0.141804 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 20.2691 | + | 11.7024i | 0.0734389 | + | 0.0424000i | ||||
\(277\) | −248.752 | + | 430.851i | −0.898022 | + | 1.55542i | −0.0680029 | + | 0.997685i | \(0.521663\pi\) |
−0.830019 | + | 0.557735i | \(0.811671\pi\) | |||||||
\(278\) | −82.0735 | + | 47.3852i | −0.295228 | + | 0.170450i | ||||
\(279\) | 32.7964i | 0.117550i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 292.779 | 1.04192 | 0.520959 | − | 0.853582i | \(-0.325574\pi\) | ||||
0.520959 | + | 0.853582i | \(0.325574\pi\) | |||||||
\(282\) | −15.7829 | − | 27.3368i | −0.0559678 | − | 0.0969391i | ||||
\(283\) | 239.686 | + | 138.383i | 0.846949 | + | 0.488986i | 0.859620 | − | 0.510934i | \(-0.170700\pi\) |
−0.0126714 | + | 0.999920i | \(0.504034\pi\) | |||||||
\(284\) | −87.4319 | + | 151.437i | −0.307859 | + | 0.533227i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 36.0087i | − | 0.125905i | ||||||
\(287\) | 108.623 | − | 74.9565i | 0.378478 | − | 0.261172i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −64.8857 | − | 112.385i | −0.224518 | − | 0.388876i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.6161 | + | 68.6171i | −0.136138 | + | 0.235798i | ||||
\(292\) | −105.508 | + | 60.9150i | −0.361329 | + | 0.208613i | ||||
\(293\) | − | 375.299i | − | 1.28088i | −0.768006 | − | 0.640442i | \(-0.778751\pi\) | ||
0.768006 | − | 0.640442i | \(-0.221249\pi\) | |||||||
\(294\) | 112.214 | + | 42.5905i | 0.381681 | + | 0.144866i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 48.6441 | + | 84.2540i | 0.164338 | + | 0.284642i | ||||
\(297\) | 14.8255 | + | 8.55952i | 0.0499176 | + | 0.0288199i | ||||
\(298\) | 36.1427 | − | 62.6009i | 0.121284 | − | 0.210070i | ||||
\(299\) | −45.2210 | + | 26.1084i | −0.151241 | + | 0.0873189i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −307.798 | − | 446.046i | −1.02259 | − | 1.48188i | ||||
\(302\) | 233.653 | 0.773687 | ||||||||
\(303\) | −79.2589 | − | 137.280i | −0.261580 | − | 0.453071i | ||||
\(304\) | −6.17214 | − | 3.56349i | −0.0203031 | − | 0.0117220i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 46.3636 | − | 26.7681i | 0.151515 | − | 0.0874773i | ||||
\(307\) | 107.784i | 0.351088i | 0.984472 | + | 0.175544i | \(0.0561684\pi\) | ||||
−0.984472 | + | 0.175544i | \(0.943832\pi\) | |||||||
\(308\) | −19.7783 | + | 41.6680i | −0.0642154 | + | 0.135286i | ||||
\(309\) | 87.4828 | 0.283116 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −499.771 | − | 288.543i | −1.60698 | − | 0.927791i | −0.990041 | − | 0.140780i | \(-0.955039\pi\) |
−0.616940 | − | 0.787010i | \(-0.711628\pi\) | |||||||
\(312\) | −18.9309 | + | 32.7893i | −0.0606759 | + | 0.105094i | ||||
\(313\) | −344.050 | + | 198.637i | −1.09920 | + | 0.634624i | −0.936011 | − | 0.351971i | \(-0.885512\pi\) |
−0.163190 | + | 0.986595i | \(0.552178\pi\) | |||||||
\(314\) | − | 269.849i | − | 0.859390i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −71.1554 | −0.225175 | ||||||||
\(317\) | 40.1851 | + | 69.6026i | 0.126767 | + | 0.219566i | 0.922422 | − | 0.386183i | \(-0.126207\pi\) |
−0.795655 | + | 0.605749i | \(0.792873\pi\) | |||||||
\(318\) | −109.647 | − | 63.3046i | −0.344801 | − | 0.199071i | ||||
\(319\) | −64.7271 | + | 112.111i | −0.202906 | + | 0.351444i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 162.725i | 0.506932i | ||||||||
\(322\) | 66.6686 | − | 5.37336i | 0.207045 | − | 0.0166874i | ||||
\(323\) | −22.4831 | −0.0696071 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −175.505 | + | 303.984i | −0.538360 | + | 0.932467i | ||||
\(327\) | 180.915 | − | 104.452i | 0.553258 | − | 0.319424i | ||||
\(328\) | − | 53.3261i | − | 0.162580i | ||||||
\(329\) | −81.4925 | − | 38.6816i | −0.247698 | − | 0.117573i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −246.021 | − | 426.121i | −0.743266 | − | 1.28737i | −0.951000 | − | 0.309189i | \(-0.899942\pi\) |
0.207734 | − | 0.978185i | \(-0.433391\pi\) | |||||||
\(332\) | −80.8474 | − | 46.6773i | −0.243516 | − | 0.140594i | ||||
\(333\) | 51.5948 | − | 89.3649i | 0.154939 | − | 0.268363i | ||||
\(334\) | 35.8818 | − | 20.7164i | 0.107431 | − | 0.0620251i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 39.9162 | − | 27.5445i | 0.118798 | − | 0.0819777i | ||||
\(337\) | 630.123 | 1.86980 | 0.934901 | − | 0.354910i | \(-0.115488\pi\) | ||||
0.934901 | + | 0.354910i | \(0.115488\pi\) | |||||||
\(338\) | 77.2657 | + | 133.828i | 0.228597 | + | 0.395941i | ||||
\(339\) | 16.0976 | + | 9.29397i | 0.0474856 | + | 0.0274159i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.1913 | + | 18.0083i | −0.0914701 | + | 0.0528103i | ||||
\(342\) | 7.55930i | 0.0221032i | ||||||||
\(343\) | 333.065 | − | 81.9559i | 0.971035 | − | 0.238938i | ||||
\(344\) | −218.976 | −0.636558 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.2817 | + | 16.3285i | 0.0817391 | + | 0.0471921i | ||||
\(347\) | −215.071 | + | 372.514i | −0.619802 | + | 1.07353i | 0.369720 | + | 0.929143i | \(0.379454\pi\) |
−0.989522 | + | 0.144385i | \(0.953880\pi\) | |||||||
\(348\) | 117.880 | − | 68.0580i | 0.338735 | − | 0.195569i | ||||
\(349\) | − | 95.1819i | − | 0.272727i | −0.990659 | − | 0.136364i | \(-0.956458\pi\) | ||
0.990659 | − | 0.136364i | \(-0.0435416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.1585 | 0.114412 | ||||||||
\(352\) | 9.31842 | + | 16.1400i | 0.0264728 | + | 0.0458522i | ||||
\(353\) | −227.710 | − | 131.469i | −0.645071 | − | 0.372432i | 0.141494 | − | 0.989939i | \(-0.454809\pi\) |
−0.786565 | + | 0.617507i | \(0.788143\pi\) | |||||||
\(354\) | 138.306 | − | 239.553i | 0.390696 | − | 0.676704i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 109.629i | − | 0.307946i | ||||||
\(357\) | 65.6045 | − | 138.212i | 0.183766 | − | 0.387150i | ||||
\(358\) | 296.186 | 0.827334 | ||||||||
\(359\) | −149.386 | − | 258.743i | −0.416116 | − | 0.720734i | 0.579429 | − | 0.815023i | \(-0.303276\pi\) |
−0.995545 | + | 0.0942890i | \(0.969942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −178.913 | + | 309.886i | −0.495603 | + | 0.858410i | ||||
\(362\) | 298.429 | − | 172.298i | 0.824391 | − | 0.475962i | ||||
\(363\) | − | 190.778i | − | 0.525560i | ||||||
\(364\) | 8.69244 | + | 107.849i | 0.0238803 | + | 0.296289i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 32.1286 | + | 55.6484i | 0.0877831 | + | 0.152045i | ||||
