Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,11,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(6.35357252674\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.7 |
Dual form | 10.11.c.a.3.1 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | + | 16.0000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −183.000 | + | 183.000i | −0.753086 | + | 0.753086i | −0.975054 | − | 0.221968i | \(-0.928752\pi\) |
0.221968 | + | 0.975054i | \(0.428752\pi\) | |||||||
\(4\) | 512.000i | 0.500000i | ||||||||
\(5\) | −1875.00 | − | 2500.00i | −0.600000 | − | 0.800000i | ||||
\(6\) | −5856.00 | −0.753086 | ||||||||
\(7\) | −8407.00 | − | 8407.00i | −0.500208 | − | 0.500208i | 0.411294 | − | 0.911503i | \(-0.365077\pi\) |
−0.911503 | + | 0.411294i | \(0.865077\pi\) | |||||||
\(8\) | −8192.00 | + | 8192.00i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 7929.00i | − | 0.134278i | ||||||
\(10\) | 10000.0 | − | 70000.0i | 0.100000 | − | 0.700000i | ||||
\(11\) | −173398. | −1.07667 | −0.538333 | − | 0.842732i | \(-0.680946\pi\) | ||||
−0.538333 | + | 0.842732i | \(0.680946\pi\) | |||||||
\(12\) | −93696.0 | − | 93696.0i | −0.376543 | − | 0.376543i | ||||
\(13\) | −232623. | + | 232623.i | −0.626521 | + | 0.626521i | −0.947191 | − | 0.320670i | \(-0.896092\pi\) |
0.320670 | + | 0.947191i | \(0.396092\pi\) | |||||||
\(14\) | − | 269024.i | − | 0.500208i | ||||||
\(15\) | 800625. | + | 114375.i | 1.05432 | + | 0.150617i | ||||
\(16\) | −262144. | −0.250000 | ||||||||
\(17\) | 1.88003e6 | + | 1.88003e6i | 1.32410 | + | 1.32410i | 0.910424 | + | 0.413676i | \(0.135755\pi\) |
0.413676 | + | 0.910424i | \(0.364245\pi\) | |||||||
\(18\) | 126864. | − | 126864.i | 0.0671392 | − | 0.0671392i | ||||
\(19\) | − | 1.10156e6i | − | 0.444877i | −0.974947 | − | 0.222439i | \(-0.928598\pi\) | ||
0.974947 | − | 0.222439i | \(-0.0714017\pi\) | |||||||
\(20\) | 1.28000e6 | − | 960000.i | 0.400000 | − | 0.300000i | ||||
\(21\) | 3.07696e6 | 0.753400 | ||||||||
\(22\) | −2.77437e6 | − | 2.77437e6i | −0.538333 | − | 0.538333i | ||||
\(23\) | −5.22826e6 | + | 5.22826e6i | −0.812303 | + | 0.812303i | −0.984979 | − | 0.172675i | \(-0.944759\pi\) |
0.172675 | + | 0.984979i | \(0.444759\pi\) | |||||||
\(24\) | − | 2.99827e6i | − | 0.376543i | ||||||
\(25\) | −2.73438e6 | + | 9.37500e6i | −0.280000 | + | 0.960000i | ||||
\(26\) | −7.44394e6 | −0.626521 | ||||||||
\(27\) | −9.35496e6 | − | 9.35496e6i | −0.651963 | − | 0.651963i | ||||
\(28\) | 4.30438e6 | − | 4.30438e6i | 0.250104 | − | 0.250104i | ||||
\(29\) | − | 2.47908e7i | − | 1.20865i | −0.796737 | − | 0.604326i | \(-0.793442\pi\) | ||
0.796737 | − | 0.604326i | \(-0.206558\pi\) | |||||||
\(30\) | 1.09800e7 | + | 1.46400e7i | 0.451852 | + | 0.602469i | ||||
\(31\) | −1.00660e7 | −0.351600 | −0.175800 | − | 0.984426i | \(-0.556251\pi\) | ||||
−0.175800 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(32\) | −4.19430e6 | − | 4.19430e6i | −0.125000 | − | 0.125000i | ||||
\(33\) | 3.17318e7 | − | 3.17318e7i | 0.810822 | − | 0.810822i | ||||
\(34\) | 6.01611e7i | 1.32410i | ||||||||
\(35\) | −5.25438e6 | + | 3.67806e7i | −0.100042 | + | 0.700292i | ||||
\(36\) | 4.05965e6 | 0.0671392 | ||||||||
\(37\) | 5.63879e7 | + | 5.63879e7i | 0.813163 | + | 0.813163i | 0.985107 | − | 0.171944i | \(-0.0550048\pi\) |
−0.171944 | + | 0.985107i | \(0.555005\pi\) | |||||||
\(38\) | 1.76250e7 | − | 1.76250e7i | 0.222439 | − | 0.222439i | ||||
\(39\) | − | 8.51400e7i | − | 0.943649i | ||||||
\(40\) | 3.58400e7 | + | 5.12000e6i | 0.350000 | + | 0.0500000i | ||||
\(41\) | −1.53004e8 | −1.32063 | −0.660317 | − | 0.750987i | \(-0.729578\pi\) | ||||
−0.660317 | + | 0.750987i | \(0.729578\pi\) | |||||||
\(42\) | 4.92314e7 | + | 4.92314e7i | 0.376700 | + | 0.376700i | ||||
\(43\) | 5.93725e7 | − | 5.93725e7i | 0.403871 | − | 0.403871i | −0.475724 | − | 0.879595i | \(-0.657814\pi\) |
0.879595 | + | 0.475724i | \(0.157814\pi\) | |||||||
\(44\) | − | 8.87798e7i | − | 0.538333i | ||||||
\(45\) | −1.98225e7 | + | 1.48669e7i | −0.107423 | + | 0.0805670i | ||||
\(46\) | −1.67304e8 | −0.812303 | ||||||||
\(47\) | 1.72339e8 | + | 1.72339e8i | 0.751441 | + | 0.751441i | 0.974748 | − | 0.223307i | \(-0.0716852\pi\) |
−0.223307 | + | 0.974748i | \(0.571685\pi\) | |||||||
\(48\) | 4.79724e7 | − | 4.79724e7i | 0.188272 | − | 0.188272i | ||||
\(49\) | − | 1.41120e8i | − | 0.499583i | ||||||
\(50\) | −1.93750e8 | + | 1.06250e8i | −0.620000 | + | 0.340000i | ||||
\(51\) | −6.88092e8 | −1.99432 | ||||||||
\(52\) | −1.19103e8 | − | 1.19103e8i | −0.313261 | − | 0.313261i | ||||
\(53\) | 1.96386e8 | − | 1.96386e8i | 0.469602 | − | 0.469602i | −0.432183 | − | 0.901786i | \(-0.642257\pi\) |
0.901786 | + | 0.432183i | \(0.142257\pi\) | |||||||
\(54\) | − | 2.99359e8i | − | 0.651963i | ||||||
\(55\) | 3.25121e8 | + | 4.33495e8i | 0.645999 | + | 0.861332i | ||||
\(56\) | 1.37740e8 | 0.250104 | ||||||||
\(57\) | 2.01585e8 | + | 2.01585e8i | 0.335031 | + | 0.335031i | ||||
\(58\) | 3.96653e8 | − | 3.96653e8i | 0.604326 | − | 0.604326i | ||||
\(59\) | 6.94069e8i | 0.970829i | 0.874284 | + | 0.485414i | \(0.161331\pi\) | ||||
−0.874284 | + | 0.485414i | \(0.838669\pi\) | |||||||
\(60\) | −5.85600e7 | + | 4.09920e8i | −0.0753086 | + | 0.527160i | ||||
\(61\) | 9.06186e8 | 1.07292 | 0.536461 | − | 0.843925i | \(-0.319761\pi\) | ||||
0.536461 | + | 0.843925i | \(0.319761\pi\) | |||||||
\(62\) | −1.61056e8 | − | 1.61056e8i | −0.175800 | − | 0.175800i | ||||
\(63\) | −6.66591e7 | + | 6.66591e7i | −0.0671671 | + | 0.0671671i | ||||
\(64\) | − | 1.34218e8i | − | 0.125000i | ||||||
\(65\) | 1.01773e9 | + | 1.45389e8i | 0.877130 | + | 0.125304i | ||||
\(66\) | 1.01542e9 | 0.810822 | ||||||||
\(67\) | −9.62074e8 | − | 9.62074e8i | −0.712581 | − | 0.712581i | 0.254493 | − | 0.967075i | \(-0.418091\pi\) |
−0.967075 | + | 0.254493i | \(0.918091\pi\) | |||||||
\(68\) | −9.62577e8 | + | 9.62577e8i | −0.662050 | + | 0.662050i | ||||
\(69\) | − | 1.91354e9i | − | 1.22347i | ||||||
\(70\) | −6.72560e8 | + | 5.04420e8i | −0.400167 | + | 0.300125i | ||||
\(71\) | −3.12088e9 | −1.72976 | −0.864878 | − | 0.501982i | \(-0.832605\pi\) | ||||
−0.864878 | + | 0.501982i | \(0.832605\pi\) | |||||||
\(72\) | 6.49544e7 | + | 6.49544e7i | 0.0335696 | + | 0.0335696i | ||||
\(73\) | −6.36339e8 | + | 6.36339e8i | −0.306955 | + | 0.306955i | −0.843727 | − | 0.536772i | \(-0.819643\pi\) |
0.536772 | + | 0.843727i | \(0.319643\pi\) | |||||||
\(74\) | 1.80441e9i | 0.813163i | ||||||||
\(75\) | −1.21523e9 | − | 2.21602e9i | −0.512099 | − | 0.933827i | ||||
\(76\) | 5.63999e8 | 0.222439 | ||||||||
\(77\) | 1.45776e9 | + | 1.45776e9i | 0.538557 | + | 0.538557i | ||||
\(78\) | 1.36224e9 | − | 1.36224e9i | 0.471825 | − | 0.471825i | ||||
\(79\) | − | 1.96800e9i | − | 0.639571i | −0.947490 | − | 0.319786i | \(-0.896389\pi\) | ||
0.947490 | − | 0.319786i | \(-0.103611\pi\) | |||||||
\(80\) | 4.91520e8 | + | 6.55360e8i | 0.150000 | + | 0.200000i | ||||
\(81\) | 3.89211e9 | 1.11625 | ||||||||
\(82\) | −2.44806e9 | − | 2.44806e9i | −0.660317 | − | 0.660317i | ||||
\(83\) | −5.18382e9 | + | 5.18382e9i | −1.31601 | + | 1.31601i | −0.399107 | + | 0.916904i | \(0.630680\pi\) |
−0.916904 | + | 0.399107i | \(0.869320\pi\) | |||||||
\(84\) | 1.57540e9i | 0.376700i | ||||||||
\(85\) | 1.17502e9 | − | 8.22514e9i | 0.264820 | − | 1.85374i | ||||
\(86\) | 1.89992e9 | 0.403871 | ||||||||
\(87\) | 4.53672e9 | + | 4.53672e9i | 0.910219 | + | 0.910219i | ||||
\(88\) | 1.42048e9 | − | 1.42048e9i | 0.269166 | − | 0.269166i | ||||
