Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 46.11 | ||
Character | \(\chi\) | \(=\) | 225.46 |
Dual form | 225.4.h.d.181.11 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.626289 | − | 1.92752i | 0.221427 | − | 0.681481i | −0.777208 | − | 0.629244i | \(-0.783365\pi\) |
0.998635 | − | 0.0522374i | \(-0.0166353\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.14904 | + | 2.28791i | 0.393630 | + | 0.285989i | ||||
\(5\) | 3.12321 | − | 10.7352i | 0.279349 | − | 0.960190i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.4425 | −0.887810 | −0.443905 | − | 0.896074i | \(-0.646407\pi\) | ||||
−0.443905 | + | 0.896074i | \(0.646407\pi\) | |||||||
\(8\) | 19.4994 | − | 14.1671i | 0.861759 | − | 0.626104i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.7364 | − | 12.7434i | −0.592496 | − | 0.402982i | ||||
\(11\) | 1.41112 | − | 4.34299i | 0.0386790 | − | 0.119042i | −0.929853 | − | 0.367932i | \(-0.880066\pi\) |
0.968532 | + | 0.248890i | \(0.0800659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.0513 | − | 52.4784i | −0.363782 | − | 1.11961i | −0.950740 | − | 0.309989i | \(-0.899675\pi\) |
0.586958 | − | 0.809617i | \(-0.300325\pi\) | |||||||
\(14\) | −10.2977 | + | 31.6932i | −0.196585 | + | 0.605026i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.47256 | − | 16.8428i | −0.0855087 | − | 0.263169i | ||||
\(17\) | 1.72699 | − | 1.25473i | 0.0246386 | − | 0.0179010i | −0.575398 | − | 0.817874i | \(-0.695153\pi\) |
0.600036 | + | 0.799973i | \(0.295153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.2151 | − | 16.1402i | 0.268237 | − | 0.194885i | −0.445534 | − | 0.895265i | \(-0.646986\pi\) |
0.713770 | + | 0.700380i | \(0.246986\pi\) | |||||||
\(20\) | 34.3964 | − | 26.6601i | 0.384564 | − | 0.298069i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.48743 | − | 5.43993i | −0.0725602 | − | 0.0527181i | ||||
\(23\) | 30.4050 | − | 93.5770i | 0.275647 | − | 0.848354i | −0.713400 | − | 0.700757i | \(-0.752846\pi\) |
0.989047 | − | 0.147598i | \(-0.0471541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −105.491 | − | 67.0569i | −0.843929 | − | 0.536455i | ||||
\(26\) | −111.832 | −0.843542 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −51.7780 | − | 37.6189i | −0.349469 | − | 0.253904i | ||||
\(29\) | −2.70250 | − | 1.96348i | −0.0173049 | − | 0.0125728i | 0.579099 | − | 0.815257i | \(-0.303404\pi\) |
−0.596404 | + | 0.802684i | \(0.703404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54.6052 | − | 39.6730i | 0.316367 | − | 0.229854i | −0.418257 | − | 0.908329i | \(-0.637359\pi\) |
0.734624 | + | 0.678475i | \(0.237359\pi\) | |||||||
\(32\) | 156.928 | 0.866914 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.33692 | − | 4.11462i | −0.00674353 | − | 0.0207545i | ||||
\(35\) | −51.3533 | + | 176.514i | −0.248008 | + | 0.852466i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −56.4702 | − | 173.797i | −0.250909 | − | 0.772219i | −0.994608 | − | 0.103704i | \(-0.966930\pi\) |
0.743699 | − | 0.668515i | \(-0.233070\pi\) | |||||||
\(38\) | −17.1975 | − | 52.9285i | −0.0734159 | − | 0.225951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −91.1869 | − | 253.578i | −0.360448 | − | 1.00235i | ||||
\(41\) | −11.7884 | − | 36.2811i | −0.0449035 | − | 0.138199i | 0.926091 | − | 0.377300i | \(-0.123147\pi\) |
−0.970995 | + | 0.239101i | \(0.923147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −252.976 | −0.897173 | −0.448586 | − | 0.893739i | \(-0.648072\pi\) | ||||
−0.448586 | + | 0.893739i | \(0.648072\pi\) | |||||||
\(44\) | 14.3801 | − | 10.4477i | 0.0492699 | − | 0.0357967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −161.329 | − | 117.213i | −0.517102 | − | 0.375697i | ||||
\(47\) | 35.6846 | + | 25.9263i | 0.110747 | + | 0.0804627i | 0.641780 | − | 0.766888i | \(-0.278196\pi\) |
−0.531033 | + | 0.847351i | \(0.678196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −72.6451 | −0.211793 | ||||||||
\(50\) | −195.321 | + | 161.339i | −0.552452 | + | 0.456336i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 66.3708 | − | 204.268i | 0.177000 | − | 0.544749i | ||||
\(53\) | 163.853 | + | 119.046i | 0.424659 | + | 0.308533i | 0.779510 | − | 0.626390i | \(-0.215468\pi\) |
−0.354851 | + | 0.934923i | \(0.615468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −42.2158 | − | 28.7128i | −0.103498 | − | 0.0703934i | ||||
\(56\) | −320.618 | + | 232.943i | −0.765078 | + | 0.555862i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.47720 | + | 3.97942i | −0.0123999 | + | 0.00900903i | ||||
\(59\) | −36.4118 | − | 112.064i | −0.0803460 | − | 0.247280i | 0.902813 | − | 0.430034i | \(-0.141499\pi\) |
−0.983159 | + | 0.182755i | \(0.941499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −248.210 | + | 763.911i | −0.520984 | + | 1.60342i | 0.251139 | + | 0.967951i | \(0.419195\pi\) |
−0.772123 | + | 0.635473i | \(0.780805\pi\) | |||||||
\(62\) | −42.2718 | − | 130.099i | −0.0865892 | − | 0.266494i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 142.063 | − | 437.225i | 0.277467 | − | 0.853954i | ||||
\(65\) | −616.623 | + | 19.1484i | −1.17666 | + | 0.0365395i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 523.504 | − | 380.348i | 0.954571 | − | 0.693536i | 0.00268734 | − | 0.999996i | \(-0.499145\pi\) |
0.951884 | + | 0.306460i | \(0.0991446\pi\) | |||||||
\(68\) | 8.30906 | 0.0148180 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 308.072 | + | 209.533i | 0.526024 | + | 0.357772i | ||||
\(71\) | 798.476 | + | 580.127i | 1.33467 | + | 0.969696i | 0.999622 | + | 0.0274953i | \(0.00875314\pi\) |
0.335050 | + | 0.942200i | \(0.391247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −256.874 | + | 790.578i | −0.411847 | + | 1.26754i | 0.503193 | + | 0.864174i | \(0.332158\pi\) |
−0.915040 | + | 0.403362i | \(0.867842\pi\) | |||||||
\(74\) | −370.365 | −0.581811 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 106.884 | 0.161321 | ||||||||
\(77\) | −23.2023 | + | 71.4095i | −0.0343396 | + | 0.105687i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 822.092 | + | 597.285i | 1.17079 | + | 0.850630i | 0.991104 | − | 0.133093i | \(-0.0424909\pi\) |
0.179689 | + | 0.983724i | \(0.442491\pi\) | |||||||
\(80\) | −197.904 | + | 6.14563i | −0.276579 | + | 0.00858878i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −77.3154 | −0.104123 | ||||||||
\(83\) | 926.758 | − | 673.329i | 1.22560 | − | 0.890452i | 0.229049 | − | 0.973415i | \(-0.426438\pi\) |
0.996553 | + | 0.0829629i | \(0.0264383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.07608 | − | 22.4584i | −0.0103056 | − | 0.0286583i | ||||
\(86\) | −158.436 | + | 487.616i | −0.198658 | + | 0.611406i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −34.0117 | − | 104.677i | −0.0412006 | − | 0.126802i | ||||
\(89\) | 349.060 | − | 1074.29i | 0.415733 | − | 1.27949i | −0.495861 | − | 0.868402i | \(-0.665147\pi\) |
0.911594 | − | 0.411093i | \(-0.134853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 280.365 | + | 862.874i | 0.322969 | + | 0.993998i | ||||
\(92\) | 309.843 | − | 225.114i | 0.351123 | − | 0.255106i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 72.3224 | − | 52.5453i | 0.0793562 | − | 0.0576557i | ||||
\(95\) | −103.887 | − | 288.894i | −0.112195 | − | 0.311999i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 457.822 | + | 332.627i | 0.479224 | + | 0.348177i | 0.801025 | − | 0.598630i | \(-0.204288\pi\) |
−0.321801 | + | 0.946807i | \(0.604288\pi\) | |||||||
\(98\) | −45.4968 | + | 140.025i | −0.0468967 | + | 0.144333i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −178.776 | − | 452.519i | −0.178776 | − | 0.452519i | ||||
\(101\) | 732.732 | 0.721877 | 0.360938 | − | 0.932590i | \(-0.382456\pi\) | ||||
0.360938 | + | 0.932590i | \(0.382456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 148.901 | + | 108.183i | 0.142443 | + | 0.103491i | 0.656725 | − | 0.754130i | \(-0.271941\pi\) |
−0.514282 | + | 0.857621i | \(0.671941\pi\) | |||||||
\(104\) | −1075.96 | − | 781.728i | −1.01448 | − | 0.737065i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 332.083 | − | 241.272i | 0.304290 | − | 0.221080i | ||||
\(107\) | 1461.97 | 1.32088 | 0.660440 | − | 0.750879i | \(-0.270370\pi\) | ||||
0.660440 | + | 0.750879i | \(0.270370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 551.250 | + | 1696.57i | 0.484405 | + | 1.49085i | 0.832840 | + | 0.553514i | \(0.186713\pi\) |
−0.348435 | + | 0.937333i | \(0.613287\pi\) | |||||||
\(110\) | −81.7838 | + | 63.3893i | −0.0708889 | + | 0.0549448i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 89.9823 | + | 276.937i | 0.0759155 | + | 0.233644i | ||||
\(113\) | −602.823 | − | 1855.30i | −0.501848 | − | 1.54453i | −0.806006 | − | 0.591907i | \(-0.798375\pi\) |
