Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), 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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.6 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.6 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.45148 | −0.786917 | −0.393459 | − | 0.919342i | \(-0.628722\pi\) | ||||
−0.393459 | + | 0.919342i | \(0.628722\pi\) | |||||||
\(3\) | 9.81167 | + | 16.9943i | 0.629419 | + | 1.09019i | 0.987669 | + | 0.156559i | \(0.0500403\pi\) |
−0.358250 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(4\) | −12.1844 | −0.380762 | ||||||||
\(5\) | −39.8809 | − | 69.0757i | −0.713411 | − | 1.23566i | −0.963569 | − | 0.267458i | \(-0.913816\pi\) |
0.250159 | − | 0.968205i | \(-0.419517\pi\) | |||||||
\(6\) | −43.6764 | − | 75.6497i | −0.495300 | − | 0.857885i | ||||
\(7\) | 8.78791 | − | 15.2211i | 0.0677861 | − | 0.117409i | −0.830140 | − | 0.557554i | \(-0.811740\pi\) |
0.897926 | + | 0.440145i | \(0.145073\pi\) | |||||||
\(8\) | 196.686 | 1.08654 | ||||||||
\(9\) | −71.0376 | + | 123.041i | −0.292336 | + | 0.506341i | ||||
\(10\) | 177.529 | + | 307.489i | 0.561395 | + | 0.972365i | ||||
\(11\) | 296.199 | 0.738077 | 0.369039 | − | 0.929414i | \(-0.379687\pi\) | ||||
0.369039 | + | 0.929414i | \(0.379687\pi\) | |||||||
\(12\) | −119.549 | − | 207.065i | −0.239658 | − | 0.415101i | ||||
\(13\) | 198.091 | − | 343.104i | 0.325093 | − | 0.563077i | −0.656438 | − | 0.754380i | \(-0.727938\pi\) |
0.981531 | + | 0.191303i | \(0.0612712\pi\) | |||||||
\(14\) | −39.1192 | + | 67.7564i | −0.0533420 | + | 0.0923911i | ||||
\(15\) | 782.595 | − | 1355.50i | 0.898068 | − | 1.55550i | ||||
\(16\) | −485.641 | −0.474259 | ||||||||
\(17\) | 676.236 | − | 1171.28i | 0.567513 | − | 0.982962i | −0.429298 | − | 0.903163i | \(-0.641239\pi\) |
0.996811 | − | 0.0797988i | \(-0.0254278\pi\) | |||||||
\(18\) | 316.222 | − | 547.713i | 0.230044 | − | 0.398448i | ||||
\(19\) | −680.888 | − | 1179.33i | −0.432704 | − | 0.749466i | 0.564401 | − | 0.825501i | \(-0.309107\pi\) |
−0.997105 | + | 0.0760348i | \(0.975774\pi\) | |||||||
\(20\) | 485.923 | + | 841.644i | 0.271639 | + | 0.470493i | ||||
\(21\) | 344.896 | 0.170663 | ||||||||
\(22\) | −1318.52 | −0.580806 | ||||||||
\(23\) | −570.380 | − | 987.927i | −0.224825 | − | 0.389408i | 0.731442 | − | 0.681904i | \(-0.238848\pi\) |
−0.956267 | + | 0.292495i | \(0.905514\pi\) | |||||||
\(24\) | 1929.81 | + | 3342.54i | 0.683892 | + | 1.18454i | ||||
\(25\) | −1618.47 | + | 2803.27i | −0.517909 | + | 0.897045i | ||||
\(26\) | −881.799 | + | 1527.32i | −0.255821 | + | 0.443095i | ||||
\(27\) | 1980.48 | 0.522831 | ||||||||
\(28\) | −107.075 | + | 185.460i | −0.0258103 | + | 0.0447048i | ||||
\(29\) | −1198.69 | + | 2076.18i | −0.264673 | + | 0.458428i | −0.967478 | − | 0.252955i | \(-0.918597\pi\) |
0.702805 | + | 0.711383i | \(0.251931\pi\) | |||||||
\(30\) | −3483.70 | + | 6033.95i | −0.706705 | + | 1.22405i | ||||
\(31\) | −2838.29 | − | 4916.07i | −0.530460 | − | 0.918784i | −0.999368 | − | 0.0355371i | \(-0.988686\pi\) |
0.468908 | − | 0.883247i | \(-0.344648\pi\) | |||||||
\(32\) | −4132.12 | −0.713342 | ||||||||
\(33\) | 2906.21 | + | 5033.70i | 0.464560 | + | 0.804641i | ||||
\(34\) | −3010.25 | + | 5213.90i | −0.446586 | + | 0.773509i | ||||
\(35\) | −1401.88 | −0.193437 | ||||||||
\(36\) | 865.548 | − | 1499.17i | 0.111310 | − | 0.192795i | ||||
\(37\) | −3038.57 | − | 5262.96i | −0.364893 | − | 0.632013i | 0.623866 | − | 0.781531i | \(-0.285561\pi\) |
−0.988759 | + | 0.149518i | \(0.952228\pi\) | |||||||
\(38\) | 3030.95 | + | 5249.77i | 0.340503 | + | 0.589768i | ||||
\(39\) | 7774.43 | 0.818478 | ||||||||
\(40\) | −7843.99 | − | 13586.2i | −0.775153 | − | 1.34260i | ||||
\(41\) | 10487.5 | 0.974345 | 0.487172 | − | 0.873306i | \(-0.338028\pi\) | ||||
0.487172 | + | 0.873306i | \(0.338028\pi\) | |||||||
\(42\) | −1535.30 | −0.134298 | ||||||||
\(43\) | 865.356 | − | 12093.8i | 0.0713713 | − | 0.997450i | ||||
\(44\) | −3609.00 | −0.281031 | ||||||||
\(45\) | 11332.2 | 0.834222 | ||||||||
\(46\) | 2539.03 | + | 4397.73i | 0.176919 | + | 0.306432i | ||||
\(47\) | −26809.0 | −1.77026 | −0.885129 | − | 0.465346i | \(-0.845930\pi\) | ||||
−0.885129 | + | 0.465346i | \(0.845930\pi\) | |||||||
\(48\) | −4764.95 | − | 8253.14i | −0.298508 | − | 0.517030i | ||||
\(49\) | 8249.05 | + | 14287.8i | 0.490810 | + | 0.850108i | ||||
\(50\) | 7204.56 | − | 12478.7i | 0.407552 | − | 0.705900i | ||||
\(51\) | 26540.0 | 1.42881 | ||||||||
\(52\) | −2413.62 | + | 4180.51i | −0.123783 | + | 0.214398i | ||||
\(53\) | 15179.4 | + | 26291.4i | 0.742273 | + | 1.28565i | 0.951458 | + | 0.307778i | \(0.0995855\pi\) |
−0.209185 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(54\) | −8816.06 | −0.411424 | ||||||||
\(55\) | −11812.7 | − | 20460.1i | −0.526552 | − | 0.912015i | ||||
\(56\) | 1728.46 | − | 2993.77i | 0.0736526 | − | 0.127570i | ||||
\(57\) | 13361.3 | − | 23142.4i | 0.544705 | − | 0.943456i | ||||
\(58\) | 5335.92 | − | 9242.08i | 0.208276 | − | 0.360745i | ||||
\(59\) | −3000.82 | −0.112230 | −0.0561152 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561152 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(60\) | −9535.43 | + | 16515.9i | −0.341950 | + | 0.592274i | ||||
\(61\) | −6411.35 | + | 11104.8i | −0.220610 | + | 0.382108i | −0.954993 | − | 0.296627i | \(-0.904138\pi\) |
0.734383 | + | 0.678735i | \(0.237471\pi\) | |||||||
\(62\) | 12634.6 | + | 21883.7i | 0.417428 | + | 0.723007i | ||||
\(63\) | 1248.54 | + | 2162.54i | 0.0396326 | + | 0.0686457i | ||||
\(64\) | 33934.6 | 1.03560 | ||||||||
\(65\) | −31600.2 | −0.927698 | ||||||||
\(66\) | −12936.9 | − | 22407.4i | −0.365570 | − | 0.633186i | ||||
\(67\) | −19495.3 | − | 33766.8i | −0.530570 | − | 0.918974i | −0.999364 | − | 0.0356661i | \(-0.988645\pi\) |
0.468794 | − | 0.883307i | \(-0.344689\pi\) | |||||||
\(68\) | −8239.51 | + | 14271.2i | −0.216087 | + | 0.374274i | ||||
\(69\) | 11192.8 | − | 19386.4i | 0.283018 | − | 0.490202i | ||||
\(70\) | 6240.42 | 0.152219 | ||||||||
\(71\) | 23187.6 | − | 40162.2i | 0.545897 | − | 0.945521i | −0.452653 | − | 0.891687i | \(-0.649522\pi\) |
0.998550 | − | 0.0538344i | \(-0.0171443\pi\) | |||||||
\(72\) | −13972.1 | + | 24200.3i | −0.317636 | + | 0.550162i | ||||
\(73\) | 14894.3 | − | 25797.6i | 0.327124 | − | 0.566595i | −0.654816 | − | 0.755788i | \(-0.727254\pi\) |
0.981940 | + | 0.189193i | \(0.0605872\pi\) | |||||||
\(74\) | 13526.1 | + | 23427.9i | 0.287140 | + | 0.497342i | ||||
\(75\) | −63519.4 | −1.30393 | ||||||||
\(76\) | 8296.19 | + | 14369.4i | 0.164757 | + | 0.285368i | ||||
\(77\) | 2602.97 | − | 4508.48i | 0.0500314 | − | 0.0866568i | ||||
\(78\) | −34607.7 | −0.644074 | ||||||||
\(79\) | 34046.1 | − | 58969.5i | 0.613761 | − | 1.06306i | −0.376840 | − | 0.926278i | \(-0.622989\pi\) |
0.990601 | − | 0.136786i | \(-0.0436774\pi\) | |||||||
\(80\) | 19367.8 | + | 33546.0i | 0.338341 | + | 0.586025i | ||||
\(81\) | 36694.0 | + | 63555.8i | 0.621415 | + | 1.07632i | ||||
\(82\) | −46684.9 | −0.766729 | ||||||||
\(83\) | 38356.7 | + | 66435.8i | 0.611148 | + | 1.05854i | 0.991047 | + | 0.133512i | \(0.0426254\pi\) |
−0.379899 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(84\) | −4202.34 | −0.0649820 | ||||||||
\(85\) | −107876. | −1.61948 | ||||||||
\(86\) | −3852.11 | + | 53835.2i | −0.0561633 | + | 0.784910i | ||||
\(87\) | −47044.4 | −0.666361 | ||||||||
\(88\) | 58258.1 | 0.801954 | ||||||||
\(89\) | 64520.1 | + | 111752.i | 0.863416 | + | 1.49548i | 0.868611 | + | 0.495494i | \(0.165013\pi\) |
−0.00519552 | + | 0.999987i | \(0.501654\pi\) | |||||||
\(90\) | −50444.8 | −0.656463 | ||||||||
\(91\) | −3481.62 | − | 6030.34i | −0.0440735 | − | 0.0763376i | ||||
\(92\) | 6949.72 | + | 12037.3i | 0.0856047 | + | 0.148272i | ||||
\(93\) | 55696.8 | − | 96469.6i | 0.667763 | − | 1.15660i | ||||
\(94\) | 119340. | 1.39305 | ||||||||
\(95\) | −54308.8 | + | 94065.5i | −0.617392 | + | 1.06935i | ||||
\(96\) | −40543.0 | − | 70222.5i | −0.448991 | − | 0.777675i | ||||
\(97\) | −57031.7 | −0.615442 | −0.307721 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307721 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(98\) | −36720.4 | − | 63601.6i | −0.386227 | − | 0.668965i | ||||
\(99\) | −21041.3 | + | 36444.5i | −0.215766 | + | 0.373718i | ||||
\(100\) | 19720.0 | − | 34156.0i | 0.197200 | − | 0.341560i | ||||
\(101\) | 8496.24 | − | 14715.9i | 0.0828749 | − | 0.143544i | −0.821609 | − | 0.570052i | \(-0.806923\pi\) |
0.904484 | + | 0.426508i | \(0.140256\pi\) | |||||||
\(102\) | −118142. | −1.12436 | ||||||||
\(103\) | −94549.7 | + | 163765.i | −0.878147 | + | 1.52099i | −0.0247742 | + | 0.999693i | \(0.507887\pi\) |
−0.853373 | + | 0.521302i | \(0.825447\pi\) | |||||||
\(104\) | 38961.7 | − | 67483.7i | 0.353228 | − | 0.611809i | ||||
\(105\) | −13754.8 | − | 23823.9i | −0.121753 | − | 0.210882i | ||||
\(106\) | −67570.5 | − | 117036.i | −0.584107 | − | 1.01170i | ||||
\(107\) | 160449. | 1.35481 | 0.677404 | − | 0.735612i | \(-0.263105\pi\) | ||||
0.677404 | + | 0.735612i | \(0.263105\pi\) | |||||||
\(108\) | −24130.9 | −0.199074 | ||||||||
\(109\) | −100638. | − | 174310.i | −0.811326 | − | 1.40526i | −0.911936 | − | 0.410331i | \(-0.865413\pi\) |
0.100611 | − | 0.994926i | \(-0.467920\pi\) | |||||||
\(110\) | 52583.8 | + | 91077.8i | 0.414353 | + | 0.717680i | ||||
\(111\) | 59626.9 | − | 103277.i | 0.459341 | − | 0.795601i | ||||
\(112\) | −4267.77 | + | 7392.00i | −0.0321482 | + | 0.0556823i | ||||
\(113\) | 213998. | 1.57657 | 0.788287 | − | 0.615308i | \(-0.210968\pi\) | ||||
0.788287 | + | 0.615308i | \(0.210968\pi\) | |||||||
\(114\) | −59477.4 | + | 103018.i | −0.428637 | + | 0.742422i | ||||
