Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,17,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.73947263140\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 55116x^{4} + 758395257x^{2} + 123254139008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(158.486i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.17.b.a.5.6 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 181.019i | − | 0.707107i | ||||||
\(3\) | 6178.01 | + | 2208.83i | 0.941626 | + | 0.336661i | ||||
\(4\) | −32768.0 | −0.500000 | ||||||||
\(5\) | 548425.i | 1.40397i | 0.712193 | + | 0.701984i | \(0.247702\pi\) | ||||
−0.712193 | + | 0.701984i | \(0.752298\pi\) | |||||||
\(6\) | 399841. | − | 1.11834e6i | 0.238055 | − | 0.665830i | ||||
\(7\) | −8.81996e6 | −1.52997 | −0.764984 | − | 0.644049i | \(-0.777253\pi\) | ||||
−0.764984 | + | 0.644049i | \(0.777253\pi\) | |||||||
\(8\) | 5.93164e6i | 0.353553i | ||||||||
\(9\) | 3.32888e7 | + | 2.72924e7i | 0.773319 | + | 0.634017i | ||||
\(10\) | 9.92755e7 | 0.992755 | ||||||||
\(11\) | 2.97767e8i | 1.38910i | 0.719442 | + | 0.694552i | \(0.244397\pi\) | ||||
−0.719442 | + | 0.694552i | \(0.755603\pi\) | |||||||
\(12\) | −2.02441e8 | − | 7.23790e7i | −0.470813 | − | 0.168330i | ||||
\(13\) | 6.77774e8 | 0.830880 | 0.415440 | − | 0.909621i | \(-0.363628\pi\) | ||||
0.415440 | + | 0.909621i | \(0.363628\pi\) | |||||||
\(14\) | 1.59658e9i | 1.08185i | ||||||||
\(15\) | −1.21138e9 | + | 3.38817e9i | −0.472661 | + | 1.32201i | ||||
\(16\) | 1.07374e9 | 0.250000 | ||||||||
\(17\) | − | 3.75977e9i | − | 0.538976i | −0.963004 | − | 0.269488i | \(-0.913146\pi\) | ||
0.963004 | − | 0.269488i | \(-0.0868545\pi\) | |||||||
\(18\) | 4.94045e9 | − | 6.02592e9i | 0.448318 | − | 0.546819i | ||||
\(19\) | −9.70862e8 | −0.0571648 | −0.0285824 | − | 0.999591i | \(-0.509099\pi\) | ||||
−0.0285824 | + | 0.999591i | \(0.509099\pi\) | |||||||
\(20\) | − | 1.79708e10i | − | 0.701984i | ||||||
\(21\) | −5.44898e10 | − | 1.94818e10i | −1.44066 | − | 0.515080i | ||||
\(22\) | 5.39016e10 | 0.982245 | ||||||||
\(23\) | − | 2.68175e10i | − | 0.342449i | −0.985232 | − | 0.171224i | \(-0.945228\pi\) | ||
0.985232 | − | 0.171224i | \(-0.0547723\pi\) | |||||||
\(24\) | −1.31020e10 | + | 3.66457e10i | −0.119028 | + | 0.332915i | ||||
\(25\) | −1.48182e11 | −0.971126 | ||||||||
\(26\) | − | 1.22690e11i | − | 0.587521i | ||||||
\(27\) | 1.45374e11 | + | 2.42142e11i | 0.514728 | + | 0.857353i | ||||
\(28\) | 2.89012e11 | 0.764984 | ||||||||
\(29\) | 3.75954e11i | 0.751538i | 0.926713 | + | 0.375769i | \(0.122621\pi\) | ||||
−0.926713 | + | 0.375769i | \(0.877379\pi\) | |||||||
\(30\) | 6.13325e11 | + | 2.19283e11i | 0.934804 | + | 0.334222i | ||||
\(31\) | −4.78969e11 | −0.561583 | −0.280791 | − | 0.959769i | \(-0.590597\pi\) | ||||
−0.280791 | + | 0.959769i | \(0.590597\pi\) | |||||||
\(32\) | − | 1.94368e11i | − | 0.176777i | ||||||
\(33\) | −6.57717e11 | + | 1.83961e12i | −0.467657 | + | 1.30802i | ||||
\(34\) | −6.80590e11 | −0.381114 | ||||||||
\(35\) | − | 4.83709e12i | − | 2.14803i | ||||||
\(36\) | −1.09081e12 | − | 8.94316e11i | −0.386659 | − | 0.317009i | ||||
\(37\) | 9.79062e11 | 0.278738 | 0.139369 | − | 0.990241i | \(-0.455493\pi\) | ||||
0.139369 | + | 0.990241i | \(0.455493\pi\) | |||||||
\(38\) | 1.75745e11i | 0.0404216i | ||||||||
\(39\) | 4.18729e12 | + | 1.49709e12i | 0.782378 | + | 0.279725i | ||||
\(40\) | −3.25306e12 | −0.496378 | ||||||||
\(41\) | − | 1.07974e13i | − | 1.35222i | −0.736802 | − | 0.676109i | \(-0.763665\pi\) | ||
0.736802 | − | 0.676109i | \(-0.236335\pi\) | |||||||
\(42\) | −3.52658e12 | + | 9.86370e12i | −0.364217 | + | 1.01870i | ||||
\(43\) | 8.94265e12 | 0.765100 | 0.382550 | − | 0.923935i | \(-0.375046\pi\) | ||||
0.382550 | + | 0.923935i | \(0.375046\pi\) | |||||||
\(44\) | − | 9.75722e12i | − | 0.694552i | ||||||
\(45\) | −1.49678e13 | + | 1.82564e13i | −0.890140 | + | 1.08571i | ||||
\(46\) | −4.85449e12 | −0.242148 | ||||||||
\(47\) | 2.80443e13i | 1.17778i | 0.808215 | + | 0.588888i | \(0.200434\pi\) | ||||
−0.808215 | + | 0.588888i | \(0.799566\pi\) | |||||||
\(48\) | 6.63359e12 | + | 2.37172e12i | 0.235406 | + | 0.0841652i | ||||
\(49\) | 4.45588e13 | 1.34080 | ||||||||
\(50\) | 2.68238e13i | 0.686690i | ||||||||
\(51\) | 8.30469e12 | − | 2.32279e13i | 0.181452 | − | 0.507514i | ||||
\(52\) | −2.22093e13 | −0.415440 | ||||||||
\(53\) | − | 7.34316e13i | − | 1.17944i | −0.807608 | − | 0.589720i | \(-0.799238\pi\) | ||
0.807608 | − | 0.589720i | \(-0.200762\pi\) | |||||||
\(54\) | 4.38324e13 | − | 2.63156e13i | 0.606240 | − | 0.363968i | ||||
\(55\) | −1.63303e14 | −1.95026 | ||||||||
\(56\) | − | 5.23168e13i | − | 0.540925i | ||||||
\(57\) | −5.99799e12 | − | 2.14447e12i | −0.0538279 | − | 0.0192452i | ||||
\(58\) | 6.80550e13 | 0.531417 | ||||||||
\(59\) | 1.35037e14i | 0.919683i | 0.888001 | + | 0.459841i | \(0.152094\pi\) | ||||
−0.888001 | + | 0.459841i | \(0.847906\pi\) | |||||||
\(60\) | 3.96945e13 | − | 1.11024e14i | 0.236331 | − | 0.661006i | ||||
\(61\) | 4.44549e13 | 0.231890 | 0.115945 | − | 0.993256i | \(-0.463010\pi\) | ||||
0.115945 | + | 0.993256i | \(0.463010\pi\) | |||||||
\(62\) | 8.67026e13i | 0.397099i | ||||||||
\(63\) | −2.93606e14 | − | 2.40718e14i | −1.18315 | − | 0.970026i | ||||
\(64\) | −3.51844e13 | −0.125000 | ||||||||
\(65\) | 3.71708e14i | 1.16653i | ||||||||
\(66\) | 3.33004e14 | + | 1.19059e14i | 0.924907 | + | 0.330683i | ||||
\(67\) | 6.70954e14 | 1.65232 | 0.826160 | − | 0.563435i | \(-0.190521\pi\) | ||||
0.826160 | + | 0.563435i | \(0.190521\pi\) | |||||||
\(68\) | 1.23200e14i | 0.269488i | ||||||||
\(69\) | 5.92354e13 | − | 1.65679e14i | 0.115289 | − | 0.322459i | ||||
\(70\) | −8.75606e14 | −1.51888 | ||||||||
\(71\) | 6.75764e14i | 1.04647i | 0.852187 | + | 0.523237i | \(0.175276\pi\) | ||||
−0.852187 | + | 0.523237i | \(0.824724\pi\) | |||||||
\(72\) | −1.61889e14 | + | 1.97457e14i | −0.224159 | + | 0.273410i | ||||
\(73\) | 4.82017e14 | 0.597695 | 0.298847 | − | 0.954301i | \(-0.403398\pi\) | ||||
0.298847 | + | 0.954301i | \(0.403398\pi\) | |||||||
\(74\) | − | 1.77229e14i | − | 0.197098i | ||||||
\(75\) | −9.15470e14 | − | 3.27309e14i | −0.914438 | − | 0.326940i | ||||
\(76\) | 3.18132e13 | 0.0285824 | ||||||||
\(77\) | − | 2.62629e15i | − | 2.12528i | ||||||
\(78\) | 2.71002e14 | − | 7.57981e14i | 0.197795 | − | 0.553225i | ||||
\(79\) | 3.05638e14 | 0.201461 | 0.100731 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100731 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(80\) | 5.88867e14i | 0.350992i | ||||||||
\(81\) | 3.63274e14 | + | 1.81706e15i | 0.196044 | + | 0.980595i | ||||
\(82\) | −1.95453e15 | −0.956162 | ||||||||
\(83\) | − | 1.62564e15i | − | 0.721773i | −0.932610 | − | 0.360886i | \(-0.882474\pi\) | ||
0.932610 | − | 0.360886i | \(-0.117526\pi\) | |||||||
\(84\) | 1.78552e15 | + | 6.38380e14i | 0.720329 | + | 0.257540i | ||||
\(85\) | 2.06195e15 | 0.756705 | ||||||||
\(86\) | − | 1.61879e15i | − | 0.541008i | ||||||
\(87\) | −8.30419e14 | + | 2.32265e15i | −0.253013 | + | 0.707667i | ||||
\(88\) | −1.76625e15 | −0.491123 | ||||||||
\(89\) | 3.89903e15i | 0.990459i | 0.868762 | + | 0.495230i | \(0.164916\pi\) | ||||
−0.868762 | + | 0.495230i | \(0.835084\pi\) | |||||||
\(90\) | 3.30477e15 | + | 2.70946e15i | 0.767716 | + | 0.629424i | ||||
\(91\) | −5.97794e15 | −1.27122 | ||||||||
\(92\) | 8.78756e14i | 0.171224i | ||||||||
\(93\) | −2.95907e15 | − | 1.05796e15i | −0.528801 | − | 0.189063i | ||||
\(94\) | 5.07657e15 | 0.832813 | ||||||||
\(95\) | − | 5.32445e14i | − | 0.0802576i | ||||||
\(96\) | 4.29326e14 | − | 1.20081e15i | 0.0595138 | − | 0.166458i | ||||
\(97\) | 1.41665e16 | 1.80754 | 0.903769 | − | 0.428021i | \(-0.140789\pi\) | ||||
0.903769 | + | 0.428021i | \(0.140789\pi\) | |||||||
\(98\) | − | 8.06600e15i | − | 0.948090i | ||||||
\(99\) | −8.12676e15 | + | 9.91231e15i | −0.880716 | + | 1.07422i | ||||
\(100\) | 4.85563e15 | 0.485563 | ||||||||
\(101\) | − | 8.68808e15i | − | 0.802330i | −0.916006 | − | 0.401165i | \(-0.868605\pi\) | ||
0.916006 | − | 0.401165i | \(-0.131395\pi\) | |||||||
\(102\) | −4.20469e15 | − | 1.50331e15i | −0.358866 | − | 0.128306i | ||||
\(103\) | −2.33033e16 | −1.83959 | −0.919794 | − | 0.392402i | \(-0.871644\pi\) | ||||
−0.919794 | + | 0.392402i | \(0.871644\pi\) | |||||||
\(104\) | 4.02031e15i | 0.293760i | ||||||||
\(105\) | 1.06843e16 | − | 2.98836e16i | 0.723156 | − | 2.02264i | ||||
\(106\) | −1.32925e16 | −0.833990 | ||||||||
\(107\) | 6.31512e15i | 0.367546i | 0.982969 | + | 0.183773i | \(0.0588311\pi\) | ||||
−0.982969 | + | 0.183773i | \(0.941169\pi\) | |||||||
\(108\) | −4.76363e15 | − | 7.93451e15i | −0.257364 | − | 0.428677i | ||||
\(109\) | 2.25696e16 | 1.13269 | 0.566347 | − | 0.824167i | \(-0.308356\pi\) | ||||
0.566347 | + | 0.824167i | \(0.308356\pi\) | |||||||
\(110\) | 2.95610e16i | 1.37904i | ||||||||
\(111\) | 6.04865e15 | + | 2.16258e15i | 0.262467 | + | 0.0938402i | ||||
\(112\) | −9.47036e15 | −0.382492 | ||||||||
