Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,13,Mod(19,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.19");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.d (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(89.5713940931\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{8}\cdot 7^{8} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Root | \(657.612 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.31 |
Dual form | 98.13.d.a.19.5 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.6274 | + | 39.1918i | 0.353553 | + | 0.612372i | ||||
\(3\) | −985.668 | − | 569.076i | −1.35208 | − | 0.780625i | −0.363542 | − | 0.931578i | \(-0.618433\pi\) |
−0.988541 | + | 0.150953i | \(0.951766\pi\) | |||||||
\(4\) | −1024.00 | + | 1773.62i | −0.250000 | + | 0.433013i | ||||
\(5\) | 12133.2 | − | 7005.11i | 0.776526 | − | 0.448327i | −0.0586719 | − | 0.998277i | \(-0.518687\pi\) |
0.835198 | + | 0.549950i | \(0.185353\pi\) | |||||||
\(6\) | − | 51506.9i | − | 1.10397i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −92681.9 | −0.353553 | ||||||||
\(9\) | 381974. | + | 661598.i | 0.718752 | + | 1.24491i | ||||
\(10\) | 549087. | + | 317015.i | 0.549087 | + | 0.317015i | ||||
\(11\) | 1.52051e6 | − | 2.63360e6i | 0.858287 | − | 1.48660i | −0.0152738 | − | 0.999883i | \(-0.504862\pi\) |
0.873561 | − | 0.486714i | \(-0.161805\pi\) | |||||||
\(12\) | 2.01865e6 | − | 1.16547e6i | 0.676041 | − | 0.390313i | ||||
\(13\) | − | 8.06298e6i | − | 1.67046i | −0.549902 | − | 0.835229i | \(-0.685335\pi\) | ||
0.549902 | − | 0.835229i | \(-0.314665\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.59458e7 | −1.39990 | ||||||||
\(16\) | −2.09715e6 | − | 3.63237e6i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.92560e6 | + | 1.68910e6i | 0.121205 | + | 0.0699779i | 0.559377 | − | 0.828913i | \(-0.311040\pi\) |
−0.438172 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(18\) | −1.72862e7 | + | 2.99405e7i | −0.508234 | + | 0.880287i | ||||
\(19\) | 1.38064e7 | − | 7.97110e6i | 0.293466 | − | 0.169433i | −0.346038 | − | 0.938221i | \(-0.612473\pi\) |
0.639504 | + | 0.768788i | \(0.279140\pi\) | |||||||
\(20\) | 2.86929e7i | 0.448327i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.37621e8 | 1.21380 | ||||||||
\(23\) | 6.09340e7 | + | 1.05541e8i | 0.411616 | + | 0.712940i | 0.995067 | − | 0.0992084i | \(-0.0316310\pi\) |
−0.583450 | + | 0.812149i | \(0.698298\pi\) | |||||||
\(24\) | 9.13536e7 | + | 5.27430e7i | 0.478033 | + | 0.275993i | ||||
\(25\) | −2.39271e7 | + | 4.14429e7i | −0.0980052 | + | 0.169750i | ||||
\(26\) | 3.16003e8 | − | 1.82444e8i | 1.02294 | − | 0.590596i | ||||
\(27\) | − | 2.64628e8i | − | 0.683052i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.10751e9 | 1.86192 | 0.930960 | − | 0.365122i | \(-0.118973\pi\) | ||||
0.930960 | + | 0.365122i | \(0.118973\pi\) | |||||||
\(30\) | −3.60811e8 | − | 6.24944e8i | −0.494940 | − | 0.857262i | ||||
\(31\) | 1.49034e8 | + | 8.60447e7i | 0.167925 | + | 0.0969513i | 0.581607 | − | 0.813470i | \(-0.302424\pi\) |
−0.413682 | + | 0.910421i | \(0.635758\pi\) | |||||||
\(32\) | 9.49063e7 | − | 1.64382e8i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −2.99743e9 | + | 1.73057e9i | −2.32095 | + | 1.34000i | ||||
\(34\) | 1.52879e8i | 0.0989637i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.56457e9 | −0.718752 | ||||||||
\(37\) | 8.32019e8 | + | 1.44110e9i | 0.324282 | + | 0.561673i | 0.981367 | − | 0.192144i | \(-0.0615440\pi\) |
−0.657085 | + | 0.753817i | \(0.728211\pi\) | |||||||
\(38\) | 6.24804e8 | + | 3.60731e8i | 0.207512 | + | 0.119807i | ||||
\(39\) | −4.58845e9 | + | 7.94742e9i | −1.30400 | + | 2.25860i | ||||
\(40\) | −1.12453e9 | + | 6.49247e8i | −0.274543 | + | 0.158508i | ||||
\(41\) | − | 2.84361e9i | − | 0.598641i | −0.954153 | − | 0.299321i | \(-0.903240\pi\) | ||
0.954153 | − | 0.299321i | \(-0.0967600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52303e9 | 0.557321 | 0.278661 | − | 0.960390i | \(-0.410110\pi\) | ||||
0.278661 | + | 0.960390i | \(0.410110\pi\) | |||||||
\(44\) | 3.11400e9 | + | 5.39361e9i | 0.429144 | + | 0.743299i | ||||
\(45\) | 9.26915e9 | + | 5.35154e9i | 1.11626 | + | 0.644472i | ||||
\(46\) | −2.75756e9 | + | 4.77623e9i | −0.291057 | + | 0.504125i | ||||
\(47\) | 4.75293e9 | − | 2.74410e9i | 0.440934 | − | 0.254574i | −0.263059 | − | 0.964780i | \(-0.584732\pi\) |
0.703994 | + | 0.710206i | \(0.251398\pi\) | |||||||
\(48\) | 4.77375e9i | 0.390313i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.16563e9 | −0.138600 | ||||||||
\(51\) | −1.92245e9 | − | 3.32978e9i | −0.109253 | − | 0.189232i | ||||
\(52\) | 1.43007e10 | + | 8.25649e9i | 0.723330 | + | 0.417614i | ||||
\(53\) | 3.54944e9 | − | 6.14782e9i | 0.160142 | − | 0.277374i | −0.774778 | − | 0.632234i | \(-0.782138\pi\) |
0.934919 | + | 0.354860i | \(0.115471\pi\) | |||||||
\(54\) | 1.03713e10 | − | 5.98786e9i | 0.418282 | − | 0.241495i | ||||
\(55\) | − | 4.26053e10i | − | 1.53917i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.81446e10 | −0.529053 | ||||||||
\(58\) | 2.50602e10 | + | 4.34055e10i | 0.658288 | + | 1.14019i | ||||
\(59\) | −2.94046e10 | − | 1.69768e10i | −0.697114 | − | 0.402479i | 0.109158 | − | 0.994024i | \(-0.465185\pi\) |
−0.806272 | + | 0.591545i | \(0.798518\pi\) | |||||||
\(60\) | 1.63285e10 | − | 2.82817e10i | 0.349976 | − | 0.606176i | ||||
\(61\) | −6.13008e10 | + | 3.53920e10i | −1.18984 | + | 0.686952i | −0.958269 | − | 0.285867i | \(-0.907719\pi\) |
−0.231567 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(62\) | 7.78787e9i | 0.137110i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.58993e9 | 0.125000 | ||||||||
\(65\) | −5.64821e10 | − | 9.78299e10i | −0.748912 | − | 1.29715i | ||||
\(66\) | −1.35648e11 | − | 7.83166e10i | −1.64116 | − | 0.947524i | ||||
\(67\) | 5.76089e10 | − | 9.97815e10i | 0.636855 | − | 1.10307i | −0.349264 | − | 0.937025i | \(-0.613568\pi\) |
0.986119 | − | 0.166041i | \(-0.0530985\pi\) | |||||||
\(68\) | −5.99163e9 | + | 3.45927e9i | −0.0606026 | + | 0.0349889i | ||||
\(69\) | − | 1.38704e11i | − | 1.28527i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.03166e10 | −0.392791 | −0.196395 | − | 0.980525i | \(-0.562924\pi\) | ||||
−0.196395 | + | 0.980525i | \(0.562924\pi\) | |||||||
\(72\) | −3.54021e10 | − | 6.13182e10i | −0.254117 | − | 0.440144i | ||||
\(73\) | 6.57596e10 | + | 3.79663e10i | 0.434532 | + | 0.250877i | 0.701276 | − | 0.712890i | \(-0.252614\pi\) |
−0.266743 | + | 0.963768i | \(0.585948\pi\) | |||||||
\(74\) | −3.76529e10 | + | 6.52167e10i | −0.229302 | + | 0.397163i | ||||
\(75\) | 4.71683e10 | − | 2.72326e10i | 0.265022 | − | 0.153011i | ||||
\(76\) | 3.26496e10i | 0.169433i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.15299e11 | −1.84414 | ||||||||
\(79\) | −1.28534e11 | − | 2.22628e11i | −0.528757 | − | 0.915835i | −0.999438 | − | 0.0335308i | \(-0.989325\pi\) |
0.470680 | − | 0.882304i | \(-0.344009\pi\) | |||||||
\(80\) | −5.08904e10 | − | 2.93816e10i | −0.194131 | − | 0.112082i | ||||
\(81\) | 5.24031e10 | − | 9.07648e10i | 0.185544 | − | 0.321372i | ||||
\(82\) | 1.11446e11 | − | 6.43435e10i | 0.366591 | − | 0.211652i | ||||
\(83\) | 2.08263e9i | 0.00637006i | 0.999995 | + | 0.00318503i | \(0.00101383\pi\) | ||||
−0.999995 | + | 0.00318503i | \(0.998986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.73292e10 | 0.125492 | ||||||||
\(86\) | 7.97171e10 | + | 1.38074e11i | 0.197043 | + | 0.341288i | ||||
\(87\) | −1.09164e12 | − | 6.30259e11i | −2.51747 | − | 1.45346i | ||||
\(88\) | −1.40924e11 | + | 2.44087e11i | −0.303450 | + | 0.525592i | ||||
\(89\) | 7.55454e11 | − | 4.36162e11i | 1.52009 | − | 0.877622i | 0.520366 | − | 0.853943i | \(-0.325795\pi\) |
0.999720 | − | 0.0236790i | \(-0.00753797\pi\) | |||||||
\(90\) | 4.84366e11i | 0.911421i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.49586e11 | −0.411616 | ||||||||
\(93\) | −9.79319e10 | − | 1.69623e11i | −0.151365 | − | 0.262172i | ||||
\(94\) | 2.15093e11 | + | 1.24184e11i | 0.311788 | + | 0.180011i | ||||
\(95\) | 1.11677e11 | − | 1.93430e11i | 0.151922 | − | 0.263137i | ||||
\(96\) | −1.87092e11 | + | 1.08018e11i | −0.239017 | + | 0.137996i | ||||
\(97\) | − | 8.85916e11i | − | 1.06356i | −0.846882 | − | 0.531780i | \(-0.821523\pi\) | ||
0.846882 | − | 0.531780i | \(-0.178477\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.32318e12 | 2.46758 | ||||||||
\(100\) | −4.90026e10 | − | 8.48750e10i | −0.0490026 | − | 0.0848750i | ||||
\(101\) | 1.00057e12 | + | 5.77677e11i | 0.942579 | + | 0.544198i | 0.890768 | − | 0.454459i | \(-0.150167\pi\) |
0.0518111 | + | 0.998657i | \(0.483501\pi\) | |||||||
\(102\) | 8.70000e10 | − | 1.50688e11i | 0.0772535 | − | 0.133807i | ||||
\(103\) | −5.71960e11 | + | 3.30221e11i | −0.479007 | + | 0.276555i | −0.720003 | − | 0.693971i | \(-0.755859\pi\) |
0.240995 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(104\) | 7.47292e11i | 0.590596i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.21259e11 | 0.226475 | ||||||||
\(107\) | −6.00582e11 | − | 1.04024e12i | −0.400193 | − | 0.693155i | 0.593556 | − | 0.804793i | \(-0.297724\pi\) |
−0.993749 | + | 0.111638i | \(0.964390\pi\) | |||||||
\(108\) | 4.69350e11 | + | 2.70979e11i | 0.295770 | + | 0.170763i | ||||
\(109\) | −9.97053e11 | + | 1.72695e12i | −0.594510 | + | 1.02972i | 0.399106 | + | 0.916905i | \(0.369321\pi\) |
−0.993616 | + | 0.112817i | \(0.964013\pi\) | |||||||
\(110\) | 1.66978e12 | − | 9.64049e11i | 0.942548 | − | 0.544181i | ||||
\(111\) | − | 1.89393e12i | − | 1.01257i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.93470e12 | 1.40959 | 0.704796 | − | 0.709410i | \(-0.251038\pi\) | ||||
