Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,8,Mod(37,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.3605132110\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(-0.389676 + 0.674939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.109 |
Dual form | 126.8.g.j.37.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | + | 6.92820i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | ||||
\(5\) | 6.21726 | + | 10.7686i | 0.0222435 | + | 0.0385269i | 0.876933 | − | 0.480613i | \(-0.159586\pi\) |
−0.854689 | + | 0.519140i | \(0.826252\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −879.593 | − | 223.290i | −0.969257 | − | 0.246052i | ||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −49.7381 | + | 86.1488i | −0.0157286 | + | 0.0272427i | ||||
\(11\) | −3361.57 | + | 5822.41i | −0.761496 | + | 1.31895i | 0.180584 | + | 0.983560i | \(0.442201\pi\) |
−0.942079 | + | 0.335390i | \(0.891132\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7231.99 | 0.912969 | 0.456485 | − | 0.889731i | \(-0.349108\pi\) | ||||
0.456485 | + | 0.889731i | \(0.349108\pi\) | |||||||
\(14\) | −1971.37 | − | 6987.16i | −0.192009 | − | 0.680539i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | 7665.42 | − | 13276.9i | 0.378412 | − | 0.655428i | −0.612420 | − | 0.790533i | \(-0.709804\pi\) |
0.990831 | + | 0.135105i | \(0.0431370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9457.32 | − | 16380.6i | −0.316323 | − | 0.547887i | 0.663395 | − | 0.748269i | \(-0.269115\pi\) |
−0.979718 | + | 0.200382i | \(0.935782\pi\) | |||||||
\(20\) | −795.809 | −0.0222435 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −53785.1 | −1.07692 | ||||||||
\(23\) | −23860.2 | − | 41327.2i | −0.408910 | − | 0.708253i | 0.585858 | − | 0.810414i | \(-0.300758\pi\) |
−0.994768 | + | 0.102161i | \(0.967424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38985.2 | − | 67524.3i | 0.499010 | − | 0.864311i | ||||
\(26\) | 28928.0 | + | 50104.7i | 0.322783 | + | 0.559077i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 40523.0 | − | 41606.7i | 0.348858 | − | 0.358188i | ||||
\(29\) | 67449.4 | 0.513553 | 0.256776 | − | 0.966471i | \(-0.417340\pi\) | ||||
0.256776 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −54888.1 | + | 95068.9i | −0.330912 | + | 0.573156i | −0.982691 | − | 0.185253i | \(-0.940690\pi\) |
0.651779 | + | 0.758409i | \(0.274023\pi\) | |||||||
\(32\) | 16384.0 | − | 28377.9i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 122647. | 0.535155 | ||||||||
\(35\) | −3064.13 | − | 10860.2i | −0.0120801 | − | 0.0428155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −304625. | − | 527626.i | −0.988688 | − | 1.71246i | −0.624235 | − | 0.781237i | \(-0.714589\pi\) |
−0.364454 | − | 0.931222i | \(-0.618744\pi\) | |||||||
\(38\) | 75658.5 | − | 131044.i | 0.223674 | − | 0.387415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3183.24 | − | 5513.53i | −0.00786428 | − | 0.0136213i | ||||
\(41\) | 808859. | 1.83286 | 0.916430 | − | 0.400195i | \(-0.131057\pi\) | ||||
0.916430 | + | 0.400195i | \(0.131057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −334949. | −0.642450 | −0.321225 | − | 0.947003i | \(-0.604095\pi\) | ||||
−0.321225 | + | 0.947003i | \(0.604095\pi\) | |||||||
\(44\) | −215140. | − | 372634.i | −0.380748 | − | 0.659475i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 190882. | − | 330617.i | 0.289143 | − | 0.500810i | ||||
\(47\) | −382587. | − | 662661.i | −0.537512 | − | 0.930998i | −0.999037 | − | 0.0438710i | \(-0.986031\pi\) |
0.461525 | − | 0.887127i | \(-0.347302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 723826. | + | 392809.i | 0.878917 | + | 0.476975i | ||||
\(50\) | 623763. | 0.705707 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −231424. | + | 400838.i | −0.228242 | + | 0.395327i | ||||
\(53\) | 622359. | − | 1.07796e6i | 0.574216 | − | 0.994572i | −0.421910 | − | 0.906638i | \(-0.638640\pi\) |
0.996126 | − | 0.0879342i | \(-0.0280265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −83598.9 | −0.0677534 | ||||||||
\(56\) | 450352. | + | 114325.i | 0.342684 | + | 0.0869924i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 269798. | + | 467303.i | 0.181568 | + | 0.314486i | ||||
\(59\) | 1.02330e6 | − | 1.77240e6i | 0.648665 | − | 1.12352i | −0.334777 | − | 0.942297i | \(-0.608661\pi\) |
0.983442 | − | 0.181223i | \(-0.0580056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −70471.7 | − | 122061.i | −0.0397521 | − | 0.0688527i | 0.845465 | − | 0.534031i | \(-0.179323\pi\) |
−0.885217 | + | 0.465178i | \(0.845990\pi\) | |||||||
\(62\) | −878209. | −0.467980 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 44963.1 | + | 77878.4i | 0.0203077 | + | 0.0351739i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.46662e6 | + | 2.54027e6i | −0.595740 | + | 1.03185i | 0.397702 | + | 0.917515i | \(0.369808\pi\) |
−0.993442 | + | 0.114338i | \(0.963525\pi\) | |||||||
\(68\) | 490587. | + | 849721.i | 0.189206 | + | 0.327714i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 62985.4 | − | 64669.9i | 0.0219481 | − | 0.0225351i | ||||
\(71\) | 615326. | 0.204033 | 0.102017 | − | 0.994783i | \(-0.467470\pi\) | ||||
0.102017 | + | 0.994783i | \(0.467470\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 711328. | − | 1.23206e6i | 0.214013 | − | 0.370681i | −0.738954 | − | 0.673756i | \(-0.764680\pi\) |
0.952967 | + | 0.303075i | \(0.0980132\pi\) | |||||||
\(74\) | 2.43700e6 | − | 4.22101e6i | 0.699108 | − | 1.21089i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21054e6 | 0.316323 | ||||||||
\(77\) | 4.25690e6 | − | 4.37075e6i | 1.06261 | − | 1.09103i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.19370e6 | + | 2.06754e6i | 0.272395 | + | 0.471802i | 0.969475 | − | 0.245192i | \(-0.0788509\pi\) |
−0.697079 | + | 0.716994i | \(0.745518\pi\) | |||||||
\(80\) | 25465.9 | − | 44108.2i | 0.00556088 | − | 0.00963173i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.23544e6 | + | 5.60394e6i | 0.648014 | + | 1.12239i | ||||
\(83\) | 7.53432e6 | 1.44634 | 0.723171 | − | 0.690669i | \(-0.242684\pi\) | ||||
0.723171 | + | 0.690669i | \(0.242684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 190631. | 0.0336689 | ||||||||
\(86\) | −1.33980e6 | − | 2.32060e6i | −0.227140 | − | 0.393419i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.72112e6 | − | 2.98107e6i | 0.269229 | − | 0.466319i | ||||
\(89\) | −2.67757e6 | − | 4.63769e6i | −0.402602 | − | 0.697327i | 0.591437 | − | 0.806351i | \(-0.298561\pi\) |
−0.994039 | + | 0.109024i | \(0.965227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.36121e6 | − | 1.61483e6i | −0.884901 | − | 0.224638i | ||||
\(92\) | 3.05411e6 | 0.408910 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.06070e6 | − | 5.30129e6i | 0.380078 | − | 0.658315i | ||||
\(95\) | 117597. | − | 203684.i | 0.0140723 | − | 0.0243739i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58174e7 | −1.75969 | −0.879843 | − | 0.475265i | \(-0.842352\pi\) | ||||
−0.879843 | + | 0.475265i | \(0.842352\pi\) | |||||||
\(98\) | 173842. | + | 6.58605e6i | 0.0186580 | + | 0.706861i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.49505e6 | + | 4.32156e6i | 0.249505 | + | 0.432156i | ||||
\(101\) | −5.82603e6 | + | 1.00910e7i | −0.562662 | + | 0.974559i | 0.434601 | + | 0.900623i | \(0.356889\pi\) |
−0.997263 | + | 0.0739362i | \(0.976444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.58003e6 | − | 6.20080e6i | −0.322817 | − | 0.559136i | 0.658251 | − | 0.752799i | \(-0.271297\pi\) |
−0.981068 | + | 0.193663i | \(0.937963\pi\) | |||||||
\(104\) | −3.70278e6 | −0.322783 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.95775e6 | 0.812065 | ||||||||
\(107\) | −2.91738e6 | − | 5.05305e6i | −0.230224 | − | 0.398759i | 0.727650 | − | 0.685948i | \(-0.240612\pi\) |
−0.957874 | + | 0.287189i | \(0.907279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.66490e6 | − | 8.07985e6i | 0.345024 | − | 0.597600i | −0.640334 | − | 0.768097i | \(-0.721204\pi\) |
0.985358 | + | 0.170497i | \(0.0545373\pi\) | |||||||
\(110\) | −334396. | − | 579190.i | −0.0239545 | − | 0.0414903i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00934e6 | + | 3.57743e6i | 0.0678853 | + | 0.240607i | ||||
\(113\) | −8.84372e6 | −0.576581 | −0.288290 | − | 0.957543i | \(-0.593087\pi\) | ||||
−0.288290 | + | 0.957543i | \(0.593087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 296691. | − | 513883.i | 0.0181912 | − | 0.0315081i | ||||
\(116\) | −2.15838e6 | + | 3.73842e6i | −0.128388 | + | 0.222375i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.63728e7 | 0.917350 | ||||||||
