Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,13,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56996908638\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 7950x^{8} + 16939113x^{6} + 4574579500x^{4} + 337520899536x^{2} + 6615595526400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2}\cdot 5^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(8.55327i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.13.c.a.2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −61.7891 | + | 61.7891i | −0.965455 | + | 0.965455i | −0.999423 | − | 0.0339683i | \(-0.989185\pi\) |
0.0339683 | + | 0.999423i | \(0.489185\pi\) | |||||||
\(3\) | 877.187 | + | 877.187i | 1.20327 | + | 1.20327i | 0.973165 | + | 0.230110i | \(0.0739085\pi\) |
0.230110 | + | 0.973165i | \(0.426092\pi\) | |||||||
\(4\) | − | 3539.78i | − | 0.864205i | ||||||
\(5\) | −13781.9 | + | 7362.02i | −0.882043 | + | 0.471170i | ||||
\(6\) | −108401. | −2.32341 | ||||||||
\(7\) | 67595.3 | − | 67595.3i | 0.574550 | − | 0.574550i | −0.358846 | − | 0.933397i | \(-0.616830\pi\) |
0.933397 | + | 0.358846i | \(0.116830\pi\) | |||||||
\(8\) | −34368.1 | − | 34368.1i | −0.131104 | − | 0.131104i | ||||
\(9\) | 1.00747e6i | 1.89574i | ||||||||
\(10\) | 396679. | − | 1.30646e6i | 0.396679 | − | 1.30646i | ||||
\(11\) | −626262. | −0.353509 | −0.176754 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176754 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(12\) | 3.10505e6 | − | 3.10505e6i | 1.03988 | − | 1.03988i | ||||
\(13\) | 3.07386e6 | + | 3.07386e6i | 0.636832 | + | 0.636832i | 0.949773 | − | 0.312941i | \(-0.101314\pi\) |
−0.312941 | + | 0.949773i | \(0.601314\pi\) | |||||||
\(14\) | 8.35330e6i | 1.10940i | ||||||||
\(15\) | −1.85472e7 | − | 5.63145e6i | −1.62829 | − | 0.494393i | ||||
\(16\) | 1.87461e7 | 1.11735 | ||||||||
\(17\) | −6.99904e6 | + | 6.99904e6i | −0.289965 | + | 0.289965i | −0.837066 | − | 0.547102i | \(-0.815731\pi\) |
0.547102 | + | 0.837066i | \(0.315731\pi\) | |||||||
\(18\) | −6.22509e7 | − | 6.22509e7i | −1.83025 | − | 1.83025i | ||||
\(19\) | 4.52415e7i | 0.961647i | 0.876817 | + | 0.480824i | \(0.159662\pi\) | ||||
−0.876817 | + | 0.480824i | \(0.840338\pi\) | |||||||
\(20\) | 2.60600e7 | + | 4.87850e7i | 0.407187 | + | 0.762266i | ||||
\(21\) | 1.18587e8 | 1.38268 | ||||||||
\(22\) | 3.86962e7 | − | 3.86962e7i | 0.341296 | − | 0.341296i | ||||
\(23\) | 5.22502e7 | + | 5.22502e7i | 0.352956 | + | 0.352956i | 0.861208 | − | 0.508252i | \(-0.169708\pi\) |
−0.508252 | + | 0.861208i | \(0.669708\pi\) | |||||||
\(24\) | − | 6.02945e7i | − | 0.315508i | ||||||
\(25\) | 1.35742e8 | − | 2.02926e8i | 0.555998 | − | 0.831183i | ||||
\(26\) | −3.79863e8 | −1.22966 | ||||||||
\(27\) | −4.17569e8 | + | 4.17569e8i | −1.07782 | + | 1.07782i | ||||
\(28\) | −2.39273e8 | − | 2.39273e8i | −0.496529 | − | 0.496529i | ||||
\(29\) | 5.40006e8i | 0.907842i | 0.891042 | + | 0.453921i | \(0.149975\pi\) | ||||
−0.891042 | + | 0.453921i | \(0.850025\pi\) | |||||||
\(30\) | 1.49398e9 | − | 7.98052e8i | 2.04935 | − | 1.09472i | ||||
\(31\) | −2.02184e8 | −0.227812 | −0.113906 | − | 0.993492i | \(-0.536336\pi\) | ||||
−0.113906 | + | 0.993492i | \(0.536336\pi\) | |||||||
\(32\) | −1.01753e9 | + | 1.01753e9i | −0.947651 | + | 0.947651i | ||||
\(33\) | −5.49349e8 | − | 5.49349e8i | −0.425368 | − | 0.425368i | ||||
\(34\) | − | 8.64929e8i | − | 0.559895i | ||||||
\(35\) | −4.33954e8 | + | 1.42923e9i | −0.236067 | + | 0.777488i | ||||
\(36\) | 3.56624e9 | 1.63831 | ||||||||
\(37\) | 2.57578e9 | − | 2.57578e9i | 1.00392 | − | 1.00392i | 0.00392644 | − | 0.999992i | \(-0.498750\pi\) |
0.999992 | − | 0.00392644i | \(-0.00124983\pi\) | |||||||
\(38\) | −2.79543e9 | − | 2.79543e9i | −0.928427 | − | 0.928427i | ||||
\(39\) | 5.39271e9i | 1.53257i | ||||||||
\(40\) | 7.26677e8 | + | 2.20639e8i | 0.177411 | + | 0.0538670i | ||||
\(41\) | 2.72921e9 | 0.574557 | 0.287279 | − | 0.957847i | \(-0.407249\pi\) | ||||
0.287279 | + | 0.957847i | \(0.407249\pi\) | |||||||
\(42\) | −7.32741e9 | + | 7.32741e9i | −1.33492 | + | 1.33492i | ||||
\(43\) | −4.70194e9 | − | 4.70194e9i | −0.743817 | − | 0.743817i | 0.229493 | − | 0.973310i | \(-0.426293\pi\) |
−0.973310 | + | 0.229493i | \(0.926293\pi\) | |||||||
\(44\) | 2.21683e9i | 0.305504i | ||||||||
\(45\) | −7.41704e9 | − | 1.38849e10i | −0.893214 | − | 1.67212i | ||||
\(46\) | −6.45699e9 | −0.681527 | ||||||||
\(47\) | 1.28054e10 | − | 1.28054e10i | 1.18797 | − | 1.18797i | 0.210340 | − | 0.977628i | \(-0.432543\pi\) |
0.977628 | − | 0.210340i | \(-0.0674571\pi\) | |||||||
\(48\) | 1.64438e10 | + | 1.64438e10i | 1.34448 | + | 1.34448i | ||||
\(49\) | 4.70305e9i | 0.339784i | ||||||||
\(50\) | 4.15123e9 | + | 2.09260e10i | 0.265679 | + | 1.33926i | ||||
\(51\) | −1.22789e10 | −0.697814 | ||||||||
\(52\) | 1.08808e10 | − | 1.08808e10i | 0.550353 | − | 0.550353i | ||||
\(53\) | 1.73523e10 | + | 1.73523e10i | 0.782890 | + | 0.782890i | 0.980317 | − | 0.197427i | \(-0.0632587\pi\) |
−0.197427 | + | 0.980317i | \(0.563259\pi\) | |||||||
\(54\) | − | 5.16024e10i | − | 2.08117i | ||||||
\(55\) | 8.63109e9 | − | 4.61056e9i | 0.311810 | − | 0.166562i | ||||
\(56\) | −4.64624e9 | −0.150652 | ||||||||
\(57\) | −3.96853e10 | + | 3.96853e10i | −1.15713 | + | 1.15713i | ||||
\(58\) | −3.33665e10 | − | 3.33665e10i | −0.876480 | − | 0.876480i | ||||
\(59\) | − | 1.93469e10i | − | 0.458670i | −0.973348 | − | 0.229335i | \(-0.926345\pi\) | ||
0.973348 | − | 0.229335i | \(-0.0736551\pi\) | |||||||
\(60\) | −1.99341e10 | + | 6.56530e10i | −0.427257 | + | 1.40717i | ||||
\(61\) | −1.74415e10 | −0.338535 | −0.169268 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169268 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(62\) | 1.24928e10 | − | 1.24928e10i | 0.219942 | − | 0.219942i | ||||
\(63\) | 6.81004e10 | + | 6.81004e10i | 1.08920 | + | 1.08920i | ||||
\(64\) | − | 4.89608e10i | − | 0.712474i | ||||||
\(65\) | −6.49936e10 | − | 1.97339e10i | −0.861768 | − | 0.261657i | ||||
\(66\) | 6.78875e10 | 0.821347 | ||||||||
\(67\) | 7.91041e10 | − | 7.91041e10i | 0.874480 | − | 0.874480i | −0.118477 | − | 0.992957i | \(-0.537801\pi\) |
0.992957 | + | 0.118477i | \(0.0378011\pi\) | |||||||
\(68\) | 2.47751e10 | + | 2.47751e10i | 0.250589 | + | 0.250589i | ||||
\(69\) | 9.16664e10i | 0.849407i | ||||||||
\(70\) | −6.14972e10 | − | 1.15124e11i | −0.522718 | − | 0.978542i | ||||
\(71\) | −1.08760e11 | −0.849026 | −0.424513 | − | 0.905422i | \(-0.639555\pi\) | ||||
−0.424513 | + | 0.905422i | \(0.639555\pi\) | |||||||
\(72\) | 3.46249e10 | − | 3.46249e10i | 0.248539 | − | 0.248539i | ||||
\(73\) | −3.78162e10 | − | 3.78162e10i | −0.249885 | − | 0.249885i | 0.571038 | − | 0.820923i | \(-0.306541\pi\) |
−0.820923 | + | 0.571038i | \(0.806541\pi\) | |||||||
\(74\) | 3.18310e11i | 1.93848i | ||||||||
\(75\) | 2.97075e11 | − | 5.89328e10i | 1.66916 | − | 0.331123i | ||||
\(76\) | 1.60145e11 | 0.831061 | ||||||||
\(77\) | −4.23323e10 | + | 4.23323e10i | −0.203108 | + | 0.203108i | ||||
\(78\) | −3.33211e11 | − | 3.33211e11i | −1.47962 | − | 1.47962i | ||||
\(79\) | 4.17485e10i | 0.171743i | 0.996306 | + | 0.0858714i | \(0.0273674\pi\) | ||||
−0.996306 | + | 0.0858714i | \(0.972633\pi\) | |||||||
\(80\) | −2.58357e11 | + | 1.38009e11i | −0.985554 | + | 0.526464i | ||||
\(81\) | −1.97160e11 | −0.698086 | ||||||||
\(82\) | −1.68635e11 | + | 1.68635e11i | −0.554709 | + | 0.554709i | ||||
\(83\) | 1.08002e11 | + | 1.08002e11i | 0.330341 | + | 0.330341i | 0.852716 | − | 0.522375i | \(-0.174954\pi\) |
−0.522375 | + | 0.852716i | \(0.674954\pi\) | |||||||
\(84\) | − | 4.19774e11i | − | 1.19492i | ||||||
\(85\) | 4.49331e10 | − | 1.47987e11i | 0.119139 | − | 0.392384i | ||||
\(86\) | 5.81057e11 | 1.43624 | ||||||||
\(87\) | −4.73686e11 | + | 4.73686e11i | −1.09238 | + | 1.09238i | ||||
\(88\) | 2.15234e10 | + | 2.15234e10i | 0.0463463 | + | 0.0463463i | ||||
\(89\) | − | 6.78885e11i | − | 1.36602i | −0.730411 | − | 0.683008i | \(-0.760671\pi\) | ||
0.730411 | − | 0.683008i | \(-0.239329\pi\) | |||||||
\(90\) | 1.31623e12 | + | 3.99644e11i | 2.47672 | + | 0.752000i | ||||
\(91\) | 4.15557e11 | 0.731784 | ||||||||
\(92\) | 1.84954e11 | − | 1.84954e11i | 0.305027 | − | 0.305027i | ||||
\(93\) | −1.77353e11 | − | 1.77353e11i | −0.274121 | − | 0.274121i | ||||
\(94\) | 1.58246e12i | 2.29386i | ||||||||
\(95\) | −3.33069e11 | − | 6.23515e11i | −0.453099 | − | 0.848214i | ||||
\(96\) | −1.78513e12 | −2.28057 | ||||||||
\(97\) | −3.15626e10 | + | 3.15626e10i | −0.0378916 | + | 0.0378916i | −0.725799 | − | 0.687907i | \(-0.758530\pi\) |
0.687907 | + | 0.725799i | \(0.258530\pi\) | |||||||
\(98\) | −2.90597e11 | − | 2.90597e11i | −0.328046 | − | 0.328046i | ||||
\(99\) | − | 6.30942e11i | − | 0.670160i | ||||||
\(100\) | −7.18313e11 | − | 4.80497e11i | −0.718313 | − | 0.480497i | ||||
\(101\) | 5.81967e11 | 0.548239 | 0.274120 | − | 0.961696i | \(-0.411614\pi\) | ||||
0.274120 | + | 0.961696i | \(0.411614\pi\) | |||||||
\(102\) | 7.58704e11 | − | 7.58704e11i | 0.673708 | − | 0.673708i | ||||
\(103\) | 1.06154e12 | + | 1.06154e12i | 0.889023 | + | 0.889023i | 0.994429 | − | 0.105406i | \(-0.0336143\pi\) |
−0.105406 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(104\) | − | 2.11286e11i | − | 0.166982i | ||||||
\(105\) | −1.63436e12 | + | 8.73043e11i | −1.21959 | + | 0.651478i | ||||
\(106\) | −2.14436e12 | −1.51169 | ||||||||
\(107\) | 7.60757e11 | − | 7.60757e11i | 0.506924 | − | 0.506924i | −0.406657 | − | 0.913581i | \(-0.633305\pi\) |
0.913581 | + | 0.406657i | \(0.133305\pi\) | |||||||
\(108\) | 1.47810e12 | + | 1.47810e12i | 0.931457 | + | 0.931457i | ||||
\(109\) | 2.13246e12i | 1.27152i | 0.771887 | + | 0.635759i | \(0.219313\pi\) | ||||
−0.771887 | + | 0.635759i | \(0.780687\pi\) | |||||||
\(110\) | −2.48425e11 | + | 8.18189e11i | −0.140230 | + | 0.461847i | ||||
\(111\) | 4.51888e12 | 2.41598 | ||||||||
\(112\) | 1.26715e12 | − | 1.26715e12i | 0.641976 | − | 0.641976i | ||||
