Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(0.500000 + 9.26410e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.2 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −521279. | − | 56087.1i | −0.994261 | − | 0.106978i | ||||
\(3\) | − | 1.48226e9i | − | 1.27532i | −0.770318 | − | 0.637660i | \(-0.779902\pi\) | ||
0.770318 | − | 0.637660i | \(-0.220098\pi\) | |||||||
\(4\) | 2.68586e11 | + | 5.84741e10i | 0.977112 | + | 0.212728i | ||||
\(5\) | 1.90217e13 | 0.997286 | 0.498643 | − | 0.866807i | \(-0.333832\pi\) | ||||
0.498643 | + | 0.866807i | \(0.333832\pi\) | |||||||
\(6\) | −8.31355e13 | + | 7.72670e14i | −0.136431 | + | 1.26800i | ||||
\(7\) | 1.45250e16i | 1.27424i | 0.770764 | + | 0.637121i | \(0.219875\pi\) | ||||
−0.770764 | + | 0.637121i | \(0.780125\pi\) | |||||||
\(8\) | −1.36729e17 | − | 4.55456e16i | −0.948747 | − | 0.316036i | ||||
\(9\) | −8.46232e17 | −0.626443 | ||||||||
\(10\) | −9.91563e18 | − | 1.06687e18i | −0.991563 | − | 0.106687i | ||||
\(11\) | 3.87139e19i | 0.633003i | 0.948592 | + | 0.316501i | \(0.102508\pi\) | ||||
−0.948592 | + | 0.316501i | \(0.897492\pi\) | |||||||
\(12\) | 8.66736e19 | − | 3.98114e20i | 0.271296 | − | 1.24613i | ||||
\(13\) | −8.59840e20 | −0.588158 | −0.294079 | − | 0.955781i | \(-0.595013\pi\) | ||||
−0.294079 | + | 0.955781i | \(0.595013\pi\) | |||||||
\(14\) | 8.14663e20 | − | 7.57156e21i | 0.136315 | − | 1.26693i | ||||
\(15\) | − | 2.81951e22i | − | 1.27186i | ||||||
\(16\) | 6.87194e22 | + | 3.14107e22i | 0.909494 | + | 0.415717i | ||||
\(17\) | −1.60298e23 | −0.670501 | −0.335251 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335251 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(18\) | 4.41123e23 | + | 4.74627e22i | 0.622849 | + | 0.0670155i | ||||
\(19\) | 1.01555e24i | 0.513313i | 0.966503 | + | 0.256657i | \(0.0826209\pi\) | ||||
−0.966503 | + | 0.256657i | \(0.917379\pi\) | |||||||
\(20\) | 5.10898e24 | + | 1.11228e24i | 0.974460 | + | 0.212150i | ||||
\(21\) | 2.15297e25 | 1.62507 | ||||||||
\(22\) | 2.17135e24 | − | 2.01807e25i | 0.0677171 | − | 0.629370i | ||||
\(23\) | − | 1.41511e26i | − | 1.89653i | −0.317475 | − | 0.948267i | \(-0.602835\pi\) | ||
0.317475 | − | 0.948267i | \(-0.397165\pi\) | |||||||
\(24\) | −6.75102e25 | + | 2.02667e26i | −0.403047 | + | 1.20996i | ||||
\(25\) | −1.97170e24 | −0.00541976 | ||||||||
\(26\) | 4.48217e26 | + | 4.82260e25i | 0.584783 | + | 0.0629198i | ||||
\(27\) | − | 7.47975e26i | − | 0.476404i | ||||||
\(28\) | −8.49334e26 | + | 3.90121e27i | −0.271066 | + | 1.24508i | ||||
\(29\) | −9.93962e27 | −1.62858 | −0.814288 | − | 0.580462i | \(-0.802872\pi\) | ||||
−0.814288 | + | 0.580462i | \(0.802872\pi\) | |||||||
\(30\) | −1.58138e27 | + | 1.46975e28i | −0.136061 | + | 1.26456i | ||||
\(31\) | − | 3.69457e28i | − | 1.70487i | −0.522831 | − | 0.852437i | \(-0.675124\pi\) | ||
0.522831 | − | 0.852437i | \(-0.324876\pi\) | |||||||
\(32\) | −3.40603e28 | − | 2.02280e28i | −0.859802 | − | 0.510627i | ||||
\(33\) | 5.73839e28 | 0.807281 | ||||||||
\(34\) | 8.35602e28 | + | 8.99067e27i | 0.666654 | + | 0.0717287i | ||||
\(35\) | 2.76290e29i | 1.27078i | ||||||||
\(36\) | −2.27286e29 | − | 4.94827e28i | −0.612105 | − | 0.133262i | ||||
\(37\) | −7.42006e29 | −1.18734 | −0.593669 | − | 0.804709i | \(-0.702321\pi\) | ||||
−0.593669 | + | 0.804709i | \(0.702321\pi\) | |||||||
\(38\) | 5.69592e28 | − | 5.29385e29i | 0.0549130 | − | 0.510368i | ||||
\(39\) | 1.27450e30i | 0.750090i | ||||||||
\(40\) | −2.60082e30 | − | 8.66355e29i | −0.946173 | − | 0.315178i | ||||
\(41\) | −6.52818e30 | −1.48559 | −0.742794 | − | 0.669520i | \(-0.766500\pi\) | ||||
−0.742794 | + | 0.669520i | \(0.766500\pi\) | |||||||
\(42\) | −1.12230e31 | − | 1.20754e30i | −1.61574 | − | 0.173846i | ||||
\(43\) | 5.95952e30i | 0.548669i | 0.961634 | + | 0.274334i | \(0.0884575\pi\) | ||||
−0.961634 | + | 0.274334i | \(0.911542\pi\) | |||||||
\(44\) | −2.26376e30 | + | 1.03980e31i | −0.134657 | + | 0.618514i | ||||
\(45\) | −1.60968e31 | −0.624744 | ||||||||
\(46\) | −7.93693e30 | + | 7.37666e31i | −0.202887 | + | 1.88565i | ||||
\(47\) | − | 9.29922e31i | − | 1.57975i | −0.613271 | − | 0.789873i | \(-0.710147\pi\) | ||
0.613271 | − | 0.789873i | \(-0.289853\pi\) | |||||||
\(48\) | 4.65587e31 | − | 1.01860e32i | 0.530173 | − | 1.15990i | ||||
\(49\) | −8.10395e31 | −0.623694 | ||||||||
\(50\) | 1.02781e30 | + | 1.10587e29i | 0.00538866 | + | 0.000579794i | ||||
\(51\) | 2.37603e32i | 0.855104i | ||||||||
\(52\) | −2.30941e32 | − | 5.02784e31i | −0.574696 | − | 0.125117i | ||||
\(53\) | 3.86726e32 | 0.670134 | 0.335067 | − | 0.942194i | \(-0.391241\pi\) | ||||
0.335067 | + | 0.942194i | \(0.391241\pi\) | |||||||
\(54\) | −4.19518e31 | + | 3.89904e32i | −0.0509646 | + | 0.473671i | ||||
\(55\) | 7.36405e32i | 0.631285i | ||||||||
\(56\) | 6.61547e32 | − | 1.98598e33i | 0.402706 | − | 1.20893i | ||||
\(57\) | 1.50530e33 | 0.654639 | ||||||||
\(58\) | 5.18132e33 | + | 5.57484e32i | 1.61923 | + | 0.174221i | ||||
\(59\) | − | 2.63935e33i | − | 0.596086i | −0.954552 | − | 0.298043i | \(-0.903666\pi\) | ||
0.954552 | − | 0.298043i | \(-0.0963339\pi\) | |||||||
\(60\) | 1.64868e33 | − | 7.57281e33i | 0.270560 | − | 1.24275i | ||||
\(61\) | 2.89103e33 | 0.346566 | 0.173283 | − | 0.984872i | \(-0.444562\pi\) | ||||
0.173283 | + | 0.984872i | \(0.444562\pi\) | |||||||
\(62\) | −2.07218e33 | + | 1.92590e34i | −0.182383 | + | 1.69509i | ||||
\(63\) | − | 1.22915e34i | − | 0.798241i | ||||||
\(64\) | 1.66204e34 | + | 1.24548e34i | 0.800243 | + | 0.599676i | ||||
\(65\) | −1.63557e34 | −0.586562 | ||||||||
\(66\) | −2.99130e34 | − | 3.21849e33i | −0.802649 | − | 0.0863611i | ||||
\(67\) | 2.95727e34i | 0.596306i | 0.954518 | + | 0.298153i | \(0.0963706\pi\) | ||||
−0.954518 | + | 0.298153i | \(0.903629\pi\) | |||||||
\(68\) | −4.30540e34 | − | 9.37330e33i | −0.655155 | − | 0.142634i | ||||
\(69\) | −2.09755e35 | −2.41869 | ||||||||
\(70\) | 1.54963e34 | − | 1.44024e35i | 0.135946 | − | 1.26349i | ||||
\(71\) | 1.32591e35i | 0.888394i | 0.895929 | + | 0.444197i | \(0.146511\pi\) | ||||
−0.895929 | + | 0.444197i | \(0.853489\pi\) | |||||||
\(72\) | 1.15704e35 | + | 3.85421e34i | 0.594336 | + | 0.197979i | ||||
\(73\) | −1.42953e34 | −0.0565013 | −0.0282506 | − | 0.999601i | \(-0.508994\pi\) | ||||
−0.0282506 | + | 0.999601i | \(0.508994\pi\) | |||||||
\(74\) | 3.86792e35 | + | 4.16170e34i | 1.18053 | + | 0.127019i | ||||
\(75\) | 2.92256e33i | 0.00691194i | ||||||||
\(76\) | −5.93833e34 | + | 2.72763e35i | −0.109196 | + | 0.501564i | ||||
\(77\) | −5.62317e35 | −0.806599 | ||||||||
\(78\) | 7.14832e34 | − | 6.64372e35i | 0.0802429 | − | 0.745786i | ||||
\(79\) | − | 5.08832e35i | − | 0.448394i | −0.974544 | − | 0.224197i | \(-0.928024\pi\) | ||
0.974544 | − | 0.224197i | \(-0.0719759\pi\) | |||||||
\(80\) | 1.30716e36 | + | 5.97486e35i | 0.907026 | + | 0.414589i | ||||
\(81\) | −2.25183e36 | −1.23401 | ||||||||
\(82\) | 3.40300e36 | + | 3.66147e35i | 1.47706 | + | 0.158925i | ||||
\(83\) | − | 2.79965e36i | − | 0.965208i | −0.875839 | − | 0.482604i | \(-0.839691\pi\) | ||
0.875839 | − | 0.482604i | \(-0.160309\pi\) | |||||||
\(84\) | 5.78259e36 | + | 1.25893e36i | 1.58787 | + | 0.345697i | ||||
\(85\) | −3.04915e36 | −0.668682 | ||||||||
\(86\) | 3.34252e35 | − | 3.10657e36i | 0.0586953 | − | 0.545520i | ||||
\(87\) | 1.47331e37i | 2.07696i | ||||||||
\(88\) | 1.76324e36 | − | 5.29330e36i | 0.200052 | − | 0.600559i | ||||
\(89\) | −4.53475e36 | −0.415091 | −0.207546 | − | 0.978225i | \(-0.566548\pi\) | ||||
−0.207546 | + | 0.978225i | \(0.566548\pi\) | |||||||
\(90\) | 8.39093e36 | + | 9.02823e35i | 0.621158 | + | 0.0668336i | ||||
\(91\) | − | 1.24891e37i | − | 0.749456i | ||||||
\(92\) | 8.27471e36 | − | 3.80078e37i | 0.403445 | − | 1.85312i | ||||
\(93\) | −5.47630e37 | −2.17426 | ||||||||
\(94\) | −5.21566e36 | + | 4.84749e37i | −0.168997 | + | 1.57068i | ||||
\(95\) | 1.93175e37i | 0.511920i | ||||||||
\(96\) | −2.99831e37 | + | 5.04861e37i | −0.651213 | + | 1.09652i | ||||
\(97\) | −9.50070e37 | −1.69470 | −0.847350 | − | 0.531035i | \(-0.821803\pi\) | ||||
−0.847350 | + | 0.531035i | \(0.821803\pi\) | |||||||
\(98\) | 4.22442e37 | + | 4.54527e36i | 0.620114 | + | 0.0667213i | ||||
\(99\) | − | 3.27609e37i | − | 0.396540i | ||||||
\(100\) | −5.29571e35 | − | 1.15293e35i | −0.00529571 | − | 0.00115293i | ||||
\(101\) | 1.51020e38 | 1.25005 | 0.625025 | − | 0.780605i | \(-0.285089\pi\) | ||||
0.625025 | + | 0.780605i | \(0.285089\pi\) | |||||||
\(102\) | 1.33265e37 | − | 1.23858e38i | 0.0914771 | − | 0.850197i | ||||
\(103\) | − | 8.62556e37i | − | 0.491904i | −0.969282 | − | 0.245952i | \(-0.920899\pi\) | ||
0.969282 | − | 0.245952i | \(-0.0791005\pi\) | |||||||
\(104\) | 1.17565e38 | + | 3.91619e37i | 0.558013 | + | 0.185879i | ||||
\(105\) | 4.09532e38 | 1.62066 | ||||||||
\(106\) | −2.01592e38 | − | 2.16903e37i | −0.666289 | − | 0.0716894i | ||||
\(107\) | 6.84920e37i | 0.189386i | 0.995507 | + | 0.0946930i | \(0.0301869\pi\) | ||||
−0.995507 | + | 0.0946930i | \(0.969813\pi\) | |||||||
\(108\) | 4.37372e37 | − | 2.00896e38i | 0.101344 | − | 0.465500i | ||||
\(109\) | 1.28382e38 | 0.249690 | 0.124845 | − | 0.992176i | \(-0.460157\pi\) | ||||
0.124845 | + | 0.992176i | \(0.460157\pi\) | |||||||
\(110\) | 4.13028e37 | − | 3.83873e38i | 0.0675334 | − | 0.627662i | ||||
\(111\) | 1.09984e39i | 1.51424i | ||||||||
\(112\) | −4.56239e38 | + | 9.98147e38i | −0.529724 | + | 1.15892i | ||||
\(113\) | 1.08233e39 | 1.06138 | 0.530688 | − | 0.847567i | \(-0.321934\pi\) | ||||
