Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,8,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), degree \(2\), not 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: | \(8.43439568807\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{21} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Root | \(0.500000 + 11.4952i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.19 |
Dual form | 27.8.c.a.10.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7051 | − | 18.5418i | 0.946207 | − | 1.63888i | 0.192890 | − | 0.981220i | \(-0.438214\pi\) |
0.753317 | − | 0.657658i | \(-0.228453\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −165.199 | − | 286.133i | −1.29061 | − | 2.23541i | ||||
\(5\) | −32.6274 | − | 56.5123i | −0.116731 | − | 0.202185i | 0.801739 | − | 0.597674i | \(-0.203908\pi\) |
−0.918471 | + | 0.395489i | \(0.870575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −118.194 | + | 204.717i | −0.130242 | + | 0.225586i | −0.923770 | − | 0.382948i | \(-0.874909\pi\) |
0.793528 | + | 0.608534i | \(0.208242\pi\) | |||||||
\(8\) | −4333.37 | −2.99234 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1397.12 | −0.441808 | ||||||||
\(11\) | 2305.59 | − | 3993.39i | 0.522284 | − | 0.904623i | −0.477379 | − | 0.878697i | \(-0.658413\pi\) |
0.999664 | − | 0.0259259i | \(-0.00825339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 68.1364 | + | 118.016i | 0.00860157 | + | 0.0148984i | 0.870294 | − | 0.492532i | \(-0.163929\pi\) |
−0.861693 | + | 0.507431i | \(0.830595\pi\) | |||||||
\(14\) | 2530.55 | + | 4383.04i | 0.246472 | + | 0.426901i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −25243.8 | + | 43723.5i | −1.54076 | + | 2.66867i | ||||
\(17\) | −5319.46 | −0.262601 | −0.131301 | − | 0.991343i | \(-0.541915\pi\) | ||||
−0.131301 | + | 0.991343i | \(0.541915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38228.5 | 1.27864 | 0.639321 | − | 0.768940i | \(-0.279215\pi\) | ||||
0.639321 | + | 0.768940i | \(0.279215\pi\) | |||||||
\(20\) | −10780.0 | + | 18671.5i | −0.301310 | + | 0.521885i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −49363.1 | − | 85499.4i | −0.988378 | − | 1.71192i | ||||
\(23\) | −36480.5 | − | 63186.1i | −0.625192 | − | 1.08286i | −0.988504 | − | 0.151197i | \(-0.951687\pi\) |
0.363311 | − | 0.931668i | \(-0.381646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 36933.4 | − | 63970.5i | 0.472748 | − | 0.818823i | ||||
\(26\) | 2917.63 | 0.0325554 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 78101.7 | 0.672369 | ||||||||
\(29\) | 35682.4 | − | 61803.7i | 0.271682 | − | 0.470567i | −0.697611 | − | 0.716477i | \(-0.745754\pi\) |
0.969293 | + | 0.245910i | \(0.0790868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28810.3 | + | 49900.8i | 0.173693 | + | 0.300844i | 0.939708 | − | 0.341978i | \(-0.111097\pi\) |
−0.766015 | + | 0.642822i | \(0.777763\pi\) | |||||||
\(32\) | 263139. | + | 455770.i | 1.41958 | + | 2.45879i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −56945.4 | + | 98632.4i | −0.248475 | + | 0.430371i | ||||
\(35\) | 15425.4 | 0.0608133 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 88485.6 | 0.287188 | 0.143594 | − | 0.989637i | \(-0.454134\pi\) | ||||
0.143594 | + | 0.989637i | \(0.454134\pi\) | |||||||
\(38\) | 409240. | − | 708824.i | 1.20986 | − | 2.09554i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 141387. | + | 244889.i | 0.349300 | + | 0.605005i | ||||
\(41\) | 127791. | + | 221341.i | 0.289573 | + | 0.501555i | 0.973708 | − | 0.227800i | \(-0.0731533\pi\) |
−0.684135 | + | 0.729356i | \(0.739820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 324806. | − | 562580.i | 0.622994 | − | 1.07906i | −0.365931 | − | 0.930642i | \(-0.619249\pi\) |
0.988925 | − | 0.148415i | \(-0.0474172\pi\) | |||||||
\(44\) | −1.52352e6 | −2.69627 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.56211e6 | −2.36624 | ||||||||
\(47\) | −522539. | + | 905063.i | −0.734135 | + | 1.27156i | 0.220967 | + | 0.975281i | \(0.429079\pi\) |
−0.955102 | + | 0.296277i | \(0.904255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 383832. | + | 664817.i | 0.466074 | + | 0.807264i | ||||
\(50\) | −790752. | − | 1.36962e6i | −0.894634 | − | 1.54955i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 22512.1 | − | 38992.1i | 0.0222026 | − | 0.0384561i | ||||
\(53\) | 777845. | 0.717675 | 0.358837 | − | 0.933400i | \(-0.383173\pi\) | ||||
0.358837 | + | 0.933400i | \(0.383173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −300901. | −0.243868 | ||||||||
\(56\) | 512177. | − | 887116.i | 0.389728 | − | 0.675029i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −763967. | − | 1.32323e6i | −0.514134 | − | 0.890507i | ||||
\(59\) | 1.01959e6 | + | 1.76598e6i | 0.646314 | + | 1.11945i | 0.983996 | + | 0.178189i | \(0.0570237\pi\) |
−0.337682 | + | 0.941260i | \(0.609643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −927927. | + | 1.60722e6i | −0.523431 | + | 0.906609i | 0.476197 | + | 0.879339i | \(0.342015\pi\) |
−0.999628 | + | 0.0272705i | \(0.991318\pi\) | |||||||
\(62\) | 1.23367e6 | 0.657396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.80532e6 | 2.29135 | ||||||||
\(65\) | 4446.23 | − | 7701.10i | 0.00200815 | − | 0.00347821i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.81717e6 | + | 3.14743e6i | 0.738131 | + | 1.27848i | 0.953336 | + | 0.301911i | \(0.0976247\pi\) |
−0.215205 | + | 0.976569i | \(0.569042\pi\) | |||||||
\(68\) | 878768. | + | 1.52207e6i | 0.338917 | + | 0.587021i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 165131. | − | 286015.i | 0.0575419 | − | 0.0996656i | ||||
\(71\) | −1.93117e6 | −0.640348 | −0.320174 | − | 0.947359i | \(-0.603741\pi\) | ||||
−0.320174 | + | 0.947359i | \(0.603741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.06016e6 | −0.619826 | −0.309913 | − | 0.950765i | \(-0.600300\pi\) | ||||
−0.309913 | + | 0.950765i | \(0.600300\pi\) | |||||||
\(74\) | 947248. | − | 1.64068e6i | 0.271740 | − | 0.470667i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.31529e6 | − | 1.09384e7i | −1.65024 | − | 2.85829i | ||||
\(77\) | 545011. | + | 943987.i | 0.136047 | + | 0.235640i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.13421e6 | − | 5.42860e6i | 0.715208 | − | 1.23878i | −0.247671 | − | 0.968844i | \(-0.579665\pi\) |
0.962879 | − | 0.269933i | \(-0.0870016\pi\) | |||||||
\(80\) | 3.29456e6 | 0.719419 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.47209e6 | 1.09598 | ||||||||
\(83\) | −568792. | + | 985177.i | −0.109189 | + | 0.189122i | −0.915442 | − | 0.402450i | \(-0.868159\pi\) |
0.806253 | + | 0.591571i | \(0.201492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 173560. | + | 300615.i | 0.0306538 | + | 0.0530939i | ||||
\(86\) | −6.95416e6 | − | 1.20450e7i | −1.17896 | − | 2.04202i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.99096e6 | + | 1.73049e7i | −1.56285 | + | 2.70694i | ||||
\(89\) | 428904. | 0.0644904 | 0.0322452 | − | 0.999480i | \(-0.489734\pi\) | ||||
0.0322452 | + | 0.999480i | \(0.489734\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −32213.2 | −0.00448114 | ||||||||
\(92\) | −1.20531e7 | + | 2.08765e7i | −1.61376 | + | 2.79512i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.11877e7 | + | 1.93776e7i | 1.38929 | + | 2.40632i | ||||
\(95\) | −1.24730e6 | − | 2.16038e6i | −0.149258 | − | 0.258522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.85362e6 | − | 1.01388e7i | 0.651214 | − | 1.12793i | −0.331615 | − | 0.943415i | \(-0.607594\pi\) |
0.982829 | − | 0.184520i | \(-0.0590731\pi\) | |||||||
\(98\) | 1.64359e7 | 1.76401 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.44054e7 | −2.44054 | ||||||||
\(101\) | 9.34885e6 | − | 1.61927e7i | 0.902887 | − | 1.56385i | 0.0791589 | − | 0.996862i | \(-0.474777\pi\) |
0.823728 | − | 0.566985i | \(-0.191890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 414577. | + | 718068.i | 0.0373830 | + | 0.0647493i | 0.884112 | − | 0.467276i | \(-0.154764\pi\) |
−0.846729 | + | 0.532025i | \(0.821431\pi\) | |||||||
\(104\) | −295260. | − | 511406.i | −0.0257388 | − | 0.0445809i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.32692e6 | − | 1.44226e7i | 0.679069 | − | 1.17618i | ||||
\(107\) | −9.20798e6 | −0.726643 | −0.363322 | − | 0.931664i | \(-0.618357\pi\) | ||||
−0.363322 | + | 0.931664i | \(0.618357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.08593e7 | −0.803174 | −0.401587 | − | 0.915821i | \(-0.631541\pi\) | ||||
−0.401587 | + | 0.915821i | \(0.631541\pi\) | |||||||
