Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,6,Mod(75,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.b (of order \(2\), degree \(1\), 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: | \(24.3783406116\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.16 | ||
Character | \(\chi\) | \(=\) | 152.75 |
Dual form | 152.6.b.b.75.15 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.93864 | + | 2.75858i | −0.873037 | + | 0.487653i | ||||
\(3\) | − | 1.79162i | − | 0.114933i | −0.998347 | − | 0.0574664i | \(-0.981698\pi\) | ||
0.998347 | − | 0.0574664i | \(-0.0183022\pi\) | |||||||
\(4\) | 16.7804 | − | 27.2473i | 0.524388 | − | 0.851479i | ||||
\(5\) | 26.9679i | 0.482417i | 0.970473 | + | 0.241208i | \(0.0775437\pi\) | ||||
−0.970473 | + | 0.241208i | \(0.922456\pi\) | |||||||
\(6\) | 4.94234 | + | 8.84819i | 0.0560473 | + | 0.100341i | ||||
\(7\) | − | 21.5599i | − | 0.166304i | −0.996537 | − | 0.0831520i | \(-0.973501\pi\) | ||
0.996537 | − | 0.0831520i | \(-0.0264987\pi\) | |||||||
\(8\) | −7.70850 | + | 180.855i | −0.0425838 | + | 0.999093i | ||||
\(9\) | 239.790 | 0.986790 | ||||||||
\(10\) | −74.3932 | − | 133.185i | −0.235252 | − | 0.421168i | ||||
\(11\) | −90.3444 | −0.225123 | −0.112561 | − | 0.993645i | \(-0.535906\pi\) | ||||
−0.112561 | + | 0.993645i | \(0.535906\pi\) | |||||||
\(12\) | −48.8170 | − | 30.0642i | −0.0978628 | − | 0.0602694i | ||||
\(13\) | −419.826 | −0.688987 | −0.344493 | − | 0.938789i | \(-0.611949\pi\) | ||||
−0.344493 | + | 0.938789i | \(0.611949\pi\) | |||||||
\(14\) | 59.4749 | + | 106.477i | 0.0810987 | + | 0.145190i | ||||
\(15\) | 48.3163 | 0.0554454 | ||||||||
\(16\) | −460.835 | − | 914.444i | −0.450034 | − | 0.893012i | ||||
\(17\) | −215.062 | −0.180485 | −0.0902427 | − | 0.995920i | \(-0.528764\pi\) | ||||
−0.0902427 | + | 0.995920i | \(0.528764\pi\) | |||||||
\(18\) | −1184.24 | + | 661.481i | −0.861505 | + | 0.481212i | ||||
\(19\) | 1355.34 | + | 799.470i | 0.861320 | + | 0.508064i | ||||
\(20\) | 734.804 | + | 452.533i | 0.410768 | + | 0.252974i | ||||
\(21\) | −38.6273 | −0.0191138 | ||||||||
\(22\) | 446.179 | − | 249.223i | 0.196541 | − | 0.109782i | ||||
\(23\) | − | 3077.62i | − | 1.21310i | −0.795046 | − | 0.606549i | \(-0.792554\pi\) | ||
0.795046 | − | 0.606549i | \(-0.207446\pi\) | |||||||
\(24\) | 324.024 | + | 13.8107i | 0.114828 | + | 0.00489428i | ||||
\(25\) | 2397.73 | 0.767274 | ||||||||
\(26\) | 2073.37 | − | 1158.13i | 0.601511 | − | 0.335987i | ||||
\(27\) | − | 864.978i | − | 0.228347i | ||||||
\(28\) | −587.451 | − | 361.785i | −0.141604 | − | 0.0872078i | ||||
\(29\) | −6155.92 | −1.35925 | −0.679623 | − | 0.733561i | \(-0.737857\pi\) | ||||
−0.679623 | + | 0.733561i | \(0.737857\pi\) | |||||||
\(30\) | −238.617 | + | 133.285i | −0.0484059 | + | 0.0270382i | ||||
\(31\) | 3059.38 | 0.571779 | 0.285890 | − | 0.958263i | \(-0.407711\pi\) | ||||
0.285890 | + | 0.958263i | \(0.407711\pi\) | |||||||
\(32\) | 4798.47 | + | 3244.86i | 0.828376 | + | 0.560172i | ||||
\(33\) | 161.863i | 0.0258740i | ||||||||
\(34\) | 1062.12 | − | 593.268i | 0.157571 | − | 0.0880144i | ||||
\(35\) | 581.426 | 0.0802278 | ||||||||
\(36\) | 4023.78 | − | 6533.64i | 0.517461 | − | 0.840232i | ||||
\(37\) | 9295.40 | 1.11626 | 0.558128 | − | 0.829755i | \(-0.311520\pi\) | ||||
0.558128 | + | 0.829755i | \(0.311520\pi\) | |||||||
\(38\) | −8898.95 | − | 209.478i | −0.999723 | − | 0.0235331i | ||||
\(39\) | 752.170i | 0.0791871i | ||||||||
\(40\) | −4877.28 | − | 207.882i | −0.481979 | − | 0.0205431i | ||||
\(41\) | 17772.2i | 1.65113i | 0.564307 | + | 0.825565i | \(0.309143\pi\) | ||||
−0.564307 | + | 0.825565i | \(0.690857\pi\) | |||||||
\(42\) | 190.767 | − | 106.557i | 0.0166870 | − | 0.00932089i | ||||
\(43\) | 7152.73 | 0.589930 | 0.294965 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294965 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(44\) | −1516.02 | + | 2461.65i | −0.118052 | + | 0.191687i | ||||
\(45\) | 6466.64i | 0.476044i | ||||||||
\(46\) | 8489.88 | + | 15199.3i | 0.591571 | + | 1.05908i | ||||
\(47\) | 23161.1i | 1.52938i | 0.644400 | + | 0.764689i | \(0.277107\pi\) | ||||
−0.644400 | + | 0.764689i | \(0.722893\pi\) | |||||||
\(48\) | −1638.34 | + | 825.642i | −0.102636 | + | 0.0517236i | ||||
\(49\) | 16342.2 | 0.972343 | ||||||||
\(50\) | −11841.5 | + | 6614.35i | −0.669859 | + | 0.374164i | ||||
\(51\) | 385.311i | 0.0207437i | ||||||||
\(52\) | −7044.86 | + | 11439.1i | −0.361297 | + | 0.586658i | ||||
\(53\) | 11807.4 | 0.577383 | 0.288691 | − | 0.957422i | \(-0.406780\pi\) | ||||
0.288691 | + | 0.957422i | \(0.406780\pi\) | |||||||
\(54\) | 2386.11 | + | 4271.82i | 0.111354 | + | 0.199356i | ||||
\(55\) | − | 2436.40i | − | 0.108603i | ||||||
\(56\) | 3899.23 | + | 166.195i | 0.166153 | + | 0.00708186i | ||||
\(57\) | 1432.35 | − | 2428.26i | 0.0583931 | − | 0.0989938i | ||||
\(58\) | 30401.9 | − | 16981.6i | 1.18667 | − | 0.662841i | ||||
\(59\) | 42428.8i | 1.58683i | 0.608680 | + | 0.793416i | \(0.291699\pi\) | ||||
−0.608680 | + | 0.793416i | \(0.708301\pi\) | |||||||
\(60\) | 810.769 | − | 1316.49i | 0.0290749 | − | 0.0472106i | ||||
\(61\) | 45648.8i | 1.57074i | 0.619025 | + | 0.785372i | \(0.287528\pi\) | ||||
−0.619025 | + | 0.785372i | \(0.712472\pi\) | |||||||
\(62\) | −15109.2 | + | 8439.54i | −0.499185 | + | 0.278830i | ||||
\(63\) | − | 5169.86i | − | 0.164107i | ||||||
\(64\) | −32649.2 | − | 2788.24i | −0.996373 | − | 0.0850904i | ||||
\(65\) | − | 11321.8i | − | 0.332379i | ||||||
\(66\) | −446.513 | − | 799.385i | −0.0126175 | − | 0.0225890i | ||||
\(67\) | − | 33058.2i | − | 0.899690i | −0.893107 | − | 0.449845i | \(-0.851479\pi\) | ||
0.893107 | − | 0.449845i | \(-0.148521\pi\) | |||||||
\(68\) | −3608.84 | + | 5859.88i | −0.0946445 | + | 0.153680i | ||||
\(69\) | −5513.94 | −0.139425 | ||||||||
\(70\) | −2871.46 | + | 1603.91i | −0.0700418 | + | 0.0391233i | ||||
\(71\) | 29886.8 | 0.703612 | 0.351806 | − | 0.936073i | \(-0.385568\pi\) | ||||
0.351806 | + | 0.936073i | \(0.385568\pi\) | |||||||
\(72\) | −1848.42 | + | 43367.3i | −0.0420213 | + | 0.985895i | ||||
\(73\) | −39654.0 | −0.870924 | −0.435462 | − | 0.900207i | \(-0.643415\pi\) | ||||
−0.435462 | + | 0.900207i | \(0.643415\pi\) | |||||||
\(74\) | −45906.7 | + | 25642.1i | −0.974533 | + | 0.544346i | ||||
\(75\) | − | 4295.83i | − | 0.0881849i | ||||||
\(76\) | 44526.6 | − | 23514.0i | 0.884272 | − | 0.466973i | ||||
\(77\) | 1947.82i | 0.0374388i | ||||||||
\(78\) | −2074.92 | − | 3714.70i | −0.0386159 | − | 0.0691333i | ||||
\(79\) | 62295.5 | 1.12302 | 0.561512 | − | 0.827469i | \(-0.310220\pi\) | ||||
0.561512 | + | 0.827469i | \(0.310220\pi\) | |||||||
\(80\) | 24660.6 | − | 12427.7i | 0.430804 | − | 0.217104i | ||||
\(81\) | 56719.3 | 0.960546 | ||||||||
\(82\) | −49026.1 | − | 87770.5i | −0.805179 | − | 1.44150i | ||||
\(83\) | 107005. | 1.70494 | 0.852468 | − | 0.522780i | \(-0.175105\pi\) | ||||
0.852468 | + | 0.522780i | \(0.175105\pi\) | |||||||
\(84\) | −648.183 | + | 1052.49i | −0.0100230 | + | 0.0162750i | ||||
\(85\) | − | 5799.78i | − | 0.0870692i | ||||||
\(86\) | −35324.8 | + | 19731.4i | −0.515031 | + | 0.287681i | ||||
\(87\) | 11029.1i | 0.156222i | ||||||||
\(88\) | 696.420 | − | 16339.3i | 0.00958660 | − | 0.224919i | ||||
\(89\) | − | 92408.3i | − | 1.23662i | −0.785935 | − | 0.618310i | \(-0.787818\pi\) | ||
0.785935 | − | 0.618310i | \(-0.212182\pi\) | |||||||
\(90\) | −17838.8 | − | 31936.4i | −0.232145 | − | 0.415604i | ||||
\(91\) | 9051.43i | 0.114581i | ||||||||
\(92\) | −83857.0 | − | 51643.8i | −1.03293 | − | 0.636134i | ||||
\(93\) | − | 5481.25i | − | 0.0657162i | ||||||
\(94\) | −63891.9 | − | 114385.i | −0.745806 | − | 1.33520i | ||||
\(95\) | −21560.0 | + | 36550.7i | −0.245098 | + | 0.415515i | ||||
\(96\) | 5813.57 | − | 8597.05i | 0.0643821 | − | 0.0952075i | ||||
\(97\) | − | 76257.9i | − | 0.822916i | −0.911429 | − | 0.411458i | \(-0.865020\pi\) | ||
0.911429 | − | 0.411458i | \(-0.134980\pi\) | |||||||
\(98\) | −80708.2 | + | 45081.2i | −0.848892 | + | 0.474166i | ||||
\(99\) | −21663.7 | −0.222149 | ||||||||
\(100\) | 40235.0 | − | 65331.8i | 0.402350 | − | 0.653318i | ||||
\(101\) | 144178.i | 1.40636i | 0.711012 | + | 0.703180i | \(0.248237\pi\) | ||||
−0.711012 | + | 0.703180i | \(0.751763\pi\) | |||||||
\(102\) | −1062.91 | − | 1902.91i | −0.0101157 | − | 0.0181100i | ||||
\(103\) | 44423.8 | 0.412594 | 0.206297 | − | 0.978489i | \(-0.433859\pi\) | ||||
0.206297 | + | 0.978489i | \(0.433859\pi\) | |||||||
\(104\) | 3236.23 | − | 75927.7i | 0.0293397 | − | 0.688362i | ||||
\(105\) | − | 1041.70i | − | 0.00922079i | ||||||
\(106\) | −58312.4 | + | 32571.6i | −0.504077 | + | 0.281563i | ||||
\(107\) | − | 64037.4i | − | 0.540722i | −0.962759 | − | 0.270361i | \(-0.912857\pi\) | ||
0.962759 | − | 0.270361i | \(-0.0871431\pi\) | |||||||
\(108\) | −23568.3 | − | 14514.7i | −0.194433 | − | 0.119743i | ||||
\(109\) | −53855.6 | −0.434175 | −0.217087 | − | 0.976152i | \(-0.569656\pi\) | ||||
−0.217087 | + | 0.976152i | \(0.569656\pi\) | |||||||
\(110\) | 6721.02 | + | 12032.5i | 0.0529606 | + | 0.0948145i | ||||
\(111\) | − | 16653.9i | − | 0.128294i | ||||||
\(112\) | −19715.4 | + | 9935.57i | −0.148511 | + | 0.0748424i | ||||
\(113\) | − | 63828.3i | − | 0.470238i | −0.971967 | − | 0.235119i | \(-0.924452\pi\) | ||
0.971967 | − | 0.235119i | \(-0.0755479\pi\) | |||||||