\(113\) | −2.60692e12 | − | 2.60692e12i | −1.25215 | − | 1.25215i | −0.954753 | − | 0.297401i | \(-0.903880\pi\) |
−0.297401 | − | 0.954753i | \(-0.596120\pi\) | |||||||
\(114\) | − | 4.90424e12i | − | 2.23430i | ||||||
\(115\) | −1.10478e12 | − | 3.35441e11i | −0.477625 | − | 0.145020i | ||||
\(116\) | 1.91150e12 | 0.784562 | ||||||||
\(117\) | −3.09684e12 | + | 3.09684e12i | −1.20727 | + | 1.20727i | ||||
\(118\) | 1.19543e12 | + | 1.19543e12i | 0.442825 | + | 0.442825i | ||||
\(119\) | 9.46204e11i | 0.333198i | ||||||||
\(120\) | 4.43889e11 | + | 8.30973e11i | 0.148658 | + | 0.278291i | ||||
\(121\) | −2.74622e12 | −0.875032 | ||||||||
\(122\) | 1.07769e12 | − | 1.07769e12i | 0.326841 | − | 0.326841i | ||||
\(123\) | 2.39403e12 | + | 2.39403e12i | 0.691350 | + | 0.691350i | ||||
\(124\) | 7.15688e11i | 0.196876i | ||||||||
\(125\) | −3.76839e11 | + | 3.79604e12i | −0.0987860 | + | 0.995109i | ||||
\(126\) | −8.41573e12 | −2.10314 | ||||||||
\(127\) | 2.09669e12 | − | 2.09669e12i | 0.499703 | − | 0.499703i | −0.411643 | − | 0.911345i | \(-0.635045\pi\) |
0.911345 | + | 0.411643i | \(0.135045\pi\) | |||||||
\(128\) | −1.14257e12 | − | 1.14257e12i | −0.259790 | − | 0.259790i | ||||
\(129\) | − | 8.24896e12i | − | 1.79003i | ||||||
\(130\) | 5.23524e12 | − | 2.79656e12i | 1.08462 | − | 0.579380i | ||||
\(131\) | −1.98696e12 | −0.393153 | −0.196577 | − | 0.980488i | \(-0.562982\pi\) | ||||
−0.196577 | + | 0.980488i | \(0.562982\pi\) | |||||||
\(132\) | −1.94458e12 | + | 1.94458e12i | −0.367605 | + | 0.367605i | ||||
\(133\) | 3.05811e12 | + | 3.05811e12i | 0.552515 | + | 0.552515i | ||||
\(134\) | 9.77554e12i | 1.68854i | ||||||||
\(135\) | 2.68075e12 | − | 8.82906e12i | 0.442847 | − | 1.45852i | ||||
\(136\) | 4.81087e11 | 0.0760309 | ||||||||
\(137\) | −7.17765e12 | + | 7.17765e12i | −1.08557 | + | 1.08557i | −0.0895941 | + | 0.995978i | \(0.528557\pi\) |
−0.995978 | + | 0.0895941i | \(0.971443\pi\) | |||||||
\(138\) | −5.66399e12 | − | 5.66399e12i | −0.820064 | − | 0.820064i | ||||
\(139\) | − | 1.60028e11i | − | 0.0221875i | −0.999938 | − | 0.0110938i | \(-0.996469\pi\) | ||
0.999938 | − | 0.0110938i | \(-0.00353132\pi\) | |||||||
\(140\) | 5.05917e12 | + | 1.53610e12i | 0.671909 | + | 0.204010i | ||||
\(141\) | 2.24654e13 | 2.85890 | ||||||||
\(142\) | 6.72021e12 | − | 6.72021e12i | 0.819696 | − | 0.819696i | ||||
\(143\) | −1.92504e12 | − | 1.92504e12i | −0.225125 | − | 0.225125i | ||||
\(144\) | 1.88862e13i | 2.11821i | ||||||||
\(145\) | −3.97553e12 | − | 7.44231e12i | −0.427747 | − | 0.800755i | ||||
\(146\) | 4.67325e12 | 0.482505 | ||||||||
\(147\) | −4.12545e12 | + | 4.12545e12i | −0.408853 | + | 0.408853i | ||||
\(148\) | −9.11771e12 | − | 9.11771e12i | −0.867592 | − | 0.867592i | ||||
\(149\) | − | 1.52562e13i | − | 1.39422i | −0.716966 | − | 0.697108i | \(-0.754470\pi\) | ||
0.716966 | − | 0.697108i | \(-0.245530\pi\) | |||||||
\(150\) | −1.47146e13 | + | 2.19974e13i | −1.29181 | + | 1.93118i | ||||
\(151\) | −2.24188e13 | −1.89126 | −0.945631 | − | 0.325242i | \(-0.894554\pi\) | ||||
−0.945631 | + | 0.325242i | \(0.894554\pi\) | |||||||
\(152\) | 1.55487e12 | − | 1.55487e12i | 0.126076 | − | 0.126076i | ||||
\(153\) | −7.05134e12 | − | 7.05134e12i | −0.549697 | − | 0.549697i | ||||
\(154\) | − | 5.23135e12i | − | 0.392184i | ||||||
\(155\) | 2.78648e12 | − | 1.48848e12i | 0.200940 | − | 0.107338i | ||||
\(156\) | 1.90890e13 | 1.32445 | ||||||||
\(157\) | −5.18200e12 | + | 5.18200e12i | −0.346019 | + | 0.346019i | −0.858624 | − | 0.512606i | \(-0.828680\pi\) |
0.512606 | + | 0.858624i | \(0.328680\pi\) | |||||||
\(158\) | −2.57960e12 | − | 2.57960e12i | −0.165810 | − | 0.165810i | ||||
\(159\) | 3.04423e13i | 1.88406i | ||||||||
\(160\) | 6.53245e12 | − | 2.15147e13i | 0.389364 | − | 1.28237i | ||||
\(161\) | 7.06374e12 | 0.405582 | ||||||||
\(162\) | 1.21823e13 | − | 1.21823e13i | 0.673970 | − | 0.673970i | ||||
\(163\) | 2.32479e13 | + | 2.32479e13i | 1.23954 | + | 1.23954i | 0.960191 | + | 0.279344i | \(0.0901171\pi\) |
0.279344 | + | 0.960191i | \(0.409883\pi\) | |||||||
\(164\) | − | 9.66081e12i | − | 0.496535i | ||||||
\(165\) | 1.16154e13 | + | 3.52676e12i | 0.575613 | + | 0.174772i | ||||
\(166\) | −1.33467e13 | −0.637859 | ||||||||
\(167\) | 6.01904e12 | − | 6.01904e12i | 0.277478 | − | 0.277478i | −0.554624 | − | 0.832101i | \(-0.687138\pi\) |
0.832101 | + | 0.554624i | \(0.187138\pi\) | |||||||
\(168\) | −4.07562e12 | − | 4.07562e12i | −0.181275 | − | 0.181275i | ||||
\(169\) | − | 4.40079e12i | − | 0.188891i | ||||||
\(170\) | 6.36763e12 | + | 1.19204e13i | 0.263806 | + | 0.493851i | ||||
\(171\) | −4.55796e13 | −1.82303 | ||||||||
\(172\) | −1.66438e13 | + | 1.66438e13i | −0.642810 | + | 0.642810i | ||||
\(173\) | 2.55096e13 | + | 2.55096e13i | 0.951538 | + | 0.951538i | 0.998879 | − | 0.0473407i | \(-0.0150746\pi\) |
−0.0473407 | + | 0.998879i | \(0.515075\pi\) | |||||||
\(174\) | − | 5.85372e13i | − | 2.10929i | ||||||
\(175\) | −4.54131e12 | − | 2.28923e13i | −0.158108 | − | 0.797006i | ||||
\(176\) | −1.17400e13 | −0.394994 | ||||||||
\(177\) | 1.69709e13 | − | 1.69709e13i | 0.551906 | − | 0.551906i | ||||
\(178\) | 4.19477e13 | + | 4.19477e13i | 1.31883 | + | 1.31883i | ||||
\(179\) | − | 2.62541e13i | − | 0.798139i | −0.916921 | − | 0.399070i | \(-0.869333\pi\) | ||
0.916921 | − | 0.399070i | \(-0.130667\pi\) | |||||||
\(180\) | −4.91496e13 | + | 2.62547e13i | −1.44506 | + | 0.771920i | ||||
\(181\) | 9.97197e12 | 0.283602 | 0.141801 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141801 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(182\) | −2.56769e13 | + | 2.56769e13i | −0.706504 | + | 0.706504i | ||||
\(183\) | −1.52994e13 | − | 1.52994e13i | −0.407351 | − | 0.407351i | ||||
\(184\) | − | 3.59148e12i | − | 0.0925479i | ||||||
\(185\) | −1.65362e13 | + | 5.44622e13i | −0.412483 | + | 1.35852i | ||||
\(186\) | 2.19170e13 | 0.529302 | ||||||||
\(187\) | 4.38323e12 | − | 4.38323e12i | 0.102505 | − | 0.102505i | ||||
\(188\) | −4.53282e13 | − | 4.53282e13i | −1.02665 | − | 1.02665i | ||||
\(189\) | 5.64514e13i | 1.23852i | ||||||||
\(190\) | 5.91065e13 | + | 1.79464e13i | 1.25636 | + | 0.381466i | ||||
\(191\) | 1.36705e13 | 0.281568 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(192\) | 4.29478e13 | − | 4.29478e13i | 0.857302 | − | 0.857302i | ||||
\(193\) | −5.46179e13 | − | 5.46179e13i | −1.05680 | − | 1.05680i | −0.998287 | − | 0.0585082i | \(-0.981366\pi\) |
−0.0585082 | − | 0.998287i | \(-0.518634\pi\) | |||||||
\(194\) | − | 3.90045e12i | − | 0.0731652i | ||||||
\(195\) | −3.97013e13 | − | 7.43219e13i | −0.722099 | − | 1.35179i | ||||
\(196\) | 1.66478e13 | 0.293643 | ||||||||
\(197\) | 3.56213e13 | − | 3.56213e13i | 0.609415 | − | 0.609415i | −0.333378 | − | 0.942793i | \(-0.608189\pi\) |
0.942793 | + | 0.333378i | \(0.108189\pi\) | |||||||
\(198\) | 3.89853e13 | + | 3.89853e13i | 0.647009 | + | 0.647009i | ||||
\(199\) | 4.38190e13i | 0.705576i | 0.935703 | + | 0.352788i | \(0.114766\pi\) | ||||
−0.935703 | + | 0.352788i | \(0.885234\pi\) | |||||||
\(200\) | −1.16394e13 | + | 2.30898e12i | −0.181865 | + | 0.0360778i | ||||
\(201\) | 1.38778e14 | 2.10448 | ||||||||
\(202\) | −3.59592e13 | + | 3.59592e13i | −0.529300 | + | 0.529300i | ||||
\(203\) | 3.65018e13 | + | 3.65018e13i | 0.521601 | + | 0.521601i | ||||
\(204\) | 4.34648e13i | 0.603054i | ||||||||
\(205\) | −3.76137e13 | + | 2.00925e13i | −0.506784 | + | 0.270714i | ||||
\(206\) | −1.31183e14 | −1.71662 | ||||||||
\(207\) | −5.26407e13 | + | 5.26407e13i | −0.669113 | + | 0.669113i | ||||
\(208\) | 5.76230e13 | + | 5.76230e13i | 0.711567 | + | 0.711567i | ||||
\(209\) | − | 2.83331e13i | − | 0.339951i | ||||||
\(210\) | 4.70412e13 | − | 1.54930e14i | 0.548482 | − | 1.80643i | ||||
\(211\) | −1.15325e14 | −1.30686 | −0.653430 | − | 0.756987i | \(-0.726671\pi\) | ||||
−0.653430 | + | 0.756987i | \(0.726671\pi\) | |||||||
\(212\) | 6.14232e13 | − | 6.14232e13i | 0.676577 | − | 0.676577i | ||||
\(213\) | −9.54033e13 | − | 9.54033e13i | −1.02161 | − | 1.02161i | ||||
\(214\) | 9.40129e13i | 0.978825i | ||||||||
\(215\) | 9.94175e13 | + | 3.01859e13i | 1.00654 | + | 0.305614i | ||||
\(216\) | 2.87021e13 | 0.282612 | ||||||||
\(217\) | −1.36667e13 | + | 1.36667e13i | −0.130890 | + | 0.130890i | ||||
\(218\) | −1.31763e14 | − | 1.31763e14i | −1.22759 | − | 1.22759i | ||||
\(219\) | − | 6.63437e13i | − | 0.601360i | ||||||
\(220\) | −1.63204e13 | − | 3.05522e13i | −0.143944 | − | 0.269467i | ||||
\(221\) | −4.30282e13 | −0.369317 | ||||||||
\(222\) | −2.79218e14 | + | 2.79218e14i | −2.33252 | + | 2.33252i | ||||
\(223\) | −4.25094e13 | − | 4.25094e13i | −0.345666 | − | 0.345666i | 0.512827 | − | 0.858492i | \(-0.328598\pi\) |
−0.858492 | + | 0.512827i | \(0.828598\pi\) | |||||||
\(224\) | 1.37561e14i | 1.08895i | ||||||||
\(225\) | 2.04442e14 | + | 1.36756e14i | 1.57571 | + | 1.05403i | ||||
\(226\) | 3.22159e14 | 2.41779 | ||||||||
\(227\) | 1.56632e14 | − | 1.56632e14i | 1.14479 | − | 1.14479i | 0.157225 | − | 0.987563i | \(-0.449745\pi\) |
0.987563 | − | 0.157225i | \(-0.0502547\pi\) | |||||||
\(228\) | 1.40477e14 | + | 1.40477e14i | 0.999994 | + | 0.999994i | ||||
\(229\) | − | 2.12425e14i | − | 1.47297i | −0.676456 | − | 0.736483i | \(-0.736485\pi\) | ||
0.676456 | − | 0.736483i | \(-0.263515\pi\) | |||||||
\(230\) | 8.89897e13 | − | 4.75365e13i | 0.601136 | − | 0.321115i | ||||
\(231\) | −7.42668e13 | −0.488790 | ||||||||
\(232\) | 1.85590e13 | − | 1.85590e13i | 0.119022 | − | 0.119022i | ||||
\(233\) | 3.32347e13 | + | 3.32347e13i | 0.207709 | + | 0.207709i | 0.803293 | − | 0.595584i | \(-0.203079\pi\) |
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(234\) | − | 3.82701e14i | − | 2.33112i | ||||||
\(235\) | −8.22091e13 | + | 2.70756e14i | −0.488104 | + | 1.60757i | ||||
\(236\) | −6.84840e13 | −0.396385 | ||||||||
\(237\) | −3.66213e13 | + | 3.66213e13i | −0.206654 | + | 0.206654i | ||||
\(238\) | −5.84651e13 | − | 5.84651e13i | −0.321688 | − | 0.321688i | ||||
