Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,7,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.8");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83113575602\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.12 | ||
Root | \(15.2632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.7.b.a.8.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.2632i | 1.90790i | 0.299965 | + | 0.953950i | \(0.403025\pi\) | ||||
−0.299965 | + | 0.953950i | \(0.596975\pi\) | |||||||
\(3\) | 26.9946 | − | 0.538759i | 0.999801 | − | 0.0199540i | ||||
\(4\) | −168.965 | −2.64009 | ||||||||
\(5\) | 118.492i | 0.947934i | 0.880543 | + | 0.473967i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473967i | \(0.842822\pi\) | |||||||
\(6\) | 8.22319 | + | 412.025i | 0.0380703 | + | 1.90752i | ||||
\(7\) | −129.642 | −0.377964 | ||||||||
\(8\) | − | 1602.11i | − | 3.12912i | ||||||
\(9\) | 728.419 | − | 29.0872i | 0.999204 | − | 0.0399002i | ||||
\(10\) | −1808.56 | −1.80856 | ||||||||
\(11\) | 356.410i | 0.267776i | 0.990996 | + | 0.133888i | \(0.0427462\pi\) | ||||
−0.990996 | + | 0.133888i | \(0.957254\pi\) | |||||||
\(12\) | −4561.16 | + | 91.0317i | −2.63956 | + | 0.0526804i | ||||
\(13\) | 2041.21 | 0.929091 | 0.464545 | − | 0.885549i | \(-0.346218\pi\) | ||||
0.464545 | + | 0.885549i | \(0.346218\pi\) | |||||||
\(14\) | − | 1978.75i | − | 0.721119i | ||||||
\(15\) | 63.8385 | + | 3198.64i | 0.0189151 | + | 0.947745i | ||||
\(16\) | 13639.5 | 3.32996 | ||||||||
\(17\) | 4813.47i | 0.979742i | 0.871795 | + | 0.489871i | \(0.162956\pi\) | ||||
−0.871795 | + | 0.489871i | \(0.837044\pi\) | |||||||
\(18\) | 443.964 | + | 11118.0i | 0.0761255 | + | 1.90638i | ||||
\(19\) | −1518.92 | −0.221449 | −0.110725 | − | 0.993851i | \(-0.535317\pi\) | ||||
−0.110725 | + | 0.993851i | \(0.535317\pi\) | |||||||
\(20\) | − | 20021.0i | − | 2.50263i | ||||||
\(21\) | −3499.63 | + | 69.8457i | −0.377889 | + | 0.00754192i | ||||
\(22\) | −5439.96 | −0.510890 | ||||||||
\(23\) | 13874.1i | 1.14031i | 0.821538 | + | 0.570154i | \(0.193116\pi\) | ||||
−0.821538 | + | 0.570154i | \(0.806884\pi\) | |||||||
\(24\) | −863.151 | − | 43248.3i | −0.0624386 | − | 3.12850i | ||||
\(25\) | 1584.72 | 0.101422 | ||||||||
\(26\) | 31155.4i | 1.77261i | ||||||||
\(27\) | 19647.7 | − | 1177.64i | 0.998209 | − | 0.0598304i | ||||
\(28\) | 21905.0 | 0.997858 | ||||||||
\(29\) | − | 42346.6i | − | 1.73630i | −0.496301 | − | 0.868151i | \(-0.665309\pi\) | ||
0.496301 | − | 0.868151i | \(-0.334691\pi\) | |||||||
\(30\) | −48821.5 | + | 974.380i | −1.80820 | + | 0.0360882i | ||||
\(31\) | 15583.3 | 0.523089 | 0.261544 | − | 0.965191i | \(-0.415768\pi\) | ||||
0.261544 | + | 0.965191i | \(0.415768\pi\) | |||||||
\(32\) | 105648.i | 3.22412i | ||||||||
\(33\) | 192.019 | + | 9621.15i | 0.00534322 | + | 0.267723i | ||||
\(34\) | −73469.0 | −1.86925 | ||||||||
\(35\) | − | 15361.5i | − | 0.358285i | ||||||
\(36\) | −123078. | + | 4914.73i | −2.63798 | + | 0.105340i | ||||
\(37\) | −7620.26 | −0.150440 | −0.0752202 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752202 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(38\) | − | 23183.6i | − | 0.422503i | ||||||
\(39\) | 55101.8 | − | 1099.72i | 0.928906 | − | 0.0185391i | ||||
\(40\) | 189837. | 2.96620 | ||||||||
\(41\) | − | 55431.0i | − | 0.804269i | −0.915581 | − | 0.402134i | \(-0.868268\pi\) | ||
0.915581 | − | 0.402134i | \(-0.131732\pi\) | |||||||
\(42\) | −1066.07 | − | 53415.6i | −0.0143892 | − | 0.720975i | ||||
\(43\) | 60273.7 | 0.758094 | 0.379047 | − | 0.925378i | \(-0.376252\pi\) | ||||
0.379047 | + | 0.925378i | \(0.376252\pi\) | |||||||
\(44\) | − | 60221.0i | − | 0.706951i | ||||||
\(45\) | 3446.59 | + | 86311.7i | 0.0378227 | + | 0.947179i | ||||
\(46\) | −211763. | −2.17559 | ||||||||
\(47\) | − | 129201.i | − | 1.24444i | −0.782843 | − | 0.622219i | \(-0.786231\pi\) | ||
0.782843 | − | 0.622219i | \(-0.213769\pi\) | |||||||
\(48\) | 368194. | − | 7348.43i | 3.32930 | − | 0.0664463i | ||||
\(49\) | 16807.0 | 0.142857 | ||||||||
\(50\) | 24187.8i | 0.193503i | ||||||||
\(51\) | 2593.30 | + | 129938.i | 0.0195498 | + | 0.979547i | ||||
\(52\) | −344894. | −2.45288 | ||||||||
\(53\) | − | 60972.9i | − | 0.409552i | −0.978809 | − | 0.204776i | \(-0.934353\pi\) | ||
0.978809 | − | 0.204776i | \(-0.0656466\pi\) | |||||||
\(54\) | 17974.6 | + | 299887.i | 0.114150 | + | 1.90448i | ||||
\(55\) | −42231.6 | −0.253834 | ||||||||
\(56\) | 207700.i | 1.18270i | ||||||||
\(57\) | −41002.7 | + | 818.332i | −0.221405 | + | 0.00441881i | ||||
\(58\) | 646346. | 3.31269 | ||||||||
\(59\) | − | 40355.4i | − | 0.196492i | −0.995162 | − | 0.0982462i | \(-0.968677\pi\) | ||
0.995162 | − | 0.0982462i | \(-0.0313233\pi\) | |||||||
\(60\) | −10786.5 | − | 540459.i | −0.0499375 | − | 2.50213i | ||||
\(61\) | −118768. | −0.523252 | −0.261626 | − | 0.965169i | \(-0.584259\pi\) | ||||
−0.261626 | + | 0.965169i | \(0.584259\pi\) | |||||||
\(62\) | 237852.i | 0.998001i | ||||||||
\(63\) | −94433.6 | + | 3770.92i | −0.377663 | + | 0.0150808i | ||||
\(64\) | −739597. | −2.82134 | ||||||||
\(65\) | 241867.i | 0.880716i | ||||||||
\(66\) | −146850. | + | 2930.83i | −0.510788 | + | 0.0101943i | ||||
\(67\) | −133205. | −0.442890 | −0.221445 | − | 0.975173i | \(-0.571077\pi\) | ||||
−0.221445 | + | 0.975173i | \(0.571077\pi\) | |||||||
\(68\) | − | 813311.i | − | 2.58660i | ||||||
\(69\) | 7474.81 | + | 374527.i | 0.0227537 | + | 1.14008i | ||||
\(70\) | 234465. | 0.683573 | ||||||||
\(71\) | 195618.i | 0.546556i | 0.961935 | + | 0.273278i | \(0.0881079\pi\) | ||||
−0.961935 | + | 0.273278i | \(0.911892\pi\) | |||||||
\(72\) | −46600.9 | − | 1.16701e6i | −0.124852 | − | 3.12663i | ||||
\(73\) | 144743. | 0.372075 | 0.186037 | − | 0.982543i | \(-0.440435\pi\) | ||||
0.186037 | + | 0.982543i | \(0.440435\pi\) | |||||||
\(74\) | − | 116310.i | − | 0.287025i | ||||||
\(75\) | 42778.8 | − | 853.780i | 0.101402 | − | 0.00202378i | ||||
\(76\) | 256645. | 0.584644 | ||||||||
\(77\) | − | 46205.6i | − | 0.101210i | ||||||
\(78\) | 16785.3 | + | 841029.i | 0.0353708 | + | 1.77226i | ||||
\(79\) | −894049. | −1.81334 | −0.906672 | − | 0.421837i | \(-0.861385\pi\) | ||||
−0.906672 | + | 0.421837i | \(0.861385\pi\) | |||||||
\(80\) | 1.61617e6i | 3.15659i | ||||||||
\(81\) | 529749. | − | 42375.4i | 0.996816 | − | 0.0797368i | ||||
\(82\) | 846055. | 1.53446 | ||||||||
\(83\) | 287164.i | 0.502223i | 0.967958 | + | 0.251111i | \(0.0807960\pi\) | ||||
−0.967958 | + | 0.251111i | \(0.919204\pi\) | |||||||
\(84\) | 591317. | − | 11801.5i | 0.997660 | − | 0.0199113i | ||||
\(85\) | −570357. | −0.928731 | ||||||||
\(86\) | 919971.i | 1.44637i | ||||||||
\(87\) | −22814.7 | − | 1.14313e6i | −0.0346462 | − | 1.73596i | ||||
\(88\) | 571008. | 0.837903 | ||||||||
\(89\) | − | 799391.i | − | 1.13394i | −0.823739 | − | 0.566969i | \(-0.808116\pi\) | ||
0.823739 | − | 0.566969i | \(-0.191884\pi\) | |||||||
\(90\) | −1.31739e6 | + | 52606.1i | −1.80712 | + | 0.0721620i | ||||
\(91\) | −264626. | −0.351163 | ||||||||
\(92\) | − | 2.34425e6i | − | 3.01051i | ||||||
\(93\) | 420666. | − | 8395.67i | 0.522985 | − | 0.0104377i | ||||
\(94\) | 1.97203e6 | 2.37426 | ||||||||
\(95\) | − | 179979.i | − | 0.209919i | ||||||
\(96\) | 56918.9 | + | 2.85193e6i | 0.0643343 | + | 3.22348i | ||||
\(97\) | 1.17586e6 | 1.28837 | 0.644184 | − | 0.764870i | \(-0.277197\pi\) | ||||
0.644184 | + | 0.764870i | \(0.277197\pi\) | |||||||
\(98\) | 256529.i | 0.272557i | ||||||||
\(99\) | 10367.0 | + | 259616.i | 0.0106843 | + | 0.267563i | ||||
\(100\) | −267762. | −0.267762 | ||||||||
\(101\) | − | 1.40394e6i | − | 1.36265i | −0.731981 | − | 0.681325i | \(-0.761404\pi\) | ||
0.731981 | − | 0.681325i | \(-0.238596\pi\) | |||||||
\(102\) | −1.98327e6 | + | 39582.1i | −1.86888 | + | 0.0372991i | ||||
\(103\) | −1.19969e6 | −1.09788 | −0.548942 | − | 0.835861i | \(-0.684969\pi\) | ||||
−0.548942 | + | 0.835861i | \(0.684969\pi\) | |||||||
\(104\) | − | 3.27024e6i | − | 2.90724i | ||||||
\(105\) | −8276.14 | − | 414677.i | −0.00714924 | − | 0.358214i | ||||
\(106\) | 930642. | 0.781385 | ||||||||
\(107\) | 1.82547e6i | 1.49013i | 0.666994 | + | 0.745063i | \(0.267581\pi\) | ||||
−0.666994 | + | 0.745063i | \(0.732419\pi\) | |||||||
\(108\) | −3.31979e6 | + | 198981.i | −2.63536 | + | 0.157957i | ||||
\(109\) | 698011. | 0.538993 | 0.269496 | − | 0.963001i | \(-0.413143\pi\) | ||||
0.269496 | + | 0.963001i | \(0.413143\pi\) | |||||||
\(110\) | − | 644590.i | − | 0.484290i | ||||||
\(111\) | −205706. | + | 4105.49i | −0.150411 | + | 0.00300190i | ||||
\(112\) | −1.76825e6 | −1.25861 | ||||||||
\(113\) | 1.85528e6i | 1.28580i | 0.765948 | + | 0.642902i | \(0.222270\pi\) | ||||
−0.765948 | + | 0.642902i | \(0.777730\pi\) | |||||||
\(114\) | −12490.4 | − | 625832.i | −0.00843064 | − | 0.422419i | ||||