\(114\) | −375.305 | + | 15943.6i | −0.00270472 | + | 0.114901i | ||||
\(115\) | 82997.0 | 0.585218 | ||||||||
\(116\) | −103299. | + | 167733.i | −0.712773 | + | 1.15737i | ||||
\(117\) | −100670. | −0.679886 | ||||||||
\(118\) | −117043. | − | 209541.i | −0.773824 | − | 1.38536i | ||||
\(119\) | 4636.73i | 0.0300154i | ||||||||
\(120\) | −372.446 | + | 8738.26i | −0.00236108 | + | 0.0553951i | ||||
\(121\) | −152889. | −0.949320 | ||||||||
\(122\) | −125926. | − | 225443.i | −0.765978 | − | 1.37132i | ||||
\(123\) | 31841.1 | 0.189769 | ||||||||
\(124\) | 51337.6 | − | 83359.8i | 0.299834 | − | 0.486858i | ||||
\(125\) | 148937.i | 0.852562i | ||||||||
\(126\) | 14261.5 | + | 25532.1i | 0.0800274 | + | 0.143272i | ||||
\(127\) | 245386. | 1.35002 | 0.675010 | − | 0.737808i | \(-0.264139\pi\) | ||||
0.675010 | + | 0.737808i | \(0.264139\pi\) | |||||||
\(128\) | 168934. | − | 76295.3i | 0.911366 | − | 0.411598i | ||||
\(129\) | − | 12815.0i | − | 0.0678023i | ||||||
\(130\) | 31232.2 | + | 55914.5i | 0.162086 | + | 0.290179i | ||||
\(131\) | −184118. | −0.937387 | −0.468693 | − | 0.883361i | \(-0.655275\pi\) | ||||
−0.468693 | + | 0.883361i | \(0.655275\pi\) | |||||||
\(132\) | 4410.34 | + | 2716.13i | 0.0220312 | + | 0.0135680i | ||||
\(133\) | 17236.5 | − | 29221.1i | 0.0844930 | − | 0.143241i | ||||
\(134\) | 91194.0 | + | 163263.i | 0.438737 | + | 0.785463i | ||||
\(135\) | 23326.6 | 0.110158 | ||||||||
\(136\) | 1657.81 | − | 38895.1i | 0.00768576 | − | 0.180322i | ||||
\(137\) | 164046. | 0.746732 | 0.373366 | − | 0.927684i | \(-0.378204\pi\) | ||||
0.373366 | + | 0.927684i | \(0.378204\pi\) | |||||||
\(138\) | 27231.4 | − | 15210.7i | 0.121723 | − | 0.0679908i | ||||
\(139\) | −87851.9 | −0.385668 | −0.192834 | − | 0.981231i | \(-0.561768\pi\) | ||||
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(140\) | 9756.58 | − | 15842.3i | 0.0420705 | − | 0.0683123i | ||||
\(141\) | 41496.0 | 0.175776 | ||||||||
\(142\) | −147600. | + | 82445.2i | −0.614280 | + | 0.343119i | ||||
\(143\) | 37928.9 | 0.155107 | ||||||||
\(144\) | −110504. | − | 219275.i | −0.444089 | − | 0.881215i | ||||
\(145\) | − | 166012.i | − | 0.655723i | ||||||
\(146\) | 195837. | − | 109389.i | 0.760349 | − | 0.424709i | ||||
\(147\) | − | 29279.0i | − | 0.111754i | ||||||
\(148\) | 155981. | − | 253275.i | 0.585351 | − | 0.950468i | ||||
\(149\) | 12580.6i | 0.0464232i | 0.999731 | + | 0.0232116i | \(0.00738915\pi\) | ||||
−0.999731 | + | 0.0232116i | \(0.992611\pi\) | |||||||
\(150\) | 11850.4 | + | 21215.6i | 0.0430037 | + | 0.0769887i | ||||
\(151\) | −6755.65 | −0.0241115 | −0.0120558 | − | 0.999927i | \(-0.503838\pi\) | ||||
−0.0120558 | + | 0.999927i | \(0.503838\pi\) | |||||||
\(152\) | −155036. | + | 238958.i | −0.544281 | + | 0.838903i | ||||
\(153\) | −51569.8 | −0.178101 | ||||||||
\(154\) | −5373.23 | − | 9619.60i | −0.0182572 | − | 0.0326855i | ||||
\(155\) | 82504.9i | 0.275836i | ||||||||
\(156\) | 20494.6 | + | 12621.7i | 0.0674262 | + | 0.0415248i | ||||
\(157\) | 298532.i | 0.966588i | 0.875458 | + | 0.483294i | \(0.160560\pi\) | ||||
−0.875458 | + | 0.483294i | \(0.839440\pi\) | |||||||
\(158\) | −307655. | + | 171847.i | −0.980441 | + | 0.547646i | ||||
\(159\) | − | 21154.4i | − | 0.0663601i | ||||||
\(160\) | −87507.1 | + | 129405.i | −0.270236 | + | 0.399622i | ||||
\(161\) | −66353.3 | −0.201743 | ||||||||
\(162\) | −280116. | + | 156465.i | −0.838592 | + | 0.468413i | ||||
\(163\) | 225736. | 0.665476 | 0.332738 | − | 0.943019i | \(-0.392028\pi\) | ||||
0.332738 | + | 0.943019i | \(0.392028\pi\) | |||||||
\(164\) | 484245. | + | 298225.i | 1.40590 | + | 0.865833i | ||||
\(165\) | −4365.11 | −0.0124820 | ||||||||
\(166\) | −528459. | + | 295182.i | −1.48847 | + | 0.831417i | ||||
\(167\) | 581701. | 1.61402 | 0.807009 | − | 0.590539i | \(-0.201085\pi\) | ||||
0.807009 | + | 0.590539i | \(0.201085\pi\) | |||||||
\(168\) | 297.758 | − | 6985.95i | 0.000813937 | − | 0.0190964i | ||||
\(169\) | −195039. | −0.525297 | ||||||||
\(170\) | 15999.2 | + | 28643.1i | 0.0424596 | + | 0.0760146i | ||||
\(171\) | 324997. | + | 191705.i | 0.849942 | + | 0.501352i | ||||
\(172\) | 120026. | − | 194893.i | 0.309352 | − | 0.502313i | ||||
\(173\) | −626577. | −1.59169 | −0.795846 | − | 0.605499i | \(-0.792974\pi\) | ||||
−0.795846 | + | 0.605499i | \(0.792974\pi\) | |||||||
\(174\) | −30424.7 | − | 54468.8i | −0.0761821 | − | 0.136388i | ||||
\(175\) | − | 51695.0i | − | 0.127601i | ||||||
\(176\) | 41633.8 | + | 82614.9i | 0.101313 | + | 0.201037i | ||||
\(177\) | 76016.4 | 0.182379 | ||||||||
\(178\) | 254916. | + | 456372.i | 0.603042 | + | 1.07961i | ||||
\(179\) | 446020.i | 1.04045i | 0.854029 | + | 0.520226i | \(0.174152\pi\) | ||||
−0.854029 | + | 0.520226i | \(0.825848\pi\) | |||||||
\(180\) | 176199. | + | 108513.i | 0.405342 | + | 0.249632i | ||||
\(181\) | −645175. | −1.46380 | −0.731899 | − | 0.681413i | \(-0.761366\pi\) | ||||
−0.731899 | + | 0.681413i | \(0.761366\pi\) | |||||||
\(182\) | −24969.1 | − | 44701.8i | −0.0558759 | − | 0.100034i | ||||
\(183\) | 81785.5 | 0.180530 | ||||||||
\(184\) | 556604. | + | 23723.8i | 1.21200 | + | 0.0516583i | ||||
\(185\) | 250677.i | 0.538500i | ||||||||
\(186\) | 15120.5 | + | 27069.9i | 0.0320467 | + | 0.0573727i | ||||
\(187\) | 19429.7 | 0.0406314 | ||||||||
\(188\) | 631079. | + | 388653.i | 1.30223 | + | 0.801988i | ||||
\(189\) | −18648.9 | −0.0379750 | ||||||||
\(190\) | 5649.17 | − | 239986.i | 0.0113527 | − | 0.482283i | ||||
\(191\) | − | 497589.i | − | 0.986932i | −0.869765 | − | 0.493466i | \(-0.835730\pi\) | ||
0.869765 | − | 0.493466i | \(-0.164270\pi\) | |||||||
\(192\) | −4995.48 | + | 58495.0i | −0.00977967 | + | 0.114516i | ||||
\(193\) | − | 41507.7i | − | 0.0802112i | −0.999195 | − | 0.0401056i | \(-0.987231\pi\) | ||
0.999195 | − | 0.0401056i | \(-0.0127694\pi\) | |||||||
\(194\) | 210364. | + | 376611.i | 0.401298 | + | 0.718437i | ||||
\(195\) | −20284.5 | −0.0382012 | ||||||||
\(196\) | 274229. | − | 445281.i | 0.509885 | − | 0.827930i | ||||
\(197\) | − | 140183.i | − | 0.257354i | −0.991687 | − | 0.128677i | \(-0.958927\pi\) | ||
0.991687 | − | 0.128677i | \(-0.0410730\pi\) | |||||||
\(198\) | 106989. | − | 59761.1i | 0.193944 | − | 0.108332i | ||||
\(199\) | − | 745266.i | − | 1.33407i | −0.745026 | − | 0.667035i | \(-0.767563\pi\) | ||
0.745026 | − | 0.667035i | \(-0.232437\pi\) | |||||||
\(200\) | −18482.9 | + | 433642.i | −0.0326735 | + | 0.766578i | ||||
\(201\) | −59227.9 | −0.103404 | ||||||||
\(202\) | −397728. | − | 712045.i | −0.685816 | − | 1.22780i | ||||
\(203\) | 132721.i | 0.226048i | ||||||||
\(204\) | 10498.7 | + | 6465.68i | 0.0176628 | + | 0.0108777i | ||||
\(205\) | −479279. | −0.796533 | ||||||||
\(206\) | −219393. | + | 122547.i | −0.360210 | + | 0.201203i | ||||
\(207\) | − | 737983.i | − | 1.19707i | ||||||
\(208\) | 193470. | + | 383907.i | 0.310067 | + | 0.615273i | ||||
\(209\) | −122447. | − | 72227.7i | −0.193903 | − | 0.114377i | ||||
\(210\) | 2873.61 | + | 5144.57i | 0.00449655 | + | 0.00805010i | ||||
\(211\) | 759403.i | 1.17426i | 0.809491 | + | 0.587132i | \(0.199743\pi\) | ||||
−0.809491 | + | 0.587132i | \(0.800257\pi\) | |||||||
\(212\) | 198133. | − | 321720.i | 0.302773 | − | 0.491629i | ||||
\(213\) | − | 53545.9i | − | 0.0808680i | ||||||
\(214\) | 176653. | + | 316258.i | 0.263685 | + | 0.472071i | ||||
\(215\) | 192894.i | 0.284592i | ||||||||
\(216\) | 156436. | + | 6667.68i | 0.228140 | + | 0.00972390i | ||||
\(217\) | − | 65960.0i | − | 0.0950892i | ||||||
\(218\) | 265974. | − | 148565.i | 0.379051 | − | 0.211727i | ||||
\(219\) | 71045.1i | 0.100098i | ||||||||
\(220\) | −66385.4 | − | 40883.8i | −0.0924732 | − | 0.0569502i | ||||
\(221\) | 90288.8 | 0.124352 | ||||||||
\(222\) | 45941.1 | + | 82247.5i | 0.0625631 | + | 0.112006i | ||||
\(223\) | 354973. | 0.478006 | 0.239003 | − | 0.971019i | \(-0.423179\pi\) | ||||
0.239003 | + | 0.971019i | \(0.423179\pi\) | |||||||
\(224\) | 69959.0 | − | 103455.i | 0.0931588 | − | 0.137762i | ||||
\(225\) | 574952. | 0.757139 | ||||||||
\(226\) | 176076. | + | 315225.i | 0.229313 | + | 0.410535i | ||||
\(227\) | 521607.i | 0.671860i | 0.941887 | + | 0.335930i | \(0.109051\pi\) | ||||
−0.941887 | + | 0.335930i | \(0.890949\pi\) | |||||||
\(228\) | −42128.2 | − | 79774.9i | −0.0536705 | − | 0.101632i | ||||
\(229\) | − | 921989.i | − | 1.16182i | −0.813969 | − | 0.580908i | \(-0.802698\pi\) | ||
0.813969 | − | 0.580908i | \(-0.197302\pi\) | |||||||
\(230\) | −409893. | + | 228954.i | −0.510917 | + | 0.285384i | ||||
\(231\) | 3489.76 | 0.00430295 | ||||||||
\(232\) | 47452.9 | − | 1.11333e6i | 0.0578819 | − | 1.35801i | ||||
\(233\) | −1.42390e6 | −1.71826 | −0.859132 | − | 0.511754i | \(-0.828996\pi\) | ||||
−0.859132 | + | 0.511754i | \(0.828996\pi\) | |||||||
\(234\) | 497174. | − | 277707.i | 0.593566 | − | 0.331549i | ||||
\(235\) | −624607. | −0.737797 | ||||||||
\(236\) | 1.15607e6 | + | 711973.i | 1.35115 | + | 0.832116i | ||||
\(237\) | − | 111610.i | − | 0.129072i | ||||||
\(238\) | −12790.8 | − | 22899.2i | −0.0146371 | − | 0.0262046i | ||||
\(239\) | 316371.i | 0.358263i | 0.983825 | + | 0.179132i | \(0.0573288\pi\) | ||||
−0.983825 | + | 0.179132i | \(0.942671\pi\) | |||||||
\(240\) | −22265.8 | − | 44182.6i | −0.0249523 | − | 0.0495134i | ||||
\(241\) | − | 485506.i | − | 0.538458i | −0.963076 | − | 0.269229i | \(-0.913231\pi\) | ||
0.963076 | − | 0.269229i | \(-0.0867689\pi\) | |||||||
