Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,17,Mod(6,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, 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("7.6");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(11.3627180700\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{5}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.7 | ||
Root | \(-1381.83i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.6 |
Dual form | 7.17.b.b.6.8 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 270.026 | 1.05479 | 0.527394 | − | 0.849621i | \(-0.323169\pi\) | ||||
0.527394 | + | 0.849621i | \(0.323169\pi\) | |||||||
\(3\) | − | 8290.96i | − | 1.26367i | −0.775101 | − | 0.631837i | \(-0.782301\pi\) | ||
0.775101 | − | 0.631837i | \(-0.217699\pi\) | |||||||
\(4\) | 7378.00 | 0.112579 | ||||||||
\(5\) | − | 234861.i | − | 0.601244i | −0.953743 | − | 0.300622i | \(-0.902806\pi\) | ||
0.953743 | − | 0.300622i | \(-0.0971943\pi\) | |||||||
\(6\) | − | 2.23878e6i | − | 1.33291i | ||||||
\(7\) | −4.98661e6 | + | 2.89252e6i | −0.865009 | + | 0.501756i | ||||
\(8\) | −1.57042e7 | −0.936041 | ||||||||
\(9\) | −2.56934e7 | −0.596872 | ||||||||
\(10\) | − | 6.34186e7i | − | 0.634186i | ||||||
\(11\) | 5.66575e7 | 0.264311 | 0.132156 | − | 0.991229i | \(-0.457810\pi\) | ||||
0.132156 | + | 0.991229i | \(0.457810\pi\) | |||||||
\(12\) | − | 6.11708e7i | − | 0.142264i | ||||||
\(13\) | − | 5.49071e8i | − | 0.673104i | −0.941665 | − | 0.336552i | \(-0.890739\pi\) | ||
0.941665 | − | 0.336552i | \(-0.109261\pi\) | |||||||
\(14\) | −1.34651e9 | + | 7.81057e8i | −0.912402 | + | 0.529247i | ||||
\(15\) | −1.94722e9 | −0.759777 | ||||||||
\(16\) | −4.72406e9 | −1.09991 | ||||||||
\(17\) | − | 1.34700e10i | − | 1.93097i | −0.260453 | − | 0.965487i | \(-0.583872\pi\) | ||
0.260453 | − | 0.965487i | \(-0.416128\pi\) | |||||||
\(18\) | −6.93787e9 | −0.629573 | ||||||||
\(19\) | 4.64514e8i | 0.0273508i | 0.999906 | + | 0.0136754i | \(0.00435315\pi\) | ||||
−0.999906 | + | 0.0136754i | \(0.995647\pi\) | |||||||
\(20\) | − | 1.73281e9i | − | 0.0676877i | ||||||
\(21\) | 2.39818e10 | + | 4.13438e10i | 0.634056 | + | 1.09309i | ||||
\(22\) | 1.52990e10 | 0.278793 | ||||||||
\(23\) | 6.50418e10 | 0.830557 | 0.415279 | − | 0.909694i | \(-0.363684\pi\) | ||||
0.415279 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(24\) | 1.30203e11i | 1.18285i | ||||||||
\(25\) | 9.74282e10 | 0.638505 | ||||||||
\(26\) | − | 1.48263e11i | − | 0.709982i | ||||||
\(27\) | − | 1.43876e11i | − | 0.509423i | ||||||
\(28\) | −3.67912e10 | + | 2.13411e10i | −0.0973822 | + | 0.0564874i | ||||
\(29\) | 8.11530e10 | 0.162226 | 0.0811130 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811130 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(30\) | −5.25801e11 | −0.801404 | ||||||||
\(31\) | 1.17487e12i | 1.37751i | 0.724993 | + | 0.688756i | \(0.241843\pi\) | ||||
−0.724993 | + | 0.688756i | \(0.758157\pi\) | |||||||
\(32\) | −2.46430e11 | −0.224126 | ||||||||
\(33\) | − | 4.69745e11i | − | 0.334003i | ||||||
\(34\) | − | 3.63725e12i | − | 2.03677i | ||||||
\(35\) | 6.79341e11 | + | 1.17116e12i | 0.301678 | + | 0.520082i | ||||
\(36\) | −1.89566e11 | −0.0671955 | ||||||||
\(37\) | −2.93669e12 | −0.836074 | −0.418037 | − | 0.908430i | \(-0.637282\pi\) | ||||
−0.418037 | + | 0.908430i | \(0.637282\pi\) | |||||||
\(38\) | 1.25431e11i | 0.0288493i | ||||||||
\(39\) | −4.55233e12 | −0.850583 | ||||||||
\(40\) | 3.68830e12i | 0.562790i | ||||||||
\(41\) | − | 7.81827e12i | − | 0.979129i | −0.871967 | − | 0.489564i | \(-0.837156\pi\) | ||
0.871967 | − | 0.489564i | \(-0.162844\pi\) | |||||||
\(42\) | 6.47571e12 | + | 1.11639e13i | 0.668795 | + | 1.15298i | ||||
\(43\) | 1.54546e13 | 1.32224 | 0.661119 | − | 0.750281i | \(-0.270082\pi\) | ||||
0.661119 | + | 0.750281i | \(0.270082\pi\) | |||||||
\(44\) | 4.18019e11 | 0.0297560 | ||||||||
\(45\) | 6.03437e12i | 0.358866i | ||||||||
\(46\) | 1.75630e13 | 0.876063 | ||||||||
\(47\) | − | 1.35043e13i | − | 0.567139i | −0.958952 | − | 0.283569i | \(-0.908481\pi\) | ||
0.958952 | − | 0.283569i | \(-0.0915186\pi\) | |||||||
\(48\) | 3.91670e13i | 1.38992i | ||||||||
\(49\) | 1.64995e13 | − | 2.88478e13i | 0.496481 | − | 0.868047i | ||||
\(50\) | 2.63081e13 | 0.673488 | ||||||||
\(51\) | −1.11679e14 | −2.44012 | ||||||||
\(52\) | − | 4.05105e12i | − | 0.0757776i | ||||||
\(53\) | −1.02111e14 | −1.64008 | −0.820038 | − | 0.572309i | \(-0.806048\pi\) | ||||
−0.820038 | + | 0.572309i | \(0.806048\pi\) | |||||||
\(54\) | − | 3.88503e13i | − | 0.537333i | ||||||
\(55\) | − | 1.33066e13i | − | 0.158916i | ||||||
\(56\) | 7.83105e13 | − | 4.54247e13i | 0.809684 | − | 0.469665i | ||||
\(57\) | 3.85127e12 | 0.0345625 | ||||||||
\(58\) | 2.19134e13 | 0.171114 | ||||||||
\(59\) | − | 1.65302e14i | − | 1.12580i | −0.826524 | − | 0.562902i | \(-0.809685\pi\) | ||
0.826524 | − | 0.562902i | \(-0.190315\pi\) | |||||||
\(60\) | −1.43666e13 | −0.0855352 | ||||||||
\(61\) | 3.07486e14i | 1.60394i | 0.597368 | + | 0.801968i | \(0.296213\pi\) | ||||
−0.597368 | + | 0.801968i | \(0.703787\pi\) | |||||||
\(62\) | 3.17245e14i | 1.45298i | ||||||||
\(63\) | 1.28123e14 | − | 7.43187e13i | 0.516299 | − | 0.299484i | ||||
\(64\) | 2.43053e14 | 0.863499 | ||||||||
\(65\) | −1.28955e14 | −0.404700 | ||||||||
\(66\) | − | 1.26843e14i | − | 0.352303i | ||||||
\(67\) | 3.75420e13 | 0.0924527 | 0.0462263 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462263 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(68\) | − | 9.93817e13i | − | 0.217388i | ||||||
\(69\) | − | 5.39259e14i | − | 1.04955i | ||||||
\(70\) | 1.83440e14 | + | 3.16243e14i | 0.318207 | + | 0.548577i | ||||
\(71\) | −1.78686e14 | −0.276709 | −0.138354 | − | 0.990383i | \(-0.544181\pi\) | ||||
−0.138354 | + | 0.990383i | \(0.544181\pi\) | |||||||
\(72\) | 4.03493e14 | 0.558696 | ||||||||
\(73\) | 8.37004e14i | 1.03787i | 0.854812 | + | 0.518937i | \(0.173672\pi\) | ||||
−0.854812 | + | 0.518937i | \(0.826328\pi\) | |||||||
\(74\) | −7.92983e14 | −0.881881 | ||||||||
\(75\) | − | 8.07773e14i | − | 0.806862i | ||||||
\(76\) | 3.42719e12i | 0.00307914i | ||||||||
\(77\) | −2.82529e14 | + | 1.63883e14i | −0.228632 | + | 0.132620i | ||||
\(78\) | −1.22925e15 | −0.897186 | ||||||||
\(79\) | 2.06130e15 | 1.35870 | 0.679350 | − | 0.733815i | \(-0.262262\pi\) | ||||
0.679350 | + | 0.733815i | \(0.262262\pi\) | |||||||
\(80\) | 1.10950e15i | 0.661312i | ||||||||
\(81\) | −2.29889e15 | −1.24062 | ||||||||
\(82\) | − | 2.11114e15i | − | 1.03277i | ||||||
\(83\) | − | 2.72376e15i | − | 1.20933i | −0.796480 | − | 0.604664i | \(-0.793307\pi\) | ||
0.796480 | − | 0.604664i | \(-0.206693\pi\) | |||||||
\(84\) | 1.76938e14 | + | 3.05034e14i | 0.0713817 | + | 0.123059i | ||||
\(85\) | −3.16358e15 | −1.16099 | ||||||||
\(86\) | 4.17314e15 | 1.39468 | ||||||||
\(87\) | − | 6.72837e14i | − | 0.205001i | ||||||
\(88\) | −8.89759e14 | −0.247406 | ||||||||
\(89\) | 6.65516e15i | 1.69059i | 0.534300 | + | 0.845295i | \(0.320575\pi\) | ||||
−0.534300 | + | 0.845295i | \(0.679425\pi\) | |||||||
\(90\) | 1.62944e15i | 0.378528i | ||||||||
\(91\) | 1.58820e15 | + | 2.73800e15i | 0.337734 | + | 0.582241i | ||||
\(92\) | 4.79878e14 | 0.0935037 | ||||||||
\(93\) | 9.74079e15 | 1.74073 | ||||||||
\(94\) | − | 3.64651e15i | − | 0.598211i | ||||||
\(95\) | 1.09096e14 | 0.0164445 | ||||||||
\(96\) | 2.04314e15i | 0.283223i | ||||||||
\(97\) | 3.48548e15i | 0.444722i | 0.974964 | + | 0.222361i | \(0.0713764\pi\) | ||||
−0.974964 | + | 0.222361i | \(0.928624\pi\) | |||||||
\(98\) | 4.45530e15 | − | 7.78964e15i | 0.523683 | − | 0.915607i | ||||
\(99\) | −1.45572e15 | −0.157760 | ||||||||
\(100\) | 7.18825e14 | 0.0718825 | ||||||||
\(101\) | − | 2.00208e15i | − | 0.184889i | −0.995718 | − | 0.0924443i | \(-0.970532\pi\) | ||
0.995718 | − | 0.0924443i | \(-0.0294680\pi\) | |||||||
\(102\) | −3.01563e16 | −2.57381 | ||||||||
\(103\) | − | 1.19192e16i | − | 0.940912i | −0.882424 | − | 0.470456i | \(-0.844089\pi\) | ||
0.882424 | − | 0.470456i | \(-0.155911\pi\) | |||||||
\(104\) | 8.62271e15i | 0.630053i | ||||||||
\(105\) | 9.71004e15 | − | 5.63240e15i | 0.657214 | − | 0.381223i | ||||
\(106\) | −2.75725e16 | −1.72993 | ||||||||
\(107\) | 1.23218e16 | 0.717141 | 0.358571 | − | 0.933503i | \(-0.383264\pi\) | ||||
0.358571 | + | 0.933503i | \(0.383264\pi\) | |||||||
\(108\) | − | 1.06152e15i | − | 0.0573505i | ||||||
