Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,5,Mod(5,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.86065933551\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.221456830464.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 38x^{6} - 100x^{5} + 449x^{4} - 736x^{3} + 1900x^{2} - 1548x + 2307 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(0.500000 + 2.20403i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 18.5 |
Dual form | 18.5.d.a.11.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).
\(n\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | − | 1.41421i | 0.612372 | − | 0.353553i | ||||
\(3\) | −1.67960 | − | 8.84189i | −0.186622 | − | 0.982432i | ||||
\(4\) | 4.00000 | − | 6.92820i | 0.250000 | − | 0.433013i | ||||
\(5\) | 6.41371 | + | 3.70296i | 0.256548 | + | 0.148118i | 0.622759 | − | 0.782414i | \(-0.286012\pi\) |
−0.366211 | + | 0.930532i | \(0.619345\pi\) | |||||||
\(6\) | −16.6185 | − | 19.2828i | −0.461624 | − | 0.535633i | ||||
\(7\) | 30.1882 | + | 52.2875i | 0.616086 | + | 1.06709i | 0.990193 | + | 0.139707i | \(0.0446161\pi\) |
−0.374107 | + | 0.927386i | \(0.622051\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | −75.3579 | + | 29.7016i | −0.930345 | + | 0.366686i | ||||
\(10\) | 20.9471 | 0.209471 | ||||||||
\(11\) | 55.2054 | − | 31.8729i | 0.456243 | − | 0.263412i | −0.254220 | − | 0.967146i | \(-0.581819\pi\) |
0.710463 | + | 0.703734i | \(0.248485\pi\) | |||||||
\(12\) | −67.9768 | − | 23.7310i | −0.472061 | − | 0.164798i | ||||
\(13\) | −144.994 | + | 251.137i | −0.857953 | + | 1.48602i | 0.0159253 | + | 0.999873i | \(0.494931\pi\) |
−0.873878 | + | 0.486145i | \(0.838403\pi\) | |||||||
\(14\) | 147.892 | + | 85.3852i | 0.754549 | + | 0.435639i | ||||
\(15\) | 21.9687 | − | 62.9288i | 0.0976386 | − | 0.279683i | ||||
\(16\) | −32.0000 | − | 55.4256i | −0.125000 | − | 0.216506i | ||||
\(17\) | − | 460.439i | − | 1.59321i | −0.604498 | − | 0.796606i | \(-0.706626\pi\) | ||
0.604498 | − | 0.796606i | \(-0.293374\pi\) | |||||||
\(18\) | −142.584 | + | 179.326i | −0.440074 | + | 0.553475i | ||||
\(19\) | 187.741 | 0.520058 | 0.260029 | − | 0.965601i | \(-0.416268\pi\) | ||||
0.260029 | + | 0.965601i | \(0.416268\pi\) | |||||||
\(20\) | 51.3097 | − | 29.6237i | 0.128274 | − | 0.0740592i | ||||
\(21\) | 411.616 | − | 354.743i | 0.933371 | − | 0.804406i | ||||
\(22\) | 90.1501 | − | 156.144i | 0.186260 | − | 0.322613i | ||||
\(23\) | −35.8618 | − | 20.7048i | −0.0677916 | − | 0.0391395i | 0.465721 | − | 0.884932i | \(-0.345795\pi\) |
−0.533513 | + | 0.845792i | \(0.679128\pi\) | |||||||
\(24\) | −200.069 | + | 38.0049i | −0.347342 | + | 0.0659808i | ||||
\(25\) | −285.076 | − | 493.766i | −0.456122 | − | 0.790026i | ||||
\(26\) | 820.210i | 1.21333i | ||||||||
\(27\) | 389.189 | + | 616.419i | 0.533867 | + | 0.845568i | ||||
\(28\) | 483.012 | 0.616086 | ||||||||
\(29\) | −1211.49 | + | 699.452i | −1.44053 | + | 0.831691i | −0.997885 | − | 0.0650051i | \(-0.979294\pi\) |
−0.442646 | + | 0.896696i | \(0.645960\pi\) | |||||||
\(30\) | −35.1827 | − | 185.212i | −0.0390918 | − | 0.205791i | ||||
\(31\) | −318.482 | + | 551.628i | −0.331407 | + | 0.574014i | −0.982788 | − | 0.184737i | \(-0.940857\pi\) |
0.651381 | + | 0.758751i | \(0.274190\pi\) | |||||||
\(32\) | −156.767 | − | 90.5097i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −374.539 | − | 434.586i | −0.343929 | − | 0.399069i | ||||
\(34\) | −651.158 | − | 1127.84i | −0.563286 | − | 0.975640i | ||||
\(35\) | 447.143i | 0.365015i | ||||||||
\(36\) | −95.6529 | + | 640.901i | −0.0738063 | + | 0.494523i | ||||
\(37\) | 847.670 | 0.619189 | 0.309594 | − | 0.950869i | \(-0.399807\pi\) | ||||
0.309594 | + | 0.950869i | \(0.399807\pi\) | |||||||
\(38\) | 459.869 | − | 265.506i | 0.318469 | − | 0.183868i | ||||
\(39\) | 2464.06 | + | 860.212i | 1.62002 | + | 0.565557i | ||||
\(40\) | 83.7884 | − | 145.126i | 0.0523677 | − | 0.0907036i | ||||
\(41\) | −438.352 | − | 253.083i | −0.260769 | − | 0.150555i | 0.363916 | − | 0.931432i | \(-0.381439\pi\) |
−0.624685 | + | 0.780877i | \(0.714773\pi\) | |||||||
\(42\) | 506.568 | − | 1451.05i | 0.287170 | − | 0.822592i | ||||
\(43\) | −702.429 | − | 1216.64i | −0.379897 | − | 0.658001i | 0.611150 | − | 0.791515i | \(-0.290707\pi\) |
−0.991047 | + | 0.133514i | \(0.957374\pi\) | |||||||
\(44\) | − | 509.966i | − | 0.263412i | ||||||
\(45\) | −593.308 | − | 88.5497i | −0.292991 | − | 0.0437282i | ||||
\(46\) | −117.124 | −0.0553516 | ||||||||
\(47\) | 2146.72 | − | 1239.41i | 0.971806 | − | 0.561073i | 0.0720198 | − | 0.997403i | \(-0.477056\pi\) |
0.899786 | + | 0.436331i | \(0.143722\pi\) | |||||||
\(48\) | −436.320 | + | 376.033i | −0.189375 | + | 0.163209i | ||||
\(49\) | −622.158 | + | 1077.61i | −0.259125 | + | 0.448817i | ||||
\(50\) | −1396.58 | − | 806.317i | −0.558633 | − | 0.322527i | ||||
\(51\) | −4071.15 | + | 773.351i | −1.56522 | + | 0.297328i | ||||
\(52\) | 1159.95 | + | 2009.10i | 0.428976 | + | 0.743009i | ||||
\(53\) | − | 773.208i | − | 0.275261i | −0.990484 | − | 0.137630i | \(-0.956051\pi\) | ||
0.990484 | − | 0.137630i | \(-0.0439486\pi\) | |||||||
\(54\) | 1825.06 | + | 959.517i | 0.625879 | + | 0.329052i | ||||
\(55\) | 472.095 | 0.156065 | ||||||||
\(56\) | 1183.13 | − | 683.082i | 0.377274 | − | 0.217819i | ||||
\(57\) | −315.329 | − | 1659.98i | −0.0970541 | − | 0.510921i | ||||
\(58\) | −1978.35 | + | 3426.60i | −0.588094 | + | 1.01861i | ||||
\(59\) | 3894.93 | + | 2248.74i | 1.11891 | + | 0.646004i | 0.941123 | − | 0.338065i | \(-0.109772\pi\) |
0.177789 | + | 0.984069i | \(0.443106\pi\) | |||||||
\(60\) | −348.109 | − | 403.919i | −0.0966968 | − | 0.112200i | ||||
\(61\) | 1301.48 | + | 2254.22i | 0.349765 | + | 0.605811i | 0.986208 | − | 0.165513i | \(-0.0529280\pi\) |
−0.636442 | + | 0.771324i | \(0.719595\pi\) | |||||||
\(62\) | 1801.61i | 0.468681i | ||||||||
\(63\) | −3827.95 | − | 3043.64i | −0.964461 | − | 0.766853i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | −1859.90 | + | 1073.81i | −0.440213 | + | 0.254157i | ||||
\(66\) | −1532.03 | − | 534.837i | −0.351705 | − | 0.122782i | ||||
\(67\) | 1691.55 | − | 2929.85i | 0.376821 | − | 0.652673i | −0.613777 | − | 0.789479i | \(-0.710351\pi\) |
0.990598 | + | 0.136807i | \(0.0436840\pi\) | |||||||
\(68\) | −3190.01 | − | 1841.75i | −0.689881 | − | 0.398303i | ||||
\(69\) | −122.836 | + | 351.862i | −0.0258005 | + | 0.0739050i | ||||
\(70\) | 632.356 | + | 1095.27i | 0.129052 | + | 0.223525i | ||||
\(71\) | − | 2771.07i | − | 0.549706i | −0.961486 | − | 0.274853i | \(-0.911371\pi\) | ||
0.961486 | − | 0.274853i | \(-0.0886292\pi\) | |||||||
\(72\) | 672.070 | + | 1705.15i | 0.129643 | + | 0.328926i | ||||
\(73\) | 3525.16 | 0.661506 | 0.330753 | − | 0.943717i | \(-0.392697\pi\) | ||||
0.330753 | + | 0.943717i | \(0.392697\pi\) | |||||||
\(74\) | 2076.36 | − | 1198.79i | 0.379174 | − | 0.218916i | ||||
\(75\) | −3887.01 | + | 3349.94i | −0.691025 | + | 0.595545i | ||||
\(76\) | 750.964 | − | 1300.71i | 0.130014 | − | 0.225192i | ||||
\(77\) | 3333.11 | + | 1924.37i | 0.562170 | + | 0.324569i | ||||
\(78\) | 7252.21 | − | 1377.62i | 1.19201 | − | 0.226434i | ||||
\(79\) | −2914.90 | − | 5048.75i | −0.467056 | − | 0.808964i | 0.532236 | − | 0.846596i | \(-0.321352\pi\) |
−0.999292 | + | 0.0376317i | \(0.988019\pi\) | |||||||
\(80\) | − | 473.979i | − | 0.0740592i | ||||||
\(81\) | 4796.63 | − | 4476.50i | 0.731082 | − | 0.682289i | ||||
\(82\) | −1431.65 | −0.212917 | ||||||||
\(83\) | −4438.63 | + | 2562.65i | −0.644307 | + | 0.371991i | −0.786272 | − | 0.617881i | \(-0.787991\pi\) |
0.141965 | + | 0.989872i | \(0.454658\pi\) | |||||||
\(84\) | −811.265 | − | 4270.73i | −0.114975 | − | 0.605263i | ||||
\(85\) | 1704.98 | − | 2953.12i | 0.235984 | − | 0.408736i | ||||
\(86\) | −3441.19 | − | 1986.77i | −0.465277 | − | 0.268628i | ||||
\(87\) | 8219.29 | + | 9537.03i | 1.08591 | + | 1.26001i | ||||
\(88\) | −721.200 | − | 1249.16i | −0.0931302 | − | 0.161306i | ||||
\(89\) | 1221.14i | 0.154164i | 0.997025 | + | 0.0770822i | \(0.0245604\pi\) | ||||
−0.997025 | + | 0.0770822i | \(0.975440\pi\) | |||||||
\(90\) | −1578.53 | + | 622.162i | −0.194880 | + | 0.0768101i | ||||
\(91\) | −17508.5 | −2.11429 | ||||||||
\(92\) | −286.894 | + | 165.638i | −0.0338958 | + | 0.0195698i | ||||
\(93\) | 5412.35 | + | 1889.47i | 0.625778 | + | 0.218461i | ||||
\(94\) | 3505.58 | − | 6071.84i | 0.396738 | − | 0.687171i | ||||
\(95\) | 1204.12 | + | 695.197i | 0.133420 | + | 0.0770301i | ||||
\(96\) | −536.970 | + | 1538.14i | −0.0582650 | + | 0.166899i | ||||
\(97\) | 7367.60 | + | 12761.1i | 0.783038 | + | 1.35626i | 0.930164 | + | 0.367144i | \(0.119664\pi\) |
−0.147126 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(98\) | 3519.46i | 0.366458i | ||||||||
\(99\) | −3213.49 | + | 4041.56i | −0.327874 | + | 0.412362i | ||||
\(100\) | −4561.22 | −0.456122 | ||||||||
\(101\) | −15034.0 | + | 8679.88i | −1.47378 | + | 0.850885i | −0.999564 | − | 0.0295251i | \(-0.990601\pi\) |
−0.474213 | + | 0.880410i | \(0.657267\pi\) | |||||||
\(102\) | −8878.54 | + | 7651.78i | −0.853378 | + | 0.735466i | ||||
\(103\) | 5164.36 | − | 8944.94i | 0.486791 | − | 0.843146i | −0.513094 | − | 0.858332i | \(-0.671501\pi\) |
0.999885 | + | 0.0151863i | \(0.00483414\pi\) | |||||||
\(104\) | 5682.58 | + | 3280.84i | 0.525387 | + | 0.303332i | ||||
\(105\) | 3953.59 | − | 751.020i | 0.358602 | − | 0.0681197i | ||||
\(106\) | −1093.48 | − | 1893.97i | −0.0973195 | − | 0.168562i | ||||
\(107\) | − | 7260.47i | − | 0.634157i | −0.948399 | − | 0.317079i | \(-0.897298\pi\) | ||
0.948399 | − | 0.317079i | \(-0.102702\pi\) | |||||||
\(108\) | 5827.44 | − | 230.703i | 0.499609 | − | 0.0197791i | ||||
\(109\) | 1894.50 | 0.159456 | 0.0797280 | − | 0.996817i | \(-0.474595\pi\) | ||||
0.0797280 | + | 0.996817i | \(0.474595\pi\) | |||||||
\(110\) | 1156.39 | − | 667.644i | 0.0955697 | − | 0.0551772i | ||||
\(111\) | −1423.74 | − | 7495.00i | −0.115554 | − | 0.608311i | ||||
\(112\) | 1932.05 | − | 3346.40i | 0.154022 | − | 0.266773i | ||||
