Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 61.8 | ||
Character | \(\chi\) | \(=\) | 80.61 |
Dual form | 80.6.l.a.21.8 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.51701 | − | 3.40538i | −0.798502 | − | 0.601992i | ||||
\(3\) | −7.38373 | − | 7.38373i | −0.473666 | − | 0.473666i | 0.429433 | − | 0.903099i | \(-0.358714\pi\) |
−0.903099 | + | 0.429433i | \(0.858714\pi\) | |||||||
\(4\) | 8.80677 | + | 30.7643i | 0.275211 | + | 0.961384i | ||||
\(5\) | 17.6777 | − | 17.6777i | 0.316228 | − | 0.316228i | ||||
\(6\) | 8.20797 | + | 58.4968i | 0.0930803 | + | 0.663367i | ||||
\(7\) | 74.1496i | 0.571958i | 0.958236 | + | 0.285979i | \(0.0923187\pi\) | ||||
−0.958236 | + | 0.285979i | \(0.907681\pi\) | |||||||
\(8\) | 64.9838 | − | 168.953i | 0.358988 | − | 0.933342i | ||||
\(9\) | − | 133.961i | − | 0.551280i | ||||||
\(10\) | −140.049 | + | 19.6510i | −0.442875 | + | 0.0621420i | ||||
\(11\) | 383.330 | − | 383.330i | 0.955193 | − | 0.955193i | −0.0438453 | − | 0.999038i | \(-0.513961\pi\) |
0.999038 | + | 0.0438453i | \(0.0139609\pi\) | |||||||
\(12\) | 162.128 | − | 292.182i | 0.325017 | − | 0.585734i | ||||
\(13\) | 289.013 | + | 289.013i | 0.474306 | + | 0.474306i | 0.903305 | − | 0.428999i | \(-0.141134\pi\) |
−0.428999 | + | 0.903305i | \(0.641134\pi\) | |||||||
\(14\) | 252.508 | − | 334.935i | 0.344314 | − | 0.456710i | ||||
\(15\) | −261.054 | −0.299573 | ||||||||
\(16\) | −868.882 | + | 541.868i | −0.848517 | + | 0.529168i | ||||
\(17\) | −206.336 | −0.173162 | −0.0865811 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865811 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(18\) | −456.188 | + | 605.104i | −0.331866 | + | 0.440198i | ||||
\(19\) | −1954.83 | − | 1954.83i | −1.24230 | − | 1.24230i | −0.959045 | − | 0.283254i | \(-0.908586\pi\) |
−0.283254 | − | 0.959045i | \(-0.591414\pi\) | |||||||
\(20\) | 699.524 | + | 388.158i | 0.391046 | + | 0.216987i | ||||
\(21\) | 547.501 | − | 547.501i | 0.270917 | − | 0.270917i | ||||
\(22\) | −3036.89 | + | 426.121i | −1.33774 | + | 0.187705i | ||||
\(23\) | 1865.72i | 0.735404i | 0.929944 | + | 0.367702i | \(0.119855\pi\) | ||||
−0.929944 | + | 0.367702i | \(0.880145\pi\) | |||||||
\(24\) | −1727.33 | + | 767.680i | −0.612134 | + | 0.272052i | ||||
\(25\) | − | 625.000i | − | 0.200000i | ||||||
\(26\) | −321.275 | − | 2289.67i | −0.0932060 | − | 0.664262i | ||||
\(27\) | −2783.38 | + | 2783.38i | −0.734789 | + | 0.734789i | ||||
\(28\) | −2281.16 | + | 653.019i | −0.549871 | + | 0.157409i | ||||
\(29\) | −2041.63 | − | 2041.63i | −0.450799 | − | 0.450799i | 0.444821 | − | 0.895620i | \(-0.353267\pi\) |
−0.895620 | + | 0.444821i | \(0.853267\pi\) | |||||||
\(30\) | 1179.18 | + | 888.989i | 0.239210 | + | 0.180341i | ||||
\(31\) | −9379.23 | −1.75292 | −0.876462 | − | 0.481471i | \(-0.840102\pi\) | ||||
−0.876462 | + | 0.481471i | \(0.840102\pi\) | |||||||
\(32\) | 5770.01 | + | 511.251i | 0.996098 | + | 0.0882590i | ||||
\(33\) | −5660.81 | −0.904886 | ||||||||
\(34\) | 932.022 | + | 702.653i | 0.138270 | + | 0.104242i | ||||
\(35\) | 1310.79 | + | 1310.79i | 0.180869 | + | 0.180869i | ||||
\(36\) | 4121.22 | − | 1179.76i | 0.529992 | − | 0.151719i | ||||
\(37\) | 444.563 | − | 444.563i | 0.0533862 | − | 0.0533862i | −0.679910 | − | 0.733296i | \(-0.737981\pi\) |
0.733296 | + | 0.679910i | \(0.237981\pi\) | |||||||
\(38\) | 2173.05 | + | 15487.0i | 0.244124 | + | 1.73983i | ||||
\(39\) | − | 4267.98i | − | 0.449325i | ||||||
\(40\) | −1837.93 | − | 4135.46i | −0.181627 | − | 0.408671i | ||||
\(41\) | − | 20896.8i | − | 1.94142i | −0.240247 | − | 0.970712i | \(-0.577228\pi\) | ||
0.240247 | − | 0.970712i | \(-0.422772\pi\) | |||||||
\(42\) | −4337.52 | + | 608.618i | −0.379418 | + | 0.0532380i | ||||
\(43\) | 6084.75 | − | 6084.75i | 0.501847 | − | 0.501847i | −0.410165 | − | 0.912012i | \(-0.634529\pi\) |
0.912012 | + | 0.410165i | \(0.134529\pi\) | |||||||
\(44\) | 15168.8 | + | 8416.97i | 1.18119 | + | 0.655427i | ||||
\(45\) | −2368.12 | − | 2368.12i | −0.174330 | − | 0.174330i | ||||
\(46\) | 6353.47 | − | 8427.46i | 0.442707 | − | 0.587222i | ||||
\(47\) | −20403.6 | −1.34729 | −0.673647 | − | 0.739053i | \(-0.735273\pi\) | ||||
−0.673647 | + | 0.739053i | \(0.735273\pi\) | |||||||
\(48\) | 10416.6 | + | 2414.58i | 0.652563 | + | 0.151265i | ||||
\(49\) | 11308.8 | 0.672864 | ||||||||
\(50\) | −2128.36 | + | 2823.13i | −0.120398 | + | 0.159700i | ||||
\(51\) | 1523.53 | + | 1523.53i | 0.0820211 | + | 0.0820211i | ||||
\(52\) | −6346.00 | + | 11436.5i | −0.325455 | + | 0.586524i | ||||
\(53\) | 6314.88 | − | 6314.88i | 0.308799 | − | 0.308799i | −0.535645 | − | 0.844443i | \(-0.679931\pi\) |
0.844443 | + | 0.535645i | \(0.179931\pi\) | |||||||
\(54\) | 22051.0 | − | 3094.09i | 1.02907 | − | 0.144394i | ||||
\(55\) | − | 13552.8i | − | 0.604117i | ||||||
\(56\) | 12527.8 | + | 4818.53i | 0.533832 | + | 0.205326i | ||||
\(57\) | 28867.9i | 1.17687i | ||||||||
\(58\) | 2269.54 | + | 16174.6i | 0.0885866 | + | 0.631341i | ||||
\(59\) | −7624.90 | + | 7624.90i | −0.285170 | + | 0.285170i | −0.835167 | − | 0.549997i | \(-0.814629\pi\) |
0.549997 | + | 0.835167i | \(0.314629\pi\) | |||||||
\(60\) | −2299.04 | − | 8031.15i | −0.0824459 | − | 0.288005i | ||||
\(61\) | 14421.3 | + | 14421.3i | 0.496225 | + | 0.496225i | 0.910261 | − | 0.414036i | \(-0.135881\pi\) |
−0.414036 | + | 0.910261i | \(0.635881\pi\) | |||||||
\(62\) | 42366.1 | + | 31939.8i | 1.39971 | + | 1.05525i | ||||
\(63\) | 9933.17 | 0.315309 | ||||||||
\(64\) | −24322.2 | − | 21958.4i | −0.742255 | − | 0.670118i | ||||
\(65\) | 10218.1 | 0.299977 | ||||||||
\(66\) | 25569.9 | + | 19277.2i | 0.722553 | + | 0.544734i | ||||
\(67\) | −20777.0 | − | 20777.0i | −0.565452 | − | 0.565452i | 0.365399 | − | 0.930851i | \(-0.380933\pi\) |
−0.930851 | + | 0.365399i | \(0.880933\pi\) | |||||||
\(68\) | −1817.15 | − | 6347.78i | −0.0476562 | − | 0.166475i | ||||
\(69\) | 13775.9 | − | 13775.9i | 0.348336 | − | 0.348336i | ||||
\(70\) | −1457.12 | − | 10384.6i | −0.0355426 | − | 0.253306i | ||||
\(71\) | − | 5076.70i | − | 0.119519i | −0.998213 | − | 0.0597593i | \(-0.980967\pi\) | ||
0.998213 | − | 0.0597593i | \(-0.0190333\pi\) | |||||||
\(72\) | −22633.1 | − | 8705.30i | −0.514533 | − | 0.197903i | ||||
\(73\) | − | 69584.3i | − | 1.52828i | −0.645048 | − | 0.764142i | \(-0.723162\pi\) | ||
0.645048 | − | 0.764142i | \(-0.276838\pi\) | |||||||
\(74\) | −3522.00 | + | 494.190i | −0.0747671 | + | 0.0104909i | ||||
\(75\) | −4614.83 | + | 4614.83i | −0.0947333 | + | 0.0947333i | ||||
\(76\) | 42923.3 | − | 77354.9i | 0.852431 | − | 1.53622i | ||||
\(77\) | 28423.8 | + | 28423.8i | 0.546330 | + | 0.546330i | ||||
\(78\) | −14534.1 | + | 19278.5i | −0.270490 | + | 0.358787i | ||||
\(79\) | −24659.6 | −0.444547 | −0.222274 | − | 0.974984i | \(-0.571348\pi\) | ||||
−0.222274 | + | 0.974984i | \(0.571348\pi\) | |||||||
\(80\) | −5780.85 | + | 24938.8i | −0.100987 | + | 0.435662i | ||||
\(81\) | 8550.88 | 0.144810 | ||||||||
\(82\) | −71161.6 | + | 94391.1i | −1.16872 | + | 1.55023i | ||||
\(83\) | 6046.41 | + | 6046.41i | 0.0963391 | + | 0.0963391i | 0.753634 | − | 0.657295i | \(-0.228299\pi\) |
−0.657295 | + | 0.753634i | \(0.728299\pi\) | |||||||
\(84\) | 21665.2 | + | 12021.8i | 0.335015 | + | 0.185896i | ||||
\(85\) | −3647.54 | + | 3647.54i | −0.0547587 | + | 0.0547587i | ||||
\(86\) | −48205.7 | + | 6763.99i | −0.702834 | + | 0.0986181i | ||||
\(87\) | 30149.7i | 0.427057i | ||||||||
\(88\) | −39854.5 | − | 89675.0i | −0.548619 | − | 1.23442i | ||||
\(89\) | 9618.79i | 0.128720i | 0.997927 | + | 0.0643599i | \(0.0205006\pi\) | ||||
−0.997927 | + | 0.0643599i | \(0.979499\pi\) | |||||||
\(90\) | 2632.47 | + | 18761.2i | 0.0342577 | + | 0.244148i | ||||
\(91\) | −21430.2 | + | 21430.2i | −0.271283 | + | 0.271283i | ||||
\(92\) | −57397.4 | + | 16430.9i | −0.707005 | + | 0.202392i | ||||
\(93\) | 69253.7 | + | 69253.7i | 0.830301 | + | 0.830301i | ||||
\(94\) | 92163.3 | + | 69482.0i | 1.07582 | + | 0.811060i | ||||
\(95\) | −69113.9 | −0.785699 | ||||||||
\(96\) | −38829.3 | − | 46379.2i | −0.430013 | − | 0.513623i | ||||
\(97\) | −108651. | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(98\) | −51082.1 | − | 38510.9i | −0.537284 | − | 0.405059i | ||||
\(99\) | −51351.3 | − | 51351.3i | −0.526579 | − | 0.526579i | ||||
\(100\) | 19227.7 | − | 5504.23i | 0.192277 | − | 0.0550423i | ||||
\(101\) | −10122.4 | + | 10122.4i | −0.0987372 | + | 0.0987372i | −0.754750 | − | 0.656013i | \(-0.772242\pi\) |
0.656013 | + | 0.754750i | \(0.272242\pi\) | |||||||
\(102\) | −1693.60 | − | 12070.0i | −0.0161180 | − | 0.114870i | ||||
\(103\) | − | 111553.i | − | 1.03607i | −0.855360 | − | 0.518034i | \(-0.826664\pi\) | ||
0.855360 | − | 0.518034i | \(-0.173336\pi\) | |||||||
\(104\) | 67610.7 | − | 30048.4i | 0.612960 | − | 0.272419i | ||||
\(105\) | − | 19357.1i | − | 0.171343i | ||||||
\(106\) | −50028.9 | + | 7019.81i | −0.432471 | + | 0.0606821i | ||||
\(107\) | −129912. | + | 129912.i | −1.09696 | + | 1.09696i | −0.102194 | + | 0.994764i | \(0.532586\pi\) |
−0.994764 | + | 0.102194i | \(0.967414\pi\) | |||||||
\(108\) | −110141. | − | 61116.1i | −0.908637 | − | 0.504192i | ||||
\(109\) | 107123. | + | 107123.i | 0.863606 | + | 0.863606i | 0.991755 | − | 0.128149i | \(-0.0409034\pi\) |
−0.128149 | + | 0.991755i | \(0.540903\pi\) | |||||||
\(110\) | −46152.3 | + | 61218.0i | −0.363674 | + | 0.482389i | ||||
\(111\) | −6565.07 | −0.0505745 | ||||||||
\(112\) | −40179.3 | − | 64427.3i | −0.302662 | − | 0.485316i | ||||
\(113\) | 257827. | 1.89947 | 0.949735 | − | 0.313056i | \(-0.101353\pi\) | ||||
0.949735 | + | 0.313056i | \(0.101353\pi\) | |||||||
\(114\) | 98306.3 | − | 130397.i | 0.708467 | − | 0.939734i | ||||
\(115\) | 32981.5 | + | 32981.5i | 0.232555 | + | 0.232555i | ||||
\(116\) | 44829.2 | − | 80789.6i | 0.309326 | − | 0.557456i | ||||
\(117\) | 38716.4 | − | 38716.4i | 0.261475 | − | 0.261475i | ||||
\(118\) | 60407.5 | − | 8476.07i | 0.399379 | − | 0.0560389i | ||||