0.704796 | + | 0.709410i | \(0.251038\pi\) | |||||||
\(114\) | −4.10567e11 | − | 7.11122e11i | −0.187049 | − | 0.323978i | ||||
\(115\) | 1.47865e12 | + | 8.53699e11i | 0.639261 | + | 0.369078i | ||||
\(116\) | −1.13409e12 | + | 1.96431e12i | −0.465480 | + | 0.806235i | ||||
\(117\) | 5.33446e12 | − | 3.07985e12i | 2.07958 | − | 1.20064i | ||||
\(118\) | − | 1.53656e12i | − | 0.569191i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.47788e12 | 0.494940 | ||||||||
\(121\) | −3.05468e12 | − | 5.29086e12i | −0.973315 | − | 1.68583i | ||||
\(122\) | −2.77416e12 | − | 1.60166e12i | −0.841341 | − | 0.485749i | ||||
\(123\) | −1.61823e12 | + | 2.80286e12i | −0.467315 | + | 0.809413i | ||||
\(124\) | −3.05221e11 | + | 1.76219e11i | −0.0839623 | + | 0.0484757i | ||||
\(125\) | 4.09091e12i | 1.07241i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.33664e12 | −1.03355 | −0.516775 | − | 0.856122i | \(-0.672867\pi\) | ||||
−0.516775 | + | 0.856122i | \(0.672867\pi\) | |||||||
\(128\) | 1.94368e11 | + | 3.36655e11i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.47254e12 | − | 2.00487e12i | −0.753544 | − | 0.435059i | ||||
\(130\) | 2.55609e12 | − | 4.42728e12i | 0.529561 | − | 0.917226i | ||||
\(131\) | −1.55731e12 | + | 8.99112e11i | −0.308139 | + | 0.177904i | −0.646093 | − | 0.763258i | \(-0.723598\pi\) |
0.337954 | + | 0.941162i | \(0.390265\pi\) | |||||||
\(132\) | − | 7.08841e12i | − | 1.34000i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.21416e12 | 0.900649 | ||||||||
\(135\) | −1.85375e12 | − | 3.21079e12i | −0.306231 | − | 0.530407i | ||||
\(136\) | −2.71150e11 | − | 1.56549e11i | −0.0428525 | − | 0.0247409i | ||||
\(137\) | −6.12087e11 | + | 1.06017e12i | −0.0925742 | + | 0.160343i | −0.908594 | − | 0.417681i | \(-0.862843\pi\) |
0.816019 | + | 0.578025i | \(0.196176\pi\) | |||||||
\(138\) | 5.43607e12 | − | 3.13852e12i | 0.787065 | − | 0.454412i | ||||
\(139\) | 4.36570e12i | 0.605292i | 0.953103 | + | 0.302646i | \(0.0978700\pi\) | ||||
−0.953103 | + | 0.302646i | \(0.902130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24641e12 | −0.794906 | ||||||||
\(142\) | −1.13853e12 | − | 1.97200e12i | −0.138872 | − | 0.240534i | ||||
\(143\) | −2.12347e13 | − | 1.22598e13i | −2.48330 | − | 1.43373i | ||||
\(144\) | 1.60212e12 | − | 2.77495e12i | 0.179688 | − | 0.311229i | ||||
\(145\) | 1.34377e13 | − | 7.75826e12i | 1.44583 | − | 0.834749i | ||||
\(146\) | 3.43632e12i | 0.354794i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.40795e12 | −0.324282 | ||||||||
\(149\) | 2.76244e12 | + | 4.78468e12i | 0.252450 | + | 0.437256i | 0.964200 | − | 0.265177i | \(-0.0854304\pi\) |
−0.711750 | + | 0.702433i | \(0.752097\pi\) | |||||||
\(150\) | 2.13459e12 | + | 1.23241e12i | 0.187399 | + | 0.108195i | ||||
\(151\) | 8.50548e12 | − | 1.47319e13i | 0.717525 | − | 1.24279i | −0.244452 | − | 0.969661i | \(-0.578608\pi\) |
0.961977 | − | 0.273129i | \(-0.0880585\pi\) | |||||||
\(152\) | −1.27960e12 | + | 7.38777e11i | −0.103756 | + | 0.0599035i | ||||
\(153\) | 2.58076e12i | 0.201187i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.41101e12 | 0.173864 | ||||||||
\(156\) | −9.39714e12 | − | 1.62763e13i | −0.652001 | − | 1.12930i | ||||
\(157\) | −1.55451e13 | − | 8.97495e12i | −1.03799 | − | 0.599286i | −0.118729 | − | 0.992927i | \(-0.537882\pi\) |
−0.919264 | + | 0.393641i | \(0.871215\pi\) | |||||||
\(158\) | 5.81680e12 | − | 1.00750e13i | 0.373888 | − | 0.647593i | ||||
\(159\) | −6.99715e12 | + | 4.03981e12i | −0.433050 | + | 0.250022i | ||||
\(160\) | − | 2.65932e12i | − | 0.158508i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.74299e12 | 0.262399 | ||||||||
\(163\) | −1.34370e13 | − | 2.32736e13i | −0.716435 | − | 1.24090i | −0.962404 | − | 0.271624i | \(-0.912439\pi\) |
0.245969 | − | 0.969278i | \(-0.420894\pi\) | |||||||
\(164\) | 5.04348e12 | + | 2.91186e12i | 0.259219 | + | 0.149660i | ||||
\(165\) | −2.42457e13 | + | 4.19947e13i | −1.20152 | + | 2.08109i | ||||
\(166\) | −8.16221e10 | + | 4.71245e10i | −0.00390085 | + | 0.00225216i | ||||
\(167\) | − | 3.87671e13i | − | 1.78716i | −0.448900 | − | 0.893582i | \(-0.648184\pi\) | ||
0.448900 | − | 0.893582i | \(-0.351816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.17136e13 | −1.79043 | ||||||||
\(170\) | 1.07094e12 | + | 1.85492e12i | 0.0443681 | + | 0.0768478i | ||||
\(171\) | 1.05473e13 | + | 6.08951e12i | 0.421858 | + | 0.243560i | ||||
\(172\) | −3.60758e12 | + | 6.24852e12i | −0.139330 | + | 0.241327i | ||||
\(173\) | −6.48299e12 | + | 3.74296e12i | −0.241824 | + | 0.139617i | −0.616015 | − | 0.787735i | \(-0.711254\pi\) |
0.374191 | + | 0.927352i | \(0.377920\pi\) | |||||||
\(174\) | − | 5.70445e13i | − | 2.05550i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.27550e13 | −0.429144 | ||||||||
\(177\) | 1.93221e13 | + | 3.34669e13i | 0.628371 | + | 1.08837i | ||||
\(178\) | 3.41880e13 | + | 1.97384e13i | 1.07486 | + | 0.620573i | ||||
\(179\) | 1.68741e13 | − | 2.92267e13i | 0.512981 | − | 0.888509i | −0.486906 | − | 0.873455i | \(-0.661874\pi\) |
0.999887 | − | 0.0150546i | \(-0.00479222\pi\) | |||||||
\(180\) | −1.89832e13 | + | 1.09600e13i | −0.558129 | + | 0.322236i | ||||
\(181\) | 2.44112e13i | 0.694252i | 0.937819 | + | 0.347126i | \(0.112842\pi\) | ||||
−0.937819 | + | 0.347126i | \(0.887158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.05630e13 | 2.14501 | ||||||||
\(184\) | −5.64748e12 | − | 9.78172e12i | −0.145528 | − | 0.252063i | ||||
\(185\) | 2.01901e13 | + | 1.16568e13i | 0.503627 | + | 0.290769i | ||||
\(186\) | 4.43189e12 | − | 7.67626e12i | 0.107031 | − | 0.185384i | ||||
\(187\) | 8.89680e12 | − | 5.13657e12i | 0.208058 | − | 0.120122i | ||||
\(188\) | 1.12399e13i | 0.254574i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.01078e13 | 0.214851 | ||||||||
\(191\) | 2.73396e13 | + | 4.73536e13i | 0.563109 | + | 0.975334i | 0.997223 | + | 0.0744756i | \(0.0237283\pi\) |
−0.434114 | + | 0.900858i | \(0.642938\pi\) | |||||||
\(192\) | −8.46683e12 | − | 4.88832e12i | −0.169010 | − | 0.0975782i | ||||
\(193\) | −1.73142e13 | + | 2.99890e13i | −0.335010 | + | 0.580254i | −0.983487 | − | 0.180980i | \(-0.942073\pi\) |
0.648477 | + | 0.761234i | \(0.275406\pi\) | |||||||
\(194\) | 3.47207e13 | − | 2.00460e13i | 0.651295 | − | 0.376025i | ||||
\(195\) | 1.28570e14i | 2.33848i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.42879e13 | 0.415521 | 0.207761 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207761 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(198\) | 5.25675e13 | + | 9.10497e13i | 0.872422 | + | 1.51108i | ||||
\(199\) | 2.96893e13 | + | 1.71411e13i | 0.478059 | + | 0.276008i | 0.719607 | − | 0.694381i | \(-0.244322\pi\) |
−0.241548 | + | 0.970389i | \(0.577655\pi\) | |||||||
\(200\) | 2.21760e12 | − | 3.84100e12i | 0.0346501 | − | 0.0600157i | ||||
\(201\) | −1.13567e14 | + | 6.55677e13i | −1.72216 | + | 0.994291i | ||||
\(202\) | 5.22854e13i | 0.769612i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.87434e12 | 0.109253 | ||||||||
\(205\) | −1.99198e13 | − | 3.45021e13i | −0.268387 | − | 0.464860i | ||||
\(206\) | −2.58839e13 | − | 1.49441e13i | −0.338709 | − | 0.195554i | ||||
\(207\) | −4.65504e13 | + | 8.06277e13i | −0.591700 | + | 1.02485i | ||||
\(208\) | −2.92878e13 | + | 1.69093e13i | −0.361665 | + | 0.208807i | ||||
\(209\) | − | 4.84805e13i | − | 0.581687i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.46496e13 | −0.505967 | −0.252984 | − | 0.967471i | \(-0.581412\pi\) | ||||
−0.252984 | + | 0.967471i | \(0.581412\pi\) | |||||||
\(212\) | 7.26926e12 | + | 1.25907e13i | 0.0800710 | + | 0.138687i | ||||
\(213\) | 4.95955e13 | + | 2.86340e13i | 0.531085 | + | 0.306622i | ||||
\(214\) | 2.71793e13 | − | 4.70759e13i | 0.282980 | − | 0.490135i | ||||
\(215\) | 4.27457e13 | − | 2.46792e13i | 0.432774 | − | 0.249862i | ||||
\(216\) | 2.45263e13i | 0.241495i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.02430e13 | −0.840764 | ||||||||
\(219\) | −4.32114e13 | − | 7.48444e13i | −0.391682 | − | 0.678414i | ||||
\(220\) | 7.55657e13 | + | 4.36279e13i | 0.666482 | + | 0.384794i | ||||
\(221\) | 1.36191e13 | − | 2.35891e13i | 0.116895 | − | 0.202468i | ||||
\(222\) | 7.42265e13 | − | 4.28547e13i | 0.620071 | − | 0.357998i | ||||
\(223\) | − | 9.08410e13i | − | 0.738674i | −0.929296 | − | 0.369337i | \(-0.879585\pi\) | ||
0.929296 | − | 0.369337i | \(-0.120415\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.65580e13 | −0.281766 | ||||||||
\(226\) | 6.64048e13 | + | 1.15016e14i | 0.498366 | + | 0.863195i | ||||
\(227\) | −1.25149e14 | − | 7.22549e13i | −0.914688 | − | 0.528095i | −0.0327514 | − | 0.999464i | \(-0.510427\pi\) |
−0.881936 | + | 0.471368i | \(0.843760\pi\) | |||||||
\(228\) | 1.85801e13 | − | 3.21817e13i | 0.132263 | − | 0.229087i | ||||
\(229\) | −1.31986e14 | + | 7.62024e13i | −0.915201 | + | 0.528391i | −0.882101 | − | 0.471061i | \(-0.843871\pi\) |
−0.0330999 | + | 0.999452i | \(0.510538\pi\) | |||||||
\(230\) | 7.72680e13i | 0.521955i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.02646e14 | −0.658288 | ||||||||
\(233\) | 6.44584e12 | + | 1.11645e13i | 0.0402851 | + | 0.0697758i | 0.885465 | − | 0.464706i | \(-0.153840\pi\) |
−0.845180 | + | 0.534482i | \(0.820507\pi\) | |||||||
\(234\) | 2.41410e14 | + | 1.39378e14i | 1.47048 | + | 0.848984i | ||||
\(235\) | 3.84455e13 | − | 6.65896e13i | 0.228265 | − | 0.395366i | ||||
\(236\) | 6.02207e13 | − | 3.47684e13i | 0.348557 | − | 0.201240i | ||||
\(237\) | 2.92583e14i | 1.65105i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.47682e14 | 0.792392 | 0.396196 | − | 0.918166i | \(-0.370330\pi\) | ||||