0.530688 | + | 0.847567i | \(0.321934\pi\) | |||||||
\(114\) | −7.84684e38 | − | 8.44281e37i | −0.650882 | − | 0.0700318i | ||||
\(115\) | − | 2.69178e39i | − | 1.89139i | ||||||
\(116\) | −2.66965e39 | − | 5.81210e38i | −1.59130 | − | 0.346443i | ||||
\(117\) | 7.27625e38 | 0.368448 | ||||||||
\(118\) | −1.48034e38 | + | 1.37584e39i | −0.0637679 | + | 0.592665i | ||||
\(119\) | − | 2.32833e39i | − | 0.854381i | ||||||
\(120\) | −1.28416e39 | + | 3.85508e39i | −0.401953 | + | 1.20667i | ||||
\(121\) | 2.24167e39 | 0.599308 | ||||||||
\(122\) | −1.50704e39 | − | 1.62150e38i | −0.344577 | − | 0.0370748i | ||||
\(123\) | 9.67643e39i | 1.89460i | ||||||||
\(124\) | 2.16037e39 | − | 9.92312e39i | 0.362673 | − | 1.66585i | ||||
\(125\) | −6.95757e39 | −1.00269 | ||||||||
\(126\) | −6.89394e38 | + | 6.40730e39i | −0.0853939 | + | 0.793660i | ||||
\(127\) | − | 4.25573e39i | − | 0.453631i | −0.973938 | − | 0.226816i | \(-0.927169\pi\) | ||
0.973938 | − | 0.226816i | \(-0.0728315\pi\) | |||||||
\(128\) | −7.96531e39 | − | 7.42461e39i | −0.731498 | − | 0.681843i | ||||
\(129\) | 8.83353e39 | 0.699729 | ||||||||
\(130\) | 8.52586e39 | + | 9.17341e38i | 0.583196 | + | 0.0627490i | ||||
\(131\) | 3.80318e39i | 0.224902i | 0.993657 | + | 0.112451i | \(0.0358701\pi\) | ||||
−0.993657 | + | 0.112451i | \(0.964130\pi\) | |||||||
\(132\) | 1.54125e40 | + | 3.35547e39i | 0.788804 | + | 0.171731i | ||||
\(133\) | −1.47508e40 | −0.654085 | ||||||||
\(134\) | 1.65865e39 | − | 1.54156e40i | 0.0637914 | − | 0.592884i | ||||
\(135\) | − | 1.42278e40i | − | 0.475112i | ||||||
\(136\) | 2.19174e40 | + | 7.30088e39i | 0.636136 | + | 0.211902i | ||||
\(137\) | 2.88810e40 | 0.729325 | 0.364662 | − | 0.931140i | \(-0.381184\pi\) | ||||
0.364662 | + | 0.931140i | \(0.381184\pi\) | |||||||
\(138\) | 1.09341e41 | + | 1.17646e40i | 2.40481 | + | 0.258746i | ||||
\(139\) | − | 5.82010e39i | − | 0.111596i | −0.998442 | − | 0.0557981i | \(-0.982230\pi\) | ||
0.998442 | − | 0.0557981i | \(-0.0177703\pi\) | |||||||
\(140\) | −1.61558e40 | + | 7.42077e40i | −0.270331 | + | 1.24170i | ||||
\(141\) | −1.37838e41 | −2.01468 | ||||||||
\(142\) | 7.43665e39 | − | 6.91170e40i | 0.0950383 | − | 0.883296i | ||||
\(143\) | − | 3.32877e40i | − | 0.372306i | ||||||
\(144\) | −5.81526e40 | − | 2.65807e40i | −0.569747 | − | 0.260423i | ||||
\(145\) | −1.89069e41 | −1.62416 | ||||||||
\(146\) | 7.45184e39 | + | 8.01781e38i | 0.0561771 | + | 0.00604438i | ||||
\(147\) | 1.20121e41i | 0.795409i | ||||||||
\(148\) | −1.99293e41 | − | 4.33881e40i | −1.16016 | − | 0.252580i | ||||
\(149\) | 9.09811e40 | 0.466028 | 0.233014 | − | 0.972473i | \(-0.425141\pi\) | ||||
0.233014 | + | 0.972473i | \(0.425141\pi\) | |||||||
\(150\) | 1.63918e38 | − | 1.52347e39i | 0.000739423 | − | 0.00687227i | ||||
\(151\) | 4.25600e41i | 1.69215i | 0.533061 | + | 0.846077i | \(0.321042\pi\) | ||||
−0.533061 | + | 0.846077i | \(0.678958\pi\) | |||||||
\(152\) | 4.62538e40 | − | 1.38855e41i | 0.162225 | − | 0.487004i | ||||
\(153\) | 1.35650e41 | 0.420031 | ||||||||
\(154\) | 2.93124e41 | + | 3.15387e40i | 0.801970 | + | 0.0862880i | ||||
\(155\) | − | 7.02772e41i | − | 1.70025i | ||||||
\(156\) | −7.45255e40 | + | 3.42314e41i | −0.159565 | + | 0.732922i | ||||
\(157\) | −4.28263e40 | −0.0812114 | −0.0406057 | − | 0.999175i | \(-0.512929\pi\) | ||||
−0.0406057 | + | 0.999175i | \(0.512929\pi\) | |||||||
\(158\) | −2.85389e40 | + | 2.65243e41i | −0.0479681 | + | 0.445821i | ||||
\(159\) | − | 5.73227e41i | − | 0.854636i | ||||||
\(160\) | −6.47885e41 | − | 3.84772e41i | −0.857469 | − | 0.509241i | ||||
\(161\) | 2.05544e42 | 2.41664 | ||||||||
\(162\) | 1.17383e42 | + | 1.26298e41i | 1.22693 | + | 0.132012i | ||||
\(163\) | − | 2.17593e41i | − | 0.202340i | −0.994869 | − | 0.101170i | \(-0.967741\pi\) | ||
0.994869 | − | 0.101170i | \(-0.0322585\pi\) | |||||||
\(164\) | −1.75338e42 | − | 3.81729e41i | −1.45159 | − | 0.316026i | ||||
\(165\) | 1.09154e42 | 0.805091 | ||||||||
\(166\) | −1.57025e41 | + | 1.45940e42i | −0.103256 | + | 0.959669i | ||||
\(167\) | 2.18212e42i | 1.28016i | 0.768308 | + | 0.640081i | \(0.221099\pi\) | ||||
−0.768308 | + | 0.640081i | \(0.778901\pi\) | |||||||
\(168\) | −2.94373e42 | − | 9.80583e41i | −1.54178 | − | 0.513580i | ||||
\(169\) | −1.39789e42 | −0.654070 | ||||||||
\(170\) | 1.58946e42 | + | 1.71018e41i | 0.664845 | + | 0.0715340i | ||||
\(171\) | − | 8.59390e41i | − | 0.321562i | ||||||
\(172\) | −3.48477e41 | + | 1.60064e42i | −0.116717 | + | 0.536111i | ||||
\(173\) | 1.95778e42 | 0.587338 | 0.293669 | − | 0.955907i | \(-0.405124\pi\) | ||||
0.293669 | + | 0.955907i | \(0.405124\pi\) | |||||||
\(174\) | 8.26335e41 | − | 7.68004e42i | 0.222188 | − | 2.06504i | ||||
\(175\) | − | 2.86388e40i | − | 0.00690609i | ||||||
\(176\) | −1.21603e42 | + | 2.66039e42i | −0.263150 | + | 0.575712i | ||||
\(177\) | −3.91219e42 | −0.760201 | ||||||||
\(178\) | 2.36387e42 | + | 2.54341e41i | 0.412709 | + | 0.0444055i | ||||
\(179\) | 1.93234e42i | 0.303302i | 0.988434 | + | 0.151651i | \(0.0484590\pi\) | ||||
−0.988434 | + | 0.151651i | \(0.951541\pi\) | |||||||
\(180\) | −4.32338e42 | − | 9.41246e41i | −0.610444 | − | 0.132900i | ||||
\(181\) | −5.26990e42 | −0.669744 | −0.334872 | − | 0.942264i | \(-0.608693\pi\) | ||||
−0.334872 | + | 0.942264i | \(0.608693\pi\) | |||||||
\(182\) | −7.00480e41 | + | 6.51033e42i | −0.0801750 | + | 0.745155i | ||||
\(183\) | − | 4.28525e42i | − | 0.441983i | ||||||
\(184\) | −6.44519e42 | + | 1.93486e43i | −0.599372 | + | 1.79933i | ||||
\(185\) | −1.41142e43 | −1.18412 | ||||||||
\(186\) | 2.85468e43 | + | 3.07150e42i | 2.16178 | + | 0.232597i | ||||
\(187\) | − | 6.20577e42i | − | 0.424429i | ||||||
\(188\) | 5.43763e42 | − | 2.49764e43i | 0.336055 | − | 1.54359i | ||||
\(189\) | 1.08643e43 | 0.607055 | ||||||||
\(190\) | 1.08346e42 | − | 1.00698e43i | 0.0547640 | − | 0.508983i | ||||
\(191\) | 4.37537e42i | 0.200161i | 0.994979 | + | 0.100081i | \(0.0319101\pi\) | ||||
−0.994979 | + | 0.100081i | \(0.968090\pi\) | |||||||
\(192\) | 1.84612e43 | − | 2.46357e43i | 0.764780 | − | 1.02057i | ||||
\(193\) | −2.22592e43 | −0.835450 | −0.417725 | − | 0.908574i | \(-0.637172\pi\) | ||||
−0.417725 | + | 0.908574i | \(0.637172\pi\) | |||||||
\(194\) | 4.95252e43 | + | 5.32867e42i | 1.68497 | + | 0.181295i | ||||
\(195\) | 2.42433e43i | 0.748055i | ||||||||
\(196\) | −2.17661e43 | − | 4.73871e42i | −0.609418 | − | 0.132677i | ||||
\(197\) | 2.14613e43 | 0.545503 | 0.272751 | − | 0.962085i | \(-0.412066\pi\) | ||||
0.272751 | + | 0.962085i | \(0.412066\pi\) | |||||||
\(198\) | −1.83746e42 | + | 1.70776e43i | −0.0424210 | + | 0.394265i | ||||
\(199\) | 4.36019e43i | 0.914737i | 0.889277 | + | 0.457369i | \(0.151208\pi\) | ||||
−0.889277 | + | 0.457369i | \(0.848792\pi\) | |||||||
\(200\) | 2.69588e41 | + | 8.98021e40i | 0.00514198 | + | 0.00171284i | ||||
\(201\) | 4.38343e43 | 0.760482 | ||||||||
\(202\) | −7.87235e43 | − | 8.47026e42i | −1.24288 | − | 0.133727i | ||||
\(203\) | − | 1.44373e44i | − | 2.07520i | ||||||
\(204\) | −1.38936e43 | + | 6.38170e43i | −0.181904 | + | 0.835532i | ||||
\(205\) | −1.24177e44 | −1.48156 | ||||||||
\(206\) | −4.83783e42 | + | 4.49633e43i | −0.0526227 | + | 0.489081i | ||||
\(207\) | 1.19751e44i | 1.18807i | ||||||||
\(208\) | −5.90877e43 | − | 2.70082e43i | −0.534926 | − | 0.244507i | ||||
\(209\) | −3.93158e43 | −0.324929 | ||||||||
\(210\) | −2.13481e44 | − | 2.29695e43i | −1.61136 | − | 0.173374i | ||||
\(211\) | − | 1.61611e44i | − | 1.11456i | −0.830324 | − | 0.557281i | \(-0.811844\pi\) | ||
0.830324 | − | 0.557281i | \(-0.188156\pi\) | |||||||
\(212\) | 1.03869e44 | + | 2.26135e43i | 0.654796 | + | 0.142556i | ||||
\(213\) | 1.96534e44 | 1.13299 | ||||||||
\(214\) | 3.84152e42 | − | 3.57035e43i | 0.0202601 | − | 0.188299i | ||||
\(215\) | 1.13360e44i | 0.547180i | ||||||||
\(216\) | −3.40670e43 | + | 1.02270e44i | −0.150561 | + | 0.451987i | ||||
\(217\) | 5.36635e44 | 2.17242 | ||||||||
\(218\) | −6.69229e43 | − | 7.20058e42i | −0.248257 | − | 0.0267112i | ||||
\(219\) | 2.11893e43i | 0.0720573i | ||||||||
\(220\) | −4.30606e43 | + | 1.97788e44i | −0.134292 | + | 0.616836i | ||||
\(221\) | 1.37831e44 | 0.394361 | ||||||||
\(222\) | 6.16870e43 | − | 5.73326e44i | 0.161990 | − | 1.50555i | ||||
\(223\) | 3.64937e44i | 0.879885i | 0.898026 | + | 0.439943i | \(0.145001\pi\) | ||||
−0.898026 | + | 0.439943i | \(0.854999\pi\) | |||||||
\(224\) | 2.93811e44 | − | 4.94724e44i | 0.650662 | − | 1.09560i | ||||
\(225\) | 1.66851e42 | 0.00339517 | ||||||||
\(226\) | −5.64196e44 | − | 6.07047e43i | −1.05528 | − | 0.113543i | ||||
\(227\) | − | 8.19663e44i | − | 1.40976i | −0.709328 | − | 0.704879i | \(-0.751001\pi\) | ||
0.709328 | − | 0.704879i | \(-0.248999\pi\) | |||||||
\(228\) | 4.04304e44 | + | 8.80213e43i | 0.639655 | + | 0.139260i | ||||
\(229\) | −8.36405e44 | −1.21771 | −0.608853 | − | 0.793283i | \(-0.708370\pi\) | ||||
−0.608853 | + | 0.793283i | \(0.708370\pi\) | |||||||
\(230\) | −1.50974e44 | + | 1.40317e45i | −0.202336 | + | 1.88053i | ||||
\(231\) | 8.33498e44i | 1.02867i | ||||||||
\(232\) | 1.35903e45 | + | 4.52706e44i | 1.54511 | + | 0.514688i | ||||
\(233\) | −3.29214e44 | −0.344917 | −0.172459 | − | 0.985017i | \(-0.555171\pi\) | ||||
−0.172459 | + | 0.985017i | \(0.555171\pi\) | |||||||
\(234\) | −3.79296e44 | − | 4.08104e43i | −0.366333 | − | 0.0394157i | ||||
\(235\) | − | 1.76887e45i | − | 1.57546i | ||||||
\(236\) | 1.54334e44 | − | 7.08894e44i | 0.126804 | − | 0.582443i | ||||
\(237\) | −7.54219e44 | −0.571846 | ||||||||