\(115\) | −45494.5 | + | 78798.8i | −0.320785 | + | 0.555616i | ||||
\(116\) | 14605.2 | − | 25297.0i | 0.100777 | − | 0.174552i | ||||
\(117\) | 28143.9 | + | 48746.6i | 0.190073 | + | 0.329215i | ||||
\(118\) | 13358.1 | 0.0883160 | ||||||||
\(119\) | −11885.4 | − | 20586.1i | −0.0769390 | − | 0.133262i | ||||
\(120\) | 153925. | − | 266606.i | 0.975791 | − | 1.69012i | ||||
\(121\) | −73317.2 | −0.455242 | ||||||||
\(122\) | 28540.0 | − | 49432.7i | 0.173602 | − | 0.300687i | ||||
\(123\) | 102900. | + | 178228.i | 0.613271 | + | 1.06222i | ||||
\(124\) | 34582.8 | + | 59899.2i | 0.201979 | + | 0.349838i | ||||
\(125\) | 8927.90 | 0.0511063 | ||||||||
\(126\) | −5557.86 | − | 9626.50i | −0.0311876 | − | 0.0540185i | ||||
\(127\) | 252575. | 1.38957 | 0.694786 | − | 0.719217i | \(-0.255499\pi\) | ||||
0.694786 | + | 0.719217i | \(0.255499\pi\) | |||||||
\(128\) | −18831.0 | −0.101589 | ||||||||
\(129\) | 214016. | − | 103954.i | 1.13233 | − | 0.550006i | ||||
\(130\) | 140668. | 0.730022 | ||||||||
\(131\) | −300526. | −1.53004 | −0.765022 | − | 0.644004i | \(-0.777272\pi\) | ||||
−0.765022 | + | 0.644004i | \(0.777272\pi\) | |||||||
\(132\) | −35410.3 | − | 61332.4i | −0.176886 | − | 0.306376i | ||||
\(133\) | −23934.3 | −0.117325 | ||||||||
\(134\) | 86782.7 | + | 150312.i | 0.417514 | + | 0.723156i | ||||
\(135\) | −78983.3 | − | 136803.i | −0.372993 | − | 0.646043i | ||||
\(136\) | 133006. | − | 230373.i | 0.616629 | − | 1.06803i | ||||
\(137\) | −329912. | −1.50174 | −0.750872 | − | 0.660447i | \(-0.770367\pi\) | ||||
−0.750872 | + | 0.660447i | \(0.770367\pi\) | |||||||
\(138\) | −49824.3 | + | 86298.2i | −0.222712 | + | 0.385748i | ||||
\(139\) | −14130.2 | − | 24474.2i | −0.0620312 | − | 0.107441i | 0.833342 | − | 0.552758i | \(-0.186424\pi\) |
−0.895373 | + | 0.445317i | \(0.853091\pi\) | |||||||
\(140\) | 17081.0 | 0.0736534 | ||||||||
\(141\) | −263041. | − | 455601.i | −1.11423 | − | 1.92991i | ||||
\(142\) | −103219. | + | 178781.i | −0.429576 | + | 0.744047i | ||||
\(143\) | 58674.5 | − | 101627.i | 0.239944 | − | 0.415594i | ||||
\(144\) | 34498.8 | − | 59753.7i | 0.138643 | − | 0.240137i | ||||
\(145\) | 191218. | 0.755283 | ||||||||
\(146\) | −66301.5 | + | 114838.i | −0.257419 | + | 0.445864i | ||||
\(147\) | −161874. | + | 280374.i | −0.617850 | + | 1.07015i | ||||
\(148\) | 37023.1 | + | 64125.9i | 0.138937 | + | 0.240646i | ||||
\(149\) | 70895.8 | + | 122795.i | 0.261610 | + | 0.453122i | 0.966670 | − | 0.256026i | \(-0.0824132\pi\) |
−0.705060 | + | 0.709148i | \(0.749080\pi\) | |||||||
\(150\) | 282755. | 1.02608 | ||||||||
\(151\) | −111899. | −0.399379 | −0.199690 | − | 0.979859i | \(-0.563993\pi\) | ||||
−0.199690 | + | 0.979859i | \(0.563993\pi\) | |||||||
\(152\) | −133921. | − | 231958.i | −0.470153 | − | 0.814329i | ||||
\(153\) | 96076.4 | + | 166409.i | 0.331809 | + | 0.574710i | ||||
\(154\) | −11587.1 | + | 20069.4i | −0.0393705 | + | 0.0681918i | ||||
\(155\) | −226387. | + | 392114.i | −0.756872 | + | 1.31094i | ||||
\(156\) | −94726.5 | −0.311645 | ||||||||
\(157\) | −95117.5 | + | 164748.i | −0.307972 | + | 0.533423i | −0.977919 | − | 0.208986i | \(-0.932984\pi\) |
0.669947 | + | 0.742409i | \(0.266317\pi\) | |||||||
\(158\) | −151555. | + | 262501.i | −0.482979 | + | 0.836544i | ||||
\(159\) | −297869. | + | 515925.i | −0.934401 | + | 1.61843i | ||||
\(160\) | 164792. | + | 285429.i | 0.508906 | + | 0.881451i | ||||
\(161\) | −20049.8 | −0.0609600 | ||||||||
\(162\) | −163342. | − | 282917.i | −0.489002 | − | 0.846977i | ||||
\(163\) | −214841. | + | 372115.i | −0.633356 | + | 1.09700i | 0.353505 | + | 0.935433i | \(0.384990\pi\) |
−0.986861 | + | 0.161572i | \(0.948344\pi\) | |||||||
\(164\) | −127784. | −0.370993 | ||||||||
\(165\) | 231804. | − | 401496.i | 0.662843 | − | 1.14808i | ||||
\(166\) | −170744. | − | 295737.i | −0.480923 | − | 0.832983i | ||||
\(167\) | −89065.7 | − | 154266.i | −0.247126 | − | 0.428036i | 0.715601 | − | 0.698509i | \(-0.246153\pi\) |
−0.962727 | + | 0.270474i | \(0.912820\pi\) | |||||||
\(168\) | 67836.1 | 0.185433 | ||||||||
\(169\) | 107166. | + | 185617.i | 0.288629 | + | 0.499921i | ||||
\(170\) | 480205. | 1.27440 | ||||||||
\(171\) | 193475. | 0.505980 | ||||||||
\(172\) | −10543.8 | + | 147355.i | −0.0271754 | + | 0.379791i | ||||
\(173\) | 210147. | 0.533836 | 0.266918 | − | 0.963719i | \(-0.413995\pi\) | ||||
0.266918 | + | 0.963719i | \(0.413995\pi\) | |||||||
\(174\) | 209417. | 0.524371 | ||||||||
\(175\) | 28445.9 | + | 49269.7i | 0.0702141 | + | 0.121614i | ||||
\(176\) | −143846. | −0.350040 | ||||||||
\(177\) | −29443.1 | − | 50996.9i | −0.0706399 | − | 0.122352i | ||||
\(178\) | −287210. | − | 497462.i | −0.679437 | − | 1.17682i | ||||
\(179\) | 206524. | − | 357710.i | 0.481767 | − | 0.834446i | −0.518014 | − | 0.855372i | \(-0.673328\pi\) |
0.999781 | + | 0.0209267i | \(0.00666166\pi\) | |||||||
\(180\) | −138075. | −0.317640 | ||||||||
\(181\) | −43809.7 | + | 75880.6i | −0.0993971 | + | 0.172161i | −0.911435 | − | 0.411444i | \(-0.865025\pi\) |
0.812038 | + | 0.583604i | \(0.198358\pi\) | |||||||
\(182\) | 15498.3 | + | 26843.9i | 0.0346822 | + | 0.0600713i | ||||
\(183\) | −251624. | −0.555424 | ||||||||
\(184\) | −112186. | − | 194311.i | −0.244283 | − | 0.423110i | ||||
\(185\) | −242362. | + | 419783.i | −0.520637 | + | 0.901769i | ||||
\(186\) | −247933. | + | 429432.i | −0.525474 | + | 0.910148i | ||||
\(187\) | 200300. | − | 346930.i | 0.418869 | − | 0.725502i | ||||
\(188\) | 326651. | 0.674046 | ||||||||
\(189\) | 17404.3 | − | 30145.1i | 0.0354406 | − | 0.0613850i | ||||
\(190\) | 241754. | − | 418730.i | 0.485836 | − | 0.841493i | ||||
\(191\) | 188778. | + | 326974.i | 0.374428 | + | 0.648529i | 0.990241 | − | 0.139364i | \(-0.0445057\pi\) |
−0.615813 | + | 0.787892i | \(0.711172\pi\) | |||||||
\(192\) | 332955. | + | 576694.i | 0.651826 | + | 1.12900i | ||||
\(193\) | 315911. | 0.610480 | 0.305240 | − | 0.952275i | \(-0.401263\pi\) | ||||
0.305240 | + | 0.952275i | \(0.401263\pi\) | |||||||
\(194\) | 253875. | 0.484302 | ||||||||
\(195\) | −310051. | − | 537024.i | −0.583911 | − | 1.01136i | ||||
\(196\) | −100509. | − | 174087.i | −0.186882 | − | 0.323688i | ||||
\(197\) | 390412. | − | 676213.i | 0.716733 | − | 1.24142i | −0.245554 | − | 0.969383i | \(-0.578970\pi\) |
0.962287 | − | 0.272035i | \(-0.0876968\pi\) | |||||||
\(198\) | 93664.7 | − | 162232.i | 0.169790 | − | 0.294085i | ||||
\(199\) | −100876. | −0.180574 | −0.0902870 | − | 0.995916i | \(-0.528778\pi\) | ||||
−0.0902870 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(200\) | −318329. | + | 551362.i | −0.562731 | + | 0.974680i | ||||
\(201\) | 382562. | − | 662617.i | 0.667901 | − | 1.15684i | ||||
\(202\) | −37820.8 | + | 65507.5i | −0.0652157 | + | 0.112957i | ||||
\(203\) | 21067.9 | + | 36490.6i | 0.0358823 | + | 0.0621500i | ||||
\(204\) | −323373. | −0.544037 | ||||||||
\(205\) | −418251. | − | 724432.i | −0.695108 | − | 1.20396i | ||||
\(206\) | 420886. | − | 728995.i | 0.691029 | − | 1.19690i | ||||
\(207\) | 162074. | 0.262898 | ||||||||
\(208\) | −96201.4 | + | 166626.i | −0.154178 | + | 0.267044i | ||||
\(209\) | −201678. | − | 349317.i | −0.319369 | − | 0.553164i | ||||
\(210\) | 61229.0 | + | 106052.i | 0.0958095 | + | 0.165947i | ||||
\(211\) | 332166. | 0.513628 | 0.256814 | − | 0.966461i | \(-0.417327\pi\) | ||||
0.256814 | + | 0.966461i | \(0.417327\pi\) | |||||||
\(212\) | −184951. | − | 320344.i | −0.282629 | − | 0.489528i | ||||
\(213\) | 910037. | 1.37439 | ||||||||
\(214\) | −714235. | −1.06612 | ||||||||
\(215\) | −869897. | + | 422535.i | −1.28343 | + | 0.623400i | ||||
\(216\) | 389532. | 0.568079 | ||||||||
\(217\) | −99770.6 | −0.143831 | ||||||||
\(218\) | 447987. | + | 775936.i | 0.638446 | + | 1.10582i | ||||
\(219\) | 584551. | 0.823592 | ||||||||
\(220\) | 143930. | + | 249294.i | 0.200491 | + | 0.347260i | ||||
\(221\) | −267913. | − | 464039.i | −0.368989 | − | 0.639107i | ||||
\(222\) | −265428. | + | 459734.i | −0.361463 | + | 0.626072i | ||||
\(223\) | 185608. | 0.249939 | 0.124970 | − | 0.992161i | \(-0.460117\pi\) | ||||
0.124970 | + | 0.992161i | \(0.460117\pi\) | |||||||
\(224\) | −36312.7 | + | 62895.4i | −0.0483547 | + | 0.0837527i | ||||
\(225\) | −229944. | − | 398275.i | −0.302807 | − | 0.524477i | ||||
\(226\) | −952608. | −1.24063 | ||||||||
\(227\) | 498203. | + | 862912.i | 0.641714 | + | 1.11148i | 0.985050 | + | 0.172268i | \(0.0551096\pi\) |
−0.343336 | + | 0.939213i | \(0.611557\pi\) | |||||||
\(228\) | −162799. | + | 281976.i | −0.207403 | + | 0.359232i | ||||
\(229\) | −77766.5 | + | 134696.i | −0.0979950 | + | 0.169732i | −0.910855 | − | 0.412727i | \(-0.864576\pi\) |
0.812860 | + | 0.582460i | \(0.197910\pi\) | |||||||
\(230\) | 202518. | − | 350771.i | 0.252431 | − | 0.437224i | ||||
\(231\) | 102158. | 0.125963 | ||||||||
\(232\) | −235764. | + | 408356.i | −0.287579 | + | 0.498102i | ||||
\(233\) | −712861. | + | 1.23471e6i | −0.860231 | + | 1.48996i | 0.0114740 | + | 0.999934i | \(0.496348\pi\) |
−0.871705 | + | 0.490030i | \(0.836986\pi\) | |||||||
\(234\) | −125282. | − | 216994.i | −0.149571 | − | 0.259065i | ||||
\(235\) | 1.06917e6 | + | 1.85185e6i | 1.26292 | + | 2.18744i | ||||
\(236\) | 36563.1 | 0.0427330 | ||||||||
\(237\) | 1.33619e6 | 1.54525 | ||||||||
\(238\) | 52907.6 | + | 91638.6i | 0.0605446 | + | 0.104866i | ||||
\(239\) | −499112. | − | 864488.i | −0.565202 | − | 0.978958i | −0.997031 | − | 0.0770026i | \(-0.975465\pi\) |
0.431829 | − | 0.901955i | \(-0.357868\pi\) | |||||||
\(240\) | −380061. | + | 658284.i | −0.425917 | + | 0.737710i | ||||
\(241\) | 368394. | − | 638077.i | 0.408573 | − | 0.707670i | −0.586157 | − | 0.810198i | \(-0.699360\pi\) |