0.396196 | + | 0.918166i | \(0.370330\pi\) | |||||||
\(240\) | 3.34407e13 | + | 5.79210e13i | 0.174988 | + | 0.303088i | ||||
\(241\) | −1.38929e14 | − | 8.02104e13i | −0.709070 | − | 0.409382i | 0.101647 | − | 0.994821i | \(-0.467589\pi\) |
−0.810717 | + | 0.585439i | \(0.800922\pi\) | |||||||
\(242\) | 1.38239e14 | − | 2.39437e14i | 0.688237 | − | 1.19206i | ||||
\(243\) | −2.25097e14 | + | 1.29960e14i | −1.09328 | + | 0.631207i | ||||
\(244\) | − | 1.44966e14i | − | 0.686952i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.46465e14 | −0.660883 | ||||||||
\(247\) | −6.42709e13 | − | 1.11320e14i | −0.283030 | − | 0.490222i | ||||
\(248\) | −1.38127e13 | − | 7.97478e12i | −0.0593703 | − | 0.0342775i | ||||
\(249\) | 1.18517e12 | − | 2.05278e12i | 0.00497263 | − | 0.00861285i | ||||
\(250\) | −1.60330e14 | + | 9.25668e13i | −0.656713 | + | 0.379154i | ||||
\(251\) | 1.81669e14i | 0.726504i | 0.931691 | + | 0.363252i | \(0.118334\pi\) | ||||
−0.931691 | + | 0.363252i | \(0.881666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.70603e14 | 1.41314 | ||||||||
\(254\) | −9.81270e13 | − | 1.69961e14i | −0.365415 | − | 0.632917i | ||||
\(255\) | −4.66509e13 | − | 2.69339e13i | −0.169676 | − | 0.0979622i | ||||
\(256\) | −8.79609e12 | + | 1.52353e13i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.16893e14 | − | 6.74882e13i | 0.405686 | − | 0.234223i | −0.283249 | − | 0.959046i | \(-0.591412\pi\) |
0.688934 | + | 0.724824i | \(0.258079\pi\) | |||||||
\(258\) | − | 1.81460e14i | − | 0.615266i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.31351e14 | 0.748912 | ||||||||
\(261\) | 4.23041e14 | + | 7.32729e14i | 1.33826 | + | 2.31793i | ||||
\(262\) | −7.04757e13 | − | 4.06891e13i | −0.217887 | − | 0.125797i | ||||
\(263\) | −1.75536e13 | + | 3.04037e13i | −0.0530433 | + | 0.0918737i | −0.891328 | − | 0.453359i | \(-0.850225\pi\) |
0.838285 | + | 0.545233i | \(0.183559\pi\) | |||||||
\(264\) | 2.77808e14 | − | 1.60392e14i | 0.820580 | − | 0.473762i | ||||
\(265\) | − | 9.94570e13i | − | 0.287184i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.92836e14 | −2.74038 | ||||||||
\(268\) | 1.17983e14 | + | 2.04353e14i | 0.318428 | + | 0.551533i | ||||
\(269\) | 5.49523e14 | + | 3.17267e14i | 1.45035 | + | 0.837358i | 0.998501 | − | 0.0547375i | \(-0.0174322\pi\) |
0.451846 | + | 0.892096i | \(0.350766\pi\) | |||||||
\(270\) | 8.38912e13 | − | 1.45304e14i | 0.216538 | − | 0.375055i | ||||
\(271\) | −2.48989e14 | + | 1.43754e14i | −0.628587 | + | 0.362915i | −0.780205 | − | 0.625525i | \(-0.784885\pi\) |
0.151618 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(272\) | − | 1.41692e13i | − | 0.0349889i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.53998e13 | −0.130920 | ||||||||
\(275\) | 7.27626e13 | + | 1.26028e14i | 0.168233 | + | 0.291389i | ||||
\(276\) | 2.46009e14 | + | 1.42033e14i | 0.556539 | + | 0.321318i | ||||
\(277\) | −3.35788e14 | + | 5.81602e14i | −0.743338 | + | 1.28750i | 0.207629 | + | 0.978208i | \(0.433425\pi\) |
−0.950967 | + | 0.309292i | \(0.899908\pi\) | |||||||
\(278\) | −1.71100e14 | + | 9.87845e13i | −0.370664 | + | 0.214003i | ||||
\(279\) | 1.31467e14i | 0.278736i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.07036e14 | 0.623665 | 0.311832 | − | 0.950137i | \(-0.399057\pi\) | ||||
0.311832 | + | 0.950137i | \(0.399057\pi\) | |||||||
\(282\) | −1.41340e14 | − | 2.44808e14i | −0.281042 | − | 0.486779i | ||||
\(283\) | −5.60549e14 | − | 3.23633e14i | −1.09118 | − | 0.629991i | −0.157286 | − | 0.987553i | \(-0.550275\pi\) |
−0.933889 | + | 0.357562i | \(0.883608\pi\) | |||||||
\(284\) | 5.15242e13 | − | 8.92425e13i | 0.0981977 | − | 0.170083i | ||||
\(285\) | −2.20153e14 | + | 1.27105e14i | −0.410824 | + | 0.237189i | ||||
\(286\) | − | 1.10963e15i | − | 2.02760i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.45007e14 | 0.254117 | ||||||||
\(289\) | −2.85605e14 | − | 4.94682e14i | −0.490206 | − | 0.849062i | ||||
\(290\) | 6.08121e14 | + | 3.51099e14i | 1.02236 | + | 0.590257i | ||||
\(291\) | −5.04153e14 | + | 8.73219e14i | −0.830242 | + | 1.43802i | ||||
\(292\) | −1.34676e14 | + | 7.77550e13i | −0.217266 | + | 0.125439i | ||||
\(293\) | 4.60155e14i | 0.727275i | 0.931541 | + | 0.363638i | \(0.118465\pi\) | ||||
−0.931541 | + | 0.363638i | \(0.881535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.75697e14 | −0.721769 | ||||||||
\(296\) | −7.71131e13 | − | 1.33564e14i | −0.114651 | − | 0.198581i | ||||
\(297\) | −6.96925e14 | − | 4.02370e14i | −1.01542 | − | 0.586255i | ||||
\(298\) | −1.25014e14 | + | 2.16530e14i | −0.178509 | + | 0.309187i | ||||
\(299\) | 8.50973e14 | − | 4.91310e14i | 1.19094 | − | 0.687588i | ||||
\(300\) | 1.11545e14i | 0.153011i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.69828e14 | 1.01473 | ||||||||
\(303\) | −6.57484e14 | − | 1.13880e15i | −0.849630 | − | 1.47160i | ||||
\(304\) | −5.79081e13 | − | 3.34332e13i | −0.0733664 | − | 0.0423581i | ||||
\(305\) | −4.95851e14 | + | 8.58838e14i | −0.615959 | + | 1.06687i | ||||
\(306\) | −1.01145e14 | + | 5.83960e13i | −0.123201 | + | 0.0711303i | ||||
\(307\) | − | 3.97752e14i | − | 0.475097i | −0.971376 | − | 0.237548i | \(-0.923656\pi\) | ||
0.971376 | − | 0.237548i | \(-0.0763438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.51683e14 | 0.863543 | ||||||||
\(310\) | 5.45549e13 | + | 9.44919e13i | 0.0614701 | + | 0.106469i | ||||
\(311\) | −9.44605e14 | − | 5.45368e14i | −1.04397 | − | 0.602736i | −0.123015 | − | 0.992405i | \(-0.539256\pi\) |
−0.920955 | + | 0.389668i | \(0.872590\pi\) | |||||||
\(312\) | 4.25266e14 | − | 7.36582e14i | 0.461034 | − | 0.798535i | ||||
\(313\) | −4.92556e14 | + | 2.84377e14i | −0.523829 | + | 0.302433i | −0.738500 | − | 0.674254i | \(-0.764465\pi\) |
0.214671 | + | 0.976686i | \(0.431132\pi\) | |||||||
\(314\) | − | 8.12320e14i | − | 0.847518i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.26476e14 | 0.528757 | ||||||||
\(317\) | −1.19437e14 | − | 2.06870e14i | −0.117701 | − | 0.203865i | 0.801155 | − | 0.598457i | \(-0.204219\pi\) |
−0.918856 | + | 0.394592i | \(0.870886\pi\) | |||||||
\(318\) | −3.16655e14 | − | 1.82821e14i | −0.306213 | − | 0.176792i | ||||
\(319\) | 1.68398e15 | − | 2.91674e15i | 1.59806 | − | 2.76792i | ||||
\(320\) | 1.04224e14 | − | 6.01735e13i | 0.0970657 | − | 0.0560409i | ||||
\(321\) | 1.36711e15i | 1.24960i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.38558e13 | 0.0474261 | ||||||||
\(324\) | 1.07322e14 | + | 1.85886e14i | 0.0927720 | + | 0.160686i | ||||
\(325\) | 3.34153e14 | + | 1.92923e14i | 0.283560 | + | 0.163714i | ||||
\(326\) | 6.08089e14 | − | 1.05324e15i | 0.506596 | − | 0.877450i | ||||
\(327\) | 1.96553e15 | − | 1.13480e15i | 1.60765 | − | 0.928179i | ||||
\(328\) | 2.63551e14i | 0.211652i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.19447e15 | −1.69920 | ||||||||
\(331\) | 3.64766e14 | + | 6.31793e14i | 0.277362 | + | 0.480405i | 0.970728 | − | 0.240181i | \(-0.0772066\pi\) |
−0.693367 | + | 0.720585i | \(0.743873\pi\) | |||||||
\(332\) | −3.69379e12 | − | 2.13261e12i | −0.00275832 | − | 0.00159252i | ||||
\(333\) | −6.35619e14 | + | 1.10093e15i | −0.466156 | + | 0.807407i | ||||
\(334\) | 1.51935e15 | − | 8.77199e14i | 1.09441 | − | 0.631858i | ||||
\(335\) | − | 1.61423e15i | − | 1.14208i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.36845e15 | 0.934218 | 0.467109 | − | 0.884200i | \(-0.345296\pi\) | ||||
0.467109 | + | 0.884200i | \(0.345296\pi\) | |||||||
\(338\) | −9.43871e14 | − | 1.63483e15i | −0.633013 | − | 1.09641i | ||||
\(339\) | −2.89264e15 | − | 1.67007e15i | −1.90589 | − | 1.10036i | ||||
\(340\) | −4.84651e13 | + | 8.39441e13i | −0.0313730 | + | 0.0543396i | ||||
\(341\) | 4.53214e14 | − | 2.61663e14i | 0.288255 | − | 0.166424i | ||||
\(342\) | 5.51160e14i | 0.344446i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.26521e14 | −0.197043 | ||||||||
\(345\) | −9.71639e14 | − | 1.68293e15i | −0.576223 | − | 0.998047i | ||||
\(346\) | −2.93387e14 | − | 1.69387e14i | −0.170995 | − | 0.0987241i | ||||
\(347\) | −5.31356e14 | + | 9.20335e14i | −0.304375 | + | 0.527192i | −0.977122 | − | 0.212680i | \(-0.931781\pi\) |
0.672747 | + | 0.739872i | \(0.265114\pi\) | |||||||
\(348\) | 2.23568e15 | − | 1.29077e15i | 1.25873 | − | 0.726731i | ||||
\(349\) | − | 2.28786e15i | − | 1.26613i | −0.774100 | − | 0.633063i | \(-0.781798\pi\) | ||
0.774100 | − | 0.633063i | \(-0.218202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.13369e15 | −1.14101 | ||||||||
\(352\) | −2.88612e14 | − | 4.99890e14i | −0.151725 | − | 0.262796i | ||||
\(353\) | 7.89328e14 | + | 4.55719e14i | 0.407952 | + | 0.235531i | 0.689910 | − | 0.723896i | \(-0.257650\pi\) |
−0.281957 | + | 0.959427i | \(0.590984\pi\) | |||||||
\(354\) | −8.74421e14 | + | 1.51454e15i | −0.444325 | + | 0.769594i | ||||
\(355\) | −6.10502e14 | + | 3.52474e14i | −0.305012 | + | 0.176099i | ||||
\(356\) | 1.78652e15i | 0.877622i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.52727e15 | 0.725465 | ||||||||
\(359\) | −1.06968e15 | − | 1.85274e15i | −0.499675 | − | 0.865462i | 0.500325 | − | 0.865838i | \(-0.333214\pi\) |
−1.00000 | 0.000375531i | \(0.999880\pi\) | ||||||||
\(360\) | −8.59082e14 | − | 4.95991e14i | −0.394657 | − | 0.227855i | ||||
\(361\) | −9.79580e14 | + | 1.69668e15i | −0.442585 | + | 0.766580i | ||||
\(362\) | −9.56718e14 | + | 5.52361e14i | −0.425141 | + | 0.245455i | ||||
\(363\) | 6.95337e15i | 3.03918i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.06383e15 | 0.449901 | ||||||||
\(366\) | 1.82293e15 | + | 3.15741e15i | 0.758375 | + | 1.31354i | ||||