\(242\) | 755064. | − | 421757.i | 0.828792 | − | 0.462939i | ||||
\(243\) | − | 311809.i | − | 0.338745i | ||||||
\(244\) | 1.24381e6 | + | 766007.i | 1.33746 | + | 0.823679i | ||||
\(245\) | 440714.i | 0.469074i | ||||||||
\(246\) | −157252. | + | 87836.3i | −0.165675 | + | 0.0925414i | ||||
\(247\) | −569007. | − | 335638.i | −0.593438 | − | 0.350049i | ||||
\(248\) | −23583.2 | + | 553304.i | −0.0243486 | + | 0.571261i | ||||
\(249\) | − | 191712.i | − | 0.195953i | ||||||
\(250\) | −410854. | − | 735545.i | −0.415755 | − | 0.744319i | ||||
\(251\) | 788575. | 0.790058 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(252\) | −140865. | − | 86752.5i | −0.139734 | − | 0.0860559i | ||||
\(253\) | 278046.i | 0.273096i | ||||||||
\(254\) | −1.21187e6 | + | 676918.i | −1.17862 | + | 0.658342i | ||||
\(255\) | −10391.0 | −0.0100071 | ||||||||
\(256\) | −623839. | + | 842815.i | −0.594939 | + | 0.803771i | ||||
\(257\) | 743793.i | 0.702456i | 0.936290 | + | 0.351228i | \(0.114236\pi\) | ||||
−0.936290 | + | 0.351228i | \(0.885764\pi\) | |||||||
\(258\) | 35351.2 | + | 63288.7i | 0.0330640 | + | 0.0591939i | ||||
\(259\) | − | 200408.i | − | 0.185638i | ||||||
\(260\) | −308490. | − | 189985.i | −0.283014 | − | 0.174296i | ||||
\(261\) | −1.47613e6 | −1.34129 | ||||||||
\(262\) | 909295. | − | 507906.i | 0.818373 | − | 0.457120i | ||||
\(263\) | − | 1.46320e6i | − | 1.30441i | −0.758043 | − | 0.652205i | \(-0.773844\pi\) | ||
0.758043 | − | 0.652205i | \(-0.226156\pi\) | |||||||
\(264\) | −29273.8 | − | 1247.72i | −0.0258505 | − | 0.00110181i | ||||
\(265\) | 318420.i | 0.278539i | ||||||||
\(266\) | −4516.32 | + | 191861.i | −0.00391364 | + | 0.166258i | ||||
\(267\) | −165561. | −0.142128 | ||||||||
\(268\) | −900749. | − | 554731.i | −0.766067 | − | 0.471787i | ||||
\(269\) | 397571. | 0.334992 | 0.167496 | − | 0.985873i | \(-0.446432\pi\) | ||||
0.167496 | + | 0.985873i | \(0.446432\pi\) | |||||||
\(270\) | −115202. | + | 64348.5i | −0.0961725 | + | 0.0537192i | ||||
\(271\) | 1.02186e6i | 0.845217i | 0.906312 | + | 0.422608i | \(0.138885\pi\) | ||||
−0.906312 | + | 0.422608i | \(0.861115\pi\) | |||||||
\(272\) | 99108.2 | + | 196663.i | 0.0812246 | + | 0.161176i | ||||
\(273\) | 16216.7 | 0.0131691 | ||||||||
\(274\) | −810165. | + | 452535.i | −0.651925 | + | 0.364146i | ||||
\(275\) | −216622. | −0.172731 | ||||||||
\(276\) | −92526.2 | + | 150240.i | −0.0731126 | + | 0.118717i | ||||
\(277\) | 482020.i | 0.377455i | 0.982029 | + | 0.188728i | \(0.0604363\pi\) | ||||
−0.982029 | + | 0.188728i | \(0.939564\pi\) | |||||||
\(278\) | 433869. | − | 242347.i | 0.336703 | − | 0.188072i | ||||
\(279\) | 733608. | 0.564227 | ||||||||
\(280\) | −4481.92 | + | 105154.i | −0.00341641 | + | 0.0801550i | ||||
\(281\) | − | 1.37395e6i | − | 1.03802i | −0.854768 | − | 0.519010i | \(-0.826301\pi\) | ||
0.854768 | − | 0.519010i | \(-0.173699\pi\) | |||||||
\(282\) | −204934. | + | 114470.i | −0.153459 | + | 0.0857175i | ||||
\(283\) | −539885. | −0.400715 | −0.200357 | − | 0.979723i | \(-0.564210\pi\) | ||||
−0.200357 | + | 0.979723i | \(0.564210\pi\) | |||||||
\(284\) | 501513. | − | 814335.i | 0.368966 | − | 0.599111i | ||||
\(285\) | 65485.1 | + | 38627.5i | 0.0477562 | + | 0.0281698i | ||||
\(286\) | −187318. | + | 104630.i | −0.135414 | + | 0.0756383i | ||||
\(287\) | 383167. | 0.274589 | ||||||||
\(288\) | 1.15063e6 | + | 778086.i | 0.817434 | + | 0.552772i | ||||
\(289\) | −1.37361e6 | −0.967425 | ||||||||
\(290\) | 457959. | + | 819876.i | 0.319766 | + | 0.572471i | ||||
\(291\) | −136626. | −0.0945800 | ||||||||
\(292\) | −665412. | + | 1.08047e6i | −0.456702 | + | 0.741574i | ||||
\(293\) | −522263. | −0.355402 | −0.177701 | − | 0.984085i | \(-0.556866\pi\) | ||||
−0.177701 | + | 0.984085i | \(0.556866\pi\) | |||||||
\(294\) | 80768.6 | + | 144599.i | 0.0544972 | + | 0.0975654i | ||||
\(295\) | −1.14422e6 | −0.765514 | ||||||||
\(296\) | −71653.5 | + | 1.68112e6i | −0.0475344 | + | 1.11524i | ||||
\(297\) | 78146.0i | 0.0514062i | ||||||||
\(298\) | −34704.6 | − | 62131.1i | −0.0226384 | − | 0.0405292i | ||||
\(299\) | 1.29207e6i | 0.835808i | ||||||||
\(300\) | −117050. | − | 72085.9i | −0.0750876 | − | 0.0462431i | ||||
\(301\) | − | 154212.i | − | 0.0981077i | ||||||
\(302\) | 33363.8 | − | 18636.0i | 0.0210503 | − | 0.0117581i | ||||
\(303\) | 258313. | 0.161637 | ||||||||
\(304\) | 106483. | − | 1.60781e6i | 0.0660838 | − | 0.997814i | ||||
\(305\) | −1.23105e6 | −0.757752 | ||||||||
\(306\) | 254685. | − | 142260.i | 0.155489 | − | 0.0868517i | ||||
\(307\) | − | 1.90603e6i | − | 1.15421i | −0.816670 | − | 0.577105i | \(-0.804182\pi\) | ||
0.816670 | − | 0.577105i | \(-0.195818\pi\) | |||||||
\(308\) | 53072.9 | + | 32685.3i | 0.0318784 | + | 0.0196325i | ||||
\(309\) | − | 79590.7i | − | 0.0474205i | ||||||
\(310\) | −227597. | − | 407463.i | −0.134512 | − | 0.240815i | ||||
\(311\) | − | 37265.3i | − | 0.0218476i | −0.999940 | − | 0.0109238i | \(-0.996523\pi\) | ||
0.999940 | − | 0.0109238i | \(-0.00347723\pi\) | |||||||
\(312\) | −136034. | − | 5798.10i | −0.0791153 | − | 0.00337209i | ||||
\(313\) | 1.34915e6 | 0.778396 | 0.389198 | − | 0.921154i | \(-0.372752\pi\) | ||||
0.389198 | + | 0.921154i | \(0.372752\pi\) | |||||||
\(314\) | −823525. | − | 1.47434e6i | −0.471360 | − | 0.843868i | ||||
\(315\) | 139420. | 0.0791680 | ||||||||
\(316\) | 1.04534e6 | − | 1.69739e6i | 0.588900 | − | 0.956231i | ||||
\(317\) | 695473. | 0.388716 | 0.194358 | − | 0.980931i | \(-0.437738\pi\) | ||||
0.194358 | + | 0.980931i | \(0.437738\pi\) | |||||||
\(318\) | 58356.1 | + | 104474.i | 0.0323608 | + | 0.0579349i | ||||
\(319\) | 556153. | 0.305998 | ||||||||
\(320\) | 75193.1 | − | 880479.i | 0.0410490 | − | 0.480667i | ||||
\(321\) | −114731. | −0.0621467 | ||||||||
\(322\) | 327696. | − | 183041.i | 0.176129 | − | 0.0983806i | ||||
\(323\) | −291483. | − | 171936.i | −0.155456 | − | 0.0916981i | ||||
\(324\) | 951774. | − | 1.54545e6i | 0.503699 | − | 0.817885i | ||||
\(325\) | −1.00663e6 | −0.528642 | ||||||||
\(326\) | −1.11483e6 | + | 622712.i | −0.580985 | + | 0.324521i | ||||
\(327\) | 96488.9i | 0.0499009i | ||||||||
\(328\) | −3.21419e6 | − | 136997.i | −1.64963 | − | 0.0703115i | ||||
\(329\) | 499352. | 0.254342 | ||||||||
\(330\) | 21557.7 | − | 12041.5i | 0.0108973 | − | 0.00608691i | ||||
\(331\) | − | 2.30186e6i | − | 1.15481i | −0.816459 | − | 0.577404i | \(-0.804066\pi\) | ||
0.816459 | − | 0.577404i | \(-0.195934\pi\) | |||||||
\(332\) | 1.79559e6 | − | 2.91559e6i | 0.894048 | − | 1.45172i | ||||
\(333\) | 2.22894e6 | 1.10151 | ||||||||
\(334\) | −2.87281e6 | + | 1.60467e6i | −1.40910 | + | 0.787082i | ||||
\(335\) | 891512. | 0.434025 | ||||||||
\(336\) | 17800.8 | + | 35322.5i | 0.00860184 | + | 0.0170688i | ||||
\(337\) | − | 3.72058e6i | − | 1.78458i | −0.451464 | − | 0.892290i | \(-0.649098\pi\) | ||
0.451464 | − | 0.892290i | \(-0.350902\pi\) | |||||||
\(338\) | 963229. | − | 538032.i | 0.458604 | − | 0.256163i | ||||
\(339\) | −114356. | −0.0540457 | ||||||||
\(340\) | −158029. | − | 97322.8i | −0.0741376 | − | 0.0456581i | ||||
\(341\) | −276398. | −0.128721 | ||||||||
\(342\) | −2.13388e6 | − | 50230.6i | −0.986517 | − | 0.0232222i | ||||
\(343\) | − | 714694.i | − | 0.328008i | ||||||
\(344\) | −55136.8 | + | 1.29361e6i | −0.0251215 | + | 0.589395i | ||||
\(345\) | − | 148699.i | − | 0.0672607i | ||||||
\(346\) | 3.09444e6 | − | 1.72847e6i | 1.38961 | − | 0.776194i | ||||
\(347\) | −102106. | −0.0455225 | −0.0227613 | − | 0.999741i | \(-0.507246\pi\) | ||||
−0.0227613 | + | 0.999741i | \(0.507246\pi\) | |||||||
\(348\) | 300513. | + | 185073.i | 0.133020 | + | 0.0819209i | ||||
\(349\) | 2.09248e6i | 0.919597i | 0.888023 | + | 0.459799i | \(0.152078\pi\) | ||||
−0.888023 | + | 0.459799i | \(0.847922\pi\) | |||||||
\(350\) | 142605. | + | 255303.i | 0.0622249 | + | 0.111400i | ||||
\(351\) | 363140.i | 0.157328i | ||||||||
\(352\) | −433515. | − | 293155.i | −0.186487 | − | 0.126108i | ||||
\(353\) | 1.29274e6 | 0.552173 | 0.276086 | − | 0.961133i | \(-0.410962\pi\) | ||||
0.276086 | + | 0.961133i | \(0.410962\pi\) | |||||||
\(354\) | −375418. | + | 209698.i | −0.159223 | + | 0.0889376i | ||||
\(355\) | 805984.i | 0.339434i | ||||||||
\(356\) | −2.51788e6 | − | 1.55065e6i | −1.05296 | − | 0.648469i | ||||
\(357\) | 8307.28 | 0.00344976 | ||||||||
\(358\) | −1.23038e6 | − | 2.20273e6i | −0.507380 | − | 0.908353i | ||||
\(359\) | 4.19203e6i | 1.71667i | 0.513086 | + | 0.858337i | \(0.328502\pi\) | ||||
−0.513086 | + | 0.858337i | \(0.671498\pi\) | |||||||
\(360\) | −1.16952e6 | − | 49848.0i | −0.475612 | − | 0.0202718i | ||||
\(361\) | 1.19779e6 | + | 2.16711e6i | 0.483743 | + | 0.875210i | ||||
\(362\) | 3.18629e6 | − | 1.77977e6i | 1.27795 | − | 0.713826i | ||||
\(363\) | 273919.i | 0.109108i | ||||||||
\(364\) | 246627. | + | 151887.i | 0.0975635 | + | 0.0600851i | ||||
\(365\) | − | 1.06939e6i | − | 0.420148i | ||||||
\(366\) | −403910. | + | 225612.i | −0.157609 | + | 0.0880359i | ||||
\(367\) | − | 1.08261e6i | − | 0.419571i | −0.977747 | − | 0.209785i | \(-0.932723\pi\) | ||
0.977747 | − | 0.209785i | \(-0.0672765\pi\) | |||||||
\(368\) | −2.81431e6 | + | 1.41827e6i | −1.08331 | + | 0.545935i | ||||
\(369\) | 4.26160e6i | 1.62932i | ||||||||
\(370\) | −691515. | − | 1.23801e6i | −0.262601 | − | 0.470131i | ||||
\(371\) | − | 254566.i | − | 0.0960210i | ||||||