\(239\) | 2.78396e14i | 1.49374i | 0.664969 | + | 0.746871i | \(0.268445\pi\) | ||||
−0.664969 | + | 0.746871i | \(0.731555\pi\) | |||||||
\(240\) | −3.47688e14 | − | 1.05568e14i | −1.81937 | − | 0.552412i | ||||
\(241\) | 1.17185e13 | 0.0598095 | 0.0299047 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299047 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(242\) | 1.69687e14 | − | 1.69687e14i | 0.844803 | − | 0.844803i | ||||
\(243\) | 4.89672e13 | + | 4.89672e13i | 0.237830 | + | 0.237830i | ||||
\(244\) | 6.17391e13i | 0.292564i | ||||||||
\(245\) | −3.46239e13 | − | 6.48170e13i | −0.160096 | − | 0.299704i | ||||
\(246\) | −2.95849e14 | −1.33493 | ||||||||
\(247\) | −1.39066e14 | + | 1.39066e14i | −0.612408 | + | 0.612408i | ||||
\(248\) | 6.94868e12 | + | 6.94868e12i | 0.0298671 | + | 0.0298671i | ||||
\(249\) | 1.89476e14i | 0.794982i | ||||||||
\(250\) | −2.11269e14 | − | 2.57838e14i | −0.865359 | − | 1.05611i | ||||
\(251\) | 1.40981e14 | 0.563792 | 0.281896 | − | 0.959445i | \(-0.409037\pi\) | ||||
0.281896 | + | 0.959445i | \(0.409037\pi\) | |||||||
\(252\) | 2.41061e14 | − | 2.41061e14i | 0.941290 | − | 0.941290i | ||||
\(253\) | −3.27223e13 | − | 3.27223e13i | −0.124773 | − | 0.124773i | ||||
\(254\) | 2.59105e14i | 0.964881i | ||||||||
\(255\) | 1.69227e14 | − | 9.03978e13i | 0.615502 | − | 0.328789i | ||||
\(256\) | 3.41740e14 | 1.21411 | ||||||||
\(257\) | −1.00683e14 | + | 1.00683e14i | −0.349428 | + | 0.349428i | −0.859896 | − | 0.510469i | \(-0.829472\pi\) |
0.510469 | + | 0.859896i | \(0.329472\pi\) | |||||||
\(258\) | 5.09695e14 | + | 5.09695e14i | 1.72819 | + | 1.72819i | ||||
\(259\) | − | 3.48221e14i | − | 1.15360i | ||||||
\(260\) | −6.98537e13 | + | 2.30063e14i | −0.226125 | + | 0.744745i | ||||
\(261\) | −5.44041e14 | −1.72103 | ||||||||
\(262\) | 1.22773e14 | − | 1.22773e14i | 0.379572 | − | 0.379572i | ||||
\(263\) | −1.47227e14 | − | 1.47227e14i | −0.444889 | − | 0.444889i | 0.448762 | − | 0.893651i | \(-0.351865\pi\) |
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(264\) | 3.77601e13i | 0.111535i | ||||||||
\(265\) | −3.66895e14 | − | 1.11400e14i | −1.05942 | − | 0.321668i | ||||
\(266\) | −3.77916e14 | −1.06686 | ||||||||
\(267\) | 5.95509e14 | − | 5.95509e14i | 1.64369 | − | 1.64369i | ||||
\(268\) | −2.80011e14 | − | 2.80011e14i | −0.755730 | − | 0.755730i | ||||
\(269\) | 5.62680e13i | 0.148507i | 0.997239 | + | 0.0742536i | \(0.0236574\pi\) | ||||
−0.997239 | + | 0.0742536i | \(0.976343\pi\) | |||||||
\(270\) | 3.79898e14 | + | 7.11181e14i | 0.980584 | + | 1.83568i | ||||
\(271\) | 6.58674e14 | 1.66286 | 0.831429 | − | 0.555632i | \(-0.187523\pi\) | ||||
0.831429 | + | 0.555632i | \(0.187523\pi\) | |||||||
\(272\) | −1.31205e14 | + | 1.31205e14i | −0.323993 | + | 0.323993i | ||||
\(273\) | 3.64522e14 | + | 3.64522e14i | 0.880537 | + | 0.880537i | ||||
\(274\) | − | 8.87001e14i | − | 2.09614i | ||||||
\(275\) | −8.50099e13 | + | 1.27085e14i | −0.196550 | + | 0.293830i | ||||
\(276\) | 3.24479e14 | 0.734062 | ||||||||
\(277\) | −2.01448e14 | + | 2.01448e14i | −0.445949 | + | 0.445949i | −0.894005 | − | 0.448056i | \(-0.852116\pi\) |
0.448056 | + | 0.894005i | \(0.352116\pi\) | |||||||
\(278\) | 9.88801e12 | + | 9.88801e12i | 0.0214210 | + | 0.0214210i | ||||
\(279\) | − | 2.03695e14i | − | 0.431872i | ||||||
\(280\) | 6.40341e13 | − | 3.42057e13i | 0.132881 | − | 0.0709824i | ||||
\(281\) | −4.59473e14 | −0.933302 | −0.466651 | − | 0.884442i | \(-0.654540\pi\) | ||||
−0.466651 | + | 0.884442i | \(0.654540\pi\) | |||||||
\(282\) | −1.38812e15 | + | 1.38812e15i | −2.76014 | + | 2.76014i | ||||
\(283\) | 7.88330e11 | + | 7.88330e11i | 0.00153458 | + | 0.00153458i | 0.707874 | − | 0.706339i | \(-0.249655\pi\) |
−0.706339 | + | 0.707874i | \(0.749655\pi\) | |||||||
\(284\) | 3.84988e14i | 0.733732i | ||||||||
\(285\) | 2.54775e14 | − | 8.39104e14i | 0.475432 | − | 1.56584i | ||||
\(286\) | 2.37894e14 | 0.434697 | ||||||||
\(287\) | 1.84482e14 | − | 1.84482e14i | 0.330112 | − | 0.330112i | ||||
\(288\) | −1.02514e15 | − | 1.02514e15i | −1.79650 | − | 1.79650i | ||||
\(289\) | 4.84649e14i | 0.831841i | ||||||||
\(290\) | 7.05498e14 | + | 2.14209e14i | 1.18606 | + | 0.360122i | ||||
\(291\) | −5.53726e13 | −0.0911879 | ||||||||
\(292\) | −1.33861e14 | + | 1.33861e14i | −0.215952 | + | 0.215952i | ||||
\(293\) | −4.07426e14 | − | 4.07426e14i | −0.643937 | − | 0.643937i | 0.307584 | − | 0.951521i | \(-0.400480\pi\) |
−0.951521 | + | 0.307584i | \(0.900480\pi\) | |||||||
\(294\) | − | 5.09816e14i | − | 0.789458i | ||||||
\(295\) | 1.42433e14 | + | 2.66638e14i | 0.216111 | + | 0.404567i | ||||
\(296\) | −1.77049e14 | −0.263235 | ||||||||
\(297\) | 2.61508e14 | − | 2.61508e14i | 0.381018 | − | 0.381018i | ||||
\(298\) | 9.42670e14 | + | 9.42670e14i | 1.34605 | + | 1.34605i | ||||
\(299\) | 3.21220e14i | 0.449548i | ||||||||
\(300\) | −2.08609e14 | − | 1.05158e15i | −0.286158 | − | 1.44250i | ||||
\(301\) | −6.35657e14 | −0.854720 | ||||||||
\(302\) | 1.38524e15 | − | 1.38524e15i | 1.82593 | − | 1.82593i | ||||
\(303\) | 5.10494e14 | + | 5.10494e14i | 0.659683 | + | 0.659683i | ||||
\(304\) | 8.48103e14i | 1.07450i | ||||||||
\(305\) | 2.40377e14 | − | 1.28405e14i | 0.298603 | − | 0.159508i | ||||
\(306\) | 8.71392e14 | 1.06141 | ||||||||
\(307\) | −8.39174e14 | + | 8.39174e14i | −1.00236 | + | 1.00236i | −0.00235845 | + | 0.999997i | \(0.500751\pi\) |
−0.999997 | + | 0.00235845i | \(0.999249\pi\) | |||||||
\(308\) | 1.49847e14 | + | 1.49847e14i | 0.175527 | + | 0.175527i | ||||
\(309\) | 1.86234e15i | 2.13948i | ||||||||
\(310\) | −8.02023e13 | + | 2.64146e14i | −0.0903684 | + | 0.297629i | ||||
\(311\) | 4.19245e14 | 0.463346 | 0.231673 | − | 0.972794i | \(-0.425580\pi\) | ||||
0.231673 | + | 0.972794i | \(0.425580\pi\) | |||||||
\(312\) | 1.85337e14 | − | 1.85337e14i | 0.200925 | − | 0.200925i | ||||
\(313\) | −6.71824e14 | − | 6.71824e14i | −0.714479 | − | 0.714479i | 0.252990 | − | 0.967469i | \(-0.418586\pi\) |
−0.967469 | + | 0.252990i | \(0.918586\pi\) | |||||||
\(314\) | − | 6.40382e14i | − | 0.668131i | ||||||
\(315\) | −1.43991e15 | − | 4.37197e14i | −1.47391 | − | 0.447522i | ||||
\(316\) | 1.47781e14 | 0.148421 | ||||||||
\(317\) | 7.72397e14 | − | 7.72397e14i | 0.761176 | − | 0.761176i | −0.215359 | − | 0.976535i | \(-0.569092\pi\) |
0.976535 | + | 0.215359i | \(0.0690922\pi\) | |||||||
\(318\) | −1.88101e15 | − | 1.88101e15i | −1.81898 | − | 1.81898i | ||||
\(319\) | − | 3.38185e14i | − | 0.320930i | ||||||
\(320\) | 3.60451e14 | + | 6.74774e14i | 0.335696 | + | 0.628432i | ||||
\(321\) | 1.33465e15 | 1.21994 | ||||||||
\(322\) | −4.36462e14 | + | 4.36462e14i | −0.391571 | + | 0.391571i | ||||
\(323\) | −3.16647e14 | − | 3.16647e14i | −0.278844 | − | 0.278844i | ||||
\(324\) | 6.97904e14i | 0.603289i | ||||||||
\(325\) | 1.04102e15 | − | 2.06514e14i | 0.883401 | − | 0.175246i | ||||
\(326\) | −2.87294e15 | −2.39343 | ||||||||
\(327\) | −1.87057e15 | + | 1.87057e15i | −1.52999 | + | 1.52999i | ||||
\(328\) | −9.37976e13 | − | 9.37976e13i | −0.0753267 | − | 0.0753267i | ||||
\(329\) | − | 1.73116e15i | − | 1.36510i | ||||||
\(330\) | −9.35620e14 | + | 4.99790e14i | −0.724463 | + | 0.386994i | ||||
\(331\) | 1.14681e15 | 0.872017 | 0.436009 | − | 0.899942i | \(-0.356392\pi\) | ||||
0.436009 | + | 0.899942i | \(0.356392\pi\) | |||||||
\(332\) | 3.82303e14 | − | 3.82303e14i | 0.285482 | − | 0.285482i | ||||
\(333\) | 2.59503e15 | + | 2.59503e15i | 1.90317 | + | 1.90317i | ||||
\(334\) | 7.43821e14i | 0.535784i | ||||||||
\(335\) | −5.07840e14 | + | 1.67257e15i | −0.359300 | + | 1.18336i | ||||
\(336\) | 2.22305e15 | 1.54495 | ||||||||
\(337\) | −3.55515e14 | + | 3.55515e14i | −0.242705 | + | 0.242705i | −0.817968 | − | 0.575263i | \(-0.804900\pi\) |
0.575263 | + | 0.817968i | \(0.304900\pi\) | |||||||
\(338\) | 2.71921e14 | + | 2.71921e14i | 0.182366 | + | 0.182366i | ||||
\(339\) | − | 4.57352e15i | − | 3.01337i | ||||||
\(340\) | −5.23843e14 | − | 1.59053e14i | −0.339100 | − | 0.102960i | ||||
\(341\) | 1.26620e14 | 0.0805336 | ||||||||
\(342\) | 2.81632e15 | − | 2.81632e15i | 1.76005 | − | 1.76005i | ||||
\(343\) | 1.25351e15 | + | 1.25351e15i | 0.769773 | + | 0.769773i | ||||
\(344\) | 3.23193e14i | 0.195035i | ||||||||
\(345\) | −6.74851e14 | − | 1.26334e15i | −0.400215 | − | 0.749213i | ||||
\(346\) | −3.15242e15 | −1.83733 | ||||||||
\(347\) | −5.71227e14 | + | 5.71227e14i | −0.327214 | + | 0.327214i | −0.851526 | − | 0.524312i | \(-0.824323\pi\) |
0.524312 | + | 0.851526i | \(0.324323\pi\) | |||||||
\(348\) | 1.67675e15 | + | 1.67675e15i | 0.944043 | + | 0.944043i | ||||
\(349\) | − | 9.84765e14i | − | 0.544980i | −0.962159 | − | 0.272490i | \(-0.912153\pi\) | ||
0.962159 | − | 0.272490i | \(-0.0878471\pi\) | |||||||
\(350\) | 1.69510e15 | + | 1.13389e15i | 0.922118 | + | 0.616827i | ||||
\(351\) | −2.56710e15 | −1.37278 | ||||||||
\(352\) | 6.37242e14 | − | 6.37242e14i | 0.335003 | − | 0.335003i | ||||
\(353\) | −1.69093e15 | − | 1.69093e15i | −0.873930 | − | 0.873930i | 0.118968 | − | 0.992898i | \(-0.462041\pi\) |
−0.992898 | + | 0.118968i | \(0.962041\pi\) | |||||||
\(354\) | 2.09723e15i | 1.06568i | ||||||||
\(355\) | 1.49893e15 | − | 8.00697e14i | 0.748877 | − | 0.400035i | ||||
\(356\) | −2.40311e15 | −1.18052 | ||||||||
\(357\) | −8.29998e14 | + | 8.29998e14i | −0.400929 | + | 0.400929i | ||||
\(358\) | 1.62222e15 | + | 1.62222e15i | 0.770567 | + | 0.770567i | ||||
\(359\) | 1.01974e15i | 0.476345i | 0.971223 | + | 0.238173i | \(0.0765484\pi\) | ||||
−0.971223 | + | 0.238173i | \(0.923452\pi\) | |||||||
\(360\) | −2.22288e14 | + | 7.32107e14i | −0.102118 | + | 0.336325i | ||||
\(361\) | 1.66517e14 | 0.0752343 | ||||||||
\(362\) | −6.16159e14 | + | 6.16159e14i | −0.273805 | + | 0.273805i | ||||
\(363\) | −2.40895e15 | − | 2.40895e15i | −1.05290 | − | 1.05290i | ||||
\(364\) | − | 1.47098e15i | − | 0.632411i | ||||||
\(365\) | 7.99583e14 | + | 2.42776e14i | 0.338147 | + | 0.102671i | ||||