\(367\) | 1.59545e15 | + | 9.21136e14i | 0.652962 | + | 0.376988i | 0.789590 | − | 0.613635i | \(-0.210293\pi\) |
−0.136628 | + | 0.990622i | \(0.543627\pi\) | |||||||
\(368\) | 2.55576e14 | − | 4.42670e14i | 0.102904 | − | 0.178235i | ||||
\(369\) | 1.88133e15 | − | 1.08618e15i | 0.745257 | − | 0.430274i | ||||
\(370\) | 1.05505e15i | 0.411210i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.01129e14 | 0.151365 | ||||||||
\(373\) | −4.78263e14 | − | 8.28376e14i | −0.177588 | − | 0.307592i | 0.763466 | − | 0.645848i | \(-0.223496\pi\) |
−0.941054 | + | 0.338257i | \(0.890163\pi\) | |||||||
\(374\) | 4.02623e14 | + | 2.32455e14i | 0.147119 | + | 0.0849393i | ||||
\(375\) | 2.32804e15 | − | 4.03228e15i | 0.837149 | − | 1.44998i | ||||
\(376\) | −4.40510e14 | + | 2.54329e14i | −0.155894 | + | 0.0900054i | ||||
\(377\) | − | 8.92986e15i | − | 3.11026i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.65431e15 | 1.23302 | 0.616510 | − | 0.787347i | \(-0.288546\pi\) | ||||
0.616510 | + | 0.787347i | \(0.288546\pi\) | |||||||
\(380\) | 2.28714e14 | + | 3.96145e14i | 0.0759612 | + | 0.131569i | ||||
\(381\) | 4.27449e15 | + | 2.46788e15i | 1.39744 | + | 0.806815i | ||||
\(382\) | −1.23725e15 | + | 2.14298e15i | −0.398178 | + | 0.689665i | ||||
\(383\) | −2.55844e15 | + | 1.47712e15i | −0.810555 | + | 0.467974i | −0.847149 | − | 0.531356i | \(-0.821683\pi\) |
0.0365933 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(384\) | − | 4.42441e14i | − | 0.137996i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.56710e15 | −0.473776 | ||||||||
\(387\) | 1.34571e15 | + | 2.33083e15i | 0.400576 | + | 0.693817i | ||||
\(388\) | 1.57128e15 | + | 9.07178e14i | 0.460535 | + | 0.265890i | ||||
\(389\) | −1.22210e15 | + | 2.11674e15i | −0.352703 | + | 0.610900i | −0.986722 | − | 0.162418i | \(-0.948071\pi\) |
0.634019 | + | 0.773318i | \(0.281404\pi\) | |||||||
\(390\) | −5.03891e15 | + | 2.90922e15i | −1.43202 | + | 0.826777i | ||||
\(391\) | 4.11693e14i | 0.115216i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.04665e15 | 0.555506 | ||||||||
\(394\) | 5.49573e14 | + | 9.51889e14i | 0.146909 | + | 0.254454i | ||||
\(395\) | −3.11907e15 | − | 1.80079e15i | −0.821187 | − | 0.474113i | ||||
\(396\) | −2.37894e15 | + | 4.12044e15i | −0.616895 | + | 1.06849i | ||||
\(397\) | −1.35832e15 | + | 7.84227e14i | −0.346944 | + | 0.200308i | −0.663338 | − | 0.748320i | \(-0.730861\pi\) |
0.316395 | + | 0.948628i | \(0.397528\pi\) | |||||||
\(398\) | 1.55144e15i | 0.390334i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00715e14 | 0.0490026 | ||||||||
\(401\) | −5.72742e14 | − | 9.92019e14i | −0.137750 | − | 0.238591i | 0.788894 | − | 0.614529i | \(-0.210654\pi\) |
−0.926645 | + | 0.375938i | \(0.877321\pi\) | |||||||
\(402\) | −5.13943e15 | − | 2.96725e15i | −1.21775 | − | 0.703070i | ||||
\(403\) | 6.93776e14 | − | 1.20166e15i | 0.161953 | − | 0.280511i | ||||
\(404\) | −2.04916e15 | + | 1.18308e15i | −0.471289 | + | 0.272099i | ||||
\(405\) | − | 1.46836e15i | − | 0.332738i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.06037e15 | 1.11331 | ||||||||
\(408\) | 1.78176e14 | + | 3.08610e14i | 0.0386268 | + | 0.0669035i | ||||
\(409\) | 7.56565e15 | + | 4.36803e15i | 1.61624 | + | 0.933138i | 0.987880 | + | 0.155216i | \(0.0496075\pi\) |
0.628362 | + | 0.777921i | \(0.283726\pi\) | |||||||
\(410\) | 9.01468e14 | − | 1.56139e15i | 0.189778 | − | 0.328706i | ||||
\(411\) | 1.20663e15 | − | 6.96648e14i | 0.250336 | − | 0.144532i | ||||
\(412\) | − | 1.35259e15i | − | 0.276555i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.21326e15 | −0.836790 | ||||||||
\(415\) | 1.45891e13 | + | 2.52690e13i | 0.00285587 | + | 0.00494652i | ||||
\(416\) | −1.32541e15 | − | 7.65227e14i | −0.255736 | − | 0.147649i | ||||
\(417\) | 2.48441e15 | − | 4.30313e15i | 0.472506 | − | 0.818405i | ||||
\(418\) | 1.90004e15 | − | 1.09699e15i | 0.356209 | − | 0.205658i | ||||
\(419\) | − | 1.57572e15i | − | 0.291203i | −0.989343 | − | 0.145601i | \(-0.953488\pi\) | ||
0.989343 | − | 0.145601i | \(-0.0465117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.93849e15 | −1.60536 | −0.802678 | − | 0.596413i | \(-0.796592\pi\) | ||||
−0.802678 | + | 0.596413i | \(0.796592\pi\) | |||||||
\(422\) | −1.01030e15 | − | 1.74990e15i | −0.178887 | − | 0.309841i | ||||
\(423\) | 3.63099e15 | + | 2.09635e15i | 0.633845 | + | 0.365950i | ||||
\(424\) | −3.28969e14 | + | 5.69791e14i | −0.0566187 | + | 0.0980665i | ||||
\(425\) | −1.40002e14 | + | 8.08302e13i | −0.0237575 | + | 0.0137164i | ||||
\(426\) | 2.59165e15i | 0.433629i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.45999e15 | 0.400193 | ||||||||
\(429\) | 1.39535e16 | + | 2.41683e16i | 2.23842 | + | 3.87705i | ||||
\(430\) | 1.93445e15 | + | 1.11685e15i | 0.306018 | + | 0.176679i | ||||
\(431\) | −7.11093e14 | + | 1.23165e15i | −0.110933 | + | 0.192142i | −0.916147 | − | 0.400843i | \(-0.868717\pi\) |
0.805213 | + | 0.592985i | \(0.202051\pi\) | |||||||
\(432\) | −9.61229e14 | + | 5.54966e14i | −0.147885 | + | 0.0853815i | ||||
\(433\) | 7.63274e15i | 1.15812i | 0.815286 | + | 0.579059i | \(0.196580\pi\) | ||||
−0.815286 | + | 0.579059i | \(0.803420\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.76601e16 | −2.60651 | ||||||||
\(436\) | −2.04197e15 | − | 3.53679e15i | −0.297255 | − | 0.514861i | ||||
\(437\) | 1.68255e15 | + | 9.71422e14i | 0.241591 | + | 0.139482i | ||||
\(438\) | 1.95553e15 | − | 3.38707e15i | 0.276961 | − | 0.479711i | ||||
\(439\) | −1.23220e15 | + | 7.11414e14i | −0.172145 | + | 0.0993882i | −0.583597 | − | 0.812043i | \(-0.698355\pi\) |
0.411452 | + | 0.911432i | \(0.365022\pi\) | |||||||
\(440\) | 3.94874e15i | 0.544181i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.23266e15 | 0.165315 | ||||||||
\(443\) | −4.15114e15 | − | 7.18999e15i | −0.549219 | − | 0.951275i | −0.998328 | − | 0.0577979i | \(-0.981592\pi\) |
0.449110 | − | 0.893477i | \(-0.351741\pi\) | |||||||
\(444\) | 3.35911e15 | + | 1.93938e15i | 0.438456 | + | 0.253143i | ||||
\(445\) | 6.11073e15 | − | 1.05841e16i | 0.786924 | − | 1.36299i | ||||
\(446\) | 3.56022e15 | − | 2.05550e15i | 0.452343 | − | 0.261161i | ||||
\(447\) | − | 6.28815e15i | − | 0.788275i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.42464e14 | 0.0662053 | 0.0331026 | − | 0.999452i | \(-0.489461\pi\) | ||||
0.0331026 | + | 0.999452i | \(0.489461\pi\) | |||||||
\(450\) | −8.27214e14 | − | 1.43278e15i | −0.0996192 | − | 0.172545i | ||||
\(451\) | −7.48892e15 | − | 4.32373e15i | −0.889939 | − | 0.513806i | ||||
\(452\) | −3.00514e15 | + | 5.20505e15i | −0.352398 | + | 0.610371i | ||||
\(453\) | −1.67672e16 | + | 9.68053e15i | −1.94031 | + | 1.12024i | ||||
\(454\) | − | 6.53977e15i | − | 0.746839i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.68168e15 | 0.187049 | ||||||||
\(457\) | −2.66405e15 | − | 4.61428e15i | −0.292446 | − | 0.506532i | 0.681941 | − | 0.731407i | \(-0.261136\pi\) |
−0.974388 | + | 0.224875i | \(0.927803\pi\) | |||||||
\(458\) | −5.97302e15 | − | 3.44853e15i | −0.647145 | − | 0.373629i | ||||
\(459\) | 4.46983e14 | − | 7.74197e14i | 0.0477985 | − | 0.0827895i | ||||
\(460\) | −3.02828e15 | + | 1.74838e15i | −0.319631 | + | 0.184539i | ||||
\(461\) | − | 1.29900e15i | − | 0.135333i | −0.997708 | − | 0.0676663i | \(-0.978445\pi\) | ||
0.997708 | − | 0.0676663i | \(-0.0215553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.49560e16 | −1.51820 | −0.759101 | − | 0.650973i | \(-0.774361\pi\) | ||||
−0.759101 | + | 0.650973i | \(0.774361\pi\) | |||||||
\(464\) | −2.32262e15 | − | 4.02290e15i | −0.232740 | − | 0.403117i | ||||
\(465\) | −2.37646e15 | − | 1.37205e15i | −0.235078 | − | 0.135722i | ||||
\(466\) | −2.91706e14 | + | 5.05249e14i | −0.0284858 | + | 0.0493389i | ||||
\(467\) | −5.32993e15 | + | 3.07724e15i | −0.513831 | + | 0.296661i | −0.734407 | − | 0.678709i | \(-0.762540\pi\) |
0.220576 | + | 0.975370i | \(0.429206\pi\) | |||||||
\(468\) | 1.26151e16i | 1.20064i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.47969e15 | 0.322815 | ||||||||
\(471\) | 1.02149e16 | + | 1.76926e16i | 0.935635 | + | 1.62057i | ||||
\(472\) | 2.72528e15 | + | 1.57344e15i | 0.246467 | + | 0.142298i | ||||
\(473\) | 5.35680e15 | − | 9.27825e15i | 0.478342 | − | 0.828512i | ||||
\(474\) | −1.14669e16 | + | 6.62040e15i | −1.01105 | + | 0.583733i | ||||
\(475\) | 7.62900e14i | 0.0664211i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.42318e15 | 0.460409 | ||||||||
\(478\) | 3.34166e15 | + | 5.78793e15i | 0.280153 | + | 0.485239i | ||||
\(479\) | 8.13481e15 | + | 4.69664e15i | 0.673495 | + | 0.388843i | 0.797400 | − | 0.603452i | \(-0.206208\pi\) |
−0.123905 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(480\) | −1.51335e15 | + | 2.62120e15i | −0.123735 | + | 0.214315i | ||||
\(481\) | 1.16196e16 | − | 6.70855e15i | 0.938251 | − | 0.541700i | ||||
\(482\) | − | 7.25982e15i | − | 0.578953i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.25120e16 | 0.973315 | ||||||||
\(485\) | −6.20594e15 | − | 1.07490e16i | −0.476823 | − | 0.825882i | ||||
\(486\) | −1.01867e16 | − | 5.88131e15i | −0.773067 | − | 0.446330i | ||||
\(487\) | 4.10445e15 | − | 7.10912e15i | 0.307667 | − | 0.532895i | −0.670184 | − | 0.742195i | \(-0.733785\pi\) |
0.977852 | + | 0.209299i | \(0.0671183\pi\) | |||||||
\(488\) | 5.68148e15 | − | 3.28020e15i | 0.420671 | − | 0.242874i | ||||
\(489\) | 3.05867e16i | 2.23707i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.70306e16 | 1.21546 | 0.607730 | − | 0.794144i | \(-0.292080\pi\) | ||||
0.607730 | + | 0.794144i | \(0.292080\pi\) | |||||||