\(115\) | −1.64397e6 | −1.08094 | ||||||||
\(116\) | 7.15512e6i | 4.58398i | ||||||||
\(117\) | 1.48686e6 | − | 59373.2i | 0.928351 | − | 0.0370709i | ||||
\(118\) | 615953. | 0.374888 | ||||||||
\(119\) | − | 624027.i | − | 0.370308i | ||||||
\(120\) | 5.12457e6 | − | 102276.i | 2.96561 | − | 0.0591877i | ||||
\(121\) | 1.64453e6 | 0.928296 | ||||||||
\(122\) | − | 1.81278e6i | − | 0.998313i | ||||||
\(123\) | −29864.0 | − | 1.49634e6i | −0.0160484 | − | 0.804108i | ||||
\(124\) | −2.63305e6 | −1.38100 | ||||||||
\(125\) | 2.03921e6i | 1.04407i | ||||||||
\(126\) | −57556.3 | − | 1.44136e6i | −0.0287727 | − | 0.720544i | ||||
\(127\) | −327129. | −0.159701 | −0.0798504 | − | 0.996807i | \(-0.525444\pi\) | ||||
−0.0798504 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(128\) | − | 4.52715e6i | − | 2.15871i | ||||||
\(129\) | 1.62707e6 | − | 32473.0i | 0.757943 | − | 0.0151270i | ||||
\(130\) | −3.69166e6 | −1.68032 | ||||||||
\(131\) | − | 70499.3i | − | 0.0313596i | −0.999877 | − | 0.0156798i | \(-0.995009\pi\) | ||
0.999877 | − | 0.0156798i | \(-0.00499124\pi\) | |||||||
\(132\) | −32444.6 | − | 1.62564e6i | −0.0141065 | − | 0.706811i | ||||
\(133\) | 196915. | 0.0836999 | ||||||||
\(134\) | − | 2.03313e6i | − | 0.844990i | ||||||
\(135\) | 139541. | + | 2.32809e6i | 0.0567152 | + | 0.946235i | ||||
\(136\) | 7.71171e6 | 3.06573 | ||||||||
\(137\) | − | 645599.i | − | 0.251074i | −0.992089 | − | 0.125537i | \(-0.959935\pi\) | ||
0.992089 | − | 0.125537i | \(-0.0400653\pi\) | |||||||
\(138\) | −5.71648e6 | + | 114090.i | −2.17516 | + | 0.0434119i | ||||
\(139\) | −3.56997e6 | −1.32929 | −0.664645 | − | 0.747159i | \(-0.731417\pi\) | ||||
−0.664645 | + | 0.747159i | \(0.731417\pi\) | |||||||
\(140\) | 2.59556e6i | 0.945904i | ||||||||
\(141\) | −69608.4 | − | 3.48774e6i | −0.0248316 | − | 1.24419i | ||||
\(142\) | −2.98576e6 | −1.04277 | ||||||||
\(143\) | 727508.i | 0.248788i | ||||||||
\(144\) | 9.93530e6 | − | 396736.i | 3.32731 | − | 0.132866i | ||||
\(145\) | 5.01773e6 | 1.64590 | ||||||||
\(146\) | 2.20925e6i | 0.709882i | ||||||||
\(147\) | 453699. | − | 9054.93i | 0.142829 | − | 0.00285058i | ||||
\(148\) | 1.28756e6 | 0.397176 | ||||||||
\(149\) | 4.81531e6i | 1.45568i | 0.685748 | + | 0.727839i | \(0.259475\pi\) | ||||
−0.685748 | + | 0.727839i | \(0.740525\pi\) | |||||||
\(150\) | 13031.4 | + | 652942.i | 0.00386116 | + | 0.193464i | ||||
\(151\) | 3.45321e6 | 1.00298 | 0.501490 | − | 0.865164i | \(-0.332785\pi\) | ||||
0.501490 | + | 0.865164i | \(0.332785\pi\) | |||||||
\(152\) | 2.43347e6i | 0.692941i | ||||||||
\(153\) | 140011. | + | 3.50623e6i | 0.0390919 | + | 0.978962i | ||||
\(154\) | 705246. | 0.193098 | ||||||||
\(155\) | 1.84650e6i | 0.495853i | ||||||||
\(156\) | −9.31029e6 | + | 185815.i | −2.45239 | + | 0.0489449i | ||||
\(157\) | −1.96644e6 | −0.508137 | −0.254068 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(158\) | − | 1.36461e7i | − | 3.45968i | ||||||
\(159\) | −32849.7 | − | 1.64594e6i | −0.00817222 | − | 0.409470i | ||||
\(160\) | −1.25184e7 | −3.05625 | ||||||||
\(161\) | − | 1.79867e6i | − | 0.430996i | ||||||
\(162\) | 646784. | + | 8.08567e6i | 0.152130 | + | 1.90183i | ||||
\(163\) | −281420. | −0.0649819 | −0.0324910 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324910 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(164\) | 9.36592e6i | 2.12334i | ||||||||
\(165\) | −1.14003e6 | + | 22752.7i | −0.253783 | + | 0.00506501i | ||||
\(166\) | −4.38305e6 | −0.958191 | ||||||||
\(167\) | − | 8.16717e6i | − | 1.75357i | −0.480885 | − | 0.876783i | \(-0.659685\pi\) | ||
0.480885 | − | 0.876783i | \(-0.340315\pi\) | |||||||
\(168\) | 111900. | + | 5.60679e6i | 0.0235996 | + | 1.18246i | ||||
\(169\) | −660262. | −0.136791 | ||||||||
\(170\) | − | 8.70547e6i | − | 1.77193i | ||||||
\(171\) | −1.10641e6 | + | 44181.1i | −0.221273 | + | 0.00883585i | ||||
\(172\) | −1.01842e7 | −2.00143 | ||||||||
\(173\) | − | 5.14129e6i | − | 0.992965i | −0.868047 | − | 0.496482i | \(-0.834625\pi\) | ||
0.868047 | − | 0.496482i | \(-0.165375\pi\) | |||||||
\(174\) | 1.74479e7 | − | 348225.i | 3.31203 | − | 0.0661016i | ||||
\(175\) | −205445. | −0.0383338 | ||||||||
\(176\) | 4.86126e6i | 0.891685i | ||||||||
\(177\) | −21741.8 | − | 1.08938e6i | −0.00392082 | − | 0.196453i | ||||
\(178\) | 1.22013e7 | 2.16344 | ||||||||
\(179\) | − | 5.56327e6i | − | 0.969999i | −0.874514 | − | 0.485000i | \(-0.838820\pi\) | ||
0.874514 | − | 0.485000i | \(-0.161180\pi\) | |||||||
\(180\) | −582355. | − | 1.45837e7i | −0.0998551 | − | 2.50063i | ||||
\(181\) | −6.72940e6 | −1.13486 | −0.567428 | − | 0.823423i | \(-0.692062\pi\) | ||||
−0.567428 | + | 0.823423i | \(0.692062\pi\) | |||||||
\(182\) | − | 4.03905e6i | − | 0.669985i | ||||||
\(183\) | −3.20610e6 | + | 63987.5i | −0.523148 | + | 0.0104410i | ||||
\(184\) | 2.22278e7 | 3.56816 | ||||||||
\(185\) | − | 902938.i | − | 0.142608i | ||||||
\(186\) | 128145. | + | 6.42072e6i | 0.0199142 | + | 0.997803i | ||||
\(187\) | −1.71557e6 | −0.262351 | ||||||||
\(188\) | 2.18305e7i | 3.28542i | ||||||||
\(189\) | −2.54717e6 | + | 152672.i | −0.377287 | + | 0.0226138i | ||||
\(190\) | 2.74706e6 | 0.400505 | ||||||||
\(191\) | − | 599009.i | − | 0.0859673i | −0.999076 | − | 0.0429836i | \(-0.986314\pi\) | ||
0.999076 | − | 0.0429836i | \(-0.0136863\pi\) | |||||||
\(192\) | −1.99651e7 | + | 398465.i | −2.82078 | + | 0.0562971i | ||||
\(193\) | 5.95379e6 | 0.828174 | 0.414087 | − | 0.910237i | \(-0.364101\pi\) | ||||
0.414087 | + | 0.910237i | \(0.364101\pi\) | |||||||
\(194\) | 1.79474e7i | 2.45808i | ||||||||
\(195\) | 130308. | + | 6.52910e6i | 0.0175739 | + | 0.880541i | ||||
\(196\) | −2.83980e6 | −0.377155 | ||||||||
\(197\) | − | 2.64933e6i | − | 0.346527i | −0.984875 | − | 0.173264i | \(-0.944569\pi\) | ||
0.984875 | − | 0.173264i | \(-0.0554313\pi\) | |||||||
\(198\) | −3.96257e6 | + | 158233.i | −0.510483 | + | 0.0203846i | ||||
\(199\) | −1.29359e7 | −1.64148 | −0.820741 | − | 0.571300i | \(-0.806439\pi\) | ||||
−0.820741 | + | 0.571300i | \(0.806439\pi\) | |||||||
\(200\) | − | 2.53889e6i | − | 0.317361i | ||||||
\(201\) | −3.59582e6 | + | 71765.4i | −0.442802 | + | 0.00883745i | ||||
\(202\) | 2.14286e7 | 2.59980 | ||||||||
\(203\) | 5.48990e6i | 0.656260i | ||||||||
\(204\) | −438179. | − | 2.19550e7i | −0.0516132 | − | 2.58609i | ||||
\(205\) | 6.56811e6 | 0.762393 | ||||||||
\(206\) | − | 1.83111e7i | − | 2.09465i | ||||||
\(207\) | 403559. | + | 1.01062e7i | 0.0454984 | + | 1.13940i | ||||
\(208\) | 2.78412e7 | 3.09384 | ||||||||
\(209\) | − | 541358.i | − | 0.0592988i | ||||||
\(210\) | 6.32931e6 | − | 126320.i | 0.683437 | − | 0.0136400i | ||||
\(211\) | 3.92825e6 | 0.418169 | 0.209084 | − | 0.977898i | \(-0.432952\pi\) | ||||
0.209084 | + | 0.977898i | \(0.432952\pi\) | |||||||
\(212\) | 1.03023e7i | 1.08125i | ||||||||
\(213\) | 105391. | + | 5.28065e6i | 0.0109060 | + | 0.546447i | ||||
\(214\) | −2.78625e7 | −2.84301 | ||||||||
\(215\) | 7.14194e6i | 0.718622i | ||||||||
\(216\) | −1.88671e6 | − | 3.14778e7i | −0.187216 | − | 3.12351i | ||||
\(217\) | −2.02025e6 | −0.197709 | ||||||||
\(218\) | 1.06539e7i | 1.02834i | ||||||||
\(219\) | 3.90729e6 | − | 77981.9i | 0.372001 | − | 0.00742440i | ||||
\(220\) | 7.13568e6 | 0.670143 | ||||||||
\(221\) | 9.82532e6i | 0.910269i | ||||||||
\(222\) | −62662.9 | − | 3.13973e6i | −0.00572732 | − | 0.286968i | ||||
\(223\) | −4.07259e6 | −0.367245 | −0.183623 | − | 0.982997i | \(-0.558782\pi\) | ||||
−0.183623 | + | 0.982997i | \(0.558782\pi\) | |||||||
\(224\) | − | 1.36964e7i | − | 1.21860i | ||||||
\(225\) | 1.15434e6 | − | 46095.0i | 0.101341 | − | 0.00404675i | ||||
\(226\) | −2.83176e7 | −2.45319 | ||||||||
\(227\) | − | 1.04706e7i | − | 0.895147i | −0.894247 | − | 0.447573i | \(-0.852288\pi\) | ||
0.894247 | − | 0.447573i | \(-0.147712\pi\) | |||||||
\(228\) | 6.92803e6 | − | 138270.i | 0.584528 | − | 0.0116660i | ||||
\(229\) | 7.40529e6 | 0.616646 | 0.308323 | − | 0.951282i | \(-0.400232\pi\) | ||||
0.308323 | + | 0.951282i | \(0.400232\pi\) | |||||||
\(230\) | − | 2.50922e7i | − | 2.06232i | ||||||
\(231\) | −24893.7 | − | 1.24730e6i | −0.00201955 | − | 0.101190i | ||||
\(232\) | −6.78440e7 | −5.43309 | ||||||||
\(233\) | − | 1.82011e7i | − | 1.43889i | −0.694547 | − | 0.719447i | \(-0.744395\pi\) | ||
0.694547 | − | 0.719447i | \(-0.255605\pi\) | |||||||
\(234\) | 906225. | + | 2.26942e7i | 0.0707275 | + | 1.77120i | ||||
\(235\) | 1.53093e7 | 1.17964 | ||||||||
\(236\) | 6.81867e6i | 0.518757i | ||||||||
\(237\) | −2.41345e7 | + | 481677.i | −1.81298 | + | 0.0361835i | ||||
\(238\) | 9.52466e6 | 0.706510 | ||||||||
\(239\) | 1.67405e7i | 1.22624i | 0.789991 | + | 0.613118i | \(0.210085\pi\) | ||||
−0.789991 | + | 0.613118i | \(0.789915\pi\) | |||||||