\(119\) | − | 15299.8i | − | 0.0990414i | ||||||
\(120\) | −16964.3 | + | 44105.9i | −0.107543 | + | 0.279604i | ||||
\(121\) | − | 132833.i | − | 0.824787i | ||||||
\(122\) | −16031.1 | − | 114251.i | −0.0975133 | − | 0.694960i | ||||
\(123\) | −154296. | + | 154296.i | −0.919587 | + | 0.919587i | ||||
\(124\) | −82600.7 | − | 288545.i | −0.482425 | − | 1.68523i | ||||
\(125\) | −11048.5 | − | 11048.5i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −44868.2 | − | 33826.2i | −0.251775 | − | 0.189813i | ||||
\(127\) | 79411.2 | 0.436890 | 0.218445 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218445 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(128\) | 35086.9 | + | 182013.i | 0.189287 | + | 0.981922i | ||||
\(129\) | −89856.2 | −0.475416 | ||||||||
\(130\) | −46155.4 | − | 34796.6i | −0.239533 | − | 0.180584i | ||||
\(131\) | 121642. | + | 121642.i | 0.619305 | + | 0.619305i | 0.945353 | − | 0.326048i | \(-0.105717\pi\) |
−0.326048 | + | 0.945353i | \(0.605717\pi\) | |||||||
\(132\) | −49853.4 | − | 174151.i | −0.249035 | − | 0.869942i | ||||
\(133\) | 144950. | − | 144950.i | 0.710543 | − | 0.710543i | ||||
\(134\) | 23096.3 | + | 164604.i | 0.111117 | + | 0.791913i | ||||
\(135\) | 98407.3i | 0.464722i | ||||||||
\(136\) | −13408.5 | + | 34861.1i | −0.0621632 | + | 0.161620i | ||||
\(137\) | 207918.i | 0.946437i | 0.880945 | + | 0.473218i | \(0.156908\pi\) | ||||
−0.880945 | + | 0.473218i | \(0.843092\pi\) | |||||||
\(138\) | −109138. | + | 15313.8i | −0.487843 | + | 0.0684516i | ||||
\(139\) | 53972.3 | − | 53972.3i | 0.236938 | − | 0.236938i | −0.578643 | − | 0.815581i | \(-0.696418\pi\) |
0.815581 | + | 0.578643i | \(0.196418\pi\) | |||||||
\(140\) | −28781.8 | + | 51869.5i | −0.124107 | + | 0.223662i | ||||
\(141\) | 150655. | + | 150655.i | 0.638168 | + | 0.638168i | ||||
\(142\) | −17288.1 | + | 22931.5i | −0.0719492 | + | 0.0954358i | ||||
\(143\) | 221574. | 0.906107 | ||||||||
\(144\) | 72589.2 | + | 116396.i | 0.291720 | + | 0.467771i | ||||
\(145\) | −72182.6 | −0.285110 | ||||||||
\(146\) | −236961. | + | 314313.i | −0.920015 | + | 1.22034i | ||||
\(147\) | −83501.3 | − | 83501.3i | −0.318713 | − | 0.318713i | ||||
\(148\) | 17591.8 | + | 9761.50i | 0.0660171 | + | 0.0366321i | ||||
\(149\) | 192403. | − | 192403.i | 0.709979 | − | 0.709979i | −0.256551 | − | 0.966531i | \(-0.582586\pi\) |
0.966531 | + | 0.256551i | \(0.0825863\pi\) | |||||||
\(150\) | 36560.5 | − | 5129.98i | 0.132673 | − | 0.0186161i | ||||
\(151\) | 113085.i | 0.403611i | 0.979426 | + | 0.201805i | \(0.0646809\pi\) | ||||
−0.979426 | + | 0.201805i | \(0.935319\pi\) | |||||||
\(152\) | −457308. | + | 203243.i | −1.60546 | + | 0.713519i | ||||
\(153\) | 27641.0i | 0.0954609i | ||||||||
\(154\) | −31596.7 | − | 225184.i | −0.107359 | − | 0.765132i | ||||
\(155\) | −165803. | + | 165803.i | −0.554323 | + | 0.554323i | ||||
\(156\) | 131301. | − | 37587.1i | 0.431974 | − | 0.123660i | ||||
\(157\) | 101388. | + | 101388.i | 0.328276 | + | 0.328276i | 0.851931 | − | 0.523655i | \(-0.175432\pi\) |
−0.523655 | + | 0.851931i | \(0.675432\pi\) | |||||||
\(158\) | 111388. | + | 83975.3i | 0.354972 | + | 0.267614i | ||||
\(159\) | −93254.7 | −0.292535 | ||||||||
\(160\) | 111038. | − | 92962.7i | 0.342904 | − | 0.287084i | ||||
\(161\) | −138342. | −0.420620 | ||||||||
\(162\) | −38624.4 | − | 29119.0i | −0.115631 | − | 0.0871744i | ||||
\(163\) | 150058. | + | 150058.i | 0.442373 | + | 0.442373i | 0.892809 | − | 0.450435i | \(-0.148731\pi\) |
−0.450435 | + | 0.892809i | \(0.648731\pi\) | |||||||
\(164\) | 642875. | − | 184033.i | 1.86645 | − | 0.534302i | ||||
\(165\) | −100070. | + | 100070.i | −0.286150 | + | 0.286150i | ||||
\(166\) | −6721.37 | − | 47902.1i | −0.0189316 | − | 0.134922i | ||||
\(167\) | − | 585530.i | − | 1.62464i | −0.583210 | − | 0.812322i | \(-0.698203\pi\) | ||
0.583210 | − | 0.812322i | \(-0.301797\pi\) | |||||||
\(168\) | −56923.2 | − | 128081.i | −0.155602 | − | 0.350115i | ||||
\(169\) | − | 204236.i | − | 0.550068i | ||||||
\(170\) | 28897.3 | − | 4054.72i | 0.0766892 | − | 0.0107606i | ||||
\(171\) | −261872. | + | 261872.i | −0.684855 | + | 0.684855i | ||||
\(172\) | 240780. | + | 133606.i | 0.620582 | + | 0.344353i | ||||
\(173\) | 195067. | + | 195067.i | 0.495528 | + | 0.495528i | 0.910043 | − | 0.414514i | \(-0.136049\pi\) |
−0.414514 | + | 0.910043i | \(0.636049\pi\) | |||||||
\(174\) | 102671. | − | 136187.i | 0.257085 | − | 0.341006i | ||||
\(175\) | 46343.5 | 0.114392 | ||||||||
\(176\) | −125354. | + | 540783.i | −0.305041 | + | 1.31596i | ||||
\(177\) | 112600. | 0.270151 | ||||||||
\(178\) | 32755.6 | − | 43448.2i | 0.0774883 | − | 0.102783i | ||||
\(179\) | −52857.4 | − | 52857.4i | −0.123303 | − | 0.123303i | 0.642763 | − | 0.766065i | \(-0.277788\pi\) |
−0.766065 | + | 0.642763i | \(0.777788\pi\) | |||||||
\(180\) | 51998.0 | − | 93709.0i | 0.119620 | − | 0.215576i | ||||
\(181\) | 408370. | − | 408370.i | 0.926526 | − | 0.926526i | −0.0709534 | − | 0.997480i | \(-0.522604\pi\) |
0.997480 | + | 0.0709534i | \(0.0226042\pi\) | |||||||
\(182\) | 169778. | − | 23822.4i | 0.379930 | − | 0.0533099i | ||||
\(183\) | − | 212965.i | − | 0.470090i | ||||||
\(184\) | 315218. | + | 121241.i | 0.686383 | + | 0.264001i | ||||
\(185\) | − | 15717.7i | − | 0.0337644i | ||||||
\(186\) | −76984.5 | − | 548655.i | −0.163163 | − | 1.16283i | ||||
\(187\) | −79094.8 | + | 79094.8i | −0.165403 | + | 0.165403i | ||||
\(188\) | −179690. | − | 627702.i | −0.370791 | − | 1.29527i | ||||
\(189\) | −206387. | − | 206387.i | −0.420269 | − | 0.420269i | ||||
\(190\) | 312188. | + | 235359.i | 0.627382 | + | 0.472984i | ||||
\(191\) | 826837. | 1.63997 | 0.819986 | − | 0.572383i | \(-0.193981\pi\) | ||||
0.819986 | + | 0.572383i | \(0.193981\pi\) | |||||||
\(192\) | 17453.6 | + | 341724.i | 0.0341690 | + | 0.668993i | ||||
\(193\) | −478446. | −0.924570 | −0.462285 | − | 0.886731i | \(-0.652970\pi\) | ||||
−0.462285 | + | 0.886731i | \(0.652970\pi\) | |||||||
\(194\) | 490777. | + | 369998.i | 0.936225 | + | 0.705821i | ||||
\(195\) | −75448.0 | − | 75448.0i | −0.142089 | − | 0.142089i | ||||
\(196\) | 99594.2 | + | 347908.i | 0.185180 | + | 0.646881i | ||||
\(197\) | −527886. | + | 527886.i | −0.969113 | + | 0.969113i | −0.999537 | − | 0.0304244i | \(-0.990314\pi\) |
0.0304244 | + | 0.999537i | \(0.490314\pi\) | |||||||
\(198\) | 57083.7 | + | 406825.i | 0.103478 | + | 0.737471i | ||||
\(199\) | − | 764647.i | − | 1.36876i | −0.729124 | − | 0.684382i | \(-0.760072\pi\) | ||
0.729124 | − | 0.684382i | \(-0.239928\pi\) | |||||||
\(200\) | −105596. | − | 40614.9i | −0.186668 | − | 0.0717976i | ||||
\(201\) | 306824.i | 0.535672i | ||||||||
\(202\) | 80193.8 | − | 11252.4i | 0.138281 | − | 0.0194029i | ||||
\(203\) | 151386. | − | 151386.i | 0.257838 | − | 0.257838i | ||||
\(204\) | −33452.9 | + | 60287.7i | −0.0562806 | + | 0.101427i | ||||
\(205\) | −369407. | − | 369407.i | −0.613932 | − | 0.613932i | ||||
\(206\) | −379881. | + | 503887.i | −0.623705 | + | 0.827303i | ||||
\(207\) | 249933. | 0.405414 | ||||||||
\(208\) | −407724. | − | 94511.2i | −0.653444 | − | 0.151469i | ||||
\(209\) | −1.49869e6 | −2.37327 | ||||||||
\(210\) | −65918.2 | + | 87436.1i | −0.103147 | + | 0.136818i | ||||
\(211\) | −352929. | − | 352929.i | −0.545734 | − | 0.545734i | 0.379470 | − | 0.925204i | \(-0.376106\pi\) |
−0.925204 | + | 0.379470i | \(0.876106\pi\) | |||||||
\(212\) | 249886. | + | 138659.i | 0.381859 | + | 0.211889i | ||||
\(213\) | −37485.0 | + | 37485.0i | −0.0566119 | + | 0.0566119i | ||||
\(214\) | 1.02921e6 | − | 144414.i | 1.53628 | − | 0.215564i | ||||
\(215\) | − | 215128.i | − | 0.317396i | ||||||
\(216\) | 289386. | + | 651135.i | 0.422029 | + | 0.949591i | ||||
\(217\) | − | 695467.i | − | 1.00260i | ||||||
\(218\) | −119081. | − | 848669.i | −0.169708 | − | 1.20948i | ||||
\(219\) | −513792. | + | 513792.i | −0.723897 | + | 0.723897i | ||||
\(220\) | 416941. | − | 119356.i | 0.580788 | − | 0.166260i | ||||
\(221\) | −59633.7 | − | 59633.7i | −0.0821318 | − | 0.0821318i | ||||
\(222\) | 29654.5 | + | 22356.5i | 0.0403839 | + | 0.0304454i | ||||
\(223\) | −23907.2 | −0.0321934 | −0.0160967 | − | 0.999870i | \(-0.505124\pi\) | ||||
−0.0160967 | + | 0.999870i | \(0.505124\pi\) | |||||||
\(224\) | −37909.1 | + | 427844.i | −0.0504804 | + | 0.569726i | ||||
\(225\) | −83725.7 | −0.110256 | ||||||||
\(226\) | −1.16461e6 | − | 877999.i | −1.51673 | − | 1.14347i | ||||
\(227\) | 345816. | + | 345816.i | 0.445432 | + | 0.445432i | 0.893833 | − | 0.448401i | \(-0.148006\pi\) |
−0.448401 | + | 0.893833i | \(0.648006\pi\) | |||||||
\(228\) | −888101. | + | 254233.i | −1.13142 | + | 0.323888i | ||||
\(229\) | −1.00330e6 | + | 1.00330e6i | −1.26427 | + | 1.26427i | −0.315268 | + | 0.949003i | \(0.602094\pi\) |
−0.949003 | + | 0.315268i | \(0.897906\pi\) | |||||||
\(230\) | −36663.2 | − | 261292.i | −0.0456995 | − | 0.325692i | ||||
\(231\) | − | 419747.i | − | 0.517557i | ||||||
\(232\) | −477613. | + | 212267.i | −0.582581 | + | 0.258918i | ||||
\(233\) | − | 903032.i | − | 1.08972i | −0.838528 | − | 0.544858i | \(-0.816584\pi\) | ||
0.838528 | − | 0.544858i | \(-0.183416\pi\) | |||||||
\(234\) | −306727. | + | 43038.4i | −0.366195 | + | 0.0513826i | ||||
\(235\) | −360688. | + | 360688.i | −0.426052 | + | 0.426052i | ||||
\(236\) | −301725. | − | 167424.i | −0.352640 | − | 0.195676i | ||||
\(237\) | 182080. | + | 182080.i | 0.210567 | + | 0.210567i | ||||
\(238\) | −52101.5 | + | 69109.1i | −0.0596221 | + | 0.0790848i | ||||
\(239\) | −391460. | −0.443294 | −0.221647 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221647 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(240\) | 226825. | − | 141457.i | 0.254193 | − | 0.158524i | ||||
\(241\) | −1.17742e6 | −1.30584 | −0.652921 | − | 0.757426i | \(-0.726457\pi\) | ||||
−0.652921 | + | 0.757426i | \(0.726457\pi\) | |||||||
\(242\) | −452346. | + | 600007.i | −0.496515 | + | 0.658595i | ||||
\(243\) | 613224. | + | 613224.i | 0.666198 | + | 0.666198i | ||||