\(109\) | −2.59830e16 | −1.30400 | −0.651999 | − | 0.758220i | \(-0.726069\pi\) | ||||
−0.651999 | + | 0.758220i | \(0.726069\pi\) | |||||||
\(110\) | − | 3.59314e15i | − | 0.167623i | ||||||
\(111\) | 2.43480e16i | 1.05652i | ||||||||
\(112\) | 2.35570e16 | − | 1.36645e16i | 0.951428 | − | 0.551884i | ||||
\(113\) | 4.55247e16 | 1.71246 | 0.856229 | − | 0.516596i | \(-0.172801\pi\) | ||||
0.856229 | + | 0.516596i | \(0.172801\pi\) | |||||||
\(114\) | 1.03994e15 | 0.0364561 | ||||||||
\(115\) | − | 1.52758e16i | − | 0.499368i | ||||||
\(116\) | 5.98747e14 | 0.0182633 | ||||||||
\(117\) | 1.41075e16i | 0.401756i | ||||||||
\(118\) | − | 4.46359e16i | − | 1.18749i | ||||||
\(119\) | 3.89623e16 | + | 6.71696e16i | 0.968878 | + | 1.67031i | ||||
\(120\) | 3.05795e16 | 0.711182 | ||||||||
\(121\) | −4.27397e16 | −0.930139 | ||||||||
\(122\) | 8.30292e16i | 1.69181i | ||||||||
\(123\) | −6.48210e16 | −1.23730 | ||||||||
\(124\) | 8.66818e15i | 0.155080i | ||||||||
\(125\) | − | 5.87190e16i | − | 0.985142i | ||||||
\(126\) | 3.45964e16 | − | 2.00680e16i | 0.544587 | − | 0.315892i | ||||
\(127\) | −4.89229e16 | −0.722907 | −0.361454 | − | 0.932390i | \(-0.617719\pi\) | ||||
−0.361454 | + | 0.932390i | \(0.617719\pi\) | |||||||
\(128\) | 8.17807e16 | 1.13494 | ||||||||
\(129\) | − | 1.28133e17i | − | 1.67088i | ||||||
\(130\) | −3.48213e16 | −0.426873 | ||||||||
\(131\) | 3.67339e16i | 0.423542i | 0.977319 | + | 0.211771i | \(0.0679231\pi\) | ||||
−0.977319 | + | 0.211771i | \(0.932077\pi\) | |||||||
\(132\) | − | 3.46578e15i | − | 0.0376019i | ||||||
\(133\) | −1.34362e15 | − | 2.31635e15i | −0.0137234 | − | 0.0236587i | ||||
\(134\) | 1.01373e16 | 0.0975180 | ||||||||
\(135\) | −3.37909e16 | −0.306288 | ||||||||
\(136\) | 2.11535e17i | 1.80747i | ||||||||
\(137\) | −6.28808e16 | −0.506703 | −0.253352 | − | 0.967374i | \(-0.581533\pi\) | ||||
−0.253352 | + | 0.967374i | \(0.581533\pi\) | |||||||
\(138\) | − | 1.45614e17i | − | 1.10706i | ||||||
\(139\) | − | 7.02978e16i | − | 0.504456i | −0.967668 | − | 0.252228i | \(-0.918837\pi\) | ||
0.967668 | − | 0.252228i | \(-0.0811633\pi\) | |||||||
\(140\) | 5.01218e15 | + | 8.64082e15i | 0.0339627 | + | 0.0585505i | ||||
\(141\) | −1.11964e17 | −0.716678 | ||||||||
\(142\) | −4.82498e16 | −0.291869 | ||||||||
\(143\) | − | 3.11090e16i | − | 0.177909i | ||||||
\(144\) | 1.21377e17 | 0.656502 | ||||||||
\(145\) | − | 1.90597e16i | − | 0.0975375i | ||||||
\(146\) | 2.26013e17i | 1.09474i | ||||||||
\(147\) | −2.39176e17 | − | 1.36797e17i | −1.09693 | − | 0.627391i | ||||
\(148\) | −2.16669e16 | −0.0941247 | ||||||||
\(149\) | 2.78521e17 | 1.14649 | 0.573243 | − | 0.819386i | \(-0.305685\pi\) | ||||
0.573243 | + | 0.819386i | \(0.305685\pi\) | |||||||
\(150\) | − | 2.18120e17i | − | 0.851069i | ||||||
\(151\) | 2.97192e17 | 1.09957 | 0.549784 | − | 0.835307i | \(-0.314710\pi\) | ||||
0.549784 | + | 0.835307i | \(0.314710\pi\) | |||||||
\(152\) | − | 7.29481e15i | − | 0.0256015i | ||||||
\(153\) | 3.46090e17i | 1.15254i | ||||||||
\(154\) | −7.62900e16 | + | 4.42527e16i | −0.241158 | + | 0.139886i | ||||
\(155\) | 2.75931e17 | 0.828222 | ||||||||
\(156\) | −3.35871e16 | −0.0957582 | ||||||||
\(157\) | − | 2.97914e17i | − | 0.807036i | −0.914972 | − | 0.403518i | \(-0.867787\pi\) | ||
0.914972 | − | 0.403518i | \(-0.132213\pi\) | |||||||
\(158\) | 5.56603e17 | 1.43314 | ||||||||
\(159\) | 8.46596e17i | 2.07252i | ||||||||
\(160\) | 5.78767e16i | 0.134755i | ||||||||
\(161\) | −3.24338e17 | + | 1.88135e17i | −0.718440 | + | 0.416737i | ||||
\(162\) | −6.20759e17 | −1.30859 | ||||||||
\(163\) | 1.69831e17 | 0.340813 | 0.170406 | − | 0.985374i | \(-0.445492\pi\) | ||||
0.170406 | + | 0.985374i | \(0.445492\pi\) | |||||||
\(164\) | − | 5.76832e16i | − | 0.110230i | ||||||
\(165\) | −1.10325e17 | −0.200818 | ||||||||
\(166\) | − | 7.35486e17i | − | 1.27559i | ||||||
\(167\) | − | 5.70061e17i | − | 0.942300i | −0.882053 | − | 0.471150i | \(-0.843839\pi\) | ||
0.882053 | − | 0.471150i | \(-0.156161\pi\) | |||||||
\(168\) | −3.76614e17 | − | 6.49269e17i | −0.593503 | − | 1.02318i | ||||
\(169\) | 3.63937e17 | 0.546931 | ||||||||
\(170\) | −8.54248e17 | −1.22460 | ||||||||
\(171\) | − | 1.19349e16i | − | 0.0163249i | ||||||
\(172\) | 1.14024e17 | 0.148857 | ||||||||
\(173\) | − | 2.23303e17i | − | 0.278308i | −0.990271 | − | 0.139154i | \(-0.955562\pi\) | ||
0.990271 | − | 0.139154i | \(-0.0444383\pi\) | |||||||
\(174\) | − | 1.81683e17i | − | 0.216233i | ||||||
\(175\) | −4.85836e17 | + | 2.81813e17i | −0.552313 | + | 0.320374i | ||||
\(176\) | −2.67653e17 | −0.290718 | ||||||||
\(177\) | −1.37052e18 | −1.42265 | ||||||||
\(178\) | 1.79707e18i | 1.78322i | ||||||||
\(179\) | 1.28169e18 | 1.21607 | 0.608033 | − | 0.793911i | \(-0.291959\pi\) | ||||
0.608033 | + | 0.793911i | \(0.291959\pi\) | |||||||
\(180\) | 4.45216e16i | 0.0404009i | ||||||||
\(181\) | − | 7.40013e17i | − | 0.642408i | −0.947010 | − | 0.321204i | \(-0.895913\pi\) | ||
0.947010 | − | 0.321204i | \(-0.104087\pi\) | |||||||
\(182\) | 4.28856e17 | + | 7.39332e17i | 0.356238 | + | 0.614141i | ||||
\(183\) | 2.54936e18 | 2.02685 | ||||||||
\(184\) | −1.02143e18 | −0.777436 | ||||||||
\(185\) | 6.89715e17i | 0.502685i | ||||||||
\(186\) | 2.63027e18 | 1.83610 | ||||||||
\(187\) | − | 7.63177e17i | − | 0.510378i | ||||||
\(188\) | − | 9.96348e16i | − | 0.0638481i | ||||||
\(189\) | 4.16165e17 | + | 7.17453e17i | 0.255606 | + | 0.440655i | ||||
\(190\) | 2.94588e16 | 0.0173455 | ||||||||
\(191\) | −5.02202e17 | −0.283538 | −0.141769 | − | 0.989900i | \(-0.545279\pi\) | ||||
−0.141769 | + | 0.989900i | \(0.545279\pi\) | |||||||
\(192\) | − | 2.01515e18i | − | 1.09118i | ||||||
\(193\) | −1.78225e18 | −0.925787 | −0.462893 | − | 0.886414i | \(-0.653189\pi\) | ||||
−0.462893 | + | 0.886414i | \(0.653189\pi\) | |||||||
\(194\) | 9.41171e17i | 0.469088i | ||||||||
\(195\) | 1.06917e18i | 0.511409i | ||||||||
\(196\) | 1.21734e17 | − | 2.12839e17i | 0.0558936 | − | 0.0977243i | ||||
\(197\) | −4.91399e16 | −0.0216623 | −0.0108311 | − | 0.999941i | \(-0.503448\pi\) | ||||
−0.0108311 | + | 0.999941i | \(0.503448\pi\) | |||||||
\(198\) | −3.93083e17 | −0.166403 | ||||||||
\(199\) | 9.47298e16i | 0.0385179i | 0.999815 | + | 0.0192589i | \(0.00613069\pi\) | ||||
−0.999815 | + | 0.0192589i | \(0.993869\pi\) | |||||||
\(200\) | −1.53003e18 | −0.597667 | ||||||||
\(201\) | − | 3.11260e17i | − | 0.116830i | ||||||
\(202\) | − | 5.40613e17i | − | 0.195019i | ||||||
\(203\) | −4.04678e17 | + | 2.34737e17i | −0.140327 | + | 0.0813979i | ||||
\(204\) | −8.23970e17 | −0.274707 | ||||||||
\(205\) | −1.83621e18 | −0.588696 | ||||||||
\(206\) | − | 3.21849e18i | − | 0.992463i | ||||||
\(207\) | −1.67114e18 | −0.495736 | ||||||||
\(208\) | 2.59384e18i | 0.740350i | ||||||||
\(209\) | 2.63182e16i | 0.00722913i | ||||||||
\(210\) | 2.62196e18 | − | 1.52089e18i | 0.693222 | − | 0.402109i | ||||
\(211\) | 3.32011e18 | 0.845070 | 0.422535 | − | 0.906347i | \(-0.361140\pi\) | ||||
0.422535 | + | 0.906347i | \(0.361140\pi\) | |||||||
\(212\) | −7.53373e17 | −0.184639 | ||||||||
\(213\) | 1.48148e18i | 0.349670i | ||||||||
\(214\) | 3.32721e18 | 0.756433 | ||||||||
\(215\) | − | 3.62968e18i | − | 0.794988i | ||||||
\(216\) | 2.25945e18i | 0.476841i | ||||||||
\(217\) | −3.39833e18 | − | 5.85860e18i | −0.691175 | − | 1.19156i | ||||
\(218\) | −7.01607e18 | −1.37544 | ||||||||
\(219\) | 6.93957e18 | 1.31153 | ||||||||
\(220\) | − | 9.81765e16i | − | 0.0178906i | ||||||
\(221\) | −7.39599e18 | −1.29975 | ||||||||
\(222\) | 6.57459e18i | 1.11441i | ||||||||
\(223\) | 9.94156e18i | 1.62561i | 0.582538 | + | 0.812804i | \(0.302060\pi\) | ||||
−0.582538 | + | 0.812804i | \(0.697940\pi\) | |||||||
\(224\) | 1.22885e18 | − | 7.12804e17i | 0.193871 | − | 0.112457i | ||||
\(225\) | −2.50326e18 | −0.381106 | ||||||||
\(226\) | 1.22929e19 | 1.80628 | ||||||||
\(227\) | 1.66245e18i | 0.235799i | 0.993026 | + | 0.117899i | \(0.0376161\pi\) | ||||
−0.993026 | + | 0.117899i | \(0.962384\pi\) | |||||||
\(228\) | 2.84147e16 | 0.00389103 | ||||||||
\(229\) | − | 8.16261e18i | − | 1.07931i | −0.841887 | − | 0.539654i | \(-0.818555\pi\) | ||
0.841887 | − | 0.539654i | \(-0.181445\pi\) | |||||||
\(230\) | − | 4.12486e18i | − | 0.526728i | ||||||
\(231\) | 1.35875e18 | + | 2.34243e18i | 0.167588 | + | 0.288916i | ||||
\(232\) | −1.27444e18 | −0.151850 | ||||||||
\(233\) | 8.50556e18 | 0.979164 | 0.489582 | − | 0.871957i | \(-0.337149\pi\) | ||||