\(89\) | 7.77138e9i | 1.39171i | 0.718183 | + | 0.695854i | \(0.244974\pi\) | ||||
−0.718183 | + | 0.695854i | \(0.755026\pi\) | |||||||
\(90\) | −5.55030e8 | − | 7.92900e7i | −0.0939948 | − | 0.0134278i | ||||
\(91\) | 3.91132e9 | 0.626782 | ||||||||
\(92\) | −2.67687e9 | − | 2.67687e9i | −0.406152 | − | 0.406152i | ||||
\(93\) | 1.84208e9 | − | 1.84208e9i | 0.264785 | − | 0.264785i | ||||
\(94\) | 5.51486e9i | 0.751441i | ||||||||
\(95\) | −2.75390e9 | + | 2.06542e9i | −0.355902 | + | 0.266926i | ||||
\(96\) | 1.53512e9 | 0.188272 | ||||||||
\(97\) | −6.40361e8 | − | 6.40361e8i | −0.0745704 | − | 0.0745704i | 0.668838 | − | 0.743408i | \(-0.266792\pi\) |
−0.743408 | + | 0.668838i | \(0.766792\pi\) | |||||||
\(98\) | 2.25792e9 | − | 2.25792e9i | 0.249792 | − | 0.249792i | ||||
\(99\) | 1.37487e9i | 0.144573i | ||||||||
\(100\) | −4.80000e9 | − | 1.40000e9i | −0.480000 | − | 0.140000i | ||||
\(101\) | 2.02434e9 | 0.192609 | 0.0963047 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963047 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(102\) | −1.10095e10 | − | 1.10095e10i | −0.997162 | − | 0.997162i | ||||
\(103\) | −1.50252e9 | + | 1.50252e9i | −0.129609 | + | 0.129609i | −0.768935 | − | 0.639326i | \(-0.779213\pi\) |
0.639326 | + | 0.768935i | \(0.279213\pi\) | |||||||
\(104\) | − | 3.81130e9i | − | 0.313261i | ||||||
\(105\) | −5.76930e9 | − | 7.69240e9i | −0.452040 | − | 0.602720i | ||||
\(106\) | 6.28434e9 | 0.469602 | ||||||||
\(107\) | 1.41812e9 | + | 1.41812e9i | 0.101110 | + | 0.101110i | 0.755852 | − | 0.654742i | \(-0.227223\pi\) |
−0.654742 | + | 0.755852i | \(0.727223\pi\) | |||||||
\(108\) | 4.78974e9 | − | 4.78974e9i | 0.325982 | − | 0.325982i | ||||
\(109\) | − | 6.21296e9i | − | 0.403800i | −0.979406 | − | 0.201900i | \(-0.935288\pi\) | ||
0.979406 | − | 0.201900i | \(-0.0647116\pi\) | |||||||
\(110\) | −1.73398e9 | + | 1.21379e10i | −0.107667 | + | 0.753666i | ||||
\(111\) | −2.06380e10 | −1.22476 | ||||||||
\(112\) | 2.20384e9 | + | 2.20384e9i | 0.125052 | + | 0.125052i | ||||
\(113\) | −1.79511e10 | + | 1.79511e10i | −0.974313 | + | 0.974313i | −0.999678 | − | 0.0253650i | \(-0.991925\pi\) |
0.0253650 | + | 0.999678i | \(0.491925\pi\) | |||||||
\(114\) | 6.45074e9i | 0.335031i | ||||||||
\(115\) | 2.28737e10 | + | 3.26766e9i | 1.13722 | + | 0.162461i | ||||
\(116\) | 1.26929e10 | 0.604326 | ||||||||
\(117\) | 1.84447e9 | + | 1.84447e9i | 0.0841282 | + | 0.0841282i | ||||
\(118\) | −1.11051e10 | + | 1.11051e10i | −0.485414 | + | 0.485414i | ||||
\(119\) | − | 3.16109e10i | − | 1.32465i | ||||||
\(120\) | −7.49568e9 | + | 5.62176e9i | −0.301235 | + | 0.225926i | ||||
\(121\) | 4.12944e9 | 0.159208 | ||||||||
\(122\) | 1.44990e10 | + | 1.44990e10i | 0.536461 | + | 0.536461i | ||||
\(123\) | 2.79997e10 | − | 2.79997e10i | 0.994551 | − | 0.994551i | ||||
\(124\) | − | 5.15379e9i | − | 0.175800i | ||||||
\(125\) | 2.85645e10 | − | 1.07422e10i | 0.936000 | − | 0.352000i | ||||
\(126\) | −2.13309e9 | −0.0671671 | ||||||||
\(127\) | 1.30621e10 | + | 1.30621e10i | 0.395362 | + | 0.395362i | 0.876593 | − | 0.481232i | \(-0.159810\pi\) |
−0.481232 | + | 0.876593i | \(0.659810\pi\) | |||||||
\(128\) | 2.14748e9 | − | 2.14748e9i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 2.17303e10i | 0.608300i | ||||||||
\(130\) | 1.39574e10 | + | 1.86098e10i | 0.375913 | + | 0.501217i | ||||
\(131\) | −5.20222e10 | −1.34844 | −0.674221 | − | 0.738530i | \(-0.735520\pi\) | ||||
−0.674221 | + | 0.738530i | \(0.735520\pi\) | |||||||
\(132\) | 1.62467e10 | + | 1.62467e10i | 0.405411 | + | 0.405411i | ||||
\(133\) | −9.26081e9 | + | 9.26081e9i | −0.222531 | + | 0.222531i | ||||
\(134\) | − | 3.07864e10i | − | 0.712581i | ||||||
\(135\) | −5.84685e9 | + | 4.09280e10i | −0.130393 | + | 0.912749i | ||||
\(136\) | −3.08025e10 | −0.662050 | ||||||||
\(137\) | −1.63815e10 | − | 1.63815e10i | −0.339429 | − | 0.339429i | 0.516723 | − | 0.856153i | \(-0.327152\pi\) |
−0.856153 | + | 0.516723i | \(0.827152\pi\) | |||||||
\(138\) | 3.06167e10 | − | 3.06167e10i | 0.611735 | − | 0.611735i | ||||
\(139\) | − | 2.61490e10i | − | 0.503942i | −0.967735 | − | 0.251971i | \(-0.918921\pi\) | ||
0.967735 | − | 0.251971i | \(-0.0810787\pi\) | |||||||
\(140\) | −1.88317e10 | − | 2.69024e9i | −0.350146 | − | 0.0500208i | ||||
\(141\) | −6.30762e10 | −1.13180 | ||||||||
\(142\) | −4.99340e10 | − | 4.99340e10i | −0.864878 | − | 0.864878i | ||||
\(143\) | 4.03364e10 | − | 4.03364e10i | 0.674554 | − | 0.674554i | ||||
\(144\) | 2.07854e9i | 0.0335696i | ||||||||
\(145\) | −6.19771e10 | + | 4.64828e10i | −0.966922 | + | 0.725191i | ||||
\(146\) | −2.03629e10 | −0.306955 | ||||||||
\(147\) | 2.58250e10 | + | 2.58250e10i | 0.376229 | + | 0.376229i | ||||
\(148\) | −2.88706e10 | + | 2.88706e10i | −0.406581 | + | 0.406581i | ||||
\(149\) | 4.31363e9i | 0.0587369i | 0.999569 | + | 0.0293685i | \(0.00934962\pi\) | ||||
−0.999569 | + | 0.0293685i | \(0.990650\pi\) | |||||||
\(150\) | 1.60125e10 | − | 5.49000e10i | 0.210864 | − | 0.722963i | ||||
\(151\) | 1.13868e11 | 1.45050 | 0.725251 | − | 0.688484i | \(-0.241724\pi\) | ||||
0.725251 | + | 0.688484i | \(0.241724\pi\) | |||||||
\(152\) | 9.02398e9 | + | 9.02398e9i | 0.111219 | + | 0.111219i | ||||
\(153\) | 1.49068e10 | − | 1.49068e10i | 0.177798 | − | 0.177798i | ||||
\(154\) | 4.66482e10i | 0.538557i | ||||||||
\(155\) | 1.88737e10 | + | 2.51650e10i | 0.210960 | + | 0.281280i | ||||
\(156\) | 4.35917e10 | 0.471825 | ||||||||
\(157\) | 1.04428e10 | + | 1.04428e10i | 0.109476 | + | 0.109476i | 0.759723 | − | 0.650247i | \(-0.225335\pi\) |
−0.650247 | + | 0.759723i | \(0.725335\pi\) | |||||||
\(158\) | 3.14879e10 | − | 3.14879e10i | 0.319786 | − | 0.319786i | ||||
\(159\) | 7.18771e10i | 0.707302i | ||||||||
\(160\) | −2.62144e9 | + | 1.83501e10i | −0.0250000 | + | 0.175000i | ||||
\(161\) | 8.79080e10 | 0.812642 | ||||||||
\(162\) | 6.22738e10 | + | 6.22738e10i | 0.558124 | + | 0.558124i | ||||
\(163\) | 4.78305e10 | − | 4.78305e10i | 0.415688 | − | 0.415688i | −0.468027 | − | 0.883714i | \(-0.655035\pi\) |
0.883714 | + | 0.468027i | \(0.155035\pi\) | |||||||
\(164\) | − | 7.83378e10i | − | 0.660317i | ||||||
\(165\) | −1.38827e11 | − | 1.98324e10i | −1.13515 | − | 0.162164i | ||||
\(166\) | −1.65882e11 | −1.31601 | ||||||||
\(167\) | −1.18281e10 | − | 1.18281e10i | −0.0910613 | − | 0.0910613i | 0.660109 | − | 0.751170i | \(-0.270510\pi\) |
−0.751170 | + | 0.660109i | \(0.770510\pi\) | |||||||
\(168\) | −2.52065e10 | + | 2.52065e10i | −0.188350 | + | 0.188350i | ||||
\(169\) | 2.96316e10i | 0.214942i | ||||||||
\(170\) | 1.50403e11 | − | 1.12802e11i | 1.05928 | − | 0.794460i | ||||
\(171\) | −8.73427e9 | −0.0597374 | ||||||||
\(172\) | 3.03987e10 | + | 3.03987e10i | 0.201936 | + | 0.201936i | ||||
\(173\) | −1.16377e11 | + | 1.16377e11i | −0.750997 | + | 0.750997i | −0.974665 | − | 0.223669i | \(-0.928197\pi\) |
0.223669 | + | 0.974665i | \(0.428197\pi\) | |||||||
\(174\) | 1.45175e11i | 0.910219i | ||||||||
\(175\) | 1.01804e11 | − | 5.58277e10i | 0.620258 | − | 0.340142i | ||||
\(176\) | 4.54552e10 | 0.269166 | ||||||||
\(177\) | −1.27015e11 | − | 1.27015e11i | −0.731118 | − | 0.731118i | ||||
\(178\) | −1.24342e11 | + | 1.24342e11i | −0.695854 | + | 0.695854i | ||||
\(179\) | − | 1.81011e11i | − | 0.985008i | −0.870310 | − | 0.492504i | \(-0.836082\pi\) | ||
0.870310 | − | 0.492504i | \(-0.163918\pi\) | |||||||
\(180\) | −7.61184e9 | − | 1.01491e10i | −0.0402835 | − | 0.0537113i | ||||
\(181\) | 1.33000e11 | 0.684636 | 0.342318 | − | 0.939584i | \(-0.388788\pi\) | ||||