\(244\) | −316655. | + | 570664.i | −0.340496 | + | 0.613629i | ||||
\(245\) | 199914. | − | 199914.i | 0.212778 | − | 0.212778i | ||||
\(246\) | 1.22240e6 | − | 171520.i | 1.28788 | − | 0.180708i | ||||
\(247\) | − | 1.12994e6i | − | 1.17846i | ||||||
\(248\) | −609498. | + | 1.58465e6i | −0.629279 | + | 1.63608i | ||||
\(249\) | − | 89290.2i | − | 0.0912652i | ||||||
\(250\) | 12281.9 | + | 87530.9i | 0.0124284 | + | 0.0885750i | ||||
\(251\) | 1.31464e6 | − | 1.31464e6i | 1.31711 | − | 1.31711i | 0.401056 | − | 0.916054i | \(-0.368643\pi\) |
0.916054 | − | 0.401056i | \(-0.131357\pi\) | |||||||
\(252\) | 87479.1 | + | 305587.i | 0.0867767 | + | 0.303133i | ||||
\(253\) | 715185. | + | 715185.i | 0.702453 | + | 0.702453i | ||||
\(254\) | −358701. | − | 270425.i | −0.348858 | − | 0.263005i | ||||
\(255\) | 53864.9 | 0.0518747 | ||||||||
\(256\) | 461335. | − | 941638.i | 0.439963 | − | 0.898016i | ||||
\(257\) | −580264. | −0.548016 | −0.274008 | − | 0.961727i | \(-0.588349\pi\) | ||||
−0.274008 | + | 0.961727i | \(0.588349\pi\) | |||||||
\(258\) | 405882. | + | 305995.i | 0.379621 | + | 0.286197i | ||||
\(259\) | 32964.2 | + | 32964.2i | 0.0305347 | + | 0.0305347i | ||||
\(260\) | 89988.8 | + | 314354.i | 0.0825572 | + | 0.288393i | ||||
\(261\) | −273499. | + | 273499.i | −0.248516 | + | 0.248516i | ||||
\(262\) | −135221. | − | 963694.i | −0.121700 | − | 0.867334i | ||||
\(263\) | 1.07031e6i | 0.954160i | 0.878860 | + | 0.477080i | \(0.158305\pi\) | ||||
−0.878860 | + | 0.477080i | \(0.841695\pi\) | |||||||
\(264\) | −367861. | + | 956411.i | −0.324843 | + | 0.844568i | ||||
\(265\) | − | 223265.i | − | 0.195301i | ||||||
\(266\) | −1.14835e6 | + | 161131.i | −0.995111 | + | 0.139629i | ||||
\(267\) | 71022.5 | − | 71022.5i | 0.0609702 | − | 0.0609702i | ||||
\(268\) | 456211. | − | 822168.i | 0.387998 | − | 0.699236i | ||||
\(269\) | 759552. | + | 759552.i | 0.639995 | + | 0.639995i | 0.950554 | − | 0.310559i | \(-0.100516\pi\) |
−0.310559 | + | 0.950554i | \(0.600516\pi\) | |||||||
\(270\) | 335114. | − | 444507.i | 0.279759 | − | 0.371081i | ||||
\(271\) | 1.26348e6 | 1.04507 | 0.522535 | − | 0.852618i | \(-0.324986\pi\) | ||||
0.522535 | + | 0.852618i | \(0.324986\pi\) | |||||||
\(272\) | 179282. | − | 111807.i | 0.146931 | − | 0.0916318i | ||||
\(273\) | 316469. | 0.256995 | ||||||||
\(274\) | 708042. | − | 939170.i | 0.569747 | − | 0.755732i | ||||
\(275\) | −239581. | − | 239581.i | −0.191039 | − | 0.191039i | ||||
\(276\) | 545128. | + | 302485.i | 0.430751 | + | 0.239019i | ||||
\(277\) | 666957. | − | 666957.i | 0.522274 | − | 0.522274i | −0.395984 | − | 0.918258i | \(-0.629596\pi\) |
0.918258 | + | 0.395984i | \(0.129596\pi\) | |||||||
\(278\) | −427590. | + | 59997.2i | −0.331830 | + | 0.0465607i | ||||
\(279\) | 1.25645e6i | 0.966352i | ||||||||
\(280\) | 306643. | − | 136282.i | 0.233742 | − | 0.103883i | ||||
\(281\) | − | 1.15737e6i | − | 0.874391i | −0.899367 | − | 0.437195i | \(-0.855972\pi\) | ||
0.899367 | − | 0.437195i | \(-0.144028\pi\) | |||||||
\(282\) | −167472. | − | 1.19355e6i | −0.125407 | − | 0.893750i | ||||
\(283\) | −263797. | + | 263797.i | −0.195796 | + | 0.195796i | −0.798195 | − | 0.602399i | \(-0.794212\pi\) |
0.602399 | + | 0.798195i | \(0.294212\pi\) | |||||||
\(284\) | 156181. | − | 44709.3i | 0.114903 | − | 0.0328929i | ||||
\(285\) | 510318. | + | 510318.i | 0.372159 | + | 0.372159i | ||||
\(286\) | −1.00085e6 | − | 754545.i | −0.723528 | − | 0.545469i | ||||
\(287\) | 1.54949e6 | 1.11041 | ||||||||
\(288\) | 68487.7 | − | 772957.i | 0.0486554 | − | 0.549129i | ||||
\(289\) | −1.37728e6 | −0.970015 | ||||||||
\(290\) | 326050. | + | 245809.i | 0.227661 | + | 0.171634i | ||||
\(291\) | 802249. | + | 802249.i | 0.555363 | + | 0.555363i | ||||
\(292\) | 2.14071e6 | − | 612813.i | 1.46927 | − | 0.420602i | ||||
\(293\) | 1.75356e6 | − | 1.75356e6i | 1.19330 | − | 1.19330i | 0.217168 | − | 0.976134i | \(-0.430318\pi\) |
0.976134 | − | 0.217168i | \(-0.0696819\pi\) | |||||||
\(294\) | 92822.6 | + | 661530.i | 0.0626304 | + | 0.446356i | ||||
\(295\) | 269581.i | 0.180358i | ||||||||
\(296\) | −46220.8 | − | 104000.i | −0.0306626 | − | 0.0689926i | ||||
\(297\) | 2.13391e6i | 1.40373i | ||||||||
\(298\) | −1.52429e6 | + | 213881.i | −0.994322 | + | 0.139518i | ||||
\(299\) | −539215. | + | 539215.i | −0.348806 | + | 0.348806i | ||||
\(300\) | −182614. | − | 101330.i | −0.117147 | − | 0.0650034i | ||||
\(301\) | 451182. | + | 451182.i | 0.287035 | + | 0.287035i | ||||
\(302\) | 385098. | − | 510806.i | 0.242970 | − | 0.322284i | ||||
\(303\) | 149482. | 0.0935370 | ||||||||
\(304\) | 2.75778e6 | + | 639258.i | 1.71150 | + | 0.396728i | ||||
\(305\) | 509868. | 0.313840 | ||||||||
\(306\) | 94128.2 | − | 124855.i | 0.0574667 | − | 0.0762257i | ||||
\(307\) | 1.57280e6 | + | 1.57280e6i | 0.952418 | + | 0.952418i | 0.998918 | − | 0.0465006i | \(-0.0148069\pi\) |
−0.0465006 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(308\) | −624116. | + | 1.12476e6i | −0.374877 | + | 0.675589i | ||||
\(309\) | −823678. | + | 823678.i | −0.490751 | + | 0.490751i | ||||
\(310\) | 1.31356e6 | − | 184312.i | 0.776326 | − | 0.108930i | ||||
\(311\) | − | 737506.i | − | 0.432379i | −0.976351 | − | 0.216190i | \(-0.930637\pi\) | ||
0.976351 | − | 0.216190i | \(-0.0693629\pi\) | |||||||
\(312\) | −721088. | − | 277350.i | −0.419374 | − | 0.161303i | ||||
\(313\) | − | 40528.1i | − | 0.0233828i | −0.999932 | − | 0.0116914i | \(-0.996278\pi\) | ||
0.999932 | − | 0.0116914i | \(-0.00372157\pi\) | |||||||
\(314\) | −112706. | − | 803239.i | −0.0645097 | − | 0.459749i | ||||
\(315\) | 175595. | − | 175595.i | 0.0997095 | − | 0.0997095i | ||||
\(316\) | −217171. | − | 758634.i | −0.122345 | − | 0.427381i | ||||
\(317\) | −424582. | − | 424582.i | −0.237309 | − | 0.237309i | 0.578426 | − | 0.815735i | \(-0.303667\pi\) |
−0.815735 | + | 0.578426i | \(0.803667\pi\) | |||||||
\(318\) | 421233. | + | 317568.i | 0.233590 | + | 0.176104i | ||||
\(319\) | −1.56524e6 | −0.861200 | ||||||||
\(320\) | −818134. | + | 41786.3i | −0.446631 | + | 0.0228118i | ||||
\(321\) | 1.91847e6 | 1.03919 | ||||||||
\(322\) | 624893. | + | 471108.i | 0.335866 | + | 0.253210i | ||||
\(323\) | 403353. | + | 403353.i | 0.215119 | + | 0.215119i | ||||
\(324\) | 75305.6 | + | 263062.i | 0.0398534 | + | 0.139218i | ||||
\(325\) | 180633. | − | 180633.i | 0.0948611 | − | 0.0948611i | ||||
\(326\) | −166809. | − | 1.18882e6i | −0.0869309 | − | 0.619541i | ||||
\(327\) | − | 1.58193e6i | − | 0.818123i | ||||||
\(328\) | −3.53058e6 | − | 1.35795e6i | −1.81201 | − | 0.696948i | ||||
\(329\) | − | 1.51292e6i | − | 0.770595i | ||||||
\(330\) | 792793. | − | 111241.i | 0.400751 | − | 0.0562314i | ||||
\(331\) | 115804. | − | 115804.i | 0.0580967 | − | 0.0580967i | −0.677461 | − | 0.735558i | \(-0.736920\pi\) |
0.735558 | + | 0.677461i | \(0.236920\pi\) | |||||||
\(332\) | −132764. | + | 239263.i | −0.0661052 | + | 0.119132i | ||||
\(333\) | −59554.1 | − | 59554.1i | −0.0294308 | − | 0.0294308i | ||||
\(334\) | −1.99395e6 | + | 2.64484e6i | −0.978022 | + | 1.29728i | ||||
\(335\) | −734578. | −0.357624 | ||||||||
\(336\) | −179040. | + | 772387.i | −0.0865173 | + | 0.373239i | ||||
\(337\) | 1.97753e6 | 0.948524 | 0.474262 | − | 0.880384i | \(-0.342715\pi\) | ||||
0.474262 | + | 0.880384i | \(0.342715\pi\) | |||||||
\(338\) | −695503. | + | 922538.i | −0.331137 | + | 0.439231i | ||||
\(339\) | −1.90372e6 | − | 1.90372e6i | −0.899715 | − | 0.899715i | ||||
\(340\) | −144337. | − | 80090.9i | −0.0677143 | − | 0.0375739i | ||||
\(341\) | −3.59534e6 | + | 3.59534e6i | −1.67438 | + | 1.67438i | ||||
\(342\) | 2.07465e6 | − | 291105.i | 0.959135 | − | 0.134581i | ||||
\(343\) | 2.08478e6i | 0.956808i | ||||||||
\(344\) | −632626. | − | 1.42345e6i | −0.288238 | − | 0.648552i | ||||
\(345\) | − | 487053.i | − | 0.220307i | ||||||
\(346\) | −216842. | − | 1.54540e6i | −0.0973764 | − | 0.693985i | ||||
\(347\) | −443493. | + | 443493.i | −0.197725 | + | 0.197725i | −0.799024 | − | 0.601299i | \(-0.794650\pi\) |
0.601299 | + | 0.799024i | \(0.294650\pi\) | |||||||
\(348\) | −927535. | + | 265522.i | −0.410565 | + | 0.117531i | ||||
\(349\) | 738430. | + | 738430.i | 0.324523 | + | 0.324523i | 0.850499 | − | 0.525976i | \(-0.176300\pi\) |
−0.525976 | + | 0.850499i | \(0.676300\pi\) | |||||||
\(350\) | −209334. | − | 157817.i | −0.0913419 | − | 0.0688628i | ||||
\(351\) | −1.60886e6 | −0.697030 | ||||||||
\(352\) | 2.40780e6 | − | 2.01584e6i | 1.03577 | − | 0.867161i | ||||
\(353\) | 3.09175e6 | 1.32059 | 0.660295 | − | 0.751006i | \(-0.270431\pi\) | ||||
0.660295 | + | 0.751006i | \(0.270431\pi\) | |||||||
\(354\) | −508617. | − | 383447.i | −0.215716 | − | 0.162629i | ||||
\(355\) | −89744.2 | − | 89744.2i | −0.0377951 | − | 0.0377951i | ||||
\(356\) | −295915. | + | 84710.4i | −0.123749 | + | 0.0354252i | ||||
\(357\) | −112969. | + | 112969.i | −0.0469126 | + | 0.0469126i | ||||
\(358\) | 58757.9 | + | 418757.i | 0.0242303 | + | 0.172685i | ||||
\(359\) | 909411.i | 0.372412i | 0.982511 | + | 0.186206i | \(0.0596192\pi\) | ||||
−0.982511 | + | 0.186206i | \(0.940381\pi\) | |||||||
\(360\) | −553990. | + | 246211.i | −0.225292 | + | 0.100127i | ||||
\(361\) | 5.16666e6i | 2.08661i | ||||||||
\(362\) | −3.23527e6 | + | 453957.i | −1.29759 | + | 0.182072i | ||||
\(363\) | −980802. | + | 980802.i | −0.390674 | + | 0.390674i | ||||
\(364\) | −848015. | − | 470553.i | −0.335467 | − | 0.186147i | ||||
\(365\) | −1.23009e6 | − | 1.23009e6i | −0.483286 | − | 0.483286i | ||||
\(366\) | −725228. | + | 961967.i | −0.282990 | + | 0.375368i | ||||
\(367\) | 929868. | 0.360376 | 0.180188 | − | 0.983632i | \(-0.442329\pi\) | ||||
0.180188 | + | 0.983632i | \(0.442329\pi\) | |||||||
\(368\) | −1.01097e6 | − | 1.62109e6i | −0.389152 | − | 0.624003i | ||||
\(369\) | −2.79936e6 | −1.07027 | ||||||||
\(370\) | −53524.7 | + | 70996.9i | −0.0203259 | + | 0.0269609i | ||||
\(371\) | 468246. | + | 468246.i | 0.176620 | + | 0.176620i | ||||
\(372\) | −1.52064e6 | + | 2.74044e6i | −0.569730 | + | 1.02675i | ||||