0.489582 | + | 0.871957i | \(0.337149\pi\) | |||||||
\(234\) | 3.80939e18i | 0.423768i | ||||||||
\(235\) | −3.17163e18 | −0.340989 | ||||||||
\(236\) | − | 1.21960e18i | − | 0.126742i | ||||||
\(237\) | − | 1.70901e19i | − | 1.71695i | ||||||
\(238\) | 1.05208e19 | + | 1.81375e19i | 1.02196 | + | 1.76182i | ||||
\(239\) | −1.32313e18 | −0.124285 | −0.0621425 | − | 0.998067i | \(-0.519793\pi\) | ||||
−0.0621425 | + | 0.998067i | \(0.519793\pi\) | |||||||
\(240\) | 9.19880e18 | 0.835683 | ||||||||
\(241\) | − | 6.05493e17i | − | 0.0532075i | −0.999646 | − | 0.0266037i | \(-0.991531\pi\) | ||
0.999646 | − | 0.0266037i | \(-0.00846923\pi\) | |||||||
\(242\) | −1.15408e19 | −0.981101 | ||||||||
\(243\) | 1.28666e19i | 1.05831i | ||||||||
\(244\) | 2.26863e18i | 0.180570i | ||||||||
\(245\) | −6.77522e18 | − | 3.87510e18i | −0.521909 | − | 0.298507i | ||||
\(246\) | −1.75033e19 | −1.30509 | ||||||||
\(247\) | 2.55051e17 | 0.0184099 | ||||||||
\(248\) | − | 1.84503e19i | − | 1.28941i | ||||||
\(249\) | −2.25826e19 | −1.52820 | ||||||||
\(250\) | − | 1.58557e19i | − | 1.03912i | ||||||
\(251\) | 1.98557e18i | 0.126036i | 0.998012 | + | 0.0630180i | \(0.0200725\pi\) | ||||
−0.998012 | + | 0.0630180i | \(0.979927\pi\) | |||||||
\(252\) | 9.45290e17 | − | 5.48324e17i | 0.0581247 | − | 0.0337157i | ||||
\(253\) | 3.68510e18 | 0.219526 | ||||||||
\(254\) | −1.32105e19 | −0.762515 | ||||||||
\(255\) | 2.62291e19i | 1.46711i | ||||||||
\(256\) | 6.15417e18 | 0.333618 | ||||||||
\(257\) | − | 6.45607e18i | − | 0.339237i | −0.985510 | − | 0.169618i | \(-0.945746\pi\) | ||
0.985510 | − | 0.169618i | \(-0.0542535\pi\) | |||||||
\(258\) | − | 3.45993e19i | − | 1.76242i | ||||||
\(259\) | 1.46441e19 | − | 8.49445e18i | 0.723211 | − | 0.419505i | ||||
\(260\) | −9.51434e17 | −0.0455609 | ||||||||
\(261\) | −2.08509e18 | −0.0968281 | ||||||||
\(262\) | 9.91911e18i | 0.446748i | ||||||||
\(263\) | 1.26128e19 | 0.551019 | 0.275510 | − | 0.961298i | \(-0.411153\pi\) | ||||
0.275510 | + | 0.961298i | \(0.411153\pi\) | |||||||
\(264\) | 7.37696e18i | 0.312641i | ||||||||
\(265\) | 2.39818e19i | 0.986087i | ||||||||
\(266\) | −3.62812e17 | − | 6.25474e17i | −0.0144753 | − | 0.0249549i | ||||
\(267\) | 5.51777e19 | 2.13635 | ||||||||
\(268\) | 2.76985e17 | 0.0104083 | ||||||||
\(269\) | 3.28477e18i | 0.119808i | 0.998204 | + | 0.0599041i | \(0.0190795\pi\) | ||||
−0.998204 | + | 0.0599041i | \(0.980921\pi\) | |||||||
\(270\) | −9.12442e18 | −0.323069 | ||||||||
\(271\) | 2.99307e19i | 1.02888i | 0.857528 | + | 0.514438i | \(0.171999\pi\) | ||||
−0.857528 | + | 0.514438i | \(0.828001\pi\) | |||||||
\(272\) | 6.36331e19i | 2.12389i | ||||||||
\(273\) | 2.27007e19 | − | 1.31677e19i | 0.735762 | − | 0.426786i | ||||
\(274\) | −1.69795e19 | −0.534465 | ||||||||
\(275\) | 5.52004e18 | 0.168764 | ||||||||
\(276\) | − | 3.97866e18i | − | 0.118158i | ||||||
\(277\) | −1.52132e18 | −0.0438918 | −0.0219459 | − | 0.999759i | \(-0.506986\pi\) | ||||
−0.0219459 | + | 0.999759i | \(0.506986\pi\) | |||||||
\(278\) | − | 1.89822e19i | − | 0.532095i | ||||||
\(279\) | − | 3.01863e19i | − | 0.822198i | ||||||
\(280\) | −1.06685e19 | − | 1.83921e19i | −0.282383 | − | 0.486818i | ||||
\(281\) | 1.56025e19 | 0.401368 | 0.200684 | − | 0.979656i | \(-0.435684\pi\) | ||||
0.200684 | + | 0.979656i | \(0.435684\pi\) | |||||||
\(282\) | −3.02331e19 | −0.755944 | ||||||||
\(283\) | − | 7.38749e19i | − | 1.79558i | −0.440422 | − | 0.897791i | \(-0.645171\pi\) | ||
0.440422 | − | 0.897791i | \(-0.354829\pi\) | |||||||
\(284\) | −1.31834e18 | −0.0311517 | ||||||||
\(285\) | − | 9.04513e17i | − | 0.0207805i | ||||||
\(286\) | − | 8.40024e18i | − | 0.187656i | ||||||
\(287\) | 2.26145e19 | + | 3.89866e19i | 0.491284 | + | 0.846955i | ||||
\(288\) | 6.33161e18 | 0.133775 | ||||||||
\(289\) | −1.32780e20 | −2.72866 | ||||||||
\(290\) | − | 5.14661e18i | − | 0.102881i | ||||||
\(291\) | 2.88980e19 | 0.561984 | ||||||||
\(292\) | 6.17542e18i | 0.116843i | ||||||||
\(293\) | 5.85744e19i | 1.07837i | 0.842188 | + | 0.539184i | \(0.181267\pi\) | ||||
−0.842188 | + | 0.539184i | \(0.818733\pi\) | |||||||
\(294\) | −6.45836e19 | − | 3.69387e19i | −1.15703 | − | 0.661765i | ||||
\(295\) | −3.88231e19 | −0.676883 | ||||||||
\(296\) | 4.61183e19 | 0.782600 | ||||||||
\(297\) | − | 8.15166e18i | − | 0.134646i | ||||||
\(298\) | 7.52080e19 | 1.20930 | ||||||||
\(299\) | − | 3.57126e19i | − | 0.559051i | ||||||
\(300\) | − | 5.95976e18i | − | 0.0908361i | ||||||
\(301\) | −7.70659e19 | + | 4.47027e19i | −1.14375 | + | 0.663441i | ||||
\(302\) | 8.02496e19 | 1.15981 | ||||||||
\(303\) | −1.65992e19 | −0.233639 | ||||||||
\(304\) | − | 2.19439e18i | − | 0.0300833i | ||||||
\(305\) | 7.22165e19 | 0.964357 | ||||||||
\(306\) | 9.34532e19i | 1.21569i | ||||||||
\(307\) | − | 6.40668e19i | − | 0.811944i | −0.913885 | − | 0.405972i | \(-0.866933\pi\) | ||
0.913885 | − | 0.405972i | \(-0.133067\pi\) | |||||||
\(308\) | −2.08450e18 | + | 1.20913e18i | −0.0257392 | + | 0.0149303i | ||||
\(309\) | −9.88216e19 | −1.18901 | ||||||||
\(310\) | 7.45085e19 | 0.873599 | ||||||||
\(311\) | 8.73913e19i | 0.998585i | 0.866434 | + | 0.499292i | \(0.166407\pi\) | ||||
−0.866434 | + | 0.499292i | \(0.833593\pi\) | |||||||
\(312\) | 7.14906e19 | 0.796181 | ||||||||
\(313\) | − | 1.21318e20i | − | 1.31696i | −0.752599 | − | 0.658479i | \(-0.771200\pi\) | ||
0.752599 | − | 0.658479i | \(-0.228800\pi\) | |||||||
\(314\) | − | 8.04444e19i | − | 0.851253i | ||||||
\(315\) | −1.74546e19 | − | 3.00910e19i | −0.180063 | − | 0.310422i | ||||
\(316\) | 1.52082e19 | 0.152962 | ||||||||
\(317\) | 3.88718e19 | 0.381207 | 0.190603 | − | 0.981667i | \(-0.438956\pi\) | ||||
0.190603 | + | 0.981667i | \(0.438956\pi\) | |||||||
\(318\) | 2.28603e20i | 2.18607i | ||||||||
\(319\) | 4.59793e18 | 0.0428782 | ||||||||
\(320\) | − | 5.70838e19i | − | 0.519174i | ||||||
\(321\) | − | 1.02160e20i | − | 0.906233i | ||||||
\(322\) | −8.75796e19 | + | 5.08013e19i | −0.757802 | + | 0.439570i | ||||
\(323\) | 6.25701e18 | 0.0528137 | ||||||||
\(324\) | −1.69612e19 | −0.139668 | ||||||||
\(325\) | − | 5.34950e19i | − | 0.429780i | ||||||
\(326\) | 4.58588e19 | 0.359486 | ||||||||
\(327\) | 2.15424e20i | 1.64783i | ||||||||
\(328\) | 1.22779e20i | 0.916505i | ||||||||
\(329\) | 3.90615e19 | + | 6.73406e19i | 0.284565 | + | 0.490580i | ||||
\(330\) | −2.97906e19 | −0.211820 | ||||||||
\(331\) | −3.75319e19 | −0.260481 | −0.130241 | − | 0.991482i | \(-0.541575\pi\) | ||||
−0.130241 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(332\) | − | 2.00959e19i | − | 0.136146i | ||||||
\(333\) | 7.54535e19 | 0.499029 | ||||||||
\(334\) | − | 1.53931e20i | − | 0.993928i | ||||||
\(335\) | − | 8.81716e18i | − | 0.0555866i | ||||||
\(336\) | −1.13291e20 | − | 1.95310e20i | −0.697402 | − | 1.20229i | ||||
\(337\) | 1.01717e20 | 0.611438 | 0.305719 | − | 0.952122i | \(-0.401103\pi\) | ||||
0.305719 | + | 0.952122i | \(0.401103\pi\) | |||||||
\(338\) | 9.82725e19 | 0.576897 | ||||||||
\(339\) | − | 3.77444e20i | − | 2.16399i | ||||||
\(340\) | −2.33409e19 | −0.130703 | ||||||||
\(341\) | 6.65651e19i | 0.364092i | ||||||||
\(342\) | − | 3.22274e18i | − | 0.0172193i | ||||||
\(343\) | 1.16619e18 | + | 1.91578e20i | 0.00608719 | + | 0.999981i | ||||
\(344\) | −2.42701e20 | −1.23767 | ||||||||
\(345\) | −1.26651e20 | −0.631038 | ||||||||
\(346\) | − | 6.02977e19i | − | 0.293556i | ||||||
\(347\) | −9.51178e19 | −0.452508 | −0.226254 | − | 0.974068i | \(-0.572648\pi\) | ||||
−0.226254 | + | 0.974068i | \(0.572648\pi\) | |||||||
\(348\) | − | 4.96419e18i | − | 0.0230789i | ||||||
\(349\) | 9.81841e19i | 0.446106i | 0.974806 | + | 0.223053i | \(0.0716022\pi\) | ||||
−0.974806 | + | 0.223053i | \(0.928398\pi\) | |||||||
\(350\) | −1.31188e20 | + | 7.60969e19i | −0.582573 | + | 0.337927i | ||||
\(351\) | −7.89982e19 | −0.342894 | ||||||||
\(352\) | −1.39621e19 | −0.0592392 | ||||||||
\(353\) | 1.35608e20i | 0.562454i | 0.959641 | + | 0.281227i | \(0.0907414\pi\) | ||||
−0.959641 | + | 0.281227i | \(0.909259\pi\) | |||||||
\(354\) | −3.70075e20 | −1.50059 | ||||||||
\(355\) | 4.19663e19i | 0.166370i | ||||||||
\(356\) | 4.91018e19i | 0.190326i | ||||||||
\(357\) | 5.56901e20 | − | 3.23035e20i | 2.11073 | − | 1.22435i | ||||
\(358\) | 3.46088e20 | 1.28269 | ||||||||
\(359\) | −3.41215e20 | −1.23672 | −0.618362 | − | 0.785894i | \(-0.712203\pi\) | ||||