\(113\) | −8274.94 | − | 4777.54i | −0.648049 | − | 0.374151i | 0.139659 | − | 0.990200i | \(-0.455399\pi\) |
−0.787708 | + | 0.616048i | \(0.788733\pi\) | |||||||
\(114\) | −3119.97 | − | 3620.17i | −0.240071 | − | 0.278560i | ||||
\(115\) | −153.338 | − | 265.589i | −0.0115946 | − | 0.0200824i | ||||
\(116\) | 11191.2i | 0.831691i | ||||||||
\(117\) | 3467.28 | − | 23231.7i | 0.253289 | − | 1.69711i | ||||
\(118\) | 12720.8 | 0.913587 | ||||||||
\(119\) | 24075.2 | − | 13899.8i | 1.70011 | − | 0.981557i | ||||
\(120\) | −1423.92 | − | 497.095i | −0.0988830 | − | 0.0345205i | ||||
\(121\) | −5288.74 | + | 9160.37i | −0.361228 | + | 0.625666i | ||||
\(122\) | 6375.91 | + | 3681.13i | 0.428373 | + | 0.247321i | ||||
\(123\) | −1501.47 | + | 4300.94i | −0.0992448 | + | 0.284284i | ||||
\(124\) | 2547.86 | + | 4413.02i | 0.165704 | + | 0.287007i | ||||
\(125\) | − | 8851.20i | − | 0.566477i | ||||||
\(126\) | −13680.9 | − | 2041.84i | −0.861733 | − | 0.128611i | ||||
\(127\) | 7548.96 | 0.468037 | 0.234018 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(128\) | −1254.14 | + | 724.077i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −9577.62 | + | 8254.27i | −0.575544 | + | 0.496020i | ||||
\(130\) | −3037.20 | + | 5260.59i | −0.179716 | + | 0.311278i | ||||
\(131\) | −4176.24 | − | 2411.15i | −0.243356 | − | 0.140502i | 0.373362 | − | 0.927686i | \(-0.378205\pi\) |
−0.616718 | + | 0.787184i | \(0.711538\pi\) | |||||||
\(132\) | −4509.06 | + | 856.537i | −0.258784 | + | 0.0491584i | ||||
\(133\) | 5667.56 | + | 9816.51i | 0.320400 | + | 0.554950i | ||||
\(134\) | − | 9568.84i | − | 0.532905i | ||||||
\(135\) | 213.571 | + | 5394.69i | 0.0117186 | + | 0.296005i | ||||
\(136\) | −10418.5 | −0.563286 | ||||||||
\(137\) | 9346.97 | − | 5396.48i | 0.498001 | − | 0.287521i | −0.229887 | − | 0.973217i | \(-0.573836\pi\) |
0.727887 | + | 0.685697i | \(0.240502\pi\) | |||||||
\(138\) | 196.721 | + | 1035.60i | 0.0103298 | + | 0.0543792i | ||||
\(139\) | −14138.6 | + | 24488.8i | −0.731774 | + | 1.26747i | 0.224350 | + | 0.974509i | \(0.427974\pi\) |
−0.956124 | + | 0.292961i | \(0.905359\pi\) | |||||||
\(140\) | 3097.90 | + | 1788.57i | 0.158056 | + | 0.0912537i | ||||
\(141\) | −14564.3 | − | 16899.3i | −0.732576 | − | 0.850025i | ||||
\(142\) | −3918.88 | − | 6787.70i | −0.194350 | − | 0.336625i | ||||
\(143\) | 18485.5i | 0.903981i | ||||||||
\(144\) | 4057.68 | + | 3226.31i | 0.195683 | + | 0.155590i | ||||
\(145\) | −10360.2 | −0.492755 | ||||||||
\(146\) | 8634.85 | − | 4985.33i | 0.405088 | − | 0.233878i | ||||
\(147\) | 10573.1 | + | 3691.10i | 0.489290 | + | 0.170813i | ||||
\(148\) | 3390.68 | − | 5872.83i | 0.154797 | − | 0.268117i | ||||
\(149\) | −8456.84 | − | 4882.56i | −0.380922 | − | 0.219925i | 0.297298 | − | 0.954785i | \(-0.403915\pi\) |
−0.678219 | + | 0.734860i | \(0.737248\pi\) | |||||||
\(150\) | −4783.67 | + | 13702.7i | −0.212608 | + | 0.609009i | ||||
\(151\) | −383.441 | − | 664.140i | −0.0168169 | − | 0.0291277i | 0.857495 | − | 0.514493i | \(-0.172020\pi\) |
−0.874311 | + | 0.485365i | \(0.838687\pi\) | |||||||
\(152\) | − | 4248.09i | − | 0.183868i | ||||||
\(153\) | 13675.8 | + | 34697.7i | 0.584210 | + | 1.48224i | ||||
\(154\) | 10885.9 | 0.459010 | ||||||||
\(155\) | −4085.31 | + | 2358.65i | −0.170044 | + | 0.0981749i | ||||
\(156\) | 15816.0 | − | 13630.6i | 0.649899 | − | 0.560102i | ||||
\(157\) | 2595.91 | − | 4496.26i | 0.105315 | − | 0.182411i | −0.808552 | − | 0.588425i | \(-0.799748\pi\) |
0.913867 | + | 0.406014i | \(0.133082\pi\) | |||||||
\(158\) | −14280.0 | − | 8244.57i | −0.572024 | − | 0.330258i | ||||
\(159\) | −6836.62 | + | 1298.68i | −0.270425 | + | 0.0513697i | ||||
\(160\) | −670.307 | − | 1161.01i | −0.0261839 | − | 0.0453518i | ||||
\(161\) | − | 2500.17i | − | 0.0964533i | ||||||
\(162\) | 5418.57 | − | 17748.6i | 0.206469 | − | 0.676292i | ||||
\(163\) | 24180.8 | 0.910113 | 0.455057 | − | 0.890462i | \(-0.349619\pi\) | ||||
0.455057 | + | 0.890462i | \(0.349619\pi\) | |||||||
\(164\) | −3506.82 | + | 2024.66i | −0.130384 | + | 0.0752775i | ||||
\(165\) | −792.930 | − | 4174.21i | −0.0291251 | − | 0.153323i | ||||
\(166\) | −7248.26 | + | 12554.3i | −0.263037 | + | 0.455594i | ||||
\(167\) | 18849.5 | + | 10882.7i | 0.675875 | + | 0.390216i | 0.798299 | − | 0.602261i | \(-0.205734\pi\) |
−0.122424 | + | 0.992478i | \(0.539067\pi\) | |||||||
\(168\) | −8026.91 | − | 9313.82i | −0.284400 | − | 0.329996i | ||||
\(169\) | −27766.0 | − | 48092.2i | −0.972166 | − | 1.68384i | ||||
\(170\) | − | 9644.85i | − | 0.333732i | ||||||
\(171\) | −14147.8 | + | 5576.20i | −0.483833 | + | 0.190698i | ||||
\(172\) | −11238.9 | −0.379897 | ||||||||
\(173\) | −20789.4 | + | 12002.8i | −0.694625 | + | 0.401042i | −0.805342 | − | 0.592810i | \(-0.798019\pi\) |
0.110717 | + | 0.993852i | \(0.464685\pi\) | |||||||
\(174\) | 33620.5 | + | 11737.0i | 1.11047 | + | 0.387668i | ||||
\(175\) | 17211.9 | − | 29811.9i | 0.562021 | − | 0.973449i | ||||
\(176\) | −3533.15 | − | 2039.86i | −0.114061 | − | 0.0658530i | ||||
\(177\) | 13341.2 | − | 38215.5i | 0.425841 | − | 1.21981i | ||||
\(178\) | 1726.95 | + | 2991.16i | 0.0545053 | + | 0.0944060i | ||||
\(179\) | 41131.4i | 1.28371i | 0.766826 | + | 0.641855i | \(0.221835\pi\) | ||||
−0.766826 | + | 0.641855i | \(0.778165\pi\) | |||||||
\(180\) | −2986.72 | + | 3756.36i | −0.0921827 | + | 0.115937i | ||||
\(181\) | 32048.3 | 0.978246 | 0.489123 | − | 0.872215i | \(-0.337317\pi\) | ||||
0.489123 | + | 0.872215i | \(0.337317\pi\) | |||||||
\(182\) | −42886.8 | + | 24760.7i | −1.29473 | + | 0.747515i | ||||
\(183\) | 17745.6 | − | 15293.7i | 0.529895 | − | 0.456678i | ||||
\(184\) | −468.496 | + | 811.459i | −0.0138379 | + | 0.0239680i | ||||
\(185\) | 5436.71 | + | 3138.88i | 0.158852 | + | 0.0917132i | ||||
\(186\) | 15929.6 | − | 3025.97i | 0.460447 | − | 0.0874660i | ||||
\(187\) | −14675.5 | − | 25418.7i | −0.419671 | − | 0.726892i | ||||
\(188\) | − | 19830.5i | − | 0.561073i | ||||||
\(189\) | −20482.1 | + | 38958.3i | −0.573392 | + | 1.09063i | ||||
\(190\) | 3932.63 | 0.108937 | ||||||||
\(191\) | 11444.3 | − | 6607.35i | 0.313705 | − | 0.181118i | −0.334878 | − | 0.942261i | \(-0.608695\pi\) |
0.648583 | + | 0.761144i | \(0.275362\pi\) | |||||||
\(192\) | 859.953 | + | 4527.05i | 0.0233277 | + | 0.122804i | ||||
\(193\) | −893.462 | + | 1547.52i | −0.0239862 | + | 0.0415453i | −0.877769 | − | 0.479083i | \(-0.840969\pi\) |
0.853783 | + | 0.520629i | \(0.174302\pi\) | |||||||
\(194\) | 36093.7 | + | 20838.7i | 0.959022 | + | 0.553691i | ||||
\(195\) | 12618.4 | + | 14641.5i | 0.331845 | + | 0.385048i | ||||
\(196\) | 4977.27 | + | 8620.88i | 0.129562 | + | 0.224408i | ||||
\(197\) | 17640.9i | 0.454557i | 0.973830 | + | 0.227278i | \(0.0729828\pi\) | ||||
−0.973830 | + | 0.227278i | \(0.927017\pi\) | |||||||
\(198\) | −2155.78 | + | 14444.3i | −0.0549888 | + | 0.368440i | ||||
\(199\) | 236.938 | 0.00598314 | 0.00299157 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299157 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(200\) | −11172.7 | + | 6450.54i | −0.279316 | + | 0.161263i | ||||
\(201\) | −28746.5 | − | 10035.5i | −0.711529 | − | 0.248398i | ||||
\(202\) | −24550.4 | + | 42522.6i | −0.601667 | + | 1.04212i | ||||
\(203\) | −73145.3 | − | 42230.4i | −1.77498 | − | 1.02479i | ||||
\(204\) | −10926.6 | + | 31299.1i | −0.262559 | + | 0.752094i | ||||
\(205\) | −1874.31 | − | 3246.40i | −0.0445999 | − | 0.0772493i | ||||
\(206\) | − | 29214.0i | − | 0.688426i | ||||||
\(207\) | 3317.43 | + | 495.119i | 0.0774215 | + | 0.0115550i | ||||
\(208\) | 18559.2 | 0.428976 | ||||||||
\(209\) | 10364.3 | − | 5983.84i | 0.237273 | − | 0.136990i | ||||
\(210\) | 8622.17 | − | 7430.83i | 0.195514 | − | 0.168500i | ||||
\(211\) | −17979.1 | + | 31140.8i | −0.403835 | + | 0.699463i | −0.994185 | − | 0.107684i | \(-0.965656\pi\) |
0.590350 | + | 0.807147i | \(0.298990\pi\) | |||||||
\(212\) | −5356.94 | − | 3092.83i | −0.119192 | − | 0.0688152i | ||||
\(213\) | −24501.5 | + | 4654.28i | −0.540049 | + | 0.102587i | ||||
\(214\) | −10267.8 | − | 17784.4i | −0.224208 | − | 0.388340i | ||||
\(215\) | − | 10404.3i | − | 0.225079i | ||||||
\(216\) | 13948.0 | − | 8806.34i | 0.298954 | − | 0.188750i | ||||
\(217\) | −38457.7 | −0.816702 | ||||||||
\(218\) | 4640.55 | − | 2679.22i | 0.0976464 | − | 0.0563762i | ||||
\(219\) | −5920.85 | − | 31169.1i | −0.123451 | − | 0.649884i | ||||
\(220\) | 1888.38 | − | 3270.77i | 0.0390162 | − | 0.0675780i | ||||
\(221\) | 115633. | + | 66760.8i | 2.36754 | + | 1.36690i | ||||
\(222\) | −14087.0 | − | 16345.4i | −0.285833 | − | 0.331658i | ||||
\(223\) | 27311.5 | + | 47305.0i | 0.549207 | + | 0.951255i | 0.998329 | + | 0.0577846i | \(0.0184036\pi\) |
−0.449122 | + | 0.893471i | \(0.648263\pi\) | |||||||
\(224\) | − | 10929.3i | − | 0.217819i | ||||||
\(225\) | 36148.4 | + | 28742.0i | 0.714043 | + | 0.567743i | ||||
\(226\) | −27025.8 | −0.529130 | ||||||||
\(227\) | 67692.0 | − | 39082.0i | 1.31367 | − | 0.758447i | 0.330967 | − | 0.943642i | \(-0.392625\pi\) |
0.982702 | + | 0.185196i | \(0.0592919\pi\) | |||||||
\(228\) | −12762.0 | − | 4455.27i | −0.245499 | − | 0.0857047i | ||||
\(229\) | 6019.52 | − | 10426.1i | 0.114787 | − | 0.198816i | −0.802908 | − | 0.596103i | \(-0.796715\pi\) |
0.917694 | + | 0.397287i | \(0.130048\pi\) | |||||||
\(230\) | −751.200 | − | 433.706i | −0.0142004 | − | 0.00819859i | ||||
\(231\) | 11416.8 | − | 32703.1i | 0.213954 | − | 0.612866i | ||||
\(232\) | 15826.8 | + | 27412.8i | 0.294047 | + | 0.509305i | ||||
\(233\) | − | 95396.0i | − | 1.75719i | −0.477568 | − | 0.878595i | \(-0.658482\pi\) | ||
0.477568 | − | 0.878595i | \(-0.341518\pi\) | |||||||
\(234\) | −24361.6 | − | 61809.3i | −0.444911 | − | 1.12881i | ||||
\(235\) | 18357.9 | 0.332421 | ||||||||
\(236\) | 31159.4 | − | 17989.9i | 0.559456 | − | 0.323002i | ||||
\(237\) | −39744.6 | + | 34253.0i | −0.707590 | + | 0.609821i | ||||
\(238\) | 39314.6 | − | 68094.9i | 0.694065 | − | 1.20216i | ||||