0.342318 | + | 0.939584i | \(0.388788\pi\) | |||||||
\(182\) | 6.25812e10 | + | 6.25812e10i | 0.313391 | + | 0.313391i | ||||
\(183\) | −1.65832e11 | + | 1.65832e11i | −0.808003 | + | 0.808003i | ||||
\(184\) | − | 8.56599e10i | − | 0.406152i | ||||||
\(185\) | 3.52424e10 | − | 2.46697e11i | 0.162633 | − | 1.13843i | ||||
\(186\) | 5.89465e10 | 0.264785 | ||||||||
\(187\) | −3.25994e11 | − | 3.25994e11i | −1.42561 | − | 1.42561i | ||||
\(188\) | −8.82377e10 | + | 8.82377e10i | −0.375721 | + | 0.375721i | ||||
\(189\) | 1.57294e11i | 0.652235i | ||||||||
\(190\) | −7.71092e10 | − | 1.10156e10i | −0.311414 | − | 0.0444877i | ||||
\(191\) | 1.31044e11 | 0.515525 | 0.257762 | − | 0.966208i | \(-0.417015\pi\) | ||||
0.257762 | + | 0.966208i | \(0.417015\pi\) | |||||||
\(192\) | 2.45618e10 | + | 2.45618e10i | 0.0941358 | + | 0.0941358i | ||||
\(193\) | 2.12792e11 | − | 2.12792e11i | 0.794639 | − | 0.794639i | −0.187606 | − | 0.982244i | \(-0.560073\pi\) |
0.982244 | + | 0.187606i | \(0.0600727\pi\) | |||||||
\(194\) | − | 2.04916e10i | − | 0.0745704i | ||||||
\(195\) | −2.12850e11 | + | 1.59638e11i | −0.754920 | + | 0.566190i | ||||
\(196\) | 7.22534e10 | 0.249792 | ||||||||
\(197\) | 7.90246e10 | + | 7.90246e10i | 0.266337 | + | 0.266337i | 0.827622 | − | 0.561285i | \(-0.189693\pi\) |
−0.561285 | + | 0.827622i | \(0.689693\pi\) | |||||||
\(198\) | −2.19980e10 | + | 2.19980e10i | −0.0722864 | + | 0.0722864i | ||||
\(199\) | 4.52657e11i | 1.45045i | 0.688510 | + | 0.725227i | \(0.258265\pi\) | ||||
−0.688510 | + | 0.725227i | \(0.741735\pi\) | |||||||
\(200\) | −5.44000e10 | − | 9.92000e10i | −0.170000 | − | 0.310000i | ||||
\(201\) | 3.52119e11 | 1.07327 | ||||||||
\(202\) | 3.23895e10 | + | 3.23895e10i | 0.0963047 | + | 0.0963047i | ||||
\(203\) | −2.08417e11 | + | 2.08417e11i | −0.604578 | + | 0.604578i | ||||
\(204\) | − | 3.52303e11i | − | 0.997162i | ||||||
\(205\) | 2.86882e11 | + | 3.82509e11i | 0.792380 | + | 1.05651i | ||||
\(206\) | −4.80808e10 | −0.129609 | ||||||||
\(207\) | 4.14549e10 | + | 4.14549e10i | 0.109075 | + | 0.109075i | ||||
\(208\) | 6.09807e10 | − | 6.09807e10i | 0.156630 | − | 0.156630i | ||||
\(209\) | 1.91008e11i | 0.478984i | ||||||||
\(210\) | 3.07696e10 | − | 2.15387e11i | 0.0753400 | − | 0.527380i | ||||
\(211\) | 1.37995e11 | 0.329951 | 0.164976 | − | 0.986298i | \(-0.447245\pi\) | ||||
0.164976 | + | 0.986298i | \(0.447245\pi\) | |||||||
\(212\) | 1.00549e11 | + | 1.00549e11i | 0.234801 | + | 0.234801i | ||||
\(213\) | 5.71121e11 | − | 5.71121e11i | 1.30266 | − | 1.30266i | ||||
\(214\) | 4.53797e10i | 0.101110i | ||||||||
\(215\) | −2.59754e11 | − | 3.71078e10i | −0.565419 | − | 0.0807742i | ||||
\(216\) | 1.53272e11 | 0.325982 | ||||||||
\(217\) | 8.46248e10 | + | 8.46248e10i | 0.175873 | + | 0.175873i | ||||
\(218\) | 9.94074e10 | − | 9.94074e10i | 0.201900 | − | 0.201900i | ||||
\(219\) | − | 2.32900e11i | − | 0.462327i | ||||||
\(220\) | −2.21949e11 | + | 1.66462e11i | −0.430666 | + | 0.323000i | ||||
\(221\) | −8.74678e11 | −1.65915 | ||||||||
\(222\) | −3.30208e11 | − | 3.30208e11i | −0.612382 | − | 0.612382i | ||||
\(223\) | −1.26054e11 | + | 1.26054e11i | −0.228576 | + | 0.228576i | −0.812098 | − | 0.583521i | \(-0.801674\pi\) |
0.583521 | + | 0.812098i | \(0.301674\pi\) | |||||||
\(224\) | 7.05230e10i | 0.125052i | ||||||||
\(225\) | 7.43344e10 | + | 2.16809e10i | 0.128907 | + | 0.0375979i | ||||
\(226\) | −5.74435e11 | −0.974313 | ||||||||
\(227\) | 1.15268e11 | + | 1.15268e11i | 0.191241 | + | 0.191241i | 0.796232 | − | 0.604991i | \(-0.206823\pi\) |
−0.604991 | + | 0.796232i | \(0.706823\pi\) | |||||||
\(228\) | −1.03212e11 | + | 1.03212e11i | −0.167515 | + | 0.167515i | ||||
\(229\) | − | 3.29124e11i | − | 0.522615i | −0.965256 | − | 0.261308i | \(-0.915846\pi\) | ||
0.965256 | − | 0.261308i | \(-0.0841537\pi\) | |||||||
\(230\) | 3.13696e11 | + | 4.18261e11i | 0.487382 | + | 0.649843i | ||||
\(231\) | −5.33539e11 | −0.811160 | ||||||||
\(232\) | 2.03087e11 | + | 2.03087e11i | 0.302163 | + | 0.302163i | ||||
\(233\) | −9.97948e10 | + | 9.97948e10i | −0.145321 | + | 0.145321i | −0.776024 | − | 0.630703i | \(-0.782767\pi\) |
0.630703 | + | 0.776024i | \(0.282767\pi\) | |||||||
\(234\) | 5.90230e10i | 0.0841282i | ||||||||
\(235\) | 1.07712e11 | − | 7.53985e11i | 0.150288 | − | 1.05202i | ||||
\(236\) | −3.55363e11 | −0.485414 | ||||||||
\(237\) | 3.60143e11 | + | 3.60143e11i | 0.481652 | + | 0.481652i | ||||
\(238\) | 5.05774e11 | − | 5.05774e11i | 0.662326 | − | 0.662326i | ||||
\(239\) | − | 3.95622e10i | − | 0.0507331i | −0.999678 | − | 0.0253665i | \(-0.991925\pi\) | ||
0.999678 | − | 0.0253665i | \(-0.00807529\pi\) | |||||||
\(240\) | −2.09879e11 | − | 2.99827e10i | −0.263580 | − | 0.0376543i | ||||
\(241\) | −8.14271e11 | −1.00158 | −0.500788 | − | 0.865570i | \(-0.666956\pi\) | ||||
−0.500788 | + | 0.865570i | \(0.666956\pi\) | |||||||
\(242\) | 6.60711e10 | + | 6.60711e10i | 0.0796039 | + | 0.0796039i | ||||
\(243\) | −1.59856e11 | + | 1.59856e11i | −0.188668 | + | 0.188668i | ||||
\(244\) | 4.63967e11i | 0.536461i | ||||||||
\(245\) | −3.52800e11 | + | 2.64600e11i | −0.399667 | + | 0.299750i | ||||
\(246\) | 8.95989e11 | 0.994551 | ||||||||
\(247\) | 2.56248e11 | + | 2.56248e11i | 0.278725 | + | 0.278725i | ||||
\(248\) | 8.24607e10 | − | 8.24607e10i | 0.0878999 | − | 0.0878999i | ||||
\(249\) | − | 1.89728e12i | − | 1.98214i | ||||||
\(250\) | 6.28906e11 | + | 2.85156e11i | 0.644000 | + | 0.292000i | ||||
\(251\) | 4.53171e11 | 0.454877 | 0.227438 | − | 0.973793i | \(-0.426965\pi\) | ||||
0.227438 | + | 0.973793i | \(0.426965\pi\) | |||||||
\(252\) | −3.41295e10 | − | 3.41295e10i | −0.0335836 | − | 0.0335836i | ||||
\(253\) | 9.06570e11 | − | 9.06570e11i | 0.874579 | − | 0.874579i | ||||
\(254\) | 4.17987e11i | 0.395362i | ||||||||
\(255\) | 1.29017e12 | + | 1.72023e12i | 1.19659 | + | 1.59546i | ||||
\(256\) | 6.87195e10 | 0.0625000 | ||||||||
\(257\) | 1.33579e12 | + | 1.33579e12i | 1.19144 | + | 1.19144i | 0.976663 | + | 0.214777i | \(0.0689025\pi\) |
0.214777 | + | 0.976663i | \(0.431098\pi\) | |||||||
\(258\) | −3.47685e11 | + | 3.47685e11i | −0.304150 | + | 0.304150i | ||||
\(259\) | − | 9.48106e11i | − | 0.813501i | ||||||
\(260\) | −7.44394e10 | + | 5.21076e11i | −0.0626521 | + | 0.438565i | ||||
\(261\) | −1.96567e11 | −0.162296 | ||||||||
\(262\) | −8.32355e11 | − | 8.32355e11i | −0.674221 | − | 0.674221i | ||||
\(263\) | −9.12065e11 | + | 9.12065e11i | −0.724848 | + | 0.724848i | −0.969589 | − | 0.244740i | \(-0.921297\pi\) |
0.244740 | + | 0.969589i | \(0.421297\pi\) | |||||||
\(264\) | 5.19894e11i | 0.405411i | ||||||||
\(265\) | −8.59187e11 | − | 1.22741e11i | −0.657443 | − | 0.0939205i | ||||
\(266\) | −2.96346e11 | −0.222531 | ||||||||
\(267\) | −1.42216e12 | − | 1.42216e12i | −1.04808 | − | 1.04808i | ||||
\(268\) | 4.92582e11 | − | 4.92582e11i | 0.356291 | − | 0.356291i | ||||
\(269\) | 1.04348e12i | 0.740835i | 0.928865 | + | 0.370417i | \(0.120785\pi\) | ||||
−0.928865 | + | 0.370417i | \(0.879215\pi\) | |||||||
\(270\) | −7.48397e11 | + | 5.61298e11i | −0.521571 | + | 0.391178i | ||||
\(271\) | 7.19445e11 | 0.492211 | 0.246105 | − | 0.969243i | \(-0.420849\pi\) | ||||
0.246105 | + | 0.969243i | \(0.420849\pi\) | |||||||
\(272\) | −4.92839e11 | − | 4.92839e11i | −0.331025 | − | 0.331025i | ||||
\(273\) | −7.15772e11 | + | 7.15772e11i | −0.472021 | + | 0.472021i | ||||
\(274\) | − | 5.24206e11i | − | 0.339429i | ||||||
\(275\) | 4.74135e11 | − | 1.62561e12i | 0.301466 | − | 1.03360i | ||||
\(276\) | 9.79735e11 | 0.611735 | ||||||||