\(367\) | 114.381 | + | 66.0380i | 0.311665 | + | 0.179940i | 0.647671 | − | 0.761920i | \(-0.275743\pi\) |
−0.336006 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(368\) | 13.5128 | − | 23.4048i | 0.0367195 | − | 0.0636000i | ||||
\(369\) | −48.9831 | + | 28.2804i | −0.132746 | + | 0.0766407i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −360.646 | + | 29.0674i | −0.972092 | + | 0.0783487i | ||||
\(372\) | 37.8701 | 0.101801 | ||||||||
\(373\) | 5.34394 | + | 9.25597i | 0.0143269 | + | 0.0248149i | 0.873100 | − | 0.487541i | \(-0.162106\pi\) |
−0.858773 | + | 0.512356i | \(0.828773\pi\) | |||||||
\(374\) | 50.9159 | + | 29.3963i | 0.136139 | + | 0.0785998i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.5659 | + | 18.2246i | −0.0839517 | + | 0.0484696i | ||||
\(377\) | 303.678i | 0.805513i | ||||||||
\(378\) | −46.4700 | − | 22.0577i | −0.122936 | − | 0.0583536i | ||||
\(379\) | 142.918 | 0.377092 | 0.188546 | − | 0.982064i | \(-0.439622\pi\) | ||||
0.188546 | + | 0.982064i | \(0.439622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −175.922 | − | 101.569i | −0.461738 | − | 0.266585i | ||||
\(382\) | −167.475 | + | 290.075i | −0.438416 | + | 0.759359i | ||||
\(383\) | 534.349 | − | 308.507i | 1.39517 | − | 0.805500i | 0.401286 | − | 0.915953i | \(-0.368563\pi\) |
0.993881 | + | 0.110452i | \(0.0352300\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −187.938 | −0.486885 | ||||||||
\(387\) | 116.130 | + | 201.142i | 0.300076 | + | 0.519748i | ||||
\(388\) | 79.2322 | + | 45.7447i | 0.204207 | + | 0.117899i | ||||
\(389\) | 346.969 | − | 600.968i | 0.891951 | − | 1.54490i | 0.0544171 | − | 0.998518i | \(-0.482670\pi\) |
0.837534 | − | 0.546386i | \(-0.183997\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 85.2560i | − | 0.218046i | ||||||
\(392\) | 49.1793 | − | 129.574i | 0.125457 | − | 0.330546i | ||||
\(393\) | −160.552 | −0.408528 | ||||||||
\(394\) | 74.7972 | + | 129.553i | 0.189841 | + | 0.328814i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.88368 | − | 17.1190i | 0.0249588 | − | 0.0432299i | ||||
\(397\) | 484.587 | − | 279.776i | 1.22062 | − | 0.704726i | 0.255571 | − | 0.966790i | \(-0.417737\pi\) |
0.965050 | + | 0.262065i | \(0.0844033\pi\) | |||||||
\(398\) | 285.024i | 0.716142i | ||||||||
\(399\) | 12.2693 | + | 17.7801i | 0.0307502 | + | 0.0445616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 80.6033 | + | 139.609i | 0.201006 | + | 0.348152i | 0.948853 | − | 0.315719i | \(-0.102246\pi\) |
−0.747847 | + | 0.663871i | \(0.768912\pi\) | |||||||
\(402\) | −42.2421 | − | 24.3885i | −0.105080 | − | 0.0606679i | ||||
\(403\) | −42.2445 | + | 73.1697i | −0.104825 | + | 0.181563i | ||||
\(404\) | −158.518 | + | 91.5203i | −0.392371 | + | 0.226535i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 166.800 | − | 351.406i | 0.410837 | − | 0.865532i | ||||
\(407\) | 113.322 | 0.278431 | ||||||||
\(408\) | −30.9091 | − | 53.5361i | −0.0757576 | − | 0.131216i | ||||
\(409\) | 398.217 | + | 229.911i | 0.973637 | + | 0.562129i | 0.900343 | − | 0.435181i | \(-0.143316\pi\) |
0.0732937 | + | 0.997310i | \(0.476649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.2111 | + | 23.7932i | −0.100270 | + | 0.0578911i | ||||
\(412\) | − | 101.016i | − | 0.245186i | ||||||
\(413\) | −63.5056 | − | 787.931i | −0.153767 | − | 1.90782i | ||||
\(414\) | −28.6649 | −0.0692389 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 37.8618 | + | 21.8595i | 0.0910139 | + | 0.0525469i | ||||
\(417\) | 58.0347 | − | 100.519i | 0.139172 | − | 0.241053i | ||||
\(418\) | −7.18933 | + | 4.15076i | −0.0171994 | + | 0.00993005i | ||||
\(419\) | 93.5818i | 0.223346i | 0.993745 | + | 0.111673i | \(0.0356208\pi\) | ||||
−0.993745 | + | 0.111673i | \(0.964379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 162.957 | 0.387072 | 0.193536 | − | 0.981093i | \(-0.438004\pi\) | ||||
0.193536 | + | 0.981093i | \(0.438004\pi\) | |||||||
\(422\) | 20.9335 | + | 36.2579i | 0.0496055 | + | 0.0859193i | ||||
\(423\) | 33.4806 | + | 19.3301i | 0.0791504 | + | 0.0456975i | ||||
\(424\) | −73.0978 | + | 126.609i | −0.172400 | + | 0.298606i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 214.164i | − | 0.502731i | ||||||
\(427\) | 165.891 | + | 78.7425i | 0.388503 | + | 0.184409i | ||||
\(428\) | 187.899 | 0.439016 | ||||||||
\(429\) | 22.0507 | + | 38.1930i | 0.0514003 | + | 0.0890280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 165.543 | − | 286.728i | 0.384090 | − | 0.665263i | −0.607553 | − | 0.794279i | \(-0.707849\pi\) |
0.991642 | + | 0.129016i | \(0.0411820\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 88.4130i | 0.204187i | 0.994775 | + | 0.102094i | \(0.0325541\pi\) | ||||
−0.994775 | + | 0.102094i | \(0.967446\pi\) | |||||||
\(434\) | 89.0735 | − | 61.4660i | 0.205238 | − | 0.141627i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −120.610 | − | 208.903i | −0.276629 | − | 0.479136i | ||||
\(437\) | 10.4253 | + | 6.01907i | 0.0238566 | + | 0.0137736i | ||||
\(438\) | 74.6054 | − | 129.220i | 0.170332 | − | 0.295024i | ||||
\(439\) | −60.4608 | + | 34.9070i | −0.137724 | + | 0.0795149i | −0.567279 | − | 0.823526i | \(-0.692004\pi\) |
0.429555 | + | 0.903041i | \(0.358670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.102 | + | 23.5429i | −0.329031 | + | 0.0533852i | ||||
\(442\) | 137.918 | 0.312032 | ||||||||
\(443\) | 330.217 | + | 571.953i | 0.745411 | + | 1.29109i | 0.950003 | + | 0.312242i | \(0.101080\pi\) |
−0.204592 | + | 0.978847i | \(0.565587\pi\) | |||||||
\(444\) | −103.190 | − | 59.5766i | −0.232409 | − | 0.134182i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −402.368 | + | 232.307i | −0.902171 | + | 0.520869i | ||||
\(447\) | 88.5311i | 0.198056i | ||||||||
\(448\) | −31.8057 | − | 46.0912i | −0.0709948 | − | 0.102882i | ||||
\(449\) | −560.274 | −1.24783 | −0.623913 | − | 0.781493i | \(-0.714458\pi\) | ||||
−0.623913 | + | 0.781493i | \(0.714458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.7926 | − | 31.0572i | −0.119274 | − | 0.0688629i | ||||
\(452\) | 10.7318 | − | 18.5879i | 0.0237428 | − | 0.0411238i | ||||
\(453\) | −247.827 | + | 143.083i | −0.547079 | + | 0.315856i | ||||
\(454\) | − | 515.418i | − | 1.13528i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.72873 | 0.0191419 | ||||||||
\(457\) | 91.8900 | + | 159.158i | 0.201072 | + | 0.348267i | 0.948874 | − | 0.315655i | \(-0.102224\pi\) |