\(239\) | −88641.6 | − | 51177.2i | −1.55182 | − | 0.895944i | −0.997994 | − | 0.0633127i | \(-0.979833\pi\) |
−0.553827 | − | 0.832632i | \(-0.686833\pi\) | |||||||
\(240\) | −4190.87 | + | 796.093i | −0.0727581 | + | 0.0138211i | ||||
\(241\) | 26833.9 | + | 46477.6i | 0.462008 | + | 0.800221i | 0.999061 | − | 0.0433274i | \(-0.0137959\pi\) |
−0.537053 | + | 0.843548i | \(0.680463\pi\) | |||||||
\(242\) | 29917.6i | 0.510854i | ||||||||
\(243\) | −47637.1 | − | 34892.5i | −0.806739 | − | 0.590908i | ||||
\(244\) | 20823.6 | 0.349765 | ||||||||
\(245\) | −7980.69 | + | 4607.65i | −0.132956 | + | 0.0767622i | ||||
\(246\) | 2404.60 | + | 12658.5i | 0.0397349 | + | 0.209176i | ||||
\(247\) | −27221.3 | + | 47148.7i | −0.446185 | + | 0.772815i | ||||
\(248\) | 12481.9 | + | 7206.43i | 0.202945 | + | 0.117170i | ||||
\(249\) | 30113.7 | + | 34941.7i | 0.485698 | + | 0.563566i | ||||
\(250\) | −12517.5 | − | 21680.9i | −0.200280 | − | 0.346895i | ||||
\(251\) | 99789.6i | 1.58394i | 0.610562 | + | 0.791969i | \(0.290944\pi\) | ||||
−0.610562 | + | 0.791969i | \(0.709056\pi\) | |||||||
\(252\) | −36398.7 | + | 14346.2i | −0.573173 | + | 0.225910i | ||||
\(253\) | −2639.69 | −0.0412393 | ||||||||
\(254\) | 18491.1 | − | 10675.8i | 0.286613 | − | 0.165476i | ||||
\(255\) | −28974.8 | − | 10115.2i | −0.445595 | − | 0.155559i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2249.40 | − | 1298.69i | −0.0340565 | − | 0.0196625i | 0.482875 | − | 0.875689i | \(-0.339593\pi\) |
−0.516932 | + | 0.856027i | \(0.672926\pi\) | |||||||
\(258\) | −11787.0 | + | 33763.6i | −0.177078 | + | 0.507234i | ||||
\(259\) | 25589.6 | + | 44322.6i | 0.381474 | + | 0.660732i | ||||
\(260\) | 17181.0i | 0.254157i | ||||||||
\(261\) | 70520.3 | − | 88692.4i | 1.03522 | − | 1.30198i | ||||
\(262\) | −13639.5 | −0.198700 | ||||||||
\(263\) | −109308. | + | 63109.2i | −1.58031 | + | 0.912392i | −0.585495 | + | 0.810676i | \(0.699100\pi\) |
−0.994814 | + | 0.101716i | \(0.967567\pi\) | |||||||
\(264\) | −9833.57 | + | 8474.85i | −0.141092 | + | 0.121597i | ||||
\(265\) | 2863.16 | − | 4959.13i | 0.0407712 | − | 0.0706178i | ||||
\(266\) | 27765.3 | + | 16030.3i | 0.392409 | + | 0.226557i | ||||
\(267\) | 10797.1 | − | 2051.01i | 0.151456 | − | 0.0287704i | ||||
\(268\) | −13532.4 | − | 23438.8i | −0.188410 | − | 0.326336i | ||||
\(269\) | − | 14374.7i | − | 0.198652i | −0.995055 | − | 0.0993262i | \(-0.968331\pi\) | ||
0.995055 | − | 0.0993262i | \(-0.0316687\pi\) | |||||||
\(270\) | 8152.38 | + | 12912.2i | 0.111830 | + | 0.177122i | ||||
\(271\) | −54121.0 | −0.736931 | −0.368466 | − | 0.929641i | \(-0.620117\pi\) | ||||
−0.368466 | + | 0.929641i | \(0.620117\pi\) | |||||||
\(272\) | −25520.1 | + | 14734.0i | −0.344941 | + | 0.199152i | ||||
\(273\) | 29407.1 | + | 154808.i | 0.394573 | + | 2.07715i | ||||
\(274\) | 15263.5 | − | 26437.2i | 0.203308 | − | 0.352140i | ||||
\(275\) | −31475.5 | − | 18172.4i | −0.416205 | − | 0.240296i | ||||
\(276\) | 1946.42 | + | 2258.48i | 0.0255517 | + | 0.0296482i | ||||
\(277\) | −15805.9 | − | 27376.6i | −0.205996 | − | 0.356796i | 0.744453 | − | 0.667674i | \(-0.232710\pi\) |
−0.950450 | + | 0.310878i | \(0.899377\pi\) | |||||||
\(278\) | 79980.0i | 1.03488i | ||||||||
\(279\) | 7615.94 | − | 51028.9i | 0.0978397 | − | 0.655553i | ||||
\(280\) | 10117.7 | 0.129052 | ||||||||
\(281\) | 88490.4 | − | 51090.0i | 1.12068 | − | 0.647028i | 0.179109 | − | 0.983829i | \(-0.442678\pi\) |
0.941576 | + | 0.336801i | \(0.109345\pi\) | |||||||
\(282\) | −59574.5 | − | 20797.7i | −0.749138 | − | 0.261527i | ||||
\(283\) | 72667.1 | − | 125863.i | 0.907329 | − | 1.57154i | 0.0895693 | − | 0.995981i | \(-0.471451\pi\) |
0.817760 | − | 0.575560i | \(-0.195216\pi\) | |||||||
\(284\) | −19198.5 | − | 11084.3i | −0.238030 | − | 0.137427i | ||||
\(285\) | 4124.42 | − | 11814.3i | 0.0507777 | − | 0.145452i | ||||
\(286\) | 26142.4 | + | 45280.0i | 0.319605 | + | 0.553573i | ||||
\(287\) | − | 30560.5i | − | 0.371019i | ||||||
\(288\) | 14501.9 | + | 2164.38i | 0.174840 | + | 0.0260945i | ||||
\(289\) | −128483. | −1.53833 | ||||||||
\(290\) | −25377.1 | + | 14651.5i | −0.301749 | + | 0.174215i | ||||
\(291\) | 100457. | − | 86576.9i | 1.18630 | − | 1.02239i | ||||
\(292\) | 14100.7 | − | 24423.1i | 0.165376 | − | 0.286440i | ||||
\(293\) | −40048.4 | − | 23122.0i | −0.466498 | − | 0.269333i | 0.248274 | − | 0.968690i | \(-0.420137\pi\) |
−0.714773 | + | 0.699357i | \(0.753470\pi\) | |||||||
\(294\) | 31118.7 | − | 5911.27i | 0.360020 | − | 0.0683890i | ||||
\(295\) | 16654.0 | + | 28845.5i | 0.191370 | + | 0.331463i | ||||
\(296\) | − | 19180.6i | − | 0.218916i | ||||||
\(297\) | 41132.4 | + | 21625.1i | 0.466306 | + | 0.245158i | ||||
\(298\) | −27619.9 | −0.311021 | ||||||||
\(299\) | 10399.5 | − | 6004.15i | 0.116324 | − | 0.0671597i | ||||
\(300\) | 7661.01 | + | 40329.8i | 0.0851223 | + | 0.448109i | ||||
\(301\) | 42410.2 | − | 73456.6i | 0.468099 | − | 0.810770i | ||||
\(302\) | −1878.47 | − | 1084.54i | −0.0205964 | − | 0.0118913i | ||||
\(303\) | 101998. | + | 118350.i | 1.11098 | + | 1.28909i | ||||
\(304\) | −6007.71 | − | 10405.7i | −0.0650072 | − | 0.112596i | ||||
\(305\) | 19277.3i | 0.207227i | ||||||||
\(306\) | 82568.6 | + | 65651.2i | 0.881804 | + | 0.701132i | ||||
\(307\) | −10736.4 | −0.113915 | −0.0569576 | − | 0.998377i | \(-0.518140\pi\) | ||||
−0.0569576 | + | 0.998377i | \(0.518140\pi\) | |||||||
\(308\) | 26664.9 | − | 15395.0i | 0.281085 | − | 0.162285i | ||||
\(309\) | −87764.2 | − | 30638.8i | −0.919179 | − | 0.320889i | ||||
\(310\) | −6671.28 | + | 11555.0i | −0.0694202 | + | 0.120239i | ||||
\(311\) | −192.300 | − | 111.025i | −0.00198820 | − | 0.00114789i | 0.499006 | − | 0.866599i | \(-0.333699\pi\) |
−0.500994 | + | 0.865451i | \(0.667032\pi\) | |||||||
\(312\) | 19464.4 | − | 55755.2i | 0.199955 | − | 0.572765i | ||||
\(313\) | −73338.2 | − | 127026.i | −0.748586 | − | 1.29659i | −0.948500 | − | 0.316776i | \(-0.897400\pi\) |
0.199914 | − | 0.979813i | \(-0.435934\pi\) | |||||||
\(314\) | − | 14684.7i | − | 0.148938i | ||||||
\(315\) | −13280.9 | − | 33695.8i | −0.133846 | − | 0.339589i | ||||
\(316\) | −46638.3 | −0.467056 | ||||||||
\(317\) | −152804. | + | 88221.5i | −1.52061 | + | 0.877922i | −0.520901 | + | 0.853617i | \(0.674404\pi\) |
−0.999705 | + | 0.0243045i | \(0.992263\pi\) | |||||||
\(318\) | −14909.6 | + | 12849.5i | −0.147439 | + | 0.127067i | ||||
\(319\) | −44587.1 | + | 77227.1i | −0.438155 | + | 0.758907i | ||||
\(320\) | −3283.82 | − | 1895.91i | −0.0320686 | − | 0.0185148i | ||||
\(321\) | −64196.2 | + | 12194.7i | −0.623016 | + | 0.118348i | ||||
\(322\) | −3535.77 | − | 6124.13i | −0.0341014 | − | 0.0590653i | ||||
\(323\) | − | 86443.1i | − | 0.828563i | ||||||
\(324\) | −11827.6 | − | 51138.0i | −0.112669 | − | 0.487140i | ||||
\(325\) | 165337. | 1.56532 | ||||||||
\(326\) | 59230.6 | − | 34196.8i | 0.557328 | − | 0.321774i | ||||
\(327\) | −3181.99 | − | 16750.9i | −0.0297580 | − | 0.156655i | ||||
\(328\) | −5726.61 | + | 9918.78i | −0.0532292 | + | 0.0921957i | ||||
\(329\) | 129611. | + | 74831.1i | 1.19743 | + | 0.691338i | ||||
\(330\) | −7845.50 | − | 9103.32i | −0.0720432 | − | 0.0835934i | ||||
\(331\) | 48118.6 | + | 83343.8i | 0.439194 | + | 0.760707i | 0.997628 | − | 0.0688427i | \(-0.0219306\pi\) |
−0.558433 | + | 0.829549i | \(0.688597\pi\) | |||||||
\(332\) | 41002.3i | 0.371991i | ||||||||
\(333\) | −63878.6 | + | 25177.1i | −0.576059 | + | 0.227048i | ||||
\(334\) | 61562.1 | 0.551849 | ||||||||
\(335\) | 21698.2 | − | 12527.5i | 0.193346 | − | 0.111628i | ||||
\(336\) | −32833.6 | − | 11462.3i | −0.290830 | − | 0.101530i | ||||
\(337\) | −59411.3 | + | 102903.i | −0.523130 | + | 0.906087i | 0.476508 | + | 0.879170i | \(0.341902\pi\) |
−0.999638 | + | 0.0269171i | \(0.991431\pi\) | |||||||
\(338\) | −136025. | − | 78534.2i | −1.19066 | − | 0.687426i | ||||
\(339\) | −28343.9 | + | 81190.4i | −0.246638 | + | 0.706489i | ||||
\(340\) | −13639.9 | − | 23625.0i | −0.117992 | − | 0.204368i | ||||
\(341\) | 40603.8i | 0.349187i | ||||||||
\(342\) | −26768.9 | + | 33666.8i | −0.228864 | + | 0.287839i | ||||
\(343\) | 69836.5 | 0.593600 | ||||||||
\(344\) | −27529.5 | + | 15894.2i | −0.232638 | + | 0.134314i | ||||
\(345\) | −2090.76 | + | 1801.88i | −0.0175658 | + | 0.0151387i | ||||
\(346\) | −33949.0 | + | 58801.4i | −0.283580 | + | 0.491174i | ||||
\(347\) | 169009. | + | 97577.4i | 1.40362 | + | 0.810383i | 0.994762 | − | 0.102214i | \(-0.0325926\pi\) |
0.408861 | + | 0.912597i | \(0.365926\pi\) | |||||||
\(348\) | 98951.6 | − | 18796.8i | 0.817080 | − | 0.155212i | ||||
\(349\) | 39097.6 | + | 67719.0i | 0.320995 | + | 0.555981i | 0.980694 | − | 0.195550i | \(-0.0626492\pi\) |
−0.659698 | + | 0.751531i | \(0.729316\pi\) | |||||||
\(350\) | − | 97365.2i | − | 0.794818i | ||||||
\(351\) | −211236. | + | 8362.65i | −1.71456 | + | 0.0678781i | ||||
\(352\) | −11539.2 | −0.0931302 | ||||||||
\(353\) | −5389.44 | + | 3111.59i | −0.0432508 | + | 0.0249708i | −0.521469 | − | 0.853270i | \(-0.674616\pi\) |
0.478219 | + | 0.878241i | \(0.341283\pi\) | |||||||
\(354\) | −21365.8 | − | 112476.i | −0.170495 | − | 0.897537i | ||||
\(355\) | 10261.1 | − | 17772.8i | 0.0814215 | − | 0.141026i | ||||
\(356\) | 8460.27 | + | 4884.54i | 0.0667551 | + | 0.0385411i | ||||
\(357\) | −163337. | − | 189524.i | −1.28159 | − | 1.48706i | ||||
\(358\) | 58168.6 | + | 100751.i | 0.453860 | + | 0.786109i | ||||
\(359\) | 126328.i | 0.980188i | 0.871670 | + | 0.490094i | \(0.163038\pi\) | ||||
−0.871670 | + | 0.490094i | \(0.836962\pi\) | |||||||
\(360\) | −2003.65 | + | 13425.0i | −0.0154603 | + | 0.103588i | ||||
\(361\) | −95074.4 | −0.729540 | ||||||||
\(362\) | 78502.0 | − | 45323.2i | 0.599051 | − | 0.345862i | ||||
\(363\) | 89877.9 | + | 31376.7i | 0.682087 | + | 0.238119i | ||||
\(364\) | −70033.8 | + | 121302.i | −0.528573 | + | 0.915515i | ||||
\(365\) | 22609.4 | + | 13053.5i | 0.169708 | + | 0.0979811i | ||||
\(366\) | 21839.2 | − | 62557.9i | 0.163033 | − | 0.467003i | ||||