\(492\) | −3.31413e15 | − | 5.74025e15i | −0.233657 | − | 0.404706i | ||||
\(493\) | 3.24014e15 | + | 1.87070e15i | 0.225674 | + | 0.130293i | ||||
\(494\) | 2.90857e15 | − | 5.03779e15i | 0.200132 | − | 0.346640i | ||||
\(495\) | 2.81876e16 | − | 1.62741e16i | 1.91614 | − | 1.10628i | ||||
\(496\) | − | 7.21795e14i | − | 0.0484757i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.07270e14 | 0.00703236 | ||||||||
\(499\) | −3.47566e15 | − | 6.02003e15i | −0.225131 | − | 0.389938i | 0.731228 | − | 0.682133i | \(-0.238948\pi\) |
−0.956359 | + | 0.292195i | \(0.905614\pi\) | |||||||
\(500\) | −7.25573e15 | − | 4.18909e15i | −0.464366 | − | 0.268102i | ||||
\(501\) | −2.20614e16 | + | 3.82115e16i | −1.39511 | + | 2.41639i | ||||
\(502\) | −7.11993e15 | + | 4.11069e15i | −0.444891 | + | 0.256858i | ||||
\(503\) | − | 1.04626e16i | − | 0.645996i | −0.946400 | − | 0.322998i | \(-0.895309\pi\) | ||
0.946400 | − | 0.322998i | \(-0.104691\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.61868e16 | 0.975916 | ||||||||
\(506\) | 8.38578e15 | + | 1.45246e16i | 0.499621 | + | 0.865368i | ||||
\(507\) | 4.11158e16 | + | 2.37382e16i | 2.42081 | + | 1.39765i | ||||
\(508\) | 4.44072e15 | − | 7.69155e15i | 0.258387 | − | 0.447540i | ||||
\(509\) | 1.63453e16 | − | 9.43694e15i | 0.939908 | − | 0.542656i | 0.0499765 | − | 0.998750i | \(-0.484085\pi\) |
0.889931 | + | 0.456094i | \(0.150752\pi\) | |||||||
\(510\) | − | 2.43778e15i | − | 0.138539i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.96131e14 | −0.0441942 | ||||||||
\(513\) | −2.10938e15 | − | 3.65355e15i | −0.115731 | − | 0.200452i | ||||
\(514\) | 5.28997e15 | + | 3.05417e15i | 0.286863 | + | 0.165620i | ||||
\(515\) | −4.62647e15 | + | 8.01329e15i | −0.247974 | + | 0.429504i | ||||
\(516\) | 7.11176e15 | − | 4.10598e15i | 0.376772 | − | 0.217530i | ||||
\(517\) | − | 1.66897e16i | − | 0.873989i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.52011e15 | 0.435954 | ||||||||
\(520\) | 5.23487e15 | + | 9.06706e15i | 0.264780 | + | 0.458613i | ||||
\(521\) | −3.28541e15 | − | 1.89683e15i | −0.164272 | − | 0.0948423i | 0.415610 | − | 0.909543i | \(-0.363568\pi\) |
−0.579882 | + | 0.814700i | \(0.696901\pi\) | |||||||
\(522\) | −1.91447e16 | + | 3.31595e16i | −0.946291 | + | 1.63902i | ||||
\(523\) | −1.44767e16 | + | 8.35814e15i | −0.707392 | + | 0.408413i | −0.810095 | − | 0.586299i | \(-0.800584\pi\) |
0.102702 | + | 0.994712i | \(0.467251\pi\) | |||||||
\(524\) | − | 3.68276e15i | − | 0.177904i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.58877e15 | −0.0750146 | ||||||||
\(527\) | 2.90675e14 | + | 5.03464e14i | 0.0135689 | + | 0.0235020i | ||||
\(528\) | 1.25721e16 | + | 7.25853e15i | 0.580238 | + | 0.335000i | ||||
\(529\) | 3.53141e15 | − | 6.11658e15i | 0.161144 | − | 0.279110i | ||||
\(530\) | 3.89790e15 | − | 2.25046e15i | 0.175864 | − | 0.101535i | ||||
\(531\) | − | 2.59388e16i | − | 1.15713i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.29280e16 | −1.00001 | ||||||||
\(534\) | −2.24653e16 | − | 3.89111e16i | −0.968869 | − | 1.67813i | ||||
\(535\) | −1.45740e16 | − | 8.41430e15i | −0.621521 | − | 0.358835i | ||||
\(536\) | −5.33930e15 | + | 9.24794e15i | −0.225162 | + | 0.389993i | ||||
\(537\) | −3.32644e16 | + | 1.92052e16i | −1.38719 | + | 0.800892i | ||||
\(538\) | 2.87157e16i | 1.18420i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.59297e15 | 0.306231 | ||||||||
\(541\) | 5.85969e15 | + | 1.01493e16i | 0.233717 | + | 0.404810i | 0.958899 | − | 0.283747i | \(-0.0915776\pi\) |
−0.725182 | + | 0.688558i | \(0.758244\pi\) | |||||||
\(542\) | −1.12680e16 | − | 6.50557e15i | −0.444478 | − | 0.256619i | ||||
\(543\) | 1.38918e16 | − | 2.40613e16i | 0.541950 | − | 0.938685i | ||||
\(544\) | 5.55315e14 | − | 3.20612e14i | 0.0214263 | − | 0.0123705i | ||||
\(545\) | 2.79379e16i | 1.06614i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.62257e16 | 1.35236 | 0.676181 | − | 0.736736i | \(-0.263634\pi\) | ||||
0.676181 | + | 0.736736i | \(0.263634\pi\) | |||||||
\(548\) | −1.25355e15 | − | 2.17122e15i | −0.0462871 | − | 0.0801716i | ||||
\(549\) | −4.68306e16 | − | 2.70377e16i | −1.71039 | − | 0.987496i | ||||
\(550\) | −3.29286e15 | + | 5.70340e15i | −0.118959 | + | 0.206043i | ||||
\(551\) | 1.52907e16 | − | 8.82810e15i | 0.546410 | − | 0.315470i | ||||
\(552\) | 1.28554e16i | 0.454412i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.03921e16 | −1.05124 | ||||||||
\(555\) | −1.32672e16 | − | 2.29794e16i | −0.453963 | − | 0.786287i | ||||
\(556\) | −7.74309e15 | − | 4.47048e15i | −0.262099 | − | 0.151323i | ||||
\(557\) | 1.92509e16 | − | 3.33435e16i | 0.644643 | − | 1.11656i | −0.339740 | − | 0.940519i | \(-0.610339\pi\) |
0.984384 | − | 0.176036i | \(-0.0563275\pi\) | |||||||
\(558\) | −5.15244e15 | + | 2.97477e15i | −0.170690 | + | 0.0985479i | ||||
\(559\) | − | 2.84061e16i | − | 0.930982i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.16924e16 | −0.375082 | ||||||||
\(562\) | 6.94743e15 | + | 1.20333e16i | 0.220499 | + | 0.381915i | ||||
\(563\) | −8.79162e15 | − | 5.07584e15i | −0.276069 | − | 0.159389i | 0.355573 | − | 0.934648i | \(-0.384286\pi\) |
−0.631643 | + | 0.775260i | \(0.717619\pi\) | |||||||
\(564\) | 6.39633e15 | − | 1.10788e16i | 0.198727 | − | 0.344205i | ||||
\(565\) | 3.56074e16 | − | 2.05579e16i | 1.09458 | − | 0.631959i | ||||
\(566\) | − | 2.92919e16i | − | 0.890941i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.66344e15 | 0.138872 | ||||||||
\(569\) | −1.72786e16 | − | 2.99274e16i | −0.509137 | − | 0.881852i | −0.999944 | − | 0.0105833i | \(-0.996631\pi\) |
0.490807 | − | 0.871269i | \(-0.336702\pi\) | |||||||
\(570\) | −9.96298e15 | − | 5.75213e15i | −0.290496 | − | 0.167718i | ||||
\(571\) | −2.59825e16 | + | 4.50030e16i | −0.749659 | + | 1.29845i | 0.198327 | + | 0.980136i | \(0.436449\pi\) |
−0.947986 | + | 0.318312i | \(0.896884\pi\) | |||||||
\(572\) | 4.34886e16 | − | 2.51081e16i | 1.24165 | − | 0.716867i | ||||
\(573\) | − | 6.22333e16i | − | 1.75831i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.83188e15 | −0.161362 | ||||||||
\(576\) | 3.28113e15 | + | 5.68309e15i | 0.0898439 | + | 0.155614i | ||||
\(577\) | −4.62325e14 | − | 2.66924e14i | −0.0125283 | − | 0.00723323i | 0.493723 | − | 0.869619i | \(-0.335636\pi\) |
−0.506251 | + | 0.862386i | \(0.668969\pi\) | |||||||
\(578\) | 1.29250e16 | − | 2.23868e16i | 0.346628 | − | 0.600378i | ||||
\(579\) | 3.41321e16 | − | 1.97061e16i | 0.905922 | − | 0.523035i | ||||
\(580\) | 3.17778e16i | 0.834749i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.56307e16 | −1.17414 | ||||||||
\(583\) | −1.07939e16 | − | 1.86956e16i | −0.274896 | − | 0.476133i | ||||
\(584\) | −6.09473e15 | − | 3.51879e15i | −0.153630 | − | 0.0886985i | ||||
\(585\) | 4.31494e16 | − | 7.47370e16i | 1.07656 | − | 1.86466i | ||||
\(586\) | −1.80343e16 | + | 1.04121e16i | −0.445363 | + | 0.257131i | ||||
\(587\) | − | 6.77758e15i | − | 0.165671i | −0.996563 | − | 0.0828354i | \(-0.973602\pi\) | ||
0.996563 | − | 0.0828354i | \(-0.0263976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.74348e15 | 0.0657068 | ||||||||
\(590\) | −1.07638e16 | − | 1.86434e16i | −0.255184 | − | 0.441992i | ||||
\(591\) | −2.39398e16 | − | 1.38217e16i | −0.561819 | − | 0.324366i | ||||
\(592\) | 3.48974e15 | − | 6.04441e15i | 0.0810705 | − | 0.140418i | ||||
\(593\) | 2.12563e15 | − | 1.22723e15i | 0.0488832 | − | 0.0282227i | −0.475359 | − | 0.879792i | \(-0.657682\pi\) |
0.524242 | + | 0.851569i | \(0.324349\pi\) | |||||||
\(594\) | − | 3.64183e16i | − | 0.829090i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.13149e16 | −0.252450 | ||||||||
\(597\) | −1.95092e16 | − | 3.37910e16i | −0.430917 | − | 0.746371i | ||||
\(598\) | 3.85107e16 | + | 2.22341e16i | 0.842120 | + | 0.486198i | ||||
\(599\) | −3.73685e16 | + | 6.47241e16i | −0.808993 | + | 1.40122i | 0.104569 | + | 0.994518i | \(0.466654\pi\) |
−0.913562 | + | 0.406699i | \(0.866680\pi\) | |||||||
\(600\) | −4.37164e15 | + | 2.52397e15i | −0.0936995 | + | 0.0540974i | ||||
\(601\) | 2.12849e16i | 0.451674i | 0.974165 | + | 0.225837i | \(0.0725116\pi\) | ||||
−0.974165 | + | 0.225837i | \(0.927488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.80204e16 | 1.83096 | ||||||||
\(604\) | 1.74192e16 | + | 3.01710e16i | 0.358763 | + | 0.621395i | ||||
\(605\) | −7.41261e16 | − | 4.27967e16i | −1.51161 | − | 0.872727i | ||||
\(606\) | 2.97543e16 | − | 5.15360e16i | 0.600779 | − | 1.04058i | ||||
\(607\) | −4.83175e16 | + | 2.78961e16i | −0.965990 | + | 0.557714i | −0.898011 | − | 0.439972i | \(-0.854988\pi\) |
−0.0679784 | + | 0.997687i | \(0.521655\pi\) | |||||||
\(608\) | − | 3.02603e15i | − | 0.0599035i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.48793e16 | −0.871098 | ||||||||
\(611\) | −2.21257e16 | − | 3.83228e16i | −0.425255 | − | 0.736563i | ||||
\(612\) | −4.57729e15 | − | 2.64270e15i | −0.0871165 | − | 0.0502967i | ||||
\(613\) | −1.41029e16 | + | 2.44269e16i | −0.265794 | + | 0.460369i | −0.967771 | − | 0.251830i | \(-0.918968\pi\) |
0.701977 | + | 0.712199i | \(0.252301\pi\) | |||||||
\(614\) | 1.55886e16 | − | 9.00009e15i | 0.290936 | − | 0.167972i | ||||
\(615\) | 4.53435e16i | 0.838040i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.54280e16 | −1.72968 | −0.864838 | − | 0.502051i | \(-0.832579\pi\) | ||||
−0.864838 | + | 0.502051i | \(0.832579\pi\) | |||||||
\(618\) | 1.70087e16 | + | 2.94599e16i | 0.305309 | + | 0.528810i | ||||
\(619\) | −2.46755e16 | − | 1.42464e16i | −0.438653 | − | 0.253257i | 0.264373 | − | 0.964421i | \(-0.414835\pi\) |
−0.703026 | + | 0.711164i | \(0.748168\pi\) | |||||||