0.994730 | + | 0.102528i | \(0.0326931\pi\) | |||||||
\(242\) | 326370. | 0.358238 | ||||||||
\(243\) | −479429. | + | 830396.i | −0.520846 | + | 0.902131i | ||||
\(244\) | 78118.3 | − | 135305.i | 0.0839998 | − | 0.145492i | ||||
\(245\) | 657958. | − | 1.13962e6i | 0.700298 | − | 1.21295i | ||||
\(246\) | −458057. | − | 793377.i | −0.482593 | − | 0.835876i | ||||
\(247\) | −539512. | −0.562676 | ||||||||
\(248\) | −558251. | − | 966919.i | −0.576369 | − | 0.998300i | ||||
\(249\) | −752687. | + | 1.30369e6i | −0.769336 | + | 1.33253i | ||||
\(250\) | −39742.3 | −0.0402164 | ||||||||
\(251\) | 582987. | − | 1.00976e6i | 0.584083 | − | 1.01166i | −0.410906 | − | 0.911678i | \(-0.634788\pi\) |
0.994989 | − | 0.0999839i | \(-0.0318791\pi\) | |||||||
\(252\) | −15212.7 | − | 26349.2i | −0.0150906 | − | 0.0261376i | ||||
\(253\) | −168946. | − | 292623.i | −0.165938 | − | 0.287414i | ||||
\(254\) | −1.12433e6 | −1.09348 | ||||||||
\(255\) | −1.05844e6 | − | 1.83327e6i | −1.01933 | − | 1.76553i | ||||
\(256\) | −1.00208e6 | −0.955658 | ||||||||
\(257\) | 809150. | 0.764181 | 0.382090 | − | 0.924125i | \(-0.375204\pi\) | ||||
0.382090 | + | 0.924125i | \(0.375204\pi\) | |||||||
\(258\) | −952687. | + | 462749.i | −0.891048 | + | 0.432809i | ||||
\(259\) | −106811. | −0.0989386 | ||||||||
\(260\) | 385029. | 0.353232 | ||||||||
\(261\) | −170303. | − | 294974.i | −0.154747 | − | 0.268030i | ||||
\(262\) | 1.33778e6 | 1.20402 | ||||||||
\(263\) | −484033. | − | 838370.i | −0.431505 | − | 0.747388i | 0.565498 | − | 0.824749i | \(-0.308684\pi\) |
−0.997003 | + | 0.0773612i | \(0.975351\pi\) | |||||||
\(264\) | 571609. | + | 990056.i | 0.504765 | + | 0.874278i | ||||
\(265\) | 1.21073e6 | − | 2.09705e6i | 1.05909 | − | 1.83440i | ||||
\(266\) | 106543. | 0.0923253 | ||||||||
\(267\) | −1.26610e6 | + | 2.19295e6i | −1.08690 | + | 1.88257i | ||||
\(268\) | 237538. | + | 411427.i | 0.202020 | + | 0.349910i | ||||
\(269\) | 55719.5 | 0.0469490 | 0.0234745 | − | 0.999724i | \(-0.492527\pi\) | ||||
0.0234745 | + | 0.999724i | \(0.492527\pi\) | |||||||
\(270\) | 351592. | + | 608975.i | 0.293515 | + | 0.508382i | ||||
\(271\) | −176169. | + | 305134.i | −0.145716 | + | 0.252388i | −0.929640 | − | 0.368469i | \(-0.879882\pi\) |
0.783924 | + | 0.620857i | \(0.213215\pi\) | |||||||
\(272\) | −328408. | + | 568820.i | −0.269148 | + | 0.466179i | ||||
\(273\) | 68321.0 | − | 118335.i | 0.0554814 | − | 0.0960966i | ||||
\(274\) | 1.46859e6 | 1.18175 | ||||||||
\(275\) | −479388. | + | 830324.i | −0.382257 | + | 0.662088i | ||||
\(276\) | −136377. | + | 236211.i | −0.107762 | + | 0.186650i | ||||
\(277\) | 636770. | + | 1.10292e6i | 0.498636 | + | 0.863662i | 0.999999 | − | 0.00157482i | \(-0.000501282\pi\) |
−0.501363 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(278\) | 62900.1 | + | 108946.i | 0.0488134 | + | 0.0845473i | ||||
\(279\) | 806502. | 0.620290 | ||||||||
\(280\) | −275729. | −0.210178 | ||||||||
\(281\) | 182712. | + | 316467.i | 0.138039 | + | 0.239091i | 0.926754 | − | 0.375668i | \(-0.122587\pi\) |
−0.788715 | + | 0.614759i | \(0.789253\pi\) | |||||||
\(282\) | 1.17092e6 | + | 2.02810e6i | 0.876809 | + | 1.51868i | ||||
\(283\) | −79267.0 | + | 137295.i | −0.0588337 | + | 0.101903i | −0.893942 | − | 0.448182i | \(-0.852072\pi\) |
0.835108 | + | 0.550085i | \(0.185405\pi\) | |||||||
\(284\) | −282527. | + | 489351.i | −0.207857 | + | 0.360018i | ||||
\(285\) | −2.13144e6 | −1.55439 | ||||||||
\(286\) | −261188. | + | 452391.i | −0.188816 | + | 0.327038i | ||||
\(287\) | 92163.3 | − | 159631.i | 0.0660470 | − | 0.114397i | ||||
\(288\) | 293536. | − | 508419.i | 0.208535 | − | 0.361194i | ||||
\(289\) | −204662. | − | 354485.i | −0.144143 | − | 0.249662i | ||||
\(290\) | −851204. | −0.594345 | ||||||||
\(291\) | −559576. | − | 969215.i | −0.387371 | − | 0.670946i | ||||
\(292\) | −181477. | + | 314328.i | −0.124556 | + | 0.215738i | ||||
\(293\) | 808240. | 0.550011 | 0.275006 | − | 0.961443i | \(-0.411320\pi\) | ||||
0.275006 | + | 0.961443i | \(0.411320\pi\) | |||||||
\(294\) | 720577. | − | 1.24808e6i | 0.486197 | − | 0.842118i | ||||
\(295\) | 119675. | + | 207284.i | 0.0800663 | + | 0.138679i | ||||
\(296\) | −597643. | − | 1.03515e6i | −0.396472 | − | 0.686710i | ||||
\(297\) | 586616. | 0.385890 | ||||||||
\(298\) | −315591. | − | 546619.i | −0.205866 | − | 0.356570i | ||||
\(299\) | −451950. | −0.292356 | ||||||||
\(300\) | 773944. | 0.496485 | ||||||||
\(301\) | −176476. | − | 119451.i | −0.112272 | − | 0.0759928i | ||||
\(302\) | 498118. | 0.314278 | ||||||||
\(303\) | 333449. | 0.208652 | ||||||||
\(304\) | 330667. | + | 572732.i | 0.205214 | + | 0.355441i | ||||
\(305\) | 1.02276e6 | 0.629542 | ||||||||
\(306\) | −427682. | − | 740766.i | −0.261106 | − | 0.452249i | ||||
\(307\) | 208378. | + | 360922.i | 0.126185 | + | 0.218558i | 0.922195 | − | 0.386724i | \(-0.126393\pi\) |
−0.796011 | + | 0.605282i | \(0.793060\pi\) | |||||||
\(308\) | −31715.5 | + | 54932.9i | −0.0190500 | + | 0.0329956i | ||||
\(309\) | −3.71076e6 | −2.21089 | ||||||||
\(310\) | 1.00776e6 | − | 1.74549e6i | 0.595595 | − | 1.03160i | ||||
\(311\) | −791941. | − | 1.37168e6i | −0.464293 | − | 0.804179i | 0.534877 | − | 0.844930i | \(-0.320358\pi\) |
−0.999169 | + | 0.0407516i | \(0.987025\pi\) | |||||||
\(312\) | 1.52912e6 | 0.889313 | ||||||||
\(313\) | −834811. | − | 1.44594e6i | −0.481645 | − | 0.834234i | 0.518133 | − | 0.855300i | \(-0.326627\pi\) |
−0.999778 | + | 0.0210658i | \(0.993294\pi\) | |||||||
\(314\) | 423413. | − | 733373.i | 0.242348 | − | 0.419760i | ||||
\(315\) | 99586.0 | − | 172488.i | 0.0565486 | − | 0.0979451i | ||||
\(316\) | −414830. | + | 718506.i | −0.233697 | + | 0.404774i | ||||
\(317\) | 2.42601e6 | 1.35595 | 0.677977 | − | 0.735083i | \(-0.262857\pi\) | ||||
0.677977 | + | 0.735083i | \(0.262857\pi\) | |||||||
\(318\) | 1.32596e6 | − | 2.29663e6i | 0.735296 | − | 1.27357i | ||||
\(319\) | −355049. | + | 614963.i | −0.195349 | + | 0.338355i | ||||
\(320\) | −1.35334e6 | − | 2.34405e6i | −0.738808 | − | 1.27965i | ||||
\(321\) | 1.57427e6 | + | 2.72672e6i | 0.852741 | + | 1.47699i | ||||
\(322\) | 89251.2 | 0.0479705 | ||||||||
\(323\) | −1.84176e6 | −0.982262 | ||||||||
\(324\) | −447093. | − | 774387.i | −0.236611 | − | 0.409822i | ||||
\(325\) | 641208. | + | 1.11061e6i | 0.336737 | + | 0.583246i | ||||
\(326\) | 956358. | − | 1.65646e6i | 0.498398 | − | 0.863251i | ||||
\(327\) | 1.97485e6 | − | 3.42054e6i | 1.02133 | − | 1.76899i | ||||
\(328\) | 2.06274e6 | 1.05867 | ||||||||
\(329\) | −235595. | + | 408063.i | −0.119999 | + | 0.207844i | ||||
\(330\) | −1.03187e6 | + | 1.78725e6i | −0.521603 | + | 0.903443i | ||||
\(331\) | 1.08077e6 | − | 1.87196e6i | 0.542207 | − | 0.939130i | −0.456570 | − | 0.889688i | \(-0.650922\pi\) |
0.998777 | − | 0.0494426i | \(-0.0157445\pi\) | |||||||
\(332\) | −467353. | − | 809479.i | −0.232702 | − | 0.403051i | ||||
\(333\) | 863412. | 0.426685 | ||||||||
\(334\) | 396474. | + | 686713.i | 0.194468 | + | 0.336829i | ||||
\(335\) | −1.55498e6 | + | 2.69330e6i | −0.757028 | + | 1.31121i | ||||
\(336\) | −167496. | −0.0809386 | ||||||||
\(337\) | −1.62857e6 | + | 2.82077e6i | −0.781145 | + | 1.35298i | 0.150130 | + | 0.988666i | \(0.452031\pi\) |
−0.931275 | + | 0.364317i | \(0.881303\pi\) | |||||||
\(338\) | −477047. | − | 826270.i | −0.227127 | − | 0.393396i | ||||
\(339\) | 2.09968e6 | + | 3.63675e6i | 0.992325 | + | 1.71876i | ||||
\(340\) | 1.31439e6 | 0.616636 | ||||||||
\(341\) | −840699. | − | 1.45613e6i | −0.391521 | − | 0.678134i | ||||
\(342\) | −861247. | −0.398164 | ||||||||
\(343\) | 585364. | 0.268652 | ||||||||
\(344\) | 170203. | − | 2.37867e6i | 0.0775481 | − | 1.08377i | ||||
\(345\) | −1.78551e6 | −0.807633 | ||||||||
\(346\) | −935465. | −0.420085 | ||||||||
\(347\) | 1.40807e6 | + | 2.43886e6i | 0.627772 | + | 1.08733i | 0.987998 | + | 0.154468i | \(0.0493664\pi\) |
−0.360226 | + | 0.932865i | \(0.617300\pi\) | |||||||
\(348\) | 573206. | 0.253725 | ||||||||
\(349\) | 1.32927e6 | + | 2.30236e6i | 0.584184 | + | 1.01184i | 0.994977 | + | 0.100108i | \(0.0319188\pi\) |
−0.410792 | + | 0.911729i | \(0.634748\pi\) | |||||||
\(350\) | −126626. | − | 219323.i | −0.0552526 | − | 0.0957004i | ||||
\(351\) | 392316. | − | 679512.i | 0.169968 | − | 0.294394i | ||||
\(352\) | −1.22393e6 | −0.526502 | ||||||||
\(353\) | −114987. | + | 199164.i | −0.0491149 | + | 0.0850695i | −0.889538 | − | 0.456862i | \(-0.848973\pi\) |
0.840423 | + | 0.541931i | \(0.182307\pi\) | |||||||
\(354\) | 131065. | + | 227011.i | 0.0555877 | + | 0.0962807i | ||||
\(355\) | −3.69897e6 | −1.55779 | ||||||||
\(356\) | −786137. | − | 1.36163e6i | −0.328756 | − | 0.569421i | ||||
\(357\) | 233231. | − | 403968.i | 0.0968537 | − | 0.167756i | ||||
\(358\) | −919335. | + | 1.59234e6i | −0.379111 | + | 0.656640i | ||||
\(359\) | −183276. | + | 317444.i | −0.0750533 | + | 0.129996i | −0.901109 | − | 0.433592i | \(-0.857246\pi\) |
0.826056 | + | 0.563588i | \(0.190579\pi\) | |||||||
\(360\) | 2.22887e6 | 0.906419 | ||||||||
\(361\) | 310834. | − | 538380.i | 0.125534 | − | 0.217431i | ||||
\(362\) | 195018. | − | 337781.i | 0.0782173 | − | 0.135476i | ||||
\(363\) | −719364. | − | 1.24597e6i | −0.286538 | − | 0.496298i | ||||
\(364\) | 42421.3 | + | 73475.9i | 0.0167815 | + | 0.0290664i | ||||
\(365\) | −2.37599e6 | −0.933495 | ||||||||
\(366\) | 1.12010e6 | 0.437073 | ||||||||
\(367\) | 492872. | + | 853679.i | 0.191015 | + | 0.330849i | 0.945587 | − | 0.325369i | \(-0.105489\pi\) |
−0.754572 | + | 0.656218i | \(0.772155\pi\) | |||||||
\(368\) | 277000. | + | 479778.i | 0.106625 | + | 0.184681i | ||||
\(369\) | −745008. | + | 1.29039e6i | −0.284836 | + | 0.493350i | ||||
