Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,35,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, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
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: | \(29.2902616171\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 72626617369828 x^{14} - 508386321588656 x^{13} + \cdots + 10\!\cdots\!04 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.11 | ||
Root | \(0.500000 - 190511. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.35.b.a.3.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 49362.6 | − | 121422.i | 0.376607 | − | 0.926373i | ||||
\(3\) | 9.14451e6i | 0.0708107i | 0.999373 | + | 0.0354054i | \(0.0112722\pi\) | ||||
−0.999373 | + | 0.0354054i | \(0.988728\pi\) | |||||||
\(4\) | −1.23065e10 | − | 1.19874e10i | −0.716335 | − | 0.697757i | ||||
\(5\) | −6.20904e11 | −0.813831 | −0.406916 | − | 0.913466i | \(-0.633396\pi\) | ||||
−0.406916 | + | 0.913466i | \(0.633396\pi\) | |||||||
\(6\) | 1.11034e12 | + | 4.51397e11i | 0.0655972 | + | 0.0266678i | ||||
\(7\) | 3.03953e14i | 1.30659i | 0.757103 | + | 0.653295i | \(0.226614\pi\) | ||||
−0.757103 | + | 0.653295i | \(0.773386\pi\) | |||||||
\(8\) | −2.06301e15 | + | 9.02552e14i | −0.916160 | + | 0.400814i | ||||
\(9\) | 1.65936e16 | 0.994986 | ||||||||
\(10\) | −3.06494e16 | + | 7.53911e16i | −0.306494 | + | 0.753911i | ||||
\(11\) | − | 4.34141e17i | − | 0.858925i | −0.903085 | − | 0.429462i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429462i | \(-0.141297\pi\) | |||||||
\(12\) | 1.09619e17 | − | 1.12537e17i | 0.0494087 | − | 0.0507242i | ||||
\(13\) | −1.62713e18 | −0.188098 | −0.0940492 | − | 0.995568i | \(-0.529981\pi\) | ||||
−0.0940492 | + | 0.995568i | \(0.529981\pi\) | |||||||
\(14\) | 3.69064e19 | + | 1.50039e19i | 1.21039 | + | 0.492071i | ||||
\(15\) | − | 5.67786e18i | − | 0.0576280i | ||||||
\(16\) | 7.75384e18 | + | 2.95046e20i | 0.0262710 | + | 0.999655i | ||||
\(17\) | 1.14730e21 | 1.38690 | 0.693449 | − | 0.720506i | \(-0.256090\pi\) | ||||
0.693449 | + | 0.720506i | \(0.256090\pi\) | |||||||
\(18\) | 8.19101e20 | − | 2.01482e21i | 0.374718 | − | 0.921728i | ||||
\(19\) | 4.29240e21i | 0.783230i | 0.920129 | + | 0.391615i | \(0.128083\pi\) | ||||
−0.920129 | + | 0.391615i | \(0.871917\pi\) | |||||||
\(20\) | 7.64118e21 | + | 7.44301e21i | 0.582976 | + | 0.567856i | ||||
\(21\) | −2.77950e21 | −0.0925206 | ||||||||
\(22\) | −5.27141e22 | − | 2.14303e22i | −0.795685 | − | 0.323477i | ||||
\(23\) | − | 1.36588e23i | − | 0.968367i | −0.874966 | − | 0.484183i | \(-0.839117\pi\) | ||
0.874966 | − | 0.484183i | \(-0.160883\pi\) | |||||||
\(24\) | −8.25339e21 | − | 1.88652e22i | −0.0283819 | − | 0.0648739i | ||||
\(25\) | −1.96555e23 | −0.337679 | ||||||||
\(26\) | −8.03194e22 | + | 1.97569e23i | −0.0708391 | + | 0.174249i | ||||
\(27\) | 3.04245e23i | 0.141266i | ||||||||
\(28\) | 3.64359e24 | − | 3.74061e24i | 0.911682 | − | 0.935956i | ||||
\(29\) | 1.10326e25 | 1.52024 | 0.760122 | − | 0.649780i | \(-0.225139\pi\) | ||||
0.760122 | + | 0.649780i | \(0.225139\pi\) | |||||||
\(30\) | −6.89415e23 | − | 2.80274e23i | −0.0533850 | − | 0.0217031i | ||||
\(31\) | − | 1.99725e25i | − | 0.885692i | −0.896598 | − | 0.442846i | \(-0.853969\pi\) | ||
0.896598 | − | 0.442846i | \(-0.146031\pi\) | |||||||
\(32\) | 3.62077e25 | + | 1.36228e25i | 0.935947 | + | 0.352140i | ||||
\(33\) | 3.97001e24 | 0.0608211 | ||||||||
\(34\) | 5.66336e25 | − | 1.39307e26i | 0.522315 | − | 1.28479i | ||||
\(35\) | − | 1.88725e26i | − | 1.06334i | ||||||
\(36\) | −2.04209e26 | − | 1.98913e26i | −0.712743 | − | 0.694258i | ||||
\(37\) | 5.08323e26 | 1.11355 | 0.556776 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556776 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(38\) | 5.21190e26 | + | 2.11884e26i | 0.725563 | + | 0.294970i | ||||
\(39\) | − | 1.48793e25i | − | 0.0133194i | ||||||
\(40\) | 1.28093e27 | − | 5.60398e26i | 0.745599 | − | 0.326195i | ||||
\(41\) | 5.95843e26 | 0.227933 | 0.113966 | − | 0.993485i | \(-0.463644\pi\) | ||||
0.113966 | + | 0.993485i | \(0.463644\pi\) | |||||||
\(42\) | −1.37203e26 | + | 3.37491e26i | −0.0348439 | + | 0.0857086i | ||||
\(43\) | − | 2.03855e26i | − | 0.0347022i | −0.999849 | − | 0.0173511i | \(-0.994477\pi\) | ||
0.999849 | − | 0.0173511i | \(-0.00552331\pi\) | |||||||
\(44\) | −5.20421e27 | + | 5.34277e27i | −0.599320 | + | 0.615278i | ||||
\(45\) | −1.03030e28 | −0.809751 | ||||||||
\(46\) | −1.65848e28 | − | 6.74235e27i | −0.897069 | − | 0.364694i | ||||
\(47\) | 3.56118e28i | 1.33638i | 0.743990 | + | 0.668191i | \(0.232931\pi\) | ||||
−0.743990 | + | 0.668191i | \(0.767069\pi\) | |||||||
\(48\) | −2.69805e27 | + | 7.09051e25i | −0.0707863 | + | 0.00186027i | ||||
\(49\) | −3.82703e28 | −0.707177 | ||||||||
\(50\) | −9.70246e27 | + | 2.38660e28i | −0.127172 | + | 0.312817i | ||||
\(51\) | 1.04915e28i | 0.0982073i | ||||||||
\(52\) | 2.00243e28 | + | 1.95050e28i | 0.134741 | + | 0.131247i | ||||
\(53\) | 2.36155e29 | 1.14949 | 0.574747 | − | 0.818331i | \(-0.305100\pi\) | ||||
0.574747 | + | 0.818331i | \(0.305100\pi\) | |||||||
\(54\) | 3.69419e28 | + | 1.50183e28i | 0.130865 | + | 0.0532019i | ||||
\(55\) | 2.69560e29i | 0.699020i | ||||||||
\(56\) | −2.74333e29 | − | 6.27057e29i | −0.523699 | − | 1.19705i | ||||
\(57\) | −3.92519e28 | −0.0554611 | ||||||||
\(58\) | 5.44600e29 | − | 1.33960e30i | 0.572534 | − | 1.40831i | ||||
\(59\) | − | 3.03266e29i | − | 0.238418i | −0.992869 | − | 0.119209i | \(-0.961964\pi\) | ||
0.992869 | − | 0.119209i | \(-0.0380359\pi\) | |||||||
\(60\) | −6.80626e28 | + | 6.98748e28i | −0.0402103 | + | 0.0412809i | ||||
\(61\) | 2.73318e30 | 1.21916 | 0.609580 | − | 0.792724i | \(-0.291338\pi\) | ||||
0.609580 | + | 0.792724i | \(0.291338\pi\) | |||||||
\(62\) | −2.42509e30 | − | 9.85893e29i | −0.820482 | − | 0.333558i | ||||
\(63\) | 5.04366e30i | 1.30004i | ||||||||
\(64\) | 3.44140e30 | − | 3.72394e30i | 0.678697 | − | 0.734418i | ||||
\(65\) | 1.01029e30 | 0.153080 | ||||||||
\(66\) | 1.95970e29 | − | 4.82044e29i | 0.0229056 | − | 0.0563430i | ||||
\(67\) | 1.85805e31i | 1.68185i | 0.541154 | + | 0.840923i | \(0.317987\pi\) | ||||
−0.541154 | + | 0.840923i | \(0.682013\pi\) | |||||||
\(68\) | −1.41193e31 | − | 1.37531e31i | −0.993483 | − | 0.967717i | ||||
\(69\) | 1.24903e30 | 0.0685708 | ||||||||
\(70\) | −2.29153e31 | − | 9.31598e30i | −0.985053 | − | 0.400462i | ||||
\(71\) | 5.00172e31i | 1.68938i | 0.535255 | + | 0.844690i | \(0.320215\pi\) | ||||
−0.535255 | + | 0.844690i | \(0.679785\pi\) | |||||||
\(72\) | −3.42326e31 | + | 1.49765e31i | −0.911566 | + | 0.398804i | ||||
\(73\) | −1.57987e31 | −0.332761 | −0.166381 | − | 0.986062i | \(-0.553208\pi\) | ||||
−0.166381 | + | 0.986062i | \(0.553208\pi\) | |||||||
\(74\) | 2.50922e31 | − | 6.17214e31i | 0.419371 | − | 1.03157i | ||||
\(75\) | − | 1.79740e30i | − | 0.0239113i | ||||||
\(76\) | 5.14546e31 | − | 5.28246e31i | 0.546504 | − | 0.561055i | ||||
\(77\) | 1.31958e32 | 1.12226 | ||||||||
\(78\) | −1.80667e30 | − | 7.34481e29i | −0.0123387 | − | 0.00501617i | ||||
\(79\) | 2.44172e32i | 1.34287i | 0.741061 | + | 0.671437i | \(0.234323\pi\) | ||||
−0.741061 | + | 0.671437i | \(0.765677\pi\) | |||||||
\(80\) | −4.81439e30 | − | 1.83195e32i | −0.0213802 | − | 0.813550i | ||||
\(81\) | 2.73952e32 | 0.984983 | ||||||||
\(82\) | 2.94124e31 | − | 7.23482e31i | 0.0858409 | − | 0.211151i | ||||
\(83\) | − | 6.99260e32i | − | 1.66078i | −0.557186 | − | 0.830388i | \(-0.688119\pi\) | ||
0.557186 | − | 0.830388i | \(-0.311881\pi\) | |||||||
\(84\) | 3.42060e31 | + | 3.33189e31i | 0.0662757 | + | 0.0645569i | ||||
\(85\) | −7.12362e32 | −1.12870 | ||||||||
\(86\) | −2.47524e31 | − | 1.00628e31i | −0.0321472 | − | 0.0130691i | ||||
\(87\) | 1.00888e32i | 0.107650i | ||||||||
\(88\) | 3.91835e32 | + | 8.95636e32i | 0.344269 | + | 0.786912i | ||||
\(89\) | −3.74683e32 | −0.271665 | −0.135833 | − | 0.990732i | \(-0.543371\pi\) | ||||
−0.135833 | + | 0.990732i | \(0.543371\pi\) | |||||||
\(90\) | −5.08583e32 | + | 1.25101e33i | −0.304957 | + | 0.750131i | ||||
\(91\) | − | 4.94571e32i | − | 0.245768i | ||||||
\(92\) | −1.63733e33 | + | 1.68093e33i | −0.675685 | + | 0.693675i | ||||
\(93\) | 1.82638e32 | 0.0627165 | ||||||||
\(94\) | 4.32404e33 | + | 1.75789e33i | 1.23799 | + | 0.503290i | ||||
\(95\) | − | 2.66517e33i | − | 0.637417i | ||||||
\(96\) | −1.24573e32 | + | 3.31102e32i | −0.0249353 | + | 0.0662751i | ||||
\(97\) | −1.01929e34 | −1.71071 | −0.855356 | − | 0.518040i | \(-0.826662\pi\) | ||||
−0.855356 | + | 0.518040i | \(0.826662\pi\) | |||||||
\(98\) | −1.88912e33 | + | 4.64684e33i | −0.266328 | + | 0.655110i | ||||
\(99\) | − | 7.20394e33i | − | 0.854618i | ||||||
\(100\) | 2.41891e33 | + | 2.35618e33i | 0.241891 | + | 0.235618i | ||||
\(101\) | 1.20668e34 | 1.01889 | 0.509445 | − | 0.860503i | \(-0.329851\pi\) | ||||
0.509445 | + | 0.860503i | \(0.329851\pi\) | |||||||
\(102\) | 1.27389e33 | + | 5.17886e32i | 0.0909766 | + | 0.0369855i | ||||
\(103\) | − | 2.46275e34i | − | 1.49000i | −0.667062 | − | 0.745002i | \(-0.732448\pi\) | ||
0.667062 | − | 0.745002i | \(-0.267552\pi\) | |||||||
\(104\) | 3.35678e33 | − | 1.46857e33i | 0.172328 | − | 0.0753924i | ||||
\(105\) | 1.72580e33 | 0.0752961 | ||||||||
\(106\) | 1.16572e34 | − | 2.86743e34i | 0.432907 | − | 1.06486i | ||||
\(107\) | 4.54571e34i | 1.43905i | 0.694464 | + | 0.719527i | \(0.255641\pi\) | ||||
−0.694464 | + | 0.719527i | \(0.744359\pi\) | |||||||
\(108\) | 3.64709e33 | − | 3.74420e33i | 0.0985696 | − | 0.101194i | ||||
\(109\) | 3.80748e34 | 0.879806 | 0.439903 | − | 0.898045i | \(-0.355013\pi\) | ||||