\(119\) | −9.70705e6 | + | 9.96665e6i | −0.528047 | + | 0.542169i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.28567e7 | − | 2.22684e7i | −0.659752 | − | 1.14272i | ||||
\(122\) | 563773. | − | 976484.i | 0.0281090 | − | 0.0486862i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.51284e6 | − | 6.08441e6i | −0.165456 | − | 0.286578i | ||||
\(125\) | 1.94097e6 | 0.0888861 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.22621e7 | −0.964393 | −0.482196 | − | 0.876063i | \(-0.660161\pi\) | ||||
−0.482196 | + | 0.876063i | \(0.660161\pi\) | |||||||
\(128\) | 1.04858e6 | + | 1.81619e6i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −359705. | + | 623027.i | −0.0143597 | + | 0.0248717i | ||||
\(131\) | 5.45088e6 | + | 9.44120e6i | 0.211844 | + | 0.366925i | 0.952292 | − | 0.305189i | \(-0.0987197\pi\) |
−0.740447 | + | 0.672114i | \(0.765386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.66098e6 | + | 1.65199e7i | 0.171789 | + | 0.608875i | ||||
\(134\) | −2.34660e7 | −0.842504 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.92469e6 | + | 6.79777e6i | −0.133789 | + | 0.231729i | ||||
\(137\) | −1.60629e7 | + | 2.78218e7i | −0.533706 | + | 0.924406i | 0.465519 | + | 0.885038i | \(0.345868\pi\) |
−0.999225 | + | 0.0393678i | \(0.987466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.89050e7 | −0.597070 | −0.298535 | − | 0.954399i | \(-0.596498\pi\) | ||||
−0.298535 | + | 0.954399i | \(0.596498\pi\) | |||||||
\(140\) | 699988. | + | 177696.i | 0.0215597 | + | 0.00547306i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.46131e6 | + | 4.26311e6i | 0.0721367 | + | 0.124944i | ||||
\(143\) | −2.43108e7 | + | 4.21076e7i | −0.695222 | + | 1.20416i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 419350. | + | 726336.i | 0.0114232 | + | 0.0197856i | ||||
\(146\) | 1.13813e7 | 0.302660 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.89920e7 | 0.988688 | ||||||||
\(149\) | −2.77312e6 | − | 4.80319e6i | −0.0686779 | − | 0.118954i | 0.829642 | − | 0.558296i | \(-0.188545\pi\) |
−0.898320 | + | 0.439343i | \(0.855211\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.13319e7 | − | 1.96275e7i | 0.267845 | − | 0.463922i | −0.700460 | − | 0.713692i | \(-0.747022\pi\) |
0.968305 | + | 0.249770i | \(0.0803550\pi\) | |||||||
\(152\) | 4.84215e6 | + | 8.38684e6i | 0.111837 | + | 0.193707i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.73090e7 | + | 1.20097e7i | 1.04381 | + | 0.264978i | ||||
\(155\) | −1.36501e6 | −0.0294426 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.25062e7 | + | 5.63025e7i | −0.670375 | + | 1.16112i | 0.307423 | + | 0.951573i | \(0.400533\pi\) |
−0.977798 | + | 0.209551i | \(0.932800\pi\) | |||||||
\(158\) | −9.54958e6 | + | 1.65404e7i | −0.192612 | + | 0.333615i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 407454. | 0.00786428 | ||||||||
\(161\) | 1.17594e7 | + | 4.16789e7i | 0.222072 | + | 0.787092i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.74670e7 | − | 3.02537e7i | −0.315908 | − | 0.547170i | 0.663722 | − | 0.747980i | \(-0.268976\pi\) |
−0.979630 | + | 0.200810i | \(0.935643\pi\) | |||||||
\(164\) | −2.58835e7 | + | 4.48315e7i | −0.458215 | + | 0.793652i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.01373e7 | + | 5.21993e7i | 0.511359 | + | 0.885700i | ||||
\(167\) | −8.89524e7 | −1.47792 | −0.738959 | − | 0.673751i | \(-0.764682\pi\) | ||||
−0.738959 | + | 0.673751i | \(0.764682\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.04468e7 | −0.166487 | ||||||||
\(170\) | 762526. | + | 1.32073e6i | 0.0119037 | + | 0.0206179i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.07184e7 | − | 1.85648e7i | 0.160612 | − | 0.278189i | ||||
\(173\) | −1.53819e7 | − | 2.66422e7i | −0.225865 | − | 0.391209i | 0.730714 | − | 0.682684i | \(-0.239187\pi\) |
−0.956578 | + | 0.291475i | \(0.905854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.93686e7 | + | 5.06889e7i | −0.696335 | + | 0.714957i | ||||
\(176\) | 2.75380e7 | 0.380748 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.14206e7 | − | 3.71015e7i | 0.284683 | − | 0.493085i | ||||
\(179\) | 5.15359e7 | − | 8.92628e7i | 0.671621 | − | 1.16328i | −0.305823 | − | 0.952088i | \(-0.598932\pi\) |
0.977444 | − | 0.211194i | \(-0.0677351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.25682e7 | −0.784294 | −0.392147 | − | 0.919903i | \(-0.628268\pi\) | ||||
−0.392147 | + | 0.919903i | \(0.628268\pi\) | |||||||
\(182\) | −1.42570e7 | − | 5.05311e7i | −0.175298 | − | 0.621311i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.22164e7 | + | 2.11595e7i | 0.144571 | + | 0.250405i | ||||
\(185\) | 3.78786e6 | − | 6.56077e6i | 0.0439838 | − | 0.0761822i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.15356e7 | + | 8.92623e7i | 0.576318 | + | 0.998212i | ||||
\(188\) | 4.89712e7 | 0.537512 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.88155e6 | 0.0199012 | ||||||||
\(191\) | 3.95503e7 | + | 6.85031e7i | 0.410707 | + | 0.711366i | 0.994967 | − | 0.100201i | \(-0.0319484\pi\) |
−0.584260 | + | 0.811567i | \(0.698615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.81447e7 | − | 4.87480e7i | 0.281803 | − | 0.488097i | −0.690026 | − | 0.723785i | \(-0.742401\pi\) |
0.971829 | + | 0.235687i | \(0.0757342\pi\) | |||||||
\(194\) | −6.32697e7 | − | 1.09586e8i | −0.622143 | − | 1.07758i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.49341e7 | + | 2.75486e7i | −0.426265 | + | 0.261339i | ||||
\(197\) | 4.91598e7 | 0.458119 | 0.229059 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.35475e7 | − | 1.44709e8i | 0.751533 | − | 1.30169i | −0.195547 | − | 0.980694i | \(-0.562648\pi\) |
0.947080 | − | 0.320998i | \(-0.104018\pi\) | |||||||
\(200\) | −1.99604e7 | + | 3.45725e7i | −0.176427 | + | 0.305580i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.32164e7 | −0.795724 | ||||||||
\(203\) | −5.93280e7 | − | 1.50608e7i | −0.497764 | − | 0.126361i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.02888e6 | + | 8.71028e6i | 0.0407693 | + | 0.0706145i | ||||
\(206\) | 2.86403e7 | − | 4.96064e7i | 0.228266 | − | 0.395369i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.48111e7 | − | 2.56536e7i | −0.114121 | − | 0.197664i | ||||
\(209\) | 1.27166e8 | 0.963513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.06109e7 | 0.517467 | 0.258734 | − | 0.965949i | \(-0.416695\pi\) | ||||
0.258734 | + | 0.965949i | \(0.416695\pi\) | |||||||
\(212\) | 3.98310e7 | + | 6.89893e7i | 0.287108 | + | 0.497286i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.33390e7 | − | 4.04244e7i | 0.162793 | − | 0.281965i | ||||
\(215\) | −2.08246e6 | − | 3.60693e6i | −0.0142904 | − | 0.0247516i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.95071e7 | − | 7.13660e7i | 0.461764 | − | 0.474114i | ||||
\(218\) | 7.46384e7 | 0.487938 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.67517e6 | − | 4.63352e6i | 0.0169384 | − | 0.0293381i | ||||
\(221\) | 5.54362e7 | − | 9.60183e7i | 0.345478 | − | 0.598386i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.49891e8 | −1.50898 | −0.754489 | − | 0.656313i | \(-0.772115\pi\) | ||||
−0.754489 | + | 0.656313i | \(0.772115\pi\) | |||||||
\(224\) | −2.07478e7 | + | 2.13026e7i | −0.123340 | + | 0.126638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.53749e7 | − | 6.12711e7i | −0.203852 | − | 0.353082i | ||||
\(227\) | 1.62335e8 | − | 2.81173e8i | 0.921133 | − | 1.59545i | 0.123468 | − | 0.992349i | \(-0.460598\pi\) |
0.797665 | − | 0.603101i | \(-0.206068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.05242e7 | + | 1.82284e7i | 0.0579115 | + | 0.100306i | 0.893528 | − | 0.449008i | \(-0.148223\pi\) |
−0.835616 | + | 0.549314i | \(0.814889\pi\) | |||||||
\(230\) | 4.74705e6 | 0.0257262 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.45341e7 | −0.181568 | ||||||||
\(233\) | −8.17424e7 | − | 1.41582e8i | −0.423352 | − | 0.733267i | 0.572913 | − | 0.819616i | \(-0.305813\pi\) |
−0.996265 | + | 0.0863491i | \(0.972480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.75729e6 | − | 8.23987e6i | 0.0239123 | − | 0.0414174i | ||||
\(236\) | 6.54911e7 | + | 1.13434e8i | 0.324332 | + | 0.561760i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.07879e8 | − | 2.73858e7i | −0.518703 | − | 0.131676i | ||||
\(239\) | 3.18177e8 | 1.50757 | 0.753784 | − | 0.657123i | \(-0.228227\pi\) | ||||
0.753784 | + | 0.657123i | \(0.228227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.47859e7 | − | 1.12213e8i | 0.298141 | − | 0.516395i | −0.677570 | − | 0.735458i | \(-0.736967\pi\) |
0.975711 | + | 0.219064i | \(0.0703003\pi\) | |||||||