\(370\) | 1.07887e6 | − | 1.86865e6i | 0.409698 | − | 0.709618i | ||||
\(371\) | 533579. | 0.201263 | ||||||||
\(372\) | −678630. | + | 1.17542e6i | −0.254259 | + | 0.440389i | ||||
\(373\) | −2.43355e6 | + | 4.21503e6i | −0.905665 | + | 1.56866i | −0.0856428 | + | 0.996326i | \(0.527294\pi\) |
−0.820022 | + | 0.572332i | \(0.806039\pi\) | |||||||
\(374\) | −891632. | + | 1.54435e6i | −0.329615 | + | 0.570910i | ||||
\(375\) | 87597.6 | + | 151724.i | 0.0321673 | + | 0.0557153i | ||||
\(376\) | −5.27295e6 | −1.92346 | ||||||||
\(377\) | 474899. | + | 822548.i | 0.172087 | + | 0.298063i | ||||
\(378\) | −77474.7 | + | 134190.i | −0.0278888 | + | 0.0483049i | ||||
\(379\) | 1.75391e6 | 0.627203 | 0.313602 | − | 0.949555i | \(-0.398464\pi\) | ||||
0.313602 | + | 0.949555i | \(0.398464\pi\) | |||||||
\(380\) | 661718. | − | 1.14613e6i | 0.235079 | − | 0.407169i | ||||
\(381\) | 2.47818e6 | + | 4.29234e6i | 0.874622 | + | 1.51489i | ||||
\(382\) | −840342. | − | 1.45551e6i | −0.294644 | − | 0.510338i | ||||
\(383\) | −2.01371e6 | −0.701456 | −0.350728 | − | 0.936477i | \(-0.614066\pi\) | ||||
−0.350728 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(384\) | −184763. | − | 320020.i | −0.0639422 | − | 0.110751i | ||||
\(385\) | −415235. | −0.142772 | ||||||||
\(386\) | −1.40627e6 | −0.480397 | ||||||||
\(387\) | 1.42656e6 | + | 965588.i | 0.484185 | + | 0.327729i | ||||
\(388\) | 694896. | 0.234337 | ||||||||
\(389\) | 4.27059e6 | 1.43092 | 0.715458 | − | 0.698656i | \(-0.246218\pi\) | ||||
0.715458 | + | 0.698656i | \(0.246218\pi\) | |||||||
\(390\) | 1.38018e6 | + | 2.39055e6i | 0.459489 | + | 0.795859i | ||||
\(391\) | −1.54285e6 | −0.510365 | ||||||||
\(392\) | 1.62247e6 | + | 2.81020e6i | 0.533287 | + | 0.923680i | ||||
\(393\) | −2.94866e6 | − | 5.10723e6i | −0.963038 | − | 1.66803i | ||||
\(394\) | −1.73791e6 | + | 3.01015e6i | −0.564010 | + | 0.976893i | ||||
\(395\) | −5.43115e6 | −1.75145 | ||||||||
\(396\) | 256375. | − | 444054.i | 0.0821556 | − | 0.142298i | ||||
\(397\) | −1.70889e6 | − | 2.95989e6i | −0.544174 | − | 0.942537i | −0.998658 | − | 0.0517826i | \(-0.983510\pi\) |
0.454484 | − | 0.890755i | \(-0.349824\pi\) | |||||||
\(398\) | 449047. | 0.142097 | ||||||||
\(399\) | −234836. | − | 406747.i | −0.0738468 | − | 0.127906i | ||||
\(400\) | 785994. | − | 1.36138e6i | 0.245623 | − | 0.425432i | ||||
\(401\) | 1.54136e6 | − | 2.66972e6i | 0.478679 | − | 0.829097i | −0.521022 | − | 0.853543i | \(-0.674449\pi\) |
0.999701 | + | 0.0244467i | \(0.00778239\pi\) | |||||||
\(402\) | −1.70297e6 | + | 2.94962e6i | −0.525583 | + | 0.910336i | ||||
\(403\) | −2.24896e6 | −0.689795 | ||||||||
\(404\) | −103521. | + | 179304.i | −0.0315556 | + | 0.0546559i | ||||
\(405\) | 2.92677e6 | − | 5.06932e6i | 0.886649 | − | 1.53572i | ||||
\(406\) | −93783.1 | − | 162437.i | −0.0282364 | − | 0.0489069i | ||||
\(407\) | −900022. | − | 1.55888e6i | −0.269319 | − | 0.466474i | ||||
\(408\) | 5.22004e6 | 1.55247 | ||||||||
\(409\) | −337991. | −0.0999071 | −0.0499535 | − | 0.998752i | \(-0.515907\pi\) | ||||
−0.0499535 | + | 0.998752i | \(0.515907\pi\) | |||||||
\(410\) | 1.86183e6 | + | 3.22479e6i | 0.546992 | + | 0.947418i | ||||
\(411\) | −3.23698e6 | − | 5.60662e6i | −0.945226 | − | 1.63718i | ||||
\(412\) | 1.15203e6 | − | 1.99537e6i | 0.334364 | − | 0.579136i | ||||
\(413\) | −26370.9 | + | 45675.8i | −0.00760765 | + | 0.0131768i | ||||
\(414\) | −721467. | −0.206879 | ||||||||
\(415\) | 3.05940e6 | − | 5.29904e6i | 0.871999 | − | 1.51035i | ||||
\(416\) | −818537. | + | 1.41775e6i | −0.231902 | + | 0.401667i | ||||
\(417\) | 277281. | − | 480265.i | 0.0780872 | − | 0.135251i | ||||
\(418\) | 897765. | + | 1.55498e6i | 0.251317 | + | 0.435294i | ||||
\(419\) | 3.63873e6 | 1.01255 | 0.506273 | − | 0.862373i | \(-0.331023\pi\) | ||||
0.506273 | + | 0.862373i | \(0.331023\pi\) | |||||||
\(420\) | 167593. | + | 290280.i | 0.0463589 | + | 0.0802959i | ||||
\(421\) | −2.31773e6 | + | 4.01443e6i | −0.637321 | + | 1.10387i | 0.348697 | + | 0.937236i | \(0.386624\pi\) |
−0.986018 | + | 0.166637i | \(0.946709\pi\) | |||||||
\(422\) | −1.47863e6 | −0.404183 | ||||||||
\(423\) | 1.90445e6 | − | 3.29860e6i | 0.517510 | − | 0.896353i | ||||
\(424\) | 2.98556e6 | + | 5.17114e6i | 0.806513 | + | 1.39692i | ||||
\(425\) | 2.18893e6 | + | 3.79134e6i | 0.587841 | + | 1.01817i | ||||
\(426\) | −4.05101e6 | −1.08153 | ||||||||
\(427\) | 112685. | + | 195176.i | 0.0299086 | + | 0.0518031i | ||||
\(428\) | −1.95497e6 | −0.515858 | ||||||||
\(429\) | 2.30278e6 | 0.604100 | ||||||||
\(430\) | 3.87233e6 | − | 1.88091e6i | 1.00995 | − | 0.490564i | ||||
\(431\) | 4.38405e6 | 1.13680 | 0.568398 | − | 0.822754i | \(-0.307563\pi\) | ||||
0.568398 | + | 0.822754i | \(0.307563\pi\) | |||||||
\(432\) | −961803. | −0.247957 | ||||||||
\(433\) | −495379. | − | 858022.i | −0.126975 | − | 0.219927i | 0.795528 | − | 0.605917i | \(-0.207193\pi\) |
−0.922503 | + | 0.385989i | \(0.873860\pi\) | |||||||
\(434\) | 444126. | 0.113183 | ||||||||
\(435\) | 1.87617e6 | + | 3.24962e6i | 0.475389 | + | 0.823398i | ||||
\(436\) | 1.22621e6 | + | 2.12386e6i | 0.308922 | + | 0.535068i | ||||
\(437\) | −776729. | + | 1.34533e6i | −0.194566 | + | 0.336998i | ||||
\(438\) | −2.60211e6 | −0.648098 | ||||||||
\(439\) | 1.80657e6 | − | 3.12907e6i | 0.447397 | − | 0.774914i | −0.550819 | − | 0.834625i | \(-0.685684\pi\) |
0.998216 | + | 0.0597107i | \(0.0190178\pi\) | |||||||
\(440\) | −2.32338e6 | − | 4.02422e6i | −0.572122 | − | 0.990945i | ||||
\(441\) | −2.34397e6 | −0.573926 | ||||||||
\(442\) | 1.19261e6 | + | 2.06566e6i | 0.290364 | + | 0.502925i | ||||
\(443\) | 2.54236e6 | − | 4.40350e6i | 0.615500 | − | 1.06608i | −0.374797 | − | 0.927107i | \(-0.622288\pi\) |
0.990297 | − | 0.138970i | \(-0.0443790\pi\) | |||||||
\(444\) | −726516. | + | 1.25836e6i | −0.174899 | + | 0.302934i | ||||
\(445\) | 5.14623e6 | − | 8.91354e6i | 1.23194 | − | 2.13378i | ||||
\(446\) | −826229. | −0.196681 | ||||||||
\(447\) | −1.39121e6 | + | 2.40965e6i | −0.329325 | + | 0.570407i | ||||
\(448\) | 298214. | − | 516521.i | 0.0701993 | − | 0.121589i | ||||
\(449\) | −54511.0 | − | 94415.9i | −0.0127605 | − | 0.0221019i | 0.859575 | − | 0.511010i | \(-0.170729\pi\) |
−0.872335 | + | 0.488908i | \(0.837395\pi\) | |||||||
\(450\) | 1.02359e6 | + | 1.77291e6i | 0.238284 | + | 0.412720i | ||||
\(451\) | 3.10639e6 | 0.719142 | ||||||||
\(452\) | −2.60743e6 | −0.600298 | ||||||||
\(453\) | −1.09792e6 | − | 1.90165e6i | −0.251377 | − | 0.435397i | ||||
\(454\) | −2.21774e6 | − | 3.84123e6i | −0.504975 | − | 0.874643i | ||||
\(455\) | −277700. | + | 480990.i | −0.0628850 | + | 0.108920i | ||||
\(456\) | 2.62797e6 | − | 4.55178e6i | 0.591846 | − | 1.02511i | ||||
\(457\) | −3.66704e6 | −0.821343 | −0.410671 | − | 0.911783i | \(-0.634706\pi\) | ||||
−0.410671 | + | 0.911783i | \(0.634706\pi\) | |||||||
\(458\) | 346176. | − | 599594.i | 0.0771139 | − | 0.133565i | ||||
\(459\) | 1.33927e6 | − | 2.31969e6i | 0.296713 | − | 0.513923i | ||||
\(460\) | 554322. | − | 960113.i | 0.122143 | − | 0.211557i | ||||
\(461\) | 3.35227e6 | + | 5.80630e6i | 0.734660 | + | 1.27247i | 0.954872 | + | 0.297016i | \(0.0959915\pi\) |
−0.220213 | + | 0.975452i | \(0.570675\pi\) | |||||||
\(462\) | −454753. | −0.0991222 | ||||||||
\(463\) | 3.94174e6 | + | 6.82729e6i | 0.854546 | + | 1.48012i | 0.877066 | + | 0.480371i | \(0.159498\pi\) |
−0.0225195 | + | 0.999746i | \(0.507169\pi\) | |||||||
\(464\) | 582131. | − | 1.00828e6i | 0.125524 | − | 0.217414i | ||||
\(465\) | −8.88494e6 | −1.90556 | ||||||||
\(466\) | 3.17328e6 | − | 5.49629e6i | 0.676931 | − | 1.17248i | ||||
\(467\) | 3.10939e6 | + | 5.38562e6i | 0.659756 | + | 1.14273i | 0.980679 | + | 0.195625i | \(0.0626735\pi\) |
−0.320923 | + | 0.947105i | \(0.603993\pi\) | |||||||
\(468\) | −342915. | − | 593947.i | −0.0723723 | − | 0.125352i | ||||
\(469\) | −685291. | −0.143861 | ||||||||
\(470\) | −4.75937e6 | − | 8.24347e6i | −0.993813 | − | 1.72134i | ||||
\(471\) | −3.73304e6 | −0.775373 | ||||||||
\(472\) | −590219. | −0.121943 | ||||||||
\(473\) | 256317. | − | 3.58217e6i | 0.0526775 | − | 0.736195i | ||||
\(474\) | −5.94804e6 | −1.21598 | ||||||||
\(475\) | 4.40797e6 | 0.896406 | ||||||||
\(476\) | 144816. | + | 250829.i | 0.0292954 | + | 0.0507411i | ||||
\(477\) | −4.31322e6 | −0.867972 | ||||||||
\(478\) | 2.22179e6 | + | 3.84825e6i | 0.444767 | + | 0.770359i | ||||
\(479\) | 1.17090e6 | + | 2.02806e6i | 0.233174 | + | 0.403869i | 0.958740 | − | 0.284283i | \(-0.0917554\pi\) |
−0.725566 | + | 0.688152i | \(0.758422\pi\) | |||||||
\(480\) | −3.23378e6 | + | 5.60107e6i | −0.640630 | + | 1.10960i | ||||
\(481\) | −2.40766e6 | −0.474496 | ||||||||
\(482\) | −1.63990e6 | + | 2.84038e6i | −0.321513 | + | 0.556877i | ||||
\(483\) | −196722. | − | 340732.i | −0.0383694 | − | 0.0664577i | ||||
\(484\) | 893324. | 0.173339 | ||||||||
\(485\) | 2.27448e6 | + | 3.93951e6i | 0.439063 | + | 0.760479i | ||||
\(486\) | 2.13417e6 | − | 3.69649e6i | 0.409862 | − | 0.709902i | ||||
\(487\) | −542302. | + | 939295.i | −0.103614 | + | 0.179465i | −0.913171 | − | 0.407576i | \(-0.866374\pi\) |
0.809557 | + | 0.587041i | \(0.199707\pi\) | |||||||
\(488\) | −1.26102e6 | + | 2.18415e6i | −0.239703 | + | 0.415177i | ||||
\(489\) | −8.43178e6 | −1.59458 | ||||||||
\(490\) | −2.92888e6 | + | 5.07298e6i | −0.551077 | + | 0.954493i | ||||
\(491\) | −1.44190e6 | + | 2.49744e6i | −0.269918 | + | 0.467511i | −0.968840 | − | 0.247686i | \(-0.920330\pi\) |
0.698923 | + | 0.715197i | \(0.253663\pi\) | |||||||
\(492\) | −1.25377e6 | − | 2.17159e6i | −0.233510 | − | 0.404451i | ||||
\(493\) | 1.62119e6 | + | 2.80798e6i | 0.300411 | + | 0.520328i | ||||
\(494\) | 2.40162e6 | 0.442780 | ||||||||