\(110\) | −3.22118e6 | + | 5.57925e6i | −0.230749 | + | 0.399670i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.96731e6 | − | 1.03357e7i | −0.401343 | − | 0.695146i | ||||
\(113\) | −3.17666e6 | − | 5.50213e6i | −0.207107 | − | 0.358720i | 0.743695 | − | 0.668519i | \(-0.233072\pi\) |
−0.950802 | + | 0.309799i | \(0.899738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.38053e6 | + | 4.12320e6i | −0.145959 | + | 0.252809i | ||||
\(116\) | −2.35787e7 | −1.40255 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.36593e7 | 2.44619 | ||||||||
\(119\) | 628726. | − | 1.08899e6i | 0.0342017 | − | 0.0592390i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −887875. | − | 1.53784e6i | −0.0455620 | − | 0.0789157i | ||||
\(122\) | 1.98671e7 | + | 3.44109e7i | 0.990548 | + | 1.71568i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.51884e6 | − | 1.64871e7i | 0.448340 | − | 0.776548i | ||||
\(125\) | −9.91820e6 | −0.454201 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79848e7 | −0.779100 | −0.389550 | − | 0.921005i | \(-0.627369\pi\) | ||||
−0.389550 | + | 0.921005i | \(0.627369\pi\) | |||||||
\(128\) | 1.77597e7 | − | 3.07606e7i | 0.748514 | − | 1.29646i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −95194.7 | − | 164882.i | −0.00380024 | − | 0.00658221i | ||||
\(131\) | 1.88048e6 | + | 3.25708e6i | 0.0730834 | + | 0.126584i | 0.900251 | − | 0.435371i | \(-0.143383\pi\) |
−0.827168 | + | 0.561955i | \(0.810049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.51836e6 | + | 7.82603e6i | −0.166533 | + | 0.288443i | ||||
\(134\) | 7.78119e7 | 2.79370 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.30512e7 | 0.785792 | ||||||||
\(137\) | 652403. | − | 1.13000e6i | 0.0216767 | − | 0.0375452i | −0.854984 | − | 0.518655i | \(-0.826433\pi\) |
0.876660 | + | 0.481110i | \(0.159766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.83704e6 | + | 1.01101e7i | 0.184349 | + | 0.319302i | 0.943357 | − | 0.331779i | \(-0.107649\pi\) |
−0.759008 | + | 0.651081i | \(0.774316\pi\) | |||||||
\(140\) | −2.54826e6 | − | 4.41371e6i | −0.0784865 | − | 0.135943i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.06734e7 | + | 3.58073e7i | −0.605902 | + | 1.04945i | ||||
\(143\) | 628378. | 0.0179699 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.65689e6 | −0.126855 | ||||||||
\(146\) | −2.20542e7 | + | 3.81990e7i | −0.586484 | + | 1.01582i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.46177e7 | − | 2.53186e7i | −0.370649 | − | 0.641984i | ||||
\(149\) | 1.59389e7 | + | 2.76070e7i | 0.394736 | + | 0.683703i | 0.993067 | − | 0.117546i | \(-0.0375027\pi\) |
−0.598331 | + | 0.801249i | \(0.704169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.55648e7 | + | 6.16000e7i | −0.840622 | + | 1.45600i | 0.0487485 | + | 0.998811i | \(0.484477\pi\) |
−0.889370 | + | 0.457188i | \(0.848857\pi\) | |||||||
\(152\) | −1.65658e8 | −3.82613 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.33376e7 | 0.514913 | ||||||||
\(155\) | 1.88001e6 | − | 3.25627e6i | 0.0405507 | − | 0.0702360i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.52217e7 | − | 6.10057e7i | −0.726375 | − | 1.25812i | −0.958405 | − | 0.285411i | \(-0.907870\pi\) |
0.232030 | − | 0.972709i | \(-0.425463\pi\) | |||||||
\(158\) | −6.71040e7 | − | 1.16228e8i | −1.35347 | − | 2.34428i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.71711e7 | − | 2.97412e7i | 0.331419 | − | 0.574035i | ||||
\(161\) | 1.72471e7 | 0.325705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.98423e7 | 0.720590 | 0.360295 | − | 0.932838i | \(-0.382676\pi\) | ||||
0.360295 | + | 0.932838i | \(0.382676\pi\) | |||||||
\(164\) | 4.22220e7 | − | 7.31306e7i | 0.747455 | − | 1.29463i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.21780e7 | + | 2.10929e7i | 0.206631 | + | 0.357896i | ||||
\(167\) | 2.58421e7 | + | 4.47599e7i | 0.429359 | + | 0.743672i | 0.996816 | − | 0.0797308i | \(-0.0254061\pi\) |
−0.567457 | + | 0.823403i | \(0.692073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.13650e7 | − | 5.43257e7i | 0.499852 | − | 0.865769i | ||||
\(170\) | 7.43193e6 | 0.116019 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.14630e8 | −3.21618 | ||||||||
\(173\) | 9.10891e6 | − | 1.57771e7i | 0.133753 | − | 0.231668i | −0.791367 | − | 0.611341i | \(-0.790630\pi\) |
0.925121 | + | 0.379673i | \(0.123964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.73059e6 | + | 1.51218e7i | 0.123143 | + | 0.213290i | ||||
\(176\) | 1.16403e8 | + | 2.01617e8i | 1.60943 | + | 2.78761i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.59147e6 | − | 7.95265e6i | 0.0610213 | − | 0.105692i | ||||
\(179\) | −1.05708e8 | −1.37759 | −0.688797 | − | 0.724955i | \(-0.741861\pi\) | ||||
−0.688797 | + | 0.724955i | \(0.741861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.29009e8 | 1.61713 | 0.808566 | − | 0.588406i | \(-0.200244\pi\) | ||||
0.808566 | + | 0.588406i | \(0.200244\pi\) | |||||||
\(182\) | −344845. | + | 597290.i | −0.00424008 | + | 0.00734404i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.58084e8 | + | 2.73809e8i | 1.87079 | + | 3.24030i | ||||
\(185\) | −2.88706e6 | − | 5.00053e6i | −0.0335239 | − | 0.0580651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.22645e7 | + | 2.12427e7i | −0.137152 | + | 0.237555i | ||||
\(188\) | 3.45291e8 | 3.78994 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.34097e7 | −0.564915 | ||||||||
\(191\) | 8.43634e6 | − | 1.46122e7i | 0.0876067 | − | 0.151739i | −0.818892 | − | 0.573947i | \(-0.805411\pi\) |
0.906499 | + | 0.422208i | \(0.138745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.10280e7 | − | 5.37420e7i | −0.310672 | − | 0.538100i | 0.667836 | − | 0.744309i | \(-0.267221\pi\) |
−0.978508 | + | 0.206208i | \(0.933888\pi\) | |||||||
\(194\) | −1.25327e8 | − | 2.17073e8i | −1.23237 | − | 2.13452i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.26817e8 | − | 2.19654e8i | 1.20304 | − | 2.08373i | ||||
\(197\) | 7.26554e6 | 0.0677074 | 0.0338537 | − | 0.999427i | \(-0.489222\pi\) | ||||
0.0338537 | + | 0.999427i | \(0.489222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.21194e7 | 0.558780 | 0.279390 | − | 0.960178i | \(-0.409868\pi\) | ||||
0.279390 | + | 0.960178i | \(0.409868\pi\) | |||||||
\(200\) | −1.60046e8 | + | 2.77208e8i | −1.41462 | + | 2.45020i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00161e8 | − | 3.46689e8i | −1.70864 | − | 2.95944i | ||||
\(203\) | 8.43485e6 | + | 1.46096e7i | 0.0707687 | + | 0.122575i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.33901e6 | − | 1.44436e7i | 0.0676045 | − | 0.117095i | ||||
\(206\) | 1.77524e7 | 0.141488 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.88008e6 | −0.0530117 | ||||||||
\(209\) | 8.81390e7 | − | 1.52661e8i | 0.667815 | − | 1.15669i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.98867e7 | + | 1.55688e8i | 0.658729 | + | 1.14095i | 0.980945 | + | 0.194286i | \(0.0622390\pi\) |
−0.322216 | + | 0.946666i | \(0.604428\pi\) | |||||||
\(212\) | −1.28499e8 | − | 2.22567e8i | −0.926241 | − | 1.60430i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.85725e7 | + | 1.70733e8i | −0.687555 | + | 1.19088i | ||||
\(215\) | −4.23903e7 | −0.290892 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.36208e7 | −0.0904882 | ||||||||
\(218\) | −1.16250e8 | + | 2.01351e8i | −0.759969 | + | 1.31630i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.97085e7 | + | 8.60976e7i | 0.314740 | + | 0.545145i | ||||
\(221\) | −362449. | − | 627780.i | −0.00225878 | − | 0.00391232i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.72429e7 | + | 6.45066e7i | −0.224893 | + | 0.389527i | −0.956287 | − | 0.292428i | \(-0.905537\pi\) |
0.731394 | + | 0.681955i | \(0.238870\pi\) | |||||||
\(224\) | −1.24405e8 | −0.739556 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.36026e8 | −0.783866 | ||||||||
\(227\) | −1.06638e8 | + | 1.84702e8i | −0.605090 | + | 1.04805i | 0.386948 | + | 0.922102i | \(0.373529\pi\) |
−0.992037 | + | 0.125944i | \(0.959804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.52916e7 | − | 1.30409e8i | −0.414307 | − | 0.717601i | 0.581048 | − | 0.813869i | \(-0.302643\pi\) |
−0.995355 | + | 0.0962682i | \(0.969309\pi\) | |||||||
\(230\) | 5.09677e7 | + | 8.82786e7i | 0.276215 | + | 0.478418i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.54625e8 | + | 2.67818e8i | −0.812964 | + | 1.40810i | ||||
\(233\) | 1.27302e8 | 0.659309 | 0.329654 | − | 0.944102i | \(-0.393068\pi\) | ||||
0.329654 | + | 0.944102i | \(0.393068\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.81963e7 | 0.342786 | ||||||||
\(236\) | 3.36870e8 | − | 5.83476e8i | 1.66828 | − | 2.88955i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.34612e7 | − | 2.33154e7i | −0.0647237 | − | 0.112105i | ||||