\(242\) | 1.02854e8 | − | 1.78148e8i | 0.466515 | − | 0.808027i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.02038e6 | 0.0397521 | ||||||||
\(245\) | 270206. | + | 1.02368e7i | 0.00117385 | + | 0.0444716i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.83952e7 | − | 1.18464e8i | −0.288793 | − | 0.500204i | ||||
\(248\) | 2.81027e7 | − | 4.86753e7i | 0.116995 | − | 0.202641i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.76388e6 | + | 1.34474e7i | 0.0314260 | + | 0.0544314i | ||||
\(251\) | 7.94873e7 | 0.317278 | 0.158639 | − | 0.987337i | \(-0.449289\pi\) | ||||
0.158639 | + | 0.987337i | \(0.449289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.20831e8 | 1.24553 | ||||||||
\(254\) | −8.90486e7 | − | 1.54237e8i | −0.340964 | − | 0.590567i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.14513e8 | − | 3.71547e8i | −0.788293 | − | 1.36536i | −0.927012 | − | 0.375032i | \(-0.877632\pi\) |
0.138719 | − | 0.990332i | \(-0.455702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50132e8 | + | 5.32116e8i | 0.536939 | + | 1.90308i | ||||
\(260\) | −5.75528e6 | −0.0203077 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.36070e7 | + | 7.55296e7i | −0.149797 | + | 0.259455i | ||||
\(263\) | −2.12061e7 | + | 3.67300e7i | −0.0718812 | + | 0.124502i | −0.899726 | − | 0.436456i | \(-0.856234\pi\) |
0.827845 | + | 0.560958i | \(0.189567\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.54775e7 | 0.0510904 | ||||||||
\(266\) | −9.58097e7 | + | 9.83720e7i | −0.312121 | + | 0.320469i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.38639e7 | − | 1.62577e8i | −0.297870 | − | 0.515926i | ||||
\(269\) | −2.60097e8 | + | 4.50501e8i | −0.814709 | + | 1.41112i | 0.0948278 | + | 0.995494i | \(0.469770\pi\) |
−0.909537 | + | 0.415624i | \(0.863563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.71406e7 | + | 1.50932e8i | 0.265967 | + | 0.460668i | 0.967817 | − | 0.251657i | \(-0.0809754\pi\) |
−0.701850 | + | 0.712325i | \(0.747642\pi\) | |||||||
\(272\) | −6.27951e7 | −0.189206 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.57006e8 | −0.754774 | ||||||||
\(275\) | 2.62103e8 | + | 4.53975e8i | 0.759989 | + | 1.31634i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.38413e8 | − | 5.86149e8i | 0.956683 | − | 1.65702i | 0.226216 | − | 0.974077i | \(-0.427365\pi\) |
0.730468 | − | 0.682947i | \(-0.239302\pi\) | |||||||
\(278\) | −7.56200e7 | − | 1.30978e8i | −0.211096 | − | 0.365629i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.56884e6 | + | 5.56045e6i | 0.00427095 | + | 0.0151376i | ||||
\(281\) | 3.51245e8 | 0.944360 | 0.472180 | − | 0.881502i | \(-0.343467\pi\) | ||||
0.472180 | + | 0.881502i | \(0.343467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.24140e8 | + | 5.61428e8i | −0.850121 | + | 1.47245i | 0.0309780 | + | 0.999520i | \(0.490138\pi\) |
−0.881099 | + | 0.472932i | \(0.843196\pi\) | |||||||
\(284\) | −1.96904e7 | + | 3.41048e7i | −0.0510083 | + | 0.0883490i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.88973e8 | −0.983193 | ||||||||
\(287\) | −7.11467e8 | − | 1.80610e8i | −1.77651 | − | 0.450979i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.76521e7 | + | 1.51818e8i | 0.213609 | + | 0.369982i | ||||
\(290\) | −3.35480e6 | + | 5.81069e6i | −0.00807744 | + | 0.0139905i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.55250e7 | + | 7.88516e7i | 0.107006 | + | 0.185341i | ||||
\(293\) | −6.35015e6 | −0.0147485 | −0.00737424 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737424 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.54484e7 | 0.0577144 | ||||||||
\(296\) | 1.55968e8 | + | 2.70144e8i | 0.349554 | + | 0.605445i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.21850e7 | − | 3.84255e7i | 0.0485626 | − | 0.0841129i | ||||
\(299\) | −1.72557e8 | − | 2.98878e8i | −0.373322 | − | 0.646613i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.94619e8 | + | 7.47908e7i | 0.622699 | + | 0.158076i | ||||
\(302\) | 1.81311e8 | 0.378791 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.87372e7 | + | 6.70947e7i | −0.0790807 | + | 0.136972i | ||||
\(305\) | 876281. | − | 1.51776e6i | 0.00176845 | − | 0.00306305i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.05452e8 | 1.58875 | 0.794375 | − | 0.607428i | \(-0.207798\pi\) | ||||
0.794375 | + | 0.607428i | \(0.207798\pi\) | |||||||
\(308\) | 1.06031e8 | + | 3.75805e8i | 0.206778 | + | 0.732884i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.46005e6 | − | 9.45709e6i | −0.0104095 | − | 0.0180298i | ||||
\(311\) | −2.12401e8 | + | 3.67889e8i | −0.400401 | + | 0.693514i | −0.993774 | − | 0.111413i | \(-0.964462\pi\) |
0.593374 | + | 0.804927i | \(0.297796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.08578e8 | + | 3.61268e8i | 0.384472 | + | 0.665924i | 0.991696 | − | 0.128606i | \(-0.0410503\pi\) |
−0.607224 | + | 0.794531i | \(0.707717\pi\) | |||||||
\(314\) | −5.20100e8 | −0.948054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.52793e8 | −0.272395 | ||||||||
\(317\) | 2.13997e8 | + | 3.70654e8i | 0.377312 | + | 0.653523i | 0.990670 | − | 0.136282i | \(-0.0435152\pi\) |
−0.613358 | + | 0.789805i | \(0.710182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.26736e8 | + | 3.92718e8i | −0.391068 | + | 0.677350i | ||||
\(320\) | 1.62982e6 | + | 2.82292e6i | 0.00278044 | + | 0.00481587i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.41722e8 | + | 2.48187e8i | −0.403479 | + | 0.414270i | ||||
\(323\) | −2.89977e8 | −0.478801 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.81941e8 | − | 4.88335e8i | 0.455581 | − | 0.789090i | ||||
\(326\) | 1.39736e8 | − | 2.42030e8i | 0.223381 | − | 0.386907i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.14136e8 | −0.648014 | ||||||||
\(329\) | 1.88556e8 | + | 6.68300e8i | 0.291913 | + | 1.03463i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.32553e8 | − | 2.29588e8i | −0.200905 | − | 0.347978i | 0.747915 | − | 0.663794i | \(-0.231055\pi\) |
−0.948820 | + | 0.315816i | \(0.897722\pi\) | |||||||
\(332\) | −2.41098e8 | + | 4.17595e8i | −0.361586 | + | 0.626284i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.55810e8 | − | 6.16281e8i | −0.522523 | − | 0.905036i | ||||
\(335\) | −3.64735e7 | −0.0530055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17646e8 | 0.309775 | 0.154887 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154887 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(338\) | −4.17874e7 | − | 7.23778e7i | −0.0588622 | − | 0.101952i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.10021e6 | + | 1.05659e7i | −0.00841721 | + | 0.0145790i | ||||
\(341\) | −3.69020e8 | − | 6.39161e8i | −0.503976 | − | 0.872911i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.48962e8 | − | 5.07136e8i | −0.734536 | − | 0.678570i | ||||
\(344\) | 1.71494e8 | 0.227140 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23055e8 | − | 2.13138e8i | 0.159710 | − | 0.276626i | ||||
\(347\) | −3.24979e8 | + | 5.62880e8i | −0.417544 | + | 0.723207i | −0.995692 | − | 0.0927250i | \(-0.970442\pi\) |
0.578148 | + | 0.815932i | \(0.303776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.11539e8 | −0.896003 | −0.448002 | − | 0.894033i | \(-0.647864\pi\) | ||||
−0.448002 | + | 0.894033i | \(0.647864\pi\) | |||||||
\(350\) | −5.48658e8 | − | 1.39280e8i | −0.684012 | − | 0.173641i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.10152e8 | + | 1.90789e8i | 0.134615 | + | 0.233160i | ||||
\(353\) | −7.74200e8 | + | 1.34095e9i | −0.936788 | + | 1.62257i | −0.165375 | + | 0.986231i | \(0.552884\pi\) |
−0.771413 | + | 0.636335i | \(0.780450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.82564e6 | + | 6.62621e6i | 0.00453842 | + | 0.00786078i | ||||
\(356\) | 3.42729e8 | 0.402602 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.24575e8 | 0.949816 | ||||||||
\(359\) | 8.43823e7 | + | 1.46154e8i | 0.0962544 | + | 0.166718i | 0.910131 | − | 0.414320i | \(-0.135980\pi\) |
−0.813877 | + | 0.581037i | \(0.802647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.68054e8 | − | 4.64284e8i | 0.299880 | − | 0.519407i | ||||
\(362\) | −2.50273e8 | − | 4.33486e8i | −0.277290 | − | 0.480280i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.93062e8 | − | 3.00899e8i | 0.318496 | − | 0.327014i | ||||
\(365\) | 1.76900e7 | 0.0190416 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71858e8 | − | 2.97666e8i | 0.181484 | − | 0.314339i | −0.760902 | − | 0.648867i | \(-0.775243\pi\) |
0.942386 | + | 0.334527i | \(0.108577\pi\) | |||||||
\(368\) | −9.77316e7 | + | 1.69276e8i | −0.102227 | + | 0.177063i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.06058e7 | 0.0622025 | ||||||||