\(238\) | −1.30589e44 | + | 1.21371e45i | −0.0913997 | + | 0.849478i | ||||
\(239\) | 1.12428e45i | 0.726632i | 0.931666 | + | 0.363316i | \(0.118356\pi\) | ||||
−0.931666 | + | 0.363316i | \(0.881644\pi\) | |||||||
\(240\) | 8.85627e44 | − | 1.93755e45i | 0.528734 | − | 1.15675i | ||||
\(241\) | −1.35363e45 | −0.746751 | −0.373375 | − | 0.927680i | \(-0.621800\pi\) | ||||
−0.373375 | + | 0.927680i | \(0.621800\pi\) | |||||||
\(242\) | −1.16854e45 | − | 1.25729e44i | −0.595869 | − | 0.0641125i | ||||
\(243\) | 2.32738e45i | 1.09736i | ||||||||
\(244\) | 7.76492e44 | + | 1.69050e44i | 0.338634 | + | 0.0737241i | ||||
\(245\) | −1.54151e45 | −0.622001 | ||||||||
\(246\) | 5.42723e44 | − | 5.04412e45i | 0.202680 | − | 1.88373i | ||||
\(247\) | − | 8.73210e44i | − | 0.301909i | ||||||
\(248\) | −1.68271e45 | + | 5.05155e45i | −0.538801 | + | 1.61749i | ||||
\(249\) | −4.14981e45 | −1.23095 | ||||||||
\(250\) | 3.62684e45 | + | 3.90230e44i | 0.996937 | + | 0.107266i | ||||
\(251\) | 3.64288e43i | 0.00928204i | 0.999989 | + | 0.00464102i | \(0.00147729\pi\) | ||||
−0.999989 | + | 0.00464102i | \(0.998523\pi\) | |||||||
\(252\) | 7.18733e44 | − | 3.30133e45i | 0.169808 | − | 0.779970i | ||||
\(253\) | 5.47843e45 | 1.20051 | ||||||||
\(254\) | −2.38691e44 | + | 2.21842e45i | −0.0485284 | + | 0.451028i | ||||
\(255\) | 4.51963e45i | 0.852784i | ||||||||
\(256\) | 3.73573e45 | + | 4.31705e45i | 0.654359 | + | 0.756184i | ||||
\(257\) | 7.62471e45 | 1.24021 | 0.620103 | − | 0.784520i | \(-0.287091\pi\) | ||||
0.620103 | + | 0.784520i | \(0.287091\pi\) | |||||||
\(258\) | −4.60474e45 | − | 4.95447e44i | −0.695713 | − | 0.0748553i | ||||
\(259\) | − | 1.07776e46i | − | 1.51296i | ||||||
\(260\) | −4.39290e45 | − | 9.56382e44i | −0.573137 | − | 0.124778i | ||||
\(261\) | 8.41123e45 | 1.02021 | ||||||||
\(262\) | 2.13309e44 | − | 1.98252e45i | 0.0240594 | − | 0.223611i | ||||
\(263\) | − | 1.22073e46i | − | 1.28073i | −0.768069 | − | 0.640367i | \(-0.778782\pi\) | ||
0.768069 | − | 0.640367i | \(-0.221218\pi\) | |||||||
\(264\) | −7.84603e45 | − | 2.61358e45i | −0.765906 | − | 0.255130i | ||||
\(265\) | 7.35620e45 | 0.668316 | ||||||||
\(266\) | 7.68929e45 | + | 8.27330e44i | 0.650332 | + | 0.0699725i | ||||
\(267\) | 6.72167e45i | 0.529375i | ||||||||
\(268\) | −1.72924e45 | + | 7.94282e45i | −0.126851 | + | 0.582658i | ||||
\(269\) | −1.62480e45 | −0.111047 | −0.0555234 | − | 0.998457i | \(-0.517683\pi\) | ||||
−0.0555234 | + | 0.998457i | \(0.517683\pi\) | |||||||
\(270\) | −7.97995e44 | + | 7.41665e45i | −0.0508263 | + | 0.472385i | ||||
\(271\) | 2.49493e46i | 1.48130i | 0.671894 | + | 0.740648i | \(0.265481\pi\) | ||||
−0.671894 | + | 0.740648i | \(0.734519\pi\) | |||||||
\(272\) | −1.10156e46 | − | 5.03508e45i | −0.609817 | − | 0.278739i | ||||
\(273\) | −1.85121e46 | −0.955797 | ||||||||
\(274\) | −1.50550e46 | − | 1.61985e45i | −0.725139 | − | 0.0780214i | ||||
\(275\) | − | 7.63321e43i | − | 0.00343072i | ||||||
\(276\) | −5.63374e46 | − | 1.22652e46i | −2.36333 | − | 0.514522i | ||||
\(277\) | −2.25070e45 | −0.0881457 | −0.0440728 | − | 0.999028i | \(-0.514033\pi\) | ||||
−0.0440728 | + | 0.999028i | \(0.514033\pi\) | |||||||
\(278\) | −3.26433e44 | + | 3.03390e45i | −0.0119383 | + | 0.110956i | ||||
\(279\) | 3.12647e46i | 1.06801i | ||||||||
\(280\) | 1.25838e46 | − | 3.77768e46i | 0.401614 | − | 1.20565i | ||||
\(281\) | 5.94139e45 | 0.177202 | 0.0886009 | − | 0.996067i | \(-0.471760\pi\) | ||||
0.0886009 | + | 0.996067i | \(0.471760\pi\) | |||||||
\(282\) | 7.18522e46 | + | 7.73095e45i | 2.00312 | + | 0.215526i | ||||
\(283\) | − | 5.89716e46i | − | 1.53709i | −0.639793 | − | 0.768547i | \(-0.720980\pi\) | ||
0.639793 | − | 0.768547i | \(-0.279020\pi\) | |||||||
\(284\) | −7.75314e45 | + | 3.56122e46i | −0.188986 | + | 0.868060i | ||||
\(285\) | 2.86335e46 | 0.652863 | ||||||||
\(286\) | −1.86701e45 | + | 1.73522e46i | −0.0398284 | + | 0.370169i | ||||
\(287\) | − | 9.48215e46i | − | 1.89300i | ||||||
\(288\) | 2.88229e46 | + | 1.71176e46i | 0.538618 | + | 0.319879i | ||||
\(289\) | −3.14601e46 | −0.550428 | ||||||||
\(290\) | 9.85576e46 | + | 1.06043e46i | 1.61484 | + | 0.173748i | ||||
\(291\) | 1.40825e47i | 2.16129i | ||||||||
\(292\) | −3.83952e45 | − | 8.35904e44i | −0.0552081 | − | 0.0120194i | ||||
\(293\) | −9.14649e46 | −1.23245 | −0.616225 | − | 0.787570i | \(-0.711339\pi\) | ||||
−0.616225 | + | 0.787570i | \(0.711339\pi\) | |||||||
\(294\) | 6.73726e45 | − | 6.26168e46i | 0.0850910 | − | 0.790845i | ||||
\(295\) | − | 5.02050e46i | − | 0.594469i | ||||||
\(296\) | 1.01454e47 | + | 3.37951e46i | 1.12648 | + | 0.375242i | ||||
\(297\) | 2.89570e46 | 0.301565 | ||||||||
\(298\) | −4.74266e46 | − | 5.10287e45i | −0.463354 | − | 0.0498546i | ||||
\(299\) | 1.21677e47i | 1.11546i | ||||||||
\(300\) | −1.70894e44 | + | 7.84960e44i | −0.00147036 | + | 0.00675373i | ||||
\(301\) | −8.65617e46 | −0.699137 | ||||||||
\(302\) | 2.38707e46 | − | 2.21857e47i | 0.181023 | − | 1.68244i | ||||
\(303\) | − | 2.23850e47i | − | 1.59422i | ||||||
\(304\) | −3.18991e46 | + | 6.97879e46i | −0.213393 | + | 0.466855i | ||||
\(305\) | 5.49924e46 | 0.345626 | ||||||||
\(306\) | −7.07114e46 | − | 7.60820e45i | −0.417621 | − | 0.0449339i | ||||
\(307\) | 2.55999e47i | 1.42105i | 0.703673 | + | 0.710524i | \(0.251542\pi\) | ||||
−0.703673 | + | 0.710524i | \(0.748458\pi\) | |||||||
\(308\) | −1.51031e47 | − | 3.28810e46i | −0.788137 | − | 0.171586i | ||||
\(309\) | −1.27853e47 | −0.627335 | ||||||||
\(310\) | −3.94164e46 | + | 3.66340e47i | −0.181888 | + | 1.69049i | ||||
\(311\) | 1.48731e47i | 0.645585i | 0.946470 | + | 0.322792i | \(0.104622\pi\) | ||||
−0.946470 | + | 0.322792i | \(0.895378\pi\) | |||||||
\(312\) | 5.80480e46 | − | 1.74261e47i | 0.237055 | − | 0.711646i | ||||
\(313\) | −1.03852e46 | −0.0399092 | −0.0199546 | − | 0.999801i | \(-0.506352\pi\) | ||||
−0.0199546 | + | 0.999801i | \(0.506352\pi\) | |||||||
\(314\) | 2.23245e46 | + | 2.40200e45i | 0.0807454 | + | 0.00868781i | ||||
\(315\) | − | 2.33805e47i | − | 0.796075i | ||||||
\(316\) | 2.97535e46 | − | 1.36665e47i | 0.0953857 | − | 0.438131i | ||||
\(317\) | 3.32562e47 | 1.00403 | 0.502015 | − | 0.864859i | \(-0.332592\pi\) | ||||
0.502015 | + | 0.864859i | \(0.332592\pi\) | |||||||
\(318\) | −3.21506e46 | + | 2.98811e47i | −0.0914270 | + | 0.849732i | ||||
\(319\) | − | 3.84801e47i | − | 1.03089i | ||||||
\(320\) | 3.16149e47 | + | 2.36912e47i | 0.798071 | + | 0.598049i | ||||
\(321\) | 1.01523e47 | 0.241528 | ||||||||
\(322\) | −1.07146e48 | − | 1.15283e47i | −2.40277 | − | 0.258527i | ||||
\(323\) | − | 1.62791e47i | − | 0.344177i | ||||||
\(324\) | −6.04810e47 | − | 1.31673e47i | −1.20577 | − | 0.262508i | ||||
\(325\) | 1.69535e45 | 0.00318768 | ||||||||
\(326\) | −1.22042e46 | + | 1.13427e47i | −0.0216458 | + | 0.201178i | ||||
\(327\) | − | 1.90295e47i | − | 0.318435i | ||||||
\(328\) | 8.92590e47 | + | 2.97330e47i | 1.40945 | + | 0.469499i | ||||
\(329\) | 1.35071e48 | 2.01298 | ||||||||
\(330\) | −5.68997e47 | − | 6.12213e46i | −0.800471 | − | 0.0861267i | ||||
\(331\) | 1.35003e48i | 1.79313i | 0.442909 | + | 0.896567i | \(0.353947\pi\) | ||||
−0.442909 | + | 0.896567i | \(0.646053\pi\) | |||||||
\(332\) | 1.63707e47 | − | 7.51949e47i | 0.205326 | − | 0.943115i | ||||
\(333\) | 6.27909e47 | 0.743801 | ||||||||
\(334\) | 1.22389e47 | − | 1.13749e48i | 0.136949 | − | 1.27282i | ||||
\(335\) | 5.62523e47i | 0.594688i | ||||||||
\(336\) | 1.47951e48 | + | 6.76263e47i | 1.47799 | + | 0.675568i | ||||
\(337\) | −1.40009e48 | −1.32187 | −0.660933 | − | 0.750445i | \(-0.729839\pi\) | ||||
−0.660933 | + | 0.750445i | \(0.729839\pi\) | |||||||
\(338\) | 7.28689e47 | + | 7.84033e46i | 0.650317 | + | 0.0699709i | ||||
\(339\) | − | 1.60429e48i | − | 1.35359i | ||||||
\(340\) | −8.18961e47 | − | 1.78296e47i | −0.653377 | − | 0.142247i | ||||
\(341\) | 1.43031e48 | 1.07919 | ||||||||
\(342\) | −4.82007e46 | + | 4.47982e47i | −0.0343999 | + | 0.319716i | ||||
\(343\) | 7.10202e47i | 0.479506i | ||||||||
\(344\) | 2.71430e47 | − | 8.14838e47i | 0.173399 | − | 0.520548i | ||||
\(345\) | −3.98991e48 | −2.41212 | ||||||||
\(346\) | −1.02055e48 | − | 1.09806e47i | −0.583967 | − | 0.0628320i | ||||
\(347\) | − | 2.20459e48i | − | 1.19418i | −0.802175 | − | 0.597088i | \(-0.796324\pi\) | ||
0.802175 | − | 0.597088i | \(-0.203676\pi\) | |||||||
\(348\) | −8.61503e47 | + | 3.95710e48i | −0.441826 | + | 2.02942i | ||||
\(349\) | −1.96796e48 | −0.955727 | −0.477863 | − | 0.878434i | \(-0.658589\pi\) | ||||
−0.477863 | + | 0.878434i | \(0.658589\pi\) | |||||||
\(350\) | −1.60627e45 | + | 1.49288e46i | −0.000738797 | + | 0.00686646i | ||||
\(351\) | 6.43139e47i | 0.280201i | ||||||||
\(352\) | 7.83105e47 | − | 1.31861e48i | 0.323228 | − | 0.544257i | ||||
\(353\) | −5.50281e47 | −0.215211 | −0.107606 | − | 0.994194i | \(-0.534318\pi\) | ||||
−0.107606 | + | 0.994194i | \(0.534318\pi\) | |||||||
\(354\) | 2.03935e48 | + | 2.19424e47i | 0.755838 | + | 0.0813245i | ||||
\(355\) | 2.52211e48i | 0.885983i | ||||||||
\(356\) | −1.21797e48 | − | 2.65166e47i | −0.405591 | − | 0.0883014i | ||||
\(357\) | −3.45118e48 | −1.08961 | ||||||||
\(358\) | 1.08379e47 | − | 1.00729e48i | 0.0324466 | − | 0.301562i | ||||
\(359\) | 2.63214e48i | 0.747334i | 0.927563 | + | 0.373667i | \(0.121900\pi\) | ||||
−0.927563 | + | 0.373667i | \(0.878100\pi\) | |||||||
\(360\) | 2.20090e48 | + | 7.33138e47i | 0.592724 | + | 0.197441i | ||||
\(361\) | 2.88280e48 | 0.736510 | ||||||||
\(362\) | 2.74709e48 | + | 2.95573e47i | 0.665901 | + | 0.0716477i | ||||