\(372\) | −149349. | − | 91977.7i | −0.0559559 | − | 0.0344608i | ||||
\(373\) | 2.51466e6 | 0.935851 | 0.467925 | − | 0.883768i | \(-0.345002\pi\) | ||||
0.467925 | + | 0.883768i | \(0.345002\pi\) | |||||||
\(374\) | −95956.4 | + | 53598.4i | −0.0354727 | + | 0.0198140i | ||||
\(375\) | 266838. | 0.0979873 | ||||||||
\(376\) | −4.18881e6 | − | 178537.i | −1.52799 | − | 0.0651268i | ||||
\(377\) | 2.58442e6 | 0.936503 | ||||||||
\(378\) | 92100.2 | − | 51444.5i | 0.0331536 | − | 0.0185187i | ||||
\(379\) | − | 2.81311e6i | − | 1.00598i | −0.864292 | − | 0.502990i | \(-0.832233\pi\) | ||
0.864292 | − | 0.502990i | \(-0.167767\pi\) | |||||||
\(380\) | 634122. | + | 1.20079e6i | 0.225276 | + | 0.426587i | ||||
\(381\) | − | 439639.i | − | 0.155161i | ||||||
\(382\) | 1.37264e6 | + | 2.45741e6i | 0.481281 | + | 0.861628i | ||||
\(383\) | −4.38136e6 | −1.52620 | −0.763101 | − | 0.646279i | \(-0.776324\pi\) | ||||
−0.763101 | + | 0.646279i | \(0.776324\pi\) | |||||||
\(384\) | −136692. | − | 302666.i | −0.0473060 | − | 0.104746i | ||||
\(385\) | −52528.6 | −0.0180611 | ||||||||
\(386\) | 114502. | + | 204992.i | 0.0391153 | + | 0.0700274i | ||||
\(387\) | 1.71515e6 | 0.582137 | ||||||||
\(388\) | −2.07783e6 | − | 1.27964e6i | −0.700696 | − | 0.431528i | ||||
\(389\) | − | 1.39789e6i | − | 0.468381i | −0.972191 | − | 0.234191i | \(-0.924756\pi\) | ||
0.972191 | − | 0.234191i | \(-0.0752440\pi\) | |||||||
\(390\) | 100178. | − | 55956.4i | 0.0333511 | − | 0.0186289i | ||||
\(391\) | 661881.i | 0.218946i | ||||||||
\(392\) | −125974. | + | 2.95557e6i | −0.0414061 | + | 0.971461i | ||||
\(393\) | 329871.i | 0.107736i | ||||||||
\(394\) | 386707. | + | 692315.i | 0.125499 | + | 0.224679i | ||||
\(395\) | 1.67998e6i | 0.541765i | ||||||||
\(396\) | −363526. | + | 590278.i | −0.116492 | + | 0.189155i | ||||
\(397\) | 139153.i | 0.0443115i | 0.999755 | + | 0.0221557i | \(0.00705297\pi\) | ||||
−0.999755 | + | 0.0221557i | \(0.992947\pi\) | |||||||
\(398\) | 2.05588e6 | + | 3.68061e6i | 0.650564 | + | 1.16469i | ||||
\(399\) | −52353.1 | − | 30881.4i | −0.0164631 | − | 0.00971101i | ||||
\(400\) | −1.10496e6 | − | 2.19259e6i | −0.345299 | − | 0.685185i | ||||
\(401\) | 2.89612e6i | 0.899404i | 0.893179 | + | 0.449702i | \(0.148470\pi\) | ||||
−0.893179 | + | 0.449702i | \(0.851530\pi\) | |||||||
\(402\) | 292506. | − | 163385.i | 0.0902754 | − | 0.0504252i | ||||
\(403\) | −1.28441e6 | −0.393949 | ||||||||
\(404\) | 3.92847e6 | + | 2.41937e6i | 1.19749 | + | 0.737479i | ||||
\(405\) | 1.52960e6i | 0.463383i | ||||||||
\(406\) | −366123. | − | 655464.i | −0.110233 | − | 0.197348i | ||||
\(407\) | −839787. | −0.251295 | ||||||||
\(408\) | −69685.5 | − | 2970.17i | −0.0207249 | − | 0.000883346i | ||||
\(409\) | − | 4.18231e6i | − | 1.23626i | −0.786078 | − | 0.618128i | \(-0.787891\pi\) | ||
0.786078 | − | 0.618128i | \(-0.212109\pi\) | |||||||
\(410\) | 2.36699e6 | − | 1.32213e6i | 0.695403 | − | 0.388432i | ||||
\(411\) | − | 293909.i | − | 0.0858239i | ||||||
\(412\) | 745450. | − | 1.21043e6i | 0.216359 | − | 0.351315i | ||||
\(413\) | 914762. | 0.263896 | ||||||||
\(414\) | 2.03579e6 | + | 3.64464e6i | 0.583757 | + | 1.04509i | ||||
\(415\) | 2.88569e6i | 0.822489i | ||||||||
\(416\) | −2.01452e6 | − | 1.36228e6i | −0.570741 | − | 0.385951i | ||||
\(417\) | 157397.i | 0.0443259i | ||||||||
\(418\) | 803971. | + | 18925.1i | 0.225061 | + | 0.00529783i | ||||
\(419\) | 5.33921e6 | 1.48574 | 0.742869 | − | 0.669437i | \(-0.233465\pi\) | ||||
0.742869 | + | 0.669437i | \(0.233465\pi\) | |||||||
\(420\) | −28383.5 | − | 17480.1i | −0.00785131 | − | 0.00483528i | ||||
\(421\) | 5.84059e6 | 1.60602 | 0.803011 | − | 0.595964i | \(-0.203230\pi\) | ||||
0.803011 | + | 0.595964i | \(0.203230\pi\) | |||||||
\(422\) | −2.09488e6 | − | 3.75042e6i | −0.572634 | − | 1.02518i | ||||
\(423\) | 5.55381e6i | 1.50918i | ||||||||
\(424\) | −91017.1 | + | 2.13542e6i | −0.0245872 | + | 0.576859i | ||||
\(425\) | −515662. | −0.138482 | ||||||||
\(426\) | 147711. | + | 264444.i | 0.0394356 | + | 0.0706008i | ||||
\(427\) | 984186. | 0.261221 | ||||||||
\(428\) | −1.74485e6 | − | 1.07457e6i | −0.460414 | − | 0.283548i | ||||
\(429\) | − | 67954.4i | − | 0.0178268i | ||||||
\(430\) | −532115. | − | 952635.i | −0.138782 | − | 0.248459i | ||||
\(431\) | −3.18075e6 | −0.824777 | −0.412388 | − | 0.911008i | \(-0.635305\pi\) | ||||
−0.412388 | + | 0.911008i | \(0.635305\pi\) | |||||||
\(432\) | −790974. | + | 398612.i | −0.203917 | + | 0.102764i | ||||
\(433\) | 2.87889e6i | 0.737913i | 0.929447 | + | 0.368956i | \(0.120285\pi\) | ||||
−0.929447 | + | 0.368956i | \(0.879715\pi\) | |||||||
\(434\) | 181956. | + | 325753.i | 0.0463706 | + | 0.0830164i | ||||
\(435\) | −297432. | −0.0753640 | ||||||||
\(436\) | −903720. | + | 1.46742e6i | −0.227676 | + | 0.369691i | ||||
\(437\) | 2.46047e6 | − | 4.17122e6i | 0.616330 | − | 1.04486i | ||||
\(438\) | −195984. | − | 350867.i | −0.0488130 | − | 0.0873890i | ||||
\(439\) | 4.54057e6 | 1.12447 | 0.562236 | − | 0.826977i | \(-0.309941\pi\) | ||||
0.562236 | + | 0.826977i | \(0.309941\pi\) | |||||||
\(440\) | 440635. | + | 18781.0i | 0.108505 | + | 0.00462473i | ||||
\(441\) | 3.91869e6 | 0.959499 | ||||||||
\(442\) | −445904. | + | 249069.i | −0.108564 | + | 0.0606407i | ||||
\(443\) | −3.58650e6 | −0.868284 | −0.434142 | − | 0.900845i | \(-0.642948\pi\) | ||||
−0.434142 | + | 0.900845i | \(0.642948\pi\) | |||||||
\(444\) | −453773. | − | 279459.i | −0.109240 | − | 0.0672760i | ||||
\(445\) | 2.49206e6 | 0.596566 | ||||||||
\(446\) | −1.75309e6 | + | 979223.i | −0.417317 | + | 0.233101i | ||||
\(447\) | 22539.7 | 0.00533555 | ||||||||
\(448\) | −60114.4 | + | 703914.i | −0.0141509 | + | 0.165701i | ||||
\(449\) | 2.78600e6i | 0.652178i | 0.945339 | + | 0.326089i | \(0.105731\pi\) | ||||
−0.945339 | + | 0.326089i | \(0.894269\pi\) | |||||||
\(450\) | −2.83949e6 | + | 1.58605e6i | −0.661011 | + | 0.369221i | ||||
\(451\) | − | 1.60562e6i | − | 0.371707i | ||||||
\(452\) | −1.73915e6 | − | 1.07107e6i | −0.400398 | − | 0.246587i | ||||
\(453\) | 12103.6i | 0.00277120i | ||||||||
\(454\) | −1.43890e6 | − | 2.57603e6i | −0.327635 | − | 0.586559i | ||||
\(455\) | −244098. | −0.0552759 | ||||||||
\(456\) | 428122. | + | 277766.i | 0.0964174 | + | 0.0625557i | ||||
\(457\) | 6.01508e6 | 1.34726 | 0.673629 | − | 0.739069i | \(-0.264734\pi\) | ||||
0.673629 | + | 0.739069i | \(0.264734\pi\) | |||||||
\(458\) | 2.54339e6 | + | 4.55338e6i | 0.566563 | + | 1.01431i | ||||
\(459\) | 186024.i | 0.0412134i | ||||||||
\(460\) | 1.39273e6 | − | 2.26145e6i | 0.306882 | − | 0.498301i | ||||
\(461\) | 5.49794e6i | 1.20489i | 0.798160 | + | 0.602445i | \(0.205807\pi\) | ||||
−0.798160 | + | 0.602445i | \(0.794193\pi\) | |||||||
\(462\) | −17234.7 | + | 9626.80i | −0.00375663 | + | 0.00209835i | ||||
\(463\) | 6.80325e6i | 1.47490i | 0.675400 | + | 0.737452i | \(0.263971\pi\) | ||||
−0.675400 | + | 0.737452i | \(0.736029\pi\) | |||||||
\(464\) | 2.83686e6 | + | 5.62925e6i | 0.611707 | + | 1.21382i | ||||
\(465\) | 147818. | 0.0317026 | ||||||||
\(466\) | 7.03214e6 | − | 3.92795e6i | 1.50011 | − | 0.837917i | ||||
\(467\) | −3.92402e6 | −0.832606 | −0.416303 | − | 0.909226i | \(-0.636674\pi\) | ||||
−0.416303 | + | 0.909226i | \(0.636674\pi\) | |||||||
\(468\) | −1.68929e6 | + | 2.74299e6i | −0.356524 | + | 0.578909i | ||||
\(469\) | −712734. | −0.149622 | ||||||||
\(470\) | 3.08471e6 | − | 1.72303e6i | 0.644125 | − | 0.359789i | ||||
\(471\) | 534857. | 0.111093 | ||||||||
\(472\) | −7.67347e6 | − | 327062.i | −1.58539 | − | 0.0675734i | ||||
\(473\) | −646209. | −0.132807 | ||||||||
\(474\) | 307886. | + | 551202.i | 0.0629425 | + | 0.112685i | ||||
\(475\) | 3.24974e6 | + | 1.91691e6i | 0.660868 | + | 0.389824i | ||||
\(476\) | 126339. | + | 77806.4i | 0.0255575 | + | 0.0157397i | ||||
\(477\) | 2.83129e6 | 0.569756 | ||||||||
\(478\) | −872737. | − | 1.56245e6i | −0.174708 | − | 0.312777i | ||||
\(479\) | − | 4.25311e6i | − | 0.846969i | −0.905903 | − | 0.423485i | \(-0.860807\pi\) | ||
0.905903 | − | 0.423485i | \(-0.139193\pi\) | |||||||
\(480\) | 231844. | + | 156780.i | 0.0459297 | + | 0.0310590i | ||||
\(481\) | −3.90245e6 | −0.769086 | ||||||||
\(482\) | 1.33931e6 | + | 2.39774e6i | 0.262581 | + | 0.470094i | ||||
\(483\) | 118880.i | 0.0231868i | ||||||||
\(484\) | −2.56554e6 | + | 4.16581e6i | −0.497812 | + | 0.808326i | ||||
\(485\) | 2.05652e6 | 0.396988 | ||||||||
\(486\) | 860152. | + | 1.53992e6i | 0.165190 | + | 0.295737i | ||||
\(487\) | −1.02183e7 | −1.95235 | −0.976174 | − | 0.216988i | \(-0.930377\pi\) | ||||
−0.976174 | + | 0.216988i | \(0.930377\pi\) | |||||||
\(488\) | −8.25583e6 | − | 351884.i | −1.56932 | − | 0.0668883i | ||||
\(489\) | − | 404434.i | − | 0.0764849i | ||||||
\(490\) | −1.21575e6 | − | 2.17653e6i | −0.228746 | − | 0.409519i | ||||
\(491\) | 3.32334e6 | 0.622116 | 0.311058 | − | 0.950391i | \(-0.399317\pi\) | ||||
0.311058 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(492\) | 534307. | − | 867584.i | 0.0995126 | − | 0.161584i | ||||
\(493\) | 1.32391e6 | 0.245324 | ||||||||
\(494\) | 3.73601e6 | + | 87944.1i | 0.688796 | + | 0.0162140i | ||||
\(495\) | − | 584225.i | − | 0.107168i | ||||||
\(496\) | −1.40987e6 | − | 2.79763e6i | −0.257320 | − | 0.510606i | ||||
\(497\) | − | 644357.i | − | 0.117013i | ||||||
\(498\) | 528854. | + | 946799.i | 0.0955571 | + | 0.171074i | ||||