\(371\) | −7.88120e8 | + | 8.09198e8i | −0.801279 | + | 0.822709i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.96771e7 | + | 1.20684e8i | 0.0695199 | + | 0.120412i | 0.898690 | − | 0.438584i | \(-0.144520\pi\) |
−0.829170 | + | 0.558996i | \(0.811187\pi\) | |||||||
\(374\) | −4.12285e8 | + | 7.14099e8i | −0.407518 | + | 0.705842i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.95885e8 | + | 3.39282e8i | 0.190039 | + | 0.329158i | ||||
\(377\) | 4.87793e8 | 0.468858 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.74462e8 | −0.730740 | −0.365370 | − | 0.930862i | \(-0.619057\pi\) | ||||
−0.365370 | + | 0.930862i | \(0.619057\pi\) | |||||||
\(380\) | 7.52621e6 | + | 1.30358e7i | 0.00703613 | + | 0.0121869i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.16402e8 | + | 5.48024e8i | −0.290414 | + | 0.503012i | ||||
\(383\) | −6.53115e8 | − | 1.13123e9i | −0.594011 | − | 1.02886i | −0.993686 | − | 0.112200i | \(-0.964210\pi\) |
0.399675 | − | 0.916657i | \(-0.369123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.35331e7 | + | 1.86668e7i | 0.0656705 | + | 0.0166709i | ||||
\(386\) | 4.50315e8 | 0.398530 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.06158e8 | − | 8.76691e8i | 0.439921 | − | 0.761966i | ||||
\(389\) | 1.10694e9 | − | 1.91728e9i | 0.953455 | − | 1.65143i | 0.215591 | − | 0.976484i | \(-0.430832\pi\) |
0.737864 | − | 0.674949i | \(-0.235834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31595e8 | −0.618945 | ||||||||
\(392\) | −3.70599e8 | − | 2.01118e8i | −0.310744 | − | 0.168636i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.96639e8 | + | 3.40589e8i | 0.161969 | + | 0.280539i | ||||
\(395\) | −1.48430e7 | + | 2.57089e7i | −0.0121181 | + | 0.0209891i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.85561e8 | − | 1.01422e9i | −0.469684 | − | 0.813516i | 0.529715 | − | 0.848176i | \(-0.322299\pi\) |
−0.999399 | + | 0.0346591i | \(0.988965\pi\) | |||||||
\(398\) | 1.33676e9 | 1.06283 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.19367e8 | −0.249505 | ||||||||
\(401\) | −7.49819e8 | − | 1.29872e9i | −0.580699 | − | 1.00580i | −0.995397 | − | 0.0958406i | \(-0.969446\pi\) |
0.414698 | − | 0.909959i | \(-0.363887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.96950e8 | + | 6.87538e8i | −0.302112 | + | 0.523274i | ||||
\(404\) | −3.72866e8 | − | 6.45822e8i | −0.281331 | − | 0.487280i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.32968e8 | − | 4.71280e8i | −0.0986066 | − | 0.349492i | ||||
\(407\) | 4.09607e9 | 3.01153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.74802e7 | − | 6.49176e7i | 0.0270876 | − | 0.0469171i | −0.852164 | − | 0.523275i | \(-0.824710\pi\) |
0.879251 | + | 0.476358i | \(0.158043\pi\) | |||||||
\(410\) | −4.02311e7 | + | 6.96823e7i | −0.0288282 | + | 0.0499320i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.58244e8 | 0.322817 | ||||||||
\(413\) | −1.29585e9 | + | 1.33050e9i | −0.905167 | + | 0.929374i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.68428e7 | + | 8.11342e7i | 0.0321718 | + | 0.0557231i | ||||
\(416\) | 1.18489e8 | − | 2.05229e8i | 0.0806958 | − | 0.139769i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.08663e8 | + | 8.81029e8i | 0.340653 | + | 0.590029i | ||||
\(419\) | 8.47037e7 | 0.0562540 | 0.0281270 | − | 0.999604i | \(-0.491046\pi\) | ||||
0.0281270 | + | 0.999604i | \(0.491046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.03152e8 | −0.393949 | −0.196974 | − | 0.980409i | \(-0.563112\pi\) | ||||
−0.196974 | + | 0.980409i | \(0.563112\pi\) | |||||||
\(422\) | 2.82443e8 | + | 4.89206e8i | 0.182952 | + | 0.316883i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.18648e8 | + | 5.51914e8i | −0.203016 | + | 0.351634i | ||||
\(425\) | −5.97675e8 | − | 1.03520e9i | −0.377663 | − | 0.654131i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47315e7 | + | 1.23099e8i | 0.0215887 | + | 0.0765170i | ||||
\(428\) | 3.73425e8 | 0.230224 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.66597e7 | − | 2.88555e7i | 0.0101048 | − | 0.0175020i | ||||
\(431\) | 1.30326e9 | − | 2.25732e9i | 0.784081 | − | 1.35807i | −0.145465 | − | 0.989363i | \(-0.546468\pi\) |
0.929546 | − | 0.368705i | \(-0.120199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.09676e9 | 1.83316 | 0.916579 | − | 0.399854i | \(-0.130939\pi\) | ||||
0.916579 | + | 0.399854i | \(0.130939\pi\) | |||||||
\(434\) | 7.72467e8 | + | 1.96095e8i | 0.453592 | + | 0.115147i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.98554e8 | + | 5.17110e8i | 0.172512 | + | 0.298800i | ||||
\(437\) | −4.51308e8 | + | 7.81688e8i | −0.258695 | + | 0.448073i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.02299e8 | + | 5.23597e8i | 0.170534 | + | 0.295374i | 0.938607 | − | 0.344989i | \(-0.112117\pi\) |
−0.768073 | + | 0.640363i | \(0.778784\pi\) | |||||||
\(440\) | 4.28026e7 | 0.0239545 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.86979e8 | 0.488580 | ||||||||
\(443\) | 1.08327e9 | + | 1.87628e9i | 0.592003 | + | 1.02538i | 0.993962 | + | 0.109722i | \(0.0349960\pi\) |
−0.401959 | + | 0.915658i | \(0.631671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.32943e7 | − | 5.76674e7i | 0.0179106 | − | 0.0310220i | ||||
\(446\) | −9.99562e8 | − | 1.73129e9i | −0.533504 | − | 0.924056i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.30580e8 | − | 5.85342e7i | −0.121157 | − | 0.0307565i | ||||
\(449\) | 1.01304e9 | 0.528161 | 0.264080 | − | 0.964501i | \(-0.414932\pi\) | ||||
0.264080 | + | 0.964501i | \(0.414932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.71903e9 | + | 4.70951e9i | −1.39572 | + | 2.41745i | ||||
\(452\) | 2.82999e8 | − | 4.90169e8i | 0.144145 | − | 0.249667i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.59736e9 | 1.30268 | ||||||||
\(455\) | −2.21598e7 | − | 7.85412e7i | −0.0110287 | − | 0.0390893i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.04203e8 | − | 1.39292e9i | −0.394148 | − | 0.682684i | 0.598844 | − | 0.800865i | \(-0.295627\pi\) |
−0.992992 | + | 0.118182i | \(0.962293\pi\) | |||||||
\(458\) | −8.41936e7 | + | 1.45828e8i | −0.0409496 | + | 0.0709268i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.89882e7 | + | 3.28885e7i | 0.00909560 | + | 0.0157540i | ||||
\(461\) | 2.98355e9 | 1.41834 | 0.709169 | − | 0.705039i | \(-0.249070\pi\) | ||||
0.709169 | + | 0.705039i | \(0.249070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.83402e9 | −1.32700 | −0.663499 | − | 0.748178i | \(-0.730929\pi\) | ||||
−0.663499 | + | 0.748178i | \(0.730929\pi\) | |||||||
\(464\) | −1.38136e8 | − | 2.39259e8i | −0.0641941 | − | 0.111187i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.53939e8 | − | 1.13266e9i | 0.299355 | − | 0.518498i | ||||
\(467\) | −2.15916e9 | − | 3.73977e9i | −0.981014 | − | 1.69917i | −0.658460 | − | 0.752616i | \(-0.728792\pi\) |
−0.322555 | − | 0.946551i | \(-0.604542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.85725e9 | − | 1.90692e9i | 0.831314 | − | 0.853547i | ||||
\(470\) | 7.61166e7 | 0.0338171 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.23929e8 | + | 9.07471e8i | −0.229338 | + | 0.397224i | ||||
\(473\) | 1.12595e9 | − | 1.95021e9i | 0.489223 | − | 0.847359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.47478e9 | −0.631393 | ||||||||
\(476\) | −2.41782e8 | − | 8.56952e8i | −0.102754 | − | 0.364194i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.27271e9 | + | 2.20440e9i | 0.533006 | + | 0.923193i | ||||
\(479\) | −4.10161e8 | + | 7.10420e8i | −0.170522 | + | 0.295353i | −0.938602 | − | 0.345001i | \(-0.887879\pi\) |
0.768081 | + | 0.640353i | \(0.221212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.20304e9 | − | 3.81578e9i | −0.902642 | − | 1.56342i | ||||
\(482\) | 1.03657e9 | 0.421634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.64566e9 | 0.659752 | ||||||||
\(485\) | −9.83410e7 | − | 1.70332e8i | −0.0391416 | − | 0.0677953i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.16713e9 | + | 3.75359e9i | −0.850226 | + | 1.47263i | 0.0307785 | + | 0.999526i | \(0.490201\pi\) |
−0.881004 | + | 0.473108i | \(0.843132\pi\) | |||||||
\(488\) | 3.60815e7 | + | 6.24950e7i | 0.0140545 | + | 0.0243431i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.98417e7 | + | 4.28192e7i | −0.0268181 | + | 0.0164419i | ||||
\(491\) | 1.79725e9 | 0.685208 | 0.342604 | − | 0.939480i | \(-0.388691\pi\) | ||||
0.342604 | + | 0.939480i | \(0.388691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.17028e8 | − | 8.95518e8i | 0.194334 | − | 0.336597i | ||||