\(239\) | 1.55897e8 | + | 2.70021e8i | 0.738659 | + | 1.27940i | 0.953099 | + | 0.302658i | \(0.0978740\pi\) |
−0.214440 | + | 0.976737i | \(0.568793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.32957e7 | + | 4.03494e7i | −0.107205 | + | 0.185685i | −0.914637 | − | 0.404276i | \(-0.867524\pi\) |
0.807432 | + | 0.589961i | \(0.200857\pi\) | |||||||
\(242\) | −3.80192e7 | −0.172444 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.13169e8 | 2.70219 | ||||||||
\(245\) | 2.50469e7 | − | 4.33825e7i | 0.108811 | − | 0.188466i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60475e6 | + | 4.51156e6i | 0.0109983 | + | 0.0190497i | ||||
\(248\) | −1.24846e8 | − | 2.16239e8i | −0.519747 | − | 0.900229i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.06175e8 | + | 1.83901e8i | −0.429768 | + | 0.744380i | ||||
\(251\) | −2.93904e8 | −1.17313 | −0.586567 | − | 0.809901i | \(-0.699521\pi\) | ||||
−0.586567 | + | 0.809901i | \(0.699521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36436e8 | −1.30611 | ||||||||
\(254\) | −1.92529e8 | + | 3.33471e8i | −0.737190 | + | 1.27685i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.26979e7 | − | 1.25916e8i | −0.270821 | − | 0.469075i | ||||
\(257\) | 1.43637e7 | + | 2.48786e7i | 0.0527837 | + | 0.0914240i | 0.891210 | − | 0.453591i | \(-0.149857\pi\) |
−0.838426 | + | 0.545015i | \(0.816524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.04584e7 | + | 1.81145e7i | −0.0374040 | + | 0.0647856i | ||||
\(260\) | −2.93805e6 | −0.0103670 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.05229e7 | 0.276608 | ||||||||
\(263\) | −1.05540e8 | + | 1.82800e8i | −0.357743 | + | 0.619630i | −0.987583 | − | 0.157095i | \(-0.949787\pi\) |
0.629840 | + | 0.776725i | \(0.283120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53791e7 | − | 4.39578e7i | −0.0837751 | − | 0.145103i | ||||
\(266\) | 9.67391e7 | + | 1.67557e8i | 0.315149 | + | 0.545854i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.00388e8 | − | 1.03990e9i | 1.90529 | − | 3.30005i | ||||
\(269\) | 3.22090e8 | 1.00889 | 0.504446 | − | 0.863444i | \(-0.331697\pi\) | ||||
0.504446 | + | 0.863444i | \(0.331697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.74530e8 | −1.14313 | −0.571563 | − | 0.820558i | \(-0.693663\pi\) | ||||
−0.571563 | + | 0.820558i | \(0.693663\pi\) | |||||||
\(272\) | 1.34283e8 | − | 2.32586e8i | 0.404605 | − | 0.700796i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.39681e7 | − | 2.41934e7i | −0.0410214 | − | 0.0710511i | ||||
\(275\) | −1.70306e8 | − | 2.94979e8i | −0.493817 | − | 0.855317i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.96175e7 | − | 1.55222e8i | 0.253346 | − | 0.438808i | −0.711099 | − | 0.703092i | \(-0.751802\pi\) |
0.964445 | + | 0.264284i | \(0.0851357\pi\) | |||||||
\(278\) | 2.49945e8 | 0.697730 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.68440e7 | −0.181974 | ||||||||
\(281\) | 1.99247e8 | − | 3.45106e8i | 0.535697 | − | 0.927854i | −0.463432 | − | 0.886132i | \(-0.653382\pi\) |
0.999129 | − | 0.0417220i | \(-0.0132844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.71350e8 | + | 2.96786e8i | 0.449397 | + | 0.778379i | 0.998347 | − | 0.0574763i | \(-0.0183054\pi\) |
−0.548949 | + | 0.835856i | \(0.684972\pi\) | |||||||
\(284\) | 3.19027e8 | + | 5.52570e8i | 0.826443 | + | 1.43144i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.72685e6 | − | 1.16512e7i | 0.0170032 | − | 0.0294504i | ||||
\(287\) | −6.04165e7 | −0.150858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.82042e8 | −0.931041 | ||||||||
\(290\) | −4.98525e7 | + | 8.63471e7i | −0.120031 | + | 0.207900i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.40335e8 | + | 5.89477e8i | 0.799957 | + | 1.38557i | ||||
\(293\) | −3.04388e8 | − | 5.27216e8i | −0.706954 | − | 1.22448i | −0.965982 | − | 0.258610i | \(-0.916735\pi\) |
0.259028 | − | 0.965870i | \(-0.416598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.65332e7 | − | 1.15239e8i | 0.150890 | − | 0.261350i | ||||
\(296\) | −3.83441e8 | −0.859365 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.82511e8 | 1.49401 | ||||||||
\(299\) | 4.97130e6 | − | 8.61055e6i | 0.0107553 | − | 0.0186287i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.67799e7 | + | 1.32987e8i | 0.162280 | + | 0.281077i | ||||
\(302\) | 7.61449e8 | + | 1.31887e9i | 1.59080 | + | 2.75535i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.65031e8 | + | 1.67148e9i | −1.97008 | + | 3.41228i | ||||
\(305\) | 1.21103e8 | 0.244403 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.84300e8 | 1.15253 | 0.576265 | − | 0.817263i | \(-0.304510\pi\) | ||||
0.576265 | + | 0.817263i | \(0.304510\pi\) | |||||||
\(308\) | 1.80070e8 | − | 3.11891e8i | 0.351168 | − | 0.608240i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.02514e7 | − | 6.97175e7i | −0.0767388 | − | 0.132915i | ||||
\(311\) | −1.46239e8 | − | 2.53294e8i | −0.275678 | − | 0.477489i | 0.694628 | − | 0.719369i | \(-0.255569\pi\) |
−0.970306 | + | 0.241881i | \(0.922236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.13742e8 | − | 7.16621e8i | 0.762648 | − | 1.32094i | −0.178834 | − | 0.983879i | \(-0.557232\pi\) |
0.941481 | − | 0.337065i | \(-0.109434\pi\) | |||||||
\(314\) | −1.50821e9 | −2.74921 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.07107e9 | −3.69223 | ||||||||
\(317\) | 1.21830e7 | − | 2.11016e7i | 0.0214807 | − | 0.0372057i | −0.855085 | − | 0.518487i | \(-0.826495\pi\) |
0.876566 | + | 0.481282i | \(0.159829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.64538e8 | − | 2.84987e8i | −0.283790 | − | 0.491539i | ||||
\(320\) | −1.56785e8 | − | 2.71560e8i | −0.267473 | − | 0.463277i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.84632e8 | − | 3.19791e8i | 0.308184 | − | 0.533791i | ||||
\(323\) | −2.03355e8 | −0.335773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00660e7 | 0.0162655 | ||||||||
\(326\) | 4.26516e8 | − | 7.38748e8i | 0.681827 | − | 1.18096i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.53768e8 | − | 9.59154e8i | −0.866501 | − | 1.50082i | ||||
\(329\) | −1.23521e8 | − | 2.13945e8i | −0.191230 | − | 0.331221i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.03016e6 | − | 1.39086e7i | 0.0121710 | − | 0.0210808i | −0.859876 | − | 0.510503i | \(-0.829459\pi\) |
0.872047 | + | 0.489423i | \(0.162792\pi\) | |||||||
\(332\) | 3.75855e8 | 0.563686 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.10657e9 | 1.62505 | ||||||||
\(335\) | 1.18579e8 | − | 2.05385e8i | 0.172326 | − | 0.298478i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21283e8 | + | 2.10068e8i | 0.172621 | + | 0.298989i | 0.939335 | − | 0.343000i | \(-0.111443\pi\) |
−0.766714 | + | 0.641988i | \(0.778110\pi\) | |||||||
\(338\) | −6.71531e8 | − | 1.16313e9i | −0.945927 | − | 1.63839i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.73439e7 | − | 9.93225e7i | 0.0791245 | − | 0.137048i | ||||
\(341\) | 2.65698e8 | 0.362868 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.76141e8 | −0.503293 | ||||||||
\(344\) | −1.40750e9 | + | 2.43787e9i | −1.86421 | + | 3.22891i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.95024e8 | − | 3.37791e8i | −0.253117 | − | 0.438411i | ||||
\(347\) | 2.06422e8 | + | 3.57534e8i | 0.265218 | + | 0.459372i | 0.967621 | − | 0.252408i | \(-0.0812226\pi\) |
−0.702402 | + | 0.711780i | \(0.747889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.60275e8 | + | 4.50809e8i | −0.327750 | + | 0.567680i | −0.982065 | − | 0.188542i | \(-0.939624\pi\) |
0.654315 | + | 0.756222i | \(0.272957\pi\) | |||||||
\(350\) | 3.73847e8 | 0.466075 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.42676e9 | 2.96570 | ||||||||
\(353\) | −7.22672e8 | + | 1.25170e9i | −0.874439 | + | 1.51457i | −0.0170799 | + | 0.999854i | \(0.505437\pi\) |
−0.857359 | + | 0.514719i | \(0.827896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.30090e7 | + | 1.09135e8i | 0.0747487 | + | 0.129469i | ||||
\(356\) | −7.08544e7 | − | 1.22723e8i | −0.0832323 | − | 0.144163i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.13161e9 | + | 1.96001e9i | −1.30349 | + | 2.25771i | ||||
\(359\) | 1.00008e9 | 1.14079 | 0.570395 | − | 0.821371i | \(-0.306790\pi\) | ||||
0.570395 | + | 0.821371i | \(0.306790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.67544e8 | 0.634927 | ||||||||
\(362\) | 1.38106e9 | − | 2.39206e9i | 1.53014 | − | 2.65028i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.32157e6 | + | 9.21723e6i | 0.00578342 | + | 0.0100172i | ||||