\(499\) | −5.52536e6 | −0.993366 | −0.496683 | − | 0.867932i | \(-0.665449\pi\) | ||||
−0.496683 | + | 0.867932i | \(0.665449\pi\) | |||||||
\(500\) | 4.05812e6 | + | 2.49922e6i | 0.725939 | + | 0.447074i | ||||
\(501\) | − | 1.04219e6i | − | 0.185504i | ||||||
\(502\) | −3.89449e6 | + | 2.17535e6i | −0.689750 | + | 0.385274i | ||||
\(503\) | − | 2.18871e6i | − | 0.385716i | −0.981227 | − | 0.192858i | \(-0.938224\pi\) | ||
0.981227 | − | 0.192858i | \(-0.0617756\pi\) | |||||||
\(504\) | 934996. | + | 39851.9i | 0.163958 | + | 0.00698831i | ||||
\(505\) | −3.88819e6 | −0.678451 | ||||||||
\(506\) | −767013. | − | 1.37317e6i | −0.133176 | − | 0.238423i | ||||
\(507\) | 349437.i | 0.0603738i | ||||||||
\(508\) | 4.11768e6 | − | 6.68611e6i | 0.707935 | − | 1.14951i | ||||
\(509\) | −6.27300e6 | −1.07320 | −0.536600 | − | 0.843836i | \(-0.680292\pi\) | ||||
−0.536600 | + | 0.843836i | \(0.680292\pi\) | |||||||
\(510\) | 51317.6 | − | 28664.5i | 0.00873657 | − | 0.00487999i | ||||
\(511\) | 854939.i | 0.144838i | ||||||||
\(512\) | 755944. | − | 5.88327e6i | 0.127443 | − | 0.991846i | ||||
\(513\) | 691524. | − | 1.17234e6i | 0.116015 | − | 0.196680i | ||||
\(514\) | −2.05182e6 | − | 3.67333e6i | −0.342555 | − | 0.613271i | ||||
\(515\) | 1.19802e6i | 0.199042i | ||||||||
\(516\) | −349174. | − | 215041.i | −0.0577322 | − | 0.0355547i | ||||
\(517\) | − | 2.09248e6i | − | 0.344298i | ||||||
\(518\) | 552843. | + | 989745.i | 0.0905268 | + | 0.162069i | ||||
\(519\) | 1.12259e6i | 0.182938i | ||||||||
\(520\) | 2.04761e6 | + | 87274.3i | 0.332077 | + | 0.0141540i | ||||
\(521\) | 1.45769e6i | 0.235273i | 0.993057 | + | 0.117636i | \(0.0375317\pi\) | ||||
−0.993057 | + | 0.117636i | \(0.962468\pi\) | |||||||
\(522\) | 7.29008e6 | − | 4.07203e6i | 1.17100 | − | 0.654085i | ||||
\(523\) | − | 1.24010e7i | − | 1.98245i | −0.132178 | − | 0.991226i | \(-0.542197\pi\) | ||
0.132178 | − | 0.991226i | \(-0.457803\pi\) | |||||||
\(524\) | −3.08958e6 | + | 5.01673e6i | −0.491555 | + | 0.798165i | ||||
\(525\) | −92617.9 | −0.0146655 | ||||||||
\(526\) | 4.03636e6 | + | 7.22622e6i | 0.636100 | + | 1.13880i | ||||
\(527\) | −657957. | −0.103198 | ||||||||
\(528\) | 148015. | − | 74592.2i | 0.0231058 | − | 0.0116442i | ||||
\(529\) | −3.03541e6 | −0.471605 | ||||||||
\(530\) | −878389. | − | 1.57256e6i | −0.135830 | − | 0.243175i | ||||
\(531\) | 1.01740e7i | 1.56587i | ||||||||
\(532\) | −506960. | − | 959991.i | −0.0776595 | − | 0.147058i | ||||
\(533\) | − | 7.46123e6i | − | 1.13761i | ||||||
\(534\) | 817647. | − | 456714.i | 0.124083 | − | 0.0693092i | ||||
\(535\) | 1.72695e6 | 0.260853 | ||||||||
\(536\) | 5.97875e6 | + | 254829.i | 0.898874 | + | 0.0383122i | ||||
\(537\) | 799100. | 0.119582 | ||||||||
\(538\) | −1.96346e6 | + | 1.09673e6i | −0.292460 | + | 0.163360i | ||||
\(539\) | −1.47642e6 | −0.218897 | ||||||||
\(540\) | 391431. | − | 635589.i | 0.0577658 | − | 0.0937976i | ||||
\(541\) | − | 6.25172e6i | − | 0.918346i | −0.888347 | − | 0.459173i | \(-0.848146\pi\) | ||
0.888347 | − | 0.459173i | \(-0.151854\pi\) | |||||||
\(542\) | −2.81889e6 | − | 5.04660e6i | −0.412173 | − | 0.737906i | ||||
\(543\) | 1.15591e6i | 0.168238i | ||||||||
\(544\) | −1.03197e6 | − | 697848.i | −0.149510 | − | 0.101103i | ||||
\(545\) | − | 1.45237e6i | − | 0.209453i | ||||||
\(546\) | −80088.7 | + | 44735.3i | −0.0114971 | + | 0.00642197i | ||||
\(547\) | − | 8.68527e6i | − | 1.24112i | −0.784158 | − | 0.620561i | \(-0.786905\pi\) | ||
0.784158 | − | 0.620561i | \(-0.213095\pi\) | |||||||
\(548\) | 2.75276e6 | − | 4.46982e6i | 0.391577 | − | 0.635826i | ||||
\(549\) | 1.09461e7i | 1.54999i | ||||||||
\(550\) | 1.06982e6 | − | 597569.i | 0.150801 | − | 0.0842329i | ||||
\(551\) | −8.34337e6 | − | 4.92147e6i | −1.17075 | − | 0.690584i | ||||
\(552\) | 42504.2 | − | 997224.i | 0.00593723 | − | 0.139298i | ||||
\(553\) | − | 1.34309e6i | − | 0.186763i | ||||||
\(554\) | −1.32969e6 | − | 2.38052e6i | −0.184067 | − | 0.329532i | ||||
\(555\) | 449120. | 0.0618913 | ||||||||
\(556\) | −1.47419e6 | + | 2.39373e6i | −0.202240 | + | 0.328389i | ||||
\(557\) | − | 1.26351e7i | − | 1.72560i | −0.505544 | − | 0.862801i | \(-0.668708\pi\) | ||
0.505544 | − | 0.862801i | \(-0.331292\pi\) | |||||||
\(558\) | −3.62303e6 | + | 2.02372e6i | −0.492591 | + | 0.275147i | ||||
\(559\) | −3.00290e6 | −0.406454 | ||||||||
\(560\) | −267941. | − | 531682.i | −0.0361052 | − | 0.0716443i | ||||
\(561\) | − | 34810.7i | − | 0.00466988i | ||||||
\(562\) | 3.79016e6 | + | 6.78546e6i | 0.506194 | + | 0.906231i | ||||
\(563\) | − | 2.22227e6i | − | 0.295478i | −0.989026 | − | 0.147739i | \(-0.952800\pi\) | ||
0.989026 | − | 0.147739i | \(-0.0471996\pi\) | |||||||
\(564\) | 696321. | − | 1.13066e6i | 0.0921746 | − | 0.149669i | ||||
\(565\) | 1.72132e6 | 0.226850 | ||||||||
\(566\) | 2.66630e6 | − | 1.48932e6i | 0.349839 | − | 0.195410i | ||||
\(567\) | − | 1.22286e6i | − | 0.159743i | ||||||
\(568\) | −230382. | + | 5.40518e6i | −0.0299625 | + | 0.702974i | ||||
\(569\) | 8.80479e6i | 1.14009i | 0.821614 | + | 0.570044i | \(0.193074\pi\) | ||||
−0.821614 | + | 0.570044i | \(0.806926\pi\) | |||||||
\(570\) | −429965. | − | 10121.2i | −0.0554301 | − | 0.00130480i | ||||
\(571\) | −1.03222e7 | −1.32490 | −0.662450 | − | 0.749106i | \(-0.730483\pi\) | ||||
−0.662450 | + | 0.749106i | \(0.730483\pi\) | |||||||
\(572\) | 636464. | − | 1.03346e6i | 0.0813362 | − | 0.132070i | ||||
\(573\) | −891491. | −0.113431 | ||||||||
\(574\) | −1.89233e6 | + | 1.05700e6i | −0.239727 | + | 0.133904i | ||||
\(575\) | − | 7.37931e6i | − | 0.930778i | ||||||
\(576\) | −7.82894e6 | − | 668593.i | −0.983212 | − | 0.0839664i | ||||
\(577\) | −2.38619e6 | −0.298378 | −0.149189 | − | 0.988809i | \(-0.547666\pi\) | ||||
−0.149189 | + | 0.988809i | \(0.547666\pi\) | |||||||
\(578\) | 6.78375e6 | − | 3.78921e6i | 0.844598 | − | 0.471768i | ||||
\(579\) | −74366.1 | −0.00921889 | ||||||||
\(580\) | −4.52339e6 | − | 2.78576e6i | −0.558334 | − | 0.343853i | ||||
\(581\) | − | 2.30702e6i | − | 0.283537i | ||||||
\(582\) | 674745. | − | 376893.i | 0.0825719 | − | 0.0461223i | ||||
\(583\) | −1.06673e6 | −0.129982 | ||||||||
\(584\) | 305673. | − | 7.17164e6i | 0.0370873 | − | 0.870134i | ||||
\(585\) | − | 2.71486e6i | − | 0.327988i | ||||||
\(586\) | 2.57927e6 | − | 1.44071e6i | 0.310279 | − | 0.173313i | ||||
\(587\) | −4.97228e6 | −0.595608 | −0.297804 | − | 0.954627i | \(-0.596254\pi\) | ||||
−0.297804 | + | 0.954627i | \(0.596254\pi\) | |||||||
\(588\) | −797775. | − | 491314.i | −0.0951562 | − | 0.0586025i | ||||
\(589\) | 4.14649e6 | + | 2.44588e6i | 0.492485 | + | 0.290500i | ||||
\(590\) | 5.65088e6 | − | 3.15642e6i | 0.668322 | − | 0.373305i | ||||
\(591\) | −251156. | −0.0295784 | ||||||||
\(592\) | −4.28364e6 | − | 8.50012e6i | −0.502353 | − | 0.996829i | ||||
\(593\) | 550883. | 0.0643313 | 0.0321657 | − | 0.999483i | \(-0.489760\pi\) | ||||
0.0321657 | + | 0.999483i | \(0.489760\pi\) | |||||||
\(594\) | −215572. | − | 385935.i | −0.0250684 | − | 0.0448795i | ||||
\(595\) | −125043. | −0.0144799 | ||||||||
\(596\) | 342788. | + | 211108.i | 0.0395284 | + | 0.0243438i | ||||
\(597\) | −1.33524e6 | −0.153328 | ||||||||
\(598\) | −3.56427e6 | − | 6.38105e6i | −0.407585 | − | 0.729692i | ||||
\(599\) | 4.35875e6 | 0.496357 | 0.248179 | − | 0.968714i | \(-0.420168\pi\) | ||||
0.248179 | + | 0.968714i | \(0.420168\pi\) | |||||||
\(600\) | 776923. | + | 33114.4i | 0.0881049 | + | 0.00375525i | ||||
\(601\) | 387678.i | 0.0437809i | 0.999760 | + | 0.0218905i | \(0.00696851\pi\) | ||||
−0.999760 | + | 0.0218905i | \(0.993031\pi\) | |||||||
\(602\) | 425408. | + | 761600.i | 0.0478425 | + | 0.0856517i | ||||
\(603\) | − | 7.92704e6i | − | 0.887805i | ||||||
\(604\) | −113363. | + | 184074.i | −0.0126438 | + | 0.0205305i | ||||
\(605\) | − | 4.12309e6i | − | 0.457968i | ||||||
\(606\) | −1.27572e6 | + | 712579.i | −0.141115 | + | 0.0788227i | ||||
\(607\) | −3.69831e6 | −0.407410 | −0.203705 | − | 0.979032i | \(-0.565298\pi\) | ||||
−0.203705 | + | 0.979032i | \(0.565298\pi\) | |||||||
\(608\) | 3.90939e6 | + | 8.23412e6i | 0.428894 | + | 0.903355i | ||||
\(609\) | 237787. | 0.0259803 | ||||||||
\(610\) | 6.07974e6 | − | 3.39596e6i | 0.661546 | − | 0.369521i | ||||
\(611\) | − | 9.72364e6i | − | 1.05372i | ||||||
\(612\) | −865364. | + | 1.40514e6i | −0.0933943 | + | 0.151650i | ||||
\(613\) | − | 2.46872e6i | − | 0.265351i | −0.991160 | − | 0.132675i | \(-0.957643\pi\) | ||
0.991160 | − | 0.132675i | \(-0.0423568\pi\) | |||||||
\(614\) | 5.25796e6 | + | 9.41323e6i | 0.562854 | + | 1.00767i | ||||
\(615\) | 858687.i | 0.0915476i | ||||||||
\(616\) | −352273. | − | 15014.8i | −0.0374049 | − | 0.00159429i | ||||
\(617\) | −6.46330e6 | −0.683504 | −0.341752 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341752 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(618\) | 219558. | + | 393070.i | 0.0231248 | + | 0.0413999i | ||||
\(619\) | 1.08579e6 | 0.113899 | 0.0569494 | − | 0.998377i | \(-0.481863\pi\) | ||||
0.0569494 | + | 0.998377i | \(0.481863\pi\) | |||||||
\(620\) | 2.24804e6 | + | 1.38447e6i | 0.234869 | + | 0.144645i | ||||
\(621\) | −2.66207e6 | −0.277007 | ||||||||
\(622\) | 102800. | + | 184040.i | 0.0106541 | + | 0.0190738i | ||||
\(623\) | −1.99232e6 | −0.205655 | ||||||||
\(624\) | 687817. | − | 346626.i | 0.0707150 | − | 0.0356369i | ||||
\(625\) | 3.47641e6 | 0.355984 | ||||||||