\(494\) | 5.47162e8 | − | 9.47712e8i | 0.204207 | − | 0.353697i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.49643e8 | 0.165456 | ||||||||
\(497\) | −5.41237e8 | − | 1.37396e8i | −0.197761 | − | 0.0502028i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.07065e8 | − | 7.05058e8i | −0.146660 | − | 0.254023i | 0.783331 | − | 0.621605i | \(-0.213519\pi\) |
−0.929991 | + | 0.367582i | \(0.880186\pi\) | |||||||
\(500\) | −6.21110e7 | + | 1.07579e8i | −0.0222215 | + | 0.0384888i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.17949e8 | + | 5.50704e8i | 0.112175 | + | 0.194292i | ||||
\(503\) | −3.03176e9 | −1.06220 | −0.531101 | − | 0.847309i | \(-0.678221\pi\) | ||||
−0.531101 | + | 0.847309i | \(0.678221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.44888e8 | −0.0500624 | ||||||||
\(506\) | 1.28333e9 | + | 2.22279e9i | 0.440362 | + | 0.762730i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.12388e8 | − | 1.23389e9i | 0.241098 | − | 0.417594i | ||||
\(509\) | −1.34515e9 | − | 2.32986e9i | −0.452124 | − | 0.783101i | 0.546394 | − | 0.837528i | \(-0.316000\pi\) |
−0.998518 | + | 0.0544271i | \(0.982667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00786e8 | + | 9.24876e8i | −0.298640 | + | 0.306627i | ||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.71610e9 | − | 2.97238e9i | 0.557407 | − | 0.965458i | ||||
\(515\) | 4.45160e7 | − | 7.71039e7i | 0.0143612 | − | 0.0248743i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.14437e9 | 1.63725 | ||||||||
\(518\) | −3.08608e9 | + | 3.16861e9i | −0.975557 | + | 1.00165i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.30211e7 | − | 3.98738e7i | −0.00717984 | − | 0.0124359i | ||||
\(521\) | −1.84690e9 | + | 3.19892e9i | −0.572152 | + | 0.990996i | 0.424193 | + | 0.905572i | \(0.360558\pi\) |
−0.996345 | + | 0.0854238i | \(0.972776\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.36893e9 | − | 2.37105e9i | −0.418432 | − | 0.724745i | 0.577350 | − | 0.816497i | \(-0.304087\pi\) |
−0.995782 | + | 0.0917518i | \(0.970753\pi\) | |||||||
\(524\) | −6.97712e8 | −0.211844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.39297e8 | −0.101655 | ||||||||
\(527\) | 8.41480e8 | + | 1.45749e9i | 0.250442 | + | 0.433778i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.63790e8 | − | 9.76512e8i | 0.165585 | − | 0.286802i | ||||
\(530\) | 6.19099e7 | + | 1.07231e8i | 0.0180632 | + | 0.0312864i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.06478e9 | − | 2.70301e8i | −0.306598 | − | 0.0778317i | ||||
\(533\) | 5.84966e9 | 1.67334 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.62762e7 | − | 6.28322e7i | 0.0102420 | − | 0.0177396i | ||||
\(536\) | 7.50912e8 | − | 1.30062e9i | 0.210626 | − | 0.364815i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.16155e9 | −1.15217 | ||||||||
\(539\) | −4.72028e9 | + | 2.89395e9i | −1.29840 | + | 0.796033i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26385e9 | − | 2.18905e9i | −0.343167 | − | 0.594382i | 0.641852 | − | 0.766828i | \(-0.278166\pi\) |
−0.985019 | + | 0.172446i | \(0.944833\pi\) | |||||||
\(542\) | −6.97124e8 | + | 1.20745e9i | −0.188067 | + | 0.325742i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.51180e8 | − | 4.35057e8i | −0.0668944 | − | 0.115864i | ||||
\(545\) | 1.16012e8 | 0.0306982 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49324e8 | 0.0390098 | 0.0195049 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195049 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(548\) | −1.02803e9 | − | 1.78059e9i | −0.266853 | − | 0.462203i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.09682e9 | + | 3.63180e9i | −0.537393 | + | 0.930792i | ||||
\(551\) | −6.37890e8 | − | 1.10486e9i | −0.162448 | − | 0.281369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.88306e8 | − | 2.08514e9i | −0.147933 | − | 0.524321i | ||||
\(554\) | 5.41461e9 | 1.35295 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.04960e8 | − | 1.04782e9i | 0.149267 | − | 0.258539i | ||||
\(557\) | −2.77646e9 | + | 4.80896e9i | −0.680766 | + | 1.17912i | 0.293982 | + | 0.955811i | \(0.405019\pi\) |
−0.974748 | + | 0.223310i | \(0.928314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.42235e9 | −0.586537 | ||||||||
\(560\) | −3.22486e7 | + | 3.31110e7i | −0.00775983 | + | 0.00796736i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.40498e9 | + | 2.43350e9i | 0.333882 | + | 0.578300i | ||||
\(563\) | −1.41867e9 | + | 2.45721e9i | −0.335045 | + | 0.580315i | −0.983493 | − | 0.180944i | \(-0.942085\pi\) |
0.648449 | + | 0.761258i | \(0.275418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.49837e7 | − | 9.52345e7i | −0.0128252 | − | 0.0222139i | ||||
\(566\) | −5.18625e9 | −1.20225 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.15047e8 | −0.0721367 | ||||||||
\(569\) | 4.10087e9 | + | 7.10291e9i | 0.933217 | + | 1.61638i | 0.777782 | + | 0.628534i | \(0.216345\pi\) |
0.155435 | + | 0.987846i | \(0.450322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.70322e7 | + | 4.68211e7i | −0.00607651 | + | 0.0105248i | −0.869048 | − | 0.494728i | \(-0.835268\pi\) |
0.862971 | + | 0.505253i | \(0.168601\pi\) | |||||||
\(572\) | −1.55589e9 | − | 2.69489e9i | −0.347611 | − | 0.602080i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.59456e9 | − | 5.65163e9i | −0.351925 | − | 1.24733i | ||||
\(575\) | −3.72079e9 | −0.816201 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.27103e8 | − | 1.25938e9i | 0.157573 | − | 0.272924i | −0.776420 | − | 0.630216i | \(-0.782967\pi\) |
0.933993 | + | 0.357292i | \(0.116300\pi\) | |||||||
\(578\) | −7.01217e8 | + | 1.21454e9i | −0.151044 | + | 0.261617i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.36768e7 | −0.0114232 | ||||||||
\(581\) | −6.62714e9 | − | 1.68234e9i | −1.40188 | − | 0.355875i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.18421e9 | + | 7.24726e9i | 0.874527 | + | 1.51472i | ||||
\(584\) | −3.64200e8 | + | 6.30813e8i | −0.0756650 | + | 0.131056i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.54006e7 | − | 4.39951e7i | −0.00521437 | − | 0.00903156i | ||||
\(587\) | 7.30976e9 | 1.49166 | 0.745830 | − | 0.666137i | \(-0.232053\pi\) | ||||
0.745830 | + | 0.666137i | \(0.232053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.07638e9 | 0.418699 | ||||||||
\(590\) | 1.01794e8 | + | 1.76312e8i | 0.0204051 | + | 0.0353427i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.24774e9 | + | 2.16116e9i | −0.247172 | + | 0.428115i | ||||
\(593\) | −2.16461e9 | − | 3.74922e9i | −0.426274 | − | 0.738329i | 0.570264 | − | 0.821461i | \(-0.306841\pi\) |
−0.996538 | + | 0.0831327i | \(0.973507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.67678e8 | − | 4.25661e7i | −0.0326338 | − | 0.00828428i | ||||
\(596\) | 3.54959e8 | 0.0686779 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.38046e9 | − | 2.39102e9i | 0.263979 | − | 0.457224i | ||||
\(599\) | −1.44898e9 | + | 2.50970e9i | −0.275466 | + | 0.477121i | −0.970253 | − | 0.242095i | \(-0.922165\pi\) |
0.694787 | + | 0.719216i | \(0.255499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.87385e9 | 1.47954 | 0.739770 | − | 0.672860i | \(-0.234935\pi\) | ||||
0.739770 | + | 0.672860i | \(0.234935\pi\) | |||||||
\(602\) | 6.60310e8 | + | 2.34034e9i | 0.123356 | + | 0.437212i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.25243e8 | + | 1.25616e9i | 0.133923 | + | 0.231961i | ||||
\(605\) | 1.59867e8 | − | 2.76897e8i | 0.0293504 | − | 0.0508364i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.80092e9 | + | 3.11928e9i | 0.326838 | + | 0.566101i | 0.981883 | − | 0.189490i | \(-0.0606834\pi\) |
−0.655044 | + | 0.755591i | \(0.727350\pi\) | |||||||
\(608\) | −6.19795e8 | −0.111837 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.40205e7 | 0.00250097 | ||||||||
\(611\) | −2.76687e9 | − | 4.79236e9i | −0.490732 | − | 0.849973i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.97224e9 | − | 3.41602e9i | 0.345819 | − | 0.598976i | −0.639683 | − | 0.768639i | \(-0.720934\pi\) |
0.985502 | + | 0.169663i | \(0.0542678\pi\) | |||||||
\(614\) | 3.22181e9 | + | 5.58034e9i | 0.561708 | + | 0.972907i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.17953e9 | + | 2.23782e9i | −0.375691 | + | 0.385738i | ||||
\(617\) | −4.54305e9 | −0.778663 | −0.389331 | − | 0.921098i | \(-0.627294\pi\) | ||||
−0.389331 | + | 0.921098i | \(0.627294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.82703e9 | + | 6.62860e9i | −0.648551 | + | 1.12332i | 0.334918 | + | 0.942247i | \(0.391291\pi\) |
−0.983469 | + | 0.181076i | \(0.942042\pi\) | |||||||
\(620\) | 4.36804e7 | − | 7.56567e7i | 0.00736064 | − | 0.0127490i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.39841e9 | −0.566252 | ||||||||