−0.747802 | + | 0.663922i | \(0.768891\pi\) | |||||||
\(458\) | −368.709 | − | 212.874i | −0.805041 | − | 0.464790i | ||||
\(459\) | −32.7840 | + | 56.7836i | −0.0714249 | + | 0.123712i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.4330i | 0.0616767i | 0.999524 | + | 0.0308384i | \(0.00981771\pi\) | ||||
−0.999524 | + | 0.0308384i | \(0.990182\pi\) | |||||||
\(462\) | −4.53826 | − | 56.3073i | −0.00982307 | − | 0.121877i | ||||
\(463\) | 269.931 | 0.583005 | 0.291503 | − | 0.956570i | \(-0.405845\pi\) | ||||
0.291503 | + | 0.956570i | \(0.405845\pi\) | |||||||
\(464\) | −78.5866 | − | 136.116i | −0.169368 | − | 0.293353i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 199.422 | − | 345.409i | 0.427944 | − | 0.741221i | ||||
\(467\) | −289.539 | + | 167.166i | −0.619999 | + | 0.357956i | −0.776868 | − | 0.629663i | \(-0.783193\pi\) |
0.156870 | + | 0.987619i | \(0.449860\pi\) | |||||||
\(468\) | − | 46.3710i | − | 0.0990834i | ||||||
\(469\) | −138.941 | + | 11.1984i | −0.296250 | + | 0.0238772i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 165.248 | + | 286.218i | 0.350845 | + | 0.607681i | ||||
\(472\) | −276.612 | − | 159.702i | −0.586043 | − | 0.338352i | ||||
\(473\) | −127.532 | + | 220.892i | −0.269624 | + | 0.467002i | ||||
\(474\) | 75.4717 | − | 43.5736i | 0.159223 | − | 0.0919274i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −159.594 | − | 75.7536i | −0.335281 | − | 0.159146i | ||||
\(477\) | 155.064 | 0.325081 | ||||||||
\(478\) | 58.7144 | + | 101.696i | 0.122833 | + | 0.212754i | ||||
\(479\) | 114.560 | + | 66.1412i | 0.239165 | + | 0.138082i | 0.614793 | − | 0.788689i | \(-0.289240\pi\) |
−0.375628 | + | 0.926771i | \(0.622573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 230.219 | − | 132.917i | 0.478626 | − | 0.276335i | ||||
\(482\) | − | 469.271i | − | 0.973592i | ||||||
\(483\) | −67.4222 | + | 46.5253i | −0.139591 | + | 0.0963257i | ||||
\(484\) | −220.292 | −0.455148 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | + | 11.0227i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −258.635 | + | 447.970i | −0.531079 | + | 0.919856i | 0.468263 | + | 0.883589i | \(0.344880\pi\) |
−0.999342 | + | 0.0362667i | \(0.988453\pi\) | |||||||
\(488\) | 64.2573 | − | 37.0989i | 0.131675 | − | 0.0760224i | ||||
\(489\) | − | 429.898i | − | 0.879138i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 484.805 | 0.987383 | 0.493692 | − | 0.869637i | \(-0.335647\pi\) | ||||
0.493692 | + | 0.869637i | \(0.335647\pi\) | |||||||
\(492\) | 32.6554 | + | 56.5609i | 0.0663728 | + | 0.114961i | ||||
\(493\) | −429.398 | − | 247.913i | −0.870989 | − | 0.502866i | ||||
\(494\) | −9.73701 | + | 16.8650i | −0.0197105 | + | 0.0341397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 43.7286i | − | 0.0881624i | ||||||
\(497\) | −347.604 | − | 503.730i | −0.699404 | − | 1.01354i | ||||
\(498\) | 114.336 | 0.229589 | ||||||||
\(499\) | 64.6450 | + | 111.968i | 0.129549 | + | 0.224385i | 0.923502 | − | 0.383594i | \(-0.125314\pi\) |
−0.793953 | + | 0.607979i | \(0.791980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.3723 | + | 43.9461i | −0.0506432 | + | 0.0877167i | ||||
\(502\) | 513.260 | − | 296.331i | 1.02243 | − | 0.590300i | ||||
\(503\) | 160.905i | 0.319890i | 0.987126 | + | 0.159945i | \(0.0511317\pi\) | ||||
−0.987126 | + | 0.159945i | \(0.948868\pi\) | |||||||
\(504\) | −25.4700 | + | 53.6589i | −0.0505357 | + | 0.106466i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.7397 | − | 27.2620i | −0.0311061 | − | 0.0538774i | ||||
\(507\) | −163.905 | − | 94.6308i | −0.323285 | − | 0.186649i | ||||
\(508\) | −117.281 | + | 203.137i | −0.230869 | + | 0.399877i | ||||
\(509\) | −320.453 | + | 185.014i | −0.629575 | + | 0.363485i | −0.780587 | − | 0.625047i | \(-0.785080\pi\) |
0.151013 | + | 0.988532i | \(0.451747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.2563 | − | 425.027i | −0.0670378 | − | 0.831755i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −4.62911 | − | 8.01785i | −0.00902360 | − | 0.0156293i | ||||
\(514\) | 409.012 | + | 236.143i | 0.795744 | + | 0.459423i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 232.259 | − | 134.095i | 0.450115 | − | 0.259874i | ||||
\(517\) | 42.4560i | 0.0821200i | ||||||||
\(518\) | −339.408 | + | 27.3556i | −0.655228 | + | 0.0528101i | ||||
\(519\) | −39.9964 | −0.0770644 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 65.1395 | + | 37.6083i | 0.125028 | + | 0.0721849i | 0.561210 | − | 0.827674i | \(-0.310336\pi\) |
−0.436182 | + | 0.899859i | \(0.643670\pi\) | |||||||
\(522\) | −83.3537 | + | 144.373i | −0.159681 | + | 0.276576i | ||||
\(523\) | −810.701 | + | 468.058i | −1.55010 | + | 0.894949i | −0.551965 | + | 0.833867i | \(0.686122\pi\) |
−0.998133 | + | 0.0610819i | \(0.980545\pi\) | |||||||
\(524\) | 185.389i | 0.353796i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 289.032 | 0.549491 | ||||||||
\(527\) | −68.9741 | − | 119.467i | −0.130881 | − | 0.226692i | ||||
\(528\) | −19.7674 | − | 11.4127i | −0.0374382 | − | 0.0216149i | ||||
\(529\) | 241.676 | − | 418.594i | 0.456854 | − | 0.791294i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 338.780i | 0.638003i | ||||||||
\(532\) | 20.5307 | − | 14.1674i | 0.0385915 | − | 0.0266304i | ||||
\(533\) | −145.710 | −0.273377 | ||||||||
\(534\) | 67.1336 | + | 116.279i | 0.125718 | + | 0.217751i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.1614 | + | 48.7770i | −0.0525399 | + | 0.0910018i | ||||
\(537\) | −314.152 | + | 181.376i | −0.585014 | + | 0.337758i | ||||
\(538\) | − | 197.214i | − | 0.366569i | ||||||
\(539\) | −102.065 | − | 125.074i | −0.189361 | − | 0.232047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 304.692 | + | 527.742i | 0.563201 | + | 0.975493i | 0.997215 | + | 0.0745867i | \(0.0237638\pi\) |
−0.434013 | + | 0.900906i | \(0.642903\pi\) | |||||||
\(542\) | −457.092 | − | 263.902i | −0.843343 | − | 0.486904i | ||||
\(543\) | −211.021 | + | 365.500i | −0.388622 | + | 0.673112i | ||||
\(544\) | −61.8182 | + | 35.6907i | −0.113636 | + | 0.0656080i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −75.2637 | − | 109.068i | −0.137846 | − | 0.199759i | ||||
\(547\) | 491.361 | 0.898283 | 0.449141 | − | 0.893461i | \(-0.351730\pi\) | ||||
0.449141 | + | 0.893461i | \(0.351730\pi\) | |||||||
\(548\) | 27.4741 | + | 47.5865i | 0.0501351 | + | 0.0868366i | ||||
