Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,37,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 37, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(24.6273775978\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 1732091138 x^{8} + \cdots + 87\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{71}\cdot 5^{4}\cdot 7^{2}\cdot 13 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(-10236.4i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.37.b.b.2.7 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 184256.i | − | 0.702881i | −0.936210 | − | 0.351441i | \(-0.885692\pi\) | ||
0.936210 | − | 0.351441i | \(-0.114308\pi\) | |||||||
\(3\) | 7.73223e7 | + | 3.79626e8i | 0.199582 | + | 0.979881i | ||||
\(4\) | 3.47692e10 | 0.505958 | ||||||||
\(5\) | − | 1.78906e12i | − | 0.468991i | −0.972117 | − | 0.234495i | \(-0.924656\pi\) | ||
0.972117 | − | 0.234495i | \(-0.0753438\pi\) | |||||||
\(6\) | 6.99484e13 | − | 1.42471e13i | 0.688740 | − | 0.140283i | ||||
\(7\) | −1.12077e15 | −0.688258 | −0.344129 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344129 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(8\) | − | 1.90684e16i | − | 1.05851i | ||||||
\(9\) | −1.38137e17 | + | 5.87071e16i | −0.920334 | + | 0.391134i | ||||
\(10\) | −3.29645e17 | −0.329645 | ||||||||
\(11\) | − | 3.23174e18i | − | 0.581256i | −0.956836 | − | 0.290628i | \(-0.906136\pi\) | ||
0.956836 | − | 0.290628i | \(-0.0938643\pi\) | |||||||
\(12\) | 2.68843e18 | + | 1.31993e19i | 0.100980 | + | 0.495779i | ||||
\(13\) | 1.98159e20 | 1.76211 | 0.881054 | − | 0.473016i | \(-0.156835\pi\) | ||||
0.881054 | + | 0.473016i | \(0.156835\pi\) | |||||||
\(14\) | 2.06509e20i | 0.483764i | ||||||||
\(15\) | 6.79173e20 | − | 1.38334e20i | 0.459555 | − | 0.0936023i | ||||
\(16\) | −1.12415e21 | −0.238048 | ||||||||
\(17\) | − | 9.74924e21i | − | 0.693251i | −0.938004 | − | 0.346625i | \(-0.887328\pi\) | ||
0.938004 | − | 0.346625i | \(-0.112672\pi\) | |||||||
\(18\) | 1.08171e22 | + | 2.54526e22i | 0.274921 | + | 0.646885i | ||||
\(19\) | −4.96441e22 | −0.476764 | −0.238382 | − | 0.971171i | \(-0.576617\pi\) | ||||
−0.238382 | + | 0.971171i | \(0.576617\pi\) | |||||||
\(20\) | − | 6.22041e22i | − | 0.237290i | ||||||
\(21\) | −8.66605e22 | − | 4.25473e23i | −0.137364 | − | 0.674411i | ||||
\(22\) | −5.95467e23 | −0.408554 | ||||||||
\(23\) | − | 1.29913e24i | − | 0.400453i | −0.979750 | − | 0.200227i | \(-0.935832\pi\) | ||
0.979750 | − | 0.200227i | \(-0.0641678\pi\) | |||||||
\(24\) | 7.23886e24 | − | 1.47441e24i | 1.03721 | − | 0.211260i | ||||
\(25\) | 1.13512e25 | 0.780048 | ||||||||
\(26\) | − | 3.65119e25i | − | 1.23855i | ||||||
\(27\) | −3.29678e25 | − | 4.79011e25i | −0.566947 | − | 0.823754i | ||||
\(28\) | −3.89682e25 | −0.348230 | ||||||||
\(29\) | − | 3.60149e26i | − | 1.71127i | −0.517579 | − | 0.855635i | \(-0.673167\pi\) | ||
0.517579 | − | 0.855635i | \(-0.326833\pi\) | |||||||
\(30\) | −2.54889e25 | − | 1.25142e26i | −0.0657913 | − | 0.323013i | ||||
\(31\) | 7.63484e26 | 1.09217 | 0.546084 | − | 0.837730i | \(-0.316118\pi\) | ||||
0.546084 | + | 0.837730i | \(0.316118\pi\) | |||||||
\(32\) | − | 1.10324e27i | − | 0.891190i | ||||||
\(33\) | 1.22685e27 | − | 2.49885e26i | 0.569562 | − | 0.116009i | ||||
\(34\) | −1.79636e27 | −0.487273 | ||||||||
\(35\) | 2.00512e27i | 0.322787i | ||||||||
\(36\) | −4.80292e27 | + | 2.04120e27i | −0.465650 | + | 0.197897i | ||||
\(37\) | −3.30211e27 | −0.195506 | −0.0977530 | − | 0.995211i | \(-0.531166\pi\) | ||||
−0.0977530 | + | 0.995211i | \(0.531166\pi\) | |||||||
\(38\) | 9.14724e27i | 0.335108i | ||||||||
\(39\) | 1.53221e28 | + | 7.52261e28i | 0.351686 | + | 1.72666i | ||||
\(40\) | −3.41145e28 | −0.496431 | ||||||||
\(41\) | 1.75258e28i | 0.163519i | 0.996652 | + | 0.0817595i | \(0.0260539\pi\) | ||||
−0.996652 | + | 0.0817595i | \(0.973946\pi\) | |||||||
\(42\) | −7.83960e28 | + | 1.59677e28i | −0.474031 | + | 0.0965508i | ||||
\(43\) | 2.19776e29 | 0.870059 | 0.435030 | − | 0.900416i | \(-0.356738\pi\) | ||||
0.435030 | + | 0.900416i | \(0.356738\pi\) | |||||||
\(44\) | − | 1.12365e29i | − | 0.294091i | ||||||
\(45\) | 1.05030e29 | + | 2.47135e29i | 0.183438 | + | 0.431628i | ||||
\(46\) | −2.39373e29 | −0.281471 | ||||||||
\(47\) | − | 2.28804e30i | − | 1.82685i | −0.407010 | − | 0.913424i | \(-0.633429\pi\) | ||
0.407010 | − | 0.913424i | \(-0.366571\pi\) | |||||||
\(48\) | −8.69219e28 | − | 4.26757e29i | −0.0475102 | − | 0.233259i | ||||
\(49\) | −1.39561e30 | −0.526300 | ||||||||
\(50\) | − | 2.09153e30i | − | 0.548281i | ||||||
\(51\) | 3.70107e30 | − | 7.53834e29i | 0.679303 | − | 0.138361i | ||||
\(52\) | 6.88981e30 | 0.891553 | ||||||||
\(53\) | 8.49778e30i | 0.780440i | 0.920722 | + | 0.390220i | \(0.127601\pi\) | ||||
−0.920722 | + | 0.390220i | \(0.872399\pi\) | |||||||
\(54\) | −8.82606e30 | + | 6.07452e30i | −0.579001 | + | 0.398497i | ||||
\(55\) | −5.78176e30 | −0.272604 | ||||||||
\(56\) | 2.13713e31i | 0.728528i | ||||||||
\(57\) | −3.83860e30 | − | 1.88462e31i | −0.0951537 | − | 0.467172i | ||||
\(58\) | −6.63597e31 | −1.20282 | ||||||||
\(59\) | 1.12146e32i | 1.49433i | 0.664638 | + | 0.747166i | \(0.268586\pi\) | ||||
−0.664638 | + | 0.747166i | \(0.731414\pi\) | |||||||
\(60\) | 2.36143e31 | − | 4.80976e30i | 0.232516 | − | 0.0473589i | ||||
\(61\) | 1.74183e32 | 1.27371 | 0.636854 | − | 0.770985i | \(-0.280236\pi\) | ||||
0.636854 | + | 0.770985i | \(0.280236\pi\) | |||||||
\(62\) | − | 1.40677e32i | − | 0.767664i | ||||||
\(63\) | 1.54820e32 | − | 6.57972e31i | 0.633427 | − | 0.269201i | ||||
\(64\) | −2.80530e32 | −0.864449 | ||||||||
\(65\) | − | 3.54517e32i | − | 0.826412i | ||||||
\(66\) | −4.60429e31 | − | 2.26055e32i | −0.0815402 | − | 0.400334i | ||||
\(67\) | −2.93948e32 | −0.397123 | −0.198561 | − | 0.980088i | \(-0.563627\pi\) | ||||
−0.198561 | + | 0.980088i | \(0.563627\pi\) | |||||||
\(68\) | − | 3.38973e32i | − | 0.350756i | ||||||
\(69\) | 4.93184e32 | − | 1.00452e32i | 0.392397 | − | 0.0799234i | ||||
\(70\) | 3.69456e32 | 0.226881 | ||||||||
\(71\) | 3.75606e32i | 0.178683i | 0.996001 | + | 0.0893413i | \(0.0284762\pi\) | ||||
−0.996001 | + | 0.0893413i | \(0.971524\pi\) | |||||||
\(72\) | 1.11945e33 | + | 2.63406e33i | 0.414019 | + | 0.974182i | ||||
\(73\) | −2.87128e33 | −0.828446 | −0.414223 | − | 0.910175i | \(-0.635947\pi\) | ||||
−0.414223 | + | 0.910175i | \(0.635947\pi\) | |||||||
\(74\) | 6.08433e32i | 0.137417i | ||||||||
\(75\) | 8.77700e32 | + | 4.30921e33i | 0.155684 | + | 0.764354i | ||||
\(76\) | −1.72609e33 | −0.241223 | ||||||||
\(77\) | 3.62203e33i | 0.400055i | ||||||||
\(78\) | 1.38609e34 | − | 2.82319e33i | 1.21363 | − | 0.247193i | ||||
\(79\) | −2.55540e34 | −1.77898 | −0.889491 | − | 0.456953i | \(-0.848941\pi\) | ||||
−0.889491 | + | 0.456953i | \(0.848941\pi\) | |||||||
\(80\) | 2.01117e33i | 0.111642i | ||||||||
\(81\) | 1.56353e34 | − | 1.62193e34i | 0.694028 | − | 0.719948i | ||||
\(82\) | 3.22923e33 | 0.114934 | ||||||||
\(83\) | − | 2.12898e34i | − | 0.609209i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985243\pi\) | |||||||
\(84\) | −3.01311e33 | − | 1.47934e34i | −0.0695006 | − | 0.341224i | ||||
\(85\) | −1.74420e34 | −0.325128 | ||||||||
\(86\) | − | 4.04951e34i | − | 0.611548i | ||||||
\(87\) | 1.36722e35 | − | 2.78476e34i | 1.67684 | − | 0.341540i | ||||
\(88\) | −6.16241e34 | −0.615265 | ||||||||
\(89\) | 1.66287e35i | 1.35468i | 0.735670 | + | 0.677340i | \(0.236867\pi\) | ||||
−0.735670 | + | 0.677340i | \(0.763133\pi\) | |||||||
\(90\) | 4.55362e34 | − | 1.93525e34i | 0.303383 | − | 0.128935i | ||||
\(91\) | −2.22090e35 | −1.21279 | ||||||||
\(92\) | − | 4.51697e34i | − | 0.202613i | ||||||
\(93\) | 5.90344e34 | + | 2.89838e35i | 0.217978 | + | 1.07019i | ||||
\(94\) | −4.21585e35 | −1.28406 | ||||||||
\(95\) | 8.88162e34i | 0.223598i | ||||||||
\(96\) | 4.18818e35 | − | 8.53051e34i | 0.873260 | − | 0.177866i | ||||
\(97\) | 3.09990e35 | 0.536360 | 0.268180 | − | 0.963369i | \(-0.413578\pi\) | ||||
0.268180 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(98\) | 2.57149e35i | 0.369926i | ||||||||
\(99\) | 1.89726e35 | + | 4.46423e35i | 0.227349 | + | 0.534950i | ||||
\(100\) | 3.94671e35 | 0.394671 | ||||||||
\(101\) | − | 1.10326e36i | − | 0.922347i | −0.887310 | − | 0.461174i | \(-0.847429\pi\) | ||
0.887310 | − | 0.461174i | \(-0.152571\pi\) | |||||||
\(102\) | −1.38899e35 | − | 6.81944e35i | −0.0972511 | − | 0.477469i | ||||
\(103\) | −1.74073e36 | −1.02249 | −0.511247 | − | 0.859434i | \(-0.670816\pi\) | ||||
−0.511247 | + | 0.859434i | \(0.670816\pi\) | |||||||
\(104\) | − | 3.77857e36i | − | 1.86521i | ||||||
\(105\) | −7.61196e35 | + | 1.55041e35i | −0.316293 | + | 0.0644226i | ||||
\(106\) | 1.56577e36 | 0.548557 | ||||||||
\(107\) | 4.62581e36i | 1.36861i | 0.729196 | + | 0.684305i | \(0.239894\pi\) | ||||
−0.729196 | + | 0.684305i | \(0.760106\pi\) | |||||||
\(108\) | −1.14626e36 | − | 1.66548e36i | −0.286852 | − | 0.416785i | ||||
\(109\) | 4.26215e36 | 0.903550 | 0.451775 | − | 0.892132i | \(-0.350791\pi\) | ||||