\(373\) | 2.11764e6 | − | 2.11764e6i | 0.788099 | − | 0.788099i | −0.193083 | − | 0.981182i | \(-0.561849\pi\) |
0.981182 | + | 0.193083i | \(0.0618488\pi\) | |||||||
\(374\) | 626620. | − | 87924.2i | 0.231646 | − | 0.0325034i | ||||
\(375\) | 163159.i | 0.0599146i | ||||||||
\(376\) | −1.32590e6 | + | 3.44725e6i | −0.483663 | + | 1.25749i | ||||
\(377\) | − | 1.18012e6i | − | 0.427633i | ||||||
\(378\) | 229425. | + | 1.63507e6i | 0.0825871 | + | 0.588584i | ||||
\(379\) | 1.77828e6 | − | 1.77828e6i | 0.635920 | − | 0.635920i | −0.313627 | − | 0.949546i | \(-0.601544\pi\) |
0.949546 | + | 0.313627i | \(0.101544\pi\) | |||||||
\(380\) | −608670. | − | 2.12624e6i | −0.216233 | − | 0.755358i | ||||
\(381\) | −586351. | − | 586351.i | −0.206940 | − | 0.206940i | ||||
\(382\) | −3.73483e6 | − | 2.81570e6i | −1.30952 | − | 0.987250i | ||||
\(383\) | −358681. | −0.124943 | −0.0624714 | − | 0.998047i | \(-0.519898\pi\) | ||||
−0.0624714 | + | 0.998047i | \(0.519898\pi\) | |||||||
\(384\) | 1.08486e6 | − | 1.60301e6i | 0.375445 | − | 0.554762i | ||||
\(385\) | 1.00493e6 | 0.345530 | ||||||||
\(386\) | 2.16115e6 | + | 1.62929e6i | 0.738271 | + | 0.556584i | ||||
\(387\) | −815119. | − | 815119.i | −0.276658 | − | 0.276658i | ||||
\(388\) | −956864. | − | 3.34257e6i | −0.322679 | − | 1.12720i | ||||
\(389\) | 2.59255e6 | − | 2.59255e6i | 0.868668 | − | 0.868668i | −0.123657 | − | 0.992325i | \(-0.539462\pi\) |
0.992325 | + | 0.123657i | \(0.0394623\pi\) | |||||||
\(390\) | 83870.2 | + | 597728.i | 0.0279220 | + | 0.198995i | ||||
\(391\) | − | 384965.i | − | 0.127344i | ||||||
\(392\) | 734891. | − | 1.91066e6i | 0.241550 | − | 0.628013i | ||||
\(393\) | − | 1.79634e6i | − | 0.586688i | ||||||
\(394\) | 4.18212e6 | − | 586813.i | 1.35724 | − | 0.190441i | ||||
\(395\) | −435924. | + | 435924.i | −0.140578 | + | 0.140578i | ||||
\(396\) | 1.12755e6 | − | 2.03203e6i | 0.361324 | − | 0.651165i | ||||
\(397\) | −2.75694e6 | − | 2.75694e6i | −0.877913 | − | 0.877913i | 0.115405 | − | 0.993318i | \(-0.463183\pi\) |
−0.993318 | + | 0.115405i | \(0.963183\pi\) | |||||||
\(398\) | −2.60392e6 | + | 3.45392e6i | −0.823985 | + | 1.09296i | ||||
\(399\) | −2.14055e6 | −0.673120 | ||||||||
\(400\) | 338667. | + | 543051.i | 0.105834 | + | 0.169703i | ||||
\(401\) | 2.18536e6 | 0.678677 | 0.339338 | − | 0.940664i | \(-0.389797\pi\) | ||||
0.339338 | + | 0.940664i | \(0.389797\pi\) | |||||||
\(402\) | 1.04485e6 | − | 1.38593e6i | 0.322470 | − | 0.427735i | ||||
\(403\) | −2.71072e6 | − | 2.71072e6i | −0.831422 | − | 0.831422i | ||||
\(404\) | −400555. | − | 222263.i | −0.122098 | − | 0.0677507i | ||||
\(405\) | 151160. | − | 151160.i | 0.0457929 | − | 0.0457929i | ||||
\(406\) | −1.19934e6 | + | 168286.i | −0.361101 | + | 0.0506678i | ||||
\(407\) | − | 340829.i | − | 0.101988i | ||||||
\(408\) | 356410. | − | 158400.i | 0.105998 | − | 0.0471091i | ||||
\(409\) | 4.12420e6i | 1.21908i | 0.792756 | + | 0.609539i | \(0.208645\pi\) | ||||
−0.792756 | + | 0.609539i | \(0.791355\pi\) | |||||||
\(410\) | 410644. | + | 2.92659e6i | 0.120644 | + | 0.859808i | ||||
\(411\) | 1.53521e6 | − | 1.53521e6i | 0.448295 | − | 0.448295i | ||||
\(412\) | 3.43185e6 | − | 982422.i | 0.996060 | − | 0.285138i | ||||
\(413\) | −565384. | − | 565384.i | −0.163105 | − | 0.163105i | ||||
\(414\) | −1.12895e6 | − | 851118.i | −0.323724 | − | 0.244056i | ||||
\(415\) | 213773. | 0.0609302 | ||||||||
\(416\) | 1.51985e6 | + | 1.81536e6i | 0.430593 | + | 0.514317i | ||||
\(417\) | −797034. | −0.224459 | ||||||||
\(418\) | 6.76962e6 | + | 5.10362e6i | 1.89506 | + | 1.42869i | ||||
\(419\) | 435793. | + | 435793.i | 0.121268 | + | 0.121268i | 0.765136 | − | 0.643868i | \(-0.222672\pi\) |
−0.643868 | + | 0.765136i | \(0.722672\pi\) | |||||||
\(420\) | 595507. | − | 170473.i | 0.164726 | − | 0.0471556i | ||||
\(421\) | −1.76441e6 | + | 1.76441e6i | −0.485171 | + | 0.485171i | −0.906778 | − | 0.421608i | \(-0.861466\pi\) |
0.421608 | + | 0.906778i | \(0.361466\pi\) | |||||||
\(422\) | 392327. | + | 2.79604e6i | 0.107242 | + | 0.764298i | ||||
\(423\) | 2.73329e6i | 0.742736i | ||||||||
\(424\) | −656553. | − | 1.47728e6i | −0.177360 | − | 0.399070i | ||||
\(425\) | 128960.i | 0.0346324i | ||||||||
\(426\) | 296971. | − | 41669.4i | 0.0792847 | − | 0.0111248i | ||||
\(427\) | −1.06933e6 | + | 1.06933e6i | −0.283820 | + | 0.283820i | ||||
\(428\) | −5.14076e6 | − | 2.85255e6i | −1.35649 | − | 0.752703i | ||||
\(429\) | −1.63605e6 | − | 1.63605e6i | −0.429193 | − | 0.429193i | ||||
\(430\) | −732594. | + | 971737.i | −0.191070 | + | 0.253441i | ||||
\(431\) | −1.24496e6 | −0.322820 | −0.161410 | − | 0.986887i | \(-0.551604\pi\) | ||||
−0.161410 | + | 0.986887i | \(0.551604\pi\) | |||||||
\(432\) | 910204. | − | 3.92665e6i | 0.234655 | − | 1.01231i | ||||
\(433\) | −2.28661e6 | −0.586101 | −0.293050 | − | 0.956097i | \(-0.594670\pi\) | ||||
−0.293050 | + | 0.956097i | \(0.594670\pi\) | |||||||
\(434\) | −2.36833e6 | + | 3.14143e6i | −0.603556 | + | 0.800577i | ||||
\(435\) | 532977. | + | 532977.i | 0.135047 | + | 0.135047i | ||||
\(436\) | −2.35215e6 | + | 4.23896e6i | −0.592583 | + | 1.06793i | ||||
\(437\) | 3.64717e6 | − | 3.64717e6i | 0.913591 | − | 0.913591i | ||||
\(438\) | 4.07046e6 | − | 571146.i | 1.01381 | − | 0.142253i | ||||
\(439\) | 1.35452e6i | 0.335446i | 0.985834 | + | 0.167723i | \(0.0536414\pi\) | ||||
−0.985834 | + | 0.167723i | \(0.946359\pi\) | |||||||
\(440\) | −2.28978e6 | − | 880710.i | −0.563848 | − | 0.216871i | ||||
\(441\) | − | 1.51494e6i | − | 0.370937i | ||||||
\(442\) | 66290.6 | + | 472442.i | 0.0161397 | + | 0.115025i | ||||
\(443\) | 134020. | − | 134020.i | 0.0324459 | − | 0.0324459i | −0.690698 | − | 0.723144i | \(-0.742696\pi\) |
0.723144 | + | 0.690698i | \(0.242696\pi\) | |||||||
\(444\) | −57817.0 | − | 201970.i | −0.0139187 | − | 0.0486215i | ||||
\(445\) | 170038. | + | 170038.i | 0.0407048 | + | 0.0407048i | ||||
\(446\) | 107989. | + | 81413.0i | 0.0257065 | + | 0.0193801i | ||||
\(447\) | −2.84130e6 | −0.672587 | ||||||||
\(448\) | 1.62821e6 | − | 1.80348e6i | 0.383279 | − | 0.424538i | ||||
\(449\) | 6.79015e6 | 1.58951 | 0.794755 | − | 0.606930i | \(-0.207599\pi\) | ||||
0.794755 | + | 0.606930i | \(0.207599\pi\) | |||||||
\(450\) | 378190. | + | 285118.i | 0.0880397 | + | 0.0663732i | ||||
\(451\) | −8.01037e6 | − | 8.01037e6i | −1.85443 | − | 1.85443i | ||||
\(452\) | 2.27062e6 | + | 7.93186e6i | 0.522756 | + | 1.82612i | ||||
\(453\) | 834989. | − | 834989.i | 0.191177 | − | 0.191177i | ||||
\(454\) | −384420. | − | 2.73969e6i | −0.0875319 | − | 0.623824i | ||||
\(455\) | 757671.i | 0.171574i | ||||||||
\(456\) | 4.87732e6 | + | 1.87595e6i | 1.09842 | + | 0.422483i | ||||
\(457\) | 5.29375e6i | 1.18569i | 0.805315 | + | 0.592847i | \(0.201996\pi\) | ||||
−0.805315 | + | 0.592847i | \(0.798004\pi\) | |||||||
\(458\) | 7.94850e6 | − | 1.11529e6i | 1.77060 | − | 0.248442i | ||||
\(459\) | 574312. | − | 574312.i | 0.127238 | − | 0.127238i | ||||
\(460\) | −724192. | + | 1.30511e6i | −0.159573 | + | 0.287577i | ||||
\(461\) | 2.35107e6 | + | 2.35107e6i | 0.515244 | + | 0.515244i | 0.916128 | − | 0.400885i | \(-0.131297\pi\) |
−0.400885 | + | 0.916128i | \(0.631297\pi\) | |||||||
\(462\) | −1.42940e6 | + | 1.89600e6i | −0.311565 | + | 0.413270i | ||||
\(463\) | −8.46006e6 | −1.83409 | −0.917046 | − | 0.398782i | \(-0.869433\pi\) | ||||
−0.917046 | + | 0.398782i | \(0.869433\pi\) | |||||||
\(464\) | 2.88023e6 | + | 667643.i | 0.621059 | + | 0.143962i | ||||
\(465\) | 2.44849e6 | 0.525128 | ||||||||
\(466\) | −3.07517e6 | + | 4.07900e6i | −0.656000 | + | 0.870140i | ||||
\(467\) | −2.15793e6 | − | 2.15793e6i | −0.457874 | − | 0.457874i | 0.440083 | − | 0.897957i | \(-0.354949\pi\) |
−0.897957 | + | 0.440083i | \(0.854949\pi\) | |||||||
\(468\) | 1.53205e6 | + | 850117.i | 0.323339 | + | 0.179417i | ||||
\(469\) | 1.54061e6 | − | 1.54061e6i | 0.323415 | − | 0.323415i | ||||
\(470\) | 2.85751e6 | − | 400952.i | 0.596683 | − | 0.0837235i | ||||
\(471\) | − | 1.49725e6i | − | 0.310987i | ||||||
\(472\) | 792755. | + | 1.78375e6i | 0.163789 | + | 0.368534i | ||||
\(473\) | − | 4.66493e6i | − | 0.958721i | ||||||
\(474\) | −202405. | − | 1.44251e6i | −0.0413786 | − | 0.294898i | ||||
\(475\) | −1.22177e6 | + | 1.22177e6i | −0.248460 | + | 0.248460i | ||||
\(476\) | 470686. | − | 134741.i | 0.0952168 | − | 0.0272573i | ||||
\(477\) | −845948. | − | 845948.i | −0.170235 | − | 0.170235i | ||||
\(478\) | 1.76823e6 | + | 1.33307e6i | 0.353972 | + | 0.266860i | ||||
\(479\) | 3.37846e6 | 0.672790 | 0.336395 | − | 0.941721i | \(-0.390792\pi\) | ||||
0.336395 | + | 0.941721i | \(0.390792\pi\) | |||||||
\(480\) | −1.50629e6 | − | 133464.i | −0.298404 | − | 0.0264400i | ||||
\(481\) | 256969. | 0.0506428 | ||||||||
\(482\) | 5.31844e6 | + | 4.00958e6i | 1.04272 | + | 0.786106i | ||||
\(483\) | 1.02148e6 | + | 1.02148e6i | 0.199234 | + | 0.199234i | ||||
\(484\) | 4.08651e6 | − | 1.16983e6i | 0.792937 | − | 0.226991i | ||||
\(485\) | −1.92070e6 | + | 1.92070e6i | −0.370770 | + | 0.370770i | ||||
\(486\) | −681678. | − | 4.85820e6i | −0.130915 | − | 0.933006i | ||||
\(487\) | − | 987375.i | − | 0.188651i | −0.995541 | − | 0.0943257i | \(-0.969931\pi\) | ||
0.995541 | − | 0.0943257i | \(-0.0300695\pi\) | |||||||
\(488\) | 3.37366e6 | − | 1.49937e6i | 0.641286 | − | 0.285009i | ||||
\(489\) | − | 2.21597e6i | − | 0.419075i | ||||||
\(490\) | −1.58379e6 | + | 222230.i | −0.297995 | + | 0.0418131i | ||||
\(491\) | 6.82185e6 | − | 6.82185e6i | 1.27702 | − | 1.27702i | 0.334695 | − | 0.942326i | \(-0.391367\pi\) |
0.942326 | − | 0.334695i | \(-0.108633\pi\) | |||||||
\(492\) | −6.10567e6 | − | 3.38796e6i | −1.13716 | − | 0.630995i | ||||
\(493\) | 421263. | + | 421263.i | 0.0780613 | + | 0.0780613i | ||||
\(494\) | −3.84789e6 | + | 5.10397e6i | −0.709423 | + | 0.941002i | ||||
\(495\) | −1.81554e6 | −0.333038 | ||||||||
\(496\) | 8.14944e6 | − | 5.08230e6i | 1.48739 | − | 0.927590i | ||||
\(497\) | 376435. | 0.0683596 | ||||||||