\(367\) | −60152.2 | − | 104187.i | −0.446601 | − | 0.773536i | 0.551561 | − | 0.834134i | \(-0.314032\pi\) |
−0.998162 | + | 0.0605988i | \(0.980699\pi\) | |||||||
\(368\) | 2650.22i | 0.0195698i | ||||||||
\(369\) | 40550.3 | + | 6052.03i | 0.297811 | + | 0.0444476i | ||||
\(370\) | 17756.2 | 0.129702 | ||||||||
\(371\) | 40429.2 | − | 23341.8i | 0.293729 | − | 0.169585i | ||||
\(372\) | 34740.0 | − | 29940.0i | 0.251041 | − | 0.216354i | ||||
\(373\) | 32755.4 | − | 56733.9i | 0.235432 | − | 0.407779i | −0.723966 | − | 0.689835i | \(-0.757683\pi\) |
0.959398 | + | 0.282056i | \(0.0910163\pi\) | |||||||
\(374\) | −71894.9 | − | 41508.6i | −0.513990 | − | 0.296753i | ||||
\(375\) | −78261.3 | + | 14866.4i | −0.556525 | + | 0.105717i | ||||
\(376\) | −28044.6 | − | 48574.7i | −0.198369 | − | 0.343585i | ||||
\(377\) | − | 405666.i | − | 2.85421i | ||||||
\(378\) | 4924.66 | + | 124394.i | 0.0344661 | + | 0.870596i | ||||
\(379\) | 129148. | 0.899106 | 0.449553 | − | 0.893254i | \(-0.351583\pi\) | ||||
0.449553 | + | 0.893254i | \(0.351583\pi\) | |||||||
\(380\) | 9632.93 | − | 5561.57i | 0.0667100 | − | 0.0385150i | ||||
\(381\) | −12679.2 | − | 66747.1i | −0.0873459 | − | 0.459814i | ||||
\(382\) | 18688.4 | − | 32369.3i | 0.128070 | − | 0.221823i | ||||
\(383\) | 61973.9 | + | 35780.7i | 0.422485 | + | 0.243922i | 0.696140 | − | 0.717906i | \(-0.254899\pi\) |
−0.273655 | + | 0.961828i | \(0.588233\pi\) | |||||||
\(384\) | 8508.66 | + | 9872.79i | 0.0577030 | + | 0.0669542i | ||||
\(385\) | 14251.7 | + | 24684.7i | 0.0961493 | + | 0.166535i | ||||
\(386\) | 5054.19i | 0.0339216i | ||||||||
\(387\) | 89069.9 | + | 70820.4i | 0.594715 | + | 0.472864i | ||||
\(388\) | 117882. | 0.783038 | ||||||||
\(389\) | −17196.4 | + | 9928.34i | −0.113642 | + | 0.0656111i | −0.555744 | − | 0.831354i | \(-0.687566\pi\) |
0.442102 | + | 0.896965i | \(0.354233\pi\) | |||||||
\(390\) | 51614.8 | + | 18018.9i | 0.339348 | + | 0.118468i | ||||
\(391\) | −9533.29 | + | 16512.1i | −0.0623576 | + | 0.108007i | ||||
\(392\) | 24383.5 | + | 14077.8i | 0.158681 | + | 0.0916144i | ||||
\(393\) | −14304.7 | + | 40975.6i | −0.0926179 | + | 0.265302i | ||||
\(394\) | 24948.0 | + | 43211.2i | 0.160710 | + | 0.278358i | ||||
\(395\) | − | 43174.9i | − | 0.276718i | ||||||
\(396\) | 15146.8 | + | 38430.0i | 0.0965896 | + | 0.245064i | ||||
\(397\) | 35293.6 | 0.223931 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(398\) | 580.378 | − | 335.081i | 0.00366391 | − | 0.00211536i | ||||
\(399\) | 77277.2 | − | 66599.7i | 0.485407 | − | 0.418337i | ||||
\(400\) | −18244.9 | + | 31601.1i | −0.114030 | + | 0.197507i | ||||
\(401\) | −12861.6 | − | 7425.63i | −0.0799844 | − | 0.0461790i | 0.459474 | − | 0.888191i | \(-0.348038\pi\) |
−0.539459 | + | 0.842012i | \(0.681371\pi\) | |||||||
\(402\) | −84606.6 | + | 16071.8i | −0.523543 | + | 0.0994517i | ||||
\(403\) | −92356.1 | − | 159965.i | −0.568664 | − | 0.984954i | ||||
\(404\) | 138878.i | 0.850885i | ||||||||
\(405\) | 47340.5 | − | 10949.3i | 0.288618 | − | 0.0667536i | ||||
\(406\) | −238891. | −1.44927 | ||||||||
\(407\) | 46795.9 | − | 27017.7i | 0.282501 | − | 0.163102i | ||||
\(408\) | 17498.9 | + | 92119.5i | 0.105121 | + | 0.553390i | ||||
\(409\) | −36029.2 | + | 62404.4i | −0.215381 | + | 0.373051i | −0.953390 | − | 0.301739i | \(-0.902433\pi\) |
0.738009 | + | 0.674791i | \(0.235766\pi\) | |||||||
\(410\) | −9182.21 | − | 5301.35i | −0.0546235 | − | 0.0315369i | ||||
\(411\) | −63414.2 | − | 73581.0i | −0.375407 | − | 0.435594i | ||||
\(412\) | −41314.9 | − | 71559.5i | −0.243395 | − | 0.421573i | ||||
\(413\) | 271542.i | 1.59198i | ||||||||
\(414\) | 8826.23 | − | 3478.77i | 0.0514961 | − | 0.0202967i | ||||
\(415\) | −37957.5 | −0.220395 | ||||||||
\(416\) | 45460.7 | − | 26246.7i | 0.262693 | − | 0.151666i | ||||
\(417\) | 240274. | + | 83880.7i | 1.38177 | + | 0.482381i | ||||
\(418\) | 16924.9 | − | 29314.7i | 0.0968662 | − | 0.167777i | ||||
\(419\) | −250399. | − | 144568.i | −1.42628 | − | 0.823462i | −0.429453 | − | 0.903089i | \(-0.641294\pi\) |
−0.996825 | + | 0.0796271i | \(0.974627\pi\) | |||||||
\(420\) | 10611.1 | − | 30395.3i | 0.0601538 | − | 0.172309i | ||||
\(421\) | −60963.3 | − | 105592.i | −0.343957 | − | 0.595751i | 0.641207 | − | 0.767368i | \(-0.278434\pi\) |
−0.985164 | + | 0.171617i | \(0.945101\pi\) | |||||||
\(422\) | 101705.i | 0.571109i | ||||||||
\(423\) | −124960. | + | 157160.i | −0.698377 | + | 0.878339i | ||||
\(424\) | −17495.7 | −0.0973195 | ||||||||
\(425\) | −227349. | + | 131260.i | −1.25868 | + | 0.726699i | ||||
\(426\) | −53434.0 | + | 46050.9i | −0.294441 | + | 0.253758i | ||||
\(427\) | −78578.6 | + | 136102.i | −0.430971 | + | 0.746464i | ||||
\(428\) | −50302.0 | − | 29041.9i | −0.274598 | − | 0.158539i | ||||
\(429\) | 163447. | − | 31048.2i | 0.888099 | − | 0.168702i | ||||
\(430\) | −14713.9 | − | 25485.1i | −0.0795774 | − | 0.137832i | ||||
\(431\) | 207467.i | 1.11685i | 0.829555 | + | 0.558426i | \(0.188594\pi\) | ||||
−0.829555 | + | 0.558426i | \(0.811406\pi\) | |||||||
\(432\) | 21711.4 | − | 41296.5i | 0.116338 | − | 0.221282i | ||||
\(433\) | 88879.4 | 0.474051 | 0.237026 | − | 0.971503i | \(-0.423827\pi\) | ||||
0.237026 | + | 0.971503i | \(0.423827\pi\) | |||||||
\(434\) | −94201.7 | + | 54387.4i | −0.500126 | + | 0.288748i | ||||
\(435\) | 17400.9 | + | 91603.4i | 0.0919588 | + | 0.484098i | ||||
\(436\) | 7577.98 | − | 13125.5i | 0.0398640 | − | 0.0690465i | ||||
\(437\) | −6732.72 | − | 3887.14i | −0.0352556 | − | 0.0203548i | ||||
\(438\) | −58582.8 | − | 67975.0i | −0.305367 | − | 0.354325i | ||||
\(439\) | −74141.8 | − | 128417.i | −0.384711 | − | 0.666339i | 0.607018 | − | 0.794688i | \(-0.292365\pi\) |
−0.991729 | + | 0.128349i | \(0.959032\pi\) | |||||||
\(440\) | − | 10682.3i | − | 0.0551772i | ||||||
\(441\) | 14877.8 | − | 99685.5i | 0.0765001 | − | 0.512572i | ||||
\(442\) | 377656. | 1.93309 | ||||||||
\(443\) | 177795. | − | 102650.i | 0.905967 | − | 0.523060i | 0.0268357 | − | 0.999640i | \(-0.491457\pi\) |
0.879131 | + | 0.476580i | \(0.158124\pi\) | |||||||
\(444\) | −57621.8 | − | 20116.0i | −0.292295 | − | 0.102041i | ||||
\(445\) | −4521.81 | + | 7832.01i | −0.0228346 | + | 0.0395506i | ||||
\(446\) | 133799. | + | 77248.7i | 0.672639 | + | 0.388348i | ||||
\(447\) | −28966.9 | + | 82975.1i | −0.144973 | + | 0.415272i | ||||
\(448\) | −15456.4 | − | 26771.2i | −0.0770108 | − | 0.133387i | ||||
\(449\) | − | 112334.i | − | 0.557211i | −0.960406 | − | 0.278606i | \(-0.910128\pi\) | ||
0.960406 | − | 0.278606i | \(-0.0898722\pi\) | |||||||
\(450\) | 129192. | + | 19281.7i | 0.637987 | + | 0.0952180i | ||||
\(451\) | −32265.9 | −0.158632 | ||||||||
\(452\) | −66199.5 | + | 38220.3i | −0.324025 | + | 0.187076i | ||||
\(453\) | −5228.22 | + | 4505.83i | −0.0254776 | + | 0.0219573i | ||||
\(454\) | 110541. | − | 191462.i | 0.536303 | − | 0.928904i | ||||
\(455\) | −112294. | − | 64833.1i | −0.542418 | − | 0.313165i | ||||
\(456\) | −37561.1 | + | 7135.08i | −0.180638 | + | 0.0343138i | ||||
\(457\) | 115511. | + | 200070.i | 0.553082 | + | 0.957967i | 0.998050 | + | 0.0624202i | \(0.0198819\pi\) |
−0.444968 | + | 0.895547i | \(0.646785\pi\) | |||||||
\(458\) | − | 34051.5i | − | 0.162333i | ||||||
\(459\) | 283823. | − | 179198.i | 1.34717 | − | 0.850564i | ||||
\(460\) | −2453.41 | −0.0115946 | ||||||||
\(461\) | −186017. | + | 107397.i | −0.875287 | + | 0.505347i | −0.869102 | − | 0.494634i | \(-0.835302\pi\) |
−0.00618557 | + | 0.999981i | \(0.501969\pi\) | |||||||
\(462\) | −18283.9 | − | 96251.7i | −0.0856613 | − | 0.450946i | ||||
\(463\) | 109663. | − | 189941.i | 0.511561 | − | 0.886049i | −0.488349 | − | 0.872648i | \(-0.662401\pi\) |
0.999910 | − | 0.0134011i | \(-0.00426582\pi\) | |||||||
\(464\) | 77535.2 | + | 44764.9i | 0.360133 | + | 0.207923i | ||||
\(465\) | 27716.6 | + | 32160.2i | 0.128184 | + | 0.148735i | ||||
\(466\) | −134910. | − | 233672.i | −0.621260 | − | 1.07605i | ||||
\(467\) | 62261.6i | 0.285487i | 0.989760 | + | 0.142744i | \(0.0455924\pi\) | ||||
−0.989760 | + | 0.142744i | \(0.954408\pi\) | |||||||
\(468\) | −147085. | − | 116949.i | −0.671547 | − | 0.533955i | ||||
\(469\) | 204259. | 0.928616 | ||||||||
\(470\) | 44967.5 | − | 25962.0i | 0.203565 | − | 0.117528i | ||||
\(471\) | −44115.5 | − | 15400.9i | −0.198861 | − | 0.0694231i | ||||
\(472\) | 50883.2 | − | 88132.2i | 0.228397 | − | 0.395595i | ||||
\(473\) | −77555.8 | − | 44776.9i | −0.346651 | − | 0.200139i | ||||
\(474\) | −48912.9 | + | 140110.i | −0.217704 | + | 0.623608i | ||||
\(475\) | −53520.5 | − | 92700.2i | −0.237210 | − | 0.410859i | ||||
\(476\) | − | 222397.i | − | 0.981557i | ||||||
\(477\) | 22965.5 | + | 58267.3i | 0.100934 | + | 0.256088i | ||||
\(478\) | −289502. | −1.26706 | ||||||||
\(479\) | 186527. | − | 107692.i | 0.812964 | − | 0.469365i | −0.0350204 | − | 0.999387i | \(-0.511150\pi\) |
0.847984 | + | 0.530022i | \(0.177816\pi\) | |||||||
\(480\) | −9139.64 | + | 7876.80i | −0.0396686 | + | 0.0341875i | ||||
\(481\) | −122907. | + | 212881.i | −0.531235 | + | 0.920126i | ||||
\(482\) | 131459. | + | 75897.7i | 0.565842 | + | 0.326689i | ||||
\(483\) | −22106.2 | + | 4199.27i | −0.0947588 | + | 0.0180003i | ||||
\(484\) | 42309.9 | + | 73283.0i | 0.180614 | + | 0.312833i | ||||
\(485\) | 109128.i | 0.463929i | ||||||||
\(486\) | −166032. | − | 18099.9i | −0.702942 | − | 0.0766307i | ||||
\(487\) | −387518. | −1.63393 | −0.816966 | − | 0.576687i | \(-0.804345\pi\) | ||||
−0.816966 | + | 0.576687i | \(0.804345\pi\) | |||||||
\(488\) | 51007.3 | − | 29449.1i | 0.214187 | − | 0.123661i | ||||
\(489\) | −40614.0 | − | 213804.i | −0.169847 | − | 0.894124i | ||||
\(490\) | −13032.4 | + | 22572.8i | −0.0542791 | + | 0.0940141i | ||||
\(491\) | 69131.7 | + | 39913.2i | 0.286757 | + | 0.165559i | 0.636478 | − | 0.771295i | \(-0.280390\pi\) |
−0.349721 | + | 0.936854i | \(0.613724\pi\) | |||||||
\(492\) | 23791.9 | + | 27606.3i | 0.0982875 | + | 0.114045i | ||||
\(493\) | 322055. | + | 557815.i | 1.32506 | + | 2.29507i | ||||