\(366\) | 1.89068e15 | 0.786558 | ||||||||
\(367\) | 1.52100e15 | − | 1.52100e15i | 0.622490 | − | 0.622490i | −0.323677 | − | 0.946168i | \(-0.604919\pi\) |
0.946168 | + | 0.323677i | \(0.104919\pi\) | |||||||
\(368\) | 9.79488e14 | + | 9.79488e14i | 0.394378 | + | 0.394378i | ||||
\(369\) | 2.74960e15i | 1.08921i | ||||||||
\(370\) | −2.34341e15 | − | 4.38693e15i | −0.913351 | − | 1.70982i | ||||
\(371\) | 2.34586e15 | 0.899619 | ||||||||
\(372\) | −6.27792e14 | + | 6.27792e14i | −0.236896 | + | 0.236896i | ||||
\(373\) | 4.81109e14 | + | 4.81109e14i | 0.178645 | + | 0.178645i | 0.790765 | − | 0.612120i | \(-0.209683\pi\) |
−0.612120 | + | 0.790765i | \(0.709683\pi\) | |||||||
\(374\) | 5.41672e14i | 0.197928i | ||||||||
\(375\) | −3.66039e15 | + | 2.99928e15i | −1.31626 | + | 1.07852i | ||||
\(376\) | −8.80192e14 | −0.311494 | ||||||||
\(377\) | −1.65990e15 | + | 1.65990e15i | −0.578142 | + | 0.578142i | ||||
\(378\) | −3.48808e15 | − | 3.48808e15i | −1.19574 | − | 1.19574i | ||||
\(379\) | − | 7.77243e14i | − | 0.262254i | −0.991366 | − | 0.131127i | \(-0.958141\pi\) | ||
0.991366 | − | 0.131127i | \(-0.0418595\pi\) | |||||||
\(380\) | −2.20711e15 | + | 1.17899e15i | −0.733031 | + | 0.391570i | ||||
\(381\) | 3.67838e15 | 1.20256 | ||||||||
\(382\) | −8.44686e14 | + | 8.44686e14i | −0.271841 | + | 0.271841i | ||||
\(383\) | 2.57180e14 | + | 2.57180e14i | 0.0814787 | + | 0.0814787i | 0.746672 | − | 0.665193i | \(-0.231651\pi\) |
−0.665193 | + | 0.746672i | \(0.731651\pi\) | |||||||
\(384\) | − | 2.00449e15i | − | 0.625198i | ||||||
\(385\) | 2.71769e14 | − | 8.95073e14i | 0.0834518 | − | 0.274849i | ||||
\(386\) | 6.74958e15 | 2.04058 | ||||||||
\(387\) | 4.73707e15 | − | 4.73707e15i | 1.41008 | − | 1.41008i | ||||
\(388\) | 1.11725e14 | + | 1.11725e14i | 0.0327461 | + | 0.0327461i | ||||
\(389\) | 1.28470e15i | 0.370769i | 0.982666 | + | 0.185384i | \(0.0593531\pi\) | ||||
−0.982666 | + | 0.185384i | \(0.940647\pi\) | |||||||
\(390\) | 7.04538e15 | + | 2.13918e15i | 2.00224 | + | 0.607937i | ||||
\(391\) | −7.31403e14 | −0.204690 | ||||||||
\(392\) | 1.61635e14 | − | 1.61635e14i | 0.0445470 | − | 0.0445470i | ||||
\(393\) | −1.74294e15 | − | 1.74294e15i | −0.473071 | − | 0.473071i | ||||
\(394\) | 4.40202e15i | 1.17672i | ||||||||
\(395\) | −3.07354e14 | − | 5.75375e14i | −0.0809200 | − | 0.151485i | ||||
\(396\) | −2.23340e15 | −0.579156 | ||||||||
\(397\) | −7.12595e14 | + | 7.12595e14i | −0.182012 | + | 0.182012i | −0.792232 | − | 0.610220i | \(-0.791081\pi\) |
0.610220 | + | 0.792232i | \(0.291081\pi\) | |||||||
\(398\) | −2.70754e15 | − | 2.70754e15i | −0.681202 | − | 0.681202i | ||||
\(399\) | 5.36508e15i | 1.32965i | ||||||||
\(400\) | 2.54463e15 | − | 3.80406e15i | 0.621247 | − | 0.928727i | ||||
\(401\) | 4.12594e15 | 0.992332 | 0.496166 | − | 0.868228i | \(-0.334741\pi\) | ||||
0.496166 | + | 0.868228i | \(0.334741\pi\) | |||||||
\(402\) | −8.57497e15 | + | 8.57497e15i | −2.03178 | + | 2.03178i | ||||
\(403\) | −6.21487e14 | − | 6.21487e14i | −0.145078 | − | 0.145078i | ||||
\(404\) | − | 2.06004e15i | − | 0.473791i | ||||||
\(405\) | 2.71724e15 | − | 1.45150e15i | 0.615741 | − | 0.328917i | ||||
\(406\) | −4.51083e15 | −1.00716 | ||||||||
\(407\) | −1.61311e15 | + | 1.61311e15i | −0.354894 | + | 0.354894i | ||||
\(408\) | 4.22003e14 | + | 4.22003e14i | 0.0914861 | + | 0.0914861i | ||||
\(409\) | − | 7.37449e14i | − | 0.157541i | −0.996893 | − | 0.0787703i | \(-0.974901\pi\) | ||
0.996893 | − | 0.0787703i | \(-0.0250994\pi\) | |||||||
\(410\) | 1.08262e15 | − | 3.56561e15i | 0.227915 | − | 0.750639i | ||||
\(411\) | −1.25923e16 | −2.61248 | ||||||||
\(412\) | 3.75762e15 | − | 3.75762e15i | 0.768298 | − | 0.768298i | ||||
\(413\) | −1.30776e15 | − | 1.30776e15i | −0.263529 | − | 0.263529i | ||||
\(414\) | − | 6.50524e15i | − | 1.29200i | ||||||
\(415\) | −2.28358e15 | − | 6.93360e14i | −0.447022 | − | 0.135728i | ||||
\(416\) | −6.25552e15 | −1.20699 | ||||||||
\(417\) | 1.40375e14 | − | 1.40375e14i | 0.0266977 | − | 0.0266977i | ||||
\(418\) | 1.75067e15 | + | 1.75067e15i | 0.328207 | + | 0.328207i | ||||
\(419\) | 1.89487e15i | 0.350183i | 0.984552 | + | 0.175092i | \(0.0560222\pi\) | ||||
−0.984552 | + | 0.175092i | \(0.943978\pi\) | |||||||
\(420\) | 3.09038e15 | + | 5.78529e15i | 0.563011 | + | 1.05397i | ||||
\(421\) | 7.70049e14 | 0.138301 | 0.0691506 | − | 0.997606i | \(-0.477971\pi\) | ||||
0.0691506 | + | 0.997606i | \(0.477971\pi\) | |||||||
\(422\) | 7.12583e15 | − | 7.12583e15i | 1.26171 | − | 1.26171i | ||||
\(423\) | 1.29011e16 | + | 1.29011e16i | 2.25208 | + | 2.25208i | ||||
\(424\) | − | 1.19273e15i | − | 0.205280i | ||||||
\(425\) | 4.70222e14 | + | 2.37035e15i | 0.0797939 | + | 0.402234i | ||||
\(426\) | 1.17898e16 | 1.97264 | ||||||||
\(427\) | −1.17896e15 | + | 1.17896e15i | −0.194506 | + | 0.194506i | ||||
\(428\) | −2.69291e15 | − | 2.69291e15i | −0.438087 | − | 0.438087i | ||||
\(429\) | − | 3.37725e15i | − | 0.541775i | ||||||
\(430\) | −8.00808e15 | + | 4.27775e15i | −1.26683 | + | 0.676714i | ||||
\(431\) | 1.23954e15 | 0.193373 | 0.0966867 | − | 0.995315i | \(-0.469175\pi\) | ||||
0.0966867 | + | 0.995315i | \(0.469175\pi\) | |||||||
\(432\) | −7.82779e15 | + | 7.82779e15i | −1.20431 | + | 1.20431i | ||||
\(433\) | −4.00108e15 | − | 4.00108e15i | −0.607085 | − | 0.607085i | 0.335098 | − | 0.942183i | \(-0.391231\pi\) |
−0.942183 | + | 0.335098i | \(0.891231\pi\) | |||||||
\(434\) | − | 1.68890e15i | − | 0.252736i | ||||||
\(435\) | 3.04101e15 | − | 1.00156e16i | 0.448831 | − | 1.47823i | ||||
\(436\) | 7.54846e15 | 1.09885 | ||||||||
\(437\) | −2.36388e15 | + | 2.36388e15i | −0.339420 | + | 0.339420i | ||||
\(438\) | 4.09932e15 | + | 4.09932e15i | 0.580586 | + | 0.580586i | ||||
\(439\) | 2.05585e15i | 0.287213i | 0.989635 | + | 0.143607i | \(0.0458700\pi\) | ||||
−0.989635 | + | 0.143607i | \(0.954130\pi\) | |||||||
\(440\) | −4.55090e14 | − | 1.38178e14i | −0.0627164 | − | 0.0190425i | ||||
\(441\) | −4.73819e15 | −0.644141 | ||||||||
\(442\) | 2.65867e15 | − | 2.65867e15i | 0.356559 | − | 0.356559i | ||||
\(443\) | −4.86246e14 | − | 4.86246e14i | −0.0643330 | − | 0.0643330i | 0.674208 | − | 0.738541i | \(-0.264485\pi\) |
−0.738541 | + | 0.674208i | \(0.764485\pi\) | |||||||
\(444\) | − | 1.59959e16i | − | 2.08790i | ||||||
\(445\) | 4.99797e15 | + | 9.35633e15i | 0.643626 | + | 1.20488i | ||||
\(446\) | 5.25324e15 | 0.667449 | ||||||||
\(447\) | 1.33826e16 | − | 1.33826e16i | 1.67762 | − | 1.67762i | ||||
\(448\) | −3.30952e15 | − | 3.30952e15i | −0.409352 | − | 0.409352i | ||||
\(449\) | 7.06392e15i | 0.862120i | 0.902323 | + | 0.431060i | \(0.141860\pi\) | ||||
−0.902323 | + | 0.431060i | \(0.858140\pi\) | |||||||
\(450\) | −2.10823e16 | + | 4.18225e15i | −2.53889 | + | 0.503657i | ||||
\(451\) | −1.70920e15 | −0.203111 | ||||||||
\(452\) | −9.22794e15 | + | 9.22794e15i | −1.08212 | + | 1.08212i | ||||
\(453\) | −1.96655e16 | − | 1.96655e16i | −2.27571 | − | 2.27571i | ||||
\(454\) | 1.93563e16i | 2.21048i | ||||||||
\(455\) | −5.72718e15 | + | 3.05934e15i | −0.645464 | + | 0.344794i | ||||
\(456\) | 2.72782e15 | 0.303407 | ||||||||
\(457\) | 7.02310e15 | − | 7.02310e15i | 0.770959 | − | 0.770959i | −0.207315 | − | 0.978274i | \(-0.566472\pi\) |
0.978274 | + | 0.207315i | \(0.0664725\pi\) | |||||||
\(458\) | 1.31256e16 | + | 1.31256e16i | 1.42208 | + | 1.42208i | ||||
\(459\) | − | 5.84517e15i | − | 0.625059i | ||||||
\(460\) | −1.18739e15 | + | 3.91067e15i | −0.125327 | + | 0.412766i | ||||
\(461\) | −1.41503e16 | −1.47422 | −0.737109 | − | 0.675774i | \(-0.763809\pi\) | ||||
−0.737109 | + | 0.675774i | \(0.763809\pi\) | |||||||
\(462\) | 4.58888e15 | − | 4.58888e15i | 0.471905 | − | 0.471905i | ||||
\(463\) | 1.23030e16 | + | 1.23030e16i | 1.24889 | + | 1.24889i | 0.956212 | + | 0.292676i | \(0.0945458\pi\) |
0.292676 | + | 0.956212i | \(0.405454\pi\) | |||||||
\(464\) | 1.01230e16i | 1.01438i | ||||||||
\(465\) | 3.74995e15 | + | 1.13859e15i | 0.370943 | + | 0.112629i | ||||
\(466\) | −4.10708e15 | −0.401068 | ||||||||
\(467\) | 1.13770e16 | − | 1.13770e16i | 1.09679 | − | 1.09679i | 0.102011 | − | 0.994783i | \(-0.467472\pi\) |
0.994783 | − | 0.102011i | \(-0.0325277\pi\) | |||||||
\(468\) | 1.09621e16 | + | 1.09621e16i | 1.04333 | + | 1.04333i | ||||
\(469\) | − | 1.06941e16i | − | 1.00487i | ||||||
\(470\) | −1.16501e16 | − | 2.18094e16i | −1.08080 | − | 2.02328i | ||||
\(471\) | −9.09117e15 | −0.832711 | ||||||||
\(472\) | −6.64918e14 | + | 6.64918e14i | −0.0601334 | + | 0.0601334i | ||||
\(473\) | 2.94464e15 | + | 2.94464e15i | 0.262946 | + | 0.262946i | ||||
\(474\) | − | 4.52559e15i | − | 0.399030i | ||||||
\(475\) | 9.18067e15 | + | 6.14117e15i | 0.799305 | + | 0.534674i | ||||
\(476\) | 3.34936e15 | 0.287952 | ||||||||
\(477\) | −1.74819e16 | + | 1.74819e16i | −1.48415 | + | 1.48415i | ||||
\(478\) | −1.72018e16 | − | 1.72018e16i | −1.44214 | − | 1.44214i | ||||
\(479\) | − | 2.02648e16i | − | 1.67776i | −0.544316 | − | 0.838880i | \(-0.683211\pi\) | ||
0.544316 | − | 0.838880i | \(-0.316789\pi\) | |||||||
\(480\) | 2.46026e16 | − | 1.31422e16i | 2.01156 | − | 1.07453i | ||||
\(481\) | 1.58352e16 | 1.27865 | ||||||||
\(482\) | −7.24076e14 | + | 7.24076e14i | −0.0577433 | + | 0.0577433i | ||||
\(483\) | 6.19622e15 | + | 6.19622e15i | 0.488027 | + | 0.488027i | ||||
\(484\) | 9.72104e15i | 0.756207i | ||||||||
\(485\) | 2.02629e14 | − | 6.67358e14i | 0.0155686 | − | 0.0512753i | ||||
\(486\) | −6.05127e15 | −0.459229 | ||||||||
\(487\) | −1.19627e16 | + | 1.19627e16i | −0.896721 | + | 0.896721i | −0.995145 | − | 0.0984239i | \(-0.968620\pi\) |
0.0984239 | + | 0.995145i | \(0.468620\pi\) | |||||||
\(488\) | 5.99430e14 | + | 5.99430e14i | 0.0443833 | + | 0.0443833i | ||||
\(489\) | 4.07856e16i | 2.98300i | ||||||||
\(490\) | 6.14437e15 | + | 1.86560e15i | 0.443916 | + | 0.134785i | ||||
\(491\) | 4.72173e15 | 0.336986 | 0.168493 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168493 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(492\) | 8.47433e15 | − | 8.47433e15i | 0.597468 | − | 0.597468i | ||||
