Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} + \cdots + 92\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.12 | ||
Root | \(15.7319 - 6.27606i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.6.d.b.32.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.46270 | 0.788902 | 0.394451 | − | 0.918917i | \(-0.370935\pi\) | ||||
0.394451 | + | 0.918917i | \(0.370935\pi\) | |||||||
\(3\) | −14.2692 | + | 6.27606i | −0.915372 | + | 0.402609i | ||||
\(4\) | −12.0843 | −0.377634 | ||||||||
\(5\) | − | 59.8956i | − | 1.07145i | −0.844394 | − | 0.535723i | \(-0.820039\pi\) | ||
0.844394 | − | 0.535723i | \(-0.179961\pi\) | |||||||
\(6\) | −63.6794 | + | 28.0082i | −0.722139 | + | 0.317619i | ||||
\(7\) | − | 169.425i | − | 1.30687i | −0.756983 | − | 0.653435i | \(-0.773327\pi\) | ||
0.756983 | − | 0.653435i | \(-0.226673\pi\) | |||||||
\(8\) | −196.735 | −1.08682 | ||||||||
\(9\) | 164.222 | − | 179.109i | 0.675811 | − | 0.737075i | ||||
\(10\) | − | 267.296i | − | 0.845265i | ||||||
\(11\) | −358.129 | + | 181.093i | −0.892397 | + | 0.451252i | ||||
\(12\) | 172.433 | − | 75.8416i | 0.345675 | − | 0.152039i | ||||
\(13\) | 838.100i | 1.37543i | 0.725983 | + | 0.687713i | \(0.241385\pi\) | ||||
−0.725983 | + | 0.687713i | \(0.758615\pi\) | |||||||
\(14\) | − | 756.094i | − | 1.03099i | ||||||
\(15\) | 375.908 | + | 854.664i | 0.431374 | + | 0.980771i | ||||
\(16\) | −491.273 | −0.479759 | ||||||||
\(17\) | −512.592 | −0.430179 | −0.215090 | − | 0.976594i | \(-0.569004\pi\) | ||||
−0.215090 | + | 0.976594i | \(0.569004\pi\) | |||||||
\(18\) | 732.875 | − | 799.311i | 0.533149 | − | 0.581480i | ||||
\(19\) | − | 1878.22i | − | 1.19361i | −0.802387 | − | 0.596804i | \(-0.796437\pi\) | ||
0.802387 | − | 0.596804i | \(-0.203563\pi\) | |||||||
\(20\) | 723.795i | 0.404614i | ||||||||
\(21\) | 1063.32 | + | 2417.57i | 0.526158 | + | 1.19627i | ||||
\(22\) | −1598.22 | + | 808.163i | −0.704013 | + | 0.355994i | ||||
\(23\) | − | 3339.01i | − | 1.31613i | −0.752963 | − | 0.658063i | \(-0.771376\pi\) | ||
0.752963 | − | 0.658063i | \(-0.228624\pi\) | |||||||
\(24\) | 2807.26 | − | 1234.72i | 0.994843 | − | 0.437563i | ||||
\(25\) | −462.483 | −0.147995 | ||||||||
\(26\) | 3740.19i | 1.08508i | ||||||||
\(27\) | −1219.22 | + | 3586.42i | −0.321865 | + | 0.946785i | ||||
\(28\) | 2047.38i | 0.493518i | ||||||||
\(29\) | −1329.42 | −0.293540 | −0.146770 | − | 0.989171i | \(-0.546888\pi\) | ||||
−0.146770 | + | 0.989171i | \(0.546888\pi\) | |||||||
\(30\) | 1677.57 | + | 3814.11i | 0.340312 | + | 0.773732i | ||||
\(31\) | 6737.49 | 1.25920 | 0.629599 | − | 0.776920i | \(-0.283219\pi\) | ||||
0.629599 | + | 0.776920i | \(0.283219\pi\) | |||||||
\(32\) | 4103.11 | 0.708335 | ||||||||
\(33\) | 3973.68 | − | 4831.69i | 0.635197 | − | 0.772351i | ||||
\(34\) | −2287.55 | −0.339369 | ||||||||
\(35\) | −10147.8 | −1.40024 | ||||||||
\(36\) | −1984.51 | + | 2164.40i | −0.255209 | + | 0.278344i | ||||
\(37\) | 4959.19 | 0.595534 | 0.297767 | − | 0.954639i | \(-0.403758\pi\) | ||||
0.297767 | + | 0.954639i | \(0.403758\pi\) | |||||||
\(38\) | − | 8381.92i | − | 0.941639i | ||||||
\(39\) | −5259.96 | − | 11959.0i | −0.553759 | − | 1.25903i | ||||
\(40\) | 11783.6i | 1.16447i | ||||||||
\(41\) | −17769.0 | −1.65083 | −0.825415 | − | 0.564527i | \(-0.809059\pi\) | ||||
−0.825415 | + | 0.564527i | \(0.809059\pi\) | |||||||
\(42\) | 4745.29 | + | 10788.9i | 0.415087 | + | 0.943741i | ||||
\(43\) | − | 7851.09i | − | 0.647528i | −0.946138 | − | 0.323764i | \(-0.895052\pi\) | ||
0.946138 | − | 0.323764i | \(-0.104948\pi\) | |||||||
\(44\) | 4327.73 | − | 2188.37i | 0.336999 | − | 0.170408i | ||||
\(45\) | −10727.8 | − | 9836.18i | −0.789735 | − | 0.724095i | ||||
\(46\) | − | 14901.0i | − | 1.03829i | ||||||
\(47\) | − | 20190.6i | − | 1.33323i | −0.745402 | − | 0.666616i | \(-0.767742\pi\) | ||
0.745402 | − | 0.666616i | \(-0.232258\pi\) | |||||||
\(48\) | 7010.10 | − | 3083.26i | 0.439158 | − | 0.193156i | ||||
\(49\) | −11897.8 | −0.707909 | ||||||||
\(50\) | −2063.92 | −0.116753 | ||||||||
\(51\) | 7314.30 | − | 3217.06i | 0.393774 | − | 0.173194i | ||||
\(52\) | − | 10127.8i | − | 0.519407i | ||||||
\(53\) | 18738.7i | 0.916325i | 0.888868 | + | 0.458163i | \(0.151492\pi\) | ||||
−0.888868 | + | 0.458163i | \(0.848508\pi\) | |||||||
\(54\) | −5441.04 | + | 16005.1i | −0.253920 | + | 0.746921i | ||||
\(55\) | 10846.7 | + | 21450.4i | 0.483492 | + | 0.956154i | ||||
\(56\) | 33331.8i | 1.42033i | ||||||||
\(57\) | 11787.8 | + | 26800.7i | 0.480557 | + | 1.09259i | ||||
\(58\) | −5932.81 | −0.231574 | ||||||||
\(59\) | − | 5842.82i | − | 0.218520i | −0.994013 | − | 0.109260i | \(-0.965152\pi\) | ||
0.994013 | − | 0.109260i | \(-0.0348482\pi\) | |||||||
\(60\) | −4542.58 | − | 10328.0i | −0.162901 | − | 0.370372i | ||||
\(61\) | 1703.10i | 0.0586026i | 0.999571 | + | 0.0293013i | \(0.00932822\pi\) | ||||
−0.999571 | + | 0.0293013i | \(0.990672\pi\) | |||||||
\(62\) | 30067.4 | 0.993384 | ||||||||
\(63\) | −30345.6 | − | 27823.3i | −0.963261 | − | 0.883198i | ||||
\(64\) | 34031.7 | 1.03857 | ||||||||
\(65\) | 50198.5 | 1.47369 | ||||||||
\(66\) | 17733.4 | − | 21562.4i | 0.501108 | − | 0.609309i | ||||
\(67\) | −29337.8 | −0.798437 | −0.399218 | − | 0.916856i | \(-0.630718\pi\) | ||||
−0.399218 | + | 0.916856i | \(0.630718\pi\) | |||||||
\(68\) | 6194.30 | 0.162450 | ||||||||
\(69\) | 20955.8 | + | 47645.1i | 0.529885 | + | 1.20475i | ||||
\(70\) | −45286.7 | −1.10465 | ||||||||
\(71\) | − | 17330.8i | − | 0.408011i | −0.978970 | − | 0.204006i | \(-0.934604\pi\) | ||
0.978970 | − | 0.204006i | \(-0.0653961\pi\) | |||||||
\(72\) | −32308.3 | + | 35237.0i | −0.734484 | + | 0.801066i | ||||
\(73\) | − | 16626.5i | − | 0.365168i | −0.983190 | − | 0.182584i | \(-0.941554\pi\) | ||
0.983190 | − | 0.182584i | \(-0.0584462\pi\) | |||||||
\(74\) | 22131.4 | 0.469818 | ||||||||
\(75\) | 6599.28 | − | 2902.57i | 0.135470 | − | 0.0595840i | ||||
\(76\) | 22696.9i | 0.450746i | ||||||||
\(77\) | 30681.6 | + | 60676.0i | 0.589728 | + | 1.16625i | ||||
\(78\) | −23473.7 | − | 53369.7i | −0.436862 | − | 0.993248i | ||||
\(79\) | 2586.42i | 0.0466263i | 0.999728 | + | 0.0233132i | \(0.00742148\pi\) | ||||
−0.999728 | + | 0.0233132i | \(0.992579\pi\) | |||||||
\(80\) | 29425.1i | 0.514036i | ||||||||
\(81\) | −5111.17 | − | 58827.4i | −0.0865581 | − | 0.996247i | ||||
\(82\) | −79297.6 | −1.30234 | ||||||||
\(83\) | −31993.8 | −0.509766 | −0.254883 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254883 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(84\) | −12849.5 | − | 29214.5i | −0.198695 | − | 0.451753i | ||||
\(85\) | 30702.0i | 0.460913i | ||||||||
\(86\) | − | 35037.1i | − | 0.510836i | ||||||
\(87\) | 18969.8 | − | 8343.52i | 0.268698 | − | 0.118182i | ||||
\(88\) | 70456.6 | − | 35627.3i | 0.969873 | − | 0.490429i | ||||
\(89\) | − | 63768.5i | − | 0.853357i | −0.904403 | − | 0.426679i | \(-0.859684\pi\) | ||
0.904403 | − | 0.426679i | \(-0.140316\pi\) | |||||||
\(90\) | −47875.2 | − | 43896.0i | −0.623024 | − | 0.571240i | ||||
\(91\) | 141995. | 1.79750 | ||||||||
\(92\) | 40349.5i | 0.497014i | ||||||||
\(93\) | −96138.9 | + | 42284.9i | −1.15263 | + | 0.506965i | ||||
\(94\) | − | 90104.9i | − | 1.05179i | ||||||
\(95\) | −112497. | −1.27888 | ||||||||
\(96\) | −58548.3 | + | 25751.4i | −0.648390 | + | 0.285182i | ||||
\(97\) | 103785. | 1.11997 | 0.559984 | − | 0.828503i | \(-0.310807\pi\) | ||||
0.559984 | + | 0.828503i | \(0.310807\pi\) | |||||||
\(98\) | −53096.5 | −0.558471 | ||||||||
\(99\) | −26377.4 | + | 93883.6i | −0.270485 | + | 0.962724i | ||||
\(100\) | 5588.77 | 0.0558877 | ||||||||
\(101\) | −24287.2 | −0.236905 | −0.118453 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118453 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(102\) | 32641.5 | − | 14356.8i | 0.310649 | − | 0.136633i | ||||
\(103\) | −108341. | −1.00624 | −0.503119 | − | 0.864217i | \(-0.667814\pi\) | ||||
−0.503119 | + | 0.864217i | \(0.667814\pi\) | |||||||
\(104\) | − | 164884.i | − | 1.49484i | ||||||
\(105\) | 144802. | − | 63688.3i | 1.28174 | − | 0.563750i | ||||
\(106\) | 83625.2i | 0.722891i | ||||||||
\(107\) | 115625. | 0.976317 | 0.488158 | − | 0.872755i | \(-0.337669\pi\) | ||||
0.488158 | + | 0.872755i | \(0.337669\pi\) | |||||||
\(108\) | 14733.4 | − | 43339.3i | 0.121547 | − | 0.357538i | ||||
\(109\) | 33180.5i | 0.267496i | 0.991015 | + | 0.133748i | \(0.0427012\pi\) | ||||
−0.991015 | + | 0.133748i | \(0.957299\pi\) | |||||||
\(110\) | 48405.4 | + | 95726.6i | 0.381427 | + | 0.754312i | ||||
\(111\) | −70763.8 | + | 31124.2i | −0.545135 | + | 0.239767i | ||||
\(112\) | 83234.0i | 0.626983i | ||||||||
\(113\) | 75910.6i | 0.559250i | 0.960109 | + | 0.279625i | \(0.0902102\pi\) | ||||
−0.960109 | + | 0.279625i | \(0.909790\pi\) | |||||||
\(114\) | 52605.4 | + | 119604.i | 0.379113 | + | 0.861950i | ||||
\(115\) | −199992. | −1.41016 | ||||||||