0.304158 | − | 0.952622i | \(-0.401625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −909.611 | − | 618.666i | −0.737580 | − | 0.501660i | ||||
\(116\) | −4.01802 | − | 12.3662i | −0.00321606 | − | 0.00989803i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −238.810 | −0.186307 | ||||||||
\(119\) | −28.3959 | + | 20.6308i | −0.0218744 | + | 0.0158926i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1059.93 | + | 770.085i | 0.796342 | + | 0.578576i | ||||
\(122\) | 1317.00 | + | 956.859i | 0.977343 | + | 0.710081i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 262.722 | 0.190267 | ||||||||
\(125\) | −1049.34 | + | 923.040i | −0.750849 | + | 0.660474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −286.464 | + | 881.645i | −0.200154 | + | 0.616011i | 0.799724 | + | 0.600368i | \(0.204979\pi\) |
−0.999878 | + | 0.0156424i | \(0.995021\pi\) | |||||||
\(128\) | 261.874 | + | 190.263i | 0.180833 | + | 0.131383i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −349.275 | + | 1200.55i | −0.235642 | + | 0.809960i | ||||
\(131\) | −2108.91 | + | 1532.21i | −1.40654 | + | 1.02191i | −0.412720 | + | 0.910858i | \(0.635421\pi\) |
−0.993815 | + | 0.111050i | \(0.964579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −365.271 | + | 265.385i | −0.238143 | + | 0.173021i | ||||
\(134\) | −405.264 | − | 1247.27i | −0.261265 | − | 0.804090i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.8992 | − | 48.9328i | 0.0100246 | − | 0.0308526i | ||||
\(137\) | 902.756 | + | 2778.40i | 0.562976 | + | 1.73266i | 0.673890 | + | 0.738831i | \(0.264622\pi\) |
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 308.366 | − | 949.054i | 0.188167 | − | 0.579120i | −0.811821 | − | 0.583906i | \(-0.801524\pi\) |
0.999989 | + | 0.00478634i | \(0.00152355\pi\) | |||||||
\(140\) | −565.562 | + | 438.358i | −0.341420 | + | 0.264629i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1618.28 | − | 1175.75i | 0.956361 | − | 0.694837i | ||||
\(143\) | −251.974 | −0.147351 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29.5190 | + | 22.8797i | −0.0169063 | + | 0.0131038i | ||||
\(146\) | 1362.98 | + | 990.261i | 0.772608 | + | 0.561333i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 219.806 | − | 676.494i | 0.122081 | − | 0.375726i | ||||
\(149\) | −2608.22 | −1.43405 | −0.717026 | − | 0.697046i | \(-0.754497\pi\) | ||||
−0.717026 | + | 0.697046i | \(0.754497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −434.771 | −0.234312 | −0.117156 | − | 0.993114i | \(-0.537378\pi\) | ||||
−0.117156 | + | 0.993114i | \(0.537378\pi\) | |||||||
\(152\) | 204.520 | − | 629.448i | 0.109137 | − | 0.335888i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 123.112 | + | 89.4459i | 0.0644197 | + | 0.0468036i | ||||
\(155\) | −255.356 | − | 710.107i | −0.132327 | − | 0.367982i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2183.01 | −1.10970 | −0.554851 | − | 0.831949i | \(-0.687225\pi\) | ||||
−0.554851 | + | 0.831949i | \(0.687225\pi\) | |||||||
\(158\) | 1666.15 | − | 1210.53i | 0.838933 | − | 0.609521i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 490.120 | − | 1684.66i | 0.242171 | − | 0.832402i | ||||
\(161\) | −499.933 | + | 1538.64i | −0.244722 | + | 0.753178i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.56141 | + | 4.80554i | 0.000750303 | + | 0.00230920i | 0.951431 | − | 0.307862i | \(-0.0996136\pi\) |
−0.950681 | + | 0.310171i | \(0.899614\pi\) | |||||||
\(164\) | 45.8856 | − | 141.221i | 0.0218480 | − | 0.0672411i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −717.437 | − | 2208.04i | −0.335445 | − | 1.03239i | ||||
\(167\) | 182.453 | − | 132.560i | 0.0845428 | − | 0.0614239i | −0.544711 | − | 0.838624i | \(-0.683361\pi\) |
0.629254 | + | 0.777200i | \(0.283361\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −685.824 | + | 498.280i | −0.312164 | + | 0.226800i | ||||
\(170\) | −48.3470 | + | 1.50135i | −0.0218120 | + | 0.000677343i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −796.631 | − | 578.786i | −0.353154 | − | 0.256582i | ||||
\(173\) | 1021.65 | − | 3144.32i | 0.448986 | − | 1.38184i | −0.429066 | − | 0.903273i | \(-0.641157\pi\) |
0.878052 | − | 0.478565i | \(-0.158843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1734.53 | + | 1102.58i | 0.749248 | + | 0.476270i | ||||
\(176\) | −80.8705 | −0.0346355 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1852.11 | − | 1345.64i | −0.779897 | − | 0.566629i | ||||
\(179\) | −1464.76 | − | 1064.21i | −0.611627 | − | 0.444373i | 0.238360 | − | 0.971177i | \(-0.423390\pi\) |
−0.849987 | + | 0.526804i | \(0.823390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1447.42 | + | 1051.61i | −0.594395 | + | 0.431854i | −0.843885 | − | 0.536524i | \(-0.819737\pi\) |
0.249490 | + | 0.968377i | \(0.419737\pi\) | |||||||
\(182\) | 1838.80 | 0.748905 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −732.838 | − | 2255.44i | −0.293617 | − | 0.903661i | ||||
\(185\) | −2042.13 | + | 63.4155i | −0.811568 | + | 0.0252022i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.01228 | − | 9.27085i | −0.00117797 | − | 0.00362541i | ||||
\(188\) | 53.0549 | + | 163.286i | 0.0205821 | + | 0.0633451i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −621.912 | + | 19.3126i | −0.237464 | + | 0.00737414i | ||||
\(191\) | 1406.35 | + | 4328.29i | 0.532774 | + | 1.63971i | 0.748411 | + | 0.663235i | \(0.230817\pi\) |
−0.215637 | + | 0.976474i | \(0.569183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3534.94 | 1.31840 | 0.659199 | − | 0.751969i | \(-0.270895\pi\) | ||||
0.659199 | + | 0.751969i | \(0.270895\pi\) | |||||||
\(194\) | 927.874 | − | 674.140i | 0.343389 | − | 0.249487i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −228.762 | − | 166.206i | −0.0833682 | − | 0.0605706i | ||||
\(197\) | 135.139 | + | 98.1842i | 0.0488744 | + | 0.0355093i | 0.611954 | − | 0.790893i | \(-0.290384\pi\) |
−0.563080 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3173.44 | −1.13045 | −0.565224 | − | 0.824937i | \(-0.691210\pi\) | ||||
−0.565224 | + | 0.824937i | \(0.691210\pi\) | |||||||
\(200\) | −3007.01 | + | 186.938i | −1.06314 | + | 0.0660925i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 458.902 | − | 1412.36i | 0.159843 | − | 0.491946i | ||||
\(203\) | 44.4358 | + | 32.2845i | 0.0153635 | + | 0.0111622i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −426.304 | + | 13.2383i | −0.145241 | + | 0.00451026i | ||||
\(206\) | 301.779 | − | 219.256i | 0.102068 | − | 0.0741566i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −790.569 | + | 574.382i | −0.263539 | + | 0.191472i | ||||
\(209\) | −38.7485 | − | 119.256i | −0.0128244 | − | 0.0394693i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 842.745 | − | 2593.70i | 0.274962 | − | 0.846245i | −0.714268 | − | 0.699873i | \(-0.753240\pi\) |
0.989229 | − | 0.146373i | \(-0.0467599\pi\) | |||||||
\(212\) | 243.612 | + | 749.762i | 0.0789215 | + | 0.242895i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 915.617 | − | 2817.98i | 0.292478 | − | 0.900154i | ||||
\(215\) | −790.097 | + | 2715.76i | −0.250624 | + | 0.861456i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −897.844 | + | 652.322i | −0.280874 | + | 0.204067i | ||||
\(218\) | 3615.42 | 1.12324 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −67.2469 | − | 187.004i | −0.0206081 | − | 0.0573082i | ||||
\(221\) | −95.2934 | − | 69.2347i | −0.0290051 | − | 0.0210734i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.6372 | + | 35.8157i | −0.00349456 | + | 0.0107551i | −0.952789 | − | 0.303634i | \(-0.901800\pi\) |
0.949294 | + | 0.314390i | \(0.101800\pi\) | |||||||
\(224\) | −2580.29 | −0.769655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3953.67 | −1.16369 | ||||||||
\(227\) | 1025.04 | − | 3154.75i | 0.299710 | − | 0.922413i | −0.681888 | − | 0.731456i | \(-0.738841\pi\) |
0.981598 | − | 0.190957i | \(-0.0611590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3988.04 | − | 2897.48i | −1.15082 | − | 0.836118i | −0.162228 | − | 0.986753i | \(-0.551868\pi\) |
−0.988589 | + | 0.150635i | \(0.951868\pi\) | |||||||
\(230\) | −1762.17 | + | 1365.83i | −0.505192 | + | 0.391566i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −80.5141 | −0.0227845 | ||||||||
\(233\) | 5.77631 | − | 4.19673i | 0.00162411 | − | 0.00117999i | −0.586973 | − | 0.809607i | \(-0.699680\pi\) |
0.588597 | + | 0.808427i | \(0.299680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 389.776 | − | 302.109i | 0.108197 | − | 0.0838614i | ||||
\(236\) | 141.730 | − | 436.201i | 0.0390926 | − | 0.120315i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 21.9823 | + | 67.6545i | 0.00598698 | + | 0.0184260i | ||||