\(494\) | 153987.i | 0.631001i | ||||||||
\(495\) | −35576.1 | + | 14022.0i | −0.145194 | + | 0.0572268i | ||||
\(496\) | 40765.7 | 0.165704 | ||||||||
\(497\) | 144892. | − | 83653.6i | 0.586587 | − | 0.338666i | ||||
\(498\) | 123178. | + | 43002.0i | 0.496679 | + | 0.173392i | ||||
\(499\) | −36722.7 | + | 63605.6i | −0.147480 | + | 0.255443i | −0.930296 | − | 0.366811i | \(-0.880450\pi\) |
0.782815 | + | 0.622254i | \(0.213783\pi\) | |||||||
\(500\) | −61322.9 | − | 35404.8i | −0.245292 | − | 0.141619i | ||||
\(501\) | 64564.5 | − | 184943.i | 0.257228 | − | 0.736824i | ||||
\(502\) | 141124. | + | 244434.i | 0.560006 | + | 0.969960i | ||||
\(503\) | − | 465077.i | − | 1.83818i | −0.394045 | − | 0.919091i | \(-0.628925\pi\) | ||
0.394045 | − | 0.919091i | \(-0.371075\pi\) | |||||||
\(504\) | −68869.7 | + | 86616.5i | −0.271124 | + | 0.340988i | ||||
\(505\) | −128565. | −0.504127 | ||||||||
\(506\) | −6465.88 | + | 3733.08i | −0.0252538 | + | 0.0145803i | ||||
\(507\) | −378590. | + | 326280.i | −1.47283 | + | 1.26933i | ||||
\(508\) | 30195.9 | − | 52300.8i | 0.117009 | − | 0.202666i | ||||
\(509\) | −82539.6 | − | 47654.3i | −0.318586 | − | 0.183936i | 0.332176 | − | 0.943217i | \(-0.392217\pi\) |
−0.650762 | + | 0.759282i | \(0.725551\pi\) | |||||||
\(510\) | −85278.7 | + | 16199.5i | −0.327869 | + | 0.0622816i | ||||
\(511\) | 106418. | + | 184322.i | 0.407545 | + | 0.705888i | ||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 73066.7 | + | 115727.i | 0.277642 | + | 0.439745i | ||||
\(514\) | −7346.50 | −0.0278070 | ||||||||
\(515\) | 66245.4 | − | 38246.8i | 0.249771 | − | 0.144205i | ||||
\(516\) | 18876.8 | + | 99372.8i | 0.0708970 | + | 0.373223i | ||||
\(517\) | 79007.0 | − | 136844.i | 0.295587 | − | 0.511971i | ||||
\(518\) | 125363. | + | 72378.4i | 0.467208 | + | 0.269743i | ||||
\(519\) | 141045. | + | 163658.i | 0.523629 | + | 0.607579i | ||||
\(520\) | 24297.6 | + | 42084.7i | 0.0898581 | + | 0.155639i | ||||
\(521\) | − | 173345.i | − | 0.638612i | −0.947652 | − | 0.319306i | \(-0.896550\pi\) | ||
0.947652 | − | 0.319306i | \(-0.103450\pi\) | |||||||
\(522\) | 47308.7 | − | 316982.i | 0.173620 | − | 1.16330i | ||||
\(523\) | −403535. | −1.47529 | −0.737646 | − | 0.675187i | \(-0.764063\pi\) | ||||
−0.737646 | + | 0.675187i | \(0.764063\pi\) | |||||||
\(524\) | −33409.9 | + | 19289.2i | −0.121678 | + | 0.0702509i | ||||
\(525\) | −292502. | − | 102114.i | −1.06123 | − | 0.370480i | ||||
\(526\) | −178500. | + | 309171.i | −0.645158 | + | 1.11745i | ||||
\(527\) | 253991. | + | 146642.i | 0.914527 | + | 0.528002i | ||||
\(528\) | −12102.0 | + | 34665.8i | −0.0434099 | + | 0.124347i | ||||
\(529\) | −139063. | − | 240864.i | −0.496936 | − | 0.860719i | ||||
\(530\) | − | 16196.5i | − | 0.0576592i | ||||||
\(531\) | −360305. | − | 53774.6i | −1.27785 | − | 0.190717i | ||||
\(532\) | 90681.0 | 0.320400 | ||||||||
\(533\) | 127117. | − | 73391.0i | 0.447455 | − | 0.258338i | ||||
\(534\) | 23546.9 | − | 20293.4i | 0.0825755 | − | 0.0711660i | ||||
\(535\) | 26885.2 | − | 46566.5i | 0.0939303 | − | 0.162692i | ||||
\(536\) | −66294.9 | − | 38275.4i | −0.230755 | − | 0.133226i | ||||
\(537\) | 363679. | − | 69084.1i | 1.26116 | − | 0.239568i | ||||
\(538\) | −20328.9 | − | 35210.6i | −0.0702342 | − | 0.121649i | ||||
\(539\) | 79319.8i | 0.273026i | ||||||||
\(540\) | 38229.8 | + | 20099.1i | 0.131103 | + | 0.0689269i | ||||
\(541\) | 280182. | 0.957295 | 0.478648 | − | 0.878007i | \(-0.341127\pi\) | ||||
0.478648 | + | 0.878007i | \(0.341127\pi\) | |||||||
\(542\) | −132569. | + | 76538.6i | −0.451276 | + | 0.260545i | ||||
\(543\) | −53828.2 | − | 283368.i | −0.182562 | − | 0.961060i | ||||
\(544\) | −41674.1 | + | 72181.7i | −0.140821 | + | 0.243910i | ||||
\(545\) | 12150.8 | + | 7015.24i | 0.0409082 | + | 0.0236183i | ||||
\(546\) | 290964. | + | 337612.i | 0.976008 | + | 1.13249i | ||||
\(547\) | 48219.9 | + | 83519.3i | 0.161158 | + | 0.279134i | 0.935284 | − | 0.353898i | \(-0.115144\pi\) |
−0.774126 | + | 0.633031i | \(0.781811\pi\) | |||||||
\(548\) | − | 86343.6i | − | 0.287521i | ||||||
\(549\) | −165031. | − | 131218.i | −0.547545 | − | 0.435359i | ||||
\(550\) | −102799. | −0.339830 | ||||||||
\(551\) | −227446. | + | 131316.i | −0.749160 | + | 0.432528i | ||||
\(552\) | 7961.72 | + | 2779.47i | 0.0261293 | + | 0.00912186i | ||||
\(553\) | 175991. | − | 304825.i | 0.575493 | − | 0.996784i | ||||
\(554\) | −77432.8 | − | 44705.8i | −0.252293 | − | 0.145661i | ||||
\(555\) | 18622.2 | − | 53342.8i | 0.0604567 | − | 0.173177i | ||||
\(556\) | 113109. | + | 195910.i | 0.365887 | + | 0.633735i | ||||
\(557\) | 403818.i | 1.30159i | 0.759252 | + | 0.650797i | \(0.225565\pi\) | ||||
−0.759252 | + | 0.650797i | \(0.774435\pi\) | |||||||
\(558\) | −53510.6 | − | 135765.i | −0.171859 | − | 0.436034i | ||||
\(559\) | 407392. | 1.30373 | ||||||||
\(560\) | 24783.2 | − | 14308.6i | 0.0790280 | − | 0.0456268i | ||||
\(561\) | −200100. | + | 172452.i | −0.635802 | + | 0.547953i | ||||
\(562\) | 144504. | − | 250289.i | 0.457518 | − | 0.792444i | ||||
\(563\) | −12809.4 | − | 7395.51i | −0.0404122 | − | 0.0233320i | 0.479658 | − | 0.877456i | \(-0.340761\pi\) |
−0.520070 | + | 0.854124i | \(0.674094\pi\) | |||||||
\(564\) | −175339. | + | 33307.3i | −0.551216 | + | 0.104708i | ||||
\(565\) | −35382.0 | − | 61283.5i | −0.110837 | − | 0.191976i | ||||
\(566\) | − | 411067.i | − | 1.28316i | ||||||
\(567\) | 378867. | + | 115666.i | 1.17848 | + | 0.359783i | ||||
\(568\) | −62702.1 | −0.194350 | ||||||||
\(569\) | 210701. | − | 121648.i | 0.650792 | − | 0.375735i | −0.137968 | − | 0.990437i | \(-0.544057\pi\) |
0.788760 | + | 0.614702i | \(0.210724\pi\) | |||||||
\(570\) | −6605.22 | − | 34771.8i | −0.0203300 | − | 0.107023i | ||||
\(571\) | 217151. | − | 376117.i | 0.666025 | − | 1.15359i | −0.312982 | − | 0.949759i | \(-0.601328\pi\) |
0.979006 | − | 0.203829i | \(-0.0653388\pi\) | |||||||
\(572\) | 128071. | + | 73942.0i | 0.391435 | + | 0.225995i | ||||
\(573\) | −77643.2 | − | 90091.3i | −0.236480 | − | 0.274393i | ||||
\(574\) | −43219.1 | − | 74857.6i | −0.131175 | − | 0.227202i | ||||
\(575\) | 23609.8i | 0.0714096i | ||||||||
\(576\) | 38583.3 | − | 15207.2i | 0.116293 | − | 0.0458358i | ||||
\(577\) | −404030. | −1.21356 | −0.606781 | − | 0.794869i | \(-0.707540\pi\) | ||||
−0.606781 | + | 0.794869i | \(0.707540\pi\) | |||||||
\(578\) | −314717. | + | 181702.i | −0.942029 | + | 0.543881i | ||||
\(579\) | 15183.7 | + | 5300.68i | 0.0452918 | + | 0.0158115i | ||||
\(580\) | −41440.7 | + | 71777.4i | −0.123189 | + | 0.213369i | ||||
\(581\) | −267989. | − | 154723.i | −0.793898 | − | 0.458357i | ||||
\(582\) | 123631. | − | 354137.i | 0.364990 | − | 1.04550i | ||||
\(583\) | −24644.4 | − | 42685.3i | −0.0725071 | − | 0.125586i | ||||
\(584\) | − | 79765.4i | − | 0.233878i | ||||||
\(585\) | 108264. | − | 136162.i | 0.316354 | − | 0.397874i | ||||
\(586\) | −130798. | −0.380894 | ||||||||
\(587\) | −176946. | + | 102160.i | −0.513528 | + | 0.296486i | −0.734283 | − | 0.678844i | \(-0.762481\pi\) |
0.220754 | + | 0.975329i | \(0.429148\pi\) | |||||||
\(588\) | 67865.0 | − | 58488.0i | 0.196287 | − | 0.169166i | ||||
\(589\) | −59792.1 | + | 103563.i | −0.172351 | + | 0.298521i | ||||
\(590\) | 81587.5 | + | 47104.6i | 0.234379 | + | 0.135319i | ||||
\(591\) | 155979. | − | 29629.6i | 0.446571 | − | 0.0848302i | ||||
\(592\) | −27125.4 | − | 46982.6i | −0.0773986 | − | 0.134058i | ||||
\(593\) | 569645.i | 1.61993i | 0.586481 | + | 0.809963i | \(0.300513\pi\) | ||||
−0.586481 | + | 0.809963i | \(0.699487\pi\) | |||||||
\(594\) | 131336. | − | 5199.48i | 0.372229 | − | 0.0147362i | ||||
\(595\) | 205882. | 0.581546 | ||||||||
\(596\) | −67654.7 | + | 39060.5i | −0.190461 | + | 0.109963i | ||||
\(597\) | −397.961 | − | 2094.98i | −0.00111658 | − | 0.00587803i | ||||
\(598\) | 16982.3 | − | 29414.2i | 0.0474891 | − | 0.0822535i | ||||
\(599\) | 242136. | + | 139797.i | 0.674846 | + | 0.389623i | 0.797910 | − | 0.602776i | \(-0.205939\pi\) |
−0.123064 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(600\) | 75800.5 | + | 87953.1i | 0.210557 | + | 0.244314i | ||||
\(601\) | −114264. | − | 197910.i | −0.316344 | − | 0.547923i | 0.663379 | − | 0.748284i | \(-0.269122\pi\) |
−0.979722 | + | 0.200361i | \(0.935789\pi\) | |||||||
\(602\) | − | 239908.i | − | 0.661991i | ||||||
\(603\) | −40450.4 | + | 271029.i | −0.111247 | + | 0.745385i | ||||
\(604\) | −6135.06 | −0.0168169 | ||||||||
\(605\) | −67840.9 | + | 39168.0i | −0.185345 | + | 0.107009i | ||||
\(606\) | 417214. | + | 145651.i | 1.13609 | + | 0.396615i | ||||
\(607\) | 95669.3 | − | 165704.i | 0.259654 | − | 0.449734i | −0.706495 | − | 0.707718i | \(-0.749725\pi\) |
0.966149 | + | 0.257984i | \(0.0830581\pi\) | |||||||
\(608\) | −29431.6 | − | 16992.4i | −0.0796173 | − | 0.0459671i | ||||
\(609\) | −250542. | + | 717672.i | −0.675533 | + | 1.93505i | ||||
\(610\) | 27262.2 | + | 47219.4i | 0.0732657 | + | 0.126900i | ||||
\(611\) | 718828.i | 1.92550i | ||||||||
\(612\) | 295096. | + | 44042.3i | 0.787880 | + | 0.117589i | ||||
\(613\) | −446105. | −1.18718 | −0.593589 | − | 0.804768i | \(-0.702290\pi\) | ||||
−0.593589 | + | 0.804768i | \(0.702290\pi\) | |||||||
\(614\) | −26298.7 | + | 15183.6i | −0.0697585 | + | 0.0402751i | ||||
\(615\) | −25556.2 | + | 22025.1i | −0.0675688 | + | 0.0582327i | ||||
\(616\) | 43543.5 | − | 75419.6i | 0.114753 | − | 0.198757i | ||||
\(617\) | −283400. | − | 163621.i | −0.744439 | − | 0.429802i | 0.0792421 | − | 0.996855i | \(-0.474750\pi\) |
−0.823681 | + | 0.567053i | \(0.808083\pi\) | |||||||
\(618\) | −258307. | + | 49067.8i | −0.676332 | + | 0.128475i | ||||
\(619\) | −55163.0 | − | 95545.2i | −0.143968 | − | 0.249360i | 0.785019 | − | 0.619471i | \(-0.212653\pi\) |
−0.928988 | + | 0.370111i | \(0.879320\pi\) | |||||||
\(620\) | 37738.5i | 0.0981749i | ||||||||
\(621\) | −1194.17 | − | 30164.0i | −0.00309658 | − | 0.0782178i | ||||
\(622\) | −628.051 | −0.00162336 | ||||||||