0.439903 | + | 0.898045i | \(0.355013\pi\) | |||||||
\(110\) | 3.27304e34 | + | 1.33062e34i | 0.647553 | + | 0.263256i | ||||
\(111\) | 4.64837e33i | 0.0788515i | ||||||||
\(112\) | −8.96800e34 | + | 2.35680e33i | −1.30614 | + | 0.0343255i | ||||
\(113\) | −5.92069e34 | −0.741377 | −0.370688 | − | 0.928757i | \(-0.620878\pi\) | ||||
−0.370688 | + | 0.928757i | \(0.620878\pi\) | |||||||
\(114\) | −1.93758e33 | + | 4.76603e33i | −0.0208870 | + | 0.0513777i | ||||
\(115\) | 8.48082e34i | 0.788087i | ||||||||
\(116\) | −1.35774e35 | − | 1.32252e35i | −1.08900 | − | 1.06076i | ||||
\(117\) | −2.69999e34 | −0.187155 | ||||||||
\(118\) | −3.68230e34 | − | 1.49700e34i | −0.220864 | − | 0.0897899i | ||||
\(119\) | 3.48724e35i | 1.81211i | ||||||||
\(120\) | 5.12456e33 | + | 1.17135e34i | 0.0230981 | + | 0.0527964i | ||||
\(121\) | 6.69984e34 | 0.262249 | ||||||||
\(122\) | 1.34917e35 | − | 3.31867e35i | 0.459144 | − | 1.12940i | ||||
\(123\) | 5.44869e33i | 0.0161401i | ||||||||
\(124\) | −2.39417e35 | + | 2.45792e35i | −0.617998 | + | 0.634452i | ||||
\(125\) | 4.83455e35 | 1.08864 | ||||||||
\(126\) | 6.12409e35 | + | 2.48968e35i | 1.20432 | + | 0.489603i | ||||
\(127\) | − | 4.67222e35i | − | 0.803267i | −0.915800 | − | 0.401634i | \(-0.868443\pi\) | ||
0.915800 | − | 0.401634i | \(-0.131557\pi\) | |||||||
\(128\) | −2.82291e35 | − | 6.01684e35i | −0.424744 | − | 0.905314i | ||||
\(129\) | 1.86415e33 | 0.00245729 | ||||||||
\(130\) | 4.98706e34 | − | 1.22671e35i | 0.0576511 | − | 0.141810i | ||||
\(131\) | − | 7.98034e35i | − | 0.809859i | −0.914348 | − | 0.404930i | \(-0.867296\pi\) | ||
0.914348 | − | 0.404930i | \(-0.132704\pi\) | |||||||
\(132\) | −4.88570e34 | − | 4.75899e34i | −0.0435683 | − | 0.0424383i | ||||
\(133\) | −1.30469e36 | −1.02336 | ||||||||
\(134\) | 2.25608e36 | + | 9.17183e35i | 1.55802 | + | 0.633395i | ||||
\(135\) | − | 1.88907e35i | − | 0.114967i | ||||||
\(136\) | −2.36688e36 | + | 1.03550e36i | −1.27062 | + | 0.555887i | ||||
\(137\) | 3.84307e35 | 0.182150 | 0.0910748 | − | 0.995844i | \(-0.470970\pi\) | ||||
0.0910748 | + | 0.995844i | \(0.470970\pi\) | |||||||
\(138\) | 6.16555e34 | − | 1.51659e35i | 0.0258242 | − | 0.0635221i | ||||
\(139\) | − | 2.30268e36i | − | 0.853065i | −0.904472 | − | 0.426533i | \(-0.859735\pi\) | ||
0.904472 | − | 0.426533i | \(-0.140265\pi\) | |||||||
\(140\) | −2.26232e36 | + | 2.32256e36i | −0.741955 | + | 0.761710i | ||||
\(141\) | −3.25652e35 | −0.0946301 | ||||||||
\(142\) | 6.07317e36 | + | 2.46898e36i | 1.56500 | + | 0.636232i | ||||
\(143\) | 7.06404e35i | 0.161562i | ||||||||
\(144\) | 1.28664e35 | + | 4.89586e36i | 0.0261393 | + | 0.994642i | ||||
\(145\) | −6.85021e36 | −1.23722 | ||||||||
\(146\) | −7.79865e35 | + | 1.91830e36i | −0.125320 | + | 0.308261i | ||||
\(147\) | − | 3.49963e35i | − | 0.0500757i | ||||||
\(148\) | −6.25570e36 | − | 6.09346e36i | −0.797677 | − | 0.776989i | ||||
\(149\) | 6.22141e35 | 0.0707494 | 0.0353747 | − | 0.999374i | \(-0.488738\pi\) | ||||
0.0353747 | + | 0.999374i | \(0.488738\pi\) | |||||||
\(150\) | −2.18243e35 | − | 8.87242e34i | −0.0221508 | − | 0.00900515i | ||||
\(151\) | − | 4.80007e36i | − | 0.435151i | −0.976044 | − | 0.217575i | \(-0.930185\pi\) | ||
0.976044 | − | 0.217575i | \(-0.0698148\pi\) | |||||||
\(152\) | −3.87411e36 | − | 8.85526e36i | −0.313929 | − | 0.717563i | ||||
\(153\) | 1.90378e37 | 1.37994 | ||||||||
\(154\) | 6.51380e36 | − | 1.60226e37i | 0.422651 | − | 1.03963i | ||||
\(155\) | 1.24010e37i | 0.720804i | ||||||||
\(156\) | −1.78364e35 | + | 1.83113e35i | −0.00929369 | + | 0.00954114i | ||||
\(157\) | −1.02909e37 | −0.481017 | −0.240509 | − | 0.970647i | \(-0.577314\pi\) | ||||
−0.240509 | + | 0.970647i | \(0.577314\pi\) | |||||||
\(158\) | 2.96478e37 | + | 1.20530e37i | 1.24400 | + | 0.505736i | ||||
\(159\) | 2.15952e36i | 0.0813966i | ||||||||
\(160\) | −2.24815e37 | − | 8.45842e36i | −0.761703 | − | 0.286582i | ||||
\(161\) | 4.15164e37 | 1.26526 | ||||||||
\(162\) | 1.35230e37 | − | 3.32636e37i | 0.370951 | − | 0.912462i | ||||
\(163\) | 4.13537e37i | 1.02170i | 0.859669 | + | 0.510852i | \(0.170670\pi\) | ||||
−0.859669 | + | 0.510852i | \(0.829330\pi\) | |||||||
\(164\) | −7.33277e36 | − | 7.14259e36i | −0.163276 | − | 0.159041i | ||||
\(165\) | −2.46499e36 | −0.0494981 | ||||||||
\(166\) | −8.49052e37 | − | 3.45173e37i | −1.53850 | − | 0.625459i | ||||
\(167\) | 2.15925e37i | 0.353284i | 0.984275 | + | 0.176642i | \(0.0565234\pi\) | ||||
−0.984275 | + | 0.176642i | \(0.943477\pi\) | |||||||
\(168\) | 5.73413e36 | − | 2.50864e36i | 0.0847636 | − | 0.0370835i | ||||
\(169\) | −7.21821e37 | −0.964619 | ||||||||
\(170\) | −3.51640e37 | + | 8.64961e37i | −0.425076 | + | 1.04560i | ||||
\(171\) | 7.12262e37i | 0.779302i | ||||||||
\(172\) | −2.44368e36 | + | 2.50875e36i | −0.0242137 | + | 0.0248584i | ||||
\(173\) | −4.35115e37 | −0.390679 | −0.195339 | − | 0.980736i | \(-0.562581\pi\) | ||||
−0.195339 | + | 0.980736i | \(0.562581\pi\) | |||||||
\(174\) | 1.22500e37 | + | 4.98010e36i | 0.0997237 | + | 0.0405416i | ||||
\(175\) | − | 5.97434e37i | − | 0.441208i | ||||||
\(176\) | 1.28092e38 | − | 3.36626e36i | 0.858628 | − | 0.0225648i | ||||
\(177\) | 2.77322e36 | 0.0168826 | ||||||||
\(178\) | −1.84953e37 | + | 4.54947e37i | −0.102311 | + | 0.251664i | ||||
\(179\) | − | 3.09126e38i | − | 1.55466i | −0.629096 | − | 0.777328i | \(-0.716575\pi\) | ||
0.629096 | − | 0.777328i | \(-0.283425\pi\) | |||||||
\(180\) | 1.26794e38 | + | 1.23506e38i | 0.580052 | + | 0.565009i | ||||
\(181\) | 2.81380e38 | 1.17154 | 0.585770 | − | 0.810477i | \(-0.300792\pi\) | ||||
0.585770 | + | 0.810477i | \(0.300792\pi\) | |||||||
\(182\) | −6.00515e37 | − | 2.44133e37i | −0.227673 | − | 0.0925577i | ||||
\(183\) | 2.49936e37i | 0.0863297i | ||||||||
\(184\) | 1.23278e38 | + | 2.81783e38i | 0.388135 | + | 0.887179i | ||||
\(185\) | −3.15620e38 | −0.906244 | ||||||||
\(186\) | 9.01551e36 | − | 2.21762e37i | 0.0236195 | − | 0.0580989i | ||||
\(187\) | − | 4.98089e38i | − | 1.19124i | ||||||
\(188\) | 4.26892e38 | − | 4.38258e38i | 0.932469 | − | 0.957296i | ||||
\(189\) | −9.24760e37 | −0.184577 | ||||||||
\(190\) | −3.23609e38 | − | 1.31560e38i | −0.590486 | − | 0.240055i | ||||
\(191\) | − | 2.50270e38i | − | 0.417677i | −0.977950 | − | 0.208839i | \(-0.933032\pi\) | ||
0.977950 | − | 0.208839i | \(-0.0669683\pi\) | |||||||
\(192\) | 3.40536e37 | + | 3.14699e37i | 0.0520047 | + | 0.0480590i | ||||
\(193\) | −1.33712e38 | −0.186937 | −0.0934687 | − | 0.995622i | \(-0.529796\pi\) | ||||
−0.0934687 | + | 0.995622i | \(0.529796\pi\) | |||||||
\(194\) | −5.03147e38 | + | 1.23763e39i | −0.644266 | + | 1.58476i | ||||
\(195\) | 9.23862e36i | 0.0108397i | ||||||||
\(196\) | 4.70975e38 | + | 4.58760e38i | 0.506576 | + | 0.493438i | ||||
\(197\) | 2.67616e38 | 0.263989 | 0.131995 | − | 0.991250i | \(-0.457862\pi\) | ||||
0.131995 | + | 0.991250i | \(0.457862\pi\) | |||||||
\(198\) | −8.74714e38 | − | 3.55605e38i | −0.791695 | − | 0.321855i | ||||
\(199\) | 1.34085e39i | 1.11398i | 0.830518 | + | 0.556991i | \(0.188044\pi\) | ||||
−0.830518 | + | 0.556991i | \(0.811956\pi\) | |||||||
\(200\) | 4.05494e38 | − | 1.77401e38i | 0.309368 | − | 0.135346i | ||||
\(201\) | −1.69910e38 | −0.119093 | ||||||||
\(202\) | 5.95646e38 | − | 1.46516e39i | 0.383721 | − | 0.943872i | ||||
\(203\) | 3.35340e39i | 1.98634i | ||||||||
\(204\) | 1.25765e38 | − | 1.29114e38i | 0.0685248 | − | 0.0703493i | ||||
\(205\) | −3.69961e38 | −0.185499 | ||||||||
\(206\) | −2.99031e39 | − | 1.21568e39i | −1.38030 | − | 0.561146i | ||||
\(207\) | − | 2.26648e39i | − | 0.963511i | ||||||
\(208\) | −1.26165e37 | − | 4.80078e38i | −0.00494154 | − | 0.188034i | ||||
\(209\) | 1.86351e39 | 0.672735 | ||||||||
\(210\) | 8.51900e37 | − | 2.09550e38i | 0.0283570 | − | 0.0697523i | ||||
\(211\) | 9.78808e38i | 0.300536i | 0.988645 | + | 0.150268i | \(0.0480136\pi\) | ||||
−0.988645 | + | 0.150268i | \(0.951986\pi\) | |||||||
\(212\) | −2.90625e39 | − | 2.83088e39i | −0.823423 | − | 0.802068i | ||||
\(213\) | −4.57383e38 | −0.119626 | ||||||||
\(214\) | 5.51947e39 | + | 2.24388e39i | 1.33310 | + | 0.541957i | ||||
\(215\) | 1.26574e38i | 0.0282418i | ||||||||
\(216\) | −2.74597e38 | − | 6.27659e38i | −0.0566215 | − | 0.129423i | ||||
\(217\) | 6.07069e39 | 1.15724 | ||||||||
\(218\) | 1.87947e39 | − | 4.62310e39i | 0.331341 | − | 0.815029i | ||||
\(219\) | − | 1.44471e38i | − | 0.0235631i | ||||||
\(220\) | 3.23131e39 | − | 3.31735e39i | 0.487746 | − | 0.500732i | ||||
\(221\) | −1.86680e39 | −0.260873 | ||||||||
\(222\) | 5.64412e38 | + | 2.29456e38i | 0.0730459 | + | 0.0296960i | ||||
\(223\) | 1.69807e38i | 0.0203598i | 0.999948 | + | 0.0101799i | \(0.00324042\pi\) | ||||
−0.999948 | + | 0.0101799i | \(0.996760\pi\) | |||||||
\(224\) | −4.14067e39 | + | 1.10054e40i | −0.460103 | + | 1.22290i | ||||
\(225\) | −3.26154e39 | −0.335986 | ||||||||
\(226\) | −2.92261e39 | + | 7.18900e39i | −0.279207 | + | 0.686791i | ||||
\(227\) | − | 8.49225e39i | − | 0.752633i | −0.926491 | − | 0.376316i | \(-0.877191\pi\) | ||
0.926491 | − | 0.376316i | \(-0.122809\pi\) | |||||||
\(228\) | 4.83055e38 | + | 4.70527e38i | 0.0397287 | + | 0.0386983i | ||||
\(229\) | −3.70477e39 | −0.282851 | −0.141426 | − | 0.989949i | \(-0.545169\pi\) | ||||
−0.141426 | + | 0.989949i | \(0.545169\pi\) | |||||||
\(230\) | 1.02975e40 | + | 4.18635e39i | 0.730063 | + | 0.296799i | ||||
\(231\) | 1.20669e39i | 0.0794682i | ||||||||
\(232\) | −2.27604e40 | + | 9.95753e39i | −1.39279 | + | 0.609334i | ||||
\(233\) | −3.15797e40 | −1.79621 | −0.898106 | − | 0.439779i | \(-0.855057\pi\) | ||||
−0.898106 | + | 0.439779i | \(0.855057\pi\) | |||||||