\(116\) | 16065.1 | 0.110851 | ||||||||
\(117\) | 150111. | + | 137635.i | 1.01379 | + | 0.929529i | ||||
\(118\) | − | 26074.8i | − | 0.172391i | ||||||
\(119\) | 86845.9i | 0.562188i | ||||||||
\(120\) | −73954.4 | − | 168142.i | −0.468825 | − | 1.06592i | ||||
\(121\) | 95461.9 | − | 129709.i | 0.592743 | − | 0.805391i | ||||
\(122\) | 7600.45i | 0.0462317i | ||||||||
\(123\) | 253549. | − | 111519.i | 1.51112 | − | 0.664640i | ||||
\(124\) | −81417.7 | −0.475515 | ||||||||
\(125\) | − | 159473.i | − | 0.912877i | ||||||
\(126\) | −135423. | − | 124167.i | −0.759918 | − | 0.696756i | ||||
\(127\) | 258255.i | 1.42082i | 0.703787 | + | 0.710411i | \(0.251491\pi\) | ||||
−0.703787 | + | 0.710411i | \(0.748509\pi\) | |||||||
\(128\) | 20573.9 | 0.110992 | ||||||||
\(129\) | 49273.9 | + | 112029.i | 0.260701 | + | 0.592729i | ||||
\(130\) | 224021. | 1.16260 | ||||||||
\(131\) | −185955. | −0.946736 | −0.473368 | − | 0.880865i | \(-0.656962\pi\) | ||||
−0.473368 | + | 0.880865i | \(0.656962\pi\) | |||||||
\(132\) | −48019.1 | + | 58387.5i | −0.239872 | + | 0.291666i | ||||
\(133\) | −318217. | −1.55989 | ||||||||
\(134\) | −130926. | −0.629888 | ||||||||
\(135\) | 214811. | + | 73026.2i | 1.01443 | + | 0.344861i | ||||
\(136\) | 100845. | 0.467527 | ||||||||
\(137\) | 79544.3i | 0.362083i | 0.983475 | + | 0.181041i | \(0.0579468\pi\) | ||||
−0.983475 | + | 0.181041i | \(0.942053\pi\) | |||||||
\(138\) | 93519.5 | + | 212626.i | 0.418027 | + | 0.950426i | ||||
\(139\) | − | 419383.i | − | 1.84109i | −0.390642 | − | 0.920543i | \(-0.627747\pi\) | ||
0.390642 | − | 0.920543i | \(-0.372253\pi\) | |||||||
\(140\) | 122629. | 0.528777 | ||||||||
\(141\) | 126718. | + | 288105.i | 0.536772 | + | 1.22040i | ||||
\(142\) | − | 77342.1i | − | 0.321881i | ||||||
\(143\) | −151774. | − | 300148.i | −0.620664 | − | 1.22743i | ||||
\(144\) | −80678.0 | + | 87991.6i | −0.324227 | + | 0.353618i | ||||
\(145\) | 79626.5i | 0.314512i | ||||||||
\(146\) | − | 74199.1i | − | 0.288082i | ||||||
\(147\) | 169773. | − | 74671.5i | 0.648000 | − | 0.285011i | ||||
\(148\) | −59928.2 | −0.224894 | ||||||||
\(149\) | −61974.2 | −0.228689 | −0.114344 | − | 0.993441i | \(-0.536477\pi\) | ||||
−0.114344 | + | 0.993441i | \(0.536477\pi\) | |||||||
\(150\) | 29450.6 | − | 12953.3i | 0.106873 | − | 0.0470059i | ||||
\(151\) | − | 36038.3i | − | 0.128624i | −0.997930 | − | 0.0643121i | \(-0.979515\pi\) | ||
0.997930 | − | 0.0643121i | \(-0.0204853\pi\) | |||||||
\(152\) | 369511.i | 1.29723i | ||||||||
\(153\) | −84179.0 | + | 91809.9i | −0.290720 | + | 0.317074i | ||||
\(154\) | 136923. | + | 270779.i | 0.465237 | + | 0.920054i | ||||
\(155\) | − | 403546.i | − | 1.34916i | ||||||
\(156\) | 63562.8 | + | 144516.i | 0.209118 | + | 0.475451i | ||||
\(157\) | −65185.9 | −0.211059 | −0.105530 | − | 0.994416i | \(-0.533654\pi\) | ||||
−0.105530 | + | 0.994416i | \(0.533654\pi\) | |||||||
\(158\) | 11542.4i | 0.0367836i | ||||||||
\(159\) | −117605. | − | 267387.i | −0.368921 | − | 0.838778i | ||||
\(160\) | − | 245758.i | − | 0.758942i | ||||||
\(161\) | −565711. | −1.72001 | ||||||||
\(162\) | −22809.6 | − | 262529.i | −0.0682859 | − | 0.785941i | ||||
\(163\) | 304117. | 0.896543 | 0.448272 | − | 0.893897i | \(-0.352040\pi\) | ||||
0.448272 | + | 0.893897i | \(0.352040\pi\) | |||||||
\(164\) | 214725. | 0.623409 | ||||||||
\(165\) | −289397. | − | 238006.i | −0.827531 | − | 0.680578i | ||||
\(166\) | −142779. | −0.402155 | ||||||||
\(167\) | −452837. | −1.25647 | −0.628233 | − | 0.778025i | \(-0.716222\pi\) | ||||
−0.628233 | + | 0.778025i | \(0.716222\pi\) | |||||||
\(168\) | −209193. | − | 475620.i | −0.571838 | − | 1.30013i | ||||
\(169\) | −331118. | −0.891797 | ||||||||
\(170\) | 137014.i | 0.363616i | ||||||||
\(171\) | −336406. | − | 308445.i | −0.879778 | − | 0.806653i | ||||
\(172\) | 94874.7i | 0.244528i | ||||||||
\(173\) | 573310. | 1.45638 | 0.728189 | − | 0.685376i | \(-0.240362\pi\) | ||||
0.728189 | + | 0.685376i | \(0.240362\pi\) | |||||||
\(174\) | 84656.7 | − | 37234.7i | 0.211977 | − | 0.0932340i | ||||
\(175\) | 78356.2i | 0.193410i | ||||||||
\(176\) | 175939. | − | 88966.0i | 0.428136 | − | 0.216492i | ||||
\(177\) | 36669.9 | + | 83372.5i | 0.0879784 | + | 0.200028i | ||||
\(178\) | − | 284580.i | − | 0.673215i | ||||||
\(179\) | 331246.i | 0.772713i | 0.922349 | + | 0.386357i | \(0.126267\pi\) | ||||
−0.922349 | + | 0.386357i | \(0.873733\pi\) | |||||||
\(180\) | 129638. | + | 118863.i | 0.298230 | + | 0.273443i | ||||
\(181\) | 593309. | 1.34612 | 0.673061 | − | 0.739587i | \(-0.264979\pi\) | ||||
0.673061 | + | 0.739587i | \(0.264979\pi\) | |||||||
\(182\) | 633682. | 1.41805 | ||||||||
\(183\) | −10688.8 | − | 24302.0i | −0.0235939 | − | 0.0536431i | ||||
\(184\) | 656900.i | 1.43039i | ||||||||
\(185\) | − | 297034.i | − | 0.638082i | ||||||
\(186\) | −429039. | + | 188705.i | −0.909316 | + | 0.399946i | ||||
\(187\) | 183574. | − | 92826.6i | 0.383891 | − | 0.194119i | ||||
\(188\) | 243989.i | 0.503473i | ||||||||
\(189\) | 607629. | + | 206567.i | 1.23733 | + | 0.420636i | ||||
\(190\) | −502040. | −1.00891 | ||||||||
\(191\) | 434454.i | 0.861709i | 0.902421 | + | 0.430855i | \(0.141788\pi\) | ||||
−0.902421 | + | 0.430855i | \(0.858212\pi\) | |||||||
\(192\) | −485607. | + | 213585.i | −0.950674 | + | 0.418136i | ||||
\(193\) | 71460.4i | 0.138093i | 0.997613 | + | 0.0690466i | \(0.0219957\pi\) | ||||
−0.997613 | + | 0.0690466i | \(0.978004\pi\) | |||||||
\(194\) | 463162. | 0.883545 | ||||||||
\(195\) | −716294. | + | 315049.i | −1.34898 | + | 0.593323i | ||||
\(196\) | 143777. | 0.267330 | ||||||||
\(197\) | 909746. | 1.67015 | 0.835073 | − | 0.550139i | \(-0.185425\pi\) | ||||
0.835073 | + | 0.550139i | \(0.185425\pi\) | |||||||
\(198\) | −117714. | + | 418975.i | −0.213387 | + | 0.759495i | ||||
\(199\) | 177806. | 0.318283 | 0.159142 | − | 0.987256i | \(-0.449127\pi\) | ||||
0.159142 | + | 0.987256i | \(0.449127\pi\) | |||||||
\(200\) | 90986.6 | 0.160843 | ||||||||
\(201\) | 418628. | − | 184126.i | 0.730866 | − | 0.321458i | ||||
\(202\) | −108387. | −0.186895 | ||||||||
\(203\) | 225237.i | 0.383619i | ||||||||
\(204\) | −88388.0 | + | 38875.8i | −0.148702 | + | 0.0654040i | ||||
\(205\) | 1.06428e6i | 1.76877i | ||||||||
\(206\) | −483495. | −0.793823 | ||||||||
\(207\) | −598047. | − | 548339.i | −0.970084 | − | 0.889453i | ||||
\(208\) | − | 411736.i | − | 0.659873i | ||||||
\(209\) | 340131. | + | 672644.i | 0.538617 | + | 1.06517i | ||||
\(210\) | 646206. | − | 284222.i | 1.01117 | − | 0.444743i | ||||
\(211\) | − | 323638.i | − | 0.500442i | −0.968189 | − | 0.250221i | \(-0.919497\pi\) | ||
0.968189 | − | 0.250221i | \(-0.0805032\pi\) | |||||||
\(212\) | − | 226444.i | − | 0.346035i | ||||||
\(213\) | 108769. | + | 247297.i | 0.164269 | + | 0.373482i | ||||
\(214\) | 515998. | 0.770218 | ||||||||
\(215\) | −470246. | −0.693791 | ||||||||
\(216\) | 239864. | − | 705574.i | 0.349809 | − | 1.02898i | ||||
\(217\) | − | 1.14150e6i | − | 1.64561i | ||||||
\(218\) | 148075.i | 0.211028i | ||||||||
\(219\) | 104349. | + | 237247.i | 0.147020 | + | 0.334265i | ||||
\(220\) | −131074. | − | 259212.i | −0.182583 | − | 0.361076i | ||||
\(221\) | − | 429603.i | − | 0.591680i | ||||||
\(222\) | −315798. | + | 138898.i | −0.430058 | + | 0.189153i | ||||
\(223\) | 13271.8 | 0.0178718 | 0.00893588 | − | 0.999960i | \(-0.497156\pi\) | ||||
0.00893588 | + | 0.999960i | \(0.497156\pi\) | |||||||
\(224\) | − | 695170.i | − | 0.925702i | ||||||
\(225\) | −75949.9 | + | 82834.9i | −0.100016 | + | 0.109083i | ||||
\(226\) | 338766.i | 0.441194i | ||||||||
\(227\) | 281859. | 0.363051 | 0.181525 | − | 0.983386i | \(-0.441897\pi\) | ||||
0.181525 | + | 0.983386i | \(0.441897\pi\) | |||||||
\(228\) | −142447. | − | 323867.i | −0.181475 | − | 0.412600i | ||||
\(229\) | −1.35791e6 | −1.71113 | −0.855566 | − | 0.517693i | \(-0.826791\pi\) | ||||
−0.855566 | + | 0.517693i | \(0.826791\pi\) | |||||||
\(230\) | −892504. | −1.11248 | ||||||||
\(231\) | −818610. | − | 673241.i | −1.00936 | − | 0.830119i | ||||
\(232\) | 261544. | 0.319025 | ||||||||
\(233\) | −66995.0 | −0.0808449 | −0.0404224 | − | 0.999183i | \(-0.512870\pi\) | ||||
−0.0404224 | + | 0.999183i | \(0.512870\pi\) | |||||||
\(234\) | 669902. | + | 614222.i | 0.799782 | + | 0.733307i | ||||
\(235\) | −1.20933e6 | −1.42848 | ||||||||
\(236\) | 70606.2i | 0.0825207i | ||||||||
\(237\) | −16232.5 | − | 36906.2i | −0.0187722 | − | 0.0426804i | ||||
\(238\) | 387567.i | 0.443512i | ||||||||
\(239\) | −383601. | −0.434395 | −0.217198 | − | 0.976128i | \(-0.569692\pi\) | ||||
−0.217198 | + | 0.976128i | \(0.569692\pi\) | |||||||
\(240\) | −184674. | − | 419874.i | −0.206956 | − | 0.470534i | ||||
\(241\) | − | 23367.5i | − | 0.0259161i | −0.999916 | − | 0.0129581i | \(-0.995875\pi\) | ||
0.999916 | − | 0.0129581i | \(-0.00412480\pi\) | |||||||