\(623\) | −63850.2 | + | 36863.9i | −0.164508 | + | 0.0949785i | ||||
\(624\) | −31172.0 | − | 164099.i | −0.0800564 | − | 0.421440i | ||||
\(625\) | −145397. | + | 251835.i | −0.372216 | + | 0.644698i | ||||
\(626\) | −359282. | − | 207432.i | −0.916827 | − | 0.529330i | ||||
\(627\) | −70316.3 | − | 81589.6i | −0.178863 | − | 0.207539i | ||||
\(628\) | −20767.3 | − | 35970.0i | −0.0526576 | − | 0.0912056i | ||||
\(629\) | − | 390300.i | − | 0.986500i | ||||||
\(630\) | −80184.3 | − | 63755.4i | −0.202027 | − | 0.160634i | ||||
\(631\) | 321684. | 0.807925 | 0.403962 | − | 0.914776i | \(-0.367633\pi\) | ||||
0.403962 | + | 0.914776i | \(0.367633\pi\) | |||||||
\(632\) | −114240. | + | 65956.5i | −0.286012 | + | 0.165129i | ||||
\(633\) | 305541. | + | 106666.i | 0.762539 | + | 0.266205i | ||||
\(634\) | −249528. | + | 432195.i | −0.620784 | + | 1.07523i | ||||
\(635\) | 48416.9 | + | 27953.5i | 0.120074 | + | 0.0693248i | ||||
\(636\) | −18349.0 | + | 52560.2i | −0.0453626 | + | 0.129940i | ||||
\(637\) | −180418. | − | 312494.i | −0.444633 | − | 0.770128i | ||||
\(638\) | 252223.i | 0.619645i | ||||||||
\(639\) | 82305.2 | + | 208822.i | 0.201570 | + | 0.511416i | ||||
\(640\) | −10724.9 | −0.0261839 | ||||||||
\(641\) | 215079. | − | 124176.i | 0.523457 | − | 0.302218i | −0.214891 | − | 0.976638i | \(-0.568940\pi\) |
0.738348 | + | 0.674420i | \(0.235606\pi\) | |||||||
\(642\) | −140002. | + | 120658.i | −0.339676 | + | 0.292742i | ||||
\(643\) | −218681. | + | 378766.i | −0.528918 | + | 0.916113i | 0.470513 | + | 0.882393i | \(0.344069\pi\) |
−0.999431 | + | 0.0337200i | \(0.989265\pi\) | |||||||
\(644\) | −17321.7 | − | 10000.7i | −0.0417655 | − | 0.0241133i | ||||
\(645\) | −91993.3 | + | 17475.0i | −0.221125 | + | 0.0420046i | ||||
\(646\) | −122249. | − | 211742.i | −0.292941 | − | 0.507389i | ||||
\(647\) | − | 721599.i | − | 1.72380i | −0.507076 | − | 0.861901i | \(-0.669274\pi\) | ||
0.507076 | − | 0.861901i | \(-0.330726\pi\) | |||||||
\(648\) | −101292. | − | 108535.i | −0.241226 | − | 0.258477i | ||||
\(649\) | 286695. | 0.680661 | ||||||||
\(650\) | 404992. | − | 233822.i | 0.958562 | − | 0.553426i | ||||
\(651\) | 64593.4 | + | 340038.i | 0.152414 | + | 0.802354i | ||||
\(652\) | 96723.2 | − | 167530.i | 0.227528 | − | 0.394091i | ||||
\(653\) | −110385. | − | 63730.7i | −0.258871 | − | 0.149459i | 0.364949 | − | 0.931028i | \(-0.381087\pi\) |
−0.623819 | + | 0.781569i | \(0.714420\pi\) | |||||||
\(654\) | −31483.6 | − | 36531.2i | −0.0736087 | − | 0.0854099i | ||||
\(655\) | −17856.8 | − | 30928.9i | −0.0416218 | − | 0.0720910i | ||||
\(656\) | 32394.6i | 0.0752775i | ||||||||
\(657\) | −265649. | + | 104703.i | −0.615428 | + | 0.242565i | ||||
\(658\) | 423309. | 0.977700 | ||||||||
\(659\) | 137086. | − | 79146.9i | 0.315663 | − | 0.182248i | −0.333795 | − | 0.942646i | \(-0.608329\pi\) |
0.649458 | + | 0.760398i | \(0.274996\pi\) | |||||||
\(660\) | −32091.5 | − | 11203.3i | −0.0736720 | − | 0.0257192i | ||||
\(661\) | 285009. | − | 493649.i | 0.652311 | − | 1.12984i | −0.330249 | − | 0.943894i | \(-0.607133\pi\) |
0.982561 | − | 0.185943i | \(-0.0595338\pi\) | |||||||
\(662\) | 235732. | + | 136100.i | 0.537901 | + | 0.310557i | ||||
\(663\) | 396075. | − | 1.13455e6i | 0.901052 | − | 2.58104i | ||||
\(664\) | 57986.0 | + | 100435.i | 0.131519 | + | 0.227797i | ||||
\(665\) | 83947.0i | 0.189829i | ||||||||
\(666\) | −120864. | + | 152009.i | −0.272489 | + | 0.342706i | ||||
\(667\) | 57928.1 | 0.130208 | ||||||||
\(668\) | 150796. | − | 87062.0i | 0.337937 | − | 0.195108i | ||||
\(669\) | 372393. | − | 320939.i | 0.832049 | − | 0.717084i | ||||
\(670\) | 35433.0 | − | 61371.8i | 0.0789330 | − | 0.136716i | ||||
\(671\) | 143697. | + | 82963.6i | 0.319156 | + | 0.184265i | ||||
\(672\) | −96635.7 | + | 18356.8i | −0.213993 | + | 0.0406499i | ||||
\(673\) | 134677. | + | 233267.i | 0.297347 | + | 0.515020i | 0.975528 | − | 0.219875i | \(-0.0705649\pi\) |
−0.678181 | + | 0.734895i | \(0.737232\pi\) | |||||||
\(674\) | 336081.i | 0.739817i | ||||||||
\(675\) | 193419. | − | 367895.i | 0.424513 | − | 0.807451i | ||||
\(676\) | −444257. | −0.972166 | ||||||||
\(677\) | 393590. | − | 227240.i | 0.858751 | − | 0.495800i | −0.00484289 | − | 0.999988i | \(-0.501542\pi\) |
0.863594 | + | 0.504188i | \(0.168208\pi\) | |||||||
\(678\) | 45392.5 | + | 238959.i | 0.0987472 | + | 0.519834i | ||||
\(679\) | −444830. | + | 770468.i | −0.964838 | + | 1.67115i | ||||
\(680\) | −66821.5 | − | 38579.4i | −0.144510 | − | 0.0834329i | ||||
\(681\) | −459254. | − | 532883.i | −0.990281 | − | 1.14905i | ||||
\(682\) | 57422.4 | + | 99458.5i | 0.123456 | + | 0.213832i | ||||
\(683\) | − | 225234.i | − | 0.482827i | −0.970422 | − | 0.241414i | \(-0.922389\pi\) | ||
0.970422 | − | 0.241414i | \(-0.0776110\pi\) | |||||||
\(684\) | −17958.0 | + | 120323.i | −0.0383835 | + | 0.257180i | ||||
\(685\) | 79931.7 | 0.170348 | ||||||||
\(686\) | 171064. | − | 98763.7i | 0.363504 | − | 0.209869i | ||||
\(687\) | −102297. | − | 35712.3i | −0.216745 | − | 0.0756665i | ||||
\(688\) | −44955.5 | + | 77865.2i | −0.0949742 | + | 0.164500i | ||||
\(689\) | 194181. | + | 112111.i | 0.409043 | + | 0.236161i | ||||
\(690\) | −2573.06 | + | 7370.48i | −0.00540446 | + | 0.0154809i | ||||
\(691\) | 252440. | + | 437240.i | 0.528692 | + | 0.915722i | 0.999440 | + | 0.0334540i | \(0.0106507\pi\) |
−0.470748 | + | 0.882268i | \(0.656016\pi\) | |||||||
\(692\) | 192045.i | 0.401042i | ||||||||
\(693\) | −308333. | − | 46017.9i | −0.642027 | − | 0.0958209i | ||||
\(694\) | 551981. | 1.14605 | ||||||||
\(695\) | −181362. | + | 104709.i | −0.375471 | + | 0.216778i | ||||
\(696\) | 215798. | − | 185981.i | 0.445482 | − | 0.383929i | ||||
\(697\) | −116529. | + | 201834.i | −0.239866 | + | 0.415460i | ||||
\(698\) | 191538. | + | 110585.i | 0.393138 | + | 0.226978i | ||||
\(699\) | −843481. | + | 160227.i | −1.72632 | + | 0.327930i | ||||
\(700\) | −137695. | − | 238495.i | −0.281010 | − | 0.486724i | ||||
\(701\) | − | 19860.8i | − | 0.0404166i | −0.999796 | − | 0.0202083i | \(-0.993567\pi\) | ||
0.999796 | − | 0.0202083i | \(-0.00643294\pi\) | |||||||
\(702\) | −505593. | + | 319217.i | −1.02595 | + | 0.647756i | ||||
\(703\) | 159142. | 0.322014 | ||||||||
\(704\) | −28265.2 | + | 16318.9i | −0.0570304 | + | 0.0329265i | ||||
\(705\) | −30833.9 | − | 162319.i | −0.0620369 | − | 0.326580i | ||||
\(706\) | −8800.91 | + | 15243.6i | −0.0176571 | + | 0.0305829i | ||||
\(707\) | −907699. | − | 524060.i | −1.81595 | − | 1.04844i | ||||
\(708\) | −211400. | − | 245292.i | −0.421734 | − | 0.489348i | ||||
\(709\) | −315420. | − | 546324.i | −0.627476 | − | 1.08682i | −0.988056 | − | 0.154093i | \(-0.950755\pi\) |
0.360580 | − | 0.932728i | \(-0.382579\pi\) | |||||||
\(710\) | − | 58045.8i | − | 0.115147i | ||||||
\(711\) | 369616. | + | 293886.i | 0.731159 | + | 0.581353i | ||||
\(712\) | 27631.1 | 0.0545053 | ||||||||
\(713\) | 22842.7 | − | 13188.2i | 0.0449333 | − | 0.0259422i | ||||
\(714\) | −668121. | − | 233244.i | −1.31056 | − | 0.457523i | ||||
\(715\) | −68451.0 | + | 118561.i | −0.133896 | + | 0.231915i | ||||
\(716\) | 284967. | + | 164526.i | 0.555863 | + | 0.320928i | ||||
\(717\) | −303621. | + | 869716.i | −0.590601 | + | 1.69176i | ||||
\(718\) | 178654. | + | 309438.i | 0.346549 | + | 0.600240i | ||||
\(719\) | − | 337555.i | − | 0.652960i | −0.945204 | − | 0.326480i | \(-0.894137\pi\) | ||
0.945204 | − | 0.326480i | \(-0.105863\pi\) | |||||||
\(720\) | 14077.9 | + | 35718.0i | 0.0271565 | + | 0.0689005i | ||||
\(721\) | 623612. | 1.19962 | ||||||||
\(722\) | −232884. | + | 134455.i | −0.446750 | + | 0.257931i | ||||
\(723\) | 365880. | − | 315326.i | 0.699942 | − | 0.603230i | ||||
\(724\) | 128193. | − | 222037.i | 0.244561 | − | 0.423593i | ||||
\(725\) | 690732. | + | 398794.i | 1.31412 | + | 0.758705i | ||||
\(726\) | 264528. | − | 50249.6i | 0.501879 | − | 0.0953365i | ||||
\(727\) | 257481. | + | 445970.i | 0.487165 | + | 0.843795i | 0.999891 | − | 0.0147576i | \(-0.00469766\pi\) |
−0.512726 | + | 0.858552i | \(0.671364\pi\) | |||||||
\(728\) | 396171.i | 0.747515i | ||||||||
\(729\) | −228505. | + | 479807.i | −0.429972 | + | 0.902842i | ||||
\(730\) | 73841.9 | 0.138566 | ||||||||
\(731\) | −560189. | + | 323426.i | −1.04834 | + | 0.605257i | ||||
\(732\) | −34975.3 | − | 184120.i | −0.0652739 | − | 0.343621i | ||||
\(733\) | −508070. | + | 880002.i | −0.945617 | + | 1.63786i | −0.191106 | + | 0.981569i | \(0.561207\pi\) |
−0.754511 | + | 0.656287i | \(0.772126\pi\) | |||||||
\(734\) | −294685. | − | 170136.i | −0.546972 | − | 0.315795i | ||||
\(735\) | 54144.7 | + | 62825.3i | 0.100226 | + | 0.116295i | ||||
\(736\) | 3747.97 | + | 6491.68i | 0.00691896 | + | 0.0119840i | ||||
\(737\) | − | 215658.i | − | 0.397036i | ||||||
\(738\) | 107886. | − | 42522.4i | 0.198086 | − | 0.0780737i | ||||
\(739\) | −663801. | −1.21548 | −0.607742 | − | 0.794135i | \(-0.707924\pi\) | ||||
−0.607742 | + | 0.794135i | \(0.707924\pi\) | |||||||
\(740\) | 43493.7 | − | 25111.1i | 0.0794260 | − | 0.0458566i | ||||
\(741\) | 462604. | + | 161497.i | 0.842506 | + | 0.294122i | ||||
\(742\) | 66020.5 | − | 114351.i | 0.119914 | − | 0.207698i | ||||
\(743\) | 619586. | + | 357718.i | 1.12234 | + | 0.647982i | 0.941997 | − | 0.335622i | \(-0.108946\pi\) |
0.180341 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(744\) | 42753.9 | − | 122467.i | 0.0772378 | − | 0.221246i | ||||
\(745\) | −36159.8 | − | 62630.6i | −0.0651499 | − | 0.112843i | ||||
\(746\) | − | 185292.i | − | 0.332950i | ||||||
\(747\) | 258371. | − | 324950.i | 0.463024 | − | 0.582338i | ||||
\(748\) | −234808. | −0.419671 | ||||||||
\(749\) | 379632. | − | 219181.i | 0.676705 | − | 0.390696i | ||||
\(750\) | −170676. | + | 147093.i | −0.303424 | + | 0.261499i | ||||
\(751\) | 221593. | − | 383811.i | 0.392895 | − | 0.680514i | −0.599935 | − | 0.800049i | \(-0.704807\pi\) |
0.992830 | + | 0.119535i | \(0.0381402\pi\) | |||||||
\(752\) | −137390. | − | 79322.2i | −0.242952 | − | 0.140268i | ||||