\(240\) | 870728. | + | 4.36279e7i | 0.0629867 | + | 3.15596i | ||||
\(241\) | 2.01770e7 | 1.44147 | 0.720735 | − | 0.693210i | \(-0.243804\pi\) | ||||
0.720735 | + | 0.693210i | \(0.243804\pi\) | |||||||
\(242\) | 2.51008e7i | 1.77110i | ||||||||
\(243\) | 1.42775e7 | − | 1.42931e6i | 0.995026 | − | 0.0996114i | ||||
\(244\) | 2.00677e7 | 1.38143 | ||||||||
\(245\) | 1.99149e6i | 0.135419i | ||||||||
\(246\) | 2.28389e7 | − | 455820.i | 1.53416 | − | 0.0306188i | ||||
\(247\) | −3.10044e6 | −0.205746 | ||||||||
\(248\) | − | 2.49662e7i | − | 1.63681i | ||||||
\(249\) | 154713. | + | 7.75190e6i | 0.0100214 | + | 0.502123i | ||||
\(250\) | −3.11249e7 | −1.99199 | ||||||||
\(251\) | − | 1.62774e7i | − | 1.02935i | −0.857384 | − | 0.514677i | \(-0.827912\pi\) | ||
0.857384 | − | 0.514677i | \(-0.172088\pi\) | |||||||
\(252\) | 1.59560e7 | − | 637155.i | 0.997064 | − | 0.0398147i | ||||
\(253\) | −4.94487e6 | −0.305347 | ||||||||
\(254\) | − | 4.99303e6i | − | 0.304693i | ||||||
\(255\) | −1.53966e7 | + | 307285.i | −0.928546 | + | 0.0185319i | ||||
\(256\) | 2.17646e7 | 1.29727 | ||||||||
\(257\) | 2.44722e7i | 1.44170i | 0.693093 | + | 0.720848i | \(0.256247\pi\) | ||||
−0.693093 | + | 0.720848i | \(0.743753\pi\) | |||||||
\(258\) | 495643. | + | 2.48343e7i | 0.0288609 | + | 1.44608i | ||||
\(259\) | 987904. | 0.0568612 | ||||||||
\(260\) | − | 4.08671e7i | − | 2.32517i | ||||||
\(261\) | −1.23175e6 | − | 3.08461e7i | −0.0692787 | − | 1.73492i | ||||
\(262\) | 1.07604e6 | 0.0598310 | ||||||||
\(263\) | − | 1.09689e7i | − | 0.602972i | −0.953471 | − | 0.301486i | \(-0.902517\pi\) | ||
0.953471 | − | 0.301486i | \(-0.0974827\pi\) | |||||||
\(264\) | 1.54141e7 | − | 307636.i | 0.837736 | − | 0.0167196i | ||||
\(265\) | 7.22478e6 | 0.388228 | ||||||||
\(266\) | 3.00556e6i | 0.159691i | ||||||||
\(267\) | −430679. | − | 2.15793e7i | −0.0226267 | − | 1.13371i | ||||
\(268\) | 2.25070e7 | 1.16927 | ||||||||
\(269\) | 2.20170e7i | 1.13110i | 0.824714 | + | 0.565549i | \(0.191336\pi\) | ||||
−0.824714 | + | 0.565549i | \(0.808664\pi\) | |||||||
\(270\) | −3.55342e7 | + | 2.12984e6i | −1.80532 | + | 0.108207i | ||||
\(271\) | 243322. | 0.0122257 | 0.00611286 | − | 0.999981i | \(-0.498054\pi\) | ||||
0.00611286 | + | 0.999981i | \(0.498054\pi\) | |||||||
\(272\) | 6.56535e7i | 3.26251i | ||||||||
\(273\) | −7.14349e6 | + | 142570.i | −0.351093 | + | 0.00700713i | ||||
\(274\) | 9.85392e6 | 0.479024 | ||||||||
\(275\) | 564808.i | 0.0271583i | ||||||||
\(276\) | −1.26298e6 | − | 6.32820e7i | −0.0600718 | − | 3.00991i | ||||
\(277\) | 1.63929e7 | 0.771289 | 0.385644 | − | 0.922648i | \(-0.373979\pi\) | ||||
0.385644 | + | 0.922648i | \(0.373979\pi\) | |||||||
\(278\) | − | 5.44891e7i | − | 2.53615i | ||||||
\(279\) | 1.13512e7 | − | 453276.i | 0.522672 | − | 0.0208713i | ||||
\(280\) | −2.46108e7 | −1.12112 | ||||||||
\(281\) | − | 1.20421e7i | − | 0.542731i | −0.962476 | − | 0.271366i | \(-0.912525\pi\) | ||
0.962476 | − | 0.271366i | \(-0.0874752\pi\) | |||||||
\(282\) | 5.32341e7 | − | 1.06245e6i | 2.37379 | − | 0.0473762i | ||||
\(283\) | −1.54181e7 | −0.680257 | −0.340128 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340128 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(284\) | − | 3.30528e7i | − | 1.44295i | ||||||
\(285\) | −96965.5 | − | 4.85847e6i | −0.00418873 | − | 0.209877i | ||||
\(286\) | −1.11041e7 | −0.474663 | ||||||||
\(287\) | 7.18617e6i | 0.303985i | ||||||||
\(288\) | 3.07301e6 | + | 7.69561e7i | 0.128643 | + | 3.22155i | ||||
\(289\) | 968044. | 0.0401053 | ||||||||
\(290\) | 7.65866e7i | 3.14021i | ||||||||
\(291\) | 3.17419e7 | − | 633505.i | 1.28811 | − | 0.0257082i | ||||
\(292\) | −2.44566e7 | −0.982309 | ||||||||
\(293\) | − | 3.13748e7i | − | 1.24732i | −0.781696 | − | 0.623659i | \(-0.785645\pi\) | ||
0.781696 | − | 0.623659i | \(-0.214355\pi\) | |||||||
\(294\) | 138207. | + | 6.92490e6i | 0.00543862 | + | 0.272503i | ||||
\(295\) | 4.78178e6 | 0.186262 | ||||||||
\(296\) | 1.22085e7i | 0.470746i | ||||||||
\(297\) | 419723. | + | 7.00265e6i | 0.0160211 | + | 0.267296i | ||||
\(298\) | −7.34971e7 | −2.77729 | ||||||||
\(299\) | 2.83200e7i | 1.05945i | ||||||||
\(300\) | −7.22814e6 | + | 144259.i | −0.267709 | + | 0.00534294i | ||||
\(301\) | −7.81400e6 | −0.286532 | ||||||||
\(302\) | 5.27071e7i | 1.91359i | ||||||||
\(303\) | −756386. | − | 3.78988e7i | −0.0271904 | − | 1.36238i | ||||
\(304\) | −2.07173e7 | −0.737418 | ||||||||
\(305\) | − | 1.40730e7i | − | 0.496008i | ||||||
\(306\) | −5.35163e7 | + | 2.13701e6i | −1.86776 | + | 0.0745834i | ||||
\(307\) | 3.26210e7 | 1.12741 | 0.563705 | − | 0.825976i | \(-0.309375\pi\) | ||||
0.563705 | + | 0.825976i | \(0.309375\pi\) | |||||||
\(308\) | 7.80715e6i | 0.267203i | ||||||||
\(309\) | −3.23851e7 | + | 646343.i | −1.09766 | + | 0.0219072i | ||||
\(310\) | −2.81835e7 | −0.946039 | ||||||||
\(311\) | 3.80992e7i | 1.26659i | 0.773912 | + | 0.633293i | \(0.218297\pi\) | ||||
−0.773912 | + | 0.633293i | \(0.781703\pi\) | |||||||
\(312\) | −1.76187e6 | − | 8.82790e7i | −0.0580111 | − | 2.90666i | ||||
\(313\) | −1.64482e7 | −0.536395 | −0.268197 | − | 0.963364i | \(-0.586428\pi\) | ||||
−0.268197 | + | 0.963364i | \(0.586428\pi\) | |||||||
\(314\) | − | 3.00141e7i | − | 0.969475i | ||||||
\(315\) | −446823. | − | 1.11896e7i | −0.0142956 | − | 0.358000i | ||||
\(316\) | 1.51063e8 | 4.78738 | ||||||||
\(317\) | 3.18719e7i | 1.00053i | 0.865872 | + | 0.500266i | \(0.166764\pi\) | ||||
−0.865872 | + | 0.500266i | \(0.833236\pi\) | |||||||
\(318\) | 2.51223e7 | − | 501392.i | 0.781229 | − | 0.0155918i | ||||
\(319\) | 1.50928e7 | 0.464940 | ||||||||
\(320\) | − | 8.76361e7i | − | 2.67444i | ||||||
\(321\) | 983489. | + | 4.92779e7i | 0.0297341 | + | 1.48983i | ||||
\(322\) | 2.74534e7 | 0.822297 | ||||||||
\(323\) | − | 7.31128e6i | − | 0.216963i | ||||||
\(324\) | −8.95093e7 | + | 7.15998e6i | −2.63168 | + | 0.210512i | ||||
\(325\) | 3.23474e6 | 0.0942300 | ||||||||
\(326\) | − | 4.29538e6i | − | 0.123979i | ||||||
\(327\) | 1.88425e7 | − | 376060.i | 0.538885 | − | 0.0107551i | ||||
\(328\) | −8.88065e7 | −2.51665 | ||||||||
\(329\) | 1.67499e7i | 0.470353i | ||||||||
\(330\) | −347279. | − | 1.74005e7i | −0.00966354 | − | 0.484193i | ||||
\(331\) | 5.26170e6 | 0.145092 | 0.0725458 | − | 0.997365i | \(-0.476888\pi\) | ||||
0.0725458 | + | 0.997365i | \(0.476888\pi\) | |||||||
\(332\) | − | 4.85209e7i | − | 1.32591i | ||||||
\(333\) | −5.55075e6 | + | 221652.i | −0.150321 | + | 0.00600260i | ||||
\(334\) | 1.24657e8 | 3.34563 | ||||||||
\(335\) | − | 1.57837e7i | − | 0.419830i | ||||||
\(336\) | −4.77333e7 | + | 952663.i | −1.25836 | + | 0.0251143i | ||||
\(337\) | −7.23973e7 | −1.89161 | −0.945807 | − | 0.324729i | \(-0.894727\pi\) | ||||
−0.945807 | + | 0.324729i | \(0.894727\pi\) | |||||||
\(338\) | − | 1.00777e7i | − | 0.260983i | ||||||
\(339\) | 999551. | + | 5.00827e7i | 0.0256570 | + | 1.28555i | ||||
\(340\) | 9.63706e7 | 2.45193 | ||||||||
\(341\) | 5.55406e6i | 0.140071i | ||||||||
\(342\) | −674346. | − | 1.68874e7i | −0.0168579 | − | 0.422166i | ||||
\(343\) | −2.17889e6 | −0.0539949 | ||||||||
\(344\) | − | 9.65651e7i | − | 2.37217i | ||||||
\(345\) | −4.43783e7 | + | 885703.i | −1.08072 | + | 0.0215690i | ||||
\(346\) | 7.84726e7 | 1.89448 | ||||||||
\(347\) | 2.29798e7i | 0.549994i | 0.961445 | + | 0.274997i | \(0.0886769\pi\) | ||||
−0.961445 | + | 0.274997i | \(0.911323\pi\) | |||||||
\(348\) | 3.85489e6 | + | 1.93150e8i | 0.0914690 | + | 4.58307i | ||||
\(349\) | −6.12628e7 | −1.44119 | −0.720594 | − | 0.693357i | \(-0.756131\pi\) | ||||
−0.720594 | + | 0.693357i | \(0.756131\pi\) | |||||||
\(350\) | − | 3.13576e6i | − | 0.0731372i | ||||||
\(351\) | 4.01052e7 | − | 2.40382e6i | 0.927426 | − | 0.0555878i | ||||
\(352\) | −3.76540e7 | −0.863342 | ||||||||
\(353\) | − | 5.32886e7i | − | 1.21146i | −0.795669 | − | 0.605732i | \(-0.792881\pi\) | ||
0.795669 | − | 0.605732i | \(-0.207119\pi\) | |||||||
\(354\) | 1.66274e7 | − | 331850.i | 0.374813 | − | 0.00748053i | ||||
\(355\) | −2.31792e7 | −0.518099 | ||||||||
\(356\) | 1.35069e8i | 2.99369i | ||||||||
\(357\) | −336201. | − | 1.68454e7i | −0.00738914 | − | 0.370234i | ||||
\(358\) | 8.49134e7 | 1.85066 | ||||||||
\(359\) | 6.23374e6i | 0.134730i | 0.997728 | + | 0.0673651i | \(0.0214592\pi\) | ||||
−0.997728 | + | 0.0673651i | \(0.978541\pi\) | |||||||
\(360\) | 1.38281e8 | − | 5.52182e6i | 2.96384 | − | 0.118352i | ||||
\(361\) | −4.47388e7 | −0.950960 | ||||||||
\(362\) | − | 1.02712e8i | − | 2.16519i | ||||||
\(363\) | 4.43936e7 | − | 886008.i | 0.928111 | − | 0.0185233i | ||||
\(364\) | 4.47127e7 | 0.927101 | ||||||||
\(365\) | 1.71509e7i | 0.352702i | ||||||||
\(366\) | −976654. | − | 4.89354e7i | −0.0199204 | − | 0.998114i | ||||
\(367\) | −5.29535e7 | −1.07126 | −0.535632 | − | 0.844452i | \(-0.679927\pi\) | ||||