\(234\) | −1.33278e39 | + | 3.27837e39i | −0.0704839 | + | 0.173376i | ||||
\(235\) | − | 2.21115e40i | − | 1.08759i | ||||||
\(236\) | −3.63536e39 | + | 3.73215e39i | −0.166358 | + | 0.170787i | ||||
\(237\) | −2.23283e39 | −0.0950899 | ||||||||
\(238\) | 4.23427e40 | + | 1.72139e40i | 1.67869 | + | 0.682452i | ||||
\(239\) | 3.46110e39i | 0.127776i | 0.997957 | + | 0.0638881i | \(0.0203501\pi\) | ||||
−0.997957 | + | 0.0638881i | \(0.979650\pi\) | |||||||
\(240\) | 1.67523e39 | − | 4.40252e37i | 0.0576081 | − | 0.00151395i | ||||
\(241\) | 4.22422e40 | 1.35350 | 0.676748 | − | 0.736214i | \(-0.263389\pi\) | ||||
0.676748 | + | 0.736214i | \(0.263389\pi\) | |||||||
\(242\) | 3.30721e39 | − | 8.13505e39i | 0.0987646 | − | 0.242940i | ||||
\(243\) | 7.57910e39i | 0.211014i | ||||||||
\(244\) | −3.36360e40 | − | 3.27636e40i | −0.873327 | − | 0.850678i | ||||
\(245\) | 2.37622e40 | 0.575523 | ||||||||
\(246\) | 6.61589e38 | + | 2.68962e38i | 0.0149517 | + | 0.00607846i | ||||
\(247\) | − | 6.98430e39i | − | 0.147324i | ||||||
\(248\) | 1.80262e40 | + | 4.12034e40i | 0.354997 | + | 0.811436i | ||||
\(249\) | 6.39439e39 | 0.117601 | ||||||||
\(250\) | 2.38646e40 | − | 5.87019e40i | 0.409991 | − | 1.00849i | ||||
\(251\) | − | 4.84791e39i | − | 0.0778219i | −0.999243 | − | 0.0389109i | \(-0.987611\pi\) | ||
0.999243 | − | 0.0389109i | \(-0.0123889\pi\) | |||||||
\(252\) | 6.04602e40 | − | 6.20700e40i | 0.907111 | − | 0.931263i | ||||
\(253\) | −5.92985e40 | −0.831754 | ||||||||
\(254\) | −5.67308e40 | − | 2.30633e40i | −0.744125 | − | 0.302516i | ||||
\(255\) | − | 6.51420e39i | − | 0.0799241i | ||||||
\(256\) | −8.69920e40 | + | 4.57548e39i | −0.998620 | + | 0.0525239i | ||||
\(257\) | 8.50841e39 | 0.0914082 | 0.0457041 | − | 0.998955i | \(-0.485447\pi\) | ||||
0.0457041 | + | 0.998955i | \(0.485447\pi\) | |||||||
\(258\) | 9.20194e37 | − | 2.26348e38i | 0.000925432 | − | 0.00227637i | ||||
\(259\) | 1.54506e41i | 1.45496i | ||||||||
\(260\) | −1.24332e40 | − | 1.21107e40i | −0.109657 | − | 0.106813i | ||||
\(261\) | 1.83071e41 | 1.51262 | ||||||||
\(262\) | −9.68986e40 | − | 3.93930e40i | −0.750232 | − | 0.304998i | ||||
\(263\) | 2.04018e41i | 1.48054i | 0.672309 | + | 0.740271i | \(0.265303\pi\) | ||||
−0.672309 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(264\) | −8.19015e39 | + | 3.58314e39i | −0.0557218 | + | 0.0243779i | ||||
\(265\) | −1.46629e41 | −0.935495 | ||||||||
\(266\) | −6.44027e40 | + | 1.58417e41i | −0.385404 | + | 0.948013i | ||||
\(267\) | − | 3.42630e39i | − | 0.0192368i | ||||||
\(268\) | 2.22732e41 | − | 2.28662e41i | 1.17352 | − | 1.20477i | ||||
\(269\) | −7.27162e40 | −0.359619 | −0.179809 | − | 0.983701i | \(-0.557548\pi\) | ||||
−0.179809 | + | 0.983701i | \(0.557548\pi\) | |||||||
\(270\) | −2.29374e40 | − | 9.32492e39i | −0.106502 | − | 0.0432973i | ||||
\(271\) | − | 2.52650e41i | − | 1.10165i | −0.834622 | − | 0.550823i | \(-0.814314\pi\) | ||
0.834622 | − | 0.550823i | \(-0.185686\pi\) | |||||||
\(272\) | 8.89596e39 | + | 3.38506e41i | 0.0364352 | + | 1.38642i | ||||
\(273\) | 4.52261e39 | 0.0174030 | ||||||||
\(274\) | 1.89704e40 | − | 4.66631e40i | 0.0685988 | − | 0.168739i | ||||
\(275\) | 8.53325e40i | 0.290041i | ||||||||
\(276\) | −1.53713e40 | − | 1.49726e40i | −0.0491196 | − | 0.0478457i | ||||
\(277\) | 2.89946e40 | 0.0871286 | 0.0435643 | − | 0.999051i | \(-0.486129\pi\) | ||||
0.0435643 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(278\) | −2.79595e41 | − | 1.13666e41i | −0.790257 | − | 0.321270i | ||||
\(279\) | − | 3.31414e41i | − | 0.881251i | ||||||
\(280\) | 1.70334e41 | + | 3.89342e41i | 0.426203 | + | 0.974193i | ||||
\(281\) | −1.14056e41 | −0.268604 | −0.134302 | − | 0.990940i | \(-0.542879\pi\) | ||||
−0.134302 | + | 0.990940i | \(0.542879\pi\) | |||||||
\(282\) | −1.60750e40 | + | 3.95412e40i | −0.0356383 | + | 0.0876628i | ||||
\(283\) | − | 8.18564e41i | − | 1.70877i | −0.519642 | − | 0.854384i | \(-0.673935\pi\) | ||
0.519642 | − | 0.854384i | \(-0.326065\pi\) | |||||||
\(284\) | 5.99575e41 | − | 6.15539e41i | 1.17878 | − | 1.21016i | ||||
\(285\) | 2.43717e40 | 0.0451360 | ||||||||
\(286\) | 8.57727e40 | + | 3.48699e40i | 0.149667 | + | 0.0608455i | ||||
\(287\) | 1.81108e41i | 0.297814i | ||||||||
\(288\) | 6.00815e41 | + | 2.26050e41i | 0.931254 | + | 0.350374i | ||||
\(289\) | 6.31966e41 | 0.923486 | ||||||||
\(290\) | −3.38144e41 | + | 8.31763e41i | −0.465946 | + | 1.14613i | ||||
\(291\) | − | 9.32088e40i | − | 0.121137i | ||||||
\(292\) | 1.94427e41 | + | 1.89385e41i | 0.238369 | + | 0.232186i | ||||
\(293\) | −1.01502e42 | −1.17415 | −0.587076 | − | 0.809532i | \(-0.699721\pi\) | ||||
−0.587076 | + | 0.809532i | \(0.699721\pi\) | |||||||
\(294\) | −4.24931e40 | − | 1.72751e40i | −0.0463888 | − | 0.0188589i | ||||
\(295\) | 1.88299e41i | 0.194032i | ||||||||
\(296\) | −1.04868e42 | + | 4.58788e41i | −1.02019 | + | 0.446327i | ||||
\(297\) | 1.32085e41 | 0.121337 | ||||||||
\(298\) | 3.07105e40 | − | 7.55414e40i | 0.0266447 | − | 0.0655403i | ||||
\(299\) | 2.22247e41i | 0.182148i | ||||||||
\(300\) | −2.15461e40 | + | 2.21197e40i | −0.0166843 | + | 0.0171285i | ||||
\(301\) | 6.19622e40 | 0.0453416 | ||||||||
\(302\) | −5.82833e41 | − | 2.36944e41i | −0.403112 | − | 0.163881i | ||||
\(303\) | 1.10345e41i | 0.0721483i | ||||||||
\(304\) | −1.26646e42 | + | 3.32826e40i | −0.782959 | + | 0.0205763i | ||||
\(305\) | −1.69704e42 | −0.992191 | ||||||||
\(306\) | 9.39753e41 | − | 2.31159e42i | 0.519696 | − | 1.27834i | ||||
\(307\) | 2.39156e42i | 1.25121i | 0.780141 | + | 0.625604i | \(0.215147\pi\) | ||||
−0.780141 | + | 0.625604i | \(0.784853\pi\) | |||||||
\(308\) | −1.62395e42 | − | 1.58183e42i | −0.803915 | − | 0.783066i | ||||
\(309\) | 2.25206e41 | 0.105508 | ||||||||
\(310\) | 1.50575e42 | + | 6.12145e41i | 0.667734 | + | 0.271460i | ||||
\(311\) | 3.93969e42i | 1.65400i | 0.562203 | + | 0.826999i | \(0.309954\pi\) | ||||
−0.562203 | + | 0.826999i | \(0.690046\pi\) | |||||||
\(312\) | 1.34293e40 | + | 3.06961e40i | 0.00533859 | + | 0.0122027i | ||||
\(313\) | 4.98442e42 | 1.87655 | 0.938276 | − | 0.345887i | \(-0.112422\pi\) | ||||
0.938276 | + | 0.345887i | \(0.112422\pi\) | |||||||
\(314\) | −5.07987e41 | + | 1.24954e42i | −0.181154 | + | 0.445602i | ||||
\(315\) | − | 3.13163e42i | − | 1.05801i | ||||||
\(316\) | 2.92698e42 | − | 3.00491e42i | 0.937000 | − | 0.961948i | ||||
\(317\) | 1.53460e42 | 0.465574 | 0.232787 | − | 0.972528i | \(-0.425216\pi\) | ||||
0.232787 | + | 0.972528i | \(0.425216\pi\) | |||||||
\(318\) | 2.62212e41 | + | 1.06600e41i | 0.0754036 | + | 0.0306545i | ||||
\(319\) | − | 4.78972e42i | − | 1.30578i | ||||||
\(320\) | −2.13678e42 | + | 2.31221e42i | −0.552345 | + | 0.597693i | ||||
\(321\) | −4.15683e41 | −0.101900 | ||||||||
\(322\) | 2.04935e42 | − | 5.04098e42i | 0.476505 | − | 1.17210i | ||||
\(323\) | 4.92466e42i | 1.08626i | ||||||||
\(324\) | −3.37140e42 | − | 3.28396e42i | −0.705577 | − | 0.687278i | ||||
\(325\) | 3.19820e41 | 0.0635168 | ||||||||
\(326\) | 5.02123e42 | + | 2.04133e42i | 0.946480 | + | 0.384781i | ||||
\(327\) | 3.48175e41i | 0.0622997i | ||||||||
\(328\) | −1.22923e42 | + | 5.37779e41i | −0.208823 | + | 0.0913585i | ||||
\(329\) | −1.08243e43 | −1.74610 | ||||||||
\(330\) | −1.21678e41 | + | 2.99303e41i | −0.0186413 | + | 0.0458537i | ||||
\(331\) | 1.35229e41i | 0.0196786i | 0.999952 | + | 0.00983928i | \(0.00313199\pi\) | ||||
−0.999952 | + | 0.00983928i | \(0.996868\pi\) | |||||||
\(332\) | −8.38228e42 | + | 8.60547e42i | −1.15882 | + | 1.18967i | ||||
\(333\) | 8.43490e42 | 1.10797 | ||||||||
\(334\) | 2.62180e42 | + | 1.06586e42i | 0.327272 | + | 0.133049i | ||||
\(335\) | − | 1.15367e43i | − | 1.36874i | ||||||
\(336\) | −2.15518e40 | − | 8.20080e41i | −0.00243061 | − | 0.0924887i | ||||
\(337\) | −5.44175e42 | −0.583485 | −0.291743 | − | 0.956497i | \(-0.594235\pi\) | ||||
−0.291743 | + | 0.956497i | \(0.594235\pi\) | |||||||
\(338\) | −3.56310e42 | + | 8.76447e42i | −0.363282 | + | 0.893597i | ||||
\(339\) | − | 5.41418e41i | − | 0.0524974i | ||||||
\(340\) | 8.76671e42 | + | 8.53934e42i | 0.808528 | + | 0.787559i | ||||
\(341\) | −8.67086e42 | −0.760743 | ||||||||
\(342\) | 8.64840e42 | + | 3.51591e42i | 0.721925 | + | 0.293491i | ||||
\(343\) | 4.81664e42i | 0.382599i | ||||||||
\(344\) | 1.83990e41 | + | 4.20554e41i | 0.0139091 | + | 0.0317928i | ||||
\(345\) | −7.75529e41 | −0.0558050 | ||||||||
\(346\) | −2.14784e42 | + | 5.28323e42i | −0.147132 | + | 0.361914i | ||||
\(347\) | − | 6.28542e42i | − | 0.409952i | −0.978767 | − | 0.204976i | \(-0.934288\pi\) | ||
0.978767 | − | 0.204976i | \(-0.0657116\pi\) | |||||||
\(348\) | 1.20938e42 | − | 1.24158e42i | 0.0751132 | − | 0.0771132i | ||||
\(349\) | −2.62369e42 | −0.155196 | −0.0775978 | − | 0.996985i | \(-0.524725\pi\) | ||||
−0.0775978 | + | 0.996985i | \(0.524725\pi\) | |||||||
\(350\) | −7.25414e42 | − | 2.94909e42i | −0.408723 | − | 0.166162i | ||||
\(351\) | − | 4.95046e41i | − | 0.0265720i | ||||||
\(352\) | 5.91419e42 | − | 1.57192e43i | 0.302462 | − | 0.803908i | ||||
\(353\) | 1.89188e43 | 0.921986 | 0.460993 | − | 0.887404i | \(-0.347493\pi\) | ||||
0.460993 | + | 0.887404i | \(0.347493\pi\) | |||||||
\(354\) | 1.36893e41 | − | 3.36729e41i | 0.00635809 | − | 0.0156396i | ||||
\(355\) | − | 3.10559e43i | − | 1.37487i | ||||||
\(356\) | 4.61106e42 | + | 4.49147e42i | 0.194603 | + | 0.189556i | ||||
\(357\) | −3.18891e42 | −0.128317 | ||||||||
\(358\) | −3.75346e43 | − | 1.52593e43i | −1.44019 | − | 0.585494i | ||||
\(359\) | 3.36230e43i | 1.23035i | 0.788389 | + | 0.615177i | \(0.210916\pi\) | ||||
−0.788389 | + | 0.615177i | \(0.789084\pi\) | |||||||