\(239\) | 2227.98 | − | 6857.03i | 0.602997 | − | 1.85583i | 0.0929815 | − | 0.995668i | \(-0.470360\pi\) |
0.510015 | − | 0.860165i | \(-0.329640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1061.81 | − | 3267.92i | −0.283806 | − | 0.873465i | −0.986754 | − | 0.162224i | \(-0.948133\pi\) |
0.702948 | − | 0.711241i | \(-0.251867\pi\) | |||||||
\(242\) | 2148.18 | − | 1560.74i | 0.570620 | − | 0.414580i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2529.39 | + | 1837.71i | −0.663637 | + | 0.482160i | ||||
\(245\) | −226.886 | + | 779.863i | −0.0591642 | + | 0.203362i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1225.81 | − | 890.601i | −0.315774 | − | 0.229424i | ||||
\(248\) | 502.715 | − | 1547.20i | 0.128719 | − | 0.396158i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1121.99 | + | 2600.72i | 0.283842 | + | 0.657936i | ||||
\(251\) | −1687.00 | −0.424233 | −0.212117 | − | 0.977244i | \(-0.568036\pi\) | ||||
−0.212117 | + | 0.977244i | \(0.568036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −363.499 | − | 264.097i | −0.0903279 | − | 0.0656271i | ||||
\(254\) | 1519.98 | + | 1104.33i | 0.375480 | + | 0.272802i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3506.15 | − | 2547.37i | 0.855993 | − | 0.621915i | ||||
\(257\) | 2098.27 | 0.509286 | 0.254643 | − | 0.967035i | \(-0.418042\pi\) | ||||
0.254643 | + | 0.967035i | \(0.418042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 928.509 | + | 2857.66i | 0.222760 | + | 0.685584i | ||||
\(260\) | −1985.58 | − | 1350.48i | −0.473617 | − | 0.322128i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1632.58 | + | 5024.57i | 0.384966 | + | 1.18480i | ||||
\(263\) | −43.9940 | − | 135.400i | −0.0103148 | − | 0.0317456i | 0.945767 | − | 0.324847i | \(-0.105313\pi\) |
−0.956081 | + | 0.293101i | \(0.905313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1789.74 | − | 1387.19i | 0.414878 | − | 0.321565i | ||||
\(266\) | 282.770 | + | 870.275i | 0.0651794 | + | 0.200601i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2518.74 | 0.574092 | ||||||||
\(269\) | 2534.35 | − | 1841.31i | 0.574432 | − | 0.417349i | −0.262281 | − | 0.964992i | \(-0.584475\pi\) |
0.836712 | + | 0.547643i | \(0.184475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2812.49 | + | 2043.40i | 0.630431 | + | 0.458035i | 0.856550 | − | 0.516065i | \(-0.172604\pi\) |
−0.226118 | + | 0.974100i | \(0.572604\pi\) | |||||||
\(272\) | −30.5841 | − | 22.2207i | −0.00681778 | − | 0.00495341i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5920.80 | 1.30543 | ||||||||
\(275\) | −440.088 | + | 363.521i | −0.0965030 | + | 0.0797133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1027.03 | + | 3160.87i | −0.222774 | + | 0.685626i | 0.775736 | + | 0.631057i | \(0.217379\pi\) |
−0.998510 | + | 0.0545694i | \(0.982621\pi\) | |||||||
\(278\) | −1636.19 | − | 1188.76i | −0.352994 | − | 0.256465i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1499.34 | + | 4169.44i | 0.320009 | + | 0.889899i | ||||
\(281\) | 2319.48 | − | 1685.20i | 0.492415 | − | 0.357760i | −0.313698 | − | 0.949523i | \(-0.601568\pi\) |
0.806112 | + | 0.591763i | \(0.201568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6659.26 | − | 4838.24i | 1.39877 | − | 1.01627i | 0.403933 | − | 0.914789i | \(-0.367643\pi\) |
0.994838 | − | 0.101478i | \(-0.0323571\pi\) | |||||||
\(284\) | 1187.15 | + | 3653.69i | 0.248045 | + | 0.763403i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −157.809 | + | 485.686i | −0.0326274 | + | 0.100417i | ||||
\(287\) | 193.831 | + | 596.550i | 0.0398658 | + | 0.122694i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1516.79 | + | 4668.21i | −0.308730 | + | 0.950174i | ||||
\(290\) | 25.6136 | + | 71.2277i | 0.00518649 | + | 0.0144229i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2617.68 | + | 1901.86i | −0.524617 | + | 0.381157i | ||||
\(293\) | 2288.26 | 0.456251 | 0.228125 | − | 0.973632i | \(-0.426740\pi\) | ||||
0.228125 | + | 0.973632i | \(0.426740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1316.76 | + | 40.8901i | −0.259880 | + | 0.00807022i | ||||
\(296\) | −3563.34 | − | 2588.92i | −0.699713 | − | 0.508371i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1633.50 | + | 5027.40i | −0.317538 | + | 0.977280i | ||||
\(299\) | −5429.21 | −1.05010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4159.55 | 0.796519 | ||||||||
\(302\) | −272.292 | + | 838.029i | −0.0518830 | + | 0.159679i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −393.420 | − | 285.836i | −0.0742242 | − | 0.0539271i | ||||
\(305\) | 7425.57 | + | 5050.45i | 1.39405 | + | 0.948157i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2783.54 | −0.517475 | −0.258737 | − | 0.965948i | \(-0.583306\pi\) | ||||
−0.258737 | + | 0.965948i | \(0.583306\pi\) | |||||||
\(308\) | −236.444 | + | 171.786i | −0.0437423 | + | 0.0317806i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1528.67 | + | 47.4709i | −0.280073 | + | 0.00869731i | ||||
\(311\) | −2462.79 | + | 7579.70i | −0.449043 | + | 1.38201i | 0.428946 | + | 0.903330i | \(0.358885\pi\) |
−0.877989 | + | 0.478681i | \(0.841115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1489.79 | − | 4585.11i | −0.269035 | − | 0.828005i | −0.990736 | − | 0.135800i | \(-0.956640\pi\) |
0.721701 | − | 0.692205i | \(-0.243360\pi\) | |||||||
\(314\) | −1367.20 | + | 4207.80i | −0.245718 | + | 0.756242i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1222.27 | + | 3761.75i | 0.217588 | + | 0.669668i | ||||
\(317\) | −6986.98 | + | 5076.34i | −1.23794 | + | 0.899418i | −0.997460 | − | 0.0712347i | \(-0.977306\pi\) |
−0.240484 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.3409 | + | 8.96622i | −0.00216602 | + | 0.00157371i | ||||
\(320\) | −4250.02 | − | 2890.63i | −0.742448 | − | 0.504971i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2652.65 | + | 1927.26i | 0.459088 | + | 0.333547i | ||||
\(323\) | 18.1136 | − | 55.7478i | 0.00312033 | − | 0.00960338i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1720.28 | + | 6679.41i | −0.293612 | + | 1.14002i | ||||
\(326\) | 10.2407 | 0.00173981 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −743.866 | − | 540.450i | −0.125223 | − | 0.0909797i | ||||
\(329\) | −586.742 | − | 426.293i | −0.0983226 | − | 0.0714356i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1556.01 | − | 1130.51i | 0.258388 | − | 0.187730i | −0.451048 | − | 0.892500i | \(-0.648950\pi\) |
0.709436 | + | 0.704770i | \(0.248950\pi\) | |||||||
\(332\) | 4458.92 | 0.737093 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −141.244 | − | 434.703i | −0.0231392 | − | 0.0712152i | ||||
\(335\) | −2448.12 | − | 6807.86i | −0.399269 | − | 1.11031i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 721.800 | + | 2221.47i | 0.116673 | + | 0.359084i | 0.992292 | − | 0.123919i | \(-0.0395462\pi\) |
−0.875619 | + | 0.483003i | \(0.839546\pi\) | |||||||
\(338\) | 530.921 | + | 1634.01i | 0.0854388 | + | 0.262953i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.9509 | − | 89.1998i | 0.00413937 | − | 0.0142280i | ||||
\(341\) | −95.2447 | − | 293.133i | −0.0151255 | − | 0.0465515i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6834.23 | 1.07584 | ||||||||
\(344\) | −4932.87 | + | 3583.94i | −0.773147 | + | 0.561724i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5420.88 | − | 3938.50i | −0.842279 | − | 0.611952i | ||||
\(347\) | −5254.02 | − | 3817.27i | −0.812826 | − | 0.590553i | 0.101822 | − | 0.994803i | \(-0.467533\pi\) |
−0.914649 | + | 0.404250i | \(0.867533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4713.73 | 0.722980 | 0.361490 | − | 0.932376i | \(-0.382268\pi\) | ||||
0.361490 | + | 0.932376i | \(0.382268\pi\) | |||||||
\(350\) | 3211.57 | − | 2652.81i | 0.490473 | − | 0.405140i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 221.445 | − | 681.537i | 0.0335314 | − | 0.103199i | ||||
\(353\) | −3185.69 | − | 2314.54i | −0.480331 | − | 0.348981i | 0.321123 | − | 0.947038i | \(-0.395940\pi\) |
−0.801454 | + | 0.598056i | \(0.795940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8721.62 | − | 6759.98i | 1.30393 | − | 1.01066i | ||||
\(356\) | 3557.10 | − | 2584.38i | 0.529567 | − | 0.384753i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2968.65 | + | 2156.85i | −0.438262 | + | 0.318416i | ||||
\(359\) | 2913.64 | + | 8967.26i | 0.428345 | + | 1.31831i | 0.899754 | + | 0.436397i | \(0.143746\pi\) |
−0.471409 | + | 0.881915i | \(0.656254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1886.54 | + | 5806.18i | −0.275046 | + | 0.846506i | ||||
\(362\) | 1120.50 | + | 3448.53i | 0.162685 | + | 0.500693i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1091.30 | + | 3358.68i | −0.157142 | + | 0.483633i | ||||