−0.535632 | + | 0.844452i | \(0.679927\pi\) | |||||||
\(368\) | 1.89236e8i | 3.79718i | ||||||||
\(369\) | −1.61233e6 | − | 4.03770e7i | −0.0320904 | − | 0.803628i | ||||
\(370\) | 1.37817e7 | 0.272081 | ||||||||
\(371\) | 7.90463e6i | 0.154796i | ||||||||
\(372\) | −7.10781e7 | + | 1.41858e6i | −1.38072 | + | 0.0275565i | ||||
\(373\) | 4.67074e7 | 0.900034 | 0.450017 | − | 0.893020i | \(-0.351418\pi\) | ||||
0.450017 | + | 0.893020i | \(0.351418\pi\) | |||||||
\(374\) | − | 2.61851e7i | − | 0.500541i | ||||||
\(375\) | 1.09864e6 | + | 5.50477e7i | 0.0208335 | + | 1.04387i | ||||
\(376\) | −2.06994e8 | −3.89399 | ||||||||
\(377\) | − | 8.64385e7i | − | 1.61318i | ||||||
\(378\) | −2.33026e6 | − | 3.88780e7i | −0.0431448 | − | 0.719827i | ||||
\(379\) | 2.19924e7 | 0.403975 | 0.201988 | − | 0.979388i | \(-0.435260\pi\) | ||||
0.201988 | + | 0.979388i | \(0.435260\pi\) | |||||||
\(380\) | 3.04103e7i | 0.554204i | ||||||||
\(381\) | −8.83071e6 | + | 176244.i | −0.159669 | + | 0.00318668i | ||||
\(382\) | 9.14280e6 | 0.164017 | ||||||||
\(383\) | − | 4.96363e7i | − | 0.883494i | −0.897140 | − | 0.441747i | \(-0.854359\pi\) | ||
0.897140 | − | 0.441747i | \(-0.145641\pi\) | |||||||
\(384\) | −2.43905e6 | − | 1.22209e8i | −0.0430751 | − | 2.15828i | ||||
\(385\) | 5.47498e6 | 0.0959402 | ||||||||
\(386\) | 9.08740e7i | 1.58007i | ||||||||
\(387\) | 4.39046e7 | − | 1.75320e6i | 0.757490 | − | 0.0302481i | ||||
\(388\) | −1.98680e8 | −3.40140 | ||||||||
\(389\) | − | 2.09851e7i | − | 0.356502i | −0.983985 | − | 0.178251i | \(-0.942956\pi\) | ||
0.983985 | − | 0.178251i | \(-0.0570439\pi\) | |||||||
\(390\) | −9.96550e7 | + | 1.98892e6i | −1.67998 | + | 0.0335292i | ||||
\(391\) | −6.67827e7 | −1.11721 | ||||||||
\(392\) | − | 2.69266e7i | − | 0.447017i | ||||||
\(393\) | −37982.1 | − | 1.90310e6i | −0.000625751 | − | 0.0313534i | ||||
\(394\) | 4.04373e7 | 0.661140 | ||||||||
\(395\) | − | 1.05937e8i | − | 1.71893i | ||||||
\(396\) | −1.75166e6 | − | 4.38661e7i | −0.0282075 | − | 0.706388i | ||||
\(397\) | 8.86430e7 | 1.41668 | 0.708342 | − | 0.705869i | \(-0.249443\pi\) | ||||
0.708342 | + | 0.705869i | \(0.249443\pi\) | |||||||
\(398\) | − | 1.97443e8i | − | 3.13179i | ||||||
\(399\) | 5.31566e6 | − | 106090.i | 0.0836832 | − | 0.00167015i | ||||
\(400\) | 2.16148e7 | 0.337731 | ||||||||
\(401\) | 5.86359e7i | 0.909349i | 0.890658 | + | 0.454675i | \(0.150244\pi\) | ||||
−0.890658 | + | 0.454675i | \(0.849756\pi\) | |||||||
\(402\) | −1.09537e6 | − | 5.48837e7i | −0.0168610 | − | 0.844822i | ||||
\(403\) | 3.18089e7 | 0.485997 | ||||||||
\(404\) | 2.37217e8i | 3.59751i | ||||||||
\(405\) | 5.02113e6 | + | 6.27708e7i | 0.0755852 | + | 0.944915i | ||||
\(406\) | −8.37934e7 | −1.25208 | ||||||||
\(407\) | − | 2.71594e6i | − | 0.0402843i | ||||||
\(408\) | 2.08175e8 | − | 4.15476e6i | 3.06512 | − | 0.0611737i | ||||
\(409\) | 8.09388e7 | 1.18301 | 0.591503 | − | 0.806303i | \(-0.298535\pi\) | ||||
0.591503 | + | 0.806303i | \(0.298535\pi\) | |||||||
\(410\) | 1.00250e8i | 1.45457i | ||||||||
\(411\) | −347823. | − | 1.74277e7i | −0.00500994 | − | 0.251024i | ||||
\(412\) | 2.02706e8 | 2.89851 | ||||||||
\(413\) | 5.23175e6i | 0.0742671i | ||||||||
\(414\) | −1.54253e8 | + | 6.15961e6i | −2.17386 | + | 0.0868065i | ||||
\(415\) | −3.40266e7 | −0.476074 | ||||||||
\(416\) | 2.15650e8i | 2.99550i | ||||||||
\(417\) | −9.63699e7 | + | 1.92335e6i | −1.32903 | + | 0.0265247i | ||||
\(418\) | 8.26286e6 | 0.113136 | ||||||||
\(419\) | 1.01481e8i | 1.37957i | 0.724015 | + | 0.689785i | \(0.242295\pi\) | ||||
−0.724015 | + | 0.689785i | \(0.757705\pi\) | |||||||
\(420\) | 1.39838e6 | + | 7.00661e7i | 0.0188746 | + | 0.945715i | ||||
\(421\) | 2.35310e7 | 0.315350 | 0.157675 | − | 0.987491i | \(-0.449600\pi\) | ||||
0.157675 | + | 0.987491i | \(0.449600\pi\) | |||||||
\(422\) | 5.99576e7i | 0.797824i | ||||||||
\(423\) | −3.75810e6 | − | 9.41127e7i | −0.0496532 | − | 1.24345i | ||||
\(424\) | −9.76852e7 | −1.28154 | ||||||||
\(425\) | 7.62799e6i | 0.0993672i | ||||||||
\(426\) | −8.05996e7 | + | 1.60861e6i | −1.04257 | + | 0.0208076i | ||||
\(427\) | 1.53973e7 | 0.197771 | ||||||||
\(428\) | − | 3.08441e8i | − | 3.93406i | ||||||
\(429\) | 391952. | + | 1.96388e7i | 0.00496433 | + | 0.248739i | ||||
\(430\) | −1.09009e8 | −1.37106 | ||||||||
\(431\) | − | 1.30255e8i | − | 1.62691i | −0.581629 | − | 0.813454i | \(-0.697585\pi\) | ||
0.581629 | − | 0.813454i | \(-0.302415\pi\) | |||||||
\(432\) | 2.67986e8 | − | 1.60625e7i | 3.32400 | − | 0.199233i | ||||
\(433\) | 3.94140e7 | 0.485497 | 0.242748 | − | 0.970089i | \(-0.421951\pi\) | ||||
0.242748 | + | 0.970089i | \(0.421951\pi\) | |||||||
\(434\) | − | 3.08355e7i | − | 0.377209i | ||||||
\(435\) | 1.35452e8 | − | 2.70335e6i | 1.64557 | − | 0.0328423i | ||||
\(436\) | −1.17940e8 | −1.42299 | ||||||||
\(437\) | − | 2.10737e7i | − | 0.252520i | ||||||
\(438\) | 1.19025e6 | + | 5.96378e7i | 0.0141650 | + | 0.709740i | ||||
\(439\) | −1.61575e8 | −1.90977 | −0.954884 | − | 0.296978i | \(-0.904021\pi\) | ||||
−0.954884 | + | 0.296978i | \(0.904021\pi\) | |||||||
\(440\) | 6.76597e7i | 0.794277i | ||||||||
\(441\) | 1.22425e7 | − | 488869.i | 0.142743 | − | 0.00570002i | ||||
\(442\) | −1.49966e8 | −1.73670 | ||||||||
\(443\) | 8.00677e7i | 0.920971i | 0.887667 | + | 0.460486i | \(0.152325\pi\) | ||||
−0.887667 | + | 0.460486i | \(0.847675\pi\) | |||||||
\(444\) | 3.47572e7 | − | 693685.i | 0.397097 | − | 0.00792526i | ||||
\(445\) | 9.47212e7 | 1.07490 | ||||||||
\(446\) | − | 6.21608e7i | − | 0.700667i | ||||||
\(447\) | 2.59429e6 | + | 1.29988e8i | 0.0290467 | + | 1.45539i | ||||
\(448\) | 9.58827e7 | 1.06637 | ||||||||
\(449\) | 1.32122e8i | 1.45961i | 0.683655 | + | 0.729805i | \(0.260389\pi\) | ||||
−0.683655 | + | 0.729805i | \(0.739611\pi\) | |||||||
\(450\) | 703557. | + | 1.76189e7i | 0.00772079 | + | 0.193349i | ||||
\(451\) | 1.97562e7 | 0.215364 | ||||||||
\(452\) | − | 3.13479e8i | − | 3.39463i | ||||||
\(453\) | 9.32181e7 | − | 1.86045e6i | 1.00278 | − | 0.0200135i | ||||
\(454\) | 1.59815e8 | 1.70785 | ||||||||
\(455\) | − | 3.13560e7i | − | 0.332879i | ||||||
\(456\) | 1.31106e6 | + | 6.56907e7i | 0.0138270 | + | 0.692803i | ||||
\(457\) | −3.56971e7 | −0.374010 | −0.187005 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187005 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(458\) | 1.13029e8i | 1.17650i | ||||||||
\(459\) | 5.66854e6 | + | 9.45739e7i | 0.0586183 | + | 0.977987i | ||||
\(460\) | 2.77774e8 | 2.85376 | ||||||||
\(461\) | − | 8.85096e7i | − | 0.903416i | −0.892166 | − | 0.451708i | \(-0.850815\pi\) | ||
0.892166 | − | 0.451708i | \(-0.149185\pi\) | |||||||
\(462\) | 1.90378e7 | − | 379958.i | 0.193060 | − | 0.00385309i | ||||
\(463\) | −9.87878e7 | −0.995315 | −0.497657 | − | 0.867374i | \(-0.665806\pi\) | ||||
−0.497657 | + | 0.867374i | \(0.665806\pi\) | |||||||
\(464\) | − | 5.77589e8i | − | 5.78182i | ||||||
\(465\) | 994817. | + | 4.98455e7i | 0.00989428 | + | 0.495755i | ||||
\(466\) | 2.77806e8 | 2.74527 | ||||||||
\(467\) | − | 8.53806e7i | − | 0.838318i | −0.907913 | − | 0.419159i | \(-0.862325\pi\) | ||
0.907913 | − | 0.419159i | \(-0.137675\pi\) | |||||||
\(468\) | −2.51228e8 | + | 1.00320e7i | −2.45092 | + | 0.0978702i | ||||
\(469\) | 1.72689e7 | 0.167397 | ||||||||
\(470\) | 2.33669e8i | 2.25064i | ||||||||
\(471\) | −5.30832e7 | + | 1.05944e6i | −0.508036 | + | 0.0101394i | ||||
\(472\) | −6.46538e7 | −0.614848 | ||||||||
\(473\) | 2.14822e7i | 0.202999i | ||||||||
\(474\) | −7.35194e6 | − | 3.68370e8i | −0.0690346 | − | 3.45899i | ||||
\(475\) | −2.40706e6 | −0.0224598 | ||||||||
\(476\) | 1.05439e8i | 0.977644i | ||||||||
\(477\) | −1.77353e6 | − | 4.44138e7i | −0.0163412 | − | 0.409226i | ||||
\(478\) | −2.55513e8 | −2.33954 | ||||||||
\(479\) | 8.18328e7i | 0.744597i | 0.928113 | + | 0.372298i | \(0.121430\pi\) | ||||
−0.928113 | + | 0.372298i | \(0.878570\pi\) | |||||||
\(480\) | −3.37930e8 | + | 6.74441e6i | −3.05564 | + | 0.0609846i | ||||
\(481\) | −1.55546e7 | −0.139773 | ||||||||
\(482\) | 3.07966e8i | 2.75018i | ||||||||
\(483\) | −969048. | − | 4.85543e7i | −0.00860011 | − | 0.430910i | ||||
\(484\) | −2.77869e8 | −2.45078 | ||||||||
\(485\) | 1.39330e8i | 1.22129i | ||||||||
\(486\) | 2.18159e7 | + | 2.17921e8i | 0.190049 | + | 1.89841i | ||||
\(487\) | −2.20121e8 | −1.90579 | −0.952894 | − | 0.303303i | \(-0.901911\pi\) | ||||
−0.952894 | + | 0.303303i | \(0.901911\pi\) | |||||||
\(488\) | 1.90280e8i | 1.63732i | ||||||||
\(489\) | −7.59684e6 | + | 151618.i | −0.0649690 | + | 0.00129665i | ||||
\(490\) | −3.03965e7 | −0.258366 | ||||||||
\(491\) | 1.16286e8i | 0.982384i | 0.871051 | + | 0.491192i | \(0.163439\pi\) | ||||
−0.871051 | + | 0.491192i | \(0.836561\pi\) | |||||||
\(492\) | 5.04598e6 | + | 2.52830e8i | 0.0423692 | + | 2.12291i | ||||