−0.618362 | + | 0.785894i | \(0.712203\pi\) | |||||||
\(360\) | − | 9.47648e19i | − | 0.335913i | ||||||
\(361\) | 2.88226e20 | 0.999252 | ||||||||
\(362\) | − | 1.99823e20i | − | 0.677604i | ||||||
\(363\) | 3.54353e20i | 1.17539i | ||||||||
\(364\) | 1.17178e19 | + | 2.02010e19i | 0.0380219 | + | 0.0655483i | ||||
\(365\) | 1.96580e20 | 0.624016 | ||||||||
\(366\) | 6.88392e20 | 2.13790 | ||||||||
\(367\) | 2.98843e20i | 0.908061i | 0.890986 | + | 0.454030i | \(0.150014\pi\) | ||||
−0.890986 | + | 0.454030i | \(0.849986\pi\) | |||||||
\(368\) | −3.07261e20 | −0.913535 | ||||||||
\(369\) | 2.00878e20i | 0.584414i | ||||||||
\(370\) | 1.86241e20i | 0.530226i | ||||||||
\(371\) | 5.09186e20 | − | 2.95358e20i | 1.41868 | − | 0.822919i | ||||
\(372\) | 7.18676e19 | 0.195970 | ||||||||
\(373\) | −1.02024e20 | −0.272291 | −0.136146 | − | 0.990689i | \(-0.543471\pi\) | ||||
−0.136146 | + | 0.990689i | \(0.543471\pi\) | |||||||
\(374\) | − | 2.06077e20i | − | 0.538341i | ||||||
\(375\) | −4.86837e20 | −1.24490 | ||||||||
\(376\) | 2.12074e20i | 0.530865i | ||||||||
\(377\) | − | 4.45588e19i | − | 0.109195i | ||||||
\(378\) | 1.12375e20 | + | 1.93731e20i | 0.269610 | + | 0.464798i | ||||
\(379\) | −5.93003e19 | −0.139297 | −0.0696487 | − | 0.997572i | \(-0.522188\pi\) | ||||
−0.0696487 | + | 0.997572i | \(0.522188\pi\) | |||||||
\(380\) | 8.04913e17 | 0.00185131 | ||||||||
\(381\) | 4.05618e20i | 0.913519i | ||||||||
\(382\) | −1.35607e20 | −0.299073 | ||||||||
\(383\) | − | 3.25031e20i | − | 0.701996i | −0.936376 | − | 0.350998i | \(-0.885842\pi\) | ||
0.936376 | − | 0.350998i | \(-0.114158\pi\) | |||||||
\(384\) | − | 6.78041e20i | − | 1.43419i | ||||||
\(385\) | 3.84898e19 | + | 6.63550e19i | 0.0797370 | + | 0.137464i | ||||
\(386\) | −4.81255e20 | −0.976510 | ||||||||
\(387\) | −3.97080e20 | −0.789206 | ||||||||
\(388\) | 2.57159e19i | 0.0500666i | ||||||||
\(389\) | −7.32963e20 | −1.39793 | −0.698964 | − | 0.715156i | \(-0.746355\pi\) | ||||
−0.698964 | + | 0.715156i | \(0.746355\pi\) | |||||||
\(390\) | 2.88702e20i | 0.539428i | ||||||||
\(391\) | − | 8.76113e20i | − | 1.60378i | ||||||
\(392\) | −2.59111e20 | + | 4.53030e20i | −0.464727 | + | 0.812528i | ||||
\(393\) | 3.04559e20 | 0.535219 | ||||||||
\(394\) | −1.32690e19 | −0.0228491 | ||||||||
\(395\) | − | 4.84118e20i | − | 0.816910i | ||||||
\(396\) | −1.07403e19 | −0.0177605 | ||||||||
\(397\) | − | 5.24892e20i | − | 0.850640i | −0.905043 | − | 0.425320i | \(-0.860161\pi\) | ||
0.905043 | − | 0.425320i | \(-0.139839\pi\) | |||||||
\(398\) | 2.55795e19i | 0.0406282i | ||||||||
\(399\) | −1.92048e19 | + | 1.11399e19i | −0.0298969 | + | 0.0173419i | ||||
\(400\) | −4.60256e20 | −0.702295 | ||||||||
\(401\) | 5.73775e20 | 0.858196 | 0.429098 | − | 0.903258i | \(-0.358831\pi\) | ||||
0.429098 | + | 0.903258i | \(0.358831\pi\) | |||||||
\(402\) | − | 8.40482e19i | − | 0.123231i | ||||||
\(403\) | 6.45086e20 | 0.927209 | ||||||||
\(404\) | − | 1.47714e19i | − | 0.0208147i | ||||||
\(405\) | 5.39919e20i | 0.745913i | ||||||||
\(406\) | −1.09274e20 | + | 6.33851e19i | −0.148015 | + | 0.0858576i | ||||
\(407\) | −1.66386e20 | −0.220984 | ||||||||
\(408\) | 1.75383e21 | 2.28405 | ||||||||
\(409\) | 6.43164e20i | 0.821363i | 0.911779 | + | 0.410682i | \(0.134709\pi\) | ||||
−0.911779 | + | 0.410682i | \(0.865291\pi\) | |||||||
\(410\) | −4.95824e20 | −0.620950 | ||||||||
\(411\) | 5.21343e20i | 0.640308i | ||||||||
\(412\) | − | 8.79398e19i | − | 0.105927i | ||||||
\(413\) | 4.78141e20 | + | 8.24297e20i | 0.564879 | + | 0.973831i | ||||
\(414\) | −4.51252e20 | −0.522897 | ||||||||
\(415\) | −6.39706e20 | −0.727102 | ||||||||
\(416\) | 1.35307e20i | 0.150860i | ||||||||
\(417\) | −5.82837e20 | −0.637468 | ||||||||
\(418\) | 7.10660e18i | 0.00762520i | ||||||||
\(419\) | − | 1.00606e20i | − | 0.105903i | −0.998597 | − | 0.0529517i | \(-0.983137\pi\) | ||
0.998597 | − | 0.0529517i | \(-0.0168630\pi\) | |||||||
\(420\) | 7.16407e19 | − | 4.15558e19i | 0.0739887 | − | 0.0429178i | ||||
\(421\) | 4.89798e20 | 0.496318 | 0.248159 | − | 0.968719i | \(-0.420174\pi\) | ||||
0.248159 | + | 0.968719i | \(0.420174\pi\) | |||||||
\(422\) | 8.96516e20 | 0.891371 | ||||||||
\(423\) | 3.46971e20i | 0.338509i | ||||||||
\(424\) | 1.60356e21 | 1.53518 | ||||||||
\(425\) | − | 1.31236e21i | − | 1.23294i | ||||||
\(426\) | 4.00037e20i | 0.368828i | ||||||||
\(427\) | −8.89411e20 | − | 1.53331e21i | −0.804784 | − | 1.38742i | ||||
\(428\) | 9.09105e19 | 0.0807354 | ||||||||
\(429\) | −2.57924e20 | −0.224819 | ||||||||
\(430\) | − | 9.80107e20i | − | 0.838544i | ||||||
\(431\) | −6.28051e20 | −0.527445 | −0.263722 | − | 0.964599i | \(-0.584950\pi\) | ||||
−0.263722 | + | 0.964599i | \(0.584950\pi\) | |||||||
\(432\) | 6.79679e20i | 0.560317i | ||||||||
\(433\) | 2.17005e21i | 1.75617i | 0.478503 | + | 0.878086i | \(0.341180\pi\) | ||||
−0.478503 | + | 0.878086i | \(0.658820\pi\) | |||||||
\(434\) | −9.17638e20 | − | 1.58197e21i | −0.729044 | − | 1.25684i | ||||
\(435\) | −1.58023e20 | −0.123256 | ||||||||
\(436\) | −1.91702e20 | −0.146803 | ||||||||
\(437\) | 3.02128e19i | 0.0227164i | ||||||||
\(438\) | 1.87386e21 | 1.38339 | ||||||||
\(439\) | 3.99198e19i | 0.0289383i | 0.999895 | + | 0.0144691i | \(0.00460583\pi\) | ||||
−0.999895 | + | 0.0144691i | \(0.995394\pi\) | |||||||
\(440\) | 2.08970e20i | 0.148752i | ||||||||
\(441\) | −4.23929e20 | + | 7.41196e20i | −0.296336 | + | 0.518113i | ||||
\(442\) | −1.99711e21 | −1.37096 | ||||||||
\(443\) | −8.43902e20 | −0.568934 | −0.284467 | − | 0.958686i | \(-0.591817\pi\) | ||||
−0.284467 | + | 0.958686i | \(0.591817\pi\) | |||||||
\(444\) | 1.79640e20i | 0.118943i | ||||||||
\(445\) | 1.56304e21 | 1.01646 | ||||||||
\(446\) | 2.68448e21i | 1.71467i | ||||||||
\(447\) | − | 2.30921e21i | − | 1.44878i | ||||||
\(448\) | −1.21201e21 | + | 7.03038e20i | −0.746935 | + | 0.433266i | ||||
\(449\) | 1.36329e21 | 0.825309 | 0.412654 | − | 0.910888i | \(-0.364602\pi\) | ||||
0.412654 | + | 0.910888i | \(0.364602\pi\) | |||||||
\(450\) | −6.75944e20 | −0.401986 | ||||||||
\(451\) | − | 4.42964e20i | − | 0.258795i | ||||||
\(452\) | 3.35882e20 | 0.192788 | ||||||||
\(453\) | − | 2.46401e21i | − | 1.38950i | ||||||
\(454\) | 4.48905e20i | 0.248718i | ||||||||
\(455\) | 6.43050e20 | − | 3.73007e20i | 0.350069 | − | 0.203061i | ||||
\(456\) | −6.04810e19 | −0.0323519 | ||||||||
\(457\) | −3.30364e21 | −1.73645 | −0.868227 | − | 0.496166i | \(-0.834741\pi\) | ||||
−0.868227 | + | 0.496166i | \(0.834741\pi\) | |||||||
\(458\) | − | 2.20412e21i | − | 1.13844i | ||||||
\(459\) | −1.93801e21 | −0.983682 | ||||||||
\(460\) | − | 1.12705e20i | − | 0.0562186i | ||||||
\(461\) | 2.21453e20i | 0.108561i | 0.998526 | + | 0.0542805i | \(0.0172865\pi\) | ||||
−0.998526 | + | 0.0542805i | \(0.982713\pi\) | |||||||
\(462\) | 3.66898e20 | + | 6.32518e20i | 0.176770 | + | 0.304745i | ||||
\(463\) | 3.87674e21 | 1.83577 | 0.917886 | − | 0.396844i | \(-0.129895\pi\) | ||||
0.917886 | + | 0.396844i | \(0.129895\pi\) | |||||||
\(464\) | −3.83371e20 | −0.178433 | ||||||||
\(465\) | − | 2.28773e21i | − | 1.04660i | ||||||
\(466\) | 2.29672e21 | 1.03281 | ||||||||
\(467\) | 4.03114e21i | 1.78194i | 0.454062 | + | 0.890970i | \(0.349975\pi\) | ||||
−0.454062 | + | 0.890970i | \(0.650025\pi\) | |||||||
\(468\) | 1.04085e20i | 0.0452295i | ||||||||
\(469\) | −1.87207e20 | + | 1.08591e20i | −0.0799724 | + | 0.0463887i | ||||
\(470\) | −8.56424e20 | −0.359671 | ||||||||
\(471\) | −2.46999e21 | −1.01983 | ||||||||
\(472\) | 2.59593e21i | 1.05380i | ||||||||
\(473\) | 8.75618e20 | 0.349482 | ||||||||
\(474\) | − | 4.61478e21i | − | 1.81102i | ||||||
\(475\) | 4.52568e19i | 0.0174636i | ||||||||
\(476\) | 2.87464e20 | + | 4.95577e20i | 0.109076 | + | 0.188042i | ||||
\(477\) | 2.62357e21 | 0.978915 | ||||||||
\(478\) | −3.57279e20 | −0.131094 | ||||||||
\(479\) | 4.96713e21i | 1.79235i | 0.443706 | + | 0.896173i | \(0.353664\pi\) | ||||
−0.443706 | + | 0.896173i | \(0.646336\pi\) | |||||||
\(480\) | 4.79854e20 | 0.170286 | ||||||||
\(481\) | 1.61245e21i | 0.562764i | ||||||||
\(482\) | − | 1.63499e20i | − | 0.0561226i | ||||||
\(483\) | 1.55982e21 | + | 2.68907e21i | 0.526620 | + | 0.907874i | ||||
\(484\) | −3.15333e20 | −0.104715 | ||||||||
\(485\) | 8.18604e20 | 0.267387 | ||||||||
\(486\) | 3.47431e21i | 1.11629i | ||||||||
\(487\) | 3.86397e21 | 1.22124 | 0.610621 | − | 0.791923i | \(-0.290920\pi\) | ||||