\(365\) | 7684.78 | + | 5226.75i | 1.10203 | + | 0.749536i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2067.94 | − | 1502.45i | 0.294130 | − | 0.213698i | −0.430927 | − | 0.902387i | \(-0.641813\pi\) |
0.725057 | + | 0.688689i | \(0.241813\pi\) | |||||||
\(368\) | −1742.49 | −0.246831 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1156.73 | + | 3975.96i | −0.162528 | + | 0.558649i | ||||
\(371\) | −2694.14 | − | 1957.41i | −0.377016 | − | 0.273918i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3360.65 | + | 10343.0i | −0.466509 | + | 1.43577i | 0.390565 | + | 0.920575i | \(0.372280\pi\) |
−0.857074 | + | 0.515193i | \(0.827720\pi\) | |||||||
\(374\) | −19.7563 | −0.00273148 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1063.13 | 0.145816 | ||||||||
\(377\) | −56.9593 | + | 175.303i | −0.00778131 | + | 0.0239484i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5989.27 | − | 4351.46i | −0.811737 | − | 0.589761i | 0.102597 | − | 0.994723i | \(-0.467285\pi\) |
−0.914334 | + | 0.404962i | \(0.867285\pi\) | |||||||
\(380\) | 333.820 | − | 1147.42i | 0.0450648 | − | 0.154899i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9223.65 | 1.23540 | ||||||||
\(383\) | −5046.70 | + | 3666.64i | −0.673301 | + | 0.489182i | −0.871128 | − | 0.491055i | \(-0.836611\pi\) |
0.197828 | + | 0.980237i | \(0.436611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 694.132 | + | 472.110i | 0.0918864 | + | 0.0624959i | ||||
\(386\) | 2213.90 | − | 6813.67i | 0.291928 | − | 0.898463i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 680.678 | + | 2094.91i | 0.0890624 | + | 0.274106i | ||||
\(389\) | 2416.91 | − | 7438.49i | 0.315019 | − | 0.969528i | −0.660728 | − | 0.750625i | \(-0.729752\pi\) |
0.975747 | − | 0.218903i | \(-0.0702477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −64.9047 | − | 199.756i | −0.00839481 | − | 0.0258366i | ||||
\(392\) | −1416.53 | + | 1029.17i | −0.182515 | + | 0.132605i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 273.888 | − | 198.991i | 0.0350210 | − | 0.0254443i | ||||
\(395\) | 8979.57 | − | 6959.92i | 1.14383 | − | 0.886560i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6541.82 | − | 4752.91i | −0.827013 | − | 0.600860i | 0.0916994 | − | 0.995787i | \(-0.470770\pi\) |
−0.918713 | + | 0.394926i | \(0.870770\pi\) | |||||||
\(398\) | −1987.49 | + | 6116.87i | −0.250311 | + | 0.770379i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −552.120 | + | 2143.74i | −0.0690150 | + | 0.267967i | ||||
\(401\) | 1345.64 | 0.167576 | 0.0837882 | − | 0.996484i | \(-0.473298\pi\) | ||||
0.0837882 | + | 0.996484i | \(0.473298\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3013.06 | − | 2189.12i | −0.372435 | − | 0.270590i | ||||
\(404\) | 2307.40 | + | 1676.43i | 0.284153 | + | 0.206449i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 90.0587 | − | 65.4315i | 0.0110087 | − | 0.00799830i | ||||
\(407\) | −834.486 | −0.101631 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 917.900 | + | 2825.00i | 0.110971 | + | 0.341534i | 0.991085 | − | 0.133228i | \(-0.0425342\pi\) |
−0.880114 | + | 0.474762i | \(0.842534\pi\) | |||||||
\(410\) | −241.472 | + | 830.000i | −0.0290865 | + | 0.0999776i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 221.382 | + | 681.344i | 0.0264726 | + | 0.0814743i | ||||
\(413\) | 598.700 | + | 1842.61i | 0.0713320 | + | 0.219537i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4333.90 | − | 12051.9i | −0.512633 | − | 1.42556i | ||||
\(416\) | −2675.82 | − | 8235.34i | −0.315368 | − | 0.970603i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −254.136 | −0.0297373 | ||||||||
\(419\) | 12542.9 | − | 9112.94i | 1.46243 | − | 1.06252i | 0.479713 | − | 0.877425i | \(-0.340741\pi\) |
0.982721 | − | 0.185095i | \(-0.0592594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1956.11 | − | 1421.19i | −0.226448 | − | 0.164524i | 0.468776 | − | 0.883317i | \(-0.344695\pi\) |
−0.695225 | + | 0.718793i | \(0.744695\pi\) | |||||||
\(422\) | −4471.61 | − | 3248.81i | −0.515816 | − | 0.374763i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4881.57 | 0.559127 | ||||||||
\(425\) | −266.320 | + | 16.5564i | −0.0303962 | + | 0.00188965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4081.18 | − | 12560.6i | 0.462535 | − | 1.42354i | ||||
\(428\) | 4603.81 | + | 3344.86i | 0.519938 | + | 0.377757i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4739.85 | + | 3223.78i | 0.531571 | + | 0.361545i | ||||
\(431\) | 6422.91 | − | 4666.52i | 0.717821 | − | 0.521527i | −0.167866 | − | 0.985810i | \(-0.553688\pi\) |
0.885687 | + | 0.464282i | \(0.153688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1146.40 | − | 832.906i | 0.127234 | − | 0.0924409i | −0.522348 | − | 0.852732i | \(-0.674944\pi\) |
0.649582 | + | 0.760291i | \(0.274944\pi\) | |||||||
\(434\) | 695.054 | + | 2139.15i | 0.0768747 | + | 0.236596i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2145.70 | + | 6603.79i | −0.235689 | + | 0.725377i | ||||
\(437\) | −834.902 | − | 2569.57i | −0.0913931 | − | 0.281279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4154.10 | − | 12785.0i | 0.451628 | − | 1.38997i | −0.423422 | − | 0.905933i | \(-0.639171\pi\) |
0.875049 | − | 0.484034i | \(-0.160829\pi\) | |||||||
\(440\) | −1229.96 | + | 38.1948i | −0.133264 | + | 0.00413833i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −193.132 | + | 140.319i | −0.0207836 | + | 0.0151002i | ||||
\(443\) | −13347.6 | −1.43152 | −0.715759 | − | 0.698347i | \(-0.753919\pi\) | ||||
−0.715759 | + | 0.698347i | \(0.753919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10442.6 | − | 7102.49i | −1.11242 | − | 0.756608i | ||||
\(446\) | 61.7472 | + | 44.8619i | 0.00655564 | + | 0.00476295i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2335.87 | + | 7189.05i | −0.246338 | + | 0.758149i | ||||
\(449\) | −3063.89 | −0.322035 | −0.161017 | − | 0.986952i | \(-0.551478\pi\) | ||||
−0.161017 | + | 0.986952i | \(0.551478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −174.203 | −0.0181883 | ||||||||
\(452\) | 2346.45 | − | 7221.62i | 0.244176 | − | 0.751496i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5438.86 | − | 3951.57i | −0.562243 | − | 0.408494i | ||||
\(455\) | 10138.8 | − | 314.847i | 1.04465 | − | 0.0324401i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −185.070 | −0.0189435 | −0.00947177 | − | 0.999955i | \(-0.503015\pi\) | ||||
−0.00947177 | + | 0.999955i | \(0.503015\pi\) | |||||||
\(458\) | −8082.62 | + | 5872.37i | −0.824620 | + | 0.599122i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1448.95 | − | 4029.31i | −0.146864 | − | 0.408408i | ||||
\(461\) | 2389.28 | − | 7353.45i | 0.241388 | − | 0.742916i | −0.754822 | − | 0.655930i | \(-0.772277\pi\) |
0.996210 | − | 0.0869857i | \(-0.0277235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4560.19 | − | 14034.8i | −0.457732 | − | 1.40875i | −0.867897 | − | 0.496744i | \(-0.834529\pi\) |
0.410165 | − | 0.912011i | \(-0.365471\pi\) | |||||||
\(464\) | −18.2810 | + | 56.2630i | −0.00182903 | + | 0.00562919i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.47165 | − | 13.7623i | −0.000444517 | − | 0.00136808i | ||||
\(467\) | −11511.6 | + | 8363.69i | −1.14067 | + | 0.828748i | −0.987213 | − | 0.159407i | \(-0.949042\pi\) |
−0.153460 | + | 0.988155i | \(0.549042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8607.71 | + | 6253.87i | −0.847478 | + | 0.615729i | ||||
\(470\) | −338.209 | − | 940.509i | −0.0331923 | − | 0.0923031i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2297.63 | − | 1669.33i | −0.224062 | − | 0.162790i | ||||
\(473\) | −356.980 | + | 1098.67i | −0.0347018 | + | 0.106801i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3425.81 | + | 212.973i | −0.330920 | + | 0.0205724i | ||||
\(476\) | −136.621 | −0.0131555 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11821.7 | − | 8588.96i | −1.13120 | − | 0.821862i | ||||
\(479\) | 13254.4 | + | 9629.85i | 1.26431 | + | 0.918578i | 0.998961 | − | 0.0455728i | \(-0.0145113\pi\) |
0.265354 | + | 0.964151i | \(0.414511\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8157.72 | + | 5926.93i | −0.773305 | + | 0.561839i | ||||
\(482\) | −6963.98 | −0.658092 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1575.88 | + | 4850.06i | 0.147998 | + | 0.455490i | ||||
\(485\) | 5000.71 | − | 3875.97i | 0.468186 | − | 0.362884i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4049.02 | − | 12461.6i | −0.376752 | − | 1.15952i | −0.942289 | − | 0.334801i | \(-0.891331\pi\) |
0.565536 | − | 0.824723i | \(-0.308669\pi\) | |||||||
\(488\) | 5982.49 | + | 18412.2i | 0.554948 | + | 1.70795i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1361.11 | + | 925.747i | 0.125487 | + | 0.0853490i | ||||