0.451775 | + | 0.892132i | \(0.350791\pi\) | |||||||
\(110\) | 1.06533e36i | 0.191608i | ||||||||
\(111\) | −2.55327e35 | − | 1.25357e36i | −0.0390196 | − | 0.191573i | ||||
\(112\) | 1.25991e36 | 0.163839 | ||||||||
\(113\) | 1.56660e37i | 1.73598i | 0.496578 | + | 0.867992i | \(0.334590\pi\) | ||||
−0.496578 | + | 0.867992i | \(0.665410\pi\) | |||||||
\(114\) | −3.47253e36 | + | 7.07285e35i | −0.328366 | + | 0.0668817i | ||||
\(115\) | −2.32422e36 | −0.187809 | ||||||||
\(116\) | − | 1.25221e37i | − | 0.865831i | ||||||
\(117\) | −2.73731e37 | + | 1.16333e37i | −1.62173 | + | 0.689220i | ||||
\(118\) | 2.06636e37 | 1.05034 | ||||||||
\(119\) | 1.09267e37i | 0.477136i | ||||||||
\(120\) | −2.63781e36 | − | 1.29507e37i | −0.0990789 | − | 0.486443i | ||||
\(121\) | 2.04686e37 | 0.662141 | ||||||||
\(122\) | − | 3.20943e37i | − | 0.895265i | ||||||
\(123\) | −6.65325e36 | + | 1.35513e36i | −0.160229 | + | 0.0326355i | ||||
\(124\) | 2.65457e37 | 0.552591 | ||||||||
\(125\) | − | 4.63421e37i | − | 0.834826i | ||||||
\(126\) | −1.21235e37 | − | 2.85265e37i | −0.189217 | − | 0.445224i | ||||
\(127\) | 1.49422e36 | 0.0202277 | 0.0101138 | − | 0.999949i | \(-0.496781\pi\) | ||||
0.0101138 | + | 0.999949i | \(0.496781\pi\) | |||||||
\(128\) | − | 2.41248e37i | − | 0.283585i | ||||||
\(129\) | 1.69936e37 | + | 8.34328e37i | 0.173649 | + | 0.852554i | ||||
\(130\) | −6.53219e37 | −0.580869 | ||||||||
\(131\) | 3.94725e37i | 0.305781i | 0.988243 | + | 0.152891i | \(0.0488582\pi\) | ||||
−0.988243 | + | 0.152891i | \(0.951142\pi\) | |||||||
\(132\) | 4.26566e37 | − | 8.68831e36i | 0.288175 | − | 0.0586955i | ||||
\(133\) | 5.56396e37 | 0.328137 | ||||||||
\(134\) | 5.41618e37i | 0.279130i | ||||||||
\(135\) | −8.56978e37 | + | 5.89814e37i | −0.386333 | + | 0.265893i | ||||
\(136\) | −1.85903e38 | −0.733813 | ||||||||
\(137\) | 4.00656e38i | 1.38612i | 0.720878 | + | 0.693062i | \(0.243739\pi\) | ||||
−0.720878 | + | 0.693062i | \(0.756261\pi\) | |||||||
\(138\) | −1.85089e37 | − | 9.08721e37i | −0.0561767 | − | 0.275808i | ||||
\(139\) | −1.96149e38 | −0.522781 | −0.261390 | − | 0.965233i | \(-0.584181\pi\) | ||||
−0.261390 | + | 0.965233i | \(0.584181\pi\) | |||||||
\(140\) | 6.97164e37i | 0.163317i | ||||||||
\(141\) | 8.68600e38 | − | 1.76917e38i | 1.79009 | − | 0.364607i | ||||
\(142\) | 6.92077e37 | 0.125593 | ||||||||
\(143\) | − | 6.40396e38i | − | 1.02424i | ||||||
\(144\) | 1.55287e38 | − | 6.59957e37i | 0.219084 | − | 0.0931088i | ||||
\(145\) | −6.44328e38 | −0.802570 | ||||||||
\(146\) | 5.29051e38i | 0.582299i | ||||||||
\(147\) | −1.07912e38 | − | 5.29809e38i | −0.105040 | − | 0.515712i | ||||
\(148\) | −1.14812e38 | −0.0989178 | ||||||||
\(149\) | − | 2.06248e39i | − | 1.57412i | −0.616878 | − | 0.787059i | \(-0.711603\pi\) | ||
0.616878 | − | 0.787059i | \(-0.288397\pi\) | |||||||
\(150\) | 7.93997e38 | − | 1.61722e38i | 0.537250 | − | 0.109427i | ||||
\(151\) | −1.90467e39 | −1.14350 | −0.571749 | − | 0.820428i | \(-0.693735\pi\) | ||||
−0.571749 | + | 0.820428i | \(0.693735\pi\) | |||||||
\(152\) | 9.46635e38i | 0.504659i | ||||||||
\(153\) | 5.72350e38 | + | 1.34673e39i | 0.271154 | + | 0.638022i | ||||
\(154\) | 6.67381e38 | 0.281191 | ||||||||
\(155\) | − | 1.36592e39i | − | 0.512217i | ||||||
\(156\) | 5.32736e38 | + | 2.61555e39i | 0.177938 | + | 0.873616i | ||||
\(157\) | 4.18282e39 | 1.24530 | 0.622651 | − | 0.782499i | \(-0.286055\pi\) | ||||
0.622651 | + | 0.782499i | \(0.286055\pi\) | |||||||
\(158\) | 4.70848e39i | 1.25041i | ||||||||
\(159\) | −3.22598e39 | + | 6.57068e38i | −0.764739 | + | 0.155762i | ||||
\(160\) | −1.97376e39 | −0.417960 | ||||||||
\(161\) | 1.45603e39i | 0.275615i | ||||||||
\(162\) | −2.98850e39 | − | 2.88091e39i | −0.506038 | − | 0.487819i | ||||
\(163\) | −8.81419e38 | −0.133600 | −0.0667999 | − | 0.997766i | \(-0.521279\pi\) | ||||
−0.0667999 | + | 0.997766i | \(0.521279\pi\) | |||||||
\(164\) | 6.09357e38i | 0.0827338i | ||||||||
\(165\) | −4.47059e38 | − | 2.19491e39i | −0.0544069 | − | 0.267119i | ||||
\(166\) | −3.92278e39 | −0.428201 | ||||||||
\(167\) | − | 1.25263e40i | − | 1.22723i | −0.789604 | − | 0.613617i | \(-0.789714\pi\) | ||
0.789604 | − | 0.613617i | \(-0.210286\pi\) | |||||||
\(168\) | −8.11310e39 | + | 1.65248e39i | −0.713871 | + | 0.145401i | ||||
\(169\) | 2.66206e40 | 2.10502 | ||||||||
\(170\) | 3.21379e39i | 0.228526i | ||||||||
\(171\) | 6.85770e39 | − | 2.91447e39i | 0.438782 | − | 0.186479i | ||||
\(172\) | 7.64144e39 | 0.440214 | ||||||||
\(173\) | 1.13842e39i | 0.0590842i | 0.999564 | + | 0.0295421i | \(0.00940491\pi\) | ||||
−0.999564 | + | 0.0295421i | \(0.990595\pi\) | |||||||
\(174\) | −5.13109e39 | − | 2.51919e40i | −0.240062 | − | 1.17862i | ||||
\(175\) | −1.27221e40 | −0.536874 | ||||||||
\(176\) | 3.63296e39i | 0.138367i | ||||||||
\(177\) | −4.25735e40 | + | 8.67138e39i | −1.46427 | + | 0.298242i | ||||
\(178\) | 3.06393e40 | 0.952179 | ||||||||
\(179\) | − | 7.98758e38i | − | 0.0224420i | −0.999937 | − | 0.0112210i | \(-0.996428\pi\) | ||
0.999937 | − | 0.0112210i | \(-0.00357182\pi\) | |||||||
\(180\) | 3.65182e39 | + | 8.59269e39i | 0.0928121 | + | 0.218386i | ||||
\(181\) | −2.00135e40 | −0.460372 | −0.230186 | − | 0.973147i | \(-0.573933\pi\) | ||||
−0.230186 | + | 0.973147i | \(0.573933\pi\) | |||||||
\(182\) | 4.09214e40i | 0.852444i | ||||||||
\(183\) | 1.34683e40 | + | 6.61245e40i | 0.254210 | + | 1.24808i | ||||
\(184\) | −2.47724e40 | −0.423884 | ||||||||
\(185\) | 5.90766e39i | 0.0916905i | ||||||||
\(186\) | 5.34045e40 | − | 1.08774e40i | 0.752220 | − | 0.153212i | ||||
\(187\) | −3.15070e40 | −0.402956 | ||||||||
\(188\) | − | 7.95533e40i | − | 0.924308i | ||||||
\(189\) | 3.69493e40 | + | 5.36861e40i | 0.390206 | + | 0.566956i | ||||
\(190\) | 1.63649e40 | 0.157163 | ||||||||
\(191\) | 7.86625e39i | 0.0687333i | 0.999409 | + | 0.0343666i | \(0.0109414\pi\) | ||||
−0.999409 | + | 0.0343666i | \(0.989059\pi\) | |||||||
\(192\) | −2.16912e40 | − | 1.06496e41i | −0.172529 | − | 0.847057i | ||||
\(193\) | −8.42492e40 | −0.610287 | −0.305143 | − | 0.952306i | \(-0.598704\pi\) | ||||
−0.305143 | + | 0.952306i | \(0.598704\pi\) | |||||||
\(194\) | − | 5.71175e40i | − | 0.376997i | ||||||
\(195\) | 1.34584e41 | − | 2.74121e40i | 0.809786 | − | 0.164937i | ||||
\(196\) | −4.85241e40 | −0.266286 | ||||||||
\(197\) | − | 2.05769e40i | − | 0.103036i | −0.998672 | − | 0.0515180i | \(-0.983594\pi\) | ||
0.998672 | − | 0.0515180i | \(-0.0164059\pi\) | |||||||
\(198\) | 8.22561e40 | − | 3.49582e40i | 0.376006 | − | 0.159799i | ||||
\(199\) | −2.79071e40 | −0.116509 | −0.0582544 | − | 0.998302i | \(-0.518553\pi\) | ||||
−0.0582544 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(200\) | − | 2.16449e41i | − | 0.825688i | ||||||
\(201\) | −2.27288e40 | − | 1.11590e41i | −0.0792587 | − | 0.389133i | ||||
\(202\) | −2.03283e41 | −0.648300 | ||||||||
\(203\) | 4.03644e41i | 1.17780i | ||||||||
\(204\) | 1.28683e41 | − | 2.62102e40i | 0.343699 | − | 0.0700047i | ||||
\(205\) | 3.13547e40 | 0.0766889 | ||||||||
\(206\) | 3.20740e41i | 0.718692i | ||||||||
\(207\) | 7.62682e40 | + | 1.79458e41i | 0.156631 | + | 0.368551i | ||||
\(208\) | −2.22760e41 | −0.419467 | ||||||||
\(209\) | 1.60437e41i | 0.277122i | ||||||||
\(210\) | 2.85672e40 | + | 1.40255e41i | 0.0452814 | + | 0.222316i | ||||
\(211\) | 2.27251e41 | 0.330690 | 0.165345 | − | 0.986236i | \(-0.447126\pi\) | ||||
0.165345 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(212\) | 2.95461e41i | 0.394870i | ||||||||
\(213\) | −1.42590e41 | + | 2.90427e40i | −0.175088 | + | 0.0356619i | ||||
\(214\) | 8.52334e41 | 0.961970 | ||||||||
\(215\) | − | 3.93193e41i | − | 0.408050i | ||||||
\(216\) | −9.13398e41 | + | 6.28644e41i | −0.871952 | + | 0.600119i | ||||
\(217\) | −8.55690e41 | −0.751694 | ||||||||
\(218\) | − | 7.85328e41i | − | 0.635088i | ||||||
\(219\) | −2.22014e41 | − | 1.09001e42i | −0.165343 | − | 0.811779i | ||||
\(220\) | −2.01027e41 | −0.137926 | ||||||||
\(221\) | − | 1.93190e42i | − | 1.22158i | ||||||
\(222\) | −2.30977e41 | + | 4.70455e40i | −0.134653 | + | 0.0274261i | ||||
\(223\) | 2.70449e42 | 1.45411 | 0.727056 | − | 0.686578i | \(-0.240888\pi\) | ||||
0.727056 | + | 0.686578i | \(0.240888\pi\) | |||||||
\(224\) | 1.23648e42i | 0.613369i | ||||||||
\(225\) | −1.56802e42 | + | 6.66396e41i | −0.717904 | + | 0.305103i | ||||
\(226\) | 2.88655e42 | 1.22019 | ||||||||
\(227\) | − | 2.11376e42i | − | 0.825257i | −0.910899 | − | 0.412629i | \(-0.864611\pi\) | ||
0.910899 | − | 0.412629i | \(-0.135389\pi\) | |||||||
\(228\) | −1.33465e41 | − | 6.55267e41i | −0.0481438 | − | 0.236369i | ||||
\(229\) | 2.93053e42 | 0.977030 | 0.488515 | − | 0.872556i | \(-0.337539\pi\) | ||||
0.488515 | + | 0.872556i | \(0.337539\pi\) | |||||||
\(230\) | 4.28252e41i | 0.132007i | ||||||||
\(231\) | −1.37502e42 | + | 2.80064e41i | −0.392006 | + | 0.0798439i | ||||
\(232\) | −6.86748e42 | −1.81140 | ||||||||
\(233\) | 3.38086e42i | 0.825316i | 0.910886 | + | 0.412658i | \(0.135399\pi\) | ||||