\(365\) | 6.72175e7 | + | 1.16424e8i | 0.0723532 | + | 0.125319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.98743e8 | + | 6.90644e8i | −0.421078 | + | 0.729328i | −0.996045 | − | 0.0888481i | \(-0.971681\pi\) |
0.574967 | + | 0.818176i | \(0.305015\pi\) | |||||||
\(368\) | 3.68362e9 | 3.85308 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.23625e8 | −0.126882 | ||||||||
\(371\) | −9.19363e7 | + | 1.59238e8i | −0.0934713 | + | 0.161897i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.30751e8 | − | 2.26468e8i | −0.130456 | − | 0.225957i | 0.793396 | − | 0.608705i | \(-0.208311\pi\) |
−0.923853 | + | 0.382749i | \(0.874978\pi\) | |||||||
\(374\) | 2.62585e8 | + | 4.54811e8i | 0.259549 | + | 0.449552i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.26435e9 | − | 3.92198e9i | 2.19678 | − | 3.80494i | ||||
\(377\) | 9.72507e6 | 0.00934756 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.42925e8 | −0.323565 | −0.161782 | − | 0.986826i | \(-0.551724\pi\) | ||||
−0.161782 | + | 0.986826i | \(0.551724\pi\) | |||||||
\(380\) | −4.12103e8 | + | 7.13784e8i | −0.385268 | + | 0.667305i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.80624e8 | − | 3.12850e8i | −0.165788 | − | 0.287153i | ||||
\(383\) | 5.05976e8 | + | 8.76376e8i | 0.460187 | + | 0.797067i | 0.998970 | − | 0.0453777i | \(-0.0144491\pi\) |
−0.538783 | + | 0.842444i | \(0.681116\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.55646e7 | − | 6.15997e7i | 0.0317618 | − | 0.0550131i | ||||
\(386\) | −1.32863e9 | −1.17584 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.86804e9 | −3.36186 | ||||||||
\(389\) | −6.08222e8 | + | 1.05347e9i | −0.523888 | + | 0.907400i | 0.475725 | + | 0.879594i | \(0.342186\pi\) |
−0.999613 | + | 0.0278066i | \(0.991148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94057e8 | + | 3.36116e8i | 0.164176 | + | 0.284361i | ||||
\(392\) | −1.66329e9 | − | 2.88090e9i | −1.39465 | − | 2.41561i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.77784e7 | − | 1.34716e8i | 0.0640652 | − | 0.110964i | ||||
\(395\) | −4.09044e8 | −0.333949 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.05353e9 | 0.845043 | 0.422522 | − | 0.906353i | \(-0.361145\pi\) | ||||
0.422522 | + | 0.906353i | \(0.361145\pi\) | |||||||
\(398\) | 6.64994e8 | − | 1.15180e9i | 0.528722 | − | 0.915773i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.86468e9 | + | 3.22972e9i | 1.45678 | + | 2.52322i | ||||
\(401\) | 8.32350e8 | + | 1.44167e9i | 0.644616 | + | 1.11651i | 0.984390 | + | 0.176000i | \(0.0563159\pi\) |
−0.339774 | + | 0.940507i | \(0.610351\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.92606e6 | + | 6.80013e6i | −0.00298806 | + | 0.00517547i | ||||
\(404\) | −6.17767e9 | −4.66112 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.61184e8 | 0.267847 | ||||||||
\(407\) | 2.04011e8 | − | 3.53358e8i | 0.149994 | − | 0.259797i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.26033e6 | + | 1.60394e7i | 0.00669260 | + | 0.0115919i | 0.869352 | − | 0.494193i | \(-0.164536\pi\) |
−0.862660 | + | 0.505785i | \(0.831203\pi\) | |||||||
\(410\) | −1.78540e8 | − | 3.09240e8i | −0.127936 | − | 0.221591i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.36975e8 | − | 2.37248e8i | 0.0964942 | − | 0.167133i | ||||
\(413\) | −4.82036e8 | −0.336709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.42329e7 | 0.0509833 | ||||||||
\(416\) | −3.58587e7 | + | 6.21091e7i | −0.0244213 | + | 0.0422988i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.88708e9 | − | 3.26851e9i | −1.26378 | − | 2.18894i | ||||
\(419\) | −7.91691e8 | − | 1.37125e9i | −0.525783 | − | 0.910683i | −0.999549 | − | 0.0300324i | \(-0.990439\pi\) |
0.473766 | − | 0.880651i | \(-0.342894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.10933e8 | + | 1.23137e9i | −0.464345 | + | 0.804270i | −0.999172 | − | 0.0406923i | \(-0.987044\pi\) |
0.534826 | + | 0.844962i | \(0.320377\pi\) | |||||||
\(422\) | 3.84899e9 | 2.49318 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.37069e9 | −2.14753 | ||||||||
\(425\) | −1.96466e8 | + | 3.40289e8i | −0.124144 | + | 0.215024i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.19350e8 | − | 3.79926e8i | −0.136345 | − | 0.236157i | ||||
\(428\) | 1.52115e9 | + | 2.63470e9i | 0.937817 | + | 1.62435i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.53792e8 | + | 7.85991e8i | −0.275244 | + | 0.476736i | ||||
\(431\) | 1.76729e9 | 1.06326 | 0.531628 | − | 0.846978i | \(-0.321580\pi\) | ||||
0.531628 | + | 0.846978i | \(0.321580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.43174e9 | 0.847535 | 0.423767 | − | 0.905771i | \(-0.360707\pi\) | ||||
0.423767 | + | 0.905771i | \(0.360707\pi\) | |||||||
\(434\) | −1.45812e8 | + | 2.52553e8i | −0.0856206 | + | 0.148299i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.79394e9 | + | 3.10720e9i | 1.03659 | + | 1.79542i | ||||
\(437\) | −1.39459e9 | − | 2.41551e9i | −0.799398 | − | 1.38460i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.70176e8 | − | 6.41164e8i | 0.208825 | − | 0.361696i | −0.742520 | − | 0.669824i | \(-0.766369\pi\) |
0.951345 | + | 0.308129i | \(0.0997027\pi\) | |||||||
\(440\) | 1.30392e9 | 0.729736 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.55202e7 | −0.00854910 | ||||||||
\(443\) | 1.16814e9 | − | 2.02328e9i | 0.638386 | − | 1.10572i | −0.347401 | − | 0.937717i | \(-0.612936\pi\) |
0.985787 | − | 0.168000i | \(-0.0537309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.39940e7 | − | 2.42384e7i | −0.00752806 | − | 0.0130390i | ||||
\(446\) | 7.97379e8 | + | 1.38110e9i | 0.425591 | + | 0.737146i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.67958e8 | + | 9.83732e8i | −0.298430 | + | 0.516897i | ||||
\(449\) | 5.43412e8 | 0.283313 | 0.141657 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141657 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.17854e9 | 0.604958 | ||||||||
\(452\) | −1.04956e9 | + | 1.81789e9i | −0.534592 | + | 0.925940i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.28313e9 | + | 3.95450e9i | 1.14508 | + | 1.98334i | ||||
\(455\) | 1.05103e6 | + | 1.82044e6i | 0.000523090 | + | 0.000906018i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.93333e8 | + | 1.54730e9i | −0.437831 | + | 0.758345i | −0.997522 | − | 0.0703559i | \(-0.977586\pi\) |
0.559691 | + | 0.828701i | \(0.310920\pi\) | |||||||
\(458\) | −3.22402e9 | −1.56808 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.57304e9 | 0.753508 | ||||||||
\(461\) | −1.17001e9 | + | 2.02652e9i | −0.556209 | + | 0.963382i | 0.441599 | + | 0.897212i | \(0.354411\pi\) |
−0.997808 | + | 0.0661700i | \(0.978922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.84161e9 | − | 3.18976e9i | −0.862312 | − | 1.49357i | −0.869692 | − | 0.493595i | \(-0.835683\pi\) |
0.00738049 | − | 0.999973i | \(-0.497651\pi\) | |||||||
\(464\) | 1.80152e9 | + | 3.12032e9i | 0.837192 | + | 1.45006i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.36278e9 | − | 2.36040e9i | 0.623843 | − | 1.08053i | ||||
\(467\) | −8.38332e8 | −0.380897 | −0.190448 | − | 0.981697i | \(-0.560994\pi\) | ||||
−0.190448 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.59111e8 | −0.384542 | ||||||||
\(470\) | 7.30049e8 | − | 1.26448e9i | 0.324347 | − | 0.561785i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.41826e9 | − | 7.65266e9i | −1.93399 | − | 3.34977i | ||||
\(473\) | −1.49773e9 | − | 2.59415e9i | −0.650760 | − | 1.12715i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41191e9 | − | 2.44550e9i | 0.604475 | − | 1.04698i | ||||
\(476\) | −4.15459e8 | −0.176565 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.67556e9 | 2.79570 | ||||||||
\(479\) | 1.38683e9 | − | 2.40207e9i | 0.576567 | − | 0.998644i | −0.419302 | − | 0.907847i | \(-0.637725\pi\) |
0.995869 | − | 0.0907972i | \(-0.0289415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.02909e6 | + | 1.04427e7i | 0.00247027 | + | 0.00427863i | ||||
\(482\) | 4.98767e8 | + | 8.63890e8i | 0.202877 | + | 0.351394i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.93352e8 | + | 5.08100e8i | −0.117606 | + | 0.203700i | ||||
\(485\) | −7.63954e8 | −0.304068 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.08195e8 | 0.238612 | 0.119306 | − | 0.992858i | \(-0.461933\pi\) | ||||
0.119306 | + | 0.992858i | \(0.461933\pi\) | |||||||
\(488\) | 4.02105e9 | − | 6.96467e9i | 1.56628 | − | 2.71288i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.36259e8 | − | 9.28828e8i | −0.205915 | − | 0.356656i | ||||
\(491\) | 1.37347e9 | + | 2.37892e9i | 0.523641 | + | 0.906973i | 0.999621 | + | 0.0275169i | \(0.00876000\pi\) |