\(495\) | 3.35658e6 | 0.615720 | ||||||||
\(496\) | 1.37839e6 | + | 2.38744e6i | 0.251576 | + | 0.435742i | ||||
\(497\) | −407542. | − | 705883.i | −0.0740084 | − | 0.128186i | ||||
\(498\) | 3.35057e6 | − | 5.80335e6i | 0.605404 | − | 1.04859i | ||||
\(499\) | 3.43988e6 | − | 5.95805e6i | 0.618433 | − | 1.07116i | −0.371339 | − | 0.928497i | \(-0.621101\pi\) |
0.989772 | − | 0.142659i | \(-0.0455653\pi\) | |||||||
\(500\) | −108781. | −0.0194593 | ||||||||
\(501\) | 1.74777e6 | − | 3.02722e6i | 0.311092 | − | 0.538827i | ||||
\(502\) | −2.59515e6 | + | 4.49494e6i | −0.459625 | + | 0.796094i | ||||
\(503\) | −4.67564e6 | + | 8.09845e6i | −0.823989 | + | 1.42719i | 0.0787012 | + | 0.996898i | \(0.474923\pi\) |
−0.902690 | + | 0.430292i | \(0.858411\pi\) | |||||||
\(504\) | 245571. | + | 425341.i | 0.0430626 | + | 0.0745866i | ||||
\(505\) | −1.35535e6 | −0.236495 | ||||||||
\(506\) | 752059. | + | 1.30260e6i | 0.130580 | + | 0.226171i | ||||
\(507\) | −2.10296e6 | + | 3.64243e6i | −0.363338 | + | 0.629319i | ||||
\(508\) | −3.07747e6 | −0.529095 | ||||||||
\(509\) | 36537.0 | − | 63283.9i | 0.00625084 | − | 0.0108268i | −0.862883 | − | 0.505404i | \(-0.831344\pi\) |
0.869134 | + | 0.494577i | \(0.164677\pi\) | |||||||
\(510\) | 4.71161e6 | + | 8.16075e6i | 0.802129 | + | 1.38933i | ||||
\(511\) | −261779. | − | 453415.i | −0.0443489 | − | 0.0768145i | ||||
\(512\) | 5.06333e6 | 0.853613 | ||||||||
\(513\) | −1.34848e6 | − | 2.33564e6i | −0.226231 | − | 0.391844i | ||||
\(514\) | −3.60191e6 | −0.601347 | ||||||||
\(515\) | 1.50829e7 | 2.50592 | ||||||||
\(516\) | −2.60765e6 | + | 1.26661e6i | −0.431147 | + | 0.209421i | ||||
\(517\) | −7.94080e6 | −1.30659 | ||||||||
\(518\) | 475466. | 0.0778565 | ||||||||
\(519\) | 2.06189e6 | + | 3.57130e6i | 0.336007 | + | 0.581981i | ||||
\(520\) | −6.21531e6 | −1.00799 | ||||||||
\(521\) | 2.77754e6 | + | 4.81083e6i | 0.448297 | + | 0.776472i | 0.998275 | − | 0.0587062i | \(-0.0186975\pi\) |
−0.549979 | + | 0.835179i | \(0.685364\pi\) | |||||||
\(522\) | 758102. | + | 1.31307e6i | 0.121773 | + | 0.210917i | ||||
\(523\) | 1.65658e6 | − | 2.86928e6i | 0.264824 | − | 0.458689i | −0.702693 | − | 0.711493i | \(-0.748019\pi\) |
0.967518 | + | 0.252804i | \(0.0813527\pi\) | |||||||
\(524\) | 3.66172e6 | 0.582582 | ||||||||
\(525\) | −558203. | + | 966835.i | −0.0883881 | + | 0.153093i | ||||
\(526\) | 2.15466e6 | + | 3.73198e6i | 0.339558 | + | 0.588133i | ||||
\(527\) | −7.67742e6 | −1.20417 | ||||||||
\(528\) | −1.41137e6 | − | 2.44457e6i | −0.220322 | − | 0.381608i | ||||
\(529\) | 2.56750e6 | − | 4.44705e6i | 0.398907 | − | 0.690928i | ||||
\(530\) | −5.38954e6 | + | 9.33496e6i | −0.833416 | + | 1.44352i | ||||
\(531\) | 213171. | − | 369223.i | 0.0328089 | − | 0.0568268i | ||||
\(532\) | 291624. | 0.0446730 | ||||||||
\(533\) | 2.07749e6 | − | 3.59831e6i | 0.316752 | − | 0.548631i | ||||
\(534\) | 5.63601e6 | − | 9.76186e6i | 0.855300 | − | 1.48142i | ||||
\(535\) | −6.39884e6 | − | 1.10831e7i | −0.966534 | − | 1.67409i | ||||
\(536\) | −3.83444e6 | − | 6.64145e6i | −0.576488 | − | 0.998506i | ||||
\(537\) | 8.10537e6 | 1.21293 | ||||||||
\(538\) | −248034. | −0.0369450 | ||||||||
\(539\) | 2.44336e6 | + | 4.23202e6i | 0.362256 | + | 0.627445i | ||||
\(540\) | 962361. | + | 1.66686e6i | 0.142021 | + | 0.245988i | ||||
\(541\) | 2.99744e6 | − | 5.19171e6i | 0.440308 | − | 0.762636i | −0.557404 | − | 0.830241i | \(-0.688203\pi\) |
0.997712 | + | 0.0676052i | \(0.0215358\pi\) | |||||||
\(542\) | 784214. | − | 1.35830e6i | 0.114666 | − | 0.198608i | ||||
\(543\) | −1.71938e6 | −0.250250 | ||||||||
\(544\) | −2.79429e6 | + | 4.83985e6i | −0.404831 | + | 0.701188i | ||||
\(545\) | −8.02705e6 | + | 1.39033e7i | −1.15762 | + | 2.00505i | ||||
\(546\) | −304129. | + | 526767.i | −0.0436593 | + | 0.0756200i | ||||
\(547\) | −5.28219e6 | − | 9.14901e6i | −0.754823 | − | 1.30739i | −0.945462 | − | 0.325732i | \(-0.894389\pi\) |
0.190639 | − | 0.981660i | \(-0.438944\pi\) | |||||||
\(548\) | 4.01976e6 | 0.571807 | ||||||||
\(549\) | −910894. | − | 1.57772e6i | −0.128984 | − | 0.223407i | ||||
\(550\) | 2.13398e6 | − | 3.69617e6i | 0.300805 | − | 0.521009i | ||||
\(551\) | 3.26468e6 | 0.458101 | ||||||||
\(552\) | 2.20145e6 | − | 3.81303e6i | 0.307512 | − | 0.532626i | ||||
\(553\) | −598387. | − | 1.03644e6i | −0.0832089 | − | 0.144122i | ||||
\(554\) | −2.83457e6 | − | 4.90961e6i | −0.392385 | − | 0.679630i | ||||
\(555\) | −9.51189e6 | −1.31079 | ||||||||
\(556\) | 172167. | + | 298202.i | 0.0236191 | + | 0.0409095i | ||||
\(557\) | 6.71609e6 | 0.917231 | 0.458615 | − | 0.888635i | \(-0.348346\pi\) | ||||
0.458615 | + | 0.888635i | \(0.348346\pi\) | |||||||
\(558\) | −3.59012e6 | −0.488117 | ||||||||
\(559\) | −3.97801e6 | − | 2.69258e6i | −0.538439 | − | 0.364451i | ||||
\(560\) | 680810. | 0.0917394 | ||||||||
\(561\) | 7.86112e6 | 1.05458 | ||||||||
\(562\) | −813339. | − | 1.40874e6i | −0.108625 | − | 0.188144i | ||||
\(563\) | −9.15631e6 | −1.21745 | −0.608723 | − | 0.793383i | \(-0.708318\pi\) | ||||
−0.608723 | + | 0.793383i | \(0.708318\pi\) | |||||||
\(564\) | 3.20499e6 | + | 5.55121e6i | 0.424257 | + | 0.734835i | ||||
\(565\) | −8.53444e6 | − | 1.47821e7i | −1.12474 | − | 1.94811i | ||||
\(566\) | 352855. | − | 611163.i | 0.0462973 | − | 0.0801892i | ||||
\(567\) | 1.28985e6 | 0.168493 | ||||||||
\(568\) | 4.56067e6 | − | 7.89932e6i | 0.593141 | − | 1.02735i | ||||
\(569\) | 6.56898e6 | + | 1.13778e7i | 0.850584 | + | 1.47325i | 0.880682 | + | 0.473708i | \(0.157085\pi\) |
−0.0300980 | + | 0.999547i | \(0.509582\pi\) | |||||||
\(570\) | 9.48804e6 | 1.22318 | ||||||||
\(571\) | −1.18937e6 | − | 2.06005e6i | −0.152661 | − | 0.264416i | 0.779544 | − | 0.626347i | \(-0.215451\pi\) |
−0.932205 | + | 0.361931i | \(0.882118\pi\) | |||||||
\(572\) | −714911. | + | 1.23826e6i | −0.0913613 | + | 0.158242i | ||||
\(573\) | −3.70446e6 | + | 6.41631e6i | −0.471344 | + | 0.816392i | ||||
\(574\) | −410263. | + | 710596.i | −0.0519735 | + | 0.0900208i | ||||
\(575\) | 3.69256e6 | 0.465756 | ||||||||
\(576\) | −2.41063e6 | + | 4.17533e6i | −0.302743 | + | 0.524366i | ||||
\(577\) | −688919. | + | 1.19324e6i | −0.0861447 | + | 0.149207i | −0.905878 | − | 0.423538i | \(-0.860788\pi\) |
0.819734 | + | 0.572745i | \(0.194121\pi\) | |||||||
\(578\) | 911048. | + | 1.57798e6i | 0.113428 | + | 0.196464i | ||||
\(579\) | 3.09961e6 | + | 5.36869e6i | 0.384248 | + | 0.665537i | ||||
\(580\) | −2.32988e6 | −0.287583 | ||||||||
\(581\) | 1.34830e6 | 0.165709 | ||||||||
\(582\) | 2.49094e6 | + | 4.31444e6i | 0.304829 | + | 0.527979i | ||||
\(583\) | 4.49611e6 | + | 7.78749e6i | 0.547855 | + | 0.948912i | ||||
\(584\) | 2.92949e6 | − | 5.07403e6i | 0.355435 | − | 0.615631i | ||||
\(585\) | 2.24480e6 | − | 3.88812e6i | 0.271199 | − | 0.469731i | ||||
\(586\) | −3.59786e6 | −0.432813 | ||||||||
\(587\) | 7.30371e6 | − | 1.26504e7i | 0.874879 | − | 1.51534i | 0.0179882 | − | 0.999838i | \(-0.494274\pi\) |
0.856891 | − | 0.515497i | \(-0.172393\pi\) | |||||||
\(588\) | 1.97233e6 | − | 3.41618e6i | 0.235254 | − | 0.407471i | ||||
\(589\) | −3.86512e6 | + | 6.69458e6i | −0.459065 | + | 0.795124i | ||||
\(590\) | −532732. | − | 922719.i | −0.0630055 | − | 0.109129i | ||||
\(591\) | 1.53224e7 | 1.80450 | ||||||||
\(592\) | 1.47566e6 | + | 2.55591e6i | 0.173054 | + | 0.299738i | ||||
\(593\) | −6.35547e6 | + | 1.10080e7i | −0.742183 | + | 1.28550i | 0.209316 | + | 0.977848i | \(0.432876\pi\) |
−0.951499 | + | 0.307651i | \(0.900457\pi\) | |||||||
\(594\) | −2.61131e6 | −0.303663 | ||||||||
\(595\) | −948000. | + | 1.64198e6i | −0.109778 | + | 0.190141i | ||||
\(596\) | −863820. | − | 1.49618e6i | −0.0996111 | − | 0.172532i | ||||
\(597\) | −989761. | − | 1.71432e6i | −0.113657 | − | 0.196859i | ||||
\(598\) | 2.01184e6 | 0.230060 | ||||||||
\(599\) | −5.86128e6 | − | 1.01520e7i | −0.667461 | − | 1.15608i | −0.978612 | − | 0.205715i | \(-0.934048\pi\) |
0.311151 | − | 0.950360i | \(-0.399285\pi\) | |||||||
\(600\) | −1.24934e7 | −1.41677 | ||||||||
\(601\) | −5.06231e6 | −0.571693 | −0.285847 | − | 0.958275i | \(-0.592275\pi\) | ||||
−0.285847 | + | 0.958275i | \(0.592275\pi\) | |||||||
\(602\) | 785579. | + | 531732.i | 0.0883484 | + | 0.0598001i | ||||
\(603\) | 5.53959e6 | 0.620418 | ||||||||
\(604\) | 1.36342e6 | 0.152068 | ||||||||
\(605\) | 2.92395e6 | + | 5.06443e6i | 0.324774 | + | 0.562526i | ||||
\(606\) | −1.48434e6 | −0.164192 | ||||||||
\(607\) | −3.05915e6 | − | 5.29861e6i | −0.337000 | − | 0.583700i | 0.646867 | − | 0.762603i | \(-0.276079\pi\) |
−0.983867 | + | 0.178902i | \(0.942745\pi\) | |||||||
\(608\) | 2.81351e6 | + | 4.87314e6i | 0.308666 | + | 0.534626i | ||||
\(609\) | −413422. | + | 716068.i | −0.0451700 | + | 0.0782368i | ||||
\(610\) | −4.55279e6 | −0.495397 | ||||||||
\(611\) | −5.31064e6 | + | 9.19829e6i | −0.575498 | + | 0.996791i | ||||
\(612\) | −1.17063e6 | − | 2.02759e6i | −0.126340 | − | 0.218827i | ||||
\(613\) | 4.53703e6 | 0.487663 | 0.243832 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243832 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(614\) | −927590. | − | 1.60663e6i | −0.0992968 | − | 0.171987i | ||||
\(615\) | 8.20748e6 | − | 1.42158e7i | 0.875028 | − | 1.51559i | ||||
\(616\) | 511967. | − | 886752.i | 0.0543613 | − | 0.0941565i | ||||
\(617\) | −1.90739e6 | + | 3.30370e6i | −0.201710 | + | 0.349371i | −0.949079 | − | 0.315037i | \(-0.897983\pi\) |
0.747370 | + | 0.664408i | \(0.231316\pi\) | |||||||
\(618\) | 1.65184e7 | 1.73979 | ||||||||
\(619\) | 7.15409e6 | − | 1.23912e7i | 0.750460 | − | 1.29983i | −0.197140 | − | 0.980375i | \(-0.563165\pi\) |
0.947600 | − | 0.319459i | \(-0.103501\pi\) | |||||||
\(620\) | 2.75838e6 | − | 4.77766e6i | 0.288188 | − | 0.499156i | ||||