−0.910886 | + | 0.412658i | \(0.864601\pi\) | |||||||
\(234\) | 2.14351e42 | + | 5.04365e42i | 0.484440 | + | 1.13988i | ||||
\(235\) | −4.09344e42 | −0.856775 | ||||||||
\(236\) | 3.89922e42i | 0.756069i | ||||||||
\(237\) | −1.97590e42 | − | 9.70097e42i | −0.355053 | − | 1.74319i | ||||
\(238\) | 2.01330e42 | 0.335370 | ||||||||
\(239\) | 6.94508e42i | 1.07279i | 0.843967 | + | 0.536396i | \(0.180215\pi\) | ||||
−0.843967 | + | 0.536396i | \(0.819785\pi\) | |||||||
\(240\) | −7.63493e41 | + | 1.55508e41i | −0.109396 | + | 0.0222819i | ||||
\(241\) | 2.49680e42 | 0.331954 | 0.165977 | − | 0.986130i | \(-0.446922\pi\) | ||||
0.165977 | + | 0.986130i | \(0.446922\pi\) | |||||||
\(242\) | − | 3.77146e42i | − | 0.465406i | ||||||
\(243\) | 7.36622e42 | + | 4.68147e42i | 0.843979 | + | 0.536376i | ||||
\(244\) | 6.05621e42 | 0.644443 | ||||||||
\(245\) | 2.49682e42i | 0.246830i | ||||||||
\(246\) | 2.49692e41 | + | 1.22590e42i | 0.0229389 | + | 0.112622i | ||||
\(247\) | −9.83741e42 | −0.840109 | ||||||||
\(248\) | − | 1.45584e43i | − | 1.15607i | ||||||
\(249\) | 8.08217e42 | − | 1.64618e42i | 0.596952 | − | 0.121587i | ||||
\(250\) | −8.53882e42 | −0.586783 | ||||||||
\(251\) | − | 2.20823e43i | − | 1.41227i | −0.708077 | − | 0.706136i | \(-0.750437\pi\) | ||
0.708077 | − | 0.706136i | \(-0.249563\pi\) | |||||||
\(252\) | 5.38296e42 | − | 2.28771e42i | 0.320488 | − | 0.136205i | ||||
\(253\) | −4.19845e42 | −0.232766 | ||||||||
\(254\) | − | 2.75318e41i | − | 0.0142177i | ||||||
\(255\) | −1.34865e42 | − | 6.62142e42i | −0.0648899 | − | 0.318587i | ||||
\(256\) | −2.37230e43 | −1.06378 | ||||||||
\(257\) | 2.21794e43i | 0.927157i | 0.886056 | + | 0.463579i | \(0.153435\pi\) | ||||
−0.886056 | + | 0.463579i | \(0.846565\pi\) | |||||||
\(258\) | 1.53730e43 | − | 3.13118e42i | 0.599244 | − | 0.122054i | ||||
\(259\) | 3.70090e42 | 0.134559 | ||||||||
\(260\) | − | 1.23263e43i | − | 0.418130i | ||||||
\(261\) | 2.11433e43 | + | 4.97500e43i | 0.669336 | + | 1.57494i | ||||
\(262\) | 7.27304e42 | 0.214928 | ||||||||
\(263\) | 3.11959e43i | 0.860785i | 0.902642 | + | 0.430392i | \(0.141625\pi\) | ||||
−0.902642 | + | 0.430392i | \(0.858375\pi\) | |||||||
\(264\) | −4.76492e42 | − | 2.33941e43i | −0.122796 | − | 0.602887i | ||||
\(265\) | 1.52030e43 | 0.366019 | ||||||||
\(266\) | − | 1.02519e43i | − | 0.230641i | ||||||
\(267\) | −6.31267e43 | + | 1.28577e43i | −1.32743 | + | 0.270370i | ||||
\(268\) | −1.02203e43 | −0.200927 | ||||||||
\(269\) | 4.50123e43i | 0.827543i | 0.910381 | + | 0.413771i | \(0.135789\pi\) | ||||
−0.910381 | + | 0.413771i | \(0.864211\pi\) | |||||||
\(270\) | 1.08677e43 | + | 1.57903e43i | 0.186891 | + | 0.271546i | ||||
\(271\) | −3.68709e42 | −0.0593248 | −0.0296624 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296624 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(272\) | 1.09596e43i | 0.165027i | ||||||||
\(273\) | −1.71725e43 | − | 8.43112e43i | −0.242051 | − | 1.18839i | ||||
\(274\) | 7.38234e43 | 0.974280 | ||||||||
\(275\) | − | 3.66841e43i | − | 0.453408i | ||||||
\(276\) | 1.71476e43 | − | 3.49263e42i | 0.198536 | − | 0.0404379i | ||||
\(277\) | −1.53564e43 | −0.166592 | −0.0832960 | − | 0.996525i | \(-0.526545\pi\) | ||||
−0.0832960 | + | 0.996525i | \(0.526545\pi\) | |||||||
\(278\) | 3.61416e43i | 0.367453i | ||||||||
\(279\) | −1.05466e44 | + | 4.48220e43i | −1.00516 | + | 0.427184i | ||||
\(280\) | 3.82345e43 | 0.341673 | ||||||||
\(281\) | − | 1.68902e44i | − | 1.41554i | −0.706445 | − | 0.707768i | \(-0.749702\pi\) | ||
0.706445 | − | 0.707768i | \(-0.250298\pi\) | |||||||
\(282\) | −3.25980e43 | − | 1.60045e44i | −0.256275 | − | 1.25822i | ||||
\(283\) | 1.87568e44 | 1.38357 | 0.691786 | − | 0.722102i | \(-0.256824\pi\) | ||||
0.691786 | + | 0.722102i | \(0.256824\pi\) | |||||||
\(284\) | 1.30595e43i | 0.0904059i | ||||||||
\(285\) | −3.37170e43 | + | 6.86748e42i | −0.219099 | + | 0.0446262i | ||||
\(286\) | −1.17997e44 | −0.719916 | ||||||||
\(287\) | − | 1.96424e43i | − | 0.112543i | ||||||
\(288\) | 6.47680e43 | + | 1.52398e44i | 0.348575 | + | 0.820192i | ||||
\(289\) | 1.02723e44 | 0.519403 | ||||||||
\(290\) | 1.18721e44i | 0.564111i | ||||||||
\(291\) | 2.39691e43 | + | 1.17680e44i | 0.107048 | + | 0.525569i | ||||
\(292\) | −9.98321e43 | −0.419159 | ||||||||
\(293\) | 6.94199e43i | 0.274073i | 0.990566 | + | 0.137037i | \(0.0437578\pi\) | ||||
−0.990566 | + | 0.137037i | \(0.956242\pi\) | |||||||
\(294\) | −9.76204e43 | + | 1.98834e43i | −0.362484 | + | 0.0738308i | ||||
\(295\) | 2.00635e44 | 0.700828 | ||||||||
\(296\) | 6.29659e43i | 0.206945i | ||||||||
\(297\) | −1.54804e44 | + | 1.06543e44i | −0.478812 | + | 0.329542i | ||||
\(298\) | −3.80025e44 | −1.10642 | ||||||||
\(299\) | − | 2.57434e44i | − | 0.705642i | ||||||
\(300\) | 3.05169e43 | + | 1.49828e44i | 0.0787695 | + | 0.386731i | ||||
\(301\) | −2.46319e44 | −0.598826 | ||||||||
\(302\) | 3.50948e44i | 0.803744i | ||||||||
\(303\) | 4.18827e44 | − | 8.53069e43i | 0.903791 | − | 0.184084i | ||||
\(304\) | 5.58075e43 | 0.113493 | ||||||||
\(305\) | − | 3.11624e44i | − | 0.597357i | ||||||
\(306\) | 2.48144e44 | − | 1.05459e44i | 0.448454 | − | 0.190589i | ||||
\(307\) | 1.59238e44 | 0.271366 | 0.135683 | − | 0.990752i | \(-0.456677\pi\) | ||||
0.135683 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(308\) | 1.25935e44i | 0.202411i | ||||||||
\(309\) | −1.34597e44 | − | 6.60825e44i | −0.204072 | − | 1.00192i | ||||
\(310\) | −2.51678e44 | −0.360027 | ||||||||
\(311\) | 2.11490e44i | 0.285498i | 0.989759 | + | 0.142749i | \(0.0455942\pi\) | ||||
−0.989759 | + | 0.142749i | \(0.954406\pi\) | |||||||
\(312\) | 1.43444e45 | − | 2.92168e44i | 1.82768 | − | 0.372263i | ||||
\(313\) | −6.34982e43 | −0.0763771 | −0.0381885 | − | 0.999271i | \(-0.512159\pi\) | ||||
−0.0381885 | + | 0.999271i | \(0.512159\pi\) | |||||||
\(314\) | − | 7.70709e44i | − | 0.875300i | ||||||
\(315\) | −1.17715e44 | − | 2.76982e44i | −0.126253 | − | 0.297072i | ||||
\(316\) | −8.88492e44 | −0.900090 | ||||||||
\(317\) | − | 2.83676e44i | − | 0.271491i | −0.990744 | − | 0.135745i | \(-0.956657\pi\) | ||
0.990744 | − | 0.135745i | \(-0.0433429\pi\) | |||||||
\(318\) | 1.21069e44 | + | 5.94406e44i | 0.109482 | + | 0.537520i | ||||
\(319\) | −1.16391e45 | −0.994687 | ||||||||
\(320\) | 5.01884e44i | 0.405418i | ||||||||
\(321\) | −1.75608e45 | + | 3.57678e44i | −1.34108 | + | 0.273151i | ||||
\(322\) | 2.68282e44 | 0.193725 | ||||||||
\(323\) | 4.83993e44i | 0.330517i | ||||||||
\(324\) | 5.43628e44 | − | 5.63931e44i | 0.351149 | − | 0.364263i | ||||
\(325\) | 2.24933e45 | 1.37453 | ||||||||
\(326\) | 1.62407e44i | 0.0939047i | ||||||||
\(327\) | 3.29560e44 | + | 1.61802e45i | 0.180333 | + | 0.885371i | ||||
\(328\) | 3.34189e44 | 0.173086 | ||||||||
\(329\) | 2.56437e45i | 1.25734i | ||||||||
\(330\) | −4.04425e44 | + | 8.23734e43i | −0.187753 | + | 0.0382416i | ||||
\(331\) | 7.89685e44 | 0.347176 | 0.173588 | − | 0.984818i | \(-0.444464\pi\) | ||||
0.173588 | + | 0.984818i | \(0.444464\pi\) | |||||||
\(332\) | − | 7.40230e44i | − | 0.308234i | ||||||
\(333\) | 4.56144e44 | − | 1.93857e44i | 0.179931 | − | 0.0764691i | ||||
\(334\) | −2.30805e45 | −0.862599 | ||||||||
\(335\) | 5.25891e44i | 0.186247i | ||||||||
\(336\) | 9.74195e43 | + | 4.78296e44i | 0.0326993 | + | 0.160542i | ||||
\(337\) | 1.86680e45 | 0.593963 | 0.296982 | − | 0.954883i | \(-0.404020\pi\) | ||||
0.296982 | + | 0.954883i | \(0.404020\pi\) | |||||||
\(338\) | − | 4.90500e45i | − | 1.47958i | ||||||
\(339\) | −5.94722e45 | + | 1.21133e45i | −1.70106 | + | 0.346472i | ||||
\(340\) | −6.06443e44 | −0.164501 | ||||||||
\(341\) | − | 2.46738e45i | − | 0.634830i | ||||||
\(342\) | −5.37008e44 | − | 1.26357e45i | −0.131072 | − | 0.308411i | ||||
\(343\) | 4.53613e45 | 1.05049 | ||||||||
\(344\) | − | 4.19079e45i | − | 0.920966i | ||||||
\(345\) | −1.79714e44 | − | 8.82334e44i | −0.0374833 | − | 0.184030i | ||||
\(346\) | 2.09760e44 | 0.0415291 | ||||||||
\(347\) | 5.41382e45i | 1.01759i | 0.860887 | + | 0.508796i | \(0.169909\pi\) | ||||
−0.860887 | + | 0.508796i | \(0.830091\pi\) | |||||||
\(348\) | 4.75371e45 | − | 9.68238e44i | 0.848412 | − | 0.172805i | ||||
\(349\) | 6.88573e45 | 1.16706 | 0.583529 | − | 0.812092i | \(-0.301672\pi\) | ||||
0.583529 | + | 0.812092i | \(0.301672\pi\) | |||||||
\(350\) | 2.34412e45i | 0.377359i | ||||||||
\(351\) | −6.53286e45 | − | 9.49201e45i | −0.999022 | − | 1.45154i | ||||
\(352\) | −3.56538e45 | −0.518010 | ||||||||
\(353\) | 1.50986e45i | 0.208446i | 0.994554 | + | 0.104223i | \(0.0332355\pi\) | ||||
−0.994554 | + | 0.104223i | \(0.966764\pi\) | |||||||
\(354\) | 1.59775e45 | + | 7.84442e45i | 0.209629 | + | 1.02921i | ||||
\(355\) | 6.71981e44 | 0.0838005 | ||||||||
\(356\) | 5.78165e45i | 0.685412i | ||||||||
\(357\) | −4.14804e45 | + | 8.44874e44i | −0.467536 | + | 0.0952279i | ||||
\(358\) | −1.47176e44 | −0.0157740 | ||||||||
\(359\) | − | 1.29291e44i | − | 0.0131785i | −0.999978 | − | 0.00658927i | \(-0.997903\pi\) | ||