\(363\) | − | 3.32273e48i | − | 0.764310i | ||||||
\(364\) | 7.30291e47 | − | 3.35441e48i | 0.159430 | − | 0.732302i | ||||
\(365\) | −2.71921e47 | −0.0563480 | ||||||||
\(366\) | −2.40347e47 | + | 2.23381e48i | −0.0472823 | + | 0.439447i | ||||
\(367\) | − | 4.67445e48i | − | 0.873122i | −0.899675 | − | 0.436561i | \(-0.856196\pi\) | ||
0.899675 | − | 0.436561i | \(-0.143804\pi\) | |||||||
\(368\) | 4.44495e48 | − | 9.72453e48i | 0.788421 | − | 1.72489i | ||||
\(369\) | 5.52435e48 | 0.930637 | ||||||||
\(370\) | 7.35746e48 | + | 7.91627e47i | 1.17732 | + | 0.126674i | ||||
\(371\) | 5.61718e48i | 0.853913i | ||||||||
\(372\) | −1.47086e49 | − | 3.20222e48i | −2.12449 | − | 0.462525i | ||||
\(373\) | 8.33802e48 | 1.14445 | 0.572223 | − | 0.820098i | \(-0.306081\pi\) | ||||
0.572223 | + | 0.820098i | \(0.306081\pi\) | |||||||
\(374\) | −3.48064e47 | + | 3.23494e48i | −0.0454044 | + | 0.421993i | ||||
\(375\) | 1.03129e49i | 1.27875i | ||||||||
\(376\) | −4.23538e48 | + | 1.27147e49i | −0.499256 | + | 1.49878i | ||||
\(377\) | 8.54649e48 | 0.957860 | ||||||||
\(378\) | −5.66334e48 | − | 6.09348e47i | −0.603571 | − | 0.0649413i | ||||
\(379\) | − | 1.67174e49i | − | 1.69443i | −0.531250 | − | 0.847215i | \(-0.678277\pi\) | ||
0.531250 | − | 0.847215i | \(-0.321723\pi\) | |||||||
\(380\) | −1.12957e48 | + | 5.18842e48i | −0.108900 | + | 0.500203i | ||||
\(381\) | −6.30808e48 | −0.578525 | ||||||||
\(382\) | 2.45402e47 | − | 2.28079e48i | 0.0214128 | − | 0.199013i | ||||
\(383\) | − | 8.37544e48i | − | 0.695394i | −0.937607 | − | 0.347697i | \(-0.886964\pi\) | ||
0.937607 | − | 0.347697i | \(-0.113036\pi\) | |||||||
\(384\) | −1.10052e49 | + | 1.18066e49i | −0.869569 | + | 0.932895i | ||||
\(385\) | −1.06962e49 | −0.804410 | ||||||||
\(386\) | 1.16033e49 | + | 1.24845e48i | 0.830656 | + | 0.0893745i | ||||
\(387\) | − | 5.04313e48i | − | 0.343710i | ||||||
\(388\) | −2.55176e49 | − | 5.55545e48i | −1.65591 | − | 0.360509i | ||||
\(389\) | 7.43652e48 | 0.459544 | 0.229772 | − | 0.973244i | \(-0.426202\pi\) | ||||
0.229772 | + | 0.973244i | \(0.426202\pi\) | |||||||
\(390\) | 1.35973e48 | − | 1.26375e49i | 0.0800252 | − | 0.743762i | ||||
\(391\) | 2.26839e49i | 1.27163i | ||||||||
\(392\) | 1.10804e49 | + | 3.69099e48i | 0.591728 | + | 0.197110i | ||||
\(393\) | 5.63729e48 | 0.286822 | ||||||||
\(394\) | −1.11873e49 | − | 1.20370e48i | −0.542373 | − | 0.0583566i | ||||
\(395\) | − | 9.67886e48i | − | 0.447177i | ||||||
\(396\) | 1.91566e48 | − | 8.79914e48i | 0.0843550 | − | 0.387464i | ||||
\(397\) | −9.64903e47 | −0.0405009 | −0.0202504 | − | 0.999795i | \(-0.506446\pi\) | ||||
−0.0202504 | + | 0.999795i | \(0.506446\pi\) | |||||||
\(398\) | 2.44550e48 | − | 2.27287e49i | 0.0978565 | − | 0.909488i | ||||
\(399\) | 2.18645e49i | 0.834169i | ||||||||
\(400\) | −1.35494e47 | − | 6.19324e46i | −0.00492924 | − | 0.00225309i | ||||
\(401\) | 3.33372e49 | 1.15661 | 0.578304 | − | 0.815821i | \(-0.303715\pi\) | ||||
0.578304 | + | 0.815821i | \(0.303715\pi\) | |||||||
\(402\) | −2.28499e49 | − | 2.45854e48i | −0.756118 | − | 0.0813546i | ||||
\(403\) | 3.17674e49i | 1.00273i | ||||||||
\(404\) | 4.05618e49 | + | 8.83074e48i | 1.22144 | + | 0.265920i | ||||
\(405\) | −4.28336e49 | −1.23066 | ||||||||
\(406\) | −8.09744e48 | + | 7.52584e49i | −0.222000 | + | 2.06329i | ||||
\(407\) | − | 2.87259e49i | − | 0.751589i | ||||||
\(408\) | 1.08218e49 | − | 3.24872e49i | 0.270244 | − | 0.811278i | ||||
\(409\) | −7.74923e49 | −1.84721 | −0.923604 | − | 0.383348i | \(-0.874771\pi\) | ||||
−0.923604 | + | 0.383348i | \(0.874771\pi\) | |||||||
\(410\) | 6.47310e49 | + | 6.96474e48i | 1.47306 | + | 0.158494i | ||||
\(411\) | − | 4.28090e49i | − | 0.930123i | ||||||
\(412\) | 5.04372e48 | − | 2.31671e49i | 0.104641 | − | 0.480645i | ||||
\(413\) | 3.83365e49 | 0.759558 | ||||||||
\(414\) | 6.71648e48 | − | 6.24237e49i | 0.127097 | − | 1.18125i | ||||
\(415\) | − | 5.32543e49i | − | 0.962588i | ||||||
\(416\) | 2.92864e49 | + | 1.73929e49i | 0.505700 | + | 0.300329i | ||||
\(417\) | −8.62688e48 | −0.142321 | ||||||||
\(418\) | 2.04945e49 | + | 2.20511e48i | 0.323064 | + | 0.0347601i | ||||
\(419\) | 2.73512e49i | 0.412013i | 0.978551 | + | 0.206006i | \(0.0660468\pi\) | ||||
−0.978551 | + | 0.206006i | \(0.933953\pi\) | |||||||
\(420\) | 1.09995e50 | + | 2.39470e49i | 1.58356 | + | 0.344759i | ||||
\(421\) | 1.25744e49 | 0.173032 | 0.0865160 | − | 0.996250i | \(-0.472427\pi\) | ||||
0.0865160 | + | 0.996250i | \(0.472427\pi\) | |||||||
\(422\) | −9.06430e48 | + | 8.42445e49i | −0.119233 | + | 1.10817i | ||||
\(423\) | 7.86930e49i | 0.989621i | ||||||||
\(424\) | −5.28766e49 | − | 1.76137e49i | −0.635788 | − | 0.211786i | ||||
\(425\) | 3.16060e47 | 0.00363396 | ||||||||
\(426\) | −1.02449e50 | − | 1.10230e49i | −1.12649 | − | 0.121204i | ||||
\(427\) | 4.19921e49i | 0.441609i | ||||||||
\(428\) | −4.00501e48 | + | 1.83960e49i | −0.0402876 | + | 0.185051i | ||||
\(429\) | −4.93410e49 | −0.474809 | ||||||||
\(430\) | 6.35805e48 | − | 5.90924e49i | 0.0585360 | − | 0.544040i | ||||
\(431\) | − | 1.63530e50i | − | 1.44055i | −0.693686 | − | 0.720277i | \(-0.744015\pi\) | ||
0.693686 | − | 0.720277i | \(-0.255985\pi\) | |||||||
\(432\) | 2.34944e49 | − | 5.14004e49i | 0.198049 | − | 0.433287i | ||||
\(433\) | −1.34096e50 | −1.08179 | −0.540897 | − | 0.841089i | \(-0.681915\pi\) | ||||
−0.540897 | + | 0.841089i | \(0.681915\pi\) | |||||||
\(434\) | −2.79737e50 | − | 3.00983e49i | −2.15995 | − | 0.232401i | ||||
\(435\) | 2.80248e50i | 2.07132i | ||||||||
\(436\) | 3.44817e49 | + | 7.50702e48i | 0.243975 | + | 0.0531159i | ||||
\(437\) | 1.43711e50 | 0.973515 | ||||||||
\(438\) | 1.18844e48 | − | 1.10455e49i | 0.00770852 | − | 0.0716438i | ||||
\(439\) | − | 1.04622e50i | − | 0.649829i | −0.945743 | − | 0.324914i | \(-0.894664\pi\) | ||
0.945743 | − | 0.324914i | \(-0.105336\pi\) | |||||||
\(440\) | 3.35400e49 | − | 1.00688e50i | 0.199509 | − | 0.598930i | ||||
\(441\) | 6.85782e49 | 0.390709 | ||||||||
\(442\) | −7.18485e49 | − | 7.73054e48i | −0.392098 | − | 0.0421878i | ||||
\(443\) | 4.66785e49i | 0.244032i | 0.992528 | + | 0.122016i | \(0.0389359\pi\) | ||||
−0.992528 | + | 0.122016i | \(0.961064\pi\) | |||||||
\(444\) | −6.43123e49 | + | 2.95403e50i | −0.322120 | + | 1.47958i | ||||
\(445\) | −8.62589e49 | −0.413965 | ||||||||
\(446\) | 2.04683e49 | − | 1.90234e50i | 0.0941281 | − | 0.874836i | ||||
\(447\) | − | 1.34857e50i | − | 0.594335i | ||||||
\(448\) | −1.80905e50 | + | 2.41410e50i | −0.764133 | + | 1.01970i | ||||
\(449\) | 2.54850e50 | 1.03182 | 0.515910 | − | 0.856643i | \(-0.327454\pi\) | ||||
0.515910 | + | 0.856643i | \(0.327454\pi\) | |||||||
\(450\) | −8.69762e47 | − | 9.35821e46i | −0.00337569 | − | 0.000363208i | ||||
\(451\) | − | 2.52731e50i | − | 0.940382i | ||||||
\(452\) | 2.90699e50 | + | 6.32882e49i | 1.03708 | + | 0.225784i | ||||
\(453\) | 6.30848e50 | 2.15804 | ||||||||
\(454\) | −4.59725e49 | + | 4.27274e50i | −0.150813 | + | 1.40167i | ||||
\(455\) | − | 2.37565e50i | − | 0.747422i | ||||||
\(456\) | −2.05819e50 | − | 6.85599e49i | −0.621087 | − | 0.206889i | ||||
\(457\) | 5.57953e50 | 1.61507 | 0.807533 | − | 0.589823i | \(-0.200802\pi\) | ||||
0.807533 | + | 0.589823i | \(0.200802\pi\) | |||||||
\(458\) | 4.36001e50 | + | 4.69115e49i | 1.21072 | + | 0.130267i | ||||
\(459\) | 1.19899e50i | 0.319430i | ||||||||
\(460\) | 1.57399e50 | − | 7.22975e50i | 0.402350 | − | 1.84810i | ||||
\(461\) | −4.09629e50 | −1.00478 | −0.502392 | − | 0.864640i | \(-0.667547\pi\) | ||||
−0.502392 | + | 0.864640i | \(0.667547\pi\) | |||||||
\(462\) | 4.67485e49 | − | 4.34485e50i | 0.110045 | − | 1.02277i | ||||
\(463\) | 2.84574e50i | 0.642919i | 0.946923 | + | 0.321460i | \(0.104173\pi\) | ||||
−0.946923 | + | 0.321460i | \(0.895827\pi\) | |||||||
\(464\) | −6.83045e50 | − | 3.12210e50i | −1.48118 | − | 0.677026i | ||||
\(465\) | −1.04169e51 | −2.16836 | ||||||||
\(466\) | 1.71612e50 | + | 1.84646e49i | 0.342938 | + | 0.0368985i | ||||
\(467\) | 5.27136e50i | 1.01135i | 0.862724 | + | 0.505676i | \(0.168757\pi\) | ||||
−0.862724 | + | 0.505676i | \(0.831243\pi\) | |||||||
\(468\) | 1.95430e50 | + | 4.25472e49i | 0.360015 | + | 0.0783790i | ||||
\(469\) | −4.29542e50 | −0.759839 | ||||||||
\(470\) | −9.92109e49 | + | 9.22077e50i | −0.168539 | + | 1.56642i | ||||
\(471\) | 6.34795e49i | 0.103571i | ||||||||
\(472\) | −1.20211e50 | + | 3.60876e50i | −0.188385 | + | 0.565535i | ||||
\(473\) | −2.30716e50 | −0.347309 | ||||||||
\(474\) | 3.93159e50 | + | 4.23020e49i | 0.568564 | + | 0.0611747i | ||||
\(475\) | − | 2.00236e48i | − | 0.00278204i | ||||||
\(476\) | 1.36147e50 | − | 6.25357e50i | 0.181750 | − | 0.834826i | ||||
\(477\) | −3.27260e50 | −0.419801 | ||||||||
\(478\) | 6.30577e49 | − | 5.86064e50i | 0.0777334 | − | 0.722463i | ||||
\(479\) | 1.02379e51i | 1.21293i | 0.795111 | + | 0.606464i | \(0.207412\pi\) | ||||
−0.795111 | + | 0.606464i | \(0.792588\pi\) | |||||||
\(480\) | −5.70331e50 | + | 9.60332e50i | −0.649446 | + | 1.09355i | ||||
\(481\) | 6.38007e50 | 0.698343 | ||||||||
\(482\) | 7.05619e50 | + | 7.59211e49i | 0.742466 | + | 0.0798857i | ||||
\(483\) | − | 3.04668e51i | − | 3.08199i | ||||||
\(484\) | 6.02082e50 | + | 1.31080e50i | 0.585591 | + | 0.127489i | ||||
\(485\) | −1.80720e51 | −1.69010 | ||||||||
\(486\) | 1.30536e50 | − | 1.21321e51i | 0.117393 | − | 1.09106i | ||||
\(487\) | 1.04852e51i | 0.906828i | 0.891300 | + | 0.453414i | \(0.149794\pi\) | ||||
−0.891300 | + | 0.453414i | \(0.850206\pi\) | |||||||
\(488\) | −3.95288e50 | − | 1.31674e50i | −0.328804 | − | 0.109527i | ||||