\(498\) | −304067. | + | 403325.i | −0.0549409 | + | 0.0728755i | ||||
\(499\) | 5.27326e6 | + | 5.27326e6i | 0.948043 | + | 0.948043i | 0.998715 | − | 0.0506726i | \(-0.0161365\pi\) |
−0.0506726 | + | 0.998715i | \(0.516136\pi\) | |||||||
\(500\) | 242599. | − | 437202.i | 0.0433973 | − | 0.0782091i | ||||
\(501\) | −4.32339e6 | + | 4.32339e6i | −0.769539 | + | 0.769539i | ||||
\(502\) | −1.04151e7 | + | 1.46139e6i | −1.84460 | + | 0.258826i | ||||
\(503\) | 7.43828e6i | 1.31085i | 0.755261 | + | 0.655424i | \(0.227510\pi\) | ||||
−0.755261 | + | 0.655424i | \(0.772490\pi\) | |||||||
\(504\) | 645495. | − | 1.67824e6i | 0.113192 | − | 0.294291i | ||||
\(505\) | 357882.i | 0.0624469i | ||||||||
\(506\) | −795021. | − | 5.66598e6i | −0.138039 | − | 0.983781i | ||||
\(507\) | −1.50803e6 | + | 1.50803e6i | −0.260549 | + | 0.260549i | ||||
\(508\) | 699356. | + | 2.44303e6i | 0.120237 | + | 0.420019i | ||||
\(509\) | −6.34354e6 | − | 6.34354e6i | −1.08527 | − | 1.08527i | −0.996008 | − | 0.0892602i | \(-0.971550\pi\) |
−0.0892602 | − | 0.996008i | \(-0.528450\pi\) | |||||||
\(510\) | −243308. | − | 183431.i | −0.0414221 | − | 0.0312281i | ||||
\(511\) | 5.15965e6 | 0.874115 | ||||||||
\(512\) | −5.29049e6 | + | 2.68237e6i | −0.891910 | + | 0.452213i | ||||
\(513\) | 1.08821e7 | 1.82566 | ||||||||
\(514\) | 2.62106e6 | + | 1.97602e6i | 0.437592 | + | 0.329901i | ||||
\(515\) | −1.97200e6 | − | 1.97200e6i | −0.327634 | − | 0.327634i | ||||
\(516\) | −791343. | − | 2.76436e6i | −0.130840 | − | 0.457057i | ||||
\(517\) | −7.82131e6 | + | 7.82131e6i | −1.28693 | + | 1.28693i | ||||
\(518\) | −36644.0 | − | 261155.i | −0.00600037 | − | 0.0427636i | ||||
\(519\) | − | 2.88064e6i | − | 0.469430i | ||||||
\(520\) | 664014. | − | 1.72638e6i | 0.107688 | − | 0.279981i | ||||
\(521\) | 3.05780e6i | 0.493531i | 0.969075 | + | 0.246766i | \(0.0793678\pi\) | ||||
−0.969075 | + | 0.246766i | \(0.920632\pi\) | |||||||
\(522\) | 2.16677e6 | − | 304030.i | 0.348046 | − | 0.0488360i | ||||
\(523\) | −7.25293e6 | + | 7.25293e6i | −1.15947 | + | 1.15947i | −0.174880 | + | 0.984590i | \(0.555954\pi\) |
−0.984590 | + | 0.174880i | \(0.944046\pi\) | |||||||
\(524\) | −2.67095e6 | + | 4.81350e6i | −0.424950 | + | 0.765830i | ||||
\(525\) | −342188. | − | 342188.i | −0.0541834 | − | 0.0541834i | ||||
\(526\) | 3.64482e6 | − | 4.83461e6i | 0.574397 | − | 0.761899i | ||||
\(527\) | 1.93527e6 | 0.303540 | ||||||||
\(528\) | 4.91857e6 | − | 3.06741e6i | 0.767811 | − | 0.478836i | ||||
\(529\) | 2.95545e6 | 0.459181 | ||||||||
\(530\) | −760301. | + | 1.00849e6i | −0.117570 | + | 0.155949i | ||||
\(531\) | 1.02144e6 | + | 1.02144e6i | 0.157209 | + | 0.157209i | ||||
\(532\) | 5.73584e6 | + | 3.18275e6i | 0.878653 | + | 0.487555i | ||||
\(533\) | 6.03944e6 | − | 6.03944e6i | 0.920828 | − | 0.920828i | ||||
\(534\) | −562668. | + | 78950.8i | −0.0853885 | + | 0.0119813i | ||||
\(535\) | 4.59309e6i | 0.693778i | ||||||||
\(536\) | −4.86051e6 | + | 2.16017e6i | −0.730751 | + | 0.324770i | ||||
\(537\) | 780570.i | 0.116809i | ||||||||
\(538\) | −844341. | − | 6.01747e6i | −0.125766 | − | 0.896310i | ||||
\(539\) | 4.33501e6 | − | 4.33501e6i | 0.642715 | − | 0.642715i | ||||
\(540\) | −3.02743e6 | + | 866650.i | −0.446776 | + | 0.127897i | ||||
\(541\) | −9.13296e6 | − | 9.13296e6i | −1.34159 | − | 1.34159i | −0.894482 | − | 0.447104i | \(-0.852455\pi\) |
−0.447104 | − | 0.894482i | \(-0.647545\pi\) | |||||||
\(542\) | −5.70715e6 | − | 4.30263e6i | −0.834491 | − | 0.629124i | ||||
\(543\) | −6.03059e6 | −0.877729 | ||||||||
\(544\) | −1.19056e6 | − | 105489.i | −0.172486 | − | 0.0152831i | ||||
\(545\) | 3.78736e6 | 0.546193 | ||||||||
\(546\) | −1.42950e6 | − | 1.07770e6i | −0.205211 | − | 0.154709i | ||||
\(547\) | 4.04115e6 | + | 4.04115e6i | 0.577480 | + | 0.577480i | 0.934208 | − | 0.356728i | \(-0.116108\pi\) |
−0.356728 | + | 0.934208i | \(0.616108\pi\) | |||||||
\(548\) | −6.39646e6 | + | 1.83109e6i | −0.909889 | + | 0.260470i | ||||
\(549\) | 1.93189e6 | − | 1.93189e6i | 0.273559 | − | 0.273559i | ||||
\(550\) | 266326. | + | 1.89806e6i | 0.0375410 | + | 0.267548i | ||||
\(551\) | 7.98211e6i | 1.12005i | ||||||||
\(552\) | −1.43227e6 | − | 3.22270e6i | −0.200068 | − | 0.450165i | ||||
\(553\) | − | 1.82850e6i | − | 0.254262i | ||||||
\(554\) | −5.28389e6 | + | 741409.i | −0.731441 | + | 0.102632i | ||||
\(555\) | −116055. | + | 116055.i | −0.0159931 | + | 0.0159931i | ||||
\(556\) | 2.13574e6 | + | 1.18510e6i | 0.292996 | + | 0.162580i | ||||
\(557\) | 4.65319e6 | + | 4.65319e6i | 0.635496 | + | 0.635496i | 0.949441 | − | 0.313945i | \(-0.101651\pi\) |
−0.313945 | + | 0.949441i | \(0.601651\pi\) | |||||||
\(558\) | 4.27870e6 | − | 5.67541e6i | 0.581736 | − | 0.771634i | ||||
\(559\) | 3.51714e6 | 0.476058 | ||||||||
\(560\) | −1.84920e6 | − | 428648.i | −0.249180 | − | 0.0577604i | ||||
\(561\) | 1.16803e6 | 0.156692 | ||||||||
\(562\) | −3.94128e6 | + | 5.22784e6i | −0.526376 | + | 0.698203i | ||||
\(563\) | −301629. | − | 301629.i | −0.0401054 | − | 0.0401054i | 0.686770 | − | 0.726875i | \(-0.259028\pi\) |
−0.726875 | + | 0.686770i | \(0.759028\pi\) | |||||||
\(564\) | −3.30800e6 | + | 5.96156e6i | −0.437893 | + | 0.789155i | ||||
\(565\) | 4.55778e6 | − | 4.55778e6i | 0.600665 | − | 0.600665i | ||||
\(566\) | 2.08990e6 | − | 293244.i | 0.274211 | − | 0.0384759i | ||||
\(567\) | 634045.i | 0.0828252i | ||||||||
\(568\) | −857723. | − | 329903.i | −0.111552 | − | 0.0429058i | ||||
\(569\) | 1.33157e6i | 0.172418i | 0.996277 | + | 0.0862089i | \(0.0274752\pi\) | ||||
−0.996277 | + | 0.0862089i | \(0.972525\pi\) | |||||||
\(570\) | −567285. | − | 4.04294e6i | −0.0731331 | − | 0.521207i | ||||
\(571\) | 9.93247e6 | − | 9.93247e6i | 1.27487 | − | 1.27487i | 0.331373 | − | 0.943500i | \(-0.392488\pi\) |
0.943500 | − | 0.331373i | \(-0.107512\pi\) | |||||||
\(572\) | 1.95135e6 | + | 6.81658e6i | 0.249371 | + | 0.871117i | ||||
\(573\) | −6.10514e6 | − | 6.10514e6i | −0.776800 | − | 0.776800i | ||||
\(574\) | −6.99907e6 | − | 5.27661e6i | −0.886667 | − | 0.668459i | ||||
\(575\) | 1.16607e6 | 0.147081 | ||||||||
\(576\) | −2.94157e6 | + | 3.25823e6i | −0.369423 | + | 0.409190i | ||||
\(577\) | −1.29022e7 | −1.61333 | −0.806665 | − | 0.591009i | \(-0.798730\pi\) | ||||
−0.806665 | + | 0.591009i | \(0.798730\pi\) | |||||||
\(578\) | 6.22120e6 | + | 4.69017e6i | 0.774559 | + | 0.583941i | ||||
\(579\) | 3.53272e6 | + | 3.53272e6i | 0.437938 | + | 0.437938i | ||||
\(580\) | −635696. | − | 2.22065e6i | −0.0784656 | − | 0.274100i | ||||
\(581\) | −448339. | + | 448339.i | −0.0551019 | + | 0.0551019i | ||||
\(582\) | −891804. | − | 6.35573e6i | −0.109135 | − | 0.777782i | ||||
\(583\) | − | 4.84137e6i | − | 0.589925i | ||||||
\(584\) | −1.17565e7 | − | 4.52186e6i | −1.42641 | − | 0.548636i | ||||
\(585\) | − | 1.36883e6i | − | 0.165372i | ||||||
\(586\) | −1.38924e7 | + | 1.94930e6i | −1.67121 | + | 0.234496i | ||||
\(587\) | 5.46386e6 | − | 5.46386e6i | 0.654492 | − | 0.654492i | −0.299579 | − | 0.954071i | \(-0.596846\pi\) |
0.954071 | + | 0.299579i | \(0.0968463\pi\) | |||||||
\(588\) | 1.83348e6 | − | 3.30424e6i | 0.218692 | − | 0.394119i | ||||
\(589\) | 1.83348e7 | + | 1.83348e7i | 2.17765 | + | 2.17765i | ||||
\(590\) | 918026. | − | 1.21770e6i | 0.108574 | − | 0.144016i | ||||
\(591\) | 7.79553e6 | 0.918072 | ||||||||
\(592\) | −145378. | + | 627167.i | −0.0170489 | + | 0.0735494i | ||||
\(593\) | −1.10740e7 | −1.29320 | −0.646602 | − | 0.762828i | \(-0.723811\pi\) | ||||
−0.646602 | + | 0.762828i | \(0.723811\pi\) | |||||||
\(594\) | 7.26676e6 | − | 9.63887e6i | 0.845035 | − | 1.12088i | ||||
\(595\) | −270464. | − | 270464.i | −0.0313197 | − | 0.0313197i | ||||
\(596\) | 7.61358e6 | + | 4.22469e6i | 0.877957 | + | 0.487168i | ||||
\(597\) | −5.64595e6 | + | 5.64595e6i | −0.648338 | + | 0.648338i | ||||
\(598\) | 4.27188e6 | − | 599408.i | 0.488501 | − | 0.0685440i | ||||
\(599\) | − | 1.29827e6i | − | 0.147842i | −0.997264 | − | 0.0739212i | \(-0.976449\pi\) | ||
0.997264 | − | 0.0739212i | \(-0.0235513\pi\) | |||||||
\(600\) | 479800. | + | 1.07958e6i | 0.0544104 | + | 0.122427i | ||||
\(601\) | 6.86733e6i | 0.775535i | 0.921757 | + | 0.387768i | \(0.126754\pi\) | ||||
−0.921757 | + | 0.387768i | \(0.873246\pi\) | |||||||
\(602\) | −501547. | − | 3.57444e6i | −0.0564054 | − | 0.401991i | ||||
\(603\) | −2.78331e6 | + | 2.78331e6i | −0.311723 | + | 0.311723i | ||||
\(604\) | −3.47898e6 | + | 995914.i | −0.388025 | + | 0.111078i | ||||
\(605\) | −2.34818e6 | − | 2.34818e6i | −0.260821 | − | 0.260821i | ||||
\(606\) | −675214. | − | 509045.i | −0.0746895 | − | 0.0563085i | ||||
\(607\) | −1.48353e7 | −1.63427 | −0.817136 | − | 0.576444i | \(-0.804440\pi\) | ||||
−0.817136 | + | 0.576444i | \(0.804440\pi\) | |||||||
\(608\) | −1.02800e7 | − | 1.22788e7i | −1.12781 | − | 1.34709i | ||||
\(609\) | −2.23559e6 | −0.244258 | ||||||||
\(610\) | −2.30308e6 | − | 1.73630e6i | −0.250602 | − | 0.188929i | ||||
\(611\) | −5.89690e6 | − | 5.89690e6i | −0.639029 | − | 0.639029i | ||||
\(612\) | −850356. | + | 243428.i | −0.0917745 | + | 0.0262719i | ||||
\(613\) | −1.12593e7 | + | 1.12593e7i | −1.21021 | + | 1.21021i | −0.239247 | + | 0.970959i | \(0.576900\pi\) |
−0.970959 | + | 0.239247i | \(0.923100\pi\) | |||||||
\(614\) | −1.74837e6 | − | 1.24603e7i | −0.187160 | − | 1.33386i | ||||
\(615\) | 5.45520e6i | 0.581598i | ||||||||
\(616\) | 6.64937e6 | − | 2.95520e6i | 0.706039 | − | 0.313787i | ||||
\(617\) | 3.07881e6i | 0.325589i | 0.986660 | + | 0.162795i | \(0.0520508\pi\) | ||||
−0.986660 | + | 0.162795i | \(0.947949\pi\) | |||||||
\(618\) | 6.52550e6 | − | 915625.i | 0.687294 | − | 0.0964376i | ||||
\(619\) | 1.12128e7 | − | 1.12128e7i | 1.17622 | − | 1.17622i | 0.195516 | − | 0.980701i | \(-0.437362\pi\) |
0.980701 | − | 0.195516i | \(-0.0626380\pi\) | |||||||
\(620\) | −6.56100e6 | − | 3.64062e6i | −0.685473 | − | 0.380361i | ||||
\(621\) | −5.19299e6 | − | 5.19299e6i | −0.540367 | − | 0.540367i | ||||
\(622\) | −2.51149e6 | + | 3.33132e6i | −0.260289 | + | 0.345256i | ||||