\(113\) | 2.00529e16i | 0.754311i | 0.926150 | + | 0.377155i | \(0.123098\pi\) | ||||
−0.926150 | + | 0.377155i | \(0.876902\pi\) | |||||||
\(114\) | −3.88191e14 | + | 1.08575e15i | −0.0136084 | + | 0.0380621i | ||||
\(115\) | 1.47074e16 | 0.480787 | ||||||||
\(116\) | − | 1.23193e16i | − | 0.375769i | ||||||
\(117\) | 2.25623e16 | + | 1.84981e16i | 0.642535 | + | 0.526792i | ||||
\(118\) | 2.44444e16 | 0.650314 | ||||||||
\(119\) | 3.31610e16i | 0.824616i | ||||||||
\(120\) | −2.00974e16 | − | 7.18546e15i | −0.467402 | − | 0.167111i | ||||
\(121\) | −4.27154e16 | −0.929611 | ||||||||
\(122\) | − | 8.04720e15i | − | 0.163971i | ||||||
\(123\) | 2.38495e16 | − | 6.67061e16i | 0.455239 | − | 1.27328i | ||||
\(124\) | 1.56949e16 | 0.280791 | ||||||||
\(125\) | 2.41626e15i | 0.0405381i | ||||||||
\(126\) | −4.35745e16 | + | 5.31484e16i | −0.685912 | + | 0.836616i | ||||
\(127\) | −1.00499e17 | −1.48501 | −0.742506 | − | 0.669839i | \(-0.766363\pi\) | ||||
−0.742506 | + | 0.669839i | \(0.766363\pi\) | |||||||
\(128\) | 6.36905e15i | 0.0883883i | ||||||||
\(129\) | 5.52477e16 | + | 1.97528e16i | 0.720438 | + | 0.257579i | ||||
\(130\) | 6.72864e16 | 0.824860 | ||||||||
\(131\) | − | 8.13030e16i | − | 0.937424i | −0.883351 | − | 0.468712i | \(-0.844718\pi\) | ||
0.883351 | − | 0.468712i | \(-0.155282\pi\) | |||||||
\(132\) | 2.15521e16 | − | 6.02802e16i | 0.233829 | − | 0.654008i | ||||
\(133\) | 8.56297e15 | 0.0874603 | ||||||||
\(134\) | − | 1.21456e17i | − | 1.16837i | ||||||
\(135\) | −1.32797e17 | + | 7.97270e16i | −1.20370 | + | 0.722662i | ||||
\(136\) | 2.23016e16 | 0.190557 | ||||||||
\(137\) | − | 1.68892e17i | − | 1.36096i | −0.732768 | − | 0.680478i | \(-0.761772\pi\) | ||
0.732768 | − | 0.680478i | \(-0.238228\pi\) | |||||||
\(138\) | −2.99911e16 | − | 1.07227e16i | −0.228013 | − | 0.0815217i | ||||
\(139\) | 1.17875e17 | 0.845867 | 0.422934 | − | 0.906161i | \(-0.361000\pi\) | ||||
0.422934 | + | 0.906161i | \(0.361000\pi\) | |||||||
\(140\) | 1.58502e17i | 1.07401i | ||||||||
\(141\) | −6.19452e16 | + | 1.73258e17i | −0.396511 | + | 1.10902i | ||||
\(142\) | 1.22326e17 | 0.739969 | ||||||||
\(143\) | 2.01819e17i | 1.15418i | ||||||||
\(144\) | 3.57436e16 | + | 2.93050e16i | 0.193330 | + | 0.158504i | ||||
\(145\) | −2.06183e17 | −1.05513 | ||||||||
\(146\) | − | 8.72544e16i | − | 0.422634i | ||||||
\(147\) | 2.75284e17 | + | 9.84228e16i | 1.26253 | + | 0.451395i | ||||
\(148\) | −3.20819e16 | −0.139369 | ||||||||
\(149\) | − | 3.69639e16i | − | 0.152156i | −0.997102 | − | 0.0760778i | \(-0.975760\pi\) | ||
0.997102 | − | 0.0760778i | \(-0.0242397\pi\) | |||||||
\(150\) | −5.92493e16 | + | 1.65718e17i | −0.231182 | + | 0.646605i | ||||
\(151\) | −2.48497e16 | −0.0919403 | −0.0459702 | − | 0.998943i | \(-0.514638\pi\) | ||||
−0.0459702 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(152\) | − | 5.75881e15i | − | 0.0202108i | ||||||
\(153\) | 1.02613e17 | − | 1.25158e17i | 0.341720 | − | 0.416800i | ||||
\(154\) | −4.75410e17 | −1.50280 | ||||||||
\(155\) | − | 2.62678e17i | − | 0.788444i | ||||||
\(156\) | −1.37209e17 | − | 4.90566e16i | −0.391189 | − | 0.139862i | ||||
\(157\) | 4.63885e17 | 1.25665 | 0.628324 | − | 0.777952i | \(-0.283741\pi\) | ||||
0.628324 | + | 0.777952i | \(0.283741\pi\) | |||||||
\(158\) | − | 5.53265e16i | − | 0.142454i | ||||||
\(159\) | 1.62198e17 | − | 4.53661e17i | 0.397071 | − | 1.11059i | ||||
\(160\) | 1.06596e17 | 0.248189 | ||||||||
\(161\) | 2.36529e17i | 0.523936i | ||||||||
\(162\) | 3.28923e17 | − | 6.57596e16i | 0.693385 | − | 0.138624i | ||||
\(163\) | 2.12872e16 | 0.0427187 | 0.0213593 | − | 0.999772i | \(-0.493201\pi\) | ||||
0.0213593 | + | 0.999772i | \(0.493201\pi\) | |||||||
\(164\) | 3.53808e17i | 0.676109i | ||||||||
\(165\) | −1.00889e18 | − | 3.60708e17i | −1.83641 | − | 0.656576i | ||||
\(166\) | −2.94273e17 | −0.510370 | ||||||||
\(167\) | 5.29792e16i | 0.0875737i | 0.999041 | + | 0.0437868i | \(0.0139422\pi\) | ||||
−0.999041 | + | 0.0437868i | \(0.986058\pi\) | |||||||
\(168\) | 1.15559e17 | − | 3.23214e17i | 0.182108 | − | 0.509349i | ||||
\(169\) | −2.06039e17 | −0.309639 | ||||||||
\(170\) | − | 3.73253e17i | − | 0.535071i | ||||||
\(171\) | −3.23189e16 | − | 2.64971e16i | −0.0442066 | − | 0.0362435i | ||||
\(172\) | −2.93033e17 | −0.382550 | ||||||||
\(173\) | 1.09697e18i | 1.36718i | 0.729867 | + | 0.683590i | \(0.239582\pi\) | ||||
−0.729867 | + | 0.683590i | \(0.760418\pi\) | |||||||
\(174\) | 4.20444e17 | + | 1.50322e17i | 0.500396 | + | 0.178907i | ||||
\(175\) | 1.30696e18 | 1.48579 | ||||||||
\(176\) | 3.19725e17i | 0.347276i | ||||||||
\(177\) | −2.98275e17 | + | 8.34262e17i | −0.309621 | + | 0.865997i | ||||
\(178\) | 7.05800e17 | 0.700360 | ||||||||
\(179\) | − | 3.50481e17i | − | 0.332537i | −0.986081 | − | 0.166269i | \(-0.946828\pi\) | ||
0.986081 | − | 0.166269i | \(-0.0531719\pi\) | |||||||
\(180\) | 4.90465e17 | − | 5.98227e17i | 0.445070 | − | 0.542857i | ||||
\(181\) | −1.16227e18 | −1.00897 | −0.504487 | − | 0.863419i | \(-0.668318\pi\) | ||||
−0.504487 | + | 0.863419i | \(0.668318\pi\) | |||||||
\(182\) | 1.08212e18i | 0.898888i | ||||||||
\(183\) | 2.74643e17 | + | 9.81935e16i | 0.218353 | + | 0.0780682i | ||||
\(184\) | 1.59072e17 | 0.121074 | ||||||||
\(185\) | 5.36942e17i | 0.391339i | ||||||||
\(186\) | −1.91512e17 | + | 5.35649e17i | −0.133688 | + | 0.373919i | ||||
\(187\) | 1.11953e18 | 0.748694 | ||||||||
\(188\) | − | 9.18957e17i | − | 0.588888i | ||||||
\(189\) | −1.28220e18 | − | 2.13568e18i | −0.787518 | − | 1.31172i | ||||
\(190\) | −9.63829e16 | −0.0567507 | ||||||||
\(191\) | − | 5.02220e17i | − | 0.283548i | −0.989899 | − | 0.141774i | \(-0.954719\pi\) | ||
0.989899 | − | 0.141774i | \(-0.0452807\pi\) | |||||||
\(192\) | −2.17369e17 | − | 7.77164e16i | −0.117703 | − | 0.0420826i | ||||
\(193\) | −1.79109e18 | −0.930379 | −0.465190 | − | 0.885211i | \(-0.654014\pi\) | ||||
−0.465190 | + | 0.885211i | \(0.654014\pi\) | |||||||
\(194\) | − | 2.56440e18i | − | 1.27812i | ||||||
\(195\) | −8.21041e17 | + | 2.29642e18i | −0.392725 | + | 1.09843i | ||||
\(196\) | −1.46010e18 | −0.670401 | ||||||||
\(197\) | − | 2.08085e18i | − | 0.917297i | −0.888618 | − | 0.458649i | \(-0.848334\pi\) | ||
0.888618 | − | 0.458649i | \(-0.151666\pi\) | |||||||
\(198\) | 1.79432e18 | + | 1.47110e18i | 0.759589 | + | 0.622760i | ||||
\(199\) | −1.32205e18 | −0.537554 | −0.268777 | − | 0.963202i | \(-0.586619\pi\) | ||||
−0.268777 | + | 0.963202i | \(0.586619\pi\) | |||||||
\(200\) | − | 8.78963e17i | − | 0.343345i | ||||||
\(201\) | 4.14516e18 | + | 1.48202e18i | 1.55587 | + | 0.556272i | ||||
\(202\) | −1.57271e18 | −0.567333 | ||||||||
\(203\) | − | 3.31590e18i | − | 1.14983i | ||||||
\(204\) | −2.72128e17 | + | 7.61131e17i | −0.0907261 | + | 0.253757i | ||||
\(205\) | 5.92154e18 | 1.89847 | ||||||||
\(206\) | 4.21836e18i | 1.30079i | ||||||||
\(207\) | 7.31913e17 | − | 8.92724e17i | 0.217119 | − | 0.264822i | ||||
\(208\) | 7.27754e17 | 0.207720 | ||||||||
\(209\) | − | 2.89091e17i | − | 0.0794079i | ||||||
\(210\) | −5.40950e18 | − | 1.93407e18i | −1.43022 | − | 0.511349i | ||||
\(211\) | −3.76539e18 | −0.958409 | −0.479204 | − | 0.877703i | \(-0.659075\pi\) | ||||
−0.479204 | + | 0.877703i | \(0.659075\pi\) | |||||||
\(212\) | 2.40621e18i | 0.589720i | ||||||||
\(213\) | −1.49265e18 | + | 4.17488e18i | −0.352307 | + | 0.985387i | ||||
\(214\) | 1.14316e18 | 0.259894 | ||||||||
\(215\) | 4.90437e18i | 1.07418i | ||||||||
\(216\) | −1.43630e18 | + | 8.62309e17i | −0.303120 | + | 0.181984i | ||||
\(217\) | 4.22449e18 | 0.859203 | ||||||||
\(218\) | − | 4.08554e18i | − | 0.800935i | ||||||
\(219\) | 2.97791e18 | + | 1.06469e18i | 0.562805 | + | 0.201220i | ||||
\(220\) | 5.35111e18 | 0.975129 | ||||||||
\(221\) | − | 2.54827e18i | − | 0.447824i | ||||||
\(222\) | 3.91469e17 | − | 1.09492e18i | 0.0663550 | − | 0.185592i | ||||
\(223\) | −7.62525e18 | −1.24685 | −0.623426 | − | 0.781882i | \(-0.714260\pi\) | ||||
−0.623426 | + | 0.781882i | \(0.714260\pi\) | |||||||
\(224\) | 1.71432e18i | 0.270463i | ||||||||
\(225\) | −4.93281e18 | − | 4.04424e18i | −0.750990 | − | 0.615711i | ||||
\(226\) | 3.62997e18 | 0.533378 | ||||||||
\(227\) | 1.03157e19i | 1.46316i | 0.681755 | + | 0.731580i | \(0.261217\pi\) | ||||
−0.681755 | + | 0.731580i | \(0.738783\pi\) | |||||||
\(228\) | 1.96542e17 | + | 7.02700e16i | 0.0269139 | + | 0.00962258i | ||||
\(229\) | −1.17626e18 | −0.155532 | −0.0777659 | − | 0.996972i | \(-0.524779\pi\) | ||||
−0.0777659 | + | 0.996972i | \(0.524779\pi\) | |||||||
\(230\) | − | 2.66232e18i | − | 0.339968i | ||||||
\(231\) | 5.80104e18 | − | 1.62252e19i | 0.715500 | − | 2.00122i | ||||
\(232\) | −2.23002e18 | −0.265709 | ||||||||
\(233\) | − | 1.08482e19i | − | 1.24885i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) | ||
0.781086 | − | 0.624423i | \(-0.214666\pi\) | |||||||
\(234\) | 3.34851e18 | − | 4.08422e18i | 0.372498 | − | 0.454341i | ||||
\(235\) | −1.53802e19 | −1.65356 | ||||||||
\(236\) | − | 4.42491e18i | − | 0.459841i | ||||||