0.610621 | + | 0.791923i | \(0.290920\pi\) | |||||||
\(488\) | − | 4.82881e21i | − | 1.50135i | ||||||
\(489\) | − | 1.40806e21i | − | 0.430676i | ||||||
\(490\) | −1.82948e21 | − | 1.04638e21i | −0.550503 | − | 0.314861i | ||||
\(491\) | 4.87646e21 | 1.44362 | 0.721810 | − | 0.692091i | \(-0.243310\pi\) | ||||
0.721810 | + | 0.692091i | \(0.243310\pi\) | |||||||
\(492\) | −4.78250e20 | −0.139294 | ||||||||
\(493\) | − | 1.09313e21i | − | 0.313254i | ||||||
\(494\) | 6.88705e19 | 0.0194186 | ||||||||
\(495\) | 3.41892e20i | 0.0948523i | ||||||||
\(496\) | − | 5.55014e21i | − | 1.51513i | ||||||
\(497\) | 8.91035e20 | − | 5.16853e20i | 0.239356 | − | 0.138840i | ||||
\(498\) | −6.09789e21 | −1.61193 | ||||||||
\(499\) | −4.46501e21 | −1.16150 | −0.580749 | − | 0.814083i | \(-0.697240\pi\) | ||||
−0.580749 | + | 0.814083i | \(0.697240\pi\) | |||||||
\(500\) | − | 4.33229e20i | − | 0.110907i | ||||||
\(501\) | −4.72635e21 | −1.19076 | ||||||||
\(502\) | 5.36154e20i | 0.132941i | ||||||||
\(503\) | − | 7.17394e20i | − | 0.175071i | −0.996161 | − | 0.0875354i | \(-0.972101\pi\) | ||
0.996161 | − | 0.0875354i | \(-0.0278991\pi\) | |||||||
\(504\) | −2.01206e21 | + | 1.16711e21i | −0.483278 | + | 0.280329i | ||||
\(505\) | −4.70211e20 | −0.111163 | ||||||||
\(506\) | 9.95074e20 | 0.231553 | ||||||||
\(507\) | − | 3.01739e21i | − | 0.691143i | ||||||
\(508\) | −3.60954e20 | −0.0813845 | ||||||||
\(509\) | 3.26039e21i | 0.723648i | 0.932247 | + | 0.361824i | \(0.117846\pi\) | ||||
−0.932247 | + | 0.361824i | \(0.882154\pi\) | |||||||
\(510\) | 7.08254e21i | 1.54749i | ||||||||
\(511\) | −2.42105e21 | − | 4.17381e21i | −0.520760 | − | 0.897770i | ||||
\(512\) | −3.69780e21 | −0.783039 | ||||||||
\(513\) | 6.68325e19 | 0.0139331 | ||||||||
\(514\) | − | 1.74331e21i | − | 0.357823i | ||||||
\(515\) | −2.79935e21 | −0.565718 | ||||||||
\(516\) | − | 9.45368e20i | − | 0.188106i | ||||||
\(517\) | − | 7.65120e20i | − | 0.149901i | ||||||
\(518\) | 3.95429e21 | − | 2.29372e21i | 0.762835 | − | 0.442489i | ||||
\(519\) | −1.85140e21 | −0.351691 | ||||||||
\(520\) | 2.02514e21 | 0.378816 | ||||||||
\(521\) | − | 6.65810e21i | − | 1.22645i | −0.789909 | − | 0.613224i | \(-0.789872\pi\) | ||
0.789909 | − | 0.613224i | \(-0.210128\pi\) | |||||||
\(522\) | −5.63029e20 | −0.102133 | ||||||||
\(523\) | 5.30443e21i | 0.947600i | 0.880632 | + | 0.473800i | \(0.157118\pi\) | ||||
−0.880632 | + | 0.473800i | \(0.842882\pi\) | |||||||
\(524\) | 2.71023e20i | 0.0476821i | ||||||||
\(525\) | 2.33650e21 | + | 4.02805e21i | 0.404848 | + | 0.697943i | ||||
\(526\) | 3.40579e21 | 0.581209 | ||||||||
\(527\) | 1.58255e22 | 2.65994 | ||||||||
\(528\) | 2.21910e21i | 0.367372i | ||||||||
\(529\) | −1.90218e21 | −0.310174 | ||||||||
\(530\) | 6.47571e21i | 1.04011i | ||||||||
\(531\) | 4.24717e21i | 0.671960i | ||||||||
\(532\) | −9.91322e18 | − | 1.70900e19i | −0.00154498 | − | 0.00266348i | ||||
\(533\) | −4.29279e21 | −0.659055 | ||||||||
\(534\) | 1.48994e22 | 2.25340 | ||||||||
\(535\) | − | 2.89392e21i | − | 0.431177i | ||||||
\(536\) | −5.89566e20 | −0.0865395 | ||||||||
\(537\) | − | 1.06264e22i | − | 1.53671i | ||||||
\(538\) | 8.86973e20i | 0.126372i | ||||||||
\(539\) | 9.34822e20 | − | 1.63444e21i | 0.131226 | − | 0.229435i | ||||
\(540\) | −2.49309e20 | −0.0344817 | ||||||||
\(541\) | −7.19478e21 | −0.980481 | −0.490241 | − | 0.871587i | \(-0.663091\pi\) | ||||
−0.490241 | + | 0.871587i | \(0.663091\pi\) | |||||||
\(542\) | 8.08207e21i | 1.08525i | ||||||||
\(543\) | −6.13542e21 | −0.811794 | ||||||||
\(544\) | 3.31941e21i | 0.432782i | ||||||||
\(545\) | 6.10239e21i | 0.784021i | ||||||||
\(546\) | 6.12977e21 | − | 3.55563e21i | 0.776074 | − | 0.450169i | ||||
\(547\) | −5.53194e21 | −0.690206 | −0.345103 | − | 0.938565i | \(-0.612156\pi\) | ||||
−0.345103 | + | 0.938565i | \(0.612156\pi\) | |||||||
\(548\) | −4.63935e20 | −0.0570444 | ||||||||
\(549\) | − | 7.90035e21i | − | 0.957343i | ||||||
\(550\) | 1.49055e21 | 0.178011 | ||||||||
\(551\) | 3.76967e19i | 0.00443701i | ||||||||
\(552\) | 8.46861e21i | 0.982426i | ||||||||
\(553\) | −1.02789e22 | + | 5.96235e21i | −1.17529 | + | 0.681736i | ||||
\(554\) | −4.10797e20 | −0.0462966 | ||||||||
\(555\) | 5.71840e21 | 0.635229 | ||||||||
\(556\) | − | 5.18658e20i | − | 0.0567914i | ||||||
\(557\) | −8.43664e21 | −0.910600 | −0.455300 | − | 0.890338i | \(-0.650468\pi\) | ||||
−0.455300 | + | 0.890338i | \(0.650468\pi\) | |||||||
\(558\) | − | 8.15109e21i | − | 0.867245i | ||||||
\(559\) | − | 8.48566e21i | − | 0.890003i | ||||||
\(560\) | −3.20925e21 | − | 5.53262e21i | −0.331817 | − | 0.572041i | ||||
\(561\) | −6.32747e21 | −0.644952 | ||||||||
\(562\) | 4.21307e21 | 0.423359 | ||||||||
\(563\) | 1.43830e22i | 1.42489i | 0.701728 | + | 0.712444i | \(0.252412\pi\) | ||||
−0.701728 | + | 0.712444i | \(0.747588\pi\) | |||||||
\(564\) | −8.26068e20 | −0.0806832 | ||||||||
\(565\) | − | 1.06920e22i | − | 1.02961i | ||||||
\(566\) | − | 1.99481e22i | − | 1.89396i | ||||||
\(567\) | 1.14636e22 | − | 6.64959e21i | 1.07314 | − | 0.622487i | ||||
\(568\) | 2.80611e21 | 0.259011 | ||||||||
\(569\) | −4.27027e21 | −0.388648 | −0.194324 | − | 0.980937i | \(-0.562251\pi\) | ||||
−0.194324 | + | 0.980937i | \(0.562251\pi\) | |||||||
\(570\) | − | 2.44242e20i | − | 0.0219190i | ||||||
\(571\) | 5.15155e21 | 0.455879 | 0.227939 | − | 0.973675i | \(-0.426801\pi\) | ||||
0.227939 | + | 0.973675i | \(0.426801\pi\) | |||||||
\(572\) | − | 2.29522e20i | − | 0.0200289i | ||||||
\(573\) | 4.16374e21i | 0.358299i | ||||||||
\(574\) | 6.10651e21 | + | 1.05274e22i | 0.518201 | + | 0.893359i | ||||
\(575\) | 6.33690e21 | 0.530315 | ||||||||
\(576\) | −6.24486e21 | −0.515398 | ||||||||
\(577\) | 9.03400e21i | 0.735316i | 0.929961 | + | 0.367658i | \(0.119840\pi\) | ||||
−0.929961 | + | 0.367658i | \(0.880160\pi\) | |||||||
\(578\) | −3.58540e22 | −2.87816 | ||||||||
\(579\) | 1.47766e22i | 1.16989i | ||||||||
\(580\) | − | 1.40622e20i | − | 0.0109807i | ||||||
\(581\) | 7.87855e21 | + | 1.35823e22i | 0.606788 | + | 1.04608i | ||||
\(582\) | 7.80321e21 | 0.592775 | ||||||||
\(583\) | −5.78533e21 | −0.433491 | ||||||||
\(584\) | − | 1.31445e22i | − | 0.971493i | ||||||
\(585\) | 3.31330e21 | 0.241554 | ||||||||
\(586\) | 1.58166e22i | 1.13745i | ||||||||
\(587\) | − | 1.47426e22i | − | 1.04585i | −0.852378 | − | 0.522926i | \(-0.824840\pi\) | ||
0.852378 | − | 0.522926i | \(-0.175160\pi\) | |||||||
\(588\) | −1.76464e21 | − | 1.00929e21i | −0.123492 | − | 0.0706313i | ||||
\(589\) | −5.45743e20 | −0.0376761 | ||||||||
\(590\) | −1.04832e22 | −0.713969 | ||||||||
\(591\) | 4.07417e20i | 0.0273741i | ||||||||
\(592\) | 1.38731e22 | 0.919602 | ||||||||
\(593\) | − | 1.70778e22i | − | 1.11685i | −0.829555 | − | 0.558425i | \(-0.811406\pi\) | ||
0.829555 | − | 0.558425i | \(-0.188594\pi\) | |||||||
\(594\) | − | 2.20116e21i | − | 0.142023i | ||||||
\(595\) | 1.57755e22 | − | 9.15073e21i | 1.00426 | − | 0.582532i | ||||
\(596\) | 2.05493e21 | 0.129071 | ||||||||
\(597\) | 7.85402e20 | 0.0486740 | ||||||||
\(598\) | − | 9.64332e21i | − | 0.589681i | ||||||
\(599\) | 2.23629e22 | 1.34931 | 0.674657 | − | 0.738131i | \(-0.264292\pi\) | ||||
0.674657 | + | 0.738131i | \(0.264292\pi\) | |||||||
\(600\) | 1.26854e22i | 0.755256i | ||||||||
\(601\) | − | 1.53685e21i | − | 0.0902890i | −0.998980 | − | 0.0451445i | \(-0.985625\pi\) | ||
0.998980 | − | 0.0451445i | \(-0.0143748\pi\) | |||||||
\(602\) | −2.08098e22 | + | 1.20709e22i | −1.20641 | + | 0.699790i | ||||
\(603\) | −9.64581e20 | −0.0551824 | ||||||||
\(604\) | 2.19269e21 | 0.123789 | ||||||||
\(605\) | 1.00379e22i | 0.559241i | ||||||||
\(606\) | −4.48221e21 | −0.246440 | ||||||||
\(607\) | 6.64708e21i | 0.360680i | 0.983604 | + | 0.180340i | \(0.0577198\pi\) | ||||
−0.983604 | + | 0.180340i | \(0.942280\pi\) | |||||||
\(608\) | − | 1.14470e20i | − | 0.00613004i | ||||||
\(609\) | 1.94620e21 | + | 3.35517e21i | 0.102860 | + | 0.177328i | ||||
\(610\) | 1.95003e22 | 1.01719 | ||||||||
\(611\) | −7.41482e21 | −0.381743 | ||||||||
\(612\) | 2.55345e21i | 0.129753i | ||||||||
\(613\) | 2.31810e22 | 1.16265 | 0.581325 | − | 0.813672i | \(-0.302535\pi\) | ||||
0.581325 | + | 0.813672i | \(0.302535\pi\) | |||||||
\(614\) | − | 1.72997e22i | − | 0.856430i | ||||||
\(615\) | 1.52239e22i | 0.743919i | ||||||||
\(616\) | 4.43688e21 | − | 2.57365e21i | 0.214009 | − | 0.124138i | ||||