\(623\) | −713230. | −0.0736223 | ||||||||
\(624\) | 2.31268e6 | + | 3.70837e6i | 0.237768 | + | 0.381260i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | −138014. | + | 183066.i | −0.0140762 | + | 0.0186712i | ||||
\(627\) | 1.10659e7 | + | 1.10659e7i | 1.12414 | + | 1.12414i | ||||
\(628\) | −2.22624e6 | + | 4.01205e6i | −0.225254 | + | 0.405945i | ||||
\(629\) | −91729.4 | + | 91729.4i | −0.00924447 | + | 0.00924447i | ||||
\(630\) | −1.39113e6 | + | 195197.i | −0.139643 | + | 0.0195939i | ||||
\(631\) | 8.75273e6i | 0.875126i | 0.899188 | + | 0.437563i | \(0.144158\pi\) | ||||
−0.899188 | + | 0.437563i | \(0.855842\pi\) | |||||||
\(632\) | −1.60247e6 | + | 4.16631e6i | −0.159587 | + | 0.414915i | ||||
\(633\) | 5.21187e6i | 0.516992i | ||||||||
\(634\) | 471978. | + | 3.36371e6i | 0.0466336 | + | 0.332349i | ||||
\(635\) | 1.40381e6 | − | 1.40381e6i | 0.138157 | − | 0.138157i | ||||
\(636\) | −821273. | − | 2.86891e6i | −0.0805090 | − | 0.281239i | ||||
\(637\) | 3.26839e6 | + | 3.26839e6i | 0.319143 | + | 0.319143i | ||||
\(638\) | 7.07020e6 | + | 5.33023e6i | 0.687670 | + | 0.518435i | ||||
\(639\) | −680080. | −0.0658882 | ||||||||
\(640\) | 3.83782e6 | + | 2.59731e6i | 0.370369 | + | 0.250653i | ||||
\(641\) | −5.52968e6 | −0.531563 | −0.265782 | − | 0.964033i | \(-0.585630\pi\) | ||||
−0.265782 | + | 0.964033i | \(0.585630\pi\) | |||||||
\(642\) | −8.66576e6 | − | 6.53313e6i | −0.829791 | − | 0.625581i | ||||
\(643\) | 4.46397e6 | + | 4.46397e6i | 0.425788 | + | 0.425788i | 0.887191 | − | 0.461403i | \(-0.152654\pi\) |
−0.461403 | + | 0.887191i | \(0.652654\pi\) | |||||||
\(644\) | −1.21835e6 | − | 4.25600e6i | −0.115759 | − | 0.404377i | ||||
\(645\) | −1.58845e6 | + | 1.58845e6i | −0.150340 | + | 0.150340i | ||||
\(646\) | −448379. | − | 3.19552e6i | −0.0422731 | − | 0.301273i | ||||
\(647\) | − | 8.74852e6i | − | 0.821625i | −0.911720 | − | 0.410813i | \(-0.865245\pi\) | ||
0.911720 | − | 0.410813i | \(-0.134755\pi\) | |||||||
\(648\) | 555669. | − | 1.44470e6i | 0.0519851 | − | 0.135157i | ||||
\(649\) | 5.84571e6i | 0.544785i | ||||||||
\(650\) | −1.43104e6 | + | 200797.i | −0.132852 | + | 0.0186412i | ||||
\(651\) | −5.13514e6 | + | 5.13514e6i | −0.474897 | + | 0.474897i | ||||
\(652\) | −3.29489e6 | + | 5.93794e6i | −0.303544 | + | 0.547037i | ||||
\(653\) | −8.59835e6 | − | 8.59835e6i | −0.789100 | − | 0.789100i | 0.192246 | − | 0.981347i | \(-0.438423\pi\) |
−0.981347 | + | 0.192246i | \(0.938423\pi\) | |||||||
\(654\) | −5.38708e6 | + | 7.14560e6i | −0.492503 | + | 0.653273i | ||||
\(655\) | 4.30069e6 | 0.391683 | ||||||||
\(656\) | 1.13233e7 | + | 1.81569e7i | 1.02734 | + | 1.64733i | ||||
\(657\) | −9.32159e6 | −0.842513 | ||||||||
\(658\) | −5.15207e6 | + | 6.83388e6i | −0.463892 | + | 0.615322i | ||||
\(659\) | 1.19553e6 | + | 1.19553e6i | 0.107238 | + | 0.107238i | 0.758690 | − | 0.651452i | \(-0.225840\pi\) |
−0.651452 | + | 0.758690i | \(0.725840\pi\) | |||||||
\(660\) | −3.95987e6 | − | 2.19729e6i | −0.353852 | − | 0.196348i | ||||
\(661\) | −1.03894e7 | + | 1.03894e7i | −0.924881 | + | 0.924881i | −0.997369 | − | 0.0724883i | \(-0.976906\pi\) |
0.0724883 | + | 0.997369i | \(0.476906\pi\) | |||||||
\(662\) | −917441. | + | 128731.i | −0.0813641 | + | 0.0114166i | ||||
\(663\) | 880639.i | 0.0778062i | ||||||||
\(664\) | 1.41448e6 | − | 628640.i | 0.124502 | − | 0.0553327i | ||||
\(665\) | − | 5.12477e6i | − | 0.449387i | ||||||
\(666\) | 66202.2 | + | 471811.i | 0.00578345 | + | 0.0412176i | ||||
\(667\) | 3.80911e6 | − | 3.80911e6i | 0.331519 | − | 0.331519i | ||||
\(668\) | 1.80134e7 | − | 5.15663e6i | 1.56191 | − | 0.447120i | ||||
\(669\) | 176524. | + | 176524.i | 0.0152489 | + | 0.0152489i | ||||
\(670\) | 3.31810e6 | + | 2.50152e6i | 0.285563 | + | 0.215286i | ||||
\(671\) | 1.10562e7 | 0.947981 | ||||||||
\(672\) | 3.43900e6 | − | 2.87918e6i | 0.293771 | − | 0.245949i | ||||
\(673\) | 1.15217e7 | 0.980567 | 0.490284 | − | 0.871563i | \(-0.336893\pi\) | ||||
0.490284 | + | 0.871563i | \(0.336893\pi\) | |||||||
\(674\) | −8.93252e6 | − | 6.73424e6i | −0.757399 | − | 0.571004i | ||||
\(675\) | 1.73961e6 | + | 1.73961e6i | 0.146958 | + | 0.146958i | ||||
\(676\) | 6.28319e6 | − | 1.79866e6i | 0.528827 | − | 0.151385i | ||||
\(677\) | 1.34224e7 | − | 1.34224e7i | 1.12553 | − | 1.12553i | 0.134640 | − | 0.990895i | \(-0.457012\pi\) |
0.990895 | − | 0.134640i | \(-0.0429878\pi\) | |||||||
\(678\) | 2.11624e6 | + | 1.50821e7i | 0.176803 | + | 1.26005i | ||||
\(679\) | − | 8.05643e6i | − | 0.670607i | ||||||
\(680\) | 379232. | + | 853294.i | 0.0314509 | + | 0.0707663i | ||||
\(681\) | − | 5.10683e6i | − | 0.421972i | ||||||
\(682\) | 2.84837e7 | − | 3.99669e6i | 2.34496 | − | 0.329033i | ||||
\(683\) | −624937. | + | 624937.i | −0.0512607 | + | 0.0512607i | −0.732272 | − | 0.681012i | \(-0.761540\pi\) |
0.681012 | + | 0.732272i | \(0.261540\pi\) | |||||||
\(684\) | −1.03625e7 | − | 5.75005e6i | −0.846888 | − | 0.469928i | ||||
\(685\) | 3.67551e6 | + | 3.67551e6i | 0.299290 | + | 0.299290i | ||||
\(686\) | 7.09947e6 | − | 9.41697e6i | 0.575991 | − | 0.764013i | ||||
\(687\) | 1.48161e7 | 1.19769 | ||||||||
\(688\) | −1.98980e6 | + | 8.58405e6i | −0.160265 | + | 0.691387i | ||||
\(689\) | 3.65016e6 | 0.292930 | ||||||||
\(690\) | −1.65860e6 | + | 2.20002e6i | −0.132623 | + | 0.175916i | ||||
\(691\) | −8.23530e6 | − | 8.23530e6i | −0.656121 | − | 0.656121i | 0.298339 | − | 0.954460i | \(-0.403567\pi\) |
−0.954460 | + | 0.298339i | \(0.903567\pi\) | |||||||
\(692\) | −4.28319e6 | + | 7.71900e6i | −0.340018 | + | 0.612768i | ||||
\(693\) | 3.80768e6 | − | 3.80768e6i | 0.301181 | − | 0.301181i | ||||
\(694\) | 3.51352e6 | − | 493000.i | 0.276913 | − | 0.0388551i | ||||
\(695\) | − | 1.90821e6i | − | 0.149852i | ||||||
\(696\) | 5.09389e6 | + | 1.95925e6i | 0.398590 | + | 0.153308i | ||||
\(697\) | 4.31177e6i | 0.336181i | ||||||||
\(698\) | −820861. | − | 5.85013e6i | −0.0637722 | − | 0.454493i | ||||
\(699\) | −6.66774e6 | + | 6.66774e6i | −0.516162 | + | 0.516162i | ||||
\(700\) | 408137. | + | 1.42573e6i | 0.0314819 | + | 0.109974i | ||||
\(701\) | 2.01546e6 | + | 2.01546e6i | 0.154910 | + | 0.154910i | 0.780307 | − | 0.625397i | \(-0.215063\pi\) |
−0.625397 | + | 0.780307i | \(0.715063\pi\) | |||||||
\(702\) | 7.26725e6 | + | 5.47879e6i | 0.556580 | + | 0.419606i | ||||
\(703\) | −1.73809e6 | −0.132643 | ||||||||
\(704\) | −1.77408e7 | + | 906113.i | −1.34909 | + | 0.0689050i | ||||
\(705\) | 5.32645e6 | 0.403613 | ||||||||
\(706\) | −1.39655e7 | − | 1.05286e7i | −1.05449 | − | 0.794985i | ||||
\(707\) | −750574. | − | 750574.i | −0.0564735 | − | 0.0564735i | ||||
\(708\) | 991646. | + | 3.46407e6i | 0.0743487 | + | 0.259719i | ||||
\(709\) | −1.70737e6 | + | 1.70737e6i | −0.127559 | + | 0.127559i | −0.768004 | − | 0.640445i | \(-0.778750\pi\) |
0.640445 | + | 0.768004i | \(0.278750\pi\) | |||||||
\(710\) | 99762.3 | + | 710989.i | 0.00742712 | + | 0.0529318i | ||||
\(711\) | 3.30342e6i | 0.245070i | ||||||||
\(712\) | 1.62512e6 | + | 625066.i | 0.120140 | + | 0.0462089i | ||||
\(713\) | − | 1.74990e7i | − | 1.28911i | ||||||
\(714\) | 894986. | − | 125580.i | 0.0657008 | − | 0.00921881i | ||||
\(715\) | 3.91692e6 | − | 3.91692e6i | 0.286536 | − | 0.286536i | ||||
\(716\) | 1.16062e6 | − | 2.09162e6i | 0.0846070 | − | 0.152476i | ||||
\(717\) | 2.89043e6 | + | 2.89043e6i | 0.209974 | + | 0.209974i | ||||
\(718\) | 3.09689e6 | − | 4.10782e6i | 0.224189 | − | 0.297372i | ||||
\(719\) | 2.07619e7 | 1.49777 | 0.748884 | − | 0.662701i | \(-0.230590\pi\) | ||||
0.748884 | + | 0.662701i | \(0.230590\pi\) | |||||||
\(720\) | 3.34082e6 | + | 774408.i | 0.240172 | + | 0.0556722i | ||||
\(721\) | 8.27162e6 | 0.592588 | ||||||||
\(722\) | 1.75944e7 | − | 2.33379e7i | 1.25612 | − | 1.66616i | ||||
\(723\) | 8.69379e6 | + | 8.69379e6i | 0.618534 | + | 0.618534i | ||||
\(724\) | 1.61596e7 | + | 8.96680e6i | 1.14574 | + | 0.635757i | ||||
\(725\) | −1.27602e6 | + | 1.27602e6i | −0.0901598 | + | 0.0901598i | ||||
\(726\) | 7.77030e6 | − | 1.09029e6i | 0.547137 | − | 0.0767715i | ||||
\(727\) | − | 2.48883e7i | − | 1.74646i | −0.487309 | − | 0.873230i | \(-0.662021\pi\) | ||
0.487309 | − | 0.873230i | \(-0.337979\pi\) | |||||||
\(728\) | 2.22808e6 | + | 5.01331e6i | 0.155812 | + | 0.350587i | ||||
\(729\) | − | 1.11336e7i | − | 0.775921i | ||||||
\(730\) | 1.36740e6 | + | 9.74524e6i | 0.0949707 | + | 0.676839i | ||||
\(731\) | −1.25550e6 | + | 1.25550e6i | −0.0869009 | + | 0.0869009i | ||||
\(732\) | 6.55172e6 | − | 1.87554e6i | 0.451937 | − | 0.129374i | ||||
\(733\) | 9.21984e6 | + | 9.21984e6i | 0.633816 | + | 0.633816i | 0.949023 | − | 0.315207i | \(-0.102074\pi\) |
−0.315207 | + | 0.949023i | \(0.602074\pi\) | |||||||
\(734\) | −4.20023e6 | − | 3.16656e6i | −0.287761 | − | 0.216944i | ||||
\(735\) | −2.95222e6 | −0.201572 | ||||||||
\(736\) | −953849. | + | 1.07652e7i | −0.0649060 | + | 0.732534i | ||||
\(737\) | −1.59289e7 | −1.08023 | ||||||||
\(738\) | 1.26447e7 | + | 9.53288e6i | 0.854612 | + | 0.644293i | ||||
\(739\) | −3.18394e6 | − | 3.18394e6i | −0.214464 | − | 0.214464i | 0.591697 | − | 0.806161i | \(-0.298458\pi\) |
−0.806161 | + | 0.591697i | \(0.798458\pi\) | |||||||
\(740\) | 483543. | − | 138422.i | 0.0324605 | − | 0.00929235i | ||||
\(741\) | −8.34320e6 | + | 8.34320e6i | −0.558196 | + | 0.558196i | ||||
\(742\) | −520516. | − | 3.70963e6i | −0.0347076 | − | 0.247355i | ||||
\(743\) | 1.30646e6i | 0.0868211i | 0.999057 | + | 0.0434106i | \(0.0138224\pi\) | ||||
−0.999057 | + | 0.0434106i | \(0.986178\pi\) | |||||||
\(744\) | 1.62010e7 | − | 7.20025e6i | 1.07302 | − | 0.476887i | ||||
\(745\) | − | 6.80247e6i | − | 0.449030i | ||||||
\(746\) | −1.67768e7 | + | 2.35404e6i | −1.10373 | + | 0.154870i | ||||
\(747\) | 809984. | − | 809984.i | 0.0531098 | − | 0.0531098i | ||||
\(748\) | −3.12987e6 | − | 1.73673e6i | −0.204537 | − | 0.113495i | ||||
\(749\) | −9.63294e6 | − | 9.63294e6i | −0.627414 | − | 0.627414i | ||||
\(750\) | 555618. | − | 736990.i | 0.0360681 | − | 0.0478419i | ||||