\(237\) | 1.88824e18 | + | 6.75104e17i | 0.189701 | + | 0.0678241i | ||||
\(238\) | 6.00278e18 | 0.583091 | ||||||||
\(239\) | 5.84823e18i | 0.549340i | 0.961539 | + | 0.274670i | \(0.0885687\pi\) | ||||
−0.961539 | + | 0.274670i | \(0.911431\pi\) | |||||||
\(240\) | −1.30071e18 | + | 3.63802e18i | −0.118165 | + | 0.330503i | ||||
\(241\) | 6.67037e18 | 0.586157 | 0.293078 | − | 0.956088i | \(-0.405320\pi\) | ||||
0.293078 | + | 0.956088i | \(0.405320\pi\) | |||||||
\(242\) | 7.73231e18i | 0.657334i | ||||||||
\(243\) | −1.76928e18 | + | 1.20282e19i | −0.145528 | + | 0.989354i | ||||
\(244\) | −1.45670e18 | −0.115945 | ||||||||
\(245\) | 2.44371e19i | 1.88244i | ||||||||
\(246\) | −1.20751e19 | − | 4.31723e18i | −0.900347 | − | 0.321902i | ||||
\(247\) | −6.58025e17 | −0.0474971 | ||||||||
\(248\) | − | 2.84107e18i | − | 0.198549i | ||||||
\(249\) | 3.59077e18 | − | 1.00432e19i | 0.242993 | − | 0.679640i | ||||
\(250\) | 4.37389e17 | 0.0286647 | ||||||||
\(251\) | − | 1.76579e19i | − | 1.12085i | −0.828205 | − | 0.560426i | \(-0.810637\pi\) | ||
0.828205 | − | 0.560426i | \(-0.189363\pi\) | |||||||
\(252\) | 9.62089e18 | + | 7.88783e18i | 0.591576 | + | 0.485013i | ||||
\(253\) | 7.98537e18 | 0.475697 | ||||||||
\(254\) | 1.81922e19i | 1.05006i | ||||||||
\(255\) | 1.27387e19 | + | 4.55450e18i | 0.712533 | + | 0.254753i | ||||
\(256\) | 1.15292e18 | 0.0625000 | ||||||||
\(257\) | 3.98050e18i | 0.209157i | 0.994517 | + | 0.104579i | \(0.0333494\pi\) | ||||
−0.994517 | + | 0.104579i | \(0.966651\pi\) | |||||||
\(258\) | 3.57564e18 | − | 1.00009e19i | 0.182136 | − | 0.509427i | ||||
\(259\) | −8.63528e18 | −0.426460 | ||||||||
\(260\) | − | 1.21801e19i | − | 0.583264i | ||||||
\(261\) | −1.02607e19 | + | 1.25151e19i | −0.476488 | + | 0.581178i | ||||
\(262\) | −1.47174e19 | −0.662859 | ||||||||
\(263\) | − | 1.01302e19i | − | 0.442559i | −0.975210 | − | 0.221279i | \(-0.928977\pi\) | ||
0.975210 | − | 0.221279i | \(-0.0710233\pi\) | |||||||
\(264\) | −1.09119e19 | − | 3.90134e18i | −0.462454 | − | 0.165342i | ||||
\(265\) | 4.02717e19 | 1.65590 | ||||||||
\(266\) | − | 1.55006e18i | − | 0.0618438i | ||||||
\(267\) | −8.61230e18 | + | 2.40882e19i | −0.333449 | + | 0.932642i | ||||
\(268\) | −2.19858e19 | −0.826160 | ||||||||
\(269\) | − | 4.60904e19i | − | 1.68109i | −0.541739 | − | 0.840547i | \(-0.682234\pi\) | ||
0.541739 | − | 0.840547i | \(-0.317766\pi\) | |||||||
\(270\) | 1.44321e19 | + | 2.40388e19i | 0.510999 | + | 0.851142i | ||||
\(271\) | 2.83745e19 | 0.975382 | 0.487691 | − | 0.873016i | \(-0.337839\pi\) | ||||
0.487691 | + | 0.873016i | \(0.337839\pi\) | |||||||
\(272\) | − | 4.03702e18i | − | 0.134744i | ||||||
\(273\) | −3.69318e19 | − | 1.32043e19i | −1.19701 | − | 0.427970i | ||||
\(274\) | −3.05727e19 | −0.962341 | ||||||||
\(275\) | − | 4.41237e19i | − | 1.34900i | ||||||
\(276\) | −1.94102e18 | + | 5.42896e18i | −0.0576446 | + | 0.161229i | ||||
\(277\) | −2.50576e19 | −0.722939 | −0.361470 | − | 0.932384i | \(-0.617725\pi\) | ||||
−0.361470 | + | 0.932384i | \(0.617725\pi\) | |||||||
\(278\) | − | 2.13376e19i | − | 0.598118i | ||||||
\(279\) | −1.59443e19 | − | 1.30722e19i | −0.434282 | − | 0.356053i | ||||
\(280\) | 2.86919e19 | 0.759442 | ||||||||
\(281\) | 3.81217e19i | 0.980668i | 0.871535 | + | 0.490334i | \(0.163125\pi\) | ||||
−0.871535 | + | 0.490334i | \(0.836875\pi\) | |||||||
\(282\) | 3.13631e19 | + | 1.12133e19i | 0.784198 | + | 0.280376i | ||||
\(283\) | −1.65340e19 | −0.401870 | −0.200935 | − | 0.979605i | \(-0.564398\pi\) | ||||
−0.200935 | + | 0.979605i | \(0.564398\pi\) | |||||||
\(284\) | − | 2.21434e19i | − | 0.523237i | ||||||
\(285\) | 1.17608e18 | − | 3.28945e18i | 0.0270196 | − | 0.0755726i | ||||
\(286\) | 3.65331e19 | 0.816128 | ||||||||
\(287\) | 9.52322e19i | 2.06885i | ||||||||
\(288\) | 5.30476e18 | − | 6.47029e18i | 0.112079 | − | 0.136705i | ||||
\(289\) | 3.45254e19 | 0.709505 | ||||||||
\(290\) | 3.73230e19i | 0.746093i | ||||||||
\(291\) | 8.75205e19 | + | 3.12913e19i | 1.70202 | + | 0.608527i | ||||
\(292\) | −1.57947e19 | −0.298847 | ||||||||
\(293\) | − | 7.32082e18i | − | 0.134778i | −0.997727 | − | 0.0673889i | \(-0.978533\pi\) | ||
0.997727 | − | 0.0673889i | \(-0.0214668\pi\) | |||||||
\(294\) | 1.78164e19 | − | 4.98318e19i | 0.319185 | − | 0.892746i | ||||
\(295\) | −7.40579e19 | −1.29120 | ||||||||
\(296\) | 5.80744e18i | 0.0985488i | ||||||||
\(297\) | −7.21018e19 | + | 4.32877e19i | −1.19095 | + | 0.715011i | ||||
\(298\) | −6.69119e18 | −0.107590 | ||||||||
\(299\) | − | 1.81762e19i | − | 0.284534i | ||||||
\(300\) | 2.99981e19 | + | 1.07253e19i | 0.457219 | + | 0.163470i | ||||
\(301\) | −7.88738e19 | −1.17058 | ||||||||
\(302\) | 4.49828e18i | 0.0650116i | ||||||||
\(303\) | 1.91905e19 | − | 5.36751e19i | 0.270113 | − | 0.755495i | ||||
\(304\) | −1.04246e18 | −0.0142912 | ||||||||
\(305\) | 2.43802e19i | 0.325566i | ||||||||
\(306\) | −2.26561e19 | − | 1.85749e19i | −0.294722 | − | 0.241633i | ||||
\(307\) | 1.46906e20 | 1.86179 | 0.930896 | − | 0.365284i | \(-0.119028\pi\) | ||||
0.930896 | + | 0.365284i | \(0.119028\pi\) | |||||||
\(308\) | 8.60583e19i | 1.06264i | ||||||||
\(309\) | −1.43968e20 | − | 5.14732e19i | −1.73220 | − | 0.619317i | ||||
\(310\) | −4.75499e19 | −0.557514 | ||||||||
\(311\) | − | 1.24018e20i | − | 1.41710i | −0.705659 | − | 0.708552i | \(-0.749349\pi\) | ||
0.705659 | − | 0.708552i | \(-0.250651\pi\) | |||||||
\(312\) | −8.88020e18 | + | 2.48375e19i | −0.0988976 | + | 0.276612i | ||||
\(313\) | 1.48074e20 | 1.60740 | 0.803700 | − | 0.595035i | \(-0.202862\pi\) | ||||
0.803700 | + | 0.595035i | \(0.202862\pi\) | |||||||
\(314\) | − | 8.39722e19i | − | 0.888584i | ||||||
\(315\) | 1.32016e20 | − | 1.61021e20i | 1.36189 | − | 1.66111i | ||||
\(316\) | −1.00152e19 | −0.100731 | ||||||||
\(317\) | 1.99460e20i | 1.95606i | 0.208460 | + | 0.978031i | \(0.433155\pi\) | ||||
−0.208460 | + | 0.978031i | \(0.566845\pi\) | |||||||
\(318\) | −8.21214e19 | − | 2.93610e19i | −0.785306 | − | 0.280772i | ||||
\(319\) | −1.11947e20 | −1.04396 | ||||||||
\(320\) | − | 1.92960e19i | − | 0.175496i | ||||||
\(321\) | −1.39490e19 | + | 3.90148e19i | −0.123738 | + | 0.346090i | ||||
\(322\) | 4.28164e19 | 0.370479 | ||||||||
\(323\) | 3.65021e18i | 0.0308105i | ||||||||
\(324\) | −1.19038e19 | − | 5.95415e19i | −0.0980221 | − | 0.490298i | ||||
\(325\) | −1.00434e20 | −0.806889 | ||||||||
\(326\) | − | 3.85340e18i | − | 0.0302067i | ||||||
\(327\) | 1.39435e20 | + | 4.98525e19i | 1.06657 | + | 0.381333i | ||||
\(328\) | 6.40460e19 | 0.478081 | ||||||||
\(329\) | − | 2.47350e20i | − | 1.80196i | ||||||
\(330\) | −6.52952e19 | + | 1.82628e20i | −0.464269 | + | 1.29854i | ||||
\(331\) | −1.27378e20 | −0.884036 | −0.442018 | − | 0.897006i | \(-0.645737\pi\) | ||||
−0.442018 | + | 0.897006i | \(0.645737\pi\) | |||||||
\(332\) | 5.32691e19i | 0.360886i | ||||||||
\(333\) | 3.25918e19 | + | 2.67209e19i | 0.215553 | + | 0.176725i | ||||
\(334\) | 9.59026e18 | 0.0619240 | ||||||||
\(335\) | 3.67968e20i | 2.31980i | ||||||||
\(336\) | −5.85080e19 | − | 2.09184e19i | −0.360164 | − | 0.128770i | ||||
\(337\) | 2.66631e20 | 1.60277 | 0.801386 | − | 0.598148i | \(-0.204096\pi\) | ||||
0.801386 | + | 0.598148i | \(0.204096\pi\) | |||||||
\(338\) | 3.72970e19i | 0.218948i | ||||||||
\(339\) | −4.42936e19 | + | 1.23887e20i | −0.253947 | + | 0.710279i | ||||
\(340\) | −6.75660e19 | −0.378353 | ||||||||
\(341\) | − | 1.42621e20i | − | 0.780097i | ||||||
\(342\) | −4.79649e18 | + | 5.85034e18i | −0.0256280 | + | 0.0312588i | ||||
\(343\) | −9.98933e19 | −0.521415 | ||||||||
\(344\) | 5.30446e19i | 0.270504i | ||||||||
\(345\) | 9.08624e19 | + | 3.24862e19i | 0.452722 | + | 0.161862i | ||||
\(346\) | 1.98573e20 | 0.966742 | ||||||||
\(347\) | − | 1.22916e20i | − | 0.584753i | −0.956303 | − | 0.292377i | \(-0.905554\pi\) | ||
0.956303 | − | 0.292377i | \(-0.0944461\pi\) | |||||||
\(348\) | 2.72112e19 | − | 7.61085e19i | 0.126507 | − | 0.353834i | ||||
\(349\) | −5.33630e19 | −0.242458 | −0.121229 | − | 0.992625i | \(-0.538684\pi\) | ||||
−0.121229 | + | 0.992625i | \(0.538684\pi\) | |||||||
\(350\) | − | 2.36585e20i | − | 1.05061i | ||||||
\(351\) | 9.85311e19 | + | 1.64118e20i | 0.427677 | + | 0.712358i | ||||
\(352\) | 5.78764e19 | 0.245561 | ||||||||
\(353\) | − | 2.08236e20i | − | 0.863689i | −0.901948 | − | 0.431844i | \(-0.857863\pi\) | ||
0.901948 | − | 0.431844i | \(-0.142137\pi\) | |||||||
\(354\) | 1.51018e20 | + | 5.39935e19i | 0.612352 | + | 0.218935i | ||||
\(355\) | −3.70606e20 | −1.46922 | ||||||||
\(356\) | − | 1.27763e20i | − | 0.495230i | ||||||
\(357\) | −7.32470e19 | + | 2.04869e20i | −0.277616 | + | 0.776480i | ||||
\(358\) | −6.34438e19 | −0.235139 | ||||||||
\(359\) | − | 5.45140e20i | − | 1.97584i | −0.154958 | − | 0.987921i | \(-0.549524\pi\) | ||
0.154958 | − | 0.987921i | \(-0.450476\pi\) | |||||||
\(360\) | −1.08291e20 | − | 8.87837e19i | −0.383858 | − | 0.314712i | ||||
\(361\) | −2.87499e20 | −0.996732 | ||||||||
\(362\) | 2.10394e20i | 0.713452i | ||||||||