\(489\) | −3.22529e50 | −0.258048 | ||||||||
\(490\) | 8.03558e50 | + | 8.64589e49i | 0.618432 | + | 0.0665402i | ||||
\(491\) | 1.72849e50i | 0.127973i | 0.997951 | + | 0.0639866i | \(0.0203815\pi\) | ||||
−0.997951 | + | 0.0639866i | \(0.979619\pi\) | |||||||
\(492\) | −5.65821e50 | + | 2.59896e51i | −0.403034 | + | 1.85124i | ||||
\(493\) | 1.59330e51 | 1.09196 | ||||||||
\(494\) | −4.89758e49 | + | 4.55186e50i | −0.0322976 | + | 0.300177i | ||||
\(495\) | − | 6.23169e50i | − | 0.395464i | ||||||
\(496\) | 1.16049e51 | − | 2.53889e51i | 0.708745 | − | 1.55057i | ||||
\(497\) | −1.92588e51 | −1.13203 | ||||||||
\(498\) | 2.16321e51 | + | 2.32751e50i | 1.22389 | + | 0.131684i | ||||
\(499\) | 1.00275e51i | 0.546111i | 0.961998 | + | 0.273056i | \(0.0880343\pi\) | ||||
−0.961998 | + | 0.273056i | \(0.911966\pi\) | |||||||
\(500\) | −1.86871e51 | − | 4.06838e50i | −0.979741 | − | 0.213300i | ||||
\(501\) | 3.23446e51 | 1.63262 | ||||||||
\(502\) | 2.04318e48 | − | 1.89896e49i | 0.000992971 | − | 0.00922878i | ||||
\(503\) | 2.34914e50i | 0.109930i | 0.998488 | + | 0.0549651i | \(0.0175047\pi\) | ||||
−0.998488 | + | 0.0549651i | \(0.982495\pi\) | |||||||
\(504\) | −5.59823e50 | + | 1.68060e51i | −0.252273 | + | 0.757329i | ||||
\(505\) | 2.87266e51 | 1.24666 | ||||||||
\(506\) | −2.85579e51 | − | 3.07269e50i | −1.19362 | − | 0.128428i | ||||
\(507\) | 2.07202e51i | 0.834149i | ||||||||
\(508\) | 2.48850e50 | − | 1.14303e51i | 0.0964998 | − | 0.443248i | ||||
\(509\) | 1.50917e50 | 0.0563768 | 0.0281884 | − | 0.999603i | \(-0.491026\pi\) | ||||
0.0281884 | + | 0.999603i | \(0.491026\pi\) | |||||||
\(510\) | 2.53493e50 | − | 2.35599e51i | 0.0912288 | − | 0.847890i | ||||
\(511\) | − | 2.07638e50i | − | 0.0719963i | ||||||
\(512\) | −1.70523e51 | − | 2.45991e51i | −0.569709 | − | 0.821847i | ||||
\(513\) | 7.59606e50 | 0.244545 | ||||||||
\(514\) | −3.97460e51 | − | 4.27648e50i | −1.23309 | − | 0.132674i | ||||
\(515\) | − | 1.64073e51i | − | 0.490569i | ||||||
\(516\) | 2.37257e51 | + | 5.16533e50i | 0.683713 | + | 0.148852i | ||||
\(517\) | 3.60009e51 | 0.999983 | ||||||||
\(518\) | −6.04485e50 | + | 5.61814e51i | −0.161853 | + | 1.50428i | ||||
\(519\) | − | 2.90193e51i | − | 0.749044i | ||||||
\(520\) | 2.23629e51 | + | 7.44927e50i | 0.556499 | + | 0.185375i | ||||
\(521\) | −1.62828e51 | −0.390673 | −0.195336 | − | 0.980736i | \(-0.562580\pi\) | ||||
−0.195336 | + | 0.980736i | \(0.562580\pi\) | |||||||
\(522\) | −4.38460e51 | − | 4.71761e50i | −1.01436 | − | 0.109140i | ||||
\(523\) | − | 4.95932e51i | − | 1.10634i | −0.833067 | − | 0.553172i | \(-0.813417\pi\) | ||
0.833067 | − | 0.553172i | \(-0.186583\pi\) | |||||||
\(524\) | −2.22388e50 | + | 1.02148e51i | −0.0478428 | + | 0.219754i | ||||
\(525\) | −4.24501e49 | −0.00880748 | ||||||||
\(526\) | −6.84670e50 | + | 6.36339e51i | −0.137010 | + | 1.27338i | ||||
\(527\) | 5.92234e51i | 1.14312i | ||||||||
\(528\) | 3.94339e51 | + | 1.80247e51i | 0.734218 | + | 0.335601i | ||||
\(529\) | −1.44578e52 | −2.59684 | ||||||||
\(530\) | −3.83463e51 | − | 4.12588e50i | −0.664481 | − | 0.0714949i | ||||
\(531\) | 2.23350e51i | 0.373414i | ||||||||
\(532\) | −3.96186e51 | − | 8.62540e50i | −0.639114 | − | 0.139142i | ||||
\(533\) | 5.61319e51 | 0.873761 | ||||||||
\(534\) | 3.76999e50 | − | 3.50387e51i | 0.0566313 | − | 0.526337i | ||||
\(535\) | 1.30284e51i | 0.188872i | ||||||||
\(536\) | 1.34690e51 | − | 4.04344e51i | 0.188454 | − | 0.565744i | ||||
\(537\) | 2.86422e51 | 0.386808 | ||||||||
\(538\) | 8.46974e50 | + | 9.11303e49i | 0.110410 | + | 0.0118795i | ||||
\(539\) | − | 3.13735e51i | − | 0.394800i | ||||||
\(540\) | 8.31957e50 | − | 3.82139e51i | 0.101069 | − | 0.464237i | ||||
\(541\) | −2.05605e51 | −0.241149 | −0.120574 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120574 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(542\) | 1.39933e51 | − | 1.30056e52i | 0.158466 | − | 1.47279i | ||||
\(543\) | 7.81134e51i | 0.854139i | ||||||||
\(544\) | 5.45981e51 | + | 3.24252e51i | 0.576499 | + | 0.342376i | ||||
\(545\) | 2.44205e51 | 0.249012 | ||||||||
\(546\) | 9.64998e51 | + | 1.03829e51i | 0.950312 | + | 0.102249i | ||||
\(547\) | − | 3.96530e51i | − | 0.377152i | −0.982059 | − | 0.188576i | \(-0.939613\pi\) | ||
0.982059 | − | 0.188576i | \(-0.0603873\pi\) | |||||||
\(548\) | 7.75703e51 | + | 1.68879e51i | 0.712631 | + | 0.155147i | ||||
\(549\) | −2.44648e51 | −0.217104 | ||||||||
\(550\) | −4.28124e48 | + | 3.97903e49i | −0.000367011 | + | 0.00341104i | ||||
\(551\) | − | 1.00942e52i | − | 0.835969i | ||||||
\(552\) | 2.86796e52 | + | 9.55342e51i | 2.29472 | + | 0.764392i | ||||
\(553\) | 7.39076e51 | 0.571362 | ||||||||
\(554\) | 1.17324e51 | + | 1.26235e50i | 0.0876399 | + | 0.00942962i | ||||
\(555\) | 2.09209e52i | 1.51013i | ||||||||
\(556\) | 3.40325e50 | − | 1.56320e51i | 0.0237396 | − | 0.109042i | ||||
\(557\) | −2.49633e52 | −1.68288 | −0.841441 | − | 0.540350i | \(-0.818292\pi\) | ||||
−0.841441 | + | 0.540350i | \(0.818292\pi\) | |||||||
\(558\) | 1.75354e51 | − | 1.62976e52i | 0.114253 | − | 1.06188i | ||||
\(559\) | − | 5.12423e51i | − | 0.322704i | ||||||
\(560\) | −8.67845e51 | + | 1.89865e52i | −0.528287 | + | 1.15577i | ||||
\(561\) | −9.19854e51 | −0.541283 | ||||||||
\(562\) | −3.09713e51 | − | 3.33236e50i | −0.176185 | − | 0.0189566i | ||||
\(563\) | − | 5.15392e51i | − | 0.283451i | −0.989906 | − | 0.141726i | \(-0.954735\pi\) | ||
0.989906 | − | 0.141726i | \(-0.0452650\pi\) | |||||||
\(564\) | −3.70215e52 | − | 8.05997e51i | −1.96857 | − | 0.428578i | ||||
\(565\) | 2.05878e52 | 1.05850 | ||||||||
\(566\) | −3.30755e51 | + | 3.07407e52i | −0.164435 | + | 1.52827i | ||||
\(567\) | − | 3.27077e52i | − | 1.57243i | ||||||
\(568\) | 6.03894e51 | − | 1.81290e52i | 0.280764 | − | 0.842862i | ||||
\(569\) | −2.78426e52 | −1.25192 | −0.625961 | − | 0.779855i | \(-0.715293\pi\) | ||||
−0.625961 | + | 0.779855i | \(0.715293\pi\) | |||||||
\(570\) | −1.49260e52 | − | 1.60597e51i | −0.649116 | − | 0.0698417i | ||||
\(571\) | 1.13401e52i | 0.477014i | 0.971141 | + | 0.238507i | \(0.0766579\pi\) | ||||
−0.971141 | + | 0.238507i | \(0.923342\pi\) | |||||||
\(572\) | 1.94647e51 | − | 8.94063e51i | 0.0791997 | − | 0.363784i | ||||
\(573\) | 6.48542e51 | 0.255270 | ||||||||
\(574\) | −5.31826e51 | + | 4.94285e52i | −0.202509 | + | 1.88214i | ||||
\(575\) | 2.79016e50i | 0.0102788i | ||||||||
\(576\) | −1.40647e52 | − | 1.05396e52i | −0.501307 | − | 0.375663i | ||||
\(577\) | 9.57231e51 | 0.330123 | 0.165062 | − | 0.986283i | \(-0.447218\pi\) | ||||
0.165062 | + | 0.986283i | \(0.447218\pi\) | |||||||
\(578\) | 1.63995e52 | + | 1.76450e51i | 0.547269 | + | 0.0588835i | ||||
\(579\) | 3.29938e52i | 1.06547i | ||||||||
\(580\) | −5.07813e52 | − | 1.10556e52i | −1.58698 | − | 0.345503i | ||||
\(581\) | 4.06649e52 | 1.22991 | ||||||||
\(582\) | 7.89845e51 | − | 7.34090e52i | 0.231209 | − | 2.14888i | ||||
\(583\) | 1.49717e52i | 0.424197i | ||||||||
\(584\) | 1.95458e51 | + | 6.51087e50i | 0.0536054 | + | 0.0178564i | ||||
\(585\) | 1.38407e52 | 0.367448 | ||||||||
\(586\) | 4.76788e52 | + | 5.13000e51i | 1.22538 | + | 0.131845i | ||||
\(587\) | 3.27860e52i | 0.815764i | 0.913035 | + | 0.407882i | \(0.133733\pi\) | ||||
−0.913035 | + | 0.407882i | \(0.866267\pi\) | |||||||
\(588\) | −7.02398e51 | + | 3.22629e52i | −0.169205 | + | 0.777204i | ||||
\(589\) | 3.75202e52 | 0.875134 | ||||||||
\(590\) | −2.81585e51 | + | 2.61708e52i | −0.0635948 | + | 0.591057i | ||||
\(591\) | − | 3.18111e52i | − | 0.695691i | ||||||
\(592\) | −5.09902e52 | − | 2.33069e52i | −1.07988 | − | 0.493597i | ||||
\(593\) | −1.87234e52 | −0.384013 | −0.192006 | − | 0.981394i | \(-0.561499\pi\) | ||||
−0.192006 | + | 0.981394i | \(0.561499\pi\) | |||||||
\(594\) | −1.50947e52 | − | 1.62412e51i | −0.299835 | − | 0.0322607i | ||||
\(595\) | − | 4.42888e52i | − | 0.852063i | ||||||
\(596\) | 2.44363e52 | + | 5.32004e51i | 0.455361 | + | 0.0991370i | ||||
\(597\) | 6.46291e52 | 1.16658 | ||||||||
\(598\) | 6.82449e51 | − | 6.34275e52i | 0.119329 | − | 1.10906i | ||||
\(599\) | − | 6.44824e52i | − | 1.09227i | −0.837696 | − | 0.546137i | \(-0.816098\pi\) | ||
0.837696 | − | 0.546137i | \(-0.183902\pi\) | |||||||
\(600\) | 1.33110e50 | − | 3.99599e50i | 0.00218442 | − | 0.00655768i | ||||
\(601\) | 8.37720e51 | 0.133194 | 0.0665969 | − | 0.997780i | \(-0.478786\pi\) | ||||
0.0665969 | + | 0.997780i | \(0.478786\pi\) | |||||||
\(602\) | 4.51228e52 | + | 4.85499e51i | 0.695125 | + | 0.0747920i | ||||
\(603\) | − | 2.50253e52i | − | 0.373552i | ||||||
\(604\) | −2.48866e52 | + | 1.14310e53i | −0.359968 | + | 1.65342i | ||||
\(605\) | 4.26405e52 | 0.597681 | ||||||||
\(606\) | −1.25551e52 | + | 1.16688e53i | −0.170545 | + | 1.58507i | ||||
\(607\) | 1.62298e52i | 0.213662i | 0.994277 | + | 0.106831i | \(0.0340704\pi\) | ||||
−0.994277 | + | 0.106831i | \(0.965930\pi\) | |||||||
\(608\) | 2.05425e52 | − | 3.45899e52i | 0.262112 | − | 0.441348i | ||||
\(609\) | −2.13997e53 | −2.64655 | ||||||||
\(610\) | −2.86664e52 | − | 3.08437e51i | −0.343642 | − | 0.0369742i | ||||
\(611\) | 7.99584e52i | 0.929140i | ||||||||
\(612\) | 3.64336e52 | + | 7.93199e51i | 0.410417 | + | 0.0893522i | ||||
\(613\) | 2.77165e52 | 0.302684 | 0.151342 | − | 0.988481i | \(-0.451641\pi\) | ||||
0.151342 | + | 0.988481i | \(0.451641\pi\) | |||||||
\(614\) | 1.43582e52 | − | 1.33447e53i | 0.152020 | − | 1.41289i | ||||
\(615\) | 1.84062e53i | 1.88946i | ||||||||
\(616\) | 7.68850e52 | + | 2.56111e52i | 0.765258 | + | 0.254914i | ||||