\(277\) | −8.62576e11 | − | 8.62576e11i | −0.528931 | − | 0.528931i | 0.391323 | − | 0.920253i | \(-0.372018\pi\) |
−0.920253 | + | 0.391323i | \(0.872018\pi\) | |||||||
\(278\) | 4.18383e11 | − | 4.18383e11i | 0.251971 | − | 0.251971i | ||||
\(279\) | 7.98133e10i | 0.0472122i | ||||||||
\(280\) | −2.58263e11 | − | 3.44351e11i | −0.150062 | − | 0.200083i | ||||
\(281\) | −7.89300e11 | −0.450516 | −0.225258 | − | 0.974299i | \(-0.572323\pi\) | ||||
−0.225258 | + | 0.974299i | \(0.572323\pi\) | |||||||
\(282\) | −1.00922e12 | − | 1.00922e12i | −0.565900 | − | 0.565900i | ||||
\(283\) | −6.60245e11 | + | 6.60245e11i | −0.363725 | + | 0.363725i | −0.865182 | − | 0.501457i | \(-0.832797\pi\) |
0.501457 | + | 0.865182i | \(0.332797\pi\) | |||||||
\(284\) | − | 1.59789e12i | − | 0.864878i | ||||||
\(285\) | 1.25991e11 | − | 8.81936e11i | 0.0670062 | − | 0.469043i | ||||
\(286\) | 1.29076e12 | 0.674554 | ||||||||
\(287\) | 1.28630e12 | + | 1.28630e12i | 0.660592 | + | 0.660592i | ||||
\(288\) | −3.32566e10 | + | 3.32566e10i | −0.0167848 | + | 0.0167848i | ||||
\(289\) | 5.05305e12i | 2.50648i | ||||||||
\(290\) | −1.73536e12 | − | 2.47908e11i | −0.846056 | − | 0.120865i | ||||
\(291\) | 2.34372e11 | 0.112316 | ||||||||
\(292\) | −3.25806e11 | − | 3.25806e11i | −0.153477 | − | 0.153477i | ||||
\(293\) | 1.79236e11 | − | 1.79236e11i | 0.0830019 | − | 0.0830019i | −0.664387 | − | 0.747389i | \(-0.731307\pi\) |
0.747389 | + | 0.664387i | \(0.231307\pi\) | |||||||
\(294\) | 8.26398e11i | 0.376229i | ||||||||
\(295\) | 1.73517e12 | − | 1.30138e12i | 0.776663 | − | 0.582497i | ||||
\(296\) | −9.23860e11 | −0.406581 | ||||||||
\(297\) | 1.62213e12 | + | 1.62213e12i | 0.701946 | + | 0.701946i | ||||
\(298\) | −6.90180e10 | + | 6.90180e10i | −0.0293685 | + | 0.0293685i | ||||
\(299\) | − | 2.43243e12i | − | 1.01785i | ||||||
\(300\) | 1.13460e12 | − | 6.22200e11i | 0.466914 | − | 0.256049i | ||||
\(301\) | −9.98288e11 | −0.404039 | ||||||||
\(302\) | 1.82189e12 | + | 1.82189e12i | 0.725251 | + | 0.725251i | ||||
\(303\) | −3.70455e11 | + | 3.70455e11i | −0.145051 | + | 0.145051i | ||||
\(304\) | 2.88767e11i | 0.111219i | ||||||||
\(305\) | −1.69910e12 | − | 2.26546e12i | −0.643753 | − | 0.858337i | ||||
\(306\) | 4.77017e11 | 0.177798 | ||||||||
\(307\) | −1.10155e12 | − | 1.10155e12i | −0.403937 | − | 0.403937i | 0.475681 | − | 0.879618i | \(-0.342202\pi\) |
−0.879618 | + | 0.475681i | \(0.842202\pi\) | |||||||
\(308\) | −7.46372e11 | + | 7.46372e11i | −0.269278 | + | 0.269278i | ||||
\(309\) | − | 5.49924e11i | − | 0.195214i | ||||||
\(310\) | −1.00660e11 | + | 7.04620e11i | −0.0351600 | + | 0.246120i | ||||
\(311\) | 5.31138e12 | 1.82560 | 0.912800 | − | 0.408406i | \(-0.133915\pi\) | ||||
0.912800 | + | 0.408406i | \(0.133915\pi\) | |||||||
\(312\) | 6.97467e11 | + | 6.97467e11i | 0.235912 | + | 0.235912i | ||||
\(313\) | −8.40078e11 | + | 8.40078e11i | −0.279639 | + | 0.279639i | −0.832965 | − | 0.553326i | \(-0.813358\pi\) |
0.553326 | + | 0.832965i | \(0.313358\pi\) | |||||||
\(314\) | 3.34169e11i | 0.109476i | ||||||||
\(315\) | 2.91634e11 | + | 4.16619e10i | 0.0940340 | + | 0.0134334i | ||||
\(316\) | 1.00761e12 | 0.319786 | ||||||||
\(317\) | −1.16635e12 | − | 1.16635e12i | −0.364361 | − | 0.364361i | 0.501055 | − | 0.865416i | \(-0.332946\pi\) |
−0.865416 | + | 0.501055i | \(0.832946\pi\) | |||||||
\(318\) | −1.15003e12 | + | 1.15003e12i | −0.353651 | + | 0.353651i | ||||
\(319\) | 4.29868e12i | 1.30131i | ||||||||
\(320\) | −3.35544e11 | + | 2.51658e11i | −0.100000 | + | 0.0750000i | ||||
\(321\) | −5.19031e11 | −0.152289 | ||||||||
\(322\) | 1.40653e12 | + | 1.40653e12i | 0.406321 | + | 0.406321i | ||||
\(323\) | 2.07097e12 | − | 2.07097e12i | 0.589062 | − | 0.589062i | ||||
\(324\) | 1.99276e12i | 0.558124i | ||||||||
\(325\) | −1.54476e12 | − | 2.81692e12i | −0.426035 | − | 0.776887i | ||||
\(326\) | 1.53058e12 | 0.415688 | ||||||||
\(327\) | 1.13697e12 | + | 1.13697e12i | 0.304096 | + | 0.304096i | ||||
\(328\) | 1.25341e12 | − | 1.25341e12i | 0.330158 | − | 0.330158i | ||||
\(329\) | − | 2.89771e12i | − | 0.751754i | ||||||
\(330\) | −1.90391e12 | − | 2.53855e12i | −0.486493 | − | 0.648658i | ||||
\(331\) | −4.82042e12 | −1.21324 | −0.606618 | − | 0.794994i | \(-0.707474\pi\) | ||||
−0.606618 | + | 0.794994i | \(0.707474\pi\) | |||||||
\(332\) | −2.65412e12 | − | 2.65412e12i | −0.658006 | − | 0.658006i | ||||
\(333\) | 4.47100e11 | − | 4.47100e11i | 0.109190 | − | 0.109190i | ||||
\(334\) | − | 3.78500e11i | − | 0.0910613i | ||||||
\(335\) | −6.01296e11 | + | 4.20907e12i | −0.142516 | + | 0.997614i | ||||
\(336\) | −8.06607e11 | −0.188350 | ||||||||
\(337\) | −3.68550e12 | − | 3.68550e12i | −0.847904 | − | 0.847904i | 0.141967 | − | 0.989871i | \(-0.454657\pi\) |
−0.989871 | + | 0.141967i | \(0.954657\pi\) | |||||||
\(338\) | −4.74105e11 | + | 4.74105e11i | −0.107471 | + | 0.107471i | ||||
\(339\) | − | 6.57010e12i | − | 1.46748i | ||||||
\(340\) | 4.21127e12 | + | 6.01611e11i | 0.926870 | + | 0.132410i | ||||
\(341\) | 1.74542e12 | 0.378555 | ||||||||
\(342\) | −1.39748e11 | − | 1.39748e11i | −0.0298687 | − | 0.0298687i | ||||
\(343\) | −3.56116e12 | + | 3.56116e12i | −0.750104 | + | 0.750104i | ||||
\(344\) | 9.72758e11i | 0.201936i | ||||||||
\(345\) | −4.78386e12 | + | 3.58790e12i | −0.978775 | + | 0.734082i | ||||
\(346\) | −3.72408e12 | −0.750997 | ||||||||
\(347\) | −5.38450e12 | − | 5.38450e12i | −1.07028 | − | 1.07028i | −0.997336 | − | 0.0729452i | \(-0.976760\pi\) |
−0.0729452 | − | 0.997336i | \(-0.523240\pi\) | |||||||
\(348\) | −2.32280e12 | + | 2.32280e12i | −0.455110 | + | 0.455110i | ||||
\(349\) | 8.12658e12i | 1.56957i | 0.619768 | + | 0.784785i | \(0.287227\pi\) | ||||
−0.619768 | + | 0.784785i | \(0.712773\pi\) | |||||||
\(350\) | 2.52210e12 | + | 7.35612e11i | 0.480200 | + | 0.140058i | ||||
\(351\) | 4.35236e12 | 0.816938 | ||||||||
\(352\) | 7.27284e11 | + | 7.27284e11i | 0.134583 | + | 0.134583i | ||||
\(353\) | 5.49274e12 | − | 5.49274e12i | 1.00211 | − | 1.00211i | 0.00211203 | − | 0.999998i | \(-0.499328\pi\) |
0.999998 | − | 0.00211203i | \(-0.000672280\pi\) | |||||||
\(354\) | − | 4.06447e12i | − | 0.731118i | ||||||
\(355\) | 5.85165e12 | + | 7.80219e12i | 1.03785 | + | 1.38381i | ||||
\(356\) | −3.97895e12 | −0.695854 | ||||||||
\(357\) | 5.78479e12 | + | 5.78479e12i | 0.997577 | + | 0.997577i | ||||
\(358\) | 2.89617e12 | − | 2.89617e12i | 0.492504 | − | 0.492504i | ||||
\(359\) | − | 5.91305e12i | − | 0.991606i | −0.868435 | − | 0.495803i | \(-0.834874\pi\) | ||
0.868435 | − | 0.495803i | \(-0.165126\pi\) | |||||||
\(360\) | 4.05965e10 | − | 2.84175e11i | 0.00671392 | − | 0.0469974i | ||||
\(361\) | 4.91763e12 | 0.802084 | ||||||||
\(362\) | 2.12801e12 | + | 2.12801e12i | 0.342318 | + | 0.342318i | ||||
\(363\) | −7.55688e11 | + | 7.55688e11i | −0.119897 | + | 0.119897i | ||||
\(364\) | 2.00260e12i | 0.313391i | ||||||||
\(365\) | 2.78398e12 | + | 3.97712e11i | 0.429737 | + | 0.0613910i | ||||
\(366\) | −5.30662e12 | −0.808003 | ||||||||
\(367\) | 1.75360e12 | + | 1.75360e12i | 0.263390 | + | 0.263390i | 0.826430 | − | 0.563040i | \(-0.190368\pi\) |
−0.563040 | + | 0.826430i | \(0.690368\pi\) | |||||||
\(368\) | 1.37056e12 | − | 1.37056e12i | 0.203076 | − | 0.203076i | ||||
\(369\) | 1.21317e12i | 0.177332i | ||||||||
\(370\) | 4.51103e12 | − | 3.38327e12i | 0.650530 | − | 0.487898i | ||||
\(371\) | −3.30203e12 | −0.469798 | ||||||||
\(372\) | 9.43144e11 | + | 9.43144e11i | 0.132392 | + | 0.132392i | ||||