\(242\) | 426018. | − | 578853.i | 0.467617 | − | 0.635375i | ||||
\(243\) | 442137. | + | 807344.i | 0.480331 | + | 0.877087i | ||||
\(244\) | − | 20580.8i | − | 0.0221303i | ||||||
\(245\) | 712628.i | 0.758486i | ||||||||
\(246\) | 1.13152e6 | − | 497676.i | 1.19213 | − | 0.524336i | ||||
\(247\) | 1.57413e6 | 1.64172 | ||||||||
\(248\) | −1.32550e6 | −1.36852 | ||||||||
\(249\) | 456527. | − | 200795.i | 0.466626 | − | 0.205237i | ||||
\(250\) | − | 711681.i | − | 0.720171i | ||||||
\(251\) | − | 1.73283e6i | − | 1.73608i | −0.496491 | − | 0.868042i | \(-0.665378\pi\) | ||
0.496491 | − | 0.868042i | \(-0.334622\pi\) | |||||||
\(252\) | 366704. | + | 336225.i | 0.363760 | + | 0.333525i | ||||
\(253\) | 604669. | + | 1.19580e6i | 0.593905 | + | 1.17451i | ||||
\(254\) | 1.15252e6i | 1.12089i | ||||||||
\(255\) | −192688. | − | 438094.i | −0.185568 | − | 0.421907i | ||||
\(256\) | −997200. | −0.951004 | ||||||||
\(257\) | 83741.8i | 0.0790878i | 0.999218 | + | 0.0395439i | \(0.0125905\pi\) | ||||
−0.999218 | + | 0.0395439i | \(0.987410\pi\) | |||||||
\(258\) | 219895. | + | 499952.i | 0.205668 | + | 0.467605i | ||||
\(259\) | − | 840210.i | − | 0.778285i | ||||||
\(260\) | −606612. | −0.556516 | ||||||||
\(261\) | −218320. | + | 238111.i | −0.198378 | + | 0.216361i | ||||
\(262\) | −829860. | −0.746882 | ||||||||
\(263\) | 1.45210e6 | 1.29451 | 0.647256 | − | 0.762272i | \(-0.275916\pi\) | ||||
0.647256 | + | 0.762272i | \(0.275916\pi\) | |||||||
\(264\) | −781762. | + | 950563.i | −0.690343 | + | 0.839404i | ||||
\(265\) | 1.12237e6 | 0.981792 | ||||||||
\(266\) | −1.42011e6 | −1.23060 | ||||||||
\(267\) | 400215. | + | 909927.i | 0.343570 | + | 0.781139i | ||||
\(268\) | 354526. | 0.301517 | ||||||||
\(269\) | − | 335334.i | − | 0.282551i | −0.989970 | − | 0.141275i | \(-0.954880\pi\) | ||
0.989970 | − | 0.141275i | \(-0.0451203\pi\) | |||||||
\(270\) | 958636. | + | 325894.i | 0.800285 | + | 0.272062i | ||||
\(271\) | − | 2.35862e6i | − | 1.95090i | −0.220227 | − | 0.975449i | \(-0.570680\pi\) | ||
0.220227 | − | 0.975449i | \(-0.429320\pi\) | |||||||
\(272\) | 251823. | 0.206382 | ||||||||
\(273\) | −2.02616e6 | + | 891169.i | −1.64538 | + | 0.723692i | ||||
\(274\) | 354983.i | 0.285648i | ||||||||
\(275\) | 165629. | − | 83752.2i | 0.132070 | − | 0.0667828i | ||||
\(276\) | −253236. | − | 575756.i | −0.200102 | − | 0.454952i | ||||
\(277\) | 1.98229e6i | 1.55227i | 0.630564 | + | 0.776137i | \(0.282824\pi\) | ||||
−0.630564 | + | 0.776137i | \(0.717176\pi\) | |||||||
\(278\) | − | 1.87158e6i | − | 1.45244i | ||||||
\(279\) | 1.10645e6 | − | 1.20675e6i | 0.850980 | − | 0.928123i | ||||
\(280\) | 1.99643e6 | 1.52181 | ||||||||
\(281\) | −119166. | −0.0900299 | −0.0450150 | − | 0.998986i | \(-0.514334\pi\) | ||||
−0.0450150 | + | 0.998986i | \(0.514334\pi\) | |||||||
\(282\) | 565504. | + | 1.28573e6i | 0.423460 | + | 0.962778i | ||||
\(283\) | 2.04647e6i | 1.51894i | 0.650544 | + | 0.759468i | \(0.274541\pi\) | ||||
−0.650544 | + | 0.759468i | \(0.725459\pi\) | |||||||
\(284\) | 209430.i | 0.154079i | ||||||||
\(285\) | 1.60524e6 | − | 706037.i | 1.17065 | − | 0.514891i | ||||
\(286\) | −677321. | − | 1.33947e6i | −0.489643 | − | 0.968319i | ||||
\(287\) | 3.01051e6i | 2.15742i | ||||||||
\(288\) | 673822. | − | 734905.i | 0.478701 | − | 0.522096i | ||||
\(289\) | −1.15711e6 | −0.814946 | ||||||||
\(290\) | 355349.i | 0.248119i | ||||||||
\(291\) | −1.48093e6 | + | 651362.i | −1.02519 | + | 0.450910i | ||||
\(292\) | 200919.i | 0.137900i | ||||||||
\(293\) | −874404. | −0.595036 | −0.297518 | − | 0.954716i | \(-0.596159\pi\) | ||||
−0.297518 | + | 0.954716i | \(0.596159\pi\) | |||||||
\(294\) | 757646. | − | 333237.i | 0.511209 | − | 0.224846i | ||||
\(295\) | −349959. | −0.234133 | ||||||||
\(296\) | −975646. | −0.647237 | ||||||||
\(297\) | −212834. | − | 1.50519e6i | −0.140007 | − | 0.990151i | ||||
\(298\) | −276572. | −0.180413 | ||||||||
\(299\) | 2.79842e6 | 1.81023 | ||||||||
\(300\) | −79747.5 | + | 35075.5i | −0.0511580 | + | 0.0225009i | ||||
\(301\) | −1.33017e6 | −0.846235 | ||||||||
\(302\) | − | 160828.i | − | 0.101472i | ||||||
\(303\) | 346560. | − | 152428.i | 0.216856 | − | 0.0953803i | ||||
\(304\) | 922717.i | 0.572644i | ||||||||
\(305\) | 102008. | 0.0627894 | ||||||||
\(306\) | −375666. | + | 409720.i | −0.229350 | + | 0.250141i | ||||
\(307\) | 2.22344e6i | 1.34642i | 0.739452 | + | 0.673209i | \(0.235085\pi\) | ||||
−0.739452 | + | 0.673209i | \(0.764915\pi\) | |||||||
\(308\) | −370765. | − | 733226.i | −0.222701 | − | 0.440414i | ||||
\(309\) | 1.54595e6 | − | 679956.i | 0.921082 | − | 0.405121i | ||||
\(310\) | − | 1.80091e6i | − | 1.06436i | ||||||
\(311\) | − | 2.04294e6i | − | 1.19772i | −0.800854 | − | 0.598860i | \(-0.795621\pi\) | ||
0.800854 | − | 0.598860i | \(-0.204379\pi\) | |||||||
\(312\) | 1.03482e6 | + | 2.35276e6i | 0.601836 | + | 1.36833i | ||||
\(313\) | 2.46189e6 | 1.42039 | 0.710195 | − | 0.704005i | \(-0.248607\pi\) | ||||
0.710195 | + | 0.704005i | \(0.248607\pi\) | |||||||
\(314\) | −290905. | −0.166505 | ||||||||
\(315\) | −1.66650e6 | + | 1.81757e6i | −0.946298 | + | 1.03208i | ||||
\(316\) | − | 31255.0i | − | 0.0176077i | ||||||
\(317\) | 59333.5i | 0.0331628i | 0.999863 | + | 0.0165814i | \(0.00527827\pi\) | ||||
−0.999863 | + | 0.0165814i | \(0.994722\pi\) | |||||||
\(318\) | −524837. | − | 1.19327e6i | −0.291043 | − | 0.661714i | ||||
\(319\) | 476104. | − | 240748.i | 0.261954 | − | 0.132461i | ||||
\(320\) | − | 2.03835e6i | − | 1.11277i | ||||||
\(321\) | −1.64987e6 | + | 725667.i | −0.893693 | + | 0.393074i | ||||
\(322\) | −2.52460e6 | −1.35692 | ||||||||
\(323\) | 962758.i | 0.513465i | ||||||||
\(324\) | 61764.8 | + | 710886.i | 0.0326872 | + | 0.376216i | ||||
\(325\) | − | 387607.i | − | 0.203556i | ||||||
\(326\) | 1.35718e6 | 0.707285 | ||||||||
\(327\) | −208243. | − | 473461.i | −0.107696 | − | 0.244858i | ||||
\(328\) | 3.49578e6 | 1.79415 | ||||||||
\(329\) | −3.42080e6 | −1.74236 | ||||||||
\(330\) | −1.29149e6 | − | 1.06215e6i | −0.652841 | − | 0.536909i | ||||
\(331\) | 1.38194e6 | 0.693297 | 0.346648 | − | 0.937995i | \(-0.387320\pi\) | ||||
0.346648 | + | 0.937995i | \(0.387320\pi\) | |||||||
\(332\) | 386622. | 0.192505 | ||||||||
\(333\) | 814409. | − | 888236.i | 0.402468 | − | 0.438953i | ||||
\(334\) | −2.02088e6 | −0.991229 | ||||||||
\(335\) | 1.75720e6i | 0.855481i | ||||||||
\(336\) | −522382. | − | 1.18769e6i | −0.252429 | − | 0.573923i | ||||
\(337\) | − | 1.39179e6i | − | 0.667572i | −0.942649 | − | 0.333786i | \(-0.891674\pi\) | ||
0.942649 | − | 0.333786i | \(-0.108326\pi\) | |||||||
\(338\) | −1.47768e6 | −0.703540 | ||||||||
\(339\) | −476419. | − | 1.08319e6i | −0.225159 | − | 0.511922i | ||||
\(340\) | − | 371011.i | − | 0.174056i | ||||||
\(341\) | −2.41289e6 | + | 1.22011e6i | −1.12370 | + | 0.568215i | ||||
\(342\) | −1.50128e6 | − | 1.37650e6i | −0.694058 | − | 0.636370i | ||||
\(343\) | − | 831736.i | − | 0.381725i | ||||||
\(344\) | 1.54458e6i | 0.703745i | ||||||||
\(345\) | 2.85373e6 | − | 1.25516e6i | 1.29082 | − | 0.567743i | ||||
\(346\) | 2.55851e6 | 1.14894 | ||||||||
\(347\) | 4.18029e6 | 1.86373 | 0.931865 | − | 0.362806i | \(-0.118181\pi\) | ||||
0.931865 | + | 0.362806i | \(0.118181\pi\) | |||||||
\(348\) | −229237. | + | 100825.i | −0.101470 | + | 0.0446295i | ||||
\(349\) | − | 1.74185e6i | − | 0.765506i | −0.923851 | − | 0.382753i | \(-0.874976\pi\) | ||
0.923851 | − | 0.382753i | \(-0.125024\pi\) | |||||||
\(350\) | 349680.i | 0.152581i | ||||||||
\(351\) | −3.00578e6 | − | 1.02183e6i | −1.30223 | − | 0.442702i | ||||
\(352\) | −1.46944e6 | + | 743044.i | −0.632116 | + | 0.319637i | ||||
\(353\) | − | 2.80701e6i | − | 1.19897i | −0.800387 | − | 0.599483i | \(-0.795373\pi\) | ||
0.800387 | − | 0.599483i | \(-0.204627\pi\) | |||||||
\(354\) | 163647. | + | 372067.i | 0.0694063 | + | 0.157802i | ||||
\(355\) | −1.03804e6 | −0.437162 | ||||||||
\(356\) | 770596.i | 0.322256i | ||||||||
\(357\) | −545050. | − | 1.23922e6i | −0.226342 | − | 0.514611i | ||||
\(358\) | 1.47825e6i | 0.609595i | ||||||||
\(359\) | 596226. | 0.244160 | 0.122080 | − | 0.992520i | \(-0.461044\pi\) | ||||
0.122080 | + | 0.992520i | \(0.461044\pi\) | |||||||
\(360\) | 2.11054e6 | + | 1.93512e6i | 0.858298 | + | 0.786959i | ||||
\(361\) | −1.05159e6 | −0.424698 | ||||||||
\(362\) | 2.64776e6 | 1.06196 | ||||||||
\(363\) | −548107. | + | 2.44997e6i | −0.218323 | + | 0.975877i | ||||
\(364\) | −1.71591e6 | −0.678798 | ||||||||
\(365\) | −995853. | −0.391258 | ||||||||
\(366\) | −47700.9 | − | 108453.i | −0.0186133 | − | 0.0423192i | ||||
\(367\) | −3.46674e6 | −1.34356 | −0.671779 | − | 0.740752i | \(-0.734470\pi\) | ||||
−0.671779 | + | 0.740752i | \(0.734470\pi\) | |||||||
\(368\) | 1.64037e6i | 0.631424i | ||||||||
\(369\) | −2.91806e6 | + | 3.18258e6i | −1.11565 | + | 1.21678i | ||||
\(370\) | − | 1.32557e6i | − | 0.503384i | ||||||
\(371\) | 3.17480e6 | 1.19752 | ||||||||