\(621\) | −1.12963e6 | − | 1.95657e6i | −0.117545 | − | 0.203595i | ||||
\(622\) | 3.52531e6 | + | 6.10601e6i | 0.365360 | + | 0.632822i | ||||
\(623\) | 2.26799e6 | 0.234110 | ||||||||
\(624\) | −3.77558e6 | −0.388171 | ||||||||
\(625\) | 4.70165e6 | + | 8.14350e6i | 0.481449 | + | 0.833895i | ||||
\(626\) | 3.71614e6 | + | 6.43655e6i | 0.379015 | + | 0.656473i | ||||
\(627\) | 3.95760e6 | − | 6.85476e6i | 0.402034 | − | 0.696343i | ||||
\(628\) | 1.15895e6 | − | 2.00735e6i | 0.117264 | − | 0.203107i | ||||
\(629\) | −8.21917e6 | −0.828326 | ||||||||
\(630\) | −443305. | + | 767826.i | −0.0444991 | + | 0.0770747i | ||||
\(631\) | −5.00017e6 | + | 8.66055e6i | −0.499932 | + | 0.865908i | −1.00000 | 7.79706e-5i | \(-0.999975\pi\) | |
0.500068 | + | 0.865986i | \(0.333309\pi\) | |||||||
\(632\) | 6.69637e6 | − | 1.15985e7i | 0.666879 | − | 1.15507i | ||||
\(633\) | 3.25910e6 | + | 5.64493e6i | 0.323287 | + | 0.559950i | ||||
\(634\) | −1.07993e7 | −1.06702 | ||||||||
\(635\) | −1.00729e7 | − | 1.74468e7i | −0.991335 | − | 1.71704i | ||||
\(636\) | 3.62935e6 | − | 6.28622e6i | 0.355784 | − | 0.616236i | ||||
\(637\) | 6.53626e6 | 0.638235 | ||||||||
\(638\) | 1.58049e6 | − | 2.73749e6i | 0.153724 | − | 0.266257i | ||||
\(639\) | 3.29439e6 | + | 5.70605e6i | 0.319170 | + | 0.552819i | ||||
\(640\) | 750996. | + | 1.30076e6i | 0.0724749 | + | 0.125530i | ||||
\(641\) | −1.66557e7 | −1.60110 | −0.800548 | − | 0.599268i | \(-0.795458\pi\) | ||||
−0.800548 | + | 0.599268i | \(0.795458\pi\) | |||||||
\(642\) | −7.00783e6 | − | 1.21379e7i | −0.671036 | − | 1.16227i | ||||
\(643\) | −1.53313e7 | −1.46235 | −0.731175 | − | 0.682190i | \(-0.761027\pi\) | ||||
−0.731175 | + | 0.682190i | \(0.761027\pi\) | |||||||
\(644\) | 244294. | 0.0232112 | ||||||||
\(645\) | −1.57158e7 | − | 1.06375e7i | −1.48744 | − | 1.00680i | ||||
\(646\) | 8.19856e6 | 0.772959 | ||||||||
\(647\) | −7.10962e6 | −0.667706 | −0.333853 | − | 0.942625i | \(-0.608349\pi\) | ||||
−0.333853 | + | 0.942625i | \(0.608349\pi\) | |||||||
\(648\) | 7.21717e6 | + | 1.25005e7i | 0.675196 | + | 1.16947i | ||||
\(649\) | −888840. | −0.0828346 | ||||||||
\(650\) | −2.85432e6 | − | 4.94383e6i | −0.264984 | − | 0.458966i | ||||
\(651\) | −978916. | − | 1.69553e6i | −0.0905301 | − | 0.156803i | ||||
\(652\) | 2.61770e6 | − | 4.53399e6i | 0.241157 | − | 0.417697i | ||||
\(653\) | −1.42306e6 | −0.130599 | −0.0652995 | − | 0.997866i | \(-0.520800\pi\) | ||||
−0.0652995 | + | 0.997866i | \(0.520800\pi\) | |||||||
\(654\) | −8.79100e6 | + | 1.52265e7i | −0.803700 | + | 1.39205i | ||||
\(655\) | 1.19852e7 | + | 2.07590e7i | 1.09155 | + | 1.89062i | ||||
\(656\) | −5.09317e6 | −0.462092 | ||||||||
\(657\) | 2.11611e6 | + | 3.66521e6i | 0.191260 | + | 0.331272i | ||||
\(658\) | 1.04875e6 | − | 1.81648e6i | 0.0944291 | − | 0.163556i | ||||
\(659\) | 341284. | − | 591120.i | 0.0306127 | − | 0.0530228i | −0.850313 | − | 0.526277i | \(-0.823587\pi\) |
0.880926 | + | 0.473254i | \(0.156921\pi\) | |||||||
\(660\) | −2.82438e6 | + | 4.89198e6i | −0.252385 | + | 0.437144i | ||||
\(661\) | 1.15905e7 | 1.03180 | 0.515902 | − | 0.856648i | \(-0.327457\pi\) | ||||
0.515902 | + | 0.856648i | \(0.327457\pi\) | |||||||
\(662\) | −4.81104e6 | + | 8.33297e6i | −0.426672 | + | 0.739018i | ||||
\(663\) | 5.25735e6 | − | 9.10599e6i | 0.464497 | − | 0.804532i | ||||
\(664\) | 7.54422e6 | + | 1.30670e7i | 0.664040 | + | 1.15015i | ||||
\(665\) | 954521. | + | 1.65328e6i | 0.0837011 | + | 0.144975i | ||||
\(666\) | −3.84346e6 | −0.335766 | ||||||||
\(667\) | 2.73483e6 | 0.238021 | ||||||||
\(668\) | 1.08521e6 | + | 1.87964e6i | 0.0940962 | + | 0.162979i | ||||
\(669\) | 1.82112e6 | + | 3.15428e6i | 0.157316 | + | 0.272480i | ||||
\(670\) | 6.92194e6 | − | 1.19892e7i | 0.595718 | − | 1.03181i | ||||
\(671\) | −1.89904e6 | + | 3.28923e6i | −0.162827 | + | 0.282025i | ||||
\(672\) | −1.42515e6 | −0.121741 | ||||||||
\(673\) | −9.68947e6 | + | 1.67827e7i | −0.824636 | + | 1.42831i | 0.0775613 | + | 0.996988i | \(0.475287\pi\) |
−0.902197 | + | 0.431324i | \(0.858047\pi\) | |||||||
\(674\) | 7.24954e6 | − | 1.25566e7i | 0.614696 | − | 1.06469i | ||||
\(675\) | −3.20534e6 | + | 5.55181e6i | −0.270779 | + | 0.469003i | ||||
\(676\) | −1.30575e6 | − | 2.26163e6i | −0.109899 | − | 0.190351i | ||||
\(677\) | 1.75397e7 | 1.47079 | 0.735395 | − | 0.677638i | \(-0.236997\pi\) | ||||
0.735395 | + | 0.677638i | \(0.236997\pi\) | |||||||
\(678\) | −9.34667e6 | − | 1.61889e7i | −0.780877 | − | 1.35252i | ||||
\(679\) | −501190. | + | 868086.i | −0.0417184 | + | 0.0722584i | ||||
\(680\) | −2.12176e7 | −1.75964 | ||||||||
\(681\) | −9.77640e6 | + | 1.69332e7i | −0.807813 | + | 1.39917i | ||||
\(682\) | 3.74235e6 | + | 6.48194e6i | 0.308094 | + | 0.533635i | ||||
\(683\) | 76409.6 | + | 132345.i | 0.00626753 | + | 0.0108557i | 0.869142 | − | 0.494562i | \(-0.164672\pi\) |
−0.862875 | + | 0.505418i | \(0.831338\pi\) | |||||||
\(684\) | −2.35736e6 | −0.192658 | ||||||||
\(685\) | 1.31572e7 | + | 2.27889e7i | 1.07136 | + | 1.85565i | ||||
\(686\) | −2.60573e6 | −0.211407 | ||||||||
\(687\) | −3.05208e6 | −0.246720 | ||||||||
\(688\) | −420252. | + | 5.87324e6i | −0.0338485 | + | 0.473050i | ||||
\(689\) | 1.20276e7 | 0.965230 | ||||||||
\(690\) | 7.94814e6 | 0.635540 | ||||||||
\(691\) | −8.17735e6 | − | 1.41636e7i | −0.651505 | − | 1.12844i | −0.982758 | − | 0.184897i | \(-0.940805\pi\) |
0.331253 | − | 0.943542i | \(-0.392529\pi\) | |||||||
\(692\) | −2.56051e6 | −0.203264 | ||||||||
\(693\) | 369817. | + | 640543.i | 0.0292519 | + | 0.0506658i | ||||
\(694\) | −6.26801e6 | − | 1.08565e7i | −0.494005 | − | 0.855641i | ||||
\(695\) | −1.12705e6 | + | 1.95210e6i | −0.0885074 | + | 0.153299i | ||||
\(696\) | −9.25296e6 | −0.724032 | ||||||||
\(697\) | 7.09203e6 | − | 1.22838e7i | 0.552954 | − | 0.957744i | ||||
\(698\) | −5.91721e6 | − | 1.02489e7i | −0.459705 | − | 0.796232i | ||||
\(699\) | −2.79774e7 | −2.16578 | ||||||||
\(700\) | −346595. | − | 600320.i | −0.0267348 | − | 0.0463060i | ||||
\(701\) | 5.61313e6 | − | 9.72223e6i | 0.431430 | − | 0.747259i | −0.565567 | − | 0.824703i | \(-0.691343\pi\) |
0.996997 | + | 0.0774439i | \(0.0246759\pi\) | |||||||
\(702\) | −1.74639e6 | + | 3.02483e6i | −0.133751 | + | 0.231664i | ||||
\(703\) | −4.13785e6 | + | 7.16697e6i | −0.315781 | + | 0.546950i | ||||
\(704\) | 1.00514e7 | 0.764353 | ||||||||
\(705\) | −2.09806e7 | + | 3.63395e7i | −1.58981 | + | 2.75363i | ||||
\(706\) | 511864. | − | 886574.i | 0.0386494 | − | 0.0669427i | ||||
\(707\) | −149328. | − | 258644.i | −0.0112355 | − | 0.0194605i | ||||
\(708\) | 358745. | + | 621365.i | 0.0268969 | + | 0.0465869i | ||||
\(709\) | 1.11943e7 | 0.836334 | 0.418167 | − | 0.908370i | \(-0.362673\pi\) | ||||
0.418167 | + | 0.908370i | \(0.362673\pi\) | |||||||
\(710\) | 1.64659e7 | 1.22585 | ||||||||
\(711\) | 4.83710e6 | + | 8.37811e6i | 0.358849 | + | 0.621544i | ||||
\(712\) | 1.26902e7 | + | 2.19800e7i | 0.938140 | + | 1.62491i | ||||
\(713\) | −3.23781e6 | + | 5.60805e6i | −0.238522 | + | 0.413131i | ||||
\(714\) | −1.03822e6 | + | 1.79825e6i | −0.0762158 | + | 0.132010i | ||||
\(715\) | −9.35995e6 | −0.684713 | ||||||||
\(716\) | −2.51636e6 | + | 4.35847e6i | −0.183439 | + | 0.317725i | ||||
\(717\) | 9.79424e6 | − | 1.69641e7i | 0.711497 | − | 1.23235i | ||||
\(718\) | 815849. | − | 1.41309e6i | 0.0590607 | − | 0.102296i | ||||
\(719\) | −5.86717e6 | − | 1.01622e7i | −0.423259 | − | 0.733107i | 0.572997 | − | 0.819558i | \(-0.305781\pi\) |
−0.996256 | + | 0.0864509i | \(0.972447\pi\) | |||||||
\(720\) | −5.50337e6 | −0.395637 | ||||||||
\(721\) | 1.66179e6 | + | 2.87830e6i | 0.119052 | + | 0.206205i | ||||
\(722\) | −1.38367e6 | + | 2.39658e6i | −0.0987846 | + | 0.171100i | ||||
\(723\) | 1.44582e7 | 1.02865 | ||||||||
\(724\) | 533793. | − | 924557.i | 0.0378466 | − | 0.0655522i | ||||
\(725\) | −3.88006e6 | − | 6.72047e6i | −0.274153 | − | 0.474848i | ||||
\(726\) | 3.20223e6 | + | 5.54643e6i | 0.225482 | + | 0.390545i | ||||
\(727\) | −1.61910e7 | −1.13616 | −0.568079 | − | 0.822974i | \(-0.692313\pi\) | ||||
−0.568079 | + | 0.822974i | \(0.692313\pi\) | |||||||
\(728\) | −684784. | − | 1.18608e6i | −0.0478879 | − | 0.0829442i | ||||
\(729\) | −982741. | −0.0684889 | ||||||||
\(730\) | 1.05766e7 | 0.734583 | ||||||||
\(731\) | −1.35800e7 | − | 9.19182e6i | −0.939951 | − | 0.636221i | ||||
\(732\) | 3.06588e6 | 0.211484 | ||||||||
\(733\) | −8.05149e6 | −0.553499 | −0.276749 | − | 0.960942i | \(-0.589257\pi\) | ||||
−0.276749 | + | 0.960942i | \(0.589257\pi\) | |||||||
\(734\) | −2.19401e6 | − | 3.80013e6i | −0.150313 | − | 0.260350i | ||||
\(735\) | 2.58227e7 | 1.76312 | ||||||||
\(736\) | 2.35688e6 | + | 4.08223e6i | 0.160377 | + | 0.277782i | ||||
\(737\) | −5.77448e6 | − | 1.00017e7i | −0.391601 | − | 0.678273i | ||||
\(738\) | 3.31638e6 | − | 5.74414e6i | 0.224142 | − | 0.388226i | ||||
\(739\) | −3.25656e6 | −0.219356 | −0.109678 | − | 0.993967i | \(-0.534982\pi\) | ||||
−0.109678 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(740\) | 2.95302e6 | − | 5.11479e6i | 0.198238 | − | 0.343359i | ||||
\(741\) | −5.29351e6 | − | 9.16863e6i | −0.354159 | − | 0.613421i | ||||
\(742\) | −2.37521e6 | −0.158377 | ||||||||
\(743\) | 3.71609e6 | + | 6.43646e6i | 0.246953 | + | 0.427735i | 0.962679 | − | 0.270646i | \(-0.0872374\pi\) |
−0.715726 | + | 0.698381i | \(0.753904\pi\) | |||||||
\(744\) | 1.09548e7 | − | 1.89742e7i | 0.725555 | − | 1.25670i | ||||
\(745\) | 5.65477e6 | − | 9.79435e6i | 0.373271 | − | 0.646524i | ||||
\(746\) | 1.08329e7 | − | 1.87631e7i | 0.712683 | − | 1.23440i | ||||
\(747\) | −1.08991e7 | −0.714642 | ||||||||
\(748\) | −2.44053e6 | + | 4.22713e6i | −0.159489 | + | 0.276243i | ||||