\(753\) | 882329. | − | 167606.i | 1.55611 | − | 0.295597i | ||||
\(754\) | −573698. | − | 993674.i | −1.00911 | − | 1.74784i | ||||
\(755\) | − | 5679.47i | − | 0.00996355i | ||||||
\(756\) | 187983. | + | 297738.i | 0.328908 | + | 0.520943i | ||||
\(757\) | −270550. | −0.472123 | −0.236061 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236061 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(758\) | 316348. | − | 182644.i | 0.550588 | − | 0.317882i | ||||
\(759\) | 4433.61 | + | 23339.8i | 0.00769615 | + | 0.0405148i | ||||
\(760\) | 15730.5 | − | 27246.0i | 0.0272343 | − | 0.0471711i | ||||
\(761\) | −507749. | − | 293149.i | −0.876758 | − | 0.506196i | −0.00716962 | − | 0.999974i | \(-0.502282\pi\) |
−0.869588 | + | 0.493778i | \(0.835616\pi\) | |||||||
\(762\) | −125452. | − | 145565.i | −0.216057 | − | 0.250696i | ||||
\(763\) | 57191.5 | + | 99058.5i | 0.0982386 | + | 0.170154i | ||||
\(764\) | − | 105718.i | − | 0.181118i | ||||||
\(765\) | −40771.7 | + | 273182.i | −0.0696684 | + | 0.466798i | ||||
\(766\) | 202406. | 0.344958 | ||||||||
\(767\) | −1.12948e6 | + | 652108.i | −1.91995 | + | 1.10848i | ||||
\(768\) | 34804.1 | + | 12150.3i | 0.0590076 | + | 0.0205998i | ||||
\(769\) | 226409. | − | 392152.i | 0.382861 | − | 0.663134i | −0.608609 | − | 0.793470i | \(-0.708272\pi\) |
0.991470 | + | 0.130336i | \(0.0416056\pi\) | |||||||
\(770\) | 69818.9 | + | 40310.0i | 0.117758 | + | 0.0679878i | ||||
\(771\) | −7704.79 | + | 22070.2i | −0.0129614 | + | 0.0371276i | ||||
\(772\) | 7147.70 | + | 12380.2i | 0.0119931 | + | 0.0207727i | ||||
\(773\) | − | 217175.i | − | 0.363455i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181728i | \(-0.0581689\pi\) | |||||||
\(774\) | 318331. | + | 47510.1i | 0.531370 | + | 0.0793056i | ||||
\(775\) | 363167. | 0.604648 | ||||||||
\(776\) | 288750. | − | 166710.i | 0.479511 | − | 0.276846i | ||||
\(777\) | 348915. | − | 300705.i | 0.577933 | − | 0.498079i | ||||
\(778\) | −28081.6 | + | 48638.7i | −0.0463941 | + | 0.0803569i | ||||
\(779\) | −82296.6 | − | 47514.0i | −0.135615 | − | 0.0782973i | ||||
\(780\) | 151913. | − | 28857.2i | 0.249692 | − | 0.0474313i | ||||
\(781\) | −88321.9 | − | 152978.i | −0.144799 | − | 0.250800i | ||||
\(782\) | 53928.4i | 0.0881870i | ||||||||
\(783\) | −902653. | − | 474565.i | −1.47230 | − | 0.774055i | ||||
\(784\) | 79636.2 | 0.129562 | ||||||||
\(785\) | 33298.9 | − | 19225.1i | 0.0540369 | − | 0.0311982i | ||||
\(786\) | 22908.9 | + | 120599.i | 0.0370817 | + | 0.195209i | ||||
\(787\) | 23419.0 | − | 40562.9i | 0.0378110 | − | 0.0654906i | −0.846501 | − | 0.532388i | \(-0.821295\pi\) |
0.884312 | + | 0.466897i | \(0.154628\pi\) | |||||||
\(788\) | 122220. | + | 70563.6i | 0.196829 | + | 0.113639i | ||||
\(789\) | 741598. | + | 860494.i | 1.19128 | + | 1.38227i | ||||
\(790\) | −61058.6 | − | 105757.i | −0.0978346 | − | 0.169455i | ||||
\(791\) | − | 576902.i | − | 0.922038i | ||||||
\(792\) | 91450.1 | + | 72713.0i | 0.145792 | + | 0.115921i | ||||
\(793\) | −754826. | −1.20033 | ||||||||
\(794\) | 86451.3 | − | 49912.7i | 0.137129 | − | 0.0791717i | ||||
\(795\) | −48657.0 | − | 16986.4i | −0.0769859 | − | 0.0268761i | ||||
\(796\) | 947.754 | − | 1641.56i | 0.00149579 | − | 0.00259078i | ||||
\(797\) | 324494. | + | 187347.i | 0.510846 | + | 0.294937i | 0.733181 | − | 0.680033i | \(-0.238035\pi\) |
−0.222335 | + | 0.974970i | \(0.571368\pi\) | |||||||
\(798\) | 95103.6 | − | 272422.i | 0.149345 | − | 0.427796i | ||||
\(799\) | −570672. | − | 988433.i | −0.893908 | − | 1.54829i | ||||
\(800\) | 103209.i | 0.161263i | ||||||||
\(801\) | −36269.7 | − | 92022.2i | −0.0565300 | − | 0.143426i | ||||
\(802\) | −42005.7 | −0.0653070 | ||||||||
\(803\) | 194608. | − | 112357.i | 0.301807 | − | 0.174249i | ||||
\(804\) | −184514. | + | 159019.i | −0.285442 | + | 0.246002i | ||||
\(805\) | 9258.01 | − | 16035.3i | 0.0142865 | − | 0.0247449i | ||||
\(806\) | −452451. | − | 261222.i | −0.696468 | − | 0.402106i | ||||
\(807\) | −127099. | + | 24143.7i | −0.195162 | + | 0.0370729i | ||||
\(808\) | 196403. | + | 340180.i | 0.300833 | + | 0.521059i | ||||
\(809\) | 1.02586e6i | 1.56745i | 0.621109 | + | 0.783724i | \(0.286682\pi\) | ||||
−0.621109 | + | 0.783724i | \(0.713318\pi\) | |||||||
\(810\) | 100475. | − | 93769.7i | 0.153140 | − | 0.142920i | ||||
\(811\) | 869028. | 1.32127 | 0.660636 | − | 0.750707i | \(-0.270287\pi\) | ||||
0.660636 | + | 0.750707i | \(0.270287\pi\) | |||||||
\(812\) | −585162. | + | 337844.i | −0.887492 | + | 0.512394i | ||||
\(813\) | 90901.4 | + | 478532.i | 0.137527 | + | 0.723985i | ||||
\(814\) | 76417.5 | − | 132359.i | 0.115330 | − | 0.199758i | ||||
\(815\) | 155089. | + | 89540.5i | 0.233488 | + | 0.134804i | ||||
\(816\) | 173140. | + | 200899.i | 0.260026 | + | 0.301715i | ||||
\(817\) | −131875. | − | 228414.i | −0.197568 | − | 0.342198i | ||||
\(818\) | 203812.i | 0.304595i | ||||||||
\(819\) | 1.31940e6 | − | 520029.i | 1.96702 | − | 0.775282i | ||||
\(820\) | −29989.0 | −0.0445999 | ||||||||
\(821\) | −469988. | + | 271348.i | −0.697269 | + | 0.402568i | −0.806329 | − | 0.591467i | \(-0.798549\pi\) |
0.109060 | + | 0.994035i | \(0.465216\pi\) | |||||||
\(822\) | −259392. | − | 90554.6i | −0.383895 | − | 0.134019i | ||||
\(823\) | 285782. | − | 494990.i | 0.421926 | − | 0.730797i | −0.574202 | − | 0.818713i | \(-0.694688\pi\) |
0.996128 | + | 0.0879170i | \(0.0280210\pi\) | |||||||
\(824\) | −202401. | − | 116856.i | −0.298097 | − | 0.172106i | ||||
\(825\) | −107812. | + | 308825.i | −0.158402 | + | 0.453737i | ||||
\(826\) | 384018. | + | 665139.i | 0.562849 | + | 0.974882i | ||||
\(827\) | 143023.i | 0.209120i | 0.994519 | + | 0.104560i | \(0.0333434\pi\) | ||||
−0.994519 | + | 0.104560i | \(0.966657\pi\) | |||||||
\(828\) | 16700.0 | − | 21003.4i | 0.0243588 | − | 0.0306358i | ||||
\(829\) | −17805.6 | −0.0259087 | −0.0129544 | − | 0.999916i | \(-0.504124\pi\) | ||||
−0.0129544 | + | 0.999916i | \(0.504124\pi\) | |||||||
\(830\) | −92976.4 | + | 53680.0i | −0.134964 | + | 0.0779213i | ||||
\(831\) | −215513. | + | 185736.i | −0.312085 | + | 0.268963i | ||||
\(832\) | 74237.0 | − | 128582.i | 0.107244 | − | 0.185752i | ||||
\(833\) | 496173. | + | 286466.i | 0.715061 | + | 0.412841i | ||||
\(834\) | 707174. | − | 134334.i | 1.01670 | − | 0.193132i | ||||
\(835\) | 80596.7 | + | 139598.i | 0.115596 | + | 0.200219i | ||||
\(836\) | − | 95741.4i | − | 0.136990i | ||||||
\(837\) | −463984. | + | 18368.7i | −0.662296 | + | 0.0262197i | ||||
\(838\) | −817799. | −1.16455 | ||||||||
\(839\) | −834828. | + | 481988.i | −1.18597 | + | 0.684719i | −0.957388 | − | 0.288806i | \(-0.906742\pi\) |
−0.228580 | + | 0.973525i | \(0.573408\pi\) | |||||||
\(840\) | −16993.6 | − | 89459.5i | −0.0240840 | − | 0.126785i | ||||
\(841\) | 624826. | − | 1.08223e6i | 0.883420 | − | 1.53013i | ||||
\(842\) | −298658. | − | 172430.i | −0.421260 | − | 0.243214i | ||||
\(843\) | −600360. | − | 696612.i | −0.844805 | − | 0.980247i | ||||
\(844\) | 143833. | + | 249126.i | 0.201918 | + | 0.349731i | ||||
\(845\) | − | 411266.i | − | 0.575983i | ||||||
\(846\) | −83829.7 | + | 561683.i | −0.117127 | + | 0.784784i | ||||
\(847\) | −638631. | −0.890191 | ||||||||
\(848\) | −42855.5 | + | 24742.7i | −0.0595958 | + | 0.0344076i | ||||
\(849\) | −1.23492e6 | − | 431115.i | −1.71326 | − | 0.598105i | ||||
\(850\) | −371260. | + | 643040.i | −0.513854 | + | 0.890021i | ||||
\(851\) | −30398.9 | − | 17550.8i | −0.0419758 | − | 0.0242348i | ||||
\(852\) | −65760.1 | + | 188368.i | −0.0905906 | + | 0.259495i | ||||
\(853\) | 536801. | + | 929767.i | 0.737760 | + | 1.27784i | 0.953502 | + | 0.301388i | \(0.0974498\pi\) |
−0.215741 | + | 0.976451i | \(0.569217\pi\) | |||||||
\(854\) | 444508.i | 0.609486i | ||||||||
\(855\) | −111388. | − | 16624.4i | −0.152372 | − | 0.0227412i | ||||
\(856\) | −164286. | −0.224208 | ||||||||
\(857\) | 951017. | − | 549070.i | 1.29487 | − | 0.747595i | 0.315358 | − | 0.948973i | \(-0.397875\pi\) |
0.979514 | + | 0.201378i | \(0.0645419\pi\) | |||||||
\(858\) | 356452. | − | 307201.i | 0.484202 | − | 0.417299i | ||||
\(859\) | 446.404 | − | 773.194i | 0.000604981 | − | 0.00104786i | −0.865723 | − | 0.500524i | \(-0.833141\pi\) |
0.866328 | + | 0.499476i | \(0.166474\pi\) | |||||||
\(860\) | −72082.9 | − | 41617.1i | −0.0974620 | − | 0.0562697i | ||||
\(861\) | −270212. | + | 51329.3i | −0.364501 | + | 0.0692403i | ||||
\(862\) | 293403. | + | 508189.i | 0.394867 | + | 0.683929i | ||||
\(863\) | 395494.i | 0.531029i | 0.964107 | + | 0.265514i | \(0.0855418\pi\) | ||||
−0.964107 | + | 0.265514i | \(0.914458\pi\) | |||||||
\(864\) | −5220.22 | − | 131860.i | −0.00699296 | − | 0.176638i | ||||
\(865\) | −177783. | −0.237607 | ||||||||
\(866\) | 217709. | − | 125694.i | 0.290296 | − | 0.167602i | ||||
\(867\) | 215799. | + | 1.13603e6i | 0.287085 | + | 1.51130i | ||||
\(868\) | −153831. | + | 266443.i | −0.204175 | + | 0.353642i | ||||
\(869\) | −321836. | − | 185812.i | −0.426182 | − | 0.246056i | ||||
\(870\) | 172170. | + | 199773.i | 0.227468 | + | 0.263936i | ||||
\(871\) | 490529. | + | 849621.i | 0.646589 | + | 1.11992i | ||||
\(872\) | − | 42867.6i | − | 0.0563762i | ||||||
\(873\) | −934231. | − | 742818.i | −1.22582 | − | 0.974661i | ||||
\(874\) | −21989.0 | −0.0287861 | ||||||||
\(875\) | 462807. | − | 267202.i | 0.604483 | − | 0.348999i | ||||
\(876\) | −239629. | − | 83655.5i | −0.312271 | − | 0.109015i | ||||
\(877\) | 330793. | − | 572951.i | 0.430088 | − | 0.744935i | −0.566792 | − | 0.823861i | \(-0.691816\pi\) |
0.996880 | + | 0.0789259i | \(0.0251491\pi\) | |||||||
\(878\) | −363219. | − | 209705.i | −0.471173 | − | 0.272032i | ||||
\(879\) | −137177. | + | 392939.i | −0.177542 | + | 0.508566i | ||||
\(880\) | −15107.1 | − | 26166.2i | −0.0195081 | − | 0.0337890i | ||||
\(881\) | 419496.i | 0.540476i | 0.962794 | + | 0.270238i | \(0.0871024\pi\) | ||||
−0.962794 | + | 0.270238i | \(0.912898\pi\) | |||||||
\(882\) | −104534. | − | 265219.i | −0.134375 | − | 0.340932i | ||||