\(363\) | −2.63896e20 | − | 9.43511e19i | −0.875346 | − | 0.312964i | ||||
\(364\) | 1.95885e20 | 0.635610 | ||||||||
\(365\) | 2.64350e20i | 0.839144i | ||||||||
\(366\) | 1.77749e19 | − | 4.97157e19i | 0.0552025 | − | 0.154399i | ||||
\(367\) | −4.49668e19 | −0.136635 | −0.0683177 | − | 0.997664i | \(-0.521763\pi\) | ||||
−0.0683177 | + | 0.997664i | \(0.521763\pi\) | |||||||
\(368\) | − | 2.87951e19i | − | 0.0856122i | ||||||
\(369\) | 2.94685e20 | − | 3.59431e20i | 0.857329 | − | 1.04570i | ||||
\(370\) | 9.71969e19 | 0.276719 | ||||||||
\(371\) | 6.47663e20i | 1.80450i | ||||||||
\(372\) | 9.69629e19 | + | 3.46673e19i | 0.264400 | + | 0.0945315i | ||||
\(373\) | 5.45992e20 | 1.45719 | 0.728593 | − | 0.684946i | \(-0.240174\pi\) | ||||
0.728593 | + | 0.684946i | \(0.240174\pi\) | |||||||
\(374\) | − | 2.02657e20i | − | 0.529406i | ||||||
\(375\) | −5.33711e18 | + | 1.49277e19i | −0.0136476 | + | 0.0381717i | ||||
\(376\) | −1.66349e20 | −0.416406 | ||||||||
\(377\) | 2.54812e20i | 0.624438i | ||||||||
\(378\) | −3.86600e20 | + | 2.32102e20i | −0.927528 | + | 0.556859i | ||||
\(379\) | −6.86587e19 | −0.161281 | −0.0806403 | − | 0.996743i | \(-0.525697\pi\) | ||||
−0.0806403 | + | 0.996743i | \(0.525697\pi\) | |||||||
\(380\) | 1.74472e19i | 0.0401288i | ||||||||
\(381\) | −6.20881e20 | − | 2.21984e20i | −1.39833 | − | 0.499946i | ||||
\(382\) | −9.09115e19 | −0.200499 | ||||||||
\(383\) | − | 4.63825e20i | − | 1.00176i | −0.865517 | − | 0.500880i | \(-0.833010\pi\) | ||
0.865517 | − | 0.500880i | \(-0.166990\pi\) | |||||||
\(384\) | −1.40682e19 | + | 3.93481e19i | −0.0297569 | + | 0.0832288i | ||||
\(385\) | 1.44032e21 | 2.98383 | ||||||||
\(386\) | 3.24223e20i | 0.657877i | ||||||||
\(387\) | 2.97690e20 | + | 2.44066e20i | 0.591667 | + | 0.485087i | ||||
\(388\) | −4.64206e20 | −0.903769 | ||||||||
\(389\) | 6.10357e20i | 1.16409i | 0.813156 | + | 0.582046i | \(0.197748\pi\) | ||||
−0.813156 | + | 0.582046i | \(0.802252\pi\) | |||||||
\(390\) | 4.15696e20 | + | 1.48624e20i | 0.776710 | + | 0.277698i | ||||
\(391\) | −1.00828e20 | −0.184572 | ||||||||
\(392\) | 2.64307e20i | 0.474045i | ||||||||
\(393\) | 1.79585e20 | − | 5.02290e20i | 0.315594 | − | 0.882703i | ||||
\(394\) | −3.76673e20 | −0.648627 | ||||||||
\(395\) | 1.67620e20i | 0.282845i | ||||||||
\(396\) | 2.66298e20 | − | 3.24807e20i | 0.440358 | − | 0.537110i | ||||
\(397\) | −6.66393e20 | −1.07996 | −0.539979 | − | 0.841679i | \(-0.681568\pi\) | ||||
−0.539979 | + | 0.841679i | \(0.681568\pi\) | |||||||
\(398\) | 2.39316e20i | 0.380108i | ||||||||
\(399\) | 5.29021e19 | + | 1.89142e19i | 0.0823549 | + | 0.0294445i | ||||
\(400\) | −1.59109e20 | −0.242782 | ||||||||
\(401\) | − | 3.54618e20i | − | 0.530403i | −0.964193 | − | 0.265201i | \(-0.914562\pi\) | ||
0.964193 | − | 0.265201i | \(-0.0854384\pi\) | |||||||
\(402\) | 2.68275e20 | − | 7.50354e20i | 0.393343 | − | 1.10016i | ||||
\(403\) | −3.24633e20 | −0.466608 | ||||||||
\(404\) | 2.84691e20i | 0.401165i | ||||||||
\(405\) | −9.96522e20 | + | 1.99229e20i | −1.37672 | + | 0.275240i | ||||
\(406\) | −6.00242e20 | −0.813052 | ||||||||
\(407\) | 2.91532e20i | 0.387196i | ||||||||
\(408\) | 1.37779e20 | + | 4.92605e19i | 0.179433 | + | 0.0641530i | ||||
\(409\) | −5.68936e19 | −0.0726569 | −0.0363284 | − | 0.999340i | \(-0.511566\pi\) | ||||
−0.0363284 | + | 0.999340i | \(0.511566\pi\) | |||||||
\(410\) | − | 1.07191e21i | − | 1.34242i | ||||||
\(411\) | 3.73054e20 | − | 1.04342e21i | 0.458181 | − | 1.28151i | ||||
\(412\) | 7.63604e20 | 0.919794 | ||||||||
\(413\) | − | 1.19102e21i | − | 1.40708i | ||||||
\(414\) | −1.61600e20 | − | 1.32490e20i | −0.187258 | − | 0.153526i | ||||
\(415\) | 8.91543e20 | 1.01335 | ||||||||
\(416\) | − | 1.31738e20i | − | 0.146880i | ||||||
\(417\) | 7.28231e20 | + | 2.60365e20i | 0.796491 | + | 0.284770i | ||||
\(418\) | −5.23310e19 | −0.0561499 | ||||||||
\(419\) | 1.43563e20i | 0.151123i | 0.997141 | + | 0.0755614i | \(0.0240749\pi\) | ||||
−0.997141 | + | 0.0755614i | \(0.975925\pi\) | |||||||
\(420\) | −3.50104e20 | + | 9.79224e20i | −0.361578 | + | 1.01132i | ||||
\(421\) | −6.44522e20 | −0.653102 | −0.326551 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326551 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(422\) | 6.81609e20i | 0.677697i | ||||||||
\(423\) | −7.65396e20 | + | 9.33564e20i | −0.746730 | + | 0.910796i | ||||
\(424\) | 4.35570e20 | 0.416995 | ||||||||
\(425\) | 5.57130e20i | 0.523414i | ||||||||
\(426\) | 7.55734e20 | + | 2.70199e20i | 0.696774 | + | 0.249119i | ||||
\(427\) | −3.92091e20 | −0.354784 | ||||||||
\(428\) | − | 2.06934e20i | − | 0.183773i | ||||||
\(429\) | −4.45784e20 | + | 1.24684e21i | −0.388567 | + | 1.08680i | ||||
\(430\) | 8.87786e20 | 0.759557 | ||||||||
\(431\) | − | 1.78139e20i | − | 0.149603i | −0.997198 | − | 0.0748017i | \(-0.976168\pi\) | ||
0.997198 | − | 0.0748017i | \(-0.0238324\pi\) | |||||||
\(432\) | 1.56095e20 | + | 2.59998e20i | 0.128682 | + | 0.214338i | ||||
\(433\) | 7.63467e20 | 0.617855 | 0.308928 | − | 0.951086i | \(-0.400030\pi\) | ||||
0.308928 | + | 0.951086i | \(0.400030\pi\) | |||||||
\(434\) | − | 7.64714e20i | − | 0.607549i | ||||||
\(435\) | −1.27380e21 | − | 4.55423e20i | −0.993542 | − | 0.355223i | ||||
\(436\) | −7.39561e20 | −0.566347 | ||||||||
\(437\) | 2.60361e19i | 0.0195760i | ||||||||
\(438\) | 1.92730e20 | − | 5.39058e20i | 0.142284 | − | 0.397963i | ||||
\(439\) | 3.77361e19 | 0.0273552 | 0.0136776 | − | 0.999906i | \(-0.495646\pi\) | ||||
0.0136776 | + | 0.999906i | \(0.495646\pi\) | |||||||
\(440\) | − | 9.68654e20i | − | 0.689520i | ||||||
\(441\) | 1.48331e21 | + | 1.21611e21i | 1.03687 | + | 0.850091i | ||||
\(442\) | −4.61287e20 | −0.316660 | ||||||||
\(443\) | 1.54395e21i | 1.04088i | 0.853897 | + | 0.520442i | \(0.174233\pi\) | ||||
−0.853897 | + | 0.520442i | \(0.825767\pi\) | |||||||
\(444\) | −1.98202e20 | − | 7.08635e19i | −0.131233 | − | 0.0469201i | ||||
\(445\) | −2.13833e21 | −1.39057 | ||||||||
\(446\) | 1.38032e21i | 0.881658i | ||||||||
\(447\) | 8.16471e19 | − | 2.28363e20i | 0.0512248 | − | 0.143274i | ||||
\(448\) | 3.10325e20 | 0.191246 | ||||||||
\(449\) | − | 1.33836e21i | − | 0.810219i | −0.914268 | − | 0.405109i | \(-0.867233\pi\) | ||
0.914268 | − | 0.405109i | \(-0.132767\pi\) | |||||||
\(450\) | −7.32086e20 | + | 8.92934e20i | −0.435373 | + | 0.531030i | ||||
\(451\) | 3.21509e21 | 1.87837 | ||||||||
\(452\) | − | 6.57095e20i | − | 0.377155i | ||||||
\(453\) | −1.53522e20 | − | 5.48889e19i | −0.0865734 | − | 0.0309527i | ||||
\(454\) | 1.86734e21 | 1.03461 | ||||||||
\(455\) | − | 3.27845e21i | − | 1.78475i | ||||||
\(456\) | 1.27202e19 | − | 3.55780e19i | 0.00680419 | − | 0.0190310i | ||||
\(457\) | −1.28524e21 | −0.675544 | −0.337772 | − | 0.941228i | \(-0.609673\pi\) | ||||
−0.337772 | + | 0.941228i | \(0.609673\pi\) | |||||||
\(458\) | 2.12926e20i | 0.109978i | ||||||||
\(459\) | 9.10397e20 | − | 5.46574e20i | 0.462093 | − | 0.277426i | ||||
\(460\) | −4.81932e20 | −0.240394 | ||||||||
\(461\) | − | 6.09388e20i | − | 0.298735i | −0.988782 | − | 0.149368i | \(-0.952276\pi\) | ||
0.988782 | − | 0.149368i | \(-0.0477238\pi\) | |||||||
\(462\) | −2.93708e21 | − | 1.05010e21i | −1.41508 | − | 0.505935i | ||||
\(463\) | 2.09033e21 | 0.989843 | 0.494922 | − | 0.868938i | \(-0.335197\pi\) | ||||
0.494922 | + | 0.868938i | \(0.335197\pi\) | |||||||
\(464\) | 4.03678e20i | 0.187884i | ||||||||
\(465\) | 5.80213e20 | − | 1.62283e21i | 0.265438 | − | 0.742419i | ||||
\(466\) | −1.96373e21 | −0.883068 | ||||||||
\(467\) | − | 1.09633e21i | − | 0.484626i | −0.970198 | − | 0.242313i | \(-0.922094\pi\) | ||
0.970198 | − | 0.242313i | \(-0.0779062\pi\) | |||||||
\(468\) | −7.39322e20 | − | 6.06144e20i | −0.321268 | − | 0.263396i | ||||
\(469\) | −5.91779e21 | −2.52800 | ||||||||
\(470\) | 2.78412e21i | 1.16924i | ||||||||
\(471\) | 2.86589e21 | + | 1.02464e21i | 1.18329 | + | 0.423064i | ||||
\(472\) | −8.00993e20 | −0.325157 | ||||||||
\(473\) | 2.66282e21i | 1.06280i | ||||||||
\(474\) | 1.22207e20 | − | 3.41807e20i | 0.0479589 | − | 0.134139i | ||||
\(475\) | 1.43864e20 | 0.0555142 | ||||||||
\(476\) | − | 1.08662e21i | − | 0.412308i | ||||||
\(477\) | 2.00412e21 | − | 2.44445e21i | 0.747785 | − | 0.912083i | ||||
\(478\) | 1.05864e21 | 0.388442 | ||||||||
\(479\) | 1.81172e21i | 0.653744i | 0.945069 | + | 0.326872i | \(0.105995\pi\) | ||||
−0.945069 | + | 0.326872i | \(0.894005\pi\) | |||||||
\(480\) | 6.58553e20 | + | 2.35453e20i | 0.233701 | + | 0.0835555i | ||||
\(481\) | 6.63583e20 | 0.231598 | ||||||||
\(482\) | − | 1.20747e21i | − | 0.414475i | ||||||
\(483\) | −5.22454e20 | + | 1.46128e21i | −0.176389 | + | 0.493352i | ||||
\(484\) | 1.39970e21 | 0.464805 | ||||||||
\(485\) | 7.76924e21i | 2.53772i | ||||||||
\(486\) | 2.17734e21 | + | 3.20273e20i | 0.699579 | + | 0.102904i | ||||
\(487\) | −6.83278e19 | −0.0215956 | −0.0107978 | − | 0.999942i | \(-0.503437\pi\) | ||||
−0.0107978 | + | 0.999942i | \(0.503437\pi\) | |||||||
\(488\) | 2.63691e20i | 0.0819854i | ||||||||