\(493\) | 2.03834e8 | 1.70113 | ||||||||
\(494\) | − | 4.73226e7i | − | 0.392543i | ||||||
\(495\) | −3.07623e7 | + | 1.22840e6i | −0.253632 | + | 0.0101280i | ||||
\(496\) | 2.12549e8 | 1.74187 | ||||||||
\(497\) | − | 2.53603e7i | − | 0.206579i | ||||||
\(498\) | −1.18319e8 | + | 2.36141e6i | −0.958000 | + | 0.0191198i | ||||
\(499\) | 1.25472e8 | 1.00982 | 0.504911 | − | 0.863171i | \(-0.331525\pi\) | ||||
0.504911 | + | 0.863171i | \(0.331525\pi\) | |||||||
\(500\) | − | 3.44556e8i | − | 2.75645i | ||||||
\(501\) | −4.40014e6 | − | 2.20470e8i | −0.0349908 | − | 1.75322i | ||||
\(502\) | 2.48446e8 | 1.96391 | ||||||||
\(503\) | − | 3.36217e7i | − | 0.264190i | −0.991237 | − | 0.132095i | \(-0.957830\pi\) | ||
0.991237 | − | 0.132095i | \(-0.0421704\pi\) | |||||||
\(504\) | 6.04142e6 | + | 1.51293e8i | 0.0471898 | + | 1.18175i | ||||
\(505\) | 1.66355e8 | 1.29170 | ||||||||
\(506\) | − | 7.54746e7i | − | 0.582572i | ||||||
\(507\) | −1.78235e7 | + | 355723.i | −0.136763 | + | 0.00272953i | ||||
\(508\) | 5.52734e7 | 0.421624 | ||||||||
\(509\) | 1.55599e8i | 1.17992i | 0.807431 | + | 0.589962i | \(0.200857\pi\) | ||||
−0.807431 | + | 0.589962i | \(0.799143\pi\) | |||||||
\(510\) | −4.69015e6 | − | 2.35001e8i | −0.0353571 | − | 1.77157i | ||||
\(511\) | −1.87648e7 | −0.140631 | ||||||||
\(512\) | 4.24602e7i | 0.316353i | ||||||||
\(513\) | −2.98433e7 | + | 1.78874e6i | −0.221052 | + | 0.0132494i | ||||
\(514\) | −3.73524e8 | −2.75061 | ||||||||
\(515\) | − | 1.42153e8i | − | 1.04072i | ||||||
\(516\) | −2.74918e8 | + | 5.48682e6i | −2.00103 | + | 0.0399367i | ||||
\(517\) | 4.60486e7 | 0.333231 | ||||||||
\(518\) | 1.50786e7i | 0.108485i | ||||||||
\(519\) | −2.76992e6 | − | 1.38787e8i | −0.0198137 | − | 0.992767i | ||||
\(520\) | 3.87497e8 | 2.75587 | ||||||||
\(521\) | − | 1.60889e8i | − | 1.13766i | −0.822454 | − | 0.568832i | \(-0.807395\pi\) | ||
0.822454 | − | 0.568832i | \(-0.192605\pi\) | |||||||
\(522\) | 4.70811e8 | − | 1.88004e7i | 3.31005 | − | 0.132177i | ||||
\(523\) | −8.06025e7 | −0.563435 | −0.281717 | − | 0.959497i | \(-0.590904\pi\) | ||||
−0.281717 | + | 0.959497i | \(0.590904\pi\) | |||||||
\(524\) | 1.19119e7i | 0.0827921i | ||||||||
\(525\) | −5.54592e6 | + | 110686.i | −0.0383262 | + | 0.000764915i | ||||
\(526\) | 1.67421e8 | 1.15041 | ||||||||
\(527\) | 7.50100e7i | 0.512492i | ||||||||
\(528\) | 2.61905e6 | + | 1.31228e8i | 0.0177927 | + | 0.891507i | ||||
\(529\) | −4.44552e7 | −0.300300 | ||||||||
\(530\) | 1.10273e8i | 0.740701i | ||||||||
\(531\) | −1.17383e6 | − | 2.93957e7i | −0.00784007 | − | 0.196336i | ||||
\(532\) | −3.32719e7 | −0.220975 | ||||||||
\(533\) | − | 1.13146e8i | − | 0.747238i | ||||||
\(534\) | 3.29369e8 | − | 6.57355e6i | 2.16301 | − | 0.0431694i | ||||
\(535\) | −2.16303e8 | −1.41254 | ||||||||
\(536\) | 2.13409e8i | 1.38586i | ||||||||
\(537\) | −2.99727e6 | − | 1.50178e8i | −0.0193554 | − | 0.969806i | ||||
\(538\) | −3.36049e8 | −2.15802 | ||||||||
\(539\) | 5.99018e6i | 0.0382537i | ||||||||
\(540\) | −2.35776e7 | − | 3.93367e8i | −0.149733 | − | 2.49814i | ||||
\(541\) | −563602. | −0.00355943 | −0.00177972 | − | 0.999998i | \(-0.500567\pi\) | ||||
−0.00177972 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(542\) | 3.71388e6i | 0.0233255i | ||||||||
\(543\) | −1.81658e8 | + | 3.62553e6i | −1.13463 | + | 0.0226450i | ||||
\(544\) | −5.08534e8 | −3.15881 | ||||||||
\(545\) | 8.27085e7i | 0.510929i | ||||||||
\(546\) | −2.17607e6 | − | 1.09033e8i | −0.0133689 | − | 0.669851i | ||||
\(547\) | 3.12342e7 | 0.190840 | 0.0954198 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954198 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(548\) | 1.09084e8i | 0.662856i | ||||||||
\(549\) | −8.65131e7 | + | 3.45464e6i | −0.522835 | + | 0.0208778i | ||||
\(550\) | −8.62079e6 | −0.0518154 | ||||||||
\(551\) | 6.43211e7i | 0.384502i | ||||||||
\(552\) | 6.00032e8 | − | 1.19755e7i | 3.56745 | − | 0.0711992i | ||||
\(553\) | 1.15906e8 | 0.685379 | ||||||||
\(554\) | 2.50208e8i | 1.47154i | ||||||||
\(555\) | −486466. | − | 2.43745e7i | −0.00284560 | − | 0.142579i | ||||
\(556\) | 6.03201e8 | 3.50944 | ||||||||
\(557\) | 8.81896e7i | 0.510331i | 0.966897 | + | 0.255165i | \(0.0821299\pi\) | ||||
−0.966897 | + | 0.255165i | \(0.917870\pi\) | |||||||
\(558\) | 6.91844e6 | + | 1.73256e8i | 0.0398204 | + | 0.997207i | ||||
\(559\) | 1.23031e8 | 0.704338 | ||||||||
\(560\) | − | 2.09523e8i | − | 1.19308i | ||||||
\(561\) | −4.63112e7 | + | 924279.i | −0.262299 | + | 0.00523497i | ||||
\(562\) | 1.83802e8 | 1.03548 | ||||||||
\(563\) | 1.70614e8i | 0.956067i | 0.878342 | + | 0.478034i | \(0.158650\pi\) | ||||
−0.878342 | + | 0.478034i | \(0.841350\pi\) | |||||||
\(564\) | 1.17614e7 | + | 5.89307e8i | 0.0655575 | + | 3.28477i | ||||
\(565\) | −2.19836e8 | −1.21886 | ||||||||
\(566\) | − | 2.35330e8i | − | 1.29786i | ||||||
\(567\) | −6.86776e7 | + | 5.49362e6i | −0.376761 | + | 0.0301377i | ||||
\(568\) | 3.13402e8 | 1.71024 | ||||||||
\(569\) | − | 1.22459e8i | − | 0.664744i | −0.943148 | − | 0.332372i | \(-0.892151\pi\) | ||
0.943148 | − | 0.332372i | \(-0.107849\pi\) | |||||||
\(570\) | 7.41559e7 | − | 1.48001e6i | 0.400425 | − | 0.00799169i | ||||
\(571\) | −1.61790e8 | −0.869050 | −0.434525 | − | 0.900660i | \(-0.643084\pi\) | ||||
−0.434525 | + | 0.900660i | \(0.643084\pi\) | |||||||
\(572\) | − | 1.22924e8i | − | 0.656822i | ||||||
\(573\) | −322722. | − | 1.61700e7i | −0.00171540 | − | 0.0859502i | ||||
\(574\) | −1.09684e8 | −0.579973 | ||||||||
\(575\) | 2.19865e7i | 0.115652i | ||||||||
\(576\) | −5.38737e8 | + | 2.15128e7i | −2.81909 | + | 0.112572i | ||||
\(577\) | 2.12745e8 | 1.10747 | 0.553736 | − | 0.832692i | \(-0.313202\pi\) | ||||
0.553736 | + | 0.832692i | \(0.313202\pi\) | |||||||
\(578\) | 1.47754e7i | 0.0765169i | ||||||||
\(579\) | 1.60720e8 | − | 3.20766e6i | 0.828010 | − | 0.0165254i | ||||
\(580\) | −8.47822e8 | −4.34531 | ||||||||
\(581\) | − | 3.72285e7i | − | 0.189822i | ||||||
\(582\) | 9.66932e6 | + | 4.84483e8i | 0.0490486 | + | 2.45759i | ||||
\(583\) | 2.17313e7 | 0.109668 | ||||||||
\(584\) | − | 2.31895e8i | − | 1.16427i | ||||||
\(585\) | 7.03523e6 | + | 1.76180e8i | 0.0351407 | + | 0.880015i | ||||
\(586\) | 4.78879e8 | 2.37976 | ||||||||
\(587\) | − | 1.05054e8i | − | 0.519397i | −0.965690 | − | 0.259698i | \(-0.916377\pi\) | ||
0.965690 | − | 0.259698i | \(-0.0836231\pi\) | |||||||
\(588\) | −7.66594e7 | + | 1.52997e6i | −0.377080 | + | 0.00752577i | ||||
\(589\) | −2.36698e7 | −0.115838 | ||||||||
\(590\) | 7.29853e7i | 0.355369i | ||||||||
\(591\) | −1.42735e6 | − | 7.15177e7i | −0.00691462 | − | 0.346458i | ||||
\(592\) | −1.03937e8 | −0.500961 | ||||||||
\(593\) | − | 1.28998e8i | − | 0.618614i | −0.950962 | − | 0.309307i | \(-0.899903\pi\) | ||
0.950962 | − | 0.309307i | \(-0.100097\pi\) | |||||||
\(594\) | −1.06883e8 | + | 6.40632e6i | −0.509975 | + | 0.0305667i | ||||
\(595\) | 7.39421e7 | 0.351027 | ||||||||
\(596\) | − | 8.13621e8i | − | 3.84312i | ||||||
\(597\) | −3.49199e8 | + | 6.96932e6i | −1.64116 | + | 0.0327542i | ||||
\(598\) | −4.32254e8 | −2.02132 | ||||||||
\(599\) | 2.22645e8i | 1.03594i | 0.855400 | + | 0.517968i | \(0.173311\pi\) | ||||
−0.855400 | + | 0.517968i | \(0.826689\pi\) | |||||||
\(600\) | −1.36785e6 | − | 6.85363e7i | −0.00633264 | − | 0.317298i | ||||
\(601\) | −1.77397e7 | −0.0817191 | −0.0408596 | − | 0.999165i | \(-0.513010\pi\) | ||||
−0.0408596 | + | 0.999165i | \(0.513010\pi\) | |||||||
\(602\) | − | 1.19267e8i | − | 0.546675i | ||||||
\(603\) | −9.70291e7 | + | 3.87456e6i | −0.442537 | + | 0.0176714i | ||||
\(604\) | −5.83473e8 | −2.64795 | ||||||||
\(605\) | 1.94864e8i | 0.879963i | ||||||||
\(606\) | 5.78457e8 | − | 1.15449e7i | 2.59928 | − | 0.0518765i | ||||
\(607\) | −2.74443e7 | −0.122712 | −0.0613559 | − | 0.998116i | \(-0.519542\pi\) | ||||
−0.0613559 | + | 0.998116i | \(0.519542\pi\) | |||||||
\(608\) | − | 1.60471e8i | − | 0.713979i | ||||||
\(609\) | 2.95773e6 | + | 1.48198e8i | 0.0130950 | + | 0.656129i | ||||
\(610\) | 2.14800e8 | 0.946334 | ||||||||
\(611\) | − | 2.63727e8i | − | 1.15620i | ||||||
\(612\) | −2.36569e7 | − | 5.92431e8i | −0.103206 | − | 2.58454i | ||||
\(613\) | 2.44566e8 | 1.06173 | 0.530867 | − | 0.847455i | \(-0.321867\pi\) | ||||
0.530867 | + | 0.847455i | \(0.321867\pi\) | |||||||
\(614\) | 4.97901e8i | 2.15099i | ||||||||
\(615\) | 1.77304e8 | − | 3.53863e6i | 0.762241 | − | 0.0152128i | ||||
\(616\) | −7.40265e7 | −0.316698 | ||||||||
\(617\) | 6.37471e7i | 0.271397i | 0.990750 | + | 0.135699i | \(0.0433279\pi\) | ||||
−0.990750 | + | 0.135699i | \(0.956672\pi\) | |||||||
\(618\) | −9.86526e6 | − | 4.94300e8i | −0.0417968 | − | 2.09424i | ||||
\(619\) | 2.88252e8 | 1.21535 | 0.607674 | − | 0.794187i | \(-0.292103\pi\) | ||||