−0.475980 | + | 0.879456i | \(0.657907\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.89811e8 | + | 3.28762e8i | −0.0713439 | + | 0.123571i | ||||
\(494\) | 1.11537e8 | 0.0416268 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.90912e9 | −1.07047 | ||||||||
\(497\) | 2.28252e8 | − | 3.95344e8i | 0.0834002 | − | 0.144453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.14164e9 | − | 1.97737e9i | −0.411316 | − | 0.712421i | 0.583718 | − | 0.811957i | \(-0.301597\pi\) |
−0.995034 | + | 0.0995360i | \(0.968264\pi\) | |||||||
\(500\) | 1.63847e9 | + | 2.83792e9i | 0.586198 | + | 1.01532i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.14627e9 | + | 5.44951e9i | −1.11003 | + | 1.92262i | ||||
\(503\) | −5.24355e9 | −1.83712 | −0.918559 | − | 0.395283i | \(-0.870647\pi\) | ||||
−0.918559 | + | 0.395283i | \(0.870647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22012e9 | −0.421581 | ||||||||
\(506\) | −3.60158e9 | + | 6.23813e9i | −1.23585 | + | 2.14056i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.97107e9 | + | 5.14604e9i | 1.00552 | + | 1.74161i | ||||
\(509\) | 7.15597e8 | + | 1.23945e9i | 0.240523 | + | 0.416598i | 0.960863 | − | 0.277023i | \(-0.0893478\pi\) |
−0.720341 | + | 0.693621i | \(0.756014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.43497e8 | − | 4.21750e8i | 0.0807274 | − | 0.139824i | ||||
\(512\) | 1.43352e9 | 0.472018 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.15059e8 | 0.199777 | ||||||||
\(515\) | 2.70531e7 | − | 4.68574e7i | 0.00872755 | − | 0.0151166i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.40952e9 | + | 4.17340e9i | 0.766854 | + | 1.32823i | ||||
\(518\) | 2.23917e8 | + | 3.87836e8i | 0.0707838 | + | 0.122601i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.92672e7 | + | 3.33717e7i | −0.00600905 | + | 0.0104080i | ||||
\(521\) | 5.00475e9 | 1.55042 | 0.775211 | − | 0.631702i | \(-0.217643\pi\) | ||||
0.775211 | + | 0.631702i | \(0.217643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.38432e9 | −1.34013 | −0.670064 | − | 0.742304i | \(-0.733733\pi\) | ||||
−0.670064 | + | 0.742304i | \(0.733733\pi\) | |||||||
\(524\) | 6.21305e8 | − | 1.07613e9i | 0.188645 | − | 0.326743i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.25963e9 | + | 3.91380e9i | 0.676998 | + | 1.17260i | ||||
\(527\) | −1.53255e8 | − | 2.65446e8i | −0.0456119 | − | 0.0790021i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.59243e8 | + | 1.66146e9i | −0.281731 | + | 0.487972i | ||||
\(530\) | −1.08674e9 | −0.317074 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.98571e9 | 0.859719 | ||||||||
\(533\) | −1.74145e7 | + | 3.01628e7i | −0.00498157 | + | 0.00862833i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00433e8 | + | 5.20365e8i | 0.0848221 | + | 0.146916i | ||||
\(536\) | −7.87447e9 | − | 1.36390e10i | −2.20874 | − | 3.82565i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.44801e9 | − | 5.97213e9i | 0.954620 | − | 1.65345i | ||||
\(539\) | 3.53983e9 | 0.973693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.37230e9 | −1.45871 | −0.729357 | − | 0.684133i | \(-0.760181\pi\) | ||||
−0.729357 | + | 0.684133i | \(0.760181\pi\) | |||||||
\(542\) | −4.00938e9 | + | 6.94446e9i | −1.08163 | + | 1.87344i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.39976e9 | − | 2.42445e9i | −0.372784 | − | 0.645680i | ||||
\(545\) | 3.54311e8 | + | 6.13685e8i | 0.0937556 | + | 0.162389i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.22120e8 | + | 2.11518e8i | −0.0319029 | + | 0.0552575i | −0.881536 | − | 0.472117i | \(-0.843490\pi\) |
0.849633 | + | 0.527374i | \(0.176823\pi\) | |||||||
\(548\) | −4.31105e8 | −0.111905 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.29259e9 | −1.86901 | ||||||||
\(551\) | 1.36408e9 | − | 2.36266e9i | 0.347384 | − | 0.601687i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.40886e8 | + | 1.28325e9i | 0.186300 | + | 0.322682i | ||||
\(554\) | −1.91873e9 | − | 3.32334e9i | −0.479435 | − | 0.830405i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.92854e9 | − | 3.34034e9i | 0.475847 | − | 0.824192i | ||||
\(557\) | −5.52077e9 | −1.35365 | −0.676825 | − | 0.736144i | \(-0.736645\pi\) | ||||
−0.676825 | + | 0.736144i | \(0.736645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.85243e7 | 0.0214349 | ||||||||
\(560\) | −3.89396e8 | + | 6.74453e8i | −0.0936986 | + | 0.162291i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.26592e9 | − | 7.38878e9i | −1.01376 | − | 1.75588i | ||||
\(563\) | 2.31199e9 | + | 4.00448e9i | 0.546017 | + | 0.945728i | 0.998542 | + | 0.0539770i | \(0.0171898\pi\) |
−0.452526 | + | 0.891751i | \(0.649477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.07292e8 | + | 3.59040e8i | −0.0483519 | + | 0.0837479i | ||||
\(566\) | 7.33726e9 | 1.70089 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.36847e9 | 1.91614 | ||||||||
\(569\) | −2.27221e9 | + | 3.93559e9i | −0.517078 | + | 0.895605i | 0.482726 | + | 0.875772i | \(0.339647\pi\) |
−0.999803 | + | 0.0198332i | \(0.993686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.39633e9 | + | 2.41851e9i | 0.313878 | + | 0.543653i | 0.979198 | − | 0.202905i | \(-0.0650383\pi\) |
−0.665320 | + | 0.746558i | \(0.731705\pi\) | |||||||
\(572\) | −1.03807e8 | − | 1.79799e8i | −0.0231922 | − | 0.0401700i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.46766e8 | + | 1.12023e9i | −0.142743 | + | 0.247238i | ||||
\(575\) | −5.38940e9 | −1.18223 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.63375e9 | 1.00419 | 0.502096 | − | 0.864812i | \(-0.332562\pi\) | ||||
0.502096 | + | 0.864812i | \(0.332562\pi\) | |||||||
\(578\) | −4.08980e9 | + | 7.08374e9i | −0.880957 | + | 1.52586i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.69312e8 | + | 1.33249e9i | 0.163721 | + | 0.283573i | ||||
\(581\) | −1.34455e8 | − | 2.32883e8i | −0.0284421 | − | 0.0492631i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79339e9 | − | 3.10624e9i | 0.374830 | − | 0.649225i | ||||
\(584\) | 8.92742e9 | 1.85473 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.30340e10 | −2.67570 | ||||||||
\(587\) | 2.49329e9 | − | 4.31850e9i | 0.508791 | − | 0.881251i | −0.491158 | − | 0.871071i | \(-0.663426\pi\) |
0.999948 | − | 0.0101804i | \(-0.00324059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.10137e9 | + | 1.90763e9i | 0.222091 | + | 0.384673i | ||||
\(590\) | −1.42449e9 | − | 2.46729e9i | −0.285547 | − | 0.494581i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.23371e9 | + | 3.86890e9i | −0.442488 | + | 0.766411i | ||||
\(593\) | 1.08733e9 | 0.214126 | 0.107063 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107063 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.20549e7 | −0.0159696 | ||||||||
\(596\) | 5.26618e9 | − | 9.12128e9i | 1.01890 | − | 1.76479i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.06437e8 | − | 1.84354e8i | −0.0203534 | − | 0.0352531i | ||||
\(599\) | 7.88181e8 | + | 1.36517e9i | 0.149841 | + | 0.259533i | 0.931169 | − | 0.364589i | \(-0.118790\pi\) |
−0.781327 | + | 0.624122i | \(0.785457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98739e9 | − | 5.17431e9i | 0.561347 | − | 0.972282i | −0.436032 | − | 0.899931i | \(-0.643617\pi\) |
0.997379 | − | 0.0723505i | \(-0.0230500\pi\) | |||||||
\(602\) | 3.28775e9 | 0.614201 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.35010e10 | 4.33967 | ||||||||
\(605\) | −5.79381e7 | + | 1.00352e8i | −0.0106370 | + | 0.0184239i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.07004e9 | + | 3.58541e9i | 0.375680 | + | 0.650696i | 0.990429 | − | 0.138027i | \(-0.0440759\pi\) |
−0.614749 | + | 0.788723i | \(0.710743\pi\) | |||||||
\(608\) | 1.00594e10 | + | 1.74234e10i | 1.81514 | + | 3.14391i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.29643e9 | − | 2.24547e9i | 0.231256 | − | 0.400547i | ||||
\(611\) | −1.42416e8 | −0.0252588 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.24640e9 | −0.569234 | −0.284617 | − | 0.958641i | \(-0.591866\pi\) | ||||
−0.284617 | + | 0.958641i | \(0.591866\pi\) | |||||||
\(614\) | 6.25500e9 | − | 1.08340e10i | 1.09053 | − | 1.88886i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.36174e9 | − | 4.09065e9i | −0.407098 | − | 0.705114i | ||||
\(617\) | 2.56649e9 | + | 4.44529e9i | 0.439887 | + | 0.761907i | 0.997680 | − | 0.0680728i | \(-0.0216850\pi\) |
−0.557793 | + | 0.829980i | \(0.688352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.08023e7 | + | 7.06717e7i | −0.00691461 | + | 0.0119765i | −0.869462 | − | 0.494000i | \(-0.835534\pi\) |
0.862547 | + | 0.505976i | \(0.168868\pi\) | |||||||
\(620\) | −1.24230e9 | −0.209342 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.26203e9 | −1.04339 | ||||||||