\(491\) | 570.719 | + | 1756.49i | 0.0524566 | + | 0.161445i | 0.973853 | − | 0.227180i | \(-0.0729504\pi\) |
−0.921396 | + | 0.388624i | \(0.872950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.13082 | −0.000651432 | ||||||||
\(494\) | −2484.36 | + | 1804.99i | −0.226269 | + | 0.164394i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −967.034 | − | 702.591i | −0.0875426 | − | 0.0636034i | ||||
\(497\) | −13128.9 | − | 9538.72i | −1.18493 | − | 0.860906i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17773.8 | 1.59451 | 0.797257 | − | 0.603640i | \(-0.206284\pi\) | ||||
0.797257 | + | 0.603640i | \(0.206284\pi\) | |||||||
\(500\) | −5416.26 | + | 505.886i | −0.484445 | + | 0.0452478i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1056.55 | + | 3251.73i | −0.0939366 | + | 0.289107i | ||||
\(503\) | −1358.97 | − | 987.353i | −0.120465 | − | 0.0875227i | 0.525922 | − | 0.850533i | \(-0.323721\pi\) |
−0.646386 | + | 0.763010i | \(0.723721\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2288.48 | − | 7866.06i | 0.201655 | − | 0.693139i | ||||
\(506\) | −736.708 | + | 535.249i | −0.0647246 | + | 0.0470252i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2919.21 | + | 2120.93i | −0.254959 | + | 0.185239i | ||||
\(509\) | 5876.65 | + | 18086.5i | 0.511744 | + | 1.57499i | 0.789129 | + | 0.614228i | \(0.210532\pi\) |
−0.277385 | + | 0.960759i | \(0.589468\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4223.65 | − | 12999.1i | 0.365642 | − | 1.12533i | ||||
\(512\) | −1914.02 | − | 5890.75i | −0.165212 | − | 0.508470i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1314.12 | − | 4044.46i | 0.112769 | − | 0.347069i | ||||
\(515\) | 1626.42 | − | 1260.61i | 0.139162 | − | 0.107862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 162.953 | − | 118.392i | 0.0138620 | − | 0.0100714i | ||||
\(518\) | 6089.71 | 0.516538 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11752.5 | + | 9109.16i | −0.991117 | + | 0.768198i | ||||
\(521\) | 1611.58 | + | 1170.88i | 0.135517 | + | 0.0984592i | 0.653479 | − | 0.756945i | \(-0.273309\pi\) |
−0.517961 | + | 0.855404i | \(0.673309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3681.59 | + | 11330.8i | −0.307810 | + | 0.947342i | 0.670803 | + | 0.741635i | \(0.265949\pi\) |
−0.978614 | + | 0.205707i | \(0.934051\pi\) | |||||||
\(524\) | −10146.6 | −0.845909 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −288.538 | −0.0239180 | ||||||||
\(527\) | 44.5235 | − | 137.029i | 0.00368022 | − | 0.0113265i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2011.12 | + | 1461.17i | 0.165293 | + | 0.120093i | ||||
\(530\) | −1552.95 | − | 4318.54i | −0.127275 | − | 0.353934i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1757.43 | −0.143222 | ||||||||
\(533\) | −1702.96 | + | 1237.28i | −0.138393 | + | 0.100549i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4566.05 | − | 15694.6i | 0.368986 | − | 1.26829i | ||||
\(536\) | 4819.57 | − | 14833.1i | 0.388384 | − | 1.19532i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1961.93 | − | 6038.21i | −0.157221 | − | 0.483876i | ||||
\(539\) | −102.511 | + | 315.497i | −0.00819196 | + | 0.0252123i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3650.27 | + | 11234.4i | 0.290088 | + | 0.892798i | 0.984827 | + | 0.173537i | \(0.0555196\pi\) |
−0.694740 | + | 0.719261i | \(0.744480\pi\) | |||||||
\(542\) | 5700.12 | − | 4141.38i | 0.451736 | − | 0.328206i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 271.013 | − | 196.902i | 0.0213595 | − | 0.0155186i | ||||
\(545\) | 19934.8 | − | 619.049i | 1.56681 | − | 0.0486553i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6225.01 | + | 4522.74i | 0.486586 | + | 0.353525i | 0.803870 | − | 0.594805i | \(-0.202771\pi\) |
−0.317284 | + | 0.948331i | \(0.602771\pi\) | |||||||
\(548\) | −3513.92 | + | 10814.7i | −0.273918 | + | 0.843033i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 425.072 | + | 1075.95i | 0.0329548 | + | 0.0834156i | ||||
\(551\) | −91.7274 | −0.00709205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13517.2 | − | 9820.84i | −1.03944 | − | 0.755198i | ||||
\(554\) | 5449.43 | + | 3959.24i | 0.417914 | + | 0.303632i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3142.41 | − | 2283.09i | 0.239690 | − | 0.174145i | ||||
\(557\) | −20699.8 | −1.57465 | −0.787324 | − | 0.616540i | \(-0.788534\pi\) | ||||
−0.787324 | + | 0.616540i | \(0.788534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4313.55 | + | 13275.8i | 0.326375 | + | 1.00448i | ||||
\(560\) | 3254.02 | − | 101.049i | 0.245549 | − | 0.00762521i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1795.59 | − | 5526.26i | −0.134773 | − | 0.414789i | ||||
\(563\) | −5732.09 | − | 17641.6i | −0.429092 | − | 1.32061i | −0.899021 | − | 0.437905i | \(-0.855721\pi\) |
0.469929 | − | 0.882704i | \(-0.344279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21799.8 | + | 676.965i | −1.62323 | + | 0.0504073i | ||||
\(566\) | −5155.18 | − | 15866.0i | −0.382841 | − | 1.17826i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23788.5 | 1.75730 | ||||||||
\(569\) | −131.419 | + | 95.4817i | −0.00968257 | + | 0.00703480i | −0.592616 | − | 0.805485i | \(-0.701905\pi\) |
0.582933 | + | 0.812520i | \(0.301905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13305.3 | + | 9666.86i | 0.975147 | + | 0.708486i | 0.956619 | − | 0.291343i | \(-0.0941020\pi\) |
0.0185281 | + | 0.999828i | \(0.494102\pi\) | |||||||
\(572\) | −793.478 | − | 576.495i | −0.0580017 | − | 0.0421407i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1271.26 | 0.0924412 | ||||||||
\(575\) | −9482.44 | + | 7832.67i | −0.687731 | + | 0.568078i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1917.80 | + | 5902.39i | −0.138369 | + | 0.425857i | −0.996099 | − | 0.0882441i | \(-0.971874\pi\) |
0.857729 | + | 0.514101i | \(0.171874\pi\) | |||||||
\(578\) | 8048.11 | + | 5847.29i | 0.579165 | + | 0.420788i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −145.303 | + | 4.51220i | −0.0104024 | + | 0.000323032i | ||||
\(581\) | −15238.2 | + | 11071.2i | −1.08810 | + | 0.790552i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 748.232 | − | 543.622i | 0.0531537 | − | 0.0386184i | ||||
\(584\) | 6191.33 | + | 19054.9i | 0.438697 | + | 1.35017i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1433.11 | − | 4410.66i | 0.101026 | − | 0.310926i | ||||
\(587\) | 4296.85 | + | 13224.4i | 0.302130 | + | 0.929860i | 0.980733 | + | 0.195354i | \(0.0625857\pi\) |
−0.678603 | + | 0.734505i | \(0.737414\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 572.729 | − | 1762.68i | 0.0400660 | − | 0.123311i | ||||
\(590\) | −745.854 | + | 2563.68i | −0.0520446 | + | 0.178890i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2618.20 | + | 1902.23i | −0.181769 | + | 0.132063i | ||||
\(593\) | −11389.2 | −0.788698 | −0.394349 | − | 0.918961i | \(-0.629030\pi\) | ||||
−0.394349 | + | 0.918961i | \(0.629030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 132.791 | + | 369.272i | 0.00914939 | + | 0.0254431i | ||||
\(596\) | −8213.40 | − | 5967.38i | −0.564486 | − | 0.410123i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3400.26 | + | 10464.9i | −0.232520 | + | 0.715622i | ||||
\(599\) | 12576.2 | 0.857844 | 0.428922 | − | 0.903342i | \(-0.358894\pi\) | ||||
0.428922 | + | 0.903342i | \(0.358894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2154.43 | 0.146225 | 0.0731124 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731124 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(602\) | 2605.08 | − | 8017.61i | 0.176371 | − | 0.542813i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1369.11 | − | 994.717i | −0.0922323 | − | 0.0670107i | ||||
\(605\) | 11577.4 | − | 8973.49i | 0.778000 | − | 0.603015i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9937.94 | 0.664528 | 0.332264 | − | 0.943186i | \(-0.392187\pi\) | ||||
0.332264 | + | 0.943186i | \(0.392187\pi\) | |||||||
\(608\) | 3486.18 | − | 2532.86i | 0.232538 | − | 0.168949i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14385.4 | − | 11149.9i | 0.954832 | − | 0.740075i | ||||
\(611\) | 752.106 | − | 2314.74i | 0.0497986 | − | 0.153264i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3184.38 | + | 9800.52i | 0.209814 | + | 0.645741i | 0.999481 | + | 0.0322059i | \(0.0102532\pi\) |
−0.789667 | + | 0.613535i | \(0.789747\pi\) | |||||||
\(614\) | −1743.30 | + | 5365.32i | −0.114583 | + | 0.352649i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 559.236 | + | 1721.15i | 0.0365783 | + | 0.112577i | ||||
\(617\) | −13637.9 | + | 9908.50i | −0.889854 | + | 0.646517i | −0.935840 | − | 0.352425i | \(-0.885357\pi\) |