\(549\) | −68.1551 | − | 39.3494i | −0.124144 | − | 0.0716746i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.6310 | − | 35.0053i | 0.110038 | − | 0.0635305i | ||||
\(552\) | 33.0994i | 0.0599626i | ||||||||
\(553\) | 106.792 | − | 224.985i | 0.193115 | − | 0.406844i | ||||
\(554\) | −703.577 | −1.27000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −116.069 | − | 67.0127i | −0.208758 | − | 0.120527i | ||||
\(557\) | −526.110 | + | 911.250i | −0.944543 | + | 1.63600i | −0.187878 | + | 0.982192i | \(0.560161\pi\) |
−0.756665 | + | 0.653803i | \(0.773172\pi\) | |||||||
\(558\) | −40.1673 | + | 23.1906i | −0.0719843 | + | 0.0415602i | ||||
\(559\) | 598.339i | 1.07037i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.0060 | −0.128353 | ||||||||
\(562\) | 207.026 | + | 358.580i | 0.368374 | + | 0.638042i | ||||
\(563\) | 670.769 | + | 387.269i | 1.19142 | + | 0.687866i | 0.958628 | − | 0.284661i | \(-0.0918810\pi\) |
0.232791 | + | 0.972527i | \(0.425214\pi\) | |||||||
\(564\) | 22.3204 | − | 38.6601i | 0.0395752 | − | 0.0685463i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 391.406i | 0.691531i | ||||||||
\(567\) | 62.7964 | − | 5.06126i | 0.110752 | − | 0.00892639i | ||||
\(568\) | −247.295 | −0.435378 | ||||||||
\(569\) | −156.525 | − | 271.109i | −0.275088 | − | 0.476466i | 0.695070 | − | 0.718942i | \(-0.255374\pi\) |
−0.970157 | + | 0.242477i | \(0.922040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −324.711 | + | 562.416i | −0.568670 | + | 0.984966i | 0.428027 | + | 0.903766i | \(0.359209\pi\) |
−0.996698 | + | 0.0812002i | \(0.974125\pi\) | |||||||
\(572\) | 44.1015 | − | 25.4620i | 0.0771005 | − | 0.0445140i | ||||
\(573\) | − | 410.228i | − | 0.715931i | ||||||
\(574\) | 168.611 | + | 80.0336i | 0.293747 | + | 0.139431i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −891.822 | − | 514.893i | −1.54562 | − | 0.892363i | −0.998468 | − | 0.0553284i | \(-0.982379\pi\) |
−0.547150 | − | 0.837035i | \(-0.684287\pi\) | |||||||
\(578\) | 91.7622 | − | 158.937i | 0.158758 | − | 0.274977i | ||||
\(579\) | 199.338 | − | 115.088i | 0.344280 | − | 0.198770i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 268.927 | − | 185.575i | 0.462868 | − | 0.319406i | ||||
\(582\) | −112.051 | −0.192528 | ||||||||
\(583\) | 85.1445 | + | 147.475i | 0.146046 | + | 0.252958i | ||||
\(584\) | −149.211 | − | 86.1469i | −0.255498 | − | 0.147512i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 459.646 | − | 265.376i | 0.784378 | − | 0.452861i | ||||
\(587\) | 791.817i | 1.34892i | 0.738311 | + | 0.674461i | \(0.235624\pi\) | ||||
−0.738311 | + | 0.674461i | \(0.764376\pi\) | |||||||
\(588\) | 27.1850 | + | 167.550i | 0.0462329 | + | 0.284949i | ||||
\(589\) | 19.4783 | 0.0330701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −158.669 | − | 91.6075i | −0.268475 | − | 0.155004i | ||||
\(592\) | −68.7931 | + | 119.153i | −0.116205 | + | 0.201272i | ||||
\(593\) | 73.1807 | − | 42.2509i | 0.123408 | − | 0.0712494i | −0.437025 | − | 0.899449i | \(-0.643968\pi\) |
0.560433 | + | 0.828200i | \(0.310635\pi\) | |||||||
\(594\) | 24.2100i | 0.0407575i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 102.227 | 0.171522 | ||||||||
\(597\) | −174.541 | − | 302.314i | −0.292364 | − | 0.506389i | ||||
\(598\) | −63.9522 | − | 36.9228i | −0.106943 | − | 0.0617438i | ||||
\(599\) | 233.463 | − | 404.369i | 0.389754 | − | 0.675074i | −0.602662 | − | 0.797997i | \(-0.705893\pi\) |
0.992416 | + | 0.122922i | \(0.0392266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1095.93i | 1.82351i | 0.410733 | + | 0.911756i | \(0.365273\pi\) | ||||
−0.410733 | + | 0.911756i | \(0.634727\pi\) | |||||||
\(602\) | 328.647 | − | 692.377i | 0.545925 | − | 1.15013i | ||||
\(603\) | 59.7394 | 0.0990702 | ||||||||
\(604\) | 165.218 | + | 286.166i | 0.273540 | + | 0.473785i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 112.089 | − | 194.144i | 0.184965 | − | 0.320369i | ||||
\(607\) | 310.815 | − | 179.449i | 0.512051 | − | 0.295633i | −0.221625 | − | 0.975132i | \(-0.571136\pi\) |
0.733676 | + | 0.679499i | \(0.237803\pi\) | |||||||
\(608\) | − | 10.0791i | − | 0.0165774i | ||||||
\(609\) | 38.2733 | + | 474.866i | 0.0628461 | + | 0.779747i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 49.7975 | + | 86.2517i | 0.0815016 | + | 0.141165i | ||||
\(612\) | 65.5681 | + | 37.8558i | 0.107137 | + | 0.0618558i | ||||
\(613\) | −231.029 | + | 400.154i | −0.376883 | + | 0.652780i | −0.990607 | − | 0.136741i | \(-0.956337\pi\) |
0.613724 | + | 0.789520i | \(0.289671\pi\) | |||||||
\(614\) | −132.008 | + | 76.2148i | −0.214996 | + | 0.124128i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −65.0181 | + | 5.24033i | −0.105549 | + | 0.00850703i | ||||
\(617\) | −219.440 | −0.355656 | −0.177828 | − | 0.984062i | \(-0.556907\pi\) | ||||
−0.177828 | + | 0.984062i | \(0.556907\pi\) | |||||||
\(618\) | 61.8597 | + | 107.144i | 0.100097 | + | 0.173372i | ||||
\(619\) | 832.792 | + | 480.813i | 1.34538 | + | 0.776757i | 0.987592 | − | 0.157044i | \(-0.0501966\pi\) |
0.357791 | + | 0.933802i | \(0.383530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.4037 | − | 17.5536i | 0.0489593 | − | 0.0282667i | ||||
\(622\) | − | 816.123i | − | 1.31209i | ||||||
\(623\) | 346.633 | + | 164.534i | 0.556393 | + | 0.264100i | ||||
\(624\) | −53.5446 | −0.0858087 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −486.560 | − | 280.915i | −0.777252 | − | 0.448747i | ||||
\(627\) | 5.08362 | − | 8.80509i | 0.00810785 | − | 0.0140432i | ||||
\(628\) | 330.496 | − | 190.812i | 0.526267 | − | 0.303840i | ||||
\(629\) | 434.036i | 0.690041i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 584.721 | 0.926658 | 0.463329 | − | 0.886186i | \(-0.346655\pi\) | ||||
0.463329 | + | 0.886186i | \(0.346655\pi\) | |||||||
\(632\) | −50.3144 | − | 87.1472i | −0.0796115 | − | 0.137891i | ||||
\(633\) | −44.4067 | − | 25.6382i | −0.0701528 | − | 0.0405027i | ||||
\(634\) | −56.8303 | + | 98.4329i | −0.0896376 | + | 0.155257i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 179.052i | − | 0.281529i | ||||||
\(637\) | −354.053 | − | 134.379i | −0.555813 | − | 0.210957i | ||||
\(638\) | −183.076 | −0.286953 | ||||||||
\(639\) | 131.148 | + | 227.155i | 0.205239 | + | 0.355485i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −269.518 | + | 466.819i | −0.420465 | + | 0.728268i | −0.995985 | − | 0.0895205i | \(-0.971467\pi\) |
0.575520 | + | 0.817788i | \(0.304800\pi\) | |||||||