\(493\) | −3.77952e15 | − | 3.77952e15i | −0.263242 | − | 0.263242i | ||||
\(494\) | − | 1.71856e16i | − | 1.18250i | ||||||
\(495\) | 4.64501e15 | + | 8.69559e15i | 0.315759 | + | 0.591110i | ||||
\(496\) | −3.79016e15 | −0.254547 | ||||||||
\(497\) | −7.35169e15 | + | 7.35169e15i | −0.487808 | + | 0.487808i | ||||
\(498\) | −1.17075e16 | − | 1.17075e16i | −0.767519 | − | 0.767519i | ||||
\(499\) | − | 1.86387e16i | − | 1.20729i | −0.797253 | − | 0.603646i | \(-0.793714\pi\) | ||
0.797253 | − | 0.603646i | \(-0.206286\pi\) | |||||||
\(500\) | 1.34372e16 | + | 1.33393e15i | 0.859978 | + | 0.0853714i | ||||
\(501\) | 1.05596e16 | 0.667764 | ||||||||
\(502\) | −8.71110e15 | + | 8.71110e15i | −0.544315 | + | 0.544315i | ||||
\(503\) | −4.21542e15 | − | 4.21542e15i | −0.260275 | − | 0.260275i | 0.564890 | − | 0.825166i | \(-0.308918\pi\) |
−0.825166 | + | 0.564890i | \(0.808918\pi\) | |||||||
\(504\) | − | 4.68096e15i | − | 0.285596i | ||||||
\(505\) | −8.02062e15 | + | 4.28446e15i | −0.483571 | + | 0.258314i | ||||
\(506\) | 4.04377e15 | 0.240926 | ||||||||
\(507\) | 3.86032e15 | − | 3.86032e15i | 0.227287 | − | 0.227287i | ||||
\(508\) | −7.42183e15 | − | 7.42183e15i | −0.431846 | − | 0.431846i | ||||
\(509\) | − | 7.67307e15i | − | 0.441228i | −0.975361 | − | 0.220614i | \(-0.929194\pi\) | ||
0.975361 | − | 0.220614i | \(-0.0708061\pi\) | |||||||
\(510\) | −4.87080e15 | + | 1.60420e16i | −0.276808 | + | 0.911669i | ||||
\(511\) | −5.11239e15 | −0.287143 | ||||||||
\(512\) | −1.64359e16 | + | 1.64359e16i | −0.912373 | + | 0.912373i | ||||
\(513\) | −1.88915e16 | − | 1.88915e16i | −1.03648 | − | 1.03648i | ||||
\(514\) | − | 1.24422e16i | − | 0.674713i | ||||||
\(515\) | −2.24451e16 | − | 6.81497e15i | −1.20304 | − | 0.365276i | ||||
\(516\) | −2.91995e16 | −1.54695 | ||||||||
\(517\) | −8.01951e15 | + | 8.01951e15i | −0.419957 | + | 0.419957i | ||||
\(518\) | 2.15163e16 | + | 2.15163e16i | 1.11375 | + | 1.11375i | ||||
\(519\) | 4.47533e16i | 2.28992i | ||||||||
\(520\) | 1.55549e15 | + | 2.91192e15i | 0.0786769 | + | 0.147285i | ||||
\(521\) | 2.97878e16 | 1.48940 | 0.744701 | − | 0.667398i | \(-0.232592\pi\) | ||||
0.744701 | + | 0.667398i | \(0.232592\pi\) | |||||||
\(522\) | 3.36158e16 | − | 3.36158e16i | 1.66158 | − | 1.66158i | ||||
\(523\) | −3.43245e15 | − | 3.43245e15i | −0.167723 | − | 0.167723i | 0.618255 | − | 0.785978i | \(-0.287840\pi\) |
−0.785978 | + | 0.618255i | \(0.787840\pi\) | |||||||
\(524\) | 7.03342e15i | 0.339765i | ||||||||
\(525\) | 1.60973e16 | − | 2.40644e16i | 0.768770 | − | 1.14926i | ||||
\(526\) | 1.81940e16 | 0.859040 | ||||||||
\(527\) | 1.41509e15 | − | 1.41509e15i | 0.0660575 | − | 0.0660575i | ||||
\(528\) | −1.02982e16 | − | 1.02982e16i | −0.475287 | − | 0.475287i | ||||
\(529\) | − | 1.64545e16i | − | 0.750843i | ||||||
\(530\) | 2.95534e16 | − | 1.57868e16i | 1.33337 | − | 0.712262i | ||||
\(531\) | 1.94915e16 | 0.869518 | ||||||||
\(532\) | 1.08251e16 | − | 1.08251e16i | 0.477486 | − | 0.477486i | ||||
\(533\) | 8.38922e15 | + | 8.38922e15i | 0.365896 | + | 0.365896i | ||||
\(534\) | 7.35919e16i | 3.17382i | ||||||||
\(535\) | −4.88398e15 | + | 1.60854e16i | −0.208282 | + | 0.685976i | ||||
\(536\) | −5.43731e15 | −0.229295 | ||||||||
\(537\) | 2.30297e16 | − | 2.30297e16i | 0.960380 | − | 0.960380i | ||||
\(538\) | −3.47675e15 | − | 3.47675e15i | −0.143377 | − | 0.143377i | ||||
\(539\) | − | 2.94534e15i | − | 0.120117i | ||||||
\(540\) | −3.12530e16 | − | 9.48927e15i | −1.26046 | − | 0.382710i | ||||
\(541\) | 6.03588e15 | 0.240745 | 0.120372 | − | 0.992729i | \(-0.461591\pi\) | ||||
0.120372 | + | 0.992729i | \(0.461591\pi\) | |||||||
\(542\) | −4.06989e16 | + | 4.06989e16i | −1.60541 | + | 1.60541i | ||||
\(543\) | 8.74728e15 | + | 8.74728e15i | 0.341251 | + | 0.341251i | ||||
\(544\) | − | 1.42435e16i | − | 0.549571i | ||||||
\(545\) | −1.56993e16 | − | 2.93894e16i | −0.599101 | − | 1.12153i | ||||
\(546\) | −4.50469e16 | −1.70024 | ||||||||
\(547\) | 1.37352e16 | − | 1.37352e16i | 0.512755 | − | 0.512755i | −0.402615 | − | 0.915370i | \(-0.631899\pi\) |
0.915370 | + | 0.402615i | \(0.131899\pi\) | |||||||
\(548\) | 2.54073e16 | + | 2.54073e16i | 0.938157 | + | 0.938157i | ||||
\(549\) | − | 1.75718e16i | − | 0.641775i | ||||||
\(550\) | −2.59976e15 | − | 1.31051e16i | −0.0939196 | − | 0.473440i | ||||
\(551\) | −2.44307e16 | −0.873024 | ||||||||
\(552\) | 3.15040e15 | − | 3.15040e15i | 0.111361 | − | 0.111361i | ||||
\(553\) | 2.82200e15 | + | 2.82200e15i | 0.0986749 | + | 0.0986749i | ||||
\(554\) | − | 2.48946e16i | − | 0.861087i | ||||||
\(555\) | −6.22789e16 | + | 3.32681e16i | −2.13100 | + | 1.13834i | ||||
\(556\) | −5.66466e14 | −0.0191746 | ||||||||
\(557\) | −2.30649e15 | + | 2.30649e15i | −0.0772362 | + | 0.0772362i | −0.744670 | − | 0.667433i | \(-0.767393\pi\) |
0.667433 | + | 0.744670i | \(0.267393\pi\) | |||||||
\(558\) | 1.25861e16 | + | 1.25861e16i | 0.416953 | + | 0.416953i | ||||
\(559\) | − | 2.89062e16i | − | 0.947372i | ||||||
\(560\) | −8.13495e15 | + | 2.67925e16i | −0.263771 | + | 0.868730i | ||||
\(561\) | 7.68983e15 | 0.246683 | ||||||||
\(562\) | 2.83904e16 | − | 2.83904e16i | 0.901060 | − | 0.901060i | ||||
\(563\) | −1.89176e15 | − | 1.89176e15i | −0.0594040 | − | 0.0594040i | 0.676781 | − | 0.736185i | \(-0.263375\pi\) |
−0.736185 | + | 0.676781i | \(0.763375\pi\) | |||||||
\(564\) | − | 7.95227e16i | − | 2.47068i | ||||||
\(565\) | 5.51206e16 | + | 1.67362e16i | 1.69443 | + | 0.514476i | ||||
\(566\) | −9.74204e13 | −0.00296314 | ||||||||
\(567\) | −1.33271e16 | + | 1.33271e16i | −0.401085 | + | 0.401085i | ||||
\(568\) | 3.73789e15 | + | 3.73789e15i | 0.111311 | + | 0.111311i | ||||
\(569\) | 6.48056e16i | 1.90959i | 0.297273 | + | 0.954793i | \(0.403923\pi\) | ||||
−0.297273 | + | 0.954793i | \(0.596077\pi\) | |||||||
\(570\) | 3.61051e16 | + | 6.75898e16i | 1.05274 | + | 1.97075i | ||||
\(571\) | −6.74108e16 | −1.94497 | −0.972485 | − | 0.232967i | \(-0.925157\pi\) | ||||
−0.972485 | + | 0.232967i | \(0.925157\pi\) | |||||||
\(572\) | −6.81424e15 | + | 6.81424e15i | −0.194555 | + | 0.194555i | ||||
\(573\) | 1.19916e16 | + | 1.19916e16i | 0.338803 | + | 0.338803i | ||||
\(574\) | 2.27979e16i | 0.637417i | ||||||||
\(575\) | 1.76954e16 | − | 3.51037e15i | 0.489615 | − | 0.0971283i | ||||
\(576\) | 4.93267e16 | 1.35066 | ||||||||
\(577\) | −2.36489e16 | + | 2.36489e16i | −0.640849 | + | 0.640849i | −0.950764 | − | 0.309915i | \(-0.899699\pi\) |
0.309915 | + | 0.950764i | \(0.399699\pi\) | |||||||
\(578\) | −2.99460e16 | − | 2.99460e16i | −0.803105 | − | 0.803105i | ||||
\(579\) | − | 9.58201e16i | − | 2.54323i | ||||||
\(580\) | −2.63442e16 | + | 1.40725e16i | −0.692017 | + | 0.369662i | ||||
\(581\) | 1.46008e16 | 0.379595 | ||||||||
\(582\) | 3.42142e15 | − | 3.42142e15i | 0.0880378 | − | 0.0880378i | ||||
\(583\) | −1.08671e16 | − | 1.08671e16i | −0.276758 | − | 0.276758i | ||||
\(584\) | 2.59934e15i | 0.0655218i | ||||||||
\(585\) | 1.98814e16 | − | 6.54793e16i | 0.496033 | − | 1.63369i | ||||
\(586\) | 5.03490e16 | 1.24338 | ||||||||
\(587\) | −1.75615e16 | + | 1.75615e16i | −0.429273 | + | 0.429273i | −0.888381 | − | 0.459108i | \(-0.848169\pi\) |
0.459108 | + | 0.888381i | \(0.348169\pi\) | |||||||
\(588\) | 1.46032e16 | + | 1.46032e16i | 0.353333 | + | 0.353333i | ||||
\(589\) | − | 9.14712e15i | − | 0.219075i | ||||||
\(590\) | −2.52761e16 | − | 7.67453e15i | −0.599236 | − | 0.181945i | ||||
\(591\) | 6.24932e16 | 1.46659 | ||||||||
\(592\) | 4.82858e16 | − | 4.82858e16i | 1.12173 | − | 1.12173i | ||||
\(593\) | 1.59726e16 | + | 1.59726e16i | 0.367322 | + | 0.367322i | 0.866500 | − | 0.499177i | \(-0.166364\pi\) |
−0.499177 | + | 0.866500i | \(0.666364\pi\) | |||||||
\(594\) | 3.23167e16i | 0.735712i | ||||||||
\(595\) | −6.96598e15 | − | 1.30405e16i | −0.156993 | − | 0.293895i | ||||
\(596\) | −5.40038e16 | −1.20489 | ||||||||
\(597\) | −3.84375e16 | + | 3.84375e16i | −0.849002 | + | 0.849002i | ||||
\(598\) | −1.98479e16 | − | 1.98479e16i | −0.434018 | − | 0.434018i | ||||
\(599\) | − | 5.40452e14i | − | 0.0117003i | −0.999983 | − | 0.00585014i | \(-0.998138\pi\) | ||
0.999983 | − | 0.00585014i | \(-0.00186217\pi\) | |||||||
\(600\) | −1.22353e16 | − | 8.18448e15i | −0.262245 | − | 0.175422i | ||||
\(601\) | −9.10704e16 | −1.93255 | −0.966274 | − | 0.257515i | \(-0.917096\pi\) | ||||
−0.966274 | + | 0.257515i | \(0.917096\pi\) | |||||||
\(602\) | 3.92767e16 | − | 3.92767e16i | 0.825194 | − | 0.825194i | ||||
\(603\) | 7.96952e16 | + | 7.96952e16i | 1.65779 | + | 1.65779i | ||||
\(604\) | 7.93579e16i | 1.63444i | ||||||||
\(605\) | 3.78482e16 | − | 2.02178e16i | 0.771815 | − | 0.412288i | ||||
\(606\) | −6.30859e16 | −1.27379 | ||||||||
\(607\) | −2.28805e16 | + | 2.28805e16i | −0.457440 | + | 0.457440i | −0.897814 | − | 0.440374i | \(-0.854846\pi\) |
0.440374 | + | 0.897814i | \(0.354846\pi\) | |||||||
\(608\) | −4.60348e16 | − | 4.60348e16i | −0.911306 | − | 0.911306i | ||||
\(609\) | 6.40378e16i | 1.25526i | ||||||||
\(610\) | −6.91867e15 | + | 2.27867e16i | −0.134290 | + | 0.442285i | ||||
\(611\) | 7.87239e16 | 1.51307 | ||||||||
\(612\) | −2.49602e16 | + | 2.49602e16i | −0.475051 | + | 0.475051i | ||||
\(613\) | 5.03246e16 | + | 5.03246e16i | 0.948456 | + | 0.948456i | 0.998735 | − | 0.0502791i | \(-0.0160111\pi\) |
−0.0502791 | + | 0.998735i | \(0.516011\pi\) | |||||||
\(614\) | − | 1.03704e17i | − | 1.93546i | ||||||
\(615\) | −5.06191e16 | − | 1.53694e16i | −0.935544 | − | 0.284057i | ||||
\(616\) | 2.90976e15 | 0.0532566 | ||||||||
\(617\) | 5.26298e16 | − | 5.26298e16i | 0.953939 | − | 0.953939i | −0.0450463 | − | 0.998985i | \(-0.514344\pi\) |
0.998985 | + | 0.0450463i | \(0.0143435\pi\) | |||||||
\(618\) | −1.15072e17 | − | 1.15072e17i | −2.06557 | − | 2.06557i | ||||
\(619\) | 5.70602e16i | 1.01435i | 0.861842 | + | 0.507177i | \(0.169311\pi\) | ||||