\(623\) | 1.31962e9 | + | 4.67716e9i | 0.218646 | + | 0.774950i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.03365e9 | − | 5.25444e9i | −0.497033 | − | 0.860887i | ||||
\(626\) | −1.66863e9 | + | 2.89015e9i | −0.271862 | + | 0.470880i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.08040e9 | − | 3.60336e9i | −0.335188 | − | 0.580562i | ||||
\(629\) | −9.34031e9 | −1.49652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.11407e9 | −1.12724 | −0.563619 | − | 0.826035i | \(-0.690591\pi\) | ||||
−0.563619 | + | 0.826035i | \(0.690591\pi\) | |||||||
\(632\) | −6.11173e8 | − | 1.05858e9i | −0.0963062 | − | 0.166807i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.71198e9 | + | 2.96523e9i | −0.266800 | + | 0.462111i | ||||
\(635\) | −1.38409e8 | − | 2.39732e8i | −0.0214515 | − | 0.0371551i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.23470e9 | + | 2.84079e9i | 0.802424 | + | 0.435463i | ||||
\(638\) | −3.62777e9 | −0.553054 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.30385e7 | + | 2.25834e7i | −0.00196607 | + | 0.00340533i | ||||
\(641\) | 1.99141e9 | − | 3.44923e9i | 0.298647 | − | 0.517271i | −0.677180 | − | 0.735818i | \(-0.736798\pi\) |
0.975827 | + | 0.218546i | \(0.0701314\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.89465e9 | 0.577737 | 0.288869 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288869 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(644\) | −2.68638e9 | − | 6.81953e8i | −0.396339 | − | 0.100613i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.15991e9 | − | 2.00902e9i | −0.169282 | − | 0.293204i | ||||
\(647\) | −2.55065e9 | + | 4.41786e9i | −0.370243 | + | 0.641279i | −0.989603 | − | 0.143828i | \(-0.954059\pi\) |
0.619360 | + | 0.785107i | \(0.287392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.87977e9 | + | 1.19161e10i | 0.987911 | + | 1.71111i | ||||
\(650\) | 4.51105e9 | 0.644289 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.23577e9 | 0.315908 | ||||||||
\(653\) | 4.67227e9 | + | 8.09262e9i | 0.656647 | + | 1.13735i | 0.981478 | + | 0.191574i | \(0.0613593\pi\) |
−0.324831 | + | 0.945772i | \(0.605307\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.77790e7 | + | 1.17397e8i | −0.00942433 | + | 0.0163234i | ||||
\(656\) | −1.65654e9 | − | 2.86922e9i | −0.229108 | − | 0.396826i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.87590e9 | + | 3.97955e9i | −0.530373 | + | 0.544557i | ||||
\(659\) | 1.00669e10 | 1.37024 | 0.685120 | − | 0.728430i | \(-0.259750\pi\) | ||||
0.685120 | + | 0.728430i | \(0.259750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.51511e8 | + | 1.30166e9i | −0.101212 | + | 0.175304i | −0.912184 | − | 0.409781i | \(-0.865605\pi\) |
0.810973 | + | 0.585084i | \(0.198939\pi\) | |||||||
\(662\) | 1.06042e9 | − | 1.83671e9i | 0.142062 | − | 0.246058i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.85757e9 | −0.511359 | ||||||||
\(665\) | −1.48918e8 | + | 1.52901e8i | −0.0196369 | + | 0.0201620i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60936e9 | − | 2.78749e9i | −0.209997 | − | 0.363725i | ||||
\(668\) | 2.84648e9 | − | 4.93024e9i | 0.369479 | − | 0.639957i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.45894e8 | − | 2.52696e8i | −0.0187403 | − | 0.0324591i | ||||
\(671\) | 9.47581e8 | 0.121084 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.90495e9 | 0.493814 | 0.246907 | − | 0.969039i | \(-0.420586\pi\) | ||||
0.246907 | + | 0.969039i | \(0.420586\pi\) | |||||||
\(674\) | 8.70584e8 | + | 1.50790e9i | 0.109522 | + | 0.189697i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.34299e8 | − | 5.79023e8i | 0.0416219 | − | 0.0720912i | ||||
\(677\) | −3.20795e9 | − | 5.55633e9i | −0.397344 | − | 0.688220i | 0.596053 | − | 0.802945i | \(-0.296735\pi\) |
−0.993397 | + | 0.114725i | \(0.963401\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.39129e10 | + | 3.53188e9i | 1.70559 | + | 0.432974i | ||||
\(680\) | −9.76033e7 | −0.0119037 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.95216e9 | − | 5.11329e9i | 0.356365 | − | 0.617242i | ||||
\(683\) | 4.58428e9 | − | 7.94021e9i | 0.550553 | − | 0.953585i | −0.447682 | − | 0.894193i | \(-0.647750\pi\) |
0.998235 | − | 0.0593923i | \(-0.0189163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.99469e8 | −0.0474860 | ||||||||
\(686\) | 1.31769e9 | − | 5.83186e9i | 0.155840 | − | 0.689720i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.85976e8 | + | 1.18814e9i | 0.0803062 | + | 0.139094i | ||||
\(689\) | 4.50090e9 | − | 7.79578e9i | 0.524242 | − | 0.908013i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.12922e9 | − | 7.15202e9i | −0.476096 | − | 0.824623i | 0.523529 | − | 0.852008i | \(-0.324615\pi\) |
−0.999625 | + | 0.0273851i | \(0.991282\pi\) | |||||||
\(692\) | 1.96888e9 | 0.225865 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.19966e9 | −0.590496 | ||||||||
\(695\) | −1.17537e8 | − | 2.03581e8i | −0.0132809 | − | 0.0230033i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.20024e9 | − | 1.07391e10i | 0.693576 | − | 1.20131i | ||||
\(698\) | −2.84615e9 | − | 4.92969e9i | −0.316785 | − | 0.548688i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.22967e9 | − | 4.35833e9i | −0.135502 | − | 0.480261i | ||||
\(701\) | 1.35693e10 | 1.48779 | 0.743897 | − | 0.668294i | \(-0.232975\pi\) | ||||
0.743897 | + | 0.668294i | \(0.232975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.76187e9 | + | 9.97985e9i | −0.625489 | + | 1.08338i | ||||
\(704\) | −8.81215e8 | + | 1.52631e9i | −0.0951870 | + | 0.164869i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23872e10 | −1.32482 | ||||||||
\(707\) | 7.37775e9 | − | 7.57506e9i | 0.785156 | − | 0.806154i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.01524e9 | − | 5.22255e9i | −0.317731 | − | 0.550327i | 0.662283 | − | 0.749254i | \(-0.269588\pi\) |
−0.980014 | + | 0.198927i | \(0.936254\pi\) | |||||||
\(710\) | −3.06051e7 | + | 5.30096e7i | −0.00320915 | + | 0.00555841i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.37092e9 | + | 2.37450e9i | 0.142341 | + | 0.246542i | ||||
\(713\) | 5.23857e9 | 0.541252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.04587e8 | −0.0618568 | ||||||||
\(716\) | 3.29830e9 | + | 5.71282e9i | 0.335811 | + | 0.581641i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.75058e8 | + | 1.16923e9i | −0.0680621 | + | 0.117887i | ||||
\(719\) | −4.88166e8 | − | 8.45527e8i | −0.0489797 | − | 0.0848353i | 0.840496 | − | 0.541818i | \(-0.182264\pi\) |
−0.889476 | + | 0.456982i | \(0.848930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.76440e9 | + | 6.25357e9i | 0.175316 | + | 0.621376i | ||||
\(722\) | 4.28887e9 | 0.424094 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.00218e9 | − | 3.46788e9i | 0.196074 | − | 0.339609i | ||||
\(725\) | 2.62953e9 | − | 4.55447e9i | 0.256268 | − | 0.443869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.25379e10 | 1.21019 | 0.605095 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605095 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(728\) | 3.25694e9 | + | 8.26794e8i | 0.312860 | + | 0.0794214i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.07602e7 | + | 1.22560e8i | 0.00673223 | + | 0.0116606i | ||||
\(731\) | −2.56752e9 | + | 4.44708e9i | −0.243111 | + | 0.421080i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.39843e9 | − | 1.10824e10i | −0.600080 | − | 1.03937i | −0.992808 | − | 0.119715i | \(-0.961802\pi\) |
0.392728 | − | 0.919655i | \(-0.371531\pi\) | |||||||
\(734\) | 2.74972e9 | 0.256657 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.56371e9 | −0.144571 | ||||||||
\(737\) | −9.86031e9 | − | 1.70786e10i | −0.907307 | − | 1.57150i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.26030e9 | − | 3.91495e9i | 0.206020 | − | 0.356838i | −0.744437 | − | 0.667693i | \(-0.767282\pi\) |
0.950457 | + | 0.310855i | \(0.100615\pi\) | |||||||
\(740\) | 2.42423e8 | + | 4.19889e8i | 0.0219919 | + | 0.0380911i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.75877e9 | − | 2.22347e9i | −0.787099 | − | 0.199810i | ||||
\(743\) | −1.42321e10 | −1.27294 | −0.636469 | − | 0.771303i | \(-0.719606\pi\) | ||||
−0.636469 | + | 0.771303i | \(0.719606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.44824e7 | − | 5.97253e7i | 0.00305528 | − | 0.00529190i | ||||
\(746\) | −5.57417e8 | + | 9.65474e8i | −0.0491580 | + | 0.0851442i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.59656e9 | −0.576318 | ||||||||