\(883\) | −498161. | −0.638923 | −0.319461 | − | 0.947599i | \(-0.603502\pi\) | ||||
−0.319461 | + | 0.947599i | \(0.603502\pi\) | |||||||
\(884\) | 925065. | − | 534087.i | 1.18377 | − | 0.683451i | ||||
\(885\) | 227077. | − | 195701.i | 0.289926 | − | 0.249866i | ||||
\(886\) | 290338. | − | 502881.i | 0.369859 | − | 0.640615i | ||||
\(887\) | 332952. | + | 192230.i | 0.423189 | + | 0.244328i | 0.696441 | − | 0.717614i | \(-0.254766\pi\) |
−0.273252 | + | 0.961942i | \(0.588099\pi\) | |||||||
\(888\) | −169592. | + | 32215.6i | −0.215070 | + | 0.0408546i | ||||
\(889\) | 227890. | + | 394717.i | 0.288351 | + | 0.499439i | ||||
\(890\) | 25579.2i | 0.0322929i | ||||||||
\(891\) | 122121. | − | 400009.i | 0.153828 | − | 0.503866i | ||||
\(892\) | 436985. | 0.549207 | ||||||||
\(893\) | 403027. | − | 232688.i | 0.505395 | − | 0.291790i | ||||
\(894\) | 46390.3 | + | 244212.i | 0.0580433 | + | 0.305557i | ||||
\(895\) | −152308. | + | 263805.i | −0.190141 | + | 0.329334i | ||||
\(896\) | −75720.5 | − | 43717.2i | −0.0943186 | − | 0.0544548i | ||||
\(897\) | −70554.9 | − | 81866.6i | −0.0876885 | − | 0.101747i | ||||
\(898\) | −158865. | − | 275162.i | −0.197004 | − | 0.341221i | ||||
\(899\) | − | 891053.i | − | 1.10251i | ||||||
\(900\) | 343724. | − | 135476.i | 0.424351 | − | 0.167254i | ||||
\(901\) | −356015. | −0.438549 | ||||||||
\(902\) | −79035.0 | + | 45630.9i | −0.0971418 | + | 0.0560849i | ||||
\(903\) | −720727. | − | 251609.i | −0.883884 | − | 0.308567i | ||||
\(904\) | −108103. | + | 187240.i | −0.132282 | + | 0.229120i | ||||
\(905\) | 205549. | + | 118674.i | 0.250967 | + | 0.144896i | ||||
\(906\) | −6434.27 | + | 18430.8i | −0.00783868 | + | 0.0224537i | ||||
\(907\) | −49856.1 | − | 86353.3i | −0.0606043 | − | 0.104970i | 0.834131 | − | 0.551566i | \(-0.185969\pi\) |
−0.894736 | + | 0.446596i | \(0.852636\pi\) | |||||||
\(908\) | − | 625312.i | − | 0.758447i | ||||||
\(909\) | 875124. | − | 1.10063e6i | 1.05911 | − | 1.33203i | ||||
\(910\) | −366751. | −0.442883 | ||||||||
\(911\) | 947426. | − | 546996.i | 1.14159 | − | 0.659095i | 0.194763 | − | 0.980850i | \(-0.437606\pi\) |
0.946823 | + | 0.321756i | \(0.104273\pi\) | |||||||
\(912\) | −81915.1 | + | 70596.8i | −0.0984860 | + | 0.0848780i | ||||
\(913\) | −163358. | + | 282944.i | −0.195974 | + | 0.339437i | ||||
\(914\) | 565885. | + | 326714.i | 0.677385 | + | 0.391088i | ||||
\(915\) | 170447. | − | 32378.0i | 0.203586 | − | 0.0386730i | ||||
\(916\) | −48156.2 | − | 83408.9i | −0.0573933 | − | 0.0994080i | ||||
\(917\) | − | 291154.i | − | 0.346245i | ||||||
\(918\) | 441798. | − | 840329.i | 0.524250 | − | 0.997159i | ||||
\(919\) | 102313. | 0.121143 | 0.0605717 | − | 0.998164i | \(-0.480708\pi\) | ||||
0.0605717 | + | 0.998164i | \(0.480708\pi\) | |||||||
\(920\) | −6009.60 | + | 3469.64i | −0.00710019 | + | 0.00409930i | ||||
\(921\) | 18032.8 | + | 94930.0i | 0.0212591 | + | 0.111914i | ||||
\(922\) | −303764. | + | 526135.i | −0.357334 | + | 0.618922i | ||||
\(923\) | 695918. | + | 401788.i | 0.816873 | + | 0.471622i | ||||
\(924\) | −180907. | − | 209910.i | −0.211890 | − | 0.245861i | ||||
\(925\) | −241650. | − | 418551.i | −0.282426 | − | 0.489176i | ||||
\(926\) | − | 620346.i | − | 0.723456i | ||||||
\(927\) | −123497. | + | 827462.i | −0.143713 | + | 0.962916i | ||||
\(928\) | 253229. | 0.294047 | ||||||||
\(929\) | −942127. | + | 543937.i | −1.09164 | + | 0.630256i | −0.934012 | − | 0.357243i | \(-0.883717\pi\) |
−0.157625 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(930\) | 113373. | + | 39579.0i | 0.131082 | + | 0.0457613i | ||||
\(931\) | −116805. | + | 202311.i | −0.134760 | + | 0.233411i | ||||
\(932\) | −660923. | − | 381584.i | −0.760885 | − | 0.439297i | ||||
\(933\) | −658.681 | + | 1886.78i | −0.000756679 | + | 0.00216749i | ||||
\(934\) | 88051.2 | + | 152509.i | 0.100935 | + | 0.174824i | ||||
\(935\) | − | 217371.i | − | 0.248644i | ||||||
\(936\) | −525674. | − | 78455.5i | −0.600018 | − | 0.0895513i | ||||
\(937\) | 1.30162e6 | 1.48253 | 0.741265 | − | 0.671213i | \(-0.234226\pi\) | ||||
0.741265 | + | 0.671213i | \(0.234226\pi\) | |||||||
\(938\) | 500331. | − | 288866.i | 0.568659 | − | 0.328315i | ||||
\(939\) | −999967. | + | 861800.i | −1.13411 | + | 0.977407i | ||||
\(940\) | 73431.7 | − | 127187.i | 0.0831051 | − | 0.143942i | ||||
\(941\) | −949282. | − | 548068.i | −1.07205 | − | 0.618950i | −0.143311 | − | 0.989678i | \(-0.545775\pi\) |
−0.928742 | + | 0.370728i | \(0.879108\pi\) | |||||||
\(942\) | −129841. | + | 24664.4i | −0.146322 | + | 0.0277951i | ||||
\(943\) | 10480.1 | + | 18152.0i | 0.0117853 | + | 0.0204127i | ||||
\(944\) | − | 287839.i | − | 0.323002i | ||||||
\(945\) | −275628. | + | 174023.i | −0.308645 | + | 0.194869i | ||||
\(946\) | −253296. | −0.283039 | ||||||||
\(947\) | 863203. | − | 498371.i | 0.962528 | − | 0.555716i | 0.0655775 | − | 0.997847i | \(-0.479111\pi\) |
0.896950 | + | 0.442132i | \(0.145778\pi\) | |||||||
\(948\) | 78333.6 | + | 412371.i | 0.0871628 | + | 0.458850i | ||||
\(949\) | −511128. | + | 885299.i | −0.567541 | + | 0.983009i | ||||
\(950\) | −262196. | − | 151379.i | −0.290521 | − | 0.167733i | ||||
\(951\) | 1.03669e6 | + | 1.20290e6i | 1.14628 | + | 1.33005i | ||||
\(952\) | −314517. | − | 544760.i | −0.347033 | − | 0.601078i | ||||
\(953\) | 501410.i | 0.552087i | 0.961145 | + | 0.276044i | \(0.0890234\pi\) | ||||
−0.961145 | + | 0.276044i | \(0.910977\pi\) | |||||||
\(954\) | 138656. | + | 110247.i | 0.152350 | + | 0.121135i | ||||
\(955\) | 97867.0 | 0.107307 | ||||||||
\(956\) | −709133. | + | 409418.i | −0.775911 | + | 0.447972i | ||||
\(957\) | 757722. | + | 264524.i | 0.827343 | + | 0.288829i | ||||
\(958\) | 304598. | − | 527579.i | 0.331891 | − | 0.574852i | ||||
\(959\) | 564337. | + | 325820.i | 0.613623 | + | 0.354275i | ||||
\(960\) | −11248.0 | + | 32219.5i | −0.0122048 | + | 0.0349604i | ||||
\(961\) | 258899. | + | 448425.i | 0.280339 | + | 0.485561i | ||||
\(962\) | 695267.i | 0.751280i | ||||||||
\(963\) | 215647. | + | 547134.i | 0.232537 | + | 0.589985i | ||||
\(964\) | 429342. | 0.462008 | ||||||||
\(965\) | −11460.8 | + | 6616.91i | −0.0123072 | + | 0.00710559i | ||||
\(966\) | −48210.2 | + | 41548.9i | −0.0516636 | + | 0.0445252i | ||||
\(967\) | −105121. | + | 182074.i | −0.112418 | + | 0.194713i | −0.916745 | − | 0.399474i | \(-0.869193\pi\) |
0.804327 | + | 0.594187i | \(0.202526\pi\) | |||||||
\(968\) | 207275. | + | 119671.i | 0.221206 | + | 0.127713i | ||||
\(969\) | −764320. | + | 145190.i | −0.814006 | + | 0.154628i | ||||
\(970\) | 154330. | + | 267307.i | 0.164024 | + | 0.284097i | ||||
\(971\) | 1.41640e6i | 1.50227i | 0.660151 | + | 0.751133i | \(0.270492\pi\) | ||||
−0.660151 | + | 0.751133i | \(0.729508\pi\) | |||||||
\(972\) | −432291. | + | 190469.i | −0.457555 | + | 0.201601i | ||||
\(973\) | −1.70728e6 | −1.80334 | ||||||||
\(974\) | −949221. | + | 548033.i | −1.00057 | + | 0.577682i | ||||
\(975\) | −277700. | − | 1.46189e6i | −0.292124 | − | 1.53782i | ||||
\(976\) | 83294.5 | − | 144270.i | 0.0874414 | − | 0.151453i | ||||
\(977\) | −1.56228e6 | − | 901983.i | −1.63670 | − | 0.944951i | −0.981958 | − | 0.189101i | \(-0.939443\pi\) |
−0.654745 | − | 0.755850i | \(-0.727224\pi\) | |||||||
\(978\) | −401848. | − | 466274.i | −0.420130 | − | 0.487487i | ||||
\(979\) | 38921.1 | + | 67413.3i | 0.0406087 | + | 0.0703364i | ||||
\(980\) | 73722.4i | 0.0767622i | ||||||||
\(981\) | −142765. | + | 56269.6i | −0.148349 | + | 0.0584703i | ||||
\(982\) | 225783. | 0.234136 | ||||||||
\(983\) | −966691. | + | 558119.i | −1.00042 | + | 0.577590i | −0.908371 | − | 0.418164i | \(-0.862674\pi\) |
−0.0920447 | + | 0.995755i | \(0.529340\pi\) | |||||||
\(984\) | 97319.1 | + | 33974.5i | 0.100510 | + | 0.0350883i | ||||
\(985\) | −65323.5 | + | 113144.i | −0.0673282 | + | 0.116616i | ||||
\(986\) | 1.57774e6 | + | 910908.i | 1.62286 | + | 0.936960i | ||||
\(987\) | 443954. | − | 1.27169e6i | 0.455726 | − | 1.30542i | ||||
\(988\) | 217770. | + | 377190.i | 0.223093 | + | 0.386408i | ||||
\(989\) | 58174.7i | 0.0594759i | ||||||||
\(990\) | −67313.3 | + | 84659.0i | −0.0686800 | + | 0.0863779i | ||||
\(991\) | −888178. | −0.904383 | −0.452192 | − | 0.891921i | \(-0.649358\pi\) | ||||
−0.452192 | + | 0.891921i | \(0.649358\pi\) | |||||||
\(992\) | 99855.2 | − | 57651.5i | 0.101472 | − | 0.0585851i | ||||
\(993\) | 656097. | − | 565443.i | 0.665379 | − | 0.573443i | ||||
\(994\) | 236608. | − | 409817.i | 0.239473 | − | 0.414780i | ||||
\(995\) | 1519.65 | + | 877.373i | 0.00153497 | + | 0.000886213i | ||||
\(996\) | 362538. | − | 68867.4i | 0.365456 | − | 0.0694216i | ||||
\(997\) | −404840. | − | 701204.i | −0.407280 | − | 0.705430i | 0.587304 | − | 0.809367i | \(-0.300190\pi\) |
−0.994584 | + | 0.103936i | \(0.966856\pi\) | |||||||
\(998\) | 207735.i | 0.208569i | ||||||||
\(999\) | 329904. | + | 522520.i | 0.330565 | + | 0.523567i |
(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 | 18.5.d.a.5.3 | ✓ | 8 | |
3.2 | odd | 2 | 54.5.d.a.17.1 | 8 | |||
4.3 | odd | 2 | 144.5.q.b.113.3 | 8 | |||
9.2 | odd | 6 | inner | 18.5.d.a.11.3 | yes | 8 | |
9.4 | even | 3 | 162.5.b.c.161.6 | 8 | |||
9.5 | odd | 6 | 162.5.b.c.161.3 | 8 | |||
9.7 | even | 3 | 54.5.d.a.35.1 | 8 | |||
12.11 | even | 2 | 432.5.q.b.17.2 | 8 | |||
36.7 | odd | 6 | 432.5.q.b.305.2 | 8 | |||
36.11 | even | 6 | 144.5.q.b.65.3 | 8 | |||
36.23 | even | 6 | 1296.5.e.e.161.6 | 8 | |||
36.31 | odd | 6 | 1296.5.e.e.161.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.5.d.a.5.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
18.5.d.a.11.3 | yes | 8 | 9.2 | odd | 6 | inner | |
54.5.d.a.17.1 | 8 | 3.2 | odd | 2 | |||
54.5.d.a.35.1 | 8 | 9.7 | even | 3 | |||
144.5.q.b.65.3 | 8 | 36.11 | even | 6 | |||
144.5.q.b.113.3 | 8 | 4.3 | odd | 2 | |||
162.5.b.c.161.3 | 8 | 9.5 | odd | 6 | |||
162.5.b.c.161.6 | 8 | 9.4 | even | 3 | |||
432.5.q.b.17.2 | 8 | 12.11 | even | 2 | |||
432.5.q.b.305.2 | 8 | 36.7 | odd | 6 | |||
1296.5.e.e.161.3 | 8 | 36.31 | odd | 6 | |||
1296.5.e.e.161.6 | 8 | 36.23 | even | 6 |