\(620\) | −2.46887e15 | + | 4.27622e15i | −0.0434659 | + | 0.0752852i | ||||
\(621\) | 2.79291e16 | − | 1.61249e16i | 0.486975 | − | 0.281155i | ||||
\(622\) | − | 4.93611e16i | − | 0.852398i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.84907e16 | 0.652001 | ||||||||
\(625\) | 2.28157e16 | + | 3.95180e16i | 0.382785 | + | 0.663003i | ||||
\(626\) | −2.22905e16 | − | 1.28694e16i | −0.370403 | − | 0.213852i | ||||
\(627\) | −2.75891e16 | + | 4.77857e16i | −0.454080 | + | 0.786489i | ||||
\(628\) | 3.18363e16 | − | 1.83807e16i | 0.518997 | − | 0.299643i | ||||
\(629\) | 5.62144e15i | 0.0907703i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.69031e16 | −1.21834 | −0.609169 | − | 0.793041i | \(-0.708497\pi\) | ||||
−0.609169 | + | 0.793041i | \(0.708497\pi\) | |||||||
\(632\) | 1.19128e16 | + | 2.06336e16i | 0.186944 | + | 0.323796i | ||||
\(633\) | 4.40097e16 | + | 2.54090e16i | 0.684110 | + | 0.394971i | ||||
\(634\) | 5.40508e15 | − | 9.36188e15i | 0.0832275 | − | 0.144154i | ||||
\(635\) | −5.26174e16 | + | 3.03787e16i | −0.802578 | + | 0.463368i | ||||
\(636\) | − | 1.65470e16i | − | 0.250022i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.52417e17 | 2.26000 | ||||||||
\(639\) | −1.92196e16 | − | 3.32894e16i | −0.282319 | − | 0.488991i | ||||
\(640\) | 4.71662e15 | + | 2.72314e15i | 0.0686358 | + | 0.0396269i | ||||
\(641\) | 5.28270e15 | − | 9.14990e15i | 0.0761566 | − | 0.131907i | −0.825432 | − | 0.564501i | \(-0.809068\pi\) |
0.901589 | + | 0.432594i | \(0.142402\pi\) | |||||||
\(642\) | −5.35795e16 | + | 3.09341e16i | −0.765223 | + | 0.441802i | ||||
\(643\) | 3.09940e16i | 0.438543i | 0.975664 | + | 0.219272i | \(0.0703681\pi\) | ||||
−0.975664 | + | 0.219272i | \(0.929632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.61774e16 | −0.780195 | ||||||||
\(646\) | 1.21862e15 | + | 2.11071e15i | 0.0167677 | + | 0.0290424i | ||||
\(647\) | 2.77746e16 | + | 1.60357e16i | 0.378637 | + | 0.218606i | 0.677225 | − | 0.735776i | \(-0.263182\pi\) |
−0.298588 | + | 0.954382i | \(0.596516\pi\) | |||||||
\(648\) | −4.85682e15 | + | 8.41225e15i | −0.0655997 | + | 0.113622i | ||||
\(649\) | −8.94200e16 | + | 5.16267e16i | −1.19665 | + | 0.690885i | ||||
\(650\) | 1.74614e16i | 0.231526i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.50380e16 | 0.716435 | ||||||||
\(653\) | 3.25065e16 | + | 5.63029e16i | 0.419267 | + | 0.726193i | 0.995866 | − | 0.0908351i | \(-0.0289536\pi\) |
−0.576599 | + | 0.817028i | \(0.695620\pi\) | |||||||
\(654\) | 8.89496e16 | + | 5.13551e16i | 1.13678 | + | 0.656322i | ||||
\(655\) | −1.25968e16 | + | 2.18182e16i | −0.159519 | + | 0.276294i | ||||
\(656\) | −1.03291e16 | + | 5.96348e15i | −0.129610 | + | 0.0748302i | ||||
\(657\) | 5.80086e16i | 0.721274i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.60030e17 | 1.95385 | 0.976923 | − | 0.213594i | \(-0.0685168\pi\) | ||||
0.976923 | + | 0.213594i | \(0.0685168\pi\) | |||||||
\(660\) | −4.96551e16 | − | 8.60052e16i | −0.600759 | − | 1.04055i | ||||
\(661\) | 1.31451e17 | + | 7.58935e16i | 1.57600 | + | 0.909904i | 0.995409 | + | 0.0957083i | \(0.0305116\pi\) |
0.580591 | + | 0.814196i | \(0.302822\pi\) | |||||||
\(662\) | −1.65074e16 | + | 2.85917e16i | −0.196124 | + | 0.339697i | ||||
\(663\) | −2.68479e16 | + | 1.55007e16i | −0.316104 | + | 0.182503i | ||||
\(664\) | − | 1.93022e14i | − | 0.00225216i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.75297e16 | −0.659245 | ||||||||
\(667\) | 6.74852e16 | + | 1.16888e17i | 0.766396 | + | 1.32744i | ||||
\(668\) | 6.87581e16 | + | 3.96975e16i | 0.773865 | + | 0.446791i | ||||
\(669\) | −5.16954e16 | + | 8.95391e16i | −0.576627 | + | 0.998748i | ||||
\(670\) | 6.32645e16 | − | 3.65258e16i | 0.699377 | − | 0.403786i | ||||
\(671\) | 2.15256e17i | 2.35841i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.64122e16 | −0.822380 | −0.411190 | − | 0.911550i | \(-0.634887\pi\) | ||||
−0.411190 | + | 0.911550i | \(0.634887\pi\) | |||||||
\(674\) | 3.09644e16 | + | 5.36319e16i | 0.330296 | + | 0.572090i | ||||
\(675\) | 1.09670e16 | + | 6.33178e15i | 0.115948 | + | 0.0669426i | ||||
\(676\) | 4.27147e16 | − | 7.39841e16i | 0.447607 | − | 0.775279i | ||||
\(677\) | 3.90256e16 | − | 2.25314e16i | 0.405338 | − | 0.234022i | −0.283447 | − | 0.958988i | \(-0.591478\pi\) |
0.688785 | + | 0.724966i | \(0.258145\pi\) | |||||||
\(678\) | − | 1.51157e17i | − | 1.55615i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.38656e15 | −0.0443681 | ||||||||
\(681\) | 8.22371e16 | + | 1.42439e17i | 0.824489 | + | 1.42806i | ||||
\(682\) | 2.05101e16 | + | 1.18415e16i | 0.203827 | + | 0.117680i | ||||
\(683\) | −6.42829e16 | + | 1.11341e17i | −0.633244 | + | 1.09681i | 0.353640 | + | 0.935381i | \(0.384944\pi\) |
−0.986884 | + | 0.161429i | \(0.948390\pi\) | |||||||
\(684\) | −2.16010e16 | + | 1.24713e16i | −0.210929 | + | 0.121780i | ||||
\(685\) | 1.71510e16i | 0.166014i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.73460e17 | 1.64990 | ||||||||
\(688\) | −7.38833e15 | − | 1.27970e16i | −0.0696652 | − | 0.120664i | ||||
\(689\) | −4.95697e16 | − | 2.86191e16i | −0.463342 | − | 0.267510i | ||||
\(690\) | 4.39714e16 | − | 7.61606e16i | 0.407451 | − | 0.705726i | ||||
\(691\) | 3.41126e16 | − | 1.96949e16i | 0.313362 | − | 0.180920i | −0.335068 | − | 0.942194i | \(-0.608759\pi\) |
0.648430 | + | 0.761274i | \(0.275426\pi\) | |||||||
\(692\) | − | 1.53312e16i | − | 0.139617i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.80928e16 | −0.430451 | ||||||||
\(695\) | 3.05822e16 | + | 5.29700e16i | 0.271369 | + | 0.470025i | ||||
\(696\) | 1.01175e17 | + | 5.84136e16i | 0.890060 | + | 0.513876i | ||||
\(697\) | 4.80313e15 | − | 8.31926e15i | 0.0418917 | − | 0.0725585i | ||||
\(698\) | 8.96654e16 | − | 5.17683e16i | 0.775340 | − | 0.447643i | ||||
\(699\) | − | 1.46727e16i | − | 0.125790i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.18834e16 | 0.437241 | 0.218620 | − | 0.975810i | \(-0.429844\pi\) | ||||
0.218620 | + | 0.975810i | \(0.429844\pi\) | |||||||
\(702\) | −4.82800e16 | − | 8.36234e16i | −0.403408 | − | 0.698723i | ||||
\(703\) | 2.29743e16 | + | 1.32642e16i | 0.190331 | + | 0.109888i | ||||
\(704\) | 1.30611e16 | − | 2.26224e16i | 0.107286 | − | 0.185825i | ||||
\(705\) | −7.57891e16 | + | 4.37568e16i | −0.617265 | + | 0.356378i | ||||
\(706\) | 4.12470e16i | 0.333092i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.91435e16 | −0.628371 | ||||||||
\(709\) | −2.92719e16 | − | 5.07003e16i | −0.230448 | − | 0.399148i | 0.727492 | − | 0.686116i | \(-0.240686\pi\) |
−0.957940 | + | 0.286969i | \(0.907352\pi\) | |||||||
\(710\) | −2.76282e16 | − | 1.59511e16i | −0.215676 | − | 0.124521i | ||||
\(711\) | 9.81935e16 | − | 1.70076e17i | 0.760090 | − | 1.31652i | ||||
\(712\) | −7.00169e16 | + | 4.04243e16i | −0.537432 | + | 0.310286i | ||||
\(713\) | 2.09722e16i | 0.159627i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.43526e17 | −2.57113 | ||||||||
\(716\) | 3.45581e16 | + | 5.98563e16i | 0.256491 | + | 0.444255i | ||||
\(717\) | −1.45565e17 | − | 8.40423e16i | −1.07138 | − | 0.618561i | ||||
\(718\) | 4.84082e16 | − | 8.38455e16i | 0.353323 | − | 0.611974i | ||||
\(719\) | 9.50918e16 | − | 5.49013e16i | 0.688287 | − | 0.397383i | −0.114683 | − | 0.993402i | \(-0.536585\pi\) |
0.802970 | + | 0.596019i | \(0.203252\pi\) | |||||||
\(720\) | − | 4.48920e16i | − | 0.322236i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.86615e16 | −0.625910 | ||||||||
\(723\) | 9.12916e16 | + | 1.58122e17i | 0.639147 | + | 1.10704i | ||||
\(724\) | −4.32961e16 | − | 2.49970e16i | −0.300620 | − | 0.173563i | ||||
\(725\) | −2.64995e16 | + | 4.58985e16i | −0.182478 | + | 0.316061i | ||||
\(726\) | −2.72516e17 | + | 1.57337e17i | −1.86111 | + | 1.07451i | ||||
\(727\) | − | 6.97698e16i | − | 0.472565i | −0.971684 | − | 0.236282i | \(-0.924071\pi\) | ||
0.971684 | − | 0.236282i | \(-0.0759290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.40130e17 | 1.59986 | ||||||||
\(730\) | 2.40718e16 | + | 4.16936e16i | 0.159064 | + | 0.275507i | ||||
\(731\) | 1.03070e16 | + | 5.95074e15i | 0.0675503 | + | 0.0390002i | ||||
\(732\) | −8.24965e16 | + | 1.42888e17i | −0.536252 | + | 0.928816i | ||||
\(733\) | −1.25691e17 | + | 7.25679e16i | −0.810366 | + | 0.467865i | −0.847083 | − | 0.531461i | \(-0.821643\pi\) |
0.0367169 | + | 0.999326i | \(0.488310\pi\) | |||||||
\(734\) | 8.33717e16i | 0.533141i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31321e16 | 0.145528 | ||||||||
\(737\) | −1.75190e17 | − | 3.03437e17i | −1.09321 | − | 1.89349i | ||||
\(738\) | 8.51392e16 | + | 4.91551e16i | 0.526976 | + | 0.304250i | ||||
\(739\) | 1.27126e17 | − | 2.20188e17i | 0.780489 | − | 1.35185i | −0.151169 | − | 0.988508i | \(-0.548304\pi\) |
0.931657 | − | 0.363338i | \(-0.118363\pi\) | |||||||
\(740\) | −4.13494e16 | + | 2.38731e16i | −0.251813 | + | 0.145385i | ||||
\(741\) | 1.46300e17i | 0.883761i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.89108e17 | −1.12403 | −0.562013 | − | 0.827128i | \(-0.689973\pi\) | ||||
−0.562013 | + | 0.827128i | \(0.689973\pi\) | |||||||
\(744\) | 9.07651e15 | + | 1.57210e16i | 0.0535157 | + | 0.0926919i | ||||
\(745\) | 6.70345e16 | + | 3.87024e16i | 0.392067 | + | 0.226360i | ||||
\(746\) | 2.16437e16 | − | 3.74880e16i | 0.125574 | − | 0.217500i | ||||
\(747\) | −1.37787e15 | + | 7.95511e14i | −0.00793018 | + | 0.00457849i | ||||
\(748\) | 2.10394e16i | 0.120122i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.10710e17 | 1.18391 | ||||||||
\(751\) | −8.78442e16 | − | 1.52151e17i | −0.489636 | − | 0.848074i | 0.510293 | − | 0.860001i | \(-0.329537\pi\) |