−0.861842 | + | 0.507177i | \(0.830689\pi\) | |||||||
\(620\) | −5.26891e15 | − | 9.86355e15i | −0.0927622 | − | 0.173653i | ||||
\(621\) | −4.36362e16 | −0.760846 | ||||||||
\(622\) | −2.59048e16 | + | 2.59048e16i | −0.447340 | + | 0.447340i | ||||
\(623\) | −4.58894e16 | − | 4.58894e16i | −0.784845 | − | 0.784845i | ||||
\(624\) | 1.01092e17i | 1.71242i | ||||||||
\(625\) | −2.27530e16 | − | 5.50910e16i | −0.381731 | − | 0.924273i | ||||
\(626\) | 8.30228e16 | 1.37959 | ||||||||
\(627\) | 2.48534e16 | − | 2.48534e16i | 0.409054 | − | 0.409054i | ||||
\(628\) | 1.83432e16 | + | 1.83432e16i | 0.299031 | + | 0.299031i | ||||
\(629\) | 3.60560e16i | 0.582202i | ||||||||
\(630\) | 1.15985e17 | − | 6.19568e16i | 1.85506 | − | 0.990936i | ||||
\(631\) | 2.30258e16 | 0.364786 | 0.182393 | − | 0.983226i | \(-0.441616\pi\) | ||||
0.182393 | + | 0.983226i | \(0.441616\pi\) | |||||||
\(632\) | 1.43482e15 | − | 1.43482e15i | 0.0225162 | − | 0.0225162i | ||||
\(633\) | −1.01162e17 | − | 1.01162e17i | −1.57251 | − | 1.57251i | ||||
\(634\) | 9.54514e16i | 1.46976i | ||||||||
\(635\) | −1.34605e16 | + | 4.43323e16i | −0.205314 | + | 0.676204i | ||||
\(636\) | 1.07759e17 | 1.62822 | ||||||||
\(637\) | −1.44565e16 | + | 1.44565e16i | −0.216385 | + | 0.216385i | ||||
\(638\) | 2.08961e16 | + | 2.08961e16i | 0.309843 | + | 0.309843i | ||||
\(639\) | − | 1.09573e17i | − | 1.60953i | ||||||
\(640\) | 2.41584e16 | + | 7.33517e15i | 0.351551 | + | 0.106741i | ||||
\(641\) | 3.74181e15 | 0.0539429 | 0.0269714 | − | 0.999636i | \(-0.491414\pi\) | ||||
0.0269714 | + | 0.999636i | \(0.491414\pi\) | |||||||
\(642\) | −8.24669e16 | + | 8.24669e16i | −1.17779 | + | 1.17779i | ||||
\(643\) | 1.66526e16 | + | 1.66526e16i | 0.235622 | + | 0.235622i | 0.815035 | − | 0.579412i | \(-0.196718\pi\) |
−0.579412 | + | 0.815035i | \(0.696718\pi\) | |||||||
\(644\) | − | 2.50041e16i | − | 0.350506i | ||||||
\(645\) | 6.07290e16 | + | 1.13686e17i | 0.843408 | + | 1.57888i | ||||
\(646\) | 3.91307e16 | 0.538422 | ||||||||
\(647\) | −1.95135e16 | + | 1.95135e16i | −0.266017 | + | 0.266017i | −0.827493 | − | 0.561476i | \(-0.810234\pi\) |
0.561476 | + | 0.827493i | \(0.310234\pi\) | |||||||
\(648\) | 6.77601e15 | + | 6.77601e15i | 0.0915217 | + | 0.0915217i | ||||
\(649\) | 1.21163e16i | 0.162144i | ||||||||
\(650\) | −5.15632e16 | + | 7.70839e16i | −0.683691 | + | 1.02208i | ||||
\(651\) | −2.39765e16 | −0.314992 | ||||||||
\(652\) | 8.22927e16 | − | 8.22927e16i | 1.07121 | − | 1.07121i | ||||
\(653\) | 1.75698e16 | + | 1.75698e16i | 0.226615 | + | 0.226615i | 0.811277 | − | 0.584662i | \(-0.198773\pi\) |
−0.584662 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(654\) | − | 2.31162e17i | − | 2.95426i | ||||||
\(655\) | 2.73842e16 | − | 1.46281e16i | 0.346778 | − | 0.185242i | ||||
\(656\) | 5.11620e16 | 0.641984 | ||||||||
\(657\) | 3.80988e16 | − | 3.80988e16i | 0.473717 | − | 0.473717i | ||||
\(658\) | 1.06967e17 | + | 1.06967e17i | 1.31794 | + | 1.31794i | ||||
\(659\) | 3.81081e16i | 0.465269i | 0.972564 | + | 0.232635i | \(0.0747346\pi\) | ||||
−0.972564 | + | 0.232635i | \(0.925265\pi\) | |||||||
\(660\) | 1.24840e16 | − | 4.11160e16i | 0.151039 | − | 0.497448i | ||||
\(661\) | −8.15161e16 | −0.977315 | −0.488657 | − | 0.872476i | \(-0.662513\pi\) | ||||
−0.488657 | + | 0.872476i | \(0.662513\pi\) | |||||||
\(662\) | −7.08606e16 | + | 7.08606e16i | −0.841893 | + | 0.841893i | ||||
\(663\) | −3.77438e16 | − | 3.77438e16i | −0.444390 | − | 0.444390i | ||||
\(664\) | − | 7.42363e15i | − | 0.0866180i | ||||||
\(665\) | −6.46606e16 | − | 1.96328e16i | −0.747670 | − | 0.227013i | ||||
\(666\) | −3.20689e17 | −3.67484 | ||||||||
\(667\) | −2.82154e16 | + | 2.82154e16i | −0.320429 | + | 0.320429i | ||||
\(668\) | −2.13061e16 | − | 2.13061e16i | −0.239798 | − | 0.239798i | ||||
\(669\) | − | 7.45774e16i | − | 0.831861i | ||||||
\(670\) | −7.19677e16 | − | 1.34726e17i | −0.795590 | − | 1.48937i | ||||
\(671\) | 1.09229e16 | 0.119675 | ||||||||
\(672\) | −1.20667e17 | + | 1.20667e17i | −1.31030 | + | 1.31030i | ||||
\(673\) | −7.90609e16 | − | 7.90609e16i | −0.850886 | − | 0.850886i | 0.139356 | − | 0.990242i | \(-0.455497\pi\) |
−0.990242 | + | 0.139356i | \(0.955497\pi\) | |||||||
\(674\) | − | 4.39339e16i | − | 0.468641i | ||||||
\(675\) | 2.80539e16 | + | 1.41417e17i | 0.296600 | + | 1.49513i | ||||
\(676\) | −1.55779e16 | −0.163240 | ||||||||
\(677\) | 2.97497e16 | − | 2.97497e16i | 0.308995 | − | 0.308995i | −0.535525 | − | 0.844519i | \(-0.679886\pi\) |
0.844519 | + | 0.535525i | \(0.179886\pi\) | |||||||
\(678\) | 2.82594e17 | + | 2.82594e17i | 2.90927 | + | 2.90927i | ||||
\(679\) | 4.26697e15i | 0.0435412i | ||||||||
\(680\) | −6.63030e15 | + | 3.54178e15i | −0.0670625 | + | 0.0358235i | ||||
\(681\) | 2.74791e17 | 2.75499 | ||||||||
\(682\) | −7.82375e15 | + | 7.82375e15i | −0.0777515 | + | 0.0777515i | ||||
\(683\) | −5.51641e15 | − | 5.51641e15i | −0.0543415 | − | 0.0543415i | 0.679414 | − | 0.733755i | \(-0.262234\pi\) |
−0.733755 | + | 0.679414i | \(0.762234\pi\) | |||||||
\(684\) | 1.61342e17i | 1.57547i | ||||||||
\(685\) | 4.60797e16 | − | 1.51764e17i | 0.446032 | − | 1.46901i | ||||
\(686\) | −1.54906e17 | −1.48636 | ||||||||
\(687\) | 1.86337e17 | − | 1.86337e17i | 1.77238 | − | 1.77238i | ||||
\(688\) | −8.81430e16 | − | 8.81430e16i | −0.831107 | − | 0.831107i | ||||
\(689\) | 1.06677e17i | 0.997138i | ||||||||
\(690\) | 1.19759e17 | + | 3.63622e16i | 1.10972 | + | 0.336942i | ||||
\(691\) | −9.43544e16 | −0.866750 | −0.433375 | − | 0.901214i | \(-0.642677\pi\) | ||||
−0.433375 | + | 0.901214i | \(0.642677\pi\) | |||||||
\(692\) | 9.02983e16 | − | 9.02983e16i | 0.822324 | − | 0.822324i | ||||
\(693\) | −4.26487e16 | − | 4.26487e16i | −0.385041 | − | 0.385041i | ||||
\(694\) | − | 7.05912e16i | − | 0.631821i | ||||||
\(695\) | 1.17813e15 | + | 2.20550e15i | 0.0104541 | + | 0.0195703i | ||||
\(696\) | 3.25594e16 | 0.286431 | ||||||||
\(697\) | −1.91018e16 | + | 1.91018e16i | −0.166601 | + | 0.166601i | ||||
\(698\) | 6.08478e16 | + | 6.08478e16i | 0.526153 | + | 0.526153i | ||||
\(699\) | 5.83061e16i | 0.499863i | ||||||||
\(700\) | −8.10339e16 | + | 1.60752e16i | −0.688776 | + | 0.136637i | ||||
\(701\) | −6.88565e16 | −0.580279 | −0.290140 | − | 0.956984i | \(-0.593702\pi\) | ||||
−0.290140 | + | 0.956984i | \(0.593702\pi\) | |||||||
\(702\) | 1.58619e17 | − | 1.58619e17i | 1.32536 | − | 1.32536i | ||||
\(703\) | 1.16532e17 | + | 1.16532e17i | 0.965416 | + | 0.965416i | ||||
\(704\) | 3.06623e16i | 0.251866i | ||||||||
\(705\) | −3.09616e17 | + | 1.65391e17i | −2.52167 | + | 1.34703i | ||||
\(706\) | 2.08962e17 | 1.68748 | ||||||||
\(707\) | 3.93382e16 | − | 3.93382e16i | 0.314991 | − | 0.314991i | ||||
\(708\) | −6.00733e16 | − | 6.00733e16i | −0.476960 | − | 0.476960i | ||||
\(709\) | − | 1.81196e17i | − | 1.42650i | −0.700909 | − | 0.713251i | \(-0.747222\pi\) | ||
0.700909 | − | 0.713251i | \(-0.252778\pi\) | |||||||
\(710\) | −4.31430e16 | + | 1.42092e17i | −0.336791 | + | 1.10922i | ||||
\(711\) | −4.20605e16 | −0.325580 | ||||||||
\(712\) | −2.33320e16 | + | 2.33320e16i | −0.179090 | + | 0.179090i | ||||
\(713\) | −1.05642e16 | − | 1.05642e16i | −0.0804078 | − | 0.0804078i | ||||
\(714\) | − | 1.02570e17i | − | 0.774158i | ||||||
\(715\) | 4.07030e16 | + | 1.23586e16i | 0.304643 | + | 0.0924980i | ||||
\(716\) | −9.29338e16 | −0.689756 | ||||||||
\(717\) | −2.44205e17 | + | 2.44205e17i | −1.79738 | + | 1.79738i | ||||
\(718\) | −6.30087e16 | − | 6.30087e16i | −0.459890 | − | 0.459890i | ||||
\(719\) | − | 5.00769e16i | − | 0.362464i | −0.983440 | − | 0.181232i | \(-0.941992\pi\) | ||
0.983440 | − | 0.181232i | \(-0.0580084\pi\) | |||||||
\(720\) | −1.39041e17 | − | 2.60288e17i | −0.998037 | − | 1.86835i | ||||
\(721\) | 1.43510e17 | 1.02158 | ||||||||
\(722\) | −1.02889e16 | + | 1.02889e16i | −0.0726353 | + | 0.0726353i | ||||
\(723\) | 1.02793e16 | + | 1.02793e16i | 0.0719672 | + | 0.0719672i | ||||
\(724\) | − | 3.52986e16i | − | 0.245090i | ||||||
\(725\) | 1.09581e17 | + | 7.33013e16i | 0.754583 | + | 0.504759i | ||||
\(726\) | 2.97694e17 | 2.03306 | ||||||||
\(727\) | 9.59203e16 | − | 9.59203e16i | 0.649687 | − | 0.649687i | −0.303231 | − | 0.952917i | \(-0.598065\pi\) |
0.952917 | + | 0.303231i | \(0.0980652\pi\) | |||||||
\(728\) | −1.42819e16 | − | 1.42819e16i | −0.0959397 | − | 0.0959397i | ||||
\(729\) | 1.90686e17i | 1.27044i | ||||||||
\(730\) | −6.44064e16 | + | 3.44046e16i | −0.425590 | + | 0.227342i | ||||
\(731\) | 6.58181e16 | 0.431361 | ||||||||
\(732\) | −5.41567e16 | + | 5.41567e16i | −0.352035 | + | 0.352035i | ||||
\(733\) | −4.57264e16 | − | 4.57264e16i | −0.294811 | − | 0.294811i | 0.544166 | − | 0.838977i | \(-0.316846\pi\) |
−0.838977 | + | 0.544166i | \(0.816846\pi\) | |||||||
\(734\) | 1.87962e17i | 1.20197i | ||||||||
\(735\) | 2.64849e16 | − | 8.72283e16i | 0.167987 | − | 0.553265i | ||||
\(736\) | −1.06333e17 | −0.668959 | ||||||||
\(737\) | −4.95399e16 | + | 4.95399e16i | −0.309136 | + | 0.309136i | ||||
\(738\) | −1.69895e17 | − | 1.69895e17i | −1.05158 | − | 1.05158i | ||||
\(739\) | 1.18384e17i | 0.726818i | 0.931630 | + | 0.363409i | \(0.118387\pi\) | ||||
−0.931630 | + | 0.363409i | \(0.881613\pi\) | |||||||
\(740\) | 1.92784e17 | + | 5.85347e16i | 1.17404 | + | 0.356470i | ||||
\(741\) | −2.43975e17 | −1.47379 | ||||||||
\(742\) | −1.44949e17 | + | 1.44949e17i | −0.868542 | + | 0.868542i | ||||
\(743\) | −8.36175e16 | − | 8.36175e16i | −0.497009 | − | 0.497009i | 0.413497 | − | 0.910506i | \(-0.364307\pi\) |
−0.910506 | + | 0.413497i | \(0.864307\pi\) | |||||||
\(744\) | 1.21906e16i | 0.0718765i | ||||||||
\(745\) | 1.12317e17 | + | 2.10260e17i | 0.656912 | + | 1.22976i | ||||
\(746\) | −5.94545e16 | −0.344947 | ||||||||
\(747\) | −1.08809e17 | + | 1.08809e17i | −0.626240 | + | 0.626240i | ||||
\(748\) | −1.55157e16 | − | 1.55157e16i | −0.0885853 | − | 0.0885853i | ||||
\(749\) | − | 1.02847e17i | − | 0.582507i | ||||||