\(373\) | 4.25717e12 | − | 4.25717e12i | 0.589627 | − | 0.589627i | −0.347904 | − | 0.937530i | \(-0.613106\pi\) |
0.937530 | + | 0.347904i | \(0.113106\pi\) | |||||||
\(374\) | − | 1.04318e13i | − | 1.42561i | ||||||
\(375\) | −3.26147e12 | + | 7.19312e12i | −0.439802 | + | 0.969975i | ||||
\(376\) | −2.82361e12 | −0.375721 | ||||||||
\(377\) | 5.76692e12 | + | 5.76692e12i | 0.757246 | + | 0.757246i | ||||
\(378\) | −2.51671e12 | + | 2.51671e12i | −0.326117 | + | 0.326117i | ||||
\(379\) | − | 7.20999e12i | − | 0.922016i | −0.887396 | − | 0.461008i | \(-0.847488\pi\) | ||
0.887396 | − | 0.461008i | \(-0.152512\pi\) | |||||||
\(380\) | −1.05750e12 | − | 1.41000e12i | −0.133463 | − | 0.177951i | ||||
\(381\) | −4.78073e12 | −0.595483 | ||||||||
\(382\) | 2.09670e12 | + | 2.09670e12i | 0.257762 | + | 0.257762i | ||||
\(383\) | −6.93832e12 | + | 6.93832e12i | −0.841900 | + | 0.841900i | −0.989106 | − | 0.147206i | \(-0.952972\pi\) |
0.147206 | + | 0.989106i | \(0.452972\pi\) | |||||||
\(384\) | 7.85979e11i | 0.0941358i | ||||||||
\(385\) | 9.11098e11 | − | 6.37769e12i | 0.107711 | − | 0.753980i | ||||
\(386\) | 6.80936e12 | 0.794639 | ||||||||
\(387\) | −4.70764e11 | − | 4.70764e11i | −0.0542311 | − | 0.0542311i | ||||
\(388\) | 3.27865e11 | − | 3.27865e11i | 0.0372852 | − | 0.0372852i | ||||
\(389\) | 1.12518e13i | 1.26320i | 0.775293 | + | 0.631601i | \(0.217602\pi\) | ||||
−0.775293 | + | 0.631601i | \(0.782398\pi\) | |||||||
\(390\) | −5.95980e12 | − | 8.51400e11i | −0.660555 | − | 0.0943649i | ||||
\(391\) | −1.96586e13 | −2.15114 | ||||||||
\(392\) | 1.15605e12 | + | 1.15605e12i | 0.124896 | + | 0.124896i | ||||
\(393\) | 9.52006e12 | − | 9.52006e12i | 1.01549 | − | 1.01549i | ||||
\(394\) | 2.52879e12i | 0.266337i | ||||||||
\(395\) | −4.91999e12 | + | 3.68999e12i | −0.511657 | + | 0.383743i | ||||
\(396\) | −7.03935e11 | −0.0722864 | ||||||||
\(397\) | −7.94628e12 | − | 7.94628e12i | −0.805770 | − | 0.805770i | 0.178221 | − | 0.983991i | \(-0.442966\pi\) |
−0.983991 | + | 0.178221i | \(0.942966\pi\) | |||||||
\(398\) | −7.24252e12 | + | 7.24252e12i | −0.725227 | + | 0.725227i | ||||
\(399\) | − | 3.38946e12i | − | 0.335171i | ||||||
\(400\) | 7.16800e11 | − | 2.45760e12i | 0.0700000 | − | 0.240000i | ||||
\(401\) | 8.81072e12 | 0.849747 | 0.424874 | − | 0.905253i | \(-0.360319\pi\) | ||||
0.424874 | + | 0.905253i | \(0.360319\pi\) | |||||||
\(402\) | 5.63391e12 | + | 5.63391e12i | 0.536635 | + | 0.536635i | ||||
\(403\) | 2.34158e12 | − | 2.34158e12i | 0.220285 | − | 0.220285i | ||||
\(404\) | 1.03646e12i | 0.0963047i | ||||||||
\(405\) | −7.29772e12 | − | 9.73029e12i | −0.669749 | − | 0.892998i | ||||
\(406\) | −6.66933e12 | −0.604578 | ||||||||
\(407\) | −9.77755e12 | − | 9.77755e12i | −0.875504 | − | 0.875504i | ||||
\(408\) | 5.63685e12 | − | 5.63685e12i | 0.498581 | − | 0.498581i | ||||
\(409\) | − | 1.00160e13i | − | 0.875141i | −0.899184 | − | 0.437571i | \(-0.855839\pi\) | ||
0.899184 | − | 0.437571i | \(-0.144161\pi\) | |||||||
\(410\) | −1.53004e12 | + | 1.07103e13i | −0.132063 | + | 0.924444i | ||||
\(411\) | 5.99561e12 | 0.511239 | ||||||||
\(412\) | −7.69293e11 | − | 7.69293e11i | −0.0648045 | − | 0.0648045i | ||||
\(413\) | 5.83504e12 | − | 5.83504e12i | 0.485616 | − | 0.485616i | ||||
\(414\) | 1.32656e12i | 0.109075i | ||||||||
\(415\) | 2.26792e13 | + | 3.23989e12i | 1.84242 | + | 0.263202i | ||||
\(416\) | 1.95138e12 | 0.156630 | ||||||||
\(417\) | 4.78526e12 | + | 4.78526e12i | 0.379512 | + | 0.379512i | ||||
\(418\) | −3.05613e12 | + | 3.05613e12i | −0.239492 | + | 0.239492i | ||||
\(419\) | 1.48244e13i | 1.14791i | 0.818888 | + | 0.573954i | \(0.194591\pi\) | ||||
−0.818888 | + | 0.573954i | \(0.805409\pi\) | |||||||
\(420\) | 3.93851e12 | − | 2.95388e12i | 0.301360 | − | 0.226020i | ||||
\(421\) | −4.68500e12 | −0.354241 | −0.177121 | − | 0.984189i | \(-0.556678\pi\) | ||||
−0.177121 | + | 0.984189i | \(0.556678\pi\) | |||||||
\(422\) | 2.20791e12 | + | 2.20791e12i | 0.164976 | + | 0.164976i | ||||
\(423\) | 1.36648e12 | − | 1.36648e12i | 0.100902 | − | 0.100902i | ||||
\(424\) | 3.21758e12i | 0.234801i | ||||||||
\(425\) | −2.27660e13 | + | 1.24846e13i | −1.64188 | + | 0.900388i | ||||
\(426\) | 1.82759e13 | 1.30266 | ||||||||
\(427\) | −7.61830e12 | − | 7.61830e12i | −0.536684 | − | 0.536684i | ||||
\(428\) | −7.26075e11 | + | 7.26075e11i | −0.0505549 | + | 0.0505549i | ||||
\(429\) | 1.47631e13i | 1.01599i | ||||||||
\(430\) | −3.56235e12 | − | 4.74980e12i | −0.242323 | − | 0.323097i | ||||
\(431\) | 2.39126e13 | 1.60783 | 0.803917 | − | 0.594741i | \(-0.202746\pi\) | ||||
0.803917 | + | 0.594741i | \(0.202746\pi\) | |||||||
\(432\) | 2.45235e12 | + | 2.45235e12i | 0.162991 | + | 0.162991i | ||||
\(433\) | −7.41823e11 | + | 7.41823e11i | −0.0487372 | + | 0.0487372i | −0.731055 | − | 0.682318i | \(-0.760972\pi\) |
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(434\) | 2.70800e12i | 0.175873i | ||||||||
\(435\) | 2.83545e12 | − | 1.98482e13i | 0.182044 | − | 1.27431i | ||||
\(436\) | 3.18104e12 | 0.201900 | ||||||||
\(437\) | 5.75925e12 | + | 5.75925e12i | 0.361375 | + | 0.361375i | ||||
\(438\) | 3.72640e12 | − | 3.72640e12i | 0.231163 | − | 0.231163i | ||||
\(439\) | 2.09704e13i | 1.28613i | 0.765811 | + | 0.643065i | \(0.222338\pi\) | ||||
−0.765811 | + | 0.643065i | \(0.777662\pi\) | |||||||
\(440\) | −6.21458e12 | − | 8.87798e11i | −0.376833 | − | 0.0538333i | ||||
\(441\) | −1.11894e12 | −0.0670832 | ||||||||
\(442\) | −1.39948e13 | − | 1.39948e13i | −0.829577 | − | 0.829577i | ||||
\(443\) | −2.38909e13 | + | 2.38909e13i | −1.40028 | + | 1.40028i | −0.601118 | + | 0.799160i | \(0.705278\pi\) |
−0.799160 | + | 0.601118i | \(0.794722\pi\) | |||||||
\(444\) | − | 1.05666e13i | − | 0.612382i | ||||||
\(445\) | 1.94285e13 | − | 1.45713e13i | 1.11337 | − | 0.835025i | ||||
\(446\) | −4.03372e12 | −0.228576 | ||||||||
\(447\) | −7.89394e11 | − | 7.89394e11i | −0.0442340 | − | 0.0442340i | ||||
\(448\) | −1.12837e12 | + | 1.12837e12i | −0.0625260 | + | 0.0625260i | ||||
\(449\) | − | 2.04535e13i | − | 1.12082i | −0.828215 | − | 0.560411i | \(-0.810643\pi\) | ||
0.828215 | − | 0.560411i | \(-0.189357\pi\) | |||||||
\(450\) | 8.42456e11 | + | 1.53624e12i | 0.0456546 | + | 0.0832526i | ||||
\(451\) | 2.65305e13 | 1.42188 | ||||||||
\(452\) | −9.19096e12 | − | 9.19096e12i | −0.487157 | − | 0.487157i | ||||
\(453\) | −2.08379e13 | + | 2.08379e13i | −1.09235 | + | 1.09235i | ||||
\(454\) | 3.68858e12i | 0.191241i | ||||||||
\(455\) | −7.33373e12 | − | 9.77831e12i | −0.376069 | − | 0.501426i | ||||
\(456\) | −3.30278e12 | −0.167515 | ||||||||
\(457\) | 6.88521e12 | + | 6.88521e12i | 0.345411 | + | 0.345411i | 0.858397 | − | 0.512986i | \(-0.171461\pi\) |
−0.512986 | + | 0.858397i | \(0.671461\pi\) | |||||||
\(458\) | 5.26598e12 | − | 5.26598e12i | 0.261308 | − | 0.261308i | ||||
\(459\) | − | 3.51753e13i | − | 1.72653i | ||||||
\(460\) | −1.67304e12 | + | 1.17113e13i | −0.0812303 | + | 0.568612i | ||||
\(461\) | −1.72039e13 | −0.826268 | −0.413134 | − | 0.910670i | \(-0.635566\pi\) | ||||
−0.413134 | + | 0.910670i | \(0.635566\pi\) | |||||||
\(462\) | −8.53662e12 | − | 8.53662e12i | −0.405580 | − | 0.405580i | ||||
\(463\) | −4.67192e11 | + | 4.67192e11i | −0.0219579 | + | 0.0219579i | −0.718000 | − | 0.696043i | \(-0.754942\pi\) |
0.696043 | + | 0.718000i | \(0.254942\pi\) | |||||||
\(464\) | 6.49877e12i | 0.302163i | ||||||||
\(465\) | −8.05909e12 | − | 1.15130e12i | −0.370699 | − | 0.0529570i | ||||
\(466\) | −3.19343e12 | −0.145321 | ||||||||