0.607674 | + | 0.794187i | \(0.292103\pi\) | |||||||
\(620\) | − | 3.11994e8i | − | 1.30910i | ||||||
\(621\) | 1.63387e7 | + | 2.72595e8i | 0.0682250 | + | 1.13826i | ||||
\(622\) | −5.81516e8 | −2.41652 | ||||||||
\(623\) | 1.03635e8i | 0.428588i | ||||||||
\(624\) | 7.51562e8 | − | 1.49997e7i | 3.09322 | − | 0.0617346i | ||||
\(625\) | −2.16868e8 | −0.888292 | ||||||||
\(626\) | − | 2.51052e8i | − | 1.02339i | ||||||
\(627\) | −291662. | − | 1.46138e7i | −0.00118325 | − | 0.0592869i | ||||
\(628\) | 3.32260e8 | 1.34152 | ||||||||
\(629\) | − | 3.66799e7i | − | 0.147393i | ||||||
\(630\) | 1.70789e8 | − | 6.81995e6i | 0.683028 | − | 0.0272747i | ||||
\(631\) | −2.57686e8 | −1.02566 | −0.512830 | − | 0.858490i | \(-0.671403\pi\) | ||||
−0.512830 | + | 0.858490i | \(0.671403\pi\) | |||||||
\(632\) | 1.43236e9i | 5.67417i | ||||||||
\(633\) | 1.06042e8 | − | 2.11638e6i | 0.418085 | − | 0.00834416i | ||||
\(634\) | −4.86468e8 | −1.90891 | ||||||||
\(635\) | − | 3.87620e7i | − | 0.151386i | ||||||
\(636\) | 5.55047e6 | + | 2.78107e8i | 0.0215754 | + | 1.08104i | ||||
\(637\) | 3.43067e7 | 0.132727 | ||||||||
\(638\) | 2.30364e8i | 0.887059i | ||||||||
\(639\) | 5.69000e6 | + | 1.42492e8i | 0.0218077 | + | 0.546121i | ||||
\(640\) | 5.36430e8 | 2.04632 | ||||||||
\(641\) | 2.04007e8i | 0.774588i | 0.921956 | + | 0.387294i | \(0.126590\pi\) | ||||
−0.921956 | + | 0.387294i | \(0.873410\pi\) | |||||||
\(642\) | −7.52138e8 | + | 1.50112e7i | −2.84245 | + | 0.0567296i | ||||
\(643\) | 4.66132e8 | 1.75338 | 0.876690 | − | 0.481055i | \(-0.159746\pi\) | ||||
0.876690 | + | 0.481055i | \(0.159746\pi\) | |||||||
\(644\) | 3.03912e8i | 1.13786i | ||||||||
\(645\) | 3.84779e6 | + | 1.92794e8i | 0.0143394 | + | 0.718479i | ||||
\(646\) | 1.11594e8 | 0.413944 | ||||||||
\(647\) | − | 7.13431e7i | − | 0.263414i | −0.991289 | − | 0.131707i | \(-0.957954\pi\) | ||
0.991289 | − | 0.131707i | \(-0.0420458\pi\) | |||||||
\(648\) | −6.78900e7 | − | 8.48716e8i | −0.249506 | − | 3.11916i | ||||
\(649\) | 1.43831e7 | 0.0526159 | ||||||||
\(650\) | 4.93725e7i | 0.179782i | ||||||||
\(651\) | −5.45359e7 | + | 1.08843e6i | −0.197670 | + | 0.00394509i | ||||
\(652\) | 4.75503e7 | 0.171558 | ||||||||
\(653\) | − | 3.40530e8i | − | 1.22297i | −0.791255 | − | 0.611486i | \(-0.790572\pi\) | ||
0.791255 | − | 0.611486i | \(-0.209428\pi\) | |||||||
\(654\) | 5.73988e6 | + | 2.87598e8i | 0.0205196 | + | 1.02814i | ||||
\(655\) | 8.35358e6 | 0.0297268 | ||||||||
\(656\) | − | 7.56053e8i | − | 2.67819i | ||||||
\(657\) | 1.05434e8 | − | 4.21018e6i | 0.371778 | − | 0.0148458i | ||||
\(658\) | −2.55657e8 | −0.897387 | ||||||||
\(659\) | − | 1.33221e8i | − | 0.465495i | −0.972537 | − | 0.232748i | \(-0.925228\pi\) | ||
0.972537 | − | 0.232748i | \(-0.0747716\pi\) | |||||||
\(660\) | 1.92625e8 | − | 3.84442e6i | 0.670010 | − | 0.0133721i | ||||
\(661\) | −1.15163e8 | −0.398758 | −0.199379 | − | 0.979922i | \(-0.563892\pi\) | ||||
−0.199379 | + | 0.979922i | \(0.563892\pi\) | |||||||
\(662\) | 8.03104e7i | 0.276820i | ||||||||
\(663\) | 5.29348e6 | + | 2.65231e8i | 0.0181636 | + | 0.910088i | ||||
\(664\) | 4.60069e8 | 1.57152 | ||||||||
\(665\) | 2.33328e7i | 0.0793419i | ||||||||
\(666\) | −3.38312e6 | − | 8.47222e7i | −0.0114524 | − | 0.286797i | ||||
\(667\) | 5.87522e8 | 1.97992 | ||||||||
\(668\) | 1.37997e9i | 4.62957i | ||||||||
\(669\) | −1.09938e8 | + | 2.19415e6i | −0.367172 | + | 0.00732803i | ||||
\(670\) | 2.40910e8 | 0.800995 | ||||||||
\(671\) | − | 4.23302e7i | − | 0.140114i | ||||||
\(672\) | −7.37906e6 | − | 3.69729e8i | −0.0243161 | − | 1.21836i | ||||
\(673\) | 1.27548e8 | 0.418436 | 0.209218 | − | 0.977869i | \(-0.432908\pi\) | ||||
0.209218 | + | 0.977869i | \(0.432908\pi\) | |||||||
\(674\) | − | 1.10501e9i | − | 3.60901i | ||||||
\(675\) | 3.11361e7 | − | 1.86623e6i | 0.101240 | − | 0.00606810i | ||||
\(676\) | 1.11562e8 | 0.361139 | ||||||||
\(677\) | − | 3.13042e8i | − | 1.00887i | −0.863448 | − | 0.504437i | \(-0.831700\pi\) | ||
0.863448 | − | 0.504437i | \(-0.168300\pi\) | |||||||
\(678\) | −7.64422e8 | + | 1.52563e7i | −2.45270 | + | 0.0489510i | ||||
\(679\) | −1.52441e8 | −0.486958 | ||||||||
\(680\) | 9.13774e8i | 2.90611i | ||||||||
\(681\) | −5.64114e6 | − | 2.82650e8i | −0.0178618 | − | 0.894968i | ||||
\(682\) | −8.47727e7 | −0.267241 | ||||||||
\(683\) | − | 3.04900e7i | − | 0.0956964i | −0.998855 | − | 0.0478482i | \(-0.984764\pi\) | ||
0.998855 | − | 0.0478482i | \(-0.0152364\pi\) | |||||||
\(684\) | 1.86945e8 | − | 7.46508e6i | 0.584179 | − | 0.0233274i | ||||
\(685\) | 7.64982e7 | 0.238001 | ||||||||
\(686\) | − | 3.32568e7i | − | 0.103017i | ||||||
\(687\) | 1.99903e8 | − | 3.98967e6i | 0.616523 | − | 0.0123046i | ||||
\(688\) | 8.22106e8 | 2.52442 | ||||||||
\(689\) | − | 1.24459e8i | − | 0.380511i | ||||||
\(690\) | −1.35187e7 | − | 6.77355e8i | −0.0411516 | − | 2.06191i | ||||
\(691\) | −4.93596e8 | −1.49602 | −0.748010 | − | 0.663688i | \(-0.768990\pi\) | ||||
−0.748010 | + | 0.663688i | \(0.768990\pi\) | |||||||
\(692\) | 8.68701e8i | 2.62151i | ||||||||
\(693\) | −1.34399e6 | − | 3.36571e7i | −0.00403829 | − | 0.101129i | ||||
\(694\) | −3.50745e8 | −1.04933 | ||||||||
\(695\) | − | 4.23011e8i | − | 1.26008i | ||||||
\(696\) | −1.83142e9 | + | 3.65516e7i | −5.43201 | + | 0.108412i | ||||
\(697\) | 2.66816e8 | 0.787976 | ||||||||
\(698\) | − | 9.35067e8i | − | 2.74965i | ||||||
\(699\) | −9.80599e6 | − | 4.91331e8i | −0.0287118 | − | 1.43861i | ||||
\(700\) | 3.47132e7 | 0.101205 | ||||||||
\(701\) | − | 4.50780e8i | − | 1.30861i | −0.756230 | − | 0.654306i | \(-0.772961\pi\) | ||
0.756230 | − | 0.654306i | \(-0.227039\pi\) | |||||||
\(702\) | 3.66899e7 | + | 6.12134e8i | 0.106056 | + | 1.76944i | ||||
\(703\) | 1.15746e7 | 0.0333149 | ||||||||
\(704\) | − | 2.63600e8i | − | 0.755487i | ||||||
\(705\) | 4.13268e8 | − | 8.24801e6i | 1.17941 | − | 0.0235387i | ||||
\(706\) | 8.13355e8 | 2.31135 | ||||||||
\(707\) | 1.82009e8i | 0.515033i | ||||||||
\(708\) | 3.67362e6 | + | 1.84067e8i | 0.0103513 | + | 0.518653i | ||||
\(709\) | −5.70371e8 | −1.60036 | −0.800182 | − | 0.599757i | \(-0.795264\pi\) | ||||
−0.800182 | + | 0.599757i | \(0.795264\pi\) | |||||||
\(710\) | − | 3.53788e8i | − | 0.988481i | ||||||
\(711\) | −6.51243e8 | + | 2.60054e7i | −1.81190 | + | 0.0723527i | ||||
\(712\) | −1.28071e9 | −3.54823 | ||||||||
\(713\) | 2.16205e8i | 0.596482i | ||||||||
\(714\) | 2.57115e8 | − | 5.13150e6i | 0.706370 | − | 0.0140977i | ||||
\(715\) | −8.62037e7 | −0.235835 | ||||||||
\(716\) | 9.40001e8i | 2.56088i | ||||||||
\(717\) | 9.01909e6 | + | 4.51903e8i | 0.0244684 | + | 1.22599i | ||||
\(718\) | −9.51468e7 | −0.257052 | ||||||||
\(719\) | 1.28727e8i | 0.346325i | 0.984893 | + | 0.173163i | \(0.0553986\pi\) | ||||
−0.984893 | + | 0.173163i | \(0.944601\pi\) | |||||||
\(720\) | 4.70099e7 | + | 1.17725e9i | 0.125948 | + | 3.15407i | ||||
\(721\) | 1.55530e8 | 0.414961 | ||||||||
\(722\) | − | 6.82857e8i | − | 1.81434i | ||||||
\(723\) | 5.44671e8 | − | 1.08706e7i | 1.44118 | − | 0.0287632i | ||||
\(724\) | 1.13704e9 | 2.99612 | ||||||||
\(725\) | − | 6.71074e7i | − | 0.176099i | ||||||
\(726\) | 1.35233e7 | + | 6.77588e8i | 0.0353405 | + | 1.77074i | ||||
\(727\) | −5.00584e8 | −1.30279 | −0.651394 | − | 0.758740i | \(-0.725815\pi\) | ||||
−0.651394 | + | 0.758740i | \(0.725815\pi\) | |||||||
\(728\) | 4.23960e8i | 1.09883i | ||||||||
\(729\) | 3.84647e8 | − | 4.62760e7i | 0.992841 | − | 0.119446i | ||||
\(730\) | −2.61778e8 | −0.672921 | ||||||||
\(731\) | 2.90126e8i | 0.742736i | ||||||||
\(732\) | 5.41721e8 | − | 1.08117e7i | 1.38115 | − | 0.0275651i | ||||
\(733\) | 5.86354e7 | 0.148884 | 0.0744420 | − | 0.997225i | \(-0.476282\pi\) | ||||
0.0744420 | + | 0.997225i | \(0.476282\pi\) | |||||||
\(734\) | − | 8.08240e8i | − | 2.04387i | ||||||
\(735\) | 1.07293e6 | + | 5.37595e7i | 0.00270216 | + | 0.135392i | ||||
\(736\) | −1.46577e9 | −3.67649 | ||||||||
\(737\) | − | 4.74756e7i | − | 0.118595i | ||||||
\(738\) | 6.16283e8 | − | 2.46094e7i | 1.53324 | − | 0.0612254i | ||||
\(739\) | 4.44555e8 | 1.10152 | 0.550760 | − | 0.834664i | \(-0.314338\pi\) | ||||
0.550760 | + | 0.834664i | \(0.314338\pi\) | |||||||
\(740\) | 1.52565e8i | 0.376496i | ||||||||
\(741\) | −8.36951e7 | + | 1.67039e6i | −0.205705 | + | 0.00410547i | ||||
\(742\) | −1.20650e8 | −0.295336 | ||||||||
\(743\) | 8.35867e6i | 0.0203784i | 0.999948 | + | 0.0101892i | \(0.00324339\pi\) | ||||
−0.999948 | + | 0.0101892i | \(0.996757\pi\) | |||||||
\(744\) | −1.34508e7 | − | 6.73953e8i | −0.0326609 | − | 1.63648i | ||||
\(745\) | −5.70574e8 | −1.37989 | ||||||||
\(746\) | 7.12904e8i | 1.71718i | ||||||||
\(747\) | 8.35281e6 | + | 2.09176e8i | 0.0200388 | + | 0.501823i | ||||
\(748\) | 2.89872e8 | 0.692630 | ||||||||
\(749\) | − | 2.36657e8i | − | 0.563215i | ||||||