\(642\) | −199.297 | + | 115.064i | −0.310431 | + | 0.179228i | ||||
\(643\) | − | 150.959i | − | 0.234773i | −0.993086 | − | 0.117386i | \(-0.962548\pi\) | ||
0.993086 | − | 0.117386i | \(-0.0374516\pi\) | |||||||
\(644\) | 53.7228 | + | 77.8525i | 0.0834205 | + | 0.120889i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.8979 | − | 27.5360i | −0.0246098 | − | 0.0426255i | ||||
\(647\) | −391.111 | − | 225.808i | −0.604499 | − | 0.349008i | 0.166310 | − | 0.986073i | \(-0.446815\pi\) |
−0.770809 | + | 0.637066i | \(0.780148\pi\) | |||||||
\(648\) | 12.7279 | − | 22.0454i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −322.199 | + | 186.022i | −0.496454 | + | 0.286628i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.8366 | + | 119.741i | −0.0873067 | + | 0.183933i | ||||
\(652\) | −496.404 | −0.761356 | ||||||||
\(653\) | 215.848 | + | 373.860i | 0.330548 | + | 0.572526i | 0.982619 | − | 0.185631i | \(-0.0594330\pi\) |
−0.652071 | + | 0.758158i | \(0.726100\pi\) | |||||||
\(654\) | 255.853 | + | 147.717i | 0.391213 | + | 0.225867i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 65.3108 | − | 37.7072i | 0.0995592 | − | 0.0574805i | ||||
\(657\) | 182.745i | 0.278151i | ||||||||
\(658\) | −10.2488 | − | 127.160i | −0.0155757 | − | 0.193252i | ||||
\(659\) | −195.185 | −0.296184 | −0.148092 | − | 0.988974i | \(-0.547313\pi\) | ||||
−0.148092 | + | 0.988974i | \(0.547313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 596.305 | + | 344.277i | 0.902126 | + | 0.520843i | 0.877889 | − | 0.478863i | \(-0.158951\pi\) |
0.0242368 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(662\) | 347.926 | − | 602.626i | 0.525569 | − | 0.910311i | ||||
\(663\) | −146.284 | + | 84.4572i | −0.220640 | + | 0.127386i | ||||
\(664\) | − | 132.023i | − | 0.198830i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 145.932 | 0.219118 | ||||||||
\(667\) | 132.740 | + | 229.913i | 0.199011 | + | 0.344697i | ||||
\(668\) | 50.7445 | + | 29.2974i | 0.0759649 | + | 0.0438583i | ||||
\(669\) | 284.517 | − | 492.799i | 0.425288 | − | 0.736620i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 86.4259i | − | 0.128802i | ||||||
\(672\) | 61.9600 | + | 29.4102i | 0.0922024 | + | 0.0437652i | ||||
\(673\) | −200.020 | −0.297206 | −0.148603 | − | 0.988897i | \(-0.547478\pi\) | ||||
−0.148603 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(674\) | 445.564 | + | 771.740i | 0.661075 | + | 1.14501i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −109.270 | + | 189.262i | −0.161642 | + | 0.279973i | ||||
\(677\) | −735.787 | + | 424.807i | −1.08683 | + | 0.627484i | −0.932732 | − | 0.360571i | \(-0.882582\pi\) |
−0.154103 | + | 0.988055i | \(0.549249\pi\) | |||||||
\(678\) | 26.2873i | 0.0387719i | ||||||||
\(679\) | −263.554 | + | 181.868i | −0.388150 | + | 0.267846i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 315.628 | + | 546.684i | 0.463477 | + | 0.802766i | ||||
\(682\) | −44.1111 | − | 25.4676i | −0.0646791 | − | 0.0373425i | ||||
\(683\) | −224.005 | + | 387.988i | −0.327972 | + | 0.568064i | −0.982109 | − | 0.188311i | \(-0.939699\pi\) |
0.654137 | + | 0.756376i | \(0.273032\pi\) | |||||||
\(684\) | −9.25821 | + | 5.34523i | −0.0135354 | + | 0.00781467i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 335.888 | + | 349.968i | 0.489632 | + | 0.510157i | ||||
\(687\) | 521.433 | 0.759000 | ||||||||
\(688\) | −154.839 | − | 268.190i | −0.225057 | − | 0.389811i | ||||
\(689\) | 345.952 | + | 199.735i | 0.502107 | + | 0.289891i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.930 | + | 195.104i | −0.489044 | + | 0.282350i | −0.724178 | − | 0.689613i | \(-0.757781\pi\) |
0.235134 | + | 0.971963i | \(0.424447\pi\) | |||||||
\(692\) | 46.1839i | 0.0667397i | ||||||||
\(693\) | 39.2946 | + | 56.9439i | 0.0567022 | + | 0.0821701i | ||||
\(694\) | −608.313 | −0.876532 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 166.707 | + | 96.2485i | 0.239522 | + | 0.138288i | ||||
\(697\) | 118.953 | − | 206.033i | 0.170664 | − | 0.295599i | ||||
\(698\) | 116.574 | − | 67.3038i | 0.167011 | − | 0.0964237i | ||||
\(699\) | 488.482i | 0.698830i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 989.018 | 1.41087 | 0.705434 | − | 0.708776i | \(-0.250752\pi\) | ||||
0.705434 | + | 0.708776i | \(0.250752\pi\) | |||||||
\(702\) | 28.3963 | + | 49.1839i | 0.0404506 | + | 0.0700625i | ||||
\(703\) | −53.0751 | − | 30.6429i | −0.0754980 | − | 0.0435888i | ||||
\(704\) | −13.1782 | + | 22.8254i | −0.0187191 | + | 0.0324224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 371.849i | − | 0.526699i | ||||||
\(707\) | −51.4676 | − | 638.571i | −0.0727971 | − | 0.903212i | ||||
\(708\) | 391.189 | 0.552527 | ||||||||
\(709\) | −554.927 | − | 961.161i | −0.782689 | − | 1.35566i | −0.930370 | − | 0.366623i | \(-0.880514\pi\) |
0.147680 | − | 0.989035i | \(-0.452819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −53.3665 | + | 92.4335i | −0.0750584 | + | 0.130005i | ||||
\(712\) | 134.267 | − | 77.5192i | 0.188578 | − | 0.108875i | ||||
\(713\) | 73.8617i | 0.103593i | ||||||||
\(714\) | 215.664 | − | 17.3821i | 0.302051 | − | 0.0243447i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 209.435 | + | 362.752i | 0.292507 | + | 0.506637i | ||||
\(717\) | −124.552 | − | 71.9101i | −0.173713 | − | 0.100293i | ||||
\(718\) | 211.263 | − | 365.918i | 0.294238 | − | 0.509636i | ||||
\(719\) | 936.393 | − | 540.627i | 1.30235 | − | 0.751915i | 0.321547 | − | 0.946894i | \(-0.395797\pi\) |
0.980807 | + | 0.194979i | \(0.0624638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 319.402 | + | 151.609i | 0.442999 | + | 0.210276i | ||||
\(722\) | −506.042 | −0.700889 | ||||||||
\(723\) | 287.369 | + | 497.737i | 0.397467 | + | 0.688433i | ||||
\(724\) | 422.043 | + | 243.667i | 0.582932 | + | 0.336556i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 233.655 | − | 134.901i | 0.321838 | − | 0.185813i | ||||
\(727\) | 491.493i | 0.676056i | 0.941136 | + | 0.338028i | \(0.109760\pi\) | ||||
−0.941136 | + | 0.338028i | \(0.890240\pi\) | |||||||
\(728\) | −125.941 | + | 86.9070i | −0.172996 | + | 0.119378i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −846.044 | − | 488.464i | −1.15738 | − | 0.668213i | ||||
\(732\) | −45.4367 | + | 78.6988i | −0.0620721 | + | 0.107512i | ||||
\(733\) | 40.4999 | − | 23.3826i | 0.0552522 | − | 0.0318999i | −0.472119 | − | 0.881535i | \(-0.656511\pi\) |