\(751\) | −1.87700e7 | −1.21441 | −0.607204 | − | 0.794546i | \(-0.707709\pi\) | ||||
−0.607204 | + | 0.794546i | \(0.707709\pi\) | |||||||
\(752\) | 1.77283e7 | − | 1.10561e7i | 1.14320 | − | 0.712944i | ||||
\(753\) | −1.94139e7 | −1.24774 | ||||||||
\(754\) | −4.01874e6 | + | 5.33059e6i | −0.257432 | + | 0.341466i | ||||
\(755\) | 1.99908e6 | + | 1.99908e6i | 0.127633 | + | 0.127633i | ||||
\(756\) | 4.53173e6 | − | 8.16693e6i | 0.288377 | − | 0.519702i | ||||
\(757\) | 1.33258e7 | − | 1.33258e7i | 0.845190 | − | 0.845190i | −0.144338 | − | 0.989528i | \(-0.546105\pi\) |
0.989528 | + | 0.144338i | \(0.0461054\pi\) | |||||||
\(758\) | −1.40882e7 | + | 1.97679e6i | −0.890602 | + | 0.124965i | ||||
\(759\) | − | 1.05615e7i | − | 0.665457i | ||||||
\(760\) | −4.49128e6 | + | 1.16770e7i | −0.282057 | + | 0.733326i | ||||
\(761\) | − | 1.03099e7i | − | 0.645345i | −0.946511 | − | 0.322673i | \(-0.895419\pi\) | ||
0.946511 | − | 0.322673i | \(-0.104581\pi\) | |||||||
\(762\) | 651805. | + | 4.64530e6i | 0.0406659 | + | 0.289819i | ||||
\(763\) | −7.94312e6 | + | 7.94312e6i | −0.493946 | + | 0.493946i | ||||
\(764\) | 7.28176e6 | + | 2.54371e7i | 0.451339 | + | 1.57664i | ||||
\(765\) | 488629. | + | 488629.i | 0.0301874 | + | 0.0301874i | ||||
\(766\) | 1.62017e6 | + | 1.22144e6i | 0.0997671 | + | 0.0752146i | ||||
\(767\) | −4.40739e6 | −0.270516 | ||||||||
\(768\) | −1.03592e7 | + | 3.54643e6i | −0.633756 | + | 0.216964i | ||||
\(769\) | −1.59550e7 | −0.972928 | −0.486464 | − | 0.873701i | \(-0.661714\pi\) | ||||
−0.486464 | + | 0.873701i | \(0.661714\pi\) | |||||||
\(770\) | −4.53929e6 | − | 3.42218e6i | −0.275906 | − | 0.208006i | ||||
\(771\) | 4.28451e6 | + | 4.28451e6i | 0.259577 | + | 0.259577i | ||||
\(772\) | −4.21356e6 | − | 1.47190e7i | −0.254452 | − | 0.888866i | ||||
\(773\) | 6.77412e6 | − | 6.77412e6i | 0.407760 | − | 0.407760i | −0.473197 | − | 0.880957i | \(-0.656900\pi\) |
0.880957 | + | 0.473197i | \(0.156900\pi\) | |||||||
\(774\) | 906111. | + | 6.45769e6i | 0.0543662 | + | 0.387458i | ||||
\(775\) | 5.86202e6i | 0.350585i | ||||||||
\(776\) | −7.06055e6 | + | 1.83569e7i | −0.420905 | + | 1.09432i | ||||
\(777\) | − | 486797.i | − | 0.0289265i | ||||||
\(778\) | −2.05392e7 | + | 2.88196e6i | −1.21656 | + | 0.170702i | ||||
\(779\) | −4.08498e7 | + | 4.08498e7i | −2.41183 | + | 2.41183i | ||||
\(780\) | 1.65665e6 | − | 2.98555e6i | 0.0974976 | − | 0.175707i | ||||
\(781\) | −1.94605e6 | − | 1.94605e6i | −0.114163 | − | 0.114163i | ||||
\(782\) | −1.31095e6 | + | 1.73889e6i | −0.0766601 | + | 0.101685i | ||||
\(783\) | 1.13653e7 | 0.662484 | ||||||||
\(784\) | −9.82603e6 | + | 6.12789e6i | −0.570937 | + | 0.356058i | ||||
\(785\) | 3.58462e6 | 0.207620 | ||||||||
\(786\) | −6.11723e6 | + | 8.11409e6i | −0.353182 | + | 0.468472i | ||||
\(787\) | −1.32067e7 | − | 1.32067e7i | −0.760079 | − | 0.760079i | 0.216257 | − | 0.976336i | \(-0.430615\pi\) |
−0.976336 | + | 0.216257i | \(0.930615\pi\) | |||||||
\(788\) | −2.08890e7 | − | 1.15911e7i | −1.19840 | − | 0.664978i | ||||
\(789\) | 7.90290e6 | − | 7.90290e6i | 0.451954 | − | 0.451954i | ||||
\(790\) | 3.45356e6 | − | 484586.i | 0.196879 | − | 0.0276251i | ||||
\(791\) | 1.91178e7i | 1.08642i | ||||||||
\(792\) | −1.20130e7 | + | 5.33895e6i | −0.680514 | + | 0.302443i | ||||
\(793\) | 8.33585e6i | 0.470725i | ||||||||
\(794\) | 3.06470e6 | + | 2.18416e7i | 0.172519 | + | 1.22951i | ||||
\(795\) | −1.64853e6 | + | 1.64853e6i | −0.0925077 | + | 0.0925077i | ||||
\(796\) | 2.35238e7 | − | 6.73407e6i | 1.31591 | − | 0.376700i | ||||
\(797\) | 1.22724e7 | + | 1.22724e7i | 0.684361 | + | 0.684361i | 0.960980 | − | 0.276619i | \(-0.0892139\pi\) |
−0.276619 | + | 0.960980i | \(0.589214\pi\) | |||||||
\(798\) | 9.66888e6 | + | 7.28938e6i | 0.537488 | + | 0.405213i | ||||
\(799\) | 4.21000e6 | 0.233300 | ||||||||
\(800\) | 319532. | − | 3.60626e6i | 0.0176518 | − | 0.199220i | ||||
\(801\) | 1.28854e6 | 0.0709607 | ||||||||
\(802\) | −9.87131e6 | − | 7.44200e6i | −0.541925 | − | 0.408558i | ||||
\(803\) | −2.66738e7 | − | 2.66738e7i | −1.45981 | − | 1.45981i | ||||
\(804\) | −9.43921e6 | + | 2.70212e6i | −0.514986 | + | 0.147423i | ||||
\(805\) | −2.44557e6 | + | 2.44557e6i | −0.133012 | + | 0.133012i | ||||
\(806\) | 3.01331e6 | + | 2.14753e7i | 0.163383 | + | 1.16440i | ||||
\(807\) | − | 1.12167e7i | − | 0.606289i | ||||||
\(808\) | 1.05242e6 | + | 2.36801e6i | 0.0567101 | + | 0.127601i | ||||
\(809\) | 2.12446e7i | 1.14124i | 0.821213 | + | 0.570621i | \(0.193298\pi\) | ||||
−0.821213 | + | 0.570621i | \(0.806702\pi\) | |||||||
\(810\) | −1.19755e6 | + | 168034.i | −0.0641327 | + | 0.00899878i | ||||
\(811\) | −2.16169e6 | + | 2.16169e6i | −0.115409 | + | 0.115409i | −0.762453 | − | 0.647044i | \(-0.776005\pi\) |
0.647044 | + | 0.762453i | \(0.276005\pi\) | |||||||
\(812\) | 5.99052e6 | + | 3.32407e6i | 0.318841 | + | 0.176921i | ||||
\(813\) | −9.32920e6 | − | 9.32920e6i | −0.495014 | − | 0.495014i | ||||
\(814\) | −1.16065e6 | + | 1.53953e6i | −0.0613961 | + | 0.0814379i | ||||
\(815\) | 5.30534e6 | 0.279782 | ||||||||
\(816\) | −2.14932e6 | − | 498216.i | −0.112999 | − | 0.0261934i | ||||
\(817\) | −2.37893e7 | −1.24689 | ||||||||
\(818\) | 1.40445e7 | − | 1.86291e7i | 0.733875 | − | 0.973436i | ||||
\(819\) | 2.87081e6 | + | 2.87081e6i | 0.149553 | + | 0.149553i | ||||
\(820\) | 8.11126e6 | − | 1.46178e7i | 0.421263 | − | 0.759185i | ||||
\(821\) | −1.86596e7 | + | 1.86596e7i | −0.966149 | + | 0.966149i | −0.999446 | − | 0.0332965i | \(-0.989399\pi\) |
0.0332965 | + | 0.999446i | \(0.489399\pi\) | |||||||
\(822\) | −1.21626e7 | + | 1.70659e6i | −0.627835 | + | 0.0880947i | ||||
\(823\) | − | 2.26427e7i | − | 1.16527i | −0.812732 | − | 0.582637i | \(-0.802021\pi\) | ||
0.812732 | − | 0.582637i | \(-0.197979\pi\) | |||||||
\(824\) | −1.88472e7 | − | 7.24915e6i | −0.967007 | − | 0.371936i | ||||
\(825\) | 3.53801e6i | 0.180977i | ||||||||
\(826\) | 628498. | + | 4.47919e6i | 0.0320519 | + | 0.228428i | ||||
\(827\) | −1.30154e7 | + | 1.30154e7i | −0.661752 | + | 0.661752i | −0.955793 | − | 0.294041i | \(-0.905000\pi\) |
0.294041 | + | 0.955793i | \(0.405000\pi\) | |||||||
\(828\) | 2.20110e6 | + | 7.68902e6i | 0.111574 | + | 0.389758i | ||||
\(829\) | 551866. | + | 551866.i | 0.0278899 | + | 0.0278899i | 0.720914 | − | 0.693024i | \(-0.243722\pi\) |
−0.693024 | + | 0.720914i | \(0.743722\pi\) | |||||||
\(830\) | −965615. | − | 727978.i | −0.0486529 | − | 0.0366795i | ||||
\(831\) | −9.84926e6 | −0.494767 | ||||||||
\(832\) | −683166. | − | 1.33757e7i | −0.0342151 | − | 0.669896i | ||||
\(833\) | −2.33342e6 | −0.116515 | ||||||||
\(834\) | 3.60021e6 | + | 2.71420e6i | 0.179231 | + | 0.135122i | ||||
\(835\) | −1.03508e7 | − | 1.03508e7i | −0.513757 | − | 0.513757i | ||||
\(836\) | −1.31986e7 | − | 4.61062e7i | −0.653151 | − | 2.28162i | ||||
\(837\) | 2.61059e7 | − | 2.61059e7i | 1.28803 | − | 1.28803i | ||||
\(838\) | −484441. | − | 3.45252e6i | −0.0238304 | − | 0.169835i | ||||
\(839\) | − | 3.46589e7i | − | 1.69985i | −0.526907 | − | 0.849923i | \(-0.676648\pi\) | ||
0.526907 | − | 0.849923i | \(-0.323352\pi\) | |||||||
\(840\) | −3.27044e6 | − | 1.25790e6i | −0.159922 | − | 0.0615102i | ||||
\(841\) | − | 1.21746e7i | − | 0.593561i | ||||||
\(842\) | 1.39784e7 | − | 1.96137e6i | 0.679479 | − | 0.0953411i | ||||
\(843\) | −8.54569e6 | + | 8.54569e6i | −0.414170 | + | 0.414170i | ||||
\(844\) | 7.74945e6 | − | 1.39658e7i | 0.374468 | − | 0.674853i | ||||
\(845\) | −3.61042e6 | − | 3.61042e6i | −0.173947 | − | 0.173947i | ||||
\(846\) | 9.30789e6 | − | 1.23463e7i | 0.447121 | − | 0.593077i | ||||
\(847\) | 9.84951e6 | 0.471744 | ||||||||
\(848\) | −2.06505e6 | + | 8.90871e6i | −0.0986147 | + | 0.425427i | ||||
\(849\) | 3.89560e6 | 0.185484 | ||||||||
\(850\) | 439158. | − | 582514.i | 0.0208484 | − | 0.0276541i | ||||
\(851\) | 829428. | + | 829428.i | 0.0392604 | + | 0.0392604i | ||||
\(852\) | −1.48332e6 | − | 823076.i | −0.0700061 | − | 0.0388455i | ||||
\(853\) | 2.05147e7 | − | 2.05147e7i | 0.965367 | − | 0.965367i | −0.0340530 | − | 0.999420i | \(-0.510842\pi\) |
0.999420 | + | 0.0340530i | \(0.0108415\pi\) | |||||||
\(854\) | 8.47166e6 | − | 1.18870e6i | 0.397488 | − | 0.0557735i | ||||
\(855\) | 9.25857e6i | 0.433140i | ||||||||
\(856\) | 1.35069e7 | + | 3.03912e7i | 0.630042 | + | 1.41763i | ||||
\(857\) | − | 2.06113e7i | − | 0.958633i | −0.877642 | − | 0.479316i | \(-0.840885\pi\) | ||
0.877642 | − | 0.479316i | \(-0.159115\pi\) | |||||||
\(858\) | 1.81868e6 | + | 1.29614e7i | 0.0843407 | + | 0.601082i | ||||
\(859\) | −2.28831e6 | + | 2.28831e6i | −0.105811 | + | 0.105811i | −0.758030 | − | 0.652219i | \(-0.773838\pi\) |
0.652219 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(860\) | 6.61827e6 | − | 1.89458e6i | 0.305139 | − | 0.0873510i | ||||
\(861\) | −1.14410e7 | − | 1.14410e7i | −0.525965 | − | 0.525965i | ||||
\(862\) | 5.62348e6 | + | 4.23955e6i | 0.257773 | + | 0.194335i | ||||
\(863\) | −2.98017e7 | −1.36212 | −0.681058 | − | 0.732229i | \(-0.738480\pi\) | ||||
−0.681058 | + | 0.732229i | \(0.738480\pi\) | |||||||
\(864\) | −1.74831e7 | + | 1.46371e7i | −0.796774 | + | 0.667070i | ||||
\(865\) | 6.89666e6 | 0.313400 | ||||||||
\(866\) | 1.03286e7 | + | 7.78678e6i | 0.468003 | + | 0.352828i | ||||
\(867\) | 1.01695e7 | + | 1.01695e7i | 0.459464 | + | 0.459464i | ||||
\(868\) | 2.13955e7 | − | 6.12481e6i | 0.963882 | − | 0.275927i | ||||
\(869\) | −9.45276e6 | + | 9.45276e6i | −0.424628 | + | 0.424628i | ||||
\(870\) | −592473. | − | 4.22245e6i | −0.0265382 | − | 0.189133i | ||||
\(871\) | − | 1.20096e7i | − | 0.536395i | ||||||
\(872\) | 2.50600e7 | − | 1.11375e7i | 1.11606 | − | 0.496016i | ||||
\(873\) | 1.45550e7i | 0.646363i | ||||||||
\(874\) | −2.88943e7 | + | 4.05430e6i | −1.27948 | + | 0.179530i | ||||
\(875\) | 819246. | − | 819246.i | 0.0361738 | − | 0.0361738i | ||||
\(876\) | −2.03313e7 | − | 1.12816e7i | −0.895168 | − | 0.496718i | ||||
\(877\) | 3.00419e7 | + | 3.00419e7i | 1.31895 | + | 1.31895i | 0.914608 | + | 0.404342i | \(0.132499\pi\) |