\(617\) | −3.43615e52 | −0.331630 | −0.165815 | − | 0.986157i | \(-0.553025\pi\) | ||||
−0.165815 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(618\) | 6.66471e52 | + | 7.17090e51i | 0.623735 | + | 0.0671108i | ||||
\(619\) | − | 1.85801e53i | − | 1.68627i | −0.537704 | − | 0.843134i | \(-0.680708\pi\) | ||
0.537704 | − | 0.843134i | \(-0.319292\pi\) | |||||||
\(620\) | 4.10939e52 | − | 1.88755e53i | 0.361689 | − | 1.66133i | ||||
\(621\) | −1.05847e53 | −0.903517 | ||||||||
\(622\) | 8.34187e51 | − | 7.75302e52i | 0.0690631 | − | 0.641880i | ||||
\(623\) | − | 6.58671e52i | − | 0.528927i | ||||||
\(624\) | −4.00330e52 | + | 8.75832e52i | −0.311825 | + | 0.682203i | ||||
\(625\) | −1.31628e53 | −0.994551 | ||||||||
\(626\) | 5.41360e51 | + | 5.82477e50i | 0.0396802 | + | 0.00426939i | ||||
\(627\) | 5.82761e52i | 0.414388i | ||||||||
\(628\) | −1.15026e52 | − | 2.50423e51i | −0.0793526 | − | 0.0172759i | ||||
\(629\) | 1.18942e53 | 0.796112 | ||||||||
\(630\) | −1.31135e52 | + | 1.21878e53i | −0.0851622 | + | 0.791506i | ||||
\(631\) | 2.72301e53i | 1.71590i | 0.513735 | + | 0.857949i | \(0.328261\pi\) | ||||
−0.513735 | + | 0.857949i | \(0.671739\pi\) | |||||||
\(632\) | −2.31750e52 | + | 6.95720e52i | −0.141708 | + | 0.425412i | ||||
\(633\) | −2.39549e53 | −1.42143 | ||||||||
\(634\) | −1.73358e53 | − | 1.86524e52i | −0.998267 | − | 0.107409i | ||||
\(635\) | − | 8.09513e52i | − | 0.452400i | ||||||
\(636\) | 3.35189e52 | − | 1.53961e53i | 0.181805 | − | 0.835075i | ||||
\(637\) | 6.96810e52 | 0.366830 | ||||||||
\(638\) | −2.15824e52 | + | 2.00589e53i | −0.110282 | + | 1.02498i | ||||
\(639\) | − | 1.12203e53i | − | 0.556529i | ||||||
\(640\) | −1.51514e53 | − | 1.41229e53i | −0.729513 | − | 0.679993i | ||||
\(641\) | 6.04692e52 | 0.282639 | 0.141319 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141319 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(642\) | −5.29217e52 | − | 5.69411e51i | −0.240142 | − | 0.0258381i | ||||
\(643\) | − | 5.90817e52i | − | 0.260282i | −0.991495 | − | 0.130141i | \(-0.958457\pi\) | ||
0.991495 | − | 0.130141i | \(-0.0415430\pi\) | |||||||
\(644\) | 5.52062e53 | + | 1.20190e53i | 2.36133 | + | 0.514086i | ||||
\(645\) | 1.68029e53 | 0.697830 | ||||||||
\(646\) | −9.13047e51 | + | 8.48595e52i | −0.0368193 | + | 0.342202i | ||||
\(647\) | 1.96965e53i | 0.771271i | 0.922651 | + | 0.385635i | \(0.126018\pi\) | ||||
−0.922651 | + | 0.385635i | \(0.873982\pi\) | |||||||
\(648\) | 3.07890e53 | + | 1.02561e53i | 1.17077 | + | 0.389992i | ||||
\(649\) | 1.02179e53 | 0.377324 | ||||||||
\(650\) | −8.83749e50 | − | 9.50870e49i | −0.00316938 | − | 0.000341010i | ||||
\(651\) | − | 7.95431e53i | − | 2.77053i | ||||||
\(652\) | 1.27236e52 | − | 5.84426e52i | 0.0430432 | − | 0.197708i | ||||
\(653\) | 5.40162e53 | 1.77490 | 0.887449 | − | 0.460906i | \(-0.152475\pi\) | ||||
0.887449 | + | 0.460906i | \(0.152475\pi\) | |||||||
\(654\) | −1.06731e52 | + | 9.91969e52i | −0.0340654 | + | 0.316607i | ||||
\(655\) | 7.23431e52i | 0.224291i | ||||||||
\(656\) | −4.48613e53 | − | 2.05055e53i | −1.35113 | − | 0.617585i | ||||
\(657\) | 1.20971e52 | 0.0353949 | ||||||||
\(658\) | −7.04096e53 | − | 7.57573e52i | −2.00143 | − | 0.215344i | ||||
\(659\) | 2.00451e53i | 0.553587i | 0.960929 | + | 0.276794i | \(0.0892718\pi\) | ||||
−0.960929 | + | 0.276794i | \(0.910728\pi\) | |||||||
\(660\) | 2.93173e53 | + | 6.38268e52i | 0.786664 | + | 0.171265i | ||||
\(661\) | 3.12269e53 | 0.814144 | 0.407072 | − | 0.913396i | \(-0.366550\pi\) | ||||
0.407072 | + | 0.913396i | \(0.366550\pi\) | |||||||
\(662\) | 7.57195e52 | − | 7.03745e53i | 0.191825 | − | 1.78284i | ||||
\(663\) | − | 2.04301e53i | − | 0.502937i | ||||||
\(664\) | −1.27512e53 | + | 3.82794e53i | −0.305040 | + | 0.915738i | ||||
\(665\) | −2.80586e53 | −0.652311 | ||||||||
\(666\) | −3.27316e53 | − | 3.52176e52i | −0.739532 | − | 0.0795701i | ||||
\(667\) | 1.40656e54i | 3.08865i | ||||||||
\(668\) | −1.27597e53 | + | 5.86087e53i | −0.272326 | + | 1.25086i | ||||
\(669\) | 5.40931e53 | 1.12214 | ||||||||
\(670\) | 3.15503e52 | − | 2.93232e53i | 0.0636183 | − | 0.591275i | ||||
\(671\) | 1.11923e53i | 0.219377i | ||||||||
\(672\) | −7.33308e53 | − | 4.35503e53i | −1.39724 | − | 0.829803i | ||||
\(673\) | −1.40702e53 | −0.260624 | −0.130312 | − | 0.991473i | \(-0.541598\pi\) | ||||
−0.130312 | + | 0.991473i | \(0.541598\pi\) | |||||||
\(674\) | 7.29837e53 | + | 7.85269e52i | 1.31428 | + | 0.141410i | ||||
\(675\) | 1.47478e51i | 0.00258200i | ||||||||
\(676\) | −3.75453e53 | − | 8.17401e52i | −0.639099 | − | 0.139139i | ||||
\(677\) | −9.24747e53 | −1.53052 | −0.765258 | − | 0.643723i | \(-0.777389\pi\) | ||||
−0.765258 | + | 0.643723i | \(0.777389\pi\) | |||||||
\(678\) | −8.99799e52 | + | 8.36283e53i | −0.144804 | + | 1.34583i | ||||
\(679\) | − | 1.37997e54i | − | 2.15946i | ||||||
\(680\) | 4.16907e53 | + | 1.38875e53i | 0.634410 | + | 0.211327i | ||||
\(681\) | −1.21495e54 | −1.79789 | ||||||||
\(682\) | −7.45592e53 | − | 8.02220e52i | −1.07300 | − | 0.115449i | ||||
\(683\) | − | 7.94333e53i | − | 1.11176i | −0.831264 | − | 0.555878i | \(-0.812382\pi\) | ||
0.831264 | − | 0.555878i | \(-0.187618\pi\) | |||||||
\(684\) | 5.02521e52 | − | 2.30821e53i | 0.0684050 | − | 0.314202i | ||||
\(685\) | 5.49366e53 | 0.727345 | ||||||||
\(686\) | 3.98332e52 | − | 3.70214e53i | 0.0512964 | − | 0.476754i | ||||
\(687\) | 1.23977e54i | 1.55297i | ||||||||
\(688\) | −1.87192e53 | + | 4.09534e53i | −0.228091 | + | 0.499011i | ||||
\(689\) | −3.32523e53 | −0.394145 | ||||||||
\(690\) | 2.07986e54 | + | 2.23782e53i | 2.39828 | + | 0.258043i | ||||
\(691\) | − | 5.60269e53i | − | 0.628512i | −0.949338 | − | 0.314256i | \(-0.898245\pi\) | ||
0.949338 | − | 0.314256i | \(-0.101755\pi\) | |||||||
\(692\) | 5.25833e53 | + | 1.14479e53i | 0.573894 | + | 0.124943i | ||||
\(693\) | 4.75851e53 | 0.505288 | ||||||||
\(694\) | −1.23649e53 | + | 1.14921e54i | −0.127750 | + | 1.18732i | ||||
\(695\) | − | 1.10708e53i | − | 0.111293i | ||||||
\(696\) | 6.71026e53 | − | 2.01444e54i | 0.656393 | − | 1.97051i | ||||
\(697\) | 1.04646e54 | 0.996089 | ||||||||
\(698\) | 1.02586e54 | + | 1.10377e53i | 0.950242 | + | 0.102241i | ||||
\(699\) | 4.87979e53i | 0.439880i | ||||||||
\(700\) | 1.67463e51 | − | 7.69200e51i | 0.00146912 | − | 0.00674802i | ||||
\(701\) | 3.82771e53 | 0.326811 | 0.163405 | − | 0.986559i | \(-0.447752\pi\) | ||||
0.163405 | + | 0.986559i | \(0.447752\pi\) | |||||||
\(702\) | 3.60718e52 | − | 3.35255e53i | 0.0299753 | − | 0.278593i | ||||
\(703\) | − | 7.53543e53i | − | 0.609477i | ||||||
\(704\) | −4.82173e53 | + | 6.43439e53i | −0.379597 | + | 0.506556i | ||||
\(705\) | −2.62192e54 | −2.00922 | ||||||||
\(706\) | 2.86850e53 | + | 3.08636e52i | 0.213976 | + | 0.0230228i | ||||
\(707\) | 2.19355e54i | 1.59287i | ||||||||
\(708\) | −1.05076e54 | − | 2.28762e53i | −0.742801 | − | 0.161716i | ||||
\(709\) | 2.39700e54 | 1.64964 | 0.824822 | − | 0.565392i | \(-0.191275\pi\) | ||||
0.824822 | + | 0.565392i | \(0.191275\pi\) | |||||||
\(710\) | 1.41458e53 | − | 1.31472e54i | 0.0947804 | − | 0.880899i | ||||
\(711\) | 4.30590e53i | 0.280893i | ||||||||
\(712\) | 6.20032e53 | + | 2.06538e53i | 0.393817 | + | 0.131184i | ||||
\(713\) | −5.22822e54 | −3.23335 | ||||||||
\(714\) | 1.79903e54 | + | 1.93567e53i | 1.08336 | + | 0.116564i | ||||
\(715\) | − | 6.33190e53i | − | 0.371295i | ||||||
\(716\) | −1.12992e53 | + | 5.19000e53i | −0.0645207 | + | 0.296360i | ||||
\(717\) | 1.66647e54 | 0.926690 | ||||||||
\(718\) | 1.47629e53 | − | 1.37208e54i | 0.0799481 | − | 0.743045i | ||||
\(719\) | − | 1.91513e54i | − | 1.01007i | −0.863100 | − | 0.505033i | \(-0.831480\pi\) | ||
0.863100 | − | 0.505033i | \(-0.168520\pi\) | |||||||
\(720\) | −1.10616e54 | − | 5.05612e53i | −0.568201 | − | 0.259717i | ||||
\(721\) | 1.25286e54 | 0.626805 | ||||||||
\(722\) | −1.50275e54 | − | 1.61688e53i | −0.732283 | − | 0.0787901i | ||||
\(723\) | 2.00642e54i | 0.952347i | ||||||||
\(724\) | −1.41542e54 | − | 3.08152e53i | −0.654415 | − | 0.142473i | ||||
\(725\) | 1.95979e52 | 0.00882649 | ||||||||
\(726\) | −1.86362e53 | + | 1.73207e54i | −0.0817641 | + | 0.759924i | ||||
\(727\) | − | 7.02587e53i | − | 0.300294i | −0.988664 | − | 0.150147i | \(-0.952025\pi\) | ||
0.988664 | − | 0.150147i | \(-0.0479747\pi\) | |||||||
\(728\) | −5.68825e53 | + | 1.70763e54i | −0.236855 | + | 0.711044i | ||||
\(729\) | 4.07890e53 | 0.165470 | ||||||||
\(730\) | 1.41747e53 | + | 1.52513e52i | 0.0560246 | + | 0.00602797i | ||||
\(731\) | − | 9.55301e53i | − | 0.367883i | ||||||
\(732\) | 2.50576e53 | − | 1.15096e54i | 0.0940219 | − | 0.431867i | ||||
\(733\) | 4.89872e54 | 1.79105 | 0.895524 | − | 0.445012i | \(-0.146801\pi\) | ||||
0.895524 | + | 0.445012i | \(0.146801\pi\) | |||||||
\(734\) | −2.62176e53 | + | 2.43669e54i | −0.0934046 | + | 0.868112i | ||||
\(735\) | 2.28492e54i | 0.793251i | ||||||||
\(736\) | −2.86248e54 | + | 4.81989e54i | −0.968421 | + | 1.63064i | ||||
\(737\) | −1.14487e54 | −0.377463 | ||||||||
\(738\) | −2.87973e54 | − | 3.09845e53i | −0.925297 | − | 0.0995574i | ||||
\(739\) | − | 5.19784e54i | − | 1.62772i | −0.581064 | − | 0.813858i | \(-0.697364\pi\) | ||
0.581064 | − | 0.813858i | \(-0.302636\pi\) | |||||||
\(740\) | −3.79089e54 | − | 8.25317e53i | −1.15701 | − | 0.251894i | ||||
\(741\) | −1.29432e54 | −0.385031 | ||||||||
\(742\) | 3.15051e53 | − | 2.92812e54i | 0.0913497 | − | 0.849013i | ||||
\(743\) | − | 3.61825e54i | − | 1.02261i | −0.859398 | − | 0.511307i | \(-0.829162\pi\) | ||