\(360\) | 2.12552e43 | − | 9.29900e42i | 0.741861 | − | 0.324559i | ||||
\(361\) | 1.16099e43 | 0.386551 | ||||||||
\(362\) | 1.38896e43 | − | 3.41656e43i | 0.441210 | − | 1.08528i | ||||
\(363\) | 6.12667e41i | 0.0185700i | ||||||||
\(364\) | −5.92860e42 | + | 6.08645e42i | −0.171486 | + | 0.176052i | ||||
\(365\) | 9.80948e42 | 0.270812 | ||||||||
\(366\) | 3.03476e42 | + | 1.23375e42i | 0.0799735 | + | 0.0325123i | ||||
\(367\) | 1.39483e43i | 0.350911i | 0.984487 | + | 0.175456i | \(0.0561398\pi\) | ||||
−0.984487 | + | 0.175456i | \(0.943860\pi\) | |||||||
\(368\) | 4.02998e43 | − | 1.05908e42i | 0.968033 | − | 0.0254400i | ||||
\(369\) | 9.88716e42 | 0.226790 | ||||||||
\(370\) | −1.55798e43 | + | 3.83231e43i | −0.341298 | + | 0.839520i | ||||
\(371\) | 7.17799e43i | 1.50192i | ||||||||
\(372\) | −2.24765e42 | − | 2.18935e42i | −0.0449260 | − | 0.0437609i | ||||
\(373\) | −6.69798e41 | −0.0127907 | −0.00639534 | − | 0.999980i | \(-0.502036\pi\) | ||||
−0.00639534 | + | 0.999980i | \(0.502036\pi\) | |||||||
\(374\) | −6.04787e43 | − | 2.45870e43i | −1.10353 | − | 0.448629i | ||||
\(375\) | 4.42096e42i | 0.0770877i | ||||||||
\(376\) | −3.21415e43 | − | 7.34674e43i | −0.535640 | − | 1.22434i | ||||
\(377\) | −1.79515e43 | −0.285956 | ||||||||
\(378\) | −4.56485e42 | + | 1.12286e43i | −0.0695130 | + | 0.170987i | ||||
\(379\) | 3.72526e43i | 0.542364i | 0.962528 | + | 0.271182i | \(0.0874145\pi\) | ||||
−0.962528 | + | 0.271182i | \(0.912586\pi\) | |||||||
\(380\) | −3.19484e43 | + | 3.27990e43i | −0.444762 | + | 0.456604i | ||||
\(381\) | 4.27252e42 | 0.0568799 | ||||||||
\(382\) | −3.03881e43 | − | 1.23540e43i | −0.386925 | − | 0.157300i | ||||
\(383\) | − | 1.10518e43i | − | 0.134603i | −0.997733 | − | 0.0673016i | \(-0.978561\pi\) | ||
0.997733 | − | 0.0673016i | \(-0.0214390\pi\) | |||||||
\(384\) | 5.50211e42 | − | 2.58141e42i | 0.0641059 | − | 0.0300764i | ||||
\(385\) | −8.19334e43 | −0.913332 | ||||||||
\(386\) | −6.60037e42 | + | 1.62355e43i | −0.0704019 | + | 0.173174i | ||||
\(387\) | − | 3.38268e42i | − | 0.0345282i | ||||||
\(388\) | 1.25439e44 | + | 1.22186e44i | 1.22544 | + | 1.19366i | ||||
\(389\) | −1.42396e43 | −0.133155 | −0.0665773 | − | 0.997781i | \(-0.521208\pi\) | ||||
−0.0665773 | + | 0.997781i | \(0.521208\pi\) | |||||||
\(390\) | 1.12177e42 | + | 4.56042e41i | 0.0100416 | + | 0.00408232i | ||||
\(391\) | − | 1.56707e44i | − | 1.34303i | ||||||
\(392\) | 7.89519e43 | − | 3.45409e43i | 0.647887 | − | 0.283446i | ||||
\(393\) | 7.29763e42 | 0.0573467 | ||||||||
\(394\) | 1.32102e43 | − | 3.24944e43i | 0.0994201 | − | 0.244553i | ||||
\(395\) | − | 1.51607e44i | − | 1.09287i | ||||||
\(396\) | −8.63563e43 | + | 8.86556e43i | −0.596315 | + | 0.612192i | ||||
\(397\) | 1.57466e44 | 1.04171 | 0.520856 | − | 0.853644i | \(-0.325613\pi\) | ||||
0.520856 | + | 0.853644i | \(0.325613\pi\) | |||||||
\(398\) | 1.62808e44 | + | 6.61879e43i | 1.03196 | + | 0.419533i | ||||
\(399\) | − | 1.19307e43i | − | 0.0724649i | ||||||
\(400\) | −1.52406e42 | − | 5.79927e43i | −0.00887117 | − | 0.337562i | ||||
\(401\) | 1.81831e44 | 1.01441 | 0.507204 | − | 0.861826i | \(-0.330679\pi\) | ||||
0.507204 | + | 0.861826i | \(0.330679\pi\) | |||||||
\(402\) | −8.38719e42 | + | 2.06307e43i | −0.0448511 | + | 0.110324i | ||||
\(403\) | 3.24978e43i | 0.166597i | ||||||||
\(404\) | −1.48500e44 | − | 1.44649e44i | −0.729866 | − | 0.710937i | ||||
\(405\) | −1.70098e44 | −0.801610 | ||||||||
\(406\) | 4.07175e44 | + | 1.65533e44i | 1.84009 | + | 0.748067i | ||||
\(407\) | − | 2.20684e44i | − | 0.956458i | ||||||
\(408\) | −9.46910e42 | − | 2.16440e43i | −0.0393628 | − | 0.0899735i | ||||
\(409\) | −4.94587e44 | −1.97218 | −0.986090 | − | 0.166213i | \(-0.946846\pi\) | ||||
−0.986090 | + | 0.166213i | \(0.946846\pi\) | |||||||
\(410\) | −1.82623e43 | + | 4.49213e43i | −0.0698600 | + | 0.171841i | ||||
\(411\) | 3.51430e42i | 0.0128981i | ||||||||
\(412\) | −2.95219e44 | + | 3.03079e44i | −1.03966 | + | 1.06734i | ||||
\(413\) | 9.21785e43 | 0.311515 | ||||||||
\(414\) | −2.75200e44 | − | 1.11880e44i | −0.892571 | − | 0.362865i | ||||
\(415\) | 4.34173e44i | 1.35159i | ||||||||
\(416\) | −5.89147e43 | − | 2.21660e43i | −0.176050 | − | 0.0662370i | ||||
\(417\) | 2.10569e43 | 0.0604062 | ||||||||
\(418\) | 9.19875e43 | − | 2.26270e44i | 0.253357 | − | 0.623204i | ||||
\(419\) | − | 4.66286e44i | − | 1.23314i | −0.787298 | − | 0.616572i | \(-0.788521\pi\) | ||
0.787298 | − | 0.616572i | \(-0.211479\pi\) | |||||||
\(420\) | −2.12386e43 | − | 2.06878e43i | −0.0539372 | − | 0.0525384i | ||||
\(421\) | 4.26948e44 | 1.04131 | 0.520655 | − | 0.853767i | \(-0.325688\pi\) | ||||
0.520655 | + | 0.853767i | \(0.325688\pi\) | |||||||
\(422\) | 1.18848e44 | + | 4.83165e43i | 0.278408 | + | 0.113184i | ||||
\(423\) | 5.90926e44i | 1.32968i | ||||||||
\(424\) | −4.87189e44 | + | 2.13142e44i | −1.05312 | + | 0.460733i | ||||
\(425\) | −2.25507e44 | −0.468326 | ||||||||
\(426\) | −2.25776e43 | + | 5.55362e43i | −0.0450521 | + | 0.110819i | ||||
\(427\) | 8.30757e44i | 1.59294i | ||||||||
\(428\) | 5.44911e44 | − | 5.59419e44i | 1.00411 | − | 1.03084i | ||||
\(429\) | −6.45972e42 | −0.0114404 | ||||||||
\(430\) | 1.53689e43 | + | 6.24804e42i | 0.0261624 | + | 0.0106360i | ||||
\(431\) | 3.36518e44i | 0.550674i | 0.961348 | + | 0.275337i | \(0.0887895\pi\) | ||||
−0.961348 | + | 0.275337i | \(0.911211\pi\) | |||||||
\(432\) | −8.97662e43 | + | 2.35906e42i | −0.141218 | + | 0.00371121i | ||||
\(433\) | 4.59142e44 | 0.694469 | 0.347234 | − | 0.937778i | \(-0.387121\pi\) | ||||
0.347234 | + | 0.937778i | \(0.387121\pi\) | |||||||
\(434\) | 2.99665e44 | − | 7.37112e44i | 0.435823 | − | 1.07203i | ||||
\(435\) | − | 6.26418e43i | − | 0.0876086i | ||||||
\(436\) | −4.68569e44 | − | 4.56416e44i | −0.630235 | − | 0.613890i | ||||
\(437\) | 5.86291e44 | 0.758454 | ||||||||
\(438\) | −1.75419e43 | − | 7.13148e42i | −0.0218282 | − | 0.00887401i | ||||
\(439\) | − | 1.46509e45i | − | 1.75375i | −0.480719 | − | 0.876875i | \(-0.659624\pi\) | ||
0.480719 | − | 0.876875i | \(-0.340376\pi\) | |||||||
\(440\) | −2.43292e44 | − | 5.56104e44i | −0.280177 | − | 0.640414i | ||||
\(441\) | −6.35040e44 | −0.703631 | ||||||||
\(442\) | −9.21502e43 | + | 2.26670e44i | −0.0982467 | + | 0.241666i | ||||
\(443\) | 2.86620e44i | 0.294064i | 0.989132 | + | 0.147032i | \(0.0469721\pi\) | ||||
−0.989132 | + | 0.147032i | \(0.953028\pi\) | |||||||
\(444\) | 5.57217e43 | − | 5.72053e43i | 0.0550192 | − | 0.0564841i | ||||
\(445\) | 2.32642e44 | 0.221090 | ||||||||
\(446\) | 2.06183e43 | + | 8.38213e42i | 0.0188608 | + | 0.00766764i | ||||
\(447\) | 5.68918e42i | 0.00500981i | ||||||||
\(448\) | 1.13190e45 | + | 1.04602e45i | 0.959584 | + | 0.886779i | ||||
\(449\) | 1.19675e44 | 0.0976826 | 0.0488413 | − | 0.998807i | \(-0.484447\pi\) | ||||
0.0488413 | + | 0.998807i | \(0.484447\pi\) | |||||||
\(450\) | −1.60998e44 | + | 3.96022e44i | −0.126534 | + | 0.311248i | ||||
\(451\) | − | 2.58680e44i | − | 0.195777i | ||||||
\(452\) | 7.28632e44 | + | 7.09735e44i | 0.531074 | + | 0.517301i | ||||
\(453\) | 4.38943e43 | 0.0308133 | ||||||||
\(454\) | −1.03114e45 | − | 4.19199e44i | −0.697219 | − | 0.283447i | ||||
\(455\) | 3.07081e44i | 0.200013i | ||||||||
\(456\) | 8.09770e43 | − | 3.54269e43i | 0.0508112 | − | 0.0222295i | ||||
\(457\) | −2.01430e45 | −1.21772 | −0.608861 | − | 0.793277i | \(-0.708373\pi\) | ||||
−0.608861 | + | 0.793277i | \(0.708373\pi\) | |||||||
\(458\) | −1.82877e44 | + | 4.49839e44i | −0.106524 | + | 0.262026i | ||||
\(459\) | 3.49059e44i | 0.195922i | ||||||||
\(460\) | 1.01663e45 | − | 1.04369e45i | 0.549893 | − | 0.564534i | ||||
\(461\) | 1.76802e45 | 0.921663 | 0.460832 | − | 0.887488i | \(-0.347551\pi\) | ||||
0.460832 | + | 0.887488i | \(0.347551\pi\) | |||||||
\(462\) | 1.46519e44 | + | 5.95655e43i | 0.0736172 | + | 0.0299283i | ||||
\(463\) | − | 1.69842e45i | − | 0.822563i | −0.911508 | − | 0.411282i | \(-0.865081\pi\) | ||
0.911508 | − | 0.411282i | \(-0.134919\pi\) | |||||||
\(464\) | 8.55453e43 | + | 3.25514e45i | 0.0399384 | + | 1.51972i | ||||
\(465\) | −1.13401e44 | −0.0510407 | ||||||||
\(466\) | −1.55886e45 | + | 3.83446e45i | −0.676465 | + | 1.66396i | ||||
\(467\) | − | 1.55014e45i | − | 0.648609i | −0.945953 | − | 0.324304i | \(-0.894870\pi\) | ||
0.945953 | − | 0.324304i | \(-0.105130\pi\) | |||||||
\(468\) | 3.32275e44 | + | 3.23658e44i | 0.134066 | + | 0.130589i | ||||
\(469\) | −5.64760e45 | −2.19748 | ||||||||
\(470\) | −2.68481e45 | − | 1.09148e45i | −1.00751 | − | 0.409593i | ||||
\(471\) | − | 9.41056e43i | − | 0.0340612i | ||||||
\(472\) | 2.73713e44 | + | 6.25640e44i | 0.0955613 | + | 0.218429i | ||||
\(473\) | −8.85017e43 | −0.0298066 | ||||||||
\(474\) | −1.10218e44 | + | 2.71114e44i | −0.0358115 | + | 0.0880888i | ||||
\(475\) | − | 8.43692e44i | − | 0.264480i | ||||||
\(476\) | 4.18029e45 | − | 4.29159e45i | 1.26441 | − | 1.29808i | ||||
\(477\) | 3.91865e45 | 1.14373 | ||||||||
\(478\) | 4.20253e44 | + | 1.70849e44i | 0.118369 | + | 0.0481214i | ||||
\(479\) | 1.05670e45i | 0.287242i | 0.989633 | + | 0.143621i | \(0.0458746\pi\) | ||||
−0.989633 | + | 0.143621i | \(0.954125\pi\) | |||||||
\(480\) | 7.73481e43 | − | 2.05582e44i | 0.0202931 | − | 0.0539368i | ||||
\(481\) | −8.27108e44 | −0.209458 | ||||||||
\(482\) | 2.08519e45 | − | 5.12912e45i | 0.509736 | − | 1.25384i | ||||
\(483\) | 3.79647e44i | 0.0895939i | ||||||||
\(484\) | −8.24518e44 | − | 8.03134e44i | −0.187858 | − | 0.182986i | ||||
\(485\) | 6.32879e45 | 1.39223 | ||||||||
\(486\) | 9.20266e44 | + | 3.74124e44i | 0.195477 | + | 0.0794692i | ||||