\(372\) | 1.16177e6 | − | 510982.i | 0.435273 | − | 0.191447i | ||||
\(373\) | − | 4.41525e6i | − | 1.64317i | −0.570085 | − | 0.821586i | \(-0.693090\pi\) | ||
0.570085 | − | 0.821586i | \(-0.306910\pi\) | |||||||
\(374\) | 819237. | − | 414258.i | 0.302852 | − | 0.153141i | ||||
\(375\) | 1.00086e6 | + | 2.27556e6i | 0.367533 | + | 0.835622i | ||||
\(376\) | 3.97221e6i | 1.44898i | ||||||||
\(377\) | − | 1.11419e6i | − | 0.403743i | ||||||
\(378\) | 2.71167e6 | + | 921848.i | 0.976129 | + | 0.331841i | ||||
\(379\) | −2.65164e6 | −0.948236 | −0.474118 | − | 0.880461i | \(-0.657233\pi\) | ||||
−0.474118 | + | 0.880461i | \(0.657233\pi\) | |||||||
\(380\) | 1.35944e6 | 0.482950 | ||||||||
\(381\) | −1.62083e6 | − | 3.68510e6i | −0.572036 | − | 1.30058i | ||||
\(382\) | 1.93884e6i | 0.679804i | ||||||||
\(383\) | 1.60664e6i | 0.559656i | 0.960050 | + | 0.279828i | \(0.0902774\pi\) | ||||
−0.960050 | + | 0.279828i | \(0.909723\pi\) | |||||||
\(384\) | −293574. | + | 129123.i | −0.101599 | + | 0.0446864i | ||||
\(385\) | 3.63423e6 | − | 1.83769e6i | 1.24957 | − | 0.631861i | ||||
\(386\) | 318907.i | 0.108942i | ||||||||
\(387\) | −1.40620e6 | − | 1.28932e6i | −0.477277 | − | 0.437607i | ||||
\(388\) | −1.25417e6 | −0.422938 | ||||||||
\(389\) | 243726.i | 0.0816634i | 0.999166 | + | 0.0408317i | \(0.0130008\pi\) | ||||
−0.999166 | + | 0.0408317i | \(0.986999\pi\) | |||||||
\(390\) | −3.19661e6 | + | 1.40597e6i | −1.06421 | + | 0.468074i | ||||
\(391\) | 1.71155e6i | 0.566170i | ||||||||
\(392\) | 2.34072e6 | 0.769368 | ||||||||
\(393\) | 2.65343e6 | − | 1.16706e6i | 0.866615 | − | 0.381165i | ||||
\(394\) | 4.05993e6 | 1.31758 | ||||||||
\(395\) | 154915. | 0.0499576 | ||||||||
\(396\) | 318752. | − | 1.13452e6i | 0.102144 | − | 0.363557i | ||||
\(397\) | 181651. | 0.0578445 | 0.0289223 | − | 0.999582i | \(-0.490792\pi\) | ||||
0.0289223 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(398\) | 793496. | 0.251094 | ||||||||
\(399\) | 4.54071e6 | − | 1.99715e6i | 1.42788 | − | 0.628026i | ||||
\(400\) | 227206. | 0.0710017 | ||||||||
\(401\) | − | 3.23285e6i | − | 1.00398i | −0.864874 | − | 0.501989i | \(-0.832602\pi\) | ||
0.864874 | − | 0.501989i | \(-0.167398\pi\) | |||||||
\(402\) | 1.86821e6 | − | 821699.i | 0.576582 | − | 0.253599i | ||||
\(403\) | 5.64669e6i | 1.73193i | ||||||||
\(404\) | 293494. | 0.0894634 | ||||||||
\(405\) | −3.52350e6 | + | 306137.i | −1.06742 | + | 0.0927423i | ||||
\(406\) | 1.00517e6i | 0.302638i | ||||||||
\(407\) | −1.77603e6 | + | 898072.i | −0.531452 | + | 0.268736i | ||||
\(408\) | −1.43898e6 | + | 632908.i | −0.427961 | + | 0.188231i | ||||
\(409\) | − | 2.73058e6i | − | 0.807135i | −0.914950 | − | 0.403567i | \(-0.867770\pi\) | ||
0.914950 | − | 0.403567i | \(-0.132230\pi\) | |||||||
\(410\) | 4.74958e6i | 1.39539i | ||||||||
\(411\) | −499225. | − | 1.13504e6i | −0.145778 | − | 0.331440i | ||||
\(412\) | 1.30923e6 | 0.379989 | ||||||||
\(413\) | −989919. | −0.285578 | ||||||||
\(414\) | −2.66890e6 | − | 2.44707e6i | −0.765301 | − | 0.701691i | ||||
\(415\) | 1.91629e6i | 0.546186i | ||||||||
\(416\) | 3.43882e6i | 0.974262i | ||||||||
\(417\) | 2.63207e6 | + | 5.98428e6i | 0.741238 | + | 1.68528i | ||||
\(418\) | 1.51790e6 | + | 3.00181e6i | 0.424916 | + | 0.840316i | ||||
\(419\) | 2.32728e6i | 0.647611i | 0.946124 | + | 0.323805i | \(0.104962\pi\) | ||||
−0.946124 | + | 0.323805i | \(0.895038\pi\) | |||||||
\(420\) | −1.74982e6 | + | 769627.i | −0.484028 | + | 0.212891i | ||||
\(421\) | 2.07600e6 | 0.570851 | 0.285425 | − | 0.958401i | \(-0.407865\pi\) | ||||
0.285425 | + | 0.958401i | \(0.407865\pi\) | |||||||
\(422\) | − | 1.44430e6i | − | 0.394799i | ||||||
\(423\) | −3.61633e6 | − | 3.31575e6i | −0.982691 | − | 0.901013i | ||||
\(424\) | − | 3.68656e6i | − | 0.995879i | ||||||
\(425\) | 237065. | 0.0636642 | ||||||||
\(426\) | 485404. | + | 1.10361e6i | 0.129592 | + | 0.294641i | ||||
\(427\) | 288548. | 0.0765859 | ||||||||
\(428\) | −1.39724e6 | −0.368690 | ||||||||
\(429\) | 4.04944e6 | + | 3.33034e6i | 1.06231 | + | 0.873666i | ||||
\(430\) | −2.09857e6 | −0.547333 | ||||||||
\(431\) | 4.32285e6 | 1.12092 | 0.560462 | − | 0.828180i | \(-0.310623\pi\) | ||||
0.560462 | + | 0.828180i | \(0.310623\pi\) | |||||||
\(432\) | 598973. | − | 1.76191e6i | 0.154418 | − | 0.454229i | ||||
\(433\) | −2.24130e6 | −0.574488 | −0.287244 | − | 0.957857i | \(-0.592739\pi\) | ||||
−0.287244 | + | 0.957857i | \(0.592739\pi\) | |||||||
\(434\) | − | 5.09417e6i | − | 1.29822i | ||||||
\(435\) | −499740. | − | 1.13621e6i | −0.126626 | − | 0.287896i | ||||
\(436\) | − | 400963.i | − | 0.101015i | ||||||
\(437\) | −6.27137e6 | −1.57094 | ||||||||
\(438\) | 465678. | + | 1.05876e6i | 0.115985 | + | 0.263702i | ||||
\(439\) | − | 771175.i | − | 0.190982i | −0.995430 | − | 0.0954908i | \(-0.969558\pi\) | ||
0.995430 | − | 0.0954908i | \(-0.0304421\pi\) | |||||||
\(440\) | −2.13392e6 | − | 4.22004e6i | −0.525467 | − | 1.03917i | ||||
\(441\) | −1.95389e6 | + | 2.13101e6i | −0.478413 | + | 0.521782i | ||||
\(442\) | − | 1.91719e6i | − | 0.466777i | ||||||
\(443\) | 4.38448e6i | 1.06147i | 0.847537 | + | 0.530737i | \(0.178085\pi\) | ||||
−0.847537 | + | 0.530737i | \(0.821915\pi\) | |||||||
\(444\) | 855130. | − | 376113.i | 0.205861 | − | 0.0905442i | ||||
\(445\) | −3.81945e6 | −0.914325 | ||||||||
\(446\) | 59228.0 | 0.0140991 | ||||||||
\(447\) | 884324. | − | 388954.i | 0.209335 | − | 0.0920723i | ||||
\(448\) | − | 5.76583e6i | − | 1.35727i | ||||||
\(449\) | − | 6.62600e6i | − | 1.55108i | −0.631295 | − | 0.775542i | \(-0.717476\pi\) | ||
0.631295 | − | 0.775542i | \(-0.282524\pi\) | |||||||
\(450\) | −338942. | + | 369668.i | −0.0789031 | + | 0.0860558i | ||||
\(451\) | 6.36358e6 | − | 3.21783e6i | 1.47319 | − | 0.744940i | ||||
\(452\) | − | 917324.i | − | 0.211192i | ||||||
\(453\) | 226179. | + | 514240.i | 0.0517853 | + | 0.117739i | ||||
\(454\) | 1.25785e6 | 0.286412 | ||||||||
\(455\) | − | 8.50488e6i | − | 1.92593i | ||||||
\(456\) | −2.31907e6 | − | 5.27264e6i | −0.522278 | − | 1.18745i | ||||
\(457\) | − | 1.04547e6i | − | 0.234164i | −0.993122 | − | 0.117082i | \(-0.962646\pi\) | ||
0.993122 | − | 0.117082i | \(-0.0373540\pi\) | |||||||
\(458\) | −6.05997e6 | −1.34992 | ||||||||
\(459\) | 624965. | − | 1.83837e6i | 0.138460 | − | 0.407287i | ||||
\(460\) | 2.41676e6 | 0.532523 | ||||||||
\(461\) | −4.96719e6 | −1.08857 | −0.544287 | − | 0.838899i | \(-0.683200\pi\) | ||||
−0.544287 | + | 0.838899i | \(0.683200\pi\) | |||||||
\(462\) | −3.65321e6 | − | 3.00447e6i | −0.796288 | − | 0.654883i | ||||
\(463\) | −3.13080e6 | −0.678739 | −0.339370 | − | 0.940653i | \(-0.610214\pi\) | ||||
−0.339370 | + | 0.940653i | \(0.610214\pi\) | |||||||
\(464\) | 653109. | 0.140829 | ||||||||
\(465\) | 2.53268e6 | + | 5.75829e6i | 0.543185 | + | 1.23498i | ||||
\(466\) | −298979. | −0.0637787 | ||||||||
\(467\) | 6.97533e6i | 1.48004i | 0.672587 | + | 0.740018i | \(0.265183\pi\) | ||||
−0.672587 | + | 0.740018i | \(0.734817\pi\) | |||||||
\(468\) | −1.81399e6 | − | 1.66321e6i | −0.382842 | − | 0.351021i | ||||
\(469\) | 4.97056e6i | 1.04345i | ||||||||
\(470\) | −5.39688e6 | −1.12693 | ||||||||
\(471\) | 930153. | − | 409110.i | 0.193198 | − | 0.0849744i | ||||
\(472\) | 1.14949e6i | 0.237492i | ||||||||
\(473\) | 1.42177e6 | + | 2.81170e6i | 0.292198 | + | 0.577852i | ||||
\(474\) | −72440.9 | − | 164702.i | −0.0148094 | − | 0.0336707i | ||||
\(475\) | 868643.i | 0.176647i | ||||||||
\(476\) | − | 1.04947e6i | − | 0.212301i | ||||||
\(477\) | 3.35627e6 | + | 3.07731e6i | 0.675400 | + | 0.619263i | ||||
\(478\) | −1.71190e6 | −0.342695 | ||||||||
\(479\) | −5.09382e6 | −1.01439 | −0.507194 | − | 0.861832i | \(-0.669317\pi\) | ||||
−0.507194 | + | 0.861832i | \(0.669317\pi\) | |||||||
\(480\) | 1.54239e6 | + | 3.50679e6i | 0.305557 | + | 0.694714i | ||||
\(481\) | 4.15629e6i | 0.819112i | ||||||||
\(482\) | − | 104282.i | − | 0.0204453i | ||||||
\(483\) | 8.07226e6 | − | 3.55044e6i | 1.57445 | − | 0.692491i | ||||
\(484\) | −1.15359e6 | + | 1.56744e6i | −0.223840 | + | 0.304143i | ||||
\(485\) | − | 6.21627e6i | − | 1.19998i | ||||||
\(486\) | 1.97312e6 | + | 3.60294e6i | 0.378934 | + | 0.691936i | ||||
\(487\) | 7.86781e6 | 1.50325 | 0.751625 | − | 0.659590i | \(-0.229270\pi\) | ||||
0.751625 | + | 0.659590i | \(0.229270\pi\) | |||||||
\(488\) | − | 335060.i | − | 0.0636903i | ||||||
\(489\) | −4.33951e6 | + | 1.90865e6i | −0.820670 | + | 0.360957i | ||||
\(490\) | 3.18025e6i | 0.598371i | ||||||||
\(491\) | 8.05135e6 | 1.50718 | 0.753590 | − | 0.657345i | \(-0.228320\pi\) | ||||
0.753590 | + | 0.657345i | \(0.228320\pi\) | |||||||
\(492\) | −3.06396e6 | + | 1.34763e6i | −0.570651 | + | 0.250990i | ||||
\(493\) | 681450. | 0.126275 | ||||||||
\(494\) | 7.02488e6 | 1.29515 | ||||||||
\(495\) | 5.62322e6 | + | 1.57989e6i | 1.03151 | + | 0.289810i | ||||
\(496\) | −3.30995e6 | −0.604112 | ||||||||