0.527372 | + | 0.849635i | \(0.323178\pi\) | |||||||
\(734\) | 186.784i | 0.254474i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.2199 | 0.0519292 | ||||||||
\(737\) | 32.8025 | + | 56.8156i | 0.0445081 | + | 0.0770903i | ||||
\(738\) | −69.2726 | − | 39.9946i | −0.0938653 | − | 0.0541932i | ||||
\(739\) | 368.856 | − | 638.878i | 0.499129 | − | 0.864517i | −0.500870 | − | 0.865522i | \(-0.666987\pi\) |
0.999999 | + | 0.00100544i | \(0.000320040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 23.8507i | − | 0.0321872i | ||||||
\(742\) | −290.615 | − | 421.146i | −0.391665 | − | 0.567582i | ||||
\(743\) | 258.593 | 0.348039 | 0.174020 | − | 0.984742i | \(-0.444324\pi\) | ||||
0.174020 | + | 0.984742i | \(0.444324\pi\) | |||||||
\(744\) | 26.7782 | + | 46.3812i | 0.0359922 | + | 0.0623403i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.55747 | + | 13.0899i | −0.0101307 | + | 0.0175468i | ||||
\(747\) | −121.271 | + | 70.0159i | −0.162344 | + | 0.0937295i | ||||
\(748\) | 83.1454i | 0.111157i | ||||||||
\(749\) | −282.005 | + | 594.114i | −0.376509 | + | 0.793210i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −175.310 | − | 303.645i | −0.233435 | − | 0.404321i | 0.725382 | − | 0.688347i | \(-0.241663\pi\) |
−0.958817 | + | 0.284025i | \(0.908330\pi\) | |||||||
\(752\) | −44.6409 | − | 25.7734i | −0.0593628 | − | 0.0342731i | ||||
\(753\) | −362.930 | + | 628.613i | −0.481978 | + | 0.834811i | ||||
\(754\) | −371.928 | + | 214.733i | −0.493274 | + | 0.284792i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.84424 | − | 72.5110i | −0.00773048 | − | 0.0959140i | ||||
\(757\) | −907.187 | −1.19840 | −0.599199 | − | 0.800600i | \(-0.704514\pi\) | ||||
−0.599199 | + | 0.800600i | \(0.704514\pi\) | |||||||
\(758\) | 101.058 | + | 175.038i | 0.133322 | + | 0.230921i | ||||
\(759\) | 33.3890 | + | 19.2771i | 0.0439907 | + | 0.0253981i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1067.66 | − | 616.416i | 1.40297 | − | 0.810007i | 0.408277 | − | 0.912858i | \(-0.366130\pi\) |
0.994697 | + | 0.102851i | \(0.0327965\pi\) | |||||||
\(762\) | − | 287.280i | − | 0.377008i | ||||||
\(763\) | 841.543 | − | 67.8267i | 1.10294 | − | 0.0888948i | ||||
\(764\) | −473.691 | −0.620014 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 755.684 | + | 436.294i | 0.986532 | + | 0.569575i | ||||
\(767\) | −436.376 | + | 755.826i | −0.568939 | + | 0.985432i | ||||
\(768\) | 24.0000 | − | 13.8564i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 685.828i | − | 0.891844i | −0.895072 | − | 0.445922i | \(-0.852876\pi\) | ||
0.895072 | − | 0.445922i | \(-0.147124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −578.431 | −0.750235 | ||||||||
\(772\) | −132.892 | − | 230.176i | −0.172140 | − | 0.298155i | ||||
\(773\) | −334.420 | − | 193.077i | −0.432625 | − | 0.249776i | 0.267839 | − | 0.963464i | \(-0.413690\pi\) |
−0.700465 | + | 0.713687i | \(0.747024\pi\) | |||||||
\(774\) | −164.232 | + | 284.458i | −0.212186 | + | 0.367517i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 129.386i | 0.166734i | ||||||||
\(777\) | 343.245 | − | 236.859i | 0.441756 | − | 0.304838i | ||||
\(778\) | 981.376 | 1.26141 | ||||||||
\(779\) | 16.7962 | + | 29.0918i | 0.0215612 | + | 0.0373451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −144.025 | + | 249.458i | −0.184411 | + | 0.319409i | ||||
\(782\) | 104.417 | − | 60.2851i | 0.133525 | − | 0.0770909i | ||||
\(783\) | − | 204.174i | − | 0.260759i | ||||||
\(784\) | 193.470 | − | 31.3905i | 0.246773 | − | 0.0400389i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −113.527 | − | 196.635i | −0.144437 | − | 0.250171i | ||||
\(787\) | −1064.42 | − | 614.543i | −1.35250 | − | 0.780867i | −0.363902 | − | 0.931437i | \(-0.618556\pi\) |
−0.988599 | + | 0.150570i | \(0.951889\pi\) | |||||||
\(788\) | −105.779 | + | 183.215i | −0.134238 | + | 0.232506i | ||||
\(789\) | −306.565 | + | 176.995i | −0.388549 | + | 0.224329i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.6663 | + | 61.8300i | 0.0539397 | + | 0.0781668i | ||||
\(792\) | 27.9553 | 0.0352971 | ||||||||
\(793\) | −101.371 | − | 175.579i | −0.127832 | − | 0.221411i | ||||
\(794\) | 685.309 | + | 395.663i | 0.863109 | + | 0.498316i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −349.082 | + | 201.543i | −0.438545 | + | 0.253194i | ||||
\(797\) | 821.718i | 1.03101i | 0.856886 | + | 0.515507i | \(0.172396\pi\) | ||||
−0.856886 | + | 0.515507i | \(0.827604\pi\) | |||||||
\(798\) | −13.1004 | + | 27.5992i | −0.0164165 | + | 0.0345855i | ||||
\(799\) | −162.612 | −0.203519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −142.412 | − | 82.2215i | −0.177793 | − | 0.102649i | ||||
\(802\) | −113.990 | + | 197.437i | −0.142132 | + | 0.246181i | ||||
\(803\) | −173.801 | + | 100.344i | −0.216440 | + | 0.124962i | ||||
\(804\) | − | 68.9811i | − | 0.0857973i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −119.486 | −0.148245 | ||||||||
\(807\) | 120.768 | + | 209.177i | 0.149651 | + | 0.259203i | ||||
\(808\) | −224.178 | − | 129.429i | −0.277448 | − | 0.160185i | ||||
\(809\) | 216.809 | − | 375.524i | 0.267996 | − | 0.464184i | −0.700348 | − | 0.713802i | \(-0.746972\pi\) |
0.968344 | + | 0.249618i | \(0.0803051\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1618.04i | 1.99512i | 0.0698416 | + | 0.997558i | \(0.477751\pi\) | ||||
−0.0698416 | + | 0.997558i | \(0.522249\pi\) | |||||||
\(812\) | 548.328 | − | 44.1941i | 0.675281 | − | 0.0544263i | ||||
\(813\) | 646.425 | 0.795111 | ||||||||
\(814\) | 80.1304 | + | 138.790i | 0.0984403 | + | 0.170504i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 43.7121 | − | 75.7115i | 0.0535687 | − | 0.0927837i | ||||
\(817\) | 119.461 | − | 68.9711i | 0.146220 | − | 0.0844199i | ||||
\(818\) | 650.286i | 0.794971i | ||||||||
\(819\) | 146.620 | + | 69.5952i | 0.179023 | + | 0.0849758i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 429.043 | + | 743.125i | 0.522586 | + | 0.905146i | 0.999655 | + | 0.0262799i | \(0.00836612\pi\) |
−0.477068 | + | 0.878866i | \(0.658301\pi\) | |||||||
\(822\) | −58.2813 | − | 33.6487i | −0.0709018 | − | 0.0409352i | ||||
\(823\) | −392.287 | + | 679.461i | −0.476655 | + | 0.825591i | −0.999642 | − | 0.0267498i | \(-0.991484\pi\) |
0.522987 | + | 0.852341i | \(0.324818\pi\) | |||||||