0.999978 | − | 0.00658927i | \(-0.00209744\pi\) | |||||||
\(360\) | 4.71248e45 | − | 2.00276e45i | 0.456882 | − | 0.194171i | ||||
\(361\) | −8.37796e45 | −0.772696 | ||||||||
\(362\) | 3.68761e45i | 0.323587i | ||||||||
\(363\) | 1.58268e45 | + | 7.77040e45i | 0.132152 | + | 0.648819i | ||||
\(364\) | −7.72189e45 | −0.613619 | ||||||||
\(365\) | 5.13689e45i | 0.388534i | ||||||||
\(366\) | 1.21838e46 | − | 2.48161e45i | 0.877253 | − | 0.178679i | ||||
\(367\) | −9.17946e45 | −0.629257 | −0.314628 | − | 0.949215i | \(-0.601880\pi\) | ||||
−0.314628 | + | 0.949215i | \(0.601880\pi\) | |||||||
\(368\) | 1.46042e45i | 0.0953272i | ||||||||
\(369\) | −1.02889e45 | − | 2.42096e45i | −0.0639579 | − | 0.150492i | ||||
\(370\) | 1.08852e45 | 0.0644475 | ||||||||
\(371\) | − | 9.52405e45i | − | 0.537145i | ||||||
\(372\) | 2.05258e45 | + | 1.00774e46i | 0.110288 | + | 0.541474i | ||||
\(373\) | 1.89617e46 | 0.970773 | 0.485387 | − | 0.874300i | \(-0.338679\pi\) | ||||
0.485387 | + | 0.874300i | \(0.338679\pi\) | |||||||
\(374\) | 5.80535e45i | 0.283230i | ||||||||
\(375\) | 1.75927e46 | − | 3.58328e45i | 0.818030 | − | 0.166617i | ||||
\(376\) | −4.36293e46 | −1.93374 | ||||||||
\(377\) | − | 7.13667e46i | − | 3.01544i | ||||||
\(378\) | 9.89198e45 | − | 6.80814e45i | 0.398502 | − | 0.274269i | ||||
\(379\) | 1.40641e46 | 0.540266 | 0.270133 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(380\) | 3.08807e45i | 0.113131i | ||||||||
\(381\) | 1.15536e44 | + | 5.67243e44i | 0.00403709 | + | 0.0198207i | ||||
\(382\) | 1.44940e45 | 0.0483113 | ||||||||
\(383\) | 3.65569e46i | 1.16250i | 0.813727 | + | 0.581248i | \(0.197435\pi\) | ||||
−0.813727 | + | 0.581248i | \(0.802565\pi\) | |||||||
\(384\) | 9.15839e45 | − | 1.86538e45i | 0.277880 | − | 0.0565986i | ||||
\(385\) | 6.48003e45 | 0.187622 | ||||||||
\(386\) | 1.55234e46i | 0.428959i | ||||||||
\(387\) | −3.03593e46 | + | 1.29024e46i | −0.800745 | + | 0.340310i | ||||
\(388\) | 1.07781e46 | 0.271376 | ||||||||
\(389\) | − | 2.13748e46i | − | 0.513819i | −0.966435 | − | 0.256910i | \(-0.917296\pi\) | ||
0.966435 | − | 0.256910i | \(-0.0827042\pi\) | |||||||
\(390\) | −5.05084e45 | − | 2.47979e46i | −0.115931 | − | 0.569183i | ||||
\(391\) | −1.26655e46 | −0.277614 | ||||||||
\(392\) | 2.66120e46i | 0.557094i | ||||||||
\(393\) | −1.49848e46 | + | 3.05210e45i | −0.299629 | + | 0.0610286i | ||||
\(394\) | −3.79143e45 | −0.0724220 | ||||||||
\(395\) | 4.57176e46i | 0.834326i | ||||||||
\(396\) | 6.59662e45 | + | 1.55218e46i | 0.115029 | + | 0.270662i | ||||
\(397\) | −3.23014e46 | −0.538260 | −0.269130 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269130 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(398\) | 5.14205e45i | 0.0818919i | ||||||||
\(399\) | 4.30219e45 | + | 2.11223e46i | 0.0654903 | + | 0.321535i | ||||
\(400\) | −1.27604e46 | −0.185689 | ||||||||
\(401\) | 5.33934e46i | 0.742829i | 0.928467 | + | 0.371414i | \(0.121127\pi\) | ||||
−0.928467 | + | 0.371414i | \(0.878873\pi\) | |||||||
\(402\) | −2.05612e46 | + | 4.18791e45i | −0.273514 | + | 0.0557095i | ||||
\(403\) | 1.51291e47 | 1.92452 | ||||||||
\(404\) | − | 3.83596e46i | − | 0.466669i | ||||||
\(405\) | −2.90172e46 | − | 2.79725e46i | −0.337649 | − | 0.325493i | ||||
\(406\) | 7.43739e46 | 0.827851 | ||||||||
\(407\) | 1.06715e46i | 0.113639i | ||||||||
\(408\) | −1.43744e46 | − | 7.05735e46i | −0.146456 | − | 0.719049i | ||||
\(409\) | 2.82102e46 | 0.275035 | 0.137517 | − | 0.990499i | \(-0.456088\pi\) | ||||
0.137517 | + | 0.990499i | \(0.456088\pi\) | |||||||
\(410\) | − | 5.77728e45i | − | 0.0539032i | ||||||
\(411\) | −1.52100e47 | + | 3.09797e46i | −1.35824 | + | 0.276646i | ||||
\(412\) | −6.05237e46 | −0.517339 | ||||||||
\(413\) | − | 1.25690e47i | − | 1.02849i | ||||||
\(414\) | 3.30663e46 | − | 1.40529e46i | 0.259047 | − | 0.110093i | ||||
\(415\) | −3.80887e46 | −0.285713 | ||||||||
\(416\) | − | 2.18616e47i | − | 1.57037i | ||||||
\(417\) | −1.51667e46 | − | 7.44633e46i | −0.104338 | − | 0.512263i | ||||
\(418\) | 2.95615e46 | 0.194784 | ||||||||
\(419\) | 1.53626e47i | 0.969647i | 0.874612 | + | 0.484823i | \(0.161116\pi\) | ||||
−0.874612 | + | 0.484823i | \(0.838884\pi\) | |||||||
\(420\) | −2.64662e46 | + | 5.39064e45i | −0.160031 | + | 0.0325951i | ||||
\(421\) | 1.84762e46 | 0.107037 | 0.0535186 | − | 0.998567i | \(-0.482956\pi\) | ||||
0.0535186 | + | 0.998567i | \(0.482956\pi\) | |||||||
\(422\) | − | 4.18723e46i | − | 0.232436i | ||||||
\(423\) | 1.34324e47 | + | 3.16063e47i | 0.714542 | + | 1.68131i | ||||
\(424\) | 1.62039e47 | 0.826104 | ||||||||
\(425\) | − | 1.10665e47i | − | 0.540769i | ||||||
\(426\) | 5.35130e45 | + | 2.62730e46i | 0.0250661 | + | 0.123066i | ||||
\(427\) | −1.95219e47 | −0.876640 | ||||||||
\(428\) | 1.60836e47i | 0.692460i | ||||||||
\(429\) | 2.43111e47 | − | 4.95169e46i | 1.00363 | − | 0.204420i | ||||
\(430\) | −7.24481e46 | −0.286810 | ||||||||
\(431\) | 2.20596e47i | 0.837542i | 0.908092 | + | 0.418771i | \(0.137539\pi\) | ||||
−0.908092 | + | 0.418771i | \(0.862461\pi\) | |||||||
\(432\) | 3.70608e46 | + | 5.38480e46i | 0.134961 | + | 0.196093i | ||||
\(433\) | −2.44161e47 | −0.852893 | −0.426447 | − | 0.904513i | \(-0.640235\pi\) | ||||
−0.426447 | + | 0.904513i | \(0.640235\pi\) | |||||||
\(434\) | 1.57666e47i | 0.528351i | ||||||||
\(435\) | −4.98209e46 | − | 2.44604e47i | −0.160179 | − | 0.786423i | ||||
\(436\) | 1.48192e47 | 0.457158 | ||||||||
\(437\) | 6.44942e46i | 0.190922i | ||||||||
\(438\) | −2.00842e47 | + | 4.09075e46i | −0.570584 | + | 0.116217i | ||||
\(439\) | −4.59501e47 | −1.25292 | −0.626462 | − | 0.779452i | \(-0.715498\pi\) | ||||
−0.626462 | + | 0.779452i | \(0.715498\pi\) | |||||||
\(440\) | 1.10249e47i | 0.288554i | ||||||||
\(441\) | 1.92785e47 | − | 8.19321e46i | 0.484372 | − | 0.205854i | ||||
\(442\) | −3.55964e47 | −0.858627 | ||||||||
\(443\) | 1.36833e47i | 0.316900i | 0.987367 | + | 0.158450i | \(0.0506497\pi\) | ||||
−0.987367 | + | 0.158450i | \(0.949350\pi\) | |||||||
\(444\) | −8.87749e45 | − | 4.35854e46i | −0.0197423 | − | 0.0969277i | ||||
\(445\) | 2.97496e47 | 0.635333 | ||||||||
\(446\) | − | 4.98319e47i | − | 1.02207i | ||||||
\(447\) | 7.82972e47 | − | 1.59476e47i | 1.54245 | − | 0.314166i | ||||
\(448\) | 3.14409e47 | 0.594964 | ||||||||
\(449\) | − | 8.45639e47i | − | 1.53727i | −0.639687 | − | 0.768636i | \(-0.720936\pi\) | ||
0.639687 | − | 0.768636i | \(-0.279064\pi\) | |||||||
\(450\) | 1.22787e47 | + | 2.88917e47i | 0.214451 | + | 0.504601i | ||||
\(451\) | 5.66388e46 | 0.0950465 | ||||||||
\(452\) | 5.44694e47i | 0.878336i | ||||||||
\(453\) | −1.47274e47 | − | 7.23064e47i | −0.228222 | − | 1.12049i | ||||
\(454\) | −3.89472e47 | −0.580058 | ||||||||
\(455\) | 3.97332e47i | 0.568785i | ||||||||
\(456\) | −3.59367e47 | + | 7.31960e46i | −0.494506 | + | 0.100721i | ||||
\(457\) | 7.90122e47 | 1.04521 | 0.522604 | − | 0.852576i | \(-0.324961\pi\) | ||||
0.522604 | + | 0.852576i | \(0.324961\pi\) | |||||||
\(458\) | − | 5.39968e47i | − | 0.686736i | ||||||
\(459\) | −4.66999e47 | + | 3.21411e47i | −0.571068 | + | 0.393037i | ||||
\(460\) | −8.08112e46 | −0.0950234 | ||||||||
\(461\) | − | 5.44752e47i | − | 0.616003i | −0.951386 | − | 0.308001i | \(-0.900340\pi\) | ||
0.951386 | − | 0.308001i | \(-0.0996601\pi\) | |||||||
\(462\) | 5.16035e46 | + | 2.53355e47i | 0.0561208 | + | 0.275534i | ||||
\(463\) | −1.52156e48 | −1.59159 | −0.795796 | − | 0.605565i | \(-0.792947\pi\) | ||||
−0.795796 | + | 0.605565i | \(0.792947\pi\) | |||||||
\(464\) | 4.04862e47i | 0.407365i | ||||||||
\(465\) | 5.18538e47 | − | 1.05616e47i | 0.501911 | − | 0.102229i | ||||
\(466\) | 6.22943e47 | 0.580099 | ||||||||
\(467\) | 6.18890e47i | 0.554511i | 0.960796 | + | 0.277255i | \(0.0894248\pi\) | ||||
−0.960796 | + | 0.277255i | \(0.910575\pi\) | |||||||
\(468\) | −9.51739e47 | + | 4.04481e47i | −0.820526 | + | 0.348717i | ||||
\(469\) | 3.29448e47 | 0.273323 | ||||||||
\(470\) | 7.54241e47i | 0.602211i | ||||||||
\(471\) | 3.23425e47 | + | 1.58791e48i | 0.248541 | + | 1.22025i | ||||
\(472\) | 2.13844e48 | 1.58176 | ||||||||
\(473\) | − | 7.10259e47i | − | 0.505727i | ||||||
\(474\) | −1.78746e48 | + | 3.64071e47i | −1.22526 | + | 0.249560i | ||||
\(475\) | −5.63520e47 | −0.371898 | ||||||||
\(476\) | 3.79911e47i | 0.241411i | ||||||||
\(477\) | −4.98880e47 | − | 1.17386e48i | −0.305257 | − | 0.718266i | ||||
\(478\) | 1.27967e48 | 0.754045 | ||||||||
\(479\) | 7.48459e47i | 0.424746i | 0.977189 | + | 0.212373i | \(0.0681191\pi\) | ||||
−0.977189 | + | 0.212373i | \(0.931881\pi\) | |||||||
\(480\) | −1.52616e47 | − | 7.49290e47i | −0.0834174 | − | 0.409551i | ||||
\(481\) | −6.54341e47 | −0.344503 | ||||||||
\(482\) | − | 4.60051e47i | − | 0.233324i | ||||||
\(483\) | −5.52745e47 | + | 1.12583e47i | −0.270070 | + | 0.0550080i | ||||
\(484\) | 7.11675e47 | 0.335016 | ||||||||
\(485\) | − | 5.54590e47i | − | 0.251548i | ||||||
\(486\) | 8.62590e47 | − | 1.35727e48i | 0.377009 | − | 0.593217i | ||||