\(623\) | −5.06937e7 | + | 8.78041e7i | −0.00839936 | + | 0.0145481i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.56182e9 | − | 4.43720e9i | −0.419728 | − | 0.726990i | ||||
\(626\) | −8.85830e9 | − | 1.53430e10i | −1.44325 | − | 2.49977i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.16371e10 | + | 2.01561e10i | −1.87494 | + | 3.24749i | ||||
\(629\) | −4.70696e8 | −0.0754160 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.87381e9 | 0.930716 | 0.465358 | − | 0.885123i | \(-0.345926\pi\) | ||||
0.465358 | + | 0.885123i | \(0.345926\pi\) | |||||||
\(632\) | −1.35817e10 | + | 2.35242e10i | −2.14015 | + | 3.70684i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.60842e8 | − | 4.51791e8i | −0.0406504 | − | 0.0704085i | ||||
\(635\) | 5.86798e8 | + | 1.01636e9i | 0.0909454 | + | 0.157522i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.23059e7 | + | 9.05964e7i | −0.00801793 | + | 0.0138875i | ||||
\(638\) | −7.04557e9 | −1.07410 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.31781e9 | −0.349500 | ||||||||
\(641\) | 8.24069e8 | − | 1.42733e9i | 0.123583 | − | 0.214053i | −0.797595 | − | 0.603193i | \(-0.793895\pi\) |
0.921178 | + | 0.389141i | \(0.127228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.07980e9 | − | 3.60232e9i | −0.308520 | − | 0.534373i | 0.669519 | − | 0.742795i | \(-0.266500\pi\) |
−0.978039 | + | 0.208422i | \(0.933167\pi\) | |||||||
\(644\) | −2.84919e9 | − | 4.93494e9i | −0.420360 | − | 0.728084i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.17694e9 | + | 3.77056e9i | −0.317711 | + | 0.550291i | ||||
\(647\) | 3.14826e9 | 0.456988 | 0.228494 | − | 0.973545i | \(-0.426620\pi\) | ||||
0.228494 | + | 0.973545i | \(0.426620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.40301e9 | 1.35024 | ||||||||
\(650\) | 1.07758e8 | − | 1.86642e8i | 0.0153905 | − | 0.0266571i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.58190e9 | − | 1.14002e10i | −0.930004 | − | 1.61081i | ||||
\(653\) | −6.14384e9 | − | 1.06414e10i | −0.863463 | − | 1.49556i | −0.868565 | − | 0.495575i | \(-0.834958\pi\) |
0.00510246 | − | 0.999987i | \(-0.498376\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.22710e8 | − | 2.12540e8i | 0.0170623 | − | 0.0295527i | ||||
\(656\) | −1.29038e10 | −1.78465 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.28924e9 | −0.723774 | ||||||||
\(659\) | 2.76278e9 | − | 4.78528e9i | 0.376052 | − | 0.651341i | −0.614432 | − | 0.788970i | \(-0.710615\pi\) |
0.990484 | + | 0.137629i | \(0.0439480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.98631e9 | + | 3.44039e9i | 0.267511 | + | 0.463342i | 0.968218 | − | 0.250106i | \(-0.0804656\pi\) |
−0.700708 | + | 0.713449i | \(0.747132\pi\) | |||||||
\(662\) | −1.71927e8 | − | 2.97787e8i | −0.0230326 | − | 0.0398936i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.46479e9 | − | 4.26914e9i | 0.326732 | − | 0.565916i | ||||
\(665\) | 5.89690e8 | 0.0777585 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.20684e9 | −0.679413 | ||||||||
\(668\) | 8.53818e9 | − | 1.47886e10i | 1.10828 | − | 1.91959i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.53880e9 | − | 4.39733e9i | −0.326112 | − | 0.564843i | ||||
\(671\) | 4.27883e9 | + | 7.41116e9i | 0.546760 | + | 0.947016i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.56024e9 | − | 1.13627e10i | 0.829597 | − | 1.43690i | −0.0687581 | − | 0.997633i | \(-0.521904\pi\) |
0.898355 | − | 0.439270i | \(-0.144763\pi\) | |||||||
\(674\) | 5.19338e9 | 0.653341 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.07258e10 | −2.58047 | ||||||||
\(677\) | −5.73199e9 | + | 9.92810e9i | −0.709978 | + | 1.22972i | 0.254886 | + | 0.966971i | \(0.417962\pi\) |
−0.964865 | + | 0.262748i | \(0.915371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.38372e9 | + | 2.39667e9i | 0.169631 | + | 0.293809i | ||||
\(680\) | −7.52101e8 | − | 1.30268e9i | −0.0917266 | − | 0.158875i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.84433e9 | − | 4.92652e9i | 0.343348 | − | 0.594696i | ||||
\(683\) | −7.63032e9 | −0.916368 | −0.458184 | − | 0.888857i | \(-0.651500\pi\) | ||||
−0.458184 | + | 0.888857i | \(0.651500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.51449e7 | −0.0101214 | ||||||||
\(686\) | −4.02663e9 | + | 6.97433e9i | −0.476220 | + | 0.824837i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.63986e10 | + | 2.84033e10i | 1.91977 | + | 3.32513i | ||||
\(689\) | 5.29996e7 | + | 9.17980e7i | 0.00617313 | + | 0.0106922i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.78482e9 | + | 8.28755e9i | −0.551686 | + | 0.955549i | 0.446467 | + | 0.894800i | \(0.352682\pi\) |
−0.998153 | + | 0.0607485i | \(0.980651\pi\) | |||||||
\(692\) | −6.01912e9 | −0.690497 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.83910e9 | 1.00381 | ||||||||
\(695\) | 3.80895e8 | − | 6.59730e8i | 0.0430387 | − | 0.0745451i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.79782e8 | − | 1.17742e9i | −0.0760422 | − | 0.131709i | ||||
\(698\) | 5.57254e9 | + | 9.65192e9i | 0.620239 | + | 1.07429i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.88456e9 | − | 4.99621e9i | 0.317861 | − | 0.550551i | ||||
\(701\) | 1.24509e10 | 1.36517 | 0.682586 | − | 0.730805i | \(-0.260855\pi\) | ||||
0.682586 | + | 0.730805i | \(0.260855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.38267e9 | 0.367211 | ||||||||
\(704\) | 1.10791e10 | − | 1.91895e10i | 1.19674 | − | 2.07281i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.54726e10 | + | 2.67993e10i | 1.65480 | + | 2.86620i | ||||
\(707\) | 2.20995e9 | + | 3.82774e9i | 0.235188 | + | 0.407357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.92899e9 | + | 1.37334e10i | −0.835518 | + | 1.44716i | 0.0580897 | + | 0.998311i | \(0.481499\pi\) |
−0.893608 | + | 0.448849i | \(0.851834\pi\) | |||||||
\(710\) | 2.69807e9 | 0.282911 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.85860e9 | −0.192977 | ||||||||
\(713\) | 2.10203e9 | − | 3.64082e9i | 0.217183 | − | 0.376171i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.05023e7 | − | 3.55111e7i | −0.00209765 | − | 0.00363323i | ||||
\(716\) | 1.74628e10 | + | 3.02464e10i | 1.77794 | + | 3.07949i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.07060e10 | − | 1.85433e10i | 1.07942 | − | 1.86962i | ||||
\(719\) | −1.79885e10 | −1.80486 | −0.902432 | − | 0.430833i | \(-0.858220\pi\) | ||||
−0.902432 | + | 0.430833i | \(0.858220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.96001e8 | −0.0194754 | ||||||||
\(722\) | 6.07562e9 | − | 1.05233e10i | 0.600773 | − | 1.04057i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.13121e10 | − | 3.69137e10i | −2.08709 | − | 3.61495i | ||||
\(725\) | −2.63574e9 | − | 4.56524e9i | −0.256874 | − | 0.444919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.60459e9 | + | 1.49036e10i | −0.830538 | + | 1.43853i | 0.0670741 | + | 0.997748i | \(0.478634\pi\) |
−0.897612 | + | 0.440786i | \(0.854700\pi\) | |||||||
\(728\) | 1.39592e8 | 0.0134091 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.87828e9 | 0.273844 | ||||||||
\(731\) | −1.72779e9 | + | 2.99262e9i | −0.163599 | + | 0.283362i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.01647e10 | − | 1.76058e10i | −0.953304 | − | 1.65117i | −0.738202 | − | 0.674580i | \(-0.764325\pi\) |
−0.215102 | − | 0.976592i | \(-0.569009\pi\) | |||||||
\(734\) | 8.53718e9 | + | 1.47868e10i | 0.796853 | + | 1.38019i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.91989e10 | − | 3.32535e10i | 1.77502 | − | 3.07443i | ||||
\(737\) | 1.67586e10 | 1.54206 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.40068e9 | −0.765700 | −0.382850 | − | 0.923810i | \(-0.625057\pi\) | ||||
−0.382850 | + | 0.923810i | \(0.625057\pi\) | |||||||
\(740\) | −9.53876e8 | + | 1.65216e9i | −0.0865328 | + | 0.149879i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.96838e9 | + | 3.40933e9i | 0.176886 | + | 0.306376i | ||||
\(743\) | −5.00275e9 | − | 8.66502e9i | −0.447454 | − | 0.775013i | 0.550766 | − | 0.834660i | \(-0.314336\pi\) |
−0.998220 | + | 0.0596473i | \(0.981002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.04009e9 | − | 1.80149e9i | 0.0921562 | − | 0.159619i | ||||
\(746\) | −5.59882e9 | −0.493754 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.10431e9 | 0.708044 | ||||||||
\(749\) | 1.08832e9 | − | 1.88503e9i | 0.0946395 | − | 0.163920i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.51619e9 | + | 1.12864e10i | 0.561376 | + | 0.972332i | 0.997377 | + | 0.0723858i | \(0.0230613\pi\) |
−0.436000 | + | 0.899946i | \(0.643605\pi\) | |||||||