\(489\) | 1.31513e20 | + | 4.70199e19i | 0.0402250 | + | 0.0143817i | ||||
\(490\) | 4.42359e21 | 1.33109 | ||||||||
\(491\) | − | 1.74579e20i | − | 0.0516820i | −0.999666 | − | 0.0258410i | \(-0.991774\pi\) | ||
0.999666 | − | 0.0258410i | \(-0.00822636\pi\) | |||||||
\(492\) | −7.81502e20 | + | 2.18583e21i | −0.227619 | + | 0.636641i | ||||
\(493\) | 1.41350e21 | 0.405061 | ||||||||
\(494\) | 1.19115e20i | 0.0335855i | ||||||||
\(495\) | −5.43616e21 | − | 4.45692e21i | −1.50817 | − | 1.23650i | ||||
\(496\) | −5.14289e20 | −0.140396 | ||||||||
\(497\) | − | 5.96021e21i | − | 1.60107i | ||||||
\(498\) | −1.81802e21 | − | 6.49999e20i | −0.480578 | − | 0.171822i | ||||
\(499\) | −1.38375e21 | −0.359960 | −0.179980 | − | 0.983670i | \(-0.557603\pi\) | ||||
−0.179980 | + | 0.983670i | \(0.557603\pi\) | |||||||
\(500\) | − | 7.91759e19i | − | 0.0202690i | ||||||
\(501\) | −1.17022e20 | + | 3.27306e20i | −0.0294826 | + | 0.0824617i | ||||
\(502\) | −3.19641e21 | −0.792562 | ||||||||
\(503\) | 6.68741e21i | 1.63198i | 0.578068 | + | 0.815988i | \(0.303807\pi\) | ||||
−0.578068 | + | 0.815988i | \(0.696193\pi\) | |||||||
\(504\) | 1.42785e21 | − | 1.74157e21i | 0.342956 | − | 0.418308i | ||||
\(505\) | 4.76476e21 | 1.12645 | ||||||||
\(506\) | − | 1.44551e21i | − | 0.336369i | ||||||
\(507\) | −1.27291e21 | − | 4.55105e20i | −0.291564 | − | 0.104243i | ||||
\(508\) | 3.29314e21 | 0.742506 | ||||||||
\(509\) | 3.92709e21i | 0.871623i | 0.900038 | + | 0.435812i | \(0.143539\pi\) | ||||
−0.900038 | + | 0.435812i | \(0.856461\pi\) | |||||||
\(510\) | 8.24453e20 | − | 2.30596e21i | 0.180138 | − | 0.503837i | ||||
\(511\) | −4.25137e21 | −0.914454 | ||||||||
\(512\) | − | 2.08701e20i | − | 0.0441942i | ||||||
\(513\) | −1.41139e20 | − | 2.35086e20i | −0.0294244 | − | 0.0490104i | ||||
\(514\) | 7.20548e20 | 0.147897 | ||||||||
\(515\) | − | 1.27801e22i | − | 2.58272i | ||||||
\(516\) | −1.81036e21 | − | 6.47260e20i | −0.360219 | − | 0.128790i | ||||
\(517\) | −8.35068e21 | −1.63605 | ||||||||
\(518\) | 1.56315e21i | 0.301553i | ||||||||
\(519\) | −2.42302e21 | + | 6.77708e21i | −0.460276 | + | 1.28737i | ||||
\(520\) | −2.20484e21 | −0.412430 | ||||||||
\(521\) | − | 1.00353e22i | − | 1.84854i | −0.381743 | − | 0.924268i | \(-0.624676\pi\) | ||
0.381743 | − | 0.924268i | \(-0.375324\pi\) | |||||||
\(522\) | 2.26547e21 | + | 1.85738e21i | 0.410955 | + | 0.336928i | ||||
\(523\) | 6.06629e21 | 1.08370 | 0.541851 | − | 0.840475i | \(-0.317724\pi\) | ||||
0.541851 | + | 0.840475i | \(0.317724\pi\) | |||||||
\(524\) | 2.66414e21i | 0.468712i | ||||||||
\(525\) | 8.07441e21 | + | 2.88686e21i | 1.39906 | + | 0.500208i | ||||
\(526\) | −1.83376e21 | −0.312936 | ||||||||
\(527\) | 1.80081e21i | 0.302680i | ||||||||
\(528\) | −7.06218e20 | + | 1.97526e21i | −0.116914 | + | 0.327004i | ||||
\(529\) | 5.41343e21 | 0.882729 | ||||||||
\(530\) | − | 7.28996e21i | − | 1.17090i | ||||||
\(531\) | −3.68549e21 | + | 4.49524e21i | −0.583095 | + | 0.711208i | ||||
\(532\) | −2.80591e20 | −0.0437302 | ||||||||
\(533\) | − | 7.31817e21i | − | 1.12353i | ||||||
\(534\) | 4.36044e21 | + | 1.55899e21i | 0.659478 | + | 0.235784i | ||||
\(535\) | −3.46337e21 | −0.516022 | ||||||||
\(536\) | 3.97986e21i | 0.584183i | ||||||||
\(537\) | 7.74153e20 | − | 2.16527e21i | 0.111952 | − | 0.313126i | ||||
\(538\) | −8.34325e21 | −1.18871 | ||||||||
\(539\) | 1.32681e22i | 1.86251i | ||||||||
\(540\) | 4.35148e21 | − | 2.61249e21i | 0.601848 | − | 0.361331i | ||||
\(541\) | 1.03705e22 | 1.41325 | 0.706626 | − | 0.707587i | \(-0.250216\pi\) | ||||
0.706626 | + | 0.707587i | \(0.250216\pi\) | |||||||
\(542\) | − | 5.13634e21i | − | 0.689699i | ||||||
\(543\) | −7.18054e21 | − | 2.56727e21i | −0.950076 | − | 0.339682i | ||||
\(544\) | −7.30778e20 | −0.0952784 | ||||||||
\(545\) | 1.23777e22i | 1.59026i | ||||||||
\(546\) | −2.39023e21 | + | 6.68536e21i | −0.302620 | + | 0.846416i | ||||
\(547\) | 8.78290e21 | 1.09582 | 0.547910 | − | 0.836537i | \(-0.315424\pi\) | ||||
0.547910 | + | 0.836537i | \(0.315424\pi\) | |||||||
\(548\) | 5.53425e21i | 0.680478i | ||||||||
\(549\) | 1.47985e21 | + | 1.21328e21i | 0.179325 | + | 0.147022i | ||||
\(550\) | −7.98724e21 | −0.953884 | ||||||||
\(551\) | − | 3.65000e20i | − | 0.0429615i | ||||||
\(552\) | 9.82747e20 | + | 3.51363e20i | 0.114006 | + | 0.0407609i | ||||
\(553\) | −2.69572e21 | −0.308229 | ||||||||
\(554\) | 4.53591e21i | 0.511195i | ||||||||
\(555\) | −1.18601e21 | + | 3.31723e21i | −0.131749 | + | 0.368495i | ||||
\(556\) | −3.86252e21 | −0.422934 | ||||||||
\(557\) | − | 1.64848e22i | − | 1.77928i | −0.456666 | − | 0.889638i | \(-0.650957\pi\) | ||
0.456666 | − | 0.889638i | \(-0.349043\pi\) | |||||||
\(558\) | −2.36632e21 | + | 2.88623e21i | −0.251768 | + | 0.307084i | ||||
\(559\) | 6.06109e21 | 0.635706 | ||||||||
\(560\) | − | 5.19378e21i | − | 0.537006i | ||||||
\(561\) | 6.91649e21 | + | 2.47286e21i | 0.704990 | + | 0.252056i | ||||
\(562\) | 6.90077e21 | 0.693437 | ||||||||
\(563\) | − | 1.09770e22i | − | 1.08746i | −0.839259 | − | 0.543732i | \(-0.817011\pi\) | ||
0.839259 | − | 0.543732i | \(-0.182989\pi\) | |||||||
\(564\) | 2.02982e21 | − | 5.67732e21i | 0.198255 | − | 0.554512i | ||||
\(565\) | −1.09975e22 | −1.05903 | ||||||||
\(566\) | 2.99297e21i | 0.284165i | ||||||||
\(567\) | −3.20406e21 | − | 1.60264e22i | −0.299941 | − | 1.50028i | ||||
\(568\) | −4.00839e21 | −0.369984 | ||||||||
\(569\) | 7.70777e21i | 0.701504i | 0.936468 | + | 0.350752i | \(0.114074\pi\) | ||||
−0.936468 | + | 0.350752i | \(0.885926\pi\) | |||||||
\(570\) | −5.95454e20 | − | 2.12894e20i | −0.0534379 | − | 0.0191057i | ||||
\(571\) | −1.24243e22 | −1.09947 | −0.549733 | − | 0.835340i | \(-0.685271\pi\) | ||||
−0.549733 | + | 0.835340i | \(0.685271\pi\) | |||||||
\(572\) | − | 6.61319e21i | − | 0.577089i | ||||||
\(573\) | 1.10932e21 | − | 3.10272e21i | 0.0954596 | − | 0.266996i | ||||
\(574\) | 1.72389e22 | 1.46290 | ||||||||
\(575\) | 3.97387e21i | 0.332561i | ||||||||
\(576\) | −1.17125e21 | − | 9.60265e20i | −0.0966649 | − | 0.0792522i | ||||
\(577\) | −5.10610e21 | −0.415607 | −0.207803 | − | 0.978171i | \(-0.566631\pi\) | ||||
−0.207803 | + | 0.978171i | \(0.566631\pi\) | |||||||
\(578\) | − | 6.24976e21i | − | 0.501696i | ||||||
\(579\) | −1.10654e22 | − | 3.95623e21i | −0.876069 | − | 0.313222i | ||||
\(580\) | 6.75619e21 | 0.527567 | ||||||||
\(581\) | 1.43381e22i | 1.10429i | ||||||||
\(582\) | 5.66433e21 | − | 1.58429e22i | 0.430294 | − | 1.20351i | ||||
\(583\) | 2.18655e22 | 1.63836 | ||||||||
\(584\) | 2.85915e21i | 0.211317i | ||||||||
\(585\) | −1.01448e22 | + | 1.23737e22i | −0.739599 | + | 0.902099i | ||||
\(586\) | −1.32521e21 | −0.0953024 | ||||||||
\(587\) | 5.19346e21i | 0.368427i | 0.982886 | + | 0.184214i | \(0.0589738\pi\) | ||||
−0.982886 | + | 0.184214i | \(0.941026\pi\) | |||||||
\(588\) | −9.02052e21 | − | 3.22512e21i | −0.631267 | − | 0.225698i | ||||
\(589\) | 4.65013e20 | 0.0321028 | ||||||||
\(590\) | 1.34059e22i | 0.913020i | ||||||||
\(591\) | 4.59624e21 | − | 1.28555e22i | 0.308818 | − | 0.863751i | ||||
\(592\) | 1.05126e21 | 0.0696845 | ||||||||
\(593\) | 4.29285e21i | 0.280743i | 0.990099 | + | 0.140371i | \(0.0448296\pi\) | ||||
−0.990099 | + | 0.140371i | \(0.955170\pi\) | |||||||
\(594\) | 7.83591e21 | + | 1.30518e22i | 0.505589 | + | 0.842131i | ||||
\(595\) | −1.81863e22 | −1.15773 | ||||||||
\(596\) | 1.21123e21i | 0.0760778i | ||||||||
\(597\) | −8.16761e21 | − | 2.92018e21i | −0.506175 | − | 0.180973i | ||||
\(598\) | −3.29025e21 | −0.201196 | ||||||||
\(599\) | 1.02183e22i | 0.616541i | 0.951299 | + | 0.308271i | \(0.0997503\pi\) | ||||
−0.951299 | + | 0.308271i | \(0.900250\pi\) | |||||||
\(600\) | 1.94148e21 | − | 5.43024e21i | 0.115591 | − | 0.323302i | ||||
\(601\) | −1.64963e22 | −0.969150 | −0.484575 | − | 0.874750i | \(-0.661026\pi\) | ||||
−0.484575 | + | 0.874750i | \(0.661026\pi\) | |||||||
\(602\) | 1.42777e22i | 0.827724i | ||||||||
\(603\) | 2.23353e22 | + | 1.83119e22i | 1.27777 | + | 1.04760i | ||||
\(604\) | 8.14276e20 | 0.0459702 | ||||||||
\(605\) | − | 2.34262e22i | − | 1.30514i | ||||||
\(606\) | −9.71622e21 | − | 3.47385e21i | −0.534215 | − | 0.190999i | ||||
\(607\) | 6.96878e21 | 0.378136 | 0.189068 | − | 0.981964i | \(-0.439453\pi\) | ||||
0.189068 | + | 0.981964i | \(0.439453\pi\) | |||||||
\(608\) | 1.88705e20i | 0.0101054i | ||||||||
\(609\) | 7.32427e21 | − | 2.04857e22i | 0.387102 | − | 1.08271i | ||||
\(610\) | 4.41329e21 | 0.230210 | ||||||||
\(611\) | 1.90077e22i | 0.978590i | ||||||||
\(612\) | −3.36242e21 | + | 4.10119e21i | −0.170860 | + | 0.208400i | ||||
\(613\) | 2.71321e22 | 1.36082 | 0.680408 | − | 0.732833i | \(-0.261802\pi\) | ||||
0.680408 | + | 0.732833i | \(0.261802\pi\) | |||||||
\(614\) | − | 2.65927e22i | − | 1.31649i | ||||||
\(615\) | 3.65833e22 | + | 1.30797e22i | 1.78765 | + | 0.639140i | ||||
\(616\) | 1.55782e22 | 0.751402 | ||||||||
\(617\) | 2.67609e22i | 1.27415i | 0.770803 | + | 0.637073i | \(0.219855\pi\) | ||||
−0.770803 | + | 0.637073i | \(0.780145\pi\) | |||||||