0.404342 | + | 0.914608i | \(0.367501\pi\) | |||||||
\(878\) | 4.61264e6 | − | 6.11836e6i | 0.201936 | − | 0.267854i | ||||
\(879\) | −2.58956e7 | −1.13045 | ||||||||
\(880\) | 7.34380e6 | + | 1.17757e7i | 0.319679 | + | 0.512604i | ||||
\(881\) | 4.34646e7 | 1.88667 | 0.943335 | − | 0.331841i | \(-0.107670\pi\) | ||||
0.943335 | + | 0.331841i | \(0.107670\pi\) | |||||||
\(882\) | −5.15896e6 | + | 6.84301e6i | −0.223301 | + | 0.296194i | ||||
\(883\) | 9.44643e6 | + | 9.44643e6i | 0.407724 | + | 0.407724i | 0.880944 | − | 0.473220i | \(-0.156909\pi\) |
−0.473220 | + | 0.880944i | \(0.656909\pi\) | |||||||
\(884\) | 1.30941e6 | − | 2.35977e6i | 0.0563566 | − | 0.101564i | ||||
\(885\) | 1.99051e6 | − | 1.99051e6i | 0.0854293 | − | 0.0854293i | ||||
\(886\) | −1.06176e6 | + | 148980.i | −0.0454403 | + | 0.00637595i | ||||
\(887\) | 1.72681e7i | 0.736945i | 0.929639 | + | 0.368472i | \(0.120119\pi\) | ||||
−0.929639 | + | 0.368472i | \(0.879881\pi\) | |||||||
\(888\) | −426623. | + | 1.10919e6i | −0.0181557 | + | 0.0472033i | ||||
\(889\) | 5.88831e6i | 0.249883i | ||||||||
\(890\) | −189019. | − | 1.34711e6i | −0.00799891 | − | 0.0570068i | ||||
\(891\) | 3.27781e6 | − | 3.27781e6i | 0.138321 | − | 0.138321i | ||||
\(892\) | −210545. | − | 735487.i | −0.00885998 | − | 0.0309502i | ||||
\(893\) | 3.98857e7 | + | 3.98857e7i | 1.67374 | + | 1.67374i | ||||
\(894\) | 1.28342e7 | + | 9.67571e6i | 0.537062 | + | 0.404892i | ||||
\(895\) | −1.86879e6 | −0.0779836 | ||||||||
\(896\) | −1.34962e7 | + | 2.60168e6i | −0.561618 | + | 0.108264i | ||||
\(897\) | 7.96284e6 | 0.330436 | ||||||||
\(898\) | −3.06712e7 | − | 2.31230e7i | −1.26923 | − | 0.956872i | ||||
\(899\) | 1.91490e7 | + | 1.91490e7i | 0.790216 | + | 0.790216i | ||||
\(900\) | −737353. | − | 2.57576e6i | −0.0303437 | − | 0.105998i | ||||
\(901\) | −1.30299e6 | + | 1.30299e6i | −0.0534722 | + | 0.0534722i | ||||
\(902\) | 8.90457e6 | + | 6.34613e7i | 0.364415 | + | 2.59712i | ||||
\(903\) | − | 6.66281e6i | − | 0.271918i | ||||||
\(904\) | 1.67546e7 | − | 4.35606e7i | 0.681887 | − | 1.77285i | ||||
\(905\) | − | 1.44381e7i | − | 0.585987i | ||||||
\(906\) | −6.61511e6 | + | 928199.i | −0.267742 | + | 0.0375682i | ||||
\(907\) | −2.80498e6 | + | 2.80498e6i | −0.113217 | + | 0.113217i | −0.761446 | − | 0.648229i | \(-0.775510\pi\) |
0.648229 | + | 0.761446i | \(0.275510\pi\) | |||||||
\(908\) | −7.59327e6 | + | 1.36843e7i | −0.305643 | + | 0.550818i | ||||
\(909\) | 1.35601e6 | + | 1.35601e6i | 0.0544319 | + | 0.0544319i | ||||
\(910\) | 2.58016e6 | − | 3.42241e6i | 0.103286 | − | 0.137002i | ||||
\(911\) | 4.53266e7 | 1.80949 | 0.904746 | − | 0.425951i | \(-0.140060\pi\) | ||||
0.904746 | + | 0.425951i | \(0.140060\pi\) | |||||||
\(912\) | −1.56426e7 | − | 2.50828e7i | −0.622762 | − | 0.998595i | ||||
\(913\) | 4.63554e6 | 0.184045 | ||||||||
\(914\) | 1.80272e7 | − | 2.39119e7i | 0.713779 | − | 0.946780i | ||||
\(915\) | −3.76473e6 | − | 3.76473e6i | −0.148656 | − | 0.148656i | ||||
\(916\) | −3.97014e7 | − | 2.20299e7i | −1.56339 | − | 0.867507i | ||||
\(917\) | −9.01970e6 | + | 9.01970e6i | −0.354217 | + | 0.354217i | ||||
\(918\) | −4.54992e6 | + | 638422.i | −0.178196 | + | 0.0250035i | ||||
\(919\) | 1.35189e7i | 0.528023i | 0.964520 | + | 0.264011i | \(0.0850457\pi\) | ||||
−0.964520 | + | 0.264011i | \(0.914954\pi\) | |||||||
\(920\) | 7.71559e6 | − | 3.42906e6i | 0.300538 | − | 0.133569i | ||||
\(921\) | − | 2.32263e7i | − | 0.902257i | ||||||
\(922\) | −2.61352e6 | − | 1.86261e7i | −0.101251 | − | 0.721596i | ||||
\(923\) | 1.46723e6 | − | 1.46723e6i | 0.0566883 | − | 0.0566883i | ||||
\(924\) | 1.29132e7 | − | 3.69662e6i | 0.497570 | − | 0.142437i | ||||
\(925\) | −277852. | − | 277852.i | −0.0106772 | − | 0.0106772i | ||||
\(926\) | 3.82142e7 | + | 2.88097e7i | 1.46453 | + | 1.10411i | ||||
\(927\) | −1.49438e7 | −0.571164 | ||||||||
\(928\) | −1.07365e7 | − | 1.28240e7i | −0.409253 | − | 0.488827i | ||||
\(929\) | −3.44513e7 | −1.30968 | −0.654842 | − | 0.755766i | \(-0.727265\pi\) | ||||
−0.654842 | + | 0.755766i | \(0.727265\pi\) | |||||||
\(930\) | −1.10598e7 | − | 8.33803e6i | −0.419316 | − | 0.316123i | ||||
\(931\) | −2.21069e7 | − | 2.21069e7i | −0.835898 | − | 0.835898i | ||||
\(932\) | 2.77811e7 | − | 7.95279e6i | 1.04763 | − | 0.299902i | ||||
\(933\) | −5.44555e6 | + | 5.44555e6i | −0.204804 | + | 0.204804i | ||||
\(934\) | 2.39882e6 | + | 1.70960e7i | 0.0899769 | + | 0.641250i | ||||
\(935\) | 2.79642e6i | 0.104610i | ||||||||
\(936\) | −4.02532e6 | − | 9.05720e6i | −0.150179 | − | 0.337913i | ||||
\(937\) | 2.75086e7i | 1.02358i | 0.859112 | + | 0.511788i | \(0.171017\pi\) | ||||
−0.859112 | + | 0.511788i | \(0.828983\pi\) | |||||||
\(938\) | −1.22053e7 | + | 1.71259e6i | −0.452941 | + | 0.0635544i | ||||
\(939\) | −299249. | + | 299249.i | −0.0110756 | + | 0.0110756i | ||||
\(940\) | −1.42728e7 | − | 7.91981e6i | −0.526853 | − | 0.292345i | ||||
\(941\) | 1.70365e7 | + | 1.70365e7i | 0.627201 | + | 0.627201i | 0.947363 | − | 0.320162i | \(-0.103737\pi\) |
−0.320162 | + | 0.947363i | \(0.603737\pi\) | |||||||
\(942\) | −5.09871e6 | + | 6.76309e6i | −0.187212 | + | 0.248324i | ||||
\(943\) | 3.89875e7 | 1.42773 | ||||||||
\(944\) | 2.49345e6 | − | 1.07568e7i | 0.0910690 | − | 0.392875i | ||||
\(945\) | −7.29687e6 | −0.265801 | ||||||||
\(946\) | −1.58859e7 | + | 2.10715e7i | −0.577143 | + | 0.765541i | ||||
\(947\) | 3.80922e7 | + | 3.80922e7i | 1.38026 | + | 1.38026i | 0.844146 | + | 0.536113i | \(0.180108\pi\) |
0.536113 | + | 0.844146i | \(0.319892\pi\) | |||||||
\(948\) | −3.99802e6 | + | 7.20508e6i | −0.144485 | + | 0.260386i | ||||
\(949\) | 2.01107e7 | − | 2.01107e7i | 0.724874 | − | 0.724874i | ||||
\(950\) | 9.67935e6 | − | 1.35816e6i | 0.347966 | − | 0.0488249i | ||||
\(951\) | 6.27000e6i | 0.224810i | ||||||||
\(952\) | −2.58494e6 | − | 994236.i | −0.0924395 | − | 0.0355547i | ||||
\(953\) | − | 6.41614e6i | − | 0.228845i | −0.993432 | − | 0.114423i | \(-0.963498\pi\) | ||
0.993432 | − | 0.114423i | \(-0.0365018\pi\) | |||||||
\(954\) | 940381. | + | 6.70193e6i | 0.0334528 | + | 0.238413i | ||||
\(955\) | 1.46166e7 | − | 1.46166e7i | 0.518605 | − | 0.518605i | ||||
\(956\) | −3.44749e6 | − | 1.20430e7i | −0.122000 | − | 0.426176i | ||||
\(957\) | 1.15573e7 | + | 1.15573e7i | 0.407921 | + | 0.407921i | ||||
\(958\) | −1.52605e7 | − | 1.15049e7i | −0.537224 | − | 0.405014i | ||||
\(959\) | −1.54171e7 | −0.541322 | ||||||||
\(960\) | 6.34942e6 | + | 5.73234e6i | 0.222359 | + | 0.200749i | ||||
\(961\) | 5.93408e7 | 2.07274 | ||||||||
\(962\) | −1.16073e6 | − | 875076.i | −0.0404384 | − | 0.0304865i | ||||
\(963\) | 1.74032e7 | + | 1.74032e7i | 0.604732 | + | 0.604732i | ||||
\(964\) | −1.03693e7 | − | 3.62226e7i | −0.359383 | − | 1.25542i | ||||
\(965\) | −8.45781e6 | + | 8.45781e6i | −0.292375 | + | 0.292375i | ||||
\(966\) | −1.13551e6 | − | 8.09257e6i | −0.0391515 | − | 0.279025i | ||||
\(967\) | − | 3.21397e7i | − | 1.10529i | −0.833417 | − | 0.552644i | \(-0.813619\pi\) | ||
0.833417 | − | 0.552644i | \(-0.186381\pi\) | |||||||
\(968\) | −2.24425e7 | − | 8.63198e6i | −0.769809 | − | 0.296089i | ||||
\(969\) | − | 5.95650e6i | − | 0.203789i | ||||||
\(970\) | 1.52165e7 | − | 2.13510e6i | 0.519261 | − | 0.0728600i | ||||
\(971\) | −7.02162e6 | + | 7.02162e6i | −0.238995 | + | 0.238995i | −0.816434 | − | 0.577439i | \(-0.804052\pi\) |
0.577439 | + | 0.816434i | \(0.304052\pi\) | |||||||
\(972\) | −1.34649e7 | + | 2.42659e7i | −0.457126 | + | 0.823817i | ||||
\(973\) | 4.00203e6 | + | 4.00203e6i | 0.135518 | + | 0.135518i | ||||
\(974\) | −3.36239e6 | + | 4.45998e6i | −0.113567 | + | 0.150639i | ||||
\(975\) | −2.66749e6 | −0.0898651 | ||||||||
\(976\) | −2.03448e7 | − | 4.71595e6i | −0.683642 | − | 0.158469i | ||||
\(977\) | −2.62900e7 | −0.881157 | −0.440579 | − | 0.897714i | \(-0.645227\pi\) | ||||
−0.440579 | + | 0.897714i | \(0.645227\pi\) | |||||||
\(978\) | −7.54622e6 | + | 1.00096e7i | −0.252280 | + | 0.334632i | ||||
\(979\) | 3.68717e6 | + | 3.68717e6i | 0.122952 | + | 0.122952i | ||||
\(980\) | 7.91080e6 | + | 4.38961e6i | 0.263121 | + | 0.146003i | ||||
\(981\) | 1.43503e7 | − | 1.43503e7i | 0.476089 | − | 0.476089i | ||||
\(982\) | −5.40453e7 | + | 7.58337e6i | −1.78846 | + | 0.250948i | ||||
\(983\) | 2.63215e7i | 0.868814i | 0.900717 | + | 0.434407i | \(0.143042\pi\) | ||||
−0.900717 | + | 0.434407i | \(0.856958\pi\) | |||||||
\(984\) | 1.60421e7 | + | 3.60956e7i | 0.528168 | + | 1.18841i | ||||
\(985\) | 1.86636e7i | 0.612921i | ||||||||
\(986\) | −468288. | − | 3.33741e6i | −0.0153398 | − | 0.109324i | ||||
\(987\) | −1.11710e7 | + | 1.11710e7i | −0.365005 | + | 0.365005i | ||||
\(988\) | 3.47619e7 | − | 9.95115e6i | 1.13295 | − | 0.324325i | ||||
\(989\) | 1.13524e7 | + | 1.13524e7i | 0.369060 | + | 0.369060i | ||||
\(990\) | 8.20083e6 | + | 6.18261e6i | 0.265931 | + | 0.200486i | ||||
\(991\) | −9.19942e6 | −0.297561 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(992\) | −5.41183e7 | − | 4.79514e6i | −1.74608 | − | 0.154711i | ||||
\(993\) | −1.71012e6 | −0.0550369 | ||||||||
\(994\) | −1.70036e6 | − | 1.28191e6i | −0.0545853 | − | 0.0411519i | ||||
\(995\) | −1.35172e7 | − | 1.35172e7i | −0.432841 | − | 0.432841i | ||||
\(996\) | 2.74695e6 | − | 786358.i | 0.0877409 | − | 0.0251172i | ||||
\(997\) | 2.01627e7 | − | 2.01627e7i | 0.642408 | − | 0.642408i | −0.308739 | − | 0.951147i | \(-0.599907\pi\) |
0.951147 | + | 0.308739i | \(0.0999068\pi\) | |||||||
\(998\) | −5.86192e6 | − | 4.17768e7i | −0.186300 | − | 1.32773i | ||||
\(999\) | 2.47477e6i | 0.0784552i |
(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 | 80.6.l.a.61.8 | yes | 80 | |
4.3 | odd | 2 | 320.6.l.a.81.27 | 80 | |||
16.5 | even | 4 | inner | 80.6.l.a.21.8 | ✓ | 80 | |
16.11 | odd | 4 | 320.6.l.a.241.27 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.8 | ✓ | 80 | 16.5 | even | 4 | inner | |
80.6.l.a.61.8 | yes | 80 | 1.1 | even | 1 | trivial | |
320.6.l.a.81.27 | 80 | 4.3 | odd | 2 | |||
320.6.l.a.241.27 | 80 | 16.11 | odd | 4 |