\(487\) | 1.72017e48 | 0.724519 | 0.362260 | − | 0.932077i | \(-0.382005\pi\) | ||||
0.362260 | + | 0.932077i | \(0.382005\pi\) | |||||||
\(488\) | − | 3.32140e48i | − | 1.34823i | ||||||
\(489\) | −6.81534e46 | − | 3.34610e47i | −0.0266642 | − | 0.130912i | ||||
\(490\) | 4.60054e47 | 0.173492 | ||||||||
\(491\) | 7.68862e47i | 0.279500i | 0.990187 | + | 0.139750i | \(0.0446299\pi\) | ||||
−0.990187 | + | 0.139750i | \(0.955370\pi\) | |||||||
\(492\) | −2.31328e47 | + | 4.71169e46i | −0.0810693 | + | 0.0165122i | ||||
\(493\) | −3.51118e48 | −1.18634 | ||||||||
\(494\) | 1.81260e48i | 0.590497i | ||||||||
\(495\) | 7.98676e47 | − | 3.39431e47i | 0.250887 | − | 0.106625i | ||||
\(496\) | −8.58271e47 | −0.259989 | ||||||||
\(497\) | − | 4.20968e47i | − | 0.122980i | ||||||
\(498\) | −3.03318e47 | − | 1.48919e48i | −0.0854615 | − | 0.419587i | ||||
\(499\) | 1.27440e48 | 0.346336 | 0.173168 | − | 0.984892i | \(-0.444600\pi\) | ||||
0.173168 | + | 0.984892i | \(0.444600\pi\) | |||||||
\(500\) | − | 1.61128e48i | − | 0.422387i | ||||||
\(501\) | 4.75532e48 | − | 9.68564e47i | 1.20254 | − | 0.244934i | ||||
\(502\) | −4.06881e48 | −0.992659 | ||||||||
\(503\) | 7.16188e48i | 1.68579i | 0.538078 | + | 0.842895i | \(0.319151\pi\) | ||||
−0.538078 | + | 0.842895i | \(0.680849\pi\) | |||||||
\(504\) | −1.25465e48 | − | 2.95217e48i | −0.284952 | − | 0.670489i | ||||
\(505\) | −1.97380e48 | −0.432572 | ||||||||
\(506\) | 7.73590e47i | 0.163607i | ||||||||
\(507\) | 2.05837e48 | + | 1.01059e49i | 0.420126 | + | 2.06267i | ||||
\(508\) | 5.19526e46 | 0.0102344 | ||||||||
\(509\) | − | 5.76516e48i | − | 1.09620i | −0.836411 | − | 0.548102i | \(-0.815350\pi\) | ||
0.836411 | − | 0.548102i | \(-0.184650\pi\) | |||||||
\(510\) | −1.22004e48 | + | 2.48497e47i | −0.223929 | + | 0.0456099i | ||||
\(511\) | 3.21805e48 | 0.570185 | ||||||||
\(512\) | 2.71326e48i | 0.464122i | ||||||||
\(513\) | 1.63666e48 | + | 2.37801e48i | 0.270300 | + | 0.392736i | ||||
\(514\) | 4.08669e48 | 0.651681 | ||||||||
\(515\) | 3.11426e48i | 0.479540i | ||||||||
\(516\) | 5.90854e47 | + | 2.90089e48i | 0.0878589 | + | 0.431357i | ||||
\(517\) | −7.39435e48 | −1.06187 | ||||||||
\(518\) | − | 6.81913e47i | − | 0.0945787i | ||||||
\(519\) | −4.32172e47 | + | 8.80250e46i | −0.0578955 | + | 0.0117922i | ||||
\(520\) | −6.76008e48 | −0.874765 | ||||||||
\(521\) | − | 9.10339e48i | − | 1.13795i | −0.822354 | − | 0.568977i | \(-0.807340\pi\) | ||
0.822354 | − | 0.568977i | \(-0.192660\pi\) | |||||||
\(522\) | 9.16674e48 | − | 3.89579e48i | 1.10700 | − | 0.470464i | ||||
\(523\) | −1.20984e49 | −1.41155 | −0.705777 | − | 0.708434i | \(-0.749402\pi\) | ||||
−0.705777 | + | 0.708434i | \(0.749402\pi\) | |||||||
\(524\) | 1.37243e48i | 0.154713i | ||||||||
\(525\) | −9.83700e47 | − | 4.82963e48i | −0.107151 | − | 0.526073i | ||||
\(526\) | 5.74804e48 | 0.605029 | ||||||||
\(527\) | − | 7.44339e48i | − | 0.757146i | ||||||
\(528\) | −1.37917e48 | + | 2.80909e47i | −0.135583 | + | 0.0276156i | ||||
\(529\) | 8.83677e48 | 0.839637 | ||||||||
\(530\) | − | 2.80125e48i | − | 0.257268i | ||||||
\(531\) | −6.58376e48 | − | 1.54915e49i | −0.584484 | − | 1.37528i | ||||
\(532\) | 1.93454e48 | 0.166023 | ||||||||
\(533\) | 3.47289e48i | 0.288138i | ||||||||
\(534\) | 2.36910e48 | + | 1.16315e49i | 0.190038 | + | 0.933022i | ||||
\(535\) | 8.27584e48 | 0.641866 | ||||||||
\(536\) | 5.60513e48i | 0.420358i | ||||||||
\(537\) | 3.03229e47 | − | 6.17618e46i | 0.0219904 | − | 0.00447902i | ||||
\(538\) | 8.29379e48 | 0.581664 | ||||||||
\(539\) | 4.51023e48i | 0.305915i | ||||||||
\(540\) | −2.97964e48 | + | 2.05073e48i | −0.195468 | + | 0.134531i | ||||
\(541\) | 1.75620e49 | 1.11435 | 0.557176 | − | 0.830395i | \(-0.311885\pi\) | ||||
0.557176 | + | 0.830395i | \(0.311885\pi\) | |||||||
\(542\) | 6.79368e47i | 0.0416983i | ||||||||
\(543\) | −1.54749e48 | − | 7.59764e48i | −0.0918821 | − | 0.451109i | ||||
\(544\) | −1.07558e49 | −0.617818 | ||||||||
\(545\) | − | 7.62524e48i | − | 0.423756i | ||||||
\(546\) | −1.55348e49 | + | 3.16414e48i | −0.835294 | + | 0.170133i | ||||
\(547\) | −1.84394e49 | −0.959346 | −0.479673 | − | 0.877447i | \(-0.659245\pi\) | ||||
−0.479673 | + | 0.877447i | \(0.659245\pi\) | |||||||
\(548\) | 1.39305e49i | 0.701320i | ||||||||
\(549\) | −2.40612e49 | + | 1.02258e49i | −1.17224 | + | 0.498190i | ||||
\(550\) | −6.75926e48 | −0.318692 | ||||||||
\(551\) | 1.78793e49i | 0.815872i | ||||||||
\(552\) | −1.91546e48 | − | 9.40423e48i | −0.0845997 | − | 0.415355i | ||||
\(553\) | 2.86402e49 | 1.22440 | ||||||||
\(554\) | 2.82951e48i | 0.117094i | ||||||||
\(555\) | −2.24270e48 | + | 4.56794e47i | −0.0898458 | + | 0.0182998i | ||||
\(556\) | −6.81994e48 | −0.264505 | ||||||||
\(557\) | 2.17422e49i | 0.816414i | 0.912889 | + | 0.408207i | \(0.133846\pi\) | ||||
−0.912889 | + | 0.408207i | \(0.866154\pi\) | |||||||
\(558\) | 8.25872e48 | + | 1.94327e49i | 0.300260 | + | 0.706507i | ||||
\(559\) | 4.35506e49 | 1.53314 | ||||||||
\(560\) | − | 2.25406e48i | − | 0.0768388i | ||||||
\(561\) | −2.43619e48 | − | 1.19609e49i | −0.0804230 | − | 0.394849i | ||||
\(562\) | −3.11212e49 | −0.994953 | ||||||||
\(563\) | − | 4.38124e49i | − | 1.35658i | −0.734794 | − | 0.678291i | \(-0.762721\pi\) | ||
0.734794 | − | 0.678291i | \(-0.237279\pi\) | |||||||
\(564\) | 3.02005e49 | − | 6.15125e48i | 0.905712 | − | 0.184476i | ||||
\(565\) | 2.80274e49 | 0.814161 | ||||||||
\(566\) | − | 3.45605e49i | − | 0.972487i | ||||||
\(567\) | −1.75236e49 | + | 1.81781e49i | −0.477671 | + | 0.495510i | ||||
\(568\) | 7.16221e48 | 0.189137 | ||||||||
\(569\) | − | 6.29187e48i | − | 0.160975i | −0.996756 | − | 0.0804876i | \(-0.974352\pi\) | ||
0.996756 | − | 0.0804876i | \(-0.0256477\pi\) | |||||||
\(570\) | 1.26537e48 | + | 6.21255e48i | 0.0313669 | + | 0.154001i | ||||
\(571\) | −4.24109e49 | −1.01866 | −0.509328 | − | 0.860573i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860573i | \(0.670106\pi\) | |||||||
\(572\) | − | 2.22661e49i | − | 0.518221i | ||||||
\(573\) | −2.98623e48 | + | 6.08236e47i | −0.0673504 | + | 0.0137180i | ||||
\(574\) | −3.61923e48 | −0.0791046 | ||||||||
\(575\) | − | 1.47467e49i | − | 0.312373i | ||||||
\(576\) | 3.87516e49 | − | 1.64691e49i | 0.795581 | − | 0.338115i | ||||
\(577\) | −5.07984e49 | −1.01085 | −0.505423 | − | 0.862872i | \(-0.668664\pi\) | ||||
−0.505423 | + | 0.862872i | \(0.668664\pi\) | |||||||
\(578\) | − | 1.89273e49i | − | 0.365079i | ||||||
\(579\) | −6.51434e48 | − | 3.19832e49i | −0.121803 | − | 0.598008i | ||||
\(580\) | −2.24028e49 | −0.406067 | ||||||||
\(581\) | 2.38610e49i | 0.419293i | ||||||||
\(582\) | 2.16833e49 | − | 4.41646e48i | 0.369412 | − | 0.0752420i | ||||
\(583\) | 2.74626e49 | 0.453636 | ||||||||
\(584\) | 5.47508e49i | 0.876918i | ||||||||
\(585\) | 2.08127e49 | + | 4.89720e49i | 0.323238 | + | 0.760575i | ||||
\(586\) | 1.27910e49 | 0.192641 | ||||||||
\(587\) | 6.76227e49i | 0.987658i | 0.869559 | + | 0.493829i | \(0.164403\pi\) | ||||
−0.869559 | + | 0.493829i | \(0.835597\pi\) | |||||||
\(588\) | −3.75200e48 | − | 1.84210e49i | −0.0531460 | − | 0.260929i | ||||
\(589\) | −3.79025e49 | −0.520706 | ||||||||
\(590\) | − | 3.69683e49i | − | 0.492599i | ||||||
\(591\) | 7.81154e48 | − | 1.59106e48i | 0.100963 | − | 0.0205642i | ||||
\(592\) | 3.71207e48 | 0.0465398 | ||||||||
\(593\) | 1.09064e50i | 1.32647i | 0.748412 | + | 0.663234i | \(0.230816\pi\) | ||||
−0.748412 | + | 0.663234i | \(0.769184\pi\) | |||||||
\(594\) | 1.96313e49 | + | 2.85235e49i | 0.231629 | + | 0.336548i | ||||
\(595\) | 1.95484e49 | 0.223772 | ||||||||
\(596\) | − | 7.17108e49i | − | 0.796438i | ||||||
\(597\) | −2.15784e48 | − | 1.05942e49i | −0.0232531 | − | 0.114165i | ||||
\(598\) | −4.74337e49 | −0.495982 | ||||||||
\(599\) | 8.77311e49i | 0.890165i | 0.895490 | + | 0.445083i | \(0.146826\pi\) | ||||
−0.895490 | + | 0.445083i | \(0.853174\pi\) | |||||||
\(600\) | 8.21697e49 | − | 1.67363e49i | 0.809076 | − | 0.164793i | ||||
\(601\) | −1.55745e50 | −1.48825 | −0.744123 | − | 0.668042i | \(-0.767132\pi\) | ||||
−0.744123 | + | 0.668042i | \(0.767132\pi\) | |||||||
\(602\) | 4.53857e49i | 0.420903i | ||||||||
\(603\) | 4.06052e49 | − | 1.72569e49i | 0.365485 | − | 0.155328i | ||||
\(604\) | −6.62240e49 | −0.578562 | ||||||||
\(605\) | − | 3.66194e49i | − | 0.310538i | ||||||
\(606\) | −1.57183e49 | − | 7.71715e49i | −0.129389 | − | 0.635257i | ||||
\(607\) | 2.05418e50 | 1.64151 | 0.820754 | − | 0.571282i | \(-0.193554\pi\) | ||||
0.820754 | + | 0.571282i | \(0.193554\pi\) | |||||||
\(608\) | 5.47694e49i | 0.424887i | ||||||||
\(609\) | −1.53234e50 | + | 3.12107e49i | −1.15410 | + | 0.235067i | ||||
\(610\) | −5.74186e49 | −0.419871 | ||||||||
\(611\) | − | 4.53395e50i | − | 3.21910i | ||||||
\(612\) | 1.99001e49 | + | 4.68248e49i | 0.137193 | + | 0.322812i | ||||
\(613\) | 2.44687e50 | 1.63803 | 0.819017 | − | 0.573769i | \(-0.194519\pi\) | ||||
0.819017 | + | 0.573769i | \(0.194519\pi\) | |||||||
\(614\) | − | 2.93406e49i | − | 0.190738i | ||||||