\(824\) | 123.719 | − | 71.4294i | 0.150145 | − | 0.0866862i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 920.109 | − | 634.929i | 1.11393 | − | 0.768680i | ||||
\(827\) | 773.795 | 0.935665 | 0.467833 | − | 0.883817i | \(-0.345035\pi\) | ||||
0.467833 | + | 0.883817i | \(0.345035\pi\) | |||||||
\(828\) | −20.2691 | − | 35.1072i | −0.0244796 | − | 0.0424000i | ||||
\(829\) | −573.640 | − | 331.191i | −0.691966 | − | 0.399507i | 0.112382 | − | 0.993665i | \(-0.464152\pi\) |
−0.804348 | + | 0.594158i | \(0.797485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 746.256 | − | 430.851i | 0.898022 | − | 0.518473i | ||||
\(832\) | 61.8280i | 0.0743125i | ||||||||
\(833\) | 479.048 | − | 390.924i | 0.575087 | − | 0.469296i | ||||
\(834\) | 164.147 | 0.196819 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.1672 | − | 5.87006i | −0.0121618 | − | 0.00702161i | ||||
\(837\) | 28.4025 | − | 49.1946i | 0.0339337 | − | 0.0587750i | ||||
\(838\) | −114.614 | + | 66.1723i | −0.136771 | + | 0.0789646i | ||||
\(839\) | 359.133i | 0.428049i | 0.976828 | + | 0.214024i | \(0.0686572\pi\) | ||||
−0.976828 | + | 0.214024i | \(0.931343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 702.963 | 0.835866 | ||||||||
\(842\) | 115.228 | + | 199.581i | 0.136851 | + | 0.237032i | ||||
\(843\) | −439.169 | − | 253.554i | −0.520959 | − | 0.300776i | ||||
\(844\) | −29.6045 | + | 51.2764i | −0.0350764 | + | 0.0607541i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 54.6737i | 0.0646261i | ||||||||
\(847\) | 330.621 | − | 696.537i | 0.390344 | − | 0.822357i | ||||
\(848\) | −206.752 | −0.243811 | ||||||||
\(849\) | −239.686 | − | 415.149i | −0.282316 | − | 0.488986i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 116.198 | − | 201.261i | 0.136543 | − | 0.236500i | ||||
\(852\) | 262.296 | − | 151.437i | 0.307859 | − | 0.177742i | ||||
\(853\) | − | 1089.78i | − | 1.27758i | −0.769379 | − | 0.638792i | \(-0.779434\pi\) | ||
0.769379 | − | 0.638792i | \(-0.220566\pi\) | |||||||
\(854\) | 20.8631 | + | 258.853i | 0.0244298 | + | 0.303107i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 132.865 | + | 230.128i | 0.155216 | + | 0.268841i | ||||
\(857\) | 56.2155 | + | 32.4560i | 0.0655956 | + | 0.0378717i | 0.532439 | − | 0.846468i | \(-0.321276\pi\) |
−0.466843 | + | 0.884340i | \(0.654609\pi\) | |||||||
\(858\) | −31.1845 | + | 54.0131i | −0.0363455 | + | 0.0629523i | ||||
\(859\) | 250.689 | − | 144.735i | 0.291838 | − | 0.168493i | −0.346933 | − | 0.937890i | \(-0.612777\pi\) |
0.638770 | + | 0.769397i | \(0.279443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −227.849 | + | 18.3642i | −0.264633 | + | 0.0213289i | ||||
\(862\) | 468.225 | 0.543185 | ||||||||
\(863\) | 469.234 | + | 812.738i | 0.543725 | + | 0.941759i | 0.998686 | + | 0.0512476i | \(0.0163198\pi\) |
−0.454961 | + | 0.890511i | \(0.650347\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −108.283 | + | 62.5174i | −0.125038 | + | 0.0721910i | ||||
\(867\) | 224.771i | 0.259251i | ||||||||
\(868\) | 138.265 | + | 65.6293i | 0.159291 | + | 0.0756098i | ||||
\(869\) | −117.213 | −0.134882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 133.280 | + | 76.9493i | 0.153020 | + | 0.0883459i | ||||
\(872\) | 170.569 | − | 295.434i | 0.195606 | − | 0.338800i | ||||
\(873\) | 118.848 | − | 68.6171i | 0.136138 | − | 0.0785992i | ||||
\(874\) | 17.0245i | 0.0194788i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 211.016 | 0.240886 | ||||||||
\(877\) | 110.543 | + | 191.465i | 0.126046 | + | 0.218318i | 0.922141 | − | 0.386853i | \(-0.126438\pi\) |
−0.796095 | + | 0.605171i | \(0.793105\pi\) | |||||||
\(878\) | −85.5044 | − | 49.3660i | −0.0973855 | − | 0.0562255i | ||||
\(879\) | −325.019 | + | 562.949i | −0.369759 | + | 0.640442i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 154.796i | 0.175704i | 0.996134 | + | 0.0878522i | \(0.0280003\pi\) | ||||
−0.996134 | + | 0.0878522i | \(0.972000\pi\) | |||||||
\(882\) | −131.437 | − | 161.066i | −0.149022 | − | 0.182615i | ||||
\(883\) | 1267.40 | 1.43534 | 0.717668 | − | 0.696385i | \(-0.245209\pi\) | ||||
0.717668 | + | 0.696385i | \(0.245209\pi\) | |||||||
\(884\) | 97.5227 | + | 168.914i | 0.110320 | + | 0.191080i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −466.997 | + | 808.863i | −0.527085 | + | 0.912938i | ||||
\(887\) | 1434.83 | − | 828.399i | 1.61762 | − | 0.933934i | 0.630087 | − | 0.776524i | \(-0.283019\pi\) |
0.987533 | − | 0.157410i | \(-0.0503143\pi\) | |||||||
\(888\) | − | 168.508i | − | 0.189761i | ||||||
\(889\) | −466.277 | − | 675.706i | −0.524496 | − | 0.760074i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.8255 | − | 25.6786i | −0.0166392 | − | 0.0288199i | ||||
\(892\) | −569.035 | − | 328.532i | −0.637931 | − | 0.368310i | ||||
\(893\) | 11.4804 | − | 19.8846i | 0.0128560 | − | 0.0222672i | ||||
\(894\) | −108.428 | + | 62.6009i | −0.121284 | + | 0.0700234i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 33.9600 | − | 71.5452i | 0.0379018 | − | 0.0798496i | ||||
\(897\) | 90.4420 | 0.100827 | ||||||||
\(898\) | −396.174 | − | 686.193i | −0.441173 | − | 0.764135i | ||||
\(899\) | 372.010 | + | 214.780i | 0.413804 | + | 0.238910i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −564.847 | + | 326.114i | −0.626911 | + | 0.361947i | ||||
\(902\) | − | 87.8430i | − | 0.0973869i | ||||||
\(903\) | 75.4099 | + | 935.630i | 0.0835105 | + | 1.03614i | ||||
\(904\) | 30.3540 | 0.0335774 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −350.480 | − | 202.350i | −0.386844 | − | 0.223344i | ||||
\(907\) | −368.230 | + | 637.793i | −0.405987 | + | 0.703190i | −0.994436 | − | 0.105345i | \(-0.966405\pi\) |
0.588449 | + | 0.808534i | \(0.299739\pi\) | |||||||
\(908\) | 631.256 | − | 364.456i | 0.695216 | − | 0.401383i | ||||
\(909\) | 274.561i | 0.302047i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 197.935 | 0.217273 | 0.108636 | − | 0.994082i | \(-0.465352\pi\) | ||||
0.108636 | + | 0.994082i | \(0.465352\pi\) | |||||||
\(912\) | 6.17214 | + | 10.6905i | 0.00676770 | + | 0.0117220i | ||||
\(913\) | −133.178 | − | 76.8905i | −0.145869 | − | 0.0842175i | ||||
\(914\) | −129.952 | + | 225.084i | −0.142180 | + | 0.246262i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 602.099i | − | 0.657313i | ||||||
\(917\) | −586.178 | − | 278.238i | −0.639235 | − | 0.303422i | ||||
\(918\) | −92.7273 | −0.101010 | ||||||||
\(919\) | −821.091 | − | 1422.17i | −0.893462 | − | 1.54752i | −0.835697 | − | 0.549191i | \(-0.814936\pi\) |