−0.999929 | + | 0.0119263i | \(0.996204\pi\) | |||||||
\(752\) | −1.99352e16 | − | 1.15096e16i | −0.110234 | − | 0.0636434i | ||||
\(753\) | 1.03383e17 | − | 1.79065e17i | 0.567127 | − | 0.982293i | ||||
\(754\) | 3.49978e17 | − | 2.02060e17i | 1.90464 | − | 1.09964i | ||||
\(755\) | − | 2.38327e17i | − | 1.28674i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.95370e16 | 0.422663 | 0.211331 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211331 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(758\) | 8.26876e16 | + | 1.43219e17i | 0.435938 | + | 0.755067i | ||||
\(759\) | −3.65291e17 | − | 2.10901e17i | −1.91068 | − | 1.10313i | ||||
\(760\) | −1.03504e16 | + | 1.79275e16i | −0.0537127 | + | 0.0930331i | ||||
\(761\) | −2.38900e17 | + | 1.37929e17i | −1.23001 | + | 0.710147i | −0.967032 | − | 0.254655i | \(-0.918038\pi\) |
−0.262978 | + | 0.964802i | \(0.584705\pi\) | |||||||
\(762\) | 2.23367e17i | 1.14101i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.11983e17 | −0.563109 | ||||||||
\(765\) | 1.80785e16 | + | 3.13130e16i | 0.0901976 | + | 0.156227i | ||||
\(766\) | −1.15782e17 | − | 6.68467e16i | −0.573149 | − | 0.330908i | ||||
\(767\) | −1.36883e17 | + | 2.37089e17i | −0.672324 | + | 1.16450i | ||||
\(768\) | 1.73401e16 | − | 1.00113e16i | 0.0845052 | − | 0.0487891i | ||||
\(769\) | 1.76448e17i | 0.853217i | 0.904436 | + | 0.426609i | \(0.140292\pi\) | ||||
−0.904436 | + | 0.426609i | \(0.859708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.53624e17 | −0.731361 | ||||||||
\(772\) | −3.54594e16 | − | 6.14175e16i | −0.167505 | − | 0.290127i | ||||
\(773\) | −1.95408e16 | − | 1.12819e16i | −0.0915937 | − | 0.0528817i | 0.453504 | − | 0.891254i | \(-0.350174\pi\) |
−0.545097 | + | 0.838373i | \(0.683507\pi\) | |||||||
\(774\) | −6.08997e16 | + | 1.05481e17i | −0.283250 | + | 0.490603i | ||||
\(775\) | −7.13187e15 | + | 4.11759e15i | −0.0329150 | + | 0.0190035i | ||||
\(776\) | 8.21084e16i | 0.376025i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.10612e17 | −0.498798 | ||||||||
\(779\) | −2.26667e16 | − | 3.92599e16i | −0.101429 | − | 0.175681i | ||||
\(780\) | −2.28035e17 | − | 1.31656e17i | −1.01259 | − | 0.584620i | ||||
\(781\) | −7.65068e16 | + | 1.32514e17i | −0.337127 | + | 0.583922i | ||||
\(782\) | −1.61350e16 | + | 9.31556e15i | −0.0705552 | + | 0.0407351i | ||||
\(783\) | − | 2.93079e17i | − | 1.27179i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.51482e17 | −1.07470 | ||||||||
\(786\) | 4.63104e16 | + | 8.02120e16i | 0.196401 | + | 0.340176i | ||||
\(787\) | 3.74906e17 | + | 2.16452e17i | 1.57788 | + | 0.910990i | 0.995155 | + | 0.0983211i | \(0.0313472\pi\) |
0.582726 | + | 0.812669i | \(0.301986\pi\) | |||||||
\(788\) | −2.48708e16 | + | 4.30776e16i | −0.103880 | + | 0.179926i | ||||
\(789\) | 3.46040e16 | − | 1.99786e16i | 0.143438 | − | 0.0828139i | ||||
\(790\) | − | 1.62989e17i | − | 0.670497i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.15317e17 | −0.872422 | ||||||||
\(793\) | 2.85365e17 | + | 4.94267e17i | 1.14752 | + | 1.98757i | ||||
\(794\) | −6.14706e16 | − | 3.54901e16i | −0.245326 | − | 0.141639i | ||||
\(795\) | −5.65986e16 | + | 9.80316e16i | −0.224183 | + | 0.388297i | ||||
\(796\) | −6.08037e16 | + | 3.51051e16i | −0.239030 | + | 0.138004i | ||||
\(797\) | − | 2.73462e17i | − | 1.06696i | −0.845813 | − | 0.533479i | \(-0.820884\pi\) | ||
0.845813 | − | 0.533479i | \(-0.179116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.85402e16 | 0.0712581 | ||||||||
\(800\) | 4.54165e15 | + | 7.86638e15i | 0.0173250 | + | 0.0300078i | ||||
\(801\) | 5.77128e17 | + | 3.33205e17i | 2.18513 | + | 1.26158i | ||||
\(802\) | 2.59194e16 | − | 4.48937e16i | 0.0974043 | − | 0.168709i | ||||
\(803\) | 1.99976e17 | − | 1.15456e17i | 0.745907 | − | 0.430650i | ||||
\(804\) | − | 2.68565e17i | − | 0.994291i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.27935e16 | 0.229036 | ||||||||
\(807\) | −3.61098e17 | − | 6.25440e17i | −1.30733 | − | 2.26436i | ||||
\(808\) | −9.27344e16 | − | 5.35402e16i | −0.333252 | − | 0.192403i | ||||
\(809\) | 8.57211e16 | − | 1.48473e17i | 0.305771 | − | 0.529611i | −0.671662 | − | 0.740858i | \(-0.734419\pi\) |
0.977433 | + | 0.211247i | \(0.0677524\pi\) | |||||||
\(810\) | 5.75477e16 | − | 3.32252e16i | 0.203759 | − | 0.117641i | ||||
\(811\) | − | 2.32308e17i | − | 0.816466i | −0.912878 | − | 0.408233i | \(-0.866145\pi\) | ||
0.912878 | − | 0.408233i | \(-0.133855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.27228e17 | 1.13320 | ||||||||
\(814\) | 1.14503e17 | + | 1.98325e17i | 0.393614 | + | 0.681760i | ||||
\(815\) | −3.26068e17 | − | 1.88255e17i | −1.11266 | − | 0.642395i | ||||
\(816\) | −8.06333e15 | + | 1.39661e16i | −0.0273132 | + | 0.0473079i | ||||
\(817\) | 4.86402e16 | − | 2.80824e16i | 0.163555 | − | 0.0944284i | ||||
\(818\) | 3.95349e17i | 1.31966i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.15915e16 | 0.268387 | ||||||||
\(821\) | 1.51474e16 | + | 2.62360e16i | 0.0494627 | + | 0.0856719i | 0.889697 | − | 0.456552i | \(-0.150916\pi\) |
−0.840234 | + | 0.542224i | \(0.817582\pi\) | |||||||
\(822\) | 5.46058e16 | + | 3.15267e16i | 0.177014 | + | 0.102199i | ||||
\(823\) | 8.12445e16 | − | 1.40720e17i | 0.261454 | − | 0.452851i | −0.705175 | − | 0.709034i | \(-0.749131\pi\) |
0.966628 | + | 0.256182i | \(0.0824648\pi\) | |||||||
\(824\) | 5.30103e16 | − | 3.06055e16i | 0.169355 | − | 0.0977770i | ||||
\(825\) | − | 1.65630e17i | − | 0.525309i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.54389e17 | 1.42035 | 0.710174 | − | 0.704026i | \(-0.248616\pi\) | ||||
0.710174 | + | 0.704026i | \(0.248616\pi\) | |||||||
\(828\) | −9.53352e16 | − | 1.65125e17i | −0.295850 | − | 0.512427i | ||||
\(829\) | 3.63717e17 | + | 2.09992e17i | 1.12056 | + | 0.646957i | 0.941544 | − | 0.336889i | \(-0.109375\pi\) |
0.179018 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(830\) | −6.60226e14 | + | 1.14354e15i | −0.00201941 | + | 0.00349772i | ||||
\(831\) | 6.61951e17 | − | 3.82178e17i | 2.01011 | − | 1.16054i | ||||
\(832\) | − | 6.92605e16i | − | 0.208807i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.24864e17 | 0.668225 | ||||||||
\(835\) | −2.71568e17 | − | 4.70369e17i | −0.801234 | − | 1.38778i | ||||
\(836\) | 8.59860e16 | + | 4.96441e16i | 0.251878 | + | 0.145422i | ||||
\(837\) | 2.27699e16 | − | 3.94385e16i | 0.0662228 | − | 0.114701i | ||||
\(838\) | 6.17554e16 | − | 3.56545e16i | 0.178324 | − | 0.102956i | ||||
\(839\) | − | 2.11535e16i | − | 0.0606473i | −0.999540 | − | 0.0303236i | \(-0.990346\pi\) | ||
0.999540 | − | 0.0303236i | \(-0.00965379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.72771e17 | 2.46674 | ||||||||
\(842\) | −2.02255e17 | − | 3.50316e17i | −0.567579 | − | 0.983076i | ||||
\(843\) | −3.02635e17 | − | 1.74727e17i | −0.843246 | − | 0.486848i | ||||
\(844\) | 4.57212e16 | − | 7.91914e16i | 0.126492 | − | 0.219090i | ||||
\(845\) | −5.06120e17 | + | 2.92208e17i | −1.39031 | + | 0.802699i | ||||
\(846\) | 1.89740e17i | 0.517532i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.97749e16 | −0.0800710 | ||||||||
\(849\) | 3.68343e17 | + | 6.37989e17i | 0.983573 | + | 1.70360i | ||||
\(850\) | −6.33576e15 | − | 3.65796e15i | −0.0167991 | − | 0.00969895i | ||||
\(851\) | −1.01396e17 | + | 1.75624e17i | −0.266960 | + | 0.462388i | ||||
\(852\) | −1.01572e17 | + | 5.86423e16i | −0.265543 | + | 0.153311i | ||||
\(853\) | − | 3.17413e17i | − | 0.824006i | −0.911183 | − | 0.412003i | \(-0.864829\pi\) | ||
0.911183 | − | 0.412003i | \(-0.135171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.70631e17 | 0.436778 | ||||||||
\(856\) | 5.56631e16 | + | 9.64114e16i | 0.141490 | + | 0.245067i | ||||
\(857\) | −3.22966e17 | − | 1.86465e17i | −0.815215 | − | 0.470665i | 0.0335487 | − | 0.999437i | \(-0.489319\pi\) |
−0.848764 | + | 0.528773i | \(0.822652\pi\) | |||||||
\(858\) | −6.31466e17 | + | 1.09373e18i | −1.58280 | + | 2.74149i | ||||
\(859\) | 3.62991e17 | − | 2.09573e17i | 0.903519 | − | 0.521647i | 0.0251784 | − | 0.999683i | \(-0.491985\pi\) |
0.878340 | + | 0.478036i | \(0.158651\pi\) | |||||||
\(860\) | 1.01086e17i | 0.249862i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.43608e16 | −0.156884 | ||||||||
\(863\) | −1.67121e17 | − | 2.89462e17i | −0.404545 | − | 0.700692i | 0.589724 | − | 0.807605i | \(-0.299237\pi\) |
−0.994268 | + | 0.106913i | \(0.965903\pi\) | |||||||
\(864\) | −4.35003e16 | − | 2.51149e16i | −0.104571 | − | 0.0603738i | ||||
\(865\) | −5.24397e16 | + | 9.08282e16i | −0.125188 | + | 0.216832i | ||||
\(866\) | −2.99141e17 | + | 1.72709e17i | −0.709200 | + | 0.409457i | ||||
\(867\) | 6.50124e17i | 1.53067i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.81750e17 | −1.81530 | ||||||||
\(870\) | −3.99603e17 | − | 6.92133e17i | −0.921539 | − | 1.59615i | ||||
\(871\) | −8.04537e17 | − | 4.64499e17i | −1.84262 | − | 1.06384i | ||||
\(872\) | 9.24088e16 | − | 1.60057e17i | 0.210191 | − | 0.364062i | ||||
\(873\) | 5.86121e17 | − | 3.38397e17i | 1.32404 | − | 0.764436i | ||||
\(874\) | 8.79231e16i | 0.197258i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.76994e17 | 0.391682 | ||||||||
\(877\) | −1.04169e17 | − | 1.80426e17i | −0.228950 | − | 0.396553i | 0.728547 | − | 0.684996i | \(-0.240196\pi\) |
−0.957497 | + | 0.288443i | \(0.906863\pi\) | |||||||
\(878\) | −5.57632e16 | − | 3.21949e16i | −0.121725 | − | 0.0702781i | ||||
\(879\) | 2.61863e17 | − | 4.53560e17i | 0.567729 | − | 0.983336i | ||||
\(880\) | −1.54759e17 | + | 8.93499e16i | −0.333241 | + | 0.192397i | ||||
\(881\) | − | 1.11446e16i | − | 0.0238347i | −0.999929 | − | 0.0119174i | \(-0.996206\pi\) | ||