\(497\) | −2.93627e6 | −0.533218 | ||||||||
\(498\) | 2.03735e6 | − | 896089.i | 0.368122 | − | 0.161912i | ||||
\(499\) | −9.10103e6 | −1.63621 | −0.818106 | − | 0.575068i | \(-0.804976\pi\) | ||||
−0.818106 | + | 0.575068i | \(0.804976\pi\) | |||||||
\(500\) | 1.92712e6i | 0.344733i | ||||||||
\(501\) | 6.46164e6 | − | 2.84203e6i | 1.15013 | − | 0.505865i | ||||
\(502\) | − | 7.73309e6i | − | 1.36960i | ||||||
\(503\) | −1.00620e6 | −0.177323 | −0.0886615 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886615 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(504\) | 5.97004e6 | + | 5.47383e6i | 1.04689 | + | 0.959875i | ||||
\(505\) | 1.45470e6i | 0.253831i | ||||||||
\(506\) | 2.69846e6 | + | 5.33648e6i | 0.468533 | + | 0.926571i | ||||
\(507\) | 4.72480e6 | − | 2.07812e6i | 0.816326 | − | 0.359046i | ||||
\(508\) | − | 3.12083e6i | − | 0.536550i | ||||||
\(509\) | 2.93973e6i | 0.502936i | 0.967866 | + | 0.251468i | \(0.0809134\pi\) | ||||
−0.967866 | + | 0.251468i | \(0.919087\pi\) | |||||||
\(510\) | −859908. | − | 1.95508e6i | −0.146395 | − | 0.332843i | ||||
\(511\) | −2.81694e6 | −0.477228 | ||||||||
\(512\) | −5.10857e6 | −0.861241 | ||||||||
\(513\) | 6.73607e6 | + | 2.28997e6i | 1.13009 | + | 0.384181i | ||||
\(514\) | 373715.i | 0.0623925i | ||||||||
\(515\) | 6.48916e6i | 1.07813i | ||||||||
\(516\) | −595439. | − | 1.35379e6i | −0.0984495 | − | 0.223834i | ||||
\(517\) | 3.65638e6 | + | 7.23086e6i | 0.601623 | + | 1.18977i | ||||
\(518\) | − | 3.74961e6i | − | 0.613991i | ||||||
\(519\) | −8.18069e6 | + | 3.59813e6i | −1.33313 | + | 0.586352i | ||||
\(520\) | −9.87580e6 | −1.60164 | ||||||||
\(521\) | 9.05577e6i | 1.46161i | 0.682587 | + | 0.730804i | \(0.260855\pi\) | ||||
−0.682587 | + | 0.730804i | \(0.739145\pi\) | |||||||
\(522\) | −974299. | + | 1.06262e6i | −0.156501 | + | 0.170688i | ||||
\(523\) | 912191.i | 0.145825i | 0.997338 | + | 0.0729124i | \(0.0232294\pi\) | ||||
−0.997338 | + | 0.0729124i | \(0.976771\pi\) | |||||||
\(524\) | 2.24713e6 | 0.357519 | ||||||||
\(525\) | −491768. | − | 1.11808e6i | −0.0778685 | − | 0.177042i | ||||
\(526\) | 6.48028e6 | 1.02124 | ||||||||
\(527\) | −3.45358e6 | −0.541681 | ||||||||
\(528\) | −1.95216e6 | + | 2.37368e6i | −0.304741 | + | 0.370542i | ||||
\(529\) | −4.71262e6 | −0.732189 | ||||||||
\(530\) | 5.00878e6 | 0.774538 | ||||||||
\(531\) | −1.04650e6 | − | 959520.i | −0.161066 | − | 0.147679i | ||||
\(532\) | 3.84542e6 | 0.589067 | ||||||||
\(533\) | − | 1.48922e7i | − | 2.27059i | ||||||
\(534\) | 1.78604e6 | + | 4.06074e6i | 0.271043 | + | 0.616242i | ||||
\(535\) | − | 6.92540e6i | − | 1.04607i | ||||||
\(536\) | 5.77177e6 | 0.867755 | ||||||||
\(537\) | −2.07892e6 | − | 4.72663e6i | −0.311102 | − | 0.707320i | ||||
\(538\) | − | 1.49649e6i | − | 0.222905i | ||||||
\(539\) | 4.26096e6 | − | 2.15461e6i | 0.631736 | − | 0.319445i | ||||
\(540\) | −2.59583e6 | − | 882469.i | −0.383082 | − | 0.130231i | ||||
\(541\) | − | 2.77036e6i | − | 0.406952i | −0.979080 | − | 0.203476i | \(-0.934776\pi\) | ||
0.979080 | − | 0.203476i | \(-0.0652238\pi\) | |||||||
\(542\) | − | 1.05258e7i | − | 1.53907i | ||||||
\(543\) | −8.46606e6 | + | 3.72364e6i | −1.23220 | + | 0.541961i | ||||
\(544\) | −2.10322e6 | −0.304711 | ||||||||
\(545\) | 1.98737e6 | 0.286607 | ||||||||
\(546\) | −9.04215e6 | + | 3.97702e6i | −1.29805 | + | 0.570922i | ||||
\(547\) | − | 9.31603e6i | − | 1.33126i | −0.746282 | − | 0.665630i | \(-0.768163\pi\) | ||
0.746282 | − | 0.665630i | \(-0.231837\pi\) | |||||||
\(548\) | − | 961236.i | − | 0.136735i | ||||||
\(549\) | 305041. | + | 279687.i | 0.0431945 | + | 0.0396043i | ||||
\(550\) | 739151. | − | 373761.i | 0.104190 | − | 0.0526851i | ||||
\(551\) | 2.49694e6i | 0.350372i | ||||||||
\(552\) | −4.12274e6 | − | 9.37345e6i | −0.575888 | − | 1.30934i | ||||
\(553\) | 438204. | 0.0609346 | ||||||||
\(554\) | 8.84639e6i | 1.22459i | ||||||||
\(555\) | 1.86420e6 | + | 4.23844e6i | 0.256898 | + | 0.584082i | ||||
\(556\) | 5.06794e6i | 0.695256i | ||||||||
\(557\) | −109865. | −0.0150045 | −0.00750225 | − | 0.999972i | \(-0.502388\pi\) | ||||
−0.00750225 | + | 0.999972i | \(0.502388\pi\) | |||||||
\(558\) | 4.93774e6 | − | 5.38535e6i | 0.671340 | − | 0.732198i | ||||
\(559\) | 6.57999e6 | 0.890627 | ||||||||
\(560\) | 4.98535e6 | 0.671778 | ||||||||
\(561\) | −2.03688e6 | + | 2.47669e6i | −0.273248 | + | 0.332249i | ||||
\(562\) | −531803. | −0.0710248 | ||||||||
\(563\) | −4.75207e6 | −0.631847 | −0.315924 | − | 0.948785i | \(-0.602314\pi\) | ||||
−0.315924 | + | 0.948785i | \(0.602314\pi\) | |||||||
\(564\) | −1.53129e6 | − | 3.48154e6i | −0.202703 | − | 0.460865i | ||||
\(565\) | 4.54671e6 | 0.599206 | ||||||||
\(566\) | 9.13279e6i | 1.19829i | ||||||||
\(567\) | −9.96683e6 | + | 865960.i | −1.30197 | + | 0.113120i | ||||
\(568\) | 3.40957e6i | 0.443434i | ||||||||
\(569\) | −76851.0 | −0.00995105 | −0.00497552 | − | 0.999988i | \(-0.501584\pi\) | ||||
−0.00497552 | + | 0.999988i | \(0.501584\pi\) | |||||||
\(570\) | 7.16373e6 | − | 3.15083e6i | 0.923532 | − | 0.406199i | ||||
\(571\) | 9.51570e6i | 1.22138i | 0.791870 | + | 0.610689i | \(0.209108\pi\) | ||||
−0.791870 | + | 0.610689i | \(0.790892\pi\) | |||||||
\(572\) | 1.83407e6 | + | 3.62707e6i | 0.234383 | + | 0.463517i | ||||
\(573\) | −2.72666e6 | − | 6.19933e6i | −0.346932 | − | 0.788784i | ||||
\(574\) | 1.34350e7i | 1.70199i | ||||||||
\(575\) | 1.54423e6i | 0.194780i | ||||||||
\(576\) | 5.58876e6 | − | 6.09539e6i | 0.701875 | − | 0.765501i | ||||
\(577\) | 3.79444e6 | 0.474470 | 0.237235 | − | 0.971452i | \(-0.423759\pi\) | ||||
0.237235 | + | 0.971452i | \(0.423759\pi\) | |||||||
\(578\) | −5.16382e6 | −0.642912 | ||||||||
\(579\) | −448490. | − | 1.01969e6i | −0.0555976 | − | 0.126407i | ||||
\(580\) | − | 962228.i | − | 0.118770i | ||||||
\(581\) | 5.42055e6i | 0.666198i | ||||||||
\(582\) | −6.60897e6 | + | 2.90683e6i | −0.808772 | + | 0.355724i | ||||
\(583\) | −3.39344e6 | − | 6.71087e6i | −0.413493 | − | 0.817726i | ||||
\(584\) | 3.27101e6i | 0.396872i | ||||||||
\(585\) | 8.24370e6 | − | 8.99101e6i | 0.995939 | − | 1.08622i | ||||
\(586\) | −3.90221e6 | −0.469425 | ||||||||
\(587\) | − | 1.06797e7i | − | 1.27927i | −0.768679 | − | 0.639635i | \(-0.779085\pi\) | ||
0.768679 | − | 0.639635i | \(-0.220915\pi\) | |||||||
\(588\) | −2.05158e6 | + | 902351.i | −0.244707 | + | 0.107630i | ||||
\(589\) | − | 1.26545e7i | − | 1.50299i | ||||||
\(590\) | −1.56176e6 | −0.184708 | ||||||||
\(591\) | −1.29814e7 | + | 5.70962e6i | −1.52880 | + | 0.672417i | ||||
\(592\) | −2.43632e6 | −0.285713 | ||||||||
\(593\) | −1.56261e6 | −0.182480 | −0.0912400 | − | 0.995829i | \(-0.529083\pi\) | ||||
−0.0912400 | + | 0.995829i | \(0.529083\pi\) | |||||||
\(594\) | −949815. | − | 6.71723e6i | −0.110452 | − | 0.781132i | ||||
\(595\) | 5.20169e6 | 0.602354 | ||||||||
\(596\) | 748913. | 0.0863606 | ||||||||
\(597\) | −2.53716e6 | + | 1.11592e6i | −0.291348 | + | 0.128144i | ||||
\(598\) | 1.24885e7 | 1.42810 | ||||||||
\(599\) | − | 8.24346e6i | − | 0.938734i | −0.883003 | − | 0.469367i | \(-0.844482\pi\) | ||
0.883003 | − | 0.469367i | \(-0.155518\pi\) | |||||||
\(600\) | −1.29831e6 | + | 571037.i | −0.147231 | + | 0.0647569i | ||||
\(601\) | 3.24701e6i | 0.366689i | 0.983049 | + | 0.183344i | \(0.0586923\pi\) | ||||
−0.983049 | + | 0.183344i | \(0.941308\pi\) | |||||||
\(602\) | −5.93616e6 | −0.667597 | ||||||||
\(603\) | −4.81792e6 | + | 5.25467e6i | −0.539593 | + | 0.588507i | ||||
\(604\) | 435497.i | 0.0485728i | ||||||||
\(605\) | −7.76900e6 | − | 5.71775e6i | −0.862933 | − | 0.635092i | ||||
\(606\) | 1.54660e6 | − | 680242.i | 0.171078 | − | 0.0752457i | ||||
\(607\) | 4.58595e6i | 0.505194i | 0.967572 | + | 0.252597i | \(0.0812846\pi\) | ||||
−0.967572 | + | 0.252597i | \(0.918715\pi\) | |||||||
\(608\) | − | 7.70653e6i | − | 0.845474i | ||||||
\(609\) | −1.41360e6 | − | 3.21396e6i | −0.154449 | − | 0.351154i | ||||
\(610\) | 455233. | 0.0495347 | ||||||||
\(611\) | 1.69218e7 | 1.83376 | ||||||||
\(612\) | 1.01724e6 | − | 1.10946e6i | 0.109786 | − | 0.119738i | ||||
\(613\) | 1.50334e7i | 1.61587i | 0.589274 | + | 0.807933i | \(0.299414\pi\) | ||||
−0.589274 | + | 0.807933i | \(0.700586\pi\) | |||||||
\(614\) | 9.92257e6i | 1.06219i | ||||||||
\(615\) | −6.67950e6 | − | 1.51865e7i | −0.712125 | − | 1.61909i | ||||
\(616\) | −6.03615e6 | − | 1.19371e7i | −0.640926 | − | 1.26750i | ||||
\(617\) | 1.03976e7i | 1.09956i | 0.835308 | + | 0.549782i | \(0.185289\pi\) | ||||
−0.835308 | + | 0.549782i | \(0.814711\pi\) | |||||||
\(618\) | 6.89910e6 | − | 3.03444e6i | 0.726643 | − | 0.319601i | ||||
\(619\) | 7.96319e6 | 0.835335 | 0.417667 | − | 0.908600i | \(-0.362848\pi\) | ||||
0.417667 | + | 0.908600i | \(0.362848\pi\) | |||||||
\(620\) | 4.87656e6i | 0.509489i | ||||||||
\(621\) | 1.19751e7 | + | 4.07100e6i | 1.24609 | + | 0.423616i | ||||
\(622\) | − | 9.11704e6i | − | 0.944883i | ||||||