\(749\) | 1.43781e9 | + | 5.09605e9i | 0.125030 | + | 0.443147i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.44123e9 | − | 1.28886e10i | −0.641069 | − | 1.11036i | −0.985194 | − | 0.171441i | \(-0.945158\pi\) |
0.344125 | − | 0.938924i | \(-0.388175\pi\) | |||||||
\(752\) | −1.56708e9 | + | 2.71426e9i | −0.134378 | + | 0.232750i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.95117e9 | + | 3.37953e9i | 0.165766 | + | 0.287116i | ||||
\(755\) | 2.81814e8 | 0.0238313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.24473e10 | 1.04289 | 0.521445 | − | 0.853285i | \(-0.325393\pi\) | ||||
0.521445 | + | 0.853285i | \(0.325393\pi\) | |||||||
\(758\) | −3.09785e9 | − | 5.36563e9i | −0.258356 | − | 0.447485i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.02097e7 | + | 1.04286e8i | −0.00497530 | + | 0.00861747i | ||||
\(761\) | 1.15160e10 | + | 1.99463e10i | 0.947230 | + | 1.64065i | 0.751223 | + | 0.660049i | \(0.229464\pi\) |
0.196007 | + | 0.980602i | \(0.437202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.90737e9 | + | 6.06535e9i | −0.481458 | + | 0.494334i | ||||
\(764\) | −5.06243e9 | −0.410707 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.22492e9 | − | 9.04983e9i | 0.420029 | − | 0.727511i | ||||
\(767\) | 7.40048e9 | − | 1.28180e10i | 0.592211 | − | 1.02574i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.08864e10 | −0.863265 | −0.431632 | − | 0.902050i | \(-0.642062\pi\) | ||||
−0.431632 | + | 0.902050i | \(0.642062\pi\) | |||||||
\(770\) | 1.64805e8 | + | 5.84119e8i | 0.0130092 | + | 0.0461088i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.80126e9 | + | 3.11987e9i | 0.140902 | + | 0.244049i | ||||
\(773\) | 7.34907e9 | − | 1.27290e10i | 0.572275 | − | 0.991209i | −0.424057 | − | 0.905635i | \(-0.639395\pi\) |
0.996332 | − | 0.0855732i | \(-0.0272722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.27964e9 | + | 7.41256e9i | 0.330257 | + | 0.572021i | ||||
\(776\) | 8.09853e9 | 0.622143 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.77110e10 | 1.34839 | ||||||||
\(779\) | −7.64964e9 | − | 1.32496e10i | −0.579775 | − | 1.00420i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.06846e9 | + | 3.58268e9i | −0.155371 | + | 0.269110i | ||||
\(782\) | −2.92638e9 | − | 5.06864e9i | −0.218830 | − | 0.379025i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.90073e7 | − | 3.37206e9i | −0.00659659 | − | 0.249913i | ||||
\(785\) | −8.08398e8 | −0.0596460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.29872e8 | − | 7.44560e8i | 0.0314360 | − | 0.0544488i | −0.849879 | − | 0.526977i | \(-0.823325\pi\) |
0.881315 | + | 0.472528i | \(0.156659\pi\) | |||||||
\(788\) | −1.57311e9 | + | 2.72471e9i | −0.114530 | + | 0.198371i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.37489e8 | −0.0171375 | ||||||||
\(791\) | 7.77888e9 | + | 1.97472e9i | 0.558855 | + | 0.141869i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.09651e8 | − | 8.82741e8i | −0.0362925 | − | 0.0628604i | ||||
\(794\) | 4.68449e9 | − | 8.11378e9i | 0.332117 | − | 0.575243i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.34704e9 | + | 9.26135e9i | 0.375766 | + | 0.650846i | ||||
\(797\) | −4.31200e9 | −0.301699 | −0.150850 | − | 0.988557i | \(-0.548201\pi\) | ||||
−0.150850 | + | 0.988557i | \(0.548201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.17308e10 | −0.813603 | ||||||||
\(800\) | −1.27747e9 | − | 2.21264e9i | −0.0882134 | − | 0.152790i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.99855e9 | − | 1.03898e10i | 0.410616 | − | 0.711208i | ||||
\(803\) | 4.78236e9 | + | 8.28329e9i | 0.325940 | + | 0.564545i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.75712e8 | + | 3.85760e8i | −0.0253846 | + | 0.0260634i | ||||
\(806\) | −6.35120e9 | −0.427251 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.98293e9 | − | 5.16658e9i | 0.198931 | − | 0.344559i | ||||
\(809\) | −9.94355e9 | + | 1.72227e10i | −0.660270 | + | 1.14362i | 0.320275 | + | 0.947325i | \(0.396225\pi\) |
−0.980545 | + | 0.196296i | \(0.937108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.58957e10 | −1.70473 | −0.852363 | − | 0.522950i | \(-0.824831\pi\) | ||||
−0.852363 | + | 0.522950i | \(0.824831\pi\) | |||||||
\(812\) | 2.73325e9 | − | 2.80635e9i | 0.179157 | − | 0.183948i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.63843e10 | + | 2.83784e10i | 1.06474 | + | 1.84418i | ||||
\(815\) | 2.17193e8 | − | 3.76190e8i | 0.0140538 | − | 0.0243420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.16772e9 | + | 5.48665e9i | 0.203221 | + | 0.351990i | ||||
\(818\) | 5.99683e8 | 0.0383076 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.43697e8 | −0.0407693 | ||||||||
\(821\) | 1.06287e9 | + | 1.84094e9i | 0.0670314 | + | 0.116102i | 0.897593 | − | 0.440825i | \(-0.145314\pi\) |
−0.830562 | + | 0.556926i | \(0.811981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.58631e9 | − | 1.31399e10i | 0.474385 | − | 0.821660i | −0.525184 | − | 0.850988i | \(-0.676004\pi\) |
0.999570 | + | 0.0293289i | \(0.00933701\pi\) | |||||||
\(824\) | 1.83298e9 | + | 3.17481e9i | 0.114133 | + | 0.197684i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.44014e10 | − | 3.65588e9i | −0.889148 | − | 0.225716i | ||||
\(827\) | −1.94463e10 | −1.19555 | −0.597776 | − | 0.801663i | \(-0.703949\pi\) | ||||
−0.597776 | + | 0.801663i | \(0.703949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.84579e9 | − | 3.19701e9i | 0.112523 | − | 0.194896i | −0.804264 | − | 0.594273i | \(-0.797440\pi\) |
0.916787 | + | 0.399376i | \(0.130773\pi\) | |||||||
\(830\) | −3.74743e8 | + | 6.49073e8i | −0.0227489 | + | 0.0394022i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.89582e9 | 0.114121 | ||||||||
\(833\) | 1.07637e10 | − | 6.59911e9i | 0.645215 | − | 0.395574i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.53040e8 | − | 9.57894e8i | −0.0328741 | − | 0.0569396i | ||||
\(836\) | −4.06930e9 | + | 7.04823e9i | −0.240878 | + | 0.417214i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.38815e8 | + | 5.86844e8i | 0.0198888 | + | 0.0344484i | ||||
\(839\) | 9.94899e9 | 0.581584 | 0.290792 | − | 0.956786i | \(-0.406081\pi\) | ||||
0.290792 | + | 0.956786i | \(0.406081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.27005e10 | −0.736264 | ||||||||
\(842\) | −2.41261e9 | − | 4.17876e9i | −0.139282 | − | 0.241243i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.25955e9 | + | 3.91365e9i | −0.129367 | + | 0.224070i | ||||
\(845\) | −6.49507e7 | − | 1.12498e8i | −0.00370327 | − | 0.00641425i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.33634e9 | + | 2.24580e10i | 0.358300 | + | 1.26993i | ||||
\(848\) | −5.09837e9 | −0.287108 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.78140e9 | − | 8.28163e9i | 0.267048 | − | 0.462541i | ||||
\(851\) | −1.45369e10 | + | 2.51786e10i | −0.808569 | + | 1.40048i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.15287e9 | 0.173934 | 0.0869669 | − | 0.996211i | \(-0.472283\pi\) | ||||
0.0869669 | + | 0.996211i | \(0.472283\pi\) | |||||||
\(854\) | −7.13931e8 | + | 7.33024e8i | −0.0392242 | + | 0.0402732i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.49370e9 | + | 2.58716e9i | 0.0813963 | + | 0.140983i | ||||
\(857\) | 8.54798e7 | − | 1.48055e8i | 0.00463907 | − | 0.00803510i | −0.863697 | − | 0.504012i | \(-0.831857\pi\) |
0.868336 | + | 0.495977i | \(0.165190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.17292e9 | + | 1.58880e10i | 0.493778 | + | 0.855248i | 0.999974 | − | 0.00717006i | \(-0.00228232\pi\) |
−0.506197 | + | 0.862418i | \(0.668949\pi\) | |||||||
\(860\) | 2.66555e8 | 0.0142904 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.08522e10 | 1.10886 | ||||||||
\(863\) | 1.05965e10 | + | 1.83536e10i | 0.561208 | + | 0.972040i | 0.997391 | + | 0.0721827i | \(0.0229965\pi\) |
−0.436184 | + | 0.899858i | \(0.643670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.91266e8 | − | 3.31283e8i | 0.0100481 | − | 0.0174037i | ||||
\(866\) | 1.23870e10 | + | 2.14550e10i | 0.648119 | + | 1.12258i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.73128e9 | + | 6.13619e9i | 0.0898562 | + | 0.318478i | ||||
\(869\) | −1.60508e10 | −0.829711 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06066e10 | + | 1.83712e10i | −0.543893 | + | 0.942049i | ||||
\(872\) | −2.38843e9 | + | 4.13688e9i | −0.121985 | + | 0.211283i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.22092e9 | −0.365850 | ||||||||
\(875\) | −1.70726e9 | − | 4.33400e8i | −0.0861534 | − | 0.0218706i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.29471e10 | − | 2.24251e10i | −0.648148 | − | 1.12263i | −0.983565 | − | 0.180556i | \(-0.942210\pi\) |
0.335417 | − | 0.942070i | \(-0.391123\pi\) | |||||||