0.999929 | − | 0.0119174i | \(-0.00379350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.76939e17 | −1.00623 | −0.503117 | − | 0.864218i | \(-0.667813\pi\) | ||||
−0.503117 | + | 0.864218i | \(0.667813\pi\) | |||||||
\(884\) | 2.78920e16 | + | 4.83104e16i | 0.0584476 | + | 0.101234i | ||||
\(885\) | 4.68880e17 | + | 2.70708e17i | 0.975892 | + | 0.563431i | ||||
\(886\) | 1.87859e17 | − | 3.25382e17i | 0.388356 | − | 0.672653i | ||||
\(887\) | −3.47506e17 | + | 2.00632e17i | −0.713543 | + | 0.411964i | −0.812372 | − | 0.583140i | \(-0.801824\pi\) |
0.0988285 | + | 0.995104i | \(0.468490\pi\) | |||||||
\(888\) | 1.75533e17i | 0.357998i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.53080e17 | 1.11288 | ||||||||
\(891\) | −1.59359e17 | − | 2.76017e17i | −0.318500 | − | 0.551658i | ||||
\(892\) | 1.61117e17 | + | 9.30212e16i | 0.319855 | + | 0.184668i | ||||
\(893\) | 4.37471e16 | − | 7.57722e16i | 0.0862661 | − | 0.149417i | ||||
\(894\) | 2.46444e17 | − | 1.42285e17i | 0.482718 | − | 0.278697i | ||||
\(895\) | − | 4.72819e17i | − | 0.919934i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.11837e18 | −2.14699 | ||||||||
\(898\) | 1.22746e16 | + | 2.12601e16i | 0.0234071 | + | 0.0405423i | ||||
\(899\) | 1.65057e17 | + | 9.52956e16i | 0.312662 | + | 0.180516i | ||||
\(900\) | 3.74354e16 | − | 6.48401e16i | 0.0704414 | − | 0.122008i | ||||
\(901\) | 2.07685e16 | − | 1.19907e16i | 0.0388201 | − | 0.0224128i | ||||
\(902\) | − | 3.91340e17i | − | 0.726632i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.71994e17 | −0.498366 | ||||||||
\(905\) | 1.71003e17 | + | 2.96186e17i | 0.311252 | + | 0.539104i | ||||
\(906\) | −7.58795e17 | − | 4.38091e17i | −1.37200 | − | 0.792127i | ||||
\(907\) | 2.11727e17 | − | 3.66722e17i | 0.380305 | − | 0.658708i | −0.610801 | − | 0.791784i | \(-0.709152\pi\) |
0.991106 | + | 0.133077i | \(0.0424856\pi\) | |||||||
\(908\) | 2.56306e17 | − | 1.47978e17i | 0.457344 | − | 0.264048i | ||||
\(909\) | 8.82631e17i | 1.56457i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.15441e16 | −0.0551834 | −0.0275917 | − | 0.999619i | \(-0.508784\pi\) | ||||
−0.0275917 | + | 0.999619i | \(0.508784\pi\) | |||||||
\(912\) | 3.80521e16 | + | 6.59082e16i | 0.0661317 | + | 0.114543i | ||||
\(913\) | 5.48481e15 | + | 3.16666e15i | 0.00946972 | + | 0.00546734i | ||||
\(914\) | 1.20561e17 | − | 2.08818e17i | 0.206791 | − | 0.358172i | ||||
\(915\) | 9.77488e17 | − | 5.64353e17i | 1.66565 | − | 0.961666i | ||||
\(916\) | − | 3.12125e17i | − | 0.528391i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.04562e16 | 0.0675973 | ||||||||
\(919\) | 1.78384e17 | + | 3.08971e17i | 0.296117 | + | 0.512890i | 0.975244 | − | 0.221131i | \(-0.0709748\pi\) |
−0.679127 | + | 0.734021i | \(0.737641\pi\) | |||||||
\(920\) | −1.37044e17 | − | 7.91225e16i | −0.226013 | − | 0.130489i | ||||
\(921\) | −2.26351e17 | + | 3.92051e17i | −0.370872 | + | 0.642370i | ||||
\(922\) | 5.09101e16 | − | 2.93929e16i | 0.0828740 | − | 0.0478473i | ||||
\(923\) | 4.05702e17i | 0.656140i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.96310e16 | −0.127125 | ||||||||
\(926\) | −3.38416e17 | − | 5.86153e17i | −0.536765 | − | 0.929705i | ||||
\(927\) | −4.36948e17 | − | 2.52272e17i | −0.688575 | − | 0.397549i | ||||
\(928\) | 1.05110e17 | − | 1.82056e17i | 0.164572 | − | 0.285047i | ||||
\(929\) | 7.87030e17 | − | 4.54392e17i | 1.22433 | − | 0.706864i | 0.258488 | − | 0.966014i | \(-0.416776\pi\) |
0.965837 | + | 0.259150i | \(0.0834424\pi\) | |||||||
\(930\) | − | 1.24184e17i | − | 0.191940i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.64022e16 | −0.0402851 | ||||||||
\(933\) | 6.20712e17 | + | 1.07510e18i | 0.941023 | + | 1.62990i | ||||
\(934\) | −2.41205e17 | − | 1.39260e17i | −0.363334 | − | 0.209771i | ||||
\(935\) | 7.19645e16 | − | 1.24646e17i | 0.107708 | − | 0.186556i | ||||
\(936\) | −4.94408e17 | + | 2.85446e17i | −0.735241 | + | 0.424492i | ||||
\(937\) | 7.52418e16i | 0.111179i | 0.998454 | + | 0.0555894i | \(0.0177038\pi\) | ||||
−0.998454 | + | 0.0555894i | \(0.982296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.47329e17 | 0.944346 | ||||||||
\(940\) | 7.87364e16 | + | 1.36376e17i | 0.114132 | + | 0.197683i | ||||
\(941\) | 1.16129e18 | + | 6.70472e17i | 1.67264 | + | 0.965701i | 0.966150 | + | 0.257982i | \(0.0830577\pi\) |
0.706494 | + | 0.707719i | \(0.250276\pi\) | |||||||
\(942\) | −4.62271e17 | + | 8.00678e17i | −0.661594 | + | 1.14591i | ||||
\(943\) | 3.00117e17 | − | 1.73272e17i | 0.426796 | − | 0.246411i | ||||
\(944\) | 1.42412e17i | 0.201240i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.84842e17 | 0.676478 | ||||||||
\(947\) | 5.24027e16 | + | 9.07641e16i | 0.0726530 | + | 0.125839i | 0.900063 | − | 0.435759i | \(-0.143520\pi\) |
−0.827410 | + | 0.561598i | \(0.810187\pi\) | |||||||
\(948\) | −5.18931e17 | − | 2.99605e17i | −0.714924 | − | 0.412761i | ||||
\(949\) | 3.06122e17 | − | 5.30218e17i | 0.419080 | − | 0.725868i | ||||
\(950\) | −2.98995e16 | + | 1.72625e16i | −0.0406744 | + | 0.0234834i | ||||
\(951\) | 2.71874e17i | 0.367523i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.53447e17 | 0.872274 | 0.436137 | − | 0.899880i | \(-0.356346\pi\) | ||||
0.436137 | + | 0.899880i | \(0.356346\pi\) | |||||||
\(954\) | 1.22713e17 | + | 2.12544e17i | 0.162779 | + | 0.281942i | ||||
\(955\) | 6.63435e17 | + | 3.83035e17i | 0.874537 | + | 0.504914i | ||||
\(956\) | −1.51226e17 | + | 2.61932e17i | −0.198098 | + | 0.343116i | ||||
\(957\) | −3.31970e18 | + | 1.91663e18i | −4.32142 | + | 2.49498i | ||||
\(958\) | 4.25091e17i | 0.549906i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.36973e17 | −0.174988 | ||||||||
\(961\) | −3.79024e17 | − | 6.56489e17i | −0.481201 | − | 0.833464i | ||||
\(962\) | 5.25841e17 | + | 3.03595e17i | 0.663444 | + | 0.383039i | ||||
\(963\) | 4.58814e17 | − | 7.94689e17i | 0.575279 | − | 0.996413i | ||||
\(964\) | 2.84526e17 | − | 1.64271e17i | 0.354535 | − | 0.204691i | ||||
\(965\) | 4.85151e17i | 0.600777i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.98974e17 | −0.365658 | −0.182829 | − | 0.983145i | \(-0.558525\pi\) | ||||
−0.182829 | + | 0.983145i | \(0.558525\pi\) | |||||||
\(968\) | 2.83113e17 | + | 4.90367e17i | 0.344119 | + | 0.596031i | ||||
\(969\) | −5.30840e16 | − | 3.06481e16i | −0.0641240 | − | 0.0370220i | ||||
\(970\) | 2.80849e17 | − | 4.86445e17i | 0.337165 | − | 0.583987i | ||||
\(971\) | −5.60125e17 | + | 3.23388e17i | −0.668297 | + | 0.385841i | −0.795431 | − | 0.606044i | \(-0.792755\pi\) |
0.127134 | + | 0.991886i | \(0.459422\pi\) | |||||||
\(972\) | − | 5.32315e17i | − | 0.631207i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.71493e17 | 0.435107 | ||||||||
\(975\) | −2.19576e17 | − | 3.80317e17i | −0.255598 | − | 0.442709i | ||||
\(976\) | 2.57114e17 | + | 1.48445e17i | 0.297459 | + | 0.171738i | ||||
\(977\) | −7.29729e17 | + | 1.26393e18i | −0.839062 | + | 1.45330i | 0.0516180 | + | 0.998667i | \(0.483562\pi\) |
−0.890680 | + | 0.454631i | \(0.849771\pi\) | |||||||
\(978\) | −1.19875e18 | + | 6.92098e17i | −1.36992 | + | 0.790923i | ||||
\(979\) | − | 2.65275e18i | − | 3.01301i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.52339e18 | −1.70922 | ||||||||
\(982\) | 3.85358e17 | + | 6.67460e17i | 0.429730 | + | 0.744314i | ||||
\(983\) | 4.19576e16 | + | 2.42242e16i | 0.0465039 | + | 0.0268490i | 0.523072 | − | 0.852289i | \(-0.324786\pi\) |
−0.476568 | + | 0.879138i | \(0.658119\pi\) | |||||||
\(984\) | 1.49981e17 | − | 2.59774e17i | 0.165221 | − | 0.286171i | ||||
\(985\) | 2.94691e17 | − | 1.70140e17i | 0.322663 | − | 0.186289i | ||||
\(986\) | 1.69316e17i | 0.184262i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.63253e17 | 0.283030 | ||||||||
\(989\) | 2.14672e17 | + | 3.71823e17i | 0.229403 | + | 0.397337i | ||||
\(990\) | 1.27563e18 | + | 7.36483e17i | 1.35492 | + | 0.782261i | ||||
\(991\) | 6.04866e17 | − | 1.04766e18i | 0.638583 | − | 1.10606i | −0.347161 | − | 0.937805i | \(-0.612854\pi\) |
0.985744 | − | 0.168252i | \(-0.0538123\pi\) | |||||||
\(992\) | 2.82885e16 | − | 1.63324e16i | 0.0296852 | − | 0.0171387i | ||||
\(993\) | − | 8.30318e17i | − | 0.866062i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.80303e17 | 0.494967 | ||||||||
\(996\) | 2.42724e15 | + | 4.20410e15i | 0.00248632 | + | 0.00430642i | ||||
\(997\) | 1.50455e18 | + | 8.68652e17i | 1.53192 | + | 0.884454i | 0.999273 | + | 0.0381148i | \(0.0121352\pi\) |
0.532645 | + | 0.846339i | \(0.321198\pi\) | |||||||
\(998\) | 1.57291e17 | − | 2.72435e17i | 0.159191 | − | 0.275728i | ||||
\(999\) | 3.81356e17 | − | 2.20176e17i | 0.383652 | − | 0.221502i |
(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 | 98.13.d.a.31.5 | 16 | ||
7.2 | even | 3 | 14.13.d.a.5.8 | yes | 16 | ||
7.3 | odd | 6 | 98.13.b.c.97.2 | 16 | |||
7.4 | even | 3 | 98.13.b.c.97.7 | 16 | |||
7.5 | odd | 6 | inner | 98.13.d.a.19.5 | 16 | ||
7.6 | odd | 2 | 14.13.d.a.3.8 | ✓ | 16 | ||
21.2 | odd | 6 | 126.13.n.a.19.3 | 16 | |||
21.20 | even | 2 | 126.13.n.a.73.3 | 16 | |||
28.23 | odd | 6 | 112.13.s.c.33.2 | 16 | |||
28.27 | even | 2 | 112.13.s.c.17.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.13.d.a.3.8 | ✓ | 16 | 7.6 | odd | 2 | ||
14.13.d.a.5.8 | yes | 16 | 7.2 | even | 3 | ||
98.13.b.c.97.2 | 16 | 7.3 | odd | 6 | |||
98.13.b.c.97.7 | 16 | 7.4 | even | 3 | |||
98.13.d.a.19.5 | 16 | 7.5 | odd | 6 | inner | ||
98.13.d.a.31.5 | 16 | 1.1 | even | 1 | trivial | ||
112.13.s.c.17.2 | 16 | 28.27 | even | 2 | |||
112.13.s.c.33.2 | 16 | 28.23 | odd | 6 | |||
126.13.n.a.19.3 | 16 | 21.2 | odd | 6 | |||
126.13.n.a.73.3 | 16 | 21.20 | even | 2 |