\(750\) | 4.08498e16 | − | 4.11495e17i | 0.229521 | − | 2.31205i | ||||
\(751\) | −5.34118e16 | −0.297713 | −0.148856 | − | 0.988859i | \(-0.547559\pi\) | ||||
−0.148856 | + | 0.988859i | \(0.547559\pi\) | |||||||
\(752\) | 2.40051e17 | − | 2.40051e17i | 1.32738 | − | 1.32738i | ||||
\(753\) | 1.23667e17 | + | 1.23667e17i | 0.678396 | + | 0.678396i | ||||
\(754\) | − | 2.05128e17i | − | 1.11634i | ||||||
\(755\) | 3.08975e17 | − | 1.65048e17i | 1.66817 | − | 0.891105i | ||||
\(756\) | 1.99826e17 | 1.07034 | ||||||||
\(757\) | 8.74072e16 | − | 8.74072e16i | 0.464485 | − | 0.464485i | −0.435637 | − | 0.900122i | \(-0.643477\pi\) |
0.900122 | + | 0.435637i | \(0.143477\pi\) | |||||||
\(758\) | 4.80251e16 | + | 4.80251e16i | 0.253194 | + | 0.253194i | ||||
\(759\) | − | 5.74072e16i | − | 0.300273i | ||||||
\(760\) | −9.98207e15 | + | 3.28760e16i | −0.0518011 | + | 0.170607i | ||||
\(761\) | −1.69256e17 | −0.871439 | −0.435720 | − | 0.900083i | \(-0.643506\pi\) | ||||
−0.435720 | + | 0.900083i | \(0.643506\pi\) | |||||||
\(762\) | −2.27284e17 | + | 2.27284e17i | −1.16102 | + | 1.16102i | ||||
\(763\) | 1.44144e17 | + | 1.44144e17i | 0.730551 | + | 0.730551i | ||||
\(764\) | − | 4.83905e16i | − | 0.243332i | ||||||
\(765\) | 1.49093e17 | + | 4.52689e16i | 0.743857 | + | 0.225856i | ||||
\(766\) | −3.17818e16 | −0.157328 | ||||||||
\(767\) | 5.94699e16 | − | 5.94699e16i | 0.292096 | − | 0.292096i | ||||
\(768\) | 2.99770e17 | + | 2.99770e17i | 1.46090 | + | 1.46090i | ||||
\(769\) | − | 1.92021e17i | − | 0.928521i | −0.885699 | − | 0.464260i | \(-0.846320\pi\) | ||
0.885699 | − | 0.464260i | \(-0.153680\pi\) | |||||||
\(770\) | 3.85134e16 | + | 7.20981e16i | 0.184785 | + | 0.345923i | ||||
\(771\) | −1.76636e17 | −0.840915 | ||||||||
\(772\) | −1.93335e17 | + | 1.93335e17i | −0.913288 | + | 0.913288i | ||||
\(773\) | −1.91520e17 | − | 1.91520e17i | −0.897714 | − | 0.897714i | 0.0975192 | − | 0.995234i | \(-0.468909\pi\) |
−0.995234 | + | 0.0975192i | \(0.968909\pi\) | |||||||
\(774\) | 5.85399e17i | 2.72274i | ||||||||
\(775\) | −2.74448e16 | + | 4.10283e16i | −0.126663 | + | 0.189354i | ||||
\(776\) | 2.16949e15 | 0.00993546 | ||||||||
\(777\) | 3.05455e17 | − | 3.05455e17i | 1.38810 | − | 1.38810i | ||||
\(778\) | −7.93803e16 | − | 7.93803e16i | −0.357961 | − | 0.357961i | ||||
\(779\) | 1.23474e17i | 0.552522i | ||||||||
\(780\) | −2.63083e17 | + | 1.40534e17i | −1.16822 | + | 0.624041i | ||||
\(781\) | 6.81125e16 | 0.300138 | ||||||||
\(782\) | 4.51927e16 | − | 4.51927e16i | 0.197619 | − | 0.197619i | ||||
\(783\) | −2.25490e17 | − | 2.25490e17i | −0.978489 | − | 0.978489i | ||||
\(784\) | 8.81638e16i | 0.379659i | ||||||||
\(785\) | 3.32679e16 | − | 1.09568e17i | 0.142170 | − | 0.468237i | ||||
\(786\) | 2.15389e17 | 0.913458 | ||||||||
\(787\) | −1.82035e17 | + | 1.82035e17i | −0.766138 | + | 0.766138i | −0.977424 | − | 0.211287i | \(-0.932235\pi\) |
0.211287 | + | 0.977424i | \(0.432235\pi\) | |||||||
\(788\) | −1.26092e17 | − | 1.26092e17i | −0.526659 | − | 0.526659i | ||||
\(789\) | − | 2.58290e17i | − | 1.07065i | ||||||
\(790\) | 5.45430e16 | + | 1.65608e16i | 0.224376 | + | 0.0681268i | ||||
\(791\) | −3.52431e17 | −1.43885 | ||||||||
\(792\) | −2.16843e16 | + | 2.16843e16i | −0.0878605 | + | 0.0878605i | ||||
\(793\) | −5.36127e16 | − | 5.36127e16i | −0.215590 | − | 0.215590i | ||||
\(794\) | − | 8.80613e16i | − | 0.351449i | ||||||
\(795\) | −2.24117e17 | − | 4.19554e17i | −0.887713 | − | 1.66182i | ||||
\(796\) | 1.55110e17 | 0.609763 | ||||||||
\(797\) | −6.96241e16 | + | 6.96241e16i | −0.271650 | + | 0.271650i | −0.829764 | − | 0.558114i | \(-0.811525\pi\) |
0.558114 | + | 0.829764i | \(0.311525\pi\) | |||||||
\(798\) | −3.31503e17 | − | 3.31503e17i | −1.28372 | − | 1.28372i | ||||
\(799\) | 1.79251e17i | 0.688937i | ||||||||
\(800\) | 6.83617e16 | + | 3.44605e17i | 0.260779 | + | 1.31456i | ||||
\(801\) | 6.83958e17 | 2.58961 | ||||||||
\(802\) | −2.54938e17 | + | 2.54938e17i | −0.958052 | + | 0.958052i | ||||
\(803\) | 2.36828e16 | + | 2.36828e16i | 0.0883365 | + | 0.0883365i | ||||
\(804\) | − | 4.91245e17i | − | 1.81870i | ||||||
\(805\) | −9.73518e16 | + | 5.20034e16i | −0.357741 | + | 0.191098i | ||||
\(806\) | 7.68022e16 | 0.280132 | ||||||||
\(807\) | −4.93575e16 | + | 4.93575e16i | −0.178695 | + | 0.178695i | ||||
\(808\) | −2.00011e16 | − | 2.00011e16i | −0.0718763 | − | 0.0718763i | ||||
\(809\) | 4.08047e17i | 1.45552i | 0.685829 | + | 0.727762i | \(0.259440\pi\) | ||||
−0.685829 | + | 0.727762i | \(0.740560\pi\) | |||||||
\(810\) | −7.82093e16 | + | 2.57583e17i | −0.276916 | + | 0.912025i | ||||
\(811\) | 2.99530e17 | 1.05272 | 0.526362 | − | 0.850260i | \(-0.323556\pi\) | ||||
0.526362 | + | 0.850260i | \(0.323556\pi\) | |||||||
\(812\) | 1.29209e17 | − | 1.29209e17i | 0.450770 | − | 0.450770i | ||||
\(813\) | 5.77781e17 | + | 5.77781e17i | 2.00087 | + | 2.00087i | ||||
\(814\) | − | 1.99346e17i | − | 0.685268i | ||||||
\(815\) | −4.91553e17 | − | 1.49249e17i | −1.67735 | − | 0.509292i | ||||
\(816\) | −2.30182e17 | −0.779706 | ||||||||
\(817\) | 2.12723e17 | − | 2.12723e17i | 0.715290 | − | 0.715290i | ||||
\(818\) | 4.55663e16 | + | 4.55663e16i | 0.152098 | + | 0.152098i | ||||
\(819\) | 4.18663e17i | 1.38727i | ||||||||
\(820\) | 7.11231e16 | + | 1.33144e17i | 0.233952 | + | 0.437965i | ||||
\(821\) | −2.94278e17 | −0.960945 | −0.480473 | − | 0.877010i | \(-0.659535\pi\) | ||||
−0.480473 | + | 0.877010i | \(0.659535\pi\) | |||||||
\(822\) | 7.78066e17 | − | 7.78066e17i | 2.52223 | − | 2.52223i | ||||
\(823\) | 3.30432e17 | + | 3.30432e17i | 1.06337 | + | 1.06337i | 0.997852 | + | 0.0655141i | \(0.0208687\pi\) |
0.0655141 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(824\) | − | 7.29662e16i | − | 0.233109i | ||||||
\(825\) | −1.86047e17 | + | 3.69074e16i | −0.590062 | + | 0.117055i | ||||
\(826\) | 1.61611e17 | 0.508851 | ||||||||
\(827\) | −1.15770e17 | + | 1.15770e17i | −0.361880 | + | 0.361880i | −0.864505 | − | 0.502625i | \(-0.832368\pi\) |
0.502625 | + | 0.864505i | \(0.332368\pi\) | |||||||
\(828\) | 1.86337e17 | + | 1.86337e17i | 0.578251 | + | 0.578251i | ||||
\(829\) | − | 5.47006e17i | − | 1.68525i | −0.538500 | − | 0.842626i | \(-0.681009\pi\) | ||
0.538500 | − | 0.842626i | \(-0.318991\pi\) | |||||||
\(830\) | 1.83943e17 | − | 9.82585e16i | 0.562619 | − | 0.300540i | ||||
\(831\) | −3.53416e17 | −1.07320 | ||||||||
\(832\) | 1.50499e17 | − | 1.50499e17i | 0.453726 | − | 0.453726i | ||||
\(833\) | −3.29168e16 | − | 3.29168e16i | −0.0985253 | − | 0.0985253i | ||||
\(834\) | 1.73473e16i | 0.0515507i | ||||||||
\(835\) | −3.86416e16 | + | 1.27266e17i | −0.114008 | + | 0.375486i | ||||
\(836\) | −1.00293e17 | −0.293787 | ||||||||
\(837\) | 8.44259e16 | − | 8.44259e16i | 0.245540 | − | 0.245540i | ||||
\(838\) | −1.17082e17 | − | 1.17082e17i | −0.338086 | − | 0.338086i | ||||
\(839\) | − | 2.08823e17i | − | 0.598697i | −0.954144 | − | 0.299348i | \(-0.903231\pi\) | ||
0.954144 | − | 0.299348i | \(-0.0967693\pi\) | |||||||
\(840\) | 8.61747e16 | + | 2.61650e16i | 0.245304 | + | 0.0744811i | ||||
\(841\) | 6.22088e16 | 0.175823 | ||||||||
\(842\) | −4.75806e16 | + | 4.75806e16i | −0.133523 | + | 0.133523i | ||||
\(843\) | −4.03044e17 | − | 4.03044e17i | −1.12302 | − | 1.12302i | ||||
\(844\) | 4.08226e17i | 1.12939i | ||||||||
\(845\) | 3.23988e16 | + | 6.06514e16i | 0.0889996 | + | 0.166610i | ||||
\(846\) | −1.59429e18 | −4.34856 | ||||||||
\(847\) | −1.85632e17 | + | 1.85632e17i | −0.502750 | + | 0.502750i | ||||
\(848\) | 3.25287e17 | + | 3.25287e17i | 0.874766 | + | 0.874766i | ||||
\(849\) | 1.38303e15i | 0.00369304i | ||||||||
\(850\) | −1.75516e17 | − | 1.17407e17i | −0.465376 | − | 0.311301i | ||||
\(851\) | 2.69170e17 | 0.708679 | ||||||||
\(852\) | −3.37707e17 | + | 3.37707e17i | −0.882881 | + | 0.882881i | ||||
\(853\) | 4.48811e16 | + | 4.48811e16i | 0.116512 | + | 0.116512i | 0.762959 | − | 0.646447i | \(-0.223746\pi\) |
−0.646447 | + | 0.762959i | \(0.723746\pi\) | |||||||
\(854\) | − | 1.45694e17i | − | 0.375573i | ||||||
\(855\) | 6.28175e17 | − | 3.35558e17i | 1.60799 | − | 0.858957i | ||||
\(856\) | −5.22915e16 | −0.132919 | ||||||||
\(857\) | −1.35142e17 | + | 1.35142e17i | −0.341118 | + | 0.341118i | −0.856788 | − | 0.515669i | \(-0.827543\pi\) |
0.515669 | + | 0.856788i | \(0.327543\pi\) | |||||||
\(858\) | 2.08677e17 | + | 2.08677e17i | 0.523060 | + | 0.523060i | ||||
\(859\) | 5.20411e17i | 1.29535i | 0.761916 | + | 0.647676i | \(0.224259\pi\) | ||||
−0.761916 | + | 0.647676i | \(0.775741\pi\) | |||||||
\(860\) | 1.06852e17 | − | 3.51916e17i | 0.264113 | − | 0.869859i | ||||
\(861\) | 3.23650e17 | 0.794431 | ||||||||
\(862\) | −7.65901e16 | + | 7.65901e16i | −0.186693 | + | 0.186693i | ||||
\(863\) | 3.52137e16 | + | 3.52137e16i | 0.0852407 | + | 0.0852407i | 0.748441 | − | 0.663201i | \(-0.230802\pi\) |
−0.663201 | + | 0.748441i | \(0.730802\pi\) | |||||||
\(864\) | − | 8.49781e17i | − | 2.04279i | ||||||
\(865\) | −5.39372e17 | − | 1.63769e17i | −1.28763 | − | 0.390961i | ||||
\(866\) | 4.94446e17 | 1.17223 | ||||||||
\(867\) | −4.25128e17 | + | 4.25128e17i | −1.00093 | + | 1.00093i | ||||
\(868\) | 4.83771e16 | + | 4.83771e16i | 0.113115 | + | 0.113115i | ||||
\(869\) | − | 2.61455e16i | − | 0.0607126i | ||||||
\(870\) | 4.30953e17 | + | 8.06755e17i | 0.993834 | + | 1.86049i | ||||
\(871\) | 4.86310e17 | 1.11379 | ||||||||
\(872\) | 7.32887e16 | − | 7.32887e16i | 0.166701 | − | 0.166701i | ||||
\(873\) | −3.17985e16 | − | 3.17985e16i | −0.0718325 | − | 0.0718325i | ||||
\(874\) | − | 2.92124e17i | − | 0.655389i | ||||||
\(875\) | 2.31122e17 | + | 2.82067e17i | 0.514982 | + | 0.628498i | ||||
\(876\) | −2.34842e17 | −0.519699 | ||||||||
\(877\) | −1.54663e17 | + | 1.54663e17i | −0.339930 | + | 0.339930i | −0.856341 | − | 0.516411i | \(-0.827268\pi\) |
0.516411 | + | 0.856341i | \(0.327268\pi\) | |||||||
\(878\) | −1.27029e17 | − | 1.27029e17i | −0.277291 | − | 0.277291i | ||||
\(879\) | − | 7.14778e17i | − | 1.54967i | ||||||