\(615\) | 2.42441e48 | + | 1.19030e49i | 0.0153058 | + | 0.0751460i | ||||
\(616\) | 6.90664e49 | 0.423462 | ||||||||
\(617\) | 1.86269e50i | 1.10920i | 0.832118 | + | 0.554598i | \(0.187128\pi\) | ||||
−0.832118 | + | 0.554598i | \(0.812872\pi\) | |||||||
\(618\) | −1.21761e50 | + | 2.48003e49i | −0.704232 | + | 0.143438i | ||||
\(619\) | −1.39441e50 | −0.783356 | −0.391678 | − | 0.920102i | \(-0.628105\pi\) | ||||
−0.391678 | + | 0.920102i | \(0.628105\pi\) | |||||||
\(620\) | − | 4.74918e49i | − | 0.259160i | ||||||
\(621\) | −6.22298e49 | + | 4.28295e49i | −0.329875 | + | 0.227036i | ||||
\(622\) | 3.89684e49 | 0.200671 | ||||||||
\(623\) | − | 1.86369e50i | − | 0.932370i | ||||||
\(624\) | −1.72243e49 | − | 8.45655e49i | −0.0837181 | − | 0.411027i | ||||
\(625\) | 8.22728e49 | 0.388522 | ||||||||
\(626\) | 1.16999e49i | 0.0536840i | ||||||||
\(627\) | −6.09060e49 | + | 1.24054e49i | −0.271547 | + | 0.0553087i | ||||
\(628\) | 1.45433e50 | 0.630071 | ||||||||
\(629\) | 3.21930e49i | 0.135535i | ||||||||
\(630\) | −5.10356e49 | + | 2.16897e49i | −0.208806 | + | 0.0887408i | ||||
\(631\) | 3.02076e50 | 1.20112 | 0.600561 | − | 0.799579i | \(-0.294944\pi\) | ||||
0.600561 | + | 0.799579i | \(0.294944\pi\) | |||||||
\(632\) | 4.87274e50i | 1.88307i | ||||||||
\(633\) | 1.75716e49 | + | 8.62703e49i | 0.0659999 | + | 0.324037i | ||||
\(634\) | −5.22690e49 | −0.190826 | ||||||||
\(635\) | − | 2.67324e48i | − | 0.00948660i | ||||||
\(636\) | −1.12165e50 | + | 2.28457e49i | −0.386926 | + | 0.0788092i | ||||
\(637\) | −2.76551e50 | −0.927398 | ||||||||
\(638\) | 2.14457e50i | 0.699147i | ||||||||
\(639\) | −2.20507e49 | − | 5.18851e49i | −0.0698888 | − | 0.164448i | ||||
\(640\) | −4.31606e49 | −0.132999 | ||||||||
\(641\) | − | 1.72071e50i | − | 0.515542i | −0.966206 | − | 0.257771i | \(-0.917012\pi\) | ||
0.966206 | − | 0.257771i | \(-0.0829880\pi\) | |||||||
\(642\) | 6.59044e49 | + | 3.23568e50i | 0.191992 | + | 0.942616i | ||||
\(643\) | −4.34040e50 | −1.22951 | −0.614755 | − | 0.788718i | \(-0.710745\pi\) | ||||
−0.614755 | + | 0.788718i | \(0.710745\pi\) | |||||||
\(644\) | 5.06248e49i | 0.139450i | ||||||||
\(645\) | 1.49266e50 | − | 3.04026e49i | 0.399840 | − | 0.0814395i | ||||
\(646\) | 8.91786e49 | 0.232314 | ||||||||
\(647\) | − | 9.80395e49i | − | 0.248384i | −0.992258 | − | 0.124192i | \(-0.960366\pi\) | ||
0.992258 | − | 0.124192i | \(-0.0396339\pi\) | |||||||
\(648\) | −3.09276e50 | − | 2.98141e50i | −0.762072 | − | 0.734636i | ||||
\(649\) | 3.62426e50 | 0.868590 | ||||||||
\(650\) | − | 4.14454e50i | − | 0.966130i | ||||||
\(651\) | −6.61639e49 | − | 3.24842e50i | −0.150025 | − | 0.736571i | ||||
\(652\) | −3.06462e49 | −0.0675959 | ||||||||
\(653\) | 5.13701e50i | 1.10223i | 0.834428 | + | 0.551116i | \(0.185798\pi\) | ||||
−0.834428 | + | 0.551116i | \(0.814202\pi\) | |||||||
\(654\) | 2.98131e50 | − | 6.07234e49i | 0.622311 | − | 0.126752i | ||||
\(655\) | 7.06185e49 | 0.143409 | ||||||||
\(656\) | − | 1.97016e49i | − | 0.0389254i | ||||||
\(657\) | 3.96631e50 | − | 1.68565e50i | 0.762447 | − | 0.324034i | ||||
\(658\) | 4.72500e50 | 0.883763 | ||||||||
\(659\) | − | 1.24566e50i | − | 0.226705i | −0.993555 | − | 0.113352i | \(-0.963841\pi\) | ||
0.993555 | − | 0.113352i | \(-0.0361589\pi\) | |||||||
\(660\) | −1.55439e49 | − | 7.63152e49i | −0.0275276 | − | 0.135151i | ||||
\(661\) | −5.32566e50 | −0.917799 | −0.458899 | − | 0.888488i | \(-0.651756\pi\) | ||||
−0.458899 | + | 0.888488i | \(0.651756\pi\) | |||||||
\(662\) | − | 1.45504e50i | − | 0.244024i | ||||||
\(663\) | 7.33398e50 | − | 1.49379e50i | 1.19701 | − | 0.243806i | ||||
\(664\) | −4.05963e50 | −0.644854 | ||||||||
\(665\) | − | 9.95425e49i | − | 0.153893i | ||||||
\(666\) | −3.57194e49 | − | 8.40472e49i | −0.0537487 | − | 0.126470i | ||||
\(667\) | −4.67881e50 | −0.685284 | ||||||||
\(668\) | − | 4.35530e50i | − | 0.620929i | ||||||
\(669\) | 2.09117e50 | + | 1.02669e51i | 0.290215 | + | 1.42486i | ||||
\(670\) | 9.68986e49 | 0.130909 | ||||||||
\(671\) | − | 5.62915e50i | − | 0.740350i | ||||||
\(672\) | −4.69399e50 | + | 9.56073e49i | −0.601029 | + | 0.122418i | ||||
\(673\) | −1.36851e51 | −1.70600 | −0.852998 | − | 0.521915i | \(-0.825218\pi\) | ||||
−0.852998 | + | 0.521915i | \(0.825218\pi\) | |||||||
\(674\) | − | 3.43969e50i | − | 0.417486i | ||||||
\(675\) | −3.74224e50 | − | 5.43734e50i | −0.442246 | − | 0.642567i | ||||
\(676\) | 9.25576e50 | 1.06505 | ||||||||
\(677\) | 1.36362e51i | 1.52790i | 0.645274 | + | 0.763951i | \(0.276743\pi\) | ||||
−0.645274 | + | 0.763951i | \(0.723257\pi\) | |||||||
\(678\) | 2.23195e50 | + | 1.09581e51i | 0.243529 | + | 1.19564i | ||||
\(679\) | −3.47427e50 | −0.369154 | ||||||||
\(680\) | 3.32590e50i | 0.344151i | ||||||||
\(681\) | 8.02437e50 | − | 1.63441e50i | 0.808654 | − | 0.164707i | ||||
\(682\) | −4.54630e50 | −0.446210 | ||||||||
\(683\) | 3.17270e50i | 0.303289i | 0.988435 | + | 0.151644i | \(0.0484568\pi\) | ||||
−0.988435 | + | 0.151644i | \(0.951543\pi\) | |||||||
\(684\) | 2.38437e50 | − | 1.01334e50i | 0.222005 | − | 0.0943504i | ||||
\(685\) | 7.16797e50 | 0.650079 | ||||||||
\(686\) | − | 8.35810e50i | − | 0.738369i | ||||||
\(687\) | 2.26596e50 | + | 1.11251e51i | 0.194998 | + | 0.957373i | ||||
\(688\) | −2.47062e50 | −0.207116 | ||||||||
\(689\) | 1.68391e51i | 1.37522i | ||||||||
\(690\) | −1.62575e50 | + | 3.31134e49i | −0.129351 | + | 0.0263463i | ||||
\(691\) | 6.64077e50 | 0.514770 | 0.257385 | − | 0.966309i | \(-0.417139\pi\) | ||||
0.257385 | + | 0.966309i | \(0.417139\pi\) | |||||||
\(692\) | 3.95818e49i | 0.0298941i | ||||||||
\(693\) | −2.12639e50 | − | 5.00337e50i | −0.156475 | − | 0.368184i | ||||
\(694\) | 9.97529e50 | 0.715246 | ||||||||
\(695\) | 3.50922e50i | 0.245179i | ||||||||
\(696\) | −5.31009e50 | − | 2.60707e51i | −0.361523 | − | 1.77495i | ||||
\(697\) | 1.70863e50 | 0.113360 | ||||||||
\(698\) | − | 1.26874e51i | − | 0.820303i | ||||||
\(699\) | −1.28346e51 | + | 2.61416e50i | −0.808711 | + | 0.164718i | ||||
\(700\) | −4.42336e50 | −0.271636 | ||||||||
\(701\) | − | 3.03202e51i | − | 1.81471i | −0.420366 | − | 0.907355i | \(-0.638098\pi\) | ||
0.420366 | − | 0.907355i | \(-0.361902\pi\) | |||||||
\(702\) | −1.74896e51 | + | 1.20372e51i | −1.02026 | + | 0.702194i | ||||
\(703\) | 1.63930e50 | 0.0932102 | ||||||||
\(704\) | 9.06598e50i | 0.502466i | ||||||||
\(705\) | −3.16514e50 | − | 1.55397e51i | −0.170997 | − | 0.839537i | ||||
\(706\) | 2.78201e50 | 0.146513 | ||||||||
\(707\) | 1.23650e51i | 0.634813i | ||||||||
\(708\) | −1.48024e51 | + | 3.01497e50i | −0.740858 | + | 0.150898i | ||||
\(709\) | 8.48005e50 | 0.413777 | 0.206888 | − | 0.978365i | \(-0.433666\pi\) | ||||
0.206888 | + | 0.978365i | \(0.433666\pi\) | |||||||
\(710\) | − | 1.23817e50i | − | 0.0589018i | ||||||
\(711\) | 3.52996e51 | − | 1.50020e51i | 1.63726 | − | 0.695820i | ||||
\(712\) | 3.17082e51 | 1.43394 | ||||||||
\(713\) | − | 9.91865e50i | − | 0.437362i | ||||||
\(714\) | 1.55673e50 | + | 7.64302e50i | 0.0669339 | + | 0.328622i | ||||
\(715\) | −1.14571e51 | −0.480357 | ||||||||
\(716\) | − | 2.77722e49i | − | 0.0113547i | ||||||
\(717\) | −2.63653e51 | + | 5.37010e50i | −1.05121 | + | 0.214110i | ||||
\(718\) | −2.38226e49 | −0.00926295 | ||||||||
\(719\) | 2.60399e51i | 0.987460i | 0.869615 | + | 0.493730i | \(0.164367\pi\) | ||||
−0.869615 | + | 0.493730i | \(0.835633\pi\) | |||||||
\(720\) | −1.18070e50 | − | 2.77817e50i | −0.0436671 | − | 0.102748i | ||||
\(721\) | 1.95095e51 | 0.703740 | ||||||||
\(722\) | 1.54369e51i | 0.543114i | ||||||||
\(723\) | 1.93059e50 | + | 9.47851e50i | 0.0662521 | + | 0.325275i | ||||
\(724\) | −6.95853e50 | −0.232929 | ||||||||
\(725\) | − | 4.08812e51i | − | 1.33487i | ||||||
\(726\) | 1.43174e51 | − | 2.91618e50i | 0.456043 | − | 0.0928869i | ||||
\(727\) | −4.00585e51 | −1.24473 | −0.622365 | − | 0.782727i | \(-0.713828\pi\) | ||||
−0.622365 | + | 0.782727i | \(0.713828\pi\) | |||||||
\(728\) | 4.23490e51i | 1.28375i | ||||||||
\(729\) | −1.20764e51 | + | 3.15839e51i | −0.357141 | + | 0.934050i | ||||
\(730\) | 9.46503e50 | 0.273093 | ||||||||
\(731\) | − | 2.14265e51i | − | 0.603169i | ||||||
\(732\) | 4.68280e50 | + | 2.29910e51i | 0.128619 | + | 0.631477i | ||||
\(733\) | −2.72371e51 | −0.729943 | −0.364971 | − | 0.931019i | \(-0.618921\pi\) | ||||
−0.364971 | + | 0.931019i | \(0.618921\pi\) | |||||||
\(734\) | 1.69137e51i | 0.442293i | ||||||||
\(735\) | −9.47858e50 | + | 1.93060e50i | −0.241864 | + | 0.0492629i | ||||
\(736\) | −1.43325e51 | −0.356880 | ||||||||
\(737\) | 9.49964e50i | 0.230830i | ||||||||
\(738\) | −4.46077e50 | + | 1.89579e50i | −0.105778 | + | 0.0449548i | ||||
\(739\) | 7.29458e51 | 1.68811 | 0.844054 | − | 0.536258i | \(-0.180163\pi\) | ||||
0.844054 | + | 0.536258i | \(0.180163\pi\) | |||||||
\(740\) | 2.05404e50i | 0.0463916i | ||||||||
\(741\) | −7.60652e50 | − | 3.73454e51i | −0.167671 | − | 0.823207i | ||||
\(742\) | −1.75486e51 | −0.377549 | ||||||||
\(743\) | − | 2.66881e51i | − | 0.560426i | −0.959938 | − | 0.280213i | \(-0.909595\pi\) | ||