0.0459856 | + | 0.998942i | \(0.485357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6572.78 | + | 4775.40i | −0.426789 | + | 0.310080i | −0.780364 | − | 0.625326i | \(-0.784966\pi\) |
0.353575 | + | 0.935406i | \(0.384966\pi\) | |||||||
\(620\) | 820.537 | − | 2820.39i | 0.0531509 | − | 0.182693i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13067.6 | + | 9494.17i | 0.842385 | + | 0.612028i | ||||
\(623\) | −5739.40 | + | 17664.1i | −0.369092 | + | 1.13595i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6631.74 | + | 14147.8i | 0.424432 | + | 0.905460i | ||||
\(626\) | −9770.92 | −0.623841 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6874.40 | − | 4994.54i | −0.436813 | − | 0.317363i | ||||
\(629\) | −315.592 | − | 229.291i | −0.0200055 | − | 0.0145348i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9984.59 | + | 7254.23i | −0.629921 | + | 0.457665i | −0.856373 | − | 0.516358i | \(-0.827287\pi\) |
0.226452 | + | 0.974022i | \(0.427287\pi\) | |||||||
\(632\) | 24492.1 | 1.54152 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5408.87 | + | 16646.8i | 0.338823 | + | 1.04279i | ||||
\(635\) | 8569.99 | + | 5828.83i | 0.535574 | + | 0.364268i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1238.69 | + | 3812.30i | 0.0770466 | + | 0.237125i | ||||
\(638\) | 9.55357 | + | 29.4029i | 0.000592836 | + | 0.00182456i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2860.41 | − | 2217.05i | 0.176668 | − | 0.136932i | ||||
\(641\) | −4664.84 | − | 14356.9i | −0.287442 | − | 0.884654i | −0.985656 | − | 0.168766i | \(-0.946022\pi\) |
0.698215 | − | 0.715889i | \(-0.253978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21379.1 | 1.31121 | 0.655606 | − | 0.755103i | \(-0.272413\pi\) | ||||
0.655606 | + | 0.755103i | \(0.272413\pi\) | |||||||
\(644\) | −5094.58 | + | 3701.43i | −0.311731 | + | 0.226486i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −96.1107 | − | 69.8285i | −0.00585360 | − | 0.00425289i | ||||
\(647\) | −7903.05 | − | 5741.90i | −0.480218 | − | 0.348899i | 0.321192 | − | 0.947014i | \(-0.395916\pi\) |
−0.801410 | + | 0.598115i | \(0.795916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −538.074 | −0.0325443 | ||||||||
\(650\) | 11797.3 | + | 7499.12i | 0.711889 | + | 0.452522i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.07770 | + | 18.7052i | −0.000365063 | + | 0.00112355i | ||||
\(653\) | −10418.9 | − | 7569.74i | −0.624382 | − | 0.453640i | 0.230068 | − | 0.973175i | \(-0.426105\pi\) |
−0.854449 | + | 0.519535i | \(0.826105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9862.10 | + | 27425.1i | 0.588312 | + | 1.63601i | ||||
\(656\) | −546.562 | + | 397.100i | −0.0325300 | + | 0.0236344i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1189.16 | + | 863.974i | −0.0704532 | + | 0.0511873i | ||||
\(659\) | −1499.44 | − | 4614.81i | −0.0886343 | − | 0.272788i | 0.896908 | − | 0.442217i | \(-0.145808\pi\) |
−0.985542 | + | 0.169429i | \(0.945808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2892.29 | + | 8901.56i | −0.170192 | + | 0.523798i | −0.999381 | − | 0.0351704i | \(-0.988803\pi\) |
0.829189 | + | 0.558968i | \(0.188803\pi\) | |||||||
\(662\) | −1204.57 | − | 3707.27i | −0.0707202 | − | 0.217655i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8532.07 | − | 26259.0i | 0.498657 | − | 1.53471i | ||||
\(665\) | 1708.16 | + | 4750.13i | 0.0996081 | + | 0.276996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −265.907 | + | 193.192i | −0.0154362 | + | 0.0112151i | ||||
\(668\) | 877.838 | 0.0508452 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14655.5 | + | 455.107i | −0.845062 | + | 0.0262423i | ||||
\(671\) | 2967.40 | + | 2155.95i | 0.170723 | + | 0.124038i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8985.41 | + | 27654.2i | −0.514654 | + | 1.58394i | 0.269257 | + | 0.963068i | \(0.413222\pi\) |
−0.783911 | + | 0.620873i | \(0.786778\pi\) | |||||||
\(674\) | 4733.99 | 0.270544 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3299.71 | −0.187740 | ||||||||
\(677\) | 1446.09 | − | 4450.60i | 0.0820940 | − | 0.252659i | −0.901582 | − | 0.432608i | \(-0.857593\pi\) |
0.983676 | + | 0.179949i | \(0.0575933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7527.72 | − | 5469.21i | −0.425460 | − | 0.309115i | ||||
\(680\) | −475.649 | − | 323.510i | −0.0268240 | − | 0.0182442i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −624.671 | −0.0350731 | ||||||||
\(683\) | 13511.7 | − | 9816.80i | 0.756968 | − | 0.549970i | −0.141011 | − | 0.990008i | \(-0.545035\pi\) |
0.897979 | + | 0.440038i | \(0.145035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32646.3 | − | 1013.79i | 1.82095 | − | 0.0565472i | ||||
\(686\) | 4280.21 | − | 13173.1i | 0.238220 | − | 0.733166i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1384.42 | + | 4260.82i | 0.0767161 | + | 0.236108i | ||||
\(689\) | 3453.45 | − | 10628.6i | 0.190952 | − | 0.587689i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3623.18 | − | 11151.0i | −0.199468 | − | 0.613899i | −0.999895 | − | 0.0144691i | \(-0.995394\pi\) |
0.800428 | − | 0.599429i | \(-0.204606\pi\) | |||||||
\(692\) | 10411.1 | − | 7564.14i | 0.571925 | − | 0.415528i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10648.4 | + | 7736.52i | −0.582432 | + | 0.423162i | ||||
\(695\) | −9225.23 | − | 6274.48i | −0.503501 | − | 0.342453i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.8813 | − | 47.8656i | −0.00358025 | − | 0.00260120i | ||||
\(698\) | 2952.16 | − | 9085.80i | 0.160087 | − | 0.492697i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2939.51 | + | 7440.54i | 0.158719 | + | 0.401751i | ||||
\(701\) | 19249.4 | 1.03714 | 0.518572 | − | 0.855034i | \(-0.326464\pi\) | ||||
0.518572 | + | 0.855034i | \(0.326464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4059.62 | − | 2949.49i | −0.217797 | − | 0.158239i | ||||
\(704\) | −1698.39 | − | 1233.95i | −0.0909242 | − | 0.0660603i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6456.48 | + | 4690.90i | −0.344182 | + | 0.250063i | ||||
\(707\) | −12047.9 | −0.640890 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1993.96 | + | 6136.79i | 0.105620 | + | 0.325066i | 0.989876 | − | 0.141938i | \(-0.0453334\pi\) |
−0.884255 | + | 0.467004i | \(0.845333\pi\) | |||||||
\(710\) | −7567.74 | − | 21044.8i | −0.400017 | − | 1.11239i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8413.23 | − | 25893.3i | −0.442836 | − | 1.36291i | ||||
\(713\) | −2052.21 | − | 6316.05i | −0.107792 | − | 0.331750i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −786.969 | + | 2705.01i | −0.0411622 | + | 0.141485i | ||||
\(716\) | −2177.77 | − | 6702.48i | −0.113669 | − | 0.349837i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19109.3 | 0.993251 | ||||||||
\(719\) | 17508.2 | − | 12720.5i | 0.908132 | − | 0.659797i | −0.0324096 | − | 0.999475i | \(-0.510318\pi\) |
0.940542 | + | 0.339678i | \(0.110318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2448.30 | − | 1778.79i | −0.126462 | − | 0.0918803i | ||||
\(722\) | 10010.0 | + | 7272.70i | 0.515975 | + | 0.374878i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6963.96 | −0.357477 | ||||||||
\(725\) | 153.425 | + | 388.352i | 0.00785939 | + | 0.0198938i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6051.62 | + | 18625.0i | −0.308724 | + | 0.950155i | 0.669537 | + | 0.742778i | \(0.266492\pi\) |
−0.978261 | + | 0.207376i | \(0.933508\pi\) | |||||||
\(728\) | 17691.4 | + | 12853.5i | 0.900668 | + | 0.654374i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14887.6 | − | 11539.1i | 0.754813 | − | 0.585043i | ||||
\(731\) | −436.885 | + | 317.416i | −0.0221050 | + | 0.0160603i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8314.98 | − | 6041.19i | 0.418992 | − | 0.304415i | −0.358240 | − | 0.933629i | \(-0.616623\pi\) |
0.777232 | + | 0.629214i | \(0.216623\pi\) | |||||||
\(734\) | −1600.87 | − | 4926.97i | −0.0805029 | − | 0.247762i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4771.40 | − | 14684.9i | 0.238962 | − | 0.735450i | ||||
\(737\) | −913.119 | − | 2810.29i | −0.0456380 | − | 0.140459i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8283.58 | − | 25494.2i | 0.412336 | − | 1.26904i | −0.502276 | − | 0.864707i | \(-0.667504\pi\) |
0.914612 | − | 0.404333i | \(-0.132496\pi\) | |||||||
\(740\) | −6575.83 | − | 4472.51i | −0.326665 | − | 0.222179i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5460.26 | + | 3967.11i | −0.270152 | + | 0.196277i | ||||
\(743\) | −3369.02 | −0.166349 | −0.0831746 | − | 0.996535i | \(-0.526506\pi\) | ||||
−0.0831746 | + | 0.996535i | \(0.526506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8146.03 | + | 27999.9i | −0.400601 | + | 1.37696i | ||||