\(467\) | 1.62768e13 | + | 1.62768e13i | 0.732799 | + | 0.732799i | 0.971173 | − | 0.238374i | \(-0.0766146\pi\) |
−0.238374 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(468\) | −9.44367e11 | + | 9.44367e11i | −0.0420641 | + | 0.0420641i | ||||
\(469\) | 1.61763e13i | 0.712878i | ||||||||
\(470\) | 1.37871e13 | − | 1.03404e13i | 0.601153 | − | 0.450865i | ||||
\(471\) | −3.82206e12 | −0.164889 | ||||||||
\(472\) | −5.68581e12 | − | 5.68581e12i | −0.242707 | − | 0.242707i | ||||
\(473\) | −1.02951e13 | + | 1.02951e13i | −0.434834 | + | 0.434834i | ||||
\(474\) | 1.15246e13i | 0.481652i | ||||||||
\(475\) | 1.03271e13 | + | 3.01208e12i | 0.427082 | + | 0.124566i | ||||
\(476\) | 1.61848e13 | 0.662326 | ||||||||
\(477\) | −1.55714e12 | − | 1.55714e12i | −0.0630574 | − | 0.0630574i | ||||
\(478\) | 6.32996e11 | − | 6.32996e11i | 0.0253665 | − | 0.0253665i | ||||
\(479\) | − | 3.26759e13i | − | 1.29584i | −0.761710 | − | 0.647918i | \(-0.775640\pi\) | ||
0.761710 | − | 0.647918i | \(-0.224360\pi\) | |||||||
\(480\) | −2.87834e12 | − | 3.83779e12i | −0.112963 | − | 0.150617i | ||||
\(481\) | −2.62343e13 | −1.01893 | ||||||||
\(482\) | −1.30283e13 | − | 1.30283e13i | −0.500788 | − | 0.500788i | ||||
\(483\) | −1.60872e13 | + | 1.60872e13i | −0.611989 | + | 0.611989i | ||||
\(484\) | 2.11427e12i | 0.0796039i | ||||||||
\(485\) | −4.00226e11 | + | 2.80158e12i | −0.0149141 | + | 0.104399i | ||||
\(486\) | −5.11539e12 | −0.188668 | ||||||||
\(487\) | 3.91617e12 | + | 3.91617e12i | 0.142961 | + | 0.142961i | 0.774965 | − | 0.632004i | \(-0.217768\pi\) |
−0.632004 | + | 0.774965i | \(0.717768\pi\) | |||||||
\(488\) | −7.42347e12 | + | 7.42347e12i | −0.268230 | + | 0.268230i | ||||
\(489\) | 1.75060e13i | 0.626098i | ||||||||
\(490\) | −9.87840e12 | − | 1.41120e12i | −0.349708 | − | 0.0499583i | ||||
\(491\) | −1.66945e12 | −0.0585015 | −0.0292508 | − | 0.999572i | \(-0.509312\pi\) | ||||
−0.0292508 | + | 0.999572i | \(0.509312\pi\) | |||||||
\(492\) | 1.43358e13 | + | 1.43358e13i | 0.497276 | + | 0.497276i | ||||
\(493\) | 4.66076e13 | − | 4.66076e13i | 1.60038 | − | 1.60038i | ||||
\(494\) | 8.19994e12i | 0.278725i | ||||||||
\(495\) | 3.43718e12 | − | 2.57789e12i | 0.115658 | − | 0.0867437i | ||||
\(496\) | 2.63874e12 | 0.0878999 | ||||||||
\(497\) | 2.62372e13 | + | 2.62372e13i | 0.865239 | + | 0.865239i | ||||
\(498\) | 3.03565e13 | − | 3.03565e13i | 0.991070 | − | 0.991070i | ||||
\(499\) | 2.69113e13i | 0.869824i | 0.900473 | + | 0.434912i | \(0.143221\pi\) | ||||
−0.900473 | + | 0.434912i | \(0.856779\pi\) | |||||||
\(500\) | 5.50000e12 | + | 1.46250e13i | 0.176000 | + | 0.468000i | ||||
\(501\) | 4.32910e12 | 0.137154 | ||||||||
\(502\) | 7.25074e12 | + | 7.25074e12i | 0.227438 | + | 0.227438i | ||||
\(503\) | 2.35501e13 | − | 2.35501e13i | 0.731397 | − | 0.731397i | −0.239499 | − | 0.970897i | \(-0.576983\pi\) |
0.970897 | + | 0.239499i | \(0.0769833\pi\) | |||||||
\(504\) | − | 1.09214e12i | − | 0.0335836i | ||||||
\(505\) | −3.79564e12 | − | 5.06086e12i | −0.115566 | − | 0.154087i | ||||
\(506\) | 2.90103e13 | 0.874579 | ||||||||
\(507\) | −5.42258e12 | − | 5.42258e12i | −0.161870 | − | 0.161870i | ||||
\(508\) | −6.68780e12 | + | 6.68780e12i | −0.197681 | + | 0.197681i | ||||
\(509\) | − | 8.63621e12i | − | 0.252775i | −0.991981 | − | 0.126388i | \(-0.959662\pi\) | ||
0.991981 | − | 0.126388i | \(-0.0403383\pi\) | |||||||
\(510\) | −6.88092e12 | + | 4.81664e13i | −0.199432 | + | 1.39603i | ||||
\(511\) | 1.06994e13 | 0.307083 | ||||||||
\(512\) | 1.09951e12 | + | 1.09951e12i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −1.03050e13 | + | 1.03050e13i | −0.290044 | + | 0.290044i | ||||
\(514\) | 4.27452e13i | 1.19144i | ||||||||
\(515\) | 6.57355e12 | + | 9.39078e11i | 0.181453 | + | 0.0259218i | ||||
\(516\) | −1.11259e13 | −0.304150 | ||||||||
\(517\) | −2.98833e13 | − | 2.98833e13i | −0.809051 | − | 0.809051i | ||||
\(518\) | 1.51697e13 | − | 1.51697e13i | 0.406751 | − | 0.406751i | ||||
\(519\) | − | 4.25941e13i | − | 1.13113i | ||||||
\(520\) | −9.52824e12 | + | 7.14618e12i | −0.250609 | + | 0.187956i | ||||
\(521\) | −6.27326e13 | −1.63420 | −0.817099 | − | 0.576497i | \(-0.804419\pi\) | ||||
−0.817099 | + | 0.576497i | \(0.804419\pi\) | |||||||
\(522\) | −3.14507e12 | − | 3.14507e12i | −0.0811479 | − | 0.0811479i | ||||
\(523\) | 1.48951e12 | − | 1.48951e12i | 0.0380659 | − | 0.0380659i | −0.687818 | − | 0.725884i | \(-0.741431\pi\) |
0.725884 | + | 0.687818i | \(0.241431\pi\) | |||||||
\(524\) | − | 2.66354e13i | − | 0.674221i | ||||||
\(525\) | −8.41357e12 | + | 2.88465e13i | −0.210952 | + | 0.723264i | ||||
\(526\) | −2.91861e13 | −0.724848 | ||||||||
\(527\) | −1.89244e13 | − | 1.89244e13i | −0.465553 | − | 0.465553i | ||||
\(528\) | −8.31831e12 | + | 8.31831e12i | −0.202705 | + | 0.202705i | ||||
\(529\) | − | 1.32430e13i | − | 0.319673i | ||||||
\(530\) | −1.17831e13 | − | 1.57108e13i | −0.281761 | − | 0.375682i | ||||
\(531\) | 5.50327e12 | 0.130361 | ||||||||
\(532\) | −4.74154e12 | − | 4.74154e12i | −0.111266 | − | 0.111266i | ||||
\(533\) | 3.55922e13 | − | 3.55922e13i | 0.827405 | − | 0.827405i | ||||
\(534\) | − | 4.55092e13i | − | 1.04808i | ||||||
\(535\) | 8.86323e11 | − | 6.20426e12i | 0.0202219 | − | 0.141554i | ||||
\(536\) | 1.57626e13 | 0.356291 | ||||||||
\(537\) | 3.31250e13 | + | 3.31250e13i | 0.741796 | + | 0.741796i | ||||
\(538\) | −1.66956e13 | + | 1.66956e13i | −0.370417 | + | 0.370417i | ||||
\(539\) | 2.44699e13i | 0.537884i | ||||||||
\(540\) | −2.09551e13 | − | 2.99359e12i | −0.456374 | − | 0.0651963i | ||||
\(541\) | −8.97115e13 | −1.93581 | −0.967903 | − | 0.251324i | \(-0.919134\pi\) | ||||
−0.967903 | + | 0.251324i | \(0.919134\pi\) | |||||||
\(542\) | 1.15111e13 | + | 1.15111e13i | 0.246105 | + | 0.246105i | ||||
\(543\) | −2.43391e13 | + | 2.43391e13i | −0.515590 | + | 0.515590i | ||||
\(544\) | − | 1.57709e13i | − | 0.331025i | ||||||
\(545\) | −1.55324e13 | + | 1.16493e13i | −0.323040 | + | 0.242280i | ||||
\(546\) | −2.29047e13 | −0.472021 | ||||||||
\(547\) | 3.39955e13 | + | 3.39955e13i | 0.694200 | + | 0.694200i | 0.963153 | − | 0.268953i | \(-0.0866777\pi\) |
−0.268953 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(548\) | 8.38730e12 | − | 8.38730e12i | 0.169715 | − | 0.169715i | ||||
\(549\) | − | 7.18515e12i | − | 0.144070i | ||||||
\(550\) | 3.35959e13 | − | 1.84235e13i | 0.667532 | − | 0.366066i | ||||
\(551\) | −2.73086e13 | −0.537702 | ||||||||
\(552\) | 1.56758e13 | + | 1.56758e13i | 0.305867 | + | 0.305867i | ||||
\(553\) | −1.65449e13 | + | 1.65449e13i | −0.319919 | + | 0.319919i | ||||
\(554\) | − | 2.76024e13i | − | 0.528931i | ||||||
\(555\) | 3.86962e13 | + | 5.15949e13i | 0.734858 | + | 0.979811i | ||||
\(556\) | 1.33883e13 | 0.251971 | ||||||||
\(557\) | 9.51915e12 | + | 9.51915e12i | 0.177551 | + | 0.177551i | 0.790287 | − | 0.612737i | \(-0.209931\pi\) |
−0.612737 | + | 0.790287i | \(0.709931\pi\) | |||||||
\(558\) | −1.27701e12 | + | 1.27701e12i | −0.0236061 | + | 0.0236061i | ||||
\(559\) | 2.76228e13i | 0.506068i | ||||||||
\(560\) | 1.37740e12 | − | 9.64182e12i | 0.0250104 | − | 0.175073i | ||||
\(561\) | 1.19314e14 | 2.14722 | ||||||||
\(562\) | −1.26288e13 | − | 1.26288e13i | −0.225258 | − | 0.225258i | ||||
\(563\) | 3.63651e13 | − | 3.63651e13i | 0.642900 | − | 0.642900i | −0.308367 | − | 0.951267i | \(-0.599783\pi\) |
0.951267 | + | 0.308367i | \(0.0997826\pi\) | |||||||
\(564\) | − | 3.22950e13i | − | 0.565900i | ||||||
\(565\) | 7.85360e13 | + | 1.12194e13i | 1.36404 | + | 0.194863i | ||||
\(566\) | −2.11278e13 | −0.363725 | ||||||||