\(750\) | −8.40204e8 | + | 1.67688e7i | −1.99159 | + | 0.0397483i | ||||
\(751\) | 2.94347e8 | 0.694929 | 0.347464 | − | 0.937693i | \(-0.387043\pi\) | ||||
0.347464 | + | 0.937693i | \(0.387043\pi\) | |||||||
\(752\) | − | 1.76224e9i | − | 4.14393i | ||||||
\(753\) | −8.76962e6 | − | 4.39403e8i | −0.0205398 | − | 1.02915i | ||||
\(754\) | 1.31933e9 | 3.07779 | ||||||||
\(755\) | 4.09177e8i | 0.950758i | ||||||||
\(756\) | 4.30383e8 | − | 2.57962e7i | 0.996071 | − | 0.0597022i | ||||
\(757\) | −2.95864e8 | −0.682031 | −0.341016 | − | 0.940058i | \(-0.610771\pi\) | ||||
−0.341016 | + | 0.940058i | \(0.610771\pi\) | |||||||
\(758\) | 3.35674e8i | 0.770745i | ||||||||
\(759\) | −1.33485e8 | + | 2.66410e6i | −0.305286 | + | 0.00609291i | ||||
\(760\) | −2.88347e8 | −0.656862 | ||||||||
\(761\) | 7.57657e8i | 1.71917i | 0.510993 | + | 0.859585i | \(0.329278\pi\) | ||||
−0.510993 | + | 0.859585i | \(0.670722\pi\) | |||||||
\(762\) | −2.69004e6 | − | 1.34785e8i | −0.00607987 | − | 0.304633i | ||||
\(763\) | −9.04914e7 | −0.203720 | ||||||||
\(764\) | 1.01212e8i | 0.226961i | ||||||||
\(765\) | −4.15459e8 | + | 1.65901e7i | −0.927991 | + | 0.0370565i | ||||
\(766\) | 7.57610e8 | 1.68562 | ||||||||
\(767\) | − | 8.23739e7i | − | 0.182559i | ||||||
\(768\) | 5.87528e8 | − | 1.17259e7i | 1.29701 | − | 0.0258858i | ||||
\(769\) | −8.35758e8 | −1.83781 | −0.918907 | − | 0.394475i | \(-0.870927\pi\) | ||||
−0.918907 | + | 0.394475i | \(0.870927\pi\) | |||||||
\(770\) | 8.35658e7i | 0.183044i | ||||||||
\(771\) | 1.31846e7 | + | 6.60618e8i | 0.0287677 | + | 1.44141i | ||||
\(772\) | −1.00599e9 | −2.18645 | ||||||||
\(773\) | 6.51151e8i | 1.40975i | 0.709329 | + | 0.704877i | \(0.248998\pi\) | ||||
−0.709329 | + | 0.704877i | \(0.751002\pi\) | |||||||
\(774\) | 2.67594e7 | + | 6.70124e8i | 0.0577103 | + | 1.44522i | ||||
\(775\) | 2.46952e7 | 0.0530526 | ||||||||
\(776\) | − | 1.88385e9i | − | 4.03146i | ||||||
\(777\) | 2.66681e7 | − | 532243.i | 0.0568498 | − | 0.00113461i | ||||
\(778\) | 3.20300e8 | 0.680171 | ||||||||
\(779\) | 8.41952e7i | 0.178105i | ||||||||
\(780\) | −2.20175e7 | − | 1.10319e9i | −0.0463965 | − | 2.32470i | ||||
\(781\) | −6.97203e7 | −0.146355 | ||||||||
\(782\) | − | 1.01932e9i | − | 2.13152i | ||||||
\(783\) | −4.98692e7 | − | 8.32016e8i | −0.103884 | − | 1.73319i | ||||
\(784\) | 2.29240e8 | 0.475709 | ||||||||
\(785\) | − | 2.33006e8i | − | 0.481680i | ||||||
\(786\) | 2.90474e7 | − | 579729.i | 0.0598191 | − | 0.00119387i | ||||
\(787\) | 2.96849e8 | 0.608991 | 0.304495 | − | 0.952514i | \(-0.401512\pi\) | ||||
0.304495 | + | 0.952514i | \(0.401512\pi\) | |||||||
\(788\) | 4.47645e8i | 0.914862i | ||||||||
\(789\) | −5.90962e6 | − | 2.96102e8i | −0.0120317 | − | 0.602852i | ||||
\(790\) | 1.61694e9 | 3.27955 | ||||||||
\(791\) | − | 2.40522e8i | − | 0.485988i | ||||||
\(792\) | 4.15933e8 | − | 1.66090e7i | 0.837236 | − | 0.0334325i | ||||
\(793\) | −2.42431e8 | −0.486148 | ||||||||
\(794\) | 1.35298e9i | 2.70289i | ||||||||
\(795\) | 1.95030e8 | − | 3.89242e6i | 0.388151 | − | 0.00774672i | ||||
\(796\) | 2.18571e9 | 4.33365 | ||||||||
\(797\) | 2.57514e7i | 0.0508659i | 0.999677 | + | 0.0254329i | \(0.00809643\pi\) | ||||
−0.999677 | + | 0.0254329i | \(0.991904\pi\) | |||||||
\(798\) | 1.61927e6 | + | 8.11340e7i | 0.00318648 | + | 0.159659i | ||||
\(799\) | 6.21907e8 | 1.21923 | ||||||||
\(800\) | 1.67422e8i | 0.326996i | ||||||||
\(801\) | −2.32521e7 | − | 5.82292e8i | −0.0452443 | − | 1.13303i | ||||
\(802\) | −8.94972e8 | −1.73495 | ||||||||
\(803\) | 5.15880e7i | 0.0996327i | ||||||||
\(804\) | 6.07569e8 | − | 1.21259e7i | 1.16903 | − | 0.0233316i | ||||
\(805\) | 2.13127e8 | 0.408555 | ||||||||
\(806\) | 4.85506e8i | 0.927234i | ||||||||
\(807\) | 1.18618e7 | + | 5.94340e8i | 0.0225700 | + | 1.13087i | ||||
\(808\) | −2.24926e9 | −4.26389 | ||||||||
\(809\) | 6.07452e8i | 1.14727i | 0.819110 | + | 0.573636i | \(0.194468\pi\) | ||||
−0.819110 | + | 0.573636i | \(0.805532\pi\) | |||||||
\(810\) | −9.58084e8 | + | 7.66386e7i | −1.80280 | + | 0.144209i | ||||
\(811\) | −1.78071e8 | −0.333835 | −0.166917 | − | 0.985971i | \(-0.553381\pi\) | ||||
−0.166917 | + | 0.985971i | \(0.553381\pi\) | |||||||
\(812\) | − | 9.27603e8i | − | 1.73258i | ||||||
\(813\) | 6.56840e6 | − | 131092.i | 0.0122233 | − | 0.000243953i | ||||
\(814\) | 4.14539e7 | 0.0768585 | ||||||||
\(815\) | − | 3.33460e7i | − | 0.0615986i | ||||||
\(816\) | 3.53715e7 | + | 1.77229e9i | 0.0651002 | + | 3.26186i | ||||
\(817\) | −9.15510e7 | −0.167879 | ||||||||
\(818\) | 1.23539e9i | 2.25706i | ||||||||
\(819\) | −1.92759e8 | + | 7.69725e6i | −0.350884 | + | 0.0140115i | ||||
\(820\) | −1.10978e9 | −2.01278 | ||||||||
\(821\) | 3.25560e8i | 0.588304i | 0.955759 | + | 0.294152i | \(0.0950372\pi\) | ||||
−0.955759 | + | 0.294152i | \(0.904963\pi\) | |||||||
\(822\) | 2.66003e8 | − | 5.30889e6i | 0.478928 | − | 0.00955847i | ||||
\(823\) | −3.15464e7 | −0.0565914 | −0.0282957 | − | 0.999600i | \(-0.509008\pi\) | ||||
−0.0282957 | + | 0.999600i | \(0.509008\pi\) | |||||||
\(824\) | 1.92203e9i | 3.43541i | ||||||||
\(825\) | 304296. | + | 1.52468e7i | 0.000541919 | + | 0.0271529i | ||||
\(826\) | −7.98532e7 | −0.141694 | ||||||||
\(827\) | − | 3.83741e8i | − | 0.678456i | −0.940704 | − | 0.339228i | \(-0.889834\pi\) | ||
0.940704 | − | 0.339228i | \(-0.110166\pi\) | |||||||
\(828\) | −6.81876e7 | − | 1.70759e9i | −0.120120 | − | 3.00811i | ||||
\(829\) | −7.83129e7 | −0.137458 | −0.0687289 | − | 0.997635i | \(-0.521894\pi\) | ||||
−0.0687289 | + | 0.997635i | \(0.521894\pi\) | |||||||
\(830\) | − | 5.19355e8i | − | 0.908302i | ||||||
\(831\) | 4.42521e8 | − | 8.83184e6i | 0.771135 | − | 0.0153903i | ||||
\(832\) | −1.50967e9 | −2.62128 | ||||||||
\(833\) | 8.09000e7i | 0.139963i | ||||||||
\(834\) | −2.93565e7 | − | 1.47091e9i | −0.0506065 | − | 2.53565i | ||||
\(835\) | 9.67742e8 | 1.66227 | ||||||||
\(836\) | 9.14708e7i | 0.156554i | ||||||||
\(837\) | 3.06177e8 | − | 1.83516e7i | 0.522152 | − | 0.0312966i | ||||
\(838\) | −1.54893e9 | −2.63208 | ||||||||
\(839\) | 5.38101e8i | 0.911125i | 0.890204 | + | 0.455562i | \(0.150562\pi\) | ||||
−0.890204 | + | 0.455562i | \(0.849438\pi\) | |||||||
\(840\) | −6.64358e8 | + | 1.32593e7i | −1.12089 | + | 0.0223708i | ||||
\(841\) | −1.19842e9 | −2.01474 | ||||||||
\(842\) | 3.59158e8i | 0.601657i | ||||||||
\(843\) | −6.48782e6 | − | 3.25073e8i | −0.0108297 | − | 0.542623i | ||||
\(844\) | −6.63738e8 | −1.10400 | ||||||||
\(845\) | − | 7.82356e7i | − | 0.129668i | ||||||
\(846\) | 1.43646e9 | − | 5.73607e7i | 2.37237 | − | 0.0947335i | ||||
\(847\) | −2.13200e8 | −0.350863 | ||||||||
\(848\) | − | 8.31642e8i | − | 1.36379i | ||||||
\(849\) | −4.16207e8 | + | 8.30667e6i | −0.680121 | + | 0.0135739i | ||||
\(850\) | −1.16428e8 | −0.189583 | ||||||||
\(851\) | − | 1.05724e8i | − | 0.171548i | ||||||
\(852\) | −1.78075e7 | − | 8.92247e8i | −0.0287928 | − | 1.44267i | ||||
\(853\) | −4.26618e8 | −0.687372 | −0.343686 | − | 0.939085i | \(-0.611676\pi\) | ||||
−0.343686 | + | 0.939085i | \(0.611676\pi\) | |||||||
\(854\) | 2.35013e8i | 0.377327i | ||||||||
\(855\) | −5.23510e6 | − | 1.31100e8i | −0.00837580 | − | 0.209752i | ||||
\(856\) | 2.92460e9 | 4.66278 | ||||||||
\(857\) | − | 5.94150e8i | − | 0.943960i | −0.881609 | − | 0.471980i | \(-0.843539\pi\) | ||
0.881609 | − | 0.471980i | \(-0.156461\pi\) | |||||||
\(858\) | −2.99751e8 | + | 5.98244e6i | −0.474569 | + | 0.00947145i | ||||
\(859\) | −7.06773e8 | −1.11507 | −0.557533 | − | 0.830155i | \(-0.688252\pi\) | ||||
−0.557533 | + | 0.830155i | \(0.688252\pi\) | |||||||
\(860\) | − | 1.20674e9i | − | 1.89722i | ||||||
\(861\) | 3.87162e6 | + | 1.93988e8i | 0.00606573 | + | 0.303924i | ||||
\(862\) | 1.98811e9 | 3.10398 | ||||||||
\(863\) | 2.61287e8i | 0.406523i | 0.979124 | + | 0.203262i | \(0.0651542\pi\) | ||||
−0.979124 | + | 0.203262i | \(0.934846\pi\) | |||||||
\(864\) | 1.24415e8 | + | 2.07574e9i | 0.192900 | + | 3.21835i | ||||
\(865\) | 6.09200e8 | 0.941265 | ||||||||
\(866\) | 6.01583e8i | 0.926280i | ||||||||
\(867\) | 2.61320e7 | − | 521542.i | 0.0400973 | − | 0.000800262i | ||||
\(868\) | 3.41353e8 | 0.521969 | ||||||||
\(869\) | − | 3.18648e8i | − | 0.485570i | ||||||
\(870\) | 4.12617e7 | + | 2.06743e9i | 0.0626599 | + | 3.13959i | ||||
\(871\) | −2.71900e8 | −0.411485 | ||||||||
\(872\) | − | 1.11829e9i | − | 1.68657i | ||||||
\(873\) | 8.56519e8 | − | 3.42025e7i | 1.28734 | − | 0.0514061i | ||||
\(874\) | 3.21652e8 | 0.481783 | ||||||||
\(875\) | − | 2.64367e8i | − | 0.394623i | ||||||
\(876\) | −6.60198e8 | + | 1.31762e7i | −0.982113 | + | 0.0196010i | ||||
\(877\) | −3.73441e8 | −0.553634 | −0.276817 | − | 0.960923i | \(-0.589280\pi\) | ||||
−0.276817 | + | 0.960923i | \(0.589280\pi\) | |||||||
\(878\) | − | 2.46615e9i | − | 3.64365i | ||||||