\(746\) | 17831.6 | + | 12955.5i | 0.875151 | + | 0.635835i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.7251 | − | 36.0861i | 0.000573144 | − | 0.00176396i | ||||
\(749\) | −24038.4 | −1.17269 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6458.58 | 0.313817 | 0.156909 | − | 0.987613i | \(-0.449847\pi\) | ||||
0.156909 | + | 0.987613i | \(0.449847\pi\) | |||||||
\(752\) | 241.386 | − | 742.911i | 0.0117054 | − | 0.0360255i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 302.227 | + | 219.581i | 0.0145974 | + | 0.0106056i | ||||
\(755\) | −1357.88 | + | 4667.37i | −0.0654548 | + | 0.224984i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5810.90 | −0.278997 | −0.139499 | − | 0.990222i | \(-0.544549\pi\) | ||||
−0.139499 | + | 0.990222i | \(0.544549\pi\) | |||||||
\(758\) | −12138.5 | + | 8819.17i | −0.581651 | + | 0.422594i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6118.52 | − | 4161.47i | −0.292029 | − | 0.198622i | ||||
\(761\) | −10479.9 | + | 32253.9i | −0.499208 | + | 1.53640i | 0.311087 | + | 0.950382i | \(0.399307\pi\) |
−0.810295 | + | 0.586023i | \(0.800693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9063.92 | − | 27895.9i | −0.430060 | − | 1.32359i | ||||
\(764\) | −5474.11 | + | 16847.6i | −0.259223 | + | 0.797806i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3906.83 | + | 12024.0i | 0.184281 | + | 0.567160i | ||||
\(767\) | −5260.07 | + | 3821.66i | −0.247627 | + | 0.179912i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29641.8 | + | 21536.0i | −1.39000 | + | 1.00990i | −0.394137 | + | 0.919052i | \(0.628956\pi\) |
−0.995865 | + | 0.0908440i | \(0.971044\pi\) | |||||||
\(770\) | 1344.73 | − | 1042.28i | 0.0629359 | − | 0.0487806i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11131.7 | + | 8087.64i | 0.518961 | + | 0.377047i | ||||
\(773\) | −136.048 | + | 418.714i | −0.00633030 | + | 0.0194827i | −0.954172 | − | 0.299259i | \(-0.903260\pi\) |
0.947841 | + | 0.318742i | \(0.103260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8420.71 | + | 523.493i | −0.390298 | + | 0.0242638i | ||||
\(776\) | 13639.6 | 0.630971 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12824.1 | − | 9317.29i | −0.590961 | − | 0.429359i | ||||
\(779\) | −847.465 | − | 615.720i | −0.0389777 | − | 0.0283189i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3646.23 | − | 2649.14i | 0.167058 | − | 0.121375i | ||||
\(782\) | −425.683 | −0.0194660 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 397.554 | + | 1223.55i | 0.0181102 | + | 0.0557374i | ||||
\(785\) | −6818.01 | + | 23435.2i | −0.309994 | + | 1.06553i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7874.56 | + | 24235.4i | 0.356668 | + | 1.09771i | 0.955036 | + | 0.296490i | \(0.0958163\pi\) |
−0.598368 | + | 0.801222i | \(0.704184\pi\) | |||||||
\(788\) | 200.921 | + | 618.372i | 0.00908316 | + | 0.0279551i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7791.57 | − | 21667.2i | −0.350901 | − | 0.975804i | ||||
\(791\) | 9911.90 | + | 30505.7i | 0.445546 | + | 1.37125i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44321.1 | 1.98473 | ||||||||
\(794\) | −13258.4 | + | 9632.79i | −0.592598 | + | 0.430548i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9993.29 | − | 7260.55i | −0.444979 | − | 0.323296i | ||||
\(797\) | −11704.4 | − | 8503.78i | −0.520192 | − | 0.377941i | 0.296484 | − | 0.955038i | \(-0.404186\pi\) |
−0.816676 | + | 0.577096i | \(0.804186\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 94.1572 | 0.00416901 | ||||||||
\(800\) | −16554.5 | − | 10523.1i | −0.731614 | − | 0.465061i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 842.761 | − | 2593.75i | 0.0371059 | − | 0.114200i | ||||
\(803\) | 3070.99 | + | 2231.20i | 0.134960 | + | 0.0980541i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14956.3 | + | 10172.4i | 0.654831 | + | 0.445379i | ||||
\(806\) | −6106.61 | + | 4436.71i | −0.266869 | + | 0.193892i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14287.8 | − | 10380.7i | 0.622084 | − | 0.451970i | ||||
\(809\) | −9487.61 | − | 29199.8i | −0.412319 | − | 1.26899i | −0.914627 | − | 0.404300i | \(-0.867515\pi\) |
0.502307 | − | 0.864689i | \(-0.332485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9430.64 | − | 29024.5i | 0.408329 | − | 1.25671i | −0.509755 | − | 0.860320i | \(-0.670264\pi\) |
0.918084 | − | 0.396387i | \(-0.129736\pi\) | |||||||
\(812\) | 66.0661 | + | 203.331i | 0.00285525 | + | 0.00878757i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −522.630 | + | 1608.49i | −0.0225039 | + | 0.0692598i | ||||
\(815\) | 56.4653 | − | 1.75346i | 0.00242686 | − | 7.53630e-5i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5619.88 | + | 4083.08i | −0.240654 | + | 0.174846i | ||||
\(818\) | 6020.12 | 0.257321 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1372.74 | − | 933.658i | −0.0584610 | − | 0.0397619i | ||||
\(821\) | 9950.34 | + | 7229.34i | 0.422983 | + | 0.307315i | 0.778837 | − | 0.627226i | \(-0.215810\pi\) |
−0.355854 | + | 0.934542i | \(0.615810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13521.5 | + | 41614.9i | −0.572697 | + | 1.76258i | 0.0711940 | + | 0.997462i | \(0.477319\pi\) |
−0.643891 | + | 0.765117i | \(0.722681\pi\) | |||||||
\(824\) | 4436.11 | 0.187548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3926.63 | 0.165405 | ||||||||
\(827\) | −10223.8 | + | 31465.7i | −0.429888 | + | 1.32306i | 0.468347 | + | 0.883545i | \(0.344850\pi\) |
−0.898235 | + | 0.439515i | \(0.855150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16695.2 | − | 12129.7i | −0.699454 | − | 0.508183i | 0.180301 | − | 0.983612i | \(-0.442293\pi\) |
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(830\) | −25944.6 | + | 805.675i | −1.08500 | + | 0.0336933i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25367.2 | −1.05703 | ||||||||
\(833\) | −125.457 | + | 91.1499i | −0.00521828 | + | 0.00379130i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −853.224 | − | 2372.69i | −0.0353617 | − | 0.0983358i | ||||
\(836\) | 150.826 | − | 464.195i | 0.00623974 | − | 0.0192040i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9709.90 | − | 29884.0i | −0.400266 | − | 1.23189i | ||||
\(839\) | 10488.9 | − | 32281.4i | 0.431605 | − | 1.32834i | −0.464922 | − | 0.885352i | \(-0.653918\pi\) |
0.896526 | − | 0.442991i | \(-0.146082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7533.17 | − | 23184.7i | −0.308876 | − | 0.950621i | ||||
\(842\) | −3964.47 | + | 2880.35i | −0.162262 | + | 0.117890i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8588.00 | − | 6239.55i | 0.350250 | − | 0.254472i | ||||
\(845\) | 3207.19 | + | 8918.73i | 0.130569 | + | 0.363093i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17427.9 | − | 12662.1i | −0.707001 | − | 0.513666i | ||||
\(848\) | 1108.37 | − | 3411.22i | 0.0448841 | − | 0.138139i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −134.880 | + | 523.706i | −0.00544278 | + | 0.0211329i | ||||
\(851\) | −17980.4 | −0.724278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28353.2 | − | 20599.8i | −1.13809 | − | 0.826873i | −0.151241 | − | 0.988497i | \(-0.548327\pi\) |
−0.986852 | + | 0.161624i | \(0.948327\pi\) | |||||||
\(854\) | −21654.8 | − | 15733.1i | −0.867695 | − | 0.630417i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28507.5 | − | 20711.9i | 1.13828 | − | 0.827008i | ||||
\(857\) | 39687.9 | 1.58193 | 0.790965 | − | 0.611862i | \(-0.209579\pi\) | ||||
0.790965 | + | 0.611862i | \(0.209579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1637.70 | + | 5040.34i | 0.0650498 | + | 0.200203i | 0.978299 | − | 0.207199i | \(-0.0664348\pi\) |
−0.913249 | + | 0.407402i | \(0.866435\pi\) | |||||||
\(860\) | −8701.46 | + | 6744.36i | −0.345020 | + | 0.267419i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4972.21 | − | 15302.9i | −0.196466 | − | 0.604662i | ||||
\(863\) | −347.117 | − | 1068.32i | −0.0136918 | − | 0.0421390i | 0.943977 | − | 0.330011i | \(-0.107052\pi\) |
−0.957669 | + | 0.287872i | \(0.907052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30564.2 | − | 20788.0i | −1.20140 | − | 0.817127i | ||||
\(866\) | −887.467 | − | 2731.34i | −0.0348237 | − | 0.107176i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4319.80 | −0.168921 | ||||||||
\(869\) | 3754.07 | − | 2727.49i | 0.146546 | − | 0.106472i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28886.5 | − | 20987.2i | −1.12374 | − | 0.816447i | ||||
\(872\) | 34784.6 | + | 25272.5i | 1.35087 | + | 0.981462i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5475.78 | −0.211923 | ||||||||
\(875\) | 17253.8 | − | 15177.1i | 0.666611 | − | 0.586375i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6273.14 | + | 19306.7i | −0.241538 | + | 0.743378i | 0.754649 | + | 0.656129i | \(0.227807\pi\) |