\(487\) | 8.02364e44i | 0.164581i | 0.996608 | + | 0.0822904i | \(0.0262235\pi\) | ||||
−0.996608 | + | 0.0822904i | \(0.973776\pi\) | |||||||
\(488\) | −5.63857e45 | + | 2.46684e45i | −1.11695 | + | 0.488656i | ||||
\(489\) | −3.78159e44 | −0.0723476 | ||||||||
\(490\) | 1.17296e45 | − | 2.88524e45i | 0.216746 | − | 0.533149i | ||||
\(491\) | 2.35961e45i | 0.421168i | 0.977576 | + | 0.210584i | \(0.0675365\pi\) | ||||
−0.977576 | + | 0.210584i | \(0.932463\pi\) | |||||||
\(492\) | 6.53155e43 | − | 6.70546e43i | 0.0112618 | − | 0.0115617i | ||||
\(493\) | 1.26577e46 | 2.10842 | ||||||||
\(494\) | −8.48044e44 | − | 3.44763e44i | −0.136477 | − | 0.0554833i | ||||
\(495\) | 4.47296e45i | 0.695515i | ||||||||
\(496\) | 5.89280e45 | − | 1.54863e44i | 0.885387 | − | 0.0232681i | ||||
\(497\) | −1.52029e46 | −2.20733 | ||||||||
\(498\) | 3.15644e44 | − | 7.76417e44i | 0.0442892 | − | 0.108942i | ||||
\(499\) | − | 7.08769e44i | − | 0.0961160i | −0.998845 | − | 0.0480580i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480580i | \(-0.0153032\pi\) | |||||||
\(500\) | −5.94966e45 | − | 5.79536e45i | −0.779834 | − | 0.759609i | ||||
\(501\) | −1.97453e44 | −0.0250163 | ||||||||
\(502\) | −5.88641e44 | − | 2.39306e44i | −0.0720921 | − | 0.0293082i | ||||
\(503\) | 8.39076e45i | 0.993449i | 0.867908 | + | 0.496724i | \(0.165464\pi\) | ||||
−0.867908 | + | 0.496724i | \(0.834536\pi\) | |||||||
\(504\) | −4.55216e45 | − | 1.04051e46i | −0.521073 | − | 1.19104i | ||||
\(505\) | −7.49230e45 | −0.829204 | ||||||||
\(506\) | −2.92713e45 | + | 7.20012e45i | −0.313244 | + | 0.770515i | ||||
\(507\) | − | 6.60070e44i | − | 0.0683054i | ||||||
\(508\) | −5.60076e45 | + | 5.74989e45i | −0.560485 | + | 0.575408i | ||||
\(509\) | 3.72541e45 | 0.360555 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(510\) | −7.90964e44 | − | 3.21558e44i | −0.0740396 | − | 0.0301000i | ||||
\(511\) | − | 4.80206e45i | − | 0.434783i | ||||||
\(512\) | −3.73859e45 | + | 1.07886e46i | −0.327430 | + | 0.944875i | ||||
\(513\) | −1.30594e45 | −0.110644 | ||||||||
\(514\) | 4.19997e44 | − | 1.03310e45i | 0.0344250 | − | 0.0846782i | ||||
\(515\) | 1.52913e46i | 1.21261i | ||||||||
\(516\) | −2.29413e43 | − | 2.23463e43i | −0.00176024 | − | 0.00171459i | ||||
\(517\) | 1.54605e46 | 1.14785 | ||||||||
\(518\) | 1.87604e46 | + | 7.62683e45i | 1.34783 | + | 0.547947i | ||||
\(519\) | − | 3.97891e44i | − | 0.0276643i | ||||||
\(520\) | −2.08424e45 | + | 9.11840e44i | −0.140246 | + | 0.0613567i | ||||
\(521\) | −1.59460e46 | −1.03851 | −0.519254 | − | 0.854620i | \(-0.673790\pi\) | ||||
−0.519254 | + | 0.854620i | \(0.673790\pi\) | |||||||
\(522\) | 9.03685e45 | − | 2.22287e46i | 0.569663 | − | 1.40125i | ||||
\(523\) | − | 2.73828e46i | − | 1.67090i | −0.549570 | − | 0.835448i | \(-0.685208\pi\) | ||
0.549570 | − | 0.835448i | \(-0.314792\pi\) | |||||||
\(524\) | −9.56633e45 | + | 9.82104e45i | −0.565085 | + | 0.580130i | ||||
\(525\) | 5.46324e44 | 0.0312422 | ||||||||
\(526\) | 2.47722e46 | + | 1.00709e46i | 1.37153 | + | 0.557582i | ||||
\(527\) | − | 2.29144e46i | − | 1.22836i | ||||||
\(528\) | 3.07828e43 | + | 1.17133e45i | 0.00159783 | + | 0.0608001i | ||||
\(529\) | 1.23878e45 | 0.0622654 | ||||||||
\(530\) | −7.23801e45 | + | 1.78040e46i | −0.352314 | + | 0.866617i | ||||
\(531\) | − | 5.03226e45i | − | 0.237223i | ||||||
\(532\) | 1.60562e46 | + | 1.56398e46i | 0.733068 | + | 0.714056i | ||||
\(533\) | −9.69514e44 | −0.0428738 | ||||||||
\(534\) | −4.16026e44 | − | 1.69131e44i | −0.0178205 | − | 0.00724472i | ||||
\(535\) | − | 2.82245e46i | − | 1.17115i | ||||||
\(536\) | −1.67699e46 | − | 3.83318e46i | −0.674107 | − | 1.54084i | ||||
\(537\) | 2.82681e45 | 0.110086 | ||||||||
\(538\) | −3.58946e45 | + | 8.82931e45i | −0.135435 | + | 0.333141i | ||||
\(539\) | 1.66147e46i | 0.607412i | ||||||||
\(540\) | −2.26449e45 | + | 2.32479e45i | −0.0802190 | + | 0.0823549i | ||||
\(541\) | 1.91364e45 | 0.0656910 | 0.0328455 | − | 0.999460i | \(-0.489543\pi\) | ||||
0.0328455 | + | 0.999460i | \(0.489543\pi\) | |||||||
\(542\) | −3.06772e46 | − | 1.24715e46i | −1.02053 | − | 0.414887i | ||||
\(543\) | 2.57308e45i | 0.0829576i | ||||||||
\(544\) | 4.15410e46 | + | 1.56294e46i | 1.29806 | + | 0.488382i | ||||
\(545\) | −2.36408e46 | −0.716013 | ||||||||
\(546\) | 2.23248e44 | − | 5.49142e44i | 0.00655408 | − | 0.0161217i | ||||
\(547\) | 9.65466e45i | 0.274759i | 0.990518 | + | 0.137380i | \(0.0438680\pi\) | ||||
−0.990518 | + | 0.137380i | \(0.956132\pi\) | |||||||
\(548\) | −4.72948e45 | − | 4.60683e45i | −0.130480 | − | 0.127096i | ||||
\(549\) | 4.53532e46 | 1.21305 | ||||||||
\(550\) | 1.03612e46 | + | 4.21223e45i | 0.268686 | + | 0.109231i | ||||
\(551\) | 4.73565e46i | 1.19070i | ||||||||
\(552\) | −2.57676e45 | + | 1.12732e45i | −0.0628218 | + | 0.0274841i | ||||
\(553\) | −7.42168e46 | −1.75459 | ||||||||
\(554\) | 1.43125e45 | − | 3.52057e45i | 0.0328132 | − | 0.0807136i | ||||
\(555\) | − | 2.88619e45i | − | 0.0641718i | ||||||
\(556\) | −2.76031e46 | + | 2.83380e46i | −0.595232 | + | 0.611080i | ||||
\(557\) | 4.10537e46 | 0.858646 | 0.429323 | − | 0.903151i | \(-0.358752\pi\) | ||||
0.429323 | + | 0.903151i | \(0.358752\pi\) | |||||||
\(558\) | −4.02409e46 | − | 1.63595e46i | −0.816368 | − | 0.331885i | ||||
\(559\) | 3.31698e44i | 0.00652744i | ||||||||
\(560\) | 5.56827e46 | − | 1.46335e45i | 1.06298 | − | 0.0279351i | ||||
\(561\) | 4.55478e45 | 0.0843526 | ||||||||
\(562\) | −5.63012e45 | + | 1.38489e46i | −0.101158 | + | 0.248827i | ||||
\(563\) | 7.07753e46i | 1.23378i | 0.787048 | + | 0.616892i | \(0.211609\pi\) | ||||
−0.787048 | + | 0.616892i | \(0.788391\pi\) | |||||||
\(564\) | 4.00765e45 | + | 3.90372e45i | 0.0677868 | + | 0.0660288i | ||||
\(565\) | 3.67618e46 | 0.603355 | ||||||||
\(566\) | −9.93913e46 | − | 4.04064e46i | −1.58296 | − | 0.643533i | ||||
\(567\) | 8.32683e46i | 1.28697i | ||||||||
\(568\) | −4.51431e46 | − | 1.03186e47i | −0.677127 | − | 1.54774i | ||||
\(569\) | −2.27536e45 | −0.0331239 | −0.0165620 | − | 0.999863i | \(-0.505272\pi\) | ||||
−0.0165620 | + | 0.999863i | \(0.505272\pi\) | |||||||
\(570\) | 1.20305e45 | − | 2.95925e45i | 0.0169985 | − | 0.0418127i | ||||
\(571\) | − | 1.09044e47i | − | 1.49550i | −0.663978 | − | 0.747752i | \(-0.731133\pi\) | ||
0.663978 | − | 0.747752i | \(-0.268867\pi\) | |||||||
\(572\) | 8.46792e45 | − | 8.69338e45i | 0.112731 | − | 0.115733i | ||||
\(573\) | 2.28859e45 | 0.0295760 | ||||||||
\(574\) | 2.19904e46 | + | 8.93997e45i | 0.275887 | + | 0.112159i | ||||
\(575\) | 2.68471e46i | 0.326997i | ||||||||
\(576\) | 5.71051e46 | − | 6.17935e46i | 0.675294 | − | 0.730736i | ||||
\(577\) | −1.23848e47 | −1.42200 | −0.710999 | − | 0.703193i | \(-0.751757\pi\) | ||||
−0.710999 | + | 0.703193i | \(0.751757\pi\) | |||||||
\(578\) | 3.11955e46 | − | 7.67343e46i | 0.347791 | − | 0.855492i | ||||
\(579\) | − | 1.22273e45i | − | 0.0132372i | ||||||
\(580\) | 8.43023e46 | + | 8.21160e46i | 0.886265 | + | 0.863280i | ||||
\(581\) | 2.12542e47 | 2.16995 | ||||||||
\(582\) | −1.13176e46 | − | 4.60103e45i | −0.112218 | − | 0.0456209i | ||||
\(583\) | − | 1.02524e47i | − | 0.987329i | ||||||
\(584\) | 3.25929e46 | − | 1.42592e46i | 0.304863 | − | 0.133375i | ||||
\(585\) | 1.67643e46 | 0.152313 | ||||||||
\(586\) | −5.01039e46 | + | 1.23245e47i | −0.442193 | + | 1.08770i | ||||
\(587\) | 5.32247e46i | 0.456316i | 0.973624 | + | 0.228158i | \(0.0732702\pi\) | ||||
−0.973624 | + | 0.228158i | \(0.926730\pi\) | |||||||
\(588\) | −4.19514e45 | + | 4.30683e45i | −0.0349407 | + | 0.0358710i | ||||
\(589\) | 8.57299e46 | 0.693701 | ||||||||
\(590\) | 2.28636e46 | + | 9.29493e45i | 0.179746 | + | 0.0730738i | ||||
\(591\) | 2.44722e45i | 0.0186933i | ||||||||
\(592\) | 3.94146e45 | + | 1.49979e47i | 0.0292542 | + | 1.11317i | ||||
\(593\) | −1.90194e47 | −1.37172 | −0.685861 | − | 0.727733i | \(-0.740574\pi\) | ||||
−0.685861 | + | 0.727733i | \(0.740574\pi\) | |||||||
\(594\) | 6.52006e45 | − | 1.60380e46i | 0.0456964 | − | 0.112404i | ||||
\(595\) | − | 2.16524e47i | − | 1.47475i | ||||||
\(596\) | −7.65641e45 | − | 7.45784e45i | −0.0506802 | − | 0.0493659i | ||||
\(597\) | −1.22614e46 | −0.0788819 | ||||||||
\(598\) | 2.69856e46 | + | 1.09707e46i | 0.168737 | + | 0.0685983i | ||||
\(599\) | − | 1.17386e47i | − | 0.713444i | −0.934211 | − | 0.356722i | \(-0.883894\pi\) | ||
0.934211 | − | 0.356722i | \(-0.116106\pi\) | |||||||
\(600\) | 1.62224e45 | + | 3.70805e45i | 0.00958396 | + | 0.0219065i | ||||
\(601\) | −2.61329e47 | −1.50079 | −0.750396 | − | 0.660988i | \(-0.770137\pi\) | ||||
−0.750396 | + | 0.660988i | \(0.770137\pi\) | |||||||
\(602\) | 3.05862e45 | − | 7.52355e45i | 0.0170759 | − | 0.0420032i | ||||
\(603\) | 3.08317e47i | 1.67341i | ||||||||
\(604\) | −5.75402e46 | + | 5.90723e46i | −0.303629 | + | 0.311714i | ||||
\(605\) | −4.15996e46 | −0.213426 | ||||||||
\(606\) | 1.33982e46 | + | 5.44689e45i | 0.0668363 | + | 0.0271715i | ||||
\(607\) | − | 1.24244e47i | − | 0.602655i | −0.953521 | − | 0.301327i | \(-0.902570\pi\) | ||
0.953521 | − | 0.301327i | \(-0.0974297\pi\) | |||||||
\(608\) | −5.84743e46 | + | 1.55418e47i | −0.275806 | + | 0.733062i | ||||
\(609\) | −3.06652e46 | −0.140654 | ||||||||
\(610\) | −8.37704e46 | + | 2.06058e47i | −0.373666 | + | 0.919139i | ||||
\(611\) | − | 5.79450e46i | − | 0.251371i | ||||||
\(612\) | −2.34289e47 | − | 2.28213e47i | −0.988502 | − | 0.962865i | ||||
\(613\) | 1.32241e46 | 0.0542673 | 0.0271336 | − | 0.999632i | \(-0.491362\pi\) | ||||
0.0271336 | + | 0.999632i | \(0.491362\pi\) | |||||||
\(614\) | 2.90388e47 | + | 1.18054e47i | 1.15909 | + | 0.471213i | ||||