\(626\) | −6.66299e6 | + | 3.72175e6i | −0.679569 | + | 0.379587i | ||||
\(627\) | −129405. | + | 219380.i | −0.0131456 | + | 0.0222858i | ||||
\(628\) | 8.13420e6 | + | 5.00949e6i | 0.823030 | + | 0.506868i | ||||
\(629\) | −1.99909e6 | −0.201468 | ||||||||
\(630\) | −688547. | + | 384603.i | −0.0691166 | + | 0.0386065i | ||||
\(631\) | 4.86063e6i | 0.485981i | 0.970029 | + | 0.242991i | \(0.0781284\pi\) | ||||
−0.970029 | + | 0.242991i | \(0.921872\pi\) | |||||||
\(632\) | −480205. | + | 1.12665e7i | −0.0478226 | + | 1.12200i | ||||
\(633\) | 1.36056e6 | 0.134961 | ||||||||
\(634\) | −3.43470e6 | + | 1.91852e6i | −0.339363 | + | 0.189559i | ||||
\(635\) | 6.61754e6i | 0.651272i | ||||||||
\(636\) | −576400. | − | 354979.i | −0.0565043 | − | 0.0347985i | ||||
\(637\) | −6.86087e6 | −0.669932 | ||||||||
\(638\) | −2.74664e6 | + | 1.53420e6i | −0.267147 | + | 0.149221i | ||||
\(639\) | 7.16655e6 | 0.694318 | ||||||||
\(640\) | 2.05752e6 | + | 4.55580e6i | 0.198562 | + | 0.439658i | ||||
\(641\) | − | 7.52432e6i | − | 0.723306i | −0.932313 | − | 0.361653i | \(-0.882212\pi\) | ||
0.932313 | − | 0.361653i | \(-0.117788\pi\) | |||||||
\(642\) | 566615. | − | 316495.i | 0.0542564 | − | 0.0303060i | ||||
\(643\) | 3.17853e6 | 0.303178 | 0.151589 | − | 0.988444i | \(-0.451561\pi\) | ||||
0.151589 | + | 0.988444i | \(0.451561\pi\) | |||||||
\(644\) | −1.11344e6 | + | 1.80795e6i | −0.105792 | + | 0.171780i | ||||
\(645\) | 345594. | 0.0327089 | ||||||||
\(646\) | 1.91383e6 | + | 45050.8i | 0.180435 | + | 0.00424738i | ||||
\(647\) | − | 1.27831e7i | − | 1.20054i | −0.799798 | − | 0.600269i | \(-0.795060\pi\) | ||
0.799798 | − | 0.600269i | \(-0.204940\pi\) | |||||||
\(648\) | −437220. | + | 1.02580e7i | −0.0409037 | + | 0.959675i | ||||
\(649\) | − | 3.83321e6i | − | 0.357232i | ||||||
\(650\) | 4.97139e6 | − | 2.77687e6i | 0.461524 | − | 0.257794i | ||||
\(651\) | −118175. | −0.0109289 | ||||||||
\(652\) | 3.78795e6 | − | 6.15071e6i | 0.348968 | − | 0.566639i | ||||
\(653\) | 1.25243e7i | 1.14940i | 0.818365 | + | 0.574699i | \(0.194881\pi\) | ||||
−0.818365 | + | 0.574699i | \(0.805119\pi\) | |||||||
\(654\) | −266173. | − | 476525.i | −0.0243343 | − | 0.0435653i | ||||
\(655\) | − | 4.96529e6i | − | 0.452211i | ||||||
\(656\) | 1.62517e7 | − | 8.19004e6i | 1.47448 | − | 0.743064i | ||||
\(657\) | −9.50865e6 | −0.859420 | ||||||||
\(658\) | −2.46612e6 | + | 1.37751e6i | −0.222050 | + | 0.124031i | ||||
\(659\) | 1.95227e7i | 1.75116i | 0.483075 | + | 0.875579i | \(0.339520\pi\) | ||||
−0.483075 | + | 0.875579i | \(0.660480\pi\) | |||||||
\(660\) | −73248.4 | + | 118938.i | −0.00654544 | + | 0.0106282i | ||||
\(661\) | 1.17749e6 | 0.104822 | 0.0524110 | − | 0.998626i | \(-0.483309\pi\) | ||||
0.0524110 | + | 0.998626i | \(0.483309\pi\) | |||||||
\(662\) | 6.34988e6 | + | 1.13681e7i | 0.563146 | + | 1.00819i | ||||
\(663\) | − | 161764.i | − | 0.0142921i | ||||||
\(664\) | −824846. | + | 1.93524e7i | −0.0726027 | + | 1.70339i | ||||
\(665\) | 788031. | + | 464833.i | 0.0691017 | + | 0.0407608i | ||||
\(666\) | −1.10080e7 | + | 6.14873e6i | −0.961660 | + | 0.537155i | ||||
\(667\) | 1.89456e7i | 1.64890i | ||||||||
\(668\) | 9.76119e6 | − | 1.58498e7i | 0.846373 | − | 1.37430i | ||||
\(669\) | − | 635978.i | − | 0.0549385i | ||||||
\(670\) | −4.40286e6 | + | 2.45931e6i | −0.378920 | + | 0.211654i | ||||
\(671\) | − | 4.12412e6i | − | 0.353610i | ||||||
\(672\) | −185352. | − | 125340.i | −0.0158334 | − | 0.0107070i | ||||
\(673\) | 1.92406e7i | 1.63750i | 0.574151 | + | 0.818749i | \(0.305332\pi\) | ||||
−0.574151 | + | 0.818749i | \(0.694668\pi\) | |||||||
\(674\) | 1.02635e7 | + | 1.83746e7i | 0.870256 | + | 1.55800i | ||||
\(675\) | − | 2.07399e6i | − | 0.175205i | ||||||
\(676\) | −3.27284e6 | + | 5.31430e6i | −0.275460 | + | 0.447279i | ||||
\(677\) | −1.22877e7 | −1.03039 | −0.515194 | − | 0.857074i | \(-0.672280\pi\) | ||||
−0.515194 | + | 0.857074i | \(0.672280\pi\) | |||||||
\(678\) | 564765. | − | 315462.i | 0.0471839 | − | 0.0263556i | ||||
\(679\) | −1.64412e6 | −0.136854 | ||||||||
\(680\) | 1.04892e6 | + | 44707.6i | 0.0869902 | + | 0.00370774i | ||||
\(681\) | 934523. | 0.0772187 | ||||||||
\(682\) | 1.36503e6 | − | 762466.i | 0.112378 | − | 0.0627711i | ||||
\(683\) | 2.78444e6i | 0.228395i | 0.993458 | + | 0.114197i | \(0.0364296\pi\) | ||||
−0.993458 | + | 0.114197i | \(0.963570\pi\) | |||||||
\(684\) | 1.06770e7 | − | 5.63842e6i | 0.872591 | − | 0.460805i | ||||
\(685\) | 4.42398e6i | 0.360236i | ||||||||
\(686\) | 1.97154e6 | + | 3.52962e6i | 0.159954 | + | 0.286364i | ||||
\(687\) | −1.65186e6 | −0.133531 | ||||||||
\(688\) | −3.29622e6 | − | 6.54077e6i | −0.265488 | − | 0.526814i | ||||
\(689\) | −4.95704e6 | −0.397809 | ||||||||
\(690\) | 410200. | + | 734373.i | 0.0327999 | + | 0.0587211i | ||||
\(691\) | −5.06792e6 | −0.403771 | −0.201885 | − | 0.979409i | \(-0.564707\pi\) | ||||
−0.201885 | + | 0.979409i | \(0.564707\pi\) | |||||||
\(692\) | −1.05142e7 | + | 1.70726e7i | −0.834665 | + | 1.35529i | ||||
\(693\) | 467068.i | 0.0369443i | ||||||||
\(694\) | 504264. | − | 281667.i | 0.0397429 | − | 0.0221992i | ||||
\(695\) | − | 2.36918e6i | − | 0.186053i | ||||||
\(696\) | −1.99467e6 | − | 85017.8i | −0.156080 | − | 0.00665253i | ||||
\(697\) | − | 3.82213e6i | − | 0.298005i | ||||||
\(698\) | −5.77228e6 | − | 1.03340e7i | −0.448445 | − | 0.802843i | ||||
\(699\) | 2.55109e6i | 0.197485i | ||||||||
\(700\) | −1.40855e6 | − | 867464.i | −0.108649 | − | 0.0669123i | ||||
\(701\) | − | 1.84189e7i | − | 1.41569i | −0.706366 | − | 0.707847i | \(-0.749667\pi\) | ||
0.706366 | − | 0.707847i | \(-0.250333\pi\) | |||||||
\(702\) | −1.00175e6 | − | 1.79342e6i | −0.0767216 | − | 0.137353i | ||||
\(703\) | 1.25984e7 | + | 7.43139e6i | 0.961453 | + | 0.567129i | ||||
\(704\) | 2.94967e6 | + | 251902.i | 0.224306 | + | 0.0191558i | ||||
\(705\) | 1.11906e6i | 0.0847970i | ||||||||
\(706\) | −6.38439e6 | + | 3.56614e6i | −0.482068 | + | 0.269269i | ||||
\(707\) | 3.10848e6 | 0.233883 | ||||||||
\(708\) | 1.27559e6 | − | 2.07125e6i | 0.0956373 | − | 0.155292i | ||||
\(709\) | 1.41054e7i | 1.05383i | 0.849918 | + | 0.526915i | \(0.176651\pi\) | ||||
−0.849918 | + | 0.526915i | \(0.823349\pi\) | |||||||
\(710\) | −2.22337e6 | − | 3.98047e6i | −0.165526 | − | 0.296339i | ||||
\(711\) | 1.49378e7 | 1.10819 | ||||||||
\(712\) | 1.67125e7 | + | 712329.i | 1.23550 | + | 0.0526600i | ||||
\(713\) | − | 9.41560e6i | − | 0.693624i | ||||||
\(714\) | −41026.7 | + | 22916.3i | −0.00301177 | + | 0.00168229i | ||||
\(715\) | 1.02286e6i | 0.0748261i | ||||||||
\(716\) | 1.21529e7 | + | 7.48441e6i | 0.885923 | + | 0.545600i | ||||
\(717\) | 566819. | 0.0411762 | ||||||||
\(718\) | −1.15641e7 | − | 2.07029e7i | −0.837142 | − | 1.49872i | ||||
\(719\) | 3.59772e6i | 0.259540i | 0.991544 | + | 0.129770i | \(0.0414240\pi\) | ||||
−0.991544 | + | 0.129770i | \(0.958576\pi\) | |||||||
\(720\) | 5.91338e6 | − | 2.98005e6i | 0.425113 | − | 0.214236i | ||||
\(721\) | − | 957774.i | − | 0.0686159i | ||||||
\(722\) | −1.18936e7 | − | 7.39835e6i | −0.849125 | − | 0.528192i | ||||
\(723\) | −869844. | −0.0618865 | ||||||||
\(724\) | −1.08263e7 | + | 1.75793e7i | −0.767598 | + | 1.24639i | ||||
\(725\) | −1.47603e7 | −1.04291 | ||||||||
\(726\) | −755629. | − | 1.35279e6i | −0.0532068 | − | 0.0952552i | ||||
\(727\) | 4.42128e6i | 0.310250i | 0.987895 | + | 0.155125i | \(0.0495781\pi\) | ||||
−0.987895 | + | 0.155125i | \(0.950422\pi\) | |||||||
\(728\) | −1.63700e6 | − | 69772.9i | −0.114477 | − | 0.00487931i | ||||
\(729\) | 1.32241e7 | 0.921613 | ||||||||
\(730\) | 2.94999e6 | + | 5.28132e6i | 0.204887 | + | 0.366805i | ||||
\(731\) | −1.53828e6 | −0.106474 | ||||||||
\(732\) | 1.37240e6 | − | 2.22844e6i | 0.0946677 | − | 0.153717i | ||||
\(733\) | 5.89336e6i | 0.405138i | 0.979268 | + | 0.202569i | \(0.0649291\pi\) | ||||
−0.979268 | + | 0.202569i | \(0.935071\pi\) | |||||||
\(734\) | 2.98646e6 | + | 5.34661e6i | 0.204605 | + | 0.366301i | ||||
\(735\) | 789594. | 0.0539120 | ||||||||
\(736\) | 9.98646e6 | − | 1.47679e7i | 0.679543 | − | 1.00490i | ||||
\(737\) | 2.98663e6i | 0.202541i | ||||||||
\(738\) | −1.17560e7 | − | 2.10465e7i | −0.794543 | − | 1.42246i | ||||
\(739\) | 2.27527e7 | 1.53258 | 0.766288 | − | 0.642497i | \(-0.222102\pi\) | ||||
0.766288 | + | 0.642497i | \(0.222102\pi\) | |||||||
\(740\) | 6.83029e6 | + | 4.20647e6i | 0.458522 | + | 0.282383i | ||||
\(741\) | −601337. | + | 1.01945e6i | −0.0402321 | + | 0.0682054i | ||||
\(742\) | 702243. | + | 1.25721e6i | 0.0468250 | + | 0.0838299i | ||||
\(743\) | 341178. | 0.0226730 | 0.0113365 | − | 0.999936i | \(-0.496391\pi\) | ||||
0.0113365 | + | 0.999936i | \(0.496391\pi\) | |||||||
\(744\) | 991312. | + | 42252.2i | 0.0656565 | + | 0.00279845i | ||||
\(745\) | −339272. | −0.0223953 | ||||||||
\(746\) | −1.24190e7 | + | 6.93689e6i | −0.817033 | + | 0.456371i | ||||
\(747\) | 2.56587e7 | 1.68241 | ||||||||
\(748\) | 326039. | − | 529407.i | 0.0213066 | − | 0.0345968i | ||||
\(749\) | −1.38064e6 | −0.0899242 | ||||||||
\(750\) | −1.31782e6 | + | 736096.i | −0.0855466 | + | 0.0477838i | ||||
\(751\) | 6.71971e6 | 0.434761 | 0.217380 | − | 0.976087i | \(-0.430249\pi\) | ||||
0.217380 | + | 0.976087i | \(0.430249\pi\) | |||||||
\(752\) | 2.11795e7 | − | 1.06734e7i | 1.36575 | − | 0.688272i | ||||
\(753\) | − | 1.41283e6i | − | 0.0908035i | ||||||