−0.0577645 | − | 0.998330i | \(-0.518397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 93.3436 | − | 161.676i | 0.101350 | − | 0.175544i | ||||
\(922\) | −34.8231 | + | 20.1051i | −0.0377691 | + | 0.0218060i | ||||
\(923\) | 675.718i | 0.732089i | ||||||||
\(924\) | 65.7531 | − | 45.3735i | 0.0711614 | − | 0.0491055i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 190.870 | + | 330.597i | 0.206123 | + | 0.357016i | ||||
\(927\) | −131.224 | − | 75.7623i | −0.141558 | − | 0.0817285i | ||||
\(928\) | 111.138 | − | 192.497i | 0.119761 | − | 0.207432i | ||||
\(929\) | 1317.18 | − | 760.473i | 1.41784 | − | 0.818593i | 0.421735 | − | 0.906719i | \(-0.361421\pi\) |
0.996109 | + | 0.0881263i | \(0.0280879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.9825 | + | 86.1785i | 0.0150188 | + | 0.0925655i | ||||
\(932\) | 564.050 | 0.605204 | ||||||||
\(933\) | 499.771 | + | 865.629i | 0.535660 | + | 0.927791i | ||||
\(934\) | −409.471 | − | 236.408i | −0.438405 | − | 0.253113i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 56.7927 | − | 32.7893i | 0.0606759 | − | 0.0350313i | ||||
\(937\) | − | 682.636i | − | 0.728534i | −0.931295 | − | 0.364267i | \(-0.881320\pi\) | ||
0.931295 | − | 0.364267i | \(-0.118680\pi\) | |||||||
\(938\) | −111.961 | − | 162.249i | −0.119362 | − | 0.172974i | ||||
\(939\) | 688.100 | 0.732800 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −248.545 | − | 143.497i | −0.264129 | − | 0.152495i | 0.362088 | − | 0.932144i | \(-0.382064\pi\) |
−0.626216 | + | 0.779649i | \(0.715397\pi\) | |||||||
\(942\) | −233.696 | + | 404.773i | −0.248085 | + | 0.429695i | ||||
\(943\) | −110.316 | + | 63.6911i | −0.116984 | + | 0.0675410i | ||||
\(944\) | − | 451.706i | − | 0.478502i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −360.715 | −0.381305 | ||||||||
\(947\) | 240.057 | + | 415.790i | 0.253492 | + | 0.439061i | 0.964485 | − | 0.264139i | \(-0.0850876\pi\) |
−0.710993 | + | 0.703199i | \(0.751754\pi\) | |||||||
\(948\) | 106.733 | + | 61.6224i | 0.112588 | + | 0.0650025i | ||||
\(949\) | −235.391 | + | 407.709i | −0.248041 | + | 0.429620i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 139.205i | − | 0.146378i | ||||||
\(952\) | −20.0711 | − | 249.028i | −0.0210831 | − | 0.261584i | ||||
\(953\) | −1147.30 | −1.20388 | −0.601941 | − | 0.798540i | \(-0.705606\pi\) | ||||
−0.601941 | + | 0.798540i | \(0.705606\pi\) | |||||||
\(954\) | 109.647 | + | 189.914i | 0.114934 | + | 0.199071i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −83.0347 | + | 143.820i | −0.0868563 | + | 0.150440i | ||||
\(957\) | 194.181 | − | 112.111i | 0.202906 | − | 0.117148i | ||||
\(958\) | 187.076i | 0.195277i | ||||||||
\(959\) | −191.697 | + | 15.4504i | −0.199892 | + | 0.0161109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −420.744 | − | 728.750i | −0.437819 | − | 0.758325i | ||||
\(962\) | 325.579 | + | 187.973i | 0.338439 | + | 0.195398i | ||||
\(963\) | 140.924 | − | 244.088i | 0.146339 | − | 0.253466i | ||||
\(964\) | 574.737 | − | 331.825i | 0.596201 | − | 0.344217i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −104.656 | − | 49.6767i | −0.108340 | − | 0.0514251i | ||||
\(967\) | 1400.07 | 1.44785 | 0.723923 | − | 0.689881i | \(-0.242337\pi\) | ||||
0.723923 | + | 0.689881i | \(0.242337\pi\) | |||||||
\(968\) | −155.770 | − | 269.801i | −0.160919 | − | 0.278720i | ||||
\(969\) | 33.7246 | + | 19.4709i | 0.0348035 | + | 0.0200938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 226.263 | − | 130.633i | 0.233020 | − | 0.134534i | −0.378944 | − | 0.925419i | \(-0.623713\pi\) |
0.611965 | + | 0.790885i | \(0.290379\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 386.087 | − | 266.423i | 0.396801 | − | 0.273816i | ||||
\(974\) | −731.532 | −0.751059 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 90.8735 | + | 52.4658i | 0.0931081 | + | 0.0537560i | ||||
\(977\) | 389.723 | − | 675.019i | 0.398897 | − | 0.690910i | −0.594693 | − | 0.803953i | \(-0.702726\pi\) |
0.993590 | + | 0.113043i | \(0.0360597\pi\) | |||||||
\(978\) | 526.516 | − | 303.984i | 0.538360 | − | 0.310822i | ||||
\(979\) | − | 180.589i | − | 0.184463i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −361.831 | −0.368839 | ||||||||
\(982\) | 342.809 | + | 593.763i | 0.349093 | + | 0.604646i | ||||
\(983\) | 1332.15 | + | 769.118i | 1.35519 | + | 0.782419i | 0.988971 | − | 0.148110i | \(-0.0473189\pi\) |
0.366219 | + | 0.930529i | \(0.380652\pi\) | |||||||
\(984\) | −46.1817 | + | 79.9891i | −0.0469327 | + | 0.0812898i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 701.204i | − | 0.711160i | ||||||
\(987\) | 88.7395 | + | 128.597i | 0.0899083 | + | 0.130291i | ||||
\(988\) | −27.5404 | −0.0278749 | ||||||||
\(989\) | 261.539 | + | 452.998i | 0.264448 | + | 0.458037i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −482.270 | + | 835.316i | −0.486650 | + | 0.842902i | −0.999882 | − | 0.0153476i | \(-0.995115\pi\) |
0.513233 | + | 0.858250i | \(0.328448\pi\) | |||||||
\(992\) | 53.5563 | − | 30.9208i | 0.0539883 | − | 0.0311701i | ||||
\(993\) | 852.242i | 0.858250i | ||||||||
\(994\) | 371.148 | − | 781.917i | 0.373389 | − | 0.786637i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 80.8474 | + | 140.032i | 0.0811721 | + | 0.140594i | ||||
\(997\) | −361.770 | − | 208.868i | −0.362858 | − | 0.209496i | 0.307476 | − | 0.951556i | \(-0.400516\pi\) |
−0.670334 | + | 0.742060i | \(0.733849\pi\) | |||||||
\(998\) | −91.4218 | + | 158.347i | −0.0916050 | + | 0.158664i | ||||
\(999\) | −154.785 | + | 89.3649i | −0.154939 | + | 0.0894543i |
(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 | 1050.3.p.c.451.3 | ✓ | 8 | |
5.2 | odd | 4 | 1050.3.q.b.199.2 | 16 | |||
5.3 | odd | 4 | 1050.3.q.b.199.7 | 16 | |||
5.4 | even | 2 | 1050.3.p.d.451.2 | yes | 8 | ||
7.5 | odd | 6 | inner | 1050.3.p.c.901.3 | yes | 8 | |
35.12 | even | 12 | 1050.3.q.b.649.7 | 16 | |||
35.19 | odd | 6 | 1050.3.p.d.901.2 | yes | 8 | ||
35.33 | even | 12 | 1050.3.q.b.649.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1050.3.p.c.901.3 | yes | 8 | 7.5 | odd | 6 | inner | |
1050.3.p.d.451.2 | yes | 8 | 5.4 | even | 2 | ||
1050.3.p.d.901.2 | yes | 8 | 35.19 | odd | 6 | ||
1050.3.q.b.199.2 | 16 | 5.2 | odd | 4 | |||
1050.3.q.b.199.7 | 16 | 5.3 | odd | 4 | |||
1050.3.q.b.649.2 | 16 | 35.33 | even | 12 | |||
1050.3.q.b.649.7 | 16 | 35.12 | even | 12 |