0.959938 | − | 0.280213i | \(-0.0904051\pi\) | |||||||
\(744\) | 5.52676e51 | − | 1.12569e51i | 1.13281 | − | 0.230731i | ||||
\(745\) | −3.68990e51 | −0.738247 | ||||||||
\(746\) | − | 3.49380e51i | − | 0.682338i | ||||||
\(747\) | 1.24986e51 | + | 2.94091e51i | 0.238282 | + | 0.560676i | ||||
\(748\) | −1.09547e51 | −0.203879 | ||||||||
\(749\) | − | 5.18447e51i | − | 0.941958i | ||||||
\(750\) | −6.60241e50 | − | 3.24156e51i | −0.117112 | − | 0.574978i | ||||
\(751\) | −7.60412e50 | −0.131683 | −0.0658416 | − | 0.997830i | \(-0.520973\pi\) | ||||
−0.0658416 | + | 0.997830i | \(0.520973\pi\) | |||||||
\(752\) | 2.57210e51i | 0.434878i | ||||||||
\(753\) | 8.38303e51 | − | 1.70746e51i | 1.38386 | − | 0.281865i | ||||
\(754\) | −1.31497e52 | −2.11950 | ||||||||
\(755\) | 3.40757e51i | 0.536290i | ||||||||
\(756\) | 1.28470e51 | + | 1.86662e51i | 0.197428 | + | 0.286856i | ||||
\(757\) | 9.95443e51 | 1.49379 | 0.746897 | − | 0.664940i | \(-0.231543\pi\) | ||||
0.746897 | + | 0.664940i | \(0.231543\pi\) | |||||||
\(758\) | − | 2.59140e51i | − | 0.379743i | ||||||
\(759\) | −3.24634e50 | − | 1.59384e51i | −0.0464560 | − | 0.228083i | ||||
\(760\) | 1.69358e51 | 0.236680 | ||||||||
\(761\) | − | 1.02462e52i | − | 1.39842i | −0.714915 | − | 0.699211i | \(-0.753535\pi\) | ||
0.714915 | − | 0.699211i | \(-0.246465\pi\) | |||||||
\(762\) | 1.04518e50 | − | 2.12882e49i | 0.0139316 | − | 0.00283760i | ||||
\(763\) | −4.77689e51 | −0.621876 | ||||||||
\(764\) | 2.73503e50i | 0.0347762i | ||||||||
\(765\) | 2.40938e51 | − | 1.02397e51i | 0.299226 | − | 0.127169i | ||||
\(766\) | 6.73583e51 | 0.817096 | ||||||||
\(767\) | 2.22227e52i | 2.63317i | ||||||||
\(768\) | −1.83432e51 | − | 9.00586e51i | −0.212311 | − | 1.04237i | ||||
\(769\) | −1.00804e52 | −1.13974 | −0.569869 | − | 0.821735i | \(-0.693006\pi\) | ||||
−0.569869 | + | 0.821735i | \(0.693006\pi\) | |||||||
\(770\) | − | 1.19398e51i | − | 0.131876i | ||||||
\(771\) | −8.41988e51 | + | 1.71496e51i | −0.908504 | + | 0.185044i | ||||
\(772\) | −2.92927e51 | −0.308780 | ||||||||
\(773\) | 1.35607e52i | 1.39654i | 0.715835 | + | 0.698269i | \(0.246046\pi\) | ||||
−0.715835 | + | 0.698269i | \(0.753954\pi\) | |||||||
\(774\) | 2.37735e51 | + | 5.59388e51i | 0.239197 | + | 0.562828i | ||||
\(775\) | 8.66645e51 | 0.851943 | ||||||||
\(776\) | − | 5.91101e51i | − | 0.567742i | ||||||
\(777\) | 2.86162e50 | + | 1.40496e51i | 0.0268555 | + | 0.131851i | ||||
\(778\) | −3.93845e51 | −0.361154 | ||||||||
\(779\) | − | 8.70053e50i | − | 0.0779599i | ||||||
\(780\) | 4.67937e51 | − | 9.53096e50i | 0.409718 | − | 0.0834514i | ||||
\(781\) | 1.21386e51 | 0.103860 | ||||||||
\(782\) | 2.33370e51i | 0.195130i | ||||||||
\(783\) | −1.72515e52 | + | 1.18733e52i | −1.40967 | + | 0.970200i | ||||
\(784\) | 1.56887e51 | 0.125285 | ||||||||
\(785\) | − | 7.48330e51i | − | 0.584035i | ||||||
\(786\) | 5.62368e50 | + | 2.76104e51i | 0.0428958 | + | 0.210604i | ||||
\(787\) | 2.46972e51 | 0.184121 | 0.0920603 | − | 0.995753i | \(-0.470655\pi\) | ||||
0.0920603 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(788\) | − | 7.15443e50i | − | 0.0521319i | ||||||
\(789\) | −1.18428e52 | + | 2.41214e51i | −0.843467 | + | 0.171798i | ||||
\(790\) | 8.42375e51 | 0.586432 | ||||||||
\(791\) | − | 1.75580e52i | − | 1.19481i | ||||||
\(792\) | 8.51258e51 | − | 3.61777e51i | 0.566249 | − | 0.240651i | ||||
\(793\) | 3.45159e52 | 2.24441 | ||||||||
\(794\) | 5.95172e51i | 0.378333i | ||||||||
\(795\) | 1.17553e51 | + | 5.77146e51i | 0.0730510 | + | 0.358655i | ||||
\(796\) | −9.70306e50 | −0.0589486 | ||||||||
\(797\) | − | 1.49302e51i | − | 0.0886780i | −0.999017 | − | 0.0443390i | \(-0.985882\pi\) | ||
0.999017 | − | 0.0443390i | \(-0.0141182\pi\) | |||||||
\(798\) | 3.89190e51 | − | 7.92704e50i | 0.226001 | − | 0.0460319i | ||||
\(799\) | −2.23067e52 | −1.26646 | ||||||||
\(800\) | − | 1.25231e52i | − | 0.695171i | ||||||
\(801\) | −9.76220e51 | − | 2.29703e52i | −0.529862 | − | 1.24676i | ||||
\(802\) | 9.83805e51 | 0.522120 | ||||||||
\(803\) | 9.27923e51i | 0.481540i | ||||||||
\(804\) | −7.90261e50 | − | 3.87991e51i | −0.0401016 | − | 0.196885i | ||||
\(805\) | 2.60491e51 | 0.129261 | ||||||||
\(806\) | − | 2.78763e52i | − | 1.35271i | ||||||
\(807\) | −1.70878e52 | + | 3.48046e51i | −0.810893 | + | 0.165163i | ||||
\(808\) | −2.10375e52 | −0.976313 | ||||||||
\(809\) | 4.45901e51i | 0.202379i | 0.994867 | + | 0.101189i | \(0.0322648\pi\) | ||||
−0.994867 | + | 0.101189i | \(0.967735\pi\) | |||||||
\(810\) | −5.15411e51 | + | 5.34660e51i | −0.228783 | + | 0.237327i | ||||
\(811\) | 1.44695e52 | 0.628172 | 0.314086 | − | 0.949395i | \(-0.398302\pi\) | ||||
0.314086 | + | 0.949395i | \(0.398302\pi\) | |||||||
\(812\) | 1.40344e52i | 0.595916i | ||||||||
\(813\) | −2.85094e50 | − | 1.39971e51i | −0.0118402 | − | 0.0581312i | ||||
\(814\) | 1.96630e51 | 0.0798748 | ||||||||
\(815\) | 1.57691e51i | 0.0626570i | ||||||||
\(816\) | −4.16056e51 | + | 8.47423e50i | −0.161707 | + | 0.0329365i | ||||
\(817\) | −1.09106e52 | −0.414813 | ||||||||
\(818\) | − | 5.19791e51i | − | 0.193317i | ||||||
\(819\) | 3.06789e52 | − | 1.30383e52i | 1.11617 | − | 0.474362i | ||||
\(820\) | 1.09018e51 | 0.0388014 | ||||||||
\(821\) | 2.38829e51i | 0.0831591i | 0.999135 | + | 0.0415795i | \(0.0132390\pi\) | ||||
−0.999135 | + | 0.0415795i | \(0.986761\pi\) | |||||||
\(822\) | 5.70819e51 | + | 2.80253e52i | 0.194449 | + | 0.954678i | ||||
\(823\) | 2.69269e52 | 0.897407 | 0.448703 | − | 0.893681i | \(-0.351886\pi\) | ||||
0.448703 | + | 0.893681i | \(0.351886\pi\) | |||||||
\(824\) | 3.31929e52i | 1.08232i | ||||||||
\(825\) | 1.39262e52 | − | 2.83650e51i | 0.444286 | − | 0.0904922i | ||||
\(826\) | −2.31591e52 | −0.722904 | ||||||||
\(827\) | 4.62393e52i | 1.41225i | 0.708086 | + | 0.706127i | \(0.249559\pi\) | ||||
−0.708086 | + | 0.706127i | \(0.750441\pi\) | |||||||
\(828\) | 2.65178e51 | + | 6.23961e51i | 0.0792487 | + | 0.186471i | ||||
\(829\) | 3.34053e52 | 0.976862 | 0.488431 | − | 0.872602i | \(-0.337569\pi\) | ||||
0.488431 | + | 0.872602i | \(0.337569\pi\) | |||||||
\(830\) | 7.01808e51i | 0.200823i | ||||||||
\(831\) | −1.18739e51 | − | 5.82969e51i | −0.0332488 | − | 0.163240i | ||||
\(832\) | −5.55893e52 | −1.52325 | ||||||||
\(833\) | 1.36061e52i | 0.364858i | ||||||||
\(834\) | −1.37203e52 | + | 2.79456e51i | −0.360060 | + | 0.0733371i | ||||
\(835\) | −2.24103e52 | −0.575561 | ||||||||
\(836\) | 5.57826e51i | 0.140212i | ||||||||
\(837\) | −2.51704e52 | − | 3.65717e52i | −0.619202 | − | 0.899678i | ||||
\(838\) | 2.83066e52 | 0.681546 | ||||||||
\(839\) | − | 6.10331e52i | − | 1.43830i | −0.694854 | − | 0.719151i | \(-0.744531\pi\) | ||
0.694854 | − | 0.719151i | \(-0.255469\pi\) | |||||||
\(840\) | 2.95638e51 | + | 1.45148e52i | 0.0681919 | + | 0.334799i | ||||
\(841\) | −8.54153e52 | −1.92845 | ||||||||
\(842\) | − | 3.40435e51i | − | 0.0752344i | ||||||
\(843\) | 6.41196e52 | − | 1.30599e52i | 1.38706 | − | 0.282516i | ||||
\(844\) | 7.90132e51 | 0.167315 | ||||||||
\(845\) | − | 4.76258e52i | − | 0.987236i | ||||||
\(846\) | 5.82366e52 | − | 2.47501e52i | 1.18176 | − | 0.502238i | ||||
\(847\) | −2.29405e52 | −0.455724 | ||||||||
\(848\) | − | 9.55278e51i | − | 0.185782i | ||||||
\(849\) | 1.45032e52 | + | 7.12056e52i | 0.276137 | + | 1.35574i | ||||
\(850\) | −2.03908e52 | −0.380096 | ||||||||
\(851\) | 4.28987e51i | 0.0782910i | ||||||||
\(852\) | −4.95773e51 | + | 1.00979e51i | −0.0885870 | + | 0.0180434i | ||||
\(853\) | −7.25447e51 | −0.126918 | −0.0634590 | − | 0.997984i | \(-0.520213\pi\) | ||||
−0.0634590 | + | 0.997984i | \(0.520213\pi\) | |||||||
\(854\) | 3.59704e52i | 0.616174i | ||||||||
\(855\) | −5.21415e51 | − | 1.22688e52i | −0.0874567 | − | 0.205785i | ||||
\(856\) | 8.82069e52 | 1.44869 | ||||||||
\(857\) | − | 8.42381e52i | − | 1.35473i | −0.735646 | − | 0.677366i | \(-0.763121\pi\) | ||
0.735646 | − | 0.677366i | \(-0.236879\pi\) | |||||||
\(858\) | −9.12380e51 | − | 4.47947e52i | −0.143683 | − | 0.705432i | ||||
\(859\) | 2.60858e52 | 0.402279 | 0.201140 | − | 0.979563i | \(-0.435536\pi\) | ||||
0.201140 | + | 0.979563i | \(0.435536\pi\) | |||||||
\(860\) | − | 1.36710e52i | − | 0.206456i | ||||||
\(861\) | 7.45676e51 | − | 1.51879e51i | 0.110279 | − | 0.0224617i | ||||
\(862\) | 4.06461e52 | 0.588692 | ||||||||
\(863\) | − | 4.81527e52i | − | 0.683009i | −0.939880 | − | 0.341505i | \(-0.889064\pi\) | ||
0.939880 | − | 0.341505i | \(-0.110936\pi\) | |||||||
\(864\) | −5.28464e52 | + | 3.63714e52i | −0.734121 | + | 0.505258i | ||||
\(865\) | 2.03669e51 | 0.0277099 | ||||||||
\(866\) | 4.49882e52i | 0.599482i | ||||||||
\(867\) | 7.94275e51 | + | 3.89962e52i | 0.103664 | + | 0.508954i | ||||
\(868\) | −2.97516e52 | −0.380326 | ||||||||
\(869\) | 8.25839e52i | 1.03404i | ||||||||
\(870\) | −4.50697e52 | + | 9.17981e51i | −0.552762 | + | 0.112587i | ||||
\(871\) | −5.82484e52 | −0.699773 | ||||||||
\(872\) | − | 8.12725e52i | − | 0.956416i | ||||||
\(873\) | −4.28211e52 | + | 1.81986e52i | −0.493630 | + | 0.209789i | ||||