\(567\) | −3.27210e13 | − | 3.27210e13i | −0.558356 | − | 0.558356i | ||||
\(568\) | 2.55662e13 | − | 2.55662e13i | 0.432439 | − | 0.432439i | ||||
\(569\) | − | 2.82859e13i | − | 0.474252i | −0.971479 | − | 0.237126i | \(-0.923795\pi\) | ||
0.971479 | − | 0.237126i | \(-0.0762054\pi\) | |||||||
\(570\) | 1.61268e13 | − | 1.20951e13i | 0.268025 | − | 0.201019i | ||||
\(571\) | 2.19201e12 | 0.0361129 | 0.0180564 | − | 0.999837i | \(-0.494252\pi\) | ||||
0.0180564 | + | 0.999837i | \(0.494252\pi\) | |||||||
\(572\) | 2.06522e13 | + | 2.06522e13i | 0.337277 | + | 0.337277i | ||||
\(573\) | −2.39810e13 | + | 2.39810e13i | −0.388235 | + | 0.388235i | ||||
\(574\) | 4.11616e13i | 0.660592i | ||||||||
\(575\) | −3.47189e13 | − | 6.33110e13i | −0.552366 | − | 1.00726i | ||||
\(576\) | −1.06421e12 | −0.0167848 | ||||||||
\(577\) | −2.97579e13 | − | 2.97579e13i | −0.465289 | − | 0.465289i | 0.435095 | − | 0.900384i | \(-0.356715\pi\) |
−0.900384 | + | 0.435095i | \(0.856715\pi\) | |||||||
\(578\) | −8.08489e13 | + | 8.08489e13i | −1.25324 | + | 1.25324i | ||||
\(579\) | 7.78821e13i | 1.19686i | ||||||||
\(580\) | −2.37992e13 | − | 3.17323e13i | −0.362596 | − | 0.483461i | ||||
\(581\) | 8.71608e13 | 1.31656 | ||||||||
\(582\) | 3.74996e12 | + | 3.74996e12i | 0.0561579 | + | 0.0561579i | ||||
\(583\) | −3.40529e13 | + | 3.40529e13i | −0.505605 | + | 0.505605i | ||||
\(584\) | − | 1.04258e13i | − | 0.153477i | ||||||
\(585\) | 1.15279e12 | − | 8.06955e12i | 0.0168256 | − | 0.117780i | ||||
\(586\) | 5.73556e12 | 0.0830019 | ||||||||
\(587\) | 4.60333e13 | + | 4.60333e13i | 0.660513 | + | 0.660513i | 0.955501 | − | 0.294988i | \(-0.0953157\pi\) |
−0.294988 | + | 0.955501i | \(0.595316\pi\) | |||||||
\(588\) | −1.32224e13 | + | 1.32224e13i | −0.188115 | + | 0.188115i | ||||
\(589\) | 1.10883e13i | 0.156419i | ||||||||
\(590\) | 4.85848e13 | + | 6.94069e12i | 0.679580 | + | 0.0970829i | ||||
\(591\) | −2.89230e13 | −0.401149 | ||||||||
\(592\) | −1.47818e13 | − | 1.47818e13i | −0.203291 | − | 0.203291i | ||||
\(593\) | −6.17714e12 | + | 6.17714e12i | −0.0842391 | + | 0.0842391i | −0.747971 | − | 0.663732i | \(-0.768972\pi\) |
0.663732 | + | 0.747971i | \(0.268972\pi\) | |||||||
\(594\) | 5.19082e13i | 0.701946i | ||||||||
\(595\) | −7.90272e13 | + | 5.92704e13i | −1.05972 | + | 0.794791i | ||||
\(596\) | −2.20858e12 | −0.0293685 | ||||||||
\(597\) | −8.28363e13 | − | 8.28363e13i | −1.09232 | − | 1.09232i | ||||
\(598\) | 3.89189e13 | − | 3.89189e13i | 0.508925 | − | 0.508925i | ||||
\(599\) | − | 5.80310e13i | − | 0.752534i | −0.926511 | − | 0.376267i | \(-0.877208\pi\) | ||
0.926511 | − | 0.376267i | \(-0.122792\pi\) | |||||||
\(600\) | 2.81088e13 | + | 8.19840e12i | 0.361481 | + | 0.105432i | ||||
\(601\) | 1.24750e14 | 1.59100 | 0.795499 | − | 0.605955i | \(-0.207209\pi\) | ||||
0.795499 | + | 0.605955i | \(0.207209\pi\) | |||||||
\(602\) | −1.59726e13 | − | 1.59726e13i | −0.202020 | − | 0.202020i | ||||
\(603\) | −7.62828e12 | + | 7.62828e12i | −0.0956842 | + | 0.0956842i | ||||
\(604\) | 5.83006e13i | 0.725251i | ||||||||
\(605\) | −7.74270e12 | − | 1.03236e13i | −0.0955247 | − | 0.127366i | ||||
\(606\) | −1.18546e13 | −0.145051 | ||||||||
\(607\) | −9.34184e13 | − | 9.34184e13i | −1.13368 | − | 1.13368i | −0.989561 | − | 0.144115i | \(-0.953967\pi\) |
−0.144115 | − | 0.989561i | \(-0.546033\pi\) | |||||||
\(608\) | −4.62028e12 | + | 4.62028e12i | −0.0556097 | + | 0.0556097i | ||||
\(609\) | − | 7.62805e13i | − | 0.910598i | ||||||
\(610\) | 9.06186e12 | − | 6.34330e13i | 0.107292 | − | 0.751045i | ||||
\(611\) | −8.01802e13 | −0.941588 | ||||||||
\(612\) | 7.63227e12 | + | 7.63227e12i | 0.0888990 | + | 0.0888990i | ||||
\(613\) | 1.42802e13 | − | 1.42802e13i | 0.164980 | − | 0.164980i | −0.619789 | − | 0.784769i | \(-0.712782\pi\) |
0.784769 | + | 0.619789i | \(0.212782\pi\) | |||||||
\(614\) | − | 3.52497e13i | − | 0.403937i | ||||||
\(615\) | −1.22499e14 | − | 1.74998e13i | −1.39237 | − | 0.198910i | ||||
\(616\) | −2.38839e13 | −0.269278 | ||||||||
\(617\) | −4.17740e12 | − | 4.17740e12i | −0.0467176 | − | 0.0467176i | 0.683362 | − | 0.730080i | \(-0.260517\pi\) |
−0.730080 | + | 0.683362i | \(0.760517\pi\) | |||||||
\(618\) | 8.79878e12 | − | 8.79878e12i | 0.0976068 | − | 0.0976068i | ||||
\(619\) | 4.07977e13i | 0.448934i | 0.974482 | + | 0.224467i | \(0.0720642\pi\) | ||||
−0.974482 | + | 0.224467i | \(0.927936\pi\) | |||||||
\(620\) | −1.28845e13 | + | 9.66336e12i | −0.140640 | + | 0.105480i | ||||
\(621\) | 9.78204e13 | 1.05918 | ||||||||
\(622\) | 8.49822e13 | + | 8.49822e13i | 0.912800 | + | 0.912800i | ||||
\(623\) | 6.53340e13 | − | 6.53340e13i | 0.696144 | − | 0.696144i | ||||
\(624\) | 2.23189e13i | 0.235912i | ||||||||
\(625\) | −8.04138e13 | − | 5.12695e13i | −0.843200 | − | 0.537600i | ||||
\(626\) | −2.68825e13 | −0.279639 | ||||||||
\(627\) | −3.49545e13 | − | 3.49545e13i | −0.360716 | − | 0.360716i | ||||
\(628\) | −5.34670e12 | + | 5.34670e12i | −0.0547379 | + | 0.0547379i | ||||
\(629\) | 2.12022e14i | 2.15342i | ||||||||
\(630\) | 3.99955e12 | + | 5.33273e12i | 0.0403003 | + | 0.0537337i | ||||
\(631\) | 8.03556e13 | 0.803284 | 0.401642 | − | 0.915797i | \(-0.368440\pi\) | ||||
0.401642 | + | 0.915797i | \(0.368440\pi\) | |||||||
\(632\) | 1.61218e13 | + | 1.61218e13i | 0.159893 | + | 0.159893i | ||||
\(633\) | −2.52530e13 | + | 2.52530e13i | −0.248482 | + | 0.248482i | ||||
\(634\) | − | 3.73231e13i | − | 0.364361i | ||||||
\(635\) | 8.16382e12 | − | 5.71467e13i | 0.0790723 | − | 0.553506i | ||||
\(636\) | −3.68011e13 | −0.353651 | ||||||||
\(637\) | 3.28277e13 | + | 3.28277e13i | 0.313000 | + | 0.313000i | ||||
\(638\) | −6.87789e13 | + | 6.87789e13i | −0.650657 | + | 0.650657i | ||||
\(639\) | 2.47454e13i | 0.232269i | ||||||||
\(640\) | −9.39524e12 | − | 1.34218e12i | −0.0875000 | − | 0.0125000i | ||||
\(641\) | 9.43477e13 | 0.871849 | 0.435924 | − | 0.899983i | \(-0.356421\pi\) | ||||
0.435924 | + | 0.899983i | \(0.356421\pi\) | |||||||
\(642\) | −8.30449e12 | − | 8.30449e12i | −0.0761444 | − | 0.0761444i | ||||
\(643\) | 1.98925e13 | − | 1.98925e13i | 0.180981 | − | 0.180981i | −0.610802 | − | 0.791783i | \(-0.709153\pi\) |
0.791783 | + | 0.610802i | \(0.209153\pi\) | |||||||
\(644\) | 4.50089e13i | 0.406321i | ||||||||
\(645\) | 5.43258e13 | − | 4.07443e13i | 0.486640 | − | 0.364980i | ||||
\(646\) | 6.62710e13 | 0.589062 | ||||||||
\(647\) | 5.97289e13 | + | 5.97289e13i | 0.526821 | + | 0.526821i | 0.919623 | − | 0.392802i | \(-0.128494\pi\) |
−0.392802 | + | 0.919623i | \(0.628494\pi\) | |||||||
\(648\) | −3.18842e13 | + | 3.18842e13i | −0.279062 | + | 0.279062i | ||||
\(649\) | − | 1.20350e14i | − | 1.04526i | ||||||
\(650\) | 2.03545e13 | − | 6.97869e13i | 0.175426 | − | 0.601461i | ||||
\(651\) | −3.09727e13 | −0.264895 | ||||||||
\(652\) | 2.44892e13 | + | 2.44892e13i | 0.207844 | + | 0.207844i | ||||
\(653\) | −9.87072e13 | + | 9.87072e13i | −0.831349 | + | 0.831349i | −0.987701 | − | 0.156353i | \(-0.950026\pi\) |
0.156353 | + | 0.987701i | \(0.450026\pi\) | |||||||
\(654\) | 3.63831e13i | 0.304096i | ||||||||
\(655\) | 9.75416e13 | + | 1.30055e14i | 0.809065 | + | 1.07875i | ||||
\(656\) | 4.01090e13 | 0.330158 | ||||||||
\(657\) | 5.04553e12 | + | 5.04553e12i | 0.0412174 | + | 0.0412174i | ||||
\(658\) | 4.63634e13 | − | 4.63634e13i | 0.375877 | − | 0.375877i | ||||
\(659\) | 5.80689e13i | 0.467215i | 0.972331 | + | 0.233607i | \(0.0750530\pi\) | ||||
−0.972331 | + | 0.233607i | \(0.924947\pi\) | |||||||
\(660\) | 1.01542e13 | − | 7.10793e13i | 0.0810822 | − | 0.567575i | ||||