\(623\) | −1.08040e7 | −1.11523 | ||||||||
\(624\) | 2.58408e6 | + | 5.87516e6i | 0.265671 | + | 0.604030i | ||||
\(625\) | −1.09970e7 | −1.12609 | ||||||||
\(626\) | 1.09867e7 | 1.12055 | ||||||||
\(627\) | −9.07496e6 | − | 7.46343e6i | −0.921883 | − | 0.758175i | ||||
\(628\) | 787724. | 0.0797031 | ||||||||
\(629\) | −2.54204e6 | −0.256186 | ||||||||
\(630\) | −7.43708e6 | + | 8.11126e6i | −0.746536 | + | 0.814211i | ||||
\(631\) | −3.40838e6 | −0.340780 | −0.170390 | − | 0.985377i | \(-0.554503\pi\) | ||||
−0.170390 | + | 0.985377i | \(0.554503\pi\) | |||||||
\(632\) | − | 508839.i | − | 0.0506743i | ||||||
\(633\) | 2.03117e6 | + | 4.61807e6i | 0.201483 | + | 0.458090i | ||||
\(634\) | 264788.i | 0.0261622i | ||||||||
\(635\) | 1.54684e7 | 1.52233 | ||||||||
\(636\) | 1.42117e6 | + | 3.23118e6i | 0.139317 | + | 0.316751i | ||||
\(637\) | − | 9.97156e6i | − | 0.973677i | ||||||
\(638\) | 2.12471e6 | − | 1.07439e6i | 0.206656 | − | 0.104498i | ||||
\(639\) | −3.10410e6 | − | 2.84610e6i | −0.300735 | − | 0.275739i | ||||
\(640\) | − | 1.23229e6i | − | 0.118922i | ||||||
\(641\) | 3.31964e6i | 0.319114i | 0.987189 | + | 0.159557i | \(0.0510066\pi\) | ||||
−0.987189 | + | 0.159557i | \(0.948993\pi\) | |||||||
\(642\) | −7.36290e6 | + | 3.23844e6i | −0.705036 | + | 0.310097i | ||||
\(643\) | 1.41646e6 | 0.135107 | 0.0675534 | − | 0.997716i | \(-0.478481\pi\) | ||||
0.0675534 | + | 0.997716i | \(0.478481\pi\) | |||||||
\(644\) | 6.83621e6 | 0.649532 | ||||||||
\(645\) | 6.71005e6 | − | 2.95129e6i | 0.635077 | − | 0.279327i | ||||
\(646\) | 4.29650e6i | 0.405074i | ||||||||
\(647\) | − | 1.40678e7i | − | 1.32119i | −0.750742 | − | 0.660596i | \(-0.770304\pi\) | ||
0.750742 | − | 0.660596i | \(-0.229696\pi\) | |||||||
\(648\) | 1.00555e6 | + | 1.15734e7i | 0.0940729 | + | 1.08274i | ||||
\(649\) | 1.05809e6 | + | 2.09248e6i | 0.0986078 | + | 0.195007i | ||||
\(650\) | − | 1.72977e6i | − | 0.160585i | ||||||
\(651\) | 7.16412e6 | + | 1.62883e7i | 0.662537 | + | 1.50634i | ||||
\(652\) | −3.67503e6 | −0.338565 | ||||||||
\(653\) | 1.38283e6i | 0.126907i | 0.997985 | + | 0.0634535i | \(0.0202114\pi\) | ||||
−0.997985 | + | 0.0634535i | \(0.979789\pi\) | |||||||
\(654\) | −929326. | − | 2.11291e6i | −0.0849618 | − | 0.193169i | ||||
\(655\) | 1.11379e7i | 1.01438i | ||||||||
\(656\) | 8.72942e6 | 0.792001 | ||||||||
\(657\) | −2.97795e6 | − | 2.73044e6i | −0.269156 | − | 0.246785i | ||||
\(658\) | −1.52660e7 | −1.37455 | ||||||||
\(659\) | −9.61639e6 | −0.862578 | −0.431289 | − | 0.902214i | \(-0.641941\pi\) | ||||
−0.431289 | + | 0.902214i | \(0.641941\pi\) | |||||||
\(660\) | 3.49715e6 | + | 2.87613e6i | 0.312504 | + | 0.257009i | ||||
\(661\) | −3.17414e6 | −0.282568 | −0.141284 | − | 0.989969i | \(-0.545123\pi\) | ||||
−0.141284 | + | 0.989969i | \(0.545123\pi\) | |||||||
\(662\) | 6.16719e6 | 0.546943 | ||||||||
\(663\) | 2.69621e6 | + | 6.13011e6i | 0.238216 | + | 0.541607i | ||||
\(664\) | 6.29431e6 | 0.554023 | ||||||||
\(665\) | 1.90598e7i | 1.67134i | ||||||||
\(666\) | 3.63446e6 | − | 3.96393e6i | 0.317508 | − | 0.346291i | ||||
\(667\) | 4.43894e6i | 0.386336i | ||||||||
\(668\) | 5.47221e6 | 0.474484 | ||||||||
\(669\) | −189378. | + | 83294.5i | −0.0163593 | + | 0.00719534i | ||||
\(670\) | 7.84188e6i | 0.674891i | ||||||||
\(671\) | −308420. | − | 609931.i | −0.0264445 | − | 0.0522967i | ||||
\(672\) | 4.36293e6 | + | 9.91955e6i | 0.372696 | + | 0.847361i | ||||
\(673\) | − | 6.37989e6i | − | 0.542969i | −0.962443 | − | 0.271485i | \(-0.912485\pi\) | ||
0.962443 | − | 0.271485i | \(-0.0875146\pi\) | |||||||
\(674\) | − | 6.21113e6i | − | 0.526649i | ||||||
\(675\) | 563871. | − | 1.65866e6i | 0.0476343 | − | 0.140119i | ||||
\(676\) | 4.00132e6 | 0.336772 | ||||||||
\(677\) | −2.33822e6 | −0.196071 | −0.0980356 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980356 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(678\) | −2.12612e6 | − | 4.83394e6i | −0.177629 | − | 0.403856i | ||||
\(679\) | − | 1.75838e7i | − | 1.46365i | ||||||
\(680\) | − | 6.04016e6i | − | 0.500929i | ||||||
\(681\) | −4.02191e6 | + | 1.76896e6i | −0.332327 | + | 0.146168i | ||||
\(682\) | −1.07680e7 | + | 5.44499e6i | −0.886492 | + | 0.448266i | ||||
\(683\) | 1.64219e7i | 1.34701i | 0.739183 | + | 0.673505i | \(0.235212\pi\) | ||||
−0.739183 | + | 0.673505i | \(0.764788\pi\) | |||||||
\(684\) | 4.06522e6 | + | 3.72733e6i | 0.332234 | + | 0.304619i | ||||
\(685\) | 4.76435e6 | 0.387952 | ||||||||
\(686\) | − | 3.71179e6i | − | 0.301143i | ||||||
\(687\) | 1.93764e7 | − | 8.52235e6i | 1.56632 | − | 0.688918i | ||||
\(688\) | 3.85703e6i | 0.310658i | ||||||||
\(689\) | −1.57049e7 | −1.26034 | ||||||||
\(690\) | 1.27354e7 | − | 5.60141e6i | 1.01833 | − | 0.447893i | ||||
\(691\) | −8.80612e6 | −0.701600 | −0.350800 | − | 0.936450i | \(-0.614090\pi\) | ||||
−0.350800 | + | 0.936450i | \(0.614090\pi\) | |||||||
\(692\) | −6.92803e6 | −0.549977 | ||||||||
\(693\) | 1.59062e7 | + | 4.46899e6i | 1.25816 | + | 0.353489i | ||||
\(694\) | 1.86554e7 | 1.47030 | ||||||||
\(695\) | −2.51192e7 | −1.97262 | ||||||||
\(696\) | −3.73203e6 | + | 1.64146e6i | −0.292026 | + | 0.128442i | ||||
\(697\) | 9.10823e6 | 0.710153 | ||||||||
\(698\) | − | 7.77338e6i | − | 0.603909i | ||||||
\(699\) | 955967. | − | 420464.i | 0.0740031 | − | 0.0325489i | ||||
\(700\) | − | 946877.i | − | 0.0730380i | ||||||
\(701\) | 1.86560e7 | 1.43392 | 0.716958 | − | 0.697117i | \(-0.245534\pi\) | ||||
0.716958 | + | 0.697117i | \(0.245534\pi\) | |||||||
\(702\) | −1.34139e7 | − | 4.56013e6i | −1.02733 | − | 0.349249i | ||||
\(703\) | − | 9.31442e6i | − | 0.710833i | ||||||
\(704\) | −1.21878e7 | + | 6.16290e6i | −0.926813 | + | 0.468655i | ||||
\(705\) | 1.72562e7 | − | 7.58983e6i | 1.30759 | − | 0.575121i | ||||
\(706\) | − | 1.25268e7i | − | 0.945867i | ||||||
\(707\) | 4.11486e6i | 0.309604i | ||||||||
\(708\) | −443129. | − | 1.00750e6i | −0.0332236 | − | 0.0755371i | ||||
\(709\) | −1.00665e7 | −0.752076 | −0.376038 | − | 0.926604i | \(-0.622714\pi\) | ||||
−0.376038 | + | 0.926604i | \(0.622714\pi\) | |||||||
\(710\) | −4.63245e6 | −0.344878 | ||||||||
\(711\) | 463251. | + | 424747.i | 0.0343671 | + | 0.0315106i | ||||
\(712\) | 1.25455e7i | 0.927444i | ||||||||
\(713\) | − | 2.24965e7i | − | 1.65726i | ||||||
\(714\) | −2.43240e6 | − | 5.53029e6i | −0.178562 | − | 0.405978i | ||||
\(715\) | −1.79775e7 | + | 9.09057e6i | −1.31512 | + | 0.665007i | ||||
\(716\) | − | 4.00287e6i | − | 0.291803i | ||||||
\(717\) | 5.47369e6 | − | 2.40750e6i | 0.397633 | − | 0.174892i | ||||
\(718\) | 2.66078e6 | 0.192618 | ||||||||
\(719\) | − | 8.33326e6i | − | 0.601164i | −0.953756 | − | 0.300582i | \(-0.902819\pi\) | ||
0.953756 | − | 0.300582i | \(-0.0971809\pi\) | |||||||
\(720\) | 5.27031e6 | + | 4.83226e6i | 0.378883 | + | 0.347391i | ||||
\(721\) | 1.83557e7i | 1.31502i | ||||||||
\(722\) | −4.69296e6 | −0.335045 | ||||||||
\(723\) | 146656. | + | 333437.i | 0.0104341 | + | 0.0237229i | ||||
\(724\) | −7.16971e6 | −0.508341 | ||||||||
\(725\) | 614834. | 0.0434423 | ||||||||
\(726\) | −2.44604e6 | + | 1.09335e7i | −0.172235 | + | 0.769871i | ||||
\(727\) | 1.38279e7 | 0.970333 | 0.485167 | − | 0.874422i | \(-0.338759\pi\) | ||||
0.485167 | + | 0.874422i | \(0.338759\pi\) | |||||||
\(728\) | −2.79354e7 | −1.95356 | ||||||||
\(729\) | −1.13759e7 | − | 8.74530e6i | −0.792805 | − | 0.609475i | ||||
\(730\) | −4.44420e6 | −0.308664 | ||||||||
\(731\) | 4.02440e6i | 0.278553i | ||||||||
\(732\) | 129166. | + | 293672.i | 0.00890987 | + | 0.0202574i | ||||
\(733\) | − | 1.35485e7i | − | 0.931390i | −0.884945 | − | 0.465695i | \(-0.845804\pi\) | ||
0.884945 | − | 0.465695i | \(-0.154196\pi\) | |||||||
\(734\) | −1.54710e7 | −1.05994 | ||||||||
\(735\) | −4.47249e6 | − | 1.01687e7i | −0.305373 | − | 0.694296i | ||||
\(736\) | − | 1.37003e7i | − | 0.932258i | ||||||
\(737\) | 1.05067e7 | − | 5.31286e6i | 0.712522 | − | 0.360296i | ||||
\(738\) | −1.30224e7 | + | 1.42029e7i | −0.880138 | + | 0.959924i | ||||
\(739\) | − | 1.17902e7i | − | 0.794164i | −0.917783 | − | 0.397082i | \(-0.870023\pi\) | ||
0.917783 | − | 0.397082i | \(-0.129977\pi\) | |||||||
\(740\) | 3.58944e6i | 0.240961i | ||||||||
\(741\) | −2.24617e7 | + | 9.87934e6i | −1.50278 | + | 0.660971i | ||||
\(742\) | 1.41682e7 | 0.944724 | ||||||||
\(743\) | −1.50901e6 | −0.100281 | −0.0501407 | − | 0.998742i | \(-0.515967\pi\) | ||||
−0.0501407 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(744\) | 1.89139e7 | − | 8.31892e6i | 1.25270 | − | 0.550979i | ||||
\(745\) | 3.71198e6i | 0.245028i | ||||||||
\(746\) | − | 1.97039e7i | − | 1.29630i | ||||||
\(747\) | −5.25409e6 | + | 5.73039e6i | −0.344506 | + | 0.375736i | ||||
\(748\) | −2.21836e6 | + | 1.12174e6i | −0.144970 | + | 0.0733059i | ||||
\(749\) | − | 1.95897e7i | − | 1.27592i | ||||||
\(750\) | 4.46655e6 | + | 1.01551e7i | 0.289947 | + | 0.659224i | ||||