\(618\) | −9.31764e21 | + | 2.60610e22i | −0.437923 | + | 1.22485i | ||||
\(619\) | −2.25075e22 | −1.04424 | −0.522122 | − | 0.852871i | \(-0.674859\pi\) | ||||
−0.522122 | + | 0.852871i | \(0.674859\pi\) | |||||||
\(620\) | 8.60745e21i | 0.394222i | ||||||||
\(621\) | 6.49364e21 | − | 3.89858e21i | 0.293600 | − | 0.176268i | ||||
\(622\) | −2.24497e22 | −1.00204 | ||||||||
\(623\) | − | 3.43893e22i | − | 1.51537i | ||||||
\(624\) | 4.49607e21 | + | 1.60749e21i | 0.195595 | + | 0.0699312i | ||||
\(625\) | −2.39359e22 | −1.02804 | ||||||||
\(626\) | − | 2.68042e22i | − | 1.13660i | ||||||
\(627\) | 6.38553e20 | − | 1.78600e21i | 0.0267335 | − | 0.0747725i | ||||
\(628\) | −1.52006e22 | −0.628324 | ||||||||
\(629\) | − | 3.68104e21i | − | 0.150233i | ||||||
\(630\) | −2.91479e22 | − | 2.38974e22i | −1.17458 | − | 0.962998i | ||||
\(631\) | −1.91478e22 | −0.761875 | −0.380938 | − | 0.924601i | \(-0.624399\pi\) | ||||
−0.380938 | + | 0.924601i | \(0.624399\pi\) | |||||||
\(632\) | 1.81294e21i | 0.0712272i | ||||||||
\(633\) | −2.32626e22 | − | 8.31712e21i | −0.902462 | − | 0.322659i | ||||
\(634\) | 3.61062e22 | 1.38314 | ||||||||
\(635\) | − | 5.51159e22i | − | 2.08491i | ||||||
\(636\) | −5.31490e21 | + | 1.48656e22i | −0.198536 | + | 0.555296i | ||||
\(637\) | 3.02008e22 | 1.11404 | ||||||||
\(638\) | 2.02645e22i | 0.738194i | ||||||||
\(639\) | −1.84432e22 | + | 2.24954e22i | −0.663483 | + | 0.809258i | ||||
\(640\) | −3.49295e21 | −0.124094 | ||||||||
\(641\) | − | 3.21010e22i | − | 1.12630i | −0.826355 | − | 0.563150i | \(-0.809589\pi\) | ||
0.826355 | − | 0.563150i | \(-0.190411\pi\) | |||||||
\(642\) | 7.06244e21 | + | 2.52505e21i | 0.244723 | + | 0.0874961i | ||||
\(643\) | 3.71143e22 | 1.27015 | 0.635073 | − | 0.772452i | \(-0.280970\pi\) | ||||
0.635073 | + | 0.772452i | \(0.280970\pi\) | |||||||
\(644\) | − | 7.75059e21i | − | 0.261968i | ||||||
\(645\) | −1.08329e22 | + | 3.02992e22i | −0.361633 | + | 1.01147i | ||||
\(646\) | 6.60759e20 | 0.0217863 | ||||||||
\(647\) | − | 1.37787e22i | − | 0.448719i | −0.974506 | − | 0.224360i | \(-0.927971\pi\) | ||
0.974506 | − | 0.224360i | \(-0.0720291\pi\) | |||||||
\(648\) | −1.07782e22 | + | 2.15481e21i | −0.346693 | + | 0.0693121i | ||||
\(649\) | −4.02097e22 | −1.27754 | ||||||||
\(650\) | 1.81805e22i | 0.570557i | ||||||||
\(651\) | 2.60989e22 | + | 9.33118e21i | 0.809048 | + | 0.289260i | ||||
\(652\) | −6.97539e20 | −0.0213593 | ||||||||
\(653\) | 4.84286e22i | 1.46486i | 0.680841 | + | 0.732431i | \(0.261614\pi\) | ||||
−0.680841 | + | 0.732431i | \(0.738386\pi\) | |||||||
\(654\) | 9.02427e21 | − | 2.52405e22i | 0.269643 | − | 0.754181i | ||||
\(655\) | 4.45886e22 | 1.31611 | ||||||||
\(656\) | − | 1.15936e22i | − | 0.338054i | ||||||
\(657\) | 1.60458e22 | + | 1.31554e22i | 0.462209 | + | 0.378949i | ||||
\(658\) | −4.47751e22 | −1.27418 | ||||||||
\(659\) | 2.62793e22i | 0.738807i | 0.929269 | + | 0.369404i | \(0.120438\pi\) | ||||
−0.929269 | + | 0.369404i | \(0.879562\pi\) | |||||||
\(660\) | 3.30592e22 | + | 1.18197e22i | 0.918207 | + | 0.328288i | ||||
\(661\) | 6.00724e21 | 0.164840 | 0.0824201 | − | 0.996598i | \(-0.473735\pi\) | ||||
0.0824201 | + | 0.996598i | \(0.473735\pi\) | |||||||
\(662\) | 2.30579e22i | 0.625108i | ||||||||
\(663\) | 5.62871e21 | − | 1.57432e22i | 0.150765 | − | 0.421683i | ||||
\(664\) | 9.64273e21 | 0.255185 | ||||||||
\(665\) | 4.69614e21i | 0.122791i | ||||||||
\(666\) | 4.83700e21 | − | 5.89975e21i | 0.124963 | − | 0.152419i | ||||
\(667\) | 1.00822e22 | 0.257363 | ||||||||
\(668\) | − | 1.73602e21i | − | 0.0437868i | ||||||
\(669\) | −4.71088e22 | − | 1.68429e22i | −1.17407 | − | 0.419766i | ||||
\(670\) | 6.66093e22 | 1.64035 | ||||||||
\(671\) | 1.32372e22i | 0.322119i | ||||||||
\(672\) | −3.78664e21 | + | 1.05911e22i | −0.0910542 | + | 0.254675i | ||||
\(673\) | −3.45462e22 | −0.820881 | −0.410440 | − | 0.911887i | \(-0.634625\pi\) | ||||
−0.410440 | + | 0.911887i | \(0.634625\pi\) | |||||||
\(674\) | − | 4.82654e22i | − | 1.13333i | ||||||
\(675\) | −2.15419e22 | − | 3.58811e22i | −0.499866 | − | 0.832598i | ||||
\(676\) | 6.75148e21 | 0.154819 | ||||||||
\(677\) | 3.42077e22i | 0.775201i | 0.921828 | + | 0.387600i | \(0.126696\pi\) | ||||
−0.921828 | + | 0.387600i | \(0.873304\pi\) | |||||||
\(678\) | 2.24260e22 | + | 8.01799e21i | 0.502243 | + | 0.179568i | ||||
\(679\) | −1.24948e23 | −2.76547 | ||||||||
\(680\) | 1.22307e22i | 0.267536i | ||||||||
\(681\) | −2.27857e22 | + | 6.37305e22i | −0.492589 | + | 1.37775i | ||||
\(682\) | −2.58172e22 | −0.551612 | ||||||||
\(683\) | 1.76733e22i | 0.373209i | 0.982435 | + | 0.186605i | \(0.0597484\pi\) | ||||
−0.982435 | + | 0.186605i | \(0.940252\pi\) | |||||||
\(684\) | 1.05903e21 | + | 8.68258e20i | 0.0221033 | + | 0.0181217i | ||||
\(685\) | 9.26245e22 | 1.91074 | ||||||||
\(686\) | 1.80826e22i | 0.368696i | ||||||||
\(687\) | −7.26694e21 | − | 2.59816e21i | −0.146453 | − | 0.0523615i | ||||
\(688\) | 9.60209e21 | 0.191275 | ||||||||
\(689\) | − | 4.97700e22i | − | 0.979973i | ||||||
\(690\) | 5.88062e21 | − | 1.64479e22i | 0.114454 | − | 0.320123i | ||||
\(691\) | 3.67658e22 | 0.707325 | 0.353663 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353663 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(692\) | − | 3.59455e22i | − | 0.683590i | ||||||
\(693\) | 7.16777e22 | − | 8.74262e22i | 1.34747 | − | 1.64352i | ||||
\(694\) | −2.22502e22 | −0.413483 | ||||||||
\(695\) | 6.46454e22i | 1.18757i | ||||||||
\(696\) | −1.37771e22 | − | 4.92575e21i | −0.250198 | − | 0.0894537i | ||||
\(697\) | −4.05955e22 | −0.728813 | ||||||||
\(698\) | 9.65974e21i | 0.171444i | ||||||||
\(699\) | 2.39618e22 | − | 6.70201e22i | 0.420438 | − | 1.17595i | ||||
\(700\) | −4.28265e22 | −0.742896 | ||||||||
\(701\) | − | 9.04977e22i | − | 1.55201i | −0.630729 | − | 0.776003i | \(-0.717244\pi\) | ||
0.630729 | − | 0.776003i | \(-0.282756\pi\) | |||||||
\(702\) | 2.97084e22 | − | 1.78360e22i | 0.503713 | − | 0.302414i | ||||
\(703\) | −9.50534e20 | −0.0159340 | ||||||||
\(704\) | − | 1.04767e22i | − | 0.173638i | ||||||
\(705\) | −9.50191e22 | − | 3.39723e22i | −1.55703 | − | 0.556689i | ||||
\(706\) | −3.76947e22 | −0.610720 | ||||||||
\(707\) | 7.66286e22i | 1.22754i | ||||||||
\(708\) | 9.77387e21 | − | 2.73371e22i | 0.154811 | − | 0.432999i | ||||
\(709\) | 1.22712e23 | 1.92185 | 0.960923 | − | 0.276816i | \(-0.0892794\pi\) | ||||
0.960923 | + | 0.276816i | \(0.0892794\pi\) | |||||||
\(710\) | 6.70869e22i | 1.03889i | ||||||||
\(711\) | 1.01743e22 | + | 8.34159e21i | 0.155794 | + | 0.127730i | ||||
\(712\) | −2.31277e22 | −0.350180 | ||||||||
\(713\) | 1.28448e22i | 0.192313i | ||||||||
\(714\) | 3.70852e22 | + | 1.32591e22i | 0.549054 | + | 0.196304i | ||||
\(715\) | −1.10682e23 | −1.62043 | ||||||||
\(716\) | 1.14846e22i | 0.166269i | ||||||||
\(717\) | −1.29178e22 | + | 3.61304e22i | −0.184941 | + | 0.517273i | ||||
\(718\) | −9.86808e22 | −1.39713 | ||||||||
\(719\) | − | 1.80138e22i | − | 0.252217i | −0.992016 | − | 0.126108i | \(-0.959751\pi\) | ||
0.992016 | − | 0.126108i | \(-0.0402487\pi\) | |||||||
\(720\) | −1.60716e22 | + | 1.96027e22i | −0.222535 | + | 0.271429i | ||||
\(721\) | 2.05535e23 | 2.81451 | ||||||||
\(722\) | 5.20428e22i | 0.704796i | ||||||||
\(723\) | 4.12096e22 | + | 1.47337e22i | 0.551940 | + | 0.197336i | ||||
\(724\) | 3.80854e22 | 0.504487 | ||||||||
\(725\) | − | 5.57097e22i | − | 0.729838i | ||||||
\(726\) | −1.70794e22 | + | 4.77702e22i | −0.221299 | + | 0.618963i | ||||
\(727\) | −7.83484e21 | −0.100405 | −0.0502024 | − | 0.998739i | \(-0.515987\pi\) | ||||
−0.0502024 | + | 0.998739i | \(0.515987\pi\) | |||||||
\(728\) | − | 3.54590e22i | − | 0.449444i | ||||||
\(729\) | −3.74990e22 | + | 7.04025e22i | −0.470109 | + | 0.882608i | ||||
\(730\) | 4.78525e22 | 0.593365 | ||||||||
\(731\) | − | 3.36223e22i | − | 0.412371i | ||||||
\(732\) | −8.99950e21 | − | 3.21760e21i | −0.109177 | − | 0.0390341i | ||||
\(733\) | 1.30423e22 | 0.156503 | 0.0782513 | − | 0.996934i | \(-0.475066\pi\) | ||||
0.0782513 | + | 0.996934i | \(0.475066\pi\) | |||||||
\(734\) | 8.13985e21i | 0.0966158i | ||||||||
\(735\) | −5.39775e22 | + | 1.50973e23i | −0.633745 | + | 1.77256i | ||||
\(736\) | −5.21247e21 | −0.0605370 | ||||||||
\(737\) | 1.99788e23i | 2.29525i | ||||||||
\(738\) | −6.50640e22 | − | 5.33437e22i | −0.739418 | − | 0.606223i | ||||
\(739\) | −7.97130e22 | −0.896135 | −0.448068 | − | 0.894000i | \(-0.647888\pi\) | ||||
−0.448068 | + | 0.894000i | \(0.647888\pi\) | |||||||
\(740\) | − | 1.75945e22i | − | 0.195670i | ||||||
\(741\) | −4.06529e21 | − | 1.45347e21i | −0.0447245 | − | 0.0159904i | ||||
\(742\) | 1.17240e23 | 1.27598 | ||||||||
\(743\) | − | 1.47795e23i | − | 1.59129i | −0.605762 | − | 0.795646i | \(-0.707131\pi\) | ||
0.605762 | − | 0.795646i | \(-0.292869\pi\) | |||||||
\(744\) | 6.27545e21 | − | 1.75522e22i | 0.0668438 | − | 0.186959i | ||||
\(745\) | 2.02719e22 | 0.213622 | ||||||||
\(746\) | − | 9.88350e22i | − | 1.03039i | ||||||