\(878\) | −2.41839e9 | + | 4.18878e9i | −0.120586 | + | 0.208861i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.71211e8 | + | 2.96545e8i | 0.00846918 | + | 0.0146690i | ||||
\(881\) | −2.45497e10 | −1.20957 | −0.604785 | − | 0.796389i | \(-0.706741\pi\) | ||||
−0.604785 | + | 0.796389i | \(0.706741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.01403e10 | 0.984473 | 0.492237 | − | 0.870461i | \(-0.336179\pi\) | ||||
0.492237 | + | 0.870461i | \(0.336179\pi\) | |||||||
\(884\) | 3.54792e9 | + | 6.14517e9i | 0.172739 | + | 0.299193i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.66617e9 | + | 1.50102e10i | −0.418609 | + | 0.725053i | ||||
\(887\) | 7.24531e8 | + | 1.25492e9i | 0.0348597 | + | 0.0603788i | 0.882929 | − | 0.469507i | \(-0.155568\pi\) |
−0.848069 | + | 0.529886i | \(0.822235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.95816e10 | + | 4.97092e9i | 0.934744 | + | 0.237291i | ||||
\(890\) | 5.32709e8 | 0.0253294 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.99650e9 | − | 1.38503e10i | 0.377244 | − | 0.653407i | ||||
\(893\) | −7.23650e9 | + | 1.25340e10i | −0.340054 | + | 0.588992i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.28165e9 | 0.0597569 | ||||||||
\(896\) | −5.16784e8 | − | 1.83164e9i | −0.0240011 | − | 0.0850673i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.05218e9 | + | 7.01858e9i | 0.186733 | + | 0.323431i | ||||
\(899\) | −3.70217e9 | + | 6.41234e9i | −0.169941 | + | 0.294346i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.54129e9 | − | 1.65260e10i | −0.434580 | − | 0.752715i | ||||
\(902\) | −4.35046e10 | −1.97384 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.52798e9 | 0.203852 | ||||||||
\(905\) | −3.89003e8 | − | 6.73773e8i | −0.0174455 | − | 0.0302164i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.54863e9 | − | 2.68231e9i | 0.0689165 | − | 0.119367i | −0.829508 | − | 0.558495i | \(-0.811379\pi\) |
0.898425 | + | 0.439128i | \(0.144712\pi\) | |||||||
\(908\) | 1.03895e10 | + | 1.79951e10i | 0.460567 | + | 0.797725i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.55510e8 | − | 4.67692e8i | 0.0200379 | − | 0.0205738i | ||||
\(911\) | −2.29298e10 | −1.00481 | −0.502406 | − | 0.864632i | \(-0.667552\pi\) | ||||
−0.502406 | + | 0.864632i | \(0.667552\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.53271e10 | + | 4.38679e10i | −1.10138 | + | 1.90765i | ||||
\(914\) | 6.43362e9 | − | 1.11434e10i | 0.278705 | − | 0.482730i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.34710e9 | −0.0579115 | ||||||||
\(917\) | −2.68643e9 | − | 9.52154e9i | −0.115049 | − | 0.407769i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.23880e10 | − | 3.87772e10i | −0.951506 | − | 1.64806i | −0.742168 | − | 0.670213i | \(-0.766203\pi\) |
−0.209338 | − | 0.977843i | \(-0.567131\pi\) | |||||||
\(920\) | −1.51906e8 | + | 2.63108e8i | −0.00643156 | + | 0.0111398i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.19342e10 | + | 2.06706e10i | 0.501458 | + | 0.868551i | ||||
\(923\) | 4.45003e9 | 0.186276 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.75034e10 | −1.97346 | ||||||||
\(926\) | −1.13361e10 | − | 1.96347e10i | −0.469164 | − | 0.812616i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.10509e9 | − | 1.91407e9i | 0.0453921 | − | 0.0786214i | ||||
\(929\) | 1.49225e10 | + | 2.58466e10i | 0.610644 | + | 1.05767i | 0.991132 | + | 0.132880i | \(0.0424226\pi\) |
−0.380488 | + | 0.924786i | \(0.624244\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.11020e8 | − | 1.55716e10i | −0.0166932 | − | 0.632425i | ||||
\(932\) | 1.04630e10 | 0.423352 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.72733e10 | − | 2.99182e10i | 0.693682 | − | 1.20149i | ||||
\(935\) | −6.40821e8 | + | 1.10993e9i | −0.0256387 | + | 0.0444075i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.43090e10 | 0.568227 | 0.284113 | − | 0.958791i | \(-0.408301\pi\) | ||||
0.284113 | + | 0.958791i | \(0.408301\pi\) | |||||||
\(938\) | 2.06405e10 | + | 5.23972e9i | 0.816603 | + | 0.207300i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.04466e8 | + | 5.27351e8i | 0.0119562 | + | 0.0207087i | ||||
\(941\) | −3.30316e9 | + | 5.72124e9i | −0.129231 | + | 0.223834i | −0.923379 | − | 0.383890i | \(-0.874584\pi\) |
0.794148 | + | 0.607724i | \(0.207917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.92996e10 | − | 3.34279e10i | −0.749475 | − | 1.29813i | ||||
\(944\) | −8.38286e9 | −0.324332 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.80153e10 | 0.691866 | ||||||||
\(947\) | −9.94687e9 | − | 1.72285e10i | −0.380594 | − | 0.659208i | 0.610553 | − | 0.791975i | \(-0.290947\pi\) |
−0.991147 | + | 0.132767i | \(0.957614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.14432e9 | − | 8.91022e9i | 0.195387 | − | 0.338421i | ||||
\(950\) | −5.89912e9 | − | 1.02176e10i | −0.223231 | − | 0.386648i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.97001e9 | − | 5.10293e9i | 0.186693 | − | 0.191686i | ||||
\(953\) | −4.15702e10 | −1.55581 | −0.777905 | − | 0.628382i | \(-0.783717\pi\) | ||||
−0.777905 | + | 0.628382i | \(0.783717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.91788e8 | + | 8.51802e8i | −0.0182712 | + | 0.0316466i | ||||
\(956\) | −1.01817e10 | + | 1.76352e10i | −0.376892 | + | 0.652796i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.56258e9 | −0.241154 | ||||||||
\(959\) | 2.03411e10 | − | 2.08851e10i | 0.744750 | − | 0.764667i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.73091e9 | + | 1.33903e10i | 0.280995 | + | 0.486698i | ||||
\(962\) | 1.76244e10 | − | 3.05263e10i | 0.638264 | − | 1.10551i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.14630e9 | + | 7.18160e9i | 0.149070 | + | 0.258197i | ||||
\(965\) | 6.99931e8 | 0.0250732 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.38376e10 | −0.847755 | −0.423877 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423877 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(968\) | 6.58263e9 | + | 1.14014e10i | 0.233257 | + | 0.404014i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.86728e8 | − | 1.36265e9i | 0.0276773 | − | 0.0479385i | ||||
\(971\) | 2.49541e10 | + | 4.32218e10i | 0.874732 | + | 1.51508i | 0.857047 | + | 0.515237i | \(0.172296\pi\) |
0.0176850 | + | 0.999844i | \(0.494370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.66287e10 | + | 4.22130e9i | 0.578714 | + | 0.146910i | ||||
\(974\) | −3.46741e10 | −1.20240 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.88652e8 | + | 4.99960e8i | −0.00993803 | + | 0.0172132i | ||||
\(977\) | −1.06421e10 | + | 1.84327e10i | −0.365087 | + | 0.632350i | −0.988790 | − | 0.149312i | \(-0.952294\pi\) |
0.623703 | + | 0.781662i | \(0.285628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.60034e10 | 1.22632 | ||||||||
\(980\) | −5.76027e8 | − | 3.12601e8i | −0.0195502 | − | 0.0106096i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.18899e9 | + | 1.24517e10i | 0.242258 | + | 0.419603i | ||||
\(983\) | 2.02849e10 | − | 3.51344e10i | 0.681138 | − | 1.17977i | −0.293496 | − | 0.955960i | \(-0.594819\pi\) |
0.974634 | − | 0.223805i | \(-0.0718479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.05639e8 | + | 5.29382e8i | 0.0101902 | + | 0.0176499i | ||||
\(986\) | 8.27244e9 | 0.274830 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.75459e9 | 0.288793 | ||||||||
\(989\) | 7.99197e9 | + | 1.38425e10i | 0.262704 | + | 0.455017i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53510e10 | − | 2.65888e10i | 0.501048 | − | 0.867841i | −0.498951 | − | 0.866630i | \(-0.666281\pi\) |
0.999999 | − | 0.00121109i | \(-0.000385502\pi\) | |||||||
\(992\) | 1.79857e9 | + | 3.11522e9i | 0.0584975 | + | 0.101321i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.21304e9 | − | 4.29938e9i | −0.0391762 | − | 0.138853i | ||||
\(995\) | 2.07775e9 | 0.0668670 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.94876e10 | + | 3.37534e10i | −0.622765 | + | 1.07866i | 0.366203 | + | 0.930535i | \(0.380657\pi\) |
−0.988968 | + | 0.148126i | \(0.952676\pi\) | |||||||
\(998\) | 3.25652e9 | − | 5.64046e9i | 0.103704 | − | 0.179621i | ||||
\(999\) | 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 | 126.8.g.j.109.3 | yes | 6 | |
3.2 | odd | 2 | 126.8.g.i.109.1 | yes | 6 | ||
7.2 | even | 3 | inner | 126.8.g.j.37.3 | yes | 6 | |
21.2 | odd | 6 | 126.8.g.i.37.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.8.g.i.37.1 | ✓ | 6 | 21.2 | odd | 6 | ||
126.8.g.i.109.1 | yes | 6 | 3.2 | odd | 2 | ||
126.8.g.j.37.3 | yes | 6 | 7.2 | even | 3 | inner | |
126.8.g.j.109.3 | yes | 6 | 1.1 | even | 1 | trivial |