\(751\) | 1.29385e7 | 0.837112 | 0.418556 | − | 0.908191i | \(-0.362536\pi\) | ||||
0.418556 | + | 0.908191i | \(0.362536\pi\) | |||||||
\(752\) | 9.91913e6i | 0.639630i | ||||||||
\(753\) | 1.08753e7 | + | 2.47261e7i | 0.698964 | + | 1.58916i | ||||
\(754\) | − | 4.97229e6i | − | 0.318513i | ||||||
\(755\) | −2.15854e6 | −0.137814 | ||||||||
\(756\) | −7.34276e6 | − | 2.49621e6i | −0.467256 | − | 0.158846i | ||||
\(757\) | −2.29160e7 | −1.45345 | −0.726724 | − | 0.686929i | \(-0.758958\pi\) | ||||
−0.726724 | + | 0.686929i | \(0.758958\pi\) | |||||||
\(758\) | −1.18335e7 | −0.748065 | ||||||||
\(759\) | −1.61331e7 | − | 1.32681e7i | −1.01651 | − | 0.835999i | ||||
\(760\) | 2.21321e7 | 1.38991 | ||||||||
\(761\) | 2.50919e7 | 1.57062 | 0.785311 | − | 0.619101i | \(-0.212503\pi\) | ||||
0.785311 | + | 0.619101i | \(0.212503\pi\) | |||||||
\(762\) | −7.23326e6 | − | 1.64455e7i | −0.451281 | − | 1.02603i | ||||
\(763\) | 5.62161e6 | 0.349582 | ||||||||
\(764\) | − | 5.25007e6i | − | 0.325410i | ||||||
\(765\) | 5.49901e6 | + | 5.04195e6i | 0.339728 | + | 0.311491i | ||||
\(766\) | 7.16995e6i | 0.441513i | ||||||||
\(767\) | 4.89686e6 | 0.300559 | ||||||||
\(768\) | 1.42293e7 | − | 6.25849e6i | 0.870523 | − | 0.382883i | ||||
\(769\) | 4.73793e6i | 0.288917i | 0.989511 | + | 0.144458i | \(0.0461440\pi\) | ||||
−0.989511 | + | 0.144458i | \(0.953856\pi\) | |||||||
\(770\) | 1.62185e7 | − | 8.20108e6i | 0.985787 | − | 0.498476i | ||||
\(771\) | −525568. | − | 1.19493e6i | −0.0318415 | − | 0.0723947i | ||||
\(772\) | − | 863548.i | − | 0.0521487i | ||||||
\(773\) | − | 2.64966e6i | − | 0.159493i | −0.996815 | − | 0.0797466i | \(-0.974589\pi\) | ||
0.996815 | − | 0.0797466i | \(-0.0254111\pi\) | |||||||
\(774\) | −6.27546e6 | − | 5.75386e6i | −0.376525 | − | 0.345229i | ||||
\(775\) | −3.11597e6 | −0.186354 | ||||||||
\(776\) | −2.04182e7 | −1.21720 | ||||||||
\(777\) | 5.27321e6 | + | 1.19892e7i | 0.313345 | + | 0.712420i | ||||
\(778\) | 1.08768e6i | 0.0644245i | ||||||||
\(779\) | 3.33739e7i | 1.97044i | ||||||||
\(780\) | 8.65589e6 | − | 3.80713e6i | 0.509419 | − | 0.224059i | ||||
\(781\) | 3.13848e6 | + | 6.20666e6i | 0.184116 | + | 0.364108i | ||||
\(782\) | 7.63813e6i | 0.446653i | ||||||||
\(783\) | 1.62086e6 | − | 4.76786e6i | 0.0944804 | − | 0.277920i | ||||
\(784\) | 5.84509e6 | 0.339626 | ||||||||
\(785\) | 3.90435e6i | 0.226138i | ||||||||
\(786\) | 1.18415e7 | − | 5.20825e6i | 0.683675 | − | 0.300702i | ||||
\(787\) | − | 6.36462e6i | − | 0.366299i | −0.983085 | − | 0.183150i | \(-0.941371\pi\) | ||
0.983085 | − | 0.183150i | \(-0.0586292\pi\) | |||||||
\(788\) | −1.09936e7 | −0.630703 | ||||||||
\(789\) | −2.07203e7 | + | 9.11345e6i | −1.18496 | + | 0.521183i | ||||
\(790\) | 691340. | 0.0394116 | ||||||||
\(791\) | 1.28611e7 | 0.730867 | ||||||||
\(792\) | 5.18936e6 | − | 1.84702e7i | 0.293968 | − | 1.04631i | ||||
\(793\) | −1.42737e6 | −0.0806035 | ||||||||
\(794\) | 810656. | 0.0456337 | ||||||||
\(795\) | −1.60153e7 | + | 7.04403e6i | −0.898705 | + | 0.395279i | ||||
\(796\) | −2.14866e6 | −0.120195 | ||||||||
\(797\) | 2.74248e7i | 1.52932i | 0.644436 | + | 0.764658i | \(0.277092\pi\) | ||||
−0.644436 | + | 0.764658i | \(0.722908\pi\) | |||||||
\(798\) | 2.02638e7 | − | 8.91267e6i | 1.12646 | − | 0.495451i | ||||
\(799\) | 1.03496e7i | 0.573529i | ||||||||
\(800\) | −1.89762e6 | −0.104830 | ||||||||
\(801\) | −1.14215e7 | − | 1.04722e7i | −0.628988 | − | 0.576709i | ||||
\(802\) | − | 1.44272e7i | − | 0.792040i | ||||||
\(803\) | 3.01093e6 | + | 5.95443e6i | 0.164783 | + | 0.325875i | ||||
\(804\) | −5.05881e6 | + | 2.22503e6i | −0.276000 | + | 0.121393i | ||||
\(805\) | 3.38836e7i | 1.84289i | ||||||||
\(806\) | 2.51995e7i | 1.36633i | ||||||||
\(807\) | 2.10457e6 | + | 4.78495e6i | 0.113758 | + | 0.258639i | ||||
\(808\) | 4.77815e6 | 0.257473 | ||||||||
\(809\) | 8.49113e6 | 0.456136 | 0.228068 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228068 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(810\) | −1.57243e7 | + | 1.36620e6i | −0.842093 | + | 0.0731646i | ||||
\(811\) | − | 1.66787e7i | − | 0.890452i | −0.895418 | − | 0.445226i | \(-0.853123\pi\) | ||
0.895418 | − | 0.445226i | \(-0.146877\pi\) | |||||||
\(812\) | − | 2.72183e6i | − | 0.144867i | ||||||
\(813\) | 1.48028e7 | + | 3.36557e7i | 0.785450 | + | 1.78580i | ||||
\(814\) | −7.92589e6 | + | 4.00783e6i | −0.419264 | + | 0.212006i | ||||
\(815\) | − | 1.82153e7i | − | 0.960597i | ||||||
\(816\) | −3.59332e6 | + | 1.58046e6i | −0.188917 | + | 0.0830915i | ||||
\(817\) | −1.47460e7 | −0.772894 | ||||||||
\(818\) | − | 1.21858e7i | − | 0.636750i | ||||||
\(819\) | 2.33187e7 | − | 2.54326e7i | 1.21477 | − | 1.32489i | ||||
\(820\) | − | 1.28611e7i | − | 0.667948i | ||||||
\(821\) | 2.77497e7 | 1.43681 | 0.718406 | − | 0.695625i | \(-0.244872\pi\) | ||||
0.718406 | + | 0.695625i | \(0.244872\pi\) | |||||||
\(822\) | −2.22789e6 | − | 5.06533e6i | −0.115004 | − | 0.261474i | ||||
\(823\) | 1.20865e7 | 0.622018 | 0.311009 | − | 0.950407i | \(-0.399333\pi\) | ||||
0.311009 | + | 0.950407i | \(0.399333\pi\) | |||||||
\(824\) | 2.13145e7 | 1.09360 | ||||||||
\(825\) | −1.83776e6 | + | 2.23458e6i | −0.0940056 | + | 0.114304i | ||||
\(826\) | −4.41772e6 | −0.225293 | ||||||||
\(827\) | 2.83484e7 | 1.44133 | 0.720667 | − | 0.693281i | \(-0.243836\pi\) | ||||
0.720667 | + | 0.693281i | \(0.243836\pi\) | |||||||
\(828\) | 7.22696e6 | + | 6.62628e6i | 0.366336 | + | 0.335887i | ||||
\(829\) | 3.06974e7 | 1.55137 | 0.775685 | − | 0.631120i | \(-0.217404\pi\) | ||||
0.775685 | + | 0.631120i | \(0.217404\pi\) | |||||||
\(830\) | 8.55183e6i | 0.430887i | ||||||||
\(831\) | −1.24410e7 | − | 2.82858e7i | −0.624960 | − | 1.42091i | ||||
\(832\) | 2.85220e7i | 1.42847i | ||||||||
\(833\) | 6.09873e6 | 0.304528 | ||||||||
\(834\) | 1.17462e7 | + | 2.67061e7i | 0.584764 | + | 1.32952i | ||||
\(835\) | 2.71230e7i | 1.34624i | ||||||||
\(836\) | −4.11024e6 | − | 8.12841e6i | −0.203400 | − | 0.402244i | ||||
\(837\) | −8.21452e6 | + | 2.41635e7i | −0.405292 | + | 1.19219i | ||||
\(838\) | 1.03860e7i | 0.510901i | ||||||||
\(839\) | 150471.i | 0.00737987i | 0.999993 | + | 0.00368993i | \(0.00117454\pi\) | ||||
−0.999993 | + | 0.00368993i | \(0.998825\pi\) | |||||||
\(840\) | −2.84875e7 | + | 1.25297e7i | −1.39302 | + | 0.612693i | ||||
\(841\) | −1.87438e7 | −0.913834 | ||||||||
\(842\) | 9.26458e6 | 0.450345 | ||||||||
\(843\) | 1.70041e6 | − | 747893.i | 0.0824108 | − | 0.0362469i | ||||
\(844\) | 3.91093e6i | 0.188984i | ||||||||
\(845\) | 1.98325e7i | 0.955511i | ||||||||
\(846\) | −1.61386e7 | − | 1.47972e7i | −0.775247 | − | 0.710811i | ||||
\(847\) | −2.19760e7 | − | 1.61736e7i | −1.05254 | − | 0.774639i | ||||
\(848\) | − | 9.20582e6i | − | 0.439615i | ||||||
\(849\) | −1.28438e7 | − | 2.92016e7i | −0.611538 | − | 1.39039i | ||||
\(850\) | 1.05795e6 | 0.0502248 | ||||||||
\(851\) | − | 1.65588e7i | − | 0.783798i | ||||||
\(852\) | −1.31439e6 | − | 2.98840e6i | −0.0620336 | − | 0.141039i | ||||
\(853\) | − | 1.36865e7i | − | 0.644048i | −0.946731 | − | 0.322024i | \(-0.895637\pi\) | ||
0.946731 | − | 0.322024i | \(-0.104363\pi\) | |||||||
\(854\) | 1.28771e6 | 0.0604188 | ||||||||
\(855\) | −1.84745e7 | + | 2.01492e7i | −0.864285 | + | 0.942633i | ||||
\(856\) | −2.27474e7 | −1.06108 | ||||||||
\(857\) | 1.37392e7 | 0.639013 | 0.319507 | − | 0.947584i | \(-0.396483\pi\) | ||||
0.319507 | + | 0.947584i | \(0.396483\pi\) | |||||||
\(858\) | 1.80714e7 | + | 1.48623e7i | 0.838059 | + | 0.689237i | ||||
\(859\) | −2.18827e7 | −1.01186 | −0.505928 | − | 0.862576i | \(-0.668850\pi\) | ||||
−0.505928 | + | 0.862576i | \(0.668850\pi\) | |||||||
\(860\) | 5.68258e6 | 0.261999 | ||||||||
\(861\) | −1.88941e7 | − | 4.29576e7i | −0.868598 | − | 1.97484i | ||||
\(862\) | 1.92916e7 | 0.884300 | ||||||||
\(863\) | − | 8.18461e6i | − | 0.374086i | −0.982352 | − | 0.187043i | \(-0.940110\pi\) | ||
0.982352 | − | 0.187043i | \(-0.0598903\pi\) | |||||||
\(864\) | −5.00262e6 | + | 1.47155e7i | −0.227989 | + | 0.670641i | ||||
\(865\) | − | 3.43387e7i | − | 1.56043i | ||||||
\(866\) | −1.00023e7 | −0.453215 | ||||||||
\(867\) | 1.65110e7 | − | 7.26207e6i | 0.745978 | − | 0.328105i | ||||
\(868\) | 1.37942e7i | 0.621437i | ||||||||
\(869\) | −468381. | − | 926272.i | −0.0210402 | − | 0.0416092i | ||||
\(870\) | −2.23019e6 | − | 5.07056e6i | −0.0998951 | − | 0.227121i | ||||
\(871\) | − | 2.45880e7i | − | 1.09819i | ||||||
\(872\) | − | 6.52777e6i | − | 0.290719i | ||||||
\(873\) | 1.70438e7 | − | 1.85889e7i | 0.756887 | − | 0.825500i | ||||
\(874\) | −2.79873e7 | −1.23932 | ||||||||
\(875\) | −2.70187e7 | −1.19301 | ||||||||
\(876\) | −1.26098e6 | − | 2.86696e6i | −0.0555198 | − | 0.126230i | ||||
\(877\) | − | 1.11241e7i | − | 0.488387i | −0.969727 | − | 0.244194i | \(-0.921477\pi\) | ||
0.969727 | − | 0.244194i | \(-0.0785232\pi\) | |||||||
\(878\) | − | 3.44153e6i | − | 0.150666i | ||||||