\(874\) | 1.18835e52 | 0.134195 | ||||||||
\(875\) | 5.19389e52i | 0.574576i | ||||||||
\(876\) | −7.71925e51 | − | 3.78989e52i | −0.0836568 | − | 0.410726i | ||||
\(877\) | −1.85957e52 | −0.197433 | −0.0987165 | − | 0.995116i | \(-0.531474\pi\) | ||||
−0.0987165 | + | 0.995116i | \(0.531474\pi\) | |||||||
\(878\) | 8.46658e52i | 0.880656i | ||||||||
\(879\) | −2.63536e52 | + | 5.36771e51i | −0.268559 | + | 0.0547002i | ||||
\(880\) | 6.49957e51 | 0.0648928 | ||||||||
\(881\) | 1.62346e53i | 1.58809i | 0.607859 | + | 0.794045i | \(0.292029\pi\) | ||||
−0.607859 | + | 0.794045i | \(0.707971\pi\) | |||||||
\(882\) | −1.50965e52 | − | 3.55218e52i | −0.144691 | − | 0.340456i | ||||
\(883\) | 1.35375e53 | 1.27130 | 0.635648 | − | 0.771979i | \(-0.280733\pi\) | ||||
0.635648 | + | 0.771979i | \(0.280733\pi\) | |||||||
\(884\) | − | 6.71704e52i | − | 0.618070i | ||||||
\(885\) | 1.55136e52 | + | 7.61664e52i | 0.139873 | + | 0.686728i | ||||
\(886\) | 2.52123e52 | 0.222743 | ||||||||
\(887\) | 8.73319e51i | 0.0756045i | 0.999285 | + | 0.0378022i | \(0.0120357\pi\) | ||||
−0.999285 | + | 0.0378022i | \(0.987964\pi\) | |||||||
\(888\) | −2.39035e52 | + | 4.86867e51i | −0.202781 | + | 0.0413026i | ||||
\(889\) | −1.67467e51 | −0.0139219 | ||||||||
\(890\) | − | 5.48155e52i | − | 0.446563i | ||||||
\(891\) | −5.24164e52 | − | 5.05293e52i | −0.418474 | − | 0.403408i | ||||
\(892\) | 9.40329e52 | 0.735720 | ||||||||
\(893\) | 1.13588e53i | 0.870975i | ||||||||
\(894\) | −2.93844e52 | − | 1.44267e53i | −0.220822 | − | 1.08416i | ||||
\(895\) | −1.42902e51 | −0.0105251 | ||||||||
\(896\) | 2.70383e52i | 0.195180i | ||||||||
\(897\) | 9.77286e52 | − | 1.99054e52i | 0.691445 | − | 0.140834i | ||||
\(898\) | −1.55814e53 | −1.08052 | ||||||||
\(899\) | − | 2.74968e53i | − | 1.86899i | ||||||
\(900\) | −5.45188e52 | + | 2.31700e52i | −0.363229 | + | 0.154369i | ||||
\(901\) | 8.28469e52 | 0.541041 | ||||||||
\(902\) | − | 1.04360e52i | − | 0.0668064i | ||||||
\(903\) | −1.90459e52 | − | 9.35090e52i | −0.119515 | − | 0.586778i | ||||
\(904\) | 2.98726e53 | 1.83756 | ||||||||
\(905\) | 3.58053e52i | 0.215910i | ||||||||
\(906\) | −1.33229e53 | + | 2.71361e52i | −0.787573 | + | 0.160413i | ||||
\(907\) | −2.38299e53 | −1.38099 | −0.690497 | − | 0.723335i | \(-0.742608\pi\) | ||||
−0.690497 | + | 0.723335i | \(0.742608\pi\) | |||||||
\(908\) | − | 7.34936e52i | − | 0.417546i | ||||||
\(909\) | 6.47694e52 | + | 1.52402e53i | 0.360761 | + | 0.848867i | ||||
\(910\) | 7.32108e52 | 0.399788 | ||||||||
\(911\) | − | 6.66896e52i | − | 0.357048i | −0.983936 | − | 0.178524i | \(-0.942868\pi\) | ||
0.983936 | − | 0.178524i | \(-0.0571323\pi\) | |||||||
\(912\) | 4.31517e51 | + | 2.11860e52i | 0.0226512 | + | 0.111209i | ||||
\(913\) | −6.88031e52 | −0.354107 | ||||||||
\(914\) | − | 1.45585e53i | − | 0.734657i | ||||||
\(915\) | 1.18301e53 | − | 2.40955e52i | 0.585339 | − | 0.119222i | ||||
\(916\) | 1.01892e53 | 0.494336 | ||||||||
\(917\) | − | 4.42395e52i | − | 0.210457i | ||||||
\(918\) | 5.92220e52 | + | 8.60475e52i | 0.276258 | + | 0.401393i | ||||
\(919\) | −2.05261e53 | −0.938915 | −0.469458 | − | 0.882955i | \(-0.655551\pi\) | ||||
−0.469458 | + | 0.882955i | \(0.655551\pi\) | |||||||
\(920\) | 4.43192e52i | 0.198797i | ||||||||
\(921\) | 1.23127e52 | + | 6.04509e52i | 0.0541600 | + | 0.265907i | ||||
\(922\) | −1.00374e53 | −0.432977 | ||||||||
\(923\) | 7.44295e52i | 0.314858i | ||||||||
\(924\) | −4.78082e52 | + | 9.73760e51i | −0.198339 | + | 0.0403977i | ||||
\(925\) | −3.74828e52 | −0.152504 | ||||||||
\(926\) | 2.80357e53i | 1.11870i | ||||||||
\(927\) | 2.40459e53 | − | 1.02193e53i | 0.941036 | − | 0.399932i | ||||
\(928\) | −3.97331e53 | −1.52507 | ||||||||
\(929\) | 1.08375e53i | 0.407986i | 0.978972 | + | 0.203993i | \(0.0653920\pi\) | ||||
−0.978972 | + | 0.203993i | \(0.934608\pi\) | |||||||
\(930\) | −1.94604e52 | − | 9.55437e52i | −0.0718551 | − | 0.352784i | ||||
\(931\) | 6.92837e52 | 0.250921 | ||||||||
\(932\) | 1.17550e53i | 0.417575i | ||||||||
\(933\) | −8.02873e52 | + | 1.63529e52i | −0.279755 | + | 0.0569805i | ||||
\(934\) | 1.14034e53 | 0.389755 | ||||||||
\(935\) | 5.63678e52i | 0.188983i | ||||||||
\(936\) | 2.21829e53 | + | 5.21961e53i | 0.729546 | + | 1.71661i | ||||
\(937\) | 1.55713e53 | 0.502356 | 0.251178 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251178 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(938\) | − | 6.07029e52i | − | 0.192114i | ||||||
\(939\) | −4.90983e51 | − | 2.41056e52i | −0.0152435 | − | 0.0748405i | ||||
\(940\) | −1.42325e53 | −0.433492 | ||||||||
\(941\) | 5.05546e52i | 0.151059i | 0.997144 | + | 0.0755296i | \(0.0240647\pi\) | ||||
−0.997144 | + | 0.0755296i | \(0.975935\pi\) | |||||||
\(942\) | 2.92581e53 | − | 5.95930e52i | 0.857690 | − | 0.174694i | ||||
\(943\) | 2.27683e52 | 0.0654817 | ||||||||
\(944\) | − | 1.26069e53i | − | 0.355723i | ||||||
\(945\) | 9.60475e52 | − | 6.61045e52i | 0.265897 | − | 0.183003i | ||||
\(946\) | −1.30870e53 | −0.355466 | ||||||||
\(947\) | − | 4.18557e53i | − | 1.11546i | −0.830022 | − | 0.557731i | \(-0.811672\pi\) | ||
0.830022 | − | 0.557731i | \(-0.188328\pi\) | |||||||
\(948\) | −6.87003e52 | − | 3.37295e53i | −0.179642 | − | 0.881981i | ||||
\(949\) | −5.68969e53 | −1.45981 | ||||||||
\(950\) | 1.03832e53i | 0.261400i | ||||||||
\(951\) | 1.07691e53 | − | 2.19345e52i | 0.266029 | − | 0.0541848i | ||||
\(952\) | 2.08354e53 | 0.505053 | ||||||||
\(953\) | 3.25845e52i | 0.0775066i | 0.999249 | + | 0.0387533i | \(0.0123386\pi\) | ||||
−0.999249 | + | 0.0387533i | \(0.987661\pi\) | |||||||
\(954\) | −2.16291e53 | + | 9.19217e52i | −0.504855 | + | 0.214559i | ||||
\(955\) | 1.40732e52 | 0.0322353 | ||||||||
\(956\) | 2.41475e53i | 0.542788i | ||||||||
\(957\) | −8.99961e52 | − | 4.41850e53i | −0.198522 | − | 0.974675i | ||||
\(958\) | 1.37908e53 | 0.298546 | ||||||||
\(959\) | − | 4.49043e53i | − | 0.954011i | ||||||
\(960\) | −1.90528e53 | + | 3.88068e52i | −0.397262 | + | 0.0809144i | ||||
\(961\) | 9.42318e52 | 0.192831 | ||||||||
\(962\) | 1.20566e53i | 0.242144i | ||||||||
\(963\) | −2.71568e53 | − | 6.38996e53i | −0.535310 | − | 1.25958i | ||||
\(964\) | 8.68118e52 | 0.167955 | ||||||||
\(965\) | 1.50727e53i | 0.286219i | ||||||||
\(966\) | 2.07442e52 | + | 1.01847e53i | 0.0386641 | + | 0.189827i | ||||
\(967\) | 8.75276e53 | 1.60129 | 0.800643 | − | 0.599142i | \(-0.204492\pi\) | ||||
0.800643 | + | 0.599142i | \(0.204492\pi\) | |||||||
\(968\) | − | 3.90303e53i | − | 0.700883i | ||||||
\(969\) | −1.83736e53 | + | 3.74235e52i | −0.323867 | + | 0.0659654i | ||||
\(970\) | −1.02187e53 | −0.176808 | ||||||||
\(971\) | 6.79262e53i | 1.15370i | 0.816852 | + | 0.576848i | \(0.195717\pi\) | ||||
−0.816852 | + | 0.576848i | \(0.804283\pi\) | |||||||
\(972\) | 2.56117e53 | + | 1.62771e53i | 0.427018 | + | 0.271384i | ||||
\(973\) | 2.19838e53 | 0.359808 | ||||||||
\(974\) | − | 3.16952e53i | − | 0.509251i | ||||||
\(975\) | 1.73924e53 | + | 8.53906e53i | 0.274332 | + | 1.34687i | ||||
\(976\) | −1.95808e53 | −0.303204 | ||||||||
\(977\) | − | 3.90925e53i | − | 0.594280i | −0.954834 | − | 0.297140i | \(-0.903967\pi\) | ||
0.954834 | − | 0.297140i | \(-0.0960327\pi\) | |||||||
\(978\) | −6.16538e52 | + | 1.25577e52i | −0.0920154 | + | 0.0187417i | ||||
\(979\) | 5.37394e53 | 0.787417 | ||||||||
\(980\) | 8.68124e52i | 0.124886i | ||||||||
\(981\) | −5.88762e53 | + | 2.50219e53i | −0.831567 | + | 0.353409i | ||||
\(982\) | 1.41668e53 | 0.196455 | ||||||||
\(983\) | 8.03195e53i | 1.09360i | 0.837264 | + | 0.546799i | \(0.184154\pi\) | ||||
−0.837264 | + | 0.546799i | \(0.815846\pi\) | |||||||
\(984\) | 2.58403e52 | + | 1.26867e53i | 0.0345450 | + | 0.169604i | ||||
\(985\) | −3.68133e52 | −0.0483229 | ||||||||
\(986\) | 6.46957e53i | 0.833856i | ||||||||
\(987\) | −9.73500e53 | + | 1.98283e53i | −1.23205 | + | 0.250944i | ||||
\(988\) | −3.42039e53 | −0.425060 | ||||||||
\(989\) | − | 2.85518e53i | − | 0.348418i | ||||||
\(990\) | −6.25422e52 | − | 1.47161e53i | −0.0749445 | − | 0.176343i | ||||
\(991\) | −1.24081e54 | −1.46009 | −0.730045 | − | 0.683399i | \(-0.760501\pi\) | ||||
−0.730045 | + | 0.683399i | \(0.760501\pi\) | |||||||
\(992\) | − | 8.42306e53i | − | 0.973329i | ||||||
\(993\) | 6.10603e52 | + | 2.99785e53i | 0.0692903 | + | 0.340191i | ||||
\(994\) | −7.75659e52 | −0.0864402 | ||||||||
\(995\) | 4.99274e52i | 0.0546416i | ||||||||
\(996\) | 2.81010e53 | − | 5.72363e52i | 0.302033 | − | 0.0615181i | ||||
\(997\) | 1.37750e54 | 1.45405 | 0.727024 | − | 0.686612i | \(-0.240903\pi\) | ||||
0.727024 | + | 0.686612i | \(0.240903\pi\) | |||||||
\(998\) | − | 2.34817e53i | − | 0.243433i | ||||||
\(999\) | 1.08863e53 | + | 1.58174e53i | 0.110842 | + | 0.161049i |
(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 | 3.37.b.b.2.4 | ✓ | 10 | |
3.2 | odd | 2 | inner | 3.37.b.b.2.7 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.37.b.b.2.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3.37.b.b.2.7 | yes | 10 | 3.2 | odd | 2 | inner |