\(749\) | 1.41001e6 | − | 2.44221e6i | 0.0918370 | − | 0.159066i | ||||
\(750\) | −389939. | − | 675393.i | −0.0253130 | − | 0.0438433i | ||||
\(751\) | 7.80320e6 | + | 1.35155e7i | 0.504862 | + | 0.874447i | 0.999984 | + | 0.00562381i | \(0.00179012\pi\) |
−0.495122 | + | 0.868824i | \(0.664877\pi\) | |||||||
\(752\) | 1.30196e7 | 0.839561 | ||||||||
\(753\) | 2.28803e7 | 1.47053 | ||||||||
\(754\) | −2.11400e6 | − | 3.66155e6i | −0.135418 | − | 0.234551i | ||||
\(755\) | 4.46265e6 | + | 7.72953e6i | 0.284921 | + | 0.493498i | ||||
\(756\) | −212060. | + | 367299.i | −0.0134944 | + | 0.0233730i | ||||
\(757\) | 1.37363e7 | − | 2.37920e7i | 0.871226 | − | 1.50901i | 0.0104957 | − | 0.999945i | \(-0.496659\pi\) |
0.860730 | − | 0.509062i | \(-0.170008\pi\) | |||||||
\(758\) | −7.80747e6 | −0.493557 | ||||||||
\(759\) | 3.31528e6 | − | 5.74224e6i | 0.208889 | − | 0.361807i | ||||
\(760\) | −1.06818e7 | + | 1.85013e7i | −0.670824 | + | 1.16190i | ||||
\(761\) | 4.67913e6 | − | 8.10448e6i | 0.292889 | − | 0.507299i | −0.681603 | − | 0.731723i | \(-0.738717\pi\) |
0.974492 | + | 0.224424i | \(0.0720500\pi\) | |||||||
\(762\) | −1.10316e7 | − | 1.91072e7i | −0.688255 | − | 1.19209i | ||||
\(763\) | −3.53759e6 | −0.219986 | ||||||||
\(764\) | −2.30014e6 | − | 3.98397e6i | −0.142568 | − | 0.246935i | ||||
\(765\) | 7.66322e6 | − | 1.32731e7i | 0.473432 | − | 0.820008i | ||||
\(766\) | 8.96399e6 | 0.551988 | ||||||||
\(767\) | −594437. | + | 1.02960e6i | −0.0364853 | + | 0.0631943i | ||||
\(768\) | −9.83207e6 | − | 1.70297e7i | −0.601509 | − | 1.04184i | ||||
\(769\) | −4.85000e6 | − | 8.40045e6i | −0.295751 | − | 0.512256i | 0.679408 | − | 0.733760i | \(-0.262236\pi\) |
−0.975159 | + | 0.221505i | \(0.928903\pi\) | |||||||
\(770\) | 1.84841e6 | 0.112349 | ||||||||
\(771\) | 7.93911e6 | + | 1.37509e7i | 0.480990 | + | 0.833099i | ||||
\(772\) | −3.84918e6 | −0.232447 | ||||||||
\(773\) | −2.66459e7 | −1.60391 | −0.801957 | − | 0.597382i | \(-0.796208\pi\) | ||||
−0.801957 | + | 0.597382i | \(0.796208\pi\) | |||||||
\(774\) | −6.35028e6 | − | 4.29829e6i | −0.381013 | − | 0.257895i | ||||
\(775\) | 1.83747e7 | 1.09892 | ||||||||
\(776\) | −1.12173e7 | −0.668706 | ||||||||
\(777\) | −1.04799e6 | − | 1.81518e6i | −0.0622738 | − | 0.107861i | ||||
\(778\) | −1.90104e7 | −1.12601 | ||||||||
\(779\) | −7.14081e6 | − | 1.23683e7i | −0.421603 | − | 0.730238i | ||||
\(780\) | 3.77777e6 | + | 6.54330e6i | 0.222331 | + | 0.385088i | ||||
\(781\) | 6.86815e6 | − | 1.18960e7i | 0.402914 | − | 0.697868i | ||||
\(782\) | 6.86794e6 | 0.401615 | ||||||||
\(783\) | −2.37397e6 | + | 4.11184e6i | −0.138379 | + | 0.239680i | ||||
\(784\) | −4.00608e6 | − | 6.93873e6i | −0.232771 | − | 0.403172i | ||||
\(785\) | 1.51735e7 | 0.878842 | ||||||||
\(786\) | 1.31259e7 | + | 2.27347e7i | 0.757831 | + | 1.31260i | ||||
\(787\) | −1.21060e6 | + | 2.09683e6i | −0.0696731 | + | 0.120677i | −0.898757 | − | 0.438446i | \(-0.855529\pi\) |
0.829084 | + | 0.559124i | \(0.188862\pi\) | |||||||
\(788\) | −4.75692e6 | + | 8.23923e6i | −0.272904 | + | 0.472684i | ||||
\(789\) | 9.49834e6 | − | 1.64516e7i | 0.543194 | − | 0.940840i | ||||
\(790\) | 2.41766e7 | 1.37825 | ||||||||
\(791\) | 1.88060e6 | − | 3.25729e6i | 0.106870 | − | 0.185104i | ||||
\(792\) | −4.13851e6 | + | 7.16812e6i | −0.234440 | + | 0.406062i | ||||
\(793\) | 2.54007e6 | + | 4.39953e6i | 0.143437 | + | 0.248441i | ||||
\(794\) | 7.60708e6 | + | 1.31759e7i | 0.428220 | + | 0.741699i | ||||
\(795\) | 4.75172e7 | 2.66645 | ||||||||
\(796\) | 1.22911e6 | 0.0687556 | ||||||||
\(797\) | −1.09162e7 | − | 1.89074e7i | −0.608730 | − | 1.05435i | −0.991450 | − | 0.130487i | \(-0.958346\pi\) |
0.382720 | − | 0.923864i | \(-0.374987\pi\) | |||||||
\(798\) | 1.04536e6 | + | 1.81062e6i | 0.0581113 | + | 0.100652i | ||||
\(799\) | −1.81292e7 | + | 3.14007e7i | −1.00464 | + | 1.74010i | ||||
\(800\) | 6.68770e6 | − | 1.15834e7i | 0.369446 | − | 0.639900i | ||||
\(801\) | −1.83334e7 | −1.00963 | ||||||||
\(802\) | −6.86135e6 | + | 1.18842e7i | −0.376681 | + | 0.652430i | ||||
\(803\) | 4.41167e6 | − | 7.64124e6i | 0.241443 | − | 0.418191i | ||||
\(804\) | −4.66128e6 | + | 8.07357e6i | −0.254311 | + | 0.440480i | ||||
\(805\) | 799603. | + | 1.38495e6i | 0.0434895 | + | 0.0753261i | ||||
\(806\) | 1.00112e7 | 0.542812 | ||||||||
\(807\) | 546701. | + | 946915.i | 0.0295506 | + | 0.0511831i | ||||
\(808\) | 1.67109e6 | − | 2.89441e6i | 0.0900473 | − | 0.155967i | ||||
\(809\) | −2.91565e7 | −1.56626 | −0.783129 | − | 0.621859i | \(-0.786378\pi\) | ||||
−0.783129 | + | 0.621859i | \(0.786378\pi\) | |||||||
\(810\) | −1.30285e7 | + | 2.25660e7i | −0.697719 | + | 1.20848i | ||||
\(811\) | 2.80916e6 | + | 4.86560e6i | 0.149977 | + | 0.259767i | 0.931219 | − | 0.364461i | \(-0.118747\pi\) |
−0.781242 | + | 0.624228i | \(0.785413\pi\) | |||||||
\(812\) | −256699. | − | 444615.i | −0.0136626 | − | 0.0236643i | ||||
\(813\) | −6.91406e6 | −0.366866 | ||||||||
\(814\) | 4.00643e6 | + | 6.93933e6i | 0.211932 | + | 0.367077i | ||||
\(815\) | 3.42721e7 | 1.80737 | ||||||||
\(816\) | −1.28889e7 | −0.677628 | ||||||||
\(817\) | −1.48518e7 | + | 7.21397e6i | −0.778438 | + | 0.378111i | ||||
\(818\) | 1.50456e6 | 0.0786186 | ||||||||
\(819\) | 989303. | 0.0515371 | ||||||||
\(820\) | 5.09612e6 | + | 8.82674e6i | 0.264670 | + | 0.458422i | ||||
\(821\) | −1.34109e6 | −0.0694384 | −0.0347192 | − | 0.999397i | \(-0.511054\pi\) | ||||
−0.0347192 | + | 0.999397i | \(0.511054\pi\) | |||||||
\(822\) | 1.44093e7 | + | 2.49577e7i | 0.743815 | + | 1.28832i | ||||
\(823\) | −3.41468e6 | − | 5.91440e6i | −0.175732 | − | 0.304377i | 0.764682 | − | 0.644407i | \(-0.222896\pi\) |
−0.940414 | + | 0.340031i | \(0.889563\pi\) | |||||||
\(824\) | −1.85966e7 | + | 3.22102e7i | −0.954146 | + | 1.65263i | ||||
\(825\) | −1.88144e7 | −0.962399 | ||||||||
\(826\) | 117390. | − | 203325.i | 0.00598659 | − | 0.0103691i | ||||
\(827\) | 6.76572e6 | + | 1.17186e7i | 0.343994 | + | 0.595815i | 0.985170 | − | 0.171579i | \(-0.0548868\pi\) |
−0.641177 | + | 0.767393i | \(0.721553\pi\) | |||||||
\(828\) | −1.97477e6 | −0.100101 | ||||||||
\(829\) | −1.35415e7 | − | 2.34545e7i | −0.684352 | − | 1.18533i | −0.973640 | − | 0.228090i | \(-0.926752\pi\) |
0.289288 | − | 0.957242i | \(-0.406582\pi\) | |||||||
\(830\) | −1.36188e7 | + | 2.35885e7i | −0.686191 | + | 1.18852i | ||||
\(831\) | −1.24956e7 | + | 2.16429e7i | −0.627701 | + | 1.08721i | ||||
\(832\) | 6.72214e6 | − | 1.16431e7i | 0.336666 | − | 0.583123i | ||||
\(833\) | 2.23132e7 | 1.11417 | ||||||||
\(834\) | −1.23431e6 | + | 2.13789e6i | −0.0614481 | + | 0.106431i | ||||
\(835\) | −7.10403e6 | + | 1.23045e7i | −0.352605 | + | 0.610730i | ||||
\(836\) | 2.45732e6 | + | 4.25621e6i | 0.121604 | + | 0.210624i | ||||
\(837\) | −5.62118e6 | − | 9.73617e6i | −0.277341 | − | 0.480369i | ||||
\(838\) | −1.61977e7 | −0.796789 | ||||||||
\(839\) | −2.43661e7 | −1.19503 | −0.597517 | − | 0.801856i | \(-0.703846\pi\) | ||||
−0.597517 | + | 0.801856i | \(0.703846\pi\) | |||||||
\(840\) | −2.70536e6 | − | 4.68583e6i | −0.132290 | − | 0.229133i | ||||
\(841\) | 7.38188e6 | + | 1.27858e7i | 0.359896 | + | 0.623358i | ||||
\(842\) | 1.03173e7 | − | 1.78702e7i | 0.501519 | − | 0.868656i | ||||
\(843\) | −3.58542e6 | + | 6.21014e6i | −0.173769 | + | 0.300976i | ||||
\(844\) | −4.04723e6 | −0.195570 | ||||||||
\(845\) | 8.54775e6 | − | 1.48051e7i | 0.411823 | − | 0.713298i | ||||
\(846\) | −8.47761e6 | + | 1.46836e7i | −0.407237 | + | 0.705355i | ||||
\(847\) | −644305. | + | 1.11597e6i | −0.0308591 | + | 0.0534495i | ||||
\(848\) | −7.37172e6 | − | 1.27682e7i | −0.352030 | − | 0.609733i | ||||
\(849\) | −3.11097e6 | −0.148124 | ||||||||
\(850\) | −9.74397e6 | − | 1.68770e7i | −0.462582 | − | 0.801215i | ||||
\(851\) | −3.46628e6 | + | 6.00378e6i | −0.164074 | + | 0.284185i | ||||
\(852\) | −1.10882e7 | −0.523315 | ||||||||
\(853\) | 1.77822e7 | − | 3.07997e7i | 0.836784 | − | 1.44935i | −0.0557860 | − | 0.998443i | \(-0.517766\pi\) |
0.892570 | − | 0.450909i | \(-0.148900\pi\) | |||||||
\(854\) | −501613. | − | 868820.i | −0.0235356 | − | 0.0407648i | ||||
\(855\) | −7.71593e6 | − | 1.33644e7i | −0.360972 | − | 0.625221i | ||||
\(856\) | 3.15580e7 | 1.47206 | ||||||||
\(857\) | −4.30970e6 | − | 7.46461e6i | −0.200445 | − | 0.347180i | 0.748227 | − | 0.663443i | \(-0.230905\pi\) |
−0.948672 | + | 0.316262i | \(0.897572\pi\) | |||||||
\(858\) | −1.02508e7 | −0.475376 | ||||||||
\(859\) | −8.11563e6 | −0.375266 | −0.187633 | − | 0.982239i | \(-0.560082\pi\) | ||||
−0.187633 | + | 0.982239i | \(0.560082\pi\) | |||||||
\(860\) | 1.05992e7 | − | 5.14833e6i | 0.488680 | − | 0.237367i | ||||
\(861\) | 3.61710e6 | 0.166285 | ||||||||
\(862\) | −1.95155e7 | −0.894564 | ||||||||
\(863\) | 4.44583e6 | + | 7.70040e6i | 0.203201 | + | 0.351955i | 0.949558 | − | 0.313591i | \(-0.101532\pi\) |
−0.746357 | + | 0.665546i | \(0.768199\pi\) | |||||||
\(864\) | −8.18358e6 | −0.372957 | ||||||||
\(865\) | −8.38085e6 | − | 1.45161e7i | −0.380845 | − | 0.659642i | ||||
\(866\) | 2.20517e6 | + | 3.81946e6i | 0.0999188 | + | 0.173064i | ||||
\(867\) | 4.01615e6 | − | 6.95618e6i | 0.181452 | − | 0.314284i | ||||
\(868\) | 1.21564e6 | 0.0547654 | ||||||||
\(869\) | 1.00844e7 | − | 1.74667e7i | 0.453003 | − | 0.784624i | ||||
\(870\) | −8.35173e6 | − | 1.44656e7i | −0.374092 | − | 0.647946i | ||||
\(871\) | −1.54474e7 | −0.689937 | ||||||||
\(872\) | −1.97940e7 | − | 3.42843e7i | −0.881542 | − | 1.52688i | ||||
\(873\) | 4.05140e6 | − | 7.01723e6i | 0.179916 | − | 0.311623i | ||||
\(874\) | 3.45759e6 | − | 5.98872e6i | 0.153107 | − | 0.265189i | ||||
\(875\) | 78457.6 | − | 135893.i | 0.00346430 | − | 0.00600034i | ||||
\(876\) | −7.12238e6 | −0.313592 | ||||||||