\(752\) | −2.63817e10 | − | 4.56944e10i | −2.26225 | − | 3.91833i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.04108e8 | − | 1.80320e8i | 0.00884472 | − | 0.0153195i | ||||
\(755\) | 4.64154e9 | 0.392508 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.11633e9 | −0.680024 | −0.340012 | − | 0.940421i | \(-0.610431\pi\) | ||||
−0.340012 | + | 0.940421i | \(0.610431\pi\) | |||||||
\(758\) | −3.67104e9 | + | 6.35843e9i | −0.306159 | + | 0.530283i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.40500e9 | + | 9.36173e9i | 0.446630 | + | 0.773586i | ||||
\(761\) | 1.10813e9 | + | 1.91934e9i | 0.0911476 | + | 0.157872i | 0.907994 | − | 0.418983i | \(-0.137613\pi\) |
−0.816847 | + | 0.576855i | \(0.804280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.28350e9 | − | 2.22309e9i | 0.104607 | − | 0.181185i | ||||
\(764\) | −5.57469e9 | −0.452266 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.16661e10 | 1.74173 | ||||||||
\(767\) | −1.38942e8 | + | 2.40655e8i | −0.0111186 | + | 0.0192580i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.59962e9 | − | 1.14309e10i | −0.523332 | − | 0.906437i | −0.999631 | − | 0.0271540i | \(-0.991356\pi\) |
0.476300 | − | 0.879283i | \(-0.341978\pi\) | |||||||
\(770\) | −7.61446e8 | − | 1.31886e9i | −0.0601065 | − | 0.104108i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.02516e10 | + | 1.77562e10i | −0.801917 | + | 1.38896i | ||||
\(773\) | −1.25254e10 | −0.975355 | −0.487677 | − | 0.873024i | \(-0.662156\pi\) | ||||
−0.487677 | + | 0.873024i | \(0.662156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.25624e9 | 0.328451 | ||||||||
\(776\) | −2.53659e10 | + | 4.39350e10i | −1.94865 | + | 3.37517i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.30222e10 | + | 2.25550e10i | 0.991413 | + | 1.71718i | ||||
\(779\) | 4.88527e9 | + | 8.46154e9i | 0.370261 | + | 0.641310i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.45248e9 | + | 7.71192e9i | −0.334444 | + | 0.579274i | ||||
\(782\) | 8.30959e9 | 0.621378 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.87575e10 | −2.87243 | ||||||||
\(785\) | −2.29838e9 | + | 3.98092e9i | −0.169582 | + | 0.293724i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.66640e9 | − | 6.35038e9i | −0.268119 | − | 0.464396i | 0.700257 | − | 0.713891i | \(-0.253069\pi\) |
−0.968376 | + | 0.249495i | \(0.919735\pi\) | |||||||
\(788\) | −1.20026e9 | − | 2.07891e9i | −0.0873841 | − | 0.151354i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.37886e9 | + | 7.58441e9i | −0.315985 | + | 0.547302i | ||||
\(791\) | 1.50184e9 | 0.107896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.52903e8 | −0.0180093 | ||||||||
\(794\) | 1.12781e10 | − | 1.95343e10i | 0.799586 | − | 1.38492i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.02620e10 | − | 1.77744e10i | −0.721170 | − | 1.24910i | ||||
\(797\) | −9.72182e9 | − | 1.68387e10i | −0.680211 | − | 1.17816i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
0.294706 | − | 0.955588i | \(-0.404778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.77962e9 | − | 4.81445e9i | 0.192785 | − | 0.333913i | ||||
\(800\) | 3.88745e10 | 2.68441 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.56416e10 | 2.43976 | ||||||||
\(803\) | −4.74987e9 | + | 8.22701e9i | −0.323726 | + | 0.560709i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.62727e8 | − | 9.74671e8i | −0.0380200 | − | 0.0658526i | ||||
\(806\) | 8.40577e7 | + | 1.45592e8i | 0.00565464 | + | 0.00979412i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.05121e10 | + | 7.01689e10i | −2.70175 | + | 4.67956i | ||||
\(809\) | 2.66596e10 | 1.77025 | 0.885123 | − | 0.465356i | \(-0.154074\pi\) | ||||
0.885123 | + | 0.465356i | \(0.154074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.23929e10 | 1.47413 | 0.737066 | − | 0.675820i | \(-0.236210\pi\) | ||||
0.737066 | + | 0.675820i | \(0.236210\pi\) | |||||||
\(812\) | 2.78685e9 | − | 4.82697e9i | 0.182670 | − | 0.316394i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.36793e9 | − | 7.56547e9i | −0.283851 | − | 0.491644i | ||||
\(815\) | −1.29995e9 | − | 2.25158e9i | −0.0841154 | − | 0.145692i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.24168e10 | − | 2.15066e10i | 0.796587 | − | 1.37973i | ||||
\(818\) | 3.96531e8 | 0.0253303 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.51037e9 | −0.349006 | ||||||||
\(821\) | 9.93766e9 | − | 1.72125e10i | 0.626734 | − | 1.08553i | −0.361469 | − | 0.932384i | \(-0.617725\pi\) |
0.988203 | − | 0.153151i | \(-0.0489420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.48625e9 | − | 1.46986e10i | −0.530660 | − | 0.919130i | −0.999360 | − | 0.0357725i | \(-0.988611\pi\) |
0.468700 | − | 0.883357i | \(-0.344723\pi\) | |||||||
\(824\) | −1.79652e9 | − | 3.11166e9i | −0.111863 | − | 0.193752i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.16025e9 | + | 8.93781e9i | −0.318596 | + | 0.551825i | ||||
\(827\) | −1.89569e10 | −1.16546 | −0.582730 | − | 0.812666i | \(-0.698015\pi\) | ||||
−0.582730 | + | 0.812666i | \(0.698015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.77995e9 | −0.230433 | −0.115217 | − | 0.993340i | \(-0.536756\pi\) | ||||
−0.115217 | + | 0.993340i | \(0.536756\pi\) | |||||||
\(830\) | 7.94671e8 | − | 1.37641e9i | 0.0482407 | − | 0.0835554i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.27417e8 | + | 5.67103e8i | 0.0197092 | + | 0.0341374i | ||||
\(833\) | −2.04178e9 | − | 3.53647e9i | −0.122392 | − | 0.211988i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68632e9 | − | 2.92080e9i | 0.100239 | − | 0.173620i | ||||
\(836\) | −5.82418e10 | −3.44757 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.39006e10 | −1.99000 | ||||||||
\(839\) | −6.28559e9 | + | 1.08870e10i | −0.367434 | + | 0.636414i | −0.989164 | − | 0.146818i | \(-0.953097\pi\) |
0.621730 | + | 0.783232i | \(0.286430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.07848e9 | + | 1.05282e10i | 0.352378 | + | 0.610337i | ||||
\(842\) | 1.52212e10 | + | 2.63639e10i | 0.878733 | + | 1.52201i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.96983e10 | − | 5.14390e10i | 1.70033 | − | 2.94506i | ||||
\(845\) | −4.09343e9 | −0.233394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.19765e8 | 0.0237363 | ||||||||
\(848\) | −1.96357e10 | + | 3.40101e10i | −1.10576 | + | 1.91524i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.20638e9 | + | 7.28566e9i | 0.234932 | + | 0.406914i | ||||
\(851\) | −3.22800e9 | − | 5.59106e9i | −0.179548 | − | 0.310986i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.38980e9 | + | 5.87130e9i | −0.187004 | + | 0.323901i | −0.944250 | − | 0.329229i | \(-0.893211\pi\) |
0.757246 | + | 0.653130i | \(0.226545\pi\) | |||||||
\(854\) | −9.39267e9 | −0.516044 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.99016e10 | 2.17436 | ||||||||
\(857\) | 1.10047e10 | − | 1.90608e10i | 0.597237 | − | 1.03445i | −0.395989 | − | 0.918255i | \(-0.629598\pi\) |
0.993227 | − | 0.116191i | \(-0.0370683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.05339e10 | + | 1.82452e10i | 0.567039 | + | 0.982140i | 0.996857 | + | 0.0792243i | \(0.0252443\pi\) |
−0.429818 | + | 0.902915i | \(0.641422\pi\) | |||||||
\(860\) | 7.00281e9 | + | 1.21292e10i | 0.375429 | + | 0.650262i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.89191e10 | − | 3.27688e10i | 1.00606 | − | 1.74255i | ||||
\(863\) | −1.10986e10 | −0.587800 | −0.293900 | − | 0.955836i | \(-0.594953\pi\) | ||||
−0.293900 | + | 0.955836i | \(0.594953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.18880e9 | −0.0624529 | ||||||||
\(866\) | 1.53270e10 | − | 2.65471e10i | 0.801943 | − | 1.38901i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.25013e9 | + | 3.89734e9i | 0.116785 | + | 0.202278i | ||||
\(869\) | −1.44524e10 | − | 2.50322e10i | −0.747084 | − | 1.29399i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.47631e8 | + | 4.28909e8i | −0.0126982 | + | 0.0219939i | ||||
\(872\) | 4.70574e10 | 2.40337 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.97171e10 | −3.02558 | ||||||||
\(875\) | 1.17227e9 | − | 2.03043e9i | 0.0591560 | − | 0.102461i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.74513e9 | + | 6.48675e9i | 0.187486 | + | 0.324735i | 0.944411 | − | 0.328766i | \(-0.106633\pi\) |
−0.756926 | + | 0.653501i | \(0.773300\pi\) | |||||||
\(878\) | −7.92555e9 | − | 1.37275e10i | −0.395184 | − | 0.684478i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.59589e9 | − | 1.31565e10i | 0.375741 | − | 0.650803i | ||||
\(881\) | 3.40216e10 | 1.67625 | 0.838124 | − | 0.545479i | \(-0.183652\pi\) | ||||