\(661\) | −1.53137e14 | −1.21360 | −0.606798 | − | 0.794856i | \(-0.707546\pi\) | ||||
−0.606798 | + | 0.794856i | \(0.707546\pi\) | |||||||
\(662\) | −7.71268e13 | − | 7.71268e13i | −0.606618 | − | 0.606618i | ||||
\(663\) | 1.60066e14 | − | 1.60066e14i | 1.24949 | − | 1.24949i | ||||
\(664\) | − | 8.49317e13i | − | 0.658006i | ||||||
\(665\) | 4.05161e13 | + | 5.78801e12i | 0.311544 | + | 0.0445062i | ||||
\(666\) | 1.43072e13 | 0.109190 | ||||||||
\(667\) | 1.29613e14 | + | 1.29613e14i | 0.981792 | + | 0.981792i | ||||
\(668\) | 6.05600e12 | − | 6.05600e12i | 0.0455306 | − | 0.0455306i | ||||
\(669\) | − | 4.61357e13i | − | 0.344275i | ||||||
\(670\) | −7.69659e13 | + | 5.77244e13i | −0.570065 | + | 0.427549i | ||||
\(671\) | −1.57131e14 | −1.15518 | ||||||||
\(672\) | −1.29057e13 | − | 1.29057e13i | −0.0941750 | − | 0.0941750i | ||||
\(673\) | −8.75360e13 | + | 8.75360e13i | −0.634032 | + | 0.634032i | −0.949077 | − | 0.315045i | \(-0.897980\pi\) |
0.315045 | + | 0.949077i | \(0.397980\pi\) | |||||||
\(674\) | − | 1.17936e14i | − | 0.847904i | ||||||
\(675\) | 1.13283e14 | − | 6.21228e13i | 0.808434 | − | 0.443335i | ||||
\(676\) | −1.51714e13 | −0.107471 | ||||||||
\(677\) | 1.59452e12 | + | 1.59452e12i | 0.0112121 | + | 0.0112121i | 0.712691 | − | 0.701478i | \(-0.247476\pi\) |
−0.701478 | + | 0.712691i | \(0.747476\pi\) | |||||||
\(678\) | 1.05122e14 | − | 1.05122e14i | 0.733742 | − | 0.733742i | ||||
\(679\) | 1.07670e13i | 0.0746014i | ||||||||
\(680\) | 5.77546e13 | + | 7.70062e13i | 0.397230 | + | 0.529640i | ||||
\(681\) | −4.21882e13 | −0.288042 | ||||||||
\(682\) | 2.79268e13 | + | 2.79268e13i | 0.189278 | + | 0.189278i | ||||
\(683\) | −5.65796e13 | + | 5.65796e13i | −0.380677 | + | 0.380677i | −0.871346 | − | 0.490669i | \(-0.836752\pi\) |
0.490669 | + | 0.871346i | \(0.336752\pi\) | |||||||
\(684\) | − | 4.47195e12i | − | 0.0298687i | ||||||
\(685\) | −1.02384e13 | + | 7.16689e13i | −0.0678859 | + | 0.475201i | ||||
\(686\) | −1.13957e14 | −0.750104 | ||||||||
\(687\) | 6.02297e13 | + | 6.02297e13i | 0.393575 | + | 0.393575i | ||||
\(688\) | −1.55641e13 | + | 1.55641e13i | −0.100968 | + | 0.100968i | ||||
\(689\) | 9.13676e13i | 0.588432i | ||||||||
\(690\) | −1.33948e14 | − | 1.91354e13i | −0.856428 | − | 0.122347i | ||||
\(691\) | 4.98558e12 | 0.0316465 | 0.0158232 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158232 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(692\) | −5.95852e13 | − | 5.95852e13i | −0.375498 | − | 0.375498i | ||||
\(693\) | 1.15586e13 | − | 1.15586e13i | 0.0723165 | − | 0.0723165i | ||||
\(694\) | − | 1.72304e14i | − | 1.07028i | ||||||
\(695\) | −6.53724e13 | + | 4.90293e13i | −0.403153 | + | 0.302365i | ||||
\(696\) | −7.43297e13 | −0.455110 | ||||||||
\(697\) | −2.87652e14 | − | 2.87652e14i | −1.74865 | − | 1.74865i | ||||
\(698\) | −1.30025e14 | + | 1.30025e14i | −0.784785 | + | 0.784785i | ||||
\(699\) | − | 3.65249e13i | − | 0.218879i | ||||||
\(700\) | 2.85838e13 | + | 5.21234e13i | 0.170071 | + | 0.310129i | ||||
\(701\) | −1.80303e14 | −1.06516 | −0.532578 | − | 0.846381i | \(-0.678777\pi\) | ||||
−0.532578 | + | 0.846381i | \(0.678777\pi\) | |||||||
\(702\) | 6.96377e13 | + | 6.96377e13i | 0.408469 | + | 0.408469i | ||||
\(703\) | 6.21147e13 | − | 6.21147e13i | 0.361758 | − | 0.361758i | ||||
\(704\) | 2.32731e13i | 0.134583i | ||||||||
\(705\) | 1.18268e14 | + | 1.57691e14i | 0.679080 | + | 0.905441i | ||||
\(706\) | 1.75768e14 | 1.00211 | ||||||||
\(707\) | −1.70187e13 | − | 1.70187e13i | −0.0963448 | − | 0.0963448i | ||||
\(708\) | 6.50315e13 | − | 6.50315e13i | 0.365559 | − | 0.365559i | ||||
\(709\) | − | 3.11543e14i | − | 1.73895i | −0.493979 | − | 0.869474i | \(-0.664458\pi\) | ||
0.493979 | − | 0.869474i | \(-0.335542\pi\) | |||||||
\(710\) | −3.12088e13 | + | 2.18461e14i | −0.172976 | + | 1.21083i | ||||
\(711\) | −1.56042e13 | −0.0858805 | ||||||||
\(712\) | −6.36632e13 | − | 6.36632e13i | −0.347927 | − | 0.347927i | ||||
\(713\) | 5.26277e13 | − | 5.26277e13i | 0.285606 | − | 0.285606i | ||||
\(714\) | 1.85113e14i | 0.997577i | ||||||||
\(715\) | −1.76472e14 | − | 2.52102e13i | −0.944375 | − | 0.134911i | ||||
\(716\) | 9.26776e13 | 0.492504 | ||||||||
\(717\) | 7.23989e12 | + | 7.23989e12i | 0.0382064 | + | 0.0382064i | ||||
\(718\) | 9.46087e13 | − | 9.46087e13i | 0.495803 | − | 0.495803i | ||||
\(719\) | − | 1.65068e14i | − | 0.859051i | −0.903055 | − | 0.429525i | \(-0.858681\pi\) | ||
0.903055 | − | 0.429525i | \(-0.141319\pi\) | |||||||
\(720\) | 5.19635e12 | − | 3.89726e12i | 0.0268557 | − | 0.0201417i | ||||
\(721\) | 2.52634e13 | 0.129663 | ||||||||
\(722\) | 7.86821e13 | + | 7.86821e13i | 0.401042 | + | 0.401042i | ||||
\(723\) | 1.49012e14 | − | 1.49012e14i | 0.754273 | − | 0.754273i | ||||
\(724\) | 6.80962e13i | 0.342318i | ||||||||
\(725\) | 2.32414e14 | + | 6.77875e13i | 1.16031 | + | 0.338423i | ||||
\(726\) | −2.41820e13 | −0.119897 | ||||||||
\(727\) | 2.15314e14 | + | 2.15314e14i | 1.06023 | + | 1.06023i | 0.998066 | + | 0.0621642i | \(0.0198002\pi\) |
0.0621642 | + | 0.998066i | \(0.480200\pi\) | |||||||
\(728\) | −3.20416e13 | + | 3.20416e13i | −0.156696 | + | 0.156696i | ||||
\(729\) | 1.71318e14i | 0.832081i | ||||||||
\(730\) | 3.81804e13 | + | 5.09071e13i | 0.184173 | + | 0.245564i | ||||
\(731\) | 2.23244e14 | 1.06953 | ||||||||
\(732\) | −8.49060e13 | − | 8.49060e13i | −0.404001 | − | 0.404001i | ||||
\(733\) | −2.78787e14 | + | 2.78787e14i | −1.31750 | + | 1.31750i | −0.401759 | + | 0.915746i | \(0.631601\pi\) |
−0.915746 | + | 0.401759i | \(0.868399\pi\) | |||||||
\(734\) | 5.61152e13i | 0.263390i | ||||||||
\(735\) | 1.61406e13 | − | 1.12984e14i | 0.0752459 | − | 0.526721i | ||||
\(736\) | 4.38578e13 | 0.203076 | ||||||||
\(737\) | 1.66822e14 | + | 1.66822e14i | 0.767212 | + | 0.767212i | ||||
\(738\) | −1.94106e13 | + | 1.94106e13i | −0.0886662 | + | 0.0886662i | ||||
\(739\) | − | 2.05171e14i | − | 0.930879i | −0.885080 | − | 0.465440i | \(-0.845896\pi\) | ||
0.885080 | − | 0.465440i | \(-0.154104\pi\) | |||||||
\(740\) | 1.26309e14 | + | 1.80441e13i | 0.569214 | + | 0.0813163i | ||||
\(741\) | −9.37868e13 | −0.419808 | ||||||||
\(742\) | −5.28324e13 | − | 5.28324e13i | −0.234899 | − | 0.234899i | ||||
\(743\) | 1.59047e14 | − | 1.59047e14i | 0.702396 | − | 0.702396i | −0.262528 | − | 0.964924i | \(-0.584556\pi\) |
0.964924 | + | 0.262528i | \(0.0845563\pi\) | |||||||
\(744\) | 3.01806e13i | 0.132392i | ||||||||
\(745\) | 1.07841e13 | − | 8.08805e12i | 0.0469895 | − | 0.0352422i | ||||
\(746\) | 1.36230e14 | 0.589627 | ||||||||
\(747\) | 4.11025e13 | + | 4.11025e13i | 0.176712 | + | 0.176712i | ||||
\(748\) | 1.66909e14 | − | 1.66909e14i | 0.712806 | − | 0.712806i | ||||
\(749\) | − | 2.38442e13i | − | 0.101152i | ||||||
\(750\) | −1.67273e14 | + | 6.29063e13i | −0.704889 | + | 0.265086i | ||||
\(751\) | −1.40008e14 | −0.586074 | −0.293037 | − | 0.956101i | \(-0.594666\pi\) | ||||
−0.293037 | + | 0.956101i | \(0.594666\pi\) | |||||||
\(752\) | −4.51777e13 | − | 4.51777e13i | −0.187860 | − | 0.187860i | ||||
\(753\) | −8.29303e13 | + | 8.29303e13i | −0.342561 | + | 0.342561i | ||||
\(754\) | 1.84541e14i | 0.757246i | ||||||||
\(755\) | −2.13503e14 | − | 2.84671e14i | −0.870302 | − | 1.16040i | ||||
\(756\) | −8.05347e13 | −0.326117 | ||||||||
\(757\) | 7.07881e13 | + | 7.07881e13i | 0.284761 | + | 0.284761i | 0.835004 | − | 0.550243i | \(-0.185465\pi\) |
−0.550243 | + | 0.835004i | \(0.685465\pi\) | |||||||
\(758\) | 1.15360e14 | − | 1.15360e14i | 0.461008 |