\(747\) | 4.43676e22 | − | 5.41158e22i | 0.457616 | − | 0.558160i | ||||
\(748\) | −3.66849e22 | −0.374347 | ||||||||
\(749\) | − | 5.56991e22i | − | 0.562333i | ||||||
\(750\) | 2.70219e21 | + | 9.66119e20i | 0.0269915 | + | 0.00965030i | ||||
\(751\) | −1.09749e21 | −0.0108463 | −0.00542315 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542315 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(752\) | 3.01124e22i | 0.294444i | ||||||||
\(753\) | 3.90032e22 | − | 1.09090e23i | 0.377347 | − | 1.05542i | ||||
\(754\) | 4.61259e22 | 0.441544 | ||||||||
\(755\) | − | 1.36282e22i | − | 0.129081i | ||||||
\(756\) | 4.20150e22 | + | 6.99820e22i | 0.393759 | + | 0.655861i | ||||
\(757\) | −2.73479e22 | −0.253604 | −0.126802 | − | 0.991928i | \(-0.540471\pi\) | ||||
−0.126802 | + | 0.991928i | \(0.540471\pi\) | |||||||
\(758\) | 1.24286e22i | 0.114043i | ||||||||
\(759\) | 4.93337e22 | + | 1.76383e22i | 0.447929 | + | 0.160149i | ||||
\(760\) | 3.15827e21 | 0.0283753 | ||||||||
\(761\) | − | 1.88562e23i | − | 1.67640i | −0.545363 | − | 0.838200i | \(-0.683608\pi\) | ||
0.545363 | − | 0.838200i | \(-0.316392\pi\) | |||||||
\(762\) | −4.01835e22 | + | 1.12391e23i | −0.353515 | + | 0.988766i | ||||
\(763\) | −1.99063e23 | −1.73298 | ||||||||
\(764\) | 1.64567e22i | 0.141774i | ||||||||
\(765\) | 6.86399e22 | + | 5.62755e22i | 0.585174 | + | 0.479764i | ||||
\(766\) | −8.39613e22 | −0.708352 | ||||||||
\(767\) | 9.15249e22i | 0.764146i | ||||||||
\(768\) | 7.12276e21 | + | 2.54661e21i | 0.0588516 | + | 0.0210413i | ||||
\(769\) | −1.56339e23 | −1.27837 | −0.639187 | − | 0.769051i | \(-0.720729\pi\) | ||||
−0.639187 | + | 0.769051i | \(0.720729\pi\) | |||||||
\(770\) | − | 2.60726e23i | − | 2.10989i | ||||||
\(771\) | −8.79226e21 | + | 2.45916e22i | −0.0704151 | + | 0.196948i | ||||
\(772\) | 5.86906e22 | 0.465190 | ||||||||
\(773\) | − | 1.68543e22i | − | 0.132213i | −0.997813 | − | 0.0661065i | \(-0.978942\pi\) | ||
0.997813 | − | 0.0661065i | \(-0.0210577\pi\) | |||||||
\(774\) | 4.41807e22 | − | 5.38877e22i | 0.343008 | − | 0.418371i | ||||
\(775\) | 7.09746e22 | 0.545368 | ||||||||
\(776\) | 8.40303e22i | 0.639061i | ||||||||
\(777\) | −5.33489e22 | − | 1.90739e22i | −0.401566 | − | 0.143572i | ||||
\(778\) | 1.10487e23 | 0.823138 | ||||||||
\(779\) | 1.04827e22i | 0.0772992i | ||||||||
\(780\) | 2.69039e22 | − | 7.52490e22i | 0.196362 | − | 0.549217i | ||||
\(781\) | −2.01220e23 | −1.45366 | ||||||||
\(782\) | 1.82517e22i | 0.130512i | ||||||||
\(783\) | −9.10342e22 | + | 5.46541e22i | −0.644333 | + | 0.386838i | ||||
\(784\) | 4.78446e22 | 0.335200 | ||||||||
\(785\) | 2.54406e23i | 1.76429i | ||||||||
\(786\) | −9.09243e22 | − | 3.25083e22i | −0.624165 | − | 0.223159i | ||||
\(787\) | 2.18785e23 | 1.48669 | 0.743344 | − | 0.668909i | \(-0.233239\pi\) | ||||
0.743344 | + | 0.668909i | \(0.233239\pi\) | |||||||
\(788\) | 6.81852e22i | 0.458649i | ||||||||
\(789\) | 2.23759e22 | − | 6.25843e22i | 0.148992 | − | 0.416725i | ||||
\(790\) | 3.03424e22 | 0.200002 | ||||||||
\(791\) | − | 1.76866e23i | − | 1.15407i | ||||||
\(792\) | −5.87963e22 | − | 4.82050e22i | −0.379794 | − | 0.311380i | ||||
\(793\) | 3.01304e22 | 0.192672 | ||||||||
\(794\) | 1.20630e23i | 0.763645i | ||||||||
\(795\) | 2.48799e23 | + | 8.89534e22i | 1.55923 | + | 0.557475i | ||||
\(796\) | 4.33208e22 | 0.268777 | ||||||||
\(797\) | 7.37996e22i | 0.453302i | 0.973976 | + | 0.226651i | \(0.0727777\pi\) | ||||
−0.973976 | + | 0.226651i | \(0.927222\pi\) | |||||||
\(798\) | 3.42383e21 | − | 9.57630e21i | 0.0208204 | − | 0.0582337i | ||||
\(799\) | 1.05440e23 | 0.634793 | ||||||||
\(800\) | 2.88019e22i | 0.171672i | ||||||||
\(801\) | −1.06414e23 | + | 1.29794e23i | −0.627968 | + | 0.765941i | ||||
\(802\) | −6.41927e22 | −0.375051 | ||||||||
\(803\) | 1.43529e23i | 0.830260i | ||||||||
\(804\) | −1.35829e23 | − | 4.85630e22i | −0.777934 | − | 0.278136i | ||||
\(805\) | −1.29719e23 | −0.735589 | ||||||||
\(806\) | 5.87648e22i | 0.329941i | ||||||||
\(807\) | 1.01806e23 | − | 2.84747e23i | 0.565959 | − | 1.58296i | ||||
\(808\) | 5.15346e22 | 0.283666 | ||||||||
\(809\) | − | 3.56571e22i | − | 0.194338i | −0.995268 | − | 0.0971690i | \(-0.969021\pi\) | ||
0.995268 | − | 0.0971690i | \(-0.0309787\pi\) | |||||||
\(810\) | 3.60642e22 | + | 1.80390e23i | 0.194624 | + | 0.973491i | ||||
\(811\) | 1.77454e23 | 0.948239 | 0.474120 | − | 0.880460i | \(-0.342766\pi\) | ||||
0.474120 | + | 0.880460i | \(0.342766\pi\) | |||||||
\(812\) | 1.08655e23i | 0.574914i | ||||||||
\(813\) | 1.75298e23 | + | 6.26746e22i | 0.918445 | + | 0.328373i | ||||
\(814\) | 5.27729e22 | 0.273789 | ||||||||
\(815\) | 1.16744e22i | 0.0599757i | ||||||||
\(816\) | 8.91709e21 | − | 2.49407e22i | 0.0453630 | − | 0.126878i | ||||
\(817\) | −8.68208e21 | −0.0437368 | ||||||||
\(818\) | 1.02988e22i | 0.0513762i | ||||||||
\(819\) | −1.98999e23 | − | 1.63152e23i | −0.983058 | − | 0.805975i | ||||
\(820\) | −1.94037e23 | −0.949235 | ||||||||
\(821\) | 2.07921e23i | 1.00728i | 0.863912 | + | 0.503642i | \(0.168007\pi\) | ||||
−0.863912 | + | 0.503642i | \(0.831993\pi\) | |||||||
\(822\) | −1.88878e23 | − | 6.75299e22i | −0.906166 | − | 0.323983i | ||||
\(823\) | −8.92072e22 | −0.423839 | −0.211920 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211920 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(824\) | − | 1.38227e23i | − | 0.650393i | ||||||
\(825\) | 9.74619e22 | − | 2.72597e23i | 0.454154 | − | 1.27025i | ||||
\(826\) | −2.15598e23 | −0.994959 | ||||||||
\(827\) | − | 1.90740e23i | − | 0.871762i | −0.900004 | − | 0.435881i | \(-0.856437\pi\) | ||
0.900004 | − | 0.435881i | \(-0.143563\pi\) | |||||||
\(828\) | −2.39833e22 | + | 2.92528e22i | −0.108559 | + | 0.132411i | ||||
\(829\) | 2.32798e22 | 0.104362 | 0.0521811 | − | 0.998638i | \(-0.483383\pi\) | ||||
0.0521811 | + | 0.998638i | \(0.483383\pi\) | |||||||
\(830\) | − | 1.61387e23i | − | 0.716544i | ||||||
\(831\) | −1.54806e23 | − | 5.53481e22i | −0.680738 | − | 0.243385i | ||||
\(832\) | −2.38471e22 | −0.103860 | ||||||||
\(833\) | − | 1.67530e23i | − | 0.722660i | ||||||
\(834\) | 4.71312e22 | − | 1.31824e23i | 0.201363 | − | 0.563204i | ||||
\(835\) | −2.90551e22 | −0.122951 | ||||||||
\(836\) | 9.47292e21i | 0.0397039i | ||||||||
\(837\) | −6.96298e22 | − | 1.15978e23i | −0.289063 | − | 0.481475i | ||||
\(838\) | 2.59876e22 | 0.106860 | ||||||||
\(839\) | 2.78947e23i | 1.13612i | 0.822986 | + | 0.568062i | \(0.192307\pi\) | ||||
−0.822986 | + | 0.568062i | \(0.807693\pi\) | |||||||
\(840\) | 1.77259e23 | + | 6.33755e22i | 0.715110 | + | 0.255674i | ||||
\(841\) | 1.08905e23 | 0.435191 | ||||||||
\(842\) | 1.16671e23i | 0.461813i | ||||||||
\(843\) | −8.42045e22 | + | 2.35516e23i | −0.330153 | + | 0.923422i | ||||
\(844\) | 1.23384e23 | 0.479204 | ||||||||
\(845\) | − | 1.12997e23i | − | 0.434723i | ||||||
\(846\) | 1.68993e23 | + | 1.38552e23i | 0.644030 | + | 0.528018i | ||||
\(847\) | 3.76748e23 | 1.42227 | ||||||||
\(848\) | − | 7.88465e22i | − | 0.294860i | ||||||
\(849\) | −1.02147e23 | − | 3.65208e22i | −0.378411 | − | 0.135294i | ||||
\(850\) | 1.00851e23 | 0.370109 | ||||||||
\(851\) | − | 2.62560e22i | − | 0.0954535i | ||||||
\(852\) | 4.89112e22 | − | 1.36802e23i | 0.176153 | − | 0.492694i | ||||
\(853\) | 5.28116e22 | 0.188424 | 0.0942121 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942121 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(854\) | 7.09760e22i | 0.250870i | ||||||||
\(855\) | 1.45317e22 | − | 1.77245e22i | 0.0508847 | − | 0.0620647i | ||||
\(856\) | −3.74590e22 | −0.129947 | ||||||||
\(857\) | − | 1.13504e23i | − | 0.390089i | −0.980794 | − | 0.195045i | \(-0.937515\pi\) | ||
0.980794 | − | 0.195045i | \(-0.0624852\pi\) | |||||||
\(858\) | 2.25702e23 | + | 8.06954e22i | 0.768487 | + | 0.274758i | ||||
\(859\) | −4.37523e23 | −1.47589 | −0.737947 | − | 0.674858i | \(-0.764205\pi\) | ||||
−0.737947 | + | 0.674858i | \(0.764205\pi\) | |||||||
\(860\) | − | 1.60706e23i | − | 0.537088i | ||||||
\(861\) | −2.10352e23 | + | 5.88345e23i | −0.696500 | + | 1.94808i | ||||
\(862\) | −3.22467e22 | −0.105786 | ||||||||
\(863\) | − | 6.38714e21i | − | 0.0207597i | −0.999946 | − | 0.0103798i | \(-0.996696\pi\) | ||
0.999946 | − | 0.0103798i | \(-0.00330406\pi\) | |||||||
\(864\) | 4.70646e22 | − | 2.82562e22i | 0.151560 | − | 0.0909920i | ||||
\(865\) | −6.01605e23 | −1.91948 | ||||||||
\(866\) | − | 1.38202e23i | − | 0.436890i | ||||||
\(867\) | 2.13298e23 | + | 7.62607e22i | 0.668088 | + | 0.238863i | ||||
\(868\) | −1.38428e23 | −0.429602 | ||||||||
\(869\) | 9.10090e22i | 0.279850i | ||||||||
\(870\) | −8.24403e22 | + | 2.30582e23i | −0.251180 | + | 0.702541i | ||||
\(871\) | 4.54755e23 | 1.37288 | ||||||||
\(872\) | 1.33875e23i | 0.400467i | ||||||||
\(873\) | 4.71585e23 | + | 3.86636e23i | 1.39780 | + | 1.14601i | ||||
\(874\) | 4.71304e21 | 0.0138423 | ||||||||
\(875\) | − | 2.13113e22i | − | 0.0620219i | ||||||
\(876\) | −9.75800e22 | − | 3.48879e22i | −0.281402 | − | 0.100610i | ||||