0.859398 | − | 0.511307i | \(-0.170838\pi\) | |||||||
\(744\) | 7.48769e54 | + | 2.49421e54i | 2.06282 | + | 0.687144i | ||||
\(745\) | 1.73062e54 | 0.464763 | ||||||||
\(746\) | −4.34644e54 | − | 4.67656e53i | −1.13788 | − | 0.122430i | ||||
\(747\) | 2.36916e54i | 0.604648i | ||||||||
\(748\) | 3.62877e53 | − | 1.66679e54i | 0.0902877 | − | 0.414715i | ||||
\(749\) | −9.94843e53 | −0.241324 | ||||||||
\(750\) | 5.78421e53 | − | 5.37590e54i | 0.136798 | − | 1.27142i | ||||
\(751\) | 6.21252e54i | 1.43255i | 0.697819 | + | 0.716274i | \(0.254154\pi\) | ||||
−0.697819 | + | 0.716274i | \(0.745846\pi\) | |||||||
\(752\) | 2.92095e54 | − | 6.39037e54i | 0.656727 | − | 1.43677i | ||||
\(753\) | 5.39968e52 | 0.0118376 | ||||||||
\(754\) | −4.45511e54 | − | 4.79348e53i | −0.952363 | − | 0.102470i | ||||
\(755\) | 8.09565e54i | 1.68756i | ||||||||
\(756\) | 2.91801e54 | + | 6.35281e53i | 0.593160 | + | 0.129137i | ||||
\(757\) | 9.25923e54 | 1.83549 | 0.917747 | − | 0.397165i | \(-0.130006\pi\) | ||||
0.917747 | + | 0.397165i | \(0.130006\pi\) | |||||||
\(758\) | −9.37631e53 | + | 8.71444e54i | −0.181266 | + | 1.68471i | ||||
\(759\) | − | 8.12043e54i | − | 1.53104i | ||||||
\(760\) | 8.79826e53 | − | 2.64126e54i | 0.161785 | − | 0.485683i | ||||
\(761\) | −4.61983e54 | −0.828548 | −0.414274 | − | 0.910152i | \(-0.635964\pi\) | ||||
−0.414274 | + | 0.910152i | \(0.635964\pi\) | |||||||
\(762\) | 3.28827e54 | + | 3.53802e53i | 0.575206 | + | 0.0618893i | ||||
\(763\) | 1.86474e54i | 0.318165i | ||||||||
\(764\) | −2.55846e53 | + | 1.17516e54i | −0.0425799 | + | 0.195580i | ||||
\(765\) | 2.58029e54 | 0.418891 | ||||||||
\(766\) | −4.69754e53 | + | 4.36594e54i | −0.0743916 | + | 0.691404i | ||||
\(767\) | 2.26942e54i | 0.350593i | ||||||||
\(768\) | 6.39897e54 | − | 5.53731e54i | 0.964378 | − | 0.834517i | ||||
\(769\) | 6.21880e54 | 0.914337 | 0.457168 | − | 0.889380i | \(-0.348864\pi\) | ||||
0.457168 | + | 0.889380i | \(0.348864\pi\) | |||||||
\(770\) | 5.57573e54 | + | 5.99921e53i | 0.799794 | + | 0.0860539i | ||||
\(771\) | − | 1.13018e55i | − | 1.58166i | ||||||
\(772\) | −5.97851e54 | − | 1.30159e54i | −0.816328 | − | 0.177723i | ||||
\(773\) | −9.51269e54 | −1.26734 | −0.633670 | − | 0.773604i | \(-0.718452\pi\) | ||||
−0.633670 | + | 0.773604i | \(0.718452\pi\) | |||||||
\(774\) | −2.82855e53 | + | 2.62888e54i | −0.0367693 | + | 0.341738i | ||||
\(775\) | 7.28458e52i | 0.00924001i | ||||||||
\(776\) | 1.29902e55 | + | 4.32715e54i | 1.60784 | + | 0.535586i | ||||
\(777\) | −1.59752e55 | −1.92951 | ||||||||
\(778\) | −3.87651e54 | − | 4.17093e53i | −0.456907 | − | 0.0491610i | ||||
\(779\) | − | 6.62968e54i | − | 0.762572i | ||||||
\(780\) | −1.41760e54 | + | 6.51141e54i | −0.159132 | + | 0.730933i | ||||
\(781\) | −5.13311e54 | −0.562356 | ||||||||
\(782\) | 1.27228e54 | − | 1.18247e55i | 0.136036 | − | 1.26433i | ||||
\(783\) | 7.43459e54i | 0.775861i | ||||||||
\(784\) | −5.56899e54 | − | 2.54551e54i | −0.567246 | − | 0.259280i | ||||
\(785\) | −8.14630e53 | −0.0809910 | ||||||||
\(786\) | −2.93860e54 | − | 3.16179e53i | −0.285176 | − | 0.0306835i | ||||
\(787\) | 1.00037e54i | 0.0947636i | 0.998877 | + | 0.0473818i | \(0.0150878\pi\) | ||||
−0.998877 | + | 0.0473818i | \(0.984912\pi\) | |||||||
\(788\) | 5.76420e54 | + | 1.25493e54i | 0.533017 | + | 0.116043i | ||||
\(789\) | −1.80943e55 | −1.63335 | ||||||||
\(790\) | −5.42859e53 | + | 5.04539e54i | −0.0478379 | + | 0.444611i | ||||
\(791\) | 1.57208e55i | 1.35245i | ||||||||
\(792\) | −1.49211e54 | + | 4.47936e54i | −0.125321 | + | 0.376217i | ||||
\(793\) | −2.48583e54 | −0.203836 | ||||||||
\(794\) | 5.02984e53 | + | 5.41186e52i | 0.0402684 | + | 0.00433269i | ||||
\(795\) | − | 1.09038e55i | − | 0.852317i | ||||||
\(796\) | −2.54958e54 | + | 1.17109e55i | −0.194590 | + | 0.893801i | ||||
\(797\) | −2.22747e54 | −0.165998 | −0.0829992 | − | 0.996550i | \(-0.526450\pi\) | ||||
−0.0829992 | + | 0.996550i | \(0.526450\pi\) | |||||||
\(798\) | 1.22631e54 | − | 1.13975e55i | 0.0892374 | − | 0.829382i | ||||
\(799\) | 1.49065e55i | 1.05922i | ||||||||
\(800\) | 6.71566e52 | + | 3.98835e52i | 0.00465992 | + | 0.00276748i | ||||
\(801\) | 3.83746e54 | 0.260031 | ||||||||
\(802\) | −1.73780e55 | − | 1.86979e54i | −1.14997 | − | 0.123731i | ||||
\(803\) | − | 5.53426e53i | − | 0.0357655i | ||||||
\(804\) | 1.17733e55 | + | 2.56317e54i | 0.743076 | + | 0.161775i | ||||
\(805\) | 3.90980e55 | 2.41008 | ||||||||
\(806\) | 1.78174e54 | − | 1.65597e55i | 0.107270 | − | 0.996981i | ||||
\(807\) | 2.40837e54i | 0.141620i | ||||||||
\(808\) | −2.06488e55 | − | 6.87828e54i | −1.18598 | − | 0.395061i | ||||
\(809\) | 5.36292e54 | 0.300870 | 0.150435 | − | 0.988620i | \(-0.451933\pi\) | ||||
0.150435 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(810\) | 2.23283e55 | + | 2.40241e54i | 1.22360 | + | 0.131653i | ||||
\(811\) | − | 2.26902e55i | − | 1.21463i | −0.794462 | − | 0.607314i | \(-0.792247\pi\) | ||
0.794462 | − | 0.607314i | \(-0.207753\pi\) | |||||||
\(812\) | 8.44205e54 | − | 3.87765e55i | 0.441452 | − | 2.02770i | ||||
\(813\) | 3.69812e55 | 1.88913 | ||||||||
\(814\) | −1.61115e54 | + | 1.49742e55i | −0.0804032 | + | 0.747276i | ||||
\(815\) | − | 4.13900e54i | − | 0.201790i | ||||||
\(816\) | −7.46328e54 | + | 1.63280e55i | −0.355481 | + | 0.777712i | ||||
\(817\) | −6.05218e54 | −0.281639 | ||||||||
\(818\) | 4.03951e55 | + | 4.34632e54i | 1.83661 | + | 0.197610i | ||||
\(819\) | 1.05687e55i | 0.469492i | ||||||||
\(820\) | −3.33523e55 | − | 7.26115e54i | −1.44765 | − | 0.315168i | ||||
\(821\) | −8.38021e54 | −0.355414 | −0.177707 | − | 0.984083i | \(-0.556868\pi\) | ||||
−0.177707 | + | 0.984083i | \(0.556868\pi\) | |||||||
\(822\) | −2.40103e54 | + | 2.23154e55i | −0.0995024 | + | 0.924785i | ||||
\(823\) | − | 3.09277e55i | − | 1.25242i | −0.779653 | − | 0.626212i | \(-0.784604\pi\) | ||
0.779653 | − | 0.626212i | \(-0.215396\pi\) | |||||||
\(824\) | −3.92856e54 | + | 1.17936e55i | −0.155459 | + | 0.466692i | ||||
\(825\) | −1.13144e53 | −0.00437527 | ||||||||
\(826\) | −1.99840e55 | − | 2.15018e54i | −0.755199 | − | 0.0812557i | ||||
\(827\) | 5.17202e54i | 0.191010i | 0.995429 | + | 0.0955048i | \(0.0304465\pi\) | ||||
−0.995429 | + | 0.0955048i | \(0.969553\pi\) | |||||||
\(828\) | −7.00233e54 | + | 3.21635e55i | −0.252735 | + | 1.16088i | ||||
\(829\) | 7.71739e53 | 0.0272229 | 0.0136114 | − | 0.999907i | \(-0.495667\pi\) | ||||
0.0136114 | + | 0.999907i | \(0.495667\pi\) | |||||||
\(830\) | −2.98688e54 | + | 2.77604e55i | −0.102975 | + | 0.957064i | ||||
\(831\) | 3.33611e54i | 0.112414i | ||||||||
\(832\) | −1.42909e55 | − | 1.07091e55i | −0.470669 | − | 0.352705i | ||||
\(833\) | 1.29905e55 | 0.418187 | ||||||||
\(834\) | 4.49702e54 | + | 4.83857e53i | 0.141504 | + | 0.0152252i | ||||
\(835\) | 4.15076e55i | 1.27669i | ||||||||
\(836\) | −1.05597e55 | − | 2.29896e54i | −0.317491 | − | 0.0691212i | ||||
\(837\) | −2.76345e55 | −0.812209 | ||||||||
\(838\) | 1.53405e54 | − | 1.42576e55i | 0.0440761 | − | 0.409648i | ||||
\(839\) | − | 5.50494e55i | − | 1.54624i | −0.634263 | − | 0.773118i | \(-0.718696\pi\) | ||
0.634263 | − | 0.773118i | \(-0.281304\pi\) | |||||||
\(840\) | −5.59949e55 | − | 1.86524e55i | −1.53759 | − | 0.512186i | ||||
\(841\) | 6.15462e55 | 1.65226 | ||||||||
\(842\) | −6.55476e54 | − | 7.05260e53i | −0.172039 | − | 0.0185106i | ||||
\(843\) | − | 8.80667e54i | − | 0.225989i | ||||||
\(844\) | 9.45006e54 | − | 4.34065e55i | 0.237098 | − | 1.08905i | ||||
\(845\) | −2.65902e55 | −0.652295 | ||||||||
\(846\) | 4.41366e54 | − | 4.10210e55i | 0.105867 | − | 0.983942i | ||||
\(847\) | 3.25602e55i | 0.763663i | ||||||||
\(848\) | 2.65756e55 | + | 1.21473e55i | 0.609483 | + | 0.278586i | ||||
\(849\) | −8.74110e55 | −1.96029 | ||||||||
\(850\) | −1.64756e53 | − | 1.77269e52i | −0.00361310 | − | 0.000388752i | ||||
\(851\) | 1.05002e56i | 2.25183i | ||||||||
\(852\) | 5.27864e55 | + | 1.14921e55i | 1.10706 | + | 0.241018i | ||||
\(853\) | −8.25808e53 | −0.0169374 | −0.00846872 | − | 0.999964i | \(-0.502696\pi\) | ||||
−0.00846872 | + | 0.999964i | \(0.502696\pi\) | |||||||
\(854\) | 2.35522e54 | − | 2.18896e55i | 0.0472423 | − | 0.439075i | ||||
\(855\) | − | 1.63471e55i | − | 0.320689i | ||||||
\(856\) | 3.11951e54 | − | 9.36483e54i | 0.0598528 | − | 0.179679i | ||||
\(857\) | 3.68402e55 | 0.691331 | 0.345666 | − | 0.938358i | \(-0.387653\pi\) | ||||
0.345666 | + | 0.938358i | \(0.387653\pi\) | |||||||
\(858\) | 2.57204e55 | + | 2.76739e54i | 0.472084 | + | 0.0507940i | ||||
\(859\) | − | 3.04325e55i | − | 0.546345i | −0.961965 | − | 0.273172i | \(-0.911927\pi\) | ||
0.961965 | − | 0.273172i | \(-0.0880730\pi\) | |||||||
\(860\) | −6.62864e54 | + | 3.04470e55i | −0.116400 | + | 0.534656i | ||||
\(861\) | −1.40550e56 | −2.41418 | ||||||||
\(862\) | −9.17193e54 | + | 8.52449e55i | −0.154107 | + | 1.43229i | ||||
\(863\) | − | 7.58901e55i | − | 1.24733i | −0.781693 | − | 0.623663i | \(-0.785644\pi\) | ||
0.781693 | − | 0.623663i | \(-0.214356\pi\) | |||||||
\(864\) | −1.51301e55 | + | 2.54763e55i | −0.243265 | + | 0.409614i | ||||
\(865\) | 3.72403e55 | 0.585744 | ||||||||
\(866\) | 6.99012e55 | + | 7.52103e54i | 1.07559 | + | 0.115728i | ||||
\(867\) | 4.66319e55i | 0.701972i | ||||||||
\(868\) | 1.44133e56 | + | 3.13792e55i | 2.12270 | + | 0.462134i | ||||
\(869\) | 1.96988e55 | 0.283834 | ||||||||
\(870\) | 1.57183e55 | − | 1.46088e56i | 0.221585 | − | 2.05943i | ||||
\(871\) | − | 2.54278e55i | − | 0.350722i | ||||||
\(872\) | −1.75535e55 | − | 5.84723e54i | −0.236892 | − | 0.0789109i | ||||