\(880\) | 1.61799e17 | − | 8.64300e16i | 0.348402 | − | 0.186109i | ||||
\(881\) | 7.40343e16 | 0.158335 | 0.0791676 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791676 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(882\) | 2.92769e17 | − | 2.92769e17i | 0.621889 | − | 0.621889i | ||||
\(883\) | −3.54003e17 | − | 3.54003e17i | −0.746866 | − | 0.746866i | 0.227024 | − | 0.973889i | \(-0.427101\pi\) |
−0.973889 | + | 0.227024i | \(0.927101\pi\) | |||||||
\(884\) | 1.52311e17i | 0.319166i | ||||||||
\(885\) | −1.08951e17 | + | 3.58832e17i | −0.226763 | + | 0.746846i | ||||
\(886\) | 6.00895e16 | 0.124221 | ||||||||
\(887\) | 5.57483e17 | − | 5.57483e17i | 1.14469 | − | 1.14469i | 0.157114 | − | 0.987580i | \(-0.449781\pi\) |
0.987580 | − | 0.157114i | \(-0.0502191\pi\) | |||||||
\(888\) | −1.55305e17 | − | 1.55305e17i | −0.316744 | − | 0.316744i | ||||
\(889\) | − | 2.83453e17i | − | 0.574209i | ||||||
\(890\) | −8.86939e17 | − | 2.69299e17i | −1.78465 | − | 0.541870i | ||||
\(891\) | 1.23474e17 | 0.246779 | ||||||||
\(892\) | −1.50474e17 | + | 1.50474e17i | −0.298726 | + | 0.298726i | ||||
\(893\) | 5.79335e17 | + | 5.79335e17i | 1.14241 | + | 1.14241i | ||||
\(894\) | 1.65380e18i | 3.23934i | ||||||||
\(895\) | 1.93283e17 | + | 3.61831e17i | 0.376059 | + | 0.703993i | ||||
\(896\) | −1.54465e17 | −0.298525 | ||||||||
\(897\) | −2.81770e17 | + | 2.81770e17i | −0.540929 | + | 0.540929i | ||||
\(898\) | −4.36473e17 | − | 4.36473e17i | −0.832337 | − | 0.832337i | ||||
\(899\) | − | 1.09181e17i | − | 0.206817i | ||||||
\(900\) | 4.84087e17 | − | 7.23681e17i | 0.910896 | − | 1.36173i | ||||
\(901\) | −2.42898e17 | −0.454021 | ||||||||
\(902\) | 1.05610e17 | − | 1.05610e17i | 0.196094 | − | 0.196094i | ||||
\(903\) | −5.57590e17 | − | 5.57590e17i | −1.02846 | − | 1.02846i | ||||
\(904\) | 1.79190e17i | 0.328324i | ||||||||
\(905\) | −1.37433e17 | + | 7.34139e16i | −0.250149 | + | 0.133625i | ||||
\(906\) | 2.43023e18 | 4.39418 | ||||||||
\(907\) | 3.40011e17 | − | 3.40011e17i | 0.610730 | − | 0.610730i | −0.332406 | − | 0.943136i | \(-0.607860\pi\) |
0.943136 | + | 0.332406i | \(0.107860\pi\) | |||||||
\(908\) | −5.54443e17 | − | 5.54443e17i | −0.989331 | − | 0.989331i | ||||
\(909\) | 5.86316e17i | 1.03932i | ||||||||
\(910\) | 1.64843e17 | − | 5.42911e17i | 0.290283 | − | 0.956050i | ||||
\(911\) | 5.97092e17 | 1.04455 | 0.522277 | − | 0.852776i | \(-0.325083\pi\) | ||||
0.522277 | + | 0.852776i | \(0.325083\pi\) | |||||||
\(912\) | −7.43945e17 | + | 7.43945e17i | −1.29292 | + | 1.29292i | ||||
\(913\) | −6.76375e16 | − | 6.76375e16i | −0.116778 | − | 0.116778i | ||||
\(914\) | 8.67902e17i | 1.48865i | ||||||||
\(915\) | 3.23490e17 | + | 9.82207e16i | 0.551232 | + | 0.167370i | ||||
\(916\) | −7.51939e17 | −1.27295 | ||||||||
\(917\) | −1.34309e17 | + | 1.34309e17i | −0.225886 | + | 0.225886i | ||||
\(918\) | 3.61168e17 | + | 3.61168e17i | 0.603466 | + | 0.603466i | ||||
\(919\) | − | 7.95352e16i | − | 0.132028i | −0.997819 | − | 0.0660140i | \(-0.978972\pi\) | ||
0.997819 | − | 0.0660140i | \(-0.0210282\pi\) | |||||||
\(920\) | 2.64406e16 | + | 4.94975e16i | 0.0436058 | + | 0.0816312i | ||||
\(921\) | −1.47223e18 | −2.41222 | ||||||||
\(922\) | 8.74337e17 | − | 8.74337e17i | 1.42329 | − | 1.42329i | ||||
\(923\) | −3.34315e17 | − | 3.34315e17i | −0.540687 | − | 0.540687i | ||||
\(924\) | 2.62888e17i | 0.422415i | ||||||||
\(925\) | −1.73051e17 | − | 8.72333e17i | −0.276263 | − | 1.39262i | ||||
\(926\) | −1.52038e18 | −2.41149 | ||||||||
\(927\) | −1.06947e18 | + | 1.06947e18i | −1.68535 | + | 1.68535i | ||||
\(928\) | −5.49473e17 | − | 5.49473e17i | −0.860318 | − | 0.860318i | ||||
\(929\) | − | 2.12697e17i | − | 0.330877i | −0.986220 | − | 0.165439i | \(-0.947096\pi\) | ||
0.986220 | − | 0.165439i | \(-0.0529040\pi\) | |||||||
\(930\) | −3.02058e17 | + | 1.61353e17i | −0.466867 | + | 0.249391i | ||||
\(931\) | −2.12773e17 | −0.326752 | ||||||||
\(932\) | 1.17644e17 | − | 1.17644e17i | 0.179504 | − | 0.179504i | ||||
\(933\) | 3.67756e17 | + | 3.67756e17i | 0.557533 | + | 0.557533i | ||||
\(934\) | 1.40594e18i | 2.11781i | ||||||||
\(935\) | −2.81399e16 | + | 9.26788e16i | −0.0421165 | + | 0.138711i | ||||
\(936\) | 2.12865e17 | 0.316555 | ||||||||
\(937\) | 8.07752e17 | − | 8.07752e17i | 1.19355 | − | 1.19355i | 0.217485 | − | 0.976064i | \(-0.430215\pi\) |
0.976064 | − | 0.217485i | \(-0.0697855\pi\) | |||||||
\(938\) | 6.60780e17 | + | 6.60780e17i | 0.970152 | + | 0.970152i | ||||
\(939\) | − | 1.17863e18i | − | 1.71943i | ||||||
\(940\) | 9.58417e17 | + | 2.91002e17i | 1.38927 | + | 0.421822i | ||||
\(941\) | 6.87254e17 | 0.989873 | 0.494936 | − | 0.868929i | \(-0.335191\pi\) | ||||
0.494936 | + | 0.868929i | \(0.335191\pi\) | |||||||
\(942\) | 5.61735e17 | − | 5.61735e17i | 0.803944 | − | 0.803944i | ||||
\(943\) | 1.42602e17 | + | 1.42602e17i | 0.202794 | + | 0.202794i | ||||
\(944\) | − | 3.62680e17i | − | 0.512497i | ||||||
\(945\) | −4.15597e17 | − | 7.78009e17i | −0.583554 | − | 1.09243i | ||||
\(946\) | −3.63894e17 | −0.507724 | ||||||||
\(947\) | −4.36393e17 | + | 4.36393e17i | −0.605031 | + | 0.605031i | −0.941643 | − | 0.336612i | \(-0.890719\pi\) |
0.336612 | + | 0.941643i | \(0.390719\pi\) | |||||||
\(948\) | 1.29631e17 | + | 1.29631e17i | 0.178591 | + | 0.178591i | ||||
\(949\) | − | 2.32484e17i | − | 0.318269i | ||||||
\(950\) | −9.46723e17 | + | 1.87808e17i | −1.28790 | + | 0.255489i | ||||
\(951\) | 1.35507e18 | 1.83181 | ||||||||
\(952\) | 3.25192e16 | − | 3.25192e16i | 0.0436836 | − | 0.0436836i | ||||
\(953\) | −4.05844e16 | − | 4.05844e16i | −0.0541753 | − | 0.0541753i | 0.679500 | − | 0.733675i | \(-0.262197\pi\) |
−0.733675 | + | 0.679500i | \(0.762197\pi\) | |||||||
\(954\) | − | 2.16039e18i | − | 2.86577i | ||||||
\(955\) | −1.88405e17 | + | 1.00642e17i | −0.248355 | + | 0.132666i | ||||
\(956\) | 9.85462e17 | 1.29090 | ||||||||
\(957\) | 2.96651e17 | − | 2.96651e17i | 0.386167 | − | 0.386167i | ||||
\(958\) | 1.25215e18 | + | 1.25215e18i | 1.61980 | + | 1.61980i | ||||
\(959\) | 9.70350e17i | 1.24743i | ||||||||
\(960\) | −2.75720e17 | + | 9.08086e17i | −0.352242 | + | 1.16011i | ||||
\(961\) | −7.46784e17 | −0.948102 | ||||||||
\(962\) | −9.78443e17 | + | 9.78443e17i | −1.23448 | + | 1.23448i | ||||
\(963\) | 7.66442e17 | + | 7.66442e17i | 0.960996 | + | 0.960996i | ||||
\(964\) | − | 4.14810e16i | − | 0.0516876i | ||||||
\(965\) | 1.15484e18 | + | 3.50641e17i | 1.43007 | + | 0.434209i | ||||
\(966\) | −7.65717e17 | −0.942336 | ||||||||
\(967\) | −2.16577e17 | + | 2.16577e17i | −0.264883 | + | 0.264883i | −0.827034 | − | 0.562152i | \(-0.809974\pi\) |
0.562152 | + | 0.827034i | \(0.309974\pi\) | |||||||
\(968\) | 9.43825e16 | + | 9.43825e16i | 0.114720 | + | 0.114720i | ||||
\(969\) | − | 5.55518e17i | − | 0.671051i | ||||||
\(970\) | 2.87152e16 | + | 5.37557e16i | 0.0344732 | + | 0.0645348i | ||||
\(971\) | 1.15067e18 | 1.37289 | 0.686445 | − | 0.727181i | \(-0.259170\pi\) | ||||
0.686445 | + | 0.727181i | \(0.259170\pi\) | |||||||
\(972\) | 1.73333e17 | − | 1.73333e17i | 0.205534 | − | 0.205534i | ||||
\(973\) | −1.08172e16 | − | 1.08172e16i | −0.0127478 | − | 0.0127478i | ||||
\(974\) | − | 1.47833e18i | − | 1.73149i | ||||||
\(975\) | 1.09432e18 | + | 7.32016e17i | 1.27384 | + | 0.852105i | ||||
\(976\) | −3.26960e17 | −0.378264 | ||||||||
\(977\) | −8.74046e17 | + | 8.74046e17i | −1.00500 | + | 1.00500i | −0.00501491 | + | 0.999987i | \(0.501596\pi\) |
−0.999987 | + | 0.00501491i | \(0.998404\pi\) | |||||||
\(978\) | −2.52010e18 | − | 2.52010e18i | −2.87995 | − | 2.87995i | ||||
\(979\) | 4.25160e17i | 0.482899i | ||||||||
\(980\) | −2.29438e17 | + | 1.22561e17i | −0.259006 | + | 0.138356i | ||||
\(981\) | −2.14840e18 | −2.41047 | ||||||||
\(982\) | −2.91752e17 | + | 2.91752e17i | −0.325345 | + | 0.325345i | ||||
\(983\) | −1.16627e18 | − | 1.16627e18i | −1.29264 | − | 1.29264i | −0.933149 | − | 0.359490i | \(-0.882951\pi\) |
−0.359490 | − | 0.933149i | \(-0.617049\pi\) | |||||||
\(984\) | − | 1.64556e17i | − | 0.181277i | ||||||
\(985\) | −2.28685e17 | + | 7.53176e17i | −0.250392 | + | 0.824667i | ||||
\(986\) | 4.67066e17 | 0.508296 | ||||||||
\(987\) | 1.51855e18 | − | 1.51855e18i | 1.64258 | − | 1.64258i | ||||
\(988\) | 4.92265e17 | + | 4.92265e17i | 0.529246 | + | 0.529246i | ||||
\(989\) | − | 4.91354e17i | − | 0.525070i | ||||||
\(990\) | −8.24304e17 | − | 2.50282e17i | −0.875540 | − | 0.265838i | ||||
\(991\) | −1.00175e18 | −1.05759 | −0.528793 | − | 0.848751i | \(-0.677355\pi\) | ||||
−0.528793 | + | 0.848751i | \(0.677355\pi\) | |||||||
\(992\) | 2.05729e17 | − | 2.05729e17i | 0.215887 | − | 0.215887i | ||||
\(993\) | 1.00597e18 | + | 1.00597e18i | 1.04928 | + | 1.04928i | ||||
\(994\) | − | 9.08509e17i | − | 0.941913i | ||||||
\(995\) | −3.22597e17 | − | 6.03910e17i | −0.332446 | − | 0.622348i | ||||
\(996\) | 6.70703e17 | 0.687027 | ||||||||
\(997\) | 8.25301e17 | − | 8.25301e17i | 0.840314 | − | 0.840314i | −0.148585 | − | 0.988900i | \(-0.547472\pi\) |
0.988900 | + | 0.148585i | \(0.0474720\pi\) | |||||||
\(998\) | 1.15167e18 | + | 1.15167e18i | 1.16559 | + | 1.16559i | ||||
\(999\) | 2.15113e18i | 2.16409i |
(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 | 5.13.c.a.3.1 | yes | 10 | |
3.2 | odd | 2 | 45.13.g.a.28.5 | 10 | |||
4.3 | odd | 2 | 80.13.p.c.33.1 | 10 | |||
5.2 | odd | 4 | inner | 5.13.c.a.2.1 | ✓ | 10 | |
5.3 | odd | 4 | 25.13.c.b.7.5 | 10 | |||
5.4 | even | 2 | 25.13.c.b.18.5 | 10 | |||
15.2 | even | 4 | 45.13.g.a.37.5 | 10 | |||
20.7 | even | 4 | 80.13.p.c.17.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.13.c.a.2.1 | ✓ | 10 | 5.2 | odd | 4 | inner | |
5.13.c.a.3.1 | yes | 10 | 1.1 | even | 1 | trivial | |
25.13.c.b.7.5 | 10 | 5.3 | odd | 4 | |||
25.13.c.b.18.5 | 10 | 5.4 | even | 2 | |||
45.13.g.a.28.5 | 10 | 3.2 | odd | 2 | |||
45.13.g.a.37.5 | 10 | 15.2 | even | 4 | |||
80.13.p.c.17.1 | 10 | 20.7 | even | 4 | |||
80.13.p.c.33.1 | 10 | 4.3 | odd | 2 |