\(617\) | 7.42512e21 | 0.353527 | 0.176763 | − | 0.984253i | \(-0.443437\pi\) | ||||
0.176763 | + | 0.984253i | \(0.443437\pi\) | |||||||
\(618\) | −2.66844e22 | −1.25415 | ||||||||
\(619\) | 3.07234e22i | 1.42543i | 0.701456 | + | 0.712713i | \(0.252534\pi\) | ||||
−0.701456 | + | 0.712713i | \(0.747466\pi\) | |||||||
\(620\) | 2.03582e21 | 0.0932407 | ||||||||
\(621\) | − | 9.35795e21i | − | 0.423105i | ||||||
\(622\) | 2.35979e22i | 1.05330i | ||||||||
\(623\) | −1.92502e22 | − | 3.31866e22i | −0.848264 | − | 1.46238i | ||||
\(624\) | 2.15055e22 | 0.935561 | ||||||||
\(625\) | 1.07554e21 | 0.0461940 | ||||||||
\(626\) | − | 3.27591e22i | − | 1.38911i | ||||||
\(627\) | 2.18203e20 | 0.00913526 | ||||||||
\(628\) | − | 2.19801e21i | − | 0.0908557i | ||||||
\(629\) | 3.95572e22i | 1.61444i | ||||||||
\(630\) | −4.71319e21 | − | 8.12536e21i | −0.189929 | − | 0.327430i | ||||
\(631\) | −4.05650e22 | −1.61405 | −0.807024 | − | 0.590519i | \(-0.798923\pi\) | ||||
−0.807024 | + | 0.590519i | \(0.798923\pi\) | |||||||
\(632\) | −3.23709e22 | −1.27180 | ||||||||
\(633\) | − | 2.75269e22i | − | 1.06789i | ||||||
\(634\) | 1.04964e22 | 0.402093 | ||||||||
\(635\) | 1.14901e22i | 0.434644i | ||||||||
\(636\) | 6.24619e21i | 0.233323i | ||||||||
\(637\) | −1.58395e22 | − | 9.05942e21i | −0.584286 | − | 0.334183i | ||||
\(638\) | 1.24156e21 | 0.0452274 | ||||||||
\(639\) | 4.59104e21 | 0.165160 | ||||||||
\(640\) | − | 1.92071e22i | − | 0.682374i | ||||||
\(641\) | −3.39412e21 | −0.119087 | −0.0595434 | − | 0.998226i | \(-0.518964\pi\) | ||||
−0.0595434 | + | 0.998226i | \(0.518964\pi\) | |||||||
\(642\) | − | 2.75858e22i | − | 0.955884i | ||||||
\(643\) | − | 3.99482e22i | − | 1.36713i | −0.729890 | − | 0.683564i | \(-0.760429\pi\) | ||
0.729890 | − | 0.683564i | \(-0.239571\pi\) | |||||||
\(644\) | −2.39296e21 | + | 1.38806e21i | −0.0808815 | + | 0.0469160i | ||||
\(645\) | −3.00935e22 | −1.00461 | ||||||||
\(646\) | 1.68955e21 | 0.0557073 | ||||||||
\(647\) | − | 1.45003e21i | − | 0.0472219i | −0.999721 | − | 0.0236109i | \(-0.992484\pi\) | ||
0.999721 | − | 0.0236109i | \(-0.00751630\pi\) | |||||||
\(648\) | 3.61021e22 | 1.16127 | ||||||||
\(649\) | − | 9.36561e21i | − | 0.297563i | ||||||
\(650\) | − | 1.44450e22i | − | 0.453327i | ||||||
\(651\) | −4.85735e22 | + | 2.81755e22i | −1.50574 | + | 0.873420i | ||||
\(652\) | 1.25301e21 | 0.0383685 | ||||||||
\(653\) | 5.55769e22 | 1.68108 | 0.840541 | − | 0.541747i | \(-0.182237\pi\) | ||||
0.840541 | + | 0.541747i | \(0.182237\pi\) | |||||||
\(654\) | 5.81700e22i | 1.73811i | ||||||||
\(655\) | 8.62736e21 | 0.254652 | ||||||||
\(656\) | 3.69340e22i | 1.07695i | ||||||||
\(657\) | − | 2.15054e22i | − | 0.619478i | ||||||
\(658\) | 1.05476e22 | + | 1.81837e22i | 0.300156 | + | 0.517458i | ||||
\(659\) | 1.64988e22 | 0.463842 | 0.231921 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231921 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(660\) | −8.13977e20 | −0.0226079 | ||||||||
\(661\) | − | 2.01529e22i | − | 0.553001i | −0.961014 | − | 0.276500i | \(-0.910825\pi\) | ||
0.961014 | − | 0.276500i | \(-0.0891747\pi\) | |||||||
\(662\) | −1.01346e22 | −0.274753 | ||||||||
\(663\) | 6.13199e22i | 1.64245i | ||||||||
\(664\) | 4.27744e22i | 1.13198i | ||||||||
\(665\) | −5.44020e20 | + | 3.15564e20i | −0.0142247 | + | 0.00825114i | ||||
\(666\) | 2.03744e22 | 0.526370 | ||||||||
\(667\) | 5.27834e21 | 0.134738 | ||||||||
\(668\) | − | 4.20591e21i | − | 0.106084i | ||||||
\(669\) | 8.24251e22 | 2.05424 | ||||||||
\(670\) | − | 2.38086e21i | − | 0.0586322i | ||||||
\(671\) | 1.74214e22i | 0.423938i | ||||||||
\(672\) | −5.90983e21 | − | 1.01883e22i | −0.142109 | − | 0.244990i | ||||
\(673\) | −2.75005e22 | −0.653462 | −0.326731 | − | 0.945117i | \(-0.605947\pi\) | ||||
−0.326731 | + | 0.945117i | \(0.605947\pi\) | |||||||
\(674\) | 2.74661e22 | 0.644938 | ||||||||
\(675\) | − | 1.40176e22i | − | 0.325269i | ||||||
\(676\) | 2.68513e21 | 0.0615732 | ||||||||
\(677\) | − | 2.28197e22i | − | 0.517131i | −0.965994 | − | 0.258566i | \(-0.916750\pi\) | ||
0.965994 | − | 0.258566i | \(-0.0832498\pi\) | |||||||
\(678\) | − | 1.01920e23i | − | 2.28255i | ||||||
\(679\) | −1.00818e22 | − | 1.73807e22i | −0.223142 | − | 0.384689i | ||||
\(680\) | 4.96814e22 | 1.08673 | ||||||||
\(681\) | 1.37833e22 | 0.297973 | ||||||||
\(682\) | 1.79743e22i | 0.384040i | ||||||||
\(683\) | 1.27757e22 | 0.269786 | 0.134893 | − | 0.990860i | \(-0.456931\pi\) | ||||
0.134893 | + | 0.990860i | \(0.456931\pi\) | |||||||
\(684\) | − | 8.80560e19i | − | 0.00183785i | ||||||
\(685\) | 1.47683e22i | 0.304652i | ||||||||
\(686\) | 3.14902e20 | + | 5.17309e22i | 0.00642070 | + | 1.05477i | ||||
\(687\) | −6.76759e22 | −1.36389 | ||||||||
\(688\) | −7.30083e22 | −1.45434 | ||||||||
\(689\) | 5.60660e22i | 1.10394i | ||||||||
\(690\) | −3.41990e22 | −0.665612 | ||||||||
\(691\) | − | 9.51389e22i | − | 1.83035i | −0.403058 | − | 0.915175i | \(-0.632053\pi\) | ||
0.403058 | − | 0.915175i | \(-0.367947\pi\) | |||||||
\(692\) | − | 1.64753e21i | − | 0.0313318i | ||||||
\(693\) | 7.25911e21 | − | 4.21071e21i | 0.136464 | − | 0.0791570i | ||||
\(694\) | −2.56843e22 | −0.477300 | ||||||||
\(695\) | −1.65102e22 | −0.303302 | ||||||||
\(696\) | 1.05663e22i | 0.191889i | ||||||||
\(697\) | −1.05312e23 | −1.89067 | ||||||||
\(698\) | 2.65123e22i | 0.470547i | ||||||||
\(699\) | − | 7.05193e22i | − | 1.23734i | ||||||
\(700\) | −3.58450e21 | + | 2.07922e21i | −0.0621790 | + | 0.0360675i | ||||
\(701\) | 3.40641e22 | 0.584188 | 0.292094 | − | 0.956390i | \(-0.405648\pi\) | ||||
0.292094 | + | 0.956390i | \(0.405648\pi\) | |||||||
\(702\) | −2.13316e22 | −0.361681 | ||||||||
\(703\) | − | 1.36413e21i | − | 0.0228673i | ||||||
\(704\) | 1.37708e22 | 0.228233 | ||||||||
\(705\) | 2.62959e22i | 0.430899i | ||||||||
\(706\) | 3.66176e22i | 0.593270i | ||||||||
\(707\) | 5.79106e21 | + | 9.98358e21i | 0.0927690 | + | 0.159930i | ||||
\(708\) | −1.01117e22 | −0.160161 | ||||||||
\(709\) | 5.37960e22 | 0.842520 | 0.421260 | − | 0.906940i | \(-0.361588\pi\) | ||||
0.421260 | + | 0.906940i | \(0.361588\pi\) | |||||||
\(710\) | 1.13320e22i | 0.175485i | ||||||||
\(711\) | −5.29616e22 | −0.810969 | ||||||||
\(712\) | − | 1.04514e23i | − | 1.58246i | ||||||
\(713\) | 7.64155e22i | 1.14410i | ||||||||
\(714\) | 1.50378e23 | − | 8.72279e22i | 2.22637 | − | 1.29143i | ||||
\(715\) | −7.30630e21 | −0.106967 | ||||||||
\(716\) | 9.45628e21 | 0.136904 | ||||||||
\(717\) | 1.09700e22i | 0.157056i | ||||||||
\(718\) | −9.21369e22 | −1.30448 | ||||||||
\(719\) | − | 2.58679e22i | − | 0.362184i | −0.983466 | − | 0.181092i | \(-0.942037\pi\) | ||
0.983466 | − | 0.181092i | \(-0.0579632\pi\) | |||||||
\(720\) | − | 2.85067e22i | − | 0.394718i | ||||||
\(721\) | 3.44765e22 | + | 5.94363e22i | 0.472108 | + | 0.813897i | ||||
\(722\) | 7.78284e22 | 1.05400 | ||||||||
\(723\) | −5.02012e21 | −0.0672369 | ||||||||
\(724\) | − | 5.45982e21i | − | 0.0723219i | ||||||
\(725\) | 7.90659e21 | 0.103582 | ||||||||
\(726\) | 9.56845e22i | 1.23979i | ||||||||
\(727\) | 5.69842e22i | 0.730263i | 0.930956 | + | 0.365132i | \(0.118976\pi\) | ||||
−0.930956 | + | 0.365132i | \(0.881024\pi\) | |||||||
\(728\) | −2.49414e22 | − | 4.29980e22i | −0.316133 | − | 0.545001i | ||||
\(729\) | 7.71693e21 | 0.0967441 | ||||||||
\(730\) | 5.30816e22 | 0.658205 | ||||||||
\(731\) | − | 2.08173e23i | − | 2.55321i | ||||||
\(732\) | 1.88092e22 | 0.228182 | ||||||||
\(733\) | 1.16231e23i | 1.39473i | 0.716718 | + | 0.697364i | \(0.245644\pi\) | ||||
−0.716718 | + | 0.697364i | \(0.754356\pi\) | |||||||
\(734\) | 8.06954e22i | 0.957812i | ||||||||
\(735\) | −3.21283e22 | + | 5.61731e22i | −0.377215 | + | 0.659522i | ||||
\(736\) | −1.60282e22 | −0.186150 | ||||||||
\(737\) | 2.12704e21 | 0.0244363 | ||||||||
\(738\) | 5.42422e22i | 0.616433i | ||||||||
\(739\) | −7.73065e22 | −0.869082 | −0.434541 | − | 0.900652i | \(-0.643089\pi\) | ||||
−0.434541 | + | 0.900652i | \(0.643089\pi\) | |||||||
\(740\) | 5.08872e21i | 0.0565919i | ||||||||
\(741\) | − | 2.11462e21i | − | 0.0232641i | ||||||
\(742\) | 1.37493e23 | − | 7.97542e22i | 1.49641 | − | 0.868005i | ||||
\(743\) | 1.03344e23 | 1.11269 | 0.556344 | − | 0.830952i | \(-0.312204\pi\) | ||||
0.556344 | + | 0.830952i | \(0.312204\pi\) | |||||||
\(744\) | −1.52971e23 | −1.62939 | ||||||||
\(745\) | − | 6.54139e22i | − | 0.689318i | ||||||
\(746\) | −2.75492e22 | −0.287210 | ||||||||