\(877\) | −4.12792e23 | −1.17960 | −0.589800 | − | 0.807550i | \(-0.700793\pi\) | ||||
−0.589800 | + | 0.807550i | \(0.700793\pi\) | |||||||
\(878\) | − | 6.83096e21i | − | 0.0193431i | ||||||
\(879\) | 1.61705e22 | − | 4.52281e22i | 0.0453744 | − | 0.126910i | ||||
\(880\) | −1.75345e23 | −0.487564 | ||||||||
\(881\) | − | 2.90893e23i | − | 0.801543i | −0.916178 | − | 0.400771i | \(-0.868742\pi\) | ||
0.916178 | − | 0.400771i | \(-0.131258\pi\) | |||||||
\(882\) | 2.20140e23 | − | 2.68508e23i | 0.601105 | − | 0.733176i | ||||
\(883\) | 1.57662e23 | 0.426621 | 0.213311 | − | 0.976984i | \(-0.431575\pi\) | ||||
0.213311 | + | 0.976984i | \(0.431575\pi\) | |||||||
\(884\) | 8.35018e22i | 0.223912i | ||||||||
\(885\) | −4.57530e23 | − | 1.63581e23i | −1.21583 | − | 0.434698i | ||||
\(886\) | 2.79484e23 | 0.736016 | ||||||||
\(887\) | 2.23947e23i | 0.584462i | 0.956348 | + | 0.292231i | \(0.0943977\pi\) | ||||
−0.956348 | + | 0.292231i | \(0.905602\pi\) | |||||||
\(888\) | −1.28277e22 | + | 3.58784e22i | −0.0331775 | + | 0.0927961i | ||||
\(889\) | 8.86393e23 | 2.27202 | ||||||||
\(890\) | 3.87078e23i | 0.983284i | ||||||||
\(891\) | −5.41061e23 | + | 1.08171e23i | −1.36215 | + | 0.272326i | ||||
\(892\) | 2.49864e23 | 0.623426 | ||||||||
\(893\) | − | 2.72272e22i | − | 0.0673273i | ||||||
\(894\) | −4.13382e22 | − | 1.47797e22i | −0.101310 | − | 0.0362214i | ||||
\(895\) | 1.92212e23 | 0.466871 | ||||||||
\(896\) | − | 5.61748e22i | − | 0.135231i | ||||||
\(897\) | 4.01482e22 | − | 1.12293e23i | 0.0957914 | − | 0.267925i | ||||
\(898\) | −2.42269e23 | −0.572911 | ||||||||
\(899\) | − | 1.80070e23i | − | 0.422051i | ||||||
\(900\) | 1.61638e23 | + | 1.32522e23i | 0.375495 | + | 0.307855i | ||||
\(901\) | −2.76085e23 | −0.635690 | ||||||||
\(902\) | − | 5.81994e23i | − | 1.32821i | ||||||
\(903\) | −4.87283e23 | − | 1.74219e23i | −1.10225 | − | 0.394088i | ||||
\(904\) | −1.18947e23 | −0.266689 | ||||||||
\(905\) | − | 6.37420e23i | − | 1.41657i | ||||||
\(906\) | −9.93595e21 | + | 2.77904e22i | −0.0218869 | + | 0.0612166i | ||||
\(907\) | −9.34461e22 | −0.204034 | −0.102017 | − | 0.994783i | \(-0.532530\pi\) | ||||
−0.102017 | + | 0.994783i | \(0.532530\pi\) | |||||||
\(908\) | − | 3.38025e23i | − | 0.731580i | ||||||
\(909\) | 2.37118e23 | − | 2.89216e23i | 0.508691 | − | 0.620457i | ||||
\(910\) | −5.93463e23 | −1.26201 | ||||||||
\(911\) | − | 7.60583e23i | − | 1.60324i | −0.597831 | − | 0.801622i | \(-0.703971\pi\) | ||
0.597831 | − | 0.801622i | \(-0.296029\pi\) | |||||||
\(912\) | −6.44030e21 | − | 2.30261e21i | −0.0134570 | − | 0.00481129i | ||||
\(913\) | 4.84062e23 | 1.00262 | ||||||||
\(914\) | 2.32653e23i | 0.477682i | ||||||||
\(915\) | −5.38518e22 | + | 1.50621e23i | −0.109605 | + | 0.306561i | ||||
\(916\) | 3.85437e22 | 0.0777659 | ||||||||
\(917\) | 7.17089e23i | 1.43423i | ||||||||
\(918\) | −9.89405e22 | − | 1.64799e23i | −0.196170 | − | 0.326749i | ||||
\(919\) | 1.08833e23 | 0.213912 | 0.106956 | − | 0.994264i | \(-0.465890\pi\) | ||||
0.106956 | + | 0.994264i | \(0.465890\pi\) | |||||||
\(920\) | 8.72390e22i | 0.169984i | ||||||||
\(921\) | 9.07584e23 | + | 3.24490e23i | 1.75311 | + | 0.626793i | ||||
\(922\) | −1.10311e23 | −0.211238 | ||||||||
\(923\) | 4.58016e23i | 0.869494i | ||||||||
\(924\) | −1.90088e23 | + | 5.31669e23i | −0.357750 | + | 1.00061i | ||||
\(925\) | −1.45079e23 | −0.270690 | ||||||||
\(926\) | − | 3.78390e23i | − | 0.699925i | ||||||
\(927\) | −7.75742e23 | − | 6.36003e23i | −1.42259 | − | 1.16633i | ||||
\(928\) | 7.30735e22 | 0.132854 | ||||||||
\(929\) | 1.08986e24i | 1.96447i | 0.187645 | + | 0.982237i | \(0.439915\pi\) | ||||
−0.187645 | + | 0.982237i | \(0.560085\pi\) | |||||||
\(930\) | −2.93764e23 | − | 1.05030e23i | −0.524970 | − | 0.187693i | ||||
\(931\) | −4.32604e22 | −0.0766467 | ||||||||
\(932\) | 3.55473e23i | 0.624423i | ||||||||
\(933\) | 2.73935e23 | − | 7.66184e23i | 0.477083 | − | 1.33438i | ||||
\(934\) | −1.98457e23 | −0.342683 | ||||||||
\(935\) | 6.13980e23i | 1.05114i | ||||||||
\(936\) | −1.09724e23 | + | 1.33832e23i | −0.186249 | + | 0.227170i | ||||
\(937\) | −5.90958e23 | −0.994581 | −0.497291 | − | 0.867584i | \(-0.665672\pi\) | ||||
−0.497291 | + | 0.867584i | \(0.665672\pi\) | |||||||
\(938\) | 1.07123e24i | 1.78756i | ||||||||
\(939\) | 9.14801e23 | + | 3.27070e23i | 1.51357 | + | 0.541148i | ||||
\(940\) | 5.03979e23 | 0.826779 | ||||||||
\(941\) | − | 1.35098e23i | − | 0.219752i | −0.993945 | − | 0.109876i | \(-0.964955\pi\) | ||
0.993945 | − | 0.109876i | \(-0.0350453\pi\) | |||||||
\(942\) | 1.85481e23 | − | 5.18781e23i | 0.299151 | − | 0.836714i | ||||
\(943\) | −2.89558e23 | −0.463065 | ||||||||
\(944\) | 1.44995e23i | 0.229921i | ||||||||
\(945\) | 1.17126e24 | − | 7.03189e23i | 1.84162 | − | 1.10565i | ||||
\(946\) | 4.82023e23 | 0.751516 | ||||||||
\(947\) | − | 1.14490e24i | − | 1.76998i | −0.465614 | − | 0.884988i | \(-0.654166\pi\) | ||
0.465614 | − | 0.884988i | \(-0.345834\pi\) | |||||||
\(948\) | −6.18737e22 | − | 2.21218e22i | −0.0948505 | − | 0.0339120i | ||||
\(949\) | 3.26699e23 | 0.496613 | ||||||||
\(950\) | − | 2.60422e22i | − | 0.0392545i | ||||||
\(951\) | −4.40575e23 | + | 1.23227e24i | −0.658530 | + | 1.84188i | ||||
\(952\) | −1.96699e23 | −0.291546 | ||||||||
\(953\) | 1.61468e23i | 0.237325i | 0.992935 | + | 0.118662i | \(0.0378606\pi\) | ||||
−0.992935 | + | 0.118662i | \(0.962139\pi\) | |||||||
\(954\) | −4.42493e23 | − | 3.62785e23i | −0.644940 | − | 0.528764i | ||||
\(955\) | 2.75430e23 | 0.398093 | ||||||||
\(956\) | − | 1.91635e23i | − | 0.274670i | ||||||
\(957\) | −6.91607e23 | − | 2.47271e23i | −0.983024 | − | 0.351462i | ||||
\(958\) | 3.27957e23 | 0.462267 | ||||||||
\(959\) | 1.48962e24i | 2.08222i | ||||||||
\(960\) | 4.26216e22 | − | 1.19211e23i | 0.0590826 | − | 0.165252i | ||||
\(961\) | −4.98012e23 | −0.684625 | ||||||||
\(962\) | − | 1.20121e23i | − | 0.163764i | ||||||
\(963\) | −1.72354e23 | + | 2.10223e23i | −0.233030 | + | 0.284230i | ||||
\(964\) | −2.18575e23 | −0.293078 | ||||||||
\(965\) | − | 9.82281e23i | − | 1.30622i | ||||||
\(966\) | 2.64520e23 | + | 9.45742e22i | 0.348852 | + | 0.124726i | ||||
\(967\) | −2.41604e23 | −0.316004 | −0.158002 | − | 0.987439i | \(-0.550505\pi\) | ||||
−0.158002 | + | 0.987439i | \(0.550505\pi\) | |||||||
\(968\) | − | 2.53372e23i | − | 0.328667i | ||||||
\(969\) | −8.06271e21 | + | 2.25511e22i | −0.0103727 | + | 0.0290119i | ||||
\(970\) | 1.40638e24 | 1.79444 | ||||||||
\(971\) | 2.11221e23i | 0.267290i | 0.991029 | + | 0.133645i | \(0.0426683\pi\) | ||||
−0.991029 | + | 0.133645i | \(0.957332\pi\) | |||||||
\(972\) | 5.79756e22 | − | 3.94141e23i | 0.0727638 | − | 0.494677i | ||||
\(973\) | −1.03965e24 | −1.29415 | ||||||||
\(974\) | 1.23687e22i | 0.0152704i | ||||||||
\(975\) | −6.20482e23 | − | 2.21842e23i | −0.759788 | − | 0.271648i | ||||
\(976\) | 4.77331e22 | 0.0579724 | ||||||||
\(977\) | − | 8.99050e21i | − | 0.0108300i | −0.999985 | − | 0.00541499i | \(-0.998276\pi\) | ||
0.999985 | − | 0.00541499i | \(-0.00172365\pi\) | |||||||
\(978\) | 8.51151e21 | − | 2.38063e22i | 0.0101694 | − | 0.0284434i | ||||
\(979\) | −1.16100e24 | −1.37585 | ||||||||
\(980\) | − | 8.00756e23i | − | 0.941221i | ||||||
\(981\) | 7.51316e23 | + | 6.15978e23i | 0.875933 | + | 0.718147i | ||||
\(982\) | −3.16021e22 | −0.0365447 | ||||||||
\(983\) | − | 2.64139e23i | − | 0.302973i | −0.988459 | − | 0.151486i | \(-0.951594\pi\) | ||
0.988459 | − | 0.151486i | \(-0.0484060\pi\) | |||||||
\(984\) | 3.95677e23 | + | 1.41467e23i | 0.450173 | + | 0.160951i | ||||
\(985\) | 1.14119e24 | 1.28786 | ||||||||
\(986\) | − | 2.55871e23i | − | 0.286421i | ||||||
\(987\) | 5.46355e23 | − | 1.52813e24i | 0.606649 | − | 1.69677i | ||||
\(988\) | 2.15622e22 | 0.0237485 | ||||||||
\(989\) | − | 2.39820e23i | − | 0.262008i | ||||||
\(990\) | −8.06788e23 | + | 9.84050e23i | −0.874336 | + | 1.06644i | ||||
\(991\) | −8.23814e23 | −0.885605 | −0.442802 | − | 0.896619i | \(-0.646016\pi\) | ||||
−0.442802 | + | 0.896619i | \(0.646016\pi\) | |||||||
\(992\) | 9.30962e22i | 0.0992747i | ||||||||
\(993\) | −7.86942e23 | − | 2.81356e23i | −0.832432 | − | 0.297620i | ||||
\(994\) | −1.07891e24 | −1.13213 | ||||||||
\(995\) | − | 7.25043e23i | − | 0.754708i | ||||||
\(996\) | −1.17662e23 | + | 3.29097e23i | −0.121496 | + | 0.339820i | ||||
\(997\) | 2.13470e22 | 0.0218663 | 0.0109332 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109332 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(998\) | 2.50486e23i | 0.254530i | ||||||||
\(999\) | 1.42331e23 | + | 2.37072e23i | 0.143474 | + | 0.238977i |
(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 | 6.17.b.a.5.3 | ✓ | 6 | |
3.2 | odd | 2 | inner | 6.17.b.a.5.6 | yes | 6 | |
4.3 | odd | 2 | 48.17.e.d.17.1 | 6 | |||
12.11 | even | 2 | 48.17.e.d.17.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.17.b.a.5.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6.17.b.a.5.6 | yes | 6 | 3.2 | odd | 2 | inner | |
48.17.e.d.17.1 | 6 | 4.3 | odd | 2 | |||
48.17.e.d.17.2 | 6 | 12.11 | even | 2 |