\(754\) | −1.27635e7 | + | 7.12933e6i | −0.817602 | + | 0.456689i | ||||
\(755\) | − | 182186.i | − | 0.0116318i | ||||||
\(756\) | −312936. | + | 508132.i | −0.0199137 | + | 0.0323350i | ||||
\(757\) | 8.93104e6i | 0.566451i | 0.959053 | + | 0.283226i | \(0.0914045\pi\) | ||||
−0.959053 | + | 0.283226i | \(0.908595\pi\) | |||||||
\(758\) | 7.76021e6 | + | 1.38930e7i | 0.490570 | + | 0.878258i | ||||
\(759\) | 498154. | 0.0313877 | ||||||||
\(760\) | −6.44418e6 | − | 4.18099e6i | −0.404701 | − | 0.262570i | ||||
\(761\) | −1.57336e7 | −0.984839 | −0.492419 | − | 0.870358i | \(-0.663887\pi\) | ||||
−0.492419 | + | 0.870358i | \(0.663887\pi\) | |||||||
\(762\) | 1.21278e6 | + | 2.17122e6i | 0.0756650 | + | 0.135462i | ||||
\(763\) | 1.16112e6i | 0.0722050i | ||||||||
\(764\) | −1.35580e7 | − | 8.34975e6i | −0.840352 | − | 0.517535i | ||||
\(765\) | − | 1.39073e6i | − | 0.0859190i | ||||||
\(766\) | 2.16380e7 | − | 1.20864e7i | 1.33243 | − | 0.744258i | ||||
\(767\) | − | 1.78127e7i | − | 1.09331i | ||||||
\(768\) | 1.51001e6 | + | 1.11768e6i | 0.0923795 | + | 0.0683780i | ||||
\(769\) | 5.08185e6 | 0.309889 | 0.154944 | − | 0.987923i | \(-0.450480\pi\) | ||||
0.154944 | + | 0.987923i | \(0.450480\pi\) | |||||||
\(770\) | 259420. | − | 144905.i | 0.0157680 | − | 0.00880756i | ||||
\(771\) | 1.33260e6 | 0.0807352 | ||||||||
\(772\) | −1.13097e6 | − | 696516.i | −0.0682982 | − | 0.0420618i | ||||
\(773\) | 1.30205e7 | 0.783755 | 0.391877 | − | 0.920017i | \(-0.371826\pi\) | ||||
0.391877 | + | 0.920017i | \(0.371826\pi\) | |||||||
\(774\) | −8.47053e6 | + | 4.73139e6i | −0.508228 | + | 0.283881i | ||||
\(775\) | 7.33556e6 | 0.438712 | ||||||||
\(776\) | 1.37916e7 | + | 587834.i | 0.822170 | + | 0.0350429i | ||||
\(777\) | −359056. | −0.0213358 | ||||||||
\(778\) | 3.85620e6 | + | 6.90369e6i | 0.228408 | + | 0.408914i | ||||
\(779\) | −1.42083e7 | + | 2.40874e7i | −0.838879 | + | 1.42215i | ||||
\(780\) | −340382. | + | 552697.i | −0.0200323 | + | 0.0325275i | ||||
\(781\) | −2.70010e6 | −0.158399 | ||||||||
\(782\) | −1.82585e6 | − | 3.26879e6i | −0.106770 | − | 0.191148i | ||||
\(783\) | 5.32474e6i | 0.310380i | ||||||||
\(784\) | −7.53104e6 | − | 1.49440e7i | −0.437587 | − | 0.868314i | ||||
\(785\) | −8.05078e6 | −0.466298 | ||||||||
\(786\) | −909976. | − | 1.62911e6i | −0.0525380 | − | 0.0940579i | ||||
\(787\) | 5.56173e6i | 0.320091i | 0.987110 | + | 0.160045i | \(0.0511641\pi\) | ||||
−0.987110 | + | 0.160045i | \(0.948836\pi\) | |||||||
\(788\) | −3.81962e6 | − | 2.35233e6i | −0.219131 | − | 0.134953i | ||||
\(789\) | −2.62150e6 | −0.149919 | ||||||||
\(790\) | −4.63436e6 | − | 8.29682e6i | −0.264194 | − | 0.472981i | ||||
\(791\) | −1.37614e6 | −0.0782024 | ||||||||
\(792\) | 166995. | − | 3.91799e6i | 0.00945996 | − | 0.221948i | ||||
\(793\) | − | 1.91646e7i | − | 1.08222i | ||||||
\(794\) | −383865. | − | 687227.i | −0.0216086 | − | 0.0386856i | ||||
\(795\) | 570489. | 0.0320132 | ||||||||
\(796\) | −2.03065e7 | − | 1.25059e7i | −1.13593 | − | 0.699571i | ||||
\(797\) | −2.16448e7 | −1.20700 | −0.603502 | − | 0.797361i | \(-0.706228\pi\) | ||||
−0.603502 | + | 0.797361i | \(0.706228\pi\) | |||||||
\(798\) | 343742. | + | 8091.55i | 0.0191085 | + | 0.000449805i | ||||
\(799\) | − | 4.98109e6i | − | 0.276031i | ||||||
\(800\) | 1.15054e7 | + | 7.78031e6i | 0.635592 | + | 0.429805i | ||||
\(801\) | − | 2.21586e7i | − | 1.22028i | ||||||
\(802\) | −7.98918e6 | − | 1.43029e7i | −0.438597 | − | 0.785213i | ||||
\(803\) | 3.58252e6 | 0.196065 | ||||||||
\(804\) | −993870. | + | 1.61380e6i | −0.0542237 | + | 0.0880462i | ||||
\(805\) | − | 1.78941e6i | − | 0.0973241i | ||||||
\(806\) | 6.34322e6 | − | 3.54314e6i | 0.343932 | − | 0.192110i | ||||
\(807\) | − | 712298.i | − | 0.0385015i | ||||||
\(808\) | −2.60754e7 | − | 1.11140e6i | −1.40508 | − | 0.0598882i | ||||
\(809\) | 2.25215e7 | 1.20983 | 0.604917 | − | 0.796289i | \(-0.293206\pi\) | ||||
0.604917 | + | 0.796289i | \(0.293206\pi\) | |||||||
\(810\) | −4.21953e6 | − | 7.55415e6i | −0.225970 | − | 0.404551i | ||||
\(811\) | − | 8.93759e6i | − | 0.477165i | −0.971122 | − | 0.238582i | \(-0.923317\pi\) | ||
0.971122 | − | 0.238582i | \(-0.0766827\pi\) | |||||||
\(812\) | 3.61630e6 | + | 2.22712e6i | 0.192475 | + | 0.118537i | ||||
\(813\) | 1.83079e6 | 0.0971430 | ||||||||
\(814\) | 4.14741e6 | − | 2.31662e6i | 0.219390 | − | 0.122545i | ||||
\(815\) | 6.08763e6i | 0.321036i | ||||||||
\(816\) | 352345. | − | 177565.i | 0.0185243 | − | 0.00933536i | ||||
\(817\) | 9.69438e6 | + | 5.71839e6i | 0.508118 | + | 0.299722i | ||||
\(818\) | 1.15373e7 | + | 2.06550e7i | 0.602864 | + | 1.07930i | ||||
\(819\) | 2.17044e6i | 0.113068i | ||||||||
\(820\) | −8.04250e6 | + | 1.30591e7i | −0.417692 | + | 0.678231i | ||||
\(821\) | 3.29211e7i | 1.70457i | 0.523074 | + | 0.852287i | \(0.324785\pi\) | ||||
−0.523074 | + | 0.852287i | \(0.675215\pi\) | |||||||
\(822\) | 810772. | + | 1.45151e6i | 0.0418523 | + | 0.0749274i | ||||
\(823\) | − | 6.73875e6i | − | 0.346801i | −0.984851 | − | 0.173400i | \(-0.944525\pi\) | ||
0.984851 | − | 0.173400i | \(-0.0554754\pi\) | |||||||
\(824\) | −342441. | + | 8.03427e6i | −0.0175698 | + | 0.412219i | ||||
\(825\) | 388105.i | 0.0198524i | ||||||||
\(826\) | −4.51769e6 | + | 2.52345e6i | −0.230391 | + | 0.128690i | ||||
\(827\) | − | 2.63122e7i | − | 1.33781i | −0.743349 | − | 0.668904i | \(-0.766764\pi\) | ||
0.743349 | − | 0.668904i | \(-0.233236\pi\) | |||||||
\(828\) | −2.01081e7 | − | 1.23837e7i | −1.01928 | − | 0.627731i | ||||
\(829\) | 5.20905e6 | 0.263252 | 0.131626 | − | 0.991299i | \(-0.457980\pi\) | ||||
0.131626 | + | 0.991299i | \(0.457980\pi\) | |||||||
\(830\) | −7.96043e6 | − | 1.42514e7i | −0.401090 | − | 0.718064i | ||||
\(831\) | 863598. | 0.0433819 | ||||||||
\(832\) | 1.37070e7 | + | 1.17058e6i | 0.686488 | + | 0.0586262i | ||||
\(833\) | −3.51459e6 | −0.175494 | ||||||||
\(834\) | −434194. | − | 777330.i | −0.0216157 | − | 0.0386982i | ||||
\(835\) | 1.56873e7i | 0.778629i | ||||||||
\(836\) | −4.02273e6 | + | 2.12436e6i | −0.199070 | + | 0.105126i | ||||
\(837\) | − | 2.64629e6i | − | 0.130564i | ||||||
\(838\) | −2.63685e7 | + | 1.47287e7i | −1.29710 | + | 0.724525i | ||||
\(839\) | 3.75422e7 | 1.84126 | 0.920630 | − | 0.390437i | \(-0.127676\pi\) | ||||
0.920630 | + | 0.390437i | \(0.127676\pi\) | |||||||
\(840\) | 188396. | + | 8029.92i | 0.00921243 | + | 0.000392657i | ||||
\(841\) | 1.73842e7 | 0.847551 | ||||||||
\(842\) | −2.88446e7 | + | 1.61118e7i | −1.40212 | + | 0.783182i | ||||
\(843\) | −2.46161e6 | −0.119302 | ||||||||
\(844\) | 2.06917e7 | + | 1.27431e7i | 0.999862 | + | 0.615771i | ||||
\(845\) | − | 5.25980e6i | − | 0.253412i | ||||||
\(846\) | −1.53206e7 | − | 2.74283e7i | −0.735955 | − | 1.31757i | ||||
\(847\) | 3.29628e6i | 0.157876i | ||||||||
\(848\) | −5.44125e6 | − | 1.07972e7i | −0.259842 | − | 0.515609i | ||||
\(849\) | 967271.i | 0.0460552i | ||||||||
\(850\) | 2.54667e6 | − | 1.42250e6i | 0.120900 | − | 0.0675311i | ||||
\(851\) | − | 2.86077e7i | − | 1.35413i | ||||||
\(852\) | −1.45898e6 | − | 898522.i | −0.0688574 | − | 0.0424062i | ||||
\(853\) | 4.33902e6i | 0.204183i | 0.994775 | + | 0.102091i | \(0.0325534\pi\) | ||||
−0.994775 | + | 0.102091i | \(0.967447\pi\) | |||||||
\(854\) | −4.86055e6 | + | 2.71496e6i | −0.228055 | + | 0.127385i | ||||
\(855\) | −5.16988e6 | + | 8.76449e6i | −0.241861 | + | 0.410026i | ||||
\(856\) | 1.15815e7 | + | 493632.i | 0.540232 | + | 0.0230260i | ||||
\(857\) | 3.19143e7i | 1.48434i | 0.670213 | + | 0.742169i | \(0.266203\pi\) | ||||
−0.670213 | + | 0.742169i | \(0.733797\pi\) | |||||||
\(858\) | 187458. | + | 335603.i | 0.00869332 | + | 0.0155635i | ||||
\(859\) | 2.97907e7 | 1.37752 | 0.688761 | − | 0.724989i | \(-0.258155\pi\) | ||||
0.688761 | + | 0.724989i | \(0.258155\pi\) | |||||||
\(860\) | 5.25585e6 | + | 3.23685e6i | 0.242324 | + | 0.149237i | ||||
\(861\) | − | 686492.i | − | 0.0315593i | ||||||
\(862\) | 1.57086e7 | − | 8.77437e6i | 0.720061 | − | 0.402205i | ||||
\(863\) | −1.38627e6 | −0.0633609 | −0.0316804 | − | 0.999498i | \(-0.510086\pi\) | ||||
−0.0316804 | + | 0.999498i | \(0.510086\pi\) | |||||||
\(864\) | 2.80673e6 | − | 4.15057e6i | 0.127914 | − | 0.189157i | ||||
\(865\) | − | 1.68975e7i | − | 0.767859i | ||||||
\(866\) | −7.94166e6 | − | 1.42178e7i | −0.359846 | − | 0.644226i | ||||
\(867\) | 2.46098e6i | 0.111189i | ||||||||
\(868\) | −1.79723e6 | − | 1.10684e6i | −0.0809664 | − | 0.0498636i | ||||
\(869\) | −5.62805e6 | −0.252818 | ||||||||
\(870\) | 1.46891e6 | − | 820490.i | 0.0657956 | − | 0.0367515i | ||||
\(871\) | 1.38787e7i | 0.619875i | ||||||||
\(872\) | 415146. | − | 9.74006e6i | 0.0184888 | − | 0.433781i | ||||
\(873\) | − | 1.82859e7i | − | 0.812046i | ||||||
\(874\) | −644693. | + | 2.73876e7i | −0.0285479 | + | 1.21276i | ||||
\(875\) | 3.21106e6 | 0.141784 | ||||||||
\(876\) | 1.93579e6 | + | 1.19217e6i | 0.0852311 | + | 0.0524900i | ||||
\(877\) | 1.65815e6 | 0.0727987 | 0.0363994 | − | 0.999337i | \(-0.488411\pi\) | ||||
0.0363994 | + | 0.999337i | \(0.488411\pi\) | |||||||
\(878\) | −2.24243e7 | + | 1.25255e7i | −0.981707 | + | 0.548353i | ||||
\(879\) | 935698.i | 0.0408473i | ||||||||
\(880\) | −2.22795e6 | + | 1.12278e6i | −0.0969838 | + | 0.0488750i | ||||
\(881\) | −2.95505e7 | −1.28270 | −0.641349 | − | 0.767249i | \(-0.721625\pi\) | ||||
−0.641349 | + | 0.767249i | \(0.721625\pi\) | |||||||