\(873\) | 8.03980e55 | 1.06163 | ||||||||
\(874\) | −7.49136e55 | − | 8.06034e54i | −0.967929 | − | 0.104144i | ||||
\(875\) | − | 1.01058e56i | − | 1.27767i | ||||||
\(876\) | −1.23902e54 | + | 5.69115e54i | −0.0153286 | + | 0.0704080i | ||||
\(877\) | −7.68908e55 | −0.930855 | −0.465427 | − | 0.885086i | \(-0.654099\pi\) | ||||
−0.465427 | + | 0.885086i | \(0.654099\pi\) | |||||||
\(878\) | −5.86797e54 | + | 5.45375e55i | −0.0695172 | + | 0.646100i | ||||
\(879\) | 1.35574e56i | 1.57177i | ||||||||
\(880\) | −2.31310e55 | + | 5.06053e55i | −0.262436 | + | 0.574150i | ||||
\(881\) | 5.04962e54 | 0.0560681 | 0.0280341 | − | 0.999607i | \(-0.491075\pi\) | ||||
0.0280341 | + | 0.999607i | \(0.491075\pi\) | |||||||
\(882\) | −3.57484e55 | − | 3.84635e54i | −0.388467 | − | 0.0417971i | ||||
\(883\) | − | 2.61388e55i | − | 0.277992i | −0.990293 | − | 0.138996i | \(-0.955612\pi\) | ||
0.990293 | − | 0.138996i | \(-0.0443875\pi\) | |||||||
\(884\) | 3.70195e55 | + | 8.05954e54i | 0.385334 | + | 0.0838914i | ||||
\(885\) | −7.44167e55 | −0.758138 | ||||||||
\(886\) | 2.61806e54 | − | 2.43325e55i | 0.0261059 | − | 0.242631i | ||||
\(887\) | − | 8.03525e55i | − | 0.784243i | −0.919913 | − | 0.392122i | \(-0.871741\pi\) | ||
0.919913 | − | 0.392122i | \(-0.128259\pi\) | |||||||
\(888\) | 5.00930e55 | − | 1.50380e56i | 0.478554 | − | 1.43663i | ||||
\(889\) | 6.18142e55 | 0.578036 | ||||||||
\(890\) | 4.49650e55 | + | 4.83801e54i | 0.411589 | + | 0.0442850i | ||||
\(891\) | − | 8.71769e55i | − | 0.781133i | ||||||
\(892\) | −2.13394e55 | + | 9.80172e55i | −0.187176 | + | 0.859746i | ||||
\(893\) | 9.44381e55 | 0.810904 | ||||||||
\(894\) | −7.56376e54 | + | 7.02983e55i | −0.0635806 | + | 0.590925i | ||||
\(895\) | 3.67564e55i | 0.302479i | ||||||||
\(896\) | 1.07842e56 | − | 1.15696e56i | 0.868833 | − | 0.932106i | ||||
\(897\) | 1.80356e56 | 1.42257 | ||||||||
\(898\) | −1.32848e56 | − | 1.42938e55i | −1.02590 | − | 0.110382i | ||||
\(899\) | 3.67227e56i | 2.77651i | ||||||||
\(900\) | 4.48140e53 | + | 9.75649e52i | 0.00331746 | + | 0.000722247i | ||||
\(901\) | −6.19915e55 | −0.449326 | ||||||||
\(902\) | −1.41749e55 | + | 1.31743e56i | −0.100600 | + | 0.934985i | ||||
\(903\) | 1.28307e56i | 0.891624i | ||||||||
\(904\) | −1.47986e56 | − | 4.92953e55i | −1.00698 | − | 0.335433i | ||||
\(905\) | −1.00243e56 | −0.667927 | ||||||||
\(906\) | −3.28848e56 | − | 3.53825e55i | −2.14565 | − | 0.230862i | ||||
\(907\) | − | 2.22949e56i | − | 1.42452i | −0.701918 | − | 0.712258i | \(-0.747673\pi\) | ||
0.701918 | − | 0.712258i | \(-0.252327\pi\) | |||||||
\(908\) | 4.79291e55 | − | 2.20150e56i | 0.299894 | − | 1.37749i | ||||
\(909\) | −1.27798e56 | −0.783086 | ||||||||
\(910\) | −1.33243e55 | + | 1.23838e56i | −0.0799575 | + | 0.743133i | ||||
\(911\) | − | 1.13569e56i | − | 0.667440i | −0.942672 | − | 0.333720i | \(-0.891696\pi\) | ||
0.942672 | − | 0.333720i | \(-0.108304\pi\) | |||||||
\(912\) | 1.03444e56 | + | 4.72826e55i | 0.595390 | + | 0.272145i | ||||
\(913\) | 1.08385e56 | 0.610979 | ||||||||
\(914\) | −2.90850e56 | − | 3.12940e55i | −1.60580 | − | 0.172776i | ||||
\(915\) | − | 8.15129e55i | − | 0.440784i | ||||||
\(916\) | −2.24647e56 | − | 4.89080e55i | −1.18983 | − | 0.259040i | ||||
\(917\) | −5.52411e55 | −0.286579 | ||||||||
\(918\) | 6.72480e54 | − | 6.25010e55i | 0.0341719 | − | 0.317597i | ||||
\(919\) | − | 5.09000e55i | − | 0.253351i | −0.991944 | − | 0.126676i | \(-0.959569\pi\) | ||
0.991944 | − | 0.126676i | \(-0.0404307\pi\) | |||||||
\(920\) | −1.22599e56 | + | 3.68044e56i | −0.597746 | + | 1.79445i | ||||
\(921\) | 3.79456e56 | 1.81229 | ||||||||
\(922\) | 2.13531e56 | + | 2.29749e55i | 0.999018 | + | 0.107489i | ||||
\(923\) | − | 1.14007e56i | − | 0.522516i | ||||||
\(924\) | −4.87380e55 | + | 2.23866e56i | −0.218827 | + | 1.00513i | ||||
\(925\) | 1.46301e54 | 0.00643510 | ||||||||
\(926\) | 1.59609e55 | − | 1.48343e56i | 0.0687780 | − | 0.639230i | ||||
\(927\) | 7.29923e55i | 0.308150i | ||||||||
\(928\) | 3.38546e56 | + | 2.01059e56i | 1.40025 | + | 0.831594i | ||||
\(929\) | −3.46567e55 | −0.140439 | −0.0702197 | − | 0.997532i | \(-0.522370\pi\) | ||||
−0.0702197 | + | 0.997532i | \(0.522370\pi\) | |||||||
\(930\) | 5.43010e56 | + | 5.84252e55i | 2.15592 | + | 0.231966i | ||||
\(931\) | − | 8.22996e55i | − | 0.320150i | ||||||
\(932\) | −8.84223e55 | − | 1.92505e55i | −0.337023 | − | 0.0733734i | ||||
\(933\) | 2.20457e56 | 0.823327 | ||||||||
\(934\) | 2.95655e55 | − | 2.74785e56i | 0.108192 | − | 1.00555i | ||||
\(935\) | − | 1.18044e56i | − | 0.423277i | ||||||
\(936\) | −9.94873e55 | − | 3.31401e55i | −0.349564 | − | 0.116443i | ||||
\(937\) | −6.42395e55 | −0.221182 | −0.110591 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110591 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(938\) | 2.23911e56 | + | 2.40918e55i | 0.755478 | + | 0.0812858i | ||||
\(939\) | 1.53936e55i | 0.0508971i | ||||||||
\(940\) | 1.03433e56 | − | 4.75095e56i | 0.335143 | − | 1.53940i | ||||
\(941\) | −5.20051e56 | −1.65136 | −0.825682 | − | 0.564135i | \(-0.809210\pi\) | ||||
−0.825682 | + | 0.564135i | \(0.809210\pi\) | |||||||
\(942\) | 3.56038e54 | − | 3.30906e55i | 0.0110797 | − | 0.102976i | ||||
\(943\) | 9.23807e56i | 2.81747i | ||||||||
\(944\) | 8.29038e55 | − | 1.81375e56i | 0.247803 | − | 0.542137i | ||||
\(945\) | 2.06658e56 | 0.605407 | ||||||||
\(946\) | 1.20267e56 | + | 1.29402e55i | 0.345316 | + | 0.0371543i | ||||
\(947\) | − | 2.24906e56i | − | 0.632923i | −0.948605 | − | 0.316462i | \(-0.897505\pi\) | ||
0.948605 | − | 0.316462i | \(-0.102495\pi\) | |||||||
\(948\) | −2.02573e56 | − | 4.41023e55i | −0.558757 | − | 0.121647i | ||||
\(949\) | 1.22917e55 | 0.0332317 | ||||||||
\(950\) | −1.12306e53 | + | 1.04379e54i | −0.000297616 | + | 0.00276607i | ||||
\(951\) | − | 4.92942e56i | − | 1.28046i | ||||||
\(952\) | −1.06045e56 | + | 3.18349e56i | −0.270015 | + | 0.810592i | ||||
\(953\) | 2.70444e56 | 0.675012 | 0.337506 | − | 0.941323i | \(-0.390417\pi\) | ||||
0.337506 | + | 0.941323i | \(0.390417\pi\) | |||||||
\(954\) | 1.70594e56 | + | 1.83551e55i | 0.417392 | + | 0.0449093i | ||||
\(955\) | 8.32271e55i | 0.199618i | ||||||||
\(956\) | −6.57413e55 | + | 3.01967e56i | −0.154575 | + | 0.710001i | ||||
\(957\) | −5.70374e56 | −1.31472 | ||||||||
\(958\) | 5.74212e55 | − | 5.33679e56i | 0.129756 | − | 1.20597i | ||||
\(959\) | 4.19495e56i | 0.929336i | ||||||||
\(960\) | 3.51164e56 | − | 4.68613e56i | 0.762704 | − | 1.01780i | ||||
\(961\) | −8.95369e56 | −1.90659 | ||||||||
\(962\) | −3.32580e56 | − | 3.57839e55i | −0.694336 | − | 0.0747071i | ||||
\(963\) | − | 5.79601e55i | − | 0.118640i | ||||||
\(964\) | −3.63566e56 | − | 7.91522e55i | −0.729659 | − | 0.158854i | ||||
\(965\) | −4.23408e56 | −0.833183 | ||||||||
\(966\) | −1.70880e56 | + | 1.58817e57i | −0.329705 | + | 3.06431i | ||||
\(967\) | − | 6.06480e56i | − | 1.14740i | −0.819066 | − | 0.573699i | \(-0.805508\pi\) | ||
0.819066 | − | 0.573699i | \(-0.194492\pi\) | |||||||
\(968\) | −3.06501e56 | − | 1.02098e56i | −0.568592 | − | 0.189403i | ||||
\(969\) | −2.41298e56 | −0.438936 | ||||||||
\(970\) | 9.42055e56 | + | 1.01360e56i | 1.68040 | + | 0.180803i | ||||
\(971\) | 8.08233e56i | 1.41375i | 0.707340 | + | 0.706873i | \(0.249895\pi\) | ||||
−0.707340 | + | 0.706873i | \(0.750105\pi\) | |||||||
\(972\) | −1.36091e56 | + | 6.25102e56i | −0.233438 | + | 1.07224i | ||||
\(973\) | 8.45367e55 | 0.142201 | ||||||||
\(974\) | 5.88082e55 | − | 5.46570e56i | 0.0970103 | − | 0.901624i | ||||
\(975\) | − | 2.51294e54i | − | 0.00406531i | ||||||
\(976\) | 1.98670e56 | + | 9.08093e55i | 0.315200 | + | 0.144073i | ||||
\(977\) | 5.76887e56 | 0.897623 | 0.448811 | − | 0.893627i | \(-0.351848\pi\) | ||||
0.448811 | + | 0.893627i | \(0.351848\pi\) | |||||||
\(978\) | 1.68128e56 | + | 1.80897e55i | 0.256567 | + | 0.0276054i | ||||
\(979\) | − | 1.75558e56i | − | 0.262754i | ||||||
\(980\) | −4.14029e56 | − | 9.01385e55i | −0.607764 | − | 0.132317i | ||||
\(981\) | −1.08641e56 | −0.156417 | ||||||||
\(982\) | 9.69460e54 | − | 9.01026e55i | 0.0136903 | − | 0.127239i | ||||
\(983\) | − | 5.52329e56i | − | 0.765034i | −0.923948 | − | 0.382517i | \(-0.875057\pi\) | ||
0.923948 | − | 0.382517i | \(-0.124943\pi\) | |||||||
\(984\) | 4.40719e56 | − | 1.32305e57i | 0.598762 | − | 1.79750i | ||||
\(985\) | 4.08230e56 | 0.544023 | ||||||||
\(986\) | −8.30557e56 | − | 8.93639e55i | −1.08570 | − | 0.116816i | ||||
\(987\) | − | 2.00209e57i | − | 2.56719i | ||||||
\(988\) | 5.10602e55 | − | 2.34532e56i | 0.0642244 | − | 0.294999i | ||||
\(989\) | 8.43335e56 | 1.04057 | ||||||||
\(990\) | −3.49518e55 | + | 3.24845e56i | −0.0423058 | + | 0.393195i | ||||
\(991\) | 1.19721e57i | 1.42158i | 0.703406 | + | 0.710788i | \(0.251662\pi\) | ||||
−0.703406 | + | 0.710788i | \(0.748338\pi\) | |||||||
\(992\) | −7.47339e56 | + | 1.25838e57i | −0.870554 | + | 1.46585i | ||||
\(993\) | 2.00110e57 | 2.28682 | ||||||||
\(994\) | 1.00392e57 | + | 1.08017e56i | 1.12553 | + | 0.121102i | ||||
\(995\) | 8.29383e56i | 0.912255i | ||||||||
\(996\) | −1.11458e57 | − | 2.42656e56i | −1.20277 | − | 0.261857i | ||||
\(997\) | −1.00088e57 | −1.05968 | −0.529841 | − | 0.848097i | \(-0.677749\pi\) | ||||
−0.529841 | + | 0.848097i | \(0.677749\pi\) | |||||||
\(998\) | 5.62412e55 | − | 5.22711e56i | 0.0584217 | − | 0.542977i | ||||
\(999\) | 5.55002e56i | 0.565654i |
(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 | 4.39.b.a.3.1 | ✓ | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4.39.b.a.3.2 | yes | 18 | 4.3 | odd | 2 | inner |