\(879\) | 1.24771e7 | − | 5.48781e6i | 0.544679 | − | 0.239567i | ||||
\(880\) | −5.32867e6 | − | 1.05380e7i | −0.231960 | − | 0.458724i | ||||
\(881\) | 4.13547e7i | 1.79509i | 0.440926 | + | 0.897544i | \(0.354650\pi\) | ||||
−0.440926 | + | 0.897544i | \(0.645350\pi\) | |||||||
\(882\) | −8.71962e6 | + | 9.51007e6i | −0.377421 | + | 0.411635i | ||||
\(883\) | 6.49069e6 | 0.280149 | 0.140074 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140074 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(884\) | 5.19144e6i | 0.223438i | ||||||||
\(885\) | 4.99365e6 | − | 2.19636e6i | 0.214318 | − | 0.0942640i | ||||
\(886\) | 1.95667e7i | 0.837399i | ||||||||
\(887\) | −2.55265e7 | −1.08939 | −0.544693 | − | 0.838636i | \(-0.683354\pi\) | ||||
−0.544693 | + | 0.838636i | \(0.683354\pi\) | |||||||
\(888\) | 1.39217e7 | − | 6.12321e6i | 0.592462 | − | 0.260584i | ||||
\(889\) | 4.37549e7 | 1.85683 | ||||||||
\(890\) | −1.70451e7 | −0.721313 | ||||||||
\(891\) | 1.24837e7 | + | 2.01422e7i | 0.526802 | + | 0.849988i | ||||
\(892\) | −160380. | −0.00674898 | ||||||||
\(893\) | −3.79224e7 | −1.59135 | ||||||||
\(894\) | 3.94648e6 | − | 1.73579e6i | 0.165145 | − | 0.0726361i | ||||
\(895\) | 1.98402e7 | 0.827920 | ||||||||
\(896\) | − | 3.48573e6i | − | 0.145052i | ||||||
\(897\) | −3.99313e7 | + | 1.75630e7i | −1.65704 | + | 0.728818i | ||||
\(898\) | − | 2.95699e7i | − | 1.22365i | ||||||
\(899\) | −8.95696e6 | −0.369625 | ||||||||
\(900\) | 917800. | − | 1.00100e6i | 0.0377695 | − | 0.0411934i | ||||
\(901\) | − | 9.60530e6i | − | 0.394184i | ||||||
\(902\) | 2.83988e7 | − | 1.43602e7i | 1.16221 | − | 0.587685i | ||||
\(903\) | 1.89805e7 | − | 8.34823e6i | 0.774620 | − | 0.340702i | ||||
\(904\) | − | 1.49343e7i | − | 0.607803i | ||||||
\(905\) | − | 3.55366e7i | − | 1.44230i | ||||||
\(906\) | 1.00937e6 | + | 2.29490e6i | 0.0408535 | + | 0.0928845i | ||||
\(907\) | −2.07306e7 | −0.836748 | −0.418374 | − | 0.908275i | \(-0.637400\pi\) | ||||
−0.418374 | + | 0.908275i | \(0.637400\pi\) | |||||||
\(908\) | −3.40606e6 | −0.137100 | ||||||||
\(909\) | −3.98850e6 | + | 4.35007e6i | −0.160103 | + | 0.174617i | ||||
\(910\) | − | 3.79547e7i | − | 1.51937i | ||||||
\(911\) | 2.89435e7i | 1.15546i | 0.816228 | + | 0.577730i | \(0.196061\pi\) | ||||
−0.816228 | + | 0.577730i | \(0.803939\pi\) | |||||||
\(912\) | −5.79103e6 | − | 1.31665e7i | −0.230552 | − | 0.524182i | ||||
\(913\) | 1.14579e7 | − | 5.79385e6i | 0.454914 | − | 0.230033i | ||||
\(914\) | − | 4.66561e6i | − | 0.184732i | ||||||
\(915\) | −1.45558e6 | + | 640211.i | −0.0574757 | + | 0.0252796i | ||||
\(916\) | 1.64094e7 | 0.646181 | ||||||||
\(917\) | 3.15054e7i | 1.23726i | ||||||||
\(918\) | 2.78903e6 | − | 8.20410e6i | 0.109231 | − | 0.321310i | ||||
\(919\) | 2.28240e7i | 0.891462i | 0.895167 | + | 0.445731i | \(0.147056\pi\) | ||||
−0.895167 | + | 0.445731i | \(0.852944\pi\) | |||||||
\(920\) | 3.93454e7 | 1.53258 | ||||||||
\(921\) | −1.39545e7 | − | 3.17268e7i | −0.542081 | − | 1.23247i | ||||
\(922\) | −2.21671e7 | −0.858779 | ||||||||
\(923\) | 1.45249e7 | 0.561189 | ||||||||
\(924\) | 9.89230e6 | + | 8.13563e6i | 0.381169 | + | 0.313481i | ||||
\(925\) | −2.29354e6 | −0.0881357 | ||||||||
\(926\) | −1.39718e7 | −0.535459 | ||||||||
\(927\) | −1.77920e7 | + | 1.94049e7i | −0.680027 | + | 0.741673i | ||||
\(928\) | −5.45477e6 | −0.207925 | ||||||||
\(929\) | − | 3.70762e7i | − | 1.40947i | −0.709470 | − | 0.704736i | \(-0.751066\pi\) | ||
0.709470 | − | 0.704736i | \(-0.248934\pi\) | |||||||
\(930\) | 1.13026e7 | + | 2.56976e7i | 0.428520 | + | 0.974282i | ||||
\(931\) | 2.23467e7i | 0.844965i | ||||||||
\(932\) | 809586. | 0.0305297 | ||||||||
\(933\) | 1.28216e7 | + | 2.91512e7i | 0.482213 | + | 1.09636i | ||||
\(934\) | 3.11288e7i | 1.16760i | ||||||||
\(935\) | −5.55991e6 | − | 1.09953e7i | −0.207988 | − | 0.411318i | ||||
\(936\) | −2.95322e7 | − | 2.70775e7i | −1.10181 | − | 1.01023i | ||||
\(937\) | 4.38476e7i | 1.63154i | 0.578379 | + | 0.815768i | \(0.303685\pi\) | ||||
−0.578379 | + | 0.815768i | \(0.696315\pi\) | |||||||
\(938\) | 2.21821e7i | 0.823182i | ||||||||
\(939\) | −3.51293e7 | + | 1.54510e7i | −1.30018 | + | 0.571862i | ||||
\(940\) | 1.46139e7 | 0.539444 | ||||||||
\(941\) | −1.41203e6 | −0.0519841 | −0.0259920 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259920 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(942\) | 4.15100e6 | − | 1.82574e6i | 0.152414 | − | 0.0670365i | ||||
\(943\) | 5.93307e7i | 2.17270i | ||||||||
\(944\) | 2.87042e6i | 0.104837i | ||||||||
\(945\) | 1.23725e7 | − | 3.63943e7i | 0.450689 | − | 1.32573i | ||||
\(946\) | 6.34496e6 | + | 1.25478e7i | 0.230516 | + | 0.455869i | ||||
\(947\) | − | 2.01772e7i | − | 0.731115i | −0.930789 | − | 0.365557i | \(-0.880878\pi\) | ||
0.930789 | − | 0.365557i | \(-0.119122\pi\) | |||||||
\(948\) | 196158. | + | 445985.i | 0.00708901 | + | 0.0161176i | ||||
\(949\) | 1.39346e7 | 0.502262 | ||||||||
\(950\) | 3.87649e6i | 0.139357i | ||||||||
\(951\) | −372381. | − | 846644.i | −0.0133517 | − | 0.0303563i | ||||
\(952\) | − | 1.70856e7i | − | 0.610996i | ||||||
\(953\) | −1.48197e6 | −0.0528577 | −0.0264289 | − | 0.999651i | \(-0.508414\pi\) | ||||
−0.0264289 | + | 0.999651i | \(0.508414\pi\) | |||||||
\(954\) | 1.49780e7 | + | 1.37331e7i | 0.532824 | + | 0.488538i | ||||
\(955\) | 2.60219e7 | 0.923274 | ||||||||
\(956\) | 4.63554e6 | 0.164042 | ||||||||
\(957\) | −5.28269e6 | + | 6.42335e6i | −0.186456 | + | 0.226716i | ||||
\(958\) | −2.27322e7 | −0.800253 | ||||||||
\(959\) | 1.34768e7 | 0.473195 | ||||||||
\(960\) | 1.27928e7 | + | 2.90857e7i | 0.448010 | + | 1.01860i | ||||
\(961\) | 1.67646e7 | 0.585580 | ||||||||
\(962\) | 1.85483e7i | 0.646199i | ||||||||
\(963\) | 1.89881e7 | − | 2.07094e7i | 0.659806 | − | 0.719618i | ||||
\(964\) | 282380.i | 0.00978681i | ||||||||
\(965\) | 4.28017e6 | 0.147959 | ||||||||
\(966\) | 3.60241e7 | − | 1.58445e7i | 1.24208 | − | 0.546307i | ||||
\(967\) | − | 3.24697e7i | − | 1.11664i | −0.829626 | − | 0.558319i | \(-0.811447\pi\) | ||
0.829626 | − | 0.558319i | \(-0.188553\pi\) | |||||||
\(968\) | −1.87807e7 | + | 2.55183e7i | −0.644204 | + | 0.875314i | ||||
\(969\) | −6.04233e6 | − | 1.37378e7i | −0.206726 | − | 0.470012i | ||||
\(970\) | − | 2.77414e7i | − | 0.946670i | ||||||
\(971\) | − | 4.12664e6i | − | 0.140459i | −0.997531 | − | 0.0702293i | \(-0.977627\pi\) | ||
0.997531 | − | 0.0702293i | \(-0.0223731\pi\) | |||||||
\(972\) | −5.34290e6 | − | 9.75616e6i | −0.181389 | − | 0.331218i | ||||
\(973\) | −7.10540e7 | −2.40606 | ||||||||
\(974\) | 3.51117e7 | 1.18592 | ||||||||
\(975\) | 2.43264e6 | + | 5.53085e6i | 0.0819534 | + | 0.186329i | ||||
\(976\) | − | 836690.i | − | 0.0281151i | ||||||
\(977\) | − | 5.18080e7i | − | 1.73644i | −0.496177 | − | 0.868221i | \(-0.665263\pi\) | ||
0.496177 | − | 0.868221i | \(-0.334737\pi\) | |||||||
\(978\) | −1.93660e7 | + | 8.51776e6i | −0.647429 | + | 0.284759i | ||||
\(979\) | 1.15480e7 | + | 2.28373e7i | 0.385079 | + | 0.761533i | ||||
\(980\) | − | 8.61159e6i | − | 0.286430i | ||||||
\(981\) | 5.94293e6 | + | 5.44898e6i | 0.197164 | + | 0.180777i | ||||
\(982\) | 3.59308e7 | 1.18902 | ||||||||
\(983\) | 1.81166e7i | 0.597990i | 0.954255 | + | 0.298995i | \(0.0966514\pi\) | ||||
−0.954255 | + | 0.298995i | \(0.903349\pi\) | |||||||
\(984\) | −4.98821e7 | + | 2.19397e7i | −1.64232 | + | 0.722342i | ||||
\(985\) | − | 5.44898e7i | − | 1.78947i | ||||||
\(986\) | 3.04111e6 | 0.0996185 | ||||||||
\(987\) | 4.88122e7 | − | 2.14691e7i | 1.59491 | − | 0.701491i | ||||
\(988\) | −1.90222e7 | −0.619968 | ||||||||
\(989\) | −2.62148e7 | −0.852229 | ||||||||
\(990\) | 2.50947e7 | + | 7.05058e6i | 0.813757 | + | 0.228632i | ||||
\(991\) | −1.89585e7 | −0.613224 | −0.306612 | − | 0.951835i | \(-0.599195\pi\) | ||||
−0.306612 | + | 0.951835i | \(0.599195\pi\) | |||||||
\(992\) | 2.76447e7 | 0.891934 | ||||||||
\(993\) | −1.97192e7 | + | 8.67314e6i | −0.634624 | + | 0.279128i | ||||
\(994\) | −1.31037e7 | −0.420656 | ||||||||
\(995\) | − | 1.06498e7i | − | 0.341023i | ||||||
\(996\) | −5.51680e6 | + | 2.42646e6i | −0.176213 | + | 0.0775042i | ||||
\(997\) | 3.68727e6i | 0.117481i | 0.998273 | + | 0.0587405i | \(0.0187084\pi\) | ||||
−0.998273 | + | 0.0587405i | \(0.981292\pi\) | |||||||
\(998\) | −4.06152e7 | −1.29081 | ||||||||
\(999\) | −6.04637e6 | + | 1.77857e7i | −0.191682 | + | 0.563843i |
(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 | 33.6.d.b.32.12 | yes | 16 | |
3.2 | odd | 2 | inner | 33.6.d.b.32.5 | ✓ | 16 | |
11.10 | odd | 2 | inner | 33.6.d.b.32.6 | yes | 16 | |
33.32 | even | 2 | inner | 33.6.d.b.32.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.d.b.32.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
33.6.d.b.32.6 | yes | 16 | 11.10 | odd | 2 | inner | |
33.6.d.b.32.11 | yes | 16 | 33.32 | even | 2 | inner | |
33.6.d.b.32.12 | yes | 16 | 1.1 | even | 1 | trivial |