\(747\) | 6.99826e22i | 0.721814i | ||||||||
\(748\) | − | 5.63072e21i | − | 0.0574581i | ||||||
\(749\) | −6.14441e22 | + | 3.56412e22i | −0.620334 | + | 0.359830i | ||||
\(750\) | −1.31459e23 | −1.31310 | ||||||||
\(751\) | 1.59317e23 | 1.57450 | 0.787248 | − | 0.616636i | \(-0.211505\pi\) | ||||
0.787248 | + | 0.616636i | \(0.211505\pi\) | |||||||
\(752\) | 6.37951e22i | 0.623799i | ||||||||
\(753\) | 1.64623e22 | 0.159268 | ||||||||
\(754\) | − | 1.20320e22i | − | 0.115178i | ||||||
\(755\) | − | 6.97989e22i | − | 0.661109i | ||||||
\(756\) | 3.07047e21 | + | 5.29337e21i | 0.0287760 | + | 0.0496087i | ||||
\(757\) | 8.52662e22 | 0.790697 | 0.395348 | − | 0.918531i | \(-0.370624\pi\) | ||||
0.395348 | + | 0.918531i | \(0.370624\pi\) | |||||||
\(758\) | −1.60126e22 | −0.146929 | ||||||||
\(759\) | − | 3.05531e22i | − | 0.277409i | ||||||
\(760\) | −1.71327e21 | −0.0153927 | ||||||||
\(761\) | − | 8.00060e22i | − | 0.711287i | −0.934622 | − | 0.355644i | \(-0.884262\pi\) | ||
0.934622 | − | 0.355644i | \(-0.115738\pi\) | |||||||
\(762\) | 1.09527e23i | 0.963570i | ||||||||
\(763\) | 1.29567e23 | − | 7.51564e22i | 1.12797 | − | 0.654289i | ||||
\(764\) | −3.70525e21 | −0.0319205 | ||||||||
\(765\) | 8.12830e22 | 0.692960 | ||||||||
\(766\) | − | 8.77669e22i | − | 0.740458i | ||||||
\(767\) | −9.07627e22 | −0.757783 | ||||||||
\(768\) | − | 5.10240e22i | − | 0.421585i | ||||||
\(769\) | − | 6.29296e22i | − | 0.514570i | −0.966336 | − | 0.257285i | \(-0.917172\pi\) | ||
0.966336 | − | 0.257285i | \(-0.0828279\pi\) | |||||||
\(770\) | 1.03932e22 | + | 1.79176e22i | 0.0841057 | + | 0.144995i | ||||
\(771\) | −5.35270e22 | −0.428685 | ||||||||
\(772\) | −1.31495e22 | −0.104225 | ||||||||
\(773\) | 2.31126e23i | 1.81306i | 0.422139 | + | 0.906531i | \(0.361279\pi\) | ||||
−0.422139 | + | 0.906531i | \(0.638721\pi\) | |||||||
\(774\) | −1.07222e23 | −0.832446 | ||||||||
\(775\) | 1.14465e23i | 0.879549i | ||||||||
\(776\) | − | 5.47366e22i | − | 0.416279i | ||||||
\(777\) | −7.04272e22 | − | 1.21414e23i | −0.530118 | − | 0.913903i | ||||
\(778\) | −1.97919e23 | −1.47452 | ||||||||
\(779\) | 3.63170e21 | 0.0267800 | ||||||||
\(780\) | 7.88831e21i | 0.0575741i | ||||||||
\(781\) | −1.01239e22 | −0.0731373 | ||||||||
\(782\) | − | 2.36573e23i | − | 1.69165i | ||||||
\(783\) | − | 1.16760e22i | − | 0.0826417i | ||||||
\(784\) | −7.79447e22 | + | 1.36278e23i | −0.546083 | + | 0.954770i | ||||
\(785\) | −6.99683e22 | −0.485226 | ||||||||
\(786\) | 8.22390e22 | 0.564543 | ||||||||
\(787\) | 2.83630e23i | 1.92732i | 0.267133 | + | 0.963660i | \(0.413924\pi\) | ||||
−0.267133 | + | 0.963660i | \(0.586076\pi\) | |||||||
\(788\) | −3.62554e20 | −0.00243873 | ||||||||
\(789\) | − | 1.04573e23i | − | 0.696309i | ||||||
\(790\) | − | 1.30724e23i | − | 0.861668i | ||||||
\(791\) | −2.27014e23 | + | 1.31681e23i | −1.48129 | + | 0.859237i | ||||
\(792\) | 2.28609e22 | 0.147670 | ||||||||
\(793\) | 1.68832e23 | 1.07961 | ||||||||
\(794\) | − | 1.41734e23i | − | 0.897246i | ||||||
\(795\) | 1.98832e23 | 1.24609 | ||||||||
\(796\) | 6.98917e20i | 0.00433632i | ||||||||
\(797\) | − | 1.11760e23i | − | 0.686468i | −0.939250 | − | 0.343234i | \(-0.888478\pi\) | ||
0.939250 | − | 0.343234i | \(-0.111522\pi\) | |||||||
\(798\) | −5.18578e21 | + | 3.00806e21i | −0.0315349 | + | 0.0182921i | ||||
\(799\) | −1.81903e23 | −1.09513 | ||||||||
\(800\) | −2.40092e22 | −0.143106 | ||||||||
\(801\) | − | 1.70993e23i | − | 1.00907i | ||||||
\(802\) | 1.54934e23 | 0.905216 | ||||||||
\(803\) | 4.74225e22i | 0.274322i | ||||||||
\(804\) | − | 2.29648e21i | − | 0.0131527i | ||||||
\(805\) | 4.41856e22 | + | 7.61743e22i | 0.250561 | + | 0.431958i | ||||
\(806\) | 1.74190e23 | 0.978009 | ||||||||
\(807\) | 2.72339e22 | 0.151399 | ||||||||
\(808\) | 3.14410e22i | 0.173063i | ||||||||
\(809\) | −1.09796e23 | −0.598407 | −0.299203 | − | 0.954189i | \(-0.596721\pi\) | ||||
−0.299203 | + | 0.954189i | \(0.596721\pi\) | |||||||
\(810\) | 1.45792e23i | 0.786781i | ||||||||
\(811\) | 1.21306e23i | 0.648209i | 0.946021 | + | 0.324105i | \(0.105063\pi\) | ||||
−0.946021 | + | 0.324105i | \(0.894937\pi\) | |||||||
\(812\) | −2.98572e21 | + | 1.73189e21i | −0.0157979 | + | 0.00916373i | ||||
\(813\) | 2.48154e23 | 1.30016 | ||||||||
\(814\) | −4.49284e22 | −0.233091 | ||||||||
\(815\) | − | 3.98867e22i | − | 0.204912i | ||||||
\(816\) | 5.27579e23 | 2.68390 | ||||||||
\(817\) | 7.17887e21i | 0.0361643i | ||||||||
\(818\) | 1.73671e23i | 0.866365i | ||||||||
\(819\) | −4.08063e22 | − | 7.03485e22i | −0.201584 | − | 0.347523i | ||||
\(820\) | −1.35475e22 | −0.0662750 | ||||||||
\(821\) | −1.80834e23 | −0.876064 | −0.438032 | − | 0.898959i | \(-0.644324\pi\) | ||||
−0.438032 | + | 0.898959i | \(0.644324\pi\) | |||||||
\(822\) | 1.40776e23i | 0.675389i | ||||||||
\(823\) | 9.66562e22 | 0.459231 | 0.229615 | − | 0.973281i | \(-0.426253\pi\) | ||||
0.229615 | + | 0.973281i | \(0.426253\pi\) | |||||||
\(824\) | 1.87181e23i | 0.880732i | ||||||||
\(825\) | − | 4.57664e22i | − | 0.213263i | ||||||
\(826\) | 1.29110e23 | + | 2.22582e23i | 0.595828 | + | 1.02719i | ||||
\(827\) | 9.96977e22 | 0.455660 | 0.227830 | − | 0.973701i | \(-0.426837\pi\) | ||||
0.227830 | + | 0.973701i | \(0.426837\pi\) | |||||||
\(828\) | −1.23297e22 | −0.0558097 | ||||||||
\(829\) | − | 3.66051e22i | − | 0.164099i | −0.996628 | − | 0.0820494i | \(-0.973853\pi\) | ||
0.996628 | − | 0.0820494i | \(-0.0261465\pi\) | |||||||
\(830\) | −1.72737e23 | −0.766939 | ||||||||
\(831\) | 1.26132e22i | 0.0554650i | ||||||||
\(832\) | − | 1.33454e23i | − | 0.581224i | ||||||
\(833\) | −3.88579e23 | − | 2.22249e23i | −1.67618 | − | 0.958692i | ||||
\(834\) | −1.57381e23 | −0.672394 | ||||||||
\(835\) | −1.33885e23 | −0.566553 | ||||||||
\(836\) | 1.94176e20i | 0.000813851i | ||||||||
\(837\) | 1.69035e23 | 0.701736 | ||||||||
\(838\) | − | 2.71661e22i | − | 0.111706i | ||||||
\(839\) | − | 1.78047e23i | − | 0.725168i | −0.931951 | − | 0.362584i | \(-0.881895\pi\) | ||
0.931951 | − | 0.362584i | \(-0.118105\pi\) | |||||||
\(840\) | −1.52488e23 | + | 8.84521e22i | −0.615179 | + | 0.356840i | ||||
\(841\) | −2.43661e23 | −0.973683 | ||||||||
\(842\) | 1.32258e23 | 0.523511 | ||||||||
\(843\) | − | 1.29360e23i | − | 0.507199i | ||||||
\(844\) | 2.44958e22 | 0.0951375 | ||||||||
\(845\) | − | 8.54747e22i | − | 0.328839i | ||||||
\(846\) | 9.36911e22i | 0.357055i | ||||||||
\(847\) | 2.13126e23 | − | 1.23626e23i | 0.804579 | − | 0.466703i | ||||
\(848\) | 4.82377e23 | 1.80393 | ||||||||
\(849\) | −6.12494e23 | −2.26903 | ||||||||
\(850\) | − | 3.54371e23i | − | 1.30049i | ||||||
\(851\) | −1.91008e23 | −0.694407 | ||||||||
\(852\) | 1.09303e22i | 0.0393656i | ||||||||
\(853\) | 1.04907e23i | 0.374294i | 0.982332 | + | 0.187147i | \(0.0599240\pi\) | ||||
−0.982332 | + | 0.187147i | \(0.940076\pi\) | |||||||
\(854\) | −2.40164e23 | − | 4.14034e23i | −0.848878 | − | 1.46343i | ||||
\(855\) | −2.80305e21 | −0.00981527 | ||||||||
\(856\) | −1.93504e23 | −0.671274 | ||||||||
\(857\) | 1.62445e23i | 0.558290i | 0.960249 | + | 0.279145i | \(0.0900510\pi\) | ||||
−0.960249 | + | 0.279145i | \(0.909949\pi\) | |||||||
\(858\) | −6.96461e22 | −0.237136 | ||||||||
\(859\) | − | 4.43943e23i | − | 1.49755i | −0.662824 | − | 0.748775i | \(-0.730642\pi\) | ||
0.662824 | − | 0.748775i | \(-0.269358\pi\) | |||||||
\(860\) | − | 2.67798e22i | − | 0.0894993i | ||||||
\(861\) | 3.23237e23 | − | 1.87496e23i | 1.07028 | − | 0.620823i | ||||
\(862\) | −1.69590e23 | −0.556343 | ||||||||
\(863\) | −6.65298e22 | −0.216237 | −0.108118 | − | 0.994138i | \(-0.534483\pi\) | ||||
−0.108118 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(864\) | 3.54553e22i | 0.114175i | ||||||||
\(865\) | −5.24452e22 | −0.167331 | ||||||||
\(866\) | 5.85970e23i | 1.85239i | ||||||||
\(867\) | 1.10087e24i | 3.44813i | ||||||||
\(868\) | −2.50729e22 | − | 4.32248e22i | −0.0778121 | − | 0.134145i | ||||
\(869\) | 1.16788e23 | 0.359120 | ||||||||
\(870\) | −4.26704e22 | −0.130009 | ||||||||
\(871\) | − | 2.06133e22i | − | 0.0622302i | ||||||
\(872\) | 4.08041e23 | 1.22060 | ||||||||
\(873\) | − | 8.95538e22i | − | 0.265442i | ||||||
\(874\) | 8.15824e21i | 0.0239610i | ||||||||
\(875\) | 1.69846e23 | + | 2.92809e23i | 0.494301 | + | 0.852157i | ||||
\(876\) | 5.12002e22 | 0.147652 | ||||||||
\(877\) | −1.76354e23 | −0.503952 | −0.251976 | − | 0.967733i | \(-0.581080\pi\) | ||||