\(615\) | − | 3.38312e45i | − | 0.0131353i | ||||||
\(616\) | −2.72231e47 | + | 1.19099e47i | −1.02817 | + | 0.449818i | ||||
\(617\) | 2.46524e47 | 0.905755 | 0.452878 | − | 0.891573i | \(-0.350397\pi\) | ||||
0.452878 | + | 0.891573i | \(0.350397\pi\) | |||||||
\(618\) | 1.11168e46 | − | 2.73449e46i | 0.0397351 | − | 0.0977401i | ||||
\(619\) | − | 1.28216e46i | − | 0.0445863i | −0.999751 | − | 0.0222931i | \(-0.992903\pi\) | ||
0.999751 | − | 0.0222931i | \(-0.00709671\pi\) | |||||||
\(620\) | 1.48655e47 | − | 1.52613e47i | 0.502946 | − | 0.516337i | ||||
\(621\) | 4.15562e46 | 0.136798 | ||||||||
\(622\) | 4.78363e47 | + | 1.94473e47i | 1.53222 | + | 0.622907i | ||||
\(623\) | − | 1.13886e47i | − | 0.354955i | ||||||
\(624\) | 4.39008e45 | − | 1.15372e44i | 0.0133148 | − | 0.000349914i | ||||
\(625\) | −1.85769e47 | −0.548294 | ||||||||
\(626\) | 2.46044e47 | − | 6.05216e47i | 0.706722 | − | 1.73839i | ||||
\(627\) | 1.70409e46i | 0.0476369i | ||||||||
\(628\) | 1.26646e47 | + | 1.23361e47i | 0.344570 | + | 0.335633i | ||||
\(629\) | 5.83198e47 | 1.54438 | ||||||||
\(630\) | −3.80247e47 | − | 1.54585e47i | −0.980114 | − | 0.398454i | ||||
\(631\) | 2.63150e47i | 0.660244i | 0.943938 | + | 0.330122i | \(0.107090\pi\) | ||||
−0.943938 | + | 0.330122i | \(0.892910\pi\) | |||||||
\(632\) | −2.20378e47 | − | 5.03729e47i | −0.538242 | − | 1.23029i | ||||
\(633\) | −8.95072e45 | −0.0212811 | ||||||||
\(634\) | 7.57519e46 | − | 1.86334e47i | 0.175338 | − | 0.431295i | ||||
\(635\) | 2.90100e47i | 0.653724i | ||||||||
\(636\) | 2.58870e46 | − | 2.65762e46i | 0.0567950 | − | 0.0583072i | ||||
\(637\) | 6.22707e46 | 0.133019 | ||||||||
\(638\) | −5.81575e47 | − | 2.36433e47i | −1.20964 | − | 0.491764i | ||||
\(639\) | 8.29964e47i | 1.68091i | ||||||||
\(640\) | 1.75275e47 | + | 3.73588e47i | 0.345670 | + | 0.736773i | ||||
\(641\) | −6.71426e46 | −0.128947 | −0.0644736 | − | 0.997919i | \(-0.520537\pi\) | ||||
−0.0644736 | + | 0.997919i | \(0.520537\pi\) | |||||||
\(642\) | −2.05192e46 | + | 5.04728e46i | −0.0383764 | + | 0.0943979i | ||||
\(643\) | − | 8.17403e47i | − | 1.48885i | −0.667708 | − | 0.744423i | \(-0.732725\pi\) | ||
0.667708 | − | 0.744423i | \(-0.267275\pi\) | |||||||
\(644\) | −5.10923e47 | − | 4.97672e47i | −0.906349 | − | 0.882843i | ||||
\(645\) | −1.15746e45 | −0.00199982 | ||||||||
\(646\) | 5.97960e47 | + | 2.43094e47i | 1.00628 | + | 0.409093i | ||||
\(647\) | − | 1.35487e47i | − | 0.222088i | −0.993816 | − | 0.111044i | \(-0.964581\pi\) | ||
0.993816 | − | 0.111044i | \(-0.0354194\pi\) | |||||||
\(648\) | −5.65164e47 | + | 2.47256e47i | −0.902401 | + | 0.394794i | ||||
\(649\) | −1.31660e47 | −0.204783 | ||||||||
\(650\) | 1.57872e46 | − | 3.88331e46i | 0.0239209 | − | 0.0588403i | ||||
\(651\) | 5.55134e46i | 0.0819448i | ||||||||
\(652\) | 4.95722e47 | − | 5.08921e47i | 0.712901 | − | 0.731882i | ||||
\(653\) | −7.17987e46 | −0.100599 | −0.0502994 | − | 0.998734i | \(-0.516018\pi\) | ||||
−0.0502994 | + | 0.998734i | \(0.516018\pi\) | |||||||
\(654\) | 4.22760e46 | + | 1.71868e46i | 0.0577128 | + | 0.0234625i | ||||
\(655\) | 4.95503e47i | 0.659089i | ||||||||
\(656\) | 4.62007e45 | + | 1.75801e47i | 0.00598802 | + | 0.227854i | ||||
\(657\) | −2.62157e47 | −0.331093 | ||||||||
\(658\) | −5.34316e47 | + | 1.31430e48i | −0.657594 | + | 1.61754i | ||||
\(659\) | 1.22313e48i | 1.46697i | 0.679707 | + | 0.733484i | \(0.262107\pi\) | ||||
−0.679707 | + | 0.733484i | \(0.737893\pi\) | |||||||
\(660\) | 3.03355e46 | + | 2.95488e46i | 0.0354572 | + | 0.0345376i | ||||
\(661\) | −6.15228e47 | −0.700828 | −0.350414 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350414 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(662\) | 1.64197e46 | + | 6.67524e45i | 0.0182297 | + | 0.00741108i | ||||
\(663\) | − | 1.70710e46i | − | 0.0184726i | ||||||
\(664\) | 6.31118e47 | + | 1.44258e48i | 0.665661 | + | 1.52154i | ||||
\(665\) | 8.10085e47 | 0.832842 | ||||||||
\(666\) | 4.16368e47 | − | 1.02418e48i | 0.417269 | − | 1.02639i | ||||
\(667\) | − | 1.50693e48i | − | 1.47215i | ||||||
\(668\) | 2.58838e47 | − | 2.65729e47i | 0.246506 | − | 0.253069i | ||||
\(669\) | −1.55280e45 | −0.00144169 | ||||||||
\(670\) | −1.40081e48 | − | 5.69483e47i | −1.26796 | − | 0.515476i | ||||
\(671\) | − | 1.18659e48i | − | 1.04717i | ||||||
\(672\) | −1.00639e47 | − | 3.78644e46i | −0.0865944 | − | 0.0325802i | ||||
\(673\) | −1.90585e47 | −0.159894 | −0.0799470 | − | 0.996799i | \(-0.525475\pi\) | ||||
−0.0799470 | + | 0.996799i | \(0.525475\pi\) | |||||||
\(674\) | −2.68619e47 | + | 6.60746e47i | −0.219745 | + | 0.540525i | ||||
\(675\) | − | 5.98008e46i | − | 0.0477027i | ||||||
\(676\) | 8.88312e47 | + | 8.65274e47i | 0.690990 | + | 0.673069i | ||||
\(677\) | −8.94804e47 | −0.678767 | −0.339383 | − | 0.940648i | \(-0.610218\pi\) | ||||
−0.339383 | + | 0.940648i | \(0.610218\pi\) | |||||||
\(678\) | −6.57399e46 | − | 2.67258e46i | −0.0486322 | − | 0.0197709i | ||||
\(679\) | − | 3.09815e48i | − | 2.23520i | ||||||
\(680\) | 1.46961e48 | − | 6.42943e47i | 1.03407 | − | 0.452399i | ||||
\(681\) | 7.76574e46 | 0.0532945 | ||||||||
\(682\) | −4.28016e47 | + | 1.05283e48i | −0.286501 | + | 0.704732i | ||||
\(683\) | 1.78816e48i | 1.16750i | 0.811935 | + | 0.583748i | \(0.198414\pi\) | ||||
−0.811935 | + | 0.583748i | \(0.801586\pi\) | |||||||
\(684\) | 8.53815e47 | − | 8.76548e47i | 0.543764 | − | 0.558241i | ||||
\(685\) | −2.38618e47 | −0.148239 | ||||||||
\(686\) | 5.84844e47 | + | 2.37762e47i | 0.354430 | + | 0.144089i | ||||
\(687\) | − | 3.38783e46i | − | 0.0200289i | ||||||
\(688\) | 6.01466e46 | − | 1.58066e45i | 0.0346903 | − | 0.000911664i | ||||
\(689\) | −3.84255e47 | −0.216218 | ||||||||
\(690\) | −3.82821e46 | + | 9.41660e46i | −0.0210166 | + | 0.0516963i | ||||
\(691\) | − | 1.83766e48i | − | 0.984323i | −0.870504 | − | 0.492162i | \(-0.836207\pi\) | ||
0.870504 | − | 0.492162i | \(-0.163793\pi\) | |||||||
\(692\) | 5.35475e47 | + | 5.21588e47i | 0.279857 | + | 0.272599i | ||||
\(693\) | 2.18966e48 | 1.11664 | ||||||||
\(694\) | −7.63185e47 | − | 3.10264e47i | −0.379769 | − | 0.154391i | ||||
\(695\) | 1.42974e48i | 0.694251i | ||||||||
\(696\) | −9.10567e46 | − | 2.08133e47i | −0.0431474 | − | 0.0986242i | ||||
\(697\) | 6.83610e47 | 0.316119 | ||||||||
\(698\) | −1.29512e47 | + | 3.18572e47i | −0.0584477 | + | 0.143769i | ||||
\(699\) | − | 2.88781e47i | − | 0.127191i | ||||||
\(700\) | −7.16166e47 | + | 7.35234e47i | −0.307856 | + | 0.316052i | ||||
\(701\) | 1.73557e48 | 0.728173 | 0.364087 | − | 0.931365i | \(-0.381381\pi\) | ||||
0.364087 | + | 0.931365i | \(0.381381\pi\) | |||||||
\(702\) | −6.01092e46 | − | 2.44367e46i | −0.0246156 | − | 0.0100072i | ||||
\(703\) | 2.18193e48i | 0.872168i | ||||||||
\(704\) | −1.61672e48 | − | 1.49405e48i | −0.630810 | − | 0.582950i | ||||
\(705\) | 2.02199e47 | 0.0770129 | ||||||||
\(706\) | 9.33882e47 | − | 2.29715e48i | 0.347226 | − | 0.854103i | ||||
\(707\) | 3.66772e48i | 1.33127i | ||||||||
\(708\) | −3.41287e46 | − | 3.32436e46i | −0.0120936 | − | 0.0117799i | ||||
\(709\) | −5.64217e48 | −1.95191 | −0.975955 | − | 0.217971i | \(-0.930056\pi\) | ||||
−0.975955 | + | 0.217971i | \(0.930056\pi\) | |||||||
\(710\) | −3.77085e48 | − | 1.53300e48i | −1.27364 | − | 0.517786i | ||||
\(711\) | 4.05168e48i | 1.33614i | ||||||||
\(712\) | 7.72975e47 | − | 3.38171e47i | 0.248889 | − | 0.108887i | ||||
\(713\) | −2.72800e48 | −0.857675 | ||||||||
\(714\) | −1.57413e47 | + | 3.87203e47i | −0.0483249 | + | 0.118869i | ||||
\(715\) | − | 4.38609e47i | − | 0.131485i | ||||||
\(716\) | −3.70561e48 | + | 3.80427e48i | −1.08477 | + | 1.11365i | ||||
\(717\) | −3.16501e46 | −0.00904793 | ||||||||
\(718\) | 4.08255e48 | + | 1.65972e48i | 1.13977 | + | 0.463360i | ||||
\(719\) | − | 3.72634e48i | − | 1.01600i | −0.861359 | − | 0.507998i | \(-0.830386\pi\) | ||
0.861359 | − | 0.507998i | \(-0.169614\pi\) | |||||||
\(720\) | −7.98879e46 | − | 3.03986e48i | −0.0212730 | − | 0.809471i | ||||
\(721\) | 7.48560e48 | 1.94683 | ||||||||
\(722\) | 5.73096e47 | − | 1.40970e48i | 0.145578 | − | 0.358091i | ||||
\(723\) | 3.86285e47i | 0.0958421i | ||||||||
\(724\) | −3.46281e48 | − | 3.37300e48i | −0.839215 | − | 0.817450i | ||||
\(725\) | −2.16852e48 | −0.513354 | ||||||||
\(726\) | 7.43910e46 | + | 3.02429e46i | 0.0172028 | + | 0.00699359i | ||||
\(727\) | 2.53261e48i | 0.572115i | 0.958212 | + | 0.286058i | \(0.0923449\pi\) | ||||
−0.958212 | + | 0.286058i | \(0.907655\pi\) | |||||||
\(728\) | 4.46376e47 | + | 1.02030e48i | 0.0985070 | + | 0.225162i | ||||
\(729\) | 4.49943e48 | 0.970041 | ||||||||
\(730\) | 4.84221e47 | − | 1.19108e48i | 0.101989 | − | 0.250873i | ||||
\(731\) | − | 2.33882e47i | − | 0.0481285i | ||||||
\(732\) | 2.99607e47 | − | 3.07585e47i | 0.0602371 | − | 0.0618409i | ||||
\(733\) | −3.90024e48 | −0.766167 | −0.383083 | − | 0.923714i | \(-0.625138\pi\) | ||||
−0.383083 | + | 0.923714i | \(0.625138\pi\) | |||||||
\(734\) | 1.69362e48 | + | 6.88523e47i | 0.325075 | + | 0.132155i | ||||
\(735\) | 2.17293e47i | 0.0407532i | ||||||||
\(736\) | 1.86071e48 | − | 4.94555e48i | 0.341001 | − | 0.906341i | ||||
\(737\) | 8.06657e48 | 1.44458 | ||||||||
\(738\) | 4.88056e47 | − | 1.20051e48i | 0.0854105 | − | 0.210092i | ||||
\(739\) | − | 2.84901e48i | − | 0.487235i | −0.969871 | − | 0.243617i | \(-0.921666\pi\) | ||
0.969871 | − | 0.243617i | \(-0.0783341\pi\) | |||||||
\(740\) | 3.88419e48 | + | 3.78345e48i | 0.649174 | + | 0.632338i | ||||
\(741\) | 6.38680e46 | 0.0104321 | ||||||||
\(742\) | 8.71563e48 | + | 3.54324e48i | 1.39134 | + | 0.565633i | ||||
\(743\) | 3.32263e48i | 0.518408i | 0.965823 | + | 0.259204i | \(0.0834602\pi\) | ||||