−0.996187 | + | 0.0872483i | \(0.972193\pi\) | |||||||
\(878\) | −22041.7 | − | 16014.2i | −0.847234 | − | 0.615551i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −252.576 | + | 868.165i | −0.00967537 | + | 0.0332566i | ||||
\(881\) | 15364.5 | − | 11163.0i | 0.587563 | − | 0.426890i | −0.253880 | − | 0.967236i | \(-0.581707\pi\) |
0.841443 | + | 0.540346i | \(0.181707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18914.0 | − | 13741.8i | 0.720845 | − | 0.523725i | −0.165809 | − | 0.986158i | \(-0.553024\pi\) |
0.886654 | + | 0.462433i | \(0.153024\pi\) | |||||||
\(884\) | −141.680 | − | 436.046i | −0.00539051 | − | 0.0165903i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8359.44 | + | 25727.7i | −0.316976 | + | 0.975553i | ||||
\(887\) | −1134.58 | − | 3491.86i | −0.0429485 | − | 0.132182i | 0.927283 | − | 0.374361i | \(-0.122138\pi\) |
−0.970232 | + | 0.242179i | \(0.922138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4710.17 | − | 14496.4i | 0.177699 | − | 0.546901i | ||||
\(890\) | −20230.3 | + | 15680.2i | −0.761934 | + | 0.590563i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −118.589 | + | 86.1601i | −0.00445141 | + | 0.00323414i | ||||
\(893\) | 1211.19 | 0.0453875 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15999.3 | + | 12400.8i | −0.597539 | + | 0.463143i | ||||
\(896\) | −4305.86 | − | 3128.39i | −0.160545 | − | 0.116643i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1918.88 | + | 5905.70i | −0.0713071 | + | 0.219461i | ||||
\(899\) | −225.468 | −0.00836460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 432.342 | 0.0159860 | ||||||||
\(902\) | −109.102 | + | 335.780i | −0.00402737 | + | 0.0123950i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38038.9 | − | 27636.9i | −1.39951 | − | 1.01680i | ||||
\(905\) | 6768.70 | + | 18822.8i | 0.248618 | + | 0.691370i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9274.11 | 0.339517 | 0.169758 | − | 0.985486i | \(-0.445701\pi\) | ||||
0.169758 | + | 0.985486i | \(0.445701\pi\) | |||||||
\(908\) | 10445.7 | − | 7589.22i | 0.381775 | − | 0.277376i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5742.95 | − | 19739.9i | 0.209205 | − | 0.719091i | ||||
\(911\) | −9464.91 | + | 29130.0i | −0.344222 | + | 1.05941i | 0.617776 | + | 0.786354i | \(0.288034\pi\) |
−0.961999 | + | 0.273054i | \(0.911966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1616.49 | − | 4975.05i | −0.0585959 | − | 0.180340i | ||||
\(914\) | −115.907 | + | 356.725i | −0.00419460 | + | 0.0129097i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5929.32 | − | 18248.6i | −0.213876 | − | 0.658242i | ||||
\(917\) | 34675.6 | − | 25193.3i | 1.24874 | − | 0.907260i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10928.5 | + | 7940.03i | −0.392272 | + | 0.285003i | −0.766386 | − | 0.642380i | \(-0.777947\pi\) |
0.374114 | + | 0.927383i | \(0.377947\pi\) | |||||||
\(920\) | −26501.6 | + | 822.971i | −0.949707 | + | 0.0294919i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12677.5 | − | 9210.77i | −0.452833 | − | 0.329003i | ||||
\(923\) | 16829.1 | − | 51794.6i | 0.600148 | − | 1.84706i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5697.21 | + | 22120.8i | −0.202511 | + | 0.786300i | ||||
\(926\) | −29908.4 | −1.06139 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −424.099 | − | 308.126i | −0.0150019 | − | 0.0108995i | ||||
\(929\) | −5704.34 | − | 4144.45i | −0.201457 | − | 0.146367i | 0.482483 | − | 0.875905i | \(-0.339735\pi\) |
−0.683940 | + | 0.729538i | \(0.739735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1613.82 | + | 1172.51i | −0.0568107 | + | 0.0412754i | ||||
\(932\) | 27.7916 | 0.000976764 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8911.56 | + | 27427.0i | 0.312200 | + | 0.960854i | ||||
\(935\) | −108.933 | + | 3.38277i | −0.00381015 | + | 0.000118319i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3108.74 | + | 9567.73i | 0.108387 | + | 0.333579i | 0.990510 | − | 0.137438i | \(-0.0438868\pi\) |
−0.882124 | + | 0.471018i | \(0.843887\pi\) | |||||||
\(938\) | 6663.54 | + | 20508.3i | 0.231953 | + | 0.713879i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1918.62 | − | 59.5802i | 0.0665729 | − | 0.00206733i | ||||
\(941\) | 17066.8 | + | 52526.1i | 0.591244 | + | 1.81966i | 0.572599 | + | 0.819835i | \(0.305935\pi\) |
0.0186448 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3753.50 | −0.129619 | ||||||||
\(944\) | −1688.21 | + | 1226.55i | −0.0582059 | + | 0.0422891i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1894.14 | + | 1376.17i | 0.0650990 | + | 0.0472972i | ||||
\(947\) | 34518.5 | + | 25079.2i | 1.18448 | + | 0.860574i | 0.992670 | − | 0.120858i | \(-0.0385646\pi\) |
0.191809 | + | 0.981432i | \(0.438565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45868.3 | 1.56896 | ||||||||
\(950\) | −1735.04 | + | 6736.70i | −0.0592548 | + | 0.230071i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −261.423 | + | 804.577i | −0.00889996 | + | 0.0273913i | ||||
\(953\) | −15050.9 | − | 10935.1i | −0.511592 | − | 0.371694i | 0.301835 | − | 0.953360i | \(-0.402401\pi\) |
−0.813427 | + | 0.581667i | \(0.802401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50857.6 | − | 1579.32i | 1.72326 | − | 0.0535136i | ||||
\(956\) | 22704.3 | − | 16495.6i | 0.768106 | − | 0.558061i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26862.8 | − | 19517.0i | 0.905947 | − | 0.658209i | ||||
\(959\) | −14843.5 | − | 45683.7i | −0.499816 | − | 1.53827i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7798.15 | + | 24000.2i | −0.261762 | + | 0.805620i | ||||
\(962\) | 6315.18 | + | 19436.1i | 0.211652 | + | 0.651399i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4133.02 | − | 12720.1i | 0.138087 | − | 0.424988i | ||||
\(965\) | 11040.4 | − | 37948.5i | 0.368293 | − | 1.26591i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 182.356 | − | 132.489i | 0.00606428 | − | 0.00440596i | −0.584749 | − | 0.811214i | \(-0.698807\pi\) |
0.590813 | + | 0.806808i | \(0.298807\pi\) | |||||||
\(968\) | 31577.9 | 1.04850 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4339.11 | − | 12066.4i | −0.143629 | − | 0.399412i | ||||
\(971\) | −30228.7 | − | 21962.4i | −0.999058 | − | 0.725858i | −0.0371718 | − | 0.999309i | \(-0.511835\pi\) |
−0.961886 | + | 0.273451i | \(0.911835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5070.30 | + | 15604.8i | −0.167057 | + | 0.514148i | ||||
\(974\) | −26555.8 | −0.873617 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14224.7 | 0.466520 | ||||||||
\(977\) | 2795.31 | − | 8603.08i | 0.0915352 | − | 0.281716i | −0.894800 | − | 0.446467i | \(-0.852682\pi\) |
0.986335 | + | 0.164751i | \(0.0526820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4173.08 | − | 3031.92i | −0.136233 | − | 0.0989793i | ||||
\(980\) | −2498.73 | + | 1936.73i | −0.0814480 | + | 0.0631290i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3743.11 | 0.121637 | ||||||||
\(983\) | 21087.0 | − | 15320.6i | 0.684201 | − | 0.497101i | −0.190548 | − | 0.981678i | \(-0.561026\pi\) |
0.874749 | + | 0.484577i | \(0.161026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1476.10 | − | 1144.10i | 0.0477487 | − | 0.0370092i | ||||
\(986\) | −4.46596 | + | 13.7448i | −0.000144244 | + | 0.000443939i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1822.50 | − | 5609.08i | −0.0586857 | − | 0.180616i | ||||
\(989\) | −7691.73 | + | 23672.7i | −0.247303 | + | 0.761120i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13152.5 | + | 40479.4i | 0.421599 | + | 1.29755i | 0.906214 | + | 0.422820i | \(0.138960\pi\) |
−0.484615 | + | 0.874727i | \(0.661040\pi\) | |||||||
\(992\) | 8569.10 | − | 6225.81i | 0.274263 | − | 0.199264i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −26608.6 | + | 19332.3i | −0.849067 | + | 0.616883i | ||||
\(995\) | −9911.32 | + | 34067.7i | −0.315789 | + | 1.08544i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18242.6 | + | 13254.0i | 0.579487 | + | 0.421022i | 0.838539 | − | 0.544841i | \(-0.183410\pi\) |
−0.259052 | + | 0.965863i | \(0.583410\pi\) | |||||||
\(998\) | 11131.5 | − | 34259.3i | 0.353068 | − | 1.08663i | ||||
\(999\) | 0 | 0 |
(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 | 225.4.h.d.46.11 | yes | 64 | |
3.2 | odd | 2 | inner | 225.4.h.d.46.6 | ✓ | 64 | |
25.6 | even | 5 | inner | 225.4.h.d.181.11 | yes | 64 | |
75.56 | odd | 10 | inner | 225.4.h.d.181.6 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.h.d.46.6 | ✓ | 64 | 3.2 | odd | 2 | inner | |
225.4.h.d.46.11 | yes | 64 | 1.1 | even | 1 | trivial | |
225.4.h.d.181.6 | yes | 64 | 75.56 | odd | 10 | inner | |
225.4.h.d.181.11 | yes | 64 | 25.6 | even | 5 | inner |