0.838124 | + | 0.545479i | \(0.183652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.52483e8 | −0.00745350 | −0.00372675 | − | 0.999993i | \(-0.501186\pi\) | ||||
−0.00372675 | + | 0.999993i | \(0.501186\pi\) | |||||||
\(884\) | −1.19752e8 | + | 2.07417e8i | −0.00583043 | + | 0.0100986i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.50102e10 | − | 4.33190e10i | −1.20809 | − | 2.09247i | ||||
\(887\) | 1.61805e10 | + | 2.80255e10i | 0.778502 | + | 1.34840i | 0.932805 | + | 0.360381i | \(0.117353\pi\) |
−0.154303 | + | 0.988024i | \(0.549313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.12569e9 | − | 3.68180e9i | 0.101471 | − | 0.175754i | ||||
\(890\) | −5.99231e8 | −0.0284924 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.46099e10 | 1.16100 | ||||||||
\(893\) | −1.99758e10 | + | 3.45992e10i | −0.938696 | + | 1.62587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.44897e9 | + | 5.97379e9i | 0.160808 | + | 0.278528i | ||||
\(896\) | 4.19816e9 | + | 7.27142e9i | 0.194976 | + | 0.337708i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.81728e9 | − | 1.00758e10i | 0.268073 | − | 0.464316i | ||||
\(899\) | 4.11207e9 | 0.188756 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.13772e9 | −0.188462 | ||||||||
\(902\) | 1.26164e10 | − | 2.18522e10i | 0.572416 | − | 0.991453i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.37656e10 | + | 2.38428e10i | 0.619736 | + | 1.07341i | ||||
\(905\) | −4.20923e9 | − | 7.29060e9i | −0.188770 | − | 0.326959i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.07730e9 | + | 8.79415e9i | −0.225948 | + | 0.391353i | −0.956603 | − | 0.291393i | \(-0.905881\pi\) |
0.730656 | + | 0.682746i | \(0.239214\pi\) | |||||||
\(908\) | 7.04656e10 | 3.12375 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.50056e7 | 0.00197980 | ||||||||
\(911\) | 2.06340e9 | − | 3.57392e9i | 0.0904210 | − | 0.156614i | −0.817267 | − | 0.576259i | \(-0.804512\pi\) |
0.907688 | + | 0.419645i | \(0.137845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.62280e9 | + | 4.54282e9i | 0.114056 | + | 0.197550i | ||||
\(914\) | 1.91264e10 | + | 3.31280e10i | 0.828557 | + | 1.43510i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.48761e10 | + | 4.30867e10i | −1.06942 | + | 1.85229i | ||||
\(917\) | −8.89042e8 | −0.0380741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.67341e9 | −0.368625 | −0.184313 | − | 0.982868i | \(-0.559006\pi\) | ||||
−0.184313 | + | 0.982868i | \(0.559006\pi\) | |||||||
\(920\) | 1.03157e10 | − | 1.78673e10i | 0.436759 | − | 0.756489i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.50503e10 | + | 4.33883e10i | 1.05258 | + | 1.82312i | ||||
\(923\) | −1.31583e8 | − | 2.27908e8i | −0.00550800 | − | 0.00954013i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.26808e9 | − | 5.66047e9i | 0.135768 | − | 0.235156i | ||||
\(926\) | −7.88585e10 | −3.26370 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.75577e10 | 1.54270 | ||||||||
\(929\) | −1.95971e10 | + | 3.39432e10i | −0.801930 | + | 1.38898i | 0.116414 | + | 0.993201i | \(0.462860\pi\) |
−0.918344 | + | 0.395783i | \(0.870473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46733e10 | + | 2.54149e10i | 0.595942 | + | 1.03220i | ||||
\(932\) | −2.10301e10 | − | 3.64252e10i | −0.850914 | − | 1.47383i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.97444e9 | + | 1.55442e10i | −0.360407 | + | 0.624243i | ||||
\(935\) | 1.60063e9 | 0.0640400 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.74627e9 | −0.347324 | −0.173662 | − | 0.984805i | \(-0.555560\pi\) | ||||
−0.173662 | + | 0.984805i | \(0.555560\pi\) | |||||||
\(938\) | −9.19688e9 | + | 1.59295e10i | −0.363857 | + | 0.630218i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.12659e10 | − | 1.95132e10i | −0.442405 | − | 0.766268i | ||||
\(941\) | 2.00195e10 | + | 3.46747e10i | 0.783229 | + | 1.35659i | 0.930051 | + | 0.367429i | \(0.119762\pi\) |
−0.146823 | + | 0.989163i | \(0.546905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.32380e9 | − | 1.61493e10i | 0.362078 | − | 0.627137i | ||||
\(944\) | −1.02953e11 | −3.98325 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.41336e10 | −2.46301 | ||||||||
\(947\) | −9.20351e9 | + | 1.59409e10i | −0.352151 | + | 0.609943i | −0.986626 | − | 0.163000i | \(-0.947883\pi\) |
0.634475 | + | 0.772943i | \(0.281216\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.40372e8 | − | 2.43131e8i | −0.00533148 | − | 0.00923439i | ||||
\(950\) | −3.02292e10 | − | 5.23586e10i | −1.14392 | − | 1.98132i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.72451e9 | + | 4.71898e9i | −0.102343 | + | 0.177263i | ||||
\(953\) | 1.36320e10 | 0.510194 | 0.255097 | − | 0.966915i | \(-0.417893\pi\) | ||||
0.255097 | + | 0.966915i | \(0.417893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.10102e9 | −0.0409058 | ||||||||
\(956\) | 5.15078e10 | − | 8.92142e10i | 1.90665 | − | 3.30241i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.96924e10 | − | 5.14288e10i | −1.09110 | − | 1.88985i | ||||
\(959\) | 1.54220e8 | + | 2.67116e8i | 0.00564644 | + | 0.00977992i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.20962e10 | − | 2.09513e10i | 0.439662 | − | 0.761517i | ||||
\(962\) | 2.58168e8 | 0.00934954 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.53937e10 | 0.553444 | ||||||||
\(965\) | −2.02472e9 | + | 3.50693e9i | −0.0725304 | + | 0.125626i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.82952e9 | + | 4.90087e9i | 0.100628 | + | 0.174293i | 0.911944 | − | 0.410315i | \(-0.134581\pi\) |
−0.811315 | + | 0.584609i | \(0.801248\pi\) | |||||||
\(968\) | 3.84749e9 | + | 6.66405e9i | 0.136337 | + | 0.236143i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.17821e9 | + | 1.41651e10i | −0.287711 | + | 0.498331i | ||||
\(971\) | 9.65547e9 | 0.338459 | 0.169230 | − | 0.985577i | \(-0.445872\pi\) | ||||
0.169230 | + | 0.985577i | \(0.445872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.75961e9 | −0.0960400 | ||||||||
\(974\) | 6.51079e9 | − | 1.12770e10i | 0.225776 | − | 0.391055i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.68488e10 | − | 8.11445e10i | −1.61296 | − | 2.79373i | ||||
\(977\) | 2.13798e10 | + | 3.70308e10i | 0.733453 | + | 1.27038i | 0.955399 | + | 0.295318i | \(0.0954257\pi\) |
−0.221946 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.88876e8 | − | 1.71278e9i | 0.0336824 | − | 0.0583395i | ||||
\(980\) | −1.65509e10 | −0.561732 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.88125e10 | 1.98189 | ||||||||
\(983\) | 1.84845e10 | − | 3.20161e10i | 0.620684 | − | 1.07506i | −0.368675 | − | 0.929558i | \(-0.620188\pi\) |
0.989359 | − | 0.145497i | \(-0.0464782\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.37056e8 | − | 4.10592e8i | −0.00790357 | − | 0.0136894i | ||||
\(986\) | 4.06389e9 | + | 7.03887e9i | 0.135012 | + | 0.233848i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.60603e8 | − | 1.49061e9i | 0.0283892 | − | 0.0491716i | ||||
\(989\) | −4.73963e10 | −1.55796 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.13146e10 | −1.67488 | −0.837440 | − | 0.546530i | \(-0.815948\pi\) | ||||
−0.837440 | + | 0.546530i | \(0.815948\pi\) | |||||||
\(992\) | −1.51622e10 | + | 2.62617e10i | −0.493142 | + | 0.854146i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.88692e9 | − | 8.46440e9i | −0.157828 | − | 0.273365i | ||||
\(995\) | −2.02679e9 | − | 3.51051e9i | −0.0652272 | − | 0.112977i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.28440e10 | + | 3.95670e10i | −0.730028 | + | 1.26445i | 0.226843 | + | 0.973931i | \(0.427160\pi\) |
−0.956871 | + | 0.290514i | \(0.906174\pi\) | |||||||
\(998\) | −4.88854e10 | −1.55676 | ||||||||
\(999\) | 0 | 0 |
(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 | 27.8.c.a.19.6 | 12 | ||
3.2 | odd | 2 | 9.8.c.a.7.1 | yes | 12 | ||
4.3 | odd | 2 | 432.8.i.c.289.4 | 12 | |||
9.2 | odd | 6 | 81.8.a.e.1.6 | 6 | |||
9.4 | even | 3 | inner | 27.8.c.a.10.6 | 12 | ||
9.5 | odd | 6 | 9.8.c.a.4.1 | ✓ | 12 | ||
9.7 | even | 3 | 81.8.a.c.1.1 | 6 | |||
12.11 | even | 2 | 144.8.i.c.97.3 | 12 | |||
36.23 | even | 6 | 144.8.i.c.49.3 | 12 | |||
36.31 | odd | 6 | 432.8.i.c.145.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.8.c.a.4.1 | ✓ | 12 | 9.5 | odd | 6 | ||
9.8.c.a.7.1 | yes | 12 | 3.2 | odd | 2 | ||
27.8.c.a.10.6 | 12 | 9.4 | even | 3 | inner | ||
27.8.c.a.19.6 | 12 | 1.1 | even | 1 | trivial | ||
81.8.a.c.1.1 | 6 | 9.7 | even | 3 | |||
81.8.a.e.1.6 | 6 | 9.2 | odd | 6 | |||
144.8.i.c.49.3 | 12 | 36.23 | even | 6 | |||
144.8.i.c.97.3 | 12 | 12.11 | even | 2 | |||
432.8.i.c.145.4 | 12 | 36.31 | odd | 6 | |||
432.8.i.c.289.4 | 12 | 4.3 | odd | 2 |