−0.965823 | + | 0.259204i | \(0.916540\pi\) | |||||||
\(744\) | −3.76785e47 | + | 1.64841e47i | −0.0574584 | + | 0.0251376i | ||||
\(745\) | −3.86290e47 | −0.0575780 | ||||||||
\(746\) | −3.30630e46 | + | 8.13280e46i | −0.00481706 | + | 0.0118490i | ||||
\(747\) | − | 1.16032e49i | − | 1.65245i | ||||||
\(748\) | −5.97078e48 | + | 6.12975e48i | −0.831196 | + | 0.853327i | ||||
\(749\) | −1.38168e49 | −1.88025 | ||||||||
\(750\) | 5.36800e47 | + | 2.18230e47i | 0.0714120 | + | 0.0290318i | ||||
\(751\) | − | 1.39345e49i | − | 1.81223i | −0.423031 | − | 0.906115i | \(-0.639034\pi\) | ||
0.423031 | − | 0.906115i | \(-0.360966\pi\) | |||||||
\(752\) | −1.05071e49 | + | 2.76128e47i | −1.33592 | + | 0.0351081i | ||||
\(753\) | 4.43318e46 | 0.00551062 | ||||||||
\(754\) | −8.86134e47 | + | 2.17970e48i | −0.107693 | + | 0.264902i | ||||
\(755\) | 2.98038e48i | 0.354139i | ||||||||
\(756\) | 1.13806e48 | + | 1.10854e48i | 0.132219 | + | 0.128790i | ||||
\(757\) | −6.26459e47 | −0.0711644 | −0.0355822 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355822 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(758\) | 4.52328e48 | + | 1.83889e48i | 0.502431 | + | 0.204258i | ||||
\(759\) | − | 5.42256e47i | − | 0.0588971i | ||||||
\(760\) | 2.40545e48 | + | 5.49827e48i | 0.255485 | + | 0.583976i | ||||
\(761\) | 1.74459e47 | 0.0181198 | 0.00905990 | − | 0.999959i | \(-0.497116\pi\) | ||||
0.00905990 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(762\) | 2.10903e47 | − | 5.18776e47i | 0.0214214 | − | 0.0526921i | ||||
\(763\) | 1.15729e49i | 1.14955i | ||||||||
\(764\) | −3.00007e48 | + | 3.07995e48i | −0.291437 | + | 0.299197i | ||||
\(765\) | −1.18206e49 | −1.12304 | ||||||||
\(766\) | −1.34193e48 | − | 5.45547e47i | −0.124693 | − | 0.0506925i | ||||
\(767\) | 4.93453e47i | 0.0448461i | ||||||||
\(768\) | −4.18405e46 | − | 7.95500e47i | −0.00371926 | − | 0.0707130i | ||||
\(769\) | 1.41354e49 | 1.22903 | 0.614514 | − | 0.788906i | \(-0.289352\pi\) | ||||
0.614514 | + | 0.788906i | \(0.289352\pi\) | |||||||
\(770\) | −4.04445e48 | + | 9.94849e48i | −0.343967 | + | 0.846086i | ||||
\(771\) | 7.78052e46i | 0.00647269i | ||||||||
\(772\) | 1.64553e48 | + | 1.60286e48i | 0.133910 | + | 0.130437i | ||||
\(773\) | −1.27804e49 | −1.01741 | −0.508703 | − | 0.860942i | \(-0.669875\pi\) | ||||
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(774\) | −4.10730e47 | − | 1.66978e47i | −0.0319860 | − | 0.0130036i | ||||
\(775\) | 3.92569e48i | 0.299079i | ||||||||
\(776\) | 2.10280e49 | − | 9.19960e48i | 1.56729 | − | 0.685677i | ||||
\(777\) | −1.41288e48 | −0.103027 | ||||||||
\(778\) | −7.02906e47 | + | 1.72900e48i | −0.0501469 | + | 0.123351i | ||||
\(779\) | 2.55760e48i | 0.178524i | ||||||||
\(780\) | 1.10747e47 | − | 1.13695e47i | 0.00756350 | − | 0.00776488i | ||||
\(781\) | 2.17145e49 | 1.45105 | ||||||||
\(782\) | −1.90277e49 | − | 7.73548e48i | −1.24414 | − | 0.505793i | ||||
\(783\) | 3.35662e48i | 0.214759i | ||||||||
\(784\) | −2.96742e47 | − | 1.12915e49i | −0.0185783 | − | 0.706933i | ||||
\(785\) | 6.38968e48 | 0.391467 | ||||||||
\(786\) | 3.60230e47 | − | 8.86090e47i | 0.0215972 | − | 0.0531245i | ||||
\(787\) | − | 1.95005e48i | − | 0.114413i | −0.998362 | − | 0.0572065i | \(-0.981781\pi\) | ||
0.998362 | − | 0.0572065i | \(-0.0182193\pi\) | |||||||
\(788\) | −3.29343e48 | − | 3.20801e48i | −0.189105 | − | 0.184200i | ||||
\(789\) | −1.86564e48 | −0.104838 | ||||||||
\(790\) | −1.84084e49 | − | 7.48374e48i | −1.01241 | − | 0.411583i | ||||
\(791\) | − | 1.79961e49i | − | 0.968675i | ||||||
\(792\) | 6.50193e48 | + | 1.48618e49i | 0.342542 | + | 0.782966i | ||||
\(793\) | −4.44724e48 | −0.229322 | ||||||||
\(794\) | 7.77293e48 | − | 1.91198e49i | 0.392316 | − | 0.965015i | ||||
\(795\) | − | 1.34085e48i | − | 0.0662431i | ||||||
\(796\) | 1.60733e49 | − | 1.65012e49i | 0.777289 | − | 0.797984i | ||||
\(797\) | 1.70069e49 | 0.805070 | 0.402535 | − | 0.915405i | \(-0.368129\pi\) | ||||
0.402535 | + | 0.915405i | \(0.368129\pi\) | |||||||
\(798\) | −1.44865e48 | − | 5.88931e47i | −0.0671295 | − | 0.0272908i | ||||
\(799\) | 4.08573e49i | 1.85342i | ||||||||
\(800\) | −7.11680e48 | − | 2.67762e48i | −0.316049 | − | 0.118910i | ||||
\(801\) | −6.21733e48 | −0.270303 | ||||||||
\(802\) | 8.97564e48 | − | 2.20782e49i | 0.382033 | − | 0.939721i | ||||
\(803\) | 6.85886e48i | 0.285817i | ||||||||
\(804\) | 2.09100e48 | + | 2.03677e48i | 0.0853103 | + | 0.0830978i | ||||
\(805\) | −2.57777e49 | −1.02971 | ||||||||
\(806\) | 3.94593e48 | + | 1.60418e48i | 0.154331 | + | 0.0627417i | ||||
\(807\) | − | 6.64954e47i | − | 0.0254649i | ||||||
\(808\) | −2.48938e49 | + | 1.08909e49i | −0.933466 | + | 0.408385i | ||||
\(809\) | 4.65753e49 | 1.71014 | 0.855068 | − | 0.518516i | \(-0.173515\pi\) | ||||
0.855068 | + | 0.518516i | \(0.173515\pi\) | |||||||
\(810\) | −8.39646e48 | + | 2.06535e49i | −0.301892 | + | 0.742590i | ||||
\(811\) | 2.02824e49i | 0.714108i | 0.934084 | + | 0.357054i | \(0.116219\pi\) | ||||
−0.934084 | + | 0.357054i | \(0.883781\pi\) | |||||||
\(812\) | 4.01984e49 | − | 4.12687e49i | 1.38598 | − | 1.42288i | ||||
\(813\) | 2.31036e48 | 0.0780083 | ||||||||
\(814\) | −2.67958e49 | − | 1.08935e49i | −0.886037 | − | 0.360208i | ||||
\(815\) | − | 2.56767e49i | − | 0.831495i | ||||||
\(816\) | −3.09547e48 | + | 8.13492e46i | −0.0981734 | + | 0.00258001i | ||||
\(817\) | 8.75027e47 | 0.0271798 | ||||||||
\(818\) | −2.44141e49 | + | 6.00535e49i | −0.742736 | + | 1.82697i | ||||
\(819\) | − | 8.20669e48i | − | 0.244535i | ||||||
\(820\) | 4.55294e48 | + | 4.43486e48i | 0.132879 | + | 0.129433i | ||||
\(821\) | −2.14727e49 | −0.613836 | −0.306918 | − | 0.951736i | \(-0.599298\pi\) | ||||
−0.306918 | + | 0.951736i | \(0.599298\pi\) | |||||||
\(822\) | 4.26711e47 | + | 1.73475e47i | 0.0119485 | + | 0.00485753i | ||||
\(823\) | 3.45556e49i | 0.947811i | 0.880576 | + | 0.473905i | \(0.157156\pi\) | ||||
−0.880576 | + | 0.473905i | \(0.842844\pi\) | |||||||
\(824\) | 2.22276e49 | + | 5.08067e49i | 0.597214 | + | 1.36508i | ||||
\(825\) | −7.80324e47 | −0.0205380 | ||||||||
\(826\) | 4.55017e48 | − | 1.11925e49i | 0.117319 | − | 0.288579i | ||||
\(827\) | − | 4.38594e49i | − | 1.10782i | −0.832577 | − | 0.553909i | \(-0.813135\pi\) | ||
0.832577 | − | 0.553909i | \(-0.186865\pi\) | |||||||
\(828\) | −2.71692e49 | + | 2.78926e49i | −0.672297 | + | 0.690197i | ||||
\(829\) | −7.66632e49 | −1.85849 | −0.929244 | − | 0.369467i | \(-0.879540\pi\) | ||||
−0.929244 | + | 0.369467i | \(0.879540\pi\) | |||||||
\(830\) | 5.27180e49 | + | 2.14319e49i | 1.25208 | + | 0.509018i | ||||
\(831\) | 2.65141e47i | 0.00616964i | ||||||||
\(832\) | −5.59961e48 | + | 6.05934e48i | −0.127662 | + | 0.138143i | ||||
\(833\) | −4.39074e49 | −0.980783 | ||||||||
\(834\) | 1.03942e48 | − | 2.55676e48i | 0.0227494 | − | 0.0559587i | ||||
\(835\) | − | 1.34069e49i | − | 0.287513i | ||||||
\(836\) | −2.29333e49 | − | 2.23385e49i | −0.481904 | − | 0.469406i | ||||
\(837\) | 6.07652e48 | 0.125119 | ||||||||
\(838\) | −5.66172e49 | − | 2.30171e49i | −1.14235 | − | 0.464411i | ||||
\(839\) | − | 6.59836e49i | − | 1.30462i | −0.757954 | − | 0.652308i | \(-0.773801\pi\) | ||
0.757954 | − | 0.652308i | \(-0.226199\pi\) | |||||||
\(840\) | −3.56034e48 | + | 1.55763e48i | −0.0689833 | + | 0.0301797i | ||||
\(841\) | 6.90529e49 | 1.31114 | ||||||||
\(842\) | 2.10753e49 | − | 5.18407e49i | 0.392164 | − | 0.964641i | ||||
\(843\) | − | 1.04299e48i | − | 0.0190200i | ||||||
\(844\) | 1.17333e49 | − | 1.20457e49i | 0.209701 | − | 0.215284i | ||||
\(845\) | 4.48182e49 | 0.785037 | ||||||||
\(846\) | 7.17512e49 | + | 2.91697e49i | 1.23178 | + | 0.500766i | ||||
\(847\) | 2.03643e49i | 0.342651i | ||||||||
\(848\) | 1.83111e48 | + | 6.96765e49i | 0.0301984 | + | 1.14910i | ||||
\(849\) | 7.48536e48 | 0.120999 | ||||||||
\(850\) | −1.11316e49 | + | 2.73814e49i | −0.176375 | + | 0.433845i | ||||
\(851\) | − | 6.94310e49i | − | 1.07833i | ||||||
\(852\) | 5.62880e48 | + | 5.48282e48i | 0.0856925 | + | 0.0834700i | ||||
\(853\) | 6.62877e48 | 0.0989235 | 0.0494617 | − | 0.998776i | \(-0.484249\pi\) | ||||
0.0494617 | + | 0.998776i | \(0.484249\pi\) | |||||||
\(854\) | 1.00872e50 | + | 4.10083e49i | 1.47566 | + | 0.599913i | ||||
\(855\) | − | 4.42246e49i | − | 0.634221i | ||||||
\(856\) | −4.10273e49 | − | 9.37783e49i | −0.576792 | − | 1.31840i | ||||
\(857\) | −3.82145e49 | −0.526690 | −0.263345 | − | 0.964702i | \(-0.584826\pi\) | ||||
−0.263345 | + | 0.964702i | \(0.584826\pi\) | |||||||
\(858\) | −3.18868e47 | + | 7.84349e47i | −0.00430851 | + | 0.0105980i | ||||
\(859\) | 8.54696e49i | 1.13221i | 0.824332 | + | 0.566106i | \(0.191551\pi\) | ||||
−0.824332 | + | 0.566106i | \(0.808449\pi\) | |||||||
\(860\) | 1.51729e48 | − | 1.55769e48i | 0.0197059 | − | 0.0202306i | ||||
\(861\) | −1.65615e48 | −0.0210885 | ||||||||
\(862\) | 4.08606e49 | + | 1.66114e49i | 0.510130 | + | 0.207388i | ||||
\(863\) | 1.86775e49i | 0.228631i | 0.993444 | + | 0.114315i | \(0.0364675\pi\) | ||||
−0.993444 | + | 0.114315i | \(0.963533\pi\) | |||||||
\(864\) | −4.14465e48 | + | 1.10160e49i | −0.0497455 | + | 0.132218i | ||||
\(865\) | 2.70164e49 | 0.317947 | ||||||||
\(866\) | 2.26644e49 | − | 5.57498e49i | 0.261542 | − | 0.643337i | ||||
\(867\) | 5.77902e48i | 0.0653927i | ||||||||
\(868\) | −7.47091e49 | − | 7.27715e49i | −0.828969 | − | 0.807470i | ||||
\(869\) | 1.06005e50 | 1.15343 | ||||||||
\(870\) | −7.60607e48 | − | 3.09216e48i | −0.0811583 | − | 0.0329940i | ||||
\(871\) | − | 3.02329e49i | − | 0.316353i | ||||||
\(872\) | −7.85486e49 | + | 3.43644e49i | −0.806043 | + | 0.352638i | ||||