\(879\) | −1.69034e7 | − | 8.46950e8i | −0.0248891 | − | 1.24707i | ||||
\(880\) | −5.76019e8 | −0.845258 | ||||||||
\(881\) | 9.23680e8i | 1.35081i | 0.737447 | + | 0.675405i | \(0.236031\pi\) | ||||
−0.737447 | + | 0.675405i | \(0.763969\pi\) | |||||||
\(882\) | 7.46170e6 | + | 1.86860e8i | 0.0108751 | + | 0.272340i | ||||
\(883\) | 3.97760e8 | 0.577749 | 0.288875 | − | 0.957367i | \(-0.406719\pi\) | ||||
0.288875 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(884\) | − | 1.66014e9i | − | 2.40319i | ||||||
\(885\) | 1.29082e8 | − | 2.57623e6i | 0.186225 | − | 0.00371668i | ||||
\(886\) | −1.22209e9 | −1.75712 | ||||||||
\(887\) | − | 1.35041e9i | − | 1.93506i | −0.252758 | − | 0.967530i | \(-0.581338\pi\) | ||
0.252758 | − | 0.967530i | \(-0.418662\pi\) | |||||||
\(888\) | 6.57744e6 | + | 3.29564e8i | 0.00939329 | + | 0.470652i | ||||
\(889\) | 4.24095e7 | 0.0603613 | ||||||||
\(890\) | 1.44575e9i | 2.05080i | ||||||||
\(891\) | 1.51030e7 | + | 1.88808e8i | 0.0213516 | + | 0.266923i | ||||
\(892\) | 6.88127e8 | 0.969559 | ||||||||
\(893\) | 1.96246e8i | 0.275580i | ||||||||
\(894\) | −1.98403e9 | + | 3.95972e7i | −2.77674 | + | 0.0554182i | ||||
\(895\) | 6.59202e8 | 0.919495 | ||||||||
\(896\) | 5.86908e8i | 0.815917i | ||||||||
\(897\) | 1.52577e7 | + | 7.64488e8i | 0.0211403 | + | 1.05924i | ||||
\(898\) | −2.01661e9 | −2.78479 | ||||||||
\(899\) | − | 6.59902e8i | − | 0.908240i | ||||||
\(900\) | −1.95043e8 | + | 7.78846e6i | −0.267549 | + | 0.0106838i | ||||
\(901\) | 2.93491e8 | 0.401255 | ||||||||
\(902\) | 3.01542e8i | 0.410893i | ||||||||
\(903\) | −2.10936e8 | + | 4.20986e6i | −0.286475 | + | 0.00571748i | ||||
\(904\) | 2.97237e9 | 4.02343 | ||||||||
\(905\) | − | 7.97379e8i | − | 1.07577i | ||||||
\(906\) | 2.83964e7 | + | 1.42281e9i | 0.0381838 | + | 1.91320i | ||||
\(907\) | −8.88661e7 | −0.119101 | −0.0595504 | − | 0.998225i | \(-0.518967\pi\) | ||||
−0.0595504 | + | 0.998225i | \(0.518967\pi\) | |||||||
\(908\) | 1.76917e9i | 2.36326i | ||||||||
\(909\) | −4.08367e7 | − | 1.02266e9i | −0.0543699 | − | 1.36156i | ||||
\(910\) | 4.78594e8 | 0.635101 | ||||||||
\(911\) | 8.00546e8i | 1.05884i | 0.848359 | + | 0.529421i | \(0.177591\pi\) | ||||
−0.848359 | + | 0.529421i | \(0.822409\pi\) | |||||||
\(912\) | −5.59257e8 | + | 1.11617e7i | −0.737271 | + | 0.0147145i | ||||
\(913\) | −1.02348e8 | −0.134483 | ||||||||
\(914\) | − | 5.44851e8i | − | 0.713575i | ||||||
\(915\) | −7.58199e6 | − | 3.79897e8i | −0.00989737 | − | 0.495909i | ||||
\(916\) | −1.25124e9 | −1.62800 | ||||||||
\(917\) | 9.13965e6i | 0.0118528i | ||||||||
\(918\) | −1.44350e9 | + | 8.65202e7i | −1.86590 | + | 0.111838i | ||||
\(919\) | 1.33761e9 | 1.72338 | 0.861691 | − | 0.507434i | \(-0.169406\pi\) | ||||
0.861691 | + | 0.507434i | \(0.169406\pi\) | |||||||
\(920\) | 2.63382e9i | 3.38238i | ||||||||
\(921\) | 8.80591e8 | − | 1.75749e7i | 1.12719 | − | 0.0224964i | ||||
\(922\) | 1.35094e9 | 1.72363 | ||||||||
\(923\) | 3.99299e8i | 0.507800i | ||||||||
\(924\) | 4.20618e6 | + | 2.10751e8i | 0.00533177 | + | 0.267149i | ||||
\(925\) | −1.20759e7 | −0.0152579 | ||||||||
\(926\) | − | 1.50782e9i | − | 1.89896i | ||||||
\(927\) | −8.73875e8 | + | 3.48956e7i | −1.09701 | + | 0.0438057i | ||||
\(928\) | 4.47384e9 | 5.59805 | ||||||||
\(929\) | − | 1.17941e9i | − | 1.47102i | −0.677513 | − | 0.735511i | \(-0.736942\pi\) | ||
0.677513 | − | 0.735511i | \(-0.263058\pi\) | |||||||
\(930\) | −7.60802e8 | + | 1.51841e7i | −0.945851 | + | 0.0188773i | ||||
\(931\) | −2.55285e7 | −0.0316356 | ||||||||
\(932\) | 3.07535e9i | 3.79880i | ||||||||
\(933\) | 2.05263e7 | + | 1.02847e9i | 0.0252735 | + | 1.26633i | ||||
\(934\) | 1.30318e9 | 1.59943 | ||||||||
\(935\) | − | 2.03281e8i | − | 0.248692i | ||||||
\(936\) | −9.51223e7 | − | 2.38211e9i | −0.115999 | − | 2.90492i | ||||
\(937\) | −6.97854e8 | −0.848293 | −0.424147 | − | 0.905594i | \(-0.639426\pi\) | ||||
−0.424147 | + | 0.905594i | \(0.639426\pi\) | |||||||
\(938\) | 2.63579e8i | 0.319376i | ||||||||
\(939\) | −4.44012e8 | + | 8.86161e6i | −0.536288 | + | 0.0107033i | ||||
\(940\) | −2.58674e9 | −3.11436 | ||||||||
\(941\) | − | 6.81654e8i | − | 0.818079i | −0.912517 | − | 0.409040i | \(-0.865864\pi\) | ||
0.912517 | − | 0.409040i | \(-0.134136\pi\) | |||||||
\(942\) | −1.61704e7 | − | 8.10219e8i | −0.0193449 | − | 0.969282i | ||||
\(943\) | 7.69056e8 | 0.917113 | ||||||||
\(944\) | − | 5.50429e8i | − | 0.654312i | ||||||
\(945\) | −1.80903e7 | − | 3.01818e8i | −0.0214363 | − | 0.357643i | ||||
\(946\) | −3.27887e8 | −0.387302 | ||||||||
\(947\) | 1.31995e9i | 1.55420i | 0.629378 | + | 0.777099i | \(0.283310\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(948\) | 4.07790e9 | − | 8.13868e7i | 4.78643 | − | 0.0955276i | ||||
\(949\) | 2.95452e8 | 0.345691 | ||||||||
\(950\) | − | 3.67394e7i | − | 0.0428510i | ||||||
\(951\) | 1.71713e7 | + | 8.60371e8i | 0.0199646 | + | 1.00033i | ||||
\(952\) | −9.99760e8 | −1.15874 | ||||||||
\(953\) | 1.01893e9i | 1.17724i | 0.808411 | + | 0.588618i | \(0.200328\pi\) | ||||
−0.808411 | + | 0.588618i | \(0.799672\pi\) | |||||||
\(954\) | 6.77897e8 | − | 2.70698e7i | 0.780762 | − | 0.0311774i | ||||
\(955\) | 7.09776e7 | 0.0814913 | ||||||||
\(956\) | − | 2.82856e9i | − | 3.23737i | ||||||
\(957\) | 4.07423e8 | − | 8.13137e6i | 0.464847 | − | 0.00927743i | ||||
\(958\) | −1.24903e9 | −1.42062 | ||||||||
\(959\) | 8.36967e7i | 0.0948970i | ||||||||
\(960\) | −4.72148e7 | − | 2.36570e9i | −0.0533660 | − | 2.67391i | ||||
\(961\) | −6.44663e8 | −0.726378 | ||||||||
\(962\) | − | 2.37413e8i | − | 0.266673i | ||||||
\(963\) | 5.30978e7 | + | 1.32971e9i | 0.0594563 | + | 1.48894i | ||||
\(964\) | −3.40922e9 | −3.80561 | ||||||||
\(965\) | 7.05475e8i | 0.785054i | ||||||||
\(966\) | 7.41094e8 | − | 1.47908e7i | 0.822133 | − | 0.0164082i | ||||
\(967\) | −7.83984e7 | −0.0867018 | −0.0433509 | − | 0.999060i | \(-0.513803\pi\) | ||||
−0.0433509 | + | 0.999060i | \(0.513803\pi\) | |||||||
\(968\) | − | 2.63472e9i | − | 2.90475i | ||||||
\(969\) | −3.93902e6 | − | 1.97365e8i | −0.00432929 | − | 0.216920i | ||||
\(970\) | −2.12662e9 | −2.33010 | ||||||||
\(971\) | 7.64016e8i | 0.834535i | 0.908784 | + | 0.417267i | \(0.137012\pi\) | ||||
−0.908784 | + | 0.417267i | \(0.862988\pi\) | |||||||
\(972\) | −2.41241e9 | + | 2.41505e8i | −2.62695 | + | 0.262983i | ||||
\(973\) | 4.62817e8 | 0.502424 | ||||||||
\(974\) | − | 3.35975e9i | − | 3.63606i | ||||||
\(975\) | 8.73206e7 | − | 1.74275e6i | 0.0942113 | − | 0.00188027i | ||||
\(976\) | −1.61994e9 | −1.74241 | ||||||||
\(977\) | − | 3.22166e8i | − | 0.345459i | −0.984969 | − | 0.172729i | \(-0.944741\pi\) | ||
0.984969 | − | 0.172729i | \(-0.0552586\pi\) | |||||||
\(978\) | −2.31417e6 | − | 1.15952e8i | −0.00247388 | − | 0.123954i | ||||
\(979\) | 2.84911e8 | 0.303641 | ||||||||
\(980\) | − | 3.36493e8i | − | 0.357518i | ||||||
\(981\) | 5.08445e8 | − | 2.03032e7i | 0.538563 | − | 0.0215059i | ||||
\(982\) | −1.77489e9 | −1.87429 | ||||||||
\(983\) | 1.94805e8i | 0.205088i | 0.994728 | + | 0.102544i | \(0.0326982\pi\) | ||||
−0.994728 | + | 0.102544i | \(0.967302\pi\) | |||||||
\(984\) | −2.39730e9 | + | 4.78453e7i | −2.51615 | + | 0.0502174i | ||||
\(985\) | 3.13924e8 | 0.328485 | ||||||||
\(986\) | 3.11117e9i | 3.24558i | ||||||||
\(987\) | 9.02416e6 | + | 4.52157e8i | 0.00938545 | + | 0.470260i | ||||
\(988\) | 5.23867e8 | 0.543188 | ||||||||
\(989\) | 8.36245e8i | 0.864459i | ||||||||
\(990\) | −1.87493e7 | − | 4.69532e8i | −0.0193232 | − | 0.483904i | ||||
\(991\) | 5.49963e8 | 0.565083 | 0.282542 | − | 0.959255i | \(-0.408822\pi\) | ||||
0.282542 | + | 0.959255i | \(0.408822\pi\) | |||||||
\(992\) | 1.64635e9i | 1.68650i | ||||||||
\(993\) | 1.42038e8 | − | 2.83479e6i | 0.145063 | − | 0.00289516i | ||||
\(994\) | 3.87080e8 | 0.394132 | ||||||||
\(995\) | − | 1.53279e9i | − | 1.55602i | ||||||
\(996\) | −2.61411e7 | − | 1.30980e9i | −0.0264573 | − | 1.32565i | ||||
\(997\) | 1.45349e9 | 1.46665 | 0.733324 | − | 0.679879i | \(-0.237968\pi\) | ||||
0.733324 | + | 0.679879i | \(0.237968\pi\) | |||||||
\(998\) | 1.91510e9i | 1.92664i | ||||||||
\(999\) | −1.49721e8 | + | 8.97393e6i | −0.150171 | + | 0.00900091i |
(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 | 21.7.b.a.8.12 | yes | 12 | |
3.2 | odd | 2 | inner | 21.7.b.a.8.1 | ✓ | 12 | |
4.3 | odd | 2 | 336.7.d.a.113.2 | 12 | |||
7.6 | odd | 2 | 147.7.b.b.50.12 | 12 | |||
12.11 | even | 2 | 336.7.d.a.113.1 | 12 | |||
21.20 | even | 2 | 147.7.b.b.50.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.b.a.8.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
21.7.b.a.8.12 | yes | 12 | 1.1 | even | 1 | trivial | |
147.7.b.b.50.1 | 12 | 21.20 | even | 2 | |||
147.7.b.b.50.12 | 12 | 7.6 | odd | 2 | |||
336.7.d.a.113.1 | 12 | 12.11 | even | 2 | |||
336.7.d.a.113.2 | 12 | 4.3 | odd | 2 |