−0.251976 | + | 0.967733i | \(0.581080\pi\) | |||||||
\(878\) | 1.07794e22i | 0.0305237i | ||||||||
\(879\) | 4.85638e23 | 1.36270 | ||||||||
\(880\) | 6.28613e22i | 0.174792i | ||||||||
\(881\) | − | 3.97774e23i | − | 1.09605i | −0.836463 | − | 0.548024i | \(-0.815380\pi\) | ||
0.836463 | − | 0.548024i | \(-0.184620\pi\) | |||||||
\(882\) | −1.14472e23 | + | 2.00142e23i | −0.312572 | + | 0.546500i | ||||
\(883\) | 5.80261e23 | 1.57014 | 0.785069 | − | 0.619408i | \(-0.212627\pi\) | ||||
0.785069 | + | 0.619408i | \(0.212627\pi\) | |||||||
\(884\) | −5.45677e22 | −0.146325 | ||||||||
\(885\) | 3.21881e23i | 0.855360i | ||||||||
\(886\) | −2.27875e23 | −0.600106 | ||||||||
\(887\) | − | 4.52350e23i | − | 1.18055i | −0.807201 | − | 0.590277i | \(-0.799019\pi\) | ||
0.807201 | − | 0.590277i | \(-0.200981\pi\) | |||||||
\(888\) | − | 3.82365e23i | − | 0.988951i | ||||||
\(889\) | 2.43959e23 | − | 1.41511e23i | 0.625321 | − | 0.362723i | ||||
\(890\) | 4.22061e23 | 1.07215 | ||||||||
\(891\) | −1.30249e23 | −0.327909 | ||||||||
\(892\) | 7.33489e22i | 0.183010i | ||||||||
\(893\) | 6.27294e21 | 0.0155117 | ||||||||
\(894\) | − | 6.23547e23i | − | 1.52816i | ||||||
\(895\) | − | 3.01018e23i | − | 0.731153i | ||||||
\(896\) | −4.07808e23 | + | 2.36553e23i | −0.981730 | + | 0.569461i | ||||
\(897\) | −2.96092e23 | −0.706458 | ||||||||
\(898\) | 3.68123e23 | 0.870527 | ||||||||
\(899\) | 9.53441e22i | 0.223468i | ||||||||
\(900\) | −1.84690e22 | −0.0429046 | ||||||||
\(901\) | 1.37543e24i | 3.16694i | ||||||||
\(902\) | − | 1.19612e23i | − | 0.272974i | ||||||
\(903\) | 3.70629e23 | + | 6.38950e23i | 0.838373 | + | 1.44532i | ||||
\(904\) | −7.14928e23 | −1.60293 | ||||||||
\(905\) | −1.73800e23 | −0.386244 | ||||||||
\(906\) | − | 6.65347e23i | − | 1.46562i | ||||||
\(907\) | 1.51743e23 | 0.331322 | 0.165661 | − | 0.986183i | \(-0.447024\pi\) | ||||
0.165661 | + | 0.986183i | \(0.447024\pi\) | |||||||
\(908\) | 1.22656e22i | 0.0265461i | ||||||||
\(909\) | 5.14402e22i | 0.110355i | ||||||||
\(910\) | 1.73640e23 | − | 1.00722e23i | 0.369249 | − | 0.214186i | ||||
\(911\) | 4.78281e23 | 1.00817 | 0.504087 | − | 0.863653i | \(-0.331829\pi\) | ||||
0.504087 | + | 0.863653i | \(0.331829\pi\) | |||||||
\(912\) | −1.81936e22 | −0.0380155 | ||||||||
\(913\) | − | 1.54322e23i | − | 0.319639i | ||||||
\(914\) | −8.92069e23 | −1.83159 | ||||||||
\(915\) | − | 5.98745e23i | − | 1.21863i | ||||||
\(916\) | − | 6.02238e22i | − | 0.121508i | ||||||
\(917\) | −1.06254e23 | − | 1.83177e23i | −0.212515 | − | 0.366368i | ||||
\(918\) | −5.23313e23 | −1.03758 | ||||||||
\(919\) | 2.52314e23 | 0.495926 | 0.247963 | − | 0.968770i | \(-0.420239\pi\) | ||||
0.247963 | + | 0.968770i | \(0.420239\pi\) | |||||||
\(920\) | 2.39893e23i | 0.467429i | ||||||||
\(921\) | −5.31176e23 | −1.02603 | ||||||||
\(922\) | 5.97980e22i | 0.114509i | ||||||||
\(923\) | 9.81112e22i | 0.186254i | ||||||||
\(924\) | 1.00249e22 | + | 1.72825e22i | 0.0188670 | + | 0.0325260i | ||||
\(925\) | −2.86117e23 | −0.533837 | ||||||||
\(926\) | 1.04682e24 | 1.93635 | ||||||||
\(927\) | 3.06244e23i | 0.561603i | ||||||||
\(928\) | −1.99985e22 | −0.0363592 | ||||||||
\(929\) | 2.89738e23i | 0.522251i | 0.965305 | + | 0.261125i | \(0.0840936\pi\) | ||||
−0.965305 | + | 0.261125i | \(0.915906\pi\) | |||||||
\(930\) | − | 6.17747e23i | − | 1.10394i | ||||||
\(931\) | 1.34002e22 | + | 7.66427e21i | 0.0237418 | + | 0.0135792i | ||||
\(932\) | 6.27541e22 | 0.110234 | ||||||||
\(933\) | 7.24558e23 | 1.26189 | ||||||||
\(934\) | 1.08851e24i | 1.87957i | ||||||||
\(935\) | −1.79240e23 | −0.306862 | ||||||||
\(936\) | − | 2.21546e23i | − | 0.376061i | ||||||
\(937\) | − | 9.00773e23i | − | 1.51600i | −0.652255 | − | 0.757999i | \(-0.726177\pi\) | ||
0.652255 | − | 0.757999i | \(-0.273823\pi\) | |||||||
\(938\) | −5.05508e22 | + | 2.93225e22i | −0.0843540 | + | 0.0489303i | ||||
\(939\) | −1.00585e24 | −1.66420 | ||||||||
\(940\) | −2.34003e22 | −0.0383883 | ||||||||
\(941\) | − | 5.79898e23i | − | 0.943267i | −0.881795 | − | 0.471634i | \(-0.843664\pi\) | ||
0.881795 | − | 0.471634i | \(-0.156336\pi\) | |||||||
\(942\) | −6.66962e23 | −1.07571 | ||||||||
\(943\) | − | 5.08514e23i | − | 0.813223i | ||||||
\(944\) | 7.80897e23i | 1.23828i | ||||||||
\(945\) | 1.68502e23 | − | 9.77410e22i | 0.264942 | − | 0.153682i | ||||
\(946\) | 2.36439e23 | 0.368630 | ||||||||
\(947\) | 1.55676e23 | 0.240669 | 0.120335 | − | 0.992733i | \(-0.461603\pi\) | ||||
0.120335 | + | 0.992733i | \(0.461603\pi\) | |||||||
\(948\) | − | 1.26091e23i | − | 0.193294i | ||||||
\(949\) | 4.59575e23 | 0.698597 | ||||||||
\(950\) | 1.22205e22i | 0.0184204i | ||||||||
\(951\) | − | 3.22285e23i | − | 0.481721i | ||||||
\(952\) | −6.11871e23 | − | 1.05484e24i | −0.906910 | − | 1.56348i | ||||
\(953\) | 1.61838e23 | 0.237869 | 0.118935 | − | 0.992902i | \(-0.462052\pi\) | ||||
0.118935 | + | 0.992902i | \(0.462052\pi\) | |||||||
\(954\) | 7.08431e23 | 1.03255 | ||||||||
\(955\) | 1.17948e23i | 0.170476i | ||||||||
\(956\) | −9.76205e21 | −0.0139919 | ||||||||
\(957\) | − | 3.81212e22i | − | 0.0541841i | ||||||
\(958\) | 1.34125e24i | 1.89055i | ||||||||
\(959\) | 3.13562e23 | − | 1.81884e23i | 0.438303 | − | 0.254242i | ||||
\(960\) | −4.73280e23 | −0.656067 | ||||||||
\(961\) | −6.52892e23 | −0.897540 | ||||||||
\(962\) | 4.35404e23i | 0.593598i | ||||||||
\(963\) | −3.16589e23 | −0.428041 | ||||||||
\(964\) | − | 4.46733e21i | − | 0.00599006i | ||||||
\(965\) | 4.18582e23i | 0.556624i | ||||||||
\(966\) | 4.21192e23 | + | 7.26119e23i | 0.555473 | + | 0.957615i | ||||
\(967\) | −6.22182e23 | −0.813778 | −0.406889 | − | 0.913478i | \(-0.633386\pi\) | ||||
−0.406889 | + | 0.913478i | \(0.633386\pi\) | |||||||
\(968\) | 6.71191e23 | 0.870649 | ||||||||
\(969\) | − | 5.18766e22i | − | 0.0667393i | ||||||
\(970\) | 2.21044e23 | 0.282037 | ||||||||
\(971\) | 1.21529e24i | 1.53789i | 0.639315 | + | 0.768945i | \(0.279218\pi\) | ||||
−0.639315 | + | 0.768945i | \(0.720782\pi\) | |||||||
\(972\) | 9.49298e22i | 0.119144i | ||||||||
\(973\) | 2.03338e23 | + | 3.50548e23i | 0.253114 | + | 0.436359i | ||||
\(974\) | 1.04337e24 | 1.28815 | ||||||||
\(975\) | −4.43525e23 | −0.543102 | ||||||||
\(976\) | − | 1.45258e24i | − | 1.76418i | ||||||
\(977\) | −1.14008e24 | −1.37334 | −0.686671 | − | 0.726968i | \(-0.740929\pi\) | ||||
−0.686671 | + | 0.726968i | \(0.740929\pi\) | |||||||
\(978\) | − | 3.80213e23i | − | 0.454272i | ||||||
\(979\) | 3.77065e23i | 0.446842i | ||||||||
\(980\) | −4.99876e22 | − | 2.85905e22i | −0.0587562 | − | 0.0336057i | ||||
\(981\) | 6.67590e23 | 0.778319 | ||||||||
\(982\) | 1.31677e24 | 1.52272 | ||||||||
\(983\) | − | 5.80105e23i | − | 0.665393i | −0.943034 | − | 0.332696i | \(-0.892042\pi\) | ||
0.943034 | − | 0.332696i | \(-0.107958\pi\) | |||||||
\(984\) | 1.01796e24 | 1.15816 | ||||||||
\(985\) | 1.15410e22i | 0.0130243i | ||||||||
\(986\) | − | 2.95174e23i | − | 0.330417i | ||||||
\(987\) | 5.58319e23 | − | 3.23858e23i | 0.619933 | − | 0.359598i | ||||
\(988\) | 1.88177e21 | 0.00207258 | ||||||||
\(989\) | 1.00519e24 | 1.09819 | ||||||||
\(990\) | 9.23198e22i | 0.100049i | ||||||||
\(991\) | 1.69694e23 | 0.182422 | 0.0912111 | − | 0.995832i | \(-0.470926\pi\) | ||||
0.0912111 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(992\) | − | 2.89522e23i | − | 0.308737i | ||||||
\(993\) | 3.11176e23i | 0.329163i | ||||||||
\(994\) | 2.40603e23 | − | 1.39564e23i | 0.252470 | − | 0.146447i | ||||
\(995\) | 2.22483e22 | 0.0231586 | ||||||||
\(996\) | −1.66615e23 | −0.172044 | ||||||||
\(997\) | − | 1.11057e23i | − | 0.113759i | −0.998381 | − | 0.0568794i | \(-0.981885\pi\) | ||
0.998381 | − | 0.0568794i | \(-0.0181150\pi\) | |||||||
\(998\) | −1.20567e24 | −1.22513 | ||||||||
\(999\) | 4.22520e23i | 0.425915i |
(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 | 7.17.b.b.6.7 | ✓ | 8 | |
3.2 | odd | 2 | 63.17.d.c.55.2 | 8 | |||
4.3 | odd | 2 | 112.17.c.b.97.8 | 8 | |||
7.6 | odd | 2 | inner | 7.17.b.b.6.8 | yes | 8 | |
21.20 | even | 2 | 63.17.d.c.55.1 | 8 | |||
28.27 | even | 2 | 112.17.c.b.97.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.17.b.b.6.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
7.17.b.b.6.8 | yes | 8 | 7.6 | odd | 2 | inner | |
63.17.d.c.55.1 | 8 | 21.20 | even | 2 | |||
63.17.d.c.55.2 | 8 | 3.2 | odd | 2 | |||
112.17.c.b.97.1 | 8 | 28.27 | even | 2 | |||
112.17.c.b.97.8 | 8 | 4.3 | odd | 2 |