\(873\) | −1.69136e50 | −1.70214 | ||||||||
\(874\) | 2.89409e49 | − | 7.11884e49i | 0.285639 | − | 0.702611i | ||||
\(875\) | 1.46948e50i | 1.42241i | ||||||||
\(876\) | −1.73183e48 | + | 1.77794e48i | −0.0164413 | + | 0.0168791i | ||||
\(877\) | 4.14203e49 | 0.385674 | 0.192837 | − | 0.981231i | \(-0.438231\pi\) | ||||
0.192837 | + | 0.981231i | \(0.438231\pi\) | |||||||
\(878\) | −1.77894e50 | − | 7.23207e49i | −1.62463 | − | 0.660474i | ||||
\(879\) | − | 9.28184e48i | − | 0.0831425i | ||||||
\(880\) | −7.95326e49 | + | 2.09012e48i | −0.698778 | + | 0.0183640i | ||||
\(881\) | −4.14674e49 | −0.357369 | −0.178684 | − | 0.983906i | \(-0.557184\pi\) | ||||
−0.178684 | + | 0.983906i | \(0.557184\pi\) | |||||||
\(882\) | −3.13472e49 | + | 7.71076e49i | −0.264992 | + | 0.651825i | ||||
\(883\) | 1.94669e50i | 1.61423i | 0.590395 | + | 0.807114i | \(0.298972\pi\) | ||||
−0.590395 | + | 0.807114i | \(0.701028\pi\) | |||||||
\(884\) | 2.29739e49 | + | 2.23781e49i | 0.186873 | + | 0.182026i | ||||
\(885\) | −1.72190e48 | −0.0137396 | ||||||||
\(886\) | 3.48018e49 | + | 1.41483e49i | 0.272413 | + | 0.110747i | ||||
\(887\) | 1.00003e50i | 0.767913i | 0.923351 | + | 0.383956i | \(0.125439\pi\) | ||||
−0.923351 | + | 0.383956i | \(0.874561\pi\) | |||||||
\(888\) | −4.19539e48 | − | 9.58962e48i | −0.0316047 | − | 0.0722406i | ||||
\(889\) | 1.42013e50 | 1.04954 | ||||||||
\(890\) | 1.14838e49 | − | 2.82478e49i | 0.0832639 | − | 0.204812i | ||||
\(891\) | − | 1.18934e50i | − | 0.846026i | ||||||
\(892\) | 2.03554e48 | − | 2.08974e48i | 0.0142062 | − | 0.0145844i | ||||
\(893\) | −1.52860e50 | −1.04669 | ||||||||
\(894\) | 6.90789e47 | + | 2.80833e47i | 0.00464096 | + | 0.00188673i | ||||
\(895\) | 1.91938e50i | 1.26523i | ||||||||
\(896\) | 1.82884e50 | − | 8.58030e49i | 1.18287 | − | 0.554966i | ||||
\(897\) | −2.03234e48 | −0.0128981 | ||||||||
\(898\) | 5.90749e48 | − | 1.45312e49i | 0.0367879 | − | 0.0904906i | ||||
\(899\) | − | 2.20349e50i | − | 1.34647i | ||||||
\(900\) | 4.01383e49 | + | 3.90973e49i | 0.240678 | + | 0.234436i | ||||
\(901\) | 2.70940e50 | 1.59423 | ||||||||
\(902\) | −3.14093e49 | − | 1.27691e49i | −0.181362 | − | 0.0737309i | ||||
\(903\) | 5.66614e47i | 0.00321067i | ||||||||
\(904\) | 1.22144e50 | − | 5.34373e49i | 0.679219 | − | 0.297154i | ||||
\(905\) | −1.74710e50 | −0.953436 | ||||||||
\(906\) | 2.16674e48 | − | 5.32972e48i | 0.0116045 | − | 0.0285447i | ||||
\(907\) | − | 1.73078e50i | − | 0.909741i | −0.890558 | − | 0.454870i | \(-0.849686\pi\) | ||
0.890558 | − | 0.454870i | \(-0.150314\pi\) | |||||||
\(908\) | −1.01800e50 | + | 1.04510e50i | −0.525155 | + | 0.539137i | ||||
\(909\) | 2.00230e50 | 1.01378 | ||||||||
\(910\) | 3.72862e49 | + | 1.51583e49i | 0.185287 | + | 0.0753264i | ||||
\(911\) | − | 1.76425e50i | − | 0.860493i | −0.902712 | − | 0.430246i | \(-0.858427\pi\) | ||
0.902712 | − | 0.430246i | \(-0.141573\pi\) | |||||||
\(912\) | −3.04353e47 | − | 1.15811e49i | −0.00145702 | − | 0.0554419i | ||||
\(913\) | −3.03577e50 | −1.42648 | ||||||||
\(914\) | −9.94309e49 | + | 2.44579e50i | −0.458602 | + | 1.12807i | ||||
\(915\) | − | 1.55186e49i | − | 0.0702578i | ||||||
\(916\) | 4.55929e49 | + | 4.44105e49i | 0.202616 | + | 0.197361i | ||||
\(917\) | 2.42565e50 | 1.05815 | ||||||||
\(918\) | 4.23833e49 | + | 1.72305e49i | 0.181497 | + | 0.0737856i | ||||
\(919\) | 8.00927e49i | 0.336689i | 0.985728 | + | 0.168345i | \(0.0538422\pi\) | ||||
−0.985728 | + | 0.168345i | \(0.946158\pi\) | |||||||
\(920\) | −7.65438e49 | − | 1.74960e50i | −0.315876 | − | 0.722014i | ||||
\(921\) | −2.18697e49 | −0.0885990 | ||||||||
\(922\) | 8.72742e49 | − | 2.14676e50i | 0.347105 | − | 0.853804i | ||||
\(923\) | − | 8.13845e49i | − | 0.317770i | ||||||
\(924\) | 1.44651e49 | − | 1.48502e49i | 0.0554495 | − | 0.0569258i | ||||
\(925\) | −9.99134e49 | −0.376023 | ||||||||
\(926\) | −2.06225e50 | − | 8.38386e49i | −0.762001 | − | 0.309783i | ||||
\(927\) | − | 4.08658e50i | − | 1.48253i | ||||||
\(928\) | 3.99467e50 | + | 1.50295e50i | 1.42287 | + | 0.535339i | ||||
\(929\) | −3.92684e50 | −1.37333 | −0.686667 | − | 0.726972i | \(-0.740927\pi\) | ||||
−0.686667 | + | 0.726972i | \(0.740927\pi\) | |||||||
\(930\) | −5.59776e48 | + | 1.37693e49i | −0.0192223 | + | 0.0472827i | ||||
\(931\) | − | 1.64271e50i | − | 0.553882i | ||||||
\(932\) | 3.88637e50 | + | 3.78558e50i | 1.28669 | + | 1.25332i | ||||
\(933\) | −3.60265e49 | −0.117121 | ||||||||
\(934\) | −1.88220e50 | − | 7.65187e49i | −0.600854 | − | 0.244270i | ||||
\(935\) | 3.09265e50i | 0.969469i | ||||||||
\(936\) | 5.57010e49 | − | 2.43688e49i | 0.171464 | − | 0.0750144i | ||||
\(937\) | 7.82422e49 | 0.236520 | 0.118260 | − | 0.992983i | \(-0.462268\pi\) | ||||
0.118260 | + | 0.992983i | \(0.462268\pi\) | |||||||
\(938\) | −2.78780e50 | + | 6.85741e50i | −0.827587 | + | 2.03569i | ||||
\(939\) | 4.55801e49i | 0.132880i | ||||||||
\(940\) | −2.65059e50 | + | 2.72116e50i | −0.758872 | + | 0.779078i | ||||
\(941\) | 2.49039e50 | 0.700235 | 0.350117 | − | 0.936706i | \(-0.386142\pi\) | ||||
0.350117 | + | 0.936706i | \(0.386142\pi\) | |||||||
\(942\) | −1.14264e49 | − | 4.64530e48i | −0.0315534 | − | 0.0128277i | ||||
\(943\) | − | 8.13851e49i | − | 0.220722i | ||||||
\(944\) | 8.94774e49 | − | 2.35148e48i | 0.238336 | − | 0.00626349i | ||||
\(945\) | 5.74187e49 | 0.150215 | ||||||||
\(946\) | −4.36868e48 | + | 1.07460e49i | −0.0112254 | + | 0.0276120i | ||||
\(947\) | 4.30190e50i | 1.08570i | 0.839829 | + | 0.542852i | \(0.182655\pi\) | ||||
−0.839829 | + | 0.542852i | \(0.817345\pi\) | |||||||
\(948\) | 2.74785e49 | + | 2.67658e49i | 0.0681162 | + | 0.0663496i | ||||
\(949\) | 2.57065e49 | 0.0625919 | ||||||||
\(950\) | −1.02442e50 | − | 4.16468e49i | −0.245007 | − | 0.0996049i | ||||
\(951\) | 1.40332e49i | 0.0329676i | ||||||||
\(952\) | −3.14742e50 | − | 7.19421e50i | −0.726317 | − | 1.66018i | ||||
\(953\) | −5.09134e50 | −1.15412 | −0.577062 | − | 0.816700i | \(-0.695801\pi\) | ||||
−0.577062 | + | 0.816700i | \(0.695801\pi\) | |||||||
\(954\) | 1.93435e50 | − | 4.75809e50i | 0.430737 | − | 1.05952i | ||||
\(955\) | 1.55393e50i | 0.339919i | ||||||||
\(956\) | 4.14895e49 | − | 4.25942e49i | 0.0891568 | − | 0.0915306i | ||||
\(957\) | 4.37996e49 | 0.0924629 | ||||||||
\(958\) | 1.28306e50 | + | 5.21614e49i | 0.266093 | + | 0.108177i | ||||
\(959\) | 1.16811e50i | 0.237995i | ||||||||
\(960\) | −2.11440e49 | − | 1.95398e49i | −0.0423230 | − | 0.0391119i | ||||
\(961\) | 1.09608e50 | 0.215549 | ||||||||
\(962\) | −4.08282e49 | + | 1.00429e50i | −0.0788831 | + | 0.194036i | ||||
\(963\) | 7.54294e50i | 1.43184i | ||||||||
\(964\) | −5.19856e50 | − | 5.06373e50i | −0.969557 | − | 0.944412i | ||||
\(965\) | 8.30223e49 | 0.152135 | ||||||||
\(966\) | 4.60973e49 | + | 1.87403e49i | 0.0829974 | + | 0.0337417i | ||||
\(967\) | − | 5.96244e50i | − | 1.05481i | −0.849614 | − | 0.527404i | \(-0.823165\pi\) | ||
0.849614 | − | 0.527404i | \(-0.176835\pi\) | |||||||
\(968\) | −1.38218e50 | + | 6.04695e49i | −0.240262 | + | 0.105113i | ||||
\(969\) | −4.50336e49 | −0.0769188 | ||||||||
\(970\) | 3.12406e50 | − | 7.68452e50i | 0.524324 | − | 1.28973i | ||||
\(971\) | − | 3.60777e50i | − | 0.594993i | −0.954723 | − | 0.297496i | \(-0.903848\pi\) | ||
0.954723 | − | 0.297496i | \(-0.0961516\pi\) | |||||||
\(972\) | 9.08534e49 | − | 9.32724e49i | 0.147236 | − | 0.151156i | ||||
\(973\) | 6.99906e50 | 1.11461 | ||||||||
\(974\) | 9.74243e49 | + | 3.96068e49i | 0.152463 | + | 0.0619822i | ||||
\(975\) | 2.92460e48i | 0.00449767i | ||||||||
\(976\) | 2.11926e49 | + | 8.06414e50i | 0.0320286 | + | 1.21874i | ||||
\(977\) | 4.28087e50 | 0.635805 | 0.317903 | − | 0.948123i | \(-0.397022\pi\) | ||||
0.317903 | + | 0.948123i | \(0.397022\pi\) | |||||||
\(978\) | −1.86669e49 | + | 4.59167e49i | −0.0272466 | + | 0.0670209i | ||||
\(979\) | 1.62665e50i | 0.233340i | ||||||||
\(980\) | −2.92430e50 | − | 2.84846e50i | −0.412267 | − | 0.401575i | ||||
\(981\) | 6.31796e50 | 0.875394 | ||||||||
\(982\) | 2.86508e50 | + | 1.16477e50i | 0.390159 | + | 0.158615i | ||||
\(983\) | 8.22664e50i | 1.10106i | 0.834814 | + | 0.550532i | \(0.185575\pi\) | ||||
−0.834814 | + | 0.550532i | \(0.814425\pi\) | |||||||
\(984\) | −4.91773e48 | − | 1.12407e49i | −0.00646916 | − | 0.0147869i | ||||
\(985\) | −1.66164e50 | −0.214843 | ||||||||
\(986\) | 6.24818e50 | − | 1.53692e51i | 0.794046 | − | 1.95319i | ||||
\(987\) | − | 9.89829e49i | − | 0.123643i | ||||||
\(988\) | −8.37233e49 | + | 8.59525e49i | −0.102797 | + | 0.105534i | ||||
\(989\) | −2.78442e49 | −0.0336045 | ||||||||
\(990\) | 5.43114e50 | + | 2.20797e50i | 0.644306 | + | 0.261935i | ||||
\(991\) | 1.40043e50i | 0.163308i | 0.996661 | + | 0.0816542i | \(0.0260203\pi\) | ||||
−0.996661 | + | 0.0816542i | \(0.973980\pi\) | |||||||
\(992\) | 2.72080e50 | − | 7.23157e50i | 0.311888 | − | 0.828961i | ||||
\(993\) | −1.23660e48 | −0.00139345 | ||||||||
\(994\) | −7.50453e50 | + | 1.84596e51i | −0.831294 | + | 2.04481i | ||||
\(995\) | − | 8.32540e50i | − | 0.906594i | ||||||
\(996\) | −7.86928e49 | − | 7.66519e49i | −0.0842415 | − | 0.0820567i | ||||
\(997\) | −1.55310e51 | −1.63448 | −0.817242 | − | 0.576295i | \(-0.804498\pi\) | ||||
−0.817242 | + | 0.576295i | \(0.804498\pi\) | |||||||
\(998\) | −8.60599e49 | − | 3.49867e49i | −0.0890393 | − | 0.0361979i | ||||
\(999\) | 1.54655e50i | 0.157308i |
(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 | 4.35.b.a.3.11 | ✓ | 16 | |
4.3 | odd | 2 | inner | 4.35.b.a.3.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.35.b.a.3.11 | ✓ | 16 | 1.1 | even | 1 | trivial | |
4.35.b.a.3.12 | yes | 16 | 4.3 | odd | 2 | inner |