\(882\) | −1.93530e7 | + | 1.08100e7i | −0.837678 | + | 0.467903i | ||||
\(883\) | −1.95346e7 | −0.843146 | −0.421573 | − | 0.906794i | \(-0.638522\pi\) | ||||
−0.421573 | + | 0.906794i | \(0.638522\pi\) | |||||||
\(884\) | 1.51508e6 | − | 2.46013e6i | 0.0652088 | − | 0.105883i | ||||
\(885\) | 2.05000e6i | 0.0879825i | ||||||||
\(886\) | 1.77125e7 | − | 9.89367e6i | 0.758044 | − | 0.423422i | ||||
\(887\) | 1.11186e7 | 0.474506 | 0.237253 | − | 0.971448i | \(-0.423753\pi\) | ||||
0.237253 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(888\) | 3.01193e6 | + | 128376.i | 0.128178 | + | 0.00546326i | ||||
\(889\) | − | 5.29051e6i | − | 0.224514i | ||||||
\(890\) | −1.23074e7 | + | 6.87455e6i | −0.520824 | + | 0.290917i | ||||
\(891\) | −5.12427e6 | −0.216241 | ||||||||
\(892\) | 5.95660e6 | − | 9.67207e6i | 0.250661 | − | 0.407012i | ||||
\(893\) | −1.85166e7 | + | 3.13912e7i | −0.777021 | + | 1.31728i | ||||
\(894\) | −111315. | + | 62177.6i | −0.00465813 | + | 0.00260190i | ||||
\(895\) | −1.20282e7 | −0.501931 | ||||||||
\(896\) | −1.64492e6 | − | 3.64221e6i | −0.0684503 | − | 0.151564i | ||||
\(897\) | 2.31489e6 | 0.0960617 | ||||||||
\(898\) | −7.68543e6 | − | 1.37591e7i | −0.318037 | − | 0.569376i | ||||
\(899\) | −1.88333e7 | −0.777189 | ||||||||
\(900\) | 9.64795e6 | − | 1.56659e7i | 0.397035 | − | 0.644688i | ||||
\(901\) | −2.53932e6 | −0.104209 | ||||||||
\(902\) | 4.42923e6 | + | 7.92958e6i | 0.181264 | + | 0.324514i | ||||
\(903\) | −276291. | −0.0112758 | ||||||||
\(904\) | 1.15437e7 | + | 492020.i | 0.469811 | + | 0.0200245i | ||||
\(905\) | − | 1.73990e7i | − | 0.706160i | ||||||
\(906\) | −33388.8 | − | 59775.3i | −0.00135139 | − | 0.00241936i | ||||
\(907\) | − | 2.35927e7i | − | 0.952270i | −0.879372 | − | 0.476135i | \(-0.842037\pi\) | ||
0.879372 | − | 0.476135i | \(-0.157963\pi\) | |||||||
\(908\) | 1.42124e7 | + | 8.75279e6i | 0.572075 | + | 0.352315i | ||||
\(909\) | 3.45725e7i | 1.38778i | ||||||||
\(910\) | 1.20551e6 | − | 673365.i | 0.0482579 | − | 0.0269555i | ||||
\(911\) | 3.38240e7 | 1.35030 | 0.675148 | − | 0.737682i | \(-0.264080\pi\) | ||||
0.675148 | + | 0.737682i | \(0.264080\pi\) | |||||||
\(912\) | −2.88058e6 | − | 190777.i | −0.114681 | − | 0.00759518i | ||||
\(913\) | −9.66729e6 | −0.383820 | ||||||||
\(914\) | −2.97063e7 | + | 1.65931e7i | −1.17621 | + | 0.656995i | ||||
\(915\) | 2.20558e6i | 0.0870905i | ||||||||
\(916\) | −2.51218e7 | − | 1.54714e7i | −0.989262 | − | 0.609243i | ||||
\(917\) | 3.96958e6i | 0.155891i | ||||||||
\(918\) | −513164. | − | 918708.i | −0.0200978 | − | 0.0359808i | ||||
\(919\) | 5.37265e6i | 0.209845i | 0.994480 | + | 0.104923i | \(0.0334595\pi\) | ||||
−0.994480 | + | 0.104923i | \(0.966540\pi\) | |||||||
\(920\) | −639782. | + | 1.50104e7i | −0.0249208 | + | 0.584687i | ||||
\(921\) | −3.41490e6 | −0.132656 | ||||||||
\(922\) | −1.51665e7 | − | 2.71524e7i | −0.587569 | − | 1.05191i | ||||
\(923\) | −1.25472e7 | −0.484779 | ||||||||
\(924\) | 58559.7 | − | 95086.7i | 0.00225641 | − | 0.00366387i | ||||
\(925\) | 2.22879e7 | 0.856474 | ||||||||
\(926\) | −1.87673e7 | − | 3.35988e7i | −0.719242 | − | 1.28765i | ||||
\(927\) | 1.06524e7 | 0.407143 | ||||||||
\(928\) | −2.95390e7 | − | 1.99751e7i | −1.12597 | − | 0.761412i | ||||
\(929\) | −1.92859e7 | −0.733164 | −0.366582 | − | 0.930386i | \(-0.619472\pi\) | ||||
−0.366582 | + | 0.930386i | \(0.619472\pi\) | |||||||
\(930\) | −730020. | + | 407768.i | −0.0276775 | + | 0.0154599i | ||||
\(931\) | 2.21492e7 | + | 1.30651e7i | 0.837498 | + | 0.494012i | ||||
\(932\) | −2.38937e7 | + | 3.87975e7i | −0.901038 | + | 1.46307i | ||||
\(933\) | −66765.5 | −0.00251101 | ||||||||
\(934\) | 1.93794e7 | − | 1.08247e7i | 0.726896 | − | 0.406023i | ||||
\(935\) | 523978.i | 0.0196013i | ||||||||
\(936\) | 776015. | − | 1.82067e7i | 0.0289521 | − | 0.679269i | ||||
\(937\) | 1.41288e7 | 0.525721 | 0.262861 | − | 0.964834i | \(-0.415334\pi\) | ||||
0.262861 | + | 0.964834i | \(0.415334\pi\) | |||||||
\(938\) | 3.51994e6 | − | 1.96614e6i | 0.130626 | − | 0.0729637i | ||||
\(939\) | − | 2.41717e6i | − | 0.0894631i | ||||||
\(940\) | −1.04812e7 | + | 1.70189e7i | −0.386892 | + | 0.628219i | ||||
\(941\) | −2.19479e7 | −0.808012 | −0.404006 | − | 0.914756i | \(-0.632383\pi\) | ||||
−0.404006 | + | 0.914756i | \(0.632383\pi\) | |||||||
\(942\) | −2.64147e6 | + | 1.47545e6i | −0.0969880 | + | 0.0541747i | ||||
\(943\) | 5.46961e7 | 2.00298 | ||||||||
\(944\) | 3.87988e7 | − | 1.95527e7i | 1.41706 | − | 0.714128i | ||||
\(945\) | − | 502921.i | − | 0.0183198i | ||||||
\(946\) | 3.19140e6 | − | 1.78262e6i | 0.115945 | − | 0.0647637i | ||||
\(947\) | −8.42285e6 | −0.305200 | −0.152600 | − | 0.988288i | \(-0.548765\pi\) | ||||
−0.152600 | + | 0.988288i | \(0.548765\pi\) | |||||||
\(948\) | −3.04108e6 | − | 1.87286e6i | −0.109902 | − | 0.0676839i | ||||
\(949\) | 1.66478e7 | 0.600055 | ||||||||
\(950\) | −2.13373e7 | − | 502271.i | −0.767062 | − | 0.0180563i | ||||
\(951\) | − | 1.24603e6i | − | 0.0446762i | ||||||
\(952\) | −838577. | − | 35742.2i | −0.0299882 | − | 0.00127817i | ||||
\(953\) | − | 4.19088e7i | − | 1.49477i | −0.664394 | − | 0.747383i | \(-0.731310\pi\) | ||
0.664394 | − | 0.747383i | \(-0.268690\pi\) | |||||||
\(954\) | −1.39827e7 | + | 7.81036e6i | −0.497418 | + | 0.277843i | ||||
\(955\) | 1.34189e7 | 0.476112 | ||||||||
\(956\) | 8.62028e6 | + | 5.30885e6i | 0.305054 | + | 0.187869i | ||||
\(957\) | − | 996418.i | − | 0.0351691i | ||||||
\(958\) | 1.17326e7 | + | 2.10046e7i | 0.413027 | + | 0.739436i | ||||
\(959\) | − | 3.53682e6i | − | 0.124184i | ||||||
\(960\) | −1.57749e6 | − | 134718.i | −0.0552444 | − | 0.00471788i | ||||
\(961\) | −1.92694e7 | −0.673068 | ||||||||
\(962\) | 1.92728e7 | − | 1.07652e7i | 0.671440 | − | 0.375047i | ||||
\(963\) | − | 1.53555e7i | − | 0.533580i | ||||||
\(964\) | −1.32287e7 | − | 8.14700e6i | −0.458486 | − | 0.282361i | ||||
\(965\) | 1.11937e6 | 0.0386952 | ||||||||
\(966\) | −327941. | − | 587107.i | −0.0113071 | − | 0.0202430i | ||||
\(967\) | − | 1.10867e7i | − | 0.381272i | −0.981661 | − | 0.190636i | \(-0.938945\pi\) | ||
0.981661 | − | 0.190636i | \(-0.0610550\pi\) | |||||||
\(968\) | 1.17854e6 | − | 2.76507e7i | 0.0404257 | − | 0.948459i | ||||
\(969\) | −308044. | + | 522227.i | −0.0105391 | + | 0.0178669i | ||||
\(970\) | −1.01564e7 | + | 5.67307e6i | −0.346586 | + | 0.193593i | ||||
\(971\) | 2.03318e7i | 0.692035i | 0.938228 | + | 0.346018i | \(0.112466\pi\) | ||||
−0.938228 | + | 0.346018i | \(0.887534\pi\) | |||||||
\(972\) | −8.49597e6 | − | 5.23229e6i | −0.288435 | − | 0.177634i | ||||
\(973\) | 1.89408e6i | 0.0641382i | ||||||||
\(974\) | 5.04647e7 | − | 2.81881e7i | 1.70447 | − | 0.952069i | ||||
\(975\) | 1.80350e6i | 0.0607582i | ||||||||
\(976\) | 4.17433e7 | − | 2.10366e7i | 1.40269 | − | 0.706887i | ||||
\(977\) | 1.13639e7i | 0.380884i | 0.981698 | + | 0.190442i | \(0.0609921\pi\) | ||||
−0.981698 | + | 0.190442i | \(0.939008\pi\) | |||||||
\(978\) | 1.11567e6 | + | 1.99736e6i | 0.0372981 | + | 0.0667742i | ||||
\(979\) | 8.34858e6i | 0.278391i | ||||||||
\(980\) | 1.20083e7 | + | 7.39537e6i | 0.399407 | + | 0.245977i | ||||
\(981\) | −1.29140e7 | −0.428439 | ||||||||
\(982\) | −1.64128e7 | + | 9.16772e6i | −0.543130 | + | 0.303377i | ||||
\(983\) | −3.96913e7 | −1.31012 | −0.655060 | − | 0.755577i | \(-0.727357\pi\) | ||||
−0.655060 | + | 0.755577i | \(0.727357\pi\) | |||||||
\(984\) | −245447. | + | 5.75862e6i | −0.00808109 | + | 0.189597i | ||||
\(985\) | 3.78045e6 | 0.124152 | ||||||||
\(986\) | −6.53831e6 | + | 3.65211e6i | −0.214177 | + | 0.119633i | ||||
\(987\) | − | 894651.i | − | 0.0292322i | ||||||
\(988\) | −1.86934e7 | + | 9.87177e6i | −0.609252 | + | 0.321738i | ||||
\(989\) | − | 2.20134e7i | − | 0.715643i | ||||||
\(990\) | 1.61163e6 | + | 2.88528e6i | 0.0522610 | + | 0.0935620i | ||||
\(991\) | −5.69524e7 | −1.84216 | −0.921081 | − | 0.389372i | \(-0.872692\pi\) | ||||
−0.921081 | + | 0.389372i | \(0.872692\pi\) | |||||||
\(992\) | 1.46803e7 | + | 9.92725e6i | 0.473649 | + | 0.320295i | ||||
\(993\) | −4.12407e6 | −0.132725 | ||||||||
\(994\) | 1.77751e6 | + | 3.18225e6i | 0.0570620 | + | 0.102157i | ||||
\(995\) | 2.00983e7 | 0.643578 | ||||||||
\(996\) | −5.22365e6 | − | 3.21701e6i | −0.166850 | − | 0.102755i | ||||
\(997\) | − | 1.02156e7i | − | 0.325483i | −0.986669 | − | 0.162741i | \(-0.947966\pi\) | ||
0.986669 | − | 0.162741i | \(-0.0520336\pi\) | |||||||
\(998\) | 2.72878e7 | − | 1.52422e7i | 0.867246 | − | 0.484418i | ||||
\(999\) | − | 8.04031e6i | − | 0.254894i |
(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 | 152.6.b.b.75.16 | yes | 96 | |
4.3 | odd | 2 | 608.6.b.b.303.52 | 96 | |||
8.3 | odd | 2 | inner | 152.6.b.b.75.82 | yes | 96 | |
8.5 | even | 2 | 608.6.b.b.303.51 | 96 | |||
19.18 | odd | 2 | inner | 152.6.b.b.75.81 | yes | 96 | |
76.75 | even | 2 | 608.6.b.b.303.46 | 96 | |||
152.37 | odd | 2 | 608.6.b.b.303.45 | 96 | |||
152.75 | even | 2 | inner | 152.6.b.b.75.15 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.6.b.b.75.15 | ✓ | 96 | 152.75 | even | 2 | inner | |
152.6.b.b.75.16 | yes | 96 | 1.1 | even | 1 | trivial | |
152.6.b.b.75.81 | yes | 96 | 19.18 | odd | 2 | inner | |
152.6.b.b.75.82 | yes | 96 | 8.3 | odd | 2 | inner | |
608.6.b.b.303.45 | 96 | 152.37 | odd | 2 | |||
608.6.b.b.303.46 | 96 | 76.75 | even | 2 | |||
608.6.b.b.303.51 | 96 | 8.5 | even | 2 | |||
608.6.b.b.303.52 | 96 | 4.3 | odd | 2 |