\(877\) | −7.34821e6 | + | 1.27275e7i | −0.322614 | + | 0.558783i | −0.981026 | − | 0.193874i | \(-0.937895\pi\) |
0.658413 | + | 0.752657i | \(0.271228\pi\) | |||||||
\(878\) | −8.04189e6 | + | 1.39290e7i | −0.352064 | + | 0.609793i | ||||
\(879\) | 7.93019e6 | + | 1.37355e7i | 0.346187 | + | 0.599614i | ||||
\(880\) | 5.73672e6 | + | 9.93629e6i | 0.249722 | + | 0.432531i | ||||
\(881\) | 3.53994e7 | 1.53658 | 0.768291 | − | 0.640100i | \(-0.221107\pi\) | ||||
0.768291 | + | 0.640100i | \(0.221107\pi\) | |||||||
\(882\) | 1.04341e7 | 0.451632 | ||||||||
\(883\) | 1.73600e7 | + | 3.00684e7i | 0.749286 | + | 1.29780i | 0.948165 | + | 0.317778i | \(0.102937\pi\) |
−0.198879 | + | 0.980024i | \(0.563730\pi\) | |||||||
\(884\) | 3.26435e6 | + | 5.65402e6i | 0.140497 | + | 0.243348i | ||||
\(885\) | −2.34843e6 | + | 4.06760e6i | −0.100790 | + | 0.174574i | ||||
\(886\) | −1.13173e7 | + | 1.96021e7i | −0.484347 | + | 0.838914i | ||||
\(887\) | 3.80231e6 | 0.162270 | 0.0811350 | − | 0.996703i | \(-0.474146\pi\) | ||||
0.0811350 | + | 0.996703i | \(0.474146\pi\) | |||||||
\(888\) | 1.17278e7 | − | 2.03131e7i | 0.499094 | − | 0.864457i | ||||
\(889\) | 2.21961e6 | − | 3.84447e6i | 0.0941936 | − | 0.163148i | ||||
\(890\) | −2.29083e7 | + | 3.96784e7i | −0.969435 | + | 1.67911i | ||||
\(891\) | 1.08687e7 | + | 1.88252e7i | 0.458653 | + | 0.794409i | ||||
\(892\) | −2.26151e6 | −0.0951672 | ||||||||
\(893\) | 1.82539e7 | + | 3.16167e7i | 0.765998 | + | 1.32675i | ||||
\(894\) | 6.19294e6 | − | 1.07265e7i | 0.259151 | − | 0.448863i | ||||
\(895\) | −3.29454e7 | −1.37479 | ||||||||
\(896\) | −165485. | + | 286628.i | −0.00688634 | + | 0.0119275i | ||||
\(897\) | −4.43438e6 | − | 7.68057e6i | −0.184014 | − | 0.318722i | ||||
\(898\) | 242655. | + | 420290.i | 0.0100415 | + | 0.0173923i | ||||
\(899\) | 1.36089e7 | 0.561595 | ||||||||
\(900\) | 2.80172e6 | + | 4.85272e6i | 0.115297 | + | 0.199701i | ||||
\(901\) | 4.10593e7 | 1.68500 | ||||||||
\(902\) | −1.38280e7 | −0.565905 | ||||||||
\(903\) | 298458. | − | 4.17110e6i | 0.0121805 | − | 0.170228i | ||||
\(904\) | 4.20904e7 | 1.71302 | ||||||||
\(905\) | 6.98867e6 | 0.283644 | ||||||||
\(906\) | 4.88736e6 | + | 8.46516e6i | 0.197813 | + | 0.342622i | ||||
\(907\) | −3.10074e7 | −1.25155 | −0.625774 | − | 0.780004i | \(-0.715217\pi\) | ||||
−0.625774 | + | 0.780004i | \(0.715217\pi\) | |||||||
\(908\) | −6.07028e6 | − | 1.05140e7i | −0.244340 | − | 0.423209i | ||||
\(909\) | 1.20710e6 | + | 2.09077e6i | 0.0484546 | + | 0.0839259i | ||||
\(910\) | 1.23617e6 | − | 2.14112e6i | 0.0494853 | − | 0.0857110i | ||||
\(911\) | −2.20777e7 | −0.881370 | −0.440685 | − | 0.897662i | \(-0.645264\pi\) | ||||
−0.440685 | + | 0.897662i | \(0.645264\pi\) | |||||||
\(912\) | −6.48879e6 | + | 1.12389e7i | −0.258331 | + | 0.447443i | ||||
\(913\) | 1.13612e7 | + | 1.96782e7i | 0.451075 | + | 0.781284i | ||||
\(914\) | 1.63237e7 | 0.646329 | ||||||||
\(915\) | 1.00350e7 | + | 1.73811e7i | 0.396245 | + | 0.686317i | ||||
\(916\) | 947536. | − | 1.64118e6i | 0.0373127 | − | 0.0646275i | ||||
\(917\) | −2.64100e6 | + | 4.57434e6i | −0.103716 | + | 0.179641i | ||||
\(918\) | −5.96174e6 | + | 1.03260e7i | −0.233489 | + | 0.404415i | ||||
\(919\) | 3.09597e7 | 1.20923 | 0.604613 | − | 0.796519i | \(-0.293328\pi\) | ||||
0.604613 | + | 0.796519i | \(0.293328\pi\) | |||||||
\(920\) | −8.94811e6 | + | 1.54986e7i | −0.348547 | + | 0.603702i | ||||
\(921\) | −4.08908e6 | + | 7.08249e6i | −0.158846 | + | 0.275129i | ||||
\(922\) | −1.49225e7 | − | 2.58466e7i | −0.578116 | − | 1.00133i | ||||
\(923\) | −9.18654e6 | − | 1.59116e7i | −0.354934 | − | 0.614764i | ||||
\(924\) | −1.24473e6 | −0.0479617 | ||||||||
\(925\) | 1.96713e7 | 0.755925 | ||||||||
\(926\) | −1.75466e7 | − | 3.03915e7i | −0.672457 | − | 1.16473i | ||||
\(927\) | −1.34332e7 | − | 2.32669e7i | −0.513428 | − | 0.889283i | ||||
\(928\) | 4.95311e6 | − | 8.57904e6i | 0.188803 | − | 0.327016i | ||||
\(929\) | −8.53168e6 | + | 1.47773e7i | −0.324336 | + | 0.561767i | −0.981378 | − | 0.192088i | \(-0.938474\pi\) |
0.657042 | + | 0.753854i | \(0.271808\pi\) | |||||||
\(930\) | 3.95511e7 | 1.49952 | ||||||||
\(931\) | 1.12333e7 | − | 1.94567e7i | 0.424751 | − | 0.735691i | ||||
\(932\) | 8.68577e6 | − | 1.50442e7i | 0.327543 | − | 0.567321i | ||||
\(933\) | 1.55405e7 | − | 2.69170e7i | 0.584469 | − | 1.01233i | ||||
\(934\) | −1.38414e7 | − | 2.39740e7i | −0.519173 | − | 0.899234i | ||||
\(935\) | −3.19526e7 | −1.19530 | ||||||||
\(936\) | 5.53550e6 | + | 9.58776e6i | 0.206522 | + | 0.357707i | ||||
\(937\) | 5.47791e6 | − | 9.48802e6i | 0.203829 | − | 0.353042i | −0.745930 | − | 0.666024i | \(-0.767995\pi\) |
0.949759 | + | 0.312982i | \(0.101328\pi\) | |||||||
\(938\) | 3.05056e6 | 0.113207 | ||||||||
\(939\) | 1.63818e7 | − | 2.83741e7i | 0.606313 | − | 1.05017i | ||||
\(940\) | −1.30271e7 | − | 2.25636e7i | −0.480871 | − | 0.832894i | ||||
\(941\) | 2.91127e6 | + | 5.04248e6i | 0.107179 | + | 0.185639i | 0.914626 | − | 0.404300i | \(-0.132485\pi\) |
−0.807447 | + | 0.589939i | \(0.799152\pi\) | |||||||
\(942\) | 1.66175e7 | 0.610154 | ||||||||
\(943\) | −5.98187e6 | − | 1.03609e7i | −0.219057 | − | 0.379418i | ||||
\(944\) | 1.45732e6 | 0.0532263 | ||||||||
\(945\) | −2.77639e6 | −0.101135 | ||||||||
\(946\) | −1.14099e6 | + | 1.59459e7i | −0.0414528 | + | 0.579324i | ||||
\(947\) | −1.89165e7 | −0.685435 | −0.342718 | − | 0.939439i | \(-0.611347\pi\) | ||||
−0.342718 | + | 0.939439i | \(0.611347\pi\) | |||||||
\(948\) | −1.62807e7 | −0.588372 | ||||||||
\(949\) | −5.90086e6 | − | 1.02206e7i | −0.212691 | − | 0.368392i | ||||
\(950\) | −1.96220e7 | −0.705398 | ||||||||
\(951\) | 2.38032e7 | + | 4.12284e7i | 0.853463 | + | 1.47824i | ||||
\(952\) | −2.33769e6 | − | 4.04899e6i | −0.0835977 | − | 0.144795i | ||||
\(953\) | 1.41673e7 | − | 2.45385e7i | 0.505307 | − | 0.875218i | −0.494674 | − | 0.869079i | \(-0.664712\pi\) |
0.999981 | − | 0.00613922i | \(-0.00195419\pi\) | |||||||
\(954\) | 1.92002e7 | 0.683022 | ||||||||
\(955\) | 1.50573e7 | − | 2.60800e7i | 0.534242 | − | 0.925335i | ||||
\(956\) | 6.08137e6 | + | 1.05332e7i | 0.215207 | + | 0.372750i | ||||
\(957\) | −1.39345e7 | −0.491826 | ||||||||
\(958\) | −5.21223e6 | − | 9.02784e6i | −0.183489 | − | 0.317812i | ||||
\(959\) | −2.89923e6 | + | 5.02162e6i | −0.101797 | + | 0.176318i | ||||
\(960\) | 2.65570e7 | − | 4.59981e7i | 0.930039 | − | 1.61088i | ||||
\(961\) | −1.79723e6 | + | 3.11289e6i | −0.0627761 | + | 0.108731i | ||||
\(962\) | 1.07176e7 | 0.373389 | ||||||||
\(963\) | −1.13979e7 | + | 1.97418e7i | −0.396059 | + | 0.685994i | ||||
\(964\) | −4.48865e6 | + | 7.77457e6i | −0.155569 | + | 0.269453i | ||||
\(965\) | −1.25988e7 | − | 2.18218e7i | −0.435523 | − | 0.754348i | ||||
\(966\) | 875703. | + | 1.51676e6i | 0.0301935 | + | 0.0522967i | ||||
\(967\) | −4.73505e7 | −1.62839 | −0.814194 | − | 0.580592i | \(-0.802821\pi\) | ||||
−0.814194 | + | 0.580592i | \(0.802821\pi\) | |||||||
\(968\) | −1.44204e7 | −0.494641 | ||||||||
\(969\) | −1.80708e7 | − | 3.12995e7i | −0.618254 | − | 1.07085i | ||||
\(970\) | −1.01248e7 | − | 1.75366e7i | −0.345506 | − | 0.598434i | ||||
\(971\) | −5.46536e6 | + | 9.46629e6i | −0.186025 | + | 0.322204i | −0.943921 | − | 0.330170i | \(-0.892894\pi\) |
0.757897 | + | 0.652375i | \(0.226227\pi\) | |||||||
\(972\) | 5.84154e6 | − | 1.01179e7i | 0.198318 | − | 0.343497i | ||||
\(973\) | −496698. | −0.0168194 | ||||||||
\(974\) | 2.41404e6 | − | 4.18125e6i | 0.0815357 | − | 0.141224i | ||||
\(975\) | −1.25826e7 | + | 2.17938e7i | −0.423897 | + | 0.734211i | ||||
\(976\) | 3.11362e6 | − | 5.39294e6i | 0.104626 | − | 0.181218i | ||||
\(977\) | 2.12669e7 | + | 3.68354e7i | 0.712801 | + | 1.23461i | 0.963802 | + | 0.266620i | \(0.0859069\pi\) |
−0.251001 | + | 0.967987i | \(0.580760\pi\) | |||||||
\(978\) | 3.75339e7 | 1.25481 | ||||||||
\(979\) | 1.91108e7 | + | 3.31009e7i | 0.637268 | + | 1.10378i | ||||
\(980\) | −8.01680e6 | + | 1.38855e7i | −0.266647 | + | 0.461845i | ||||
\(981\) | 2.85963e7 | 0.948718 | ||||||||
\(982\) | 6.41858e6 | − | 1.11173e7i | 0.212403 | − | 0.367892i | ||||
\(983\) | 1.01962e7 | + | 1.76604e7i | 0.336555 | + | 0.582931i | 0.983782 | − | 0.179366i | \(-0.0574047\pi\) |
−0.647227 | + | 0.762297i | \(0.724071\pi\) | |||||||
\(984\) | 2.02389e7 | + | 3.50549e7i | 0.666346 | + | 1.15415i | ||||
\(985\) | −6.22799e7 | −2.04530 | ||||||||
\(986\) | −7.21668e6 | − | 1.24997e7i | −0.236399 | − | 0.409455i | ||||
\(987\) | −9.24633e6 | −0.302118 | ||||||||
\(988\) | 6.57361e6 | 0.214245 | ||||||||
\(989\) | −1.24414e7 | + | 6.04315e6i | −0.404461 | + | 0.196459i | ||||
\(990\) | −1.49417e7 | −0.484521 | ||||||||
\(991\) | 1.45760e6 | 0.0471470 | 0.0235735 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235735 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(992\) | 1.17282e7 | + | 2.03138e7i | 0.378400 | + | 0.655407i | ||||
\(993\) | 4.24168e7 | 1.36510 | ||||||||
\(994\) | 1.81416e6 | + | 3.14222e6i | 0.0582385 | + | 0.100872i | ||||
\(995\) | 4.02302e6 | + | 6.96808e6i | 0.128823 | + | 0.223129i | ||||
\(996\) | 9.17102e6 | − | 1.58847e7i | 0.292934 | − | 0.507376i | ||||
\(997\) | 4.09018e7 | 1.30318 | 0.651591 | − | 0.758571i | \(-0.274102\pi\) | ||||
0.651591 | + | 0.758571i | \(0.274102\pi\) | |||||||
\(998\) | −1.53126e7 | + | 2.65221e7i | −0.486655 | + | 0.842911i | ||||
\(999\) | −6.01783e6 | − | 1.04232e7i | −0.190777 | − | 0.330436i |
(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 | 43.6.c.a.36.6 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.6 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.6 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.6 | yes | 34 | 1.1 | even | 1 | trivial |